LMFDB - Embedded newform 196.8.e.b.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,8,Mod(165,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("196.165");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not 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:	$61.2274649949$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{1009})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 253x^{2} + 252x + 63504 $ x^4 - x^3 + 253x^2 + 252x + 63504
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$8.19119 - 14.1876i$ of defining polynomial
Character	$\chi$	$=$	196.165
Dual form			196.8.e.b.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-19.3824 + 33.5713i) q^{3} +(248.206 + 429.906i) q^{5} +(342.147 + 592.615i) q^{9} +(-2017.59 + 3494.57i) q^{11} -14469.7 q^{13} -19243.3 q^{15} +(13375.1 - 23166.3i) q^{17} +(-18305.0 - 31705.2i) q^{19} +(17460.0 + 30241.7i) q^{23} +(-84150.1 + 145752. i) q^{25} -111305. q^{27} +35874.3 q^{29} +(-99299.2 + 171991. i) q^{31} +(-78211.5 - 135466. i) q^{33} +(57206.6 + 99084.7i) q^{37} +(280458. - 485767. i) q^{39} +245990. q^{41} +30224.0 q^{43} +(-169846. + 294182. i) q^{45} +(152616. + 264339. i) q^{47} +(518481. + 898036. i) q^{51} +(605264. - 1.04835e6i) q^{53} -2.00312e6 q^{55} +1.41918e6 q^{57} +(767785. - 1.32984e6i) q^{59} +(22543.2 + 39045.9i) q^{61} +(-3.59147e6 - 6.22061e6i) q^{65} +(-1.54250e6 + 2.67169e6i) q^{67} -1.35367e6 q^{69} -1.69051e6 q^{71} +(1.93466e6 - 3.35093e6i) q^{73} +(-3.26206e6 - 5.65005e6i) q^{75} +(-1.00455e6 - 1.73993e6i) q^{79} +(1.40908e6 - 2.44060e6i) q^{81} -8.28720e6 q^{83} +1.32791e7 q^{85} +(-695328. + 1.20434e6i) q^{87} +(3.25312e6 + 5.63457e6i) q^{89} +(-3.84931e6 - 6.66720e6i) q^{93} +(9.08683e6 - 1.57389e7i) q^{95} -1.14882e7 q^{97} -2.76125e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 14 q^{3} + 294 q^{5} + 2258 q^{9} + 3492 q^{11} - 32340 q^{13} - 48512 q^{15} + 29232 q^{17} + 3206 q^{19} + 9360 q^{23} - 131146 q^{25} - 36344 q^{27} + 369408 q^{29} - 165060 q^{31} - 342832 q^{33}+ \cdots + 18168664 q^{99}+O(q^{100}) $ 4 * q - 14 * q^3 + 294 * q^5 + 2258 * q^9 + 3492 * q^11 - 32340 * q^13 - 48512 * q^15 + 29232 * q^17 + 3206 * q^19 + 9360 * q^23 - 131146 * q^25 - 36344 * q^27 + 369408 * q^29 - 165060 * q^31 - 342832 * q^33 - 286144 * q^37 + 518808 * q^39 - 233520 * q^41 - 588856 * q^43 - 21154 * q^45 + 1014132 * q^47 + 975500 * q^51 + 1396452 * q^53 - 7053424 * q^55 + 4810424 * q^57 + 2729286 * q^59 - 2466954 * q^61 - 6838788 * q^65 - 225176 * q^67 - 3973312 * q^69 + 3060624 * q^71 - 1143548 * q^73 - 7444234 * q^75 - 7951176 * q^79 + 1682882 * q^81 - 36975708 * q^83 + 25553480 * q^85 + 2295076 * q^87 + 4652508 * q^89 - 8529192 * q^93 + 26232912 * q^95 - 53404736 * q^97 + 18168664 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−19.3824	+	33.5713i	−0.414460	+	0.717866i	−0.995372	−	0.0961008i	$-0.969363\pi$
$3$	−19.3824	+	33.5713i	−0.414460	+	0.717866i	0.580912	+	0.813967i	$0.302696\pi$
$4$		0			0
$5$	248.206	+	429.906i	0.888009	+	1.53808i	0.842225	+	0.539126i	$0.181245\pi$
$5$	248.206	+	429.906i	0.888009	+	1.53808i	0.0457844	+	0.998951i	$0.485421\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	342.147	+	592.615i	0.156446	+	0.270972i
$10$		0			0
$11$	−2017.59	+	3494.57i	−0.457045	+	0.791626i	−0.998803	−	0.0489089i	$-0.984426\pi$
$11$	−2017.59	+	3494.57i	−0.457045	+	0.791626i	0.541758	+	0.840535i	$0.317759\pi$
$12$		0			0
$13$	−14469.7			−1.82666			−0.913331	−	0.407217i	$-0.866499\pi$
$13$	−14469.7			−1.82666			−0.913331	+	0.407217i	$0.866499\pi$
$14$		0			0
$15$	−19243.3			−1.47218
$16$		0			0
$17$	13375.1	−	23166.3i	0.660275	−	1.14363i	−0.320268	−	0.947327i	$-0.603773\pi$
$17$	13375.1	−	23166.3i	0.660275	−	1.14363i	0.980543	−	0.196303i	$-0.0628936\pi$
$18$		0			0
$19$	−18305.0	−	31705.2i	−0.612255	−	1.06046i	−0.990859	−	0.134898i	$-0.956929\pi$
$19$	−18305.0	−	31705.2i	−0.612255	−	1.06046i	0.378605	−	0.925558i	$-0.376404\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	17460.0	+	30241.7i	0.299225	+	0.518272i	0.975959	−	0.217955i	$-0.0699386\pi$
$23$	17460.0	+	30241.7i	0.299225	+	0.518272i	−0.676734	+	0.736228i	$0.736605\pi$
$24$		0			0
$25$	−84150.1	+	145752.i	−1.07712	+	1.86563i
$26$		0			0
$27$	−111305.			−1.08828
$28$		0			0
$29$	35874.3			0.273143			0.136571	−	0.990630i	$-0.456392\pi$
$29$	35874.3			0.273143			0.136571	+	0.990630i	$0.456392\pi$
$30$		0			0
$31$	−99299.2	+	171991.i	−0.598660	+	1.03691i	0.394360	+	0.918956i	$0.370966\pi$
$31$	−99299.2	+	171991.i	−0.598660	+	1.03691i	−0.993019	+	0.117953i	$0.962367\pi$
$32$		0			0
$33$	−78211.5	−	135466.i	−0.378854	−	0.656194i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	57206.6	+	99084.7i	0.185669	+	0.321589i	0.943802	−	0.330512i	$-0.107221\pi$
$37$	57206.6	+	99084.7i	0.185669	+	0.321589i	−0.758133	+	0.652100i	$0.773888\pi$
$38$		0			0
$39$	280458.	−	485767.i	0.757079	−	1.31130i
$40$		0			0
$41$	245990.			0.557409			0.278704	−	0.960377i	$-0.410095\pi$
$41$	245990.			0.557409			0.278704	+	0.960377i	$0.410095\pi$
$42$		0			0
$43$	30224.0			0.0579711			0.0289856	−	0.999580i	$-0.490772\pi$
$43$	30224.0			0.0579711			0.0289856	+	0.999580i	$0.490772\pi$
$44$		0			0
$45$	−169846.	+	294182.i	−0.277850	+	0.481251i
$46$		0			0
$47$	152616.	+	264339.i	0.214417	+	0.371381i	0.953092	−	0.302681i	$-0.0978816\pi$
$47$	152616.	+	264339.i	0.214417	+	0.371381i	−0.738675	+	0.674061i	$0.764548\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	518481.	+	898036.i	0.547315	+	0.947978i
$52$		0			0
$53$	605264.	−	1.04835e6i	0.558444	−	0.967253i	−0.439183	−	0.898398i	$-0.644732\pi$
$53$	605264.	−	1.04835e6i	0.558444	−	0.967253i	0.997627	−	0.0688551i	$-0.0219346\pi$
$54$		0			0
$55$	−2.00312e6			−1.62344
$56$		0			0
$57$	1.41918e6			1.01502
$58$		0			0
$59$	767785.	−	1.32984e6i	0.486696	−	0.842981i	−0.513188	−	0.858277i	$-0.671535\pi$
$59$	767785.	−	1.32984e6i	0.486696	−	0.842981i	0.999883	+	0.0152952i	$0.00486879\pi$
$60$		0			0
$61$	22543.2	+	39045.9i	0.0127163	+	0.0220253i	0.872314	−	0.488947i	$-0.162619\pi$
$61$	22543.2	+	39045.9i	0.0127163	+	0.0220253i	−0.859597	+	0.510972i	$0.829285\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.59147e6	−	6.22061e6i	−1.62209	−	2.80955i
$66$		0			0
$67$	−1.54250e6	+	2.67169e6i	−0.626562	+	1.08524i	0.361674	+	0.932305i	$0.382205\pi$
$67$	−1.54250e6	+	2.67169e6i	−0.626562	+	1.08524i	−0.988236	+	0.152933i	$0.951128\pi$
$68$		0			0
$69$	−1.35367e6			−0.496067
$70$		0			0
$71$	−1.69051e6			−0.560550			−0.280275	−	0.959920i	$-0.590426\pi$
$71$	−1.69051e6			−0.560550			−0.280275	+	0.959920i	$0.590426\pi$
$72$		0			0
$73$	1.93466e6	−	3.35093e6i	0.582069	−	1.00817i	−0.413165	−	0.910656i	$-0.635577\pi$
$73$	1.93466e6	−	3.35093e6i	0.582069	−	1.00817i	0.995234	−	0.0975172i	$-0.0310901\pi$
$74$		0			0
$75$	−3.26206e6	−	5.65005e6i	−0.892848	−	1.54646i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.00455e6	−	1.73993e6i	−0.229232	−	0.397042i	0.728349	−	0.685207i	$-0.240288\pi$
$79$	−1.00455e6	−	1.73993e6i	−0.229232	−	0.397042i	−0.957581	+	0.288165i	$0.906955\pi$
$80$		0			0
$81$	1.40908e6	−	2.44060e6i	0.294604	−	0.510269i
$82$		0			0
$83$	−8.28720e6			−1.59087			−0.795435	−	0.606039i	$-0.792758\pi$
$83$	−8.28720e6			−1.59087			−0.795435	+	0.606039i	$0.792758\pi$
$84$		0			0
$85$	1.32791e7			2.34532
$86$		0			0
$87$	−695328.	+	1.20434e6i	−0.113207	+	0.196080i
$88$		0			0
$89$	3.25312e6	+	5.63457e6i	0.489142	+	0.847219i	0.999922	−	0.0124923i	$-0.00397654\pi$
$89$	3.25312e6	+	5.63457e6i	0.489142	+	0.847219i	−0.510780	+	0.859712i	$0.670643\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.84931e6	−	6.66720e6i	−0.496241	−	0.859515i
$94$		0			0
$95$	9.08683e6	−	1.57389e7i	1.08738	−	1.88339i
$96$		0			0
$97$	−1.14882e7			−1.27806			−0.639028	−	0.769183i	$-0.720663\pi$
$97$	−1.14882e7			−1.27806			−0.639028	+	0.769183i	$0.720663\pi$
$98$		0			0
$99$	−2.76125e6			−0.286011
$100$		0			0
$101$	3.45226e6	−	5.97950e6i	0.333410	−	0.577484i	−0.649768	−	0.760133i	$-0.725134\pi$
$101$	3.45226e6	−	5.97950e6i	0.333410	−	0.577484i	0.983178	+	0.182649i	$0.0584672\pi$
$102$		0			0
$103$	−2.08698e6	−	3.61475e6i	−0.188186	−	0.325948i	0.756459	−	0.654041i	$-0.226928\pi$
$103$	−2.08698e6	−	3.61475e6i	−0.188186	−	0.325948i	−0.944646	+	0.328093i	$0.893594\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.32843e6	+	5.76501e6i	0.262661	+	0.454942i	0.966948	−	0.254973i	$-0.0820665\pi$
$107$	3.32843e6	+	5.76501e6i	0.262661	+	0.454942i	−0.704287	+	0.709915i	$0.748733\pi$
$108$		0			0
$109$	5.56972e6	−	9.64704e6i	0.411946	−	0.713512i	−0.583156	−	0.812360i	$-0.698182\pi$
$109$	5.56972e6	−	9.64704e6i	0.411946	−	0.713512i	0.995103	+	0.0988480i	$0.0315158\pi$
$110$		0			0
$111$	−4.43520e6			−0.307810
$112$		0			0
$113$	4.18354e6			0.272753			0.136377	−	0.990657i	$-0.456454\pi$
$113$	4.18354e6			0.272753			0.136377	+	0.990657i	$0.456454\pi$
$114$		0			0
$115$	−8.66737e6	+	1.50123e7i	−0.531429	+	0.920462i
$116$		0			0
$117$	−4.95077e6	−	8.57498e6i	−0.285773	−	0.494974i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.60222e6	+	2.77513e6i	0.0822193	+	0.142408i
$122$		0			0
$123$	−4.76787e6	+	8.25819e6i	−0.231024	+	0.400145i
$124$		0			0
$125$	−4.47641e7			−2.04996
$126$		0			0
$127$	3.65300e7			1.58247			0.791237	−	0.611510i	$-0.209438\pi$
$127$	3.65300e7			1.58247			0.791237	+	0.611510i	$0.209438\pi$
$128$		0			0
$129$	−585812.	+	1.01466e6i	−0.0240267	+	0.0416155i
$130$		0			0
$131$	−2.54084e7	−	4.40087e7i	−0.987479	−	1.71036i	−0.630353	−	0.776308i	$-0.717090\pi$
$131$	−2.54084e7	−	4.40087e7i	−0.987479	−	1.71036i	−0.357126	−	0.934056i	$-0.616243\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.76266e7	−	4.78507e7i	−0.966405	−	1.67386i
$136$		0			0
$137$	−1.51976e7	+	2.63230e7i	−0.504955	+	0.874608i	0.495028	+	0.868877i	$0.335158\pi$
$137$	−1.51976e7	+	2.63230e7i	−0.504955	+	0.874608i	−0.999984	+	0.00573133i	$0.998176\pi$
$138$		0			0
$139$	−2.92052e7			−0.922377			−0.461189	−	0.887302i	$-0.652577\pi$
$139$	−2.92052e7			−0.922377			−0.461189	+	0.887302i	$0.652577\pi$
$140$		0			0
$141$	−1.18323e7			−0.355469
$142$		0			0
$143$	2.91940e7	−	5.05655e7i	0.834867	−	1.44603i
$144$		0			0
$145$	8.90421e6	+	1.54225e7i	0.242553	+	0.420115i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.85475e7	+	3.21252e7i	0.459339	+	0.795598i	0.998926	−	0.0463317i	$-0.0147531\pi$
$149$	1.85475e7	+	3.21252e7i	0.459339	+	0.795598i	−0.539588	+	0.841930i	$0.681420\pi$
$150$		0			0
$151$	−9.11971e6	+	1.57958e7i	−0.215557	+	0.373356i	−0.953445	−	0.301568i	$-0.902490\pi$
$151$	−9.11971e6	+	1.57958e7i	−0.215557	+	0.373356i	0.737888	+	0.674923i	$0.235823\pi$
$152$		0			0
$153$	1.83049e7			0.413189
$154$		0			0
$155$	−9.85867e7			−2.12646
$156$		0			0
$157$	−1.06032e7	+	1.83653e7i	−0.218670	+	0.378747i	−0.954402	−	0.298526i	$-0.903505\pi$
$157$	−1.06032e7	+	1.83653e7i	−0.218670	+	0.378747i	0.735732	+	0.677273i	$0.236838\pi$
$158$		0			0
$159$	2.34629e7	+	4.06390e7i	0.462905	+	0.801775i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.25476e7	−	3.90537e7i	−0.407797	−	0.706326i	0.586845	−	0.809699i	$-0.300370\pi$
$163$	−2.25476e7	−	3.90537e7i	−0.407797	−	0.706326i	−0.994643	+	0.103373i	$0.967036\pi$
$164$		0			0
$165$	3.88252e7	−	6.72472e7i	0.672852	−	1.16541i
$166$		0			0
$167$	6.32823e7			1.05142			0.525708	−	0.850665i	$-0.323801\pi$
$167$	6.32823e7			1.05142			0.525708	+	0.850665i	$0.323801\pi$
$168$		0			0
$169$	1.46624e8			2.33670
$170$		0			0
$171$	1.25260e7	−	2.16957e7i	0.191569	−	0.331808i
$172$		0			0
$173$	1.67096e7	+	2.89420e7i	0.245361	+	0.424978i	0.962233	−	0.272227i	$-0.0877601\pi$
$173$	1.67096e7	+	2.89420e7i	0.245361	+	0.424978i	−0.716872	+	0.697205i	$0.754427\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.97630e7	+	5.15510e7i	0.403432	+	0.698764i
$178$		0			0
$179$	6.49827e7	−	1.12553e8i	0.846861	−	1.46681i	−0.0371339	−	0.999310i	$-0.511823\pi$
$179$	6.49827e7	−	1.12553e8i	0.846861	−	1.46681i	0.883995	−	0.467496i	$-0.154844\pi$
$180$		0			0
$181$	1.91607e7			0.240180			0.120090	−	0.992763i	$-0.461682\pi$
$181$	1.91607e7			0.240180			0.120090	+	0.992763i	$0.461682\pi$
$182$		0			0
$183$	−1.74776e6			−0.0210816
$184$		0			0
$185$	−2.83981e7	+	4.91869e7i	−0.329752	+	0.571147i
$186$		0			0
$187$	5.39709e7	+	9.34803e7i	0.603551	+	1.04538i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.77182e7	−	3.06888e7i	−0.183994	−	0.318686i	0.759243	−	0.650807i	$-0.225569\pi$
$191$	−1.77182e7	−	3.06888e7i	−0.183994	−	0.318686i	−0.943237	+	0.332121i	$0.892236\pi$
$192$		0			0
$193$	−9.01695e7	+	1.56178e8i	−0.902837	+	1.56376i	−0.0790419	+	0.996871i	$0.525186\pi$
$193$	−9.01695e7	+	1.56178e8i	−0.902837	+	1.56376i	−0.823795	+	0.566888i	$0.808147\pi$
$194$		0			0
$195$	2.78445e8			2.68917
$196$		0			0
$197$	−1.39463e8			−1.29965			−0.649826	−	0.760083i	$-0.725158\pi$
$197$	−1.39463e8			−1.29965			−0.649826	+	0.760083i	$0.725158\pi$
$198$		0			0
$199$	−7.31562e7	+	1.26710e8i	−0.658060	+	1.13979i	0.323057	+	0.946379i	$0.395289\pi$
$199$	−7.31562e7	+	1.26710e8i	−0.658060	+	1.13979i	−0.981117	+	0.193414i	$0.938044\pi$
$200$		0			0
$201$	−5.97948e7	−	1.03568e8i	−0.519370	−	0.899576i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	6.10562e7	+	1.05752e8i	0.494984	+	0.857338i
$206$		0			0
$207$	−1.19478e7	+	2.06942e7i	−0.0936248	+	0.162163i
$208$		0			0
$209$	1.47728e8			1.11931
$210$		0			0
$211$	−1.02935e8			−0.754351			−0.377176	−	0.926142i	$-0.623105\pi$
$211$	−1.02935e8			−0.754351			−0.377176	+	0.926142i	$0.623105\pi$
$212$		0			0
$213$	3.27662e7	−	5.67527e7i	0.232326	−	0.402400i
$214$		0			0
$215$	7.50177e6	+	1.29934e7i	0.0514789	+	0.0891641i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	7.49966e7	+	1.29898e8i	0.482489	+	0.835695i
$220$		0			0
$221$	−1.93533e8	+	3.35210e8i	−1.20610	+	2.08903i
$222$		0			0
$223$	−3.26446e8			−1.97126			−0.985632	−	0.168906i	$-0.945977\pi$
$223$	−3.26446e8			−1.97126			−0.985632	+	0.168906i	$0.945977\pi$
$224$		0			0
$225$	−1.15167e8			−0.674044
$226$		0			0
$227$	4.49769e7	−	7.79023e7i	0.255211	−	0.442038i	−0.709742	−	0.704462i	$-0.751188\pi$
$227$	4.49769e7	−	7.79023e7i	0.255211	−	0.442038i	0.964953	+	0.262424i	$0.0845218\pi$
$228$		0			0
$229$	5.09646e7	+	8.82734e7i	0.280443	+	0.485742i	0.971494	−	0.237064i	$-0.0761853\pi$
$229$	5.09646e7	+	8.82734e7i	0.280443	+	0.485742i	−0.691051	+	0.722806i	$0.742852\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.13457e7	+	3.69719e7i	0.110552	+	0.191481i	0.915993	−	0.401195i	$-0.131405\pi$
$233$	2.13457e7	+	3.69719e7i	0.110552	+	0.191481i	−0.805441	+	0.592676i	$0.798072\pi$
$234$		0			0
$235$	−7.57606e7	+	1.31221e8i	−0.380808	+	0.659579i
$236$		0			0
$237$	7.78821e7			0.380030
$238$		0			0
$239$	−6.02163e7			−0.285313			−0.142656	−	0.989772i	$-0.545564\pi$
$239$	−6.02163e7			−0.285313			−0.142656	+	0.989772i	$0.545564\pi$
$240$		0			0
$241$	2.35768e7	−	4.08362e7i	0.108499	−	0.187926i	−0.806663	−	0.591011i	$-0.798729\pi$
$241$	2.35768e7	−	4.08362e7i	0.108499	−	0.187926i	0.915162	+	0.403086i	$0.132062\pi$
$242$		0			0
$243$	−6.70893e7	−	1.16202e8i	−0.299938	−	0.519508i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.64868e8	+	4.58765e8i	1.11838	+	1.93710i
$248$		0			0
$249$	1.60626e8	−	2.78212e8i	0.659352	−	1.14203i
$250$		0			0
$251$	1.94014e8			0.774416			0.387208	−	0.921992i	$-0.373440\pi$
$251$	1.94014e8			0.774416			0.387208	+	0.921992i	$0.373440\pi$
$252$		0			0
$253$	−1.40909e8			−0.547037
$254$		0			0
$255$	−2.57381e8	+	4.45796e8i	−0.972042	+	1.68363i
$256$		0			0
$257$	3.39371e7	+	5.87809e7i	0.124712	+	0.216008i	0.921620	−	0.388092i	$-0.126866\pi$
$257$	3.39371e7	+	5.87809e7i	0.124712	+	0.216008i	−0.796908	+	0.604101i	$0.793533\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.22743e7	+	2.12596e7i	0.0427320	+	0.0740140i
$262$		0			0
$263$	−8.05998e7	+	1.39603e8i	−0.273205	+	0.473205i	−0.969681	−	0.244375i	$-0.921417\pi$
$263$	−8.05998e7	+	1.39603e8i	−0.273205	+	0.473205i	0.696476	+	0.717580i	$0.254750\pi$
$264$		0			0
$265$	6.00921e8			1.98361
$266$		0			0
$267$	−2.52213e8			−0.810920
$268$		0			0
$269$	1.32052e8	−	2.28721e8i	0.413631	−	0.716429i	−0.581653	−	0.813437i	$-0.697594\pi$
$269$	1.32052e8	−	2.28721e8i	0.413631	−	0.716429i	0.995284	+	0.0970078i	$0.0309272\pi$
$270$		0			0
$271$	2.46217e7	+	4.26460e7i	0.0751493	+	0.130162i	0.901151	−	0.433505i	$-0.142723\pi$
$271$	2.46217e7	+	4.26460e7i	0.0751493	+	0.130162i	−0.826002	+	0.563667i	$0.809390\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.39561e8	−	5.88138e8i	−0.984587	−	1.70535i
$276$		0			0
$277$	1.42902e8	−	2.47513e8i	0.403978	−	0.699711i	−0.590224	−	0.807240i	$-0.700960\pi$
$277$	1.42902e8	−	2.47513e8i	0.403978	−	0.699711i	0.994202	+	0.107529i	$0.0342938\pi$
$278$		0			0
$279$	−1.35900e8			−0.374631
$280$		0			0
$281$	5.50944e8			1.48127			0.740637	−	0.671905i	$-0.234524\pi$
$281$	5.50944e8			1.48127			0.740637	+	0.671905i	$0.234524\pi$
$282$		0			0
$283$	−1.42073e8	+	2.46077e8i	−0.372613	+	0.645385i	−0.989967	−	0.141301i	$-0.954871\pi$
$283$	−1.42073e8	+	2.46077e8i	−0.372613	+	0.645385i	0.617354	+	0.786686i	$0.288205\pi$
$284$		0			0
$285$	3.52249e8	+	6.10113e8i	0.901348	+	1.56118i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.52616e8	−	2.64338e8i	−0.371926	−	0.644195i
$290$		0			0
$291$	2.22668e8	−	3.85673e8i	0.529704	−	0.917474i
$292$		0			0
$293$	4.33632e7			0.100713			0.0503564	−	0.998731i	$-0.483964\pi$
$293$	4.33632e7			0.100713			0.0503564	+	0.998731i	$0.483964\pi$
$294$		0			0
$295$	7.62276e8			1.72876
$296$		0			0
$297$	2.24568e8	−	3.88964e8i	0.497394	−	0.861512i
$298$		0			0
$299$	−2.52642e8	−	4.37588e8i	−0.546583	−	0.946709i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.33826e8	+	2.31794e8i	0.276371	+	0.478688i
$304$		0			0
$305$	−1.11907e7	+	1.93829e7i	−0.0225844	+	0.0391173i
$306$		0			0
$307$	−4.07582e8			−0.803954			−0.401977	−	0.915650i	$-0.631677\pi$
$307$	−4.07582e8			−0.803954			−0.401977	+	0.915650i	$0.631677\pi$
$308$		0			0
$309$	1.61802e8			0.311983
$310$		0			0
$311$	−3.84132e8	+	6.65336e8i	−0.724134	+	1.25424i	0.235195	+	0.971948i	$0.424427\pi$
$311$	−3.84132e8	+	6.65336e8i	−0.724134	+	1.25424i	−0.959329	+	0.282289i	$0.908906\pi$
$312$		0			0
$313$	−2.15655e8	−	3.73525e8i	−0.397515	−	0.688517i	0.595903	−	0.803056i	$-0.296794\pi$
$313$	−2.15655e8	−	3.73525e8i	−0.397515	−	0.688517i	−0.993419	+	0.114539i	$0.963461\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.89918e7	−	1.36818e8i	−0.139276	−	0.241232i	0.787947	−	0.615743i	$-0.211144\pi$
$317$	−7.89918e7	−	1.36818e8i	−0.139276	−	0.241232i	−0.927223	+	0.374511i	$0.877811\pi$
$318$		0			0
$319$	−7.23797e7	+	1.25365e8i	−0.124839	+	0.216227i
$320$		0			0
$321$	−2.58051e8			−0.435450
$322$		0			0
$323$	−9.79323e8			−1.61703
$324$		0			0
$325$	1.21763e9	−	2.10899e9i	1.96754	−	3.40787i
$326$		0			0
$327$	2.15909e8	+	3.73965e8i	0.341471	+	0.591445i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4.87683e8	−	8.44692e8i	−0.739162	−	1.28027i	−0.952873	−	0.303370i	$-0.901888\pi$
$331$	−4.87683e8	−	8.44692e8i	−0.739162	−	1.28027i	0.213711	−	0.976897i	$-0.431445\pi$
$332$		0			0
$333$	−3.91461e7	+	6.78030e7i	−0.0580943	+	0.100622i
$334$		0			0
$335$	−1.53144e9			−2.22557
$336$		0			0
$337$	−9.07880e8			−1.29218			−0.646091	−	0.763260i	$-0.723597\pi$
$337$	−9.07880e8			−1.29218			−0.646091	+	0.763260i	$0.723597\pi$
$338$		0			0
$339$	−8.10870e7	+	1.40447e8i	−0.113045	+	0.195800i
$340$		0			0
$341$	−4.00691e8	−	6.94017e8i	−0.547229	−	0.947828i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.35989e8	−	5.81949e8i	−0.440512	−	0.762989i
$346$		0			0
$347$	2.89860e7	−	5.02052e7i	0.0372422	−	0.0645053i	−0.846804	−	0.531906i	$-0.821476\pi$
$347$	2.89860e7	−	5.02052e7i	0.0372422	−	0.0645053i	0.884046	+	0.467400i	$0.154809\pi$
$348$		0			0
$349$	−1.33879e9			−1.68587			−0.842935	−	0.538016i	$-0.819174\pi$
$349$	−1.33879e9			−1.68587			−0.842935	+	0.538016i	$0.819174\pi$
$350$		0			0
$351$	1.61055e9			1.98792
$352$		0			0
$353$	−2.91117e8	+	5.04230e8i	−0.352254	+	0.610122i	−0.986644	−	0.162891i	$-0.947918\pi$
$353$	−2.91117e8	+	5.04230e8i	−0.352254	+	0.610122i	0.634390	+	0.773013i	$0.281251\pi$
$354$		0			0
$355$	−4.19596e8	−	7.26762e8i	−0.497774	−	0.862170i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.60217e8	+	2.77505e8i	0.182759	+	0.316548i	0.942819	−	0.333305i	$-0.108164\pi$
$359$	1.60217e8	+	2.77505e8i	0.182759	+	0.316548i	−0.760060	+	0.649853i	$0.774830\pi$
$360$		0			0
$361$	−2.23210e8	+	3.86612e8i	−0.249712	+	0.432514i
$362$		0			0
$363$	−1.24219e8			−0.136306
$364$		0			0
$365$	1.92078e9			2.06753
$366$		0			0
$367$	−3.27639e8	+	5.67487e8i	−0.345990	+	0.599273i	−0.985533	−	0.169483i	$-0.945790\pi$
$367$	−3.27639e8	+	5.67487e8i	−0.345990	+	0.599273i	0.639543	+	0.768755i	$0.279124\pi$
$368$		0			0
$369$	8.41646e7	+	1.45777e8i	0.0872042	+	0.151042i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.71464e8	+	4.70189e8i	0.270851	+	0.469128i	0.969080	−	0.246746i	$-0.0793615\pi$
$373$	2.71464e8	+	4.70189e8i	0.270851	+	0.469128i	−0.698229	+	0.715875i	$0.746028\pi$
$374$		0			0
$375$	8.67635e8	−	1.50279e9i	0.849626	−	1.47159i
$376$		0			0
$377$	−5.19090e8			−0.498940
$378$		0			0
$379$	−1.57480e9			−1.48590			−0.742949	−	0.669348i	$-0.766573\pi$
$379$	−1.57480e9			−1.48590			−0.742949	+	0.669348i	$0.766573\pi$
$380$		0			0
$381$	−7.08038e8	+	1.22636e9i	−0.655872	+	1.13600i
$382$		0			0
$383$	4.44411e8	+	7.69742e8i	0.404193	+	0.700083i	0.994227	−	0.107295i	$-0.0342190\pi$
$383$	4.44411e8	+	7.69742e8i	0.404193	+	0.700083i	−0.590034	+	0.807378i	$0.700886\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.03410e7	+	1.79112e7i	0.00906933	+	0.0157085i
$388$		0			0
$389$	−6.73363e8	+	1.16630e9i	−0.579997	+	1.00458i	0.415482	+	0.909601i	$0.363613\pi$
$389$	−6.73363e8	+	1.16630e9i	−0.579997	+	1.00458i	−0.995479	+	0.0949829i	$0.969720\pi$
$390$		0			0
$391$	9.34116e8			0.790282
$392$		0			0
$393$	1.96990e9			1.63708
$394$		0			0
$395$	4.98670e8	−	8.63722e8i	0.407121	−	0.705154i
$396$		0			0
$397$	−1.07964e9	−	1.86998e9i	−0.865985	−	1.49993i	−0.866066	−	0.499930i	$-0.833359\pi$
$397$	−1.07964e9	−	1.86998e9i	−0.865985	−	1.49993i	8.13447e−5	−	1.00000i	$-0.499974\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.38083e8	+	1.62481e9i	0.726500	+	1.25834i	0.958354	+	0.285585i	$0.0921877\pi$
$401$	9.38083e8	+	1.62481e9i	0.726500	+	1.25834i	−0.231853	+	0.972751i	$0.574479\pi$
$402$		0			0
$403$	1.43683e9	−	2.48867e9i	1.09355	−	1.89408i
$404$		0			0
$405$	1.39897e9			1.04644
$406$		0			0
$407$	−4.61678e8			−0.339437
$408$		0			0
$409$	−1.13724e6	+	1.96976e6i	−0.000821906	+	0.00142358i	−0.866436	−	0.499288i	$-0.833595\pi$
$409$	−1.13724e6	+	1.96976e6i	−0.000821906	+	0.00142358i	0.865614	+	0.500712i	$0.166928\pi$
$410$		0			0
$411$	−5.89131e8	−	1.02041e9i	−0.418568	−	0.724980i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.05694e9	−	3.56272e9i	−1.41271	−	2.44688i
$416$		0			0
$417$	5.66067e8	−	9.80456e8i	0.382289	−	0.662143i
$418$		0			0
$419$	−2.40944e9			−1.60017			−0.800087	−	0.599884i	$-0.795213\pi$
$419$	−2.40944e9			−1.60017			−0.800087	+	0.599884i	$0.795213\pi$
$420$		0			0
$421$	−1.08307e9			−0.707404			−0.353702	−	0.935358i	$-0.615077\pi$
$421$	−1.08307e9			−0.707404			−0.353702	+	0.935358i	$0.615077\pi$
$422$		0			0
$423$	−1.04434e8	+	1.80886e8i	−0.0670891	+	0.116202i
$424$		0			0
$425$	2.25103e9	+	3.89889e9i	1.42239	+	2.46366i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.13170e9	+	1.96016e9i	0.692038	+	1.19865i
$430$		0			0
$431$	−2.52993e8	+	4.38197e8i	−0.152208	+	0.263633i	−0.932039	−	0.362358i	$-0.881972\pi$
$431$	−2.52993e8	+	4.38197e8i	−0.152208	+	0.263633i	0.779831	+	0.625991i	$0.215305\pi$
$432$		0			0
$433$	3.73323e8			0.220992			0.110496	−	0.993877i	$-0.464756\pi$
$433$	3.73323e8			0.220992			0.110496	+	0.993877i	$0.464756\pi$
$434$		0			0
$435$	−6.90339e8			−0.402115
$436$		0			0
$437$	6.39212e8	−	1.10715e9i	0.366404	−	0.634630i
$438$		0			0
$439$	4.44465e6	+	7.69836e6i	0.00250733	+	0.00434283i	0.867276	−	0.497827i	$-0.165869\pi$
$439$	4.44465e6	+	7.69836e6i	0.00250733	+	0.00434283i	−0.864769	+	0.502170i	$0.832535\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.12024e8	−	8.86851e8i	−0.279819	−	0.484661i	0.691521	−	0.722357i	$-0.256941\pi$
$443$	−5.12024e8	−	8.86851e8i	−0.279819	−	0.484661i	−0.971340	+	0.237696i	$0.923608\pi$
$444$		0			0
$445$	−1.61489e9	+	2.79707e9i	−0.868726	+	1.50468i
$446$		0			0
$447$	−1.43798e9			−0.761510
$448$		0			0
$449$	8.32711e8			0.434142			0.217071	−	0.976156i	$-0.430350\pi$
$449$	8.32711e8			0.434142			0.217071	+	0.976156i	$0.430350\pi$
$450$		0			0
$451$	−4.96308e8	+	8.59630e8i	−0.254761	+	0.441259i
$452$		0			0
$453$	−3.53524e8	−	6.12321e8i	−0.178679	−	0.309482i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.14391e9	+	1.98130e9i	0.560639	+	0.971055i	0.997441	+	0.0714976i	$0.0227778\pi$
$457$	1.14391e9	+	1.98130e9i	0.560639	+	0.971055i	−0.436802	+	0.899558i	$0.643889\pi$
$458$		0			0
$459$	−1.48871e9	+	2.57852e9i	−0.718565	+	1.24459i
$460$		0			0
$461$	7.84459e8			0.372921			0.186461	−	0.982462i	$-0.440298\pi$
$461$	7.84459e8			0.372921			0.186461	+	0.982462i	$0.440298\pi$
$462$		0			0
$463$	−2.31590e9			−1.08439			−0.542196	−	0.840252i	$-0.682407\pi$
$463$	−2.31590e9			−1.08439			−0.542196	+	0.840252i	$0.682407\pi$
$464$		0			0
$465$	1.91085e9	−	3.30968e9i	0.881333	−	1.52651i
$466$		0			0
$467$	3.06330e8	+	5.30578e8i	0.139181	+	0.241068i	0.927187	−	0.374599i	$-0.122220\pi$
$467$	3.06330e8	+	5.30578e8i	0.139181	+	0.241068i	−0.788006	+	0.615668i	$0.788886\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.11031e8	−	7.11927e8i	−0.181260	−	0.313951i
$472$		0			0
$473$	−6.09796e7	+	1.05620e8i	−0.0264954	+	0.0458914i
$474$		0			0
$475$	6.16147e9			2.63789
$476$		0			0
$477$	8.28356e8			0.349464
$478$		0			0
$479$	−3.64475e8	+	6.31289e8i	−0.151528	+	0.262454i	−0.931789	−	0.362999i	$-0.881753\pi$
$479$	−3.64475e8	+	6.31289e8i	−0.151528	+	0.262454i	0.780261	+	0.625454i	$0.215086\pi$
$480$		0			0
$481$	−8.27763e8	−	1.43373e9i	−0.339155	−	0.587434i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.85144e9	−	4.93883e9i	−1.13493	−	1.96575i
$486$		0			0
$487$	4.34192e8	−	7.52043e8i	0.170346	−	0.295047i	−0.768195	−	0.640216i	$-0.778845\pi$
$487$	4.34192e8	−	7.52043e8i	0.170346	−	0.295047i	0.938541	+	0.345169i	$0.112178\pi$
$488$		0			0
$489$	1.74811e9			0.676063
$490$		0			0
$491$	−3.47503e9			−1.32487			−0.662435	−	0.749119i	$-0.730477\pi$
$491$	−3.47503e9			−1.32487			−0.662435	+	0.749119i	$0.730477\pi$
$492$		0			0
$493$	4.79821e8	−	8.31074e8i	0.180349	−	0.312374i
$494$		0			0
$495$	−6.85360e8	−	1.18708e9i	−0.253980	−	0.439907i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.84086e9	+	3.18846e9i	0.663236	+	1.14876i	0.979760	+	0.200174i	$0.0641507\pi$
$499$	1.84086e9	+	3.18846e9i	0.663236	+	1.14876i	−0.316524	+	0.948584i	$0.602516\pi$
$500$		0			0
$501$	−1.22656e9	+	2.12447e9i	−0.435770	+	0.754775i
$502$		0			0
$503$	3.79099e9			1.32820			0.664102	−	0.747642i	$-0.268814\pi$
$503$	3.79099e9			1.32820			0.664102	+	0.747642i	$0.268814\pi$
$504$		0			0
$505$	3.42749e9			1.18429
$506$		0			0
$507$	−2.84193e9	+	4.92236e9i	−0.968467	+	1.67743i
$508$		0			0
$509$	2.04656e9	+	3.54475e9i	0.687880	+	1.19144i	0.972522	+	0.232810i	$0.0747920\pi$
$509$	2.04656e9	+	3.54475e9i	0.687880	+	1.19144i	−0.284642	+	0.958634i	$0.591875\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.03744e9	+	3.52895e9i	0.666306	+	1.15408i
$514$		0			0
$515$	1.03600e9	−	1.79441e9i	0.334222	−	0.578890i
$516$		0			0
$517$	−1.23167e9			−0.391993
$518$		0			0
$519$	−1.29549e9			−0.406770
$520$		0			0
$521$	−8.47729e8	+	1.46831e9i	−0.262618	+	0.454868i	−0.966937	−	0.255016i	$-0.917919\pi$
$521$	−8.47729e8	+	1.46831e9i	−0.262618	+	0.454868i	0.704319	+	0.709884i	$0.251253\pi$
$522$		0			0
$523$	7.68571e8	+	1.33120e9i	0.234924	+	0.406901i	0.959251	−	0.282556i	$-0.0911824\pi$
$523$	7.68571e8	+	1.33120e9i	0.234924	+	0.406901i	−0.724326	+	0.689457i	$0.757849\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.65627e9	+	4.60079e9i	0.790560	+	1.36929i
$528$		0			0
$529$	1.09271e9	−	1.89263e9i	0.320929	−	0.555866i
$530$		0			0
$531$	1.05078e9			0.304566
$532$		0			0
$533$	−3.55940e9			−1.01820
$534$		0			0
$535$	−1.65227e9	+	2.86182e9i	−0.466491	+	0.807986i
$536$		0			0
$537$	2.51904e9	+	4.36310e9i	0.701980	+	1.21587i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.17255e9	+	3.76296e9i	0.589901	+	1.02174i	0.994245	+	0.107131i	$0.0341664\pi$
$541$	2.17255e9	+	3.76296e9i	0.589901	+	1.02174i	−0.404344	+	0.914607i	$0.632500\pi$
$542$		0			0
$543$	−3.71380e8	+	6.43249e8i	−0.0995449	+	0.172417i
$544$		0			0
$545$	5.52976e9			1.46325
$546$		0			0
$547$	2.30195e9			0.601367			0.300683	−	0.953724i	$-0.402785\pi$
$547$	2.30195e9			0.601367			0.300683	+	0.953724i	$0.402785\pi$
$548$		0			0
$549$	−1.54262e7	+	2.67189e7i	−0.00397882	+	0.00689152i
$550$		0			0
$551$	−6.56678e8	−	1.13740e9i	−0.167233	−	0.289656i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.10084e9	−	1.90672e9i	−0.273338	−	0.473435i
$556$		0			0
$557$	−8.55534e8	+	1.48183e9i	−0.209770	+	0.363333i	−0.951642	−	0.307209i	$-0.900605\pi$
$557$	−8.55534e8	+	1.48183e9i	−0.209770	+	0.363333i	0.741872	+	0.670542i	$0.233938\pi$
$558$		0			0
$559$	−4.37332e8			−0.105894
$560$		0			0
$561$	−4.18434e9			−1.00059
$562$		0			0
$563$	−1.08317e9	+	1.87610e9i	−0.255809	+	0.443074i	−0.965115	−	0.261827i	$-0.915675\pi$
$563$	−1.08317e9	+	1.87610e9i	−0.255809	+	0.443074i	0.709306	+	0.704901i	$0.249008\pi$
$564$		0			0
$565$	1.03838e9	+	1.79853e9i	0.242207	+	0.419515i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.38031e9	+	2.39077e9i	0.314112	+	0.544059i	0.979248	−	0.202664i	$-0.0649598\pi$
$569$	1.38031e9	+	2.39077e9i	0.314112	+	0.544059i	−0.665136	+	0.746722i	$0.731626\pi$
$570$		0			0
$571$	−3.62954e8	+	6.28654e8i	−0.0815877	+	0.141314i	−0.903932	−	0.427676i	$-0.859332\pi$
$571$	−3.62954e8	+	6.28654e8i	−0.0815877	+	0.141314i	0.822344	+	0.568990i	$0.192666\pi$
$572$		0			0
$573$	1.37368e9			0.305032
$574$		0			0
$575$	−5.87705e9			−1.28921
$576$		0			0
$577$	2.68517e9	−	4.65086e9i	0.581911	−	1.00790i	−0.413341	−	0.910576i	$-0.635638\pi$
$577$	2.68517e9	−	4.65086e9i	0.581911	−	1.00790i	0.995253	−	0.0973240i	$-0.0310283\pi$
$578$		0			0
$579$	−3.49540e9	−	6.05421e9i	−0.748380	−	1.29623i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.44235e9	+	4.23028e9i	0.510468	+	0.884157i
$584$		0			0
$585$	2.45762e9	−	4.25672e9i	0.507539	−	0.879083i
$586$		0			0
$587$	−7.86145e9			−1.60424			−0.802120	−	0.597163i	$-0.796295\pi$
$587$	−7.86145e9			−1.60424			−0.802120	+	0.597163i	$0.796295\pi$
$588$		0			0
$589$	7.27069e9			1.46613
$590$		0			0
$591$	2.70313e9	−	4.68195e9i	0.538654	−	0.932976i
$592$		0			0
$593$	−2.72206e9	−	4.71475e9i	−0.536051	−	0.928468i	−0.999112	−	0.0421412i	$-0.986582\pi$
$593$	−2.72206e9	−	4.71475e9i	−0.536051	−	0.928468i	0.463060	−	0.886327i	$-0.346751\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.83588e9	−	4.91189e9i	−0.545479	−	0.944798i
$598$		0			0
$599$	−3.98704e9	+	6.90575e9i	−0.757978	+	1.31286i	0.185902	+	0.982568i	$0.440479\pi$
$599$	−3.98704e9	+	6.90575e9i	−0.757978	+	1.31286i	−0.943880	+	0.330288i	$0.892854\pi$
$600$		0			0
$601$	−6.27378e8			−0.117888			−0.0589439	−	0.998261i	$-0.518773\pi$
$601$	−6.27378e8			−0.117888			−0.0589439	+	0.998261i	$0.518773\pi$
$602$		0			0
$603$	−2.11105e9			−0.392092
$604$		0			0
$605$	−7.95362e8	+	1.37761e9i	−0.146023	+	0.252919i
$606$		0			0
$607$	−1.89879e9	−	3.28880e9i	−0.344601	−	0.596866i	0.640680	−	0.767808i	$-0.278652\pi$
$607$	−1.89879e9	−	3.28880e9i	−0.344601	−	0.596866i	−0.985281	+	0.170941i	$0.945319\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.20832e9	−	3.82491e9i	−0.391667	−	0.678387i
$612$		0			0
$613$	−5.30599e9	+	9.19025e9i	−0.930369	+	1.61145i	−0.147677	+	0.989036i	$0.547180\pi$
$613$	−5.30599e9	+	9.19025e9i	−0.930369	+	1.61145i	−0.782691	+	0.622410i	$0.786154\pi$
$614$		0			0
$615$	−4.73366e9			−0.820605
$616$		0			0
$617$	2.26828e8			0.0388776			0.0194388	−	0.999811i	$-0.493812\pi$
$617$	2.26828e8			0.0388776			0.0194388	+	0.999811i	$0.493812\pi$
$618$		0			0
$619$	−2.45900e9	+	4.25912e9i	−0.416718	+	0.721776i	−0.995607	−	0.0936299i	$-0.970153\pi$
$619$	−2.45900e9	+	4.25912e9i	−0.416718	+	0.721776i	0.578889	+	0.815406i	$0.303486\pi$
$620$		0			0
$621$	−1.94339e9	−	3.36605e9i	−0.325641	−	0.564027i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−4.53650e9	−	7.85745e9i	−0.743260	−	1.28736i
$626$		0			0
$627$	−2.86332e9	+	4.95942e9i	−0.463910	+	0.803516i
$628$		0			0
$629$	3.06057e9			0.490371
$630$		0			0
$631$	6.22228e9			0.985931			0.492966	−	0.870049i	$-0.335913\pi$
$631$	6.22228e9			0.985931			0.492966	+	0.870049i	$0.335913\pi$
$632$		0			0
$633$	1.99512e9	−	3.45565e9i	0.312648	−	0.541523i
$634$		0			0
$635$	9.06697e9	+	1.57044e10i	1.40525	+	2.43397i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−5.78404e8	−	1.00182e9i	−0.0876957	−	0.151893i
$640$		0			0
$641$	1.35677e9	−	2.35000e9i	0.203472	−	0.352424i	−0.746173	−	0.665752i	$-0.768111\pi$
$641$	1.35677e9	−	2.35000e9i	0.203472	−	0.352424i	0.949645	+	0.313328i	$0.101444\pi$
$642$		0			0
$643$	−5.96086e9			−0.884240			−0.442120	−	0.896956i	$-0.645774\pi$
$643$	−5.96086e9			−0.884240			−0.442120	+	0.896956i	$0.645774\pi$
$644$		0			0
$645$	−5.81609e8			−0.0853438
$646$		0			0
$647$	−9.35684e8	+	1.62065e9i	−0.135820	+	0.235247i	−0.925910	−	0.377743i	$-0.876700\pi$
$647$	−9.35684e8	+	1.62065e9i	−0.135820	+	0.235247i	0.790090	+	0.612990i	$0.210034\pi$
$648$		0			0
$649$	3.09815e9	+	5.36616e9i	0.444884	+	0.770561i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.34121e9	−	7.51920e9i	−0.610120	−	1.05676i	−0.991220	−	0.132225i	$-0.957788\pi$
$653$	−4.34121e9	−	7.51920e9i	−0.610120	−	1.05676i	0.381100	−	0.924534i	$-0.375545\pi$
$654$		0			0
$655$	1.26131e10	−	2.18464e10i	1.75378	−	3.03764i
$656$		0			0
$657$	2.64775e9			0.364249
$658$		0			0
$659$	1.17028e10			1.59291			0.796457	−	0.604696i	$-0.206705\pi$
$659$	1.17028e10			1.59291			0.796457	+	0.604696i	$0.206705\pi$
$660$		0			0
$661$	2.11762e9	−	3.66782e9i	0.285195	−	0.493973i	−0.687461	−	0.726221i	$-0.741275\pi$
$661$	2.11762e9	−	3.66782e9i	0.285195	−	0.493973i	0.972657	+	0.232248i	$0.0746082\pi$
$662$		0			0
$663$	−7.50228e9	−	1.29943e10i	−0.999760	−	1.73164i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.26365e8	+	1.08490e9i	0.0817311	+	0.141562i
$668$		0			0
$669$	6.32731e9	−	1.09592e10i	0.817010	−	1.41510i
$670$		0			0
$671$	−1.81932e8			−0.0232477
$672$		0			0
$673$	−1.64366e9			−0.207854			−0.103927	−	0.994585i	$-0.533141\pi$
$673$	−1.64366e9			−0.207854			−0.103927	+	0.994585i	$0.533141\pi$
$674$		0			0
$675$	9.36633e9	−	1.62230e10i	1.17221	−	2.03033i
$676$		0			0
$677$	−5.44190e9	−	9.42565e9i	−0.674048	−	1.16748i	−0.976746	−	0.214398i	$-0.931221\pi$
$677$	−5.44190e9	−	9.42565e9i	−0.674048	−	1.16748i	0.302699	−	0.953086i	$-0.402112\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.74352e9	+	3.01986e9i	0.211549	+	0.366414i
$682$		0			0
$683$	1.92639e9	−	3.33660e9i	0.231351	−	0.400711i	−0.726855	−	0.686791i	$-0.759019\pi$
$683$	1.92639e9	−	3.33660e9i	0.231351	−	0.400711i	0.958206	+	0.286080i	$0.0923522\pi$
$684$		0			0
$685$	−1.50885e10			−1.79362
$686$		0			0
$687$	−3.95126e9			−0.464930
$688$		0			0
$689$	−8.75800e9	+	1.51693e10i	−1.02009	+	1.76684i
$690$		0			0
$691$	7.77195e9	+	1.34614e10i	0.896100	+	1.55209i	0.832437	+	0.554120i	$0.186945\pi$
$691$	7.77195e9	+	1.34614e10i	0.896100	+	1.55209i	0.0636633	+	0.997971i	$0.479722\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.24892e9	−	1.25555e10i	−0.819080	−	1.41869i
$696$		0			0
$697$	3.29013e9	−	5.69868e9i	0.368043	−	0.637469i
$698$		0			0
$699$	−1.65493e9			−0.183277
$700$		0			0
$701$	−7.75099e9			−0.849854			−0.424927	−	0.905228i	$-0.639700\pi$
$701$	−7.75099e9			−0.849854			−0.424927	+	0.905228i	$0.639700\pi$
$702$		0			0
$703$	2.09433e9	−	3.62749e9i	0.227354	−	0.393788i
$704$		0			0
$705$	−2.93684e9	−	5.08676e9i	−0.315660	−	0.546738i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.73320e9	+	9.93020e9i	0.604137	+	1.04640i	0.992187	+	0.124758i	$0.0398154\pi$
$709$	5.73320e9	+	9.93020e9i	0.604137	+	1.04640i	−0.388050	+	0.921638i	$0.626851\pi$
$710$		0			0
$711$	6.87405e8	−	1.19062e9i	0.0717248	−	0.124231i
$712$		0			0
$713$	−6.93507e9			−0.716535
$714$		0			0
$715$	2.89845e10			2.96548
$716$		0			0
$717$	1.16713e9	−	2.02154e9i	0.118251	−	0.204816i
$718$		0			0
$719$	8.19259e9	+	1.41900e10i	0.821997	+	1.42374i	0.904193	+	0.427125i	$0.140473\pi$
$719$	8.19259e9	+	1.41900e10i	0.821997	+	1.42374i	−0.0821957	+	0.996616i	$0.526193\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	9.13949e8	+	1.58301e9i	0.0899369	+	0.155775i
$724$		0			0
$725$	−3.01882e9	+	5.22875e9i	−0.294208	+	0.509583i
$726$		0			0
$727$	1.66277e10			1.60495			0.802474	−	0.596687i	$-0.203517\pi$
$727$	1.66277e10			1.60495			0.802474	+	0.596687i	$0.203517\pi$
$728$		0			0
$729$	1.13647e10			1.08646
$730$		0			0
$731$	4.04247e8	−	7.00177e8i	0.0382769	−	0.0662975i
$732$		0			0
$733$	−7.28863e9	−	1.26243e10i	−0.683568	−	1.18398i	−0.973884	−	0.227044i	$-0.927094\pi$
$733$	−7.28863e9	−	1.26243e10i	−0.683568	−	1.18398i	0.290316	−	0.956931i	$-0.406240\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.22429e9	−	1.07808e10i	−0.572735	−	0.992006i
$738$		0			0
$739$	−2.15001e9	+	3.72393e9i	−0.195968	+	0.339427i	−0.947218	−	0.320592i	$-0.896118\pi$
$739$	−2.15001e9	+	3.72393e9i	−0.195968	+	0.339427i	0.751249	+	0.660019i	$0.229452\pi$
$740$		0			0
$741$	−2.05351e10			−1.85410
$742$		0			0
$743$	−9.14731e9			−0.818150			−0.409075	−	0.912501i	$-0.634148\pi$
$743$	−9.14731e9			−0.818150			−0.409075	+	0.912501i	$0.634148\pi$
$744$		0			0
$745$	−9.20720e9	+	1.59473e10i	−0.815794	+	1.41300i
$746$		0			0
$747$	−2.83544e9	−	4.91113e9i	−0.248885	−	0.431081i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.59368e8	−	1.48847e9i	−0.0740354	−	0.128233i	0.826631	−	0.562744i	$-0.190254\pi$
$751$	−8.59368e8	−	1.48847e9i	−0.0740354	−	0.128233i	−0.900666	+	0.434511i	$0.856921\pi$
$752$		0			0
$753$	−3.76045e9	+	6.51328e9i	−0.320964	+	0.555927i
$754$		0			0
$755$	−9.05428e9			−0.765666
$756$		0			0
$757$	−1.58386e10			−1.32703			−0.663517	−	0.748161i	$-0.730937\pi$
$757$	−1.58386e10			−1.32703			−0.663517	+	0.748161i	$0.730937\pi$
$758$		0			0
$759$	2.73115e9	−	4.73049e9i	0.226725	−	0.392699i
$760$		0			0
$761$	−1.64664e9	−	2.85207e9i	−0.135442	−	0.234592i	0.790324	−	0.612689i	$-0.209912\pi$
$761$	−1.64664e9	−	2.85207e9i	−0.135442	−	0.234592i	−0.925766	+	0.378096i	$0.876579\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	4.54340e9	+	7.86940e9i	0.366915	+	0.635516i
$766$		0			0
$767$	−1.11096e10	+	1.92424e10i	−0.889028	+	1.53984i
$768$		0			0
$769$	−1.80581e10			−1.43196			−0.715978	−	0.698123i	$-0.754019\pi$
$769$	−1.80581e10			−1.43196			−0.715978	+	0.698123i	$0.754019\pi$
$770$		0			0
$771$	−2.63113e9			−0.206753
$772$		0			0
$773$	7.87646e9	−	1.36424e10i	0.613342	−	1.06234i	−0.377331	−	0.926079i	$-0.623158\pi$
$773$	7.87646e9	−	1.36424e10i	0.613342	−	1.06234i	0.990673	−	0.136261i	$-0.0435087\pi$
$774$		0			0
$775$	−1.67121e10	−	2.89462e10i	−1.28966	−	2.23375i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.50285e9	−	7.79916e9i	−0.341276	−	0.591108i
$780$		0			0
$781$	3.41077e9	−	5.90763e9i	0.256197	−	0.443746i
$782$		0			0
$783$	−3.99298e9			−0.297257
$784$		0			0
$785$	−1.05271e10			−0.776724
$786$		0			0
$787$	−5.11120e9	+	8.85285e9i	−0.373776	+	0.647398i	−0.990143	−	0.140060i	$-0.955270\pi$
$787$	−5.11120e9	+	8.85285e9i	−0.373776	+	0.647398i	0.616367	+	0.787459i	$0.288604\pi$
$788$		0			0
$789$	−3.12443e9	−	5.41167e9i	−0.226465	−	0.392249i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.26193e8	−	5.64984e8i	−0.0232284	−	0.0402328i
$794$		0			0
$795$	−1.16473e10	+	2.01737e10i	−0.822128	+	1.42397i
$796$		0			0
$797$	1.44391e10			1.01027			0.505134	−	0.863041i	$-0.331443\pi$
$797$	1.44391e10			1.01027			0.505134	+	0.863041i	$0.331443\pi$
$798$		0			0
$799$	8.16502e9			0.566296
$800$		0			0
$801$	−2.22609e9	+	3.85570e9i	−0.153048	+	0.265088i
$802$		0			0
$803$	7.80672e9	+	1.35216e10i	0.532064	+	0.921562i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.11897e9	+	8.86632e9i	0.342867	+	0.593863i
$808$		0			0
$809$	5.04427e9	−	8.73692e9i	0.334949	−	0.580148i	−0.648526	−	0.761192i	$-0.724614\pi$
$809$	5.04427e9	−	8.73692e9i	0.334949	−	0.580148i	0.983475	+	0.181044i	$0.0579477\pi$
$810$		0			0
$811$	1.35981e9			0.0895172			0.0447586	−	0.998998i	$-0.485748\pi$
$811$	1.35981e9			0.0895172			0.0447586	+	0.998998i	$0.485748\pi$
$812$		0			0
$813$	−1.90890e9			−0.124585
$814$		0			0
$815$	1.11929e10	−	1.93867e10i	0.724256	−	1.25445i
$816$		0			0
$817$	−5.53250e8	−	9.58256e8i	−0.0354931	−	0.0614758i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.49011e9	+	1.29733e10i	0.472375	+	0.818178i	0.999500	−	0.0316097i	$-0.0100633\pi$
$821$	7.49011e9	+	1.29733e10i	0.472375	+	0.818178i	−0.527125	+	0.849788i	$0.676730\pi$
$822$		0			0
$823$	9.80080e9	−	1.69755e10i	0.612861	−	1.06151i	−0.377895	−	0.925849i	$-0.623352\pi$
$823$	9.80080e9	−	1.69755e10i	0.612861	−	1.06151i	0.990756	−	0.135658i	$-0.0433148\pi$
$824$		0			0
$825$	2.63260e10			1.63229
$826$		0			0
$827$	1.68768e9			0.103758			0.0518789	−	0.998653i	$-0.483479\pi$
$827$	1.68768e9			0.103758			0.0518789	+	0.998653i	$0.483479\pi$
$828$		0			0
$829$	8.22703e8	−	1.42496e9i	0.0501536	−	0.0868686i	−0.839859	−	0.542805i	$-0.817362\pi$
$829$	8.22703e8	−	1.42496e9i	0.0501536	−	0.0868686i	0.890012	+	0.455936i	$0.150696\pi$
$830$		0			0
$831$	5.53955e9	+	9.59478e9i	0.334866	+	0.580005i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.57071e10	+	2.72054e10i	0.933667	+	1.61716i
$836$		0			0
$837$	1.10525e10	−	1.91435e10i	0.651510	−	1.12845i
$838$		0			0
$839$	−3.49725e9			−0.204437			−0.102219	−	0.994762i	$-0.532594\pi$
$839$	−3.49725e9			−0.204437			−0.102219	+	0.994762i	$0.532594\pi$
$840$		0			0
$841$	−1.59629e10			−0.925393
$842$		0			0
$843$	−1.06786e10	+	1.84959e10i	−0.613929	+	1.06336i
$844$		0			0
$845$	3.63930e10	+	6.30346e10i	2.07501	+	3.59402i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−5.50741e9	−	9.53912e9i	−0.308866	−	0.534972i
$850$		0			0
$851$	−1.99766e9	+	3.46004e9i	−0.111114	+	0.192454i
$852$		0			0
$853$	2.86798e10			1.58218			0.791088	−	0.611702i	$-0.209515\pi$
$853$	2.86798e10			1.58218			0.791088	+	0.611702i	$0.209515\pi$
$854$		0			0
$855$	1.24361e10			0.680461
$856$		0			0
$857$	−1.83667e10	+	3.18120e10i	−0.996776	+	1.72647i	−0.428901	+	0.903351i	$0.641099\pi$
$857$	−1.83667e10	+	3.18120e10i	−0.996776	+	1.72647i	−0.567875	+	0.823115i	$0.692234\pi$
$858$		0			0
$859$	−2.77367e9	−	4.80413e9i	−0.149306	−	0.258606i	0.781665	−	0.623699i	$-0.214371\pi$
$859$	−2.77367e9	−	4.80413e9i	−0.149306	−	0.258606i	−0.930971	+	0.365092i	$0.881037\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.63029e9	−	4.55579e9i	−0.139305	−	0.241283i	0.787929	−	0.615766i	$-0.211153\pi$
$863$	−2.63029e9	−	4.55579e9i	−0.139305	−	0.241283i	−0.927234	+	0.374484i	$0.877820\pi$
$864$		0			0
$865$	−8.29487e9	+	1.43671e10i	−0.435766	+	0.754769i
$866$		0			0
$867$	1.18322e10			0.616594
$868$		0			0
$869$	8.10707e9			0.419078
$870$		0			0
$871$	2.23196e10	−	3.86587e10i	1.14452	−	1.98236i
$872$		0			0
$873$	−3.93064e9	−	6.80807e9i	−0.199946	−	0.346317i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.41580e10	−	2.45224e10i	−0.708767	−	1.22762i	−0.965315	−	0.261089i	$-0.915918\pi$
$877$	−1.41580e10	−	2.45224e10i	−0.708767	−	1.22762i	0.256548	−	0.966532i	$-0.417415\pi$
$878$		0			0
$879$	−8.40482e8	+	1.45576e9i	−0.0417414	+	0.0722983i
$880$		0			0
$881$	−5.58205e9			−0.275029			−0.137514	−	0.990500i	$-0.543911\pi$
$881$	−5.58205e9			−0.275029			−0.137514	+	0.990500i	$0.543911\pi$
$882$		0			0
$883$	−2.81316e10			−1.37509			−0.687547	−	0.726140i	$-0.741312\pi$
$883$	−2.81316e10			−1.37509			−0.687547	+	0.726140i	$0.741312\pi$
$884$		0			0
$885$	−1.47747e10	+	2.55906e10i	−0.716502	+	1.24102i
$886$		0			0
$887$	4.96052e6	+	8.59188e6i	0.000238668	+	0.000413386i	0.866145	−	0.499793i	$-0.166591\pi$
$887$	4.96052e6	+	8.59188e6i	0.000238668	+	0.000413386i	−0.865906	+	0.500207i	$0.833257\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.68590e9	+	9.84828e9i	0.269295	+	0.466432i
$892$		0			0
$893$	5.58729e9	−	9.67746e9i	0.262555	−	0.454759i
$894$		0			0
$895$	6.45164e10			3.00808
$896$		0			0
$897$	1.95872e10			0.906147
$898$		0			0
$899$	−3.56229e9	+	6.17006e9i	−0.163520	+	0.283224i
$900$		0			0
$901$	−1.61909e10	−	2.80435e10i	−0.737453	−	1.27731i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.75580e9	+	8.23730e9i	0.213282	+	0.369415i
$906$		0			0
$907$	8.05863e8	−	1.39579e9i	0.0358621	−	0.0621149i	−0.847537	−	0.530736i	$-0.821916\pi$
$907$	8.05863e8	−	1.39579e9i	0.0358621	−	0.0621149i	0.883399	+	0.468621i	$0.155249\pi$
$908$		0			0
$909$	4.72472e9			0.208642
$910$		0			0
$911$	−2.31768e10			−1.01564			−0.507818	−	0.861464i	$-0.669548\pi$
$911$	−2.31768e10			−1.01564			−0.507818	+	0.861464i	$0.669548\pi$
$912$		0			0
$913$	1.67202e10	−	2.89602e10i	0.727100	−	1.25937i
$914$		0			0
$915$	−4.33805e8	−	7.51373e8i	−0.0187207	−	0.0324251i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	6.83205e9	+	1.18335e10i	0.290367	+	0.502930i	0.973896	−	0.226993i	$-0.0728894\pi$
$919$	6.83205e9	+	1.18335e10i	0.290367	+	0.502930i	−0.683530	+	0.729923i	$0.739556\pi$
$920$		0			0
$921$	7.89992e9	−	1.36831e10i	0.333207	−	0.577131i
$922$		0			0
$923$	2.44613e10			1.02394
$924$		0			0
$925$	−1.92558e10			−0.799953
$926$		0			0
$927$	1.42811e9	−	2.47355e9i	0.0588818	−	0.101986i
$928$		0			0
$929$	1.67141e10	+	2.89497e10i	0.683956	+	1.18465i	0.973764	+	0.227562i	$0.0730753\pi$
$929$	1.67141e10	+	2.89497e10i	0.683956	+	1.18465i	−0.289808	+	0.957085i	$0.593591\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.48908e10	−	2.57916e10i	−0.600250	−	1.03966i
$934$		0			0
$935$	−2.67918e10	+	4.64048e10i	−1.07192	+	1.85662i
$936$		0			0
$937$	1.04114e10			0.413450			0.206725	−	0.978399i	$-0.433720\pi$
$937$	1.04114e10			0.413450			0.206725	+	0.978399i	$0.433720\pi$
$938$		0			0
$939$	1.67196e10			0.659017
$940$		0			0
$941$	−2.50008e10	+	4.33027e10i	−0.978117	+	1.69415i	−0.308877	+	0.951102i	$0.599953\pi$
$941$	−2.50008e10	+	4.33027e10i	−0.978117	+	1.69415i	−0.669240	+	0.743047i	$0.733380\pi$
$942$		0			0
$943$	4.29499e9	+	7.43914e9i	0.166790	+	0.288890i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.13649e9	+	1.58249e10i	0.349586	+	0.605501i	0.986176	−	0.165702i	$-0.0529888\pi$
$947$	9.13649e9	+	1.58249e10i	0.349586	+	0.605501i	−0.636590	+	0.771203i	$0.719656\pi$
$948$		0			0
$949$	−2.79940e10	+	4.84870e10i	−1.06324	+	1.84159i
$950$		0			0
$951$	6.12420e9			0.230897
$952$		0			0
$953$	−1.24663e10			−0.466565			−0.233282	−	0.972409i	$-0.574947\pi$
$953$	−1.24663e10			−0.466565			−0.233282	+	0.972409i	$0.574947\pi$
$954$		0			0
$955$	8.79553e9	−	1.52343e10i	0.326776	−	0.565993i
$956$		0			0
$957$	−2.80578e9	−	4.85975e9i	−0.103481	−	0.179235i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−5.96436e9	−	1.03306e10i	−0.216786	−	0.375485i
$962$		0			0
$963$	−2.27762e9	+	3.94495e9i	−0.0821844	+	0.142348i
$964$		0			0
$965$	−8.95225e10			−3.20691
$966$		0			0
$967$	4.12045e9			0.146539			0.0732693	−	0.997312i	$-0.476657\pi$
$967$	4.12045e9			0.146539			0.0732693	+	0.997312i	$0.476657\pi$
$968$		0			0
$969$	1.89816e10	−	3.28771e10i	0.670193	−	1.16081i
$970$		0			0
$971$	6.21190e9	+	1.07593e10i	0.217749	+	0.377153i	0.954120	−	0.299426i	$-0.0967951\pi$
$971$	6.21190e9	+	1.07593e10i	0.217749	+	0.377153i	−0.736370	+	0.676579i	$0.763462\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	4.72011e10	+	8.17547e10i	1.63093	+	2.82486i
$976$		0			0
$977$	−2.25652e10	+	3.90840e10i	−0.774119	+	1.34081i	0.161170	+	0.986927i	$0.448473\pi$
$977$	−2.25652e10	+	3.90840e10i	−0.774119	+	1.34081i	−0.935289	+	0.353886i	$0.884860\pi$
$978$		0			0
$979$	−2.62539e10			−0.894241
$980$		0			0
$981$	7.62265e9			0.257789
$982$		0			0
$983$	−2.87779e9	+	4.98448e9i	−0.0966321	+	0.167372i	−0.910289	−	0.413974i	$-0.864140\pi$
$983$	−2.87779e9	+	4.98448e9i	−0.0966321	+	0.167372i	0.813656	+	0.581346i	$0.197474\pi$
$984$		0			0
$985$	−3.46156e10	−	5.99560e10i	−1.15410	−	1.99897i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.27711e8	+	9.14022e8i	0.0173464	+	0.0300448i
$990$		0			0
$991$	1.82054e10	−	3.15327e10i	0.594214	−	1.02921i	−0.399443	−	0.916758i	$-0.630797\pi$
$991$	1.82054e10	−	3.15327e10i	0.594214	−	1.02921i	0.993657	−	0.112451i	$-0.0358701\pi$
$992$		0			0
$993$	3.78098e10			1.22541
$994$		0			0
$995$	−7.26313e10			−2.33745
$996$		0			0
$997$	−5.65165e9	+	9.78895e9i	−0.180610	+	0.312826i	−0.942089	−	0.335364i	$-0.891141\pi$
$997$	−5.65165e9	+	9.78895e9i	−0.180610	+	0.312826i	0.761478	+	0.648190i	$0.224474\pi$
$998$		0			0
$999$	−6.36738e9	−	1.10286e10i	−0.202060	−	0.349979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.8.e.b.165.1		4
7.2	even	3	inner	196.8.e.b.177.1		4
7.3	odd	6		196.8.a.a.1.1		2
7.4	even	3		28.8.a.b.1.2	✓	2
7.5	odd	6		196.8.e.c.177.2		4
7.6	odd	2		196.8.e.c.165.2		4
21.11	odd	6		252.8.a.f.1.2		2
28.11	odd	6		112.8.a.h.1.1		2
56.11	odd	6		448.8.a.q.1.2		2
56.53	even	6		448.8.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.8.a.b.1.2	✓	2	7.4	even	3
112.8.a.h.1.1		2	28.11	odd	6
196.8.a.a.1.1		2	7.3	odd	6
196.8.e.b.165.1		4	1.1	even	1	trivial
196.8.e.b.177.1		4	7.2	even	3	inner
196.8.e.c.165.2		4	7.6	odd	2
196.8.e.c.177.2		4	7.5	odd	6
252.8.a.f.1.2		2	21.11	odd	6
448.8.a.o.1.1		2	56.53	even	6
448.8.a.q.1.2		2	56.11	odd	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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-19.3824 + 33.5713i) q^{3} +(248.206 + 429.906i) q^{5} +(342.147 + 592.615i) q^{9} +(-2017.59 + 3494.57i) q^{11} -14469.7 q^{13} -19243.3 q^{15} +(13375.1 - 23166.3i) q^{17} +(-18305.0 - 31705.2i) q^{19} +(17460.0 + 30241.7i) q^{23} +(-84150.1 + 145752. i) q^{25} -111305. q^{27} +35874.3 q^{29} +(-99299.2 + 171991. i) q^{31} +(-78211.5 - 135466. i) q^{33} +(57206.6 + 99084.7i) q^{37} +(280458. - 485767. i) q^{39} +245990. q^{41} +30224.0 q^{43} +(-169846. + 294182. i) q^{45} +(152616. + 264339. i) q^{47} +(518481. + 898036. i) q^{51} +(605264. - 1.04835e6i) q^{53} -2.00312e6 q^{55} +1.41918e6 q^{57} +(767785. - 1.32984e6i) q^{59} +(22543.2 + 39045.9i) q^{61} +(-3.59147e6 - 6.22061e6i) q^{65} +(-1.54250e6 + 2.67169e6i) q^{67} -1.35367e6 q^{69} -1.69051e6 q^{71} +(1.93466e6 - 3.35093e6i) q^{73} +(-3.26206e6 - 5.65005e6i) q^{75} +(-1.00455e6 - 1.73993e6i) q^{79} +(1.40908e6 - 2.44060e6i) q^{81} -8.28720e6 q^{83} +1.32791e7 q^{85} +(-695328. + 1.20434e6i) q^{87} +(3.25312e6 + 5.63457e6i) q^{89} +(-3.84931e6 - 6.66720e6i) q^{93} +(9.08683e6 - 1.57389e7i) q^{95} -1.14882e7 q^{97} -2.76125e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 14 q^{3} + 294 q^{5} + 2258 q^{9} + 3492 q^{11} - 32340 q^{13} - 48512 q^{15} + 29232 q^{17} + 3206 q^{19} + 9360 q^{23} - 131146 q^{25} - 36344 q^{27} + 369408 q^{29} - 165060 q^{31} - 342832 q^{33}+ \cdots + 18168664 q^{99}+O(q^{100}) \) 4 * q - 14 * q^3 + 294 * q^5 + 2258 * q^9 + 3492 * q^11 - 32340 * q^13 - 48512 * q^15 + 29232 * q^17 + 3206 * q^19 + 9360 * q^23 - 131146 * q^25 - 36344 * q^27 + 369408 * q^29 - 165060 * q^31 - 342832 * q^33 - 286144 * q^37 + 518808 * q^39 - 233520 * q^41 - 588856 * q^43 - 21154 * q^45 + 1014132 * q^47 + 975500 * q^51 + 1396452 * q^53 - 7053424 * q^55 + 4810424 * q^57 + 2729286 * q^59 - 2466954 * q^61 - 6838788 * q^65 - 225176 * q^67 - 3973312 * q^69 + 3060624 * q^71 - 1143548 * q^73 - 7444234 * q^75 - 7951176 * q^79 + 1682882 * q^81 - 36975708 * q^83 + 25553480 * q^85 + 2295076 * q^87 + 4652508 * q^89 - 8529192 * q^93 + 26232912 * q^95 - 53404736 * q^97 + 18168664 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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