LMFDB - Embedded newform 425.2.n.f.399.4

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			399.4
Character	$\chi$	$=$	425.399
Dual form			425.2.n.f.49.4

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$

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	$-0.139429\pi$
$2$	0.680853	+	0.680853i	0.481435	+	0.481435i	−0.424154	+	0.905590i	$0.639429\pi$
$3$	2.44733	+	1.01372i	1.41297	+	0.585271i	0.953083	−	0.302708i	$-0.0978907\pi$
$3$	2.44733	+	1.01372i	1.41297	+	0.585271i	0.459885	+	0.887979i	$0.347891\pi$
$4$		−	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	0.973215	+	0.229896i	$0.0738387\pi$
$7$	1.18426	+	2.85906i	0.447609	+	1.08062i	−0.525606	+	0.850728i	$0.676161\pi$
$8$	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	−0.706442	−	0.707771i	$-0.749701\pi$
$11$	−2.34612	−	5.66403i	−0.707382	−	1.70777i	−0.000939675	−	1.00000i	$-0.500299\pi$
$12$	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	−0.993553	−	0.113365i	$-0.963837\pi$
$19$	−3.83665	+	3.83665i	−0.880188	+	0.880188i	0.113365	+	0.993553i	$0.463837\pi$
$20$		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	$-0.730370\pi$
$23$	−2.88015	+	1.19300i	−0.600552	+	0.248757i	0.0616306	+	0.998099i	$0.480370\pi$
$24$	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	0.767644	−	0.640877i	$-0.221429\pi$
$29$	4.61660	+	1.91226i	0.857282	+	0.355098i	0.0896380	+	0.995974i	$0.471429\pi$
$30$		0			0
$31$	−1.42666	+	3.44426i	−0.256236	+	0.618608i	−0.998683	−	0.0512962i	$-0.983665\pi$
$31$	−1.42666	+	3.44426i	−0.256236	+	0.618608i	0.742448	+	0.669904i	$0.233665\pi$
$32$	−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	$-0.385382\pi$
$37$	−0.366518	−	0.151817i	−0.0602551	−	0.0249585i	−0.412607	+	0.910909i	$0.635382\pi$
$38$	−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	−0.256453	−	0.966557i	$-0.582554\pi$
$41$	1.57303	−	0.651568i	0.245665	−	0.101758i	0.502119	+	0.864799i	$0.332554\pi$
$42$	−5.58135	+	5.58135i	−0.861221	+	0.861221i
$43$	0.0189720	−	0.0189720i	0.00289320	−	0.00289320i	−0.705659	−	0.708552i	$-0.749349\pi$
$43$	0.0189720	−	0.0189720i	0.00289320	−	0.00289320i	0.708552	+	0.705659i	$0.249349\pi$
$44$	−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	0.723667	−	0.690149i	$-0.242455\pi$
$53$	0.244014	+	0.244014i	0.0335179	+	0.0335179i	−0.690149	+	0.723667i	$0.742455\pi$
$54$	−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	0.495054	−	0.868862i	$-0.335148\pi$
$59$	−2.87128	−	2.87128i	−0.373808	−	0.373808i	−0.868862	+	0.495054i	$0.835148\pi$
$60$		0			0
$61$	−11.4953	+	4.76149i	−1.47182	+	0.609646i	−0.967273	−	0.253740i	$-0.918339\pi$
$61$	−11.4953	+	4.76149i	−1.47182	+	0.609646i	−0.504544	+	0.863386i	$0.668339\pi$
$62$	−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	−0.465383	−	0.885110i	$-0.654083\pi$
$71$	4.12510	−	9.95888i	0.489560	−	1.18190i	0.954942	−	0.296792i	$-0.0959167\pi$
$72$	11.8856			1.40073
$73$	−0.633083	+	1.52840i	−0.0740968	+	0.178886i	−0.956588	−	0.291443i	$-0.905865\pi$
$73$	−0.633083	+	1.52840i	−0.0740968	+	0.178886i	0.882491	+	0.470329i	$0.155865\pi$
$74$	−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	0.768787	−	0.639505i	$-0.220861\pi$
$79$	−2.01785	−	4.87153i	−0.227026	−	0.548090i	−0.995813	+	0.0914157i	$0.970861\pi$
$80$		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	$-0.0111299\pi$
$83$	8.78638	+	8.78638i	0.964430	+	0.964430i	−0.0349583	+	0.999389i	$0.511130\pi$
$84$	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	$-0.945251\pi$
$89$		−	3.22930i		−	0.342305i	0.985245	−	0.171152i	$-0.0547490\pi$
$90$		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	0.445476	+	0.895294i	$0.353035\pi$
$97$	−4.94995	+	11.9502i	−0.502592	+	1.21336i	−0.948067	+	0.318070i	$0.896965\pi$
$98$	−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	$-0.830428\pi$
$107$	1.10497	−	2.66763i	0.106821	−	0.257889i	0.968248	+	0.249993i	$0.0804284\pi$
$108$	2.67049	−	1.10615i	0.256968	−	0.106440i
$109$	−5.32460	+	2.20552i	−0.510004	+	0.211251i	−0.622820	−	0.782365i	$-0.714013\pi$
$109$	−5.32460	+	2.20552i	−0.510004	+	0.211251i	0.112816	+	0.993616i	$0.464013\pi$
$110$		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	$-0.485525\pi$
$113$	8.33379	−	3.45197i	0.783977	−	0.324734i	0.738519	+	0.674232i	$0.235525\pi$
$114$	−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	$-0.536681\pi$
$127$	9.89892	−	9.89892i	0.878387	−	0.878387i	0.993368	+	0.114980i	$0.0366805\pi$
$128$	−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	0.830091	−	0.557628i	$-0.188288\pi$
$131$	11.7059	+	4.84875i	1.02275	+	0.423638i	0.192661	+	0.981265i	$0.438288\pi$
$132$	−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	0.192423	+	0.981312i	$0.438365\pi$
$139$	−7.51640	+	18.1462i	−0.637533	+	1.53914i	−0.829956	+	0.557829i	$0.811635\pi$
$140$		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	$-0.961367\pi$
$149$		−	2.95573i		−	0.242143i	0.992644	−	0.121072i	$-0.0386330\pi$
$150$		0			0
$151$	15.5848	−	15.5848i	1.26828	−	1.26828i	0.321298	−	0.946978i	$-0.395881\pi$
$151$	15.5848	−	15.5848i	1.26828	−	1.26828i	0.946978	−	0.321298i	$-0.104119\pi$
$152$			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	0.894361	+	0.447347i	$0.147631\pi$
$163$	7.38291	+	17.8239i	0.578274	+	1.39608i	−0.316087	+	0.948730i	$0.602369\pi$
$164$	−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	$-0.635332\pi$
$167$	−17.4236	−	7.21707i	−1.34828	−	0.558474i	−0.935812	+	0.352500i	$0.885332\pi$
$168$	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	$-0.0465524\pi$
$173$	20.8584	+	8.63985i	1.58584	+	0.656876i	0.596513	+	0.802603i	$0.296552\pi$
$174$			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	0.757018	−	0.653393i	$-0.226655\pi$
$179$	1.38641	+	1.38641i	0.103625	+	0.103625i	−0.653393	+	0.757018i	$0.726655\pi$
$180$		0			0
$181$	0.272363	+	0.657542i	0.0202446	+	0.0488747i	0.933679	−	0.358112i	$-0.116579\pi$
$181$	0.272363	+	0.657542i	0.0202446	+	0.0488747i	−0.913434	+	0.406987i	$0.866579\pi$
$182$	−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	$0.0609861\pi$
$191$			5.26341i			0.380847i	−0.981702	+	0.190423i	$0.939014\pi$
$192$	6.54079	−	15.7909i	0.472041	−	1.13961i
$193$	13.7936	−	5.71352i	0.992888	−	0.411268i	0.173704	−	0.984798i	$-0.444426\pi$
$193$	13.7936	−	5.71352i	0.992888	−	0.411268i	0.819184	+	0.573530i	$0.194426\pi$
$194$	−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	$-0.0525978\pi$
$197$	2.42244	+	5.84828i	0.172592	+	0.416673i	−0.813787	+	0.581163i	$0.802598\pi$
$198$	21.9080	−	9.07458i	1.55693	−	0.644902i
$199$	13.7796	+	5.70769i	0.976809	+	0.404607i	0.813243	−	0.581925i	$-0.197700\pi$
$199$	13.7796	+	5.70769i	0.976809	+	0.404607i	0.163566	+	0.986532i	$0.447700\pi$
$200$		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	0.0865417	−	0.996248i	$-0.472418\pi$
$211$	12.3788	−	5.12746i	0.852190	−	0.352989i	0.765648	+	0.643260i	$0.222418\pi$
$212$	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	$-0.272539\pi$
$223$	−1.49410	−	1.49410i	−0.100053	−	0.100053i	−0.755361	+	0.655309i	$0.772539\pi$
$224$	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	$-0.785516\pi$
$227$	−13.4512	+	5.57168i	−0.892789	+	0.369805i	−0.111346	+	0.993782i	$0.535516\pi$
$228$	5.90114	+	14.2466i	0.390812	+	0.943505i
$229$	1.87412	+	1.87412i	0.123845	+	0.123845i	0.766313	−	0.642468i	$-0.222089\pi$
$229$	1.87412	+	1.87412i	0.123845	+	0.123845i	−0.642468	+	0.766313i	$0.722089\pi$
$230$		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	$-0.907790\pi$
$233$	−1.20133	+	2.90028i	−0.0787021	+	0.190004i	0.879631	+	0.475657i	$0.157790\pi$
$234$			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	0.691943	+	0.721952i	$0.256755\pi$
$241$	−4.77884	+	11.5371i	−0.307832	+	0.743173i	−0.999775	+	0.0212201i	$0.993245\pi$
$242$	−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	$0.185541\pi$
$251$			17.4413i			1.10088i	−0.834874	+	0.550441i	$0.814459\pi$
$252$	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	$-0.318849\pi$
$257$	−4.86561	−	4.86561i	−0.303508	−	0.303508i	−0.842385	+	0.538876i	$0.818849\pi$
$258$	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	$-0.688396\pi$
$263$	4.41100	−	4.41100i	0.271994	−	0.271994i	0.829902	+	0.557909i	$0.188396\pi$
$264$	−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	−0.938224	−	0.346030i	$-0.887530\pi$
$269$	−0.493996	+	1.19261i	−0.0301194	+	0.0727148i	0.908104	+	0.418744i	$0.137530\pi$
$270$		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	0.305982	+	0.952037i	$0.401015\pi$
$277$	−9.71258	+	23.4482i	−0.583572	+	1.40887i	−0.889554	+	0.456831i	$0.848985\pi$
$278$	−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	0.571743	−	0.820433i	$-0.306267\pi$
$281$	−4.16880	−	4.16880i	−0.248690	−	0.248690i	−0.820433	+	0.571743i	$0.806267\pi$
$282$	5.30710	+	12.8125i	0.316033	+	0.762971i
$283$	−17.0606	+	7.06675i	−1.01415	+	0.420075i	−0.826967	−	0.562250i	$-0.809936\pi$
$283$	−17.0606	+	7.06675i	−1.01415	+	0.420075i	−0.187183	+	0.982325i	$0.559936\pi$
$284$	−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	$-0.886454\pi$
$307$		−	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	−0.999993	−	0.00381046i	$-0.998787\pi$
$311$	−30.1525	−	12.4896i	−1.70979	−	0.708218i	−0.709796	−	0.704407i	$-0.751213\pi$
$312$	8.40098	−	3.47980i	0.475612	−	0.197005i
$313$	5.13906	+	12.4068i	0.290477	+	0.701273i	0.999994	−	0.00341475i	$-0.00108695\pi$
$313$	5.13906	+	12.4068i	0.290477	+	0.701273i	−0.709517	+	0.704688i	$0.751087\pi$
$314$	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	$-0.535568\pi$
$317$	9.12199	−	3.77845i	0.512342	−	0.212219i	0.623849	+	0.781545i	$0.285568\pi$
$318$	−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	0.588890	−	0.808213i	$-0.299565\pi$
$331$	−3.99024	−	3.99024i	−0.219323	−	0.219323i	−0.808213	+	0.588890i	$0.799565\pi$
$332$	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	$-0.225737\pi$
$337$	15.3295	+	6.34969i	0.835051	+	0.345890i	0.0761510	+	0.997096i	$0.475737\pi$
$338$	−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	$-0.0451845\pi$
$347$	3.53762	+	8.54057i	0.189909	+	0.458482i	−0.800032	+	0.599957i	$0.795184\pi$
$348$	10.0420	−	10.0420i	0.538309	−	0.538309i
$349$	19.0405	+	19.0405i	1.01921	+	1.01921i	0.999812	+	0.0194030i	$0.00617656\pi$
$349$	19.0405	+	19.0405i	1.01921	+	1.01921i	0.0194030	+	0.999812i	$0.493823\pi$
$350$		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	0.328394	−	0.944541i	$-0.393493\pi$
$359$	24.1187	−	24.1187i	1.27293	−	1.27293i	0.944541	−	0.328394i	$-0.106507\pi$
$360$		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	$-0.0471624\pi$
$367$	3.54981	+	8.57000i	0.185299	+	0.447351i	−0.803745	+	0.594974i	$0.797162\pi$
$368$	−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	−0.999215	−	0.0396029i	$-0.987391\pi$
$379$	−33.7529	−	13.9809i	−1.73377	−	0.718151i	−0.734556	−	0.678549i	$-0.762609\pi$
$380$		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	$-0.673458\pi$
$383$	6.59130	−	6.59130i	0.336800	−	0.336800i	0.855161	+	0.518362i	$0.173458\pi$
$384$	−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	−0.211559	+	0.977365i	$0.567854\pi$
$389$	−23.4493	+	23.4493i	−1.18892	+	1.18892i	−0.977365	+	0.211559i	$0.932146\pi$
$390$		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	$-0.553915\pi$
$397$	8.15361	−	3.37734i	0.409218	−	0.169504i	0.577790	+	0.816186i	$0.303915\pi$
$398$	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	0.116109	−	0.993236i	$-0.462958\pi$
$401$	18.0332	−	7.46960i	0.900535	−	0.373014i	0.784426	+	0.620223i	$0.212958\pi$
$402$	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	−0.797288	−	0.603599i	$-0.793733\pi$
$419$	−13.5166	−	32.6320i	−0.660329	−	1.59418i	0.136958	−	0.990577i	$-0.456267\pi$
$420$		0			0
$421$		−	15.0205i		−	0.732052i	−0.930605	−	0.366026i	$-0.880718\pi$
$421$		−	15.0205i		−	0.732052i	0.930605	−	0.366026i	$-0.119282\pi$
$422$	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	−0.979143	−	0.203171i	$-0.934875\pi$
$431$	−8.93633	−	21.5742i	−0.430448	−	1.03919i	0.548695	−	0.836022i	$-0.315125\pi$
$432$	0.724977	+	1.75025i	0.0348805	+	0.0842090i
$433$	−12.9455	+	12.9455i	−0.622120	+	0.622120i	−0.946073	−	0.323953i	$-0.894988\pi$
$433$	−12.9455	+	12.9455i	−0.622120	+	0.622120i	0.323953	+	0.946073i	$0.394988\pi$
$434$	−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	0.623497	+	0.781826i	$0.285711\pi$
$439$	−7.75689	+	18.7268i	−0.370216	+	0.893780i	−0.993713	+	0.111955i	$0.964289\pi$
$440$		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	0.467543	−	0.883970i	$-0.345139\pi$
$449$	30.1572	−	12.4915i	1.42321	−	0.589512i	0.955664	+	0.294459i	$0.0951394\pi$
$450$		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	$-0.313335\pi$
$457$	−5.97585	−	5.97585i	−0.279538	−	0.279538i	−0.832925	+	0.553386i	$0.813335\pi$
$458$			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	0.308863	−	0.951106i	$-0.400051\pi$
$461$	27.0527	−	27.0527i	1.25997	−	1.25997i	0.951106	−	0.308863i	$-0.0999486\pi$
$462$	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	−0.761223	−	0.648491i	$-0.775401\pi$
$467$	−2.43616	+	2.43616i	−0.112732	+	0.112732i	0.648491	+	0.761223i	$0.275401\pi$
$468$	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	−0.999416	−	0.0341684i	$-0.989122\pi$
$479$	−5.87776	+	14.1902i	−0.268562	+	0.648365i	0.730855	+	0.682533i	$0.239122\pi$
$480$		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	$-0.421717\pi$
$487$	24.3068	−	10.0682i	1.10145	−	0.456234i	0.857984	+	0.513676i	$0.171717\pi$
$488$	−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	−0.997484	−	0.0708885i	$-0.977417\pi$
$491$	−20.5320	+	20.5320i	−0.926596	+	0.926596i	0.0708885	+	0.997484i	$0.477417\pi$
$492$		−	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	−0.911098	−	0.412189i	$-0.864764\pi$
$499$	−12.4718	−	30.1097i	−0.558316	−	1.34789i	0.352782	−	0.935706i	$-0.385236\pi$
$500$		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	−0.987266	−	0.159077i	$-0.949148\pi$
$503$	−9.00803	−	21.7473i	−0.401648	−	0.969665i	0.585618	−	0.810587i	$-0.300852\pi$
$504$	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	−0.997325	−	0.0730986i	$-0.976711\pi$
$521$	−7.84734	−	18.9452i	−0.343798	−	0.830002i	0.653527	−	0.756904i	$-0.273289\pi$
$522$	−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	−0.996761	−	0.0804201i	$-0.974374\pi$
$541$	−5.46780	+	13.2004i	−0.235079	+	0.567531i	0.761682	+	0.647951i	$0.224374\pi$
$542$	−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	$-0.205869\pi$
$547$	21.8969	+	9.06998i	0.936243	+	0.387805i	0.138199	+	0.990404i	$0.455869\pi$
$548$	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	0.831536	−	0.555472i	$-0.187462\pi$
$563$	6.55034	+	6.55034i	0.276064	+	0.276064i	−0.555472	+	0.831536i	$0.687462\pi$
$564$	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	0.616619	−	0.787262i	$-0.288502\pi$
$569$	−4.07046	−	4.07046i	−0.170643	−	0.170643i	−0.787262	+	0.616619i	$0.788502\pi$
$570$		0			0
$571$	−12.9331	+	5.35705i	−0.541232	+	0.224186i	−0.636515	−	0.771265i	$-0.719625\pi$
$571$	−12.9331	+	5.35705i	−0.541232	+	0.224186i	0.0952826	+	0.995450i	$0.469625\pi$
$572$	−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	$-0.723485\pi$
$587$	2.85082	−	2.85082i	0.117666	−	0.117666i	0.763488	+	0.645822i	$0.223485\pi$
$588$	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	$-0.207231\pi$
$593$	4.61328	+	4.61328i	0.189445	+	0.189445i	−0.606011	+	0.795456i	$0.707231\pi$
$594$	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	$0.0444413\pi$
$599$			6.81189i			0.278326i	−0.990269	+	0.139163i	$0.955559\pi$
$600$		0			0
$601$	14.6029	+	35.2545i	0.595664	+	1.43806i	0.877961	+	0.478732i	$0.158904\pi$
$601$	14.6029	+	35.2545i	0.595664	+	1.43806i	−0.282297	+	0.959327i	$0.591096\pi$
$602$	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	−0.559996	−	0.828495i	$-0.689197\pi$
$607$	10.3924	−	25.0895i	0.421816	−	1.01835i	0.981812	−	0.189858i	$-0.0608027\pi$
$608$	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	0.123661	+	0.992325i	$0.460536\pi$
$617$	−16.5297	+	39.9062i	−0.665460	+	1.60656i	−0.789121	+	0.614238i	$0.789464\pi$
$618$	23.1164	−	9.57513i	0.929878	−	0.385168i
$619$	1.27211	−	0.526923i	0.0511302	−	0.0211788i	−0.356972	−	0.934115i	$-0.616191\pi$
$619$	1.27211	−	0.526923i	0.0511302	−	0.0211788i	0.408102	+	0.912936i	$0.366191\pi$
$620$		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	−0.0834781	−	0.996510i	$-0.526603\pi$
$631$	22.9351	−	22.9351i	0.913032	−	0.913032i	0.996510	+	0.0834781i	$0.0266029\pi$
$632$	−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	0.750437	−	0.660942i	$-0.229843\pi$
$641$	20.6017	+	8.53352i	0.813719	+	0.337054i	0.0632825	+	0.997996i	$0.479843\pi$
$642$	7.36471			0.290662
$643$	10.8335	+	4.48736i	0.427230	+	0.176964i	0.585929	−	0.810363i	$-0.300730\pi$
$643$	10.8335	+	4.48736i	0.427230	+	0.176964i	−0.158699	+	0.987327i	$0.550730\pi$
$644$	−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	$-0.114063\pi$
$653$	0.671889	+	1.62208i	0.0262931	+	0.0634771i	−0.910188	+	0.414196i	$0.864063\pi$
$654$	−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	$-0.962539\pi$
$659$		−	6.02834i		−	0.234831i	0.993083	−	0.117415i	$-0.0374609\pi$
$660$		0			0
$661$	22.6415	−	22.6415i	0.880652	−	0.880652i	−0.112949	−	0.993601i	$-0.536030\pi$
$661$	22.6415	−	22.6415i	0.880652	−	0.880652i	0.993601	+	0.112949i	$0.0360296\pi$
$662$		−	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	0.889150	+	0.457615i	$0.151296\pi$
$673$	15.1505	+	36.5765i	0.584009	+	1.40992i	−0.305142	+	0.952307i	$0.598704\pi$
$674$	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	$-0.332085\pi$
$677$	6.46223	+	2.67674i	0.248364	+	0.102876i	−0.255029	+	0.966933i	$0.582085\pi$
$678$	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	$-0.627213\pi$
$683$	−34.3826	−	14.2417i	−1.31561	−	0.544945i	−0.926518	+	0.376251i	$0.877213\pi$
$684$			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	0.768104	−	0.640325i	$-0.221200\pi$
$691$	−5.98831	−	14.4571i	−0.227806	−	0.549972i	−0.995910	+	0.0903530i	$0.971200\pi$
$692$	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	$0.0366622\pi$
$701$			6.08551i			0.229847i	−0.993374	+	0.114923i	$0.963338\pi$
$702$	−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	0.0136069	−	0.999907i	$-0.495669\pi$
$709$	−18.2079	−	7.54197i	−0.683813	−	0.283245i	−0.697420	+	0.716663i	$0.745669\pi$
$710$		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	0.639640	−	0.768675i	$-0.279083\pi$
$719$	14.7049	+	6.09095i	0.548399	+	0.227154i	−0.0912412	+	0.995829i	$0.529083\pi$
$720$		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	0.629125	−	0.777304i	$-0.283413\pi$
$733$	−4.01178	−	4.01178i	−0.148178	−	0.148178i	−0.777304	+	0.629125i	$0.783413\pi$
$734$	−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	0.999358	+	0.0358281i	$0.0114069\pi$
$739$	28.1411	+	28.1411i	1.03519	+	1.03519i	0.0358281	+	0.999358i	$0.488593\pi$
$740$		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	$-0.937586\pi$
$743$	−4.07556	+	9.83928i	−0.149518	+	0.360968i	0.831320	+	0.555794i	$0.187586\pi$
$744$			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	−0.745419	−	0.666596i	$-0.767751\pi$
$751$	6.93403	−	16.7402i	0.253026	−	0.610860i	0.998446	+	0.0557362i	$0.0177506\pi$
$752$	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	$-0.850442\pi$
$757$	−12.0753	+	12.0753i	−0.438885	+	0.438885i	0.452752	+	0.891637i	$0.350442\pi$
$758$	−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	$-0.803251\pi$
$761$		−	31.9719i		−	1.15898i	0.814979	−	0.579491i	$-0.196749\pi$
$762$	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	$-0.783248\pi$
$769$		−	34.9147i		−	1.25906i	0.776977	−	0.629529i	$-0.216752\pi$
$770$		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	$-0.724260\pi$
$773$	3.17604	−	3.17604i	0.114234	−	0.114234i	0.761913	+	0.647679i	$0.224260\pi$
$774$	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	$-0.825722\pi$
$787$	3.31075	−	7.99286i	0.118016	−	0.284915i	0.971838	+	0.235649i	$0.0757217\pi$
$788$	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	$-0.140672\pi$
$797$	13.4447	+	13.4447i	0.476236	+	0.476236i	−0.427689	+	0.903926i	$0.640672\pi$
$798$		−	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	0.0172227	−	0.999852i	$-0.494518\pi$
$809$	20.9455	−	8.67589i	0.736403	−	0.305028i	0.719180	+	0.694824i	$0.244518\pi$
$810$		0			0
$811$	−22.2809	−	9.22904i	−0.782388	−	0.324076i	−0.0445090	−	0.999009i	$-0.514172\pi$
$811$	−22.2809	−	9.22904i	−0.782388	−	0.324076i	−0.737879	+	0.674933i	$0.764172\pi$
$812$	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	0.380834	−	0.924644i	$-0.375637\pi$
$821$	−0.105957	−	0.0438888i	−0.00369792	−	0.00153173i	−0.384532	+	0.923112i	$0.625637\pi$
$822$	−7.01962	+	2.90762i	−0.244838	+	0.101415i
$823$	12.9581	+	31.2835i	0.451689	+	1.09047i	0.971680	+	0.236302i	$0.0759356\pi$
$823$	12.9581	+	31.2835i	0.451689	+	1.09047i	−0.519990	+	0.854172i	$0.674064\pi$
$824$	−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	$-0.508612\pi$
$827$	18.9992	−	7.86974i	0.660668	−	0.273658i	0.687720	+	0.725976i	$0.258612\pi$
$828$	−5.14160	+	12.4129i	−0.178683	+	0.431379i
$829$		−	26.7935i		−	0.930576i	−0.885159	−	0.465288i	$-0.845951\pi$
$829$		−	26.7935i		−	0.930576i	0.885159	−	0.465288i	$-0.154049\pi$
$830$		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	0.805773	−	0.592224i	$-0.201750\pi$
$839$	−5.29374	−	12.7802i	−0.182760	−	0.441222i	−0.988533	+	0.151002i	$0.951750\pi$
$840$		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	$-0.445219\pi$
$853$	−11.8086	−	4.89128i	−0.404319	−	0.167474i	−0.575569	+	0.817753i	$0.695219\pi$
$854$		−	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	$-0.0905977\pi$
$857$	2.41686	+	5.83483i	0.0825585	+	0.199314i	−0.877210	+	0.480107i	$0.840598\pi$
$858$	12.8282	−	12.8282i	0.437946	−	0.437946i
$859$	−24.8431	−	24.8431i	−0.847636	−	0.847636i	0.142202	−	0.989838i	$-0.454582\pi$
$859$	−24.8431	−	24.8431i	−0.847636	−	0.847636i	−0.989838	+	0.142202i	$0.954582\pi$
$860$		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	0.999851	+	0.0172700i	$0.00549748\pi$
$877$	9.03414	+	21.8103i	0.305061	+	0.736483i	−0.694790	+	0.719213i	$0.744503\pi$
$878$	−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	0.554189	+	0.832391i	$0.313029\pi$
$881$	−12.6524	+	30.5457i	−0.426271	+	1.02911i	−0.980460	+	0.196719i	$0.936971\pi$
$882$	−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	$-0.530832\pi$
$887$	−25.8776	−	10.7189i	−0.868885	−	0.359904i	−0.772176	+	0.635409i	$0.780832\pi$
$888$	−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	$-0.935970\pi$
$907$	−46.1204	+	19.1037i	−1.53140	+	0.634328i	−0.551568	+	0.834130i	$0.685970\pi$
$908$	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	−0.691526	−	0.722352i	$-0.743061\pi$
$911$	−20.2142	+	8.37302i	−0.669728	+	0.277410i	0.0217976	+	0.999762i	$0.493061\pi$
$912$	−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	−0.983494	−	0.180941i	$-0.942086\pi$
$929$	−12.6796	−	30.6112i	−0.416003	−	1.00432i	0.567491	−	0.823380i	$-0.307914\pi$
$930$		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	0.887159	+	0.461465i	$0.152676\pi$
$937$	41.2820	+	41.2820i	1.34862	+	1.34862i	0.461465	+	0.887159i	$0.347324\pi$
$938$	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	0.881257	−	0.472638i	$-0.156698\pi$
$941$	−2.33416	−	5.63515i	−0.0760913	−	0.183701i	−0.957348	+	0.288937i	$0.906698\pi$
$942$	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	0.300683	+	0.953724i	$0.402785\pi$
$947$	−18.0429	+	43.5595i	−0.586317	+	1.41549i	−0.887000	+	0.461770i	$0.847215\pi$
$948$	−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	$-0.434808\pi$
$967$	−24.1223	−	24.1223i	−0.775722	−	0.775722i	−0.979100	+	0.203378i	$0.934808\pi$
$968$			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	−0.917819	−	0.396999i	$-0.870052\pi$
$971$	−16.2292	+	16.2292i	−0.520821	+	0.520821i	0.396999	+	0.917819i	$0.370052\pi$
$972$	−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	$-0.852982\pi$
$977$	−14.0530	+	14.0530i	−0.449595	+	0.449595i	0.445625	+	0.895220i	$0.352982\pi$
$978$	−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	0.998723	+	0.0505223i	$0.0160886\pi$
$983$	54.5743	+	22.6054i	1.74065	+	0.721001i	0.741928	+	0.670479i	$0.233911\pi$
$984$	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	0.221768	−	0.975099i	$-0.428817\pi$
$991$	−9.78771	−	4.05420i	−0.310917	−	0.128786i	−0.532685	+	0.846313i	$0.678817\pi$
$992$	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	$-0.848501\pi$
$997$	−37.6817	+	15.6083i	−1.19339	+	0.494319i	−0.304534	+	0.952501i	$0.598501\pi$
$998$	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.399.4		24
5.2	odd	4		425.2.m.b.76.3		24
5.3	odd	4		85.2.l.a.76.4	yes	24
5.4	even	2		425.2.n.c.399.3		24
15.8	even	4		765.2.be.b.586.3		24
17.15	even	8		425.2.n.c.49.3		24
85.7	even	16		7225.2.a.bs.1.7		12
85.23	even	16		1445.2.d.j.866.14		24
85.27	even	16		7225.2.a.bq.1.7		12
85.28	even	16		1445.2.d.j.866.13		24
85.32	odd	8		425.2.m.b.151.3		24
85.49	even	8	inner	425.2.n.f.49.4		24
85.58	even	16		1445.2.a.p.1.6		12
85.78	even	16		1445.2.a.q.1.6		12
85.83	odd	8		85.2.l.a.66.4	✓	24
255.83	even	8		765.2.be.b.406.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.4	✓	24	85.83	odd	8
85.2.l.a.76.4	yes	24	5.3	odd	4
425.2.m.b.76.3		24	5.2	odd	4
425.2.m.b.151.3		24	85.32	odd	8
425.2.n.c.49.3		24	17.15	even	8
425.2.n.c.399.3		24	5.4	even	2
425.2.n.f.49.4		24	85.49	even	8	inner
425.2.n.f.399.4		24	1.1	even	1	trivial
765.2.be.b.406.3		24	255.83	even	8
765.2.be.b.586.3		24	15.8	even	4
1445.2.a.p.1.6		12	85.58	even	16
1445.2.a.q.1.6		12	85.78	even	16
1445.2.d.j.866.13		24	85.28	even	16
1445.2.d.j.866.14		24	85.23	even	16
7225.2.a.bq.1.7		12	85.27	even	16
7225.2.a.bs.1.7		12	85.7	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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 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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