LMFDB - Embedded newform 59.7.d.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [59,7,Mod(2,59)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(59, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("59.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	59.d (of order $58$, degree $28$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.5731909336$
Analytic rank:	$0$
Dimension:	$812$
Relative dimension:	$29$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	59.11
Dual form			59.7.d.a.43.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.744271 - 3.38126i) q^{2} +(-0.974635 + 5.94501i) q^{3} +(47.2059 - 21.8398i) q^{4} +(44.0346 - 158.598i) q^{5} +(20.8270 - 1.12921i) q^{6} +(-67.3470 + 63.7945i) q^{7} +(-243.075 - 319.760i) q^{8} +(656.446 + 221.182i) q^{9} +(-569.035 - 30.8522i) q^{10} +(-412.587 + 350.455i) q^{11} +(83.8291 + 301.925i) q^{12} +(-410.310 - 1217.76i) q^{13} +(265.830 + 180.237i) q^{14} +(899.950 + 416.361i) q^{15} +(1254.77 - 1477.23i) q^{16} +(638.219 + 604.553i) q^{17} +(259.301 - 2384.23i) q^{18} +(-3078.55 - 7726.57i) q^{19} +(-1385.06 - 8448.47i) q^{20} +(-313.620 - 462.555i) q^{21} +(1492.06 + 1134.23i) q^{22} +(-1173.87 - 10793.5i) q^{23} +(2137.88 - 1133.43i) q^{24} +(-9825.94 - 5912.07i) q^{25} +(-3812.17 + 2293.71i) q^{26} +(-4011.87 + 7567.19i) q^{27} +(-1785.92 + 4482.32i) q^{28} +(-43458.6 - 9565.96i) q^{29} +(738.018 - 3352.85i) q^{30} +(25302.2 + 10081.3i) q^{31} +(-28640.6 - 15184.3i) q^{32} +(-1681.34 - 2794.40i) q^{33} +(1569.14 - 2607.93i) q^{34} +(7152.09 + 13490.3i) q^{35} +(35818.7 - 3895.51i) q^{36} +(50587.2 - 66546.3i) q^{37} +(-23834.3 + 16160.0i) q^{38} +(7639.48 - 1252.43i) q^{39} +(-61417.0 + 24470.8i) q^{40} +(35018.8 + 3808.52i) q^{41} +(-1330.60 + 1404.70i) q^{42} +(94558.4 + 80318.6i) q^{43} +(-11822.7 + 25554.3i) q^{44} +(63985.4 - 94371.4i) q^{45} +(-35622.0 + 12002.4i) q^{46} +(-50790.3 + 14101.9i) q^{47} +(7559.21 + 8899.38i) q^{48} +(-5903.50 + 108884. i) q^{49} +(-12677.1 + 37624.2i) q^{50} +(-4216.10 + 3205.00i) q^{51} +(-45964.6 - 48524.2i) q^{52} +(-2666.14 - 49174.1i) q^{53} +(28572.5 + 7933.12i) q^{54} +(37413.4 + 80867.7i) q^{55} +(36769.3 + 6028.02i) q^{56} +(48935.0 - 10771.4i) q^{57} +154064. i q^{58} +(134980. + 154793. i) q^{59} +51576.2 q^{60} +(53953.2 + 245112. i) q^{61} +(15255.9 - 93056.6i) q^{62} +(-58319.9 + 26981.7i) q^{63} +(3160.03 - 11381.4i) q^{64} +(-211202. + 11451.0i) q^{65} +(-8197.22 + 7764.82i) q^{66} +(13107.8 + 17243.0i) q^{67} +(43330.9 + 14599.9i) q^{68} +(65311.7 + 3541.10i) q^{69} +(40291.0 - 34223.5i) q^{70} +(78763.3 + 283680. i) q^{71} +(-88840.3 - 263669. i) q^{72} +(-398311. - 270062. i) q^{73} +(-262661. - 121520. i) q^{74} +(44724.1 - 52653.2i) q^{75} +(-314072. - 297505. i) q^{76} +(5429.44 - 49922.9i) q^{77} +(-9920.64 - 24898.9i) q^{78} +(81377.9 + 496383. i) q^{79} +(-179033. - 264053. i) q^{80} +(360937. + 274377. i) q^{81} +(-13185.9 - 121242. i) q^{82} +(426775. - 226262. i) q^{83} +(-24906.8 - 14985.9i) q^{84} +(123985. - 74599.1i) q^{85} +(201201. - 379505. i) q^{86} +(99226.0 - 249039. i) q^{87} +(212351. + 46742.0i) q^{88} +(88683.3 - 402892. i) q^{89} +(-366717. - 146113. i) q^{90} +(105319. + 55836.8i) q^{91} +(-291141. - 483880. i) q^{92} +(-84594.1 + 140596. i) q^{93} +(85483.8 + 161240. i) q^{94} +(-1.36098e6 + 148016. i) q^{95} +(118185. - 155470. i) q^{96} +(673183. - 456429. i) q^{97} +(372558. - 61077.7i) q^{98} +(-348356. + 138798. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 812 q - 29 q^{2} - 39 q^{3} + 869 q^{4} - 171 q^{5} - 29 q^{6} - 435 q^{7} - 29 q^{8} - 7648 q^{9} - 29 q^{10} - 29 q^{11} + 1095 q^{12} - 29 q^{13} - 29 q^{14} - 569 q^{15} - 25051 q^{16} - 9071 q^{17}+ \cdots + 9513421 q^{99}+O(q^{100}) $ 812 * q - 29 * q^2 - 39 * q^3 + 869 * q^4 - 171 * q^5 - 29 * q^6 - 435 * q^7 - 29 * q^8 - 7648 * q^9 - 29 * q^10 - 29 * q^11 + 1095 * q^12 - 29 * q^13 - 29 * q^14 - 569 * q^15 - 25051 * q^16 - 9071 * q^17 - 29 * q^18 - 3879 * q^19 + 46867 * q^20 - 3729 * q^21 - 11267 * q^22 - 29 * q^23 - 29 * q^24 - 65696 * q^25 + 64561 * q^26 - 36009 * q^27 + 45513 * q^28 + 31701 * q^29 - 29 * q^30 - 29 * q^31 - 29 * q^32 - 29 * q^33 - 29 * q^34 - 46305 * q^35 + 185269 * q^36 - 29 * q^37 - 29 * q^38 - 29 * q^39 - 29 * q^40 - 91943 * q^41 - 29 * q^42 - 29 * q^43 - 29 * q^44 + 1328609 * q^45 + 122071 * q^46 - 472149 * q^47 - 4460721 * q^48 - 992540 * q^49 - 1117341 * q^50 - 161065 * q^51 + 1336291 * q^52 + 1079813 * q^53 + 4504947 * q^54 + 1872907 * q^55 + 3956963 * q^56 + 2677007 * q^57 - 302138 * q^59 - 4965482 * q^60 - 1574381 * q^61 - 2444409 * q^62 - 5085047 * q^63 - 5066455 * q^64 - 1422653 * q^65 + 433939 * q^66 + 876931 * q^67 + 3018437 * q^68 + 5706243 * q^69 + 6798499 * q^70 + 3537645 * q^71 + 6041251 * q^72 - 396749 * q^73 - 3448403 * q^74 - 9552475 * q^75 - 247173 * q^76 - 29 * q^77 + 375035 * q^78 - 4731 * q^79 - 1921013 * q^80 + 841594 * q^81 - 29 * q^82 - 29 * q^83 - 2367333 * q^84 - 864073 * q^85 - 5031139 * q^86 + 4790463 * q^87 - 726023 * q^88 - 29 * q^89 - 29 * q^90 - 29 * q^91 - 29 * q^92 - 29 * q^93 - 2835797 * q^94 - 1047881 * q^95 - 29 * q^96 - 29 * q^97 + 29127484 * q^98 + 9513421 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/59\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{25}{58}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.744271	−	3.38126i	−0.0930339	−	0.422657i	−0.999999	−	0.00145139i	$-0.999538\pi$
$2$	−0.744271	−	3.38126i	−0.0930339	−	0.422657i	0.906965	−	0.421206i	$-0.138393\pi$
$3$	−0.974635	+	5.94501i	−0.0360976	+	0.220186i	−0.998715	−	0.0506793i	$-0.983861\pi$
$3$	−0.974635	+	5.94501i	−0.0360976	+	0.220186i	0.962617	+	0.270865i	$0.0873097\pi$
$4$	47.2059	−	21.8398i	0.737592	−	0.341246i
$5$	44.0346	−	158.598i	0.352277	−	1.26879i	−0.549103	−	0.835755i	$-0.685030\pi$
$5$	44.0346	−	158.598i	0.352277	−	1.26879i	0.901379	−	0.433030i	$-0.142556\pi$
$6$	20.8270	−	1.12921i	0.0964214	−	0.00522781i
$7$	−67.3470	+	63.7945i	−0.196347	+	0.185990i	−0.779556	−	0.626332i	$-0.784555\pi$
$7$	−67.3470	+	63.7945i	−0.196347	+	0.185990i	0.583209	+	0.812322i	$0.301797\pi$
$8$	−243.075	−	319.760i	−0.474756	−	0.624530i
$9$	656.446	+	221.182i	0.900475	+	0.303405i
$10$	−569.035	−	30.8522i	−0.569035	−	0.0308522i
$11$	−412.587	+	350.455i	−0.309983	+	0.263302i	−0.788850	−	0.614585i	$-0.789323\pi$
$11$	−412.587	+	350.455i	−0.309983	+	0.263302i	0.478867	+	0.877887i	$0.341047\pi$
$12$	83.8291	+	301.925i	0.0485122	+	0.174725i
$13$	−410.310	−	1217.76i	−0.186759	−	0.554282i	0.812843	−	0.582483i	$-0.197919\pi$
$13$	−410.310	−	1217.76i	−0.186759	−	0.554282i	−0.999602	+	0.0282010i	$0.991022\pi$
$14$	265.830	+	180.237i	0.0968769	+	0.0656842i
$15$	899.950	+	416.361i	0.266652	+	0.123366i
$16$	1254.77	−	1477.23i	0.306340	−	0.360652i
$17$	638.219	+	604.553i	0.129904	+	0.123052i	0.749894	−	0.661558i	$-0.230105\pi$
$17$	638.219	+	604.553i	0.129904	+	0.123052i	−0.619990	+	0.784610i	$0.712863\pi$
$18$	259.301	−	2384.23i	0.0444618	−	0.408819i
$19$	−3078.55	−	7726.57i	−0.448833	−	1.12649i	−0.963169	−	0.268897i	$-0.913341\pi$
$19$	−3078.55	−	7726.57i	−0.448833	−	1.12649i	0.514336	−	0.857589i	$-0.328039\pi$
$20$	−1385.06	−	8448.47i	−0.173132	−	1.05606i
$21$	−313.620	−	462.555i	−0.0338646	−	0.0499466i
$22$	1492.06	+	1134.23i	0.140125	+	0.106521i
$23$	−1173.87	−	10793.5i	−0.0964795	−	0.887114i	−0.937940	−	0.346796i	$-0.887270\pi$
$23$	−1173.87	−	10793.5i	−0.0964795	−	0.887114i	0.841461	−	0.540318i	$-0.181696\pi$
$24$	2137.88	−	1133.43i	0.154650	−	0.0819903i
$25$	−9825.94	−	5912.07i	−0.628860	−	0.378373i
$26$	−3812.17	+	2293.71i	−0.216896	+	0.130502i
$27$	−4011.87	+	7567.19i	−0.203824	+	0.384453i
$28$	−1785.92	+	4482.32i	−0.0813556	+	0.204187i
$29$	−43458.6	−	9565.96i	−1.78189	−	0.392224i	−0.802899	−	0.596115i	$-0.796710\pi$
$29$	−43458.6	−	9565.96i	−1.78189	−	0.392224i	−0.978994	+	0.203890i	$0.934641\pi$
$30$	738.018	−	3352.85i	0.0273340	−	0.124180i
$31$	25302.2	+	10081.3i	0.849325	+	0.338402i	0.753863	−	0.657031i	$-0.228188\pi$
$31$	25302.2	+	10081.3i	0.849325	+	0.338402i	0.0954615	+	0.995433i	$0.469567\pi$
$32$	−28640.6	−	15184.3i	−0.874042	−	0.463388i
$33$	−1681.34	−	2794.40i	−0.0467856	−	0.0777584i
$34$	1569.14	−	2607.93i	0.0399232	−	0.0663529i
$35$	7152.09	+	13490.3i	0.166813	+	0.314642i
$36$	35818.7	−	3895.51i	0.767718	−	0.0834944i
$37$	50587.2	−	66546.3i	0.998700	−	1.31377i	0.0496084	−	0.998769i	$-0.484203\pi$
$37$	50587.2	−	66546.3i	0.998700	−	1.31377i	0.949092	−	0.314999i	$-0.102004\pi$
$38$	−23834.3	+	16160.0i	−0.434361	+	0.294504i
$39$	7639.48	−	1252.43i	0.128786	−	0.0211135i
$40$	−61417.0	+	24470.8i	−0.959640	+	0.382356i
$41$	35018.8	+	3808.52i	0.508100	+	0.0552592i	0.358579	−	0.933499i	$-0.383261\pi$
$41$	35018.8	+	3808.52i	0.508100	+	0.0552592i	0.149521	+	0.988759i	$0.452227\pi$
$42$	−1330.60	+	1404.70i	−0.0179597	+	0.0189599i
$43$	94558.4	+	80318.6i	1.18931	+	1.01021i	0.999598	+	0.0283678i	$0.00903095\pi$
$43$	94558.4	+	80318.6i	1.18931	+	1.01021i	0.189711	+	0.981840i	$0.439245\pi$
$44$	−11822.7	+	25554.3i	−0.138790	+	0.299990i
$45$	63985.4	−	94371.4i	0.702172	−	1.03563i
$46$	−35622.0	+	12002.4i	−0.365969	+	0.123309i
$47$	−50790.3	+	14101.9i	−0.489201	+	0.135826i	−0.503365	−	0.864074i	$-0.667905\pi$
$47$	−50790.3	+	14101.9i	−0.489201	+	0.135826i	0.0141643	+	0.999900i	$0.495491\pi$
$48$	7559.21	+	8899.38i	0.0683522	+	0.0804704i
$49$	−5903.50	+	108884.i	−0.0501790	+	0.925496i
$50$	−12677.1	+	37624.2i	−0.101417	+	0.300994i
$51$	−4216.10	+	3205.00i	−0.0317834	+	0.0241611i
$52$	−45964.6	−	48524.2i	−0.326899	−	0.345103i
$53$	−2666.14	−	49174.1i	−0.0179084	−	0.330301i	−0.993736	−	0.111757i	$-0.964352\pi$
$53$	−2666.14	−	49174.1i	−0.0179084	−	0.330301i	0.975827	−	0.218544i	$-0.0701306\pi$
$54$	28572.5	+	7933.12i	0.181454	+	0.0503806i
$55$	37413.4	+	80867.7i	0.224874	+	0.486057i
$56$	36769.3	+	6028.02i	0.209373	+	0.0343250i
$57$	48935.0	−	10771.4i	0.264238	−	0.0581632i
$58$			154064.i			0.789620i
$59$	134980.	+	154793.i	0.657224	+	0.753696i
$59$	134980.	+	154793.i	0.657224	+	0.753696i
$60$	51576.2			0.238779
$61$	53953.2	+	245112.i	0.237699	+	1.07988i	0.932639	+	0.360810i	$0.117500\pi$
$61$	53953.2	+	245112.i	0.237699	+	1.07988i	−0.694940	+	0.719068i	$0.744569\pi$
$62$	15255.9	−	93056.6i	0.0640120	−	0.390456i
$63$	−58319.9	+	26981.7i	−0.233236	+	0.107906i
$64$	3160.03	−	11381.4i	0.0120546	−	0.0434166i
$65$	−211202.	+	11451.0i	−0.769056	+	0.0416970i
$66$	−8197.22	+	7764.82i	−0.0285125	+	0.0270085i
$67$	13107.8	+	17243.0i	0.0435819	+	0.0573310i	0.817368	−	0.576116i	$-0.195432\pi$
$67$	13107.8	+	17243.0i	0.0435819	+	0.0573310i	−0.773786	+	0.633447i	$0.781639\pi$
$68$	43330.9	+	14599.9i	0.137807	+	0.0464326i
$69$	65311.7	+	3541.10i	0.198812	+	0.0107793i
$70$	40291.0	−	34223.5i	0.117467	−	0.0997770i
$71$	78763.3	+	283680.i	0.220064	+	0.792599i	0.988312	+	0.152446i	$0.0487150\pi$
$71$	78763.3	+	283680.i	0.220064	+	0.792599i	−0.768248	+	0.640152i	$0.778871\pi$
$72$	−88840.3	−	263669.i	−0.238020	−	0.706417i
$73$	−398311.	−	270062.i	−1.02389	−	0.694215i	−0.0709838	−	0.997477i	$-0.522614\pi$
$73$	−398311.	−	270062.i	−1.02389	−	0.694215i	−0.952907	+	0.303262i	$0.901924\pi$
$74$	−262661.	−	121520.i	−0.648187	−	0.299883i
$75$	44724.1	−	52653.2i	0.106013	−	0.124808i
$76$	−314072.	−	297505.i	−0.715465	−	0.677724i
$77$	5429.44	−	49922.9i	0.0118928	−	0.109352i
$78$	−9920.64	−	24898.9i	−0.0209053	−	0.0524683i
$79$	81377.9	+	496383.i	0.165054	+	1.00678i	0.931305	+	0.364242i	$0.118672\pi$
$79$	81377.9	+	496383.i	0.165054	+	1.00678i	−0.766251	+	0.642542i	$0.777880\pi$
$80$	−179033.	−	264053.i	−0.349673	−	0.515729i
$81$	360937.	+	274377.i	0.679166	+	0.516289i
$82$	−13185.9	−	121242.i	−0.0239148	−	0.219893i
$83$	426775.	−	226262.i	0.746387	−	0.395710i	−0.0513767	−	0.998679i	$-0.516361\pi$
$83$	426775.	−	226262.i	0.746387	−	0.395710i	0.797764	+	0.602970i	$0.206016\pi$
$84$	−24906.8	−	14985.9i	−0.0420223	−	0.0252840i
$85$	123985.	−	74599.1i	0.201888	−	0.121472i
$86$	201201.	−	379505.i	0.316326	−	0.596653i
$87$	99226.0	−	249039.i	0.150684	−	0.378189i
$88$	212351.	+	46742.0i	0.311606	+	0.0685897i
$89$	88683.3	−	402892.i	0.125797	−	0.571504i	−0.870982	−	0.491315i	$-0.836517\pi$
$89$	88683.3	−	402892.i	0.125797	−	0.571504i	0.996780	−	0.0801891i	$-0.0255524\pi$
$90$	−366717.	−	146113.i	−0.503041	−	0.200430i
$91$	105319.	+	55836.8i	0.139760	+	0.0740963i
$92$	−291141.	−	483880.i	−0.373887	−	0.621405i
$93$	−84594.1	+	140596.i	−0.105170	+	0.174794i
$94$	85483.8	+	161240.i	0.102920	+	0.194128i
$95$	−1.36098e6	+	148016.i	−1.58738	+	0.172638i
$96$	118185.	−	155470.i	0.133582	−	0.175724i
$97$	673183.	−	456429.i	0.737595	−	0.500102i	−0.133602	−	0.991035i	$-0.542655\pi$
$97$	673183.	−	456429.i	0.737595	−	0.500102i	0.871197	+	0.490933i	$0.163344\pi$
$98$	372558.	−	61077.7i	0.395836	−	0.0648940i
$99$	−348356.	+	138798.i	−0.359019	+	0.143046i
$100$	−592960.	−	64488.3i	−0.592960	−	0.0644883i
$101$	954182.	−	1.00732e6i	0.926119	−	0.977692i	−0.0736887	−	0.997281i	$-0.523477\pi$
$101$	954182.	−	1.00732e6i	0.926119	−	0.977692i	0.999808	+	0.0195889i	$0.00623574\pi$
$102$	13974.9	+	11870.3i	0.0131688	+	0.0111857i
$103$	−106562.	+	230331.i	−0.0975196	+	0.210785i	−0.950195	−	0.311656i	$-0.899116\pi$
$103$	−106562.	+	230331.i	−0.0975196	+	0.210785i	0.852675	+	0.522441i	$0.174978\pi$
$104$	−289653.	+	427207.i	−0.257501	+	0.379785i
$105$	−87170.6	+	29371.2i	−0.0753012	+	0.0253719i
$106$	−164286.	+	45613.8i	−0.137938	+	0.0382983i
$107$	470930.	+	554422.i	0.384419	+	0.452574i	0.920005	−	0.391908i	$-0.128185\pi$
$107$	470930.	+	554422.i	0.384419	+	0.452574i	−0.535585	+	0.844481i	$0.679909\pi$
$108$	−24118.2	+	444834.i	−0.0191458	+	0.353123i
$109$	11882.4	−	35265.8i	0.00917542	−	0.0272317i	−0.942968	−	0.332884i	$-0.891978\pi$
$109$	11882.4	−	35265.8i	0.00917542	−	0.0272317i	0.952143	+	0.305653i	$0.0988747\pi$
$110$	245589.	−	186692.i	0.184515	−	0.140264i
$111$	346314.	+	365600.i	0.253222	+	0.267323i
$112$	9734.08	+	179535.i	0.00692853	+	0.127789i
$113$	344319.	+	95599.8i	0.238631	+	0.0662555i	0.384785	−	0.923006i	$-0.374276\pi$
$113$	344319.	+	95599.8i	0.238631	+	0.0662555i	−0.146154	+	0.989262i	$0.546690\pi$
$114$	−72841.8	−	157445.i	−0.0491662	−	0.106271i
$115$	−1.76352e6	−	289115.i	−1.15954	−	0.190098i
$116$	−2.26042e6	+	497556.i	−1.44815	+	0.318763i
$117$		−	890145.i		−	0.555780i
$118$	422934.	−	571610.i	0.257411	−	0.347900i
$119$	−81549.3			−0.0483926
$120$	−85619.8	−	388975.i	−0.0495485	−	0.225101i
$121$	−239197.	+	1.45904e6i	−0.135020	+	0.823588i
$122$	788630.	−	364859.i	0.434304	−	0.200931i
$123$	−56772.2	+	204475.i	−0.0305085	+	0.109882i
$124$	1.41459e6	−	76696.7i	0.741933	−	0.0402264i
$125$	496819.	−	470612.i	0.254371	−	0.240953i
$126$	134638.	+	177113.i	0.0673063	+	0.0885399i
$127$	2.83042e6	+	953681.i	1.38178	+	0.465577i	0.909439	−	0.415836i	$-0.136511\pi$
$127$	2.83042e6	+	953681.i	1.38178	+	0.465577i	0.472345	+	0.881414i	$0.343408\pi$
$128$	−2.11247e6	−	114535.i	−1.00730	−	0.0546144i
$129$	−569655.	+	483869.i	−0.265364	+	0.225403i
$130$	195910.	+	705605.i	0.0891718	+	0.321168i
$131$	255610.	+	758623.i	0.113701	+	0.337452i	0.989362	−	0.145474i	$-0.0464706\pi$
$131$	255610.	+	758623.i	0.113701	+	0.337452i	−0.875661	+	0.482926i	$0.839574\pi$
$132$	−140398.	−	95192.2i	−0.0610434	−	0.0413885i
$133$	700244.	+	323967.i	0.297642	+	0.137704i
$134$	48547.4	−	57154.4i	0.0201768	−	0.0237539i
$135$	1.02348e6	+	969493.i	0.415986	+	0.394043i
$136$	38176.6	−	351028.i	0.0151768	−	0.139549i
$137$	586420.	+	1.47180e6i	0.228059	+	0.572385i	0.997823	−	0.0659431i	$-0.0210056\pi$
$137$	586420.	+	1.47180e6i	0.228059	+	0.572385i	−0.769764	+	0.638328i	$0.779626\pi$
$138$	−36636.2	−	223471.i	−0.0139404	−	0.0850324i
$139$	2.08374e6	+	3.07329e6i	0.775890	+	1.14435i	0.986012	+	0.166676i	$0.0533035\pi$
$139$	2.08374e6	+	3.07329e6i	0.775890	+	1.14435i	−0.210122	+	0.977675i	$0.567386\pi$
$140$	632245.	+	480620.i	0.230410	+	0.175153i
$141$	−34333.7	−	315693.i	−0.0122480	−	0.112618i
$142$	900573.	−	477454.i	0.314524	−	0.166750i
$143$	596058.	+	358636.i	0.203836	+	0.122644i
$144$	1.15043e6	−	692188.i	0.385275	−	0.231813i
$145$	−3.43082e6	+	6.47122e6i	−1.12537	+	2.12267i
$146$	−616696.	+	1.54779e6i	−0.198159	+	0.497341i
$147$	−641561.	−	141218.i	−0.201970	−	0.0444569i
$148$	934656.	−	4.24619e6i	0.288315	−	1.30983i
$149$	−3.56242e6	−	1.41940e6i	−1.07693	−	0.429087i	−0.236845	−	0.971547i	$-0.576114\pi$
$149$	−3.56242e6	−	1.41940e6i	−1.07693	−	0.429087i	−0.840081	+	0.542460i	$0.817493\pi$
$150$	−211321.	−	112035.i	−0.0626136	−	0.0331956i
$151$	−1.15076e6	−	1.91258e6i	−0.334237	−	0.555506i	0.643472	−	0.765469i	$-0.277493\pi$
$151$	−1.15076e6	−	1.91258e6i	−0.334237	−	0.555506i	−0.977709	+	0.209963i	$0.932666\pi$
$152$	−1.72233e6	+	2.86253e6i	−0.490439	+	0.815116i
$153$	285240.	+	538019.i	0.0796408	+	0.150218i
$154$	−172843.	+	18797.8i	−0.0473250	+	0.00514690i
$155$	2.71305e6	−	3.56896e6i	0.728557	−	0.958400i
$156$	333276.	−	225966.i	0.0877869	−	0.0595210i
$157$	408804.	−	67020.0i	0.105637	−	0.0173183i	−0.108732	−	0.994071i	$-0.534679\pi$
$157$	408804.	−	67020.0i	0.105637	−	0.0173183i	0.214369	+	0.976753i	$0.431231\pi$
$158$	1.61783e6	−	644604.i	0.410169	−	0.163426i
$159$	294939.	+	32076.6i	0.0733739	+	0.00797989i
$160$	−3.66938e6	+	3.87372e6i	−0.895844	+	0.945731i
$161$	767624.	+	652025.i	0.183938	+	0.156238i
$162$	659105.	−	1.42463e6i	0.155028	−	0.335087i
$163$	715906.	−	1.05588e6i	0.165308	−	0.243811i	−0.736009	−	0.676972i	$-0.763292\pi$
$163$	715906.	−	1.05588e6i	0.165308	−	0.243811i	0.901316	+	0.433162i	$0.142602\pi$
$164$	1.73627e6	−	585017.i	0.393627	−	0.132628i
$165$	−517224.	+	143607.i	−0.115140	+	0.0319685i
$166$	−1.08268e6	−	1.27464e6i	−0.236689	−	0.278652i
$167$	147072.	−	2.71258e6i	0.0315776	−	0.582415i	−0.939338	−	0.342993i	$-0.888559\pi$
$167$	147072.	−	2.71258e6i	0.0315776	−	0.582415i	0.970916	−	0.239422i	$-0.0769580\pi$
$168$	−71673.3	+	212719.i	−0.0151157	+	0.0448619i
$169$	2.52801e6	−	1.92174e6i	0.523744	−	0.398140i
$170$	−344517.	−	363702.i	−0.0701236	−	0.0740285i
$171$	−311918.	−	5.75300e6i	−0.0623810	−	1.15055i
$172$	6.21785e6	+	1.72638e6i	1.22195	+	0.339274i
$173$	−454798.	−	983029.i	−0.0878375	−	0.189858i	0.858678	−	0.512515i	$-0.171286\pi$
$173$	−454798.	−	983029.i	−0.0878375	−	0.189858i	−0.946516	+	0.322657i	$0.895424\pi$
$174$	−915915.	−	150157.i	−0.173863	−	0.0285034i
$175$	1.03891e6	−	228681.i	0.193848	−	0.0426693i
$176$			1.04923e6i			0.192456i
$177$	−1.05180e6	+	651590.i	−0.189677	+	0.117505i
$178$	−1.42829e6			−0.253254
$179$	461970.	+	2.09875e6i	0.0805480	+	0.365933i	0.999602	−	0.0281975i	$-0.00897675\pi$
$179$	461970.	+	2.09875e6i	0.0805480	+	0.365933i	−0.919054	+	0.394131i	$0.871046\pi$
$180$	959438.	−	5.85231e6i	0.164513	−	1.00348i
$181$	1.65220e6	−	764390.i	0.278630	−	0.128908i	−0.275598	−	0.961273i	$-0.588876\pi$
$181$	1.65220e6	−	764390.i	0.278630	−	0.128908i	0.554228	+	0.832365i	$0.313014\pi$
$182$	110412.	−	397670.i	0.0183149	−	0.0659642i
$183$	−1.50978e6	+	81857.7i	−0.246354	+	0.0133569i
$184$	−3.16599e6	+	2.99899e6i	−0.508226	+	0.481417i
$185$	−8.32653e6	−	1.09534e7i	−1.31507	−	1.72995i
$186$	538354.	+	181393.i	0.0836622	+	0.0281891i
$187$	−475189.	−	25764.0i	−0.0726678	−	0.00393993i
$188$	−2.08962e6	+	1.77494e6i	−0.314480	+	0.267122i
$189$	−212557.	−	765563.i	−0.0314841	−	0.113395i
$190$	1.51342e6	+	4.49167e6i	0.220647	+	0.654858i
$191$	−9.60739e6	−	6.51397e6i	−1.37881	−	0.934858i	−0.999956	−	0.00940325i	$-0.997007\pi$
$191$	−9.60739e6	−	6.51397e6i	−1.37881	−	0.934858i	−0.378857	−	0.925455i	$-0.623683\pi$
$192$	64582.7	+	29879.1i	0.00912457	+	0.00422148i
$193$	−6.66279e6	+	7.84404e6i	−0.926796	+	1.09111i	0.0688248	+	0.997629i	$0.478075\pi$
$193$	−6.66279e6	+	7.84404e6i	−0.926796	+	1.09111i	−0.995621	+	0.0934802i	$0.970201\pi$
$194$	−2.04434e6	−	1.93650e6i	−0.279993	−	0.265223i
$195$	137768.	−	1.26676e6i	0.0185800	−	0.170840i
$196$	2.09931e6	+	5.26888e6i	0.278811	+	0.699762i
$197$	−621306.	−	3.78980e6i	−0.0812656	−	0.495698i	−0.995828	−	0.0912529i	$-0.970913\pi$
$197$	−621306.	−	3.78980e6i	−0.0812656	−	0.495698i	0.914562	−	0.404445i	$-0.132535\pi$
$198$	728582.	+	1.07458e6i	0.0938605	+	0.138434i
$199$	4.42728e6	+	3.36553e6i	0.561795	+	0.427065i	0.847148	−	0.531357i	$-0.178318\pi$
$199$	4.42728e6	+	3.36553e6i	0.561795	+	0.427065i	−0.285353	+	0.958422i	$0.592111\pi$
$200$	497998.	+	4.57902e6i	0.0622498	+	0.572377i
$201$	−115285.	+	61120.5i	−0.0141967	+	0.00752660i
$202$	−4.11617e6	−	2.47662e6i	−0.499389	−	0.300473i
$203$	3.53706e6	−	2.12818e6i	0.422819	−	0.254402i
$204$	−129028.	+	243373.i	−0.0151983	+	0.0286670i
$205$	2.14606e6	−	5.38620e6i	0.249104	−	0.625203i
$206$	858119.	+	188886.i	0.0981625	+	0.0216072i
$207$	1.61676e6	−	7.34500e6i	0.182278	−	0.828096i
$208$	−2.31375e6	−	921883.i	−0.257115	−	0.102444i
$209$	3.97798e6	+	2.10899e6i	0.435737	+	0.231013i
$210$	164190.	+	272886.i	0.0177292	+	0.0294662i
$211$	−7.68347e6	+	1.27700e7i	−0.817919	+	1.35939i	0.112786	+	0.993619i	$0.464023\pi$
$211$	−7.68347e6	+	1.27700e7i	−0.817919	+	1.35939i	−0.930704	+	0.365772i	$0.880805\pi$
$212$	−1.19981e6	−	2.26308e6i	−0.125923	−	0.237516i
$213$	−1.76324e6	+	191764.i	−0.182463	+	0.0198440i
$214$	1.52414e6	−	2.00498e6i	0.155519	−	0.204582i
$215$	1.69022e7	−	1.14600e7i	1.70070	−	1.15310i
$216$	3.39487e6	−	556560.i	0.336869	−	0.0552269i
$217$	−2.34716e6	+	935196.i	−0.229702	+	0.0915216i
$218$	−128087.	−	13930.3i	−0.0123633	−	0.00134459i
$219$	1.99373e6	−	2.10475e6i	0.189816	−	0.200387i
$220$	3.53226e6	+	3.00033e6i	0.331730	+	0.281774i
$221$	474331.	−	1.02525e6i	0.0439445	−	0.0949845i
$222$	978435.	−	1.44308e6i	0.0894279	−	0.131896i
$223$	−8.86224e6	+	2.98604e6i	−0.799151	+	0.269265i	−0.689105	−	0.724661i	$-0.741996\pi$
$223$	−8.86224e6	+	2.98604e6i	−0.799151	+	0.269265i	−0.110046	+	0.993927i	$0.535100\pi$
$224$	2.89754e6	−	804497.i	0.257801	−	0.0715781i
$225$	−5.14255e6	−	6.05428e6i	−0.451472	−	0.531514i
$226$	66980.6	−	1.23538e6i	0.00580262	−	0.107023i
$227$	3.40275e6	−	1.00990e7i	0.290906	−	0.863379i	−0.698165	−	0.715937i	$-0.746000\pi$
$227$	3.40275e6	−	1.00990e7i	0.290906	−	0.863379i	0.989071	−	0.147442i	$-0.0471038\pi$
$228$	2.07477e6	−	1.57720e6i	0.175052	−	0.133071i
$229$	−768153.	−	810929.i	−0.0639648	−	0.0675269i	0.693228	−	0.720719i	$-0.256188\pi$
$229$	−768153.	−	810929.i	−0.0639648	−	0.0675269i	−0.757192	+	0.653192i	$0.773429\pi$
$230$	334967.	+	6.17811e6i	0.0275308	+	0.507776i
$231$	291501.	+	80934.7i	0.0236485	+	0.00656597i
$232$	7.50489e6	+	1.62215e7i	0.601008	+	1.29906i
$233$	−2.08594e6	−	341973.i	−0.164905	−	0.0270349i	0.0787636	−	0.996893i	$-0.474903\pi$
$233$	−2.08594e6	−	341973.i	−0.164905	−	0.0270349i	−0.243669	+	0.969858i	$0.578351\pi$
$234$	−3.00981e6	+	662509.i	−0.234905	+	0.0517064i
$235$			8.67622e6i			0.668540i
$236$	9.75249e6	+	4.35922e6i	0.741958	+	0.331644i
$237$	−3.03032e6			−0.227637
$238$	60694.8	+	275739.i	0.00450216	+	0.0204535i
$239$	−4.11925e6	+	2.51263e7i	−0.301734	+	1.84050i	0.205459	+	0.978666i	$0.434131\pi$
$239$	−4.11925e6	+	2.51263e7i	−0.301734	+	1.84050i	−0.507194	+	0.861832i	$0.669317\pi$
$240$	1.74429e6	−	806996.i	0.126179	−	0.0583764i
$241$	−1.43917e6	+	5.18341e6i	−0.102816	+	0.370309i	−0.997001	−	0.0773880i	$-0.975342\pi$
$241$	−1.43917e6	+	5.18341e6i	−0.102816	+	0.370309i	0.894185	+	0.447697i	$0.147756\pi$
$242$	5.11141e6	−	277133.i	0.360657	−	0.0195543i
$243$	−6.51593e6	+	6.17222e6i	−0.454107	+	0.430153i
$244$	7.90009e6	+	1.03924e7i	0.543829	+	0.715395i
$245$	1.70088e7	+	5.73093e6i	1.15658	+	0.389697i
$246$	733637.	+	39776.6i	0.0492806	+	0.00267192i
$247$	−8.14593e6	+	6.91921e6i	−0.540567	+	0.459162i
$248$	−2.92674e6	−	1.05412e7i	−0.191879	−	0.691087i
$249$	929178.	+	2.75770e6i	0.0601868	+	0.178628i
$250$	−1.96103e6	−	1.32961e6i	−0.125506	−	0.0850951i
$251$	−1.93629e6	−	895825.i	−0.122448	−	0.0566503i	0.357709	−	0.933833i	$-0.383558\pi$
$251$	−1.93629e6	−	895825.i	−0.122448	−	0.0566503i	−0.480156	+	0.877183i	$0.659420\pi$
$252$	−2.16377e6	+	2.54739e6i	−0.135210	+	0.159182i
$253$	4.26696e6	+	4.04188e6i	0.263486	+	0.249587i
$254$	1.11804e6	−	1.02802e7i	0.0682269	−	0.627336i
$255$	322653.	+	809797.i	0.0194587	+	0.0488378i
$256$	1.06268e6	+	6.48203e6i	0.0633404	+	0.386359i
$257$	1.32708e7	+	1.95729e7i	0.781802	+	1.15307i	0.984766	+	0.173885i	$0.0556322\pi$
$257$	1.32708e7	+	1.95729e7i	0.781802	+	1.15307i	−0.202964	+	0.979186i	$0.565057\pi$
$258$	2.06006e6	+	1.56602e6i	0.119956	+	0.0911881i
$259$	838391.	+	7.70888e6i	0.0482556	+	0.443703i
$260$	−9.71988e6	+	5.15315e6i	−0.553020	+	0.293193i
$261$	−2.64124e7	−	1.58918e7i	−1.48555	−	0.893824i
$262$	2.37486e6	−	1.42890e6i	0.132049	−	0.0794509i
$263$	1.29000e7	−	2.43319e7i	0.709122	−	1.33755i	−0.222792	−	0.974866i	$-0.571517\pi$
$263$	1.29000e7	−	2.43319e7i	0.709122	−	1.33755i	0.931914	−	0.362680i	$-0.118138\pi$
$264$	−484846.	+	1.21687e6i	−0.0263507	+	0.0661353i
$265$	−7.91633e6	−	1.74252e6i	−0.425389	−	0.0936352i
$266$	574246.	−	2.60882e6i	0.0305108	−	0.138612i
$267$	2.30877e6	+	919896.i	0.121296	+	0.0483287i
$268$	995350.	+	527701.i	0.0517096	+	0.0274147i
$269$	−1.67742e7	−	2.78790e7i	−0.861758	−	1.43225i	−0.901376	−	0.433038i	$-0.857442\pi$
$269$	−1.67742e7	−	2.78790e7i	−0.861758	−	1.43225i	0.0396180	−	0.999215i	$-0.487386\pi$
$270$	2.51636e6	−	4.18222e6i	0.127844	−	0.212479i
$271$	6.17981e6	+	1.16564e7i	0.310504	+	0.585673i	0.988823	−	0.149095i	$-0.0476360\pi$
$271$	6.17981e6	+	1.16564e7i	0.310504	+	0.585673i	−0.678319	+	0.734768i	$0.737291\pi$
$272$	1.69388e6	−	184221.i	0.0841737	−	0.00915444i
$273$	−434599.	+	571705.i	−0.0213600	+	0.0280985i
$274$	4.54009e6	−	3.07826e6i	0.220705	−	0.149642i
$275$	6.12597e6	−	1.00430e6i	0.294562	−	0.0482910i
$276$	3.16043e6	−	1.25923e6i	0.150321	−	0.0598933i
$277$	−1.74816e7	−	1.90124e6i	−0.822513	−	0.0894537i	−0.312823	−	0.949812i	$-0.601275\pi$
$277$	−1.74816e7	−	1.90124e6i	−0.822513	−	0.0894537i	−0.509690	+	0.860358i	$0.670240\pi$
$278$	8.84072e6	−	9.33304e6i	0.411484	−	0.434399i
$279$	1.43797e7	+	1.22143e7i	0.662122	+	0.562412i
$280$	2.57515e6	−	5.56610e6i	0.117308	−	0.253558i
$281$	−7.93778e6	+	1.17073e7i	−0.357750	+	0.527642i	−0.963392	−	0.268095i	$-0.913606\pi$
$281$	−7.93778e6	+	1.17073e7i	−0.357750	+	0.527642i	0.605642	+	0.795737i	$0.292916\pi$
$282$	−1.04189e6	+	351053.i	−0.0464594	+	0.0156540i
$283$	−1.20955e6	+	335831.i	−0.0533662	+	0.0148170i	−0.294109	−	0.955772i	$-0.595023\pi$
$283$	−1.20955e6	+	335831.i	−0.0533662	+	0.0148170i	0.240743	+	0.970589i	$0.422609\pi$
$284$	9.91358e6	+	1.16712e7i	0.432789	+	0.509518i
$285$	446506.	−	8.23532e6i	0.0192882	−	0.355751i
$286$	769012.	−	2.28235e6i	0.0328727	−	0.0975627i
$287$	−2.60137e6	+	1.97751e6i	−0.110042	+	0.0836515i
$288$	−1.54425e7	−	1.63025e7i	−0.646459	−	0.682458i
$289$	−1.26494e6	−	2.33305e7i	−0.0524056	−	0.966564i
$290$	2.44343e7	+	6.78416e6i	1.00186	+	0.278165i
$291$	2.05737e6	+	4.44693e6i	0.0834898	+	0.180460i
$292$	−2.47007e7	−	4.04947e6i	−0.992112	−	0.162648i
$293$	−2.93900e7	+	6.46923e6i	−1.16841	+	0.257188i	−0.756475	−	0.654023i	$-0.773080\pi$
$293$	−2.93900e7	+	6.46923e6i	−1.16841	+	0.257188i	−0.411940	+	0.911211i	$0.635149\pi$
$294$			2.27439e6i			0.0894999i
$295$	3.04937e7	−	1.45913e7i	1.18780	−	0.568367i
$296$	−3.35753e7			−1.29463
$297$	−996711.	−	4.52810e6i	−0.0380452	−	0.172841i
$298$	−2.14794e6	+	1.31019e7i	−0.0811660	+	0.495091i
$299$	−1.26622e7	+	5.85817e6i	−0.473693	+	0.219154i
$300$	961304.	−	3.46230e6i	0.0356038	−	0.128233i
$301$	−1.14921e7	+	623084.i	−0.421406	+	0.0228479i
$302$	−5.61045e6	+	5.31450e6i	−0.203693	+	0.192949i
$303$	5.05853e6	+	6.65439e6i	0.181843	+	0.239211i
$304$	−1.52768e7	−	5.14735e6i	−0.543765	−	0.183216i
$305$	4.12501e7	+	2.23651e6i	1.45387	+	0.0788265i
$306$	1.60689e6	−	1.36490e6i	0.0560816	−	0.0476362i
$307$	−3.85305e6	−	1.38774e7i	−0.133165	−	0.479616i	0.866649	−	0.498919i	$-0.166269\pi$
$307$	−3.85305e6	−	1.38774e7i	−0.133165	−	0.479616i	−0.999814	+	0.0193021i	$0.993856\pi$
$308$	−834003.	−	2.47523e6i	−0.0285440	−	0.0847156i
$309$	−1.26546e6	−	858003.i	−0.0428916	−	0.0290813i
$310$	−1.40868e7	−	6.51726e6i	−0.472855	−	0.218766i
$311$	−1.20425e7	+	1.41775e7i	−0.400345	+	0.471322i	−0.924986	−	0.380001i	$-0.875924\pi$
$311$	−1.20425e7	+	1.41775e7i	−0.400345	+	0.471322i	0.524641	+	0.851323i	$0.324199\pi$
$312$	−2.25744e6	−	2.13836e6i	−0.0743281	−	0.0704073i
$313$	4.73814e6	−	4.35665e7i	0.154516	−	1.42076i	−0.618208	−	0.786014i	$-0.712141\pi$
$313$	4.73814e6	−	4.35665e7i	0.154516	−	1.42076i	0.772725	−	0.634741i	$-0.218893\pi$
$314$	−530873.	−	1.33239e6i	−0.0171475	−	0.0430371i
$315$	1.71115e6	+	1.04376e7i	0.0547465	+	0.333939i
$316$	1.46824e7	+	2.16549e7i	0.465303	+	0.686271i
$317$	−3.64704e7	−	2.77241e7i	−1.14489	−	0.870322i	−0.151884	−	0.988398i	$-0.548534\pi$
$317$	−3.64704e7	−	2.77241e7i	−1.14489	−	0.870322i	−0.993004	+	0.118077i	$0.962327\pi$
$318$	−111056.	−	1.02114e6i	−0.00345350	−	0.0317544i
$319$	2.12829e7	−	1.12835e7i	0.655630	−	0.347593i
$320$	−1.66592e6	−	1.00235e6i	−0.0508398	−	0.0305893i
$321$	−3.75503e6	+	2.25933e6i	−0.113527	+	0.0683068i
$322$	1.63335e6	−	3.08082e6i	0.0489227	−	0.0922780i
$323$	2.70633e6	−	6.79239e6i	0.0803108	−	0.201565i
$324$	2.30307e7	+	5.06943e6i	0.677129	+	0.149047i
$325$	−3.16779e6	+	1.43914e7i	−0.0922796	+	0.419230i
$326$	−4.10304e6	−	1.63480e6i	−0.118428	−	0.0471859i
$327$	198075.	+	105012.i	0.00566481	+	0.00300329i
$328$	−7.29437e6	−	1.21233e7i	−0.206712	−	0.343559i
$329$	2.52096e6	−	4.18986e6i	0.0707910	−	0.117655i
$330$	870526.	+	1.64199e6i	0.0242237	+	0.0456907i
$331$	6.42036e7	−	6.98256e6i	1.77042	−	0.192544i	0.836000	−	0.548729i	$-0.184888\pi$
$331$	6.42036e7	−	6.98256e6i	1.77042	−	0.192544i	0.934416	+	0.356185i	$0.115923\pi$
$332$	1.52048e7	−	2.00015e7i	0.415495	−	0.546574i
$333$	4.79266e7	−	3.24950e7i	1.29791	−	0.880004i
$334$	−9.28139e6	+	1.52161e6i	−0.249100	+	0.0408379i
$335$	3.31191e6	−	1.31959e6i	0.0880936	−	0.0350997i
$336$	−1.07682e6	−	117111.i	−0.0283874	−	0.00308732i
$337$	−4.63827e7	+	4.89657e7i	−1.21190	+	1.27939i	−0.262640	+	0.964894i	$0.584593\pi$
$337$	−4.63827e7	+	4.89657e7i	−1.21190	+	1.27939i	−0.949260	+	0.314493i	$0.898166\pi$
$338$	−8.37944e6	−	7.11756e6i	−0.217003	−	0.184324i
$339$	−903928.	+	1.95381e6i	−0.0232025	+	0.0501514i
$340$	4.22358e6	−	6.22931e6i	0.107459	−	0.158490i
$341$	−1.39724e7	+	4.70786e6i	−0.352378	+	0.118730i
$342$	−1.92202e7	+	5.33647e6i	−0.480485	+	0.133406i
$343$	−1.36140e7	−	1.60276e7i	−0.337367	−	0.397180i
$344$	2.69787e6	−	4.97594e7i	0.0662745	−	1.22236i
$345$	3.43758e6	−	1.02024e7i	0.0837136	−	0.248453i
$346$	−2.98538e6	+	2.26943e6i	−0.0720728	+	0.0547883i
$347$	−1.65836e7	−	1.75070e7i	−0.396907	−	0.419010i	0.496656	−	0.867948i	$-0.334561\pi$
$347$	−1.65836e7	−	1.75070e7i	−0.396907	−	0.419010i	−0.893563	+	0.448938i	$0.851803\pi$
$348$	−754891.	−	1.39231e7i	−0.0179121	−	0.330369i
$349$	4.08852e7	+	1.13517e7i	0.961812	+	0.267046i	0.712731	−	0.701437i	$-0.247458\pi$
$349$	4.08852e7	+	1.13517e7i	0.961812	+	0.267046i	0.249080	+	0.968483i	$0.419872\pi$
$350$	−1.54646e6	−	3.34261e6i	−0.0360689	−	0.0779617i
$351$	1.08611e7	+	1.78059e6i	0.251161	+	0.0411758i
$352$	1.71382e7	−	3.77240e6i	0.392949	−	0.0864946i
$353$			3.93377e7i			0.894304i	0.894458	+	0.447152i	$0.147562\pi$
$353$			3.93377e7i			0.894304i	−0.894458	+	0.447152i	$0.852438\pi$
$354$	2.98602e6	+	3.07146e6i	0.0673106	+	0.0692365i
$355$	4.84594e7			1.08316
$356$	−4.61270e6	−	2.09557e7i	−0.102236	−	0.464464i
$357$	79480.8	−	484812.i	0.00174686	−	0.0106554i
$358$	6.75259e6	−	3.12408e6i	0.147171	−	0.0680884i
$359$	−1.98385e7	+	7.14518e7i	−0.428771	+	1.54429i	0.361999	+	0.932179i	$0.382095\pi$
$359$	−1.98385e7	+	7.14518e7i	−0.428771	+	1.54429i	−0.790769	+	0.612114i	$0.790319\pi$
$360$	−4.57294e7	+	2.47938e6i	−0.980140	+	0.0531417i
$361$	−1.60673e7	+	1.52198e7i	−0.341525	+	0.323509i
$362$	−3.81429e6	−	5.01761e6i	−0.0804059	−	0.105772i
$363$	−8.44086e6	−	2.84406e6i	−0.176468	−	0.0594591i
$364$	6.19116e6	+	335675.i	0.128371	+	0.00696008i
$365$	−6.03707e7	+	5.12794e7i	−1.24150	+	1.05454i
$366$	1.40047e6	+	5.04402e6i	0.0285647	+	0.102881i
$367$	2.45450e7	+	7.28469e7i	0.496552	+	1.47371i	0.844169	+	0.536077i	$0.180094\pi$
$367$	2.45450e7	+	7.28469e7i	0.496552	+	1.47371i	−0.347618	+	0.937636i	$0.613009\pi$
$368$	−1.74174e7	−	1.18093e7i	−0.349495	−	0.236963i
$369$	2.21455e7	+	1.02456e7i	0.440765	+	0.203920i
$370$	−3.08390e7	+	3.63064e7i	−0.608828	+	0.716768i
$371$	3.31660e6	+	3.14165e6i	0.0649488	+	0.0615228i
$372$	−922744.	+	8.48449e6i	−0.0179247	+	0.164815i
$373$	−2.61556e7	−	6.56455e7i	−0.504008	−	1.26497i	−0.932418	−	0.361381i	$-0.882305\pi$
$373$	−2.61556e7	−	6.56455e7i	−0.504008	−	1.26497i	0.428410	−	0.903584i	$-0.359074\pi$
$374$	266555.	+	1.62591e6i	0.00509533	+	0.0310801i
$375$	2.31358e6	+	3.41227e6i	0.0438723	+	0.0647068i
$376$	1.68551e7	+	1.28129e7i	0.317079	+	0.241037i
$377$	6.18249e6	+	5.68470e7i	0.115382	+	1.06092i
$378$	−2.43037e6	+	1.28850e6i	−0.0449983	+	0.0238566i
$379$	−1.06441e7	−	6.40432e6i	−0.195519	−	0.117640i	0.414428	−	0.910082i	$-0.363982\pi$
$379$	−1.06441e7	−	6.40432e6i	−0.195519	−	0.117640i	−0.609947	+	0.792442i	$0.708809\pi$
$380$	−6.10137e7	+	3.67107e7i	−1.11193	+	0.669025i
$381$	−8.42827e6	+	1.58974e7i	−0.152393	+	0.287443i
$382$	−1.48749e7	+	3.73332e7i	−0.266848	+	0.669739i
$383$	5.09359e7	+	1.12118e7i	0.906624	+	0.199563i	0.643722	−	0.765259i	$-0.277389\pi$
$383$	5.09359e7	+	1.12118e7i	0.906624	+	0.199563i	0.262902	+	0.964822i	$0.415320\pi$
$384$	2.73979e6	−	1.24470e7i	0.0483865	−	0.219822i
$385$	−7.67860e6	−	3.05943e6i	−0.134555	−	0.0536116i
$386$	3.14817e7	+	1.66905e7i	0.547389	+	0.290207i
$387$	4.43074e7	+	7.36395e7i	0.764440	+	1.27051i
$388$	2.18099e7	−	3.62483e7i	0.373386	−	0.620572i
$389$	−2.83303e7	−	5.34367e7i	−0.481286	−	0.907801i	−0.998645	−	0.0520332i	$-0.983430\pi$
$389$	−2.83303e7	−	5.34367e7i	−0.481286	−	0.907801i	0.517360	−	0.855768i	$-0.326915\pi$
$390$	−4.38577e6	+	476982.i	−0.0739354	+	0.00804096i
$391$	5.77607e6	−	7.59829e6i	0.0966278	−	0.127112i
$392$	3.62516e7	−	2.45792e7i	0.601823	−	0.408046i
$393$	−4.75915e6	+	780223.i	−0.0784064	+	0.0128541i
$394$	−1.23519e7	+	4.92143e6i	−0.201950	+	0.0804643i
$395$	8.23089e7	+	8.95164e6i	1.33554	+	0.145248i
$396$	−1.34131e7	+	1.41601e7i	−0.215995	+	0.228023i
$397$	4.37235e7	+	3.71391e7i	0.698785	+	0.593553i	0.924747	−	0.380583i	$-0.124277\pi$
$397$	4.37235e7	+	3.71391e7i	0.698785	+	0.593553i	−0.225962	+	0.974136i	$0.572553\pi$
$398$	8.08463e6	−	1.74746e7i	0.128236	−	0.277178i
$399$	−2.60847e6	+	3.84721e6i	−0.0410646	+	0.0605657i
$400$	−2.10628e7	+	7.09688e6i	−0.329106	+	0.110889i
$401$	−9.07046e6	+	2.51840e6i	−0.140668	+	0.0390564i	−0.337149	−	0.941451i	$-0.609463\pi$
$401$	−9.07046e6	+	2.51840e6i	−0.140668	+	0.0390564i	0.196480	+	0.980508i	$0.437049\pi$
$402$	292468.	+	344320.i	0.00450194	+	0.00530010i
$403$	1.89485e6	−	3.49485e7i	0.0289507	−	0.533965i
$404$	2.30434e7	−	6.83904e7i	0.349464	−	1.03717i
$405$	5.94094e7	−	4.51618e7i	0.894314	−	0.679840i
$406$	−9.82846e6	−	1.03758e7i	−0.146861	−	0.155040i
$407$	2.44984e6	+	4.51847e7i	0.0363375	+	0.670205i
$408$	2.04966e6	+	569085.i	0.0301787	+	0.00837908i
$409$	8.26766e6	+	1.78703e7i	0.120841	+	0.261193i	0.958550	−	0.284923i	$-0.0919680\pi$
$409$	8.26766e6	+	1.78703e7i	0.120841	+	0.261193i	−0.837710	+	0.546116i	$0.816106\pi$
$410$	−1.98094e7	−	3.24759e6i	−0.287422	−	0.0471204i
$411$	−9.32144e6	+	2.05180e6i	−0.134263	+	0.0295536i
$412$			1.32003e7i			0.188752i
$413$	−1.89655e7	−	1.81389e6i	−0.269224	−	0.0257490i
$414$	−2.60386e7			−0.366959
$415$	−1.70918e7	−	7.76490e7i	−0.239136	−	1.08640i
$416$	−6.73925e6	+	4.11076e7i	−0.0936120	+	0.571008i
$417$	−2.03016e7	+	9.39254e6i	−0.279977	+	0.129531i
$418$	4.17035e6	−	1.50203e7i	0.0571010	−	0.205659i
$419$	7.35225e7	−	3.98628e6i	0.999490	−	0.0541908i	0.452874	−	0.891574i	$-0.350399\pi$
$419$	7.35225e7	−	3.98628e6i	0.999490	−	0.0541908i	0.546616	+	0.837384i	$0.315916\pi$
$420$	−3.47350e6	+	3.29028e6i	−0.0468835	+	0.0444104i
$421$	9.52926e6	+	1.25355e7i	0.127706	+	0.167995i	0.855503	−	0.517799i	$-0.173248\pi$
$421$	9.52926e6	+	1.25355e7i	0.127706	+	0.167995i	−0.727796	+	0.685794i	$0.759455\pi$
$422$	4.88974e7	+	1.64754e7i	0.650651	+	0.219230i
$423$	−3.64602e7	−	1.97681e6i	−0.481723	−	0.0261183i
$424$	−1.50758e7	+	1.28055e7i	−0.197781	+	0.167996i
$425$	−2.69694e6	−	9.71350e6i	−0.0351321	−	0.126534i
$426$	1.96074e6	+	5.81926e6i	0.0253624	+	0.0752730i
$427$	−1.92704e7	−	1.30656e7i	−0.247518	−	0.167821i
$428$	3.43391e7	+	1.58870e7i	0.437984	+	0.202633i
$429$	−2.71303e6	+	3.19403e6i	−0.0343624	+	0.0404545i
$430$	−5.13290e7	−	4.86214e7i	−0.645591	−	0.611536i
$431$	8.02934e6	−	7.38286e7i	0.100288	−	0.922131i	−0.830611	−	0.556853i	$-0.812009\pi$
$431$	8.02934e6	−	7.38286e7i	0.100288	−	0.922131i	0.930899	−	0.365278i	$-0.119026\pi$
$432$	6.14450e6	+	1.54215e7i	0.0762141	+	0.191283i
$433$	−3.18977e6	−	1.94568e7i	−0.0392913	−	0.239666i	0.959878	−	0.280418i	$-0.0904730\pi$
$433$	−3.18977e6	−	1.94568e7i	−0.0392913	−	0.239666i	−0.999169	+	0.0407517i	$0.987025\pi$
$434$	4.90907e6	+	7.24033e6i	0.0600523	+	0.0885705i
$435$	−3.51277e7	−	2.67034e7i	−0.426758	−	0.324413i
$436$	−209276.	−	1.92426e6i	−0.00252499	−	0.0232169i
$437$	−7.97831e7	+	4.22983e7i	−0.956019	+	0.506849i
$438$	−8.60058e6	−	5.17480e6i	−0.102354	−	0.0615845i
$439$	6.91557e7	−	4.16096e7i	0.817400	−	0.491813i	−0.0444291	−	0.999013i	$-0.514147\pi$
$439$	6.91557e7	−	4.16096e7i	0.817400	−	0.491813i	0.861829	+	0.507200i	$0.169319\pi$
$440$	1.67640e7	−	3.16202e7i	0.196797	−	0.371199i
$441$	−2.79585e7	+	7.01705e7i	−0.325985	+	0.818161i
$442$	−3.81966e6	−	840772.i	−0.0442342	−	0.00973669i
$443$	−5.28687e6	+	2.40185e7i	−0.0608118	+	0.276271i	−0.997208	−	0.0746739i	$-0.976208\pi$
$443$	−5.28687e6	+	2.40185e7i	−0.0608118	+	0.276271i	0.936396	+	0.350945i	$0.114139\pi$
$444$	2.43327e7	+	9.69502e6i	0.277998	+	0.110764i
$445$	−5.99929e7	−	3.18062e7i	−0.680800	−	0.360937i
$446$	1.66925e7	+	2.77431e7i	0.188155	+	0.312716i
$447$	1.19104e7	−	1.97952e7i	0.133353	−	0.221635i
$448$	513252.	+	968096.i	0.00570817	+	0.0107667i
$449$	7.46492e6	−	811858.i	0.0824681	−	0.00896894i	−0.0667919	−	0.997767i	$-0.521276\pi$
$449$	7.46492e6	−	811858.i	0.0824681	−	0.00896894i	0.149260	+	0.988798i	$0.452311\pi$
$450$	−1.66436e7	+	2.18943e7i	−0.182646	+	0.240267i
$451$	−1.57830e7	+	1.07011e7i	−0.172052	+	0.116654i
$452$	1.83418e7	−	3.00698e6i	0.198621	−	0.0325623i
$453$	1.24919e7	−	4.97722e6i	0.134380	−	0.0535417i
$454$	−3.66799e7	−	3.98918e6i	−0.391978	−	0.0426301i
$455$	1.34933e7	−	1.42447e7i	0.143247	−	0.151224i
$456$	−1.53391e7	−	1.30292e7i	−0.161773	−	0.137411i
$457$	5.83750e7	−	1.26176e8i	0.611615	−	1.32199i	−0.316110	−	0.948722i	$-0.602377\pi$
$457$	5.83750e7	−	1.26176e8i	0.611615	−	1.32199i	0.927726	−	0.373263i	$-0.121761\pi$
$458$	−2.17025e6	+	3.20088e6i	−0.0225898	+	0.0333175i
$459$	−7.13521e6	+	2.40413e6i	−0.0737851	+	0.0248611i
$460$	−8.95628e7	+	2.48670e7i	−0.920141	+	0.255476i
$461$	1.93385e6	+	2.27671e6i	0.0197388	+	0.0232383i	0.771943	−	0.635692i	$-0.219285\pi$
$461$	1.93385e6	+	2.27671e6i	0.0197388	+	0.0232383i	−0.752204	+	0.658930i	$0.771009\pi$
$462$	56705.7	−	1.04588e6i	0.000575044	−	0.0106061i
$463$	2.59578e7	−	7.70399e7i	0.261532	−	0.776199i	−0.733772	−	0.679396i	$-0.762242\pi$
$463$	2.59578e7	−	7.70399e7i	0.261532	−	0.776199i	0.995304	−	0.0968027i	$-0.0308616\pi$
$464$	−6.86617e7	+	5.21952e7i	−0.687322	+	0.522489i
$465$	1.85733e7	+	1.96076e7i	0.184727	+	0.195014i
$466$	396208.	+	7.30763e6i	0.00391531	+	0.0722136i
$467$	−8.27497e6	−	2.29753e6i	−0.0812486	−	0.0225586i	0.226666	−	0.973973i	$-0.427217\pi$
$467$	−8.27497e6	−	2.29753e6i	−0.0812486	−	0.0225586i	−0.307915	+	0.951414i	$0.599631\pi$
$468$	−1.94406e7	−	4.20201e7i	−0.189658	−	0.409939i
$469$	−1.98278e6	−	325061.i	−0.0192202	−	0.00315099i
$470$	2.93366e7	−	6.45746e6i	0.282563	−	0.0621968i
$471$			2.49566e6i			0.0238849i
$472$	1.66864e7	−	8.07875e7i	0.158685	−	0.768277i
$473$	−6.71616e7			−0.634655
$474$	2.25538e6	+	1.02463e7i	0.0211780	+	0.0962125i
$475$	−1.54304e7	+	9.41214e7i	−0.143978	+	0.878229i
$476$	−3.84960e6	+	1.78102e6i	−0.0356940	+	0.0165138i
$477$	9.12628e6	−	3.28699e7i	0.0840889	−	0.302861i
$478$	8.80244e7	−	4.77255e6i	0.805971	−	0.0436985i
$479$	9.31701e7	−	8.82554e7i	0.847754	−	0.803036i	−0.134436	−	0.990922i	$-0.542922\pi$
$479$	9.31701e7	−	8.82554e7i	0.847754	−	0.803036i	0.982191	+	0.187887i	$0.0601638\pi$
$480$	−1.94530e7	−	2.55900e7i	−0.175899	−	0.231391i
$481$	−1.01794e8	−	3.42983e7i	−0.914714	−	0.308203i
$482$	1.85976e7	+	1.00833e6i	0.166079	+	0.00900456i
$483$	−4.62445e6	+	3.92804e6i	−0.0410411	+	0.0348606i
$484$	2.05735e7	+	7.40991e7i	0.181456	+	0.653547i
$485$	−4.27455e7	−	1.26864e8i	−0.374684	−	1.11202i
$486$	2.57195e7	+	1.74382e7i	0.224054	+	0.151913i
$487$	−1.10865e8	−	5.12914e7i	−0.959856	−	0.444077i	−0.123549	−	0.992338i	$-0.539428\pi$
$487$	−1.10865e8	−	5.12914e7i	−0.959856	−	0.444077i	−0.836307	+	0.548262i	$0.815290\pi$
$488$	6.52622e7	−	7.68326e7i	0.561568	−	0.661129i
$489$	5.57949e6	+	5.28517e6i	0.0477164	+	0.0451994i
$490$	6.71860e6	−	6.17765e7i	0.0571072	−	0.525092i
$491$	1.79150e7	+	4.49632e7i	0.151346	+	0.379851i	0.985028	−	0.172395i	$-0.0551504\pi$
$491$	1.79150e7	+	4.49632e7i	0.151346	+	0.379851i	−0.833682	+	0.552246i	$0.813771\pi$
$492$	1.78570e6	+	1.08923e7i	0.0149939	+	0.0914586i
$493$	−2.19530e7	−	3.23782e7i	−0.183211	−	0.270216i
$494$	2.94584e7	+	2.23937e7i	0.244359	+	0.185757i
$495$	6.67335e6	+	6.13605e7i	0.0550210	+	0.505910i
$496$	4.66409e7	−	2.47275e7i	0.382228	−	0.202644i
$497$	−2.34017e7	−	1.40803e7i	−0.190624	−	0.114695i
$498$	8.63294e6	−	5.19427e6i	0.0698990	−	0.0420568i
$499$	−9.79561e7	+	1.84765e8i	−0.788369	+	1.48702i	0.0830830	+	0.996543i	$0.473523\pi$
$499$	−9.79561e7	+	1.84765e8i	−0.788369	+	1.48702i	−0.871452	+	0.490480i	$0.836821\pi$
$500$	1.31747e7	−	3.30661e7i	0.105398	−	0.264528i
$501$	1.59830e7	+	3.51812e6i	0.127100	+	0.0279767i
$502$	−1.58789e6	+	7.21385e6i	−0.0125519	+	0.0570237i
$503$	−1.85648e8	−	7.39688e7i	−1.45877	−	0.581226i	−0.500153	−	0.865937i	$-0.666723\pi$
$503$	−1.85648e8	−	7.39688e7i	−1.45877	−	0.581226i	−0.958613	+	0.284711i	$0.908102\pi$
$504$	2.28038e7	+	1.20898e7i	0.178121	+	0.0944337i
$505$	−1.17742e8	−	1.95688e8i	−0.914232	−	1.51946i
$506$	1.04909e7	−	1.74360e7i	0.0809767	−	0.134584i
$507$	8.96090e6	+	1.69021e7i	0.0687587	+	0.129693i
$508$	1.54441e8	−	1.67964e7i	1.17807	−	0.128123i
$509$	−1.41880e8	+	1.86640e8i	−1.07589	+	1.41531i	−0.173273	+	0.984874i	$0.555434\pi$
$509$	−1.41880e8	+	1.86640e8i	−1.07589	+	1.41531i	−0.902620	+	0.430439i	$0.858359\pi$
$510$	2.49799e6	−	1.69368e6i	0.0188313	−	0.0127679i
$511$	4.40535e7	−	7.22221e6i	0.330155	−	0.0541262i
$512$	−1.04654e8	+	4.16978e7i	−0.779730	+	0.310673i
$513$	7.08191e7	+	7.70204e6i	0.524564	+	0.0570498i
$514$	5.63040e7	−	5.94395e7i	0.414620	−	0.437709i
$515$	3.18376e7	+	2.70431e7i	0.233087	+	0.197986i
$516$	−1.63235e7	+	3.52826e7i	−0.118813	+	0.256810i
$517$	1.60134e7	−	2.36180e7i	0.115881	−	0.170911i
$518$	2.54417e7	−	8.57232e6i	0.183045	−	0.0616750i
$519$	6.28738e6	−	1.74568e6i	0.0449746	−	0.0124871i
$520$	5.49995e7	+	6.47504e7i	0.391155	+	0.460503i
$521$	−1.19101e7	+	2.19669e8i	−0.0842176	+	1.55330i	0.585491	+	0.810679i	$0.300902\pi$
$521$	−1.19101e7	+	2.19669e8i	−0.0842176	+	1.55330i	−0.669709	+	0.742624i	$0.733581\pi$
$522$	−3.40763e7	+	1.01135e8i	−0.239575	+	0.711033i
$523$	9.08643e7	−	6.90732e7i	0.635167	−	0.482842i	−0.237350	−	0.971424i	$-0.576279\pi$
$523$	9.08643e7	−	6.90732e7i	0.635167	−	0.482842i	0.872518	+	0.488582i	$0.162486\pi$
$524$	2.86344e7	+	3.02290e7i	0.199019	+	0.210102i
$525$	346954.	+	6.39919e6i	0.00239769	+	0.0442229i
$526$	−9.18735e7	−	2.55085e7i	−0.631296	−	0.175278i
$527$	1.00537e7	+	2.17306e7i	0.0686898	+	0.148471i
$528$	−6.23766e6	−	1.02261e6i	−0.0423760	−	0.00694720i
$529$	2.94528e7	−	6.48306e6i	0.198957	−	0.0437938i
$530$			2.80641e7i			0.188505i
$531$	5.43695e7	+	1.31469e8i	0.363138	+	0.878089i
$532$	4.01310e7			0.266529
$533$	−9.73070e6	−	4.42070e7i	−0.0642632	−	0.291951i
$534$	1.39206e6	−	8.49119e6i	0.00914185	−	0.0557628i
$535$	1.08668e8	−	5.02750e7i	0.709641	−	0.328315i
$536$	2.32745e6	−	8.38270e6i	0.0151142	−	0.0544364i
$537$	−1.29274e7	+	700901.i	−0.0834808	+	0.00452620i
$538$	−8.17814e7	+	7.74674e7i	−0.525179	+	0.497476i
$539$	−3.57231e7	−	4.69929e7i	−0.228130	−	0.300100i
$540$	6.94878e7	+	2.34132e7i	0.441293	+	0.148689i
$541$	−7.10524e6	−	385235.i	−0.0448732	−	0.00243295i	0.0316886	−	0.999498i	$-0.489912\pi$
$541$	−7.10524e6	−	385235.i	−0.0448732	−	0.00243295i	−0.0765618	+	0.997065i	$0.524394\pi$
$542$	3.48137e7	−	2.95710e7i	0.218652	−	0.185724i
$543$	2.93401e6	+	1.05674e7i	0.0183258	+	0.0660035i
$544$	−9.09927e6	−	2.70057e7i	−0.0565210	−	0.167748i
$545$	−5.06985e6	−	3.43745e6i	−0.0313189	−	0.0212347i
$546$	2.25654e6	+	1.04399e6i	0.0138633	+	0.00641382i
$547$	9.34951e7	−	1.10071e8i	0.571251	−	0.672529i	−0.398346	−	0.917235i	$-0.630416\pi$
$547$	9.34951e7	−	1.10071e8i	0.571251	−	0.672529i	0.969597	+	0.244706i	$0.0786916\pi$
$548$	5.98263e7	+	5.66705e7i	0.363539	+	0.344362i
$549$	−1.87971e7	+	1.72836e8i	−0.113599	+	1.04452i
$550$	−7.95519e6	−	1.99660e7i	−0.0478148	−	0.120006i
$551$	5.98773e7	+	3.65235e8i	0.357937	+	2.18332i
$552$	−1.47433e7	−	2.17448e7i	−0.0876553	−	0.129282i
$553$	−3.71471e7	−	2.82385e7i	−0.219659	−	0.166981i
$554$	6.58249e6	+	6.05250e7i	0.0387133	+	0.355963i
$555$	7.32332e7	−	3.88258e7i	0.428380	−	0.227113i
$556$	1.65485e8	+	9.95689e7i	0.962795	+	0.579295i
$557$	−4.98512e7	+	2.99944e7i	−0.288476	+	0.173570i	−0.652435	−	0.757845i	$-0.726252\pi$
$557$	−4.98512e7	+	2.99944e7i	−0.288476	+	0.173570i	0.363959	+	0.931415i	$0.381425\pi$
$558$	3.05971e7	−	5.77123e7i	0.176108	−	0.332174i
$559$	5.90103e7	−	1.48105e8i	0.337825	−	0.847878i
$560$	2.89025e7	+	6.36192e6i	0.164578	+	0.0362263i
$561$	616304.	−	2.79990e6i	0.00349065	−	0.0158582i
$562$	4.54934e7	+	1.81262e7i	0.256295	+	0.102117i
$563$	−2.78905e7	−	1.47866e7i	−0.156290	−	0.0828597i	0.388428	−	0.921479i	$-0.373018\pi$
$563$	−2.78905e7	−	1.47866e7i	−0.156290	−	0.0828597i	−0.544718	+	0.838620i	$0.683363\pi$
$564$	−8.51542e6	−	1.41527e7i	−0.0474645	−	0.0788865i
$565$	3.03239e7	−	5.03987e7i	0.168128	−	0.279431i
$566$	2.03577e6	+	3.83986e6i	0.0112274	+	0.0211771i
$567$	−4.18118e7	+	4.54731e6i	−0.229377	+	0.0249462i
$568$	7.15639e7	−	9.41407e7i	0.390525	−	0.513727i
$569$	5.63486e7	−	3.82053e7i	0.305876	−	0.207389i	−0.398585	−	0.917131i	$-0.630499\pi$
$569$	5.63486e7	−	3.82053e7i	0.305876	−	0.207389i	0.704462	+	0.709742i	$0.251188\pi$
$570$	−2.81781e7	+	4.61956e6i	−0.152155	+	0.0249446i
$571$	−1.50152e8	+	5.98260e7i	−0.806534	+	0.321353i	−0.736712	−	0.676207i	$-0.763623\pi$
$571$	−1.50152e8	+	5.98260e7i	−0.806534	+	0.321353i	−0.0698224	+	0.997559i	$0.522243\pi$
$572$	3.59699e7	+	3.91197e6i	0.192199	+	0.0209029i
$573$	4.80893e7	−	5.07673e7i	0.255614	−	0.269849i
$574$	8.62261e6	+	7.32411e6i	0.0455935	+	0.0387275i
$575$	−5.22777e7	+	1.12996e8i	−0.274988	+	0.594376i
$576$	4.59175e6	−	6.77233e6i	0.0240276	−	0.0354381i
$577$	−1.14879e8	+	3.87071e7i	−0.598014	+	0.201494i	−0.601998	−	0.798498i	$-0.705628\pi$
$577$	−1.14879e8	+	3.87071e7i	−0.598014	+	0.201494i	0.00398382	+	0.999992i	$0.498732\pi$
$578$	−7.79450e7	+	2.16413e7i	−0.403650	+	0.112073i
$579$	−4.01391e7	−	4.72555e7i	−0.206791	−	0.243454i
$580$	−2.06251e7	+	3.80408e8i	−0.105709	+	1.94969i
$581$	−1.43078e7	+	4.24639e7i	−0.0729530	+	0.216517i
$582$	1.35050e7	−	1.02662e7i	0.0685054	−	0.0520765i
$583$	1.83333e7	+	1.93543e7i	0.0925200	+	0.0976722i
$584$	1.04646e7	+	1.93009e8i	0.0525395	+	0.969034i
$585$	−1.41175e8	−	3.91972e7i	−0.705166	−	0.195788i
$586$	4.37483e7	+	9.45604e7i	0.217404	+	0.469912i
$587$	3.13209e8	+	5.13480e7i	1.54853	+	0.253869i	0.874571	−	0.484898i	$-0.161143\pi$
$587$	3.13209e8	+	5.13480e7i	1.54853	+	0.253869i	0.673961	+	0.738767i	$0.264591\pi$
$588$	−3.33696e7	+	7.34521e6i	−0.164142	+	0.0361303i
$589$		−	2.26535e8i		−	1.10864i
$590$	−7.20326e7	−	9.22472e7i	−0.350730	−	0.449156i
$591$	2.31359e7			0.112079
$592$	−3.48289e7	−	1.58229e8i	−0.167870	−	0.762643i
$593$	4.73050e7	−	2.88548e8i	0.226852	−	1.38374i	−0.590239	−	0.807228i	$-0.700967\pi$
$593$	4.73050e7	−	2.88548e8i	0.226852	−	1.38374i	0.817091	−	0.576508i	$-0.195585\pi$
$594$	−1.45689e7	+	6.74027e6i	−0.0695131	+	0.0321602i
$595$	−3.59099e6	+	1.29336e7i	−0.0170476	+	0.0613999i
$596$	−1.99166e8	+	1.07985e7i	−0.940756	+	0.0510063i
$597$	−2.43231e7	+	2.30401e7i	−0.114313	+	0.108283i
$598$	2.92321e7	+	3.84542e7i	0.136696	+	0.179821i
$599$	−2.88497e8	−	9.72059e7i	−1.34233	−	0.452285i	−0.445750	−	0.895158i	$-0.647063\pi$
$599$	−2.88497e8	−	9.72059e7i	−1.34233	−	0.452285i	−0.896585	+	0.442872i	$0.853959\pi$
$600$	−2.77077e7	−	1.50227e6i	−0.128276	−	0.00695494i
$601$	1.47177e8	−	1.25013e8i	0.677979	−	0.575880i	−0.240838	−	0.970565i	$-0.577422\pi$
$601$	1.47177e8	−	1.25013e8i	0.677979	−	0.575880i	0.918816	+	0.394685i	$0.129146\pi$
$602$	1.06601e7	+	3.83941e7i	0.0488619	+	0.175985i
$603$	4.79072e6	+	1.42183e7i	0.0218499	+	0.0648481i
$604$	−9.60929e7	−	6.51526e7i	−0.436095	−	0.295679i
$605$	2.20868e8	+	1.02184e8i	0.997392	+	0.461443i
$606$	1.87353e7	−	2.20569e7i	0.0841865	−	0.0991120i
$607$	−1.14242e8	−	1.08216e8i	−0.510811	−	0.483866i	0.388333	−	0.921519i	$-0.373051\pi$
$607$	−1.14242e8	−	1.08216e8i	−0.510811	−	0.483866i	−0.899144	+	0.437653i	$0.855810\pi$
$608$	−2.91510e7	+	2.68039e8i	−0.129701	+	1.19258i
$609$	9.20471e6	+	2.31021e7i	0.0407529	+	0.102282i
$610$	−2.31390e7	−	1.41142e8i	−0.101943	−	0.621822i
$611$	3.80124e7	+	5.60641e7i	0.166649	+	0.245789i
$612$	2.52152e7	+	1.91681e7i	0.110004	+	0.0836227i
$613$	−3.34523e7	−	3.07589e8i	−0.145226	−	1.33533i	−0.809181	−	0.587559i	$-0.800089\pi$
$613$	−3.34523e7	−	3.07589e8i	−0.145226	−	1.33533i	0.663955	−	0.747773i	$-0.268877\pi$
$614$	−4.40555e7	+	2.33567e7i	−0.190325	+	0.100904i
$615$	2.99294e7	+	1.80079e7i	0.128669	+	0.0774174i
$616$	−1.72831e7	+	1.03989e7i	−0.0739400	+	0.0444882i
$617$	−1.13053e8	+	2.13240e8i	−0.481311	+	0.907848i	0.517333	+	0.855784i	$0.326925\pi$
$617$	−1.13053e8	+	2.13240e8i	−0.481311	+	0.907848i	−0.998644	+	0.0520642i	$0.983420\pi$
$618$	−1.95928e6	+	4.91743e6i	−0.00830103	+	0.0208340i
$619$	−2.63461e8	−	5.79922e7i	−1.11082	−	0.244511i	−0.378590	−	0.925564i	$-0.623591\pi$
$619$	−2.63461e8	−	5.79922e7i	−1.11082	−	0.244511i	−0.732233	+	0.681054i	$0.761522\pi$
$620$	5.01268e7	−	2.27728e8i	0.210327	−	0.955525i
$621$	8.63860e7	+	3.44193e7i	0.360718	+	0.143723i
$622$	5.69006e7	+	3.01668e7i	0.236453	+	0.125360i
$623$	1.97298e7	+	3.27911e7i	0.0815939	+	0.135610i
$624$	7.73567e6	−	1.28568e7i	0.0318379	−	0.0529150i
$625$	−1.36690e8	−	2.57824e8i	−0.559881	−	1.05605i
$626$	−1.50836e8	+	1.64044e7i	−0.614868	+	0.0668709i
$627$	−1.64151e7	+	2.15937e7i	−0.0665948	+	0.0876039i
$628$	1.78342e7	−	1.20919e7i	0.0720072	−	0.0488221i
$629$	7.25164e7	−	1.18885e7i	0.291397	−	0.0477720i
$630$	3.40185e7	−	1.35542e7i	0.136049	−	0.0542067i
$631$	4.45704e7	+	4.84733e6i	0.177402	+	0.0192936i	0.196389	−	0.980526i	$-0.437079\pi$
$631$	4.45704e7	+	4.84733e6i	0.177402	+	0.0192936i	−0.0189867	+	0.999820i	$0.506044\pi$
$632$	1.38942e8	−	1.46680e8i	0.550406	−	0.581057i
$633$	−6.84294e7	−	5.81245e7i	−0.269794	−	0.229165i
$634$	−6.65985e7	+	1.43950e8i	−0.261334	+	0.564865i
$635$	2.75888e8	−	4.06905e8i	1.07749	−	1.58918i
$636$	1.46234e7	−	4.92720e6i	0.0568431	−	0.0191527i
$637$	1.35016e8	−	3.74871e7i	0.522357	−	0.145032i
$638$	−5.39926e7	−	6.35650e7i	−0.207909	−	0.244769i
$639$	−1.10411e7	+	2.03641e8i	−0.0423166	+	0.780483i
$640$	−1.11187e8	+	3.29990e8i	−0.424143	+	1.25881i
$641$	−9.25123e6	+	7.03260e6i	−0.0351257	+	0.0267019i	−0.622590	−	0.782548i	$-0.713919\pi$
$641$	−9.25123e6	+	7.03260e6i	−0.0351257	+	0.0267019i	0.587464	+	0.809250i	$0.300126\pi$
$642$	1.04341e7	+	1.10152e7i	0.0394322	+	0.0416281i
$643$	−4.79145e6	−	8.83731e7i	−0.0180233	−	0.332420i	−0.993615	−	0.112826i	$-0.964010\pi$
$643$	−4.79145e6	−	8.83731e7i	−0.0180233	−	0.332420i	0.975591	−	0.219594i	$-0.0704731\pi$
$644$	5.04764e7	+	1.40147e7i	0.188987	+	0.0524719i
$645$	5.16563e7	+	1.11653e8i	0.192506	+	0.416094i
$646$	−2.49811e7	−	4.09544e6i	−0.0926645	−	0.0151916i
$647$	−2.46937e7	+	5.43550e6i	−0.0911746	+	0.0200691i	−0.260323	−	0.965521i	$-0.583829\pi$
$647$	−2.46937e7	+	5.43550e6i	−0.0911746	+	0.0200691i	0.169149	+	0.985591i	$0.445898\pi$
$648$		−	1.82107e8i		−	0.669271i
$649$	−1.09939e8	−	1.65614e7i	−0.402178	−	0.0605845i
$650$	5.10187e7			0.185776
$651$	−3.27212e6	−	1.48654e7i	−0.0118600	−	0.0538807i
$652$	1.07347e7	−	6.54791e7i	0.0387301	−	0.236243i
$653$	3.56935e8	−	1.65136e8i	1.28189	−	0.593064i	0.343663	−	0.939093i	$-0.388332\pi$
$653$	3.56935e8	−	1.65136e8i	1.28189	−	0.593064i	0.938224	+	0.346029i	$0.112470\pi$
$654$	207653.	−	747899.i	0.000742344	−	0.00267368i
$655$	1.31572e8	−	7.13362e6i	0.468208	−	0.0253855i
$656$	4.95666e7	−	4.69519e7i	0.175581	−	0.166319i
$657$	−2.01737e8	−	2.65380e8i	−0.711359	−	0.935777i
$658$	−1.60433e7	−	5.40561e6i	−0.0563139	−	0.0189744i
$659$	−4.70302e8	−	2.54990e7i	−1.64331	−	0.0890978i	−0.790892	−	0.611955i	$-0.790383\pi$
$659$	−4.70302e8	−	2.54990e7i	−1.64331	−	0.0890978i	−0.852420	+	0.522857i	$0.824866\pi$
$660$	−2.12797e7	+	1.80751e7i	−0.0740173	+	0.0628708i
$661$	8.84926e7	+	3.18722e8i	0.306410	+	1.10359i	0.943111	+	0.332478i	$0.107885\pi$
$661$	8.84926e7	+	3.18722e8i	0.306410	+	1.10359i	−0.636701	+	0.771111i	$0.719701\pi$
$662$	−7.13947e7	−	2.11892e8i	−0.246089	−	0.730366i
$663$	5.63282e6	+	3.81915e6i	0.0193279	+	0.0131047i
$664$	−1.76087e8	−	8.14667e7i	−0.601484	−	0.278276i
$665$	8.22155e7	−	9.67916e7i	0.279569	−	0.329134i
$666$	−1.45545e8	−	1.37867e8i	−0.492689	−	0.466700i
$667$	−5.22358e7	+	4.80300e8i	−0.176032	+	1.61858i
$668$	−5.22994e7	−	1.31262e8i	−0.175456	−	0.440360i
$669$	−9.11457e6	−	5.55964e7i	−0.0304409	−	0.185681i
$670$	−6.92682e6	−	1.02163e7i	−0.0230308	−	0.0339679i
$671$	−1.08161e8	−	8.22219e7i	−0.358017	−	0.272157i
$672$	1.95870e6	+	1.80100e7i	0.00645447	+	0.0593479i
$673$	−4.06561e8	+	2.15545e8i	−1.33377	+	0.707120i	−0.974134	−	0.225973i	$-0.927444\pi$
$673$	−4.06561e8	+	2.15545e8i	−1.33377	+	0.707120i	−0.359636	+	0.933093i	$0.617099\pi$
$674$	2.00087e8	+	1.20388e8i	0.653490	+	0.393192i
$675$	8.41582e7	−	5.06363e7i	0.273643	−	0.164646i
$676$	7.73665e7	−	1.45929e8i	0.250445	−	0.472390i
$677$	−1.21197e8	+	3.04182e8i	−0.390595	+	0.980319i	0.593842	+	0.804581i	$0.297610\pi$
$677$	−1.21197e8	+	3.04182e8i	−0.390595	+	0.980319i	−0.984437	+	0.175737i	$0.943769\pi$
$678$	7.27910e6	+	1.60225e6i	0.0233555	+	0.00514093i
$679$	−1.62192e7	+	7.36845e7i	−0.0518108	+	0.235379i
$680$	−5.39913e7	−	2.15121e7i	−0.171711	−	0.0684158i
$681$	5.67223e7	+	3.00723e7i	0.179603	+	0.0952193i
$682$	2.63178e7	+	4.37405e7i	0.0829652	+	0.137889i
$683$	2.42468e8	−	4.02986e8i	0.761015	−	1.26482i	−0.197648	−	0.980273i	$-0.563330\pi$
$683$	2.42468e8	−	4.02986e8i	0.761015	−	1.26482i	0.958663	−	0.284543i	$-0.0918420\pi$
$684$	−1.40368e8	−	2.64763e8i	−0.438633	−	0.827349i
$685$	2.59248e8	−	2.81949e7i	0.806574	−	0.0877202i
$686$	−4.40611e7	+	5.79613e7i	−0.136484	+	0.179542i
$687$	5.56965e6	−	3.77632e6i	0.0171774	−	0.0116466i
$688$	2.37298e8	−	3.89030e7i	0.728667	−	0.119459i
$689$	−5.87882e7	+	2.34234e7i	−0.179735	+	0.0716130i
$690$	−3.70554e7	−	4.03002e6i	−0.112799	−	0.0122676i
$691$	−2.39419e8	+	2.52752e8i	−0.725645	+	0.766055i	−0.979556	−	0.201173i	$-0.935525\pi$
$691$	−2.39419e8	+	2.52752e8i	−0.725645	+	0.766055i	0.253910	+	0.967228i	$0.418283\pi$
$692$	−4.29382e7	−	3.64721e7i	−0.129576	−	0.110063i
$693$	1.46062e7	−	3.15708e7i	0.0438872	−	0.0948606i
$694$	−4.68532e7	+	6.91033e7i	−0.140172	+	0.206738i
$695$	5.79175e8	−	1.95147e8i	1.72526	−	0.581309i
$696$	−1.03752e8	+	2.88065e7i	−0.307729	+	0.0854404i
$697$	2.00472e7	+	2.36014e7i	0.0592045	+	0.0697010i
$698$	7.95342e6	−	1.46692e8i	0.0233877	−	0.431361i
$699$	4.06607e6	−	1.20677e7i	0.0119054	−	0.0353339i
$700$	4.40481e7	−	3.34845e7i	0.128420	−	0.0976225i
$701$	2.11599e8	+	2.23382e8i	0.614270	+	0.648477i	0.956703	−	0.291065i	$-0.0940097\pi$
$701$	2.11599e8	+	2.23382e8i	0.614270	+	0.648477i	−0.342433	+	0.939542i	$0.611251\pi$
$702$	−2.06298e6	−	3.80494e7i	−0.00596326	−	0.109986i
$703$	−6.69910e8	−	1.85999e8i	−1.92819	−	0.535360i
$704$	2.68488e6	+	5.80327e6i	0.00769497	+	0.0166324i
$705$	−5.15802e7	−	8.45615e6i	−0.147203	−	0.0241327i
$706$	1.33011e8	−	2.92779e7i	0.377984	−	0.0832006i
$707$			1.28711e8i			0.364216i
$708$	−3.54207e7	+	5.37300e7i	−0.0998062	+	0.151397i
$709$	3.15742e8			0.885919			0.442960	−	0.896542i	$-0.353928\pi$
$709$	3.15742e8			0.885919			0.442960	+	0.896542i	$0.353928\pi$
$710$	−3.60669e7	−	1.63854e8i	−0.100771	−	0.457806i
$711$	−5.63710e7	+	3.43848e8i	−0.156837	+	0.956661i
$712$	−1.50385e8	+	6.95757e7i	−0.416644	+	0.192760i
$713$	7.91116e7	−	2.84934e8i	0.218259	−	0.786097i
$714$	−1.69843e6	+	92086.1i	−0.00466608	+	0.000252988i
$715$	8.31261e7	−	7.87413e7i	0.227415	−	0.215419i
$716$	6.76439e7	+	8.89840e7i	0.184285	+	0.242423i
$717$	−1.45362e8	−	4.89780e7i	−0.394359	−	0.132875i
$718$	2.56362e8	+	1.38996e7i	0.692597	+	0.0375515i
$719$	1.76154e8	−	1.49627e8i	0.473921	−	0.402552i	−0.378342	−	0.925666i	$-0.623506\pi$
$719$	1.76154e8	−	1.49627e8i	0.473921	−	0.402552i	0.852263	+	0.523114i	$0.175230\pi$
$720$	−5.91213e7	−	2.12936e8i	−0.158397	−	0.570494i
$721$	−7.51718e6	−	2.23102e7i	−0.0200562	−	0.0595247i
$722$	6.34205e7	+	4.30002e7i	0.168507	+	0.114251i
$723$	−2.94128e7	−	1.36078e7i	−0.0778254	−	0.0360058i
$724$	6.12995e7	−	7.21674e7i	0.161526	−	0.190163i
$725$	3.70467e8	+	3.50925e8i	0.972155	+	0.920874i
$726$	−3.33420e6	+	3.06575e7i	−0.00871329	+	0.0801174i
$727$	2.09123e8	+	5.24859e8i	0.544250	+	1.36597i	0.901833	+	0.432084i	$0.142222\pi$
$727$	2.09123e8	+	5.24859e8i	0.544250	+	1.36597i	−0.357583	+	0.933881i	$0.616399\pi$
$728$	−7.74615e6	−	4.72494e7i	−0.0200767	−	0.122462i
$729$	1.55139e8	+	2.28813e8i	0.400441	+	0.590606i
$730$	2.18321e8	+	1.65963e8i	0.561212	+	0.426622i
$731$	1.17921e7	+	1.08426e8i	0.0301883	+	0.277576i
$732$	−6.94826e7	+	3.68373e7i	−0.177151	+	0.0939193i
$733$	6.36545e8	+	3.82996e8i	1.61628	+	0.972484i	0.979501	+	0.201440i	$0.0645619\pi$
$733$	6.36545e8	+	3.82996e8i	1.61628	+	0.972484i	0.636781	+	0.771045i	$0.280266\pi$
$734$	2.28046e8	−	1.37211e8i	0.576679	−	0.346977i
$735$	−5.06478e7	+	9.55319e7i	−0.127555	+	0.240595i
$736$	−1.30272e8	+	3.26957e8i	−0.326751	+	0.820083i
$737$	−1.14510e7	−	2.52056e6i	−0.0286050	−	0.00629644i
$738$	1.81608e7	−	8.25053e7i	0.0451820	−	0.205264i
$739$	−1.84198e8	−	7.33911e7i	−0.456406	−	0.181849i	0.130594	−	0.991436i	$-0.458312\pi$
$739$	−1.84198e8	−	7.33911e7i	−0.456406	−	0.181849i	−0.586999	+	0.809587i	$0.699691\pi$
$740$	−6.32280e8	−	3.35214e8i	−1.56032	−	0.827231i
$741$	−3.31955e7	−	5.51713e7i	−0.0815877	−	0.135600i
$742$	8.15428e6	−	1.35525e7i	0.0199606	−	0.0331748i
$743$	1.27914e8	+	2.41271e8i	0.311853	+	0.588218i	0.989049	−	0.147585i	$-0.0471499\pi$
$743$	1.27914e8	+	2.41271e8i	0.311853	+	0.588218i	−0.677196	+	0.735803i	$0.736805\pi$
$744$	6.55198e7	−	7.12570e6i	0.159094	−	0.0173025i
$745$	−3.81983e8	+	5.02491e8i	−0.923795	+	1.21523i
$746$	−2.02498e8	+	1.37297e8i	−0.487757	+	0.330707i
$747$	3.30199e8	−	5.41335e7i	0.792163	−	0.129869i
$748$	−2.29944e7	+	9.16181e6i	−0.0549436	+	0.0218915i
$749$	−6.70849e7	−	7.29592e6i	−0.159654	−	0.0173634i
$750$	9.81584e6	−	1.03625e7i	0.0232672	−	0.0245629i
$751$	−5.06749e8	−	4.30436e8i	−1.19639	−	1.01622i	−0.999358	−	0.0358260i	$-0.988594\pi$
$751$	−5.06749e8	−	4.30436e8i	−1.19639	−	1.01622i	−0.197032	−	0.980397i	$-0.563130\pi$
$752$	−4.28985e7	+	9.27236e7i	−0.100876	+	0.218040i
$753$	7.21287e6	−	1.06382e7i	0.0168936	−	0.0249162i
$754$	1.87613e8	−	6.32142e7i	0.437672	−	0.147469i
$755$	−3.54005e8	+	9.82890e7i	−0.822562	+	0.228383i
$756$	−2.67537e7	−	3.14968e7i	−0.0619181	−	0.0728957i
$757$	−3.72058e7	+	6.86221e8i	−0.0857676	+	1.58189i	0.566604	+	0.823990i	$0.308257\pi$
$757$	−3.72058e7	+	6.86221e8i	−0.0857676	+	1.58189i	−0.652372	+	0.757899i	$0.726226\pi$
$758$	−1.37326e7	+	4.07569e7i	−0.0315315	+	0.0935822i
$759$	−2.81878e7	+	2.14278e7i	−0.0644667	+	0.0490063i
$760$	3.78150e8	+	3.99208e8i	0.861437	+	0.909408i
$761$	1.32294e7	+	2.44002e8i	0.0300183	+	0.553655i	0.974402	+	0.224811i	$0.0721764\pi$
$761$	1.32294e7	+	2.44002e8i	0.0300183	+	0.553655i	−0.944384	+	0.328844i	$0.893341\pi$
$762$	6.00262e7	+	1.66662e7i	0.135667	+	0.0376679i
$763$	1.44952e6	+	3.13308e6i	0.00326325	+	0.00705339i
$764$	−5.95789e8	−	9.76746e7i	−1.33602	−	0.219029i
$765$	9.78892e7	−	2.15470e7i	0.218651	−	0.0481286i
$766$		−	1.80572e8i		−	0.401757i
$767$	1.33117e8	−	2.27886e8i	0.295017	−	0.505047i
$768$	−3.95715e7			−0.0873572
$769$	7.95038e7	+	3.61189e8i	0.174827	+	0.794247i	0.979647	+	0.200728i	$0.0643308\pi$
$769$	7.95038e7	+	3.61189e8i	0.174827	+	0.794247i	−0.804820	+	0.593519i	$0.797738\pi$
$770$	−4.62977e6	+	2.82404e7i	−0.0101412	+	0.0618583i
$771$	−1.29295e8	+	5.98184e7i	−0.282111	+	0.130518i
$772$	−1.43211e8	+	5.15799e8i	−0.311260	+	1.12106i
$773$	1.94765e8	−	1.05598e7i	0.421669	−	0.0228622i	0.157916	−	0.987453i	$-0.449522\pi$
$773$	1.94765e8	−	1.05598e7i	0.421669	−	0.0228622i	0.263753	+	0.964590i	$0.415040\pi$
$774$	2.16017e8	−	2.04622e8i	0.465871	−	0.441296i
$775$	−1.89017e8	−	2.48647e8i	−0.406065	−	0.534169i
$776$	−3.09581e8	−	1.04310e8i	−0.662506	−	0.223224i
$777$	−4.66465e7	−	2.52910e6i	−0.0994388	−	0.00539142i
$778$	−1.59598e8	+	1.35564e8i	−0.338913	+	0.287875i
$779$	−7.83801e7	−	2.82300e8i	−0.165803	−	0.597170i
$780$	−2.11622e7	−	6.28072e7i	−0.0445941	−	0.132351i
$781$	−1.31914e8	−	8.94397e7i	−0.276909	−	0.187749i
$782$	−2.99907e7	−	1.38752e7i	−0.0627144	−	0.0290147i
$783$	2.46738e8	−	2.90482e8i	0.513984	−	0.605109i
$784$	1.53439e8	+	1.45345e8i	0.318410	+	0.301614i
$785$	7.37225e6	−	6.77868e7i	0.0152402	−	0.140132i
$786$	6.18023e6	+	1.55112e7i	0.0127273	+	0.0319432i
$787$	−2.62915e7	−	1.60371e8i	−0.0539375	−	0.329004i	−0.999988	−	0.00498386i	$-0.998414\pi$
$787$	−2.62915e7	−	1.60371e8i	−0.0539375	−	0.329004i	0.946050	−	0.324021i	$-0.105035\pi$
$788$	−1.12098e8	−	1.65332e8i	−0.229096	−	0.337891i
$789$	1.32081e8	+	1.00405e8i	0.268911	+	0.204421i
$790$	−3.09924e7	−	2.84970e8i	−0.0628599	−	0.577987i
$791$	−2.92876e7	+	1.55273e7i	−0.0591773	+	0.0313738i
$792$	1.29058e8	+	7.76519e7i	0.259783	+	0.156306i
$793$	2.76349e8	−	1.66274e8i	0.554164	−	0.333430i
$794$	9.30347e7	−	1.75482e8i	0.185859	−	0.350567i
$795$	1.80748e7	−	4.53644e7i	0.0359727	−	0.0902846i
$796$	2.82496e8	+	6.21821e7i	0.560110	+	0.123289i
$797$	−2.01452e8	+	9.15207e8i	−0.397921	+	1.80777i	0.170872	+	0.985293i	$0.445342\pi$
$797$	−2.01452e8	+	9.15207e8i	−0.397921	+	1.80777i	−0.568793	+	0.822481i	$0.692589\pi$
$798$	1.49498e7	+	5.95655e6i	0.0294189	+	0.0117216i
$799$	−4.09407e7	−	2.17054e7i	−0.0802628	−	0.0425527i
$800$	1.91650e8	+	3.18525e8i	0.374317	+	0.622120i
$801$	1.47328e8	−	2.44862e8i	0.286675	−	0.476457i
$802$	1.52663e7	+	2.87952e7i	0.0295944	+	0.0558209i
$803$	2.58982e8	−	2.81660e7i	0.500177	−	0.0543975i
$804$	−4.10729e6	+	5.40305e6i	−0.00790292	+	0.0103961i
$805$	1.37212e8	−	9.30320e7i	0.263030	−	0.178338i
$806$	−1.19580e8	+	1.96042e7i	−0.228378	+	0.0374406i
$807$	1.82089e8	−	7.25511e7i	0.346469	−	0.138046i
$808$	−5.54037e8	−	6.02552e7i	−1.05028	−	0.114225i
$809$	−1.95353e8	+	2.06231e8i	−0.368955	+	0.389501i	−0.883864	−	0.467744i	$-0.845067\pi$
$809$	−1.95353e8	+	2.06231e8i	−0.368955	+	0.389501i	0.514909	+	0.857245i	$0.327826\pi$
$810$	−1.96921e8	−	1.67266e8i	−0.370541	−	0.314740i
$811$	−7.90667e7	+	1.70900e8i	−0.148228	+	0.320390i	−0.967440	−	0.253101i	$-0.918549\pi$
$811$	−7.90667e7	+	1.70900e8i	−0.148228	+	0.320390i	0.819212	+	0.573491i	$0.194411\pi$
$812$	1.20491e8	−	1.77711e8i	0.225054	−	0.331930i
$813$	−7.53203e7	+	2.53784e7i	−0.140165	+	0.0472272i
$814$	1.50958e8	−	4.19132e7i	0.279887	−	0.0777101i
$815$	−1.35936e8	−	1.60037e8i	−0.251109	−	0.295629i
$816$	−555722.	+	1.02497e7i	−0.00102279	+	0.0188643i
$817$	3.29485e8	−	9.77876e8i	0.604184	−	1.79315i
$818$	5.42706e7	−	4.12554e7i	0.0991527	−	0.0753739i
$819$	5.67864e7	+	5.99486e7i	0.103370	+	0.109126i
$820$	−1.63268e7	−	3.01130e8i	−0.0296114	−	0.546150i
$821$	−3.75196e8	−	1.04173e8i	−0.677999	−	0.188245i	−0.0885750	−	0.996070i	$-0.528231\pi$
$821$	−3.75196e8	−	1.04173e8i	−0.677999	−	0.188245i	−0.589424	+	0.807824i	$0.700645\pi$
$822$	1.38754e7	+	2.99911e7i	0.0249821	+	0.0539979i
$823$	4.40177e8	+	7.21634e7i	0.789638	+	0.129455i	0.543088	−	0.839676i	$-0.317255\pi$
$823$	4.40177e8	+	7.21634e7i	0.789638	+	0.129455i	0.246550	+	0.969130i	$0.420703\pi$
$824$	9.95531e7	−	2.19133e7i	0.177940	−	0.0391675i
$825$			3.73978e7i			0.0666016i
$826$	7.98223e6	+	6.54771e7i	0.0141639	+	0.116185i
$827$	5.32582e8			0.941608			0.470804	−	0.882238i	$-0.343964\pi$
$827$	5.32582e8			0.941608			0.470804	+	0.882238i	$0.343964\pi$
$828$	−8.40926e7	−	3.82037e8i	−0.148138	−	0.672998i
$829$	3.69608e7	−	2.25451e8i	0.0648751	−	0.395720i	−0.934350	−	0.356357i	$-0.884019\pi$
$829$	3.69608e7	−	2.25451e8i	0.0648751	−	0.395720i	0.999225	−	0.0393635i	$-0.0125330\pi$
$830$	−2.49830e8	+	1.15584e8i	−0.436929	+	0.202145i
$831$	2.83411e7	−	1.02076e8i	0.0493872	−	0.177876i
$832$	−1.51564e7	+	821755.i	−0.0263163	+	0.00142683i
$833$	−6.95937e7	+	6.59226e7i	−0.120402	+	0.114051i
$834$	4.68685e7	+	6.16545e7i	0.0807948	+	0.106284i
$835$	−4.23734e8	−	1.42772e8i	−0.727836	−	0.245237i
$836$	2.33844e8	+	1.26787e7i	0.400228	+	0.0216997i
$837$	−1.77797e8	+	1.51022e8i	−0.303212	+	0.257551i
$838$	−6.81993e7	−	2.45632e8i	−0.115891	−	0.417400i
$839$	7.81163e6	+	2.31841e7i	0.0132268	+	0.0392558i	0.954063	−	0.299605i	$-0.0968549\pi$
$839$	7.81163e6	+	2.31841e7i	0.0132268	+	0.0392558i	−0.940836	+	0.338861i	$0.889958\pi$
$840$	3.05807e7	+	2.07342e7i	0.0515952	+	0.0349824i
$841$	1.25729e9	+	5.81686e8i	2.11373	+	0.977915i
$842$	3.52935e7	−	4.15507e7i	0.0591233	−	0.0696053i
$843$	−6.18639e7	−	5.86006e7i	−0.103265	−	0.0978181i
$844$	−8.38106e7	+	7.70625e8i	−0.139403	+	1.28179i
$845$	−1.93465e8	−	4.85561e8i	−0.320651	−	0.804774i
$846$	2.04522e7	+	1.24753e8i	0.0337775	+	0.206034i
$847$	−7.69693e7	−	1.13521e8i	−0.126668	−	0.186822i
$848$	−7.59869e7	−	5.77638e7i	−0.124610	−	0.0947257i
$849$	−817645.	−	7.51812e6i	−0.00133611	−	0.0122853i
$850$	−3.08366e7	+	1.63485e7i	−0.0502122	+	0.0266208i
$851$	−7.77651e8	−	4.67897e8i	−1.26182	−	0.759210i
$852$	−7.90474e7	+	4.75612e7i	−0.127811	+	0.0769014i
$853$	2.70377e8	−	5.09985e8i	0.435635	−	0.821695i	−0.564357	−	0.825531i	$-0.690876\pi$
$853$	2.70377e8	−	5.09985e8i	0.435635	−	0.821695i	0.999993	+	0.00383541i	$0.00122085\pi$
$854$	−2.98359e7	+	7.48825e7i	−0.0479033	+	0.120228i
$855$	−9.26150e8	−	2.03861e8i	−1.48178	−	0.326164i
$856$	6.28104e7	−	2.85351e8i	0.100141	−	0.454944i
$857$	−1.00340e9	−	3.99792e8i	−1.59416	−	0.635172i	−0.606972	−	0.794723i	$-0.707616\pi$
$857$	−1.00340e9	−	3.99792e8i	−1.59416	−	0.635172i	−0.987190	+	0.159551i	$0.948995\pi$
$858$	1.28191e7	+	6.79624e6i	0.0202953	+	0.0107599i
$859$	3.67000e8	+	6.09959e8i	0.579011	+	0.962324i	0.998510	+	0.0545682i	$0.0173782\pi$
$859$	3.67000e8	+	6.09959e8i	0.579011	+	0.962324i	−0.419499	+	0.907756i	$0.637794\pi$
$860$	5.47600e8	−	9.10119e8i	0.860931	−	1.43088i
$861$	−9.22094e6	−	1.73925e7i	−0.0144466	−	0.0272492i
$862$	−2.55610e8	+	2.77992e7i	−0.399076	+	0.0434021i
$863$	−1.37878e8	+	1.81376e8i	−0.214518	+	0.282194i	−0.890749	−	0.454496i	$-0.849819\pi$
$863$	−1.37878e8	+	1.81376e8i	−0.214518	+	0.282194i	0.676230	+	0.736690i	$0.263612\pi$
$864$	2.29805e8	−	1.55812e8i	0.356302	−	0.241579i
$865$	−1.75933e8	+	2.88428e7i	−0.271832	+	0.0445645i
$866$	−6.34142e7	+	2.52665e7i	−0.0976412	+	0.0389038i
$867$	1.39933e8	+	1.52186e7i	0.214715	+	0.0233517i
$868$	−9.03755e7	+	9.54082e7i	−0.138195	+	0.145890i
$869$	−2.07535e8	−	1.76282e8i	−0.316252	−	0.268627i
$870$	−6.41465e7	+	1.38650e8i	−0.0974126	+	0.210554i
$871$	1.56196e7	−	2.30371e7i	0.0236382	−	0.0348638i
$872$	−1.41649e7	+	4.77271e6i	−0.0213631	+	0.00719806i
$873$	5.42862e8	−	1.50725e8i	0.815919	−	0.226539i
$874$	2.02402e8	+	2.38286e8i	0.303166	+	0.356914i
$875$	−3.43683e6	+	6.33887e7i	−0.00513020	+	0.0946210i
$876$	4.81483e7	−	1.42899e8i	0.0716257	−	0.212577i
$877$	4.09418e8	−	3.11232e8i	0.606972	−	0.461408i	−0.255988	−	0.966680i	$-0.582401\pi$
$877$	4.09418e8	−	3.11232e8i	0.606972	−	0.461408i	0.862960	+	0.505272i	$0.168608\pi$
$878$	−1.92163e8	−	2.02864e8i	−0.283914	−	0.299725i
$879$	−9.81512e6	−	1.81029e8i	−0.0144520	−	0.266552i
$880$	1.66405e8	+	4.62022e7i	0.244185	+	0.0677977i
$881$	5.06465e8	+	1.09471e9i	0.740666	+	1.60092i	0.798065	+	0.602571i	$0.205857\pi$
$881$	5.06465e8	+	1.09471e9i	0.740666	+	1.60092i	−0.0573998	+	0.998351i	$0.518281\pi$
$882$	2.58073e8	+	4.23090e7i	0.376130	+	0.0616633i
$883$	−8.32094e8	+	1.83158e8i	−1.20862	+	0.266038i	−0.773184	−	0.634182i	$-0.781337\pi$
$883$	−8.32094e8	+	1.83158e8i	−1.20862	+	0.266038i	−0.435437	+	0.900219i	$0.643406\pi$
$884$		−	5.87571e7i		−	0.0850557i
$885$	5.70253e7	+	1.95507e8i	0.0822693	+	0.282054i
$886$	8.51476e7			0.122425
$887$	−3.23976e7	−	1.47184e8i	−0.0464239	−	0.210906i	0.947699	−	0.319167i	$-0.103403\pi$
$887$	−3.23976e7	−	1.47184e8i	−0.0464239	−	0.210906i	−0.994123	+	0.108261i	$0.965472\pi$
$888$	3.27237e7	−	1.99605e8i	0.0467329	−	0.285058i
$889$	−2.51460e8	+	1.16338e8i	−0.357902	+	0.165583i
$890$	−6.28940e7	+	2.26524e8i	−0.0892153	+	0.321324i
$891$	−2.45075e8	+	1.32876e7i	−0.346470	+	0.0187850i
$892$	−3.53135e8	+	3.34508e8i	−0.497561	+	0.471315i
$893$	2.65319e8	+	3.49022e8i	0.372576	+	0.490115i
$894$	−7.57973e7	−	2.55391e7i	−0.106082	−	0.0357432i
$895$	3.53201e8	+	1.91500e7i	0.492666	+	0.0267116i
$896$	1.49575e8	−	1.27050e8i	0.207939	−	0.176625i
$897$	−2.24859e7	−	8.09867e7i	−0.0311553	−	0.112211i
$898$	−8.30102e6	−	2.46366e7i	−0.0114631	−	0.0340213i
$899$	−1.00316e9	−	6.80161e8i	−1.38068	−	0.936122i
$900$	−3.74983e8	−	1.73485e8i	−0.514380	−	0.237977i
$901$	2.80268e7	−	3.29957e7i	0.0383177	−	0.0451110i
$902$	4.79302e7	+	4.54019e7i	0.0653115	+	0.0618663i
$903$	7.49637e6	−	6.89280e7i	0.0101809	−	0.0936122i
$904$	−5.31265e7	−	1.33337e8i	−0.0719127	−	0.180487i
$905$	−4.84769e7	−	2.95696e8i	−0.0654017	−	0.398933i
$906$	−2.61266e7	−	3.85339e7i	−0.0351316	−	0.0518153i
$907$	−6.35769e8	−	4.83299e8i	−0.852074	−	0.647730i	0.0851845	−	0.996365i	$-0.472852\pi$
$907$	−6.35769e8	−	4.83299e8i	−0.852074	−	0.647730i	−0.937258	+	0.348635i	$0.886645\pi$
$908$	−5.99301e7	−	5.51048e8i	−0.0800548	−	0.736092i
$909$	8.49170e8	−	4.50201e8i	1.13058	−	0.599398i
$910$	−5.82077e7	−	3.50224e7i	−0.0772426	−	0.0464753i
$911$	−6.70207e8	+	4.03250e8i	−0.886449	+	0.533359i	−0.884448	−	0.466639i	$-0.845465\pi$
$911$	−6.70207e8	+	4.03250e8i	−0.886449	+	0.533359i	−0.00200159	+	0.999998i	$0.500637\pi$
$912$	4.54904e7	−	8.58039e7i	0.0599701	−	0.113116i
$913$	−9.67873e7	+	2.42918e8i	−0.127176	+	0.319188i
$914$	−4.70079e8	−	1.03472e8i	−0.615648	−	0.135514i
$915$	−5.34999e7	+	2.43052e8i	−0.0698376	+	0.317276i
$916$	−5.39718e7	−	2.15043e7i	−0.0702232	−	0.0279795i
$917$	−6.56105e7	−	3.47845e7i	−0.0850875	−	0.0451105i
$918$	1.34395e7	+	2.23367e7i	0.0173722	+	0.0288729i
$919$	6.16364e8	−	1.02440e9i	0.794128	−	1.31985i	−0.149473	−	0.988766i	$-0.547758\pi$
$919$	6.16364e8	−	1.02440e9i	0.794128	−	1.31985i	0.943601	−	0.331085i	$-0.107415\pi$
$920$	3.36221e8	+	6.34180e8i	0.431779	+	0.814421i
$921$	8.62568e7	−	9.38100e6i	0.110412	−	0.0120080i
$922$	6.25883e6	−	8.23335e6i	0.00798547	−	0.0105047i
$923$	3.13136e8	−	2.12311e8i	0.398224	−	0.270003i
$924$	1.55281e7	−	2.54571e6i	0.0196835	−	0.00322695i
$925$	−8.90493e8	+	3.54805e8i	−1.12514	+	0.448296i
$926$	−2.79812e8	−	3.04313e7i	−0.352397	−	0.0383255i
$927$	−1.20897e8	+	1.27630e8i	−0.151767	+	0.160219i
$928$	1.09943e9	+	9.33863e8i	1.37570	+	1.16853i
$929$	3.68376e8	−	7.96233e8i	0.459457	−	0.993100i	−0.529963	−	0.848021i	$-0.677794\pi$
$929$	3.68376e8	−	7.96233e8i	0.459457	−	0.993100i	0.989420	−	0.145079i	$-0.0463437\pi$
$930$	5.24747e7	−	7.73944e7i	0.0652381	−	0.0962190i
$931$	8.59472e8	−	2.89590e8i	1.06508	−	0.358868i
$932$	−1.05937e8	+	2.94134e7i	−0.130858	+	0.0363326i
$933$	−7.25483e7	−	8.54105e7i	−0.0893269	−	0.105164i
$934$	−1.60973e6	+	2.96898e7i	−0.00197567	+	0.0364390i
$935$	−2.50109e7	+	7.42297e7i	−0.0305981	+	0.0908119i
$936$	−2.84632e8	+	2.16372e8i	−0.347102	+	0.263860i
$937$	−7.07285e7	−	7.46671e7i	−0.0859757	−	0.0907634i	0.681588	−	0.731736i	$-0.261290\pi$
$937$	−7.07285e7	−	7.46671e7i	−0.0859757	−	0.0907634i	−0.767564	+	0.640973i	$0.778531\pi$
$938$	376614.	+	6.94624e6i	0.000456340	+	0.00841669i
$939$	2.54385e8	+	7.06297e7i	0.307252	+	0.0853082i
$940$	1.89487e8	+	4.09569e8i	0.228137	+	0.493109i
$941$	1.18053e9	+	1.93539e8i	1.41680	+	0.232273i	0.821032	−	0.570882i	$-0.193399\pi$
$941$	1.18053e9	+	1.93539e8i	1.41680	+	0.232273i	0.595770	+	0.803155i	$0.296847\pi$
$942$	8.43849e6	−	1.85745e6i	0.0100951	−	0.00222211i
$943$		−	3.82446e8i		−	0.456074i
$944$	3.98034e8	−	5.16645e6i	0.473156	−	0.00614153i
$945$	−1.30777e8			−0.154966
$946$	4.99865e7	+	2.27091e8i	0.0590444	+	0.268242i
$947$	−3.92861e7	+	2.39635e8i	−0.0462582	+	0.282163i	−0.999819	−	0.0190387i	$-0.993939\pi$
$947$	−3.92861e7	+	2.39635e8i	−0.0462582	+	0.282163i	0.953561	+	0.301202i	$0.0973877\pi$
$948$	−1.43049e8	+	6.61814e7i	−0.167903	+	0.0776803i
$949$	−1.65438e8	+	5.95855e8i	−0.193570	+	0.697175i
$950$	3.29733e8	−	1.78776e7i	0.384585	−	0.0208516i
$951$	2.00366e8	−	1.89796e8i	0.232960	−	0.220671i
$952$	1.98226e7	+	2.60762e7i	0.0229747	+	0.0302227i
$953$	−1.12031e9	−	3.77477e8i	−1.29438	−	0.436126i	−0.413946	−	0.910301i	$-0.635850\pi$
$953$	−1.12031e9	−	3.77477e8i	−1.29438	−	0.436126i	−0.880431	+	0.474175i	$0.842746\pi$
$954$	−1.17934e8	−	6.39419e6i	−0.135829	−	0.00736446i
$955$	−1.45616e9	+	1.23687e9i	−1.67186	+	1.42009i
$956$	3.54300e8	+	1.27607e9i	0.405506	+	1.46050i
$957$	4.63374e7	+	1.37524e8i	0.0528683	+	0.156908i
$958$	−3.67758e8	−	2.49346e8i	−0.418279	−	0.283600i
$959$	−1.33387e8	−	6.17113e7i	−0.151237	−	0.0699695i
$960$	7.58265e6	−	8.92698e6i	0.00857052	−	0.0100900i
$961$	−1.05754e8	−	1.00175e8i	−0.119159	−	0.112873i
$962$	−4.02092e7	+	3.69718e8i	−0.0451649	+	0.415284i
$963$	1.86512e8	+	4.68110e8i	0.208847	+	0.524166i
$964$	4.52673e7	+	2.76118e8i	0.0505305	+	0.308222i
$965$	9.50658e8	+	1.40212e9i	1.05789	+	1.56028i
$966$	1.67236e7	+	1.27129e7i	0.0185523	+	0.0141031i
$967$	1.77246e8	+	1.62975e9i	0.196018	+	1.80236i	0.517754	+	0.855530i	$0.326768\pi$
$967$	1.77246e8	+	1.62975e9i	0.196018	+	1.80236i	−0.321736	+	0.946830i	$0.604266\pi$
$968$	5.24684e8	−	2.78170e8i	0.578458	−	0.306679i
$969$	3.77431e7	+	2.27093e7i	0.0414827	+	0.0249593i
$970$	−3.97146e8	+	2.38955e8i	−0.435146	+	0.261819i
$971$	5.42905e8	−	1.02403e9i	0.593016	−	1.11855i	−0.387456	−	0.921888i	$-0.626646\pi$
$971$	5.42905e8	−	1.02403e9i	0.593016	−	1.11855i	0.980472	−	0.196659i	$-0.0630090\pi$
$972$	−1.72790e8	+	4.33671e8i	−0.188157	+	0.472239i
$973$	−3.36393e8	−	7.40457e7i	−0.365181	−	0.0803825i
$974$	−9.09162e7	+	4.13037e8i	−0.0983931	+	0.447004i
$975$	−8.24696e7	−	3.28589e7i	−0.0889774	−	0.0354519i
$976$	4.29785e8	+	2.27858e8i	0.462277	+	0.245084i
$977$	1.42606e7	+	2.37013e7i	0.0152916	+	0.0254149i	0.864409	−	0.502790i	$-0.167693\pi$
$977$	1.42606e7	+	2.37013e7i	0.0152916	+	0.0254149i	−0.849117	+	0.528205i	$0.822865\pi$
$978$	1.37179e7	−	2.27993e7i	0.0146646	−	0.0243728i
$979$	1.04606e8	+	1.97308e8i	0.111483	+	0.210279i
$980$	9.28077e8	−	1.00934e8i	0.986066	−	0.107241i
$981$	1.56003e7	−	2.05219e7i	0.0165245	−	0.0217376i
$982$	1.38699e8	−	9.40401e7i	0.146466	−	0.0993067i
$983$	−8.06920e8	+	1.32288e8i	−0.849513	+	0.139271i	−0.570785	−	0.821100i	$-0.693361\pi$
$983$	−8.06920e8	+	1.32288e8i	−0.849513	+	0.139271i	−0.278728	+	0.960370i	$0.589913\pi$
$984$	7.91827e7	−	3.15493e7i	0.0831085	−	0.0331134i
$985$	−6.28414e8	−	6.83442e7i	−0.657563	−	0.0715143i
$986$	−9.31401e7	+	9.83268e7i	−0.0971641	+	0.102575i
$987$	2.24518e7	+	1.90707e7i	0.0233507	+	0.0198342i
$988$	−2.33422e8	+	5.04532e8i	−0.242031	+	0.523140i
$989$	7.55921e8	−	1.11490e9i	0.781426	−	1.15252i
$990$	2.02509e8	−	6.82332e7i	0.208708	−	0.0703218i
$991$	−6.65625e8	+	1.84810e8i	−0.683926	+	0.189891i	−0.592076	−	0.805882i	$-0.701692\pi$
$991$	−6.65625e8	+	1.84810e8i	−0.683926	+	0.189891i	−0.0918494	+	0.995773i	$0.529278\pi$
$992$	−5.71594e8	−	6.72932e8i	−0.585534	−	0.689344i
$993$	−2.10637e7	+	3.88497e8i	−0.0215123	+	0.396771i
$994$	−3.01920e7	+	8.96067e7i	−0.0307421	+	0.0912392i
$995$	7.28720e8	−	5.53959e8i	0.739761	−	0.562352i
$996$	1.04090e8	+	1.09887e8i	0.105349	+	0.111216i
$997$	−7.83239e7	−	1.44460e9i	−0.0790330	−	1.45768i	−0.722058	−	0.691833i	$-0.756803\pi$
$997$	−7.83239e7	−	1.44460e9i	−0.0790330	−	1.45768i	0.643024	−	0.765846i	$-0.277679\pi$
$998$	6.97643e8	+	1.93700e8i	0.701846	+	0.194867i
$999$	3.00619e8	+	6.49778e8i	0.301523	+	0.651731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.7.d.a.11.12	✓	812
59.43	odd	58	inner	59.7.d.a.43.12	yes	812

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.7.d.a.11.12	✓	812	1.1	even	1	trivial
59.7.d.a.43.12	yes	812	59.43	odd	58	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	59.d (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.744271 - 3.38126i) q^{2} +(-0.974635 + 5.94501i) q^{3} +(47.2059 - 21.8398i) q^{4} +(44.0346 - 158.598i) q^{5} +(20.8270 - 1.12921i) q^{6} +(-67.3470 + 63.7945i) q^{7} +(-243.075 - 319.760i) q^{8} +(656.446 + 221.182i) q^{9} +(-569.035 - 30.8522i) q^{10} +(-412.587 + 350.455i) q^{11} +(83.8291 + 301.925i) q^{12} +(-410.310 - 1217.76i) q^{13} +(265.830 + 180.237i) q^{14} +(899.950 + 416.361i) q^{15} +(1254.77 - 1477.23i) q^{16} +(638.219 + 604.553i) q^{17} +(259.301 - 2384.23i) q^{18} +(-3078.55 - 7726.57i) q^{19} +(-1385.06 - 8448.47i) q^{20} +(-313.620 - 462.555i) q^{21} +(1492.06 + 1134.23i) q^{22} +(-1173.87 - 10793.5i) q^{23} +(2137.88 - 1133.43i) q^{24} +(-9825.94 - 5912.07i) q^{25} +(-3812.17 + 2293.71i) q^{26} +(-4011.87 + 7567.19i) q^{27} +(-1785.92 + 4482.32i) q^{28} +(-43458.6 - 9565.96i) q^{29} +(738.018 - 3352.85i) q^{30} +(25302.2 + 10081.3i) q^{31} +(-28640.6 - 15184.3i) q^{32} +(-1681.34 - 2794.40i) q^{33} +(1569.14 - 2607.93i) q^{34} +(7152.09 + 13490.3i) q^{35} +(35818.7 - 3895.51i) q^{36} +(50587.2 - 66546.3i) q^{37} +(-23834.3 + 16160.0i) q^{38} +(7639.48 - 1252.43i) q^{39} +(-61417.0 + 24470.8i) q^{40} +(35018.8 + 3808.52i) q^{41} +(-1330.60 + 1404.70i) q^{42} +(94558.4 + 80318.6i) q^{43} +(-11822.7 + 25554.3i) q^{44} +(63985.4 - 94371.4i) q^{45} +(-35622.0 + 12002.4i) q^{46} +(-50790.3 + 14101.9i) q^{47} +(7559.21 + 8899.38i) q^{48} +(-5903.50 + 108884. i) q^{49} +(-12677.1 + 37624.2i) q^{50} +(-4216.10 + 3205.00i) q^{51} +(-45964.6 - 48524.2i) q^{52} +(-2666.14 - 49174.1i) q^{53} +(28572.5 + 7933.12i) q^{54} +(37413.4 + 80867.7i) q^{55} +(36769.3 + 6028.02i) q^{56} +(48935.0 - 10771.4i) q^{57} +154064. i q^{58} +(134980. + 154793. i) q^{59} +51576.2 q^{60} +(53953.2 + 245112. i) q^{61} +(15255.9 - 93056.6i) q^{62} +(-58319.9 + 26981.7i) q^{63} +(3160.03 - 11381.4i) q^{64} +(-211202. + 11451.0i) q^{65} +(-8197.22 + 7764.82i) q^{66} +(13107.8 + 17243.0i) q^{67} +(43330.9 + 14599.9i) q^{68} +(65311.7 + 3541.10i) q^{69} +(40291.0 - 34223.5i) q^{70} +(78763.3 + 283680. i) q^{71} +(-88840.3 - 263669. i) q^{72} +(-398311. - 270062. i) q^{73} +(-262661. - 121520. i) q^{74} +(44724.1 - 52653.2i) q^{75} +(-314072. - 297505. i) q^{76} +(5429.44 - 49922.9i) q^{77} +(-9920.64 - 24898.9i) q^{78} +(81377.9 + 496383. i) q^{79} +(-179033. - 264053. i) q^{80} +(360937. + 274377. i) q^{81} +(-13185.9 - 121242. i) q^{82} +(426775. - 226262. i) q^{83} +(-24906.8 - 14985.9i) q^{84} +(123985. - 74599.1i) q^{85} +(201201. - 379505. i) q^{86} +(99226.0 - 249039. i) q^{87} +(212351. + 46742.0i) q^{88} +(88683.3 - 402892. i) q^{89} +(-366717. - 146113. i) q^{90} +(105319. + 55836.8i) q^{91} +(-291141. - 483880. i) q^{92} +(-84594.1 + 140596. i) q^{93} +(85483.8 + 161240. i) q^{94} +(-1.36098e6 + 148016. i) q^{95} +(118185. - 155470. i) q^{96} +(673183. - 456429. i) q^{97} +(372558. - 61077.7i) q^{98} +(-348356. + 138798. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 812 q - 29 q^{2} - 39 q^{3} + 869 q^{4} - 171 q^{5} - 29 q^{6} - 435 q^{7} - 29 q^{8} - 7648 q^{9} - 29 q^{10} - 29 q^{11} + 1095 q^{12} - 29 q^{13} - 29 q^{14} - 569 q^{15} - 25051 q^{16} - 9071 q^{17}+ \cdots + 9513421 q^{99}+O(q^{100}) \) 812 * q - 29 * q^2 - 39 * q^3 + 869 * q^4 - 171 * q^5 - 29 * q^6 - 435 * q^7 - 29 * q^8 - 7648 * q^9 - 29 * q^10 - 29 * q^11 + 1095 * q^12 - 29 * q^13 - 29 * q^14 - 569 * q^15 - 25051 * q^16 - 9071 * q^17 - 29 * q^18 - 3879 * q^19 + 46867 * q^20 - 3729 * q^21 - 11267 * q^22 - 29 * q^23 - 29 * q^24 - 65696 * q^25 + 64561 * q^26 - 36009 * q^27 + 45513 * q^28 + 31701 * q^29 - 29 * q^30 - 29 * q^31 - 29 * q^32 - 29 * q^33 - 29 * q^34 - 46305 * q^35 + 185269 * q^36 - 29 * q^37 - 29 * q^38 - 29 * q^39 - 29 * q^40 - 91943 * q^41 - 29 * q^42 - 29 * q^43 - 29 * q^44 + 1328609 * q^45 + 122071 * q^46 - 472149 * q^47 - 4460721 * q^48 - 992540 * q^49 - 1117341 * q^50 - 161065 * q^51 + 1336291 * q^52 + 1079813 * q^53 + 4504947 * q^54 + 1872907 * q^55 + 3956963 * q^56 + 2677007 * q^57 - 302138 * q^59 - 4965482 * q^60 - 1574381 * q^61 - 2444409 * q^62 - 5085047 * q^63 - 5066455 * q^64 - 1422653 * q^65 + 433939 * q^66 + 876931 * q^67 + 3018437 * q^68 + 5706243 * q^69 + 6798499 * q^70 + 3537645 * q^71 + 6041251 * q^72 - 396749 * q^73 - 3448403 * q^74 - 9552475 * q^75 - 247173 * q^76 - 29 * q^77 + 375035 * q^78 - 4731 * q^79 - 1921013 * q^80 + 841594 * q^81 - 29 * q^82 - 29 * q^83 - 2367333 * q^84 - 864073 * q^85 - 5031139 * q^86 + 4790463 * q^87 - 726023 * q^88 - 29 * q^89 - 29 * q^90 - 29 * q^91 - 29 * q^92 - 29 * q^93 - 2835797 * q^94 - 1047881 * q^95 - 29 * q^96 - 29 * q^97 + 29127484 * q^98 + 9513421 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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