LMFDB - Embedded newform 945.2.g.b.944.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(944,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("945.944");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.g (of order $2$, degree $1$, 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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			944.7
Character	$\chi$	$=$	945.944
Dual form			945.2.g.b.944.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92418 q^{2} +1.70246 q^{4} +(1.22993 - 1.86742i) q^{5} +(-2.62359 - 0.341697i) q^{7} +0.572523 q^{8} +O(q^{10})$	\(q-1.92418 q^{2} +1.70246 q^{4} +(1.22993 - 1.86742i) q^{5} +(-2.62359 - 0.341697i) q^{7} +0.572523 q^{8} +(-2.36661 + 3.59325i) q^{10} -3.13927i q^{11} -3.49574 q^{13} +(5.04826 + 0.657486i) q^{14} -4.50655 q^{16} -0.661056i q^{17} +4.05658i q^{19} +(2.09391 - 3.17921i) q^{20} +6.04051i q^{22} -2.99686 q^{23} +(-1.97454 - 4.59360i) q^{25} +6.72642 q^{26} +(-4.46656 - 0.581726i) q^{28} -0.604649i q^{29} +1.99580i q^{31} +7.52636 q^{32} +1.27199i q^{34} +(-3.86493 + 4.47910i) q^{35} +8.98387i q^{37} -7.80558i q^{38} +(0.704164 - 1.06914i) q^{40} -2.09391 q^{41} -8.55335i q^{43} -5.34448i q^{44} +5.76649 q^{46} +6.12795i q^{47} +(6.76649 + 1.79295i) q^{49} +(3.79936 + 8.83891i) q^{50} -5.95135 q^{52} +5.42119 q^{53} +(-5.86235 - 3.86109i) q^{55} +(-1.50207 - 0.195630i) q^{56} +1.16345i q^{58} -5.81619 q^{59} +4.13408i q^{61} -3.84027i q^{62} -5.46894 q^{64} +(-4.29952 + 6.52803i) q^{65} +10.7638i q^{67} -1.12542i q^{68} +(7.43682 - 8.61857i) q^{70} -10.5090i q^{71} +2.64580 q^{73} -17.2866i q^{74} +6.90616i q^{76} +(-1.07268 + 8.23617i) q^{77} -10.1581 q^{79} +(-5.54275 + 8.41564i) q^{80} +4.02905 q^{82} +14.4489i q^{83} +(-1.23447 - 0.813054i) q^{85} +16.4582i q^{86} -1.79731i q^{88} -11.6461 q^{89} +(9.17140 + 1.19449i) q^{91} -5.10202 q^{92} -11.7913i q^{94} +(7.57535 + 4.98931i) q^{95} -7.70280 q^{97} +(-13.0199 - 3.44995i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4}+O(q^{10}) $ 32 * q + 32 * q^4	$ 32 q + 32 q^{4} + 32 q^{16} + 20 q^{25} - 24 q^{46} + 8 q^{49} + 56 q^{64} + 40 q^{79} + 76 q^{85} + 40 q^{91}+O(q^{100}) $ 32 * q + 32 * q^4 + 32 * q^16 + 20 * q^25 - 24 * q^46 + 8 * q^49 + 56 * q^64 + 40 * q^79 + 76 * q^85 + 40 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.92418			−1.36060			−0.680299	−	0.732934i	$-0.738150\pi$
$2$	−1.92418			−1.36060			−0.680299	+	0.732934i	$0.738150\pi$
$3$		0			0
$3$		0			0
$4$	1.70246			0.851229
$5$	1.22993	−	1.86742i	0.550042	−	0.835137i
$5$	1.22993	−	1.86742i	0.550042	−	0.835137i
$6$		0			0
$7$	−2.62359	−	0.341697i	−0.991625	−	0.129149i
$7$	−2.62359	−	0.341697i	−0.991625	−	0.129149i
$8$	0.572523			0.202418
$9$		0			0
$10$	−2.36661	+	3.59325i	−0.748386	+	1.13629i
$11$		−	3.13927i		−	0.946526i	−0.880921	−	0.473263i	$-0.843076\pi$
$11$		−	3.13927i		−	0.946526i	0.880921	−	0.473263i	$-0.156924\pi$
$12$		0			0
$13$	−3.49574			−0.969544			−0.484772	−	0.874641i	$-0.661097\pi$
$13$	−3.49574			−0.969544			−0.484772	+	0.874641i	$0.661097\pi$
$14$	5.04826	+	0.657486i	1.34920	+	0.175721i
$15$		0			0
$16$	−4.50655			−1.12664
$17$		−	0.661056i		−	0.160330i	−0.996782	−	0.0801649i	$-0.974455\pi$
$17$		−	0.661056i		−	0.160330i	0.996782	−	0.0801649i	$-0.0255447\pi$
$18$		0			0
$19$			4.05658i			0.930643i	0.885142	+	0.465322i	$0.154061\pi$
$19$			4.05658i			0.930643i	−0.885142	+	0.465322i	$0.845939\pi$
$20$	2.09391	−	3.17921i	0.468212	−	0.710893i
$21$		0			0
$22$			6.04051i			1.28784i
$23$	−2.99686			−0.624888			−0.312444	−	0.949936i	$-0.601148\pi$
$23$	−2.99686			−0.624888			−0.312444	+	0.949936i	$0.601148\pi$
$24$		0			0
$25$	−1.97454	−	4.59360i	−0.394908	−	0.918721i
$26$	6.72642			1.31916
$27$		0			0
$28$	−4.46656	−	0.581726i	−0.844100	−	0.109936i
$29$		−	0.604649i		−	0.112280i	−0.998423	−	0.0561402i	$-0.982121\pi$
$29$		−	0.604649i		−	0.112280i	0.998423	−	0.0561402i	$-0.0178794\pi$
$30$		0			0
$31$			1.99580i			0.358456i	0.983808	+	0.179228i	$0.0573599\pi$
$31$			1.99580i			0.358456i	−0.983808	+	0.179228i	$0.942640\pi$
$32$	7.52636			1.33048
$33$		0			0
$34$			1.27199i			0.218144i
$35$	−3.86493	+	4.47910i	−0.653293	+	0.757105i
$36$		0			0
$37$			8.98387i			1.47694i	0.674287	+	0.738469i	$0.264451\pi$
$37$			8.98387i			1.47694i	−0.674287	+	0.738469i	$0.735549\pi$
$38$		−	7.80558i		−	1.26623i
$39$		0			0
$40$	0.704164	−	1.06914i	0.111338	−	0.169046i
$41$	−2.09391			−0.327013			−0.163507	−	0.986542i	$-0.552281\pi$
$41$	−2.09391			−0.327013			−0.163507	+	0.986542i	$0.552281\pi$
$42$		0			0
$43$		−	8.55335i		−	1.30437i	−0.758058	−	0.652187i	$-0.773852\pi$
$43$		−	8.55335i		−	1.30437i	0.758058	−	0.652187i	$-0.226148\pi$
$44$		−	5.34448i		−	0.805710i
$45$		0			0
$46$	5.76649			0.850222
$47$			6.12795i			0.893854i	0.894570	+	0.446927i	$0.147482\pi$
$47$			6.12795i			0.893854i	−0.894570	+	0.446927i	$0.852518\pi$
$48$		0			0
$49$	6.76649	+	1.79295i	0.966641	+	0.256136i
$50$	3.79936	+	8.83891i	0.537311	+	1.25001i
$51$		0			0
$52$	−5.95135			−0.825304
$53$	5.42119			0.744658			0.372329	−	0.928101i	$-0.378559\pi$
$53$	5.42119			0.744658			0.372329	+	0.928101i	$0.378559\pi$
$54$		0			0
$55$	−5.86235	−	3.86109i	−0.790479	−	0.520629i
$56$	−1.50207	−	0.195630i	−0.200722	−	0.0261421i
$57$		0			0
$58$			1.16345i			0.152769i
$59$	−5.81619			−0.757204			−0.378602	−	0.925560i	$-0.623595\pi$
$59$	−5.81619			−0.757204			−0.378602	+	0.925560i	$0.623595\pi$
$60$		0			0
$61$			4.13408i			0.529315i	0.964342	+	0.264658i	$0.0852589\pi$
$61$			4.13408i			0.529315i	−0.964342	+	0.264658i	$0.914741\pi$
$62$		−	3.84027i		−	0.487714i
$63$		0			0
$64$	−5.46894			−0.683618
$65$	−4.29952	+	6.52803i	−0.533290	+	0.809702i
$66$		0			0
$67$			10.7638i			1.31500i	0.753453	+	0.657502i	$0.228387\pi$
$67$			10.7638i			1.31500i	−0.753453	+	0.657502i	$0.771613\pi$
$68$		−	1.12542i		−	0.136477i
$69$		0			0
$70$	7.43682	−	8.61857i	0.888870	−	1.03012i
$71$		−	10.5090i		−	1.24719i	−0.781746	−	0.623597i	$-0.785671\pi$
$71$		−	10.5090i		−	1.24719i	0.781746	−	0.623597i	$-0.214329\pi$
$72$		0			0
$73$	2.64580			0.309667			0.154834	−	0.987941i	$-0.450516\pi$
$73$	2.64580			0.309667			0.154834	+	0.987941i	$0.450516\pi$
$74$		−	17.2866i		−	2.00952i
$75$		0			0
$76$			6.90616i			0.792191i
$77$	−1.07268	+	8.23617i	−0.122243	+	0.938599i
$78$		0			0
$79$	−10.1581			−1.14287			−0.571437	−	0.820646i	$-0.693614\pi$
$79$	−10.1581			−1.14287			−0.571437	+	0.820646i	$0.693614\pi$
$80$	−5.54275	+	8.41564i	−0.619698	+	0.940897i
$81$		0			0
$82$	4.02905			0.444934
$83$			14.4489i			1.58597i	0.609240	+	0.792986i	$0.291475\pi$
$83$			14.4489i			1.58597i	−0.609240	+	0.792986i	$0.708525\pi$
$84$		0			0
$85$	−1.23447	−	0.813054i	−0.133897	−	0.0881881i
$86$			16.4582i			1.77473i
$87$		0			0
$88$		−	1.79731i		−	0.191593i
$89$	−11.6461			−1.23449			−0.617245	−	0.786771i	$-0.711751\pi$
$89$	−11.6461			−1.23449			−0.617245	+	0.786771i	$0.711751\pi$
$90$		0			0
$91$	9.17140	+	1.19449i	0.961424	+	0.125216i
$92$	−5.10202			−0.531923
$93$		0			0
$94$		−	11.7913i		−	1.21618i
$95$	7.57535	+	4.98931i	0.777215	+	0.511893i
$96$		0			0
$97$	−7.70280			−0.782101			−0.391050	−	0.920369i	$-0.627888\pi$
$97$	−7.70280			−0.782101			−0.391050	+	0.920369i	$0.627888\pi$
$98$	−13.0199	−	3.44995i	−1.31521	−	0.348498i
$99$		0			0
$100$	−3.36157	−	7.82042i	−0.336157	−	0.782042i
$101$	−14.6503			−1.45776			−0.728879	−	0.684643i	$-0.759958\pi$
$101$	−14.6503			−1.45776			−0.728879	+	0.684643i	$0.759958\pi$
$102$		0			0
$103$	−18.3995			−1.81296			−0.906480	−	0.422248i	$-0.861241\pi$
$103$	−18.3995			−1.81296			−0.906480	+	0.422248i	$0.861241\pi$
$104$	−2.00139			−0.196253
$105$		0			0
$106$	−10.4313			−1.01318
$107$	−15.0527			−1.45520			−0.727601	−	0.686001i	$-0.759365\pi$
$107$	−15.0527			−1.45520			−0.727601	+	0.686001i	$0.759365\pi$
$108$		0			0
$109$	0.404916			0.0387839			0.0193920	−	0.999812i	$-0.493827\pi$
$109$	0.404916			0.0387839			0.0193920	+	0.999812i	$0.493827\pi$
$110$	11.2802	+	7.42941i	1.07552	+	0.708367i
$111$		0			0
$112$	11.8234	+	1.53988i	1.11720	+	0.145505i
$113$	7.73297			0.727456			0.363728	−	0.931505i	$-0.381504\pi$
$113$	7.73297			0.727456			0.363728	+	0.931505i	$0.381504\pi$
$114$		0			0
$115$	−3.68593	+	5.59640i	−0.343715	+	0.521867i
$116$		−	1.02939i		−	0.0955764i
$117$		0			0
$118$	11.1914			1.03025
$119$	−0.225881	+	1.73434i	−0.0207065	+	0.158987i
$120$		0			0
$121$	1.14498			0.104089
$122$		−	7.95471i		−	0.720186i
$123$		0			0
$124$			3.39776i			0.305128i
$125$	−11.0067	−	1.96252i	−0.984474	−	0.175533i
$126$		0			0
$127$			22.3821i			1.98609i	0.117719	+	0.993047i	$0.462442\pi$
$127$			22.3821i			1.98609i	−0.117719	+	0.993047i	$0.537558\pi$
$128$	−4.52950			−0.400355
$129$		0			0
$130$	8.27304	−	12.5611i	0.725593	−	1.10168i
$131$	−6.36047			−0.555717			−0.277858	−	0.960622i	$-0.589625\pi$
$131$	−6.36047			−0.555717			−0.277858	+	0.960622i	$0.589625\pi$
$132$		0			0
$133$	1.38612	−	10.6428i	0.120192	−	0.922849i
$134$		−	20.7114i		−	1.78919i
$135$		0			0
$136$		−	0.378470i		−	0.0324536i
$137$	20.7166			1.76994			0.884970	−	0.465647i	$-0.154178\pi$
$137$	20.7166			1.76994			0.884970	+	0.465647i	$0.154178\pi$
$138$		0			0
$139$			20.5176i			1.74028i	0.492805	+	0.870140i	$0.335972\pi$
$139$			20.5176i			1.74028i	−0.492805	+	0.870140i	$0.664028\pi$
$140$	−6.57989	+	7.62547i	−0.556102	+	0.644470i
$141$		0			0
$142$			20.2213i			1.69693i
$143$			10.9741i			0.917698i
$144$		0			0
$145$	−1.12913	−	0.743676i	−0.0937696	−	0.0617589i
$146$	−5.09099			−0.421333
$147$		0			0
$148$			15.2947i			1.25721i
$149$			5.38831i			0.441427i	0.975339	+	0.220714i	$0.0708386\pi$
$149$			5.38831i			0.441427i	−0.975339	+	0.220714i	$0.929161\pi$
$150$		0			0
$151$	−2.54416			−0.207041			−0.103520	−	0.994627i	$-0.533011\pi$
$151$	−2.54416			−0.207041			−0.103520	+	0.994627i	$0.533011\pi$
$152$			2.32249i			0.188379i
$153$		0			0
$154$	2.06403	−	15.8478i	0.166324	−	1.27706i
$155$	3.72700	+	2.45469i	0.299360	+	0.197166i
$156$		0			0
$157$	8.03876			0.641563			0.320782	−	0.947153i	$-0.396054\pi$
$157$	8.03876			0.641563			0.320782	+	0.947153i	$0.396054\pi$
$158$	19.5460			1.55499
$159$		0			0
$160$	9.25690	−	14.0549i	0.731822	−	1.11114i
$161$	7.86254	+	1.02402i	0.619655	+	0.0807040i
$162$		0			0
$163$		−	8.98387i		−	0.703671i	−0.936062	−	0.351835i	$-0.885558\pi$
$163$		−	8.98387i		−	0.703671i	0.936062	−	0.351835i	$-0.114442\pi$
$164$	−3.56479			−0.278363
$165$		0			0
$166$		−	27.8022i		−	2.15787i
$167$		−	13.7368i		−	1.06299i	−0.847062	−	0.531494i	$-0.821631\pi$
$167$		−	13.7368i		−	1.06299i	0.847062	−	0.531494i	$-0.178369\pi$
$168$		0			0
$169$	−0.779799			−0.0599845
$170$	2.37534	+	1.56446i	0.182180	+	0.119989i
$171$		0			0
$172$		−	14.5617i		−	1.11032i
$173$		−	10.2128i		−	0.776467i	−0.921561	−	0.388234i	$-0.873085\pi$
$173$		−	10.2128i		−	0.776467i	0.921561	−	0.388234i	$-0.126915\pi$
$174$		0			0
$175$	3.61076	+	12.7264i	0.272948	+	0.962029i
$176$			14.1473i			1.06639i
$177$		0			0
$178$	22.4093			1.67964
$179$		−	22.6310i		−	1.69152i	−0.533561	−	0.845761i	$-0.679147\pi$
$179$		−	22.6310i		−	1.69152i	0.533561	−	0.845761i	$-0.320853\pi$
$180$		0			0
$181$		−	17.9861i		−	1.33690i	−0.743758	−	0.668449i	$-0.766958\pi$
$181$		−	17.9861i		−	1.33690i	0.743758	−	0.668449i	$-0.233042\pi$
$182$	−17.6474	−	2.29840i	−1.30811	−	0.170369i
$183$		0			0
$184$	−1.71577			−0.126488
$185$	16.7767	+	11.0495i	1.23345	+	0.812378i
$186$		0			0
$187$	−2.07523			−0.151756
$188$			10.4326i			0.760874i
$189$		0			0
$190$	−14.5763	−	9.60032i	−1.05748	−	0.696481i
$191$			21.8465i			1.58076i	0.612620	+	0.790378i	$0.290116\pi$
$191$			21.8465i			1.58076i	−0.612620	+	0.790378i	$0.709884\pi$
$192$		0			0
$193$		−	20.5848i		−	1.48173i	−0.671655	−	0.740864i	$-0.734416\pi$
$193$		−	20.5848i		−	1.48173i	0.671655	−	0.740864i	$-0.265584\pi$
$194$	14.8215			1.06413
$195$		0			0
$196$	11.5197	+	3.05242i	0.822833	+	0.218030i
$197$	8.02652			0.571866			0.285933	−	0.958250i	$-0.407697\pi$
$197$	8.02652			0.571866			0.285933	+	0.958250i	$0.407697\pi$
$198$		0			0
$199$		−	1.01886i		−	0.0722252i	−0.999348	−	0.0361126i	$-0.988503\pi$
$199$		−	1.01886i		−	0.0722252i	0.999348	−	0.0361126i	$-0.0114975\pi$
$200$	−1.13047	−	2.62995i	−0.0799363	−	0.185965i
$201$		0			0
$202$	28.1897			1.98342
$203$	−0.206607	+	1.58635i	−0.0145010	+	0.111340i
$204$		0			0
$205$	−2.57536	+	3.91021i	−0.179871	+	0.273101i
$206$	35.4040			2.46671
$207$		0			0
$208$	15.7537			1.09233
$209$	12.7347			0.880878
$210$		0			0
$211$	−18.5518			−1.27716			−0.638580	−	0.769556i	$-0.720478\pi$
$211$	−18.5518			−1.27716			−0.638580	+	0.769556i	$0.720478\pi$
$212$	9.22935			0.633875
$213$		0			0
$214$	28.9641			1.97994
$215$	−15.9727	−	10.5200i	−1.08933	−	0.717460i
$216$		0			0
$217$	0.681959	−	5.23616i	0.0462944	−	0.355454i
$218$	−0.779130			−0.0527694
$219$		0			0
$220$	−9.98040	−	6.57334i	−0.672878	−	0.443174i
$221$			2.31088i			0.155447i
$222$		0			0
$223$	0.711317			0.0476333			0.0238167	−	0.999716i	$-0.492418\pi$
$223$	0.711317			0.0476333			0.0238167	+	0.999716i	$0.492418\pi$
$224$	−19.7461	−	2.57174i	−1.31934	−	0.171831i
$225$		0			0
$226$	−14.8796			−0.989776
$227$		−	27.6259i		−	1.83359i	−0.399353	−	0.916797i	$-0.630765\pi$
$227$		−	27.6259i		−	1.83359i	0.399353	−	0.916797i	$-0.369235\pi$
$228$		0			0
$229$		−	19.0281i		−	1.25741i	−0.777644	−	0.628705i	$-0.783585\pi$
$229$		−	19.0281i		−	1.25741i	0.777644	−	0.628705i	$-0.216415\pi$
$230$	7.09238	−	10.7685i	0.467658	−	0.710052i
$231$		0			0
$232$		−	0.346176i		−	0.0227275i
$233$	−18.7201			−1.22639			−0.613197	−	0.789930i	$-0.710117\pi$
$233$	−18.7201			−1.22639			−0.613197	+	0.789930i	$0.710117\pi$
$234$		0			0
$235$	11.4435	+	7.53696i	0.746490	+	0.491657i
$236$	−9.90182			−0.644554
$237$		0			0
$238$	0.434636	−	3.33718i	0.0281732	−	0.216317i
$239$		−	13.0561i		−	0.844526i	−0.906473	−	0.422263i	$-0.861236\pi$
$239$		−	13.0561i		−	0.844526i	0.906473	−	0.422263i	$-0.138764\pi$
$240$		0			0
$241$		−	1.99580i		−	0.128561i	−0.997932	−	0.0642803i	$-0.979525\pi$
$241$		−	1.99580i		−	0.128561i	0.997932	−	0.0642803i	$-0.0204752\pi$
$242$	−2.20315			−0.141624
$243$		0			0
$244$			7.03810i			0.450568i
$245$	11.6705	−	10.4307i	0.745601	−	0.666392i
$246$		0			0
$247$		−	14.1807i		−	0.902299i
$248$			1.14264i			0.0725577i
$249$		0			0
$250$	21.1789	+	3.77623i	1.33947	+	0.238830i
$251$	29.7453			1.87751			0.938753	−	0.344592i	$-0.111983\pi$
$251$	29.7453			1.87751			0.938753	+	0.344592i	$0.111983\pi$
$252$		0			0
$253$			9.40795i			0.591473i
$254$		−	43.0672i		−	2.70228i
$255$		0			0
$256$	19.6535			1.22834
$257$			15.6886i			0.978631i	0.872107	+	0.489315i	$0.162753\pi$
$257$			15.6886i			0.978631i	−0.872107	+	0.489315i	$0.837247\pi$
$258$		0			0
$259$	3.06977	−	23.5700i	0.190746	−	1.46457i
$260$	−7.31975	+	11.1137i	−0.453952	+	0.689242i
$261$		0			0
$262$	12.2387			0.756107
$263$	−2.38808			−0.147255			−0.0736276	−	0.997286i	$-0.523458\pi$
$263$	−2.38808			−0.147255			−0.0736276	+	0.997286i	$0.523458\pi$
$264$		0			0
$265$	6.66769	−	10.1237i	0.409593	−	0.621892i
$266$	−2.66715	+	20.4787i	−0.163533	+	1.25563i
$267$		0			0
$268$			18.3249i			1.11937i
$269$	14.4720			0.882371			0.441186	−	0.897416i	$-0.354558\pi$
$269$	14.4720			0.882371			0.441186	+	0.897416i	$0.354558\pi$
$270$		0			0
$271$			23.6328i			1.43559i	0.696254	+	0.717796i	$0.254849\pi$
$271$			23.6328i			1.43559i	−0.696254	+	0.717796i	$0.745151\pi$
$272$			2.97909i			0.180634i
$273$		0			0
$274$	−39.8625			−2.40818
$275$	−14.4206	+	6.19861i	−0.869593	+	0.373790i
$276$		0			0
$277$			16.1640i			0.971200i	0.874181	+	0.485600i	$0.161399\pi$
$277$			16.1640i			0.971200i	−0.874181	+	0.485600i	$0.838601\pi$
$278$		−	39.4795i		−	2.36782i
$279$		0			0
$280$	−2.21276	+	2.56439i	−0.132238	+	0.153251i
$281$		−	6.17286i		−	0.368242i	−0.982904	−	0.184121i	$-0.941056\pi$
$281$		−	6.17286i		−	0.368242i	0.982904	−	0.184121i	$-0.0589439\pi$
$282$		0			0
$283$	−9.98040			−0.593273			−0.296637	−	0.954990i	$-0.595865\pi$
$283$	−9.98040			−0.593273			−0.296637	+	0.954990i	$0.595865\pi$
$284$		−	17.8912i		−	1.06165i
$285$		0			0
$286$		−	21.1161i		−	1.24862i
$287$	5.49356	+	0.715482i	0.324275	+	0.0422336i
$288$		0			0
$289$	16.5630			0.974294
$290$	2.17266	+	1.43096i	0.127583	+	0.0840291i
$291$		0			0
$292$	4.50436			0.263598
$293$		−	4.09686i		−	0.239341i	−0.992814	−	0.119671i	$-0.961816\pi$
$293$		−	4.09686i		−	0.239341i	0.992814	−	0.119671i	$-0.0381839\pi$
$294$		0			0
$295$	−7.15352	+	10.8613i	−0.416494	+	0.632369i
$296$			5.14348i			0.298958i
$297$		0			0
$298$		−	10.3681i		−	0.600606i
$299$	10.4762			0.605856
$300$		0			0
$301$	−2.92266	+	22.4405i	−0.168459	+	1.29345i
$302$	4.89542			0.281700
$303$		0			0
$304$		−	18.2812i		−	1.04850i
$305$	7.72008	+	5.08464i	0.442051	+	0.291146i
$306$		0			0
$307$	−14.8966			−0.850196			−0.425098	−	0.905147i	$-0.639760\pi$
$307$	−14.8966			−0.850196			−0.425098	+	0.905147i	$0.639760\pi$
$308$	−1.82619	+	14.0217i	−0.104057	+	0.798962i
$309$		0			0
$310$	−7.17140	−	4.72326i	−0.407308	−	0.268263i
$311$	−2.00810			−0.113869			−0.0569344	−	0.998378i	$-0.518133\pi$
$311$	−2.00810			−0.113869			−0.0569344	+	0.998378i	$0.518133\pi$
$312$		0			0
$313$	16.9790			0.959712			0.479856	−	0.877347i	$-0.340689\pi$
$313$	16.9790			0.959712			0.479856	+	0.877347i	$0.340689\pi$
$314$	−15.4680			−0.872910
$315$		0			0
$316$	−17.2937			−0.972848
$317$	−21.9597			−1.23338			−0.616689	−	0.787207i	$-0.711526\pi$
$317$	−21.9597			−1.23338			−0.616689	+	0.787207i	$0.711526\pi$
$318$		0			0
$319$	−1.89816			−0.106276
$320$	−6.72642	+	10.2128i	−0.376019	+	0.570915i
$321$		0			0
$322$	−15.1289	−	1.97039i	−0.843101	−	0.109806i
$323$	2.68163			0.149210
$324$		0			0
$325$	6.90248	+	16.0580i	0.382880	+	0.890740i
$326$			17.2866i			0.957414i
$327$		0			0
$328$	−1.19881			−0.0661932
$329$	2.09391	−	16.0773i	0.115441	−	0.886368i
$330$		0			0
$331$	29.6968			1.63228			0.816142	−	0.577852i	$-0.196109\pi$
$331$	29.6968			1.63228			0.816142	+	0.577852i	$0.196109\pi$
$332$			24.5986i			1.35003i
$333$		0			0
$334$			26.4321i			1.44630i
$335$	20.1005	+	13.2387i	1.09821	+	0.723308i
$336$		0			0
$337$		−	1.34939i		−	0.0735059i	−0.999324	−	0.0367530i	$-0.988299\pi$
$337$		−	1.34939i		−	0.0735059i	0.999324	−	0.0367530i	$-0.0117015\pi$
$338$	1.50047			0.0816149
$339$		0			0
$340$	−2.10164	−	1.38419i	−0.113977	−	0.0750682i
$341$	6.26534			0.339287
$342$		0			0
$343$	−17.1399	−	7.01606i	−0.925466	−	0.378832i
$344$		−	4.89700i		−	0.264028i
$345$		0			0
$346$			19.6513i			1.05646i
$347$	−24.1372			−1.29575			−0.647876	−	0.761746i	$-0.724343\pi$
$347$	−24.1372			−1.29575			−0.647876	+	0.761746i	$0.724343\pi$
$348$		0			0
$349$			29.7146i			1.59059i	0.606225	+	0.795293i	$0.292683\pi$
$349$			29.7146i			1.59059i	−0.606225	+	0.795293i	$0.707317\pi$
$350$	−6.94775	−	24.4879i	−0.371373	−	1.30894i
$351$		0			0
$352$		−	23.6273i		−	1.25934i
$353$		−	9.13010i		−	0.485946i	−0.970033	−	0.242973i	$-0.921877\pi$
$353$		−	9.13010i		−	0.485946i	0.970033	−	0.242973i	$-0.0781227\pi$
$354$		0			0
$355$	−19.6248	−	12.9254i	−1.04158	−	0.686009i
$356$	−19.8271			−1.05083
$357$		0			0
$358$			43.5461i			2.30148i
$359$			11.4431i			0.603944i	0.953317	+	0.301972i	$0.0976449\pi$
$359$			11.4431i			0.603944i	−0.953317	+	0.301972i	$0.902355\pi$
$360$		0			0
$361$	2.54416			0.133903
$362$			34.6085i			1.81898i
$363$		0			0
$364$	15.6139	+	2.03356i	0.818392	+	0.106588i
$365$	3.25415	−	4.94083i	0.170330	−	0.258615i
$366$		0			0
$367$	−31.8191			−1.66094			−0.830471	−	0.557061i	$-0.811929\pi$
$367$	−31.8191			−1.66094			−0.830471	+	0.557061i	$0.811929\pi$
$368$	13.5055			0.704023
$369$		0			0
$370$	−32.2813	−	21.2613i	−1.67823	−	1.10532i
$371$	−14.2230	−	1.85241i	−0.738422	−	0.0961722i
$372$		0			0
$373$		−	15.0739i		−	0.780498i	−0.920709	−	0.390249i	$-0.872389\pi$
$373$		−	15.0739i		−	0.780498i	0.920709	−	0.390249i	$-0.127611\pi$
$374$	3.99312			0.206479
$375$		0			0
$376$			3.50840i			0.180932i
$377$			2.11369i			0.108861i
$378$		0			0
$379$	−19.9058			−1.02249			−0.511246	−	0.859434i	$-0.670816\pi$
$379$	−19.9058			−1.02249			−0.511246	+	0.859434i	$0.670816\pi$
$380$	12.8967	+	8.49410i	0.661588	+	0.435738i
$381$		0			0
$382$		−	42.0365i		−	2.15077i
$383$		−	17.3312i		−	0.885584i	−0.896624	−	0.442792i	$-0.853988\pi$
$383$		−	17.3312i		−	0.885584i	0.896624	−	0.442792i	$-0.146012\pi$
$384$		0			0
$385$	14.0611	+	12.1331i	0.716619	+	0.618358i
$386$			39.6089i			2.01604i
$387$		0			0
$388$	−13.1137			−0.665747
$389$			8.09249i			0.410305i	0.978730	+	0.205153i	$0.0657691\pi$
$389$			8.09249i			0.410305i	−0.978730	+	0.205153i	$0.934231\pi$
$390$		0			0
$391$			1.98109i			0.100188i
$392$	3.87397	+	1.02651i	0.195665	+	0.0518464i
$393$		0			0
$394$	−15.4444			−0.778080
$395$	−12.4937	+	18.9695i	−0.628629	+	0.954457i
$396$		0			0
$397$	28.5579			1.43328			0.716641	−	0.697442i	$-0.245679\pi$
$397$	28.5579			1.43328			0.716641	+	0.697442i	$0.245679\pi$
$398$			1.96047i			0.0982695i
$399$		0			0
$400$	8.89836	+	20.7013i	0.444918	+	1.03507i
$401$		−	29.0771i		−	1.45204i	−0.687673	−	0.726020i	$-0.741368\pi$
$401$		−	29.0771i		−	1.45204i	0.687673	−	0.726020i	$-0.258632\pi$
$402$		0			0
$403$		−	6.97679i		−	0.347538i
$404$	−24.9415			−1.24089
$405$		0			0
$406$	0.397548	−	3.05242i	0.0197300	−	0.151489i
$407$	28.2028			1.39796
$408$		0			0
$409$		−	24.4967i		−	1.21128i	−0.795738	−	0.605641i	$-0.792917\pi$
$409$		−	24.4967i		−	1.21128i	0.795738	−	0.605641i	$-0.207083\pi$
$410$	4.95545	−	7.52394i	0.244732	−	0.371581i
$411$		0			0
$412$	−31.3244			−1.54324
$413$	15.2593	+	1.98738i	0.750862	+	0.0977925i
$414$		0			0
$415$	26.9822	+	17.7711i	1.32450	+	0.872351i
$416$	−26.3102			−1.28996
$417$		0			0
$418$	−24.5038			−1.19852
$419$	−19.2966			−0.942699			−0.471350	−	0.881947i	$-0.656233\pi$
$419$	−19.2966			−0.942699			−0.471350	+	0.881947i	$0.656233\pi$
$420$		0			0
$421$	−17.6837			−0.861850			−0.430925	−	0.902388i	$-0.641813\pi$
$421$	−17.6837			−0.861850			−0.430925	+	0.902388i	$0.641813\pi$
$422$	35.6970			1.73770
$423$		0			0
$424$	3.10376			0.150732
$425$	−3.03663	+	1.30528i	−0.147298	+	0.0633154i
$426$		0			0
$427$	1.41261	−	10.8462i	0.0683608	−	0.524882i
$428$	−25.6266			−1.23871
$429$		0			0
$430$	30.7344	+	20.2424i	1.48214	+	0.976176i
$431$		−	17.4541i		−	0.840733i	−0.907354	−	0.420367i	$-0.861901\pi$
$431$		−	17.4541i		−	0.840733i	0.907354	−	0.420367i	$-0.138099\pi$
$432$		0			0
$433$	−11.4152			−0.548580			−0.274290	−	0.961647i	$-0.588443\pi$
$433$	−11.4152			−0.548580			−0.274290	+	0.961647i	$0.588443\pi$
$434$	−1.31221	+	10.0753i	−0.0629881	+	0.483630i
$435$		0			0
$436$	0.689353			0.0330140
$437$		−	12.1570i		−	0.581548i
$438$		0			0
$439$			29.6077i			1.41310i	0.707664	+	0.706549i	$0.249749\pi$
$439$			29.6077i			1.41310i	−0.707664	+	0.706549i	$0.750251\pi$
$440$	−3.35633	−	2.21056i	−0.160007	−	0.105384i
$441$		0			0
$442$		−	4.44655i		−	0.211501i
$443$	16.1469			0.767164			0.383582	−	0.923507i	$-0.374690\pi$
$443$	16.1469			0.767164			0.383582	+	0.923507i	$0.374690\pi$
$444$		0			0
$445$	−14.3240	+	21.7483i	−0.679021	+	1.03097i
$446$	−1.36870			−0.0648098
$447$		0			0
$448$	14.3483	+	1.86872i	0.677893	+	0.0882889i
$449$			19.2784i			0.909803i	0.890542	+	0.454901i	$0.150325\pi$
$449$			19.2784i			0.909803i	−0.890542	+	0.454901i	$0.849675\pi$
$450$		0			0
$451$			6.57334i			0.309526i
$452$	13.1651			0.619232
$453$		0			0
$454$			53.1571i			2.49479i
$455$	13.5108	−	15.6578i	0.633396	−	0.734047i
$456$		0			0
$457$		−	21.3242i		−	0.997505i	−0.866745	−	0.498752i	$-0.833792\pi$
$457$		−	21.3242i		−	0.997505i	0.866745	−	0.498752i	$-0.166208\pi$
$458$			36.6134i			1.71083i
$459$		0			0
$460$	−6.27514	+	9.52764i	−0.292580	+	0.444228i
$461$	−16.7304			−0.779214			−0.389607	−	0.920981i	$-0.627389\pi$
$461$	−16.7304			−0.779214			−0.389607	+	0.920981i	$0.627389\pi$
$462$		0			0
$463$		−	0.715535i		−	0.0332537i	−0.999862	−	0.0166269i	$-0.994707\pi$
$463$		−	0.715535i		−	0.0332537i	0.999862	−	0.0166269i	$-0.00529274\pi$
$464$			2.72488i			0.126499i
$465$		0			0
$466$	36.0208			1.66863
$467$		−	3.40444i		−	0.157539i	−0.996893	−	0.0787694i	$-0.974901\pi$
$467$		−	3.40444i		−	0.157539i	0.996893	−	0.0787694i	$-0.0250991\pi$
$468$		0			0
$469$	3.67795	−	28.2398i	0.169832	−	1.30399i
$470$	−22.0193	−	14.5024i	−1.01567	−	0.668948i
$471$		0			0
$472$	−3.32991			−0.153271
$473$	−26.8513			−1.23462
$474$		0			0
$475$	18.6343	−	8.00987i	0.855001	−	0.367518i
$476$	−0.384553	+	2.95265i	−0.0176260	+	0.135334i
$477$		0			0
$478$			25.1222i			1.14906i
$479$	4.53739			0.207319			0.103659	−	0.994613i	$-0.466945\pi$
$479$	4.53739			0.207319			0.103659	+	0.994613i	$0.466945\pi$
$480$		0			0
$481$		−	31.4053i		−	1.43196i
$482$			3.84027i			0.174919i
$483$		0			0
$484$	1.94929			0.0886039
$485$	−9.47391	+	14.3844i	−0.430188	+	0.653161i
$486$		0			0
$487$		−	17.9439i		−	0.813116i	−0.913625	−	0.406558i	$-0.866729\pi$
$487$		−	17.9439i		−	0.813116i	0.913625	−	0.406558i	$-0.133271\pi$
$488$			2.36686i			0.107143i
$489$		0			0
$490$	−22.4561	+	20.0705i	−1.01446	+	0.906692i
$491$		−	20.0964i		−	0.906938i	−0.891272	−	0.453469i	$-0.850186\pi$
$491$		−	20.0964i		−	0.906938i	0.891272	−	0.453469i	$-0.149814\pi$
$492$		0			0
$493$	−0.399707			−0.0180019
$494$			27.2863i			1.22767i
$495$		0			0
$496$		−	8.99416i		−	0.403850i
$497$	−3.59091	+	27.5715i	−0.161074	+	1.23675i
$498$		0			0
$499$	18.8060			0.841873			0.420936	−	0.907090i	$-0.361702\pi$
$499$	18.8060			0.841873			0.420936	+	0.907090i	$0.361702\pi$
$500$	−18.7385	−	3.34110i	−0.838012	−	0.149419i
$501$		0			0
$502$	−57.2352			−2.55453
$503$			9.23004i			0.411547i	0.978600	+	0.205774i	$0.0659710\pi$
$503$			9.23004i			0.411547i	−0.978600	+	0.205774i	$0.934029\pi$
$504$		0			0
$505$	−18.0188	+	27.3583i	−0.801828	+	1.21743i
$506$		−	18.1026i		−	0.804757i
$507$		0			0
$508$			38.1047i			1.69062i
$509$	−10.4461			−0.463015			−0.231508	−	0.972833i	$-0.574366\pi$
$509$	−10.4461			−0.463015			−0.231508	+	0.972833i	$0.574366\pi$
$510$		0			0
$511$	−6.94150	−	0.904063i	−0.307074	−	0.0399934i
$512$	−28.7577			−1.27092
$513$		0			0
$514$		−	30.1877i		−	1.33152i
$515$	−22.6302	+	34.3597i	−0.997204	+	1.51407i
$516$		0			0
$517$	19.2373			0.846056
$518$	−5.90677	+	45.3529i	−0.259529	+	1.99269i
$519$		0			0
$520$	−2.46158	+	3.73745i	−0.107947	+	0.163898i
$521$	19.9427			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$521$	19.9427			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$522$		0			0
$523$	−7.65839			−0.334878			−0.167439	−	0.985882i	$-0.553550\pi$
$523$	−7.65839			−0.334878			−0.167439	+	0.985882i	$0.553550\pi$
$524$	−10.8284			−0.473042
$525$		0			0
$526$	4.59508			0.200355
$527$	1.31933			0.0574711
$528$		0			0
$529$	−14.0188			−0.609515
$530$	−12.8298	+	19.4797i	−0.557292	+	0.846145i
$531$		0			0
$532$	2.35982	−	18.1189i	0.102311	−	0.785556i
$533$	7.31975			0.317054
$534$		0			0
$535$	−18.5138	+	28.1098i	−0.800422	+	1.21529i
$536$			6.16251i			0.266180i
$537$		0			0
$538$	−27.8466			−1.20055
$539$	5.62856	−	21.2418i	0.242439	−	0.914950i
$540$		0			0
$541$	−38.6516			−1.66176			−0.830881	−	0.556450i	$-0.812163\pi$
$541$	−38.6516			−1.66176			−0.830881	+	0.556450i	$0.812163\pi$
$542$		−	45.4737i		−	1.95326i
$543$		0			0
$544$		−	4.97535i		−	0.213316i
$545$	0.498019	−	0.756150i	0.0213328	−	0.0323899i
$546$		0			0
$547$		−	4.29919i		−	0.183820i	−0.995767	−	0.0919099i	$-0.970703\pi$
$547$		−	4.29919i		−	0.183820i	0.995767	−	0.0919099i	$-0.0292972\pi$
$548$	35.2692			1.50663
$549$		0			0
$550$	27.7477	−	11.9272i	1.18317	−	0.508579i
$551$	2.45281			0.104493
$552$		0			0
$553$	26.6507	+	3.47099i	1.13330	+	0.147602i
$554$		−	31.1024i		−	1.32141i
$555$		0			0
$556$			34.9303i			1.48138i
$557$	−22.3874			−0.948587			−0.474293	−	0.880367i	$-0.657296\pi$
$557$	−22.3874			−0.948587			−0.474293	+	0.880367i	$0.657296\pi$
$558$		0			0
$559$			29.9003i			1.26465i
$560$	17.4175	−	20.1853i	0.736025	−	0.852984i
$561$		0			0
$562$			11.8777i			0.501030i
$563$		−	4.17615i		−	0.176004i	−0.996120	−	0.0880019i	$-0.971952\pi$
$563$		−	4.17615i		−	0.176004i	0.996120	−	0.0880019i	$-0.0280482\pi$
$564$		0			0
$565$	9.51102	−	14.4407i	0.400131	−	0.607526i
$566$	19.2041			0.807207
$567$		0			0
$568$		−	6.01667i		−	0.252454i
$569$			26.8177i			1.12426i	0.827050	+	0.562128i	$0.190017\pi$
$569$			26.8177i			1.12426i	−0.827050	+	0.562128i	$0.809983\pi$
$570$		0			0
$571$	−7.86812			−0.329271			−0.164635	−	0.986355i	$-0.552645\pi$
$571$	−7.86812			−0.329271			−0.164635	+	0.986355i	$0.552645\pi$
$572$			18.6829i			0.781171i
$573$		0			0
$574$	−10.5706	−	1.37671i	−0.441207	−	0.0574630i
$575$	5.91741	+	13.7664i	0.246773	+	0.574098i
$576$		0			0
$577$	22.7595			0.947491			0.473746	−	0.880662i	$-0.342902\pi$
$577$	22.7595			0.947491			0.473746	+	0.880662i	$0.342902\pi$
$578$	−31.8702			−1.32562
$579$		0			0
$580$	−1.92230	−	1.26608i	−0.0798194	−	0.0525710i
$581$	4.93715	−	37.9080i	0.204827	−	1.57269i
$582$		0			0
$583$		−	17.0186i		−	0.704838i
$584$	1.51478			0.0626821
$585$		0			0
$586$			7.88309i			0.325648i
$587$		−	24.9697i		−	1.03061i	−0.857007	−	0.515304i	$-0.827679\pi$
$587$		−	24.9697i		−	1.03061i	0.857007	−	0.515304i	$-0.172321\pi$
$588$		0			0
$589$	−8.09611			−0.333594
$590$	13.7646	−	20.8991i	0.566681	−	0.860400i
$591$		0			0
$592$		−	40.4863i		−	1.66398i
$593$		−	41.6715i		−	1.71124i	−0.517603	−	0.855621i	$-0.673176\pi$
$593$		−	41.6715i		−	1.71124i	0.517603	−	0.855621i	$-0.326824\pi$
$594$		0			0
$595$	2.96093	+	2.55494i	0.121386	+	0.104742i
$596$			9.17337i			0.375756i
$597$		0			0
$598$	−20.1581			−0.824328
$599$			16.6201i			0.679077i	0.940592	+	0.339539i	$0.110271\pi$
$599$			16.6201i			0.679077i	−0.940592	+	0.339539i	$0.889729\pi$
$600$		0			0
$601$		−	5.48113i		−	0.223580i	−0.993732	−	0.111790i	$-0.964342\pi$
$601$		−	5.48113i		−	0.223580i	0.993732	−	0.111790i	$-0.0356584\pi$
$602$	5.62371	−	43.1795i	0.229205	−	1.75987i
$603$		0			0
$604$	−4.33133			−0.176239
$605$	1.40825	−	2.13817i	0.0572535	−	0.0869289i
$606$		0			0
$607$	−19.8129			−0.804180			−0.402090	−	0.915600i	$-0.631716\pi$
$607$	−19.8129			−0.804180			−0.402090	+	0.915600i	$0.631716\pi$
$608$			30.5313i			1.23821i
$609$		0			0
$610$	−14.8548	−	9.78374i	−0.601454	−	0.396132i
$611$		−	21.4217i		−	0.866631i
$612$		0			0
$613$			17.3448i			0.700552i	0.936647	+	0.350276i	$0.113912\pi$
$613$			17.3448i			0.700552i	−0.936647	+	0.350276i	$0.886088\pi$
$614$	28.6638			1.15678
$615$		0			0
$616$	−0.614135	+	4.71540i	−0.0247442	+	0.189989i
$617$	−12.6138			−0.507813			−0.253906	−	0.967229i	$-0.581716\pi$
$617$	−12.6138			−0.507813			−0.253906	+	0.967229i	$0.581716\pi$
$618$		0			0
$619$		−	18.3018i		−	0.735612i	−0.929903	−	0.367806i	$-0.880109\pi$
$619$		−	18.3018i		−	0.735612i	0.929903	−	0.367806i	$-0.119891\pi$
$620$	6.34506	+	4.17901i	0.254824	+	0.167833i
$621$		0			0
$622$	3.86394			0.154930
$623$	30.5548	+	3.97946i	1.22415	+	0.159434i
$624$		0			0
$625$	−17.2024	+	18.1405i	−0.688096	+	0.725620i
$626$	−32.6707			−1.30578
$627$		0			0
$628$	13.6857			0.546117
$629$	5.93884			0.236797
$630$		0			0
$631$	14.7646			0.587771			0.293886	−	0.955841i	$-0.405052\pi$
$631$	14.7646			0.587771			0.293886	+	0.955841i	$0.405052\pi$
$632$	−5.81574			−0.231338
$633$		0			0
$634$	42.2543			1.67813
$635$	41.7969	+	27.5285i	1.65866	+	1.09243i
$636$		0			0
$637$	−23.6539	−	6.26769i	−0.937201	−	0.248335i
$638$	3.65239			0.144599
$639$		0			0
$640$	−5.57097	+	8.45850i	−0.220212	+	0.334351i
$641$			0.636092i			0.0251241i	0.999921	+	0.0125621i	$0.00399873\pi$
$641$			0.636092i			0.0251241i	−0.999921	+	0.0125621i	$0.996001\pi$
$642$		0			0
$643$	26.4634			1.04361			0.521807	−	0.853064i	$-0.325258\pi$
$643$	26.4634			1.04361			0.521807	+	0.853064i	$0.325258\pi$
$644$	13.3856	+	1.74335i	0.527468	+	0.0686976i
$645$		0			0
$646$	−5.15993			−0.203015
$647$		−	7.10184i		−	0.279202i	−0.990208	−	0.139601i	$-0.955418\pi$
$647$		−	7.10184i		−	0.279202i	0.990208	−	0.139601i	$-0.0445820\pi$
$648$		0			0
$649$			18.2586i			0.716713i
$650$	−13.2816	−	30.8985i	−0.520947	−	1.21194i
$651$		0			0
$652$		−	15.2947i		−	0.598985i
$653$	−14.4439			−0.565235			−0.282617	−	0.959233i	$-0.591203\pi$
$653$	−14.4439			−0.565235			−0.282617	+	0.959233i	$0.591203\pi$
$654$		0			0
$655$	−7.82294	+	11.8777i	−0.305667	+	0.464100i
$656$	9.43630			0.368426
$657$		0			0
$658$	−4.02905	+	30.9355i	−0.157069	+	1.20599i
$659$			27.4765i			1.07033i	0.844746	+	0.535167i	$0.179751\pi$
$659$			27.4765i			1.07033i	−0.844746	+	0.535167i	$0.820249\pi$
$660$		0			0
$661$		−	20.3876i		−	0.792987i	−0.918038	−	0.396493i	$-0.870227\pi$
$661$		−	20.3876i		−	0.792987i	0.918038	−	0.396493i	$-0.129773\pi$
$662$	−57.1419			−2.22088
$663$		0			0
$664$			8.27233i			0.321029i
$665$	−18.1698	−	15.6784i	−0.704595	−	0.607983i
$666$		0			0
$667$			1.81205i			0.0701627i
$668$		−	23.3864i		−	0.904847i
$669$		0			0
$670$	−38.6770	−	25.4736i	−1.49422	−	0.984131i
$671$	12.9780			0.501010
$672$		0			0
$673$		−	30.9355i		−	1.19248i	−0.802808	−	0.596238i	$-0.796662\pi$
$673$		−	30.9355i		−	1.19248i	0.802808	−	0.596238i	$-0.203338\pi$
$674$			2.59647i			0.100012i
$675$		0			0
$676$	−1.32758			−0.0510606
$677$			18.6143i			0.715407i	0.933835	+	0.357703i	$0.116440\pi$
$677$			18.6143i			0.715407i	−0.933835	+	0.357703i	$0.883560\pi$
$678$		0			0
$679$	20.2090	+	2.63203i	0.775551	+	0.101008i
$680$	−0.706764	−	0.465492i	−0.0271032	−	0.0178508i
$681$		0			0
$682$	−12.0556			−0.461634
$683$	−28.5767			−1.09346			−0.546729	−	0.837310i	$-0.684127\pi$
$683$	−28.5767			−1.09346			−0.546729	+	0.837310i	$0.684127\pi$
$684$		0			0
$685$	25.4800	−	38.6867i	0.973542	−	1.47814i
$686$	32.9801	+	13.5002i	1.25919	+	0.515438i
$687$		0			0
$688$			38.5461i			1.46956i
$689$	−18.9511			−0.721979
$690$		0			0
$691$			11.3878i			0.433211i	0.976259	+	0.216605i	$0.0694985\pi$
$691$			11.3878i			0.433211i	−0.976259	+	0.216605i	$0.930501\pi$
$692$		−	17.3869i		−	0.660951i
$693$		0			0
$694$	46.4442			1.76300
$695$	38.3150	+	25.2352i	1.45337	+	0.957227i
$696$		0			0
$697$			1.38419i			0.0524299i
$698$		−	57.1762i		−	2.16415i
$699$		0			0
$700$	6.14718	+	21.6662i	0.232341	+	0.818907i
$701$		−	36.3021i		−	1.37111i	−0.728020	−	0.685555i	$-0.759559\pi$
$701$		−	36.3021i		−	1.37111i	0.728020	−	0.685555i	$-0.240441\pi$
$702$		0			0
$703$	−36.4438			−1.37450
$704$			17.1685i			0.647062i
$705$		0			0
$706$			17.5679i			0.661178i
$707$	38.4364	+	5.00597i	1.44555	+	0.188269i
$708$		0			0
$709$	2.29733			0.0862782			0.0431391	−	0.999069i	$-0.486264\pi$
$709$	2.29733			0.0862782			0.0431391	+	0.999069i	$0.486264\pi$
$710$	37.7617	+	24.8708i	1.41717	+	0.933383i
$711$		0			0
$712$	−6.66769			−0.249882
$713$		−	5.98112i		−	0.223995i
$714$		0			0
$715$	20.4932	+	13.4974i	0.766404	+	0.504772i
$716$		−	38.5284i		−	1.43987i
$717$		0			0
$718$		−	22.0186i		−	0.821726i
$719$	22.2501			0.829789			0.414894	−	0.909870i	$-0.363819\pi$
$719$	22.2501			0.829789			0.414894	+	0.909870i	$0.363819\pi$
$720$		0			0
$721$	48.2729	+	6.28708i	1.79778	+	0.234143i
$722$	−4.89542			−0.182189
$723$		0			0
$724$		−	30.6206i		−	1.13801i
$725$	−2.77752	+	1.19390i	−0.103154	+	0.0443404i
$726$		0			0
$727$	−10.2920			−0.381709			−0.190855	−	0.981618i	$-0.561126\pi$
$727$	−10.2920			−0.381709			−0.190855	+	0.981618i	$0.561126\pi$
$728$	5.25084	+	0.683871i	0.194609	+	0.0253459i
$729$		0			0
$730$	−6.26156	+	9.50703i	−0.231751	+	0.351871i
$731$	−5.65425			−0.209130
$732$		0			0
$733$	19.9343			0.736291			0.368145	−	0.929768i	$-0.379993\pi$
$733$	19.9343			0.736291			0.368145	+	0.929768i	$0.379993\pi$
$734$	61.2256			2.25988
$735$		0			0
$736$	−22.5554			−0.831404
$737$	33.7904			1.24469
$738$		0			0
$739$	−20.9588			−0.770981			−0.385491	−	0.922712i	$-0.625968\pi$
$739$	−20.9588			−0.770981			−0.385491	+	0.922712i	$0.625968\pi$
$740$	28.5616	+	18.8114i	1.04995	+	0.691520i
$741$		0			0
$742$	27.3676	+	3.56436i	1.00470	+	0.130852i
$743$	−1.74974			−0.0641918			−0.0320959	−	0.999485i	$-0.510218\pi$
$743$	−1.74974			−0.0641918			−0.0320959	+	0.999485i	$0.510218\pi$
$744$		0			0
$745$	10.0623	+	6.62725i	0.368652	+	0.242804i
$746$			29.0049i			1.06194i
$747$		0			0
$748$	−3.53300			−0.129179
$749$	39.4922	+	5.14348i	1.44301	+	0.187939i
$750$		0			0
$751$	25.3616			0.925460			0.462730	−	0.886499i	$-0.346870\pi$
$751$	25.3616			0.925460			0.462730	+	0.886499i	$0.346870\pi$
$752$		−	27.6159i		−	1.00705i
$753$		0			0
$754$		−	4.06712i		−	0.148116i
$755$	−3.12914	+	4.75103i	−0.113881	+	0.172908i
$756$		0			0
$757$		−	30.7496i		−	1.11761i	−0.829299	−	0.558806i	$-0.811260\pi$
$757$		−	30.7496i		−	1.11761i	0.829299	−	0.558806i	$-0.188740\pi$
$758$	38.3023			1.39120
$759$		0			0
$760$	4.33707	+	2.85650i	0.157322	+	0.103616i
$761$	6.92782			0.251133			0.125567	−	0.992085i	$-0.459925\pi$
$761$	6.92782			0.251133			0.125567	+	0.992085i	$0.459925\pi$
$762$		0			0
$763$	−1.06234	−	0.138359i	−0.0384591	−	0.00500893i
$764$			37.1927i			1.34558i
$765$		0			0
$766$			33.3483i			1.20492i
$767$	20.3319			0.734142
$768$		0			0
$769$			21.9821i			0.792695i	0.918101	+	0.396347i	$0.129722\pi$
$769$			21.9821i			0.792695i	−0.918101	+	0.396347i	$0.870278\pi$
$770$	−27.0560	−	23.3462i	−0.975032	−	0.841338i
$771$		0			0
$772$		−	35.0448i		−	1.26129i
$773$			6.86090i			0.246769i	0.992359	+	0.123385i	$0.0393749\pi$
$773$			6.86090i			0.246769i	−0.992359	+	0.123385i	$0.960625\pi$
$774$		0			0
$775$	9.16790	−	3.94078i	0.329321	−	0.141557i
$776$	−4.41003			−0.158311
$777$		0			0
$778$		−	15.5714i		−	0.558261i
$779$		−	8.49410i		−	0.304333i
$780$		0			0
$781$	−32.9907			−1.18050
$782$		−	3.81197i		−	0.136316i
$783$		0			0
$784$	−30.4935	−	8.08003i	−1.08905	−	0.288572i
$785$	9.88712	−	15.0118i	0.352887	−	0.535793i
$786$		0			0
$787$	38.6576			1.37800			0.688998	−	0.724763i	$-0.258051\pi$
$787$	38.6576			1.37800			0.688998	+	0.724763i	$0.258051\pi$
$788$	13.6648			0.486789
$789$		0			0
$790$	24.0402	−	36.5006i	0.855311	−	1.29863i
$791$	−20.2882	−	2.64233i	−0.721364	−	0.0939506i
$792$		0			0
$793$		−	14.4517i		−	0.513194i
$794$	−54.9506			−1.95012
$795$		0			0
$796$		−	1.73457i		−	0.0614802i
$797$		−	19.6764i		−	0.696974i	−0.937314	−	0.348487i	$-0.886696\pi$
$797$		−	19.6764i		−	0.696974i	0.937314	−	0.348487i	$-0.113304\pi$
$798$		0			0
$799$	4.05092			0.143311
$800$	−14.8611	−	34.5731i	−0.525419	−	1.22234i
$801$		0			0
$802$			55.9495i			1.97564i
$803$		−	8.30588i		−	0.293108i
$804$		0			0
$805$	11.5827	−	13.4232i	0.408235	−	0.473106i
$806$			13.4246i			0.472860i
$807$		0			0
$808$	−8.38763			−0.295076
$809$			44.6802i			1.57087i	0.618944	+	0.785435i	$0.287561\pi$
$809$			44.6802i			1.57087i	−0.618944	+	0.785435i	$0.712439\pi$
$810$		0			0
$811$		−	40.7880i		−	1.43226i	−0.697967	−	0.716130i	$-0.745912\pi$
$811$		−	40.7880i		−	1.43226i	0.697967	−	0.716130i	$-0.254088\pi$
$812$	−0.351740	+	2.70070i	−0.0123436	+	0.0947759i
$813$		0			0
$814$	−54.2672			−1.90206
$815$	−16.7767	−	11.0495i	−0.587662	−	0.387049i
$816$		0			0
$817$	34.6974			1.21391
$818$			47.1359i			1.64807i
$819$		0			0
$820$	−4.38444	+	6.65697i	−0.153111	+	0.232471i
$821$		−	24.0078i		−	0.837880i	−0.908014	−	0.418940i	$-0.862402\pi$
$821$		−	24.0078i		−	0.837880i	0.908014	−	0.418940i	$-0.137598\pi$
$822$		0			0
$823$			6.66793i			0.232429i	0.993224	+	0.116215i	$0.0370761\pi$
$823$			6.66793i			0.232429i	−0.993224	+	0.116215i	$0.962924\pi$
$824$	−10.5342			−0.366975
$825$		0			0
$826$	−29.3616	−	3.82407i	−1.02162	−	0.133056i
$827$	−2.45651			−0.0854211			−0.0427105	−	0.999087i	$-0.513599\pi$
$827$	−2.45651			−0.0854211			−0.0427105	+	0.999087i	$0.513599\pi$
$828$		0			0
$829$		−	22.7766i		−	0.791064i	−0.918452	−	0.395532i	$-0.870560\pi$
$829$		−	22.7766i		−	0.791064i	0.918452	−	0.395532i	$-0.129440\pi$
$830$	−51.9185	−	34.1948i	−1.80212	−	1.18692i
$831$		0			0
$832$	19.1180			0.662798
$833$	1.18524	−	4.47303i	0.0410662	−	0.154981i
$834$		0			0
$835$	−25.6525	−	16.8954i	−0.887741	−	0.584688i
$836$	21.6803			0.749829
$837$		0			0
$838$	37.1300			1.28264
$839$	6.82825			0.235738			0.117869	−	0.993029i	$-0.462394\pi$
$839$	6.82825			0.235738			0.117869	+	0.993029i	$0.462394\pi$
$840$		0			0
$841$	28.6344			0.987393
$842$	34.0266			1.17263
$843$		0			0
$844$	−31.5837			−1.08716
$845$	−0.959099	+	1.45621i	−0.0329940	+	0.0500953i
$846$		0			0
$847$	−3.00397	−	0.391238i	−0.103218	−	0.0134431i
$848$	−24.4309			−0.838960
$849$		0			0
$850$	5.84302	−	2.51159i	0.200414	−	0.0861469i
$851$		−	26.9234i		−	0.922922i
$852$		0			0
$853$	46.5327			1.59325			0.796625	−	0.604474i	$-0.206617\pi$
$853$	46.5327			1.59325			0.796625	+	0.604474i	$0.206617\pi$
$854$	−2.71810	+	20.8699i	−0.0930116	+	0.714154i
$855$		0			0
$856$	−8.61803			−0.294558
$857$			41.7342i			1.42561i	0.701361	+	0.712806i	$0.252576\pi$
$857$			41.7342i			1.42561i	−0.701361	+	0.712806i	$0.747424\pi$
$858$		0			0
$859$		−	29.6077i		−	1.01020i	−0.863060	−	0.505101i	$-0.831455\pi$
$859$		−	29.6077i		−	1.01020i	0.863060	−	0.505101i	$-0.168545\pi$
$860$	−27.1929	−	17.9099i	−0.927270	−	0.610723i
$861$		0			0
$862$			33.5847i			1.14390i
$863$	−18.3099			−0.623276			−0.311638	−	0.950201i	$-0.600878\pi$
$863$	−18.3099			−0.623276			−0.311638	+	0.950201i	$0.600878\pi$
$864$		0			0
$865$	−19.0717	−	12.5611i	−0.648457	−	0.427090i
$866$	21.9649			0.746397
$867$		0			0
$868$	1.16101	−	8.91434i	0.0394071	−	0.302572i
$869$			31.8890i			1.08176i
$870$		0			0
$871$		−	37.6274i		−	1.27495i
$872$	0.231824			0.00785055
$873$		0			0
$874$			23.3922i			0.791253i
$875$	28.2066	+	8.90982i	0.953559	+	0.301207i
$876$		0			0
$877$			32.6607i			1.10287i	0.834217	+	0.551436i	$0.185920\pi$
$877$			32.6607i			1.10287i	−0.834217	+	0.551436i	$0.814080\pi$
$878$		−	56.9704i		−	1.92266i
$879$		0			0
$880$	26.4190	+	17.4002i	0.890583	+	0.586560i
$881$	−43.5574			−1.46749			−0.733743	−	0.679428i	$-0.762228\pi$
$881$	−43.5574			−1.46749			−0.733743	+	0.679428i	$0.762228\pi$
$882$		0			0
$883$			17.3274i			0.583115i	0.956553	+	0.291557i	$0.0941735\pi$
$883$			17.3274i			0.583115i	−0.956553	+	0.291557i	$0.905827\pi$
$884$			3.93418i			0.132321i
$885$		0			0
$886$	−31.0696			−1.04380
$887$			34.1745i			1.14747i	0.819042	+	0.573734i	$0.194505\pi$
$887$			34.1745i			1.14747i	−0.819042	+	0.573734i	$0.805495\pi$
$888$		0			0
$889$	7.64792	−	58.7216i	0.256503	−	1.96946i
$890$	27.5618	−	41.8476i	0.923875	−	1.40273i
$891$		0			0
$892$	1.21099			0.0405469
$893$	−24.8585			−0.831859
$894$		0			0
$895$	−42.2617	−	27.8346i	−1.41265	−	0.930408i
$896$	11.8836	+	1.54772i	0.397002	+	0.0517057i
$897$		0			0
$898$		−	37.0950i		−	1.23788i
$899$	1.20676			0.0402476
$900$		0			0
$901$		−	3.58371i		−	0.119391i
$902$		−	12.6483i		−	0.421141i
$903$		0			0
$904$	4.42730			0.147250
$905$	−33.5877	−	22.1217i	−1.11649	−	0.735350i
$906$		0			0
$907$			10.8417i			0.359992i	0.983667	+	0.179996i	$0.0576085\pi$
$907$			10.8417i			0.359992i	−0.983667	+	0.179996i	$0.942392\pi$
$908$		−	47.0319i		−	1.56081i
$909$		0			0
$910$	−25.9972	+	30.1283i	−0.861798	+	0.998743i
$911$			15.6964i			0.520043i	0.965603	+	0.260022i	$0.0837297\pi$
$911$			15.6964i			0.520043i	−0.965603	+	0.260022i	$0.916270\pi$
$912$		0			0
$913$	45.3590			1.50116
$914$			41.0316i			1.35720i
$915$		0			0
$916$		−	32.3945i		−	1.07034i
$917$	16.6873	+	2.17336i	0.551063	+	0.0717705i
$918$		0			0
$919$	16.0285			0.528733			0.264366	−	0.964422i	$-0.414837\pi$
$919$	16.0285			0.528733			0.264366	+	0.964422i	$0.414837\pi$
$920$	−2.11028	+	3.20407i	−0.0695739	+	0.105635i
$921$		0			0
$922$	32.1923			1.06020
$923$			36.7369i			1.20921i
$924$		0			0
$925$	41.2683	−	17.7390i	1.35689	−	0.583255i
$926$			1.37682i			0.0452450i
$927$		0			0
$928$		−	4.55080i		−	0.149387i
$929$	−23.0233			−0.755370			−0.377685	−	0.925934i	$-0.623280\pi$
$929$	−23.0233			−0.755370			−0.377685	+	0.925934i	$0.623280\pi$
$930$		0			0
$931$	−7.27325	+	27.4488i	−0.238371	+	0.899598i
$932$	−31.8702			−1.04394
$933$		0			0
$934$			6.55075i			0.214347i
$935$	−2.55240	+	3.87534i	−0.0834723	+	0.126737i
$936$		0			0
$937$	31.8119			1.03925			0.519625	−	0.854394i	$-0.326072\pi$
$937$	31.8119			1.03925			0.519625	+	0.854394i	$0.326072\pi$
$938$	−7.07704	+	54.3383i	−0.231073	+	1.77421i
$939$		0			0
$940$	19.4820	+	12.8314i	0.635434	+	0.418513i
$941$	−5.99712			−0.195501			−0.0977503	−	0.995211i	$-0.531165\pi$
$941$	−5.99712			−0.195501			−0.0977503	+	0.995211i	$0.531165\pi$
$942$		0			0
$943$	6.27514			0.204347
$944$	26.2110			0.853095
$945$		0			0
$946$	51.6666			1.67983
$947$	−49.3510			−1.60369			−0.801846	−	0.597531i	$-0.796149\pi$
$947$	−49.3510			−1.60369			−0.801846	+	0.597531i	$0.796149\pi$
$948$		0			0
$949$	−9.24903			−0.300236
$950$	−35.8557	+	15.4124i	−1.16331	+	0.500045i
$951$		0			0
$952$	−0.129322	+	0.992952i	−0.00419136	+	0.0321818i
$953$	26.3001			0.851945			0.425973	−	0.904736i	$-0.359932\pi$
$953$	26.3001			0.851945			0.425973	+	0.904736i	$0.359932\pi$
$954$		0			0
$955$	40.7966	+	26.8697i	1.32015	+	0.869482i
$956$		−	22.2274i		−	0.718885i
$957$		0			0
$958$	−8.73075			−0.282078
$959$	−54.3520	−	7.07882i	−1.75512	−	0.228587i
$960$		0			0
$961$	27.0168			0.871510
$962$			60.4293i			1.94832i
$963$		0			0
$964$		−	3.39776i		−	0.109434i
$965$	−38.4406	−	25.3179i	−1.23745	−	0.815013i
$966$		0			0
$967$			9.19365i			0.295648i	0.989014	+	0.147824i	$0.0472269\pi$
$967$			9.19365i			0.295648i	−0.989014	+	0.147824i	$0.952773\pi$
$968$	0.655530			0.0210695
$969$		0			0
$970$	18.2295	−	27.6781i	0.585313	−	0.888690i
$971$	−58.3370			−1.87212			−0.936062	−	0.351835i	$-0.885558\pi$
$971$	−58.3370			−1.87212			−0.936062	+	0.351835i	$0.885558\pi$
$972$		0			0
$973$	7.01081	−	53.8298i	0.224756	−	1.72571i
$974$			34.5272i			1.10632i
$975$		0			0
$976$		−	18.6305i		−	0.596347i
$977$	−36.6463			−1.17242			−0.586210	−	0.810159i	$-0.699381\pi$
$977$	−36.6463			−1.17242			−0.586210	+	0.810159i	$0.699381\pi$
$978$		0			0
$979$			36.5604i			1.16848i
$980$	19.8686	−	17.7578i	0.634678	−	0.567252i
$981$		0			0
$982$			38.6691i			1.23398i
$983$		−	14.6373i		−	0.466857i	−0.972374	−	0.233428i	$-0.925006\pi$
$983$		−	14.6373i		−	0.466857i	0.972374	−	0.233428i	$-0.0749944\pi$
$984$		0			0
$985$	9.87206	−	14.9889i	0.314550	−	0.477586i
$986$	0.769107			0.0244933
$987$		0			0
$988$		−	24.1421i		−	0.768064i
$989$			25.6332i			0.815088i
$990$		0			0
$991$	−21.8306			−0.693472			−0.346736	−	0.937963i	$-0.612710\pi$
$991$	−21.8306			−0.693472			−0.346736	+	0.937963i	$0.612710\pi$
$992$			15.0211i			0.476920i
$993$		0			0
$994$	6.90955	−	53.0524i	0.219158	−	1.68272i
$995$	−1.90265	−	1.25313i	−0.0603179	−	0.0397269i
$996$		0			0
$997$	−4.01687			−0.127216			−0.0636078	−	0.997975i	$-0.520261\pi$
$997$	−4.01687			−0.127216			−0.0636078	+	0.997975i	$0.520261\pi$
$998$	−36.1861			−1.14545
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.g.b.944.7	yes	32
3.2	odd	2	inner	945.2.g.b.944.26	yes	32
5.4	even	2	inner	945.2.g.b.944.28	yes	32
7.6	odd	2	inner	945.2.g.b.944.6	yes	32
15.14	odd	2	inner	945.2.g.b.944.5	✓	32
21.20	even	2	inner	945.2.g.b.944.27	yes	32
35.34	odd	2	inner	945.2.g.b.944.25	yes	32
105.104	even	2	inner	945.2.g.b.944.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.g.b.944.5	✓	32	15.14	odd	2	inner
945.2.g.b.944.6	yes	32	7.6	odd	2	inner
945.2.g.b.944.7	yes	32	1.1	even	1	trivial
945.2.g.b.944.8	yes	32	105.104	even	2	inner
945.2.g.b.944.25	yes	32	35.34	odd	2	inner
945.2.g.b.944.26	yes	32	3.2	odd	2	inner
945.2.g.b.944.27	yes	32	21.20	even	2	inner
945.2.g.b.944.28	yes	32	5.4	even	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.92418 q^{2} +1.70246 q^{4} +(1.22993 - 1.86742i) q^{5} +(-2.62359 - 0.341697i) q^{7} +0.572523 q^{8} +O(q^{10})\)	\(q-1.92418 q^{2} +1.70246 q^{4} +(1.22993 - 1.86742i) q^{5} +(-2.62359 - 0.341697i) q^{7} +0.572523 q^{8} +(-2.36661 + 3.59325i) q^{10} -3.13927i q^{11} -3.49574 q^{13} +(5.04826 + 0.657486i) q^{14} -4.50655 q^{16} -0.661056i q^{17} +4.05658i q^{19} +(2.09391 - 3.17921i) q^{20} +6.04051i q^{22} -2.99686 q^{23} +(-1.97454 - 4.59360i) q^{25} +6.72642 q^{26} +(-4.46656 - 0.581726i) q^{28} -0.604649i q^{29} +1.99580i q^{31} +7.52636 q^{32} +1.27199i q^{34} +(-3.86493 + 4.47910i) q^{35} +8.98387i q^{37} -7.80558i q^{38} +(0.704164 - 1.06914i) q^{40} -2.09391 q^{41} -8.55335i q^{43} -5.34448i q^{44} +5.76649 q^{46} +6.12795i q^{47} +(6.76649 + 1.79295i) q^{49} +(3.79936 + 8.83891i) q^{50} -5.95135 q^{52} +5.42119 q^{53} +(-5.86235 - 3.86109i) q^{55} +(-1.50207 - 0.195630i) q^{56} +1.16345i q^{58} -5.81619 q^{59} +4.13408i q^{61} -3.84027i q^{62} -5.46894 q^{64} +(-4.29952 + 6.52803i) q^{65} +10.7638i q^{67} -1.12542i q^{68} +(7.43682 - 8.61857i) q^{70} -10.5090i q^{71} +2.64580 q^{73} -17.2866i q^{74} +6.90616i q^{76} +(-1.07268 + 8.23617i) q^{77} -10.1581 q^{79} +(-5.54275 + 8.41564i) q^{80} +4.02905 q^{82} +14.4489i q^{83} +(-1.23447 - 0.813054i) q^{85} +16.4582i q^{86} -1.79731i q^{88} -11.6461 q^{89} +(9.17140 + 1.19449i) q^{91} -5.10202 q^{92} -11.7913i q^{94} +(7.57535 + 4.98931i) q^{95} -7.70280 q^{97} +(-13.0199 - 3.44995i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4}+O(q^{10}) \) 32 * q + 32 * q^4	\( 32 q + 32 q^{4} + 32 q^{16} + 20 q^{25} - 24 q^{46} + 8 q^{49} + 56 q^{64} + 40 q^{79} + 76 q^{85} + 40 q^{91}+O(q^{100}) \) 32 * q + 32 * q^4 + 32 * q^16 + 20 * q^25 - 24 * q^46 + 8 * q^49 + 56 * q^64 + 40 * q^79 + 76 * q^85 + 40 * q^91

Introduction

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