LMFDB - Embedded newform 702.2.bb.a.89.4

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			89.4
Character	$\chi$	$=$	702.89
Dual form			702.2.bb.a.71.4

$q$-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 $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−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	0.110382	−	0.993889i	$-0.464793\pi$
$5$	−0.650628	−	0.174335i	−0.290970	−	0.0779651i	−0.401351	+	0.915924i	$0.631459\pi$
$6$		0			0
$7$	−1.73068	−	0.463733i	−0.654134	−	0.175275i	−0.0835368	−	0.996505i	$-0.526622\pi$
$7$	−1.73068	−	0.463733i	−0.654134	−	0.175275i	−0.570597	+	0.821230i	$0.693288\pi$
$8$	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	0.594183	−	0.804330i	$-0.297475\pi$
$11$	−0.696978	−	0.696978i	−0.210147	−	0.210147i	−0.804330	+	0.594183i	$0.797475\pi$
$12$		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	−0.681260	−	0.732042i	$-0.738568\pi$
$17$	1.20946	−	2.09485i	0.293337	−	0.508075i	0.974597	+	0.223967i	$0.0719009\pi$
$18$		0			0
$19$	6.33213	−	1.69669i	1.45269	−	0.389247i	0.555732	−	0.831361i	$-0.312438\pi$
$19$	6.33213	−	1.69669i	1.45269	−	0.389247i	0.896959	+	0.442114i	$0.145771\pi$
$20$	−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	−0.321200	−	0.947011i	$-0.604086\pi$
$23$	3.16302	−	5.47852i	0.659536	−	1.14235i	0.980736	−	0.195338i	$-0.0625805\pi$
$24$		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	$-0.869512\pi$
$29$		−	4.29257i		−	0.797111i	0.917144	−	0.398555i	$-0.130488\pi$
$30$		0			0
$31$	1.49861	−	5.59289i	0.269158	−	1.00451i	−0.690498	−	0.723335i	$-0.742608\pi$
$31$	1.49861	−	5.59289i	0.269158	−	1.00451i	0.959656	−	0.281178i	$-0.0907250\pi$
$32$	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	0.772096	−	0.635505i	$-0.219208\pi$
$37$	6.83094	+	1.83034i	1.12300	+	0.300907i	0.350902	+	0.936412i	$0.385875\pi$
$38$	−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	−0.990595	−	0.136830i	$-0.956309\pi$
$41$	−1.28786	−	4.80634i	−0.201129	−	0.750625i	0.789465	−	0.613795i	$-0.210358\pi$
$42$		0			0
$43$	−0.772736	+	0.446139i	−0.117841	+	0.0680356i	−0.557762	−	0.830001i	$-0.688340\pi$
$43$	−0.772736	+	0.446139i	−0.117841	+	0.0680356i	0.439921	+	0.898037i	$0.355006\pi$
$44$	−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	0.0184899	−	0.999829i	$-0.494114\pi$
$47$	3.66378	−	0.981707i	0.534417	−	0.143197i	0.515927	+	0.856632i	$0.327447\pi$
$48$		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	$-0.787890\pi$
$53$		−	9.00014i		−	1.23626i	0.786074	−	0.618132i	$-0.212110\pi$
$54$		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	0.890250	−	0.455473i	$-0.150530\pi$
$59$	3.33959	+	3.33959i	0.434777	+	0.434777i	−0.455473	+	0.890250i	$0.650530\pi$
$60$		0			0
$61$	−2.38199	−	4.12572i	−0.304982	−	0.528245i	0.672275	−	0.740301i	$-0.265317\pi$
$61$	−2.38199	−	4.12572i	−0.304982	−	0.528245i	−0.977257	+	0.212057i	$0.931984\pi$
$62$	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	0.462658	−	0.886537i	$-0.346896\pi$
$67$	10.6950	−	2.86571i	1.30660	−	0.350102i	0.843942	+	0.536434i	$0.180229\pi$
$68$	−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	0.990103	+	0.140345i	$0.0448212\pi$
$71$	1.70900	+	6.37808i	0.202821	+	0.756939i	−0.787281	+	0.616594i	$0.788512\pi$
$72$		0			0
$73$	−8.01788	+	8.01788i	−0.938421	+	0.938421i	−0.998211	−	0.0597896i	$-0.980957\pi$
$73$	−8.01788	+	8.01788i	−0.938421	+	0.938421i	0.0597896	+	0.998211i	$0.480957\pi$
$74$	−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	−0.907851	−	0.419292i	$-0.862278\pi$
$79$	−0.807117	+	1.39797i	−0.0908078	+	0.157284i	0.817043	+	0.576576i	$0.195612\pi$
$80$	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	0.986162	+	0.165783i	$0.0530152\pi$
$83$	1.95885	+	7.31055i	0.215012	+	0.802437i	−0.771150	+	0.636653i	$0.780318\pi$
$84$		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	−0.938615	−	0.344967i	$-0.887890\pi$
$89$	0.440877	−	1.64537i	0.0467329	−	0.174409i	0.985348	+	0.170557i	$0.0545568\pi$
$90$		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	−0.986562	−	0.163386i	$-0.947758\pi$
$97$	−0.497183	+	1.85551i	−0.0504812	+	0.188399i	0.936081	+	0.351785i	$0.114425\pi$
$98$	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	0.0197081	−	0.999806i	$-0.493726\pi$
$103$	9.08751	−	5.24668i	0.895419	−	0.516971i	0.875711	+	0.482835i	$0.160393\pi$
$104$	−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	−0.406418	−	0.913687i	$-0.633222\pi$
$107$	1.87899	−	1.08484i	0.181649	−	0.104875i	0.588067	+	0.808812i	$0.299889\pi$
$108$		0			0
$109$	−8.28528	−	8.28528i	−0.793586	−	0.793586i	0.188489	−	0.982075i	$-0.439641\pi$
$109$	−8.28528	−	8.28528i	−0.793586	−	0.793586i	−0.982075	+	0.188489i	$0.939641\pi$
$110$	−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	$0.174600\pi$
$113$			11.0857i			1.04285i	−0.853296	+	0.521427i	$0.825400\pi$
$114$		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	−0.295331	−	0.955395i	$-0.595430\pi$
$127$	4.33197	−	2.50106i	0.384400	−	0.221933i	0.679731	+	0.733462i	$0.262097\pi$
$128$	−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	−0.692010	+	0.721888i	$0.743275\pi$
$131$	−19.0361	+	10.9905i	−1.66319	+	0.960242i	−0.971178	+	0.238354i	$0.923392\pi$
$132$		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	0.675172	+	0.737660i	$0.264069\pi$
$137$	−3.25829	+	12.1601i	−0.278374	+	1.03891i	−0.953546	+	0.301246i	$0.902597\pi$
$138$		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	−0.369197	−	0.929351i	$-0.620367\pi$
$149$	6.83755	−	6.83755i	0.560154	−	0.560154i	0.929351	+	0.369197i	$0.120367\pi$
$150$		0			0
$151$	−1.28698	−	4.80308i	−0.104733	−	0.390869i	0.893582	−	0.448900i	$-0.148184\pi$
$151$	−1.28698	−	4.80308i	−0.104733	−	0.390869i	−0.998315	+	0.0580316i	$0.981518\pi$
$152$	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	0.604168	−	0.796857i	$-0.293506\pi$
$157$	−4.86181	−	8.42090i	−0.388015	−	0.672061i	−0.992182	+	0.124796i	$0.960172\pi$
$158$	−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	0.997413	−	0.0718838i	$-0.0229011\pi$
$163$	1.24717	+	4.65451i	0.0976861	+	0.364570i	−0.899727	+	0.436453i	$0.856234\pi$
$164$	−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	−0.745403	−	0.666614i	$-0.767743\pi$
$167$	−13.6676	+	3.66224i	−1.05763	+	0.283392i	−0.312231	+	0.950006i	$0.601076\pi$
$168$		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	−0.849280	−	0.527942i	$-0.822964\pi$
$173$	−11.5989	−	20.0900i	−0.881852	−	1.52741i	−0.0325714	−	0.999469i	$-0.510370\pi$
$174$		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	0.951146	−	0.308742i	$-0.0999080\pi$
$179$	2.78545	+	4.82455i	0.208194	+	0.360603i	−0.742951	+	0.669345i	$0.766575\pi$
$180$		0			0
$181$			20.8410i			1.54910i	0.632514	+	0.774549i	$0.282023\pi$
$181$			20.8410i			1.54910i	−0.632514	+	0.774549i	$0.717977\pi$
$182$	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	0.187935	−	0.982181i	$-0.439821\pi$
$191$	15.6514	−	9.03635i	1.13250	−	0.653847i	0.944562	+	0.328334i	$0.106487\pi$
$192$		0			0
$193$	1.90556	+	7.11166i	0.137165	+	0.511908i	0.999980	+	0.00638720i	$0.00203312\pi$
$193$	1.90556	+	7.11166i	0.137165	+	0.511908i	−0.862814	+	0.505521i	$0.831300\pi$
$194$	−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	−0.715761	−	0.698345i	$-0.753920\pi$
$197$	−23.6473	−	6.33628i	−1.68480	−	0.451441i	−0.969040	+	0.246904i	$0.920587\pi$
$198$		0			0
$199$	−6.97794	−	4.02871i	−0.494653	−	0.285588i	0.231850	−	0.972752i	$-0.425522\pi$
$199$	−6.97794	−	4.02871i	−0.494653	−	0.285588i	−0.726503	+	0.687164i	$0.758856\pi$
$200$	−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	−0.515130	−	0.857112i	$-0.672256\pi$
$211$	7.04091	−	12.1952i	0.484716	−	0.839553i	0.999846	+	0.0175594i	$0.00558961\pi$
$212$	−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	0.991103	+	0.133096i	$0.0424918\pi$
$223$	16.7879	+	16.7879i	1.12420	+	1.12420i	0.133096	+	0.991103i	$0.457508\pi$
$224$	−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	0.924616	−	0.380901i	$-0.124386\pi$
$227$	23.1257	+	6.19651i	1.53491	+	0.411277i	0.610291	+	0.792178i	$0.291053\pi$
$228$		0			0
$229$	−19.8362	−	5.31509i	−1.31081	−	0.351231i	−0.465284	−	0.885161i	$-0.654048\pi$
$229$	−19.8362	−	5.31509i	−1.31081	−	0.351231i	−0.845529	+	0.533930i	$0.820714\pi$
$230$		−	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	0.00489453	−	0.999988i	$-0.498442\pi$
$239$	−7.58852	−	2.03334i	−0.490861	−	0.131526i	−0.495755	+	0.868462i	$0.665109\pi$
$240$		0			0
$241$	22.4869	+	6.02534i	1.44851	+	0.388126i	0.895504	−	0.445054i	$-0.146815\pi$
$241$	22.4869	+	6.02534i	1.44851	+	0.388126i	0.553002	+	0.833180i	$0.313482\pi$
$242$	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	−0.0820668	−	0.996627i	$-0.526152\pi$
$251$	13.0241	−	22.5583i	0.822071	−	1.42387i	0.904138	−	0.427241i	$-0.140515\pi$
$252$		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	−0.731592	−	0.681743i	$-0.761222\pi$
$257$	3.60078	−	6.23673i	0.224610	−	0.389036i	0.956202	+	0.292706i	$0.0945558\pi$
$258$		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	$-0.885103\pi$
$263$		−	11.4549i		−	0.706342i	0.935559	−	0.353171i	$-0.114897\pi$
$264$		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	−0.342941	−	0.939357i	$-0.611423\pi$
$269$	−21.7795	−	12.5744i	−1.32792	−	0.766674i	−0.984977	+	0.172683i	$0.944756\pi$
$270$		0			0
$271$	6.17248	+	1.65391i	0.374952	+	0.100468i	0.441373	−	0.897324i	$-0.354492\pi$
$271$	6.17248	+	1.65391i	0.374952	+	0.100468i	−0.0664215	+	0.997792i	$0.521158\pi$
$272$	−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	0.100010	−	0.994986i	$-0.468113\pi$
$277$	16.8380	−	9.72143i	1.01170	−	0.584104i	0.911688	+	0.410882i	$0.134779\pi$
$278$	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	−0.977263	−	0.212030i	$-0.931993\pi$
$281$	−28.7919	+	7.71478i	−1.71758	+	0.460225i	−0.740320	+	0.672255i	$0.765326\pi$
$282$		0			0
$283$	19.1183	+	11.0380i	1.13647	+	0.656139i	0.945553	−	0.325467i	$-0.105522\pi$
$283$	19.1183	+	11.0380i	1.13647	+	0.656139i	0.190914	+	0.981607i	$0.438855\pi$
$284$	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	0.875378	−	0.483440i	$-0.160613\pi$
$293$	6.70889	+	6.70889i	0.391938	+	0.391938i	−0.483440	+	0.875378i	$0.660613\pi$
$294$		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	−0.604790	−	0.796385i	$-0.706743\pi$
$307$	3.35703	−	3.35703i	0.191596	−	0.191596i	0.796385	+	0.604790i	$0.206743\pi$
$308$	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	0.992970	+	0.118370i	$0.0377669\pi$
$311$	10.5634	+	18.2964i	0.598996	+	1.03749i	−0.393973	+	0.919122i	$0.628900\pi$
$312$		0			0
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	−0.974281	−	0.225336i	$-0.927652\pi$
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	0.682287	+	0.731084i	$0.260985\pi$
$314$	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	0.974084	+	0.226185i	$0.0726253\pi$
$317$	4.33708	+	16.1862i	0.243595	+	0.909108i	−0.730490	+	0.682924i	$0.760708\pi$
$318$		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	−0.778001	−	0.628263i	$-0.783766\pi$
$331$	3.81878	−	14.2519i	0.209899	−	0.783354i	0.987900	−	0.155091i	$-0.0495671\pi$
$332$	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	−0.405544	−	0.914076i	$-0.632918\pi$
$337$	3.36489	−	1.94272i	0.183297	−	0.105827i	0.588841	+	0.808249i	$0.299584\pi$
$338$	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	$0.334248\pi$
$347$			32.3179i			1.73492i	−0.497510	+	0.867459i	$0.665752\pi$
$348$		0			0
$349$	13.4101	−	13.4101i	0.717828	−	0.717828i	−0.250332	−	0.968160i	$-0.580540\pi$
$349$	13.4101	−	13.4101i	0.717828	−	0.717828i	0.968160	+	0.250332i	$0.0805399\pi$
$350$	−8.14572			−0.435407
$351$		0			0
$352$	−0.985676			−0.0525367
$353$	13.8574	−	13.8574i	0.737554	−	0.737554i	−0.234550	−	0.972104i	$-0.575362\pi$
$353$	13.8574	−	13.8574i	0.737554	−	0.737554i	0.972104	+	0.234550i	$0.0753617\pi$
$354$		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	−0.999904	−	0.0138835i	$-0.995581\pi$
$359$	−19.2085	−	19.2085i	−1.01379	−	1.01379i	−0.0138835	−	0.999904i	$-0.504419\pi$
$360$		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	−0.547305	−	0.836933i	$-0.684346\pi$
$379$	6.71919	−	25.0764i	0.345142	−	1.28809i	0.892446	−	0.451153i	$-0.148987\pi$
$380$			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	0.147581	−	0.989050i	$-0.452851\pi$
$383$	22.2443	−	22.2443i	1.13663	−	1.13663i	0.989050	−	0.147581i	$-0.0471487\pi$
$384$		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	0.340733	+	0.940160i	$0.389325\pi$
$389$	−12.6984	+	21.9943i	−0.643836	+	1.11516i	−0.984569	+	0.174997i	$0.944009\pi$
$390$		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	0.973870	−	0.227108i	$-0.0729270\pi$
$397$	0.337126	+	1.25817i	0.0169199	+	0.0631458i	−0.956950	+	0.290254i	$0.906260\pi$
$398$	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	−0.293324	−	0.956013i	$-0.594761\pi$
$401$	−1.38859	+	0.372073i	−0.0693431	+	0.0185804i	0.223981	+	0.974594i	$0.428095\pi$
$402$		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	0.983593	−	0.180404i	$-0.0577405\pi$
$409$	16.2435	+	16.2435i	0.803189	+	0.803189i	−0.180404	+	0.983593i	$0.557741\pi$
$410$	−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	0.633182	−	0.774003i	$-0.281749\pi$
$419$	5.72052	+	3.30274i	0.279466	+	0.161350i	−0.353716	+	0.935353i	$0.615082\pi$
$420$		0			0
$421$	9.08681	−	2.43480i	0.442864	−	0.118665i	−0.0304944	−	0.999535i	$-0.509708\pi$
$421$	9.08681	−	2.43480i	0.442864	−	0.118665i	0.473359	+	0.880870i	$0.343042\pi$
$422$	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	0.304970	−	0.952362i	$-0.401354\pi$
$431$	1.92865	+	0.516780i	0.0928998	+	0.0248924i	−0.212070	+	0.977255i	$0.568020\pi$
$432$		0			0
$433$	−27.7623	−	16.0286i	−1.33417	−	0.770285i	−0.348236	−	0.937407i	$-0.613219\pi$
$433$	−27.7623	−	16.0286i	−1.33417	−	0.770285i	−0.985936	+	0.167122i	$0.946553\pi$
$434$	−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	$0.214307\pi$
$439$			26.1293i			1.24708i	−0.781790	+	0.623542i	$0.785693\pi$
$440$	−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	0.247209	−	0.968962i	$-0.420487\pi$
$443$	−9.85727	−	5.69110i	−0.468333	−	0.270392i	−0.715542	+	0.698570i	$0.753820\pi$
$444$		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	−0.560238	−	0.828331i	$-0.689290\pi$
$449$	−13.3760	+	3.58409i	−0.631253	+	0.169144i	−0.0710148	+	0.997475i	$0.522624\pi$
$450$		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	0.992609	+	0.121357i	$0.0387244\pi$
$457$	23.8139	+	23.8139i	1.11397	+	1.11397i	0.121357	+	0.992609i	$0.461276\pi$
$458$	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	0.0507728	−	0.998710i	$-0.483832\pi$
$461$	−8.68738	−	2.32778i	−0.404612	−	0.108415i	−0.455385	+	0.890295i	$0.650498\pi$
$462$		0			0
$463$	−18.3164	−	4.90786i	−0.851234	−	0.228087i	−0.193278	−	0.981144i	$-0.561912\pi$
$463$	−18.3164	−	4.90786i	−0.851234	−	0.228087i	−0.657956	+	0.753057i	$0.728579\pi$
$464$			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	0.999993	−	0.00379781i	$-0.00120888\pi$
$479$	21.8028	+	21.8028i	0.996195	+	0.996195i	−0.00379781	+	0.999993i	$0.501209\pi$
$480$		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	−0.672787	−	0.739836i	$-0.734903\pi$
$487$	−19.5417	+	5.23619i	−0.885520	+	0.237274i	−0.212733	+	0.977110i	$0.568236\pi$
$488$	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	−0.643797	−	0.765196i	$-0.722642\pi$
$491$	7.55120	−	13.0791i	0.340781	−	0.590250i	0.984578	+	0.174946i	$0.0559752\pi$
$492$		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	0.0914956	+	0.995805i	$0.470835\pi$
$499$	−10.8485	+	40.4871i	−0.485645	+	1.81245i	−0.577140	+	0.816645i	$0.695831\pi$
$500$	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	0.722963	−	0.690886i	$-0.242780\pi$
$503$	10.9025	+	6.29458i	0.486120	+	0.280661i	−0.236843	+	0.971548i	$0.576113\pi$
$504$		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	−0.844309	−	0.535857i	$-0.819989\pi$
$509$	−8.59675	−	32.0835i	−0.381044	−	1.42208i	0.463264	−	0.886220i	$-0.346678\pi$
$510$		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	$0.125642\pi$
$521$			17.5549i			0.769094i	−0.923105	+	0.384547i	$0.874358\pi$
$522$		0			0
$523$	−4.19432	−	7.26477i	−0.183405	−	0.317666i	0.759633	−	0.650352i	$-0.225379\pi$
$523$	−4.19432	−	7.26477i	−0.183405	−	0.317666i	−0.943038	+	0.332686i	$0.892045\pi$
$524$	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	−0.675531	−	0.737332i	$-0.736086\pi$
$541$	1.43745	−	1.43745i	0.0618007	−	0.0618007i	0.737332	+	0.675531i	$0.236086\pi$
$542$	−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	−0.710848	−	0.703345i	$-0.751689\pi$
$547$	5.93332	−	10.2768i	0.253691	−	0.439405i	0.964539	+	0.263940i	$0.0850222\pi$
$548$	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	0.442470	+	0.896783i	$0.354102\pi$
$557$	−9.18337	+	34.2728i	−0.389112	+	1.45219i	−0.831582	+	0.555402i	$0.812564\pi$
$558$		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	−0.647315	−	0.762223i	$-0.724108\pi$
$571$	−7.42838	+	4.28878i	−0.310868	+	0.179480i	0.336447	+	0.941702i	$0.390775\pi$
$572$	−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	0.686174	−	0.727437i	$-0.259289\pi$
$577$	−0.991168	−	0.991168i	−0.0412629	−	0.0412629i	−0.727437	+	0.686174i	$0.759289\pi$
$578$	−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	0.120743	−	0.992684i	$-0.461472\pi$
$587$	26.9762	−	26.9762i	1.11343	−	1.11343i	0.992684	−	0.120743i	$-0.0385277\pi$
$588$		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	0.997139	−	0.0755923i	$-0.0240847\pi$
$593$	22.4411	+	22.4411i	0.921547	+	0.921547i	−0.0755923	+	0.997139i	$0.524085\pi$
$594$		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	−0.740464	−	0.672096i	$-0.765394\pi$
$599$	−12.9383	+	7.46992i	−0.528644	+	0.305213i	0.211820	+	0.977309i	$0.432061\pi$
$600$		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	0.774280	+	0.632843i	$0.218112\pi$
$613$	−5.26589	+	19.6526i	−0.212687	+	0.793760i	−0.986968	+	0.160918i	$0.948555\pi$
$614$			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	−0.997853	−	0.0654935i	$-0.979138\pi$
$617$	−23.1593	+	23.1593i	−0.932360	+	0.932360i	0.0654935	+	0.997853i	$0.479138\pi$
$618$		0			0
$619$	2.50985	+	9.36687i	0.100879	+	0.376486i	0.997845	−	0.0656133i	$-0.0209004\pi$
$619$	2.50985	+	9.36687i	0.100879	+	0.376486i	−0.896966	+	0.442100i	$0.854234\pi$
$620$	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	−0.978991	−	0.203906i	$-0.934636\pi$
$631$	−5.85572	−	21.8539i	−0.233113	−	0.869988i	0.745878	−	0.666083i	$-0.232030\pi$
$632$	−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	0.739618	−	0.673027i	$-0.235006\pi$
$641$	−5.39399	−	9.34267i	−0.213050	−	0.369013i	−0.952668	+	0.304014i	$0.901673\pi$
$642$		0			0
$643$	7.58253	+	7.58253i	0.299026	+	0.299026i	0.840632	−	0.541606i	$-0.182184\pi$
$643$	7.58253	+	7.58253i	0.299026	+	0.299026i	−0.541606	+	0.840632i	$0.682184\pi$
$644$	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	0.814037	−	0.580813i	$-0.197265\pi$
$647$	−2.44136	−	4.22856i	−0.0959799	−	0.166242i	−0.910017	+	0.414571i	$0.863932\pi$
$648$		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	0.823403	−	0.567457i	$-0.192073\pi$
$653$	19.0037	+	10.9718i	0.743673	+	0.429360i	−0.0797303	+	0.996816i	$0.525406\pi$
$654$		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	−0.996905	−	0.0786138i	$-0.974951\pi$
$659$	−36.6396	+	21.1539i	−1.42728	+	0.824038i	−0.430371	+	0.902652i	$0.641617\pi$
$660$		0			0
$661$	−8.10585	−	30.2514i	−0.315281	−	1.17664i	−0.923728	−	0.383050i	$-0.874874\pi$
$661$	−8.10585	−	30.2514i	−0.315281	−	1.17664i	0.608447	−	0.793595i	$-0.291793\pi$
$662$	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	$0.261915\pi$
$673$			38.0352i			1.46615i	−0.680148	+	0.733075i	$0.738085\pi$
$674$	−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	0.588291	−	0.808649i	$-0.299801\pi$
$677$	4.73877	+	2.73593i	0.182126	+	0.105150i	−0.406165	+	0.913800i	$0.633134\pi$
$678$		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	0.252775	−	0.967525i	$-0.418657\pi$
$683$	24.9699	−	6.69067i	0.955447	−	0.256011i	0.702672	+	0.711514i	$0.251990\pi$
$684$		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	0.0855252	−	0.996336i	$-0.472743\pi$
$691$	−23.9424	−	23.9424i	−0.910811	−	0.910811i	−0.996336	+	0.0855252i	$0.972743\pi$
$692$	−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	0.0156169	−	0.999878i	$-0.495029\pi$
$709$	−12.5359	−	3.35900i	−0.470797	−	0.126150i	−0.486414	+	0.873728i	$0.661695\pi$
$710$	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	−0.892101	−	0.451837i	$-0.850769\pi$
$719$	−1.46802	+	2.54269i	−0.0547480	+	0.0948263i	0.837353	+	0.546663i	$0.184102\pi$
$720$		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	−0.311569	−	0.950224i	$-0.600854\pi$
$727$	−34.7895	−	20.0857i	−1.29027	−	0.744938i	−0.978702	+	0.205285i	$0.934188\pi$
$728$	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	−0.999850	−	0.0173384i	$-0.994481\pi$
$733$	−3.39197	+	12.6590i	−0.125285	+	0.467571i	0.874564	+	0.484909i	$0.161147\pi$
$734$	−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	−0.132990	−	0.991117i	$-0.542458\pi$
$739$	−20.2177	−	5.41732i	−0.743721	−	0.199279i	−0.610731	+	0.791838i	$0.709124\pi$
$740$	−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	0.998726	+	0.0504696i	$0.0160718\pi$
$743$	4.33508	+	16.1787i	0.159039	+	0.593540i	−0.839687	+	0.543071i	$0.817262\pi$
$744$		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	0.344605	−	0.938748i	$-0.388013\pi$
$751$	−8.11367	−	4.68443i	−0.296072	−	0.170937i	−0.640677	+	0.767810i	$0.721346\pi$
$752$	−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	0.891490	−	0.453041i	$-0.149661\pi$
$757$	1.46922	+	2.54477i	0.0533999	+	0.0924913i	−0.838090	+	0.545532i	$0.816328\pi$
$758$	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	0.827106	−	0.562045i	$-0.189985\pi$
$761$	7.31204	+	7.31204i	0.265061	+	0.265061i	−0.562045	+	0.827106i	$0.689985\pi$
$762$		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	−0.260036	−	0.965599i	$-0.583734\pi$
$769$	−0.0675077	+	0.0180886i	−0.00243439	+	0.000652292i	0.257602	+	0.966251i	$0.417068\pi$
$770$	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	0.978227	+	0.207536i	$0.0665445\pi$
$773$	6.52883	+	24.3659i	0.234826	+	0.876382i	−0.743402	+	0.668845i	$0.766789\pi$
$774$		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	−0.217506	−	0.976059i	$-0.569792\pi$
$787$	21.2801	−	21.2801i	0.758554	−	0.758554i	0.976059	+	0.217506i	$0.0697920\pi$
$788$	−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	−0.936624	−	0.350336i	$-0.886067\pi$
$809$	−31.3309	+	18.0889i	−1.10154	+	0.635972i	−0.164912	+	0.986308i	$0.552734\pi$
$810$		0			0
$811$	0.803239	+	0.803239i	0.0282055	+	0.0282055i	0.721069	−	0.692863i	$-0.243651\pi$
$811$	0.803239	+	0.803239i	0.0282055	+	0.0282055i	−0.692863	+	0.721069i	$0.743651\pi$
$812$	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	0.220656	−	0.975352i	$-0.429180\pi$
$821$	34.2693	−	34.2693i	1.19601	−	1.19601i	0.975352	−	0.220656i	$-0.0708198\pi$
$822$		0			0
$823$		−	28.2827i		−	0.985873i	−0.870065	−	0.492937i	$-0.835923\pi$
$823$		−	28.2827i		−	0.985873i	0.870065	−	0.492937i	$-0.164077\pi$
$824$	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	0.441467	−	0.897277i	$-0.354458\pi$
$827$	−13.1080	−	13.1080i	−0.455810	−	0.455810i	−0.897277	+	0.441467i	$0.854458\pi$
$828$		0			0
$829$	46.5863	−	26.8966i	1.61801	−	0.934159i	0.630577	−	0.776127i	$-0.282818\pi$
$829$	46.5863	−	26.8966i	1.61801	−	0.934159i	0.987434	−	0.158032i	$-0.0505148\pi$
$830$	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	−0.943723	−	0.330736i	$-0.892703\pi$
$839$	1.12772	−	4.20871i	0.0389332	−	0.145301i	0.982656	+	0.185436i	$0.0593696\pi$
$840$		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	0.997745	−	0.0671200i	$-0.0213810\pi$
$853$	2.92390	+	10.9121i	0.100112	+	0.373625i	−0.897632	+	0.440745i	$0.854714\pi$
$854$	−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	−0.672726	−	0.739891i	$-0.734877\pi$
$857$	8.91122	−	15.4347i	0.304401	−	0.527239i	0.977128	+	0.212653i	$0.0682103\pi$
$858$		0			0
$859$	−12.6436	−	21.8993i	−0.431393	−	0.747194i	0.565601	−	0.824679i	$-0.308644\pi$
$859$	−12.6436	−	21.8993i	−0.431393	−	0.747194i	−0.996994	+	0.0774851i	$0.975311\pi$
$860$	−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	−0.844750	−	0.535161i	$-0.820251\pi$
$863$	−9.09474	+	9.09474i	−0.309589	+	0.309589i	0.535161	+	0.844750i	$0.320251\pi$
$864$		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	0.962791	+	0.270247i	$0.0871052\pi$
$877$	36.5154	+	36.5154i	1.23304	+	1.23304i	0.270247	+	0.962791i	$0.412895\pi$
$878$	−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	0.961782	+	0.273816i	$0.0882860\pi$
$881$	21.3121	+	36.9136i	0.718023	+	1.24365i	−0.243759	+	0.969836i	$0.578381\pi$
$882$		0			0
$883$			33.4740i			1.12649i	0.826290	+	0.563245i	$0.190447\pi$
$883$			33.4740i			1.12649i	−0.826290	+	0.563245i	$0.809553\pi$
$884$	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	0.566930	−	0.823766i	$-0.308131\pi$
$887$	4.08001	+	2.35559i	0.136993	+	0.0790931i	−0.429937	+	0.902859i	$0.641464\pi$
$888$		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	$-0.988229\pi$
$907$		−	2.22688i		−	0.0739424i	0.999316	−	0.0369712i	$-0.0117710\pi$
$908$	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	0.661571	−	0.749882i	$-0.269890\pi$
$911$	10.3509	+	5.97609i	0.342940	+	0.197997i	−0.318631	+	0.947879i	$0.603223\pi$
$912$		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	−0.825822	−	0.563930i	$-0.809289\pi$
$919$	2.28777	−	3.96254i	0.0754667	−	0.130712i	0.901289	+	0.433218i	$0.142622\pi$
$920$	−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	−0.584805	−	0.811174i	$-0.698829\pi$
$929$	−45.6232	−	12.2247i	−1.49685	−	0.401079i	−0.912043	+	0.410095i	$0.865495\pi$
$930$		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	0.687728	−	0.725968i	$-0.258608\pi$
$941$	28.2319	+	7.56472i	0.920334	+	0.246603i	0.232606	+	0.972571i	$0.425275\pi$
$942$		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	0.949107	−	0.314953i	$-0.101989\pi$
$947$	19.5151	+	19.5151i	0.634154	+	0.634154i	−0.314953	+	0.949107i	$0.601989\pi$
$948$		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	−0.705261	−	0.708948i	$-0.749170\pi$
$953$	8.06765	−	13.9736i	0.261337	−	0.452649i	0.966597	+	0.256299i	$0.0825033\pi$
$954$		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	0.689442	+	0.724341i	$0.257856\pi$
$967$	−8.38995	+	31.3117i	−0.269803	+	1.00692i	−0.959245	+	0.282576i	$0.908811\pi$
$968$	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	0.0765068	−	0.997069i	$-0.475623\pi$
$971$	−23.3310	−	13.4701i	−0.748727	−	0.432278i	−0.825234	+	0.564791i	$0.808957\pi$
$972$		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	0.873335	−	0.487120i	$-0.161952\pi$
$977$	−3.95573	−	14.7630i	−0.126555	−	0.472310i	−0.999890	+	0.0148095i	$0.995286\pi$
$978$		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	−0.213508	−	0.976941i	$-0.568489\pi$
$983$	2.82359	−	0.756578i	0.0900584	−	0.0241311i	0.303567	+	0.952810i	$0.401822\pi$
$984$		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	0.985918	+	0.167229i	$0.0534821\pi$
$991$	20.0775	+	34.7753i	0.637784	+	1.10467i	−0.348134	+	0.937445i	$0.613185\pi$
$992$	−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	0.715222	−	0.698897i	$-0.246325\pi$
$997$	−7.81967	−	13.5441i	−0.247651	−	0.428945i	−0.962874	+	0.269952i	$0.912992\pi$
$998$	−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.89.4		56
3.2	odd	2		234.2.y.a.11.13	✓	56
9.4	even	3		234.2.z.a.167.1	yes	56
9.5	odd	6		702.2.bc.a.557.11		56
13.6	odd	12		702.2.bc.a.305.11		56
39.32	even	12		234.2.z.a.227.1	yes	56
117.32	even	12	inner	702.2.bb.a.71.4		56
117.58	odd	12		234.2.y.a.149.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.13	✓	56	3.2	odd	2
234.2.y.a.149.13	yes	56	117.58	odd	12
234.2.z.a.167.1	yes	56	9.4	even	3
234.2.z.a.227.1	yes	56	39.32	even	12
702.2.bb.a.71.4		56	117.32	even	12	inner
702.2.bb.a.89.4		56	1.1	even	1	trivial
702.2.bc.a.305.11		56	13.6	odd	12
702.2.bc.a.557.11		56	9.5	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 $\F_{q}$
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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