LMFDB - Embedded newform 525.2.j.c.407.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			407.14
Character	$\chi$	$=$	525.407
Dual form			525.2.j.c.218.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27211 - 1.27211i) q^{2} +(1.54904 + 0.774907i) q^{3} -1.23654i q^{4} +(2.95632 - 0.984783i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.971203 + 0.971203i) q^{8} +(1.79904 + 2.40072i) q^{9} +O(q^{10})$	\(q+(1.27211 - 1.27211i) q^{2} +(1.54904 + 0.774907i) q^{3} -1.23654i q^{4} +(2.95632 - 0.984783i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.971203 + 0.971203i) q^{8} +(1.79904 + 2.40072i) q^{9} -0.596077i q^{11} +(0.958205 - 1.91545i) q^{12} +(0.651688 - 0.651688i) q^{13} -1.79904 q^{14} +4.94405 q^{16} +(2.63250 - 2.63250i) q^{17} +(5.34257 + 0.765406i) q^{18} +1.16418i q^{19} +(-0.547394 - 1.64328i) q^{21} +(-0.758277 - 0.758277i) q^{22} +(-2.83371 - 2.83371i) q^{23} +(0.751839 + 2.25702i) q^{24} -1.65804i q^{26} +(0.926447 + 5.11290i) q^{27} +(-0.874368 + 0.874368i) q^{28} -9.57511 q^{29} -7.54990 q^{31} +(4.34698 - 4.34698i) q^{32} +(0.461904 - 0.923346i) q^{33} -6.69767i q^{34} +(2.96859 - 2.22459i) q^{36} +(7.81453 + 7.81453i) q^{37} +(1.48096 + 1.48096i) q^{38} +(1.51449 - 0.504492i) q^{39} -8.32646i q^{41} +(-2.78678 - 1.39409i) q^{42} +(-7.71640 + 7.71640i) q^{43} -0.737075 q^{44} -7.20959 q^{46} +(5.33798 - 5.33798i) q^{47} +(7.65852 + 3.83117i) q^{48} +1.00000i q^{49} +(6.11778 - 2.03790i) q^{51} +(-0.805840 - 0.805840i) q^{52} +(-2.54423 - 2.54423i) q^{53} +(7.68273 + 5.32563i) q^{54} -1.37349i q^{56} +(-0.902128 + 1.80335i) q^{57} +(-12.1806 + 12.1806i) q^{58} -4.37549 q^{59} -15.0140 q^{61} +(-9.60433 + 9.60433i) q^{62} +(0.425452 - 2.96968i) q^{63} -1.17161i q^{64} +(-0.587007 - 1.76220i) q^{66} +(1.26066 + 1.26066i) q^{67} +(-3.25520 - 3.25520i) q^{68} +(-2.19366 - 6.58538i) q^{69} +7.16919i q^{71} +(-0.584354 + 4.07882i) q^{72} +(5.66151 - 5.66151i) q^{73} +19.8819 q^{74} +1.43955 q^{76} +(-0.421490 + 0.421490i) q^{77} +(1.28483 - 2.56837i) q^{78} -3.85224i q^{79} +(-2.52691 + 8.63798i) q^{81} +(-10.5922 - 10.5922i) q^{82} +(-4.70691 - 4.70691i) q^{83} +(-2.03198 + 0.676876i) q^{84} +19.6323i q^{86} +(-14.8322 - 7.41982i) q^{87} +(0.578912 - 0.578912i) q^{88} -2.19762 q^{89} -0.921626 q^{91} +(-3.50400 + 3.50400i) q^{92} +(-11.6951 - 5.85047i) q^{93} -13.5810i q^{94} +(10.1021 - 3.36514i) q^{96} +(7.69844 + 7.69844i) q^{97} +(1.27211 + 1.27211i) q^{98} +(1.43101 - 1.07237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{6}+O(q^{10}) $ 32 * q - 16 * q^6	$ 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) $ 32 * q - 16 * q^6 - 16 * q^16 - 8 * q^21 + 16 * q^31 + 48 * q^36 + 144 * q^46 - 64 * q^51 - 112 * q^61 - 192 * q^76 - 64 * q^81 + 64 * q^91 + 360 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.27211	−	1.27211i	0.899520	−	0.899520i	−0.0958737	−	0.995394i	$-0.530565\pi$
$2$	1.27211	−	1.27211i	0.899520	−	0.899520i	0.995394	+	0.0958737i	$0.0305645\pi$
$3$	1.54904	+	0.774907i	0.894338	+	0.447393i
$3$	1.54904	+	0.774907i	0.894338	+	0.447393i
$4$		−	1.23654i		−	0.618272i
$5$		0			0
$5$		0			0
$6$	2.95632	−	0.984783i	1.20691	−	0.402036i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.971203	+	0.971203i	0.343372	+	0.343372i
$9$	1.79904	+	2.40072i	0.599680	+	0.800240i
$10$		0			0
$11$		−	0.596077i		−	0.179724i	−0.995954	−	0.0898620i	$-0.971357\pi$
$11$		−	0.596077i		−	0.179724i	0.995954	−	0.0898620i	$-0.0286426\pi$
$12$	0.958205	−	1.91545i	0.276610	−	0.552944i
$13$	0.651688	−	0.651688i	0.180746	−	0.180746i	−0.610935	−	0.791681i	$-0.709206\pi$
$13$	0.651688	−	0.651688i	0.180746	−	0.180746i	0.791681	+	0.610935i	$0.209206\pi$
$14$	−1.79904			−0.480814
$15$		0			0
$16$	4.94405			1.23601
$17$	2.63250	−	2.63250i	0.638474	−	0.638474i	−0.311705	−	0.950179i	$-0.600900\pi$
$17$	2.63250	−	2.63250i	0.638474	−	0.638474i	0.950179	+	0.311705i	$0.100900\pi$
$18$	5.34257	+	0.765406i	1.25926	+	0.180408i
$19$			1.16418i			0.267081i	0.991043	+	0.133540i	$0.0426345\pi$
$19$			1.16418i			0.267081i	−0.991043	+	0.133540i	$0.957365\pi$
$20$		0			0
$21$	−0.547394	−	1.64328i	−0.119451	−	0.358592i
$22$	−0.758277	−	0.758277i	−0.161665	−	0.161665i
$23$	−2.83371	−	2.83371i	−0.590869	−	0.590869i	0.346997	−	0.937866i	$-0.387201\pi$
$23$	−2.83371	−	2.83371i	−0.590869	−	0.590869i	−0.937866	+	0.346997i	$0.887201\pi$
$24$	0.751839	+	2.25702i	0.153469	+	0.460713i
$25$		0			0
$26$		−	1.65804i		−	0.325169i
$27$	0.926447	+	5.11290i	0.178295	+	0.983977i
$28$	−0.874368	+	0.874368i	−0.165240	+	0.165240i
$29$	−9.57511			−1.77805			−0.889027	−	0.457855i	$-0.848618\pi$
$29$	−9.57511			−1.77805			−0.889027	+	0.457855i	$0.848618\pi$
$30$		0			0
$31$	−7.54990			−1.35600			−0.678001	−	0.735061i	$-0.737154\pi$
$31$	−7.54990			−1.35600			−0.678001	+	0.735061i	$0.737154\pi$
$32$	4.34698	−	4.34698i	0.768445	−	0.768445i
$33$	0.461904	−	0.923346i	0.0804072	−	0.160734i
$34$		−	6.69767i		−	1.14864i
$35$		0			0
$36$	2.96859	−	2.22459i	0.494766	−	0.370765i
$37$	7.81453	+	7.81453i	1.28470	+	1.28470i	0.937961	+	0.346740i	$0.112711\pi$
$37$	7.81453	+	7.81453i	1.28470	+	1.28470i	0.346740	+	0.937961i	$0.387289\pi$
$38$	1.48096	+	1.48096i	0.240244	+	0.240244i
$39$	1.51449	−	0.504492i	0.242512	−	0.0807834i
$40$		0			0
$41$		−	8.32646i		−	1.30037i	−0.759774	−	0.650187i	$-0.774691\pi$
$41$		−	8.32646i		−	1.30037i	0.759774	−	0.650187i	$-0.225309\pi$
$42$	−2.78678	−	1.39409i	−0.430010	−	0.215112i
$43$	−7.71640	+	7.71640i	−1.17674	+	1.17674i	−0.196171	+	0.980570i	$0.562851\pi$
$43$	−7.71640	+	7.71640i	−1.17674	+	1.17674i	−0.980570	+	0.196171i	$0.937149\pi$
$44$	−0.737075			−0.111118
$45$		0			0
$46$	−7.20959			−1.06300
$47$	5.33798	−	5.33798i	0.778624	−	0.778624i	−0.200972	−	0.979597i	$-0.564410\pi$
$47$	5.33798	−	5.33798i	0.778624	−	0.778624i	0.979597	+	0.200972i	$0.0644102\pi$
$48$	7.65852	+	3.83117i	1.10541	+	0.552982i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	6.11778	−	2.03790i	0.856660	−	0.285363i
$52$	−0.805840	−	0.805840i	−0.111750	−	0.111750i
$53$	−2.54423	−	2.54423i	−0.349476	−	0.349476i	0.510438	−	0.859914i	$-0.329483\pi$
$53$	−2.54423	−	2.54423i	−0.349476	−	0.349476i	−0.859914	+	0.510438i	$0.829483\pi$
$54$	7.68273	+	5.32563i	1.04549	+	0.724727i
$55$		0			0
$56$		−	1.37349i		−	0.183540i
$57$	−0.902128	+	1.80335i	−0.119490	+	0.238860i
$58$	−12.1806	+	12.1806i	−1.59939	+	1.59939i
$59$	−4.37549			−0.569640			−0.284820	−	0.958581i	$-0.591934\pi$
$59$	−4.37549			−0.569640			−0.284820	+	0.958581i	$0.591934\pi$
$60$		0			0
$61$	−15.0140			−1.92235			−0.961173	−	0.275946i	$-0.911009\pi$
$61$	−15.0140			−1.92235			−0.961173	+	0.275946i	$0.911009\pi$
$62$	−9.60433	+	9.60433i	−1.21975	+	1.21975i
$63$	0.425452	−	2.96968i	0.0536020	−	0.374144i
$64$		−	1.17161i		−	0.146451i
$65$		0			0
$66$	−0.587007	−	1.76220i	−0.0722555	−	0.216911i
$67$	1.26066	+	1.26066i	0.154015	+	0.154015i	0.779908	−	0.625894i	$-0.215266\pi$
$67$	1.26066	+	1.26066i	0.154015	+	0.154015i	−0.625894	+	0.779908i	$0.715266\pi$
$68$	−3.25520	−	3.25520i	−0.394751	−	0.394751i
$69$	−2.19366	−	6.58538i	−0.264086	−	0.792786i
$70$		0			0
$71$			7.16919i			0.850826i	0.904999	+	0.425413i	$0.139871\pi$
$71$			7.16919i			0.850826i	−0.904999	+	0.425413i	$0.860129\pi$
$72$	−0.584354	+	4.07882i	−0.0688668	+	0.480694i
$73$	5.66151	−	5.66151i	0.662629	−	0.662629i	−0.293370	−	0.955999i	$-0.594777\pi$
$73$	5.66151	−	5.66151i	0.662629	−	0.662629i	0.955999	+	0.293370i	$0.0947768\pi$
$74$	19.8819			2.31123
$75$		0			0
$76$	1.43955			0.165128
$77$	−0.421490	+	0.421490i	−0.0480333	+	0.0480333i
$78$	1.28483	−	2.56837i	0.145478	−	0.290811i
$79$		−	3.85224i		−	0.433410i	−0.976237	−	0.216705i	$-0.930469\pi$
$79$		−	3.85224i		−	0.433410i	0.976237	−	0.216705i	$-0.0695311\pi$
$80$		0			0
$81$	−2.52691	+	8.63798i	−0.280768	+	0.959776i
$82$	−10.5922	−	10.5922i	−1.16971	−	1.16971i
$83$	−4.70691	−	4.70691i	−0.516651	−	0.516651i	0.399905	−	0.916556i	$-0.369043\pi$
$83$	−4.70691	−	4.70691i	−0.516651	−	0.516651i	−0.916556	+	0.399905i	$0.869043\pi$
$84$	−2.03198	+	0.676876i	−0.221708	+	0.0738532i
$85$		0			0
$86$			19.6323i			2.11700i
$87$	−14.8322	−	7.41982i	−1.59018	−	0.795488i
$88$	0.578912	−	0.578912i	0.0617122	−	0.0617122i
$89$	−2.19762			−0.232947			−0.116474	−	0.993194i	$-0.537159\pi$
$89$	−2.19762			−0.232947			−0.116474	+	0.993194i	$0.537159\pi$
$90$		0			0
$91$	−0.921626			−0.0966127
$92$	−3.50400	+	3.50400i	−0.365317	+	0.365317i
$93$	−11.6951	−	5.85047i	−1.21272	−	0.606666i
$94$		−	13.5810i		−	1.40078i
$95$		0			0
$96$	10.1021	−	3.36514i	1.03105	−	0.343453i
$97$	7.69844	+	7.69844i	0.781658	+	0.781658i	0.980111	−	0.198452i	$-0.0635914\pi$
$97$	7.69844	+	7.69844i	0.781658	+	0.781658i	−0.198452	+	0.980111i	$0.563591\pi$
$98$	1.27211	+	1.27211i	0.128503	+	0.128503i
$99$	1.43101	−	1.07237i	0.143822	−	0.107777i
$100$		0			0
$101$		−	12.7638i		−	1.27005i	−0.772493	−	0.635023i	$-0.780991\pi$
$101$		−	12.7638i		−	1.27005i	0.772493	−	0.635023i	$-0.219009\pi$
$102$	5.19007	−	10.3749i	0.513893	−	1.02727i
$103$	6.78916	−	6.78916i	0.668956	−	0.668956i	−0.288518	−	0.957474i	$-0.593163\pi$
$103$	6.78916	−	6.78916i	0.668956	−	0.668956i	0.957474	+	0.288518i	$0.0931626\pi$
$104$	1.26584			0.124126
$105$		0			0
$106$	−6.47309			−0.628722
$107$	−0.176542	+	0.176542i	−0.0170670	+	0.0170670i	−0.715589	−	0.698522i	$-0.753842\pi$
$107$	−0.176542	+	0.176542i	−0.0170670	+	0.0170670i	0.698522	+	0.715589i	$0.253842\pi$
$108$	6.32232	−	1.14559i	0.608365	−	0.110235i
$109$			11.2027i			1.07303i	0.843892	+	0.536513i	$0.180259\pi$
$109$			11.2027i			1.07303i	−0.843892	+	0.536513i	$0.819741\pi$
$110$		0			0
$111$	6.04948	+	18.1605i	0.574191	+	1.72372i
$112$	−3.49597	−	3.49597i	−0.330338	−	0.330338i
$113$	0.553500	+	0.553500i	0.0520689	+	0.0520689i	0.732662	−	0.680593i	$-0.238278\pi$
$113$	0.553500	+	0.553500i	0.0520689	+	0.0520689i	−0.680593	+	0.732662i	$0.738278\pi$
$114$	1.14646	+	3.44168i	0.107376	+	0.322343i
$115$		0			0
$116$			11.8400i			1.09932i
$117$	2.73693	+	0.392108i	0.253030	+	0.0362504i
$118$	−5.56612	+	5.56612i	−0.512403	+	0.512403i
$119$	−3.72291			−0.341279
$120$		0			0
$121$	10.6447			0.967699
$122$	−19.0995	+	19.0995i	−1.72919	+	1.72919i
$123$	6.45223	−	12.8980i	0.581778	−	1.16297i
$124$			9.33578i			0.838378i
$125$		0			0
$126$	−3.23654	−	4.31899i	−0.288334	−	0.384766i
$127$	−2.62625	−	2.62625i	−0.233042	−	0.233042i	0.580919	−	0.813961i	$-0.302693\pi$
$127$	−2.62625	−	2.62625i	−0.233042	−	0.233042i	−0.813961	+	0.580919i	$0.802693\pi$
$128$	7.20355	+	7.20355i	0.636709	+	0.636709i
$129$	−17.9325	+	5.97351i	−1.57887	+	0.525938i
$130$		0			0
$131$			16.5281i			1.44406i	0.691859	+	0.722032i	$0.256792\pi$
$131$			16.5281i			1.44406i	−0.691859	+	0.722032i	$0.743208\pi$
$132$	−1.14176	−	0.571164i	−0.0993772	−	0.0497135i
$133$	0.823197	−	0.823197i	0.0713803	−	0.0713803i
$134$	3.20741			0.277078
$135$		0			0
$136$	5.11338			0.438469
$137$	11.1583	−	11.1583i	0.953316	−	0.953316i	−0.0456415	−	0.998958i	$-0.514533\pi$
$137$	11.1583	−	11.1583i	0.953316	−	0.953316i	0.998958	+	0.0456415i	$0.0145332\pi$
$138$	−11.1679	−	5.58676i	−0.950677	−	0.475576i
$139$		−	2.90366i		−	0.246285i	−0.992389	−	0.123142i	$-0.960703\pi$
$139$		−	2.90366i		−	0.246285i	0.992389	−	0.123142i	$-0.0392972\pi$
$140$		0			0
$141$	12.4052	−	4.13230i	1.04470	−	0.348002i
$142$	9.12001	+	9.12001i	0.765335	+	0.765335i
$143$	−0.388456	−	0.388456i	−0.0324843	−	0.0324843i
$144$	8.89454	+	11.8693i	0.741211	+	0.989106i
$145$		0			0
$146$		−	14.4041i		−	1.19210i
$147$	−0.774907	+	1.54904i	−0.0639132	+	0.127763i
$148$	9.66301	−	9.66301i	0.794294	−	0.794294i
$149$	2.77395			0.227251			0.113625	−	0.993524i	$-0.463754\pi$
$149$	2.77395			0.227251			0.113625	+	0.993524i	$0.463754\pi$
$150$		0			0
$151$	2.07180			0.168600			0.0843002	−	0.996440i	$-0.473135\pi$
$151$	2.07180			0.168600			0.0843002	+	0.996440i	$0.473135\pi$
$152$	−1.13065	+	1.13065i	−0.0917080	+	0.0917080i
$153$	11.0559	+	1.58392i	0.893813	+	0.128053i
$154$			1.07237i			0.0864137i
$155$		0			0
$156$	−0.623827	−	1.87273i	−0.0499461	−	0.149938i
$157$	−9.28263	−	9.28263i	−0.740834	−	0.740834i	0.231904	−	0.972739i	$-0.425504\pi$
$157$	−9.28263	−	9.28263i	−0.740834	−	0.740834i	−0.972739	+	0.231904i	$0.925504\pi$
$158$	−4.90048	−	4.90048i	−0.389861	−	0.389861i
$159$	−1.96957	−	5.91264i	−0.156197	−	0.468903i
$160$		0			0
$161$			4.00747i			0.315833i
$162$	7.77397	+	14.2030i	0.610781	+	1.11589i
$163$	9.40972	−	9.40972i	0.737026	−	0.737026i	−0.234975	−	0.972001i	$-0.575501\pi$
$163$	9.40972	−	9.40972i	0.737026	−	0.737026i	0.972001	+	0.234975i	$0.0755009\pi$
$164$	−10.2960			−0.803984
$165$		0			0
$166$	−11.9755			−0.929475
$167$	−10.4473	+	10.4473i	−0.808437	+	0.808437i	−0.984397	−	0.175960i	$-0.943697\pi$
$167$	−10.4473	+	10.4473i	−0.808437	+	0.808437i	0.175960	+	0.984397i	$0.443697\pi$
$168$	1.06433	−	2.12759i	0.0821145	−	0.164147i
$169$			12.1506i			0.934662i
$170$		0			0
$171$	−2.79486	+	2.09440i	−0.213729	+	0.160163i
$172$	9.54166	+	9.54166i	0.727545	+	0.727545i
$173$	18.0363	+	18.0363i	1.37127	+	1.37127i	0.858563	+	0.512707i	$0.171357\pi$
$173$	18.0363	+	18.0363i	1.37127	+	1.37127i	0.512707	+	0.858563i	$0.328643\pi$
$174$	−28.3071	+	9.42941i	−2.14596	+	0.714841i
$175$		0			0
$176$		−	2.94703i		−	0.222141i
$177$	−6.77780	−	3.39060i	−0.509451	−	0.254853i
$178$	−2.79562	+	2.79562i	−0.209540	+	0.209540i
$179$	18.2401			1.36333			0.681663	−	0.731666i	$-0.261257\pi$
$179$	18.2401			1.36333			0.681663	+	0.731666i	$0.261257\pi$
$180$		0			0
$181$	5.06040			0.376137			0.188068	−	0.982156i	$-0.439777\pi$
$181$	5.06040			0.376137			0.188068	+	0.982156i	$0.439777\pi$
$182$	−1.17241	+	1.17241i	−0.0869050	+	0.0869050i
$183$	−23.2573	−	11.6345i	−1.71923	−	0.860043i
$184$		−	5.50421i		−	0.405776i
$185$		0			0
$186$	−22.3199	+	7.43502i	−1.63658	+	0.545162i
$187$	−1.56917	−	1.56917i	−0.114749	−	0.114749i
$188$	−6.60064	−	6.60064i	−0.481401	−	0.481401i
$189$	2.96027	−	4.27046i	0.215328	−	0.310630i
$190$		0			0
$191$		−	4.33413i		−	0.313607i	−0.987630	−	0.156803i	$-0.949881\pi$
$191$		−	4.33413i		−	0.313607i	0.987630	−	0.156803i	$-0.0501189\pi$
$192$	0.907885	−	1.81486i	0.0655210	−	0.130976i
$193$	−11.7911	+	11.7911i	−0.848741	+	0.848741i	−0.989976	−	0.141235i	$-0.954893\pi$
$193$	−11.7911	+	11.7911i	−0.848741	+	0.848741i	0.141235	+	0.989976i	$0.454893\pi$
$194$	19.5866			1.40623
$195$		0			0
$196$	1.23654			0.0883245
$197$	−5.36265	+	5.36265i	−0.382073	+	0.382073i	−0.871848	−	0.489776i	$-0.837079\pi$
$197$	−5.36265	+	5.36265i	−0.382073	+	0.382073i	0.489776	+	0.871848i	$0.337079\pi$
$198$	0.456241	−	3.18458i	0.0324236	−	0.226318i
$199$		−	0.778449i		−	0.0551828i	−0.999619	−	0.0275914i	$-0.991216\pi$
$199$		−	0.778449i		−	0.0551828i	0.999619	−	0.0275914i	$-0.00878373\pi$
$200$		0			0
$201$	0.975920	+	2.92971i	0.0688361	+	0.206646i
$202$	−16.2370	−	16.2370i	−1.14243	−	1.14243i
$203$	6.77063	+	6.77063i	0.475205	+	0.475205i
$204$	−2.51995	−	7.56490i	−0.176432	−	0.529649i
$205$		0			0
$206$		−	17.2732i		−	1.20348i
$207$	1.70499	−	11.9009i	0.118505	−	0.827169i
$208$	3.22198	−	3.22198i	0.223404	−	0.223404i
$209$	0.693939			0.0480008
$210$		0			0
$211$	3.91922			0.269810			0.134905	−	0.990859i	$-0.456927\pi$
$211$	3.91922			0.269810			0.134905	+	0.990859i	$0.456927\pi$
$212$	−3.14605	+	3.14605i	−0.216071	+	0.216071i
$213$	−5.55545	+	11.1053i	−0.380653	+	0.760926i
$214$			0.449163i			0.0307042i
$215$		0			0
$216$	−4.06589	+	5.86543i	−0.276649	+	0.399092i
$217$	5.33859	+	5.33859i	0.362407	+	0.362407i
$218$	14.2511	+	14.2511i	0.965209	+	0.965209i
$219$	13.1570	−	4.38275i	0.889069	−	0.296159i
$220$		0			0
$221$		−	3.43113i		−	0.230803i
$222$	30.7979	+	15.4066i	2.06702	+	1.03403i
$223$	−4.95226	+	4.95226i	−0.331628	+	0.331628i	−0.853204	−	0.521577i	$-0.825344\pi$
$223$	−4.95226	+	4.95226i	−0.331628	+	0.331628i	0.521577	+	0.853204i	$0.325344\pi$
$224$	−6.14756			−0.410751
$225$		0			0
$226$	1.40823			0.0936740
$227$	10.4264	−	10.4264i	0.692027	−	0.692027i	−0.270651	−	0.962678i	$-0.587239\pi$
$227$	10.4264	−	10.4264i	0.692027	−	0.692027i	0.962678	+	0.270651i	$0.0872389\pi$
$228$	2.22993	+	1.11552i	0.147680	+	0.0738772i
$229$		−	18.3432i		−	1.21215i	−0.795406	−	0.606077i	$-0.792742\pi$
$229$		−	18.3432i		−	1.21215i	0.795406	−	0.606077i	$-0.207258\pi$
$230$		0			0
$231$	−0.979520	+	0.326289i	−0.0644477	+	0.0214682i
$232$	−9.29938	−	9.29938i	−0.610534	−	0.610534i
$233$	8.53926	+	8.53926i	0.559426	+	0.559426i	0.929144	−	0.369718i	$-0.120546\pi$
$233$	8.53926	+	8.53926i	0.559426	+	0.559426i	−0.369718	+	0.929144i	$0.620546\pi$
$234$	3.98049	−	2.98288i	0.260213	−	0.194997i
$235$		0			0
$236$			5.41048i			0.352192i
$237$	2.98512	−	5.96726i	0.193905	−	0.387615i
$238$	−4.73597	+	4.73597i	−0.306987	+	0.306987i
$239$	−5.98239			−0.386968			−0.193484	−	0.981103i	$-0.561979\pi$
$239$	−5.98239			−0.386968			−0.193484	+	0.981103i	$0.561979\pi$
$240$		0			0
$241$	5.05823			0.325829			0.162914	−	0.986640i	$-0.447911\pi$
$241$	5.05823			0.325829			0.162914	+	0.986640i	$0.447911\pi$
$242$	13.5413	−	13.5413i	0.870465	−	0.870465i
$243$	−10.6079	+	11.4224i	−0.680498	+	0.732750i
$244$			18.5655i			1.18853i
$245$		0			0
$246$	−8.19975	−	24.6157i	−0.522797	−	1.56944i
$247$	0.758680	+	0.758680i	0.0482737	+	0.0482737i
$248$	−7.33249	−	7.33249i	−0.465614	−	0.465614i
$249$	−3.64377	−	10.9386i	−0.230915	−	0.693206i
$250$		0			0
$251$		−	26.3582i		−	1.66372i	−0.554989	−	0.831858i	$-0.687277\pi$
$251$		−	26.3582i		−	1.66372i	0.554989	−	0.831858i	$-0.312723\pi$
$252$	−3.67214	−	0.526090i	−0.231323	−	0.0331406i
$253$	−1.68911	+	1.68911i	−0.106193	+	0.106193i
$254$	−6.68178			−0.419252
$255$		0			0
$256$	20.6707			1.29192
$257$	12.5808	−	12.5808i	0.784766	−	0.784766i	−0.195865	−	0.980631i	$-0.562751\pi$
$257$	12.5808	−	12.5808i	0.784766	−	0.784766i	0.980631	+	0.195865i	$0.0627514\pi$
$258$	−15.2132	+	30.4111i	−0.947131	+	1.89332i
$259$		−	11.0514i		−	0.686702i
$260$		0			0
$261$	−17.2260	−	22.9872i	−1.06626	−	1.42287i
$262$	21.0256	+	21.0256i	1.29896	+	1.29896i
$263$	−7.32034	−	7.32034i	−0.451391	−	0.451391i	0.444425	−	0.895816i	$-0.353408\pi$
$263$	−7.32034	−	7.32034i	−0.451391	−	0.451391i	−0.895816	+	0.444425i	$0.853408\pi$
$264$	1.34536	−	0.448154i	0.0828012	−	0.0275820i
$265$		0			0
$266$		−	2.09440i		−	0.128416i
$267$	−3.40419	−	1.70295i	−0.208333	−	0.104219i
$268$	1.55886	−	1.55886i	0.0952228	−	0.0952228i
$269$	7.34074			0.447573			0.223786	−	0.974638i	$-0.428158\pi$
$269$	7.34074			0.447573			0.223786	+	0.974638i	$0.428158\pi$
$270$		0			0
$271$	−7.40673			−0.449927			−0.224963	−	0.974367i	$-0.572226\pi$
$271$	−7.40673			−0.449927			−0.224963	+	0.974367i	$0.572226\pi$
$272$	13.0152	−	13.0152i	0.789162	−	0.789162i
$273$	−1.42763	−	0.714174i	−0.0864043	−	0.0432238i
$274$		−	28.3892i		−	1.71505i
$275$		0			0
$276$	−8.14310	+	2.71256i	−0.490157	+	0.163277i
$277$	11.1225	+	11.1225i	0.668289	+	0.668289i	0.957320	−	0.289031i	$-0.0933331\pi$
$277$	11.1225	+	11.1225i	0.668289	+	0.668289i	−0.289031	+	0.957320i	$0.593333\pi$
$278$	−3.69378	−	3.69378i	−0.221538	−	0.221538i
$279$	−13.5826	−	18.1252i	−0.813168	−	1.08513i
$280$		0			0
$281$		−	17.1123i		−	1.02084i	−0.859927	−	0.510418i	$-0.829491\pi$
$281$		−	17.1123i		−	1.02084i	0.859927	−	0.510418i	$-0.170509\pi$
$282$	10.5240	−	21.0375i	0.626697	−	1.25277i
$283$	−10.9094	+	10.9094i	−0.648494	+	0.648494i	−0.952629	−	0.304135i	$-0.901633\pi$
$283$	−10.9094	+	10.9094i	−0.648494	+	0.648494i	0.304135	+	0.952629i	$0.401633\pi$
$284$	8.86501			0.526041
$285$		0			0
$286$	−0.988321			−0.0584406
$287$	−5.88769	+	5.88769i	−0.347540	+	0.347540i
$288$	18.2563	+	2.61549i	1.07576	+	0.154119i
$289$			3.13992i			0.184701i
$290$		0			0
$291$	5.95961	+	17.8908i	0.349358	+	1.04877i
$292$	−7.00070	−	7.00070i	−0.409685	−	0.409685i
$293$	−15.3592	−	15.3592i	−0.897295	−	0.897295i	0.0979008	−	0.995196i	$-0.468787\pi$
$293$	−15.3592	−	15.3592i	−0.897295	−	0.897295i	−0.995196	+	0.0979008i	$0.968787\pi$
$294$	0.984783	+	2.95632i	0.0574337	+	0.172416i
$295$		0			0
$296$			15.1790i			0.882262i
$297$	3.04768	−	0.552234i	0.176844	−	0.0320439i
$298$	3.52878	−	3.52878i	0.204417	−	0.204417i
$299$	−3.69338			−0.213594
$300$		0			0
$301$	10.9126			0.628994
$302$	2.63556	−	2.63556i	0.151659	−	0.151659i
$303$	9.89076	−	19.7716i	0.568209	−	1.13585i
$304$			5.75575i			0.330115i
$305$		0			0
$306$	16.0792	−	12.0494i	0.919188	−	0.688817i
$307$	−15.5878	−	15.5878i	−0.889641	−	0.889641i	0.104848	−	0.994488i	$-0.466564\pi$
$307$	−15.5878	−	15.5878i	−0.889641	−	0.889641i	−0.994488	+	0.104848i	$0.966564\pi$
$308$	0.521191	+	0.521191i	0.0296976	+	0.0296976i
$309$	15.7776	−	5.25571i	0.897558	−	0.298987i
$310$		0			0
$311$			21.7724i			1.23460i	0.786729	+	0.617299i	$0.211773\pi$
$311$			21.7724i			1.23460i	−0.786729	+	0.617299i	$0.788227\pi$
$312$	1.96084	+	0.980910i	0.111011	+	0.0555331i
$313$	16.7825	−	16.7825i	0.948603	−	0.948603i	−0.0501392	−	0.998742i	$-0.515966\pi$
$313$	16.7825	−	16.7825i	0.948603	−	0.948603i	0.998742	+	0.0501392i	$0.0159665\pi$
$314$	−23.6171			−1.33279
$315$		0			0
$316$	−4.76346			−0.267965
$317$	19.4564	−	19.4564i	1.09278	−	1.09278i	0.0975486	−	0.995231i	$-0.468900\pi$
$317$	19.4564	−	19.4564i	1.09278	−	1.09278i	0.995231	−	0.0975486i	$-0.0311002\pi$
$318$	−10.0271	−	5.01604i	−0.562290	−	0.281285i
$319$			5.70750i			0.319559i
$320$		0			0
$321$	−0.410274	+	0.136667i	−0.0228993	+	0.00762800i
$322$	5.09795	+	5.09795i	0.284098	+	0.284098i
$323$	3.06469	+	3.06469i	0.170524	+	0.170524i
$324$	10.6812	+	3.12464i	0.593402	+	0.173591i
$325$		0			0
$326$		−	23.9405i		−	1.32594i
$327$	−8.68107	+	17.3535i	−0.480064	+	0.959648i
$328$	8.08668	−	8.08668i	0.446512	−	0.446512i
$329$	−7.54904			−0.416192
$330$		0			0
$331$	−20.0430			−1.10166			−0.550830	−	0.834617i	$-0.685689\pi$
$331$	−20.0430			−1.10166			−0.550830	+	0.834617i	$0.685689\pi$
$332$	−5.82030	+	5.82030i	−0.319431	+	0.319431i
$333$	−4.70185	+	32.8192i	−0.257660	+	1.79848i
$334$			26.5803i			1.45441i
$335$		0			0
$336$	−2.70634	−	8.12444i	−0.147643	−	0.443225i
$337$	−5.35404	−	5.35404i	−0.291653	−	0.291653i	0.546080	−	0.837733i	$-0.316119\pi$
$337$	−5.35404	−	5.35404i	−0.291653	−	0.291653i	−0.837733	+	0.546080i	$0.816119\pi$
$338$	15.4569	+	15.4569i	0.840747	+	0.840747i
$339$	0.428482	+	1.28630i	0.0232720	+	0.0698624i
$340$		0			0
$341$			4.50033i			0.243706i
$342$	−0.891068	+	6.21970i	−0.0481834	+	0.336323i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−14.9884			−0.808120
$345$		0			0
$346$	45.8883			2.46697
$347$	−20.2180	+	20.2180i	−1.08536	+	1.08536i	−0.0893604	+	0.995999i	$0.528482\pi$
$347$	−20.2180	+	20.2180i	−1.08536	+	1.08536i	−0.995999	+	0.0893604i	$0.971518\pi$
$348$	−9.17492	+	18.3407i	−0.491828	+	0.983163i
$349$			14.0744i			0.753386i	0.926338	+	0.376693i	$0.122939\pi$
$349$			14.0744i			0.753386i	−0.926338	+	0.376693i	$0.877061\pi$
$350$		0			0
$351$	3.93577	+	2.72826i	0.210076	+	0.145624i
$352$	−2.59114	−	2.59114i	−0.138108	−	0.138108i
$353$	7.05174	+	7.05174i	0.375326	+	0.375326i	0.869413	−	0.494087i	$-0.164497\pi$
$353$	7.05174	+	7.05174i	0.375326	+	0.375326i	−0.494087	+	0.869413i	$0.664497\pi$
$354$	−12.9354	+	4.30891i	−0.687506	+	0.229016i
$355$		0			0
$356$			2.71745i			0.144025i
$357$	−5.76694	−	2.88491i	−0.305219	−	0.152686i
$358$	23.2034	−	23.2034i	1.22634	−	1.22634i
$359$	15.8072			0.834270			0.417135	−	0.908844i	$-0.363034\pi$
$359$	15.8072			0.834270			0.417135	+	0.908844i	$0.363034\pi$
$360$		0			0
$361$	17.6447			0.928668
$362$	6.43741	−	6.43741i	0.338343	−	0.338343i
$363$	16.4890	+	8.24864i	0.865450	+	0.432941i
$364$			1.13963i			0.0597329i
$365$		0			0
$366$	−44.3862	+	14.7855i	−2.32010	+	0.772853i
$367$	13.4893	+	13.4893i	0.704138	+	0.704138i	0.965296	−	0.261158i	$-0.0841043\pi$
$367$	13.4893	+	13.4893i	0.704138	+	0.704138i	−0.261158	+	0.965296i	$0.584104\pi$
$368$	−14.0100	−	14.0100i	−0.730321	−	0.730321i
$369$	19.9895	−	14.9796i	1.04061	−	0.779808i
$370$		0			0
$371$			3.59808i			0.186803i
$372$	−7.23436	+	14.4615i	−0.375084	+	0.749793i
$373$	14.7655	−	14.7655i	0.764527	−	0.764527i	−0.212610	−	0.977137i	$-0.568197\pi$
$373$	14.7655	−	14.7655i	0.764527	−	0.764527i	0.977137	+	0.212610i	$0.0681965\pi$
$374$	−3.99233			−0.206438
$375$		0			0
$376$	10.3685			0.534716
$377$	−6.23998	+	6.23998i	−0.321376	+	0.321376i
$378$	−1.66672	−	9.19830i	−0.0857266	−	0.473110i
$379$			31.9071i			1.63896i	0.573109	+	0.819479i	$0.305737\pi$
$379$			31.9071i			1.63896i	−0.573109	+	0.819479i	$0.694263\pi$
$380$		0			0
$381$	−2.03307	−	6.10327i	−0.104157	−	0.312680i
$382$	−5.51350	−	5.51350i	−0.282095	−	0.282095i
$383$	−10.5821	−	10.5821i	−0.540720	−	0.540720i	0.383020	−	0.923740i	$-0.374884\pi$
$383$	−10.5821	−	10.5821i	−0.540720	−	0.540720i	−0.923740	+	0.383020i	$0.874884\pi$
$384$	5.57649	+	16.7406i	0.284574	+	0.854292i
$385$		0			0
$386$			29.9992i			1.52692i
$387$	−32.4070	−	4.64281i	−1.64734	−	0.236007i
$388$	9.51946	−	9.51946i	0.483277	−	0.483277i
$389$	−22.7753			−1.15475			−0.577376	−	0.816478i	$-0.695923\pi$
$389$	−22.7753			−1.15475			−0.577376	+	0.816478i	$0.695923\pi$
$390$		0			0
$391$	−14.9194			−0.754509
$392$	−0.971203	+	0.971203i	−0.0490532	+	0.0490532i
$393$	−12.8077	+	25.6026i	−0.646064	+	1.29148i
$394$			13.6438i			0.687364i
$395$		0			0
$396$	−1.32603	−	1.76951i	−0.0666354	−	0.0889213i
$397$	14.8873	+	14.8873i	0.747172	+	0.747172i	0.973947	−	0.226775i	$-0.0728181\pi$
$397$	14.8873	+	14.8873i	0.747172	+	0.747172i	−0.226775	+	0.973947i	$0.572818\pi$
$398$	−0.990276	−	0.990276i	−0.0496380	−	0.0496380i
$399$	1.91307	−	0.637263i	0.0957731	−	0.0319031i
$400$		0			0
$401$		−	15.0691i		−	0.752513i	−0.926515	−	0.376257i	$-0.877211\pi$
$401$		−	15.0691i		−	0.752513i	0.926515	−	0.376257i	$-0.122789\pi$
$402$	4.96841	+	2.48545i	0.247802	+	0.123963i
$403$	−4.92018	+	4.92018i	−0.245092	+	0.245092i
$404$	−15.7830			−0.785233
$405$		0			0
$406$	17.2260			0.854912
$407$	4.65806	−	4.65806i	0.230892	−	0.230892i
$408$	7.92082	+	3.96239i	0.392139	+	0.196168i
$409$			25.3358i			1.25277i	0.779512	+	0.626387i	$0.215467\pi$
$409$			25.3358i			1.25277i	−0.779512	+	0.626387i	$0.784533\pi$
$410$		0			0
$411$	25.9312	−	8.63798i	1.27909	−	0.426080i
$412$	−8.39509	−	8.39509i	−0.413596	−	0.413596i
$413$	3.09394	+	3.09394i	0.152243	+	0.152243i
$414$	−12.9703	−	17.3082i	−0.637457	−	0.850652i
$415$		0			0
$416$		−	5.66575i		−	0.277786i
$417$	2.25006	−	4.49788i	0.110186	−	0.220262i
$418$	0.882769	−	0.882769i	0.0431776	−	0.0431776i
$419$	19.4078			0.948133			0.474067	−	0.880489i	$-0.342786\pi$
$419$	19.4078			0.948133			0.474067	+	0.880489i	$0.342786\pi$
$420$		0			0
$421$	−9.18958			−0.447872			−0.223936	−	0.974604i	$-0.571891\pi$
$421$	−9.18958			−0.447872			−0.223936	+	0.974604i	$0.571891\pi$
$422$	4.98569	−	4.98569i	0.242700	−	0.242700i
$423$	22.4182	+	3.21176i	1.09001	+	0.156161i
$424$		−	4.94192i		−	0.240001i
$425$		0			0
$426$	7.06009	+	21.1944i	0.342063	+	1.02687i
$427$	10.6165	+	10.6165i	0.513769	+	0.513769i
$428$	0.218302	+	0.218302i	0.0105520	+	0.0105520i
$429$	−0.300716	−	0.902751i	−0.0145187	−	0.0435852i
$430$		0			0
$431$			17.0854i			0.822972i	0.911416	+	0.411486i	$0.134990\pi$
$431$			17.0854i			0.822972i	−0.911416	+	0.411486i	$0.865010\pi$
$432$	4.58040	+	25.2784i	0.220375	+	1.21621i
$433$	20.7996	−	20.7996i	0.999563	−	0.999563i	−0.000437230	−	1.00000i	$-0.500139\pi$
$433$	20.7996	−	20.7996i	0.999563	−	0.999563i	1.00000		0.000437230i	$0.000139175\pi$
$434$	13.5826			0.651985
$435$		0			0
$436$	13.8527			0.663422
$437$	3.29894	−	3.29894i	0.157809	−	0.157809i
$438$	11.1619	−	22.3126i	0.533335	−	1.06614i
$439$			12.3529i			0.589572i	0.955563	+	0.294786i	$0.0952483\pi$
$439$			12.3529i			0.589572i	−0.955563	+	0.294786i	$0.904752\pi$
$440$		0			0
$441$	−2.40072	+	1.79904i	−0.114320	+	0.0856685i
$442$	−4.36479	−	4.36479i	−0.207612	−	0.207612i
$443$	−6.57501	−	6.57501i	−0.312388	−	0.312388i	0.533446	−	0.845834i	$-0.320897\pi$
$443$	−6.57501	−	6.57501i	−0.312388	−	0.312388i	−0.845834	+	0.533446i	$0.820897\pi$
$444$	22.4563	−	7.48044i	1.06573	−	0.355006i
$445$		0			0
$446$			12.5997i			0.596611i
$447$	4.29696	+	2.14955i	0.203239	+	0.101670i
$448$	−0.828450	+	0.828450i	−0.0391406	+	0.0391406i
$449$	−14.2416			−0.672104			−0.336052	−	0.941843i	$-0.609092\pi$
$449$	−14.2416			−0.672104			−0.336052	+	0.941843i	$0.609092\pi$
$450$		0			0
$451$	−4.96321			−0.233708
$452$	0.684427	−	0.684427i	0.0321927	−	0.0321927i
$453$	3.20929	+	1.60545i	0.150786	+	0.0754306i
$454$		−	26.5272i		−	1.24498i
$455$		0			0
$456$	−2.62757	+	0.875274i	−0.123047	+	0.0409885i
$457$	−17.6696	−	17.6696i	−0.826550	−	0.826550i	0.160488	−	0.987038i	$-0.448693\pi$
$457$	−17.6696	−	17.6696i	−0.826550	−	0.826550i	−0.987038	+	0.160488i	$0.948693\pi$
$458$	−23.3346	−	23.3346i	−1.09036	−	1.09036i
$459$	15.8986	+	11.0208i	0.742081	+	0.514407i
$460$		0			0
$461$		−	21.7105i		−	1.01116i	−0.862780	−	0.505580i	$-0.831279\pi$
$461$		−	21.7105i		−	1.01116i	0.862780	−	0.505580i	$-0.168721\pi$
$462$	−0.830984	+	1.66114i	−0.0386609	+	0.0772831i
$463$	−1.05768	+	1.05768i	−0.0491547	+	0.0491547i	−0.731257	−	0.682102i	$-0.761066\pi$
$463$	−1.05768	+	1.05768i	−0.0491547	+	0.0491547i	0.682102	+	0.731257i	$0.261066\pi$
$464$	−47.3398			−2.19770
$465$		0			0
$466$	21.7258			1.00643
$467$	−26.8566	+	26.8566i	−1.24278	+	1.24278i	−0.283932	+	0.958844i	$0.591639\pi$
$467$	−26.8566	+	26.8566i	−1.24278	+	1.24278i	−0.958844	+	0.283932i	$0.908361\pi$
$468$	0.484858	−	3.38434i	0.0224126	−	0.156441i
$469$		−	1.78285i		−	0.0823242i
$470$		0			0
$471$	−7.18597	−	21.5723i	−0.331112	−	0.994000i
$472$	−4.24949	−	4.24949i	−0.195599	−	0.195599i
$473$	4.59957	+	4.59957i	0.211488	+	0.211488i
$474$	−3.79362	−	11.3884i	−0.174247	−	0.523089i
$475$		0			0
$476$			4.60354i			0.211003i
$477$	1.53081	−	10.6851i	0.0700910	−	0.489239i
$478$	−7.61027	+	7.61027i	−0.348086	+	0.348086i
$479$	2.38823			0.109121			0.0545605	−	0.998510i	$-0.482624\pi$
$479$	2.38823			0.109121			0.0545605	+	0.998510i	$0.482624\pi$
$480$		0			0
$481$	10.1853			0.464409
$482$	6.43463	−	6.43463i	0.293090	−	0.293090i
$483$	−3.10541	+	6.20772i	−0.141301	+	0.282461i
$484$		−	13.1626i		−	0.598301i
$485$		0			0
$486$	1.03617	+	28.0251i	0.0470016	+	1.27124i
$487$	15.5114	+	15.5114i	0.702890	+	0.702890i	0.965030	−	0.262140i	$-0.0844281\pi$
$487$	15.5114	+	15.5114i	0.702890	+	0.702890i	−0.262140	+	0.965030i	$0.584428\pi$
$488$	−14.5817	−	14.5817i	−0.660080	−	0.660080i
$489$	21.8677	−	7.28436i	0.988890	−	0.329410i
$490$		0			0
$491$			33.8566i			1.52793i	0.645259	+	0.763964i	$0.276749\pi$
$491$			33.8566i			1.52793i	−0.645259	+	0.763964i	$0.723251\pi$
$492$	−15.9489	−	7.97846i	−0.719033	−	0.359697i
$493$	−25.2065	+	25.2065i	−1.13524	+	1.13524i
$494$	1.93025			0.0868462
$495$		0			0
$496$	−37.3271			−1.67604
$497$	5.06938	−	5.06938i	0.227393	−	0.227393i
$498$	−18.5504	−	9.27986i	−0.831265	−	0.415840i
$499$		−	3.55804i		−	0.159280i	−0.996824	−	0.0796398i	$-0.974623\pi$
$499$		−	3.55804i		−	0.159280i	0.996824	−	0.0796398i	$-0.0253770\pi$
$500$		0			0
$501$	−24.2790	+	8.08760i	−1.08470	+	0.361327i
$502$	−33.5306	−	33.5306i	−1.49655	−	1.49655i
$503$	−8.89336	−	8.89336i	−0.396535	−	0.396535i	0.480474	−	0.877009i	$-0.340465\pi$
$503$	−8.89336	−	8.89336i	−0.396535	−	0.396535i	−0.877009	+	0.480474i	$0.840465\pi$
$504$	3.29736	−	2.47096i	0.146876	−	0.110065i
$505$		0			0
$506$			4.29747i			0.191046i
$507$	−9.41558	+	18.8218i	−0.418161	+	0.835903i
$508$	−3.24747	+	3.24747i	−0.144083	+	0.144083i
$509$	24.4919			1.08558			0.542791	−	0.839868i	$-0.317367\pi$
$509$	24.4919			1.08558			0.542791	+	0.839868i	$0.317367\pi$
$510$		0			0
$511$	−8.00658			−0.354190
$512$	11.8883	−	11.8883i	0.525395	−	0.525395i
$513$	−5.95231	+	1.07855i	−0.262801	+	0.0476191i
$514$		−	32.0083i		−	1.41182i
$515$		0			0
$516$	7.38651	+	22.1743i	0.325173	+	0.976169i
$517$	−3.18185	−	3.18185i	−0.139938	−	0.139938i
$518$	−14.0587	−	14.0587i	−0.617702	−	0.617702i
$519$	13.9624	+	41.9153i	0.612883	+	1.83988i
$520$		0			0
$521$			28.4652i			1.24708i	0.781790	+	0.623541i	$0.214307\pi$
$521$			28.4652i			1.24708i	−0.781790	+	0.623541i	$0.785693\pi$
$522$	−51.1557	−	7.32884i	−2.23902	−	0.320775i
$523$	−7.00886	+	7.00886i	−0.306476	+	0.306476i	−0.843541	−	0.537065i	$-0.819533\pi$
$523$	−7.00886	+	7.00886i	−0.306476	+	0.306476i	0.537065	+	0.843541i	$0.319533\pi$
$524$	20.4377			0.892824
$525$		0			0
$526$	−18.6246			−0.812071
$527$	−19.8751	+	19.8751i	−0.865773	+	0.865773i
$528$	2.28368	−	4.56507i	0.0993842	−	0.198669i
$529$		−	6.94022i		−	0.301749i
$530$		0			0
$531$	−7.87168	−	10.5043i	−0.341602	−	0.455849i
$532$	−1.01792	−	1.01792i	−0.0441324	−	0.0441324i
$533$	−5.42625	−	5.42625i	−0.235037	−	0.235037i
$534$	−6.49686	+	2.16418i	−0.281147	+	0.0936531i
$535$		0			0
$536$			2.44872i			0.105769i
$537$	28.2546	+	14.1343i	1.21927	+	0.609942i
$538$	9.33825	−	9.33825i	0.402600	−	0.402600i
$539$	0.596077			0.0256749
$540$		0			0
$541$	−5.17756			−0.222601			−0.111300	−	0.993787i	$-0.535502\pi$
$541$	−5.17756			−0.222601			−0.111300	+	0.993787i	$0.535502\pi$
$542$	−9.42220	+	9.42220i	−0.404718	+	0.404718i
$543$	7.83876	+	3.92134i	0.336393	+	0.168281i
$544$		−	22.8868i		−	0.981265i
$545$		0			0
$546$	−2.72462	+	0.907602i	−0.116603	+	0.0388418i
$547$	−3.24667	−	3.24667i	−0.138818	−	0.138818i	0.634283	−	0.773101i	$-0.281295\pi$
$547$	−3.24667	−	3.24667i	−0.138818	−	0.138818i	−0.773101	+	0.634283i	$0.781295\pi$
$548$	−13.7977	−	13.7977i	−0.589408	−	0.589408i
$549$	−27.0108	−	36.0444i	−1.15279	−	1.53834i
$550$		0			0
$551$		−	11.1471i		−	0.474883i
$552$	4.26525	−	8.52623i	0.181541	−	0.362901i
$553$	−2.72394	+	2.72394i	−0.115834	+	0.115834i
$554$	28.2982			1.20228
$555$		0			0
$556$	−3.59050			−0.152271
$557$	−9.93063	+	9.93063i	−0.420774	+	0.420774i	−0.885470	−	0.464696i	$-0.846164\pi$
$557$	−9.93063	+	9.93063i	−0.420774	+	0.420774i	0.464696	+	0.885470i	$0.346164\pi$
$558$	−40.3359	−	5.77874i	−1.70755	−	0.244634i
$559$			10.0574i			0.425382i
$560$		0			0
$561$	−1.21475	−	3.64667i	−0.0512866	−	0.153962i
$562$	−21.7688	−	21.7688i	−0.918262	−	0.918262i
$563$	11.8553	+	11.8553i	0.499641	+	0.499641i	0.911326	−	0.411685i	$-0.135060\pi$
$563$	11.8553	+	11.8553i	0.499641	+	0.499641i	−0.411685	+	0.911326i	$0.635060\pi$
$564$	−5.10977	−	15.3395i	−0.215160	−	0.645911i
$565$		0			0
$566$			27.7559i			1.16667i
$567$	7.89477	−	4.32118i	0.331549	−	0.181472i
$568$	−6.96274	+	6.96274i	−0.292150	+	0.292150i
$569$	19.3729			0.812155			0.406077	−	0.913839i	$-0.366896\pi$
$569$	19.3729			0.812155			0.406077	+	0.913839i	$0.366896\pi$
$570$		0			0
$571$	−10.8864			−0.455581			−0.227791	−	0.973710i	$-0.573150\pi$
$571$	−10.8864			−0.455581			−0.227791	+	0.973710i	$0.573150\pi$
$572$	−0.480343	+	0.480343i	−0.0200841	+	0.0200841i
$573$	3.35855	−	6.71373i	0.140305	−	0.280470i
$574$			14.9796i			0.625237i
$575$		0			0
$576$	2.81270	−	2.10777i	0.117196	−	0.0878235i
$577$	3.36353	+	3.36353i	0.140025	+	0.140025i	0.773645	−	0.633619i	$-0.218431\pi$
$577$	3.36353	+	3.36353i	0.140025	+	0.140025i	−0.633619	+	0.773645i	$0.718431\pi$
$578$	3.99433	+	3.99433i	0.166142	+	0.166142i
$579$	−27.4018	+	9.12785i	−1.13878	+	0.379341i
$580$		0			0
$581$			6.65658i			0.276162i
$582$	30.3404	+	15.1778i	1.25765	+	0.629139i
$583$	−1.51655	+	1.51655i	−0.0628093	+	0.0628093i
$584$	10.9969			0.455057
$585$		0			0
$586$	−39.0773			−1.61427
$587$	−11.6266	+	11.6266i	−0.479883	+	0.479883i	−0.905094	−	0.425211i	$-0.860200\pi$
$587$	−11.6266	+	11.6266i	−0.479883	+	0.479883i	0.425211	+	0.905094i	$0.360200\pi$
$588$	1.91545	+	0.958205i	0.0789919	+	0.0395157i
$589$		−	8.78942i		−	0.362162i
$590$		0			0
$591$	−12.4625	+	4.15140i	−0.512639	+	0.170766i
$592$	38.6354	+	38.6354i	1.58791	+	1.58791i
$593$	18.7263	+	18.7263i	0.768999	+	0.768999i	0.977930	−	0.208932i	$-0.0669986\pi$
$593$	18.7263	+	18.7263i	0.768999	+	0.768999i	−0.208932	+	0.977930i	$0.566999\pi$
$594$	3.17449	−	4.57950i	0.130251	−	0.187899i
$595$		0			0
$596$		−	3.43011i		−	0.140503i
$597$	0.603226	−	1.20585i	0.0246884	−	0.0493521i
$598$	−4.69840	+	4.69840i	−0.192132	+	0.192132i
$599$	−27.9518			−1.14208			−0.571041	−	0.820922i	$-0.693460\pi$
$599$	−27.9518			−1.14208			−0.571041	+	0.820922i	$0.693460\pi$
$600$		0			0
$601$	19.9760			0.814837			0.407418	−	0.913242i	$-0.366429\pi$
$601$	19.9760			0.814837			0.407418	+	0.913242i	$0.366429\pi$
$602$	13.8821	−	13.8821i	0.565793	−	0.565793i
$603$	−0.758517	+	5.29448i	−0.0308892	+	0.215608i
$604$		−	2.56187i		−	0.104241i
$605$		0			0
$606$	−12.5696	−	37.7339i	−0.510604	−	1.53283i
$607$	−23.8478	−	23.8478i	−0.967953	−	0.967953i	0.0315491	−	0.999502i	$-0.489956\pi$
$607$	−23.8478	−	23.8478i	−0.967953	−	0.967953i	−0.999502	+	0.0315491i	$0.989956\pi$
$608$	5.06065	+	5.06065i	0.205237	+	0.205237i
$609$	5.24136	+	15.7346i	0.212390	+	0.637597i
$610$		0			0
$611$		−	6.95740i		−	0.281466i
$612$	1.95859	−	13.6710i	0.0791712	−	0.552619i
$613$	−11.8807	+	11.8807i	−0.479858	+	0.479858i	−0.905086	−	0.425228i	$-0.860194\pi$
$613$	−11.8807	+	11.8807i	−0.479858	+	0.479858i	0.425228	+	0.905086i	$0.360194\pi$
$614$	−39.6588			−1.60050
$615$		0			0
$616$	−0.818705			−0.0329866
$617$	−7.72276	+	7.72276i	−0.310906	+	0.310906i	−0.845261	−	0.534354i	$-0.820555\pi$
$617$	−7.72276	+	7.72276i	−0.310906	+	0.310906i	0.534354	+	0.845261i	$0.320555\pi$
$618$	13.3851	−	26.7568i	0.538427	−	1.07632i
$619$			7.02322i			0.282287i	0.989989	+	0.141144i	$0.0450779\pi$
$619$			7.02322i			0.282287i	−0.989989	+	0.141144i	$0.954922\pi$
$620$		0			0
$621$	11.8632	−	17.1137i	0.476052	−	0.686750i
$622$	27.6969	+	27.6969i	1.11054	+	1.11054i
$623$	1.55395	+	1.55395i	0.0622577	+	0.0622577i
$624$	7.48770	−	2.49423i	0.299748	−	0.0998493i
$625$		0			0
$626$		−	42.6985i		−	1.70657i
$627$	1.07494	+	0.537738i	0.0429289	+	0.0214752i
$628$	−11.4784	+	11.4784i	−0.458037	+	0.458037i
$629$	41.1435			1.64050
$630$		0			0
$631$	−23.6907			−0.943111			−0.471555	−	0.881836i	$-0.656307\pi$
$631$	−23.6907			−0.943111			−0.471555	+	0.881836i	$0.656307\pi$
$632$	3.74131	−	3.74131i	0.148821	−	0.148821i
$633$	6.07102	+	3.03703i	0.241301	+	0.120711i
$634$		−	49.5014i		−	1.96595i
$635$		0			0
$636$	−7.31124	+	2.43545i	−0.289909	+	0.0965720i
$637$	0.651688	+	0.651688i	0.0258208	+	0.0258208i
$638$	7.26059	+	7.26059i	0.287450	+	0.287450i
$639$	−17.2112	+	12.8976i	−0.680865	+	0.510223i
$640$		0			0
$641$			0.574461i			0.0226898i	0.999936	+	0.0113449i	$0.00361128\pi$
$641$			0.574461i			0.0226898i	−0.999936	+	0.0113449i	$0.996389\pi$
$642$	−0.348059	+	0.695771i	−0.0137368	+	0.0274599i
$643$	4.70272	−	4.70272i	0.185457	−	0.185457i	−0.608272	−	0.793729i	$-0.708137\pi$
$643$	4.70272	−	4.70272i	0.185457	−	0.185457i	0.793729	+	0.608272i	$0.208137\pi$
$644$	4.95540			0.195270
$645$		0			0
$646$	7.79727			0.306779
$647$	4.55125	−	4.55125i	0.178928	−	0.178928i	−0.611960	−	0.790888i	$-0.709619\pi$
$647$	4.55125	−	4.55125i	0.178928	−	0.178928i	0.790888	+	0.611960i	$0.209619\pi$
$648$	−10.8434	+	5.93509i	−0.425968	+	0.233152i
$649$			2.60813i			0.102378i
$650$		0			0
$651$	4.13277	+	12.4066i	0.161976	+	0.486252i
$652$	−11.6355	−	11.6355i	−0.455682	−	0.455682i
$653$	−18.2705	−	18.2705i	−0.714980	−	0.714980i	0.252593	−	0.967573i	$-0.418717\pi$
$653$	−18.2705	−	18.2705i	−0.714980	−	0.714980i	−0.967573	+	0.252593i	$0.918717\pi$
$654$	11.0323	+	33.1189i	0.431395	+	1.29505i
$655$		0			0
$656$		−	41.1664i		−	1.60728i
$657$	23.7770	+	3.40642i	0.927628	+	0.132897i
$658$	−9.60324	+	9.60324i	−0.374373	+	0.374373i
$659$	23.1110			0.900276			0.450138	−	0.892959i	$-0.351375\pi$
$659$	23.1110			0.900276			0.450138	+	0.892959i	$0.351375\pi$
$660$		0			0
$661$	16.9566			0.659537			0.329768	−	0.944062i	$-0.393029\pi$
$661$	16.9566			0.659537			0.329768	+	0.944062i	$0.393029\pi$
$662$	−25.4969	+	25.4969i	−0.990965	+	0.990965i
$663$	2.65881	−	5.31496i	0.103260	−	0.206416i
$664$		−	9.14274i		−	0.354807i
$665$		0			0
$666$	35.7684	+	47.7310i	1.38600	+	1.84954i
$667$	27.1331	+	27.1331i	1.05060	+	1.05060i
$668$	12.9186	+	12.9186i	0.499834	+	0.499834i
$669$	−11.5088	+	3.83370i	−0.444955	+	0.148219i
$670$		0			0
$671$			8.94951i			0.345492i
$672$	−9.52280	−	4.76378i	−0.367350	−	0.183767i
$673$	20.0108	−	20.0108i	0.771359	−	0.771359i	−0.206985	−	0.978344i	$-0.566365\pi$
$673$	20.0108	−	20.0108i	0.771359	−	0.771359i	0.978344	+	0.206985i	$0.0663653\pi$
$674$	−13.6219			−0.524696
$675$		0			0
$676$	15.0247			0.577875
$677$	−9.33392	+	9.33392i	−0.358732	+	0.358732i	−0.863345	−	0.504614i	$-0.831635\pi$
$677$	−9.33392	+	9.33392i	−0.358732	+	0.358732i	0.504614	+	0.863345i	$0.331635\pi$
$678$	2.18140	+	1.09125i	0.0837762	+	0.0419091i
$679$		−	10.8872i		−	0.417814i
$680$		0			0
$681$	24.2305	−	8.07143i	0.928513	−	0.309298i
$682$	5.72492	+	5.72492i	0.219219	+	0.219219i
$683$	34.9400	+	34.9400i	1.33694	+	1.33694i	0.899005	+	0.437939i	$0.144291\pi$
$683$	34.9400	+	34.9400i	1.33694	+	1.33694i	0.437939	+	0.899005i	$0.355709\pi$
$684$	2.58982	+	3.45597i	0.0990241	+	0.132142i
$685$		0			0
$686$		−	1.79904i		−	0.0686876i
$687$	14.2143	−	28.4143i	0.542308	−	1.08407i
$688$	−38.1503	+	38.1503i	−1.45447	+	1.45447i
$689$	−3.31608			−0.126333
$690$		0			0
$691$	−35.0437			−1.33313			−0.666563	−	0.745449i	$-0.732235\pi$
$691$	−35.0437			−1.33313			−0.666563	+	0.745449i	$0.732235\pi$
$692$	22.3026	−	22.3026i	0.847818	−	0.847818i
$693$	−1.77016	−	0.253602i	−0.0672427	−	0.00963356i
$694$			51.4392i			1.95261i
$695$		0			0
$696$	−7.19895	−	21.6112i	−0.272875	−	0.819172i
$697$	−21.9194	−	21.9194i	−0.830255	−	0.830255i
$698$	17.9042	+	17.9042i	0.677686	+	0.677686i
$699$	6.61051	+	19.8448i	0.250033	+	0.750598i
$700$		0			0
$701$		−	52.2978i		−	1.97526i	−0.156805	−	0.987630i	$-0.550119\pi$
$701$		−	52.2978i		−	1.97526i	0.156805	−	0.987630i	$-0.449881\pi$
$702$	8.47739	−	1.53609i	0.319959	−	0.0579759i
$703$	−9.09750	+	9.09750i	−0.343119	+	0.343119i
$704$	−0.698367			−0.0263207
$705$		0			0
$706$	17.9412			0.675227
$707$	−9.02537	+	9.02537i	−0.339434	+	0.339434i
$708$	−4.19262	+	8.38105i	−0.157568	+	0.314979i
$709$			22.2416i			0.835302i	0.908608	+	0.417651i	$0.137146\pi$
$709$			22.2416i			0.835302i	−0.908608	+	0.417651i	$0.862854\pi$
$710$		0			0
$711$	9.24814	−	6.93033i	0.346832	−	0.259908i
$712$	−2.13433	−	2.13433i	−0.0799875	−	0.0799875i
$713$	21.3942	+	21.3942i	0.801219	+	0.801219i
$714$	−11.0061	+	3.66626i	−0.411894	+	0.137206i
$715$		0			0
$716$		−	22.5546i		−	0.842906i
$717$	−9.26695	−	4.63579i	−0.346080	−	0.173127i
$718$	20.1085	−	20.1085i	0.750443	−	0.750443i
$719$	−40.5531			−1.51238			−0.756188	−	0.654354i	$-0.772941\pi$
$719$	−40.5531			−1.51238			−0.756188	+	0.654354i	$0.772941\pi$
$720$		0			0
$721$	−9.60132			−0.357572
$722$	22.4460	−	22.4460i	0.835355	−	0.835355i
$723$	7.83539	+	3.91965i	0.291401	+	0.145773i
$724$		−	6.25741i		−	0.232555i
$725$		0			0
$726$	31.4691	−	10.4827i	1.16793	−	0.389050i
$727$	25.9411	+	25.9411i	0.962103	+	0.962103i	0.999308	−	0.0372050i	$-0.0118454\pi$
$727$	25.9411	+	25.9411i	0.962103	+	0.962103i	−0.0372050	+	0.999308i	$0.511845\pi$
$728$	−0.895086	−	0.895086i	−0.0331741	−	0.0331741i
$729$	−25.2834	+	9.47366i	−0.936422	+	0.350876i
$730$		0			0
$731$			40.6268i			1.50264i
$732$	−14.3865	+	28.7586i	−0.531740	+	1.06295i
$733$	20.5005	−	20.5005i	0.757205	−	0.757205i	−0.218608	−	0.975813i	$-0.570152\pi$
$733$	20.5005	−	20.5005i	0.757205	−	0.757205i	0.975813	+	0.218608i	$0.0701515\pi$
$734$	34.3199			1.26677
$735$		0			0
$736$	−24.6361			−0.908100
$737$	0.751453	−	0.751453i	0.0276801	−	0.0276801i
$738$	6.37312	−	44.4847i	0.234598	−	1.63750i
$739$		−	11.5622i		−	0.425323i	−0.977126	−	0.212661i	$-0.931787\pi$
$739$		−	11.5622i		−	0.425323i	0.977126	−	0.212661i	$-0.0682131\pi$
$740$		0			0
$741$	0.587318	+	1.76313i	0.0215757	+	0.0647702i
$742$	4.57716	+	4.57716i	0.168033	+	0.168033i
$743$	−24.6182	−	24.6182i	−0.903153	−	0.903153i	0.0925542	−	0.995708i	$-0.470497\pi$
$743$	−24.6182	−	24.6182i	−0.903153	−	0.903153i	−0.995708	+	0.0925542i	$0.970497\pi$
$744$	−5.67632	−	17.0403i	−0.208104	−	0.624728i
$745$		0			0
$746$		−	37.5667i		−	1.37541i
$747$	2.83206	−	19.7679i	0.103620	−	0.723270i
$748$	−1.94035	+	1.94035i	−0.0709461	+	0.0709461i
$749$	0.249668			0.00912268
$750$		0			0
$751$	40.1876			1.46647			0.733233	−	0.679977i	$-0.238010\pi$
$751$	40.1876			1.46647			0.733233	+	0.679977i	$0.238010\pi$
$752$	26.3912	−	26.3912i	0.962389	−	0.962389i
$753$	20.4252	−	40.8299i	0.744334	−	1.48792i
$754$			15.8759i			0.578167i
$755$		0			0
$756$	−5.28061	−	3.66050i	−0.192054	−	0.133131i
$757$	4.46261	+	4.46261i	0.162196	+	0.162196i	0.783539	−	0.621343i	$-0.213412\pi$
$757$	4.46261	+	4.46261i	0.162196	+	0.162196i	−0.621343	+	0.783539i	$0.713412\pi$
$758$	40.5895	+	40.5895i	1.47428	+	1.47428i
$759$	−3.92539	+	1.30759i	−0.142483	+	0.0474626i
$760$		0			0
$761$			27.3558i			0.991646i	0.868424	+	0.495823i	$0.165133\pi$
$761$			27.3558i			0.991646i	−0.868424	+	0.495823i	$0.834867\pi$
$762$	−10.3503	−	5.17775i	−0.374953	−	0.187570i
$763$	7.92153	−	7.92153i	0.286779	−	0.286779i
$764$	−5.35934			−0.193894
$765$		0			0
$766$	−26.9232			−0.972776
$767$	−2.85145	+	2.85145i	−0.102960	+	0.102960i
$768$	32.0196	+	16.0178i	1.15541	+	0.577994i
$769$		−	10.3542i		−	0.373382i	−0.982419	−	0.186691i	$-0.940224\pi$
$769$		−	10.3542i		−	0.373382i	0.982419	−	0.186691i	$-0.0597762\pi$
$770$		0			0
$771$	29.2370	−	9.73916i	1.05294	−	0.350747i
$772$	14.5802	+	14.5802i	0.524752	+	0.524752i
$773$	−1.59901	−	1.59901i	−0.0575125	−	0.0575125i	0.677766	−	0.735278i	$-0.262948\pi$
$773$	−1.59901	−	1.59901i	−0.0575125	−	0.0575125i	−0.735278	+	0.677766i	$0.762948\pi$
$774$	−47.1316	+	35.3192i	−1.69411	+	1.26952i
$775$		0			0
$776$			14.9535i			0.536800i
$777$	8.56382	−	17.1191i	0.307225	−	0.614143i
$778$	−28.9727	+	28.9727i	−1.03872	+	1.03872i
$779$	9.69347			0.347305
$780$		0			0
$781$	4.27339			0.152914
$782$	−18.9792	+	18.9792i	−0.678696	+	0.678696i
$783$	−8.87084	−	48.9565i	−0.317018	−	1.74956i
$784$			4.94405i			0.176573i
$785$		0			0
$786$	16.2766	+	48.8623i	0.580566	+	1.74286i
$787$	−6.16607	−	6.16607i	−0.219797	−	0.219797i	0.588616	−	0.808413i	$-0.299673\pi$
$787$	−6.16607	−	6.16607i	−0.219797	−	0.219797i	−0.808413	+	0.588616i	$0.799673\pi$
$788$	6.63114	+	6.63114i	0.236225	+	0.236225i
$789$	−5.66691	−	17.0121i	−0.201747	−	0.605646i
$790$		0			0
$791$		−	0.782768i		−	0.0278320i
$792$	2.43129	+	0.348320i	0.0863922	+	0.0123770i
$793$	−9.78445	+	9.78445i	−0.347456	+	0.347456i
$794$	37.8767			1.34419
$795$		0			0
$796$	−0.962586			−0.0341180
$797$	24.9323	−	24.9323i	0.883148	−	0.883148i	−0.110705	−	0.993853i	$-0.535311\pi$
$797$	24.9323	−	24.9323i	0.883148	−	0.883148i	0.993853	+	0.110705i	$0.0353109\pi$
$798$	1.62296	−	3.24431i	0.0574523	−	0.114847i
$799$		−	28.1044i		−	0.994263i
$800$		0			0
$801$	−3.95360	−	5.27587i	−0.139694	−	0.186414i
$802$	−19.1696	−	19.1696i	−0.676901	−	0.676901i
$803$	−3.37469	−	3.37469i	−0.119090	−	0.119090i
$804$	3.62272	−	1.20677i	0.127763	−	0.0425594i
$805$		0			0
$806$			12.5181i			0.440930i
$807$	11.3711	+	5.68839i	0.400281	+	0.200241i
$808$	12.3962	−	12.3962i	0.436099	−	0.436099i
$809$	−21.2421			−0.746831			−0.373416	−	0.927664i	$-0.621813\pi$
$809$	−21.2421			−0.746831			−0.373416	+	0.927664i	$0.621813\pi$
$810$		0			0
$811$	−20.9414			−0.735351			−0.367675	−	0.929954i	$-0.619846\pi$
$811$	−20.9414			−0.735351			−0.367675	+	0.929954i	$0.619846\pi$
$812$	8.37217	−	8.37217i	0.293806	−	0.293806i
$813$	−11.4733	−	5.73952i	−0.402386	−	0.201294i
$814$		−	11.8512i		−	0.415383i
$815$		0			0
$816$	30.2466	−	10.0755i	1.05884	−	0.352712i
$817$	−8.98326	−	8.98326i	−0.314284	−	0.314284i
$818$	32.2300	+	32.2300i	1.12689	+	1.12689i
$819$	−1.65804	−	2.21257i	−0.0579367	−	0.0773133i
$820$		0			0
$821$			13.9737i			0.487684i	0.969815	+	0.243842i	$0.0784078\pi$
$821$			13.9737i			0.487684i	−0.969815	+	0.243842i	$0.921592\pi$
$822$	21.9990	−	43.9759i	0.767302	−	1.53384i
$823$	9.64020	−	9.64020i	0.336036	−	0.336036i	−0.518837	−	0.854873i	$-0.673635\pi$
$823$	9.64020	−	9.64020i	0.336036	−	0.336036i	0.854873	+	0.518837i	$0.173635\pi$
$824$	13.1873			0.459402
$825$		0			0
$826$	7.87168			0.273891
$827$	−11.2829	+	11.2829i	−0.392345	+	0.392345i	−0.875522	−	0.483178i	$-0.839482\pi$
$827$	−11.2829	+	11.2829i	−0.392345	+	0.392345i	0.483178	+	0.875522i	$0.339482\pi$
$828$	−14.7160	−	2.10829i	−0.511415	−	0.0732681i
$829$			18.8442i			0.654485i	0.944940	+	0.327242i	$0.106119\pi$
$829$			18.8442i			0.654485i	−0.944940	+	0.327242i	$0.893881\pi$
$830$		0			0
$831$	8.61031	+	25.8482i	0.298688	+	0.896663i
$832$	−0.763521	−	0.763521i	−0.0264703	−	0.0264703i
$833$	2.63250	+	2.63250i	0.0912106	+	0.0912106i
$834$	−2.85947	−	8.58414i	−0.0990154	−	0.297244i
$835$		0			0
$836$		−	0.858086i		−	0.0296775i
$837$	−6.99459	−	38.6019i	−0.241768	−	1.33428i
$838$	24.6889	−	24.6889i	0.852865	−	0.852865i
$839$	−46.9582			−1.62118			−0.810588	−	0.585617i	$-0.800852\pi$
$839$	−46.9582			−1.62118			−0.810588	+	0.585617i	$0.800852\pi$
$840$		0			0
$841$	62.6827			2.16147
$842$	−11.6902	+	11.6902i	−0.402870	+	0.402870i
$843$	13.2605	−	26.5076i	0.456714	−	0.912972i
$844$		−	4.84628i		−	0.166816i
$845$		0			0
$846$	32.6042	−	24.4328i	1.12096	−	0.840017i
$847$	−7.52693	−	7.52693i	−0.258629	−	0.258629i
$848$	−12.5788	−	12.5788i	−0.431957	−	0.431957i
$849$	−25.3527	+	8.44528i	−0.870104	+	0.289841i
$850$		0			0
$851$		−	44.2882i		−	1.51818i
$852$	13.7322	+	6.86955i	0.470459	+	0.235347i
$853$	−26.8180	+	26.8180i	−0.918232	+	0.918232i	−0.996901	−	0.0786690i	$-0.974933\pi$
$853$	−26.8180	+	26.8180i	−0.918232	+	0.918232i	0.0786690	+	0.996901i	$0.474933\pi$
$854$	27.0108			0.924290
$855$		0			0
$856$	−0.342917			−0.0117207
$857$	24.3943	−	24.3943i	0.833293	−	0.833293i	−0.154673	−	0.987966i	$-0.549432\pi$
$857$	24.3943	−	24.3943i	0.833293	−	0.833293i	0.987966	+	0.154673i	$0.0494324\pi$
$858$	−1.53095	−	0.765856i	−0.0522657	−	0.0261459i
$859$		−	1.97722i		−	0.0674617i	−0.999431	−	0.0337309i	$-0.989261\pi$
$859$		−	1.97722i		−	0.0674617i	0.999431	−	0.0337309i	$-0.0107389\pi$
$860$		0			0
$861$	−13.6827	+	4.55785i	−0.466304	+	0.155331i
$862$	21.7345	+	21.7345i	0.740280	+	0.740280i
$863$	−17.7690	−	17.7690i	−0.604863	−	0.604863i	0.336736	−	0.941599i	$-0.390677\pi$
$863$	−17.7690	−	17.7690i	−0.604863	−	0.604863i	−0.941599	+	0.336736i	$0.890677\pi$
$864$	26.2529	+	18.1984i	0.893142	+	0.619122i
$865$		0			0
$866$		−	52.9188i		−	1.79825i
$867$	−2.43314	+	4.86385i	−0.0826339	+	0.165185i
$868$	6.60140	−	6.60140i	0.224066	−	0.224066i
$869$	−2.29623			−0.0778943
$870$		0			0
$871$	1.64312			0.0556749
$872$	−10.8801	+	10.8801i	−0.368448	+	0.368448i
$873$	−4.63200	+	32.3316i	−0.156770	+	1.09426i
$874$		−	8.39324i		−	0.283905i
$875$		0			0
$876$	−5.41946	−	16.2692i	−0.183107	−	0.549686i
$877$	30.0684	+	30.0684i	1.01534	+	1.01534i	0.999881	+	0.0154576i	$0.00492051\pi$
$877$	30.0684	+	30.0684i	1.01534	+	1.01534i	0.0154576	+	0.999881i	$0.495079\pi$
$878$	15.7143	+	15.7143i	0.530331	+	0.530331i
$879$	−11.8901	−	35.6940i	−0.401042	−	1.20393i
$880$		0			0
$881$			34.7319i			1.17015i	0.810980	+	0.585074i	$0.198934\pi$
$881$			34.7319i			1.17015i	−0.810980	+	0.585074i	$0.801066\pi$
$882$	−0.765406	+	5.34257i	−0.0257726	+	0.179894i
$883$	−0.424655	+	0.424655i	−0.0142908	+	0.0142908i	−0.714216	−	0.699925i	$-0.753217\pi$
$883$	−0.424655	+	0.424655i	−0.0142908	+	0.0142908i	0.699925	+	0.714216i	$0.253217\pi$
$884$	−4.24274			−0.142699
$885$		0			0
$886$	−16.7283			−0.561999
$887$	39.8779	−	39.8779i	1.33897	−	1.33897i	0.441912	−	0.897059i	$-0.354300\pi$
$887$	39.8779	−	39.8779i	1.33897	−	1.33897i	0.897059	−	0.441912i	$-0.145700\pi$
$888$	−11.7623	+	23.5129i	−0.394717	+	0.789040i
$889$			3.71408i			0.124566i
$890$		0			0
$891$	5.14890	+	1.50624i	0.172495	+	0.0504608i
$892$	6.12368	+	6.12368i	0.205036	+	0.205036i
$893$	6.21435	+	6.21435i	0.207955	+	0.207955i
$894$	8.20069	−	2.73174i	0.274272	−	0.0913630i
$895$		0			0
$896$		−	10.1874i		−	0.340336i
$897$	−5.72119	−	2.86203i	−0.191025	−	0.0955603i
$898$	−18.1170	+	18.1170i	−0.604571	+	0.604571i
$899$	72.2912			2.41105
$900$		0			0
$901$	−13.3953			−0.446263
$902$	−6.31376	+	6.31376i	−0.210225	+	0.210225i
$903$	16.9041	+	8.45628i	0.562533	+	0.281407i
$904$			1.07512i			0.0357580i
$905$		0			0
$906$	6.12490	−	2.04027i	0.203486	−	0.0677834i
$907$	−12.8493	−	12.8493i	−0.426653	−	0.426653i	0.460834	−	0.887487i	$-0.347550\pi$
$907$	−12.8493	−	12.8493i	−0.426653	−	0.426653i	−0.887487	+	0.460834i	$0.847550\pi$
$908$	−12.8927	−	12.8927i	−0.427860	−	0.427860i
$909$	30.6423	−	22.9626i	1.01634	−	0.761621i
$910$		0			0
$911$		−	15.5488i		−	0.515156i	−0.966258	−	0.257578i	$-0.917076\pi$
$911$		−	15.5488i		−	0.515156i	0.966258	−	0.257578i	$-0.0829244\pi$
$912$	−4.46017	+	8.91587i	−0.147691	+	0.295234i
$913$	−2.80568	+	2.80568i	−0.0928546	+	0.0928546i
$914$	−44.9555			−1.48700
$915$		0			0
$916$	−22.6822			−0.749440
$917$	11.6871	−	11.6871i	0.385943	−	0.385943i
$918$	34.2445	−	6.20504i	1.13024	−	0.204797i
$919$		−	53.8863i		−	1.77755i	−0.458348	−	0.888773i	$-0.651559\pi$
$919$		−	53.8863i		−	1.77755i	0.458348	−	0.888773i	$-0.348441\pi$
$920$		0			0
$921$	−12.0670	−	36.2251i	−0.397621	−	1.19366i
$922$	−27.6182	−	27.6182i	−0.909558	−	0.909558i
$923$	4.67207	+	4.67207i	0.153783	+	0.153783i
$924$	0.403470	+	1.21122i	0.0132732	+	0.0398462i
$925$		0			0
$926$			2.69098i			0.0884313i
$927$	28.5128	+	4.08491i	0.936485	+	0.134166i
$928$	−41.6228	+	41.6228i	−1.36634	+	1.36634i
$929$	14.9417			0.490220			0.245110	−	0.969495i	$-0.421176\pi$
$929$	14.9417			0.490220			0.245110	+	0.969495i	$0.421176\pi$
$930$		0			0
$931$	−1.16418			−0.0381544
$932$	10.5592	−	10.5592i	0.345877	−	0.345877i
$933$	−16.8715	+	33.7262i	−0.552350	+	1.10415i
$934$			68.3293i			2.23580i
$935$		0			0
$936$	2.27730	+	3.03894i	0.0744359	+	0.0993307i
$937$	−13.0089	−	13.0089i	−0.424981	−	0.424981i	0.461933	−	0.886915i	$-0.347156\pi$
$937$	−13.0089	−	13.0089i	−0.424981	−	0.424981i	−0.886915	+	0.461933i	$0.847156\pi$
$938$	−2.26798	−	2.26798i	−0.0740523	−	0.0740523i
$939$	39.0016	−	12.9919i	1.27277	−	0.423974i
$940$		0			0
$941$			3.15194i			0.102750i	0.998679	+	0.0513751i	$0.0163604\pi$
$941$			3.15194i			0.102750i	−0.998679	+	0.0513751i	$0.983640\pi$
$942$	−36.5838	−	18.3010i	−1.19196	−	0.596280i
$943$	−23.5947	+	23.5947i	−0.768350	+	0.768350i
$944$	−21.6326			−0.704082
$945$		0			0
$946$	11.7023			0.380476
$947$	−14.6574	+	14.6574i	−0.476302	+	0.476302i	−0.903947	−	0.427645i	$-0.859343\pi$
$947$	−14.6574	+	14.6574i	−0.476302	+	0.476302i	0.427645	+	0.903947i	$0.359343\pi$
$948$	−7.37878	−	3.69123i	−0.239652	−	0.119886i
$949$		−	7.37907i		−	0.239535i
$950$		0			0
$951$	45.2156	−	15.0618i	1.46622	−	0.488412i
$952$	−3.61571	−	3.61571i	−0.117186	−	0.117186i
$953$	9.88130	+	9.88130i	0.320087	+	0.320087i	0.848800	−	0.528714i	$-0.177325\pi$
$953$	9.88130	+	9.88130i	0.320087	+	0.320087i	−0.528714	+	0.848800i	$0.677325\pi$
$954$	−11.6453	−	15.5401i	−0.377032	−	0.503128i
$955$		0			0
$956$			7.39748i			0.239252i
$957$	−4.42278	+	8.84114i	−0.142968	+	0.285794i
$958$	3.03810	−	3.03810i	0.0981565	−	0.0981565i
$959$	−15.7802			−0.509569
$960$		0			0
$961$	26.0011			0.838744
$962$	12.9568	−	12.9568i	0.417745	−	0.417745i
$963$	−0.741435	−	0.106222i	−0.0238924	−	0.00342296i
$964$		−	6.25471i		−	0.201451i
$965$		0			0
$966$	3.94648	+	11.8474i	0.126976	+	0.381182i
$967$	−1.97663	−	1.97663i	−0.0635642	−	0.0635642i	0.674610	−	0.738174i	$-0.264312\pi$
$967$	−1.97663	−	1.97663i	−0.0635642	−	0.0635642i	−0.738174	+	0.674610i	$0.764312\pi$
$968$	10.3382	+	10.3382i	0.332281	+	0.332281i
$969$	2.37248	+	7.12218i	0.0762149	+	0.228797i
$970$		0			0
$971$		−	3.57758i		−	0.114810i	−0.998351	−	0.0574051i	$-0.981717\pi$
$971$		−	3.57758i		−	0.114810i	0.998351	−	0.0574051i	$-0.0182827\pi$
$972$	14.1243	+	13.1171i	0.453038	+	0.420733i
$973$	−2.05320	+	2.05320i	−0.0658224	+	0.0658224i
$974$	39.4646			1.26453
$975$		0			0
$976$	−74.2300			−2.37604
$977$	−23.9909	+	23.9909i	−0.767537	+	0.767537i	−0.977672	−	0.210135i	$-0.932610\pi$
$977$	−23.9909	+	23.9909i	−0.767537	+	0.767537i	0.210135	+	0.977672i	$0.432610\pi$
$978$	18.5516	−	37.0847i	0.593215	−	1.18584i
$979$			1.30995i			0.0418662i
$980$		0			0
$981$	−26.8946	+	20.1542i	−0.858679	+	0.643473i
$982$	43.0694	+	43.0694i	1.37440	+	1.37440i
$983$	−24.6787	−	24.6787i	−0.787127	−	0.787127i	0.193895	−	0.981022i	$-0.437888\pi$
$983$	−24.6787	−	24.6787i	−0.787127	−	0.787127i	−0.981022	+	0.193895i	$0.937888\pi$
$984$	18.7930	−	6.26016i	0.599099	−	0.199567i
$985$		0			0
$986$			64.1309i			2.04234i
$987$	−11.6938	−	5.84980i	−0.372216	−	0.186201i
$988$	0.938141	−	0.938141i	0.0298462	−	0.0298462i
$989$	43.7320			1.39060
$990$		0			0
$991$	−25.6595			−0.815102			−0.407551	−	0.913182i	$-0.633617\pi$
$991$	−25.6595			−0.815102			−0.407551	+	0.913182i	$0.633617\pi$
$992$	−32.8193	+	32.8193i	−1.04201	+	1.04201i
$993$	−31.0473	−	15.5314i	−0.985256	−	0.492875i
$994$		−	12.8976i		−	0.409089i
$995$		0			0
$996$	−13.5261	+	4.50568i	−0.428590	+	0.142768i
$997$	−17.2215	−	17.2215i	−0.545409	−	0.545409i	0.379701	−	0.925109i	$-0.376027\pi$
$997$	−17.2215	−	17.2215i	−0.545409	−	0.545409i	−0.925109	+	0.379701i	$0.876027\pi$
$998$	−4.52623	−	4.52623i	−0.143275	−	0.143275i
$999$	−32.7151	+	47.1946i	−1.03506	+	1.49317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.c.407.14	yes	32
3.2	odd	2	inner	525.2.j.c.407.4	yes	32
5.2	odd	4	inner	525.2.j.c.218.13	yes	32
5.3	odd	4	inner	525.2.j.c.218.4	yes	32
5.4	even	2	inner	525.2.j.c.407.3	yes	32
15.2	even	4	inner	525.2.j.c.218.3	✓	32
15.8	even	4	inner	525.2.j.c.218.14	yes	32
15.14	odd	2	inner	525.2.j.c.407.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.j.c.218.3	✓	32	15.2	even	4	inner
525.2.j.c.218.4	yes	32	5.3	odd	4	inner
525.2.j.c.218.13	yes	32	5.2	odd	4	inner
525.2.j.c.218.14	yes	32	15.8	even	4	inner
525.2.j.c.407.3	yes	32	5.4	even	2	inner
525.2.j.c.407.4	yes	32	3.2	odd	2	inner
525.2.j.c.407.13	yes	32	15.14	odd	2	inner
525.2.j.c.407.14	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27211 - 1.27211i) q^{2} +(1.54904 + 0.774907i) q^{3} -1.23654i q^{4} +(2.95632 - 0.984783i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.971203 + 0.971203i) q^{8} +(1.79904 + 2.40072i) q^{9} +O(q^{10})\)	\(q+(1.27211 - 1.27211i) q^{2} +(1.54904 + 0.774907i) q^{3} -1.23654i q^{4} +(2.95632 - 0.984783i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.971203 + 0.971203i) q^{8} +(1.79904 + 2.40072i) q^{9} -0.596077i q^{11} +(0.958205 - 1.91545i) q^{12} +(0.651688 - 0.651688i) q^{13} -1.79904 q^{14} +4.94405 q^{16} +(2.63250 - 2.63250i) q^{17} +(5.34257 + 0.765406i) q^{18} +1.16418i q^{19} +(-0.547394 - 1.64328i) q^{21} +(-0.758277 - 0.758277i) q^{22} +(-2.83371 - 2.83371i) q^{23} +(0.751839 + 2.25702i) q^{24} -1.65804i q^{26} +(0.926447 + 5.11290i) q^{27} +(-0.874368 + 0.874368i) q^{28} -9.57511 q^{29} -7.54990 q^{31} +(4.34698 - 4.34698i) q^{32} +(0.461904 - 0.923346i) q^{33} -6.69767i q^{34} +(2.96859 - 2.22459i) q^{36} +(7.81453 + 7.81453i) q^{37} +(1.48096 + 1.48096i) q^{38} +(1.51449 - 0.504492i) q^{39} -8.32646i q^{41} +(-2.78678 - 1.39409i) q^{42} +(-7.71640 + 7.71640i) q^{43} -0.737075 q^{44} -7.20959 q^{46} +(5.33798 - 5.33798i) q^{47} +(7.65852 + 3.83117i) q^{48} +1.00000i q^{49} +(6.11778 - 2.03790i) q^{51} +(-0.805840 - 0.805840i) q^{52} +(-2.54423 - 2.54423i) q^{53} +(7.68273 + 5.32563i) q^{54} -1.37349i q^{56} +(-0.902128 + 1.80335i) q^{57} +(-12.1806 + 12.1806i) q^{58} -4.37549 q^{59} -15.0140 q^{61} +(-9.60433 + 9.60433i) q^{62} +(0.425452 - 2.96968i) q^{63} -1.17161i q^{64} +(-0.587007 - 1.76220i) q^{66} +(1.26066 + 1.26066i) q^{67} +(-3.25520 - 3.25520i) q^{68} +(-2.19366 - 6.58538i) q^{69} +7.16919i q^{71} +(-0.584354 + 4.07882i) q^{72} +(5.66151 - 5.66151i) q^{73} +19.8819 q^{74} +1.43955 q^{76} +(-0.421490 + 0.421490i) q^{77} +(1.28483 - 2.56837i) q^{78} -3.85224i q^{79} +(-2.52691 + 8.63798i) q^{81} +(-10.5922 - 10.5922i) q^{82} +(-4.70691 - 4.70691i) q^{83} +(-2.03198 + 0.676876i) q^{84} +19.6323i q^{86} +(-14.8322 - 7.41982i) q^{87} +(0.578912 - 0.578912i) q^{88} -2.19762 q^{89} -0.921626 q^{91} +(-3.50400 + 3.50400i) q^{92} +(-11.6951 - 5.85047i) q^{93} -13.5810i q^{94} +(10.1021 - 3.36514i) q^{96} +(7.69844 + 7.69844i) q^{97} +(1.27211 + 1.27211i) q^{98} +(1.43101 - 1.07237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{6}+O(q^{10}) \) 32 * q - 16 * q^6	\( 32 q - 16 q^{6} - 16 q^{16} - 8 q^{21} + 16 q^{31} + 48 q^{36} + 144 q^{46} - 64 q^{51} - 112 q^{61} - 192 q^{76} - 64 q^{81} + 64 q^{91} + 360 q^{96}+O(q^{100}) \) 32 * q - 16 * q^6 - 16 * q^16 - 8 * q^21 + 16 * q^31 + 48 * q^36 + 144 * q^46 - 64 * q^51 - 112 * q^61 - 192 * q^76 - 64 * q^81 + 64 * q^91 + 360 * q^96

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