LMFDB - Embedded newform 702.2.bb.a.71.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.650628 + 0.174335i) q^{5} +(-1.73068 + 0.463733i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.583337 + 0.336790i) q^{10} +(-0.696978 + 0.696978i) q^{11} +(0.391864 - 3.58419i) q^{13} +(1.55168 + 0.895864i) q^{14} -1.00000 q^{16} +(1.20946 + 2.09485i) q^{17} +(6.33213 + 1.69669i) q^{19} +(-0.174335 - 0.650628i) q^{20} +0.985676 q^{22} +(3.16302 + 5.47852i) q^{23} +(-3.93720 + 2.27315i) q^{25} +(-2.81150 + 2.25732i) q^{26} +(-0.463733 - 1.73068i) q^{28} +4.29257i q^{29} +(1.49861 + 5.59289i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.626062 - 2.33650i) q^{34} +(1.04518 - 0.603436i) q^{35} +(6.83094 - 1.83034i) q^{37} +(-3.27775 - 5.67724i) q^{38} +(-0.336790 + 0.583337i) q^{40} +(-1.28786 + 4.80634i) q^{41} +(-0.772736 - 0.446139i) q^{43} +(-0.696978 - 0.696978i) q^{44} +(1.63730 - 6.11049i) q^{46} +(3.66378 + 0.981707i) q^{47} +(-3.28199 + 1.89486i) q^{49} +(4.39138 + 1.17667i) q^{50} +(3.58419 + 0.391864i) q^{52} +9.00014i q^{53} +(0.331966 - 0.574981i) q^{55} +(-0.895864 + 1.55168i) q^{56} +(3.03531 - 3.03531i) q^{58} +(3.33959 - 3.33959i) q^{59} +(-2.38199 + 4.12572i) q^{61} +(2.89509 - 5.01445i) q^{62} -1.00000i q^{64} +(0.369894 + 2.40029i) q^{65} +(10.6950 + 2.86571i) q^{67} +(-2.09485 + 1.20946i) q^{68} +(-1.16575 - 0.312361i) q^{70} +(1.70900 - 6.37808i) q^{71} +(-8.01788 - 8.01788i) q^{73} +(-6.12445 - 3.53595i) q^{74} +(-1.69669 + 6.33213i) q^{76} +(0.883031 - 1.52946i) q^{77} +(-0.807117 - 1.39797i) q^{79} +(0.650628 - 0.174335i) q^{80} +(4.30925 - 2.48795i) q^{82} +(1.95885 - 7.31055i) q^{83} +(-1.15211 - 1.15211i) q^{85} +(0.230939 + 0.861875i) q^{86} +0.985676i q^{88} +(0.440877 + 1.64537i) q^{89} +(0.983920 + 6.38480i) q^{91} +(-5.47852 + 3.16302i) q^{92} +(-1.89651 - 3.28485i) q^{94} -4.41566 q^{95} +(-0.497183 - 1.85551i) q^{97} +(3.66058 + 0.980849i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.650628	+	0.174335i	−0.290970	+	0.0779651i	−0.401351	−	0.915924i	$-0.631459\pi$
$5$	−0.650628	+	0.174335i	−0.290970	+	0.0779651i	0.110382	+	0.993889i	$0.464793\pi$
$6$		0			0
$7$	−1.73068	+	0.463733i	−0.654134	+	0.175275i	−0.570597	−	0.821230i	$-0.693288\pi$
$7$	−1.73068	+	0.463733i	−0.654134	+	0.175275i	−0.0835368	+	0.996505i	$0.526622\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	0.583337	+	0.336790i	0.184467	+	0.106502i
$11$	−0.696978	+	0.696978i	−0.210147	+	0.210147i	−0.804330	−	0.594183i	$-0.797475\pi$
$11$	−0.696978	+	0.696978i	−0.210147	+	0.210147i	0.594183	+	0.804330i	$0.297475\pi$
$12$		0			0
$13$	0.391864	−	3.58419i	0.108684	−	0.994076i
$13$	0.391864	−	3.58419i	0.108684	−	0.994076i
$14$	1.55168	+	0.895864i	0.414704	+	0.239430i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.20946	+	2.09485i	0.293337	+	0.508075i	0.974597	−	0.223967i	$-0.0719009\pi$
$17$	1.20946	+	2.09485i	0.293337	+	0.508075i	−0.681260	+	0.732042i	$0.738568\pi$
$18$		0			0
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.896959	−	0.442114i	$-0.145771\pi$
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.555732	+	0.831361i	$0.312438\pi$
$20$	−0.174335	−	0.650628i	−0.0389826	−	0.145485i
$21$		0			0
$22$	0.985676			0.210147
$23$	3.16302	+	5.47852i	0.659536	+	1.14235i	0.980736	+	0.195338i	$0.0625805\pi$
$23$	3.16302	+	5.47852i	0.659536	+	1.14235i	−0.321200	+	0.947011i	$0.604086\pi$
$24$		0			0
$25$	−3.93720	+	2.27315i	−0.787441	+	0.454629i
$26$	−2.81150	+	2.25732i	−0.551380	+	0.442696i
$27$		0			0
$28$	−0.463733	−	1.73068i	−0.0876374	−	0.327067i
$29$			4.29257i			0.797111i	0.917144	+	0.398555i	$0.130488\pi$
$29$			4.29257i			0.797111i	−0.917144	+	0.398555i	$0.869512\pi$
$30$		0			0
$31$	1.49861	+	5.59289i	0.269158	+	1.00451i	0.959656	+	0.281178i	$0.0907250\pi$
$31$	1.49861	+	5.59289i	0.269158	+	1.00451i	−0.690498	+	0.723335i	$0.742608\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	0.626062	−	2.33650i	0.107369	−	0.400706i
$35$	1.04518	−	0.603436i	0.176668	−	0.101999i
$36$		0			0
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.350902	−	0.936412i	$-0.385875\pi$
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.772096	+	0.635505i	$0.219208\pi$
$38$	−3.27775	−	5.67724i	−0.531722	−	0.920969i
$39$		0			0
$40$	−0.336790	+	0.583337i	−0.0532512	+	0.0922337i
$41$	−1.28786	+	4.80634i	−0.201129	+	0.750625i	0.789465	+	0.613795i	$0.210358\pi$
$41$	−1.28786	+	4.80634i	−0.201129	+	0.750625i	−0.990595	+	0.136830i	$0.956309\pi$
$42$		0			0
$43$	−0.772736	−	0.446139i	−0.117841	−	0.0680356i	0.439921	−	0.898037i	$-0.355006\pi$
$43$	−0.772736	−	0.446139i	−0.117841	−	0.0680356i	−0.557762	+	0.830001i	$0.688340\pi$
$44$	−0.696978	−	0.696978i	−0.105073	−	0.105073i
$45$		0			0
$46$	1.63730	−	6.11049i	0.241407	−	0.900943i
$47$	3.66378	+	0.981707i	0.534417	+	0.143197i	0.515927	−	0.856632i	$-0.327447\pi$
$47$	3.66378	+	0.981707i	0.534417	+	0.143197i	0.0184899	+	0.999829i	$0.494114\pi$
$48$		0			0
$49$	−3.28199	+	1.89486i	−0.468855	+	0.270694i
$50$	4.39138	+	1.17667i	0.621035	+	0.166406i
$51$		0			0
$52$	3.58419	+	0.391864i	0.497038	+	0.0543418i
$53$			9.00014i			1.23626i	0.786074	+	0.618132i	$0.212110\pi$
$53$			9.00014i			1.23626i	−0.786074	+	0.618132i	$0.787890\pi$
$54$		0			0
$55$	0.331966	−	0.574981i	0.0447622	−	0.0775305i
$56$	−0.895864	+	1.55168i	−0.119715	+	0.207352i
$57$		0			0
$58$	3.03531	−	3.03531i	0.398555	−	0.398555i
$59$	3.33959	−	3.33959i	0.434777	−	0.434777i	−0.455473	−	0.890250i	$-0.650530\pi$
$59$	3.33959	−	3.33959i	0.434777	−	0.434777i	0.890250	+	0.455473i	$0.150530\pi$
$60$		0			0
$61$	−2.38199	+	4.12572i	−0.304982	+	0.528245i	−0.977257	−	0.212057i	$-0.931984\pi$
$61$	−2.38199	+	4.12572i	−0.304982	+	0.528245i	0.672275	+	0.740301i	$0.265317\pi$
$62$	2.89509	−	5.01445i	0.367677	−	0.636835i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.369894	+	2.40029i	0.0458797	+	0.297720i
$66$		0			0
$67$	10.6950	+	2.86571i	1.30660	+	0.350102i	0.843942	−	0.536434i	$-0.180229\pi$
$67$	10.6950	+	2.86571i	1.30660	+	0.350102i	0.462658	+	0.886537i	$0.346896\pi$
$68$	−2.09485	+	1.20946i	−0.254037	+	0.146669i
$69$		0			0
$70$	−1.16575	−	0.312361i	−0.139334	−	0.0373343i
$71$	1.70900	−	6.37808i	0.202821	−	0.756939i	−0.787281	−	0.616594i	$-0.788512\pi$
$71$	1.70900	−	6.37808i	0.202821	−	0.756939i	0.990103	−	0.140345i	$-0.0448212\pi$
$72$		0			0
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	0.0597896	−	0.998211i	$-0.480957\pi$
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	−0.998211	+	0.0597896i	$0.980957\pi$
$74$	−6.12445	−	3.53595i	−0.711953	−	0.411046i
$75$		0			0
$76$	−1.69669	+	6.33213i	−0.194624	+	0.726346i
$77$	0.883031	−	1.52946i	0.100631	−	0.174298i
$78$		0			0
$79$	−0.807117	−	1.39797i	−0.0908078	−	0.157284i	0.817043	−	0.576576i	$-0.195612\pi$
$79$	−0.807117	−	1.39797i	−0.0908078	−	0.157284i	−0.907851	+	0.419292i	$0.862278\pi$
$80$	0.650628	−	0.174335i	0.0727424	−	0.0194913i
$81$		0			0
$82$	4.30925	−	2.48795i	0.475877	−	0.274748i
$83$	1.95885	−	7.31055i	0.215012	−	0.802437i	−0.771150	−	0.636653i	$-0.780318\pi$
$83$	1.95885	−	7.31055i	0.215012	−	0.802437i	0.986162	−	0.165783i	$-0.0530152\pi$
$84$		0			0
$85$	−1.15211	−	1.15211i	−0.124964	−	0.124964i
$86$	0.230939	+	0.861875i	0.0249028	+	0.0929384i
$87$		0			0
$88$			0.985676i			0.105073i
$89$	0.440877	+	1.64537i	0.0467329	+	0.174409i	0.985348	−	0.170557i	$-0.0545568\pi$
$89$	0.440877	+	1.64537i	0.0467329	+	0.174409i	−0.938615	+	0.344967i	$0.887890\pi$
$90$		0			0
$91$	0.983920	+	6.38480i	0.103143	+	0.669309i
$92$	−5.47852	+	3.16302i	−0.571175	+	0.329768i
$93$		0			0
$94$	−1.89651	−	3.28485i	−0.195610	−	0.338807i
$95$	−4.41566			−0.453037
$96$		0			0
$97$	−0.497183	−	1.85551i	−0.0504812	−	0.188399i	0.936081	−	0.351785i	$-0.114425\pi$
$97$	−0.497183	−	1.85551i	−0.0504812	−	0.188399i	−0.986562	+	0.163386i	$0.947758\pi$
$98$	3.66058	+	0.980849i	0.369774	+	0.0990807i
$99$		0			0
$100$	−2.27315	−	3.93720i	−0.227315	−	0.393720i
$101$	14.8919			1.48180			0.740902	−	0.671613i	$-0.234398\pi$
$101$	14.8919			1.48180			0.740902	+	0.671613i	$0.234398\pi$
$102$		0			0
$103$	9.08751	+	5.24668i	0.895419	+	0.516971i	0.875711	−	0.482835i	$-0.160393\pi$
$103$	9.08751	+	5.24668i	0.895419	+	0.516971i	0.0197081	+	0.999806i	$0.493726\pi$
$104$	−2.25732	−	2.81150i	−0.221348	−	0.275690i
$105$		0			0
$106$	6.36406	−	6.36406i	0.618132	−	0.618132i
$107$	1.87899	+	1.08484i	0.181649	+	0.104875i	0.588067	−	0.808812i	$-0.299889\pi$
$107$	1.87899	+	1.08484i	0.181649	+	0.104875i	−0.406418	+	0.913687i	$0.633222\pi$
$108$		0			0
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	−0.982075	−	0.188489i	$-0.939641\pi$
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	0.188489	+	0.982075i	$0.439641\pi$
$110$	−0.641308	+	0.171838i	−0.0611463	+	0.0163841i
$111$		0			0
$112$	1.73068	−	0.463733i	0.163534	−	0.0438187i
$113$		−	11.0857i		−	1.04285i	−0.853296	−	0.521427i	$-0.825400\pi$
$113$		−	11.0857i		−	1.04285i	0.853296	−	0.521427i	$-0.174600\pi$
$114$		0			0
$115$	−3.01305	−	3.01305i	−0.280968	−	0.280968i
$116$	−4.29257			−0.398555
$117$		0			0
$118$	−4.72289			−0.434777
$119$	−3.06463	−	3.06463i	−0.280934	−	0.280934i
$120$		0			0
$121$			10.0284i			0.911677i
$122$	4.60165	−	1.23301i	0.416614	−	0.111631i
$123$		0			0
$124$	−5.59289	+	1.49861i	−0.502256	+	0.134579i
$125$	4.54683	−	4.54683i	0.406681	−	0.406681i
$126$		0			0
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	0.679731	−	0.733462i	$-0.262097\pi$
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	−0.295331	+	0.955395i	$0.595430\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	1.43571	−	1.95882i	0.125920	−	0.171800i
$131$	−19.0361	−	10.9905i	−1.66319	−	0.960242i	−0.971178	−	0.238354i	$-0.923392\pi$
$131$	−19.0361	−	10.9905i	−1.66319	−	0.960242i	−0.692010	−	0.721888i	$-0.743275\pi$
$132$		0			0
$133$	−11.7457			−1.01848
$134$	−5.53613	−	9.58886i	−0.478249	−	0.828351i
$135$		0			0
$136$	2.33650	+	0.626062i	0.200353	+	0.0536844i
$137$	−3.25829	−	12.1601i	−0.278374	−	1.03891i	−0.953546	−	0.301246i	$-0.902597\pi$
$137$	−3.25829	−	12.1601i	−0.278374	−	1.03891i	0.675172	−	0.737660i	$-0.264069\pi$
$138$		0			0
$139$	−19.6965			−1.67063			−0.835316	−	0.549770i	$-0.814715\pi$
$139$	−19.6965			−1.67063			−0.835316	+	0.549770i	$0.814715\pi$
$140$	0.603436	+	1.04518i	0.0509996	+	0.0883340i
$141$		0			0
$142$	−5.71843	+	3.30154i	−0.479880	+	0.277059i
$143$	2.22498	+	2.77122i	0.186062	+	0.231741i
$144$		0			0
$145$	−0.748347	−	2.79287i	−0.0621468	−	0.231935i
$146$			11.3390i			0.938421i
$147$		0			0
$148$	1.83034	+	6.83094i	0.150453	+	0.561499i
$149$	6.83755	+	6.83755i	0.560154	+	0.560154i	0.929351	−	0.369197i	$-0.120367\pi$
$149$	6.83755	+	6.83755i	0.560154	+	0.560154i	−0.369197	+	0.929351i	$0.620367\pi$
$150$		0			0
$151$	−1.28698	+	4.80308i	−0.104733	+	0.390869i	−0.998315	−	0.0580316i	$-0.981518\pi$
$151$	−1.28698	+	4.80308i	−0.104733	+	0.390869i	0.893582	+	0.448900i	$0.148184\pi$
$152$	5.67724	−	3.27775i	0.460485	−	0.265861i
$153$		0			0
$154$	−1.70589	+	0.457091i	−0.137464	+	0.0368334i
$155$	−1.95008	−	3.37763i	−0.156634	−	0.271298i
$156$		0			0
$157$	−4.86181	+	8.42090i	−0.388015	+	0.672061i	−0.992182	−	0.124796i	$-0.960172\pi$
$157$	−4.86181	+	8.42090i	−0.388015	+	0.672061i	0.604168	+	0.796857i	$0.293506\pi$
$158$	−0.417795	+	1.55923i	−0.0332380	+	0.124046i
$159$		0			0
$160$	−0.583337	−	0.336790i	−0.0461169	−	0.0266256i
$161$	−8.01474	−	8.01474i	−0.631650	−	0.631650i
$162$		0			0
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	−0.899727	−	0.436453i	$-0.856234\pi$
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	0.997413	+	0.0718838i	$0.0229011\pi$
$164$	−4.80634	−	1.28786i	−0.375312	−	0.100565i
$165$		0			0
$166$	−6.55446	+	3.78422i	−0.508724	+	0.293712i
$167$	−13.6676	−	3.66224i	−1.05763	−	0.283392i	−0.312231	−	0.950006i	$-0.601076\pi$
$167$	−13.6676	−	3.66224i	−1.05763	−	0.283392i	−0.745403	+	0.666614i	$0.767743\pi$
$168$		0			0
$169$	−12.6929	−	2.80903i	−0.976376	−	0.216079i
$170$			1.62934i			0.124964i
$171$		0			0
$172$	0.446139	−	0.772736i	0.0340178	−	0.0589206i
$173$	−11.5989	+	20.0900i	−0.881852	+	1.52741i	−0.0325714	+	0.999469i	$0.510370\pi$
$173$	−11.5989	+	20.0900i	−0.881852	+	1.52741i	−0.849280	+	0.527942i	$0.822964\pi$
$174$		0			0
$175$	5.75989	−	5.75989i	0.435407	−	0.435407i
$176$	0.696978	−	0.696978i	0.0525367	−	0.0525367i
$177$		0			0
$178$	0.851709	−	1.47520i	0.0638383	−	0.110571i
$179$	2.78545	−	4.82455i	0.208194	−	0.360603i	−0.742951	−	0.669345i	$-0.766575\pi$
$179$	2.78545	−	4.82455i	0.208194	−	0.360603i	0.951146	+	0.308742i	$0.0999080\pi$
$180$		0			0
$181$		−	20.8410i		−	1.54910i	−0.632514	−	0.774549i	$-0.717977\pi$
$181$		−	20.8410i		−	1.54910i	0.632514	−	0.774549i	$-0.282023\pi$
$182$	3.81900	−	5.21047i	0.283083	−	0.386226i
$183$		0			0
$184$	6.11049	+	1.63730i	0.450471	+	0.120703i
$185$	−4.12531	+	2.38175i	−0.303298	+	0.175109i
$186$		0			0
$187$	−2.30303	−	0.617094i	−0.168414	−	0.0451264i
$188$	−0.981707	+	3.66378i	−0.0715983	+	0.267209i
$189$		0			0
$190$	3.12234	+	3.12234i	0.226518	+	0.226518i
$191$	15.6514	+	9.03635i	1.13250	+	0.653847i	0.944562	−	0.328334i	$-0.106487\pi$
$191$	15.6514	+	9.03635i	1.13250	+	0.653847i	0.187935	+	0.982181i	$0.439821\pi$
$192$		0			0
$193$	1.90556	−	7.11166i	0.137165	−	0.511908i	−0.862814	−	0.505521i	$-0.831300\pi$
$193$	1.90556	−	7.11166i	0.137165	−	0.511908i	0.999980	−	0.00638720i	$-0.00203312\pi$
$194$	−0.960483	+	1.66361i	−0.0689587	+	0.119440i
$195$		0			0
$196$	−1.89486	−	3.28199i	−0.135347	−	0.234428i
$197$	−23.6473	+	6.33628i	−1.68480	+	0.451441i	−0.969040	−	0.246904i	$-0.920587\pi$
$197$	−23.6473	+	6.33628i	−1.68480	+	0.451441i	−0.715761	+	0.698345i	$0.753920\pi$
$198$		0			0
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	−0.726503	−	0.687164i	$-0.758856\pi$
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	0.231850	+	0.972752i	$0.425522\pi$
$200$	−1.17667	+	4.39138i	−0.0832029	+	0.310517i
$201$		0			0
$202$	−10.5302	−	10.5302i	−0.740902	−	0.740902i
$203$	−1.99061	−	7.42905i	−0.139713	−	0.521417i
$204$		0			0
$205$		−	3.35166i		−	0.234090i
$206$	−2.71588	−	10.1358i	−0.189224	−	0.706195i
$207$		0			0
$208$	−0.391864	+	3.58419i	−0.0271709	+	0.248519i
$209$	−5.59591	+	3.23080i	−0.387077	+	0.223479i
$210$		0			0
$211$	7.04091	+	12.1952i	0.484716	+	0.839553i	0.999846	−	0.0175594i	$-0.00558961\pi$
$211$	7.04091	+	12.1952i	0.484716	+	0.839553i	−0.515130	+	0.857112i	$0.672256\pi$
$212$	−9.00014			−0.618132
$213$		0			0
$214$	−0.561553	−	2.09574i	−0.0383870	−	0.143262i
$215$	0.580542	+	0.155556i	0.0395926	+	0.0106088i
$216$		0			0
$217$	−5.18722	−	8.98452i	−0.352131	−	0.609909i
$218$	11.7172			0.793586
$219$		0			0
$220$	0.574981	+	0.331966i	0.0387652	+	0.0223811i
$221$	7.98227	−	3.51404i	0.536946	−	0.236380i
$222$		0			0
$223$	16.7879	−	16.7879i	1.12420	−	1.12420i	0.133096	−	0.991103i	$-0.457508\pi$
$223$	16.7879	−	16.7879i	1.12420	−	1.12420i	0.991103	−	0.133096i	$-0.0424918\pi$
$224$	−1.55168	−	0.895864i	−0.103676	−	0.0598574i
$225$		0			0
$226$	−7.83876	+	7.83876i	−0.521427	+	0.521427i
$227$	23.1257	−	6.19651i	1.53491	−	0.411277i	0.610291	−	0.792178i	$-0.291053\pi$
$227$	23.1257	−	6.19651i	1.53491	−	0.411277i	0.924616	+	0.380901i	$0.124386\pi$
$228$		0			0
$229$	−19.8362	+	5.31509i	−1.31081	+	0.351231i	−0.845529	−	0.533930i	$-0.820714\pi$
$229$	−19.8362	+	5.31509i	−1.31081	+	0.351231i	−0.465284	+	0.885161i	$0.654048\pi$
$230$			4.26110i			0.280968i
$231$		0			0
$232$	3.03531	+	3.03531i	0.199278	+	0.199278i
$233$	−2.79071			−0.182825			−0.0914126	−	0.995813i	$-0.529138\pi$
$233$	−2.79071			−0.182825			−0.0914126	+	0.995813i	$0.529138\pi$
$234$		0			0
$235$	−2.55490			−0.166664
$236$	3.33959	+	3.33959i	0.217389	+	0.217389i
$237$		0			0
$238$			4.33405i			0.280934i
$239$	−7.58852	+	2.03334i	−0.490861	+	0.131526i	−0.495755	−	0.868462i	$-0.665109\pi$
$239$	−7.58852	+	2.03334i	−0.490861	+	0.131526i	0.00489453	+	0.999988i	$0.498442\pi$
$240$		0			0
$241$	22.4869	−	6.02534i	1.44851	−	0.388126i	0.553002	−	0.833180i	$-0.313482\pi$
$241$	22.4869	−	6.02534i	1.44851	−	0.388126i	0.895504	+	0.445054i	$0.146815\pi$
$242$	7.09118	−	7.09118i	0.455838	−	0.455838i
$243$		0			0
$244$	−4.12572	−	2.38199i	−0.264122	−	0.152491i
$245$	1.80501	−	1.80501i	0.115318	−	0.115318i
$246$		0			0
$247$	8.56260	−	22.0307i	0.544825	−	1.40178i
$248$	5.01445	+	2.89509i	0.318418	+	0.183839i
$249$		0			0
$250$	−6.43019			−0.406681
$251$	13.0241	+	22.5583i	0.822071	+	1.42387i	0.904138	+	0.427241i	$0.140515\pi$
$251$	13.0241	+	22.5583i	0.822071	+	1.42387i	−0.0820668	+	0.996627i	$0.526152\pi$
$252$		0			0
$253$	−6.02296	−	1.61385i	−0.378660	−	0.101462i
$254$	−1.29465	−	4.83168i	−0.0812333	−	0.303167i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.60078	+	6.23673i	0.224610	+	0.389036i	0.956202	−	0.292706i	$-0.0945558\pi$
$257$	3.60078	+	6.23673i	0.224610	+	0.389036i	−0.731592	+	0.681743i	$0.761222\pi$
$258$		0			0
$259$	−10.9733	+	6.33546i	−0.681851	+	0.393667i
$260$	−2.40029	+	0.369894i	−0.148860	+	0.0229398i
$261$		0			0
$262$	5.68909	+	21.2320i	0.351473	+	1.31172i
$263$			11.4549i			0.706342i	0.935559	+	0.353171i	$0.114897\pi$
$263$			11.4549i			0.706342i	−0.935559	+	0.353171i	$0.885103\pi$
$264$		0			0
$265$	−1.56904	−	5.85574i	−0.0963855	−	0.359715i
$266$	8.30546	+	8.30546i	0.509240	+	0.509240i
$267$		0			0
$268$	−2.86571	+	10.6950i	−0.175051	+	0.653300i
$269$	−21.7795	+	12.5744i	−1.32792	+	0.766674i	−0.984977	−	0.172683i	$-0.944756\pi$
$269$	−21.7795	+	12.5744i	−1.32792	+	0.766674i	−0.342941	+	0.939357i	$0.611423\pi$
$270$		0			0
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	−0.0664215	−	0.997792i	$-0.521158\pi$
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	0.441373	+	0.897324i	$0.354492\pi$
$272$	−1.20946	−	2.09485i	−0.0733343	−	0.127019i
$273$		0			0
$274$	−6.29452	+	10.9024i	−0.380266	+	0.658640i
$275$	1.15981	−	4.32848i	0.0699393	−	0.261017i
$276$		0			0
$277$	16.8380	+	9.72143i	1.01170	+	0.584104i	0.911688	−	0.410882i	$-0.134779\pi$
$277$	16.8380	+	9.72143i	1.01170	+	0.584104i	0.100010	+	0.994986i	$0.468113\pi$
$278$	13.9275	+	13.9275i	0.835316	+	0.835316i
$279$		0			0
$280$	0.312361	−	1.16575i	0.0186672	−	0.0696668i
$281$	−28.7919	−	7.71478i	−1.71758	−	0.460225i	−0.740320	−	0.672255i	$-0.765326\pi$
$281$	−28.7919	−	7.71478i	−1.71758	−	0.460225i	−0.977263	+	0.212030i	$0.931993\pi$
$282$		0			0
$283$	19.1183	−	11.0380i	1.13647	−	0.656139i	0.190914	−	0.981607i	$-0.438855\pi$
$283$	19.1183	−	11.0380i	1.13647	−	0.656139i	0.945553	+	0.325467i	$0.105522\pi$
$284$	6.37808	+	1.70900i	0.378470	+	0.101411i
$285$		0			0
$286$	0.386251	−	3.53285i	0.0228395	−	0.208902i
$287$		−	8.91545i		−	0.526262i
$288$		0			0
$289$	5.57442	−	9.65517i	0.327907	−	0.567951i
$290$	−1.44570	+	2.50402i	−0.0848941	+	0.147041i
$291$		0			0
$292$	8.01788	−	8.01788i	0.469211	−	0.469211i
$293$	6.70889	−	6.70889i	0.391938	−	0.391938i	−0.483440	−	0.875378i	$-0.660613\pi$
$293$	6.70889	−	6.70889i	0.391938	−	0.391938i	0.875378	+	0.483440i	$0.160613\pi$
$294$		0			0
$295$	−1.59062	+	2.75504i	−0.0926096	+	0.160404i
$296$	3.53595	−	6.12445i	0.205523	−	0.355976i
$297$		0			0
$298$		−	9.66976i		−	0.560154i
$299$	20.8755	−	9.19005i	1.20726	−	0.531475i
$300$		0			0
$301$	1.54425	+	0.413779i	0.0890088	+	0.0238498i
$302$	4.30632	−	2.48626i	0.247801	−	0.143068i
$303$		0			0
$304$	−6.33213	−	1.69669i	−0.363173	−	0.0973119i
$305$	0.830529	−	3.09958i	0.0475560	−	0.177481i
$306$		0			0
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	0.796385	−	0.604790i	$-0.206743\pi$
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	−0.604790	+	0.796385i	$0.706743\pi$
$308$	1.52946	+	0.883031i	0.0871488	+	0.0503154i
$309$		0			0
$310$	−1.00943	+	3.76726i	−0.0573320	+	0.213966i
$311$	10.5634	−	18.2964i	0.598996	−	1.03749i	−0.393973	−	0.919122i	$-0.628900\pi$
$311$	10.5634	−	18.2964i	0.598996	−	1.03749i	0.992970	−	0.118370i	$-0.0377669\pi$
$312$		0			0
$313$	−5.16590	−	8.94760i	−0.291994	−	0.505748i	0.682287	−	0.731084i	$-0.260985\pi$
$313$	−5.16590	−	8.94760i	−0.291994	−	0.505748i	−0.974281	+	0.225336i	$0.927652\pi$
$314$	9.39229	−	2.51666i	0.530038	−	0.142023i
$315$		0			0
$316$	1.39797	−	0.807117i	0.0786419	−	0.0454039i
$317$	4.33708	−	16.1862i	0.243595	−	0.909108i	−0.730490	−	0.682924i	$-0.760708\pi$
$317$	4.33708	−	16.1862i	0.243595	−	0.909108i	0.974084	−	0.226185i	$-0.0726253\pi$
$318$		0			0
$319$	−2.99183	−	2.99183i	−0.167510	−	0.167510i
$320$	0.174335	+	0.650628i	0.00974564	+	0.0363712i
$321$		0			0
$322$			11.3346i			0.631650i
$323$	4.10416	+	15.3169i	0.228361	+	0.852256i
$324$		0			0
$325$	6.60454	+	15.0025i	0.366354	+	0.832187i
$326$	−4.17312	+	2.40935i	−0.231128	+	0.133442i
$327$		0			0
$328$	2.48795	+	4.30925i	0.137374	+	0.237939i
$329$	−6.79607			−0.374679
$330$		0			0
$331$	3.81878	+	14.2519i	0.209899	+	0.783354i	0.987900	+	0.155091i	$0.0495671\pi$
$331$	3.81878	+	14.2519i	0.209899	+	0.783354i	−0.778001	+	0.628263i	$0.783766\pi$
$332$	7.31055	+	1.95885i	0.401218	+	0.107506i
$333$		0			0
$334$	7.07490	+	12.2541i	0.387121	+	0.670513i
$335$	−7.45805			−0.407477
$336$		0			0
$337$	3.36489	+	1.94272i	0.183297	+	0.105827i	0.588841	−	0.808249i	$-0.299584\pi$
$337$	3.36489	+	1.94272i	0.183297	+	0.105827i	−0.405544	+	0.914076i	$0.632918\pi$
$338$	6.98894	+	10.9615i	0.380148	+	0.596228i
$339$		0			0
$340$	1.15211	−	1.15211i	0.0624822	−	0.0624822i
$341$	−4.94262	−	2.85362i	−0.267658	−	0.154532i
$342$		0			0
$343$	13.6699	−	13.6699i	0.738108	−	0.738108i
$344$	−0.861875	+	0.230939i	−0.0464692	+	0.0124514i
$345$		0			0
$346$	22.4074	−	6.00406i	1.20463	−	0.322780i
$347$		−	32.3179i		−	1.73492i	−0.497510	−	0.867459i	$-0.665752\pi$
$347$		−	32.3179i		−	1.73492i	0.497510	−	0.867459i	$-0.334248\pi$
$348$		0			0
$349$	13.4101	+	13.4101i	0.717828	+	0.717828i	0.968160	−	0.250332i	$-0.0805399\pi$
$349$	13.4101	+	13.4101i	0.717828	+	0.717828i	−0.250332	+	0.968160i	$0.580540\pi$
$350$	−8.14572			−0.435407
$351$		0			0
$352$	−0.985676			−0.0525367
$353$	13.8574	+	13.8574i	0.737554	+	0.737554i	0.972104	−	0.234550i	$-0.0753617\pi$
$353$	13.8574	+	13.8574i	0.737554	+	0.737554i	−0.234550	+	0.972104i	$0.575362\pi$
$354$		0			0
$355$			4.44770i			0.236059i
$356$	−1.64537	+	0.440877i	−0.0872047	+	0.0233664i
$357$		0			0
$358$	−5.38108	+	1.44186i	−0.284399	+	0.0762045i
$359$	−19.2085	+	19.2085i	−1.01379	+	1.01379i	−0.0138835	+	0.999904i	$0.504419\pi$
$359$	−19.2085	+	19.2085i	−1.01379	+	1.01379i	−0.999904	+	0.0138835i	$0.995581\pi$
$360$		0			0
$361$	20.7627	+	11.9873i	1.09277	+	0.630913i
$362$	−14.7368	+	14.7368i	−0.774549	+	0.774549i
$363$		0			0
$364$	−6.38480	+	0.983920i	−0.334654	+	0.0515714i
$365$	6.61445	+	3.81886i	0.346216	+	0.199888i
$366$		0			0
$367$	7.69429			0.401639			0.200819	−	0.979628i	$-0.435640\pi$
$367$	7.69429			0.401639			0.200819	+	0.979628i	$0.435640\pi$
$368$	−3.16302	−	5.47852i	−0.164884	−	0.285587i
$369$		0			0
$370$	4.60118	+	1.23288i	0.239204	+	0.0640945i
$371$	−4.17366	−	15.5763i	−0.216686	−	0.808683i
$372$		0			0
$373$	−16.0980			−0.833521			−0.416760	−	0.909016i	$-0.636835\pi$
$373$	−16.0980			−0.833521			−0.416760	+	0.909016i	$0.636835\pi$
$374$	1.19213	+	2.06484i	0.0616438	+	0.106770i
$375$		0			0
$376$	3.28485	−	1.89651i	0.169403	−	0.0978051i
$377$	15.3854	+	1.68210i	0.792389	+	0.0866328i
$378$		0			0
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	0.892446	+	0.451153i	$0.148987\pi$
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	−0.547305	+	0.836933i	$0.684346\pi$
$380$		−	4.41566i		−	0.226518i
$381$		0			0
$382$	−4.67756	−	17.4569i	−0.239325	−	0.893172i
$383$	22.2443	+	22.2443i	1.13663	+	1.13663i	0.989050	+	0.147581i	$0.0471487\pi$
$383$	22.2443	+	22.2443i	1.13663	+	1.13663i	0.147581	+	0.989050i	$0.452851\pi$
$384$		0			0
$385$	−0.307887	+	1.14905i	−0.0156914	+	0.0585610i
$386$	−6.37614	+	3.68127i	−0.324537	+	0.187372i
$387$		0			0
$388$	1.85551	−	0.497183i	0.0941993	−	0.0252406i
$389$	−12.6984	−	21.9943i	−0.643836	−	1.11516i	−0.984569	−	0.174997i	$-0.944009\pi$
$389$	−12.6984	−	21.9943i	−0.643836	−	1.11516i	0.340733	−	0.940160i	$-0.389325\pi$
$390$		0			0
$391$	−7.65110	+	13.2521i	−0.386933	+	0.670187i
$392$	−0.980849	+	3.66058i	−0.0495404	+	0.184887i
$393$		0			0
$394$	21.2016	+	12.2407i	1.06812	+	0.616680i
$395$	0.768848	+	0.768848i	0.0386850	+	0.0386850i
$396$		0			0
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	−0.956950	−	0.290254i	$-0.906260\pi$
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	0.973870	+	0.227108i	$0.0729270\pi$
$398$	7.78288	+	2.08542i	0.390120	+	0.104532i
$399$		0			0
$400$	3.93720	−	2.27315i	0.196860	−	0.113657i
$401$	−1.38859	−	0.372073i	−0.0693431	−	0.0185804i	0.223981	−	0.974594i	$-0.428095\pi$
$401$	−1.38859	−	0.372073i	−0.0693431	−	0.0185804i	−0.293324	+	0.956013i	$0.594761\pi$
$402$		0			0
$403$	20.6332	−	3.17966i	1.02782	−	0.158390i
$404$			14.8919i			0.740902i
$405$		0			0
$406$	−3.84556	+	6.66071i	−0.190852	+	0.330565i
$407$	−3.48530	+	6.03672i	−0.172760	+	0.299229i
$408$		0			0
$409$	16.2435	−	16.2435i	0.803189	−	0.803189i	−0.180404	−	0.983593i	$-0.557741\pi$
$409$	16.2435	−	16.2435i	0.803189	−	0.803189i	0.983593	+	0.180404i	$0.0577405\pi$
$410$	−2.36998	+	2.36998i	−0.117045	+	0.117045i
$411$		0			0
$412$	−5.24668	+	9.08751i	−0.258485	+	0.447710i
$413$	−4.23107	+	7.32842i	−0.208197	+	0.360608i
$414$		0			0
$415$			5.09794i			0.250248i
$416$	2.81150	−	2.25732i	0.137845	−	0.110674i
$417$		0			0
$418$	6.24143	+	1.67239i	0.305278	+	0.0817991i
$419$	5.72052	−	3.30274i	0.279466	−	0.161350i	−0.353716	−	0.935353i	$-0.615082\pi$
$419$	5.72052	−	3.30274i	0.279466	−	0.161350i	0.633182	+	0.774003i	$0.281749\pi$
$420$		0			0
$421$	9.08681	+	2.43480i	0.442864	+	0.118665i	0.473359	−	0.880870i	$-0.343042\pi$
$421$	9.08681	+	2.43480i	0.442864	+	0.118665i	−0.0304944	+	0.999535i	$0.509708\pi$
$422$	3.64464	−	13.6020i	0.177418	−	0.662134i
$423$		0			0
$424$	6.36406	+	6.36406i	0.309066	+	0.309066i
$425$	−9.52378	−	5.49855i	−0.461971	−	0.266719i
$426$		0			0
$427$	2.20921	−	8.24490i	0.106911	−	0.398999i
$428$	−1.08484	+	1.87899i	−0.0524376	+	0.0908246i
$429$		0			0
$430$	−0.300510	−	0.520499i	−0.0144919	−	0.0251007i
$431$	1.92865	−	0.516780i	0.0928998	−	0.0248924i	−0.212070	−	0.977255i	$-0.568020\pi$
$431$	1.92865	−	0.516780i	0.0928998	−	0.0248924i	0.304970	+	0.952362i	$0.401354\pi$
$432$		0			0
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.985936	−	0.167122i	$-0.946553\pi$
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.348236	+	0.937407i	$0.613219\pi$
$434$	−2.68510	+	10.0209i	−0.128889	+	0.481020i
$435$		0			0
$436$	−8.28528	−	8.28528i	−0.396793	−	0.396793i
$437$	10.7333	+	40.0574i	0.513445	+	1.91620i
$438$		0			0
$439$		−	26.1293i		−	1.24708i	−0.781790	−	0.623542i	$-0.785693\pi$
$439$		−	26.1293i		−	1.24708i	0.781790	−	0.623542i	$-0.214307\pi$
$440$	−0.171838	−	0.641308i	−0.00819206	−	0.0305732i
$441$		0			0
$442$	−8.12912	−	3.15952i	−0.386663	−	0.150283i
$443$	−9.85727	+	5.69110i	−0.468333	+	0.270392i	−0.715542	−	0.698570i	$-0.753820\pi$
$443$	−9.85727	+	5.69110i	−0.468333	+	0.270392i	0.247209	+	0.968962i	$0.420487\pi$
$444$		0			0
$445$	−0.573694	−	0.993667i	−0.0271957	−	0.0471043i
$446$	−23.7416			−1.12420
$447$		0			0
$448$	0.463733	+	1.73068i	0.0219093	+	0.0817668i
$449$	−13.3760	−	3.58409i	−0.631253	−	0.169144i	−0.0710148	−	0.997475i	$-0.522624\pi$
$449$	−13.3760	−	3.58409i	−0.631253	−	0.169144i	−0.560238	+	0.828331i	$0.689290\pi$
$450$		0			0
$451$	−2.45231	−	4.24752i	−0.115475	−	0.200008i
$452$	11.0857			0.521427
$453$		0			0
$454$	−20.7339	−	11.9707i	−0.973092	−	0.561815i
$455$	−1.75326	−	3.98260i	−0.0821942	−	0.186707i
$456$		0			0
$457$	23.8139	−	23.8139i	1.11397	−	1.11397i	0.121357	−	0.992609i	$-0.461276\pi$
$457$	23.8139	−	23.8139i	1.11397	−	1.11397i	0.992609	−	0.121357i	$-0.0387244\pi$
$458$	17.7846	+	10.2680i	0.831022	+	0.479791i
$459$		0			0
$460$	3.01305	−	3.01305i	0.140484	−	0.140484i
$461$	−8.68738	+	2.32778i	−0.404612	+	0.108415i	−0.455385	−	0.890295i	$-0.650498\pi$
$461$	−8.68738	+	2.32778i	−0.404612	+	0.108415i	0.0507728	+	0.998710i	$0.483832\pi$
$462$		0			0
$463$	−18.3164	+	4.90786i	−0.851234	+	0.228087i	−0.657956	−	0.753057i	$-0.728579\pi$
$463$	−18.3164	+	4.90786i	−0.851234	+	0.228087i	−0.193278	+	0.981144i	$0.561912\pi$
$464$		−	4.29257i		−	0.199278i
$465$		0			0
$466$	1.97333	+	1.97333i	0.0914126	+	0.0914126i
$467$	33.1417			1.53362			0.766808	−	0.641877i	$-0.221844\pi$
$467$	33.1417			1.53362			0.766808	+	0.641877i	$0.221844\pi$
$468$		0			0
$469$	−19.8385			−0.916056
$470$	1.80659	+	1.80659i	0.0833318	+	0.0833318i
$471$		0			0
$472$		−	4.72289i		−	0.217389i
$473$	0.849529	−	0.227631i	0.0390614	−	0.0104665i
$474$		0			0
$475$	−28.7877	+	7.71365i	−1.32087	+	0.353926i
$476$	3.06463	−	3.06463i	0.140467	−	0.140467i
$477$		0			0
$478$	6.80368	+	3.92811i	0.311193	+	0.179667i
$479$	21.8028	−	21.8028i	0.996195	−	0.996195i	−0.00379781	−	0.999993i	$-0.501209\pi$
$479$	21.8028	−	21.8028i	0.996195	−	0.996195i	0.999993	+	0.00379781i	$0.00120888\pi$
$480$		0			0
$481$	−3.88351	−	25.2006i	−0.177073	−	1.14905i
$482$	−20.1612	−	11.6401i	−0.918316	−	0.530190i
$483$		0			0
$484$	−10.0284			−0.455838
$485$	0.646962	+	1.12057i	0.0293770	+	0.0508825i
$486$		0			0
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.212733	−	0.977110i	$-0.568236\pi$
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.672787	+	0.739836i	$0.734903\pi$
$488$	1.23301	+	4.60165i	0.0558156	+	0.208307i
$489$		0			0
$490$	−2.55267			−0.115318
$491$	7.55120	+	13.0791i	0.340781	+	0.590250i	0.984578	−	0.174946i	$-0.0559752\pi$
$491$	7.55120	+	13.0791i	0.340781	+	0.590250i	−0.643797	+	0.765196i	$0.722642\pi$
$492$		0			0
$493$	−8.99228	+	5.19169i	−0.404992	+	0.233822i
$494$	−21.6327	+	9.52340i	−0.973303	+	0.428478i
$495$		0			0
$496$	−1.49861	−	5.59289i	−0.0672896	−	0.251128i
$497$			11.8309i			0.530689i
$498$		0			0
$499$	−10.8485	−	40.4871i	−0.485645	−	1.81245i	−0.577140	−	0.816645i	$-0.695831\pi$
$499$	−10.8485	−	40.4871i	−0.485645	−	1.81245i	0.0914956	−	0.995805i	$-0.470835\pi$
$500$	4.54683	+	4.54683i	0.203340	+	0.203340i
$501$		0			0
$502$	6.74174	−	25.1605i	0.300899	−	1.12297i
$503$	10.9025	−	6.29458i	0.486120	−	0.280661i	−0.236843	−	0.971548i	$-0.576113\pi$
$503$	10.9025	−	6.29458i	0.486120	−	0.280661i	0.722963	+	0.690886i	$0.242780\pi$
$504$		0			0
$505$	−9.68912	+	2.59619i	−0.431160	+	0.115529i
$506$	3.11771	+	5.40004i	0.138599	+	0.240061i
$507$		0			0
$508$	−2.50106	+	4.33197i	−0.110967	+	0.192200i
$509$	−8.59675	+	32.0835i	−0.381044	+	1.42208i	0.463264	+	0.886220i	$0.346678\pi$
$509$	−8.59675	+	32.0835i	−0.381044	+	1.42208i	−0.844309	+	0.535857i	$0.819989\pi$
$510$		0			0
$511$	17.5945	+	10.1582i	0.778335	+	0.449372i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	1.86390	−	6.95616i	0.0822130	−	0.306823i
$515$	−6.82727	−	1.82936i	−0.300846	−	0.0806113i
$516$		0			0
$517$	−3.23780	+	1.86935i	−0.142398	+	0.0822137i
$518$	12.2392	+	3.27948i	0.537759	+	0.144092i
$519$		0			0
$520$	1.95882	+	1.43571i	0.0858998	+	0.0629600i
$521$		−	17.5549i		−	0.769094i	−0.923105	−	0.384547i	$-0.874358\pi$
$521$		−	17.5549i		−	0.769094i	0.923105	−	0.384547i	$-0.125642\pi$
$522$		0			0
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	−0.943038	−	0.332686i	$-0.892045\pi$
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	0.759633	+	0.650352i	$0.225379\pi$
$524$	10.9905	−	19.0361i	0.480121	−	0.831594i
$525$		0			0
$526$	8.09986	−	8.09986i	0.353171	−	0.353171i
$527$	−9.90373	+	9.90373i	−0.431413	+	0.431413i
$528$		0			0
$529$	−8.50943	+	14.7388i	−0.369975	+	0.640816i
$530$	−3.03116	+	5.25012i	−0.131665	+	0.228050i
$531$		0			0
$532$		−	11.7457i		−	0.509240i
$533$	16.7222	+	6.49936i	0.724319	+	0.281518i
$534$		0			0
$535$	−1.41165	−	0.378251i	−0.0610310	−	0.0163532i
$536$	9.58886	−	5.53613i	0.414176	−	0.239124i
$537$		0			0
$538$	24.2918	+	6.50898i	1.04730	+	0.280622i
$539$	0.966799	−	3.60814i	0.0416430	−	0.155414i
$540$		0			0
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	0.737332	−	0.675531i	$-0.236086\pi$
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	−0.675531	+	0.737332i	$0.736086\pi$
$542$	−5.53410	−	3.19511i	−0.237710	−	0.137242i
$543$		0			0
$544$	−0.626062	+	2.33650i	−0.0268422	+	0.100176i
$545$	3.94622	−	6.83505i	0.169037	−	0.292781i
$546$		0			0
$547$	5.93332	+	10.2768i	0.253691	+	0.439405i	0.964539	−	0.263940i	$-0.0850222\pi$
$547$	5.93332	+	10.2768i	0.253691	+	0.439405i	−0.710848	+	0.703345i	$0.751689\pi$
$548$	12.1601	−	3.25829i	0.519453	−	0.139187i
$549$		0			0
$550$	−3.88080	+	2.24058i	−0.165478	+	0.0955388i
$551$	−7.28317	+	27.1811i	−0.310273	+	1.15796i
$552$		0			0
$553$	2.04514	+	2.04514i	0.0869683	+	0.0869683i
$554$	−5.03218	−	18.7804i	−0.213797	−	0.797901i
$555$		0			0
$556$		−	19.6965i		−	0.835316i
$557$	−9.18337	−	34.2728i	−0.389112	−	1.45219i	−0.831582	−	0.555402i	$-0.812564\pi$
$557$	−9.18337	−	34.2728i	−0.389112	−	1.45219i	0.442470	−	0.896783i	$-0.354102\pi$
$558$		0			0
$559$	−1.90186	+	2.59481i	−0.0804400	+	0.109749i
$560$	−1.04518	+	0.603436i	−0.0441670	+	0.0254998i
$561$		0			0
$562$	14.9038	+	25.8141i	0.628679	+	1.08890i
$563$	−36.9752			−1.55832			−0.779159	−	0.626826i	$-0.784353\pi$
$563$	−36.9752			−1.55832			−0.779159	+	0.626826i	$0.784353\pi$
$564$		0			0
$565$	1.93263	+	7.21266i	0.0813062	+	0.303439i
$566$	−21.3237	−	5.71368i	−0.896303	−	0.240164i
$567$		0			0
$568$	−3.30154	−	5.71843i	−0.138529	−	0.239940i
$569$	−24.5310			−1.02840			−0.514198	−	0.857672i	$-0.671910\pi$
$569$	−24.5310			−1.02840			−0.514198	+	0.857672i	$0.671910\pi$
$570$		0			0
$571$	−7.42838	−	4.28878i	−0.310868	−	0.179480i	0.336447	−	0.941702i	$-0.390775\pi$
$571$	−7.42838	−	4.28878i	−0.310868	−	0.179480i	−0.647315	+	0.762223i	$0.724108\pi$
$572$	−2.77122	+	2.22498i	−0.115871	+	0.0930312i
$573$		0			0
$574$	−6.30417	+	6.30417i	−0.263131	+	0.263131i
$575$	−24.9069	−	14.3800i	−1.03869	−	0.599688i
$576$		0			0
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	−0.727437	−	0.686174i	$-0.759289\pi$
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	0.686174	+	0.727437i	$0.259289\pi$
$578$	−10.7689	+	2.88553i	−0.447929	+	0.120022i
$579$		0			0
$580$	2.79287	−	0.748347i	0.115968	−	0.0310734i
$581$			13.5606i			0.562587i
$582$		0			0
$583$	−6.27290	−	6.27290i	−0.259797	−	0.259797i
$584$	−11.3390			−0.469211
$585$		0			0
$586$	−9.48781			−0.391938
$587$	26.9762	+	26.9762i	1.11343	+	1.11343i	0.992684	+	0.120743i	$0.0385277\pi$
$587$	26.9762	+	26.9762i	1.11343	+	1.11343i	0.120743	+	0.992684i	$0.461472\pi$
$588$		0			0
$589$			37.9576i			1.56402i
$590$	3.07284	−	0.823366i	0.126507	−	0.0338975i
$591$		0			0
$592$	−6.83094	+	1.83034i	−0.280750	+	0.0752267i
$593$	22.4411	−	22.4411i	0.921547	−	0.921547i	−0.0755923	−	0.997139i	$-0.524085\pi$
$593$	22.4411	−	22.4411i	0.921547	−	0.921547i	0.997139	+	0.0755923i	$0.0240847\pi$
$594$		0			0
$595$	2.52821	+	1.45966i	0.103647	+	0.0598403i
$596$	−6.83755	+	6.83755i	−0.280077	+	0.280077i
$597$		0			0
$598$	−21.2596	−	8.26289i	−0.869369	−	0.337895i
$599$	−12.9383	−	7.46992i	−0.528644	−	0.305213i	0.211820	−	0.977309i	$-0.432061\pi$
$599$	−12.9383	−	7.46992i	−0.528644	−	0.305213i	−0.740464	+	0.672096i	$0.765394\pi$
$600$		0			0
$601$	−9.43517			−0.384869			−0.192434	−	0.981310i	$-0.561638\pi$
$601$	−9.43517			−0.384869			−0.192434	+	0.981310i	$0.561638\pi$
$602$	−0.799360	−	1.38453i	−0.0325795	−	0.0564293i
$603$		0			0
$604$	−4.80308	−	1.28698i	−0.195434	−	0.0523665i
$605$	−1.74831	−	6.52479i	−0.0710790	−	0.265270i
$606$		0			0
$607$	8.22930			0.334017			0.167008	−	0.985955i	$-0.446589\pi$
$607$	8.22930			0.334017			0.167008	+	0.985955i	$0.446589\pi$
$608$	3.27775	+	5.67724i	0.132930	+	0.230242i
$609$		0			0
$610$	−2.77901	+	1.60446i	−0.112519	+	0.0649627i
$611$	4.95433	−	12.7470i	0.200431	−	0.515688i
$612$		0			0
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	−0.986968	−	0.160918i	$-0.948555\pi$
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	0.774280	−	0.632843i	$-0.218112\pi$
$614$		−	4.74755i		−	0.191596i
$615$		0			0
$616$	−0.457091	−	1.70589i	−0.0184167	−	0.0687321i
$617$	−23.1593	−	23.1593i	−0.932360	−	0.932360i	0.0654935	−	0.997853i	$-0.479138\pi$
$617$	−23.1593	−	23.1593i	−0.932360	−	0.932360i	−0.997853	+	0.0654935i	$0.979138\pi$
$618$		0			0
$619$	2.50985	−	9.36687i	0.100879	−	0.376486i	−0.896966	−	0.442100i	$-0.854234\pi$
$619$	2.50985	−	9.36687i	0.100879	−	0.376486i	0.997845	+	0.0656133i	$0.0209004\pi$
$620$	3.37763	−	1.95008i	0.135649	−	0.0783169i
$621$		0			0
$622$	−20.4069	+	5.46802i	−0.818244	+	0.219248i
$623$	−1.52603	−	2.64316i	−0.0611391	−	0.105896i
$624$		0			0
$625$	9.20010	−	15.9350i	0.368004	−	0.637402i
$626$	−2.67407	+	9.97975i	−0.106877	+	0.398871i
$627$		0			0
$628$	−8.42090	−	4.86181i	−0.336030	−	0.194007i
$629$	12.0960	+	12.0960i	0.482300	+	0.482300i
$630$		0			0
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	0.745878	+	0.666083i	$0.232030\pi$
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	−0.978991	+	0.203906i	$0.934636\pi$
$632$	−1.55923	−	0.417795i	−0.0620229	−	0.0166190i
$633$		0			0
$634$	−14.5122	+	8.37860i	−0.576352	+	0.332757i
$635$	−3.25452	−	0.872047i	−0.129152	−	0.0346061i
$636$		0			0
$637$	5.50544	+	12.5058i	0.218133	+	0.495498i
$638$			4.23108i			0.167510i
$639$		0			0
$640$	0.336790	−	0.583337i	0.0133128	−	0.0230584i
$641$	−5.39399	+	9.34267i	−0.213050	+	0.369013i	−0.952668	−	0.304014i	$-0.901673\pi$
$641$	−5.39399	+	9.34267i	−0.213050	+	0.369013i	0.739618	+	0.673027i	$0.235006\pi$
$642$		0			0
$643$	7.58253	−	7.58253i	0.299026	−	0.299026i	−0.541606	−	0.840632i	$-0.682184\pi$
$643$	7.58253	−	7.58253i	0.299026	−	0.299026i	0.840632	+	0.541606i	$0.182184\pi$
$644$	8.01474	−	8.01474i	0.315825	−	0.315825i
$645$		0			0
$646$	7.92862	−	13.7328i	0.311947	−	0.540309i
$647$	−2.44136	+	4.22856i	−0.0959799	+	0.166242i	−0.910017	−	0.414571i	$-0.863932\pi$
$647$	−2.44136	+	4.22856i	−0.0959799	+	0.166242i	0.814037	+	0.580813i	$0.197265\pi$
$648$		0			0
$649$			4.65524i			0.182734i
$650$	5.93822	−	15.2785i	0.232916	−	0.599270i
$651$		0			0
$652$	4.65451	+	1.24717i	0.182285	+	0.0488431i
$653$	19.0037	−	10.9718i	0.743673	−	0.429360i	−0.0797303	−	0.996816i	$-0.525406\pi$
$653$	19.0037	−	10.9718i	0.743673	−	0.429360i	0.823403	+	0.567457i	$0.192073\pi$
$654$		0			0
$655$	14.3014	+	3.83206i	0.558803	+	0.149731i
$656$	1.28786	−	4.80634i	0.0502823	−	0.187656i
$657$		0			0
$658$	4.80554	+	4.80554i	0.187340	+	0.187340i
$659$	−36.6396	−	21.1539i	−1.42728	−	0.824038i	−0.430371	−	0.902652i	$-0.641617\pi$
$659$	−36.6396	−	21.1539i	−1.42728	−	0.824038i	−0.996905	+	0.0786138i	$0.974951\pi$
$660$		0			0
$661$	−8.10585	+	30.2514i	−0.315281	+	1.17664i	0.608447	+	0.793595i	$0.291793\pi$
$661$	−8.10585	+	30.2514i	−0.315281	+	1.17664i	−0.923728	+	0.383050i	$0.874874\pi$
$662$	7.37732	−	12.7779i	0.286728	−	0.496627i
$663$		0			0
$664$	−3.78422	−	6.55446i	−0.146856	−	0.254362i
$665$	7.64207	−	2.04769i	0.296347	−	0.0794059i
$666$		0			0
$667$	−23.5169	+	13.5775i	−0.910579	+	0.525723i
$668$	3.66224	−	13.6676i	0.141696	−	0.528817i
$669$		0			0
$670$	5.27364	+	5.27364i	0.203738	+	0.203738i
$671$	−1.21535	−	4.53573i	−0.0469179	−	0.175100i
$672$		0			0
$673$		−	38.0352i		−	1.46615i	−0.680148	−	0.733075i	$-0.738085\pi$
$673$		−	38.0352i		−	1.46615i	0.680148	−	0.733075i	$-0.261915\pi$
$674$	−1.00563	−	3.75304i	−0.0387352	−	0.144562i
$675$		0			0
$676$	2.80903	−	12.6929i	0.108040	−	0.488188i
$677$	4.73877	−	2.73593i	0.182126	−	0.105150i	−0.406165	−	0.913800i	$-0.633134\pi$
$677$	4.73877	−	2.73593i	0.182126	−	0.105150i	0.588291	+	0.808649i	$0.299801\pi$
$678$		0			0
$679$	1.72092	+	2.98073i	0.0660430	+	0.114390i
$680$	−1.62934			−0.0624822
$681$		0			0
$682$	1.47714	+	5.51277i	0.0565627	+	0.211095i
$683$	24.9699	+	6.69067i	0.955447	+	0.256011i	0.702672	−	0.711514i	$-0.251990\pi$
$683$	24.9699	+	6.69067i	0.955447	+	0.256011i	0.252775	+	0.967525i	$0.418657\pi$
$684$		0			0
$685$	4.23986	+	7.34366i	0.161997	+	0.280587i
$686$	−19.3322			−0.738108
$687$		0			0
$688$	0.772736	+	0.446139i	0.0294603	+	0.0170089i
$689$	32.2582	+	3.52683i	1.22894	+	0.134362i
$690$		0			0
$691$	−23.9424	+	23.9424i	−0.910811	+	0.910811i	−0.996336	−	0.0855252i	$-0.972743\pi$
$691$	−23.9424	+	23.9424i	−0.910811	+	0.910811i	0.0855252	+	0.996336i	$0.472743\pi$
$692$	−20.0900	−	11.5989i	−0.763706	−	0.440926i
$693$		0			0
$694$	−22.8522	+	22.8522i	−0.867459	+	0.867459i
$695$	12.8151	−	3.43379i	0.486103	−	0.130251i
$696$		0			0
$697$	−11.6262	+	3.11522i	−0.440372	+	0.117997i
$698$		−	18.9648i		−	0.717828i
$699$		0			0
$700$	5.75989	+	5.75989i	0.217703	+	0.217703i
$701$	29.4689			1.11303			0.556513	−	0.830839i	$-0.312139\pi$
$701$	29.4689			1.11303			0.556513	+	0.830839i	$0.312139\pi$
$702$		0			0
$703$	46.3599			1.74850
$704$	0.696978	+	0.696978i	0.0262683	+	0.0262683i
$705$		0			0
$706$		−	19.5973i		−	0.737554i
$707$	−25.7731	+	6.90589i	−0.969298	+	0.259723i
$708$		0			0
$709$	−12.5359	+	3.35900i	−0.470797	+	0.126150i	−0.486414	−	0.873728i	$-0.661695\pi$
$709$	−12.5359	+	3.35900i	−0.470797	+	0.126150i	0.0156169	+	0.999878i	$0.495029\pi$
$710$	3.14500	−	3.14500i	0.118030	−	0.118030i
$711$		0			0
$712$	1.47520	+	0.851709i	0.0552856	+	0.0319191i
$713$	−25.9006	+	25.9006i	−0.969985	+	0.969985i
$714$		0			0
$715$	−1.93076	−	1.41514i	−0.0722063	−	0.0529234i
$716$	4.82455	+	2.78545i	0.180302	+	0.104097i
$717$		0			0
$718$	27.1650			1.01379
$719$	−1.46802	−	2.54269i	−0.0547480	−	0.0948263i	0.837353	−	0.546663i	$-0.184102\pi$
$719$	−1.46802	−	2.54269i	−0.0547480	−	0.0948263i	−0.892101	+	0.451837i	$0.850769\pi$
$720$		0			0
$721$	−18.1606	−	4.86612i	−0.676336	−	0.181224i
$722$	−6.20510	−	23.1578i	−0.230930	−	0.861843i
$723$		0			0
$724$	20.8410			0.774549
$725$	−9.75764	−	16.9007i	−0.362390	−	0.627677i
$726$		0			0
$727$	−34.7895	+	20.0857i	−1.29027	+	0.744938i	−0.978702	−	0.205285i	$-0.934188\pi$
$727$	−34.7895	+	20.0857i	−1.29027	+	0.744938i	−0.311569	+	0.950224i	$0.600854\pi$
$728$	5.21047	+	3.81900i	0.193113	+	0.141541i
$729$		0			0
$730$	−1.97679	−	7.37746i	−0.0731641	−	0.273052i
$731$		−	2.15835i		−	0.0798294i
$732$		0			0
$733$	−3.39197	−	12.6590i	−0.125285	−	0.467571i	0.874564	−	0.484909i	$-0.161147\pi$
$733$	−3.39197	−	12.6590i	−0.125285	−	0.467571i	−0.999850	+	0.0173384i	$0.994481\pi$
$734$	−5.44068	−	5.44068i	−0.200819	−	0.200819i
$735$		0			0
$736$	−1.63730	+	6.11049i	−0.0603517	+	0.225236i
$737$	−9.45150	+	5.45683i	−0.348151	+	0.201005i
$738$		0			0
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.610731	−	0.791838i	$-0.709124\pi$
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.132990	+	0.991117i	$0.542458\pi$
$740$	−2.38175	−	4.12531i	−0.0875547	−	0.151649i
$741$		0			0
$742$	−8.06290	+	13.9654i	−0.295998	+	0.512684i
$743$	4.33508	−	16.1787i	0.159039	−	0.593540i	−0.839687	−	0.543071i	$-0.817262\pi$
$743$	4.33508	−	16.1787i	0.159039	−	0.593540i	0.998726	−	0.0504696i	$-0.0160718\pi$
$744$		0			0
$745$	−5.64073	−	3.25668i	−0.206660	−	0.119315i
$746$	11.3830	+	11.3830i	0.416760	+	0.416760i
$747$		0			0
$748$	0.617094	−	2.30303i	0.0225632	−	0.0842070i
$749$	−3.75500	−	1.00615i	−0.137205	−	0.0367639i
$750$		0			0
$751$	−8.11367	+	4.68443i	−0.296072	+	0.170937i	−0.640677	−	0.767810i	$-0.721346\pi$
$751$	−8.11367	+	4.68443i	−0.296072	+	0.170937i	0.344605	+	0.938748i	$0.388013\pi$
$752$	−3.66378	−	0.981707i	−0.133604	−	0.0357992i
$753$		0			0
$754$	−9.68970	−	12.0686i	−0.352878	−	0.439511i
$755$		−	3.34938i		−	0.121897i
$756$		0			0
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	−0.838090	−	0.545532i	$-0.816328\pi$
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	0.891490	+	0.453041i	$0.149661\pi$
$758$	12.9805	−	22.4829i	0.471472	−	0.816614i
$759$		0			0
$760$	−3.12234	+	3.12234i	−0.113259	+	0.113259i
$761$	7.31204	−	7.31204i	0.265061	−	0.265061i	−0.562045	−	0.827106i	$-0.689985\pi$
$761$	7.31204	−	7.31204i	0.265061	−	0.265061i	0.827106	+	0.562045i	$0.189985\pi$
$762$		0			0
$763$	10.4970	−	18.1813i	0.380016	−	0.658207i
$764$	−9.03635	+	15.6514i	−0.326924	+	0.566248i
$765$		0			0
$766$		−	31.4582i		−	1.13663i
$767$	−10.6611	−	13.2784i	−0.384949	−	0.479455i
$768$		0			0
$769$	−0.0675077	−	0.0180886i	−0.00243439	−	0.000652292i	0.257602	−	0.966251i	$-0.417068\pi$
$769$	−0.0675077	−	0.0180886i	−0.00243439	−	0.000652292i	−0.260036	+	0.965599i	$0.583734\pi$
$770$	1.03021	−	0.594792i	0.0371262	−	0.0214348i
$771$		0			0
$772$	7.11166	+	1.90556i	0.255954	+	0.0685827i
$773$	6.52883	−	24.3659i	0.234826	−	0.876382i	−0.743402	−	0.668845i	$-0.766789\pi$
$773$	6.52883	−	24.3659i	0.234826	−	0.876382i	0.978227	−	0.207536i	$-0.0665445\pi$
$774$		0			0
$775$	−18.6138	−	18.6138i	−0.668627	−	0.668627i
$776$	−1.66361	−	0.960483i	−0.0597199	−	0.0344793i
$777$		0			0
$778$	−6.57319	+	24.5315i	−0.235660	+	0.879496i
$779$	−16.3098	+	28.2493i	−0.584358	+	1.01214i
$780$		0			0
$781$	3.25425	+	5.63652i	0.116446	+	0.201691i
$782$	14.7808	−	3.96050i	0.528560	−	0.141627i
$783$		0			0
$784$	3.28199	−	1.89486i	0.117214	−	0.0676734i
$785$	1.69517	−	6.32646i	0.0605032	−	0.225801i
$786$		0			0
$787$	21.2801	+	21.2801i	0.758554	+	0.758554i	0.976059	−	0.217506i	$-0.0697920\pi$
$787$	21.2801	+	21.2801i	0.758554	+	0.758554i	−0.217506	+	0.976059i	$0.569792\pi$
$788$	−6.33628	−	23.6473i	−0.225721	−	0.842401i
$789$		0			0
$790$		−	1.08732i		−	0.0386850i
$791$	5.14080	+	19.1857i	0.182786	+	0.682166i
$792$		0			0
$793$	13.8540	+	10.1542i	0.491969	+	0.360587i
$794$	−1.12805	+	0.651278i	−0.0400329	+	0.0231130i
$795$		0			0
$796$	−4.02871	−	6.97794i	−0.142794	−	0.247326i
$797$	27.5921			0.977363			0.488682	−	0.872462i	$-0.337478\pi$
$797$	27.5921			0.977363			0.488682	+	0.872462i	$0.337478\pi$
$798$		0			0
$799$	2.37467	+	8.86239i	0.0840098	+	0.313529i
$800$	−4.39138	−	1.17667i	−0.155259	−	0.0416014i
$801$		0			0
$802$	0.718789	+	1.24498i	0.0253813	+	0.0439618i
$803$	11.1766			0.394412
$804$		0			0
$805$	6.61187	+	3.81736i	0.233038	+	0.134544i
$806$	−16.8383	−	12.3415i	−0.593102	−	0.434713i
$807$		0			0
$808$	10.5302	−	10.5302i	0.370451	−	0.370451i
$809$	−31.3309	−	18.0889i	−1.10154	−	0.635972i	−0.164912	−	0.986308i	$-0.552734\pi$
$809$	−31.3309	−	18.0889i	−1.10154	−	0.635972i	−0.936624	+	0.350336i	$0.886067\pi$
$810$		0			0
$811$	0.803239	−	0.803239i	0.0282055	−	0.0282055i	−0.692863	−	0.721069i	$-0.743651\pi$
$811$	0.803239	−	0.803239i	0.0282055	−	0.0282055i	0.721069	+	0.692863i	$0.243651\pi$
$812$	7.42905	−	1.99061i	0.260709	−	0.0698567i
$813$		0			0
$814$	6.73309	−	1.80412i	0.235995	−	0.0632345i
$815$			3.24578i			0.113695i
$816$		0			0
$817$	−4.13611	−	4.13611i	−0.144704	−	0.144704i
$818$	−22.9718			−0.803189
$819$		0			0
$820$	3.35166			0.117045
$821$	34.2693	+	34.2693i	1.19601	+	1.19601i	0.975352	+	0.220656i	$0.0708198\pi$
$821$	34.2693	+	34.2693i	1.19601	+	1.19601i	0.220656	+	0.975352i	$0.429180\pi$
$822$		0			0
$823$			28.2827i			0.985873i	0.870065	+	0.492937i	$0.164077\pi$
$823$			28.2827i			0.985873i	−0.870065	+	0.492937i	$0.835923\pi$
$824$	10.1358	−	2.71588i	0.353098	−	0.0946122i
$825$		0			0
$826$	8.17379	−	2.19016i	0.284403	−	0.0762055i
$827$	−13.1080	+	13.1080i	−0.455810	+	0.455810i	−0.897277	−	0.441467i	$-0.854458\pi$
$827$	−13.1080	+	13.1080i	−0.455810	+	0.455810i	0.441467	+	0.897277i	$0.354458\pi$
$828$		0			0
$829$	46.5863	+	26.8966i	1.61801	+	0.934159i	0.987434	+	0.158032i	$0.0505148\pi$
$829$	46.5863	+	26.8966i	1.61801	+	0.934159i	0.630577	+	0.776127i	$0.282818\pi$
$830$	3.60479	−	3.60479i	0.125124	−	0.125124i
$831$		0			0
$832$	−3.58419	−	0.391864i	−0.124260	−	0.0135854i
$833$	−7.93886	−	4.58350i	−0.275065	−	0.158809i
$834$		0			0
$835$	9.53101			0.329834
$836$	−3.23080	−	5.59591i	−0.111740	−	0.193539i
$837$		0			0
$838$	−6.38041	−	1.70963i	−0.220408	−	0.0590581i
$839$	1.12772	+	4.20871i	0.0389332	+	0.145301i	0.982656	−	0.185436i	$-0.0593696\pi$
$839$	1.12772	+	4.20871i	0.0389332	+	0.145301i	−0.943723	+	0.330736i	$0.892703\pi$
$840$		0			0
$841$	10.5738			0.364614
$842$	−4.70368	−	8.14701i	−0.162100	−	0.280765i
$843$		0			0
$844$	−12.1952	+	7.04091i	−0.419776	+	0.242358i
$845$	8.74806	−	0.385182i	0.300942	−	0.0132507i
$846$		0			0
$847$	−4.65052	−	17.3560i	−0.159794	−	0.596359i
$848$		−	9.00014i		−	0.309066i
$849$		0			0
$850$	2.84626	+	10.6224i	0.0976260	+	0.364345i
$851$	31.6340	+	31.6340i	1.08440	+	1.08440i
$852$		0			0
$853$	2.92390	−	10.9121i	0.100112	−	0.373625i	−0.897632	−	0.440745i	$-0.854714\pi$
$853$	2.92390	−	10.9121i	0.100112	−	0.373625i	0.997745	+	0.0671200i	$0.0213810\pi$
$854$	−7.39218	+	4.26788i	−0.252955	+	0.146044i
$855$		0			0
$856$	2.09574	−	0.561553i	0.0716311	−	0.0191935i
$857$	8.91122	+	15.4347i	0.304401	+	0.527239i	0.977128	−	0.212653i	$-0.0682103\pi$
$857$	8.91122	+	15.4347i	0.304401	+	0.527239i	−0.672726	+	0.739891i	$0.734877\pi$
$858$		0			0
$859$	−12.6436	+	21.8993i	−0.431393	+	0.747194i	−0.996994	−	0.0774851i	$-0.975311\pi$
$859$	−12.6436	+	21.8993i	−0.431393	+	0.747194i	0.565601	+	0.824679i	$0.308644\pi$
$860$	−0.155556	+	0.580542i	−0.00530440	+	0.0197963i
$861$		0			0
$862$	−1.72918	−	0.998343i	−0.0588961	−	0.0340037i
$863$	−9.09474	−	9.09474i	−0.309589	−	0.309589i	0.535161	−	0.844750i	$-0.320251\pi$
$863$	−9.09474	−	9.09474i	−0.309589	−	0.309589i	−0.844750	+	0.535161i	$0.820251\pi$
$864$		0			0
$865$	4.04421	−	15.0932i	0.137507	−	0.513184i
$866$	30.9649	+	8.29701i	1.05223	+	0.281944i
$867$		0			0
$868$	8.98452	−	5.18722i	0.304955	−	0.176066i
$869$	1.53690	+	0.411810i	0.0521356	+	0.0139697i
$870$		0			0
$871$	14.4622	−	37.2099i	0.490034	−	1.26081i
$872$			11.7172i			0.396793i
$873$		0			0
$874$	20.7352	−	35.9145i	0.701379	−	1.21482i
$875$	−5.76057	+	9.97761i	−0.194743	+	0.337305i
$876$		0			0
$877$	36.5154	−	36.5154i	1.23304	−	1.23304i	0.270247	−	0.962791i	$-0.412895\pi$
$877$	36.5154	−	36.5154i	1.23304	−	1.23304i	0.962791	−	0.270247i	$-0.0871052\pi$
$878$	−18.4762	+	18.4762i	−0.623542	+	0.623542i
$879$		0			0
$880$	−0.331966	+	0.574981i	−0.0111906	+	0.0193826i
$881$	21.3121	−	36.9136i	0.718023	−	1.24365i	−0.243759	−	0.969836i	$-0.578381\pi$
$881$	21.3121	−	36.9136i	0.718023	−	1.24365i	0.961782	−	0.273816i	$-0.0882860\pi$
$882$		0			0
$883$		−	33.4740i		−	1.12649i	−0.826290	−	0.563245i	$-0.809553\pi$
$883$		−	33.4740i		−	1.12649i	0.826290	−	0.563245i	$-0.190447\pi$
$884$	3.51404	+	7.98227i	0.118190	+	0.268473i
$885$		0			0
$886$	10.9944	+	2.94593i	0.369363	+	0.0989704i
$887$	4.08001	−	2.35559i	0.136993	−	0.0790931i	−0.429937	−	0.902859i	$-0.641464\pi$
$887$	4.08001	−	2.35559i	0.136993	−	0.0790931i	0.566930	+	0.823766i	$0.308131\pi$
$888$		0			0
$889$	−8.65706	−	2.31965i	−0.290349	−	0.0777987i
$890$	−0.296966	+	1.10829i	−0.00995431	+	0.0371500i
$891$		0			0
$892$	16.7879	+	16.7879i	0.562099	+	0.562099i
$893$	21.5339	+	12.4326i	0.720604	+	0.416041i
$894$		0			0
$895$	−0.971205	+	3.62459i	−0.0324638	+	0.121157i
$896$	0.895864	−	1.55168i	0.0299287	−	0.0518381i
$897$		0			0
$898$	6.92393	+	11.9926i	0.231055	+	0.400198i
$899$	−24.0079	+	6.43289i	−0.800708	+	0.214549i
$900$		0			0
$901$	−18.8539	+	10.8853i	−0.628115	+	0.362642i
$902$	−1.26941	+	4.73750i	−0.0422667	+	0.157741i
$903$		0			0
$904$	−7.83876	−	7.83876i	−0.260713	−	0.260713i
$905$	3.63332	+	13.5597i	0.120776	+	0.450740i
$906$		0			0
$907$			2.22688i			0.0739424i	0.999316	+	0.0369712i	$0.0117710\pi$
$907$			2.22688i			0.0739424i	−0.999316	+	0.0369712i	$0.988229\pi$
$908$	6.19651	+	23.1257i	0.205638	+	0.767453i
$909$		0			0
$910$	−1.57638	+	4.05587i	−0.0522564	+	0.134451i
$911$	10.3509	−	5.97609i	0.342940	−	0.197997i	−0.318631	−	0.947879i	$-0.603223\pi$
$911$	10.3509	−	5.97609i	0.342940	−	0.197997i	0.661571	+	0.749882i	$0.269890\pi$
$912$		0			0
$913$	3.73001	+	6.46057i	0.123445	+	0.213814i
$914$	−33.6779			−1.11397
$915$		0			0
$916$	−5.31509	−	19.8362i	−0.175616	−	0.655406i
$917$	38.0419	+	10.1933i	1.25625	+	0.336612i
$918$		0			0
$919$	2.28777	+	3.96254i	0.0754667	+	0.130712i	0.901289	−	0.433218i	$-0.142622\pi$
$919$	2.28777	+	3.96254i	0.0754667	+	0.130712i	−0.825822	+	0.563930i	$0.809289\pi$
$920$	−4.26110			−0.140484
$921$		0			0
$922$	7.78890	+	4.49692i	0.256514	+	0.148098i
$923$	−22.1906	−	8.62473i	−0.730412	−	0.283887i
$924$		0			0
$925$	−22.7341	+	22.7341i	−0.747494	+	0.747494i
$926$	16.4220	+	9.48125i	0.539661	+	0.311573i
$927$		0			0
$928$	−3.03531	+	3.03531i	−0.0996388	+	0.0996388i
$929$	−45.6232	+	12.2247i	−1.49685	+	0.401079i	−0.912043	−	0.410095i	$-0.865495\pi$
$929$	−45.6232	+	12.2247i	−1.49685	+	0.401079i	−0.584805	+	0.811174i	$0.698829\pi$
$930$		0			0
$931$	−23.9970	+	6.42997i	−0.786469	+	0.210734i
$932$		−	2.79071i		−	0.0914126i
$933$		0			0
$934$	−23.4347	−	23.4347i	−0.766808	−	0.766808i
$935$	1.60600			0.0525217
$936$		0			0
$937$	34.1939			1.11707			0.558533	−	0.829482i	$-0.311365\pi$
$937$	34.1939			1.11707			0.558533	+	0.829482i	$0.311365\pi$
$938$	14.0279	+	14.0279i	0.458028	+	0.458028i
$939$		0			0
$940$		−	2.55490i		−	0.0833318i
$941$	28.2319	−	7.56472i	0.920334	−	0.246603i	0.232606	−	0.972571i	$-0.425275\pi$
$941$	28.2319	−	7.56472i	0.920334	−	0.246603i	0.687728	+	0.725968i	$0.258608\pi$
$942$		0			0
$943$	−30.4052	+	8.14704i	−0.990128	+	0.265304i
$944$	−3.33959	+	3.33959i	−0.108694	+	0.108694i
$945$		0			0
$946$	−0.761667	−	0.439749i	−0.0247639	−	0.0142975i
$947$	19.5151	−	19.5151i	0.634154	−	0.634154i	−0.314953	−	0.949107i	$-0.601989\pi$
$947$	19.5151	−	19.5151i	0.634154	−	0.634154i	0.949107	+	0.314953i	$0.101989\pi$
$948$		0			0
$949$	−31.8795	+	25.5957i	−1.03485	+	0.830872i
$950$	25.8104	+	14.9016i	0.837399	+	0.483472i
$951$		0			0
$952$	−4.33405			−0.140467
$953$	8.06765	+	13.9736i	0.261337	+	0.452649i	0.966597	−	0.256299i	$-0.0825033\pi$
$953$	8.06765	+	13.9736i	0.261337	+	0.452649i	−0.705261	+	0.708948i	$0.749170\pi$
$954$		0			0
$955$	−11.7586	−	3.15071i	−0.380500	−	0.101955i
$956$	−2.03334	−	7.58852i	−0.0657629	−	0.245430i
$957$		0			0
$958$	−30.8338			−0.996195
$959$	11.2781	+	19.5342i	0.364188	+	0.630792i
$960$		0			0
$961$	−2.18777	+	1.26311i	−0.0705733	+	0.0407455i
$962$	−15.0735	+	20.5656i	−0.485989	+	0.663061i
$963$		0			0
$964$	6.02534	+	22.4869i	0.194063	+	0.724253i
$965$			4.95925i			0.159644i
$966$		0			0
$967$	−8.38995	−	31.3117i	−0.269803	−	1.00692i	−0.959245	−	0.282576i	$-0.908811\pi$
$967$	−8.38995	−	31.3117i	−0.269803	−	1.00692i	0.689442	−	0.724341i	$-0.257856\pi$
$968$	7.09118	+	7.09118i	0.227919	+	0.227919i
$969$		0			0
$970$	0.334892	−	1.24983i	0.0107527	−	0.0401298i
$971$	−23.3310	+	13.4701i	−0.748727	+	0.432278i	−0.825234	−	0.564791i	$-0.808957\pi$
$971$	−23.3310	+	13.4701i	−0.748727	+	0.432278i	0.0765068	+	0.997069i	$0.475623\pi$
$972$		0			0
$973$	34.0882	−	9.13391i	1.09282	−	0.292820i
$974$	10.1155	+	17.5206i	0.324123	+	0.561397i
$975$		0			0
$976$	2.38199	−	4.12572i	0.0762456	−	0.132061i
$977$	−3.95573	+	14.7630i	−0.126555	+	0.472310i	−0.999890	−	0.0148095i	$-0.995286\pi$
$977$	−3.95573	+	14.7630i	−0.126555	+	0.472310i	0.873335	+	0.487120i	$0.161952\pi$
$978$		0			0
$979$	−1.45407	−	0.839508i	−0.0464723	−	0.0268308i
$980$	1.80501	+	1.80501i	0.0576590	+	0.0576590i
$981$		0			0
$982$	3.90879	−	14.5878i	0.124735	−	0.465516i
$983$	2.82359	+	0.756578i	0.0900584	+	0.0241311i	0.303567	−	0.952810i	$-0.401822\pi$
$983$	2.82359	+	0.756578i	0.0900584	+	0.0241311i	−0.213508	+	0.976941i	$0.568489\pi$
$984$		0			0
$985$	14.2810	−	8.24512i	0.455030	−	0.262711i
$986$	10.0296	+	2.68742i	0.319407	+	0.0855848i
$987$		0			0
$988$	22.0307	+	8.56260i	0.700891	+	0.272413i
$989$		−	5.64460i		−	0.179488i
$990$		0			0
$991$	20.0775	−	34.7753i	0.637784	−	1.10467i	−0.348134	−	0.937445i	$-0.613185\pi$
$991$	20.0775	−	34.7753i	0.637784	−	1.10467i	0.985918	−	0.167229i	$-0.0534821\pi$
$992$	−2.89509	+	5.01445i	−0.0919193	+	0.159209i
$993$		0			0
$994$	8.36572	−	8.36572i	0.265345	−	0.265345i
$995$	3.83769	−	3.83769i	0.121663	−	0.121663i
$996$		0			0
$997$	−7.81967	+	13.5441i	−0.247651	+	0.428945i	−0.962874	−	0.269952i	$-0.912992\pi$
$997$	−7.81967	+	13.5441i	−0.247651	+	0.428945i	0.715222	+	0.698897i	$0.246325\pi$
$998$	−20.9577	+	36.2997i	−0.663403	+	1.14905i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.71.4		56
3.2	odd	2		234.2.y.a.149.13	yes	56
9.2	odd	6		702.2.bc.a.305.11		56
9.7	even	3		234.2.z.a.227.1	yes	56
13.11	odd	12		702.2.bc.a.557.11		56
39.11	even	12		234.2.z.a.167.1	yes	56
117.11	even	12	inner	702.2.bb.a.89.4		56
117.115	odd	12		234.2.y.a.11.13	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.13	✓	56	117.115	odd	12
234.2.y.a.149.13	yes	56	3.2	odd	2
234.2.z.a.167.1	yes	56	39.11	even	12
234.2.z.a.227.1	yes	56	9.7	even	3
702.2.bb.a.71.4		56	1.1	even	1	trivial
702.2.bb.a.89.4		56	117.11	even	12	inner
702.2.bc.a.305.11		56	9.2	odd	6
702.2.bc.a.557.11		56	13.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.650628 + 0.174335i) q^{5} +(-1.73068 + 0.463733i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.583337 + 0.336790i) q^{10} +(-0.696978 + 0.696978i) q^{11} +(0.391864 - 3.58419i) q^{13} +(1.55168 + 0.895864i) q^{14} -1.00000 q^{16} +(1.20946 + 2.09485i) q^{17} +(6.33213 + 1.69669i) q^{19} +(-0.174335 - 0.650628i) q^{20} +0.985676 q^{22} +(3.16302 + 5.47852i) q^{23} +(-3.93720 + 2.27315i) q^{25} +(-2.81150 + 2.25732i) q^{26} +(-0.463733 - 1.73068i) q^{28} +4.29257i q^{29} +(1.49861 + 5.59289i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.626062 - 2.33650i) q^{34} +(1.04518 - 0.603436i) q^{35} +(6.83094 - 1.83034i) q^{37} +(-3.27775 - 5.67724i) q^{38} +(-0.336790 + 0.583337i) q^{40} +(-1.28786 + 4.80634i) q^{41} +(-0.772736 - 0.446139i) q^{43} +(-0.696978 - 0.696978i) q^{44} +(1.63730 - 6.11049i) q^{46} +(3.66378 + 0.981707i) q^{47} +(-3.28199 + 1.89486i) q^{49} +(4.39138 + 1.17667i) q^{50} +(3.58419 + 0.391864i) q^{52} +9.00014i q^{53} +(0.331966 - 0.574981i) q^{55} +(-0.895864 + 1.55168i) q^{56} +(3.03531 - 3.03531i) q^{58} +(3.33959 - 3.33959i) q^{59} +(-2.38199 + 4.12572i) q^{61} +(2.89509 - 5.01445i) q^{62} -1.00000i q^{64} +(0.369894 + 2.40029i) q^{65} +(10.6950 + 2.86571i) q^{67} +(-2.09485 + 1.20946i) q^{68} +(-1.16575 - 0.312361i) q^{70} +(1.70900 - 6.37808i) q^{71} +(-8.01788 - 8.01788i) q^{73} +(-6.12445 - 3.53595i) q^{74} +(-1.69669 + 6.33213i) q^{76} +(0.883031 - 1.52946i) q^{77} +(-0.807117 - 1.39797i) q^{79} +(0.650628 - 0.174335i) q^{80} +(4.30925 - 2.48795i) q^{82} +(1.95885 - 7.31055i) q^{83} +(-1.15211 - 1.15211i) q^{85} +(0.230939 + 0.861875i) q^{86} +0.985676i q^{88} +(0.440877 + 1.64537i) q^{89} +(0.983920 + 6.38480i) q^{91} +(-5.47852 + 3.16302i) q^{92} +(-1.89651 - 3.28485i) q^{94} -4.41566 q^{95} +(-0.497183 - 1.85551i) q^{97} +(3.66058 + 0.980849i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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