LMFDB - Embedded newform 684.2.ce.a.575.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(35,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 4]))

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

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

chi := DirichletCharacter("684.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.ce (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			575.18
Character	$\chi$	$=$	684.575
Dual form			684.2.ce.a.251.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.268384 + 1.38851i) q^{2} +(-1.85594 - 0.745309i) q^{4} +(0.280698 - 0.334522i) q^{5} +(-1.12035 + 0.646834i) q^{7} +(1.53298 - 2.37697i) q^{8} +O(q^{10})$	\(q+(-0.268384 + 1.38851i) q^{2} +(-1.85594 - 0.745309i) q^{4} +(0.280698 - 0.334522i) q^{5} +(-1.12035 + 0.646834i) q^{7} +(1.53298 - 2.37697i) q^{8} +(0.389154 + 0.479533i) q^{10} +(0.842516 - 1.45928i) q^{11} +(0.944062 + 5.35404i) q^{13} +(-0.597454 - 1.72922i) q^{14} +(2.88903 + 2.76650i) q^{16} +(0.614700 + 1.68887i) q^{17} +(-3.19522 + 2.96489i) q^{19} +(-0.770281 + 0.411647i) q^{20} +(1.80011 + 1.56149i) q^{22} +(-1.92647 + 1.61650i) q^{23} +(0.835127 + 4.73624i) q^{25} +(-7.68753 - 0.126095i) q^{26} +(2.56139 - 0.365479i) q^{28} +(0.0255800 - 0.0702806i) q^{29} +(-2.87590 + 1.66040i) q^{31} +(-4.61669 + 3.26897i) q^{32} +(-2.51000 + 0.400253i) q^{34} +(-0.0980989 + 0.556347i) q^{35} +5.65252 q^{37} +(-3.25924 - 5.23234i) q^{38} +(-0.364847 - 1.18002i) q^{40} +(-6.88524 - 1.21405i) q^{41} +(-3.06284 + 3.65015i) q^{43} +(-2.65127 + 2.08040i) q^{44} +(-1.72750 - 3.10878i) q^{46} +(10.3436 + 3.76477i) q^{47} +(-2.66321 + 4.61282i) q^{49} +(-6.80047 - 0.111545i) q^{50} +(2.23829 - 10.6404i) q^{52} +(-2.66483 - 3.17582i) q^{53} +(-0.251670 - 0.691457i) q^{55} +(-0.179964 + 3.65462i) q^{56} +(0.0907203 + 0.0543804i) q^{58} +(-0.983482 + 0.357958i) q^{59} +(1.05962 - 0.889126i) q^{61} +(-1.53365 - 4.43886i) q^{62} +(-3.29997 - 7.28767i) q^{64} +(2.05604 + 1.18706i) q^{65} +(-4.42587 + 12.1600i) q^{67} +(0.117887 - 3.59259i) q^{68} +(-0.746167 - 0.285526i) q^{70} +(3.20103 + 2.68598i) q^{71} +(1.72543 - 9.78538i) q^{73} +(-1.51705 + 7.84861i) q^{74} +(8.13990 - 3.12123i) q^{76} +2.17987i q^{77} +(3.47382 + 0.612528i) q^{79} +(1.73640 - 0.189895i) q^{80} +(3.53362 - 9.23442i) q^{82} +(-4.00659 - 6.93962i) q^{83} +(0.737511 + 0.268432i) q^{85} +(-4.24627 - 5.23244i) q^{86} +(-2.17711 - 4.23968i) q^{88} +(2.01566 - 0.355415i) q^{89} +(-4.52085 - 5.38774i) q^{91} +(4.78022 - 1.56432i) q^{92} +(-8.00349 + 13.3519i) q^{94} +(0.0949310 + 1.90111i) q^{95} +(4.95301 - 1.80275i) q^{97} +(-5.69020 - 4.93591i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{4}+O(q^{10}) $ 240 * q + 12 * q^4	$ 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) $ 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.268384	+	1.38851i	−0.189776	+	0.981827i
$2$	−0.268384	+	1.38851i	−0.189776	+	0.981827i
$3$		0			0
$3$		0			0
$4$	−1.85594	−	0.745309i	−0.927970	−	0.372654i
$5$	0.280698	−	0.334522i	0.125532	−	0.149603i	−0.699618	−	0.714517i	$-0.746646\pi$
$5$	0.280698	−	0.334522i	0.125532	−	0.149603i	0.825150	+	0.564914i	$0.191091\pi$
$6$		0			0
$7$	−1.12035	+	0.646834i	−0.423452	+	0.244480i	−0.696553	−	0.717505i	$-0.745284\pi$
$7$	−1.12035	+	0.646834i	−0.423452	+	0.244480i	0.273101	+	0.961985i	$0.411951\pi$
$8$	1.53298	−	2.37697i	0.541989	−	0.840386i
$9$		0			0
$10$	0.389154	+	0.479533i	0.123061	+	0.151642i
$11$	0.842516	−	1.45928i	0.254028	−	0.439990i	−0.710603	−	0.703593i	$-0.751578\pi$
$11$	0.842516	−	1.45928i	0.254028	−	0.439990i	0.964631	+	0.263604i	$0.0849111\pi$
$12$		0			0
$13$	0.944062	+	5.35404i	0.261836	+	1.48494i	0.777897	+	0.628392i	$0.216287\pi$
$13$	0.944062	+	5.35404i	0.261836	+	1.48494i	−0.516061	+	0.856552i	$0.672602\pi$
$14$	−0.597454	−	1.72922i	−0.159676	−	0.462154i
$15$		0			0
$16$	2.88903	+	2.76650i	0.722257	+	0.691625i
$17$	0.614700	+	1.68887i	0.149087	+	0.409612i	0.991646	−	0.128992i	$-0.0411741\pi$
$17$	0.614700	+	1.68887i	0.149087	+	0.409612i	−0.842559	+	0.538604i	$0.818952\pi$
$18$		0			0
$19$	−3.19522	+	2.96489i	−0.733034	+	0.680192i
$19$	−3.19522	+	2.96489i	−0.733034	+	0.680192i
$20$	−0.770281	+	0.411647i	−0.172240	+	0.0920471i
$21$		0			0
$22$	1.80011	+	1.56149i	0.383786	+	0.332911i
$23$	−1.92647	+	1.61650i	−0.401698	+	0.337064i	−0.821149	−	0.570713i	$-0.806667\pi$
$23$	−1.92647	+	1.61650i	−0.401698	+	0.337064i	0.419452	+	0.907778i	$0.362222\pi$
$24$		0			0
$25$	0.835127	+	4.73624i	0.167025	+	0.947248i
$26$	−7.68753	−	0.126095i	−1.50765	−	0.0247292i
$27$		0			0
$28$	2.56139	−	0.365479i	0.484058	−	0.0690690i
$29$	0.0255800	−	0.0702806i	0.00475009	−	0.0130508i	−0.937295	−	0.348537i	$-0.886678\pi$
$29$	0.0255800	−	0.0702806i	0.00475009	−	0.0130508i	0.942045	+	0.335487i	$0.108901\pi$
$30$		0			0
$31$	−2.87590	+	1.66040i	−0.516527	+	0.298217i	−0.735513	−	0.677511i	$-0.763059\pi$
$31$	−2.87590	+	1.66040i	−0.516527	+	0.298217i	0.218985	+	0.975728i	$0.429725\pi$
$32$	−4.61669	+	3.26897i	−0.816123	+	0.577878i
$33$		0			0
$34$	−2.51000	+	0.400253i	−0.430462	+	0.0686428i
$35$	−0.0980989	+	0.556347i	−0.0165817	+	0.0940398i
$36$		0			0
$37$	5.65252			0.929269			0.464635	−	0.885503i	$-0.346186\pi$
$37$	5.65252			0.929269			0.464635	+	0.885503i	$0.346186\pi$
$38$	−3.25924	−	5.23234i	−0.528719	−	0.848797i
$39$		0			0
$40$	−0.364847	−	1.18002i	−0.0576874	−	0.186578i
$41$	−6.88524	−	1.21405i	−1.07529	−	0.189603i	−0.392160	−	0.919897i	$-0.628272\pi$
$41$	−6.88524	−	1.21405i	−1.07529	−	0.189603i	−0.683133	+	0.730294i	$0.739383\pi$
$42$		0			0
$43$	−3.06284	+	3.65015i	−0.467079	+	0.556643i	−0.947235	−	0.320540i	$-0.896136\pi$
$43$	−3.06284	+	3.65015i	−0.467079	+	0.556643i	0.480156	+	0.877183i	$0.340580\pi$
$44$	−2.65127	+	2.08040i	−0.399695	+	0.313633i
$45$		0			0
$46$	−1.72750	−	3.10878i	−0.254706	−	0.458365i
$47$	10.3436	+	3.76477i	1.50877	+	0.549148i	0.958315	−	0.285715i	$-0.0922311\pi$
$47$	10.3436	+	3.76477i	1.50877	+	0.549148i	0.550458	+	0.834863i	$0.314453\pi$
$48$		0			0
$49$	−2.66321	+	4.61282i	−0.380459	+	0.658974i
$50$	−6.80047	−	0.111545i	−0.961731	−	0.0157748i
$51$		0			0
$52$	2.23829	−	10.6404i	0.310395	−	1.47556i
$53$	−2.66483	−	3.17582i	−0.366042	−	0.436232i	0.551315	−	0.834297i	$-0.314126\pi$
$53$	−2.66483	−	3.17582i	−0.366042	−	0.436232i	−0.917357	+	0.398065i	$0.869682\pi$
$54$		0			0
$55$	−0.251670	−	0.691457i	−0.0339352	−	0.0932361i
$56$	−0.179964	+	3.65462i	−0.0240487	+	0.488369i
$57$		0			0
$58$	0.0907203	+	0.0543804i	0.0119122	+	0.00714050i
$59$	−0.983482	+	0.357958i	−0.128038	+	0.0466022i	−0.405245	−	0.914208i	$-0.632814\pi$
$59$	−0.983482	+	0.357958i	−0.128038	+	0.0466022i	0.277206	+	0.960810i	$0.410591\pi$
$60$		0			0
$61$	1.05962	−	0.889126i	0.135670	−	0.113841i	−0.572427	−	0.819955i	$-0.693998\pi$
$61$	1.05962	−	0.889126i	0.135670	−	0.113841i	0.708098	+	0.706115i	$0.249554\pi$
$62$	−1.53365	−	4.43886i	−0.194773	−	0.563735i
$63$		0			0
$64$	−3.29997	−	7.28767i	−0.412496	−	0.910959i
$65$	2.05604	+	1.18706i	0.255021	+	0.147236i
$66$		0			0
$67$	−4.42587	+	12.1600i	−0.540706	+	1.48558i	0.305222	+	0.952281i	$0.401269\pi$
$67$	−4.42587	+	12.1600i	−0.540706	+	1.48558i	−0.845928	+	0.533296i	$0.820953\pi$
$68$	0.117887	−	3.59259i	0.0142959	−	0.435666i
$69$		0			0
$70$	−0.746167	−	0.285526i	−0.0891840	−	0.0341269i
$71$	3.20103	+	2.68598i	0.379892	+	0.318767i	0.812660	−	0.582738i	$-0.198019\pi$
$71$	3.20103	+	2.68598i	0.379892	+	0.318767i	−0.432768	+	0.901505i	$0.642463\pi$
$72$		0			0
$73$	1.72543	−	9.78538i	0.201946	−	1.14529i	−0.700228	−	0.713920i	$-0.746918\pi$
$73$	1.72543	−	9.78538i	0.201946	−	1.14529i	0.902174	−	0.431373i	$-0.141971\pi$
$74$	−1.51705	+	7.84861i	−0.176353	+	0.912382i
$75$		0			0
$76$	8.13990	−	3.12123i	0.933710	−	0.358030i
$77$			2.17987i			0.248420i
$78$		0			0
$79$	3.47382	+	0.612528i	0.390835	+	0.0689148i	0.365613	−	0.930767i	$-0.380859\pi$
$79$	3.47382	+	0.612528i	0.390835	+	0.0689148i	0.0252225	+	0.999682i	$0.491971\pi$
$80$	1.73640	−	0.189895i	0.194135	−	0.0212310i
$81$		0			0
$82$	3.53362	−	9.23442i	0.390223	−	1.01977i
$83$	−4.00659	−	6.93962i	−0.439781	−	0.761722i	0.557892	−	0.829914i	$-0.311610\pi$
$83$	−4.00659	−	6.93962i	−0.439781	−	0.761722i	−0.997672	+	0.0681914i	$0.978277\pi$
$84$		0			0
$85$	0.737511	+	0.268432i	0.0799943	+	0.0291155i
$86$	−4.24627	−	5.23244i	−0.457887	−	0.564229i
$87$		0			0
$88$	−2.17711	−	4.23968i	−0.232081	−	0.451951i
$89$	2.01566	−	0.355415i	0.213659	−	0.0376739i	−0.0657939	−	0.997833i	$-0.520958\pi$
$89$	2.01566	−	0.355415i	0.213659	−	0.0376739i	0.279453	+	0.960159i	$0.409847\pi$
$90$		0			0
$91$	−4.52085	−	5.38774i	−0.473914	−	0.564789i
$92$	4.78022	−	1.56432i	0.498372	−	0.163091i
$93$		0			0
$94$	−8.00349	+	13.3519i	−0.825497	+	1.37714i
$95$	0.0949310	+	1.90111i	0.00973972	+	0.195050i
$96$		0			0
$97$	4.95301	−	1.80275i	0.502902	−	0.183041i	−0.0780969	−	0.996946i	$-0.524884\pi$
$97$	4.95301	−	1.80275i	0.502902	−	0.183041i	0.580999	+	0.813905i	$0.302662\pi$
$98$	−5.69020	−	4.93591i	−0.574797	−	0.498602i
$99$		0			0
$100$	1.98002	−	9.41261i	0.198002	−	0.941261i
$101$	13.0045	−	2.29305i	1.29400	−	0.228167i	0.516086	−	0.856537i	$-0.327389\pi$
$101$	13.0045	−	2.29305i	1.29400	−	0.228167i	0.777915	+	0.628370i	$0.216277\pi$
$102$		0			0
$103$	−10.7583	−	6.21128i	−1.06004	−	0.612016i	−0.134599	−	0.990900i	$-0.542974\pi$
$103$	−10.7583	−	6.21128i	−1.06004	−	0.612016i	−0.925444	+	0.378884i	$0.876308\pi$
$104$	14.1736	+	5.96361i	1.38984	+	0.584780i
$105$		0			0
$106$	5.12486	−	2.84781i	0.497771	−	0.276604i
$107$	7.92487	+	13.7263i	0.766126	+	1.32697i	0.939649	+	0.342140i	$0.111152\pi$
$107$	7.92487	+	13.7263i	0.766126	+	1.32697i	−0.173523	+	0.984830i	$0.555515\pi$
$108$		0			0
$109$	−7.79153	−	6.53787i	−0.746293	−	0.626214i	0.188227	−	0.982126i	$-0.439726\pi$
$109$	−7.79153	−	6.53787i	−0.746293	−	0.626214i	−0.934520	+	0.355911i	$0.884171\pi$
$110$	1.02764	−	0.163871i	0.0979818	−	0.0156245i
$111$		0			0
$112$	−5.02619	−	1.23072i	−0.474930	−	0.116292i
$113$		−	14.3705i		−	1.35186i	−0.736965	−	0.675930i	$-0.763742\pi$
$113$		−	14.3705i		−	1.35186i	0.736965	−	0.675930i	$-0.236258\pi$
$114$		0			0
$115$			1.09820i			0.102407i
$116$	−0.0998558	+	0.111372i	−0.00927138	+	0.0103406i
$117$		0			0
$118$	−0.233079	−	1.46165i	−0.0214567	−	0.134556i
$119$	−1.78110	−	1.49452i	−0.163273	−	0.137002i
$120$		0			0
$121$	4.08033	+	7.06734i	0.370939	+	0.642486i
$122$	0.950179	+	1.70992i	0.0860252	+	0.154809i
$123$		0			0
$124$	6.57502	−	0.938173i	0.590454	−	0.0842504i
$125$	3.70971	+	2.14180i	0.331807	+	0.191569i
$126$		0			0
$127$	−1.34284	+	0.236779i	−0.119158	+	0.0210107i	−0.232909	−	0.972499i	$-0.574824\pi$
$127$	−1.34284	+	0.236779i	−0.119158	+	0.0210107i	0.113751	+	0.993509i	$0.463713\pi$
$128$	11.0047	−	2.62616i	0.972687	−	0.232122i
$129$		0			0
$130$	−2.20005	+	2.53626i	−0.192957	+	0.222444i
$131$	−11.5538	+	4.20524i	−1.00946	+	0.367413i	−0.793225	−	0.608928i	$-0.791600\pi$
$131$	−11.5538	+	4.20524i	−1.00946	+	0.367413i	−0.216234	+	0.976342i	$0.569377\pi$
$132$		0			0
$133$	1.66197	−	5.38849i	0.144111	−	0.467241i
$134$	−15.6965	−	9.40892i	−1.35597	−	0.812807i
$135$		0			0
$136$	4.95672	+	1.12788i	0.425036	+	0.0967150i
$137$	3.94038	+	4.69596i	0.336649	+	0.401203i	0.907637	−	0.419756i	$-0.137884\pi$
$137$	3.94038	+	4.69596i	0.336649	+	0.401203i	−0.570988	+	0.820958i	$0.693440\pi$
$138$		0			0
$139$	18.2340	−	3.21514i	1.54658	−	0.272705i	0.665767	−	0.746160i	$-0.268105\pi$
$139$	18.2340	−	3.21514i	1.54658	−	0.272705i	0.880818	+	0.473455i	$0.156993\pi$
$140$	0.596716	−	0.959432i	0.0504317	−	0.0810868i
$141$		0			0
$142$	−4.58862	+	3.72379i	−0.385069	+	0.312494i
$143$	8.60844	+	3.13321i	0.719874	+	0.262013i
$144$		0			0
$145$	−0.0163302	−	0.0282847i	−0.00135615	−	0.00234892i
$146$	13.1241	+	5.02202i	1.08616	+	0.415625i
$147$		0			0
$148$	−10.4907	−	4.21288i	−0.862334	−	0.346296i
$149$	2.29903	+	0.405381i	0.188344	+	0.0332101i	0.267024	−	0.963690i	$-0.413960\pi$
$149$	2.29903	+	0.405381i	0.188344	+	0.0332101i	−0.0786805	+	0.996900i	$0.525071\pi$
$150$		0			0
$151$			8.42166i			0.685345i	0.939455	+	0.342673i	$0.111332\pi$
$151$			8.42166i			0.685345i	−0.939455	+	0.342673i	$0.888668\pi$
$152$	2.14926	+	12.1400i	0.174328	+	0.984688i
$153$		0			0
$154$	−3.02678	−	0.585042i	−0.243905	−	0.0471441i
$155$	−0.251817	+	1.42813i	−0.0202264	+	0.114710i
$156$		0			0
$157$	3.71526	+	3.11747i	0.296510	+	0.248801i	0.778890	−	0.627161i	$-0.215783\pi$
$157$	3.71526	+	3.11747i	0.296510	+	0.248801i	−0.482380	+	0.875962i	$0.660228\pi$
$158$	−1.78282	+	4.65905i	−0.141834	+	0.370654i
$159$		0			0
$160$	−0.202349	+	2.46198i	−0.0159971	+	0.194637i
$161$	1.11271	−	3.05716i	0.0876942	−	0.240938i
$162$		0			0
$163$	13.9115	+	8.03182i	1.08964	+	0.629101i	0.933479	−	0.358631i	$-0.116756\pi$
$163$	13.9115	+	8.03182i	1.08964	+	0.629101i	0.156156	+	0.987732i	$0.450090\pi$
$164$	11.8737	+	7.38484i	0.927184	+	0.576659i
$165$		0			0
$166$	10.7111	−	3.70073i	0.831340	−	0.287232i
$167$	18.0065	−	15.1093i	1.39339	−	1.16919i	0.429438	−	0.903096i	$-0.358712\pi$
$167$	18.0065	−	15.1093i	1.39339	−	1.16919i	0.963947	−	0.266093i	$-0.0857328\pi$
$168$		0			0
$169$	−15.5585	+	5.66283i	−1.19681	+	0.435602i
$170$	−0.570658	+	0.952001i	−0.0437674	+	0.0730152i
$171$		0			0
$172$	8.40495	−	4.49170i	0.640871	−	0.342489i
$173$	0.446636	+	1.22712i	0.0339571	+	0.0932964i	0.955513	−	0.294950i	$-0.0953031\pi$
$173$	0.446636	+	1.22712i	0.0339571	+	0.0932964i	−0.921555	+	0.388247i	$0.873081\pi$
$174$		0			0
$175$	−3.99919	−	4.76605i	−0.302311	−	0.360280i
$176$	6.47115	−	1.88509i	0.487781	−	0.142094i
$177$		0			0
$178$	−0.0474714	+	2.89415i	−0.00355813	+	0.216926i
$179$	−4.49861	+	7.79182i	−0.336242	+	0.582388i	−0.983723	−	0.179694i	$-0.942489\pi$
$179$	−4.49861	+	7.79182i	−0.336242	+	0.582388i	0.647481	+	0.762082i	$0.275823\pi$
$180$		0			0
$181$	−3.90388	−	1.42090i	−0.290173	−	0.105614i	0.192832	−	0.981232i	$-0.438233\pi$
$181$	−3.90388	−	1.42090i	−0.290173	−	0.105614i	−0.483006	+	0.875617i	$0.660455\pi$
$182$	8.69428	−	4.83128i	0.644463	−	0.358119i
$183$		0			0
$184$	0.889142	+	7.05723i	0.0655484	+	0.520266i
$185$	1.58665	−	1.89090i	0.116653	−	0.139021i
$186$		0			0
$187$	2.98244	+	0.525884i	0.218097	+	0.0384564i
$188$	−16.3912	−	14.6964i	−1.19545	−	1.07184i
$189$		0			0
$190$	−2.66520	−	0.378414i	−0.193354	−	0.0274530i
$191$	−14.3080			−1.03529			−0.517646	−	0.855595i	$-0.673192\pi$
$191$	−14.3080			−1.03529			−0.517646	+	0.855595i	$0.673192\pi$
$192$		0			0
$193$	−1.33390	+	7.56491i	−0.0960161	+	0.544534i	0.898415	+	0.439147i	$0.144719\pi$
$193$	−1.33390	+	7.56491i	−0.0960161	+	0.544534i	−0.994431	+	0.105387i	$0.966392\pi$
$194$	1.17383	+	7.36115i	0.0842763	+	0.528500i
$195$		0			0
$196$	8.38074	−	6.57620i	0.598624	−	0.469728i
$197$	6.91429	−	3.99197i	0.492623	−	0.284416i	−0.233039	−	0.972467i	$-0.574867\pi$
$197$	6.91429	−	3.99197i	0.492623	−	0.284416i	0.725662	+	0.688051i	$0.241534\pi$
$198$		0			0
$199$	1.97419	−	5.42404i	0.139947	−	0.384500i	−0.849843	−	0.527036i	$-0.823303\pi$
$199$	1.97419	−	5.42404i	0.139947	−	0.384500i	0.989790	+	0.142536i	$0.0455256\pi$
$200$	12.5381	+	5.27547i	0.886579	+	0.373032i
$201$		0			0
$202$	−0.306274	+	18.6724i	−0.0215494	+	1.31379i
$203$	0.0168013	+	0.0952848i	0.00117922	+	0.00668768i
$204$		0			0
$205$	−2.33880	+	1.96248i	−0.163349	+	0.137066i
$206$	11.5118	−	13.2710i	0.802065	−	0.924633i
$207$		0			0
$208$	−12.0845	+	18.0797i	−0.837911	+	1.25360i
$209$	1.63458	+	7.16069i	0.113066	+	0.495315i
$210$		0			0
$211$	−2.09008	−	5.74244i	−0.143887	−	0.395326i	0.846725	−	0.532031i	$-0.178571\pi$
$211$	−2.09008	−	5.74244i	−0.143887	−	0.395326i	−0.990612	+	0.136705i	$0.956349\pi$
$212$	2.57880	+	7.88025i	0.177112	+	0.541218i
$213$		0			0
$214$	−21.1860	+	7.31988i	−1.44825	+	0.500377i
$215$	0.361326	+	2.04918i	0.0246422	+	0.139753i
$216$		0			0
$217$	2.14801	−	3.72046i	0.145816	−	0.252562i
$218$	11.1690	−	9.06399i	0.756463	−	0.613891i
$219$		0			0
$220$	−0.0482651	+	1.47088i	−0.00325403	+	0.0991664i
$221$	−8.46199	+	4.88553i	−0.569215	+	0.328636i
$222$		0			0
$223$	16.7105	−	19.9148i	1.11902	−	1.33359i	0.182402	−	0.983224i	$-0.441613\pi$
$223$	16.7105	−	19.9148i	1.11902	−	1.33359i	0.936613	−	0.350366i	$-0.113943\pi$
$224$	3.05782	−	6.64862i	0.204309	−	0.444230i
$225$		0			0
$226$	19.9536	+	3.85680i	1.32729	+	0.256551i
$227$	−24.7680			−1.64391			−0.821956	−	0.569551i	$-0.807117\pi$
$227$	−24.7680			−1.64391			−0.821956	+	0.569551i	$0.807117\pi$
$228$		0			0
$229$	−10.3731			−0.685471			−0.342736	−	0.939432i	$-0.611354\pi$
$229$	−10.3731			−0.685471			−0.342736	+	0.939432i	$0.611354\pi$
$230$	−1.52486	−	0.294738i	−0.100546	−	0.0194345i
$231$		0			0
$232$	−0.127841	−	0.168541i	−0.00839319	−	0.0110653i
$233$	8.26912	−	9.85475i	0.541728	−	0.645606i	−0.423846	−	0.905734i	$-0.639320\pi$
$233$	8.26912	−	9.85475i	0.541728	−	0.645606i	0.965574	+	0.260128i	$0.0837647\pi$
$234$		0			0
$235$	4.16283	−	2.40341i	0.271553	−	0.156781i
$236$	2.09207	+	0.0686490i	0.136182	+	0.00446867i
$237$		0			0
$238$	2.55318	−	2.07198i	0.165498	−	0.134306i
$239$	7.66779	−	13.2810i	0.495988	−	0.859077i	−0.504001	−	0.863703i	$-0.668139\pi$
$239$	7.66779	−	13.2810i	0.495988	−	0.859077i	0.999989	+	0.00462626i	$0.00147259\pi$
$240$		0			0
$241$	−3.64743	−	20.6856i	−0.234951	−	1.33248i	−0.842716	−	0.538358i	$-0.819045\pi$
$241$	−3.64743	−	20.6856i	−0.234951	−	1.33248i	0.607765	−	0.794117i	$-0.292066\pi$
$242$	−10.9082	+	3.76884i	−0.701206	+	0.242270i
$243$		0			0
$244$	−2.62926	+	0.860421i	−0.168321	+	0.0550828i
$245$	0.795534	+	2.18571i	0.0508248	+	0.139640i
$246$		0			0
$247$	−18.8906	−	14.3083i	−1.20198	−	0.910415i
$248$	−0.461962	+	9.38129i	−0.0293346	+	0.595713i
$249$		0			0
$250$	−3.96955	+	4.57616i	−0.251056	+	0.289422i
$251$	−8.32334	+	6.98411i	−0.525365	+	0.440833i	−0.866497	−	0.499182i	$-0.833634\pi$
$251$	−8.32334	+	6.98411i	−0.525365	+	0.440833i	0.341132	+	0.940015i	$0.389190\pi$
$252$		0			0
$253$	0.735847	+	4.17320i	0.0462623	+	0.262367i
$254$	0.0316256	−	1.92810i	0.00198437	−	0.120980i
$255$		0			0
$256$	0.692977	+	15.9850i	0.0433111	+	0.999062i
$257$	−7.90479	+	21.7182i	−0.493087	+	1.35475i	0.404754	+	0.914426i	$0.367357\pi$
$257$	−7.90479	+	21.7182i	−0.493087	+	1.35475i	−0.897841	+	0.440320i	$0.854865\pi$
$258$		0			0
$259$	−6.33280	+	3.65624i	−0.393501	+	0.227188i
$260$	−2.93117	−	3.73549i	−0.181783	−	0.231665i
$261$		0			0
$262$	−2.73818	−	17.1712i	−0.169165	−	1.06084i
$263$	4.57866	−	25.9669i	0.282332	−	1.60119i	−0.432329	−	0.901716i	$-0.642308\pi$
$263$	4.57866	−	25.9669i	0.282332	−	1.60119i	0.714662	−	0.699470i	$-0.246581\pi$
$264$		0			0
$265$	−1.81039			−0.111212
$266$	7.03594	+	3.75385i	0.431401	+	0.230164i
$267$		0			0
$268$	17.2771	−	19.2695i	1.05537	−	1.17708i
$269$	−9.98073	−	1.75987i	−0.608536	−	0.107301i	−0.139115	−	0.990276i	$-0.544426\pi$
$269$	−9.98073	−	1.75987i	−0.608536	−	0.107301i	−0.469420	+	0.882975i	$0.655537\pi$
$270$		0			0
$271$	7.92276	−	9.44197i	0.481273	−	0.573559i	−0.469702	−	0.882825i	$-0.655639\pi$
$271$	7.92276	−	9.44197i	0.481273	−	0.573559i	0.950976	+	0.309266i	$0.100083\pi$
$272$	−2.89638	+	6.57977i	−0.175619	+	0.398957i
$273$		0			0
$274$	−7.57793	+	4.21095i	−0.457800	+	0.254393i
$275$	7.61511	+	2.77167i	0.459209	+	0.167138i
$276$		0			0
$277$	11.1327	−	19.2825i	0.668902	−	1.15857i	−0.309310	−	0.950961i	$-0.600098\pi$
$277$	11.1327	−	19.2825i	0.668902	−	1.15857i	0.978212	−	0.207611i	$-0.0665687\pi$
$278$	−0.429434	+	26.1810i	−0.0257557	+	1.57023i
$279$		0			0
$280$	1.17204	+	1.08604i	0.0700425	+	0.0649036i
$281$	8.98278	+	10.7053i	0.535868	+	0.638623i	0.964256	−	0.264972i	$-0.0853628\pi$
$281$	8.98278	+	10.7053i	0.535868	+	0.638623i	−0.428388	+	0.903595i	$0.640918\pi$
$282$		0			0
$283$	3.95075	+	10.8546i	0.234848	+	0.645239i	0.999999	+	0.00138840i	$0.000441942\pi$
$283$	3.95075	+	10.8546i	0.234848	+	0.645239i	−0.765151	+	0.643851i	$0.777336\pi$
$284$	−3.93903	−	7.37077i	−0.233738	−	0.437375i
$285$		0			0
$286$	−6.66087	+	11.1120i	−0.393866	+	0.657068i
$287$	8.49916	−	3.09344i	0.501690	−	0.182600i
$288$		0			0
$289$	10.5483	−	8.85109i	0.620489	−	0.520652i
$290$	0.0436564	−	0.0150835i	0.00256359	−	0.000885735i
$291$		0			0
$292$	−10.4954	+	16.8751i	−0.614198	+	0.987541i
$293$	−15.7120	−	9.07131i	−0.917903	−	0.529952i	−0.0349375	−	0.999389i	$-0.511123\pi$
$293$	−15.7120	−	9.07131i	−0.917903	−	0.529952i	−0.882965	+	0.469438i	$0.844457\pi$
$294$		0			0
$295$	−0.156316	+	0.429475i	−0.00910107	+	0.0250050i
$296$	8.66518	−	13.4359i	0.503653	−	0.780944i
$297$		0			0
$298$	−1.17990	+	3.08344i	−0.0683498	+	0.178619i
$299$	−10.4735	−	8.78834i	−0.605700	−	0.508243i
$300$		0			0
$301$	1.07041	−	6.07060i	0.0616974	−	0.349904i
$302$	−11.6936	−	2.26024i	−0.672891	−	0.130062i
$303$		0			0
$304$	−17.4334	−	0.273920i	−0.999877	−	0.0157104i
$305$		−	0.604042i		−	0.0345873i
$306$		0			0
$307$	25.6795	+	4.52799i	1.46561	+	0.258426i	0.848810	−	0.528697i	$-0.177319\pi$
$307$	25.6795	+	4.52799i	1.46561	+	0.258426i	0.616796	+	0.787123i	$0.288430\pi$
$308$	1.62468	−	4.04571i	0.0925747	−	0.230526i
$309$		0			0
$310$	−1.91539	−	0.732937i	−0.108787	−	0.0416280i
$311$	−3.77869	−	6.54489i	−0.214270	−	0.371127i	0.738776	−	0.673951i	$-0.235404\pi$
$311$	−3.77869	−	6.54489i	−0.214270	−	0.371127i	−0.953047	+	0.302824i	$0.902071\pi$
$312$		0			0
$313$	−4.08409	−	1.48649i	−0.230846	−	0.0840211i	0.224007	−	0.974587i	$-0.428086\pi$
$313$	−4.08409	−	1.48649i	−0.230846	−	0.0840211i	−0.454853	+	0.890566i	$0.650308\pi$
$314$	−5.32577	+	4.32201i	−0.300550	+	0.243905i
$315$		0			0
$316$	−5.99068	−	3.72588i	−0.337002	−	0.209597i
$317$	−31.8664	+	5.61891i	−1.78980	+	0.315589i	−0.967386	−	0.253306i	$-0.918482\pi$
$317$	−31.8664	+	5.61891i	−1.78980	+	0.315589i	−0.822410	+	0.568895i	$0.807371\pi$
$318$		0			0
$319$	−0.0810075	−	0.0965410i	−0.00453555	−	0.00540526i
$320$	−3.36418	−	0.941719i	−0.188064	−	0.0526437i
$321$		0			0
$322$	3.94627	+	2.36551i	0.219917	+	0.131825i
$323$	−6.97143	−	3.57381i	−0.387901	−	0.198852i
$324$		0			0
$325$	−24.5696	+	8.94260i	−1.36288	+	0.496046i
$326$	−14.8859	+	17.1607i	−0.824455	+	0.950445i
$327$		0			0
$328$	−13.4407	+	14.5049i	−0.742137	+	0.800898i
$329$	−14.0237	+	2.47275i	−0.773149	+	0.136327i
$330$		0			0
$331$	−12.9904	−	7.50001i	−0.714017	−	0.412238i	0.0985297	−	0.995134i	$-0.468586\pi$
$331$	−12.9904	−	7.50001i	−0.714017	−	0.412238i	−0.812547	+	0.582896i	$0.801919\pi$
$332$	2.26383	+	15.8657i	0.124244	+	0.870742i
$333$		0			0
$334$	16.1468	+	29.0574i	0.883511	+	1.58995i
$335$	2.82545	+	4.89383i	0.154371	+	0.267378i
$336$		0			0
$337$	9.08533	+	7.62350i	0.494910	+	0.415279i	0.855782	−	0.517337i	$-0.173077\pi$
$337$	9.08533	+	7.62350i	0.494910	+	0.415279i	−0.360872	+	0.932615i	$0.617521\pi$
$338$	−3.68727	−	23.1230i	−0.200561	−	1.25772i
$339$		0			0
$340$	−1.16871	−	1.04787i	−0.0633823	−	0.0568286i
$341$			5.59567i			0.303022i
$342$		0			0
$343$		−	15.9463i		−	0.861019i
$344$	3.98104	+	12.8759i	0.214643	+	0.694221i
$345$		0			0
$346$	−1.82375	+	0.290821i	−0.0980452	+	0.0156346i
$347$	−26.8273	−	22.5108i	−1.44017	−	1.20844i	−0.939383	−	0.342868i	$-0.888602\pi$
$347$	−26.8273	−	22.5108i	−1.44017	−	1.20844i	−0.500782	−	0.865574i	$-0.666954\pi$
$348$		0			0
$349$	1.85477	+	3.21256i	0.0992836	+	0.171964i	0.911388	−	0.411547i	$-0.135012\pi$
$349$	1.85477	+	3.21256i	0.0992836	+	0.171964i	−0.812105	+	0.583512i	$0.801678\pi$
$350$	7.69105	−	4.27380i	0.411104	−	0.228444i
$351$		0			0
$352$	0.880715	+	9.49121i	0.0469423	+	0.505883i
$353$	−29.5978	−	17.0883i	−1.57533	−	0.909518i	−0.995498	−	0.0947838i	$-0.969784\pi$
$353$	−29.5978	−	17.0883i	−1.57533	−	0.909518i	−0.579834	−	0.814735i	$-0.696883\pi$
$354$		0			0
$355$	1.79704	−	0.316867i	0.0953770	−	0.0168175i
$356$	−4.00583	−	0.842659i	−0.212309	−	0.0446608i
$357$		0			0
$358$	−9.61170	−	8.33758i	−0.507994	−	0.440655i
$359$	0.109011	−	0.0396768i	0.00575339	−	0.00209406i	−0.339142	−	0.940735i	$-0.610137\pi$
$359$	0.109011	−	0.0396768i	0.00575339	−	0.00209406i	0.344895	+	0.938641i	$0.387914\pi$
$360$		0			0
$361$	1.41887	−	18.9469i	0.0746772	−	0.997208i
$362$	3.02067	−	5.03925i	0.158763	−	0.264857i
$363$		0			0
$364$	4.37490	+	13.3688i	0.229307	+	0.700714i
$365$	−2.78911	−	3.32393i	−0.145989	−	0.173982i
$366$		0			0
$367$	27.3399	−	4.82077i	1.42713	−	0.251642i	0.593888	−	0.804548i	$-0.297592\pi$
$367$	27.3399	−	4.82077i	1.42713	−	0.251642i	0.833244	+	0.552906i	$0.186481\pi$
$368$	−10.0377	−	0.659461i	−0.523251	−	0.0343768i
$369$		0			0
$370$	2.19970	+	2.71057i	0.114357	+	0.140916i
$371$	5.03977	+	1.83432i	0.261652	+	0.0952334i
$372$		0			0
$373$	14.6786	+	25.4241i	0.760030	+	1.31641i	0.942835	+	0.333261i	$0.108149\pi$
$373$	14.6786	+	25.4241i	0.760030	+	1.31641i	−0.182805	+	0.983149i	$0.558518\pi$
$374$	−1.53063	+	4.00002i	−0.0791472	+	0.206836i
$375$		0			0
$376$	24.8053	−	18.8152i	1.27923	−	0.970318i
$377$	0.400434	+	0.0706073i	0.0206234	+	0.00363646i
$378$		0			0
$379$			24.2068i			1.24342i	0.783247	+	0.621710i	$0.213562\pi$
$379$			24.2068i			1.24342i	−0.783247	+	0.621710i	$0.786438\pi$
$380$	1.24073	−	3.59910i	0.0636480	−	0.184630i
$381$		0			0
$382$	3.84004	−	19.8669i	0.196474	−	1.01648i
$383$	−3.36713	+	19.0959i	−0.172052	+	0.975757i	0.769439	+	0.638720i	$0.220536\pi$
$383$	−3.36713	+	19.0959i	−0.172052	+	0.975757i	−0.941491	+	0.337037i	$0.890575\pi$
$384$		0			0
$385$	0.729216	+	0.611885i	0.0371643	+	0.0311845i
$386$	−10.1460	−	3.88244i	−0.516417	−	0.197611i
$387$		0			0
$388$	−10.5361	−	0.345730i	−0.534889	−	0.0175518i
$389$	−12.0380	+	33.0742i	−0.610352	+	1.67693i	0.119089	+	0.992884i	$0.462003\pi$
$389$	−12.0380	+	33.0742i	−0.610352	+	1.67693i	−0.729440	+	0.684044i	$0.760219\pi$
$390$		0			0
$391$	−3.91428	−	2.25991i	−0.197953	−	0.114288i
$392$	6.88189	+	13.4017i	0.347588	+	0.676889i
$393$		0			0
$394$	3.68722	+	10.6720i	0.185759	+	0.537646i
$395$	1.18000	−	0.990135i	0.0593721	−	0.0498191i
$396$		0			0
$397$	−15.3344	+	5.58127i	−0.769612	+	0.280116i	−0.696834	−	0.717232i	$-0.745409\pi$
$397$	−15.3344	+	5.58127i	−0.769612	+	0.280116i	−0.0727776	+	0.997348i	$0.523186\pi$
$398$	7.00151	+	4.19691i	0.350954	+	0.210372i
$399$		0			0
$400$	−10.6901	+	15.9935i	−0.534505	+	0.799675i
$401$	8.29356	+	22.7864i	0.414161	+	1.13790i	0.954957	+	0.296744i	$0.0959007\pi$
$401$	8.29356	+	22.7864i	0.414161	+	1.13790i	−0.540797	+	0.841153i	$0.681877\pi$
$402$		0			0
$403$	−11.6049	−	13.8302i	−0.578081	−	0.688930i
$404$	−25.8447	−	5.43664i	−1.28582	−	0.270483i
$405$		0			0
$406$	−0.136813	−	0.00224408i	−0.00678994	−	0.000111372i
$407$	4.76234	−	8.24862i	0.236061	−	0.408869i
$408$		0			0
$409$	−16.5160	−	6.01132i	−0.816661	−	0.297240i	−0.100289	−	0.994958i	$-0.531977\pi$
$409$	−16.5160	−	6.01132i	−0.816661	−	0.297240i	−0.716373	+	0.697718i	$0.754199\pi$
$410$	−2.09724	−	3.77415i	−0.103575	−	0.186392i
$411$		0			0
$412$	15.3374	+	19.5460i	0.755617	+	0.962962i
$413$	0.870304	−	1.03719i	0.0428249	−	0.0510367i
$414$		0			0
$415$	−3.44610	−	0.607640i	−0.169162	−	0.0298279i
$416$	−21.8607	−	21.6318i	−1.07181	−	1.06059i
$417$		0			0
$418$	−10.3814	+	0.347825i	−0.507771	+	0.0170127i
$419$	−28.3296			−1.38399			−0.691996	−	0.721901i	$-0.743269\pi$
$419$	−28.3296			−1.38399			−0.691996	+	0.721901i	$0.743269\pi$
$420$		0			0
$421$	−0.834505	+	4.73271i	−0.0406713	+	0.230658i	−0.998367	−	0.0571242i	$-0.981807\pi$
$421$	−0.834505	+	4.73271i	−0.0406713	+	0.230658i	0.957696	+	0.287782i	$0.0929180\pi$
$422$	8.53440	−	1.36092i	0.415448	−	0.0662487i
$423$		0			0
$424$	−11.6339	+	1.46576i	−0.564994	+	0.0711837i
$425$	−7.48556	+	4.32179i	−0.363103	+	0.209638i
$426$		0			0
$427$	−0.612027	+	1.68153i	−0.0296180	+	0.0813749i
$428$	−4.47777	−	31.3816i	−0.216441	−	1.51689i
$429$		0			0
$430$	−2.94229	−	0.0482609i	−0.141890	−	0.00232735i
$431$	5.31875	+	30.1641i	0.256195	+	1.45295i	0.792986	+	0.609239i	$0.208525\pi$
$431$	5.31875	+	30.1641i	0.256195	+	1.45295i	−0.536791	+	0.843715i	$0.680364\pi$
$432$		0			0
$433$	−11.5436	+	9.68620i	−0.554748	+	0.465489i	−0.876545	−	0.481320i	$-0.840158\pi$
$433$	−11.5436	+	9.68620i	−0.554748	+	0.465489i	0.321797	+	0.946809i	$0.395713\pi$
$434$	4.58942	+	3.98105i	0.220299	+	0.191097i
$435$		0			0
$436$	9.58788	+	17.9410i	0.459176	+	0.859218i
$437$	1.36276	−	10.8769i	0.0651894	−	0.520311i
$438$		0			0
$439$	−0.978288	−	2.68782i	−0.0466911	−	0.128283i	0.914155	−	0.405364i	$-0.132855\pi$
$439$	−0.978288	−	2.68782i	−0.0466911	−	0.128283i	−0.960847	+	0.277081i	$0.910633\pi$
$440$	−2.02938	−	0.461776i	−0.0967467	−	0.0220143i
$441$		0			0
$442$	−4.51257	−	13.0608i	−0.214641	−	0.621238i
$443$	−5.08925	−	28.8625i	−0.241797	−	1.37130i	−0.827814	−	0.561002i	$-0.810416\pi$
$443$	−5.08925	−	28.8625i	−0.241797	−	1.37130i	0.586017	−	0.810299i	$-0.300695\pi$
$444$		0			0
$445$	0.446896	−	0.774046i	0.0211849	−	0.0366933i
$446$	23.1671	+	28.5475i	1.09699	+	1.35176i
$447$		0			0
$448$	8.41103	+	6.03021i	0.397384	+	0.284901i
$449$	22.5140	−	12.9984i	1.06250	−	0.613434i	0.136377	−	0.990657i	$-0.456454\pi$
$449$	22.5140	−	12.9984i	1.06250	−	0.613434i	0.926122	+	0.377223i	$0.123121\pi$
$450$		0			0
$451$	−7.57257	+	9.02464i	−0.356578	+	0.424954i
$452$	−10.7104	+	26.6707i	−0.503777	+	1.25449i
$453$		0			0
$454$	6.64734	−	34.3907i	0.311975	−	1.61404i
$455$	−3.07131			−0.143985
$456$		0			0
$457$	16.7074			0.781541			0.390771	−	0.920488i	$-0.372209\pi$
$457$	16.7074			0.781541			0.390771	+	0.920488i	$0.372209\pi$
$458$	2.78396	−	14.4031i	0.130086	−	0.673015i
$459$		0			0
$460$	0.818497	−	2.03819i	0.0381626	−	0.0950311i
$461$	13.9038	−	16.5699i	0.647563	−	0.771735i	−0.337982	−	0.941153i	$-0.609744\pi$
$461$	13.9038	−	16.5699i	0.647563	−	0.771735i	0.985544	+	0.169418i	$0.0541887\pi$
$462$		0			0
$463$	−10.2339	+	5.90856i	−0.475611	+	0.274594i	−0.718585	−	0.695439i	$-0.755210\pi$
$463$	−10.2339	+	5.90856i	−0.475611	+	0.274594i	0.242975	+	0.970033i	$0.421877\pi$
$464$	0.268333	−	0.132276i	0.0124570	−	0.00614074i
$465$		0			0
$466$	11.4642	+	14.1266i	0.531067	+	0.654404i
$467$	−3.56373	+	6.17257i	−0.164910	+	0.285632i	−0.936623	−	0.350338i	$-0.886067\pi$
$467$	−3.56373	+	6.17257i	−0.164910	+	0.285632i	0.771713	+	0.635971i	$0.219400\pi$
$468$		0			0
$469$	−2.90697	−	16.4862i	−0.134231	−	0.761263i
$470$	2.21993	+	6.42518i	0.102398	+	0.296372i
$471$		0			0
$472$	−0.656799	+	2.88645i	−0.0302316	+	0.132860i
$473$	2.74611	+	7.54486i	0.126266	+	0.346913i
$474$		0			0
$475$	−16.7108	−	12.6573i	−0.766746	−	0.580755i
$476$	2.19174	+	4.10121i	0.100458	+	0.187979i
$477$		0			0
$478$	16.3829	+	14.2112i	0.749338	+	0.650007i
$479$	28.8104	−	24.1748i	1.31638	−	1.10458i	0.329323	−	0.944217i	$-0.393180\pi$
$479$	28.8104	−	24.1748i	1.31638	−	1.10458i	0.987059	−	0.160358i	$-0.0512649\pi$
$480$		0			0
$481$	5.33633	+	30.2638i	0.243316	+	1.37991i
$482$	29.7011	+	0.487173i	1.35285	+	0.0221901i
$483$		0			0
$484$	−2.30550	−	16.1577i	−0.104795	−	0.734440i
$485$	0.787238	−	2.16292i	0.0357466	−	0.0982131i
$486$		0			0
$487$	21.6997	−	12.5283i	0.983309	−	0.567713i	0.0800412	−	0.996792i	$-0.474495\pi$
$487$	21.6997	−	12.5283i	0.983309	−	0.567713i	0.903267	+	0.429078i	$0.141161\pi$
$488$	−0.489055	−	3.88169i	−0.0221385	−	0.175716i
$489$		0			0
$490$	−3.24840	+	0.518000i	−0.146748	+	0.0234009i
$491$	1.43612	−	8.14466i	0.0648114	−	0.367563i	−0.935102	−	0.354379i	$-0.884692\pi$
$491$	1.43612	−	8.14466i	0.0648114	−	0.367563i	0.999913	−	0.0131841i	$-0.00419674\pi$
$492$		0			0
$493$	0.134419			0.00605393
$494$	24.9372	−	22.3898i	1.12198	−	1.00736i
$495$		0			0
$496$	−12.9021	−	3.15923i	−0.579320	−	0.141853i
$497$	−5.32365	−	0.938703i	−0.238798	−	0.0421066i
$498$		0			0
$499$	−2.88822	+	3.44205i	−0.129294	+	0.154087i	−0.826808	−	0.562485i	$-0.809845\pi$
$499$	−2.88822	+	3.44205i	−0.129294	+	0.154087i	0.697513	+	0.716572i	$0.254290\pi$
$500$	−5.28870	−	6.73994i	−0.236518	−	0.301419i
$501$		0			0
$502$	−7.46369	−	13.4315i	−0.333121	−	0.599477i
$503$	38.5883	+	14.0450i	1.72057	+	0.626235i	0.997889	−	0.0649489i	$-0.0206884\pi$
$503$	38.5883	+	14.0450i	1.72057	+	0.626235i	0.722679	+	0.691184i	$0.242911\pi$
$504$		0			0
$505$	2.88327	−	4.99397i	0.128304	−	0.222229i
$506$	−5.99203	−	0.0982844i	−0.266378	−	0.00436927i
$507$		0			0
$508$	2.66870	+	0.561383i	0.118405	+	0.0249073i
$509$	23.3085	+	27.7780i	1.03313	+	1.23124i	0.972458	+	0.233080i	$0.0748804\pi$
$509$	23.3085	+	27.7780i	1.03313	+	1.23124i	0.0606736	+	0.998158i	$0.480675\pi$
$510$		0			0
$511$	4.39644	+	12.0791i	0.194487	+	0.534349i
$512$	−22.3814	−	3.32790i	−0.989126	−	0.147074i
$513$		0			0
$514$	−28.0345	−	16.8047i	−1.23655	−	0.741224i
$515$	−5.09763	+	1.85539i	−0.224628	+	0.0817581i
$516$		0			0
$517$	14.2085	−	11.9224i	0.624890	−	0.524345i
$518$	−3.37712	−	9.77446i	−0.148382	−	0.429465i
$519$		0			0
$520$	5.97346	−	3.06742i	0.261954	−	0.134515i
$521$	24.5148	+	14.1536i	1.07401	+	0.620081i	0.929275	−	0.369389i	$-0.120433\pi$
$521$	24.5148	+	14.1536i	1.07401	+	0.620081i	0.144737	+	0.989470i	$0.453766\pi$
$522$		0			0
$523$	−4.60927	+	12.6639i	−0.201549	+	0.553752i	−0.998751	−	0.0499610i	$-0.984090\pi$
$523$	−4.60927	+	12.6639i	−0.201549	+	0.553752i	0.797202	+	0.603713i	$0.206313\pi$
$524$	24.5773	+	0.806477i	1.07367	+	0.0352311i
$525$		0			0
$526$	34.8265	+	13.3266i	1.51851	+	0.581068i
$527$	−4.57203	−	3.83639i	−0.199161	−	0.167116i
$528$		0			0
$529$	−2.89569	+	16.4223i	−0.125900	+	0.714012i
$530$	0.485880	−	2.51376i	0.0211053	−	0.109191i
$531$		0			0
$532$	−7.10061	+	8.76203i	−0.307851	+	0.379882i
$533$		−	38.0100i		−	1.64640i
$534$		0			0
$535$	6.81624	+	1.20189i	0.294692	+	0.0519621i
$536$	22.1191	+	29.1611i	0.955401	+	1.25957i
$537$		0			0
$538$	5.12227	−	13.3861i	0.220837	−	0.577114i
$539$	4.48760	+	7.77275i	0.193295	+	0.334796i
$540$		0			0
$541$	37.2863	+	13.5711i	1.60306	+	0.583467i	0.980051	−	0.198746i	$-0.0636870\pi$
$541$	37.2863	+	13.5711i	1.60306	+	0.583467i	0.623011	+	0.782213i	$0.285909\pi$
$542$	10.9840	+	13.5349i	0.471802	+	0.581375i
$543$		0			0
$544$	−8.35876	−	5.78757i	−0.358379	−	0.248140i
$545$	−4.37413	+	0.771277i	−0.187367	+	0.0330379i
$546$		0			0
$547$	25.2994	+	30.1506i	1.08172	+	1.28915i	0.954805	+	0.297234i	$0.0960640\pi$
$547$	25.2994	+	30.1506i	1.08172	+	1.28915i	0.126918	+	0.991913i	$0.459492\pi$
$548$	−3.81316	−	11.6522i	−0.162890	−	0.497758i
$549$		0			0
$550$	−5.89228	+	9.82981i	−0.251248	+	0.419145i
$551$	0.126640	+	0.300404i	0.00539506	+	0.0127976i
$552$		0			0
$553$	−4.28810	+	1.56074i	−0.182348	+	0.0663694i
$554$	23.7861	+	20.6331i	1.01058	+	0.876615i
$555$		0			0
$556$	−36.2374	−	7.62283i	−1.53681	−	0.323280i
$557$	39.8256	−	7.02233i	1.68746	−	0.297546i	0.754176	−	0.656672i	$-0.228037\pi$
$557$	39.8256	−	7.02233i	1.68746	−	0.297546i	0.933289	+	0.359127i	$0.116925\pi$
$558$		0			0
$559$	−22.4346	−	12.9526i	−0.948882	−	0.547837i
$560$	−1.82254	+	1.33591i	−0.0770165	+	0.0564526i
$561$		0			0
$562$	−17.2752	+	9.59960i	−0.728712	+	0.404935i
$563$	6.36319	+	11.0214i	0.268177	+	0.464495i	0.968391	−	0.249437i	$-0.0802456\pi$
$563$	6.36319	+	11.0214i	0.268177	+	0.464495i	−0.700214	+	0.713933i	$0.746912\pi$
$564$		0			0
$565$	−4.80725	−	4.03376i	−0.202242	−	0.169702i
$566$	−16.1321	+	2.57247i	−0.678082	+	0.108129i
$567$		0			0
$568$	11.2916	−	3.49120i	0.473784	−	0.146487i
$569$		−	34.1940i		−	1.43349i	−0.697336	−	0.716744i	$-0.745632\pi$
$569$		−	34.1940i		−	1.43349i	0.697336	−	0.716744i	$-0.254368\pi$
$570$		0			0
$571$			13.6509i			0.571272i	0.958338	+	0.285636i	$0.0922048\pi$
$571$			13.6509i			0.571272i	−0.958338	+	0.285636i	$0.907795\pi$
$572$	−13.6415	−	12.2310i	−0.570381	−	0.511404i
$573$		0			0
$574$	2.01425	+	12.6314i	0.0840732	+	0.527226i
$575$	−9.26500	−	7.77426i	−0.386377	−	0.324209i
$576$		0			0
$577$	−5.84007	−	10.1153i	−0.243125	−	0.421105i	0.718478	−	0.695550i	$-0.244839\pi$
$577$	−5.84007	−	10.1153i	−0.243125	−	0.421105i	−0.961603	+	0.274445i	$0.911506\pi$
$578$	9.45886	+	17.0220i	0.393437	+	0.708021i
$579$		0			0
$580$	0.00922699	+	0.0646657i	0.000383130	+	0.00268510i
$581$	8.97757	+	5.18320i	0.372452	+	0.215035i
$582$		0			0
$583$	−6.87957	+	1.21305i	−0.284923	+	0.0502396i
$584$	−20.6145	−	19.1020i	−0.853035	−	0.790448i
$585$		0			0
$586$	16.8125	−	19.3817i	0.694517	−	0.800650i
$587$	−7.93169	+	2.88690i	−0.327376	+	0.119155i	−0.500479	−	0.865749i	$-0.666843\pi$
$587$	−7.93169	+	2.88690i	−0.327376	+	0.119155i	0.173103	+	0.984904i	$0.444621\pi$
$588$		0			0
$589$	4.26623	−	13.8321i	0.175787	−	0.569941i
$590$	−0.554379	−	0.332311i	−0.0228234	−	0.0136810i
$591$		0			0
$592$	16.3303	+	15.6377i	0.671171	+	0.642705i
$593$	−16.8272	−	20.0539i	−0.691012	−	0.823516i	0.300466	−	0.953793i	$-0.402858\pi$
$593$	−16.8272	−	20.0539i	−0.691012	−	0.823516i	−0.991478	+	0.130277i	$0.958413\pi$
$594$		0			0
$595$	−0.999901	+	0.176310i	−0.0409919	+	0.00722799i
$596$	−3.96473	−	2.46585i	−0.162402	−	0.101005i
$597$		0			0
$598$	15.0137	−	12.1840i	0.613954	−	0.498241i
$599$	21.7722	+	7.92445i	0.889590	+	0.323784i	0.746073	−	0.665864i	$-0.231937\pi$
$599$	21.7722	+	7.92445i	0.889590	+	0.323784i	0.143516	+	0.989648i	$0.454159\pi$
$600$		0			0
$601$	1.58823	+	2.75090i	0.0647854	+	0.112212i	0.896599	−	0.442844i	$-0.146030\pi$
$601$	1.58823	+	2.75090i	0.0647854	+	0.112212i	−0.831813	+	0.555055i	$0.812697\pi$
$602$	8.14183	+	3.11553i	0.331836	+	0.126980i
$603$		0			0
$604$	6.27674	−	15.6301i	0.255397	−	0.635980i
$605$	3.50952	+	0.618824i	0.142682	+	0.0251588i
$606$		0			0
$607$		−	1.98537i		−	0.0805836i	−0.999188	−	0.0402918i	$-0.987171\pi$
$607$		−	1.98537i		−	0.0805836i	0.999188	−	0.0402918i	$-0.0128287\pi$
$608$	5.05920	−	24.1331i	0.205177	−	0.978725i
$609$		0			0
$610$	0.838720	+	0.162115i	0.0339588	+	0.00656384i
$611$	−10.3917	+	58.9343i	−0.420404	+	2.38423i
$612$		0			0
$613$	10.9345	+	9.17511i	0.441639	+	0.370579i	0.836322	−	0.548238i	$-0.184701\pi$
$613$	10.9345	+	9.17511i	0.441639	+	0.370579i	−0.394683	+	0.918817i	$0.629146\pi$
$614$	−13.1791	+	34.4411i	−0.531866	+	1.38993i
$615$		0			0
$616$	5.18149	+	3.34169i	0.208768	+	0.134641i
$617$	8.17276	−	22.4545i	0.329023	−	0.903983i	−0.659337	−	0.751848i	$-0.729163\pi$
$617$	8.17276	−	22.4545i	0.329023	−	0.903983i	0.988360	−	0.152135i	$-0.0486150\pi$
$618$		0			0
$619$	−6.83693	−	3.94730i	−0.274799	−	0.158655i	0.356267	−	0.934384i	$-0.384049\pi$
$619$	−6.83693	−	3.94730i	−0.274799	−	0.158655i	−0.631067	+	0.775729i	$0.717383\pi$
$620$	1.53175	−	2.46283i	0.0615166	−	0.0989098i
$621$		0			0
$622$	10.1018	−	3.49023i	0.405046	−	0.139945i
$623$	−2.02835	+	1.70198i	−0.0812640	+	0.0681886i
$624$		0			0
$625$	−20.8385	+	7.58461i	−0.833542	+	0.303384i
$626$	3.16011	−	5.27186i	0.126303	−	0.210706i
$627$		0			0
$628$	−4.57182	−	8.55486i	−0.182435	−	0.341376i
$629$	3.47461	+	9.54640i	0.138542	+	0.380640i
$630$		0			0
$631$	−17.4503	−	20.7965i	−0.694687	−	0.827896i	0.297227	−	0.954807i	$-0.403938\pi$
$631$	−17.4503	−	20.7965i	−0.694687	−	0.827896i	−0.991914	+	0.126911i	$0.959494\pi$
$632$	6.78124	−	7.31817i	0.269743	−	0.291101i
$633$		0			0
$634$	0.750496	−	45.7550i	0.0298060	−	1.81716i
$635$	−0.297724	+	0.515673i	−0.0118148	+	0.0204639i
$636$		0			0
$637$	−27.2114	−	9.90416i	−1.07816	−	0.392417i
$638$	0.155790	−	0.0865700i	0.00616777	−	0.00342734i
$639$		0			0
$640$	2.21048	−	4.41847i	0.0873770	−	0.174655i
$641$	−17.6122	+	20.9894i	−0.695641	+	0.829032i	−0.992026	−	0.126036i	$-0.959774\pi$
$641$	−17.6122	+	20.9894i	−0.695641	+	0.829032i	0.296385	+	0.955069i	$0.404219\pi$
$642$		0			0
$643$	−17.2352	−	3.03903i	−0.679689	−	0.119848i	−0.176864	−	0.984235i	$-0.556595\pi$
$643$	−17.2352	−	3.03903i	−0.679689	−	0.119848i	−0.502826	+	0.864388i	$0.667706\pi$
$644$	−4.34366	+	4.84459i	−0.171164	+	0.190904i
$645$		0			0
$646$	6.83330	−	8.72077i	0.268853	−	0.343114i
$647$	26.6467			1.04759			0.523796	−	0.851844i	$-0.324516\pi$
$647$	26.6467			1.04759			0.523796	+	0.851844i	$0.324516\pi$
$648$		0			0
$649$	−0.306238	+	1.73676i	−0.0120209	+	0.0681739i
$650$	−5.82285	−	36.5153i	−0.228391	−	1.43225i
$651$		0			0
$652$	−19.8328	−	25.2750i	−0.776711	−	0.989844i
$653$	24.1438	−	13.9394i	0.944821	−	0.545493i	0.0533528	−	0.998576i	$-0.483009\pi$
$653$	24.1438	−	13.9394i	0.944821	−	0.545493i	0.891468	+	0.453083i	$0.149676\pi$
$654$		0			0
$655$	−1.83638	+	5.04540i	−0.0717531	+	0.197140i
$656$	−16.5330	−	22.5554i	−0.645504	−	0.880642i
$657$		0			0
$658$	0.330276	−	20.1357i	0.0128755	−	0.784970i
$659$	8.26906	+	46.8962i	0.322117	+	1.82682i	0.529206	+	0.848493i	$0.322490\pi$
$659$	8.26906	+	46.8962i	0.322117	+	1.82682i	−0.207089	+	0.978322i	$0.566399\pi$
$660$		0			0
$661$	−18.5666	+	15.5792i	−0.722157	+	0.605962i	−0.927981	−	0.372627i	$-0.878457\pi$
$661$	−18.5666	+	15.5792i	−0.722157	+	0.605962i	0.205824	+	0.978589i	$0.434013\pi$
$662$	13.9003	−	16.0245i	0.540250	−	0.622809i
$663$		0			0
$664$	−22.6373	−	1.11472i	−0.878497	−	0.0432597i
$665$	−1.33606	−	2.06850i	−0.0518101	−	0.0802131i
$666$		0			0
$667$	0.0643295	+	0.176744i	0.00249085	+	0.00684355i
$668$	−44.6801	+	14.6215i	−1.72872	+	0.565721i
$669$		0			0
$670$	−7.55345	+	2.60976i	−0.291815	+	0.100824i
$671$	−0.404738	−	2.29538i	−0.0156247	−	0.0886123i
$672$		0			0
$673$	16.7270	−	28.9720i	0.644779	−	1.11679i	−0.339573	−	0.940580i	$-0.610283\pi$
$673$	16.7270	−	28.9720i	0.644779	−	1.11679i	0.984352	−	0.176211i	$-0.0563840\pi$
$674$	−13.0237	+	10.5691i	−0.501654	+	0.407106i
$675$		0			0
$676$	33.0962	+	1.08601i	1.27293	+	0.0417697i
$677$	−23.7742	+	13.7261i	−0.913718	+	0.527536i	−0.881626	−	0.471949i	$-0.843550\pi$
$677$	−23.7742	+	13.7261i	−0.913718	+	0.527536i	−0.0320927	+	0.999485i	$0.510217\pi$
$678$		0			0
$679$	−4.38302	+	5.22348i	−0.168205	+	0.200459i
$680$	1.76864	−	1.34154i	0.0678243	−	0.0514458i
$681$		0			0
$682$	−7.76966	−	1.50179i	−0.297516	−	0.0575064i
$683$	−4.82120			−0.184478			−0.0922390	−	0.995737i	$-0.529402\pi$
$683$	−4.82120			−0.184478			−0.0922390	+	0.995737i	$0.529402\pi$
$684$		0			0
$685$	2.67696			0.102281
$686$	22.1417	+	4.27973i	0.845372	+	0.163401i
$687$		0			0
$688$	−18.9468	+	2.07205i	−0.722339	+	0.0789962i
$689$	14.4877	−	17.2658i	0.551937	−	0.657773i
$690$		0			0
$691$	11.8770	−	6.85720i	0.451823	−	0.260860i	−0.256777	−	0.966471i	$-0.582660\pi$
$691$	11.8770	−	6.85720i	0.451823	−	0.260860i	0.708600	+	0.705610i	$0.249327\pi$
$692$	0.0856555	−	2.61035i	0.00325614	−	0.0992305i
$693$		0			0
$694$	38.4565	−	31.2085i	1.45979	−	1.18466i
$695$	4.04269	−	7.00215i	0.153348	−	0.265607i
$696$		0			0
$697$	−2.18197	−	12.3746i	−0.0826481	−	0.468721i
$698$	−4.95847	+	1.71318i	−0.187681	+	0.0648447i
$699$		0			0
$700$	3.87008	+	11.8261i	0.146275	+	0.446986i
$701$	−2.32355	−	6.38391i	−0.0877594	−	0.241117i	0.888047	−	0.459752i	$-0.152062\pi$
$701$	−2.32355	−	6.38391i	−0.0877594	−	0.241117i	−0.975807	+	0.218635i	$0.929840\pi$
$702$		0			0
$703$	−18.0611	+	16.7591i	−0.681186	+	0.632082i
$704$	−13.4150	−	1.32440i	−0.505598	−	0.0499153i
$705$		0			0
$706$	31.6709	−	36.5107i	1.19195	−	1.37410i
$707$	−13.0864	+	10.9808i	−0.492165	+	0.412976i
$708$		0			0
$709$	6.42719	+	36.4504i	0.241378	+	1.36892i	0.828756	+	0.559610i	$0.189049\pi$
$709$	6.42719	+	36.4504i	0.241378	+	1.36892i	−0.587378	+	0.809313i	$0.699840\pi$
$710$	−0.0423227	+	2.58026i	−0.00158834	+	0.0968353i
$711$		0			0
$712$	2.24514	−	5.33600i	0.0841403	−	0.199975i
$713$	2.85631	−	7.84763i	0.106969	−	0.293896i
$714$		0			0
$715$	3.46450	−	2.00023i	0.129565	−	0.0748043i
$716$	14.1565	−	11.1083i	0.529052	−	0.415137i
$717$		0			0
$718$	0.0258350	+	0.162012i	0.000964152	+	0.00604624i
$719$	−0.996312	+	5.65037i	−0.0371562	+	0.210723i	−0.997733	−	0.0672900i	$-0.978565\pi$
$719$	−0.996312	+	5.65037i	−0.0371562	+	0.210723i	0.960577	+	0.278013i	$0.0896759\pi$
$720$		0			0
$721$	16.0707			0.598503
$722$	25.9273	+	7.05517i	0.964914	+	0.262566i
$723$		0			0
$724$	6.18636	+	5.54670i	0.229914	+	0.206141i
$725$	0.354228	+	0.0624600i	0.0131557	+	0.00231971i
$726$		0			0
$727$	−10.4537	+	12.4582i	−0.387706	+	0.462050i	−0.924231	−	0.381835i	$-0.875292\pi$
$727$	−10.4537	+	12.4582i	−0.387706	+	0.462050i	0.536525	+	0.843885i	$0.319737\pi$
$728$	−19.7369	+	2.48665i	−0.731497	+	0.0921614i
$729$		0			0
$730$	5.36387	−	2.98062i	0.198526	−	0.110318i
$731$	−8.04738	−	2.92901i	−0.297643	−	0.108333i
$732$		0			0
$733$	11.1038	−	19.2323i	0.410127	−	0.710360i	−0.584777	−	0.811194i	$-0.698818\pi$
$733$	11.1038	−	19.2323i	0.410127	−	0.710360i	0.994903	+	0.100834i	$0.0321512\pi$
$734$	−0.643891	+	39.2557i	−0.0237665	+	1.44895i
$735$		0			0
$736$	3.60962	−	13.7605i	0.133053	−	0.507218i
$737$	14.0160	+	16.7036i	0.516284	+	0.615284i
$738$		0			0
$739$	17.3331	+	47.6223i	0.637608	+	1.75181i	0.659112	+	0.752045i	$0.270933\pi$
$739$	17.3331	+	47.6223i	0.637608	+	1.75181i	−0.0215034	+	0.999769i	$0.506845\pi$
$740$	−4.35403	+	2.32684i	−0.160057	+	0.0855365i
$741$		0			0
$742$	−3.89958	+	6.50548i	−0.143158	+	0.238824i
$743$	48.5951	−	17.6872i	1.78278	−	0.648880i	0.783148	−	0.621836i	$-0.213613\pi$
$743$	48.5951	−	17.6872i	1.78278	−	0.648880i	0.999634	−	0.0270440i	$-0.00860942\pi$
$744$		0			0
$745$	0.780942	−	0.655288i	0.0286115	−	0.0240079i
$746$	−39.2412	+	13.5580i	−1.43672	+	0.496395i
$747$		0			0
$748$	−5.14328	−	3.19885i	−0.188057	−	0.116961i
$749$	−17.7573	−	10.2522i	−0.648836	−	0.374606i
$750$		0			0
$751$	−3.52032	+	9.67200i	−0.128458	+	0.352936i	−0.987203	−	0.159467i	$-0.949022\pi$
$751$	−3.52032	+	9.67200i	−0.128458	+	0.352936i	0.858745	+	0.512403i	$0.171245\pi$
$752$	19.4678	+	39.4921i	0.709917	+	1.44013i
$753$		0			0
$754$	−0.205509	+	0.537058i	−0.00748421	+	0.0195585i
$755$	2.81724	+	2.36394i	0.102530	+	0.0860326i
$756$		0			0
$757$	7.10267	−	40.2813i	0.258151	−	1.46405i	−0.529702	−	0.848184i	$-0.677696\pi$
$757$	7.10267	−	40.2813i	0.258151	−	1.46405i	0.787853	−	0.615864i	$-0.211193\pi$
$758$	−33.6115	−	6.49672i	−1.22082	−	0.235971i
$759$		0			0
$760$	4.66441	+	2.68871i	0.169196	+	0.0975297i
$761$			25.1303i			0.910973i	0.890243	+	0.455486i	$0.150535\pi$
$761$			25.1303i			0.910973i	−0.890243	+	0.455486i	$0.849465\pi$
$762$		0			0
$763$	12.9582	+	2.28487i	0.469117	+	0.0827179i
$764$	26.5548	+	10.6639i	0.960720	+	0.385806i
$765$		0			0
$766$	−25.6113	−	9.80035i	−0.925374	−	0.354101i
$767$	−2.84499	−	4.92767i	−0.102727	−	0.177928i
$768$		0			0
$769$	−1.12642	−	0.409982i	−0.0406196	−	0.0147843i	0.321630	−	0.946865i	$-0.395769\pi$
$769$	−1.12642	−	0.409982i	−0.0406196	−	0.0147843i	−0.362250	+	0.932081i	$0.617991\pi$
$770$	−1.04532	+	0.848307i	−0.0376707	+	0.0305708i
$771$		0			0
$772$	8.11384	−	13.0459i	0.292023	−	0.469531i
$773$	9.78659	−	1.72564i	0.351999	−	0.0620670i	0.00514704	−	0.999987i	$-0.498362\pi$
$773$	9.78659	−	1.72564i	0.351999	−	0.0620670i	0.346852	+	0.937920i	$0.387251\pi$
$774$		0			0
$775$	−10.2658	−	12.2343i	−0.368759	−	0.439470i
$776$	3.30777	−	14.5367i	0.118742	−	0.521838i
$777$		0			0
$778$	−42.6932	−	25.5915i	−1.53062	−	0.917501i
$779$	25.5994	−	16.5348i	0.917193	−	0.592421i
$780$		0			0
$781$	6.61651	−	2.40821i	0.236758	−	0.0861727i
$782$	4.18844	−	4.82850i	0.149778	−	0.172667i
$783$		0			0
$784$	−20.4554	+	5.95879i	−0.730552	+	0.212814i
$785$	2.08573	−	0.367770i	0.0744428	−	0.0131263i
$786$		0			0
$787$	31.9287	+	18.4341i	1.13814	+	0.657103i	0.945968	−	0.324259i	$-0.105115\pi$
$787$	31.9287	+	18.4341i	1.13814	+	0.657103i	0.192168	+	0.981362i	$0.438448\pi$
$788$	−15.8078	+	2.25557i	−0.563128	+	0.0803514i
$789$		0			0
$790$	1.05812	+	1.90418i	0.0376464	+	0.0677476i
$791$	9.29531	+	16.1000i	0.330503	+	0.572449i
$792$		0			0
$793$	5.76076	+	4.83385i	0.204571	+	0.171655i
$794$	−3.63416	−	22.7899i	−0.128972	−	0.808785i
$795$		0			0
$796$	−7.70656	+	8.59531i	−0.273152	+	0.304653i
$797$		−	41.9806i		−	1.48703i	−0.668720	−	0.743514i	$-0.733158\pi$
$797$		−	41.9806i		−	1.48703i	0.668720	−	0.743514i	$-0.266842\pi$
$798$		0			0
$799$			19.7833i			0.699882i
$800$	−19.3382	−	19.1357i	−0.683707	−	0.676550i
$801$		0			0
$802$	−33.8650	+	5.40023i	−1.19582	+	0.190689i
$803$	−12.8259	−	10.7622i	−0.452617	−	0.379791i
$804$		0			0
$805$	−0.710352	−	1.23037i	−0.0250366	−	0.0433647i
$806$	22.3180	−	12.4018i	0.786116	−	0.436833i
$807$		0			0
$808$	14.4851	−	34.4266i	0.509585	−	1.21112i
$809$	10.7776	+	6.22247i	0.378921	+	0.218770i	0.677349	−	0.735662i	$-0.263129\pi$
$809$	10.7776	+	6.22247i	0.378921	+	0.218770i	−0.298428	+	0.954432i	$0.596462\pi$
$810$		0			0
$811$	−43.5005	+	7.67030i	−1.52751	+	0.269341i	−0.873379	−	0.487042i	$-0.838076\pi$
$811$	−43.5005	+	7.67030i	−1.52751	+	0.269341i	−0.654129	+	0.756383i	$0.726965\pi$
$812$	0.0398345	−	0.189365i	0.00139792	−	0.00664541i
$813$		0			0
$814$	10.1752	+	8.82637i	0.356640	+	0.309364i
$815$	6.59176	−	2.39920i	0.230899	−	0.0840404i
$816$		0			0
$817$	−1.03584	−	20.7440i	−0.0362396	−	0.725742i
$818$	12.7794	−	21.3193i	0.446822	−	0.745412i
$819$		0			0
$820$	5.80333	−	1.89913i	0.202661	−	0.0663204i
$821$	11.4126	+	13.6011i	0.398304	+	0.474680i	0.927502	−	0.373818i	$-0.121952\pi$
$821$	11.4126	+	13.6011i	0.398304	+	0.474680i	−0.529198	+	0.848498i	$0.677507\pi$
$822$		0			0
$823$	3.86108	−	0.680812i	0.134589	−	0.0237316i	−0.105948	−	0.994372i	$-0.533788\pi$
$823$	3.86108	−	0.680812i	0.134589	−	0.0237316i	0.240537	+	0.970640i	$0.422677\pi$
$824$	−31.2562	+	16.0503i	−1.08886	+	0.559139i
$825$		0			0
$826$	1.20657	+	1.48679i	0.0419821	+	0.0517322i
$827$	16.9309	+	6.16235i	0.588746	+	0.214286i	0.619178	−	0.785251i	$-0.287466\pi$
$827$	16.9309	+	6.16235i	0.588746	+	0.214286i	−0.0304318	+	0.999537i	$0.509688\pi$
$828$		0			0
$829$	3.62712	+	6.28236i	0.125975	+	0.218195i	0.922114	−	0.386919i	$-0.126461\pi$
$829$	3.62712	+	6.28236i	0.125975	+	0.218195i	−0.796139	+	0.605114i	$0.793127\pi$
$830$	1.76859	−	4.62188i	0.0613888	−	0.160428i
$831$		0			0
$832$	35.9031	−	24.5482i	1.24472	−	0.851055i
$833$	−9.42754	−	1.66233i	−0.326645	−	0.0575963i
$834$		0			0
$835$		−	10.2647i		−	0.355225i
$836$	2.30324	−	14.5081i	0.0796593	−	0.501773i
$837$		0			0
$838$	7.60321	−	39.3361i	0.262649	−	1.35884i
$839$	−0.359087	+	2.03648i	−0.0123971	+	0.0703072i	−0.990379	−	0.138384i	$-0.955809\pi$
$839$	−0.359087	+	2.03648i	−0.0123971	+	0.0703072i	0.977982	+	0.208691i	$0.0669203\pi$
$840$		0			0
$841$	22.2110	+	18.6372i	0.765897	+	0.642664i
$842$	−6.34747	−	2.42890i	−0.218748	−	0.0837056i
$843$		0			0
$844$	−0.400833	+	12.2154i	−0.0137973	+	0.420471i
$845$	−2.47289	+	6.79420i	−0.0850699	+	0.233728i
$846$		0			0
$847$	−9.14280	−	5.27860i	−0.314150	−	0.181375i
$848$	1.08713	−	16.5473i	0.0373322	−	0.568236i
$849$		0			0
$850$	−3.99186	−	11.5537i	−0.136920	−	0.396289i
$851$	−10.8894	+	9.13733i	−0.373285	+	0.313224i
$852$		0			0
$853$	−41.4770	+	15.0964i	−1.42015	+	0.516891i	−0.934090	−	0.357037i	$-0.883787\pi$
$853$	−41.4770	+	15.0964i	−1.42015	+	0.516891i	−0.486055	+	0.873928i	$0.661565\pi$
$854$	−2.17057	−	1.30110i	−0.0742753	−	0.0445228i
$855$		0			0
$856$	44.7756	+	2.20488i	1.53040	+	0.0753612i
$857$	−2.59576	−	7.13179i	−0.0886694	−	0.243617i	0.887430	−	0.460943i	$-0.152489\pi$
$857$	−2.59576	−	7.13179i	−0.0886694	−	0.243617i	−0.976099	+	0.217326i	$0.930267\pi$
$858$		0			0
$859$	−4.44327	−	5.29529i	−0.151603	−	0.180673i	0.684898	−	0.728639i	$-0.259847\pi$
$859$	−4.44327	−	5.29529i	−0.151603	−	0.180673i	−0.836501	+	0.547966i	$0.815402\pi$
$860$	0.856673	−	4.07245i	0.0292123	−	0.138870i
$861$		0			0
$862$	−43.3108	−	0.710405i	−1.47517	−	0.0241965i
$863$	−6.70188	+	11.6080i	−0.228135	+	0.395141i	−0.957255	−	0.289244i	$-0.906596\pi$
$863$	−6.70188	+	11.6080i	−0.228135	+	0.395141i	0.729121	+	0.684385i	$0.239929\pi$
$864$		0			0
$865$	0.535870	+	0.195041i	0.0182201	+	0.00663158i
$866$	−10.3513	−	18.6280i	−0.351752	−	0.633006i
$867$		0			0
$868$	−6.75948	+	5.30403i	−0.229432	+	0.180030i
$869$	3.82060	−	4.55321i	0.129605	−	0.154457i
$870$		0			0
$871$	−69.2833	−	12.2165i	−2.34757	−	0.413941i
$872$	−27.4845	+	8.49783i	−0.930744	+	0.287773i
$873$		0			0
$874$	14.7369	+	4.81138i	0.498484	+	0.162747i
$875$	−5.54156			−0.187339
$876$		0			0
$877$	1.40120	−	7.94658i	0.0473151	−	0.268337i	−0.951968	−	0.306198i	$-0.900943\pi$
$877$	1.40120	−	7.94658i	0.0473151	−	0.268337i	0.999283	+	0.0378606i	$0.0120543\pi$
$878$	3.99464	−	0.636998i	0.134812	−	0.0214976i
$879$		0			0
$880$	1.18583	−	2.69388i	0.0399744	−	0.0908108i
$881$	32.2729	−	18.6328i	1.08730	−	0.627753i	0.154444	−	0.988001i	$-0.450641\pi$
$881$	32.2729	−	18.6328i	1.08730	−	0.627753i	0.932857	+	0.360248i	$0.117308\pi$
$882$		0			0
$883$	−0.535500	+	1.47127i	−0.0180210	+	0.0495123i	−0.948377	−	0.317145i	$-0.897276\pi$
$883$	−0.535500	+	1.47127i	−0.0180210	+	0.0495123i	0.930356	+	0.366658i	$0.119498\pi$
$884$	19.3462	−	2.76046i	0.650682	−	0.0928442i
$885$		0			0
$886$	41.4419	+	0.679751i	1.39227	+	0.0228367i
$887$	−5.30178	−	30.0679i	−0.178016	−	1.00958i	−0.934604	−	0.355689i	$-0.884246\pi$
$887$	−5.30178	−	30.0679i	−0.178016	−	1.00958i	0.756588	−	0.653892i	$-0.226865\pi$
$888$		0			0
$889$	1.35129	−	1.13387i	0.0453209	−	0.0380287i
$890$	0.954834	+	0.828262i	0.0320061	+	0.0277634i
$891$		0			0
$892$	−45.8563	+	24.5061i	−1.53538	+	0.820526i
$893$	−44.2123	+	18.6384i	−1.47951	+	0.623711i
$894$		0			0
$895$	1.34379	+	3.69203i	0.0449179	+	0.123411i
$896$	−10.6304	+	10.0604i	−0.355137	+	0.336095i
$897$		0			0
$898$	12.0061	+	34.7495i	0.400650	+	1.15961i
$899$	0.0431284	+	0.244593i	0.00143841	+	0.00815764i
$900$		0			0
$901$	3.72549	−	6.45274i	0.124114	−	0.214972i
$902$	−10.4985	−	12.9367i	−0.349561	−	0.430744i
$903$		0			0
$904$	−34.1582	−	22.0296i	−1.13608	−	0.732693i
$905$	−1.57113	+	0.907094i	−0.0522262	+	0.0301528i
$906$		0			0
$907$	−14.5264	+	17.3118i	−0.482340	+	0.574831i	−0.951252	−	0.308414i	$-0.900202\pi$
$907$	−14.5264	+	17.3118i	−0.482340	+	0.574831i	0.468912	+	0.883245i	$0.344646\pi$
$908$	45.9680	+	18.4598i	1.52550	+	0.612611i
$909$		0			0
$910$	0.824291	−	4.26456i	0.0273250	−	0.141369i
$911$	−55.4920			−1.83853			−0.919266	−	0.393637i	$-0.871217\pi$
$911$	−55.4920			−1.83853			−0.919266	+	0.393637i	$0.871217\pi$
$912$		0			0
$913$	−13.5025			−0.446867
$914$	−4.48401	+	23.1985i	−0.148318	+	0.767339i
$915$		0			0
$916$	19.2518	+	7.73114i	0.636097	+	0.255444i
$917$	10.2242	−	12.1847i	0.337633	−	0.402375i
$918$		0			0
$919$	40.3293	−	23.2841i	1.33034	−	0.768072i	0.344988	−	0.938607i	$-0.387883\pi$
$919$	40.3293	−	23.2841i	1.33034	−	0.768072i	0.985352	+	0.170535i	$0.0545497\pi$
$920$	2.61038	+	1.68351i	0.0860618	+	0.0555037i
$921$		0			0
$922$	19.2759	+	23.7526i	0.634819	+	0.782251i
$923$	−11.3589	+	19.6741i	−0.373882	+	0.647583i
$924$		0			0
$925$	4.72057	+	26.7717i	0.155212	+	0.880248i
$926$	−5.45750	−	15.7957i	−0.179344	−	0.519079i
$927$		0			0
$928$	0.111650	+	0.408084i	0.00366510	+	0.0133960i
$929$	14.3635	+	39.4634i	0.471251	+	1.29475i	0.916747	+	0.399467i	$0.130805\pi$
$929$	14.3635	+	39.4634i	0.471251	+	1.29475i	−0.445497	+	0.895284i	$0.646973\pi$
$930$		0			0
$931$	−5.16694	−	22.6351i	−0.169340	−	0.741835i
$932$	−22.6918	+	12.1268i	−0.743295	+	0.397226i
$933$		0			0
$934$	−7.61425	−	6.60491i	−0.249146	−	0.216119i
$935$	1.01308	−	0.850077i	0.0331314	−	0.0278005i
$936$		0			0
$937$	10.3380	+	58.6298i	0.337728	+	1.91535i	0.398436	+	0.917196i	$0.369553\pi$
$937$	10.3380	+	58.6298i	0.337728	+	1.91535i	−0.0607077	+	0.998156i	$0.519336\pi$
$938$	23.6715	+	0.388272i	0.772903	+	0.0126775i
$939$		0			0
$940$	−9.51725	+	1.35799i	−0.310418	+	0.0442928i
$941$	−16.7209	+	45.9404i	−0.545086	+	1.49761i	0.295181	+	0.955441i	$0.404620\pi$
$941$	−16.7209	+	45.9404i	−0.545086	+	1.49761i	−0.840268	+	0.542171i	$0.817602\pi$
$942$		0			0
$943$	15.2268	−	8.79117i	0.495851	−	0.286280i
$944$	−3.83160	−	1.68665i	−0.124708	−	0.0548958i
$945$		0			0
$946$	−11.2132	+	1.78809i	−0.364571	+	0.0581357i
$947$	2.66296	−	15.1024i	0.0865346	−	0.490762i	−0.910480	−	0.413552i	$-0.864288\pi$
$947$	2.66296	−	15.1024i	0.0865346	−	0.490762i	0.997015	−	0.0772096i	$-0.0246010\pi$
$948$		0			0
$949$	54.0202			1.75357
$950$	22.0597	−	19.8062i	0.715712	−	0.642599i
$951$		0			0
$952$	−6.28281	+	1.94256i	−0.203627	+	0.0629586i
$953$	−43.7491	−	7.71415i	−1.41717	−	0.249886i	−0.587992	−	0.808867i	$-0.700081\pi$
$953$	−43.7491	−	7.71415i	−1.41717	−	0.249886i	−0.829180	+	0.558981i	$0.811192\pi$
$954$		0			0
$955$	−4.01623	+	4.78635i	−0.129962	+	0.154883i
$956$	−24.1294	+	18.9339i	−0.780401	+	0.612365i
$957$		0			0
$958$	25.8348	+	46.4918i	0.834685	+	1.50208i
$959$	−7.45210	−	2.71234i	−0.240641	−	0.0875862i
$960$		0			0
$961$	−9.98612	+	17.2965i	−0.322133	+	0.557951i
$962$	−43.4539	−	0.712753i	−1.40101	−	0.0229801i
$963$		0			0
$964$	−8.64774	+	41.1097i	−0.278525	+	1.32405i
$965$	2.15621	+	2.56967i	0.0694109	+	0.0827207i
$966$		0			0
$967$	6.69124	+	18.3840i	0.215176	+	0.591190i	0.999578	−	0.0290625i	$-0.00925217\pi$
$967$	6.69124	+	18.3840i	0.215176	+	0.591190i	−0.784402	+	0.620253i	$0.787030\pi$
$968$	23.0539	+	1.13524i	0.740981	+	0.0364880i
$969$		0			0
$970$	2.79196	+	1.67358i	0.0896444	+	0.0537355i
$971$	12.2064	−	4.44276i	0.391722	−	0.142575i	−0.138647	−	0.990342i	$-0.544275\pi$
$971$	12.2064	−	4.44276i	0.391722	−	0.142575i	0.530369	+	0.847767i	$0.322053\pi$
$972$		0			0
$973$	−18.3487	+	15.3964i	−0.588234	+	0.493587i
$974$	11.5719	+	33.4928i	0.370788	+	1.07318i
$975$		0			0
$976$	5.52103	+	0.362723i	0.176724	+	0.0116105i
$977$	−14.3531	−	8.28675i	−0.459196	−	0.265117i	0.252510	−	0.967594i	$-0.418744\pi$
$977$	−14.3531	−	8.28675i	−0.459196	−	0.265117i	−0.711706	+	0.702478i	$0.752077\pi$
$978$		0			0
$979$	1.17957	−	3.24085i	0.0376993	−	0.103578i
$980$	0.152567	−	4.64947i	0.00487357	−	0.148522i
$981$		0			0
$982$	10.9235	+	4.17997i	0.348584	+	0.133388i
$983$	24.4165	+	20.4878i	0.778764	+	0.653461i	0.942937	−	0.332971i	$-0.108051\pi$
$983$	24.4165	+	20.4878i	0.778764	+	0.653461i	−0.164173	+	0.986432i	$0.552496\pi$
$984$		0			0
$985$	0.605422	−	3.43352i	0.0192904	−	0.109401i
$986$	−0.0360759	+	0.186643i	−0.00114889	+	0.00594392i
$987$		0			0
$988$	24.3958	+	40.6347i	0.776132	+	1.29276i
$989$		−	11.9830i		−	0.381038i
$990$		0			0
$991$	−12.2280	−	2.15613i	−0.388435	−	0.0684916i	−0.0239798	−	0.999712i	$-0.507634\pi$
$991$	−12.2280	−	2.15613i	−0.388435	−	0.0684916i	−0.364455	+	0.931221i	$0.618745\pi$
$992$	7.84934	−	17.0668i	0.249217	−	0.541872i
$993$		0			0
$994$	2.73218	−	7.14003i	0.0866596	−	0.226468i
$995$	−1.26031	−	2.18292i	−0.0399546	−	0.0692034i
$996$		0			0
$997$	22.3628	+	8.13938i	0.708236	+	0.257777i	0.670923	−	0.741527i	$-0.265898\pi$
$997$	22.3628	+	8.13938i	0.708236	+	0.257777i	0.0373129	+	0.999304i	$0.488120\pi$
$998$	−4.00418	−	4.93412i	−0.126750	−	0.156187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.ce.a.575.18	yes	240
3.2	odd	2	inner	684.2.ce.a.575.23	yes	240
4.3	odd	2	inner	684.2.ce.a.575.33	yes	240
12.11	even	2	inner	684.2.ce.a.575.8	yes	240
19.4	even	9	inner	684.2.ce.a.251.8	✓	240
57.23	odd	18	inner	684.2.ce.a.251.33	yes	240
76.23	odd	18	inner	684.2.ce.a.251.23	yes	240
228.23	even	18	inner	684.2.ce.a.251.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.ce.a.251.8	✓	240	19.4	even	9	inner
684.2.ce.a.251.18	yes	240	228.23	even	18	inner
684.2.ce.a.251.23	yes	240	76.23	odd	18	inner
684.2.ce.a.251.33	yes	240	57.23	odd	18	inner
684.2.ce.a.575.8	yes	240	12.11	even	2	inner
684.2.ce.a.575.18	yes	240	1.1	even	1	trivial
684.2.ce.a.575.23	yes	240	3.2	odd	2	inner
684.2.ce.a.575.33	yes	240	4.3	odd	2	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.ce (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.268384 + 1.38851i) q^{2} +(-1.85594 - 0.745309i) q^{4} +(0.280698 - 0.334522i) q^{5} +(-1.12035 + 0.646834i) q^{7} +(1.53298 - 2.37697i) q^{8} +O(q^{10})\)	\(q+(-0.268384 + 1.38851i) q^{2} +(-1.85594 - 0.745309i) q^{4} +(0.280698 - 0.334522i) q^{5} +(-1.12035 + 0.646834i) q^{7} +(1.53298 - 2.37697i) q^{8} +(0.389154 + 0.479533i) q^{10} +(0.842516 - 1.45928i) q^{11} +(0.944062 + 5.35404i) q^{13} +(-0.597454 - 1.72922i) q^{14} +(2.88903 + 2.76650i) q^{16} +(0.614700 + 1.68887i) q^{17} +(-3.19522 + 2.96489i) q^{19} +(-0.770281 + 0.411647i) q^{20} +(1.80011 + 1.56149i) q^{22} +(-1.92647 + 1.61650i) q^{23} +(0.835127 + 4.73624i) q^{25} +(-7.68753 - 0.126095i) q^{26} +(2.56139 - 0.365479i) q^{28} +(0.0255800 - 0.0702806i) q^{29} +(-2.87590 + 1.66040i) q^{31} +(-4.61669 + 3.26897i) q^{32} +(-2.51000 + 0.400253i) q^{34} +(-0.0980989 + 0.556347i) q^{35} +5.65252 q^{37} +(-3.25924 - 5.23234i) q^{38} +(-0.364847 - 1.18002i) q^{40} +(-6.88524 - 1.21405i) q^{41} +(-3.06284 + 3.65015i) q^{43} +(-2.65127 + 2.08040i) q^{44} +(-1.72750 - 3.10878i) q^{46} +(10.3436 + 3.76477i) q^{47} +(-2.66321 + 4.61282i) q^{49} +(-6.80047 - 0.111545i) q^{50} +(2.23829 - 10.6404i) q^{52} +(-2.66483 - 3.17582i) q^{53} +(-0.251670 - 0.691457i) q^{55} +(-0.179964 + 3.65462i) q^{56} +(0.0907203 + 0.0543804i) q^{58} +(-0.983482 + 0.357958i) q^{59} +(1.05962 - 0.889126i) q^{61} +(-1.53365 - 4.43886i) q^{62} +(-3.29997 - 7.28767i) q^{64} +(2.05604 + 1.18706i) q^{65} +(-4.42587 + 12.1600i) q^{67} +(0.117887 - 3.59259i) q^{68} +(-0.746167 - 0.285526i) q^{70} +(3.20103 + 2.68598i) q^{71} +(1.72543 - 9.78538i) q^{73} +(-1.51705 + 7.84861i) q^{74} +(8.13990 - 3.12123i) q^{76} +2.17987i q^{77} +(3.47382 + 0.612528i) q^{79} +(1.73640 - 0.189895i) q^{80} +(3.53362 - 9.23442i) q^{82} +(-4.00659 - 6.93962i) q^{83} +(0.737511 + 0.268432i) q^{85} +(-4.24627 - 5.23244i) q^{86} +(-2.17711 - 4.23968i) q^{88} +(2.01566 - 0.355415i) q^{89} +(-4.52085 - 5.38774i) q^{91} +(4.78022 - 1.56432i) q^{92} +(-8.00349 + 13.3519i) q^{94} +(0.0949310 + 1.90111i) q^{95} +(4.95301 - 1.80275i) q^{97} +(-5.69020 - 4.93591i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{4}+O(q^{10}) \) 240 * q + 12 * q^4	\( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Introduction

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