LMFDB - Embedded newform 972.2.l.d.107.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,3,0,3,6,0,0,-9,0,-3,0,0,6,33] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	972.107
Dual form			972.2.l.d.863.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.612484 + 1.27470i) q^{2} +(-1.24973 - 1.56147i) q^{4} +(0.840877 - 2.31029i) q^{5} +(3.82489 + 0.674430i) q^{7} +(2.75584 - 0.636655i) q^{8} +(2.42991 + 2.48688i) q^{10} +(0.0547511 - 0.0199278i) q^{11} +(-3.53434 + 2.96567i) q^{13} +(-3.20238 + 4.46251i) q^{14} +(-0.876364 + 3.90282i) q^{16} +(1.79249 - 1.03489i) q^{17} +(2.46167 + 1.42125i) q^{19} +(-4.65831 + 1.57423i) q^{20} +(-0.00813220 + 0.0819967i) q^{22} +(-0.991876 - 5.62521i) q^{23} +(-0.800144 - 0.671401i) q^{25} +(-1.61561 - 6.32166i) q^{26} +(-3.72696 - 6.81529i) q^{28} +(2.57867 - 3.07314i) q^{29} +(7.51076 - 1.32435i) q^{31} +(-4.43817 - 3.50751i) q^{32} +(0.221310 + 2.91874i) q^{34} +(4.77439 - 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(-3.31940 + 2.26740i) q^{38} +(0.846466 - 6.90215i) q^{40} +(-0.705325 - 0.840573i) q^{41} +(-3.29941 - 9.06505i) q^{43} +(-0.0995405 - 0.0605878i) q^{44} +(7.77797 + 2.18100i) q^{46} +(0.948548 - 5.37948i) q^{47} +(7.59704 + 2.76510i) q^{49} +(1.34591 - 0.608723i) q^{50} +(9.04776 + 1.81249i) q^{52} +10.5337i q^{53} -0.143248i q^{55} +(10.9702 - 0.576509i) q^{56} +(2.33794 + 5.16928i) q^{58} +(-1.50332 - 0.547162i) q^{59} +(-0.366631 + 2.07927i) q^{61} +(-2.91207 + 10.3851i) q^{62} +(7.18934 - 3.50904i) q^{64} +(3.87960 + 10.6591i) q^{65} +(4.85766 + 5.78913i) q^{67} +(-3.85607 - 1.50558i) q^{68} +(7.61689 + 11.1508i) q^{70} +(-4.08357 - 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(-6.79844 + 0.515484i) q^{74} +(-0.857186 - 5.61999i) q^{76} +(0.222856 - 0.0392956i) q^{77} +(4.45402 - 5.30809i) q^{79} +(8.27973 + 5.30644i) q^{80} +(1.50348 - 0.384241i) q^{82} +(8.72941 + 7.32485i) q^{83} +(-0.883642 - 5.01138i) q^{85} +(13.5761 + 1.34644i) q^{86} +(0.138198 - 0.0897753i) q^{88} +(-1.85844 - 1.07297i) q^{89} +(-15.5186 + 8.95967i) q^{91} +(-7.54401 + 8.57876i) q^{92} +(6.27626 + 4.50396i) q^{94} +(5.35345 - 4.49208i) q^{95} +(4.84352 - 1.76290i) q^{97} +(-8.17774 + 7.99038i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) $ 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−0.612484	+	1.27470i	−0.433091	+	0.901350i
$2$	−0.612484	+	1.27470i	−0.433091	+	0.901350i
$3$		0			0
$3$		0			0
$4$	−1.24973	−	1.56147i	−0.624864	−	0.780734i
$5$	0.840877	−	2.31029i	0.376052	−	1.03319i	−0.596927	−	0.802296i	$-0.703612\pi$
$5$	0.840877	−	2.31029i	0.376052	−	1.03319i	0.972978	−	0.230897i	$-0.0741661\pi$
$6$		0			0
$7$	3.82489	+	0.674430i	1.44567	+	0.254911i	0.840771	−	0.541391i	$-0.182102\pi$
$7$	3.82489	+	0.674430i	1.44567	+	0.254911i	0.604900	+	0.796302i	$0.293213\pi$
$8$	2.75584	−	0.636655i	0.974338	−	0.225092i
$9$		0			0
$10$	2.42991	+	2.48688i	0.768404	+	0.786421i
$11$	0.0547511	−	0.0199278i	0.0165081	−	0.00600845i	−0.333753	−	0.942661i	$-0.608315\pi$
$11$	0.0547511	−	0.0199278i	0.0165081	−	0.00600845i	0.350261	+	0.936652i	$0.386093\pi$
$12$		0			0
$13$	−3.53434	+	2.96567i	−0.980251	+	0.822528i	−0.984127	−	0.177465i	$-0.943210\pi$
$13$	−3.53434	+	2.96567i	−0.980251	+	0.822528i	0.00387662	+	0.999992i	$0.498766\pi$
$14$	−3.20238	+	4.46251i	−0.855871	+	1.19266i
$15$		0			0
$16$	−0.876364	+	3.90282i	−0.219091	+	0.975704i
$17$	1.79249	−	1.03489i	0.434742	−	0.250998i	−0.266623	−	0.963801i	$-0.585908\pi$
$17$	1.79249	−	1.03489i	0.434742	−	0.250998i	0.701365	+	0.712803i	$0.252574\pi$
$18$		0			0
$19$	2.46167	+	1.42125i	0.564746	+	0.326056i	0.755048	−	0.655669i	$-0.227613\pi$
$19$	2.46167	+	1.42125i	0.564746	+	0.326056i	−0.190302	+	0.981726i	$0.560947\pi$
$20$	−4.65831	+	1.57423i	−1.04163	+	0.352009i
$21$		0			0
$22$	−0.00813220	+	0.0819967i	−0.00173379	+	0.0174818i
$23$	−0.991876	−	5.62521i	−0.206820	−	1.17294i	−0.894549	−	0.446969i	$-0.852503\pi$
$23$	−0.991876	−	5.62521i	−0.206820	−	1.17294i	0.687729	−	0.725968i	$-0.258608\pi$
$24$		0			0
$25$	−0.800144	−	0.671401i	−0.160029	−	0.134280i
$26$	−1.61561	−	6.32166i	−0.316847	−	1.23978i
$27$		0			0
$28$	−3.72696	−	6.81529i	−0.704330	−	1.28797i
$29$	2.57867	−	3.07314i	0.478847	−	0.570668i	−0.471497	−	0.881867i	$-0.656286\pi$
$29$	2.57867	−	3.07314i	0.478847	−	0.570668i	0.950345	+	0.311200i	$0.100731\pi$
$30$		0			0
$31$	7.51076	−	1.32435i	1.34897	−	0.237860i	0.547958	−	0.836506i	$-0.315405\pi$
$31$	7.51076	−	1.32435i	1.34897	−	0.237860i	0.801014	+	0.598645i	$0.204294\pi$
$32$	−4.43817	−	3.50751i	−0.784565	−	0.620047i
$33$		0			0
$34$	0.221310	+	2.91874i	0.0379544	+	0.500560i
$35$	4.77439	−	8.26948i	0.807019	−	1.39780i
$36$		0			0
$37$	2.41051	+	4.17513i	0.396286	+	0.686387i	0.993264	−	0.115870i	$-0.0369656\pi$
$37$	2.41051	+	4.17513i	0.396286	+	0.686387i	−0.596979	+	0.802257i	$0.703632\pi$
$38$	−3.31940	+	2.26740i	−0.538477	+	0.367822i
$39$		0			0
$40$	0.846466	−	6.90215i	0.133838	−	1.09132i
$41$	−0.705325	−	0.840573i	−0.110153	−	0.131275i	0.708151	−	0.706061i	$-0.249530\pi$
$41$	−0.705325	−	0.840573i	−0.110153	−	0.131275i	−0.818304	+	0.574786i	$0.805085\pi$
$42$		0			0
$43$	−3.29941	−	9.06505i	−0.503155	−	1.38241i	−0.888178	−	0.459500i	$-0.848028\pi$
$43$	−3.29941	−	9.06505i	−0.503155	−	1.38241i	0.385022	−	0.922907i	$-0.374194\pi$
$44$	−0.0995405	−	0.0605878i	−0.0150063	−	0.00913395i
$45$		0			0
$46$	7.77797	+	2.18100i	1.14680	+	0.321571i
$47$	0.948548	−	5.37948i	0.138360	−	0.784678i	−0.834101	−	0.551612i	$-0.814013\pi$
$47$	0.948548	−	5.37948i	0.138360	−	0.784678i	0.972461	−	0.233066i	$-0.0748759\pi$
$48$		0			0
$49$	7.59704	+	2.76510i	1.08529	+	0.395014i
$50$	1.34591	−	0.608723i	0.190341	−	0.0860864i
$51$		0			0
$52$	9.04776	+	1.81249i	1.25470	+	0.251347i
$53$			10.5337i			1.44692i	0.690367	+	0.723459i	$0.257449\pi$
$53$			10.5337i			1.44692i	−0.690367	+	0.723459i	$0.742551\pi$
$54$		0			0
$55$		−	0.143248i		−	0.0193155i
$56$	10.9702	−	0.576509i	1.46595	−	0.0770393i
$57$		0			0
$58$	2.33794	+	5.16928i	0.306987	+	0.678760i
$59$	−1.50332	−	0.547162i	−0.195715	−	0.0712344i	0.242303	−	0.970201i	$-0.422097\pi$
$59$	−1.50332	−	0.547162i	−0.195715	−	0.0712344i	−0.438018	+	0.898966i	$0.644319\pi$
$60$		0			0
$61$	−0.366631	+	2.07927i	−0.0469423	+	0.266223i	−0.999241	−	0.0389431i	$-0.987601\pi$
$61$	−0.366631	+	2.07927i	−0.0469423	+	0.266223i	0.952299	+	0.305166i	$0.0987120\pi$
$62$	−2.91207	+	10.3851i	−0.369833	+	1.31891i
$63$		0			0
$64$	7.18934	−	3.50904i	0.898668	−	0.438630i
$65$	3.87960	+	10.6591i	0.481205	+	1.32210i
$66$		0			0
$67$	4.85766	+	5.78913i	0.593457	+	0.707255i	0.976266	−	0.216573i	$-0.0694879\pi$
$67$	4.85766	+	5.78913i	0.593457	+	0.707255i	−0.382809	+	0.923827i	$0.625043\pi$
$68$	−3.85607	−	1.50558i	−0.467617	−	0.182578i
$69$		0			0
$70$	7.61689	+	11.1508i	0.910392	+	1.33278i
$71$	−4.08357	−	7.07295i	−0.484630	−	0.839404i	0.515214	−	0.857062i	$-0.327712\pi$
$71$	−4.08357	−	7.07295i	−0.484630	−	0.839404i	−0.999844	+	0.0176575i	$0.994379\pi$
$72$		0			0
$73$	3.26625	−	5.65731i	0.382286	−	0.662138i	−0.609103	−	0.793091i	$-0.708470\pi$
$73$	3.26625	−	5.65731i	0.382286	−	0.662138i	0.991389	+	0.130953i	$0.0418037\pi$
$74$	−6.79844	+	0.515484i	−0.790303	+	0.0599238i
$75$		0			0
$76$	−0.857186	−	5.61999i	−0.0983260	−	0.644657i
$77$	0.222856	−	0.0392956i	0.0253968	−	0.00447815i
$78$		0			0
$79$	4.45402	−	5.30809i	0.501116	−	0.597207i	−0.454892	−	0.890546i	$-0.650322\pi$
$79$	4.45402	−	5.30809i	0.501116	−	0.597207i	0.956008	+	0.293340i	$0.0947667\pi$
$80$	8.27973	+	5.30644i	0.925702	+	0.593278i
$81$		0			0
$82$	1.50348	−	0.384241i	0.166032	−	0.0424323i
$83$	8.72941	+	7.32485i	0.958178	+	0.804006i	0.980656	−	0.195741i	$-0.0627111\pi$
$83$	8.72941	+	7.32485i	0.958178	+	0.804006i	−0.0224781	+	0.999747i	$0.507156\pi$
$84$		0			0
$85$	−0.883642	−	5.01138i	−0.0958444	−	0.543561i
$86$	13.5761	+	1.34644i	1.46395	+	0.145190i
$87$		0			0
$88$	0.138198	−	0.0897753i	0.0147320	−	0.00957008i
$89$	−1.85844	−	1.07297i	−0.196995	−	0.113735i	0.398258	−	0.917273i	$-0.369615\pi$
$89$	−1.85844	−	1.07297i	−0.196995	−	0.113735i	−0.595253	+	0.803538i	$0.702948\pi$
$90$		0			0
$91$	−15.5186	+	8.95967i	−1.62679	+	0.939228i
$92$	−7.54401	+	8.57876i	−0.786517	+	0.894397i
$93$		0			0
$94$	6.27626	+	4.50396i	0.647347	+	0.464548i
$95$	5.35345	−	4.49208i	0.549253	−	0.460878i
$96$		0			0
$97$	4.84352	−	1.76290i	0.491785	−	0.178995i	−0.0842102	−	0.996448i	$-0.526837\pi$
$97$	4.84352	−	1.76290i	0.491785	−	0.178995i	0.575996	+	0.817453i	$0.304615\pi$
$98$	−8.17774	+	7.99038i	−0.826076	+	0.807151i
$99$		0			0
$100$	−0.0484086	+	2.08847i	−0.00484086	+	0.208847i
$101$	−13.0167	−	2.29520i	−1.29521	−	0.228381i	−0.516784	−	0.856116i	$-0.672871\pi$
$101$	−13.0167	−	2.29520i	−1.29521	−	0.228381i	−0.778427	+	0.627735i	$0.783982\pi$
$102$		0			0
$103$	0.356687	−	0.979989i	0.0351454	−	0.0965612i	−0.920879	−	0.389849i	$-0.872527\pi$
$103$	0.356687	−	0.979989i	0.0351454	−	0.0965612i	0.956024	+	0.293288i	$0.0947494\pi$
$104$	−7.85199	+	10.4231i	−0.769951	+	1.02207i
$105$		0			0
$106$	−13.4274	−	6.45173i	−1.30418	−	0.626648i
$107$	12.4850			1.20697			0.603485	−	0.797375i	$-0.293778\pi$
$107$	12.4850			1.20697			0.603485	+	0.797375i	$0.293778\pi$
$108$		0			0
$109$	−19.2545			−1.84425			−0.922123	−	0.386896i	$-0.873547\pi$
$109$	−19.2545			−1.84425			−0.922123	+	0.386896i	$0.873547\pi$
$110$	0.182598	+	0.0877369i	0.0174100	+	0.00836538i
$111$		0			0
$112$	−5.98417	+	14.3368i	−0.565451	+	1.35470i
$113$	−1.78289	+	4.89846i	−0.167721	+	0.460809i	−0.994869	−	0.101176i	$-0.967740\pi$
$113$	−1.78289	+	4.89846i	−0.167721	+	0.460809i	0.827148	+	0.561984i	$0.189962\pi$
$114$		0			0
$115$	−13.8299	−	2.43859i	−1.28965	−	0.227399i
$116$	−8.02124	−	0.185925i	−0.744754	−	0.0172627i
$117$		0			0
$118$	1.61822	−	1.58115i	0.148970	−	0.145557i
$119$	7.55402	−	2.74944i	0.692476	−	0.252041i
$120$		0			0
$121$	−8.42389	+	7.06848i	−0.765808	+	0.642589i
$122$	−2.42589	−	1.74086i	−0.219630	−	0.157610i
$123$		0			0
$124$	−11.4543	−	10.0727i	−1.02863	−	0.904559i
$125$	8.42192	−	4.86240i	0.753279	−	0.434906i
$126$		0			0
$127$	−1.67801	−	0.968801i	−0.148900	−	0.0859672i	0.423699	−	0.905803i	$-0.360731\pi$
$127$	−1.67801	−	0.968801i	−0.148900	−	0.0859672i	−0.572599	+	0.819836i	$0.694065\pi$
$128$	0.0696290	+	11.3135i	0.00615439	+	0.999981i
$129$		0			0
$130$	−15.9634	−	1.58320i	−1.40008	−	0.138856i
$131$	0.0812185	+	0.460613i	0.00709609	+	0.0402440i	0.988150	−	0.153490i	$-0.0490513\pi$
$131$	0.0812185	+	0.460613i	0.00709609	+	0.0402440i	−0.981054	+	0.193734i	$0.937940\pi$
$132$		0			0
$133$	8.45707	+	7.09633i	0.733321	+	0.615330i
$134$	−10.3546	+	2.64631i	−0.894505	+	0.228607i
$135$		0			0
$136$	4.28094	−	3.99320i	0.367088	−	0.342414i
$137$	2.82207	−	3.36321i	0.241105	−	0.287338i	−0.631899	−	0.775051i	$-0.717724\pi$
$137$	2.82207	−	3.36321i	0.241105	−	0.287338i	0.873004	+	0.487713i	$0.162169\pi$
$138$		0			0
$139$	8.31937	−	1.46693i	0.705639	−	0.124423i	0.190698	−	0.981649i	$-0.438925\pi$
$139$	8.31937	−	1.46693i	0.705639	−	0.124423i	0.514941	+	0.857225i	$0.327814\pi$
$140$	−18.8792	+	2.87954i	−1.59558	+	0.243366i
$141$		0			0
$142$	11.5170	−	0.873264i	0.966486	−	0.0732827i
$143$	−0.134410	+	0.232805i	−0.0112399	+	0.0194681i
$144$		0			0
$145$	−4.93150	−	8.54161i	−0.409539	−	0.709342i
$146$	5.21086	+	7.62851i	0.431254	+	0.631340i
$147$		0			0
$148$	3.50685	−	8.98171i	0.288261	−	0.738292i
$149$	6.53498	+	7.78809i	0.535367	+	0.638025i	0.964142	−	0.265386i	$-0.0854994\pi$
$149$	6.53498	+	7.78809i	0.535367	+	0.638025i	−0.428776	+	0.903411i	$0.641055\pi$
$150$		0			0
$151$	0.816192	+	2.24247i	0.0664208	+	0.182490i	0.968463	−	0.249159i	$-0.0801542\pi$
$151$	0.816192	+	2.24247i	0.0664208	+	0.182490i	−0.902042	+	0.431649i	$0.857932\pi$
$152$	7.68882	+	2.34950i	0.623646	+	0.190569i
$153$		0			0
$154$	−0.0864058	+	0.308143i	−0.00696278	+	0.0248309i
$155$	3.25599	−	18.4657i	0.261528	−	1.48320i
$156$		0			0
$157$	5.11743	+	1.86259i	0.408416	+	0.148651i	0.538054	−	0.842910i	$-0.319160\pi$
$157$	5.11743	+	1.86259i	0.408416	+	0.148651i	−0.129639	+	0.991561i	$0.541382\pi$
$158$	4.03822	+	8.92866i	0.321263	+	0.710326i
$159$		0			0
$160$	−11.8353	+	7.30407i	−0.935665	+	0.577437i
$161$		−	22.1847i		−	1.74840i
$162$		0			0
$163$			9.76328i			0.764719i	0.924014	+	0.382360i	$0.124888\pi$
$163$			9.76328i			0.764719i	−0.924014	+	0.382360i	$0.875112\pi$
$164$	−0.431065	+	2.15183i	−0.0336605	+	0.168030i
$165$		0			0
$166$	−14.6836	+	6.64104i	−1.13967	+	0.515445i
$167$	4.36568	+	1.58898i	0.337826	+	0.122959i	0.505362	−	0.862907i	$-0.331359\pi$
$167$	4.36568	+	1.58898i	0.337826	+	0.122959i	−0.167536	+	0.985866i	$0.553581\pi$
$168$		0			0
$169$	1.43898	−	8.16087i	0.110691	−	0.627759i
$170$	6.92923	+	1.94301i	0.531448	+	0.149022i
$171$		0			0
$172$	−10.0314	+	16.4808i	−0.764889	+	1.25665i
$173$	−0.301382	−	0.828041i	−0.0229137	−	0.0629548i	0.927708	−	0.373306i	$-0.121776\pi$
$173$	−0.301382	−	0.828041i	−0.0229137	−	0.0629548i	−0.950622	+	0.310351i	$0.899553\pi$
$174$		0			0
$175$	−2.60765	−	3.10767i	−0.197120	−	0.234918i
$176$	0.0297926	+	0.231147i	0.00224570	+	0.0174234i
$177$		0			0
$178$	2.50599	−	1.71178i	0.187832	−	0.128304i
$179$	6.34874	+	10.9963i	0.474527	+	0.821905i	0.999575	−	0.0291678i	$-0.00928571\pi$
$179$	6.34874	+	10.9963i	0.474527	+	0.821905i	−0.525047	+	0.851073i	$0.675952\pi$
$180$		0			0
$181$	−3.30529	+	5.72493i	−0.245680	+	0.425530i	−0.962323	−	0.271910i	$-0.912345\pi$
$181$	−3.30529	+	5.72493i	−0.245680	+	0.425530i	0.716643	+	0.697441i	$0.245678\pi$
$182$	−1.91601	−	25.2692i	−0.142024	−	1.87308i
$183$		0			0
$184$	−6.31477	−	14.8707i	−0.465531	−	1.09628i
$185$	11.6727	−	2.05821i	0.858194	−	0.151323i
$186$		0			0
$187$	0.0775175	−	0.0923817i	0.00566864	−	0.00675562i
$188$	−9.58531	+	5.24176i	−0.699081	+	0.382294i
$189$		0			0
$190$	2.44716	+	9.57538i	0.177535	+	0.694671i
$191$	−19.5133	−	16.3736i	−1.41193	−	1.18475i	−0.955500	−	0.294990i	$-0.904684\pi$
$191$	−19.5133	−	16.3736i	−1.41193	−	1.18475i	−0.456429	−	0.889760i	$-0.650872\pi$
$192$		0			0
$193$	−3.57625	−	20.2819i	−0.257424	−	1.45993i	−0.789772	−	0.613400i	$-0.789801\pi$
$193$	−3.57625	−	20.2819i	−0.257424	−	1.45993i	0.532348	−	0.846526i	$-0.321310\pi$
$194$	−0.719411	+	7.25379i	−0.0516507	+	0.520792i
$195$		0			0
$196$	−5.17662	−	15.3182i	−0.369759	−	1.09415i
$197$	6.00833	+	3.46891i	0.428076	+	0.247150i	0.698526	−	0.715584i	$-0.253839\pi$
$197$	6.00833	+	3.46891i	0.428076	+	0.247150i	−0.270451	+	0.962734i	$0.587173\pi$
$198$		0			0
$199$	10.0244	−	5.78756i	0.710608	−	0.410270i	−0.100678	−	0.994919i	$-0.532101\pi$
$199$	10.0244	−	5.78756i	0.710608	−	0.410270i	0.811286	+	0.584650i	$0.198768\pi$
$200$	−2.63252	−	1.34086i	−0.186147	−	0.0948131i
$201$		0			0
$202$	10.8982	−	15.1866i	0.766796	−	1.06853i
$203$	11.9357	−	10.0153i	0.837725	−	0.702934i
$204$		0			0
$205$	−2.53506	+	0.922686i	−0.177056	+	0.0644432i
$206$	1.03073	+	1.05490i	0.0718143	+	0.0734981i
$207$		0			0
$208$	−8.47709	−	16.3929i	−0.587780	−	1.13664i
$209$	0.163101	+	0.0287592i	0.0112820	+	0.00198931i
$210$		0			0
$211$	−5.16932	+	14.2026i	−0.355871	+	0.977747i	0.624576	+	0.780964i	$0.285272\pi$
$211$	−5.16932	+	14.2026i	−0.355871	+	0.977747i	−0.980447	+	0.196783i	$0.936951\pi$
$212$	16.4481	−	13.1643i	1.12966	−	0.904127i
$213$		0			0
$214$	−7.64685	+	15.9146i	−0.522728	+	1.08790i
$215$	−23.7173			−1.61751
$216$		0			0
$217$	29.6210			2.01080
$218$	11.7931	−	24.5437i	0.798728	−	1.66231i
$219$		0			0
$220$	−0.223677	+	0.179020i	−0.0150803	+	0.0120696i
$221$	−3.26612	+	8.97359i	−0.219703	+	0.603629i
$222$		0			0
$223$	−1.61660	−	0.285051i	−0.108256	−	0.0190884i	0.119258	−	0.992863i	$-0.461949\pi$
$223$	−1.61660	−	0.285051i	−0.108256	−	0.0190884i	−0.227514	+	0.973775i	$0.573060\pi$
$224$	−14.6099	−	16.4091i	−0.976166	−	1.09638i
$225$		0			0
$226$	−5.15208	−	5.27289i	−0.342711	−	0.350747i
$227$	−25.6644	+	9.34108i	−1.70341	+	0.619989i	−0.996206	−	0.0870239i	$-0.972264\pi$
$227$	−25.6644	+	9.34108i	−1.70341	+	0.619989i	−0.707200	+	0.707013i	$0.750042\pi$
$228$		0			0
$229$	−4.83939	+	4.06073i	−0.319796	+	0.268340i	−0.788527	−	0.615000i	$-0.789156\pi$
$229$	−4.83939	+	4.06073i	−0.319796	+	0.268340i	0.468731	+	0.883341i	$0.344711\pi$
$230$	11.5791	−	16.1354i	0.763501	−	1.06394i
$231$		0			0
$232$	5.14988	−	10.1108i	0.338106	−	0.663807i
$233$	−25.6785	+	14.8255i	−1.68226	+	0.971251i	−0.722099	+	0.691790i	$0.756822\pi$
$233$	−25.6785	+	14.8255i	−1.68226	+	0.971251i	−0.960157	+	0.279461i	$0.909844\pi$
$234$		0			0
$235$	−11.6306	−	6.71490i	−0.758693	−	0.438032i
$236$	1.02436	+	3.03118i	0.0666800	+	0.197313i
$237$		0			0
$238$	−1.12200	+	11.3131i	−0.0727286	+	0.733320i
$239$	1.61593	+	9.16442i	0.104526	+	0.592797i	0.991409	+	0.130802i	$0.0417552\pi$
$239$	1.61593	+	9.16442i	0.104526	+	0.592797i	−0.886882	+	0.461995i	$0.847134\pi$
$240$		0			0
$241$	−10.7714	−	9.03831i	−0.693849	−	0.582209i	0.226167	−	0.974089i	$-0.427380\pi$
$241$	−10.7714	−	9.03831i	−0.693849	−	0.582209i	−0.920016	+	0.391880i	$0.871825\pi$
$242$	−3.85071	−	15.0673i	−0.247533	−	0.968561i
$243$		0			0
$244$	3.70490	−	2.02604i	0.237182	−	0.129704i
$245$	12.7764	−	15.2263i	0.816251	−	0.972771i
$246$		0			0
$247$	−12.9153	+	2.27732i	−0.821783	+	0.144902i
$248$	19.8553	−	8.43147i	1.26081	−	0.535399i
$249$		0			0
$250$	1.03982	+	13.7136i	0.0657637	+	0.867323i
$251$	−7.60386	+	13.1703i	−0.479951	+	0.831300i	−0.999736	−	0.0229974i	$-0.992679\pi$
$251$	−7.60386	+	13.1703i	−0.479951	+	0.831300i	0.519784	+	0.854298i	$0.326012\pi$
$252$		0			0
$253$	−0.166404	−	0.288220i	−0.0104617	−	0.0181203i
$254$	2.26269	−	1.54559i	0.141974	−	0.0969789i
$255$		0			0
$256$	−14.4640	−	6.84058i	−0.903998	−	0.427536i
$257$	−4.55275	−	5.42575i	−0.283992	−	0.338449i	0.605123	−	0.796132i	$-0.293124\pi$
$257$	−4.55275	−	5.42575i	−0.283992	−	0.338449i	−0.889115	+	0.457683i	$0.848679\pi$
$258$		0			0
$259$	6.40410	+	17.5951i	0.397931	+	1.09331i
$260$	11.7954	−	19.3789i	0.731521	−	1.20183i
$261$		0			0
$262$	−0.636889	−	0.178589i	−0.0393471	−	0.0110332i
$263$	−0.345233	+	1.95791i	−0.0212880	+	0.120730i	−0.993600	−	0.112957i	$-0.963968\pi$
$263$	−0.345233	+	1.95791i	−0.0212880	+	0.120730i	0.972312	+	0.233687i	$0.0750790\pi$
$264$		0			0
$265$	24.3360	+	8.85756i	1.49495	+	0.544116i
$266$	−14.2255	+	6.43386i	−0.872223	+	0.394485i
$267$		0			0
$268$	2.96879	−	14.8199i	0.181348	−	0.905270i
$269$		−	1.18433i		−	0.0722097i	−0.999348	−	0.0361048i	$-0.988505\pi$
$269$		−	1.18433i		−	0.0722097i	0.999348	−	0.0361048i	$-0.0114950\pi$
$270$		0			0
$271$		−	10.9019i		−	0.662245i	−0.943588	−	0.331122i	$-0.892573\pi$
$271$		−	10.9019i		−	0.662245i	0.943588	−	0.331122i	$-0.107427\pi$
$272$	2.46813	+	7.90269i	0.149652	+	0.479171i
$273$		0			0
$274$	2.55861	+	5.65720i	0.154572	+	0.341764i
$275$	−0.0571883	−	0.0208148i	−0.00344858	−	0.00125518i
$276$		0			0
$277$	−0.982411	+	5.57153i	−0.0590274	+	0.334761i	−0.999993	−	0.00374124i	$-0.998809\pi$
$277$	−0.982411	+	5.57153i	−0.0590274	+	0.334761i	0.940966	+	0.338502i	$0.109920\pi$
$278$	−3.22558	+	11.5032i	−0.193457	+	0.689915i
$279$		0			0
$280$	7.89265	−	25.8290i	0.471676	−	1.54358i
$281$	4.23708	+	11.6413i	0.252763	+	0.694460i	0.999567	+	0.0294162i	$0.00936483\pi$
$281$	4.23708	+	11.6413i	0.252763	+	0.694460i	−0.746805	+	0.665044i	$0.768413\pi$
$282$		0			0
$283$	−14.4882	−	17.2663i	−0.861233	−	1.02638i	−0.999353	−	0.0359618i	$-0.988551\pi$
$283$	−14.4882	−	17.2663i	−0.861233	−	1.02638i	0.138120	−	0.990415i	$-0.455894\pi$
$284$	−5.94083	+	15.2156i	−0.352524	+	0.902880i
$285$		0			0
$286$	−0.214433	−	0.313922i	−0.0126797	−	0.0185626i
$287$	−2.13088	−	3.69079i	−0.125782	−	0.217860i
$288$		0			0
$289$	−6.35799	+	11.0124i	−0.374000	+	0.647786i
$290$	13.9085	−	1.05459i	0.816733	−	0.0619278i
$291$		0			0
$292$	−12.9156	+	1.96995i	−0.755830	+	0.115283i
$293$	−24.7027	+	4.35575i	−1.44315	+	0.254466i	−0.839749	−	0.542975i	$-0.817298\pi$
$293$	−24.7027	+	4.35575i	−1.44315	+	0.254466i	−0.603398	+	0.797440i	$0.706187\pi$
$294$		0			0
$295$	−2.52821	+	3.01300i	−0.147198	+	0.175424i
$296$	9.30111	+	9.97134i	0.540616	+	0.579572i
$297$		0			0
$298$	−13.9301	+	3.56007i	−0.806946	+	0.206229i
$299$	20.1881	+	16.9398i	1.16751	+	0.979657i
$300$		0			0
$301$	−6.50611	−	36.8980i	−0.375006	−	2.12677i
$302$	−3.35838	−	0.333075i	−0.193253	−	0.0191663i
$303$		0			0
$304$	−7.70418	+	8.36192i	−0.441865	+	0.479589i
$305$	4.49542	+	2.59543i	0.257407	+	0.148614i
$306$		0			0
$307$	7.99858	−	4.61798i	0.456503	−	0.263562i	−0.254070	−	0.967186i	$-0.581769\pi$
$307$	7.99858	−	4.61798i	0.456503	−	0.263562i	0.710573	+	0.703624i	$0.248436\pi$
$308$	−0.339869	−	0.298874i	−0.0193658	−	0.0170299i
$309$		0			0
$310$	21.5440	+	15.4603i	1.22361	+	0.878088i
$311$	−19.9420	+	16.7333i	−1.13080	+	0.948858i	−0.999099	−	0.0424309i	$-0.986490\pi$
$311$	−19.9420	+	16.7333i	−1.13080	+	0.948858i	−0.131706	+	0.991289i	$0.542045\pi$
$312$		0			0
$313$	−21.0105	+	7.64718i	−1.18758	+	0.432244i	−0.858874	−	0.512187i	$-0.828835\pi$
$313$	−21.0105	+	7.64718i	−1.18758	+	0.432244i	−0.328708	+	0.944432i	$0.606613\pi$
$314$	−5.50859	+	5.38239i	−0.310868	+	0.303746i
$315$		0			0
$316$	−13.8547	−	0.321139i	−0.779389	−	0.0180655i
$317$	11.4763	+	2.02358i	0.644574	+	0.113656i	0.486373	−	0.873751i	$-0.338320\pi$
$317$	11.4763	+	2.02358i	0.644574	+	0.113656i	0.158201	+	0.987407i	$0.449431\pi$
$318$		0			0
$319$	0.0799442	−	0.219645i	0.00447601	−	0.0122977i
$320$	−2.06156	−	19.5601i	−0.115245	−	1.09344i
$321$		0			0
$322$	28.2789	+	13.5878i	1.57592	+	0.757218i
$323$	5.88335			0.327358
$324$		0			0
$325$	4.81914			0.267318
$326$	−12.4453	−	5.97985i	−0.689280	−	0.331193i
$327$		0			0
$328$	−2.47892	−	1.86744i	−0.136875	−	0.103112i
$329$	7.25617	−	19.9362i	0.400046	−	1.09912i
$330$		0			0
$331$	4.32184	+	0.762057i	0.237550	+	0.0418864i	0.291155	−	0.956676i	$-0.405960\pi$
$331$	4.32184	+	0.762057i	0.237550	+	0.0418864i	−0.0536058	+	0.998562i	$0.517071\pi$
$332$	0.528128	−	22.7848i	0.0289848	−	1.25048i
$333$		0			0
$334$	−4.69938	+	4.59171i	−0.257139	+	0.251247i
$335$	17.4593	−	6.35465i	0.953901	−	0.347192i
$336$		0			0
$337$	−25.7716	+	21.6249i	−1.40387	+	1.17799i	−0.444517	+	0.895771i	$0.646625\pi$
$337$	−25.7716	+	21.6249i	−1.40387	+	1.17799i	−0.959351	+	0.282214i	$0.908931\pi$
$338$	9.52132	+	6.83267i	0.517891	+	0.371648i
$339$		0			0
$340$	−6.72080	+	7.64264i	−0.364487	+	0.414480i
$341$	0.384831	−	0.222182i	0.0208398	−	0.0120318i
$342$		0			0
$343$	3.64812	+	2.10624i	0.196980	+	0.113726i
$344$	−14.8640	−	22.8813i	−0.801411	−	1.23368i
$345$		0			0
$346$	1.24010	+	0.122989i	0.0666680	+	0.00661194i
$347$	−2.59951	−	14.7425i	−0.139549	−	0.791421i	−0.971583	−	0.236697i	$-0.923935\pi$
$347$	−2.59951	−	14.7425i	−0.139549	−	0.791421i	0.832035	−	0.554724i	$-0.187176\pi$
$348$		0			0
$349$	−8.14865	−	6.83753i	−0.436187	−	0.366005i	0.398093	−	0.917345i	$-0.369672\pi$
$349$	−8.14865	−	6.83753i	−0.436187	−	0.366005i	−0.834280	+	0.551340i	$0.814117\pi$
$350$	5.55850	−	1.42057i	0.297114	−	0.0759328i
$351$		0			0
$352$	−0.312891	−	0.103597i	−0.0166772	−	0.00552176i
$353$	−7.07097	+	8.42685i	−0.376350	+	0.448516i	−0.920659	−	0.390369i	$-0.872348\pi$
$353$	−7.07097	+	8.42685i	−0.376350	+	0.448516i	0.544309	+	0.838885i	$0.316792\pi$
$354$		0			0
$355$	−19.7743	+	3.48675i	−1.04951	+	0.185057i
$356$	0.647135	+	4.24282i	0.0342981	+	0.224869i
$357$		0			0
$358$	−17.9056	+	1.35767i	−0.946338	+	0.0717550i
$359$	−8.75833	+	15.1699i	−0.462247	+	0.800636i	−0.999073	−	0.0430578i	$-0.986290\pi$
$359$	−8.75833	+	15.1699i	−0.462247	+	0.800636i	0.536825	+	0.843693i	$0.319623\pi$
$360$		0			0
$361$	−5.46012	−	9.45721i	−0.287375	−	0.497748i
$362$	−5.27314	−	7.71968i	−0.277150	−	0.405737i
$363$		0			0
$364$	33.3842	+	13.0347i	1.74981	+	0.683201i
$365$	−10.3235	−	12.3031i	−0.540358	−	0.643973i
$366$		0			0
$367$	−1.77877	−	4.88714i	−0.0928511	−	0.255106i	0.884570	−	0.466408i	$-0.154452\pi$
$367$	−1.77877	−	4.88714i	−0.0928511	−	0.255106i	−0.977421	+	0.211301i	$0.932230\pi$
$368$	22.8234	+	1.05862i	1.18975	+	0.0551842i
$369$		0			0
$370$	−4.52574	+	16.1398i	−0.235282	+	0.839070i
$371$	−7.10426	+	40.2903i	−0.368835	+	2.09177i
$372$		0			0
$373$	14.9141	+	5.42829i	0.772223	+	0.281066i	0.697926	−	0.716170i	$-0.254107\pi$
$373$	14.9141	+	5.42829i	0.772223	+	0.281066i	0.0742970	+	0.997236i	$0.476329\pi$
$374$	0.0702809	+	0.155394i	0.00363414	+	0.00803523i
$375$		0			0
$376$	−0.810827	−	15.4289i	−0.0418152	−	0.795685i
$377$			18.5090i			0.953262i
$378$		0			0
$379$			13.3564i			0.686073i	0.939322	+	0.343037i	$0.111456\pi$
$379$			13.3564i			0.686073i	−0.939322	+	0.343037i	$0.888544\pi$
$380$	−13.7046	−	2.74537i	−0.703031	−	0.140834i
$381$		0			0
$382$	32.8230	−	14.8450i	1.67937	−	0.759538i
$383$	7.59874	+	2.76571i	0.388277	+	0.141321i	0.528780	−	0.848759i	$-0.322650\pi$
$383$	7.59874	+	2.76571i	0.388277	+	0.141321i	−0.140503	+	0.990080i	$0.544872\pi$
$384$		0			0
$385$	0.0966106	−	0.547906i	0.00492373	−	0.0279239i
$386$	28.0438	+	7.86371i	1.42739	+	0.400252i
$387$		0			0
$388$	−8.80579	−	5.35987i	−0.447046	−	0.272106i
$389$	−6.72162	−	18.4675i	−0.340799	−	0.936339i	−0.985163	−	0.171620i	$-0.945100\pi$
$389$	−6.72162	−	18.4675i	−0.340799	−	0.936339i	0.644364	−	0.764719i	$-0.277122\pi$
$390$		0			0
$391$	−7.59941	−	9.05663i	−0.384319	−	0.458013i
$392$	22.6967	+	2.78348i	1.14636	+	0.140587i
$393$		0			0
$394$	−8.10183	+	5.53417i	−0.408164	+	0.278808i
$395$	−8.51795	−	14.7535i	−0.428585	−	0.742330i
$396$		0			0
$397$	12.3726	−	21.4299i	0.620961	−	1.07554i	−0.368346	−	0.929689i	$-0.620076\pi$
$397$	12.3726	−	21.4299i	0.620961	−	1.07554i	0.989307	−	0.145848i	$-0.0465910\pi$
$398$	1.23766	+	16.3228i	0.0620383	+	0.818190i
$399$		0			0
$400$	3.32157	−	2.53443i	0.166079	−	0.126721i
$401$	11.9917	−	2.11446i	0.598836	−	0.105591i	0.133990	−	0.990983i	$-0.457221\pi$
$401$	11.9917	−	2.11446i	0.598836	−	0.105591i	0.464846	+	0.885392i	$0.346110\pi$
$402$		0			0
$403$	−22.6180	+	26.9551i	−1.12668	+	1.34273i
$404$	12.6835	+	23.1935i	0.631026	+	1.15392i
$405$		0			0
$406$	5.45604	+	21.3487i	0.270779	+	1.05952i
$407$	0.215179	+	0.180557i	0.0106660	+	0.00894986i
$408$		0			0
$409$	5.39760	+	30.6113i	0.266894	+	1.51363i	0.763586	+	0.645706i	$0.223437\pi$
$409$	5.39760	+	30.6113i	0.266894	+	1.51363i	−0.496692	+	0.867927i	$0.665452\pi$
$410$	0.376533	−	3.79657i	0.0185957	−	0.187499i
$411$		0			0
$412$	−1.97598	+	0.667764i	−0.0973497	+	0.0328984i
$413$	−5.38099	−	3.10671i	−0.264781	−	0.152871i
$414$		0			0
$415$	24.2629	−	14.0082i	1.19102	−	0.687635i
$416$	26.0881	−	0.765366i	1.27908	−	0.0375252i
$417$		0			0
$418$	−0.136556	+	0.190291i	−0.00667918	+	0.00930743i
$419$	−28.2403	+	23.6964i	−1.37963	+	1.15765i	−0.410281	+	0.911959i	$0.634569\pi$
$419$	−28.2403	+	23.6964i	−1.37963	+	1.15765i	−0.969349	+	0.245688i	$0.920986\pi$
$420$		0			0
$421$	34.6191	−	12.6003i	1.68723	−	0.614102i	0.692960	−	0.720976i	$-0.256306\pi$
$421$	34.6191	−	12.6003i	1.68723	−	0.614102i	0.994273	+	0.106874i	$0.0340842\pi$
$422$	−14.9379	−	15.2882i	−0.727167	−	0.744218i
$423$		0			0
$424$	6.70635	+	29.0293i	0.325689	+	1.40979i
$425$	−2.12908	−	0.375414i	−0.103275	−	0.0182102i
$426$		0			0
$427$	−2.80464	+	7.70569i	−0.135726	+	0.372905i
$428$	−15.6028	−	19.4949i	−0.754191	−	0.942322i
$429$		0			0
$430$	14.5265	−	30.2325i	0.700528	−	1.45794i
$431$	11.3781			0.548063			0.274032	−	0.961721i	$-0.411643\pi$
$431$	11.3781			0.548063			0.274032	+	0.961721i	$0.411643\pi$
$432$		0			0
$433$	−7.27646			−0.349684			−0.174842	−	0.984596i	$-0.555941\pi$
$433$	−7.27646			−0.349684			−0.174842	+	0.984596i	$0.555941\pi$
$434$	−18.1424	+	37.7579i	−0.870862	+	1.81244i
$435$		0			0
$436$	24.0629	+	30.0653i	1.15240	+	1.43987i
$437$	5.55313	−	15.2571i	0.265642	−	0.729846i
$438$		0			0
$439$	29.3104	+	5.16822i	1.39891	+	0.246665i	0.821695	−	0.569927i	$-0.193029\pi$
$439$	29.3104	+	5.16822i	1.39891	+	0.246665i	0.577214	+	0.816593i	$0.304140\pi$
$440$	−0.0911994	−	0.394768i	−0.00434776	−	0.0188198i
$441$		0			0
$442$	−9.43820	−	9.65950i	−0.448929	−	0.459456i
$443$	−16.1633	+	5.88296i	−0.767941	+	0.279508i	−0.696135	−	0.717911i	$-0.745099\pi$
$443$	−16.1633	+	5.88296i	−0.767941	+	0.279508i	−0.0718063	+	0.997419i	$0.522876\pi$
$444$		0			0
$445$	−4.04160	+	3.39131i	−0.191590	+	0.160763i
$446$	1.35350	−	1.88610i	0.0640900	−	0.0893094i
$447$		0			0
$448$	29.8650	−	8.57298i	1.41099	−	0.405035i
$449$	18.8763	−	10.8982i	0.890826	−	0.514319i	0.0166137	−	0.999862i	$-0.494711\pi$
$449$	18.8763	−	10.8982i	0.890826	−	0.514319i	0.874213	+	0.485543i	$0.161378\pi$
$450$		0			0
$451$	−0.0553680	−	0.0319667i	−0.00260718	−	0.00150525i
$452$	9.87692	−	3.33781i	0.464571	−	0.156997i
$453$		0			0
$454$	3.81195	−	38.4357i	0.178903	−	1.80388i
$455$	7.65020	+	43.3864i	0.358647	+	2.03399i
$456$		0			0
$457$	7.39792	+	6.20759i	0.346060	+	0.290379i	0.799206	−	0.601058i	$-0.205254\pi$
$457$	7.39792	+	6.20759i	0.346060	+	0.290379i	−0.453146	+	0.891436i	$0.649698\pi$
$458$	−2.21217	−	8.65590i	−0.103368	−	0.404464i
$459$		0			0
$460$	13.4758	+	24.6425i	0.628314	+	1.14896i
$461$	−21.0745	+	25.1156i	−0.981536	+	1.16975i	0.00395005	+	0.999992i	$0.498743\pi$
$461$	−21.0745	+	25.1156i	−0.981536	+	1.16975i	−0.985486	+	0.169757i	$0.945702\pi$
$462$		0			0
$463$	37.7572	−	6.65762i	1.75473	−	0.309406i	0.798493	−	0.602005i	$-0.205631\pi$
$463$	37.7572	−	6.65762i	1.75473	−	0.309406i	0.956235	+	0.292599i	$0.0945201\pi$
$464$	9.73405	+	12.7573i	0.451892	+	0.592241i
$465$		0			0
$466$	−3.17041	−	41.8128i	−0.146866	−	1.93694i
$467$	5.79199	−	10.0320i	0.268021	−	0.464227i	−0.700329	−	0.713820i	$-0.746964\pi$
$467$	5.79199	−	10.0320i	0.268021	−	0.464227i	0.968351	+	0.249593i	$0.0802969\pi$
$468$		0			0
$469$	14.6756	+	25.4189i	0.677657	+	1.17374i
$470$	15.6830	−	10.7127i	0.723404	−	0.494140i
$471$		0			0
$472$	−4.49125	−	0.550799i	−0.206727	−	0.0253526i
$473$	−0.361292	−	0.430571i	−0.0166122	−	0.0197977i
$474$		0			0
$475$	−1.01547	−	2.78997i	−0.0465928	−	0.128013i
$476$	−13.7336	−	8.35931i	−0.629480	−	0.383148i
$477$		0			0
$478$	−12.6716	−	3.55323i	−0.579587	−	0.162521i
$479$	−3.11270	+	17.6530i	−0.142223	+	0.806585i	0.827332	+	0.561713i	$0.189857\pi$
$479$	−3.11270	+	17.6530i	−0.142223	+	0.806585i	−0.969555	+	0.244873i	$0.921254\pi$
$480$		0			0
$481$	−20.9016	−	7.60757i	−0.953032	−	0.346875i
$482$	18.1185	−	8.19455i	0.825274	−	0.373252i
$483$		0			0
$484$	21.5648	+	4.31996i	0.980217	+	0.196362i
$485$		−	12.6723i		−	0.575421i
$486$		0			0
$487$		−	22.6464i		−	1.02621i	−0.858327	−	0.513104i	$-0.828496\pi$
$487$		−	22.6464i		−	1.02621i	0.858327	−	0.513104i	$-0.171504\pi$
$488$	0.313399	+	5.96355i	0.0141869	+	0.269957i
$489$		0			0
$490$	11.5836	+	25.6119i	0.523295	+	1.15703i
$491$	−24.1565	−	8.79224i	−1.09017	−	0.396788i	−0.266484	−	0.963839i	$-0.585862\pi$
$491$	−24.1565	−	8.79224i	−1.09017	−	0.396788i	−0.823683	+	0.567051i	$0.808084\pi$
$492$		0			0
$493$	1.44186	−	8.17721i	0.0649382	−	0.368283i
$494$	5.00753	−	17.8580i	0.225299	−	0.803470i
$495$		0			0
$496$	−1.41346	+	30.4737i	−0.0634663	+	1.36831i
$497$	−10.8490	−	29.8073i	−0.486643	−	1.33704i
$498$		0			0
$499$	−4.64688	−	5.53794i	−0.208023	−	0.247912i	0.651938	−	0.758273i	$-0.273956\pi$
$499$	−4.64688	−	5.53794i	−0.208023	−	0.247912i	−0.859961	+	0.510360i	$0.829512\pi$
$500$	−18.1176	−	7.07389i	−0.810243	−	0.316354i
$501$		0			0
$502$	−12.1309	−	17.7592i	−0.541430	−	0.792633i
$503$	19.3621	+	33.5362i	0.863314	+	1.49530i	0.868712	+	0.495318i	$0.164949\pi$
$503$	19.3621	+	33.5362i	0.863314	+	1.49530i	−0.00539768	+	0.999985i	$0.501718\pi$
$504$		0			0
$505$	−16.2480	+	28.1424i	−0.723027	+	1.25232i
$506$	0.469315	−	0.0355852i	0.0208636	−	0.00158196i
$507$		0			0
$508$	0.584306	+	3.83090i	0.0259244	+	0.169969i
$509$	−18.8059	+	3.31600i	−0.833559	+	0.146979i	−0.574110	−	0.818778i	$-0.694652\pi$
$509$	−18.8059	+	3.31600i	−0.833559	+	0.146979i	−0.259449	+	0.965757i	$0.583541\pi$
$510$		0			0
$511$	16.3085	−	19.4357i	0.721446	−	0.859785i
$512$	17.5786	−	14.2475i	0.776873	−	0.629657i
$513$		0			0
$514$	9.70469	−	2.48021i	0.428056	−	0.109397i
$515$	−1.96413	−	1.64810i	−0.0865499	−	0.0726240i
$516$		0			0
$517$	−0.0552670	−	0.313435i	−0.00243064	−	0.0137848i
$518$	−26.3509	−	2.61341i	−1.15779	−	0.114827i
$519$		0			0
$520$	17.4778	+	26.9049i	0.766450	+	1.17986i
$521$	−19.0779	−	11.0146i	−0.835817	−	0.482559i	0.0200233	−	0.999800i	$-0.493626\pi$
$521$	−19.0779	−	11.0146i	−0.835817	−	0.482559i	−0.855840	+	0.517240i	$0.826959\pi$
$522$		0			0
$523$	3.75661	−	2.16888i	0.164265	−	0.0948384i	−0.415614	−	0.909541i	$-0.636433\pi$
$523$	3.75661	−	2.16888i	0.164265	−	0.0948384i	0.579879	+	0.814703i	$0.303100\pi$
$524$	0.617732	−	0.702461i	0.0269857	−	0.0306871i
$525$		0			0
$526$	−2.28430	−	1.63926i	−0.0996004	−	0.0714750i
$527$	12.0924	−	10.1467i	0.526752	−	0.441998i
$528$		0			0
$529$	−9.04622	+	3.29256i	−0.393314	+	0.143155i
$530$	−26.1961	+	25.5960i	−1.13789	+	1.11182i
$531$		0			0
$532$	0.511652	−	22.0739i	0.0221829	−	0.957026i
$533$	4.98572	+	0.879117i	0.215955	+	0.0380788i
$534$		0			0
$535$	10.4983	−	28.8439i	0.453883	−	1.24703i
$536$	17.0726	+	12.8613i	0.737425	+	0.555523i
$537$		0			0
$538$	1.50966	+	0.725381i	0.0650862	+	0.0312734i
$539$	0.471048			0.0202895
$540$		0			0
$541$	−2.88802			−0.124166			−0.0620829	−	0.998071i	$-0.519774\pi$
$541$	−2.88802			−0.124166			−0.0620829	+	0.998071i	$0.519774\pi$
$542$	13.8967	+	6.67725i	0.596915	+	0.286813i
$543$		0			0
$544$	−11.5853	−	1.69415i	−0.496714	−	0.0726359i
$545$	−16.1907	+	44.4835i	−0.693532	+	1.90546i
$546$		0			0
$547$	22.9975	+	4.05508i	0.983303	+	0.173383i	0.642112	−	0.766611i	$-0.278059\pi$
$547$	22.9975	+	4.05508i	0.983303	+	0.173383i	0.341191	+	0.939994i	$0.389170\pi$
$548$	−8.77835	−	0.203474i	−0.374993	−	0.00869196i
$549$		0			0
$550$	0.0615596	−	0.0601492i	0.00262491	−	0.00256477i
$551$	10.7155	−	3.90013i	0.456497	−	0.166151i
$552$		0			0
$553$	20.6160	−	17.2989i	0.876683	−	0.735625i
$554$	−6.50033	−	4.66475i	−0.276172	−	0.198186i
$555$		0			0
$556$	−12.6875	−	11.1572i	−0.538070	−	0.473169i
$557$	−7.72227	+	4.45845i	−0.327203	+	0.188911i	−0.654599	−	0.755977i	$-0.727162\pi$
$557$	−7.72227	+	4.45845i	−0.327203	+	0.188911i	0.327396	+	0.944887i	$0.393829\pi$
$558$		0			0
$559$	38.5452	+	22.2541i	1.63029	+	0.941247i
$560$	28.0902	+	25.8806i	1.18703	+	1.09366i
$561$		0			0
$562$	−17.4343	−	1.72908i	−0.735421	−	0.0729369i
$563$	−3.80400	−	21.5736i	−0.160320	−	0.909218i	−0.953760	−	0.300570i	$-0.902823\pi$
$563$	−3.80400	−	21.5736i	−0.160320	−	0.909218i	0.793440	−	0.608648i	$-0.208288\pi$
$564$		0			0
$565$	9.81767	+	8.23801i	0.413033	+	0.346576i
$566$	30.8832	−	7.89275i	1.29812	−	0.331757i
$567$		0			0
$568$	−15.7567	−	16.8921i	−0.661136	−	0.708777i
$569$	−12.7365	+	15.1788i	−0.533943	+	0.636329i	−0.963818	−	0.266560i	$-0.914113\pi$
$569$	−12.7365	+	15.1788i	−0.533943	+	0.636329i	0.429875	+	0.902888i	$0.358558\pi$
$570$		0			0
$571$	−27.0599	+	4.77140i	−1.13242	+	0.199677i	−0.708289	−	0.705923i	$-0.750533\pi$
$571$	−27.0599	+	4.77140i	−1.13242	+	0.199677i	−0.424134	+	0.905599i	$0.639421\pi$
$572$	0.531493	−	0.0810658i	0.0222229	−	0.00338953i
$573$		0			0
$574$	6.00978	−	0.455685i	0.250843	−	0.0190199i
$575$	−2.98313	+	5.16693i	−0.124405	+	0.215476i
$576$		0			0
$577$	1.20328	+	2.08414i	0.0500931	+	0.0867638i	0.889985	−	0.455990i	$-0.150715\pi$
$577$	1.20328	+	2.08414i	0.0500931	+	0.0867638i	−0.839892	+	0.542754i	$0.817382\pi$
$578$	−10.1433	−	14.8494i	−0.421906	−	0.617655i
$579$		0			0
$580$	−7.17442	+	18.3751i	−0.297901	+	0.762983i
$581$	28.4489	+	33.9041i	1.18026	+	1.40658i
$582$		0			0
$583$	0.209913	+	0.576733i	0.00869373	+	0.0238858i
$584$	5.39952	−	17.6701i	0.223434	−	0.731196i
$585$		0			0
$586$	9.57772	−	34.1564i	0.395652	−	1.41099i
$587$	−2.24123	+	12.7106i	−0.0925054	+	0.524624i	0.902978	+	0.429687i	$0.141376\pi$
$587$	−2.24123	+	12.7106i	−0.0925054	+	0.524624i	−0.995483	+	0.0949372i	$0.969735\pi$
$588$		0			0
$589$	20.3712	+	7.41453i	0.839383	+	0.305510i
$590$	−2.29219	−	5.06812i	−0.0943679	−	0.208651i
$591$		0			0
$592$	−18.4073	+	5.74886i	−0.756534	+	0.236277i
$593$			27.2738i			1.12000i	0.828493	+	0.560000i	$0.189199\pi$
$593$			27.2738i			1.12000i	−0.828493	+	0.560000i	$0.810801\pi$
$594$		0			0
$595$		−	19.7639i		−	0.810242i
$596$	3.99390	−	19.9371i	0.163597	−	0.816657i
$597$		0			0
$598$	−33.9581	+	15.3584i	−1.38865	+	0.628054i
$599$	19.1994	+	6.98801i	0.784466	+	0.285522i	0.703034	−	0.711157i	$-0.251828\pi$
$599$	19.1994	+	6.98801i	0.784466	+	0.285522i	0.0814322	+	0.996679i	$0.474051\pi$
$600$		0			0
$601$	−7.63059	+	43.2752i	−0.311258	+	1.76523i	0.281216	+	0.959645i	$0.409262\pi$
$601$	−7.63059	+	43.2752i	−0.311258	+	1.76523i	−0.592474	+	0.805589i	$0.701849\pi$
$602$	51.0188	+	14.3061i	2.07937	+	0.583072i
$603$		0			0
$604$	2.48153	−	4.07693i	0.100972	−	0.165888i
$605$	9.24679	+	25.4053i	0.375935	+	1.03287i
$606$		0			0
$607$	24.2266	+	28.8721i	0.983326	+	1.17188i	0.985117	+	0.171884i	$0.0549854\pi$
$607$	24.2266	+	28.8721i	0.983326	+	1.17188i	−0.00179117	+	0.999998i	$0.500570\pi$
$608$	−5.94027	−	14.9421i	−0.240910	−	0.605981i
$609$		0			0
$610$	−6.06177	+	4.14066i	−0.245434	+	0.167650i
$611$	12.6013	+	21.8260i	0.509792	+	0.882986i
$612$		0			0
$613$	1.70832	−	2.95890i	0.0689984	−	0.119509i	−0.829462	−	0.558563i	$-0.811353\pi$
$613$	1.70832	−	2.95890i	0.0689984	−	0.119509i	0.898461	+	0.439054i	$0.144686\pi$
$614$	0.987548	+	13.0242i	0.0398542	+	0.525616i
$615$		0			0
$616$	0.589140	−	0.250175i	0.0237371	−	0.0100798i
$617$	28.4409	−	5.01489i	1.14499	−	0.201892i	0.431200	−	0.902256i	$-0.358090\pi$
$617$	28.4409	−	5.01489i	1.14499	−	0.201892i	0.713786	+	0.700364i	$0.246979\pi$
$618$		0			0
$619$	−11.5574	+	13.7736i	−0.464533	+	0.553609i	−0.946552	−	0.322552i	$-0.895459\pi$
$619$	−11.5574	+	13.7736i	−0.464533	+	0.553609i	0.482019	+	0.876161i	$0.339904\pi$
$620$	−32.9026	+	17.9929i	−1.32140	+	0.722612i
$621$		0			0
$622$	−9.11582	−	35.6689i	−0.365511	−	1.43019i
$623$	−6.38469	−	5.35739i	−0.255797	−	0.214639i
$624$		0			0
$625$	−5.05864	−	28.6890i	−0.202346	−	1.14756i
$626$	3.12069	−	31.4658i	0.124728	−	1.25763i
$627$		0			0
$628$	−3.48702	−	10.3184i	−0.139147	−	0.411751i
$629$	8.64162	+	4.98924i	0.344564	+	0.198934i
$630$		0			0
$631$	10.4847	−	6.05333i	0.417388	−	0.240979i	−0.276571	−	0.960994i	$-0.589198\pi$
$631$	10.4847	−	6.05333i	0.417388	−	0.240979i	0.693959	+	0.720014i	$0.255865\pi$
$632$	8.89515	−	17.4639i	0.353830	−	0.694678i
$633$		0			0
$634$	−9.60852	+	13.3895i	−0.381603	+	0.531763i
$635$	−3.64921	+	3.06205i	−0.144815	+	0.121514i
$636$		0			0
$637$	−35.0509	+	12.7575i	−1.38877	+	0.505470i
$638$	0.231017	+	0.236434i	0.00914605	+	0.00936050i
$639$		0			0
$640$	26.1960	+	9.35239i	1.03549	+	0.369686i
$641$	−18.9399	−	3.33962i	−0.748081	−	0.131907i	−0.213405	−	0.976964i	$-0.568455\pi$
$641$	−18.9399	−	3.33962i	−0.748081	−	0.131907i	−0.534676	+	0.845057i	$0.679566\pi$
$642$		0			0
$643$	−0.978566	+	2.68859i	−0.0385909	+	0.106028i	−0.957491	−	0.288462i	$-0.906856\pi$
$643$	−0.978566	+	2.68859i	−0.0385909	+	0.106028i	0.918901	+	0.394489i	$0.129078\pi$
$644$	−34.6407	+	27.7249i	−1.36504	+	1.09251i
$645$		0			0
$646$	−3.60346	+	7.49951i	−0.141776	+	0.295064i
$647$	−36.4238			−1.43197			−0.715984	−	0.698117i	$-0.754022\pi$
$647$	−36.4238			−1.43197			−0.715984	+	0.698117i	$0.754022\pi$
$648$		0			0
$649$	−0.0932118			−0.00365888
$650$	−2.95164	+	6.14296i	−0.115773	+	0.240947i
$651$		0			0
$652$	15.2451	−	12.2014i	0.597042	−	0.477845i
$653$	7.46684	−	20.5150i	0.292200	−	0.802813i	−0.703544	−	0.710652i	$-0.748400\pi$
$653$	7.46684	−	20.5150i	0.292200	−	0.802813i	0.995744	−	0.0921615i	$-0.0293776\pi$
$654$		0			0
$655$	1.13244	+	0.199681i	0.0442483	+	0.00780216i
$656$	3.89872	−	2.01611i	0.152220	−	0.0787157i
$657$		0			0
$658$	20.9684	+	21.4600i	0.817432	+	0.836599i
$659$	−0.310964	+	0.113182i	−0.0121134	+	0.00440894i	−0.348070	−	0.937469i	$-0.613163\pi$
$659$	−0.310964	+	0.113182i	−0.0121134	+	0.00440894i	0.335956	+	0.941878i	$0.390941\pi$
$660$		0			0
$661$	18.1399	−	15.2212i	0.705561	−	0.592036i	−0.217789	−	0.975996i	$-0.569884\pi$
$661$	18.1399	−	15.2212i	0.705561	−	0.592036i	0.923350	+	0.383960i	$0.125440\pi$
$662$	−3.61845	+	5.04230i	−0.140635	+	0.195975i
$663$		0			0
$664$	28.7203	+	14.6285i	1.11456	+	0.567696i
$665$	23.5059	−	13.5712i	0.911521	−	0.526267i
$666$		0			0
$667$	−19.8448	−	11.4574i	−0.768393	−	0.443632i
$668$	−2.97477	−	8.80266i	−0.115097	−	0.340585i
$669$		0			0
$670$	−2.59323	+	26.1475i	−0.100185	+	1.01016i
$671$	0.0213617	+	0.121148i	0.000824660	+	0.00467688i
$672$		0			0
$673$	2.82408	+	2.36968i	0.108860	+	0.0913446i	0.695593	−	0.718436i	$-0.255142\pi$
$673$	2.82408	+	2.36968i	0.108860	+	0.0913446i	−0.586733	+	0.809781i	$0.699586\pi$
$674$	−11.7806	−	46.0960i	−0.453774	−	1.77555i
$675$		0			0
$676$	−14.5413	+	7.95194i	−0.559280	+	0.305844i
$677$	−6.13883	+	7.31597i	−0.235934	+	0.281176i	−0.871001	−	0.491282i	$-0.836528\pi$
$677$	−6.13883	+	7.31597i	−0.235934	+	0.281176i	0.635066	+	0.772458i	$0.280973\pi$
$678$		0			0
$679$	19.7149	−	3.47627i	0.756588	−	0.133407i
$680$	−5.62570	−	13.2480i	−0.215736	−	0.508038i
$681$		0			0
$682$	0.0475133	+	0.626628i	0.00181938	+	0.0239948i
$683$	14.0206	−	24.2843i	0.536482	−	0.929214i	−0.462608	−	0.886563i	$-0.653086\pi$
$683$	14.0206	−	24.2843i	0.536482	−	0.929214i	0.999090	−	0.0426510i	$-0.0135804\pi$
$684$		0			0
$685$	−5.39697	−	9.34783i	−0.206208	−	0.357162i
$686$	−4.91925	+	3.36022i	−0.187818	+	0.128294i
$687$		0			0
$688$	38.2707	−	4.93271i	1.45906	−	0.188058i
$689$	−31.2395	−	37.2298i	−1.19013	−	1.41834i
$690$		0			0
$691$	13.8412	+	38.0284i	0.526545	+	1.44667i	0.863113	+	0.505011i	$0.168512\pi$
$691$	13.8412	+	38.0284i	0.526545	+	1.44667i	−0.336568	+	0.941659i	$0.609266\pi$
$692$	−0.916314	+	1.50542i	−0.0348330	+	0.0572276i
$693$		0			0
$694$	20.3845	+	5.71597i	0.773785	+	0.216975i
$695$	3.60653	−	20.4537i	0.136804	−	0.775851i
$696$		0			0
$697$	−2.13419	−	0.776781i	−0.0808381	−	0.0294227i
$698$	13.7067	−	6.19922i	0.518807	−	0.234644i
$699$		0			0
$700$	−1.59368	+	7.95550i	−0.0602356	+	0.300690i
$701$		−	13.2691i		−	0.501165i	−0.968095	−	0.250583i	$-0.919378\pi$
$701$		−	13.2691i		−	0.501165i	0.968095	−	0.250583i	$-0.0806222\pi$
$702$		0			0
$703$			13.7037i			0.516846i
$704$	0.323697	−	0.335391i	0.0121998	−	0.0126405i
$705$		0			0
$706$	−6.41087	−	14.1747i	−0.241276	−	0.533471i
$707$	−48.2395	−	17.5577i	−1.81423	−	0.660326i
$708$		0			0
$709$	2.29730	−	13.0286i	0.0862768	−	0.489300i	−0.910797	−	0.412855i	$-0.864532\pi$
$709$	2.29730	−	13.0286i	0.0862768	−	0.489300i	0.997074	−	0.0764456i	$-0.0243571\pi$
$710$	7.66689	−	27.3419i	0.287733	−	1.02612i
$711$		0			0
$712$	−5.80469	−	1.77376i	−0.217540	−	0.0664744i
$713$	−14.8995	−	40.9360i	−0.557990	−	1.53307i
$714$		0			0
$715$	0.424825	+	0.506286i	0.0158875	+	0.0189340i
$716$	9.23624	−	23.6558i	0.345175	−	0.884058i
$717$		0			0
$718$	−13.9727	−	20.4556i	−0.521458	−	0.763395i
$719$	−20.7715	−	35.9773i	−0.774647	−	1.34173i	−0.934992	−	0.354668i	$-0.884594\pi$
$719$	−20.7715	−	35.9773i	−0.774647	−	1.34173i	0.160345	−	0.987061i	$-0.448739\pi$
$720$		0			0
$721$	2.02522	−	3.50779i	0.0754232	−	0.130637i
$722$	15.3993	−	1.16764i	0.573104	−	0.0434550i
$723$		0			0
$724$	13.0700	−	1.99350i	0.485743	−	0.0740877i
$725$	−4.12662	+	0.727634i	−0.153259	+	0.0270236i
$726$		0			0
$727$	22.0411	−	26.2675i	0.817458	−	0.974208i	−0.182502	−	0.983206i	$-0.558420\pi$
$727$	22.0411	−	26.2675i	0.817458	−	0.974208i	0.999960	+	0.00899729i	$0.00286396\pi$
$728$	−37.0626	+	34.5714i	−1.37363	+	1.28130i
$729$		0			0
$730$	22.0058	−	5.62396i	0.814470	−	0.208152i
$731$	−15.2955	−	12.8345i	−0.565725	−	0.474699i
$732$		0			0
$733$	3.79927	+	21.5467i	0.140329	+	0.795846i	0.970999	+	0.239082i	$0.0768464\pi$
$733$	3.79927	+	21.5467i	0.140329	+	0.795846i	−0.830670	+	0.556765i	$0.812043\pi$
$734$	7.31911	+	0.725888i	0.270153	+	0.0267930i
$735$		0			0
$736$	−15.3284	+	28.4446i	−0.565012	+	1.04848i
$737$	0.381326	+	0.220159i	0.0140463	+	0.00810965i
$738$		0			0
$739$	−23.8855	+	13.7903i	−0.878644	+	0.507285i	−0.870211	−	0.492679i	$-0.836018\pi$
$739$	−23.8855	+	13.7903i	−0.878644	+	0.507285i	−0.00843293	+	0.999964i	$0.502684\pi$
$740$	−17.8015	−	15.6543i	−0.654397	−	0.575465i
$741$		0			0
$742$	−47.0068	−	33.7330i	−1.72568	−	1.23838i
$743$	16.1814	−	13.5778i	0.593637	−	0.498121i	−0.295756	−	0.955263i	$-0.595572\pi$
$743$	16.1814	−	13.5778i	0.593637	−	0.498121i	0.889393	+	0.457143i	$0.151127\pi$
$744$		0			0
$745$	23.4879	−	8.54888i	0.860528	−	0.313207i
$746$	−16.0541	+	15.6863i	−0.587782	+	0.574316i
$747$		0			0
$748$	−0.241127	−	0.00558908i	−0.00881647	−	0.000204357i
$749$	47.7537	+	8.42026i	1.74488	+	0.307670i
$750$		0			0
$751$	−5.22592	+	14.3581i	−0.190696	+	0.523934i	−0.997787	−	0.0664938i	$-0.978819\pi$
$751$	−5.22592	+	14.3581i	−0.190696	+	0.523934i	0.807090	+	0.590428i	$0.201041\pi$
$752$	20.1639	+	8.41639i	0.735300	+	0.306914i
$753$		0			0
$754$	−23.5935	−	11.3365i	−0.859223	−	0.412850i
$755$	5.86707			0.213525
$756$		0			0
$757$	−29.8309			−1.08422			−0.542112	−	0.840306i	$-0.682375\pi$
$757$	−29.8309			−1.08422			−0.542112	+	0.840306i	$0.682375\pi$
$758$	−17.0254	−	8.18059i	−0.618392	−	0.297132i
$759$		0			0
$760$	11.8934	−	15.7878i	0.431418	−	0.572683i
$761$	3.25292	−	8.93733i	0.117918	−	0.323978i	−0.866666	−	0.498889i	$-0.833742\pi$
$761$	3.25292	−	8.93733i	0.117918	−	0.323978i	0.984584	+	0.174911i	$0.0559638\pi$
$762$		0			0
$763$	−73.6463	−	12.9858i	−2.66617	−	0.470118i
$764$	−1.18055	+	50.9318i	−0.0427108	+	1.84265i
$765$		0			0
$766$	−8.17956	+	7.99217i	−0.295540	+	0.288769i
$767$	6.93593	−	2.52447i	0.250442	−	0.0911534i
$768$		0			0
$769$	4.27261	−	3.58514i	0.154074	−	0.129284i	−0.562492	−	0.826803i	$-0.690157\pi$
$769$	4.27261	−	3.58514i	0.154074	−	0.129284i	0.716566	+	0.697519i	$0.245713\pi$
$770$	0.639244	+	0.458733i	0.0230368	+	0.0165316i
$771$		0			0
$772$	−27.2003	+	30.9311i	−0.978959	+	1.11323i
$773$	15.2614	−	8.81115i	0.548913	−	0.316915i	−0.199770	−	0.979843i	$-0.564020\pi$
$773$	15.2614	−	8.81115i	0.548913	−	0.316915i	0.748683	+	0.662928i	$0.230686\pi$
$774$		0			0
$775$	−6.89886	−	3.98306i	−0.247815	−	0.143076i
$776$	12.2256	−	7.94193i	0.438875	−	0.285099i
$777$		0			0
$778$	27.6574	+	2.74298i	0.991566	+	0.0983407i
$779$	−0.541615	−	3.07165i	−0.0194054	−	0.110053i
$780$		0			0
$781$	−0.364528	−	0.305875i	−0.0130438	−	0.0109451i
$782$	16.1990	−	4.13994i	0.579275	−	0.148044i
$783$		0			0
$784$	−17.4494	+	27.2266i	−0.623194	+	0.972380i
$785$	8.60626	−	10.2565i	0.307171	−	0.366072i
$786$		0			0
$787$	−38.0897	+	6.71624i	−1.35775	+	0.239408i	−0.804672	−	0.593720i	$-0.797659\pi$
$787$	−38.0897	+	6.71624i	−1.35775	+	0.239408i	−0.553080	+	0.833128i	$0.686547\pi$
$788$	−2.09218	−	13.7170i	−0.0745308	−	0.488648i
$789$		0			0
$790$	24.0234	−	1.82155i	0.854716	−	0.0648078i
$791$	−10.1230	+	17.5336i	−0.359934	+	0.623424i
$792$		0			0
$793$	−4.87062	−	8.43615i	−0.172961	−	0.299577i
$794$	19.7387	+	28.8968i	0.700502	+	1.02551i
$795$		0			0
$796$	−21.5648	−	8.41983i	−0.764344	−	0.298433i
$797$	−2.14341	−	2.55442i	−0.0759236	−	0.0904822i	0.726746	−	0.686907i	$-0.241032\pi$
$797$	−2.14341	−	2.55442i	−0.0759236	−	0.0904822i	−0.802669	+	0.596425i	$0.796587\pi$
$798$		0			0
$799$	−3.86693	−	10.6243i	−0.136802	−	0.375861i
$800$	1.19623	+	5.78631i	0.0422930	+	0.204577i
$801$		0			0
$802$	−4.64941	+	16.5809i	−0.164176	+	0.585492i
$803$	0.0660932	−	0.374833i	0.00233238	−	0.0132276i
$804$		0			0
$805$	−51.2532	−	18.6546i	−1.80644	−	0.657489i
$806$	−20.5066	−	45.3408i	−0.722313	−	1.59706i
$807$		0			0
$808$	−37.3333	+	1.96195i	−1.31338	+	0.0690213i
$809$		−	5.26208i		−	0.185005i	−0.995712	−	0.0925025i	$-0.970513\pi$
$809$		−	5.26208i		−	0.185005i	0.995712	−	0.0925025i	$-0.0294866\pi$
$810$		0			0
$811$		−	3.33372i		−	0.117063i	−0.998286	−	0.0585314i	$-0.981358\pi$
$811$		−	3.33372i		−	0.117063i	0.998286	−	0.0585314i	$-0.0186418\pi$
$812$	−30.5549	−	6.12091i	−1.07227	−	0.214802i
$813$		0			0
$814$	−0.361950	+	0.163701i	−0.0126863	+	0.00573772i
$815$	22.5560	+	8.20972i	0.790103	+	0.287574i
$816$		0			0
$817$	4.76161	−	27.0044i	0.166588	−	0.944766i
$818$	−42.3263	−	11.8686i	−1.47990	−	0.414976i
$819$		0			0
$820$	4.60888	+	2.80531i	0.160949	+	0.0979656i
$821$	−8.98195	−	24.6777i	−0.313472	−	0.861258i	−0.991949	−	0.126636i	$-0.959582\pi$
$821$	−8.98195	−	24.6777i	−0.313472	−	0.861258i	0.678477	−	0.734622i	$-0.262640\pi$
$822$		0			0
$823$	−24.7575	−	29.5048i	−0.862991	−	1.02847i	−0.999285	−	0.0378043i	$-0.987964\pi$
$823$	−24.7575	−	29.5048i	−0.862991	−	1.02847i	0.136294	−	0.990668i	$-0.456481\pi$
$824$	0.359058	−	2.92778i	0.0125084	−	0.101994i
$825$		0			0
$826$	7.25590	−	4.95634i	0.252465	−	0.172453i
$827$	−16.3619	−	28.3397i	−0.568960	−	0.985467i	−0.996669	−	0.0815507i	$-0.974013\pi$
$827$	−16.3619	−	28.3397i	−0.568960	−	0.985467i	0.427710	−	0.903916i	$-0.359321\pi$
$828$		0			0
$829$	13.4083	−	23.2238i	0.465688	−	0.806595i	−0.533544	−	0.845772i	$-0.679140\pi$
$829$	13.4083	−	23.2238i	0.465688	−	0.806595i	0.999232	+	0.0391769i	$0.0124736\pi$
$830$	2.99563	+	39.5077i	0.103980	+	1.37133i
$831$		0			0
$832$	−15.0029	+	33.7234i	−0.520134	+	1.16915i
$833$	16.4792	−	2.90572i	0.570970	−	0.100677i
$834$		0			0
$835$	7.34200	−	8.74985i	0.254080	−	0.302801i
$836$	−0.158926	−	0.290619i	−0.00549656	−	0.0100513i
$837$		0			0
$838$	−12.9091	−	50.5117i	−0.445939	−	1.74490i
$839$	−4.82314	−	4.04709i	−0.166513	−	0.139721i	0.555723	−	0.831367i	$-0.312441\pi$
$839$	−4.82314	−	4.04709i	−0.166513	−	0.139721i	−0.722237	+	0.691646i	$0.756886\pi$
$840$		0			0
$841$	2.24115	+	12.7102i	0.0772811	+	0.438283i
$842$	−5.14199	+	51.8465i	−0.177205	+	1.78675i
$843$		0			0
$844$	28.6371	−	9.67764i	0.985731	−	0.333118i
$845$	−17.6440	−	10.1867i	−0.606971	−	0.350435i
$846$		0			0
$847$	−36.9876	+	21.3548i	−1.27091	+	0.733760i
$848$	−41.1112	−	9.23137i	−1.41176	−	0.317007i
$849$		0			0
$850$	1.78256	−	2.48400i	0.0611415	−	0.0852006i
$851$	21.0950	−	17.7008i	0.723129	−	0.606777i
$852$		0			0
$853$	−0.675411	+	0.245829i	−0.0231256	+	0.00841704i	−0.353557	−	0.935413i	$-0.615028\pi$
$853$	−0.675411	+	0.245829i	−0.0231256	+	0.00841704i	0.330431	+	0.943830i	$0.392806\pi$
$854$	−8.10466	−	8.29470i	−0.277336	−	0.283839i
$855$		0			0
$856$	34.4067	−	7.94863i	1.17600	−	0.271679i
$857$	53.7149	+	9.47138i	1.83486	+	0.323536i	0.980557	−	0.196232i	$-0.0628706\pi$
$857$	53.7149	+	9.47138i	1.83486	+	0.323536i	0.854307	+	0.519768i	$0.173982\pi$
$858$		0			0
$859$	−10.4149	+	28.6147i	−0.355352	+	0.976322i	0.625269	+	0.780409i	$0.284989\pi$
$859$	−10.4149	+	28.6147i	−0.355352	+	0.976322i	−0.980621	+	0.195913i	$0.937233\pi$
$860$	29.6402	+	37.0338i	1.01072	+	1.26284i
$861$		0			0
$862$	−6.96890	+	14.5037i	−0.237362	+	0.493997i
$863$	30.5772			1.04086			0.520430	−	0.853904i	$-0.325772\pi$
$863$	30.5772			1.04086			0.520430	+	0.853904i	$0.325772\pi$
$864$		0			0
$865$	−2.16644			−0.0736612
$866$	4.45671	−	9.27531i	0.151445	−	0.315188i
$867$		0			0
$868$	−37.0182	−	46.2522i	−1.25648	−	1.56990i
$869$	0.138084	−	0.379382i	0.00468417	−	0.0128697i
$870$		0			0
$871$	−34.3372	−	6.05458i	−1.16347	−	0.205152i
$872$	−53.0624	+	12.2585i	−1.79692	+	0.415125i
$873$		0			0
$874$	16.0471	+	16.4233i	0.542800	+	0.555527i
$875$	35.4922	−	12.9181i	1.19986	−	0.436712i
$876$		0			0
$877$	−25.9234	+	21.7523i	−0.875372	+	0.734524i	−0.965222	−	0.261431i	$-0.915806\pi$
$877$	−25.9234	+	21.7523i	−0.875372	+	0.734524i	0.0898503	+	0.995955i	$0.471361\pi$
$878$	−24.5401	+	34.1966i	−0.828188	+	1.15408i
$879$		0			0
$880$	0.559069	+	0.125537i	0.0188462	+	0.00423185i
$881$	−10.3117	+	5.95348i	−0.347411	+	0.200578i	−0.663544	−	0.748137i	$-0.730949\pi$
$881$	−10.3117	+	5.95348i	−0.347411	+	0.200578i	0.316133	+	0.948715i	$0.397615\pi$
$882$		0			0
$883$	10.5936	+	6.11620i	0.356502	+	0.205827i	0.667545	−	0.744569i	$-0.267345\pi$
$883$	10.5936	+	6.11620i	0.356502	+	0.205827i	−0.311043	+	0.950396i	$0.600678\pi$
$884$	18.0937	−	6.11460i	0.608558	−	0.205656i
$885$		0			0
$886$	2.40074	−	24.2066i	0.0806545	−	0.813236i
$887$	2.31672	+	13.1388i	0.0777879	+	0.441157i	0.998681	+	0.0513422i	$0.0163499\pi$
$887$	2.31672	+	13.1388i	0.0777879	+	0.441157i	−0.920893	+	0.389815i	$0.872539\pi$
$888$		0			0
$889$	−5.76482	−	4.83725i	−0.193346	−	0.162236i
$890$	−1.84749	−	7.22896i	−0.0619279	−	0.242315i
$891$		0			0
$892$	1.57522	+	2.88051i	0.0527422	+	0.0964467i
$893$	9.98058	−	11.8944i	0.333987	−	0.398031i
$894$		0			0
$895$	30.7433	−	5.42086i	1.02763	−	0.181200i
$896$	−7.36384	+	43.3198i	−0.246009	+	1.44721i
$897$		0			0
$898$	2.33057	+	30.7366i	0.0777720	+	1.02569i
$899$	15.2979	−	26.4967i	0.510212	−	0.883714i
$900$		0			0
$901$	10.9013	+	18.8816i	0.363174	+	0.629036i
$902$	0.0746600	−	0.0509986i	0.00248591	−	0.00169807i
$903$		0			0
$904$	−1.79475	+	14.6345i	−0.0596923	+	0.486736i
$905$	10.4469	+	12.4501i	0.347267	+	0.413856i
$906$		0			0
$907$	−6.89696	−	18.9492i	−0.229010	−	0.629199i	0.770961	−	0.636883i	$-0.219776\pi$
$907$	−6.89696	−	18.9492i	−0.229010	−	0.629199i	−0.999970	+	0.00768346i	$0.997554\pi$
$908$	46.6593	+	28.4003i	1.54844	+	0.942499i
$909$		0			0
$910$	−59.9904	−	16.8218i	−1.98866	−	0.557636i
$911$	5.48881	−	31.1286i	0.181852	−	1.03134i	−0.748081	−	0.663607i	$-0.769025\pi$
$911$	5.48881	−	31.1286i	0.181852	−	1.03134i	0.929933	−	0.367728i	$-0.119864\pi$
$912$		0			0
$913$	0.623912	+	0.227086i	0.0206485	+	0.00751544i
$914$	−12.4439	+	5.62809i	−0.411608	+	0.186161i
$915$		0			0
$916$	12.3886	+	2.48175i	0.409331	+	0.0819992i
$917$			1.81657i			0.0599884i
$918$		0			0
$919$		−	3.86720i		−	0.127567i	−0.997964	−	0.0637835i	$-0.979683\pi$
$919$		−	3.86720i		−	0.127567i	0.997964	−	0.0637835i	$-0.0203167\pi$
$920$	−39.6656	+	2.08452i	−1.30774	+	0.0687247i
$921$		0			0
$922$	−19.1071	−	42.2465i	−0.629258	−	1.39132i
$923$	35.4087	+	12.8877i	1.16549	+	0.424205i
$924$		0			0
$925$	0.874428	−	4.95913i	0.0287510	−	0.163055i
$926$	−14.6392	+	52.2069i	−0.481075	+	1.71562i
$927$		0			0
$928$	−22.2237	+	4.59439i	−0.729527	+	0.150818i
$929$	17.2575	+	47.4145i	0.566200	+	1.55562i	0.810388	+	0.585893i	$0.199256\pi$
$929$	17.2575	+	47.4145i	0.566200	+	1.55562i	−0.244189	+	0.969728i	$0.578522\pi$
$930$		0			0
$931$	14.7715	+	17.6040i	0.484117	+	0.576949i
$932$	55.2407	+	21.5684i	1.80947	+	0.706495i
$933$		0			0
$934$	9.24034	+	13.5275i	0.302353	+	0.442634i
$935$	−0.148246	−	0.256770i	−0.00484816	−	0.00839726i
$936$		0			0
$937$	24.0457	−	41.6483i	0.785538	−	1.36059i	−0.143139	−	0.989703i	$-0.545720\pi$
$937$	24.0457	−	41.6483i	0.785538	−	1.36059i	0.928677	−	0.370890i	$-0.120947\pi$
$938$	−41.3901	+	3.13836i	−1.35143	+	0.102471i
$939$		0			0
$940$	4.04991	+	26.5525i	0.132094	+	0.866048i
$941$	−7.23098	+	1.27502i	−0.235723	+	0.0415644i	−0.290262	−	0.956947i	$-0.593742\pi$
$941$	−7.23098	+	1.27502i	−0.235723	+	0.0415644i	0.0545385	+	0.998512i	$0.482631\pi$
$942$		0			0
$943$	−4.02880	+	4.80134i	−0.131196	+	0.156353i
$944$	3.45292	−	5.38765i	0.112383	−	0.175353i
$945$		0			0
$946$	0.770136	−	0.196822i	0.0250393	−	0.00639923i
$947$	−24.3956	−	20.4704i	−0.792752	−	0.665198i	0.153673	−	0.988122i	$-0.450890\pi$
$947$	−24.3956	−	20.4704i	−0.792752	−	0.665198i	−0.946425	+	0.322924i	$0.895334\pi$
$948$		0			0
$949$	5.23365	+	29.6815i	0.169891	+	0.963502i
$950$	4.17833	+	0.414395i	0.135563	+	0.0134448i
$951$		0			0
$952$	19.0672	−	12.3863i	0.617973	−	0.401443i
$953$	13.1967	+	7.61912i	0.427483	+	0.246807i	0.698274	−	0.715831i	$-0.253952\pi$
$953$	13.1967	+	7.61912i	0.427483	+	0.246807i	−0.270791	+	0.962638i	$0.587285\pi$
$954$		0			0
$955$	−54.2359	+	31.3131i	−1.75503	+	1.01327i
$956$	12.2905	−	13.9763i	0.397502	−	0.452025i
$957$		0			0
$958$	−20.5958	−	14.7799i	−0.665420	−	0.477518i
$959$	13.0623	−	10.9606i	0.421804	−	0.353936i
$960$		0			0
$961$	25.5272	−	9.29113i	0.823457	−	0.299714i
$962$	22.4993	−	21.9838i	0.725406	−	0.708787i
$963$		0			0
$964$	−0.651671	+	28.1147i	−0.0209889	+	0.905513i
$965$	−49.8644	−	8.79243i	−1.60519	−	0.283038i
$966$		0			0
$967$	14.7610	−	40.5556i	0.474683	−	1.30418i	−0.439268	−	0.898356i	$-0.644762\pi$
$967$	14.7610	−	40.5556i	0.474683	−	1.30418i	0.913951	−	0.405825i	$-0.133016\pi$
$968$	−18.7147	+	24.8427i	−0.601514	+	0.798476i
$969$		0			0
$970$	16.1534	+	7.76160i	0.518656	+	0.249210i
$971$	32.9105			1.05615			0.528074	−	0.849198i	$-0.322914\pi$
$971$	32.9105			1.05615			0.528074	+	0.849198i	$0.322914\pi$
$972$		0			0
$973$	32.8100			1.05184
$974$	28.8674	+	13.8706i	0.924972	+	0.444442i
$975$		0			0
$976$	−7.79370	−	3.25309i	−0.249470	−	0.104129i
$977$	−19.4179	+	53.3502i	−0.621234	+	1.70683i	0.0827138	+	0.996573i	$0.473641\pi$
$977$	−19.4179	+	53.3502i	−0.621234	+	1.70683i	−0.703947	+	0.710252i	$0.748581\pi$
$978$		0			0
$979$	−0.123134	−	0.0217118i	−0.00393537	−	0.000693912i
$980$	−39.7423	−	0.921187i	−1.26952	−	0.0294262i
$981$		0			0
$982$	26.0029	−	25.4072i	0.829787	−	0.810776i
$983$	30.4707	−	11.0904i	0.971864	−	0.353730i	0.193192	−	0.981161i	$-0.438116\pi$
$983$	30.4707	−	11.0904i	0.971864	−	0.353730i	0.778672	+	0.627431i	$0.215894\pi$
$984$		0			0
$985$	13.0665	−	10.9641i	0.416332	−	0.349344i
$986$	9.54038	+	6.84635i	0.303828	+	0.218032i
$987$		0			0
$988$	19.6966	+	17.3208i	0.626632	+	0.551049i
$989$	−47.7202	+	27.5513i	−1.51741	+	0.876080i
$990$		0			0
$991$	−36.6324	−	21.1497i	−1.16367	−	0.671843i	−0.211486	−	0.977381i	$-0.567830\pi$
$991$	−36.6324	−	21.1497i	−1.16367	−	0.671843i	−0.952180	+	0.305539i	$0.901164\pi$
$992$	−37.9792	−	20.4664i	−1.20584	−	0.649809i
$993$		0			0
$994$	44.6402	+	4.42729i	1.41590	+	0.140425i
$995$	−4.94170	−	28.0258i	−0.156663	−	0.888477i
$996$		0			0
$997$	−25.8985	−	21.7314i	−0.820213	−	0.688241i	0.132809	−	0.991142i	$-0.457600\pi$
$997$	−25.8985	−	21.7314i	−0.820213	−	0.688241i	−0.953022	+	0.302901i	$0.902045\pi$
$998$	9.90536	−	2.53149i	0.313549	−	0.0801329i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.d.107.6		96
3.2	odd	2		972.2.l.a.107.11		96
4.3	odd	2	inner	972.2.l.d.107.4		96
9.2	odd	6		972.2.l.b.755.1		96
9.4	even	3		108.2.l.a.47.6	yes	96
9.5	odd	6		324.2.l.a.143.11		96
9.7	even	3		972.2.l.c.755.16		96
12.11	even	2		972.2.l.a.107.13		96
27.4	even	9		972.2.l.b.215.2		96
27.5	odd	18	inner	972.2.l.d.863.4		96
27.13	even	9		324.2.l.a.179.10		96
27.14	odd	18		108.2.l.a.23.7	yes	96
27.22	even	9		972.2.l.a.863.13		96
27.23	odd	18		972.2.l.c.215.15		96
36.7	odd	6		972.2.l.c.755.15		96
36.11	even	6		972.2.l.b.755.2		96
36.23	even	6		324.2.l.a.143.10		96
36.31	odd	6		108.2.l.a.47.7	yes	96
108.23	even	18		972.2.l.c.215.16		96
108.31	odd	18		972.2.l.b.215.1		96
108.59	even	18	inner	972.2.l.d.863.6		96
108.67	odd	18		324.2.l.a.179.11		96
108.95	even	18		108.2.l.a.23.6	✓	96
108.103	odd	18		972.2.l.a.863.11		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.6	✓	96	108.95	even	18
108.2.l.a.23.7	yes	96	27.14	odd	18
108.2.l.a.47.6	yes	96	9.4	even	3
108.2.l.a.47.7	yes	96	36.31	odd	6
324.2.l.a.143.10		96	36.23	even	6
324.2.l.a.143.11		96	9.5	odd	6
324.2.l.a.179.10		96	27.13	even	9
324.2.l.a.179.11		96	108.67	odd	18
972.2.l.a.107.11		96	3.2	odd	2
972.2.l.a.107.13		96	12.11	even	2
972.2.l.a.863.11		96	108.103	odd	18
972.2.l.a.863.13		96	27.22	even	9
972.2.l.b.215.1		96	108.31	odd	18
972.2.l.b.215.2		96	27.4	even	9
972.2.l.b.755.1		96	9.2	odd	6
972.2.l.b.755.2		96	36.11	even	6
972.2.l.c.215.15		96	27.23	odd	18
972.2.l.c.215.16		96	108.23	even	18
972.2.l.c.755.15		96	36.7	odd	6
972.2.l.c.755.16		96	9.7	even	3
972.2.l.d.107.4		96	4.3	odd	2	inner
972.2.l.d.107.6		96	1.1	even	1	trivial
972.2.l.d.863.4		96	27.5	odd	18	inner
972.2.l.d.863.6		96	108.59	even	18	inner

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.612484 + 1.27470i) q^{2} +(-1.24973 - 1.56147i) q^{4} +(0.840877 - 2.31029i) q^{5} +(3.82489 + 0.674430i) q^{7} +(2.75584 - 0.636655i) q^{8} +(2.42991 + 2.48688i) q^{10} +(0.0547511 - 0.0199278i) q^{11} +(-3.53434 + 2.96567i) q^{13} +(-3.20238 + 4.46251i) q^{14} +(-0.876364 + 3.90282i) q^{16} +(1.79249 - 1.03489i) q^{17} +(2.46167 + 1.42125i) q^{19} +(-4.65831 + 1.57423i) q^{20} +(-0.00813220 + 0.0819967i) q^{22} +(-0.991876 - 5.62521i) q^{23} +(-0.800144 - 0.671401i) q^{25} +(-1.61561 - 6.32166i) q^{26} +(-3.72696 - 6.81529i) q^{28} +(2.57867 - 3.07314i) q^{29} +(7.51076 - 1.32435i) q^{31} +(-4.43817 - 3.50751i) q^{32} +(0.221310 + 2.91874i) q^{34} +(4.77439 - 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(-3.31940 + 2.26740i) q^{38} +(0.846466 - 6.90215i) q^{40} +(-0.705325 - 0.840573i) q^{41} +(-3.29941 - 9.06505i) q^{43} +(-0.0995405 - 0.0605878i) q^{44} +(7.77797 + 2.18100i) q^{46} +(0.948548 - 5.37948i) q^{47} +(7.59704 + 2.76510i) q^{49} +(1.34591 - 0.608723i) q^{50} +(9.04776 + 1.81249i) q^{52} +10.5337i q^{53} -0.143248i q^{55} +(10.9702 - 0.576509i) q^{56} +(2.33794 + 5.16928i) q^{58} +(-1.50332 - 0.547162i) q^{59} +(-0.366631 + 2.07927i) q^{61} +(-2.91207 + 10.3851i) q^{62} +(7.18934 - 3.50904i) q^{64} +(3.87960 + 10.6591i) q^{65} +(4.85766 + 5.78913i) q^{67} +(-3.85607 - 1.50558i) q^{68} +(7.61689 + 11.1508i) q^{70} +(-4.08357 - 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(-6.79844 + 0.515484i) q^{74} +(-0.857186 - 5.61999i) q^{76} +(0.222856 - 0.0392956i) q^{77} +(4.45402 - 5.30809i) q^{79} +(8.27973 + 5.30644i) q^{80} +(1.50348 - 0.384241i) q^{82} +(8.72941 + 7.32485i) q^{83} +(-0.883642 - 5.01138i) q^{85} +(13.5761 + 1.34644i) q^{86} +(0.138198 - 0.0897753i) q^{88} +(-1.85844 - 1.07297i) q^{89} +(-15.5186 + 8.95967i) q^{91} +(-7.54401 + 8.57876i) q^{92} +(6.27626 + 4.50396i) q^{94} +(5.35345 - 4.49208i) q^{95} +(4.84352 - 1.76290i) q^{97} +(-8.17774 + 7.99038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more