LMFDB - Embedded newform 400.2.q.g.149.2

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			149.2
Root			$1.32070 - 0.505727i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.g.349.2

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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	0.999250	−	0.0387330i	$-0.0123322\pi$
$3$	1.66366	+	1.66366i	0.960517	+	0.960517i	−0.0387330	+	0.999250i	$0.512332\pi$
$4$	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	0.928216	−	0.372041i	$-0.121342\pi$
$11$	1.84462	+	1.84462i	0.556175	+	0.556175i	−0.372041	+	0.928216i	$0.621342\pi$
$12$	1.91744	+	4.29717i	0.553518	+	1.24048i
$13$	3.08011	+	3.08011i	0.854268	+	0.854268i	0.990656	−	0.136388i	$-0.0435493\pi$
$13$	3.08011	+	3.08011i	0.854268	+	0.854268i	−0.136388	+	0.990656i	$0.543549\pi$
$14$	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	$0.345913\pi$
$17$			7.29875i			1.77021i	−0.465393	+	0.885104i	$0.654087\pi$
$18$	0.652018	−	3.52604i	0.153682	−	0.831095i
$19$	1.23593	−	1.23593i	0.283542	−	0.283542i	−0.550978	−	0.834520i	$-0.685745\pi$
$19$	1.23593	−	1.23593i	0.283542	−	0.283542i	0.834520	+	0.550978i	$0.185745\pi$
$20$		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	−0.981266	−	0.192656i	$-0.938290\pi$
$29$	−4.24680	+	4.24680i	−0.788611	+	0.788611i	0.192656	+	0.981266i	$0.438290\pi$
$30$		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	−0.603522	−	0.797346i	$-0.706236\pi$
$37$	1.17899	−	1.17899i	0.193825	−	0.193825i	0.797346	+	0.603522i	$0.206236\pi$
$38$	−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	$0.117346\pi$
$41$			4.61484i			0.720717i	−0.932814	+	0.360359i	$0.882654\pi$
$42$	5.45738	+	7.93357i	0.842092	+	1.22418i
$43$	3.03019	−	3.03019i	0.462099	−	0.462099i	−0.437244	−	0.899343i	$-0.644045\pi$
$43$	3.03019	−	3.03019i	0.462099	−	0.462099i	0.899343	+	0.437244i	$0.144045\pi$
$44$	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	$-0.674098\pi$
$47$		−	11.7111i		−	1.70823i	0.520081	−	0.854117i	$-0.325902\pi$
$48$	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	−0.494256	−	0.869316i	$-0.664559\pi$
$53$	2.73048	−	2.73048i	0.375061	−	0.375061i	0.869316	+	0.494256i	$0.164559\pi$
$54$	−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	0.474805	−	0.880091i	$-0.342518\pi$
$59$	−3.11306	−	3.11306i	−0.405285	−	0.405285i	−0.880091	+	0.474805i	$0.842518\pi$
$60$		0			0
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	−0.540503	−	0.841342i	$-0.681766\pi$
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	0.841342	+	0.540503i	$0.181766\pi$
$62$	−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	0.999975	+	0.00708173i	$0.00225420\pi$
$67$	8.24311	+	8.24311i	1.00706	+	1.00706i	0.00708173	+	0.999975i	$0.497746\pi$
$68$	−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	$-0.938046\pi$
$71$		−	3.25937i		−	0.386816i	0.981118	−	0.193408i	$-0.0619541\pi$
$72$	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	−0.997183	−	0.0750089i	$-0.976101\pi$
$83$	−9.76813	−	9.76813i	−1.07219	−	1.07219i	−0.0750089	−	0.997183i	$-0.523899\pi$
$84$	−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	$0.0636180\pi$
$89$			3.74593i			0.397068i	−0.980094	+	0.198534i	$0.936382\pi$
$90$		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	$-0.748697\pi$
$97$		−	13.9853i		−	1.41999i	0.704206	−	0.709995i	$-0.251303\pi$
$98$	−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	0.860288	−	0.509808i	$-0.170284\pi$
$101$	3.52228	+	3.52228i	0.350480	+	0.350480i	−0.509808	+	0.860288i	$0.670284\pi$
$102$	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	−0.561539	−	0.827451i	$-0.689790\pi$
$107$	2.75062	−	2.75062i	0.265912	−	0.265912i	0.827451	+	0.561539i	$0.189790\pi$
$108$	1.99580	−	0.890550i	0.192046	−	0.0856932i
$109$	6.90778	−	6.90778i	0.661646	−	0.661646i	−0.294122	−	0.955768i	$-0.595027\pi$
$109$	6.90778	−	6.90778i	0.661646	−	0.661646i	0.955768	+	0.294122i	$0.0950273\pi$
$110$		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	$0.0525669\pi$
$113$			3.49507i			0.328788i	−0.986395	+	0.164394i	$0.947433\pi$
$114$	−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	$0.0894918\pi$
$127$			6.25357i			0.554915i	−0.960738	+	0.277458i	$0.910508\pi$
$128$	−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	−0.895772	−	0.444513i	$-0.853377\pi$
$131$	−5.16490	+	5.16490i	−0.451259	+	0.451259i	0.444513	+	0.895772i	$0.353377\pi$
$132$	−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	0.578786	−	0.815479i	$-0.303527\pi$
$139$	−2.79057	−	2.79057i	−0.236693	−	0.236693i	−0.815479	+	0.578786i	$0.803527\pi$
$140$		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	0.769740	−	0.638358i	$-0.220386\pi$
$149$	1.60372	+	1.60372i	0.131382	+	0.131382i	−0.638358	+	0.769740i	$0.720386\pi$
$150$		0			0
$151$			2.53754i			0.206502i	0.994655	+	0.103251i	$0.0329245\pi$
$151$			2.53754i			0.206502i	−0.994655	+	0.103251i	$0.967076\pi$
$152$	−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	0.985713	−	0.168435i	$-0.0538712\pi$
$157$	10.2405	+	10.2405i	0.817278	+	0.817278i	−0.168435	+	0.985713i	$0.553871\pi$
$158$	−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	0.319078	−	0.947728i	$-0.396627\pi$
$163$	−8.02607	−	8.02607i	−0.628650	−	0.628650i	−0.947728	+	0.319078i	$0.896627\pi$
$164$	−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	0.486674	−	0.873584i	$-0.338210\pi$
$173$	−5.08901	−	5.08901i	−0.386910	−	0.386910i	−0.873584	+	0.486674i	$0.838210\pi$
$174$	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	−0.765666	−	0.643238i	$-0.777590\pi$
$179$	−1.63797	+	1.63797i	−0.122428	+	0.122428i	0.643238	+	0.765666i	$0.277590\pi$
$180$		0			0
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.957071	−	0.289855i	$-0.906393\pi$
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.289855	−	0.957071i	$-0.593607\pi$
$182$	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	$0.000276272\pi$
$193$			0.0241155i			0.00173587i	−1.00000		0.000867935i	$0.999724\pi$
$194$	−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	−0.0642576	+	0.997933i	$0.520468\pi$
$197$	−14.9086	+	14.9086i	−1.06219	+	1.06219i	−0.997933	+	0.0642576i	$0.979532\pi$
$198$	7.70694	−	5.30149i	0.547708	−	0.376760i
$199$		−	13.6525i		−	0.967801i	−0.875123	−	0.483900i	$-0.839220\pi$
$199$		−	13.6525i		−	0.967801i	0.875123	−	0.483900i	$-0.160780\pi$
$200$		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	−0.786424	−	0.617688i	$-0.788070\pi$
$211$	−2.45103	+	2.45103i	−0.168736	+	0.168736i	0.617688	+	0.786424i	$0.288070\pi$
$212$	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	$-0.845327\pi$
$223$		−	13.9483i		−	0.934045i	0.884245	−	0.467023i	$-0.154673\pi$
$224$	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	0.838901	−	0.544285i	$-0.183199\pi$
$227$	4.43883	+	4.43883i	0.294616	+	0.294616i	−0.544285	+	0.838901i	$0.683199\pi$
$228$	7.68083	+	2.94117i	0.508675	+	0.194784i
$229$	5.35068	+	5.35068i	0.353583	+	0.353583i	0.861441	−	0.507858i	$-0.169562\pi$
$229$	5.35068	+	5.35068i	0.353583	+	0.353583i	−0.507858	+	0.861441i	$0.669562\pi$
$230$		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	0.884882	−	0.465816i	$-0.154239\pi$
$251$	6.63925	+	6.63925i	0.419066	+	0.419066i	−0.465816	+	0.884882i	$0.654239\pi$
$252$	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	$-0.927312\pi$
$257$		−	7.25821i		−	0.452755i	0.974040	−	0.226377i	$-0.0726883\pi$
$258$	−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	−0.167648	−	0.985847i	$-0.553617\pi$
$269$	13.4195	−	13.4195i	0.818199	−	0.818199i	0.985847	+	0.167648i	$0.0536173\pi$
$270$		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	−0.999657	−	0.0262056i	$-0.991658\pi$
$277$	−16.2015	+	16.2015i	−0.973451	+	0.973451i	0.0262056	+	0.999657i	$0.491658\pi$
$278$	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	$-0.914987\pi$
$281$		−	8.84793i		−	0.527824i	0.964547	−	0.263912i	$-0.0850128\pi$
$282$	−32.1043	+	22.0840i	−1.91178	+	1.31509i
$283$	−20.3062	+	20.3062i	−1.20708	+	1.20708i	−0.235109	+	0.971969i	$0.575545\pi$
$283$	−20.3062	+	20.3062i	−1.20708	+	1.20708i	−0.971969	+	0.235109i	$0.924455\pi$
$284$	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	−0.884803	−	0.465965i	$-0.845707\pi$
$293$	−7.16936	+	7.16936i	−0.418839	+	0.418839i	0.465965	+	0.884803i	$0.345707\pi$
$294$	−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	−0.998577	−	0.0533241i	$-0.983018\pi$
$307$	−18.4308	−	18.4308i	−1.05190	−	1.05190i	−0.0533241	−	0.998577i	$-0.516982\pi$
$308$	−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	$0.0644215\pi$
$311$			7.08961i			0.402015i	−0.979590	+	0.201007i	$0.935578\pi$
$312$	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	0.511338	−	0.859380i	$-0.329150\pi$
$317$	−6.19670	−	6.19670i	−0.348042	−	0.348042i	−0.859380	+	0.511338i	$0.829150\pi$
$318$	−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	−0.999722	−	0.0235823i	$-0.992493\pi$
$331$	−18.6174	−	18.6174i	−1.02330	−	1.02330i	−0.0235823	−	0.999722i	$-0.507507\pi$
$332$	−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	$0.126949\pi$
$337$			14.2577i			0.776666i	−0.921519	+	0.388333i	$0.873051\pi$
$338$	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	0.314363	−	0.949303i	$-0.398209\pi$
$347$	23.5395	−	23.5395i	1.26367	−	1.26367i	0.949303	−	0.314363i	$-0.101791\pi$
$348$	−26.3922	−	10.1062i	−1.41477	−	0.541749i
$349$	1.56682	−	1.56682i	0.0838701	−	0.0838701i	−0.663927	−	0.747797i	$-0.731112\pi$
$349$	1.56682	−	1.56682i	0.0838701	−	0.0838701i	0.747797	+	0.663927i	$0.231112\pi$
$350$		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	$-0.919109\pi$
$353$		−	9.44678i		−	0.502801i	0.967883	−	0.251401i	$-0.0808912\pi$
$354$	−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	$0.157985\pi$
$359$			18.0452i			0.952392i	−0.879339	+	0.476196i	$0.842015\pi$
$360$		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	$0.274979\pi$
$367$			29.1329i			1.52073i	−0.649498	+	0.760363i	$0.725021\pi$
$368$	−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	−0.614866	−	0.788632i	$-0.710790\pi$
$373$	3.35598	−	3.35598i	0.173766	−	0.173766i	0.788632	+	0.614866i	$0.210790\pi$
$374$	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	0.341445	−	0.939902i	$-0.389084\pi$
$379$	−11.6507	−	11.6507i	−0.598457	−	0.598457i	−0.939902	+	0.341445i	$0.889084\pi$
$380$		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	$0.188077\pi$
$383$			21.8044i			1.11415i	−0.830461	+	0.557077i	$0.811923\pi$
$384$	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	0.941066	−	0.338224i	$-0.109826\pi$
$389$	11.8899	+	11.8899i	0.602842	+	0.602842i	−0.338224	+	0.941066i	$0.609826\pi$
$390$		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	0.436170	−	0.899864i	$-0.356335\pi$
$397$	−9.23905	−	9.23905i	−0.463694	−	0.463694i	−0.899864	+	0.436170i	$0.856335\pi$
$398$	−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	$0.0758006\pi$
$409$			9.54117i			0.471781i	−0.971780	+	0.235890i	$0.924199\pi$
$410$		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	−0.727272	−	0.686349i	$-0.759212\pi$
$419$	−0.837667	+	0.837667i	−0.0409227	+	0.0409227i	0.686349	+	0.727272i	$0.259212\pi$
$420$		0			0
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	0.993087	−	0.117385i	$-0.0374511\pi$
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	−0.117385	+	0.993087i	$0.537451\pi$
$422$	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	$0.210557\pi$
$433$			25.5651i			1.22858i	−0.789081	+	0.614289i	$0.789443\pi$
$434$	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	$0.255418\pi$
$439$			30.1311i			1.43808i	−0.694970	+	0.719039i	$0.744582\pi$
$440$		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	−0.0412027	−	0.999151i	$-0.513119\pi$
$443$	20.1625	−	20.1625i	0.957948	−	0.957948i	0.999151	+	0.0412027i	$0.0131189\pi$
$444$	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	−0.375491	−	0.926826i	$-0.622526\pi$
$461$	11.8377	−	11.8377i	0.551335	−	0.551335i	0.926826	+	0.375491i	$0.122526\pi$
$462$	−4.56764	+	24.7013i	−0.212506	+	1.14921i
$463$			32.2711i			1.49976i	0.661572	+	0.749882i	$0.269890\pi$
$463$			32.2711i			1.49976i	−0.661572	+	0.749882i	$0.730110\pi$
$464$	−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	0.734896	−	0.678180i	$-0.237231\pi$
$467$	1.22565	+	1.22565i	0.0567163	+	0.0567163i	−0.678180	+	0.734896i	$0.737231\pi$
$468$	−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	0.573723	−	0.819049i	$-0.305499\pi$
$491$	−5.43607	−	5.43607i	−0.245326	−	0.245326i	−0.819049	+	0.573723i	$0.805499\pi$
$492$	−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	−0.210773	−	0.977535i	$-0.567598\pi$
$499$	17.1282	−	17.1282i	0.766762	−	0.766762i	0.977535	+	0.210773i	$0.0675981\pi$
$500$		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	−0.995474	−	0.0950391i	$-0.969702\pi$
$509$	−20.3147	+	20.3147i	−0.900434	+	0.900434i	0.0950391	+	0.995474i	$0.469702\pi$
$510$		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	$-0.716325\pi$
$521$		−	35.5082i		−	1.55564i	0.628487	−	0.777820i	$-0.283675\pi$
$522$	12.2054	+	17.7434i	0.534215	+	0.776606i
$523$	0.677766	−	0.677766i	0.0296366	−	0.0296366i	−0.692133	−	0.721770i	$-0.743329\pi$
$523$	0.677766	−	0.677766i	0.0296366	−	0.0296366i	0.721770	+	0.692133i	$0.243329\pi$
$524$	−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	−0.582158	−	0.813075i	$-0.697792\pi$
$541$	5.37099	−	5.37099i	0.230917	−	0.230917i	0.813075	+	0.582158i	$0.197792\pi$
$542$	−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	0.870799	−	0.491639i	$-0.163602\pi$
$547$	8.86782	+	8.86782i	0.379161	+	0.379161i	−0.491639	+	0.870799i	$0.663602\pi$
$548$	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	0.0330091	−	0.999455i	$-0.489491\pi$
$557$	−22.8089	−	22.8089i	−0.966446	−	0.966446i	−0.999455	+	0.0330091i	$0.989491\pi$
$558$	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	0.110095	−	0.993921i	$-0.464884\pi$
$563$	−20.9711	−	20.9711i	−0.883826	−	0.883826i	−0.993921	+	0.110095i	$0.964884\pi$
$564$	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	$0.0539888\pi$
$569$			8.05295i			0.337597i	−0.985651	+	0.168799i	$0.946011\pi$
$570$		0			0
$571$	−22.5040	−	22.5040i	−0.941762	−	0.941762i	0.0566333	−	0.998395i	$-0.481963\pi$
$571$	−22.5040	−	22.5040i	−0.941762	−	0.941762i	−0.998395	+	0.0566333i	$0.981963\pi$
$572$	−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	$0.107949\pi$
$577$			15.9819i			0.665334i	−0.943044	+	0.332667i	$0.892051\pi$
$578$	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	−0.590232	−	0.807233i	$-0.700964\pi$
$587$	5.25752	−	5.25752i	0.217001	−	0.217001i	0.807233	+	0.590232i	$0.200964\pi$
$588$	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	$-0.974053\pi$
$593$		−	3.96571i		−	0.162852i	0.996679	−	0.0814260i	$-0.0259474\pi$
$594$	−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	$-0.945658\pi$
$599$		−	8.31600i		−	0.339783i	0.985463	−	0.169891i	$-0.0543417\pi$
$600$		0			0
$601$		−	46.0550i		−	1.87862i	−0.343068	−	0.939310i	$-0.611466\pi$
$601$		−	46.0550i		−	1.87862i	0.343068	−	0.939310i	$-0.388534\pi$
$602$	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	$-0.967271\pi$
$607$		−	5.05760i		−	0.205282i	0.994718	−	0.102641i	$-0.0327292\pi$
$608$	−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	0.309141	−	0.951016i	$-0.399958\pi$
$613$	31.2000	−	31.2000i	1.26016	−	1.26016i	0.951016	−	0.309141i	$-0.100042\pi$
$614$	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	0.959622	−	0.281293i	$-0.0907632\pi$
$619$	16.8766	+	16.8766i	0.678329	+	0.678329i	−0.281293	+	0.959622i	$0.590763\pi$
$620$		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	$0.209517\pi$
$631$			30.7318i			1.22342i	−0.791084	+	0.611708i	$0.790483\pi$
$632$	−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	0.687605	−	0.726085i	$-0.258662\pi$
$643$	−0.975773	−	0.975773i	−0.0384807	−	0.0384807i	−0.726085	+	0.687605i	$0.758662\pi$
$644$	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	0.998115	−	0.0613792i	$-0.0195499\pi$
$653$	23.9372	+	23.9372i	0.936735	+	0.936735i	−0.0613792	+	0.998115i	$0.519550\pi$
$654$	−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	−0.376790	−	0.926299i	$-0.622972\pi$
$659$	14.1064	−	14.1064i	0.549508	−	0.549508i	0.926299	+	0.376790i	$0.122972\pi$
$660$		0			0
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	0.645484	−	0.763774i	$-0.276656\pi$
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	−0.763774	+	0.645484i	$0.776656\pi$
$662$	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	$0.162577\pi$
$673$			25.3628i			0.977662i	−0.872378	+	0.488831i	$0.837423\pi$
$674$	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	−0.863789	−	0.503853i	$-0.831915\pi$
$677$	−9.36526	+	9.36526i	−0.359936	+	0.359936i	0.503853	+	0.863789i	$0.331915\pi$
$678$	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	−0.622059	−	0.782970i	$-0.713704\pi$
$683$	4.20530	−	4.20530i	0.160911	−	0.160911i	0.782970	+	0.622059i	$0.213704\pi$
$684$	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	−0.588282	−	0.808656i	$-0.700195\pi$
$691$	5.79295	−	5.79295i	0.220374	−	0.220374i	0.808656	+	0.588282i	$0.200195\pi$
$692$	−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	−0.711981	−	0.702199i	$-0.752202\pi$
$701$	−0.258991	+	0.258991i	−0.00978196	+	0.00978196i	0.702199	+	0.711981i	$0.252202\pi$
$702$	−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	0.721081	−	0.692851i	$-0.243646\pi$
$709$	0.751674	+	0.751674i	0.0282297	+	0.0282297i	−0.692851	+	0.721081i	$0.743646\pi$
$710$		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	−0.999045	−	0.0436851i	$-0.986090\pi$
$733$	−28.2309	−	28.2309i	−1.04273	−	1.04273i	−0.0436851	−	0.999045i	$-0.513910\pi$
$734$	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	−0.599695	−	0.800228i	$-0.704712\pi$
$739$	5.45140	−	5.45140i	0.200533	−	0.200533i	0.800228	+	0.599695i	$0.204712\pi$
$740$		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	−0.660719	−	0.750634i	$-0.729748\pi$
$757$	2.47389	−	2.47389i	0.0899152	−	0.0899152i	0.750634	+	0.660719i	$0.229748\pi$
$758$	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	$-0.985666\pi$
$761$		−	2.48375i		−	0.0900358i	0.998986	−	0.0450179i	$-0.0143345\pi$
$762$	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	−0.701745	−	0.712428i	$-0.747595\pi$
$773$	0.297026	−	0.297026i	0.0106833	−	0.0106833i	0.712428	+	0.701745i	$0.247595\pi$
$774$	−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	0.144882	−	0.989449i	$-0.453720\pi$
$787$	−23.6931	−	23.6931i	−0.844567	−	0.844567i	−0.989449	+	0.144882i	$0.953720\pi$
$788$	−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	0.880963	+	0.473186i	$0.156896\pi$
$797$	38.2292	+	38.2292i	1.35415	+	1.35415i	0.473186	+	0.880963i	$0.343104\pi$
$798$	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	$-0.604791\pi$
$809$		−	53.8310i		−	1.89260i	0.323296	−	0.946298i	$-0.395209\pi$
$810$		0			0
$811$	27.0549	+	27.0549i	0.950025	+	0.950025i	0.998809	−	0.0487847i	$-0.0155348\pi$
$811$	27.0549	+	27.0549i	0.950025	+	0.950025i	−0.0487847	+	0.998809i	$0.515535\pi$
$812$	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	0.144347	−	0.989527i	$-0.453892\pi$
$821$	−24.2170	−	24.2170i	−0.845180	−	0.845180i	−0.989527	+	0.144347i	$0.953892\pi$
$822$	−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	−0.925532	−	0.378670i	$-0.876382\pi$
$827$	−15.7264	+	15.7264i	−0.546862	+	0.546862i	0.378670	+	0.925532i	$0.376382\pi$
$828$	8.35072	−	21.8078i	0.290208	−	0.757873i
$829$	20.7323	−	20.7323i	0.720061	−	0.720061i	−0.248556	−	0.968618i	$-0.579956\pi$
$829$	20.7323	−	20.7323i	0.720061	−	0.720061i	0.968618	+	0.248556i	$0.0799560\pi$
$830$		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	$-0.728022\pi$
$839$		−	43.6919i		−	1.50841i	0.656638	−	0.754206i	$-0.271978\pi$
$840$		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	−0.226439	+	0.974025i	$0.572708\pi$
$853$	−35.0610	+	35.0610i	−1.20046	+	1.20046i	−0.974025	+	0.226439i	$0.927292\pi$
$854$	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	−0.994871	−	0.101147i	$-0.967749\pi$
$859$	−32.1229	−	32.1229i	−1.09602	−	1.09602i	−0.101147	−	0.994871i	$-0.532251\pi$
$860$		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	$-0.783756\pi$
$863$		−	36.9142i		−	1.25657i	0.777981	−	0.628287i	$-0.216244\pi$
$864$	−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	0.390044	−	0.920796i	$-0.372460\pi$
$877$	−15.7178	−	15.7178i	−0.530753	−	0.530753i	−0.920796	+	0.390044i	$0.872460\pi$
$878$	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	−0.996035	−	0.0889621i	$-0.971645\pi$
$883$	−32.2410	−	32.2410i	−1.08500	−	1.08500i	−0.0889621	−	0.996035i	$-0.528355\pi$
$884$	−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	−0.727287	−	0.686334i	$-0.759219\pi$
$907$	−1.23335	+	1.23335i	−0.0409528	+	0.0409528i	0.686334	+	0.727287i	$0.259219\pi$
$908$	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	$0.269248\pi$
$919$			45.3844i			1.49709i	−0.663082	+	0.748546i	$0.730752\pi$
$920$		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	−0.688841	−	0.724912i	$-0.741880\pi$
$941$	1.10649	−	1.10649i	0.0360705	−	0.0360705i	0.724912	+	0.688841i	$0.241880\pi$
$942$	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	0.548768	−	0.835975i	$-0.315097\pi$
$947$	−8.83833	−	8.83833i	−0.287207	−	0.287207i	−0.835975	+	0.548768i	$0.815097\pi$
$948$	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	0.0654740	−	0.997854i	$-0.479144\pi$
$971$	−29.0538	−	29.0538i	−0.932380	−	0.932380i	−0.997854	+	0.0654740i	$0.979144\pi$
$972$	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	$0.135955\pi$
$977$			25.8962i			0.828494i	−0.910164	+	0.414247i	$0.864045\pi$
$978$	−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	−0.824210	−	0.566285i	$-0.808380\pi$
$997$	−8.14405	+	8.14405i	−0.257925	+	0.257925i	0.566285	+	0.824210i	$0.308380\pi$
$998$	−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.149.2		16
4.3	odd	2		1600.2.q.h.49.2		16
5.2	odd	4		400.2.l.h.101.5		16
5.3	odd	4		80.2.l.a.21.4	✓	16
5.4	even	2		400.2.q.h.149.7		16
15.8	even	4		720.2.t.c.181.5		16
16.3	odd	4		1600.2.q.g.849.7		16
16.13	even	4		400.2.q.h.349.7		16
20.3	even	4		320.2.l.a.241.7		16
20.7	even	4		1600.2.l.i.1201.2		16
20.19	odd	2		1600.2.q.g.49.7		16
40.3	even	4		640.2.l.a.481.2		16
40.13	odd	4		640.2.l.b.481.7		16
60.23	odd	4		2880.2.t.c.2161.6		16
80.3	even	4		320.2.l.a.81.7		16
80.13	odd	4		80.2.l.a.61.4	yes	16
80.19	odd	4		1600.2.q.h.849.2		16
80.29	even	4	inner	400.2.q.g.349.2		16
80.43	even	4		640.2.l.a.161.2		16
80.53	odd	4		640.2.l.b.161.7		16
80.67	even	4		1600.2.l.i.401.2		16
80.77	odd	4		400.2.l.h.301.5		16
160.3	even	8		5120.2.a.t.1.8		8
160.13	odd	8		5120.2.a.s.1.8		8
160.83	even	8		5120.2.a.u.1.1		8
160.93	odd	8		5120.2.a.v.1.1		8
240.83	odd	4		2880.2.t.c.721.7		16
240.173	even	4		720.2.t.c.541.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.4	✓	16	5.3	odd	4
80.2.l.a.61.4	yes	16	80.13	odd	4
320.2.l.a.81.7		16	80.3	even	4
320.2.l.a.241.7		16	20.3	even	4
400.2.l.h.101.5		16	5.2	odd	4
400.2.l.h.301.5		16	80.77	odd	4
400.2.q.g.149.2		16	1.1	even	1	trivial
400.2.q.g.349.2		16	80.29	even	4	inner
400.2.q.h.149.7		16	5.4	even	2
400.2.q.h.349.7		16	16.13	even	4
640.2.l.a.161.2		16	80.43	even	4
640.2.l.a.481.2		16	40.3	even	4
640.2.l.b.161.7		16	80.53	odd	4
640.2.l.b.481.7		16	40.13	odd	4
720.2.t.c.181.5		16	15.8	even	4
720.2.t.c.541.5		16	240.173	even	4
1600.2.l.i.401.2		16	80.67	even	4
1600.2.l.i.1201.2		16	20.7	even	4
1600.2.q.g.49.7		16	20.19	odd	2
1600.2.q.g.849.7		16	16.3	odd	4
1600.2.q.h.49.2		16	4.3	odd	2
1600.2.q.h.849.2		16	80.19	odd	4
2880.2.t.c.721.7		16	240.83	odd	4
2880.2.t.c.2161.6		16	60.23	odd	4
5120.2.a.s.1.8		8	160.13	odd	8
5120.2.a.t.1.8		8	160.3	even	8
5120.2.a.u.1.1		8	160.83	even	8
5120.2.a.v.1.1		8	160.93	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

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