LMFDB - Embedded newform 945.2.cj.e.388.34

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			388.34
Character	$\chi$	$=$	945.388
Dual form			945.2.cj.e.397.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.544675 + 2.03275i) q^{2} +(-2.10336 + 1.21438i) q^{4} +(2.13753 - 0.656469i) q^{5} +(0.310030 - 2.62752i) q^{7} +(-0.638021 - 0.638021i) q^{8} +O(q^{10})$	\(q+(0.544675 + 2.03275i) q^{2} +(-2.10336 + 1.21438i) q^{4} +(2.13753 - 0.656469i) q^{5} +(0.310030 - 2.62752i) q^{7} +(-0.638021 - 0.638021i) q^{8} +(2.49870 + 3.98751i) q^{10} +0.0883552 q^{11} +(-1.37787 - 5.14229i) q^{13} +(5.50997 - 0.800930i) q^{14} +(-1.47933 + 2.56227i) q^{16} +(3.40854 - 0.913316i) q^{17} +(2.57895 + 4.46688i) q^{19} +(-3.69881 + 3.97657i) q^{20} +(0.0481248 + 0.179604i) q^{22} +(2.62082 + 2.62082i) q^{23} +(4.13810 - 2.80645i) q^{25} +(9.70252 - 5.60175i) q^{26} +(2.53870 + 5.90313i) q^{28} +(-0.609023 + 0.351619i) q^{29} +(4.22275 - 2.43801i) q^{31} +(-7.75733 - 2.07857i) q^{32} +(3.71309 + 6.43126i) q^{34} +(-1.06219 - 5.81994i) q^{35} +(8.44603 + 2.26311i) q^{37} +(-7.67537 + 7.67537i) q^{38} +(-1.78263 - 0.944950i) q^{40} +(-2.57843 - 1.48865i) q^{41} +(-0.595563 + 2.22267i) q^{43} +(-0.185843 + 0.107297i) q^{44} +(-3.89998 + 6.75496i) q^{46} +(5.54877 - 1.48679i) q^{47} +(-6.80776 - 1.62922i) q^{49} +(7.95874 + 6.88312i) q^{50} +(9.14285 + 9.14285i) q^{52} +(-13.5481 + 3.63020i) q^{53} +(0.188862 - 0.0580025i) q^{55} +(-1.87422 + 1.47861i) q^{56} +(-1.04647 - 1.04647i) q^{58} +(1.73147 + 2.99899i) q^{59} +(-1.18197 - 0.682409i) q^{61} +(7.25589 + 7.25589i) q^{62} -10.9836i q^{64} +(-6.32101 - 10.0873i) q^{65} +(5.78303 + 1.54956i) q^{67} +(-6.06029 + 6.06029i) q^{68} +(11.2520 - 5.32914i) q^{70} -13.4890 q^{71} +(-0.285680 - 1.06617i) q^{73} +18.4014i q^{74} +(-10.8489 - 6.26364i) q^{76} +(0.0273928 - 0.232155i) q^{77} +(-3.07762 - 1.77687i) q^{79} +(-1.48006 + 6.44808i) q^{80} +(1.62166 - 6.05214i) q^{82} +(-0.319553 - 0.0856239i) q^{83} +(6.68631 - 4.18985i) q^{85} -4.84253 q^{86} +(-0.0563725 - 0.0563725i) q^{88} +(-5.71165 - 9.89286i) q^{89} +(-13.9387 + 2.02613i) q^{91} +(-8.69519 - 2.32987i) q^{92} +(6.04455 + 10.4695i) q^{94} +(8.44496 + 7.85509i) q^{95} +(-2.70245 + 10.0857i) q^{97} +(-0.396205 - 14.7259i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.544675	+	2.03275i	0.385143	+	1.43737i	0.837941	+	0.545760i	$0.183759\pi$
$2$	0.544675	+	2.03275i	0.385143	+	1.43737i	−0.452798	+	0.891613i	$0.649574\pi$
$3$		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
$7$	0.310030	−	2.62752i	0.117180	−	0.993111i
$7$	0.310030	−	2.62752i	0.117180	−	0.993111i
$8$	−0.638021	−	0.638021i	−0.225575	−	0.225575i
$9$		0			0
$10$	2.49870	+	3.98751i	0.790158	+	1.26096i
$11$	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
$13$	−1.37787	−	5.14229i	−0.382153	−	1.42622i	−0.842606	−	0.538531i	$-0.818979\pi$
$13$	−1.37787	−	5.14229i	−0.382153	−	1.42622i	0.460452	−	0.887684i	$-0.347687\pi$
$14$	5.50997	−	0.800930i	1.47260	−	0.214058i
$15$		0			0
$16$	−1.47933	+	2.56227i	−0.369832	+	0.640568i
$17$	3.40854	−	0.913316i	0.826693	−	0.221512i	0.179422	−	0.983772i	$-0.442577\pi$
$17$	3.40854	−	0.913316i	0.826693	−	0.221512i	0.647270	+	0.762260i	$0.275910\pi$
$18$		0			0
$19$	2.57895	+	4.46688i	0.591652	+	1.02477i	0.994010	+	0.109289i	$0.0348574\pi$
$19$	2.57895	+	4.46688i	0.591652	+	1.02477i	−0.402358	+	0.915482i	$0.631809\pi$
$20$	−3.69881	+	3.97657i	−0.827079	+	0.889187i
$21$		0			0
$22$	0.0481248	+	0.179604i	0.0102602	+	0.0382918i
$23$	2.62082	+	2.62082i	0.546478	+	0.546478i	0.925420	−	0.378942i	$-0.123712\pi$
$23$	2.62082	+	2.62082i	0.546478	+	0.546478i	−0.378942	+	0.925420i	$0.623712\pi$
$24$		0			0
$25$	4.13810	−	2.80645i	0.827619	−	0.561290i
$26$	9.70252	−	5.60175i	1.90282	−	1.09859i
$27$		0			0
$28$	2.53870	+	5.90313i	0.479769	+	1.11559i
$29$	−0.609023	+	0.351619i	−0.113093	+	0.0652941i	−0.555479	−	0.831530i	$-0.687465\pi$
$29$	−0.609023	+	0.351619i	−0.113093	+	0.0652941i	0.442387	+	0.896824i	$0.354132\pi$
$30$		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	$0.189063\pi$
$32$	−7.75733	−	2.07857i	−1.37132	−	0.367443i
$33$		0			0
$34$	3.71309	+	6.43126i	0.636790	+	1.10295i
$35$	−1.06219	−	5.81994i	−0.179543	−	0.983750i
$36$		0			0
$37$	8.44603	+	2.26311i	1.38852	+	0.372053i	0.874208	−	0.485551i	$-0.161381\pi$
$37$	8.44603	+	2.26311i	1.38852	+	0.372053i	0.514311	+	0.857604i	$0.328048\pi$
$38$	−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
$43$	−0.595563	+	2.22267i	−0.0908225	+	0.338954i	−0.996353	−	0.0853269i	$-0.972807\pi$
$43$	−0.595563	+	2.22267i	−0.0908225	+	0.338954i	0.905530	+	0.424281i	$0.139473\pi$
$44$	−0.185843	+	0.107297i	−0.0280169	+	0.0161756i
$45$		0			0
$46$	−3.89998	+	6.75496i	−0.575021	+	0.995965i
$47$	5.54877	−	1.48679i	0.809372	−	0.216870i	0.169677	−	0.985500i	$-0.445728\pi$
$47$	5.54877	−	1.48679i	0.809372	−	0.216870i	0.639695	+	0.768629i	$0.279061\pi$
$48$		0			0
$49$	−6.80776	−	1.62922i	−0.972537	−	0.232746i
$50$	7.95874	+	6.88312i	1.12554	+	0.973421i
$51$		0			0
$52$	9.14285	+	9.14285i	1.26789	+	1.26789i
$53$	−13.5481	+	3.63020i	−1.86097	+	0.498646i	−0.999951	−	0.00992346i	$-0.996841\pi$
$53$	−13.5481	+	3.63020i	−1.86097	+	0.498646i	−0.861021	+	0.508569i	$0.830175\pi$
$54$		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	0.956445	−	0.291913i	$-0.0942918\pi$
$59$	1.73147	+	2.99899i	0.225418	+	0.390436i	−0.731027	+	0.682349i	$0.760959\pi$
$60$		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
$65$	−6.32101	−	10.0873i	−0.784024	−	1.25117i
$66$		0			0
$67$	5.78303	+	1.54956i	0.706509	+	0.189309i	0.594144	−	0.804359i	$-0.297491\pi$
$67$	5.78303	+	1.54956i	0.706509	+	0.189309i	0.112365	+	0.993667i	$0.464157\pi$
$68$	−6.06029	+	6.06029i	−0.734918	+	0.734918i
$69$		0			0
$70$	11.2520	−	5.32914i	1.34487	−	0.636954i
$71$	−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
$73$	−0.285680	−	1.06617i	−0.0334363	−	0.124786i	0.947190	−	0.320672i	$-0.103909\pi$
$73$	−0.285680	−	1.06617i	−0.0334363	−	0.124786i	−0.980627	+	0.195886i	$0.937242\pi$
$74$			18.4014i			2.13911i
$75$		0			0
$76$	−10.8489	−	6.26364i	−1.24446	−	0.718489i
$77$	0.0273928	−	0.232155i	0.00312170	−	0.0264566i
$78$		0			0
$79$	−3.07762	−	1.77687i	−0.346260	−	0.199913i	0.316777	−	0.948500i	$-0.397399\pi$
$79$	−3.07762	−	1.77687i	−0.346260	−	0.199913i	−0.663037	+	0.748587i	$0.730733\pi$
$80$	−1.48006	+	6.44808i	−0.165476	+	0.720917i
$81$		0			0
$82$	1.62166	−	6.05214i	0.179083	−	0.668347i
$83$	−0.319553	−	0.0856239i	−0.0350755	−	0.00939845i	0.241239	−	0.970466i	$-0.422446\pi$
$83$	−0.319553	−	0.0856239i	−0.0350755	−	0.00939845i	−0.276314	+	0.961067i	$0.589113\pi$
$84$		0			0
$85$	6.68631	−	4.18985i	0.725232	−	0.454453i
$86$	−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	$-0.959666\pi$
$89$	−5.71165	−	9.89286i	−0.605434	−	1.04864i	0.386549	−	0.922269i	$-0.373667\pi$
$90$		0			0
$91$	−13.9387	+	2.02613i	−1.46117	+	0.212396i
$92$	−8.69519	−	2.32987i	−0.906536	−	0.242906i
$93$		0			0
$94$	6.04455	+	10.4695i	0.623448	+	1.07984i
$95$	8.44496	+	7.85509i	0.866435	+	0.805915i
$96$		0			0
$97$	−2.70245	+	10.0857i	−0.274393	+	1.02405i	0.681855	+	0.731488i	$0.261174\pi$
$97$	−2.70245	+	10.0857i	−0.274393	+	1.02405i	−0.956247	+	0.292559i	$0.905493\pi$
$98$	−0.396205	−	14.7259i	−0.0400227	−	1.48754i
$99$		0			0
$100$	−5.29583	+	10.9282i	−0.529583	+	1.09282i
$101$			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	$-0.972788\pi$
$103$	−9.24526	+	9.24526i	−0.910963	+	0.910963i	0.0853854	+	0.996348i	$0.472788\pi$
$104$	−2.40178	+	4.16000i	−0.235514	+	0.407922i
$105$		0			0
$106$	−14.7586	−	25.5626i	−1.43348	−	2.48286i
$107$	11.6419	+	3.11943i	1.12546	+	0.301567i	0.773092	−	0.634294i	$-0.218709\pi$
$107$	11.6419	+	3.11943i	1.12546	+	0.301567i	0.352371	+	0.935860i	$0.385376\pi$
$108$		0			0
$109$	−11.5914	−	6.69232i	−1.11026	−	0.641008i	−0.171363	−	0.985208i	$-0.554817\pi$
$109$	−11.5914	−	6.69232i	−1.11026	−	0.641008i	−0.938897	+	0.344200i	$0.888150\pi$
$110$	0.220773	+	0.352318i	0.0210499	+	0.0335922i
$111$		0			0
$112$	6.27380	+	4.68136i	0.592818	+	0.442347i
$113$	−14.4209	+	3.86407i	−1.35660	+	0.363501i	−0.862568	−	0.505941i	$-0.831145\pi$
$113$	−14.4209	+	3.86407i	−1.35660	+	0.363501i	−0.494035	+	0.869442i	$0.664479\pi$
$114$		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
$122$	0.743382	−	2.77434i	0.0673026	−	0.251177i
$123$		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	−0.470255	−	0.882531i	$-0.655838\pi$
$127$	4.64611	−	4.64611i	0.412276	−	0.412276i	0.882531	+	0.470255i	$0.155838\pi$
$128$	6.81221	−	1.82533i	0.602120	−	0.161337i
$129$		0			0
$130$	17.0621	−	18.3433i	1.49644	−	1.60882i
$131$		−	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
$133$	12.5364	−	5.39139i	1.08704	−	0.467493i
$134$			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	−0.128000	−	0.991774i	$-0.540856\pi$
$137$	10.1102	−	10.1102i	0.863775	−	0.863775i	0.991774	+	0.128000i	$0.0408556\pi$
$138$		0			0
$139$	8.63234	−	14.9516i	0.732185	−	1.26818i	−0.223762	−	0.974644i	$-0.571834\pi$
$139$	8.63234	−	14.9516i	0.732185	−	1.26818i	0.955947	−	0.293538i	$-0.0948328\pi$
$140$	9.30178	+	10.9516i	0.786144	+	0.925576i
$141$		0			0
$142$	−7.34711	−	27.4198i	−0.616556	−	2.30102i
$143$	−0.121742	−	0.454348i	−0.0101806	−	0.0379945i
$144$		0			0
$145$	−1.07098	+	1.15140i	−0.0889400	+	0.0956188i
$146$	2.01166	−	1.16143i	0.166486	−	0.0961209i
$147$		0			0
$148$	−20.5133	+	5.49653i	−1.68619	+	0.451812i
$149$		−	2.82533i		−	0.231460i	−0.993281	−	0.115730i	$-0.963079\pi$
$149$		−	2.82533i		−	0.231460i	0.993281	−	0.115730i	$-0.0369207\pi$
$150$		0			0
$151$	5.89991			0.480128			0.240064	−	0.970757i	$-0.422832\pi$
$151$	5.89991			0.480128			0.240064	+	0.970757i	$0.422832\pi$
$152$	1.20454	−	4.49539i	0.0977007	−	0.364624i
$153$		0			0
$154$	0.486835	−	0.0707663i	0.0392302	−	0.00570251i
$155$	7.42580	−	7.98343i	0.596454	−	0.641244i
$156$		0			0
$157$	−3.05331	+	11.3951i	−0.243680	+	0.909427i	0.730362	+	0.683060i	$0.239351\pi$
$157$	−3.05331	+	11.3951i	−0.243680	+	0.909427i	−0.974042	+	0.226367i	$0.927315\pi$
$158$	1.93563	−	7.22386i	0.153990	−	0.574700i
$159$		0			0
$160$	−17.9461	+	0.649437i	−1.41876	+	0.0513425i
$161$	7.69879	−	6.07372i	0.606750	−	0.478677i
$162$		0			0
$163$	2.60174	−	9.70984i	0.203784	−	0.760533i	−0.786032	−	0.618185i	$-0.787868\pi$
$163$	2.60174	−	9.70984i	0.203784	−	0.760533i	0.989817	−	0.142348i	$-0.0454652\pi$
$164$	7.23116			0.564658
$165$		0			0
$166$		−	0.696209i		−	0.0540363i
$167$	1.04965	−	0.281253i	0.0812244	−	0.0217640i	−0.217978	−	0.975954i	$-0.569946\pi$
$167$	1.04965	−	0.281253i	0.0812244	−	0.0217640i	0.299202	+	0.954190i	$0.403279\pi$
$168$		0			0
$169$	−13.2863	+	7.67086i	−1.02202	+	0.590066i
$170$	12.1588	+	11.3095i	0.932536	+	0.867400i
$171$		0			0
$172$	−1.44648	−	5.39833i	−0.110293	−	0.411619i
$173$	2.64924	+	9.88708i	0.201418	+	0.751701i	0.990512	+	0.137428i	$0.0438837\pi$
$173$	2.64924	+	9.88708i	0.201418	+	0.751701i	−0.789094	+	0.614272i	$0.789450\pi$
$174$		0			0
$175$	−6.09108	−	11.7430i	−0.460442	−	0.887690i
$176$	−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	0.312426	−	0.949942i	$-0.398858\pi$
$179$	−4.73666	−	2.73471i	−0.354034	−	0.204402i	−0.666461	+	0.745540i	$0.732192\pi$
$180$		0			0
$181$			17.8425i			1.32622i	0.748520	+	0.663112i	$0.230765\pi$
$181$			17.8425i			1.32622i	−0.748520	+	0.663112i	$0.769235\pi$
$182$	−11.7107	−	27.2303i	−0.868052	−	2.01845i
$183$		0			0
$184$		−	3.34427i		−	0.246543i
$185$	19.5393	−	0.707094i	1.43656	−	0.0519866i
$186$		0			0
$187$	0.301162	−	0.0806962i	0.0220232	−	0.00590109i
$188$	−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
$193$	−3.18008	+	11.8682i	−0.228907	+	0.854294i	0.751894	+	0.659284i	$0.229141\pi$
$193$	−3.18008	+	11.8682i	−0.228907	+	0.854294i	−0.980801	+	0.195010i	$0.937526\pi$
$194$	−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	−0.835761	−	0.549093i	$-0.814973\pi$
$197$	−4.02358	+	4.02358i	−0.286668	+	0.286668i	0.549093	+	0.835761i	$0.314973\pi$
$198$		0			0
$199$	−11.9528	+	20.7029i	−0.847314	+	1.46759i	0.0362825	+	0.999342i	$0.488448\pi$
$199$	−11.9528	+	20.7029i	−0.847314	+	1.46759i	−0.883596	+	0.468249i	$0.844885\pi$
$200$	−4.43077	−	0.849618i	−0.313303	−	0.0600771i
$201$		0			0
$202$	−23.3599	+	6.25926i	−1.64359	+	0.440400i
$203$	0.735073	+	1.70923i	0.0515920	+	0.119965i
$204$		0			0
$205$	−6.48873	−	1.48939i	−0.453192	−	0.104024i
$206$	−23.8290	−	13.7577i	−1.66024	−	0.958542i
$207$		0			0
$208$	15.2143	+	4.07666i	1.05492	+	0.282665i
$209$	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
$215$	0.186080	+	5.14200i	0.0126906	+	0.350682i
$216$		0			0
$217$	−5.09674	−	11.8512i	−0.345989	−	0.804514i
$218$	7.29028	−	27.2077i	0.493760	−	1.84274i
$219$		0			0
$220$	−0.326809	+	0.351350i	−0.0220334	+	0.0236880i
$221$	−9.39308	−	16.2693i	−0.631847	−	1.09439i
$222$		0			0
$223$	24.5939	+	6.58992i	1.64693	+	0.441294i	0.958751	−	0.284247i	$-0.0917434\pi$
$223$	24.5939	+	6.58992i	1.64693	+	0.441294i	0.688180	+	0.725540i	$0.258410\pi$
$224$	−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	$-0.183083\pi$
$227$	4.44644	+	4.44644i	0.295120	+	0.295120i	−0.543979	+	0.839099i	$0.683083\pi$
$228$		0			0
$229$	−3.42981			−0.226649			−0.113324	−	0.993558i	$-0.536150\pi$
$229$	−3.42981			−0.226649			−0.113324	+	0.993558i	$0.536150\pi$
$230$	−3.90191	+	16.9992i	−0.257284	+	1.12089i
$231$		0			0
$232$	0.612910	+	0.164229i	0.0402395	+	0.0107821i
$233$	2.45042	−	9.14509i	0.160532	−	0.599115i	−0.838036	−	0.545616i	$-0.816296\pi$
$233$	2.45042	−	9.14509i	0.160532	−	0.599115i	0.998568	−	0.0534991i	$-0.0170374\pi$
$234$		0			0
$235$	10.8847	−	6.82066i	0.710037	−	0.444931i
$236$	−7.28382	−	4.20532i	−0.474136	−	0.273743i
$237$		0			0
$238$	18.0495	−	7.76235i	1.16997	−	0.503158i
$239$	−1.38131	−	0.797500i	−0.0893495	−	0.0515860i	0.454660	−	0.890665i	$-0.349761\pi$
$239$	−1.38131	−	0.797500i	−0.0893495	−	0.0515860i	−0.544009	+	0.839079i	$0.683094\pi$
$240$		0			0
$241$			22.3460i			1.43943i	0.694268	+	0.719716i	$0.255728\pi$
$241$			22.3460i			1.43943i	−0.694268	+	0.719716i	$0.744272\pi$
$242$	−5.98717	−	22.3444i	−0.384870	−	1.43635i
$243$		0			0
$244$	3.31481			0.212209
$245$	−15.6214	+	0.986567i	−0.998012	+	0.0630295i
$246$		0			0
$247$	19.4165	−	19.4165i	1.23544	−	1.23544i
$248$	−4.24970	−	1.13871i	−0.269857	−	0.0723078i
$249$		0			0
$250$	21.5306	+	9.48824i	1.36172	+	0.600089i
$251$			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	$-0.330721\pi$
$257$	−5.68790	−	5.68790i	−0.354801	−	0.354801i	−0.861892	+	0.507091i	$0.830721\pi$
$258$		0			0
$259$	8.56489	−	21.4905i	0.532197	−	1.33536i
$260$	25.5452	+	13.5411i	1.58424	+	0.839786i
$261$		0			0
$262$	38.9570	−	10.4385i	2.40677	−	0.644892i
$263$	14.7998	+	14.7998i	0.912598	+	0.912598i	0.996476	−	0.0838785i	$-0.0267308\pi$
$263$	14.7998	+	14.7998i	0.912598	+	0.912598i	−0.0838785	+	0.996476i	$0.526731\pi$
$264$		0			0
$265$	−26.5764	+	16.6536i	−1.63257	+	1.02302i
$266$	17.7876	+	22.5468i	1.09063	+	1.38243i
$267$		0			0
$268$	−14.0456	+	3.76349i	−0.857969	+	0.229892i
$269$	−3.69593	+	6.40154i	−0.225345	+	0.390309i	−0.956423	−	0.291985i	$-0.905684\pi$
$269$	−3.69593	+	6.40154i	−0.225345	+	0.390309i	0.731078	+	0.682294i	$0.239018\pi$
$270$		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	$0.325796\pi$
$272$	−2.70219	+	10.0847i	−0.163844	+	0.611476i
$273$		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	−0.880060	−	0.474862i	$-0.842498\pi$
$277$	−6.74383	+	6.74383i	−0.405198	+	0.405198i	0.474862	+	0.880060i	$0.342498\pi$
$278$	35.0948	+	9.40363i	2.10485	+	0.563992i
$279$		0			0
$280$	−3.03555	+	4.39095i	−0.181409	+	0.262409i
$281$	−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
$283$	−21.6896	−	5.81172i	−1.28931	−	0.345471i	−0.451915	−	0.892061i	$-0.649259\pi$
$283$	−21.6896	−	5.81172i	−1.28931	−	0.345471i	−0.837400	+	0.546590i	$0.815926\pi$
$284$	28.3723	−	16.3807i	1.68358	−	0.972018i
$285$		0			0
$286$	0.857268	−	0.494944i	0.0506913	−	0.0292666i
$287$	−4.71087	+	6.31335i	−0.278074	+	0.372665i
$288$		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
$293$	−2.45679	−	9.16886i	−0.143527	−	0.535651i	−0.999817	−	0.0191543i	$-0.993903\pi$
$293$	−2.45679	−	9.16886i	−0.143527	−	0.535651i	0.856289	−	0.516496i	$-0.172764\pi$
$294$		0			0
$295$	5.66982	+	5.27379i	0.330110	+	0.307052i
$296$	−3.94484	−	6.83266i	−0.229289	−	0.397140i
$297$		0			0
$298$	5.74319	−	1.53888i	0.332694	−	0.0891452i
$299$	9.86585	−	17.0882i	0.570557	−	0.988234i
$300$		0			0
$301$	5.65548	+	2.25395i	0.325977	+	0.129916i
$302$	3.21353	+	11.9931i	0.184918	+	0.690123i
$303$		0			0
$304$	−15.2605			−0.875249
$305$	−2.97447	−	0.682747i	−0.170318	−	0.0390940i
$306$		0			0
$307$	−4.02496	−	4.02496i	−0.229717	−	0.229717i	0.582858	−	0.812574i	$-0.301935\pi$
$307$	−4.02496	−	4.02496i	−0.229717	−	0.229717i	−0.812574	+	0.582858i	$0.801935\pi$
$308$	0.224307	+	0.521572i	0.0127811	+	0.0297193i
$309$		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
$313$	−8.39639	−	31.3358i	−0.474592	−	1.77120i	−0.622943	−	0.782267i	$-0.714063\pi$
$313$	−8.39639	−	31.3358i	−0.474592	−	1.77120i	0.148351	−	0.988935i	$-0.452603\pi$
$314$	−24.8265			−1.40104
$315$		0			0
$316$	8.63115			0.485540
$317$	1.65952	+	6.19342i	0.0932080	+	0.347857i	0.996742	−	0.0806600i	$-0.0257028\pi$
$317$	1.65952	+	6.19342i	0.0932080	+	0.347857i	−0.903534	+	0.428517i	$0.859036\pi$
$318$		0			0
$319$	−0.0538103	+	0.0310674i	−0.00301280	+	0.00173944i
$320$	−7.21037	−	23.4777i	−0.403072	−	1.31244i
$321$		0			0
$322$	16.5397	+	12.3415i	0.921722	+	0.687767i
$323$	12.8701	+	12.8701i	0.716113	+	0.716113i
$324$		0			0
$325$	−20.1334	−	17.4124i	−1.11680	−	0.965864i
$326$	21.1548			1.17166
$327$		0			0
$328$	0.695297	+	2.59488i	0.0383914	+	0.143278i
$329$	−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	$0.114553\pi$
$332$	0.776116	−	0.207960i	0.0425949	−	0.0114133i
$333$		0			0
$334$	1.14344	+	1.98049i	0.0625660	+	0.108368i
$335$	13.3786	−	0.484150i	0.730953	−	0.0264519i
$336$		0			0
$337$	−2.50004	−	9.33028i	−0.136186	−	0.508253i	−0.999990	−	0.00442531i	$-0.998591\pi$
$337$	−2.50004	−	9.33028i	−0.136186	−	0.508253i	0.863804	−	0.503828i	$-0.168075\pi$
$338$	−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
$343$	−6.39144	+	17.3824i	−0.345105	+	0.938564i
$344$	1.79809	−	1.03813i	0.0969467	−	0.0559722i
$345$		0			0
$346$	−18.6550	+	10.7705i	−1.00290	+	0.579025i
$347$	−29.7420	−	7.96934i	−1.59663	−	0.427816i	−0.652609	−	0.757695i	$-0.726326\pi$
$347$	−29.7420	−	7.96934i	−1.59663	−	0.427816i	−0.944023	+	0.329879i	$0.892992\pi$
$348$		0			0
$349$	−5.20858	−	9.02153i	−0.278809	−	0.482911i	0.692280	−	0.721629i	$-0.256606\pi$
$349$	−5.20858	−	9.02153i	−0.278809	−	0.482911i	−0.971089	+	0.238718i	$0.923273\pi$
$350$	20.5530	−	18.7778i	1.09861	−	1.00372i
$351$		0			0
$352$	−0.685400	−	0.183652i	−0.0365320	−	0.00978871i
$353$	22.7835	−	22.7835i	1.21265	−	1.21265i	0.242492	−	0.970153i	$-0.422035\pi$
$353$	22.7835	−	22.7835i	1.21265	−	1.21265i	0.970153	−	0.242492i	$-0.0779648\pi$
$354$		0			0
$355$	−28.8332	+	8.85511i	−1.53031	+	0.469981i
$356$	24.0273	+	13.8722i	1.27345	+	0.735225i
$357$		0			0
$358$	2.97905	−	11.1180i	0.157448	−	0.587604i
$359$	−6.83504	+	3.94621i	−0.360739	+	0.208273i	−0.669405	−	0.742898i	$-0.733451\pi$
$359$	−6.83504	+	3.94621i	−0.360739	+	0.208273i	0.308666	+	0.951171i	$0.400118\pi$
$360$		0			0
$361$	−3.80199	+	6.58524i	−0.200105	+	0.346591i
$362$	−36.2694	+	9.71837i	−1.90628	+	0.510786i
$363$		0			0
$364$	26.8576	−	21.1885i	1.40772	−	1.11058i
$365$	−1.31056	−	2.09144i	−0.0685978	−	0.109471i
$366$		0			0
$367$	−6.37922	−	6.37922i	−0.332992	−	0.332992i	0.520729	−	0.853722i	$-0.325660\pi$
$367$	−6.37922	−	6.37922i	−0.332992	−	0.332992i	−0.853722	+	0.520729i	$0.825660\pi$
$368$	−10.5923	+	2.83820i	−0.552162	+	0.147951i
$369$		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	0.643692	−	0.765285i	$-0.277402\pi$
$373$	−2.34834	−	2.34834i	−0.121592	−	0.121592i	−0.765285	+	0.643692i	$0.777402\pi$
$374$	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	$-0.924883\pi$
$379$		−	9.10326i		−	0.467603i	0.972284	−	0.233802i	$-0.0751166\pi$
$380$	−27.3019	−	6.26674i	−1.40056	−	0.321477i
$381$		0			0
$382$	1.74598	+	0.467835i	0.0893323	+	0.0239365i
$383$	−14.4171	+	14.4171i	−0.736677	+	0.736677i	−0.971933	−	0.235256i	$-0.924407\pi$
$383$	−14.4171	+	14.4171i	−0.736677	+	0.736677i	0.235256	+	0.971933i	$0.424407\pi$
$384$		0			0
$385$	−0.0938499	−	0.514222i	−0.00478303	−	0.0262072i
$386$	−25.8573			−1.31610
$387$		0			0
$388$	−6.56360	−	24.4957i	−0.333216	−	1.24358i
$389$			12.0832i			0.612642i	0.951928	+	0.306321i	$0.0990981\pi$
$389$			12.0832i			0.612642i	−0.951928	+	0.306321i	$0.900902\pi$
$390$		0			0
$391$	11.3268	+	6.53953i	0.572821	+	0.330718i
$392$	3.30402	+	5.38298i	0.166878	+	0.271881i
$393$		0			0
$394$	−10.3705	−	5.98741i	−0.522458	−	0.301641i
$395$	−7.74498	−	1.77775i	−0.389692	−	0.0894481i
$396$		0			0
$397$	−7.12359	+	26.5856i	−0.357523	+	1.33429i	0.519757	+	0.854314i	$0.326022\pi$
$397$	−7.12359	+	26.5856i	−0.357523	+	1.33429i	−0.877280	+	0.479979i	$0.840644\pi$
$398$	−48.5943	−	13.0208i	−2.43581	−	0.652674i
$399$		0			0
$400$	1.06929	+	14.7546i	0.0534643	+	0.737730i
$401$	−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
$407$	0.746251	+	0.199957i	0.0369903	+	0.00991151i
$408$		0			0
$409$	−1.38540	−	2.39958i	−0.0685036	−	0.118652i	0.829739	−	0.558151i	$-0.188489\pi$
$409$	−1.38540	−	2.39958i	−0.0685036	−	0.118652i	−0.898243	+	0.439500i	$0.855156\pi$
$410$	−0.506679	−	14.0012i	−0.0250231	−	0.691471i
$411$		0			0
$412$	8.21891	−	30.6734i	0.404917	−	1.51117i
$413$	8.41673	−	3.61970i	0.414160	−	0.178114i
$414$		0			0
$415$	−0.739264	+	0.0267527i	−0.0362891	+	0.00131324i
$416$			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	−0.674527	−	0.738250i	$-0.735653\pi$
$419$	6.18341	−	10.7100i	0.302079	−	0.523217i	0.976607	+	0.215033i	$0.0689859\pi$
$420$		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	$0.744547\pi$
$422$	22.8294	+	6.11713i	1.11132	+	0.297777i
$423$		0			0
$424$	10.9601	+	6.32782i	0.532270	+	0.307306i
$425$	11.5417	−	13.3453i	0.559855	−	0.647342i
$426$		0			0
$427$	−2.15949	+	2.89408i	−0.104505	+	0.140054i
$428$	−28.2753	+	7.57634i	−1.36674	+	0.366216i
$429$		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	$-0.677870\pi$
$433$	6.61149	−	6.61149i	0.317728	−	0.317728i	0.847894	+	0.530166i	$0.177870\pi$
$434$	21.3146	−	16.8155i	1.02313	−	0.807169i
$435$		0			0
$436$	32.5080			1.55685
$437$	−4.94790	+	18.4658i	−0.236690	+	0.883340i
$438$		0			0
$439$	−4.69348	+	8.12935i	−0.224008	+	0.387993i	−0.956021	−	0.293297i	$-0.905247\pi$
$439$	−4.69348	+	8.12935i	−0.224008	+	0.387993i	0.732014	+	0.681290i	$0.238581\pi$
$440$	−0.157505	−	0.0834912i	−0.00750875	−	0.00398029i
$441$		0			0
$442$	27.9553	−	27.9553i	1.32970	−	1.32970i
$443$	24.4659	−	6.55561i	1.16241	−	0.311467i	0.374481	−	0.927234i	$-0.377821\pi$
$443$	24.4659	−	6.55561i	1.16241	−	0.311467i	0.787928	+	0.615768i	$0.211154\pi$
$444$		0			0
$445$	−18.7032	−	17.3968i	−0.886617	−	0.824688i
$446$			53.5827i			2.53722i
$447$		0			0
$448$	−28.8596	−	3.40524i	−1.36349	−	0.160882i
$449$		−	7.88064i		−	0.371910i	−0.982558	−	0.185955i	$-0.940462\pi$
$449$		−	7.88064i		−	0.371910i	0.982558	−	0.185955i	$-0.0595379\pi$
$450$		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
$455$	−28.4643	+	13.4812i	−1.33443	+	0.632010i
$456$		0			0
$457$	10.6289	+	39.6678i	0.497201	+	1.85558i	0.517336	+	0.855782i	$0.326924\pi$
$457$	10.6289	+	39.6678i	0.497201	+	1.85558i	−0.0201351	+	0.999797i	$0.506410\pi$
$458$	−1.86813	−	6.97197i	−0.0872921	−	0.325779i
$459$		0			0
$460$	−20.1157	+	0.727953i	−0.937901	+	0.0339410i
$461$	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
$463$	−4.55437	+	1.22034i	−0.211659	+	0.0567140i	−0.363091	−	0.931754i	$-0.618278\pi$
$463$	−4.55437	+	1.22034i	−0.211659	+	0.0567140i	0.151431	+	0.988468i	$0.451612\pi$
$464$		−	2.08064i		−	0.0965915i
$465$		0			0
$466$	19.9244			0.922979
$467$	−4.40276	+	16.4313i	−0.203735	+	0.760350i	0.786096	+	0.618104i	$0.212099\pi$
$467$	−4.40276	+	16.4313i	−0.203735	+	0.760350i	−0.989831	+	0.142246i	$0.954568\pi$
$468$		0			0
$469$	5.86441	−	14.7146i	0.270793	−	0.679458i
$470$	19.7933	+	18.4108i	0.912997	+	0.849226i
$471$		0			0
$472$	0.808707	−	3.01814i	0.0372238	−	0.138921i
$473$	−0.0526211	+	0.196385i	−0.00241952	+	0.00902977i
$474$		0			0
$475$	23.2080	+	11.2467i	1.06486	+	0.516032i
$476$	14.0447	+	17.8024i	0.643737	+	0.815973i
$477$		0			0
$478$	0.868755	−	3.24224i	0.0397359	−	0.148297i
$479$	−4.74183			−0.216660			−0.108330	−	0.994115i	$-0.534550\pi$
$479$	−4.74183			−0.216660			−0.108330	+	0.994115i	$0.534550\pi$
$480$		0			0
$481$		−	46.5502i		−	2.12251i
$482$	−45.4239	+	12.1713i	−2.06900	+	0.554387i
$483$		0			0
$484$	23.1206	−	13.3487i	1.05094	−	0.606758i
$485$	0.844365	+	23.3326i	0.0383407	+	1.05948i
$486$		0			0
$487$	−5.49403	−	20.5040i	−0.248958	−	0.929125i	−0.971352	−	0.237644i	$-0.923625\pi$
$487$	−5.49403	−	20.5040i	−0.248958	−	0.929125i	0.722394	−	0.691482i	$-0.243042\pi$
$488$	0.318729	+	1.18951i	0.0144282	+	0.0538467i
$489$		0			0
$490$	−10.5140	−	31.2170i	−0.474974	−	1.41024i
$491$	−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
$497$	−4.18200	+	35.4427i	−0.187588	+	1.58982i
$498$		0			0
$499$			42.5764i			1.90598i	0.302996	+	0.952992i	$0.402013\pi$
$499$			42.5764i			1.90598i	−0.302996	+	0.952992i	$0.597987\pi$
$500$	−4.14599	+	26.8359i	−0.185414	+	1.20014i
$501$		0			0
$502$	−41.1840	+	11.0352i	−1.83813	+	0.492526i
$503$	−7.74911	+	7.74911i	−0.345516	+	0.345516i	−0.858436	−	0.512920i	$-0.828564\pi$
$503$	−7.74911	+	7.74911i	−0.345516	+	0.345516i	0.512920	+	0.858436i	$0.328564\pi$
$504$		0			0
$505$	7.54397	+	24.5640i	0.335702	+	1.09308i
$506$	−0.344583	+	0.596836i	−0.0153186	+	0.0265326i
$507$		0			0
$508$	−4.13033	+	15.4146i	−0.183254	+	0.683912i
$509$	−4.48049			−0.198594			−0.0992972	−	0.995058i	$-0.531659\pi$
$509$	−4.48049			−0.198594			−0.0992972	+	0.995058i	$0.531659\pi$
$510$		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
$517$	0.490263	−	0.131366i	0.0215617	−	0.00577745i
$518$	48.3500	+	5.70498i	2.12438	+	0.250662i
$519$		0			0
$520$	−2.40297	+	10.4688i	−0.105377	+	0.459089i
$521$	−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
$523$	6.48593	+	1.73790i	0.283610	+	0.0759931i	0.397820	−	0.917464i	$-0.369767\pi$
$523$	6.48593	+	1.73790i	0.283610	+	0.0759931i	−0.114210	+	0.993457i	$0.536434\pi$
$524$	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
$530$	−48.3280	−	44.9524i	−2.09924	−	1.95261i
$531$		0			0
$532$	−19.8214	+	26.5639i	−0.859366	+	1.15169i
$533$	−4.10236	+	15.3102i	−0.177693	+	0.663158i
$534$		0			0
$535$	26.9327	−	0.974648i	1.16440	−	0.0421377i
$536$	−2.70104	−	4.67834i	−0.116667	−	0.202074i
$537$		0			0
$538$	−15.0258	−	4.02616i	−0.647809	−	0.173580i
$539$	−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
$545$	−29.1704	−	6.69564i	−1.24952	−	0.286810i
$546$		0			0
$547$	6.16965	+	1.65315i	0.263795	+	0.0706837i	0.388292	−	0.921536i	$-0.373065\pi$
$547$	6.16965	+	1.65315i	0.263795	+	0.0706837i	−0.124497	+	0.992220i	$0.539732\pi$
$548$	−8.98785	+	33.5431i	−0.383942	+	1.43289i
$549$		0			0
$550$	0.703195	+	0.608160i	0.0299844	+	0.0259320i
$551$	−3.14128	−	1.81362i	−0.133823	−	0.0772628i
$552$		0			0
$553$	−5.62292	+	7.53565i	−0.239111	+	0.320448i
$554$	−17.3817	−	10.0354i	−0.738479	−	0.426361i
$555$		0			0
$556$			41.9317i			1.77830i
$557$	−5.29513	−	19.7617i	−0.224362	−	0.837329i	−0.982659	−	0.185421i	$-0.940635\pi$
$557$	−5.29513	−	19.7617i	−0.224362	−	0.837329i	0.758298	−	0.651909i	$-0.226031\pi$
$558$		0			0
$559$	12.2502			0.518130
$560$	16.4836	+	5.88800i	0.696560	+	0.248813i
$561$		0			0
$562$	28.2693	−	28.2693i	1.19247	−	1.19247i
$563$	20.5724	+	5.51236i	0.867024	+	0.232318i	0.664800	−	0.747021i	$-0.268517\pi$
$563$	20.5724	+	5.51236i	0.867024	+	0.232318i	0.202223	+	0.979339i	$0.435183\pi$
$564$		0			0
$565$	−28.2885	+	17.7264i	−1.19011	+	0.745757i
$566$		−	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	−0.111275	−	0.993790i	$-0.535494\pi$
$569$	−24.5111	−	14.1515i	−1.02756	−	0.593262i	−0.916285	+	0.400528i	$0.868827\pi$
$570$		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
$577$	1.72908	−	0.463305i	0.0719825	−	0.0192876i	−0.222648	−	0.974899i	$-0.571470\pi$
$577$	1.72908	−	0.463305i	0.0719825	−	0.0192876i	0.294631	+	0.955611i	$0.404803\pi$
$578$	−6.76733	−	6.76733i	−0.281484	−	0.281484i
$579$		0			0
$580$	0.854420	−	3.72239i	0.0354779	−	0.154564i
$581$	−0.324050	+	0.813087i	−0.0134439	+	0.0337325i
$582$		0			0
$583$	−1.19704	+	0.320747i	−0.0495765	+	0.0132840i
$584$	−0.497970	+	0.862510i	−0.0206062	+	0.0356909i
$585$		0			0
$586$	17.2999	−	9.98809i	0.714652	−	0.412604i
$587$	1.76127	−	6.57314i	0.0726953	−	0.271302i	−0.920006	−	0.391905i	$-0.871816\pi$
$587$	1.76127	−	6.57314i	0.0726953	−	0.271302i	0.992701	+	0.120603i	$0.0384828\pi$
$588$		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
$593$	23.7495	+	6.36367i	0.975277	+	0.261325i	0.711054	−	0.703137i	$-0.248218\pi$
$593$	23.7495	+	6.36367i	0.975277	+	0.261325i	0.264223	+	0.964462i	$0.414885\pi$
$594$		0			0
$595$	−8.93596	−	18.8674i	−0.366339	−	0.773488i
$596$	3.43102	+	5.94269i	0.140540	+	0.243422i
$597$		0			0
$598$	40.1097	+	10.7474i	1.64021	+	0.439492i
$599$	19.9787	−	11.5347i	0.816309	−	0.471296i	−0.0328327	−	0.999461i	$-0.510453\pi$
$599$	19.9787	−	11.5347i	0.816309	−	0.471296i	0.849142	+	0.528164i	$0.177120\pi$
$600$		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	$0.194251\pi$
$602$	−1.50133	+	12.7239i	−0.0611897	+	0.518586i
$603$		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	$-0.0281386\pi$
$607$	22.3661	+	22.3661i	0.907810	+	0.907810i	−0.0882849	+	0.996095i	$0.528139\pi$
$608$	−10.7211	−	40.0116i	−0.434797	−	1.62268i
$609$		0			0
$610$	−0.232265	−	6.41825i	−0.00940414	−	0.259867i
$611$	−15.2910	−	26.4848i	−0.618608	−	1.07146i
$612$		0			0
$613$	−22.5570	+	6.04412i	−0.911067	+	0.244120i	−0.683763	−	0.729704i	$-0.739658\pi$
$613$	−22.5570	+	6.04412i	−0.911067	+	0.244120i	−0.227304	+	0.973824i	$0.572991\pi$
$614$	5.98946	−	10.3740i	0.241715	−	0.418662i
$615$		0			0
$616$	−0.165597	+	0.130643i	−0.00667210	+	0.00526375i
$617$	0.258887	+	0.966179i	0.0104224	+	0.0388969i	0.970941	−	0.239318i	$-0.0769239\pi$
$617$	0.258887	+	0.966179i	0.0104224	+	0.0388969i	−0.960519	+	0.278215i	$0.910257\pi$
$618$		0			0
$619$	12.4971			0.502303			0.251151	−	0.967948i	$-0.419191\pi$
$619$	12.4971			0.502303			0.251151	+	0.967948i	$0.419191\pi$
$620$	−5.92425	+	25.8098i	−0.237924	+	1.03655i
$621$		0			0
$622$	−8.30415	−	8.30415i	−0.332966	−	0.332966i
$623$	−27.7645	+	11.9404i	−1.11236	+	0.478382i
$624$		0			0
$625$	9.24768	−	23.2267i	0.369907	−	0.929069i
$626$	59.1246	−	34.1356i	2.36309	−	1.36433i
$627$		0			0
$628$	−7.41573	−	27.6759i	−0.295920	−	1.10439i
$629$	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	$0.323470\pi$
$632$	0.829910	+	3.09727i	0.0330121	+	0.123203i
$633$		0			0
$634$	−11.6858	+	6.74680i	−0.464102	+	0.267950i
$635$	6.88119	−	12.9813i	0.273072	−	0.515145i
$636$		0			0
$637$	1.00229	+	37.2524i	0.0397120	+	1.47599i
$638$	−0.0924615	−	0.0924615i	−0.00366058	−	0.00366058i
$639$		0			0
$640$	13.3630	−	8.37370i	0.528221	−	0.330999i
$641$	−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
$643$	−6.04998	−	22.5788i	−0.238588	−	0.890422i	−0.976499	−	0.215524i	$-0.930854\pi$
$643$	−6.04998	−	22.5788i	−0.238588	−	0.890422i	0.737911	−	0.674898i	$-0.235812\pi$
$644$	−8.81756	+	22.1245i	−0.347460	+	0.871827i
$645$		0			0
$646$	−19.1518	+	33.1718i	−0.753516	+	1.30513i
$647$	7.74958	−	2.07649i	0.304667	−	0.0816354i	−0.103246	−	0.994656i	$-0.532923\pi$
$647$	7.74958	−	2.07649i	0.304667	−	0.0816354i	0.407914	+	0.913020i	$0.366256\pi$
$648$		0			0
$649$	0.152984	+	0.264977i	0.00600516	+	0.0104012i
$650$	24.4289	−	50.4102i	0.958181	−	1.97725i
$651$		0			0
$652$	6.31900	+	23.5828i	0.247471	+	0.923575i
$653$	−12.2599	−	12.2599i	−0.479765	−	0.479765i	0.425291	−	0.905057i	$-0.360172\pi$
$653$	−12.2599	−	12.2599i	−0.479765	−	0.479765i	−0.905057	+	0.425291i	$0.860172\pi$
$654$		0			0
$655$	−12.5810	−	40.9650i	−0.491580	−	1.60064i
$656$	7.62868	−	4.40442i	0.297850	−	0.171964i
$657$		0			0
$658$	29.3828	−	12.6363i	1.14546	−	0.492616i
$659$	−27.0155	+	15.5974i	−1.05237	+	0.607588i	−0.923313	−	0.384049i	$-0.874529\pi$
$659$	−27.0155	+	15.5974i	−1.05237	+	0.607588i	−0.129060	+	0.991637i	$0.541196\pi$
$660$		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	$0.237547\pi$
$662$	12.0557	+	3.23030i	0.468556	+	0.125549i
$663$		0			0
$664$	0.149252	+	0.258511i	0.00579208	+	0.0100322i
$665$	23.2576	−	19.7540i	0.901892	−	0.766028i
$666$		0			0
$667$	−2.51767	−	0.674607i	−0.0974844	−	0.0261209i
$668$	−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
$673$	−10.3359	+	38.5740i	−0.398418	+	1.48692i	0.417461	+	0.908695i	$0.362920\pi$
$673$	−10.3359	+	38.5740i	−0.398418	+	1.48692i	−0.815879	+	0.578223i	$0.803746\pi$
$674$	17.6044	−	10.1639i	0.678098	−	0.391500i
$675$		0			0
$676$	18.6306	−	32.2692i	0.716563	−	1.24112i
$677$	0.396426	−	0.106222i	0.0152359	−	0.00408244i	−0.251193	−	0.967937i	$-0.580823\pi$
$677$	0.396426	−	0.106222i	0.0152359	−	0.00408244i	0.266429	+	0.963855i	$0.414156\pi$
$678$		0			0
$679$	25.6626	+	10.2276i	0.984839	+	0.392500i
$680$	−6.93922	−	1.59279i	−0.266107	−	0.0610809i
$681$		0			0
$682$	0.641096	+	0.641096i	0.0245488	+	0.0245488i
$683$	−29.7361	+	7.96776i	−1.13782	+	0.304878i	−0.778074	−	0.628173i	$-0.783803\pi$
$683$	−29.7361	+	7.96776i	−1.13782	+	0.304878i	−0.359746	+	0.933050i	$0.617137\pi$
$684$		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
$695$	8.63661	−	37.6265i	0.327605	−	1.42725i
$696$		0			0
$697$	−10.1483	−	2.71922i	−0.384394	−	0.102998i
$698$	15.5016	−	15.5016i	0.586743	−	0.586743i
$699$		0			0
$700$	27.0722	+	17.3030i	1.02323	+	0.653992i
$701$	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
$703$	11.6729	+	43.5638i	0.440251	+	1.64304i
$704$		−	0.970454i		−	0.0365754i
$705$		0			0
$706$	58.7229	+	33.9037i	2.21007	+	1.27598i
$707$	30.1948	+	3.56279i	1.13559	+	0.133992i
$708$		0			0
$709$	4.78195	+	2.76086i	0.179590	+	0.103686i	0.587100	−	0.809514i	$-0.300270\pi$
$709$	4.78195	+	2.76086i	0.179590	+	0.103686i	−0.407510	+	0.913201i	$0.633603\pi$
$710$	−33.7050	−	53.7876i	−1.26492	−	2.01861i
$711$		0			0
$712$	−2.66770	+	9.95601i	−0.0999765	+	0.373117i
$713$	17.4566	+	4.67749i	0.653756	+	0.175173i
$714$		0			0
$715$	−0.558494	−	0.891264i	−0.0208865	−	0.0333314i
$716$	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	0.999635	−	0.0270154i	$-0.00860032\pi$
$719$	12.7748	+	22.1267i	0.476421	+	0.825186i	−0.523214	+	0.852202i	$0.675267\pi$
$720$		0			0
$721$	21.4258	+	27.1585i	0.797940	+	1.01143i
$722$	−15.4570	−	4.14169i	−0.575250	−	0.154138i
$723$		0			0
$724$	−21.6676	−	37.5293i	−0.805268	−	1.39477i
$725$	−1.53339	+	3.16423i	−0.0569488	+	0.117516i
$726$		0			0
$727$	5.90847	−	22.0507i	0.219133	−	0.817816i	−0.765537	−	0.643391i	$-0.777527\pi$
$727$	5.90847	−	22.0507i	0.219133	−	0.817816i	0.984671	−	0.174425i	$-0.0558066\pi$
$728$	10.1859	+	7.60046i	0.377514	+	0.281692i
$729$		0			0
$730$	3.53755	−	3.80320i	0.130930	−	0.140763i
$731$			8.12001i			0.300329i
$732$		0			0
$733$	27.2649	−	27.2649i	1.00705	−	1.00705i	0.00707692	−	0.999975i	$-0.497747\pi$
$733$	27.2649	−	27.2649i	1.00705	−	1.00705i	0.999975	−	0.00707692i	$-0.00225267\pi$
$734$	9.49278	−	16.4420i	0.350385	−	0.606884i
$735$		0			0
$736$	−14.8830	−	25.7781i	−0.548594	−	0.950193i
$737$	0.510960	+	0.136911i	0.0188215	+	0.00504320i
$738$		0			0
$739$	15.5491	+	8.97729i	0.571984	+	0.330235i	0.757941	−	0.652323i	$-0.226205\pi$
$739$	15.5491	+	8.97729i	0.571984	+	0.330235i	−0.185958	+	0.982558i	$0.559539\pi$
$740$	−40.2396	+	25.2154i	−1.47924	+	0.926937i
$741$		0			0
$742$	−71.7420	+	30.8534i	−2.63373	+	1.13266i
$743$	31.1560	−	8.34823i	1.14300	−	0.306267i	0.362845	−	0.931849i	$-0.381805\pi$
$743$	31.1560	−	8.34823i	1.14300	−	0.306267i	0.780158	+	0.625583i	$0.215139\pi$
$744$		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	$0.671745\pi$
$752$	−4.39890	+	16.4169i	−0.160411	+	0.598664i
$753$		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	−0.844424	−	0.535675i	$-0.820057\pi$
$757$	−8.49483	+	8.49483i	−0.308750	+	0.308750i	0.535675	+	0.844424i	$0.320057\pi$
$758$	18.5047	−	4.95832i	0.672121	−	0.180094i
$759$		0			0
$760$	−0.376350	−	10.3998i	−0.0136516	−	0.377240i
$761$		−	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
$763$	−21.1779	+	28.3820i	−0.766693	+	1.02750i
$764$			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	$-0.610856\pi$
$769$	17.8420	−	30.9033i	0.643401	−	1.11440i	0.984668	−	0.174436i	$-0.0558103\pi$
$770$	0.994169	−	0.470857i	0.0358274	−	0.0169685i
$771$		0			0
$772$	−7.72364	−	28.8250i	−0.277980	−	1.03744i
$773$	5.62676	+	20.9993i	0.202380	+	0.755294i	0.990232	+	0.139429i	$0.0445266\pi$
$773$	5.62676	+	20.9993i	0.202380	+	0.755294i	−0.787852	+	0.615865i	$0.788807\pi$
$774$		0			0
$775$	10.6320	−	21.9396i	0.381913	−	0.788095i
$776$	8.15911	−	4.71066i	0.292895	−	0.169103i
$777$		0			0
$778$	−24.5621	+	6.58140i	−0.880595	+	0.235955i
$779$		−	15.3567i		−	0.550210i
$780$		0			0
$781$	−1.19182			−0.0426468
$782$	−7.12383	+	26.5865i	−0.254748	+	0.950731i
$783$		0			0
$784$	14.2454	−	15.0332i	0.508766	−	0.536900i
$785$	0.953987	+	26.3618i	0.0340492	+	0.940892i
$786$		0			0
$787$	4.65509	−	17.3730i	0.165936	−	0.619282i	−0.831983	−	0.554801i	$-0.812794\pi$
$787$	4.65509	−	17.3730i	0.165936	−	0.619282i	0.997919	−	0.0644806i	$-0.0205391\pi$
$788$	3.57691	−	13.3492i	0.127422	−	0.475546i
$789$		0			0
$790$	−0.604775	−	16.7119i	−0.0215169	−	0.594584i
$791$	5.68201	+	39.0892i	0.202029	+	1.38985i
$792$		0			0
$793$	−1.88055	+	7.01830i	−0.0667802	+	0.249227i
$794$	−57.9220			−2.05558
$795$		0			0
$796$		−	58.0610i		−	2.05792i
$797$	39.3012	−	10.5307i	1.39212	−	0.373017i	0.516611	−	0.856220i	$-0.327193\pi$
$797$	39.3012	−	10.5307i	1.39212	−	0.373017i	0.875509	+	0.483203i	$0.160527\pi$
$798$		0			0
$799$	17.5553	−	10.1356i	0.621062	−	0.358571i
$800$	−37.9340	+	13.1692i	−1.34117	+	0.465603i
$801$		0			0
$802$	−3.38324	−	12.6264i	−0.119466	−	0.445854i
$803$	−0.0252413	−	0.0942018i	−0.000890746	−	0.00332431i
$804$		0			0
$805$	12.4692	−	18.0368i	0.439482	−	0.635714i
$806$	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	−0.00187764	−	0.999998i	$-0.500598\pi$
$809$	−24.7124	−	14.2677i	−0.868840	−	0.501625i	−0.866963	+	0.498373i	$0.833931\pi$
$810$		0			0
$811$		−	48.5126i		−	1.70351i	−0.523941	−	0.851755i	$-0.675539\pi$
$811$		−	48.5126i		−	1.70351i	0.523941	−	0.851755i	$-0.324461\pi$
$812$	−3.62178	−	2.70249i	−0.127100	−	0.0948386i
$813$		0			0
$814$			1.62585i			0.0569862i
$815$	−0.812899	−	22.4631i	−0.0284746	−	0.786847i
$816$		0			0
$817$	−11.4643	+	3.07186i	−0.401086	+	0.107471i
$818$	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
$823$	−7.54502	+	28.1584i	−0.263003	+	0.981540i	0.700459	+	0.713693i	$0.252979\pi$
$823$	−7.54502	+	28.1584i	−0.263003	+	0.981540i	−0.963461	+	0.267847i	$0.913688\pi$
$824$	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	−0.285259	−	0.958450i	$-0.592080\pi$
$827$	19.3594	−	19.3594i	0.673191	−	0.673191i	0.958450	+	0.285259i	$0.0920797\pi$
$828$		0			0
$829$	−15.8644	+	27.4780i	−0.550994	+	0.954350i	0.447209	+	0.894430i	$0.352418\pi$
$829$	−15.8644	+	27.4780i	−0.550994	+	0.954350i	−0.998203	+	0.0599208i	$0.980915\pi$
$830$	−0.457040	−	1.48817i	−0.0158641	−	0.0516551i
$831$		0			0
$832$	−56.4807	+	15.1340i	−1.95812	+	0.524675i
$833$	−24.6925	+	0.664360i	−0.855546	+	0.0230187i
$834$		0			0
$835$	2.05903	−	1.29025i	0.0712556	−	0.0446510i
$836$	−0.958561	−	0.553425i	−0.0331525	−	0.0191406i
$837$		0			0
$838$	25.1387	+	6.73589i	0.868401	+	0.232687i
$839$	−6.71273	−	11.6268i	−0.231749	−	0.401401i	0.726574	−	0.687088i	$-0.241112\pi$
$839$	−6.71273	−	11.6268i	−0.231749	−	0.401401i	−0.958323	+	0.285687i	$0.907778\pi$
$840$		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
$845$	−23.3642	+	25.1188i	−0.803755	+	0.864112i
$846$		0			0
$847$	−3.40791	+	28.8822i	−0.117097	+	0.992406i
$848$	10.7405	−	40.0841i	0.368831	−	1.37650i
$849$		0			0
$850$	33.4141	+	16.1926i	1.14610	+	0.555401i
$851$	16.2043	+	28.0667i	0.555477	+	0.962114i
$852$		0			0
$853$	40.5841	+	10.8745i	1.38957	+	0.372335i	0.874590	−	0.484864i	$-0.161131\pi$
$853$	40.5841	+	10.8745i	1.38957	+	0.372335i	0.514985	+	0.857199i	$0.327798\pi$
$854$	−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	$-0.369564\pi$
$857$	−15.1878	−	15.1878i	−0.518806	−	0.518806i	−0.917210	+	0.398404i	$0.869564\pi$
$858$		0			0
$859$	−3.55514			−0.121300			−0.0606499	−	0.998159i	$-0.519317\pi$
$859$	−3.55514			−0.121300			−0.0606499	+	0.998159i	$0.519317\pi$
$860$	−6.63573	−	10.5895i	−0.226276	−	0.361100i
$861$		0			0
$862$	−64.6953	−	17.3351i	−2.20353	−	0.590435i
$863$	13.0583	−	48.7342i	0.444509	−	1.65893i	−0.272719	−	0.962094i	$-0.587923\pi$
$863$	13.0583	−	48.7342i	0.444509	−	1.65893i	0.717229	−	0.696838i	$-0.245410\pi$
$864$		0			0
$865$	12.1534	+	19.3948i	0.413228	+	0.659444i
$866$	17.0406	+	9.83842i	0.579065	+	0.334323i
$867$		0			0
$868$	25.1122	+	18.7381i	0.852363	+	0.636012i
$869$	−0.271924	−	0.156995i	−0.00922439	−	0.00532570i
$870$		0			0
$871$		−	31.8731i		−	1.07998i
$872$	3.12574	+	11.6654i	0.105851	+	0.395041i
$873$		0			0
$874$	−40.2314			−1.36085
$875$	−20.7288	−	21.1025i	−0.700762	−	0.713395i
$876$		0			0
$877$	30.5289	−	30.5289i	1.03089	−	1.03089i	0.0313812	−	0.999507i	$-0.490009\pi$
$877$	30.5289	−	30.5289i	1.03089	−	1.03089i	0.999507	−	0.0313812i	$-0.00999058\pi$
$878$	−19.0814	−	5.11284i	−0.643965	−	0.172550i
$879$		0			0
$880$	−0.130771	+	0.569721i	−0.00440829	+	0.0192053i
$881$		−	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	0.403633	−	0.914921i	$-0.367747\pi$
$883$	−15.1931	−	15.1931i	−0.511288	−	0.511288i	−0.914921	+	0.403633i	$0.867747\pi$
$884$	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	$-0.0719553\pi$
$887$	22.3495	+	22.3495i	0.750424	+	0.750424i	−0.224134	+	0.974558i	$0.571955\pi$
$888$		0			0
$889$	−10.7673	−	13.6482i	−0.361125	−	0.457746i
$890$	25.1762	−	47.4946i	0.843910	−	1.59202i
$891$		0			0
$892$	−59.7326	+	16.0053i	−2.00000	+	0.535897i
$893$	20.9513	+	20.9513i	0.701109	+	0.701109i
$894$		0			0
$895$	−11.9200	−	2.73606i	−0.398442	−	0.0914565i
$896$	−2.68409	−	18.4651i	−0.0896693	−	0.616877i
$897$		0			0
$898$	16.0194	−	4.29238i	0.534574	−	0.143239i
$899$	−1.71450	+	2.96960i	−0.0571818	+	0.0990418i
$900$		0			0
$901$	−42.8637	+	24.7474i	−1.42800	+	0.824454i
$902$	0.143282	−	0.534737i	0.00477078	−	0.0178048i
$903$		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	−0.498124	−	0.867106i	$-0.665978\pi$
$907$	11.1124	−	11.1124i	0.368982	−	0.368982i	0.867106	+	0.498124i	$0.165978\pi$
$908$	−14.7521	−	3.95282i	−0.489566	−	0.131179i
$909$		0			0
$910$	−42.9078	−	50.5180i	−1.42238	−	1.67466i
$911$	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
$913$	−0.0282341	−	0.00756532i	−0.000934414	−	0.000250375i
$914$	−74.8454	+	43.2120i	−2.47567	+	1.42933i
$915$		0			0
$916$	7.21415	−	4.16509i	0.238362	−	0.137618i
$917$	−50.3555	−	5.94162i	−1.66289	−	0.196209i
$918$		0			0
$919$	−1.01486	+	0.585929i	−0.0334771	+	0.0193280i	−0.516645	−	0.856200i	$-0.672819\pi$
$919$	−1.01486	+	0.585929i	−0.0334771	+	0.0193280i	0.483168	+	0.875528i	$0.339486\pi$
$920$	−2.19541	−	7.14849i	−0.0723806	−	0.235679i
$921$		0			0
$922$	24.8025	+	24.8025i	0.816826	+	0.816826i
$923$	18.5861	+	69.3644i	0.611770	+	2.28316i
$924$		0			0
$925$	41.3018	−	14.3384i	1.35799	−	0.471444i
$926$	−4.96130	−	8.59322i	−0.163038	−	0.282391i
$927$		0			0
$928$	5.45526	−	1.46173i	0.179078	−	0.0479837i
$929$	−0.674615	+	1.16847i	−0.0221334	+	0.0383362i	−0.876880	−	0.480709i	$-0.840379\pi$
$929$	−0.674615	+	1.16847i	−0.0221334	+	0.0383362i	0.854747	+	0.519046i	$0.173713\pi$
$930$		0			0
$931$	−10.2794	−	34.6111i	−0.336892	−	1.13433i
$932$	5.95147	+	22.2112i	0.194947	+	0.727551i
$933$		0			0
$934$	−35.7989			−1.17137
$935$	0.590770	−	0.370195i	0.0193202	−	0.0121067i
$936$		0			0
$937$	25.3539	+	25.3539i	0.828277	+	0.828277i	0.987278	−	0.159001i	$-0.0508274\pi$
$937$	25.3539	+	25.3539i	0.828277	+	0.828277i	−0.159001	+	0.987278i	$0.550827\pi$
$938$	33.1054	+	3.90622i	1.08093	+	0.127542i
$939$		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
$943$	−2.85609	−	10.6591i	−0.0930071	−	0.347107i
$944$	−10.2457			−0.333468
$945$		0			0
$946$	−0.427863			−0.0139110
$947$	5.57439	+	20.8039i	0.181143	+	0.676036i	0.995423	+	0.0955637i	$0.0304654\pi$
$947$	5.57439	+	20.8039i	0.181143	+	0.676036i	−0.814280	+	0.580472i	$0.802868\pi$
$948$		0			0
$949$	−5.08894	+	2.93810i	−0.165194	+	0.0953747i
$950$	−10.2209	+	53.3019i	−0.331609	+	1.72934i
$951$		0			0
$952$	−5.03792	+	6.75166i	−0.163280	+	0.218823i
$953$	7.79646	+	7.79646i	0.252552	+	0.252552i	0.822016	−	0.569464i	$-0.192849\pi$
$953$	7.79646	+	7.79646i	0.252552	+	0.252552i	−0.569464	+	0.822016i	$0.692849\pi$
$954$		0			0
$955$	0.429675	−	1.87194i	0.0139040	−	0.0605744i
$956$	3.87386			0.125290
$957$		0			0
$958$	−2.58275	−	9.63897i	−0.0834450	−	0.311421i
$959$	−23.4304	−	29.6993i	−0.756606	−	0.959041i
$960$		0			0
$961$	−3.61224	+	6.25659i	−0.116524	+	0.201826i
$962$	94.6252	−	25.3547i	3.05084	−	0.817469i
$963$		0			0
$964$	−27.1365	−	47.0018i	−0.874007	−	1.51382i
$965$	0.993598	+	27.4564i	0.0319850	+	0.883852i
$966$		0			0
$967$	9.76493	+	36.4432i	0.314019	+	1.17193i	0.924899	+	0.380212i	$0.124149\pi$
$967$	9.76493	+	36.4432i	0.314019	+	1.17193i	−0.610880	+	0.791723i	$0.709184\pi$
$968$	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
$973$	−36.6095	−	27.3171i	−1.17365	−	0.875747i
$974$	38.6871	−	22.3360i	1.23962	−	0.715692i
$975$		0			0
$976$	3.49704	−	2.01902i	0.111937	−	0.0646271i
$977$	−15.4124	−	4.12974i	−0.493086	−	0.132122i	0.00370333	−	0.999993i	$-0.498821\pi$
$977$	−15.4124	−	4.12974i	−0.493086	−	0.132122i	−0.496789	+	0.867871i	$0.665488\pi$
$978$		0			0
$979$	−0.504654	−	0.874086i	−0.0161288	−	0.0279359i
$980$	31.6593	−	21.0453i	1.01132	−	0.672268i
$981$		0			0
$982$	−38.6447	−	10.3548i	−1.23320	−	0.330436i
$983$	0.502961	−	0.502961i	0.0160420	−	0.0160420i	−0.699040	−	0.715082i	$-0.746389\pi$
$983$	0.502961	−	0.502961i	0.0160420	−	0.0160420i	0.715082	+	0.699040i	$0.246389\pi$
$984$		0			0
$985$	−5.95918	+	11.2419i	−0.189875	+	0.358197i
$986$	−4.52271	−	2.61119i	−0.144033	−	0.0831572i
$987$		0			0
$988$	−17.2610	+	64.4190i	−0.549146	+	2.04944i
$989$	−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	$0.907192\pi$
$992$	−37.8248	+	10.1351i	−1.20094	+	0.321791i
$993$		0			0
$994$	−74.3240	+	10.8037i	−2.35741	+	0.342674i
$995$	−11.9587	+	52.0998i	−0.379118	+	1.65168i
$996$		0			0
$997$	5.33194	+	5.33194i	0.168864	+	0.168864i	0.786480	−	0.617616i	$-0.211901\pi$
$997$	5.33194	+	5.33194i	0.168864	+	0.168864i	−0.617616	+	0.786480i	$0.711901\pi$
$998$	−86.5474	+	23.1903i	−2.73961	+	0.734076i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cj.e.388.34		160
3.2	odd	2		315.2.cg.e.283.7	yes	160
5.2	odd	4	inner	945.2.cj.e.577.7		160
7.5	odd	6		945.2.bv.e.523.34		160
9.2	odd	6		315.2.bs.e.178.7	yes	160
9.7	even	3		945.2.bv.e.73.34		160
15.2	even	4		315.2.cg.e.157.34	yes	160
21.5	even	6		315.2.bs.e.103.7	yes	160
35.12	even	12		945.2.bv.e.712.34		160
45.2	even	12		315.2.bs.e.52.7	✓	160
45.7	odd	12		945.2.bv.e.262.34		160
63.47	even	6		315.2.cg.e.313.34	yes	160
63.61	odd	6	inner	945.2.cj.e.208.7		160
105.47	odd	12		315.2.bs.e.292.7	yes	160
315.47	odd	12		315.2.cg.e.187.7	yes	160
315.187	even	12	inner	945.2.cj.e.397.34		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.7	✓	160	45.2	even	12
315.2.bs.e.103.7	yes	160	21.5	even	6
315.2.bs.e.178.7	yes	160	9.2	odd	6
315.2.bs.e.292.7	yes	160	105.47	odd	12
315.2.cg.e.157.34	yes	160	15.2	even	4
315.2.cg.e.187.7	yes	160	315.47	odd	12
315.2.cg.e.283.7	yes	160	3.2	odd	2
315.2.cg.e.313.34	yes	160	63.47	even	6
945.2.bv.e.73.34		160	9.7	even	3
945.2.bv.e.262.34		160	45.7	odd	12
945.2.bv.e.523.34		160	7.5	odd	6
945.2.bv.e.712.34		160	35.12	even	12
945.2.cj.e.208.7		160	63.61	odd	6	inner
945.2.cj.e.388.34		160	1.1	even	1	trivial
945.2.cj.e.397.34		160	315.187	even	12	inner
945.2.cj.e.577.7		160	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.544675 + 2.03275i) q^{2} +(-2.10336 + 1.21438i) q^{4} +(2.13753 - 0.656469i) q^{5} +(0.310030 - 2.62752i) q^{7} +(-0.638021 - 0.638021i) q^{8} +O(q^{10})\)	\(q+(0.544675 + 2.03275i) q^{2} +(-2.10336 + 1.21438i) q^{4} +(2.13753 - 0.656469i) q^{5} +(0.310030 - 2.62752i) q^{7} +(-0.638021 - 0.638021i) q^{8} +(2.49870 + 3.98751i) q^{10} +0.0883552 q^{11} +(-1.37787 - 5.14229i) q^{13} +(5.50997 - 0.800930i) q^{14} +(-1.47933 + 2.56227i) q^{16} +(3.40854 - 0.913316i) q^{17} +(2.57895 + 4.46688i) q^{19} +(-3.69881 + 3.97657i) q^{20} +(0.0481248 + 0.179604i) q^{22} +(2.62082 + 2.62082i) q^{23} +(4.13810 - 2.80645i) q^{25} +(9.70252 - 5.60175i) q^{26} +(2.53870 + 5.90313i) q^{28} +(-0.609023 + 0.351619i) q^{29} +(4.22275 - 2.43801i) q^{31} +(-7.75733 - 2.07857i) q^{32} +(3.71309 + 6.43126i) q^{34} +(-1.06219 - 5.81994i) q^{35} +(8.44603 + 2.26311i) q^{37} +(-7.67537 + 7.67537i) q^{38} +(-1.78263 - 0.944950i) q^{40} +(-2.57843 - 1.48865i) q^{41} +(-0.595563 + 2.22267i) q^{43} +(-0.185843 + 0.107297i) q^{44} +(-3.89998 + 6.75496i) q^{46} +(5.54877 - 1.48679i) q^{47} +(-6.80776 - 1.62922i) q^{49} +(7.95874 + 6.88312i) q^{50} +(9.14285 + 9.14285i) q^{52} +(-13.5481 + 3.63020i) q^{53} +(0.188862 - 0.0580025i) q^{55} +(-1.87422 + 1.47861i) q^{56} +(-1.04647 - 1.04647i) q^{58} +(1.73147 + 2.99899i) q^{59} +(-1.18197 - 0.682409i) q^{61} +(7.25589 + 7.25589i) q^{62} -10.9836i q^{64} +(-6.32101 - 10.0873i) q^{65} +(5.78303 + 1.54956i) q^{67} +(-6.06029 + 6.06029i) q^{68} +(11.2520 - 5.32914i) q^{70} -13.4890 q^{71} +(-0.285680 - 1.06617i) q^{73} +18.4014i q^{74} +(-10.8489 - 6.26364i) q^{76} +(0.0273928 - 0.232155i) q^{77} +(-3.07762 - 1.77687i) q^{79} +(-1.48006 + 6.44808i) q^{80} +(1.62166 - 6.05214i) q^{82} +(-0.319553 - 0.0856239i) q^{83} +(6.68631 - 4.18985i) q^{85} -4.84253 q^{86} +(-0.0563725 - 0.0563725i) q^{88} +(-5.71165 - 9.89286i) q^{89} +(-13.9387 + 2.02613i) q^{91} +(-8.69519 - 2.32987i) q^{92} +(6.04455 + 10.4695i) q^{94} +(8.44496 + 7.85509i) q^{95} +(-2.70245 + 10.0857i) q^{97} +(-0.396205 - 14.7259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 6 q^{7} + 16 q^{8}+O(q^{10}) \) 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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