LMFDB - Embedded newform 945.2.cj.e.577.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(208,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 10]))

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

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

chi := DirichletCharacter("945.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cj (of order $12$, degree $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			577.7
Character	$\chi$	$=$	945.577
Dual form			945.2.cj.e.208.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03275 + 0.544675i) q^{2} +(2.10336 - 1.21438i) q^{4} +(-2.13753 - 0.656469i) q^{5} +(2.62752 + 0.310030i) q^{7} +(-0.638021 + 0.638021i) q^{8} +O(q^{10})$	\(q+(-2.03275 + 0.544675i) q^{2} +(2.10336 - 1.21438i) q^{4} +(-2.13753 - 0.656469i) q^{5} +(2.62752 + 0.310030i) q^{7} +(-0.638021 + 0.638021i) q^{8} +(4.70264 + 0.170180i) q^{10} +0.0883552 q^{11} +(-5.14229 + 1.37787i) q^{13} +(-5.50997 + 0.800930i) q^{14} +(-1.47933 + 2.56227i) q^{16} +(0.913316 + 3.40854i) q^{17} +(-2.57895 - 4.46688i) q^{19} +(-5.29321 + 1.21498i) q^{20} +(-0.179604 + 0.0481248i) q^{22} +(2.62082 - 2.62082i) q^{23} +(4.13810 + 2.80645i) q^{25} +(9.70252 - 5.60175i) q^{26} +(5.90313 - 2.53870i) q^{28} +(0.609023 - 0.351619i) q^{29} +(4.22275 - 2.43801i) q^{31} +(2.07857 - 7.75733i) q^{32} +(-3.71309 - 6.43126i) q^{34} +(-5.41289 - 2.38759i) q^{35} +(-2.26311 + 8.44603i) q^{37} +(7.67537 + 7.67537i) q^{38} +(1.78263 - 0.944950i) q^{40} +(-2.57843 - 1.48865i) q^{41} +(2.22267 + 0.595563i) q^{43} +(0.185843 - 0.107297i) q^{44} +(-3.89998 + 6.75496i) q^{46} +(1.48679 + 5.54877i) q^{47} +(6.80776 + 1.62922i) q^{49} +(-9.94033 - 3.45090i) q^{50} +(-9.14285 + 9.14285i) q^{52} +(3.63020 + 13.5481i) q^{53} +(-0.188862 - 0.0580025i) q^{55} +(-1.87422 + 1.47861i) q^{56} +(-1.04647 + 1.04647i) q^{58} +(-1.73147 - 2.99899i) q^{59} +(-1.18197 - 0.682409i) q^{61} +(-7.25589 + 7.25589i) q^{62} +10.9836i q^{64} +(11.8964 + 0.430508i) q^{65} +(-1.54956 + 5.78303i) q^{67} +(6.06029 + 6.06029i) q^{68} +(12.3035 + 1.90511i) q^{70} -13.4890 q^{71} +(-1.06617 + 0.285680i) q^{73} -18.4014i q^{74} +(-10.8489 - 6.26364i) q^{76} +(0.232155 + 0.0273928i) q^{77} +(3.07762 + 1.77687i) q^{79} +(4.84417 - 4.50581i) q^{80} +(6.05214 + 1.62166i) q^{82} +(-0.0856239 + 0.319553i) q^{83} +(0.285360 - 7.88543i) q^{85} -4.84253 q^{86} +(-0.0563725 + 0.0563725i) q^{88} +(5.71165 + 9.89286i) q^{89} +(-13.9387 + 2.02613i) q^{91} +(2.32987 - 8.69519i) q^{92} +(-6.04455 - 10.4695i) q^{94} +(2.58023 + 11.2411i) q^{95} +(-10.0857 - 2.70245i) q^{97} +(-14.7259 + 0.396205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) $ 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8	$ 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8} - 24 q^{10} - 32 q^{11} + 76 q^{16} + 6 q^{17} + 60 q^{20} + 8 q^{22} + 16 q^{23} - 4 q^{25} + 36 q^{26} + 22 q^{28} + 48 q^{31} + 6 q^{32} + 36 q^{35} - 4 q^{37} - 12 q^{41} - 4 q^{43} - 16 q^{46} + 54 q^{47} + 44 q^{50} - 8 q^{53} + 92 q^{56} - 56 q^{58} - 24 q^{61} - 62 q^{65} + 12 q^{67} + 2 q^{70} + 40 q^{71} + 36 q^{73} - 96 q^{76} + 110 q^{77} - 36 q^{80} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 32 q^{86} - 92 q^{88} - 48 q^{91} + 26 q^{92} + 94 q^{95} - 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8 - 24 * q^10 - 32 * q^11 + 76 * q^16 + 6 * q^17 + 60 * q^20 + 8 * q^22 + 16 * q^23 - 4 * q^25 + 36 * q^26 + 22 * q^28 + 48 * q^31 + 6 * q^32 + 36 * q^35 - 4 * q^37 - 12 * q^41 - 4 * q^43 - 16 * q^46 + 54 * q^47 + 44 * q^50 - 8 * q^53 + 92 * q^56 - 56 * q^58 - 24 * q^61 - 62 * q^65 + 12 * q^67 + 2 * q^70 + 40 * q^71 + 36 * q^73 - 96 * q^76 + 110 * q^77 - 36 * q^80 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 32 * q^86 - 92 * q^88 - 48 * q^91 + 26 * q^92 + 94 * q^95 - 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.03275	+	0.544675i	−1.43737	+	0.385143i	−0.891613	−	0.452798i	$-0.850426\pi$
$2$	−2.03275	+	0.544675i	−1.43737	+	0.385143i	−0.545760	+	0.837941i	$0.683759\pi$
$3$		0			0
$3$		0			0
$4$	2.10336	−	1.21438i	1.05168	−	0.607189i
$5$	−2.13753	−	0.656469i	−0.955934	−	0.293582i
$5$	−2.13753	−	0.656469i	−0.955934	−	0.293582i
$6$		0			0
$7$	2.62752	+	0.310030i	0.993111	+	0.117180i
$7$	2.62752	+	0.310030i	0.993111	+	0.117180i
$8$	−0.638021	+	0.638021i	−0.225575	+	0.225575i
$9$		0			0
$10$	4.70264	+	0.170180i	1.48711	+	0.0538157i
$11$	0.0883552			0.0266401			0.0133200	−	0.999911i	$-0.495760\pi$
$11$	0.0883552			0.0266401			0.0133200	+	0.999911i	$0.495760\pi$
$12$		0			0
$13$	−5.14229	+	1.37787i	−1.42622	+	0.382153i	−0.887684	−	0.460452i	$-0.847687\pi$
$13$	−5.14229	+	1.37787i	−1.42622	+	0.382153i	−0.538531	+	0.842606i	$0.681021\pi$
$14$	−5.50997	+	0.800930i	−1.47260	+	0.214058i
$15$		0			0
$16$	−1.47933	+	2.56227i	−0.369832	+	0.640568i
$17$	0.913316	+	3.40854i	0.221512	+	0.826693i	0.983772	+	0.179422i	$0.0574229\pi$
$17$	0.913316	+	3.40854i	0.221512	+	0.826693i	−0.762260	+	0.647270i	$0.775910\pi$
$18$		0			0
$19$	−2.57895	−	4.46688i	−0.591652	−	1.02477i	−0.994010	−	0.109289i	$-0.965143\pi$
$19$	−2.57895	−	4.46688i	−0.591652	−	1.02477i	0.402358	−	0.915482i	$-0.368191\pi$
$20$	−5.29321	+	1.21498i	−1.18360	+	0.271677i
$21$		0			0
$22$	−0.179604	+	0.0481248i	−0.0382918	+	0.0102602i
$23$	2.62082	−	2.62082i	0.546478	−	0.546478i	−0.378942	−	0.925420i	$-0.623712\pi$
$23$	2.62082	−	2.62082i	0.546478	−	0.546478i	0.925420	+	0.378942i	$0.123712\pi$
$24$		0			0
$25$	4.13810	+	2.80645i	0.827619	+	0.561290i
$26$	9.70252	−	5.60175i	1.90282	−	1.09859i
$27$		0			0
$28$	5.90313	−	2.53870i	1.11559	−	0.479769i
$29$	0.609023	−	0.351619i	0.113093	−	0.0652941i	−0.442387	−	0.896824i	$-0.645868\pi$
$29$	0.609023	−	0.351619i	0.113093	−	0.0652941i	0.555479	+	0.831530i	$0.312535\pi$
$30$		0			0
$31$	4.22275	−	2.43801i	0.758429	−	0.437879i	−0.0703027	−	0.997526i	$-0.522397\pi$
$31$	4.22275	−	2.43801i	0.758429	−	0.437879i	0.828731	+	0.559647i	$0.189063\pi$
$32$	2.07857	−	7.75733i	0.367443	−	1.37132i
$33$		0			0
$34$	−3.71309	−	6.43126i	−0.636790	−	1.10295i
$35$	−5.41289	−	2.38759i	−0.914946	−	0.403576i
$36$		0			0
$37$	−2.26311	+	8.44603i	−0.372053	+	1.38852i	0.485551	+	0.874208i	$0.338619\pi$
$37$	−2.26311	+	8.44603i	−0.372053	+	1.38852i	−0.857604	+	0.514311i	$0.828048\pi$
$38$	7.67537	+	7.67537i	1.24511	+	1.24511i
$39$		0			0
$40$	1.78263	−	0.944950i	0.281859	−	0.149410i
$41$	−2.57843	−	1.48865i	−0.402682	−	0.232489i	0.284958	−	0.958540i	$-0.408020\pi$
$41$	−2.57843	−	1.48865i	−0.402682	−	0.232489i	−0.687641	+	0.726051i	$0.741354\pi$
$42$		0			0
$43$	2.22267	+	0.595563i	0.338954	+	0.0908225i	0.424281	−	0.905530i	$-0.360527\pi$
$43$	2.22267	+	0.595563i	0.338954	+	0.0908225i	−0.0853269	+	0.996353i	$0.527193\pi$
$44$	0.185843	−	0.107297i	0.0280169	−	0.0161756i
$45$		0			0
$46$	−3.89998	+	6.75496i	−0.575021	+	0.995965i
$47$	1.48679	+	5.54877i	0.216870	+	0.809372i	0.985500	+	0.169677i	$0.0542725\pi$
$47$	1.48679	+	5.54877i	0.216870	+	0.809372i	−0.768629	+	0.639695i	$0.779061\pi$
$48$		0			0
$49$	6.80776	+	1.62922i	0.972537	+	0.232746i
$50$	−9.94033	−	3.45090i	−1.40577	−	0.488032i
$51$		0			0
$52$	−9.14285	+	9.14285i	−1.26789	+	1.26789i
$53$	3.63020	+	13.5481i	0.498646	+	1.86097i	0.508569	+	0.861021i	$0.330175\pi$
$53$	3.63020	+	13.5481i	0.498646	+	1.86097i	−0.00992346	+	0.999951i	$0.503159\pi$
$54$		0			0
$55$	−0.188862	−	0.0580025i	−0.0254662	−	0.00782105i
$56$	−1.87422	+	1.47861i	−0.250453	+	0.197588i
$57$		0			0
$58$	−1.04647	+	1.04647i	−0.137409	+	0.137409i
$59$	−1.73147	−	2.99899i	−0.225418	−	0.390436i	0.731027	−	0.682349i	$-0.239041\pi$
$59$	−1.73147	−	2.99899i	−0.225418	−	0.390436i	−0.956445	+	0.291913i	$0.905708\pi$
$60$		0			0
$61$	−1.18197	−	0.682409i	−0.151335	−	0.0873735i	0.422420	−	0.906400i	$-0.361181\pi$
$61$	−1.18197	−	0.682409i	−0.151335	−	0.0873735i	−0.573756	+	0.819027i	$0.694514\pi$
$62$	−7.25589	+	7.25589i	−0.921499	+	0.921499i
$63$		0			0
$64$			10.9836i			1.37295i
$65$	11.8964	+	0.430508i	1.47556	+	0.0533980i
$66$		0			0
$67$	−1.54956	+	5.78303i	−0.189309	+	0.706509i	0.804359	+	0.594144i	$0.202509\pi$
$67$	−1.54956	+	5.78303i	−0.189309	+	0.706509i	−0.993667	+	0.112365i	$0.964157\pi$
$68$	6.06029	+	6.06029i	0.734918	+	0.734918i
$69$		0			0
$70$	12.3035	+	1.90511i	1.47055	+	0.227705i
$71$	−13.4890			−1.60085			−0.800425	−	0.599433i	$-0.795393\pi$
$71$	−13.4890			−1.60085			−0.800425	+	0.599433i	$0.795393\pi$
$72$		0			0
$73$	−1.06617	+	0.285680i	−0.124786	+	0.0334363i	−0.320672	−	0.947190i	$-0.603909\pi$
$73$	−1.06617	+	0.285680i	−0.124786	+	0.0334363i	0.195886	+	0.980627i	$0.437242\pi$
$74$		−	18.4014i		−	2.13911i
$75$		0			0
$76$	−10.8489	−	6.26364i	−1.24446	−	0.718489i
$77$	0.232155	+	0.0273928i	0.0264566	+	0.00312170i
$78$		0			0
$79$	3.07762	+	1.77687i	0.346260	+	0.199913i	0.663037	−	0.748587i	$-0.269267\pi$
$79$	3.07762	+	1.77687i	0.346260	+	0.199913i	−0.316777	+	0.948500i	$0.602601\pi$
$80$	4.84417	−	4.50581i	0.541595	−	0.503765i
$81$		0			0
$82$	6.05214	+	1.62166i	0.668347	+	0.179083i
$83$	−0.0856239	+	0.319553i	−0.00939845	+	0.0350755i	−0.970466	−	0.241239i	$-0.922446\pi$
$83$	−0.0856239	+	0.319553i	−0.00939845	+	0.0350755i	0.961067	+	0.276314i	$0.0891130\pi$
$84$		0			0
$85$	0.285360	−	7.88543i	0.0309516	−	0.855295i
$86$	−4.84253			−0.522184
$87$		0			0
$88$	−0.0563725	+	0.0563725i	−0.00600933	+	0.00600933i
$89$	5.71165	+	9.89286i	0.605434	+	1.04864i	0.991983	+	0.126373i	$0.0403336\pi$
$89$	5.71165	+	9.89286i	0.605434	+	1.04864i	−0.386549	+	0.922269i	$0.626333\pi$
$90$		0			0
$91$	−13.9387	+	2.02613i	−1.46117	+	0.212396i
$92$	2.32987	−	8.69519i	0.242906	−	0.906536i
$93$		0			0
$94$	−6.04455	−	10.4695i	−0.623448	−	1.07984i
$95$	2.58023	+	11.2411i	0.264726	+	1.15331i
$96$		0			0
$97$	−10.0857	−	2.70245i	−1.02405	−	0.274393i	−0.292559	−	0.956247i	$-0.594507\pi$
$97$	−10.0857	−	2.70245i	−1.02405	−	0.274393i	−0.731488	+	0.681855i	$0.761174\pi$
$98$	−14.7259	+	0.396205i	−1.48754	+	0.0400227i
$99$		0			0
$100$	12.1120	+	0.877774i	1.21120	+	0.0877774i
$101$			11.4917i			1.14347i	0.820438	+	0.571735i	$0.193730\pi$
$101$			11.4917i			1.14347i	−0.820438	+	0.571735i	$0.806270\pi$
$102$		0			0
$103$	9.24526	+	9.24526i	0.910963	+	0.910963i	0.996348	−	0.0853854i	$-0.0272122\pi$
$103$	9.24526	+	9.24526i	0.910963	+	0.910963i	−0.0853854	+	0.996348i	$0.527212\pi$
$104$	2.40178	−	4.16000i	0.235514	−	0.407922i
$105$		0			0
$106$	−14.7586	−	25.5626i	−1.43348	−	2.48286i
$107$	−3.11943	+	11.6419i	−0.301567	+	1.12546i	0.634294	+	0.773092i	$0.281291\pi$
$107$	−3.11943	+	11.6419i	−0.301567	+	1.12546i	−0.935860	+	0.352371i	$0.885376\pi$
$108$		0			0
$109$	11.5914	+	6.69232i	1.11026	+	0.641008i	0.938897	−	0.344200i	$-0.111850\pi$
$109$	11.5914	+	6.69232i	1.11026	+	0.641008i	0.171363	+	0.985208i	$0.445183\pi$
$110$	0.415502	+	0.0150363i	0.0396166	+	0.00143366i
$111$		0			0
$112$	−4.68136	+	6.27380i	−0.442347	+	0.592818i
$113$	3.86407	+	14.4209i	0.363501	+	1.35660i	0.869442	+	0.494035i	$0.164479\pi$
$113$	3.86407	+	14.4209i	0.363501	+	1.35660i	−0.505941	+	0.862568i	$0.668855\pi$
$114$		0			0
$115$	−7.32257	+	3.88160i	−0.682833	+	0.361961i
$116$	0.853998	−	1.47917i	0.0792917	−	0.137337i
$117$		0			0
$118$	5.15313	+	5.15313i	0.474384	+	0.474384i
$119$	1.34301	+	9.23918i	0.123113	+	0.846954i
$120$		0			0
$121$	−10.9922			−0.999290
$122$	2.77434	+	0.743382i	0.251177	+	0.0673026i
$123$		0			0
$124$	5.92132	−	10.2560i	0.531750	−	0.921019i
$125$	−7.00297	−	8.71541i	−0.626365	−	0.779530i
$126$		0			0
$127$	4.64611	+	4.64611i	0.412276	+	0.412276i	0.882531	−	0.470255i	$-0.155838\pi$
$127$	4.64611	+	4.64611i	0.412276	+	0.412276i	−0.470255	+	0.882531i	$0.655838\pi$
$128$	−1.82533	−	6.81221i	−0.161337	−	0.602120i
$129$		0			0
$130$	−24.4168	+	5.60452i	−2.14150	+	0.491549i
$131$		−	19.1646i		−	1.67442i	−0.546880	−	0.837211i	$-0.684185\pi$
$131$		−	19.1646i		−	1.67442i	0.546880	−	0.837211i	$-0.315815\pi$
$132$		0			0
$133$	−5.39139	−	12.5364i	−0.467493	−	1.08704i
$134$		−	12.5995i		−	1.08843i
$135$		0			0
$136$	−2.75744	−	1.59201i	−0.236448	−	0.136513i
$137$	10.1102	+	10.1102i	0.863775	+	0.863775i	0.991774	−	0.128000i	$-0.0408556\pi$
$137$	10.1102	+	10.1102i	0.863775	+	0.863775i	−0.128000	+	0.991774i	$0.540856\pi$
$138$		0			0
$139$	−8.63234	+	14.9516i	−0.732185	+	1.26818i	0.223762	+	0.974644i	$0.428166\pi$
$139$	−8.63234	+	14.9516i	−0.732185	+	1.26818i	−0.955947	+	0.293538i	$0.905167\pi$
$140$	−14.2847	+	1.55133i	−1.20728	+	0.131111i
$141$		0			0
$142$	27.4198	−	7.34711i	2.30102	−	0.616556i
$143$	−0.454348	+	0.121742i	−0.0379945	+	0.0101806i
$144$		0			0
$145$	−1.53263	+	0.351793i	−0.127278	+	0.0292149i
$146$	2.01166	−	1.16143i	0.166486	−	0.0961209i
$147$		0			0
$148$	5.49653	+	20.5133i	0.451812	+	1.68619i
$149$			2.82533i			0.231460i	0.993281	+	0.115730i	$0.0369207\pi$
$149$			2.82533i			0.231460i	−0.993281	+	0.115730i	$0.963079\pi$
$150$		0			0
$151$	5.89991			0.480128			0.240064	−	0.970757i	$-0.422832\pi$
$151$	5.89991			0.480128			0.240064	+	0.970757i	$0.422832\pi$
$152$	4.49539	+	1.20454i	0.364624	+	0.0977007i
$153$		0			0
$154$	−0.486835	+	0.0707663i	−0.0392302	+	0.00570251i
$155$	−10.6267	+	2.43921i	−0.853561	+	0.195922i
$156$		0			0
$157$	−11.3951	−	3.05331i	−0.909427	−	0.243680i	−0.226367	−	0.974042i	$-0.572685\pi$
$157$	−11.3951	−	3.05331i	−0.909427	−	0.243680i	−0.683060	+	0.730362i	$0.739351\pi$
$158$	−7.22386	−	1.93563i	−0.574700	−	0.153990i
$159$		0			0
$160$	−9.53546	+	15.2170i	−0.753844	+	1.20301i
$161$	7.69879	−	6.07372i	0.606750	−	0.478677i
$162$		0			0
$163$	−9.70984	−	2.60174i	−0.760533	−	0.203784i	−0.142348	−	0.989817i	$-0.545465\pi$
$163$	−9.70984	−	2.60174i	−0.760533	−	0.203784i	−0.618185	+	0.786032i	$0.712132\pi$
$164$	−7.23116			−0.564658
$165$		0			0
$166$		−	0.696209i		−	0.0540363i
$167$	0.281253	+	1.04965i	0.0217640	+	0.0812244i	0.975954	−	0.217978i	$-0.0699461\pi$
$167$	0.281253	+	1.04965i	0.0217640	+	0.0812244i	−0.954190	+	0.299202i	$0.903279\pi$
$168$		0			0
$169$	13.2863	−	7.67086i	1.02202	−	0.590066i
$170$	3.71493	+	16.1846i	0.284922	+	1.24130i
$171$		0			0
$172$	5.39833	−	1.44648i	0.411619	−	0.110293i
$173$	9.88708	−	2.64924i	0.751701	−	0.201418i	0.137428	−	0.990512i	$-0.456116\pi$
$173$	9.88708	−	2.64924i	0.751701	−	0.201418i	0.614272	+	0.789094i	$0.289450\pi$
$174$		0			0
$175$	10.0029	+	8.65695i	0.756145	+	0.654404i
$176$	−0.130706	+	0.226390i	−0.00985237	+	0.0170648i
$177$		0			0
$178$	−16.9988	−	16.9988i	−1.27411	−	1.27411i
$179$	4.73666	+	2.73471i	0.354034	+	0.204402i	0.666461	−	0.745540i	$-0.267808\pi$
$179$	4.73666	+	2.73471i	0.354034	+	0.204402i	−0.312426	+	0.949942i	$0.601142\pi$
$180$		0			0
$181$			17.8425i			1.32622i	0.748520	+	0.663112i	$0.230765\pi$
$181$			17.8425i			1.32622i	−0.748520	+	0.663112i	$0.769235\pi$
$182$	27.2303	−	11.7107i	2.01845	−	0.868052i
$183$		0			0
$184$			3.34427i			0.246543i
$185$	10.3820	−	16.5680i	0.763302	−	1.21810i
$186$		0			0
$187$	0.0806962	+	0.301162i	0.00590109	+	0.0220232i
$188$	9.86556	+	9.86556i	0.719520	+	0.719520i
$189$		0			0
$190$	−11.3677	−	21.4450i	−0.824700	−	1.55578i
$191$	0.429463	−	0.743851i	0.0310748	−	0.0538232i	−0.850070	−	0.526670i	$-0.823440\pi$
$191$	0.429463	−	0.743851i	0.0310748	−	0.0538232i	0.881145	+	0.472847i	$0.156774\pi$
$192$		0			0
$193$	11.8682	+	3.18008i	0.854294	+	0.228907i	0.659284	−	0.751894i	$-0.270859\pi$
$193$	11.8682	+	3.18008i	0.854294	+	0.228907i	0.195010	+	0.980801i	$0.437526\pi$
$194$	21.9737			1.57762
$195$		0			0
$196$	16.2977	−	4.84034i	1.16412	−	0.345739i
$197$	−4.02358	−	4.02358i	−0.286668	−	0.286668i	0.549093	−	0.835761i	$-0.314973\pi$
$197$	−4.02358	−	4.02358i	−0.286668	−	0.286668i	−0.835761	+	0.549093i	$0.814973\pi$
$198$		0			0
$199$	11.9528	−	20.7029i	0.847314	−	1.46759i	−0.0362825	−	0.999342i	$-0.511552\pi$
$199$	11.9528	−	20.7029i	0.847314	−	1.46759i	0.883596	−	0.468249i	$-0.155115\pi$
$200$	−4.43077	+	0.849618i	−0.313303	+	0.0600771i
$201$		0			0
$202$	−6.25926	−	23.3599i	−0.440400	−	1.64359i
$203$	1.70923	−	0.735073i	0.119965	−	0.0515920i
$204$		0			0
$205$	4.53421	+	4.87471i	0.316683	+	0.340464i
$206$	−23.8290	−	13.7577i	−1.66024	−	0.958542i
$207$		0			0
$208$	4.07666	−	15.2143i	0.282665	−	1.05492i
$209$	−0.227864	−	0.394672i	−0.0157617	−	0.0273000i
$210$		0			0
$211$	5.61540	−	9.72616i	0.386580	−	0.669576i	−0.605407	−	0.795916i	$-0.706990\pi$
$211$	5.61540	−	9.72616i	0.386580	−	0.669576i	0.991987	+	0.126340i	$0.0403229\pi$
$212$	24.0881	+	24.0881i	1.65438	+	1.65438i
$213$		0			0
$214$		−	25.3641i		−	1.73386i
$215$	−4.36007	−	2.73215i	−0.297354	−	0.186331i
$216$		0			0
$217$	11.8512	−	5.09674i	0.804514	−	0.345989i
$218$	−27.2077	−	7.29028i	−1.84274	−	0.493760i
$219$		0			0
$220$	−0.467683	+	0.107350i	−0.0315312	+	0.00723751i
$221$	−9.39308	−	16.2693i	−0.631847	−	1.09439i
$222$		0			0
$223$	6.58992	−	24.5939i	0.441294	−	1.64693i	−0.284247	−	0.958751i	$-0.591743\pi$
$223$	6.58992	−	24.5939i	0.441294	−	1.64693i	0.725540	−	0.688180i	$-0.241590\pi$
$224$	7.86650	−	19.7381i	0.525603	−	1.31881i
$225$		0			0
$226$	−15.7094	−	27.2094i	−1.04497	−	1.80995i
$227$	−4.44644	+	4.44644i	−0.295120	+	0.295120i	−0.839099	−	0.543979i	$-0.816917\pi$
$227$	−4.44644	+	4.44644i	−0.295120	+	0.295120i	0.543979	+	0.839099i	$0.316917\pi$
$228$		0			0
$229$	3.42981			0.226649			0.113324	−	0.993558i	$-0.463850\pi$
$229$	3.42981			0.226649			0.113324	+	0.993558i	$0.463850\pi$
$230$	12.7708	−	11.8787i	0.842079	−	0.783261i
$231$		0			0
$232$	−0.164229	+	0.612910i	−0.0107821	+	0.0402395i
$233$	−9.14509	−	2.45042i	−0.599115	−	0.160532i	−0.0534991	−	0.998568i	$-0.517037\pi$
$233$	−9.14509	−	2.45042i	−0.599115	−	0.160532i	−0.545616	+	0.838036i	$0.683704\pi$
$234$		0			0
$235$	0.464538	−	12.8367i	0.0303031	−	0.837375i
$236$	−7.28382	−	4.20532i	−0.474136	−	0.273743i
$237$		0			0
$238$	−7.76235	−	18.0495i	−0.503158	−	1.16997i
$239$	1.38131	+	0.797500i	0.0893495	+	0.0515860i	0.544009	−	0.839079i	$-0.316906\pi$
$239$	1.38131	+	0.797500i	0.0893495	+	0.0515860i	−0.454660	+	0.890665i	$0.650239\pi$
$240$		0			0
$241$			22.3460i			1.43943i	0.694268	+	0.719716i	$0.255728\pi$
$241$			22.3460i			1.43943i	−0.694268	+	0.719716i	$0.744272\pi$
$242$	22.3444	−	5.98717i	1.43635	−	0.384870i
$243$		0			0
$244$	−3.31481			−0.212209
$245$	−13.4823	−	7.95161i	−0.861351	−	0.508010i
$246$		0			0
$247$	19.4165	+	19.4165i	1.23544	+	1.23544i
$248$	−1.13871	+	4.24970i	−0.0723078	+	0.269857i
$249$		0			0
$250$	18.9824	+	13.9019i	1.20055	+	0.879236i
$251$			20.2602i			1.27881i	0.768869	+	0.639406i	$0.220820\pi$
$251$			20.2602i			1.27881i	−0.768869	+	0.639406i	$0.779180\pi$
$252$		0			0
$253$	0.231563	−	0.231563i	0.0145582	−	0.0145582i
$254$	−11.9750	−	6.91378i	−0.751380	−	0.433809i
$255$		0			0
$256$	−3.56269	−	6.17076i	−0.222668	−	0.385672i
$257$	5.68790	−	5.68790i	0.354801	−	0.354801i	−0.507091	−	0.861892i	$-0.669279\pi$
$257$	5.68790	−	5.68790i	0.354801	−	0.354801i	0.861892	+	0.507091i	$0.169279\pi$
$258$		0			0
$259$	−8.56489	+	21.4905i	−0.532197	+	1.33536i
$260$	25.5452	−	13.5411i	1.58424	−	0.839786i
$261$		0			0
$262$	10.4385	+	38.9570i	0.644892	+	2.40677i
$263$	14.7998	−	14.7998i	0.912598	−	0.912598i	−0.0838785	−	0.996476i	$-0.526731\pi$
$263$	14.7998	−	14.7998i	0.912598	−	0.912598i	0.996476	+	0.0838785i	$0.0267308\pi$
$264$		0			0
$265$	1.13423	−	31.3426i	0.0696754	−	1.92536i
$266$	17.7876	+	22.5468i	1.09063	+	1.38243i
$267$		0			0
$268$	3.76349	+	14.0456i	0.229892	+	0.857969i
$269$	3.69593	−	6.40154i	0.225345	−	0.390309i	−0.731078	−	0.682294i	$-0.760982\pi$
$269$	3.69593	−	6.40154i	0.225345	−	0.390309i	0.956423	+	0.291985i	$0.0943158\pi$
$270$		0			0
$271$	0.675089	−	0.389763i	0.0410087	−	0.0236764i	−0.479355	−	0.877621i	$-0.659130\pi$
$271$	0.675089	−	0.389763i	0.0410087	−	0.0236764i	0.520364	+	0.853944i	$0.325796\pi$
$272$	−10.0847	−	2.70219i	−0.611476	−	0.163844i
$273$		0			0
$274$	−26.0584	−	15.0448i	−1.57424	−	0.908890i
$275$	0.365622	+	0.247964i	0.0220478	+	0.0149528i
$276$		0			0
$277$	−6.74383	−	6.74383i	−0.405198	−	0.405198i	0.474862	−	0.880060i	$-0.342498\pi$
$277$	−6.74383	−	6.74383i	−0.405198	−	0.405198i	−0.880060	+	0.474862i	$0.842498\pi$
$278$	9.40363	−	35.0948i	0.563992	−	2.10485i
$279$		0			0
$280$	4.97687	−	1.93021i	0.297425	−	0.115352i
$281$	−9.49861	−	16.4521i	−0.566639	−	0.981448i	−0.996895	−	0.0787411i	$-0.974910\pi$
$281$	−9.49861	−	16.4521i	−0.566639	−	0.981448i	0.430256	−	0.902707i	$-0.358423\pi$
$282$		0			0
$283$	−5.81172	+	21.6896i	−0.345471	+	1.28931i	0.546590	+	0.837400i	$0.315926\pi$
$283$	−5.81172	+	21.6896i	−0.345471	+	1.28931i	−0.892061	+	0.451915i	$0.850741\pi$
$284$	−28.3723	+	16.3807i	−1.68358	+	0.972018i
$285$		0			0
$286$	0.857268	−	0.494944i	0.0506913	−	0.0292666i
$287$	−6.31335	−	4.71087i	−0.372665	−	0.278074i
$288$		0			0
$289$	3.93842	−	2.27385i	0.231672	−	0.133756i
$290$	2.92385	−	1.54990i	0.171695	−	0.0910130i
$291$		0			0
$292$	−1.89562	+	1.89562i	−0.110933	+	0.110933i
$293$	−9.16886	+	2.45679i	−0.535651	+	0.143527i	−0.516496	−	0.856289i	$-0.672764\pi$
$293$	−9.16886	+	2.45679i	−0.535651	+	0.143527i	−0.0191543	+	0.999817i	$0.506097\pi$
$294$		0			0
$295$	1.73233	+	7.54710i	0.100860	+	0.439409i
$296$	−3.94484	−	6.83266i	−0.229289	−	0.397140i
$297$		0			0
$298$	−1.53888	−	5.74319i	−0.0891452	−	0.332694i
$299$	−9.86585	+	17.0882i	−0.570557	+	0.988234i
$300$		0			0
$301$	5.65548	+	2.25395i	0.325977	+	0.129916i
$302$	−11.9931	+	3.21353i	−0.690123	+	0.184918i
$303$		0			0
$304$	15.2605			0.875249
$305$	2.07851	+	2.23460i	0.119015	+	0.127953i
$306$		0			0
$307$	4.02496	−	4.02496i	0.229717	−	0.229717i	−0.582858	−	0.812574i	$-0.698065\pi$
$307$	4.02496	−	4.02496i	0.229717	−	0.229717i	0.812574	+	0.582858i	$0.198065\pi$
$308$	0.521572	−	0.224307i	0.0297193	−	0.0127811i
$309$		0			0
$310$	20.2730	−	10.7464i	1.15143	−	0.610357i
$311$	−4.83281	+	2.79023i	−0.274044	+	0.158219i	−0.630724	−	0.776007i	$-0.717242\pi$
$311$	−4.83281	+	2.79023i	−0.274044	+	0.158219i	0.356680	+	0.934227i	$0.383909\pi$
$312$		0			0
$313$	−31.3358	+	8.39639i	−1.77120	+	0.474592i	−0.988935	−	0.148351i	$-0.952603\pi$
$313$	−31.3358	+	8.39639i	−1.77120	+	0.474592i	−0.782267	+	0.622943i	$0.785937\pi$
$314$	24.8265			1.40104
$315$		0			0
$316$	8.63115			0.485540
$317$	−6.19342	+	1.65952i	−0.347857	+	0.0932080i	−0.428517	−	0.903534i	$-0.640964\pi$
$317$	−6.19342	+	1.65952i	−0.347857	+	0.0932080i	0.0806600	+	0.996742i	$0.474297\pi$
$318$		0			0
$319$	0.0538103	−	0.0310674i	0.00301280	−	0.00173944i
$320$	7.21037	−	23.4777i	0.403072	−	1.31244i
$321$		0			0
$322$	−12.3415	+	16.5397i	−0.687767	+	0.921722i
$323$	12.8701	−	12.8701i	0.716113	−	0.716113i
$324$		0			0
$325$	−25.1462	−	8.72982i	−1.39486	−	0.484243i
$326$	21.1548			1.17166
$327$		0			0
$328$	2.59488	−	0.695297i	0.143278	−	0.0383914i
$329$	2.18629	+	15.0405i	0.120534	+	0.829209i
$330$		0			0
$331$	2.96535	−	5.13614i	0.162990	−	0.282308i	−0.772949	−	0.634468i	$-0.781219\pi$
$331$	2.96535	−	5.13614i	0.162990	−	0.282308i	0.935940	+	0.352160i	$0.114553\pi$
$332$	0.207960	+	0.776116i	0.0114133	+	0.0425949i
$333$		0			0
$334$	−1.14344	−	1.98049i	−0.0625660	−	0.108368i
$335$	7.10861	−	11.3442i	0.388385	−	0.619798i
$336$		0			0
$337$	9.33028	−	2.50004i	0.508253	−	0.136186i	0.00442531	−	0.999990i	$-0.498591\pi$
$337$	9.33028	−	2.50004i	0.508253	−	0.136186i	0.503828	+	0.863804i	$0.331925\pi$
$338$	−22.8297	+	22.8297i	−1.24177	+	1.24177i
$339$		0			0
$340$	−8.97568	−	16.9325i	−0.486775	−	0.918292i
$341$	0.373102	−	0.215411i	0.0202046	−	0.0116651i
$342$		0			0
$343$	17.3824	+	6.39144i	0.938564	+	0.345105i
$344$	−1.79809	+	1.03813i	−0.0969467	+	0.0559722i
$345$		0			0
$346$	−18.6550	+	10.7705i	−1.00290	+	0.579025i
$347$	7.96934	−	29.7420i	0.427816	−	1.59663i	−0.329879	−	0.944023i	$-0.607008\pi$
$347$	7.96934	−	29.7420i	0.427816	−	1.59663i	0.757695	−	0.652609i	$-0.226326\pi$
$348$		0			0
$349$	5.20858	+	9.02153i	0.278809	+	0.482911i	0.971089	−	0.238718i	$-0.0767270\pi$
$349$	5.20858	+	9.02153i	0.278809	+	0.482911i	−0.692280	+	0.721629i	$0.743394\pi$
$350$	−25.0486	−	12.1491i	−1.33890	−	0.649399i
$351$		0			0
$352$	0.183652	−	0.685400i	0.00978871	−	0.0365320i
$353$	−22.7835	−	22.7835i	−1.21265	−	1.21265i	−0.970153	−	0.242492i	$-0.922035\pi$
$353$	−22.7835	−	22.7835i	−1.21265	−	1.21265i	−0.242492	−	0.970153i	$-0.577965\pi$
$354$		0			0
$355$	28.8332	+	8.85511i	1.53031	+	0.469981i
$356$	24.0273	+	13.8722i	1.27345	+	0.735225i
$357$		0			0
$358$	−11.1180	−	2.97905i	−0.587604	−	0.157448i
$359$	6.83504	−	3.94621i	0.360739	−	0.208273i	−0.308666	−	0.951171i	$-0.599882\pi$
$359$	6.83504	−	3.94621i	0.360739	−	0.208273i	0.669405	+	0.742898i	$0.266549\pi$
$360$		0			0
$361$	−3.80199	+	6.58524i	−0.200105	+	0.346591i
$362$	−9.71837	−	36.2694i	−0.510786	−	1.90628i
$363$		0			0
$364$	−26.8576	+	21.1885i	−1.40772	+	1.11058i
$365$	2.46652	+	0.0892589i	0.129103	+	0.00467203i
$366$		0			0
$367$	6.37922	−	6.37922i	0.332992	−	0.332992i	−0.520729	−	0.853722i	$-0.674340\pi$
$367$	6.37922	−	6.37922i	0.332992	−	0.332992i	0.853722	+	0.520729i	$0.174340\pi$
$368$	2.83820	+	10.5923i	0.147951	+	0.552162i
$369$		0			0
$370$	−12.0799	+	39.3335i	−0.628005	+	2.04485i
$371$	5.33811	+	36.7234i	0.277141	+	1.90658i
$372$		0			0
$373$	−2.34834	+	2.34834i	−0.121592	+	0.121592i	−0.765285	−	0.643692i	$-0.777402\pi$
$373$	−2.34834	+	2.34834i	−0.121592	+	0.121592i	0.643692	+	0.765285i	$0.277402\pi$
$374$	−0.328071	−	0.568235i	−0.0169641	−	0.0293828i
$375$		0			0
$376$	−4.48884	−	2.59163i	−0.231494	−	0.133653i
$377$	−2.64729	+	2.64729i	−0.136342	+	0.136342i
$378$		0			0
$379$			9.10326i			0.467603i	0.972284	+	0.233802i	$0.0751166\pi$
$379$			9.10326i			0.467603i	−0.972284	+	0.233802i	$0.924883\pi$
$380$	19.0781	+	20.5107i	0.978686	+	1.05218i
$381$		0			0
$382$	−0.467835	+	1.74598i	−0.0239365	+	0.0893323i
$383$	14.4171	+	14.4171i	0.736677	+	0.736677i	0.971933	−	0.235256i	$-0.0755930\pi$
$383$	14.4171	+	14.4171i	0.736677	+	0.736677i	−0.235256	+	0.971933i	$0.575593\pi$
$384$		0			0
$385$	−0.478257	−	0.210956i	−0.0243742	−	0.0107513i
$386$	−25.8573			−1.31610
$387$		0			0
$388$	−24.4957	+	6.56360i	−1.24358	+	0.333216i
$389$		−	12.0832i		−	0.612642i	−0.951928	−	0.306321i	$-0.900902\pi$
$389$		−	12.0832i		−	0.612642i	0.951928	−	0.306321i	$-0.0990981\pi$
$390$		0			0
$391$	11.3268	+	6.53953i	0.572821	+	0.330718i
$392$	−5.38298	+	3.30402i	−0.271881	+	0.166878i
$393$		0			0
$394$	10.3705	+	5.98741i	0.522458	+	0.301641i
$395$	−5.41206	−	5.81848i	−0.272310	−	0.292759i
$396$		0			0
$397$	−26.5856	−	7.12359i	−1.33429	−	0.357523i	−0.479979	−	0.877280i	$-0.659356\pi$
$397$	−26.5856	−	7.12359i	−1.33429	−	0.357523i	−0.854314	+	0.519757i	$0.826022\pi$
$398$	−13.0208	+	48.5943i	−0.652674	+	2.43581i
$399$		0			0
$400$	−13.3125	+	6.45127i	−0.665625	+	0.322564i
$401$	−6.21149			−0.310187			−0.155093	−	0.987900i	$-0.549568\pi$
$401$	−6.21149			−0.310187			−0.155093	+	0.987900i	$0.549568\pi$
$402$		0			0
$403$	−18.3554	+	18.3554i	−0.914346	+	0.914346i
$404$	13.9553	+	24.1713i	0.694302	+	1.20257i
$405$		0			0
$406$	−3.07408	+	2.42520i	−0.152564	+	0.120361i
$407$	−0.199957	+	0.746251i	−0.00991151	+	0.0369903i
$408$		0			0
$409$	1.38540	+	2.39958i	0.0685036	+	0.118652i	0.898243	−	0.439500i	$-0.144844\pi$
$409$	1.38540	+	2.39958i	0.0685036	+	0.118652i	−0.829739	+	0.558151i	$0.811511\pi$
$410$	−11.8721	−	7.43940i	−0.586320	−	0.367406i
$411$		0			0
$412$	30.6734	+	8.21891i	1.51117	+	0.404917i
$413$	−3.61970	−	8.41673i	−0.178114	−	0.414160i
$414$		0			0
$415$	0.392801	−	0.626845i	0.0192818	−	0.0307706i
$416$			42.7545i			2.09621i
$417$		0			0
$418$	0.678158	+	0.678158i	0.0331698	+	0.0331698i
$419$	−6.18341	+	10.7100i	−0.302079	+	0.523217i	−0.976607	−	0.215033i	$-0.931014\pi$
$419$	−6.18341	+	10.7100i	−0.302079	+	0.523217i	0.674527	+	0.738250i	$0.264347\pi$
$420$		0			0
$421$	5.64924	+	9.78478i	0.275327	+	0.476881i	0.970218	−	0.242235i	$-0.0778804\pi$
$421$	5.64924	+	9.78478i	0.275327	+	0.476881i	−0.694890	+	0.719116i	$0.744547\pi$
$422$	−6.11713	+	22.8294i	−0.297777	+	1.11132i
$423$		0			0
$424$	−10.9601	−	6.32782i	−0.532270	−	0.307306i
$425$	−5.78651	+	16.6680i	−0.280687	+	0.808519i
$426$		0			0
$427$	−2.89408	−	2.15949i	−0.140054	−	0.104505i
$428$	7.57634	+	28.2753i	0.366216	+	1.36674i
$429$		0			0
$430$	10.3511	+	3.17897i	0.499173	+	0.153304i
$431$	−15.9132	+	27.5625i	−0.766513	+	1.32764i	0.172929	+	0.984934i	$0.444677\pi$
$431$	−15.9132	+	27.5625i	−0.766513	+	1.32764i	−0.939443	+	0.342706i	$0.888657\pi$
$432$		0			0
$433$	−6.61149	−	6.61149i	−0.317728	−	0.317728i	0.530166	−	0.847894i	$-0.322130\pi$
$433$	−6.61149	−	6.61149i	−0.317728	−	0.317728i	−0.847894	+	0.530166i	$0.822130\pi$
$434$	−21.3146	+	16.8155i	−1.02313	+	0.807169i
$435$		0			0
$436$	32.5080			1.55685
$437$	−18.4658	−	4.94790i	−0.883340	−	0.236690i
$438$		0			0
$439$	4.69348	−	8.12935i	0.224008	−	0.387993i	−0.732014	−	0.681290i	$-0.761419\pi$
$439$	4.69348	−	8.12935i	0.224008	−	0.387993i	0.956021	+	0.293297i	$0.0947526\pi$
$440$	0.157505	−	0.0834912i	0.00750875	−	0.00398029i
$441$		0			0
$442$	27.9553	+	27.9553i	1.32970	+	1.32970i
$443$	−6.55561	−	24.4659i	−0.311467	−	1.16241i	−0.927234	−	0.374481i	$-0.877821\pi$
$443$	−6.55561	−	24.4659i	−0.311467	−	1.16241i	0.615768	−	0.787928i	$-0.288846\pi$
$444$		0			0
$445$	−5.71447	−	24.8958i	−0.270892	−	1.18018i
$446$			53.5827i			2.53722i
$447$		0			0
$448$	−3.40524	+	28.8596i	−0.160882	+	1.36349i
$449$			7.88064i			0.371910i	0.982558	+	0.185955i	$0.0595379\pi$
$449$			7.88064i			0.371910i	−0.982558	+	0.185955i	$0.940462\pi$
$450$		0			0
$451$	−0.227817	−	0.131530i	−0.0107275	−	0.00619352i
$452$	25.6399	+	25.6399i	1.20600	+	1.20600i
$453$		0			0
$454$	6.61665	−	11.4604i	0.310535	−	0.537862i
$455$	31.1245	+	4.81940i	1.45914	+	0.225937i
$456$		0			0
$457$	−39.6678	+	10.6289i	−1.85558	+	0.497201i	−0.999797	−	0.0201351i	$-0.993590\pi$
$457$	−39.6678	+	10.6289i	−1.85558	+	0.497201i	−0.855782	+	0.517336i	$0.826924\pi$
$458$	−6.97197	+	1.86813i	−0.325779	+	0.0872921i
$459$		0			0
$460$	−10.6883	+	17.0568i	−0.498344	+	0.795276i
$461$	14.4344	−	8.33373i	0.672279	−	0.388140i	−0.124661	−	0.992199i	$-0.539784\pi$
$461$	14.4344	−	8.33373i	0.672279	−	0.388140i	0.796940	+	0.604059i	$0.206451\pi$
$462$		0			0
$463$	1.22034	+	4.55437i	0.0567140	+	0.211659i	0.988468	−	0.151431i	$-0.0483882\pi$
$463$	1.22034	+	4.55437i	0.0567140	+	0.211659i	−0.931754	+	0.363091i	$0.881722\pi$
$464$			2.08064i			0.0965915i
$465$		0			0
$466$	19.9244			0.922979
$467$	−16.4313	−	4.40276i	−0.760350	−	0.203735i	−0.142246	−	0.989831i	$-0.545432\pi$
$467$	−16.4313	−	4.40276i	−0.760350	−	0.203735i	−0.618104	+	0.786096i	$0.712099\pi$
$468$		0			0
$469$	−5.86441	+	14.7146i	−0.270793	+	0.679458i
$470$	6.04754	+	26.3469i	0.278952	+	1.21529i
$471$		0			0
$472$	3.01814	+	0.808707i	0.138921	+	0.0372238i
$473$	0.196385	+	0.0526211i	0.00902977	+	0.00241952i
$474$		0			0
$475$	1.86411	−	25.7221i	0.0855314	−	1.18021i
$476$	14.0447	+	17.8024i	0.643737	+	0.815973i
$477$		0			0
$478$	−3.24224	−	0.868755i	−0.148297	−	0.0397359i
$479$	4.74183			0.216660			0.108330	−	0.994115i	$-0.465450\pi$
$479$	4.74183			0.216660			0.108330	+	0.994115i	$0.465450\pi$
$480$		0			0
$481$		−	46.5502i		−	2.12251i
$482$	−12.1713	−	45.4239i	−0.554387	−	2.06900i
$483$		0			0
$484$	−23.1206	+	13.3487i	−1.05094	+	0.606758i
$485$	19.7844	+	12.3975i	0.898365	+	0.562943i
$486$		0			0
$487$	20.5040	−	5.49403i	0.929125	−	0.248958i	0.237644	−	0.971352i	$-0.423625\pi$
$487$	20.5040	−	5.49403i	0.929125	−	0.248958i	0.691482	+	0.722394i	$0.256958\pi$
$488$	1.18951	−	0.318729i	0.0538467	−	0.0144282i
$489$		0			0
$490$	31.7372	+	8.82020i	1.43374	+	0.398456i
$491$	−9.50551	+	16.4640i	−0.428978	+	0.743011i	−0.996783	−	0.0801518i	$-0.974459\pi$
$491$	−9.50551	+	16.4640i	−0.428978	+	0.743011i	0.567805	+	0.823163i	$0.307793\pi$
$492$		0			0
$493$	1.75474	+	1.75474i	0.0790295	+	0.0790295i
$494$	−50.0447	−	28.8933i	−2.25162	−	1.29997i
$495$		0			0
$496$			14.4265i			0.647767i
$497$	−35.4427	−	4.18200i	−1.58982	−	0.187588i
$498$		0			0
$499$		−	42.5764i		−	1.90598i	−0.302996	−	0.952992i	$-0.597987\pi$
$499$		−	42.5764i		−	1.90598i	0.302996	−	0.952992i	$-0.402013\pi$
$500$	−25.3136	−	9.82744i	−1.13206	−	0.439496i
$501$		0			0
$502$	−11.0352	−	41.1840i	−0.492526	−	1.83813i
$503$	7.74911	+	7.74911i	0.345516	+	0.345516i	0.858436	−	0.512920i	$-0.171436\pi$
$503$	7.74911	+	7.74911i	0.345516	+	0.345516i	−0.512920	+	0.858436i	$0.671436\pi$
$504$		0			0
$505$	7.54397	−	24.5640i	0.335702	−	1.09308i
$506$	−0.344583	+	0.596836i	−0.0153186	+	0.0265326i
$507$		0			0
$508$	15.4146	+	4.13033i	0.683912	+	0.183254i
$509$	4.48049			0.198594			0.0992972	−	0.995058i	$-0.468341\pi$
$509$	4.48049			0.198594			0.0992972	+	0.995058i	$0.468341\pi$
$510$		0			0
$511$	−2.88996	+	0.420085i	−0.127844	+	0.0185835i
$512$	20.5769	+	20.5769i	0.909378	+	0.909378i
$513$		0			0
$514$	−8.46403	+	14.6601i	−0.373333	+	0.646631i
$515$	−13.6928	−	25.8313i	−0.603378	−	1.13826i
$516$		0			0
$517$	0.131366	+	0.490263i	0.00577745	+	0.0215617i
$518$	5.70498	−	48.3500i	0.250662	−	2.12438i
$519$		0			0
$520$	−7.86480	+	7.31545i	−0.344894	+	0.320804i
$521$	−25.1653	−	14.5292i	−1.10251	−	0.636534i	−0.165631	−	0.986188i	$-0.552966\pi$
$521$	−25.1653	−	14.5292i	−1.10251	−	0.636534i	−0.936879	+	0.349653i	$0.886299\pi$
$522$		0			0
$523$	1.73790	−	6.48593i	0.0759931	−	0.283610i	−0.917464	−	0.397820i	$-0.869767\pi$
$523$	1.73790	−	6.48593i	0.0759931	−	0.283610i	0.993457	+	0.114210i	$0.0364336\pi$
$524$	−23.2731	−	40.3102i	−1.01669	−	1.76096i
$525$		0			0
$526$	−22.0233	+	38.1455i	−0.960263	+	1.66322i
$527$	12.1668	+	12.1668i	0.529992	+	0.529992i
$528$		0			0
$529$			9.26264i			0.402724i
$530$	14.7659	+	64.3295i	0.641389	+	2.79430i
$531$		0			0
$532$	−26.5639	−	19.8214i	−1.15169	−	0.859366i
$533$	15.3102	+	4.10236i	0.663158	+	0.177693i
$534$		0			0
$535$	14.3104	−	22.8371i	0.618694	−	0.987334i
$536$	−2.70104	−	4.67834i	−0.116667	−	0.202074i
$537$		0			0
$538$	−4.02616	+	15.0258i	−0.173580	+	0.647809i
$539$	0.601501	+	0.143950i	0.0259085	+	0.00620038i
$540$		0			0
$541$	−12.0145	−	20.8098i	−0.516544	−	0.894681i	−0.999815	−	0.0192104i	$-0.993885\pi$
$541$	−12.0145	−	20.8098i	−0.516544	−	0.894681i	0.483271	−	0.875471i	$-0.339449\pi$
$542$	−1.15999	+	1.15999i	−0.0498260	+	0.0498260i
$543$		0			0
$544$	28.3396			1.21505
$545$	−20.3838	−	21.9145i	−0.873146	−	0.938714i
$546$		0			0
$547$	−1.65315	+	6.16965i	−0.0706837	+	0.263795i	−0.992220	−	0.124497i	$-0.960268\pi$
$547$	−1.65315	+	6.16965i	−0.0706837	+	0.263795i	0.921536	+	0.388292i	$0.126935\pi$
$548$	33.5431	+	8.98785i	1.43289	+	0.383942i
$549$		0			0
$550$	−0.878279	−	0.304905i	−0.0374500	−	0.0130012i
$551$	−3.14128	−	1.81362i	−0.133823	−	0.0772628i
$552$		0			0
$553$	7.53565	+	5.62292i	0.320448	+	0.239111i
$554$	17.3817	+	10.0354i	0.738479	+	0.426361i
$555$		0			0
$556$			41.9317i			1.77830i
$557$	19.7617	−	5.29513i	0.837329	−	0.224362i	0.185421	−	0.982659i	$-0.440635\pi$
$557$	19.7617	−	5.29513i	0.837329	−	0.224362i	0.651909	+	0.758298i	$0.273969\pi$
$558$		0			0
$559$	−12.2502			−0.518130
$560$	14.1251	−	10.3373i	0.596895	−	0.436830i
$561$		0			0
$562$	28.2693	+	28.2693i	1.19247	+	1.19247i
$563$	5.51236	−	20.5724i	0.232318	−	0.867024i	−0.747021	−	0.664800i	$-0.768517\pi$
$563$	5.51236	−	20.5724i	0.232318	−	0.867024i	0.979339	−	0.202223i	$-0.0648167\pi$
$564$		0			0
$565$	1.20730	−	33.3618i	0.0507917	−	1.40354i
$566$		−	47.2552i		−	1.98628i
$567$		0			0
$568$	8.60627	−	8.60627i	0.361111	−	0.361111i
$569$	24.5111	+	14.1515i	1.02756	+	0.593262i	0.916285	−	0.400528i	$-0.131173\pi$
$569$	24.5111	+	14.1515i	1.02756	+	0.593262i	0.111275	+	0.993790i	$0.464506\pi$
$570$		0			0
$571$	20.0348	+	34.7013i	0.838430	+	1.45220i	0.891207	+	0.453596i	$0.149859\pi$
$571$	20.0348	+	34.7013i	0.838430	+	1.45220i	−0.0527777	+	0.998606i	$0.516807\pi$
$572$	−0.807818	+	0.807818i	−0.0337766	+	0.0337766i
$573$		0			0
$574$	15.3994	+	6.13731i	0.642757	+	0.256166i
$575$	18.2004	−	3.49000i	0.759008	−	0.145543i
$576$		0			0
$577$	0.463305	+	1.72908i	0.0192876	+	0.0719825i	0.974899	−	0.222648i	$-0.0714701\pi$
$577$	0.463305	+	1.72908i	0.0192876	+	0.0719825i	−0.955611	+	0.294631i	$0.904803\pi$
$578$	−6.76733	+	6.76733i	−0.281484	+	0.281484i
$579$		0			0
$580$	−2.79648	+	2.60115i	−0.116117	+	0.108007i
$581$	−0.324050	+	0.813087i	−0.0134439	+	0.0337325i
$582$		0			0
$583$	0.320747	+	1.19704i	0.0132840	+	0.0495765i
$584$	0.497970	−	0.862510i	0.0206062	−	0.0356909i
$585$		0			0
$586$	17.2999	−	9.98809i	0.714652	−	0.412604i
$587$	6.57314	+	1.76127i	0.271302	+	0.0726953i	0.391905	−	0.920006i	$-0.371816\pi$
$587$	6.57314	+	1.76127i	0.271302	+	0.0726953i	−0.120603	+	0.992701i	$0.538483\pi$
$588$		0			0
$589$	−21.7805	−	12.5750i	−0.897452	−	0.518144i
$590$	−7.63211	−	14.3978i	−0.314209	−	0.592750i
$591$		0			0
$592$	−18.2932	−	18.2932i	−0.751844	−	0.751844i
$593$	6.36367	−	23.7495i	0.261325	−	0.975277i	−0.703137	−	0.711054i	$-0.748218\pi$
$593$	6.36367	−	23.7495i	0.261325	−	0.975277i	0.964462	−	0.264223i	$-0.0851154\pi$
$594$		0			0
$595$	3.19451	−	20.6307i	0.130962	−	0.845776i
$596$	3.43102	+	5.94269i	0.140540	+	0.243422i
$597$		0			0
$598$	10.7474	−	40.1097i	0.439492	−	1.64021i
$599$	−19.9787	+	11.5347i	−0.816309	+	0.471296i	−0.849142	−	0.528164i	$-0.822880\pi$
$599$	−19.9787	+	11.5347i	−0.816309	+	0.471296i	0.0328327	+	0.999461i	$0.489547\pi$
$600$		0			0
$601$	17.9685	−	10.3741i	0.732951	−	0.423169i	−0.0865498	−	0.996248i	$-0.527584\pi$
$601$	17.9685	−	10.3741i	0.732951	−	0.423169i	0.819501	+	0.573078i	$0.194251\pi$
$602$	−12.7239	−	1.50133i	−0.518586	−	0.0611897i
$603$		0			0
$604$	12.4097	−	7.16472i	0.504942	−	0.291528i
$605$	23.4962	+	7.21604i	0.955255	+	0.293374i
$606$		0			0
$607$	−22.3661	+	22.3661i	−0.907810	+	0.907810i	−0.996095	−	0.0882849i	$-0.971861\pi$
$607$	−22.3661	+	22.3661i	−0.907810	+	0.907810i	0.0882849	+	0.996095i	$0.471861\pi$
$608$	−40.0116	+	10.7211i	−1.62268	+	0.434797i
$609$		0			0
$610$	−5.44223	−	3.41027i	−0.220350	−	0.138078i
$611$	−15.2910	−	26.4848i	−0.618608	−	1.07146i
$612$		0			0
$613$	6.04412	+	22.5570i	0.244120	+	0.911067i	0.973824	+	0.227304i	$0.0729912\pi$
$613$	6.04412	+	22.5570i	0.244120	+	0.911067i	−0.729704	+	0.683763i	$0.760342\pi$
$614$	−5.98946	+	10.3740i	−0.241715	+	0.418662i
$615$		0			0
$616$	−0.165597	+	0.130643i	−0.00667210	+	0.00526375i
$617$	−0.966179	+	0.258887i	−0.0388969	+	0.0104224i	−0.278215	−	0.960519i	$-0.589743\pi$
$617$	−0.966179	+	0.258887i	−0.0388969	+	0.0104224i	0.239318	+	0.970941i	$0.423076\pi$
$618$		0			0
$619$	−12.4971			−0.502303			−0.251151	−	0.967948i	$-0.580809\pi$
$619$	−12.4971			−0.502303			−0.251151	+	0.967948i	$0.580809\pi$
$620$	−19.3898	+	18.0354i	−0.778713	+	0.724321i
$621$		0			0
$622$	8.30415	−	8.30415i	0.332966	−	0.332966i
$623$	11.9404	+	27.7645i	0.478382	+	1.11236i
$624$		0			0
$625$	9.24768	+	23.2267i	0.369907	+	0.929069i
$626$	59.1246	−	34.1356i	2.36309	−	1.36433i
$627$		0			0
$628$	−27.6759	+	7.41573i	−1.10439	+	0.295920i
$629$	−30.8556			−1.23029
$630$		0			0
$631$	26.4557			1.05318			0.526592	−	0.850118i	$-0.323470\pi$
$631$	26.4557			1.05318			0.526592	+	0.850118i	$0.323470\pi$
$632$	−3.09727	+	0.829910i	−0.123203	+	0.0330121i
$633$		0			0
$634$	11.6858	−	6.74680i	0.464102	−	0.267950i
$635$	−6.88119	−	12.9813i	−0.273072	−	0.515145i
$636$		0			0
$637$	−37.2524	+	1.00229i	−1.47599	+	0.0397120i
$638$	−0.0924615	+	0.0924615i	−0.00366058	+	0.00366058i
$639$		0			0
$640$	−0.570312	+	15.7596i	−0.0225436	+	0.622952i
$641$	−47.7088			−1.88438			−0.942192	−	0.335072i	$-0.891239\pi$
$641$	−47.7088			−1.88438			−0.942192	+	0.335072i	$0.891239\pi$
$642$		0			0
$643$	−22.5788	+	6.04998i	−0.890422	+	0.238588i	−0.674898	−	0.737911i	$-0.735812\pi$
$643$	−22.5788	+	6.04998i	−0.890422	+	0.238588i	−0.215524	+	0.976499i	$0.569146\pi$
$644$	8.81756	−	22.1245i	0.347460	−	0.871827i
$645$		0			0
$646$	−19.1518	+	33.1718i	−0.753516	+	1.30513i
$647$	2.07649	+	7.74958i	0.0816354	+	0.304667i	0.994656	−	0.103246i	$-0.0329230\pi$
$647$	2.07649	+	7.74958i	0.0816354	+	0.304667i	−0.913020	+	0.407914i	$0.866256\pi$
$648$		0			0
$649$	−0.152984	−	0.264977i	−0.00600516	−	0.0104012i
$650$	55.8710	+	4.04905i	2.19144	+	0.158817i
$651$		0			0
$652$	−23.5828	+	6.31900i	−0.923575	+	0.247471i
$653$	−12.2599	+	12.2599i	−0.479765	+	0.479765i	−0.905057	−	0.425291i	$-0.860172\pi$
$653$	−12.2599	+	12.2599i	−0.479765	+	0.479765i	0.425291	+	0.905057i	$0.360172\pi$
$654$		0			0
$655$	−12.5810	+	40.9650i	−0.491580	+	1.60064i
$656$	7.62868	−	4.40442i	0.297850	−	0.171964i
$657$		0			0
$658$	−12.6363	−	29.3828i	−0.492616	−	1.14546i
$659$	27.0155	−	15.5974i	1.05237	−	0.607588i	0.129060	−	0.991637i	$-0.458804\pi$
$659$	27.0155	−	15.5974i	1.05237	−	0.607588i	0.923313	+	0.384049i	$0.125471\pi$
$660$		0			0
$661$	13.1989	−	7.62041i	0.513379	−	0.296400i	−0.220842	−	0.975309i	$-0.570881\pi$
$661$	13.1989	−	7.62041i	0.513379	−	0.296400i	0.734222	+	0.678910i	$0.237547\pi$
$662$	−3.23030	+	12.0557i	−0.125549	+	0.468556i
$663$		0			0
$664$	−0.149252	−	0.258511i	−0.00579208	−	0.0100322i
$665$	3.29453	+	30.3362i	0.127756	+	1.17639i
$666$		0			0
$667$	0.674607	−	2.51767i	0.0261209	−	0.0974844i
$668$	1.86625	+	1.86625i	0.0722074	+	0.0722074i
$669$		0			0
$670$	−8.27116	+	26.9318i	−0.319543	+	1.04047i
$671$	−0.104433	−	0.0602944i	−0.00403159	−	0.00232764i
$672$		0			0
$673$	38.5740	+	10.3359i	1.48692	+	0.398418i	0.908695	−	0.417461i	$-0.137080\pi$
$673$	38.5740	+	10.3359i	1.48692	+	0.398418i	0.578223	+	0.815879i	$0.303746\pi$
$674$	−17.6044	+	10.1639i	−0.678098	+	0.391500i
$675$		0			0
$676$	18.6306	−	32.2692i	0.716563	−	1.24112i
$677$	0.106222	+	0.396426i	0.00408244	+	0.0152359i	0.967937	−	0.251193i	$-0.0808229\pi$
$677$	0.106222	+	0.396426i	0.00408244	+	0.0152359i	−0.963855	+	0.266429i	$0.914156\pi$
$678$		0			0
$679$	−25.6626	−	10.2276i	−0.984839	−	0.392500i
$680$	4.84901	+	5.21314i	0.185951	+	0.199915i
$681$		0			0
$682$	−0.641096	+	0.641096i	−0.0245488	+	0.0245488i
$683$	7.96776	+	29.7361i	0.304878	+	1.13782i	0.933050	+	0.359746i	$0.117137\pi$
$683$	7.96776	+	29.7361i	0.304878	+	1.13782i	−0.628173	+	0.778074i	$0.716197\pi$
$684$		0			0
$685$	−14.9739	−	28.2480i	−0.572123	−	1.07930i
$686$	−38.8155	−	3.52444i	−1.48198	−	0.134564i
$687$		0			0
$688$	−4.81406	+	4.81406i	−0.183534	+	0.183534i
$689$	−37.3351	−	64.6662i	−1.42235	−	2.46359i
$690$		0			0
$691$	17.5381	+	10.1256i	0.667180	+	0.385197i	0.795007	−	0.606600i	$-0.207467\pi$
$691$	17.5381	+	10.1256i	0.667180	+	0.385197i	−0.127827	+	0.991796i	$0.540800\pi$
$692$	17.5790	−	17.5790i	0.668252	−	0.668252i
$693$		0			0
$694$			64.7988i			2.45973i
$695$	28.2672	−	26.2928i	1.07224	−	0.997342i
$696$		0			0
$697$	2.71922	−	10.1483i	0.102998	−	0.384394i
$698$	−15.5016	−	15.5016i	−0.586743	−	0.586743i
$699$		0			0
$700$	31.5525	+	6.06146i	1.19257	+	0.229102i
$701$	33.6028			1.26916			0.634581	−	0.772856i	$-0.281173\pi$
$701$	33.6028			1.26916			0.634581	+	0.772856i	$0.281173\pi$
$702$		0			0
$703$	43.5638	−	11.6729i	1.64304	−	0.440251i
$704$			0.970454i			0.0365754i
$705$		0			0
$706$	58.7229	+	33.9037i	2.21007	+	1.27598i
$707$	−3.56279	+	30.1948i	−0.133992	+	1.13559i
$708$		0			0
$709$	−4.78195	−	2.76086i	−0.179590	−	0.103686i	0.407510	−	0.913201i	$-0.366397\pi$
$709$	−4.78195	−	2.76086i	−0.179590	−	0.103686i	−0.587100	+	0.809514i	$0.699730\pi$
$710$	−63.4339	−	2.29556i	−2.38063	−	0.0861509i
$711$		0			0
$712$	−9.95601	−	2.66770i	−0.373117	−	0.0999765i
$713$	4.67749	−	17.4566i	0.175173	−	0.653756i
$714$		0			0
$715$	1.05110	+	0.0380376i	0.0393091	+	0.00142253i
$716$	13.2839			0.496442
$717$		0			0
$718$	−11.7445	+	11.7445i	−0.438302	+	0.438302i
$719$	−12.7748	−	22.1267i	−0.476421	−	0.825186i	0.523214	−	0.852202i	$-0.324733\pi$
$719$	−12.7748	−	22.1267i	−0.476421	−	0.825186i	−0.999635	+	0.0270154i	$0.991400\pi$
$720$		0			0
$721$	21.4258	+	27.1585i	0.797940	+	1.01143i
$722$	4.14169	−	15.4570i	0.154138	−	0.575250i
$723$		0			0
$724$	21.6676	+	37.5293i	0.805268	+	1.39477i
$725$	3.50700	+	0.254157i	0.130247	+	0.00943915i
$726$		0			0
$727$	22.0507	+	5.90847i	0.817816	+	0.219133i	0.643391	−	0.765537i	$-0.277527\pi$
$727$	22.0507	+	5.90847i	0.817816	+	0.219133i	0.174425	+	0.984671i	$0.444193\pi$
$728$	7.60046	−	10.1859i	0.281692	−	0.377514i
$729$		0			0
$730$	−5.06244	+	1.16201i	−0.187369	+	0.0430078i
$731$			8.12001i			0.300329i
$732$		0			0
$733$	−27.2649	−	27.2649i	−1.00705	−	1.00705i	−0.999975	−	0.00707692i	$-0.997747\pi$
$733$	−27.2649	−	27.2649i	−1.00705	−	1.00705i	−0.00707692	−	0.999975i	$-0.502253\pi$
$734$	−9.49278	+	16.4420i	−0.350385	+	0.606884i
$735$		0			0
$736$	−14.8830	−	25.7781i	−0.548594	−	0.950193i
$737$	−0.136911	+	0.510960i	−0.00504320	+	0.0188215i
$738$		0			0
$739$	−15.5491	−	8.97729i	−0.571984	−	0.330235i	0.185958	−	0.982558i	$-0.440461\pi$
$739$	−15.5491	−	8.97729i	−0.571984	−	0.330235i	−0.757941	+	0.652323i	$0.773795\pi$
$740$	1.71736	−	47.4563i	0.0631314	−	1.74453i
$741$		0			0
$742$	−30.8534	−	71.7420i	−1.13266	−	2.63373i
$743$	−8.34823	−	31.1560i	−0.306267	−	1.14300i	−0.931849	−	0.362845i	$-0.881805\pi$
$743$	−8.34823	−	31.1560i	−0.306267	−	1.14300i	0.625583	−	0.780158i	$-0.284861\pi$
$744$		0			0
$745$	1.85474	−	6.03923i	0.0679525	−	0.221260i
$746$	3.49451	−	6.05267i	0.127943	−	0.221604i
$747$		0			0
$748$	0.535458	+	0.535458i	0.0195783	+	0.0195783i
$749$	−11.8057	+	29.6222i	−0.431372	+	1.08237i
$750$		0			0
$751$	−28.1581			−1.02750			−0.513752	−	0.857939i	$-0.671745\pi$
$751$	−28.1581			−1.02750			−0.513752	+	0.857939i	$0.671745\pi$
$752$	−16.4169	−	4.39890i	−0.598664	−	0.160411i
$753$		0			0
$754$	3.93937	−	6.82319i	0.143463	−	0.248486i
$755$	−12.6113	−	3.87311i	−0.458971	−	0.140957i
$756$		0			0
$757$	−8.49483	−	8.49483i	−0.308750	−	0.308750i	0.535675	−	0.844424i	$-0.320057\pi$
$757$	−8.49483	−	8.49483i	−0.308750	−	0.308750i	−0.844424	+	0.535675i	$0.820057\pi$
$758$	−4.95832	−	18.5047i	−0.180094	−	0.672121i
$759$		0			0
$760$	−8.81830	−	5.52582i	−0.319873	−	0.200443i
$761$		−	25.4992i		−	0.924344i	−0.886790	−	0.462172i	$-0.847070\pi$
$761$		−	25.4992i		−	0.924344i	0.886790	−	0.462172i	$-0.152930\pi$
$762$		0			0
$763$	28.3820	+	21.1779i	1.02750	+	0.766693i
$764$		−	2.08612i		−	0.0754732i
$765$		0			0
$766$	−37.1589	−	21.4537i	−1.34261	−	0.775154i
$767$	13.0360	+	13.0360i	0.470701	+	0.470701i
$768$		0			0
$769$	−17.8420	+	30.9033i	−0.643401	+	1.11440i	0.341268	+	0.939966i	$0.389144\pi$
$769$	−17.8420	+	30.9033i	−0.643401	+	1.11440i	−0.984668	+	0.174436i	$0.944190\pi$
$770$	1.08708	+	0.168327i	0.0391757	+	0.00606607i
$771$		0			0
$772$	28.8250	−	7.72364i	1.03744	−	0.277980i
$773$	20.9993	−	5.62676i	0.755294	−	0.202380i	0.139429	−	0.990232i	$-0.455473\pi$
$773$	20.9993	−	5.62676i	0.755294	−	0.202380i	0.615865	+	0.787852i	$0.288807\pi$
$774$		0			0
$775$	24.3163	+	1.76224i	0.873467	+	0.0633014i
$776$	8.15911	−	4.71066i	0.292895	−	0.169103i
$777$		0			0
$778$	6.58140	+	24.5621i	0.235955	+	0.880595i
$779$			15.3567i			0.550210i
$780$		0			0
$781$	−1.19182			−0.0426468
$782$	−26.5865	−	7.12383i	−0.950731	−	0.254748i
$783$		0			0
$784$	−14.2454	+	15.0332i	−0.508766	+	0.536900i
$785$	22.3530	+	14.0071i	0.797812	+	0.499934i
$786$		0			0
$787$	17.3730	+	4.65509i	0.619282	+	0.165936i	0.554801	−	0.831983i	$-0.312794\pi$
$787$	17.3730	+	4.65509i	0.619282	+	0.165936i	0.0644806	+	0.997919i	$0.479461\pi$
$788$	−13.3492	−	3.57691i	−0.475546	−	0.127422i
$789$		0			0
$790$	14.1706	+	8.87971i	0.504166	+	0.315926i
$791$	5.68201	+	39.0892i	0.202029	+	1.38985i
$792$		0			0
$793$	7.01830	+	1.88055i	0.249227	+	0.0667802i
$794$	57.9220			2.05558
$795$		0			0
$796$		−	58.0610i		−	2.05792i
$797$	10.5307	+	39.3012i	0.373017	+	1.39212i	0.856220	+	0.516611i	$0.172807\pi$
$797$	10.5307	+	39.3012i	0.373017	+	1.39212i	−0.483203	+	0.875509i	$0.660527\pi$
$798$		0			0
$799$	−17.5553	+	10.1356i	−0.621062	+	0.358571i
$800$	30.3719	−	26.2672i	1.07381	−	0.928685i
$801$		0			0
$802$	12.6264	−	3.38324i	0.445854	−	0.119466i
$803$	−0.0942018	+	0.0252413i	−0.00332431	+	0.000890746i
$804$		0			0
$805$	−20.4436	+	7.92877i	−0.720543	+	0.279452i
$806$	27.3142	−	47.3096i	0.962102	−	1.66641i
$807$		0			0
$808$	−7.33197	−	7.33197i	−0.257938	−	0.257938i
$809$	24.7124	+	14.2677i	0.868840	+	0.501625i	0.866963	−	0.498373i	$-0.166069\pi$
$809$	24.7124	+	14.2677i	0.868840	+	0.501625i	0.00187764	+	0.999998i	$0.499402\pi$
$810$		0			0
$811$		−	48.5126i		−	1.70351i	−0.523941	−	0.851755i	$-0.675539\pi$
$811$		−	48.5126i		−	1.70351i	0.523941	−	0.851755i	$-0.324461\pi$
$812$	2.70249	−	3.62178i	0.0948386	−	0.127100i
$813$		0			0
$814$		−	1.62585i		−	0.0569862i
$815$	19.0471	+	11.9355i	0.667192	+	0.418083i
$816$		0			0
$817$	−3.07186	−	11.4643i	−0.107471	−	0.401086i
$818$	−4.12317	−	4.12317i	−0.144163	−	0.144163i
$819$		0			0
$820$	15.4568	+	4.74703i	0.539776	+	0.165774i
$821$	2.54586	−	4.40956i	0.0888512	−	0.153895i	−0.818175	−	0.574970i	$-0.805014\pi$
$821$	2.54586	−	4.40956i	0.0888512	−	0.153895i	0.907026	+	0.421075i	$0.138347\pi$
$822$		0			0
$823$	28.1584	+	7.54502i	0.981540	+	0.263003i	0.713693	−	0.700459i	$-0.247021\pi$
$823$	28.1584	+	7.54502i	0.981540	+	0.263003i	0.267847	+	0.963461i	$0.413688\pi$
$824$	−11.7973			−0.410980
$825$		0			0
$826$	11.9423	+	15.1376i	0.415527	+	0.526704i
$827$	19.3594	+	19.3594i	0.673191	+	0.673191i	0.958450	−	0.285259i	$-0.0920797\pi$
$827$	19.3594	+	19.3594i	0.673191	+	0.673191i	−0.285259	+	0.958450i	$0.592080\pi$
$828$		0			0
$829$	15.8644	−	27.4780i	0.550994	−	0.954350i	−0.447209	−	0.894430i	$-0.647582\pi$
$829$	15.8644	−	27.4780i	0.550994	−	0.954350i	0.998203	−	0.0599208i	$-0.0190848\pi$
$830$	−0.457040	+	1.48817i	−0.0158641	+	0.0516551i
$831$		0			0
$832$	−15.1340	−	56.4807i	−0.524675	−	1.95812i
$833$	0.664360	+	24.6925i	0.0230187	+	0.855546i
$834$		0			0
$835$	0.0878758	−	2.42830i	0.00304107	−	0.0840347i
$836$	−0.958561	−	0.553425i	−0.0331525	−	0.0191406i
$837$		0			0
$838$	6.73589	−	25.1387i	0.232687	−	0.868401i
$839$	6.71273	+	11.6268i	0.231749	+	0.401401i	0.958323	−	0.285687i	$-0.0922218\pi$
$839$	6.71273	+	11.6268i	0.231749	+	0.401401i	−0.726574	+	0.687088i	$0.758888\pi$
$840$		0			0
$841$	−14.2527	+	24.6864i	−0.491473	+	0.851257i
$842$	−16.8130	−	16.8130i	−0.579416	−	0.579416i
$843$		0			0
$844$		−	27.2769i		−	0.938908i
$845$	−33.4356	+	7.67465i	−1.15022	+	0.264016i
$846$		0			0
$847$	−28.8822	−	3.40791i	−0.992406	−	0.117097i
$848$	−40.0841	−	10.7405i	−1.37650	−	0.368831i
$849$		0			0
$850$	2.68389	−	37.0338i	0.0920567	−	1.27025i
$851$	16.2043	+	28.0667i	0.555477	+	0.962114i
$852$		0			0
$853$	10.8745	−	40.5841i	0.372335	−	1.38957i	−0.484864	−	0.874590i	$-0.661131\pi$
$853$	10.8745	−	40.5841i	0.372335	−	1.38957i	0.857199	−	0.514985i	$-0.172202\pi$
$854$	7.05917	+	2.81338i	0.241560	+	0.0962720i
$855$		0			0
$856$	−5.43750	−	9.41803i	−0.185850	−	0.321902i
$857$	15.1878	−	15.1878i	0.518806	−	0.518806i	−0.398404	−	0.917210i	$-0.630436\pi$
$857$	15.1878	−	15.1878i	0.518806	−	0.518806i	0.917210	+	0.398404i	$0.130436\pi$
$858$		0			0
$859$	3.55514			0.121300			0.0606499	−	0.998159i	$-0.480683\pi$
$859$	3.55514			0.121300			0.0606499	+	0.998159i	$0.480683\pi$
$860$	−12.4887	−	0.451943i	−0.425860	−	0.0154111i
$861$		0			0
$862$	17.3351	−	64.6953i	0.590435	−	2.20353i
$863$	−48.7342	−	13.0583i	−1.65893	−	0.444509i	−0.696838	−	0.717229i	$-0.745410\pi$
$863$	−48.7342	−	13.0583i	−1.65893	−	0.444509i	−0.962094	+	0.272719i	$0.912077\pi$
$864$		0			0
$865$	−22.8731	−	0.827738i	−0.777709	−	0.0281439i
$866$	17.0406	+	9.83842i	0.579065	+	0.334323i
$867$		0			0
$868$	18.7381	−	25.1122i	0.636012	−	0.852363i
$869$	0.271924	+	0.156995i	0.00922439	+	0.00532570i
$870$		0			0
$871$		−	31.8731i		−	1.07998i
$872$	−11.6654	+	3.12574i	−0.395041	+	0.105851i
$873$		0			0
$874$	40.2314			1.36085
$875$	−15.6984	−	25.0711i	−0.530704	−	0.847557i
$876$		0			0
$877$	30.5289	+	30.5289i	1.03089	+	1.03089i	0.999507	+	0.0313812i	$0.00999058\pi$
$877$	30.5289	+	30.5289i	1.03089	+	1.03089i	0.0313812	+	0.999507i	$0.490009\pi$
$878$	−5.11284	+	19.0814i	−0.172550	+	0.643965i
$879$		0			0
$880$	0.428008	−	0.398112i	0.0144281	−	0.0134203i
$881$		−	44.2073i		−	1.48938i	−0.667409	−	0.744691i	$-0.732597\pi$
$881$		−	44.2073i		−	1.48938i	0.667409	−	0.744691i	$-0.267403\pi$
$882$		0			0
$883$	−15.1931	+	15.1931i	−0.511288	+	0.511288i	−0.914921	−	0.403633i	$-0.867747\pi$
$883$	−15.1931	+	15.1931i	−0.511288	+	0.511288i	0.403633	+	0.914921i	$0.367747\pi$
$884$	−39.5141	−	22.8135i	−1.32900	−	0.767300i
$885$		0			0
$886$	26.6519	+	46.1624i	0.895388	+	1.55086i
$887$	−22.3495	+	22.3495i	−0.750424	+	0.750424i	−0.974558	−	0.224134i	$-0.928045\pi$
$887$	−22.3495	+	22.3495i	−0.750424	+	0.750424i	0.224134	+	0.974558i	$0.428045\pi$
$888$		0			0
$889$	10.7673	+	13.6482i	0.361125	+	0.457746i
$890$	25.1762	+	47.4946i	0.843910	+	1.59202i
$891$		0			0
$892$	−16.0053	−	59.7326i	−0.535897	−	2.00000i
$893$	20.9513	−	20.9513i	0.701109	−	0.701109i
$894$		0			0
$895$	−8.32951	−	8.95501i	−0.278425	−	0.299333i
$896$	−2.68409	−	18.4651i	−0.0896693	−	0.616877i
$897$		0			0
$898$	−4.29238	−	16.0194i	−0.143239	−	0.534574i
$899$	1.71450	−	2.96960i	0.0571818	−	0.0990418i
$900$		0			0
$901$	−42.8637	+	24.7474i	−1.42800	+	0.824454i
$902$	0.534737	+	0.143282i	0.0178048	+	0.00477078i
$903$		0			0
$904$	−11.6662	−	6.73548i	−0.388012	−	0.224019i
$905$	11.7131	−	38.1390i	0.389356	−	1.26778i
$906$		0			0
$907$	11.1124	+	11.1124i	0.368982	+	0.368982i	0.867106	−	0.498124i	$-0.165978\pi$
$907$	11.1124	+	11.1124i	0.368982	+	0.368982i	−0.498124	+	0.867106i	$0.665978\pi$
$908$	−3.95282	+	14.7521i	−0.131179	+	0.489566i
$909$		0			0
$910$	−65.8934	+	7.15606i	−2.18434	+	0.237221i
$911$	12.1778	+	21.0926i	0.403468	+	0.698828i	0.994142	−	0.108083i	$-0.0344712\pi$
$911$	12.1778	+	21.0926i	0.403468	+	0.698828i	−0.590673	+	0.806911i	$0.701138\pi$
$912$		0			0
$913$	−0.00756532	+	0.0282341i	−0.000250375	+	0.000934414i
$914$	74.8454	−	43.2120i	2.47567	−	1.42933i
$915$		0			0
$916$	7.21415	−	4.16509i	0.238362	−	0.137618i
$917$	5.94162	−	50.3555i	0.196209	−	1.66289i
$918$		0			0
$919$	1.01486	−	0.585929i	0.0334771	−	0.0193280i	−0.483168	−	0.875528i	$-0.660514\pi$
$919$	1.01486	−	0.585929i	0.0334771	−	0.0193280i	0.516645	+	0.856200i	$0.327181\pi$
$920$	2.19541	−	7.14849i	0.0723806	−	0.235679i
$921$		0			0
$922$	−24.8025	+	24.8025i	−0.816826	+	0.816826i
$923$	69.3644	−	18.5861i	2.28316	−	0.611770i
$924$		0			0
$925$	−33.0683	+	28.5992i	−1.08728	+	0.940336i
$926$	−4.96130	−	8.59322i	−0.163038	−	0.282391i
$927$		0			0
$928$	−1.46173	−	5.45526i	−0.0479837	−	0.179078i
$929$	0.674615	−	1.16847i	0.0221334	−	0.0383362i	−0.854747	−	0.519046i	$-0.826287\pi$
$929$	0.674615	−	1.16847i	0.0221334	−	0.0383362i	0.876880	+	0.480709i	$0.159621\pi$
$930$		0			0
$931$	−10.2794	−	34.6111i	−0.336892	−	1.13433i
$932$	−22.2112	+	5.95147i	−0.727551	+	0.194947i
$933$		0			0
$934$	35.7989			1.17137
$935$	0.0252130	−	0.696719i	0.000824554	−	0.0227851i
$936$		0			0
$937$	−25.3539	+	25.3539i	−0.828277	+	0.828277i	−0.987278	−	0.159001i	$-0.949173\pi$
$937$	−25.3539	+	25.3539i	−0.828277	+	0.828277i	0.159001	+	0.987278i	$0.449173\pi$
$938$	3.90622	−	33.1054i	0.127542	−	1.08093i
$939$		0			0
$940$	−14.6115	−	27.5644i	−0.476576	−	0.899052i
$941$	25.5785	−	14.7677i	0.833834	−	0.481414i	−0.0213296	−	0.999772i	$-0.506790\pi$
$941$	25.5785	−	14.7677i	0.833834	−	0.481414i	0.855164	+	0.518358i	$0.173457\pi$
$942$		0			0
$943$	−10.6591	+	2.85609i	−0.347107	+	0.0930071i
$944$	10.2457			0.333468
$945$		0			0
$946$	−0.427863			−0.0139110
$947$	−20.8039	+	5.57439i	−0.676036	+	0.181143i	−0.580472	−	0.814280i	$-0.697132\pi$
$947$	−20.8039	+	5.57439i	−0.676036	+	0.181143i	−0.0955637	+	0.995423i	$0.530465\pi$
$948$		0			0
$949$	5.08894	−	2.93810i	0.165194	−	0.0953747i
$950$	10.2209	+	53.3019i	0.331609	+	1.72934i
$951$		0			0
$952$	−6.75166	−	5.03792i	−0.218823	−	0.163280i
$953$	7.79646	−	7.79646i	0.252552	−	0.252552i	−0.569464	−	0.822016i	$-0.692849\pi$
$953$	7.79646	−	7.79646i	0.252552	−	0.252552i	0.822016	+	0.569464i	$0.192849\pi$
$954$		0			0
$955$	−1.40631	+	1.30808i	−0.0455070	+	0.0423284i
$956$	3.87386			0.125290
$957$		0			0
$958$	−9.63897	+	2.58275i	−0.311421	+	0.0834450i
$959$	23.4304	+	29.6993i	0.756606	+	0.959041i
$960$		0			0
$961$	−3.61224	+	6.25659i	−0.116524	+	0.201826i
$962$	25.3547	+	94.6252i	0.817469	+	3.05084i
$963$		0			0
$964$	27.1365	+	47.0018i	0.874007	+	1.51382i
$965$	−23.2811	−	14.5887i	−0.749445	−	0.469626i
$966$		0			0
$967$	−36.4432	+	9.76493i	−1.17193	+	0.314019i	−0.791723	−	0.610880i	$-0.790816\pi$
$967$	−36.4432	+	9.76493i	−1.17193	+	0.314019i	−0.380212	+	0.924899i	$0.624149\pi$
$968$	7.01325	−	7.01325i	0.225414	−	0.225414i
$969$		0			0
$970$	−46.9695	−	14.4250i	−1.50810	−	0.463160i
$971$	−2.41770	+	1.39586i	−0.0775877	+	0.0447953i	−0.538292	−	0.842758i	$-0.680930\pi$
$971$	−2.41770	+	1.39586i	−0.0775877	+	0.0447953i	0.460704	+	0.887554i	$0.347597\pi$
$972$		0			0
$973$	−27.3171	+	36.6095i	−0.875747	+	1.17365i
$974$	−38.6871	+	22.3360i	−1.23962	+	0.715692i
$975$		0			0
$976$	3.49704	−	2.01902i	0.111937	−	0.0646271i
$977$	4.12974	−	15.4124i	0.132122	−	0.493086i	−0.867871	−	0.496789i	$-0.834512\pi$
$977$	4.12974	−	15.4124i	0.132122	−	0.493086i	0.999993	+	0.00370333i	$0.00117881\pi$
$978$		0			0
$979$	0.504654	+	0.874086i	0.0161288	+	0.0279359i
$980$	−38.0144	−	0.352542i	−1.21433	−	0.0112615i
$981$		0			0
$982$	10.3548	−	38.6447i	0.330436	−	1.23320i
$983$	−0.502961	−	0.502961i	−0.0160420	−	0.0160420i	0.699040	−	0.715082i	$-0.253611\pi$
$983$	−0.502961	−	0.502961i	−0.0160420	−	0.0160420i	−0.715082	+	0.699040i	$0.753611\pi$
$984$		0			0
$985$	5.95918	+	11.2419i	0.189875	+	0.358197i
$986$	−4.52271	−	2.61119i	−0.144033	−	0.0831572i
$987$		0			0
$988$	64.4190	+	17.2610i	2.04944	+	0.549146i
$989$	7.38608	−	4.26435i	0.234864	−	0.135599i
$990$		0			0
$991$	−22.9124	+	39.6855i	−0.727837	+	1.26065i	0.229959	+	0.973200i	$0.426141\pi$
$991$	−22.9124	+	39.6855i	−0.727837	+	1.26065i	−0.957796	+	0.287450i	$0.907192\pi$
$992$	−10.1351	−	37.8248i	−0.321791	−	1.20094i
$993$		0			0
$994$	74.3240	−	10.8037i	2.35741	−	0.342674i
$995$	−39.1404	+	36.4065i	−1.24083	+	1.15416i
$996$		0			0
$997$	−5.33194	+	5.33194i	−0.168864	+	0.168864i	−0.786480	−	0.617616i	$-0.788099\pi$
$997$	−5.33194	+	5.33194i	−0.168864	+	0.168864i	0.617616	+	0.786480i	$0.288099\pi$
$998$	23.1903	+	86.5474i	0.734076	+	2.73961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cj.e.577.7		160
3.2	odd	2		315.2.cg.e.157.34	yes	160
5.3	odd	4	inner	945.2.cj.e.388.34		160
7.5	odd	6		945.2.bv.e.712.34		160
9.2	odd	6		315.2.bs.e.52.7	✓	160
9.7	even	3		945.2.bv.e.262.34		160
15.8	even	4		315.2.cg.e.283.7	yes	160
21.5	even	6		315.2.bs.e.292.7	yes	160
35.33	even	12		945.2.bv.e.523.34		160
45.38	even	12		315.2.bs.e.178.7	yes	160
45.43	odd	12		945.2.bv.e.73.34		160
63.47	even	6		315.2.cg.e.187.7	yes	160
63.61	odd	6	inner	945.2.cj.e.397.34		160
105.68	odd	12		315.2.bs.e.103.7	yes	160
315.173	odd	12		315.2.cg.e.313.34	yes	160
315.313	even	12	inner	945.2.cj.e.208.7		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.7	✓	160	9.2	odd	6
315.2.bs.e.103.7	yes	160	105.68	odd	12
315.2.bs.e.178.7	yes	160	45.38	even	12
315.2.bs.e.292.7	yes	160	21.5	even	6
315.2.cg.e.157.34	yes	160	3.2	odd	2
315.2.cg.e.187.7	yes	160	63.47	even	6
315.2.cg.e.283.7	yes	160	15.8	even	4
315.2.cg.e.313.34	yes	160	315.173	odd	12
945.2.bv.e.73.34		160	45.43	odd	12
945.2.bv.e.262.34		160	9.7	even	3
945.2.bv.e.523.34		160	35.33	even	12
945.2.bv.e.712.34		160	7.5	odd	6
945.2.cj.e.208.7		160	315.313	even	12	inner
945.2.cj.e.388.34		160	5.3	odd	4	inner
945.2.cj.e.397.34		160	63.61	odd	6	inner
945.2.cj.e.577.7		160	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cj (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.03275 + 0.544675i) q^{2} +(2.10336 - 1.21438i) q^{4} +(-2.13753 - 0.656469i) q^{5} +(2.62752 + 0.310030i) q^{7} +(-0.638021 + 0.638021i) q^{8} +O(q^{10})\)	\(q+(-2.03275 + 0.544675i) q^{2} +(2.10336 - 1.21438i) q^{4} +(-2.13753 - 0.656469i) q^{5} +(2.62752 + 0.310030i) q^{7} +(-0.638021 + 0.638021i) q^{8} +(4.70264 + 0.170180i) q^{10} +0.0883552 q^{11} +(-5.14229 + 1.37787i) q^{13} +(-5.50997 + 0.800930i) q^{14} +(-1.47933 + 2.56227i) q^{16} +(0.913316 + 3.40854i) q^{17} +(-2.57895 - 4.46688i) q^{19} +(-5.29321 + 1.21498i) q^{20} +(-0.179604 + 0.0481248i) q^{22} +(2.62082 - 2.62082i) q^{23} +(4.13810 + 2.80645i) q^{25} +(9.70252 - 5.60175i) q^{26} +(5.90313 - 2.53870i) q^{28} +(0.609023 - 0.351619i) q^{29} +(4.22275 - 2.43801i) q^{31} +(2.07857 - 7.75733i) q^{32} +(-3.71309 - 6.43126i) q^{34} +(-5.41289 - 2.38759i) q^{35} +(-2.26311 + 8.44603i) q^{37} +(7.67537 + 7.67537i) q^{38} +(1.78263 - 0.944950i) q^{40} +(-2.57843 - 1.48865i) q^{41} +(2.22267 + 0.595563i) q^{43} +(0.185843 - 0.107297i) q^{44} +(-3.89998 + 6.75496i) q^{46} +(1.48679 + 5.54877i) q^{47} +(6.80776 + 1.62922i) q^{49} +(-9.94033 - 3.45090i) q^{50} +(-9.14285 + 9.14285i) q^{52} +(3.63020 + 13.5481i) q^{53} +(-0.188862 - 0.0580025i) q^{55} +(-1.87422 + 1.47861i) q^{56} +(-1.04647 + 1.04647i) q^{58} +(-1.73147 - 2.99899i) q^{59} +(-1.18197 - 0.682409i) q^{61} +(-7.25589 + 7.25589i) q^{62} +10.9836i q^{64} +(11.8964 + 0.430508i) q^{65} +(-1.54956 + 5.78303i) q^{67} +(6.06029 + 6.06029i) q^{68} +(12.3035 + 1.90511i) q^{70} -13.4890 q^{71} +(-1.06617 + 0.285680i) q^{73} -18.4014i q^{74} +(-10.8489 - 6.26364i) q^{76} +(0.232155 + 0.0273928i) q^{77} +(3.07762 + 1.77687i) q^{79} +(4.84417 - 4.50581i) q^{80} +(6.05214 + 1.62166i) q^{82} +(-0.0856239 + 0.319553i) q^{83} +(0.285360 - 7.88543i) q^{85} -4.84253 q^{86} +(-0.0563725 + 0.0563725i) q^{88} +(5.71165 + 9.89286i) q^{89} +(-13.9387 + 2.02613i) q^{91} +(2.32987 - 8.69519i) q^{92} +(-6.04455 - 10.4695i) q^{94} +(2.58023 + 11.2411i) q^{95} +(-10.0857 - 2.70245i) q^{97} +(-14.7259 + 0.396205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) \) 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8} - 24 q^{10} - 32 q^{11} + 76 q^{16} + 6 q^{17} + 60 q^{20} + 8 q^{22} + 16 q^{23} - 4 q^{25} + 36 q^{26} + 22 q^{28} + 48 q^{31} + 6 q^{32} + 36 q^{35} - 4 q^{37} - 12 q^{41} - 4 q^{43} - 16 q^{46} + 54 q^{47} + 44 q^{50} - 8 q^{53} + 92 q^{56} - 56 q^{58} - 24 q^{61} - 62 q^{65} + 12 q^{67} + 2 q^{70} + 40 q^{71} + 36 q^{73} - 96 q^{76} + 110 q^{77} - 36 q^{80} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 32 q^{86} - 92 q^{88} - 48 q^{91} + 26 q^{92} + 94 q^{95} - 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q + 2 * q^2 + 6 * q^7 + 16 * q^8 - 24 * q^10 - 32 * q^11 + 76 * q^16 + 6 * q^17 + 60 * q^20 + 8 * q^22 + 16 * q^23 - 4 * q^25 + 36 * q^26 + 22 * q^28 + 48 * q^31 + 6 * q^32 + 36 * q^35 - 4 * q^37 - 12 * q^41 - 4 * q^43 - 16 * q^46 + 54 * q^47 + 44 * q^50 - 8 * q^53 + 92 * q^56 - 56 * q^58 - 24 * q^61 - 62 * q^65 + 12 * q^67 + 2 * q^70 + 40 * q^71 + 36 * q^73 - 96 * q^76 + 110 * q^77 - 36 * q^80 - 66 * q^82 - 138 * q^83 - 20 * q^85 - 32 * q^86 - 92 * q^88 - 48 * q^91 + 26 * q^92 + 94 * q^95 - 48 * q^97 - 102 * q^98

Introduction

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