LMFDB - Embedded newform 26.8.e.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,8,Mod(17,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("26.17");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	26.e (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:	$8.12201066259$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22180 x^{14} + 184473654 x^{12} + 707524481236 x^{10} + \cdots + 18\!\cdots\!76 $ x^16 + 22180x^14 + 184473654x^12 + 707524481236x^10 + 1235305573179121x^8 + 834592841081820432x^6 + 142296444753813668448x^4 + 5907885179463590558976*x^2 + 18970385728293762437376
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.5
Root			$-79.3738i$ of defining polynomial
Character	$\chi$	$=$	26.17
Dual form			26.8.e.a.23.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.92820 + 4.00000i) q^{2} +(-39.6869 + 68.7398i) q^{3} +(32.0000 + 55.4256i) q^{4} -12.5639i q^{5} +(-549.918 + 317.495i) q^{6} +(-93.7198 + 54.1091i) q^{7} +512.000i q^{8} +(-2056.60 - 3562.14i) q^{9} +(50.2557 - 87.0454i) q^{10} +(-5776.62 - 3335.13i) q^{11} -5079.93 q^{12} +(5200.37 + 5975.34i) q^{13} -865.746 q^{14} +(863.641 + 498.623i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(8266.62 + 14318.2i) q^{17} -32905.7i q^{18} +(-30598.6 + 17666.1i) q^{19} +(696.363 - 402.045i) q^{20} -8589.70i q^{21} +(-26681.1 - 46212.9i) q^{22} +(-13987.1 + 24226.4i) q^{23} +(-35194.8 - 20319.7i) q^{24} +77967.1 q^{25} +(12127.8 + 62199.8i) q^{26} +152890. q^{27} +(-5998.07 - 3462.98i) q^{28} +(-16627.8 + 28800.2i) q^{29} +(3988.99 + 6909.13i) q^{30} +220834. i q^{31} +(-28377.9 + 16384.0i) q^{32} +(458512. - 264722. i) q^{33} +132266. i q^{34} +(679.823 + 1177.49i) q^{35} +(131623. - 227977. i) q^{36} +(165533. + 95570.7i) q^{37} -282658. q^{38} +(-617130. + 120329. i) q^{39} +6432.73 q^{40} +(-70555.0 - 40734.9i) q^{41} +(34358.8 - 59511.2i) q^{42} +(-484095. - 838477. i) q^{43} -426897. i q^{44} +(-44754.5 + 25839.0i) q^{45} +(-193811. + 111897. i) q^{46} +1.10569e6i q^{47} +(-162558. - 281558. i) q^{48} +(-405916. + 703067. i) q^{49} +(540172. + 311869. i) q^{50} -1.31231e6 q^{51} +(-164775. + 479445. i) q^{52} +160288. q^{53} +(1.05926e6 + 611562. i) q^{54} +(-41902.3 + 72577.0i) q^{55} +(-27703.9 - 47984.5i) q^{56} -2.80446e6i q^{57} +(-230402. + 133023. i) q^{58} +(1.93517e6 - 1.11727e6i) q^{59} +63823.8i q^{60} +(-934692. - 1.61893e6i) q^{61} +(-883335. + 1.52998e6i) q^{62} +(385489. + 222562. i) q^{63} -262144. q^{64} +(75073.7 - 65337.0i) q^{65} +4.23556e6 q^{66} +(3.10630e6 + 1.79343e6i) q^{67} +(-529064. + 916365. i) q^{68} +(-1.11021e6 - 1.92294e6i) q^{69} +10877.2i q^{70} +(640083. - 369552. i) q^{71} +(1.82382e6 - 1.05298e6i) q^{72} +4.24974e6i q^{73} +(764566. + 1.32427e6i) q^{74} +(-3.09428e6 + 5.35944e6i) q^{75} +(-1.95831e6 - 1.13063e6i) q^{76} +721844. q^{77} +(-4.75692e6 - 1.63486e6i) q^{78} +2.45055e6 q^{79} +(44567.2 + 25730.9i) q^{80} +(-1.56996e6 + 2.71925e6i) q^{81} +(-325879. - 564440. i) q^{82} -5.19912e6i q^{83} +(476089. - 274870. i) q^{84} +(179893. - 103861. i) q^{85} -7.74552e6i q^{86} +(-1.31981e6 - 2.28599e6i) q^{87} +(1.70759e6 - 2.95763e6i) q^{88} +(3.73776e6 + 2.15800e6i) q^{89} -413424. q^{90} +(-810698. - 278620. i) q^{91} -1.79035e6 q^{92} +(-1.51801e7 - 8.76421e6i) q^{93} +(-4.42278e6 + 7.66047e6i) q^{94} +(221956. + 384439. i) q^{95} -2.60092e6i q^{96} +(7.39963e6 - 4.27218e6i) q^{97} +(-5.62454e6 + 3.24733e6i) q^{98} +2.74362e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 512 q^{4} + 2520 q^{7} - 4684 q^{9} + 2432 q^{10} - 8496 q^{11} - 3620 q^{13} + 34560 q^{14} + 51648 q^{15} - 32768 q^{16} + 41520 q^{17} - 54432 q^{19} - 16128 q^{20} - 17280 q^{22} - 7560 q^{23}+ \cdots + 19031040 q^{98}+O(q^{100}) $ 16 * q + 512 * q^4 + 2520 * q^7 - 4684 * q^9 + 2432 * q^10 - 8496 * q^11 - 3620 * q^13 + 34560 * q^14 + 51648 * q^15 - 32768 * q^16 + 41520 * q^17 - 54432 * q^19 - 16128 * q^20 - 17280 * q^22 - 7560 * q^23 - 273960 * q^25 + 51072 * q^26 + 133920 * q^27 + 161280 * q^28 - 346056 * q^29 + 170368 * q^30 + 486300 * q^33 - 283248 * q^35 + 299776 * q^36 - 68280 * q^37 - 1059840 * q^38 - 1122680 * q^39 + 311296 * q^40 - 1288008 * q^41 + 408320 * q^42 + 285360 * q^43 + 5743980 * q^45 - 188928 * q^46 - 2131660 * q^49 + 85248 * q^50 + 957280 * q^51 + 354560 * q^52 + 3666600 * q^53 - 4074624 * q^54 - 1091472 * q^55 + 1105920 * q^56 + 3504000 * q^58 + 1799280 * q^59 - 4626000 * q^61 - 2770560 * q^62 - 8609760 * q^63 - 4194304 * q^64 - 11518020 * q^65 + 7941120 * q^66 - 7094400 * q^67 - 2657280 * q^68 + 18027316 * q^69 + 25958520 * q^71 + 4423680 * q^72 - 1142400 * q^74 - 10898032 * q^75 - 3483648 * q^76 - 20577480 * q^77 - 22023040 * q^78 + 34143488 * q^79 - 1032192 * q^80 - 15745864 * q^81 + 12202240 * q^82 + 17311488 * q^84 + 7123932 * q^85 - 10460440 * q^87 + 1105920 * q^88 + 10609452 * q^89 + 4070656 * q^90 - 38683952 * q^91 - 967680 * q^92 - 52747080 * q^93 - 14303616 * q^94 + 33837504 * q^95 + 83706300 * q^97 + 19031040 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	6.92820	+	4.00000i	0.612372	+	0.353553i
$2$	6.92820	+	4.00000i	0.612372	+	0.353553i
$3$	−39.6869	+	68.7398i	−0.848639	+	1.46989i	0.0337840	+	0.999429i	$0.489244\pi$
$3$	−39.6869	+	68.7398i	−0.848639	+	1.46989i	−0.882423	+	0.470457i	$0.844089\pi$
$4$	32.0000	+	55.4256i	0.250000	+	0.433013i
$5$		−	12.5639i		−	0.0449500i	−0.999747	−	0.0224750i	$-0.992845\pi$
$5$		−	12.5639i		−	0.0449500i	0.999747	−	0.0224750i	$-0.00715462\pi$
$6$	−549.918	+	317.495i	−1.03937	+	0.600078i
$7$	−93.7198	+	54.1091i	−0.103273	+	0.0596249i	−0.550747	−	0.834672i	$-0.685657\pi$
$7$	−93.7198	+	54.1091i	−0.103273	+	0.0596249i	0.447474	+	0.894297i	$0.352324\pi$
$8$			512.000i			0.353553i
$9$	−2056.60	−	3562.14i	−0.940377	−	1.62878i
$10$	50.2557	−	87.0454i	0.0158922	−	0.0275262i
$11$	−5776.62	−	3335.13i	−1.30858	−	0.755507i	−0.326718	−	0.945122i	$-0.605943\pi$
$11$	−5776.62	−	3335.13i	−1.30858	−	0.755507i	−0.981859	+	0.189614i	$0.939276\pi$
$12$	−5079.93			−0.848639
$13$	5200.37	+	5975.34i	0.656496	+	0.754329i
$13$	5200.37	+	5975.34i	0.656496	+	0.754329i
$14$	−865.746			−0.0843223
$15$	863.641	+	498.623i	0.0660714	+	0.0381464i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	8266.62	+	14318.2i	0.408091	+	0.706834i	0.994676	−	0.103054i	$-0.0328613\pi$
$17$	8266.62	+	14318.2i	0.408091	+	0.706834i	−0.586585	+	0.809888i	$0.699528\pi$
$18$		−	32905.7i		−	1.32989i
$19$	−30598.6	+	17666.1i	−1.02344	+	0.590886i	−0.915100	−	0.403227i	$-0.867888\pi$
$19$	−30598.6	+	17666.1i	−1.02344	+	0.590886i	−0.108345	+	0.994113i	$0.534555\pi$
$20$	696.363	−	402.045i	0.0194639	−	0.0112375i
$21$		−	8589.70i		−	0.202400i
$22$	−26681.1	−	46212.9i	−0.534224	−	0.925304i
$23$	−13987.1	+	24226.4i	−0.239707	+	0.415185i	−0.960630	−	0.277830i	$-0.910385\pi$
$23$	−13987.1	+	24226.4i	−0.239707	+	0.415185i	0.720923	+	0.693015i	$0.243718\pi$
$24$	−35194.8	−	20319.7i	−0.519683	−	0.300039i
$25$	77967.1			0.997979
$26$	12127.8	+	62199.8i	0.135325	+	0.694037i
$27$	152890.			1.49488
$28$	−5998.07	−	3462.98i	−0.0516367	−	0.0298124i
$29$	−16627.8	+	28800.2i	−0.126603	+	0.219282i	−0.922358	−	0.386336i	$-0.873741\pi$
$29$	−16627.8	+	28800.2i	−0.126603	+	0.219282i	0.795756	+	0.605618i	$0.207074\pi$
$30$	3988.99	+	6909.13i	0.0269736	+	0.0467196i
$31$			220834.i			1.33137i	0.746232	+	0.665686i	$0.231861\pi$
$31$			220834.i			1.33137i	−0.746232	+	0.665686i	$0.768139\pi$
$32$	−28377.9	+	16384.0i	−0.153093	+	0.0883883i
$33$	458512.	−	264722.i	2.22102	−	1.28231i
$34$			132266.i			0.577128i
$35$	679.823	+	1177.49i	0.00268014	+	0.00464214i
$36$	131623.	−	227977.i	0.470188	−	0.814390i
$37$	165533.	+	95570.7i	0.537254	+	0.310183i	0.743965	−	0.668218i	$-0.232943\pi$
$37$	165533.	+	95570.7i	0.537254	+	0.310183i	−0.206712	+	0.978402i	$0.566276\pi$
$38$	−282658.			−0.835639
$39$	−617130.	+	120329.i	−1.66591	+	0.324821i
$40$	6432.73			0.0158922
$41$	−70555.0	−	40734.9i	−0.159876	−	0.0923046i	0.417927	−	0.908480i	$-0.362757\pi$
$41$	−70555.0	−	40734.9i	−0.159876	−	0.0923046i	−0.577804	+	0.816176i	$0.696090\pi$
$42$	34358.8	−	59511.2i	0.0715592	−	0.123944i
$43$	−484095.	−	838477.i	−0.928519	−	1.60824i	−0.785802	−	0.618478i	$-0.787749\pi$
$43$	−484095.	−	838477.i	−0.928519	−	1.60824i	−0.142717	−	0.989764i	$-0.545584\pi$
$44$		−	426897.i		−	0.755507i
$45$	−44754.5	+	25839.0i	−0.0732137	+	0.0422700i
$46$	−193811.	+	111897.i	−0.293580	+	0.169499i
$47$			1.10569e6i			1.55343i	0.629851	+	0.776716i	$0.283116\pi$
$47$			1.10569e6i			1.55343i	−0.629851	+	0.776716i	$0.716884\pi$
$48$	−162558.	−	281558.i	−0.212160	−	0.367471i
$49$	−405916.	+	703067.i	−0.492890	+	0.853710i
$50$	540172.	+	311869.i	0.611135	+	0.352839i
$51$	−1.31231e6			−1.38529
$52$	−164775.	+	479445.i	−0.162510	+	0.472854i
$53$	160288.			0.147889			0.0739443	−	0.997262i	$-0.476441\pi$
$53$	160288.			0.147889			0.0739443	+	0.997262i	$0.476441\pi$
$54$	1.05926e6	+	611562.i	0.915425	+	0.528521i
$55$	−41902.3	+	72577.0i	−0.0339601	+	0.0588206i
$56$	−27703.9	−	47984.5i	−0.0210806	−	0.0365126i
$57$		−	2.80446e6i		−	2.00580i
$58$	−230402.	+	133023.i	−0.155056	+	0.0895216i
$59$	1.93517e6	−	1.11727e6i	1.22670	−	0.708235i	0.260361	−	0.965511i	$-0.416159\pi$
$59$	1.93517e6	−	1.11727e6i	1.22670	−	0.708235i	0.966338	+	0.257277i	$0.0828252\pi$
$60$			63823.8i			0.0381464i
$61$	−934692.	−	1.61893e6i	−0.527247	−	0.913219i	−0.999496	−	0.0317533i	$-0.989891\pi$
$61$	−934692.	−	1.61893e6i	−0.527247	−	0.913219i	0.472249	−	0.881465i	$-0.343442\pi$
$62$	−883335.	+	1.52998e6i	−0.470711	+	0.815295i
$63$	385489.	+	222562.i	0.194232	+	0.112140i
$64$	−262144.			−0.125000
$65$	75073.7	−	65337.0i	0.0339071	−	0.0295095i
$66$	4.23556e6			1.81345
$67$	3.10630e6	+	1.79343e6i	1.26178	+	0.728486i	0.973418	−	0.229036i	$-0.0735574\pi$
$67$	3.10630e6	+	1.79343e6i	1.26178	+	0.728486i	0.288358	+	0.957523i	$0.406891\pi$
$68$	−529064.	+	916365.i	−0.204045	+	0.353417i
$69$	−1.11021e6	−	1.92294e6i	−0.406850	−	0.704685i
$70$			10877.2i			0.00379029i
$71$	640083.	−	369552.i	0.212242	−	0.122538i	−0.390111	−	0.920768i	$-0.627563\pi$
$71$	640083.	−	369552.i	0.212242	−	0.122538i	0.602353	+	0.798230i	$0.294230\pi$
$72$	1.82382e6	−	1.05298e6i	0.575861	−	0.332473i
$73$			4.24974e6i			1.27859i	0.768960	+	0.639297i	$0.220774\pi$
$73$			4.24974e6i			1.27859i	−0.768960	+	0.639297i	$0.779226\pi$
$74$	764566.	+	1.32427e6i	0.219333	+	0.379896i
$75$	−3.09428e6	+	5.35944e6i	−0.846924	+	1.46692i
$76$	−1.95831e6	−	1.13063e6i	−0.511722	−	0.295443i
$77$	721844.			0.180188
$78$	−4.75692e6	−	1.63486e6i	−1.13500	−	0.390075i
$79$	2.45055e6			0.559202			0.279601	−	0.960116i	$-0.409798\pi$
$79$	2.45055e6			0.559202			0.279601	+	0.960116i	$0.409798\pi$
$80$	44567.2	+	25730.9i	0.00973197	+	0.00561876i
$81$	−1.56996e6	+	2.71925e6i	−0.328239	+	0.568527i
$82$	−325879.	−	564440.i	−0.0652692	−	0.113050i
$83$		−	5.19912e6i		−	0.998060i	−0.866585	−	0.499030i	$-0.833690\pi$
$83$		−	5.19912e6i		−	0.998060i	0.866585	−	0.499030i	$-0.166310\pi$
$84$	476089.	−	274870.i	0.0876418	−	0.0506000i
$85$	179893.	−	103861.i	0.0317722	−	0.0183437i
$86$		−	7.74552e6i		−	1.31312i
$87$	−1.31981e6	−	2.28599e6i	−0.214880	−	0.372183i
$88$	1.70759e6	−	2.95763e6i	0.267112	−	0.462652i
$89$	3.73776e6	+	2.15800e6i	0.562013	+	0.324479i	0.753953	−	0.656928i	$-0.228145\pi$
$89$	3.73776e6	+	2.15800e6i	0.562013	+	0.324479i	−0.191940	+	0.981407i	$0.561478\pi$
$90$	−413424.			−0.0597788
$91$	−810698.	−	278620.i	−0.112775	−	0.0387586i
$92$	−1.79035e6			−0.239707
$93$	−1.51801e7	−	8.76421e6i	−1.95696	−	1.12985i
$94$	−4.42278e6	+	7.66047e6i	−0.549221	+	0.951279i
$95$	221956.	+	384439.i	0.0265603	+	0.0460039i
$96$		−	2.60092e6i		−	0.300039i
$97$	7.39963e6	−	4.27218e6i	0.823206	−	0.475278i	−0.0283145	−	0.999599i	$-0.509014\pi$
$97$	7.39963e6	−	4.27218e6i	0.823206	−	0.475278i	0.851521	+	0.524321i	$0.175681\pi$
$98$	−5.62454e6	+	3.24733e6i	−0.603664	+	0.348526i
$99$			2.74362e7i			2.84185i
$100$	2.49495e6	+	4.32138e6i	0.249495	+	0.432138i
$101$	9.46833e6	−	1.63996e7i	0.914426	−	1.58383i	0.106687	−	0.994293i	$-0.465976\pi$
$101$	9.46833e6	−	1.63996e7i	0.914426	−	1.58383i	0.807739	−	0.589540i	$-0.200691\pi$
$102$	−9.09193e6	−	5.24923e6i	−0.848312	−	0.489773i
$103$	1.11380e7			1.00433			0.502166	−	0.864771i	$-0.332537\pi$
$103$	1.11380e7			1.00433			0.502166	+	0.864771i	$0.332537\pi$
$104$	−3.05937e6	+	2.66259e6i	−0.266696	+	0.232106i
$105$	−107920.			−0.00909789
$106$	1.11051e6	+	641151.i	0.0905629	+	0.0522865i
$107$	−1.83954e6	+	3.18618e6i	−0.145166	+	0.251435i	−0.929435	−	0.368986i	$-0.879705\pi$
$107$	−1.83954e6	+	3.18618e6i	−0.145166	+	0.251435i	0.784269	+	0.620421i	$0.213038\pi$
$108$	4.89249e6	+	8.47405e6i	0.373721	+	0.647303i
$109$			1.55046e7i			1.14675i	0.819293	+	0.573375i	$0.194366\pi$
$109$			1.55046e7i			1.14675i	−0.819293	+	0.573375i	$0.805634\pi$
$110$	−580616.	+	335219.i	−0.0415924	+	0.0240134i
$111$	−1.31390e7	+	7.58581e6i	−0.911869	+	0.526468i
$112$		−	443262.i		−	0.0298124i
$113$	−9.63829e6	−	1.66940e7i	−0.628385	−	1.08839i	−0.987876	−	0.155246i	$-0.950383\pi$
$113$	−9.63829e6	−	1.66940e7i	−0.628385	−	1.08839i	0.359491	−	0.933148i	$-0.382950\pi$
$114$	1.12178e7	−	1.94298e7i	0.709156	−	1.22829i
$115$	304379.	+	175733.i	0.0186626	+	0.0107749i
$116$	−2.12836e6			−0.126603
$117$	1.05899e7	−	3.08134e7i	0.611283	−	1.77864i
$118$	1.78764e7			1.00160
$119$	−1.54949e6	−	894600.i	−0.0842898	−	0.0486647i
$120$	−255295.	+	442184.i	−0.0134868	+	0.0233598i
$121$	1.25026e7	+	2.16552e7i	0.641582	+	1.11125i
$122$		−	1.49551e7i		−	0.745640i
$123$	5.60022e6	−	3.23329e6i	0.271355	−	0.156667i
$124$	−1.22398e7	+	7.06668e6i	−0.576501	+	0.332843i
$125$		−	1.96113e6i		−	0.0898093i
$126$	1.78050e6	+	3.08391e6i	0.0792947	+	0.137342i
$127$	−1.93352e7	+	3.34895e7i	−0.837596	+	1.45076i	0.0543027	+	0.998525i	$0.482706\pi$
$127$	−1.93352e7	+	3.34895e7i	−0.837596	+	1.45076i	−0.891899	+	0.452235i	$0.850627\pi$
$128$	−1.81619e6	−	1.04858e6i	−0.0765466	−	0.0441942i
$129$	7.68489e7			3.15191
$130$	781474.	−	152373.i	0.0311970	−	0.00608284i
$131$	−4.18957e7			−1.62825			−0.814123	−	0.580693i	$-0.802782\pi$
$131$	−4.18957e7			−1.62825			−0.814123	+	0.580693i	$0.802782\pi$
$132$	2.93448e7	+	1.69422e7i	1.11051	+	0.641153i
$133$	1.91180e6	−	3.31133e6i	0.0704630	−	0.122045i
$134$	1.43474e7	+	2.48504e7i	0.515118	+	0.892210i
$135$		−	1.92090e6i		−	0.0671951i
$136$	−7.33092e6	+	4.23251e6i	−0.249904	+	0.144282i
$137$	−5.46930e6	+	3.15770e6i	−0.181723	+	0.104918i	−0.588102	−	0.808787i	$-0.700125\pi$
$137$	−5.46930e6	+	3.15770e6i	−0.181723	+	0.104918i	0.406379	+	0.913705i	$0.366791\pi$
$138$		−	1.77634e7i		−	0.575373i
$139$	1.36659e7	+	2.36701e7i	0.431607	+	0.747564i	0.997012	−	0.0772488i	$-0.0246136\pi$
$139$	1.36659e7	+	2.36701e7i	0.431607	+	0.747564i	−0.565405	+	0.824813i	$0.691280\pi$
$140$	−43508.7	+	75359.2i	−0.00134007	+	0.00232107i
$141$	−7.60051e7	−	4.38816e7i	−2.28337	−	1.31830i
$142$	5.91283e6			0.173295
$143$	−1.01120e7	−	5.18612e7i	−0.289175	−	1.48309i
$144$	1.68477e7			0.470188
$145$	361844.	+	208911.i	0.00985674	+	0.00569079i
$146$	−1.69990e7	+	2.94431e7i	−0.452051	+	0.782975i
$147$	−3.22191e7	−	5.58051e7i	−0.836571	−	1.44898i
$148$			1.22330e7i			0.310183i
$149$	−1.92420e7	+	1.11094e7i	−0.476539	+	0.275130i	−0.718973	−	0.695038i	$-0.755388\pi$
$149$	−1.92420e7	+	1.11094e7i	−0.476539	+	0.275130i	0.242434	+	0.970168i	$0.422054\pi$
$150$	−4.28755e7	+	2.47542e7i	−1.03727	+	0.598866i
$151$			4.67506e7i			1.10501i	0.833508	+	0.552507i	$0.186329\pi$
$151$			4.67506e7i			1.10501i	−0.833508	+	0.552507i	$0.813671\pi$
$152$	−9.04505e6	−	1.56665e7i	−0.208910	−	0.361842i
$153$	3.40023e7	−	5.88938e7i	0.767518	−	1.32938i
$154$	5.00109e6	+	2.88738e6i	0.110342	+	0.0637061i
$155$	2.77454e6			0.0598452
$156$	−2.64175e7	−	3.03543e7i	−0.557128	−	0.640153i
$157$	−5.59114e7			−1.15306			−0.576530	−	0.817076i	$-0.695594\pi$
$157$	−5.59114e7			−1.15306			−0.576530	+	0.817076i	$0.695594\pi$
$158$	1.69779e7	+	9.80220e6i	0.342440	+	0.197708i
$159$	−6.36132e6	+	1.10181e7i	−0.125504	+	0.217379i
$160$	205847.	+	356538.i	0.00397306	+	0.00688154i
$161$		−	3.02733e6i		−	0.0571701i
$162$	−2.17540e7	+	1.25597e7i	−0.402010	+	0.232100i
$163$	−3.14275e7	+	1.81447e7i	−0.568399	+	0.328166i	−0.756510	−	0.653982i	$-0.773097\pi$
$163$	−3.14275e7	+	1.81447e7i	−0.568399	+	0.328166i	0.188110	+	0.982148i	$0.439764\pi$
$164$		−	5.21407e6i		−	0.0923046i
$165$	−3.32595e6	−	5.76071e6i	−0.0576397	−	0.0998349i
$166$	2.07965e7	−	3.60206e7i	0.352867	−	0.611184i
$167$	6.06842e7	+	3.50360e7i	1.00825	+	0.582113i	0.910679	−	0.413116i	$-0.135559\pi$
$167$	6.06842e7	+	3.50360e7i	1.00825	+	0.582113i	0.0975708	+	0.995229i	$0.468893\pi$
$168$	4.39793e6			0.0715592
$169$	−8.66088e6	+	6.21479e7i	−0.138025	+	0.990429i
$170$	1.66178e6			0.0259419
$171$	1.25858e8	+	7.26644e7i	1.92485	+	1.11131i
$172$	3.09821e7	−	5.36625e7i	0.464259	−	0.804121i
$173$	−3.16133e7	−	5.47559e7i	−0.464204	−	0.804025i	0.534961	−	0.844877i	$-0.320326\pi$
$173$	−3.16133e7	−	5.47559e7i	−0.464204	−	0.804025i	−0.999165	+	0.0408514i	$0.986993\pi$
$174$		−	2.11170e7i		−	0.303886i
$175$	−7.30706e6	+	4.21873e6i	−0.103065	+	0.0595044i
$176$	2.36610e7	−	1.36607e7i	0.327144	−	0.188877i
$177$			1.77364e8i			2.40414i
$178$	1.72640e7	+	2.99021e7i	0.229441	+	0.397404i
$179$	2.80744e7	−	4.86262e7i	0.365868	−	0.633702i	−0.623047	−	0.782184i	$-0.714106\pi$
$179$	2.80744e7	−	4.86262e7i	0.365868	−	0.633702i	0.988915	+	0.148483i	$0.0474389\pi$
$180$	−2.86429e6	−	1.65370e6i	−0.0366069	−	0.0211350i
$181$	1.03528e8			1.29773			0.648864	−	0.760904i	$-0.275244\pi$
$181$	1.03528e8			1.29773			0.648864	+	0.760904i	$0.275244\pi$
$182$	−4.50220e6	−	5.17313e6i	−0.0553573	−	0.0636068i
$183$	1.48380e8			1.78977
$184$	−1.24039e7	−	7.16141e6i	−0.146790	−	0.0847493i
$185$	1.20074e6	−	2.07975e6i	0.0139428	−	0.0241496i
$186$	−7.01137e7	−	1.21440e8i	−0.798927	−	1.38378i
$187$		−	1.10281e8i		−	1.23326i
$188$	−6.12838e7	+	3.53822e7i	−0.672656	+	0.388358i
$189$	−1.43289e7	+	8.27277e6i	−0.154381	+	0.0891322i
$190$			3.55129e6i			0.0375620i
$191$	−2.49874e7	−	4.32795e7i	−0.259481	−	0.449434i	0.706622	−	0.707591i	$-0.250218\pi$
$191$	−2.49874e7	−	4.32795e7i	−0.259481	−	0.449434i	−0.966103	+	0.258157i	$0.916885\pi$
$192$	1.04037e7	−	1.80197e7i	0.106080	−	0.183736i
$193$	4.14043e7	+	2.39048e7i	0.414567	+	0.239350i	0.692750	−	0.721178i	$-0.256399\pi$
$193$	4.14043e7	+	2.39048e7i	0.414567	+	0.239350i	−0.278183	+	0.960528i	$0.589732\pi$
$194$	6.83548e7			0.672145
$195$	1.51181e6	+	7.75357e6i	0.0146007	+	0.0748826i
$196$	−5.19572e7			−0.492890
$197$	−2.06870e7	−	1.19437e7i	−0.192782	−	0.111303i	0.400502	−	0.916296i	$-0.368836\pi$
$197$	−2.06870e7	−	1.19437e7i	−0.192782	−	0.111303i	−0.593284	+	0.804993i	$0.702169\pi$
$198$	−1.09745e8	+	1.90083e8i	−1.00474	+	1.74027i
$199$	−8.06424e7	−	1.39677e8i	−0.725400	−	1.25643i	−0.958809	−	0.284051i	$-0.908321\pi$
$199$	−8.06424e7	−	1.39677e8i	−0.725400	−	1.25643i	0.233409	−	0.972379i	$-0.425012\pi$
$200$			3.99192e7i			0.352839i
$201$	−2.46559e8	+	1.42351e8i	−2.14158	+	1.23644i
$202$	1.31197e8	−	7.57466e7i	1.11994	−	0.646597i
$203$		−	3.59887e6i		−	0.0301947i
$204$	−4.19938e7	−	7.27354e7i	−0.346322	−	0.599847i
$205$	−511790.	+	886447.i	−0.00414910	+	0.00718645i
$206$	7.71664e7	+	4.45520e7i	0.615025	+	0.355085i
$207$	1.15064e8			0.901660
$208$	−3.18463e7	+	6.20945e6i	−0.245379	+	0.0478445i
$209$	2.35675e8			1.78567
$210$	−747694.	−	431681.i	−0.00557130	−	0.00321659i
$211$	−3.89068e7	+	6.73886e7i	−0.285126	+	0.493853i	−0.972640	−	0.232318i	$-0.925369\pi$
$211$	−3.89068e7	+	6.73886e7i	−0.285126	+	0.493853i	0.687514	+	0.726172i	$0.258702\pi$
$212$	5.12921e6	+	8.88404e6i	0.0369721	+	0.0640376i
$213$			5.86655e7i			0.415962i
$214$	−2.54894e7	+	1.47163e7i	−0.177792	+	0.102648i
$215$	−1.05346e7	+	6.08213e6i	−0.0722905	+	0.0417370i
$216$			7.82799e7i			0.528521i
$217$	−1.19491e7	−	2.06965e7i	−0.0793829	−	0.137495i
$218$	−6.20185e7	+	1.07419e8i	−0.405437	+	0.702238i
$219$	−2.92126e8	−	1.68659e8i	−1.87939	−	1.08506i
$220$	−5.36350e6			−0.0339601
$221$	−4.25667e7	+	1.23856e8i	−0.265276	+	0.771869i
$222$	−1.21373e8			−0.744538
$223$	5.97190e7	+	3.44788e7i	0.360617	+	0.208202i	0.669351	−	0.742946i	$-0.266572\pi$
$223$	5.97190e7	+	3.44788e7i	0.360617	+	0.208202i	−0.308735	+	0.951148i	$0.599905\pi$
$224$	1.77305e6	−	3.07101e6i	0.0105403	−	0.0182563i
$225$	−1.60348e8	−	2.77730e8i	−0.938476	−	1.62549i
$226$		−	1.54213e8i		−	0.888670i
$227$	−1.27607e7	+	7.36742e6i	−0.0724079	+	0.0418047i	−0.535767	−	0.844366i	$-0.679977\pi$
$227$	−1.27607e7	+	7.36742e6i	−0.0724079	+	0.0418047i	0.463359	+	0.886171i	$0.346644\pi$
$228$	1.55439e8	−	8.97426e7i	0.868535	−	0.501449i
$229$		−	1.39239e8i		−	0.766188i	−0.923709	−	0.383094i	$-0.874859\pi$
$229$		−	1.39239e8i		−	0.766188i	0.923709	−	0.383094i	$-0.125141\pi$
$230$	1.40587e6	+	2.43503e6i	0.00761897	+	0.0131964i
$231$	−2.86478e7	+	4.96194e7i	−0.152915	+	0.264856i
$232$	−1.47457e7	−	8.51345e6i	−0.0775279	−	0.0447608i
$233$	−6.42701e6			−0.0332861			−0.0166431	−	0.999861i	$-0.505298\pi$
$233$	−6.42701e6			−0.0332861			−0.0166431	+	0.999861i	$0.505298\pi$
$234$	1.96623e8	−	1.71121e8i	1.00318	−	0.873070i
$235$	1.38918e7			0.0698269
$236$	1.23851e8	+	7.15055e7i	0.613349	+	0.354117i
$237$	−9.72548e7	+	1.68450e8i	−0.474561	+	0.821964i
$238$	−7.15680e6	−	1.23959e7i	−0.0344112	−	0.0596019i
$239$		−	2.32090e8i		−	1.09967i	−0.835272	−	0.549837i	$-0.814690\pi$
$239$		−	2.32090e8i		−	1.09967i	0.835272	−	0.549837i	$-0.185310\pi$
$240$	−3.53747e6	+	2.04236e6i	−0.0165179	+	0.00953659i
$241$	−1.64784e8	+	9.51384e7i	−0.758327	+	0.437820i	−0.828695	−	0.559701i	$-0.810916\pi$
$241$	−1.64784e8	+	9.51384e7i	−0.758327	+	0.437820i	0.0703677	+	0.997521i	$0.477583\pi$
$242$			2.00042e8i			0.907335i
$243$	4.25720e7	+	7.37369e7i	0.190328	+	0.329657i
$244$	5.98203e7	−	1.03612e8i	0.263624	−	0.456609i
$245$	8.83328e6	+	5.09989e6i	0.0383743	+	0.0221554i
$246$	5.17326e7			0.221560
$247$	−2.64685e8	−	9.09669e7i	−1.11761	−	0.384100i
$248$	−1.13067e8			−0.470711
$249$	3.57386e8	+	2.06337e8i	1.46703	+	0.846992i
$250$	7.84452e6	−	1.35871e7i	0.0317524	−	0.0549967i
$251$	9.40925e7	+	1.62973e8i	0.375575	+	0.650516i	0.990413	−	0.138138i	$-0.0441118\pi$
$251$	9.40925e7	+	1.62973e8i	0.375575	+	0.650516i	−0.614838	+	0.788654i	$0.710778\pi$
$252$			2.84879e7i			0.112140i
$253$	1.61597e8	−	9.32978e7i	0.627351	−	0.362201i
$254$	−2.67916e8	+	1.54681e8i	−1.02584	+	0.592270i
$255$			1.64877e7i			0.0622687i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	7.14981e7	−	1.23838e8i	0.262741	−	0.455081i	−0.704228	−	0.709974i	$-0.748707\pi$
$257$	7.14981e7	−	1.23838e8i	0.262741	−	0.455081i	0.966969	+	0.254892i	$0.0820401\pi$
$258$	5.32425e8	+	3.07396e8i	1.93014	+	1.11437i
$259$	−2.06850e7			−0.0739786
$260$	6.02370e6	+	2.07022e6i	0.0212548	+	0.00730484i
$261$	1.36787e8			0.476216
$262$	−2.90262e8	−	1.67583e8i	−0.997093	−	0.575672i
$263$	1.87354e8	−	3.24506e8i	0.635063	−	1.09996i	−0.351438	−	0.936211i	$-0.614307\pi$
$263$	1.87354e8	−	3.24506e8i	0.635063	−	1.09996i	0.986502	−	0.163751i	$-0.0523594\pi$
$264$	1.35538e8	+	2.34758e8i	0.453364	+	0.785249i
$265$		−	2.01384e6i		−	0.00664760i
$266$	2.64906e7	−	1.52944e7i	0.0862992	−	0.0498249i
$267$	−2.96681e8	+	1.71289e8i	−0.953893	+	0.550730i
$268$			2.29558e8i			0.728486i
$269$	3.12901e8	+	5.41961e8i	0.980108	+	1.69760i	0.661928	+	0.749567i	$0.269738\pi$
$269$	3.12901e8	+	5.41961e8i	0.980108	+	1.69760i	0.318180	+	0.948030i	$0.396928\pi$
$270$	7.68361e6	−	1.33084e7i	0.0237570	−	0.0411484i
$271$	−1.80927e8	−	1.04458e8i	−0.552218	−	0.318823i	0.197798	−	0.980243i	$-0.436621\pi$
$271$	−1.80927e8	−	1.04458e8i	−0.552218	−	0.318823i	−0.750016	+	0.661419i	$0.769954\pi$
$272$	−6.77202e7			−0.204045
$273$	5.13264e7	−	4.46696e7i	0.152676	−	0.132875i
$274$	−5.05233e7			−0.148376
$275$	−4.50386e8	−	2.60031e8i	−1.30593	−	0.753981i
$276$	7.10536e7	−	1.23068e8i	0.203425	−	0.352342i
$277$	6.99093e7	+	1.21087e8i	0.197631	+	0.342308i	0.947760	−	0.318984i	$-0.103342\pi$
$277$	6.99093e7	+	1.21087e8i	0.197631	+	0.342308i	−0.750129	+	0.661292i	$0.770008\pi$
$278$			2.18655e8i			0.610384i
$279$	7.86641e8	−	4.54167e8i	2.16851	−	1.25199i
$280$	−602874.	+	348069.i	−0.00164124	+	0.000947573i
$281$		−	9.44593e7i		−	0.253964i	−0.991905	−	0.126982i	$-0.959471\pi$
$281$		−	9.44593e7i		−	0.253964i	0.991905	−	0.126982i	$-0.0405291\pi$
$282$	−3.51053e8	−	6.08041e8i	−0.932181	−	1.61459i
$283$	1.65237e8	−	2.86200e8i	0.433367	−	0.750614i	−0.563794	−	0.825916i	$-0.690659\pi$
$283$	1.65237e8	−	2.86200e8i	0.433367	−	0.750614i	0.997161	+	0.0753019i	$0.0239921\pi$
$284$	4.09653e7	+	2.36513e7i	0.106121	+	0.0612690i
$285$	−3.52350e7			−0.0901606
$286$	1.37387e8	−	3.99753e8i	0.347267	−	1.01044i
$287$	8.81653e6			0.0220146
$288$	1.16724e8	+	6.73908e7i	0.287930	+	0.166237i
$289$	6.84952e7	−	1.18637e8i	0.166924	−	0.289120i
$290$	1.67129e6	+	2.89475e6i	0.00402400	+	0.00696977i
$291$			6.78198e8i			1.61336i
$292$	−2.35545e8	+	1.35992e8i	−0.553647	+	0.319648i
$293$	−1.45881e8	+	8.42243e7i	−0.338814	+	0.195614i	−0.659747	−	0.751487i	$-0.729337\pi$
$293$	−1.45881e8	+	8.42243e7i	−0.338814	+	0.195614i	0.320934	+	0.947102i	$0.396003\pi$
$294$		−	5.15506e8i		−	1.18309i
$295$	−1.40373e7	−	2.43134e7i	−0.0318352	−	0.0551401i
$296$	−4.89322e7	+	8.47530e7i	−0.109666	+	0.189948i
$297$	−8.83190e8	−	5.09910e8i	−1.95617	−	1.12939i
$298$	−1.77750e8			−0.389093
$299$	−2.17499e8	+	4.24084e7i	−0.470553	+	0.0917493i
$300$	−3.96067e8			−0.846924
$301$	9.07385e7	+	5.23879e7i	0.191782	+	0.110726i
$302$	−1.87002e8	+	3.23898e8i	−0.390682	+	0.676680i
$303$	7.51538e8	+	1.30170e9i	1.55204	+	2.68820i
$304$		−	1.44721e8i		−	0.295443i
$305$	−2.03402e7	+	1.17434e7i	−0.0410492	+	0.0236998i
$306$	4.71150e8	−	2.72019e8i	0.940014	−	0.542717i
$307$			1.35886e8i			0.268034i	0.990979	+	0.134017i	$0.0427877\pi$
$307$			1.35886e8i			0.268034i	−0.990979	+	0.134017i	$0.957212\pi$
$308$	2.30990e7	+	4.00087e7i	0.0450470	+	0.0780237i
$309$	−4.42033e8	+	7.65624e8i	−0.852315	+	1.47625i
$310$	1.92226e7	+	1.10981e7i	0.0366476	+	0.0211585i
$311$	5.41703e8			1.02117			0.510587	−	0.859826i	$-0.329428\pi$
$311$	5.41703e8			1.02117			0.510587	+	0.859826i	$0.329428\pi$
$312$	−6.16085e7	−	3.15971e8i	−0.114842	−	0.588987i
$313$	−7.16256e8			−1.32027			−0.660135	−	0.751147i	$-0.729501\pi$
$313$	−7.16256e8			−1.32027			−0.660135	+	0.751147i	$0.729501\pi$
$314$	−3.87366e8	−	2.23646e8i	−0.706102	−	0.407668i
$315$	2.79625e6	−	4.84325e6i	0.00504068	−	0.00873072i
$316$	7.84176e7	+	1.35823e8i	0.139801	+	0.242142i
$317$			5.13860e6i			0.00906020i	0.999990	+	0.00453010i	$0.00144198\pi$
$317$			5.13860e6i			0.00906020i	−0.999990	+	0.00453010i	$0.998558\pi$
$318$	−8.81451e7	+	5.08906e7i	−0.153710	+	0.0887447i
$319$	1.92105e8	−	1.10912e8i	0.331338	−	0.191298i
$320$			3.29356e6i			0.00561876i
$321$	−1.46011e8	−	2.52899e8i	−0.246388	−	0.426756i
$322$	1.21093e7	−	2.09739e7i	0.0202127	−	0.0350094i
$323$	−5.05894e8	−	2.92078e8i	−0.835317	−	0.482270i
$324$	−2.00955e8			−0.328239
$325$	4.05458e8	+	4.65880e8i	0.655170	+	0.752805i
$326$	−2.90315e8			−0.464096
$327$	−1.06578e9	−	6.15331e8i	−1.68559	−	0.973176i
$328$	2.08563e7	−	3.61241e7i	0.0326346	−	0.0565248i
$329$	−5.98281e7	−	1.03625e8i	−0.0926232	−	0.160428i
$330$		−	5.32152e7i		−	0.0815149i
$331$	3.08173e8	−	1.77924e8i	0.467085	−	0.269672i	−0.247934	−	0.968777i	$-0.579751\pi$
$331$	3.08173e8	−	1.77924e8i	0.467085	−	0.269672i	0.715019	+	0.699105i	$0.246418\pi$
$332$	2.88164e8	−	1.66372e8i	0.432172	−	0.249515i
$333$		−	7.86204e8i		−	1.16676i
$334$	2.80288e8	+	4.85474e8i	0.411616	+	0.712940i
$335$	2.25325e7	−	3.90274e7i	0.0327455	−	0.0567169i
$336$	3.04697e7	+	1.75917e7i	0.0438209	+	0.0253000i
$337$	−4.39540e8			−0.625596			−0.312798	−	0.949820i	$-0.601266\pi$
$337$	−4.39540e8			−0.625596			−0.312798	+	0.949820i	$0.601266\pi$
$338$	−3.08596e8	+	3.95930e8i	−0.434692	+	0.557712i
$339$	1.53006e9			2.13309
$340$	1.15131e7	+	6.64712e6i	0.0158861	+	0.00917185i
$341$	7.36509e8	−	1.27567e9i	1.00586	−	1.74220i
$342$	5.81315e8	+	1.00687e9i	0.785815	+	1.36107i
$343$		−	1.76977e8i		−	0.236804i
$344$	4.29300e8	−	2.47857e8i	0.568599	−	0.328281i
$345$	−2.41597e7	+	1.39486e7i	−0.0316756	+	0.0182879i
$346$		−	5.05814e8i		−	0.656484i
$347$	−3.55843e8	−	6.16339e8i	−0.457199	−	0.791893i	0.541612	−	0.840628i	$-0.317814\pi$
$347$	−3.55843e8	−	6.16339e8i	−0.457199	−	0.791893i	−0.998812	+	0.0487358i	$0.984481\pi$
$348$	8.44682e7	−	1.46303e8i	0.107440	−	0.186091i
$349$	1.32703e9	+	7.66162e8i	1.67106	+	0.964787i	0.967046	+	0.254602i	$0.0819444\pi$
$349$	1.32703e9	+	7.66162e8i	1.67106	+	0.964787i	0.704015	+	0.710186i	$0.251389\pi$
$350$	−6.74998e7			−0.0841519
$351$	7.95086e8	+	9.13573e8i	0.981385	+	1.12763i
$352$	2.18571e8			0.267112
$353$	5.75284e7	+	3.32140e7i	0.0696099	+	0.0401893i	0.534401	−	0.845231i	$-0.320537\pi$
$353$	5.75284e7	+	3.32140e7i	0.0696099	+	0.0401893i	−0.464791	+	0.885420i	$0.653871\pi$
$354$	−7.09458e8	+	1.22882e9i	−0.849993	+	1.47223i
$355$	−4.64302e6	−	8.04195e6i	−0.00550809	−	0.00954030i
$356$			2.76224e8i			0.324479i
$357$	1.22989e8	−	7.10078e7i	0.143063	−	0.0825976i
$358$	3.89010e8	−	2.24595e8i	0.448095	−	0.258708i
$359$			1.24265e9i			1.41748i	0.705468	+	0.708742i	$0.250737\pi$
$359$			1.24265e9i			1.41748i	−0.705468	+	0.708742i	$0.749263\pi$
$360$	−1.32296e7	−	2.29143e7i	−0.0149447	−	0.0258850i
$361$	1.77248e8	−	3.07002e8i	0.198292	−	0.343452i
$362$	7.17265e8	+	4.14113e8i	0.794693	+	0.458816i
$363$	−1.98476e9			−2.17789
$364$	−1.04996e7	−	5.38493e7i	−0.0114109	−	0.0585228i
$365$	5.33934e7			0.0574728
$366$	1.02801e9	+	5.93521e8i	1.09601	+	0.632779i
$367$	−1.15229e7	+	1.99583e7i	−0.0121684	+	0.0210762i	−0.872045	−	0.489425i	$-0.837207\pi$
$367$	−1.15229e7	+	1.99583e7i	−0.0121684	+	0.0210762i	0.859877	+	0.510501i	$0.170540\pi$
$368$	−5.72913e7	−	9.92314e7i	−0.0599268	−	0.103796i
$369$			3.35102e8i			0.347204i
$370$	1.66380e7	−	9.60594e6i	0.0170763	−	0.00985902i
$371$	−1.50221e7	+	8.67303e6i	−0.0152729	+	0.00881784i
$372$		−	1.12182e9i		−	1.12985i
$373$	3.56036e8	+	6.16672e8i	0.355232	+	0.615280i	0.987158	−	0.159749i	$-0.0510684\pi$
$373$	3.56036e8	+	6.16672e8i	0.355232	+	0.615280i	−0.631925	+	0.775029i	$0.717735\pi$
$374$	4.41124e8	−	7.64050e8i	0.436024	−	0.755216i
$375$	1.34808e8	+	7.78312e7i	0.132009	+	0.0762157i
$376$	−5.66115e8			−0.549221
$377$	−2.58562e8	+	5.04149e7i	−0.248525	+	0.0484579i
$378$	−1.32364e8			−0.126052
$379$	−8.78626e8	−	5.07275e8i	−0.829023	−	0.478637i	0.0244948	−	0.999700i	$-0.492202\pi$
$379$	−8.78626e8	−	5.07275e8i	−0.829023	−	0.478637i	−0.853518	+	0.521063i	$0.825536\pi$
$380$	−1.42052e7	+	2.46041e7i	−0.0132802	+	0.0230019i
$381$	−1.53471e9	−	2.65819e9i	−1.42163	−	2.46234i
$382$		−	3.99799e8i		−	0.366961i
$383$	9.35938e8	−	5.40364e8i	0.851238	−	0.491463i	−0.00983015	−	0.999952i	$-0.503129\pi$
$383$	9.35938e8	−	5.40364e8i	0.851238	−	0.491463i	0.861068	+	0.508489i	$0.169796\pi$
$384$	1.44158e8	−	8.32295e7i	0.129921	−	0.0750098i
$385$		−	9.06920e6i		−	0.00809946i
$386$	1.91238e8	+	3.31234e8i	0.169246	+	0.293143i
$387$	−1.99118e9	+	3.44883e9i	−1.74631	+	3.02471i
$388$	4.73576e8	+	2.73419e8i	0.411603	+	0.237639i
$389$	−8.28300e8			−0.713450			−0.356725	−	0.934209i	$-0.616107\pi$
$389$	−8.28300e8			−0.713450			−0.356725	+	0.934209i	$0.616107\pi$
$390$	−2.05402e7	+	5.97655e7i	−0.0175339	+	0.0510182i
$391$	−4.62505e8			−0.391289
$392$	−3.59970e8	−	2.07829e8i	−0.301832	−	0.174263i
$393$	1.66271e9	−	2.87990e9i	1.38179	−	2.39334i
$394$	−9.55492e7	−	1.65496e8i	−0.0787028	−	0.136317i
$395$		−	3.07885e7i		−	0.0251362i
$396$	−1.52067e9	+	8.77958e8i	−1.23056	+	0.710461i
$397$	−7.06056e6	+	4.07642e6i	−0.00566334	+	0.00326973i	−0.502829	−	0.864386i	$-0.667707\pi$
$397$	−7.06056e6	+	4.07642e6i	−0.00566334	+	0.00326973i	0.497166	+	0.867656i	$0.334374\pi$
$398$		−	1.29028e9i		−	1.02587i
$399$	1.51747e8	+	2.62833e8i	0.119595	+	0.207145i
$400$	−1.59677e8	+	2.76568e8i	−0.124747	+	0.216069i
$401$	4.29147e8	+	2.47768e8i	0.332354	+	0.191885i	0.656886	−	0.753990i	$-0.271873\pi$
$401$	4.29147e8	+	2.47768e8i	0.332354	+	0.191885i	−0.324532	+	0.945875i	$0.605207\pi$
$402$	−2.27762e9			−1.74860
$403$	−1.31956e9	+	1.14842e9i	−1.00429	+	0.874041i
$404$	1.21195e9			0.914426
$405$	3.41644e7	+	1.97248e7i	0.0255553	+	0.0147544i
$406$	1.43955e7	−	2.49337e7i	0.0106754	−	0.0184904i
$407$	−6.37482e8	−	1.10415e9i	−0.468692	−	0.811798i
$408$		−	6.71901e8i		−	0.489773i
$409$	3.33752e8	−	1.92692e8i	0.241208	−	0.139262i	−0.374524	−	0.927217i	$-0.622194\pi$
$409$	3.33752e8	−	1.92692e8i	0.241208	−	0.139262i	0.615732	+	0.787956i	$0.288860\pi$
$410$	−7.09158e6	+	4.09432e6i	−0.00508159	+	0.00293386i
$411$		−	5.01278e8i		−	0.356149i
$412$	3.56416e8	+	6.17331e8i	0.251083	+	0.434888i
$413$	−1.20909e8	+	2.09421e8i	−0.0844568	+	0.146283i
$414$	7.97186e8	+	4.60256e8i	0.552152	+	0.318785i
$415$	−6.53213e7			−0.0448628
$416$	−2.45476e8	−	8.43649e7i	−0.167179	−	0.0574560i
$417$	−2.16944e9			−1.46511
$418$	1.63281e9	+	9.42702e8i	1.09350	+	0.631331i
$419$	−1.03381e9	+	1.79061e9i	−0.686579	+	1.18919i	0.286359	+	0.958122i	$0.407555\pi$
$419$	−1.03381e9	+	1.79061e9i	−0.686579	+	1.18919i	−0.972938	+	0.231067i	$0.925778\pi$
$420$	−3.45345e6	−	5.98155e6i	−0.00227447	−	0.00393950i
$421$			9.36163e8i			0.611454i	0.952119	+	0.305727i	$0.0988996\pi$
$421$			9.36163e8i			0.611454i	−0.952119	+	0.305727i	$0.901100\pi$
$422$	−5.39109e8	+	3.11255e8i	−0.349207	+	0.201615i
$423$	3.93864e9	−	2.27397e9i	2.53020	−	1.46081i
$424$			8.20673e7i			0.0522865i
$425$	6.44525e8	+	1.11635e9i	0.407266	+	0.705406i
$426$	−2.34662e8	+	4.06446e8i	−0.147065	+	0.254724i
$427$	1.75198e8	+	1.01151e8i	0.108901	+	0.0628741i
$428$	−2.35461e8			−0.145166
$429$	3.96624e9	+	1.36312e9i	2.42537	+	0.833551i
$430$	−9.73140e7			−0.0590250
$431$	−4.32169e8	−	2.49513e8i	−0.260006	−	0.150114i	0.364331	−	0.931269i	$-0.381298\pi$
$431$	−4.32169e8	−	2.49513e8i	−0.260006	−	0.150114i	−0.624337	+	0.781155i	$0.714631\pi$
$432$	−3.13120e8	+	5.42339e8i	−0.186860	+	0.323652i
$433$	−5.31056e8	−	9.19815e8i	−0.314364	−	0.544494i	0.664938	−	0.746898i	$-0.268458\pi$
$433$	−5.31056e8	−	9.19815e8i	−0.314364	−	0.544494i	−0.979302	+	0.202404i	$0.935124\pi$
$434$		−	1.91186e8i		−	0.112264i
$435$	−2.87209e7	+	1.65820e7i	−0.0167296	+	0.00965886i
$436$	−8.59353e8	+	4.96148e8i	−0.496557	+	0.286687i
$437$		−	9.88393e8i		−	0.566558i
$438$	−1.34927e9	−	2.33701e9i	−0.767256	−	1.32893i
$439$	−4.98585e8	+	8.63575e8i	−0.281264	+	0.487163i	−0.971696	−	0.236234i	$-0.924087\pi$
$439$	−4.98585e8	+	8.63575e8i	−0.281264	+	0.487163i	0.690433	+	0.723397i	$0.257420\pi$
$440$	−3.71594e7	−	2.14540e7i	−0.0207962	−	0.0120067i
$441$	3.33923e9			1.85401
$442$	−7.90334e8	+	6.87832e8i	−0.435344	+	0.378882i
$443$	3.24508e8			0.177342			0.0886711	−	0.996061i	$-0.471738\pi$
$443$	3.24508e8			0.177342			0.0886711	+	0.996061i	$0.471738\pi$
$444$	−8.40897e8	−	4.85492e8i	−0.455934	−	0.263234i
$445$	2.71129e7	−	4.69609e7i	0.0145853	−	0.0252625i
$446$	2.75830e8	+	4.77752e8i	0.147221	+	0.254994i
$447$		−	1.76359e9i		−	0.933944i
$448$	2.45681e7	−	1.41844e7i	0.0129092	−	0.00745311i
$449$	7.38956e8	−	4.26636e8i	0.385262	−	0.222431i	−0.294843	−	0.955546i	$-0.595267\pi$
$449$	7.38956e8	−	4.26636e8i	0.385262	−	0.222431i	0.680105	+	0.733115i	$0.261934\pi$
$450$		−	2.56556e9i		−	1.32721i
$451$	2.71713e8	+	4.70620e8i	0.139474	+	0.241575i
$452$	6.16851e8	−	1.06842e9i	0.314192	−	0.544197i
$453$	−3.21363e9	−	1.85539e9i	−1.62425	−	0.937759i
$454$	−1.17879e8			−0.0591208
$455$	−3.50056e6	+	1.01855e7i	−0.00174220	+	0.00506926i
$456$	1.43588e9			0.709156
$457$	1.20028e9	+	6.92980e8i	0.588267	+	0.339636i	0.764412	−	0.644728i	$-0.223029\pi$
$457$	1.20028e9	+	6.92980e8i	0.588267	+	0.339636i	−0.176145	+	0.984364i	$0.556363\pi$
$458$	5.56954e8	−	9.64673e8i	0.270888	−	0.469192i
$459$	1.26389e9	+	2.18912e9i	0.610048	+	1.05663i
$460$			2.24938e7i			0.0107749i
$461$	−2.17739e9	+	1.25712e9i	−1.03510	+	0.597616i	−0.918442	−	0.395556i	$-0.870552\pi$
$461$	−2.17739e9	+	1.25712e9i	−1.03510	+	0.597616i	−0.116659	+	0.993172i	$0.537219\pi$
$462$	−3.96955e8	+	2.29182e8i	−0.187281	+	0.108127i
$463$			3.33173e9i			1.56004i	0.625753	+	0.780021i	$0.284792\pi$
$463$			3.33173e9i			1.56004i	−0.625753	+	0.780021i	$0.715208\pi$
$464$	−6.81076e7	−	1.17966e8i	−0.0316506	−	0.0548205i
$465$	−1.10113e8	+	1.90721e8i	−0.0507870	+	0.0879656i
$466$	−4.45276e7	−	2.57080e7i	−0.0203835	−	0.0117684i
$467$	−1.46658e9			−0.666342			−0.333171	−	0.942866i	$-0.608119\pi$
$467$	−1.46658e9			−0.666342			−0.333171	+	0.942866i	$0.608119\pi$
$468$	2.04673e9	−	3.99074e8i	0.922995	−	0.179967i
$469$	−3.88163e8			−0.173744
$470$	9.62456e7	+	5.55674e7i	0.0427600	+	0.0246875i
$471$	2.21895e9	−	3.84334e9i	0.978531	−	1.69487i
$472$	5.72044e8	+	9.90809e8i	0.250399	+	0.433703i
$473$			6.45808e9i			2.80601i
$474$	−1.34760e9	+	7.78039e8i	−0.581216	+	0.335565i
$475$	−2.38569e9	+	1.37738e9i	−1.02138	+	0.589692i
$476$		−	1.14509e8i		−	0.0486647i
$477$	−3.29648e8	−	5.70967e8i	−0.139071	−	0.240878i
$478$	9.28361e8	−	1.60797e9i	0.388794	−	0.673410i
$479$	3.18752e9	+	1.84031e9i	1.32519	+	0.765099i	0.984552	−	0.175095i	$-0.0560232\pi$
$479$	3.18752e9	+	1.84031e9i	1.32519	+	0.765099i	0.340639	+	0.940194i	$0.389357\pi$
$480$	−3.26778e7			−0.0134868
$481$	2.89766e8	+	1.48612e9i	0.118724	+	0.608900i
$482$	−1.52221e9			−0.619172
$483$	2.08098e8	+	1.20145e8i	0.0840335	+	0.0485167i
$484$	−8.00168e8	+	1.38593e9i	−0.320791	+	0.555627i
$485$	−5.36753e7	−	9.29683e7i	−0.0213638	−	0.0370032i
$486$			6.81152e8i			0.269164i
$487$	3.30378e9	−	1.90744e9i	1.29616	−	0.748340i	0.316424	−	0.948618i	$-0.397518\pi$
$487$	3.30378e9	−	1.90744e9i	1.29616	−	0.748340i	0.979739	+	0.200278i	$0.0641845\pi$
$488$	8.28894e8	−	4.78562e8i	0.322872	−	0.186410i
$489$		−	2.88043e9i		−	1.11398i
$490$	4.07992e7	+	7.06662e7i	0.0156662	+	0.0271347i
$491$	2.14842e9	−	3.72118e9i	0.819096	−	1.41872i	−0.0872534	−	0.996186i	$-0.527809\pi$
$491$	2.14842e9	−	3.72118e9i	0.819096	−	1.41872i	0.906349	−	0.422529i	$-0.138858\pi$
$492$	3.58414e8	+	2.06930e8i	0.135677	+	0.0783333i
$493$	−5.49824e8			−0.206661
$494$	−1.46993e9	−	1.68898e9i	−0.548594	−	0.630347i
$495$	3.44706e8			0.127741
$496$	−7.83350e8	−	4.52267e8i	−0.288250	−	0.166421i
$497$	−3.99923e7	+	6.92686e7i	−0.0146126	+	0.0253098i
$498$	1.65070e9	+	2.85909e9i	0.598914	+	1.03735i
$499$		−	1.52473e9i		−	0.549341i	−0.961538	−	0.274670i	$-0.911431\pi$
$499$		−	1.52473e9i		−	0.549341i	0.961538	−	0.274670i	$-0.0885687\pi$
$500$	1.08697e8	−	6.27561e7i	0.0388886	−	0.0224523i
$501$	−4.81674e9	+	2.78095e9i	−1.71128	+	0.988008i
$502$			1.50548e9i			0.531144i
$503$	−1.40843e9	−	2.43947e9i	−0.493454	−	0.854687i	0.506518	−	0.862229i	$-0.330932\pi$
$503$	−1.40843e9	−	2.43947e9i	−0.493454	−	0.854687i	−0.999972	+	0.00754273i	$0.997599\pi$
$504$	−1.13952e8	+	1.97370e8i	−0.0396474	+	0.0686712i
$505$	−2.06044e8	−	1.18959e8i	−0.0711933	−	0.0411035i
$506$	1.49277e9			0.512230
$507$	−3.92831e9	−	3.06181e9i	−1.33868	−	1.04340i
$508$	−2.47490e9			−0.837596
$509$	−4.95616e9	−	2.86144e9i	−1.66584	−	0.961772i	−0.969844	−	0.243725i	$-0.921630\pi$
$509$	−4.95616e9	−	2.86144e9i	−1.66584	−	0.961772i	−0.695994	−	0.718047i	$-0.745036\pi$
$510$	−6.59509e7	+	1.14230e8i	−0.0220153	+	0.0381317i
$511$	−2.29950e8	−	3.98285e8i	−0.0762360	−	0.132045i
$512$		−	1.34218e8i		−	0.0441942i
$513$	−4.67824e9	+	2.70098e9i	−1.52993	+	0.883305i
$514$	9.90707e8	−	5.71985e8i	0.321791	−	0.185786i
$515$		−	1.39937e8i		−	0.0451448i
$516$	2.45917e9	+	4.25940e9i	0.787977	+	1.36482i
$517$	3.68764e9	−	6.38717e9i	1.17363	−	2.03279i
$518$	−1.43310e8	−	8.27400e7i	−0.0453025	−	0.0261554i
$519$	5.01855e9			1.57577
$520$	3.34525e7	+	3.84377e7i	0.0104332	+	0.0119880i
$521$	−1.74794e9			−0.541496			−0.270748	−	0.962650i	$-0.587271\pi$
$521$	−1.74794e9			−0.541496			−0.270748	+	0.962650i	$0.587271\pi$
$522$	9.47691e8	+	5.47150e8i	0.291622	+	0.168368i
$523$	8.72984e8	−	1.51205e9i	0.266840	−	0.462180i	−0.701204	−	0.712960i	$-0.747354\pi$
$523$	8.72984e8	−	1.51205e9i	0.266840	−	0.462180i	0.968044	+	0.250781i	$0.0806873\pi$
$524$	−1.34066e9	−	2.32210e9i	−0.407061	−	0.705051i
$525$		−	6.69714e8i		−	0.201991i
$526$	2.59605e9	−	1.49883e9i	0.777791	−	0.449058i
$527$	−3.16194e9	+	1.82555e9i	−0.941059	+	0.543321i
$528$			2.16860e9i			0.641153i
$529$	1.31113e9	+	2.27095e9i	0.385081	+	0.666980i
$530$	8.05536e6	−	1.39523e7i	0.00235028	−	0.00407081i
$531$	−7.95977e9	−	4.59557e9i	−2.30712	−	1.33201i
$532$	2.44710e8			0.0704630
$533$	−1.23507e8	−	6.33427e8i	−0.0353301	−	0.181197i
$534$	−2.74062e9			−0.778850
$535$	4.00309e7	+	2.31118e7i	0.0113020	+	0.00652523i
$536$	−9.18234e8	+	1.59043e9i	−0.257559	+	0.446105i
$537$	2.22837e9	+	3.85965e9i	0.620979	+	1.07557i
$538$			5.00642e9i			1.38608i
$539$	4.68964e9	−	2.70757e9i	1.28997	−	0.744764i
$540$	1.06467e8	−	6.14689e7i	0.0290963	−	0.0167988i
$541$			3.07314e8i			0.0834433i	0.999129	+	0.0417217i	$0.0132843\pi$
$541$			3.07314e8i			0.0834433i	−0.999129	+	0.0417217i	$0.986716\pi$
$542$	−8.35666e8	−	1.44742e9i	−0.225442	−	0.390477i
$543$	−4.10872e9	+	7.11651e9i	−1.10130	+	1.90751i
$544$	−4.69179e8	−	2.70881e8i	−0.124952	−	0.0721410i
$545$	1.94799e8			0.0515464
$546$	5.34278e8	−	1.04174e8i	0.140473	−	0.0273897i
$547$	2.37307e9			0.619947			0.309973	−	0.950745i	$-0.399680\pi$
$547$	2.37307e9			0.619947			0.309973	+	0.950745i	$0.399680\pi$
$548$	−3.50035e8	−	2.02093e8i	−0.0908615	−	0.0524589i
$549$	−3.84458e9	+	6.65901e9i	−0.991621	+	1.71754i
$550$	−2.08025e9	−	3.60309e9i	−0.533145	−	0.923434i
$551$		−	1.17500e9i		−	0.299231i
$552$	9.84547e8	−	5.68429e8i	0.249144	−	0.143843i
$553$	−2.29665e8	+	1.32597e8i	−0.0577507	+	0.0333424i
$554$			1.11855e9i			0.279493i
$555$	9.53075e7	+	1.65078e8i	0.0236647	+	0.0409885i
$556$	−8.74621e8	+	1.51489e9i	−0.215803	+	0.373782i
$557$	2.40567e9	+	1.38891e9i	0.589851	+	0.340551i	0.765039	−	0.643984i	$-0.222720\pi$
$557$	2.40567e9	+	1.38891e9i	0.589851	+	0.340551i	−0.175188	+	0.984535i	$0.556053\pi$
$558$	7.26668e9			1.77058
$559$	2.49271e9	−	7.25302e9i	0.603575	−	1.75621i
$560$	−5.56911e6			−0.00134007
$561$	7.58070e9	+	4.37672e9i	1.81276	+	1.04659i
$562$	3.77837e8	−	6.54433e8i	0.0897899	−	0.155521i
$563$	3.36862e9	+	5.83462e9i	0.795559	+	1.37795i	0.922484	+	0.386036i	$0.126156\pi$
$563$	3.36862e9	+	5.83462e9i	0.795559	+	1.37795i	−0.126924	+	0.991912i	$0.540511\pi$
$564$		−	5.61684e9i		−	1.31830i
$565$	−2.09742e8	+	1.21095e8i	−0.0489234	+	0.0282459i
$566$	2.28960e9	−	1.32190e9i	0.530764	−	0.306437i
$567$		−	3.39797e8i		−	0.0782849i
$568$	1.89211e8	+	3.27722e8i	0.0433238	+	0.0750390i
$569$	2.30137e9	−	3.98610e9i	0.523714	−	0.907100i	−0.475905	−	0.879497i	$-0.657879\pi$
$569$	2.30137e9	−	3.98610e9i	0.523714	−	0.907100i	0.999619	−	0.0276028i	$-0.00878735\pi$
$570$	−2.44115e8	−	1.40940e8i	−0.0552119	−	0.0318766i
$571$	−5.31765e9			−1.19535			−0.597673	−	0.801740i	$-0.703908\pi$
$571$	−5.31765e9			−1.19535			−0.597673	+	0.801740i	$0.703908\pi$
$572$	2.55085e9	−	2.22002e9i	0.569901	−	0.495988i
$573$	3.96670e9			0.880821
$574$	6.10827e7	+	3.52661e7i	0.0134811	+	0.00778334i
$575$	−1.09054e9	+	1.88886e9i	−0.239223	+	0.414346i
$576$	5.39126e8	+	9.33794e8i	0.117547	+	0.203597i
$577$		−	2.20076e9i		−	0.476934i	−0.971151	−	0.238467i	$-0.923355\pi$
$577$		−	2.20076e9i		−	0.476934i	0.971151	−	0.238467i	$-0.0766449\pi$
$578$	9.49098e8	−	5.47962e8i	0.204439	−	0.118033i
$579$	−3.28642e9	+	1.89741e9i	−0.703635	+	0.406244i
$580$			2.67406e7i			0.00569079i
$581$	2.81320e8	+	4.87260e8i	0.0595092	+	0.103073i
$582$	−2.71279e9	+	4.69869e9i	−0.570409	+	0.987977i
$583$	−9.25921e8	−	5.34581e8i	−0.193524	−	0.111731i
$584$	−2.17587e9			−0.452051
$585$	−3.87136e8	−	1.33051e8i	−0.0799500	−	0.0274772i
$586$	−1.34759e9			−0.276640
$587$	4.80872e9	+	2.77632e9i	0.981287	+	0.566546i	0.902658	−	0.430358i	$-0.141613\pi$
$587$	4.80872e9	+	2.77632e9i	0.981287	+	0.566546i	0.0786286	+	0.996904i	$0.474946\pi$
$588$	2.06202e9	−	3.57153e9i	0.418285	−	0.724492i
$589$	−3.90127e9	−	6.75721e9i	−0.786689	−	1.36258i
$590$		−	2.24597e8i		−	0.0450217i
$591$	1.64201e9	−	9.48014e8i	0.327204	−	0.188912i
$592$	−6.78024e8	+	3.91458e8i	−0.134313	+	0.0775459i
$593$			5.70359e9i			1.12320i	0.827409	+	0.561600i	$0.189814\pi$
$593$			5.70359e9i			1.12320i	−0.827409	+	0.561600i	$0.810186\pi$
$594$	−4.07928e9	−	7.06552e9i	−0.798603	−	1.38322i
$595$	−1.12397e7	+	1.94677e7i	−0.00218748	+	0.00378883i
$596$	−1.23149e9	−	7.11000e8i	−0.238270	−	0.137565i
$597$	1.28018e10			2.46241
$598$	−1.67651e9	−	5.76183e8i	−0.320592	−	0.110181i
$599$	3.84338e9			0.730666			0.365333	−	0.930877i	$-0.380955\pi$
$599$	3.84338e9			0.730666			0.365333	+	0.930877i	$0.380955\pi$
$600$	−2.74403e9	−	1.58427e9i	−0.518633	−	0.299433i
$601$	5.56311e8	−	9.63559e8i	0.104534	−	0.181058i	−0.809014	−	0.587790i	$-0.799998\pi$
$601$	5.56311e8	−	9.63559e8i	0.104534	−	0.181058i	0.913548	+	0.406732i	$0.133332\pi$
$602$	4.19103e8	+	7.25908e8i	0.0782949	+	0.135611i
$603$		−	1.47535e10i		−	2.74021i
$604$	−2.59118e9	+	1.49602e9i	−0.478485	+	0.276254i
$605$	2.72074e8	−	1.57082e8i	0.0499509	−	0.0288392i
$606$			1.20246e10i			2.19491i
$607$	−1.02746e8	−	1.77961e8i	−0.0186468	−	0.0322972i	0.856551	−	0.516062i	$-0.172602\pi$
$607$	−1.02746e8	−	1.77961e8i	−0.0186468	−	0.0322972i	−0.875198	+	0.483764i	$0.839269\pi$
$608$	5.78883e8	−	1.00266e9i	0.104455	−	0.180921i
$609$	2.47385e8	+	1.42828e8i	0.0443827	+	0.0256244i
$610$	−1.87894e8			−0.0335165
$611$	−6.60690e9	+	5.75001e9i	−1.17180	+	1.01982i
$612$	4.35230e9			0.767518
$613$	2.52066e9	+	1.45530e9i	0.441979	+	0.255177i	0.704437	−	0.709767i	$-0.251200\pi$
$613$	2.52066e9	+	1.45530e9i	0.441979	+	0.255177i	−0.262458	+	0.964944i	$0.584533\pi$
$614$	−5.43543e8	+	9.41444e8i	−0.0947643	+	0.164137i
$615$	−4.06228e7	−	7.03607e7i	−0.00704217	−	0.0121974i
$616$			3.69584e8i			0.0637061i
$617$	−6.36384e9	+	3.67416e9i	−1.09074	+	0.629739i	−0.933773	−	0.357865i	$-0.883505\pi$
$617$	−6.36384e9	+	3.67416e9i	−1.09074	+	0.629739i	−0.156966	+	0.987604i	$0.550171\pi$
$618$	−6.12499e9	+	3.53627e9i	−1.04387	+	0.602678i
$619$		−	1.10538e9i		−	0.187324i	−0.995604	−	0.0936619i	$-0.970143\pi$
$619$		−	1.10538e9i		−	0.187324i	0.995604	−	0.0936619i	$-0.0298573\pi$
$620$	8.87852e7	+	1.53780e8i	0.0149613	+	0.0259137i
$621$	−2.13850e9	+	3.70399e9i	−0.358334	+	0.620653i
$622$	3.75303e9	+	2.16681e9i	0.625339	+	0.361040i
$623$	−4.67070e8			−0.0773880
$624$	8.37046e8	−	2.43554e9i	0.137912	−	0.401282i
$625$	6.06654e9			0.993943
$626$	−4.96237e9	−	2.86502e9i	−0.808497	−	0.466786i
$627$	−9.35323e9	+	1.62003e10i	−1.51539	+	2.62474i
$628$	−1.78917e9	−	3.09893e9i	−0.288265	−	0.499289i
$629$			3.16019e9i			0.506332i
$630$	3.87460e7	−	2.23700e7i	0.00617355	−	0.00356430i
$631$	3.96548e9	−	2.28947e9i	0.628337	−	0.362771i	−0.151771	−	0.988416i	$-0.548498\pi$
$631$	3.96548e9	−	2.28947e9i	0.628337	−	0.362771i	0.780108	+	0.625645i	$0.215164\pi$
$632$			1.25468e9i			0.197708i
$633$	−3.08818e9	−	5.34889e9i	−0.483938	−	0.838206i
$634$	−2.05544e7	+	3.56013e7i	−0.00320326	+	0.00554822i
$635$	4.20759e8	+	2.42925e8i	0.0652117	+	0.0376500i
$636$	−8.14249e8			−0.125504
$637$	−6.31198e9	+	1.23072e9i	−0.967559	+	0.188656i
$638$	1.77459e9			0.270537
$639$	−2.63279e9	−	1.52004e9i	−0.399175	−	0.230464i
$640$	−1.31742e7	+	2.28184e7i	−0.00198653	+	0.00344077i
$641$	−4.74954e9	−	8.22645e9i	−0.712277	−	1.23370i	−0.964001	−	0.265900i	$-0.914331\pi$
$641$	−4.74954e9	−	8.22645e9i	−0.712277	−	1.23370i	0.251724	−	0.967799i	$-0.419003\pi$
$642$		−	2.33618e9i		−	0.348445i
$643$	−2.50812e9	+	1.44807e9i	−0.372058	+	0.214808i	−0.674357	−	0.738405i	$-0.735579\pi$
$643$	−2.50812e9	+	1.44807e9i	−0.372058	+	0.214808i	0.302299	+	0.953213i	$0.402246\pi$
$644$	1.67791e8	−	9.68744e7i	0.0247554	−	0.0142925i
$645$		−	9.65524e8i		−	0.141678i
$646$	−2.33663e9	−	4.04716e9i	−0.341017	−	0.590658i
$647$	6.01700e9	−	1.04217e10i	0.873403	−	1.51278i	0.0149496	−	0.999888i	$-0.495241\pi$
$647$	6.01700e9	−	1.04217e10i	0.873403	−	1.51278i	0.858454	−	0.512891i	$-0.171425\pi$
$648$	−1.39226e9	−	8.03819e8i	−0.201005	−	0.116050i
$649$	−1.49050e10			−2.14031
$650$	9.45573e8	+	4.84954e9i	0.135051	+	0.692635i
$651$	1.89689e9			0.269470
$652$	−2.01136e9	−	1.16126e9i	−0.284200	−	0.164083i
$653$	−3.16905e9	+	5.48896e9i	−0.445383	+	0.771426i	−0.998079	−	0.0619574i	$-0.980266\pi$
$653$	−3.16905e9	+	5.48896e9i	−0.445383	+	0.771426i	0.552696	+	0.833383i	$0.313599\pi$
$654$	−4.92265e9	−	8.52627e9i	−0.688140	−	1.19189i
$655$			5.26374e8i			0.0731897i
$656$	2.88993e8	−	1.66850e8i	0.0399691	−	0.0230762i
$657$	1.51382e10	−	8.74003e9i	2.08255	−	1.20236i
$658$		−	9.57250e8i		−	0.130989i
$659$	4.10410e9	+	7.10851e9i	0.558623	+	0.967564i	0.997612	+	0.0690711i	$0.0220035\pi$
$659$	4.10410e9	+	7.10851e9i	0.558623	+	0.967564i	−0.438989	+	0.898493i	$0.644663\pi$
$660$	2.12861e8	−	3.68686e8i	0.0288199	−	0.0499175i
$661$	7.68984e8	+	4.43973e8i	0.103565	+	0.0597931i	0.550888	−	0.834579i	$-0.314289\pi$
$661$	7.68984e8	+	4.43973e8i	0.103565	+	0.0597931i	−0.447323	+	0.894372i	$0.647623\pi$
$662$	2.84678e9			0.381373
$663$	−6.82448e9	−	7.84148e9i	−0.909436	−	1.04496i
$664$	2.66195e9			0.352867
$665$	−4.16033e7	−	2.40197e7i	−0.00548595	−	0.00316731i
$666$	3.14482e9	−	5.44698e9i	0.412511	−	0.714490i
$667$	−4.65151e8	−	8.05666e8i	−0.0606951	−	0.105127i
$668$			4.48461e9i			0.582113i
$669$	−4.74013e9	+	2.73672e9i	−0.612067	+	0.353377i
$670$	3.12219e8	−	1.80260e8i	0.0401049	−	0.0231546i
$671$			1.24693e10i			1.59336i
$672$	1.40734e8	+	2.43758e8i	0.0178898	+	0.0309860i
$673$	1.94451e9	−	3.36798e9i	0.245899	−	0.425909i	−0.716485	−	0.697602i	$-0.754250\pi$
$673$	1.94451e9	−	3.36798e9i	0.245899	−	0.425909i	0.962384	+	0.271693i	$0.0875836\pi$
$674$	−3.04523e9	−	1.75816e9i	−0.383098	−	0.221182i
$675$	1.19204e10			1.49186
$676$	−3.72174e9	+	1.50870e9i	−0.463375	+	0.187840i
$677$	2.22163e9			0.275176			0.137588	−	0.990490i	$-0.456065\pi$
$677$	2.22163e9			0.275176			0.137588	+	0.990490i	$0.456065\pi$
$678$	1.06005e10	+	6.12023e9i	1.30624	+	0.754160i
$679$	−4.62328e8	+	8.00775e8i	−0.0566768	+	0.0981672i
$680$	5.31769e7	+	9.21051e7i	0.00648548	+	0.0112332i
$681$		−	1.16956e9i		−	0.141908i
$682$	1.02054e10	−	5.89208e9i	1.23192	−	0.711251i
$683$	4.37929e8	−	2.52838e8i	0.0525934	−	0.0303648i	−0.473473	−	0.880808i	$-0.657000\pi$
$683$	4.37929e8	−	2.52838e8i	0.0525934	−	0.0303648i	0.526066	+	0.850444i	$0.323666\pi$
$684$			9.30105e9i			1.11131i
$685$	3.96731e7	+	6.87159e7i	0.00471606	+	0.00816846i
$686$	7.07910e8	−	1.22614e9i	0.0837227	−	0.145012i
$687$	9.57122e9	+	5.52595e9i	1.12621	+	0.650217i
$688$	3.96570e9			0.464259
$689$	8.33555e8	+	9.57773e8i	0.0970883	+	0.111557i
$690$	−2.23178e8			−0.0258630
$691$	−2.74012e8	−	1.58201e8i	−0.0315934	−	0.0182405i	0.484120	−	0.875002i	$-0.339140\pi$
$691$	−2.74012e8	−	1.58201e8i	−0.0315934	−	0.0182405i	−0.515714	+	0.856761i	$0.672473\pi$
$692$	2.02325e9	−	3.50438e9i	0.232102	−	0.402013i
$693$	−1.48455e9	−	2.57131e9i	−0.169445	−	0.293487i
$694$		−	5.69349e9i		−	0.646578i
$695$	2.97389e8	−	1.71698e8i	0.0336031	−	0.0194007i
$696$	1.17043e9	−	6.75745e8i	0.131586	−	0.0759715i
$697$		−	1.34696e9i		−	0.150675i
$698$	6.12930e9	+	1.06163e10i	0.682208	+	1.18162i
$699$	2.55068e8	−	4.41791e8i	0.0282479	−	0.0489268i
$700$	−4.67652e8	−	2.69999e8i	−0.0515323	−	0.0297522i
$701$	1.61152e9			0.176695			0.0883474	−	0.996090i	$-0.471841\pi$
$701$	1.61152e9			0.176695			0.0883474	+	0.996090i	$0.471841\pi$
$702$	1.85423e9	+	9.50976e9i	0.202294	+	1.03750i
$703$	−6.75345e9			−0.733132
$704$	1.51431e9	+	8.74285e8i	0.163572	+	0.0944384i
$705$	−5.51325e8	+	9.54922e8i	−0.0592578	+	0.102638i
$706$	2.65712e8	+	4.60227e8i	0.0284181	+	0.0492216i
$707$			2.04929e9i			0.218090i
$708$	−9.83054e9	+	5.67566e9i	−1.04102	+	0.601036i
$709$	−3.75698e9	+	2.16909e9i	−0.395892	+	0.228568i	−0.684710	−	0.728816i	$-0.740071\pi$
$709$	−3.75698e9	+	2.16909e9i	−0.395892	+	0.228568i	0.288818	+	0.957384i	$0.406738\pi$
$710$		−	7.42883e7i		−	0.00778962i
$711$	−5.03981e9	−	8.72921e9i	−0.525861	−	0.910817i
$712$	−1.10490e9	+	1.91373e9i	−0.114721	+	0.198702i
$713$	−5.35001e9	−	3.08883e9i	−0.552766	−	0.319139i
$714$	1.13612e9			0.116811
$715$	−6.51580e8	+	1.27046e8i	−0.0666648	+	0.0129984i
$716$	3.59352e9			0.365868
$717$	1.59538e10	+	9.21094e9i	1.61640	+	0.933227i
$718$	−4.97060e9	+	8.60932e9i	−0.501156	+	0.868028i
$719$	3.85660e9	+	6.67982e9i	0.386949	+	0.670215i	0.992037	−	0.125943i	$-0.0401958\pi$
$719$	3.85660e9	+	6.67982e9i	0.386949	+	0.670215i	−0.605089	+	0.796158i	$0.706862\pi$
$720$		−	2.11673e8i		−	0.0211350i
$721$	−1.04385e9	+	6.02668e8i	−0.103721	+	0.0598832i
$722$	2.45602e9	−	1.41798e9i	0.242857	−	0.140214i
$723$		−	1.51030e10i		−	1.48621i
$724$	3.31290e9	+	5.73812e9i	0.324432	+	0.561933i
$725$	−1.29642e9	+	2.24547e9i	−0.126347	+	0.218839i
$726$	−1.37508e10	−	7.93905e9i	−1.33368	−	0.770000i
$727$	5.18765e9			0.500726			0.250363	−	0.968152i	$-0.419450\pi$
$727$	5.18765e9			0.500726			0.250363	+	0.968152i	$0.419450\pi$
$728$	1.42654e8	−	4.15077e8i	0.0137032	−	0.0398721i
$729$	−1.36252e10			−1.30256
$730$	3.69920e8	+	2.13574e8i	0.0351948	+	0.0203197i
$731$	8.00366e9	−	1.38627e10i	0.757840	−	1.31262i
$732$	4.74817e9	+	8.22407e9i	0.447442	+	0.774993i
$733$		−	8.08992e9i		−	0.758718i	−0.925250	−	0.379359i	$-0.876145\pi$
$733$		−	8.08992e9i		−	0.758718i	0.925250	−	0.379359i	$-0.123855\pi$
$734$	−1.59667e8	+	9.21836e7i	−0.0149031	+	0.00860434i
$735$	−7.01131e8	+	4.04798e8i	−0.0651319	+	0.0376039i
$736$		−	9.16660e8i		−	0.0847493i
$737$	−1.19626e10	−	2.07199e10i	−1.10075	−	1.90656i
$738$	−1.34041e9	+	2.32166e9i	−0.122755	+	0.212618i
$739$	1.33487e10	+	7.70687e9i	1.21670	+	0.702461i	0.964210	−	0.265139i	$-0.0854177\pi$
$739$	1.33487e10	+	7.70687e9i	1.21670	+	0.702461i	0.252488	+	0.967600i	$0.418751\pi$
$740$	1.53695e8			0.0139428
$741$	1.67576e10	−	1.45842e10i	1.51303	−	1.31680i
$742$	−1.38768e8			−0.0124703
$743$	−1.46083e10	−	8.43411e9i	−1.30659	−	0.754360i	−0.325064	−	0.945692i	$-0.605386\pi$
$743$	−1.46083e10	−	8.43411e9i	−1.30659	−	0.754360i	−0.981525	+	0.191332i	$0.938719\pi$
$744$	4.48727e9	−	7.77219e9i	0.399464	−	0.691891i
$745$	1.39577e8	+	2.41755e8i	0.0123671	+	0.0214205i
$746$			5.69657e9i			0.502374i
$747$	−1.85200e10	+	1.06925e10i	−1.62562	+	0.938552i
$748$	6.11240e9	−	3.52900e9i	0.534018	−	0.308316i
$749$		−	3.98144e8i		−	0.0346221i
$750$	6.22649e8	+	1.07846e9i	0.0538926	+	0.0933447i
$751$	−8.99510e9	+	1.55800e10i	−0.774937	+	1.34223i	0.159894	+	0.987134i	$0.448885\pi$
$751$	−8.99510e9	+	1.55800e10i	−0.774937	+	1.34223i	−0.934830	+	0.355095i	$0.884448\pi$
$752$	−3.92216e9	−	2.26446e9i	−0.336328	−	0.194179i
$753$	−1.49370e10			−1.27491
$754$	−1.99303e9	−	6.84964e8i	−0.169322	−	0.0581926i
$755$	5.87371e8			0.0496705
$756$	−9.17047e8	−	5.29457e8i	−0.0771907	−	0.0445661i
$757$	5.08895e9	−	8.81431e9i	0.426375	−	0.738504i	−0.570172	−	0.821525i	$-0.693124\pi$
$757$	5.08895e9	−	8.81431e9i	0.426375	−	0.738504i	0.996548	+	0.0830211i	$0.0264569\pi$
$758$	−4.05820e9	−	7.02901e9i	−0.338447	−	0.586208i
$759$			1.48108e10i			1.22951i
$760$	−1.96833e8	+	1.13641e8i	−0.0162648	+	0.00939050i
$761$	−1.78234e10	+	1.02904e10i	−1.46604	+	0.846417i	−0.999279	−	0.0379689i	$-0.987911\pi$
$761$	−1.78234e10	+	1.02904e10i	−1.46604	+	0.846417i	−0.466757	+	0.884385i	$0.654578\pi$
$762$		−	2.45553e10i		−	2.01049i
$763$	−8.38942e8	−	1.45309e9i	−0.0683748	−	0.118429i
$764$	1.59920e9	−	2.76989e9i	0.129740	−	0.224717i
$765$	−7.39936e8	−	4.27203e8i	−0.0597557	−	0.0345000i
$766$	8.64582e9			0.695033
$767$	1.67397e10	+	5.75309e9i	1.33957	+	0.460381i
$768$	1.33167e9			0.106080
$769$	7.04864e9	+	4.06953e9i	0.558937	+	0.322702i	0.752719	−	0.658342i	$-0.228742\pi$
$769$	7.04864e9	+	4.06953e9i	0.558937	+	0.322702i	−0.193782	+	0.981045i	$0.562075\pi$
$770$	3.62768e7	−	6.28332e7i	0.00286359	−	0.00495989i
$771$	5.67508e9	+	9.82952e9i	0.445945	+	0.772400i
$772$			3.05981e9i			0.239350i
$773$	1.14818e10	−	6.62903e9i	0.894093	−	0.516205i	0.0188138	−	0.999823i	$-0.494011\pi$
$773$	1.14818e10	−	6.62903e9i	0.894093	−	0.516205i	0.875279	+	0.483618i	$0.160678\pi$
$774$	−2.75906e10	+	1.59295e10i	−2.13879	+	1.23483i
$775$			1.72178e10i			1.32868i
$776$	2.18735e9	+	3.78861e9i	0.168036	+	0.291047i
$777$	8.20924e8	−	1.42188e9i	0.0627811	−	0.108740i
$778$	−5.73863e9	−	3.31320e9i	−0.436897	−	0.252243i
$779$	2.87851e9			0.218166
$780$	−3.81369e8	+	3.31907e8i	−0.0287749	+	0.0250429i
$781$	−4.93002e9			−0.370314
$782$	−3.20433e9	−	1.85002e9i	−0.239615	−	0.138342i
$783$	−2.54224e9	+	4.40328e9i	−0.189256	+	0.327801i
$784$	−1.66263e9	−	2.87976e9i	−0.123222	−	0.213428i
$785$			7.02467e8i			0.0518301i
$786$	2.30392e10	−	1.33017e10i	1.69234	−	0.977075i
$787$	−6.09232e9	+	3.51740e9i	−0.445524	+	0.257223i	−0.705938	−	0.708274i	$-0.749474\pi$
$787$	−6.09232e9	+	3.51740e9i	−0.445524	+	0.257223i	0.260414	+	0.965497i	$0.416141\pi$
$788$		−	1.52879e9i		−	0.111303i
$789$	1.48710e10	+	2.57573e10i	1.07788	+	1.86694i
$790$	1.23154e8	−	2.13309e8i	0.00888698	−	0.0153927i
$791$	1.80660e9	+	1.04304e9i	0.129791	+	0.0749347i
$792$	−1.40473e10			−1.00474
$793$	4.81294e9	−	1.40042e10i	0.342732	−	0.997242i
$794$	−6.52227e7			−0.00462410
$795$	1.38431e8	+	7.99232e7i	0.00977121	+	0.00564141i
$796$	5.16111e9	−	8.93931e9i	0.362700	−	0.628215i
$797$	2.43301e9	+	4.21410e9i	0.170232	+	0.294850i	0.938501	−	0.345277i	$-0.112215\pi$
$797$	2.43301e9	+	4.21410e9i	0.170232	+	0.294850i	−0.768269	+	0.640127i	$0.778882\pi$
$798$			2.42795e9i			0.169133i
$799$	−1.58316e10	+	9.14035e9i	−1.09802	+	0.633942i
$800$	−2.21255e9	+	1.27741e9i	−0.152784	+	0.0882098i
$801$		−	1.77526e10i		−	1.22053i
$802$	1.98215e9	+	3.43318e9i	0.135683	+	0.235010i
$803$	1.41734e10	−	2.45491e10i	0.965987	−	1.67314i
$804$	−1.57798e10	−	9.11047e9i	−1.07079	−	0.618222i
$805$	−3.80351e7			−0.00256980
$806$	−1.37358e10	+	2.67823e9i	−0.924021	+	0.180167i
$807$	−4.96723e10			−3.32703
$808$	8.39661e9	+	4.84779e9i	0.559969	+	0.323298i
$809$	−6.03124e8	+	1.04464e9i	−0.0400485	+	0.0693661i	−0.885355	−	0.464916i	$-0.846085\pi$
$809$	−6.03124e8	+	1.04464e9i	−0.0400485	+	0.0693661i	0.845306	+	0.534282i	$0.179418\pi$
$810$	1.57799e8	+	2.73315e8i	0.0104329	+	0.0180703i
$811$			8.41139e9i			0.553726i	0.960909	+	0.276863i	$0.0892948\pi$
$811$			8.41139e9i			0.553726i	−0.960909	+	0.276863i	$0.910705\pi$
$812$	1.99470e8	−	1.15164e8i	0.0130747	−	0.00754866i
$813$	1.43609e10	−	8.29125e9i	0.937268	−	0.541132i
$814$		−	1.01997e10i		−	0.662830i
$815$	2.27968e8	+	3.94853e8i	0.0147511	+	0.0255496i
$816$	2.68761e9	−	4.65507e9i	0.173161	−	0.299924i
$817$	2.96253e10	+	1.71042e10i	1.90057	+	1.09730i
$818$	3.08307e9			0.196946
$819$	6.74799e8	+	3.46083e9i	0.0429221	+	0.220134i
$820$	−6.55092e7			−0.00414910
$821$	−2.23410e10	−	1.28986e10i	−1.40897	−	0.813469i	−0.413681	−	0.910422i	$-0.635757\pi$
$821$	−2.23410e10	−	1.28986e10i	−1.40897	−	0.813469i	−0.995289	+	0.0969528i	$0.969090\pi$
$822$	2.00511e9	−	3.47296e9i	0.125918	−	0.218096i
$823$	−9.10197e7	−	1.57651e8i	−0.00569162	−	0.00985818i	0.863166	−	0.504921i	$-0.168478\pi$
$823$	−9.10197e7	−	1.57651e8i	−0.00569162	−	0.00985818i	−0.868857	+	0.495063i	$0.835145\pi$
$824$			5.70266e9i			0.355085i
$825$	3.57489e10	−	2.06396e10i	2.21653	−	1.27972i
$826$	−1.67537e9	+	9.67275e8i	−0.103438	+	0.0597200i
$827$		−	2.35099e10i		−	1.44538i	−0.691175	−	0.722688i	$-0.742906\pi$
$827$		−	2.35099e10i		−	1.44538i	0.691175	−	0.722688i	$-0.257094\pi$
$828$	3.68204e9	+	6.37749e9i	0.225415	+	0.390430i
$829$	2.15503e9	−	3.73263e9i	0.131375	−	0.227548i	−0.792832	−	0.609441i	$-0.791394\pi$
$829$	2.15503e9	−	3.73263e9i	0.131375	−	0.227548i	0.924207	+	0.381892i	$0.124727\pi$
$830$	−4.52559e8	−	2.61285e8i	−0.0274728	−	0.0158614i
$831$	−1.10979e10			−0.670871
$832$	−1.36324e9	−	1.56640e9i	−0.0820620	−	0.0942912i
$833$	−1.34222e10			−0.804575
$834$	−1.50303e10	−	8.67775e9i	−0.897195	−	0.517996i
$835$	4.40190e8	−	7.62431e8i	0.0261660	−	0.0453209i
$836$	7.54161e9	+	1.30625e10i	0.446419	+	0.773220i
$837$			3.37634e10i			1.99024i
$838$	−1.43249e10	+	8.27046e9i	−0.840884	+	0.485485i
$839$	2.63154e10	−	1.51932e10i	1.53831	−	0.888142i	0.539368	−	0.842070i	$-0.318663\pi$
$839$	2.63154e10	−	1.51932e10i	1.53831	−	0.888142i	0.998938	−	0.0460715i	$-0.0146702\pi$
$840$		−	5.52552e7i		−	0.00321659i
$841$	8.07197e9	+	1.39811e10i	0.467944	+	0.810502i
$842$	−3.74465e9	+	6.48593e9i	−0.216182	+	0.374438i
$843$	6.49311e9	+	3.74880e9i	0.373298	+	0.215524i
$844$	−4.98007e9			−0.285126
$845$	7.80822e8	+	1.08815e8i	0.0445198	+	0.00620424i
$846$	3.63836e10			2.06590
$847$	−2.34349e9	−	1.35301e9i	−0.132517	−	0.0765085i
$848$	−3.28269e8	+	5.68579e8i	−0.0184861	+	0.0320188i
$849$	1.31155e10	+	2.27168e10i	0.735544	+	1.27400i
$850$			1.03124e10i			0.575962i
$851$	−4.63067e9	+	2.67352e9i	−0.257567	+	0.148706i
$852$	−3.25157e9	+	1.87730e9i	−0.180117	+	0.103991i
$853$			5.71921e9i			0.315511i	0.987478	+	0.157756i	$0.0504258\pi$
$853$			5.71921e9i			0.315511i	−0.987478	+	0.157756i	$0.949574\pi$
$854$	8.09206e8	+	1.40159e9i	0.0444587	+	0.0770047i
$855$	9.12950e8	−	1.58128e9i	0.0499535	−	0.0865219i
$856$	−1.63132e9	−	9.41844e8i	−0.0888958	−	0.0513240i
$857$	1.49325e10			0.810401			0.405201	−	0.914228i	$-0.367202\pi$
$857$	1.49325e10			0.810401			0.405201	+	0.914228i	$0.367202\pi$
$858$	2.20264e10	+	2.53089e10i	1.19053	+	1.36794i
$859$	1.66438e10			0.895932			0.447966	−	0.894051i	$-0.352149\pi$
$859$	1.66438e10			0.895932			0.447966	+	0.894051i	$0.352149\pi$
$860$	−6.74211e8	−	3.89256e8i	−0.0361453	−	0.0208685i
$861$	−3.49901e8	+	6.06046e8i	−0.0186825	+	0.0323590i
$862$	−1.99610e9	−	3.45735e9i	−0.106147	−	0.183852i
$863$		−	1.42938e10i		−	0.757023i	−0.925597	−	0.378512i	$-0.876436\pi$
$863$		−	1.42938e10i		−	0.757023i	0.925597	−	0.378512i	$-0.123564\pi$
$864$	−4.33871e9	+	2.50496e9i	−0.228856	+	0.132130i
$865$	−6.87949e8	+	3.97188e8i	−0.0361410	+	0.0208660i
$866$		−	8.49689e9i		−	0.444577i
$867$	5.43673e9	+	9.41669e9i	0.283316	+	0.490718i
$868$	7.64744e8	−	1.32457e9i	0.0396914	−	0.0687476i
$869$	−1.41559e10	−	8.17291e9i	−0.731759	−	0.422481i
$870$	−2.65313e8			−0.0136597
$871$	5.43759e9	+	2.78877e10i	0.278832	+	1.43004i
$872$	−7.93837e9			−0.405437
$873$	−3.04362e10	−	1.75723e10i	−1.54825	−	0.893881i
$874$	3.95357e9	−	6.84779e9i	0.200309	−	0.346945i
$875$	1.06115e8	+	1.83797e8i	0.00535487	+	0.00927490i
$876$		−	2.15884e10i		−	1.08506i
$877$	1.08404e10	−	6.25868e9i	0.542681	−	0.313317i	−0.203484	−	0.979078i	$-0.565226\pi$
$877$	1.08404e10	−	6.25868e9i	0.542681	−	0.313317i	0.746165	+	0.665761i	$0.231893\pi$
$878$	−6.90860e9	+	3.98868e9i	−0.344476	+	0.198883i
$879$		−	1.33704e10i		−	0.664024i
$880$	−1.71632e8	−	2.97275e8i	−0.00849002	−	0.0147051i
$881$	−7.73880e9	+	1.34040e10i	−0.381292	+	0.660417i	−0.991247	−	0.132019i	$-0.957854\pi$
$881$	−7.73880e9	+	1.34040e10i	−0.381292	+	0.660417i	0.609955	+	0.792436i	$0.291187\pi$
$882$	2.31349e10	+	1.33569e10i	1.13534	+	0.655491i
$883$	1.77069e9			0.0865525			0.0432762	−	0.999063i	$-0.486220\pi$
$883$	1.77069e9			0.0865525			0.0432762	+	0.999063i	$0.486220\pi$
$884$	−8.22692e9	+	1.60410e9i	−0.400548	+	0.0780995i
$885$	2.22839e9			0.108066
$886$	2.24826e9	+	1.29803e9i	0.108600	+	0.0627000i
$887$	−1.35468e9	+	2.34638e9i	−0.0651787	+	0.112893i	−0.896773	−	0.442490i	$-0.854095\pi$
$887$	−1.35468e9	+	2.34638e9i	−0.0651787	+	0.112893i	0.831595	+	0.555383i	$0.187428\pi$
$888$	−3.88394e9	−	6.72717e9i	−0.186134	−	0.322394i
$889$		−	4.18483e9i		−	0.199766i
$890$	3.75688e8	−	2.16903e8i	0.0178633	−	0.0103134i
$891$	1.81381e10	−	1.04720e10i	0.859053	−	0.495975i
$892$			4.41329e9i			0.208202i
$893$	−1.95333e10	−	3.38327e10i	−0.917901	−	1.58985i
$894$	7.05435e9	−	1.22185e10i	0.330199	−	0.571922i
$895$	−6.10936e8	−	3.52724e8i	−0.0284849	−	0.0164458i
$896$	2.26950e8			0.0105403
$897$	5.71673e9	−	1.66339e10i	0.264469	−	0.769522i
$898$	6.82618e9			0.314565
$899$	−6.36006e9	−	3.67198e9i	−0.291946	−	0.168555i
$900$	1.02622e10	−	1.77747e10i	0.469238	−	0.812744i
$901$	1.32504e9	+	2.29503e9i	0.0603520	+	0.104533i
$902$			4.34740e9i			0.197246i
$903$	−7.20226e9	+	4.15823e9i	−0.325508	+	0.187932i
$904$	8.54733e9	−	4.93481e9i	0.384805	−	0.222167i
$905$		−	1.30072e9i		−	0.0583330i
$906$	−1.48431e10	−	2.57090e10i	−0.663095	−	1.14851i
$907$	−1.75120e10	+	3.03316e10i	−0.779308	+	1.34980i	0.153033	+	0.988221i	$0.451096\pi$
$907$	−1.75120e10	+	3.03316e10i	−0.779308	+	1.34980i	−0.932341	+	0.361580i	$0.882237\pi$
$908$	−8.16688e8	−	4.71515e8i	−0.0362039	−	0.0209023i
$909$	−7.78904e10			−3.43962
$910$	−6.49948e7	+	5.65652e7i	−0.00285913	+	0.00248831i
$911$	6.59923e9			0.289187			0.144594	−	0.989491i	$-0.453813\pi$
$911$	6.59923e9			0.289187			0.144594	+	0.989491i	$0.453813\pi$
$912$	9.94808e9	+	5.74353e9i	0.434267	+	0.250724i
$913$	−1.73398e10	+	3.00333e10i	−0.754041	+	1.30604i
$914$	5.54384e9	+	9.60221e9i	0.240159	+	0.415968i
$915$		−	1.86424e9i		−	0.0804502i
$916$	7.71738e9	−	4.45563e9i	0.331769	−	0.191547i
$917$	3.92646e9	−	2.26694e9i	0.168154	−	0.0970839i
$918$			2.02222e10i			0.862738i
$919$	−1.24901e10	−	2.16334e10i	−0.530836	−	0.919435i	−0.999352	−	0.0359803i	$-0.988545\pi$
$919$	−1.24901e10	−	2.16334e10i	−0.530836	−	0.919435i	0.468516	−	0.883455i	$-0.344789\pi$
$920$	−8.99754e7	+	1.55842e8i	−0.00380948	+	0.00659822i
$921$	−9.34076e9	−	5.39289e9i	−0.393979	−	0.227464i
$922$	−2.01139e10			−0.845157
$923$	5.53686e9	+	1.90291e9i	0.231770	+	0.0796547i
$924$	−3.66692e9			−0.152915
$925$	1.29062e10	+	7.45137e9i	0.536168	+	0.309557i
$926$	−1.33269e10	+	2.30829e10i	−0.551558	+	0.955327i
$927$	−2.29065e10	−	3.96752e10i	−0.944450	−	1.63584i
$928$		−	1.08972e9i		−	0.0447608i
$929$	−3.42370e10	+	1.97667e10i	−1.40101	+	0.808872i	−0.994496	−	0.104773i	$-0.966588\pi$
$929$	−3.42370e10	+	1.97667e10i	−1.40101	+	0.808872i	−0.406512	+	0.913645i	$0.633255\pi$
$930$	−1.52577e9	+	8.80902e8i	−0.0622011	+	0.0359118i
$931$		−	2.86838e10i		−	1.16497i
$932$	−2.05664e8	−	3.56221e8i	−0.00832153	−	0.0144133i
$933$	−2.14985e10	+	3.72365e10i	−0.866609	+	1.50101i
$934$	−1.01608e10	−	5.86633e9i	−0.408050	−	0.235588i
$935$	−1.38556e9			−0.0554352
$936$	1.57764e10	+	5.42204e9i	0.628845	+	0.216121i
$937$	2.31754e10			0.920319			0.460159	−	0.887836i	$-0.347792\pi$
$937$	2.31754e10			0.920319			0.460159	+	0.887836i	$0.347792\pi$
$938$	−2.68927e9	−	1.55265e9i	−0.106396	−	0.0614277i
$939$	2.84260e10	−	4.92353e10i	1.12043	−	1.94065i
$940$	4.44539e8	+	7.69964e8i	0.0174567	+	0.0302359i
$941$		−	8.48646e9i		−	0.332019i	−0.986124	−	0.166009i	$-0.946912\pi$
$941$		−	8.48646e9i		−	0.332019i	0.986124	−	0.166009i	$-0.0530882\pi$
$942$	3.07467e10	−	1.77516e10i	1.19845	−	0.691926i
$943$	1.97372e9	−	1.13953e9i	0.0766470	−	0.0442522i
$944$			9.15270e9i			0.354117i
$945$	1.03938e8	+	1.80027e8i	0.00400650	+	0.00693946i
$946$	−2.58323e10	+	4.47429e10i	−0.992075	+	1.71832i
$947$	3.26354e10	+	1.88420e10i	1.24872	+	0.720946i	0.970853	−	0.239674i	$-0.0770407\pi$
$947$	3.26354e10	+	1.88420e10i	1.24872	+	0.720946i	0.277863	+	0.960621i	$0.410374\pi$
$948$	−1.24486e10			−0.474561
$949$	−2.53937e10	+	2.21002e10i	−0.964481	+	0.839392i
$950$	−2.20380e10			−0.833950
$951$	−3.53226e8	−	2.03935e8i	−0.0133175	−	0.00768884i
$952$	4.58035e8	−	7.93340e8i	0.0172056	−	0.0298009i
$953$	2.21260e10	+	3.83234e10i	0.828091	+	1.43429i	0.899534	+	0.436850i	$0.143906\pi$
$953$	2.21260e10	+	3.83234e10i	0.828091	+	1.43429i	−0.0714438	+	0.997445i	$0.522761\pi$
$954$		−	5.27437e9i		−	0.196676i
$955$	−5.43760e8	+	3.13940e8i	−0.0202021	+	0.0116637i
$956$	1.28637e10	−	7.42689e9i	0.476173	−	0.274919i
$957$			1.76070e10i			0.649373i
$958$	1.47225e10	+	2.55001e10i	0.541007	+	0.937051i
$959$	3.41721e8	−	5.91878e8i	0.0125114	−	0.0216704i
$960$	−2.26398e8	−	1.30711e8i	−0.00825893	−	0.00476830i
$961$	−2.12549e10			−0.772551
$962$	−3.93692e9	+	1.14552e10i	−0.142575	+	0.414849i
$963$	1.51328e10			0.546044
$964$	−1.05462e10	−	6.08885e9i	−0.379164	−	0.218910i
$965$	3.00338e8	−	5.20200e8i	0.0107588	−	0.0186348i
$966$	9.61162e8	+	1.66478e9i	0.0343065	+	0.0594206i
$967$		−	4.11792e10i		−	1.46449i	−0.681044	−	0.732243i	$-0.738474\pi$
$967$		−	4.11792e10i		−	1.46449i	0.681044	−	0.732243i	$-0.261526\pi$
$968$	−1.10875e10	+	6.40135e9i	−0.392887	+	0.226834i
$969$	4.01548e10	−	2.31834e10i	1.41776	−	0.818547i
$970$		−	8.58805e8i		−	0.0302130i
$971$	1.49333e10	+	2.58652e10i	0.523466	+	0.906669i	0.999627	+	0.0273114i	$0.00869456\pi$
$971$	1.49333e10	+	2.58652e10i	0.523466	+	0.906669i	−0.476161	+	0.879358i	$0.657972\pi$
$972$	−2.72461e9	+	4.71916e9i	−0.0951639	+	0.164829i
$973$	−2.56154e9	−	1.47891e9i	−0.0891469	−	0.0514690i
$974$	3.05190e10			1.05831
$975$	−4.81159e10	+	9.38172e9i	−1.66254	+	0.324165i
$976$	7.65700e9			0.263624
$977$	2.70722e10	+	1.56301e10i	0.928735	+	0.536205i	0.886411	−	0.462899i	$-0.153191\pi$
$977$	2.70722e10	+	1.56301e10i	0.928735	+	0.536205i	0.0423237	+	0.999104i	$0.486524\pi$
$978$	1.15217e10	−	1.99562e10i	0.393850	−	0.682169i
$979$	−1.43944e10	−	2.49319e10i	−0.490292	−	0.849210i
$980$			6.52787e8i			0.0221554i
$981$	5.52297e10	−	3.18869e10i	1.86780	−	1.07838i
$982$	2.97694e10	−	1.71874e10i	1.00318	−	0.579188i
$983$		−	2.53290e10i		−	0.850514i	−0.905073	−	0.425257i	$-0.860184\pi$
$983$		−	2.53290e10i		−	0.850514i	0.905073	−	0.425257i	$-0.139816\pi$
$984$	1.65544e9	+	2.86731e9i	0.0553900	+	0.0959383i
$985$	−1.50059e8	+	2.59910e8i	−0.00500306	+	0.00866555i
$986$	−3.80929e9	−	2.19930e9i	−0.126554	−	0.0730659i
$987$	9.49758e9			0.314415
$988$	−3.42803e9	−	1.75813e10i	−0.113082	−	0.579964i
$989$	2.70844e10			0.890291
$990$	2.38819e9	+	1.37882e9i	0.0782251	+	0.0451633i
$991$	1.59473e10	−	2.76216e10i	0.520512	−	0.901553i	−0.479204	−	0.877704i	$-0.659075\pi$
$991$	1.59473e10	−	2.76216e10i	0.520512	−	0.901553i	0.999716	−	0.0238492i	$-0.00759214\pi$
$992$	−3.61814e9	−	6.26680e9i	−0.117678	−	0.203824i
$993$			2.82449e10i			0.915416i
$994$	−5.54149e8	+	3.19938e8i	−0.0178968	+	0.0103327i
$995$	−1.75489e9	+	1.01318e9i	−0.0564766	+	0.0326068i
$996$			2.64111e10i			0.846992i
$997$	−2.74162e10	−	4.74863e10i	−0.876143	−	1.51752i	−0.855540	−	0.517736i	$-0.826775\pi$
$997$	−2.74162e10	−	4.74863e10i	−0.876143	−	1.51752i	−0.0206024	−	0.999788i	$-0.506558\pi$
$998$	6.09893e9	−	1.05637e10i	0.194221	−	0.336401i
$999$	2.53085e10	+	1.46118e10i	0.803131	+	0.463688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.e.a.17.5	✓	16
3.2	odd	2		234.8.l.c.199.3		16
4.3	odd	2		208.8.w.b.17.8		16
13.4	even	6		338.8.b.i.337.16		16
13.6	odd	12		338.8.a.m.1.8		8
13.7	odd	12		338.8.a.n.1.8		8
13.9	even	3		338.8.b.i.337.8		16
13.10	even	6	inner	26.8.e.a.23.5	yes	16
39.23	odd	6		234.8.l.c.127.2		16
52.23	odd	6		208.8.w.b.49.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.e.a.17.5	✓	16	1.1	even	1	trivial
26.8.e.a.23.5	yes	16	13.10	even	6	inner
208.8.w.b.17.8		16	4.3	odd	2
208.8.w.b.49.8		16	52.23	odd	6
234.8.l.c.127.2		16	39.23	odd	6
234.8.l.c.199.3		16	3.2	odd	2
338.8.a.m.1.8		8	13.6	odd	12
338.8.a.n.1.8		8	13.7	odd	12
338.8.b.i.337.8		16	13.9	even	3
338.8.b.i.337.16		16	13.4	even	6

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	26.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.92820 + 4.00000i) q^{2} +(-39.6869 + 68.7398i) q^{3} +(32.0000 + 55.4256i) q^{4} -12.5639i q^{5} +(-549.918 + 317.495i) q^{6} +(-93.7198 + 54.1091i) q^{7} +512.000i q^{8} +(-2056.60 - 3562.14i) q^{9} +(50.2557 - 87.0454i) q^{10} +(-5776.62 - 3335.13i) q^{11} -5079.93 q^{12} +(5200.37 + 5975.34i) q^{13} -865.746 q^{14} +(863.641 + 498.623i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(8266.62 + 14318.2i) q^{17} -32905.7i q^{18} +(-30598.6 + 17666.1i) q^{19} +(696.363 - 402.045i) q^{20} -8589.70i q^{21} +(-26681.1 - 46212.9i) q^{22} +(-13987.1 + 24226.4i) q^{23} +(-35194.8 - 20319.7i) q^{24} +77967.1 q^{25} +(12127.8 + 62199.8i) q^{26} +152890. q^{27} +(-5998.07 - 3462.98i) q^{28} +(-16627.8 + 28800.2i) q^{29} +(3988.99 + 6909.13i) q^{30} +220834. i q^{31} +(-28377.9 + 16384.0i) q^{32} +(458512. - 264722. i) q^{33} +132266. i q^{34} +(679.823 + 1177.49i) q^{35} +(131623. - 227977. i) q^{36} +(165533. + 95570.7i) q^{37} -282658. q^{38} +(-617130. + 120329. i) q^{39} +6432.73 q^{40} +(-70555.0 - 40734.9i) q^{41} +(34358.8 - 59511.2i) q^{42} +(-484095. - 838477. i) q^{43} -426897. i q^{44} +(-44754.5 + 25839.0i) q^{45} +(-193811. + 111897. i) q^{46} +1.10569e6i q^{47} +(-162558. - 281558. i) q^{48} +(-405916. + 703067. i) q^{49} +(540172. + 311869. i) q^{50} -1.31231e6 q^{51} +(-164775. + 479445. i) q^{52} +160288. q^{53} +(1.05926e6 + 611562. i) q^{54} +(-41902.3 + 72577.0i) q^{55} +(-27703.9 - 47984.5i) q^{56} -2.80446e6i q^{57} +(-230402. + 133023. i) q^{58} +(1.93517e6 - 1.11727e6i) q^{59} +63823.8i q^{60} +(-934692. - 1.61893e6i) q^{61} +(-883335. + 1.52998e6i) q^{62} +(385489. + 222562. i) q^{63} -262144. q^{64} +(75073.7 - 65337.0i) q^{65} +4.23556e6 q^{66} +(3.10630e6 + 1.79343e6i) q^{67} +(-529064. + 916365. i) q^{68} +(-1.11021e6 - 1.92294e6i) q^{69} +10877.2i q^{70} +(640083. - 369552. i) q^{71} +(1.82382e6 - 1.05298e6i) q^{72} +4.24974e6i q^{73} +(764566. + 1.32427e6i) q^{74} +(-3.09428e6 + 5.35944e6i) q^{75} +(-1.95831e6 - 1.13063e6i) q^{76} +721844. q^{77} +(-4.75692e6 - 1.63486e6i) q^{78} +2.45055e6 q^{79} +(44567.2 + 25730.9i) q^{80} +(-1.56996e6 + 2.71925e6i) q^{81} +(-325879. - 564440. i) q^{82} -5.19912e6i q^{83} +(476089. - 274870. i) q^{84} +(179893. - 103861. i) q^{85} -7.74552e6i q^{86} +(-1.31981e6 - 2.28599e6i) q^{87} +(1.70759e6 - 2.95763e6i) q^{88} +(3.73776e6 + 2.15800e6i) q^{89} -413424. q^{90} +(-810698. - 278620. i) q^{91} -1.79035e6 q^{92} +(-1.51801e7 - 8.76421e6i) q^{93} +(-4.42278e6 + 7.66047e6i) q^{94} +(221956. + 384439. i) q^{95} -2.60092e6i q^{96} +(7.39963e6 - 4.27218e6i) q^{97} +(-5.62454e6 + 3.24733e6i) q^{98} +2.74362e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 512 q^{4} + 2520 q^{7} - 4684 q^{9} + 2432 q^{10} - 8496 q^{11} - 3620 q^{13} + 34560 q^{14} + 51648 q^{15} - 32768 q^{16} + 41520 q^{17} - 54432 q^{19} - 16128 q^{20} - 17280 q^{22} - 7560 q^{23}+ \cdots + 19031040 q^{98}+O(q^{100}) \) 16 * q + 512 * q^4 + 2520 * q^7 - 4684 * q^9 + 2432 * q^10 - 8496 * q^11 - 3620 * q^13 + 34560 * q^14 + 51648 * q^15 - 32768 * q^16 + 41520 * q^17 - 54432 * q^19 - 16128 * q^20 - 17280 * q^22 - 7560 * q^23 - 273960 * q^25 + 51072 * q^26 + 133920 * q^27 + 161280 * q^28 - 346056 * q^29 + 170368 * q^30 + 486300 * q^33 - 283248 * q^35 + 299776 * q^36 - 68280 * q^37 - 1059840 * q^38 - 1122680 * q^39 + 311296 * q^40 - 1288008 * q^41 + 408320 * q^42 + 285360 * q^43 + 5743980 * q^45 - 188928 * q^46 - 2131660 * q^49 + 85248 * q^50 + 957280 * q^51 + 354560 * q^52 + 3666600 * q^53 - 4074624 * q^54 - 1091472 * q^55 + 1105920 * q^56 + 3504000 * q^58 + 1799280 * q^59 - 4626000 * q^61 - 2770560 * q^62 - 8609760 * q^63 - 4194304 * q^64 - 11518020 * q^65 + 7941120 * q^66 - 7094400 * q^67 - 2657280 * q^68 + 18027316 * q^69 + 25958520 * q^71 + 4423680 * q^72 - 1142400 * q^74 - 10898032 * q^75 - 3483648 * q^76 - 20577480 * q^77 - 22023040 * q^78 + 34143488 * q^79 - 1032192 * q^80 - 15745864 * q^81 + 12202240 * q^82 + 17311488 * q^84 + 7123932 * q^85 - 10460440 * q^87 + 1105920 * q^88 + 10609452 * q^89 + 4070656 * q^90 - 38683952 * q^91 - 967680 * q^92 - 52747080 * q^93 - 14303616 * q^94 + 33837504 * q^95 + 83706300 * q^97 + 19031040 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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