LMFDB - Embedded newform 975.2.n.q.749.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(749,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("975.749");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.n (of order $4$, 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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			749.13
Character	$\chi$	$=$	975.749
Dual form			975.2.n.q.824.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483812 + 0.483812i) q^{2} +(-0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(0.361045 - 1.12876i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(1.70875 - 1.70875i) q^{8} +(-1.74104 + 2.44311i) q^{9} +O(q^{10})$	\(q+(0.483812 + 0.483812i) q^{2} +(-0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(0.361045 - 1.12876i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(1.70875 - 1.70875i) q^{8} +(-1.74104 + 2.44311i) q^{9} +(0.387103 + 0.387103i) q^{11} +(-2.35852 + 1.21537i) q^{12} +(-3.49780 + 0.874878i) q^{13} -1.20499i q^{14} -1.41028 q^{16} -6.75010i q^{17} +(-2.02434 + 0.339668i) q^{18} +(-1.33304 - 1.33304i) q^{19} +(-0.929314 + 2.90536i) q^{21} +0.374570i q^{22} +1.69635i q^{23} +(-3.98660 - 1.27516i) q^{24} +(-2.11555 - 1.26900i) q^{26} +(5.14287 + 0.742237i) q^{27} +(-1.90763 + 1.90763i) q^{28} +3.85370i q^{29} +(4.06109 + 4.06109i) q^{31} +(-4.09981 - 4.09981i) q^{32} +(0.288877 - 0.903130i) q^{33} +(3.26578 - 3.26578i) q^{34} +(3.74248 + 2.66702i) q^{36} +(-2.36718 - 2.36718i) q^{37} -1.28988i q^{38} +(4.12215 + 4.69126i) q^{39} +(-5.72121 + 5.72121i) q^{41} +(-1.85526 + 0.956036i) q^{42} -11.7392 q^{43} +(0.592985 - 0.592985i) q^{44} +(-0.820713 + 0.820713i) q^{46} +(-5.99016 + 5.99016i) q^{47} +(1.11891 + 2.17133i) q^{48} -3.89841i q^{49} +(-10.3928 + 5.35551i) q^{51} +(1.34018 + 5.35811i) q^{52} +8.81372 q^{53} +(2.12908 + 2.84728i) q^{54} -4.25585 q^{56} +(-0.994786 + 3.11005i) q^{57} +(-1.86446 + 1.86446i) q^{58} +(1.30531 + 1.30531i) q^{59} -1.16343 q^{61} +3.92960i q^{62} +(5.21056 - 0.874290i) q^{63} -1.14652i q^{64} +(0.576707 - 0.297183i) q^{66} +(4.66845 - 4.66845i) q^{67} -10.3402 q^{68} +(2.61178 - 1.34588i) q^{69} +(0.915921 - 0.915921i) q^{71} +(1.19966 + 7.14967i) q^{72} +(-8.11348 - 8.11348i) q^{73} -2.29054i q^{74} +(-2.04202 + 2.04202i) q^{76} -0.964126i q^{77} +(-0.275341 + 4.26403i) q^{78} +3.85408 q^{79} +(-2.93755 - 8.50710i) q^{81} -5.53597 q^{82} +(-11.9347 - 11.9347i) q^{83} +(4.45059 + 1.42357i) q^{84} +(-5.67957 - 5.67957i) q^{86} +(5.93334 - 3.05751i) q^{87} +1.32293 q^{88} +(-5.99694 - 5.99694i) q^{89} +(5.44533 + 3.26635i) q^{91} +2.59855 q^{92} +(3.03059 - 9.47471i) q^{93} -5.79622 q^{94} +(-3.05949 + 9.56505i) q^{96} +(-1.03487 + 1.03487i) q^{97} +(1.88610 - 1.88610i) q^{98} +(-1.61970 + 0.271772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 40 * q + 12 * q^6 - 16 * q^7	$ 40 q + 12 q^{6} - 16 q^{7} - 24 q^{12} + 24 q^{13} - 64 q^{16} + 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} + 32 q^{28} + 32 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{37} + 8 q^{39} - 32 q^{43} - 40 q^{46} - 8 q^{52} + 32 q^{54} + 36 q^{57} + 24 q^{58} + 8 q^{61} - 8 q^{63} - 48 q^{66} + 32 q^{67} + 132 q^{72} + 64 q^{73} + 16 q^{76} - 108 q^{78} - 40 q^{79} + 72 q^{81} - 128 q^{82} - 124 q^{84} - 80 q^{88} + 8 q^{91} - 108 q^{93} + 32 q^{94} - 76 q^{96} - 24 q^{97} + 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 - 16 * q^7 - 24 * q^12 + 24 * q^13 - 64 * q^16 + 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 + 32 * q^28 + 32 * q^31 + 4 * q^33 + 16 * q^34 + 32 * q^37 + 8 * q^39 - 32 * q^43 - 40 * q^46 - 8 * q^52 + 32 * q^54 + 36 * q^57 + 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 + 132 * q^72 + 64 * q^73 + 16 * q^76 - 108 * q^78 - 40 * q^79 + 72 * q^81 - 128 * q^82 - 124 * q^84 - 80 * q^88 + 8 * q^91 - 108 * q^93 + 32 * q^94 - 76 * q^96 - 24 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.483812	+	0.483812i	0.342107	+	0.342107i	0.857159	−	0.515052i	$-0.172227\pi$
$2$	0.483812	+	0.483812i	0.342107	+	0.342107i	−0.515052	+	0.857159i	$0.672227\pi$
$3$	−0.793397	−	1.53965i	−0.458068	−	0.888917i
$3$	−0.793397	−	1.53965i	−0.458068	−	0.888917i
$4$		−	1.53185i		−	0.765926i
$5$		0			0
$5$		0			0
$6$	0.361045	−	1.12876i	0.147396	−	0.460813i
$7$	−1.24531	−	1.24531i	−0.470683	−	0.470683i	0.431453	−	0.902135i	$-0.358001\pi$
$7$	−1.24531	−	1.24531i	−0.470683	−	0.470683i	−0.902135	+	0.431453i	$0.858001\pi$
$8$	1.70875	−	1.70875i	0.604135	−	0.604135i
$9$	−1.74104	+	2.44311i	−0.580347	+	0.814369i
$10$		0			0
$11$	0.387103	+	0.387103i	0.116716	+	0.116716i	0.763053	−	0.646337i	$-0.223700\pi$
$11$	0.387103	+	0.387103i	0.116716	+	0.116716i	−0.646337	+	0.763053i	$0.723700\pi$
$12$	−2.35852	+	1.21537i	−0.680845	+	0.350846i
$13$	−3.49780	+	0.874878i	−0.970115	+	0.242647i
$13$	−3.49780	+	0.874878i	−0.970115	+	0.242647i
$14$		−	1.20499i		−	0.322047i
$15$		0			0
$16$	−1.41028			−0.352569
$17$		−	6.75010i		−	1.63714i	−0.574407	−	0.818570i	$-0.694767\pi$
$17$		−	6.75010i		−	1.63714i	0.574407	−	0.818570i	$-0.305233\pi$
$18$	−2.02434	+	0.339668i	−0.477142	+	0.0800606i
$19$	−1.33304	−	1.33304i	−0.305821	−	0.305821i	0.537465	−	0.843286i	$-0.319382\pi$
$19$	−1.33304	−	1.33304i	−0.305821	−	0.305821i	−0.843286	+	0.537465i	$0.819382\pi$
$20$		0			0
$21$	−0.929314	+	2.90536i	−0.202793	+	0.634003i
$22$			0.374570i			0.0798586i
$23$			1.69635i			0.353713i	0.984237	+	0.176856i	$0.0565928\pi$
$23$			1.69635i			0.353713i	−0.984237	+	0.176856i	$0.943407\pi$
$24$	−3.98660	−	1.27516i	−0.813761	−	0.260291i
$25$		0			0
$26$	−2.11555	−	1.26900i	−0.414894	−	0.248871i
$27$	5.14287	+	0.742237i	0.989745	+	0.142844i
$28$	−1.90763	+	1.90763i	−0.360508	+	0.360508i
$29$			3.85370i			0.715614i	0.933796	+	0.357807i	$0.116475\pi$
$29$			3.85370i			0.715614i	−0.933796	+	0.357807i	$0.883525\pi$
$30$		0			0
$31$	4.06109	+	4.06109i	0.729393	+	0.729393i	0.970499	−	0.241106i	$-0.0775102\pi$
$31$	4.06109	+	4.06109i	0.729393	+	0.729393i	−0.241106	+	0.970499i	$0.577510\pi$
$32$	−4.09981	−	4.09981i	−0.724751	−	0.724751i
$33$	0.288877	−	0.903130i	0.0502869	−	0.157215i
$34$	3.26578	−	3.26578i	0.560076	−	0.560076i
$35$		0			0
$36$	3.74248	+	2.66702i	0.623747	+	0.444503i
$37$	−2.36718	−	2.36718i	−0.389163	−	0.389163i	0.485226	−	0.874389i	$-0.338737\pi$
$37$	−2.36718	−	2.36718i	−0.389163	−	0.389163i	−0.874389	+	0.485226i	$0.838737\pi$
$38$		−	1.28988i		−	0.209247i
$39$	4.12215	+	4.69126i	0.660072	+	0.751202i
$40$		0			0
$41$	−5.72121	+	5.72121i	−0.893502	+	0.893502i	−0.994851	−	0.101349i	$-0.967684\pi$
$41$	−5.72121	+	5.72121i	−0.893502	+	0.893502i	0.101349	+	0.994851i	$0.467684\pi$
$42$	−1.85526	+	0.956036i	−0.286273	+	0.147520i
$43$	−11.7392			−1.79021			−0.895106	−	0.445853i	$-0.852900\pi$
$43$	−11.7392			−1.79021			−0.895106	+	0.445853i	$0.852900\pi$
$44$	0.592985	−	0.592985i	0.0893958	−	0.0893958i
$45$		0			0
$46$	−0.820713	+	0.820713i	−0.121008	+	0.121008i
$47$	−5.99016	+	5.99016i	−0.873755	+	0.873755i	−0.992879	−	0.119124i	$-0.961991\pi$
$47$	−5.99016	+	5.99016i	−0.873755	+	0.873755i	0.119124	+	0.992879i	$0.461991\pi$
$48$	1.11891	+	2.17133i	0.161501	+	0.313405i
$49$		−	3.89841i		−	0.556916i
$50$		0			0
$51$	−10.3928	+	5.35551i	−1.45528	+	0.749922i
$52$	1.34018	+	5.35811i	0.185850	+	0.743036i
$53$	8.81372			1.21066			0.605328	−	0.795976i	$-0.293042\pi$
$53$	8.81372			1.21066			0.605328	+	0.795976i	$0.293042\pi$
$54$	2.12908	+	2.84728i	0.289731	+	0.387466i
$55$		0			0
$56$	−4.25585			−0.568712
$57$	−0.994786	+	3.11005i	−0.131763	+	0.411936i
$58$	−1.86446	+	1.86446i	−0.244816	+	0.244816i
$59$	1.30531	+	1.30531i	0.169937	+	0.169937i	0.786952	−	0.617015i	$-0.211658\pi$
$59$	1.30531	+	1.30531i	0.169937	+	0.169937i	−0.617015	+	0.786952i	$0.711658\pi$
$60$		0			0
$61$	−1.16343			−0.148961			−0.0744807	−	0.997222i	$-0.523730\pi$
$61$	−1.16343			−0.148961			−0.0744807	+	0.997222i	$0.523730\pi$
$62$			3.92960i			0.499060i
$63$	5.21056	−	0.874290i	0.656469	−	0.110150i
$64$		−	1.14652i		−	0.143315i
$65$		0			0
$66$	0.576707	−	0.297183i	0.0709877	−	0.0365807i
$67$	4.66845	−	4.66845i	0.570341	−	0.570341i	−0.361882	−	0.932224i	$-0.617866\pi$
$67$	4.66845	−	4.66845i	0.570341	−	0.570341i	0.932224	+	0.361882i	$0.117866\pi$
$68$	−10.3402			−1.25393
$69$	2.61178	−	1.34588i	0.314421	−	0.162025i
$70$		0			0
$71$	0.915921	−	0.915921i	0.108700	−	0.108700i	−0.650665	−	0.759365i	$-0.725510\pi$
$71$	0.915921	−	0.915921i	0.108700	−	0.108700i	0.759365	+	0.650665i	$0.225510\pi$
$72$	1.19966	+	7.14967i	0.141381	+	0.842597i
$73$	−8.11348	−	8.11348i	−0.949611	−	0.949611i	0.0491790	−	0.998790i	$-0.484340\pi$
$73$	−8.11348	−	8.11348i	−0.949611	−	0.949611i	−0.998790	+	0.0491790i	$0.984340\pi$
$74$		−	2.29054i		−	0.266270i
$75$		0			0
$76$	−2.04202	+	2.04202i	−0.234236	+	0.234236i
$77$		−	0.964126i		−	0.109872i
$78$	−0.275341	+	4.26403i	−0.0311762	+	0.482806i
$79$	3.85408			0.433617			0.216809	−	0.976214i	$-0.430435\pi$
$79$	3.85408			0.433617			0.216809	+	0.976214i	$0.430435\pi$
$80$		0			0
$81$	−2.93755	−	8.50710i	−0.326395	−	0.945234i
$82$	−5.53597			−0.611346
$83$	−11.9347	−	11.9347i	−1.31000	−	1.31000i	−0.921412	−	0.388586i	$-0.872964\pi$
$83$	−11.9347	−	11.9347i	−1.31000	−	1.31000i	−0.388586	−	0.921412i	$-0.627036\pi$
$84$	4.45059	+	1.42357i	0.485599	+	0.155325i
$85$		0			0
$86$	−5.67957	−	5.67957i	−0.612443	−	0.612443i
$87$	5.93334	−	3.05751i	0.636121	−	0.327800i
$88$	1.32293			0.141024
$89$	−5.99694	−	5.99694i	−0.635674	−	0.635674i	0.313811	−	0.949485i	$-0.398394\pi$
$89$	−5.99694	−	5.99694i	−0.635674	−	0.635674i	−0.949485	+	0.313811i	$0.898394\pi$
$90$		0			0
$91$	5.44533	+	3.26635i	0.570826	+	0.342406i
$92$	2.59855			0.270918
$93$	3.03059	−	9.47471i	0.314258	−	0.982481i
$94$	−5.79622			−0.597835
$95$		0			0
$96$	−3.05949	+	9.56505i	−0.312258	+	0.976229i
$97$	−1.03487	+	1.03487i	−0.105075	+	0.105075i	−0.757690	−	0.652615i	$-0.773672\pi$
$97$	−1.03487	+	1.03487i	−0.105075	+	0.105075i	0.652615	+	0.757690i	$0.273672\pi$
$98$	1.88610	−	1.88610i	0.190525	−	0.190525i
$99$	−1.61970	+	0.271772i	−0.162786	+	0.0273141i
$100$		0			0
$101$	18.2471			1.81565			0.907826	−	0.419347i	$-0.137741\pi$
$101$	18.2471			1.81565			0.907826	+	0.419347i	$0.137741\pi$
$102$	−7.61921	−	2.43709i	−0.754415	−	0.241308i
$103$	3.65487			0.360125			0.180063	−	0.983655i	$-0.442370\pi$
$103$	3.65487			0.360125			0.180063	+	0.983655i	$0.442370\pi$
$104$	−4.48192	+	7.47182i	−0.439488	+	0.732672i
$105$		0			0
$106$	4.26418	+	4.26418i	0.414174	+	0.414174i
$107$	14.9588			1.44612			0.723060	−	0.690786i	$-0.242735\pi$
$107$	14.9588			1.44612			0.723060	+	0.690786i	$0.242735\pi$
$108$	1.13700	−	7.87811i	0.109408	−	0.758072i
$109$	−5.41443	−	5.41443i	−0.518609	−	0.518609i	0.398542	−	0.917150i	$-0.369516\pi$
$109$	−5.41443	−	5.41443i	−0.518609	−	0.518609i	−0.917150	+	0.398542i	$0.869516\pi$
$110$		0			0
$111$	−1.76652	+	5.52275i	−0.167670	+	0.524196i
$112$	1.75623	+	1.75623i	0.165948	+	0.165948i
$113$	5.56044			0.523083			0.261541	−	0.965192i	$-0.415769\pi$
$113$	5.56044			0.523083			0.261541	+	0.965192i	$0.415769\pi$
$114$	−1.98597	+	1.02339i	−0.186003	+	0.0958493i
$115$		0			0
$116$	5.90330			0.548107
$117$	3.95239	−	10.0687i	0.365398	−	0.930851i
$118$			1.26305i			0.116273i
$119$	−8.40596	+	8.40596i	−0.770573	+	0.770573i
$120$		0			0
$121$		−	10.7003i		−	0.972755i
$122$	−0.562879	−	0.562879i	−0.0509607	−	0.0509607i
$123$	13.3478	+	4.26946i	1.20353	+	0.384964i
$124$	6.22098	−	6.22098i	0.558661	−	0.558661i
$125$		0			0
$126$	2.94392	+	2.09794i	0.262265	+	0.186899i
$127$	0.0349646			0.00310261			0.00155130	−	0.999999i	$-0.499506\pi$
$127$	0.0349646			0.00310261			0.00155130	+	0.999999i	$0.499506\pi$
$128$	−7.64492	+	7.64492i	−0.675722	+	0.675722i
$129$	9.31386	+	18.0743i	0.820039	+	1.59135i
$130$		0			0
$131$			1.11950i			0.0978111i	0.998803	+	0.0489056i	$0.0155733\pi$
$131$			1.11950i			0.0978111i	−0.998803	+	0.0489056i	$0.984427\pi$
$132$	−1.38346	−	0.442516i	−0.120415	−	0.0385161i
$133$			3.32010i			0.287889i
$134$	4.51730			0.390235
$135$		0			0
$136$	−11.5342	−	11.5342i	−0.989054	−	0.989054i
$137$	2.58611	−	2.58611i	0.220946	−	0.220946i	−0.587950	−	0.808897i	$-0.700065\pi$
$137$	2.58611	−	2.58611i	0.220946	−	0.220946i	0.808897	+	0.587950i	$0.200065\pi$
$138$	1.91476	+	0.612459i	0.162995	+	0.0521359i
$139$	−16.6867			−1.41535			−0.707673	−	0.706540i	$-0.750255\pi$
$139$	−16.6867			−1.41535			−0.707673	+	0.706540i	$0.750255\pi$
$140$		0			0
$141$	13.9753	+	4.47017i	1.17694	+	0.376456i
$142$	0.886267			0.0743739
$143$	−1.69268	−	1.01534i	−0.141549	−	0.0849071i
$144$	2.45535	−	3.44546i	0.204612	−	0.287121i
$145$		0			0
$146$		−	7.85079i		−	0.649736i
$147$	−6.00219	+	3.09299i	−0.495052	+	0.255105i
$148$	−3.62618	+	3.62618i	−0.298070	+	0.298070i
$149$	16.9396	−	16.9396i	1.38775	−	1.38775i	0.557719	−	0.830030i	$-0.311677\pi$
$149$	16.9396	−	16.9396i	1.38775	−	1.38775i	0.830030	−	0.557719i	$-0.188323\pi$
$150$		0			0
$151$	−5.21274	+	5.21274i	−0.424207	+	0.424207i	−0.886649	−	0.462442i	$-0.846973\pi$
$151$	−5.21274	+	5.21274i	−0.424207	+	0.424207i	0.462442	+	0.886649i	$0.346973\pi$
$152$	−4.55568			−0.369514
$153$	16.4912	+	11.7522i	1.33324	+	0.950109i
$154$	0.466456	−	0.466456i	0.0375881	−	0.0375881i
$155$		0			0
$156$	7.18631	−	6.31452i	0.575366	−	0.505566i
$157$		−	13.0314i		−	1.04002i	−0.854161	−	0.520008i	$-0.825929\pi$
$157$		−	13.0314i		−	1.04002i	0.854161	−	0.520008i	$-0.174071\pi$
$158$	1.86465	+	1.86465i	0.148343	+	0.148343i
$159$	−6.99278	−	13.5700i	−0.554563	−	1.07617i
$160$		0			0
$161$	2.11248	−	2.11248i	0.166487	−	0.166487i
$162$	2.69461	−	5.53706i	0.211709	−	0.435032i
$163$	−3.83399	−	3.83399i	−0.300301	−	0.300301i	0.540830	−	0.841132i	$-0.318110\pi$
$163$	−3.83399	−	3.83399i	−0.300301	−	0.300301i	−0.841132	+	0.540830i	$0.818110\pi$
$164$	8.76404	+	8.76404i	0.684357	+	0.684357i
$165$		0			0
$166$		−	11.5483i		−	0.896318i
$167$	−9.06688	+	9.06688i	−0.701616	+	0.701616i	−0.964757	−	0.263141i	$-0.915242\pi$
$167$	−9.06688	+	9.06688i	−0.701616	+	0.701616i	0.263141	+	0.964757i	$0.415242\pi$
$168$	3.37658	+	6.55251i	0.260509	+	0.505537i
$169$	11.4692	−	6.12029i	0.882244	−	0.470792i
$170$		0			0
$171$	5.57765	−	0.935885i	0.426534	−	0.0715689i
$172$			17.9827i			1.37117i
$173$			4.63904i			0.352700i	0.984328	+	0.176350i	$0.0564291\pi$
$173$			4.63904i			0.352700i	−0.984328	+	0.176350i	$0.943571\pi$
$174$	4.34988	+	1.39136i	0.329764	+	0.105479i
$175$		0			0
$176$	−0.545923	−	0.545923i	−0.0411505	−	0.0411505i
$177$	0.974090	−	3.04535i	0.0732171	−	0.228902i
$178$		−	5.80278i		−	0.434936i
$179$	−13.2894			−0.993298			−0.496649	−	0.867951i	$-0.665436\pi$
$179$	−13.2894			−0.993298			−0.496649	+	0.867951i	$0.665436\pi$
$180$		0			0
$181$		−	23.3132i		−	1.73286i	−0.499299	−	0.866429i	$-0.666409\pi$
$181$		−	23.3132i		−	1.73286i	0.499299	−	0.866429i	$-0.333591\pi$
$182$	1.05422	+	4.21481i	0.0781439	+	0.312423i
$183$	0.923059	+	1.79127i	0.0682345	+	0.132414i
$184$	2.89864	+	2.89864i	0.213690	+	0.213690i
$185$		0			0
$186$	6.05021	−	3.11774i	0.443623	−	0.228604i
$187$	2.61299	−	2.61299i	0.191080	−	0.191080i
$188$	9.17605	+	9.17605i	0.669232	+	0.669232i
$189$	−5.48014	−	7.32877i	−0.398622	−	0.533090i
$190$		0			0
$191$		−	6.40782i		−	0.463654i	−0.972757	−	0.231827i	$-0.925530\pi$
$191$		−	6.40782i		−	0.463654i	0.972757	−	0.231827i	$-0.0744703\pi$
$192$	−1.76524	+	0.909647i	−0.127395	+	0.0656481i
$193$	16.1130	+	16.1130i	1.15984	+	1.15984i	0.984509	+	0.175332i	$0.0561000\pi$
$193$	16.1130	+	16.1130i	1.15984	+	1.15984i	0.175332	+	0.984509i	$0.443900\pi$
$194$	−1.00136			−0.0718936
$195$		0			0
$196$	−5.97179			−0.426556
$197$	−11.3286	−	11.3286i	−0.807127	−	0.807127i	0.177071	−	0.984198i	$-0.443338\pi$
$197$	−11.3286	−	11.3286i	−0.807127	−	0.807127i	−0.984198	+	0.177071i	$0.943338\pi$
$198$	−0.915115	−	0.652142i	−0.0650344	−	0.0463457i
$199$		−	23.0814i		−	1.63620i	−0.575079	−	0.818098i	$-0.695029\pi$
$199$		−	23.0814i		−	1.63620i	0.575079	−	0.818098i	$-0.304971\pi$
$200$		0			0
$201$	−10.8917	−	3.48384i	−0.768242	−	0.245731i
$202$	8.82815	+	8.82815i	0.621147	+	0.621147i
$203$	4.79904	−	4.79904i	0.336827	−	0.336827i
$204$	8.20386	+	15.9202i	0.574385	+	1.11464i
$205$		0			0
$206$	1.76827	+	1.76827i	0.123201	+	0.123201i
$207$	−4.14436	−	2.95341i	−0.288053	−	0.205276i
$208$	4.93286	−	1.23382i	0.342032	−	0.0855500i
$209$		−	1.03205i		−	0.0713884i
$210$		0			0
$211$	−9.04618			−0.622765			−0.311382	−	0.950285i	$-0.600792\pi$
$211$	−9.04618			−0.622765			−0.311382	+	0.950285i	$0.600792\pi$
$212$		−	13.5013i		−	0.927274i
$213$	−2.13689	−	0.683508i	−0.146417	−	0.0468332i
$214$	7.23723	+	7.23723i	0.494727	+	0.494727i
$215$		0			0
$216$	10.0562	−	7.51958i	0.684237	−	0.511643i
$217$		−	10.1146i		−	0.686625i
$218$		−	5.23913i		−	0.354839i
$219$	−6.05470	+	18.9291i	−0.409139	+	1.27911i
$220$		0			0
$221$	5.90551	+	23.6105i	0.397248	+	1.58821i
$222$	−3.52663	+	1.81731i	−0.236692	+	0.121970i
$223$	12.2488	−	12.2488i	0.820241	−	0.820241i	−0.165901	−	0.986142i	$-0.553053\pi$
$223$	12.2488	−	12.2488i	0.820241	−	0.820241i	0.986142	+	0.165901i	$0.0530532\pi$
$224$			10.2111i			0.682256i
$225$		0			0
$226$	2.69021	+	2.69021i	0.178950	+	0.178950i
$227$	10.5073	+	10.5073i	0.697394	+	0.697394i	0.963848	−	0.266454i	$-0.0858519\pi$
$227$	10.5073	+	10.5073i	0.697394	+	0.697394i	−0.266454	+	0.963848i	$0.585852\pi$
$228$	4.76414	+	1.52387i	0.315513	+	0.100920i
$229$	4.44578	−	4.44578i	0.293785	−	0.293785i	−0.544788	−	0.838574i	$-0.683390\pi$
$229$	4.44578	−	4.44578i	0.293785	−	0.293785i	0.838574	+	0.544788i	$0.183390\pi$
$230$		0			0
$231$	−1.48442	+	0.764935i	−0.0976674	+	0.0503290i
$232$	6.58501	+	6.58501i	0.432327	+	0.432327i
$233$			17.6896i			1.15888i	0.815014	+	0.579441i	$0.196729\pi$
$233$			17.6896i			1.15888i	−0.815014	+	0.579441i	$0.803271\pi$
$234$	6.78357	−	2.95914i	0.443456	−	0.193445i
$235$		0			0
$236$	1.99954	−	1.99954i	0.130159	−	0.130159i
$237$	−3.05781	−	5.93393i	−0.198626	−	0.385450i
$238$	−8.13381			−0.527236
$239$	−4.70800	+	4.70800i	−0.304535	+	0.304535i	−0.842785	−	0.538250i	$-0.819086\pi$
$239$	−4.70800	+	4.70800i	−0.304535	+	0.304535i	0.538250	+	0.842785i	$0.319086\pi$
$240$		0			0
$241$	13.7965	−	13.7965i	0.888710	−	0.888710i	−0.105689	−	0.994399i	$-0.533705\pi$
$241$	13.7965	−	13.7965i	0.888710	−	0.888710i	0.994399	+	0.105689i	$0.0337048\pi$
$242$	5.17693	−	5.17693i	0.332786	−	0.332786i
$243$	−10.7673	+	11.2723i	−0.690723	+	0.723119i
$244$			1.78220i			0.114093i
$245$		0			0
$246$	4.39223	+	8.52346i	0.280038	+	0.543436i
$247$	5.82896	+	3.49647i	0.370888	+	0.222475i
$248$	13.8788			0.881303
$249$	−8.90626	+	27.8441i	−0.564411	+	1.76455i
$250$		0			0
$251$	−5.80617			−0.366482			−0.183241	−	0.983068i	$-0.558659\pi$
$251$	−5.80617			−0.366482			−0.183241	+	0.983068i	$0.558659\pi$
$252$	−1.33928	−	7.98181i	−0.0843670	−	0.502807i
$253$	−0.656662	+	0.656662i	−0.0412840	+	0.0412840i
$254$	0.0169163	+	0.0169163i	0.00106142	+	0.00106142i
$255$		0			0
$256$	−9.69045			−0.605653
$257$			8.29597i			0.517488i	0.965946	+	0.258744i	$0.0833087\pi$
$257$			8.29597i			0.517488i	−0.965946	+	0.258744i	$0.916691\pi$
$258$	−4.23839	+	13.2507i	−0.263870	+	0.824952i
$259$			5.89575i			0.366344i
$260$		0			0
$261$	−9.41500	−	6.70944i	−0.582774	−	0.415304i
$262$	−0.541627	+	0.541627i	−0.0334618	+	0.0334618i
$263$	10.8718			0.670383			0.335191	−	0.942150i	$-0.391199\pi$
$263$	10.8718			0.670383			0.335191	+	0.942150i	$0.391199\pi$
$264$	−1.04961	−	2.03684i	−0.0645988	−	0.125359i
$265$		0			0
$266$	−1.60630	+	1.60630i	−0.0984888	+	0.0984888i
$267$	−4.47522	+	13.9911i	−0.273879	+	0.856243i
$268$	−7.15137	−	7.15137i	−0.436839	−	0.436839i
$269$		−	21.6607i		−	1.32068i	−0.750968	−	0.660339i	$-0.770413\pi$
$269$		−	21.6607i		−	1.32068i	0.750968	−	0.660339i	$-0.229587\pi$
$270$		0			0
$271$	−3.57577	+	3.57577i	−0.217213	+	0.217213i	−0.807323	−	0.590110i	$-0.799084\pi$
$271$	−3.57577	+	3.57577i	−0.217213	+	0.217213i	0.590110	+	0.807323i	$0.299084\pi$
$272$			9.51951i			0.577205i
$273$	0.708715	−	10.9754i	0.0428934	−	0.664262i
$274$	2.50238			0.151174
$275$		0			0
$276$	−2.06169	−	4.00086i	−0.124099	−	0.240824i
$277$	17.4880			1.05075			0.525377	−	0.850870i	$-0.323924\pi$
$277$	17.4880			1.05075			0.525377	+	0.850870i	$0.323924\pi$
$278$	−8.07321	−	8.07321i	−0.484199	−	0.484199i
$279$	−16.9922	+	2.85115i	−1.01730	+	0.170694i
$280$		0			0
$281$	−3.48513	−	3.48513i	−0.207906	−	0.207906i	0.595471	−	0.803377i	$-0.296965\pi$
$281$	−3.48513	−	3.48513i	−0.207906	−	0.207906i	−0.803377	+	0.595471i	$0.796965\pi$
$282$	4.59871	+	8.92415i	0.273849	+	0.531426i
$283$	9.47252			0.563083			0.281541	−	0.959549i	$-0.409154\pi$
$283$	9.47252			0.563083			0.281541	+	0.959549i	$0.409154\pi$
$284$	−1.40306	−	1.40306i	−0.0832561	−	0.0832561i
$285$		0			0
$286$	−0.327703	−	1.31017i	−0.0193775	−	0.0774720i
$287$	14.2493			0.841112
$288$	17.1542	−	2.87834i	1.01082	−	0.169608i
$289$	−28.5639			−1.68023
$290$		0			0
$291$	2.41439	+	0.772272i	0.141534	+	0.0452714i
$292$	−12.4287	+	12.4287i	−0.727332	+	0.727332i
$293$	−15.2096	+	15.2096i	−0.888556	+	0.888556i	−0.994384	−	0.105828i	$-0.966251\pi$
$293$	−15.2096	+	15.2096i	−0.888556	+	0.888556i	0.105828	+	0.994384i	$0.466251\pi$
$294$	−4.40035	−	1.40750i	−0.256634	−	0.0820873i
$295$		0			0
$296$	−8.08986			−0.470214
$297$	1.70350	+	2.27814i	0.0988470	+	0.132191i
$298$	16.3912			0.949516
$299$	−1.48410	−	5.93348i	−0.0858275	−	0.343142i
$300$		0			0
$301$	14.6189	+	14.6189i	0.842622	+	0.842622i
$302$	−5.04397			−0.290248
$303$	−14.4772	−	28.0941i	−0.831693	−	1.61396i
$304$	1.87996	+	1.87996i	0.107823	+	0.107823i
$305$		0			0
$306$	2.29280	+	13.6645i	0.131070	+	0.781148i
$307$	−8.64829	−	8.64829i	−0.493584	−	0.493584i	0.415850	−	0.909433i	$-0.363484\pi$
$307$	−8.64829	−	8.64829i	−0.493584	−	0.493584i	−0.909433	+	0.415850i	$0.863484\pi$
$308$	−1.47690			−0.0841541
$309$	−2.89976	−	5.62722i	−0.164962	−	0.320121i
$310$		0			0
$311$	1.51624			0.0859779			0.0429890	−	0.999076i	$-0.486312\pi$
$311$	1.51624			0.0859779			0.0429890	+	0.999076i	$0.486312\pi$
$312$	15.0599	+	0.972464i	0.852600	+	0.0550550i
$313$		−	0.929202i		−	0.0525216i	−0.999655	−	0.0262608i	$-0.991640\pi$
$313$		−	0.929202i		−	0.0525216i	0.999655	−	0.0262608i	$-0.00836004\pi$
$314$	6.30473	−	6.30473i	0.355796	−	0.355796i
$315$		0			0
$316$		−	5.90388i		−	0.332119i
$317$	15.3001	+	15.3001i	0.859342	+	0.859342i	0.991261	−	0.131919i	$-0.0421138\pi$
$317$	15.3001	+	15.3001i	0.859342	+	0.859342i	−0.131919	+	0.991261i	$0.542114\pi$
$318$	3.18215	−	9.94853i	0.178446	−	0.557886i
$319$	−1.49178	+	1.49178i	−0.0835236	+	0.0835236i
$320$		0			0
$321$	−11.8683	−	23.0313i	−0.662421	−	1.28548i
$322$	2.04408			0.113912
$323$	−8.99818	+	8.99818i	−0.500672	+	0.500672i
$324$	−13.0316	+	4.49990i	−0.723979	+	0.249994i
$325$		0			0
$326$		−	3.70986i		−	0.205470i
$327$	−4.04053	+	12.6321i	−0.223442	+	0.698558i
$328$			19.5522i			1.07959i
$329$	14.9192			0.822523
$330$		0			0
$331$	22.1751	+	22.1751i	1.21885	+	1.21885i	0.968034	+	0.250818i	$0.0806997\pi$
$331$	22.1751	+	22.1751i	1.21885	+	1.21885i	0.250818	+	0.968034i	$0.419300\pi$
$332$	−18.2821	+	18.2821i	−1.00336	+	1.00336i
$333$	9.90465	−	1.66192i	0.542771	−	0.0910727i
$334$	−8.77333			−0.480055
$335$		0			0
$336$	1.31059	−	4.09737i	0.0714986	−	0.223530i
$337$	−1.11379			−0.0606718			−0.0303359	−	0.999540i	$-0.509658\pi$
$337$	−1.11379			−0.0606718			−0.0303359	+	0.999540i	$0.509658\pi$
$338$	8.50999	+	2.58785i	0.462883	+	0.140761i
$339$	−4.41164	−	8.56113i	−0.239607	−	0.464977i
$340$		0			0
$341$			3.14412i			0.170264i
$342$	3.15132	+	2.24574i	0.170404	+	0.121436i
$343$	−13.5719	+	13.5719i	−0.732813	+	0.732813i
$344$	−20.0594	+	20.0594i	−1.08153	+	1.08153i
$345$		0			0
$346$	−2.24442	+	2.24442i	−0.120661	+	0.120661i
$347$	−14.9572			−0.802946			−0.401473	−	0.915871i	$-0.631502\pi$
$347$	−14.9572			−0.802946			−0.401473	+	0.915871i	$0.631502\pi$
$348$	−4.68366	−	9.08901i	−0.251071	−	0.487222i
$349$	−8.13022	+	8.13022i	−0.435201	+	0.435201i	−0.890393	−	0.455192i	$-0.849570\pi$
$349$	−8.13022	+	8.13022i	−0.435201	+	0.435201i	0.455192	+	0.890393i	$0.349570\pi$
$350$		0			0
$351$	−18.6381	+	1.90318i	−0.994827	+	0.101584i
$352$		−	3.17410i		−	0.169180i
$353$	14.0281	+	14.0281i	0.746638	+	0.746638i	0.973846	−	0.227208i	$-0.0729598\pi$
$353$	14.0281	+	14.0281i	0.746638	+	0.746638i	−0.227208	+	0.973846i	$0.572960\pi$
$354$	1.94465	−	1.00210i	0.103357	−	0.0532610i
$355$		0			0
$356$	−9.18642	+	9.18642i	−0.486879	+	0.486879i
$357$	19.6115	+	6.27297i	1.03795	+	0.332001i
$358$	−6.42958	−	6.42958i	−0.339814	−	0.339814i
$359$	14.0085	+	14.0085i	0.739341	+	0.739341i	0.972451	−	0.233109i	$-0.0748900\pi$
$359$	14.0085	+	14.0085i	0.739341	+	0.739341i	−0.233109	+	0.972451i	$0.574890\pi$
$360$		0			0
$361$		−	15.4460i		−	0.812947i
$362$	11.2792	−	11.2792i	0.592822	−	0.592822i
$363$	−16.4747	+	8.48959i	−0.864698	+	0.445588i
$364$	5.00356	−	8.34145i	0.262258	−	0.437211i
$365$		0			0
$366$	−0.420050	+	1.31322i	−0.0219564	+	0.0686433i
$367$		−	26.2282i		−	1.36910i	−0.728966	−	0.684549i	$-0.759999\pi$
$367$		−	26.2282i		−	1.36910i	0.728966	−	0.684549i	$-0.240001\pi$
$368$		−	2.39232i		−	0.124708i
$369$	−4.01667	−	23.9384i	−0.209099	−	1.24618i
$370$		0			0
$371$	−10.9758	−	10.9758i	−0.569835	−	0.569835i
$372$	−14.5138	−	4.64242i	−0.752508	−	0.240698i
$373$		−	6.83702i		−	0.354007i	−0.984210	−	0.177004i	$-0.943360\pi$
$373$		−	6.83702i		−	0.354007i	0.984210	−	0.177004i	$-0.0566404\pi$
$374$	2.52839			0.130740
$375$		0			0
$376$			20.4714i			1.05573i
$377$	−3.37151	−	13.4795i	−0.173642	−	0.694227i
$378$	0.894389	−	6.19711i	0.0460024	−	0.318745i
$379$	24.8881	+	24.8881i	1.27842	+	1.27842i	0.941553	+	0.336864i	$0.109366\pi$
$379$	24.8881	+	24.8881i	1.27842	+	1.27842i	0.336864	+	0.941553i	$0.390634\pi$
$380$		0			0
$381$	−0.0277408	−	0.0538332i	−0.00142121	−	0.00275796i
$382$	3.10018	−	3.10018i	0.158619	−	0.158619i
$383$	−7.76391	−	7.76391i	−0.396717	−	0.396717i	0.480356	−	0.877073i	$-0.340507\pi$
$383$	−7.76391	−	7.76391i	−0.396717	−	0.396717i	−0.877073	+	0.480356i	$0.840507\pi$
$384$	17.8360	+	5.70504i	0.910188	+	0.291134i
$385$		0			0
$386$			15.5914i			0.793579i
$387$	20.4384	−	28.6801i	1.03894	−	1.45789i
$388$	1.58526	+	1.58526i	0.0804796	+	0.0804796i
$389$	−6.30333			−0.319591			−0.159796	−	0.987150i	$-0.551084\pi$
$389$	−6.30333			−0.319591			−0.159796	+	0.987150i	$0.551084\pi$
$390$		0			0
$391$	11.4505			0.579078
$392$	−6.66141	−	6.66141i	−0.336452	−	0.336452i
$393$	1.72364	−	0.888208i	0.0869460	−	0.0448042i
$394$		−	10.9618i		−	0.552247i
$395$		0			0
$396$	0.416315	+	2.48114i	0.0209206	+	0.124682i
$397$	−24.3714	−	24.3714i	−1.22317	−	1.22317i	−0.966500	−	0.256665i	$-0.917376\pi$
$397$	−24.3714	−	24.3714i	−1.22317	−	1.22317i	−0.256665	−	0.966500i	$-0.582624\pi$
$398$	11.1670	−	11.1670i	0.559753	−	0.559753i
$399$	5.11179	−	2.63416i	0.255910	−	0.131873i
$400$		0			0
$401$	−8.82040	−	8.82040i	−0.440470	−	0.440470i	0.451700	−	0.892170i	$-0.350818\pi$
$401$	−8.82040	−	8.82040i	−0.440470	−	0.440470i	−0.892170	+	0.451700i	$0.850818\pi$
$402$	−3.58401	−	6.95506i	−0.178754	−	0.346887i
$403$	−17.7578	−	10.6519i	−0.884580	−	0.530609i
$404$		−	27.9518i		−	1.39066i
$405$		0			0
$406$	4.64367			0.230461
$407$		−	1.83269i		−	0.0908430i
$408$	−8.60746	+	26.9099i	−0.426133	+	1.33224i
$409$	10.2362	+	10.2362i	0.506149	+	0.506149i	0.913342	−	0.407193i	$-0.133492\pi$
$409$	10.2362	+	10.2362i	0.506149	+	0.506149i	−0.407193	+	0.913342i	$0.633492\pi$
$410$		0			0
$411$	−6.03352	−	1.92989i	−0.297612	−	0.0951945i
$412$		−	5.59872i		−	0.275829i
$413$		−	3.25103i		−	0.159973i
$414$	−0.576195	−	3.43398i	−0.0283185	−	0.168771i
$415$		0			0
$416$	17.9271	+	10.7535i	0.878951	+	0.527233i
$417$	13.2392	+	25.6916i	0.648325	+	1.25812i
$418$	0.499318	−	0.499318i	0.0244224	−	0.0244224i
$419$		−	39.8238i		−	1.94552i	−0.231818	−	0.972759i	$-0.574467\pi$
$419$		−	39.8238i		−	1.94552i	0.231818	−	0.972759i	$-0.425533\pi$
$420$		0			0
$421$	−11.1187	−	11.1187i	−0.541893	−	0.541893i	0.382190	−	0.924084i	$-0.375170\pi$
$421$	−11.1187	−	11.1187i	−0.541893	−	0.541893i	−0.924084	+	0.382190i	$0.875170\pi$
$422$	−4.37665	−	4.37665i	−0.213052	−	0.213052i
$423$	−4.20550	−	25.0637i	−0.204478	−	1.21864i
$424$	15.0605	−	15.0605i	0.731400	−	0.731400i
$425$		0			0
$426$	−0.703162	−	1.36454i	−0.0340683	−	0.0661122i
$427$	1.44883	+	1.44883i	0.0701136	+	0.0701136i
$428$		−	22.9146i		−	1.10762i
$429$	−0.220304	+	3.41170i	−0.0106364	+	0.164718i
$430$		0			0
$431$	−5.22718	+	5.22718i	−0.251784	+	0.251784i	−0.821702	−	0.569917i	$-0.806975\pi$
$431$	−5.22718	+	5.22718i	−0.251784	+	0.251784i	0.569917	+	0.821702i	$0.306975\pi$
$432$	−7.25286	−	1.04676i	−0.348954	−	0.0503623i
$433$	2.96201			0.142345			0.0711727	−	0.997464i	$-0.477326\pi$
$433$	2.96201			0.142345			0.0711727	+	0.997464i	$0.477326\pi$
$434$	4.89357	−	4.89357i	0.234899	−	0.234899i
$435$		0			0
$436$	−8.29411	+	8.29411i	−0.397216	+	0.397216i
$437$	2.26130	−	2.26130i	0.108173	−	0.108173i
$438$	−12.0875	+	6.22880i	−0.577562	+	0.297624i
$439$			21.3756i			1.02020i	0.860114	+	0.510101i	$0.170392\pi$
$439$			21.3756i			1.02020i	−0.860114	+	0.510101i	$0.829608\pi$
$440$		0			0
$441$	9.52424	+	6.78729i	0.453535	+	0.323204i
$442$	−8.56588	+	14.2802i	−0.407437	+	0.679239i
$443$	−20.6824			−0.982650			−0.491325	−	0.870976i	$-0.663487\pi$
$443$	−20.6824			−0.982650			−0.491325	+	0.870976i	$0.663487\pi$
$444$	8.46004	+	2.70604i	0.401496	+	0.128423i
$445$		0			0
$446$	11.8522			0.561220
$447$	−39.5210	−	12.6412i	−1.86928	−	0.597910i
$448$	−1.42777	+	1.42777i	−0.0674559	+	0.0674559i
$449$	29.1294	+	29.1294i	1.37470	+	1.37470i	0.853328	+	0.521375i	$0.174581\pi$
$449$	29.1294	+	29.1294i	1.37470	+	1.37470i	0.521375	+	0.853328i	$0.325419\pi$
$450$		0			0
$451$	−4.42939			−0.208572
$452$		−	8.51778i		−	0.400643i
$453$	12.1616	+	3.89002i	0.571401	+	0.182769i
$454$			10.1671i			0.477166i
$455$		0			0
$456$	3.61446	+	7.01415i	0.169263	+	0.328468i
$457$	2.59392	−	2.59392i	0.121338	−	0.121338i	−0.643830	−	0.765168i	$-0.722656\pi$
$457$	2.59392	−	2.59392i	0.121338	−	0.121338i	0.765168	+	0.643830i	$0.222656\pi$
$458$	4.30184			0.201012
$459$	5.01018	−	34.7149i	0.233855	−	1.62035i
$460$		0			0
$461$	18.1031	−	18.1031i	0.843144	−	0.843144i	−0.146123	−	0.989266i	$-0.546679\pi$
$461$	18.1031	−	18.1031i	0.843144	−	0.843144i	0.989266	+	0.146123i	$0.0466794\pi$
$462$	−1.08826	−	0.348093i	−0.0506306	−	0.0161948i
$463$	−19.7500	−	19.7500i	−0.917862	−	0.917862i	0.0790114	−	0.996874i	$-0.474824\pi$
$463$	−19.7500	−	19.7500i	−0.917862	−	0.917862i	−0.996874	+	0.0790114i	$0.974824\pi$
$464$		−	5.43478i		−	0.252303i
$465$		0			0
$466$	−8.55842	+	8.55842i	−0.396461	+	0.396461i
$467$			2.98569i			0.138161i	0.997611	+	0.0690807i	$0.0220066\pi$
$467$			2.98569i			0.138161i	−0.997611	+	0.0690807i	$0.977993\pi$
$468$	−15.4238	−	6.05448i	−0.712963	−	0.279868i
$469$	−11.6273			−0.536900
$470$		0			0
$471$	−20.0637	+	10.3391i	−0.924488	+	0.476398i
$472$	4.46090			0.205330
$473$	−4.54428	−	4.54428i	−0.208946	−	0.208946i
$474$	1.39150	−	4.35031i	0.0639136	−	0.199816i
$475$		0			0
$476$	12.8767	+	12.8767i	0.590202	+	0.590202i
$477$	−15.3450	+	21.5329i	−0.702601	+	0.985922i
$478$	−4.55557			−0.208367
$479$	−4.61160	−	4.61160i	−0.210710	−	0.210710i	0.593859	−	0.804569i	$-0.297604\pi$
$479$	−4.61160	−	4.61160i	−0.210710	−	0.210710i	−0.804569	+	0.593859i	$0.797604\pi$
$480$		0			0
$481$	10.3509	+	6.20893i	0.471962	+	0.283103i
$482$	13.3498			0.608067
$483$	−4.92851	−	1.57644i	−0.224255	−	0.0717305i
$484$	−16.3913			−0.745058
$485$		0			0
$486$	−10.6630	+	0.244328i	−0.483685	+	0.0110829i
$487$	−22.7100	+	22.7100i	−1.02909	+	1.02909i	−0.0295239	+	0.999564i	$0.509399\pi$
$487$	−22.7100	+	22.7100i	−1.02909	+	1.02909i	−0.999564	+	0.0295239i	$0.990601\pi$
$488$	−1.98801	+	1.98801i	−0.0899928	+	0.0899928i
$489$	−2.86112	+	8.94488i	−0.129384	+	0.404501i
$490$		0			0
$491$	−32.8134			−1.48085			−0.740423	−	0.672141i	$-0.765375\pi$
$491$	−32.8134			−1.48085			−0.740423	+	0.672141i	$0.765375\pi$
$492$	6.54019	−	20.4469i	0.294854	−	0.921819i
$493$	26.0128			1.17156
$494$	1.12849	+	4.51175i	0.0507732	+	0.202993i
$495$		0			0
$496$	−5.72725	−	5.72725i	−0.257161	−	0.257161i
$497$	−2.28121			−0.102326
$498$	−17.7803	+	9.16235i	−0.796753	+	0.410575i
$499$	−0.358414	−	0.358414i	−0.0160448	−	0.0160448i	0.699039	−	0.715084i	$-0.253611\pi$
$499$	−0.358414	−	0.358414i	−0.0160448	−	0.0160448i	−0.715084	+	0.699039i	$0.753611\pi$
$500$		0			0
$501$	21.1535	+	6.76618i	0.945067	+	0.302291i
$502$	−2.80909	−	2.80909i	−0.125376	−	0.125376i
$503$	−1.20071			−0.0535371			−0.0267685	−	0.999642i	$-0.508522\pi$
$503$	−1.20071			−0.0535371			−0.0267685	+	0.999642i	$0.508522\pi$
$504$	7.40961	−	10.3975i	0.330050	−	0.463141i
$505$		0			0
$506$	−0.635401			−0.0282470
$507$	−18.5227	−	12.8027i	−0.822623	−	0.568587i
$508$		−	0.0535606i		−	0.00237637i
$509$	−16.5736	+	16.5736i	−0.734613	+	0.734613i	−0.971530	−	0.236917i	$-0.923863\pi$
$509$	−16.5736	+	16.5736i	−0.734613	+	0.734613i	0.236917	+	0.971530i	$0.423863\pi$
$510$		0			0
$511$			20.2076i			0.893931i
$512$	10.6015	+	10.6015i	0.468524	+	0.468524i
$513$	−5.86623	−	7.84510i	−0.259000	−	0.346369i
$514$	−4.01369	+	4.01369i	−0.177036	+	0.177036i
$515$		0			0
$516$	27.6871	−	14.2675i	1.21886	−	0.628090i
$517$	−4.63762			−0.203962
$518$	−2.85243	+	2.85243i	−0.125329	+	0.125329i
$519$	7.14250	−	3.68061i	0.313521	−	0.161561i
$520$		0			0
$521$		−	24.5938i		−	1.07747i	−0.842474	−	0.538736i	$-0.818902\pi$
$521$		−	24.5938i		−	1.07747i	0.842474	−	0.538736i	$-0.181098\pi$
$522$	−1.30898	−	7.80120i	−0.0572924	−	0.341449i
$523$			38.6626i			1.69060i	0.534294	+	0.845299i	$0.320578\pi$
$523$			38.6626i			1.69060i	−0.534294	+	0.845299i	$0.679422\pi$
$524$	1.71491			0.0749161
$525$		0			0
$526$	5.25989	+	5.25989i	0.229342	+	0.229342i
$527$	27.4127	−	27.4127i	1.19412	−	1.19412i
$528$	−0.407396	+	1.27366i	−0.0177296	+	0.0554291i
$529$	20.1224			0.874887
$530$		0			0
$531$	−5.46161	+	0.916415i	−0.237014	+	0.0397690i
$532$	5.08590			0.220502
$533$	15.0063	−	25.0170i	0.649994	−	1.08361i
$534$	−8.93424	+	4.60391i	−0.386622	+	0.199231i
$535$		0			0
$536$		−	15.9544i		−	0.689126i
$537$	10.5438	+	20.4611i	0.454998	+	0.882960i
$538$	10.4797	−	10.4797i	0.451812	−	0.451812i
$539$	1.50909	−	1.50909i	0.0650010	−	0.0650010i
$540$		0			0
$541$	−1.35568	+	1.35568i	−0.0582854	+	0.0582854i	−0.735649	−	0.677363i	$-0.763123\pi$
$541$	−1.35568	+	1.35568i	−0.0582854	+	0.0582854i	0.677363	+	0.735649i	$0.263123\pi$
$542$	−3.46000			−0.148620
$543$	−35.8942	+	18.4967i	−1.54037	+	0.793768i
$544$	−27.6741	+	27.6741i	−1.18652	+	1.18652i
$545$		0			0
$546$	5.65292	−	4.96715i	0.241923	−	0.212574i
$547$			19.9892i			0.854675i	0.904092	+	0.427338i	$0.140548\pi$
$547$			19.9892i			0.854675i	−0.904092	+	0.427338i	$0.859452\pi$
$548$	−3.96154	−	3.96154i	−0.169229	−	0.169229i
$549$	2.02557	−	2.84238i	0.0864493	−	0.121310i
$550$		0			0
$551$	5.13714	−	5.13714i	0.218850	−	0.218850i
$552$	2.16311	−	6.76266i	0.0920682	−	0.287838i
$553$	−4.79952	−	4.79952i	−0.204096	−	0.204096i
$554$	8.46092	+	8.46092i	0.359470	+	0.359470i
$555$		0			0
$556$			25.5615i			1.08405i
$557$	−9.29058	+	9.29058i	−0.393655	+	0.393655i	−0.875988	−	0.482333i	$-0.839789\pi$
$557$	−9.29058	+	9.29058i	−0.393655	+	0.393655i	0.482333	+	0.875988i	$0.339789\pi$
$558$	−9.60044	−	6.84160i	−0.406419	−	0.289628i
$559$	41.0614	−	10.2704i	1.73671	−	0.434390i
$560$		0			0
$561$	−6.09622	−	1.94995i	−0.257383	−	0.0823268i
$562$		−	3.37230i		−	0.142252i
$563$		−	43.3391i		−	1.82653i	−0.407370	−	0.913263i	$-0.633554\pi$
$563$		−	43.3391i		−	1.82653i	0.407370	−	0.913263i	$-0.366446\pi$
$564$	6.84764	−	21.4081i	0.288338	−	0.901446i
$565$		0			0
$566$	4.58292	+	4.58292i	0.192634	+	0.192634i
$567$	−6.93581	+	14.2521i	−0.291277	+	0.598533i
$568$		−	3.13016i		−	0.131339i
$569$	7.47436			0.313342			0.156671	−	0.987651i	$-0.449924\pi$
$569$	7.47436			0.313342			0.156671	+	0.987651i	$0.449924\pi$
$570$		0			0
$571$			20.1324i			0.842516i	0.906941	+	0.421258i	$0.138411\pi$
$571$			20.1324i			0.842516i	−0.906941	+	0.421258i	$0.861589\pi$
$572$	−1.55535	+	2.59293i	−0.0650325	+	0.108416i
$573$	−9.86580	+	5.08395i	−0.412150	+	0.212385i
$574$	6.89400	+	6.89400i	0.287750	+	0.287750i
$575$		0			0
$576$	2.80107	+	1.99614i	0.116711	+	0.0831725i
$577$	−12.5798	+	12.5798i	−0.523705	+	0.523705i	−0.918688	−	0.394983i	$-0.870750\pi$
$577$	−12.5798	+	12.5798i	−0.523705	+	0.523705i	0.394983	+	0.918688i	$0.370750\pi$
$578$	−13.8195	−	13.8195i	−0.574817	−	0.574817i
$579$	12.0244	−	37.5925i	0.499716	−	1.56229i
$580$		0			0
$581$			29.7247i			1.23319i
$582$	0.794478	+	1.54175i	0.0329322	+	0.0639075i
$583$	3.41182	+	3.41182i	0.141303	+	0.141303i
$584$	−27.7278			−1.14739
$585$		0			0
$586$	−14.7172			−0.607962
$587$	0.511868	+	0.511868i	0.0211270	+	0.0211270i	0.717591	−	0.696464i	$-0.245245\pi$
$587$	0.511868	+	0.511868i	0.0211270	+	0.0211270i	−0.696464	+	0.717591i	$0.745245\pi$
$588$	4.73800	+	9.19446i	0.195392	+	0.379173i
$589$		−	10.8272i		−	0.446127i
$590$		0			0
$591$	−8.45397	+	26.4301i	−0.347750	+	1.08719i
$592$	3.33838	+	3.33838i	0.137207	+	0.137207i
$593$	−13.2208	+	13.2208i	−0.542911	+	0.542911i	−0.924381	−	0.381470i	$-0.875418\pi$
$593$	−13.2208	+	13.2208i	−0.542911	+	0.542911i	0.381470	+	0.924381i	$0.375418\pi$
$594$	−0.278020	+	1.92636i	−0.0114073	+	0.0790397i
$595$		0			0
$596$	−25.9490	−	25.9490i	−1.06291	−	1.06291i
$597$	−35.5372	+	18.3127i	−1.45444	+	0.749489i
$598$	2.15266	−	3.58871i	0.0880290	−	0.146753i
$599$			32.7474i			1.33802i	0.743253	+	0.669011i	$0.233282\pi$
$599$			32.7474i			1.33802i	−0.743253	+	0.669011i	$0.766718\pi$
$600$		0			0
$601$	11.3682			0.463718			0.231859	−	0.972749i	$-0.425519\pi$
$601$	11.3682			0.463718			0.231859	+	0.972749i	$0.425519\pi$
$602$			14.1456i			0.576533i
$603$	3.27756	+	19.5335i	0.133473	+	0.795465i
$604$	7.98515	+	7.98515i	0.324911	+	0.324911i
$605$		0			0
$606$	6.58803	−	20.5965i	0.267620	−	0.836675i
$607$		−	17.5226i		−	0.711221i	−0.934634	−	0.355610i	$-0.884273\pi$
$607$		−	17.5226i		−	0.711221i	0.934634	−	0.355610i	$-0.115727\pi$
$608$			10.9304i			0.443288i
$609$	−11.1964	−	3.58130i	−0.453701	−	0.145121i
$610$		0			0
$611$	15.7117	−	26.1930i	0.635628	−	1.05966i
$612$	18.0026	−	25.2621i	0.727714	−	1.02116i
$613$	22.5157	−	22.5157i	0.909399	−	0.909399i	−0.0868247	−	0.996224i	$-0.527672\pi$
$613$	22.5157	−	22.5157i	0.909399	−	0.909399i	0.996224	+	0.0868247i	$0.0276720\pi$
$614$		−	8.36829i		−	0.337717i
$615$		0			0
$616$	−1.64745	−	1.64745i	−0.0663777	−	0.0663777i
$617$	−3.20157	−	3.20157i	−0.128891	−	0.128891i	0.639719	−	0.768609i	$-0.279051\pi$
$617$	−3.20157	−	3.20157i	−0.128891	−	0.128891i	−0.768609	+	0.639719i	$0.779051\pi$
$618$	1.31957	−	4.12545i	0.0530811	−	0.165950i
$619$	−6.99088	+	6.99088i	−0.280987	+	0.280987i	−0.833503	−	0.552515i	$-0.813668\pi$
$619$	−6.99088	+	6.99088i	−0.280987	+	0.280987i	0.552515	+	0.833503i	$0.313668\pi$
$620$		0			0
$621$	−1.25909	+	8.72409i	−0.0505256	+	0.350086i
$622$	0.733573	+	0.733573i	0.0294136	+	0.0294136i
$623$			14.9361i			0.598401i
$624$	−5.81337	−	6.61597i	−0.232721	−	0.264851i
$625$		0			0
$626$	0.449559	−	0.449559i	0.0179680	−	0.0179680i
$627$	−1.58900	+	0.818826i	−0.0634584	+	0.0327008i
$628$	−19.9621			−0.796576
$629$	−15.9787	+	15.9787i	−0.637114	+	0.637114i
$630$		0			0
$631$	19.6866	−	19.6866i	0.783711	−	0.783711i	−0.196744	−	0.980455i	$-0.563037\pi$
$631$	19.6866	−	19.6866i	0.783711	−	0.783711i	0.980455	+	0.196744i	$0.0630369\pi$
$632$	6.58566	−	6.58566i	0.261963	−	0.261963i
$633$	7.17722	+	13.9279i	0.285269	+	0.553586i
$634$			14.8048i			0.587973i
$635$		0			0
$636$	−20.7873	+	10.7119i	−0.824270	+	0.424755i
$637$	3.41063	+	13.6359i	0.135134	+	0.540272i
$638$	−1.44348			−0.0571479
$639$	0.643038	+	3.83235i	0.0254382	+	0.151605i
$640$		0			0
$641$	7.99599			0.315822			0.157911	−	0.987453i	$-0.449524\pi$
$641$	7.99599			0.315822			0.157911	+	0.987453i	$0.449524\pi$
$642$	5.40080	−	16.8848i	0.213153	−	0.666390i
$643$	−15.0350	+	15.0350i	−0.592922	+	0.592922i	−0.938420	−	0.345498i	$-0.887710\pi$
$643$	−15.0350	+	15.0350i	−0.592922	+	0.592922i	0.345498	+	0.938420i	$0.387710\pi$
$644$	−3.23600	−	3.23600i	−0.127516	−	0.127516i
$645$		0			0
$646$	−8.70685			−0.342566
$647$			5.28617i			0.207821i	0.994587	+	0.103910i	$0.0331355\pi$
$647$			5.28617i			0.207821i	−0.994587	+	0.103910i	$0.966864\pi$
$648$	−19.5561	−	9.51698i	−0.768235	−	0.373862i
$649$			1.01058i			0.0396687i
$650$		0			0
$651$	−15.5730	+	8.02491i	−0.610353	+	0.314521i
$652$	−5.87311	+	5.87311i	−0.230009	+	0.230009i
$653$	−26.0947			−1.02116			−0.510581	−	0.859829i	$-0.670570\pi$
$653$	−26.0947			−1.02116			−0.510581	+	0.859829i	$0.670570\pi$
$654$	−8.06643	+	4.15671i	−0.315422	+	0.162540i
$655$		0			0
$656$	8.06848	−	8.06848i	0.315021	−	0.315021i
$657$	33.9480	−	5.69621i	1.32444	−	0.222230i
$658$	7.21809	+	7.21809i	0.281390	+	0.281390i
$659$			10.5160i			0.409646i	0.978799	+	0.204823i	$0.0656618\pi$
$659$			10.5160i			0.409646i	−0.978799	+	0.204823i	$0.934338\pi$
$660$		0			0
$661$	−19.9999	+	19.9999i	−0.777907	+	0.777907i	−0.979475	−	0.201567i	$-0.935397\pi$
$661$	−19.9999	+	19.9999i	−0.777907	+	0.777907i	0.201567	+	0.979475i	$0.435397\pi$
$662$			21.4571i			0.833955i
$663$	31.6665	−	27.8249i	1.22982	−	1.08063i
$664$	−40.7867			−1.58283
$665$		0			0
$666$	5.59604	+	3.98793i	0.216842	+	0.154529i
$667$	−6.53721			−0.253122
$668$	13.8891	+	13.8891i	0.537386	+	0.537386i
$669$	−28.5771	−	9.14070i	−1.10485	−	0.353400i
$670$		0			0
$671$	−0.450366	−	0.450366i	−0.0173862	−	0.0173862i
$672$	15.7215	−	8.10143i	0.606469	−	0.312520i
$673$	−0.230805			−0.00889689			−0.00444844	−	0.999990i	$-0.501416\pi$
$673$	−0.230805			−0.00889689			−0.00444844	+	0.999990i	$0.501416\pi$
$674$	−0.538863	−	0.538863i	−0.0207562	−	0.0207562i
$675$		0			0
$676$	−9.37538	−	17.5691i	−0.360592	−	0.675734i
$677$	−41.4875			−1.59449			−0.797247	−	0.603654i	$-0.793711\pi$
$677$	−41.4875			−1.59449			−0.797247	+	0.603654i	$0.793711\pi$
$678$	2.00757	−	6.27638i	0.0771004	−	0.241043i
$679$	2.57746			0.0989138
$680$		0			0
$681$	7.84109	−	24.5140i	0.300471	−	0.939379i
$682$	−1.52116	+	1.52116i	−0.0582483	+	0.0582483i
$683$	31.7789	−	31.7789i	1.21599	−	1.21599i	0.246960	−	0.969026i	$-0.420568\pi$
$683$	31.7789	−	31.7789i	1.21599	−	1.21599i	0.969026	−	0.246960i	$-0.0794317\pi$
$684$	−1.43364	−	8.54414i	−0.0548165	−	0.326693i
$685$		0			0
$686$	−13.1325			−0.501400
$687$	−10.3722	−	3.31767i	−0.395724	−	0.126577i
$688$	16.5555			0.631174
$689$	−30.8286	+	7.71092i	−1.17448	+	0.293763i
$690$		0			0
$691$	25.0328	+	25.0328i	0.952293	+	0.952293i	0.998913	−	0.0466196i	$-0.0148449\pi$
$691$	25.0328	+	25.0328i	0.952293	+	0.952293i	−0.0466196	+	0.998913i	$0.514845\pi$
$692$	7.10633			0.270142
$693$	2.35546	+	1.67858i	0.0894767	+	0.0637641i
$694$	−7.23648	−	7.23648i	−0.274693	−	0.274693i
$695$		0			0
$696$	4.91408	−	15.3631i	0.186268	−	0.582338i
$697$	38.6187	+	38.6187i	1.46279	+	1.46279i
$698$	−7.86699			−0.297770
$699$	27.2357	−	14.0349i	1.03015	−	0.530847i
$700$		0			0
$701$	−27.4234			−1.03577			−0.517883	−	0.855451i	$-0.673280\pi$
$701$	−27.4234			−1.03577			−0.517883	+	0.855451i	$0.673280\pi$
$702$	−9.93810	−	8.09654i	−0.375090	−	0.305584i
$703$			6.31112i			0.238028i
$704$	0.443822	−	0.443822i	0.0167272	−	0.0167272i
$705$		0			0
$706$			13.5739i			0.510859i
$707$	−22.7233	−	22.7233i	−0.854596	−	0.854596i
$708$	−4.66502	−	1.49216i	−0.175322	−	0.0560789i
$709$	0.997734	−	0.997734i	0.0374707	−	0.0374707i	−0.688123	−	0.725594i	$-0.741565\pi$
$709$	0.997734	−	0.997734i	0.0374707	−	0.0374707i	0.725594	+	0.688123i	$0.241565\pi$
$710$		0			0
$711$	−6.71010	+	9.41592i	−0.251649	+	0.353125i
$712$	−20.4945			−0.768066
$713$	−6.88901	+	6.88901i	−0.257996	+	0.257996i
$714$	6.45334	+	12.5232i	0.241510	+	0.468669i
$715$		0			0
$716$			20.3574i			0.760793i
$717$	10.9840	+	3.51336i	0.410205	+	0.131209i
$718$			13.5550i			0.505867i
$719$	13.8518			0.516585			0.258292	−	0.966067i	$-0.416840\pi$
$719$	13.8518			0.516585			0.258292	+	0.966067i	$0.416840\pi$
$720$		0			0
$721$	−4.55144	−	4.55144i	−0.169505	−	0.169505i
$722$	7.47295	−	7.47295i	0.278115	−	0.278115i
$723$	−32.1879	−	10.2957i	−1.19708	−	0.382900i
$724$	−35.7124			−1.32724
$725$		0			0
$726$	−12.0780	−	3.86330i	−0.448258	−	0.143380i
$727$	36.0915			1.33856			0.669280	−	0.743010i	$-0.266603\pi$
$727$	36.0915			1.33856			0.669280	+	0.743010i	$0.266603\pi$
$728$	14.8861	−	3.72335i	0.551715	−	0.137996i
$729$	25.8982	+	7.63446i	0.959191	+	0.282758i
$730$		0			0
$731$			79.2408i			2.93083i
$732$	2.74396	−	1.41399i	0.101420	−	0.0522626i
$733$	13.0564	−	13.0564i	0.482248	−	0.482248i	−0.423601	−	0.905849i	$-0.639234\pi$
$733$	13.0564	−	13.0564i	0.482248	−	0.482248i	0.905849	+	0.423601i	$0.139234\pi$
$734$	12.6895	−	12.6895i	0.468378	−	0.468378i
$735$		0			0
$736$	6.95471	−	6.95471i	0.256354	−	0.256354i
$737$	3.61434			0.133136
$738$	9.63836	−	13.5250i	0.354793	−	0.497861i
$739$	−12.8744	+	12.8744i	−0.473592	+	0.473592i	−0.903075	−	0.429483i	$-0.858696\pi$
$739$	−12.8744	+	12.8744i	−0.473592	+	0.473592i	0.429483	+	0.903075i	$0.358696\pi$
$740$		0			0
$741$	0.758645	−	11.7486i	0.0278695	−	0.431597i
$742$		−	10.6204i		−	0.389889i
$743$	20.7742	+	20.7742i	0.762133	+	0.762133i	0.976708	−	0.214575i	$-0.0688366\pi$
$743$	20.7742	+	20.7742i	0.762133	+	0.762133i	−0.214575	+	0.976708i	$0.568837\pi$
$744$	−11.0114	−	21.3685i	−0.403697	−	0.783405i
$745$		0			0
$746$	3.30783	−	3.30783i	0.121108	−	0.121108i
$747$	49.9364	−	8.37893i	1.82708	−	0.306569i
$748$	−4.00271	−	4.00271i	−0.146354	−	0.146354i
$749$	−18.6283	−	18.6283i	−0.680663	−	0.680663i
$750$		0			0
$751$			14.1702i			0.517080i	0.966001	+	0.258540i	$0.0832413\pi$
$751$			14.1702i			0.517080i	−0.966001	+	0.258540i	$0.916759\pi$
$752$	8.44779	−	8.44779i	0.308059	−	0.308059i
$753$	4.60660	+	8.93946i	0.167874	+	0.325772i
$754$	4.89034	−	8.15270i	0.178096	−	0.296904i
$755$		0			0
$756$	−11.2266	+	8.39477i	−0.408308	+	0.305315i
$757$		−	27.8108i		−	1.01080i	−0.862885	−	0.505400i	$-0.831345\pi$
$757$		−	27.8108i		−	1.01080i	0.862885	−	0.505400i	$-0.168655\pi$
$758$			24.0823i			0.874710i
$759$	1.53202	+	0.490035i	0.0556089	+	0.0177871i
$760$		0			0
$761$	−3.88054	−	3.88054i	−0.140669	−	0.140669i	0.633265	−	0.773935i	$-0.281714\pi$
$761$	−3.88054	−	3.88054i	−0.140669	−	0.140669i	−0.773935	+	0.633265i	$0.781714\pi$
$762$	0.0126238	−	0.0394665i	0.000457313	−	0.00142972i
$763$			13.4853i			0.488200i
$764$	−9.81584			−0.355125
$765$		0			0
$766$		−	7.51254i		−	0.271439i
$767$	−5.70769	−	3.42372i	−0.206093	−	0.123623i
$768$	7.68838	+	14.9199i	0.277430	+	0.538375i
$769$	22.5865	+	22.5865i	0.814491	+	0.814491i	0.985304	−	0.170813i	$-0.0546393\pi$
$769$	22.5865	+	22.5865i	0.814491	+	0.814491i	−0.170813	+	0.985304i	$0.554639\pi$
$770$		0			0
$771$	12.7729	−	6.58200i	0.460004	−	0.237045i
$772$	24.6828	−	24.6828i	0.888353	−	0.888353i
$773$	25.7487	+	25.7487i	0.926116	+	0.926116i	0.997452	−	0.0713367i	$-0.0227265\pi$
$773$	25.7487	+	25.7487i	0.926116	+	0.926116i	−0.0713367	+	0.997452i	$0.522726\pi$
$774$	23.7642	−	3.98744i	0.854185	−	0.143325i
$775$		0			0
$776$			3.53666i			0.126959i
$777$	9.07739	−	4.67767i	0.325650	−	0.167811i
$778$	−3.04962	−	3.04962i	−0.109334	−	0.109334i
$779$	15.2532			0.546504
$780$		0			0
$781$	0.709112			0.0253740
$782$	5.53990	+	5.53990i	0.198106	+	0.198106i
$783$	−2.86036	+	19.8191i	−0.102221	+	0.708275i
$784$			5.49784i			0.196351i
$785$		0			0
$786$	1.26364	+	0.404190i	0.0450726	+	0.0144170i
$787$	−19.7231	−	19.7231i	−0.703054	−	0.703054i	0.262011	−	0.965065i	$-0.415614\pi$
$787$	−19.7231	−	19.7231i	−0.703054	−	0.703054i	−0.965065	+	0.262011i	$0.915614\pi$
$788$	−17.3537	+	17.3537i	−0.618200	+	0.618200i
$789$	−8.62564	−	16.7387i	−0.307081	−	0.595915i
$790$		0			0
$791$	−6.92447	−	6.92447i	−0.246206	−	0.246206i
$792$	−2.30327	+	3.23205i	−0.0818431	+	0.114846i
$793$	4.06943	−	1.01786i	0.144510	−	0.0361451i
$794$		−	23.5823i		−	0.836906i
$795$		0			0
$796$	−35.3573			−1.25321
$797$			27.0871i			0.959474i	0.877412	+	0.479737i	$0.159268\pi$
$797$			27.0871i			0.959474i	−0.877412	+	0.479737i	$0.840732\pi$
$798$	3.74758	+	1.19871i	0.132663	+	0.0424338i
$799$	40.4342	+	40.4342i	1.43046	+	1.43046i
$800$		0			0
$801$	25.0921	−	4.21025i	0.886585	−	0.148762i
$802$		−	8.53483i		−	0.301375i
$803$		−	6.28151i		−	0.221670i
$804$	−5.33672	+	16.6845i	−0.188212	+	0.588416i
$805$		0			0
$806$	−3.43792	−	13.7450i	−0.121096	−	0.484145i
$807$	−33.3499	+	17.1856i	−1.17397	+	0.604960i
$808$	31.1797	−	31.1797i	1.09690	−	1.09690i
$809$			12.8814i			0.452886i	0.974024	+	0.226443i	$0.0727097\pi$
$809$			12.8814i			0.452886i	−0.974024	+	0.226443i	$0.927290\pi$
$810$		0			0
$811$	−37.1318	−	37.1318i	−1.30387	−	1.30387i	−0.925758	−	0.378116i	$-0.876572\pi$
$811$	−37.1318	−	37.1318i	−1.30387	−	1.30387i	−0.378116	−	0.925758i	$-0.623428\pi$
$812$	−7.35143	−	7.35143i	−0.257985	−	0.257985i
$813$	8.34244	+	2.66843i	0.292582	+	0.0935858i
$814$	0.886676	−	0.886676i	0.0310780	−	0.0310780i
$815$		0			0
$816$	14.6567	−	7.55275i	0.513087	−	0.264399i
$817$	15.6489	+	15.6489i	0.547485	+	0.547485i
$818$			9.90483i			0.346314i
$819$	−17.4606	+	7.61669i	−0.610122	+	0.266149i
$820$		0			0
$821$	−10.6744	+	10.6744i	−0.372540	+	0.372540i	−0.868402	−	0.495861i	$-0.834852\pi$
$821$	−10.6744	+	10.6744i	−0.372540	+	0.372540i	0.495861	+	0.868402i	$0.334852\pi$
$822$	−1.98538	−	3.85279i	−0.0692482	−	0.134382i
$823$	22.6990			0.791236			0.395618	−	0.918415i	$-0.370530\pi$
$823$	22.6990			0.791236			0.395618	+	0.918415i	$0.370530\pi$
$824$	6.24527	−	6.24527i	0.217564	−	0.217564i
$825$		0			0
$826$	1.57289	−	1.57289i	0.0547277	−	0.0547277i
$827$	−13.2802	+	13.2802i	−0.461799	+	0.461799i	−0.899245	−	0.437446i	$-0.855883\pi$
$827$	−13.2802	+	13.2802i	−0.461799	+	0.461799i	0.437446	+	0.899245i	$0.355883\pi$
$828$	−4.52419	+	6.34855i	−0.157226	+	0.220627i
$829$		−	11.0522i		−	0.383858i	−0.981409	−	0.191929i	$-0.938526\pi$
$829$		−	11.0522i		−	0.383858i	0.981409	−	0.191929i	$-0.0614743\pi$
$830$		0			0
$831$	−13.8750	−	26.9254i	−0.481317	−	0.934033i
$832$	1.00307	+	4.01030i	0.0347750	+	0.139032i
$833$	−26.3147			−0.911749
$834$	−6.02465	+	18.8352i	−0.208617	+	0.652209i
$835$		0			0
$836$	−1.58095			−0.0546783
$837$	17.8713	+	23.8999i	0.617724	+	0.826102i
$838$	19.2672	−	19.2672i	0.665575	−	0.665575i
$839$	2.03658	+	2.03658i	0.0703107	+	0.0703107i	0.741388	−	0.671077i	$-0.234168\pi$
$839$	2.03658	+	2.03658i	0.0703107	+	0.0703107i	−0.671077	+	0.741388i	$0.734168\pi$
$840$		0			0
$841$	14.1490			0.487897
$842$		−	10.7587i		−	0.370771i
$843$	−2.60079	+	8.13098i	−0.0895759	+	0.280046i
$844$			13.8574i			0.476992i
$845$		0			0
$846$	10.0915	−	14.1608i	0.346952	−	0.486858i
$847$	−13.3252	+	13.3252i	−0.457859	+	0.457859i
$848$	−12.4298			−0.426840
$849$	−7.51547	−	14.5844i	−0.257930	−	0.500534i
$850$		0			0
$851$	4.01557	−	4.01557i	0.137652	−	0.137652i
$852$	−1.04703	+	3.27340i	−0.0358708	+	0.112145i
$853$	26.1501	+	26.1501i	0.895364	+	0.895364i	0.995022	−	0.0996578i	$-0.0317748\pi$
$853$	26.1501	+	26.1501i	0.895364	+	0.895364i	−0.0996578	+	0.995022i	$0.531775\pi$
$854$			1.40192i			0.0479726i
$855$		0			0
$856$	25.5608	−	25.5608i	0.873651	−	0.873651i
$857$		−	21.8580i		−	0.746653i	−0.927700	−	0.373327i	$-0.878217\pi$
$857$		−	21.8580i		−	0.746653i	0.927700	−	0.373327i	$-0.121783\pi$
$858$	−1.75720	+	1.54403i	−0.0599900	+	0.0527124i
$859$	−3.08718			−0.105333			−0.0526666	−	0.998612i	$-0.516772\pi$
$859$	−3.08718			−0.105333			−0.0526666	+	0.998612i	$0.516772\pi$
$860$		0			0
$861$	−11.3054	−	21.9390i	−0.385287	−	0.747679i
$862$	−5.05794			−0.172274
$863$	16.2854	+	16.2854i	0.554363	+	0.554363i	0.927697	−	0.373334i	$-0.121786\pi$
$863$	16.2854	+	16.2854i	0.554363	+	0.554363i	−0.373334	+	0.927697i	$0.621786\pi$
$864$	−18.0418	−	24.1278i	−0.613793	−	0.820845i
$865$		0			0
$866$	1.43306	+	1.43306i	0.0486973	+	0.0486973i
$867$	22.6625	+	43.9784i	0.769659	+	1.49358i
$868$	−15.4941			−0.525904
$869$	1.49193	+	1.49193i	0.0506101	+	0.0506101i
$870$		0			0
$871$	−12.2450	+	20.4136i	−0.414905	+	0.691688i
$872$	−18.5038			−0.626619
$873$	−0.726546	−	4.33004i	−0.0245899	−	0.146550i
$874$	2.18809			0.0740133
$875$		0			0
$876$	28.9966	+	9.27491i	0.979705	+	0.313370i
$877$	9.53726	−	9.53726i	0.322050	−	0.322050i	−0.527503	−	0.849553i	$-0.676872\pi$
$877$	9.53726	−	9.53726i	0.322050	−	0.322050i	0.849553	+	0.527503i	$0.176872\pi$
$878$	−10.3418	+	10.3418i	−0.349018	+	0.349018i
$879$	35.4848	+	11.3502i	1.19687	+	0.382833i
$880$		0			0
$881$	45.3231			1.52697			0.763487	−	0.645823i	$-0.223486\pi$
$881$	45.3231			1.52697			0.763487	+	0.645823i	$0.223486\pi$
$882$	1.32417	+	7.89171i	0.0445870	+	0.265728i
$883$	39.8456			1.34091			0.670456	−	0.741949i	$-0.266098\pi$
$883$	39.8456			1.34091			0.670456	+	0.741949i	$0.266098\pi$
$884$	36.1678	−	9.04637i	1.21645	−	0.304263i
$885$		0			0
$886$	−10.0064	−	10.0064i	−0.336171	−	0.336171i
$887$	3.65752			0.122807			0.0614037	−	0.998113i	$-0.480442\pi$
$887$	3.65752			0.122807			0.0614037	+	0.998113i	$0.480442\pi$
$888$	6.41847	+	12.4555i	0.215390	+	0.417981i
$889$	−0.0435418	−	0.0435418i	−0.00146034	−	0.00146034i
$890$		0			0
$891$	2.15599	−	4.43026i	0.0722284	−	0.148419i
$892$	−18.7634	−	18.7634i	−0.628244	−	0.628244i
$893$	15.9703			0.534425
$894$	−13.0047	−	25.2367i	−0.434943	−	0.844041i
$895$		0			0
$896$	19.0406			0.636101
$897$	−7.95800	+	6.99260i	−0.265710	+	0.233476i
$898$			28.1863i			0.940590i
$899$	−15.6502	+	15.6502i	−0.521963	+	0.521963i
$900$		0			0
$901$		−	59.4935i		−	1.98202i
$902$	−2.14299	−	2.14299i	−0.0713539	−	0.0713539i
$903$	10.9094	−	34.1067i	0.363043	−	1.13500i
$904$	9.50142	−	9.50142i	0.316012	−	0.316012i
$905$		0			0
$906$	4.00188	+	7.76595i	0.132953	+	0.258006i
$907$	−22.0580			−0.732422			−0.366211	−	0.930532i	$-0.619345\pi$
$907$	−22.0580			−0.732422			−0.366211	+	0.930532i	$0.619345\pi$
$908$	16.0956	−	16.0956i	0.534152	−	0.534152i
$909$	−31.7689	+	44.5796i	−1.05371	+	1.47861i
$910$		0			0
$911$			9.96697i			0.330220i	0.986275	+	0.165110i	$0.0527980\pi$
$911$			9.96697i			0.330220i	−0.986275	+	0.165110i	$0.947202\pi$
$912$	1.40292	−	4.38603i	0.0464554	−	0.145236i
$913$		−	9.23989i		−	0.305796i
$914$	2.50993			0.0830212
$915$		0			0
$916$	−6.81027	−	6.81027i	−0.225018	−	0.225018i
$917$	1.39412	−	1.39412i	0.0460380	−	0.0460380i
$918$	19.2194	−	14.3715i	0.634336	−	0.474330i
$919$	−44.1088			−1.45502			−0.727508	−	0.686100i	$-0.759321\pi$
$919$	−44.1088			−1.45502			−0.727508	+	0.686100i	$0.759321\pi$
$920$		0			0
$921$	−6.45380	+	20.1769i	−0.212660	+	0.664850i
$922$	17.5169			0.576890
$923$	−2.40239	+	4.00503i	−0.0790756	+	0.131827i
$924$	1.17177	+	2.27391i	0.0385483	+	0.0748060i
$925$		0			0
$926$		−	19.1106i		−	0.628013i
$927$	−6.36328	+	8.92924i	−0.208997	+	0.293275i
$928$	15.7994	−	15.7994i	0.518642	−	0.518642i
$929$	−13.0994	+	13.0994i	−0.429776	+	0.429776i	−0.888552	−	0.458776i	$-0.848288\pi$
$929$	−13.0994	+	13.0994i	−0.429776	+	0.429776i	0.458776	+	0.888552i	$0.348288\pi$
$930$		0			0
$931$	−5.19675	+	5.19675i	−0.170317	+	0.170317i
$932$	27.0978			0.887618
$933$	−1.20298	−	2.33447i	−0.0393838	−	0.0764272i
$934$	−1.44451	+	1.44451i	−0.0472659	+	0.0472659i
$935$		0			0
$936$	−10.4512	−	23.9586i	−0.341610	−	0.783110i
$937$			23.1567i			0.756496i	0.925704	+	0.378248i	$0.123473\pi$
$937$			23.1567i			0.756496i	−0.925704	+	0.378248i	$0.876527\pi$
$938$	−5.62543	−	5.62543i	−0.183677	−	0.183677i
$939$	−1.43065	+	0.737227i	−0.0466874	+	0.0240585i
$940$		0			0
$941$	14.3573	−	14.3573i	0.468035	−	0.468035i	−0.433242	−	0.901277i	$-0.642631\pi$
$941$	14.3573	−	14.3573i	0.468035	−	0.468035i	0.901277	+	0.433242i	$0.142631\pi$
$942$	−14.7092	−	4.70492i	−0.479253	−	0.153294i
$943$	−9.70515	−	9.70515i	−0.316043	−	0.316043i
$944$	−1.84085	−	1.84085i	−0.0599145	−	0.0599145i
$945$		0			0
$946$		−	4.39716i		−	0.142964i
$947$	−0.485543	+	0.485543i	−0.0157780	+	0.0157780i	−0.714952	−	0.699174i	$-0.753551\pi$
$947$	−0.485543	+	0.485543i	−0.0157780	+	0.0157780i	0.699174	+	0.714952i	$0.253551\pi$
$948$	−9.08990	+	4.68412i	−0.295226	+	0.152133i
$949$	35.4776	+	21.2810i	1.15165	+	0.690811i
$950$		0			0
$951$	11.4178	−	35.6960i	0.370246	−	1.15752i
$952$			28.7274i			0.931061i
$953$			29.1833i			0.945339i	0.881240	+	0.472670i	$0.156710\pi$
$953$			29.1833i			0.945339i	−0.881240	+	0.472670i	$0.843290\pi$
$954$	−17.8420	+	2.99374i	−0.577655	+	0.0969259i
$955$		0			0
$956$	7.21196	+	7.21196i	0.233252	+	0.233252i
$957$	3.48039	+	1.11324i	0.112505	+	0.0359860i
$958$		−	4.46230i		−	0.144170i
$959$	−6.44102			−0.207991
$960$		0			0
$961$			1.98485i			0.0640273i
$962$	2.00394	+	8.01186i	0.0646098	+	0.258313i
$963$	−26.0438	+	36.5459i	−0.839251	+	1.17768i
$964$	−21.1342	−	21.1342i	−0.680687	−	0.680687i
$965$		0			0
$966$	−1.62177	−	3.14717i	−0.0521796	−	0.101259i
$967$	−14.9051	+	14.9051i	−0.479316	+	0.479316i	−0.904913	−	0.425597i	$-0.860064\pi$
$967$	−14.9051	+	14.9051i	−0.479316	+	0.479316i	0.425597	+	0.904913i	$0.360064\pi$
$968$	−18.2842	−	18.2842i	−0.587675	−	0.587675i
$969$	20.9932	+	6.71491i	0.674398	+	0.215714i
$970$		0			0
$971$		−	46.0892i		−	1.47907i	−0.673116	−	0.739537i	$-0.735045\pi$
$971$		−	46.0892i		−	1.47907i	0.673116	−	0.739537i	$-0.264955\pi$
$972$	17.2675	+	16.4939i	0.553856	+	0.529043i
$973$	20.7801	+	20.7801i	0.666179	+	0.666179i
$974$	−21.9747			−0.704116
$975$		0			0
$976$	1.64075			0.0525192
$977$	−11.8734	−	11.8734i	−0.379864	−	0.379864i	0.491189	−	0.871053i	$-0.336562\pi$
$977$	−11.8734	−	11.8734i	−0.379864	−	0.379864i	−0.871053	+	0.491189i	$0.836562\pi$
$978$	−5.71188	+	2.94339i	−0.182646	+	0.0941193i
$979$		−	4.64287i		−	0.148387i
$980$		0			0
$981$	22.6548	−	3.80129i	0.723312	−	0.121366i
$982$	−15.8755	−	15.8755i	−0.506607	−	0.506607i
$983$	−8.05185	+	8.05185i	−0.256814	+	0.256814i	−0.823757	−	0.566943i	$-0.808126\pi$
$983$	−8.05185	+	8.05185i	−0.256814	+	0.256814i	0.566943	+	0.823757i	$0.308126\pi$
$984$	30.1036	−	15.5127i	0.959668	−	0.494527i
$985$		0			0
$986$	12.5853	+	12.5853i	0.400798	+	0.400798i
$987$	−11.8369	−	22.9704i	−0.376772	−	0.731155i
$988$	5.35607	−	8.92911i	0.170399	−	0.284073i
$989$		−	19.9138i		−	0.633221i
$990$		0			0
$991$	52.2270			1.65905			0.829523	−	0.558473i	$-0.188612\pi$
$991$	52.2270			1.65905			0.829523	+	0.558473i	$0.188612\pi$
$992$		−	33.2994i		−	1.05726i
$993$	16.5482	−	51.7355i	0.525141	−	1.64178i
$994$	−1.10368	−	1.10368i	−0.0350065	−	0.0350065i
$995$		0			0
$996$	42.6531	+	13.6431i	1.35151	+	0.432297i
$997$		−	28.9060i		−	0.915462i	−0.889091	−	0.457731i	$-0.848662\pi$
$997$		−	28.9060i		−	0.915462i	0.889091	−	0.457731i	$-0.151338\pi$
$998$		−	0.346810i		−	0.0109781i
$999$	−10.4171	−	13.9311i	−0.329582	−	0.440761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.n.q.749.13		40
3.2	odd	2	inner	975.2.n.q.749.8		40
5.2	odd	4		975.2.o.p.476.8		40
5.3	odd	4		195.2.o.a.86.13	yes	40
5.4	even	2		975.2.n.r.749.8		40
13.5	odd	4		975.2.n.r.824.13		40
15.2	even	4		975.2.o.p.476.13		40
15.8	even	4		195.2.o.a.86.8	✓	40
15.14	odd	2		975.2.n.r.749.13		40
39.5	even	4		975.2.n.r.824.8		40
65.18	even	4		195.2.o.a.161.8	yes	40
65.44	odd	4	inner	975.2.n.q.824.8		40
65.57	even	4		975.2.o.p.551.13		40
195.44	even	4	inner	975.2.n.q.824.13		40
195.83	odd	4		195.2.o.a.161.13	yes	40
195.122	odd	4		975.2.o.p.551.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.8	✓	40	15.8	even	4
195.2.o.a.86.13	yes	40	5.3	odd	4
195.2.o.a.161.8	yes	40	65.18	even	4
195.2.o.a.161.13	yes	40	195.83	odd	4
975.2.n.q.749.8		40	3.2	odd	2	inner
975.2.n.q.749.13		40	1.1	even	1	trivial
975.2.n.q.824.8		40	65.44	odd	4	inner
975.2.n.q.824.13		40	195.44	even	4	inner
975.2.n.r.749.8		40	5.4	even	2
975.2.n.r.749.13		40	15.14	odd	2
975.2.n.r.824.8		40	39.5	even	4
975.2.n.r.824.13		40	13.5	odd	4
975.2.o.p.476.8		40	5.2	odd	4
975.2.o.p.476.13		40	15.2	even	4
975.2.o.p.551.8		40	195.122	odd	4
975.2.o.p.551.13		40	65.57	even	4

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.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.483812 + 0.483812i) q^{2} +(-0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(0.361045 - 1.12876i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(1.70875 - 1.70875i) q^{8} +(-1.74104 + 2.44311i) q^{9} +O(q^{10})\)	\(q+(0.483812 + 0.483812i) q^{2} +(-0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(0.361045 - 1.12876i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(1.70875 - 1.70875i) q^{8} +(-1.74104 + 2.44311i) q^{9} +(0.387103 + 0.387103i) q^{11} +(-2.35852 + 1.21537i) q^{12} +(-3.49780 + 0.874878i) q^{13} -1.20499i q^{14} -1.41028 q^{16} -6.75010i q^{17} +(-2.02434 + 0.339668i) q^{18} +(-1.33304 - 1.33304i) q^{19} +(-0.929314 + 2.90536i) q^{21} +0.374570i q^{22} +1.69635i q^{23} +(-3.98660 - 1.27516i) q^{24} +(-2.11555 - 1.26900i) q^{26} +(5.14287 + 0.742237i) q^{27} +(-1.90763 + 1.90763i) q^{28} +3.85370i q^{29} +(4.06109 + 4.06109i) q^{31} +(-4.09981 - 4.09981i) q^{32} +(0.288877 - 0.903130i) q^{33} +(3.26578 - 3.26578i) q^{34} +(3.74248 + 2.66702i) q^{36} +(-2.36718 - 2.36718i) q^{37} -1.28988i q^{38} +(4.12215 + 4.69126i) q^{39} +(-5.72121 + 5.72121i) q^{41} +(-1.85526 + 0.956036i) q^{42} -11.7392 q^{43} +(0.592985 - 0.592985i) q^{44} +(-0.820713 + 0.820713i) q^{46} +(-5.99016 + 5.99016i) q^{47} +(1.11891 + 2.17133i) q^{48} -3.89841i q^{49} +(-10.3928 + 5.35551i) q^{51} +(1.34018 + 5.35811i) q^{52} +8.81372 q^{53} +(2.12908 + 2.84728i) q^{54} -4.25585 q^{56} +(-0.994786 + 3.11005i) q^{57} +(-1.86446 + 1.86446i) q^{58} +(1.30531 + 1.30531i) q^{59} -1.16343 q^{61} +3.92960i q^{62} +(5.21056 - 0.874290i) q^{63} -1.14652i q^{64} +(0.576707 - 0.297183i) q^{66} +(4.66845 - 4.66845i) q^{67} -10.3402 q^{68} +(2.61178 - 1.34588i) q^{69} +(0.915921 - 0.915921i) q^{71} +(1.19966 + 7.14967i) q^{72} +(-8.11348 - 8.11348i) q^{73} -2.29054i q^{74} +(-2.04202 + 2.04202i) q^{76} -0.964126i q^{77} +(-0.275341 + 4.26403i) q^{78} +3.85408 q^{79} +(-2.93755 - 8.50710i) q^{81} -5.53597 q^{82} +(-11.9347 - 11.9347i) q^{83} +(4.45059 + 1.42357i) q^{84} +(-5.67957 - 5.67957i) q^{86} +(5.93334 - 3.05751i) q^{87} +1.32293 q^{88} +(-5.99694 - 5.99694i) q^{89} +(5.44533 + 3.26635i) q^{91} +2.59855 q^{92} +(3.03059 - 9.47471i) q^{93} -5.79622 q^{94} +(-3.05949 + 9.56505i) q^{96} +(-1.03487 + 1.03487i) q^{97} +(1.88610 - 1.88610i) q^{98} +(-1.61970 + 0.271772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 40 * q + 12 * q^6 - 16 * q^7	\( 40 q + 12 q^{6} - 16 q^{7} - 24 q^{12} + 24 q^{13} - 64 q^{16} + 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} + 32 q^{28} + 32 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{37} + 8 q^{39} - 32 q^{43} - 40 q^{46} - 8 q^{52} + 32 q^{54} + 36 q^{57} + 24 q^{58} + 8 q^{61} - 8 q^{63} - 48 q^{66} + 32 q^{67} + 132 q^{72} + 64 q^{73} + 16 q^{76} - 108 q^{78} - 40 q^{79} + 72 q^{81} - 128 q^{82} - 124 q^{84} - 80 q^{88} + 8 q^{91} - 108 q^{93} + 32 q^{94} - 76 q^{96} - 24 q^{97} + 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 - 16 * q^7 - 24 * q^12 + 24 * q^13 - 64 * q^16 + 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 + 32 * q^28 + 32 * q^31 + 4 * q^33 + 16 * q^34 + 32 * q^37 + 8 * q^39 - 32 * q^43 - 40 * q^46 - 8 * q^52 + 32 * q^54 + 36 * q^57 + 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 + 132 * q^72 + 64 * q^73 + 16 * q^76 - 108 * q^78 - 40 * q^79 + 72 * q^81 - 128 * q^82 - 124 * q^84 - 80 * q^88 + 8 * q^91 - 108 * q^93 + 32 * q^94 - 76 * q^96 - 24 * q^97 + 20 * q^99

Introduction

L-functions

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