LMFDB - Embedded newform 117.3.m.a.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(23,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.m (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	117.23
Dual form			117.3.m.a.56.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21581 + 2.10585i) q^{2} +(-2.69201 - 1.32405i) q^{3} +(-0.956401 - 1.65653i) q^{4} +(-3.20934 + 5.55874i) q^{5} +(6.06122 - 4.05917i) q^{6} -7.16022i q^{7} -5.07529 q^{8} +(5.49381 + 7.12868i) q^{9} +(-7.80391 - 13.5168i) q^{10} +(7.11261 - 12.3194i) q^{11} +(0.381310 + 5.72572i) q^{12} +(-6.53109 - 11.2403i) q^{13} +(15.0784 + 8.70549i) q^{14} +(15.9996 - 10.7149i) q^{15} +(9.99620 - 17.3139i) q^{16} +(-14.2712 - 8.23946i) q^{17} +(-21.6914 + 2.90199i) q^{18} +(4.94498 + 2.85499i) q^{19} +12.2777 q^{20} +(-9.48046 + 19.2754i) q^{21} +(17.2952 + 29.9562i) q^{22} +14.3327i q^{23} +(13.6627 + 6.71991i) q^{24} +(-8.09972 - 14.0291i) q^{25} +(31.6110 - 0.0873511i) q^{26} +(-5.35066 - 26.4645i) q^{27} +(-11.8612 + 6.84804i) q^{28} +(-4.22551 - 2.43960i) q^{29} +(3.11136 + 46.7200i) q^{30} +(-44.9926 - 25.9765i) q^{31} +(14.1564 + 24.5197i) q^{32} +(-35.4586 + 23.7465i) q^{33} +(34.7021 - 20.0353i) q^{34} +(39.8018 + 22.9796i) q^{35} +(6.55463 - 15.9186i) q^{36} +(-46.8401 + 27.0432i) q^{37} +(-12.0243 + 6.94225i) q^{38} +(2.69902 + 38.9065i) q^{39} +(16.2883 - 28.2122i) q^{40} -51.5357 q^{41} +(-29.0646 - 43.3997i) q^{42} -2.41011 q^{43} -27.2100 q^{44} +(-57.2580 + 7.66027i) q^{45} +(-30.1824 - 17.4258i) q^{46} +(0.709869 + 1.22953i) q^{47} +(-49.8343 + 33.3738i) q^{48} -2.26880 q^{49} +39.3910 q^{50} +(27.5087 + 41.0764i) q^{51} +(-12.3737 + 21.5692i) q^{52} -80.9755i q^{53} +(62.2357 + 20.9082i) q^{54} +(45.6535 + 79.0743i) q^{55} +36.3402i q^{56} +(-9.53179 - 14.2330i) q^{57} +(10.2748 - 5.93219i) q^{58} +(-9.09833 - 15.7588i) q^{59} +(-33.0515 - 16.2562i) q^{60} +113.582 q^{61} +(109.405 - 63.1651i) q^{62} +(51.0430 - 39.3369i) q^{63} +11.1233 q^{64} +(83.4425 - 0.230578i) q^{65} +(-6.89547 - 103.542i) q^{66} -33.8467i q^{67} +31.5209i q^{68} +(18.9771 - 38.5836i) q^{69} +(-96.7831 + 55.8777i) q^{70} +(-59.6642 + 103.341i) q^{71} +(-27.8826 - 36.1801i) q^{72} +52.2658i q^{73} -131.518i q^{74} +(3.22930 + 48.4909i) q^{75} -10.9220i q^{76} +(-88.2097 - 50.9279i) q^{77} +(-85.2127 - 41.6193i) q^{78} +(10.6829 + 18.5033i) q^{79} +(64.1624 + 111.133i) q^{80} +(-20.6362 + 78.3272i) q^{81} +(62.6578 - 108.527i) q^{82} +(-55.2653 - 95.7223i) q^{83} +(40.9974 - 2.73026i) q^{84} +(91.6020 - 52.8865i) q^{85} +(2.93025 - 5.07534i) q^{86} +(8.14495 + 12.1622i) q^{87} +(-36.0985 + 62.5245i) q^{88} +(-12.1907 - 21.1149i) q^{89} +(53.4836 - 129.890i) q^{90} +(-80.4832 + 46.7640i) q^{91} +(23.7426 - 13.7078i) q^{92} +(86.7264 + 129.501i) q^{93} -3.45227 q^{94} +(-31.7402 + 18.3252i) q^{95} +(-5.64407 - 84.7509i) q^{96} -45.1850i q^{97} +(2.75844 - 4.77775i) q^{98} +(126.896 - 16.9769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{2} - q^{3} - 47 q^{4} - 3 q^{6} + 78 q^{8} + q^{9} + 2 q^{10} - 3 q^{11} + 13 q^{12} - 6 q^{13} - 6 q^{14} + 24 q^{15} - 75 q^{16} - 12 q^{18} + 15 q^{19} - 6 q^{20} + 69 q^{21} + 17 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - 3 * q^2 - q^3 - 47 * q^4 - 3 * q^6 + 78 * q^8 + q^9 + 2 * q^10 - 3 * q^11 + 13 * q^12 - 6 * q^13 - 6 * q^14 + 24 * q^15 - 75 * q^16 - 12 * q^18 + 15 * q^19 - 6 * q^20 + 69 * q^21 + 17 * q^22 - 42 * q^24 - 92 * q^25 + 12 * q^26 + 14 * q^27 - 18 * q^28 + 24 * q^29 + 147 * q^30 - 48 * q^31 - 159 * q^32 - 120 * q^33 + 12 * q^34 - 78 * q^35 - 181 * q^36 + 27 * q^37 - 36 * q^38 - 35 * q^39 - 44 * q^40 + 66 * q^41 + 300 * q^42 + 62 * q^43 + 120 * q^44 + 117 * q^45 - 6 * q^46 - 153 * q^47 - 244 * q^48 - 146 * q^49 + 432 * q^50 - 63 * q^51 + 128 * q^52 - 132 * q^54 + 23 * q^55 - 171 * q^57 - 3 * q^58 - 3 * q^59 - 207 * q^60 + 12 * q^61 + 201 * q^62 - 192 * q^63 + 270 * q^64 - 3 * q^65 + 48 * q^66 - 48 * q^69 + 159 * q^70 - 432 * q^71 + 93 * q^72 + 346 * q^75 + 138 * q^77 - 93 * q^78 + 9 * q^79 - 84 * q^80 - 215 * q^81 - 85 * q^82 - 135 * q^83 - 246 * q^84 - 24 * q^85 - 306 * q^86 - 123 * q^87 + 145 * q^88 - 441 * q^89 + 543 * q^90 - 138 * q^91 + 864 * q^92 + 183 * q^93 + 362 * q^94 + 252 * q^95 + 747 * q^96 + 147 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.21581	+	2.10585i	−0.607906	+	1.05292i	0.383679	+	0.923467i	$0.374657\pi$
$2$	−1.21581	+	2.10585i	−0.607906	+	1.05292i	−0.991585	+	0.129458i	$0.958676\pi$
$3$	−2.69201	−	1.32405i	−0.897336	−	0.441349i
$3$	−2.69201	−	1.32405i	−0.897336	−	0.441349i
$4$	−0.956401	−	1.65653i	−0.239100	−	0.414134i
$5$	−3.20934	+	5.55874i	−0.641868	+	1.11175i	0.343148	+	0.939282i	$0.388507\pi$
$5$	−3.20934	+	5.55874i	−0.641868	+	1.11175i	−0.985015	+	0.172466i	$0.944826\pi$
$6$	6.06122	−	4.05917i	1.01020	−	0.676528i
$7$		−	7.16022i		−	1.02289i	−0.859316	−	0.511445i	$-0.829111\pi$
$7$		−	7.16022i		−	1.02289i	0.859316	−	0.511445i	$-0.170889\pi$
$8$	−5.07529			−0.634411
$9$	5.49381	+	7.12868i	0.610423	+	0.792076i
$10$	−7.80391	−	13.5168i	−0.780391	−	1.35168i
$11$	7.11261	−	12.3194i	0.646601	−	1.11995i	−0.337329	−	0.941387i	$-0.609523\pi$
$11$	7.11261	−	12.3194i	0.646601	−	1.11995i	0.983929	−	0.178558i	$-0.0571433\pi$
$12$	0.381310	+	5.72572i	0.0317758	+	0.477143i
$13$	−6.53109	−	11.2403i	−0.502391	−	0.864640i
$13$	−6.53109	−	11.2403i	−0.502391	−	0.864640i
$14$	15.0784	+	8.70549i	1.07703	+	0.621821i
$15$	15.9996	−	10.7149i	1.06664	−	0.714323i
$16$	9.99620	−	17.3139i	0.624762	−	1.08212i
$17$	−14.2712	−	8.23946i	−0.839480	−	0.484674i	0.0176072	−	0.999845i	$-0.494395\pi$
$17$	−14.2712	−	8.23946i	−0.839480	−	0.484674i	−0.857088	+	0.515171i	$0.827728\pi$
$18$	−21.6914	+	2.90199i	−1.20508	+	0.161221i
$19$	4.94498	+	2.85499i	0.260262	+	0.150262i	0.624454	−	0.781061i	$-0.285321\pi$
$19$	4.94498	+	2.85499i	0.260262	+	0.150262i	−0.364192	+	0.931324i	$0.618655\pi$
$20$	12.2777			0.613883
$21$	−9.48046	+	19.2754i	−0.451451	+	0.917875i
$22$	17.2952	+	29.9562i	0.786145	+	1.36164i
$23$			14.3327i			0.623159i	0.950220	+	0.311580i	$0.100858\pi$
$23$			14.3327i			0.623159i	−0.950220	+	0.311580i	$0.899142\pi$
$24$	13.6627	+	6.71991i	0.569279	+	0.279996i
$25$	−8.09972	−	14.0291i	−0.323989	−	0.561165i
$26$	31.6110	−	0.0873511i	1.21581	−	0.00335966i
$27$	−5.35066	−	26.4645i	−0.198173	−	0.980167i
$28$	−11.8612	+	6.84804i	−0.423613	+	0.244573i
$29$	−4.22551	−	2.43960i	−0.145707	−	0.0841240i	0.425374	−	0.905018i	$-0.360143\pi$
$29$	−4.22551	−	2.43960i	−0.145707	−	0.0841240i	−0.571081	+	0.820894i	$0.693476\pi$
$30$	3.11136	+	46.7200i	0.103712	+	1.55733i
$31$	−44.9926	−	25.9765i	−1.45138	−	0.837952i	−0.452815	−	0.891604i	$-0.649580\pi$
$31$	−44.9926	−	25.9765i	−1.45138	−	0.837952i	−0.998560	+	0.0536525i	$0.982914\pi$
$32$	14.1564	+	24.5197i	0.442389	+	0.766240i
$33$	−35.4586	+	23.7465i	−1.07450	+	0.719591i
$34$	34.7021	−	20.0353i	1.02065	−	0.589273i
$35$	39.8018	+	22.9796i	1.13719	+	0.656560i
$36$	6.55463	−	15.9186i	0.182073	−	0.442182i
$37$	−46.8401	+	27.0432i	−1.26595	+	0.730896i	−0.974219	−	0.225604i	$-0.927564\pi$
$37$	−46.8401	+	27.0432i	−1.26595	+	0.730896i	−0.291730	+	0.956501i	$0.594231\pi$
$38$	−12.0243	+	6.94225i	−0.316430	+	0.182691i
$39$	2.69902	+	38.9065i	0.0692057	+	0.997602i
$40$	16.2883	−	28.2122i	0.407208	−	0.705305i
$41$	−51.5357			−1.25697			−0.628485	−	0.777822i	$-0.716325\pi$
$41$	−51.5357			−1.25697			−0.628485	+	0.777822i	$0.716325\pi$
$42$	−29.0646	−	43.3997i	−0.692013	−	1.03333i
$43$	−2.41011			−0.0560491			−0.0280246	−	0.999607i	$-0.508922\pi$
$43$	−2.41011			−0.0560491			−0.0280246	+	0.999607i	$0.508922\pi$
$44$	−27.2100			−0.618409
$45$	−57.2580	+	7.66027i	−1.27240	+	0.170228i
$46$	−30.1824	−	17.4258i	−0.656140	−	0.378822i
$47$	0.709869	+	1.22953i	0.0151036	+	0.0261602i	0.873478	−	0.486863i	$-0.161859\pi$
$47$	0.709869	+	1.22953i	0.0151036	+	0.0261602i	−0.858375	+	0.513023i	$0.828526\pi$
$48$	−49.8343	+	33.3738i	−1.03821	+	0.695287i
$49$	−2.26880			−0.0463021
$50$	39.3910			0.787819
$51$	27.5087	+	41.0764i	0.539385	+	0.805419i
$52$	−12.3737	+	21.5692i	−0.237955	+	0.414793i
$53$		−	80.9755i		−	1.52784i	−0.645312	−	0.763919i	$-0.723272\pi$
$53$		−	80.9755i		−	1.52784i	0.645312	−	0.763919i	$-0.276728\pi$
$54$	62.2357	+	20.9082i	1.15251	+	0.387189i
$55$	45.6535	+	79.0743i	0.830064	+	1.43771i
$56$			36.3402i			0.648932i
$57$	−9.53179	−	14.2330i	−0.167224	−	0.249702i
$58$	10.2748	−	5.93219i	0.177153	−	0.102279i
$59$	−9.09833	−	15.7588i	−0.154209	−	0.267098i	0.778562	−	0.627568i	$-0.215950\pi$
$59$	−9.09833	−	15.7588i	−0.154209	−	0.267098i	−0.932771	+	0.360470i	$0.882616\pi$
$60$	−33.0515	−	16.2562i	−0.550859	−	0.270936i
$61$	113.582			1.86200			0.931002	−	0.365015i	$-0.118936\pi$
$61$	113.582			1.86200			0.931002	+	0.365015i	$0.118936\pi$
$62$	109.405	−	63.1651i	1.76460	−	1.01879i
$63$	51.0430	−	39.3369i	0.810206	−	0.624395i
$64$	11.1233			0.173801
$65$	83.4425	−	0.230578i	1.28373	−	0.00354735i
$66$	−6.89547	−	103.542i	−0.104477	−	1.56882i
$67$		−	33.8467i		−	0.505175i	−0.967574	−	0.252588i	$-0.918718\pi$
$67$		−	33.8467i		−	0.505175i	0.967574	−	0.252588i	$-0.0812816\pi$
$68$			31.5209i			0.463543i
$69$	18.9771	−	38.5836i	0.275030	−	0.559183i
$70$	−96.7831	+	55.8777i	−1.38262	+	0.798253i
$71$	−59.6642	+	103.341i	−0.840341	+	1.45551i	0.0492649	+	0.998786i	$0.484312\pi$
$71$	−59.6642	+	103.341i	−0.840341	+	1.45551i	−0.889606	+	0.456728i	$0.849021\pi$
$72$	−27.8826	−	36.1801i	−0.387259	−	0.502501i
$73$			52.2658i			0.715969i	0.933727	+	0.357985i	$0.116536\pi$
$73$			52.2658i			0.715969i	−0.933727	+	0.357985i	$0.883464\pi$
$74$		−	131.518i		−	1.77727i
$75$	3.22930	+	48.4909i	0.0430573	+	0.646545i
$76$		−	10.9220i		−	0.143711i
$77$	−88.2097	−	50.9279i	−1.14558	−	0.661401i
$78$	−85.2127	−	41.6193i	−1.09247	−	0.533580i
$79$	10.6829	+	18.5033i	0.135226	+	0.234219i	0.925684	−	0.378298i	$-0.123491\pi$
$79$	10.6829	+	18.5033i	0.135226	+	0.234219i	−0.790458	+	0.612517i	$0.790157\pi$
$80$	64.1624	+	111.133i	0.802030	+	1.38916i
$81$	−20.6362	+	78.3272i	−0.254768	+	0.967002i
$82$	62.6578	−	108.527i	0.764120	−	1.32349i
$83$	−55.2653	−	95.7223i	−0.665847	−	1.15328i	−0.979055	−	0.203596i	$-0.934737\pi$
$83$	−55.2653	−	95.7223i	−0.665847	−	1.15328i	0.313208	−	0.949685i	$-0.398596\pi$
$84$	40.9974	−	2.73026i	0.488065	−	0.0325031i
$85$	91.6020	−	52.8865i	1.07767	−	0.622194i
$86$	2.93025	−	5.07534i	0.0340726	−	0.0590155i
$87$	8.14495	+	12.1622i	0.0936202	+	0.139795i
$88$	−36.0985	+	62.5245i	−0.410210	+	0.710505i
$89$	−12.1907	−	21.1149i	−0.136974	−	0.237246i	0.789376	−	0.613910i	$-0.210404\pi$
$89$	−12.1907	−	21.1149i	−0.136974	−	0.237246i	−0.926350	+	0.376664i	$0.877071\pi$
$90$	53.4836	−	129.890i	0.594262	−	1.44322i
$91$	−80.4832	+	46.7640i	−0.884431	+	0.513890i
$92$	23.7426	−	13.7078i	0.258071	−	0.148997i
$93$	86.7264	+	129.501i	0.932542	+	1.39249i
$94$	−3.45227			−0.0367263
$95$	−31.7402	+	18.3252i	−0.334108	+	0.192897i
$96$	−5.64407	−	84.7509i	−0.0587924	−	0.882822i
$97$		−	45.1850i		−	0.465825i	−0.972498	−	0.232912i	$-0.925174\pi$
$97$		−	45.1850i		−	0.465825i	0.972498	−	0.232912i	$-0.0748255\pi$
$98$	2.75844	−	4.77775i	0.0281473	−	0.0487526i
$99$	126.896	−	16.9769i	1.28178	−	0.171483i
$100$	−15.4931	+	26.8349i	−0.154931	+	0.268349i
$101$	−137.614	−	79.4512i	−1.36251	−	0.786646i	−0.372553	−	0.928011i	$-0.621517\pi$
$101$	−137.614	−	79.4512i	−1.36251	−	0.786646i	−0.989957	+	0.141365i	$0.954851\pi$
$102$	−119.946	+	7.98792i	−1.17594	+	0.0783129i
$103$	−51.6241	+	89.4157i	−0.501205	+	0.868113i	0.498794	+	0.866721i	$0.333777\pi$
$103$	−51.6241	+	89.4157i	−0.501205	+	0.868113i	−0.999999	+	0.00139237i	$0.999557\pi$
$104$	33.1471	+	57.0479i	0.318722	+	0.548537i
$105$	−76.7207	−	114.561i	−0.730674	−	1.09105i
$106$	170.522	+	98.4510i	1.60870	+	0.928783i
$107$	109.254	−	63.0780i	1.02107	−	0.589514i	0.106654	−	0.994296i	$-0.465986\pi$
$107$	109.254	−	63.0780i	1.02107	−	0.589514i	0.914413	+	0.404783i	$0.132653\pi$
$108$	−38.7220	+	34.1742i	−0.358537	+	0.316428i
$109$		−	83.1109i		−	0.762485i	−0.924475	−	0.381243i	$-0.875496\pi$
$109$		−	83.1109i		−	0.762485i	0.924475	−	0.381243i	$-0.124504\pi$
$110$	−222.025			−2.01841
$111$	161.900	−	10.7819i	1.45856	−	0.0971343i
$112$	−123.972	−	71.5750i	−1.10689	−	0.639063i
$113$	−1.78506	+	1.03061i	−0.0157970	+	0.00912042i	−0.507878	−	0.861429i	$-0.669570\pi$
$113$	−1.78506	+	1.03061i	−0.0157970	+	0.00912042i	0.492081	+	0.870550i	$0.336236\pi$
$114$	41.5615	−	2.76783i	0.364574	−	0.0242792i
$115$	−79.6715	−	45.9984i	−0.692796	−	0.399986i
$116$			9.33293i			0.0804563i
$117$	44.2482	−	108.310i	0.378190	−	0.925728i
$118$	44.2475			0.374979
$119$	−58.9964	+	102.185i	−0.495768	+	0.858695i
$120$	−81.2025	+	54.3809i	−0.676687	+	0.453174i
$121$	−40.6784	−	70.4571i	−0.336185	−	0.582290i
$122$	−138.095	+	239.187i	−1.13192	+	1.96055i
$123$	138.735	+	68.2357i	1.12792	+	0.554762i
$124$			99.3758i			0.801418i
$125$	−56.4880			−0.451904
$126$	20.7789	+	155.315i	0.164912	+	1.23266i
$127$	−21.3143	−	36.9174i	−0.167829	−	0.290688i	0.769827	−	0.638252i	$-0.220342\pi$
$127$	−21.3143	−	36.9174i	−0.167829	−	0.290688i	−0.937656	+	0.347564i	$0.887009\pi$
$128$	−70.1496	+	121.503i	−0.548044	+	0.949239i
$129$	6.48804	+	3.19110i	0.0502949	+	0.0247372i
$130$	−100.965	+	175.998i	−0.776653	+	1.35383i
$131$	−41.0008	−	23.6718i	−0.312984	−	0.180701i	0.335277	−	0.942120i	$-0.391170\pi$
$131$	−41.0008	−	23.6718i	−0.312984	−	0.180701i	−0.648261	+	0.761418i	$0.724503\pi$
$132$	73.2495	+	36.0273i	0.554921	+	0.272934i
$133$	20.4423	−	35.4072i	0.153702	−	0.266219i
$134$	71.2761	+	41.1513i	0.531911	+	0.307099i
$135$	164.281	+	55.1907i	1.21690	+	0.408820i
$136$	72.4302	+	41.8176i	0.532575	+	0.307482i
$137$	−10.8548			−0.0792322			−0.0396161	−	0.999215i	$-0.512613\pi$
$137$	−10.8548			−0.0792322			−0.0396161	+	0.999215i	$0.512613\pi$
$138$	58.1787	+	86.8734i	0.421585	+	0.629517i
$139$	81.1348	+	140.530i	0.583703	+	1.01100i	0.995036	+	0.0995185i	$0.0317303\pi$
$139$	81.1348	+	140.530i	0.583703	+	1.01100i	−0.411332	+	0.911485i	$0.634936\pi$
$140$		−	87.9108i		−	0.627934i
$141$	−0.283020	−	4.24980i	−0.00200723	−	0.0301404i
$142$	−145.081	−	251.288i	−1.02170	−	1.76963i
$143$	−184.927	+	0.511011i	−1.29320	+	0.00357350i
$144$	178.343	−	23.8596i	1.23849	−	0.165692i
$145$	27.1222	−	15.6590i	0.187049	−	0.107993i
$146$	−110.064	−	63.5454i	−0.753862	−	0.435242i
$147$	6.10763	+	3.00400i	0.0415485	+	0.0204354i
$148$	89.5958	+	51.7282i	0.605377	+	0.349515i
$149$	72.2235	+	125.095i	0.484721	+	0.839562i	0.999846	−	0.0175534i	$-0.00558771\pi$
$149$	72.2235	+	125.095i	0.484721	+	0.839562i	−0.515125	+	0.857115i	$0.672254\pi$
$150$	−106.041	−	52.1554i	−0.706938	−	0.347703i
$151$	33.4959	−	19.3389i	0.221827	−	0.128072i	−0.384969	−	0.922930i	$-0.625788\pi$
$151$	33.4959	−	19.3389i	0.221827	−	0.128072i	0.606796	+	0.794858i	$0.292454\pi$
$152$	−25.0972	−	14.4899i	−0.165113	−	0.0953281i
$153$	−19.6665	−	147.001i	−0.128539	−	0.960788i
$154$	214.493	−	123.837i	1.39281	−	0.804140i
$155$	288.793	−	166.735i	1.86318	−	1.07571i
$156$	61.8686	−	41.6812i	0.396594	−	0.267187i
$157$	−82.4092	+	142.737i	−0.524899	+	0.909152i	0.474680	+	0.880158i	$0.342564\pi$
$157$	−82.4092	+	142.737i	−0.524899	+	0.909152i	−0.999580	+	0.0289938i	$0.990770\pi$
$158$	−51.9535			−0.328819
$159$	−107.215	+	217.987i	−0.674310	+	1.37098i
$160$	−181.731			−1.13582
$161$	102.625			0.637423
$162$	−139.855	−	138.688i	−0.863305	−	0.856098i
$163$	81.8644	+	47.2644i	0.502236	+	0.289966i	0.729636	−	0.683835i	$-0.239689\pi$
$163$	81.8644	+	47.2644i	0.502236	+	0.289966i	−0.227401	+	0.973801i	$0.573023\pi$
$164$	49.2888	+	85.3707i	0.300542	+	0.520553i
$165$	−18.2017	−	273.316i	−0.110314	−	1.65646i
$166$	268.769			1.61909
$167$	236.911			1.41863			0.709314	−	0.704893i	$-0.249005\pi$
$167$	236.911			1.41863			0.709314	+	0.704893i	$0.249005\pi$
$168$	48.1161	−	97.8280i	0.286405	−	0.582310i
$169$	−83.6898	+	146.823i	−0.495206	+	0.868775i
$170$			257.200i			1.51294i
$171$	6.81448	+	50.9359i	0.0398507	+	0.297871i
$172$	2.30503	+	3.99244i	0.0134014	+	0.0232118i
$173$			198.418i			1.14693i	0.819231	+	0.573464i	$0.194401\pi$
$173$			198.418i			1.14693i	−0.819231	+	0.573464i	$0.805599\pi$
$174$	−35.5144	+	2.36512i	−0.204106	+	0.0135926i
$175$	−100.452	+	57.9958i	−0.574009	+	0.331404i
$176$	−142.198	−	246.294i	−0.807944	−	1.39940i
$177$	3.62744	+	54.4693i	0.0204940	+	0.307736i
$178$	59.2864			0.333070
$179$	114.644	−	66.1898i	0.640470	−	0.369775i	−0.144326	−	0.989530i	$-0.546101\pi$
$179$	114.644	−	66.1898i	0.640470	−	0.369775i	0.784795	+	0.619755i	$0.212768\pi$
$180$	67.4511	+	87.5235i	0.374728	+	0.486242i
$181$	−25.7631			−0.142338			−0.0711688	−	0.997464i	$-0.522673\pi$
$181$	−25.7631			−0.142338			−0.0711688	+	0.997464i	$0.522673\pi$
$182$	−0.625453	−	226.342i	−0.00343656	−	1.24364i
$183$	−305.764	−	150.388i	−1.67084	−	0.821792i
$184$		−	72.7424i		−	0.395339i
$185$		−	347.163i		−	1.87656i
$186$	−378.153	+	25.1835i	−2.03308	+	0.135395i
$187$	−203.010	+	117.208i	−1.08562	+	0.626781i
$188$	1.35784	−	2.35184i	0.00722254	−	0.0125098i
$189$	−189.492	+	38.3119i	−1.00260	+	0.202709i
$190$		−	89.1202i		−	0.469054i
$191$		−	4.20261i		−	0.0220032i	−0.999939	−	0.0110016i	$-0.996498\pi$
$191$		−	4.20261i		−	0.0220032i	0.999939	−	0.0110016i	$-0.00350199\pi$
$192$	−29.9440	−	14.7277i	−0.155958	−	0.0767070i
$193$			294.252i			1.52462i	0.647212	+	0.762310i	$0.275935\pi$
$193$			294.252i			1.52462i	−0.647212	+	0.762310i	$0.724065\pi$
$194$	95.1528	+	54.9365i	0.490478	+	0.283178i
$195$	−224.933	−	109.861i	−1.15350	−	0.563390i
$196$	2.16988	+	3.75835i	0.0110708	+	0.0191752i
$197$	−79.4500	−	137.611i	−0.403299	−	0.698535i	0.590822	−	0.806802i	$-0.298803\pi$
$197$	−79.4500	−	137.611i	−0.403299	−	0.698535i	−0.994122	+	0.108266i	$0.965470\pi$
$198$	−118.531	+	287.865i	−0.598644	+	1.45387i
$199$	121.034	−	209.636i	0.608209	−	1.05345i	−0.383326	−	0.923613i	$-0.625221\pi$
$199$	121.034	−	209.636i	0.608209	−	1.05345i	0.991535	−	0.129836i	$-0.0414452\pi$
$200$	41.1084	+	71.2018i	0.205542	+	0.356009i
$201$	−44.8146	+	91.1157i	−0.222958	+	0.453312i
$202$	334.625	−	193.196i	1.65656	−	0.956414i
$203$	−17.4681	+	30.2556i	−0.0860496	+	0.149042i
$204$	41.7351	−	84.8545i	0.204584	−	0.415953i
$205$	165.396	−	286.474i	0.806808	−	1.39743i
$206$	−125.531	−	217.425i	−0.609372	−	1.05546i
$207$	−102.173	+	78.7409i	−0.493589	+	0.380391i
$208$	−259.900	+	0.718185i	−1.24952	+	0.00345281i
$209$	70.3434	−	40.6128i	0.336571	−	0.194320i
$210$	334.525	−	22.2780i	1.59298	−	0.106086i
$211$	74.7094			0.354073			0.177036	−	0.984204i	$-0.443349\pi$
$211$	74.7094			0.354073			0.177036	+	0.984204i	$0.443349\pi$
$212$	−134.139	+	77.4450i	−0.632729	+	0.365306i
$213$	297.445	−	199.198i	1.39646	−	0.935201i
$214$			306.764i			1.43348i
$215$	7.73487	−	13.3972i	0.0359761	−	0.0623125i
$216$	27.1561	+	134.315i	0.125723	+	0.621828i
$217$	−185.998	+	322.157i	−0.857132	+	1.48460i
$218$	175.019	+	101.047i	0.802840	+	0.463520i
$219$	69.2023	−	140.700i	0.315992	−	0.642465i
$220$	87.3262	−	151.253i	0.396937	−	0.687515i
$221$	0.591971	+	214.225i	0.00267860	+	0.969345i
$222$	−174.135	+	354.046i	−0.784394	+	1.59480i
$223$	−247.147	−	142.690i	−1.10828	−	0.639866i	−0.169897	−	0.985462i	$-0.554343\pi$
$223$	−247.147	−	142.690i	−1.10828	−	0.639866i	−0.938383	+	0.345596i	$0.887677\pi$
$224$	175.566	−	101.363i	0.783778	−	0.452515i
$225$	55.5109	−	134.814i	0.246715	−	0.599171i
$226$		−	5.01210i		−	0.0221774i
$227$	366.576			1.61487			0.807437	−	0.589954i	$-0.200854\pi$
$227$	366.576			1.61487			0.807437	+	0.589954i	$0.200854\pi$
$228$	−14.4613	+	29.4022i	−0.0634267	+	0.128957i
$229$	−380.993	−	219.966i	−1.66373	−	0.960552i	−0.970913	−	0.239434i	$-0.923038\pi$
$229$	−380.993	−	219.966i	−1.66373	−	0.960552i	−0.692812	−	0.721118i	$-0.743629\pi$
$230$	193.731	−	111.851i	0.842310	−	0.486308i
$231$	170.030	+	253.892i	0.736061	+	1.09910i
$232$	21.4456	+	12.3817i	0.0924381	+	0.0533692i
$233$		−	65.5461i		−	0.281314i	−0.990058	−	0.140657i	$-0.955079\pi$
$233$		−	65.5461i		−	0.281314i	0.990058	−	0.140657i	$-0.0449215\pi$
$234$	174.287	+	224.865i	0.744818	+	0.960961i
$235$	−9.11284			−0.0387780
$236$	−17.4033	+	30.1434i	−0.0737428	+	0.127726i
$237$	−4.25918	−	63.9555i	−0.0179712	−	0.269855i
$238$	−143.457	−	248.475i	−0.602761	−	1.04401i
$239$	40.5565	−	70.2459i	0.169692	−	0.293916i	−0.768619	−	0.639706i	$-0.779056\pi$
$239$	40.5565	−	70.2459i	0.169692	−	0.293916i	0.938312	+	0.345791i	$0.112389\pi$
$240$	−25.5811	−	384.123i	−0.106588	−	1.60051i
$241$		−	229.538i		−	0.952439i	−0.879327	−	0.476219i	$-0.842007\pi$
$241$		−	229.538i		−	0.952439i	0.879327	−	0.476219i	$-0.157993\pi$
$242$	197.829			0.817476
$243$	159.262	−	183.534i	0.655397	−	0.755284i
$244$	−108.630	−	188.153i	−0.445205	−	0.771118i
$245$	7.28136	−	12.6117i	0.0297198	−	0.0514762i
$246$	−312.369	+	209.192i	−1.26979	+	0.850375i
$247$	−0.205119	−	74.2293i	−0.000830440	−	0.300524i
$248$	228.350	+	131.838i	0.920768	+	0.531606i
$249$	22.0339	+	330.859i	0.0884894	+	1.32875i
$250$	68.6788	−	118.955i	0.274715	−	0.475821i
$251$	42.8006	+	24.7109i	0.170520	+	0.0984499i	0.582831	−	0.812593i	$-0.301945\pi$
$251$	42.8006	+	24.7109i	0.170520	+	0.0984499i	−0.412311	+	0.911043i	$0.635278\pi$
$252$	−113.980	−	46.9326i	−0.452303	−	0.186240i
$253$	176.570	+	101.943i	0.697904	+	0.402935i
$254$	103.657			0.408097
$255$	−316.617	+	21.0854i	−1.24164	+	0.0826880i
$256$	−148.331	−	256.917i	−0.579418	−	1.00358i
$257$			242.011i			0.941677i	0.882219	+	0.470838i	$0.156049\pi$
$257$			242.011i			0.941677i	−0.882219	+	0.470838i	$0.843951\pi$
$258$	−14.6082	+	9.78306i	−0.0566210	+	0.0379188i
$259$	193.635	+	335.386i	0.747626	+	1.29493i
$260$	−80.1864	−	138.005i	−0.308409	−	0.530788i
$261$	−5.82300	−	43.5250i	−0.0223103	−	0.166762i
$262$	99.6987	−	57.5611i	0.380529	−	0.219699i
$263$	−189.816	−	109.591i	−0.721736	−	0.416694i	0.0936555	−	0.995605i	$-0.470145\pi$
$263$	−189.816	−	109.591i	−0.721736	−	0.416694i	−0.815391	+	0.578910i	$0.803478\pi$
$264$	179.963	−	120.520i	0.681677	−	0.456516i
$265$	450.121	+	259.878i	1.69857	+	0.980671i
$266$	49.7081	+	86.0969i	0.186873	+	0.323673i
$267$	4.86034	+	72.9825i	0.0182035	+	0.273343i
$268$	−56.0683	+	32.3710i	−0.209210	+	0.120787i
$269$	−14.9001	−	8.60259i	−0.0553908	−	0.0319799i	0.472049	−	0.881572i	$-0.343515\pi$
$269$	−14.9001	−	8.60259i	−0.0553908	−	0.0319799i	−0.527440	+	0.849592i	$0.676848\pi$
$270$	−315.959	+	278.850i	−1.17022	+	1.03278i
$271$	−239.798	+	138.447i	−0.884862	+	0.510875i	−0.872259	−	0.489045i	$-0.837345\pi$
$271$	−239.798	+	138.447i	−0.884862	+	0.510875i	−0.0126038	+	0.999921i	$0.504012\pi$
$272$	−285.315	+	164.727i	−1.04895	+	0.605612i
$273$	278.579	−	19.3256i	1.02044	−	0.0707898i
$274$	13.1974	−	22.8586i	0.0481657	−	0.0834255i
$275$	−230.440			−0.837965
$276$	−82.0648	+	5.46519i	−0.297336	+	0.0198014i
$277$	269.158			0.971688			0.485844	−	0.874045i	$-0.338512\pi$
$277$	269.158			0.971688			0.485844	+	0.874045i	$0.338512\pi$
$278$	−394.579			−1.41935
$279$	−62.0025	−	463.448i	−0.222231	−	1.66110i
$280$	−202.006	−	116.628i	−0.721448	−	0.416528i
$281$	73.8243	+	127.867i	0.262720	+	0.455044i	0.966964	−	0.254914i	$-0.0820472\pi$
$281$	73.8243	+	127.867i	0.262720	+	0.455044i	−0.704244	+	0.709958i	$0.748714\pi$
$282$	9.29354	+	4.57096i	0.0329558	+	0.0162091i
$283$	−56.2713			−0.198839			−0.0994193	−	0.995046i	$-0.531699\pi$
$283$	−56.2713			−0.198839			−0.0994193	+	0.995046i	$0.531699\pi$
$284$	228.252			0.803703
$285$	109.708	−	7.30614i	0.384942	−	0.0256356i
$286$	223.761	−	390.050i	0.782380	−	1.36381i
$287$			369.007i			1.28574i
$288$	−97.0202	+	235.623i	−0.336876	+	0.818135i
$289$	−8.72255	−	15.1079i	−0.0301818	−	0.0522765i
$290$			76.1536i			0.262599i
$291$	−59.8270	+	121.638i	−0.205591	+	0.418001i
$292$	86.5800	−	49.9870i	0.296507	−	0.171188i
$293$	−134.704	−	233.314i	−0.459740	−	0.796292i	0.539207	−	0.842173i	$-0.318724\pi$
$293$	−134.704	−	233.314i	−0.459740	−	0.796292i	−0.998947	+	0.0458808i	$0.985391\pi$
$294$	−13.7517	+	9.20945i	−0.0467745	+	0.0313247i
$295$	116.799			0.395927
$296$	237.727	−	137.252i	0.803132	−	0.463688i
$297$	−364.084	−	122.315i	−1.22587	−	0.411834i
$298$	−351.241			−1.17866
$299$	161.104	−	93.6079i	0.538809	−	0.313070i
$300$	77.2383	−	51.7262i	0.257461	−	0.172421i
$301$			17.2570i			0.0573321i
$302$			94.0497i			0.311423i
$303$	265.260	+	396.090i	0.875444	+	1.30723i
$304$	98.8620	−	57.0780i	0.325204	−	0.187757i
$305$	−364.524	+	631.374i	−1.19516	+	2.07008i
$306$	333.472	+	137.310i	1.08978	+	0.448727i
$307$		−	268.115i		−	0.873340i	−0.899622	−	0.436670i	$-0.856158\pi$
$307$		−	268.115i		−	0.873340i	0.899622	−	0.436670i	$-0.143842\pi$
$308$			194.830i			0.632564i
$309$	257.363	−	172.355i	0.832890	−	0.557783i
$310$			810.873i			2.61572i
$311$	180.662	+	104.305i	0.580908	+	0.335387i	0.761494	−	0.648172i	$-0.224466\pi$
$311$	180.662	+	104.305i	0.580908	+	0.335387i	−0.180586	+	0.983559i	$0.557799\pi$
$312$	−13.6983	−	197.462i	−0.0439048	−	0.632890i
$313$	−90.2731	−	156.358i	−0.288412	−	0.499545i	0.685019	−	0.728526i	$-0.259794\pi$
$313$	−90.2731	−	156.358i	−0.288412	−	0.499545i	−0.973431	+	0.228981i	$0.926461\pi$
$314$	−200.388	−	347.083i	−0.638179	−	1.10536i
$315$	54.8493	+	409.980i	0.174125	+	1.30152i
$316$	20.4342	−	35.3931i	0.0646652	−	0.112003i
$317$	77.4399	+	134.130i	0.244290	+	0.423123i	0.961932	−	0.273290i	$-0.0881118\pi$
$317$	77.4399	+	134.130i	0.244290	+	0.423123i	−0.717642	+	0.696412i	$0.754778\pi$
$318$	−328.693	−	490.810i	−1.03363	−	1.54343i
$319$	−60.1087	+	34.7038i	−0.188429	+	0.108789i
$320$	−35.6984	+	61.8315i	−0.111558	+	0.193223i
$321$	−377.631	+	25.1487i	−1.17642	+	0.0783449i
$322$	−124.773	+	216.113i	−0.387493	+	0.671158i
$323$	−47.0471	−	81.4879i	−0.145657	−	0.252285i
$324$	149.488	−	40.7276i	0.461383	−	0.125702i
$325$	−104.792	+	182.669i	−0.322437	+	0.562058i
$326$	−199.064	+	114.929i	−0.610624	+	0.352544i
$327$	−110.043	+	223.735i	−0.336522	+	0.684205i
$328$	261.559			0.797435
$329$	8.80370	−	5.08282i	0.0267590	−	0.0154493i
$330$	597.692	+	293.971i	1.81119	+	0.890821i
$331$		−	255.948i		−	0.773257i	−0.922236	−	0.386629i	$-0.873640\pi$
$331$		−	255.948i		−	0.773257i	0.922236	−	0.386629i	$-0.126360\pi$
$332$	−105.712	+	183.098i	−0.318408	+	0.551499i
$333$	−450.113	−	185.338i	−1.35169	−	0.556572i
$334$	−288.039	+	498.898i	−0.862393	+	1.49371i
$335$	188.145	+	108.626i	0.561627	+	0.324256i
$336$	238.964	+	356.824i	0.711202	+	1.06198i
$337$	−243.708	+	422.115i	−0.723170	+	1.25257i	0.236553	+	0.971619i	$0.423982\pi$
$337$	−243.708	+	422.115i	−0.723170	+	1.25257i	−0.959723	+	0.280949i	$0.909351\pi$
$338$	−207.436	−	354.748i	−0.613716	−	1.04955i
$339$	6.16997	−	0.410895i	0.0182005	−	0.00121208i
$340$	−175.216	−	101.161i	−0.515343	−	0.297533i
$341$	−640.030	+	369.521i	−1.87692	+	1.08364i
$342$	−115.548	−	47.5783i	−0.337861	−	0.139118i
$343$		−	334.606i		−	0.975527i
$344$	12.2320			0.0355582
$345$	153.572	+	229.317i	0.445137	+	0.664686i
$346$	−417.839	−	241.240i	−1.20763	−	0.697224i
$347$	200.945	−	116.016i	0.579092	−	0.334339i	−0.181680	−	0.983358i	$-0.558154\pi$
$347$	200.945	−	116.016i	0.579092	−	0.334339i	0.760772	+	0.649019i	$0.224820\pi$
$348$	12.3572	−	25.1243i	0.0355093	−	0.0721963i
$349$	−127.011	−	73.3300i	−0.363929	−	0.210115i	0.306874	−	0.951750i	$-0.400717\pi$
$349$	−127.011	−	73.3300i	−0.363929	−	0.210115i	−0.670803	+	0.741636i	$0.734050\pi$
$350$		−	282.048i		−	0.805851i
$351$	−262.524	+	232.985i	−0.747932	+	0.663775i
$352$	402.757			1.14420
$353$	299.125	−	518.100i	0.847381	−	1.46771i	−0.0361569	−	0.999346i	$-0.511512\pi$
$353$	299.125	−	518.100i	0.847381	−	1.46771i	0.883538	−	0.468360i	$-0.155155\pi$
$354$	−119.115	−	58.5857i	−0.336482	−	0.165496i
$355$	−382.966	−	663.316i	−1.07878	−	1.86850i
$356$	−23.3184	+	40.3886i	−0.0655011	+	0.113451i
$357$	294.116	−	196.968i	0.823854	−	0.551731i
$358$			321.898i			0.899155i
$359$	542.212			1.51034			0.755169	−	0.655530i	$-0.227555\pi$
$359$	542.212			1.51034			0.755169	+	0.655530i	$0.227555\pi$
$360$	290.601	−	38.8781i	0.807224	−	0.107995i
$361$	−164.198	−	284.399i	−0.454842	−	0.787810i
$362$	31.3231	−	54.2532i	0.0865279	−	0.149871i
$363$	16.2182	+	243.531i	0.0446782	+	0.670884i
$364$	154.440	+	88.5981i	0.424287	+	0.243401i
$365$	−290.532	−	167.739i	−0.795977	−	0.459558i
$366$	688.446	−	461.049i	1.88100	−	1.25970i
$367$	−131.013	+	226.920i	−0.356983	+	0.618312i	−0.987455	−	0.157900i	$-0.949528\pi$
$367$	−131.013	+	226.920i	−0.356983	+	0.618312i	0.630473	+	0.776211i	$0.282861\pi$
$368$	248.155	+	143.272i	0.674333	+	0.389327i
$369$	−283.127	−	367.382i	−0.767283	−	0.995615i
$370$	731.072	+	422.085i	1.97587	+	1.14077i
$371$	−579.802			−1.56281
$372$	131.578	−	267.520i	0.353705	−	0.719141i
$373$	−301.271	−	521.816i	−0.807696	−	1.39897i	−0.914456	−	0.404685i	$-0.867381\pi$
$373$	−301.271	−	521.816i	−0.807696	−	1.39897i	0.106760	−	0.994285i	$-0.465952\pi$
$374$		−	570.012i		−	1.52410i
$375$	152.066	+	74.7927i	0.405510	+	0.199447i
$376$	−3.60279	−	6.24021i	−0.00958188	−	0.0165963i
$377$	0.175275	+	63.4293i	0.000464920	+	0.168247i
$378$	149.707	−	445.621i	0.396051	−	1.17889i
$379$	119.275	−	68.8634i	0.314710	−	0.181698i	−0.334322	−	0.942459i	$-0.608507\pi$
$379$	119.275	−	68.8634i	0.314710	−	0.181698i	0.649032	+	0.760761i	$0.275174\pi$
$380$	60.7128	+	35.0525i	0.159770	+	0.0922435i
$381$	8.49784	+	127.603i	0.0223041	+	0.334916i
$382$	8.85006	+	5.10959i	0.0231677	+	0.0133759i
$383$	−262.183	−	454.114i	−0.684551	−	1.18568i	−0.973578	−	0.228356i	$-0.926665\pi$
$383$	−262.183	−	454.114i	−0.684551	−	1.18568i	0.289027	−	0.957321i	$-0.406668\pi$
$384$	349.718	−	234.205i	0.910725	−	0.609908i
$385$	566.189	−	326.890i	1.47062	−	0.849064i
$386$	−619.650	−	357.755i	−1.60531	−	0.926826i
$387$	−13.2407	−	17.1809i	−0.0342137	−	0.0443952i
$388$	−74.8505	+	43.2150i	−0.192914	+	0.111379i
$389$	108.679	−	62.7461i	0.279381	−	0.161301i	−0.353762	−	0.935336i	$-0.615098\pi$
$389$	108.679	−	62.7461i	0.279381	−	0.161301i	0.633143	+	0.774035i	$0.281764\pi$
$390$	504.827	−	340.105i	1.29443	−	0.872064i
$391$	118.093	−	204.544i	0.302029	−	0.523130i
$392$	11.5148			0.0293745
$393$	79.0320	+	118.012i	0.201099	+	0.300284i
$394$	386.385			0.980673
$395$	−137.140			−0.347189
$396$	−149.487	−	193.972i	−0.377491	−	0.489827i
$397$	662.206	+	382.325i	1.66802	+	0.963035i	0.968701	+	0.248230i	$0.0798487\pi$
$397$	662.206	+	382.325i	1.66802	+	0.963035i	0.699324	+	0.714805i	$0.253485\pi$
$398$	294.308	+	509.757i	0.739469	+	1.28080i
$399$	−101.912	+	68.2497i	−0.255418	+	0.171052i
$400$	−323.866			−0.809664
$401$	129.690			0.323417			0.161709	−	0.986839i	$-0.448300\pi$
$401$	129.690			0.323417			0.161709	+	0.986839i	$0.448300\pi$
$402$	−137.390	−	205.152i	−0.341765	−	0.510329i
$403$	1.86630	+	675.387i	0.00463103	+	1.67590i
$404$			303.949i			0.752348i
$405$	−369.172	−	366.090i	−0.911535	−	0.903925i
$406$	−42.4758	−	73.5702i	−0.104620	−	0.181207i
$407$			769.390i			1.89039i
$408$	−139.614	−	208.474i	−0.342192	−	0.510966i
$409$	250.275	−	144.496i	0.611920	−	0.353292i	−0.161797	−	0.986824i	$-0.551729\pi$
$409$	250.275	−	144.496i	0.611920	−	0.353292i	0.773716	+	0.633532i	$0.218396\pi$
$410$	402.180	+	696.597i	0.980928	+	1.69902i
$411$	29.2212	+	14.3723i	0.0710979	+	0.0349690i
$412$	197.493			0.479353
$413$	−112.836	+	65.1461i	−0.273212	+	0.157739i
$414$	−41.5932	−	310.895i	−0.100467	−	0.750954i
$415$	709.460			1.70954
$416$	183.152	−	319.263i	0.440270	−	0.767459i
$417$	−32.3478	−	485.733i	−0.0775728	−	1.16483i
$418$			197.510i			0.472512i
$419$		−	575.942i		−	1.37456i	−0.726391	−	0.687282i	$-0.758804\pi$
$419$		−	575.942i		−	1.37456i	0.726391	−	0.687282i	$-0.241196\pi$
$420$	−116.398	+	236.656i	−0.277138	+	0.563468i
$421$	−305.681	+	176.485i	−0.726083	+	0.419204i	−0.816987	−	0.576655i	$-0.804358\pi$
$421$	−305.681	+	176.485i	−0.726083	+	0.419204i	0.0909046	+	0.995860i	$0.471024\pi$
$422$	−90.8326	+	157.327i	−0.215243	+	0.372812i
$423$	−4.86504	+	11.8152i	−0.0115013	+	0.0279320i
$424$			410.974i			0.969277i
$425$			266.949i			0.628116i
$426$	57.8428	+	868.562i	0.135781	+	2.03888i
$427$		−	813.274i		−	1.90462i
$428$	−208.982	−	120.656i	−0.488275	−	0.281906i
$429$	498.502	+	243.476i	1.16201	+	0.567544i
$430$	18.8083	+	32.5769i	0.0437403	+	0.0757603i
$431$	−72.1138	−	124.905i	−0.167317	−	0.289802i	0.770158	−	0.637853i	$-0.220177\pi$
$431$	−72.1138	−	124.905i	−0.167317	−	0.289802i	−0.937476	+	0.348051i	$0.886844\pi$
$432$	−511.691	−	171.904i	−1.18447	−	0.397925i
$433$	−137.768	+	238.621i	−0.318171	+	0.551088i	−0.980106	−	0.198473i	$-0.936402\pi$
$433$	−137.768	+	238.621i	−0.318171	+	0.551088i	0.661936	+	0.749561i	$0.269735\pi$
$434$	−452.276	−	783.366i	−1.04211	−	1.80499i
$435$	−93.7463	+	6.24312i	−0.215509	+	0.0143520i
$436$	−137.676	+	79.4873i	−0.315771	+	0.182310i
$437$	−40.9195	+	70.8747i	−0.0936374	+	0.162185i
$438$	212.156	+	316.794i	0.484374	+	0.723274i
$439$	−355.754	+	616.183i	−0.810373	+	1.40361i	0.102231	+	0.994761i	$0.467402\pi$
$439$	−355.754	+	616.183i	−0.810373	+	1.40361i	−0.912604	+	0.408846i	$0.865931\pi$
$440$	−231.705	−	401.324i	−0.526602	−	0.912101i
$441$	−12.4644	−	16.1736i	−0.0282638	−	0.0366748i
$442$	−451.846	−	259.211i	−1.02228	−	0.586450i
$443$	−111.062	+	64.1214i	−0.250703	+	0.144744i	−0.620086	−	0.784534i	$-0.712902\pi$
$443$	−111.062	+	64.1214i	−0.250703	+	0.144744i	0.369383	+	0.929277i	$0.379569\pi$
$444$	−172.702	−	257.882i	−0.388969	−	0.580815i
$445$	156.496			0.351677
$446$	600.968	−	346.969i	1.34746	−	0.777957i
$447$	−28.7950	−	432.383i	−0.0644183	−	0.967300i
$448$		−	79.6452i		−	0.177780i
$449$	−2.55946	+	4.43311i	−0.00570035	+	0.00987329i	−0.868862	−	0.495055i	$-0.835148\pi$
$449$	−2.55946	+	4.43311i	−0.00570035	+	0.00987329i	0.863161	+	0.504929i	$0.168481\pi$
$450$	216.406	+	280.806i	0.480903	+	0.624012i
$451$	−366.554	+	634.889i	−0.812757	+	1.40774i
$452$	3.41447	+	1.97135i	0.00755414	+	0.00436139i
$453$	−115.777	+	7.71026i	−0.255578	+	0.0170204i
$454$	−445.688	+	771.955i	−0.981692	+	1.70034i
$455$	−1.65099	−	597.467i	−0.00362854	−	1.31311i
$456$	48.3765	+	72.2366i	0.106089	+	0.158414i
$457$	−81.8086	−	47.2322i	−0.179012	−	0.103353i	0.407816	−	0.913064i	$-0.366290\pi$
$457$	−81.8086	−	47.2322i	−0.179012	−	0.103353i	−0.586829	+	0.809711i	$0.699624\pi$
$458$	926.432	−	534.876i	2.02278	−	1.16785i
$459$	−141.693	+	421.766i	−0.308700	+	0.918880i
$460$			175.972i			0.382547i
$461$	−581.747			−1.26192			−0.630962	−	0.775813i	$-0.717340\pi$
$461$	−581.747			−1.26192			−0.630962	+	0.775813i	$0.717340\pi$
$462$	−741.383	+	49.3731i	−1.60472	+	0.106868i
$463$	536.960	+	310.014i	1.15974	+	0.669576i	0.951242	−	0.308446i	$-0.0998091\pi$
$463$	536.960	+	310.014i	1.15974	+	0.669576i	0.208498	+	0.978023i	$0.433142\pi$
$464$	−84.4780	+	48.7734i	−0.182065	+	0.105115i
$465$	−998.198	+	66.4760i	−2.14666	+	0.142959i
$466$	138.030	+	79.6918i	0.296202	+	0.171013i
$467$		−	499.899i		−	1.07045i	−0.844710	−	0.535224i	$-0.820227\pi$
$467$		−	499.899i		−	1.07045i	0.844710	−	0.535224i	$-0.179773\pi$
$468$	−221.739	+	30.2893i	−0.473800	+	0.0647207i
$469$	−242.350			−0.516738
$470$	11.0795	−	19.1903i	0.0235734	−	0.0408304i
$471$	410.836	−	275.135i	0.872264	−	0.584151i
$472$	46.1766	+	79.9803i	0.0978319	+	0.169450i
$473$	−17.1422	+	29.6911i	−0.0362414	+	0.0627720i
$474$	139.859	+	68.7888i	0.295061	+	0.145124i
$475$		−	92.4983i		−	0.194733i
$476$	225.697			0.474153
$477$	577.248	−	444.863i	1.21016	−	0.932628i
$478$	98.6182	+	170.812i	0.206314	+	0.357347i
$479$	−205.302	+	355.594i	−0.428606	+	0.742367i	−0.996750	−	0.0805622i	$-0.974328\pi$
$479$	−205.302	+	355.594i	−0.428606	+	0.742367i	0.568144	+	0.822929i	$0.307662\pi$
$480$	489.222	+	240.620i	1.01921	+	0.501293i
$481$	609.891	+	349.877i	1.26796	+	0.727395i
$482$	483.372	+	279.075i	1.00285	+	0.578994i
$483$	−276.267	−	135.880i	−0.571982	−	0.281326i
$484$	−77.8097	+	134.770i	−0.160764	+	0.278451i
$485$	251.172	+	145.014i	0.517879	+	0.298998i
$486$	192.863	+	558.524i	0.396837	+	1.14923i
$487$	244.715	+	141.286i	0.502495	+	0.290116i	0.729743	−	0.683721i	$-0.239640\pi$
$487$	244.715	+	141.286i	0.502495	+	0.290116i	−0.227248	+	0.973837i	$0.572973\pi$
$488$	−576.462			−1.18127
$489$	−157.799	−	235.628i	−0.322698	−	0.481858i
$490$	17.7055	+	30.6669i	0.0361337	+	0.0625855i
$491$			42.1387i			0.0858222i	0.999079	+	0.0429111i	$0.0136632\pi$
$491$			42.1387i			0.0858222i	−0.999079	+	0.0429111i	$0.986337\pi$
$492$	−19.6511	−	295.079i	−0.0399412	−	0.599755i
$493$	40.2019	+	69.6318i	0.0815455	+	0.141241i
$494$	156.565	+	89.8170i	0.316934	+	0.181816i
$495$	−312.884	+	759.868i	−0.632088	+	1.53509i
$496$	−899.510	+	519.333i	−1.81353	+	1.04704i
$497$	739.948	+	427.209i	1.48883	+	0.859576i
$498$	−723.528	−	355.862i	−1.45287	−	0.714583i
$499$	−284.623	−	164.327i	−0.570386	−	0.329312i	0.186918	−	0.982376i	$-0.440150\pi$
$499$	−284.623	−	164.327i	−0.570386	−	0.329312i	−0.757303	+	0.653063i	$0.773484\pi$
$500$	54.0252	+	93.5743i	0.108050	+	0.187149i
$501$	−637.766	−	313.681i	−1.27299	−	0.626109i
$502$	−104.075	+	60.0877i	−0.207321	+	0.119697i
$503$	81.9945	+	47.3395i	0.163011	+	0.0941144i	0.579286	−	0.815124i	$-0.303331\pi$
$503$	81.9945	+	47.3395i	0.163011	+	0.0941144i	−0.416275	+	0.909239i	$0.636665\pi$
$504$	−259.058	+	199.646i	−0.514003	+	0.396123i
$505$	883.297	−	509.972i	1.74910	−	1.00985i
$506$	−429.352	+	247.886i	−0.848521	+	0.489894i
$507$	419.694	−	284.440i	0.827799	−	0.561025i
$508$	−40.7700	+	70.6157i	−0.0802558	+	0.139007i
$509$	−810.940			−1.59320			−0.796601	−	0.604506i	$-0.793371\pi$
$509$	−810.940			−1.59320			−0.796601	+	0.604506i	$0.793371\pi$
$510$	340.545	−	692.384i	0.667735	−	1.35762i
$511$	374.235			0.732357
$512$	160.174			0.312839
$513$	49.0969	−	146.143i	0.0957054	−	0.284878i
$514$	−509.639	−	294.240i	−0.991515	−	0.572451i
$515$	−331.359	−	573.930i	−0.643415	−	1.11443i
$516$	−0.919000	−	13.7996i	−0.00178101	−	0.0267435i
$517$	20.1961			0.0390640
$518$	−941.696			−1.81795
$519$	262.715	−	534.144i	0.506195	−	1.02918i
$520$	−423.495	+	1.17025i	−0.814413	+	0.00225048i
$521$		−	49.2103i		−	0.0944536i	−0.998884	−	0.0472268i	$-0.984962\pi$
$521$		−	49.2103i		−	0.0944536i	0.998884	−	0.0472268i	$-0.0150384\pi$
$522$	98.7367	+	40.6558i	0.189151	+	0.0778847i
$523$	−470.200	−	814.410i	−0.899043	−	1.55719i	−0.828719	−	0.559664i	$-0.810930\pi$
$523$	−470.200	−	814.410i	−0.899043	−	1.55719i	−0.0703240	−	0.997524i	$-0.522403\pi$
$524$			90.5591i			0.172823i
$525$	347.206	−	23.1225i	0.661344	−	0.0440428i
$526$	461.563	−	266.483i	0.877495	−	0.506622i
$527$	428.065	+	741.430i	0.812267	+	1.40689i
$528$	56.6933	+	851.303i	0.107374	+	1.61232i
$529$	323.575			0.611672
$530$	−1094.53	+	631.925i	−2.06514	+	1.19231i
$531$	62.3548	−	151.435i	0.117429	−	0.285188i
$532$	−78.2042			−0.147000
$533$	336.584	+	579.279i	0.631490	+	1.08683i
$534$	−159.599	−	78.4979i	−0.298875	−	0.147000i
$535$			809.754i			1.51356i
$536$			171.782i			0.320489i
$537$	−396.261	+	26.3894i	−0.737916	+	0.0491422i
$538$	36.2315	−	20.9183i	0.0673448	−	0.0388816i
$539$	−16.1371	+	27.9503i	−0.0299390	+	0.0518558i
$540$	−65.6936	−	324.922i	−0.121655	−	0.601708i
$541$		−	706.936i		−	1.30672i	−0.757047	−	0.653361i	$-0.773358\pi$
$541$		−	706.936i		−	1.30672i	0.757047	−	0.653361i	$-0.226642\pi$
$542$		−	673.304i		−	1.24226i
$543$	69.3545	+	34.1115i	0.127725	+	0.0628205i
$544$		−	466.566i		−	0.857657i
$545$	461.992	+	266.731i	0.847691	+	0.489415i
$546$	−298.003	+	610.142i	−0.545794	+	1.11748i
$547$	99.7575	+	172.785i	0.182372	+	0.315878i	0.942688	−	0.333676i	$-0.108289\pi$
$547$	99.7575	+	172.785i	0.182372	+	0.315878i	−0.760316	+	0.649554i	$0.774956\pi$
$548$	10.3815	+	17.9814i	0.0189444	+	0.0328127i
$549$	623.998	+	809.691i	1.13661	+	1.47485i
$550$	280.172	−	485.273i	0.509404	−	0.882314i
$551$	−13.9300	−	24.1275i	−0.0252814	−	0.0437886i
$552$	−96.3142	+	195.823i	−0.174482	+	0.354752i
$553$	132.488	−	76.4917i	0.239580	−	0.138321i
$554$	−327.245	+	566.805i	−0.590695	+	1.02311i
$555$	−459.659	+	934.564i	−0.828215	+	1.68390i
$556$	155.195	−	268.805i	0.279127	−	0.483462i
$557$	524.367	+	908.230i	0.941413	+	1.63057i	0.762779	+	0.646659i	$0.223834\pi$
$557$	524.367	+	908.230i	0.941413	+	1.63057i	0.178634	+	0.983916i	$0.442832\pi$
$558$	1051.34	+	432.898i	1.88411	+	0.775803i
$559$	15.7407	+	27.0905i	0.0281586	+	0.0484624i
$560$	795.734	−	459.417i	1.42095	−	0.820388i
$561$	701.694	−	46.7300i	1.25079	−	0.0832977i
$562$	−359.026			−0.638836
$563$	950.599	−	548.829i	1.68845	−	0.974829i	0.732749	−	0.680499i	$-0.238237\pi$
$563$	950.599	−	548.829i	1.68845	−	0.974829i	0.955704	−	0.294329i	$-0.0950962\pi$
$564$	−6.76926	+	4.53334i	−0.0120022	+	0.00803784i
$565$		−	13.2303i		−	0.0234164i
$566$	68.4154	−	118.499i	0.120875	−	0.209362i
$567$	560.840	+	147.760i	0.989136	+	0.260599i
$568$	302.813	−	524.488i	0.533122	−	0.923394i
$569$	62.6306	+	36.1598i	0.110071	+	0.0635497i	0.554025	−	0.832500i	$-0.313091\pi$
$569$	62.6306	+	36.1598i	0.110071	+	0.0635497i	−0.443954	+	0.896050i	$0.646425\pi$
$570$	−117.999	+	239.912i	−0.207016	+	0.420899i
$571$	217.151	−	376.116i	0.380299	−	0.658697i	−0.610806	−	0.791780i	$-0.709154\pi$
$571$	217.151	−	376.116i	0.380299	−	0.658697i	0.991105	+	0.133083i	$0.0424878\pi$
$572$	177.711	+	305.849i	0.310683	+	0.534702i
$573$	−5.56445	+	11.3135i	−0.00971108	+	0.0197443i
$574$	−777.074	−	448.644i	−1.35379	−	0.781610i
$575$	201.075	−	116.091i	0.349695	−	0.201897i
$576$	61.1092	+	79.2944i	0.106092	+	0.137664i
$577$			704.900i			1.22166i	0.791760	+	0.610832i	$0.209165\pi$
$577$			704.900i			1.22166i	−0.791760	+	0.610832i	$0.790835\pi$
$578$	42.4199			0.0733909
$579$	389.603	−	792.128i	0.672889	−	1.36810i
$580$	−51.8793	−	29.9525i	−0.0894471	−	0.0516423i
$581$	−685.393	+	395.712i	−1.17968	+	0.681088i
$582$	−183.414	−	273.876i	−0.315144	−	0.470577i
$583$	−997.569	−	575.947i	−1.71110	−	0.987902i
$584$		−	265.264i		−	0.454219i
$585$	460.061	+	593.568i	0.786428	+	1.01465i
$586$	655.098			1.11791
$587$	177.011	−	306.592i	0.301552	−	0.522303i	−0.674936	−	0.737876i	$-0.735829\pi$
$587$	177.011	−	306.592i	0.301552	−	0.522303i	0.976488	+	0.215573i	$0.0691620\pi$
$588$	−0.865117	−	12.9905i	−0.00147129	−	0.0220927i
$589$	−148.325	−	256.907i	−0.251825	−	0.436174i
$590$	−142.005	+	245.960i	−0.240687	+	0.416882i
$591$	31.6761	+	475.646i	0.0535975	+	0.804816i
$592$			1081.32i			1.82655i
$593$	−533.102			−0.898992			−0.449496	−	0.893282i	$-0.648396\pi$
$593$	−533.102			−0.898992			−0.449496	+	0.893282i	$0.648396\pi$
$594$	700.234	−	617.994i	1.17885	−	1.04039i
$595$	−378.679	−	655.891i	−0.636435	−	1.10234i
$596$	138.149	−	239.281i	0.231794	−	0.401479i
$597$	−603.392	+	404.089i	−1.01071	+	0.676866i
$598$	1.25197	+	453.070i	0.00209360	+	0.757642i
$599$	−834.351	−	481.713i	−1.39291	−	0.804195i	−0.399270	−	0.916833i	$-0.630736\pi$
$599$	−834.351	−	481.713i	−1.39291	−	0.804195i	−0.993636	+	0.112638i	$0.964070\pi$
$600$	−16.3896	−	246.105i	−0.0273160	−	0.410175i
$601$	414.212	−	717.435i	0.689204	−	1.19374i	−0.282892	−	0.959152i	$-0.591294\pi$
$601$	414.212	−	717.435i	0.689204	−	1.19374i	0.972096	−	0.234584i	$-0.0753729\pi$
$602$	−36.3405	−	20.9812i	−0.0603663	−	0.0348525i
$603$	241.283	−	185.947i	0.400137	−	0.308371i
$604$	−64.0710	−	36.9914i	−0.106078	−	0.0612440i
$605$	522.203			0.863146
$606$	−1156.61	+	77.0257i	−1.90860	+	0.127105i
$607$	33.5138	+	58.0477i	0.0552122	+	0.0956304i	0.892311	−	0.451422i	$-0.149083\pi$
$607$	33.5138	+	58.0477i	0.0552122	+	0.0956304i	−0.837098	+	0.547053i	$0.815750\pi$
$608$			161.666i			0.265897i
$609$	87.0839	−	58.3197i	0.142995	−	0.0957631i
$610$	−886.385	−	1535.26i	−1.45309	−	2.51683i
$611$	9.18409	−	16.0093i	0.0150312	−	0.0262018i
$612$	−224.702	+	173.170i	−0.367161	+	0.282957i
$613$	242.597	−	140.063i	0.395753	−	0.228488i	−0.288897	−	0.957360i	$-0.593288\pi$
$613$	242.597	−	140.063i	0.395753	−	0.228488i	0.684650	+	0.728872i	$0.259955\pi$
$614$	564.611	+	325.978i	0.919561	+	0.530909i
$615$	−824.551	+	552.198i	−1.34073	+	0.897883i
$616$	447.689	+	258.473i	0.726768	+	0.419600i
$617$	136.829	+	236.996i	0.221766	+	0.384110i	0.955344	−	0.295495i	$-0.0954846\pi$
$617$	136.829	+	236.996i	0.221766	+	0.384110i	−0.733578	+	0.679605i	$0.762151\pi$
$618$	50.0481	+	751.519i	0.0809840	+	1.21605i
$619$	545.006	−	314.660i	0.880463	−	0.508335i	0.00965176	−	0.999953i	$-0.496928\pi$
$619$	545.006	−	314.660i	0.880463	−	0.508335i	0.870811	+	0.491618i	$0.163594\pi$
$620$	−552.404	−	318.931i	−0.890974	−	0.514404i
$621$	379.307	−	76.6893i	0.610800	−	0.123493i
$622$	−439.303	+	253.632i	−0.706275	+	0.407768i
$623$	−151.187	+	87.2881i	−0.242677	+	0.140109i
$624$	700.604	+	342.186i	1.12276	+	0.548376i
$625$	383.782	−	664.730i	0.614051	−	1.06357i
$626$	439.021			0.701311
$627$	−243.138	+	16.1920i	−0.387780	+	0.0258246i
$628$	315.265			0.502014
$629$	891.284			1.41699
$630$	−930.042	−	382.954i	−1.47626	−	0.607864i
$631$	−573.158	−	330.913i	−0.908333	−	0.524426i	−0.0284384	−	0.999596i	$-0.509053\pi$
$631$	−573.158	−	330.913i	−0.908333	−	0.524426i	−0.879894	+	0.475169i	$0.842387\pi$
$632$	−54.2186	−	93.9094i	−0.0857889	−	0.148591i
$633$	−201.118	−	98.9186i	−0.317722	−	0.156270i
$634$	−376.610			−0.594022
$635$	273.619			0.430896
$636$	463.643	−	30.8767i	0.728998	−	0.0485483i
$637$	14.8177	+	25.5021i	0.0232618	+	0.0400347i
$638$		−	168.773i		−	0.264535i
$639$	−1064.47	+	142.411i	−1.66584	+	0.222865i
$640$	−450.268	−	779.886i	−0.703543	−	1.21857i
$641$		−	407.959i		−	0.636441i	−0.948017	−	0.318220i	$-0.896915\pi$
$641$		−	407.959i		−	0.636441i	0.948017	−	0.318220i	$-0.103085\pi$
$642$	406.169	−	825.811i	0.632663	−	1.28631i
$643$	−773.235	+	446.427i	−1.20254	+	0.694288i	−0.961120	−	0.276132i	$-0.910947\pi$
$643$	−773.235	+	446.427i	−1.20254	+	0.694288i	−0.241423	+	0.970420i	$0.577614\pi$
$644$	−98.1507	−	170.002i	−0.152408	−	0.263978i
$645$	−38.5608	+	25.8240i	−0.0597842	+	0.0400372i
$646$	228.802			0.354182
$647$	341.098	−	196.933i	0.527199	−	0.304378i	−0.212676	−	0.977123i	$-0.568218\pi$
$647$	341.098	−	196.933i	0.527199	−	0.304378i	0.739875	+	0.672744i	$0.234885\pi$
$648$	104.735	−	397.533i	0.161627	−	0.613477i
$649$	−258.852			−0.398847
$650$	−257.266	−	442.767i	−0.395793	−	0.681180i
$651$	927.258	−	620.980i	1.42436	−	0.953887i
$652$		−	180.815i		−	0.277324i
$653$			1115.79i			1.70872i	0.519681	+	0.854361i	$0.326051\pi$
$653$			1115.79i			1.70872i	−0.519681	+	0.854361i	$0.673949\pi$
$654$	−337.361	−	503.753i	−0.515843	−	0.770265i
$655$	263.171	−	151.942i	0.401788	−	0.231972i
$656$	−515.162	+	892.286i	−0.785307	+	1.36019i
$657$	−372.586	+	287.138i	−0.567102	+	0.437044i
$658$			24.7190i			0.0375669i
$659$		−	201.860i		−	0.306313i	−0.988202	−	0.153157i	$-0.951056\pi$
$659$		−	201.860i		−	0.306313i	0.988202	−	0.153157i	$-0.0489439\pi$
$660$	−435.349	+	291.551i	−0.659620	+	0.441744i
$661$			192.489i			0.291209i	0.989343	+	0.145604i	$0.0465126\pi$
$661$			192.489i			0.291209i	−0.989343	+	0.145604i	$0.953487\pi$
$662$	538.988	+	311.185i	0.814182	+	0.470068i
$663$	282.050	−	577.480i	0.425415	−	0.871010i
$664$	280.487	+	485.818i	0.422420	+	0.731654i
$665$	131.213	+	227.267i	0.197312	+	0.341755i
$666$	937.548	−	722.532i	1.40773	−	1.08488i
$667$	34.9659	−	60.5628i	0.0524227	−	0.0907987i
$668$	−226.582	−	392.451i	−0.339194	−	0.587501i
$669$	476.392	+	711.356i	0.712096	+	1.06331i
$670$	−457.499	+	264.137i	−0.682834	+	0.394234i
$671$	807.866	−	1399.26i	1.20397	−	2.08534i
$672$	−606.835	+	40.4128i	−0.903029	+	0.0601381i
$673$	−238.997	+	413.955i	−0.355122	+	0.615089i	−0.987139	−	0.159865i	$-0.948894\pi$
$673$	−238.997	+	413.955i	−0.355122	+	0.615089i	0.632017	+	0.774955i	$0.282227\pi$
$674$	−592.607	−	1026.43i	−0.879239	−	1.52289i
$675$	−327.935	+	289.420i	−0.485830	+	0.428771i
$676$	323.258	−	1.78654i	0.478193	−	0.00264281i
$677$	36.4414	−	21.0394i	0.0538277	−	0.0310774i	−0.472845	−	0.881146i	$-0.656773\pi$
$677$	36.4414	−	21.0394i	0.0538277	−	0.0310774i	0.526672	+	0.850068i	$0.323439\pi$
$678$	−6.63625	+	13.4926i	−0.00978798	+	0.0199006i
$679$	−323.535			−0.476487
$680$	−464.906	+	268.414i	−0.683686	+	0.394726i
$681$	−986.826	−	485.364i	−1.44908	−	0.712722i
$682$		−	1797.08i		−	2.63501i
$683$	−262.088	+	453.949i	−0.383730	+	0.664640i	−0.991592	−	0.129403i	$-0.958694\pi$
$683$	−262.088	+	453.949i	−0.383730	+	0.664640i	0.607862	+	0.794043i	$0.292027\pi$
$684$	77.8597	−	60.0036i	0.113830	−	0.0877245i
$685$	34.8368	−	60.3390i	0.0508566	−	0.0880862i
$686$	704.629	+	406.818i	1.02716	+	0.593029i
$687$	734.390	+	1096.60i	1.06898	+	1.59622i
$688$	−24.0920	+	41.7285i	−0.0350174	+	0.0606519i
$689$	−910.191	+	528.858i	−1.32103	+	0.767573i
$690$	−669.622	+	44.5941i	−0.970466	+	0.0646291i
$691$	−295.209	−	170.439i	−0.427220	−	0.246656i	0.270941	−	0.962596i	$-0.412665\pi$
$691$	−295.209	−	170.439i	−0.427220	−	0.246656i	−0.698162	+	0.715940i	$0.745998\pi$
$692$	328.687	−	189.767i	0.474981	−	0.274230i
$693$	−121.558	−	908.606i	−0.175409	−	1.31112i
$694$			564.213i			0.812987i
$695$	−1041.56			−1.49864
$696$	−41.3380	−	61.7265i	−0.0593936	−	0.0886875i
$697$	735.475	+	424.627i	1.05520	+	0.609221i
$698$	308.844	−	178.311i	0.442469	−	0.255460i
$699$	−86.7861	+	176.451i	−0.124158	+	0.252433i
$700$	192.144	+	110.934i	0.274491	+	0.158478i
$701$		−	223.372i		−	0.318647i	−0.987226	−	0.159324i	$-0.949069\pi$
$701$		−	223.372i		−	0.318647i	0.987226	−	0.159324i	$-0.0509313\pi$
$702$	−171.452	−	836.102i	−0.244233	−	1.19103i
$703$	−308.831			−0.439305
$704$	79.1156	−	137.032i	0.112380	−	0.194648i
$705$	24.5318	+	12.0658i	0.0347969	+	0.0171146i
$706$	727.361	+	1259.83i	1.03026	+	1.78446i
$707$	−568.888	+	985.344i	−0.804651	+	1.39370i
$708$	86.7611	−	58.1035i	0.122544	−	0.0820671i
$709$			450.877i			0.635933i	0.948102	+	0.317967i	$0.103000\pi$
$709$			450.877i			0.635933i	−0.948102	+	0.317967i	$0.897000\pi$
$710$	1862.46			2.62318
$711$	−73.2143	+	177.808i	−0.102974	+	0.250082i
$712$	61.8713	+	107.164i	0.0868979	+	0.150511i
$713$	372.313	−	644.864i	0.522177	−	0.904438i
$714$	57.1953	+	858.840i	0.0801055	+	1.20286i
$715$	590.653	−	1029.60i	0.826088	−	1.44000i
$716$	−219.291	−	126.608i	−0.306273	−	0.176827i
$717$	−202.187	+	135.404i	−0.281990	+	0.188848i
$718$	−659.228	+	1141.82i	−0.918144	+	1.59027i
$719$	0.356771	+	0.205982i	0.000496205	+	0.000286484i	0.500248	−	0.865882i	$-0.333242\pi$
$719$	0.356771	+	0.205982i	0.000496205	+	0.000286484i	−0.499752	+	0.866169i	$0.666575\pi$
$720$	−439.733	+	1067.93i	−0.610740	+	1.48324i
$721$	640.236	+	369.640i	0.887983	+	0.512677i
$722$	798.537			1.10601
$723$	−303.918	+	617.917i	−0.420357	+	0.854657i
$724$	24.6398	+	42.6775i	0.0340329	+	0.0589468i
$725$			79.0402i			0.109021i
$726$	−532.558	−	261.935i	−0.733551	−	0.360792i
$727$	−154.985	−	268.443i	−0.213185	−	0.369247i	0.739525	−	0.673129i	$-0.235050\pi$
$727$	−154.985	−	268.443i	−0.213185	−	0.369247i	−0.952710	+	0.303882i	$0.901717\pi$
$728$	408.475	−	237.341i	0.561093	−	0.326018i
$729$	−671.741	+	283.205i	−0.921455	+	0.388485i
$730$	706.464	−	407.877i	0.967759	−	0.558736i
$731$	34.3951	+	19.8580i	0.0470522	+	0.0271656i
$732$	43.3100	+	650.340i	0.0591667	+	0.888442i
$733$	894.231	+	516.284i	1.21996	+	0.704344i	0.964909	−	0.262584i	$-0.0845745\pi$
$733$	894.231	+	516.284i	1.21996	+	0.704344i	0.255051	+	0.966928i	$0.417908\pi$
$734$	−318.574	−	551.786i	−0.434024	−	0.751751i
$735$	−36.2999	+	24.3099i	−0.0493876	+	0.0330747i
$736$	−351.432	+	202.899i	−0.477489	+	0.275679i
$737$	−416.972	−	240.739i	−0.565769	−	0.326647i
$738$	1117.88	−	149.556i	1.51474	−	0.202650i
$739$	−38.9096	+	22.4645i	−0.0526517	+	0.0303985i	−0.526095	−	0.850426i	$-0.676344\pi$
$739$	−38.9096	+	22.4645i	−0.0526517	+	0.0303985i	0.473443	+	0.880824i	$0.343011\pi$
$740$	−575.087	+	332.027i	−0.777145	+	0.448685i
$741$	−97.7309	+	200.097i	−0.131890	+	0.270037i
$742$	704.931	−	1220.98i	0.950042	−	1.64552i
$743$	946.018			1.27324			0.636621	−	0.771177i	$-0.280332\pi$
$743$	946.018			1.27324			0.636621	+	0.771177i	$0.280332\pi$
$744$	−440.161	−	657.256i	−0.591615	−	0.883408i
$745$	−927.158			−1.24451
$746$	1465.15			1.96401
$747$	378.757	−	919.848i	0.507037	−	1.23139i
$748$	388.319	+	224.196i	0.519142	+	0.299727i
$749$	−451.652	−	782.285i	−0.603007	−	1.04444i
$750$	−342.386	+	229.294i	−0.456515	+	0.305726i
$751$	−1183.78			−1.57627			−0.788136	−	0.615502i	$-0.788953\pi$
$751$	−1183.78			−1.57627			−0.788136	+	0.615502i	$0.788953\pi$
$752$	28.3840			0.0377446
$753$	−82.5011	−	123.192i	−0.109563	−	0.163602i
$754$	−133.786	−	76.7490i	−0.177434	−	0.101789i
$755$			248.260i			0.328821i
$756$	244.695	+	277.258i	0.323671	+	0.366744i
$757$	228.146	+	395.161i	0.301382	+	0.522010i	0.976449	−	0.215747i	$-0.0692186\pi$
$757$	228.146	+	395.161i	0.301382	+	0.522010i	−0.675067	+	0.737756i	$0.735885\pi$
$758$			334.900i			0.441821i
$759$	−340.351	−	508.217i	−0.448420	−	0.669587i
$760$	161.091	−	93.0058i	0.211961	−	0.122376i
$761$	−114.372	−	198.099i	−0.150292	−	0.260313i	0.781043	−	0.624478i	$-0.214688\pi$
$761$	−114.372	−	198.099i	−0.150292	−	0.260313i	−0.931335	+	0.364164i	$0.881355\pi$
$762$	−279.044	−	137.246i	−0.366200	−	0.180113i
$763$	−595.093			−0.779938
$764$	−6.96177	+	4.01938i	−0.00911226	+	0.00526097i
$765$	880.254	+	362.454i	1.15066	+	0.473796i
$766$	1275.06			1.66457
$767$	−117.712	+	205.190i	−0.153470	+	0.267523i
$768$	59.1384	+	888.018i	0.0770032	+	1.15627i
$769$			1268.37i			1.64937i	0.565592	+	0.824685i	$0.308648\pi$
$769$			1268.37i			1.64937i	−0.565592	+	0.824685i	$0.691352\pi$
$770$			1589.75i			2.06461i
$771$	320.434	−	651.495i	0.415608	−	0.845000i
$772$	487.438	−	281.422i	0.631396	−	0.364537i
$773$	198.313	−	343.488i	0.256550	−	0.444357i	−0.708765	−	0.705444i	$-0.750748\pi$
$773$	198.313	−	343.488i	0.256550	−	0.444357i	0.965315	+	0.261087i	$0.0840809\pi$
$774$	52.2787	−	6.99411i	0.0675435	−	0.00903632i
$775$			841.609i			1.08595i
$776$			229.327i			0.295524i
$777$	−77.2009	−	1159.24i	−0.0993576	−	1.49195i
$778$			305.150i			0.392224i
$779$	−254.843	−	147.134i	−0.327141	−	0.188875i
$780$	33.1377	+	477.681i	0.0424842	+	0.612411i
$781$	848.737	+	1470.06i	1.08673	+	1.88227i
$782$	287.159	+	497.374i	0.367211	+	0.636028i
$783$	−41.9535	+	124.879i	−0.0535804	+	0.159488i
$784$	−22.6794	+	39.2819i	−0.0289278	+	0.0501044i
$785$	−528.958	−	916.182i	−0.673832	−	1.16711i
$786$	−344.603	+	22.9492i	−0.438426	+	0.0291974i
$787$	286.703	−	165.528i	0.364298	−	0.210328i	−0.306666	−	0.951817i	$-0.599214\pi$
$787$	286.703	−	165.528i	0.364298	−	0.210328i	0.670965	+	0.741489i	$0.265880\pi$
$788$	−151.972	+	263.223i	−0.192858	+	0.334040i
$789$	365.884	+	546.344i	0.463732	+	0.692452i
$790$	166.736	−	288.796i	0.211059	−	0.365564i
$791$	7.37938	+	12.7815i	0.00932917	+	0.0161586i
$792$	−644.035	+	86.1624i	−0.813176	+	0.108791i
$793$	−741.815	−	1276.70i	−0.935454	−	1.60996i
$794$	−1610.24	+	929.671i	−2.02801	+	1.17087i
$795$	−867.640	−	1295.57i	−1.09137	−	1.62965i
$796$	−463.027			−0.581692
$797$	156.545	−	90.3810i	0.196417	−	0.113402i	−0.398566	−	0.917140i	$-0.630492\pi$
$797$	156.545	−	90.3810i	0.196417	−	0.113402i	0.594983	+	0.803738i	$0.297159\pi$
$798$	−19.8183	−	297.589i	−0.0248349	−	0.372919i
$799$		−	23.3957i		−	0.0292813i
$800$	229.326	−	397.205i	0.286658	−	0.496506i
$801$	83.5481	−	202.905i	0.104305	−	0.253314i
$802$	−157.679	+	273.108i	−0.196607	+	0.340534i
$803$	643.883	+	371.746i	0.801847	+	0.462946i
$804$	193.797	−	12.9061i	0.241041	−	0.0160524i
$805$	−329.359	+	570.466i	−0.409141	+	0.708653i
$806$	−1424.53	−	817.213i	−1.76741	−	1.01391i
$807$	28.7210	+	42.8867i	0.0355899	+	0.0531434i
$808$	698.428	+	403.238i	0.864391	+	0.499056i
$809$	341.944	−	197.422i	0.422675	−	0.244032i	−0.273546	−	0.961859i	$-0.588197\pi$
$809$	341.944	−	197.422i	0.422675	−	0.244032i	0.696221	+	0.717827i	$0.254863\pi$
$810$	1219.77	−	332.324i	1.50589	−	0.410276i
$811$		−	55.3650i		−	0.0682676i	−0.999417	−	0.0341338i	$-0.989133\pi$
$811$		−	55.3650i		−	0.0682676i	0.999417	−	0.0341338i	$-0.0108672\pi$
$812$	66.8259			0.0822978
$813$	828.848	−	55.1979i	1.01949	−	0.0678941i
$814$	−1620.22	−	935.434i	−1.99044	−	1.14918i
$815$	−525.461	+	303.375i	−0.644738	+	0.372240i
$816$	986.175	−	65.6753i	1.20855	−	0.0804844i
$817$	−11.9180	−	6.88084i	−0.0145875	−	0.00842208i
$818$			702.722i			0.859074i
$819$	−775.525	−	316.827i	−0.946917	−	0.386846i
$820$	−632.738			−0.771632
$821$	386.359	−	669.193i	0.470596	−	0.815095i	−0.528839	−	0.848722i	$-0.677372\pi$
$821$	386.359	−	669.193i	0.470596	−	0.815095i	0.999434	+	0.0336268i	$0.0107058\pi$
$822$	−65.7933	+	44.0615i	−0.0800406	+	0.0536028i
$823$	136.989	+	237.273i	0.166451	+	0.288302i	0.937170	−	0.348874i	$-0.113436\pi$
$823$	136.989	+	237.273i	0.166451	+	0.288302i	−0.770718	+	0.637176i	$0.780102\pi$
$824$	262.007	−	453.810i	0.317970	−	0.550740i
$825$	620.347	+	305.114i	0.751936	+	0.369835i
$826$		−	316.822i		−	0.383562i
$827$	−744.269			−0.899963			−0.449981	−	0.893038i	$-0.648569\pi$
$827$	−744.269			−0.899963			−0.449981	+	0.893038i	$0.648569\pi$
$828$	228.155	+	93.9453i	0.275550	+	0.113460i
$829$	421.820	+	730.613i	0.508829	+	0.881318i	0.999948	+	0.0102254i	$0.00325490\pi$
$829$	421.820	+	730.613i	0.508829	+	0.881318i	−0.491118	+	0.871093i	$0.663412\pi$
$830$	−862.571	+	1494.02i	−1.03924	+	1.80002i
$831$	−724.574	−	356.377i	−0.871931	−	0.428853i
$832$	−72.6471	−	125.029i	−0.0873163	−	0.150276i
$833$	32.3784	+	18.6937i	0.0388697	+	0.0224414i
$834$	1062.21	+	522.440i	1.27363	+	0.626427i
$835$	−760.327	+	1316.93i	−0.910571	+	1.57716i
$836$	−134.553	−	77.6842i	−0.160948	−	0.0929237i
$837$	−446.715	+	1329.70i	−0.533710	+	1.58865i
$838$	1212.85	+	700.238i	1.44731	+	0.835606i
$839$	957.235			1.14092			0.570462	−	0.821324i	$-0.306764\pi$
$839$	957.235			1.14092			0.570462	+	0.821324i	$0.306764\pi$
$840$	389.380	+	581.428i	0.463547	+	0.692176i
$841$	−408.597	−	707.710i	−0.485846	−	0.841510i
$842$		−	858.290i		−	1.01935i
$843$	−29.4332	−	441.967i	−0.0349148	−	0.524278i
$844$	−71.4521	−	123.759i	−0.0846589	−	0.146633i
$845$	−547.562	−	936.415i	−0.648002	−	1.10818i
$846$	−18.9661	−	24.6101i	−0.0224186	−	0.0290900i
$847$	−504.488	+	291.266i	−0.595618	+	0.343880i
$848$	−1402.00	−	809.447i	−1.65331	−	0.954536i
$849$	151.483	+	74.5058i	0.178425	+	0.0877571i
$850$	−562.155	−	324.560i	−0.661359	−	0.381836i
$851$	−387.601	−	671.344i	−0.455465	−	0.788888i
$852$	−614.455	−	302.216i	−0.721191	−	0.354713i
$853$	−98.7338	+	57.0040i	−0.115749	+	0.0668276i	−0.556757	−	0.830676i	$-0.687954\pi$
$853$	−98.7338	+	57.0040i	−0.115749	+	0.0668276i	0.441008	+	0.897503i	$0.354621\pi$
$854$	1712.63	+	988.789i	2.00542	+	1.15783i
$855$	−305.009	−	125.591i	−0.356736	−	0.146890i
$856$	−554.496	+	320.139i	−0.647776	+	0.373994i
$857$	−234.477	+	135.376i	−0.273603	+	0.157965i	−0.630524	−	0.776170i	$-0.717160\pi$
$857$	−234.477	+	135.376i	−0.273603	+	0.157965i	0.356921	+	0.934135i	$0.383827\pi$
$858$	−1118.81	+	753.748i	−1.30397	+	0.878494i
$859$	−206.165	+	357.089i	−0.240006	+	0.415703i	−0.960716	−	0.277534i	$-0.910483\pi$
$859$	−206.165	+	357.089i	−0.240006	+	0.415703i	0.720710	+	0.693237i	$0.243816\pi$
$860$	−29.5905			−0.0344076
$861$	488.583	−	993.371i	0.567460	−	1.15374i
$862$	350.707			0.406853
$863$	−213.008			−0.246823			−0.123412	−	0.992356i	$-0.539384\pi$
$863$	−213.008			−0.246823			−0.123412	+	0.992356i	$0.539384\pi$
$864$	573.155	−	505.840i	0.663374	−	0.585463i
$865$	−1102.96	−	636.792i	−1.27509	−	0.736176i
$866$	−335.000	−	580.237i	−0.386836	−	0.670019i
$867$	3.47762	+	52.2196i	0.00401109	+	0.0602303i
$868$	711.553			0.819761
$869$	303.932			0.349749
$870$	100.831	−	205.006i	0.115898	−	0.235639i
$871$	−380.448	+	221.056i	−0.436795	+	0.253796i
$872$			421.812i			0.483729i
$873$	322.109	−	248.238i	0.368968	−	0.284350i
$874$	−99.5010	−	172.341i	−0.113846	−	0.197186i
$875$			404.467i			0.462248i
$876$	−299.259	+	19.9295i	−0.341620	+	0.0227505i
$877$	803.725	−	464.031i	0.916448	−	0.529112i	0.0339480	−	0.999424i	$-0.489192\pi$
$877$	803.725	−	464.031i	0.916448	−	0.529112i	0.882500	+	0.470312i	$0.155859\pi$
$878$	−865.059	−	1498.33i	−0.985261	−	1.70652i
$879$	53.7054	+	806.436i	0.0610983	+	0.917447i
$880$	1825.45			2.07437
$881$	−217.258	+	125.434i	−0.246603	+	0.142377i	−0.618208	−	0.786015i	$-0.712141\pi$
$881$	−217.258	+	125.434i	−0.246603	+	0.142377i	0.371605	+	0.928391i	$0.378808\pi$
$882$	49.2134	−	6.58403i	0.0557975	−	0.00746489i
$883$	−15.6013			−0.0176685			−0.00883423	−	0.999961i	$-0.502812\pi$
$883$	−15.6013			−0.0176685			−0.00883423	+	0.999961i	$0.502812\pi$
$884$	354.305	−	205.866i	0.400798	−	0.232880i
$885$	−314.423	−	154.647i	−0.355280	−	0.174742i
$886$		−	311.838i		−	0.351962i
$887$			700.604i			0.789858i	0.918712	+	0.394929i	$0.129231\pi$
$887$			700.604i			0.789858i	−0.918712	+	0.394929i	$0.870769\pi$
$888$	−821.690	+	54.7213i	−0.925327	+	0.0616230i
$889$	−264.337	+	152.615i	−0.297342	+	0.171670i
$890$	−190.270	+	329.558i	−0.213787	+	0.370290i
$891$	818.167	+	811.336i	0.918257	+	0.910591i
$892$			545.876i			0.611968i
$893$			8.10666i			0.00907801i
$894$	945.543	+	465.059i	1.05765	+	0.520200i
$895$			849.702i			0.949388i
$896$	869.986	+	502.287i	0.970967	+	0.560588i
$897$	−557.634	+	38.6842i	−0.621665	+	0.0431262i
$898$	−6.22364	−	10.7797i	−0.00693055	−	0.0120041i
$899$	126.744	+	219.528i	0.140984	+	0.244191i
$900$	−276.414	+	36.9801i	−0.307127	+	0.0410890i
$901$	−667.194	+	1155.61i	−0.740504	+	1.28259i
$902$	−891.321	−	1543.81i	−0.988161	−	1.71154i
$903$	22.8490	−	46.4558i	0.0253034	−	0.0514461i
$904$	9.05971	−	5.23062i	0.0100218	−	0.00578609i
$905$	82.6825	−	143.210i	0.0913619	−	0.158244i
$906$	124.526	−	253.183i	0.137446	−	0.279451i
$907$	756.422	−	1310.16i	0.833983	−	1.44450i	−0.0608732	−	0.998146i	$-0.519389\pi$
$907$	756.422	−	1310.16i	0.833983	−	1.44450i	0.894856	−	0.446355i	$-0.147278\pi$
$908$	−350.594	−	607.246i	−0.386117	−	0.668774i
$909$	−189.640	−	1417.49i	−0.208624	−	1.55940i
$910$	1260.18	+	722.931i	1.38482	+	0.794430i
$911$	−667.209	+	385.213i	−0.732392	+	0.422846i	−0.819296	−	0.573370i	$-0.805636\pi$
$911$	−667.209	+	385.213i	−0.732392	+	0.422846i	0.0869049	+	0.996217i	$0.472302\pi$
$912$	−341.711	+	22.7566i	−0.374683	+	0.0249524i
$913$	−1572.32			−1.72215
$914$	198.928	−	114.851i	0.217645	−	0.125658i
$915$	1817.27	−	1217.02i	1.98609	−	1.33007i
$916$			841.504i			0.918673i
$917$	−169.496	+	293.575i	−0.184837	+	0.320147i
$918$	−715.903	−	811.173i	−0.779851	−	0.883630i
$919$	−91.8891	+	159.157i	−0.0999881	+	0.173184i	−0.911679	−	0.410902i	$-0.865214\pi$
$919$	−91.8891	+	159.157i	−0.0999881	+	0.173184i	0.811691	+	0.584087i	$0.198547\pi$
$920$	404.356	+	233.455i	0.439517	+	0.253755i
$921$	−354.997	+	721.769i	−0.385447	+	0.783679i
$922$	707.296	−	1225.07i	0.767132	−	1.32871i
$923$	1551.26	−	4.28663i	1.68068	−	0.00464423i
$924$	257.964	−	524.483i	0.279181	−	0.567622i
$925$	758.784	+	438.084i	0.820307	+	0.473604i
$926$	−1305.68	+	753.837i	−1.41003	+	0.814079i
$927$	−921.029	+	123.220i	−0.993559	+	0.132923i
$928$		−	138.144i		−	0.148862i
$929$	1623.41			1.74748			0.873740	−	0.486394i	$-0.161688\pi$
$929$	1623.41			1.74748			0.873740	+	0.486394i	$0.161688\pi$
$930$	1073.63	−	2182.88i	1.15444	−	2.34718i
$931$	−11.2192	−	6.47740i	−0.0120507	−	0.00695746i
$932$	−108.579	+	62.6884i	−0.116502	+	0.0672622i
$933$	−348.239	−	519.996i	−0.373247	−	0.557338i
$934$	1052.71	+	607.784i	1.12710	+	0.650732i
$935$		−	1504.64i		−	1.60924i
$936$	−224.572	+	549.705i	−0.239928	+	0.587292i
$937$	−914.127			−0.975589			−0.487795	−	0.872958i	$-0.662199\pi$
$937$	−914.127			−0.975589			−0.487795	+	0.872958i	$0.662199\pi$
$938$	294.652	−	510.353i	0.314128	−	0.544086i
$939$	35.9912	+	540.441i	0.0383293	+	0.575550i
$940$	8.71553	+	15.0957i	0.00927184	+	0.0160593i
$941$	−442.075	+	765.697i	−0.469793	+	0.813706i	−0.999403	−	0.0345354i	$-0.989005\pi$
$941$	−442.075	+	765.697i	−0.469793	+	0.813706i	0.529610	+	0.848241i	$0.322338\pi$
$942$	79.8933	+	1199.67i	0.0848124	+	1.27354i
$943$		−	738.645i		−	0.783292i
$944$	−363.795			−0.385376
$945$	395.177	−	1176.29i	0.418177	−	1.24475i
$946$	−41.6834	−	72.1977i	−0.0440628	−	0.0763190i
$947$	−174.337	+	301.961i	−0.184094	+	0.318861i	−0.943271	−	0.332024i	$-0.892269\pi$
$947$	−174.337	+	301.961i	−0.184094	+	0.318861i	0.759177	+	0.650885i	$0.225602\pi$
$948$	−101.871	+	68.2226i	−0.107459	+	0.0719648i
$949$	587.484	−	341.352i	0.619056	−	0.359697i
$950$	194.787	+	112.461i	0.205039	+	0.118380i
$951$	−30.8747	−	463.613i	−0.0324655	−	0.487500i
$952$	299.423	−	518.617i	0.314520	−	0.544765i
$953$	−69.3765	−	40.0546i	−0.0727980	−	0.0420300i	0.463159	−	0.886275i	$-0.346716\pi$
$953$	−69.3765	−	40.0546i	−0.0727980	−	0.0420300i	−0.535957	+	0.844245i	$0.680049\pi$
$954$	234.990	+	1756.47i	0.246320	+	1.84116i
$955$	23.3612	+	13.4876i	0.0244620	+	0.0141231i
$956$	−155.153			−0.162294
$957$	207.763	−	13.8361i	0.217098	−	0.0144578i
$958$	−499.218	−	864.671i	−0.521104	−	0.902579i
$959$			77.7228i			0.0810457i
$960$	177.968	−	119.184i	0.185383	−	0.124150i
$961$	869.058	+	1505.25i	0.904326	+	1.56634i
$962$	−1478.30	+	858.953i	−1.53670	+	0.892883i
$963$	1049.88	+	432.301i	1.09022	+	0.448910i
$964$	−380.237	+	219.530i	−0.394437	+	0.227728i
$965$	−1635.67	−	944.354i	−1.69499	−	0.978605i
$966$	622.033	−	416.573i	0.643926	−	0.431235i
$967$	−907.640	−	524.026i	−0.938615	−	0.541909i	−0.0490889	−	0.998794i	$-0.515632\pi$
$967$	−907.640	−	524.026i	−0.938615	−	0.541909i	−0.889526	+	0.456885i	$0.848965\pi$
$968$	206.454	+	357.590i	0.213279	+	0.369411i
$969$	18.7573	+	281.659i	0.0193574	+	0.290669i
$970$	−610.755	+	352.620i	−0.629644	+	0.363525i
$971$	−829.665	−	479.008i	−0.854444	−	0.493314i	0.00770360	−	0.999970i	$-0.497548\pi$
$971$	−829.665	−	479.008i	−0.854444	−	0.493314i	−0.862148	+	0.506657i	$0.830881\pi$
$972$	−456.348	−	88.2902i	−0.469494	−	0.0908335i
$973$	1006.22	−	580.943i	1.03414	−	0.597064i
$974$	−595.055	+	343.555i	−0.610940	+	0.352726i
$975$	523.963	−	352.997i	0.537398	−	0.362048i
$976$	1135.39	−	1966.55i	1.16331	−	2.01491i
$977$	−100.112			−0.102468			−0.0512342	−	0.998687i	$-0.516315\pi$
$977$	−100.112			−0.102468			−0.0512342	+	0.998687i	$0.516315\pi$
$978$	688.052	−	45.8215i	0.703530	−	0.0468523i
$979$	−346.831			−0.354270
$980$	−27.8556			−0.0284240
$981$	592.471	−	456.595i	0.603946	−	0.465439i
$982$	−88.7377	−	51.2327i	−0.0903643	−	0.0521718i
$983$	313.749	+	543.430i	0.319175	+	0.552828i	0.980316	−	0.197434i	$-0.0632608\pi$
$983$	313.749	+	543.430i	0.319175	+	0.552828i	−0.661141	+	0.750262i	$0.729927\pi$
$984$	−704.118	−	346.316i	−0.715567	−	0.351947i
$985$	1019.93			1.03546
$986$	−195.512			−0.198288
$987$	−30.4295	+	2.02648i	−0.0308303	+	0.00205317i
$988$	−122.767	+	71.3328i	−0.124258	+	0.0721992i
$989$		−	34.5433i		−	0.0349275i
$990$	−1219.76	−	1582.74i	−1.23208	−	1.59873i
$991$	−639.887	−	1108.32i	−0.645698	−	1.11838i	−0.984140	−	0.177394i	$-0.943233\pi$
$991$	−639.887	−	1108.32i	−0.645698	−	1.11838i	0.338442	−	0.940987i	$-0.390100\pi$
$992$		−	1470.94i		−	1.48280i
$993$	−338.887	+	689.014i	−0.341276	+	0.693871i
$994$	−1799.28	+	1038.81i	−1.81014	+	1.04508i
$995$	776.876	+	1345.59i	0.780780	+	1.35235i
$996$	527.006	−	352.933i	0.529122	−	0.354351i
$997$	−1.55999			−0.00156468			−0.000782342	−	1.00000i	$-0.500249\pi$
$997$	−1.55999			−0.00156468			−0.000782342		1.00000i	$0.500249\pi$
$998$	692.095	−	399.581i	0.693482	−	0.400382i
$999$	966.310	+	1094.90i	0.967277	+	1.09600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.m.a.23.7	✓	52
3.2	odd	2		351.3.m.a.179.20		52
9.2	odd	6		117.3.v.a.101.7	yes	52
9.7	even	3		351.3.v.a.62.20		52
13.4	even	6		117.3.v.a.95.7	yes	52
39.17	odd	6		351.3.v.a.17.20		52
117.43	even	6		351.3.m.a.251.20		52
117.56	odd	6	inner	117.3.m.a.56.7	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.m.a.23.7	✓	52	1.1	even	1	trivial
117.3.m.a.56.7	yes	52	117.56	odd	6	inner
117.3.v.a.95.7	yes	52	13.4	even	6
117.3.v.a.101.7	yes	52	9.2	odd	6
351.3.m.a.179.20		52	3.2	odd	2
351.3.m.a.251.20		52	117.43	even	6
351.3.v.a.17.20		52	39.17	odd	6
351.3.v.a.62.20		52	9.7	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21581 + 2.10585i) q^{2} +(-2.69201 - 1.32405i) q^{3} +(-0.956401 - 1.65653i) q^{4} +(-3.20934 + 5.55874i) q^{5} +(6.06122 - 4.05917i) q^{6} -7.16022i q^{7} -5.07529 q^{8} +(5.49381 + 7.12868i) q^{9} +(-7.80391 - 13.5168i) q^{10} +(7.11261 - 12.3194i) q^{11} +(0.381310 + 5.72572i) q^{12} +(-6.53109 - 11.2403i) q^{13} +(15.0784 + 8.70549i) q^{14} +(15.9996 - 10.7149i) q^{15} +(9.99620 - 17.3139i) q^{16} +(-14.2712 - 8.23946i) q^{17} +(-21.6914 + 2.90199i) q^{18} +(4.94498 + 2.85499i) q^{19} +12.2777 q^{20} +(-9.48046 + 19.2754i) q^{21} +(17.2952 + 29.9562i) q^{22} +14.3327i q^{23} +(13.6627 + 6.71991i) q^{24} +(-8.09972 - 14.0291i) q^{25} +(31.6110 - 0.0873511i) q^{26} +(-5.35066 - 26.4645i) q^{27} +(-11.8612 + 6.84804i) q^{28} +(-4.22551 - 2.43960i) q^{29} +(3.11136 + 46.7200i) q^{30} +(-44.9926 - 25.9765i) q^{31} +(14.1564 + 24.5197i) q^{32} +(-35.4586 + 23.7465i) q^{33} +(34.7021 - 20.0353i) q^{34} +(39.8018 + 22.9796i) q^{35} +(6.55463 - 15.9186i) q^{36} +(-46.8401 + 27.0432i) q^{37} +(-12.0243 + 6.94225i) q^{38} +(2.69902 + 38.9065i) q^{39} +(16.2883 - 28.2122i) q^{40} -51.5357 q^{41} +(-29.0646 - 43.3997i) q^{42} -2.41011 q^{43} -27.2100 q^{44} +(-57.2580 + 7.66027i) q^{45} +(-30.1824 - 17.4258i) q^{46} +(0.709869 + 1.22953i) q^{47} +(-49.8343 + 33.3738i) q^{48} -2.26880 q^{49} +39.3910 q^{50} +(27.5087 + 41.0764i) q^{51} +(-12.3737 + 21.5692i) q^{52} -80.9755i q^{53} +(62.2357 + 20.9082i) q^{54} +(45.6535 + 79.0743i) q^{55} +36.3402i q^{56} +(-9.53179 - 14.2330i) q^{57} +(10.2748 - 5.93219i) q^{58} +(-9.09833 - 15.7588i) q^{59} +(-33.0515 - 16.2562i) q^{60} +113.582 q^{61} +(109.405 - 63.1651i) q^{62} +(51.0430 - 39.3369i) q^{63} +11.1233 q^{64} +(83.4425 - 0.230578i) q^{65} +(-6.89547 - 103.542i) q^{66} -33.8467i q^{67} +31.5209i q^{68} +(18.9771 - 38.5836i) q^{69} +(-96.7831 + 55.8777i) q^{70} +(-59.6642 + 103.341i) q^{71} +(-27.8826 - 36.1801i) q^{72} +52.2658i q^{73} -131.518i q^{74} +(3.22930 + 48.4909i) q^{75} -10.9220i q^{76} +(-88.2097 - 50.9279i) q^{77} +(-85.2127 - 41.6193i) q^{78} +(10.6829 + 18.5033i) q^{79} +(64.1624 + 111.133i) q^{80} +(-20.6362 + 78.3272i) q^{81} +(62.6578 - 108.527i) q^{82} +(-55.2653 - 95.7223i) q^{83} +(40.9974 - 2.73026i) q^{84} +(91.6020 - 52.8865i) q^{85} +(2.93025 - 5.07534i) q^{86} +(8.14495 + 12.1622i) q^{87} +(-36.0985 + 62.5245i) q^{88} +(-12.1907 - 21.1149i) q^{89} +(53.4836 - 129.890i) q^{90} +(-80.4832 + 46.7640i) q^{91} +(23.7426 - 13.7078i) q^{92} +(86.7264 + 129.501i) q^{93} -3.45227 q^{94} +(-31.7402 + 18.3252i) q^{95} +(-5.64407 - 84.7509i) q^{96} -45.1850i q^{97} +(2.75844 - 4.77775i) q^{98} +(126.896 - 16.9769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{2} - q^{3} - 47 q^{4} - 3 q^{6} + 78 q^{8} + q^{9} + 2 q^{10} - 3 q^{11} + 13 q^{12} - 6 q^{13} - 6 q^{14} + 24 q^{15} - 75 q^{16} - 12 q^{18} + 15 q^{19} - 6 q^{20} + 69 q^{21} + 17 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - 3 * q^2 - q^3 - 47 * q^4 - 3 * q^6 + 78 * q^8 + q^9 + 2 * q^10 - 3 * q^11 + 13 * q^12 - 6 * q^13 - 6 * q^14 + 24 * q^15 - 75 * q^16 - 12 * q^18 + 15 * q^19 - 6 * q^20 + 69 * q^21 + 17 * q^22 - 42 * q^24 - 92 * q^25 + 12 * q^26 + 14 * q^27 - 18 * q^28 + 24 * q^29 + 147 * q^30 - 48 * q^31 - 159 * q^32 - 120 * q^33 + 12 * q^34 - 78 * q^35 - 181 * q^36 + 27 * q^37 - 36 * q^38 - 35 * q^39 - 44 * q^40 + 66 * q^41 + 300 * q^42 + 62 * q^43 + 120 * q^44 + 117 * q^45 - 6 * q^46 - 153 * q^47 - 244 * q^48 - 146 * q^49 + 432 * q^50 - 63 * q^51 + 128 * q^52 - 132 * q^54 + 23 * q^55 - 171 * q^57 - 3 * q^58 - 3 * q^59 - 207 * q^60 + 12 * q^61 + 201 * q^62 - 192 * q^63 + 270 * q^64 - 3 * q^65 + 48 * q^66 - 48 * q^69 + 159 * q^70 - 432 * q^71 + 93 * q^72 + 346 * q^75 + 138 * q^77 - 93 * q^78 + 9 * q^79 - 84 * q^80 - 215 * q^81 - 85 * q^82 - 135 * q^83 - 246 * q^84 - 24 * q^85 - 306 * q^86 - 123 * q^87 + 145 * q^88 - 441 * q^89 + 543 * q^90 - 138 * q^91 + 864 * q^92 + 183 * q^93 + 362 * q^94 + 252 * q^95 + 747 * q^96 + 147 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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