LMFDB - Embedded newform 315.3.ca.b.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, 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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.14
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.87375 - 0.770020i) q^{2} +(4.20143 - 2.42570i) q^{4} +(-3.78688 - 3.26489i) q^{5} +(-1.65502 - 6.80154i) q^{7} +(1.79111 - 1.79111i) q^{8} +O(q^{10})$	\(q+(2.87375 - 0.770020i) q^{2} +(4.20143 - 2.42570i) q^{4} +(-3.78688 - 3.26489i) q^{5} +(-1.65502 - 6.80154i) q^{7} +(1.79111 - 1.79111i) q^{8} +(-13.3966 - 6.46653i) q^{10} +(-6.96127 - 12.0573i) q^{11} +(7.79302 - 7.79302i) q^{13} +(-9.99344 - 18.2715i) q^{14} +(-5.93477 + 10.2793i) q^{16} +(6.92421 - 25.8415i) q^{17} +(28.5616 + 16.4901i) q^{19} +(-23.8300 - 4.53140i) q^{20} +(-29.2893 - 29.2893i) q^{22} +(5.48688 + 20.4773i) q^{23} +(3.68094 + 24.7275i) q^{25} +(16.3944 - 28.3960i) q^{26} +(-23.4519 - 24.5616i) q^{28} +18.1531i q^{29} +(-11.5772 - 20.0522i) q^{31} +(-11.7622 + 43.8970i) q^{32} -79.5940i q^{34} +(-15.9389 + 31.1601i) q^{35} +(-20.1574 + 5.40117i) q^{37} +(94.7768 + 25.3954i) q^{38} +(-12.6305 + 0.934937i) q^{40} +1.69819 q^{41} +(26.7992 - 26.7992i) q^{43} +(-58.4946 - 33.7719i) q^{44} +(31.5359 + 54.6218i) q^{46} +(10.2827 - 2.75524i) q^{47} +(-43.5218 + 22.5134i) q^{49} +(29.6188 + 68.2264i) q^{50} +(13.8383 - 51.6453i) q^{52} +(43.0869 + 11.5451i) q^{53} +(-13.0042 + 68.3872i) q^{55} +(-15.1466 - 9.21797i) q^{56} +(13.9783 + 52.1677i) q^{58} +(-9.04603 + 5.22273i) q^{59} +(40.5827 - 70.2914i) q^{61} +(-48.7105 - 48.7105i) q^{62} +87.7280i q^{64} +(-54.9546 + 4.06786i) q^{65} +(10.9599 - 40.9029i) q^{67} +(-33.5921 - 125.367i) q^{68} +(-21.8107 + 101.820i) q^{70} +20.1105 q^{71} +(6.28085 + 1.68295i) q^{73} +(-53.7685 + 31.0433i) q^{74} +160.000 q^{76} +(-70.4869 + 67.3023i) q^{77} +(10.5341 + 6.08184i) q^{79} +(56.0352 - 19.5502i) q^{80} +(4.88019 - 1.30764i) q^{82} +(-20.6649 + 20.6649i) q^{83} +(-110.591 + 75.2519i) q^{85} +(56.3783 - 97.6501i) q^{86} +(-34.0643 - 9.12749i) q^{88} +(145.002 + 83.7168i) q^{89} +(-65.9021 - 40.1069i) q^{91} +(72.7245 + 72.7245i) q^{92} +(27.4284 - 15.8358i) q^{94} +(-54.3212 - 155.697i) q^{95} +(-66.3082 - 66.3082i) q^{97} +(-107.735 + 98.2105i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	2.87375	−	0.770020i	1.43688	−	0.385010i	0.545438	−	0.838151i	$-0.316363\pi$
$2$	2.87375	−	0.770020i	1.43688	−	0.385010i	0.891439	+	0.453141i	$0.149697\pi$
$3$		0			0
$3$		0			0
$4$	4.20143	−	2.42570i	1.05036	−	0.606424i
$5$	−3.78688	−	3.26489i	−0.757376	−	0.652979i
$5$	−3.78688	−	3.26489i	−0.757376	−	0.652979i
$6$		0			0
$7$	−1.65502	−	6.80154i	−0.236431	−	0.971648i
$7$	−1.65502	−	6.80154i	−0.236431	−	0.971648i
$8$	1.79111	−	1.79111i	0.223889	−	0.223889i
$9$		0			0
$10$	−13.3966	−	6.46653i	−1.33966	−	0.646653i
$11$	−6.96127	−	12.0573i	−0.632842	−	1.09612i	−0.986968	−	0.160917i	$-0.948555\pi$
$11$	−6.96127	−	12.0573i	−0.632842	−	1.09612i	0.354126	−	0.935198i	$-0.384779\pi$
$12$		0			0
$13$	7.79302	−	7.79302i	0.599463	−	0.599463i	−0.340707	−	0.940170i	$-0.610666\pi$
$13$	7.79302	−	7.79302i	0.599463	−	0.599463i	0.940170	+	0.340707i	$0.110666\pi$
$14$	−9.99344	−	18.2715i	−0.713817	−	1.30511i
$15$		0			0
$16$	−5.93477	+	10.2793i	−0.370923	+	0.642458i
$17$	6.92421	−	25.8415i	0.407307	−	1.52009i	−0.392455	−	0.919771i	$-0.628374\pi$
$17$	6.92421	−	25.8415i	0.407307	−	1.52009i	0.799761	−	0.600318i	$-0.204959\pi$
$18$		0			0
$19$	28.5616	+	16.4901i	1.50324	+	0.867898i	0.999993	+	0.00375778i	$0.00119614\pi$
$19$	28.5616	+	16.4901i	1.50324	+	0.867898i	0.503251	+	0.864140i	$0.332137\pi$
$20$	−23.8300	−	4.53140i	−1.19150	−	0.226570i
$21$		0			0
$22$	−29.2893	−	29.2893i	−1.33133	−	1.33133i
$23$	5.48688	+	20.4773i	0.238560	+	0.890318i	0.976512	+	0.215464i	$0.0691265\pi$
$23$	5.48688	+	20.4773i	0.238560	+	0.890318i	−0.737952	+	0.674854i	$0.764207\pi$
$24$		0			0
$25$	3.68094	+	24.7275i	0.147238	+	0.989101i
$26$	16.3944	−	28.3960i	0.630555	−	1.09215i
$27$		0			0
$28$	−23.4519	−	24.5616i	−0.837569	−	0.877201i
$29$			18.1531i			0.625971i	0.949758	+	0.312985i	$0.101329\pi$
$29$			18.1531i			0.625971i	−0.949758	+	0.312985i	$0.898671\pi$
$30$		0			0
$31$	−11.5772	−	20.0522i	−0.373457	−	0.646846i	0.616638	−	0.787247i	$-0.288494\pi$
$31$	−11.5772	−	20.0522i	−0.373457	−	0.646846i	−0.990095	+	0.140401i	$0.955161\pi$
$32$	−11.7622	+	43.8970i	−0.367567	+	1.37178i
$33$		0			0
$34$		−	79.5940i		−	2.34100i
$35$	−15.9389	+	31.1601i	−0.455398	+	0.890288i
$36$		0			0
$37$	−20.1574	+	5.40117i	−0.544796	+	0.145978i	−0.520712	−	0.853732i	$-0.674333\pi$
$37$	−20.1574	+	5.40117i	−0.544796	+	0.145978i	−0.0240837	+	0.999710i	$0.507667\pi$
$38$	94.7768	+	25.3954i	2.49413	+	0.668299i
$39$		0			0
$40$	−12.6305	+	0.934937i	−0.315762	+	0.0233734i
$41$	1.69819			0.0414193			0.0207097	−	0.999786i	$-0.493407\pi$
$41$	1.69819			0.0414193			0.0207097	+	0.999786i	$0.493407\pi$
$42$		0			0
$43$	26.7992	−	26.7992i	0.623236	−	0.623236i	−0.323121	−	0.946358i	$-0.604732\pi$
$43$	26.7992	−	26.7992i	0.623236	−	0.623236i	0.946358	+	0.323121i	$0.104732\pi$
$44$	−58.4946	−	33.7719i	−1.32942	−	0.767542i
$45$		0			0
$46$	31.5359	+	54.6218i	0.685563	+	1.18743i
$47$	10.2827	−	2.75524i	0.218781	−	0.0586222i	−0.147763	−	0.989023i	$-0.547207\pi$
$47$	10.2827	−	2.75524i	0.218781	−	0.0586222i	0.366544	+	0.930401i	$0.380541\pi$
$48$		0			0
$49$	−43.5218	+	22.5134i	−0.888200	+	0.459456i
$50$	29.6188	+	68.2264i	0.592376	+	1.36453i
$51$		0			0
$52$	13.8383	−	51.6453i	0.266122	−	0.993179i
$53$	43.0869	+	11.5451i	0.812961	+	0.217832i	0.641267	−	0.767318i	$-0.278409\pi$
$53$	43.0869	+	11.5451i	0.812961	+	0.217832i	0.171694	+	0.985150i	$0.445076\pi$
$54$		0			0
$55$	−13.0042	+	68.3872i	−0.236440	+	1.24340i
$56$	−15.1466	−	9.21797i	−0.270475	−	0.164607i
$57$		0			0
$58$	13.9783	+	52.1677i	0.241005	+	0.899443i
$59$	−9.04603	+	5.22273i	−0.153323	+	0.0885208i	−0.574698	−	0.818365i	$-0.694881\pi$
$59$	−9.04603	+	5.22273i	−0.153323	+	0.0885208i	0.421376	+	0.906886i	$0.361547\pi$
$60$		0			0
$61$	40.5827	−	70.2914i	0.665291	−	1.15232i	−0.313915	−	0.949451i	$-0.601641\pi$
$61$	40.5827	−	70.2914i	0.665291	−	1.15232i	0.979206	−	0.202867i	$-0.0650258\pi$
$62$	−48.7105	−	48.7105i	−0.785654	−	0.785654i
$63$		0			0
$64$			87.7280i			1.37075i
$65$	−54.9546	+	4.06786i	−0.845455	+	0.0625825i
$66$		0			0
$67$	10.9599	−	40.9029i	0.163581	−	0.610491i	−0.834636	−	0.550801i	$-0.814322\pi$
$67$	10.9599	−	40.9029i	0.163581	−	0.610491i	0.998217	−	0.0596898i	$-0.0190112\pi$
$68$	−33.5921	−	125.367i	−0.494001	−	1.84364i
$69$		0			0
$70$	−21.8107	+	101.820i	−0.311581	+	1.45457i
$71$	20.1105			0.283247			0.141623	−	0.989921i	$-0.454768\pi$
$71$	20.1105			0.283247			0.141623	+	0.989921i	$0.454768\pi$
$72$		0			0
$73$	6.28085	+	1.68295i	0.0860390	+	0.0230541i	0.301582	−	0.953440i	$-0.402485\pi$
$73$	6.28085	+	1.68295i	0.0860390	+	0.0230541i	−0.215543	+	0.976494i	$0.569152\pi$
$74$	−53.7685	+	31.0433i	−0.726602	+	0.419504i
$75$		0			0
$76$	160.000			2.10526
$77$	−70.4869	+	67.3023i	−0.915415	+	0.874056i
$78$		0			0
$79$	10.5341	+	6.08184i	0.133342	+	0.0769853i	0.565187	−	0.824963i	$-0.308804\pi$
$79$	10.5341	+	6.08184i	0.133342	+	0.0769853i	−0.431845	+	0.901948i	$0.642137\pi$
$80$	56.0352	−	19.5502i	0.700440	−	0.244377i
$81$		0			0
$82$	4.88019	−	1.30764i	0.0595145	−	0.0159469i
$83$	−20.6649	+	20.6649i	−0.248975	+	0.248975i	−0.820550	−	0.571575i	$-0.806333\pi$
$83$	−20.6649	+	20.6649i	−0.248975	+	0.248975i	0.571575	+	0.820550i	$0.306333\pi$
$84$		0			0
$85$	−110.591	+	75.2519i	−1.30107	+	0.885317i
$86$	56.3783	−	97.6501i	0.655562	−	1.13547i
$87$		0			0
$88$	−34.0643	−	9.12749i	−0.387094	−	0.103721i
$89$	145.002	+	83.7168i	1.62923	+	0.940638i	0.984322	+	0.176381i	$0.0564390\pi$
$89$	145.002	+	83.7168i	1.62923	+	0.940638i	0.644911	+	0.764257i	$0.276894\pi$
$90$		0			0
$91$	−65.9021	−	40.1069i	−0.724199	−	0.440735i
$92$	72.7245	+	72.7245i	0.790484	+	0.790484i
$93$		0			0
$94$	27.4284	−	15.8358i	0.291791	−	0.168466i
$95$	−54.3212	−	155.697i	−0.571802	−	1.63891i
$96$		0			0
$97$	−66.3082	−	66.3082i	−0.683589	−	0.683589i	0.277218	−	0.960807i	$-0.410588\pi$
$97$	−66.3082	−	66.3082i	−0.683589	−	0.683589i	−0.960807	+	0.277218i	$0.910588\pi$
$98$	−107.735	+	98.2105i	−1.09934	+	1.00215i
$99$		0			0
$100$	75.4467	+	94.9622i	0.754467	+	0.949622i
$101$	22.9150	+	39.6899i	0.226881	+	0.392969i	0.956882	−	0.290477i	$-0.0938138\pi$
$101$	22.9150	+	39.6899i	0.226881	+	0.392969i	−0.730001	+	0.683446i	$0.760481\pi$
$102$		0			0
$103$	5.67468	+	21.1782i	0.0550940	+	0.205614i	0.987986	−	0.154542i	$-0.0493902\pi$
$103$	5.67468	+	21.1782i	0.0550940	+	0.205614i	−0.932892	+	0.360156i	$0.882724\pi$
$104$		−	27.9163i		−	0.268426i
$105$		0			0
$106$	132.711			1.25199
$107$	97.5490	−	26.1382i	0.911673	−	0.244282i	0.227650	−	0.973743i	$-0.426896\pi$
$107$	97.5490	−	26.1382i	0.911673	−	0.244282i	0.684022	+	0.729461i	$0.260229\pi$
$108$		0			0
$109$	−109.890	+	63.4449i	−1.00816	+	0.582064i	−0.910654	−	0.413171i	$-0.864421\pi$
$109$	−109.890	+	63.4449i	−1.00816	+	0.582064i	−0.0975104	+	0.995235i	$0.531088\pi$
$110$	15.2887	+	206.542i	0.138988	+	1.87765i
$111$		0			0
$112$	79.7374	+	23.3531i	0.711941	+	0.208510i
$113$	10.2422	−	10.2422i	0.0906391	−	0.0906391i	−0.660333	−	0.750973i	$-0.729585\pi$
$113$	10.2422	−	10.2422i	0.0906391	−	0.0906391i	0.750973	+	0.660333i	$0.229585\pi$
$114$		0			0
$115$	46.0781	−	95.4592i	0.400679	−	0.830080i
$116$	44.0340	+	76.2692i	0.379604	+	0.657493i
$117$		0			0
$118$	−21.9745	+	21.9745i	−0.186224	+	0.186224i
$119$	−187.222	−	4.32709i	−1.57329	−	0.0363621i
$120$		0			0
$121$	−36.4184	+	63.0786i	−0.300979	+	0.521311i
$122$	62.4991	−	233.250i	0.512287	−	1.91188i
$123$		0			0
$124$	−97.2812	−	56.1654i	−0.784526	−	0.452946i
$125$	66.7935	−	105.658i	0.534348	−	0.845265i
$126$		0			0
$127$	138.223	+	138.223i	1.08837	+	1.08837i	0.995697	+	0.0926732i	$0.0295412\pi$
$127$	138.223	+	138.223i	1.08837	+	1.08837i	0.0926732	+	0.995697i	$0.470459\pi$
$128$	20.5037	+	76.5208i	0.160185	+	0.597819i
$129$		0			0
$130$	−154.794	+	54.0062i	−1.19072	+	0.415432i
$131$	−11.0263	+	19.0981i	−0.0841704	+	0.145787i	−0.905037	−	0.425332i	$-0.860157\pi$
$131$	−11.0263	+	19.0981i	−0.0841704	+	0.145787i	0.820867	+	0.571119i	$0.193491\pi$
$132$		0			0
$133$	64.8877	−	221.554i	0.487878	−	1.66582i
$134$		−	125.984i		−	0.940181i
$135$		0			0
$136$	−33.8829	−	58.6870i	−0.249139	−	0.431522i
$137$	55.4894	−	207.089i	0.405032	−	1.51160i	−0.398965	−	0.916966i	$-0.630630\pi$
$137$	55.4894	−	207.089i	0.405032	−	1.51160i	0.803997	−	0.594634i	$-0.202703\pi$
$138$		0			0
$139$		−	203.695i		−	1.46543i	−0.680534	−	0.732716i	$-0.738252\pi$
$139$		−	203.695i		−	1.46543i	0.680534	−	0.732716i	$-0.261748\pi$
$140$	8.61859	+	169.580i	0.0615613	+	1.21129i
$141$		0			0
$142$	57.7926	−	15.4855i	0.406990	−	0.109053i
$143$	−148.212	−	39.7132i	−1.03645	−	0.277715i
$144$		0			0
$145$	59.2681	−	68.7438i	0.408745	−	0.474095i
$146$	19.3455			0.132504
$147$		0			0
$148$	−71.5885	+	71.5885i	−0.483706	+	0.483706i
$149$	−106.635	−	61.5658i	−0.715672	−	0.413193i	0.0974859	−	0.995237i	$-0.468920\pi$
$149$	−106.635	−	61.5658i	−0.715672	−	0.413193i	−0.813157	+	0.582044i	$0.802253\pi$
$150$		0			0
$151$	−50.6434	−	87.7170i	−0.335387	−	0.580907i	0.648172	−	0.761494i	$-0.275534\pi$
$151$	−50.6434	−	87.7170i	−0.335387	−	0.580907i	−0.983559	+	0.180587i	$0.942200\pi$
$152$	80.6925	−	21.6215i	0.530872	−	0.142247i
$153$		0			0
$154$	−150.738	+	247.687i	−0.978818	+	1.60836i
$155$	−21.6271	+	113.734i	−0.139529	+	0.733765i
$156$		0			0
$157$	−18.7602	+	70.0141i	−0.119492	+	0.445950i	−0.999584	−	0.0288540i	$-0.990814\pi$
$157$	−18.7602	+	70.0141i	−0.119492	+	0.445950i	0.880092	+	0.474804i	$0.157481\pi$
$158$	34.9554	+	9.36628i	0.221237	+	0.0592802i
$159$		0			0
$160$	187.861	−	127.830i	1.17413	−	0.798940i
$161$	130.196	−	71.2096i	0.808673	−	0.442295i
$162$		0			0
$163$	47.1369	+	175.917i	0.289183	+	1.07925i	0.945728	+	0.324960i	$0.105351\pi$
$163$	47.1369	+	175.917i	0.289183	+	1.07925i	−0.656545	+	0.754287i	$0.727983\pi$
$164$	7.13484	−	4.11930i	0.0435051	−	0.0251177i
$165$		0			0
$166$	−43.4735	+	75.2984i	−0.261889	+	0.453605i
$167$	188.951	+	188.951i	1.13144	+	1.13144i	0.989938	+	0.141505i	$0.0451940\pi$
$167$	188.951	+	188.951i	1.13144	+	1.13144i	0.141505	+	0.989938i	$0.454806\pi$
$168$		0			0
$169$			47.5377i			0.281288i
$170$	−259.866	+	301.413i	−1.52862	+	1.77302i
$171$		0			0
$172$	47.5882	−	177.601i	0.276675	−	1.03257i
$173$	2.36194	+	8.81487i	0.0136528	+	0.0509530i	0.972416	−	0.233253i	$-0.0749369\pi$
$173$	2.36194	+	8.81487i	0.0136528	+	0.0509530i	−0.958763	+	0.284206i	$0.908270\pi$
$174$		0			0
$175$	162.093	−	65.9606i	0.926247	−	0.376918i
$176$	165.254			0.938944
$177$		0			0
$178$	481.163	+	128.927i	2.70316	+	0.724310i
$179$	−232.008	+	133.950i	−1.29613	+	0.748322i	−0.979734	−	0.200304i	$-0.935807\pi$
$179$	−232.008	+	133.950i	−1.29613	+	0.748322i	−0.316398	+	0.948626i	$0.602474\pi$
$180$		0			0
$181$	−226.975			−1.25401			−0.627004	−	0.779016i	$-0.715719\pi$
$181$	−226.975			−1.25401			−0.627004	+	0.779016i	$0.715719\pi$
$182$	−220.270	−	64.5115i	−1.21027	−	0.354459i
$183$		0			0
$184$	46.5047	+	26.8495i	0.252743	+	0.145921i
$185$	93.9681	+	45.3583i	0.507936	+	0.245180i
$186$		0			0
$187$	−359.779	+	96.4026i	−1.92395	+	0.515522i
$188$	36.5187	−	36.5187i	0.194248	−	0.194248i
$189$		0			0
$190$	−275.995	−	405.605i	−1.45261	−	2.13477i
$191$	−77.8090	+	134.769i	−0.407377	+	0.705597i	−0.994595	−	0.103831i	$-0.966890\pi$
$191$	−77.8090	+	134.769i	−0.407377	+	0.705597i	0.587218	+	0.809429i	$0.300223\pi$
$192$		0			0
$193$	−203.169	−	54.4390i	−1.05269	−	0.282067i	−0.309327	−	0.950956i	$-0.600104\pi$
$193$	−203.169	−	54.4390i	−1.05269	−	0.282067i	−0.743363	+	0.668889i	$0.766770\pi$
$194$	−241.612	−	139.495i	−1.24542	−	0.719045i
$195$		0			0
$196$	−128.243	+	200.159i	−0.654303	+	1.02122i
$197$	98.6199	+	98.6199i	0.500609	+	0.500609i	0.911627	−	0.411018i	$-0.134827\pi$
$197$	98.6199	+	98.6199i	0.500609	+	0.500609i	−0.411018	+	0.911627i	$0.634827\pi$
$198$		0			0
$199$	−35.8210	+	20.6813i	−0.180005	+	0.103926i	−0.587295	−	0.809373i	$-0.699807\pi$
$199$	−35.8210	+	20.6813i	−0.180005	+	0.103926i	0.407290	+	0.913299i	$0.366474\pi$
$200$	50.8826	+	37.6967i	0.254413	+	0.188484i
$201$		0			0
$202$	96.4140	+	96.4140i	0.477297	+	0.477297i
$203$	123.469	−	30.0438i	0.608223	−	0.147999i
$204$		0			0
$205$	−6.43085	−	5.54442i	−0.0313700	−	0.0270459i
$206$	32.6153	+	56.4913i	0.158327	+	0.274230i
$207$		0			0
$208$	33.8572	+	126.357i	0.162775	+	0.607485i
$209$		−	459.167i		−	2.19697i
$210$		0			0
$211$	326.483			1.54731			0.773655	−	0.633607i	$-0.218426\pi$
$211$	326.483			1.54731			0.773655	+	0.633607i	$0.218426\pi$
$212$	209.032	−	56.0099i	0.985999	−	0.264198i
$213$		0			0
$214$	260.205	−	150.229i	1.21591	−	0.702006i
$215$	−188.982	+	13.9888i	−0.878984	+	0.0650644i
$216$		0			0
$217$	−117.226	+	111.929i	−0.540210	+	0.515803i
$218$	−266.943	+	266.943i	−1.22451	+	1.22451i
$219$		0			0
$220$	111.250	+	318.868i	0.505684	+	1.44940i
$221$	−147.423	−	255.344i	−0.667072	−	1.15540i
$222$		0			0
$223$	−39.2007	+	39.2007i	−0.175788	+	0.175788i	−0.789517	−	0.613729i	$-0.789669\pi$
$223$	−39.2007	+	39.2007i	−0.175788	+	0.175788i	0.613729	+	0.789517i	$0.289669\pi$
$224$	318.033	+	7.35042i	1.41979	+	0.0328144i
$225$		0			0
$226$	21.5469	−	37.3203i	0.0953403	−	0.165134i
$227$	−0.933082	+	3.48231i	−0.00411049	+	0.0153406i	−0.967951	−	0.251141i	$-0.919194\pi$
$227$	−0.933082	+	3.48231i	−0.00411049	+	0.0153406i	0.963840	+	0.266481i	$0.0858610\pi$
$228$		0			0
$229$	−46.0053	−	26.5612i	−0.200896	−	0.115988i	0.396177	−	0.918174i	$-0.370337\pi$
$229$	−46.0053	−	26.5612i	−0.200896	−	0.115988i	−0.597074	+	0.802186i	$0.703670\pi$
$230$	58.9116	−	309.807i	0.256137	−	1.34699i
$231$		0			0
$232$	32.5143	+	32.5143i	0.140148	+	0.140148i
$233$	33.4506	+	124.839i	0.143565	+	0.535791i	0.999815	+	0.0192298i	$0.00612140\pi$
$233$	33.4506	+	124.839i	0.143565	+	0.535791i	−0.856250	+	0.516561i	$0.827212\pi$
$234$		0			0
$235$	−47.9350	−	23.1382i	−0.203979	−	0.0984603i
$236$	−25.3375	+	43.8859i	−0.107362	+	0.185957i
$237$		0			0
$238$	−541.361	+	131.730i	−2.27463	+	0.553485i
$239$		−	365.148i		−	1.52782i	−0.645325	−	0.763908i	$-0.723278\pi$
$239$		−	365.148i		−	1.52782i	0.645325	−	0.763908i	$-0.276722\pi$
$240$		0			0
$241$	−196.782	−	340.837i	−0.816525	−	1.41426i	−0.908228	−	0.418476i	$-0.862564\pi$
$241$	−196.782	−	340.837i	−0.816525	−	1.41426i	0.0917031	−	0.995786i	$-0.470769\pi$
$242$	−56.0859	+	209.315i	−0.231760	+	0.864939i
$243$		0			0
$244$		−	393.766i		−	1.61379i
$245$	238.316	+	56.8387i	0.972717	+	0.231995i
$246$		0			0
$247$	351.089	−	94.0739i	1.42141	−	0.380866i
$248$	−56.6516	−	15.1798i	−0.228434	−	0.0612087i
$249$		0			0
$250$	110.589	−	355.068i	0.442357	−	1.42027i
$251$	−353.349			−1.40777			−0.703883	−	0.710316i	$-0.748552\pi$
$251$	−353.349			−1.40777			−0.703883	+	0.710316i	$0.748552\pi$
$252$		0			0
$253$	208.705	−	208.705i	0.824920	−	0.824920i
$254$	503.653	+	290.784i	1.98289	+	1.14482i
$255$		0			0
$256$	−57.6108	−	99.7848i	−0.225042	−	0.389784i
$257$	−54.4792	+	14.5977i	−0.211981	+	0.0568002i	−0.363247	−	0.931693i	$-0.618332\pi$
$257$	−54.4792	+	14.5977i	−0.211981	+	0.0568002i	0.151266	+	0.988493i	$0.451665\pi$
$258$		0			0
$259$	70.0972	+	128.163i	0.270646	+	0.494836i
$260$	−221.021	+	150.394i	−0.850079	+	0.578439i
$261$		0			0
$262$	−16.9810	+	63.3739i	−0.0648129	+	0.241885i
$263$	274.512	+	73.5553i	1.04377	+	0.279678i	0.739676	−	0.672963i	$-0.234979\pi$
$263$	274.512	+	73.5553i	1.04377	+	0.279678i	0.304097	+	0.952641i	$0.401645\pi$
$264$		0			0
$265$	−125.472	−	184.394i	−0.473477	−	0.695827i
$266$	15.8701	−	686.658i	0.0596620	−	2.58142i
$267$		0			0
$268$	−53.1708	−	198.436i	−0.198399	−	0.740433i
$269$	−228.544	+	131.950i	−0.849607	+	0.490521i	−0.860518	−	0.509419i	$-0.829860\pi$
$269$	−228.544	+	131.950i	−0.849607	+	0.490521i	0.0109111	+	0.999940i	$0.496527\pi$
$270$		0			0
$271$	50.4495	−	87.3810i	0.186160	−	0.322439i	−0.757807	−	0.652479i	$-0.773729\pi$
$271$	50.4495	−	87.3810i	0.186160	−	0.322439i	0.943967	+	0.330040i	$0.107062\pi$
$272$	224.540	+	224.540i	0.825514	+	0.825514i
$273$		0			0
$274$		−	637.851i		−	2.32792i
$275$	272.522	−	216.517i	0.990991	−	0.787334i
$276$		0			0
$277$	−67.8808	+	253.335i	−0.245057	+	0.914566i	0.728297	+	0.685261i	$0.240312\pi$
$277$	−67.8808	+	253.335i	−0.245057	+	0.914566i	−0.973355	+	0.229305i	$0.926355\pi$
$278$	−156.849	−	585.370i	−0.564206	−	2.10565i
$279$		0			0
$280$	27.2627	+	84.3594i	0.0973669	+	0.301284i
$281$	−394.591			−1.40424			−0.702119	−	0.712060i	$-0.747762\pi$
$281$	−394.591			−1.40424			−0.702119	+	0.712060i	$0.747762\pi$
$282$		0			0
$283$	295.210	+	79.1013i	1.04315	+	0.279510i	0.739416	−	0.673249i	$-0.235102\pi$
$283$	295.210	+	79.1013i	1.04315	+	0.279510i	0.303729	+	0.952758i	$0.401768\pi$
$284$	84.4929	−	48.7820i	0.297510	−	0.171768i
$285$		0			0
$286$	−456.504			−1.59617
$287$	−2.81054	−	11.5503i	−0.00979282	−	0.0402450i
$288$		0			0
$289$	−369.558	−	213.364i	−1.27875	−	0.738285i
$290$	117.388	−	243.190i	0.404786	−	0.838588i
$291$		0			0
$292$	30.4709	−	8.16464i	0.104352	−	0.0279611i
$293$	−232.731	+	232.731i	−0.794304	+	0.794304i	−0.982191	−	0.187887i	$-0.939836\pi$
$293$	−232.731	+	232.731i	−0.794304	+	0.794304i	0.187887	+	0.982191i	$0.439836\pi$
$294$		0			0
$295$	51.3079	+	9.75647i	0.173925	+	0.0330728i
$296$	−26.4301	+	45.7782i	−0.0892908	+	0.154656i
$297$		0			0
$298$	−353.850	−	94.8138i	−1.18742	−	0.318167i
$299$	202.339	+	116.821i	0.676720	+	0.390705i
$300$		0			0
$301$	−226.629	−	137.922i	−0.752919	−	0.458214i
$302$	−213.081	−	213.081i	−0.705565	−	0.705565i
$303$		0			0
$304$	−339.014	+	195.730i	−1.11518	+	0.643847i
$305$	−383.176	+	133.687i	−1.25631	+	0.438317i
$306$		0			0
$307$	192.175	+	192.175i	0.625976	+	0.625976i	0.947053	−	0.321077i	$-0.104045\pi$
$307$	192.175	+	192.175i	0.625976	+	0.625976i	−0.321077	+	0.947053i	$0.604045\pi$
$308$	−132.891	+	453.746i	−0.431464	+	1.47320i
$309$		0			0
$310$	25.4263	+	343.496i	0.0820203	+	1.10805i
$311$	−69.8332	−	120.955i	−0.224544	−	0.388922i	0.731638	−	0.681693i	$-0.238756\pi$
$311$	−69.8332	−	120.955i	−0.224544	−	0.388922i	−0.956183	+	0.292771i	$0.905423\pi$
$312$		0			0
$313$	12.6561	+	47.2333i	0.0404349	+	0.150905i	0.983192	−	0.182576i	$-0.0584434\pi$
$313$	12.6561	+	47.2333i	0.0404349	+	0.150905i	−0.942757	+	0.333481i	$0.891777\pi$
$314$			215.649i			0.686780i
$315$		0			0
$316$	59.0108			0.186743
$317$	−288.036	+	77.1789i	−0.908630	+	0.243467i	−0.682719	−	0.730681i	$-0.739203\pi$
$317$	−288.036	+	77.1789i	−0.908630	+	0.243467i	−0.225911	+	0.974148i	$0.572536\pi$
$318$		0			0
$319$	218.877	−	126.369i	0.686136	−	0.396141i
$320$	286.423	−	332.215i	0.895070	−	1.03817i
$321$		0			0
$322$	319.319	−	304.893i	0.991675	−	0.946871i
$323$	623.895	−	623.895i	1.93156	−	1.93156i
$324$		0			0
$325$	221.388	+	164.016i	0.681193	+	0.504666i
$326$	270.920	+	469.247i	0.831042	+	1.43941i
$327$		0			0
$328$	3.04165	−	3.04165i	0.00927331	−	0.00927331i
$329$	−35.7580	−	65.3782i	−0.108687	−	0.198718i
$330$		0			0
$331$	−43.7659	+	75.8048i	−0.132223	+	0.229018i	−0.924533	−	0.381101i	$-0.875545\pi$
$331$	−43.7659	+	75.8048i	−0.132223	+	0.229018i	0.792310	+	0.610119i	$0.208878\pi$
$332$	−36.6954	+	136.949i	−0.110528	+	0.412498i
$333$		0			0
$334$	688.494	+	397.502i	2.06136	+	1.19013i
$335$	−175.047	+	119.112i	−0.522530	+	0.355557i
$336$		0			0
$337$	170.978	+	170.978i	0.507354	+	0.507354i	0.913713	−	0.406359i	$-0.133202\pi$
$337$	170.978	+	170.978i	0.507354	+	0.507354i	−0.406359	+	0.913713i	$0.633202\pi$
$338$	36.6050	+	136.612i	0.108299	+	0.404177i
$339$		0			0
$340$	−282.102	+	584.426i	−0.829712	+	1.71890i
$341$	−161.183	+	279.178i	−0.472678	+	0.818703i
$342$		0			0
$343$	225.155	+	258.755i	0.656428	+	0.754389i
$344$		−	96.0004i		−	0.279071i
$345$		0			0
$346$	13.5753	+	23.5130i	0.0392348	+	0.0679567i
$347$	17.2634	−	64.4278i	0.0497504	−	0.185671i	−0.936579	−	0.350456i	$-0.886026\pi$
$347$	17.2634	−	64.4278i	0.0497504	−	0.185671i	0.986329	+	0.164785i	$0.0526932\pi$
$348$		0			0
$349$			445.265i			1.27583i	0.770106	+	0.637915i	$0.220203\pi$
$349$			445.265i			1.27583i	−0.770106	+	0.637915i	$0.779797\pi$
$350$	415.025	−	314.370i	1.18579	−	0.898199i
$351$		0			0
$352$	611.157	−	163.759i	1.73624	−	0.465224i
$353$	357.784	+	95.8678i	1.01355	+	0.271580i	0.727112	−	0.686518i	$-0.240862\pi$
$353$	357.784	+	95.8678i	1.01355	+	0.271580i	0.286439	+	0.958099i	$0.407529\pi$
$354$		0			0
$355$	−76.1561	−	65.6587i	−0.214524	−	0.184954i
$356$	812.287			2.28170
$357$		0			0
$358$	−563.589	+	563.589i	−1.57427	+	1.57427i
$359$	507.313	+	292.897i	1.41313	+	0.815870i	0.995682	−	0.0928320i	$-0.0295919\pi$
$359$	507.313	+	292.897i	1.41313	+	0.815870i	0.417446	+	0.908702i	$0.362925\pi$
$360$		0			0
$361$	363.345	+	629.331i	1.00649	+	1.74330i
$362$	−652.272	+	174.776i	−1.80186	+	0.482806i
$363$		0			0
$364$	−374.170	−	8.64786i	−1.02794	−	0.0237579i
$365$	−18.2902	−	26.8794i	−0.0501101	−	0.0736422i
$366$		0			0
$367$	78.0318	−	291.219i	0.212621	−	0.793511i	−0.774370	−	0.632733i	$-0.781933\pi$
$367$	78.0318	−	291.219i	0.212621	−	0.793511i	0.986991	−	0.160778i	$-0.0514003\pi$
$368$	−243.056	−	65.1268i	−0.660479	−	0.176975i
$369$		0			0
$370$	304.968	+	57.9913i	0.824238	+	0.156733i
$371$	7.21478	−	312.165i	0.0194469	−	0.841414i
$372$		0			0
$373$	136.663	+	510.035i	0.366390	+	1.36739i	0.865527	+	0.500862i	$0.166984\pi$
$373$	136.663	+	510.035i	0.366390	+	1.36739i	−0.499137	+	0.866523i	$0.666350\pi$
$374$	−959.686	+	554.075i	−2.56600	+	1.48148i
$375$		0			0
$376$	13.4825	−	23.3524i	0.0358577	−	0.0621074i
$377$	141.468	+	141.468i	0.375246	+	0.375246i
$378$		0			0
$379$			177.062i			0.467182i	0.972335	+	0.233591i	$0.0750476\pi$
$379$			177.062i			0.467182i	−0.972335	+	0.233591i	$0.924952\pi$
$380$	−605.900	−	522.382i	−1.59447	−	1.37469i
$381$		0			0
$382$	−119.829	+	447.208i	−0.313688	+	1.17070i
$383$	69.8407	+	260.649i	0.182352	+	0.680545i	0.995182	+	0.0980450i	$0.0312589\pi$
$383$	69.8407	+	260.649i	0.182352	+	0.680545i	−0.812830	+	0.582500i	$0.802074\pi$
$384$		0			0
$385$	486.661	−	24.7336i	1.26405	−	0.0642432i
$386$	−625.777			−1.62118
$387$		0			0
$388$	−439.433	−	117.746i	−1.13256	−	0.303468i
$389$	−161.408	+	93.1891i	−0.414931	+	0.239561i	−0.692906	−	0.721028i	$-0.743670\pi$
$389$	−161.408	+	93.1891i	−0.414931	+	0.239561i	0.277975	+	0.960588i	$0.410337\pi$
$390$		0			0
$391$	567.157			1.45053
$392$	−37.6284	+	118.276i	−0.0959909	+	0.301725i
$393$		0			0
$394$	359.349	+	207.470i	0.912053	+	0.526574i
$395$	−20.0347	−	57.4238i	−0.0507206	−	0.145377i
$396$		0			0
$397$	−659.091	+	176.603i	−1.66018	+	0.444844i	−0.962437	−	0.271506i	$-0.912478\pi$
$397$	−659.091	+	176.603i	−1.66018	+	0.444844i	−0.697742	+	0.716349i	$0.745812\pi$
$398$	−87.0158	+	87.0158i	−0.218633	+	0.218633i
$399$		0			0
$400$	−276.028	−	108.915i	−0.690070	−	0.272287i
$401$	−63.9305	+	110.731i	−0.159428	+	0.276137i	−0.934662	−	0.355536i	$-0.884298\pi$
$401$	−63.9305	+	110.731i	−0.159428	+	0.276137i	0.775235	+	0.631673i	$0.217632\pi$
$402$		0			0
$403$	−246.488	−	66.0463i	−0.611634	−	0.163887i
$404$	192.551	+	111.170i	0.476612	+	0.275172i
$405$		0			0
$406$	331.686	−	181.412i	0.816961	−	0.446829i
$407$	205.445	+	205.445i	0.504778	+	0.504778i
$408$		0			0
$409$	67.5742	−	39.0140i	0.165218	−	0.0953887i	−0.415111	−	0.909771i	$-0.636257\pi$
$409$	67.5742	−	39.0140i	0.165218	−	0.0953887i	0.580329	+	0.814382i	$0.302924\pi$
$410$	−22.7500	−	10.9814i	−0.0554878	−	0.0267839i
$411$		0			0
$412$	75.2137	+	75.2137i	0.182558	+	0.182558i
$413$	50.4939	+	52.8832i	0.122261	+	0.128046i
$414$		0			0
$415$	145.725	−	10.7868i	0.351143	−	0.0259924i
$416$	250.427	+	433.752i	0.601988	+	1.04267i
$417$		0			0
$418$	−353.568	−	1319.53i	−0.845856	−	3.15678i
$419$			38.0855i			0.0908962i	0.998967	+	0.0454481i	$0.0144716\pi$
$419$			38.0855i			0.0908962i	−0.998967	+	0.0454481i	$0.985528\pi$
$420$		0			0
$421$	−151.613			−0.360126			−0.180063	−	0.983655i	$-0.557630\pi$
$421$	−151.613			−0.360126			−0.180063	+	0.983655i	$0.557630\pi$
$422$	938.231	−	251.398i	2.22330	−	0.595730i
$423$		0			0
$424$	97.8519	−	56.4948i	0.230783	−	0.133242i
$425$	664.484	+	76.0976i	1.56349	+	0.179053i
$426$		0			0
$427$	−545.255	−	159.691i	−1.27694	−	0.373985i
$428$	346.442	−	346.442i	0.809444	−	0.809444i
$429$		0			0
$430$	−532.315	+	185.720i	−1.23794	+	0.431907i
$431$	268.299	+	464.707i	0.622503	+	1.07821i	0.989018	+	0.147795i	$0.0472175\pi$
$431$	268.299	+	464.707i	0.622503	+	1.07821i	−0.366515	+	0.930412i	$0.619449\pi$
$432$		0			0
$433$	421.429	−	421.429i	0.973278	−	0.973278i	−0.0263739	−	0.999652i	$-0.508396\pi$
$433$	421.429	−	421.429i	0.973278	−	0.973278i	0.999652	+	0.0263739i	$0.00839605\pi$
$434$	−250.690	+	411.923i	−0.577626	+	0.949132i
$435$		0			0
$436$	−307.796	+	533.119i	−0.705955	+	1.22275i
$437$	−180.958	+	675.344i	−0.414092	+	1.54541i
$438$		0			0
$439$	411.292	+	237.460i	0.936884	+	0.540910i	0.888982	−	0.457942i	$-0.151413\pi$
$439$	411.292	+	237.460i	0.936884	+	0.540910i	0.0479017	+	0.998852i	$0.484747\pi$
$440$	99.1970	+	145.781i	0.225448	+	0.331320i
$441$		0			0
$442$	−620.277	−	620.277i	−1.40334	−	1.40334i
$443$	−24.3833	−	90.9998i	−0.0550414	−	0.205417i	0.932929	−	0.360060i	$-0.117244\pi$
$443$	−24.3833	−	90.9998i	−0.0550414	−	0.205417i	−0.987970	+	0.154643i	$0.950577\pi$
$444$		0			0
$445$	−275.778	−	790.441i	−0.619726	−	1.77627i
$446$	−82.4678	+	142.839i	−0.184905	+	0.320266i
$447$		0			0
$448$	596.685	−	145.192i	1.33189	−	0.324088i
$449$		−	521.631i		−	1.16176i	−0.813989	−	0.580881i	$-0.802708\pi$
$449$		−	521.631i		−	1.16176i	0.813989	−	0.580881i	$-0.197292\pi$
$450$		0			0
$451$	−11.8216	−	20.4756i	−0.0262119	−	0.0454003i
$452$	18.1875	−	67.8765i	0.0402377	−	0.150169i
$453$		0			0
$454$			10.7258i			0.0236251i
$455$	118.619	+	367.043i	0.260700	+	0.806689i
$456$		0			0
$457$	401.339	−	107.539i	0.878204	−	0.235314i	0.208572	−	0.978007i	$-0.433118\pi$
$457$	401.339	−	107.539i	0.878204	−	0.235314i	0.669632	+	0.742693i	$0.266452\pi$
$458$	−152.661	−	40.9053i	−0.333320	−	0.0893128i
$459$		0			0
$460$	−37.9613	−	512.837i	−0.0825246	−	1.11486i
$461$	−280.539			−0.608544			−0.304272	−	0.952585i	$-0.598413\pi$
$461$	−280.539			−0.608544			−0.304272	+	0.952585i	$0.598413\pi$
$462$		0			0
$463$	−326.436	+	326.436i	−0.705045	+	0.705045i	−0.965489	−	0.260444i	$-0.916131\pi$
$463$	−326.436	+	326.436i	−0.705045	+	0.705045i	0.260444	+	0.965489i	$0.416131\pi$
$464$	−186.602	−	107.735i	−0.402160	−	0.232187i
$465$		0			0
$466$	192.257	+	333.000i	0.412570	+	0.714592i
$467$	410.520	−	109.999i	0.879058	−	0.235543i	0.209057	−	0.977903i	$-0.432960\pi$
$467$	410.520	−	109.999i	0.879058	−	0.235543i	0.670001	+	0.742360i	$0.266294\pi$
$468$		0			0
$469$	−296.342	−	6.84907i	−0.631858	−	0.0146036i
$470$	−155.570	−	29.5825i	−0.331000	−	0.0629415i
$471$		0			0
$472$	−6.84795	+	25.5569i	−0.0145084	+	0.0541459i
$473$	−509.681	−	136.569i	−1.07755	−	0.288728i
$474$		0			0
$475$	−302.625	+	766.958i	−0.637105	+	1.61465i
$476$	−797.096	+	435.963i	−1.67457	+	0.915889i
$477$		0			0
$478$	−281.171	−	1049.35i	−0.588225	−	2.19529i
$479$	183.280	−	105.817i	0.382630	−	0.220912i	−0.296332	−	0.955085i	$-0.595763\pi$
$479$	183.280	−	105.817i	0.382630	−	0.220912i	0.678962	+	0.734173i	$0.262430\pi$
$480$		0			0
$481$	−114.996	+	199.179i	−0.239077	+	0.414093i
$482$	−827.956	−	827.956i	−1.71775	−	1.71775i
$483$		0			0
$484$			353.361i			0.730084i
$485$	34.6121	+	467.590i	0.0713651	+	0.964104i
$486$		0			0
$487$	12.4096	−	46.3134i	0.0254818	−	0.0950993i	−0.952014	−	0.306055i	$-0.900991\pi$
$487$	12.4096	−	46.3134i	0.0254818	−	0.0950993i	0.977496	+	0.210956i	$0.0676575\pi$
$488$	−53.2114	−	198.588i	−0.109040	−	0.406942i
$489$		0			0
$490$	728.628	−	20.1673i	1.48700	−	0.0411578i
$491$	784.457			1.59767			0.798836	−	0.601549i	$-0.205449\pi$
$491$	784.457			1.59767			0.798836	+	0.601549i	$0.205449\pi$
$492$		0			0
$493$	469.105	+	125.696i	0.951531	+	0.254962i
$494$	936.504	−	540.691i	1.89576	−	1.09452i
$495$		0			0
$496$	274.831			0.554095
$497$	−33.2833	−	136.782i	−0.0669684	−	0.275216i
$498$		0			0
$499$	−50.6730	−	29.2561i	−0.101549	−	0.0586294i	0.448365	−	0.893850i	$-0.352006\pi$
$499$	−50.6730	−	29.2561i	−0.101549	−	0.0586294i	−0.549914	+	0.835221i	$0.685340\pi$
$500$	24.3336	−	605.936i	0.0486671	−	1.21187i
$501$		0			0
$502$	−1015.44	+	272.086i	−2.02279	+	0.542004i
$503$	−144.269	+	144.269i	−0.286816	+	0.286816i	−0.835820	−	0.549004i	$-0.815007\pi$
$503$	−144.269	+	144.269i	−0.286816	+	0.286816i	0.549004	+	0.835820i	$0.315007\pi$
$504$		0			0
$505$	42.8070	−	225.116i	0.0847664	−	0.445774i
$506$	439.059	−	760.473i	0.867706	−	1.50291i
$507$		0			0
$508$	916.021	+	245.447i	1.80319	+	0.483164i
$509$	38.7059	+	22.3469i	0.0760431	+	0.0439035i	0.537539	−	0.843239i	$-0.319354\pi$
$509$	38.7059	+	22.3469i	0.0760431	+	0.0439035i	−0.461496	+	0.887142i	$0.652687\pi$
$510$		0			0
$511$	1.05171	−	45.5047i	0.00205814	−	0.0890503i
$512$	−466.464	−	466.464i	−0.911063	−	0.911063i
$513$		0			0
$514$	−145.319	+	83.9001i	−0.282722	+	0.163230i
$515$	47.6552	−	98.7266i	0.0925344	−	0.191702i
$516$		0			0
$517$	−104.801	−	104.801i	−0.202711	−	0.202711i
$518$	300.130	+	314.331i	0.579401	+	0.606817i
$519$		0			0
$520$	−91.1437	+	105.716i	−0.175276	+	0.203299i
$521$	−139.872	−	242.266i	−0.268469	−	0.465001i	0.699998	−	0.714145i	$-0.253184\pi$
$521$	−139.872	−	242.266i	−0.268469	−	0.465001i	−0.968467	+	0.249143i	$0.919851\pi$
$522$		0			0
$523$	63.7856	+	238.051i	0.121961	+	0.455165i	0.999713	−	0.0239502i	$-0.00762432\pi$
$523$	63.7856	+	238.051i	0.121961	+	0.455165i	−0.877752	+	0.479115i	$0.840958\pi$
$524$			106.986i			0.204172i
$525$		0			0
$526$	845.520			1.60745
$527$	−598.343	+	160.325i	−1.13537	+	0.304223i
$528$		0			0
$529$	68.9129	−	39.7869i	0.130270	−	0.0752115i
$530$	−502.562	−	433.288i	−0.948229	−	0.817524i
$531$		0			0
$532$	−264.802	−	1088.24i	−0.497749	−	2.04557i
$533$	13.2340	−	13.2340i	0.0248293	−	0.0248293i
$534$		0			0
$535$	−454.745	−	219.505i	−0.849990	−	0.410289i
$536$	−53.6312	−	92.8919i	−0.100058	−	0.173306i
$537$		0			0
$538$	−555.176	+	555.176i	−1.03193	+	1.03193i
$539$	574.416	+	368.033i	1.06571	+	0.682807i
$540$		0			0
$541$	−391.651	+	678.360i	−0.723939	+	1.25390i	0.235470	+	0.971882i	$0.424337\pi$
$541$	−391.651	+	678.360i	−0.723939	+	1.25390i	−0.959409	+	0.282018i	$0.908996\pi$
$542$	77.6942	−	289.959i	0.143347	−	0.534979i
$543$		0			0
$544$	1052.92	+	607.904i	1.93552	+	1.11747i
$545$	623.281	+	118.520i	1.14363	+	0.217468i
$546$		0			0
$547$	−32.2224	−	32.2224i	−0.0589074	−	0.0589074i	0.677039	−	0.735947i	$-0.263263\pi$
$547$	−32.2224	−	32.2224i	−0.0589074	−	0.0589074i	−0.735947	+	0.677039i	$0.763263\pi$
$548$	−269.201	−	1004.67i	−0.491243	−	1.83334i
$549$		0			0
$550$	616.440	−	832.064i	1.12080	−	1.51284i
$551$	−299.347	+	518.484i	−0.543279	+	0.940986i
$552$		0			0
$553$	23.9318	−	81.7133i	0.0432763	−	0.147764i
$554$			780.291i			1.40847i
$555$		0			0
$556$	−494.103	−	855.811i	−0.888674	−	1.53923i
$557$	215.849	−	805.560i	0.387521	−	1.44625i	−0.446634	−	0.894717i	$-0.647377\pi$
$557$	215.849	−	805.560i	0.387521	−	1.44625i	0.834155	−	0.551531i	$-0.185956\pi$
$558$		0			0
$559$		−	417.693i		−	0.747214i
$560$	−225.711	−	348.770i	−0.403055	−	0.622803i
$561$		0			0
$562$	−1133.96	+	303.843i	−2.01772	+	0.540646i
$563$	810.525	+	217.180i	1.43965	+	0.385754i	0.892412	−	0.451221i	$-0.149011\pi$
$563$	810.525	+	217.180i	1.43965	+	0.385754i	0.547241	+	0.836975i	$0.315678\pi$
$564$		0			0
$565$	−72.2258	+	5.34631i	−0.127833	+	0.00946250i
$566$	909.271			1.60649
$567$		0			0
$568$	36.0201	−	36.0201i	0.0634157	−	0.0634157i
$569$	−663.998	−	383.359i	−1.16696	−	0.673742i	−0.213995	−	0.976835i	$-0.568648\pi$
$569$	−663.998	−	383.359i	−1.16696	−	0.673742i	−0.952961	+	0.303093i	$0.901981\pi$
$570$		0			0
$571$	−525.520	−	910.227i	−0.920350	−	1.59409i	−0.798874	−	0.601498i	$-0.794571\pi$
$571$	−525.520	−	910.227i	−0.920350	−	1.59409i	−0.121476	−	0.992594i	$-0.538763\pi$
$572$	−719.034	+	192.665i	−1.25705	+	0.336826i
$573$		0			0
$574$	−16.9708	−	31.0286i	−0.0295658	−	0.0540568i
$575$	−486.156	+	211.053i	−0.845490	+	0.367048i
$576$		0			0
$577$	51.2986	−	191.449i	0.0889058	−	0.331801i	−0.907119	−	0.420873i	$-0.861724\pi$
$577$	51.2986	−	191.449i	0.0889058	−	0.331801i	0.996025	+	0.0890726i	$0.0283903\pi$
$578$	−1226.31	−	328.590i	−2.12165	−	0.568494i
$579$		0			0
$580$	82.2591	−	432.589i	0.141826	−	0.745843i
$581$	174.754	+	106.352i	0.300782	+	0.183051i
$582$		0			0
$583$	−160.737	−	599.879i	−0.275707	−	1.02895i
$584$	14.2640	−	8.23534i	0.0244247	−	0.0141016i
$585$		0			0
$586$	−489.604	+	848.019i	−0.835502	+	1.44713i
$587$	−425.592	−	425.592i	−0.725029	−	0.725029i	0.244596	−	0.969625i	$-0.421345\pi$
$587$	−425.592	−	425.592i	−0.725029	−	0.725029i	−0.969625	+	0.244596i	$0.921345\pi$
$588$		0			0
$589$		−	763.632i		−	1.29649i
$590$	154.959	−	11.4704i	0.262642	−	0.0194414i
$591$		0			0
$592$	64.1094	−	239.260i	0.108293	−	0.404155i
$593$	−139.637	−	521.131i	−0.235475	−	0.878805i	−0.977934	−	0.208914i	$-0.933007\pi$
$593$	−139.637	−	521.131i	−0.235475	−	0.878805i	0.742459	−	0.669892i	$-0.233659\pi$
$594$		0			0
$595$	694.859	+	627.645i	1.16783	+	1.05487i
$596$	−597.360			−1.00228
$597$		0			0
$598$	671.428	+	179.909i	1.12279	+	0.300851i
$599$	329.578	−	190.282i	0.550213	−	0.317666i	−0.198995	−	0.980001i	$-0.563768\pi$
$599$	329.578	−	190.282i	0.550213	−	0.317666i	0.749208	+	0.662335i	$0.230434\pi$
$600$		0			0
$601$	−566.492			−0.942582			−0.471291	−	0.881978i	$-0.656212\pi$
$601$	−566.492			−0.942582			−0.471291	+	0.881978i	$0.656212\pi$
$602$	−757.478	−	221.846i	−1.25827	−	0.368516i
$603$		0			0
$604$	−425.550	−	245.691i	−0.704552	−	0.406773i
$605$	343.857	−	119.969i	0.568359	−	0.198296i
$606$		0			0
$607$	1039.09	−	278.422i	1.71184	−	0.458685i	0.735963	−	0.677021i	$-0.236730\pi$
$607$	1039.09	−	278.422i	1.71184	−	0.458685i	0.975874	+	0.218336i	$0.0700629\pi$
$608$	−1059.81	+	1059.81i	−1.74311	+	1.74311i
$609$		0			0
$610$	−998.212	+	679.236i	−1.63641	+	1.11350i
$611$	58.6616	−	101.605i	0.0960092	−	0.166293i
$612$		0			0
$613$	405.242	+	108.584i	0.661079	+	0.177136i	0.573733	−	0.819042i	$-0.305495\pi$
$613$	405.242	+	108.584i	0.661079	+	0.177136i	0.0873463	+	0.996178i	$0.472161\pi$
$614$	700.241	+	404.284i	1.14046	+	0.658444i
$615$		0			0
$616$	−5.70396	+	246.795i	−0.00925968	+	0.400642i
$617$	504.052	+	504.052i	0.816940	+	0.816940i	0.985663	−	0.168724i	$-0.0539645\pi$
$617$	504.052	+	504.052i	0.816940	+	0.816940i	−0.168724	+	0.985663i	$0.553965\pi$
$618$		0			0
$619$	−210.689	+	121.641i	−0.340369	+	0.196512i	−0.660435	−	0.750883i	$-0.729628\pi$
$619$	−210.689	+	121.641i	−0.340369	+	0.196512i	0.320066	+	0.947395i	$0.396295\pi$
$620$	185.019	+	530.304i	0.298417	+	0.855330i
$621$		0			0
$622$	−293.821	−	293.821i	−0.472381	−	0.472381i
$623$	329.422	−	1124.79i	0.528768	−	1.80544i
$624$		0			0
$625$	−597.901	+	182.041i	−0.956642	+	0.291266i
$626$	72.7413	+	125.992i	0.116200	+	0.201264i
$627$		0			0
$628$	91.0132	+	339.666i	0.144926	+	0.540869i
$629$			558.298i			0.887596i
$630$		0			0
$631$	912.593			1.44626			0.723132	−	0.690710i	$-0.242702\pi$
$631$	912.593			1.44626			0.723132	+	0.690710i	$0.242702\pi$
$632$	29.7609	−	7.97440i	0.0470900	−	0.0126177i
$633$		0			0
$634$	−768.315	+	443.587i	−1.21185	+	0.699663i
$635$	−72.1507	−	974.717i	−0.113623	−	1.53499i
$636$		0			0
$637$	−163.719	+	514.613i	−0.257016	+	0.807870i
$638$	531.693	−	531.693i	0.833375	−	0.833375i
$639$		0			0
$640$	172.187	−	356.718i	0.269043	−	0.557371i
$641$	−114.103	−	197.632i	−0.178007	−	0.308318i	0.763191	−	0.646173i	$-0.223632\pi$
$641$	−114.103	−	197.632i	−0.178007	−	0.308318i	−0.941198	+	0.337856i	$0.890298\pi$
$642$		0			0
$643$	434.914	−	434.914i	0.676382	−	0.676382i	−0.282797	−	0.959180i	$-0.591262\pi$
$643$	434.914	−	434.914i	0.676382	−	0.676382i	0.959180	+	0.282797i	$0.0912624\pi$
$644$	374.278	−	614.999i	0.581177	−	0.954967i
$645$		0			0
$646$	1312.51	−	2273.33i	2.03175	−	3.51909i
$647$	−92.6027	+	345.598i	−0.143126	+	0.534155i	0.856705	+	0.515806i	$0.172508\pi$
$647$	−92.6027	+	345.598i	−0.143126	+	0.534155i	−0.999832	+	0.0183485i	$0.994159\pi$
$648$		0			0
$649$	125.944	+	72.7136i	0.194058	+	0.112039i
$650$	762.510	+	300.870i	1.17309	+	0.462877i
$651$		0			0
$652$	624.764	+	624.764i	0.958228	+	0.958228i
$653$	−177.811	−	663.599i	−0.272298	−	1.01623i	−0.957630	−	0.288000i	$-0.907010\pi$
$653$	−177.811	−	663.599i	−0.272298	−	1.01623i	0.685332	−	0.728231i	$-0.259657\pi$
$654$		0			0
$655$	104.109	−	36.3226i	0.158945	−	0.0554544i
$656$	−10.0784	+	17.4563i	−0.0153634	+	0.0266102i
$657$		0			0
$658$	−153.102	−	160.347i	−0.232678	−	0.243688i
$659$			619.112i			0.939471i	0.882807	+	0.469736i	$0.155651\pi$
$659$			619.112i			0.939471i	−0.882807	+	0.469736i	$0.844349\pi$
$660$		0			0
$661$	−249.541	−	432.217i	−0.377520	−	0.653884i	0.613181	−	0.789943i	$-0.289890\pi$
$661$	−249.541	−	432.217i	−0.377520	−	0.653884i	−0.990701	+	0.136059i	$0.956556\pi$
$662$	−67.4013	+	251.545i	−0.101815	+	0.379978i
$663$		0			0
$664$			74.0263i			0.111485i
$665$	−969.074	+	627.149i	−1.45725	+	0.943081i
$666$		0			0
$667$	−371.728	+	99.6041i	−0.557313	+	0.149332i
$668$	1252.20	+	335.526i	1.87455	+	0.502285i
$669$		0			0
$670$	−411.325	+	477.087i	−0.613918	+	0.712071i
$671$	−1130.03			−1.68410
$672$		0			0
$673$	588.355	−	588.355i	0.874227	−	0.874227i	−0.118703	−	0.992930i	$-0.537874\pi$
$673$	588.355	−	588.355i	0.874227	−	0.874227i	0.992930	+	0.118703i	$0.0378735\pi$
$674$	623.006	+	359.693i	0.924341	+	0.533669i
$675$		0			0
$676$	115.312	+	199.727i	0.170580	+	0.295454i
$677$	−825.046	+	221.070i	−1.21868	+	0.326544i	−0.810162	−	0.586206i	$-0.800621\pi$
$677$	−825.046	+	221.070i	−1.21868	+	0.326544i	−0.408518	+	0.912750i	$0.633954\pi$
$678$		0			0
$679$	−341.256	+	560.739i	−0.502586	+	0.825830i
$680$	−63.2961	+	332.865i	−0.0930824	+	0.489507i
$681$		0			0
$682$	−248.229	+	926.403i	−0.363972	+	1.35836i
$683$	−289.626	−	77.6050i	−0.424050	−	0.113624i	0.0404821	−	0.999180i	$-0.487111\pi$
$683$	−289.626	−	77.6050i	−0.424050	−	0.113624i	−0.464532	+	0.885557i	$0.653777\pi$
$684$		0			0
$685$	−886.256	+	603.055i	−1.29380	+	0.880373i
$686$	846.287	+	570.225i	1.23365	+	0.831232i
$687$		0			0
$688$	116.430	+	434.524i	0.169230	+	0.631576i
$689$	425.748	−	245.806i	0.617922	−	0.356758i
$690$		0			0
$691$	−422.621	+	732.000i	−0.611607	+	1.05933i	0.379363	+	0.925248i	$0.376143\pi$
$691$	−422.621	+	732.000i	−0.611607	+	1.05933i	−0.990970	+	0.134086i	$0.957190\pi$
$692$	31.3057	+	31.3057i	0.0452395	+	0.0452395i
$693$		0			0
$694$		−	198.443i		−	0.285941i
$695$	−665.043	+	771.369i	−0.956896	+	1.10988i
$696$		0			0
$697$	11.7586	−	43.8839i	0.0168704	−	0.0629611i
$698$	342.863	+	1279.58i	0.491208	+	1.83321i
$699$		0			0
$700$	521.023	−	670.318i	0.744318	−	0.957597i
$701$	177.525			0.253245			0.126623	−	0.991951i	$-0.459586\pi$
$701$	177.525			0.253245			0.126623	+	0.991951i	$0.459586\pi$
$702$		0			0
$703$	−664.795	−	178.131i	−0.945654	−	0.253387i
$704$	1057.76	−	610.698i	1.50250	−	0.867469i
$705$		0			0
$706$	1102.00			1.56091
$707$	232.028	−	221.545i	0.328186	−	0.313359i
$708$		0			0
$709$	−488.278	−	281.907i	−0.688685	−	0.397613i	0.114434	−	0.993431i	$-0.463495\pi$
$709$	−488.278	−	281.907i	−0.688685	−	0.397613i	−0.803119	+	0.595818i	$0.796828\pi$
$710$	−269.412	−	130.045i	−0.379454	−	0.183162i
$711$		0			0
$712$	409.660	−	109.768i	0.575365	−	0.154169i
$713$	347.093	−	347.093i	0.486807	−	0.486807i
$714$		0			0
$715$	431.601	+	634.285i	0.603638	+	0.887112i
$716$	−649.843	+	1125.56i	−0.907602	+	1.57201i
$717$		0			0
$718$	1683.43	+	451.074i	2.34461	+	0.628236i
$719$	340.465	+	196.567i	0.473525	+	0.273390i	0.717714	−	0.696338i	$-0.245188\pi$
$719$	340.465	+	196.567i	0.473525	+	0.273390i	−0.244189	+	0.969728i	$0.578522\pi$
$720$		0			0
$721$	134.653	−	73.6469i	0.186758	−	0.102146i
$722$	1528.76	+	1528.76i	2.11740	+	2.11740i
$723$		0			0
$724$	−953.622	+	550.574i	−1.31716	+	0.760461i
$725$	−448.882	+	66.8207i	−0.619148	+	0.0921664i
$726$		0			0
$727$	−110.762	−	110.762i	−0.152356	−	0.152356i	0.626814	−	0.779169i	$-0.284359\pi$
$727$	−110.762	−	110.762i	−0.152356	−	0.152356i	−0.779169	+	0.626814i	$0.784359\pi$
$728$	−189.874	+	46.2020i	−0.260815	+	0.0634643i
$729$		0			0
$730$	−73.2592	−	63.1610i	−0.100355	−	0.0865220i
$731$	−506.968	−	878.094i	−0.693527	−	1.20122i
$732$		0			0
$733$	−180.535	−	673.766i	−0.246296	−	0.919190i	−0.972727	−	0.231951i	$-0.925489\pi$
$733$	−180.535	−	673.766i	−0.246296	−	0.919190i	0.726431	−	0.687239i	$-0.241178\pi$
$734$		−	896.977i		−	1.22204i
$735$		0			0
$736$	−963.429			−1.30901
$737$	−569.472	+	152.590i	−0.772689	+	0.207042i
$738$		0			0
$739$	701.070	−	404.763i	0.948675	−	0.547717i	0.0560056	−	0.998430i	$-0.482164\pi$
$739$	701.070	−	404.763i	0.948675	−	0.547717i	0.892669	+	0.450713i	$0.148830\pi$
$740$	504.826	−	37.3683i	0.682197	−	0.0504977i
$741$		0			0
$742$	−219.640	−	902.640i	−0.296010	−	1.21650i
$743$	−615.379	+	615.379i	−0.828235	+	0.828235i	−0.987273	−	0.159037i	$-0.949161\pi$
$743$	−615.379	+	615.379i	−0.828235	+	0.828235i	0.159037	+	0.987273i	$0.449161\pi$
$744$		0			0
$745$	202.809	+	581.294i	0.272226	+	0.780261i
$746$	785.474	+	1360.48i	1.05291	+	1.82370i
$747$		0			0
$748$	−1277.74	+	1277.74i	−1.70821	+	1.70821i
$749$	−339.225	−	620.224i	−0.452904	−	0.828069i
$750$		0			0
$751$	−666.673	+	1154.71i	−0.887713	+	1.53756i	−0.0451417	+	0.998981i	$0.514374\pi$
$751$	−666.673	+	1154.71i	−0.887713	+	1.53756i	−0.842572	+	0.538584i	$0.818959\pi$
$752$	−32.7035	+	122.051i	−0.0434887	+	0.162302i
$753$		0			0
$754$	515.477	+	297.611i	0.683656	+	0.394709i
$755$	−94.6059	+	497.519i	−0.125306	+	0.658966i
$756$		0			0
$757$	897.927	+	897.927i	1.18617	+	1.18617i	0.978119	+	0.208047i	$0.0667106\pi$
$757$	897.927	+	897.927i	1.18617	+	1.18617i	0.208047	+	0.978119i	$0.433289\pi$
$758$	136.341	+	508.832i	0.179870	+	0.671283i
$759$		0			0
$760$	−376.165	−	181.574i	−0.494954	−	0.238914i
$761$	19.9063	−	34.4788i	0.0261581	−	0.0453072i	−0.852650	−	0.522483i	$-0.825006\pi$
$761$	19.9063	−	34.4788i	0.0261581	−	0.0453072i	0.878808	+	0.477175i	$0.158339\pi$
$762$		0			0
$763$	613.393	+	642.417i	0.803923	+	0.841963i
$764$			754.964i			0.988173i
$765$		0			0
$766$	401.410	+	695.262i	0.524034	+	0.907653i
$767$	−29.7951	+	111.197i	−0.0388462	+	0.144976i
$768$		0			0
$769$			246.046i			0.319956i	0.987121	+	0.159978i	$0.0511424\pi$
$769$			246.046i			0.319956i	−0.987121	+	0.159978i	$0.948858\pi$
$770$	1379.50	−	445.817i	1.79155	−	0.578983i
$771$		0			0
$772$	−985.653	+	264.105i	−1.27675	+	0.342105i
$773$	−760.894	−	203.881i	−0.984339	−	0.263753i	−0.269468	−	0.963009i	$-0.586848\pi$
$773$	−760.894	−	203.881i	−0.984339	−	0.263753i	−0.714871	+	0.699257i	$0.753515\pi$
$774$		0			0
$775$	453.227	−	360.086i	0.584809	−	0.464626i
$776$	−237.530			−0.306096
$777$		0			0
$778$	−392.090	+	392.090i	−0.503972	+	0.503972i
$779$	48.5031	+	28.0033i	0.0622633	+	0.0359477i
$780$		0			0
$781$	−139.995	−	242.478i	−0.179250	−	0.310471i
$782$	1629.87	−	436.722i	2.08423	−	0.558469i
$783$		0			0
$784$	26.8700	−	580.987i	0.0342730	−	0.741055i
$785$	299.631	−	203.885i	0.381696	−	0.259726i
$786$		0			0
$787$	222.827	−	831.602i	0.283135	−	1.05667i	−0.667057	−	0.745007i	$-0.732446\pi$
$787$	222.827	−	831.602i	0.283135	−	1.05667i	0.950192	−	0.311667i	$-0.100887\pi$
$788$	653.567	+	175.123i	0.829400	+	0.222237i
$789$		0			0
$790$	−101.792	−	149.595i	−0.128851	−	0.189360i
$791$	−86.6139	−	52.7118i	−0.109499	−	0.0666394i
$792$		0			0
$793$	−231.520	−	864.044i	−0.291954	−	1.08959i
$794$	−1758.08	+	1015.03i	−2.21420	+	1.27837i
$795$		0			0
$796$	−100.333	+	173.782i	−0.126046	+	0.218319i
$797$	−710.464	−	710.464i	−0.891423	−	0.891423i	0.103234	−	0.994657i	$-0.467081\pi$
$797$	−710.464	−	710.464i	−0.891423	−	0.891423i	−0.994657	+	0.103234i	$0.967081\pi$
$798$		0			0
$799$		−	284.799i		−	0.356444i
$800$	−1128.76	−	129.267i	−1.41095	−	0.161584i
$801$		0			0
$802$	−98.4556	+	367.441i	−0.122763	+	0.458156i
$803$	−23.4309	−	87.4453i	−0.0291792	−	0.108898i
$804$		0			0
$805$	−725.530	−	155.415i	−0.901279	−	0.193062i
$806$	−759.204			−0.941940
$807$		0			0
$808$	112.132	+	30.0457i	0.138777	+	0.0371853i
$809$	−836.414	+	482.904i	−1.03389	+	0.596914i	−0.918095	−	0.396359i	$-0.870273\pi$
$809$	−836.414	+	482.904i	−1.03389	+	0.596914i	−0.115790	+	0.993274i	$0.536940\pi$
$810$		0			0
$811$	−632.087			−0.779392			−0.389696	−	0.920944i	$-0.627420\pi$
$811$	−632.087			−0.779392			−0.389696	+	0.920944i	$0.627420\pi$
$812$	445.871	−	425.726i	0.549102	−	0.524293i
$813$		0			0
$814$	748.594	+	432.201i	0.919649	+	0.530959i
$815$	395.849	−	820.075i	0.485705	−	1.00623i
$816$		0			0
$817$	1207.35	−	323.508i	1.47778	−	0.395970i
$818$	164.150	−	164.150i	0.200673	−	0.200673i
$819$		0			0
$820$	−40.4679	−	7.69518i	−0.0493510	−	0.00938437i
$821$	518.747	−	898.496i	0.631848	−	1.09439i	−0.355326	−	0.934742i	$-0.615630\pi$
$821$	518.747	−	898.496i	0.631848	−	1.09439i	0.987174	−	0.159650i	$-0.0510365\pi$
$822$		0			0
$823$	−1433.38	−	384.072i	−1.74165	−	0.466673i	−0.758837	−	0.651281i	$-0.774232\pi$
$823$	−1433.38	−	384.072i	−1.74165	−	0.466673i	−0.982812	+	0.184607i	$0.940899\pi$
$824$	48.0964	+	27.7685i	0.0583695	+	0.0336996i
$825$		0			0
$826$	185.828	+	113.092i	0.224974	+	0.136915i
$827$	896.076	+	896.076i	1.08353	+	1.08353i	0.996178	+	0.0873480i	$0.0278392\pi$
$827$	896.076	+	896.076i	1.08353	+	1.08353i	0.0873480	+	0.996178i	$0.472161\pi$
$828$		0			0
$829$	−566.312	+	326.960i	−0.683127	+	0.394403i	−0.801032	−	0.598621i	$-0.795715\pi$
$829$	−566.312	+	326.960i	−0.683127	+	0.394403i	0.117905	+	0.993025i	$0.462382\pi$
$830$	410.470	−	143.210i	0.494543	−	0.172542i
$831$		0			0
$832$	683.666	+	683.666i	0.821714	+	0.821714i
$833$	280.425	+	1280.56i	0.336644	+	1.53728i
$834$		0			0
$835$	−98.6300	−	1332.44i	−0.118120	−	1.59574i
$836$	−1113.80	−	1929.16i	−1.33230	−	2.30761i
$837$		0			0
$838$	29.3266	+	109.448i	0.0349959	+	0.130607i
$839$		−	1045.69i		−	1.24636i	−0.782079	−	0.623179i	$-0.785841\pi$
$839$		−	1045.69i		−	1.24636i	0.782079	−	0.623179i	$-0.214159\pi$
$840$		0			0
$841$	511.463			0.608161
$842$	−435.699	+	116.745i	−0.517457	+	0.138652i
$843$		0			0
$844$	1371.69	−	791.948i	1.62523	−	0.938327i
$845$	155.206	−	180.020i	0.183675	−	0.213041i
$846$		0			0
$847$	489.305	+	143.305i	0.577692	+	0.169191i
$848$	−374.387	+	374.387i	−0.441494	+	0.441494i
$849$		0			0
$850$	1968.16	−	292.981i	2.31548	−	0.344683i
$851$	−221.203	−	383.135i	−0.259933	−	0.450217i
$852$		0			0
$853$	−707.639	+	707.639i	−0.829588	+	0.829588i	−0.987460	−	0.157871i	$-0.949537\pi$
$853$	−707.639	+	707.639i	−0.829588	+	0.829588i	0.157871	+	0.987460i	$0.449537\pi$
$854$	−1689.89	−	39.0570i	−1.97880	−	0.0457342i
$855$		0			0
$856$	127.904	−	221.537i	0.149421	−	0.258805i
$857$	318.658	−	1189.25i	0.371829	−	1.38769i	−0.486093	−	0.873907i	$-0.661579\pi$
$857$	318.658	−	1189.25i	0.371829	−	1.38769i	0.857923	−	0.513779i	$-0.171755\pi$
$858$		0			0
$859$	268.193	+	154.841i	0.312215	+	0.180258i	0.647917	−	0.761711i	$-0.275640\pi$
$859$	268.193	+	154.841i	0.312215	+	0.180258i	−0.335702	+	0.941968i	$0.608974\pi$
$860$	−760.061	+	517.185i	−0.883792	+	0.601378i
$861$		0			0
$862$	1128.86	+	1128.86i	1.30958	+	1.30958i
$863$	−363.183	−	1355.42i	−0.420837	−	1.57059i	−0.772849	−	0.634590i	$-0.781169\pi$
$863$	−363.183	−	1355.42i	−0.420837	−	1.57059i	0.352011	−	0.935996i	$-0.385498\pi$
$864$		0			0
$865$	19.8352	−	41.0923i	0.0229309	−	0.0475056i
$866$	886.576	−	1535.59i	1.02376	−	1.77320i
$867$		0			0
$868$	−221.008	+	754.617i	−0.254618	+	0.869374i
$869$		−	169.349i		−	0.194878i
$870$		0			0
$871$	−233.346	−	404.168i	−0.267906	−	0.464027i
$872$	−83.1879	+	310.461i	−0.0953990	+	0.356034i
$873$		0			0
$874$			2080.12i			2.37999i
$875$	−829.182	−	279.432i	−0.947637	−	0.319351i
$876$		0			0
$877$	614.493	−	164.653i	0.700676	−	0.187746i	0.109143	−	0.994026i	$-0.465189\pi$
$877$	614.493	−	164.653i	0.700676	−	0.187746i	0.591533	+	0.806281i	$0.298523\pi$
$878$	1364.80	+	365.697i	1.55444	+	0.416512i
$879$		0			0
$880$	−625.798	−	539.537i	−0.711134	−	0.613110i
$881$	947.178			1.07512			0.537559	−	0.843226i	$-0.319347\pi$
$881$	947.178			1.07512			0.537559	+	0.843226i	$0.319347\pi$
$882$		0			0
$883$	−1152.12	+	1152.12i	−1.30478	+	1.30478i	−0.379646	+	0.925132i	$0.623954\pi$
$883$	−1152.12	+	1152.12i	−1.30478	+	1.30478i	−0.925132	+	0.379646i	$0.876046\pi$
$884$	−1238.77	−	715.207i	−1.40133	−	0.809057i
$885$		0			0
$886$	−140.143	−	242.735i	−0.158175	−	0.273968i
$887$	−40.1181	+	10.7496i	−0.0452290	+	0.0121191i	−0.281363	−	0.959602i	$-0.590786\pi$
$887$	−40.1181	+	10.7496i	−0.0452290	+	0.0121191i	0.236134	+	0.971721i	$0.424120\pi$
$888$		0			0
$889$	711.367	−	1168.89i	0.800188	−	1.31484i
$890$	−1401.17	−	2059.18i	−1.57435	−	2.31368i
$891$		0			0
$892$	−69.6100	+	259.788i	−0.0780381	+	0.291242i
$893$	339.125	+	90.8683i	0.379759	+	0.101756i
$894$		0			0
$895$	1315.92	+	250.229i	1.47030	+	0.279585i
$896$	486.525	−	266.100i	0.542997	−	0.296987i
$897$		0			0
$898$	−401.666	−	1499.04i	−0.447290	−	1.66931i
$899$	364.011	−	210.162i	0.404907	−	0.233773i
$900$		0			0
$901$	596.686	−	1033.49i	0.662249	−	1.14705i
$902$	−49.7389	−	49.7389i	−0.0551429	−	0.0551429i
$903$		0			0
$904$		−	36.6899i		−	0.0405861i
$905$	859.529	+	741.051i	0.949756	+	0.818841i
$906$		0			0
$907$	−407.585	+	1521.13i	−0.449377	+	1.67710i	0.254735	+	0.967011i	$0.418012\pi$
$907$	−407.585	+	1521.13i	−0.449377	+	1.67710i	−0.704112	+	0.710088i	$0.748655\pi$
$908$	4.52675	+	16.8941i	0.00498541	+	0.0186058i
$909$		0			0
$910$	623.512	+	963.454i	0.685178	+	1.05874i
$911$	1032.26			1.13311			0.566556	−	0.824023i	$-0.308276\pi$
$911$	1032.26			1.13311			0.566556	+	0.824023i	$0.308276\pi$
$912$		0			0
$913$	393.017	+	105.309i	0.430468	+	0.115343i
$914$	1070.54	−	618.079i	1.17127	−	0.676235i
$915$		0			0
$916$	−257.717			−0.281351
$917$	148.145	+	43.3881i	0.161555	+	0.0473153i
$918$		0			0
$919$	−181.801	−	104.963i	−0.197824	−	0.114214i	0.397816	−	0.917465i	$-0.369768\pi$
$919$	−181.801	−	104.963i	−0.197824	−	0.114214i	−0.595640	+	0.803251i	$0.703102\pi$
$920$	−88.4470	−	253.509i	−0.0961380	−	0.275553i
$921$		0			0
$922$	−806.199	+	216.020i	−0.874403	+	0.234295i
$923$	156.722	−	156.722i	0.169796	−	0.169796i
$924$		0			0
$925$	−207.756	−	478.562i	−0.224601	−	0.517365i
$926$	−686.735	+	1189.46i	−0.741614	+	1.28451i
$927$		0			0
$928$	−796.868	−	213.520i	−0.858694	−	0.230086i
$929$	−194.809	−	112.473i	−0.209698	−	0.121069i	0.391473	−	0.920189i	$-0.371966\pi$
$929$	−194.809	−	112.473i	−0.209698	−	0.121069i	−0.601171	+	0.799121i	$0.705299\pi$
$930$		0			0
$931$	−1614.30	−	74.6596i	−1.73394	−	0.0801930i
$932$	443.363	+	443.363i	0.475711	+	0.475711i
$933$		0			0
$934$	1095.03	−	632.218i	1.17241	−	0.676893i
$935$	1677.19	+	809.576i	1.79378	+	0.865857i
$936$		0			0
$937$	−650.762	−	650.762i	−0.694516	−	0.694516i	0.268706	−	0.963222i	$-0.413404\pi$
$937$	−650.762	−	650.762i	−0.694516	−	0.694516i	−0.963222	+	0.268706i	$0.913404\pi$
$938$	−856.887	+	208.506i	−0.913525	+	0.222288i
$939$		0			0
$940$	−257.522	+	19.0623i	−0.273959	+	0.0202791i
$941$	−175.589	−	304.130i	−0.186599	−	0.323199i	0.757515	−	0.652817i	$-0.226413\pi$
$941$	−175.589	−	304.130i	−0.186599	−	0.323199i	−0.944114	+	0.329619i	$0.893080\pi$
$942$		0			0
$943$	9.31777	+	34.7744i	0.00988099	+	0.0368764i
$944$		−	123.983i		−	0.131338i
$945$		0			0
$946$	−1569.86			−1.65947
$947$	375.151	−	100.521i	0.396147	−	0.106147i	−0.0552454	−	0.998473i	$-0.517594\pi$
$947$	375.151	−	100.521i	0.396147	−	0.106147i	0.451392	+	0.892326i	$0.350927\pi$
$948$		0			0
$949$	62.0620	−	35.8315i	0.0653973	−	0.0377571i
$950$	−279.097	+	2437.07i	−0.293786	+	2.56534i
$951$		0			0
$952$	−343.085	+	327.584i	−0.360383	+	0.344101i
$953$	−413.158	+	413.158i	−0.433535	+	0.433535i	−0.889829	−	0.456294i	$-0.849176\pi$
$953$	−413.158	+	413.158i	−0.433535	+	0.433535i	0.456294	+	0.889829i	$0.349176\pi$
$954$		0			0
$955$	734.660	−	256.317i	0.769278	−	0.268394i
$956$	−885.739	−	1534.15i	−0.926505	−	1.60475i
$957$		0			0
$958$	445.221	−	445.221i	0.464740	−	0.464740i
$959$	−1500.36	−	34.6765i	−1.56451	−	0.0361590i
$960$		0			0
$961$	212.439	−	367.955i	0.221060	−	0.382888i
$962$	−177.098	+	660.940i	−0.184094	+	0.687048i
$963$		0			0
$964$	−1653.54	−	954.669i	−1.71529	−	0.990321i
$965$	591.640	+	869.479i	0.613098	+	0.901015i
$966$		0			0
$967$	−967.834	−	967.834i	−1.00086	−	1.00086i	−1.00000		0.000862358i	$-0.999726\pi$
$967$	−967.834	−	967.834i	−1.00086	−	1.00086i	−0.000862358	−	1.00000i	$-0.500274\pi$
$968$	47.7512	+	178.210i	0.0493298	+	0.184101i
$969$		0			0
$970$	459.520	+	1317.09i	0.473732	+	1.35782i
$971$	−540.722	+	936.558i	−0.556871	+	0.964529i	0.440884	+	0.897564i	$0.354665\pi$
$971$	−540.722	+	936.558i	−0.556871	+	0.964529i	−0.997755	+	0.0669653i	$0.978668\pi$
$972$		0			0
$973$	−1385.44	+	337.119i	−1.42389	+	0.346474i
$974$		−	142.649i		−	0.146457i
$975$		0			0
$976$	481.699	+	834.327i	0.493544	+	0.854843i
$977$	−84.3325	+	314.733i	−0.0863178	+	0.322143i	−0.995560	−	0.0941240i	$-0.969995\pi$
$977$	−84.3325	+	314.733i	−0.0863178	+	0.322143i	0.909243	+	0.416266i	$0.136662\pi$
$978$		0			0
$979$		−	2331.10i		−	2.38110i
$980$	1139.14	−	339.278i	1.16239	−	0.346202i
$981$		0			0
$982$	2254.34	−	604.048i	2.29566	−	0.615120i
$983$	−966.073	−	258.858i	−0.982780	−	0.263335i	−0.268565	−	0.963261i	$-0.586549\pi$
$983$	−966.073	−	258.858i	−0.982780	−	0.263335i	−0.714215	+	0.699926i	$0.753216\pi$
$984$		0			0
$985$	−51.4784	−	695.445i	−0.0522623	−	0.706036i
$986$	1444.88			1.46540
$987$		0			0
$988$	1246.88	−	1246.88i	1.26202	−	1.26202i
$989$	695.819	+	401.731i	0.703558	+	0.406199i
$990$		0			0
$991$	770.884	+	1335.21i	0.777885	+	1.34734i	0.933158	+	0.359465i	$0.117041\pi$
$991$	770.884	+	1335.21i	0.777885	+	1.34734i	−0.155273	+	0.987872i	$0.549626\pi$
$992$	1016.40	−	272.345i	1.02460	−	0.274541i
$993$		0			0
$994$	−200.973	−	367.450i	−0.202186	−	0.369668i
$995$	203.172	+	38.6343i	0.204193	+	0.0388284i
$996$		0			0
$997$	225.145	−	840.254i	0.225823	−	0.842782i	−0.756250	−	0.654282i	$-0.772971\pi$
$997$	225.145	−	840.254i	0.225823	−	0.842782i	0.982073	−	0.188500i	$-0.0603625\pi$
$998$	−168.150	−	45.0555i	−0.168486	−	0.0451458i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.14		64
3.2	odd	2		105.3.v.a.37.3	✓	64
5.3	odd	4	inner	315.3.ca.b.163.3		64
7.4	even	3	inner	315.3.ca.b.172.3		64
15.8	even	4		105.3.v.a.58.14	yes	64
21.11	odd	6		105.3.v.a.67.14	yes	64
35.18	odd	12	inner	315.3.ca.b.298.14		64
105.53	even	12		105.3.v.a.88.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.3	✓	64	3.2	odd	2
105.3.v.a.58.14	yes	64	15.8	even	4
105.3.v.a.67.14	yes	64	21.11	odd	6
105.3.v.a.88.3	yes	64	105.53	even	12
315.3.ca.b.37.14		64	1.1	even	1	trivial
315.3.ca.b.163.3		64	5.3	odd	4	inner
315.3.ca.b.172.3		64	7.4	even	3	inner
315.3.ca.b.298.14		64	35.18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.87375 - 0.770020i) q^{2} +(4.20143 - 2.42570i) q^{4} +(-3.78688 - 3.26489i) q^{5} +(-1.65502 - 6.80154i) q^{7} +(1.79111 - 1.79111i) q^{8} +O(q^{10})\)	\(q+(2.87375 - 0.770020i) q^{2} +(4.20143 - 2.42570i) q^{4} +(-3.78688 - 3.26489i) q^{5} +(-1.65502 - 6.80154i) q^{7} +(1.79111 - 1.79111i) q^{8} +(-13.3966 - 6.46653i) q^{10} +(-6.96127 - 12.0573i) q^{11} +(7.79302 - 7.79302i) q^{13} +(-9.99344 - 18.2715i) q^{14} +(-5.93477 + 10.2793i) q^{16} +(6.92421 - 25.8415i) q^{17} +(28.5616 + 16.4901i) q^{19} +(-23.8300 - 4.53140i) q^{20} +(-29.2893 - 29.2893i) q^{22} +(5.48688 + 20.4773i) q^{23} +(3.68094 + 24.7275i) q^{25} +(16.3944 - 28.3960i) q^{26} +(-23.4519 - 24.5616i) q^{28} +18.1531i q^{29} +(-11.5772 - 20.0522i) q^{31} +(-11.7622 + 43.8970i) q^{32} -79.5940i q^{34} +(-15.9389 + 31.1601i) q^{35} +(-20.1574 + 5.40117i) q^{37} +(94.7768 + 25.3954i) q^{38} +(-12.6305 + 0.934937i) q^{40} +1.69819 q^{41} +(26.7992 - 26.7992i) q^{43} +(-58.4946 - 33.7719i) q^{44} +(31.5359 + 54.6218i) q^{46} +(10.2827 - 2.75524i) q^{47} +(-43.5218 + 22.5134i) q^{49} +(29.6188 + 68.2264i) q^{50} +(13.8383 - 51.6453i) q^{52} +(43.0869 + 11.5451i) q^{53} +(-13.0042 + 68.3872i) q^{55} +(-15.1466 - 9.21797i) q^{56} +(13.9783 + 52.1677i) q^{58} +(-9.04603 + 5.22273i) q^{59} +(40.5827 - 70.2914i) q^{61} +(-48.7105 - 48.7105i) q^{62} +87.7280i q^{64} +(-54.9546 + 4.06786i) q^{65} +(10.9599 - 40.9029i) q^{67} +(-33.5921 - 125.367i) q^{68} +(-21.8107 + 101.820i) q^{70} +20.1105 q^{71} +(6.28085 + 1.68295i) q^{73} +(-53.7685 + 31.0433i) q^{74} +160.000 q^{76} +(-70.4869 + 67.3023i) q^{77} +(10.5341 + 6.08184i) q^{79} +(56.0352 - 19.5502i) q^{80} +(4.88019 - 1.30764i) q^{82} +(-20.6649 + 20.6649i) q^{83} +(-110.591 + 75.2519i) q^{85} +(56.3783 - 97.6501i) q^{86} +(-34.0643 - 9.12749i) q^{88} +(145.002 + 83.7168i) q^{89} +(-65.9021 - 40.1069i) q^{91} +(72.7245 + 72.7245i) q^{92} +(27.4284 - 15.8358i) q^{94} +(-54.3212 - 155.697i) q^{95} +(-66.3082 - 66.3082i) q^{97} +(-107.735 + 98.2105i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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