LMFDB - Embedded newform 400.2.q.g.349.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(149,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			349.2
Root			$1.32070 + 0.505727i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.g.149.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39064 + 0.257150i) q^{2} +(1.66366 - 1.66366i) q^{3} +(1.86775 - 0.715205i) q^{4} +(-1.88574 + 2.74137i) q^{6} -2.89402 q^{7} +(-2.41345 + 1.47488i) q^{8} -2.53555i q^{9} +(1.84462 - 1.84462i) q^{11} +(1.91744 - 4.29717i) q^{12} +(3.08011 - 3.08011i) q^{13} +(4.02454 - 0.744198i) q^{14} +(2.97696 - 2.67165i) q^{16} -7.29875i q^{17} +(0.652018 + 3.52604i) q^{18} +(1.23593 + 1.23593i) q^{19} +(-4.81468 + 4.81468i) q^{21} +(-2.09086 + 3.03955i) q^{22} -4.60490 q^{23} +(-1.56145 + 6.46887i) q^{24} +(-3.49126 + 5.07536i) q^{26} +(0.772683 + 0.772683i) q^{27} +(-5.40530 + 2.06982i) q^{28} +(-4.24680 - 4.24680i) q^{29} +2.06299 q^{31} +(-3.45286 + 4.48082i) q^{32} -6.13767i q^{33} +(1.87688 + 10.1499i) q^{34} +(-1.81344 - 4.73577i) q^{36} +(1.17899 + 1.17899i) q^{37} +(-2.03655 - 1.40091i) q^{38} -10.2485i q^{39} -4.61484i q^{41} +(5.45738 - 7.93357i) q^{42} +(3.03019 + 3.03019i) q^{43} +(2.12601 - 4.76458i) q^{44} +(6.40375 - 1.18415i) q^{46} +11.7111i q^{47} +(0.507943 - 9.39739i) q^{48} +1.37537 q^{49} +(-12.1427 - 12.1427i) q^{51} +(3.54995 - 7.95577i) q^{52} +(2.73048 + 2.73048i) q^{53} +(-1.27322 - 0.875827i) q^{54} +(6.98457 - 4.26835i) q^{56} +4.11235 q^{57} +(6.99782 + 4.81369i) q^{58} +(-3.11306 + 3.11306i) q^{59} +(2.34962 + 2.34962i) q^{61} +(-2.86887 + 0.530498i) q^{62} +7.33795i q^{63} +(3.64944 - 7.11910i) q^{64} +(1.57830 + 8.53528i) q^{66} +(8.24311 - 8.24311i) q^{67} +(-5.22011 - 13.6322i) q^{68} +(-7.66101 + 7.66101i) q^{69} +3.25937i q^{71} +(3.73965 + 6.11942i) q^{72} +12.6877 q^{73} +(-1.94272 - 1.33637i) q^{74} +(3.19235 + 1.42446i) q^{76} +(-5.33839 + 5.33839i) q^{77} +(2.63541 + 14.2520i) q^{78} +0.113885 q^{79} +10.1776 q^{81} +(1.18671 + 6.41758i) q^{82} +(-9.76813 + 9.76813i) q^{83} +(-5.54912 + 12.4361i) q^{84} +(-4.99310 - 3.43468i) q^{86} -14.1305 q^{87} +(-1.73129 + 7.17251i) q^{88} -3.74593i q^{89} +(-8.91390 + 8.91390i) q^{91} +(-8.60080 + 3.29345i) q^{92} +(3.43212 - 3.43212i) q^{93} +(-3.01150 - 16.2858i) q^{94} +(1.71017 + 13.1990i) q^{96} +13.9853i q^{97} +(-1.91264 + 0.353676i) q^{98} +(-4.67714 - 4.67714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 4 q^{4} - 12 q^{6} - 8 q^{7} + 8 q^{8} - 8 q^{11} - 20 q^{12} - 4 q^{14} + 16 q^{16} - 12 q^{18} + 8 q^{19} + 20 q^{22} - 24 q^{23} - 8 q^{24} - 16 q^{26} - 24 q^{27} - 20 q^{28} + 16 q^{29}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 4 * q^4 - 12 * q^6 - 8 * q^7 + 8 * q^8 - 8 * q^11 - 20 * q^12 - 4 * q^14 + 16 * q^16 - 12 * q^18 + 8 * q^19 + 20 * q^22 - 24 * q^23 - 8 * q^24 - 16 * q^26 - 24 * q^27 - 20 * q^28 + 16 * q^29 - 24 * q^32 - 16 * q^34 - 4 * q^36 + 16 * q^37 + 20 * q^38 + 20 * q^42 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 16 * q^49 - 32 * q^51 + 16 * q^52 + 16 * q^53 - 32 * q^54 + 16 * q^56 + 28 * q^58 + 8 * q^59 + 16 * q^61 - 48 * q^62 + 16 * q^64 + 40 * q^67 + 8 * q^68 - 16 * q^69 + 96 * q^72 + 72 * q^74 + 16 * q^77 - 24 * q^78 - 16 * q^79 - 16 * q^81 - 44 * q^82 - 40 * q^83 + 64 * q^84 + 28 * q^86 + 16 * q^88 + 32 * q^91 - 20 * q^92 + 48 * q^93 + 36 * q^94 + 8 * q^96 + 32 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.39064	+	0.257150i	−0.983329	+	0.181833i
$2$	−1.39064	+	0.257150i	−0.983329	+	0.181833i
$3$	1.66366	−	1.66366i	0.960517	−	0.960517i	−0.0387330	−	0.999250i	$-0.512332\pi$
$3$	1.66366	−	1.66366i	0.960517	−	0.960517i	0.999250	+	0.0387330i	$0.0123322\pi$
$4$	1.86775	−	0.715205i	0.933874	−	0.357603i
$5$		0			0
$5$		0			0
$6$	−1.88574	+	2.74137i	−0.769851	+	1.11916i
$7$	−2.89402			−1.09384			−0.546919	−	0.837186i	$-0.684199\pi$
$7$	−2.89402			−1.09384			−0.546919	+	0.837186i	$0.684199\pi$
$8$	−2.41345	+	1.47488i	−0.853282	+	0.521450i
$9$		−	2.53555i		−	0.845184i
$10$		0			0
$11$	1.84462	−	1.84462i	0.556175	−	0.556175i	−0.372041	−	0.928216i	$-0.621342\pi$
$11$	1.84462	−	1.84462i	0.556175	−	0.556175i	0.928216	+	0.372041i	$0.121342\pi$
$12$	1.91744	−	4.29717i	0.553518	−	1.24048i
$13$	3.08011	−	3.08011i	0.854268	−	0.854268i	−0.136388	−	0.990656i	$-0.543549\pi$
$13$	3.08011	−	3.08011i	0.854268	−	0.854268i	0.990656	+	0.136388i	$0.0435493\pi$
$14$	4.02454	−	0.744198i	1.07560	−	0.198895i
$15$		0			0
$16$	2.97696	−	2.67165i	0.744241	−	0.667912i
$17$		−	7.29875i		−	1.77021i	−0.465393	−	0.885104i	$-0.654087\pi$
$17$		−	7.29875i		−	1.77021i	0.465393	−	0.885104i	$-0.345913\pi$
$18$	0.652018	+	3.52604i	0.153682	+	0.831095i
$19$	1.23593	+	1.23593i	0.283542	+	0.283542i	0.834520	−	0.550978i	$-0.185745\pi$
$19$	1.23593	+	1.23593i	0.283542	+	0.283542i	−0.550978	+	0.834520i	$0.685745\pi$
$20$		0			0
$21$	−4.81468	+	4.81468i	−1.05065	+	1.05065i
$22$	−2.09086	+	3.03955i	−0.445773	+	0.648034i
$23$	−4.60490			−0.960189			−0.480094	−	0.877217i	$-0.659398\pi$
$23$	−4.60490			−0.960189			−0.480094	+	0.877217i	$0.659398\pi$
$24$	−1.56145	+	6.46887i	−0.318730	+	1.32045i
$25$		0			0
$26$	−3.49126	+	5.07536i	−0.684693	+	0.995360i
$27$	0.772683	+	0.772683i	0.148703	+	0.148703i
$28$	−5.40530	+	2.06982i	−1.02151	+	0.391159i
$29$	−4.24680	−	4.24680i	−0.788611	−	0.788611i	0.192656	−	0.981266i	$-0.438290\pi$
$29$	−4.24680	−	4.24680i	−0.788611	−	0.788611i	−0.981266	+	0.192656i	$0.938290\pi$
$30$		0			0
$31$	2.06299			0.370524			0.185262	−	0.982689i	$-0.440687\pi$
$31$	2.06299			0.370524			0.185262	+	0.982689i	$0.440687\pi$
$32$	−3.45286	+	4.48082i	−0.610386	+	0.792104i
$33$		−	6.13767i		−	1.06843i
$34$	1.87688	+	10.1499i	0.321882	+	1.74070i
$35$		0			0
$36$	−1.81344	−	4.73577i	−0.302240	−	0.789296i
$37$	1.17899	+	1.17899i	0.193825	+	0.193825i	0.797346	−	0.603522i	$-0.206236\pi$
$37$	1.17899	+	1.17899i	0.193825	+	0.193825i	−0.603522	+	0.797346i	$0.706236\pi$
$38$	−2.03655	−	1.40091i	−0.330373	−	0.227258i
$39$		−	10.2485i		−	1.64108i
$40$		0			0
$41$		−	4.61484i		−	0.720717i	−0.932814	−	0.360359i	$-0.882654\pi$
$41$		−	4.61484i		−	0.720717i	0.932814	−	0.360359i	$-0.117346\pi$
$42$	5.45738	−	7.93357i	0.842092	−	1.22418i
$43$	3.03019	+	3.03019i	0.462099	+	0.462099i	0.899343	−	0.437244i	$-0.144045\pi$
$43$	3.03019	+	3.03019i	0.462099	+	0.462099i	−0.437244	+	0.899343i	$0.644045\pi$
$44$	2.12601	−	4.76458i	0.320508	−	0.718287i
$45$		0			0
$46$	6.40375	−	1.18415i	0.944182	−	0.174594i
$47$			11.7111i			1.70823i	0.520081	+	0.854117i	$0.325902\pi$
$47$			11.7111i			1.70823i	−0.520081	+	0.854117i	$0.674098\pi$
$48$	0.507943	−	9.39739i	0.0733152	−	1.35640i
$49$	1.37537			0.196481
$50$		0			0
$51$	−12.1427	−	12.1427i	−1.70031	−	1.70031i
$52$	3.54995	−	7.95577i	0.492290	−	1.10327i
$53$	2.73048	+	2.73048i	0.375061	+	0.375061i	0.869316	−	0.494256i	$-0.164559\pi$
$53$	2.73048	+	2.73048i	0.375061	+	0.375061i	−0.494256	+	0.869316i	$0.664559\pi$
$54$	−1.27322	−	0.875827i	−0.173263	−	0.119185i
$55$		0			0
$56$	6.98457	−	4.26835i	0.933352	−	0.570382i
$57$	4.11235			0.544694
$58$	6.99782	+	4.81369i	0.918859	+	0.632069i
$59$	−3.11306	+	3.11306i	−0.405285	+	0.405285i	−0.880091	−	0.474805i	$-0.842518\pi$
$59$	−3.11306	+	3.11306i	−0.405285	+	0.405285i	0.474805	+	0.880091i	$0.342518\pi$
$60$		0			0
$61$	2.34962	+	2.34962i	0.300838	+	0.300838i	0.841342	−	0.540503i	$-0.181766\pi$
$61$	2.34962	+	2.34962i	0.300838	+	0.300838i	−0.540503	+	0.841342i	$0.681766\pi$
$62$	−2.86887	+	0.530498i	−0.364347	+	0.0673733i
$63$			7.33795i			0.924495i
$64$	3.64944	−	7.11910i	0.456180	−	0.889888i
$65$		0			0
$66$	1.57830	+	8.53528i	0.194276	+	1.05062i
$67$	8.24311	−	8.24311i	1.00706	−	1.00706i	0.00708173	−	0.999975i	$-0.497746\pi$
$67$	8.24311	−	8.24311i	1.00706	−	1.00706i	0.999975	−	0.00708173i	$-0.00225420\pi$
$68$	−5.22011	−	13.6322i	−0.633031	−	1.65315i
$69$	−7.66101	+	7.66101i	−0.922277	+	0.922277i
$70$		0			0
$71$			3.25937i			0.386816i	0.981118	+	0.193408i	$0.0619541\pi$
$71$			3.25937i			0.386816i	−0.981118	+	0.193408i	$0.938046\pi$
$72$	3.73965	+	6.11942i	0.440721	+	0.721180i
$73$	12.6877			1.48499			0.742494	−	0.669853i	$-0.233643\pi$
$73$	12.6877			1.48499			0.742494	+	0.669853i	$0.233643\pi$
$74$	−1.94272	−	1.33637i	−0.225837	−	0.155350i
$75$		0			0
$76$	3.19235	+	1.42446i	0.366188	+	0.163397i
$77$	−5.33839	+	5.33839i	−0.608365	+	0.608365i
$78$	2.63541	+	14.2520i	0.298401	+	1.61372i
$79$	0.113885			0.0128130			0.00640652	−	0.999979i	$-0.497961\pi$
$79$	0.113885			0.0128130			0.00640652	+	0.999979i	$0.497961\pi$
$80$		0			0
$81$	10.1776			1.13085
$82$	1.18671	+	6.41758i	0.131050	+	0.708703i
$83$	−9.76813	+	9.76813i	−1.07219	+	1.07219i	−0.0750089	+	0.997183i	$0.523899\pi$
$83$	−9.76813	+	9.76813i	−1.07219	+	1.07219i	−0.997183	+	0.0750089i	$0.976101\pi$
$84$	−5.54912	+	12.4361i	−0.605459	+	1.35689i
$85$		0			0
$86$	−4.99310	−	3.43468i	−0.538420	−	0.370371i
$87$	−14.1305			−1.51495
$88$	−1.73129	+	7.17251i	−0.184557	+	0.764592i
$89$		−	3.74593i		−	0.397068i	−0.980094	−	0.198534i	$-0.936382\pi$
$89$		−	3.74593i		−	0.397068i	0.980094	−	0.198534i	$-0.0636180\pi$
$90$		0			0
$91$	−8.91390	+	8.91390i	−0.934430	+	0.934430i
$92$	−8.60080	+	3.29345i	−0.896695	+	0.343366i
$93$	3.43212	−	3.43212i	0.355894	−	0.355894i
$94$	−3.01150	−	16.2858i	−0.310613	−	1.67976i
$95$		0			0
$96$	1.71017	+	13.1990i	0.174544	+	1.34711i
$97$			13.9853i			1.41999i	0.704206	+	0.709995i	$0.251303\pi$
$97$			13.9853i			1.41999i	−0.704206	+	0.709995i	$0.748697\pi$
$98$	−1.91264	+	0.353676i	−0.193206	+	0.0357267i
$99$	−4.67714	−	4.67714i	−0.470071	−	0.470071i
$100$		0			0
$101$	3.52228	−	3.52228i	0.350480	−	0.350480i	−0.509808	−	0.860288i	$-0.670284\pi$
$101$	3.52228	−	3.52228i	0.350480	−	0.350480i	0.860288	+	0.509808i	$0.170284\pi$
$102$	20.0085	+	13.7636i	1.98114	+	1.36280i
$103$	0.150216			0.0148013			0.00740063	−	0.999973i	$-0.497644\pi$
$103$	0.150216			0.0148013			0.00740063	+	0.999973i	$0.497644\pi$
$104$	−2.89087	+	11.9765i	−0.283473	+	1.17439i
$105$		0			0
$106$	−4.49926	−	3.09497i	−0.437006	−	0.300610i
$107$	2.75062	+	2.75062i	0.265912	+	0.265912i	0.827451	−	0.561539i	$-0.189790\pi$
$107$	2.75062	+	2.75062i	0.265912	+	0.265912i	−0.561539	+	0.827451i	$0.689790\pi$
$108$	1.99580	+	0.890550i	0.192046	+	0.0856932i
$109$	6.90778	+	6.90778i	0.661646	+	0.661646i	0.955768	−	0.294122i	$-0.0950273\pi$
$109$	6.90778	+	6.90778i	0.661646	+	0.661646i	−0.294122	+	0.955768i	$0.595027\pi$
$110$		0			0
$111$	3.92288			0.372344
$112$	−8.61540	+	7.73181i	−0.814078	+	0.730587i
$113$		−	3.49507i		−	0.328788i	−0.986395	−	0.164394i	$-0.947433\pi$
$113$		−	3.49507i		−	0.328788i	0.986395	−	0.164394i	$-0.0525669\pi$
$114$	−5.71879	+	1.05749i	−0.535614	+	0.0990431i
$115$		0			0
$116$	−10.9693	−	4.89461i	−1.01847	−	0.454454i
$117$	−7.80977	−	7.80977i	−0.722014	−	0.722014i
$118$	3.52861	−	5.12966i	0.324835	−	0.472223i
$119$			21.1228i			1.93632i
$120$		0			0
$121$			4.19472i			0.381338i
$122$	−3.87168	−	2.66327i	−0.350526	−	0.241121i
$123$	−7.67755	−	7.67755i	−0.692261	−	0.692261i
$124$	3.85314	−	1.47546i	0.346022	−	0.132500i
$125$		0			0
$126$	−1.88695	−	10.2044i	−0.168103	−	0.909083i
$127$		−	6.25357i		−	0.554915i	−0.960738	−	0.277458i	$-0.910508\pi$
$127$		−	6.25357i		−	0.554915i	0.960738	−	0.277458i	$-0.0894918\pi$
$128$	−3.24437	+	10.8385i	−0.286764	+	0.958001i
$129$	10.0824			0.887708
$130$		0			0
$131$	−5.16490	−	5.16490i	−0.451259	−	0.451259i	0.444513	−	0.895772i	$-0.353377\pi$
$131$	−5.16490	−	5.16490i	−0.451259	−	0.451259i	−0.895772	+	0.444513i	$0.853377\pi$
$132$	−4.38969	−	11.4636i	−0.382074	−	0.997780i
$133$	−3.57681	−	3.57681i	−0.310149	−	0.310149i
$134$	−9.34347	+	13.5829i	−0.807153	+	1.17338i
$135$		0			0
$136$	10.7648	+	17.6151i	0.923075	+	1.51049i
$137$	18.9408			1.61823			0.809113	−	0.587654i	$-0.199948\pi$
$137$	18.9408			1.61823			0.809113	+	0.587654i	$0.199948\pi$
$138$	8.68366	−	12.6237i	0.739203	−	1.07460i
$139$	−2.79057	+	2.79057i	−0.236693	+	0.236693i	−0.815479	−	0.578786i	$-0.803527\pi$
$139$	−2.79057	+	2.79057i	−0.236693	+	0.236693i	0.578786	+	0.815479i	$0.303527\pi$
$140$		0			0
$141$	19.4833	+	19.4833i	1.64079	+	1.64079i
$142$	−0.838147	−	4.53260i	−0.0703357	−	0.380367i
$143$		−	11.3633i		−	0.950245i
$144$	−6.77410	−	7.54825i	−0.564509	−	0.629021i
$145$		0			0
$146$	−17.6441	+	3.26265i	−1.46023	+	0.270019i
$147$	2.28815	−	2.28815i	0.188723	−	0.188723i
$148$	3.04527	+	1.35883i	0.250320	+	0.111696i
$149$	1.60372	−	1.60372i	0.131382	−	0.131382i	−0.638358	−	0.769740i	$-0.720386\pi$
$149$	1.60372	−	1.60372i	0.131382	−	0.131382i	0.769740	+	0.638358i	$0.220386\pi$
$150$		0			0
$151$		−	2.53754i		−	0.206502i	−0.994655	−	0.103251i	$-0.967076\pi$
$151$		−	2.53754i		−	0.206502i	0.994655	−	0.103251i	$-0.0329245\pi$
$152$	−4.80571	−	1.16000i	−0.389794	−	0.0940883i
$153$	−18.5064			−1.49615
$154$	6.05099	−	8.79653i	0.487603	−	0.708844i
$155$		0			0
$156$	−7.32980	−	19.1417i	−0.586854	−	1.53256i
$157$	10.2405	−	10.2405i	0.817278	−	0.817278i	−0.168435	−	0.985713i	$-0.553871\pi$
$157$	10.2405	−	10.2405i	0.817278	−	0.817278i	0.985713	+	0.168435i	$0.0538712\pi$
$158$	−0.158373	+	0.0292855i	−0.0125994	+	0.00232983i
$159$	9.08521			0.720504
$160$		0			0
$161$	13.3267			1.05029
$162$	−14.1534	+	2.61718i	−1.11200	+	0.205625i
$163$	−8.02607	+	8.02607i	−0.628650	+	0.628650i	−0.947728	−	0.319078i	$-0.896627\pi$
$163$	−8.02607	+	8.02607i	−0.628650	+	0.628650i	0.319078	+	0.947728i	$0.396627\pi$
$164$	−3.30056	−	8.61936i	−0.257731	−	0.673059i
$165$		0			0
$166$	11.0721	−	16.0958i	0.859358	−	1.24928i
$167$	6.82611			0.528221			0.264110	−	0.964492i	$-0.414922\pi$
$167$	6.82611			0.528221			0.264110	+	0.964492i	$0.414922\pi$
$168$	4.51888	−	18.7211i	0.348639	−	1.44436i
$169$		−	5.97411i		−	0.459547i
$170$		0			0
$171$	3.13377	−	3.13377i	0.239645	−	0.239645i
$172$	7.82683	+	3.49242i	0.596790	+	0.266294i
$173$	−5.08901	+	5.08901i	−0.386910	+	0.386910i	−0.873584	−	0.486674i	$-0.838210\pi$
$173$	−5.08901	+	5.08901i	−0.386910	+	0.386910i	0.486674	+	0.873584i	$0.338210\pi$
$174$	19.6504	−	3.63366i	1.48969	−	0.275467i
$175$		0			0
$176$	0.563193	−	10.4196i	0.0424523	−	0.785404i
$177$			10.3582i			0.778567i
$178$	0.963267	+	5.20924i	0.0721999	+	0.390449i
$179$	−1.63797	−	1.63797i	−0.122428	−	0.122428i	0.643238	−	0.765666i	$-0.277590\pi$
$179$	−1.63797	−	1.63797i	−0.122428	−	0.122428i	−0.765666	+	0.643238i	$0.777590\pi$
$180$		0			0
$181$	−16.7757	+	16.7757i	−1.24693	+	1.24693i	−0.289855	+	0.957071i	$0.593607\pi$
$181$	−16.7757	+	16.7757i	−1.24693	+	1.24693i	−0.957071	+	0.289855i	$0.906393\pi$
$182$	10.1038	−	14.6882i	0.748943	−	1.08876i
$183$	7.81797			0.577921
$184$	11.1137	−	6.79170i	0.819312	−	0.500691i
$185$		0			0
$186$	−3.89026	+	5.65540i	−0.285248	+	0.414674i
$187$	−13.4635	−	13.4635i	−0.984546	−	0.984546i
$188$	8.37582	+	21.8733i	0.610869	+	1.59527i
$189$	−2.23616	−	2.23616i	−0.162657	−	0.162657i
$190$		0			0
$191$	5.85815			0.423881			0.211940	−	0.977283i	$-0.432022\pi$
$191$	5.85815			0.423881			0.211940	+	0.977283i	$0.432022\pi$
$192$	−5.77235	−	17.9152i	−0.416584	−	1.29292i
$193$		−	0.0241155i		−	0.00173587i	−1.00000		0.000867935i	$-0.999724\pi$
$193$		−	0.0241155i		−	0.00173587i	1.00000		0.000867935i	$-0.000276272\pi$
$194$	−3.59632	−	19.4485i	−0.258201	−	1.39632i
$195$		0			0
$196$	2.56884	−	0.983671i	0.183489	−	0.0702622i
$197$	−14.9086	−	14.9086i	−1.06219	−	1.06219i	−0.997933	−	0.0642576i	$-0.979532\pi$
$197$	−14.9086	−	14.9086i	−1.06219	−	1.06219i	−0.0642576	−	0.997933i	$-0.520468\pi$
$198$	7.70694	+	5.30149i	0.547708	+	0.376760i
$199$			13.6525i			0.967801i	0.875123	+	0.483900i	$0.160780\pi$
$199$			13.6525i			0.967801i	−0.875123	+	0.483900i	$0.839220\pi$
$200$		0			0
$201$		−	27.4275i		−	1.93459i
$202$	−3.99246	+	5.80397i	−0.280909	+	0.408366i
$203$	12.2903	+	12.2903i	0.862612	+	0.862612i
$204$	−31.3640	−	13.9949i	−2.19592	−	0.979842i
$205$		0			0
$206$	−0.208897	+	0.0386282i	−0.0145545	+	0.00269135i
$207$			11.6760i			0.811537i
$208$	0.940405	−	17.3983i	0.0652053	−	1.20636i
$209$	4.55966			0.315398
$210$		0			0
$211$	−2.45103	−	2.45103i	−0.168736	−	0.168736i	0.617688	−	0.786424i	$-0.288070\pi$
$211$	−2.45103	−	2.45103i	−0.168736	−	0.168736i	−0.786424	+	0.617688i	$0.788070\pi$
$212$	7.05271	+	3.14700i	0.484382	+	0.216137i
$213$	5.42249	+	5.42249i	0.371543	+	0.371543i
$214$	−4.53243	−	3.11779i	−0.309831	−	0.213128i
$215$		0			0
$216$	−3.00445	−	0.725211i	−0.204427	−	0.0493444i
$217$	−5.97033			−0.405293
$218$	−11.3826	−	7.82989i	−0.770924	−	0.530307i
$219$	21.1081	−	21.1081i	1.42636	−	1.42636i
$220$		0			0
$221$	−22.4809	−	22.4809i	−1.51223	−	1.51223i
$222$	−5.45531	+	1.00877i	−0.366136	+	0.0677042i
$223$			13.9483i			0.934045i	0.884245	+	0.467023i	$0.154673\pi$
$223$			13.9483i			0.934045i	−0.884245	+	0.467023i	$0.845327\pi$
$224$	9.99266	−	12.9676i	0.667663	−	0.866434i
$225$		0			0
$226$	0.898758	+	4.86038i	0.0597845	+	0.323307i
$227$	4.43883	−	4.43883i	0.294616	−	0.294616i	−0.544285	−	0.838901i	$-0.683199\pi$
$227$	4.43883	−	4.43883i	0.294616	−	0.294616i	0.838901	+	0.544285i	$0.183199\pi$
$228$	7.68083	−	2.94117i	0.508675	−	0.194784i
$229$	5.35068	−	5.35068i	0.353583	−	0.353583i	−0.507858	−	0.861441i	$-0.669562\pi$
$229$	5.35068	−	5.35068i	0.353583	−	0.353583i	0.861441	+	0.507858i	$0.169562\pi$
$230$		0			0
$231$			17.7626i			1.16869i
$232$	16.5129	+	3.98588i	1.08413	+	0.261686i
$233$	−11.9370			−0.782019			−0.391010	−	0.920387i	$-0.627874\pi$
$233$	−11.9370			−0.782019			−0.391010	+	0.920387i	$0.627874\pi$
$234$	12.8689	+	8.85228i	0.841263	+	0.578692i
$235$		0			0
$236$	−3.58793	+	8.04088i	−0.233554	+	0.523416i
$237$	0.189466	−	0.189466i	0.0123071	−	0.0123071i
$238$	−5.43172	−	29.3741i	−0.352086	−	1.90404i
$239$	16.7720			1.08489			0.542445	−	0.840091i	$-0.317499\pi$
$239$	16.7720			1.08489			0.542445	+	0.840091i	$0.317499\pi$
$240$		0			0
$241$	−22.0294			−1.41904			−0.709519	−	0.704686i	$-0.751088\pi$
$241$	−22.0294			−1.41904			−0.709519	+	0.704686i	$0.751088\pi$
$242$	−1.07867	−	5.83334i	−0.0693397	−	0.374981i
$243$	14.6141	−	14.6141i	0.937495	−	0.937495i
$244$	6.06897	+	2.70804i	0.388526	+	0.173365i
$245$		0			0
$246$	12.6510	+	8.70241i	0.806596	+	0.554845i
$247$	7.61360			0.484442
$248$	−4.97891	+	3.04267i	−0.316161	+	0.193210i
$249$			32.5018i			2.05972i
$250$		0			0
$251$	6.63925	−	6.63925i	0.419066	−	0.419066i	−0.465816	−	0.884882i	$-0.654239\pi$
$251$	6.63925	−	6.63925i	0.419066	−	0.419066i	0.884882	+	0.465816i	$0.154239\pi$
$252$	5.24814	+	13.7054i	0.330602	+	0.863361i
$253$	−8.49432	+	8.49432i	−0.534033	+	0.534033i
$254$	1.60811	+	8.69646i	0.100902	+	0.545664i
$255$		0			0
$256$	1.72461	−	15.9068i	0.107788	−	0.994174i
$257$			7.25821i			0.452755i	0.974040	+	0.226377i	$0.0726883\pi$
$257$			7.25821i			0.452755i	−0.974040	+	0.226377i	$0.927312\pi$
$258$	−14.0210	+	2.59270i	−0.872909	+	0.161414i
$259$	−3.41202	−	3.41202i	−0.212013	−	0.212013i
$260$		0			0
$261$	−10.7680	+	10.7680i	−0.666521	+	0.666521i
$262$	8.51066	+	5.85435i	0.525790	+	0.361683i
$263$	−9.27431			−0.571878			−0.285939	−	0.958248i	$-0.592306\pi$
$263$	−9.27431			−0.571878			−0.285939	+	0.958248i	$0.592306\pi$
$264$	9.05235	+	14.8129i	0.557133	+	0.911673i
$265$		0			0
$266$	5.89383	+	4.05428i	0.361374	+	0.248584i
$267$	−6.23197	−	6.23197i	−0.381390	−	0.381390i
$268$	9.50054	−	21.2916i	0.580338	−	1.30059i
$269$	13.4195	+	13.4195i	0.818199	+	0.818199i	0.985847	−	0.167648i	$-0.0536173\pi$
$269$	13.4195	+	13.4195i	0.818199	+	0.818199i	−0.167648	+	0.985847i	$0.553617\pi$
$270$		0			0
$271$	22.5999			1.37285			0.686423	−	0.727202i	$-0.259180\pi$
$271$	22.5999			1.37285			0.686423	+	0.727202i	$0.259180\pi$
$272$	−19.4997	−	21.7281i	−1.18234	−	1.31746i
$273$			29.6595i			1.79507i
$274$	−26.3399	+	4.87064i	−1.59125	+	0.294246i
$275$		0			0
$276$	−8.82964	+	19.7880i	−0.531482	+	1.19110i
$277$	−16.2015	−	16.2015i	−0.973451	−	0.973451i	0.0262056	−	0.999657i	$-0.491658\pi$
$277$	−16.2015	−	16.2015i	−0.973451	−	0.973451i	−0.999657	+	0.0262056i	$0.991658\pi$
$278$	3.16308	−	4.59827i	0.189709	−	0.275786i
$279$		−	5.23082i		−	0.313161i
$280$		0			0
$281$			8.84793i			0.527824i	0.964547	+	0.263912i	$0.0850128\pi$
$281$			8.84793i			0.527824i	−0.964547	+	0.263912i	$0.914987\pi$
$282$	−32.1043	−	22.0840i	−1.91178	−	1.31509i
$283$	−20.3062	−	20.3062i	−1.20708	−	1.20708i	−0.971969	−	0.235109i	$-0.924455\pi$
$283$	−20.3062	−	20.3062i	−1.20708	−	1.20708i	−0.235109	−	0.971969i	$-0.575545\pi$
$284$	2.33112	+	6.08768i	0.138326	+	0.361237i
$285$		0			0
$286$	2.92207	+	15.8022i	0.172786	+	0.934404i
$287$			13.3555i			0.788348i
$288$	11.3614	+	8.75492i	0.669474	+	0.515888i
$289$	−36.2718			−2.13364
$290$		0			0
$291$	23.2668	+	23.2668i	1.36392	+	1.36392i
$292$	23.6975	−	9.07434i	1.38679	−	0.531036i
$293$	−7.16936	−	7.16936i	−0.418839	−	0.418839i	0.465965	−	0.884803i	$-0.345707\pi$
$293$	−7.16936	−	7.16936i	−0.418839	−	0.418839i	−0.884803	+	0.465965i	$0.845707\pi$
$294$	−2.59359	+	3.77039i	−0.151261	+	0.219893i
$295$		0			0
$296$	−4.58430	−	1.10655i	−0.266457	−	0.0643172i
$297$	2.85062			0.165410
$298$	−1.81779	+	2.64259i	−0.105302	+	0.153081i
$299$	−14.1836	+	14.1836i	−0.820258	+	0.820258i
$300$		0			0
$301$	−8.76943	−	8.76943i	−0.505461	−	0.505461i
$302$	0.652528	+	3.52880i	0.0375488	+	0.203059i
$303$		−	11.7198i		−	0.673284i
$304$	6.98129	+	0.377349i	0.400405	+	0.0216425i
$305$		0			0
$306$	25.7357	−	4.75892i	1.47121	−	0.272049i
$307$	−18.4308	+	18.4308i	−1.05190	+	1.05190i	−0.0533241	+	0.998577i	$0.516982\pi$
$307$	−18.4308	+	18.4308i	−1.05190	+	1.05190i	−0.998577	+	0.0533241i	$0.983018\pi$
$308$	−6.15271	+	13.7888i	−0.350583	+	0.785690i
$309$	0.249910	−	0.249910i	0.0142169	−	0.0142169i
$310$		0			0
$311$		−	7.08961i		−	0.402015i	−0.979590	−	0.201007i	$-0.935578\pi$
$311$		−	7.08961i		−	0.402015i	0.979590	−	0.201007i	$-0.0644215\pi$
$312$	15.1154	+	24.7342i	0.855739	+	1.40030i
$313$	22.0477			1.24621			0.623104	−	0.782139i	$-0.285871\pi$
$313$	22.0477			1.24621			0.623104	+	0.782139i	$0.285871\pi$
$314$	−11.6074	+	16.8741i	−0.655046	+	0.952262i
$315$		0			0
$316$	0.212708	−	0.0814510i	0.0119658	−	0.00458198i
$317$	−6.19670	+	6.19670i	−0.348042	+	0.348042i	−0.859380	−	0.511338i	$-0.829150\pi$
$317$	−6.19670	+	6.19670i	−0.348042	+	0.348042i	0.511338	+	0.859380i	$0.329150\pi$
$318$	−12.6342	+	2.33626i	−0.708493	+	0.131011i
$319$	−15.6675			−0.877211
$320$		0			0
$321$	9.15220			0.510826
$322$	−18.5326	+	3.42696i	−1.03278	+	0.190977i
$323$	9.02076	−	9.02076i	0.501929	−	0.501929i
$324$	19.0092	−	7.27910i	1.05607	−	0.404394i
$325$		0			0
$326$	9.09745	−	13.2253i	0.503861	−	0.732479i
$327$	22.9845			1.27104
$328$	6.80636	+	11.1377i	0.375818	+	0.614975i
$329$		−	33.8921i		−	1.86853i
$330$		0			0
$331$	−18.6174	+	18.6174i	−1.02330	+	1.02330i	−0.0235823	+	0.999722i	$0.507507\pi$
$331$	−18.6174	+	18.6174i	−1.02330	+	1.02330i	−0.999722	+	0.0235823i	$0.992493\pi$
$332$	−11.2582	+	25.2306i	−0.617873	+	1.38471i
$333$	2.98939	−	2.98939i	0.163818	−	0.163818i
$334$	−9.49265	+	1.75534i	−0.519415	+	0.0960477i
$335$		0			0
$336$	−1.47000	+	27.1962i	−0.0801949	+	1.48368i
$337$		−	14.2577i		−	0.776666i	−0.921519	−	0.388333i	$-0.873051\pi$
$337$		−	14.2577i		−	0.776666i	0.921519	−	0.388333i	$-0.126949\pi$
$338$	1.53624	+	8.30782i	0.0835606	+	0.451886i
$339$	−5.81462	−	5.81462i	−0.315807	−	0.315807i
$340$		0			0
$341$	3.80544	−	3.80544i	0.206076	−	0.206076i
$342$	−3.55209	+	5.16379i	−0.192075	+	0.279226i
$343$	16.2778			0.878919
$344$	−11.7824	−	2.84402i	−0.635262	−	0.153339i
$345$		0			0
$346$	5.76833	−	8.38561i	0.310107	−	0.450813i
$347$	23.5395	+	23.5395i	1.26367	+	1.26367i	0.949303	+	0.314363i	$0.101791\pi$
$347$	23.5395	+	23.5395i	1.26367	+	1.26367i	0.314363	+	0.949303i	$0.398209\pi$
$348$	−26.3922	+	10.1062i	−1.41477	+	0.541749i
$349$	1.56682	+	1.56682i	0.0838701	+	0.0838701i	0.747797	−	0.663927i	$-0.231112\pi$
$349$	1.56682	+	1.56682i	0.0838701	+	0.0838701i	−0.663927	+	0.747797i	$0.731112\pi$
$350$		0			0
$351$	4.75989			0.254064
$352$	1.89619	+	14.6347i	0.101068	+	0.780030i
$353$			9.44678i			0.502801i	0.967883	+	0.251401i	$0.0808912\pi$
$353$			9.44678i			0.502801i	−0.967883	+	0.251401i	$0.919109\pi$
$354$	−2.66360	−	14.4044i	−0.141569	−	0.765588i
$355$		0			0
$356$	−2.67911	−	6.99646i	−0.141993	−	0.370811i
$357$	35.1412	+	35.1412i	1.85987	+	1.85987i
$358$	2.69903	+	1.85662i	0.142648	+	0.0981256i
$359$		−	18.0452i		−	0.952392i	−0.879339	−	0.476196i	$-0.842015\pi$
$359$		−	18.0452i		−	0.952392i	0.879339	−	0.476196i	$-0.157985\pi$
$360$		0			0
$361$		−	15.9449i		−	0.839208i
$362$	19.0150	−	27.6427i	0.999407	−	1.45287i
$363$	6.97860	+	6.97860i	0.366282	+	0.366282i
$364$	−10.2736	+	23.0242i	−0.538485	+	1.20679i
$365$		0			0
$366$	−10.8720	+	2.01039i	−0.568286	+	0.105085i
$367$		−	29.1329i		−	1.52073i	−0.649498	−	0.760363i	$-0.725021\pi$
$367$		−	29.1329i		−	1.52073i	0.649498	−	0.760363i	$-0.274979\pi$
$368$	−13.7086	+	12.3027i	−0.714612	+	0.641321i
$369$	−11.7012			−0.609139
$370$		0			0
$371$	−7.90208	−	7.90208i	−0.410255	−	0.410255i
$372$	3.95566	−	8.86500i	0.205091	−	0.459629i
$373$	3.35598	+	3.35598i	0.173766	+	0.173766i	0.788632	−	0.614866i	$-0.210790\pi$
$373$	3.35598	+	3.35598i	0.173766	+	0.173766i	−0.614866	+	0.788632i	$0.710790\pi$
$374$	22.1849	+	15.2607i	1.14716	+	0.789110i
$375$		0			0
$376$	−17.2725	−	28.2640i	−0.890759	−	1.45760i
$377$	−26.1612			−1.34737
$378$	3.68472	+	2.53466i	0.189522	+	0.130369i
$379$	−11.6507	+	11.6507i	−0.598457	+	0.598457i	−0.939902	−	0.341445i	$-0.889084\pi$
$379$	−11.6507	+	11.6507i	−0.598457	+	0.598457i	0.341445	+	0.939902i	$0.389084\pi$
$380$		0			0
$381$	−10.4038	−	10.4038i	−0.533005	−	0.533005i
$382$	−8.14656	+	1.50642i	−0.416814	+	0.0770753i
$383$		−	21.8044i		−	1.11415i	−0.830461	−	0.557077i	$-0.811923\pi$
$383$		−	21.8044i		−	1.11415i	0.830461	−	0.557077i	$-0.188077\pi$
$384$	12.6342	+	23.4292i	0.644734	+	1.19562i
$385$		0			0
$386$	0.00620130	+	0.0335359i	0.000315638	+	0.00170693i
$387$	7.68320	−	7.68320i	0.390559	−	0.390559i
$388$	10.0024	+	26.1210i	0.507793	+	1.32609i
$389$	11.8899	−	11.8899i	0.602842	−	0.602842i	−0.338224	−	0.941066i	$-0.609826\pi$
$389$	11.8899	−	11.8899i	0.602842	−	0.602842i	0.941066	+	0.338224i	$0.109826\pi$
$390$		0			0
$391$			33.6101i			1.69973i
$392$	−3.31938	+	2.02851i	−0.167654	+	0.102455i
$393$	−17.1853			−0.866884
$394$	24.5661	+	16.8987i	1.23762	+	0.851343i
$395$		0			0
$396$	−12.0808	−	5.39061i	−0.607085	−	0.270888i
$397$	−9.23905	+	9.23905i	−0.463694	+	0.463694i	−0.899864	−	0.436170i	$-0.856335\pi$
$397$	−9.23905	+	9.23905i	−0.463694	+	0.463694i	0.436170	+	0.899864i	$0.356335\pi$
$398$	−3.51074	−	18.9857i	−0.175978	−	0.951667i
$399$	−11.9012			−0.595807
$400$		0			0
$401$	−14.4744			−0.722818			−0.361409	−	0.932407i	$-0.617704\pi$
$401$	−14.4744			−0.722818			−0.361409	+	0.932407i	$0.617704\pi$
$402$	7.05300	+	38.1418i	0.351771	+	1.90234i
$403$	6.35422	−	6.35422i	0.316526	−	0.316526i
$404$	4.05958	−	9.09789i	0.201972	−	0.452637i
$405$		0			0
$406$	−20.2519	−	13.9309i	−1.00508	−	0.691381i
$407$	4.34958			0.215601
$408$	47.2147	+	11.3967i	2.33748	+	0.564218i
$409$		−	9.54117i		−	0.471781i	−0.971780	−	0.235890i	$-0.924199\pi$
$409$		−	9.54117i		−	0.471781i	0.971780	−	0.235890i	$-0.0758006\pi$
$410$		0			0
$411$	31.5112	−	31.5112i	1.55433	−	1.55433i
$412$	0.280566	−	0.107436i	0.0138225	−	0.00529297i
$413$	9.00925	−	9.00925i	0.443316	−	0.443316i
$414$	−3.00248	−	16.2371i	−0.147564	−	0.798008i
$415$		0			0
$416$	3.16622	+	24.4366i	0.155237	+	1.19810i
$417$			9.28514i			0.454695i
$418$	−6.34083	+	1.17252i	−0.310140	+	0.0573497i
$419$	−0.837667	−	0.837667i	−0.0409227	−	0.0409227i	0.686349	−	0.727272i	$-0.259212\pi$
$419$	−0.837667	−	0.837667i	−0.0409227	−	0.0409227i	−0.727272	+	0.686349i	$0.759212\pi$
$420$		0			0
$421$	17.9679	−	17.9679i	0.875702	−	0.875702i	−0.117385	−	0.993087i	$-0.537451\pi$
$421$	17.9679	−	17.9679i	0.875702	−	0.875702i	0.993087	+	0.117385i	$0.0374511\pi$
$422$	4.03878	+	2.77822i	0.196605	+	0.135241i
$423$	29.6940			1.44377
$424$	−10.6170	−	2.56273i	−0.515608	−	0.124457i
$425$		0			0
$426$	−8.93512	−	6.14633i	−0.432908	−	0.297791i
$427$	−6.79986	−	6.79986i	−0.329068	−	0.329068i
$428$	7.10471	+	3.17020i	0.343419	+	0.153237i
$429$	−18.9047	−	18.9047i	−0.912726	−	0.912726i
$430$		0			0
$431$	−3.85473			−0.185676			−0.0928380	−	0.995681i	$-0.529594\pi$
$431$	−3.85473			−0.185676			−0.0928380	+	0.995681i	$0.529594\pi$
$432$	4.36459	+	0.235912i	0.209991	+	0.0113503i
$433$		−	25.5651i		−	1.22858i	−0.789081	−	0.614289i	$-0.789443\pi$
$433$		−	25.5651i		−	1.22858i	0.789081	−	0.614289i	$-0.210557\pi$
$434$	8.30257	−	1.53527i	0.398536	−	0.0736954i
$435$		0			0
$436$	17.8425	+	7.96151i	0.854500	+	0.381287i
$437$	−5.69135	−	5.69135i	−0.272254	−	0.272254i
$438$	−23.9258	+	34.7817i	−1.14322	+	1.66194i
$439$		−	30.1311i		−	1.43808i	−0.694970	−	0.719039i	$-0.744582\pi$
$439$		−	30.1311i		−	1.43808i	0.694970	−	0.719039i	$-0.255418\pi$
$440$		0			0
$441$		−	3.48732i		−	0.166063i
$442$	37.0438	+	25.4819i	1.76199	+	1.21205i
$443$	20.1625	+	20.1625i	0.957948	+	0.957948i	0.999151	−	0.0412027i	$-0.0131189\pi$
$443$	20.1625	+	20.1625i	0.957948	+	0.957948i	−0.0412027	+	0.999151i	$0.513119\pi$
$444$	7.32695	−	2.80567i	0.347722	−	0.133151i
$445$		0			0
$446$	−3.58680	−	19.3970i	−0.169840	−	0.918474i
$447$		−	5.33610i		−	0.252389i
$448$	−10.5616	+	20.6028i	−0.498987	+	0.973393i
$449$	36.5827			1.72644			0.863221	−	0.504826i	$-0.168443\pi$
$449$	36.5827			1.72644			0.863221	+	0.504826i	$0.168443\pi$
$450$		0			0
$451$	−8.51265	−	8.51265i	−0.400845	−	0.400845i
$452$	−2.49969	−	6.52791i	−0.117576	−	0.307047i
$453$	−4.22161	−	4.22161i	−0.198349	−	0.198349i
$454$	−5.03136	+	7.31426i	−0.236134	+	0.343275i
$455$		0			0
$456$	−9.92493	+	6.06523i	−0.464777	+	0.284031i
$457$	16.7340			0.782785			0.391392	−	0.920224i	$-0.371994\pi$
$457$	16.7340			0.782785			0.391392	+	0.920224i	$0.371994\pi$
$458$	−6.06493	+	8.81679i	−0.283396	+	0.411982i
$459$	5.63962	−	5.63962i	0.263235	−	0.263235i
$460$		0			0
$461$	11.8377	+	11.8377i	0.551335	+	0.551335i	0.926826	−	0.375491i	$-0.122526\pi$
$461$	11.8377	+	11.8377i	0.551335	+	0.551335i	−0.375491	+	0.926826i	$0.622526\pi$
$462$	−4.56764	−	24.7013i	−0.212506	−	1.14921i
$463$		−	32.2711i		−	1.49976i	−0.661572	−	0.749882i	$-0.730110\pi$
$463$		−	32.2711i		−	1.49976i	0.661572	−	0.749882i	$-0.269890\pi$
$464$	−23.9885	−	1.29661i	−1.11364	−	0.0601938i
$465$		0			0
$466$	16.6000	−	3.06960i	0.768982	−	0.142197i
$467$	1.22565	−	1.22565i	0.0567163	−	0.0567163i	−0.678180	−	0.734896i	$-0.737231\pi$
$467$	1.22565	−	1.22565i	0.0567163	−	0.0567163i	0.734896	+	0.678180i	$0.237231\pi$
$468$	−20.1723	−	9.00109i	−0.932464	−	0.416076i
$469$	−23.8558	+	23.8558i	−1.10156	+	1.10156i
$470$		0			0
$471$		−	34.0734i		−	1.57002i
$472$	2.92180	−	12.1046i	0.134487	−	0.557159i
$473$	11.1791			0.514016
$474$	−0.214757	+	0.312200i	−0.00986413	+	0.0143398i
$475$		0			0
$476$	15.1071	+	39.4520i	0.692433	+	1.80828i
$477$	6.92328	−	6.92328i	0.316995	−	0.316995i
$478$	−23.3238	+	4.31292i	−1.06680	+	0.197268i
$479$	−28.8399			−1.31773			−0.658865	−	0.752261i	$-0.728963\pi$
$479$	−28.8399			−1.31773			−0.658865	+	0.752261i	$0.728963\pi$
$480$		0			0
$481$	7.26282			0.331156
$482$	30.6349	−	5.66486i	1.39538	−	0.258027i
$483$	22.1711	−	22.1711i	1.00882	−	1.00882i
$484$	3.00009	+	7.83468i	0.136368	+	0.356122i
$485$		0			0
$486$	−16.5649	+	24.0809i	−0.751399	+	1.09233i
$487$	−32.1668			−1.45762			−0.728808	−	0.684718i	$-0.759925\pi$
$487$	−32.1668			−1.45762			−0.728808	+	0.684718i	$0.759925\pi$
$488$	−9.13611	−	2.20527i	−0.413572	−	0.0998278i
$489$			26.7054i			1.20766i
$490$		0			0
$491$	−5.43607	+	5.43607i	−0.245326	+	0.245326i	−0.819049	−	0.573723i	$-0.805499\pi$
$491$	−5.43607	+	5.43607i	−0.245326	+	0.245326i	0.573723	+	0.819049i	$0.305499\pi$
$492$	−19.8307	−	8.84870i	−0.894039	−	0.398930i
$493$	−30.9963	+	30.9963i	−1.39600	+	1.39600i
$494$	−10.5878	+	1.95784i	−0.476366	+	0.0880873i
$495$		0			0
$496$	6.14144	−	5.51157i	0.275759	−	0.247477i
$497$		−	9.43268i		−	0.423114i
$498$	−8.35783	−	45.1982i	−0.374524	−	2.02538i
$499$	17.1282	+	17.1282i	0.766762	+	0.766762i	0.977535	−	0.210773i	$-0.0675981\pi$
$499$	17.1282	+	17.1282i	0.766762	+	0.766762i	−0.210773	+	0.977535i	$0.567598\pi$
$500$		0			0
$501$	11.3564	−	11.3564i	0.507365	−	0.507365i
$502$	−7.52551	+	10.9401i	−0.335880	+	0.488280i
$503$	−23.5180			−1.04862			−0.524308	−	0.851529i	$-0.675676\pi$
$503$	−23.5180			−1.04862			−0.524308	+	0.851529i	$0.675676\pi$
$504$	−10.8226	−	17.7097i	−0.482078	−	0.788855i
$505$		0			0
$506$	9.62821	−	13.9968i	0.428026	−	0.622235i
$507$	−9.93890	−	9.93890i	−0.441402	−	0.441402i
$508$	−4.47259	−	11.6801i	−0.198439	−	0.518221i
$509$	−20.3147	−	20.3147i	−0.900434	−	0.900434i	0.0950391	−	0.995474i	$-0.469702\pi$
$509$	−20.3147	−	20.3147i	−0.900434	−	0.900434i	−0.995474	+	0.0950391i	$0.969702\pi$
$510$		0			0
$511$	−36.7186			−1.62434
$512$	1.69212	+	22.5641i	0.0747820	+	0.997200i
$513$			1.90997i			0.0843271i
$514$	−1.86645	−	10.0935i	−0.0823256	−	0.445207i
$515$		0			0
$516$	18.8314	−	7.21100i	0.829007	−	0.317447i
$517$	21.6025	+	21.6025i	0.950077	+	0.950077i
$518$	5.62229	+	3.86748i	0.247029	+	0.169928i
$519$			16.9328i			0.743268i
$520$		0			0
$521$			35.5082i			1.55564i	0.628487	+	0.777820i	$0.283675\pi$
$521$			35.5082i			1.55564i	−0.628487	+	0.777820i	$0.716325\pi$
$522$	12.2054	−	17.7434i	0.534215	−	0.776606i
$523$	0.677766	+	0.677766i	0.0296366	+	0.0296366i	0.721770	−	0.692133i	$-0.243329\pi$
$523$	0.677766	+	0.677766i	0.0296366	+	0.0296366i	−0.692133	+	0.721770i	$0.743329\pi$
$524$	−13.3407	−	5.95276i	−0.582791	−	0.260048i
$525$		0			0
$526$	12.8972	−	2.38489i	0.562345	−	0.103986i
$527$		−	15.0572i		−	0.655904i
$528$	−16.3977	−	18.2716i	−0.713618	−	0.795170i
$529$	−1.79485			−0.0780371
$530$		0			0
$531$	7.89332	+	7.89332i	0.342541	+	0.342541i
$532$	−9.23874	−	4.12243i	−0.400550	−	0.178730i
$533$	−14.2142	−	14.2142i	−0.615686	−	0.615686i
$534$	10.2690	+	7.06386i	0.444382	+	0.305683i
$535$		0			0
$536$	−7.73667	+	32.0519i	−0.334173	+	1.38443i
$537$	−5.45007			−0.235188
$538$	−22.1124	−	15.2108i	−0.953334	−	0.655784i
$539$	2.53704	−	2.53704i	0.109278	−	0.109278i
$540$		0			0
$541$	5.37099	+	5.37099i	0.230917	+	0.230917i	0.813075	−	0.582158i	$-0.197792\pi$
$541$	5.37099	+	5.37099i	0.230917	+	0.230917i	−0.582158	+	0.813075i	$0.697792\pi$
$542$	−31.4283	+	5.81157i	−1.34996	+	0.249628i
$543$			55.8181i			2.39539i
$544$	32.7044	+	25.2016i	1.40219	+	1.08051i
$545$		0			0
$546$	−7.62693	−	41.2456i	−0.326403	−	1.76515i
$547$	8.86782	−	8.86782i	0.379161	−	0.379161i	−0.491639	−	0.870799i	$-0.663602\pi$
$547$	8.86782	−	8.86782i	0.379161	−	0.379161i	0.870799	+	0.491639i	$0.163602\pi$
$548$	35.3767	−	13.5466i	1.51122	−	0.578682i
$549$	5.95760	−	5.95760i	0.254264	−	0.254264i
$550$		0			0
$551$		−	10.4975i		−	0.447209i
$552$	7.19034	−	29.7885i	0.306041	−	1.26788i
$553$	−0.329585			−0.0140154
$554$	26.6966	+	18.3641i	1.13423	+	0.780218i
$555$		0			0
$556$	−3.21625	+	7.20791i	−0.136399	+	0.305684i
$557$	−22.8089	+	22.8089i	−0.966446	+	0.966446i	−0.999455	−	0.0330091i	$-0.989491\pi$
$557$	−22.8089	+	22.8089i	−0.966446	+	0.966446i	0.0330091	+	0.999455i	$0.489491\pi$
$558$	1.34510	+	7.27417i	0.0569428	+	0.307940i
$559$	18.6666			0.789513
$560$		0			0
$561$	−44.7973			−1.89135
$562$	−2.27525	−	12.3043i	−0.0959755	−	0.519024i
$563$	−20.9711	+	20.9711i	−0.883826	+	0.883826i	−0.993921	−	0.110095i	$-0.964884\pi$
$563$	−20.9711	+	20.9711i	−0.883826	+	0.883826i	0.110095	+	0.993921i	$0.464884\pi$
$564$	50.3244	+	22.4553i	2.11904	+	0.945538i
$565$		0			0
$566$	33.4603	+	23.0168i	1.40644	+	0.967469i
$567$	−29.4543			−1.23696
$568$	−4.80719	−	7.86630i	−0.201705	−	0.330063i
$569$		−	8.05295i		−	0.337597i	−0.985651	−	0.168799i	$-0.946011\pi$
$569$		−	8.05295i		−	0.337597i	0.985651	−	0.168799i	$-0.0539888\pi$
$570$		0			0
$571$	−22.5040	+	22.5040i	−0.941762	+	0.941762i	−0.998395	−	0.0566333i	$-0.981963\pi$
$571$	−22.5040	+	22.5040i	−0.941762	+	0.941762i	0.0566333	+	0.998395i	$0.481963\pi$
$572$	−8.12708	−	21.2237i	−0.339810	−	0.887409i
$573$	9.74599	−	9.74599i	0.407144	−	0.407144i
$574$	−3.43436	−	18.5726i	−0.143347	−	0.775206i
$575$		0			0
$576$	−18.0509	−	9.25334i	−0.752119	−	0.385556i
$577$		−	15.9819i		−	0.665334i	−0.943044	−	0.332667i	$-0.892051\pi$
$577$		−	15.9819i		−	0.665334i	0.943044	−	0.332667i	$-0.107949\pi$
$578$	50.4410	−	9.32730i	2.09807	−	0.387965i
$579$	−0.0401200	−	0.0401200i	−0.00166733	−	0.00166733i
$580$		0			0
$581$	28.2692	−	28.2692i	1.17280	−	1.17280i
$582$	−38.3388	−	26.3727i	−1.58919	−	1.09318i
$583$	10.0734			0.417199
$584$	−30.6212	+	18.7129i	−1.26711	+	0.774347i
$585$		0			0
$586$	11.8136	+	8.12638i	0.488015	+	0.335698i
$587$	5.25752	+	5.25752i	0.217001	+	0.217001i	0.807233	−	0.590232i	$-0.200964\pi$
$587$	5.25752	+	5.25752i	0.217001	+	0.217001i	−0.590232	+	0.807233i	$0.700964\pi$
$588$	2.63719	−	5.91018i	0.108756	−	0.243732i
$589$	2.54971	+	2.54971i	0.105059	+	0.105059i
$590$		0			0
$591$	−49.6057			−2.04050
$592$	6.65965	+	0.359964i	0.273710	+	0.0147944i
$593$			3.96571i			0.162852i	0.996679	+	0.0814260i	$0.0259474\pi$
$593$			3.96571i			0.162852i	−0.996679	+	0.0814260i	$0.974053\pi$
$594$	−3.96418	+	0.733038i	−0.162652	+	0.0300769i
$595$		0			0
$596$	1.84835	−	4.14233i	0.0757115	−	0.169676i
$597$	22.7132	+	22.7132i	0.929589	+	0.929589i
$598$	16.0769	−	23.3716i	0.657435	−	0.955734i
$599$			8.31600i			0.339783i	0.985463	+	0.169891i	$0.0543417\pi$
$599$			8.31600i			0.339783i	−0.985463	+	0.169891i	$0.945658\pi$
$600$		0			0
$601$			46.0550i			1.87862i	0.343068	+	0.939310i	$0.388534\pi$
$601$			46.0550i			1.87862i	−0.343068	+	0.939310i	$0.611466\pi$
$602$	14.4502	+	9.94004i	0.588944	+	0.405126i
$603$	−20.9009	−	20.9009i	−0.851149	−	0.851149i
$604$	−1.81486	−	4.73948i	−0.0738456	−	0.192847i
$605$		0			0
$606$	3.01374	+	16.2980i	0.122425	+	0.662060i
$607$			5.05760i			0.205282i	0.994718	+	0.102641i	$0.0327292\pi$
$607$			5.05760i			0.205282i	−0.994718	+	0.102641i	$0.967271\pi$
$608$	−9.80549	+	1.27048i	−0.397665	+	0.0515249i
$609$	40.8940			1.65711
$610$		0			0
$611$	36.0713	+	36.0713i	1.45929	+	1.45929i
$612$	−34.5652	+	13.2359i	−1.39722	+	0.535028i
$613$	31.2000	+	31.2000i	1.26016	+	1.26016i	0.951016	+	0.309141i	$0.100042\pi$
$613$	31.2000	+	31.2000i	1.26016	+	1.26016i	0.309141	+	0.951016i	$0.399958\pi$
$614$	20.8911	−	30.3701i	0.843096	−	1.22564i
$615$		0			0
$616$	5.01041	−	20.7574i	0.201875	−	0.836339i
$617$	−30.7412			−1.23759			−0.618796	−	0.785551i	$-0.712379\pi$
$617$	−30.7412			−1.23759			−0.618796	+	0.785551i	$0.712379\pi$
$618$	−0.283269	+	0.411798i	−0.0113948	+	0.0165649i
$619$	16.8766	−	16.8766i	0.678329	−	0.678329i	−0.281293	−	0.959622i	$-0.590763\pi$
$619$	16.8766	−	16.8766i	0.678329	−	0.678329i	0.959622	+	0.281293i	$0.0907632\pi$
$620$		0			0
$621$	−3.55813	−	3.55813i	−0.142783	−	0.142783i
$622$	1.82309	+	9.85908i	0.0730994	+	0.395313i
$623$			10.8408i			0.434328i
$624$	−27.3804	−	30.5095i	−1.09609	−	1.22136i
$625$		0			0
$626$	−30.6603	+	5.66956i	−1.22543	+	0.226601i
$627$	7.58574	−	7.58574i	0.302945	−	0.302945i
$628$	11.8026	−	26.4506i	0.470974	−	1.05550i
$629$	8.60515	−	8.60515i	0.343110	−	0.343110i
$630$		0			0
$631$		−	30.7318i		−	1.22342i	−0.791084	−	0.611708i	$-0.790483\pi$
$631$		−	30.7318i		−	1.22342i	0.791084	−	0.611708i	$-0.209517\pi$
$632$	−0.274855	+	0.167967i	−0.0109331	+	0.00668136i
$633$	−8.15539			−0.324147
$634$	7.02389	−	10.2109i	0.278954	−	0.405525i
$635$		0			0
$636$	16.9689	−	6.49779i	0.672860	−	0.257654i
$637$	4.23628	−	4.23628i	0.167848	−	0.167848i
$638$	21.7878	−	4.02890i	0.862588	−	0.159506i
$639$	8.26430			0.326931
$640$		0			0
$641$	22.1658			0.875496			0.437748	−	0.899098i	$-0.355776\pi$
$641$	22.1658			0.875496			0.437748	+	0.899098i	$0.355776\pi$
$642$	−12.7274	+	2.35349i	−0.502310	+	0.0928848i
$643$	−0.975773	+	0.975773i	−0.0384807	+	0.0384807i	−0.726085	−	0.687605i	$-0.758662\pi$
$643$	−0.975773	+	0.975773i	−0.0384807	+	0.0384807i	0.687605	+	0.726085i	$0.258662\pi$
$644$	24.8909	−	9.53133i	0.980839	−	0.375587i
$645$		0			0
$646$	−10.2249	+	14.8643i	−0.402294	+	0.584828i
$647$	23.2610			0.914484			0.457242	−	0.889342i	$-0.348837\pi$
$647$	23.2610			0.914484			0.457242	+	0.889342i	$0.348837\pi$
$648$	−24.5632	+	15.0108i	−0.964932	+	0.589681i
$649$			11.4848i			0.450819i
$650$		0			0
$651$	−9.93263	+	9.93263i	−0.389290	+	0.389290i
$652$	−9.25038	+	20.7310i	−0.362273	+	0.811887i
$653$	23.9372	−	23.9372i	0.936735	−	0.936735i	−0.0613792	−	0.998115i	$-0.519550\pi$
$653$	23.9372	−	23.9372i	0.936735	−	0.936735i	0.998115	+	0.0613792i	$0.0195499\pi$
$654$	−31.9631	+	5.91046i	−1.24985	+	0.231117i
$655$		0			0
$656$	−12.3292	−	13.7382i	−0.481376	−	0.536387i
$657$		−	32.1704i		−	1.25509i
$658$	8.71535	+	47.1316i	0.339760	+	1.83738i
$659$	14.1064	+	14.1064i	0.549508	+	0.549508i	0.926299	−	0.376790i	$-0.122972\pi$
$659$	14.1064	+	14.1064i	0.549508	+	0.549508i	−0.376790	+	0.926299i	$0.622972\pi$
$660$		0			0
$661$	−3.04121	+	3.04121i	−0.118289	+	0.118289i	−0.763774	−	0.645484i	$-0.776656\pi$
$661$	−3.04121	+	3.04121i	−0.118289	+	0.118289i	0.645484	+	0.763774i	$0.276656\pi$
$662$	21.1026	−	30.6775i	0.820175	−	1.19232i
$663$	−74.8014			−2.90505
$664$	9.16800	−	37.9817i	0.355787	−	1.47398i
$665$		0			0
$666$	−3.38844	+	4.92588i	−0.131299	+	0.190874i
$667$	19.5561	+	19.5561i	0.757215	+	0.757215i
$668$	12.7495	−	4.88207i	0.493291	−	0.188893i
$669$	23.2052	+	23.2052i	0.897166	+	0.897166i
$670$		0			0
$671$	8.66835			0.334638
$672$	−4.94928	−	38.1981i	−0.190923	−	1.47353i
$673$		−	25.3628i		−	0.977662i	−0.872378	−	0.488831i	$-0.837423\pi$
$673$		−	25.3628i		−	0.977662i	0.872378	−	0.488831i	$-0.162577\pi$
$674$	3.66637	+	19.8273i	0.141223	+	0.763719i
$675$		0			0
$676$	−4.27271	−	11.1581i	−0.164335	−	0.429159i
$677$	−9.36526	−	9.36526i	−0.359936	−	0.359936i	0.503853	−	0.863789i	$-0.331915\pi$
$677$	−9.36526	−	9.36526i	−0.359936	−	0.359936i	−0.863789	+	0.503853i	$0.831915\pi$
$678$	9.58126	+	6.59080i	0.367966	+	0.253118i
$679$		−	40.4737i		−	1.55324i
$680$		0			0
$681$		−	14.7695i		−	0.565967i
$682$	−4.31342	+	6.27056i	−0.165169	+	0.240112i
$683$	4.20530	+	4.20530i	0.160911	+	0.160911i	0.782970	−	0.622059i	$-0.213704\pi$
$683$	4.20530	+	4.20530i	0.160911	+	0.160911i	−0.622059	+	0.782970i	$0.713704\pi$
$684$	3.61180	−	8.09438i	0.138101	−	0.309496i
$685$		0			0
$686$	−22.6365	+	4.18584i	−0.864267	+	0.159816i
$687$		−	17.8035i		−	0.679245i
$688$	17.1163	+	0.925163i	0.652554	+	0.0352715i
$689$	16.8204			0.640804
$690$		0			0
$691$	5.79295	+	5.79295i	0.220374	+	0.220374i	0.808656	−	0.588282i	$-0.200195\pi$
$691$	5.79295	+	5.79295i	0.220374	+	0.220374i	−0.588282	+	0.808656i	$0.700195\pi$
$692$	−5.86530	+	13.1447i	−0.222965	+	0.499686i
$693$	13.5358	+	13.5358i	0.514181	+	0.514181i
$694$	−38.7881	−	26.6817i	−1.47238	−	1.01282i
$695$		0			0
$696$	34.1032	−	20.8408i	1.29268	−	0.789969i
$697$	−33.6826			−1.27582
$698$	−2.58179	−	1.77598i	−0.0977223	−	0.0672217i
$699$	−19.8592	+	19.8592i	−0.751142	+	0.751142i
$700$		0			0
$701$	−0.258991	−	0.258991i	−0.00978196	−	0.00978196i	0.702199	−	0.711981i	$-0.252202\pi$
$701$	−0.258991	−	0.258991i	−0.00978196	−	0.00978196i	−0.711981	+	0.702199i	$0.752202\pi$
$702$	−6.61929	+	1.22401i	−0.249829	+	0.0461972i
$703$			2.91430i			0.109915i
$704$	−6.40023	−	19.8639i	−0.241218	−	0.748649i
$705$		0			0
$706$	−2.42924	−	13.1370i	−0.0914257	−	0.494419i
$707$	−10.1936	+	10.1936i	−0.383368	+	0.383368i
$708$	7.40821	+	19.3464i	0.278418	+	0.727083i
$709$	0.751674	−	0.751674i	0.0282297	−	0.0282297i	−0.692851	−	0.721081i	$-0.743646\pi$
$709$	0.751674	−	0.751674i	0.0282297	−	0.0282297i	0.721081	+	0.692851i	$0.243646\pi$
$710$		0			0
$711$		−	0.288761i		−	0.0108294i
$712$	5.52481	+	9.04060i	0.207051	+	0.338811i
$713$	−9.49986			−0.355773
$714$	−57.9052	−	39.8321i	−2.16705	−	1.49068i
$715$		0			0
$716$	−4.23081	−	1.88783i	−0.158113	−	0.0705516i
$717$	27.9029	−	27.9029i	1.04205	−	1.04205i
$718$	4.64034	+	25.0944i	0.173176	+	0.936515i
$719$	−39.6557			−1.47891			−0.739455	−	0.673206i	$-0.764917\pi$
$719$	−39.6557			−1.47891			−0.739455	+	0.673206i	$0.764917\pi$
$720$		0			0
$721$	−0.434730			−0.0161902
$722$	4.10025	+	22.1736i	0.152595	+	0.825218i
$723$	−36.6495	+	36.6495i	−1.36301	+	1.36301i
$724$	−19.3347	+	43.3308i	−0.718567	+	1.61037i
$725$		0			0
$726$	−11.4993	−	7.91016i	−0.426778	−	0.293574i
$727$	−22.2952			−0.826881			−0.413441	−	0.910531i	$-0.635673\pi$
$727$	−22.2952			−0.826881			−0.413441	+	0.910531i	$0.635673\pi$
$728$	8.36625	−	34.6602i	0.310074	−	1.28459i
$729$		−	18.0930i		−	0.670112i
$730$		0			0
$731$	22.1166	−	22.1166i	0.818011	−	0.818011i
$732$	14.6020	−	5.59145i	0.539705	−	0.206666i
$733$	−28.2309	+	28.2309i	−1.04273	+	1.04273i	−0.0436851	+	0.999045i	$0.513910\pi$
$733$	−28.2309	+	28.2309i	−1.04273	+	1.04273i	−0.999045	+	0.0436851i	$0.986090\pi$
$734$	7.49154	+	40.5134i	0.276518	+	1.49538i
$735$		0			0
$736$	15.9001	−	20.6337i	0.586086	−	0.760570i
$737$		−	30.4109i		−	1.12020i
$738$	16.2721	−	3.00896i	0.598985	−	0.110761i
$739$	5.45140	+	5.45140i	0.200533	+	0.200533i	0.800228	−	0.599695i	$-0.204712\pi$
$739$	5.45140	+	5.45140i	0.200533	+	0.200533i	−0.599695	+	0.800228i	$0.704712\pi$
$740$		0			0
$741$	12.6665	−	12.6665i	0.465314	−	0.465314i
$742$	13.0210	+	8.95691i	0.478014	+	0.328819i
$743$	52.5667			1.92849			0.964243	−	0.265020i	$-0.0853786\pi$
$743$	52.5667			1.92849			0.964243	+	0.265020i	$0.0853786\pi$
$744$	−3.22126	+	13.3452i	−0.118097	+	0.489259i
$745$		0			0
$746$	−5.52994	−	3.80396i	−0.202466	−	0.139273i
$747$	24.7676	+	24.7676i	0.906200	+	0.906200i
$748$	−34.7755	−	15.5172i	−1.27152	−	0.567365i
$749$	−7.96035	−	7.96035i	−0.290865	−	0.290865i
$750$		0			0
$751$	31.0189			1.13190			0.565948	−	0.824441i	$-0.308510\pi$
$751$	31.0189			1.13190			0.565948	+	0.824441i	$0.308510\pi$
$752$	31.2878	+	34.8634i	1.14095	+	1.27134i
$753$		−	22.0910i		−	0.805040i
$754$	36.3807	−	6.72735i	1.32491	−	0.244996i
$755$		0			0
$756$	−5.77590	−	2.57727i	−0.210068	−	0.0937345i
$757$	2.47389	+	2.47389i	0.0899152	+	0.0899152i	0.750634	−	0.660719i	$-0.229748\pi$
$757$	2.47389	+	2.47389i	0.0899152	+	0.0899152i	−0.660719	+	0.750634i	$0.729748\pi$
$758$	13.2059	−	19.1979i	0.479662	−	0.697300i
$759$			28.2634i			1.02590i
$760$		0			0
$761$			2.48375i			0.0900358i	0.998986	+	0.0450179i	$0.0143345\pi$
$761$			2.48375i			0.0900358i	−0.998986	+	0.0450179i	$0.985666\pi$
$762$	17.1433	+	11.7926i	0.621037	+	0.427202i
$763$	−19.9913	−	19.9913i	−0.723733	−	0.723733i
$764$	10.9415	−	4.18978i	0.395851	−	0.151581i
$765$		0			0
$766$	5.60701	+	30.3221i	0.202590	+	1.09558i
$767$			19.1771i			0.692444i
$768$	−23.5944	−	29.3327i	−0.851388	−	1.05845i
$769$	−43.4690			−1.56753			−0.783767	−	0.621055i	$-0.786704\pi$
$769$	−43.4690			−1.56753			−0.783767	+	0.621055i	$0.786704\pi$
$770$		0			0
$771$	12.0752	+	12.0752i	0.434879	+	0.434879i
$772$	−0.0172475	−	0.0450416i	−0.000620752	−	0.00162108i
$773$	0.297026	+	0.297026i	0.0106833	+	0.0106833i	0.712428	−	0.701745i	$-0.247595\pi$
$773$	0.297026	+	0.297026i	0.0106833	+	0.0106833i	−0.701745	+	0.712428i	$0.747595\pi$
$774$	−8.70881	+	12.6603i	−0.313032	+	0.455064i
$775$		0			0
$776$	−20.6267	−	33.7527i	−0.740454	−	1.21165i
$777$	−11.3529			−0.407283
$778$	−13.4771	+	19.5920i	−0.483176	+	0.702409i
$779$	5.70363	−	5.70363i	0.204354	−	0.204354i
$780$		0			0
$781$	6.01231	+	6.01231i	0.215137	+	0.215137i
$782$	−8.64283	−	46.7394i	−0.309067	−	1.67140i
$783$		−	6.56286i		−	0.234537i
$784$	4.09442	−	3.67450i	0.146229	−	0.131232i
$785$		0			0
$786$	23.8985	−	4.41920i	0.852433	−	0.157628i
$787$	−23.6931	+	23.6931i	−0.844567	+	0.844567i	−0.989449	−	0.144882i	$-0.953720\pi$
$787$	−23.6931	+	23.6931i	−0.844567	+	0.844567i	0.144882	+	0.989449i	$0.453720\pi$
$788$	−38.5081	−	17.1827i	−1.37179	−	0.612110i
$789$	−15.4293	+	15.4293i	−0.549299	+	0.549299i
$790$		0			0
$791$			10.1148i			0.359641i
$792$	18.1863	+	4.38979i	0.646221	+	0.155984i
$793$	14.4742			0.513993
$794$	10.4723	−	15.2240i	0.371650	−	0.540279i
$795$		0			0
$796$	9.76435	+	25.4994i	0.346088	+	0.903804i
$797$	38.2292	−	38.2292i	1.35415	−	1.35415i	0.473186	−	0.880963i	$-0.343104\pi$
$797$	38.2292	−	38.2292i	1.35415	−	1.35415i	0.880963	−	0.473186i	$-0.156896\pi$
$798$	16.5503	−	3.06040i	0.585874	−	0.108337i
$799$	85.4762			3.02393
$800$		0			0
$801$	−9.49801			−0.335596
$802$	20.1287	−	3.72210i	0.710768	−	0.131432i
$803$	23.4041	−	23.4041i	0.825913	−	0.825913i
$804$	−19.6163	−	51.2277i	−0.691814	−	1.80666i
$805$		0			0
$806$	−7.20243	+	10.4704i	−0.253695	+	0.368804i
$807$	44.6509			1.57179
$808$	−3.30588	+	13.6958i	−0.116300	+	0.481816i
$809$			53.8310i			1.89260i	0.323296	+	0.946298i	$0.395209\pi$
$809$			53.8310i			1.89260i	−0.323296	+	0.946298i	$0.604791\pi$
$810$		0			0
$811$	27.0549	−	27.0549i	0.950025	−	0.950025i	−0.0487847	−	0.998809i	$-0.515535\pi$
$811$	27.0549	−	27.0549i	0.950025	−	0.950025i	0.998809	+	0.0487847i	$0.0155348\pi$
$812$	31.7454	+	14.1651i	1.11404	+	0.497098i
$813$	37.5986	−	37.5986i	1.31864	−	1.31864i
$814$	−6.04870	+	1.11850i	−0.212007	+	0.0392033i
$815$		0			0
$816$	−68.5892	−	3.70735i	−2.40110	−	0.129783i
$817$			7.49020i			0.262049i
$818$	2.45351	+	13.2683i	0.0857851	+	0.463916i
$819$	22.6017	+	22.6017i	0.789766	+	0.789766i
$820$		0			0
$821$	−24.2170	+	24.2170i	−0.845180	+	0.845180i	−0.989527	−	0.144347i	$-0.953892\pi$
$821$	−24.2170	+	24.2170i	−0.845180	+	0.845180i	0.144347	+	0.989527i	$0.453892\pi$
$822$	−35.7175	+	51.9238i	−1.24579	+	1.81105i
$823$	−41.3013			−1.43967			−0.719836	−	0.694144i	$-0.755783\pi$
$823$	−41.3013			−1.43967			−0.719836	+	0.694144i	$0.755783\pi$
$824$	−0.362539	+	0.221552i	−0.0126296	+	0.00771812i
$825$		0			0
$826$	−10.2119	+	14.8453i	−0.355317	+	0.516535i
$827$	−15.7264	−	15.7264i	−0.546862	−	0.546862i	0.378670	−	0.925532i	$-0.376382\pi$
$827$	−15.7264	−	15.7264i	−0.546862	−	0.546862i	−0.925532	+	0.378670i	$0.876382\pi$
$828$	8.35072	+	21.8078i	0.290208	+	0.757873i
$829$	20.7323	+	20.7323i	0.720061	+	0.720061i	0.968618	−	0.248556i	$-0.0799560\pi$
$829$	20.7323	+	20.7323i	0.720061	+	0.720061i	−0.248556	+	0.968618i	$0.579956\pi$
$830$		0			0
$831$	−53.9075			−1.87003
$832$	−10.6869	−	33.1682i	−0.370503	−	1.14990i
$833$		−	10.0385i		−	0.347813i
$834$	−2.38767	−	12.9123i	−0.0826784	−	0.447115i
$835$		0			0
$836$	8.51629	−	3.26109i	0.294542	−	0.112787i
$837$	1.59404	+	1.59404i	0.0550980	+	0.0550980i
$838$	1.38030	+	0.949485i	0.0476816	+	0.0327994i
$839$			43.6919i			1.50841i	0.656638	+	0.754206i	$0.271978\pi$
$839$			43.6919i			1.50841i	−0.656638	+	0.754206i	$0.728022\pi$
$840$		0			0
$841$			7.07060i			0.243814i
$842$	−20.3664	+	29.6073i	−0.701872	+	1.02033i
$843$	14.7200	+	14.7200i	0.506983	+	0.506983i
$844$	−6.33090	−	2.82492i	−0.217919	−	0.0972377i
$845$		0			0
$846$	−41.2936	+	7.63582i	−1.41970	+	0.262525i
$847$		−	12.1396i		−	0.417122i
$848$	15.4234	+	0.833659i	0.529643	+	0.0286280i
$849$	−67.5654			−2.31884
$850$		0			0
$851$	−5.42913	−	5.42913i	−0.186108	−	0.186108i
$852$	14.0060	+	6.24965i	0.479839	+	0.214109i
$853$	−35.0610	−	35.0610i	−1.20046	−	1.20046i	−0.974025	−	0.226439i	$-0.927292\pi$
$853$	−35.0610	−	35.0610i	−1.20046	−	1.20046i	−0.226439	−	0.974025i	$-0.572708\pi$
$854$	11.2047	+	7.70756i	0.383418	+	0.263747i
$855$		0			0
$856$	−10.6953	−	2.58162i	−0.365558	−	0.0882381i
$857$	45.3397			1.54878			0.774388	−	0.632711i	$-0.218058\pi$
$857$	45.3397			1.54878			0.774388	+	0.632711i	$0.218058\pi$
$858$	31.1509	+	21.4282i	1.06347	+	0.731547i
$859$	−32.1229	+	32.1229i	−1.09602	+	1.09602i	−0.101147	+	0.994871i	$0.532251\pi$
$859$	−32.1229	+	32.1229i	−1.09602	+	1.09602i	−0.994871	+	0.101147i	$0.967749\pi$
$860$		0			0
$861$	22.2190	+	22.2190i	0.757221	+	0.757221i
$862$	5.36054	−	0.991245i	0.182581	−	0.0337619i
$863$			36.9142i			1.25657i	0.777981	+	0.628287i	$0.216244\pi$
$863$			36.9142i			1.25657i	−0.777981	+	0.628287i	$0.783756\pi$
$864$	−6.13022	+	0.794285i	−0.208554	+	0.0270221i
$865$		0			0
$866$	6.57406	+	35.5517i	0.223396	+	1.20810i
$867$	−60.3441	+	60.3441i	−2.04939	+	2.04939i
$868$	−11.1511	+	4.27002i	−0.378492	+	0.144934i
$869$	0.210075	−	0.210075i	0.00712630	−	0.00712630i
$870$		0			0
$871$		−	50.7793i		−	1.72059i
$872$	−26.8597	−	6.48338i	−0.909585	−	0.219555i
$873$	35.4604			1.20015
$874$	9.37813	+	6.45107i	0.317220	+	0.218211i
$875$		0			0
$876$	24.3280	−	54.5213i	0.821967	−	1.84210i
$877$	−15.7178	+	15.7178i	−0.530753	+	0.530753i	−0.920796	−	0.390044i	$-0.872460\pi$
$877$	−15.7178	+	15.7178i	−0.530753	+	0.530753i	0.390044	+	0.920796i	$0.372460\pi$
$878$	7.74821	+	41.9014i	0.261490	+	1.41410i
$879$	−23.8548			−0.804603
$880$		0			0
$881$	1.16748			0.0393335			0.0196667	−	0.999807i	$-0.493739\pi$
$881$	1.16748			0.0393335			0.0196667	+	0.999807i	$0.493739\pi$
$882$	0.896765	+	4.84960i	0.0301956	+	0.163294i
$883$	−32.2410	+	32.2410i	−1.08500	+	1.08500i	−0.0889621	+	0.996035i	$0.528355\pi$
$883$	−32.2410	+	32.2410i	−1.08500	+	1.08500i	−0.996035	+	0.0889621i	$0.971645\pi$
$884$	−58.0672	−	25.9102i	−1.95301	−	0.871455i
$885$		0			0
$886$	−33.2235	−	22.8539i	−1.11616	−	0.767792i
$887$	42.7282			1.43467			0.717336	−	0.696728i	$-0.245361\pi$
$887$	42.7282			1.43467			0.717336	+	0.696728i	$0.245361\pi$
$888$	−9.46766	+	5.78579i	−0.317714	+	0.194159i
$889$			18.0980i			0.606987i
$890$		0			0
$891$	18.7739	−	18.7739i	0.628949	−	0.628949i
$892$	9.97588	+	26.0518i	0.334017	+	0.872280i
$893$	−14.4741	+	14.4741i	−0.484356	+	0.484356i
$894$	1.37218	+	7.42058i	0.0458925	+	0.248181i
$895$		0			0
$896$	9.38928	−	31.3670i	0.313674	−	1.04790i
$897$			47.1935i			1.57574i
$898$	−50.8732	+	9.40724i	−1.69766	+	0.313924i
$899$	−8.76109	−	8.76109i	−0.292199	−	0.292199i
$900$		0			0
$901$	19.9291	−	19.9291i	0.663935	−	0.663935i
$902$	14.0270	+	9.64899i	0.467050	+	0.321276i
$903$	−29.1788			−0.971008
$904$	5.15482	+	8.43516i	0.171447	+	0.280549i
$905$		0			0
$906$	6.95632	+	4.78514i	0.231108	+	0.158976i
$907$	−1.23335	−	1.23335i	−0.0409528	−	0.0409528i	0.686334	−	0.727287i	$-0.259219\pi$
$907$	−1.23335	−	1.23335i	−0.0409528	−	0.0409528i	−0.727287	+	0.686334i	$0.759219\pi$
$908$	5.11594	−	11.4653i	0.169779	−	0.380489i
$909$	−8.93093	−	8.93093i	−0.296220	−	0.296220i
$910$		0			0
$911$	23.9284			0.792785			0.396392	−	0.918081i	$-0.370262\pi$
$911$	23.9284			0.792785			0.396392	+	0.918081i	$0.370262\pi$
$912$	12.2423	−	10.9867i	0.405383	−	0.363807i
$913$			36.0371i			1.19265i
$914$	−23.2710	+	4.30316i	−0.769735	+	0.142336i
$915$		0			0
$916$	6.16689	−	13.8206i	0.203760	−	0.456644i
$917$	14.9473	+	14.9473i	0.493605	+	0.493605i
$918$	−6.39245	+	9.29291i	−0.210982	+	0.306712i
$919$		−	45.3844i		−	1.49709i	−0.663082	−	0.748546i	$-0.730752\pi$
$919$		−	45.3844i		−	1.49709i	0.663082	−	0.748546i	$-0.269248\pi$
$920$		0			0
$921$			61.3253i			2.02074i
$922$	−19.5060	−	13.4179i	−0.642395	−	0.441893i
$923$	10.0392	+	10.0392i	0.330444	+	0.330444i
$924$	12.7039	+	33.1760i	0.417927	+	1.09141i
$925$		0			0
$926$	8.29851	+	44.8774i	0.272706	+	1.47476i
$927$		−	0.380882i		−	0.0125098i
$928$	33.6927	−	4.36553i	1.10602	−	0.143305i
$929$	6.51036			0.213598			0.106799	−	0.994281i	$-0.465940\pi$
$929$	6.51036			0.213598			0.106799	+	0.994281i	$0.465940\pi$
$930$		0			0
$931$	1.69986	+	1.69986i	0.0557107	+	0.0557107i
$932$	−22.2953	+	8.53741i	−0.730307	+	0.279652i
$933$	−11.7947	−	11.7947i	−0.386142	−	0.386142i
$934$	−1.38926	+	2.01961i	−0.0454579	+	0.0660837i
$935$		0			0
$936$	30.3670	+	7.32996i	0.992575	+	0.239587i
$937$	40.2986			1.31650			0.658248	−	0.752801i	$-0.271298\pi$
$937$	40.2986			1.31650			0.658248	+	0.752801i	$0.271298\pi$
$938$	27.0402	−	39.3092i	0.882894	−	1.28349i
$939$	36.6799	−	36.6799i	1.19700	−	1.19700i
$940$		0			0
$941$	1.10649	+	1.10649i	0.0360705	+	0.0360705i	0.724912	−	0.688841i	$-0.241880\pi$
$941$	1.10649	+	1.10649i	0.0360705	+	0.0360705i	−0.688841	+	0.724912i	$0.741880\pi$
$942$	8.76198	+	47.3837i	0.285481	+	1.54385i
$943$			21.2509i			0.692025i
$944$	−0.950465	+	17.5844i	−0.0309350	+	0.572325i
$945$		0			0
$946$	−15.5461	+	2.87471i	−0.505447	+	0.0934649i
$947$	−8.83833	+	8.83833i	−0.287207	+	0.287207i	−0.835975	−	0.548768i	$-0.815097\pi$
$947$	−8.83833	+	8.83833i	−0.287207	+	0.287207i	0.548768	+	0.835975i	$0.315097\pi$
$948$	0.218368	−	0.489382i	0.00709225	−	0.0158944i
$949$	39.0796	−	39.0796i	1.26858	−	1.26858i
$950$		0			0
$951$			20.6185i			0.668600i
$952$	−31.1536	−	50.9786i	−1.00969	−	1.65223i
$953$	14.9610			0.484636			0.242318	−	0.970197i	$-0.422092\pi$
$953$	14.9610			0.484636			0.242318	+	0.970197i	$0.422092\pi$
$954$	−7.84746	+	11.4081i	−0.254071	+	0.369351i
$955$		0			0
$956$	31.3258	−	11.9954i	1.01315	−	0.387959i
$957$	−26.0654	+	26.0654i	−0.842576	+	0.842576i
$958$	40.1059	−	7.41620i	1.29576	−	0.239606i
$959$	−54.8152			−1.77008
$960$		0			0
$961$	−26.7441			−0.862712
$962$	−10.1000	+	1.86764i	−0.325636	+	0.0602150i
$963$	6.97433	−	6.97433i	0.224745	−	0.224745i
$964$	−41.1453	+	15.7555i	−1.32520	+	0.507452i
$965$		0			0
$966$	−25.1307	+	36.5333i	−0.808568	+	1.17544i
$967$	3.95287			0.127116			0.0635578	−	0.997978i	$-0.479755\pi$
$967$	3.95287			0.127116			0.0635578	+	0.997978i	$0.479755\pi$
$968$	−6.18672	−	10.1237i	−0.198849	−	0.325389i
$969$		−	30.0150i		−	0.964221i
$970$		0			0
$971$	−29.0538	+	29.0538i	−0.932380	+	0.932380i	−0.997854	−	0.0654740i	$-0.979144\pi$
$971$	−29.0538	+	29.0538i	−0.932380	+	0.932380i	0.0654740	+	0.997854i	$0.479144\pi$
$972$	16.8434	−	37.7475i	0.540251	−	1.21075i
$973$	8.07597	−	8.07597i	0.258904	−	0.258904i
$974$	44.7323	−	8.27169i	1.43332	−	0.265042i
$975$		0			0
$976$	13.2721	+	0.717377i	0.424830	+	0.0229627i
$977$		−	25.8962i		−	0.828494i	−0.910164	−	0.414247i	$-0.864045\pi$
$977$		−	25.8962i		−	0.828494i	0.910164	−	0.414247i	$-0.135955\pi$
$978$	−6.86729	−	37.1375i	−0.219592	−	1.18753i
$979$	−6.90984	−	6.90984i	−0.220839	−	0.220839i
$980$		0			0
$981$	17.5151	−	17.5151i	0.559213	−	0.559213i
$982$	6.16172	−	8.95749i	0.196628	−	0.285845i
$983$	22.0151			0.702173			0.351087	−	0.936343i	$-0.385812\pi$
$983$	22.0151			0.702173			0.351087	+	0.936343i	$0.385812\pi$
$984$	29.8528	+	7.20585i	0.951673	+	0.229714i
$985$		0			0
$986$	35.1340	−	51.0754i	1.11889	−	1.62657i
$987$	−56.3850	−	56.3850i	−1.79476	−	1.79476i
$988$	14.2203	−	5.44529i	0.452407	−	0.173238i
$989$	−13.9537	−	13.9537i	−0.443702	−	0.443702i
$990$		0			0
$991$	−54.3207			−1.72556			−0.862778	−	0.505583i	$-0.831277\pi$
$991$	−54.3207			−1.72556			−0.862778	+	0.505583i	$0.831277\pi$
$992$	−7.12321	+	9.24388i	−0.226162	+	0.293493i
$993$			61.9461i			1.96580i
$994$	2.42562	+	13.1174i	0.0769359	+	0.416060i
$995$		0			0
$996$	23.2454	+	60.7051i	0.736560	+	1.92351i
$997$	−8.14405	−	8.14405i	−0.257925	−	0.257925i	0.566285	−	0.824210i	$-0.308380\pi$
$997$	−8.14405	−	8.14405i	−0.257925	−	0.257925i	−0.824210	+	0.566285i	$0.808380\pi$
$998$	−28.2236	−	19.4146i	−0.893402	−	0.614557i
$999$			1.82197i			0.0576446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.g.349.2		16
4.3	odd	2		1600.2.q.h.849.2		16
5.2	odd	4		80.2.l.a.61.4	yes	16
5.3	odd	4		400.2.l.h.301.5		16
5.4	even	2		400.2.q.h.349.7		16
15.2	even	4		720.2.t.c.541.5		16
16.5	even	4		400.2.q.h.149.7		16
16.11	odd	4		1600.2.q.g.49.7		16
20.3	even	4		1600.2.l.i.401.2		16
20.7	even	4		320.2.l.a.81.7		16
20.19	odd	2		1600.2.q.g.849.7		16
40.27	even	4		640.2.l.a.161.2		16
40.37	odd	4		640.2.l.b.161.7		16
60.47	odd	4		2880.2.t.c.721.7		16
80.27	even	4		320.2.l.a.241.7		16
80.37	odd	4		80.2.l.a.21.4	✓	16
80.43	even	4		1600.2.l.i.1201.2		16
80.53	odd	4		400.2.l.h.101.5		16
80.59	odd	4		1600.2.q.h.49.2		16
80.67	even	4		640.2.l.a.481.2		16
80.69	even	4	inner	400.2.q.g.149.2		16
80.77	odd	4		640.2.l.b.481.7		16
160.27	even	8		5120.2.a.u.1.1		8
160.37	odd	8		5120.2.a.s.1.8		8
160.107	even	8		5120.2.a.t.1.8		8
160.117	odd	8		5120.2.a.v.1.1		8
240.107	odd	4		2880.2.t.c.2161.6		16
240.197	even	4		720.2.t.c.181.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.4	✓	16	80.37	odd	4
80.2.l.a.61.4	yes	16	5.2	odd	4
320.2.l.a.81.7		16	20.7	even	4
320.2.l.a.241.7		16	80.27	even	4
400.2.l.h.101.5		16	80.53	odd	4
400.2.l.h.301.5		16	5.3	odd	4
400.2.q.g.149.2		16	80.69	even	4	inner
400.2.q.g.349.2		16	1.1	even	1	trivial
400.2.q.h.149.7		16	16.5	even	4
400.2.q.h.349.7		16	5.4	even	2
640.2.l.a.161.2		16	40.27	even	4
640.2.l.a.481.2		16	80.67	even	4
640.2.l.b.161.7		16	40.37	odd	4
640.2.l.b.481.7		16	80.77	odd	4
720.2.t.c.181.5		16	240.197	even	4
720.2.t.c.541.5		16	15.2	even	4
1600.2.l.i.401.2		16	20.3	even	4
1600.2.l.i.1201.2		16	80.43	even	4
1600.2.q.g.49.7		16	16.11	odd	4
1600.2.q.g.849.7		16	20.19	odd	2
1600.2.q.h.49.2		16	80.59	odd	4
1600.2.q.h.849.2		16	4.3	odd	2
2880.2.t.c.721.7		16	60.47	odd	4
2880.2.t.c.2161.6		16	240.107	odd	4
5120.2.a.s.1.8		8	160.37	odd	8
5120.2.a.t.1.8		8	160.107	even	8
5120.2.a.u.1.1		8	160.27	even	8
5120.2.a.v.1.1		8	160.117	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39064 + 0.257150i) q^{2} +(1.66366 - 1.66366i) q^{3} +(1.86775 - 0.715205i) q^{4} +(-1.88574 + 2.74137i) q^{6} -2.89402 q^{7} +(-2.41345 + 1.47488i) q^{8} -2.53555i q^{9} +(1.84462 - 1.84462i) q^{11} +(1.91744 - 4.29717i) q^{12} +(3.08011 - 3.08011i) q^{13} +(4.02454 - 0.744198i) q^{14} +(2.97696 - 2.67165i) q^{16} -7.29875i q^{17} +(0.652018 + 3.52604i) q^{18} +(1.23593 + 1.23593i) q^{19} +(-4.81468 + 4.81468i) q^{21} +(-2.09086 + 3.03955i) q^{22} -4.60490 q^{23} +(-1.56145 + 6.46887i) q^{24} +(-3.49126 + 5.07536i) q^{26} +(0.772683 + 0.772683i) q^{27} +(-5.40530 + 2.06982i) q^{28} +(-4.24680 - 4.24680i) q^{29} +2.06299 q^{31} +(-3.45286 + 4.48082i) q^{32} -6.13767i q^{33} +(1.87688 + 10.1499i) q^{34} +(-1.81344 - 4.73577i) q^{36} +(1.17899 + 1.17899i) q^{37} +(-2.03655 - 1.40091i) q^{38} -10.2485i q^{39} -4.61484i q^{41} +(5.45738 - 7.93357i) q^{42} +(3.03019 + 3.03019i) q^{43} +(2.12601 - 4.76458i) q^{44} +(6.40375 - 1.18415i) q^{46} +11.7111i q^{47} +(0.507943 - 9.39739i) q^{48} +1.37537 q^{49} +(-12.1427 - 12.1427i) q^{51} +(3.54995 - 7.95577i) q^{52} +(2.73048 + 2.73048i) q^{53} +(-1.27322 - 0.875827i) q^{54} +(6.98457 - 4.26835i) q^{56} +4.11235 q^{57} +(6.99782 + 4.81369i) q^{58} +(-3.11306 + 3.11306i) q^{59} +(2.34962 + 2.34962i) q^{61} +(-2.86887 + 0.530498i) q^{62} +7.33795i q^{63} +(3.64944 - 7.11910i) q^{64} +(1.57830 + 8.53528i) q^{66} +(8.24311 - 8.24311i) q^{67} +(-5.22011 - 13.6322i) q^{68} +(-7.66101 + 7.66101i) q^{69} +3.25937i q^{71} +(3.73965 + 6.11942i) q^{72} +12.6877 q^{73} +(-1.94272 - 1.33637i) q^{74} +(3.19235 + 1.42446i) q^{76} +(-5.33839 + 5.33839i) q^{77} +(2.63541 + 14.2520i) q^{78} +0.113885 q^{79} +10.1776 q^{81} +(1.18671 + 6.41758i) q^{82} +(-9.76813 + 9.76813i) q^{83} +(-5.54912 + 12.4361i) q^{84} +(-4.99310 - 3.43468i) q^{86} -14.1305 q^{87} +(-1.73129 + 7.17251i) q^{88} -3.74593i q^{89} +(-8.91390 + 8.91390i) q^{91} +(-8.60080 + 3.29345i) q^{92} +(3.43212 - 3.43212i) q^{93} +(-3.01150 - 16.2858i) q^{94} +(1.71017 + 13.1990i) q^{96} +13.9853i q^{97} +(-1.91264 + 0.353676i) q^{98} +(-4.67714 - 4.67714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 4 q^{4} - 12 q^{6} - 8 q^{7} + 8 q^{8} - 8 q^{11} - 20 q^{12} - 4 q^{14} + 16 q^{16} - 12 q^{18} + 8 q^{19} + 20 q^{22} - 24 q^{23} - 8 q^{24} - 16 q^{26} - 24 q^{27} - 20 q^{28} + 16 q^{29}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 4 * q^4 - 12 * q^6 - 8 * q^7 + 8 * q^8 - 8 * q^11 - 20 * q^12 - 4 * q^14 + 16 * q^16 - 12 * q^18 + 8 * q^19 + 20 * q^22 - 24 * q^23 - 8 * q^24 - 16 * q^26 - 24 * q^27 - 20 * q^28 + 16 * q^29 - 24 * q^32 - 16 * q^34 - 4 * q^36 + 16 * q^37 + 20 * q^38 + 20 * q^42 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 16 * q^49 - 32 * q^51 + 16 * q^52 + 16 * q^53 - 32 * q^54 + 16 * q^56 + 28 * q^58 + 8 * q^59 + 16 * q^61 - 48 * q^62 + 16 * q^64 + 40 * q^67 + 8 * q^68 - 16 * q^69 + 96 * q^72 + 72 * q^74 + 16 * q^77 - 24 * q^78 - 16 * q^79 - 16 * q^81 - 44 * q^82 - 40 * q^83 + 64 * q^84 + 28 * q^86 + 16 * q^88 + 32 * q^91 - 20 * q^92 + 48 * q^93 + 36 * q^94 + 8 * q^96 + 32 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more