LMFDB - Embedded newform 975.2.w.i.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.191102976.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 $ x^8 - 6x^6 + 6x^4 + 36*x^2 + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$0.291439 + 1.08766i$ of defining polynomial
Character	$\chi$	$=$	975.199
Dual form			975.2.w.i.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08766 - 1.88389i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.36603 - 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.221638 + 0.383889i) q^{7} -1.59245 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.08766 - 1.88389i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.36603 - 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.221638 + 0.383889i) q^{7} -1.59245 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.37910 - 0.796225i) q^{11} -2.73205i q^{12} +(1.20856 - 3.39697i) q^{13} +0.964273 q^{14} +(1.00000 - 1.73205i) q^{16} +(3.26299 - 1.88389i) q^{17} +2.17533 q^{18} +(1.33987 - 0.773575i) q^{19} +0.443277i q^{21} +(-3.00000 + 1.73205i) q^{22} +(0.611324 + 0.352948i) q^{23} +(-1.37910 - 0.796225i) q^{24} +(-5.08500 - 5.97155i) q^{26} +1.00000i q^{27} +(0.605528 - 1.04880i) q^{28} +(1.24991 - 2.16492i) q^{29} -6.18490i q^{31} +(-3.76778 - 6.52598i) q^{32} +(-0.796225 - 1.37910i) q^{33} -8.19615i q^{34} +(1.36603 - 2.36603i) q^{36} +(-5.17533 + 8.96393i) q^{37} -3.36556i q^{38} +(2.74513 - 2.33758i) q^{39} +(5.21419 + 3.01041i) q^{41} +(0.835085 + 0.482136i) q^{42} +(-4.08979 + 2.36124i) q^{43} +4.35066i q^{44} +(1.32983 - 0.767778i) q^{46} +5.41712 q^{47} +(1.73205 - 1.00000i) q^{48} +(3.40175 - 5.89201i) q^{49} +3.76778 q^{51} +(-9.68823 + 1.78086i) q^{52} +5.51641i q^{53} +(1.88389 + 1.08766i) q^{54} +(-0.352948 - 0.611324i) q^{56} +1.54715 q^{57} +(-2.71897 - 4.70940i) q^{58} +(-7.55359 + 4.36107i) q^{59} +(4.86603 + 8.42820i) q^{61} +(-11.6517 - 6.72709i) q^{62} +(-0.221638 + 0.383889i) q^{63} -12.3923 q^{64} -3.46410 q^{66} +(-6.84799 + 11.8611i) q^{67} +(-8.91466 - 5.14688i) q^{68} +(0.352948 + 0.611324i) q^{69} +(13.1193 - 7.57442i) q^{71} +(-0.796225 - 1.37910i) q^{72} -10.7939 q^{73} +(11.2580 + 19.4995i) q^{74} +(-3.66060 - 2.11345i) q^{76} -0.705897i q^{77} +(-1.41796 - 7.71402i) q^{78} -10.7317 q^{79} +(-0.500000 + 0.866025i) q^{81} +(11.3426 - 6.54863i) q^{82} -9.12801 q^{83} +(1.04880 - 0.605528i) q^{84} +10.2729i q^{86} +(2.16492 - 1.24991i) q^{87} +(2.19615 + 1.26795i) q^{88} +(4.11927 + 2.37826i) q^{89} +(1.57192 - 0.288945i) q^{91} -1.92855i q^{92} +(3.09245 - 5.35628i) q^{93} +(5.89201 - 10.2053i) q^{94} -7.53556i q^{96} +(4.20856 + 7.28944i) q^{97} +(-7.39993 - 12.8170i) q^{98} -1.59245i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 + 4 * q^9	$ 8 q - 4 q^{4} + 4 q^{9} + 12 q^{13} + 24 q^{14} + 8 q^{16} + 12 q^{19} - 24 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{28} - 12 q^{29} + 4 q^{36} - 24 q^{37} + 4 q^{39} + 36 q^{41} + 12 q^{42} - 12 q^{43} + 48 q^{47} + 4 q^{49} - 12 q^{52} + 24 q^{57} - 12 q^{58} - 36 q^{59} + 32 q^{61} - 48 q^{62} - 16 q^{64} - 12 q^{67} + 36 q^{71} - 48 q^{73} + 24 q^{74} - 48 q^{76} - 12 q^{78} + 16 q^{79} - 4 q^{81} - 12 q^{82} - 12 q^{84} + 12 q^{87} - 24 q^{88} - 36 q^{89} + 12 q^{93} - 12 q^{94} + 36 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q - 4 * q^4 + 4 * q^9 + 12 * q^13 + 24 * q^14 + 8 * q^16 + 12 * q^19 - 24 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^28 - 12 * q^29 + 4 * q^36 - 24 * q^37 + 4 * q^39 + 36 * q^41 + 12 * q^42 - 12 * q^43 + 48 * q^47 + 4 * q^49 - 12 * q^52 + 24 * q^57 - 12 * q^58 - 36 * q^59 + 32 * q^61 - 48 * q^62 - 16 * q^64 - 12 * q^67 + 36 * q^71 - 48 * q^73 + 24 * q^74 - 48 * q^76 - 12 * q^78 + 16 * q^79 - 4 * q^81 - 12 * q^82 - 12 * q^84 + 12 * q^87 - 24 * q^88 - 36 * q^89 + 12 * q^93 - 12 * q^94 + 36 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	1.08766	−	1.88389i	0.769095	−	1.33211i	−0.168960	−	0.985623i	$-0.554041\pi$
$2$	1.08766	−	1.88389i	0.769095	−	1.33211i	0.938054	−	0.346488i	$-0.112626\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.36603	−	2.36603i	−0.683013	−	1.18301i
$5$		0			0
$5$		0			0
$6$	1.88389	−	1.08766i	0.769095	−	0.444037i
$7$	0.221638	+	0.383889i	0.0837715	+	0.145096i	0.904867	−	0.425694i	$-0.139970\pi$
$7$	0.221638	+	0.383889i	0.0837715	+	0.145096i	−0.821096	+	0.570791i	$0.806637\pi$
$8$	−1.59245			−0.563016
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.37910	−	0.796225i	−0.415815	−	0.240071i	0.277470	−	0.960734i	$-0.410504\pi$
$11$	−1.37910	−	0.796225i	−0.415815	−	0.240071i	−0.693285	+	0.720663i	$0.743837\pi$
$12$		−	2.73205i		−	0.788675i
$13$	1.20856	−	3.39697i	0.335195	−	0.942149i
$13$	1.20856	−	3.39697i	0.335195	−	0.942149i
$14$	0.964273			0.257713
$15$		0			0
$16$	1.00000	−	1.73205i	0.250000	−	0.433013i
$17$	3.26299	−	1.88389i	0.791392	−	0.456910i	−0.0490606	−	0.998796i	$-0.515623\pi$
$17$	3.26299	−	1.88389i	0.791392	−	0.456910i	0.840452	+	0.541886i	$0.182289\pi$
$18$	2.17533			0.512730
$19$	1.33987	−	0.773575i	0.307388	−	0.177470i	−0.338369	−	0.941013i	$-0.609875\pi$
$19$	1.33987	−	0.773575i	0.307388	−	0.177470i	0.645757	+	0.763543i	$0.276542\pi$
$20$		0			0
$21$			0.443277i			0.0967310i
$22$	−3.00000	+	1.73205i	−0.639602	+	0.369274i
$23$	0.611324	+	0.352948i	0.127470	+	0.0735948i	0.562379	−	0.826880i	$-0.309886\pi$
$23$	0.611324	+	0.352948i	0.127470	+	0.0735948i	−0.434909	+	0.900474i	$0.643220\pi$
$24$	−1.37910	−	0.796225i	−0.281508	−	0.162529i
$25$		0			0
$26$	−5.08500	−	5.97155i	−0.997250	−	1.17112i
$27$			1.00000i			0.192450i
$28$	0.605528	−	1.04880i	0.114434	−	0.198205i
$29$	1.24991	−	2.16492i	0.232103	−	0.402015i	−0.726324	−	0.687353i	$-0.758773\pi$
$29$	1.24991	−	2.16492i	0.232103	−	0.402015i	0.958427	+	0.285338i	$0.0921059\pi$
$30$		0			0
$31$		−	6.18490i		−	1.11084i	−0.831570	−	0.555420i	$-0.812557\pi$
$31$		−	6.18490i		−	1.11084i	0.831570	−	0.555420i	$-0.187443\pi$
$32$	−3.76778	−	6.52598i	−0.666055	−	1.15364i
$33$	−0.796225	−	1.37910i	−0.138605	−	0.240071i
$34$		−	8.19615i		−	1.40563i
$35$		0			0
$36$	1.36603	−	2.36603i	0.227671	−	0.394338i
$37$	−5.17533	+	8.96393i	−0.850819	+	1.47366i	0.0296519	+	0.999560i	$0.490560\pi$
$37$	−5.17533	+	8.96393i	−0.850819	+	1.47366i	−0.880471	+	0.474101i	$0.842773\pi$
$38$		−	3.36556i		−	0.545966i
$39$	2.74513	−	2.33758i	0.439572	−	0.374312i
$40$		0			0
$41$	5.21419	+	3.01041i	0.814319	+	0.470147i	0.848454	−	0.529270i	$-0.177534\pi$
$41$	5.21419	+	3.01041i	0.814319	+	0.470147i	−0.0341343	+	0.999417i	$0.510867\pi$
$42$	0.835085	+	0.482136i	0.128856	+	0.0743952i
$43$	−4.08979	+	2.36124i	−0.623686	+	0.360086i	−0.778303	−	0.627889i	$-0.783919\pi$
$43$	−4.08979	+	2.36124i	−0.623686	+	0.360086i	0.154616	+	0.987975i	$0.450586\pi$
$44$			4.35066i			0.655886i
$45$		0			0
$46$	1.32983	−	0.767778i	0.196073	−	0.113203i
$47$	5.41712			0.790169			0.395084	−	0.918645i	$-0.370715\pi$
$47$	5.41712			0.790169			0.395084	+	0.918645i	$0.370715\pi$
$48$	1.73205	−	1.00000i	0.250000	−	0.144338i
$49$	3.40175	−	5.89201i	0.485965	−	0.841716i
$50$		0			0
$51$	3.76778			0.527594
$52$	−9.68823	+	1.78086i	−1.34352	+	0.246960i
$53$			5.51641i			0.757737i	0.925450	+	0.378869i	$0.123687\pi$
$53$			5.51641i			0.757737i	−0.925450	+	0.378869i	$0.876313\pi$
$54$	1.88389	+	1.08766i	0.256365	+	0.148012i
$55$		0			0
$56$	−0.352948	−	0.611324i	−0.0471647	−	0.0816917i
$57$	1.54715			0.204925
$58$	−2.71897	−	4.70940i	−0.357019	−	0.618375i
$59$	−7.55359	+	4.36107i	−0.983394	+	0.567763i	−0.903293	−	0.429024i	$-0.858858\pi$
$59$	−7.55359	+	4.36107i	−0.983394	+	0.567763i	−0.0801008	+	0.996787i	$0.525524\pi$
$60$		0			0
$61$	4.86603	+	8.42820i	0.623031	+	1.07912i	0.988918	+	0.148462i	$0.0474322\pi$
$61$	4.86603	+	8.42820i	0.623031	+	1.07912i	−0.365887	+	0.930659i	$0.619234\pi$
$62$	−11.6517	−	6.72709i	−1.47976	−	0.854342i
$63$	−0.221638	+	0.383889i	−0.0279238	+	0.0483655i
$64$	−12.3923			−1.54904
$65$		0			0
$66$	−3.46410			−0.426401
$67$	−6.84799	+	11.8611i	−0.836615	+	1.44906i	0.0560933	+	0.998426i	$0.482136\pi$
$67$	−6.84799	+	11.8611i	−0.836615	+	1.44906i	−0.892709	+	0.450635i	$0.851198\pi$
$68$	−8.91466	−	5.14688i	−1.08106	−	0.624151i
$69$	0.352948	+	0.611324i	0.0424900	+	0.0735948i
$70$		0			0
$71$	13.1193	−	7.57442i	1.55697	−	0.898918i	0.559427	−	0.828880i	$-0.311021\pi$
$71$	13.1193	−	7.57442i	1.55697	−	0.898918i	0.997544	−	0.0700381i	$-0.0223121\pi$
$72$	−0.796225	−	1.37910i	−0.0938360	−	0.162529i
$73$	−10.7939			−1.26333			−0.631667	−	0.775240i	$-0.717629\pi$
$73$	−10.7939			−1.26333			−0.631667	+	0.775240i	$0.717629\pi$
$74$	11.2580	+	19.4995i	1.30872	+	2.26677i
$75$		0			0
$76$	−3.66060	−	2.11345i	−0.419899	−	0.242429i
$77$		−	0.705897i		−	0.0804444i
$78$	−1.41796	−	7.71402i	−0.160553	−	0.873440i
$79$	−10.7317			−1.20741			−0.603706	−	0.797207i	$-0.706310\pi$
$79$	−10.7317			−1.20741			−0.603706	+	0.797207i	$0.706310\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	11.3426	−	6.54863i	1.25258	−	0.723176i
$83$	−9.12801			−1.00193			−0.500964	−	0.865468i	$-0.667021\pi$
$83$	−9.12801			−1.00193			−0.500964	+	0.865468i	$0.667021\pi$
$84$	1.04880	−	0.605528i	0.114434	−	0.0660685i
$85$		0			0
$86$			10.2729i			1.10776i
$87$	2.16492	−	1.24991i	0.232103	−	0.134005i
$88$	2.19615	+	1.26795i	0.234111	+	0.135164i
$89$	4.11927	+	2.37826i	0.436642	+	0.252095i	0.702172	−	0.712007i	$-0.252214\pi$
$89$	4.11927	+	2.37826i	0.436642	+	0.252095i	−0.265530	+	0.964103i	$0.585547\pi$
$90$		0			0
$91$	1.57192	−	0.288945i	0.164782	−	0.0302897i
$92$		−	1.92855i		−	0.201065i
$93$	3.09245	−	5.35628i	0.320672	−	0.555420i
$94$	5.89201	−	10.2053i	0.607714	−	1.05259i
$95$		0			0
$96$		−	7.53556i		−	0.769095i
$97$	4.20856	+	7.28944i	0.427315	+	0.740131i	0.996633	−	0.0819861i	$-0.0261263\pi$
$97$	4.20856	+	7.28944i	0.427315	+	0.740131i	−0.569319	+	0.822117i	$0.692793\pi$
$98$	−7.39993	−	12.8170i	−0.747506	−	1.29472i
$99$		−	1.59245i		−	0.160047i
$100$		0			0
$101$	−3.35295	+	5.80748i	−0.333631	+	0.577866i	−0.983221	−	0.182419i	$-0.941607\pi$
$101$	−3.35295	+	5.80748i	−0.333631	+	0.577866i	0.649590	+	0.760285i	$0.274941\pi$
$102$	4.09808	−	7.09808i	0.405770	−	0.702814i
$103$		−	1.74197i		−	0.171641i	−0.996311	−	0.0858205i	$-0.972649\pi$
$103$		−	1.74197i		−	0.171641i	0.996311	−	0.0858205i	$-0.0273512\pi$
$104$	−1.92457	+	5.40950i	−0.188720	+	0.530445i
$105$		0			0
$106$	10.3923	+	6.00000i	1.00939	+	0.582772i
$107$	10.3218	+	5.95932i	0.997850	+	0.576109i	0.907611	−	0.419811i	$-0.137904\pi$
$107$	10.3218	+	5.95932i	0.997850	+	0.576109i	0.0902383	+	0.995920i	$0.471237\pi$
$108$	2.36603	−	1.36603i	0.227671	−	0.131446i
$109$			17.0407i			1.63220i	0.577908	+	0.816102i	$0.303869\pi$
$109$			17.0407i			1.63220i	−0.577908	+	0.816102i	$0.696131\pi$
$110$		0			0
$111$	−8.96393	+	5.17533i	−0.850819	+	0.491220i
$112$	0.886554			0.0837715
$113$	−3.00000	+	1.73205i	−0.282216	+	0.162938i	−0.634426	−	0.772983i	$-0.718764\pi$
$113$	−3.00000	+	1.73205i	−0.282216	+	0.162938i	0.352210	+	0.935921i	$0.385430\pi$
$114$	1.68278	−	2.91466i	0.157607	−	0.272983i
$115$		0			0
$116$	−6.82966			−0.634118
$117$	3.54614	−	0.651838i	0.327841	−	0.0602625i
$118$			18.9735i			1.74665i
$119$	1.44641	+	0.835085i	0.132592	+	0.0765521i
$120$		0			0
$121$	−4.23205	−	7.33013i	−0.384732	−	0.666375i
$122$	21.1704			1.91668
$123$	3.01041	+	5.21419i	0.271440	+	0.470147i
$124$	−14.6336	+	8.44873i	−1.31414	+	0.758719i
$125$		0			0
$126$	0.482136	+	0.835085i	0.0429521	+	0.0743952i
$127$	−12.3418	−	7.12551i	−1.09515	−	0.632287i	−0.160210	−	0.987083i	$-0.551217\pi$
$127$	−12.3418	−	7.12551i	−1.09515	−	0.632287i	−0.934944	+	0.354796i	$0.884550\pi$
$128$	−5.94311	+	10.2938i	−0.525301	+	0.909849i
$129$	−4.72248			−0.415791
$130$		0			0
$131$	10.0354			0.876796			0.438398	−	0.898781i	$-0.355546\pi$
$131$	10.0354			0.876796			0.438398	+	0.898781i	$0.355546\pi$
$132$	−2.17533	+	3.76778i	−0.189338	+	0.327943i
$133$	0.593934	+	0.342908i	0.0515006	+	0.0297339i
$134$	14.8966	+	25.8017i	1.28687	+	2.22893i
$135$		0			0
$136$	−5.19615	+	3.00000i	−0.445566	+	0.257248i
$137$	4.64209	+	8.04034i	0.396601	+	0.686933i	0.993304	−	0.115529i	$-0.0368564\pi$
$137$	4.64209	+	8.04034i	0.396601	+	0.686933i	−0.596703	+	0.802462i	$0.703523\pi$
$138$	1.53556			0.130715
$139$	−3.25821	−	5.64338i	−0.276357	−	0.478665i	0.694119	−	0.719860i	$-0.255794\pi$
$139$	−3.25821	−	5.64338i	−0.276357	−	0.478665i	−0.970477	+	0.241195i	$0.922461\pi$
$140$		0			0
$141$	4.69137	+	2.70856i	0.395084	+	0.228102i
$142$		−	32.9537i		−	2.76541i
$143$	−4.37148	+	3.72248i	−0.365562	+	0.311289i
$144$	2.00000			0.166667
$145$		0			0
$146$	−11.7402	+	20.3346i	−0.971623	+	1.68290i
$147$	5.89201	−	3.40175i	0.485965	−	0.280572i
$148$	28.2785			2.32448
$149$	0.0492717	−	0.0284470i	0.00403650	−	0.00233047i	−0.497980	−	0.867188i	$-0.665925\pi$
$149$	0.0492717	−	0.0284470i	0.00403650	−	0.00233047i	0.502017	+	0.864858i	$0.332592\pi$
$150$		0			0
$151$		−	17.3004i		−	1.40789i	−0.710255	−	0.703944i	$-0.751420\pi$
$151$		−	17.3004i		−	1.40789i	0.710255	−	0.703944i	$-0.248580\pi$
$152$	−2.13368	+	1.23188i	−0.173064	+	0.0999186i
$153$	3.26299	+	1.88389i	0.263797	+	0.152303i
$154$	−1.32983	−	0.767778i	−0.107161	−	0.0618693i
$155$		0			0
$156$	−9.28068	−	3.30185i	−0.743049	−	0.264360i
$157$			1.34898i			0.107660i	0.998550	+	0.0538300i	$0.0171429\pi$
$157$			1.34898i			0.107660i	−0.998550	+	0.0538300i	$0.982857\pi$
$158$	−11.6725	+	20.2173i	−0.928614	+	1.60841i
$159$	−2.75821	+	4.77735i	−0.218740	+	0.378869i
$160$		0			0
$161$			0.312908i			0.0246606i
$162$	1.08766	+	1.88389i	0.0854549	+	0.148012i
$163$	1.48959	+	2.58004i	0.116674	+	0.202084i	0.918447	−	0.395543i	$-0.129444\pi$
$163$	1.48959	+	2.58004i	0.116674	+	0.202084i	−0.801774	+	0.597627i	$0.796110\pi$
$164$		−	16.4492i		−	1.28447i
$165$		0			0
$166$	−9.92820	+	17.1962i	−0.770578	+	1.33468i
$167$	−11.9070	+	20.6236i	−0.921394	+	1.59590i	−0.124134	+	0.992265i	$0.539615\pi$
$167$	−11.9070	+	20.6236i	−0.921394	+	1.59590i	−0.797260	+	0.603636i	$0.793718\pi$
$168$		−	0.705897i		−	0.0544611i
$169$	−10.0788	−	8.21088i	−0.775289	−	0.631606i
$170$		0			0
$171$	1.33987	+	0.773575i	0.102463	+	0.0591568i
$172$	11.1735	+	6.45102i	0.851972	+	0.491886i
$173$	21.3702	−	12.3381i	1.62474	−	0.938047i	0.639117	−	0.769109i	$-0.279300\pi$
$173$	21.3702	−	12.3381i	1.62474	−	0.938047i	0.985627	−	0.168937i	$-0.0540336\pi$
$174$		−	5.43795i		−	0.412250i
$175$		0			0
$176$	−2.75821	+	1.59245i	−0.207908	+	0.120035i
$177$	−8.72214			−0.655596
$178$	8.96077	−	5.17350i	0.671638	−	0.387770i
$179$	1.44244	−	2.49838i	0.107813	−	0.186737i	−0.807071	−	0.590454i	$-0.798949\pi$
$179$	1.44244	−	2.49838i	0.107813	−	0.186737i	0.914884	+	0.403717i	$0.132282\pi$
$180$		0			0
$181$	−7.41086			−0.550845			−0.275422	−	0.961323i	$-0.588818\pi$
$181$	−7.41086			−0.550845			−0.275422	+	0.961323i	$0.588818\pi$
$182$	1.16538	−	3.27560i	0.0863839	−	0.242804i
$183$			9.73205i			0.719414i
$184$	−0.973504	−	0.562053i	−0.0717676	−	0.0414351i
$185$		0			0
$186$	−6.72709	−	11.6517i	−0.493254	−	0.854342i
$187$	−6.00000			−0.438763
$188$	−7.39993	−	12.8170i	−0.539695	−	0.934779i
$189$	−0.383889	+	0.221638i	−0.0279238	+	0.0161218i
$190$		0			0
$191$	8.12885	+	14.0796i	0.588183	+	1.01876i	0.994470	+	0.105017i	$0.0334897\pi$
$191$	8.12885	+	14.0796i	0.588183	+	1.01876i	−0.406288	+	0.913745i	$0.633177\pi$
$192$	−10.7321	−	6.19615i	−0.774519	−	0.447169i
$193$	5.63876	−	9.76662i	0.405887	−	0.703017i	−0.588537	−	0.808470i	$-0.700296\pi$
$193$	5.63876	−	9.76662i	0.405887	−	0.703017i	0.994424	+	0.105453i	$0.0336293\pi$
$194$	18.3100			1.31458
$195$		0			0
$196$	−18.5875			−1.32768
$197$	−12.3335	+	21.3622i	−0.878723	+	1.52199i	−0.0259791	+	0.999662i	$0.508270\pi$
$197$	−12.3335	+	21.3622i	−0.878723	+	1.52199i	−0.852744	+	0.522330i	$0.825063\pi$
$198$	−3.00000	−	1.73205i	−0.213201	−	0.123091i
$199$	11.0356	+	19.1141i	0.782290	+	1.35497i	0.930605	+	0.366026i	$0.119282\pi$
$199$	11.0356	+	19.1141i	0.782290	+	1.35497i	−0.148315	+	0.988940i	$0.547385\pi$
$200$		0			0
$201$	−11.8611	+	6.84799i	−0.836615	+	0.483020i
$202$	7.29376	+	12.6332i	0.513187	+	0.888866i
$203$	1.10812			0.0777745
$204$	−5.14688	−	8.91466i	−0.360354	−	0.624151i
$205$		0			0
$206$	−3.28167	−	1.89467i	−0.228645	−	0.132008i
$207$			0.705897i			0.0490632i
$208$	−4.67516	−	5.49026i	−0.324164	−	0.380681i
$209$	−2.46376			−0.170422
$210$		0			0
$211$	10.7580	−	18.6335i	0.740614	−	1.28278i	−0.211603	−	0.977356i	$-0.567868\pi$
$211$	10.7580	−	18.6335i	0.740614	−	1.28278i	0.952216	−	0.305425i	$-0.0987984\pi$
$212$	13.0520	−	7.53556i	0.896413	−	0.517544i
$213$	15.1488			1.03798
$214$	22.4534	−	12.9635i	1.53488	−	0.886164i
$215$		0			0
$216$		−	1.59245i		−	0.108353i
$217$	2.37432	−	1.37081i	0.161179	−	0.0930568i
$218$	32.1028	+	18.5346i	2.17428	+	1.25532i
$219$	−9.34782	−	5.39697i	−0.631667	−	0.364693i
$220$		0			0
$221$	−2.45598	−	13.3611i	−0.165207	−	0.898763i
$222$			22.5161i			1.51118i
$223$	−10.6183	+	18.3914i	−0.711051	+	1.23158i	0.253411	+	0.967359i	$0.418447\pi$
$223$	−10.6183	+	18.3914i	−0.711051	+	1.23158i	−0.964463	+	0.264219i	$0.914886\pi$
$224$	1.67017	−	2.89282i	0.111593	−	0.193285i
$225$		0			0
$226$			7.53556i			0.501258i
$227$	−5.22497	−	9.04992i	−0.346794	−	0.600664i	0.638884	−	0.769303i	$-0.279396\pi$
$227$	−5.22497	−	9.04992i	−0.346794	−	0.600664i	−0.985678	+	0.168639i	$0.946063\pi$
$228$	−2.11345	−	3.66060i	−0.139966	−	0.242429i
$229$		−	21.4135i		−	1.41505i	−0.706690	−	0.707523i	$-0.749813\pi$
$229$		−	21.4135i		−	1.41505i	0.706690	−	0.707523i	$-0.250187\pi$
$230$		0			0
$231$	0.352948	−	0.611324i	0.0232223	−	0.0402222i
$232$	−1.99043	+	3.44752i	−0.130678	+	0.226341i
$233$		−	3.24179i		−	0.212377i	−0.994346	−	0.106189i	$-0.966135\pi$
$233$		−	3.24179i		−	0.212377i	0.994346	−	0.106189i	$-0.0338647\pi$
$234$	2.62902	−	7.38951i	0.171864	−	0.483068i
$235$		0			0
$236$	20.6368	+	11.9147i	1.34334	+	0.775578i
$237$	−9.29393	−	5.36585i	−0.603706	−	0.348550i
$238$	3.14641	−	1.81658i	0.203952	−	0.117752i
$239$		−	18.3129i		−	1.18456i	−0.805731	−	0.592282i	$-0.798227\pi$
$239$		−	18.3129i		−	1.18456i	0.805731	−	0.592282i	$-0.201773\pi$
$240$		0			0
$241$	−5.74816	+	3.31870i	−0.370272	+	0.213777i	−0.673577	−	0.739117i	$-0.735243\pi$
$241$	−5.74816	+	3.31870i	−0.370272	+	0.213777i	0.303305	+	0.952893i	$0.401910\pi$
$242$	−18.4122			−1.18358
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	13.2942	−	23.0263i	0.851076	−	1.47411i
$245$		0			0
$246$	13.0973			0.835051
$247$	−1.00849	−	5.48641i	−0.0641688	−	0.349092i
$248$			9.84915i			0.625422i
$249$	−7.90509	−	4.56400i	−0.500964	−	0.289232i
$250$		0			0
$251$	−9.94081	−	17.2180i	−0.627459	−	1.08679i	−0.988060	−	0.154070i	$-0.950762\pi$
$251$	−9.94081	−	17.2180i	−0.627459	−	1.08679i	0.360601	−	0.932720i	$-0.382571\pi$
$252$	1.21106			0.0762893
$253$	−0.562053	−	0.973504i	−0.0353359	−	0.0612037i
$254$	−26.8474	+	15.5003i	−1.68455	+	0.972577i
$255$		0			0
$256$	0.535898	+	0.928203i	0.0334936	+	0.0580127i
$257$	−0.874316	−	0.504787i	−0.0545383	−	0.0314877i	0.472483	−	0.881340i	$-0.343358\pi$
$257$	−0.874316	−	0.504787i	−0.0545383	−	0.0314877i	−0.527021	+	0.849852i	$0.676691\pi$
$258$	−5.13647	+	8.89662i	−0.319783	+	0.553880i
$259$	−4.58821			−0.285097
$260$		0			0
$261$	2.49983			0.154736
$262$	10.9151	−	18.9056i	0.674339	−	1.16799i
$263$	18.6818	+	10.7859i	1.15197	+	0.665089i	0.949366	−	0.314172i	$-0.101727\pi$
$263$	18.6818	+	10.7859i	1.15197	+	0.665089i	0.202602	+	0.979261i	$0.435060\pi$
$264$	1.26795	+	2.19615i	0.0780369	+	0.135164i
$265$		0			0
$266$	1.29200	−	0.745937i	0.0792177	−	0.0457363i
$267$	2.37826	+	4.11927i	0.145547	+	0.252095i
$268$	37.4181			2.28568
$269$	−2.32534	−	4.02761i	−0.141779	−	0.245568i	0.786388	−	0.617733i	$-0.211949\pi$
$269$	−2.32534	−	4.02761i	−0.141779	−	0.245568i	−0.928166	+	0.372165i	$0.878615\pi$
$270$		0			0
$271$	4.60718	+	2.65996i	0.279866	+	0.161581i	0.633363	−	0.773855i	$-0.281674\pi$
$271$	4.60718	+	2.65996i	0.279866	+	0.161581i	−0.353497	+	0.935436i	$0.615007\pi$
$272$		−	7.53556i		−	0.456910i
$273$	1.50580	+	0.535727i	0.0911350	+	0.0324237i
$274$	20.1962			1.22009
$275$		0			0
$276$	0.964273	−	1.67017i	0.0580424	−	0.100532i
$277$	8.10555	−	4.67974i	0.487015	−	0.281178i	−0.236320	−	0.971675i	$-0.575941\pi$
$277$	8.10555	−	4.67974i	0.487015	−	0.281178i	0.723335	+	0.690497i	$0.242608\pi$
$278$	−14.1753			−0.850180
$279$	5.35628	−	3.09245i	0.320672	−	0.185140i
$280$		0			0
$281$			13.1449i			0.784161i	0.919931	+	0.392080i	$0.128244\pi$
$281$			13.1449i			0.784161i	−0.919931	+	0.392080i	$0.871756\pi$
$282$	10.2053	−	5.89201i	0.607714	−	0.350864i
$283$	−3.15551	−	1.82184i	−0.187576	−	0.108297i	0.403271	−	0.915080i	$-0.367873\pi$
$283$	−3.15551	−	1.82184i	−0.187576	−	0.108297i	−0.590847	+	0.806783i	$0.701206\pi$
$284$	−35.8425	−	20.6937i	−2.12686	−	1.22794i
$285$		0			0
$286$	2.25803	+	12.2842i	0.133520	+	0.726379i
$287$			2.66889i			0.157540i
$288$	3.76778	−	6.52598i	0.222018	−	0.384547i
$289$	−1.40192	+	2.42820i	−0.0824661	+	0.142835i
$290$		0			0
$291$			8.41712i			0.493420i
$292$	14.7448	+	25.5387i	0.862873	+	1.49454i
$293$	9.81742	+	17.0043i	0.573540	+	0.993400i	0.996199	+	0.0871113i	$0.0277636\pi$
$293$	9.81742	+	17.0043i	0.573540	+	0.993400i	−0.422659	+	0.906289i	$0.638903\pi$
$294$		−	14.7999i		−	0.863145i
$295$		0			0
$296$	8.24145	−	14.2746i	0.479025	−	0.829695i
$297$	0.796225	−	1.37910i	0.0462017	−	0.0800236i
$298$		−	0.123763i		−	0.00716941i
$299$	1.93778	−	1.65009i	0.112064	−	0.0954271i
$300$		0			0
$301$	−1.81291	−	1.04668i	−0.104494	−	0.0603298i
$302$	−32.5921	−	18.8170i	−1.87546	−	1.08280i
$303$	−5.80748	+	3.35295i	−0.333631	+	0.192622i
$304$		−	3.09430i		−	0.177470i
$305$		0			0
$306$	7.09808	−	4.09808i	0.405770	−	0.234271i
$307$	4.74863			0.271019			0.135509	−	0.990776i	$-0.456733\pi$
$307$	4.74863			0.271019			0.135509	+	0.990776i	$0.456733\pi$
$308$	−1.67017	+	0.964273i	−0.0951667	+	0.0549445i
$309$	0.870983	−	1.50859i	0.0495485	−	0.0858205i
$310$		0			0
$311$	−5.45512			−0.309332			−0.154666	−	0.987967i	$-0.549430\pi$
$311$	−5.45512			−0.309332			−0.154666	+	0.987967i	$0.549430\pi$
$312$	−4.37148	+	3.72248i	−0.247486	+	0.210744i
$313$		−	7.23855i		−	0.409147i	−0.978851	−	0.204573i	$-0.934419\pi$
$313$		−	7.23855i		−	0.409147i	0.978851	−	0.204573i	$-0.0655807\pi$
$314$	2.54132	+	1.46723i	0.143415	+	0.0828008i
$315$		0			0
$316$	14.6598	+	25.3915i	0.824677	+	1.42838i
$317$	21.0142			1.18028			0.590138	−	0.807302i	$-0.299073\pi$
$317$	21.0142			1.18028			0.590138	+	0.807302i	$0.299073\pi$
$318$	6.00000	+	10.3923i	0.336463	+	0.582772i
$319$	−3.44752	+	1.99043i	−0.193024	+	0.111443i
$320$		0			0
$321$	5.95932	+	10.3218i	0.332617	+	0.576109i
$322$	0.589483	+	0.340338i	0.0328506	+	0.0189663i
$323$	2.91466	−	5.04834i	0.162176	−	0.280897i
$324$	2.73205			0.151781
$325$		0			0
$326$	6.48068			0.358932
$327$	−8.52036	+	14.7577i	−0.471177	+	0.816102i
$328$	−8.30333	−	4.79393i	−0.458475	−	0.264701i
$329$	1.20064	+	2.07957i	0.0661936	+	0.114651i
$330$		0			0
$331$	−13.4352	+	7.75682i	−0.738466	+	0.426354i	−0.821511	−	0.570192i	$-0.806869\pi$
$331$	−13.4352	+	7.75682i	−0.738466	+	0.426354i	0.0830453	+	0.996546i	$0.473535\pi$
$332$	12.4691	+	21.5971i	0.684330	+	1.18529i
$333$	−10.3507			−0.567212
$334$	25.9017	+	44.8631i	1.41728	+	2.45480i
$335$		0			0
$336$	0.767778	+	0.443277i	0.0418857	+	0.0241827i
$337$		−	32.8124i		−	1.78741i	−0.448660	−	0.893703i	$-0.648099\pi$
$337$		−	32.8124i		−	1.78741i	0.448660	−	0.893703i	$-0.351901\pi$
$338$	−26.4307	+	10.0566i	−1.43764	+	0.547006i
$339$	−3.46410			−0.188144
$340$		0			0
$341$	−4.92457	+	8.52961i	−0.266681	+	0.461904i
$342$	2.91466	−	1.68278i	0.157607	−	0.0909943i
$343$	6.11878			0.330383
$344$	6.51278	−	3.76016i	0.351146	−	0.202734i
$345$		0			0
$346$		−	53.6787i		−	2.88579i
$347$	16.8558	−	9.73171i	0.904868	−	0.522426i	0.0260913	−	0.999660i	$-0.491694\pi$
$347$	16.8558	−	9.73171i	0.904868	−	0.522426i	0.878776	+	0.477234i	$0.158361\pi$
$348$	−5.91466	−	3.41483i	−0.317059	−	0.183054i
$349$	8.41876	+	4.86057i	0.450646	+	0.260180i	0.708103	−	0.706109i	$-0.249551\pi$
$349$	8.41876	+	4.86057i	0.450646	+	0.260180i	−0.257457	+	0.966290i	$0.582885\pi$
$350$		0			0
$351$	3.39697	+	1.20856i	0.181317	+	0.0645082i
$352$			12.0000i			0.639602i
$353$	−11.5088	+	19.9338i	−0.612551	+	1.06097i	0.378258	+	0.925700i	$0.376523\pi$
$353$	−11.5088	+	19.9338i	−0.612551	+	1.06097i	−0.990809	+	0.135269i	$0.956810\pi$
$354$	−9.48675	+	16.4315i	−0.504215	+	0.873326i
$355$		0			0
$356$		−	12.9951i		−	0.688737i
$357$	0.835085	+	1.44641i	0.0441974	+	0.0765521i
$358$	−3.13777	−	5.43479i	−0.165837	−	0.287237i
$359$		−	10.4131i		−	0.549584i	−0.961504	−	0.274792i	$-0.911391\pi$
$359$		−	10.4131i		−	0.549584i	0.961504	−	0.274792i	$-0.0886090\pi$
$360$		0			0
$361$	−8.30316	+	14.3815i	−0.437009	+	0.756921i
$362$	−8.06052	+	13.9612i	−0.423652	+	0.733786i
$363$		−	8.46410i		−	0.444250i
$364$	−2.83094	−	3.32450i	−0.148381	−	0.174251i
$365$		0			0
$366$	18.3341	+	10.5852i	0.958339	+	0.553297i
$367$	−3.14500	−	1.81577i	−0.164168	−	0.0947823i	0.415665	−	0.909518i	$-0.363549\pi$
$367$	−3.14500	−	1.81577i	−0.164168	−	0.0947823i	−0.579833	+	0.814735i	$0.696882\pi$
$368$	1.22265	−	0.705897i	0.0637350	−	0.0367974i
$369$			6.02082i			0.313432i
$370$		0			0
$371$	−2.11769	+	1.22265i	−0.109945	+	0.0634768i
$372$	−16.8975			−0.876093
$373$	17.1810	−	9.91945i	0.889598	−	0.513609i	0.0157867	−	0.999875i	$-0.494975\pi$
$373$	17.1810	−	9.91945i	0.889598	−	0.513609i	0.873811	+	0.486266i	$0.161641\pi$
$374$	−6.52598	+	11.3033i	−0.337451	+	0.584482i
$375$		0			0
$376$	−8.62650			−0.444878
$377$	−5.84355	−	6.86235i	−0.300958	−	0.353429i
$378$			0.964273i			0.0495968i
$379$	5.91833	+	3.41695i	0.304004	+	0.175517i	0.644240	−	0.764823i	$-0.277174\pi$
$379$	5.91833	+	3.41695i	0.304004	+	0.175517i	−0.340236	+	0.940340i	$0.610507\pi$
$380$		0			0
$381$	−7.12551	−	12.3418i	−0.365051	−	0.632287i
$382$	35.3658			1.80947
$383$	−19.4419	−	33.6744i	−0.993437	−	1.72068i	−0.595774	−	0.803152i	$-0.703155\pi$
$383$	−19.4419	−	33.6744i	−0.993437	−	1.72068i	−0.397663	−	0.917531i	$-0.630179\pi$
$384$	−10.2938	+	5.94311i	−0.525301	+	0.303283i
$385$		0			0
$386$	−12.2662	−	21.2456i	−0.624331	−	1.08137i
$387$	−4.08979	−	2.36124i	−0.207895	−	0.120029i
$388$	11.4980	−	19.9151i	0.583723	−	1.01104i
$389$	8.84881			0.448652			0.224326	−	0.974514i	$-0.427982\pi$
$389$	8.84881			0.448652			0.224326	+	0.974514i	$0.427982\pi$
$390$		0			0
$391$	2.65966			0.134505
$392$	−5.41712	+	9.38273i	−0.273606	+	0.473900i
$393$	8.69090	+	5.01769i	0.438398	+	0.253109i
$394$	26.8293	+	46.4697i	1.35164	+	2.34111i
$395$		0			0
$396$	−3.76778	+	2.17533i	−0.189338	+	0.109314i
$397$	8.51890	+	14.7552i	0.427552	+	0.740541i	0.996655	−	0.0817250i	$-0.0260429\pi$
$397$	8.51890	+	14.7552i	0.427552	+	0.740541i	−0.569103	+	0.822266i	$0.692710\pi$
$398$	48.0119			2.40662
$399$	0.342908	+	0.593934i	0.0171669	+	0.0297339i
$400$		0			0
$401$	−6.66060	−	3.84550i	−0.332614	−	0.192035i	0.324387	−	0.945924i	$-0.394842\pi$
$401$	−6.66060	−	3.84550i	−0.332614	−	0.192035i	−0.657001	+	0.753890i	$0.728175\pi$
$402$			29.7932i			1.48595i
$403$	−21.0099	−	7.47483i	−1.04658	−	0.372348i
$404$	18.3209			0.911496
$405$		0			0
$406$	1.20526	−	2.08757i	0.0598160	−	0.103604i
$407$	14.2746	−	8.24145i	0.707566	−	0.408514i
$408$	−6.00000			−0.297044
$409$	−7.86637	+	4.54165i	−0.388967	+	0.224570i	−0.681712	−	0.731620i	$-0.738764\pi$
$409$	−7.86637	+	4.54165i	−0.388967	+	0.224570i	0.292746	+	0.956190i	$0.405431\pi$
$410$		0			0
$411$			9.28419i			0.457955i
$412$	−4.12154	+	2.37957i	−0.203053	+	0.117233i
$413$	−3.34833	−	1.93316i	−0.164761	−	0.0951246i
$414$	1.32983	+	0.767778i	0.0653576	+	0.0377342i
$415$		0			0
$416$	−26.7221	+	4.91196i	−1.31016	+	0.240829i
$417$		−	6.51641i		−	0.319110i
$418$	−2.67974	+	4.64145i	−0.131070	+	0.227021i
$419$	−6.49534	+	11.2503i	−0.317318	+	0.549611i	−0.979928	−	0.199354i	$-0.936116\pi$
$419$	−6.49534	+	11.2503i	−0.317318	+	0.549611i	0.662609	+	0.748965i	$0.269449\pi$
$420$		0			0
$421$			19.8859i			0.969178i	0.874742	+	0.484589i	$0.161031\pi$
$421$			19.8859i			0.969178i	−0.874742	+	0.484589i	$0.838969\pi$
$422$	−23.4022	−	40.5339i	−1.13920	−	1.97316i
$423$	2.70856	+	4.69137i	0.131695	+	0.228102i
$424$		−	8.78461i		−	0.426618i
$425$		0			0
$426$	16.4768	−	28.5387i	0.798305	−	1.38271i
$427$	−2.15700	+	3.73603i	−0.104384	+	0.180799i
$428$		−	32.5623i		−	1.57396i
$429$	−5.64705	+	1.03802i	−0.272642	+	0.0501161i
$430$		0			0
$431$	−33.8858	−	19.5640i	−1.63222	−	0.942365i	−0.983405	−	0.181422i	$-0.941930\pi$
$431$	−33.8858	−	19.5640i	−1.63222	−	0.942365i	−0.648818	−	0.760943i	$-0.724737\pi$
$432$	1.73205	+	1.00000i	0.0833333	+	0.0481125i
$433$	−33.0301	+	19.0700i	−1.58733	+	0.916444i	−0.593581	+	0.804774i	$0.702287\pi$
$433$	−33.0301	+	19.0700i	−1.58733	+	0.916444i	−0.993745	+	0.111670i	$0.964380\pi$
$434$		−	5.96393i		−	0.286278i
$435$		0			0
$436$	40.3188	−	23.2780i	1.93092	−	1.11482i
$437$	1.09213			0.0522436
$438$	−20.3346	+	11.7402i	−0.971623	+	0.560967i
$439$	−3.37543	+	5.84641i	−0.161100	+	0.279034i	−0.935264	−	0.353952i	$-0.884838\pi$
$439$	−3.37543	+	5.84641i	−0.161100	+	0.279034i	0.774163	+	0.632986i	$0.218171\pi$
$440$		0			0
$441$	6.80351			0.323976
$442$	−27.8421	−	9.90555i	−1.32431	−	0.471159i
$443$		−	12.2647i		−	0.582713i	−0.956614	−	0.291357i	$-0.905893\pi$
$443$		−	12.2647i		−	0.582713i	0.956614	−	0.291357i	$-0.0941067\pi$
$444$	24.4899	+	14.1393i	1.16224	+	0.671020i
$445$		0			0
$446$	23.0982	+	40.0073i	1.09373	+	1.89440i
$447$	0.0568941			0.00269100
$448$	−2.74661	−	4.75727i	−0.129765	−	0.224760i
$449$	−20.2673	+	11.7013i	−0.956471	+	0.552219i	−0.895085	−	0.445895i	$-0.852885\pi$
$449$	−20.2673	+	11.7013i	−0.956471	+	0.552219i	−0.0613861	+	0.998114i	$0.519552\pi$
$450$		0			0
$451$	−4.79393	−	8.30333i	−0.225737	−	0.390989i
$452$	8.19615	+	4.73205i	0.385515	+	0.222577i
$453$	8.65021	−	14.9826i	0.406422	−	0.703944i
$454$	−22.7321			−1.06687
$455$		0			0
$456$	−2.46376			−0.115376
$457$	14.7815	−	25.6023i	0.691451	−	1.19763i	−0.279912	−	0.960026i	$-0.590305\pi$
$457$	14.7815	−	25.6023i	0.691451	−	1.19763i	0.971363	−	0.237602i	$-0.0763613\pi$
$458$	−40.3407	−	23.2907i	−1.88500	−	1.08830i
$459$	1.88389	+	3.26299i	0.0879324	+	0.152303i
$460$		0			0
$461$	−8.29218	+	4.78749i	−0.386205	+	0.222976i	−0.680515	−	0.732735i	$-0.738244\pi$
$461$	−8.29218	+	4.78749i	−0.386205	+	0.222976i	0.294309	+	0.955710i	$0.404910\pi$
$462$	−0.767778	−	1.32983i	−0.0357203	−	0.0618693i
$463$	−20.0241			−0.930600			−0.465300	−	0.885153i	$-0.654054\pi$
$463$	−20.0241			−0.930600			−0.465300	+	0.885153i	$0.654054\pi$
$464$	−2.49983	−	4.32983i	−0.116052	−	0.201007i
$465$		0			0
$466$	−6.10718	−	3.52598i	−0.282910	−	0.163338i
$467$			15.7942i			0.730868i	0.930837	+	0.365434i	$0.119079\pi$
$467$			15.7942i			0.730868i	−0.930837	+	0.365434i	$0.880921\pi$
$468$	−6.38638	−	7.49983i	−0.295211	−	0.346680i
$469$	−6.07111			−0.280338
$470$		0			0
$471$	−0.674489	+	1.16825i	−0.0310788	+	0.0538300i
$472$	12.0287	−	6.94478i	0.553667	−	0.319660i
$473$	7.52031			0.345784
$474$	−20.2173	+	11.6725i	−0.928614	+	0.536135i
$475$		0			0
$476$		−	4.56299i		−	0.209144i
$477$	−4.77735	+	2.75821i	−0.218740	+	0.126290i
$478$	−34.4995	−	19.9183i	−1.57797	−	0.911041i
$479$	−23.1649	−	13.3743i	−1.05843	−	0.611086i	−0.133434	−	0.991058i	$-0.542600\pi$
$479$	−23.1649	−	13.3743i	−1.05843	−	0.611086i	−0.924998	+	0.379972i	$0.875934\pi$
$480$		0			0
$481$	24.1955	+	28.4139i	1.10322	+	1.29556i
$482$			14.4385i			0.657657i
$483$	−0.156454	+	0.270986i	−0.00711890	+	0.0123303i
$484$	−11.5622	+	20.0263i	−0.525554	+	0.910285i
$485$		0			0
$486$			2.17533i			0.0986749i
$487$	−14.1619	−	24.5291i	−0.641737	−	1.11152i	−0.985045	−	0.172299i	$-0.944881\pi$
$487$	−14.1619	−	24.5291i	−0.641737	−	1.11152i	0.343307	−	0.939223i	$-0.388453\pi$
$488$	−7.74890	−	13.4215i	−0.350776	−	0.607563i
$489$			2.97918i			0.134723i
$490$		0			0
$491$	4.75009	−	8.22739i	0.214368	−	0.371297i	−0.738709	−	0.674025i	$-0.764564\pi$
$491$	4.75009	−	8.22739i	0.214368	−	0.371297i	0.953077	+	0.302728i	$0.0978974\pi$
$492$	8.22460	−	14.2454i	0.370794	−	0.642233i
$493$		−	9.41880i		−	0.424201i
$494$	−11.4327	−	4.06748i	−0.514381	−	0.183005i
$495$		0			0
$496$	−10.7126	−	6.18490i	−0.481008	−	0.277710i
$497$	5.81547	+	3.35756i	0.260860	+	0.150607i
$498$	−17.1962	+	9.92820i	−0.770578	+	0.444893i
$499$			23.1767i			1.03753i	0.854917	+	0.518765i	$0.173608\pi$
$499$			23.1767i			1.03753i	−0.854917	+	0.518765i	$0.826392\pi$
$500$		0			0
$501$	−20.6236	+	11.9070i	−0.921394	+	0.531967i
$502$	−43.2491			−1.93030
$503$	−34.9470	+	20.1767i	−1.55821	+	0.899633i	−0.560782	+	0.827964i	$0.689499\pi$
$503$	−34.9470	+	20.1767i	−1.55821	+	0.899633i	−0.997428	+	0.0716692i	$0.977167\pi$
$504$	0.352948	−	0.611324i	0.0157216	−	0.0272306i
$505$		0			0
$506$	−2.44530			−0.108707
$507$	−4.62302	−	12.1502i	−0.205315	−	0.539610i
$508$			38.9345i			1.72744i
$509$	8.91466	+	5.14688i	0.395135	+	0.228131i	0.684383	−	0.729123i	$-0.260072\pi$
$509$	8.91466	+	5.14688i	0.395135	+	0.228131i	−0.289248	+	0.957254i	$0.593405\pi$
$510$		0			0
$511$	−2.39235	−	4.14367i	−0.105831	−	0.183305i
$512$	−21.4409			−0.947564
$513$	0.773575	+	1.33987i	0.0341542	+	0.0591568i
$514$	−1.90192	+	1.09808i	−0.0838903	+	0.0484341i
$515$		0			0
$516$	6.45102	+	11.1735i	0.283991	+	0.491886i
$517$	−7.47077	−	4.31325i	−0.328564	−	0.189697i
$518$	−4.99043	+	8.64367i	−0.219267	+	0.379781i
$519$	24.6762			1.08316
$520$		0			0
$521$	43.7218			1.91549			0.957743	−	0.287624i	$-0.0928655\pi$
$521$	43.7218			1.91549			0.957743	+	0.287624i	$0.0928655\pi$
$522$	2.71897	−	4.70940i	0.119006	−	0.206125i
$523$	−6.23154	−	3.59778i	−0.272486	−	0.157320i	0.357531	−	0.933901i	$-0.383619\pi$
$523$	−6.23154	−	3.59778i	−0.272486	−	0.157320i	−0.630017	+	0.776581i	$0.716952\pi$
$524$	−13.7086	−	23.7440i	−0.598863	−	1.03726i
$525$		0			0
$526$	40.6390	−	23.4630i	1.77195	−	1.02303i
$527$	−11.6517	−	20.1813i	−0.507555	−	0.879110i
$528$	−3.18490			−0.138605
$529$	−11.2509	−	19.4871i	−0.489168	−	0.847263i
$530$		0			0
$531$	−7.55359	−	4.36107i	−0.327798	−	0.189254i
$532$		−	1.87368i		−	0.0812345i
$533$	16.5279	−	14.0741i	0.715904	−	0.609619i
$534$	10.3470			0.447759
$535$		0			0
$536$	10.9051	−	18.8882i	0.471028	−	0.815844i
$537$	2.49838	−	1.44244i	0.107813	−	0.0622458i
$538$	−10.1168			−0.436164
$539$	−9.38273	+	5.41712i	−0.404143	+	0.233332i
$540$		0			0
$541$		−	24.7159i		−	1.06262i	−0.847177	−	0.531310i	$-0.821700\pi$
$541$		−	24.7159i		−	1.06262i	0.847177	−	0.531310i	$-0.178300\pi$
$542$	10.0221	−	5.78628i	0.430487	−	0.248542i
$543$	−6.41799	−	3.70543i	−0.275422	−	0.159015i
$544$	−24.5885	−	14.1962i	−1.05422	−	0.608655i
$545$		0			0
$546$	2.64705	−	2.25406i	0.113283	−	0.0964650i
$547$			6.97187i			0.298096i	0.988830	+	0.149048i	$0.0476209\pi$
$547$			6.97187i			0.298096i	−0.988830	+	0.149048i	$0.952379\pi$
$548$	12.6824	−	21.9666i	0.541767	−	0.938368i
$549$	−4.86603	+	8.42820i	−0.207677	+	0.359707i
$550$		0			0
$551$		−	3.86761i		−	0.164766i
$552$	−0.562053	−	0.973504i	−0.0239225	−	0.0414351i
$553$	−2.37856	−	4.11979i	−0.101147	−	0.175191i
$554$		−	20.3599i		−	0.865011i
$555$		0			0
$556$	−8.90158	+	15.4180i	−0.377511	+	0.653869i
$557$	−0.837875	+	1.45124i	−0.0355019	+	0.0614911i	−0.883230	−	0.468939i	$-0.844636\pi$
$557$	−0.837875	+	1.45124i	−0.0355019	+	0.0614911i	0.847729	+	0.530430i	$0.177970\pi$
$558$		−	13.4542i		−	0.569561i
$559$	3.07829	+	16.7466i	0.130198	+	0.708304i
$560$		0			0
$561$	−5.19615	−	3.00000i	−0.219382	−	0.126660i
$562$	24.7636	+	14.2973i	1.04459	+	0.603094i
$563$	−1.77735	+	1.02615i	−0.0749064	+	0.0432472i	−0.536985	−	0.843592i	$-0.680437\pi$
$563$	−1.77735	+	1.02615i	−0.0749064	+	0.0432472i	0.462079	+	0.886839i	$0.347104\pi$
$564$		−	14.7999i		−	0.623186i
$565$		0			0
$566$	−6.86428	+	3.96309i	−0.288527	+	0.166581i
$567$	−0.443277			−0.0186159
$568$	−20.8918	+	12.0619i	−0.876600	+	0.506105i
$569$	20.6095	−	35.6968i	0.863996	−	1.49649i	−0.00404386	−	0.999992i	$-0.501287\pi$
$569$	20.6095	−	35.6968i	0.863996	−	1.49649i	0.868040	−	0.496494i	$-0.165379\pi$
$570$		0			0
$571$	−30.7115			−1.28524			−0.642619	−	0.766186i	$-0.722152\pi$
$571$	−30.7115			−1.28524			−0.642619	+	0.766186i	$0.722152\pi$
$572$	14.7790	+	5.25803i	0.617942	+	0.219849i
$573$			16.2577i			0.679175i
$574$	5.02790	+	2.90286i	0.209860	+	0.121163i
$575$		0			0
$576$	−6.19615	−	10.7321i	−0.258173	−	0.447169i
$577$	−44.8752			−1.86818			−0.934090	−	0.357038i	$-0.883787\pi$
$577$	−44.8752			−1.86818			−0.934090	+	0.357038i	$0.883787\pi$
$578$	3.04964	+	5.28214i	0.126848	+	0.219708i
$579$	9.76662	−	5.63876i	0.405887	−	0.234339i
$580$		0			0
$581$	−2.02312	−	3.50414i	−0.0839331	−	0.145376i
$582$	15.8569	+	9.15500i	0.657291	+	0.379487i
$583$	4.39230	−	7.60770i	0.181911	−	0.315079i
$584$	17.1888			0.711278
$585$		0			0
$586$	42.7122			1.76443
$587$	−11.9359	+	20.6735i	−0.492645	+	0.853287i	−0.999964	−	0.00847155i	$-0.997303\pi$
$587$	−11.9359	+	20.6735i	−0.492645	+	0.853287i	0.507319	+	0.861759i	$0.330637\pi$
$588$	−16.0973	−	9.29376i	−0.663840	−	0.383268i
$589$	−4.78448	−	8.28697i	−0.197141	−	0.341459i
$590$		0			0
$591$	−21.3622	+	12.3335i	−0.878723	+	0.507331i
$592$	10.3507	+	17.9279i	0.425409	+	0.736831i
$593$	26.8263			1.10162			0.550811	−	0.834630i	$-0.314318\pi$
$593$	26.8263			1.10162			0.550811	+	0.834630i	$0.314318\pi$
$594$	−1.73205	−	3.00000i	−0.0710669	−	0.123091i
$595$		0			0
$596$	−0.134613	−	0.0777187i	−0.00551396	−	0.00318348i
$597$			22.0711i			0.903311i
$598$	−1.00093	−	5.44530i	−0.0409313	−	0.222675i
$599$	26.4919			1.08243			0.541215	−	0.840885i	$-0.317965\pi$
$599$	26.4919			1.08243			0.541215	+	0.840885i	$0.317965\pi$
$600$		0			0
$601$	−11.6145	+	20.1169i	−0.473765	+	0.820585i	−0.999549	−	0.0300334i	$-0.990439\pi$
$601$	−11.6145	+	20.1169i	−0.473765	+	0.820585i	0.525784	+	0.850618i	$0.323772\pi$
$602$	−3.94367	+	2.27688i	−0.160732	+	0.0927986i
$603$	−13.6960			−0.557743
$604$	−40.9333	+	23.6328i	−1.66555	+	0.961606i
$605$		0			0
$606$			14.5875i			0.592578i
$607$	−9.16359	+	5.29060i	−0.371939	+	0.214739i	−0.674305	−	0.738453i	$-0.735557\pi$
$607$	−9.16359	+	5.29060i	−0.371939	+	0.214739i	0.302366	+	0.953192i	$0.402223\pi$
$608$	−10.0967	−	5.82932i	−0.409474	−	0.236410i
$609$	0.959657	+	0.554058i	0.0388873	+	0.0224516i
$610$		0			0
$611$	6.54693	−	18.4018i	0.264860	−	0.744456i
$612$		−	10.2938i		−	0.416101i
$613$	−3.15868	+	5.47099i	−0.127578	+	0.220971i	−0.922738	−	0.385429i	$-0.874054\pi$
$613$	−3.15868	+	5.47099i	−0.127578	+	0.220971i	0.795160	+	0.606400i	$0.207387\pi$
$614$	5.16492	−	8.94590i	0.208439	−	0.361027i
$615$		0			0
$616$			1.12411i			0.0452915i
$617$	−16.3639	−	28.3430i	−0.658784	−	1.14105i	−0.980931	−	0.194358i	$-0.937738\pi$
$617$	−16.3639	−	28.3430i	−0.658784	−	1.14105i	0.322147	−	0.946690i	$-0.395596\pi$
$618$	−1.89467	−	3.28167i	−0.0762149	−	0.132008i
$619$		−	21.0143i		−	0.844635i	−0.906448	−	0.422317i	$-0.861217\pi$
$619$		−	21.0143i		−	0.844635i	0.906448	−	0.422317i	$-0.138783\pi$
$620$		0			0
$621$	−0.352948	+	0.611324i	−0.0141633	+	0.0245316i
$622$	−5.93334	+	10.2768i	−0.237905	+	0.412064i
$623$			2.10846i			0.0844736i
$624$	−1.30368	−	7.09228i	−0.0521888	−	0.283918i
$625$		0			0
$626$	−13.6366	−	7.87310i	−0.545029	−	0.314673i
$627$	−2.13368	−	1.23188i	−0.0852109	−	0.0491965i
$628$	3.19171	−	1.84274i	0.127363	−	0.0735332i
$629$			38.9990i			1.55499i
$630$		0			0
$631$	13.4803	−	7.78285i	0.536642	−	0.309830i	−0.207075	−	0.978325i	$-0.566394\pi$
$631$	13.4803	−	7.78285i	0.536642	−	0.309830i	0.743717	+	0.668495i	$0.233061\pi$
$632$	17.0897			0.679792
$633$	18.6335	−	10.7580i	0.740614	−	0.427593i
$634$	22.8564	−	39.5885i	0.907744	−	1.57226i
$635$		0			0
$636$	15.0711			0.597608
$637$	−15.9037	−	18.6765i	−0.630129	−	0.739990i
$638$			8.65966i			0.342839i
$639$	13.1193	+	7.57442i	0.518990	+	0.299639i
$640$		0			0
$641$	6.89551	+	11.9434i	0.272356	+	0.471735i	0.969465	−	0.245231i	$-0.0788637\pi$
$641$	6.89551	+	11.9434i	0.272356	+	0.471735i	−0.697108	+	0.716966i	$0.745530\pi$
$642$	25.9269			1.02325
$643$	13.8349	+	23.9628i	0.545596	+	0.945000i	0.998569	+	0.0534755i	$0.0170299\pi$
$643$	13.8349	+	23.9628i	0.545596	+	0.945000i	−0.452973	+	0.891524i	$0.649637\pi$
$644$	0.740347	−	0.427440i	0.0291738	−	0.0168435i
$645$		0			0
$646$	−6.34034	−	10.9818i	−0.249457	−	0.432073i
$647$	31.0291	+	17.9147i	1.21988	+	0.704298i	0.964892	−	0.262646i	$-0.0845953\pi$
$647$	31.0291	+	17.9147i	1.21988	+	0.704298i	0.254988	+	0.966944i	$0.417929\pi$
$648$	0.796225	−	1.37910i	0.0312787	−	0.0541763i
$649$	13.8896			0.545213
$650$		0			0
$651$	2.74162			0.107453
$652$	4.06963	−	7.04880i	0.159379	−	0.276052i
$653$	39.1708	+	22.6153i	1.53287	+	0.885003i	0.999228	+	0.0392935i	$0.0125107\pi$
$653$	39.1708	+	22.6153i	1.53287	+	0.885003i	0.533643	+	0.845710i	$0.320823\pi$
$654$	18.5346	+	32.1028i	0.724759	+	1.25532i
$655$		0			0
$656$	10.4284	−	6.02082i	0.407160	−	0.235074i
$657$	−5.39697	−	9.34782i	−0.210556	−	0.364693i
$658$	5.22358			0.203636
$659$	−1.18658	−	2.05522i	−0.0462226	−	0.0800598i	0.841988	−	0.539496i	$-0.181385\pi$
$659$	−1.18658	−	2.05522i	−0.0462226	−	0.0800598i	−0.888211	+	0.459436i	$0.848052\pi$
$660$		0			0
$661$	11.4110	+	6.58816i	0.443838	+	0.256250i	0.705224	−	0.708984i	$-0.250846\pi$
$661$	11.4110	+	6.58816i	0.443838	+	0.256250i	−0.261386	+	0.965234i	$0.584180\pi$
$662$			33.7473i			1.31162i
$663$	4.55359	−	12.7990i	0.176847	−	0.497073i
$664$	14.5359			0.564102
$665$		0			0
$666$	−11.2580	+	19.4995i	−0.436240	+	0.755590i
$667$	1.52821	−	0.882310i	0.0591724	−	0.0341632i
$668$	65.0613			2.51730
$669$	−18.3914	+	10.6183i	−0.711051	+	0.410526i
$670$		0			0
$671$		−	15.4978i		−	0.598286i
$672$	2.89282	−	1.67017i	0.111593	−	0.0644282i
$673$	11.0738	+	6.39346i	0.426864	+	0.246450i	0.698010	−	0.716088i	$-0.254069\pi$
$673$	11.0738	+	6.39346i	0.426864	+	0.246450i	−0.271146	+	0.962538i	$0.587403\pi$
$674$	−61.8149	−	35.6889i	−2.38102	−	1.37468i
$675$		0			0
$676$	−5.65932	+	35.0629i	−0.217666	+	1.34857i
$677$		−	16.0794i		−	0.617981i	−0.951065	−	0.308991i	$-0.900009\pi$
$677$		−	16.0794i		−	0.617981i	0.951065	−	0.308991i	$-0.0999912\pi$
$678$	−3.76778	+	6.52598i	−0.144701	+	0.250629i
$679$	−1.86556	+	3.23124i	−0.0715936	+	0.124004i
$680$		0			0
$681$		−	10.4499i		−	0.400443i
$682$	10.7126	+	18.5547i	0.410205	+	0.710496i
$683$	−3.15581	−	5.46602i	−0.120754	−	0.209152i	0.799311	−	0.600917i	$-0.205198\pi$
$683$	−3.15581	−	5.46602i	−0.120754	−	0.209152i	−0.920065	+	0.391765i	$0.871864\pi$
$684$		−	4.22689i		−	0.161619i
$685$		0			0
$686$	6.65517	−	11.5271i	0.254096	−	0.440107i
$687$	10.7068	−	18.5447i	0.408489	−	0.707523i
$688$			9.44496i			0.360086i
$689$	18.7391	+	6.66692i	0.713901	+	0.253989i
$690$		0			0
$691$	−31.7955	−	18.3572i	−1.20956	−	0.698339i	−0.246896	−	0.969042i	$-0.579410\pi$
$691$	−31.7955	−	18.3572i	−1.20956	−	0.698339i	−0.962663	+	0.270703i	$0.912744\pi$
$692$	−58.3844	−	33.7082i	−2.21944	−	1.28140i
$693$	0.611324	−	0.352948i	0.0232223	−	0.0134074i
$694$		−	42.3393i		−	1.60718i
$695$		0			0
$696$	−3.44752	+	1.99043i	−0.130678	+	0.0754469i
$697$	22.6851			0.859261
$698$	18.3136	−	10.5733i	0.693178	−	0.400207i
$699$	1.62090	−	2.80748i	0.0613080	−	0.106189i
$700$		0			0
$701$	52.0509			1.96594			0.982968	−	0.183774i	$-0.0588316\pi$
$701$	52.0509			1.96594			0.982968	+	0.183774i	$0.0588316\pi$
$702$	5.97155	−	5.08500i	0.225382	−	0.191921i
$703$			16.0140i			0.603980i
$704$	17.0903	+	9.86707i	0.644113	+	0.371879i
$705$		0			0
$706$	25.0354	+	43.3626i	0.942219	+	1.63197i
$707$	−2.97257			−0.111795
$708$	11.9147	+	20.6368i	0.447780	+	0.775578i
$709$	−0.810685	+	0.468049i	−0.0304459	+	0.0175779i	−0.515146	−	0.857103i	$-0.672262\pi$
$709$	−0.810685	+	0.468049i	−0.0304459	+	0.0175779i	0.484700	+	0.874681i	$0.338929\pi$
$710$		0			0
$711$	−5.36585	−	9.29393i	−0.201235	−	0.348550i
$712$	−6.55974	−	3.78727i	−0.245837	−	0.141934i
$713$	2.18295	−	3.78098i	0.0817521	−	0.141599i
$714$	3.63317			0.135968
$715$		0			0
$716$	−7.88163			−0.294550
$717$	9.15645	−	15.8594i	0.341954	−	0.592282i
$718$	−19.6172	−	11.3260i	−0.732107	−	0.422682i
$719$	−0.498717	−	0.863804i	−0.0185990	−	0.0322145i	0.856576	−	0.516021i	$-0.172587\pi$
$719$	−0.498717	−	0.863804i	−0.0185990	−	0.0322145i	−0.875175	+	0.483806i	$0.839254\pi$
$720$		0			0
$721$	0.668722	−	0.386087i	0.0249045	−	0.0143786i
$722$	18.0621	+	31.2845i	0.672202	+	1.16429i
$723$	−6.63741			−0.246848
$724$	10.1234	+	17.5343i	0.376234	+	0.651656i
$725$		0			0
$726$	−15.9454	−	9.20610i	−0.591790	−	0.341670i
$727$			15.4879i			0.574416i	0.957868	+	0.287208i	$0.0927271\pi$
$727$			15.4879i			0.574416i	−0.957868	+	0.287208i	$0.907273\pi$
$728$	−2.50321	+	0.460130i	−0.0927751	+	0.0170536i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−8.89662	+	15.4094i	−0.329054	+	0.569937i
$732$	23.0263	−	13.2942i	0.851076	−	0.491369i
$733$	−3.34533			−0.123562			−0.0617812	−	0.998090i	$-0.519678\pi$
$733$	−3.34533			−0.123562			−0.0617812	+	0.998090i	$0.519678\pi$
$734$	−6.84141	+	3.94989i	−0.252521	+	0.145793i
$735$		0			0
$736$		−	5.31932i		−	0.196073i
$737$	18.8882	−	10.9051i	0.695754	−	0.401694i
$738$	11.3426	+	6.54863i	0.417526	+	0.241059i
$739$	11.3394	+	6.54681i	0.417127	+	0.240828i	0.693847	−	0.720122i	$-0.255914\pi$
$739$	11.3394	+	6.54681i	0.417127	+	0.240828i	−0.276721	+	0.960950i	$0.589248\pi$
$740$		0			0
$741$	1.86983	−	5.25562i	0.0686898	−	0.193070i
$742$			5.31932i			0.195279i
$743$	−2.53686	+	4.39398i	−0.0930685	+	0.161199i	−0.908801	−	0.417230i	$-0.863001\pi$
$743$	−2.53686	+	4.39398i	−0.0930685	+	0.161199i	0.815732	+	0.578430i	$0.196334\pi$
$744$	−4.92457	+	8.52961i	−0.180544	+	0.312711i
$745$		0			0
$746$		−	43.1561i		−	1.58006i
$747$	−4.56400	−	7.90509i	−0.166988	−	0.289232i
$748$	8.19615	+	14.1962i	0.299681	+	0.519063i
$749$			5.28325i			0.193046i
$750$		0			0
$751$	9.51688	−	16.4837i	0.347276	−	0.601499i	−0.638489	−	0.769631i	$-0.720440\pi$
$751$	9.51688	−	16.4837i	0.347276	−	0.601499i	0.985765	+	0.168132i	$0.0537734\pi$
$752$	5.41712	−	9.38273i	0.197542	−	0.342153i
$753$		−	19.8816i		−	0.724527i
$754$	−19.2837	+	3.54466i	−0.702272	+	0.129089i
$755$		0			0
$756$	1.04880	+	0.605528i	0.0381447	+	0.0220228i
$757$	38.8056	+	22.4044i	1.41042	+	0.814303i	0.995427	−	0.0955235i	$-0.0304525\pi$
$757$	38.8056	+	22.4044i	1.41042	+	0.814303i	0.414988	+	0.909827i	$0.363786\pi$
$758$	12.8743	−	7.43299i	0.467616	−	0.269978i
$759$		−	1.12411i		−	0.0408024i
$760$		0			0
$761$	32.8763	−	18.9811i	1.19176	−	0.688065i	0.233058	−	0.972463i	$-0.425127\pi$
$761$	32.8763	−	18.9811i	1.19176	−	0.688065i	0.958706	+	0.284398i	$0.0917936\pi$
$762$	−31.0007			−1.12304
$763$	−6.54174	+	3.77688i	−0.236827	+	0.136732i
$764$	22.2084	−	38.4661i	0.803472	−	1.39166i
$765$		0			0
$766$	−84.5852			−3.05619
$767$	5.68542	+	30.9299i	0.205289	+	1.11681i
$768$			1.07180i			0.0386751i
$769$	−21.5337	−	12.4325i	−0.776525	−	0.448327i	0.0586721	−	0.998277i	$-0.481313\pi$
$769$	−21.5337	−	12.4325i	−0.776525	−	0.448327i	−0.835197	+	0.549950i	$0.814647\pi$
$770$		0			0
$771$	−0.504787	−	0.874316i	−0.0181794	−	0.0314877i
$772$	−30.8108			−1.10890
$773$	−14.6513	−	25.3768i	−0.526970	−	0.912740i	−0.999506	−	0.0314280i	$-0.989995\pi$
$773$	−14.6513	−	25.3768i	−0.526970	−	0.912740i	0.472536	−	0.881312i	$-0.343339\pi$
$774$	−8.89662	+	5.13647i	−0.319783	+	0.184627i
$775$		0			0
$776$	−6.70193	−	11.6081i	−0.240585	−	0.416706i
$777$	−3.97350	−	2.29410i	−0.142549	−	0.0823005i
$778$	9.62453	−	16.6702i	0.345056	−	0.597655i
$779$	9.31512			0.333749
$780$		0			0
$781$	−24.1238			−0.863216
$782$	2.89282	−	5.01051i	0.103447	−	0.179175i
$783$	2.16492	+	1.24991i	0.0773678	+	0.0446683i
$784$	−6.80351	−	11.7840i	−0.242982	−	0.420858i
$785$		0			0
$786$	18.9056	−	10.9151i	0.674339	−	0.389330i
$787$	−5.33508	−	9.24064i	−0.190175	−	0.329393i	0.755133	−	0.655572i	$-0.227572\pi$
$787$	−5.33508	−	9.24064i	−0.190175	−	0.329393i	−0.945308	+	0.326179i	$0.894239\pi$
$788$	67.3913			2.40071
$789$	10.7859	+	18.6818i	0.383990	+	0.665089i
$790$		0			0
$791$	−1.32983	−	0.767778i	−0.0472833	−	0.0272990i
$792$			2.53590i			0.0901092i
$793$	34.5112	−	6.34372i	1.22553	−	0.225272i
$794$	37.0628			1.31531
$795$		0			0
$796$	30.1497	−	52.2208i	1.06863	−	1.85092i
$797$	16.3506	−	9.44000i	0.579166	−	0.334382i	−0.181636	−	0.983366i	$-0.558139\pi$
$797$	16.3506	−	9.44000i	0.579166	−	0.334382i	0.760802	+	0.648984i	$0.224806\pi$
$798$	1.49187			0.0528118
$799$	17.6760	−	10.2053i	0.625333	−	0.361036i
$800$		0			0
$801$			4.75653i			0.168064i
$802$	−14.4890	+	8.36522i	−0.511624	+	0.295386i
$803$	14.8859	+	8.59440i	0.525313	+	0.303290i
$804$	32.4050	+	18.7091i	1.14284	+	0.659818i
$805$		0			0
$806$	−36.9335	+	31.4502i	−1.30093	+	1.10779i
$807$		−	4.65068i		−	0.163712i
$808$	5.33940	−	9.24812i	0.187840	−	0.325348i
$809$	21.8102	−	37.7763i	0.766805	−	1.32814i	−0.172482	−	0.985013i	$-0.555179\pi$
$809$	21.8102	−	37.7763i	0.766805	−	1.32814i	0.939287	−	0.343132i	$-0.111488\pi$
$810$		0			0
$811$		−	3.31656i		−	0.116460i	−0.998303	−	0.0582301i	$-0.981454\pi$
$811$		−	3.31656i		−	0.116460i	0.998303	−	0.0582301i	$-0.0185457\pi$
$812$	−1.51372	−	2.62183i	−0.0531210	−	0.0920083i
$813$	2.65996	+	4.60718i	0.0932888	+	0.161581i
$814$		−	35.8557i		−	1.25674i
$815$		0			0
$816$	3.76778	−	6.52598i	0.131899	−	0.228455i
$817$	−3.65319	+	6.32751i	−0.127809	+	0.221372i
$818$			19.7592i			0.690863i
$819$	1.03619	+	1.21685i	0.0362076	+	0.0425202i
$820$		0			0
$821$	6.24179	+	3.60370i	0.217840	+	0.125770i	0.604950	−	0.796264i	$-0.293193\pi$
$821$	6.24179	+	3.60370i	0.217840	+	0.125770i	−0.387110	+	0.922034i	$0.626527\pi$
$822$	17.4904	+	10.0981i	0.610047	+	0.352211i
$823$	−8.48957	+	4.90146i	−0.295928	+	0.170854i	−0.640612	−	0.767865i	$-0.721319\pi$
$823$	−8.48957	+	4.90146i	−0.295928	+	0.170854i	0.344684	+	0.938719i	$0.387986\pi$
$824$			2.77399i			0.0966367i
$825$		0			0
$826$	−7.28372	+	4.20526i	−0.253433	+	0.146320i
$827$	−3.92322			−0.136424			−0.0682118	−	0.997671i	$-0.521729\pi$
$827$	−3.92322			−0.136424			−0.0682118	+	0.997671i	$0.521729\pi$
$828$	1.67017	−	0.964273i	0.0580424	−	0.0335108i
$829$	−5.21210	+	9.02761i	−0.181024	+	0.313542i	−0.942229	−	0.334968i	$-0.891274\pi$
$829$	−5.21210	+	9.02761i	−0.181024	+	0.313542i	0.761206	+	0.648510i	$0.224608\pi$
$830$		0			0
$831$	9.35948			0.324677
$832$	−14.9769	+	42.0962i	−0.519229	+	1.45942i
$833$		−	25.6341i		−	0.888169i
$834$	−12.2762	−	7.08766i	−0.425090	−	0.245426i
$835$		0			0
$836$	3.36556	+	5.82932i	0.116400	+	0.201611i
$837$	6.18490			0.213781
$838$	14.1295	+	24.4730i	0.488095	+	0.845406i
$839$	8.87859	−	5.12606i	0.306523	−	0.176971i	−0.338847	−	0.940842i	$-0.610037\pi$
$839$	8.87859	−	5.12606i	0.306523	−	0.176971i	0.645369	+	0.763871i	$0.276703\pi$
$840$		0			0
$841$	11.3754	+	19.7028i	0.392256	+	0.679408i
$842$	37.4628	+	21.6291i	1.29105	+	0.745389i
$843$	−6.57246	+	11.3838i	−0.226368	+	0.392080i
$844$	−58.7830			−2.02339
$845$		0			0
$846$	11.7840			0.405143
$847$	1.87597	−	3.24928i	0.0644591	−	0.111646i
$848$	9.55470	+	5.51641i	0.328110	+	0.189434i
$849$	−1.82184	−	3.15551i	−0.0625253	−	0.108297i
$850$		0			0
$851$	−6.32761	+	3.65325i	−0.216908	+	0.125232i
$852$	−20.6937	−	35.8425i	−0.708954	−	1.22794i
$853$	26.3671			0.902792			0.451396	−	0.892324i	$-0.350926\pi$
$853$	26.3671			0.902792			0.451396	+	0.892324i	$0.350926\pi$
$854$	4.69218	+	8.12709i	0.160563	+	0.278103i
$855$		0			0
$856$	−16.4370	−	9.48991i	−0.561806	−	0.324359i
$857$			1.04855i			0.0358178i	0.999840	+	0.0179089i	$0.00570088\pi$
$857$			1.04855i			0.0358178i	−0.999840	+	0.0179089i	$0.994299\pi$
$858$	−4.18658	+	11.7674i	−0.142927	+	0.401734i
$859$	19.6076			0.669003			0.334501	−	0.942395i	$-0.391432\pi$
$859$	19.6076			0.669003			0.334501	+	0.942395i	$0.391432\pi$
$860$		0			0
$861$	−1.33445	+	2.31133i	−0.0454778	+	0.0787699i
$862$	−73.7128	+	42.5581i	−2.51067	+	1.44954i
$863$	−25.6925			−0.874582			−0.437291	−	0.899320i	$-0.644062\pi$
$863$	−25.6925			−0.874582			−0.437291	+	0.899320i	$0.644062\pi$
$864$	6.52598	−	3.76778i	0.222018	−	0.128182i
$865$		0			0
$866$			82.9668i			2.81933i
$867$	−2.42820	+	1.40192i	−0.0824661	+	0.0476118i
$868$	−6.48675	−	3.74513i	−0.220175	−	0.127118i
$869$	14.8001	+	8.54486i	0.502060	+	0.289864i
$870$		0			0
$871$	32.0154	+	37.5972i	1.08480	+	1.27393i
$872$		−	27.1365i		−	0.918958i
$873$	−4.20856	+	7.28944i	−0.142438	+	0.246710i
$874$	1.18787	−	2.05745i	0.0401802	−	0.0695942i
$875$		0			0
$876$			29.4896i			0.996360i
$877$	18.2071	+	31.5356i	0.614809	+	1.06488i	0.990418	+	0.138102i	$0.0441002\pi$
$877$	18.2071	+	31.5356i	0.614809	+	1.06488i	−0.375609	+	0.926778i	$0.622567\pi$
$878$	7.34266	+	12.7179i	0.247803	+	0.429207i
$879$			19.6348i			0.662267i
$880$		0			0
$881$	8.01915	−	13.8896i	0.270172	−	0.467951i	−0.698734	−	0.715382i	$-0.746253\pi$
$881$	8.01915	−	13.8896i	0.270172	−	0.467951i	0.968906	+	0.247430i	$0.0795861\pi$
$882$	7.39993	−	12.8170i	0.249169	−	0.431573i
$883$		−	27.4548i		−	0.923927i	−0.886899	−	0.461963i	$-0.847145\pi$
$883$		−	27.4548i		−	0.923927i	0.886899	−	0.461963i	$-0.152855\pi$
$884$	−28.2577	+	24.0625i	−0.950409	+	0.809309i
$885$		0			0
$886$	−23.1053	−	13.3399i	−0.776239	−	0.448162i
$887$	−27.6818	−	15.9821i	−0.929464	−	0.536626i	−0.0428217	−	0.999083i	$-0.513635\pi$
$887$	−27.6818	−	15.9821i	−0.929464	−	0.536626i	−0.886642	+	0.462457i	$0.846968\pi$
$888$	14.2746	−	8.24145i	0.479025	−	0.276565i
$889$		−	6.31715i		−	0.211870i
$890$		0			0
$891$	1.37910	−	0.796225i	0.0462017	−	0.0266745i
$892$	58.0193			1.94263
$893$	7.25825	−	4.19055i	0.242888	−	0.140231i
$894$	0.0618816	−	0.107182i	0.00206963	−	0.00358471i
$895$		0			0
$896$	−5.26888			−0.176021
$897$	2.50321	−	0.460130i	0.0835797	−	0.0153633i
$898$			50.9084i			1.69883i
$899$	−13.3898	−	7.73060i	−0.446574	−	0.257830i
$900$		0			0
$901$	10.3923	+	18.0000i	0.346218	+	0.599667i
$902$	−20.8567			−0.694454
$903$	−1.04668	−	1.81291i	−0.0348314	−	0.0603298i
$904$	4.77735	−	2.75821i	0.158892	−	0.0917365i
$905$		0			0
$906$	−18.8170	−	32.5921i	−0.625155	−	1.08280i
$907$	−27.4354	−	15.8398i	−0.910977	−	0.525953i	−0.0302317	−	0.999543i	$-0.509625\pi$
$907$	−27.4354	−	15.8398i	−0.910977	−	0.525953i	−0.880745	+	0.473590i	$0.842958\pi$
$908$	−14.2749	+	24.7248i	−0.473729	+	0.820522i
$909$	−6.70590			−0.222421
$910$		0			0
$911$	−25.9227			−0.858858			−0.429429	−	0.903101i	$-0.641285\pi$
$911$	−25.9227			−0.858858			−0.429429	+	0.903101i	$0.641285\pi$
$912$	1.54715	−	2.67974i	0.0512313	−	0.0887351i
$913$	12.5885	+	7.26795i	0.416617	+	0.240534i
$914$	−32.1547	−	55.6935i	−1.06358	−	1.84218i
$915$		0			0
$916$	−50.6650	+	29.2514i	−1.67402	+	0.966494i
$917$	2.22423	+	3.85247i	0.0734505	+	0.127220i
$918$	8.19615			0.270513
$919$	−6.00970	−	10.4091i	−0.198242	−	0.343365i	0.749717	−	0.661759i	$-0.230190\pi$
$919$	−6.00970	−	10.4091i	−0.198242	−	0.343365i	−0.947958	+	0.318394i	$0.896856\pi$
$920$		0			0
$921$	4.11244	+	2.37432i	0.135509	+	0.0782364i
$922$			20.8287i			0.685958i
$923$	−9.87459	−	53.7199i	−0.325026	−	1.76821i
$924$	−1.92855			−0.0634445
$925$		0			0
$926$	−21.7795	+	37.7232i	−0.715720	+	1.23966i
$927$	1.50859	−	0.870983i	0.0495485	−	0.0286068i
$928$	−18.8376			−0.618375
$929$	18.4962	−	10.6788i	0.606842	−	0.350360i	−0.164887	−	0.986313i	$-0.552726\pi$
$929$	18.4962	−	10.6788i	0.606842	−	0.350360i	0.771728	+	0.635952i	$0.219392\pi$
$930$		0			0
$931$		−	10.5260i		−	0.344977i
$932$	−7.67017	+	4.42837i	−0.251245	+	0.145056i
$933$	−4.72427	−	2.72756i	−0.154666	−	0.0892963i
$934$	29.7545	+	17.1788i	0.973597	+	0.562106i
$935$		0			0
$936$	−5.64705	+	1.03802i	−0.184580	+	0.0339288i
$937$		−	15.8029i		−	0.516259i	−0.966110	−	0.258129i	$-0.916894\pi$
$937$		−	15.8029i		−	0.516259i	0.966110	−	0.258129i	$-0.0831061\pi$
$938$	−6.60333	+	11.4373i	−0.215606	+	0.373441i
$939$	3.61927	−	6.26876i	0.118111	−	0.204573i
$940$		0			0
$941$		−	6.50590i		−	0.212086i	−0.994362	−	0.106043i	$-0.966182\pi$
$941$		−	6.50590i		−	0.212086i	0.994362	−	0.106043i	$-0.0338182\pi$
$942$	1.46723	+	2.54132i	0.0478051	+	0.0828008i
$943$	2.12504	+	3.68068i	0.0692008	+	0.119859i
$944$			17.4443i			0.567763i
$945$		0			0
$946$	8.17957	−	14.1674i	0.265941	−	0.460623i
$947$	13.9418	−	24.1479i	0.453048	−	0.784701i	−0.545526	−	0.838094i	$-0.683670\pi$
$947$	13.9418	−	24.1479i	0.453048	−	0.784701i	0.998574	+	0.0533924i	$0.0170034\pi$
$948$			29.3196i			0.952255i
$949$	−13.0451	+	36.6666i	−0.423463	+	1.19025i
$950$		0			0
$951$	18.1988	+	10.5071i	0.590138	+	0.340716i
$952$	−2.30333	−	1.32983i	−0.0746515	−	0.0431001i
$953$	−44.9347	+	25.9430i	−1.45558	+	0.840377i	−0.998789	−	0.0491986i	$-0.984333\pi$
$953$	−44.9347	+	25.9430i	−1.45558	+	0.840377i	−0.456787	+	0.889576i	$0.651000\pi$
$954$			12.0000i			0.388514i
$955$		0			0
$956$	−43.3288	+	25.0159i	−1.40135	+	0.809072i
$957$	−3.98085			−0.128683
$958$	−50.3913	+	29.0934i	−1.62807	+	0.939966i
$959$	−2.05773	+	3.56410i	−0.0664477	+	0.115091i
$960$		0			0
$961$	−7.25300			−0.233968
$962$	79.8451	−	14.6768i	2.57431	−	0.473200i
$963$			11.9186i			0.384072i
$964$	15.7043	+	9.06687i	0.505801	+	0.292024i
$965$		0			0
$966$	0.340338	+	0.589483i	0.0109502	+	0.0189663i
$967$	−21.4251			−0.688986			−0.344493	−	0.938789i	$-0.611949\pi$
$967$	−21.4251			−0.688986			−0.344493	+	0.938789i	$0.611949\pi$
$968$	6.73933	+	11.6729i	0.216610	+	0.375180i
$969$	5.04834	−	2.91466i	0.162176	−	0.0936323i
$970$		0			0
$971$	3.33637	+	5.77876i	0.107069	+	0.185449i	0.914582	−	0.404401i	$-0.132520\pi$
$971$	3.33637	+	5.77876i	0.107069	+	0.185449i	−0.807513	+	0.589850i	$0.799187\pi$
$972$	2.36603	+	1.36603i	0.0758903	+	0.0438153i
$973$	1.44429	−	2.50158i	0.0463017	−	0.0801969i
$974$	−61.6136			−1.97423
$975$		0			0
$976$	19.4641			0.623031
$977$	4.91271	−	8.50906i	0.157171	−	0.272229i	−0.776676	−	0.629900i	$-0.783096\pi$
$977$	4.91271	−	8.50906i	0.157171	−	0.272229i	0.933848	+	0.357671i	$0.116429\pi$
$978$	5.61244	+	3.24034i	0.179466	+	0.103615i
$979$	−3.78727	−	6.55974i	−0.121042	−	0.209650i
$980$		0			0
$981$	−14.7577	+	8.52036i	−0.471177	+	0.272034i
$982$	−10.3330	−	17.8973i	−0.329739	−	0.571125i
$983$	−8.83034			−0.281644			−0.140822	−	0.990035i	$-0.544975\pi$
$983$	−8.83034			−0.281644			−0.140822	+	0.990035i	$0.544975\pi$
$984$	−4.79393	−	8.30333i	−0.152825	−	0.264701i
$985$		0			0
$986$	−17.7440	−	10.2445i	−0.565083	−	0.326251i
$987$			2.40129i			0.0764338i
$988$	−11.6034	+	9.88069i	−0.369152	+	0.314347i
$989$	−3.33358			−0.106002
$990$		0			0
$991$	−6.16662	+	10.6809i	−0.195889	+	0.339290i	−0.947192	−	0.320668i	$-0.896093\pi$
$991$	−6.16662	+	10.6809i	−0.195889	+	0.339290i	0.751302	+	0.659958i	$0.229426\pi$
$992$	−40.3626	+	23.3033i	−1.28151	+	0.739882i
$993$	−15.5136			−0.492311
$994$	12.6506	−	7.30380i	0.401251	−	0.231663i
$995$		0			0
$996$			24.9382i			0.790196i
$997$	11.3019	−	6.52517i	0.357935	−	0.206654i	−0.310239	−	0.950658i	$-0.600409\pi$
$997$	11.3019	−	6.52517i	0.357935	−	0.206654i	0.668175	+	0.744004i	$0.267076\pi$
$998$	43.6623	+	25.2084i	1.38210	+	0.797959i
$999$	−8.96393	−	5.17533i	−0.283606	−	0.163740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.w.i.199.4		8
5.2	odd	4		195.2.bb.b.121.4	✓	8
5.3	odd	4		975.2.bc.j.901.1		8
5.4	even	2		975.2.w.h.199.1		8
13.10	even	6		975.2.w.h.49.1		8
15.2	even	4		585.2.bu.d.316.1		8
65.7	even	12		2535.2.a.bj.1.4		4
65.23	odd	12		975.2.bc.j.751.1		8
65.32	even	12		2535.2.a.bk.1.1		4
65.49	even	6	inner	975.2.w.i.49.4		8
65.62	odd	12		195.2.bb.b.166.4	yes	8
195.32	odd	12		7605.2.a.ch.1.4		4
195.62	even	12		585.2.bu.d.361.1		8
195.137	odd	12		7605.2.a.ci.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.4	✓	8	5.2	odd	4
195.2.bb.b.166.4	yes	8	65.62	odd	12
585.2.bu.d.316.1		8	15.2	even	4
585.2.bu.d.361.1		8	195.62	even	12
975.2.w.h.49.1		8	13.10	even	6
975.2.w.h.199.1		8	5.4	even	2
975.2.w.i.49.4		8	65.49	even	6	inner
975.2.w.i.199.4		8	1.1	even	1	trivial
975.2.bc.j.751.1		8	65.23	odd	12
975.2.bc.j.901.1		8	5.3	odd	4
2535.2.a.bj.1.4		4	65.7	even	12
2535.2.a.bk.1.1		4	65.32	even	12
7605.2.a.ch.1.4		4	195.32	odd	12
7605.2.a.ci.1.1		4	195.137	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.08766 - 1.88389i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.36603 - 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.221638 + 0.383889i) q^{7} -1.59245 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.08766 - 1.88389i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.36603 - 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.221638 + 0.383889i) q^{7} -1.59245 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.37910 - 0.796225i) q^{11} -2.73205i q^{12} +(1.20856 - 3.39697i) q^{13} +0.964273 q^{14} +(1.00000 - 1.73205i) q^{16} +(3.26299 - 1.88389i) q^{17} +2.17533 q^{18} +(1.33987 - 0.773575i) q^{19} +0.443277i q^{21} +(-3.00000 + 1.73205i) q^{22} +(0.611324 + 0.352948i) q^{23} +(-1.37910 - 0.796225i) q^{24} +(-5.08500 - 5.97155i) q^{26} +1.00000i q^{27} +(0.605528 - 1.04880i) q^{28} +(1.24991 - 2.16492i) q^{29} -6.18490i q^{31} +(-3.76778 - 6.52598i) q^{32} +(-0.796225 - 1.37910i) q^{33} -8.19615i q^{34} +(1.36603 - 2.36603i) q^{36} +(-5.17533 + 8.96393i) q^{37} -3.36556i q^{38} +(2.74513 - 2.33758i) q^{39} +(5.21419 + 3.01041i) q^{41} +(0.835085 + 0.482136i) q^{42} +(-4.08979 + 2.36124i) q^{43} +4.35066i q^{44} +(1.32983 - 0.767778i) q^{46} +5.41712 q^{47} +(1.73205 - 1.00000i) q^{48} +(3.40175 - 5.89201i) q^{49} +3.76778 q^{51} +(-9.68823 + 1.78086i) q^{52} +5.51641i q^{53} +(1.88389 + 1.08766i) q^{54} +(-0.352948 - 0.611324i) q^{56} +1.54715 q^{57} +(-2.71897 - 4.70940i) q^{58} +(-7.55359 + 4.36107i) q^{59} +(4.86603 + 8.42820i) q^{61} +(-11.6517 - 6.72709i) q^{62} +(-0.221638 + 0.383889i) q^{63} -12.3923 q^{64} -3.46410 q^{66} +(-6.84799 + 11.8611i) q^{67} +(-8.91466 - 5.14688i) q^{68} +(0.352948 + 0.611324i) q^{69} +(13.1193 - 7.57442i) q^{71} +(-0.796225 - 1.37910i) q^{72} -10.7939 q^{73} +(11.2580 + 19.4995i) q^{74} +(-3.66060 - 2.11345i) q^{76} -0.705897i q^{77} +(-1.41796 - 7.71402i) q^{78} -10.7317 q^{79} +(-0.500000 + 0.866025i) q^{81} +(11.3426 - 6.54863i) q^{82} -9.12801 q^{83} +(1.04880 - 0.605528i) q^{84} +10.2729i q^{86} +(2.16492 - 1.24991i) q^{87} +(2.19615 + 1.26795i) q^{88} +(4.11927 + 2.37826i) q^{89} +(1.57192 - 0.288945i) q^{91} -1.92855i q^{92} +(3.09245 - 5.35628i) q^{93} +(5.89201 - 10.2053i) q^{94} -7.53556i q^{96} +(4.20856 + 7.28944i) q^{97} +(-7.39993 - 12.8170i) q^{98} -1.59245i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 + 4 * q^9	\( 8 q - 4 q^{4} + 4 q^{9} + 12 q^{13} + 24 q^{14} + 8 q^{16} + 12 q^{19} - 24 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{28} - 12 q^{29} + 4 q^{36} - 24 q^{37} + 4 q^{39} + 36 q^{41} + 12 q^{42} - 12 q^{43} + 48 q^{47} + 4 q^{49} - 12 q^{52} + 24 q^{57} - 12 q^{58} - 36 q^{59} + 32 q^{61} - 48 q^{62} - 16 q^{64} - 12 q^{67} + 36 q^{71} - 48 q^{73} + 24 q^{74} - 48 q^{76} - 12 q^{78} + 16 q^{79} - 4 q^{81} - 12 q^{82} - 12 q^{84} + 12 q^{87} - 24 q^{88} - 36 q^{89} + 12 q^{93} - 12 q^{94} + 36 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q - 4 * q^4 + 4 * q^9 + 12 * q^13 + 24 * q^14 + 8 * q^16 + 12 * q^19 - 24 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^28 - 12 * q^29 + 4 * q^36 - 24 * q^37 + 4 * q^39 + 36 * q^41 + 12 * q^42 - 12 * q^43 + 48 * q^47 + 4 * q^49 - 12 * q^52 + 24 * q^57 - 12 * q^58 - 36 * q^59 + 32 * q^61 - 48 * q^62 - 16 * q^64 - 12 * q^67 + 36 * q^71 - 48 * q^73 + 24 * q^74 - 48 * q^76 - 12 * q^78 + 16 * q^79 - 4 * q^81 - 12 * q^82 - 12 * q^84 + 12 * q^87 - 24 * q^88 - 36 * q^89 + 12 * q^93 - 12 * q^94 + 36 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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