LMFDB - Embedded newform 425.2.n.c.49.3

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			49.3
Character	$\chi$	$=$	425.49
Dual form			425.2.n.c.399.3

$q$-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	−0.905590	−	0.424154i	$-0.860571\pi$
$2$	−0.680853	+	0.680853i	−0.481435	+	0.481435i	0.424154	+	0.905590i	$0.360571\pi$
$3$	−2.44733	+	1.01372i	−1.41297	+	0.585271i	−0.953083	−	0.302708i	$-0.902109\pi$
$3$	−2.44733	+	1.01372i	−1.41297	+	0.585271i	−0.459885	+	0.887979i	$0.652109\pi$
$4$			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	$0.323839\pi$
$7$	−1.18426	+	2.85906i	−0.447609	+	1.08062i	−0.973215	+	0.229896i	$0.926161\pi$
$8$	−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	$-0.551436\pi$
$13$	−1.16017			−0.321775			−0.160887	+	0.986973i	$0.551436\pi$
$14$	−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	0.662183	−	0.749342i	$-0.269630\pi$
$23$	2.88015	+	1.19300i	0.600552	+	0.248757i	−0.0616306	+	0.998099i	$0.519630\pi$
$24$	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	−0.352352	−	0.935867i	$-0.614618\pi$
$37$	0.366518	−	0.151817i	0.0602551	−	0.0249585i	0.412607	+	0.910909i	$0.364618\pi$
$38$	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	0.705659	−	0.708552i	$-0.250651\pi$
$43$	−0.0189720	−	0.0189720i	−0.00289320	−	0.00289320i	−0.708552	+	0.705659i	$0.750651\pi$
$44$	−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	$-0.629791\pi$
$47$	−5.43715			−0.793090			−0.396545	+	0.918015i	$0.629791\pi$
$48$	−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	−0.723667	−	0.690149i	$-0.757545\pi$
$53$	−0.244014	+	0.244014i	−0.0335179	+	0.0335179i	0.690149	+	0.723667i	$0.257545\pi$
$54$	−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	$-0.888351\pi$
$67$		−	5.62508i		−	0.687213i	0.939114	−	0.343607i	$-0.111649\pi$
$68$	−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	0.956588	−	0.291443i	$-0.0941354\pi$
$73$	0.633083	+	1.52840i	0.0740968	+	0.178886i	−0.882491	+	0.470329i	$0.844135\pi$
$74$	−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	−0.999389	−	0.0349583i	$-0.988870\pi$
$83$	−8.78638	+	8.78638i	−0.964430	+	0.964430i	0.0349583	+	0.999389i	$0.488870\pi$
$84$	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	$0.103035\pi$
$97$	4.94995	+	11.9502i	0.502592	+	1.21336i	−0.445476	+	0.895294i	$0.646965\pi$
$98$	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	$-0.839441\pi$
$103$		−	9.80978i		−	0.966586i	0.875459	−	0.483293i	$-0.160559\pi$
$104$	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	0.861426	−	0.507882i	$-0.169572\pi$
$107$	−1.10497	−	2.66763i	−0.106821	−	0.257889i	−0.968248	+	0.249993i	$0.919572\pi$
$108$	−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	−0.0454578	−	0.998966i	$-0.514475\pi$
$113$	−8.33379	−	3.45197i	−0.783977	−	0.324734i	−0.738519	+	0.674232i	$0.764475\pi$
$114$	−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	0.114980	−	0.993368i	$-0.463319\pi$
$127$	−9.89892	−	9.89892i	−0.878387	−	0.878387i	−0.993368	+	0.114980i	$0.963319\pi$
$128$	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	$0.0406155\pi$
$137$			2.97888i			0.254503i	−0.991870	+	0.127251i	$0.959384\pi$
$138$	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	$-0.671626\pi$
$157$	−12.8666			−1.02686			−0.513432	+	0.858130i	$0.671626\pi$
$158$	−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	$0.397631\pi$
$163$	−7.38291	+	17.8239i	−0.578274	+	1.39608i	−0.894361	+	0.447347i	$0.852369\pi$
$164$	−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	0.412464	−	0.910974i	$-0.364668\pi$
$167$	17.4236	−	7.21707i	1.34828	−	0.558474i	0.935812	+	0.352500i	$0.114668\pi$
$168$	−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	−0.989325	−	0.145728i	$-0.953448\pi$
$173$	−20.8584	+	8.63985i	−1.58584	+	0.656876i	−0.596513	+	0.802603i	$0.703448\pi$
$174$		−	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	−0.173704	−	0.984798i	$-0.555574\pi$
$193$	−13.7936	−	5.71352i	−0.992888	−	0.411268i	−0.819184	+	0.573530i	$0.805574\pi$
$194$	−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	−0.986379	−	0.164490i	$-0.947402\pi$
$197$	−2.42244	+	5.84828i	−0.172592	+	0.416673i	0.813787	+	0.581163i	$0.197402\pi$
$198$	−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	−0.655309	−	0.755361i	$-0.727461\pi$
$223$	1.49410	−	1.49410i	0.100053	−	0.100053i	0.755361	+	0.655309i	$0.227461\pi$
$224$	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	0.781443	−	0.623976i	$-0.214484\pi$
$227$	13.4512	+	5.57168i	0.892789	+	0.369805i	0.111346	+	0.993782i	$0.464484\pi$
$228$	−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	0.958333	−	0.285653i	$-0.0922105\pi$
$233$	1.20133	+	2.90028i	0.0787021	+	0.190004i	−0.879631	+	0.475657i	$0.842210\pi$
$234$		−	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	−0.538876	−	0.842385i	$-0.681151\pi$
$257$	4.86561	−	4.86561i	0.303508	−	0.303508i	0.842385	+	0.538876i	$0.181151\pi$
$258$	−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	0.557909	−	0.829902i	$-0.311604\pi$
$263$	−4.41100	−	4.41100i	−0.271994	−	0.271994i	−0.829902	+	0.557909i	$0.811604\pi$
$264$	−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	$0.151015\pi$
$277$	9.71258	+	23.4482i	0.583572	+	1.40887i	−0.305982	+	0.952037i	$0.598985\pi$
$278$	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	0.826967	−	0.562250i	$-0.190064\pi$
$283$	17.0606	+	7.06675i	1.01415	+	0.420075i	0.187183	+	0.982325i	$0.440064\pi$
$284$	−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	$-0.421869\pi$
$293$	8.31894			0.485998			0.242999	+	0.970027i	$0.421869\pi$
$294$	−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	$-0.886454\pi$
$307$		−	12.2369i		−	0.698398i	0.937049	−	0.349199i	$-0.113546\pi$
$308$	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	−0.999994	−	0.00341475i	$-0.998913\pi$
$313$	−5.13906	+	12.4068i	−0.290477	+	0.701273i	0.709517	+	0.704688i	$0.248913\pi$
$314$	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	0.111507	−	0.993764i	$-0.464432\pi$
$317$	−9.12199	−	3.77845i	−0.512342	−	0.212219i	−0.623849	+	0.781545i	$0.714432\pi$
$318$	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	−0.758900	−	0.651207i	$-0.774263\pi$
$337$	−15.3295	+	6.34969i	−0.835051	+	0.345890i	−0.0761510	+	0.997096i	$0.524263\pi$
$338$	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	−0.989942	−	0.141475i	$-0.954816\pi$
$347$	−3.53762	+	8.54057i	−0.189909	+	0.458482i	0.800032	+	0.599957i	$0.204816\pi$
$348$	−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	$-0.290630\pi$
$353$	22.9722			1.22269			0.611343	+	0.791366i	$0.290630\pi$
$354$	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	−0.989044	−	0.147623i	$-0.952838\pi$
$367$	−3.54981	+	8.57000i	−0.185299	+	0.447351i	0.803745	+	0.594974i	$0.202838\pi$
$368$	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	$-0.974686\pi$
$373$		−	3.06857i		−	0.158884i	0.996839	−	0.0794422i	$-0.0253139\pi$
$374$	−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	0.518362	−	0.855161i	$-0.326542\pi$
$383$	−6.59130	−	6.59130i	−0.336800	−	0.336800i	−0.855161	+	0.518362i	$0.826542\pi$
$384$	−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	0.168572	−	0.985689i	$-0.446085\pi$
$397$	−8.15361	−	3.37734i	−0.409218	−	0.169504i	−0.577790	+	0.816186i	$0.696085\pi$
$398$	−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	0.946073	−	0.323953i	$-0.105012\pi$
$433$	12.9455	+	12.9455i	0.622120	+	0.622120i	−0.323953	+	0.946073i	$0.605012\pi$
$434$	−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	$-0.754048\pi$
$443$		−	29.3849i		−	1.39612i	0.716041	−	0.698058i	$-0.245952\pi$
$444$	−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	−0.553386	−	0.832925i	$-0.686665\pi$
$457$	5.97585	−	5.97585i	0.279538	−	0.279538i	0.832925	+	0.553386i	$0.186665\pi$
$458$			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	$-0.282443\pi$
$463$	27.1761			1.26298			0.631491	+	0.775383i	$0.282443\pi$
$464$	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	0.761223	−	0.648491i	$-0.224599\pi$
$467$	2.43616	+	2.43616i	0.112732	+	0.112732i	−0.648491	+	0.761223i	$0.724599\pi$
$468$	−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	−0.243463	−	0.969910i	$-0.578283\pi$
$487$	−24.3068	−	10.0682i	−1.10145	−	0.456234i	−0.857984	+	0.513676i	$0.828283\pi$
$488$	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	$-0.699148\pi$
$503$	9.00803	−	21.7473i	0.401648	−	0.969665i	0.987266	−	0.159077i	$-0.0508519\pi$
$504$	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	$-0.564455\pi$
$523$	−9.19853			−0.402224			−0.201112	+	0.979568i	$0.564455\pi$
$524$	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	−0.798043	−	0.602600i	$-0.794131\pi$
$547$	−21.8969	+	9.06998i	−0.936243	+	0.387805i	−0.138199	+	0.990404i	$0.544131\pi$
$548$	−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	$-0.497304\pi$
$557$	0.399812			0.0169406			0.00847028	+	0.999964i	$0.497304\pi$
$558$	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	−0.831536	−	0.555472i	$-0.812538\pi$
$563$	−6.55034	+	6.55034i	−0.276064	+	0.276064i	0.555472	+	0.831536i	$0.312538\pi$
$564$	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	$-0.874592\pi$
$577$		−	18.4417i		−	0.767736i	0.923388	−	0.383868i	$-0.125408\pi$
$578$	−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	0.645822	−	0.763488i	$-0.276515\pi$
$587$	−2.85082	−	2.85082i	−0.117666	−	0.117666i	−0.763488	+	0.645822i	$0.776515\pi$
$588$	−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	−0.795456	−	0.606011i	$-0.792769\pi$
$593$	−4.61328	+	4.61328i	−0.189445	+	0.189445i	0.606011	+	0.795456i	$0.292769\pi$
$594$	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	$-0.939197\pi$
$607$	−10.3924	−	25.0895i	−0.421816	−	1.01835i	0.559996	−	0.828495i	$-0.310803\pi$
$608$	−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	$-0.984013\pi$
$613$		−	2.48591i		−	0.100405i	0.998739	−	0.0502025i	$-0.0159867\pi$
$614$	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	$0.210536\pi$
$617$	16.5297	+	39.9062i	0.665460	+	1.60656i	−0.123661	+	0.992325i	$0.539464\pi$
$618$	−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	−0.585929	−	0.810363i	$-0.699270\pi$
$643$	−10.8335	+	4.48736i	−0.427230	+	0.176964i	0.158699	+	0.987327i	$0.449270\pi$
$644$	−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	$-0.737823\pi$
$647$		−	37.3217i		−	1.46727i	0.679544	−	0.733634i	$-0.262177\pi$
$648$	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	−0.936481	−	0.350719i	$-0.885937\pi$
$653$	−0.671889	+	1.62208i	−0.0262931	+	0.0634771i	0.910188	+	0.414196i	$0.135937\pi$
$654$	−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	$0.401296\pi$
$673$	−15.1505	+	36.5765i	−0.584009	+	1.40992i	−0.889150	+	0.457615i	$0.848704\pi$
$674$	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	−0.503393	−	0.864058i	$-0.667915\pi$
$677$	−6.46223	+	2.67674i	−0.248364	+	0.102876i	0.255029	+	0.966933i	$0.417915\pi$
$678$	−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	0.389097	−	0.921197i	$-0.372787\pi$
$683$	34.3826	−	14.2417i	1.31561	−	0.544945i	0.926518	+	0.376251i	$0.122787\pi$
$684$		−	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	$-0.364527\pi$
$727$	22.2643			0.825736			0.412868	+	0.910791i	$0.364527\pi$
$728$	−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	−0.629125	−	0.777304i	$-0.716587\pi$
$733$	4.01178	−	4.01178i	0.148178	−	0.148178i	0.777304	+	0.629125i	$0.216587\pi$
$734$	−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	0.980838	−	0.194826i	$-0.0624142\pi$
$743$	4.07556	+	9.83928i	0.149518	+	0.360968i	−0.831320	+	0.555794i	$0.812414\pi$
$744$		−	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	0.891637	−	0.452752i	$-0.149558\pi$
$757$	12.0753	+	12.0753i	0.438885	+	0.438885i	−0.452752	+	0.891637i	$0.649558\pi$
$758$	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	0.647679	−	0.761913i	$-0.275740\pi$
$773$	−3.17604	−	3.17604i	−0.114234	−	0.114234i	−0.761913	+	0.647679i	$0.775740\pi$
$774$	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	0.853823	−	0.520564i	$-0.174278\pi$
$787$	−3.31075	−	7.99286i	−0.118016	−	0.284915i	−0.971838	+	0.235649i	$0.924278\pi$
$788$	−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	−0.903926	−	0.427689i	$-0.859328\pi$
$797$	−13.4447	+	13.4447i	−0.476236	+	0.476236i	0.427689	+	0.903926i	$0.359328\pi$
$798$		−	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	$0.325936\pi$
$823$	−12.9581	+	31.2835i	−0.451689	+	1.09047i	−0.971680	+	0.236302i	$0.924064\pi$
$824$	−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	0.0270516	−	0.999634i	$-0.491388\pi$
$827$	−18.9992	−	7.86974i	−0.660668	−	0.273658i	−0.687720	+	0.725976i	$0.741388\pi$
$828$	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	−0.171250	−	0.985228i	$-0.554781\pi$
$853$	11.8086	−	4.89128i	0.404319	−	0.167474i	0.575569	+	0.817753i	$0.304781\pi$
$854$			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	−0.959768	−	0.280794i	$-0.909402\pi$
$857$	−2.41686	+	5.83483i	−0.0825585	+	0.199314i	0.877210	+	0.480107i	$0.159402\pi$
$858$	−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	$-0.228864\pi$
$863$	44.2102			1.50493			0.752466	+	0.658632i	$0.228864\pi$
$864$	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	$0.255497\pi$
$877$	−9.03414	+	21.8103i	−0.305061	+	0.736483i	−0.999851	+	0.0172700i	$0.994503\pi$
$878$	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	$0.432875\pi$
$883$			58.1141i			1.95569i	−0.209320	+	0.977847i	$0.567125\pi$
$884$	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	0.0967091	−	0.995313i	$-0.469168\pi$
$887$	25.8776	−	10.7189i	0.868885	−	0.359904i	0.772176	+	0.635409i	$0.219168\pi$
$888$	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	0.979836	−	0.199802i	$-0.0640298\pi$
$907$	46.1204	+	19.1037i	1.53140	+	0.634328i	0.551568	+	0.834130i	$0.314030\pi$
$908$	−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	$0.652676\pi$
$937$	−41.2820	+	41.2820i	−1.34862	+	1.34862i	−0.887159	+	0.461465i	$0.847324\pi$
$938$	−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	$0.152785\pi$
$947$	18.0429	+	43.5595i	0.586317	+	1.41549i	−0.300683	+	0.953724i	$0.597215\pi$
$948$	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	$-0.856815\pi$
$953$		−	26.8459i		−	0.869625i	0.900521	−	0.434812i	$-0.143185\pi$
$954$	−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	−0.203378	−	0.979100i	$-0.565192\pi$
$967$	24.1223	−	24.1223i	0.775722	−	0.775722i	0.979100	+	0.203378i	$0.0651920\pi$
$968$			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	0.895220	−	0.445625i	$-0.147018\pi$
$977$	14.0530	+	14.0530i	0.449595	+	0.449595i	−0.445625	+	0.895220i	$0.647018\pi$
$978$	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	$0.766089\pi$
$983$	−54.5743	+	22.6054i	−1.74065	+	0.721001i	−0.998723	+	0.0505223i	$0.983911\pi$
$984$	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	0.888858	−	0.458182i	$-0.151499\pi$
$997$	37.6817	+	15.6083i	1.19339	+	0.494319i	0.304534	+	0.952501i	$0.401499\pi$
$998$	−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.c.49.3		24
5.2	odd	4		425.2.m.b.151.3		24
5.3	odd	4		85.2.l.a.66.4	✓	24
5.4	even	2		425.2.n.f.49.4		24
15.8	even	4		765.2.be.b.406.3		24
17.8	even	8		425.2.n.f.399.4		24
85.3	even	16		1445.2.d.j.866.13		24
85.8	odd	8		85.2.l.a.76.4	yes	24
85.12	even	16		7225.2.a.bq.1.7		12
85.22	even	16		7225.2.a.bs.1.7		12
85.42	odd	8		425.2.m.b.76.3		24
85.48	even	16		1445.2.d.j.866.14		24
85.59	even	8	inner	425.2.n.c.399.3		24
85.63	even	16		1445.2.a.q.1.6		12
85.73	even	16		1445.2.a.p.1.6		12
255.8	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	5.3	odd	4
85.2.l.a.76.4	yes	24	85.8	odd	8
425.2.m.b.76.3		24	85.42	odd	8
425.2.m.b.151.3		24	5.2	odd	4
425.2.n.c.49.3		24	1.1	even	1	trivial
425.2.n.c.399.3		24	85.59	even	8	inner
425.2.n.f.49.4		24	5.4	even	2
425.2.n.f.399.4		24	17.8	even	8
765.2.be.b.406.3		24	15.8	even	4
765.2.be.b.586.3		24	255.8	even	8
1445.2.a.p.1.6		12	85.73	even	16
1445.2.a.q.1.6		12	85.63	even	16
1445.2.d.j.866.13		24	85.3	even	16
1445.2.d.j.866.14		24	85.48	even	16
7225.2.a.bq.1.7		12	85.12	even	16
7225.2.a.bs.1.7		12	85.22	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

Introduction

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