LMFDB - Embedded newform 425.2.m.c.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.5
Character	$\chi$	$=$	425.151
Dual form			425.2.m.c.76.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.921271 + 0.921271i) q^{2} +(-0.128082 - 0.309218i) q^{3} -0.302521i q^{4} +(0.166875 - 0.402872i) q^{6} +(-3.60742 - 1.49424i) q^{7} +(2.12124 - 2.12124i) q^{8} +(2.04211 - 2.04211i) q^{9} +(0.0518326 - 0.125135i) q^{11} +(-0.0935451 + 0.0387477i) q^{12} -6.65628i q^{13} +(-1.94681 - 4.70001i) q^{14} +3.30344 q^{16} +(0.550463 + 4.08620i) q^{17} +3.76267 q^{18} +(3.65065 + 3.65065i) q^{19} +1.30686i q^{21} +(0.163035 - 0.0675313i) q^{22} +(-1.65462 + 3.99461i) q^{23} +(-0.927622 - 0.384234i) q^{24} +(6.13224 - 6.13224i) q^{26} +(-1.82067 - 0.754146i) q^{27} +(-0.452040 + 1.09132i) q^{28} +(1.98471 - 0.822093i) q^{29} +(-3.29770 - 7.96135i) q^{31} +(-1.19913 - 1.19913i) q^{32} -0.0453329 q^{33} +(-3.25737 + 4.27162i) q^{34} +(-0.617782 - 0.617782i) q^{36} +(-0.0897069 - 0.216572i) q^{37} +6.72648i q^{38} +(-2.05824 + 0.852553i) q^{39} +(7.70637 + 3.19208i) q^{41} +(-1.20398 + 1.20398i) q^{42} +(1.34097 - 1.34097i) q^{43} +(-0.0378560 - 0.0156805i) q^{44} +(-5.20447 + 2.15576i) q^{46} +9.86840i q^{47} +(-0.423112 - 1.02148i) q^{48} +(5.83095 + 5.83095i) q^{49} +(1.19302 - 0.693583i) q^{51} -2.01367 q^{52} +(1.01016 + 1.01016i) q^{53} +(-0.982557 - 2.37210i) q^{54} +(-10.8219 + 4.48256i) q^{56} +(0.661264 - 1.59643i) q^{57} +(2.58582 + 1.07108i) q^{58} +(-2.55310 + 2.55310i) q^{59} +(-5.04635 - 2.09027i) q^{61} +(4.29648 - 10.3726i) q^{62} +(-10.4181 + 4.31534i) q^{63} -8.81632i q^{64} +(-0.0417638 - 0.0417638i) q^{66} +8.10531 q^{67} +(1.23616 - 0.166527i) q^{68} +1.44714 q^{69} +(3.98597 + 9.62298i) q^{71} -8.66363i q^{72} +(-1.16860 + 0.484052i) q^{73} +(0.116877 - 0.282165i) q^{74} +(1.10440 - 1.10440i) q^{76} +(-0.373964 + 0.373964i) q^{77} +(-2.68163 - 1.11077i) q^{78} +(-4.65072 + 11.2278i) q^{79} -8.00436i q^{81} +(4.15888 + 10.0404i) q^{82} +(-1.01268 - 1.01268i) q^{83} +0.395354 q^{84} +2.47080 q^{86} +(-0.508412 - 0.508412i) q^{87} +(-0.155492 - 0.375392i) q^{88} -4.30811i q^{89} +(-9.94609 + 24.0120i) q^{91} +(1.20846 + 0.500559i) q^{92} +(-2.03942 + 2.03942i) q^{93} +(-9.09146 + 9.09146i) q^{94} +(-0.217205 + 0.524380i) q^{96} +(-0.437000 + 0.181011i) q^{97} +10.7438i q^{98} +(-0.149691 - 0.361387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} - 12 q^{12} - 24 q^{14} - 24 q^{16} + 4 q^{17} - 40 q^{18} - 20 q^{19} + 16 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{26} - 12 q^{27} + 48 q^{28} + 4 q^{29} + 24 q^{31}+ \cdots - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 - 12 * q^12 - 24 * q^14 - 24 * q^16 + 4 * q^17 - 40 * q^18 - 20 * q^19 + 16 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^26 - 12 * q^27 + 48 * q^28 + 4 * q^29 + 24 * q^31 - 60 * q^32 + 48 * q^33 + 16 * q^34 + 60 * q^36 - 12 * q^37 + 8 * q^39 - 20 * q^41 + 12 * q^42 + 32 * q^43 + 64 * q^44 - 40 * q^46 - 40 * q^48 + 24 * q^49 + 16 * q^51 - 48 * q^52 - 12 * q^53 - 20 * q^54 - 32 * q^56 + 68 * q^57 - 16 * q^58 - 16 * q^59 - 64 * q^61 + 100 * q^62 - 44 * q^63 - 72 * q^66 + 40 * q^67 + 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 + 24 * q^77 - 16 * q^78 - 48 * q^79 + 100 * q^82 + 12 * q^83 - 40 * q^84 - 16 * q^86 + 24 * q^87 + 4 * q^88 + 24 * q^91 - 88 * q^92 - 32 * q^93 - 40 * q^94 + 132 * q^96 - 88 * q^97 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.921271	+	0.921271i	0.651437	+	0.651437i	0.953339	−	0.301902i	$-0.0976216\pi$
$2$	0.921271	+	0.921271i	0.651437	+	0.651437i	−0.301902	+	0.953339i	$0.597622\pi$
$3$	−0.128082	−	0.309218i	−0.0739484	−	0.178527i	0.882583	−	0.470157i	$-0.155803\pi$
$3$	−0.128082	−	0.309218i	−0.0739484	−	0.178527i	−0.956531	+	0.291629i	$0.905803\pi$
$4$		−	0.302521i		−	0.151261i
$5$		0			0
$5$		0			0
$6$	0.166875	−	0.402872i	0.0681265	−	0.164472i
$7$	−3.60742	−	1.49424i	−1.36348	−	0.564770i	−0.423464	−	0.905913i	$-0.639186\pi$
$7$	−3.60742	−	1.49424i	−1.36348	−	0.564770i	−0.940011	+	0.341143i	$0.889186\pi$
$8$	2.12124	−	2.12124i	0.749973	−	0.749973i
$9$	2.04211	−	2.04211i	0.680703	−	0.680703i
$10$		0			0
$11$	0.0518326	−	0.125135i	0.0156281	−	0.0377296i	−0.915873	−	0.401468i	$-0.868500\pi$
$11$	0.0518326	−	0.125135i	0.0156281	−	0.0377296i	0.931501	+	0.363739i	$0.118500\pi$
$12$	−0.0935451	+	0.0387477i	−0.0270041	+	0.0111855i
$13$		−	6.65628i		−	1.84612i	−0.384655	−	0.923060i	$-0.625680\pi$
$13$		−	6.65628i		−	1.84612i	0.384655	−	0.923060i	$-0.374320\pi$
$14$	−1.94681	−	4.70001i	−0.520306	−	1.25613i
$15$		0			0
$16$	3.30344			0.825860
$17$	0.550463	+	4.08620i	0.133507	+	0.991048i
$17$	0.550463	+	4.08620i	0.133507	+	0.991048i
$18$	3.76267			0.886870
$19$	3.65065	+	3.65065i	0.837517	+	0.837517i	0.988532	−	0.151014i	$-0.0482540\pi$
$19$	3.65065	+	3.65065i	0.837517	+	0.837517i	−0.151014	+	0.988532i	$0.548254\pi$
$20$		0			0
$21$			1.30686i			0.285181i
$22$	0.163035	−	0.0675313i	0.0347592	−	0.0143977i
$23$	−1.65462	+	3.99461i	−0.345013	+	0.832934i	0.652181	+	0.758064i	$0.273854\pi$
$23$	−1.65462	+	3.99461i	−0.345013	+	0.832934i	−0.997193	+	0.0748706i	$0.976146\pi$
$24$	−0.927622	−	0.384234i	−0.189350	−	0.0784313i
$25$		0			0
$26$	6.13224	−	6.13224i	1.20263	−	1.20263i
$27$	−1.82067	−	0.754146i	−0.350388	−	0.145136i
$28$	−0.452040	+	1.09132i	−0.0854275	+	0.206240i
$29$	1.98471	−	0.822093i	0.368551	−	0.152659i	−0.190718	−	0.981645i	$-0.561082\pi$
$29$	1.98471	−	0.822093i	0.368551	−	0.152659i	0.559269	+	0.828986i	$0.311082\pi$
$30$		0			0
$31$	−3.29770	−	7.96135i	−0.592284	−	1.42990i	−0.881291	−	0.472573i	$-0.843325\pi$
$31$	−3.29770	−	7.96135i	−0.592284	−	1.42990i	0.289008	−	0.957327i	$-0.406675\pi$
$32$	−1.19913	−	1.19913i	−0.211978	−	0.211978i
$33$	−0.0453329			−0.00789144
$34$	−3.25737	+	4.27162i	−0.558634	+	0.732576i
$35$		0			0
$36$	−0.617782	−	0.617782i	−0.102964	−	0.102964i
$37$	−0.0897069	−	0.216572i	−0.0147477	−	0.0356041i	0.916334	−	0.400414i	$-0.131134\pi$
$37$	−0.0897069	−	0.216572i	−0.0147477	−	0.0356041i	−0.931082	+	0.364810i	$0.881134\pi$
$38$			6.72648i			1.09118i
$39$	−2.05824	+	0.852553i	−0.329583	+	0.136518i
$40$		0			0
$41$	7.70637	+	3.19208i	1.20353	+	0.498520i	0.892139	−	0.451761i	$-0.149204\pi$
$41$	7.70637	+	3.19208i	1.20353	+	0.498520i	0.311394	+	0.950281i	$0.399204\pi$
$42$	−1.20398	+	1.20398i	−0.185778	+	0.185778i
$43$	1.34097	−	1.34097i	0.204497	−	0.204497i	−0.597427	−	0.801923i	$-0.703810\pi$
$43$	1.34097	−	1.34097i	0.204497	−	0.204497i	0.801923	+	0.597427i	$0.203810\pi$
$44$	−0.0378560	−	0.0156805i	−0.00570701	−	0.00236392i
$45$		0			0
$46$	−5.20447	+	2.15576i	−0.767358	+	0.317850i
$47$			9.86840i			1.43945i	0.694257	+	0.719727i	$0.255733\pi$
$47$			9.86840i			1.43945i	−0.694257	+	0.719727i	$0.744267\pi$
$48$	−0.423112	−	1.02148i	−0.0610710	−	0.147438i
$49$	5.83095	+	5.83095i	0.832992	+	0.832992i
$50$		0			0
$51$	1.19302	−	0.693583i	0.167056	−	0.0971210i
$52$	−2.01367			−0.279245
$53$	1.01016	+	1.01016i	0.138756	+	0.138756i	0.773073	−	0.634317i	$-0.218719\pi$
$53$	1.01016	+	1.01016i	0.138756	+	0.138756i	−0.634317	+	0.773073i	$0.718719\pi$
$54$	−0.982557	−	2.37210i	−0.133709	−	0.322802i
$55$		0			0
$56$	−10.8219	+	4.48256i	−1.44613	+	0.599008i
$57$	0.661264	−	1.59643i	0.0875866	−	0.211453i
$58$	2.58582	+	1.07108i	0.339535	+	0.140640i
$59$	−2.55310	+	2.55310i	−0.332385	+	0.332385i	−0.853492	−	0.521107i	$-0.825519\pi$
$59$	−2.55310	+	2.55310i	−0.332385	+	0.332385i	0.521107	+	0.853492i	$0.325519\pi$
$60$		0			0
$61$	−5.04635	−	2.09027i	−0.646119	−	0.267631i	0.0354651	−	0.999371i	$-0.488709\pi$
$61$	−5.04635	−	2.09027i	−0.646119	−	0.267631i	−0.681584	+	0.731740i	$0.738709\pi$
$62$	4.29648	−	10.3726i	0.545654	−	1.31732i
$63$	−10.4181	+	4.31534i	−1.31256	+	0.543681i
$64$		−	8.81632i		−	1.10204i
$65$		0			0
$66$	−0.0417638	−	0.0417638i	−0.00514077	−	0.00514077i
$67$	8.10531			0.990221			0.495110	−	0.868830i	$-0.335128\pi$
$67$	8.10531			0.990221			0.495110	+	0.868830i	$0.335128\pi$
$68$	1.23616	−	0.166527i	0.149907	−	0.0201943i
$69$	1.44714			0.174215
$70$		0			0
$71$	3.98597	+	9.62298i	0.473048	+	1.14204i	0.962809	+	0.270182i	$0.0870838\pi$
$71$	3.98597	+	9.62298i	0.473048	+	1.14204i	−0.489762	+	0.871856i	$0.662916\pi$
$72$		−	8.66363i		−	1.02102i
$73$	−1.16860	+	0.484052i	−0.136775	+	0.0566540i	−0.450021	−	0.893018i	$-0.648584\pi$
$73$	−1.16860	+	0.484052i	−0.136775	+	0.0566540i	0.313246	+	0.949672i	$0.398584\pi$
$74$	0.116877	−	0.282165i	0.0135866	−	0.0328010i
$75$		0			0
$76$	1.10440	−	1.10440i	0.126683	−	0.126683i
$77$	−0.373964	+	0.373964i	−0.0426171	+	0.0426171i
$78$	−2.68163	−	1.11077i	−0.303635	−	0.125770i
$79$	−4.65072	+	11.2278i	−0.523247	+	1.26323i	0.412628	+	0.910900i	$0.364611\pi$
$79$	−4.65072	+	11.2278i	−0.523247	+	1.26323i	−0.935875	+	0.352331i	$0.885389\pi$
$80$		0			0
$81$		−	8.00436i		−	0.889373i
$82$	4.15888	+	10.0404i	0.459272	+	1.10878i
$83$	−1.01268	−	1.01268i	−0.111156	−	0.111156i	0.649341	−	0.760497i	$-0.275045\pi$
$83$	−1.01268	−	1.01268i	−0.111156	−	0.111156i	−0.760497	+	0.649341i	$0.775045\pi$
$84$	0.395354			0.0431367
$85$		0			0
$86$	2.47080			0.266433
$87$	−0.508412	−	0.508412i	−0.0545075	−	0.0545075i
$88$	−0.155492	−	0.375392i	−0.0165755	−	0.0400169i
$89$		−	4.30811i		−	0.456658i	−0.973584	−	0.228329i	$-0.926674\pi$
$89$		−	4.30811i		−	0.456658i	0.973584	−	0.228329i	$-0.0733263\pi$
$90$		0			0
$91$	−9.94609	+	24.0120i	−1.04263	+	2.51714i
$92$	1.20846	+	0.500559i	0.125990	+	0.0521868i
$93$	−2.03942	+	2.03942i	−0.211478	+	0.211478i
$94$	−9.09146	+	9.09146i	−0.937713	+	0.937713i
$95$		0			0
$96$	−0.217205	+	0.524380i	−0.0221684	+	0.0535193i
$97$	−0.437000	+	0.181011i	−0.0443706	+	0.0183789i	−0.404758	−	0.914424i	$-0.632644\pi$
$97$	−0.437000	+	0.181011i	−0.0443706	+	0.0183789i	0.360388	+	0.932803i	$0.382644\pi$
$98$			10.7438i			1.08528i
$99$	−0.149691	−	0.361387i	−0.0150446	−	0.0363208i
$100$		0			0
$101$	−12.0896			−1.20296			−0.601480	−	0.798888i	$-0.705422\pi$
$101$	−12.0896			−1.20296			−0.601480	+	0.798888i	$0.705422\pi$
$102$	1.73807	+	0.460118i	0.172095	+	0.0455585i
$103$	−3.87759			−0.382070			−0.191035	−	0.981583i	$-0.561184\pi$
$103$	−3.87759			−0.382070			−0.191035	+	0.981583i	$0.561184\pi$
$104$	−14.1196	−	14.1196i	−1.38454	−	1.38454i
$105$		0			0
$106$			1.86126i			0.180782i
$107$	15.8039	−	6.54619i	1.52782	−	0.632844i	0.548682	−	0.836031i	$-0.315130\pi$
$107$	15.8039	−	6.54619i	1.52782	−	0.632844i	0.979140	+	0.203187i	$0.0651299\pi$
$108$	−0.228145	+	0.550792i	−0.0219533	+	0.0530000i
$109$	11.7677	+	4.87433i	1.12714	+	0.466876i	0.866807	−	0.498644i	$-0.166168\pi$
$109$	11.7677	+	4.87433i	1.12714	+	0.466876i	0.260331	+	0.965520i	$0.416168\pi$
$110$		0			0
$111$	−0.0554780	+	0.0554780i	−0.00526574	+	0.00526574i
$112$	−11.9169	−	4.93613i	−1.12604	−	0.466421i
$113$	5.36383	−	12.9494i	0.504586	−	1.21818i	−0.442375	−	0.896830i	$-0.645864\pi$
$113$	5.36383	−	12.9494i	0.504586	−	1.21818i	0.946961	−	0.321349i	$-0.104136\pi$
$114$	2.07995	−	0.861543i	0.194805	−	0.0806909i
$115$		0			0
$116$	−0.248701	−	0.600416i	−0.0230913	−	0.0557472i
$117$	−13.5929	−	13.5929i	−1.25666	−	1.25666i
$118$	−4.70418			−0.433055
$119$	4.12001	−	15.5631i	0.377681	−	1.42667i
$120$		0			0
$121$	7.76520	+	7.76520i	0.705927	+	0.705927i
$122$	−2.72335	−	6.57476i	−0.246561	−	0.595251i
$123$		−	2.79180i		−	0.251728i
$124$	−2.40848	+	0.997624i	−0.216288	+	0.0895892i
$125$		0			0
$126$	−13.5735	−	5.62233i	−1.20923	−	0.500877i
$127$	2.26901	−	2.26901i	0.201342	−	0.201342i	−0.599233	−	0.800575i	$-0.704528\pi$
$127$	2.26901	−	2.26901i	0.201342	−	0.201342i	0.800575	+	0.599233i	$0.204528\pi$
$128$	5.72396	−	5.72396i	0.505931	−	0.505931i
$129$	−0.586409	−	0.242899i	−0.0516305	−	0.0213860i
$130$		0			0
$131$	−9.02065	+	3.73648i	−0.788138	+	0.326458i	−0.740195	−	0.672393i	$-0.765267\pi$
$131$	−9.02065	+	3.73648i	−0.788138	+	0.326458i	−0.0479434	+	0.998850i	$0.515267\pi$
$132$			0.0137142i			0.00119366i
$133$	−7.71447	−	18.6244i	−0.668929	−	1.61494i
$134$	7.46718	+	7.46718i	0.645066	+	0.645066i
$135$		0			0
$136$	9.83549	+	7.50015i	0.843386	+	0.643133i
$137$	9.08620			0.776287			0.388143	−	0.921599i	$-0.373117\pi$
$137$	9.08620			0.776287			0.388143	+	0.921599i	$0.373117\pi$
$138$	1.33320	+	1.33320i	0.113490	+	0.113490i
$139$	3.02355	+	7.29950i	0.256454	+	0.619136i	0.998699	−	0.0509933i	$-0.0162387\pi$
$139$	3.02355	+	7.29950i	0.256454	+	0.619136i	−0.742245	+	0.670129i	$0.766239\pi$
$140$		0			0
$141$	3.05149	−	1.26397i	0.256982	−	0.106445i
$142$	−5.19321	+	12.5375i	−0.435805	+	1.05213i
$143$	−0.832934	−	0.345013i	−0.0696534	−	0.0288514i
$144$	6.74598	−	6.74598i	0.562165	−	0.562165i
$145$		0			0
$146$	−1.52254	−	0.630658i	−0.126007	−	0.0521936i
$147$	1.05619	−	2.54988i	0.0871134	−	0.210310i
$148$	−0.0655175	+	0.0271382i	−0.00538551	+	0.00223075i
$149$			5.90087i			0.483418i	0.970349	+	0.241709i	$0.0777079\pi$
$149$			5.90087i			0.483418i	−0.970349	+	0.241709i	$0.922292\pi$
$150$		0			0
$151$	−0.994085	−	0.994085i	−0.0808975	−	0.0808975i	0.665500	−	0.746398i	$-0.268218\pi$
$151$	−0.994085	−	0.994085i	−0.0808975	−	0.0808975i	−0.746398	+	0.665500i	$0.768218\pi$
$152$	15.4879			1.25623
$153$	9.46856	+	7.22035i	0.765488	+	0.583731i
$154$	−0.689043			−0.0555247
$155$		0			0
$156$	0.257915	+	0.622663i	0.0206498	+	0.0498529i
$157$			21.1248i			1.68594i	0.537961	+	0.842970i	$0.319195\pi$
$157$			21.1248i			1.68594i	−0.537961	+	0.842970i	$0.680805\pi$
$158$	−14.6285	+	6.05930i	−1.16378	+	0.482052i
$159$	0.182976	−	0.441744i	0.0145110	−	0.0350325i
$160$		0			0
$161$	11.9378	−	11.9378i	0.940832	−	0.940832i
$162$	7.37418	−	7.37418i	0.579370	−	0.579370i
$163$	7.33924	+	3.04001i	0.574854	+	0.238112i	0.651119	−	0.758975i	$-0.274300\pi$
$163$	7.33924	+	3.04001i	0.574854	+	0.238112i	−0.0762657	+	0.997088i	$0.524300\pi$
$164$	0.965674	−	2.33134i	0.0754064	−	0.182047i
$165$		0			0
$166$		−	1.86591i		−	0.144823i
$167$	1.11637	+	2.69514i	0.0863870	+	0.208557i	0.961169	−	0.275960i	$-0.0889956\pi$
$167$	1.11637	+	2.69514i	0.0863870	+	0.208557i	−0.874782	+	0.484516i	$0.838996\pi$
$168$	2.77218	+	2.77218i	0.213878	+	0.213878i
$169$	−31.3061			−2.40816
$170$		0			0
$171$	14.9101			1.14020
$172$	−0.405673	−	0.405673i	−0.0309323	−	0.0309323i
$173$	6.93025	+	16.7311i	0.526897	+	1.27204i	0.933546	+	0.358458i	$0.116697\pi$
$173$	6.93025	+	16.7311i	0.526897	+	1.27204i	−0.406649	+	0.913585i	$0.633303\pi$
$174$		−	0.936770i		−	0.0710164i
$175$		0			0
$176$	0.171226	−	0.413376i	0.0129066	−	0.0311594i
$177$	1.11647	+	0.462457i	0.0839191	+	0.0347604i
$178$	3.96893	−	3.96893i	0.297484	−	0.297484i
$179$	4.22369	−	4.22369i	0.315693	−	0.315693i	−0.531417	−	0.847110i	$-0.678340\pi$
$179$	4.22369	−	4.22369i	0.315693	−	0.315693i	0.847110	+	0.531417i	$0.178340\pi$
$180$		0			0
$181$	9.05185	−	21.8531i	0.672819	−	1.62433i	−0.103980	−	0.994579i	$-0.533158\pi$
$181$	9.05185	−	21.8531i	0.672819	−	1.62433i	0.776799	−	0.629749i	$-0.216842\pi$
$182$	−31.2846	+	12.9585i	−2.31897	+	0.960547i
$183$			1.82815i			0.135141i
$184$	4.96369	+	11.9834i	0.365928	+	0.883429i
$185$		0			0
$186$	−3.75771			−0.275529
$187$	0.539858	+	0.142916i	0.0394783	+	0.0104511i
$188$	2.98540			0.217733
$189$	5.44104	+	5.44104i	0.395777	+	0.395777i
$190$		0			0
$191$		−	14.2162i		−	1.02865i	−0.857595	−	0.514326i	$-0.828042\pi$
$191$		−	14.2162i		−	1.02865i	0.857595	−	0.514326i	$-0.171958\pi$
$192$	−2.72617	+	1.12922i	−0.196744	+	0.0814941i
$193$	−4.45325	+	10.7511i	−0.320552	+	0.773880i	0.678670	+	0.734443i	$0.262557\pi$
$193$	−4.45325	+	10.7511i	−0.320552	+	0.773880i	−0.999222	+	0.0394372i	$0.987443\pi$
$194$	−0.569355	−	0.235835i	−0.0408773	−	0.0169319i
$195$		0			0
$196$	1.76399	−	1.76399i	0.125999	−	0.125999i
$197$	−17.3686	−	7.19431i	−1.23746	−	0.512574i	−0.334542	−	0.942381i	$-0.608581\pi$
$197$	−17.3686	−	7.19431i	−1.23746	−	0.512574i	−0.902921	+	0.429807i	$0.858581\pi$
$198$	0.195029	−	0.470842i	0.0138601	−	0.0334613i
$199$	4.96849	−	2.05802i	0.352207	−	0.145889i	−0.199563	−	0.979885i	$-0.563952\pi$
$199$	4.96849	−	2.05802i	0.352207	−	0.145889i	0.551771	+	0.833996i	$0.313952\pi$
$200$		0			0
$201$	−1.03815	−	2.50631i	−0.0732252	−	0.176781i
$202$	−11.1378	−	11.1378i	−0.783652	−	0.783652i
$203$	−8.38807			−0.588727
$204$	−0.209824	−	0.360914i	−0.0146906	−	0.0252691i
$205$		0			0
$206$	−3.57231	−	3.57231i	−0.248894	−	0.248894i
$207$	4.77852	+	11.5364i	0.332130	+	0.801832i
$208$		−	21.9886i		−	1.52464i
$209$	0.646047	−	0.267602i	0.0446880	−	0.0185104i
$210$		0			0
$211$	−11.2112	−	4.64382i	−0.771809	−	0.319694i	−0.0382042	−	0.999270i	$-0.512164\pi$
$211$	−11.2112	−	4.64382i	−0.771809	−	0.319694i	−0.733605	+	0.679576i	$0.762164\pi$
$212$	0.305595	−	0.305595i	0.0209883	−	0.0209883i
$213$	2.46507	−	2.46507i	0.168904	−	0.168904i
$214$	20.5905	+	8.52886i	1.40754	+	0.583021i
$215$		0			0
$216$	−5.46182	+	2.26236i	−0.371630	+	0.153934i
$217$			33.6474i			2.28414i
$218$	6.35063	+	15.3318i	0.430119	+	1.03840i
$219$	0.299355	+	0.299355i	0.0202286	+	0.0202286i
$220$		0			0
$221$	27.1989	−	3.66404i	1.82959	−	0.246470i
$222$	−0.102221			−0.00686059
$223$	6.30566	+	6.30566i	0.422258	+	0.422258i	0.885981	−	0.463722i	$-0.153486\pi$
$223$	6.30566	+	6.30566i	0.422258	+	0.422258i	−0.463722	+	0.885981i	$0.653486\pi$
$224$	2.53397	+	6.11755i	0.169308	+	0.408746i
$225$		0			0
$226$	16.8715	−	6.98839i	1.12227	−	0.464861i
$227$	1.14283	−	2.75903i	0.0758522	−	0.183123i	−0.881405	−	0.472361i	$-0.843402\pi$
$227$	1.14283	−	2.75903i	0.0758522	−	0.183123i	0.957257	+	0.289238i	$0.0934018\pi$
$228$	−0.482955	−	0.200046i	−0.0319845	−	0.0132484i
$229$	9.34813	−	9.34813i	0.617742	−	0.617742i	−0.327210	−	0.944952i	$-0.606108\pi$
$229$	9.34813	−	9.34813i	0.617742	−	0.617742i	0.944952	+	0.327210i	$0.106108\pi$
$230$		0			0
$231$	0.163535	+	0.0677382i	0.0107598	+	0.00445685i
$232$	2.46619	−	5.95391i	0.161913	−	0.390893i
$233$	18.1457	−	7.51620i	1.18876	−	0.492403i	0.301412	−	0.953494i	$-0.402542\pi$
$233$	18.1457	−	7.51620i	1.18876	−	0.492403i	0.887353	+	0.461091i	$0.152542\pi$
$234$		−	25.0454i		−	1.63727i
$235$		0			0
$236$	0.772366	+	0.772366i	0.0502767	+	0.0502767i
$237$	4.06753			0.264214
$238$	18.1335	−	10.5422i	1.17542	−	0.683350i
$239$	−16.0062			−1.03536			−0.517678	−	0.855575i	$-0.673204\pi$
$239$	−16.0062			−1.03536			−0.517678	+	0.855575i	$0.673204\pi$
$240$		0			0
$241$	3.80069	+	9.17567i	0.244824	+	0.591057i	0.997750	−	0.0670483i	$-0.0213582\pi$
$241$	3.80069	+	9.17567i	0.244824	+	0.591057i	−0.752926	+	0.658105i	$0.771358\pi$
$242$			14.3077i			0.919734i
$243$	−7.93711	+	3.28766i	−0.509166	+	0.210903i
$244$	−0.632351	+	1.52663i	−0.0404821	+	0.0977324i
$245$		0			0
$246$	2.57200	−	2.57200i	0.163985	−	0.163985i
$247$	24.2998	−	24.2998i	1.54616	−	1.54616i
$248$	−23.8832	−	9.89274i	−1.51658	−	0.628190i
$249$	−0.183433	+	0.442847i	−0.0116246	+	0.0280643i
$250$		0			0
$251$			25.5571i			1.61315i	0.591130	+	0.806576i	$0.298682\pi$
$251$			25.5571i			1.61315i	−0.591130	+	0.806576i	$0.701318\pi$
$252$	1.30548	+	3.15171i	0.0822376	+	0.198539i
$253$	0.414102	+	0.414102i	0.0260344	+	0.0260344i
$254$	4.18074			0.262323
$255$		0			0
$256$	−7.08602			−0.442876
$257$	0.954995	+	0.954995i	0.0595710	+	0.0595710i	0.736265	−	0.676694i	$-0.236588\pi$
$257$	0.954995	+	0.954995i	0.0595710	+	0.0595710i	−0.676694	+	0.736265i	$0.736588\pi$
$258$	−0.316466	−	0.764017i	−0.0197023	−	0.0475656i
$259$			0.915307i			0.0568744i
$260$		0			0
$261$	2.37419	−	5.73179i	0.146958	−	0.354789i
$262$	−11.7528	−	4.86816i	−0.726088	−	0.300756i
$263$	12.6821	−	12.6821i	0.782014	−	0.782014i	−0.198157	−	0.980170i	$-0.563496\pi$
$263$	12.6821	−	12.6821i	0.782014	−	0.782014i	0.980170	+	0.198157i	$0.0634955\pi$
$264$	−0.0961621	+	0.0961621i	−0.00591837	+	0.00591837i
$265$		0			0
$266$	10.0510	−	24.2652i	0.616265	−	1.48779i
$267$	−1.33215	+	0.551793i	−0.0815260	+	0.0337692i
$268$		−	2.45203i		−	0.149781i
$269$	−6.86275	−	16.5681i	−0.418429	−	1.01018i	−0.982803	−	0.184658i	$-0.940882\pi$
$269$	−6.86275	−	16.5681i	−0.418429	−	1.01018i	0.564374	−	0.825519i	$-0.309118\pi$
$270$		0			0
$271$	−11.6637			−0.708520			−0.354260	−	0.935147i	$-0.615267\pi$
$271$	−11.6637			−0.708520			−0.354260	+	0.935147i	$0.615267\pi$
$272$	1.81842	+	13.4985i	0.110258	+	0.818466i
$273$	8.69886			0.526479
$274$	8.37085	+	8.37085i	0.505702	+	0.505702i
$275$		0			0
$276$		−	0.437789i		−	0.0263518i
$277$	−10.9399	+	4.53147i	−0.657317	+	0.272270i	−0.686309	−	0.727310i	$-0.740770\pi$
$277$	−10.9399	+	4.53147i	−0.657317	+	0.272270i	0.0289920	+	0.999580i	$0.490770\pi$
$278$	−3.93931	+	9.51033i	−0.236264	+	0.570392i
$279$	−22.9922	−	9.52368i	−1.37651	−	0.570168i
$280$		0			0
$281$	11.1238	−	11.1238i	0.663589	−	0.663589i	−0.292635	−	0.956224i	$-0.594532\pi$
$281$	11.1238	−	11.1238i	0.663589	−	0.663589i	0.956224	+	0.292635i	$0.0945322\pi$
$282$	3.97570	+	1.64679i	0.236750	+	0.0980649i
$283$	5.76360	−	13.9146i	0.342611	−	0.827135i	−0.654840	−	0.755768i	$-0.727264\pi$
$283$	5.76360	−	13.9146i	0.342611	−	0.827135i	0.997450	−	0.0713671i	$-0.0227362\pi$
$284$	2.91116	−	1.20584i	0.172745	−	0.0715535i
$285$		0			0
$286$	−0.449508	−	1.08521i	−0.0265799	−	0.0641697i
$287$	−23.0304	−	23.0304i	−1.35944	−	1.35944i
$288$	−4.89751			−0.288588
$289$	−16.3940	+	4.49860i	−0.964352	+	0.264623i
$290$		0			0
$291$	0.111944	+	0.111944i	0.00656227	+	0.00656227i
$292$	0.146436	+	0.353528i	0.00856952	+	0.0206886i
$293$			4.85089i			0.283392i	0.989910	+	0.141696i	$0.0452555\pi$
$293$			4.85089i			0.283392i	−0.989910	+	0.141696i	$0.954744\pi$
$294$	3.32217	−	1.37609i	0.193753	−	0.0802550i
$295$		0			0
$296$	−0.649692	−	0.269111i	−0.0377626	−	0.0156418i
$297$	−0.188740	+	0.188740i	−0.0109518	+	0.0109518i
$298$	−5.43630	+	5.43630i	−0.314916	+	0.314916i
$299$	26.5893	+	11.0136i	1.53770	+	0.636935i
$300$		0			0
$301$	−6.84119	+	2.83372i	−0.394320	+	0.163333i
$302$		−	1.83164i		−	0.105399i
$303$	1.54846	+	3.73832i	0.0889569	+	0.214761i
$304$	12.0597	+	12.0597i	0.691672	+	0.691672i
$305$		0			0
$306$	2.07121	+	15.3750i	0.118403	+	0.878931i
$307$	−6.92516			−0.395240			−0.197620	−	0.980279i	$-0.563321\pi$
$307$	−6.92516			−0.395240			−0.197620	+	0.980279i	$0.563321\pi$
$308$	0.113132	+	0.113132i	0.00644629	+	0.00644629i
$309$	0.496651	+	1.19902i	0.0282535	+	0.0682099i
$310$		0			0
$311$	−26.9785	+	11.1748i	−1.52981	+	0.633668i	−0.979527	−	0.201312i	$-0.935480\pi$
$311$	−26.9785	+	11.1748i	−1.52981	+	0.633668i	−0.550281	+	0.834979i	$0.685480\pi$
$312$	−2.55757	+	6.17451i	−0.144794	+	0.349563i
$313$	−21.0514	−	8.71976i	−1.18989	−	0.492870i	−0.302173	−	0.953253i	$-0.597712\pi$
$313$	−21.0514	−	8.71976i	−1.18989	−	0.492870i	−0.887720	+	0.460383i	$0.847712\pi$
$314$	−19.4616	+	19.4616i	−1.09828	+	1.09828i
$315$		0			0
$316$	3.39666	+	1.40694i	0.191077	+	0.0791467i
$317$	8.10639	−	19.5706i	0.455300	−	1.09919i	−0.514979	−	0.857203i	$-0.672200\pi$
$317$	8.10639	−	19.5706i	0.455300	−	1.09919i	0.970279	−	0.241989i	$-0.0777999\pi$
$318$	0.575536	−	0.238395i	0.0322744	−	0.0133685i
$319$		−	0.290968i		−	0.0162911i
$320$		0			0
$321$	−4.04841	−	4.04841i	−0.225960	−	0.225960i
$322$	21.9959			1.22579
$323$	−12.9077	+	16.9268i	−0.718205	+	0.941834i
$324$	−2.42149			−0.134527
$325$		0			0
$326$	3.96075	+	9.56210i	0.219366	+	0.529596i
$327$		−	4.26309i		−	0.235750i
$328$	23.1183	−	9.57591i	1.27649	−	0.528741i
$329$	14.7458	−	35.5994i	0.812960	−	1.96266i
$330$		0			0
$331$	0.486915	−	0.486915i	0.0267633	−	0.0267633i	−0.693599	−	0.720362i	$-0.743976\pi$
$331$	0.486915	−	0.486915i	0.0267633	−	0.0267633i	0.720362	+	0.693599i	$0.243976\pi$
$332$	−0.306358	+	0.306358i	−0.0168136	+	0.0168136i
$333$	−0.625454	−	0.259072i	−0.0342747	−	0.0141970i
$334$	−1.45448	+	3.51143i	−0.0795858	+	0.192137i
$335$		0			0
$336$			4.31715i			0.235520i
$337$	−0.495589	−	1.19646i	−0.0269964	−	0.0651752i	0.909806	−	0.415033i	$-0.136230\pi$
$337$	−0.495589	−	1.19646i	−0.0269964	−	0.0651752i	−0.936803	+	0.349858i	$0.886230\pi$
$338$	−28.8414	−	28.8414i	−1.56876	−	1.56876i
$339$	−4.69121			−0.254792
$340$		0			0
$341$	−1.16717			−0.0632059
$342$	13.7362	+	13.7362i	0.742769	+	0.742769i
$343$	−1.86213	−	4.49558i	−0.100546	−	0.242738i
$344$		−	5.68907i		−	0.306734i
$345$		0			0
$346$	−9.02924	+	21.7985i	−0.485415	+	1.17190i
$347$	−2.62317	−	1.08655i	−0.140819	−	0.0583291i	0.311161	−	0.950357i	$-0.399282\pi$
$347$	−2.62317	−	1.08655i	−0.140819	−	0.0583291i	−0.451980	+	0.892028i	$0.649282\pi$
$348$	−0.153805	+	0.153805i	−0.00824484	+	0.00824484i
$349$	−2.95570	+	2.95570i	−0.158215	+	0.158215i	−0.781775	−	0.623560i	$-0.785686\pi$
$349$	−2.95570	+	2.95570i	−0.158215	+	0.158215i	0.623560	+	0.781775i	$0.285686\pi$
$350$		0			0
$351$	−5.01981	+	12.1189i	−0.267938	+	0.646859i
$352$	−0.212207	+	0.0878991i	−0.0113107	+	0.00468504i
$353$		−	1.12941i		−	0.0601125i	−0.999548	−	0.0300562i	$-0.990431\pi$
$353$		−	1.12941i		−	0.0601125i	0.999548	−	0.0300562i	$-0.00956864\pi$
$354$	0.602523	+	1.45462i	0.0320238	+	0.0773122i
$355$		0			0
$356$	−1.30329			−0.0690745
$357$	−5.34010	+	0.719381i	−0.282628	+	0.0380737i
$358$	7.78232			0.411308
$359$	−11.9203	−	11.9203i	−0.629130	−	0.629130i	0.318719	−	0.947849i	$-0.396747\pi$
$359$	−11.9203	−	11.9203i	−0.629130	−	0.629130i	−0.947849	+	0.318719i	$0.896747\pi$
$360$		0			0
$361$			7.65453i			0.402870i
$362$	28.4718	−	11.7934i	1.49645	−	0.619848i
$363$	1.40656	−	3.39573i	0.0738251	−	0.178230i
$364$	7.26414	+	3.00890i	0.380744	+	0.157709i
$365$		0			0
$366$	−1.68422	+	1.68422i	−0.0880357	+	0.0880357i
$367$	−20.3487	−	8.42869i	−1.06219	−	0.439974i	−0.217963	−	0.975957i	$-0.569941\pi$
$367$	−20.3487	−	8.42869i	−1.06219	−	0.439974i	−0.844229	+	0.535983i	$0.819941\pi$
$368$	−5.46594	+	13.1960i	−0.284932	+	0.687887i
$369$	22.2558	−	9.21867i	1.15859	−	0.479905i
$370$		0			0
$371$	−2.13464	−	5.15349i	−0.110825	−	0.267556i
$372$	0.616967	+	0.616967i	0.0319882	+	0.0319882i
$373$	19.3712			1.00300			0.501502	−	0.865157i	$-0.332781\pi$
$373$	19.3712			1.00300			0.501502	+	0.865157i	$0.332781\pi$
$374$	0.365691	+	0.629019i	0.0189094	+	0.0325258i
$375$		0			0
$376$	20.9333	+	20.9333i	1.07955	+	1.07955i
$377$	−5.47208	−	13.2108i	−0.281827	−	0.680389i
$378$			10.0253i			0.515648i
$379$	−19.3174	+	8.00151i	−0.992266	+	0.411010i	−0.818955	−	0.573857i	$-0.805446\pi$
$379$	−19.3174	+	8.00151i	−0.992266	+	0.411010i	−0.173310	+	0.984867i	$0.555446\pi$
$380$		0			0
$381$	−0.992240	−	0.410999i	−0.0508340	−	0.0210561i
$382$	13.0970	−	13.0970i	0.670101	−	0.670101i
$383$	3.04778	−	3.04778i	0.155734	−	0.155734i	−0.624939	−	0.780673i	$-0.714876\pi$
$383$	3.04778	−	3.04778i	0.155734	−	0.155734i	0.780673	+	0.624939i	$0.214876\pi$
$384$	−2.50309	−	1.03681i	−0.127735	−	0.0529097i
$385$		0			0
$386$	−14.0073	+	5.80202i	−0.712953	+	0.295315i
$387$		−	5.47684i		−	0.278403i
$388$	0.0547597	+	0.132202i	0.00278000	+	0.00671152i
$389$	10.3508	+	10.3508i	0.524804	+	0.524804i	0.919018	−	0.394214i	$-0.128983\pi$
$389$	10.3508	+	10.3508i	0.524804	+	0.524804i	−0.394214	+	0.919018i	$0.628983\pi$
$390$		0			0
$391$	−17.2336	−	4.56222i	−0.871539	−	0.230722i
$392$	24.7377			1.24944
$393$	2.31077	+	2.31077i	0.116563	+	0.116563i
$394$	−9.37328	−	22.6291i	−0.472219	−	1.14004i
$395$		0			0
$396$	−0.109327	+	0.0452849i	−0.00549390	+	0.00227565i
$397$	−4.30511	+	10.3935i	−0.216067	+	0.521633i	−0.994334	−	0.106301i	$-0.966099\pi$
$397$	−4.30511	+	10.3935i	−0.216067	+	0.521633i	0.778267	+	0.627934i	$0.216099\pi$
$398$	6.47332	+	2.68134i	0.324478	+	0.134403i
$399$	−4.77091	+	4.77091i	−0.238844	+	0.238844i
$400$		0			0
$401$	−28.9519	−	11.9923i	−1.44579	−	0.598865i	−0.484594	−	0.874739i	$-0.661032\pi$
$401$	−28.9519	−	11.9923i	−1.44579	−	0.598865i	−0.961194	+	0.275875i	$0.911032\pi$
$402$	1.35257	−	3.26540i	0.0674603	−	0.162863i
$403$	−52.9930	+	21.9504i	−2.63977	+	1.09343i
$404$			3.65736i			0.181960i
$405$		0			0
$406$	−7.72768	−	7.72768i	−0.383518	−	0.383518i
$407$	−0.0317504			−0.00157381
$408$	1.05943	−	4.00195i	0.0524497	−	0.198126i
$409$	−11.1397			−0.550823			−0.275412	−	0.961326i	$-0.588814\pi$
$409$	−11.1397			−0.550823			−0.275412	+	0.961326i	$0.588814\pi$
$410$		0			0
$411$	−1.16378	−	2.80962i	−0.0574052	−	0.138588i
$412$			1.17305i			0.0577921i
$413$	13.0250	−	5.39514i	0.640919	−	0.265477i
$414$	−6.22580	+	15.0304i	−0.305981	+	0.738704i
$415$		0			0
$416$	−7.98175	+	7.98175i	−0.391337	+	0.391337i
$417$	1.86988	−	1.86988i	0.0915682	−	0.0915682i
$418$	0.841718	+	0.348651i	0.0411698	+	0.0170531i
$419$	−12.7585	+	30.8017i	−0.623293	+	1.50476i	0.224520	+	0.974469i	$0.427918\pi$
$419$	−12.7585	+	30.8017i	−0.623293	+	1.50476i	−0.847814	+	0.530294i	$0.822082\pi$
$420$		0			0
$421$		−	2.41522i		−	0.117711i	−0.998267	−	0.0588553i	$-0.981255\pi$
$421$		−	2.41522i		−	0.117711i	0.998267	−	0.0588553i	$-0.0187451\pi$
$422$	−6.05031	−	14.6067i	−0.294524	−	0.711045i
$423$	20.1523	+	20.1523i	0.979841	+	0.979841i
$424$	4.28559			0.208127
$425$		0			0
$426$	4.54199			0.220060
$427$	15.0809	+	15.0809i	0.729817	+	0.729817i
$428$	−1.98036	−	4.78102i	−0.0957245	−	0.231099i
$429$			0.301748i			0.0145686i
$430$		0			0
$431$	−5.42084	+	13.0871i	−0.261113	+	0.630382i	−0.999008	−	0.0445336i	$-0.985820\pi$
$431$	−5.42084	+	13.0871i	−0.261113	+	0.630382i	0.737895	+	0.674915i	$0.235820\pi$
$432$	−6.01447	−	2.49128i	−0.289371	−	0.119862i
$433$	−25.3112	+	25.3112i	−1.21638	+	1.21638i	−0.247485	+	0.968892i	$0.579604\pi$
$433$	−25.3112	+	25.3112i	−1.21638	+	1.21638i	−0.968892	+	0.247485i	$0.920396\pi$
$434$	−30.9984	+	30.9984i	−1.48797	+	1.48797i
$435$		0			0
$436$	1.47459	−	3.55997i	0.0706199	−	0.170492i
$437$	−20.6234	+	8.54249i	−0.986551	+	0.408643i
$438$			0.551574i			0.0263552i
$439$	−4.80085	−	11.5903i	−0.229132	−	0.553174i	0.766940	−	0.641719i	$-0.221778\pi$
$439$	−4.80085	−	11.5903i	−0.229132	−	0.553174i	−0.996072	+	0.0885450i	$0.971778\pi$
$440$		0			0
$441$	23.8149			1.13404
$442$	28.4331	+	21.6819i	1.35242	+	1.03131i
$443$	−6.21505			−0.295286			−0.147643	−	0.989041i	$-0.547169\pi$
$443$	−6.21505			−0.295286			−0.147643	+	0.989041i	$0.547169\pi$
$444$	0.0167833	+	0.0167833i	0.000796499	+	0.000796499i
$445$		0			0
$446$			11.6184i			0.550149i
$447$	1.82466	−	0.755797i	0.0863033	−	0.0357480i
$448$	−13.1737	+	31.8041i	−0.622399	+	1.50260i
$449$	29.0859	+	12.0478i	1.37265	+	0.568569i	0.942505	−	0.334192i	$-0.108463\pi$
$449$	29.0859	+	12.0478i	1.37265	+	0.568569i	0.430142	+	0.902761i	$0.358463\pi$
$450$		0			0
$451$	0.798883	−	0.798883i	0.0376179	−	0.0376179i
$452$	−3.91748	−	1.62267i	−0.184263	−	0.0763241i
$453$	−0.180064	+	0.434714i	−0.00846017	+	0.0204246i
$454$	3.59467	−	1.48896i	0.168706	−	0.0698804i
$455$		0			0
$456$	−1.98372	−	4.78913i	−0.0928963	−	0.224271i
$457$	4.93483	+	4.93483i	0.230842	+	0.230842i	0.813044	−	0.582202i	$-0.197809\pi$
$457$	4.93483	+	4.93483i	0.230842	+	0.230842i	−0.582202	+	0.813044i	$0.697809\pi$
$458$	17.2243			0.804839
$459$	2.07938	−	7.85475i	0.0970570	−	0.366628i
$460$		0			0
$461$	−16.8525	−	16.8525i	−0.784899	−	0.784899i	0.195754	−	0.980653i	$-0.437285\pi$
$461$	−16.8525	−	16.8525i	−0.784899	−	0.784899i	−0.980653	+	0.195754i	$0.937285\pi$
$462$	0.0882543	+	0.213065i	0.00410596	+	0.00991267i
$463$			27.8631i			1.29491i	0.762104	+	0.647454i	$0.224166\pi$
$463$			27.8631i			1.29491i	−0.762104	+	0.647454i	$0.775834\pi$
$464$	6.55636	−	2.71573i	0.304371	−	0.126075i
$465$		0			0
$466$	23.6416	+	9.79265i	1.09517	+	0.453636i
$467$	−24.8120	+	24.8120i	−1.14816	+	1.14816i	−0.161247	+	0.986914i	$0.551552\pi$
$467$	−24.8120	+	24.8120i	−1.14816	+	1.14816i	−0.986914	+	0.161247i	$0.948448\pi$
$468$	−4.11213	+	4.11213i	−0.190083	+	0.190083i
$469$	−29.2392	−	12.1113i	−1.35014	−	0.559247i
$470$		0			0
$471$	6.53216	−	2.70571i	0.300986	−	0.124673i
$472$			10.8315i			0.498560i
$473$	−0.0982967	−	0.237309i	−0.00451969	−	0.0109115i
$474$	3.74729	+	3.74729i	0.172119	+	0.172119i
$475$		0			0
$476$	−4.70818	−	1.24639i	−0.215799	−	0.0571282i
$477$	4.12571			0.188903
$478$	−14.7461	−	14.7461i	−0.674469	−	0.674469i
$479$	−2.94944	−	7.12058i	−0.134763	−	0.325347i	0.842064	−	0.539378i	$-0.181341\pi$
$479$	−2.94944	−	7.12058i	−0.134763	−	0.325347i	−0.976827	+	0.214031i	$0.931341\pi$
$480$		0			0
$481$	−1.44156	+	0.597114i	−0.0657295	+	0.0272261i
$482$	−4.95181	+	11.9547i	−0.225549	+	0.544523i
$483$	−5.22042	−	2.16237i	−0.237537	−	0.0983912i
$484$	2.34914	−	2.34914i	0.106779	−	0.106779i
$485$		0			0
$486$	−10.3410	−	4.28340i	−0.469079	−	0.194299i
$487$	14.5641	−	35.1609i	0.659964	−	1.59329i	−0.137893	−	0.990447i	$-0.544033\pi$
$487$	14.5641	−	35.1609i	0.659964	−	1.59329i	0.797857	−	0.602847i	$-0.205967\pi$
$488$	−15.1385	+	6.27058i	−0.685289	+	0.283856i
$489$		−	2.65880i		−	0.120235i
$490$		0			0
$491$	−21.6157	−	21.6157i	−0.975505	−	0.975505i	0.0242025	−	0.999707i	$-0.492295\pi$
$491$	−21.6157	−	21.6157i	−0.975505	−	0.975505i	−0.999707	+	0.0242025i	$0.992295\pi$
$492$	−0.844579			−0.0380766
$493$	4.45174	+	7.65737i	0.200496	+	0.344871i
$494$	44.7733			2.01445
$495$		0			0
$496$	−10.8937	−	26.2998i	−0.489143	−	1.18090i
$497$		−	40.6701i		−	1.82430i
$498$	−0.576973	+	0.238990i	−0.0258548	+	0.0107094i
$499$	−0.427196	+	1.03134i	−0.0191239	+	0.0461692i	−0.933153	−	0.359479i	$-0.882954\pi$
$499$	−0.427196	+	1.03134i	−0.0191239	+	0.0461692i	0.914029	+	0.405649i	$0.132954\pi$
$500$		0			0
$501$	0.690401	−	0.690401i	0.0308449	−	0.0308449i
$502$	−23.5450	+	23.5450i	−1.05087	+	1.05087i
$503$	20.2920	+	8.40521i	0.904774	+	0.374770i	0.786054	−	0.618158i	$-0.212121\pi$
$503$	20.2920	+	8.40521i	0.904774	+	0.374770i	0.118720	+	0.992928i	$0.462121\pi$
$504$	−12.9455	+	31.2533i	−0.576640	+	1.39213i
$505$		0			0
$506$			0.763001i			0.0339195i
$507$	4.00976	+	9.68042i	0.178080	+	0.429922i
$508$	−0.686424	−	0.686424i	−0.0304551	−	0.0304551i
$509$	25.0162			1.10882			0.554411	−	0.832243i	$-0.312944\pi$
$509$	25.0162			1.10882			0.554411	+	0.832243i	$0.312944\pi$
$510$		0			0
$511$	4.93893			0.218485
$512$	−17.9761	−	17.9761i	−0.794437	−	0.794437i
$513$	−3.89351	−	9.39976i	−0.171903	−	0.415010i
$514$			1.75962i			0.0776134i
$515$		0			0
$516$	−0.0734820	+	0.177401i	−0.00323487	+	0.00780966i
$517$	1.23488	+	0.511505i	0.0543100	+	0.0224960i
$518$	−0.843246	+	0.843246i	−0.0370501	+	0.0370501i
$519$	4.28592	−	4.28592i	0.188131	−	0.188131i
$520$		0			0
$521$	−5.06417	+	12.2260i	−0.221865	+	0.535630i	−0.995143	−	0.0984369i	$-0.968616\pi$
$521$	−5.06417	+	12.2260i	−0.221865	+	0.535630i	0.773278	+	0.634067i	$0.218616\pi$
$522$	7.46780	−	3.09326i	0.326857	−	0.135388i
$523$			12.6357i			0.552522i	0.961083	+	0.276261i	$0.0890955\pi$
$523$			12.6357i			0.552522i	−0.961083	+	0.276261i	$0.910905\pi$
$524$	1.13036	+	2.72894i	0.0493802	+	0.119214i
$525$		0			0
$526$	23.3673			1.01886
$527$	30.7164	−	17.8575i	1.33803	−	0.777883i
$528$	−0.149754			−0.00651722
$529$	3.04431	+	3.04431i	0.132361	+	0.132361i
$530$		0			0
$531$			10.4274i			0.452511i
$532$	−5.63427	+	2.33379i	−0.244277	+	0.101183i
$533$	21.2474	−	51.2958i	0.920328	−	2.22187i
$534$	−1.73562	−	0.718916i	−0.0751075	−	0.0311105i
$535$		0			0
$536$	17.1933	−	17.1933i	0.742639	−	0.742639i
$537$	−1.84702	−	0.765061i	−0.0797049	−	0.0330148i
$538$	8.94129	−	21.5862i	0.385486	−	0.930647i
$539$	1.03189	−	0.427422i	0.0444466	−	0.0184104i
$540$		0			0
$541$	15.4030	+	37.1862i	0.662228	+	1.59876i	0.794305	+	0.607519i	$0.207835\pi$
$541$	15.4030	+	37.1862i	0.662228	+	1.59876i	−0.132077	+	0.991239i	$0.542165\pi$
$542$	−10.7454	−	10.7454i	−0.461556	−	0.461556i
$543$	−7.91676			−0.339741
$544$	4.23980	−	5.55995i	0.181780	−	0.238381i
$545$		0			0
$546$	8.01400	+	8.01400i	0.342968	+	0.342968i
$547$	4.92726	+	11.8954i	0.210674	+	0.508613i	0.993527	−	0.113594i	$-0.0362363\pi$
$547$	4.92726	+	11.8954i	0.210674	+	0.508613i	−0.782853	+	0.622207i	$0.786236\pi$
$548$		−	2.74877i		−	0.117422i
$549$	−14.5738	+	6.03665i	−0.621993	+	0.257638i
$550$		0			0
$551$	10.2467	+	4.24430i	0.436522	+	0.180813i
$552$	3.06973	−	3.06973i	0.130656	−	0.130656i
$553$	33.5542	−	33.5542i	1.42687	−	1.42687i
$554$	−14.2533	−	5.90393i	−0.605567	−	0.250834i
$555$		0			0
$556$	2.20826	−	0.914689i	0.0936509	−	0.0387915i
$557$			31.7092i			1.34356i	0.740749	+	0.671782i	$0.234471\pi$
$557$			31.7092i			1.34356i	−0.740749	+	0.671782i	$0.765529\pi$
$558$	−12.4081	−	29.9559i	−0.525279	−	1.26814i
$559$	−8.92591	−	8.92591i	−0.377526	−	0.377526i
$560$		0			0
$561$	−0.0249541	−	0.185239i	−0.00105356	−	0.00782079i
$562$	20.4960			0.864572
$563$	9.36930	+	9.36930i	0.394869	+	0.394869i	0.876419	−	0.481550i	$-0.159926\pi$
$563$	9.36930	+	9.36930i	0.394869	+	0.394869i	−0.481550	+	0.876419i	$0.659926\pi$
$564$	−0.382377	−	0.923140i	−0.0161010	−	0.0388712i
$565$		0			0
$566$	18.1289	−	7.50924i	0.762015	−	0.315637i
$567$	−11.9604	+	28.8751i	−0.502291	+	1.21264i
$568$	28.8679	+	11.9575i	1.21127	+	0.501725i
$569$	−16.0326	+	16.0326i	−0.672122	+	0.672122i	−0.958205	−	0.286083i	$-0.907647\pi$
$569$	−16.0326	+	16.0326i	−0.672122	+	0.672122i	0.286083	+	0.958205i	$0.407647\pi$
$570$		0			0
$571$	−21.9759	−	9.10272i	−0.919663	−	0.380937i	−0.127915	−	0.991785i	$-0.540829\pi$
$571$	−21.9759	−	9.10272i	−0.919663	−	0.380937i	−0.791748	+	0.610848i	$0.790829\pi$
$572$	−0.104374	+	0.251980i	−0.00436408	+	0.0105358i
$573$	−4.39592	+	1.82085i	−0.183642	+	0.0760671i
$574$		−	42.4344i		−	1.77118i
$575$		0			0
$576$	−18.0039	−	18.0039i	−0.750162	−	0.750162i
$577$	−19.5196			−0.812613			−0.406307	−	0.913737i	$-0.633184\pi$
$577$	−19.5196			−0.812613			−0.406307	+	0.913737i	$0.633184\pi$
$578$	−19.2477	−	10.9589i	−0.800600	−	0.455829i
$579$	3.89482			0.161863
$580$		0			0
$581$	2.13997	+	5.16636i	0.0887811	+	0.214337i
$582$			0.206261i			0.00854980i
$583$	0.178766	−	0.0740471i	0.00740371	−	0.00306672i
$584$	−1.45210	+	3.50569i	−0.0600885	+	0.145066i
$585$		0			0
$586$	−4.46898	+	4.46898i	−0.184612	+	0.184612i
$587$	12.9236	−	12.9236i	0.533415	−	0.533415i	−0.388172	−	0.921587i	$-0.626893\pi$
$587$	12.9236	−	12.9236i	0.533415	−	0.533415i	0.921587	+	0.388172i	$0.126893\pi$
$588$	−0.771392	−	0.319521i	−0.0318117	−	0.0131768i
$589$	17.0254	−	41.1029i	0.701518	−	1.69361i
$590$		0			0
$591$			6.29216i			0.258825i
$592$	−0.296341	−	0.715431i	−0.0121795	−	0.0294040i
$593$	−5.56675	−	5.56675i	−0.228599	−	0.228599i	0.583508	−	0.812107i	$-0.301680\pi$
$593$	−5.56675	−	5.56675i	−0.228599	−	0.228599i	−0.812107	+	0.583508i	$0.801680\pi$
$594$	−0.347762			−0.0142688
$595$		0			0
$596$	1.78514			0.0731221
$597$	−1.27275	−	1.27275i	−0.0520903	−	0.0520903i
$598$	14.3494	+	34.6424i	0.586789	+	1.41663i
$599$		−	9.39234i		−	0.383760i	−0.981418	−	0.191880i	$-0.938541\pi$
$599$		−	9.39234i		−	0.383760i	0.981418	−	0.191880i	$-0.0614585\pi$
$600$		0			0
$601$	15.1883	−	36.6678i	0.619544	−	1.49571i	−0.232690	−	0.972551i	$-0.574753\pi$
$601$	15.1883	−	36.6678i	0.619544	−	1.49571i	0.852234	−	0.523161i	$-0.175247\pi$
$602$	−8.91321	−	3.69197i	−0.363275	−	0.150474i
$603$	16.5519	−	16.5519i	0.674046	−	0.674046i
$604$	−0.300732	+	0.300732i	−0.0122366	+	0.0122366i
$605$		0			0
$606$	−2.01745	+	4.87056i	−0.0819534	+	0.197853i
$607$	−9.65164	+	3.99784i	−0.391748	+	0.162267i	−0.569858	−	0.821743i	$-0.693002\pi$
$607$	−9.65164	+	3.99784i	−0.391748	+	0.162267i	0.178110	+	0.984011i	$0.443002\pi$
$608$		−	8.75521i		−	0.355071i
$609$	1.07436	+	2.59374i	0.0435354	+	0.105104i
$610$		0			0
$611$	65.6868			2.65740
$612$	2.18431	−	2.86444i	0.0882955	−	0.115788i
$613$	−3.66845			−0.148167			−0.0740836	−	0.997252i	$-0.523603\pi$
$613$	−3.66845			−0.148167			−0.0740836	+	0.997252i	$0.523603\pi$
$614$	−6.37995	−	6.37995i	−0.257474	−	0.257474i
$615$		0			0
$616$			1.58654i			0.0639234i
$617$	−43.0594	+	17.8358i	−1.73351	+	0.718042i	−0.734276	+	0.678851i	$0.762478\pi$
$617$	−43.0594	+	17.8358i	−1.73351	+	0.718042i	−0.999232	+	0.0391908i	$0.987522\pi$
$618$	−0.647073	+	1.56217i	−0.0260291	+	0.0628398i
$619$	10.3175	+	4.27364i	0.414695	+	0.171772i	0.580269	−	0.814425i	$-0.302948\pi$
$619$	10.3175	+	4.27364i	0.414695	+	0.171772i	−0.165574	+	0.986197i	$0.552948\pi$
$620$		0			0
$621$	6.02505	−	6.02505i	0.241777	−	0.241777i
$622$	−35.1495	−	14.5594i	−1.40937	−	0.583779i
$623$	−6.43735	+	15.5411i	−0.257907	+	0.622642i
$624$	−6.79928	+	2.81636i	−0.272189	+	0.112744i
$625$		0			0
$626$	−11.3607	−	27.4273i	−0.454067	−	1.09621i
$627$	−0.165495	−	0.165495i	−0.00660922	−	0.00660922i
$628$	6.39069			0.255016
$629$	0.835573	−	0.485774i	0.0333165	−	0.0193691i
$630$		0			0
$631$	−9.85360	−	9.85360i	−0.392266	−	0.392266i	0.483229	−	0.875494i	$-0.339464\pi$
$631$	−9.85360	−	9.85360i	−0.392266	−	0.392266i	−0.875494	+	0.483229i	$0.839464\pi$
$632$	13.9517	+	33.6823i	0.554968	+	1.33981i
$633$			4.06149i			0.161430i
$634$	25.4980	−	10.5616i	1.01265	−	0.419455i
$635$		0			0
$636$	−0.133637	−	0.0553542i	−0.00529904	−	0.00219494i
$637$	38.8124	−	38.8124i	1.53780	−	1.53780i
$638$	0.268060	−	0.268060i	0.0106126	−	0.0106126i
$639$	27.7910	+	11.5114i	1.09939	+	0.455384i
$640$		0			0
$641$	0.998509	−	0.413596i	0.0394387	−	0.0163361i	−0.362877	−	0.931837i	$-0.618205\pi$
$641$	0.998509	−	0.413596i	0.0394387	−	0.0163361i	0.402316	+	0.915501i	$0.368205\pi$
$642$		−	7.45935i		−	0.294397i
$643$	−1.47605	−	3.56349i	−0.0582095	−	0.140530i	0.892099	−	0.451840i	$-0.149232\pi$
$643$	−1.47605	−	3.56349i	−0.0582095	−	0.140530i	−0.950308	+	0.311310i	$0.899232\pi$
$644$	−3.61145	−	3.61145i	−0.142311	−	0.142311i
$645$		0			0
$646$	−27.4857	+	3.70268i	−1.08141	+	0.145680i
$647$	−37.1748			−1.46149			−0.730746	−	0.682649i	$-0.760828\pi$
$647$	−37.1748			−1.46149			−0.730746	+	0.682649i	$0.760828\pi$
$648$	−16.9792	−	16.9792i	−0.667006	−	0.667006i
$649$	0.187148	+	0.451815i	0.00734620	+	0.0177353i
$650$		0			0
$651$	10.4044	−	4.30964i	0.407781	−	0.168908i
$652$	0.919669	−	2.22028i	0.0360170	−	0.0869527i
$653$	−23.6453	−	9.79421i	−0.925313	−	0.383277i	−0.131414	−	0.991328i	$-0.541952\pi$
$653$	−23.6453	−	9.79421i	−0.925313	−	0.383277i	−0.793898	+	0.608050i	$0.791952\pi$
$654$	3.92746	−	3.92746i	0.153576	−	0.153576i
$655$		0			0
$656$	25.4575	+	10.5449i	0.993950	+	0.411707i
$657$	−1.39793	+	3.37491i	−0.0545385	+	0.131668i
$658$	46.3815	−	19.2119i	1.80814	−	0.748956i
$659$			31.9659i			1.24521i	0.782535	+	0.622607i	$0.213926\pi$
$659$			31.9659i			1.24521i	−0.782535	+	0.622607i	$0.786074\pi$
$660$		0			0
$661$	−5.09233	−	5.09233i	−0.198069	−	0.198069i	0.601103	−	0.799172i	$-0.294728\pi$
$661$	−5.09233	−	5.09233i	−0.198069	−	0.198069i	−0.799172	+	0.601103i	$0.794728\pi$
$662$	0.897161			0.0348692
$663$	−4.61668	−	7.94109i	−0.179297	−	0.308406i
$664$	−4.29629			−0.166729
$665$		0			0
$666$	−0.337537	−	0.814887i	−0.0130793	−	0.0315762i
$667$			9.28839i			0.359648i
$668$	0.815339	−	0.337724i	0.0315464	−	0.0130669i
$669$	1.14218	−	2.75747i	0.0441593	−	0.106610i
$670$		0			0
$671$	−0.523131	+	0.523131i	−0.0201953	+	0.0201953i
$672$	1.56710	−	1.56710i	0.0604522	−	0.0604522i
$673$	−20.0780	−	8.31658i	−0.773950	−	0.320581i	−0.0394787	−	0.999220i	$-0.512570\pi$
$673$	−20.0780	−	8.31658i	−0.773950	−	0.320581i	−0.734471	+	0.678640i	$0.762570\pi$
$674$	0.645689	−	1.55883i	0.0248710	−	0.0600439i
$675$		0			0
$676$			9.47076i			0.364260i
$677$	3.07525	+	7.42431i	0.118192	+	0.285340i	0.971893	−	0.235423i	$-0.0756476\pi$
$677$	3.07525	+	7.42431i	0.118192	+	0.285340i	−0.853701	+	0.520763i	$0.825648\pi$
$678$	−4.32187	−	4.32187i	−0.165981	−	0.165981i
$679$	1.84691			0.0708780
$680$		0			0
$681$	−0.999519			−0.0383017
$682$	−1.07528	−	1.07528i	−0.0411746	−	0.0411746i
$683$	−17.3337	−	41.8473i	−0.663256	−	1.60124i	−0.792670	−	0.609651i	$-0.791310\pi$
$683$	−17.3337	−	41.8473i	−0.663256	−	1.60124i	0.129414	−	0.991591i	$-0.458690\pi$
$684$		−	4.51061i		−	0.172468i
$685$		0			0
$686$	2.42612	−	5.85717i	0.0926296	−	0.223628i
$687$	−4.08794	−	1.69328i	−0.155965	−	0.0646027i
$688$	4.42983	−	4.42983i	0.168886	−	0.168886i
$689$	6.72391	−	6.72391i	0.256161	−	0.256161i
$690$		0			0
$691$	8.60500	−	20.7743i	0.327350	−	0.790292i	−0.671438	−	0.741061i	$-0.734323\pi$
$691$	8.60500	−	20.7743i	0.327350	−	0.790292i	0.998787	−	0.0492308i	$-0.0156770\pi$
$692$	5.06152	−	2.09655i	0.192410	−	0.0796988i
$693$			1.52735i			0.0580192i
$694$	−1.41564	−	3.41765i	−0.0537369	−	0.129732i
$695$		0			0
$696$	−2.15693			−0.0817584
$697$	−8.80141	+	33.2469i	−0.333377	+	1.25932i
$698$	−5.44600			−0.206134
$699$	−4.64829	−	4.64829i	−0.175815	−	0.175815i
$700$		0			0
$701$			27.9289i			1.05486i	0.849599	+	0.527429i	$0.176844\pi$
$701$			27.9289i			1.05486i	−0.849599	+	0.527429i	$0.823156\pi$
$702$	−15.7894	+	6.54018i	−0.595932	+	0.246843i
$703$	0.463139	−	1.11812i	0.0174676	−	0.0421706i
$704$	−1.10323	−	0.456973i	−0.0415796	−	0.0172228i
$705$		0			0
$706$	1.04049	−	1.04049i	0.0391595	−	0.0391595i
$707$	43.6122	+	18.0648i	1.64021	+	0.679395i
$708$	0.139903	−	0.337756i	0.00525788	−	0.0126937i
$709$	20.5831	−	8.52578i	0.773013	−	0.320193i	0.0389210	−	0.999242i	$-0.487608\pi$
$709$	20.5831	−	8.52578i	0.773013	−	0.320193i	0.734092	+	0.679050i	$0.237608\pi$
$710$		0			0
$711$	13.4312	+	32.4258i	0.503709	+	1.21606i
$712$	−9.13855	−	9.13855i	−0.342482	−	0.342482i
$713$	37.2589			1.39536
$714$	−5.58243	−	4.25694i	−0.208917	−	0.159312i
$715$		0			0
$716$	−1.27776	−	1.27776i	−0.0477520	−	0.0477520i
$717$	2.05012	+	4.94942i	0.0765630	+	0.184839i
$718$		−	21.9637i		−	0.819677i
$719$	−1.26482	+	0.523906i	−0.0471698	+	0.0195384i	−0.406144	−	0.913809i	$-0.633127\pi$
$719$	−1.26482	+	0.523906i	−0.0471698	+	0.0195384i	0.358974	+	0.933348i	$0.383127\pi$
$720$		0			0
$721$	13.9881	+	5.79405i	0.520943	+	0.215782i
$722$	−7.05189	+	7.05189i	−0.262444	+	0.262444i
$723$	2.35048	−	2.35048i	0.0874154	−	0.0874154i
$724$	−6.61103	−	2.73838i	−0.245697	−	0.101771i
$725$		0			0
$726$	4.42420	−	1.83257i	0.164198	−	0.0680129i
$727$		−	42.8600i		−	1.58959i	−0.606878	−	0.794795i	$-0.707578\pi$
$727$		−	42.8600i		−	1.58959i	0.606878	−	0.794795i	$-0.292422\pi$
$728$	29.8372	+	72.0334i	1.10584	+	2.66973i
$729$	−14.9466	−	14.9466i	−0.553578	−	0.553578i
$730$		0			0
$731$	6.21764	+	4.74133i	0.229968	+	0.175364i
$732$	0.553055			0.0204415
$733$	22.9957	+	22.9957i	0.849367	+	0.849367i	0.990054	−	0.140687i	$-0.0449312\pi$
$733$	22.9957	+	22.9957i	0.849367	+	0.849367i	−0.140687	+	0.990054i	$0.544931\pi$
$734$	−10.9815	−	26.5117i	−0.405335	−	0.978566i
$735$		0			0
$736$	6.77416	−	2.80595i	0.249699	−	0.103429i
$737$	0.420119	−	1.01426i	0.0154753	−	0.0373607i
$738$	28.9965	+	12.0108i	1.06738	+	0.442122i
$739$	25.4716	−	25.4716i	0.936989	−	0.936989i	−0.0611400	−	0.998129i	$-0.519474\pi$
$739$	25.4716	−	25.4716i	0.936989	−	0.936989i	0.998129	+	0.0611400i	$0.0194736\pi$
$740$		0			0
$741$	−10.6263	−	4.40156i	−0.390367	−	0.161695i
$742$	2.78117	−	6.71434i	0.102100	−	0.246491i
$743$	30.2631	−	12.5354i	1.11024	−	0.459879i	0.249223	−	0.968446i	$-0.419825\pi$
$743$	30.2631	−	12.5354i	1.11024	−	0.459879i	0.861022	+	0.508568i	$0.169825\pi$
$744$			8.65220i			0.317205i
$745$		0			0
$746$	17.8461	+	17.8461i	0.653393	+	0.653393i
$747$	−4.13602			−0.151329
$748$	0.0432351	−	0.163319i	0.00158083	−	0.00597152i
$749$	−66.7929			−2.44056
$750$		0			0
$751$	−17.6375	−	42.5806i	−0.643600	−	1.55379i	−0.821789	−	0.569792i	$-0.807024\pi$
$751$	−17.6375	−	42.5806i	−0.643600	−	1.55379i	0.178189	−	0.983996i	$-0.442976\pi$
$752$			32.5996i			1.18879i
$753$	7.90274	−	3.27342i	0.287992	−	0.119290i
$754$	7.12943	−	17.2120i	0.259638	−	0.626823i
$755$		0			0
$756$	1.64603	−	1.64603i	0.0598655	−	0.0598655i
$757$	21.7165	−	21.7165i	0.789301	−	0.789301i	−0.192079	−	0.981379i	$-0.561523\pi$
$757$	21.7165	−	21.7165i	0.789301	−	0.789301i	0.981379	+	0.192079i	$0.0615230\pi$
$758$	−25.1681	−	10.4250i	−0.914145	−	0.378651i
$759$	0.0750088	−	0.181087i	0.00272265	−	0.00657305i
$760$		0			0
$761$		−	22.0653i		−	0.799865i	−0.916545	−	0.399932i	$-0.869034\pi$
$761$		−	22.0653i		−	0.799865i	0.916545	−	0.399932i	$-0.130966\pi$
$762$	−0.535480	−	1.29276i	−0.0193984	−	0.0468318i
$763$	−35.1674	−	35.1674i	−1.27315	−	1.27315i
$764$	−4.30072			−0.155594
$765$		0			0
$766$	5.61565			0.202902
$767$	16.9941	+	16.9941i	0.613622	+	0.613622i
$768$	0.907594	+	2.19113i	0.0327500	+	0.0790654i
$769$			29.4440i			1.06178i	0.847441	+	0.530889i	$0.178142\pi$
$769$			29.4440i			1.06178i	−0.847441	+	0.530889i	$0.821858\pi$
$770$		0			0
$771$	0.172984	−	0.417620i	0.00622986	−	0.0150402i
$772$	3.25243	+	1.34720i	0.117058	+	0.0484869i
$773$	−5.63855	+	5.63855i	−0.202805	+	0.202805i	−0.801201	−	0.598396i	$-0.795805\pi$
$773$	−5.63855	+	5.63855i	−0.202805	+	0.202805i	0.598396	+	0.801201i	$0.295805\pi$
$774$	5.04565	−	5.04565i	0.181362	−	0.181362i
$775$		0			0
$776$	−0.543014	+	1.31095i	−0.0194931	+	0.0470604i
$777$	0.283030	−	0.117235i	0.0101536	−	0.00420577i
$778$			19.0717i			0.683753i
$779$	16.4801	+	39.7865i	0.590461	+	1.42550i
$780$		0			0
$781$	1.41078			0.0504815
$782$	−11.6737	−	20.0798i	−0.417452	−	0.718053i
$783$	−4.23348			−0.151292
$784$	19.2622	+	19.2622i	0.687935	+	0.687935i
$785$		0			0
$786$			4.25770i			0.151867i
$787$	3.00460	−	1.24455i	0.107103	−	0.0443633i	−0.328489	−	0.944508i	$-0.606539\pi$
$787$	3.00460	−	1.24455i	0.107103	−	0.0443633i	0.435591	+	0.900145i	$0.356539\pi$
$788$	−2.17643	+	5.25437i	−0.0775322	+	0.187179i
$789$	−5.54590	−	2.29719i	−0.197439	−	0.0817821i
$790$		0			0
$791$	−38.6991	+	38.6991i	−1.37598	+	1.37598i
$792$	−1.08412	−	0.449059i	−0.0385226	−	0.0159566i
$793$	−13.9134	+	33.5900i	−0.494080	+	1.19281i
$794$	−13.5414	+	5.60902i	−0.480565	+	0.199056i
$795$		0			0
$796$	−0.622594	−	1.50308i	−0.0220673	−	0.0532751i
$797$	27.8278	+	27.8278i	0.985713	+	0.985713i	0.999899	−	0.0141865i	$-0.00451586\pi$
$797$	27.8278	+	27.8278i	0.985713	+	0.985713i	−0.0141865	+	0.999899i	$0.504516\pi$
$798$	−8.79060			−0.311184
$799$	−40.3242	+	5.43219i	−1.42657	+	0.192177i
$800$		0			0
$801$	−8.79763	−	8.79763i	−0.310849	−	0.310849i
$802$	−15.6244	−	37.7206i	−0.551716	−	1.33196i
$803$			0.171323i			0.00604586i
$804$	−0.758212	+	0.314062i	−0.0267401	+	0.0110761i
$805$		0			0
$806$	−69.0431	−	28.5986i	−2.43194	−	1.00734i
$807$	−4.24417	+	4.24417i	−0.149402	+	0.149402i
$808$	−25.6450	+	25.6450i	−0.902187	+	0.902187i
$809$	39.9675	+	16.5551i	1.40518	+	0.582045i	0.951091	−	0.308910i	$-0.0999643\pi$
$809$	39.9675	+	16.5551i	1.40518	+	0.582045i	0.454091	+	0.890956i	$0.349964\pi$
$810$		0			0
$811$	−10.7333	+	4.44587i	−0.376896	+	0.156115i	−0.563086	−	0.826398i	$-0.690386\pi$
$811$	−10.7333	+	4.44587i	−0.376896	+	0.156115i	0.186190	+	0.982514i	$0.440386\pi$
$812$			2.53757i			0.0890512i
$813$	1.49392	+	3.60663i	0.0523939	+	0.126490i
$814$	−0.0292507	−	0.0292507i	−0.00102524	−	0.00102524i
$815$		0			0
$816$	3.94107	−	2.29121i	0.137965	−	0.0802083i
$817$	9.79087			0.342539
$818$	−10.2627	−	10.2627i	−0.358826	−	0.358826i
$819$	28.7241	+	69.3461i	1.00370	+	2.42315i
$820$		0			0
$821$	42.2106	−	17.4842i	1.47316	−	0.610203i	0.505583	−	0.862778i	$-0.331277\pi$
$821$	42.2106	−	17.4842i	1.47316	−	0.610203i	0.967577	+	0.252575i	$0.0812775\pi$
$822$	1.51626	−	3.66058i	0.0528857	−	0.127677i
$823$	−19.5158	−	8.08372i	−0.680279	−	0.281781i	0.0156645	−	0.999877i	$-0.495014\pi$
$823$	−19.5158	−	8.08372i	−0.680279	−	0.281781i	−0.695944	+	0.718096i	$0.745014\pi$
$824$	−8.22531	+	8.22531i	−0.286542	+	0.286542i
$825$		0			0
$826$	16.9700	+	7.02918i	0.590460	+	0.244577i
$827$	−7.17270	+	17.3164i	−0.249419	+	0.602151i	−0.998155	−	0.0607172i	$-0.980661\pi$
$827$	−7.17270	+	17.3164i	−0.249419	+	0.602151i	0.748736	+	0.662869i	$0.230661\pi$
$828$	3.48999	−	1.44560i	0.121286	−	0.0502382i
$829$			34.5201i			1.19893i	0.800401	+	0.599466i	$0.204620\pi$
$829$			34.5201i			1.19893i	−0.800401	+	0.599466i	$0.795380\pi$
$830$		0			0
$831$	2.80243	+	2.80243i	0.0972151	+	0.0972151i
$832$	−58.6839			−2.03450
$833$	−20.6167	+	27.0361i	−0.714325	+	0.936746i
$834$	3.44532			0.119302
$835$		0			0
$836$	−0.0809552	−	0.195443i	−0.00279989	−	0.00675954i
$837$			16.9819i			0.586982i
$838$	−40.1308	+	16.6227i	−1.38629	+	0.574222i
$839$	14.2356	−	34.3677i	0.491467	−	1.18651i	−0.462507	−	0.886616i	$-0.653050\pi$
$839$	14.2356	−	34.3677i	0.491467	−	1.18651i	0.953974	−	0.299890i	$-0.0969499\pi$
$840$		0			0
$841$	−17.2429	+	17.2429i	−0.594582	+	0.594582i
$842$	2.22507	−	2.22507i	0.0766810	−	0.0766810i
$843$	−4.86444	−	2.01492i	−0.167540	−	0.0693974i
$844$	−1.40485	+	3.39162i	−0.0483571	+	0.116744i
$845$		0			0
$846$			37.1315i			1.27661i
$847$	−16.4092	−	39.6154i	−0.563828	−	1.36120i
$848$	3.33700	+	3.33700i	0.114593	+	0.114593i
$849$	−5.04085			−0.173002
$850$		0			0
$851$	1.01355			0.0347441
$852$	−0.745736	−	0.745736i	−0.0255485	−	0.0255485i
$853$	9.04063	+	21.8260i	0.309545	+	0.747309i	0.999720	+	0.0236657i	$0.00753372\pi$
$853$	9.04063	+	21.8260i	0.309545	+	0.747309i	−0.690175	+	0.723643i	$0.742466\pi$
$854$			27.7872i			0.950860i
$855$		0			0
$856$	19.6379	−	47.4100i	0.671209	−	1.62044i
$857$	−4.05182	−	1.67832i	−0.138407	−	0.0573303i	0.312405	−	0.949949i	$-0.398866\pi$
$857$	−4.05182	−	1.67832i	−0.138407	−	0.0573303i	−0.450812	+	0.892619i	$0.648866\pi$
$858$	−0.277992	+	0.277992i	−0.00949049	+	0.00949049i
$859$	25.3082	−	25.3082i	0.863506	−	0.863506i	−0.128238	−	0.991743i	$-0.540932\pi$
$859$	25.3082	−	25.3082i	0.863506	−	0.863506i	0.991743	+	0.128238i	$0.0409321\pi$
$860$		0			0
$861$	−4.17162	+	10.0712i	−0.142169	+	0.343225i
$862$	−17.0508	+	7.06267i	−0.580752	+	0.240555i
$863$			41.4427i			1.41073i	0.708846	+	0.705363i	$0.249216\pi$
$863$			41.4427i			1.41073i	−0.708846	+	0.705363i	$0.750784\pi$
$864$	1.27890	+	3.08754i	0.0435091	+	0.105040i
$865$		0			0
$866$	−46.6369			−1.58479
$867$	3.49083	+	4.49313i	0.118555	+	0.152595i
$868$	10.1791			0.345500
$869$	1.16394	+	1.16394i	0.0394838	+	0.0394838i
$870$		0			0
$871$		−	53.9512i		−	1.82807i
$872$	35.3017	−	14.6225i	1.19547	−	0.495179i
$873$	−0.522756	+	1.26205i	−0.0176926	+	0.0427138i
$874$	−26.8697	−	11.1298i	−0.908880	−	0.376470i
$875$		0			0
$876$	0.0905614	−	0.0905614i	0.00305978	−	0.00305978i
$877$	45.6223	+	18.8974i	1.54056	+	0.638119i	0.981578	−	0.191063i	$-0.0611935\pi$
$877$	45.6223	+	18.8974i	1.54056	+	0.638119i	0.558978	+	0.829182i	$0.311193\pi$
$878$	6.25490	−	15.1007i	0.211093	−	0.509623i
$879$	1.49998	−	0.621313i	0.0505932	−	0.0209564i
$880$		0			0
$881$	10.7287	+	25.9015i	0.361461	+	0.872643i	0.995087	+	0.0990039i	$0.0315656\pi$
$881$	10.7287	+	25.9015i	0.361461	+	0.872643i	−0.633627	+	0.773639i	$0.718434\pi$
$882$	21.9399	+	21.9399i	0.738756	+	0.738756i
$883$	−4.33207			−0.145786			−0.0728929	−	0.997340i	$-0.523223\pi$
$883$	−4.33207			−0.145786			−0.0728929	+	0.997340i	$0.523223\pi$
$884$	−1.10845	−	8.22824i	−0.0372812	−	0.276746i
$885$		0			0
$886$	−5.72574	−	5.72574i	−0.192360	−	0.192360i
$887$	11.7656	+	28.4047i	0.395051	+	0.953738i	0.988822	+	0.149103i	$0.0476387\pi$
$887$	11.7656	+	28.4047i	0.395051	+	0.953738i	−0.593771	+	0.804634i	$0.702361\pi$
$888$			0.235365i			0.00789833i
$889$	−11.5757	+	4.79482i	−0.388237	+	0.160813i
$890$		0			0
$891$	−1.00163	−	0.414887i	−0.0335557	−	0.0138992i
$892$	1.90760	−	1.90760i	0.0638710	−	0.0638710i
$893$	−36.0261	+	36.0261i	−1.20557	+	1.20557i
$894$	2.37730	+	0.984708i	0.0795087	+	0.0329336i
$895$		0			0
$896$	−29.2017	+	12.0957i	−0.975559	+	0.404090i
$897$		−	9.63254i		−	0.321621i
$898$	15.6967	+	37.8952i	0.523806	+	1.26458i
$899$	−13.0899	−	13.0899i	−0.436574	−	0.436574i
$900$		0			0
$901$	−3.57165	+	4.68377i	−0.118989	+	0.156039i
$902$	1.47197			0.0490114
$903$	1.75247	+	1.75247i	0.0583187	+	0.0583187i
$904$	−16.0909	−	38.8469i	−0.535176	−	1.29203i
$905$		0			0
$906$	−0.566377	+	0.234601i	−0.0188166	+	0.00779410i
$907$	13.3891	−	32.3241i	0.444577	−	1.07330i	−0.529747	−	0.848156i	$-0.677713\pi$
$907$	13.3891	−	32.3241i	0.444577	−	1.07330i	0.974324	−	0.225149i	$-0.0722868\pi$
$908$	−0.834666	−	0.345730i	−0.0276994	−	0.0114735i
$909$	−24.6883	+	24.6883i	−0.818858	+	0.818858i
$910$		0			0
$911$	44.9596	+	18.6229i	1.48958	+	0.617003i	0.971225	−	0.238164i	$-0.0765456\pi$
$911$	44.9596	+	18.6229i	1.48958	+	0.617003i	0.518352	+	0.855167i	$0.326546\pi$
$912$	2.18445	−	5.27372i	0.0723342	−	0.174630i
$913$	−0.179212	+	0.0742320i	−0.00593105	+	0.00245672i
$914$			9.09262i			0.300757i
$915$		0			0
$916$	−2.82801	−	2.82801i	−0.0934400	−	0.0934400i
$917$	38.1244			1.25898
$918$	9.15201	−	5.32068i	0.302061	−	0.175608i
$919$	−3.76108			−0.124067			−0.0620334	−	0.998074i	$-0.519759\pi$
$919$	−3.76108			−0.124067			−0.0620334	+	0.998074i	$0.519759\pi$
$920$		0			0
$921$	0.886992	+	2.14139i	0.0292274	+	0.0705611i
$922$		−	31.0514i		−	1.02262i
$923$	64.0533	−	26.5317i	2.10834	−	0.873303i
$924$	0.0204923	−	0.0494727i	0.000674146	−	0.00162753i
$925$		0			0
$926$	−25.6695	+	25.6695i	−0.843551	+	0.843551i
$927$	−7.91846	+	7.91846i	−0.260076	+	0.260076i
$928$	−3.36572	−	1.39413i	−0.110485	−	0.0457644i
$929$	−0.250915	+	0.605762i	−0.00823225	+	0.0198744i	−0.927942	−	0.372724i	$-0.878424\pi$
$929$	−0.250915	+	0.605762i	−0.00823225	+	0.0198744i	0.919710	+	0.392598i	$0.128424\pi$
$930$		0			0
$931$			42.5735i			1.39529i
$932$	−2.27381	−	5.48946i	−0.0744811	−	0.179813i
$933$	6.91093	+	6.91093i	0.226254	+	0.226254i
$934$	−45.7171			−1.49591
$935$		0			0
$936$	−57.6676			−1.88492
$937$	−13.7961	−	13.7961i	−0.450698	−	0.450698i	0.444888	−	0.895586i	$-0.353244\pi$
$937$	−13.7961	−	13.7961i	−0.450698	−	0.450698i	−0.895586	+	0.444888i	$0.853244\pi$
$938$	−15.7795	−	38.0950i	−0.515218	−	1.24385i
$939$			7.62631i			0.248875i
$940$		0			0
$941$	−5.66685	+	13.6810i	−0.184734	+	0.445988i	−0.988931	−	0.148375i	$-0.952596\pi$
$941$	−5.66685	+	13.6810i	−0.184734	+	0.445988i	0.804197	+	0.594363i	$0.202596\pi$
$942$	8.51058	+	3.52520i	0.277290	+	0.114857i
$943$	−25.5023	+	25.5023i	−0.830468	+	0.830468i
$944$	−8.43400	+	8.43400i	−0.274503	+	0.274503i
$945$		0			0
$946$	0.128068	−	0.309184i	0.00416385	−	0.0100524i
$947$	11.8904	−	4.92517i	0.386386	−	0.160046i	−0.181030	−	0.983478i	$-0.557943\pi$
$947$	11.8904	−	4.92517i	0.386386	−	0.160046i	0.567416	+	0.823431i	$0.307943\pi$
$948$		−	1.23051i		−	0.0399652i
$949$	3.22199	+	7.77856i	0.104590	+	0.252503i
$950$		0			0
$951$	−7.08986			−0.229905
$952$	−24.2737	−	41.7528i	−0.786714	−	1.35321i
$953$	−43.1347			−1.39727			−0.698635	−	0.715478i	$-0.746209\pi$
$953$	−43.1347			−1.39727			−0.698635	+	0.715478i	$0.746209\pi$
$954$	3.80090	+	3.80090i	0.123059	+	0.123059i
$955$		0			0
$956$			4.84223i			0.156609i
$957$	−0.0899725	+	0.0372678i	−0.00290840	+	0.00120470i
$958$	3.84274	−	9.27721i	0.124153	−	0.299733i
$959$	−32.7777	−	13.5770i	−1.05845	−	0.438423i
$960$		0			0
$961$	−30.5879	+	30.5879i	−0.986707	+	0.986707i
$962$	−1.87817	−	0.777964i	−0.0605547	−	0.0250826i
$963$	18.9053	−	45.6414i	0.609214	−	1.47077i
$964$	2.77584	−	1.14979i	0.0894037	−	0.0370322i
$965$		0			0
$966$	−2.81729	−	6.80154i	−0.0906449	−	0.218836i
$967$	−1.13385	−	1.13385i	−0.0364621	−	0.0364621i	0.688641	−	0.725103i	$-0.258208\pi$
$967$	−1.13385	−	1.13385i	−0.0364621	−	0.0364621i	−0.725103	+	0.688641i	$0.758208\pi$
$968$	32.9438			1.05885
$969$	6.88734	+	1.82328i	0.221253	+	0.0585721i
$970$		0			0
$971$	22.0166	+	22.0166i	0.706546	+	0.706546i	0.965807	−	0.259261i	$-0.0834791\pi$
$971$	22.0166	+	22.0166i	0.706546	+	0.706546i	−0.259261	+	0.965807i	$0.583479\pi$
$972$	0.994586	+	2.40114i	0.0319014	+	0.0770167i
$973$		−	30.8503i		−	0.989014i
$974$	45.8102	−	18.9752i	1.46786	−	0.608005i
$975$		0			0
$976$	−16.6703	−	6.90507i	−0.533604	−	0.221026i
$977$	4.87861	−	4.87861i	0.156081	−	0.156081i	−0.624747	−	0.780827i	$-0.714798\pi$
$977$	4.87861	−	4.87861i	0.156081	−	0.156081i	0.780827	+	0.624747i	$0.214798\pi$
$978$	2.44947	−	2.44947i	0.0783255	−	0.0783255i
$979$	−0.539095	−	0.223300i	−0.0172296	−	0.00713671i
$980$		0			0
$981$	33.9848	−	14.0769i	1.08505	−	0.449442i
$982$		−	39.8279i		−	1.27096i
$983$	−11.5969	−	27.9974i	−0.369884	−	0.892978i	−0.993769	−	0.111462i	$-0.964447\pi$
$983$	−11.5969	−	27.9974i	−0.369884	−	0.892978i	0.623885	−	0.781516i	$-0.285553\pi$
$984$	−5.92209	−	5.92209i	−0.188789	−	0.188789i
$985$		0			0
$986$	−2.95325	+	11.1558i	−0.0940507	+	0.355272i
$987$	−12.8967			−0.410505
$988$	−7.35120	−	7.35120i	−0.233873	−	0.233873i
$989$	3.13787	+	7.57548i	0.0997784	+	0.240886i
$990$		0			0
$991$	8.21733	−	3.40373i	0.261032	−	0.108123i	−0.248330	−	0.968676i	$-0.579882\pi$
$991$	8.21733	−	3.40373i	0.261032	−	0.108123i	0.509362	+	0.860553i	$0.329882\pi$
$992$	−5.59232	+	13.5011i	−0.177556	+	0.428659i
$993$	−0.212928	−	0.0881978i	−0.00675708	−	0.00279887i
$994$	37.4682	−	37.4682i	1.18842	−	1.18842i
$995$		0			0
$996$	0.133971	+	0.0554924i	0.00424502	+	0.00175834i
$997$	−10.9328	+	26.3941i	−0.346245	+	0.835909i	0.650812	+	0.759239i	$0.274429\pi$
$997$	−10.9328	+	26.3941i	−0.346245	+	0.835909i	−0.997057	+	0.0766701i	$0.975571\pi$
$998$	−1.34371	+	0.556582i	−0.0425343	+	0.0176183i
$999$			0.461958i			0.0146157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.c.151.5	yes	24
5.2	odd	4		425.2.n.e.49.2		24
5.3	odd	4		425.2.n.d.49.5		24
5.4	even	2		425.2.m.d.151.2	yes	24
17.5	odd	16		7225.2.a.bx.1.10		24
17.8	even	8	inner	425.2.m.c.76.5	✓	24
17.12	odd	16		7225.2.a.bx.1.9		24
85.8	odd	8		425.2.n.e.399.2		24
85.29	odd	16		7225.2.a.cb.1.16		24
85.39	odd	16		7225.2.a.cb.1.15		24
85.42	odd	8		425.2.n.d.399.5		24
85.59	even	8		425.2.m.d.76.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.5	✓	24	17.8	even	8	inner
425.2.m.c.151.5	yes	24	1.1	even	1	trivial
425.2.m.d.76.2	yes	24	85.59	even	8
425.2.m.d.151.2	yes	24	5.4	even	2
425.2.n.d.49.5		24	5.3	odd	4
425.2.n.d.399.5		24	85.42	odd	8
425.2.n.e.49.2		24	5.2	odd	4
425.2.n.e.399.2		24	85.8	odd	8
7225.2.a.bx.1.9		24	17.12	odd	16
7225.2.a.bx.1.10		24	17.5	odd	16
7225.2.a.cb.1.15		24	85.39	odd	16
7225.2.a.cb.1.16		24	85.29	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.921271 + 0.921271i) q^{2} +(-0.128082 - 0.309218i) q^{3} -0.302521i q^{4} +(0.166875 - 0.402872i) q^{6} +(-3.60742 - 1.49424i) q^{7} +(2.12124 - 2.12124i) q^{8} +(2.04211 - 2.04211i) q^{9} +(0.0518326 - 0.125135i) q^{11} +(-0.0935451 + 0.0387477i) q^{12} -6.65628i q^{13} +(-1.94681 - 4.70001i) q^{14} +3.30344 q^{16} +(0.550463 + 4.08620i) q^{17} +3.76267 q^{18} +(3.65065 + 3.65065i) q^{19} +1.30686i q^{21} +(0.163035 - 0.0675313i) q^{22} +(-1.65462 + 3.99461i) q^{23} +(-0.927622 - 0.384234i) q^{24} +(6.13224 - 6.13224i) q^{26} +(-1.82067 - 0.754146i) q^{27} +(-0.452040 + 1.09132i) q^{28} +(1.98471 - 0.822093i) q^{29} +(-3.29770 - 7.96135i) q^{31} +(-1.19913 - 1.19913i) q^{32} -0.0453329 q^{33} +(-3.25737 + 4.27162i) q^{34} +(-0.617782 - 0.617782i) q^{36} +(-0.0897069 - 0.216572i) q^{37} +6.72648i q^{38} +(-2.05824 + 0.852553i) q^{39} +(7.70637 + 3.19208i) q^{41} +(-1.20398 + 1.20398i) q^{42} +(1.34097 - 1.34097i) q^{43} +(-0.0378560 - 0.0156805i) q^{44} +(-5.20447 + 2.15576i) q^{46} +9.86840i q^{47} +(-0.423112 - 1.02148i) q^{48} +(5.83095 + 5.83095i) q^{49} +(1.19302 - 0.693583i) q^{51} -2.01367 q^{52} +(1.01016 + 1.01016i) q^{53} +(-0.982557 - 2.37210i) q^{54} +(-10.8219 + 4.48256i) q^{56} +(0.661264 - 1.59643i) q^{57} +(2.58582 + 1.07108i) q^{58} +(-2.55310 + 2.55310i) q^{59} +(-5.04635 - 2.09027i) q^{61} +(4.29648 - 10.3726i) q^{62} +(-10.4181 + 4.31534i) q^{63} -8.81632i q^{64} +(-0.0417638 - 0.0417638i) q^{66} +8.10531 q^{67} +(1.23616 - 0.166527i) q^{68} +1.44714 q^{69} +(3.98597 + 9.62298i) q^{71} -8.66363i q^{72} +(-1.16860 + 0.484052i) q^{73} +(0.116877 - 0.282165i) q^{74} +(1.10440 - 1.10440i) q^{76} +(-0.373964 + 0.373964i) q^{77} +(-2.68163 - 1.11077i) q^{78} +(-4.65072 + 11.2278i) q^{79} -8.00436i q^{81} +(4.15888 + 10.0404i) q^{82} +(-1.01268 - 1.01268i) q^{83} +0.395354 q^{84} +2.47080 q^{86} +(-0.508412 - 0.508412i) q^{87} +(-0.155492 - 0.375392i) q^{88} -4.30811i q^{89} +(-9.94609 + 24.0120i) q^{91} +(1.20846 + 0.500559i) q^{92} +(-2.03942 + 2.03942i) q^{93} +(-9.09146 + 9.09146i) q^{94} +(-0.217205 + 0.524380i) q^{96} +(-0.437000 + 0.181011i) q^{97} +10.7438i q^{98} +(-0.149691 - 0.361387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} - 12 q^{12} - 24 q^{14} - 24 q^{16} + 4 q^{17} - 40 q^{18} - 20 q^{19} + 16 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{26} - 12 q^{27} + 48 q^{28} + 4 q^{29} + 24 q^{31}+ \cdots - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 - 12 * q^12 - 24 * q^14 - 24 * q^16 + 4 * q^17 - 40 * q^18 - 20 * q^19 + 16 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^26 - 12 * q^27 + 48 * q^28 + 4 * q^29 + 24 * q^31 - 60 * q^32 + 48 * q^33 + 16 * q^34 + 60 * q^36 - 12 * q^37 + 8 * q^39 - 20 * q^41 + 12 * q^42 + 32 * q^43 + 64 * q^44 - 40 * q^46 - 40 * q^48 + 24 * q^49 + 16 * q^51 - 48 * q^52 - 12 * q^53 - 20 * q^54 - 32 * q^56 + 68 * q^57 - 16 * q^58 - 16 * q^59 - 64 * q^61 + 100 * q^62 - 44 * q^63 - 72 * q^66 + 40 * q^67 + 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 + 24 * q^77 - 16 * q^78 - 48 * q^79 + 100 * q^82 + 12 * q^83 - 40 * q^84 - 16 * q^86 + 24 * q^87 + 4 * q^88 + 24 * q^91 - 88 * q^92 - 32 * q^93 - 40 * q^94 + 132 * q^96 - 88 * q^97 - 80 * q^99

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