LMFDB - Embedded newform 975.2.n.q.749.8

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			749.8
Character	$\chi$	$=$	975.749
Dual form			975.2.n.q.824.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483812 - 0.483812i) q^{2} +(0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(-1.12876 + 0.361045i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(-1.74104 - 2.44311i) q^{9} +O(q^{10})$	\(q+(-0.483812 - 0.483812i) q^{2} +(0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(-1.12876 + 0.361045i) 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} +(-0.339668 + 2.02434i) q^{18} +(-1.33304 - 1.33304i) q^{19} +(-2.90536 + 0.929314i) q^{21} +0.374570i q^{22} -1.69635i q^{23} +(1.27516 + 3.98660i) 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} +(-0.903130 + 0.288877i) q^{33} +(3.26578 - 3.26578i) q^{34} +(-3.74248 + 2.66702i) q^{36} +(-2.36718 - 2.36718i) q^{37} +1.28988i q^{38} +(-1.42814 + 6.07951i) 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} +(2.84728 + 2.12908i) q^{54} +4.25585 q^{56} +(-3.11005 + 0.994786i) q^{57} +(-1.86446 + 1.86446i) q^{58} +(-1.30531 - 1.30531i) q^{59} -1.16343 q^{61} -3.92960i q^{62} +(-0.874290 + 5.21056i) 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} +(7.14967 + 1.19966i) q^{72} +(-8.11348 - 8.11348i) q^{73} +2.29054i q^{74} +(-2.04202 + 2.04202i) q^{76} +0.964126i q^{77} +(3.63229 - 2.25039i) q^{78} +3.85408 q^{79} +(-2.93755 + 8.50710i) q^{81} -5.53597 q^{82} +(11.9347 + 11.9347i) q^{83} +(1.42357 + 4.45059i) 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} +(9.47471 - 3.03059i) q^{93} -5.79622 q^{94} +(9.56505 - 3.05949i) q^{96} +(-1.03487 + 1.03487i) q^{97} +(-1.88610 + 1.88610i) q^{98} +(-0.271772 + 1.61970i) 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	0.515052	−	0.857159i	$-0.327773\pi$
$2$	−0.483812	−	0.483812i	−0.342107	−	0.342107i	−0.857159	+	0.515052i	$0.827773\pi$
$3$	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
$6$	−1.12876	+	0.361045i	−0.460813	+	0.147396i
$7$	−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	0.646337	−	0.763053i	$-0.276300\pi$
$11$	−0.387103	−	0.387103i	−0.116716	−	0.116716i	−0.763053	+	0.646337i	$0.776300\pi$
$12$	−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	$0.305233\pi$
$17$			6.75010i			1.63714i	−0.574407	+	0.818570i	$0.694767\pi$
$18$	−0.339668	+	2.02434i	−0.0800606	+	0.477142i
$19$	−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
$21$	−2.90536	+	0.929314i	−0.634003	+	0.202793i
$22$			0.374570i			0.0798586i
$23$		−	1.69635i		−	0.353713i	−0.984237	−	0.176856i	$-0.943407\pi$
$23$		−	1.69635i		−	0.353713i	0.984237	−	0.176856i	$-0.0565928\pi$
$24$	1.27516	+	3.98660i	0.260291	+	0.813761i
$25$		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	$-0.883525\pi$
$29$		−	3.85370i		−	0.715614i	0.933796	−	0.357807i	$-0.116475\pi$
$30$		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
$33$	−0.903130	+	0.288877i	−0.157215	+	0.0502869i
$34$	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
$39$	−1.42814	+	6.07951i	−0.228685	+	0.973500i
$40$		0			0
$41$	5.72121	−	5.72121i	0.893502	−	0.893502i	−0.101349	−	0.994851i	$-0.532316\pi$
$41$	5.72121	−	5.72121i	0.893502	−	0.893502i	0.994851	+	0.101349i	$0.0323158\pi$
$42$	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	−0.119124	−	0.992879i	$-0.538009\pi$
$47$	5.99016	−	5.99016i	0.873755	−	0.873755i	0.992879	+	0.119124i	$0.0380087\pi$
$48$	−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	$-0.706958\pi$
$53$	−8.81372			−1.21066			−0.605328	+	0.795976i	$0.706958\pi$
$54$	2.84728	+	2.12908i	0.387466	+	0.289731i
$55$		0			0
$56$	4.25585			0.568712
$57$	−3.11005	+	0.994786i	−0.411936	+	0.131763i
$58$	−1.86446	+	1.86446i	−0.244816	+	0.244816i
$59$	−1.30531	−	1.30531i	−0.169937	−	0.169937i	0.617015	−	0.786952i	$-0.288342\pi$
$59$	−1.30531	−	1.30531i	−0.169937	−	0.169937i	−0.786952	+	0.617015i	$0.788342\pi$
$60$		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
$63$	−0.874290	+	5.21056i	−0.110150	+	0.656469i
$64$		−	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	−0.759365	−	0.650665i	$-0.774490\pi$
$71$	−0.915921	+	0.915921i	−0.108700	+	0.108700i	0.650665	+	0.759365i	$0.274490\pi$
$72$	7.14967	+	1.19966i	0.842597	+	0.141381i
$73$	−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
$78$	3.63229	−	2.25039i	0.411276	−	0.254806i
$79$	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	$0.127036\pi$
$83$	11.9347	+	11.9347i	1.31000	+	1.31000i	0.388586	+	0.921412i	$0.372964\pi$
$84$	1.42357	+	4.45059i	0.155325	+	0.485599i
$85$		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	0.949485	−	0.313811i	$-0.101606\pi$
$89$	5.99694	+	5.99694i	0.635674	+	0.635674i	−0.313811	+	0.949485i	$0.601606\pi$
$90$		0			0
$91$	5.44533	+	3.26635i	0.570826	+	0.342406i
$92$	−2.59855			−0.270918
$93$	9.47471	−	3.03059i	0.982481	−	0.314258i
$94$	−5.79622			−0.597835
$95$		0			0
$96$	9.56505	−	3.05949i	0.976229	−	0.312258i
$97$	−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
$99$	−0.271772	+	1.61970i	−0.0273141	+	0.162786i
$100$		0			0
$101$	−18.2471			−1.81565			−0.907826	−	0.419347i	$-0.862259\pi$
$101$	−18.2471			−1.81565			−0.907826	+	0.419347i	$0.862259\pi$
$102$	−2.43709	−	7.61921i	−0.241308	−	0.754415i
$103$	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	$-0.757265\pi$
$107$	−14.9588			−1.44612			−0.723060	+	0.690786i	$0.757265\pi$
$108$	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
$111$	−5.52275	+	1.76652i	−0.524196	+	0.167670i
$112$	1.75623	+	1.75623i	0.165948	+	0.165948i
$113$	−5.56044			−0.523083			−0.261541	−	0.965192i	$-0.584231\pi$
$113$	−5.56044			−0.523083			−0.261541	+	0.965192i	$0.584231\pi$
$114$	1.98597	+	1.02339i	0.186003	+	0.0958493i
$115$		0			0
$116$	−5.90330			−0.548107
$117$	8.22723	+	7.02230i	0.760608	+	0.649212i
$118$			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
$123$	−4.26946	−	13.3478i	−0.384964	−	1.20353i
$124$	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	$-0.984427\pi$
$131$		−	1.11950i		−	0.0978111i	0.998803	−	0.0489056i	$-0.0155733\pi$
$132$	0.442516	+	1.38346i	0.0385161	+	0.120415i
$133$			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	−0.808897	−	0.587950i	$-0.799935\pi$
$137$	−2.58611	+	2.58611i	−0.220946	+	0.220946i	0.587950	+	0.808897i	$0.299935\pi$
$138$	0.612459	+	1.91476i	0.0521359	+	0.162995i
$139$	−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
$141$	−4.47017	−	13.9753i	−0.376456	−	1.17694i
$142$	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	$0.688323\pi$
$149$	−16.9396	+	16.9396i	−1.38775	+	1.38775i	−0.830030	+	0.557719i	$0.811677\pi$
$150$		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
$156$	9.31291	+	2.18770i	0.745629	+	0.175156i
$157$		−	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
$162$	5.53706	−	2.69461i	0.435032	−	0.211709i
$163$	−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	−0.263141	−	0.964757i	$-0.584758\pi$
$167$	9.06688	−	9.06688i	0.701616	−	0.701616i	0.964757	+	0.263141i	$0.0847584\pi$
$168$	3.37658	−	6.55251i	0.260509	−	0.505537i
$169$	11.4692	−	6.12029i	0.882244	−	0.470792i
$170$		0			0
$171$	−0.935885	+	5.57765i	−0.0715689	+	0.426534i
$172$			17.9827i			1.37117i
$173$		−	4.63904i		−	0.352700i	−0.984328	−	0.176350i	$-0.943571\pi$
$173$		−	4.63904i		−	0.352700i	0.984328	−	0.176350i	$-0.0564291\pi$
$174$	1.39136	+	4.34988i	0.105479	+	0.329764i
$175$		0			0
$176$	0.545923	+	0.545923i	0.0411505	+	0.0411505i
$177$	−3.04535	+	0.974090i	−0.228902	+	0.0732171i
$178$		−	5.80278i		−	0.434936i
$179$	13.2894			0.993298			0.496649	−	0.867951i	$-0.334564\pi$
$179$	13.2894			0.993298			0.496649	+	0.867951i	$0.334564\pi$
$180$		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
$189$	7.32877	+	5.48014i	0.533090	+	0.398622i
$190$		0			0
$191$			6.40782i			0.463654i	0.972757	+	0.231827i	$0.0744703\pi$
$191$			6.40782i			0.463654i	−0.972757	+	0.231827i	$0.925530\pi$
$192$	−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	0.984198	−	0.177071i	$-0.0566622\pi$
$197$	11.3286	+	11.3286i	0.807127	+	0.807127i	−0.177071	+	0.984198i	$0.556662\pi$
$198$	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
$201$	−3.48384	−	10.8917i	−0.245731	−	0.768242i
$202$	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
$213$	0.683508	+	2.13689i	0.0468332	+	0.146417i
$214$	7.23723	+	7.23723i	0.494727	+	0.494727i
$215$		0			0
$216$	7.51958	−	10.0562i	0.511643	−	0.684237i
$217$		−	10.1146i		−	0.686625i
$218$			5.23913i			0.354839i
$219$	−18.9291	+	6.05470i	−1.27911	+	0.409139i
$220$		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	0.266454	−	0.963848i	$-0.414148\pi$
$227$	−10.5073	−	10.5073i	−0.697394	−	0.697394i	−0.963848	+	0.266454i	$0.914148\pi$
$228$	1.52387	+	4.76414i	0.100920	+	0.315513i
$229$	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	$-0.803271\pi$
$233$		−	17.6896i		−	1.15888i	0.815014	−	0.579441i	$-0.196729\pi$
$234$	−0.582959	−	7.37790i	−0.0381092	−	0.482309i
$235$		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	−0.538250	−	0.842785i	$-0.680914\pi$
$239$	4.70800	−	4.70800i	0.304535	−	0.304535i	0.842785	+	0.538250i	$0.180914\pi$
$240$		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
$249$	27.8441	−	8.90626i	1.76455	−	0.564411i
$250$		0			0
$251$	5.80617			0.366482			0.183241	−	0.983068i	$-0.441341\pi$
$251$	5.80617			0.366482			0.183241	+	0.983068i	$0.441341\pi$
$252$	7.98181	+	1.33928i	0.502807	+	0.0843670i
$253$	−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	$-0.916691\pi$
$257$		−	8.29597i		−	0.517488i	0.965946	−	0.258744i	$-0.0833087\pi$
$258$	13.2507	−	4.23839i	0.824952	−	0.263870i
$259$			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	$-0.608801\pi$
$263$	−10.8718			−0.670383			−0.335191	+	0.942150i	$0.608801\pi$
$264$	1.04961	−	2.03684i	0.0645988	−	0.125359i
$265$		0			0
$266$	1.60630	−	1.60630i	0.0984888	−	0.0984888i
$267$	13.9911	−	4.47522i	0.856243	−	0.273879i
$268$	−7.15137	−	7.15137i	−0.436839	−	0.436839i
$269$			21.6607i			1.32068i	0.750968	+	0.660339i	$0.229587\pi$
$269$			21.6607i			1.32068i	−0.750968	+	0.660339i	$0.770413\pi$
$270$		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
$273$	9.34934	−	5.79239i	0.565848	−	0.350572i
$274$	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
$279$	2.85115	−	16.9922i	0.170694	−	1.01730i
$280$		0			0
$281$	3.48513	+	3.48513i	0.207906	+	0.207906i	0.803377	−	0.595471i	$-0.203035\pi$
$281$	3.48513	+	3.48513i	0.207906	+	0.207906i	−0.595471	+	0.803377i	$0.703035\pi$
$282$	−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
$288$	2.87834	−	17.1542i	0.169608	−	1.01082i
$289$	−28.5639			−1.68023
$290$		0			0
$291$	0.772272	+	2.41439i	0.0452714	+	0.141534i
$292$	−12.4287	+	12.4287i	−0.727332	+	0.727332i
$293$	15.2096	−	15.2096i	0.888556	−	0.888556i	−0.105828	−	0.994384i	$-0.533749\pi$
$293$	15.2096	−	15.2096i	0.888556	−	0.888556i	0.994384	+	0.105828i	$0.0337494\pi$
$294$	1.40750	+	4.40035i	0.0820873	+	0.256634i
$295$		0			0
$296$	8.08986			0.470214
$297$	2.27814	+	1.70350i	0.132191	+	0.0988470i
$298$	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
$306$	−13.6645	−	2.29280i	−0.781148	−	0.131070i
$307$	−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	$-0.513688\pi$
$311$	−1.51624			−0.0859779			−0.0429890	+	0.999076i	$0.513688\pi$
$312$	−7.94804	−	12.8287i	−0.449969	−	0.726282i
$313$		−	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	0.131919	−	0.991261i	$-0.457886\pi$
$317$	−15.3001	−	15.3001i	−0.859342	−	0.859342i	−0.991261	+	0.131919i	$0.957886\pi$
$318$	9.94853	−	3.18215i	0.557886	−	0.178446i
$319$	−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
$327$	−12.6321	+	4.04053i	−0.698558	+	0.223442i
$328$			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
$333$	−1.66192	+	9.90465i	−0.0910727	+	0.542771i
$334$	−8.77333			−0.480055
$335$		0			0
$336$	4.09737	−	1.31059i	0.223530	−	0.0714986i
$337$	−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	$-0.368498\pi$
$347$	14.9572			0.802946			0.401473	+	0.915871i	$0.368498\pi$
$348$	−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
$351$	17.3393	−	7.09558i	0.925506	−	0.378734i
$352$		−	3.17410i		−	0.169180i
$353$	−14.0281	−	14.0281i	−0.746638	−	0.746638i	0.227208	−	0.973846i	$-0.427040\pi$
$353$	−14.0281	−	14.0281i	−0.746638	−	0.746638i	−0.973846	+	0.227208i	$0.927040\pi$
$354$	1.94465	+	1.00210i	0.103357	+	0.0532610i
$355$		0			0
$356$	9.18642	−	9.18642i	0.486879	−	0.486879i
$357$	−6.27297	−	19.6115i	−0.332001	−	1.03795i
$358$	−6.42958	−	6.42958i	−0.339814	−	0.339814i
$359$	−14.0085	−	14.0085i	−0.739341	−	0.739341i	0.233109	−	0.972451i	$-0.425110\pi$
$359$	−14.0085	−	14.0085i	−0.739341	−	0.739341i	−0.972451	+	0.233109i	$0.925110\pi$
$360$		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
$366$	1.31322	−	0.420050i	0.0686433	−	0.0219564i
$367$		−	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
$369$	−23.9384	−	4.01667i	−1.24618	−	0.209099i
$370$		0			0
$371$	10.9758	+	10.9758i	0.569835	+	0.569835i
$372$	−4.64242	−	14.5138i	−0.240698	−	0.752508i
$373$		−	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	0.877073	−	0.480356i	$-0.159493\pi$
$383$	7.76391	+	7.76391i	0.396717	+	0.396717i	−0.480356	+	0.877073i	$0.659493\pi$
$384$	−5.70504	−	17.8360i	−0.291134	−	0.910188i
$385$		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	$-0.448916\pi$
$389$	6.30333			0.319591			0.159796	+	0.987150i	$0.448916\pi$
$390$		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
$396$	2.48114	+	0.416315i	0.124682	+	0.0209206i
$397$	−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	0.892170	−	0.451700i	$-0.149182\pi$
$401$	8.82040	+	8.82040i	0.440470	+	0.440470i	−0.451700	+	0.892170i	$0.649182\pi$
$402$	−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
$408$	−26.9099	+	8.60746i	−1.33224	+	0.426133i
$409$	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
$411$	1.92989	+	6.03352i	0.0951945	+	0.297612i
$412$		−	5.59872i		−	0.275829i
$413$			3.25103i			0.159973i
$414$	3.43398	+	0.576195i	0.168771	+	0.0283185i
$415$		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	$0.425533\pi$
$419$			39.8238i			1.94552i	−0.231818	+	0.972759i	$0.574467\pi$
$420$		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
$423$	−25.0637	−	4.20550i	−1.21864	−	0.204478i
$424$	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
$429$	2.90623	−	1.80056i	0.140314	−	0.0869318i
$430$		0			0
$431$	5.22718	−	5.22718i	0.251784	−	0.251784i	−0.569917	−	0.821702i	$-0.693025\pi$
$431$	5.22718	−	5.22718i	0.251784	−	0.251784i	0.821702	+	0.569917i	$0.193025\pi$
$432$	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	$-0.336513\pi$
$443$	20.6824			0.982650			0.491325	+	0.870976i	$0.336513\pi$
$444$	2.70604	+	8.46004i	0.128423	+	0.401496i
$445$		0			0
$446$	−11.8522			−0.561220
$447$	12.6412	+	39.5210i	0.597910	+	1.86928i
$448$	−1.42777	+	1.42777i	−0.0674559	+	0.0674559i
$449$	−29.1294	−	29.1294i	−1.37470	−	1.37470i	−0.853328	−	0.521375i	$-0.825419\pi$
$449$	−29.1294	−	29.1294i	−1.37470	−	1.37470i	−0.521375	−	0.853328i	$-0.674581\pi$
$450$		0			0
$451$	−4.42939			−0.208572
$452$			8.51778i			0.400643i
$453$	3.89002	+	12.1616i	0.182769	+	0.571401i
$454$			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	−0.989266	−	0.146123i	$-0.953321\pi$
$461$	−18.1031	+	18.1031i	−0.843144	+	0.843144i	0.146123	+	0.989266i	$0.453321\pi$
$462$	−0.348093	−	1.08826i	−0.0161948	−	0.0506306i
$463$	−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	$-0.977993\pi$
$467$		−	2.98569i		−	0.138161i	0.997611	−	0.0690807i	$-0.0220066\pi$
$468$	10.7571	−	12.6029i	0.497248	−	0.582569i
$469$	−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
$474$	−4.35031	+	1.39150i	−0.199816	+	0.0639136i
$475$		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	0.804569	−	0.593859i	$-0.202396\pi$
$479$	4.61160	+	4.61160i	0.210710	+	0.210710i	−0.593859	+	0.804569i	$0.702396\pi$
$480$		0			0
$481$	10.3509	+	6.20893i	0.471962	+	0.283103i
$482$	−13.3498			−0.608067
$483$	1.57644	+	4.92851i	0.0717305	+	0.224255i
$484$	−16.3913			−0.745058
$485$		0			0
$486$	0.244328	−	10.6630i	0.0110829	−	0.483685i
$487$	−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
$489$	−8.94488	+	2.86112i	−0.404501	+	0.129384i
$490$		0			0
$491$	32.8134			1.48085			0.740423	−	0.672141i	$-0.234625\pi$
$491$	32.8134			1.48085			0.740423	+	0.672141i	$0.234625\pi$
$492$	−20.4469	+	6.54019i	−0.921819	+	0.294854i
$493$	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
$501$	−6.76618	−	21.1535i	−0.302291	−	0.945067i
$502$	−2.80909	−	2.80909i	−0.125376	−	0.125376i
$503$	1.20071			0.0535371			0.0267685	−	0.999642i	$-0.491478\pi$
$503$	1.20071			0.0535371			0.0267685	+	0.999642i	$0.491478\pi$
$504$	−7.40961	−	10.3975i	−0.330050	−	0.463141i
$505$		0			0
$506$	0.635401			0.0282470
$507$	−0.323485	−	22.5143i	−0.0143665	−	0.999897i
$508$		−	0.0535606i		−	0.00237637i
$509$	16.5736	−	16.5736i	0.734613	−	0.734613i	−0.236917	−	0.971530i	$-0.576137\pi$
$509$	16.5736	−	16.5736i	0.734613	−	0.734613i	0.971530	+	0.236917i	$0.0761368\pi$
$510$		0			0
$511$			20.2076i			0.893931i
$512$	−10.6015	−	10.6015i	−0.468524	−	0.468524i
$513$	7.84510	+	5.86623i	0.346369	+	0.259000i
$514$	−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	$0.181098\pi$
$521$			24.5938i			1.07747i	−0.842474	+	0.538736i	$0.818902\pi$
$522$	7.80120	+	1.30898i	0.341449	+	0.0572924i
$523$			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
$528$	1.27366	−	0.407396i	0.0554291	−	0.0177296i
$529$	20.1224			0.874887
$530$		0			0
$531$	−0.916415	+	5.46161i	−0.0397690	+	0.237014i
$532$	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
$546$	−7.32575	−	1.72089i	−0.313513	−	0.0736475i
$547$			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
$552$	6.76266	−	2.16311i	0.287838	−	0.0920682i
$553$	−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	−0.482333	−	0.875988i	$-0.660211\pi$
$557$	9.29058	−	9.29058i	0.393655	−	0.393655i	0.875988	+	0.482333i	$0.160211\pi$
$558$	−9.60044	+	6.84160i	−0.406419	+	0.289628i
$559$	41.0614	−	10.2704i	1.73671	−	0.434390i
$560$		0			0
$561$	−1.94995	−	6.09622i	−0.0823268	−	0.257383i
$562$		−	3.37230i		−	0.142252i
$563$			43.3391i			1.82653i	0.407370	+	0.913263i	$0.366446\pi$
$563$			43.3391i			1.82653i	−0.407370	+	0.913263i	$0.633554\pi$
$564$	−21.4081	+	6.84764i	−0.901446	+	0.288338i
$565$		0			0
$566$	−4.58292	−	4.58292i	−0.192634	−	0.192634i
$567$	14.2521	−	6.93581i	0.598533	−	0.291277i
$568$		−	3.13016i		−	0.131339i
$569$	−7.47436			−0.313342			−0.156671	−	0.987651i	$-0.550076\pi$
$569$	−7.47436			−0.313342			−0.156671	+	0.987651i	$0.550076\pi$
$570$		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
$579$	37.5925	−	12.0244i	1.56229	−	0.499716i
$580$		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	0.696464	−	0.717591i	$-0.254755\pi$
$587$	−0.511868	−	0.511868i	−0.0211270	−	0.0211270i	−0.717591	+	0.696464i	$0.754755\pi$
$588$	−4.73800	+	9.19446i	−0.195392	+	0.379173i
$589$		−	10.8272i		−	0.446127i
$590$		0			0
$591$	26.4301	−	8.45397i	1.08719	−	0.347750i
$592$	3.33838	+	3.33838i	0.137207	+	0.137207i
$593$	13.2208	−	13.2208i	0.542911	−	0.542911i	−0.381470	−	0.924381i	$-0.624582\pi$
$593$	13.2208	−	13.2208i	0.542911	−	0.542911i	0.924381	+	0.381470i	$0.124582\pi$
$594$	−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	$-0.766718\pi$
$599$		−	32.7474i		−	1.33802i	0.743253	−	0.669011i	$-0.233282\pi$
$600$		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
$603$	−19.5335	−	3.27756i	−0.795465	−	0.133473i
$604$	7.98515	+	7.98515i	0.324911	+	0.324911i
$605$		0			0
$606$	20.5965	−	6.58803i	0.836675	−	0.267620i
$607$		−	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
$609$	3.58130	+	11.1964i	0.145121	+	0.453701i
$610$		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	0.768609	−	0.639719i	$-0.220949\pi$
$617$	3.20157	+	3.20157i	0.128891	+	0.128891i	−0.639719	+	0.768609i	$0.720949\pi$
$618$	−4.12545	+	1.31957i	−0.165950	+	0.0530811i
$619$	−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
$624$	2.01407	−	8.57379i	0.0806274	−	0.343226i
$625$		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
$639$	3.83235	+	0.643038i	0.151605	+	0.0254382i
$640$		0			0
$641$	−7.99599			−0.315822			−0.157911	−	0.987453i	$-0.550476\pi$
$641$	−7.99599			−0.315822			−0.157911	+	0.987453i	$0.550476\pi$
$642$	16.8848	−	5.40080i	0.666390	−	0.213153i
$643$	−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	$-0.966864\pi$
$647$		−	5.28617i		−	0.207821i	0.994587	−	0.103910i	$-0.0331355\pi$
$648$	−9.51698	−	19.5561i	−0.373862	−	0.768235i
$649$			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	$-0.329430\pi$
$653$	26.0947			1.02116			0.510581	+	0.859829i	$0.329430\pi$
$654$	8.06643	+	4.15671i	0.315422	+	0.162540i
$655$		0			0
$656$	−8.06848	+	8.06848i	−0.315021	+	0.315021i
$657$	−5.69621	+	33.9480i	−0.222230	+	1.32444i
$658$	7.21809	+	7.21809i	0.281390	+	0.281390i
$659$		−	10.5160i		−	0.409646i	−0.978799	−	0.204823i	$-0.934338\pi$
$659$		−	10.5160i		−	0.409646i	0.978799	−	0.204823i	$-0.0656618\pi$
$660$		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
$663$	−41.0373	−	9.64008i	−1.59376	−	0.374390i
$664$	−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
$669$	−9.14070	−	28.5771i	−0.353400	−	1.10485i
$670$		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	$-0.206289\pi$
$677$	41.4875			1.59449			0.797247	+	0.603654i	$0.206289\pi$
$678$	6.27638	−	2.00757i	0.241043	−	0.0771004i
$679$	2.57746			0.0989138
$680$		0			0
$681$	−24.5140	+	7.84109i	−0.939379	+	0.300471i
$682$	−1.52116	+	1.52116i	−0.0582483	+	0.0582483i
$683$	−31.7789	+	31.7789i	−1.21599	+	1.21599i	−0.246960	+	0.969026i	$0.579432\pi$
$683$	−31.7789	+	31.7789i	−1.21599	+	1.21599i	−0.969026	+	0.246960i	$0.920568\pi$
$684$	8.54414	+	1.43364i	0.326693	+	0.0548165i
$685$		0			0
$686$	13.1325			0.501400
$687$	−3.31767	−	10.3722i	−0.126577	−	0.395724i
$688$	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
$696$	15.3631	−	4.91408i	0.582338	−	0.186268i
$697$	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	$-0.326720\pi$
$701$	27.4234			1.03577			0.517883	+	0.855451i	$0.326720\pi$
$702$	−11.8219	−	4.95606i	−0.446189	−	0.187054i
$703$			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
$708$	1.49216	+	4.66502i	0.0560789	+	0.175322i
$709$	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
$717$	−3.51336	−	10.9840i	−0.131209	−	0.410205i
$718$			13.5550i			0.505867i
$719$	−13.8518			−0.516585			−0.258292	−	0.966067i	$-0.583160\pi$
$719$	−13.8518			−0.516585			−0.258292	+	0.966067i	$0.583160\pi$
$720$		0			0
$721$	−4.55144	−	4.55144i	−0.169505	−	0.169505i
$722$	−7.47295	+	7.47295i	−0.278115	+	0.278115i
$723$	−10.2957	−	32.1879i	−0.382900	−	1.19708i
$724$	−35.7124			−1.32724
$725$		0			0
$726$	3.86330	+	12.0780i	0.143380	+	0.448258i
$727$	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
$741$	10.0080	−	6.20047i	0.367654	−	0.227780i
$742$		−	10.6204i		−	0.389889i
$743$	−20.7742	−	20.7742i	−0.762133	−	0.762133i	0.214575	−	0.976708i	$-0.431163\pi$
$743$	−20.7742	−	20.7742i	−0.762133	−	0.762133i	−0.976708	+	0.214575i	$0.931163\pi$
$744$	−11.0114	+	21.3685i	−0.403697	+	0.783405i
$745$		0			0
$746$	−3.30783	+	3.30783i	−0.121108	+	0.121108i
$747$	8.37893	−	49.9364i	0.306569	−	1.82708i
$748$	−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
$756$	8.39477	−	11.2266i	0.305315	−	0.408308i
$757$		−	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
$759$	0.490035	+	1.53202i	0.0177871	+	0.0556089i
$760$		0			0
$761$	3.88054	+	3.88054i	0.140669	+	0.140669i	0.773935	−	0.633265i	$-0.218286\pi$
$761$	3.88054	+	3.88054i	0.140669	+	0.140669i	−0.633265	+	0.773935i	$0.718286\pi$
$762$	−0.0394665	+	0.0126238i	−0.00142972	+	0.000457313i
$763$			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	0.0713367	−	0.997452i	$-0.477274\pi$
$773$	−25.7487	−	25.7487i	−0.926116	−	0.926116i	−0.997452	+	0.0713367i	$0.977274\pi$
$774$	3.98744	−	23.7642i	0.143325	−	0.854185i
$775$		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
$786$	0.404190	+	1.26364i	0.0144170	+	0.0450726i
$787$	−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	$-0.840732\pi$
$797$		−	27.0871i		−	0.959474i	0.877412	−	0.479737i	$-0.159268\pi$
$798$	−1.19871	−	3.74758i	−0.0424338	−	0.132663i
$799$	40.4342	+	40.4342i	1.43046	+	1.43046i
$800$		0			0
$801$	4.21025	−	25.0921i	0.148762	−	0.886585i
$802$		−	8.53483i		−	0.301375i
$803$			6.28151i			0.221670i
$804$	−16.6845	+	5.33672i	−0.588416	+	0.188212i
$805$		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	$-0.927290\pi$
$809$		−	12.8814i		−	0.452886i	0.974024	−	0.226443i	$-0.0727097\pi$
$810$		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
$813$	2.66843	+	8.34244i	0.0935858	+	0.292582i
$814$	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
$819$	−1.50051	−	18.9904i	−0.0524321	−	0.663578i
$820$		0			0
$821$	10.6744	−	10.6744i	0.372540	−	0.372540i	−0.495861	−	0.868402i	$-0.665148\pi$
$821$	10.6744	−	10.6744i	0.372540	−	0.372540i	0.868402	+	0.495861i	$0.165148\pi$
$822$	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	−0.437446	−	0.899245i	$-0.644117\pi$
$827$	13.2802	−	13.2802i	0.461799	−	0.461799i	0.899245	+	0.437446i	$0.144117\pi$
$828$	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
$834$	18.8352	−	6.02465i	0.652209	−	0.208617i
$835$		0			0
$836$	1.58095			0.0546783
$837$	−23.8999	−	17.8713i	−0.826102	−	0.617724i
$838$	19.2672	−	19.2672i	0.665575	−	0.665575i
$839$	−2.03658	−	2.03658i	−0.0703107	−	0.0703107i	0.671077	−	0.741388i	$-0.265832\pi$
$839$	−2.03658	−	2.03658i	−0.0703107	−	0.0703107i	−0.741388	+	0.671077i	$0.765832\pi$
$840$		0			0
$841$	14.1490			0.487897
$842$			10.7587i			0.370771i
$843$	8.13098	−	2.60079i	0.280046	−	0.0895759i
$844$			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
$852$	3.27340	−	1.04703i	0.112145	−	0.0358708i
$853$	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	$0.121783\pi$
$857$			21.8580i			0.746653i	−0.927700	+	0.373327i	$0.878217\pi$
$858$	−2.27720	−	0.534938i	−0.0777424	−	0.0182625i
$859$	−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	0.373334	−	0.927697i	$-0.378214\pi$
$863$	−16.2854	−	16.2854i	−0.554363	−	0.554363i	−0.927697	+	0.373334i	$0.878214\pi$
$864$	−24.1278	−	18.0418i	−0.820845	−	0.613793i
$865$		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
$873$	4.33004	+	0.726546i	0.146550	+	0.0245899i
$874$	2.18809			0.0740133
$875$		0			0
$876$	9.27491	+	28.9966i	0.313370	+	0.979705i
$877$	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
$879$	−11.3502	−	35.4848i	−0.382833	−	1.19687i
$880$		0			0
$881$	−45.3231			−1.52697			−0.763487	−	0.645823i	$-0.776514\pi$
$881$	−45.3231			−1.52697			−0.763487	+	0.645823i	$0.776514\pi$
$882$	7.89171	+	1.32417i	0.265728	+	0.0445870i
$883$	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	$-0.519558\pi$
$887$	−3.65752			−0.122807			−0.0614037	+	0.998113i	$0.519558\pi$
$888$	6.41847	−	12.4555i	0.215390	−	0.417981i
$889$	−0.0435418	−	0.0435418i	−0.00146034	−	0.00146034i
$890$		0			0
$891$	4.43026	−	2.15599i	0.148419	−	0.0722284i
$892$	−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
$897$	10.3130	+	2.42262i	0.344340	+	0.0808889i
$898$			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
$903$	34.1067	−	10.9094i	1.13500	−	0.363043i
$904$	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	$-0.947202\pi$
$911$		−	9.96697i		−	0.330220i	0.986275	−	0.165110i	$-0.0527980\pi$
$912$	4.38603	−	1.40292i	0.145236	−	0.0464554i
$913$		−	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
$918$	−14.3715	+	19.2194i	−0.474330	+	0.634336i
$919$	−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
$921$	−20.1769	+	6.45380i	−0.664850	+	0.212660i
$922$	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	−0.458776	−	0.888552i	$-0.651712\pi$
$929$	13.0994	−	13.0994i	0.429776	−	0.429776i	0.888552	+	0.458776i	$0.151712\pi$
$930$		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
$936$	−26.0577	+	2.05893i	−0.851721	+	0.0672981i
$937$			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	−0.901277	−	0.433242i	$-0.857369\pi$
$941$	−14.3573	+	14.3573i	−0.468035	+	0.468035i	0.433242	+	0.901277i	$0.357369\pi$
$942$	4.70492	+	14.7092i	0.153294	+	0.479253i
$943$	−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	−0.699174	−	0.714952i	$-0.746449\pi$
$947$	0.485543	−	0.485543i	0.0157780	−	0.0157780i	0.714952	+	0.699174i	$0.246449\pi$
$948$	−9.08990	−	4.68412i	−0.295226	−	0.152133i
$949$	35.4776	+	21.2810i	1.15165	+	0.690811i
$950$		0			0
$951$	−35.6960	+	11.4178i	−1.15752	+	0.370246i
$952$			28.7274i			0.931061i
$953$		−	29.1833i		−	0.945339i	−0.881240	−	0.472670i	$-0.843290\pi$
$953$		−	29.1833i		−	0.945339i	0.881240	−	0.472670i	$-0.156710\pi$
$954$	2.99374	−	17.8420i	0.0969259	−	0.577655i
$955$		0			0
$956$	−7.21196	−	7.21196i	−0.233252	−	0.233252i
$957$	1.11324	+	3.48039i	0.0359860	+	0.112505i
$958$		−	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
$969$	−6.71491	−	20.9932i	−0.215714	−	0.674398i
$970$		0			0
$971$			46.0892i			1.47907i	0.673116	+	0.739537i	$0.264955\pi$
$971$			46.0892i			1.47907i	−0.673116	+	0.739537i	$0.735045\pi$
$972$	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	0.871053	−	0.491189i	$-0.163438\pi$
$977$	11.8734	+	11.8734i	0.379864	+	0.379864i	−0.491189	+	0.871053i	$0.663438\pi$
$978$	5.71188	+	2.94339i	0.182646	+	0.0941193i
$979$		−	4.64287i		−	0.148387i
$980$		0			0
$981$	−3.80129	+	22.6548i	−0.121366	+	0.723312i
$982$	−15.8755	−	15.8755i	−0.506607	−	0.506607i
$983$	8.05185	−	8.05185i	0.256814	−	0.256814i	−0.566943	−	0.823757i	$-0.691874\pi$
$983$	8.05185	−	8.05185i	0.256814	−	0.256814i	0.823757	+	0.566943i	$0.191874\pi$
$984$	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
$993$	51.7355	−	16.5482i	1.64178	−	0.525141i
$994$	−1.10368	−	1.10368i	−0.0350065	−	0.0350065i
$995$		0			0
$996$	−13.6431	−	42.6531i	−0.432297	−	1.35151i
$997$		−	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
$999$	13.9311	+	10.4171i	0.440761	+	0.329582i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.483812 - 0.483812i) q^{2} +(0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(-1.12876 + 0.361045i) q^{6} +(-1.24531 - 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(-1.74104 - 2.44311i) q^{9} +O(q^{10})\)	\(q+(-0.483812 - 0.483812i) q^{2} +(0.793397 - 1.53965i) q^{3} -1.53185i q^{4} +(-1.12876 + 0.361045i) 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} +(-0.339668 + 2.02434i) q^{18} +(-1.33304 - 1.33304i) q^{19} +(-2.90536 + 0.929314i) q^{21} +0.374570i q^{22} -1.69635i q^{23} +(1.27516 + 3.98660i) 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} +(-0.903130 + 0.288877i) q^{33} +(3.26578 - 3.26578i) q^{34} +(-3.74248 + 2.66702i) q^{36} +(-2.36718 - 2.36718i) q^{37} +1.28988i q^{38} +(-1.42814 + 6.07951i) 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} +(2.84728 + 2.12908i) q^{54} +4.25585 q^{56} +(-3.11005 + 0.994786i) q^{57} +(-1.86446 + 1.86446i) q^{58} +(-1.30531 - 1.30531i) q^{59} -1.16343 q^{61} -3.92960i q^{62} +(-0.874290 + 5.21056i) 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} +(7.14967 + 1.19966i) q^{72} +(-8.11348 - 8.11348i) q^{73} +2.29054i q^{74} +(-2.04202 + 2.04202i) q^{76} +0.964126i q^{77} +(3.63229 - 2.25039i) q^{78} +3.85408 q^{79} +(-2.93755 + 8.50710i) q^{81} -5.53597 q^{82} +(11.9347 + 11.9347i) q^{83} +(1.42357 + 4.45059i) 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} +(9.47471 - 3.03059i) q^{93} -5.79622 q^{94} +(9.56505 - 3.05949i) q^{96} +(-1.03487 + 1.03487i) q^{97} +(-1.88610 + 1.88610i) q^{98} +(-0.271772 + 1.61970i) 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

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