LMFDB - Embedded newform 405.3.l.m.298.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(28,405)] 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("405.28"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,6,0,0,-12,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 256x^{12} + 15630x^{8} + 235936x^{4} + 28561 $ x^16 + 256x^12 + 15630x^8 + 235936*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			298.4
Root			$-2.56790 + 2.56790i$ of defining polynomial
Character	$\chi$	$=$	405.298
Dual form			405.3.l.m.352.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939918 + 3.50782i) q^{2} +(-7.95726 + 4.59412i) q^{4} +(-4.78634 - 1.44602i) q^{5} +(-1.66244 - 6.20430i) q^{7} +(-13.3229 - 13.3229i) q^{8} +(0.573606 - 18.1488i) q^{10} +(3.66378 - 6.34586i) q^{11} +(-5.08326 + 18.9710i) q^{13} +(20.2010 - 11.6631i) q^{14} +(15.8355 - 27.4278i) q^{16} +(20.9110 - 20.9110i) q^{17} -0.814832i q^{19} +(44.7293 - 10.4827i) q^{20} +(25.7038 + 6.88731i) q^{22} +(5.74237 - 21.4308i) q^{23} +(20.8181 + 13.8423i) q^{25} -71.3246 q^{26} +(41.7318 + 41.7318i) q^{28} +(-19.8352 - 11.4518i) q^{29} +(-23.7301 - 41.1018i) q^{31} +(38.2981 + 10.2620i) q^{32} +(93.0066 + 53.6974i) q^{34} +(-1.01454 + 32.0998i) q^{35} +(11.0786 - 11.0786i) q^{37} +(2.85828 - 0.765875i) q^{38} +(44.5028 + 83.0332i) q^{40} +(-1.40488 - 2.43332i) q^{41} +(-56.3479 + 15.0984i) q^{43} +67.3275i q^{44} +80.5728 q^{46} +(-19.0278 - 71.0129i) q^{47} +(6.70561 - 3.87149i) q^{49} +(-28.9889 + 86.0366i) q^{50} +(-46.7063 - 174.310i) q^{52} +(-20.9617 - 20.9617i) q^{53} +(-26.7123 + 25.0755i) q^{55} +(-60.5109 + 104.808i) q^{56} +(21.5276 - 80.3420i) q^{58} +(-33.7253 + 19.4713i) q^{59} +(2.86576 - 4.96364i) q^{61} +(121.873 - 121.873i) q^{62} +17.3046i q^{64} +(51.7626 - 83.4511i) q^{65} +(-75.0726 - 20.1156i) q^{67} +(-70.3264 + 262.462i) q^{68} +(-113.554 + 26.6123i) q^{70} +62.1816 q^{71} +(8.47426 + 8.47426i) q^{73} +(49.2748 + 28.4488i) q^{74} +(3.74344 + 6.48382i) q^{76} +(-45.4624 - 12.1816i) q^{77} +(23.0227 + 13.2922i) q^{79} +(-115.455 + 108.380i) q^{80} +(7.21519 - 7.21519i) q^{82} +(-70.8625 + 18.9875i) q^{83} +(-130.325 + 69.8494i) q^{85} +(-105.925 - 183.467i) q^{86} +(-133.358 + 35.7331i) q^{88} +79.7031i q^{89} +126.152 q^{91} +(52.7623 + 196.912i) q^{92} +(231.216 - 133.493i) q^{94} +(-1.17826 + 3.90006i) q^{95} +(22.5867 + 84.2946i) q^{97} +(19.8832 + 19.8832i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 12 q^{5} - 20 q^{7} - 56 q^{10} + 22 q^{13} + 168 q^{14} + 16 q^{16} + 96 q^{20} - 16 q^{22} - 36 q^{23} + 46 q^{25} + 176 q^{28} + 252 q^{29} - 160 q^{31} + 114 q^{32} + 4 q^{37} - 192 q^{38}+ \cdots - 152 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 - 12 * q^5 - 20 * q^7 - 56 * q^10 + 22 * q^13 + 168 * q^14 + 16 * q^16 + 96 * q^20 - 16 * q^22 - 36 * q^23 + 46 * q^25 + 176 * q^28 + 252 * q^29 - 160 * q^31 + 114 * q^32 + 4 * q^37 - 192 * q^38 + 264 * q^40 - 128 * q^43 - 16 * q^46 - 204 * q^47 - 540 * q^50 + 154 * q^52 - 364 * q^55 - 246 * q^58 - 36 * q^59 - 4 * q^61 - 24 * q^65 - 44 * q^67 - 966 * q^68 + 18 * q^70 + 364 * q^73 - 288 * q^74 + 456 * q^76 + 204 * q^77 + 32 * q^82 - 12 * q^83 - 32 * q^85 - 420 * q^88 + 224 * q^91 + 960 * q^92 - 114 * q^95 - 152 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.939918	+	3.50782i	0.469959	+	1.75391i	0.639902	+	0.768456i	$0.278975\pi$
$2$	0.939918	+	3.50782i	0.469959	+	1.75391i	−0.169943	+	0.985454i	$0.554358\pi$
$3$		0			0
$3$		0			0
$4$	−7.95726	+	4.59412i	−1.98931	+	1.14853i
$5$	−4.78634	−	1.44602i	−0.957268	−	0.289203i
$5$	−4.78634	−	1.44602i	−0.957268	−	0.289203i
$6$		0			0
$7$	−1.66244	−	6.20430i	−0.237491	−	0.886328i	−0.977010	−	0.213193i	$-0.931614\pi$
$7$	−1.66244	−	6.20430i	−0.237491	−	0.886328i	0.739519	−	0.673136i	$-0.235053\pi$
$8$	−13.3229	−	13.3229i	−1.66536	−	1.66536i
$9$		0			0
$10$	0.573606	−	18.1488i	0.0573606	−	1.81488i
$11$	3.66378	−	6.34586i	0.333071	−	0.576896i	−0.650041	−	0.759899i	$-0.725248\pi$
$11$	3.66378	−	6.34586i	0.333071	−	0.576896i	0.983112	+	0.183003i	$0.0585817\pi$
$12$		0			0
$13$	−5.08326	+	18.9710i	−0.391020	+	1.45931i	0.437435	+	0.899250i	$0.355887\pi$
$13$	−5.08326	+	18.9710i	−0.391020	+	1.45931i	−0.828455	+	0.560056i	$0.810780\pi$
$14$	20.2010	−	11.6631i	1.44293	−	0.833076i
$15$		0			0
$16$	15.8355	−	27.4278i	0.989716	−	1.71424i
$17$	20.9110	−	20.9110i	1.23006	−	1.23006i	0.266117	−	0.963941i	$-0.414259\pi$
$17$	20.9110	−	20.9110i	1.23006	−	1.23006i	0.963941	−	0.266117i	$-0.0857408\pi$
$18$		0			0
$19$		−	0.814832i		−	0.0428859i	−0.999770	−	0.0214429i	$-0.993174\pi$
$19$		−	0.814832i		−	0.0428859i	0.999770	−	0.0214429i	$-0.00682602\pi$
$20$	44.7293	−	10.4827i	2.23647	−	0.524135i
$21$		0			0
$22$	25.7038	+	6.88731i	1.16835	+	0.313060i
$23$	5.74237	−	21.4308i	0.249668	−	0.931774i	−0.721311	−	0.692611i	$-0.756460\pi$
$23$	5.74237	−	21.4308i	0.249668	−	0.931774i	0.970979	−	0.239163i	$-0.0768731\pi$
$24$		0			0
$25$	20.8181	+	13.8423i	0.832723	+	0.553690i
$26$	−71.3246			−2.74326
$27$		0			0
$28$	41.7318	+	41.7318i	1.49042	+	1.49042i
$29$	−19.8352	−	11.4518i	−0.683972	−	0.394891i	0.117378	−	0.993087i	$-0.462551\pi$
$29$	−19.8352	−	11.4518i	−0.683972	−	0.394891i	−0.801350	+	0.598196i	$0.795884\pi$
$30$		0			0
$31$	−23.7301	−	41.1018i	−0.765487	−	1.32586i	−0.939988	−	0.341206i	$-0.889165\pi$
$31$	−23.7301	−	41.1018i	−0.765487	−	1.32586i	0.174501	−	0.984657i	$-0.444169\pi$
$32$	38.2981	+	10.2620i	1.19682	+	0.320686i
$33$		0			0
$34$	93.0066	+	53.6974i	2.73549	+	1.57933i
$35$	−1.01454	+	32.0998i	−0.0289868	+	0.917137i
$36$		0			0
$37$	11.0786	−	11.0786i	0.299422	−	0.299422i	−0.541365	−	0.840787i	$-0.682092\pi$
$37$	11.0786	−	11.0786i	0.299422	−	0.299422i	0.840787	+	0.541365i	$0.182092\pi$
$38$	2.85828	−	0.765875i	0.0752180	−	0.0201546i
$39$		0			0
$40$	44.5028	+	83.0332i	1.11257	+	2.07583i
$41$	−1.40488	−	2.43332i	−0.0342653	−	0.0593493i	0.848384	−	0.529381i	$-0.177576\pi$
$41$	−1.40488	−	2.43332i	−0.0342653	−	0.0593493i	−0.882650	+	0.470032i	$0.844242\pi$
$42$		0			0
$43$	−56.3479	+	15.0984i	−1.31042	+	0.351125i	−0.845379	−	0.534166i	$-0.820626\pi$
$43$	−56.3479	+	15.0984i	−1.31042	+	0.351125i	−0.465037	+	0.885291i	$0.653959\pi$
$44$			67.3275i			1.53017i
$45$		0			0
$46$	80.5728			1.75158
$47$	−19.0278	−	71.0129i	−0.404848	−	1.51091i	−0.804336	−	0.594174i	$-0.797479\pi$
$47$	−19.0278	−	71.0129i	−0.404848	−	1.51091i	0.399489	−	0.916738i	$-0.369188\pi$
$48$		0			0
$49$	6.70561	−	3.87149i	0.136849	−	0.0790099i
$50$	−28.9889	+	86.0366i	−0.579778	+	1.72073i
$51$		0			0
$52$	−46.7063	−	174.310i	−0.898197	−	3.35212i
$53$	−20.9617	−	20.9617i	−0.395504	−	0.395504i	0.481140	−	0.876644i	$-0.340223\pi$
$53$	−20.9617	−	20.9617i	−0.395504	−	0.395504i	−0.876644	+	0.481140i	$0.840223\pi$
$54$		0			0
$55$	−26.7123	+	25.0755i	−0.485679	+	0.455919i
$56$	−60.5109	+	104.808i	−1.08055	+	1.87157i
$57$		0			0
$58$	21.5276	−	80.3420i	0.371165	−	1.38521i
$59$	−33.7253	+	19.4713i	−0.571616	+	0.330023i	−0.757794	−	0.652493i	$-0.773723\pi$
$59$	−33.7253	+	19.4713i	−0.571616	+	0.330023i	0.186179	+	0.982516i	$0.440390\pi$
$60$		0			0
$61$	2.86576	−	4.96364i	0.0469797	−	0.0813712i	−0.841579	−	0.540134i	$-0.818374\pi$
$61$	2.86576	−	4.96364i	0.0469797	−	0.0813712i	0.888559	+	0.458762i	$0.151707\pi$
$62$	121.873	−	121.873i	1.96570	−	1.96570i
$63$		0			0
$64$			17.3046i			0.270385i
$65$	51.7626	−	83.4511i	0.796347	−	1.28386i
$66$		0			0
$67$	−75.0726	−	20.1156i	−1.12049	−	0.300234i	−0.349406	−	0.936971i	$-0.613617\pi$
$67$	−75.0726	−	20.1156i	−1.12049	−	0.300234i	−0.771080	+	0.636738i	$0.780283\pi$
$68$	−70.3264	+	262.462i	−1.03421	+	3.85973i
$69$		0			0
$70$	−113.554	+	26.6123i	−1.62220	+	0.380176i
$71$	62.1816			0.875797			0.437899	−	0.899024i	$-0.355723\pi$
$71$	62.1816			0.875797			0.437899	+	0.899024i	$0.355723\pi$
$72$		0			0
$73$	8.47426	+	8.47426i	0.116086	+	0.116086i	0.762763	−	0.646678i	$-0.223842\pi$
$73$	8.47426	+	8.47426i	0.116086	+	0.116086i	−0.646678	+	0.762763i	$0.723842\pi$
$74$	49.2748	+	28.4488i	0.665876	+	0.384443i
$75$		0			0
$76$	3.74344	+	6.48382i	0.0492558	+	0.0853135i
$77$	−45.4624	−	12.1816i	−0.590421	−	0.158203i
$78$		0			0
$79$	23.0227	+	13.2922i	0.291426	+	0.168255i	0.638585	−	0.769551i	$-0.279520\pi$
$79$	23.0227	+	13.2922i	0.291426	+	0.168255i	−0.347159	+	0.937806i	$0.612853\pi$
$80$	−115.455	+	108.380i	−1.44319	+	1.35476i
$81$		0			0
$82$	7.21519	−	7.21519i	0.0879901	−	0.0879901i
$83$	−70.8625	+	18.9875i	−0.853765	+	0.228766i	−0.659055	−	0.752095i	$-0.729043\pi$
$83$	−70.8625	+	18.9875i	−0.853765	+	0.228766i	−0.194710	+	0.980861i	$0.562377\pi$
$84$		0			0
$85$	−130.325	+	69.8494i	−1.53323	+	0.821758i
$86$	−105.925	−	183.467i	−1.23168	−	2.13334i
$87$		0			0
$88$	−133.358	+	35.7331i	−1.51543	+	0.406058i
$89$			79.7031i			0.895540i	0.894149	+	0.447770i	$0.147782\pi$
$89$			79.7031i			0.895540i	−0.894149	+	0.447770i	$0.852218\pi$
$90$		0			0
$91$	126.152			1.38629
$92$	52.7623	+	196.912i	0.573503	+	2.14034i
$93$		0			0
$94$	231.216	−	133.493i	2.45974	−	1.42013i
$95$	−1.17826	+	3.90006i	−0.0124027	+	0.0410533i
$96$		0			0
$97$	22.5867	+	84.2946i	0.232852	+	0.869016i	0.979105	+	0.203354i	$0.0651842\pi$
$97$	22.5867	+	84.2946i	0.232852	+	0.869016i	−0.746253	+	0.665662i	$0.768149\pi$
$98$	19.8832	+	19.8832i	0.202890	+	0.202890i
$99$		0			0
$100$	−229.248	−	14.5056i	−2.29248	−	0.145056i
$101$	43.0866	−	74.6281i	0.426600	−	0.738892i	−0.569969	−	0.821666i	$-0.693045\pi$
$101$	43.0866	−	74.6281i	0.426600	−	0.738892i	0.996568	+	0.0827742i	$0.0263780\pi$
$102$		0			0
$103$	5.51914	−	20.5977i	0.0535838	−	0.199978i	−0.933945	−	0.357417i	$-0.883657\pi$
$103$	5.51914	−	20.5977i	0.0535838	−	0.199978i	0.987529	+	0.157440i	$0.0503240\pi$
$104$	320.473	−	185.025i	3.08147	−	1.77909i
$105$		0			0
$106$	53.8276	−	93.2321i	0.507808	−	0.879548i
$107$	−44.8261	+	44.8261i	−0.418935	+	0.418935i	−0.884837	−	0.465902i	$-0.845730\pi$
$107$	−44.8261	+	44.8261i	−0.418935	+	0.418935i	0.465902	+	0.884837i	$0.345730\pi$
$108$		0			0
$109$			37.1212i			0.340562i	0.985396	+	0.170281i	$0.0544675\pi$
$109$			37.1212i			0.340562i	−0.985396	+	0.170281i	$0.945532\pi$
$110$	−113.068	−	70.1331i	−1.02789	−	0.637574i
$111$		0			0
$112$	−196.496	−	52.6509i	−1.75443	−	0.470097i
$113$	25.0254	−	93.3962i	0.221464	−	0.826515i	−0.762326	−	0.647193i	$-0.775943\pi$
$113$	25.0254	−	93.3962i	0.221464	−	0.826515i	0.983790	−	0.179322i	$-0.0573905\pi$
$114$		0			0
$115$	−58.4742	+	94.2715i	−0.508472	+	0.819752i
$116$	210.445			1.81418
$117$		0			0
$118$	−100.001	−	100.001i	−0.847466	−	0.847466i
$119$	−164.501	−	94.9748i	−1.38236	−	0.798108i
$120$		0			0
$121$	33.6534	+	58.2894i	0.278127	+	0.481730i
$122$	20.1051	+	5.38716i	0.164796	+	0.0441570i
$123$		0			0
$124$	377.653	+	218.038i	3.04559	+	1.75837i
$125$	−79.6262	−	96.3570i	−0.637009	−	0.770856i
$126$		0			0
$127$	3.48585	−	3.48585i	0.0274476	−	0.0274476i	−0.693250	−	0.720697i	$-0.743822\pi$
$127$	3.48585	−	3.48585i	0.0274476	−	0.0274476i	0.720697	+	0.693250i	$0.243822\pi$
$128$	92.4909	−	24.7829i	0.722585	−	0.193616i
$129$		0			0
$130$	341.384	+	103.137i	2.62603	+	0.793359i
$131$	−3.42728	−	5.93623i	−0.0261625	−	0.0453147i	0.852648	−	0.522486i	$-0.174995\pi$
$131$	−3.42728	−	5.93623i	−0.0261625	−	0.0453147i	−0.878810	+	0.477171i	$0.841662\pi$
$132$		0			0
$133$	−5.05546	+	1.35461i	−0.0380110	+	0.0101850i
$134$		−	282.248i		−	2.10633i
$135$		0			0
$136$	−557.191			−4.09699
$137$	1.34726	+	5.02805i	0.00983402	+	0.0367011i	0.970669	−	0.240422i	$-0.0772858\pi$
$137$	1.34726	+	5.02805i	0.00983402	+	0.0367011i	−0.960834	+	0.277123i	$0.910619\pi$
$138$		0			0
$139$	−108.729	+	62.7750i	−0.782226	+	0.451619i	−0.837219	−	0.546868i	$-0.815820\pi$
$139$	−108.729	+	62.7750i	−0.782226	+	0.451619i	0.0549925	+	0.998487i	$0.482487\pi$
$140$	−139.397	−	260.087i	−0.995696	−	1.85777i
$141$		0			0
$142$	58.4456	+	218.122i	0.411589	+	1.53607i
$143$	101.763	+	101.763i	0.711631	+	0.711631i
$144$		0			0
$145$	78.3783	+	83.4944i	0.540540	+	0.575824i
$146$	−21.7611	+	37.6913i	−0.149049	+	0.258160i
$147$		0			0
$148$	−37.2589	+	139.052i	−0.251749	+	0.939540i
$149$	232.521	−	134.246i	1.56054	−	0.900979i	0.563340	−	0.826225i	$-0.309516\pi$
$149$	232.521	−	134.246i	1.56054	−	0.900979i	0.997202	−	0.0747545i	$-0.0238173\pi$
$150$		0			0
$151$	116.580	−	201.923i	0.772055	−	1.33724i	−0.164379	−	0.986397i	$-0.552562\pi$
$151$	116.580	−	201.923i	0.772055	−	1.33724i	0.936435	−	0.350842i	$-0.114105\pi$
$152$	−10.8559	+	10.8559i	−0.0714206	+	0.0714206i
$153$		0			0
$154$		−	170.924i		−	1.10989i
$155$	54.1465	+	231.041i	0.349332	+	1.49059i
$156$		0			0
$157$	−237.815	−	63.7223i	−1.51474	−	0.405875i	−0.596737	−	0.802437i	$-0.703536\pi$
$157$	−237.815	−	63.7223i	−1.51474	−	0.405875i	−0.918008	+	0.396563i	$0.870203\pi$
$158$	−24.9871	+	93.2530i	−0.158146	+	0.590209i
$159$		0			0
$160$	−168.469	−	104.497i	−1.05293	−	0.653106i
$161$	−142.509			−0.885152
$162$		0			0
$163$	−113.042	−	113.042i	−0.693510	−	0.693510i	0.269493	−	0.963002i	$-0.413144\pi$
$163$	−113.042	−	113.042i	−0.693510	−	0.693510i	−0.963002	+	0.269493i	$0.913144\pi$
$164$	22.3580	+	12.9084i	0.136329	+	0.0787096i
$165$		0			0
$166$	−133.210	−	230.726i	−0.802469	−	1.38992i
$167$	−72.1456	−	19.3314i	−0.432009	−	0.115757i	0.0362598	−	0.999342i	$-0.488456\pi$
$167$	−72.1456	−	19.3314i	−0.432009	−	0.115757i	−0.468269	+	0.883586i	$0.655122\pi$
$168$		0			0
$169$	−187.700	−	108.369i	−1.11065	−	0.641236i
$170$	−367.514	−	391.503i	−2.16184	−	2.30296i
$171$		0			0
$172$	379.011	−	379.011i	2.20355	−	2.20355i
$173$	19.1882	−	5.14146i	0.110914	−	0.0297194i	−0.202935	−	0.979192i	$-0.565048\pi$
$173$	19.1882	−	5.14146i	0.110914	−	0.0297194i	0.313849	+	0.949473i	$0.398381\pi$
$174$		0			0
$175$	51.2728	−	152.173i	0.292987	−	0.869562i
$176$	−116.035	−	200.979i	−0.659292	−	1.14193i
$177$		0			0
$178$	−279.584	+	74.9143i	−1.57070	+	0.420867i
$179$			20.5177i			0.114624i	0.998356	+	0.0573119i	$0.0182529\pi$
$179$			20.5177i			0.114624i	−0.998356	+	0.0573119i	$0.981747\pi$
$180$		0			0
$181$	−169.531			−0.936637			−0.468319	−	0.883560i	$-0.655140\pi$
$181$	−169.531			−0.936637			−0.468319	+	0.883560i	$0.655140\pi$
$182$	118.573	+	442.519i	0.651498	+	2.43143i
$183$		0			0
$184$	−362.026	+	209.016i	−1.96753	+	1.13596i
$185$	−69.0459	+	37.0061i	−0.373221	+	0.200033i
$186$		0			0
$187$	−56.0848	−	209.312i	−0.299919	−	1.11931i
$188$	477.651	+	477.651i	2.54070	+	2.54070i
$189$		0			0
$190$	−14.7882	−	0.467392i	−0.0778325	−	0.00245996i
$191$	74.8869	−	129.708i	0.392078	−	0.679099i	−0.600645	−	0.799516i	$-0.705090\pi$
$191$	74.8869	−	129.708i	0.392078	−	0.679099i	0.992723	+	0.120416i	$0.0384230\pi$
$192$		0			0
$193$	−40.7967	+	152.255i	−0.211382	+	0.788887i	0.776027	+	0.630699i	$0.217232\pi$
$193$	−40.7967	+	152.255i	−0.211382	+	0.788887i	−0.987409	+	0.158188i	$0.949435\pi$
$194$	−274.461	+	158.460i	−1.41475	+	0.816804i
$195$		0			0
$196$	−35.5722	+	61.6128i	−0.181491	+	0.314351i
$197$	−31.3880	+	31.3880i	−0.159330	+	0.159330i	−0.782270	−	0.622940i	$-0.785938\pi$
$197$	−31.3880	+	31.3880i	−0.159330	+	0.159330i	0.622940	+	0.782270i	$0.285938\pi$
$198$		0			0
$199$			154.114i			0.774440i	0.921987	+	0.387220i	$0.126565\pi$
$199$			154.114i			0.774440i	−0.921987	+	0.387220i	$0.873435\pi$
$200$	−92.9381	−	461.777i	−0.464691	−	2.30888i
$201$		0			0
$202$	302.280	+	80.9956i	1.49643	+	0.400968i
$203$	−38.0759	+	142.101i	−0.187566	+	0.700007i
$204$		0			0
$205$	3.20560	+	13.6782i	0.0156371	+	0.0667228i
$206$	77.4405			0.375925
$207$		0			0
$208$	439.837	+	439.837i	2.11460	+	2.11460i
$209$	−5.17081	−	2.98537i	−0.0247407	−	0.0142841i
$210$		0			0
$211$	113.886	+	197.257i	0.539745	+	0.934866i	0.998917	+	0.0465188i	$0.0148127\pi$
$211$	113.886	+	197.257i	0.539745	+	0.934866i	−0.459172	+	0.888347i	$0.651854\pi$
$212$	263.098	+	70.4970i	1.24103	+	0.332533i
$213$		0			0
$214$	−199.375	−	115.109i	−0.931657	−	0.537892i
$215$	291.533	+	9.21412i	1.35597	+	0.0428564i
$216$		0			0
$217$	−215.558	+	215.558i	−0.993354	+	0.993354i
$218$	−130.215	+	34.8909i	−0.597315	+	0.160050i
$219$		0			0
$220$	97.3568	−	322.252i	0.442531	−	1.46478i
$221$	290.406	+	502.998i	1.31405	+	2.27601i
$222$		0			0
$223$	108.787	−	29.1494i	0.487834	−	0.130715i	−0.00651402	−	0.999979i	$-0.502073\pi$
$223$	108.787	−	29.1494i	0.487834	−	0.130715i	0.494348	+	0.869264i	$0.335407\pi$
$224$		−	254.673i		−	1.13693i
$225$		0			0
$226$	351.139			1.55371
$227$	32.9751	+	123.065i	0.145265	+	0.542136i	0.999743	+	0.0226491i	$0.00721005\pi$
$227$	32.9751	+	123.065i	0.145265	+	0.542136i	−0.854479	+	0.519486i	$0.826123\pi$
$228$		0			0
$229$	163.909	−	94.6330i	0.715760	−	0.413244i	−0.0974299	−	0.995242i	$-0.531062\pi$
$229$	163.909	−	94.6330i	0.715760	−	0.413244i	0.813190	+	0.581998i	$0.197729\pi$
$230$	−385.649	−	116.510i	−1.67673	−	0.506564i
$231$		0			0
$232$	111.690	+	416.834i	0.481424	+	1.79670i
$233$	−33.8562	−	33.8562i	−0.145306	−	0.145306i	0.630712	−	0.776017i	$-0.282763\pi$
$233$	−33.8562	−	33.8562i	−0.145306	−	0.145306i	−0.776017	+	0.630712i	$0.782763\pi$
$234$		0			0
$235$	−11.6122	+	367.406i	−0.0494135	+	1.56343i
$236$	178.907	−	309.877i	0.758083	−	1.31304i
$237$		0			0
$238$	178.537	−	666.309i	0.750155	−	2.79962i
$239$	267.952	−	154.702i	1.12114	−	0.647290i	0.179448	−	0.983768i	$-0.442569\pi$
$239$	267.952	−	154.702i	1.12114	−	0.647290i	0.941692	+	0.336478i	$0.109236\pi$
$240$		0			0
$241$	7.89303	−	13.6711i	0.0327512	−	0.0567267i	−0.849185	−	0.528095i	$-0.822906\pi$
$241$	7.89303	−	13.6711i	0.0327512	−	0.0567267i	0.881936	+	0.471368i	$0.156240\pi$
$242$	−172.837	+	172.837i	−0.714203	+	0.714203i
$243$		0			0
$244$			52.6626i			0.215830i
$245$	−37.6936	+	8.83381i	−0.153851	+	0.0360564i
$246$		0			0
$247$	15.4582	+	4.14200i	0.0625836	+	0.0167692i
$248$	−231.441	+	863.750i	−0.933230	+	3.48286i
$249$		0			0
$250$	263.161	−	369.882i	1.05264	−	1.47953i
$251$	−188.942			−0.752756			−0.376378	−	0.926466i	$-0.622831\pi$
$251$	−188.942			−0.752756			−0.376378	+	0.926466i	$0.622831\pi$
$252$		0			0
$253$	−114.958	−	114.958i	−0.454380	−	0.454380i
$254$	15.5041	+	8.95132i	0.0610400	+	0.0352414i
$255$		0			0
$256$	208.477	+	361.093i	0.814363	+	1.41052i
$257$	2.28265	+	0.611634i	0.00888191	+	0.00237990i	0.263257	−	0.964726i	$-0.415203\pi$
$257$	2.28265	+	0.611634i	0.00888191	+	0.00237990i	−0.254375	+	0.967106i	$0.581870\pi$
$258$		0			0
$259$	−87.1526	−	50.3176i	−0.336496	−	0.194276i
$260$	−28.5035	+	901.845i	−0.109629	+	3.46864i
$261$		0			0
$262$	17.6019	−	17.6019i	0.0671826	−	0.0671826i
$263$	−369.570	+	99.0260i	−1.40521	+	0.376525i	−0.880213	−	0.474579i	$-0.842600\pi$
$263$	−369.570	+	99.0260i	−1.40521	+	0.376525i	−0.524997	+	0.851104i	$0.675934\pi$
$264$		0			0
$265$	70.0188	+	130.641i	0.264222	+	0.492984i
$266$	−9.50343	−	16.4604i	−0.0357272	−	0.0618813i
$267$		0			0
$268$	689.786	−	184.828i	2.57383	−	0.689655i
$269$			276.206i			1.02679i	0.858153	+	0.513394i	$0.171612\pi$
$269$			276.206i			1.02679i	−0.858153	+	0.513394i	$0.828388\pi$
$270$		0			0
$271$	485.044			1.78983			0.894915	−	0.446237i	$-0.147236\pi$
$271$	485.044			1.78983			0.894915	+	0.446237i	$0.147236\pi$
$272$	−242.408	−	904.678i	−0.891205	−	3.32602i
$273$		0			0
$274$	−16.3712	+	9.45190i	−0.0597488	+	0.0344960i
$275$	164.114	−	81.3935i	0.596778	−	0.295976i
$276$		0			0
$277$	85.0622	+	317.456i	0.307084	+	1.14605i	0.931137	+	0.364670i	$0.118818\pi$
$277$	85.0622	+	317.456i	0.307084	+	1.14605i	−0.624053	+	0.781382i	$0.714515\pi$
$278$	−322.400	−	322.400i	−1.15971	−	1.15971i
$279$		0			0
$280$	441.179	−	414.146i	1.57564	−	1.47909i
$281$	−236.323	+	409.324i	−0.841009	+	1.45667i	0.0480345	+	0.998846i	$0.484704\pi$
$281$	−236.323	+	409.324i	−0.841009	+	1.45667i	−0.889043	+	0.457824i	$0.848629\pi$
$282$		0			0
$283$	66.9326	−	249.796i	0.236511	−	0.882671i	−0.740951	−	0.671559i	$-0.765625\pi$
$283$	66.9326	−	249.796i	0.236511	−	0.882671i	0.977462	−	0.211112i	$-0.0677084\pi$
$284$	−494.795	+	285.670i	−1.74224	+	1.00588i
$285$		0			0
$286$	−261.318	+	452.616i	−0.913700	+	1.58257i
$287$	−12.7615	+	12.7615i	−0.0444653	+	0.0444653i
$288$		0			0
$289$		−	585.538i		−	2.02608i
$290$	−219.214	+	353.415i	−0.755911	+	1.21867i
$291$		0			0
$292$	−106.364	−	28.5001i	−0.364259	−	0.0976030i
$293$	62.1506	−	231.949i	0.212118	−	0.791635i	−0.775043	−	0.631908i	$-0.782272\pi$
$293$	62.1506	−	231.949i	0.212118	−	0.791635i	0.987161	−	0.159727i	$-0.0510614\pi$
$294$		0			0
$295$	189.577	−	44.4290i	0.642633	−	0.150607i
$296$	−295.199			−0.997294
$297$		0			0
$298$	689.461	+	689.461i	2.31363	+	2.31363i
$299$	377.374	+	217.877i	1.26212	+	0.728685i
$300$		0			0
$301$	187.350	+	324.499i	0.622424	+	1.07807i
$302$	817.886	+	219.152i	2.70823	+	0.725668i
$303$		0			0
$304$	−22.3491	−	12.9032i	−0.0735166	−	0.0424448i
$305$	−20.8940	+	19.6137i	−0.0685049	+	0.0643073i
$306$		0			0
$307$	−338.921	+	338.921i	−1.10398	+	1.10398i	−0.110051	+	0.993926i	$0.535101\pi$
$307$	−338.921	+	338.921i	−1.10398	+	1.10398i	−0.993926	+	0.110051i	$0.964899\pi$
$308$	417.720	−	111.928i	1.35623	−	0.363402i
$309$		0			0
$310$	−759.557	+	407.096i	−2.45018	+	1.31321i
$311$	−70.9256	−	122.847i	−0.228057	−	0.395006i	0.729176	−	0.684327i	$-0.239904\pi$
$311$	−70.9256	−	122.847i	−0.228057	−	0.395006i	−0.957232	+	0.289321i	$0.906570\pi$
$312$		0			0
$313$	−601.729	+	161.233i	−1.92246	+	0.515121i	−0.935735	+	0.352704i	$0.885262\pi$
$313$	−601.729	+	161.233i	−1.92246	+	0.515121i	−0.986722	+	0.162417i	$0.948071\pi$
$314$		−	894.106i		−	2.84747i
$315$		0			0
$316$	−244.263			−0.772985
$317$	−50.3762	−	188.007i	−0.158916	−	0.593081i	−0.998738	−	0.0502200i	$-0.984008\pi$
$317$	−50.3762	−	188.007i	−0.158916	−	0.593081i	0.839823	−	0.542861i	$-0.182659\pi$
$318$		0			0
$319$	−145.344	+	83.9142i	−0.455623	+	0.263054i
$320$	25.0228	−	82.8258i	0.0781963	−	0.258831i
$321$		0			0
$322$	−133.947	−	499.898i	−0.415985	−	1.55248i
$323$	−17.0389	−	17.0389i	−0.0527521	−	0.0527521i
$324$		0			0
$325$	−368.425	+	324.575i	−1.13361	+	0.998693i
$326$	290.281	−	502.782i	0.890433	−	1.54228i
$327$		0			0
$328$	−13.7019	+	51.1360i	−0.0417740	+	0.155903i
$329$	−408.953	+	236.109i	−1.24302	+	0.717656i
$330$		0			0
$331$	269.674	−	467.089i	0.814726	−	1.41115i	−0.0947991	−	0.995496i	$-0.530221\pi$
$331$	269.674	−	467.089i	0.814726	−	1.41115i	0.909525	−	0.415650i	$-0.136446\pi$
$332$	476.640	−	476.640i	1.43566	−	1.43566i
$333$		0			0
$334$		−	271.244i		−	0.812107i
$335$	330.235	+	204.837i	0.985777	+	0.611453i
$336$		0			0
$337$	463.642	+	124.232i	1.37579	+	0.368642i	0.869591	−	0.493773i	$-0.164383\pi$
$337$	463.642	+	124.232i	1.37579	+	0.368642i	0.506201	+	0.862415i	$0.331049\pi$
$338$	203.716	−	760.277i	0.602709	−	2.24934i
$339$		0			0
$340$	716.130	−	1154.54i	2.10627	−	3.39570i
$341$	−347.768			−1.01985
$342$		0			0
$343$	−257.719	−	257.719i	−0.751367	−	0.751367i
$344$	951.873	+	549.564i	2.76707	+	1.59757i
$345$		0			0
$346$	36.0707	+	62.4762i	0.104250	+	0.180567i
$347$	26.4700	+	7.09262i	0.0762825	+	0.0204398i	0.296758	−	0.954953i	$-0.404094\pi$
$347$	26.4700	+	7.09262i	0.0762825	+	0.0204398i	−0.220476	+	0.975392i	$0.570761\pi$
$348$		0			0
$349$	−401.697	−	231.920i	−1.15099	−	0.664526i	−0.201864	−	0.979414i	$-0.564700\pi$
$349$	−401.697	−	231.920i	−1.15099	−	0.664526i	−0.949129	+	0.314888i	$0.898033\pi$
$350$	581.989	+	36.8253i	1.66283	+	0.105215i
$351$		0			0
$352$	205.437	−	205.437i	0.583628	−	0.583628i
$353$	−87.0482	+	23.3245i	−0.246596	+	0.0660751i	−0.380000	−	0.924987i	$-0.624076\pi$
$353$	−87.0482	+	23.3245i	−0.246596	+	0.0660751i	0.133404	+	0.991062i	$0.457409\pi$
$354$		0			0
$355$	−297.622	−	89.9157i	−0.838372	−	0.253284i
$356$	−366.166	−	634.218i	−1.02856	−	1.78151i
$357$		0			0
$358$	−71.9723	+	19.2849i	−0.201040	+	0.0538685i
$359$		−	94.1221i		−	0.262179i	−0.991371	−	0.131089i	$-0.958153\pi$
$359$		−	94.1221i		−	0.262179i	0.991371	−	0.131089i	$-0.0418475\pi$
$360$		0			0
$361$	360.336			0.998161
$362$	−159.345	−	594.685i	−0.440181	−	1.64278i
$363$		0			0
$364$	−1003.83	+	579.559i	−2.75776	+	1.59220i
$365$	−28.3068	−	52.8146i	−0.0775528	−	0.144698i
$366$		0			0
$367$	44.0767	+	164.496i	0.120100	+	0.448219i	0.999618	−	0.0276468i	$-0.00880136\pi$
$367$	44.0767	+	164.496i	0.120100	+	0.448219i	−0.879518	+	0.475866i	$0.842135\pi$
$368$	−496.867	−	496.867i	−1.35018	−	1.35018i
$369$		0			0
$370$	−194.708	−	207.418i	−0.526239	−	0.560589i
$371$	−95.2051	+	164.900i	−0.256618	+	0.444475i
$372$		0			0
$373$	−25.4843	+	95.1089i	−0.0683227	+	0.254984i	−0.991636	−	0.129063i	$-0.958803\pi$
$373$	−25.4843	+	95.1089i	−0.0683227	+	0.254984i	0.923314	+	0.384046i	$0.125470\pi$
$374$	681.512	−	393.471i	1.82222	−	1.05206i
$375$		0			0
$376$	−692.592	+	1199.61i	−1.84200	+	3.19044i
$377$	318.080	−	318.080i	0.843714	−	0.843714i
$378$		0			0
$379$		−	321.363i		−	0.847923i	−0.905680	−	0.423961i	$-0.860639\pi$
$379$		−	321.363i		−	0.847923i	0.905680	−	0.423961i	$-0.139361\pi$
$380$	−8.54164	−	36.4469i	−0.0224780	−	0.0959128i
$381$		0			0
$382$	525.380	+	140.775i	1.37534	+	0.368521i
$383$	39.0699	−	145.811i	0.102010	−	0.380707i	−0.895979	−	0.444097i	$-0.853525\pi$
$383$	39.0699	−	145.811i	0.102010	−	0.380707i	0.997989	+	0.0633900i	$0.0201912\pi$
$384$		0			0
$385$	199.984	+	124.045i	0.519438	+	0.322194i
$386$	−572.429			−1.48298
$387$		0			0
$388$	−566.988	−	566.988i	−1.46131	−	1.46131i
$389$	278.850	+	160.994i	0.716837	+	0.413866i	0.813588	−	0.581442i	$-0.197511\pi$
$389$	278.850	+	160.994i	0.716837	+	0.413866i	−0.0967501	+	0.995309i	$0.530845\pi$
$390$		0			0
$391$	−328.061	−	568.218i	−0.839030	−	1.45324i
$392$	−140.918	−	37.7588i	−0.359484	−	0.0963235i
$393$		0			0
$394$	−139.606	−	80.6014i	−0.354329	−	0.204572i
$395$	−90.9737	−	96.9119i	−0.230313	−	0.245347i
$396$		0			0
$397$	312.981	−	312.981i	0.788366	−	0.788366i	−0.192860	−	0.981226i	$-0.561776\pi$
$397$	312.981	−	312.981i	0.788366	−	0.788366i	0.981226	+	0.192860i	$0.0617763\pi$
$398$	−540.603	+	144.854i	−1.35830	+	0.363955i
$399$		0			0
$400$	709.327	−	351.796i	1.77332	−	0.879489i
$401$	199.861	+	346.169i	0.498405	+	0.863263i	0.999998	−	0.00184042i	$-0.000585824\pi$
$401$	199.861	+	346.169i	0.498405	+	0.863263i	−0.501593	+	0.865104i	$0.667252\pi$
$402$		0			0
$403$	900.367	−	241.253i	2.23416	−	0.598642i
$404$			791.780i			1.95985i
$405$		0			0
$406$	−534.254			−1.31590
$407$	−29.7137	−	110.893i	−0.0730066	−	0.272464i
$408$		0			0
$409$	244.425	−	141.119i	0.597615	−	0.345033i	−0.170488	−	0.985360i	$-0.554534\pi$
$409$	244.425	−	141.119i	0.597615	−	0.345033i	0.768103	+	0.640327i	$0.221201\pi$
$410$	−44.9676	+	24.1010i	−0.109677	+	0.0587830i
$411$		0			0
$412$	50.7112	+	189.257i	0.123085	+	0.459361i
$413$	176.872	+	176.872i	0.428262	+	0.428262i
$414$		0			0
$415$	366.628	+	11.5876i	0.883441	+	0.0279219i
$416$	−389.359	+	674.389i	−0.935958	+	1.62113i
$417$		0			0
$418$	5.61200	−	20.9443i	0.0134258	−	0.0501059i
$419$	182.930	−	105.615i	0.436587	−	0.252064i	−0.265562	−	0.964094i	$-0.585557\pi$
$419$	182.930	−	105.615i	0.436587	−	0.252064i	0.702149	+	0.712030i	$0.252224\pi$
$420$		0			0
$421$	−61.2403	+	106.071i	−0.145464	+	0.251951i	−0.929546	−	0.368706i	$-0.879801\pi$
$421$	−61.2403	+	106.071i	−0.145464	+	0.251951i	0.784082	+	0.620657i	$0.213134\pi$
$422$	−584.897	+	584.897i	−1.38601	+	1.38601i
$423$		0			0
$424$			558.542i			1.31732i
$425$	724.781	−	145.871i	1.70537	−	0.343226i
$426$		0			0
$427$	−35.5601	−	9.52829i	−0.0832788	−	0.0223145i
$428$	150.756	−	562.629i	0.352234	−	1.31455i
$429$		0			0
$430$	241.695	+	1031.30i	0.562082	+	2.39838i
$431$	−681.441			−1.58107			−0.790535	−	0.612417i	$-0.790197\pi$
$431$	−681.441			−1.58107			−0.790535	+	0.612417i	$0.790197\pi$
$432$		0			0
$433$	−176.936	−	176.936i	−0.408628	−	0.408628i	0.472632	−	0.881260i	$-0.343304\pi$
$433$	−176.936	−	176.936i	−0.408628	−	0.408628i	−0.881260	+	0.472632i	$0.843304\pi$
$434$	−958.745	−	553.531i	−2.20909	−	1.27542i
$435$		0			0
$436$	−170.540	−	295.383i	−0.391146	−	0.677484i
$437$	−17.4625	−	4.67906i	−0.0399600	−	0.0107072i
$438$		0			0
$439$	−1.32220	−	0.763370i	−0.00301184	−	0.00173888i	0.498493	−	0.866894i	$-0.333887\pi$
$439$	−1.32220	−	0.763370i	−0.00301184	−	0.00173888i	−0.501505	+	0.865155i	$0.667220\pi$
$440$	689.966	+	21.8069i	1.56810	+	0.0495612i
$441$		0			0
$442$	−1491.47	+	1491.47i	−3.37436	+	3.37436i
$443$	−365.850	+	98.0293i	−0.825847	+	0.221285i	−0.646901	−	0.762574i	$-0.723935\pi$
$443$	−365.850	+	98.0293i	−0.825847	+	0.221285i	−0.178946	+	0.983859i	$0.557269\pi$
$444$		0			0
$445$	115.252	−	381.486i	0.258993	−	0.857272i
$446$	204.502	+	354.207i	0.458524	+	0.794187i
$447$		0			0
$448$	107.363	−	28.7679i	0.239650	−	0.0642140i
$449$			282.215i			0.628540i	0.949334	+	0.314270i	$0.101760\pi$
$449$			282.215i			0.628540i	−0.949334	+	0.314270i	$0.898240\pi$
$450$		0			0
$451$	−20.5887			−0.0456512
$452$	229.940	+	858.148i	0.508717	+	1.89856i
$453$		0			0
$454$	−400.695	+	231.341i	−0.882589	+	0.509563i
$455$	−603.807	−	182.418i	−1.32705	−	0.400919i
$456$		0			0
$457$	215.556	+	804.467i	0.471677	+	1.76032i	0.633744	+	0.773543i	$0.281517\pi$
$457$	215.556	+	804.467i	0.471677	+	1.76032i	−0.162067	+	0.986780i	$0.551816\pi$
$458$	486.017	+	486.017i	1.06117	+	1.06117i
$459$		0			0
$460$	32.1994	−	1018.78i	0.0699987	−	2.21474i
$461$	280.597	−	486.008i	0.608670	−	1.05425i	−0.382790	−	0.923835i	$-0.625037\pi$
$461$	280.597	−	486.008i	0.608670	−	1.05425i	0.991460	−	0.130412i	$-0.0416300\pi$
$462$		0			0
$463$	−53.3611	+	199.146i	−0.115251	+	0.430122i	−0.999306	−	0.0372615i	$-0.988137\pi$
$463$	−53.3611	+	199.146i	−0.115251	+	0.430122i	0.884055	+	0.467383i	$0.154803\pi$
$464$	−628.198	+	362.691i	−1.35388	+	0.781661i
$465$		0			0
$466$	86.9395	−	150.584i	0.186565	−	0.323141i
$467$	635.592	−	635.592i	1.36101	−	1.36101i	0.488377	−	0.872633i	$-0.337589\pi$
$467$	635.592	−	635.592i	1.36101	−	1.36101i	0.872633	−	0.488377i	$-0.162411\pi$
$468$		0			0
$469$			499.214i			1.06442i
$470$	−1299.71	+	304.598i	−2.76534	+	0.648081i
$471$		0			0
$472$	708.735	+	189.905i	1.50156	+	0.402341i
$473$	−110.634	+	412.893i	−0.233899	+	0.872924i
$474$		0			0
$475$	11.2791	−	16.9632i	0.0237455	−	0.0357120i
$476$	1745.30			3.66661
$477$		0			0
$478$	794.521	+	794.521i	1.66218	+	1.66218i
$479$	−567.637	−	327.725i	−1.18505	−	0.684186i	−0.227869	−	0.973692i	$-0.573176\pi$
$479$	−567.637	−	327.725i	−1.18505	−	0.684186i	−0.957176	+	0.289506i	$0.906509\pi$
$480$		0			0
$481$	153.857	+	266.488i	0.319869	+	0.554029i
$482$	55.3747	+	14.8376i	0.114885	+	0.0307834i
$483$		0			0
$484$	−535.577	−	309.216i	−1.10656	−	0.638875i
$485$	13.7840	−	436.123i	0.0284207	−	0.899223i
$486$		0			0
$487$	623.917	−	623.917i	1.28114	−	1.28114i	0.341125	−	0.940018i	$-0.389192\pi$
$487$	623.917	−	623.917i	1.28114	−	1.28114i	0.940018	−	0.341125i	$-0.110808\pi$
$488$	−104.310	+	27.9499i	−0.213751	+	0.0572744i
$489$		0			0
$490$	−66.4163	−	123.919i	−0.135543	−	0.252896i
$491$	−67.7145	−	117.285i	−0.137911	−	0.238870i	0.788794	−	0.614657i	$-0.210706\pi$
$491$	−67.7145	−	117.285i	−0.137911	−	0.238870i	−0.926706	+	0.375788i	$0.877372\pi$
$492$		0			0
$493$	−654.242	+	175.304i	−1.32706	+	0.355586i
$494$			58.1176i			0.117647i
$495$		0			0
$496$	−1503.11			−3.03046
$497$	−103.373	−	385.793i	−0.207994	−	0.776244i
$498$		0			0
$499$	733.886	−	423.709i	1.47071	−	0.849117i	0.471254	−	0.881997i	$-0.343801\pi$
$499$	733.886	−	423.709i	1.47071	−	0.849117i	0.999459	+	0.0328807i	$0.0104681\pi$
$500$	1076.28	+	400.925i	2.15256	+	0.801850i
$501$		0			0
$502$	−177.590	−	662.773i	−0.353764	−	1.32027i
$503$	361.616	+	361.616i	0.718919	+	0.718919i	0.968384	−	0.249465i	$-0.0802548\pi$
$503$	361.616	+	361.616i	0.718919	+	0.718919i	−0.249465	+	0.968384i	$0.580255\pi$
$504$		0			0
$505$	−314.140	+	294.891i	−0.622060	+	0.583943i
$506$	295.201	−	511.304i	0.583402	−	1.01048i
$507$		0			0
$508$	−11.7234	+	43.7522i	−0.0230775	+	0.0861264i
$509$	−629.959	+	363.707i	−1.23764	+	0.714553i	−0.968612	−	0.248579i	$-0.920036\pi$
$509$	−629.959	+	363.707i	−1.23764	+	0.714553i	−0.269030	+	0.963132i	$0.586703\pi$
$510$		0			0
$511$	38.4889	−	66.6648i	0.0753208	−	0.130459i
$512$	−799.865	+	799.865i	−1.56224	+	1.56224i
$513$		0			0
$514$			8.58201i			0.0166965i
$515$	−56.2011	+	90.6068i	−0.109128	+	0.175935i
$516$		0			0
$517$	−520.352	−	139.428i	−1.00648	−	0.269686i
$518$	94.5887	−	353.010i	0.182604	−	0.681486i
$519$		0			0
$520$	−1801.44	+	422.183i	−3.46431	+	0.811891i
$521$	79.7796			0.153128			0.0765640	−	0.997065i	$-0.475605\pi$
$521$	79.7796			0.153128			0.0765640	+	0.997065i	$0.475605\pi$
$522$		0			0
$523$	−30.3255	−	30.3255i	−0.0579837	−	0.0579837i	0.677520	−	0.735504i	$-0.263055\pi$
$523$	−30.3255	−	30.3255i	−0.0579837	−	0.0579837i	−0.735504	+	0.677520i	$0.763055\pi$
$524$	54.5435	+	31.4907i	0.104091	+	0.0600968i
$525$		0			0
$526$	−694.731	−	1203.31i	−1.32078	−	2.28766i
$527$	−1355.70	−	363.258i	−2.57248	−	0.689295i
$528$		0			0
$529$	31.8227	+	18.3728i	0.0601563	+	0.0347313i
$530$	−392.452	+	368.405i	−0.740476	+	0.695104i
$531$		0			0
$532$	34.0044	−	34.0044i	0.0639180	−	0.0639180i
$533$	53.3039	−	14.2827i	0.100007	−	0.0267969i
$534$		0			0
$535$	279.372	−	149.733i	0.522190	−	0.279875i
$536$	732.187	+	1268.19i	1.36602	+	2.36602i
$537$		0			0
$538$	−968.881	+	259.611i	−1.80089	+	0.482548i
$539$		−	56.7372i		−	0.105264i
$540$		0			0
$541$	437.642			0.808950			0.404475	−	0.914549i	$-0.367454\pi$
$541$	437.642			0.808950			0.404475	+	0.914549i	$0.367454\pi$
$542$	455.901	+	1701.45i	0.841146	+	3.13920i
$543$		0			0
$544$	1015.44	−	586.264i	1.86662	−	1.07769i
$545$	53.6780	−	177.675i	0.0984917	−	0.326009i
$546$		0			0
$547$	−61.4542	−	229.350i	−0.112348	−	0.419287i	0.886727	−	0.462293i	$-0.152973\pi$
$547$	−61.4542	−	229.350i	−0.112348	−	0.419287i	−0.999075	+	0.0430060i	$0.986307\pi$
$548$	−33.8200	−	33.8200i	−0.0617153	−	0.0617153i
$549$		0			0
$550$	439.767	+	499.179i	0.799577	+	0.907598i
$551$	−9.33133	+	16.1623i	−0.0169353	+	0.0293327i
$552$		0			0
$553$	44.1947	−	164.937i	0.0799181	−	0.298259i
$554$	−1033.63	+	596.766i	−1.86576	+	1.07719i
$555$		0			0
$556$	576.792	−	999.033i	1.03740	−	1.79682i
$557$	−219.091	+	219.091i	−0.393341	+	0.393341i	−0.875877	−	0.482535i	$-0.839716\pi$
$557$	−219.091	+	219.091i	−0.393341	+	0.393341i	0.482535	+	0.875877i	$0.339716\pi$
$558$		0			0
$559$		−	1145.72i		−	2.04960i
$560$	864.362	+	536.142i	1.54350	+	0.957396i
$561$		0			0
$562$	−1657.96	−	444.249i	−2.95011	−	0.790479i
$563$	98.1479	−	366.293i	0.174330	−	0.650609i	−0.822335	−	0.569004i	$-0.807329\pi$
$563$	98.1479	−	366.293i	0.174330	−	0.650609i	0.996665	−	0.0816047i	$-0.0260045\pi$
$564$		0			0
$565$	−254.833	+	410.839i	−0.451032	+	0.727148i
$566$	939.150			1.65928
$567$		0			0
$568$	−828.441	−	828.441i	−1.45852	−	1.45852i
$569$	−164.452	−	94.9462i	−0.289019	−	0.166865i	0.348481	−	0.937316i	$-0.386698\pi$
$569$	−164.452	−	94.9462i	−0.289019	−	0.166865i	−0.637499	+	0.770451i	$0.720031\pi$
$570$		0			0
$571$	485.836	+	841.493i	0.850851	+	1.47372i	0.880441	+	0.474155i	$0.157247\pi$
$571$	485.836	+	841.493i	0.850851	+	1.47372i	−0.0295899	+	0.999562i	$0.509420\pi$
$572$	−1277.27	−	342.243i	−2.23299	−	0.598327i
$573$		0			0
$574$	−56.7600	−	32.7704i	−0.0988850	−	0.0570913i
$575$	416.196	−	366.661i	0.723819	−	0.637671i
$576$		0			0
$577$	390.924	−	390.924i	0.677510	−	0.677510i	−0.281926	−	0.959436i	$-0.590973\pi$
$577$	390.924	−	390.924i	0.677510	−	0.677510i	0.959436	+	0.281926i	$0.0909732\pi$
$578$	2053.96	−	550.358i	3.55357	−	0.952176i
$579$		0			0
$580$	−1007.26	−	304.307i	−1.73666	−	0.524667i
$581$	235.609	+	408.087i	0.405523	+	0.702386i
$582$		0			0
$583$	−209.819	+	56.2209i	−0.359896	+	0.0964337i
$584$		−	225.804i		−	0.386650i
$585$		0			0
$586$	872.052			1.48814
$587$	−65.1224	−	243.040i	−0.110941	−	0.414038i	0.888010	−	0.459824i	$-0.152087\pi$
$587$	−65.1224	−	243.040i	−0.110941	−	0.414038i	−0.998951	+	0.0457860i	$0.985421\pi$
$588$		0			0
$589$	−33.4910	+	19.3360i	−0.0568608	+	0.0328286i
$590$	334.035	+	623.242i	0.566162	+	1.05634i
$591$		0			0
$592$	−128.427	−	479.297i	−0.216938	−	0.809624i
$593$	−619.877	−	619.877i	−1.04532	−	1.04532i	−0.998923	−	0.0464018i	$-0.985225\pi$
$593$	−619.877	−	619.877i	−1.04532	−	1.04532i	−0.0464018	−	0.998923i	$-0.514775\pi$
$594$		0			0
$595$	650.023	+	692.453i	1.09248	+	1.16379i
$596$	−1233.49	+	2136.46i	−2.06961	+	3.58466i
$597$		0			0
$598$	−409.572	+	1528.54i	−0.684904	+	2.55609i
$599$	884.670	−	510.764i	1.47691	−	0.852695i	0.477251	−	0.878767i	$-0.341633\pi$
$599$	884.670	−	510.764i	1.47691	−	0.852695i	0.999660	+	0.0260719i	$0.00829987\pi$
$600$		0			0
$601$	−175.183	+	303.426i	−0.291486	+	0.504869i	−0.974161	−	0.225853i	$-0.927483\pi$
$601$	−175.183	+	303.426i	−0.291486	+	0.504869i	0.682675	+	0.730722i	$0.260816\pi$
$602$	−962.191	+	962.191i	−1.59832	+	1.59832i
$603$		0			0
$604$			2142.34i			3.54692i
$605$	−76.7890	−	327.656i	−0.126924	−	0.541580i
$606$		0			0
$607$	−667.777	−	178.930i	−1.10013	−	0.294778i	−0.337311	−	0.941393i	$-0.609517\pi$
$607$	−667.777	−	178.930i	−1.10013	−	0.294778i	−0.762816	+	0.646615i	$0.776184\pi$
$608$	8.36176	−	31.2065i	0.0137529	−	0.0513265i
$609$		0			0
$610$	−88.4401	−	54.8571i	−0.144984	−	0.0899297i
$611$	1443.91			2.36319
$612$		0			0
$613$	−691.311	−	691.311i	−1.12775	−	1.12775i	−0.990542	−	0.137207i	$-0.956187\pi$
$613$	−691.311	−	691.311i	−1.12775	−	1.12775i	−0.137207	−	0.990542i	$-0.543813\pi$
$614$	−1507.43	−	870.316i	−2.45510	−	1.41745i
$615$		0			0
$616$	443.397	+	767.987i	0.719801	+	1.24673i
$617$	−163.775	−	43.8833i	−0.265437	−	0.0711237i	0.123646	−	0.992326i	$-0.460541\pi$
$617$	−163.775	−	43.8833i	−0.265437	−	0.0711237i	−0.389083	+	0.921203i	$0.627208\pi$
$618$		0			0
$619$	724.843	+	418.488i	1.17099	+	0.676071i	0.953913	−	0.300083i	$-0.0970144\pi$
$619$	724.843	+	418.488i	1.17099	+	0.676071i	0.217077	+	0.976154i	$0.430348\pi$
$620$	−1492.29	−	1589.70i	−2.40692	−	2.56403i
$621$		0			0
$622$	364.260	−	364.260i	0.585627	−	0.585627i
$623$	494.502	−	132.501i	0.793743	−	0.212683i
$624$		0			0
$625$	241.784	+	576.338i	0.386854	+	0.922141i
$626$	−1131.15	−	1959.21i	−1.80695	−	3.12973i
$627$		0			0
$628$	2185.10	−	585.496i	3.47946	−	0.932319i
$629$		−	463.330i		−	0.736613i
$630$		0			0
$631$	−249.800			−0.395880			−0.197940	−	0.980214i	$-0.563425\pi$
$631$	−249.800			−0.395880			−0.197940	+	0.980214i	$0.563425\pi$
$632$	−129.639	−	483.820i	−0.205125	−	0.765537i
$633$		0			0
$634$	612.144	−	353.422i	0.965527	−	0.557447i
$635$	−21.7251	+	11.6439i	−0.0342127	+	0.0183368i
$636$		0			0
$637$	39.3595	+	146.892i	0.0617889	+	0.230599i
$638$	−430.967	−	430.967i	−0.675497	−	0.675497i
$639$		0			0
$640$	−478.529	−	15.1243i	−0.747702	−	0.0236317i
$641$	606.068	−	1049.74i	0.945503	−	1.63766i	0.190763	−	0.981636i	$-0.438904\pi$
$641$	606.068	−	1049.74i	0.945503	−	1.63766i	0.754740	−	0.656024i	$-0.227763\pi$
$642$		0			0
$643$	304.854	−	1137.73i	0.474112	−	1.76941i	−0.150642	−	0.988588i	$-0.548134\pi$
$643$	304.854	−	1137.73i	0.474112	−	1.76941i	0.624754	−	0.780822i	$-0.285199\pi$
$644$	1133.98	−	654.706i	1.76085	−	1.01662i
$645$		0			0
$646$	43.7543	−	75.7847i	0.0677311	−	0.117314i
$647$	−2.27470	+	2.27470i	−0.00351577	+	0.00351577i	−0.708862	−	0.705347i	$-0.750791\pi$
$647$	−2.27470	+	2.27470i	−0.00351577	+	0.00351577i	0.705347	+	0.708862i	$0.250791\pi$
$648$		0			0
$649$			285.355i			0.439684i
$650$	−1484.84	−	987.294i	−2.28437	−	1.51891i
$651$		0			0
$652$	1418.83	+	380.176i	2.17613	+	0.583091i
$653$	−247.567	+	923.932i	−0.379122	+	1.41490i	0.468105	+	0.883673i	$0.344937\pi$
$653$	−247.567	+	923.932i	−0.379122	+	1.41490i	−0.847228	+	0.531230i	$0.821730\pi$
$654$		0			0
$655$	7.82024	+	33.3687i	0.0119393	+	0.0509446i
$656$	−88.9876			−0.135652
$657$		0			0
$658$	−1212.61	−	1212.61i	−1.84287	−	1.84287i
$659$	471.459	+	272.197i	0.715416	+	0.413045i	0.813063	−	0.582176i	$-0.197798\pi$
$659$	471.459	+	272.197i	0.715416	+	0.413045i	−0.0976474	+	0.995221i	$0.531132\pi$
$660$		0			0
$661$	188.615	+	326.690i	0.285347	+	0.494236i	0.972693	−	0.232094i	$-0.0745577\pi$
$661$	188.615	+	326.690i	0.285347	+	0.494236i	−0.687346	+	0.726330i	$0.741224\pi$
$662$	1891.94	+	506.943i	2.85791	+	0.765775i
$663$		0			0
$664$	1197.06	+	691.126i	1.80281	+	1.04085i
$665$	26.1559	+	0.826679i	0.0393322	+	0.00124313i
$666$		0			0
$667$	−359.323	+	359.323i	−0.538715	+	0.538715i
$668$	662.892	−	177.621i	0.992353	−	0.265900i
$669$		0			0
$670$	−408.136	+	1350.94i	−0.609158	+	2.01632i
$671$	−20.9990	−	36.3714i	−0.0312952	−	0.0542048i
$672$		0			0
$673$	681.161	−	182.517i	1.01213	−	0.271199i	0.285609	−	0.958346i	$-0.407804\pi$
$673$	681.161	−	182.517i	1.01213	−	0.271199i	0.726518	+	0.687148i	$0.241138\pi$
$674$			1743.14i			2.58626i
$675$		0			0
$676$	1991.44			2.94592
$677$	−67.7970	−	253.022i	−0.100143	−	0.373740i	0.897606	−	0.440799i	$-0.145305\pi$
$677$	−67.7970	−	253.022i	−0.100143	−	0.373740i	−0.997749	+	0.0670595i	$0.978638\pi$
$678$		0			0
$679$	485.440	−	280.269i	0.714933	−	0.412767i
$680$	2666.90	+	805.707i	3.92192	+	1.18486i
$681$		0			0
$682$	−326.873	−	1219.91i	−0.479286	−	1.78872i
$683$	334.973	+	334.973i	0.490443	+	0.490443i	0.908446	−	0.418003i	$-0.137270\pi$
$683$	334.973	+	334.973i	0.490443	+	0.490443i	−0.418003	+	0.908446i	$0.637270\pi$
$684$		0			0
$685$	0.822197	−	26.0141i	0.00120029	−	0.0379768i
$686$	661.797	−	1146.27i	0.964718	−	1.67094i
$687$		0			0
$688$	−478.179	+	1784.59i	−0.695028	+	2.59388i
$689$	504.218	−	291.110i	0.731811	−	0.422511i
$690$		0			0
$691$	429.525	−	743.960i	0.621600	−	1.07664i	−0.367588	−	0.929989i	$-0.619816\pi$
$691$	429.525	−	743.960i	0.621600	−	1.07664i	0.989188	−	0.146654i	$-0.0468503\pi$
$692$	−129.065	+	129.065i	−0.186510	+	0.186510i
$693$		0			0
$694$			99.5185i			0.143398i
$695$	611.190	−	143.238i	0.879409	−	0.206097i
$696$		0			0
$697$	−80.2606	−	21.5058i	−0.115151	−	0.0308547i
$698$	435.971	−	1627.06i	0.624600	−	2.33104i
$699$		0			0
$700$	291.113	+	1446.44i	0.415875	+	2.06634i
$701$	−492.085			−0.701975			−0.350988	−	0.936380i	$-0.614154\pi$
$701$	−492.085			−0.701975			−0.350988	+	0.936380i	$0.614154\pi$
$702$		0			0
$703$	−9.02721	−	9.02721i	−0.0128410	−	0.0128410i
$704$	109.813	+	63.4005i	0.155984	+	0.0900575i
$705$		0			0
$706$	−163.636	−	283.426i	−0.231779	−	0.401454i
$707$	−534.644	−	143.257i	−0.756215	−	0.202627i
$708$		0			0
$709$	762.679	+	440.333i	1.07571	+	0.621062i	0.929736	−	0.368226i	$-0.120035\pi$
$709$	762.679	+	440.333i	1.07571	+	0.621062i	0.145975	+	0.989288i	$0.453368\pi$
$710$	35.6677	−	1128.52i	0.0502362	−	1.58946i
$711$		0			0
$712$	1061.88	−	1061.88i	1.49140	−	1.49140i
$713$	−1017.11	+	272.534i	−1.42652	+	0.382236i
$714$		0			0
$715$	−339.922	−	634.225i	−0.475415	−	0.887028i
$716$	−94.2607	−	163.264i	−0.131649	−	0.228023i
$717$		0			0
$718$	330.163	−	88.4670i	0.459838	−	0.123213i
$719$		−	212.916i		−	0.296128i	−0.988978	−	0.148064i	$-0.952696\pi$
$719$		−	212.916i		−	0.296128i	0.988978	−	0.148064i	$-0.0473042\pi$
$720$		0			0
$721$	−136.969			−0.189972
$722$	338.686	+	1263.99i	0.469094	+	1.75068i
$723$		0			0
$724$	1349.00	−	778.848i	1.86327	−	1.07576i
$725$	−254.411	−	512.969i	−0.350911	−	0.707543i
$726$		0			0
$727$	81.3033	+	303.428i	0.111834	+	0.417370i	0.999031	−	0.0440214i	$-0.0140170\pi$
$727$	81.3033	+	303.428i	0.111834	+	0.417370i	−0.887197	+	0.461392i	$0.847350\pi$
$728$	−1680.72	−	1680.72i	−2.30868	−	2.30868i
$729$		0			0
$730$	158.658	−	148.936i	0.217340	−	0.204022i
$731$	−862.568	+	1494.01i	−1.17998	+	2.04379i
$732$		0			0
$733$	−142.552	+	532.013i	−0.194478	+	0.725802i	0.797923	+	0.602759i	$0.205932\pi$
$733$	−142.552	+	532.013i	−0.194478	+	0.725802i	−0.992401	+	0.123043i	$0.960735\pi$
$734$	−535.596	+	309.226i	−0.729694	+	0.421289i
$735$		0			0
$736$	439.844	−	761.832i	0.597614	−	1.03510i
$737$	−402.701	+	402.701i	−0.546406	+	0.546406i
$738$		0			0
$739$			399.157i			0.540131i	0.962842	+	0.270066i	$0.0870454\pi$
$739$			399.157i			0.540131i	−0.962842	+	0.270066i	$0.912955\pi$
$740$	379.405	−	611.673i	0.512710	−	0.826585i
$741$		0			0
$742$	−667.925	−	178.970i	−0.900169	−	0.241199i
$743$	−50.7168	+	189.278i	−0.0682595	+	0.254748i	−0.991621	−	0.129185i	$-0.958764\pi$
$743$	−50.7168	+	189.278i	−0.0682595	+	0.254748i	0.923361	+	0.383933i	$0.125431\pi$
$744$		0			0
$745$	−1307.05	+	306.317i	−1.75442	+	0.411164i
$746$	−357.578			−0.479327
$747$		0			0
$748$	1407.88	+	1407.88i	1.88220	+	1.88220i
$749$	352.635	+	203.594i	0.470807	+	0.271821i
$750$		0			0
$751$	−406.615	−	704.278i	−0.541431	−	0.937787i	−0.998822	−	0.0485210i	$-0.984549\pi$
$751$	−406.615	−	704.278i	−0.541431	−	0.937787i	0.457391	−	0.889266i	$-0.348784\pi$
$752$	−2249.04	−	602.629i	−2.99075	−	0.801369i
$753$		0			0
$754$	1414.74	+	816.799i	1.87631	+	1.08329i
$755$	−849.977	+	797.895i	−1.12580	+	1.05681i
$756$		0			0
$757$	−25.9855	+	25.9855i	−0.0343270	+	0.0343270i	−0.724062	−	0.689735i	$-0.757727\pi$
$757$	−25.9855	+	25.9855i	−0.0343270	+	0.0343270i	0.689735	+	0.724062i	$0.257727\pi$
$758$	1127.28	−	302.055i	1.48718	−	0.398489i
$759$		0			0
$760$	67.6580	−	36.2623i	0.0890237	−	0.0477136i
$761$	−195.191	−	338.082i	−0.256493	−	0.444260i	0.708807	−	0.705403i	$-0.249234\pi$
$761$	−195.191	−	338.082i	−0.256493	−	0.444260i	−0.965300	+	0.261143i	$0.915901\pi$
$762$		0			0
$763$	230.311	−	61.7117i	0.301850	−	0.0808804i
$764$			1376.16i			1.80126i
$765$		0			0
$766$	548.201			0.715667
$767$	−197.956	−	738.781i	−0.258091	−	0.963208i
$768$		0			0
$769$	−535.244	+	309.023i	−0.696025	+	0.401850i	−0.805865	−	0.592099i	$-0.798299\pi$
$769$	−535.244	+	309.023i	−0.696025	+	0.401850i	0.109840	+	0.993949i	$0.464966\pi$
$770$	−247.159	+	818.099i	−0.320985	+	1.06247i
$771$		0			0
$772$	−374.850	−	1398.96i	−0.485557	−	1.81212i
$773$	−929.795	−	929.795i	−1.20284	−	1.20284i	−0.973299	−	0.229541i	$-0.926278\pi$
$773$	−929.795	−	929.795i	−1.20284	−	1.20284i	−0.229541	−	0.973299i	$-0.573722\pi$
$774$		0			0
$775$	74.9261	−	1184.14i	0.0966788	−	1.52792i
$776$	822.129	−	1423.97i	1.05945	−	1.83501i
$777$		0			0
$778$	−302.642	+	1129.48i	−0.389000	+	1.45177i
$779$	−1.98275	+	1.14474i	−0.00254525	+	0.00146950i
$780$		0			0
$781$	227.820	−	394.596i	0.291703	−	0.505244i
$782$	1684.86	−	1684.86i	2.15455	−	2.15455i
$783$		0			0
$784$		−	245.227i		−	0.312790i
$785$	1046.12	+	648.881i	1.33264	+	0.826600i
$786$		0			0
$787$	−360.308	−	96.5441i	−0.457824	−	0.122674i	0.0225339	−	0.999746i	$-0.492827\pi$
$787$	−360.308	−	96.5441i	−0.457824	−	0.122674i	−0.480358	+	0.877072i	$0.659493\pi$
$788$	105.562	−	393.963i	0.133962	−	0.499953i
$789$		0			0
$790$	254.442	−	410.209i	0.322078	−	0.519251i
$791$	−621.061			−0.785160
$792$		0			0
$793$	79.5977	+	79.5977i	0.100375	+	0.100375i
$794$	1392.06	+	803.706i	1.75322	+	1.01222i
$795$		0			0
$796$	−708.017	−	1226.32i	−0.889469	−	1.54060i
$797$	−19.5942	−	5.25026i	−0.0245850	−	0.00658753i	0.246506	−	0.969141i	$-0.420718\pi$
$797$	−19.5942	−	5.25026i	−0.0245850	−	0.00658753i	−0.271091	+	0.962554i	$0.587384\pi$
$798$		0			0
$799$	−1882.84	−	1087.06i	−2.35650	−	1.36052i
$800$	655.244	+	743.766i	0.819055	+	0.929708i
$801$		0			0
$802$	−1026.44	+	1026.44i	−1.27986	+	1.27986i
$803$	84.8244	−	22.7286i	0.105634	−	0.0283046i
$804$		0			0
$805$	682.099	+	206.071i	0.847327	+	0.255989i
$806$	1692.54	+	2931.57i	2.09993	+	3.63718i
$807$		0			0
$808$	−1568.30	+	420.225i	−1.94097	+	0.520081i
$809$		−	259.909i		−	0.321272i	−0.987014	−	0.160636i	$-0.948645\pi$
$809$		−	259.909i		−	0.321272i	0.987014	−	0.160636i	$-0.0513545\pi$
$810$		0			0
$811$	−114.146			−0.140747			−0.0703734	−	0.997521i	$-0.522419\pi$
$811$	−114.146			−0.140747			−0.0703734	+	0.997521i	$0.522419\pi$
$812$	−349.851	−	1305.66i	−0.430851	−	1.60796i
$813$		0			0
$814$	361.064	−	208.461i	0.443568	−	0.256094i
$815$	377.597	+	704.519i	0.463309	+	0.864440i
$816$		0			0
$817$	12.3026	+	45.9140i	0.0150583	+	0.0561983i
$818$	724.758	+	724.758i	0.886012	+	0.886012i
$819$		0			0
$820$	−88.3471	−	94.1139i	−0.107740	−	0.114773i
$821$	−509.691	+	882.810i	−0.620817	+	1.07529i	0.368517	+	0.929621i	$0.379866\pi$
$821$	−509.691	+	882.810i	−0.620817	+	1.07529i	−0.989334	+	0.145666i	$0.953468\pi$
$822$		0			0
$823$	−142.374	+	531.348i	−0.172994	+	0.645624i	0.823890	+	0.566749i	$0.191799\pi$
$823$	−142.374	+	531.348i	−0.172994	+	0.645624i	−0.996885	+	0.0788743i	$0.974867\pi$
$824$	−347.952	+	200.890i	−0.422272	+	0.243799i
$825$		0			0
$826$	−454.191	+	786.681i	−0.549868	+	0.952399i
$827$	681.141	−	681.141i	0.823629	−	0.823629i	−0.162998	−	0.986626i	$-0.552116\pi$
$827$	681.141	−	681.141i	0.823629	−	0.823629i	0.986626	+	0.162998i	$0.0521163\pi$
$828$		0			0
$829$		−	89.2952i		−	0.107714i	−0.998549	−	0.0538572i	$-0.982848\pi$
$829$		−	89.2952i		−	0.107714i	0.998549	−	0.0538572i	$-0.0171516\pi$
$830$	303.953	+	1296.96i	0.366209	+	1.56260i
$831$		0			0
$832$	−328.286	−	87.9640i	−0.394574	−	0.105726i
$833$	59.2643	−	221.177i	0.0711457	−	0.265519i
$834$		0			0
$835$	317.360	+	196.850i	0.380071	+	0.235749i
$836$	54.8606			0.0656227
$837$		0			0
$838$	542.416	+	542.416i	0.647275	+	0.647275i
$839$	−691.396	−	399.178i	−0.824072	−	0.475778i	0.0277467	−	0.999615i	$-0.491167\pi$
$839$	−691.396	−	399.178i	−0.824072	−	0.475778i	−0.851819	+	0.523837i	$0.824500\pi$
$840$		0			0
$841$	−158.210	−	274.028i	−0.188122	−	0.325836i
$842$	−429.640	−	115.122i	−0.510261	−	0.136724i
$843$		0			0
$844$	−1812.44	−	1046.41i	−2.14745	−	1.23983i
$845$	741.694	+	790.108i	0.877744	+	0.935039i
$846$		0			0
$847$	305.698	−	305.698i	0.360919	−	0.360919i
$848$	−906.872	+	242.996i	−1.06942	+	0.286551i
$849$		0			0
$850$	1192.92	+	2405.30i	1.40344	+	2.82976i
$851$	−173.806	−	301.041i	−0.204238	−	0.353750i
$852$		0			0
$853$	−858.032	+	229.909i	−1.00590	+	0.269530i	−0.723915	−	0.689889i	$-0.757659\pi$
$853$	−858.032	+	229.909i	−1.00590	+	0.269530i	−0.281984	+	0.959419i	$0.590993\pi$
$854$		−	133.694i		−	0.156550i
$855$		0			0
$856$	1194.43			1.39536
$857$	183.846	+	686.124i	0.214523	+	0.800611i	0.986334	+	0.164759i	$0.0526846\pi$
$857$	183.846	+	686.124i	0.214523	+	0.800611i	−0.771811	+	0.635852i	$0.780649\pi$
$858$		0			0
$859$	−468.890	+	270.714i	−0.545855	+	0.315150i	−0.747449	−	0.664320i	$-0.768721\pi$
$859$	−468.890	+	270.714i	−0.545855	+	0.315150i	0.201593	+	0.979469i	$0.435388\pi$
$860$	−2362.13	+	1266.02i	−2.74666	+	1.47211i
$861$		0			0
$862$	−640.499	−	2390.37i	−0.743038	−	2.77305i
$863$	929.292	+	929.292i	1.07682	+	1.07682i	0.996793	+	0.0800229i	$0.0254993\pi$
$863$	929.292	+	929.292i	1.07682	+	1.07682i	0.0800229	+	0.996793i	$0.474501\pi$
$864$		0			0
$865$	−99.2759	−	3.13769i	−0.114770	−	0.00362739i
$866$	454.354	−	786.965i	0.524659	−	0.908736i
$867$		0			0
$868$	724.949	−	2705.55i	0.835195	−	3.11699i
$869$	168.700	−	97.3992i	0.194132	−	0.112082i
$870$		0			0
$871$	763.227	−	1321.95i	0.876265	−	1.51774i
$872$	494.563	−	494.563i	0.567160	−	0.567160i
$873$		0			0
$874$		−	65.6532i		−	0.0751181i
$875$	−465.454	+	654.212i	−0.531948	+	0.747671i
$876$		0			0
$877$	1011.34	+	270.987i	1.15318	+	0.308993i	0.784238	−	0.620461i	$-0.213054\pi$
$877$	1011.34	+	270.987i	1.15318	+	0.308993i	0.368939	+	0.929454i	$0.379721\pi$
$878$	1.43501	−	5.35553i	0.00163441	−	0.00609969i
$879$		0			0
$880$	264.765	+	1129.74i	0.300870	+	1.28380i
$881$	195.699			0.222133			0.111066	−	0.993813i	$-0.464573\pi$
$881$	195.699			0.222133			0.111066	+	0.993813i	$0.464573\pi$
$882$		0			0
$883$	771.971	+	771.971i	0.874260	+	0.874260i	0.992933	−	0.118674i	$-0.0378642\pi$
$883$	771.971	+	771.971i	0.874260	+	0.874260i	−0.118674	+	0.992933i	$0.537864\pi$
$884$	−4621.67	−	2668.32i	−5.22813	−	3.01846i
$885$		0			0
$886$	−687.738	−	1191.20i	−0.776228	−	1.34447i
$887$	561.906	+	150.562i	0.633491	+	0.169743i	0.561253	−	0.827644i	$-0.310319\pi$
$887$	561.906	+	150.562i	0.633491	+	0.169743i	0.0722376	+	0.997387i	$0.476986\pi$
$888$		0			0
$889$	−27.4223	−	15.8323i	−0.0308462	−	0.0178091i
$890$	1446.51	+	45.7182i	1.62529	+	0.0513687i
$891$		0			0
$892$	−731.730	+	731.730i	−0.820325	+	0.820325i
$893$	−57.8635	+	15.5045i	−0.0647968	+	0.0173622i
$894$		0			0
$895$	29.6689	−	98.2044i	0.0331496	−	0.109726i
$896$	−307.521	−	532.641i	−0.343215	−	0.594466i
$897$		0			0
$898$	−989.958	+	265.258i	−1.10240	+	0.295388i
$899$			1087.01i			1.20914i
$900$		0			0
$901$	−876.659			−0.972985
$902$	−19.3517	−	72.2215i	−0.0214542	−	0.0800681i
$903$		0			0
$904$	−1577.72	+	910.898i	−1.74527	+	1.00763i
$905$	811.434	+	245.145i	0.896612	+	0.270879i
$906$		0			0
$907$	19.8979	+	74.2598i	0.0219381	+	0.0818741i	0.976027	−	0.217649i	$-0.0698390\pi$
$907$	19.8979	+	74.2598i	0.0219381	+	0.0818741i	−0.954089	+	0.299524i	$0.903172\pi$
$908$	−827.766	−	827.766i	−0.911637	−	0.911637i
$909$		0			0
$910$	72.3617	−	2289.51i	0.0795183	−	2.51594i
$911$	−649.456	+	1124.89i	−0.712905	+	1.23479i	0.250857	+	0.968024i	$0.419288\pi$
$911$	−649.456	+	1124.89i	−0.712905	+	1.23479i	−0.963762	+	0.266763i	$0.914046\pi$
$912$		0			0
$913$	−139.133	+	519.250i	−0.152391	+	0.568729i
$914$	−2619.32	+	1512.27i	−2.86578	+	1.65456i
$915$		0			0
$916$	−869.511	+	1506.04i	−0.949248	+	1.64415i
$917$	−31.1325	+	31.1325i	−0.0339504	+	0.0339504i
$918$		0			0
$919$			1764.81i			1.92036i	0.279385	+	0.960179i	$0.409869\pi$
$919$			1764.81i			1.92036i	−0.279385	+	0.960179i	$0.590131\pi$
$920$	2035.02	−	476.924i	2.21198	−	0.518396i
$921$		0			0
$922$	1968.57	+	527.476i	2.13511	+	0.572100i
$923$	−316.085	+	1179.65i	−0.342454	+	1.27806i
$924$		0			0
$925$	383.988	−	77.2823i	0.415123	−	0.0835485i
$926$	−748.725			−0.808558
$927$		0			0
$928$	−642.132	−	642.132i	−0.691952	−	0.691952i
$929$	894.515	+	516.449i	0.962880	+	0.555919i	0.897058	−	0.441913i	$-0.145700\pi$
$929$	894.515	+	516.449i	0.962880	+	0.555919i	0.0658215	+	0.997831i	$0.479033\pi$
$930$		0			0
$931$	−3.15461	−	5.46394i	−0.00338841	−	0.00586890i
$932$	424.942	+	113.863i	0.455947	+	0.122171i
$933$		0			0
$934$	2826.94	+	1632.14i	3.02671	+	1.74747i
$935$	−34.2270	+	1082.94i	−0.0366065	+	1.15822i
$936$		0			0
$937$	−258.161	+	258.161i	−0.275519	+	0.275519i	−0.831317	−	0.555798i	$-0.812413\pi$
$937$	−258.161	+	258.161i	−0.275519	+	0.275519i	0.555798	+	0.831317i	$0.312413\pi$
$938$	−1751.15	+	469.220i	−1.86690	+	0.500235i
$939$		0			0
$940$	−1595.51	−	2976.89i	−1.69735	−	3.16691i
$941$	226.133	+	391.675i	0.240312	+	0.416232i	0.960803	−	0.277232i	$-0.0894170\pi$
$941$	226.133	+	391.675i	0.240312	+	0.416232i	−0.720491	+	0.693464i	$0.756084\pi$
$942$		0			0
$943$	−60.2154	+	16.1347i	−0.0638551	+	0.0171099i
$944$			1233.35i			1.30652i
$945$		0			0
$946$	−1552.34			−1.64095
$947$	−47.4308	−	177.014i	−0.0500854	−	0.186921i	0.936351	−	0.351065i	$-0.114180\pi$
$947$	−47.4308	−	177.014i	−0.0500854	−	0.186921i	−0.986436	+	0.164144i	$0.947514\pi$
$948$		0			0
$949$	−203.842	+	117.688i	−0.214797	+	0.124013i
$950$	70.1054	+	23.6211i	0.0737951	+	0.0248643i
$951$		0			0
$952$	926.294	+	3456.98i	0.972998	+	3.63128i
$953$	−681.132	−	681.132i	−0.714724	−	0.714724i	0.252796	−	0.967520i	$-0.418650\pi$
$953$	−681.132	−	681.132i	−0.714724	−	0.714724i	−0.967520	+	0.252796i	$0.918650\pi$
$954$		0			0
$955$	−545.994	+	512.538i	−0.571721	+	0.536689i
$956$	−1421.44	+	2462.01i	−1.48687	+	2.57533i
$957$		0			0
$958$	616.069	−	2299.20i	0.643079	−	2.40000i
$959$	28.9558	−	16.7176i	0.0301937	−	0.0174324i
$960$		0			0
$961$	−645.736	+	1118.45i	−0.671942	+	1.16384i
$962$	−790.178	+	790.178i	−0.821391	+	0.821391i
$963$		0			0
$964$			145.046i			0.150463i
$965$	415.430	−	669.752i	0.430498	−	0.694044i
$966$		0			0
$967$	669.698	+	179.445i	0.692553	+	0.185569i	0.587892	−	0.808939i	$-0.299958\pi$
$967$	669.698	+	179.445i	0.692553	+	0.185569i	0.104660	+	0.994508i	$0.466624\pi$
$968$	328.223	−	1224.95i	0.339073	−	1.26544i
$969$		0			0
$970$	1542.80	−	361.568i	1.59051	−	0.372750i
$971$	−1004.15			−1.03414			−0.517070	−	0.855943i	$-0.672977\pi$
$971$	−1004.15			−1.03414			−0.517070	+	0.855943i	$0.672977\pi$
$972$		0			0
$973$	570.231	+	570.231i	0.586054	+	0.586054i
$974$	2775.02	+	1602.16i	2.84909	+	1.64493i
$975$		0			0
$976$	−90.7612	−	157.203i	−0.0929931	−	0.161069i
$977$	1283.24	+	343.843i	1.31345	+	0.351937i	0.846519	−	0.532358i	$-0.178694\pi$
$977$	1283.24	+	343.843i	1.31345	+	0.351937i	0.466928	+	0.884295i	$0.345361\pi$
$978$		0			0
$979$	505.785	+	292.015i	0.516634	+	0.298279i
$980$	259.354	−	243.462i	0.264647	−	0.248430i
$981$		0			0
$982$	347.768	−	347.768i	0.354143	−	0.354143i
$983$	−1233.76	+	330.584i	−1.25509	+	0.336301i	−0.824302	−	0.566150i	$-0.808432\pi$
$983$	−1233.76	+	330.584i	−1.25509	+	0.336301i	−0.430791	+	0.902452i	$0.641766\pi$
$984$		0			0
$985$	195.621	−	104.846i	0.198600	−	0.106443i
$986$	−1229.87	−	2130.19i	−1.24733	−	2.16044i
$987$		0			0
$988$	−142.033	+	38.0577i	−0.143758	+	0.0385200i
$989$			1294.28i			1.30868i
$990$		0			0
$991$	−1001.31			−1.01040			−0.505201	−	0.863002i	$-0.668581\pi$
$991$	−1001.31			−1.01040			−0.505201	+	0.863002i	$0.668581\pi$
$992$	−487.034	−	1817.64i	−0.490962	−	1.83230i
$993$		0			0
$994$	1256.13	−	725.228i	1.26371	−	0.729606i
$995$	222.851	−	737.640i	0.223971	−	0.741346i
$996$		0			0
$997$	−151.601	−	565.782i	−0.152057	−	0.567485i	−0.999339	−	0.0363420i	$-0.988429\pi$
$997$	−151.601	−	565.782i	−0.152057	−	0.567485i	0.847282	−	0.531143i	$-0.178237\pi$
$998$	2176.09	+	2176.09i	2.18045	+	2.18045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.m.298.4		16
3.2	odd	2		405.3.l.j.298.1		16
5.2	odd	4		405.3.l.j.217.1		16
9.2	odd	6		405.3.g.f.163.1	yes	16
9.4	even	3		405.3.l.j.28.1		16
9.5	odd	6	inner	405.3.l.m.28.4		16
9.7	even	3		405.3.g.f.163.8	yes	16
15.2	even	4	inner	405.3.l.m.217.4		16
45.2	even	12		405.3.g.f.82.1	✓	16
45.7	odd	12		405.3.g.f.82.8	yes	16
45.22	odd	12	inner	405.3.l.m.352.4		16
45.32	even	12		405.3.l.j.352.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.f.82.1	✓	16	45.2	even	12
405.3.g.f.82.8	yes	16	45.7	odd	12
405.3.g.f.163.1	yes	16	9.2	odd	6
405.3.g.f.163.8	yes	16	9.7	even	3
405.3.l.j.28.1		16	9.4	even	3
405.3.l.j.217.1		16	5.2	odd	4
405.3.l.j.298.1		16	3.2	odd	2
405.3.l.j.352.1		16	45.32	even	12
405.3.l.m.28.4		16	9.5	odd	6	inner
405.3.l.m.217.4		16	15.2	even	4	inner
405.3.l.m.298.4		16	1.1	even	1	trivial
405.3.l.m.352.4		16	45.22	odd	12	inner

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939918 + 3.50782i) q^{2} +(-7.95726 + 4.59412i) q^{4} +(-4.78634 - 1.44602i) q^{5} +(-1.66244 - 6.20430i) q^{7} +(-13.3229 - 13.3229i) q^{8} +(0.573606 - 18.1488i) q^{10} +(3.66378 - 6.34586i) q^{11} +(-5.08326 + 18.9710i) q^{13} +(20.2010 - 11.6631i) q^{14} +(15.8355 - 27.4278i) q^{16} +(20.9110 - 20.9110i) q^{17} -0.814832i q^{19} +(44.7293 - 10.4827i) q^{20} +(25.7038 + 6.88731i) q^{22} +(5.74237 - 21.4308i) q^{23} +(20.8181 + 13.8423i) q^{25} -71.3246 q^{26} +(41.7318 + 41.7318i) q^{28} +(-19.8352 - 11.4518i) q^{29} +(-23.7301 - 41.1018i) q^{31} +(38.2981 + 10.2620i) q^{32} +(93.0066 + 53.6974i) q^{34} +(-1.01454 + 32.0998i) q^{35} +(11.0786 - 11.0786i) q^{37} +(2.85828 - 0.765875i) q^{38} +(44.5028 + 83.0332i) q^{40} +(-1.40488 - 2.43332i) q^{41} +(-56.3479 + 15.0984i) q^{43} +67.3275i q^{44} +80.5728 q^{46} +(-19.0278 - 71.0129i) q^{47} +(6.70561 - 3.87149i) q^{49} +(-28.9889 + 86.0366i) q^{50} +(-46.7063 - 174.310i) q^{52} +(-20.9617 - 20.9617i) q^{53} +(-26.7123 + 25.0755i) q^{55} +(-60.5109 + 104.808i) q^{56} +(21.5276 - 80.3420i) q^{58} +(-33.7253 + 19.4713i) q^{59} +(2.86576 - 4.96364i) q^{61} +(121.873 - 121.873i) q^{62} +17.3046i q^{64} +(51.7626 - 83.4511i) q^{65} +(-75.0726 - 20.1156i) q^{67} +(-70.3264 + 262.462i) q^{68} +(-113.554 + 26.6123i) q^{70} +62.1816 q^{71} +(8.47426 + 8.47426i) q^{73} +(49.2748 + 28.4488i) q^{74} +(3.74344 + 6.48382i) q^{76} +(-45.4624 - 12.1816i) q^{77} +(23.0227 + 13.2922i) q^{79} +(-115.455 + 108.380i) q^{80} +(7.21519 - 7.21519i) q^{82} +(-70.8625 + 18.9875i) q^{83} +(-130.325 + 69.8494i) q^{85} +(-105.925 - 183.467i) q^{86} +(-133.358 + 35.7331i) q^{88} +79.7031i q^{89} +126.152 q^{91} +(52.7623 + 196.912i) q^{92} +(231.216 - 133.493i) q^{94} +(-1.17826 + 3.90006i) q^{95} +(22.5867 + 84.2946i) q^{97} +(19.8832 + 19.8832i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 12 q^{5} - 20 q^{7} - 56 q^{10} + 22 q^{13} + 168 q^{14} + 16 q^{16} + 96 q^{20} - 16 q^{22} - 36 q^{23} + 46 q^{25} + 176 q^{28} + 252 q^{29} - 160 q^{31} + 114 q^{32} + 4 q^{37} - 192 q^{38}+ \cdots - 152 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 - 12 * q^5 - 20 * q^7 - 56 * q^10 + 22 * q^13 + 168 * q^14 + 16 * q^16 + 96 * q^20 - 16 * q^22 - 36 * q^23 + 46 * q^25 + 176 * q^28 + 252 * q^29 - 160 * q^31 + 114 * q^32 + 4 * q^37 - 192 * q^38 + 264 * q^40 - 128 * q^43 - 16 * q^46 - 204 * q^47 - 540 * q^50 + 154 * q^52 - 364 * q^55 - 246 * q^58 - 36 * q^59 - 4 * q^61 - 24 * q^65 - 44 * q^67 - 966 * q^68 + 18 * q^70 + 364 * q^73 - 288 * q^74 + 456 * q^76 + 204 * q^77 + 32 * q^82 - 12 * q^83 - 32 * q^85 - 420 * q^88 + 224 * q^91 + 960 * q^92 - 114 * q^95 - 152 * q^97

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