LMFDB - Embedded newform 425.2.n.f.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not 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:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	425.49
Dual form			425.2.n.f.399.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.680853 - 0.680853i) q^{2} +(2.44733 - 1.01372i) q^{3} +1.07288i q^{4} +(0.976080 - 2.35647i) q^{6} +(1.18426 - 2.85906i) q^{7} +(2.09218 + 2.09218i) q^{8} +(2.84049 - 2.84049i) q^{9} +O(q^{10})$	\(q+(0.680853 - 0.680853i) q^{2} +(2.44733 - 1.01372i) q^{3} +1.07288i q^{4} +(0.976080 - 2.35647i) q^{6} +(1.18426 - 2.85906i) q^{7} +(2.09218 + 2.09218i) q^{8} +(2.84049 - 2.84049i) q^{9} +(-2.34612 + 5.66403i) q^{11} +(1.08760 + 2.62569i) q^{12} +1.16017 q^{13} +(-1.14029 - 2.75291i) q^{14} +0.703170 q^{16} +(-3.92649 - 1.25804i) q^{17} -3.86791i q^{18} +(-3.83665 - 3.83665i) q^{19} -8.19759i q^{21} +(2.25901 + 5.45373i) q^{22} +(-2.88015 - 1.19300i) q^{23} +(7.24113 + 2.99938i) q^{24} +(0.789908 - 0.789908i) q^{26} +(1.03101 - 2.48908i) q^{27} +(3.06743 + 1.27057i) q^{28} +(4.61660 - 1.91226i) q^{29} +(-1.42666 - 3.44426i) q^{31} +(-3.70560 + 3.70560i) q^{32} +16.2401i q^{33} +(-3.52990 + 1.81682i) q^{34} +(3.04750 + 3.04750i) q^{36} +(-0.366518 + 0.151817i) q^{37} -5.22439 q^{38} +(2.83933 - 1.17609i) q^{39} +(1.57303 + 0.651568i) q^{41} +(-5.58135 - 5.58135i) q^{42} +(0.0189720 + 0.0189720i) q^{43} +(-6.07683 - 2.51710i) q^{44} +(-2.77321 + 1.14870i) q^{46} +5.43715 q^{47} +(1.72089 - 0.712817i) q^{48} +(-1.82202 - 1.82202i) q^{49} +(-10.8847 + 0.901513i) q^{51} +1.24473i q^{52} +(0.244014 - 0.244014i) q^{53} +(-0.992732 - 2.39667i) q^{54} +(8.45936 - 3.50398i) q^{56} +(-13.2788 - 5.50028i) q^{57} +(1.84126 - 4.44519i) q^{58} +(-2.87128 + 2.87128i) q^{59} +(-11.4953 - 4.76149i) q^{61} +(-3.31638 - 1.37369i) q^{62} +(-4.75726 - 11.4850i) q^{63} +6.45228i q^{64} +(11.0571 + 11.0571i) q^{66} +5.62508i q^{67} +(1.34973 - 4.21265i) q^{68} -8.25804 q^{69} +(4.12510 + 9.95888i) q^{71} +11.8856 q^{72} +(-0.633083 - 1.52840i) q^{73} +(-0.146180 + 0.352909i) q^{74} +(4.11627 - 4.11627i) q^{76} +(13.4154 + 13.4154i) q^{77} +(1.13242 - 2.73391i) q^{78} +(-2.01785 + 4.87153i) q^{79} +4.91441i q^{81} +(1.51462 - 0.627376i) q^{82} +(8.78638 - 8.78638i) q^{83} +8.79502 q^{84} +0.0258342 q^{86} +(9.35987 - 9.35987i) q^{87} +(-16.7587 + 6.94167i) q^{88} +3.22930i q^{89} +(1.37395 - 3.31701i) q^{91} +(1.27994 - 3.09005i) q^{92} +(-6.98302 - 6.98302i) q^{93} +(3.70190 - 3.70190i) q^{94} +(-5.31240 + 12.8253i) q^{96} +(-4.94995 - 11.9502i) q^{97} -2.48105 q^{98} +(9.42450 + 22.7528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9	$ 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37} + 48 q^{38} - 8 q^{39} + 16 q^{41} + 24 q^{42} + 8 q^{43} - 16 q^{44} + 8 q^{46} + 64 q^{47} + 8 q^{48} - 56 q^{51} - 24 q^{53} + 32 q^{54} + 64 q^{56} - 16 q^{57} - 56 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 80 q^{63} + 96 q^{66} - 24 q^{68} - 96 q^{69} - 24 q^{71} + 24 q^{72} + 64 q^{73} + 64 q^{74} - 8 q^{76} - 24 q^{77} - 8 q^{78} + 16 q^{82} + 96 q^{83} + 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} - 112 q^{92} + 64 q^{93} - 56 q^{94} - 168 q^{96} - 48 q^{97} - 120 q^{98} + 8 q^{99}+O(q^{100}) $ 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.680853	−	0.680853i	0.481435	−	0.481435i	−0.424154	−	0.905590i	$-0.639429\pi$
$2$	0.680853	−	0.680853i	0.481435	−	0.481435i	0.905590	+	0.424154i	$0.139429\pi$
$3$	2.44733	−	1.01372i	1.41297	−	0.585271i	0.459885	−	0.887979i	$-0.347891\pi$
$3$	2.44733	−	1.01372i	1.41297	−	0.585271i	0.953083	+	0.302708i	$0.0978907\pi$
$4$			1.07288i			0.536440i
$5$		0			0
$5$		0			0
$6$	0.976080	−	2.35647i	0.398483	−	0.962023i
$7$	1.18426	−	2.85906i	0.447609	−	1.08062i	−0.525606	−	0.850728i	$-0.676161\pi$
$7$	1.18426	−	2.85906i	0.447609	−	1.08062i	0.973215	−	0.229896i	$-0.0738387\pi$
$8$	2.09218	+	2.09218i	0.739697	+	0.739697i
$9$	2.84049	−	2.84049i	0.946830	−	0.946830i
$10$		0			0
$11$	−2.34612	+	5.66403i	−0.707382	+	1.70777i	−0.000939675		1.00000i	$0.500299\pi$
$11$	−2.34612	+	5.66403i	−0.707382	+	1.70777i	−0.706442	+	0.707771i	$0.749701\pi$
$12$	1.08760	+	2.62569i	0.313962	+	0.757972i
$13$	1.16017			0.321775			0.160887	−	0.986973i	$-0.448564\pi$
$13$	1.16017			0.321775			0.160887	+	0.986973i	$0.448564\pi$
$14$	−1.14029	−	2.75291i	−0.304756	−	0.735746i
$15$		0			0
$16$	0.703170			0.175793
$17$	−3.92649	−	1.25804i	−0.952314	−	0.305120i
$17$	−3.92649	−	1.25804i	−0.952314	−	0.305120i
$18$		−	3.86791i		−	0.911675i
$19$	−3.83665	−	3.83665i	−0.880188	−	0.880188i	0.113365	−	0.993553i	$-0.463837\pi$
$19$	−3.83665	−	3.83665i	−0.880188	−	0.880188i	−0.993553	+	0.113365i	$0.963837\pi$
$20$		0			0
$21$		−	8.19759i		−	1.78886i
$22$	2.25901	+	5.45373i	0.481623	+	1.16274i
$23$	−2.88015	−	1.19300i	−0.600552	−	0.248757i	0.0616306	−	0.998099i	$-0.480370\pi$
$23$	−2.88015	−	1.19300i	−0.600552	−	0.248757i	−0.662183	+	0.749342i	$0.730370\pi$
$24$	7.24113	+	2.99938i	1.47809	+	0.612245i
$25$		0			0
$26$	0.789908	−	0.789908i	0.154914	−	0.154914i
$27$	1.03101	−	2.48908i	0.198418	−	0.479025i
$28$	3.06743	+	1.27057i	0.579690	+	0.240115i
$29$	4.61660	−	1.91226i	0.857282	−	0.355098i	0.0896380	−	0.995974i	$-0.471429\pi$
$29$	4.61660	−	1.91226i	0.857282	−	0.355098i	0.767644	+	0.640877i	$0.221429\pi$
$30$		0			0
$31$	−1.42666	−	3.44426i	−0.256236	−	0.618608i	0.742448	−	0.669904i	$-0.233665\pi$
$31$	−1.42666	−	3.44426i	−0.256236	−	0.618608i	−0.998683	+	0.0512962i	$0.983665\pi$
$32$	−3.70560	+	3.70560i	−0.655064	+	0.655064i
$33$			16.2401i			2.82703i
$34$	−3.52990	+	1.81682i	−0.605373	+	0.311582i
$35$		0			0
$36$	3.04750	+	3.04750i	0.507917	+	0.507917i
$37$	−0.366518	+	0.151817i	−0.0602551	+	0.0249585i	−0.412607	−	0.910909i	$-0.635382\pi$
$37$	−0.366518	+	0.151817i	−0.0602551	+	0.0249585i	0.352352	+	0.935867i	$0.385382\pi$
$38$	−5.22439			−0.847508
$39$	2.83933	−	1.17609i	0.454657	−	0.188325i
$40$		0			0
$41$	1.57303	+	0.651568i	0.245665	+	0.101758i	0.502119	−	0.864799i	$-0.332554\pi$
$41$	1.57303	+	0.651568i	0.245665	+	0.101758i	−0.256453	+	0.966557i	$0.582554\pi$
$42$	−5.58135	−	5.58135i	−0.861221	−	0.861221i
$43$	0.0189720	+	0.0189720i	0.00289320	+	0.00289320i	0.708552	−	0.705659i	$-0.249349\pi$
$43$	0.0189720	+	0.0189720i	0.00289320	+	0.00289320i	−0.705659	+	0.708552i	$0.749349\pi$
$44$	−6.07683	−	2.51710i	−0.916116	−	0.379468i
$45$		0			0
$46$	−2.77321	+	1.14870i	−0.408888	+	0.169367i
$47$	5.43715			0.793090			0.396545	−	0.918015i	$-0.370209\pi$
$47$	5.43715			0.793090			0.396545	+	0.918015i	$0.370209\pi$
$48$	1.72089	−	0.712817i	0.248389	−	0.102886i
$49$	−1.82202	−	1.82202i	−0.260288	−	0.260288i
$50$		0			0
$51$	−10.8847	+	0.901513i	−1.52417	+	0.126237i
$52$			1.24473i			0.172613i
$53$	0.244014	−	0.244014i	0.0335179	−	0.0335179i	−0.690149	−	0.723667i	$-0.742455\pi$
$53$	0.244014	−	0.244014i	0.0335179	−	0.0335179i	0.723667	+	0.690149i	$0.242455\pi$
$54$	−0.992732	−	2.39667i	−0.135094	−	0.326145i
$55$		0			0
$56$	8.45936	−	3.50398i	1.13043	−	0.468239i
$57$	−13.2788	−	5.50028i	−1.75883	−	0.728530i
$58$	1.84126	−	4.44519i	0.241769	−	0.583683i
$59$	−2.87128	+	2.87128i	−0.373808	+	0.373808i	−0.868862	−	0.495054i	$-0.835148\pi$
$59$	−2.87128	+	2.87128i	−0.373808	+	0.373808i	0.495054	+	0.868862i	$0.335148\pi$
$60$		0			0
$61$	−11.4953	−	4.76149i	−1.47182	−	0.609646i	−0.504544	−	0.863386i	$-0.668339\pi$
$61$	−11.4953	−	4.76149i	−1.47182	−	0.609646i	−0.967273	+	0.253740i	$0.918339\pi$
$62$	−3.31638	−	1.37369i	−0.421181	−	0.174459i
$63$	−4.75726	−	11.4850i	−0.599358	−	1.44698i
$64$			6.45228i			0.806534i
$65$		0			0
$66$	11.0571	+	11.0571i	1.36103	+	1.36103i
$67$			5.62508i			0.687213i	0.939114	+	0.343607i	$0.111649\pi$
$67$			5.62508i			0.687213i	−0.939114	+	0.343607i	$0.888351\pi$
$68$	1.34973	−	4.21265i	0.163678	−	0.510859i
$69$	−8.25804			−0.994152
$70$		0			0
$71$	4.12510	+	9.95888i	0.489560	+	1.18190i	0.954942	+	0.296792i	$0.0959167\pi$
$71$	4.12510	+	9.95888i	0.489560	+	1.18190i	−0.465383	+	0.885110i	$0.654083\pi$
$72$	11.8856			1.40073
$73$	−0.633083	−	1.52840i	−0.0740968	−	0.178886i	0.882491	−	0.470329i	$-0.155865\pi$
$73$	−0.633083	−	1.52840i	−0.0740968	−	0.178886i	−0.956588	+	0.291443i	$0.905865\pi$
$74$	−0.146180	+	0.352909i	−0.0169931	+	0.0410249i
$75$		0			0
$76$	4.11627	−	4.11627i	0.472168	−	0.472168i
$77$	13.4154	+	13.4154i	1.52883	+	1.52883i
$78$	1.13242	−	2.73391i	0.128222	−	0.309554i
$79$	−2.01785	+	4.87153i	−0.227026	+	0.548090i	−0.995813	−	0.0914157i	$-0.970861\pi$
$79$	−2.01785	+	4.87153i	−0.227026	+	0.548090i	0.768787	+	0.639505i	$0.220861\pi$
$80$		0			0
$81$			4.91441i			0.546045i
$82$	1.51462	−	0.627376i	0.167262	−	0.0692821i
$83$	8.78638	−	8.78638i	0.964430	−	0.964430i	−0.0349583	−	0.999389i	$-0.511130\pi$
$83$	8.78638	−	8.78638i	0.964430	−	0.964430i	0.999389	+	0.0349583i	$0.0111299\pi$
$84$	8.79502			0.959616
$85$		0			0
$86$	0.0258342			0.00278577
$87$	9.35987	−	9.35987i	1.00348	−	1.00348i
$88$	−16.7587	+	6.94167i	−1.78648	+	0.739984i
$89$			3.22930i			0.342305i	0.985245	+	0.171152i	$0.0547490\pi$
$89$			3.22930i			0.342305i	−0.985245	+	0.171152i	$0.945251\pi$
$90$		0			0
$91$	1.37395	−	3.31701i	0.144029	−	0.347717i
$92$	1.27994	−	3.09005i	0.133443	−	0.322160i
$93$	−6.98302	−	6.98302i	−0.724106	−	0.724106i
$94$	3.70190	−	3.70190i	0.381822	−	0.381822i
$95$		0			0
$96$	−5.31240	+	12.8253i	−0.542195	+	1.30897i
$97$	−4.94995	−	11.9502i	−0.502592	−	1.21336i	−0.948067	−	0.318070i	$-0.896965\pi$
$97$	−4.94995	−	11.9502i	−0.502592	−	1.21336i	0.445476	−	0.895294i	$-0.353035\pi$
$98$	−2.48105			−0.250624
$99$	9.42450	+	22.7528i	0.947198	+	2.28674i
$100$		0			0
$101$	1.46947			0.146218			0.0731088	−	0.997324i	$-0.476708\pi$
$101$	1.46947			0.146218			0.0731088	+	0.997324i	$0.476708\pi$
$102$	−6.79710	+	8.02469i	−0.673013	+	0.794563i
$103$			9.80978i			0.966586i	0.875459	+	0.483293i	$0.160559\pi$
$103$			9.80978i			0.966586i	−0.875459	+	0.483293i	$0.839441\pi$
$104$	2.42729	+	2.42729i	0.238016	+	0.238016i
$105$		0			0
$106$		−	0.332275i		−	0.0322734i
$107$	1.10497	+	2.66763i	0.106821	+	0.257889i	0.968248	−	0.249993i	$-0.0804284\pi$
$107$	1.10497	+	2.66763i	0.106821	+	0.257889i	−0.861426	+	0.507882i	$0.830428\pi$
$108$	2.67049	+	1.10615i	0.256968	+	0.106440i
$109$	−5.32460	−	2.20552i	−0.510004	−	0.211251i	0.112816	−	0.993616i	$-0.464013\pi$
$109$	−5.32460	−	2.20552i	−0.510004	−	0.211251i	−0.622820	+	0.782365i	$0.714013\pi$
$110$		0			0
$111$	−0.743091	+	0.743091i	−0.0705311	+	0.0705311i
$112$	0.832738	−	2.01041i	0.0786864	−	0.189966i
$113$	8.33379	+	3.45197i	0.783977	+	0.324734i	0.738519	−	0.674232i	$-0.235525\pi$
$113$	8.33379	+	3.45197i	0.783977	+	0.324734i	0.0454578	+	0.998966i	$0.485525\pi$
$114$	−12.7858	+	5.29606i	−1.19750	+	0.496021i
$115$		0			0
$116$	2.05162	+	4.95306i	0.190489	+	0.459880i
$117$	3.29547	−	3.29547i	0.304666	−	0.304666i
$118$			3.90983i			0.359929i
$119$	−8.24682	+	9.73624i	−0.755984	+	0.892519i
$120$		0			0
$121$	−18.7988	−	18.7988i	−1.70898	−	1.70898i
$122$	−11.0684	+	4.58470i	−1.00209	+	0.415079i
$123$	4.51022			0.406673
$124$	3.69528	−	1.53063i	0.331846	−	0.137455i
$125$		0			0
$126$	−11.0586	−	4.58062i	−0.985179	−	0.408074i
$127$	9.89892	+	9.89892i	0.878387	+	0.878387i	0.993368	−	0.114980i	$-0.0366805\pi$
$127$	9.89892	+	9.89892i	0.878387	+	0.878387i	−0.114980	+	0.993368i	$0.536681\pi$
$128$	−3.01815	−	3.01815i	−0.266770	−	0.266770i
$129$	0.0656629	+	0.0271985i	0.00578129	+	0.00239469i
$130$		0			0
$131$	11.7059	−	4.84875i	1.02275	−	0.423638i	0.192661	−	0.981265i	$-0.438288\pi$
$131$	11.7059	−	4.84875i	1.02275	−	0.423638i	0.830091	+	0.557628i	$0.188288\pi$
$132$	−17.4236			−1.51653
$133$	−15.5128	+	6.42563i	−1.34513	+	0.557173i
$134$	3.82985	+	3.82985i	0.330849	+	0.330849i
$135$		0			0
$136$	−5.58287	−	10.8470i	−0.478728	−	0.930119i
$137$		−	2.97888i		−	0.254503i	−0.991870	−	0.127251i	$-0.959384\pi$
$137$		−	2.97888i		−	0.254503i	0.991870	−	0.127251i	$-0.0406155\pi$
$138$	−5.62251	+	5.62251i	−0.478620	+	0.478620i
$139$	−7.51640	−	18.1462i	−0.637533	−	1.53914i	−0.829956	−	0.557829i	$-0.811635\pi$
$139$	−7.51640	−	18.1462i	−0.637533	−	1.53914i	0.192423	−	0.981312i	$-0.438365\pi$
$140$		0			0
$141$	13.3065	−	5.51174i	1.12061	−	0.464172i
$142$	9.58911	+	3.97194i	0.804700	+	0.333318i
$143$	−2.72191	+	6.57127i	−0.227617	+	0.549517i
$144$	1.99735	−	1.99735i	0.166446	−	0.166446i
$145$		0			0
$146$	−1.47165	−	0.609578i	−0.121795	−	0.0504490i
$147$	−6.30610	−	2.61207i	−0.520118	−	0.215440i
$148$	−0.162881	−	0.393229i	−0.0133887	−	0.0323232i
$149$			2.95573i			0.242143i	0.992644	+	0.121072i	$0.0386330\pi$
$149$			2.95573i			0.242143i	−0.992644	+	0.121072i	$0.961367\pi$
$150$		0			0
$151$	15.5848	+	15.5848i	1.26828	+	1.26828i	0.946978	+	0.321298i	$0.104119\pi$
$151$	15.5848	+	15.5848i	1.26828	+	1.26828i	0.321298	+	0.946978i	$0.395881\pi$
$152$		−	16.0539i		−	1.30214i
$153$	−14.7266	+	7.57971i	−1.19058	+	0.612783i
$154$	18.2678			1.47206
$155$		0			0
$156$	1.26180	+	3.04626i	0.101025	+	0.243896i
$157$	12.8666			1.02686			0.513432	−	0.858130i	$-0.328374\pi$
$157$	12.8666			1.02686			0.513432	+	0.858130i	$0.328374\pi$
$158$	1.94293	+	4.69065i	0.154571	+	0.373168i
$159$	0.349821	−	0.844544i	0.0277426	−	0.0669767i
$160$		0			0
$161$	−6.82171	+	6.82171i	−0.537626	+	0.537626i
$162$	3.34599	+	3.34599i	0.262886	+	0.262886i
$163$	7.38291	−	17.8239i	0.578274	−	1.39608i	−0.316087	−	0.948730i	$-0.602369\pi$
$163$	7.38291	−	17.8239i	0.578274	−	1.39608i	0.894361	−	0.447347i	$-0.147631\pi$
$164$	−0.699055	+	1.68767i	−0.0545870	+	0.131785i
$165$		0			0
$166$		−	11.9645i		−	0.928622i
$167$	−17.4236	+	7.21707i	−1.34828	+	0.558474i	−0.935812	−	0.352500i	$-0.885332\pi$
$167$	−17.4236	+	7.21707i	−1.34828	+	0.558474i	−0.412464	+	0.910974i	$0.635332\pi$
$168$	17.1508	−	17.1508i	1.32321	−	1.32321i
$169$	−11.6540			−0.896461
$170$		0			0
$171$	−21.7960			−1.66678
$172$	−0.0203546	+	0.0203546i	−0.00155203	+	0.00155203i
$173$	20.8584	−	8.63985i	1.58584	−	0.656876i	0.596513	−	0.802603i	$-0.296552\pi$
$173$	20.8584	−	8.63985i	1.58584	−	0.656876i	0.989325	+	0.145728i	$0.0465524\pi$
$174$		−	12.7454i		−	0.966225i
$175$		0			0
$176$	−1.64972	+	3.98278i	−0.124352	+	0.300213i
$177$	−4.11630	+	9.93763i	−0.309400	+	0.746958i
$178$	2.19867	+	2.19867i	0.164798	+	0.164798i
$179$	1.38641	−	1.38641i	0.103625	−	0.103625i	−0.653393	−	0.757018i	$-0.726655\pi$
$179$	1.38641	−	1.38641i	0.103625	−	0.103625i	0.757018	+	0.653393i	$0.226655\pi$
$180$		0			0
$181$	0.272363	−	0.657542i	0.0202446	−	0.0488747i	−0.913434	−	0.406987i	$-0.866579\pi$
$181$	0.272363	−	0.657542i	0.0202446	−	0.0488747i	0.933679	+	0.358112i	$0.116579\pi$
$182$	−1.32294	−	3.19386i	−0.0980627	−	0.236744i
$183$	−32.9595			−2.43644
$184$	−3.52982	−	8.52174i	−0.260222	−	0.628231i
$185$		0			0
$186$	−9.50882			−0.697220
$187$	16.3376	−	19.2883i	1.19472	−	1.41050i
$188$			5.83341i			0.425445i
$189$	−5.89546	−	5.89546i	−0.428832	−	0.428832i
$190$		0			0
$191$		−	5.26341i		−	0.380847i	−0.981702	−	0.190423i	$-0.939014\pi$
$191$		−	5.26341i		−	0.380847i	0.981702	−	0.190423i	$-0.0609861\pi$
$192$	6.54079	+	15.7909i	0.472041	+	1.13961i
$193$	13.7936	+	5.71352i	0.992888	+	0.411268i	0.819184	−	0.573530i	$-0.194426\pi$
$193$	13.7936	+	5.71352i	0.992888	+	0.411268i	0.173704	+	0.984798i	$0.444426\pi$
$194$	−11.5065	−	4.76617i	−0.826122	−	0.342191i
$195$		0			0
$196$	1.95481	−	1.95481i	0.139629	−	0.139629i
$197$	2.42244	−	5.84828i	0.172592	−	0.416673i	−0.813787	−	0.581163i	$-0.802598\pi$
$197$	2.42244	−	5.84828i	0.172592	−	0.416673i	0.986379	+	0.164490i	$0.0525978\pi$
$198$	21.9080	+	9.07458i	1.55693	+	0.644902i
$199$	13.7796	−	5.70769i	0.976809	−	0.404607i	0.163566	−	0.986532i	$-0.447700\pi$
$199$	13.7796	−	5.70769i	0.976809	−	0.404607i	0.813243	+	0.581925i	$0.197700\pi$
$200$		0			0
$201$	5.70225	+	13.7664i	0.402206	+	0.971010i
$202$	1.00049	−	1.00049i	0.0703943	−	0.0703943i
$203$		−	15.4638i		−	1.08534i
$204$	−0.967215	−	11.6780i	−0.0677186	−	0.817624i
$205$		0			0
$206$	6.67901	+	6.67901i	0.465349	+	0.465349i
$207$	−11.5697	+	4.79234i	−0.804152	+	0.333091i
$208$	0.815800			0.0565656
$209$	30.7322	−	12.7297i	2.12579	−	0.880531i
$210$		0			0
$211$	12.3788	+	5.12746i	0.852190	+	0.352989i	0.765648	−	0.643260i	$-0.222418\pi$
$211$	12.3788	+	5.12746i	0.852190	+	0.352989i	0.0865417	+	0.996248i	$0.472418\pi$
$212$	0.261797	+	0.261797i	0.0179803	+	0.0179803i
$213$	20.1910	+	20.1910i	1.38346	+	1.38346i
$214$	2.56858	+	1.06394i	0.175585	+	0.0727295i
$215$		0			0
$216$	7.36467	−	3.05055i	0.501102	−	0.207563i
$217$	−11.5369			−0.783176
$218$	−5.12690	+	2.12363i	−0.347238	+	0.143830i
$219$	−3.09873	−	3.09873i	−0.209393	−	0.209393i
$220$		0			0
$221$	−4.55542	−	1.45955i	−0.306430	−	0.0981797i
$222$			1.01187i			0.0679123i
$223$	−1.49410	+	1.49410i	−0.100053	+	0.100053i	−0.755361	−	0.655309i	$-0.772539\pi$
$223$	−1.49410	+	1.49410i	−0.100053	+	0.100053i	0.655309	+	0.755361i	$0.272539\pi$
$224$	6.20614	+	14.9830i	0.414665	+	1.00109i
$225$		0			0
$226$	8.02437	−	3.32380i	0.533773	−	0.221096i
$227$	−13.4512	−	5.57168i	−0.892789	−	0.369805i	−0.111346	−	0.993782i	$-0.535516\pi$
$227$	−13.4512	−	5.57168i	−0.892789	−	0.369805i	−0.781443	+	0.623976i	$0.785516\pi$
$228$	5.90114	−	14.2466i	0.390812	−	0.943505i
$229$	1.87412	−	1.87412i	0.123845	−	0.123845i	−0.642468	−	0.766313i	$-0.722089\pi$
$229$	1.87412	−	1.87412i	0.123845	−	0.123845i	0.766313	+	0.642468i	$0.222089\pi$
$230$		0			0
$231$	46.4314	+	19.2325i	3.05496	+	1.26541i
$232$	13.6595	+	5.65797i	0.896793	+	0.371464i
$233$	−1.20133	−	2.90028i	−0.0787021	−	0.190004i	0.879631	−	0.475657i	$-0.157790\pi$
$233$	−1.20133	−	2.90028i	−0.0787021	−	0.190004i	−0.958333	+	0.285653i	$0.907790\pi$
$234$		−	4.48745i		−	0.293354i
$235$		0			0
$236$	−3.08053	−	3.08053i	−0.200526	−	0.200526i
$237$			13.9678i			0.907305i
$238$	1.01408	+	12.2438i	0.0657328	+	0.793648i
$239$	−13.7090			−0.886760			−0.443380	−	0.896334i	$-0.646221\pi$
$239$	−13.7090			−0.886760			−0.443380	+	0.896334i	$0.646221\pi$
$240$		0			0
$241$	−4.77884	−	11.5371i	−0.307832	−	0.743173i	−0.999775	−	0.0212201i	$-0.993245\pi$
$241$	−4.77884	−	11.5371i	−0.307832	−	0.743173i	0.691943	−	0.721952i	$-0.256755\pi$
$242$	−25.5985			−1.64553
$243$	8.07486	+	19.4944i	0.518003	+	1.25057i
$244$	5.10851	−	12.3330i	0.327039	−	0.789541i
$245$		0			0
$246$	3.07080	−	3.07080i	0.195787	−	0.195787i
$247$	−4.45119	−	4.45119i	−0.283222	−	0.283222i
$248$	4.22118	−	10.1908i	0.268045	−	0.647119i
$249$	12.5963	−	30.4101i	0.798257	−	1.92716i
$250$		0			0
$251$		−	17.4413i		−	1.10088i	−0.834874	−	0.550441i	$-0.814459\pi$
$251$		−	17.4413i		−	1.10088i	0.834874	−	0.550441i	$-0.185541\pi$
$252$	12.3221	−	5.10396i	0.776217	−	0.321519i
$253$	13.5143	−	13.5143i	0.849640	−	0.849640i
$254$	13.4794			0.845774
$255$		0			0
$256$	−17.0144			−1.06340
$257$	−4.86561	+	4.86561i	−0.303508	+	0.303508i	−0.842385	−	0.538876i	$-0.818849\pi$
$257$	−4.86561	+	4.86561i	−0.303508	+	0.303508i	0.538876	+	0.842385i	$0.318849\pi$
$258$	0.0632249	−	0.0261886i	0.00393621	−	0.00163043i
$259$			1.22769i			0.0762848i
$260$		0			0
$261$	7.68166	−	18.5452i	0.475483	−	1.14792i
$262$	4.66872	−	11.2713i	0.288435	−	0.696343i
$263$	4.41100	+	4.41100i	0.271994	+	0.271994i	0.829902	−	0.557909i	$-0.188396\pi$
$263$	4.41100	+	4.41100i	0.271994	+	0.271994i	−0.557909	+	0.829902i	$0.688396\pi$
$264$	−33.9771	+	33.9771i	−2.09115	+	2.09115i
$265$		0			0
$266$	−6.18705	+	14.9369i	−0.379352	+	0.915838i
$267$	3.27360	+	7.90316i	0.200341	+	0.483666i
$268$	−6.03504			−0.368648
$269$	−0.493996	−	1.19261i	−0.0301194	−	0.0727148i	0.908104	−	0.418744i	$-0.137530\pi$
$269$	−0.493996	−	1.19261i	−0.0301194	−	0.0727148i	−0.938224	+	0.346030i	$0.887530\pi$
$270$		0			0
$271$	−10.2849			−0.624764			−0.312382	−	0.949957i	$-0.601127\pi$
$271$	−10.2849			−0.624764			−0.312382	+	0.949957i	$0.601127\pi$
$272$	−2.76099	−	0.884617i	−0.167410	−	0.0536378i
$273$		−	9.51063i		−	0.575610i
$274$	−2.02818	−	2.02818i	−0.122527	−	0.122527i
$275$		0			0
$276$		−	8.85989i		−	0.533302i
$277$	−9.71258	−	23.4482i	−0.583572	−	1.40887i	−0.889554	−	0.456831i	$-0.848985\pi$
$277$	−9.71258	−	23.4482i	−0.583572	−	1.40887i	0.305982	−	0.952037i	$-0.401015\pi$
$278$	−17.4724	−	7.23733i	−1.04793	−	0.434066i
$279$	−13.8358	−	5.73098i	−0.828328	−	0.343105i
$280$		0			0
$281$	−4.16880	+	4.16880i	−0.248690	+	0.248690i	−0.820433	−	0.571743i	$-0.806267\pi$
$281$	−4.16880	+	4.16880i	−0.248690	+	0.248690i	0.571743	+	0.820433i	$0.306267\pi$
$282$	5.30710	−	12.8125i	0.316033	−	0.762971i
$283$	−17.0606	−	7.06675i	−1.01415	−	0.420075i	−0.187183	−	0.982325i	$-0.559936\pi$
$283$	−17.0606	−	7.06675i	−1.01415	−	0.420075i	−0.826967	+	0.562250i	$0.809936\pi$
$284$	−10.6847	+	4.42574i	−0.634019	+	0.262619i
$285$		0			0
$286$	2.62085	+	6.32728i	0.154974	+	0.374140i
$287$	3.72575	−	3.72575i	0.219924	−	0.219924i
$288$			21.0514i			1.24047i
$289$	13.8347	+	9.87937i	0.813804	+	0.581139i
$290$		0			0
$291$	−24.2284	−	24.2284i	−1.42029	−	1.42029i
$292$	1.63979	−	0.679222i	0.0959613	−	0.0397485i
$293$	−8.31894			−0.485998			−0.242999	−	0.970027i	$-0.578131\pi$
$293$	−8.31894			−0.485998			−0.242999	+	0.970027i	$0.578131\pi$
$294$	−6.07196	+	2.51509i	−0.354124	+	0.146683i
$295$		0			0
$296$	−1.08445	−	0.449193i	−0.0630322	−	0.0261088i
$297$	11.6794	+	11.6794i	0.677706	+	0.677706i
$298$	2.01242	+	2.01242i	0.116576	+	0.116576i
$299$	−3.34148	−	1.38408i	−0.193243	−	0.0800437i
$300$		0			0
$301$	0.0767098	−	0.0317742i	0.00442148	−	0.00183144i
$302$	21.2220			1.22119
$303$	3.59628	−	1.48963i	0.206601	−	0.0855768i
$304$	−2.69782	−	2.69782i	−0.154731	−	0.154731i
$305$		0			0
$306$	−4.86599	+	15.1873i	−0.278170	+	0.868201i
$307$			12.2369i			0.698398i	0.937049	+	0.349199i	$0.113546\pi$
$307$			12.2369i			0.698398i	−0.937049	+	0.349199i	$0.886454\pi$
$308$	−14.3931	+	14.3931i	−0.820124	+	0.820124i
$309$	9.94435	+	24.0078i	0.565715	+	1.36576i
$310$		0			0
$311$	−30.1525	+	12.4896i	−1.70979	+	0.708218i	−0.709796	+	0.704407i	$0.751213\pi$
$311$	−30.1525	+	12.4896i	−1.70979	+	0.708218i	−0.999993	+	0.00381046i	$0.998787\pi$
$312$	8.40098	+	3.47980i	0.475612	+	0.197005i
$313$	5.13906	−	12.4068i	0.290477	−	0.701273i	−0.709517	−	0.704688i	$-0.751087\pi$
$313$	5.13906	−	12.4068i	0.290477	−	0.701273i	0.999994	+	0.00341475i	$0.00108695\pi$
$314$	8.76024	−	8.76024i	0.494369	−	0.494369i
$315$		0			0
$316$	−5.22656	−	2.16491i	−0.294017	−	0.121786i
$317$	9.12199	+	3.77845i	0.512342	+	0.212219i	0.623849	−	0.781545i	$-0.285568\pi$
$317$	9.12199	+	3.77845i	0.512342	+	0.212219i	−0.111507	+	0.993764i	$0.535568\pi$
$318$	−0.336833	−	0.813186i	−0.0188886	−	0.0456012i
$319$			30.6350i			1.71523i
$320$		0			0
$321$	5.40844	+	5.40844i	0.301870	+	0.301870i
$322$			9.28915i			0.517664i
$323$	10.2379	+	19.8912i	0.569653	+	1.10678i
$324$	−5.27257			−0.292920
$325$		0			0
$326$	−7.10879	−	17.1621i	−0.393719	−	0.950523i
$327$	−15.2668			−0.844258
$328$	1.92785	+	4.65425i	0.106448	+	0.256988i
$329$	6.43902	−	15.5452i	0.354995	−	0.857033i
$330$		0			0
$331$	−3.99024	+	3.99024i	−0.219323	+	0.219323i	−0.808213	−	0.588890i	$-0.799565\pi$
$331$	−3.99024	+	3.99024i	−0.219323	+	0.219323i	0.588890	+	0.808213i	$0.299565\pi$
$332$	9.42673	+	9.42673i	0.517359	+	0.517359i
$333$	−0.609856	+	1.47232i	−0.0334199	+	0.0806828i
$334$	−6.94911	+	16.7766i	−0.380238	+	0.917977i
$335$		0			0
$336$		−	5.76430i		−	0.314468i
$337$	15.3295	−	6.34969i	0.835051	−	0.345890i	0.0761510	−	0.997096i	$-0.475737\pi$
$337$	15.3295	−	6.34969i	0.835051	−	0.345890i	0.758900	+	0.651207i	$0.225737\pi$
$338$	−7.93465	+	7.93465i	−0.431588	+	0.431588i
$339$	23.8949			1.29779
$340$		0			0
$341$	22.8555			1.23770
$342$	−14.8398	+	14.8398i	−0.802446	+	0.802446i
$343$	12.6464	−	5.23832i	0.682843	−	0.282843i
$344$			0.0793854i			0.00428017i
$345$		0			0
$346$	8.31906	−	20.0840i	0.447235	−	1.07972i
$347$	3.53762	−	8.54057i	0.189909	−	0.458482i	−0.800032	−	0.599957i	$-0.795184\pi$
$347$	3.53762	−	8.54057i	0.189909	−	0.458482i	0.989942	+	0.141475i	$0.0451845\pi$
$348$	10.0420	+	10.0420i	0.538309	+	0.538309i
$349$	19.0405	−	19.0405i	1.01921	−	1.01921i	0.0194030	−	0.999812i	$-0.493823\pi$
$349$	19.0405	−	19.0405i	1.01921	−	1.01921i	0.999812	−	0.0194030i	$-0.00617656\pi$
$350$		0			0
$351$	1.19615	−	2.88777i	0.0638460	−	0.154138i
$352$	−12.2949	−	29.6824i	−0.655319	−	1.58208i
$353$	−22.9722			−1.22269			−0.611343	−	0.791366i	$-0.709370\pi$
$353$	−22.9722			−1.22269			−0.611343	+	0.791366i	$0.709370\pi$
$354$	3.96347	+	9.56866i	0.210656	+	0.508568i
$355$		0			0
$356$	−3.46465			−0.183626
$357$	−10.3129	+	32.1878i	−0.545816	+	1.70356i
$358$		−	1.88788i		−	0.0997775i
$359$	24.1187	+	24.1187i	1.27293	+	1.27293i	0.944541	+	0.328394i	$0.106507\pi$
$359$	24.1187	+	24.1187i	1.27293	+	1.27293i	0.328394	+	0.944541i	$0.393493\pi$
$360$		0			0
$361$			10.4398i			0.549463i
$362$	−0.262250	−	0.633128i	−0.0137836	−	0.0332765i
$363$	−65.0637	−	26.9503i	−3.41496	−	1.41452i
$364$	3.55876	+	1.47408i	0.186529	+	0.0772630i
$365$		0			0
$366$	−22.4406	+	22.4406i	−1.17299	+	1.17299i
$367$	3.54981	−	8.57000i	0.185299	−	0.447351i	−0.803745	−	0.594974i	$-0.797162\pi$
$367$	3.54981	−	8.57000i	0.185299	−	0.447351i	0.989044	+	0.147623i	$0.0471624\pi$
$368$	−2.02523	−	0.838880i	−0.105573	−	0.0437296i
$369$	6.31894	−	2.61739i	0.328951	−	0.136256i
$370$		0			0
$371$	−0.408674	−	0.986627i	−0.0212173	−	0.0512231i
$372$	7.49194	−	7.49194i	0.388439	−	0.388439i
$373$			3.06857i			0.158884i	0.996839	+	0.0794422i	$0.0253139\pi$
$373$			3.06857i			0.158884i	−0.996839	+	0.0794422i	$0.974686\pi$
$374$	−2.00897	−	24.2560i	−0.103881	−	1.25425i
$375$		0			0
$376$	11.3755	+	11.3755i	0.586646	+	0.586646i
$377$	5.35607	−	2.21856i	0.275851	−	0.114261i
$378$	−8.02788			−0.412910
$379$	−33.7529	+	13.9809i	−1.73377	+	0.718151i	−0.734556	+	0.678549i	$0.762609\pi$
$379$	−33.7529	+	13.9809i	−1.73377	+	0.718151i	−0.999215	+	0.0396029i	$0.987391\pi$
$380$		0			0
$381$	34.2607	+	14.1912i	1.75523	+	0.727039i
$382$	−3.58361	−	3.58361i	−0.183353	−	0.183353i
$383$	6.59130	+	6.59130i	0.336800	+	0.336800i	0.855161	−	0.518362i	$-0.173458\pi$
$383$	6.59130	+	6.59130i	0.336800	+	0.336800i	−0.518362	+	0.855161i	$0.673458\pi$
$384$	−10.4460	−	4.32687i	−0.533069	−	0.220804i
$385$		0			0
$386$	13.2815	−	5.50138i	0.676011	−	0.280013i
$387$	0.107779			0.00547873
$388$	12.8212	−	5.31071i	0.650897	−	0.269610i
$389$	−23.4493	−	23.4493i	−1.18892	−	1.18892i	−0.977365	−	0.211559i	$-0.932146\pi$
$389$	−23.4493	−	23.4493i	−1.18892	−	1.18892i	−0.211559	−	0.977365i	$-0.567854\pi$
$390$		0			0
$391$	9.80804	+	8.30763i	0.496014	+	0.420135i
$392$		−	7.62397i		−	0.385069i
$393$	23.7330	−	23.7330i	1.19717	−	1.19717i
$394$	−2.33250	−	5.63114i	−0.117509	−	0.283693i
$395$		0			0
$396$	−24.4110	+	10.1114i	−1.22670	+	0.508115i
$397$	8.15361	+	3.37734i	0.409218	+	0.169504i	0.577790	−	0.816186i	$-0.303915\pi$
$397$	8.15361	+	3.37734i	0.409218	+	0.169504i	−0.168572	+	0.985689i	$0.553915\pi$
$398$	5.49577	−	13.2680i	0.275478	−	0.665063i
$399$	−31.4513	+	31.4513i	−1.57453	+	1.57453i
$400$		0			0
$401$	18.0332	+	7.46960i	0.900535	+	0.373014i	0.784426	−	0.620223i	$-0.212958\pi$
$401$	18.0332	+	7.46960i	0.900535	+	0.373014i	0.116109	+	0.993236i	$0.462958\pi$
$402$	13.2553	+	5.49053i	0.661115	+	0.273843i
$403$	−1.65518	−	3.99595i	−0.0824501	−	0.199052i
$404$			1.57656i			0.0784369i
$405$		0			0
$406$	−10.5286	−	10.5286i	−0.522523	−	0.522523i
$407$		−	2.43215i		−	0.120557i
$408$	−24.6589	−	20.8867i	−1.22080	−	1.03404i
$409$	−10.4152			−0.514998			−0.257499	−	0.966279i	$-0.582898\pi$
$409$	−10.4152			−0.514998			−0.257499	+	0.966279i	$0.582898\pi$
$410$		0			0
$411$	−3.01974	−	7.29031i	−0.148953	−	0.359604i
$412$	−10.5247			−0.518515
$413$	4.80881	+	11.6095i	0.236626	+	0.571266i
$414$	−4.61440	+	11.1402i	−0.226786	+	0.547509i
$415$		0			0
$416$	−4.29914	+	4.29914i	−0.210783	+	0.210783i
$417$	−36.7903	−	36.7903i	−1.80163	−	1.80163i
$418$	12.2570	−	29.5911i	0.599512	−	1.44735i
$419$	−13.5166	+	32.6320i	−0.660329	+	1.59418i	0.136958	+	0.990577i	$0.456267\pi$
$419$	−13.5166	+	32.6320i	−0.660329	+	1.59418i	−0.797288	+	0.603599i	$0.793733\pi$
$420$		0			0
$421$			15.0205i			0.732052i	0.930605	+	0.366026i	$0.119282\pi$
$421$			15.0205i			0.732052i	−0.930605	+	0.366026i	$0.880718\pi$
$422$	11.9192	−	4.93708i	0.580216	−	0.240333i
$423$	15.4442	−	15.4442i	0.750922	−	0.750922i
$424$	1.02104			0.0495861
$425$		0			0
$426$	27.4942			1.33210
$427$	−27.2268	+	27.2268i	−1.31760	+	1.31760i
$428$	−2.86204	+	1.18550i	−0.138342	+	0.0573031i
$429$			18.8413i			0.909668i
$430$		0			0
$431$	−8.93633	+	21.5742i	−0.430448	+	1.03919i	0.548695	+	0.836022i	$0.315125\pi$
$431$	−8.93633	+	21.5742i	−0.430448	+	1.03919i	−0.979143	+	0.203171i	$0.934875\pi$
$432$	0.724977	−	1.75025i	0.0348805	−	0.0842090i
$433$	−12.9455	−	12.9455i	−0.622120	−	0.622120i	0.323953	−	0.946073i	$-0.394988\pi$
$433$	−12.9455	−	12.9455i	−0.622120	−	0.622120i	−0.946073	+	0.323953i	$0.894988\pi$
$434$	−7.85493	+	7.85493i	−0.377049	+	0.377049i
$435$		0			0
$436$	2.36626	−	5.71265i	0.113323	−	0.273586i
$437$	6.47302	+	15.6272i	0.309646	+	0.747552i
$438$	−4.21956			−0.201618
$439$	−7.75689	−	18.7268i	−0.370216	−	0.893780i	−0.993713	−	0.111955i	$-0.964289\pi$
$439$	−7.75689	−	18.7268i	−0.370216	−	0.893780i	0.623497	−	0.781826i	$-0.285711\pi$
$440$		0			0
$441$	−10.3509			−0.492898
$442$	−4.09530	+	2.10783i	−0.194794	+	0.100259i
$443$			29.3849i			1.39612i	0.716041	+	0.698058i	$0.245952\pi$
$443$			29.3849i			1.39612i	−0.716041	+	0.698058i	$0.754048\pi$
$444$	−0.797247	−	0.797247i	−0.0378357	−	0.0378357i
$445$		0			0
$446$			2.03453i			0.0963376i
$447$	2.99628	+	7.23366i	0.141719	+	0.342140i
$448$	18.4475	+	7.64119i	0.871561	+	0.361012i
$449$	30.1572	+	12.4915i	1.42321	+	0.589512i	0.955664	−	0.294459i	$-0.0951394\pi$
$449$	30.1572	+	12.4915i	1.42321	+	0.589512i	0.467543	+	0.883970i	$0.345139\pi$
$450$		0			0
$451$	−7.38101	+	7.38101i	−0.347558	+	0.347558i
$452$	−3.70355	+	8.94115i	−0.174200	+	0.420557i
$453$	53.9399	+	22.3426i	2.53432	+	1.04975i
$454$	−12.9518	+	5.36481i	−0.607858	+	0.251783i
$455$		0			0
$456$	−16.2742	−	39.2893i	−0.762107	−	1.83989i
$457$	−5.97585	+	5.97585i	−0.279538	+	0.279538i	−0.832925	−	0.553386i	$-0.813335\pi$
$457$	−5.97585	+	5.97585i	−0.279538	+	0.279538i	0.553386	+	0.832925i	$0.313335\pi$
$458$		−	2.55199i		−	0.119247i
$459$	−7.17963	+	8.47631i	−0.335116	+	0.395640i
$460$		0			0
$461$	27.0527	+	27.0527i	1.25997	+	1.25997i	0.951106	+	0.308863i	$0.0999486\pi$
$461$	27.0527	+	27.0527i	1.25997	+	1.25997i	0.308863	+	0.951106i	$0.400051\pi$
$462$	44.7075	−	18.5184i	2.07998	−	0.861556i
$463$	−27.1761			−1.26298			−0.631491	−	0.775383i	$-0.717557\pi$
$463$	−27.1761			−1.26298			−0.631491	+	0.775383i	$0.717557\pi$
$464$	3.24626	−	1.34464i	0.150704	−	0.0624235i
$465$		0			0
$466$	−2.79259	−	1.15673i	−0.129364	−	0.0535845i
$467$	−2.43616	−	2.43616i	−0.112732	−	0.112732i	0.648491	−	0.761223i	$-0.275401\pi$
$467$	−2.43616	−	2.43616i	−0.112732	−	0.112732i	−0.761223	+	0.648491i	$0.775401\pi$
$468$	3.53564	+	3.53564i	0.163435	+	0.163435i
$469$	16.0825	+	6.66158i	0.742619	+	0.307603i
$470$		0			0
$471$	31.4888	−	13.0431i	1.45093	−	0.600994i
$472$	−12.0144			−0.553009
$473$	−0.151968	+	0.0629473i	−0.00698751	+	0.00289432i
$474$	9.51000	+	9.51000i	0.436809	+	0.436809i
$475$		0			0
$476$	−10.4458	−	8.84784i	−0.478783	−	0.405540i
$477$		−	1.38624i		−	0.0634714i
$478$	−9.33380	+	9.33380i	−0.426918	+	0.426918i
$479$	−5.87776	−	14.1902i	−0.268562	−	0.648365i	0.730855	−	0.682533i	$-0.239122\pi$
$479$	−5.87776	−	14.1902i	−0.268562	−	0.648365i	−0.999416	+	0.0341684i	$0.989122\pi$
$480$		0			0
$481$	−0.425224	+	0.176134i	−0.0193886	+	0.00803101i
$482$	−11.1088	−	4.60141i	−0.505991	−	0.209588i
$483$	−9.77969	+	23.6103i	−0.444992	+	1.07430i
$484$	20.1689	−	20.1689i	0.916767	−	0.916767i
$485$		0			0
$486$	18.7706	+	7.77505i	0.851453	+	0.352683i
$487$	24.3068	+	10.0682i	1.10145	+	0.456234i	0.857984	−	0.513676i	$-0.171717\pi$
$487$	24.3068	+	10.0682i	1.10145	+	0.456234i	0.243463	+	0.969910i	$0.421717\pi$
$488$	−14.0882	−	34.0120i	−0.637744	−	1.53965i
$489$		−	51.1052i		−	2.31106i
$490$		0			0
$491$	−20.5320	−	20.5320i	−0.926596	−	0.926596i	0.0708885	−	0.997484i	$-0.477417\pi$
$491$	−20.5320	−	20.5320i	−0.926596	−	0.926596i	−0.997484	+	0.0708885i	$0.977417\pi$
$492$			4.83893i			0.218156i
$493$	−20.5328	+	1.70060i	−0.924749	+	0.0765911i
$494$	−6.06120			−0.272706
$495$		0			0
$496$	−1.00319	−	2.42190i	−0.0450443	−	0.108747i
$497$	33.3583			1.49632
$498$	−12.1286	−	29.2810i	−0.543495	−	1.31211i
$499$	−12.4718	+	30.1097i	−0.558316	+	1.34789i	0.352782	+	0.935706i	$0.385236\pi$
$499$	−12.4718	+	30.1097i	−0.558316	+	1.34789i	−0.911098	+	0.412189i	$0.864764\pi$
$500$		0			0
$501$	−35.3252	+	35.3252i	−1.57821	+	1.57821i
$502$	−11.8749	−	11.8749i	−0.530004	−	0.530004i
$503$	−9.00803	+	21.7473i	−0.401648	+	0.969665i	0.585618	+	0.810587i	$0.300852\pi$
$503$	−9.00803	+	21.7473i	−0.401648	+	0.969665i	−0.987266	+	0.159077i	$0.949148\pi$
$504$	14.0757	−	33.9818i	0.626982	−	1.51367i
$505$		0			0
$506$		−	18.4026i		−	0.818093i
$507$	−28.5212	+	11.8139i	−1.26667	+	0.524672i
$508$	−10.6204	+	10.6204i	−0.471202	+	0.471202i
$509$	−17.5818			−0.779300			−0.389650	−	0.920963i	$-0.627404\pi$
$509$	−17.5818			−0.779300			−0.389650	+	0.920963i	$0.627404\pi$
$510$		0			0
$511$	−5.11953			−0.226474
$512$	−5.54798	+	5.54798i	−0.245189	+	0.245189i
$513$	−13.5054	+	5.59412i	−0.596278	+	0.246986i
$514$			6.62553i			0.292239i
$515$		0			0
$516$	−0.0291807	+	0.0704484i	−0.00128461	+	0.00310132i
$517$	−12.7562	+	30.7962i	−0.561018	+	1.35442i
$518$	0.835874	+	0.835874i	0.0367262	+	0.0367262i
$519$	42.2892	−	42.2892i	1.85629	−	1.85629i
$520$		0			0
$521$	−7.84734	+	18.9452i	−0.343798	+	0.830002i	0.653527	+	0.756904i	$0.273289\pi$
$521$	−7.84734	+	18.9452i	−0.343798	+	0.830002i	−0.997325	+	0.0730986i	$0.976711\pi$
$522$	−7.39645	−	17.8566i	−0.323734	−	0.781563i
$523$	9.19853			0.402224			0.201112	−	0.979568i	$-0.435545\pi$
$523$	9.19853			0.402224			0.201112	+	0.979568i	$0.435545\pi$
$524$	5.20213	+	12.5591i	0.227256	+	0.548645i
$525$		0			0
$526$	6.00648			0.261895
$527$	1.26875	+	15.3187i	0.0552675	+	0.667291i
$528$			11.4195i			0.496972i
$529$	−9.39144	−	9.39144i	−0.408324	−	0.408324i
$530$		0			0
$531$			16.3117i			0.707866i
$532$	−6.89393	−	16.6434i	−0.298890	−	0.721583i
$533$	1.82498	+	0.755933i	0.0790488	+	0.0327431i
$534$	7.60972	+	3.15205i	0.329305	+	0.136403i
$535$		0			0
$536$	−11.7687	+	11.7687i	−0.508329	+	0.508329i
$537$	1.98757	−	4.79843i	0.0857702	−	0.207068i
$538$	−1.14833	−	0.475654i	−0.0495080	−	0.0205069i
$539$	14.5946	−	6.04530i	0.628636	−	0.260390i
$540$		0			0
$541$	−5.46780	−	13.2004i	−0.235079	−	0.567531i	0.761682	−	0.647951i	$-0.224374\pi$
$541$	−5.46780	−	13.2004i	−0.235079	−	0.567531i	−0.996761	+	0.0804201i	$0.974374\pi$
$542$	−7.00251	+	7.00251i	−0.300784	+	0.300784i
$543$		−	1.88532i		−	0.0809070i
$544$	19.2118	−	9.88821i	0.823699	−	0.423954i
$545$		0			0
$546$	−6.47534	−	6.47534i	−0.277119	−	0.277119i
$547$	21.8969	−	9.06998i	0.936243	−	0.387805i	0.138199	−	0.990404i	$-0.455869\pi$
$547$	21.8969	−	9.06998i	0.936243	−	0.387805i	0.798043	+	0.602600i	$0.205869\pi$
$548$	3.19598			0.136525
$549$	−46.1771	+	19.1272i	−1.97079	+	0.816329i
$550$		0			0
$551$	−25.0490	−	10.3756i	−1.06712	−	0.442017i
$552$	−17.2773	−	17.2773i	−0.735371	−	0.735371i
$553$	11.5383	+	11.5383i	0.490660	+	0.490660i
$554$	−22.5776	−	9.35196i	−0.959231	−	0.397327i
$555$		0			0
$556$	19.4687	−	8.06419i	0.825656	−	0.341998i
$557$	−0.399812			−0.0169406			−0.00847028	−	0.999964i	$-0.502696\pi$
$557$	−0.399812			−0.0169406			−0.00847028	+	0.999964i	$0.502696\pi$
$558$	−13.3221	+	5.51819i	−0.563969	+	0.233604i
$559$	0.0220108	+	0.0220108i	0.000930957	+	0.000930957i
$560$		0			0
$561$	20.4307	−	63.7665i	0.862584	−	2.69222i
$562$			5.67668i			0.239456i
$563$	6.55034	−	6.55034i	0.276064	−	0.276064i	−0.555472	−	0.831536i	$-0.687462\pi$
$563$	6.55034	−	6.55034i	0.276064	−	0.276064i	0.831536	+	0.555472i	$0.187462\pi$
$564$	5.91343	+	14.2763i	0.249001	+	0.601140i
$565$		0			0
$566$	−16.4272	+	6.80437i	−0.690487	+	0.286009i
$567$	14.0506	+	5.81995i	0.590070	+	0.244415i
$568$	−12.2053	+	29.4662i	−0.512123	+	1.23637i
$569$	−4.07046	+	4.07046i	−0.170643	+	0.170643i	−0.787262	−	0.616619i	$-0.788502\pi$
$569$	−4.07046	+	4.07046i	−0.170643	+	0.170643i	0.616619	+	0.787262i	$0.288502\pi$
$570$		0			0
$571$	−12.9331	−	5.35705i	−0.541232	−	0.224186i	0.0952826	−	0.995450i	$-0.469625\pi$
$571$	−12.9331	−	5.35705i	−0.541232	−	0.224186i	−0.636515	+	0.771265i	$0.719625\pi$
$572$	−7.05018	−	2.92028i	−0.294783	−	0.122103i
$573$	−5.33561	−	12.8813i	−0.222899	−	0.538125i
$574$		−	5.07337i		−	0.211759i
$575$		0			0
$576$	18.3276	+	18.3276i	0.763651	+	0.763651i
$577$			18.4417i			0.767736i	0.923388	+	0.383868i	$0.125408\pi$
$577$			18.4417i			0.767736i	−0.923388	+	0.383868i	$0.874592\pi$
$578$	16.1458	−	2.69298i	0.671575	−	0.112013i
$579$	39.5495			1.64362
$580$		0			0
$581$	−14.7154	−	35.5262i	−0.610499	−	1.47388i
$582$	−32.9919			−1.36756
$583$	0.809616	+	1.95459i	0.0335309	+	0.0809507i
$584$	1.87316	−	4.52220i	0.0775118	−	0.187130i
$585$		0			0
$586$	−5.66397	+	5.66397i	−0.233977	+	0.233977i
$587$	2.85082	+	2.85082i	0.117666	+	0.117666i	0.763488	−	0.645822i	$-0.223485\pi$
$587$	2.85082	+	2.85082i	0.117666	+	0.117666i	−0.645822	+	0.763488i	$0.723485\pi$
$588$	2.80244	−	6.76568i	0.115571	−	0.279012i
$589$	−7.74084	+	18.6880i	−0.318956	+	0.770027i
$590$		0			0
$591$		−	16.7684i		−	0.689758i
$592$	−0.257724	+	0.106753i	−0.0105924	+	0.00438752i
$593$	4.61328	−	4.61328i	0.189445	−	0.189445i	−0.606011	−	0.795456i	$-0.707231\pi$
$593$	4.61328	−	4.61328i	0.189445	−	0.189445i	0.795456	+	0.606011i	$0.207231\pi$
$594$	15.9039			0.652544
$595$		0			0
$596$	−3.17114			−0.129895
$597$	27.9372	−	27.9372i	1.14339	−	1.14339i
$598$	−3.21741	+	1.33269i	−0.131570	+	0.0544979i
$599$		−	6.81189i		−	0.278326i	−0.990269	−	0.139163i	$-0.955559\pi$
$599$		−	6.81189i		−	0.278326i	0.990269	−	0.139163i	$-0.0444413\pi$
$600$		0			0
$601$	14.6029	−	35.2545i	0.595664	−	1.43806i	−0.282297	−	0.959327i	$-0.591096\pi$
$601$	14.6029	−	35.2545i	0.595664	−	1.43806i	0.877961	−	0.478732i	$-0.158904\pi$
$602$	0.0305945	−	0.0738616i	0.00124694	−	0.00301038i
$603$	15.9780	+	15.9780i	0.650674	+	0.650674i
$604$	−16.7207	+	16.7207i	−0.680354	+	0.680354i
$605$		0			0
$606$	1.43432	−	3.46275i	0.0582652	−	0.140665i
$607$	10.3924	+	25.0895i	0.421816	+	1.01835i	0.981812	+	0.189858i	$0.0608027\pi$
$607$	10.3924	+	25.0895i	0.421816	+	1.01835i	−0.559996	+	0.828495i	$0.689197\pi$
$608$	28.4342			1.15316
$609$	−15.6759	−	37.8450i	−0.635220	−	1.53356i
$610$		0			0
$611$	6.30805			0.255196
$612$	−8.13212	−	15.7999i	−0.328721	−	0.638672i
$613$			2.48591i			0.100405i	0.998739	+	0.0502025i	$0.0159867\pi$
$613$			2.48591i			0.100405i	−0.998739	+	0.0502025i	$0.984013\pi$
$614$	8.33154	+	8.33154i	0.336233	+	0.336233i
$615$		0			0
$616$			56.1349i			2.26174i
$617$	−16.5297	−	39.9062i	−0.665460	−	1.60656i	−0.789121	−	0.614238i	$-0.789464\pi$
$617$	−16.5297	−	39.9062i	−0.665460	−	1.60656i	0.123661	−	0.992325i	$-0.460536\pi$
$618$	23.1164	+	9.57513i	0.929878	+	0.385168i
$619$	1.27211	+	0.526923i	0.0511302	+	0.0211788i	0.408102	−	0.912936i	$-0.366191\pi$
$619$	1.27211	+	0.526923i	0.0511302	+	0.0211788i	−0.356972	+	0.934115i	$0.616191\pi$
$620$		0			0
$621$	−5.93894	+	5.93894i	−0.238321	+	0.238321i
$622$	−12.0258	+	29.0329i	−0.482192	+	1.16411i
$623$	9.23276	+	3.82434i	0.369903	+	0.153219i
$624$	1.99653	−	0.826992i	0.0799253	−	0.0331062i
$625$		0			0
$626$	−4.94825	−	11.9461i	−0.197772	−	0.477464i
$627$	62.3075	−	62.3075i	2.48832	−	2.48832i
$628$			13.8043i			0.550851i
$629$	1.63012	−	0.135012i	0.0649971	−	0.00538330i
$630$		0			0
$631$	22.9351	+	22.9351i	0.913032	+	0.913032i	0.996510	−	0.0834781i	$-0.0266029\pi$
$631$	22.9351	+	22.9351i	0.913032	+	0.913032i	−0.0834781	+	0.996510i	$0.526603\pi$
$632$	−14.4138	+	5.97040i	−0.573351	+	0.237490i
$633$	35.4928			1.41071
$634$	8.78330	−	3.63816i	0.348829	−	0.144490i
$635$		0			0
$636$	0.906094	+	0.375316i	0.0359289	+	0.0148823i
$637$	−2.11386	−	2.11386i	−0.0837542	−	0.0837542i
$638$	20.8579	+	20.8579i	0.825773	+	0.825773i
$639$	40.0054	+	16.5708i	1.58259	+	0.655530i
$640$		0			0
$641$	20.6017	−	8.53352i	0.813719	−	0.337054i	0.0632825	−	0.997996i	$-0.479843\pi$
$641$	20.6017	−	8.53352i	0.813719	−	0.337054i	0.750437	+	0.660942i	$0.229843\pi$
$642$	7.36471			0.290662
$643$	10.8335	−	4.48736i	0.427230	−	0.176964i	−0.158699	−	0.987327i	$-0.550730\pi$
$643$	10.8335	−	4.48736i	0.427230	−	0.176964i	0.585929	+	0.810363i	$0.300730\pi$
$644$	−7.31887	−	7.31887i	−0.288404	−	0.288404i
$645$		0			0
$646$	20.5135	+	6.57249i	0.807094	+	0.258591i
$647$			37.3217i			1.46727i	0.679544	+	0.733634i	$0.262177\pi$
$647$			37.3217i			1.46727i	−0.679544	+	0.733634i	$0.737823\pi$
$648$	−10.2818	+	10.2818i	−0.403908	+	0.403908i
$649$	−9.52665	−	22.9994i	−0.373954	−	0.902804i
$650$		0			0
$651$	−28.2346	+	11.6952i	−1.10660	+	0.458370i
$652$	19.1229	+	7.92097i	0.748911	+	0.310209i
$653$	0.671889	−	1.62208i	0.0262931	−	0.0634771i	−0.910188	−	0.414196i	$-0.864063\pi$
$653$	0.671889	−	1.62208i	0.0262931	−	0.0634771i	0.936481	+	0.350719i	$0.114063\pi$
$654$	−10.3945	+	10.3945i	−0.406456	+	0.406456i
$655$		0			0
$656$	1.10610	+	0.458164i	0.0431861	+	0.0178883i
$657$	−6.13967	−	2.54313i	−0.239531	−	0.0992171i
$658$	−6.19994	−	14.9680i	−0.241699	−	0.583513i
$659$			6.02834i			0.234831i	0.993083	+	0.117415i	$0.0374609\pi$
$659$			6.02834i			0.234831i	−0.993083	+	0.117415i	$0.962539\pi$
$660$		0			0
$661$	22.6415	+	22.6415i	0.880652	+	0.880652i	0.993601	−	0.112949i	$-0.0360296\pi$
$661$	22.6415	+	22.6415i	0.880652	+	0.880652i	−0.112949	+	0.993601i	$0.536030\pi$
$662$			5.43353i			0.211180i
$663$	−12.6282	+	1.04591i	−0.490438	+	0.0406199i
$664$	36.7653			1.42677
$665$		0			0
$666$	0.587213	+	1.41766i	0.0227540	+	0.0549331i
$667$	−15.5778			−0.603176
$668$	−7.74305	−	18.6934i	−0.299588	−	0.723269i
$669$	−2.14197	+	5.17116i	−0.0828132	+	0.199929i
$670$		0			0
$671$	53.9385	−	53.9385i	2.08227	−	2.08227i
$672$	30.3770	+	30.3770i	1.17182	+	1.17182i
$673$	15.1505	−	36.5765i	0.584009	−	1.40992i	−0.305142	−	0.952307i	$-0.598704\pi$
$673$	15.1505	−	36.5765i	0.584009	−	1.40992i	0.889150	−	0.457615i	$-0.151296\pi$
$674$	6.11393	−	14.7603i	0.235500	−	0.568547i
$675$		0			0
$676$		−	12.5033i		−	0.480897i
$677$	6.46223	−	2.67674i	0.248364	−	0.102876i	−0.255029	−	0.966933i	$-0.582085\pi$
$677$	6.46223	−	2.67674i	0.248364	−	0.102876i	0.503393	+	0.864058i	$0.332085\pi$
$678$	16.2689	−	16.2689i	0.624803	−	0.624803i
$679$	−40.0286			−1.53616
$680$		0			0
$681$	−38.5677			−1.47792
$682$	15.5613	−	15.5613i	0.595871	−	0.595871i
$683$	−34.3826	+	14.2417i	−1.31561	+	0.544945i	−0.926518	−	0.376251i	$-0.877213\pi$
$683$	−34.3826	+	14.2417i	−1.31561	+	0.544945i	−0.389097	+	0.921197i	$0.627213\pi$
$684$		−	23.3844i		−	0.894126i
$685$		0			0
$686$	5.04383	−	12.1769i	0.192574	−	0.464915i
$687$	2.68676	−	6.48641i	0.102506	−	0.247472i
$688$	0.0133405	+	0.0133405i	0.000508602	+	0.000508602i
$689$	0.283098	−	0.283098i	0.0107852	−	0.0107852i
$690$		0			0
$691$	−5.98831	+	14.4571i	−0.227806	+	0.549972i	−0.995910	−	0.0903530i	$-0.971200\pi$
$691$	−5.98831	+	14.4571i	−0.227806	+	0.549972i	0.768104	+	0.640325i	$0.221200\pi$
$692$	9.26952	+	22.3786i	0.352374	+	0.850706i
$693$	76.2127			2.89508
$694$	−3.40627	−	8.22347i	−0.129300	−	0.312158i
$695$		0			0
$696$	39.1650			1.48455
$697$	−5.35677	−	4.53731i	−0.202902	−	0.171863i
$698$		−	25.9276i		−	0.981372i
$699$	−5.88013	−	5.88013i	−0.222407	−	0.222407i
$700$		0			0
$701$		−	6.08551i		−	0.229847i	−0.993374	−	0.114923i	$-0.963338\pi$
$701$		−	6.08551i		−	0.229847i	0.993374	−	0.114923i	$-0.0366622\pi$
$702$	−1.15174	−	2.78055i	−0.0434697	−	0.104945i
$703$	1.98867	+	0.823733i	0.0750040	+	0.0310677i
$704$	−36.5459	−	15.1378i	−1.37738	−	0.570528i
$705$		0			0
$706$	−15.6407	+	15.6407i	−0.588644	+	0.588644i
$707$	1.74024	−	4.20130i	0.0654483	−	0.158006i
$708$	−10.6619	−	4.41630i	−0.400698	−	0.165975i
$709$	−18.2079	+	7.54197i	−0.683813	+	0.283245i	−0.697420	−	0.716663i	$-0.745669\pi$
$709$	−18.2079	+	7.54197i	−0.683813	+	0.283245i	0.0136069	+	0.999907i	$0.495669\pi$
$710$		0			0
$711$	8.10584	+	19.5692i	0.303993	+	0.733903i
$712$	−6.75626	+	6.75626i	−0.253202	+	0.253202i
$713$			11.6220i			0.435247i
$714$	14.8936	+	28.9367i	0.557377	+	1.08293i
$715$		0			0
$716$	1.48745	+	1.48745i	0.0555886	+	0.0555886i
$717$	−33.5504	+	13.8970i	−1.25296	+	0.518995i
$718$	32.8425			1.22567
$719$	14.7049	−	6.09095i	0.548399	−	0.227154i	−0.0912412	−	0.995829i	$-0.529083\pi$
$719$	14.7049	−	6.09095i	0.548399	−	0.227154i	0.639640	+	0.768675i	$0.279083\pi$
$720$		0			0
$721$	28.0468	+	11.6174i	1.04452	+	0.432653i
$722$	7.10797	+	7.10797i	0.264531	+	0.264531i
$723$	−23.3908	−	23.3908i	−0.869914	−	0.869914i
$724$	0.705464	+	0.292213i	0.0262184	+	0.0108600i
$725$		0			0
$726$	−62.6479	+	25.9496i	−2.32508	+	0.963081i
$727$	−22.2643			−0.825736			−0.412868	−	0.910791i	$-0.635473\pi$
$727$	−22.2643			−0.825736			−0.412868	+	0.910791i	$0.635473\pi$
$728$	9.81433	−	4.06523i	0.363743	−	0.150667i
$729$	29.0987	+	29.0987i	1.07773	+	1.07773i
$730$		0			0
$731$	−0.0506257	−	0.0983607i	−0.00187246	−	0.00363800i
$732$		−	35.3616i		−	1.30700i
$733$	−4.01178	+	4.01178i	−0.148178	+	0.148178i	−0.777304	−	0.629125i	$-0.783413\pi$
$733$	−4.01178	+	4.01178i	−0.148178	+	0.148178i	0.629125	+	0.777304i	$0.283413\pi$
$734$	−3.41801	−	8.25181i	−0.126161	−	0.304580i
$735$		0			0
$736$	15.0934	−	6.25191i	0.556352	−	0.230449i
$737$	−31.8607	−	13.1971i	−1.17360	−	0.486122i
$738$	2.52021	−	6.08432i	0.0927702	−	0.223967i
$739$	28.1411	−	28.1411i	1.03519	−	1.03519i	0.0358281	−	0.999358i	$-0.488593\pi$
$739$	28.1411	−	28.1411i	1.03519	−	1.03519i	0.999358	−	0.0358281i	$-0.0114069\pi$
$740$		0			0
$741$	−15.4058	−	6.38128i	−0.565946	−	0.234422i
$742$	−0.949994	−	0.393501i	−0.0348754	−	0.0144459i
$743$	−4.07556	−	9.83928i	−0.149518	−	0.360968i	0.831320	−	0.555794i	$-0.187586\pi$
$743$	−4.07556	−	9.83928i	−0.149518	−	0.360968i	−0.980838	+	0.194826i	$0.937586\pi$
$744$		−	29.2195i		−	1.07124i
$745$		0			0
$746$	2.08924	+	2.08924i	0.0764926	+	0.0764926i
$747$		−	49.9153i		−	1.82630i
$748$	20.6940	+	17.5283i	0.756647	+	0.640897i
$749$	8.93549			0.326496
$750$		0			0
$751$	6.93403	+	16.7402i	0.253026	+	0.610860i	0.998446	−	0.0557362i	$-0.0177506\pi$
$751$	6.93403	+	16.7402i	0.253026	+	0.610860i	−0.745419	+	0.666596i	$0.767751\pi$
$752$	3.82324			0.139419
$753$	−17.6805	−	42.6846i	−0.644314	−	1.55551i
$754$	2.13618	−	5.15720i	0.0777952	−	0.187814i
$755$		0			0
$756$	6.32512	−	6.32512i	0.230042	−	0.230042i
$757$	−12.0753	−	12.0753i	−0.438885	−	0.438885i	0.452752	−	0.891637i	$-0.350442\pi$
$757$	−12.0753	−	12.0753i	−0.438885	−	0.438885i	−0.891637	+	0.452752i	$0.850442\pi$
$758$	−13.4618	+	32.4997i	−0.488955	+	1.18044i
$759$	19.3744	−	46.7738i	0.703245	−	1.69778i
$760$		0			0
$761$			31.9719i			1.15898i	0.814979	+	0.579491i	$0.196749\pi$
$761$			31.9719i			1.15898i	−0.814979	+	0.579491i	$0.803251\pi$
$762$	32.9886	−	13.6643i	1.19505	−	0.495006i
$763$	−12.6114	+	12.6114i	−0.456565	+	0.456565i
$764$	5.64701			0.204301
$765$		0			0
$766$	8.97540			0.324294
$767$	−3.33118	+	3.33118i	−0.120282	+	0.120282i
$768$	−41.6399	+	17.2478i	−1.50255	+	0.622376i
$769$			34.9147i			1.25906i	0.776977	+	0.629529i	$0.216752\pi$
$769$			34.9147i			1.25906i	−0.776977	+	0.629529i	$0.783248\pi$
$770$		0			0
$771$	−6.97541	+	16.8401i	−0.251213	+	0.606482i
$772$	−6.12991	+	14.7989i	−0.220620	+	0.532625i
$773$	3.17604	+	3.17604i	0.114234	+	0.114234i	0.761913	−	0.647679i	$-0.224260\pi$
$773$	3.17604	+	3.17604i	0.114234	+	0.114234i	−0.647679	+	0.761913i	$0.724260\pi$
$774$	0.0733818	−	0.0733818i	0.00263765	−	0.00263765i
$775$		0			0
$776$	14.6459	−	35.3582i	0.525756	−	1.26929i
$777$	1.24453	+	3.00456i	0.0446472	+	0.107788i
$778$	−31.9310			−1.14478
$779$	−3.53531	−	8.53499i	−0.126666	−	0.305798i
$780$		0			0
$781$	−66.0854			−2.36472
$782$	12.3341	−	1.02156i	0.441067	−	0.0365308i
$783$		−	13.4627i		−	0.481117i
$784$	−1.28119	−	1.28119i	−0.0457568	−	0.0457568i
$785$		0			0
$786$		−	32.3174i		−	1.15272i
$787$	3.31075	+	7.99286i	0.118016	+	0.284915i	0.971838	−	0.235649i	$-0.0757217\pi$
$787$	3.31075	+	7.99286i	0.118016	+	0.284915i	−0.853823	+	0.520564i	$0.825722\pi$
$788$	6.27451	+	2.59899i	0.223520	+	0.0925850i
$789$	15.2667	+	6.32367i	0.543508	+	0.225129i
$790$		0			0
$791$	19.7388	−	19.7388i	0.701831	−	0.701831i
$792$	−27.8851	+	67.3206i	−0.990854	+	2.39213i
$793$	−13.3365	−	5.52416i	−0.473593	−	0.196169i
$794$	7.85087	−	3.25194i	0.278617	−	0.115407i
$795$		0			0
$796$	6.12366	+	14.7838i	0.217048	+	0.523999i
$797$	13.4447	−	13.4447i	0.476236	−	0.476236i	−0.427689	−	0.903926i	$-0.640672\pi$
$797$	13.4447	−	13.4447i	0.476236	−	0.476236i	0.903926	+	0.427689i	$0.140672\pi$
$798$			42.8274i			1.51607i
$799$	−21.3489	−	6.84016i	−0.755271	−	0.241987i
$800$		0			0
$801$	9.17279	+	9.17279i	0.324104	+	0.324104i
$802$	17.3636	−	7.19226i	0.613132	−	0.253967i
$803$	10.1422			0.357910
$804$	−14.7697	+	6.11783i	−0.520888	+	0.215759i
$805$		0			0
$806$	−3.84758	−	1.59372i	−0.135525	−	0.0561364i
$807$	−2.41794	−	2.41794i	−0.0851156	−	0.0851156i
$808$	3.07439	+	3.07439i	0.108157	+	0.108157i
$809$	20.9455	+	8.67589i	0.736403	+	0.305028i	0.719180	−	0.694824i	$-0.244518\pi$
$809$	20.9455	+	8.67589i	0.736403	+	0.305028i	0.0172227	+	0.999852i	$0.494518\pi$
$810$		0			0
$811$	−22.2809	+	9.22904i	−0.782388	+	0.324076i	−0.737879	−	0.674933i	$-0.764172\pi$
$811$	−22.2809	+	9.22904i	−0.782388	+	0.324076i	−0.0445090	+	0.999009i	$0.514172\pi$
$812$	16.5908			0.582222
$813$	−25.1706	+	10.4260i	−0.882772	+	0.365656i
$814$	−1.65593	−	1.65593i	−0.0580405	−	0.0580405i
$815$		0			0
$816$	−7.65382	+	0.633917i	−0.267937	+	0.0221915i
$817$		−	0.145578i		−	0.00509311i
$818$	−7.09121	+	7.09121i	−0.247938	+	0.247938i
$819$	−5.51925	−	13.3246i	−0.192858	−	0.465601i
$820$		0			0
$821$	−0.105957	+	0.0438888i	−0.00369792	+	0.00153173i	−0.384532	−	0.923112i	$-0.625637\pi$
$821$	−0.105957	+	0.0438888i	−0.00369792	+	0.00153173i	0.380834	+	0.924644i	$0.375637\pi$
$822$	−7.01962	−	2.90762i	−0.244838	−	0.101415i
$823$	12.9581	−	31.2835i	0.451689	−	1.09047i	−0.519990	−	0.854172i	$-0.674064\pi$
$823$	12.9581	−	31.2835i	0.451689	−	1.09047i	0.971680	−	0.236302i	$-0.0759356\pi$
$824$	−20.5238	+	20.5238i	−0.714981	+	0.714981i
$825$		0			0
$826$	11.1785	+	4.63027i	0.388948	+	0.161108i
$827$	18.9992	+	7.86974i	0.660668	+	0.273658i	0.687720	−	0.725976i	$-0.258612\pi$
$827$	18.9992	+	7.86974i	0.660668	+	0.273658i	−0.0270516	+	0.999634i	$0.508612\pi$
$828$	−5.14160	−	12.4129i	−0.178683	−	0.431379i
$829$			26.7935i			0.930576i	0.885159	+	0.465288i	$0.154049\pi$
$829$			26.7935i			0.930576i	−0.885159	+	0.465288i	$0.845951\pi$
$830$		0			0
$831$	−47.5398	−	47.5398i	−1.64914	−	1.64914i
$832$			7.48577i			0.259522i
$833$	4.86197	+	9.44631i	0.168457	+	0.327295i
$834$	−50.0975			−1.73473
$835$		0			0
$836$	13.6574	+	32.9719i	0.472352	+	1.14036i
$837$	−10.0440			−0.347170
$838$	13.0147	+	31.4204i	0.449587	+	1.08540i
$839$	−5.29374	+	12.7802i	−0.182760	+	0.441222i	−0.988533	−	0.151002i	$-0.951750\pi$
$839$	−5.29374	+	12.7802i	−0.182760	+	0.441222i	0.805773	+	0.592224i	$0.201750\pi$
$840$		0			0
$841$	−2.84980	+	2.84980i	−0.0982690	+	0.0982690i
$842$	10.2267	+	10.2267i	0.352436	+	0.352436i
$843$	−5.97645	+	14.4284i	−0.205840	+	0.496942i
$844$	−5.50114	+	13.2809i	−0.189357	+	0.457149i
$845$		0			0
$846$		−	21.0304i		−	0.723041i
$847$	−76.0098	+	31.4843i	−2.61173	+	1.08181i
$848$	0.171583	−	0.171583i	0.00589219	−	0.00589219i
$849$	−48.9168			−1.67882
$850$		0			0
$851$	1.23674			0.0423950
$852$	−21.6625	+	21.6625i	−0.742145	+	0.742145i
$853$	−11.8086	+	4.89128i	−0.404319	+	0.167474i	−0.575569	−	0.817753i	$-0.695219\pi$
$853$	−11.8086	+	4.89128i	−0.404319	+	0.167474i	0.171250	+	0.985228i	$0.445219\pi$
$854$			37.0749i			1.26868i
$855$		0			0
$856$	−3.26936	+	7.89294i	−0.111744	+	0.269775i
$857$	2.41686	−	5.83483i	0.0825585	−	0.199314i	−0.877210	−	0.480107i	$-0.840598\pi$
$857$	2.41686	−	5.83483i	0.0825585	−	0.199314i	0.959768	+	0.280794i	$0.0905977\pi$
$858$	12.8282	+	12.8282i	0.437946	+	0.437946i
$859$	−24.8431	+	24.8431i	−0.847636	+	0.847636i	−0.989838	−	0.142202i	$-0.954582\pi$
$859$	−24.8431	+	24.8431i	−0.847636	+	0.847636i	0.142202	+	0.989838i	$0.454582\pi$
$860$		0			0
$861$	5.34129	−	12.8950i	0.182031	−	0.439461i
$862$	8.60453	+	20.7732i	0.293072	+	0.707537i
$863$	−44.2102			−1.50493			−0.752466	−	0.658632i	$-0.771136\pi$
$863$	−44.2102			−1.50493			−0.752466	+	0.658632i	$0.771136\pi$
$864$	5.40303	+	13.0441i	0.183815	+	0.443768i
$865$		0			0
$866$	−17.6279			−0.599022
$867$	43.8729	+	10.1536i	1.49000	+	0.344836i
$868$		−	12.3777i		−	0.420127i
$869$	−22.8584	−	22.8584i	−0.775417	−	0.775417i
$870$		0			0
$871$			6.52608i			0.221128i
$872$	−6.52566	−	15.7543i	−0.220987	−	0.533510i
$873$	−48.0049	−	19.8843i	−1.62472	−	0.672980i
$874$	15.0470	+	6.23268i	0.508973	+	0.210824i
$875$		0			0
$876$	3.32456	−	3.32456i	0.112327	−	0.112327i
$877$	9.03414	−	21.8103i	0.305061	−	0.736483i	−0.694790	−	0.719213i	$-0.744503\pi$
$877$	9.03414	−	21.8103i	0.305061	−	0.736483i	0.999851	−	0.0172700i	$-0.00549748\pi$
$878$	−18.0315	−	7.46888i	−0.608533	−	0.252063i
$879$	−20.3592	+	8.43306i	−0.686699	+	0.284440i
$880$		0			0
$881$	−12.6524	−	30.5457i	−0.426271	−	1.02911i	−0.980460	−	0.196719i	$-0.936971\pi$
$881$	−12.6524	−	30.5457i	−0.426271	−	1.02911i	0.554189	−	0.832391i	$-0.313029\pi$
$882$	−7.04741	+	7.04741i	−0.237298	+	0.237298i
$883$		−	58.1141i		−	1.95569i	−0.209320	−	0.977847i	$-0.567125\pi$
$883$		−	58.1141i		−	1.95569i	0.209320	−	0.977847i	$-0.432875\pi$
$884$	1.56592	−	4.88741i	0.0526675	−	0.164381i
$885$		0			0
$886$	20.0068	+	20.0068i	0.672140	+	0.672140i
$887$	−25.8776	+	10.7189i	−0.868885	+	0.359904i	−0.772176	−	0.635409i	$-0.780832\pi$
$887$	−25.8776	+	10.7189i	−0.868885	+	0.359904i	−0.0967091	+	0.995313i	$0.530832\pi$
$888$	−3.10936			−0.104343
$889$	40.0246	−	16.5787i	1.34238	−	0.556033i
$890$		0			0
$891$	−27.8354	−	11.5298i	−0.932520	−	0.386262i
$892$	−1.60299	−	1.60299i	−0.0536721	−	0.0536721i
$893$	−20.8605	−	20.8605i	−0.698069	−	0.698069i
$894$	6.96508	+	2.88503i	0.232947	+	0.0964899i
$895$		0			0
$896$	−12.2034	+	5.05480i	−0.407686	+	0.168869i
$897$	−9.58077			−0.319893
$898$	29.0375	−	12.0277i	0.968994	−	0.401371i
$899$	−13.1727	−	13.1727i	−0.439333	−	0.439333i
$900$		0			0
$901$	−1.26510	+	0.651138i	−0.0421465	+	0.0216926i
$902$			10.0508i			0.334654i
$903$	0.155524	−	0.155524i	0.00517552	−	0.00517552i
$904$	10.2136	+	24.6579i	0.339701	+	0.820110i
$905$		0			0
$906$	51.9372	−	21.5131i	1.72550	−	0.714724i
$907$	−46.1204	−	19.1037i	−1.53140	−	0.634328i	−0.551568	−	0.834130i	$-0.685970\pi$
$907$	−46.1204	−	19.1037i	−1.53140	−	0.634328i	−0.979836	+	0.199802i	$0.935970\pi$
$908$	5.97774	−	14.4315i	0.198378	−	0.478928i
$909$	4.17401	−	4.17401i	0.138443	−	0.138443i
$910$		0			0
$911$	−20.2142	−	8.37302i	−0.669728	−	0.277410i	0.0217976	−	0.999762i	$-0.493061\pi$
$911$	−20.2142	−	8.37302i	−0.669728	−	0.277410i	−0.691526	+	0.722352i	$0.743061\pi$
$912$	−9.33729	−	3.86763i	−0.309189	−	0.128070i
$913$	29.1525	+	70.3802i	0.964805	+	2.32925i
$914$			8.13734i			0.269159i
$915$		0			0
$916$	2.01070	+	2.01070i	0.0664354	+	0.0664354i
$917$		−	39.2102i		−	1.29483i
$918$	0.882850	+	10.6594i	0.0291384	+	0.351812i
$919$	11.0529			0.364600			0.182300	−	0.983243i	$-0.441646\pi$
$919$	11.0529			0.364600			0.182300	+	0.983243i	$0.441646\pi$
$920$		0			0
$921$	12.4048	+	29.9478i	0.408752	+	0.986814i
$922$	36.8378			1.21319
$923$	4.78584	+	11.5540i	0.157528	+	0.380306i
$924$	−20.6342	+	49.8153i	−0.678815	+	1.63880i
$925$		0			0
$926$	−18.5029	+	18.5029i	−0.608045	+	0.608045i
$927$	27.8646	+	27.8646i	0.915193	+	0.915193i
$928$	−10.0212	+	24.1934i	−0.328963	+	0.794186i
$929$	−12.6796	+	30.6112i	−0.416003	+	1.00432i	0.567491	+	0.823380i	$0.307914\pi$
$929$	−12.6796	+	30.6112i	−0.416003	+	1.00432i	−0.983494	+	0.180941i	$0.942086\pi$
$930$		0			0
$931$			13.9809i			0.458206i
$932$	3.11165	−	1.28889i	0.101925	−	0.0422189i
$933$	−61.1322	+	61.1322i	−2.00138	+	2.00138i
$934$	−3.31733			−0.108546
$935$		0			0
$936$	13.7894			0.450721
$937$	41.2820	−	41.2820i	1.34862	−	1.34862i	0.461465	−	0.887159i	$-0.347324\pi$
$937$	41.2820	−	41.2820i	1.34862	−	1.34862i	0.887159	−	0.461465i	$-0.152676\pi$
$938$	15.4853	−	6.41424i	0.505614	−	0.209432i
$939$		−	35.5731i		−	1.16088i
$940$		0			0
$941$	−2.33416	+	5.63515i	−0.0760913	+	0.183701i	−0.957348	−	0.288937i	$-0.906698\pi$
$941$	−2.33416	+	5.63515i	−0.0760913	+	0.183701i	0.881257	+	0.472638i	$0.156698\pi$
$942$	12.5588	−	30.3196i	0.409188	−	0.987867i
$943$	−3.75323	−	3.75323i	−0.122222	−	0.122222i
$944$	−2.01900	+	2.01900i	−0.0657127	+	0.0657127i
$945$		0			0
$946$	−0.0606101	+	0.146326i	−0.00197061	+	0.00475746i
$947$	−18.0429	−	43.5595i	−0.586317	−	1.41549i	−0.887000	−	0.461770i	$-0.847215\pi$
$947$	−18.0429	−	43.5595i	−0.586317	−	1.41549i	0.300683	−	0.953724i	$-0.402785\pi$
$948$	−14.9857			−0.486714
$949$	−0.734487	−	1.77321i	−0.0238425	−	0.0575608i
$950$		0			0
$951$	26.1548			0.848129
$952$	−37.6237	+	3.11614i	−1.21939	+	0.100995i
$953$			26.8459i			0.869625i	0.900521	+	0.434812i	$0.143185\pi$
$953$			26.8459i			0.869625i	−0.900521	+	0.434812i	$0.856815\pi$
$954$	−0.943823	−	0.943823i	−0.0305574	−	0.0305574i
$955$		0			0
$956$		−	14.7081i		−	0.475694i
$957$	31.0553	+	74.9740i	1.00387	+	2.42357i
$958$	−13.6633	−	5.65952i	−0.441441	−	0.182851i
$959$	−8.51680	−	3.52778i	−0.275022	−	0.113918i
$960$		0			0
$961$	12.0927	−	12.0927i	0.390088	−	0.390088i
$962$	−0.169594	+	0.409436i	−0.00546793	+	0.0132008i
$963$	10.7160	+	4.43872i	0.345319	+	0.143036i
$964$	12.3780	−	5.12712i	0.398667	−	0.165133i
$965$		0			0
$966$	9.41658	+	22.7336i	0.302974	+	0.731443i
$967$	−24.1223	+	24.1223i	−0.775722	+	0.775722i	−0.979100	−	0.203378i	$-0.934808\pi$
$967$	−24.1223	+	24.1223i	−0.775722	+	0.775722i	0.203378	+	0.979100i	$0.434808\pi$
$968$		−	78.6610i		−	2.52826i
$969$	45.2197	+	38.3021i	1.45267	+	1.23044i
$970$		0			0
$971$	−16.2292	−	16.2292i	−0.520821	−	0.520821i	0.396999	−	0.917819i	$-0.370052\pi$
$971$	−16.2292	−	16.2292i	−0.520821	−	0.520821i	−0.917819	+	0.396999i	$0.870052\pi$
$972$	−20.9152	+	8.66335i	−0.670855	+	0.277877i
$973$	−60.7825			−1.94860
$974$	23.4043	−	9.69439i	0.749923	−	0.310628i
$975$		0			0
$976$	−8.08312	−	3.34814i	−0.258734	−	0.107171i
$977$	−14.0530	−	14.0530i	−0.449595	−	0.449595i	0.445625	−	0.895220i	$-0.352982\pi$
$977$	−14.0530	−	14.0530i	−0.449595	−	0.449595i	−0.895220	+	0.445625i	$0.852982\pi$
$978$	−34.7951	−	34.7951i	−1.11263	−	1.11263i
$979$	−18.2908	−	7.57632i	−0.584578	−	0.242140i
$980$		0			0
$981$	−21.3892	+	8.85971i	−0.682906	+	0.282869i
$982$	−27.9585			−0.892192
$983$	54.5743	−	22.6054i	1.74065	−	0.721001i	0.741928	−	0.670479i	$-0.233911\pi$
$983$	54.5743	−	22.6054i	1.74065	−	0.721001i	0.998723	−	0.0505223i	$-0.0160886\pi$
$984$	9.43619	+	9.43619i	0.300815	+	0.300815i
$985$		0			0
$986$	−12.8219	+	15.1376i	−0.408333	+	0.482081i
$987$		−	44.5715i		−	1.41873i
$988$	4.77559	−	4.77559i	0.151932	−	0.151932i
$989$	−0.0320086	−	0.0772755i	−0.00101781	−	0.00245722i
$990$		0			0
$991$	−9.78771	+	4.05420i	−0.310917	+	0.128786i	−0.532685	−	0.846313i	$-0.678817\pi$
$991$	−9.78771	+	4.05420i	−0.310917	+	0.128786i	0.221768	+	0.975099i	$0.428817\pi$
$992$	18.0497	+	7.47643i	0.573078	+	0.237377i
$993$	−5.72046	+	13.8104i	−0.181533	+	0.438261i
$994$	22.7121	−	22.7121i	0.720383	−	0.720383i
$995$		0			0
$996$	32.6264	+	13.5143i	1.03381	+	0.428217i
$997$	−37.6817	−	15.6083i	−1.19339	−	0.494319i	−0.304534	−	0.952501i	$-0.598501\pi$
$997$	−37.6817	−	15.6083i	−1.19339	−	0.494319i	−0.888858	+	0.458182i	$0.848501\pi$
$998$	12.0088	+	28.9917i	0.380131	+	0.917718i
$999$			1.06882i			0.0338159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.f.49.4		24
5.2	odd	4		85.2.l.a.66.4	✓	24
5.3	odd	4		425.2.m.b.151.3		24
5.4	even	2		425.2.n.c.49.3		24
15.2	even	4		765.2.be.b.406.3		24
17.8	even	8		425.2.n.c.399.3		24
85.8	odd	8		425.2.m.b.76.3		24
85.12	even	16		1445.2.a.q.1.6		12
85.22	even	16		1445.2.a.p.1.6		12
85.37	even	16		1445.2.d.j.866.13		24
85.42	odd	8		85.2.l.a.76.4	yes	24
85.59	even	8	inner	425.2.n.f.399.4		24
85.63	even	16		7225.2.a.bq.1.7		12
85.73	even	16		7225.2.a.bs.1.7		12
85.82	even	16		1445.2.d.j.866.14		24
255.212	even	8		765.2.be.b.586.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.4	✓	24	5.2	odd	4
85.2.l.a.76.4	yes	24	85.42	odd	8
425.2.m.b.76.3		24	85.8	odd	8
425.2.m.b.151.3		24	5.3	odd	4
425.2.n.c.49.3		24	5.4	even	2
425.2.n.c.399.3		24	17.8	even	8
425.2.n.f.49.4		24	1.1	even	1	trivial
425.2.n.f.399.4		24	85.59	even	8	inner
765.2.be.b.406.3		24	15.2	even	4
765.2.be.b.586.3		24	255.212	even	8
1445.2.a.p.1.6		12	85.22	even	16
1445.2.a.q.1.6		12	85.12	even	16
1445.2.d.j.866.13		24	85.37	even	16
1445.2.d.j.866.14		24	85.82	even	16
7225.2.a.bq.1.7		12	85.63	even	16
7225.2.a.bs.1.7		12	85.73	even	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.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.680853 - 0.680853i) q^{2} +(2.44733 - 1.01372i) q^{3} +1.07288i q^{4} +(0.976080 - 2.35647i) q^{6} +(1.18426 - 2.85906i) q^{7} +(2.09218 + 2.09218i) q^{8} +(2.84049 - 2.84049i) q^{9} +O(q^{10})\)	\(q+(0.680853 - 0.680853i) q^{2} +(2.44733 - 1.01372i) q^{3} +1.07288i q^{4} +(0.976080 - 2.35647i) q^{6} +(1.18426 - 2.85906i) q^{7} +(2.09218 + 2.09218i) q^{8} +(2.84049 - 2.84049i) q^{9} +(-2.34612 + 5.66403i) q^{11} +(1.08760 + 2.62569i) q^{12} +1.16017 q^{13} +(-1.14029 - 2.75291i) q^{14} +0.703170 q^{16} +(-3.92649 - 1.25804i) q^{17} -3.86791i q^{18} +(-3.83665 - 3.83665i) q^{19} -8.19759i q^{21} +(2.25901 + 5.45373i) q^{22} +(-2.88015 - 1.19300i) q^{23} +(7.24113 + 2.99938i) q^{24} +(0.789908 - 0.789908i) q^{26} +(1.03101 - 2.48908i) q^{27} +(3.06743 + 1.27057i) q^{28} +(4.61660 - 1.91226i) q^{29} +(-1.42666 - 3.44426i) q^{31} +(-3.70560 + 3.70560i) q^{32} +16.2401i q^{33} +(-3.52990 + 1.81682i) q^{34} +(3.04750 + 3.04750i) q^{36} +(-0.366518 + 0.151817i) q^{37} -5.22439 q^{38} +(2.83933 - 1.17609i) q^{39} +(1.57303 + 0.651568i) q^{41} +(-5.58135 - 5.58135i) q^{42} +(0.0189720 + 0.0189720i) q^{43} +(-6.07683 - 2.51710i) q^{44} +(-2.77321 + 1.14870i) q^{46} +5.43715 q^{47} +(1.72089 - 0.712817i) q^{48} +(-1.82202 - 1.82202i) q^{49} +(-10.8847 + 0.901513i) q^{51} +1.24473i q^{52} +(0.244014 - 0.244014i) q^{53} +(-0.992732 - 2.39667i) q^{54} +(8.45936 - 3.50398i) q^{56} +(-13.2788 - 5.50028i) q^{57} +(1.84126 - 4.44519i) q^{58} +(-2.87128 + 2.87128i) q^{59} +(-11.4953 - 4.76149i) q^{61} +(-3.31638 - 1.37369i) q^{62} +(-4.75726 - 11.4850i) q^{63} +6.45228i q^{64} +(11.0571 + 11.0571i) q^{66} +5.62508i q^{67} +(1.34973 - 4.21265i) q^{68} -8.25804 q^{69} +(4.12510 + 9.95888i) q^{71} +11.8856 q^{72} +(-0.633083 - 1.52840i) q^{73} +(-0.146180 + 0.352909i) q^{74} +(4.11627 - 4.11627i) q^{76} +(13.4154 + 13.4154i) q^{77} +(1.13242 - 2.73391i) q^{78} +(-2.01785 + 4.87153i) q^{79} +4.91441i q^{81} +(1.51462 - 0.627376i) q^{82} +(8.78638 - 8.78638i) q^{83} +8.79502 q^{84} +0.0258342 q^{86} +(9.35987 - 9.35987i) q^{87} +(-16.7587 + 6.94167i) q^{88} +3.22930i q^{89} +(1.37395 - 3.31701i) q^{91} +(1.27994 - 3.09005i) q^{92} +(-6.98302 - 6.98302i) q^{93} +(3.70190 - 3.70190i) q^{94} +(-5.31240 + 12.8253i) q^{96} +(-4.94995 - 11.9502i) q^{97} -2.48105 q^{98} +(9.42450 + 22.7528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9	\( 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37} + 48 q^{38} - 8 q^{39} + 16 q^{41} + 24 q^{42} + 8 q^{43} - 16 q^{44} + 8 q^{46} + 64 q^{47} + 8 q^{48} - 56 q^{51} - 24 q^{53} + 32 q^{54} + 64 q^{56} - 16 q^{57} - 56 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 80 q^{63} + 96 q^{66} - 24 q^{68} - 96 q^{69} - 24 q^{71} + 24 q^{72} + 64 q^{73} + 64 q^{74} - 8 q^{76} - 24 q^{77} - 8 q^{78} + 16 q^{82} + 96 q^{83} + 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} - 112 q^{92} + 64 q^{93} - 56 q^{94} - 168 q^{96} - 48 q^{97} - 120 q^{98} + 8 q^{99}+O(q^{100}) \) 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 8 * q^99

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