LMFDB - Embedded newform 400.2.l.h.301.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,2,Mod(101,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == 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			301.6
Root			$1.21331 + 0.726558i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.h.101.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.376912 - 1.36306i) q^{2} +(-1.82762 - 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-3.18001 + 1.80230i) q^{6} +4.50961i q^{7} +(-2.04729 + 1.95156i) q^{8} +3.68037i q^{9} +(-1.64080 + 1.64080i) q^{11} +(1.25807 + 5.01385i) q^{12} +(-1.51857 - 1.51857i) q^{13} +(6.14687 + 1.69972i) q^{14} +(1.88845 + 3.52615i) q^{16} -1.45616 q^{17} +(5.01657 + 1.38717i) q^{18} +(-2.67964 - 2.67964i) q^{19} +(8.24183 - 8.24183i) q^{21} +(1.61808 + 2.85495i) q^{22} +2.37423i q^{23} +(7.30837 + 0.174953i) q^{24} +(-2.64228 + 1.49754i) q^{26} +(1.24345 - 1.24345i) q^{27} +(4.63366 - 7.73792i) q^{28} +(0.924966 + 0.924966i) q^{29} -7.20435 q^{31} +(5.51814 - 1.24503i) q^{32} +5.99752 q^{33} +(-0.548843 + 1.98483i) q^{34} +(3.78161 - 6.31505i) q^{36} +(5.21123 - 5.21123i) q^{37} +(-4.66251 + 2.64253i) q^{38} +5.55074i q^{39} +6.41166i q^{41} +(-8.12768 - 14.3406i) q^{42} +(-7.65800 + 7.65800i) q^{43} +(4.50135 - 1.12947i) q^{44} +(3.23622 + 0.894875i) q^{46} +2.51027 q^{47} +(2.99308 - 9.89582i) q^{48} -13.3366 q^{49} +(2.66130 + 2.66130i) q^{51} +(1.04534 + 4.16603i) q^{52} +(-1.50312 + 1.50312i) q^{53} +(-1.22623 - 2.16357i) q^{54} +(-8.80078 - 9.23248i) q^{56} +9.79472i q^{57} +(1.60942 - 0.912155i) q^{58} +(-5.31807 + 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +(-2.71541 + 9.81998i) q^{62} -16.5970 q^{63} +(0.382800 - 7.99084i) q^{64} +(2.26054 - 8.17499i) q^{66} +(-5.22745 - 5.22745i) q^{67} +(2.49859 + 1.49622i) q^{68} +(4.33918 - 4.33918i) q^{69} +1.92097i q^{71} +(-7.18247 - 7.53478i) q^{72} -1.39412i q^{73} +(-5.13905 - 9.06740i) q^{74} +(1.84458 + 7.35129i) q^{76} +(-7.39938 - 7.39938i) q^{77} +(7.56600 + 2.09214i) q^{78} +5.06317 q^{79} +6.49599 q^{81} +(8.73949 + 2.41663i) q^{82} +(2.44974 + 2.44974i) q^{83} +(-22.6105 + 5.67340i) q^{84} +(7.55194 + 13.3247i) q^{86} -3.38097i q^{87} +(0.157070 - 6.56133i) q^{88} -9.36007i q^{89} +(6.84817 - 6.84817i) q^{91} +(2.43954 - 4.07388i) q^{92} +(13.1668 + 13.1668i) q^{93} +(0.946152 - 3.42166i) q^{94} +(-12.3605 - 7.80961i) q^{96} -18.6313 q^{97} +(-5.02671 + 18.1785i) q^{98} +(-6.03876 - 6.03876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * 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 $

$2$	0.376912	−	1.36306i	0.266517	−	0.963830i
$2$	0.376912	−	1.36306i	0.266517	−	0.963830i
$3$	−1.82762	−	1.82762i	−1.05518	−	1.05518i	−0.998386	−	0.0567890i	$-0.981914\pi$
$3$	−1.82762	−	1.82762i	−1.05518	−	1.05518i	−0.0567890	−	0.998386i	$-0.518086\pi$
$4$	−1.71587	−	1.02751i	−0.857937	−	0.513754i
$5$		0			0
$5$		0			0
$6$	−3.18001	+	1.80230i	−1.29823	+	0.735788i
$7$			4.50961i			1.70447i	0.523158	+	0.852236i	$0.324754\pi$
$7$			4.50961i			1.70447i	−0.523158	+	0.852236i	$0.675246\pi$
$8$	−2.04729	+	1.95156i	−0.723827	+	0.689982i
$9$			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	$0.363757\pi$
$12$	1.25807	+	5.01385i	0.363174	+	1.44737i
$13$	−1.51857	−	1.51857i	−0.421176	−	0.421176i	0.464432	−	0.885609i	$-0.346258\pi$
$13$	−1.51857	−	1.51857i	−0.421176	−	0.421176i	−0.885609	+	0.464432i	$0.846258\pi$
$14$	6.14687	+	1.69972i	1.64282	+	0.454270i
$15$		0			0
$16$	1.88845	+	3.52615i	0.472113	+	0.881538i
$17$	−1.45616			−0.353170			−0.176585	−	0.984285i	$-0.556505\pi$
$17$	−1.45616			−0.353170			−0.176585	+	0.984285i	$0.556505\pi$
$18$	5.01657	+	1.38717i	1.18242	+	0.326960i
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	0.329428	−	0.944181i	$-0.393144\pi$
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	−0.944181	+	0.329428i	$0.893144\pi$
$20$		0			0
$21$	8.24183	−	8.24183i	1.79852	−	1.79852i
$22$	1.61808	+	2.85495i	0.344975	+	0.608678i
$23$			2.37423i			0.495061i	0.968880	+	0.247530i	$0.0796190\pi$
$23$			2.37423i			0.495061i	−0.968880	+	0.247530i	$0.920381\pi$
$24$	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
$28$	4.63366	−	7.73792i	0.875679	−	1.46233i
$29$	0.924966	+	0.924966i	0.171762	+	0.171762i	0.787753	−	0.615991i	$-0.211244\pi$
$29$	0.924966	+	0.924966i	0.171762	+	0.171762i	−0.615991	+	0.787753i	$0.711244\pi$
$30$		0			0
$31$	−7.20435			−1.29394			−0.646970	−	0.762515i	$-0.723964\pi$
$31$	−7.20435			−1.29394			−0.646970	+	0.762515i	$0.723964\pi$
$32$	5.51814	−	1.24503i	0.975479	−	0.220092i
$33$	5.99752			1.04403
$34$	−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	−0.134230	−	0.990950i	$-0.542856\pi$
$37$	5.21123	−	5.21123i	0.856720	−	0.856720i	0.990950	+	0.134230i	$0.0428560\pi$
$38$	−4.66251	+	2.64253i	−0.756359	+	0.428675i
$39$			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	$0.833088\pi$
$42$	−8.12768	−	14.3406i	−1.25413	−	2.21280i
$43$	−7.65800	+	7.65800i	−1.16783	+	1.16783i	−0.185118	+	0.982716i	$0.559267\pi$
$43$	−7.65800	+	7.65800i	−1.16783	+	1.16783i	−0.982716	+	0.185118i	$0.940733\pi$
$44$	4.50135	−	1.12947i	0.678604	−	0.170275i
$45$		0			0
$46$	3.23622	+	0.894875i	0.477155	+	0.131942i
$47$	2.51027			0.366161			0.183081	−	0.983098i	$-0.441393\pi$
$47$	2.51027			0.366161			0.183081	+	0.983098i	$0.441393\pi$
$48$	2.99308	−	9.89582i	0.432015	−	1.42834i
$49$	−13.3366			−1.90522
$50$		0			0
$51$	2.66130	+	2.66130i	0.372657	+	0.372657i
$52$	1.04534	+	4.16603i	0.144962	+	0.577724i
$53$	−1.50312	+	1.50312i	−0.206470	+	0.206470i	−0.802765	−	0.596295i	$-0.796639\pi$
$53$	−1.50312	+	1.50312i	−0.206470	+	0.206470i	0.596295	+	0.802765i	$0.296639\pi$
$54$	−1.22623	−	2.16357i	−0.166869	−	0.294425i
$55$		0			0
$56$	−8.80078	−	9.23248i	−1.17605	−	1.23374i
$57$			9.79472i			1.29734i
$58$	1.60942	−	0.912155i	0.211327	−	0.119772i
$59$	−5.31807	+	5.31807i	−0.692353	+	0.692353i	−0.962749	−	0.270396i	$-0.912845\pi$
$59$	−5.31807	+	5.31807i	−0.692353	+	0.692353i	0.270396	+	0.962749i	$0.412845\pi$
$60$		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	$0.779486\pi$
$62$	−2.71541	+	9.81998i	−0.344857	+	1.24714i
$63$	−16.5970			−2.09103
$64$	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	$-0.399141\pi$
$67$	−5.22745	−	5.22745i	−0.638635	−	0.638635i	−0.950219	+	0.311584i	$0.899141\pi$
$68$	2.49859	+	1.49622i	0.302998	+	0.181443i
$69$	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	$0.963637\pi$
$72$	−7.18247	−	7.53478i	−0.846462	−	0.887983i
$73$		−	1.39412i		−	0.163169i	−0.996666	−	0.0815847i	$-0.974002\pi$
$73$		−	1.39412i		−	0.163169i	0.996666	−	0.0815847i	$-0.0259981\pi$
$74$	−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
$78$	7.56600	+	2.09214i	0.856681	+	0.236888i
$79$	5.06317			0.569651			0.284825	−	0.958579i	$-0.408064\pi$
$79$	5.06317			0.569651			0.284825	+	0.958579i	$0.408064\pi$
$80$		0			0
$81$	6.49599			0.721777
$82$	8.73949	+	2.41663i	0.965115	+	0.266872i
$83$	2.44974	+	2.44974i	0.268894	+	0.268894i	0.828654	−	0.559761i	$-0.189107\pi$
$83$	2.44974	+	2.44974i	0.268894	+	0.268894i	−0.559761	+	0.828654i	$0.689107\pi$
$84$	−22.6105	+	5.67340i	−2.46701	+	0.619019i
$85$		0			0
$86$	7.55194	+	13.3247i	0.814347	+	1.43684i
$87$		−	3.38097i		−	0.362478i
$88$	0.157070	−	6.56133i	0.0167437	−	0.699440i
$89$		−	9.36007i		−	0.992165i	−0.868275	−	0.496083i	$-0.834771\pi$
$89$		−	9.36007i		−	0.992165i	0.868275	−	0.496083i	$-0.165229\pi$
$90$		0			0
$91$	6.84817	−	6.84817i	0.717883	−	0.717883i
$92$	2.43954	−	4.07388i	0.254340	−	0.424731i
$93$	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
$97$	−18.6313			−1.89172			−0.945859	−	0.324579i	$-0.894777\pi$
$97$	−18.6313			−1.89172			−0.945859	+	0.324579i	$0.894777\pi$
$98$	−5.02671	+	18.1785i	−0.507774	+	1.83631i
$99$	−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	$0.360636\pi$
$102$	4.63059	−	2.62444i	0.458497	−	0.259858i
$103$		−	9.12540i		−	0.899153i	−0.893242	−	0.449576i	$-0.851575\pi$
$103$		−	9.12540i		−	0.899153i	0.893242	−	0.449576i	$-0.148425\pi$
$104$	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	−0.0185385	−	0.999828i	$-0.505901\pi$
$107$	10.1505	−	10.1505i	0.981290	−	0.981290i	0.999828	+	0.0185385i	$0.00590132\pi$
$108$	−3.41127	+	0.855951i	−0.328249	+	0.0823639i
$109$	1.35489	+	1.35489i	0.129775	+	0.129775i	0.769011	−	0.639236i	$-0.220749\pi$
$109$	1.35489	+	1.35489i	0.129775	+	0.129775i	−0.639236	+	0.769011i	$0.720749\pi$
$110$		0			0
$111$	−19.0483			−1.80798
$112$	−15.9016	+	8.51618i	−1.50256	+	0.804704i
$113$	2.56039			0.240861			0.120431	−	0.992722i	$-0.461572\pi$
$113$	2.56039			0.240861			0.120431	+	0.992722i	$0.461572\pi$
$114$	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
$118$	5.24441	+	9.25329i	0.482787	+	0.851835i
$119$		−	6.56670i		−	0.601969i
$120$		0			0
$121$			5.61553i			0.510503i
$122$	−1.77772	+	1.00754i	−0.160947	+	0.0912188i
$123$	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
$127$	−13.7354			−1.21882			−0.609409	−	0.792856i	$-0.708593\pi$
$127$	−13.7354			−1.21882			−0.609409	+	0.792856i	$0.708593\pi$
$128$	−10.7477	−	3.53362i	−0.949973	−	0.312331i
$129$	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	$0.645744\pi$
$132$	−10.2910	−	6.16250i	−0.895716	−	0.536377i
$133$	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
$137$			22.7563i			1.94420i	0.234559	+	0.972102i	$0.424635\pi$
$137$			22.7563i			1.94420i	−0.234559	+	0.972102i	$0.575365\pi$
$138$	−4.27908	−	7.55006i	−0.364260	−	0.642704i
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	−0.388651	−	0.921385i	$-0.627059\pi$
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	0.921385	+	0.388651i	$0.127059\pi$
$140$		0			0
$141$	−4.58782	−	4.58782i	−0.386364	−	0.386364i
$142$	2.61841	+	0.724038i	0.219732	+	0.0607599i
$143$	4.98336			0.416729
$144$	−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
$148$	−14.2964	+	3.58723i	−1.17516	+	0.294869i
$149$	−12.9574	+	12.9574i	−1.06151	+	1.06151i	−0.0635329	+	0.997980i	$0.520237\pi$
$149$	−12.9574	+	12.9574i	−1.06151	+	1.06151i	−0.997980	+	0.0635329i	$0.979763\pi$
$150$		0			0
$151$		−	14.3417i		−	1.16711i	−0.812073	−	0.583555i	$-0.801661\pi$
$151$		−	14.3417i		−	1.16711i	0.812073	−	0.583555i	$-0.198339\pi$
$152$	10.7155	+	0.256515i	0.869142	+	0.0208061i
$153$		−	5.35920i		−	0.433266i
$154$	−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	$-0.212086\pi$
$157$	2.10564	+	2.10564i	0.168049	+	0.168049i	−0.618073	+	0.786121i	$0.712086\pi$
$158$	1.90837	−	6.90141i	0.151822	−	0.549047i
$159$	5.49426			0.435723
$160$		0			0
$161$	−10.7068			−0.843817
$162$	2.44842	−	8.85444i	0.192366	−	0.695671i
$163$	5.34004	+	5.34004i	0.418265	+	0.418265i	0.884605	−	0.466341i	$-0.154428\pi$
$163$	5.34004	+	5.34004i	0.418265	+	0.418265i	−0.466341	+	0.884605i	$0.654428\pi$
$164$	6.58804	−	11.0016i	0.514439	−	0.859081i
$165$		0			0
$166$	4.26248	−	2.41581i	0.330833	−	0.187503i
$167$		−	16.0686i		−	1.24343i	−0.783245	−	0.621714i	$-0.786437\pi$
$167$		−	16.0686i		−	1.24343i	0.783245	−	0.621714i	$-0.213563\pi$
$168$	−0.788969	+	32.9579i	−0.0608702	+	2.54276i
$169$		−	8.38787i		−	0.645221i
$170$		0			0
$171$	9.86207	−	9.86207i	0.754171	−	0.754171i
$172$	21.0088	−	5.27151i	1.60191	−	0.401949i
$173$	−17.1133	−	17.1133i	−1.30110	−	1.30110i	−0.927649	−	0.373453i	$-0.878174\pi$
$173$	−17.1133	−	17.1133i	−1.30110	−	1.30110i	−0.373453	−	0.927649i	$-0.621826\pi$
$174$	−4.60847	−	1.27433i	−0.349367	−	0.0966065i
$175$		0			0
$176$	−8.88430	−	2.68714i	−0.669679	−	0.202551i
$177$	19.4388			1.46111
$178$	−12.7584	−	3.52792i	−0.956279	−	0.264429i
$179$	1.04482	+	1.04482i	0.0780933	+	0.0780933i	0.745075	−	0.666981i	$-0.232414\pi$
$179$	1.04482	+	1.04482i	0.0780933	+	0.0780933i	−0.666981	+	0.745075i	$0.732414\pi$
$180$		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	$0.0330115\pi$
$182$	−6.75332	−	11.9156i	−0.500589	−	0.883245i
$183$			3.73453i			0.276065i
$184$	−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
$188$	−4.30732	−	2.57933i	−0.314143	−	0.188117i
$189$	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	$0.499231\pi$
$192$	−15.3038	+	13.9046i	−1.10446	+	1.00348i
$193$	1.09895			0.0791039			0.0395520	−	0.999218i	$-0.487407\pi$
$193$	1.09895			0.0791039			0.0395520	+	0.999218i	$0.487407\pi$
$194$	−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	−0.990120	−	0.140222i	$-0.955218\pi$
$197$	−11.9289	+	11.9289i	−0.849899	+	0.849899i	0.140222	+	0.990120i	$0.455218\pi$
$198$	−10.5073	+	5.95512i	−0.746720	+	0.423212i
$199$			11.0397i			0.782584i	0.920267	+	0.391292i	$0.127972\pi$
$199$			11.0397i			0.782584i	−0.920267	+	0.391292i	$0.872028\pi$
$200$		0			0
$201$			19.1076i			1.34774i
$202$	4.77403	+	8.42334i	0.335899	+	0.592664i
$203$	−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
$207$	−8.73803			−0.607335
$208$	2.48696	−	8.22247i	0.172440	−	0.570126i
$209$	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	$0.887449\pi$
$212$	4.12364	−	1.03470i	0.283213	−	0.0710634i
$213$	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
$217$		−	32.4888i		−	2.20548i
$218$	2.35748	−	1.33613i	0.159669	−	0.0904941i
$219$	−2.54792	+	2.54792i	−0.172172	+	0.172172i
$220$		0			0
$221$	2.21128	+	2.21128i	0.148747	+	0.148747i
$222$	−7.17951	+	25.9639i	−0.481857	+	1.74259i
$223$	21.4238			1.43465			0.717323	−	0.696741i	$-0.245367\pi$
$223$	21.4238			1.43465			0.717323	+	0.696741i	$0.245367\pi$
$224$	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	$-0.126464\pi$
$227$	8.06331	+	8.06331i	0.535181	+	0.535181i	−0.386929	+	0.922110i	$0.626464\pi$
$228$	10.0642	−	16.8065i	0.666515	−	1.11304i
$229$	4.63169	−	4.63169i	0.306071	−	0.306071i	−0.537313	−	0.843383i	$-0.680560\pi$
$229$	4.63169	−	4.63169i	0.306071	−	0.306071i	0.843383	+	0.537313i	$0.180560\pi$
$230$		0			0
$231$			27.0465i			1.77953i
$232$	−3.69880	−	0.0885445i	−0.242838	−	0.00581323i
$233$			26.0672i			1.70772i	0.520502	+	0.853860i	$0.325745\pi$
$233$			26.0672i			1.70772i	−0.520502	+	0.853860i	$0.674255\pi$
$234$	−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
$238$	−8.95082	−	2.47507i	−0.580196	−	0.160435i
$239$	5.12209			0.331320			0.165660	−	0.986183i	$-0.447025\pi$
$239$	5.12209			0.331320			0.165660	+	0.986183i	$0.447025\pi$
$240$		0			0
$241$	11.4987			0.740695			0.370347	−	0.928893i	$-0.379239\pi$
$241$	11.4987			0.740695			0.370347	+	0.928893i	$0.379239\pi$
$242$	7.65432	+	2.11656i	0.492038	+	0.136058i
$243$	−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
$247$			8.13847i			0.517838i
$248$	14.7494	−	14.0598i	0.936588	−	0.892795i
$249$		−	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	$0.904211\pi$
$252$	28.4784	+	17.0536i	1.79397	+	1.07427i
$253$	−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
$257$	24.2494			1.51264			0.756319	−	0.654203i	$-0.226996\pi$
$257$	24.2494			1.51264			0.756319	+	0.654203i	$0.226996\pi$
$258$	10.5504	−	38.1545i	0.656842	−	2.37540i
$259$	23.5006	+	23.5006i	1.46026	+	1.46026i
$260$		0			0
$261$	−3.40422	+	3.40422i	−0.210716	+	0.210716i
$262$	9.06049	−	5.13514i	0.559759	−	0.317250i
$263$			22.5680i			1.39160i	0.718234	+	0.695802i	$0.244951\pi$
$263$			22.5680i			1.39160i	−0.718234	+	0.695802i	$0.755049\pi$
$264$	−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
$268$	3.59840	+	14.3409i	0.219807	+	0.876010i
$269$	−5.10558	−	5.10558i	−0.311293	−	0.311293i	0.534117	−	0.845410i	$-0.320644\pi$
$269$	−5.10558	−	5.10558i	−0.311293	−	0.311293i	−0.845410	+	0.534117i	$0.820644\pi$
$270$		0			0
$271$	6.67920			0.405733			0.202866	−	0.979206i	$-0.434974\pi$
$271$	6.67920			0.405733			0.202866	+	0.979206i	$0.434974\pi$
$272$	−2.74989	−	5.13464i	−0.166736	−	0.311333i
$273$	−25.0317			−1.51498
$274$	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	−0.254842	−	0.966983i	$-0.582023\pi$
$277$	11.8524	−	11.8524i	0.712141	−	0.712141i	0.966983	+	0.254842i	$0.0820234\pi$
$278$	−6.19386	−	10.9285i	−0.371483	−	0.655448i
$279$		−	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	$-0.00453334\pi$
$282$	−7.98269	+	4.52428i	−0.475362	+	0.269417i
$283$	0.482914	−	0.482914i	0.0287063	−	0.0287063i	−0.692608	−	0.721314i	$-0.743538\pi$
$283$	0.482914	−	0.482914i	0.0287063	−	0.0287063i	0.721314	+	0.692608i	$0.243538\pi$
$284$	1.97382	−	3.29615i	0.117124	−	0.195591i
$285$		0			0
$286$	1.87829	−	6.79263i	0.111065	−	0.401656i
$287$	−28.9141			−1.70674
$288$	4.58217	+	20.3088i	0.270007	+	1.19671i
$289$	−14.8796			−0.875271
$290$		0			0
$291$	34.0508	+	34.0508i	1.99609	+	1.99609i
$292$	−1.43247	+	2.39214i	−0.0838290	+	0.139989i
$293$	−7.46638	+	7.46638i	−0.436190	+	0.436190i	−0.890728	−	0.454537i	$-0.849805\pi$
$293$	−7.46638	+	7.46638i	−0.436190	+	0.436190i	0.454537	+	0.890728i	$0.349805\pi$
$294$	42.4103	−	24.0365i	2.47342	−	1.40184i
$295$		0			0
$296$	−0.498857	+	20.8389i	−0.0289955	+	1.21124i
$297$			4.08052i			0.236776i
$298$	12.7780	+	22.5456i	0.740207	+	1.30603i
$299$	3.60544	−	3.60544i	0.208508	−	0.208508i
$300$		0			0
$301$	−34.5346	−	34.5346i	−1.99054	−	1.99054i
$302$	−19.5486	−	5.40556i	−1.12490	−	0.311055i
$303$	17.6953			1.01657
$304$	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	$-0.280795\pi$
$307$	−2.39349	−	2.39349i	−0.136604	−	0.136604i	−0.772102	+	0.635498i	$0.780795\pi$
$308$	5.09348	+	20.2993i	0.290228	+	1.15666i
$309$	−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	$-0.196765\pi$
$312$	−10.8326	−	11.3640i	−0.613276	−	0.643359i
$313$		−	2.46975i		−	0.139598i	−0.997561	−	0.0697992i	$-0.977764\pi$
$313$		−	2.46975i		−	0.139598i	0.997561	−	0.0697992i	$-0.0222359\pi$
$314$	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	$-0.0271322\pi$
$317$	16.2241	+	16.2241i	0.911234	+	0.911234i	−0.0851350	+	0.996369i	$0.527132\pi$
$318$	2.07085	−	7.48902i	0.116128	−	0.419963i
$319$	−3.03537			−0.169948
$320$		0			0
$321$	−37.1026			−2.07086
$322$	−4.03553	+	14.5941i	−0.224891	+	0.813296i
$323$	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
$327$		−	4.95246i		−	0.273871i
$328$	−12.5128	−	13.1265i	−0.690902	−	0.724792i
$329$			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	$0.207521\pi$
$332$	−1.68632	−	6.72057i	−0.0925487	−	0.368839i
$333$	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
$337$	5.40017			0.294166			0.147083	−	0.989124i	$-0.453012\pi$
$337$	5.40017			0.294166			0.147083	+	0.989124i	$0.453012\pi$
$338$	−11.4332	−	3.16149i	−0.621883	−	0.171962i
$339$	−4.67941	−	4.67941i	−0.254151	−	0.254151i
$340$		0			0
$341$	11.8209	−	11.8209i	0.640139	−	0.640139i
$342$	−9.72548	−	17.1597i	−0.525894	−	0.927893i
$343$		−	28.5754i		−	1.54292i
$344$	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	−0.589208	−	0.807982i	$-0.700560\pi$
$347$	4.07531	−	4.07531i	0.218774	−	0.218774i	0.807982	+	0.589208i	$0.200560\pi$
$348$	−3.47397	+	5.80132i	−0.186224	+	0.310983i
$349$	1.55681	+	1.55681i	0.0833339	+	0.0833339i	0.747545	−	0.664211i	$-0.231232\pi$
$349$	1.55681	+	1.55681i	0.0833339	+	0.0833339i	−0.664211	+	0.747545i	$0.731232\pi$
$350$		0			0
$351$	−3.77655			−0.201577
$352$	−7.01133	+	11.0970i	−0.373705	+	0.591474i
$353$	−1.34919			−0.0718103			−0.0359052	−	0.999355i	$-0.511431\pi$
$353$	−1.34919			−0.0718103			−0.0359052	+	0.999355i	$0.511431\pi$
$354$	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
$358$	1.81795	−	1.03035i	0.0960819	−	0.0544555i
$359$		−	23.2192i		−	1.22546i	−0.790291	−	0.612732i	$-0.790071\pi$
$359$		−	23.2192i		−	1.22546i	0.790291	−	0.612732i	$-0.209929\pi$
$360$		0			0
$361$		−	4.63903i		−	0.244159i
$362$	−11.8225	−	20.8598i	−0.621379	−	1.09637i
$363$	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
$367$	5.16452			0.269586			0.134793	−	0.990874i	$-0.456963\pi$
$367$	5.16452			0.269586			0.134793	+	0.990874i	$0.456963\pi$
$368$	−8.37189	+	4.48362i	−0.436415	+	0.233725i
$369$	−23.5973			−1.22843
$370$		0			0
$371$	−6.77849	−	6.77849i	−0.351922	−	0.351922i
$372$	−9.06359	−	36.1216i	−0.469925	−	1.87282i
$373$	−18.5056	+	18.5056i	−0.958185	+	0.958185i	−0.999160	−	0.0409750i	$-0.986954\pi$
$373$	−18.5056	+	18.5056i	−0.958185	+	0.958185i	0.0409750	+	0.999160i	$0.486954\pi$
$374$	−2.35618	−	4.15727i	−0.121835	−	0.214967i
$375$		0			0
$376$	−5.13926	+	4.89896i	−0.265037	+	0.252645i
$377$		−	2.80926i		−	0.144684i
$378$	9.75687	−	5.52982i	0.501839	−	0.284423i
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	−0.963274	−	0.268520i	$-0.913465\pi$
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	0.268520	+	0.963274i	$0.413465\pi$
$380$		0			0
$381$	25.1030	+	25.1030i	1.28607	+	1.28607i
$382$	0.0251578	−	0.0909805i	0.00128718	−	0.00465497i
$383$	−21.9051			−1.11930			−0.559650	−	0.828729i	$-0.689064\pi$
$383$	−21.9051			−1.11930			−0.559650	+	0.828729i	$0.689064\pi$
$384$	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
$388$	31.9689	+	19.1438i	1.62298	+	0.971878i
$389$	4.48844	−	4.48844i	0.227573	−	0.227573i	−0.584105	−	0.811678i	$-0.698554\pi$
$389$	4.48844	−	4.48844i	0.227573	−	0.227573i	0.811678	+	0.584105i	$0.198554\pi$
$390$		0			0
$391$		−	3.45725i		−	0.174841i
$392$	27.3038	−	26.0271i	1.37905	−	1.31457i
$393$		−	19.0337i		−	0.960126i
$394$	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	$-0.387403\pi$
$397$	−11.7892	−	11.7892i	−0.591682	−	0.591682i	−0.938086	+	0.346404i	$0.887403\pi$
$398$	15.0478	+	4.16100i	0.754278	+	0.208572i
$399$	−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	$0.286170\pi$
$402$	26.0448	+	7.20187i	1.29900	+	0.359196i
$403$	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
$407$			17.1012i			0.847675i
$408$	−10.6422	−	0.254759i	−0.526865	−	0.0126125i
$409$			21.5355i			1.06486i	0.846474	+	0.532430i	$0.178721\pi$
$409$			21.5355i			1.06486i	−0.846474	+	0.532430i	$0.821279\pi$
$410$		0			0
$411$	41.5898	−	41.5898i	2.05148	−	2.05148i
$412$	−9.37643	+	15.6581i	−0.461943	+	0.771417i
$413$	−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
$417$	−22.9580			−1.12426
$418$	3.31439	−	11.9861i	0.162112	−	0.586261i
$419$	−17.2979	−	17.2979i	−0.845060	−	0.845060i	0.144452	−	0.989512i	$-0.453858\pi$
$419$	−17.2979	−	17.2979i	−0.845060	−	0.845060i	−0.989512	+	0.144452i	$0.953858\pi$
$420$		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	$0.483579\pi$
$422$	−14.9592	+	8.47830i	−0.728203	+	0.412717i
$423$			9.23874i			0.449203i
$424$	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
$428$	−27.8468	+	6.98729i	−1.34603	+	0.337744i
$429$	−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	$0.260486\pi$
$432$	6.73280	+	2.03640i	0.323932	+	0.0979763i
$433$	−9.04007			−0.434438			−0.217219	−	0.976123i	$-0.569699\pi$
$433$	−9.04007			−0.434438			−0.217219	+	0.976123i	$0.569699\pi$
$434$	−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
$438$	2.51263	+	4.43331i	0.120058	+	0.211832i
$439$			28.2949i			1.35044i	0.737615	+	0.675221i	$0.235952\pi$
$439$			28.2949i			1.35044i	−0.737615	+	0.675221i	$0.764048\pi$
$440$		0			0
$441$		−	49.0834i		−	2.33731i
$442$	3.84757	−	2.18066i	0.183010	−	0.103723i
$443$	13.1232	−	13.1232i	0.623504	−	0.623504i	−0.322922	−	0.946426i	$-0.604665\pi$
$443$	13.1232	−	13.1232i	0.623504	−	0.623504i	0.946426	+	0.322922i	$0.104665\pi$
$444$	32.6844	+	19.5722i	1.55113	+	0.928857i
$445$		0			0
$446$	8.07489	−	29.2020i	0.382357	−	1.38275i
$447$	47.3624			2.24016
$448$	36.0355	+	1.72628i	1.70252	+	0.0815588i
$449$	−14.3902			−0.679116			−0.339558	−	0.940585i	$-0.610277\pi$
$449$	−14.3902			−0.679116			−0.339558	+	0.940585i	$0.610277\pi$
$450$		0			0
$451$	−10.5203	−	10.5203i	−0.495380	−	0.495380i
$452$	−4.39331	−	2.63082i	−0.206644	−	0.123743i
$453$	−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
$457$			4.54538i			0.212624i	0.994333	+	0.106312i	$0.0339042\pi$
$457$			4.54538i			0.212624i	−0.994333	+	0.106312i	$0.966096\pi$
$458$	−4.56754	−	8.05902i	−0.213427	−	0.376573i
$459$	−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	$0.523833\pi$
$462$	36.8660	+	10.1941i	1.71516	+	0.474274i
$463$	14.5997			0.678506			0.339253	−	0.940695i	$-0.389826\pi$
$463$	14.5997			0.678506			0.339253	+	0.940695i	$0.389826\pi$
$464$	−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	$-0.474487\pi$
$467$	−19.8105	−	19.8105i	−0.916722	−	0.916722i	−0.996789	+	0.0800671i	$0.974487\pi$
$468$	−15.3325	+	3.84722i	−0.708746	+	0.177838i
$469$	23.5738	−	23.5738i	1.08853	−	1.08853i
$470$		0			0
$471$		−	7.69661i		−	0.354641i
$472$	0.509084	−	21.2662i	0.0234325	−	0.978855i
$473$		−	25.1306i		−	1.15550i
$474$	−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
$478$	1.93058	−	6.98172i	0.0883025	−	0.319337i
$479$	21.0378			0.961243			0.480621	−	0.876928i	$-0.340411\pi$
$479$	21.0378			0.961243			0.480621	+	0.876928i	$0.340411\pi$
$480$		0			0
$481$	−15.8273			−0.721661
$482$	4.33399	−	15.6734i	0.197408	−	0.713904i
$483$	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
$487$		−	10.2724i		−	0.465485i	−0.972538	−	0.232743i	$-0.925230\pi$
$487$		−	10.2724i		−	0.465485i	0.972538	−	0.232743i	$-0.0747699\pi$
$488$	4.08561	+	0.0978041i	0.184947	+	0.00442738i
$489$		−	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	$0.310878\pi$
$492$	−32.1471	+	8.06632i	−1.44930	+	0.363658i
$493$	−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
$497$	−8.66284			−0.388581
$498$	−12.2054	−	3.37501i	−0.546935	−	0.151238i
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	0.641294	−	0.767295i	$-0.278398\pi$
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	−0.767295	+	0.641294i	$0.778398\pi$
$500$		0			0
$501$	−29.3673	+	29.3673i	−1.31203	+	1.31203i
$502$	19.5524	+	34.4985i	0.872666	+	1.53974i
$503$			5.49759i			0.245125i	0.992461	+	0.122563i	$0.0391113\pi$
$503$			5.49759i			0.245125i	−0.992461	+	0.122563i	$0.960889\pi$
$504$	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
$508$	23.5682	+	14.1132i	1.04567	+	0.626173i
$509$	−4.37578	−	4.37578i	−0.193953	−	0.193953i	0.603449	−	0.797402i	$-0.293793\pi$
$509$	−4.37578	−	4.37578i	−0.193953	−	0.193953i	−0.797402	+	0.603449i	$0.793793\pi$
$510$		0			0
$511$	6.28693			0.278118
$512$	14.8109	+	17.1066i	0.654556	+	0.756013i
$513$	−6.66402			−0.294224
$514$	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
$518$	40.8904	−	23.1751i	1.79662	−	1.01826i
$519$			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	$0.733878\pi$
$522$	3.35707	+	5.92325i	0.146935	+	0.259253i
$523$	−27.8060	+	27.8060i	−1.21587	+	1.21587i	−0.246804	+	0.969065i	$0.579380\pi$
$523$	−27.8060	+	27.8060i	−1.21587	+	1.21587i	−0.969065	+	0.246804i	$0.920620\pi$
$524$	−3.58450	−	14.2855i	−0.156590	−	0.624065i
$525$		0			0
$526$	30.7616	+	8.50615i	1.34127	+	0.370886i
$527$	10.4907			0.456981
$528$	11.3260	+	21.1482i	0.492902	+	0.920356i
$529$	17.3630			0.754915
$530$		0			0
$531$	−19.5724	−	19.5724i	−0.849372	−	0.849372i
$532$	−33.1514	+	8.31832i	−1.43730	+	0.360645i
$533$	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
$537$		−	3.81905i		−	0.164804i
$538$	−8.88358	+	5.03487i	−0.382998	+	0.217069i
$539$	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	$0.720631\pi$
$542$	2.51747	−	9.10416i	0.108135	−	0.391057i
$543$	−43.8211			−1.88054
$544$	−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	$-0.0613131\pi$
$547$	18.4783	+	18.4783i	0.790074	+	0.790074i	−0.191432	+	0.981506i	$0.561313\pi$
$548$	23.3823	−	39.0470i	0.998843	−	1.66801i
$549$	3.76021	−	3.76021i	0.160482	−	0.160482i
$550$		0			0
$551$		−	4.95716i		−	0.211182i
$552$	−0.415378	+	17.3517i	−0.0176797	+	0.738539i
$553$			22.8329i			0.970953i
$554$	−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	0.940741	+	0.339127i	$0.110132\pi$
$557$	30.2060	+	30.2060i	1.27987	+	1.27987i	0.339127	+	0.940741i	$0.389868\pi$
$558$	−36.1411	−	9.99370i	−1.52998	−	0.423067i
$559$	23.2585			0.983729
$560$		0			0
$561$	−8.73334			−0.368722
$562$	−0.650807	−	0.179960i	−0.0274526	−	0.00759117i
$563$	−2.86747	−	2.86747i	−0.120850	−	0.120850i	0.644095	−	0.764945i	$-0.277234\pi$
$563$	−2.86747	−	2.86747i	−0.120850	−	0.120850i	−0.764945	+	0.644095i	$0.777234\pi$
$564$	3.15810	+	12.5862i	0.132980	+	0.529973i
$565$		0			0
$566$	−0.476226	−	0.840258i	−0.0200173	−	0.0353187i
$567$			29.2944i			1.23025i
$568$	−3.74890	−	3.93279i	−0.157300	−	0.165016i
$569$			35.8628i			1.50345i	0.659479	+	0.751723i	$0.270777\pi$
$569$			35.8628i			1.50345i	−0.659479	+	0.751723i	$0.729223\pi$
$570$		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	$0.424932\pi$
$572$	−8.55082	−	5.12044i	−0.357528	−	0.214096i
$573$	−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
$577$	−36.1387			−1.50448			−0.752238	−	0.658892i	$-0.771025\pi$
$577$	−36.1387			−1.50448			−0.752238	+	0.658892i	$0.771025\pi$
$578$	−5.60830	+	20.2818i	−0.233274	+	0.843612i
$579$	−2.00845	−	2.00845i	−0.0834685	−	0.0834685i
$580$		0			0
$581$	−11.0474	+	11.0474i	−0.458322	+	0.458322i
$582$	59.2475	−	33.5792i	2.45589	−	1.39190i
$583$		−	4.93265i		−	0.204290i
$584$	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	−0.431542	−	0.902093i	$-0.642030\pi$
$587$	11.4005	−	11.4005i	0.470550	−	0.470550i	0.902093	+	0.431542i	$0.142030\pi$
$588$	−16.7783	−	66.8675i	−0.691927	−	2.75757i
$589$	19.3051	+	19.3051i	0.795453	+	0.795453i
$590$		0			0
$591$	43.6029			1.79358
$592$	28.2167	+	8.53441i	1.15970	+	0.350762i
$593$	35.0454			1.43914			0.719572	−	0.694418i	$-0.244338\pi$
$593$	35.0454			1.43914			0.719572	+	0.694418i	$0.244338\pi$
$594$	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
$598$	−3.55550	−	6.27337i	−0.145395	−	0.256537i
$599$			18.2753i			0.746707i	0.927689	+	0.373354i	$0.121792\pi$
$599$			18.2753i			0.746707i	−0.927689	+	0.373354i	$0.878208\pi$
$600$		0			0
$601$		−	0.480142i		−	0.0195854i	−0.999952	−	0.00979269i	$-0.996883\pi$
$601$		−	0.480142i		−	0.0195854i	0.999952	−	0.00979269i	$-0.00311716\pi$
$602$	−60.0893	+	34.0563i	−2.44906	+	1.38803i
$603$	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
$607$	38.6107			1.56716			0.783581	−	0.621290i	$-0.213391\pi$
$607$	38.6107			1.56716			0.783581	+	0.621290i	$0.213391\pi$
$608$	−18.1229	−	11.4504i	−0.734980	−	0.464376i
$609$	15.2468			0.617833
$610$		0			0
$611$	−3.81204	−	3.81204i	−0.154218	−	0.154218i
$612$	−5.50662	+	9.19572i	−0.222592	+	0.371715i
$613$	5.53592	−	5.53592i	0.223594	−	0.223594i	−0.586416	−	0.810010i	$-0.699462\pi$
$613$	5.53592	−	5.53592i	0.223594	−	0.223594i	0.810010	+	0.586416i	$0.199462\pi$
$614$	−4.16461	+	2.36034i	−0.168070	+	0.0952557i
$615$		0			0
$616$	29.5890	+	0.708322i	1.19218	+	0.0285391i
$617$			31.8836i			1.28358i	0.766879	+	0.641792i	$0.221809\pi$
$617$			31.8836i			1.28358i	−0.766879	+	0.641792i	$0.778191\pi$
$618$	16.4468	+	29.0188i	0.661586	+	1.16731i
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.202650	+	0.979251i	$0.564955\pi$
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.979251	+	0.202650i	$0.935045\pi$
$620$		0			0
$621$	2.95224	+	2.95224i	0.118469	+	0.118469i
$622$	−27.8615	−	7.70422i	−1.11714	−	0.308911i
$623$	42.2102			1.69112
$624$	−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
$628$	−1.44945	−	5.77658i	−0.0578395	−	0.230511i
$629$	−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	$0.790432\pi$
$632$	−10.3658	+	9.88109i	−0.412328	+	0.393049i
$633$			31.4254i			1.24905i
$634$	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
$638$	−1.14407	+	4.13740i	−0.0452941	+	0.163801i
$639$	−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	$0.413218\pi$
$642$	−13.9844	+	50.5731i	−0.551921	+	1.99596i
$643$	−14.9224	−	14.9224i	−0.588480	−	0.588480i	0.348740	−	0.937220i	$-0.386610\pi$
$643$	−14.9224	−	14.9224i	−0.588480	−	0.588480i	−0.937220	+	0.348740i	$0.886610\pi$
$644$	18.3716	+	11.0014i	0.723942	+	0.433514i
$645$		0			0
$646$	6.78935	−	3.84794i	0.267123	−	0.151395i
$647$		−	4.87972i		−	0.191841i	−0.995389	−	0.0959207i	$-0.969420\pi$
$647$		−	4.87972i		−	0.191841i	0.995389	−	0.0959207i	$-0.0305795\pi$
$648$	−13.2992	+	12.6773i	−0.522442	+	0.498013i
$649$		−	17.4518i		−	0.685043i
$650$		0			0
$651$	−59.3771	+	59.3771i	−2.32717	+	2.32717i
$652$	−3.67591	−	14.6498i	−0.143960	−	0.573730i
$653$	10.2913	+	10.2913i	0.402731	+	0.402731i	0.879194	−	0.476463i	$-0.158081\pi$
$653$	10.2913	+	10.2913i	0.402731	+	0.402731i	−0.476463	+	0.879194i	$0.658081\pi$
$654$	−6.75050	−	1.86664i	−0.263966	−	0.0729914i
$655$		0			0
$656$	−22.6085	+	12.1081i	−0.882713	+	0.472743i
$657$	5.13088			0.200174
$658$	15.4303	+	4.26677i	0.601537	+	0.166336i
$659$	−21.9025	−	21.9025i	−0.853201	−	0.853201i	0.137325	−	0.990526i	$-0.456149\pi$
$659$	−21.9025	−	21.9025i	−0.853201	−	0.853201i	−0.990526	+	0.137325i	$0.956149\pi$
$660$		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	$0.202497\pi$
$662$	−3.37599	−	5.95663i	−0.131212	−	0.231511i
$663$		−	8.08276i		−	0.313908i
$664$	−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
$668$	−16.5106	+	27.5717i	−0.638816	+	1.06678i
$669$	−39.1546	−	39.1546i	−1.51380	−	1.51380i
$670$		0			0
$671$	3.35280			0.129433
$672$	35.2183	−	55.7410i	1.35857	−	2.15025i
$673$	−35.3820			−1.36388			−0.681938	−	0.731410i	$-0.738862\pi$
$673$	−35.3820			−1.36388			−0.681938	+	0.731410i	$0.738862\pi$
$674$	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	−0.799452	−	0.600730i	$-0.794877\pi$
$677$	−5.17061	+	5.17061i	−0.198723	+	0.198723i	0.600730	+	0.799452i	$0.294877\pi$
$678$	−8.14205	+	4.61460i	−0.312694	+	0.177223i
$679$		−	84.0196i		−	3.22438i
$680$		0			0
$681$		−	29.4733i		−	1.12942i
$682$	−11.6572	−	20.5681i	−0.446377	−	0.787593i
$683$	−26.5989	+	26.5989i	−1.01778	+	1.01778i	−0.0179409	+	0.999839i	$0.505711\pi$
$683$	−26.5989	+	26.5989i	−1.01778	+	1.01778i	−0.999839	+	0.0179409i	$0.994289\pi$
$684$	−27.0554	+	6.78872i	−1.03449	+	0.259573i
$685$		0			0
$686$	−38.9500	−	10.7704i	−1.48712	−	0.411216i
$687$	−16.9299			−0.645916
$688$	−41.4651	−	12.5415i	−1.58084	−	0.478140i
$689$	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	$0.949448\pi$
$692$	11.7802	+	46.9484i	0.447818	+	1.78471i
$693$	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
$697$		−	9.33640i		−	0.353641i
$698$	2.70880	−	1.53524i	0.102530	−	0.0581099i
$699$	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	$0.883221\pi$
$702$	−1.42343	+	5.14767i	−0.0537237	+	0.194286i
$703$	−27.9285			−1.05334
$704$	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
$708$	−33.3545	−	19.9735i	−1.25354	−	0.750650i
$709$	4.87350	−	4.87350i	0.183028	−	0.183028i	−0.609646	−	0.792674i	$-0.708688\pi$
$709$	4.87350	−	4.87350i	0.183028	−	0.183028i	0.792674	+	0.609646i	$0.208688\pi$
$710$		0			0
$711$			18.6343i			0.698842i
$712$	18.2668	+	19.1628i	0.684576	+	0.718156i
$713$		−	17.1048i		−	0.640579i
$714$	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
$718$	−31.6492	−	8.75160i	−1.18114	−	0.326607i
$719$	9.27351			0.345843			0.172922	−	0.984936i	$-0.444679\pi$
$719$	9.27351			0.345843			0.172922	+	0.984936i	$0.444679\pi$
$720$		0			0
$721$	41.1520			1.53258
$722$	−6.32328	−	1.74850i	−0.235328	−	0.0650726i
$723$	−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
$727$		−	10.6056i		−	0.393341i	−0.980470	−	0.196670i	$-0.936987\pi$
$727$		−	10.6056i		−	0.393341i	0.980470	−	0.196670i	$-0.0630129\pi$
$728$	−0.655557	+	27.3848i	−0.0242965	+	1.01495i
$729$			37.5430i			1.39048i
$730$		0			0
$731$	11.1513	−	11.1513i	0.412445	−	0.412445i
$732$	3.83726	−	6.40799i	0.141829	−	0.236846i
$733$	29.6530	+	29.6530i	1.09526	+	1.09526i	0.994957	+	0.100301i	$0.0319806\pi$
$733$	29.6530	+	29.6530i	1.09526	+	1.09526i	0.100301	+	0.994957i	$0.468019\pi$
$734$	1.94657	−	7.03956i	0.0718492	−	0.259835i
$735$		0			0
$736$	2.95599	+	13.1013i	0.108959	+	0.482921i
$737$	17.1544			0.631892
$738$	−8.89409	+	32.1645i	−0.327396	+	1.18399i
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.989202	+	0.146559i	$0.0468197\pi$
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.146559	+	0.989202i	$0.453180\pi$
$740$		0			0
$741$	14.8740	−	14.8740i	0.546410	−	0.546410i
$742$	−11.7944	+	6.68461i	−0.432986	+	0.245400i
$743$		−	22.3956i		−	0.821617i	−0.911722	−	0.410808i	$-0.865247\pi$
$743$		−	22.3956i		−	0.821617i	0.911722	−	0.410808i	$-0.134753\pi$
$744$	−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
$748$	−6.55468	+	1.64469i	−0.239663	+	0.0601359i
$749$	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	$0.377069\pi$
$752$	4.74054	+	8.85161i	0.172870	+	0.322785i
$753$	72.4724			2.64104
$754$	−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	−0.993234	−	0.116130i	$-0.962951\pi$
$757$	−24.1323	+	24.1323i	−0.877104	+	0.877104i	0.116130	+	0.993234i	$0.462951\pi$
$758$	13.3381	+	23.5339i	0.484461	+	0.854788i
$759$			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	$-0.363648\pi$
$762$	43.6786	−	24.7554i	1.58231	−	0.896792i
$763$	−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
$767$	16.1517			0.583206
$768$	40.5465	−	8.13374i	1.46309	−	0.293501i
$769$	−28.6887			−1.03454			−0.517270	−	0.855822i	$-0.673052\pi$
$769$	−28.6887			−1.03454			−0.517270	+	0.855822i	$0.673052\pi$
$770$		0			0
$771$	−44.3187	−	44.3187i	−1.59610	−	1.59610i
$772$	−1.88565	−	1.12918i	−0.0678662	−	0.0406400i
$773$	37.5957	−	37.5957i	1.35222	−	1.35222i	0.469052	−	0.883171i	$-0.344596\pi$
$773$	37.5957	−	37.5957i	1.35222	−	1.35222i	0.883171	−	0.469052i	$-0.155404\pi$
$774$	−49.0399	+	27.7939i	−1.76270	+	0.999032i
$775$		0			0
$776$	38.1436	−	36.3601i	1.36928	−	1.30525i
$777$		−	85.9001i		−	3.08165i
$778$	−4.42628	−	7.80977i	−0.158690	−	0.279994i
$779$	17.1810	−	17.1810i	0.615572	−	0.615572i
$780$		0			0
$781$	−3.15194	−	3.15194i	−0.112785	−	0.112785i
$782$	−4.71245	−	1.30308i	−0.168517	−	0.0465980i
$783$	2.30030			0.0822061
$784$	−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	$-0.224838\pi$
$787$	3.13285	+	3.13285i	0.111674	+	0.111674i	−0.649062	+	0.760736i	$0.724838\pi$
$788$	32.7255	−	8.21145i	1.16580	−	0.292521i
$789$	41.2457	−	41.2457i	1.46839	−	1.46839i
$790$		0			0
$791$			11.5463i			0.410541i
$792$	24.1481	+	0.578074i	0.858066	+	0.0205410i
$793$			3.10304i			0.110192i
$794$	−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	$-0.250448\pi$
$797$	−0.0562195	−	0.0562195i	−0.00199140	−	0.00199140i	−0.708102	+	0.706110i	$0.750448\pi$
$798$	−16.6483	+	60.2069i	−0.589344	+	2.13130i
$799$	−3.65536			−0.129317
$800$		0			0
$801$	34.4485			1.21718
$802$	9.39488	−	33.9756i	0.331745	−	1.19972i
$803$	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
$807$			18.6621i			0.656937i
$808$	0.463423	−	19.3588i	0.0163032	−	0.681039i
$809$			3.59856i			0.126518i	0.997997	+	0.0632592i	$0.0201495\pi$
$809$			3.59856i			0.126518i	−0.997997	+	0.0632592i	$0.979851\pi$
$810$		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	$0.308521\pi$
$812$	11.4433	−	2.87134i	0.401581	−	0.100764i
$813$	−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
$817$	41.0414			1.43586
$818$	29.3542	+	8.11697i	1.02634	+	0.283803i
$819$	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	$0.131157\pi$
$822$	−41.0138	−	72.3652i	−1.43052	−	2.52403i
$823$		−	52.7544i		−	1.83890i	−0.393203	−	0.919452i	$-0.628633\pi$
$823$		−	52.7544i		−	1.83890i	0.393203	−	0.919452i	$-0.371367\pi$
$824$	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	−0.936890	−	0.349625i	$-0.886309\pi$
$827$	−16.8883	+	16.8883i	−0.587265	+	0.587265i	0.349625	+	0.936890i	$0.386309\pi$
$828$	14.9934	+	8.97840i	0.521056	+	0.312021i
$829$	−8.55974	−	8.55974i	−0.297292	−	0.297292i	0.542660	−	0.839952i	$-0.317417\pi$
$829$	−8.55974	−	8.55974i	−0.297292	−	0.297292i	−0.839952	+	0.542660i	$0.817417\pi$
$830$		0			0
$831$	−43.3232			−1.50287
$832$	−12.7160	+	11.5534i	−0.440847	+	0.400541i
$833$	19.4201			0.672868
$834$	−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
$838$	−30.0980	+	17.0584i	−1.03972	+	0.589271i
$839$			17.5407i			0.605572i	0.953059	+	0.302786i	$0.0979168\pi$
$839$			17.5407i			0.605572i	−0.953059	+	0.302786i	$0.902083\pi$
$840$		0			0
$841$		−	27.2889i		−	0.940996i
$842$	19.1638	+	33.8129i	0.660429	+	1.16527i
$843$	−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
$847$	−25.3238			−0.870137
$848$	−8.13881	−	2.46166i	−0.279488	−	0.0845337i
$849$	−1.76516			−0.0605803
$850$		0			0
$851$	12.3726	+	12.3726i	0.424129	+	0.424129i
$852$	−9.63148	+	2.41672i	−0.329969	+	0.0827955i
$853$	15.3577	−	15.3577i	0.525839	−	0.525839i	−0.393490	−	0.919329i	$-0.628732\pi$
$853$	15.3577	−	15.3577i	0.525839	−	0.525839i	0.919329	+	0.393490i	$0.128732\pi$
$854$	−4.54363	−	8.01683i	−0.155480	−	0.274330i
$855$		0			0
$856$	−0.971684	+	40.5905i	−0.0332115	+	1.38736i
$857$		−	17.9553i		−	0.613341i	−0.951816	−	0.306671i	$-0.900785\pi$
$857$		−	17.9553i		−	0.613341i	0.951816	−	0.306671i	$-0.0992150\pi$
$858$	−15.8471	+	8.98153i	−0.541011	+	0.306624i
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.147245	+	0.989100i	$0.547040\pi$
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.989100	+	0.147245i	$0.952960\pi$
$860$		0			0
$861$	52.8439	+	52.8439i	1.80091	+	1.80091i
$862$	10.6956	−	38.6795i	0.364293	−	1.31743i
$863$	32.3557			1.10140			0.550701	−	0.834703i	$-0.314361\pi$
$863$	32.3557			1.10140			0.550701	+	0.834703i	$0.314361\pi$
$864$	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
$868$	−33.3825	+	55.7467i	−1.13308	+	1.89217i
$869$	−8.30766	+	8.30766i	−0.281818	+	0.281818i
$870$		0			0
$871$			15.8765i			0.537956i
$872$	−5.41803	−	0.129700i	−0.183477	−	0.00439221i
$873$		−	68.5699i		−	2.32074i
$874$	−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	$-0.465429\pi$
$877$	−26.2297	−	26.2297i	−0.885714	−	0.885714i	−0.994108	+	0.108394i	$0.965429\pi$
$878$	38.5677	+	10.6647i	1.30160	+	0.359916i
$879$	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	$0.793789\pi$
$882$	−66.9037	−	18.5001i	−2.25277	−	0.622932i
$883$	−8.08371	−	8.08371i	−0.272039	−	0.272039i	0.557882	−	0.829920i	$-0.311614\pi$
$883$	−8.08371	−	8.08371i	−0.272039	−	0.272039i	−0.829920	+	0.557882i	$0.811614\pi$
$884$	−1.52217	−	6.06640i	−0.0511962	−	0.204035i
$885$		0			0
$886$	−12.9415	−	22.8341i	−0.434778	−	0.767127i
$887$		−	12.9255i		−	0.433994i	−0.976172	−	0.216997i	$-0.930374\pi$
$887$		−	12.9255i		−	0.433994i	0.976172	−	0.216997i	$-0.0696263\pi$
$888$	38.9973	−	37.1739i	1.30866	−	1.24747i
$889$		−	61.9412i		−	2.07744i
$890$		0			0
$891$	−10.6586	+	10.6586i	−0.357078	+	0.357078i
$892$	−36.7606	−	22.0132i	−1.23084	−	0.737055i
$893$	−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
$897$	−13.1787			−0.440025
$898$	−5.42384	+	19.6147i	−0.180996	+	0.654553i
$899$	−6.66378	−	6.66378i	−0.222250	−	0.222250i
$900$		0			0
$901$	2.18878	−	2.18878i	0.0729190	−	0.0729190i
$902$	−18.3050	+	10.3746i	−0.609490	+	0.345435i
$903$			126.232i			4.20074i
$904$	−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	−0.925817	−	0.377973i	$-0.876621\pi$
$907$	−16.4991	+	16.4991i	−0.547844	+	0.547844i	0.377973	+	0.925817i	$0.376621\pi$
$908$	−5.55051	−	22.1207i	−0.184200	−	0.734103i
$909$	−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	$0.645689\pi$
$912$	−34.5377	+	18.4969i	−1.14366	+	0.612493i
$913$	−8.03908			−0.266055
$914$	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
$918$	1.78559	+	3.15051i	0.0589331	+	0.103982i
$919$		−	57.7425i		−	1.90475i	−0.304932	−	0.952374i	$-0.598634\pi$
$919$		−	57.7425i		−	1.90475i	0.304932	−	0.952374i	$-0.401366\pi$
$920$		0			0
$921$			8.74878i			0.288282i
$922$	34.4595	−	19.5303i	1.13486	−	0.643197i
$923$	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
$927$	33.5848			1.10307
$928$	6.25571	+	3.95248i	0.205354	+	0.129747i
$929$	42.5386			1.39565			0.697823	−	0.716270i	$-0.254152\pi$
$929$	42.5386			1.39565			0.697823	+	0.716270i	$0.254152\pi$
$930$		0			0
$931$	35.7372	+	35.7372i	1.17124	+	1.17124i
$932$	26.7843	−	44.7281i	0.877349	−	1.46512i
$933$	−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
$937$		−	16.6795i		−	0.544894i	−0.962171	−	0.272447i	$-0.912167\pi$
$937$		−	16.6795i		−	0.544894i	0.962171	−	0.272447i	$-0.0878330\pi$
$938$	−23.2473	−	41.0177i	−0.759050	−	1.33928i
$939$	−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	$0.678736\pi$
$942$	−10.4910	−	2.90094i	−0.341814	−	0.0945179i
$943$	−15.2227			−0.495721
$944$	−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	$-0.224811\pi$
$947$	3.44034	+	3.44034i	0.111796	+	0.111796i	−0.648996	+	0.760792i	$0.724811\pi$
$948$	6.36982	+	25.3860i	0.206882	+	0.824498i
$949$	−2.11707	+	2.11707i	−0.0687231	+	0.0687231i
$950$		0			0
$951$		−	59.3028i		−	1.92302i
$952$	12.8153	+	13.4440i	0.415347	+	0.435721i
$953$			17.6965i			0.573247i	0.958043	+	0.286623i	$0.0925328\pi$
$953$			17.6965i			0.573247i	−0.958043	+	0.286623i	$0.907467\pi$
$954$	−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
$958$	7.92940	−	28.6759i	0.256187	−	0.926475i
$959$	−102.622			−3.31384
$960$		0			0
$961$	20.9027			0.674281
$962$	−5.96548	+	21.5735i	−0.192335	+	0.695559i
$963$	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
$967$		−	15.0023i		−	0.482442i	−0.970470	−	0.241221i	$-0.922452\pi$
$967$		−	15.0023i		−	0.482442i	0.970470	−	0.241221i	$-0.0775479\pi$
$968$	−10.9591	−	11.4966i	−0.352238	−	0.369516i
$969$		−	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	$0.355298\pi$
$972$	10.7403	+	42.8038i	0.344494	+	1.37293i
$973$	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
$977$	−48.1433			−1.54024			−0.770120	−	0.637900i	$-0.779804\pi$
$977$	−48.1433			−1.54024			−0.770120	+	0.637900i	$0.779804\pi$
$978$	−26.6058	−	7.35698i	−0.850758	−	0.235250i
$979$	15.3580	+	15.3580i	0.490845	+	0.490845i
$980$		0			0
$981$	−4.98651	+	4.98651i	−0.159207	+	0.159207i
$982$	5.87430	+	10.3647i	0.187457	+	0.330750i
$983$			0.791292i			0.0252383i	0.999920	+	0.0126191i	$0.00401690\pi$
$983$			0.791292i			0.0252383i	−0.999920	+	0.0126191i	$0.995983\pi$
$984$	−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
$988$	8.36234	−	13.9646i	0.266042	−	0.444273i
$989$	−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	$0.906131\pi$
$992$	−39.7547	+	8.96964i	−1.26221	+	0.284786i
$993$	−12.5133			−0.397099
$994$	−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	−0.725202	−	0.688536i	$-0.758254\pi$
$997$	−1.15773	+	1.15773i	−0.0366655	+	0.0366655i	0.688536	+	0.725202i	$0.258254\pi$
$998$	−4.89744	+	2.77568i	−0.155026	+	0.0878626i
$999$		−	12.9598i		−	0.410031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.h.301.6		16
4.3	odd	2		1600.2.l.i.401.8		16
5.2	odd	4		400.2.q.g.349.8		16
5.3	odd	4		400.2.q.h.349.1		16
5.4	even	2		80.2.l.a.61.3	yes	16
15.14	odd	2		720.2.t.c.541.6		16
16.5	even	4	inner	400.2.l.h.101.6		16
16.11	odd	4		1600.2.l.i.1201.8		16
20.3	even	4		1600.2.q.g.849.1		16
20.7	even	4		1600.2.q.h.849.8		16
20.19	odd	2		320.2.l.a.81.1		16
40.19	odd	2		640.2.l.a.161.8		16
40.29	even	2		640.2.l.b.161.1		16
60.59	even	2		2880.2.t.c.721.8		16
80.19	odd	4		640.2.l.a.481.8		16
80.27	even	4		1600.2.q.g.49.1		16
80.29	even	4		640.2.l.b.481.1		16
80.37	odd	4		400.2.q.h.149.1		16
80.43	even	4		1600.2.q.h.49.8		16
80.53	odd	4		400.2.q.g.149.8		16
80.59	odd	4		320.2.l.a.241.1		16
80.69	even	4		80.2.l.a.21.3	✓	16
160.59	odd	8		5120.2.a.u.1.7		8
160.69	even	8		5120.2.a.s.1.2		8
160.139	odd	8		5120.2.a.t.1.2		8
160.149	even	8		5120.2.a.v.1.7		8
240.59	even	4		2880.2.t.c.2161.5		16
240.149	odd	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	80.69	even	4
80.2.l.a.61.3	yes	16	5.4	even	2
320.2.l.a.81.1		16	20.19	odd	2
320.2.l.a.241.1		16	80.59	odd	4
400.2.l.h.101.6		16	16.5	even	4	inner
400.2.l.h.301.6		16	1.1	even	1	trivial
400.2.q.g.149.8		16	80.53	odd	4
400.2.q.g.349.8		16	5.2	odd	4
400.2.q.h.149.1		16	80.37	odd	4
400.2.q.h.349.1		16	5.3	odd	4
640.2.l.a.161.8		16	40.19	odd	2
640.2.l.a.481.8		16	80.19	odd	4
640.2.l.b.161.1		16	40.29	even	2
640.2.l.b.481.1		16	80.29	even	4
720.2.t.c.181.6		16	240.149	odd	4
720.2.t.c.541.6		16	15.14	odd	2
1600.2.l.i.401.8		16	4.3	odd	2
1600.2.l.i.1201.8		16	16.11	odd	4
1600.2.q.g.49.1		16	80.27	even	4
1600.2.q.g.849.1		16	20.3	even	4
1600.2.q.h.49.8		16	80.43	even	4
1600.2.q.h.849.8		16	20.7	even	4
2880.2.t.c.721.8		16	60.59	even	2
2880.2.t.c.2161.5		16	240.59	even	4
5120.2.a.s.1.2		8	160.69	even	8
5120.2.a.t.1.2		8	160.139	odd	8
5120.2.a.u.1.7		8	160.59	odd	8
5120.2.a.v.1.7		8	160.149	even	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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.376912 - 1.36306i) q^{2} +(-1.82762 - 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-3.18001 + 1.80230i) q^{6} +4.50961i q^{7} +(-2.04729 + 1.95156i) q^{8} +3.68037i q^{9} +(-1.64080 + 1.64080i) q^{11} +(1.25807 + 5.01385i) q^{12} +(-1.51857 - 1.51857i) q^{13} +(6.14687 + 1.69972i) q^{14} +(1.88845 + 3.52615i) q^{16} -1.45616 q^{17} +(5.01657 + 1.38717i) q^{18} +(-2.67964 - 2.67964i) q^{19} +(8.24183 - 8.24183i) q^{21} +(1.61808 + 2.85495i) q^{22} +2.37423i q^{23} +(7.30837 + 0.174953i) q^{24} +(-2.64228 + 1.49754i) q^{26} +(1.24345 - 1.24345i) q^{27} +(4.63366 - 7.73792i) q^{28} +(0.924966 + 0.924966i) q^{29} -7.20435 q^{31} +(5.51814 - 1.24503i) q^{32} +5.99752 q^{33} +(-0.548843 + 1.98483i) q^{34} +(3.78161 - 6.31505i) q^{36} +(5.21123 - 5.21123i) q^{37} +(-4.66251 + 2.64253i) q^{38} +5.55074i q^{39} +6.41166i q^{41} +(-8.12768 - 14.3406i) q^{42} +(-7.65800 + 7.65800i) q^{43} +(4.50135 - 1.12947i) q^{44} +(3.23622 + 0.894875i) q^{46} +2.51027 q^{47} +(2.99308 - 9.89582i) q^{48} -13.3366 q^{49} +(2.66130 + 2.66130i) q^{51} +(1.04534 + 4.16603i) q^{52} +(-1.50312 + 1.50312i) q^{53} +(-1.22623 - 2.16357i) q^{54} +(-8.80078 - 9.23248i) q^{56} +9.79472i q^{57} +(1.60942 - 0.912155i) q^{58} +(-5.31807 + 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +(-2.71541 + 9.81998i) q^{62} -16.5970 q^{63} +(0.382800 - 7.99084i) q^{64} +(2.26054 - 8.17499i) q^{66} +(-5.22745 - 5.22745i) q^{67} +(2.49859 + 1.49622i) q^{68} +(4.33918 - 4.33918i) q^{69} +1.92097i q^{71} +(-7.18247 - 7.53478i) q^{72} -1.39412i q^{73} +(-5.13905 - 9.06740i) q^{74} +(1.84458 + 7.35129i) q^{76} +(-7.39938 - 7.39938i) q^{77} +(7.56600 + 2.09214i) q^{78} +5.06317 q^{79} +6.49599 q^{81} +(8.73949 + 2.41663i) q^{82} +(2.44974 + 2.44974i) q^{83} +(-22.6105 + 5.67340i) q^{84} +(7.55194 + 13.3247i) q^{86} -3.38097i q^{87} +(0.157070 - 6.56133i) q^{88} -9.36007i q^{89} +(6.84817 - 6.84817i) q^{91} +(2.43954 - 4.07388i) q^{92} +(13.1668 + 13.1668i) q^{93} +(0.946152 - 3.42166i) q^{94} +(-12.3605 - 7.80961i) q^{96} -18.6313 q^{97} +(-5.02671 + 18.1785i) q^{98} +(-6.03876 - 6.03876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6} - 8 q^{11} + 12 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 20 q^{22} + 8 q^{24} - 16 q^{26} - 24 q^{27} + 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} + 16 q^{37} - 20 q^{38} - 60 q^{42}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 - 8 * q^11 + 12 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 20 * q^22 + 8 * q^24 - 16 * q^26 - 24 * q^27 + 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 + 16 * q^37 - 20 * q^38 - 60 * q^42 - 8 * q^43 + 40 * q^44 - 4 * q^46 + 40 * q^47 + 40 * q^48 - 16 * q^49 - 32 * q^51 - 56 * q^52 - 16 * q^53 + 32 * q^54 + 16 * q^56 + 12 * q^58 - 8 * q^59 + 16 * q^61 + 8 * q^62 - 40 * q^63 - 16 * q^64 - 40 * q^67 + 48 * q^68 + 16 * q^69 + 40 * q^72 - 72 * q^74 - 16 * q^77 + 16 * q^78 + 16 * q^79 - 16 * q^81 + 76 * q^82 - 40 * q^83 - 64 * q^84 + 28 * q^86 + 32 * q^91 + 52 * q^92 + 48 * q^93 - 36 * q^94 + 8 * q^96 - 60 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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