LMFDB - Embedded newform 400.2.q.g.349.8

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			349.8
Root			$1.21331 - 0.726558i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.g.149.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36306 + 0.376912i) q^{2} +(-1.82762 + 1.82762i) q^{3} +(1.71587 + 1.02751i) q^{4} +(-3.18001 + 1.80230i) q^{6} -4.50961 q^{7} +(1.95156 + 2.04729i) q^{8} -3.68037i q^{9} +(-1.64080 + 1.64080i) q^{11} +(-5.01385 + 1.25807i) q^{12} +(-1.51857 + 1.51857i) q^{13} +(-6.14687 - 1.69972i) q^{14} +(1.88845 + 3.52615i) q^{16} -1.45616i q^{17} +(1.38717 - 5.01657i) q^{18} +(2.67964 + 2.67964i) q^{19} +(8.24183 - 8.24183i) q^{21} +(-2.85495 + 1.61808i) q^{22} +2.37423 q^{23} +(-7.30837 - 0.174953i) q^{24} +(-2.64228 + 1.49754i) q^{26} +(1.24345 + 1.24345i) q^{27} +(-7.73792 - 4.63366i) q^{28} +(-0.924966 - 0.924966i) q^{29} -7.20435 q^{31} +(1.24503 + 5.51814i) q^{32} -5.99752i q^{33} +(0.548843 - 1.98483i) q^{34} +(3.78161 - 6.31505i) q^{36} +(5.21123 + 5.21123i) q^{37} +(2.64253 + 4.66251i) q^{38} -5.55074i q^{39} +6.41166i q^{41} +(14.3406 - 8.12768i) q^{42} +(7.65800 + 7.65800i) q^{43} +(-4.50135 + 1.12947i) q^{44} +(3.23622 + 0.894875i) q^{46} +2.51027i q^{47} +(-9.89582 - 2.99308i) q^{48} +13.3366 q^{49} +(2.66130 + 2.66130i) q^{51} +(-4.16603 + 1.04534i) q^{52} +(1.50312 + 1.50312i) q^{53} +(1.22623 + 2.16357i) q^{54} +(-8.80078 - 9.23248i) q^{56} -9.79472 q^{57} +(-0.912155 - 1.60942i) q^{58} +(5.31807 - 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +(-9.81998 - 2.71541i) q^{62} +16.5970i q^{63} +(-0.382800 + 7.99084i) q^{64} +(2.26054 - 8.17499i) q^{66} +(5.22745 - 5.22745i) q^{67} +(1.49622 - 2.49859i) q^{68} +(-4.33918 + 4.33918i) q^{69} +1.92097i q^{71} +(7.53478 - 7.18247i) q^{72} -1.39412 q^{73} +(5.13905 + 9.06740i) q^{74} +(1.84458 + 7.35129i) q^{76} +(7.39938 - 7.39938i) q^{77} +(2.09214 - 7.56600i) q^{78} -5.06317 q^{79} +6.49599 q^{81} +(-2.41663 + 8.73949i) q^{82} +(2.44974 - 2.44974i) q^{83} +(22.6105 - 5.67340i) q^{84} +(7.55194 + 13.3247i) q^{86} +3.38097 q^{87} +(-6.56133 - 0.157070i) q^{88} +9.36007i q^{89} +(6.84817 - 6.84817i) q^{91} +(4.07388 + 2.43954i) q^{92} +(13.1668 - 13.1668i) q^{93} +(-0.946152 + 3.42166i) q^{94} +(-12.3605 - 7.80961i) q^{96} -18.6313i q^{97} +(18.1785 + 5.02671i) q^{98} +(6.03876 + 6.03876i) 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 $

$2$	1.36306	+	0.376912i	0.963830	+	0.266517i
$2$	1.36306	+	0.376912i	0.963830	+	0.266517i
$3$	−1.82762	+	1.82762i	−1.05518	+	1.05518i	−0.0567890	+	0.998386i	$0.518086\pi$
$3$	−1.82762	+	1.82762i	−1.05518	+	1.05518i	−0.998386	+	0.0567890i	$0.981914\pi$
$4$	1.71587	+	1.02751i	0.857937	+	0.513754i
$5$		0			0
$5$		0			0
$6$	−3.18001	+	1.80230i	−1.29823	+	0.735788i
$7$	−4.50961			−1.70447			−0.852236	−	0.523158i	$-0.824754\pi$
$7$	−4.50961			−1.70447			−0.852236	+	0.523158i	$0.824754\pi$
$8$	1.95156	+	2.04729i	0.689982	+	0.723827i
$9$		−	3.68037i		−	1.22679i
$10$		0			0
$11$	−1.64080	+	1.64080i	−0.494721	+	0.494721i	−0.909790	−	0.415069i	$-0.863757\pi$
$11$	−1.64080	+	1.64080i	−0.494721	+	0.494721i	0.415069	+	0.909790i	$0.363757\pi$
$12$	−5.01385	+	1.25807i	−1.44737	+	0.363174i
$13$	−1.51857	+	1.51857i	−0.421176	+	0.421176i	−0.885609	−	0.464432i	$-0.846258\pi$
$13$	−1.51857	+	1.51857i	−0.421176	+	0.421176i	0.464432	+	0.885609i	$0.346258\pi$
$14$	−6.14687	−	1.69972i	−1.64282	−	0.454270i
$15$		0			0
$16$	1.88845	+	3.52615i	0.472113	+	0.881538i
$17$		−	1.45616i		−	0.353170i	−0.984285	−	0.176585i	$-0.943495\pi$
$17$		−	1.45616i		−	0.353170i	0.984285	−	0.176585i	$-0.0565051\pi$
$18$	1.38717	−	5.01657i	0.326960	−	1.18242i
$19$	2.67964	+	2.67964i	0.614752	+	0.614752i	0.944181	−	0.329428i	$-0.106856\pi$
$19$	2.67964	+	2.67964i	0.614752	+	0.614752i	−0.329428	+	0.944181i	$0.606856\pi$
$20$		0			0
$21$	8.24183	−	8.24183i	1.79852	−	1.79852i
$22$	−2.85495	+	1.61808i	−0.608678	+	0.344975i
$23$	2.37423			0.495061			0.247530	−	0.968880i	$-0.420381\pi$
$23$	2.37423			0.495061			0.247530	+	0.968880i	$0.420381\pi$
$24$	−7.30837	−	0.174953i	−1.49182	−	0.0357121i
$25$		0			0
$26$	−2.64228	+	1.49754i	−0.518193	+	0.293692i
$27$	1.24345	+	1.24345i	0.239303	+	0.239303i
$28$	−7.73792	−	4.63366i	−1.46233	−	0.875679i
$29$	−0.924966	−	0.924966i	−0.171762	−	0.171762i	0.615991	−	0.787753i	$-0.288756\pi$
$29$	−0.924966	−	0.924966i	−0.171762	−	0.171762i	−0.787753	+	0.615991i	$0.788756\pi$
$30$		0			0
$31$	−7.20435			−1.29394			−0.646970	−	0.762515i	$-0.723964\pi$
$31$	−7.20435			−1.29394			−0.646970	+	0.762515i	$0.723964\pi$
$32$	1.24503	+	5.51814i	0.220092	+	0.975479i
$33$		−	5.99752i		−	1.04403i
$34$	0.548843	−	1.98483i	0.0941259	−	0.340396i
$35$		0			0
$36$	3.78161	−	6.31505i	0.630268	−	1.05251i
$37$	5.21123	+	5.21123i	0.856720	+	0.856720i	0.990950	−	0.134230i	$-0.0428560\pi$
$37$	5.21123	+	5.21123i	0.856720	+	0.856720i	−0.134230	+	0.990950i	$0.542856\pi$
$38$	2.64253	+	4.66251i	0.428675	+	0.756359i
$39$		−	5.55074i		−	0.888830i
$40$		0			0
$41$			6.41166i			1.00133i	0.865640	+	0.500667i	$0.166912\pi$
$41$			6.41166i			1.00133i	−0.865640	+	0.500667i	$0.833088\pi$
$42$	14.3406	−	8.12768i	2.21280	−	1.25413i
$43$	7.65800	+	7.65800i	1.16783	+	1.16783i	0.982716	+	0.185118i	$0.0592669\pi$
$43$	7.65800	+	7.65800i	1.16783	+	1.16783i	0.185118	+	0.982716i	$0.440733\pi$
$44$	−4.50135	+	1.12947i	−0.678604	+	0.170275i
$45$		0			0
$46$	3.23622	+	0.894875i	0.477155	+	0.131942i
$47$			2.51027i			0.366161i	0.983098	+	0.183081i	$0.0586069\pi$
$47$			2.51027i			0.366161i	−0.983098	+	0.183081i	$0.941393\pi$
$48$	−9.89582	−	2.99308i	−1.42834	−	0.432015i
$49$	13.3366			1.90522
$50$		0			0
$51$	2.66130	+	2.66130i	0.372657	+	0.372657i
$52$	−4.16603	+	1.04534i	−0.577724	+	0.144962i
$53$	1.50312	+	1.50312i	0.206470	+	0.206470i	0.802765	−	0.596295i	$-0.203361\pi$
$53$	1.50312	+	1.50312i	0.206470	+	0.206470i	−0.596295	+	0.802765i	$0.703361\pi$
$54$	1.22623	+	2.16357i	0.166869	+	0.294425i
$55$		0			0
$56$	−8.80078	−	9.23248i	−1.17605	−	1.23374i
$57$	−9.79472			−1.29734
$58$	−0.912155	−	1.60942i	−0.119772	−	0.211327i
$59$	5.31807	−	5.31807i	0.692353	−	0.692353i	−0.270396	−	0.962749i	$-0.587155\pi$
$59$	5.31807	−	5.31807i	0.692353	−	0.692353i	0.962749	+	0.270396i	$0.0871546\pi$
$60$		0			0
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	0.638668	−	0.769483i	$-0.279486\pi$
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	−0.769483	+	0.638668i	$0.779486\pi$
$62$	−9.81998	−	2.71541i	−1.24714	−	0.344857i
$63$			16.5970i			2.09103i
$64$	−0.382800	+	7.99084i	−0.0478499	+	0.998855i
$65$		0			0
$66$	2.26054	−	8.17499i	0.278253	−	1.00627i
$67$	5.22745	−	5.22745i	0.638635	−	0.638635i	−0.311584	−	0.950219i	$-0.600859\pi$
$67$	5.22745	−	5.22745i	0.638635	−	0.638635i	0.950219	+	0.311584i	$0.100859\pi$
$68$	1.49622	−	2.49859i	0.181443	−	0.302998i
$69$	−4.33918	+	4.33918i	−0.522376	+	0.522376i
$70$		0			0
$71$			1.92097i			0.227978i	0.993482	+	0.113989i	$0.0363628\pi$
$71$			1.92097i			0.227978i	−0.993482	+	0.113989i	$0.963637\pi$
$72$	7.53478	−	7.18247i	0.887983	−	0.846462i
$73$	−1.39412			−0.163169			−0.0815847	−	0.996666i	$-0.525998\pi$
$73$	−1.39412			−0.163169			−0.0815847	+	0.996666i	$0.525998\pi$
$74$	5.13905	+	9.06740i	0.597403	+	1.05406i
$75$		0			0
$76$	1.84458	+	7.35129i	0.211587	+	0.843250i
$77$	7.39938	−	7.39938i	0.843237	−	0.843237i
$78$	2.09214	−	7.56600i	0.236888	−	0.856681i
$79$	−5.06317			−0.569651			−0.284825	−	0.958579i	$-0.591936\pi$
$79$	−5.06317			−0.569651			−0.284825	+	0.958579i	$0.591936\pi$
$80$		0			0
$81$	6.49599			0.721777
$82$	−2.41663	+	8.73949i	−0.266872	+	0.965115i
$83$	2.44974	−	2.44974i	0.268894	−	0.268894i	−0.559761	−	0.828654i	$-0.689107\pi$
$83$	2.44974	−	2.44974i	0.268894	−	0.268894i	0.828654	+	0.559761i	$0.189107\pi$
$84$	22.6105	−	5.67340i	2.46701	−	0.619019i
$85$		0			0
$86$	7.55194	+	13.3247i	0.814347	+	1.43684i
$87$	3.38097			0.362478
$88$	−6.56133	−	0.157070i	−0.699440	−	0.0167437i
$89$			9.36007i			0.992165i	0.868275	+	0.496083i	$0.165229\pi$
$89$			9.36007i			0.992165i	−0.868275	+	0.496083i	$0.834771\pi$
$90$		0			0
$91$	6.84817	−	6.84817i	0.717883	−	0.717883i
$92$	4.07388	+	2.43954i	0.424731	+	0.254340i
$93$	13.1668	−	13.1668i	1.36533	−	1.36533i
$94$	−0.946152	+	3.42166i	−0.0975882	+	0.352917i
$95$		0			0
$96$	−12.3605	−	7.80961i	−1.26154	−	0.797065i
$97$		−	18.6313i		−	1.89172i	−0.324579	−	0.945859i	$-0.605223\pi$
$97$		−	18.6313i		−	1.89172i	0.324579	−	0.945859i	$-0.394777\pi$
$98$	18.1785	+	5.02671i	1.83631	+	0.507774i
$99$	6.03876	+	6.03876i	0.606918	+	0.606918i
$100$		0			0
$101$	−4.84108	+	4.84108i	−0.481705	+	0.481705i	−0.905676	−	0.423971i	$-0.860636\pi$
$101$	−4.84108	+	4.84108i	−0.481705	+	0.481705i	0.423971	+	0.905676i	$0.360636\pi$
$102$	2.62444	+	4.63059i	0.259858	+	0.458497i
$103$	−9.12540			−0.899153			−0.449576	−	0.893242i	$-0.648425\pi$
$103$	−9.12540			−0.899153			−0.449576	+	0.893242i	$0.648425\pi$
$104$	−6.07255	−	0.145369i	−0.595463	−	0.0142546i
$105$		0			0
$106$	1.48230	+	2.61539i	0.143974	+	0.254029i
$107$	10.1505	+	10.1505i	0.981290	+	0.981290i	0.999828	−	0.0185385i	$-0.00590132\pi$
$107$	10.1505	+	10.1505i	0.981290	+	0.981290i	−0.0185385	+	0.999828i	$0.505901\pi$
$108$	0.855951	+	3.41127i	0.0823639	+	0.328249i
$109$	−1.35489	−	1.35489i	−0.129775	−	0.129775i	0.639236	−	0.769011i	$-0.279251\pi$
$109$	−1.35489	−	1.35489i	−0.129775	−	0.129775i	−0.769011	+	0.639236i	$0.779251\pi$
$110$		0			0
$111$	−19.0483			−1.80798
$112$	−8.51618	−	15.9016i	−0.804704	−	1.50256i
$113$		−	2.56039i		−	0.240861i	−0.992722	−	0.120431i	$-0.961572\pi$
$113$		−	2.56039i		−	0.240861i	0.992722	−	0.120431i	$-0.0384275\pi$
$114$	−13.3508	−	3.69175i	−1.25042	−	0.345764i
$115$		0			0
$116$	−0.636716	−	2.53754i	−0.0591176	−	0.235604i
$117$	5.58891	+	5.58891i	0.516695	+	0.516695i
$118$	9.25329	−	5.24441i	0.851835	−	0.482787i
$119$			6.56670i			0.601969i
$120$		0			0
$121$			5.61553i			0.510503i
$122$	−1.00754	−	1.77772i	−0.0912188	−	0.160947i
$123$	−11.7181	−	11.7181i	−1.05658	−	1.05658i
$124$	−12.3618	−	7.40253i	−1.11012	−	0.664767i
$125$		0			0
$126$	−6.25561	+	22.6228i	−0.557294	+	2.01540i
$127$		−	13.7354i		−	1.21882i	−0.792856	−	0.609409i	$-0.791407\pi$
$127$		−	13.7354i		−	1.21882i	0.792856	−	0.609409i	$-0.208593\pi$
$128$	−3.53362	+	10.7477i	−0.312331	+	0.949973i
$129$	−27.9918			−2.46454
$130$		0			0
$131$	5.20726	+	5.20726i	0.454960	+	0.454960i	0.896997	−	0.442037i	$-0.145744\pi$
$131$	5.20726	+	5.20726i	0.454960	+	0.454960i	−0.442037	+	0.896997i	$0.645744\pi$
$132$	6.16250	−	10.2910i	0.536377	−	0.895716i
$133$	−12.0841	−	12.0841i	−1.04783	−	1.04783i
$134$	9.09563	−	5.15505i	0.785743	−	0.445329i
$135$		0			0
$136$	2.98118	−	2.84179i	0.255634	−	0.243681i
$137$	−22.7563			−1.94420			−0.972102	−	0.234559i	$-0.924635\pi$
$137$	−22.7563			−1.94420			−0.972102	+	0.234559i	$0.924635\pi$
$138$	−7.55006	+	4.27908i	−0.642704	+	0.364260i
$139$	−6.28085	+	6.28085i	−0.532734	+	0.532734i	−0.921385	−	0.388651i	$-0.872941\pi$
$139$	−6.28085	+	6.28085i	−0.532734	+	0.532734i	0.388651	+	0.921385i	$0.372941\pi$
$140$		0			0
$141$	−4.58782	−	4.58782i	−0.386364	−	0.386364i
$142$	−0.724038	+	2.61841i	−0.0607599	+	0.219732i
$143$		−	4.98336i		−	0.416729i
$144$	12.9775	−	6.95020i	1.08146	−	0.579184i
$145$		0			0
$146$	−1.90027	−	0.525460i	−0.157268	−	0.0434874i
$147$	−24.3741	+	24.3741i	−2.01034	+	2.01034i
$148$	3.58723	+	14.2964i	0.294869	+	1.17516i
$149$	12.9574	−	12.9574i	1.06151	−	1.06151i	0.0635329	−	0.997980i	$-0.479763\pi$
$149$	12.9574	−	12.9574i	1.06151	−	1.06151i	0.997980	−	0.0635329i	$-0.0202368\pi$
$150$		0			0
$151$		−	14.3417i		−	1.16711i	−0.812073	−	0.583555i	$-0.801661\pi$
$151$		−	14.3417i		−	1.16711i	0.812073	−	0.583555i	$-0.198339\pi$
$152$	−0.256515	+	10.7155i	−0.0208061	+	0.869142i
$153$	−5.35920			−0.433266
$154$	12.8747	−	7.29689i	1.03747	−	0.588001i
$155$		0			0
$156$	5.70343	−	9.52438i	0.456640	−	0.762560i
$157$	−2.10564	+	2.10564i	−0.168049	+	0.168049i	−0.786121	−	0.618073i	$-0.787914\pi$
$157$	−2.10564	+	2.10564i	−0.168049	+	0.168049i	0.618073	+	0.786121i	$0.287914\pi$
$158$	−6.90141	−	1.90837i	−0.549047	−	0.151822i
$159$	−5.49426			−0.435723
$160$		0			0
$161$	−10.7068			−0.843817
$162$	8.85444	+	2.44842i	0.695671	+	0.192366i
$163$	5.34004	−	5.34004i	0.418265	−	0.418265i	−0.466341	−	0.884605i	$-0.654428\pi$
$163$	5.34004	−	5.34004i	0.418265	−	0.418265i	0.884605	+	0.466341i	$0.154428\pi$
$164$	−6.58804	+	11.0016i	−0.514439	+	0.859081i
$165$		0			0
$166$	4.26248	−	2.41581i	0.330833	−	0.187503i
$167$	16.0686			1.24343			0.621714	−	0.783245i	$-0.286437\pi$
$167$	16.0686			1.24343			0.621714	+	0.783245i	$0.286437\pi$
$168$	32.9579	+	0.788969i	2.54276	+	0.0608702i
$169$			8.38787i			0.645221i
$170$		0			0
$171$	9.86207	−	9.86207i	0.754171	−	0.754171i
$172$	5.27151	+	21.0088i	0.401949	+	1.60191i
$173$	−17.1133	+	17.1133i	−1.30110	+	1.30110i	−0.373453	+	0.927649i	$0.621826\pi$
$173$	−17.1133	+	17.1133i	−1.30110	+	1.30110i	−0.927649	+	0.373453i	$0.878174\pi$
$174$	4.60847	+	1.27433i	0.349367	+	0.0966065i
$175$		0			0
$176$	−8.88430	−	2.68714i	−0.669679	−	0.202551i
$177$			19.4388i			1.46111i
$178$	−3.52792	+	12.7584i	−0.264429	+	0.956279i
$179$	−1.04482	−	1.04482i	−0.0780933	−	0.0780933i	0.666981	−	0.745075i	$-0.267586\pi$
$179$	−1.04482	−	1.04482i	−0.0780933	−	0.0780933i	−0.745075	+	0.666981i	$0.767586\pi$
$180$		0			0
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	−0.103523	−	0.994627i	$-0.533012\pi$
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	0.994627	+	0.103523i	$0.0330115\pi$
$182$	11.9156	−	6.75332i	0.883245	−	0.500589i
$183$	3.73453			0.276065
$184$	4.63346	+	4.86074i	0.341583	+	0.358338i
$185$		0			0
$186$	22.9099	−	12.9844i	1.67983	−	0.952065i
$187$	2.38927	+	2.38927i	0.174721	+	0.174721i
$188$	−2.57933	+	4.30732i	−0.188117	+	0.314143i
$189$	−5.60748	−	5.60748i	−0.407884	−	0.407884i
$190$		0			0
$191$	0.0667471			0.00482965			0.00241483	−	0.999997i	$-0.499231\pi$
$191$	0.0667471			0.00482965			0.00241483	+	0.999997i	$0.499231\pi$
$192$	−13.9046	−	15.3038i	−1.00348	−	1.10446i
$193$		−	1.09895i		−	0.0791039i	−0.999218	−	0.0395520i	$-0.987407\pi$
$193$		−	1.09895i		−	0.0791039i	0.999218	−	0.0395520i	$-0.0125931\pi$
$194$	7.02234	−	25.3956i	0.504175	−	1.82329i
$195$		0			0
$196$	22.8839	+	13.7034i	1.63456	+	0.978816i
$197$	−11.9289	−	11.9289i	−0.849899	−	0.849899i	0.140222	−	0.990120i	$-0.455218\pi$
$197$	−11.9289	−	11.9289i	−0.849899	−	0.849899i	−0.990120	+	0.140222i	$0.955218\pi$
$198$	5.95512	+	10.5073i	0.423212	+	0.746720i
$199$		−	11.0397i		−	0.782584i	−0.920267	−	0.391292i	$-0.872028\pi$
$199$		−	11.0397i		−	0.782584i	0.920267	−	0.391292i	$-0.127972\pi$
$200$		0			0
$201$			19.1076i			1.34774i
$202$	−8.42334	+	4.77403i	−0.592664	+	0.335899i
$203$	4.17123	+	4.17123i	0.292763	+	0.292763i
$204$	1.83195	+	7.30097i	0.128262	+	0.511170i
$205$		0			0
$206$	−12.4385	−	3.43947i	−0.866631	−	0.239639i
$207$		−	8.73803i		−	0.607335i
$208$	−8.22247	−	2.48696i	−0.570126	−	0.172440i
$209$	−8.79353			−0.608261
$210$		0			0
$211$	−8.59737	−	8.59737i	−0.591868	−	0.591868i	0.346268	−	0.938136i	$-0.387449\pi$
$211$	−8.59737	−	8.59737i	−0.591868	−	0.591868i	−0.938136	+	0.346268i	$0.887449\pi$
$212$	1.03470	+	4.12364i	0.0710634	+	0.283213i
$213$	−3.51080	−	3.51080i	−0.240556	−	0.240556i
$214$	10.0100	+	17.6617i	0.684266	+	1.20733i
$215$		0			0
$216$	−0.119032	+	4.97238i	−0.00809912	+	0.338328i
$217$	32.4888			2.20548
$218$	−1.33613	−	2.35748i	−0.0904941	−	0.159669i
$219$	2.54792	−	2.54792i	0.172172	−	0.172172i
$220$		0			0
$221$	2.21128	+	2.21128i	0.148747	+	0.148747i
$222$	−25.9639	−	7.17951i	−1.74259	−	0.481857i
$223$		−	21.4238i		−	1.43465i	−0.696741	−	0.717323i	$-0.745367\pi$
$223$		−	21.4238i		−	1.43465i	0.696741	−	0.717323i	$-0.254633\pi$
$224$	−5.61460	−	24.8847i	−0.375141	−	1.66268i
$225$		0			0
$226$	0.965041	−	3.48997i	0.0641936	−	0.232149i
$227$	−8.06331	+	8.06331i	−0.535181	+	0.535181i	−0.922110	−	0.386929i	$-0.873536\pi$
$227$	−8.06331	+	8.06331i	−0.535181	+	0.535181i	0.386929	+	0.922110i	$0.373536\pi$
$228$	−16.8065	−	10.0642i	−1.11304	−	0.666515i
$229$	−4.63169	+	4.63169i	−0.306071	+	0.306071i	−0.843383	−	0.537313i	$-0.819440\pi$
$229$	−4.63169	+	4.63169i	−0.306071	+	0.306071i	0.537313	+	0.843383i	$0.319440\pi$
$230$		0			0
$231$			27.0465i			1.77953i
$232$	0.0885445	−	3.69880i	0.00581323	−	0.242838i
$233$	26.0672			1.70772			0.853860	−	0.520502i	$-0.174255\pi$
$233$	26.0672			1.70772			0.853860	+	0.520502i	$0.174255\pi$
$234$	5.51150	+	9.72455i	0.360298	+	0.635714i
$235$		0			0
$236$	14.5895	−	3.66078i	0.949695	−	0.238296i
$237$	9.25353	−	9.25353i	0.601081	−	0.601081i
$238$	−2.47507	+	8.95082i	−0.160435	+	0.580196i
$239$	−5.12209			−0.331320			−0.165660	−	0.986183i	$-0.552975\pi$
$239$	−5.12209			−0.331320			−0.165660	+	0.986183i	$0.552975\pi$
$240$		0			0
$241$	11.4987			0.740695			0.370347	−	0.928893i	$-0.379239\pi$
$241$	11.4987			0.740695			0.370347	+	0.928893i	$0.379239\pi$
$242$	−2.11656	+	7.65432i	−0.136058	+	0.492038i
$243$	−15.6025	+	15.6025i	−1.00090	+	1.00090i
$244$	−0.703301	−	2.80290i	−0.0450242	−	0.179437i
$245$		0			0
$246$	−11.5558	−	20.3891i	−0.736769	−	1.29996i
$247$	−8.13847			−0.517838
$248$	−14.0598	−	14.7494i	−0.892795	−	0.936588i
$249$			8.95437i			0.567460i
$250$		0			0
$251$	−19.8270	+	19.8270i	−1.25147	+	1.25147i	−0.296408	+	0.955061i	$0.595789\pi$
$251$	−19.8270	+	19.8270i	−1.25147	+	1.25147i	−0.955061	+	0.296408i	$0.904211\pi$
$252$	−17.0536	+	28.4784i	−1.07427	+	1.79397i
$253$	−3.89564	+	3.89564i	−0.244917	+	0.244917i
$254$	5.17703	−	18.7222i	0.324836	−	1.17473i
$255$		0			0
$256$	−8.86749	+	13.3179i	−0.554218	+	0.832372i
$257$			24.2494i			1.51264i	0.654203	+	0.756319i	$0.273004\pi$
$257$			24.2494i			1.51264i	−0.654203	+	0.756319i	$0.726996\pi$
$258$	−38.1545	−	10.5504i	−2.37540	−	0.656842i
$259$	−23.5006	−	23.5006i	−1.46026	−	1.46026i
$260$		0			0
$261$	−3.40422	+	3.40422i	−0.210716	+	0.210716i
$262$	5.13514	+	9.06049i	0.317250	+	0.559759i
$263$	22.5680			1.39160			0.695802	−	0.718234i	$-0.255049\pi$
$263$	22.5680			1.39160			0.695802	+	0.718234i	$0.255049\pi$
$264$	12.2787	−	11.7045i	0.755700	−	0.720365i
$265$		0			0
$266$	−11.9168	−	21.0261i	−0.730664	−	1.28919i
$267$	−17.1066	−	17.1066i	−1.04691	−	1.04691i
$268$	14.3409	−	3.59840i	0.876010	−	0.219807i
$269$	5.10558	+	5.10558i	0.311293	+	0.311293i	0.845410	−	0.534117i	$-0.179356\pi$
$269$	5.10558	+	5.10558i	0.311293	+	0.311293i	−0.534117	+	0.845410i	$0.679356\pi$
$270$		0			0
$271$	6.67920			0.405733			0.202866	−	0.979206i	$-0.434974\pi$
$271$	6.67920			0.405733			0.202866	+	0.979206i	$0.434974\pi$
$272$	5.13464	−	2.74989i	0.311333	−	0.166736i
$273$			25.0317i			1.51498i
$274$	−31.0183	−	8.57713i	−1.87388	−	0.518163i
$275$		0			0
$276$	−11.9040	+	2.98695i	−0.716539	+	0.179793i
$277$	11.8524	+	11.8524i	0.712141	+	0.712141i	0.966983	−	0.254842i	$-0.0820234\pi$
$277$	11.8524	+	11.8524i	0.712141	+	0.712141i	−0.254842	+	0.966983i	$0.582023\pi$
$278$	−10.9285	+	6.19386i	−0.655448	+	0.371483i
$279$			26.5147i			1.58739i
$280$		0			0
$281$		−	0.477460i		−	0.0284829i	−0.999899	−	0.0142414i	$-0.995467\pi$
$281$		−	0.477460i		−	0.0284829i	0.999899	−	0.0142414i	$-0.00453334\pi$
$282$	−4.52428	−	7.98269i	−0.269417	−	0.475362i
$283$	−0.482914	−	0.482914i	−0.0287063	−	0.0287063i	0.692608	−	0.721314i	$-0.256462\pi$
$283$	−0.482914	−	0.482914i	−0.0287063	−	0.0287063i	−0.721314	+	0.692608i	$0.756462\pi$
$284$	−1.97382	+	3.29615i	−0.117124	+	0.195591i
$285$		0			0
$286$	1.87829	−	6.79263i	0.111065	−	0.401656i
$287$		−	28.9141i		−	1.70674i
$288$	20.3088	−	4.58217i	1.19671	−	0.270007i
$289$	14.8796			0.875271
$290$		0			0
$291$	34.0508	+	34.0508i	1.99609	+	1.99609i
$292$	−2.39214	−	1.43247i	−0.139989	−	0.0838290i
$293$	7.46638	+	7.46638i	0.436190	+	0.436190i	0.890728	−	0.454537i	$-0.150195\pi$
$293$	7.46638	+	7.46638i	0.436190	+	0.436190i	−0.454537	+	0.890728i	$0.650195\pi$
$294$	−42.4103	+	24.0365i	−2.47342	+	1.40184i
$295$		0			0
$296$	−0.498857	+	20.8389i	−0.0289955	+	1.21124i
$297$	−4.08052			−0.236776
$298$	22.5456	−	12.7780i	1.30603	−	0.740207i
$299$	−3.60544	+	3.60544i	−0.208508	+	0.208508i
$300$		0			0
$301$	−34.5346	−	34.5346i	−1.99054	−	1.99054i
$302$	5.40556	−	19.5486i	0.311055	−	1.12490i
$303$		−	17.6953i		−	1.01657i
$304$	−4.38845	+	14.5092i	−0.251695	+	0.832160i
$305$		0			0
$306$	−7.30492	−	2.01995i	−0.417595	−	0.115473i
$307$	2.39349	−	2.39349i	0.136604	−	0.136604i	−0.635498	−	0.772102i	$-0.719205\pi$
$307$	2.39349	−	2.39349i	0.136604	−	0.136604i	0.772102	+	0.635498i	$0.219205\pi$
$308$	20.2993	−	5.09348i	1.15666	−	0.290228i
$309$	16.6777	−	16.6777i	0.948764	−	0.948764i
$310$		0			0
$311$		−	20.4404i		−	1.15907i	−0.814948	−	0.579534i	$-0.803235\pi$
$311$		−	20.4404i		−	1.15907i	0.814948	−	0.579534i	$-0.196765\pi$
$312$	11.3640	−	10.8326i	0.643359	−	0.613276i
$313$	−2.46975			−0.139598			−0.0697992	−	0.997561i	$-0.522236\pi$
$313$	−2.46975			−0.139598			−0.0697992	+	0.997561i	$0.522236\pi$
$314$	−3.66376	+	2.07648i	−0.206758	+	0.117182i
$315$		0			0
$316$	−8.68776	−	5.20245i	−0.488725	−	0.292660i
$317$	−16.2241	+	16.2241i	−0.911234	+	0.911234i	−0.996369	−	0.0851350i	$-0.972868\pi$
$317$	−16.2241	+	16.2241i	−0.911234	+	0.911234i	0.0851350	+	0.996369i	$0.472868\pi$
$318$	−7.48902	−	2.07085i	−0.419963	−	0.116128i
$319$	3.03537			0.169948
$320$		0			0
$321$	−37.1026			−2.07086
$322$	−14.5941	−	4.03553i	−0.813296	−	0.224891i
$323$	3.90198	−	3.90198i	0.217112	−	0.217112i
$324$	11.1463	+	6.67469i	0.619240	+	0.370816i
$325$		0			0
$326$	9.29154	−	5.26608i	0.514611	−	0.291661i
$327$	4.95246			0.273871
$328$	−13.1265	+	12.5128i	−0.724792	+	0.690902i
$329$		−	11.3204i		−	0.624111i
$330$		0			0
$331$	3.42340	−	3.42340i	0.188167	−	0.188167i	−0.606736	−	0.794903i	$-0.707521\pi$
$331$	3.42340	−	3.42340i	0.188167	−	0.188167i	0.794903	+	0.606736i	$0.207521\pi$
$332$	6.72057	−	1.68632i	0.368839	−	0.0925487i
$333$	19.1792	−	19.1792i	1.05102	−	1.05102i
$334$	21.9025	+	6.05645i	1.19845	+	0.331394i
$335$		0			0
$336$	44.6263	+	13.4976i	2.43456	+	0.736356i
$337$			5.40017i			0.294166i	0.989124	+	0.147083i	$0.0469884\pi$
$337$			5.40017i			0.294166i	−0.989124	+	0.147083i	$0.953012\pi$
$338$	−3.16149	+	11.4332i	−0.171962	+	0.621883i
$339$	4.67941	+	4.67941i	0.254151	+	0.254151i
$340$		0			0
$341$	11.8209	−	11.8209i	0.640139	−	0.640139i
$342$	17.1597	−	9.72548i	0.927893	−	0.525894i
$343$	−28.5754			−1.54292
$344$	−0.733080	+	30.6232i	−0.0395250	+	1.65109i
$345$		0			0
$346$	−29.7767	+	16.8763i	−1.60081	+	0.907276i
$347$	4.07531	+	4.07531i	0.218774	+	0.218774i	0.807982	−	0.589208i	$-0.200560\pi$
$347$	4.07531	+	4.07531i	0.218774	+	0.218774i	−0.589208	+	0.807982i	$0.700560\pi$
$348$	5.80132	+	3.47397i	0.310983	+	0.186224i
$349$	−1.55681	−	1.55681i	−0.0833339	−	0.0833339i	0.664211	−	0.747545i	$-0.268768\pi$
$349$	−1.55681	−	1.55681i	−0.0833339	−	0.0833339i	−0.747545	+	0.664211i	$0.768768\pi$
$350$		0			0
$351$	−3.77655			−0.201577
$352$	−11.0970	−	7.01133i	−0.591474	−	0.373705i
$353$			1.34919i			0.0718103i	0.999355	+	0.0359052i	$0.0114314\pi$
$353$			1.34919i			0.0718103i	−0.999355	+	0.0359052i	$0.988569\pi$
$354$	−7.32670	+	26.4963i	−0.389410	+	1.40826i
$355$		0			0
$356$	−9.61755	+	16.0607i	−0.509729	+	0.851216i
$357$	−12.0014	−	12.0014i	−0.635182	−	0.635182i
$358$	−1.03035	−	1.81795i	−0.0544555	−	0.0960819i
$359$			23.2192i			1.22546i	0.790291	+	0.612732i	$0.209929\pi$
$359$			23.2192i			1.22546i	−0.790291	+	0.612732i	$0.790071\pi$
$360$		0			0
$361$		−	4.63903i		−	0.244159i
$362$	20.8598	−	11.8225i	1.09637	−	0.621379i
$363$	−10.2630	−	10.2630i	−0.538670	−	0.538670i
$364$	18.7871	−	4.71405i	0.984714	−	0.247083i
$365$		0			0
$366$	5.09040	+	1.40759i	0.266080	+	0.0735759i
$367$			5.16452i			0.269586i	0.990874	+	0.134793i	$0.0430369\pi$
$367$			5.16452i			0.269586i	−0.990874	+	0.134793i	$0.956963\pi$
$368$	4.48362	+	8.37189i	0.233725	+	0.436415i
$369$	23.5973			1.22843
$370$		0			0
$371$	−6.77849	−	6.77849i	−0.351922	−	0.351922i
$372$	36.1216	−	9.06359i	1.87282	−	0.469925i
$373$	18.5056	+	18.5056i	0.958185	+	0.958185i	0.999160	−	0.0409750i	$-0.0130464\pi$
$373$	18.5056	+	18.5056i	0.958185	+	0.958185i	−0.0409750	+	0.999160i	$0.513046\pi$
$374$	2.35618	+	4.15727i	0.121835	+	0.214967i
$375$		0			0
$376$	−5.13926	+	4.89896i	−0.265037	+	0.252645i
$377$	2.80926			0.144684
$378$	−5.52982	−	9.75687i	−0.284423	−	0.501839i
$379$	13.5254	−	13.5254i	0.694754	−	0.694754i	−0.268520	−	0.963274i	$-0.586535\pi$
$379$	13.5254	−	13.5254i	0.694754	−	0.694754i	0.963274	+	0.268520i	$0.0865346\pi$
$380$		0			0
$381$	25.1030	+	25.1030i	1.28607	+	1.28607i
$382$	0.0909805	+	0.0251578i	0.00465497	+	0.00128718i
$383$			21.9051i			1.11930i	0.828729	+	0.559650i	$0.189064\pi$
$383$			21.9051i			1.11930i	−0.828729	+	0.559650i	$0.810936\pi$
$384$	−13.1846	−	26.1008i	−0.672825	−	1.33195i
$385$		0			0
$386$	0.414206	−	1.49793i	0.0210825	−	0.0762427i
$387$	28.1843	−	28.1843i	1.43269	−	1.43269i
$388$	19.1438	−	31.9689i	0.971878	−	1.62298i
$389$	−4.48844	+	4.48844i	−0.227573	+	0.227573i	−0.811678	−	0.584105i	$-0.801446\pi$
$389$	−4.48844	+	4.48844i	−0.227573	+	0.227573i	0.584105	+	0.811678i	$0.301446\pi$
$390$		0			0
$391$		−	3.45725i		−	0.174841i
$392$	26.0271	+	27.3038i	1.31457	+	1.37905i
$393$	−19.0337			−0.960126
$394$	−11.7637	−	20.7560i	−0.592646	−	1.04567i
$395$		0			0
$396$	4.15688	+	16.5666i	0.208891	+	0.832504i
$397$	11.7892	−	11.7892i	0.591682	−	0.591682i	−0.346404	−	0.938086i	$-0.612597\pi$
$397$	11.7892	−	11.7892i	0.591682	−	0.591682i	0.938086	+	0.346404i	$0.112597\pi$
$398$	4.16100	−	15.0478i	0.208572	−	0.754278i
$399$	44.1703			2.21128
$400$		0			0
$401$	24.9259			1.24474			0.622371	−	0.782722i	$-0.286170\pi$
$401$	24.9259			1.24474			0.622371	+	0.782722i	$0.286170\pi$
$402$	−7.20187	+	26.0448i	−0.359196	+	1.29900i
$403$	10.9403	−	10.9403i	0.544977	−	0.544977i
$404$	−13.2809	+	3.33244i	−0.660751	+	0.165795i
$405$		0			0
$406$	4.11346	+	7.25784i	0.204148	+	0.360200i
$407$	−17.1012			−0.847675
$408$	−0.254759	+	10.6422i	−0.0126125	+	0.526865i
$409$		−	21.5355i		−	1.06486i	−0.846474	−	0.532430i	$-0.821279\pi$
$409$		−	21.5355i		−	1.06486i	0.846474	−	0.532430i	$-0.178721\pi$
$410$		0			0
$411$	41.5898	−	41.5898i	2.05148	−	2.05148i
$412$	−15.6581	−	9.37643i	−0.771417	−	0.461943i
$413$	−23.9824	+	23.9824i	−1.18010	+	1.18010i
$414$	3.29347	−	11.9105i	0.161865	−	0.585368i
$415$		0			0
$416$	−10.2704	−	6.48903i	−0.503546	−	0.318151i
$417$		−	22.9580i		−	1.12426i
$418$	−11.9861	−	3.31439i	−0.586261	−	0.162112i
$419$	17.2979	+	17.2979i	0.845060	+	0.845060i	0.989512	−	0.144452i	$-0.0461419\pi$
$419$	17.2979	+	17.2979i	0.845060	+	0.845060i	−0.144452	+	0.989512i	$0.546142\pi$
$420$		0			0
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	−0.998670	−	0.0515648i	$-0.983579\pi$
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	0.0515648	+	0.998670i	$0.483579\pi$
$422$	−8.47830	−	14.9592i	−0.412717	−	0.728203i
$423$	9.23874			0.449203
$424$	−0.143890	+	6.01077i	−0.00698791	+	0.291909i
$425$		0			0
$426$	−3.46218	−	6.10871i	−0.167743	−	0.295968i
$427$	4.60744	+	4.60744i	0.222970	+	0.222970i
$428$	6.98729	+	27.8468i	0.337744	+	1.34603i
$429$	9.10767	+	9.10767i	0.439723	+	0.439723i
$430$		0			0
$431$	28.3769			1.36687			0.683433	−	0.730013i	$-0.260486\pi$
$431$	28.3769			1.36687			0.683433	+	0.730013i	$0.260486\pi$
$432$	−2.03640	+	6.73280i	−0.0979763	+	0.323932i
$433$			9.04007i			0.434438i	0.976123	+	0.217219i	$0.0696986\pi$
$433$			9.04007i			0.434438i	−0.976123	+	0.217219i	$0.930301\pi$
$434$	44.2842	+	12.2454i	2.12571	+	0.587799i
$435$		0			0
$436$	−0.932664	−	3.71699i	−0.0446665	−	0.178012i
$437$	6.36208	+	6.36208i	0.304340	+	0.304340i
$438$	4.43331	−	2.51263i	0.211832	−	0.120058i
$439$		−	28.2949i		−	1.35044i	−0.737615	−	0.675221i	$-0.764048\pi$
$439$		−	28.2949i		−	1.35044i	0.737615	−	0.675221i	$-0.235952\pi$
$440$		0			0
$441$		−	49.0834i		−	2.33731i
$442$	2.18066	+	3.84757i	0.103723	+	0.183010i
$443$	−13.1232	−	13.1232i	−0.623504	−	0.623504i	0.322922	−	0.946426i	$-0.395335\pi$
$443$	−13.1232	−	13.1232i	−0.623504	−	0.623504i	−0.946426	+	0.322922i	$0.895335\pi$
$444$	−32.6844	−	19.5722i	−1.55113	−	0.928857i
$445$		0			0
$446$	8.07489	−	29.2020i	0.382357	−	1.38275i
$447$			47.3624i			2.24016i
$448$	1.72628	−	36.0355i	0.0815588	−	1.70252i
$449$	14.3902			0.679116			0.339558	−	0.940585i	$-0.389723\pi$
$449$	14.3902			0.679116			0.339558	+	0.940585i	$0.389723\pi$
$450$		0			0
$451$	−10.5203	−	10.5203i	−0.495380	−	0.495380i
$452$	2.63082	−	4.39331i	0.123743	−	0.206644i
$453$	26.2111	+	26.2111i	1.23151	+	1.23151i
$454$	−14.0299	+	7.95163i	−0.658458	+	0.373189i
$455$		0			0
$456$	−19.1150	−	20.0526i	−0.895143	−	0.939051i
$457$	−4.54538			−0.212624			−0.106312	−	0.994333i	$-0.533904\pi$
$457$	−4.54538			−0.212624			−0.106312	+	0.994333i	$0.533904\pi$
$458$	−8.05902	+	4.56754i	−0.376573	+	0.213427i
$459$	1.81066	−	1.81066i	0.0845146	−	0.0845146i
$460$		0			0
$461$	19.8046	+	19.8046i	0.922393	+	0.922393i	0.997198	−	0.0748050i	$-0.0238334\pi$
$461$	19.8046	+	19.8046i	0.922393	+	0.922393i	−0.0748050	+	0.997198i	$0.523833\pi$
$462$	−10.1941	+	36.8660i	−0.474274	+	1.71516i
$463$		−	14.5997i		−	0.678506i	−0.940695	−	0.339253i	$-0.889826\pi$
$463$		−	14.5997i		−	0.678506i	0.940695	−	0.339253i	$-0.110174\pi$
$464$	1.51481	−	5.00833i	0.0703235	−	0.232506i
$465$		0			0
$466$	35.5312	+	9.82505i	1.64595	+	0.455137i
$467$	19.8105	−	19.8105i	0.916722	−	0.916722i	−0.0800671	−	0.996789i	$-0.525513\pi$
$467$	19.8105	−	19.8105i	0.916722	−	0.916722i	0.996789	+	0.0800671i	$0.0255135\pi$
$468$	3.84722	+	15.3325i	0.177838	+	0.708746i
$469$	−23.5738	+	23.5738i	−1.08853	+	1.08853i
$470$		0			0
$471$		−	7.69661i		−	0.354641i
$472$	21.2662	+	0.509084i	0.978855	+	0.0234325i
$473$	−25.1306			−1.15550
$474$	16.1009	−	9.12537i	0.739539	−	0.419142i
$475$		0			0
$476$	−6.74734	+	11.2676i	−0.309264	+	0.516451i
$477$	5.53204	−	5.53204i	0.253295	−	0.253295i
$478$	−6.98172	−	1.93058i	−0.319337	−	0.0883025i
$479$	−21.0378			−0.961243			−0.480621	−	0.876928i	$-0.659589\pi$
$479$	−21.0378			−0.961243			−0.480621	+	0.876928i	$0.659589\pi$
$480$		0			0
$481$	−15.8273			−0.721661
$482$	15.6734	+	4.33399i	0.713904	+	0.197408i
$483$	19.5680	−	19.5680i	0.890375	−	0.890375i
$484$	−5.77000	+	9.63555i	−0.262273	+	0.437980i
$485$		0			0
$486$	−27.1480	+	15.3865i	−1.23146	+	0.697944i
$487$	10.2724			0.465485			0.232743	−	0.972538i	$-0.425230\pi$
$487$	10.2724			0.465485			0.232743	+	0.972538i	$0.425230\pi$
$488$	0.0978041	−	4.08561i	0.00442738	−	0.184947i
$489$			19.5191i			0.882685i
$490$		0			0
$491$	−5.95681	+	5.95681i	−0.268827	+	0.268827i	−0.828627	−	0.559801i	$-0.810878\pi$
$491$	−5.95681	+	5.95681i	−0.268827	+	0.268827i	0.559801	+	0.828627i	$0.310878\pi$
$492$	−8.06632	−	32.1471i	−0.363658	−	1.44930i
$493$	−1.34690	+	1.34690i	−0.0606612	+	0.0606612i
$494$	−11.0932	−	3.06748i	−0.499108	−	0.138013i
$495$		0			0
$496$	−13.6051	−	25.4036i	−0.610886	−	1.14066i
$497$		−	8.66284i		−	0.388581i
$498$	−3.37501	+	12.2054i	−0.151238	+	0.546935i
$499$	2.81466	+	2.81466i	0.126002	+	0.126002i	0.767295	−	0.641294i	$-0.221602\pi$
$499$	2.81466	+	2.81466i	0.126002	+	0.126002i	−0.641294	+	0.767295i	$0.721602\pi$
$500$		0			0
$501$	−29.3673	+	29.3673i	−1.31203	+	1.31203i
$502$	−34.4985	+	19.5524i	−1.53974	+	0.872666i
$503$	5.49759			0.245125			0.122563	−	0.992461i	$-0.460889\pi$
$503$	5.49759			0.245125			0.122563	+	0.992461i	$0.460889\pi$
$504$	−33.9789	+	32.3901i	−1.51354	+	1.44277i
$505$		0			0
$506$	−6.77831	+	3.84169i	−0.301333	+	0.170784i
$507$	−15.3298	−	15.3298i	−0.680821	−	0.680821i
$508$	14.1132	−	23.5682i	0.626173	−	1.04567i
$509$	4.37578	+	4.37578i	0.193953	+	0.193953i	0.797402	−	0.603449i	$-0.206207\pi$
$509$	4.37578	+	4.37578i	0.193953	+	0.193953i	−0.603449	+	0.797402i	$0.706207\pi$
$510$		0			0
$511$	6.28693			0.278118
$512$	−17.1066	+	14.8109i	−0.756013	+	0.654556i
$513$			6.66402i			0.294224i
$514$	−9.13990	+	33.0535i	−0.403144	+	1.45793i
$515$		0			0
$516$	−48.0304	−	28.7618i	−2.11442	−	1.26617i
$517$	−4.11887	−	4.11887i	−0.181148	−	0.181148i
$518$	−23.1751	−	40.8904i	−1.01826	−	1.79662i
$519$		−	62.5532i		−	2.74578i
$520$		0			0
$521$			33.8729i			1.48400i	0.670401	+	0.741999i	$0.266122\pi$
$521$			33.8729i			1.48400i	−0.670401	+	0.741999i	$0.733878\pi$
$522$	−5.92325	+	3.35707i	−0.259253	+	0.146935i
$523$	27.8060	+	27.8060i	1.21587	+	1.21587i	0.969065	+	0.246804i	$0.0793803\pi$
$523$	27.8060	+	27.8060i	1.21587	+	1.21587i	0.246804	+	0.969065i	$0.420620\pi$
$524$	3.58450	+	14.2855i	0.156590	+	0.624065i
$525$		0			0
$526$	30.7616	+	8.50615i	1.34127	+	0.370886i
$527$			10.4907i			0.456981i
$528$	21.1482	−	11.3260i	0.920356	−	0.492902i
$529$	−17.3630			−0.754915
$530$		0			0
$531$	−19.5724	−	19.5724i	−0.849372	−	0.849372i
$532$	−8.31832	−	33.1514i	−0.360645	−	1.43730i
$533$	−9.73658	−	9.73658i	−0.421738	−	0.421738i
$534$	−16.8697	−	29.7651i	−0.730023	−	1.28806i
$535$		0			0
$536$	20.9038	+	0.500410i	0.902907	+	0.0216144i
$537$	3.81905			0.164804
$538$	5.03487	+	8.88358i	0.217069	+	0.382998i
$539$	−21.8827	+	21.8827i	−0.942553	+	0.942553i
$540$		0			0
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	0.769248	−	0.638950i	$-0.220631\pi$
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	−0.638950	+	0.769248i	$0.720631\pi$
$542$	9.10416	+	2.51747i	0.391057	+	0.108135i
$543$			43.8211i			1.88054i
$544$	8.03529	−	1.81296i	0.344510	−	0.0777301i
$545$		0			0
$546$	−9.43473	+	34.1197i	−0.403769	+	1.46019i
$547$	−18.4783	+	18.4783i	−0.790074	+	0.790074i	−0.981506	−	0.191432i	$-0.938687\pi$
$547$	−18.4783	+	18.4783i	−0.790074	+	0.790074i	0.191432	+	0.981506i	$0.438687\pi$
$548$	−39.0470	−	23.3823i	−1.66801	−	0.998843i
$549$	−3.76021	+	3.76021i	−0.160482	+	0.160482i
$550$		0			0
$551$		−	4.95716i		−	0.211182i
$552$	−17.3517	−	0.415378i	−0.738539	−	0.0176797i
$553$	22.8329			0.970953
$554$	11.6882	+	20.6228i	0.496585	+	0.876181i
$555$		0			0
$556$	−17.2308	+	4.32353i	−0.730747	+	0.183358i
$557$	−30.2060	+	30.2060i	−1.27987	+	1.27987i	−0.339127	+	0.940741i	$0.610132\pi$
$557$	−30.2060	+	30.2060i	−1.27987	+	1.27987i	−0.940741	+	0.339127i	$0.889868\pi$
$558$	−9.99370	+	36.1411i	−0.423067	+	1.52998i
$559$	−23.2585			−0.983729
$560$		0			0
$561$	−8.73334			−0.368722
$562$	0.179960	−	0.650807i	0.00759117	−	0.0274526i
$563$	−2.86747	+	2.86747i	−0.120850	+	0.120850i	−0.764945	−	0.644095i	$-0.777234\pi$
$563$	−2.86747	+	2.86747i	−0.120850	+	0.120850i	0.644095	+	0.764945i	$0.277234\pi$
$564$	−3.15810	−	12.5862i	−0.132980	−	0.529973i
$565$		0			0
$566$	−0.476226	−	0.840258i	−0.0200173	−	0.0353187i
$567$	−29.2944			−1.23025
$568$	−3.93279	+	3.74890i	−0.165016	+	0.157300i
$569$		−	35.8628i		−	1.50345i	−0.659479	−	0.751723i	$-0.729223\pi$
$569$		−	35.8628i		−	1.50345i	0.659479	−	0.751723i	$-0.270777\pi$
$570$		0			0
$571$	−17.6509	+	17.6509i	−0.738667	+	0.738667i	−0.972320	−	0.233653i	$-0.924932\pi$
$571$	−17.6509	+	17.6509i	−0.738667	+	0.738667i	0.233653	+	0.972320i	$0.424932\pi$
$572$	5.12044	−	8.55082i	0.214096	−	0.357528i
$573$	−0.121988	+	0.121988i	−0.00509613	+	0.00509613i
$574$	10.8981	−	39.4117i	0.454876	−	1.64501i
$575$		0			0
$576$	29.4092	+	1.40884i	1.22538	+	0.0587018i
$577$		−	36.1387i		−	1.50448i	−0.658892	−	0.752238i	$-0.728975\pi$
$577$		−	36.1387i		−	1.50448i	0.658892	−	0.752238i	$-0.271025\pi$
$578$	20.2818	+	5.60830i	0.843612	+	0.233274i
$579$	2.00845	+	2.00845i	0.0834685	+	0.0834685i
$580$		0			0
$581$	−11.0474	+	11.0474i	−0.458322	+	0.458322i
$582$	33.5792	+	59.2475i	1.39190	+	2.45589i
$583$	−4.93265			−0.204290
$584$	−2.72071	−	2.85417i	−0.112584	−	0.118106i
$585$		0			0
$586$	7.36297	+	12.9913i	0.304161	+	0.536666i
$587$	11.4005	+	11.4005i	0.470550	+	0.470550i	0.902093	−	0.431542i	$-0.142030\pi$
$587$	11.4005	+	11.4005i	0.470550	+	0.470550i	−0.431542	+	0.902093i	$0.642030\pi$
$588$	−66.8675	+	16.7783i	−2.75757	+	0.691927i
$589$	−19.3051	−	19.3051i	−0.795453	−	0.795453i
$590$		0			0
$591$	43.6029			1.79358
$592$	−8.53441	+	28.2167i	−0.350762	+	1.15970i
$593$		−	35.0454i		−	1.43914i	−0.694418	−	0.719572i	$-0.744338\pi$
$593$		−	35.0454i		−	1.43914i	0.694418	−	0.719572i	$-0.255662\pi$
$594$	−5.56200	−	1.53800i	−0.228212	−	0.0631048i
$595$		0			0
$596$	35.5472	−	8.91945i	1.45607	−	0.365355i
$597$	20.1764	+	20.1764i	0.825764	+	0.825764i
$598$	−6.27337	+	3.55550i	−0.256537	+	0.145395i
$599$		−	18.2753i		−	0.746707i	−0.927689	−	0.373354i	$-0.878208\pi$
$599$		−	18.2753i		−	0.746707i	0.927689	−	0.373354i	$-0.121792\pi$
$600$		0			0
$601$		−	0.480142i		−	0.0195854i	−0.999952	−	0.00979269i	$-0.996883\pi$
$601$		−	0.480142i		−	0.0195854i	0.999952	−	0.00979269i	$-0.00311716\pi$
$602$	−34.0563	−	60.0893i	−1.38803	−	2.44906i
$603$	−19.2389	−	19.2389i	−0.783470	−	0.783470i
$604$	14.7362	−	24.6086i	0.599608	−	1.00131i
$605$		0			0
$606$	6.66956	−	24.1197i	0.270932	−	0.979798i
$607$			38.6107i			1.56716i	0.621290	+	0.783581i	$0.286609\pi$
$607$			38.6107i			1.56716i	−0.621290	+	0.783581i	$0.713391\pi$
$608$	−11.4504	+	18.1229i	−0.464376	+	0.734980i
$609$	−15.2468			−0.617833
$610$		0			0
$611$	−3.81204	−	3.81204i	−0.154218	−	0.154218i
$612$	−9.19572	−	5.50662i	−0.371715	−	0.222592i
$613$	−5.53592	−	5.53592i	−0.223594	−	0.223594i	0.586416	−	0.810010i	$-0.300538\pi$
$613$	−5.53592	−	5.53592i	−0.223594	−	0.223594i	−0.810010	+	0.586416i	$0.800538\pi$
$614$	4.16461	−	2.36034i	0.168070	−	0.0952557i
$615$		0			0
$616$	29.5890	+	0.708322i	1.19218	+	0.0285391i
$617$	−31.8836			−1.28358			−0.641792	−	0.766879i	$-0.721809\pi$
$617$	−31.8836			−1.28358			−0.641792	+	0.766879i	$0.721809\pi$
$618$	29.0188	−	16.4468i	1.16731	−	0.661586i
$619$	29.4054	−	29.4054i	1.18190	−	1.18190i	0.202650	−	0.979251i	$-0.435045\pi$
$619$	29.4054	−	29.4054i	1.18190	−	1.18190i	0.979251	−	0.202650i	$-0.0649553\pi$
$620$		0			0
$621$	2.95224	+	2.95224i	0.118469	+	0.118469i
$622$	7.70422	−	27.8615i	0.308911	−	1.11714i
$623$		−	42.2102i		−	1.69112i
$624$	19.5728	−	10.4823i	0.783537	−	0.419628i
$625$		0			0
$626$	−3.36642	−	0.930878i	−0.134549	−	0.0372054i
$627$	16.0712	−	16.0712i	0.641822	−	0.641822i
$628$	−5.77658	+	1.44945i	−0.230511	+	0.0578395i
$629$	7.58837	−	7.58837i	0.302568	−	0.302568i
$630$		0			0
$631$			30.7381i			1.22367i	0.790987	+	0.611833i	$0.209568\pi$
$631$			30.7381i			1.22367i	−0.790987	+	0.611833i	$0.790432\pi$
$632$	−9.88109	−	10.3658i	−0.393049	−	0.412328i
$633$	31.4254			1.24905
$634$	−28.2294	+	15.9994i	−1.12113	+	0.635416i
$635$		0			0
$636$	−9.42747	−	5.64540i	−0.373823	−	0.223855i
$637$	−20.2525	+	20.2525i	−0.802435	+	0.802435i
$638$	4.13740	+	1.14407i	0.163801	+	0.0452941i
$639$	7.06989			0.279681
$640$		0			0
$641$	13.6348			0.538540			0.269270	−	0.963065i	$-0.413218\pi$
$641$	13.6348			0.538540			0.269270	+	0.963065i	$0.413218\pi$
$642$	−50.5731	−	13.9844i	−1.99596	−	0.551921i
$643$	−14.9224	+	14.9224i	−0.588480	+	0.588480i	−0.937220	−	0.348740i	$-0.886610\pi$
$643$	−14.9224	+	14.9224i	−0.588480	+	0.588480i	0.348740	+	0.937220i	$0.386610\pi$
$644$	−18.3716	−	11.0014i	−0.723942	−	0.433514i
$645$		0			0
$646$	6.78935	−	3.84794i	0.267123	−	0.151395i
$647$	4.87972			0.191841			0.0959207	−	0.995389i	$-0.469420\pi$
$647$	4.87972			0.191841			0.0959207	+	0.995389i	$0.469420\pi$
$648$	12.6773	+	13.2992i	0.498013	+	0.522442i
$649$			17.4518i			0.685043i
$650$		0			0
$651$	−59.3771	+	59.3771i	−2.32717	+	2.32717i
$652$	14.6498	−	3.67591i	0.573730	−	0.143960i
$653$	10.2913	−	10.2913i	0.402731	−	0.402731i	−0.476463	−	0.879194i	$-0.658081\pi$
$653$	10.2913	−	10.2913i	0.402731	−	0.402731i	0.879194	+	0.476463i	$0.158081\pi$
$654$	6.75050	+	1.86664i	0.263966	+	0.0729914i
$655$		0			0
$656$	−22.6085	+	12.1081i	−0.882713	+	0.472743i
$657$			5.13088i			0.200174i
$658$	4.26677	−	15.4303i	0.166336	−	0.601537i
$659$	21.9025	+	21.9025i	0.853201	+	0.853201i	0.990526	−	0.137325i	$-0.0438505\pi$
$659$	21.9025	+	21.9025i	0.853201	+	0.853201i	−0.137325	+	0.990526i	$0.543851\pi$
$660$		0			0
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	−0.594114	−	0.804381i	$-0.702497\pi$
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	0.804381	+	0.594114i	$0.202497\pi$
$662$	5.95663	−	3.37599i	0.231511	−	0.131212i
$663$	−8.08276			−0.313908
$664$	9.79615	+	0.234507i	0.380164	+	0.00910063i
$665$		0			0
$666$	33.3714	−	18.9136i	1.29311	−	0.732887i
$667$	−2.19608	−	2.19608i	−0.0850326	−	0.0850326i
$668$	27.5717	+	16.5106i	1.06678	+	0.638816i
$669$	39.1546	+	39.1546i	1.51380	+	1.51380i
$670$		0			0
$671$	3.35280			0.129433
$672$	55.7410	+	35.2183i	2.15025	+	1.35857i
$673$			35.3820i			1.36388i	0.731410	+	0.681938i	$0.238862\pi$
$673$			35.3820i			1.36388i	−0.731410	+	0.681938i	$0.761138\pi$
$674$	−2.03539	+	7.36076i	−0.0784002	+	0.283526i
$675$		0			0
$676$	−8.61861	+	14.3925i	−0.331485	+	0.553559i
$677$	−5.17061	−	5.17061i	−0.198723	−	0.198723i	0.600730	−	0.799452i	$-0.294877\pi$
$677$	−5.17061	−	5.17061i	−0.198723	−	0.198723i	−0.799452	+	0.600730i	$0.794877\pi$
$678$	4.61460	+	8.14205i	0.177223	+	0.312694i
$679$			84.0196i			3.22438i
$680$		0			0
$681$		−	29.4733i		−	1.12942i
$682$	20.5681	−	11.6572i	0.787593	−	0.446377i
$683$	26.5989	+	26.5989i	1.01778	+	1.01778i	0.999839	+	0.0179409i	$0.00571108\pi$
$683$	26.5989	+	26.5989i	1.01778	+	1.01778i	0.0179409	+	0.999839i	$0.494289\pi$
$684$	27.0554	−	6.78872i	1.03449	−	0.259573i
$685$		0			0
$686$	−38.9500	−	10.7704i	−1.48712	−	0.411216i
$687$		−	16.9299i		−	0.645916i
$688$	−12.5415	+	41.4651i	−0.478140	+	1.58084i
$689$	−4.56520			−0.173920
$690$		0			0
$691$	−21.7989	−	21.7989i	−0.829270	−	0.829270i	0.158146	−	0.987416i	$-0.449448\pi$
$691$	−21.7989	−	21.7989i	−0.829270	−	0.829270i	−0.987416	+	0.158146i	$0.949448\pi$
$692$	−46.9484	+	11.7802i	−1.78471	+	0.447818i
$693$	−27.2324	−	27.2324i	−1.03447	−	1.03447i
$694$	4.01887	+	7.09093i	0.152554	+	0.269168i
$695$		0			0
$696$	6.59817	+	6.92182i	0.250103	+	0.262371i
$697$	9.33640			0.353641
$698$	−1.53524	−	2.70880i	−0.0581099	−	0.102530i
$699$	−47.6409	+	47.6409i	−1.80194	+	1.80194i
$700$		0			0
$701$	−15.2175	−	15.2175i	−0.574756	−	0.574756i	0.358698	−	0.933454i	$-0.383221\pi$
$701$	−15.2175	−	15.2175i	−0.574756	−	0.574756i	−0.933454	+	0.358698i	$0.883221\pi$
$702$	−5.14767	−	1.42343i	−0.194286	−	0.0537237i
$703$			27.9285i			1.05334i
$704$	−12.4833	−	13.7395i	−0.470482	−	0.517826i
$705$		0			0
$706$	−0.508527	+	1.83903i	−0.0191387	+	0.0692130i
$707$	21.8313	−	21.8313i	0.821052	−	0.821052i
$708$	−19.9735	+	33.3545i	−0.750650	+	1.25354i
$709$	−4.87350	+	4.87350i	−0.183028	+	0.183028i	−0.792674	−	0.609646i	$-0.791312\pi$
$709$	−4.87350	+	4.87350i	−0.183028	+	0.183028i	0.609646	+	0.792674i	$0.291312\pi$
$710$		0			0
$711$			18.6343i			0.698842i
$712$	−19.1628	+	18.2668i	−0.718156	+	0.684576i
$713$	−17.1048			−0.640579
$714$	−11.8352	−	20.8822i	−0.442921	−	0.781495i
$715$		0			0
$716$	−0.719218	−	2.86633i	−0.0268784	−	0.107120i
$717$	9.36121	−	9.36121i	0.349601	−	0.349601i
$718$	−8.75160	+	31.6492i	−0.326607	+	1.18114i
$719$	−9.27351			−0.345843			−0.172922	−	0.984936i	$-0.555321\pi$
$719$	−9.27351			−0.345843			−0.172922	+	0.984936i	$0.555321\pi$
$720$		0			0
$721$	41.1520			1.53258
$722$	1.74850	−	6.32328i	0.0650726	−	0.235328i
$723$	−21.0152	+	21.0152i	−0.781563	+	0.781563i
$724$	32.8893	−	8.25254i	1.22232	−	0.306703i
$725$		0			0
$726$	−10.1209	−	17.8574i	−0.375622	−	0.662751i
$727$	10.6056			0.393341			0.196670	−	0.980470i	$-0.436987\pi$
$727$	10.6056			0.393341			0.196670	+	0.980470i	$0.436987\pi$
$728$	27.3848	+	0.655557i	1.01495	+	0.0242965i
$729$		−	37.5430i		−	1.39048i
$730$		0			0
$731$	11.1513	−	11.1513i	0.412445	−	0.412445i
$732$	6.40799	+	3.83726i	0.236846	+	0.141829i
$733$	29.6530	−	29.6530i	1.09526	−	1.09526i	0.100301	−	0.994957i	$-0.468019\pi$
$733$	29.6530	−	29.6530i	1.09526	−	1.09526i	0.994957	−	0.100301i	$-0.0319806\pi$
$734$	−1.94657	+	7.03956i	−0.0718492	+	0.259835i
$735$		0			0
$736$	2.95599	+	13.1013i	0.108959	+	0.482921i
$737$			17.1544i			0.631892i
$738$	32.1645	+	8.89409i	1.18399	+	0.327396i
$739$	−30.8751	−	30.8751i	−1.13576	−	1.13576i	−0.989202	−	0.146559i	$-0.953180\pi$
$739$	−30.8751	−	30.8751i	−1.13576	−	1.13576i	−0.146559	−	0.989202i	$-0.546820\pi$
$740$		0			0
$741$	14.8740	−	14.8740i	0.546410	−	0.546410i
$742$	−6.68461	−	11.7944i	−0.245400	−	0.432986i
$743$	−22.3956			−0.821617			−0.410808	−	0.911722i	$-0.634753\pi$
$743$	−22.3956			−0.821617			−0.410808	+	0.911722i	$0.634753\pi$
$744$	52.6521	+	1.26042i	1.93032	+	0.0462093i
$745$		0			0
$746$	18.2493	+	32.1993i	0.668155	+	1.17890i
$747$	−9.01594	−	9.01594i	−0.329876	−	0.329876i
$748$	1.64469	+	6.55468i	0.0601359	+	0.239663i
$749$	−45.7749	−	45.7749i	−1.67258	−	1.67258i
$750$		0			0
$751$	20.6448			0.753341			0.376670	−	0.926347i	$-0.377069\pi$
$751$	20.6448			0.753341			0.376670	+	0.926347i	$0.377069\pi$
$752$	−8.85161	+	4.74054i	−0.322785	+	0.172870i
$753$		−	72.4724i		−	2.64104i
$754$	3.82919	+	1.05884i	0.139451	+	0.0385608i
$755$		0			0
$756$	−3.86000	−	15.3835i	−0.140387	−	0.559491i
$757$	−24.1323	−	24.1323i	−0.877104	−	0.877104i	0.116130	−	0.993234i	$-0.462951\pi$
$757$	−24.1323	−	24.1323i	−0.877104	−	0.877104i	−0.993234	+	0.116130i	$0.962951\pi$
$758$	23.5339	−	13.3381i	0.854788	−	0.484461i
$759$		−	14.2395i		−	0.516860i
$760$		0			0
$761$		−	50.1874i		−	1.81929i	−0.415383	−	0.909647i	$-0.636352\pi$
$761$		−	50.1874i		−	1.81929i	0.415383	−	0.909647i	$-0.363648\pi$
$762$	24.7554	+	43.6786i	0.896792	+	1.58231i
$763$	6.11004	+	6.11004i	0.221198	+	0.221198i
$764$	0.114530	+	0.0685832i	0.00414354	+	0.00248125i
$765$		0			0
$766$	−8.25631	+	29.8581i	−0.298312	+	1.07882i
$767$			16.1517i			0.583206i
$768$	−8.13374	−	40.5465i	−0.293501	−	1.46309i
$769$	28.6887			1.03454			0.517270	−	0.855822i	$-0.326948\pi$
$769$	28.6887			1.03454			0.517270	+	0.855822i	$0.326948\pi$
$770$		0			0
$771$	−44.3187	−	44.3187i	−1.59610	−	1.59610i
$772$	1.12918	−	1.88565i	0.0406400	−	0.0678662i
$773$	−37.5957	−	37.5957i	−1.35222	−	1.35222i	−0.883171	−	0.469052i	$-0.844596\pi$
$773$	−37.5957	−	37.5957i	−1.35222	−	1.35222i	−0.469052	−	0.883171i	$-0.655404\pi$
$774$	49.0399	−	27.7939i	1.76270	−	0.999032i
$775$		0			0
$776$	38.1436	−	36.3601i	1.36928	−	1.30525i
$777$	85.9001			3.08165
$778$	−7.80977	+	4.42628i	−0.279994	+	0.158690i
$779$	−17.1810	+	17.1810i	−0.615572	+	0.615572i
$780$		0			0
$781$	−3.15194	−	3.15194i	−0.112785	−	0.112785i
$782$	1.30308	−	4.71245i	0.0465980	−	0.168517i
$783$		−	2.30030i		−	0.0822061i
$784$	25.1855	+	47.0267i	0.899481	+	1.67953i
$785$		0			0
$786$	−25.9442	−	7.17404i	−0.925398	−	0.255890i
$787$	−3.13285	+	3.13285i	−0.111674	+	0.111674i	−0.760736	−	0.649062i	$-0.775162\pi$
$787$	−3.13285	+	3.13285i	−0.111674	+	0.111674i	0.649062	+	0.760736i	$0.275162\pi$
$788$	−8.21145	−	32.7255i	−0.292521	−	1.16580i
$789$	−41.2457	+	41.2457i	−1.46839	+	1.46839i
$790$		0			0
$791$			11.5463i			0.410541i
$792$	−0.578074	+	24.1481i	−0.0205410	+	0.858066i
$793$	3.10304			0.110192
$794$	20.5129	−	11.6259i	0.727974	−	0.412588i
$795$		0			0
$796$	11.3434	−	18.9428i	0.402056	−	0.671408i
$797$	0.0562195	−	0.0562195i	0.00199140	−	0.00199140i	−0.706110	−	0.708102i	$-0.749552\pi$
$797$	0.0562195	−	0.0562195i	0.00199140	−	0.00199140i	0.708102	+	0.706110i	$0.249552\pi$
$798$	60.2069	+	16.6483i	2.13130	+	0.589344i
$799$	3.65536			0.129317
$800$		0			0
$801$	34.4485			1.21718
$802$	33.9756	+	9.39488i	1.19972	+	0.331745i
$803$	2.28748	−	2.28748i	0.0807233	−	0.0807233i
$804$	−19.6332	+	32.7862i	−0.692409	+	1.15628i
$805$		0			0
$806$	19.0359	−	10.7888i	0.670511	−	0.380020i
$807$	−18.6621			−0.656937
$808$	−19.3588	−	0.463423i	−0.681039	−	0.0163032i
$809$		−	3.59856i		−	0.126518i	−0.997997	−	0.0632592i	$-0.979851\pi$
$809$		−	3.59856i		−	0.126518i	0.997997	−	0.0632592i	$-0.0201495\pi$
$810$		0			0
$811$	−7.36274	+	7.36274i	−0.258541	+	0.258541i	−0.824460	−	0.565920i	$-0.808521\pi$
$811$	−7.36274	+	7.36274i	−0.258541	+	0.258541i	0.565920	+	0.824460i	$0.308521\pi$
$812$	2.87134	+	11.4433i	0.100764	+	0.401581i
$813$	−12.2070	+	12.2070i	−0.428119	+	0.428119i
$814$	−23.3100	−	6.44564i	−0.817014	−	0.225920i
$815$		0			0
$816$	−4.35841	+	14.4099i	−0.152575	+	0.504447i
$817$			41.0414i			1.43586i
$818$	8.11697	−	29.3542i	0.283803	−	1.02634i
$819$	−25.2038	−	25.2038i	−0.880691	−	0.880691i
$820$		0			0
$821$	14.7799	−	14.7799i	0.515824	−	0.515824i	−0.400481	−	0.916305i	$-0.631157\pi$
$821$	14.7799	−	14.7799i	0.515824	−	0.515824i	0.916305	+	0.400481i	$0.131157\pi$
$822$	72.3652	−	41.0138i	2.52403	−	1.43052i
$823$	−52.7544			−1.83890			−0.919452	−	0.393203i	$-0.871367\pi$
$823$	−52.7544			−1.83890			−0.919452	+	0.393203i	$0.871367\pi$
$824$	−17.8088	−	18.6824i	−0.620399	−	0.650831i
$825$		0			0
$826$	−41.7287	+	23.6502i	−1.45193	+	0.822897i
$827$	−16.8883	−	16.8883i	−0.587265	−	0.587265i	0.349625	−	0.936890i	$-0.386309\pi$
$827$	−16.8883	−	16.8883i	−0.587265	−	0.587265i	−0.936890	+	0.349625i	$0.886309\pi$
$828$	8.97840	−	14.9934i	0.312021	−	0.521056i
$829$	8.55974	+	8.55974i	0.297292	+	0.297292i	0.839952	−	0.542660i	$-0.182583\pi$
$829$	8.55974	+	8.55974i	0.297292	+	0.297292i	−0.542660	+	0.839952i	$0.682583\pi$
$830$		0			0
$831$	−43.3232			−1.50287
$832$	−11.5534	−	12.7160i	−0.400541	−	0.440847i
$833$		−	19.4201i		−	0.672868i
$834$	8.65313	−	31.2931i	0.299633	−	1.08359i
$835$		0			0
$836$	−15.0886	−	9.03543i	−0.521850	−	0.312497i
$837$	−8.95827	−	8.95827i	−0.309643	−	0.309643i
$838$	17.0584	+	30.0980i	0.589271	+	1.03972i
$839$		−	17.5407i		−	0.605572i	−0.953059	−	0.302786i	$-0.902083\pi$
$839$		−	17.5407i		−	0.605572i	0.953059	−	0.302786i	$-0.0979168\pi$
$840$		0			0
$841$		−	27.2889i		−	0.940996i
$842$	−33.8129	+	19.1638i	−1.16527	+	0.660429i
$843$	0.872614	+	0.872614i	0.0300544	+	0.0300544i
$844$	−5.91814	−	23.5859i	−0.203711	−	0.811860i
$845$		0			0
$846$	12.5930	+	3.48219i	0.432955	+	0.119720i
$847$		−	25.3238i		−	0.870137i
$848$	−2.46166	+	8.13881i	−0.0845337	+	0.279488i
$849$	1.76516			0.0605803
$850$		0			0
$851$	12.3726	+	12.3726i	0.424129	+	0.424129i
$852$	−2.41672	−	9.63148i	−0.0827955	−	0.329969i
$853$	−15.3577	−	15.3577i	−0.525839	−	0.525839i	0.393490	−	0.919329i	$-0.371268\pi$
$853$	−15.3577	−	15.3577i	−0.525839	−	0.525839i	−0.919329	+	0.393490i	$0.871268\pi$
$854$	4.54363	+	8.01683i	0.155480	+	0.274330i
$855$		0			0
$856$	−0.971684	+	40.5905i	−0.0332115	+	1.38736i
$857$	17.9553			0.613341			0.306671	−	0.951816i	$-0.400785\pi$
$857$	17.9553			0.613341			0.306671	+	0.951816i	$0.400785\pi$
$858$	8.98153	+	15.8471i	0.306624	+	0.541011i
$859$	33.3048	−	33.3048i	1.13634	−	1.13634i	0.147245	−	0.989100i	$-0.452960\pi$
$859$	33.3048	−	33.3048i	1.13634	−	1.13634i	0.989100	−	0.147245i	$-0.0470405\pi$
$860$		0			0
$861$	52.8439	+	52.8439i	1.80091	+	1.80091i
$862$	38.6795	+	10.6956i	1.31743	+	0.364293i
$863$		−	32.3557i		−	1.10140i	−0.834703	−	0.550701i	$-0.814361\pi$
$863$		−	32.3557i		−	1.10140i	0.834703	−	0.550701i	$-0.185639\pi$
$864$	−5.31341	+	8.40968i	−0.180766	+	0.286103i
$865$		0			0
$866$	−3.40731	+	12.3222i	−0.115785	+	0.418724i
$867$	−27.1942	+	27.1942i	−0.923564	+	0.923564i
$868$	55.7467	+	33.3825i	1.89217	+	1.13308i
$869$	8.30766	−	8.30766i	0.281818	−	0.281818i
$870$		0			0
$871$			15.8765i			0.537956i
$872$	0.129700	−	5.41803i	0.00439221	−	0.183477i
$873$	−68.5699			−2.32074
$874$	6.27397	+	11.0699i	0.212220	+	0.374444i
$875$		0			0
$876$	6.98991	−	1.75390i	0.236167	−	0.0592588i
$877$	26.2297	−	26.2297i	0.885714	−	0.885714i	−0.108394	−	0.994108i	$-0.534571\pi$
$877$	26.2297	−	26.2297i	0.885714	−	0.885714i	0.994108	+	0.108394i	$0.0345707\pi$
$878$	10.6647	−	38.5677i	0.359916	−	1.30160i
$879$	−27.2914			−0.920515
$880$		0			0
$881$	−47.3359			−1.59479			−0.797394	−	0.603459i	$-0.793789\pi$
$881$	−47.3359			−1.59479			−0.797394	+	0.603459i	$0.793789\pi$
$882$	18.5001	−	66.9037i	0.622932	−	2.25277i
$883$	−8.08371	+	8.08371i	−0.272039	+	0.272039i	−0.829920	−	0.557882i	$-0.811614\pi$
$883$	−8.08371	+	8.08371i	−0.272039	+	0.272039i	0.557882	+	0.829920i	$0.311614\pi$
$884$	1.52217	+	6.06640i	0.0511962	+	0.204035i
$885$		0			0
$886$	−12.9415	−	22.8341i	−0.434778	−	0.767127i
$887$	12.9255			0.433994			0.216997	−	0.976172i	$-0.430374\pi$
$887$	12.9255			0.433994			0.216997	+	0.976172i	$0.430374\pi$
$888$	−37.1739	−	38.9973i	−1.24747	−	1.30866i
$889$			61.9412i			2.07744i
$890$		0			0
$891$	−10.6586	+	10.6586i	−0.357078	+	0.357078i
$892$	22.0132	−	36.7606i	0.737055	−	1.23084i
$893$	−6.72664	+	6.72664i	−0.225098	+	0.225098i
$894$	−17.8514	+	64.5578i	−0.597042	+	2.15914i
$895$		0			0
$896$	15.9352	−	48.4680i	0.532359	−	1.61920i
$897$		−	13.1787i		−	0.440025i
$898$	19.6147	+	5.42384i	0.654553	+	0.180996i
$899$	6.66378	+	6.66378i	0.222250	+	0.222250i
$900$		0			0
$901$	2.18878	−	2.18878i	0.0729190	−	0.0729190i
$902$	−10.3746	−	18.3050i	−0.345435	−	0.609490i
$903$	126.232			4.20074
$904$	5.24186	−	4.99676i	0.174342	−	0.166190i
$905$		0			0
$906$	25.8481	+	45.6067i	0.858746	+	1.51518i
$907$	−16.4991	−	16.4991i	−0.547844	−	0.547844i	0.377973	−	0.925817i	$-0.376621\pi$
$907$	−16.4991	−	16.4991i	−0.547844	−	0.547844i	−0.925817	+	0.377973i	$0.876621\pi$
$908$	−22.1207	+	5.55051i	−0.734103	+	0.184200i
$909$	17.8169	+	17.8169i	0.590951	+	0.590951i
$910$		0			0
$911$	−26.6745			−0.883765			−0.441883	−	0.897073i	$-0.645689\pi$
$911$	−26.6745			−0.883765			−0.441883	+	0.897073i	$0.645689\pi$
$912$	−18.4969	−	34.5377i	−0.612493	−	1.14366i
$913$			8.03908i			0.266055i
$914$	−6.19563	−	1.71321i	−0.204933	−	0.0566678i
$915$		0			0
$916$	−12.7065	+	3.18830i	−0.419834	+	0.105344i
$917$	−23.4827	−	23.4827i	−0.775467	−	0.775467i
$918$	3.15051	−	1.78559i	0.103982	−	0.0589331i
$919$			57.7425i			1.90475i	0.304932	+	0.952374i	$0.401366\pi$
$919$			57.7425i			1.90475i	−0.304932	+	0.952374i	$0.598634\pi$
$920$		0			0
$921$			8.74878i			0.288282i
$922$	19.5303	+	34.4595i	0.643197	+	1.13486i
$923$	−2.91714	−	2.91714i	−0.0960188	−	0.0960188i
$924$	−27.7905	+	46.4083i	−0.914239	+	1.52672i
$925$		0			0
$926$	5.50280	−	19.9003i	0.180833	−	0.653965i
$927$			33.5848i			1.10307i
$928$	3.95248	−	6.25571i	0.129747	−	0.205354i
$929$	−42.5386			−1.39565			−0.697823	−	0.716270i	$-0.745848\pi$
$929$	−42.5386			−1.39565			−0.697823	+	0.716270i	$0.745848\pi$
$930$		0			0
$931$	35.7372	+	35.7372i	1.17124	+	1.17124i
$932$	44.7281	+	26.7843i	1.46512	+	0.877349i
$933$	37.3572	+	37.3572i	1.22302	+	1.22302i
$934$	34.4698	−	19.5362i	1.12789	−	0.639243i
$935$		0			0
$936$	−0.535011	+	22.3492i	−0.0174874	+	0.730507i
$937$	16.6795			0.544894			0.272447	−	0.962171i	$-0.412167\pi$
$937$	16.6795			0.544894			0.272447	+	0.962171i	$0.412167\pi$
$938$	−41.0177	+	23.2473i	−1.33928	+	0.759050i
$939$	4.51376	−	4.51376i	0.147301	−	0.147301i
$940$		0			0
$941$	9.63152	+	9.63152i	0.313979	+	0.313979i	0.846449	−	0.532470i	$-0.178736\pi$
$941$	9.63152	+	9.63152i	0.313979	+	0.313979i	−0.532470	+	0.846449i	$0.678736\pi$
$942$	2.90094	−	10.4910i	0.0945179	−	0.341814i
$943$			15.2227i			0.495721i
$944$	28.7952	+	8.70938i	0.937205	+	0.283466i
$945$		0			0
$946$	−34.2545	−	9.47200i	−1.11371	−	0.307961i
$947$	−3.44034	+	3.44034i	−0.111796	+	0.111796i	−0.760792	−	0.648996i	$-0.775189\pi$
$947$	−3.44034	+	3.44034i	−0.111796	+	0.111796i	0.648996	+	0.760792i	$0.275189\pi$
$948$	25.3860	−	6.36982i	0.824498	−	0.206882i
$949$	2.11707	−	2.11707i	0.0687231	−	0.0687231i
$950$		0			0
$951$		−	59.3028i		−	1.92302i
$952$	−13.4440	+	12.8153i	−0.435721	+	0.415347i
$953$	17.6965			0.573247			0.286623	−	0.958043i	$-0.407467\pi$
$953$	17.6965			0.573247			0.286623	+	0.958043i	$0.407467\pi$
$954$	9.62561	−	5.45542i	0.311641	−	0.176626i
$955$		0			0
$956$	−8.78886	−	5.26299i	−0.284252	−	0.170217i
$957$	−5.54750	+	5.54750i	−0.179325	+	0.179325i
$958$	−28.6759	−	7.92940i	−0.926475	−	0.256187i
$959$	102.622			3.31384
$960$		0			0
$961$	20.9027			0.674281
$962$	−21.5735	−	5.96548i	−0.695559	−	0.192335i
$963$	37.3577	−	37.3577i	1.20384	−	1.20384i
$964$	19.7303	+	11.8150i	0.635470	+	0.380535i
$965$		0			0
$966$	34.0478	−	19.2970i	1.09547	−	0.620870i
$967$	15.0023			0.482442			0.241221	−	0.970470i	$-0.422452\pi$
$967$	15.0023			0.482442			0.241221	+	0.970470i	$0.422452\pi$
$968$	−11.4966	+	10.9591i	−0.369516	+	0.352238i
$969$			14.2627i			0.458183i
$970$		0			0
$971$	−14.3135	+	14.3135i	−0.459340	+	0.459340i	−0.898439	−	0.439098i	$-0.855298\pi$
$971$	−14.3135	+	14.3135i	−0.459340	+	0.459340i	0.439098	+	0.898439i	$0.355298\pi$
$972$	−42.8038	+	10.7403i	−1.37293	+	0.344494i
$973$	28.3241	−	28.3241i	0.908030	−	0.908030i
$974$	14.0019	+	3.87177i	0.448649	+	0.124060i
$975$		0			0
$976$	1.67323	−	5.53207i	0.0535587	−	0.177077i
$977$		−	48.1433i		−	1.54024i	−0.637900	−	0.770120i	$-0.720196\pi$
$977$		−	48.1433i		−	1.54024i	0.637900	−	0.770120i	$-0.279804\pi$
$978$	−7.35698	+	26.6058i	−0.235250	+	0.850758i
$979$	−15.3580	−	15.3580i	−0.490845	−	0.490845i
$980$		0			0
$981$	−4.98651	+	4.98651i	−0.159207	+	0.159207i
$982$	−10.3647	+	5.87430i	−0.330750	+	0.187457i
$983$	0.791292			0.0252383			0.0126191	−	0.999920i	$-0.495983\pi$
$983$	0.791292			0.0252383			0.0126191	+	0.999920i	$0.495983\pi$
$984$	1.12174	−	46.8588i	0.0357597	−	1.49380i
$985$		0			0
$986$	−2.34357	+	1.32824i	−0.0746343	+	0.0422999i
$987$	20.6893	+	20.6893i	0.658547	+	0.658547i
$988$	−13.9646	−	8.36234i	−0.444273	−	0.266042i
$989$	18.1818	+	18.1818i	0.578149	+	0.578149i
$990$		0			0
$991$	−60.2424			−1.91366			−0.956832	−	0.290643i	$-0.906131\pi$
$991$	−60.2424			−1.91366			−0.956832	+	0.290643i	$0.906131\pi$
$992$	−8.96964	−	39.7547i	−0.284786	−	1.26221i
$993$			12.5133i			0.397099i
$994$	3.26513	−	11.8080i	0.103563	−	0.374526i
$995$		0			0
$996$	−9.20069	+	15.3646i	−0.291535	+	0.486845i
$997$	−1.15773	−	1.15773i	−0.0366655	−	0.0366655i	0.688536	−	0.725202i	$-0.258254\pi$
$997$	−1.15773	−	1.15773i	−0.0366655	−	0.0366655i	−0.725202	+	0.688536i	$0.758254\pi$
$998$	2.77568	+	4.89744i	0.0878626	+	0.155026i
$999$			12.9598i			0.410031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.g.349.8		16
4.3	odd	2		1600.2.q.h.849.8		16
5.2	odd	4		80.2.l.a.61.3	yes	16
5.3	odd	4		400.2.l.h.301.6		16
5.4	even	2		400.2.q.h.349.1		16
15.2	even	4		720.2.t.c.541.6		16
16.5	even	4		400.2.q.h.149.1		16
16.11	odd	4		1600.2.q.g.49.1		16
20.3	even	4		1600.2.l.i.401.8		16
20.7	even	4		320.2.l.a.81.1		16
20.19	odd	2		1600.2.q.g.849.1		16
40.27	even	4		640.2.l.a.161.8		16
40.37	odd	4		640.2.l.b.161.1		16
60.47	odd	4		2880.2.t.c.721.8		16
80.27	even	4		320.2.l.a.241.1		16
80.37	odd	4		80.2.l.a.21.3	✓	16
80.43	even	4		1600.2.l.i.1201.8		16
80.53	odd	4		400.2.l.h.101.6		16
80.59	odd	4		1600.2.q.h.49.8		16
80.67	even	4		640.2.l.a.481.8		16
80.69	even	4	inner	400.2.q.g.149.8		16
80.77	odd	4		640.2.l.b.481.1		16
160.27	even	8		5120.2.a.u.1.7		8
160.37	odd	8		5120.2.a.s.1.2		8
160.107	even	8		5120.2.a.t.1.2		8
160.117	odd	8		5120.2.a.v.1.7		8
240.107	odd	4		2880.2.t.c.2161.5		16
240.197	even	4		720.2.t.c.181.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.3	✓	16	80.37	odd	4
80.2.l.a.61.3	yes	16	5.2	odd	4
320.2.l.a.81.1		16	20.7	even	4
320.2.l.a.241.1		16	80.27	even	4
400.2.l.h.101.6		16	80.53	odd	4
400.2.l.h.301.6		16	5.3	odd	4
400.2.q.g.149.8		16	80.69	even	4	inner
400.2.q.g.349.8		16	1.1	even	1	trivial
400.2.q.h.149.1		16	16.5	even	4
400.2.q.h.349.1		16	5.4	even	2
640.2.l.a.161.8		16	40.27	even	4
640.2.l.a.481.8		16	80.67	even	4
640.2.l.b.161.1		16	40.37	odd	4
640.2.l.b.481.1		16	80.77	odd	4
720.2.t.c.181.6		16	240.197	even	4
720.2.t.c.541.6		16	15.2	even	4
1600.2.l.i.401.8		16	20.3	even	4
1600.2.l.i.1201.8		16	80.43	even	4
1600.2.q.g.49.1		16	16.11	odd	4
1600.2.q.g.849.1		16	20.19	odd	2
1600.2.q.h.49.8		16	80.59	odd	4
1600.2.q.h.849.8		16	4.3	odd	2
2880.2.t.c.721.8		16	60.47	odd	4
2880.2.t.c.2161.5		16	240.107	odd	4
5120.2.a.s.1.2		8	160.37	odd	8
5120.2.a.t.1.2		8	160.107	even	8
5120.2.a.u.1.7		8	160.27	even	8
5120.2.a.v.1.7		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+(1.36306 + 0.376912i) q^{2} +(-1.82762 + 1.82762i) q^{3} +(1.71587 + 1.02751i) q^{4} +(-3.18001 + 1.80230i) q^{6} -4.50961 q^{7} +(1.95156 + 2.04729i) q^{8} -3.68037i q^{9} +(-1.64080 + 1.64080i) q^{11} +(-5.01385 + 1.25807i) q^{12} +(-1.51857 + 1.51857i) q^{13} +(-6.14687 - 1.69972i) q^{14} +(1.88845 + 3.52615i) q^{16} -1.45616i q^{17} +(1.38717 - 5.01657i) q^{18} +(2.67964 + 2.67964i) q^{19} +(8.24183 - 8.24183i) q^{21} +(-2.85495 + 1.61808i) q^{22} +2.37423 q^{23} +(-7.30837 - 0.174953i) q^{24} +(-2.64228 + 1.49754i) q^{26} +(1.24345 + 1.24345i) q^{27} +(-7.73792 - 4.63366i) q^{28} +(-0.924966 - 0.924966i) q^{29} -7.20435 q^{31} +(1.24503 + 5.51814i) q^{32} -5.99752i q^{33} +(0.548843 - 1.98483i) q^{34} +(3.78161 - 6.31505i) q^{36} +(5.21123 + 5.21123i) q^{37} +(2.64253 + 4.66251i) q^{38} -5.55074i q^{39} +6.41166i q^{41} +(14.3406 - 8.12768i) q^{42} +(7.65800 + 7.65800i) q^{43} +(-4.50135 + 1.12947i) q^{44} +(3.23622 + 0.894875i) q^{46} +2.51027i q^{47} +(-9.89582 - 2.99308i) q^{48} +13.3366 q^{49} +(2.66130 + 2.66130i) q^{51} +(-4.16603 + 1.04534i) q^{52} +(1.50312 + 1.50312i) q^{53} +(1.22623 + 2.16357i) q^{54} +(-8.80078 - 9.23248i) q^{56} -9.79472 q^{57} +(-0.912155 - 1.60942i) q^{58} +(5.31807 - 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +(-9.81998 - 2.71541i) q^{62} +16.5970i q^{63} +(-0.382800 + 7.99084i) q^{64} +(2.26054 - 8.17499i) q^{66} +(5.22745 - 5.22745i) q^{67} +(1.49622 - 2.49859i) q^{68} +(-4.33918 + 4.33918i) q^{69} +1.92097i q^{71} +(7.53478 - 7.18247i) q^{72} -1.39412 q^{73} +(5.13905 + 9.06740i) q^{74} +(1.84458 + 7.35129i) q^{76} +(7.39938 - 7.39938i) q^{77} +(2.09214 - 7.56600i) q^{78} -5.06317 q^{79} +6.49599 q^{81} +(-2.41663 + 8.73949i) q^{82} +(2.44974 - 2.44974i) q^{83} +(22.6105 - 5.67340i) q^{84} +(7.55194 + 13.3247i) q^{86} +3.38097 q^{87} +(-6.56133 - 0.157070i) q^{88} +9.36007i q^{89} +(6.84817 - 6.84817i) q^{91} +(4.07388 + 2.43954i) q^{92} +(13.1668 - 13.1668i) q^{93} +(-0.946152 + 3.42166i) q^{94} +(-12.3605 - 7.80961i) q^{96} -18.6313i q^{97} +(18.1785 + 5.02671i) q^{98} +(6.03876 + 6.03876i) 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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