LMFDB - Embedded newform 756.2.bf.d.271.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.10
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.d.703.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.444821 - 1.34244i) q^{2} +(-1.60427 - 1.19429i) q^{4} +(1.00309 + 0.579135i) q^{5} +(-0.250854 + 2.63383i) q^{7} +(-2.31687 + 1.62238i) q^{8} +O(q^{10})$	\(q+(0.444821 - 1.34244i) q^{2} +(-1.60427 - 1.19429i) q^{4} +(1.00309 + 0.579135i) q^{5} +(-0.250854 + 2.63383i) q^{7} +(-2.31687 + 1.62238i) q^{8} +(1.22365 - 1.08897i) q^{10} +(1.17740 - 0.679774i) q^{11} -3.61225i q^{13} +(3.42417 + 1.50834i) q^{14} +(1.14735 + 3.83192i) q^{16} +(6.02963 - 3.48121i) q^{17} +(3.04436 - 5.27298i) q^{19} +(-0.917574 - 2.12707i) q^{20} +(-0.388819 - 1.88297i) q^{22} +(2.38891 + 1.37924i) q^{23} +(-1.82920 - 3.16828i) q^{25} +(-4.84922 - 1.60681i) q^{26} +(3.54799 - 3.92578i) q^{28} +5.87724 q^{29} +(2.09009 + 3.62014i) q^{31} +(5.65447 + 0.164272i) q^{32} +(-1.99119 - 9.64291i) q^{34} +(-1.77697 + 2.49670i) q^{35} +(1.83360 - 3.17589i) q^{37} +(-5.72445 - 6.43239i) q^{38} +(-3.26361 + 0.285618i) q^{40} +5.72144i q^{41} -5.96527i q^{43} +(-2.70072 - 0.315619i) q^{44} +(2.91417 - 2.59344i) q^{46} +(-6.26664 + 10.8541i) q^{47} +(-6.87415 - 1.32141i) q^{49} +(-5.06688 + 1.04627i) q^{50} +(-4.31407 + 5.79502i) q^{52} +(4.95261 + 8.57816i) q^{53} +1.57472 q^{55} +(-3.69189 - 6.50922i) q^{56} +(2.61432 - 7.88981i) q^{58} +(0.862393 + 1.49371i) q^{59} +(-2.23245 - 1.28891i) q^{61} +(5.78952 - 1.19549i) q^{62} +(2.73575 - 7.51769i) q^{64} +(2.09198 - 3.62342i) q^{65} +(-6.37655 + 3.68150i) q^{67} +(-13.8307 - 1.61632i) q^{68} +(2.56122 + 3.49606i) q^{70} -15.8728i q^{71} +(-3.53385 + 2.04027i) q^{73} +(-3.44780 - 3.87420i) q^{74} +(-11.1814 + 4.82344i) q^{76} +(1.49505 + 3.27161i) q^{77} +(-0.0869902 - 0.0502238i) q^{79} +(-1.06830 + 4.50824i) q^{80} +(7.68067 + 2.54502i) q^{82} -3.12931 q^{83} +8.06436 q^{85} +(-8.00800 - 2.65348i) q^{86} +(-1.62503 + 3.48514i) q^{88} +(2.78884 + 1.61014i) q^{89} +(9.51407 + 0.906147i) q^{91} +(-2.18524 - 5.06571i) q^{92} +(11.7835 + 13.2407i) q^{94} +(6.10754 - 3.52619i) q^{95} -1.23090i q^{97} +(-4.83168 + 8.64031i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{7}+O(q^{10}) $ 32 * q + 2 * q^7	$ 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) $ 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.444821	−	1.34244i	0.314536	−	0.949245i
$2$	0.444821	−	1.34244i	0.314536	−	0.949245i
$3$		0			0
$3$		0			0
$4$	−1.60427	−	1.19429i	−0.802134	−	0.597144i
$5$	1.00309	+	0.579135i	0.448596	+	0.258997i	0.707237	−	0.706976i	$-0.249941\pi$
$5$	1.00309	+	0.579135i	0.448596	+	0.258997i	−0.258641	+	0.965974i	$0.583275\pi$
$6$		0			0
$7$	−0.250854	+	2.63383i	−0.0948137	+	0.995495i
$7$	−0.250854	+	2.63383i	−0.0948137	+	0.995495i
$8$	−2.31687	+	1.62238i	−0.819136	+	0.573599i
$9$		0			0
$10$	1.22365	−	1.08897i	0.386952	−	0.344364i
$11$	1.17740	−	0.679774i	0.355000	−	0.204960i	−0.311885	−	0.950120i	$-0.600960\pi$
$11$	1.17740	−	0.679774i	0.355000	−	0.204960i	0.666885	+	0.745160i	$0.267627\pi$
$12$		0			0
$13$		−	3.61225i		−	1.00186i	−0.865488	−	0.500930i	$-0.832992\pi$
$13$		−	3.61225i		−	1.00186i	0.865488	−	0.500930i	$-0.167008\pi$
$14$	3.42417	+	1.50834i	0.915147	+	0.403121i
$15$		0			0
$16$	1.14735	+	3.83192i	0.286838	+	0.957979i
$17$	6.02963	−	3.48121i	1.46240	−	0.844317i	0.463278	−	0.886213i	$-0.346673\pi$
$17$	6.02963	−	3.48121i	1.46240	−	0.844317i	0.999122	+	0.0418962i	$0.0133399\pi$
$18$		0			0
$19$	3.04436	−	5.27298i	0.698424	−	1.20971i	−0.270589	−	0.962695i	$-0.587219\pi$
$19$	3.04436	−	5.27298i	0.698424	−	1.20971i	0.969013	−	0.247010i	$-0.0794481\pi$
$20$	−0.917574	−	2.12707i	−0.205176	−	0.475627i
$21$		0			0
$22$	−0.388819	−	1.88297i	−0.0828965	−	0.401450i
$23$	2.38891	+	1.37924i	0.498122	+	0.287591i	0.727937	−	0.685644i	$-0.240479\pi$
$23$	2.38891	+	1.37924i	0.498122	+	0.287591i	−0.229816	+	0.973234i	$0.573812\pi$
$24$		0			0
$25$	−1.82920	−	3.16828i	−0.365841	−	0.633655i
$26$	−4.84922	−	1.60681i	−0.951010	−	0.315121i
$27$		0			0
$28$	3.54799	−	3.92578i	0.670507	−	0.741903i
$29$	5.87724			1.09138			0.545688	−	0.837989i	$-0.316268\pi$
$29$	5.87724			1.09138			0.545688	+	0.837989i	$0.316268\pi$
$30$		0			0
$31$	2.09009	+	3.62014i	0.375391	+	0.650196i	0.990385	−	0.138335i	$-0.0441751\pi$
$31$	2.09009	+	3.62014i	0.375391	+	0.650196i	−0.614995	+	0.788531i	$0.710842\pi$
$32$	5.65447	+	0.164272i	0.999578	+	0.0290395i
$33$		0			0
$34$	−1.99119	−	9.64291i	−0.341486	−	1.65374i
$35$	−1.77697	+	2.49670i	−0.300364	+	0.422019i
$36$		0			0
$37$	1.83360	−	3.17589i	0.301442	−	0.522113i	−0.675021	−	0.737799i	$-0.735865\pi$
$37$	1.83360	−	3.17589i	0.301442	−	0.522113i	0.976463	+	0.215686i	$0.0691987\pi$
$38$	−5.72445	−	6.43239i	−0.928628	−	1.04347i
$39$		0			0
$40$	−3.26361	+	0.285618i	−0.516022	+	0.0451602i
$41$			5.72144i			0.893539i	0.894649	+	0.446770i	$0.147426\pi$
$41$			5.72144i			0.893539i	−0.894649	+	0.446770i	$0.852574\pi$
$42$		0			0
$43$		−	5.96527i		−	0.909696i	−0.890569	−	0.454848i	$-0.849694\pi$
$43$		−	5.96527i		−	0.909696i	0.890569	−	0.454848i	$-0.150306\pi$
$44$	−2.70072	−	0.315619i	−0.407148	−	0.0475813i
$45$		0			0
$46$	2.91417	−	2.59344i	0.429671	−	0.382382i
$47$	−6.26664	+	10.8541i	−0.914084	+	1.58324i	−0.105846	+	0.994383i	$0.533755\pi$
$47$	−6.26664	+	10.8541i	−0.914084	+	1.58324i	−0.808238	+	0.588857i	$0.799578\pi$
$48$		0			0
$49$	−6.87415	−	1.32141i	−0.982021	−	0.188773i
$50$	−5.06688	+	1.04627i	−0.716564	+	0.147965i
$51$		0			0
$52$	−4.31407	+	5.79502i	−0.598254	+	0.803625i
$53$	4.95261	+	8.57816i	0.680293	+	1.17830i	0.974892	+	0.222680i	$0.0714806\pi$
$53$	4.95261	+	8.57816i	0.680293	+	1.17830i	−0.294599	+	0.955621i	$0.595186\pi$
$54$		0			0
$55$	1.57472			0.212336
$56$	−3.69189	−	6.50922i	−0.493349	−	0.869831i
$57$		0			0
$58$	2.61432	−	7.88981i	0.343277	−	1.03598i
$59$	0.862393	+	1.49371i	0.112274	+	0.194464i	0.916687	−	0.399606i	$-0.130853\pi$
$59$	0.862393	+	1.49371i	0.112274	+	0.194464i	−0.804413	+	0.594071i	$0.797520\pi$
$60$		0			0
$61$	−2.23245	−	1.28891i	−0.285836	−	0.165027i	0.350227	−	0.936665i	$-0.386105\pi$
$61$	−2.23245	−	1.28891i	−0.285836	−	0.165027i	−0.636062	+	0.771638i	$0.719438\pi$
$62$	5.78952	−	1.19549i	0.735270	−	0.151828i
$63$		0			0
$64$	2.73575	−	7.51769i	0.341969	−	0.939711i
$65$	2.09198	−	3.62342i	0.259479	−	0.449430i
$66$		0			0
$67$	−6.37655	+	3.68150i	−0.779019	+	0.449767i	−0.836083	−	0.548604i	$-0.815160\pi$
$67$	−6.37655	+	3.68150i	−0.779019	+	0.449767i	0.0570634	+	0.998371i	$0.481826\pi$
$68$	−13.8307	−	1.61632i	−1.67722	−	0.196008i
$69$		0			0
$70$	2.56122	+	3.49606i	0.306124	+	0.417859i
$71$		−	15.8728i		−	1.88375i	−0.335964	−	0.941875i	$-0.609062\pi$
$71$		−	15.8728i		−	1.88375i	0.335964	−	0.941875i	$-0.390938\pi$
$72$		0			0
$73$	−3.53385	+	2.04027i	−0.413606	+	0.238795i	−0.692338	−	0.721574i	$-0.743419\pi$
$73$	−3.53385	+	2.04027i	−0.413606	+	0.238795i	0.278732	+	0.960369i	$0.410086\pi$
$74$	−3.44780	−	3.87420i	−0.400799	−	0.450366i
$75$		0			0
$76$	−11.1814	+	4.82344i	−1.28260	+	0.553286i
$77$	1.49505	+	3.27161i	0.170377	+	0.372834i
$78$		0			0
$79$	−0.0869902	−	0.0502238i	−0.00978717	−	0.00565062i	0.495098	−	0.868837i	$-0.335132\pi$
$79$	−0.0869902	−	0.0502238i	−0.00978717	−	0.00565062i	−0.504886	+	0.863186i	$0.668465\pi$
$80$	−1.06830	+	4.50824i	−0.119439	+	0.504036i
$81$		0			0
$82$	7.68067	+	2.54502i	0.848188	+	0.281050i
$83$	−3.12931			−0.343486			−0.171743	−	0.985142i	$-0.554940\pi$
$83$	−3.12931			−0.343486			−0.171743	+	0.985142i	$0.554940\pi$
$84$		0			0
$85$	8.06436			0.874703
$86$	−8.00800	−	2.65348i	−0.863524	−	0.286132i
$87$		0			0
$88$	−1.62503	+	3.48514i	−0.173229	+	0.371518i
$89$	2.78884	+	1.61014i	0.295617	+	0.170674i	0.640472	−	0.767981i	$-0.278739\pi$
$89$	2.78884	+	1.61014i	0.295617	+	0.170674i	−0.344855	+	0.938656i	$0.612072\pi$
$90$		0			0
$91$	9.51407	+	0.906147i	0.997346	+	0.0949900i
$92$	−2.18524	−	5.06571i	−0.227827	−	0.528137i
$93$		0			0
$94$	11.7835	+	13.2407i	1.21537	+	1.36568i
$95$	6.10754	−	3.52619i	0.626620	−	0.361780i
$96$		0			0
$97$		−	1.23090i		−	0.124979i	−0.998046	−	0.0624896i	$-0.980096\pi$
$97$		−	1.23090i		−	0.124979i	0.998046	−	0.0624896i	$-0.0199040\pi$
$98$	−4.83168	+	8.64031i	−0.488073	+	0.872803i
$99$		0			0
$100$	−0.849299	+	7.26736i	−0.0849299	+	0.726736i
$101$	−6.53900	+	3.77530i	−0.650655	+	0.375656i	−0.788707	−	0.614769i	$-0.789249\pi$
$101$	−6.53900	+	3.77530i	−0.650655	+	0.375656i	0.138052	+	0.990425i	$0.455916\pi$
$102$		0			0
$103$	−3.79081	+	6.56588i	−0.373520	+	0.646956i	−0.990104	−	0.140333i	$-0.955183\pi$
$103$	−3.79081	+	6.56588i	−0.373520	+	0.646956i	0.616584	+	0.787289i	$0.288516\pi$
$104$	5.86046	+	8.36912i	0.574665	+	0.820659i
$105$		0			0
$106$	13.7187	−	2.83280i	1.33247	−	0.275146i
$107$	−8.48341	−	4.89790i	−0.820122	−	0.473498i	0.0303366	−	0.999540i	$-0.490342\pi$
$107$	−8.48341	−	4.89790i	−0.820122	−	0.473498i	−0.850459	+	0.526042i	$0.823675\pi$
$108$		0			0
$109$	4.12235	+	7.14013i	0.394850	+	0.683900i	0.993082	−	0.117423i	$-0.0374633\pi$
$109$	4.12235	+	7.14013i	0.394850	+	0.683900i	−0.598232	+	0.801323i	$0.704130\pi$
$110$	0.700471	−	2.11397i	0.0667873	−	0.201559i
$111$		0			0
$112$	−10.3804	+	2.06068i	−0.980860	+	0.194716i
$113$	14.8028			1.39253			0.696266	−	0.717783i	$-0.254843\pi$
$113$	14.8028			1.39253			0.696266	+	0.717783i	$0.254843\pi$
$114$		0			0
$115$	1.59753	+	2.76700i	0.148970	+	0.258024i
$116$	−9.42866	−	7.01911i	−0.875429	−	0.651708i
$117$		0			0
$118$	2.38882	−	0.493274i	0.219909	−	0.0454095i
$119$	7.65636	+	16.7543i	0.701858	+	1.53586i
$120$		0			0
$121$	−4.57582	+	7.92554i	−0.415983	+	0.720504i
$122$	−2.72331	+	2.42359i	−0.246557	+	0.219421i
$123$		0			0
$124$	0.970428	−	8.30384i	0.0871470	−	0.745707i
$125$		−	10.0288i		−	0.897001i
$126$		0			0
$127$		−	13.9057i		−	1.23393i	−0.786991	−	0.616964i	$-0.788362\pi$
$127$		−	13.9057i		−	1.23393i	0.786991	−	0.616964i	$-0.211638\pi$
$128$	−8.87509	−	7.01660i	−0.784455	−	0.620186i
$129$		0			0
$130$	−3.93365	−	4.42013i	−0.345004	−	0.387671i
$131$	3.30349	−	5.72181i	0.288627	−	0.499917i	−0.684855	−	0.728679i	$-0.740135\pi$
$131$	3.30349	−	5.72181i	0.288627	−	0.499917i	0.973482	+	0.228762i	$0.0734679\pi$
$132$		0			0
$133$	13.1245	+	9.34107i	1.13804	+	0.809974i
$134$	2.10575	+	10.1977i	0.181910	+	0.880948i
$135$		0			0
$136$	−8.32200	+	17.8479i	−0.713606	+	1.53044i
$137$	6.46461	+	11.1970i	0.552309	+	0.956627i	0.998107	+	0.0614936i	$0.0195864\pi$
$137$	6.46461	+	11.1970i	0.552309	+	0.956627i	−0.445799	+	0.895133i	$0.647080\pi$
$138$		0			0
$139$	−13.4368			−1.13969			−0.569847	−	0.821751i	$-0.692997\pi$
$139$	−13.4368			−1.13969			−0.569847	+	0.821751i	$0.692997\pi$
$140$	5.83252	−	1.88315i	0.492938	−	0.159155i
$141$		0			0
$142$	−21.3082	−	7.06054i	−1.78814	−	0.592507i
$143$	−2.45552	−	4.25308i	−0.205341	−	0.355660i
$144$		0			0
$145$	5.89541	+	3.40372i	0.489587	+	0.282663i
$146$	1.16700	+	5.65152i	0.0965815	+	0.467723i
$147$		0			0
$148$	−6.73451	+	2.90513i	−0.553574	+	0.238800i
$149$	2.57773	−	4.46476i	0.211176	−	0.365767i	−0.740907	−	0.671608i	$-0.765604\pi$
$149$	2.57773	−	4.46476i	0.211176	−	0.365767i	0.952083	+	0.305840i	$0.0989374\pi$
$150$		0			0
$151$	−18.9645	+	10.9492i	−1.54331	+	0.891030i	−0.544683	+	0.838642i	$0.683350\pi$
$151$	−18.9645	+	10.9492i	−1.54331	+	0.891030i	−0.998627	+	0.0523881i	$0.983317\pi$
$152$	1.50142	+	17.1559i	0.121781	+	1.39153i
$153$		0			0
$154$	5.05695	−	0.551735i	0.407501	−	0.0444601i
$155$			4.84178i			0.388901i
$156$		0			0
$157$	−2.39277	+	1.38147i	−0.190964	+	0.110253i	−0.592434	−	0.805619i	$-0.701833\pi$
$157$	−2.39277	+	1.38147i	−0.190964	+	0.110253i	0.401470	+	0.915872i	$0.368500\pi$
$158$	−0.106117	+	0.0944382i	−0.00844225	+	0.00751310i
$159$		0			0
$160$	5.57682	+	3.43948i	0.440886	+	0.271915i
$161$	−4.23194	+	5.94599i	−0.333524	+	0.468610i
$162$		0			0
$163$	3.87942	+	2.23978i	0.303860	+	0.175433i	0.644175	−	0.764878i	$-0.277201\pi$
$163$	3.87942	+	2.23978i	0.303860	+	0.175433i	−0.340316	+	0.940311i	$0.610534\pi$
$164$	6.83305	−	9.17873i	0.533572	−	0.716738i
$165$		0			0
$166$	−1.39198	+	4.20090i	−0.108039	+	0.326053i
$167$	−24.1008			−1.86498			−0.932488	−	0.361202i	$-0.882367\pi$
$167$	−24.1008			−1.86498			−0.932488	+	0.361202i	$0.882367\pi$
$168$		0			0
$169$	−0.0483818			−0.00372167
$170$	3.58720	−	10.8259i	0.275126	−	0.830308i
$171$		0			0
$172$	−7.12425	+	9.56990i	−0.543219	+	0.729698i
$173$	−5.03887	−	2.90919i	−0.383098	−	0.221182i	0.296067	−	0.955167i	$-0.404325\pi$
$173$	−5.03887	−	2.90919i	−0.383098	−	0.221182i	−0.679165	+	0.733985i	$0.737658\pi$
$174$		0			0
$175$	8.80357	−	4.02304i	0.665487	−	0.304114i
$176$	3.95573	+	3.73177i	0.298174	+	0.281293i
$177$		0			0
$178$	3.40204	−	3.02762i	0.254994	−	0.226929i
$179$	12.1143	−	6.99419i	0.905464	−	0.522770i	0.0264953	−	0.999649i	$-0.491565\pi$
$179$	12.1143	−	6.99419i	0.905464	−	0.522770i	0.878969	+	0.476879i	$0.158232\pi$
$180$		0			0
$181$			10.2103i			0.758924i	0.925207	+	0.379462i	$0.123891\pi$
$181$			10.2103i			0.758924i	−0.925207	+	0.379462i	$0.876109\pi$
$182$	5.44851	−	12.3690i	0.403870	−	0.916848i
$183$		0			0
$184$	−7.77243	+	0.680212i	−0.572991	+	0.0501459i
$185$	3.67854	−	2.12381i	0.270452	−	0.156145i
$186$		0			0
$187$	4.73287	−	8.19757i	0.346102	−	0.599466i
$188$	23.0163	−	9.92878i	1.67864	−	0.724130i
$189$		0			0
$190$	−2.01692	−	9.76751i	−0.146323	−	0.708609i
$191$	18.0141	+	10.4004i	1.30345	+	0.752548i	0.980994	−	0.194037i	$-0.0621580\pi$
$191$	18.0141	+	10.4004i	1.30345	+	0.752548i	0.322457	+	0.946584i	$0.395491\pi$
$192$		0			0
$193$	−11.5929	−	20.0795i	−0.834476	−	1.44536i	−0.894456	−	0.447156i	$-0.852437\pi$
$193$	−11.5929	−	20.0795i	−0.834476	−	1.44536i	0.0599800	−	0.998200i	$-0.480896\pi$
$194$	−1.65241	−	0.547532i	−0.118636	−	0.0393105i
$195$		0			0
$196$	9.44982	+	10.3296i	0.674987	+	0.737829i
$197$	−7.91608			−0.563998			−0.281999	−	0.959415i	$-0.590997\pi$
$197$	−7.91608			−0.563998			−0.281999	+	0.959415i	$0.590997\pi$
$198$		0			0
$199$	1.73074	+	2.99773i	0.122689	+	0.212504i	0.920827	−	0.389971i	$-0.127515\pi$
$199$	1.73074	+	2.99773i	0.122689	+	0.212504i	−0.798138	+	0.602474i	$0.794182\pi$
$200$	9.37818	+	4.37281i	0.663137	+	0.309204i
$201$		0			0
$202$	2.15940	+	10.4575i	0.151935	+	0.735789i
$203$	−1.47433	+	15.4797i	−0.103477	+	1.08646i
$204$		0			0
$205$	−3.31349	+	5.73913i	−0.231424	+	0.400838i
$206$	7.12804	+	8.00957i	0.496634	+	0.558053i
$207$		0			0
$208$	13.8419	−	4.14453i	0.959760	−	0.287371i
$209$		−	8.27790i		−	0.572594i
$210$		0			0
$211$		−	2.99740i		−	0.206349i	−0.994663	−	0.103175i	$-0.967100\pi$
$211$		−	2.99740i		−	0.206349i	0.994663	−	0.103175i	$-0.0329001\pi$
$212$	2.29949	−	19.6765i	0.157930	−	1.35139i
$213$		0			0
$214$	−10.3487	+	9.20974i	−0.707423	+	0.629565i
$215$	3.45470	−	5.98372i	0.235609	−	0.408086i
$216$		0			0
$217$	−10.0591	+	4.59682i	−0.682859	+	0.312052i
$218$	11.4189	−	2.35792i	0.773384	−	0.159698i
$219$		0			0
$220$	−2.52628	−	1.88067i	−0.170322	−	0.126795i
$221$	−12.5750	−	21.7806i	−0.845887	−	1.46512i
$222$		0			0
$223$	15.9964			1.07120			0.535598	−	0.844473i	$-0.320086\pi$
$223$	15.9964			1.07120			0.535598	+	0.844473i	$0.320086\pi$
$224$	−1.85111	+	14.8517i	−0.123682	+	0.992322i
$225$		0			0
$226$	6.58461	−	19.8718i	0.438002	−	1.32186i
$227$	12.8944	+	22.3338i	0.855832	+	1.48235i	0.875871	+	0.482546i	$0.160288\pi$
$227$	12.8944	+	22.3338i	0.855832	+	1.48235i	−0.0200383	+	0.999799i	$0.506379\pi$
$228$		0			0
$229$	19.1866	+	11.0774i	1.26789	+	0.732014i	0.974588	−	0.224007i	$-0.0719137\pi$
$229$	19.1866	+	11.0774i	1.26789	+	0.732014i	0.293298	+	0.956021i	$0.405247\pi$
$230$	4.42514	−	0.913759i	0.291785	−	0.0602515i
$231$		0			0
$232$	−13.6168	+	9.53512i	−0.893985	+	0.626011i
$233$	2.09023	−	3.62038i	0.136935	−	0.237179i	−0.789400	−	0.613880i	$-0.789608\pi$
$233$	2.09023	−	3.62038i	0.136935	−	0.237179i	0.926335	+	0.376700i	$0.122941\pi$
$234$		0			0
$235$	−12.5720	+	7.25847i	−0.820109	+	0.473490i
$236$	0.400409	−	3.42625i	0.0260644	−	0.223030i
$237$		0			0
$238$	25.8973	−	2.82551i	1.67867	−	0.183150i
$239$		−	18.9785i		−	1.22762i	−0.789454	−	0.613810i	$-0.789636\pi$
$239$		−	18.9785i		−	1.22762i	0.789454	−	0.613810i	$-0.210364\pi$
$240$		0			0
$241$	−4.95053	+	2.85819i	−0.318892	+	0.184112i	−0.650899	−	0.759165i	$-0.725608\pi$
$241$	−4.95053	+	2.85819i	−0.318892	+	0.184112i	0.332007	+	0.943277i	$0.392274\pi$
$242$	8.60411	+	9.66819i	0.553093	+	0.621495i
$243$		0			0
$244$	2.04212	+	4.73394i	0.130734	+	0.303059i
$245$	−6.13012	−	5.30656i	−0.391639	−	0.339024i
$246$		0			0
$247$	−19.0474	−	10.9970i	−1.21195	−	0.699722i
$248$	−10.7157	−	4.99646i	−0.680448	−	0.317276i
$249$		0			0
$250$	−13.4630	−	4.46102i	−0.851475	−	0.282139i
$251$	−9.26670			−0.584909			−0.292455	−	0.956279i	$-0.594472\pi$
$251$	−9.26670			−0.584909			−0.292455	+	0.956279i	$0.594472\pi$
$252$		0			0
$253$	3.75027			0.235778
$254$	−18.6675	−	6.18554i	−1.17130	−	0.388115i
$255$		0			0
$256$	−13.3672	+	8.79311i	−0.835448	+	0.549569i
$257$	−11.7697	−	6.79523i	−0.734173	−	0.423875i	0.0857741	−	0.996315i	$-0.472664\pi$
$257$	−11.7697	−	6.79523i	−0.734173	−	0.423875i	−0.819947	+	0.572440i	$0.805997\pi$
$258$		0			0
$259$	7.90480	+	5.62608i	0.491180	+	0.349588i
$260$	−7.68351	+	3.31451i	−0.476511	+	0.205557i
$261$		0			0
$262$	−6.21170	−	6.97990i	−0.383760	−	0.431220i
$263$	1.01439	−	0.585656i	0.0625497	−	0.0361131i	−0.468399	−	0.883517i	$-0.655169\pi$
$263$	1.01439	−	0.585656i	0.0625497	−	0.0361131i	0.530949	+	0.847404i	$0.321836\pi$
$264$		0			0
$265$			11.4729i			0.704776i
$266$	18.3778	−	13.4636i	1.12682	−	0.825509i
$267$		0			0
$268$	14.6265	+	1.70932i	0.893453	+	0.104413i
$269$	−2.07519	+	1.19811i	−0.126527	+	0.0730501i	−0.561927	−	0.827187i	$-0.689940\pi$
$269$	−2.07519	+	1.19811i	−0.126527	+	0.0730501i	0.435401	+	0.900237i	$0.356607\pi$
$270$		0			0
$271$	−0.964402	+	1.67039i	−0.0585833	+	0.101469i	−0.893830	−	0.448407i	$-0.851992\pi$
$271$	−0.964402	+	1.67039i	−0.0585833	+	0.101469i	0.835246	+	0.549876i	$0.185325\pi$
$272$	20.2578	+	19.1109i	1.22831	+	1.15877i
$273$		0			0
$274$	17.9069	−	3.69764i	1.08179	−	0.223383i
$275$	−4.30742	−	2.48689i	−0.259747	−	0.149965i
$276$		0			0
$277$	3.63574	+	6.29729i	0.218451	+	0.378368i	0.954335	−	0.298740i	$-0.0965664\pi$
$277$	3.63574	+	6.29729i	0.218451	+	0.378368i	−0.735884	+	0.677108i	$0.763233\pi$
$278$	−5.97697	+	18.0380i	−0.358475	+	1.08185i
$279$		0			0
$280$	0.0664179	−	8.66745i	0.00396923	−	0.517979i
$281$	−17.3716			−1.03630			−0.518152	−	0.855288i	$-0.673380\pi$
$281$	−17.3716			−1.03630			−0.518152	+	0.855288i	$0.673380\pi$
$282$		0			0
$283$	10.9210	+	18.9157i	0.649185	+	1.12442i	0.983318	+	0.181895i	$0.0582231\pi$
$283$	10.9210	+	18.9157i	0.649185	+	1.12442i	−0.334133	+	0.942526i	$0.608444\pi$
$284$	−18.9566	+	25.4642i	−1.12487	+	1.51102i
$285$		0			0
$286$	−6.80175	+	1.40451i	−0.402196	+	0.0830506i
$287$	−15.0693	−	1.43524i	−0.889514	−	0.0847198i
$288$		0			0
$289$	15.7376	−	27.2583i	0.925742	−	1.60343i
$290$	7.19167	−	6.40016i	0.422310	−	0.375830i
$291$		0			0
$292$	8.10591	+	0.947296i	0.474362	+	0.0554363i
$293$			23.9126i			1.39699i	0.715616	+	0.698493i	$0.246146\pi$
$293$			23.9126i			1.39699i	−0.715616	+	0.698493i	$0.753854\pi$
$294$		0			0
$295$			1.99777i			0.116315i
$296$	0.904296	+	10.3329i	0.0525611	+	0.600589i
$297$		0			0
$298$	−4.84702	−	5.44645i	−0.280780	−	0.315505i
$299$	4.98215	−	8.62934i	0.288125	−	0.499048i
$300$		0			0
$301$	15.7115	+	1.49641i	0.905597	+	0.0862516i
$302$	6.26273	+	30.3291i	0.360380	+	1.74524i
$303$		0			0
$304$	23.6986	+	5.61576i	1.35921	+	0.322086i
$305$	−1.49290	−	2.58578i	−0.0854833	−	0.148061i
$306$		0			0
$307$	−6.65724			−0.379949			−0.189974	−	0.981789i	$-0.560841\pi$
$307$	−6.65724			−0.379949			−0.189974	+	0.981789i	$0.560841\pi$
$308$	1.50877	−	7.03406i	0.0859702	−	0.400803i
$309$		0			0
$310$	6.49977	+	2.15373i	0.369162	+	0.122323i
$311$	−5.91371	−	10.2428i	−0.335336	−	0.580818i	0.648214	−	0.761459i	$-0.275516\pi$
$311$	−5.91371	−	10.2428i	−0.335336	−	0.580818i	−0.983549	+	0.180640i	$0.942183\pi$
$312$		0			0
$313$	−27.5277	−	15.8931i	−1.55596	−	0.898333i	−0.997637	−	0.0687080i	$-0.978112\pi$
$313$	−27.5277	−	15.8931i	−1.55596	−	0.898333i	−0.558321	−	0.829625i	$-0.688554\pi$
$314$	0.790176	+	3.82665i	0.0445922	+	0.215950i
$315$		0			0
$316$	0.0795739	+	0.184464i	0.00447638	+	0.0103769i
$317$	−10.4062	+	18.0240i	−0.584468	+	1.01233i	0.410473	+	0.911873i	$0.365363\pi$
$317$	−10.4062	+	18.0240i	−0.584468	+	1.01233i	−0.994942	+	0.100456i	$0.967970\pi$
$318$		0			0
$319$	6.91987	−	3.99519i	0.387439	−	0.223688i
$320$	7.09797	−	5.95656i	0.396789	−	0.332982i
$321$		0			0
$322$	6.09966	+	8.32602i	0.339921	+	0.463991i
$323$		−	42.3922i		−	2.35876i
$324$		0			0
$325$	−11.4446	+	6.60755i	−0.634833	+	0.366521i
$326$	4.73242	−	4.21157i	0.262104	−	0.233257i
$327$		0			0
$328$	−9.28237	−	13.2558i	−0.512533	−	0.731931i
$329$	−27.0160	−	19.2281i	−1.48944	−	1.06008i
$330$		0			0
$331$	−23.3464	−	13.4790i	−1.28323	−	0.740874i	−0.305794	−	0.952098i	$-0.598922\pi$
$331$	−23.3464	−	13.4790i	−1.28323	−	0.740874i	−0.977438	+	0.211224i	$0.932255\pi$
$332$	5.02025	+	3.73730i	0.275522	+	0.205111i
$333$		0			0
$334$	−10.7205	+	32.3538i	−0.586602	+	1.77032i
$335$	−8.52835			−0.465953
$336$		0			0
$337$	−28.8579			−1.57199			−0.785994	−	0.618234i	$-0.787848\pi$
$337$	−28.8579			−1.57199			−0.785994	+	0.618234i	$0.787848\pi$
$338$	−0.0215212	+	0.0649494i	−0.00117060	+	0.00353278i
$339$		0			0
$340$	−12.9374	−	9.63117i	−0.701629	−	0.522324i
$341$	4.92175	+	2.84157i	0.266528	+	0.153880i
$342$		0			0
$343$	5.20478	−	17.7739i	0.281032	−	0.959698i
$344$	9.67795	+	13.8207i	0.521800	+	0.745165i
$345$		0			0
$346$	−6.14680	+	5.47029i	−0.330454	+	0.294084i
$347$	20.6499	−	11.9222i	1.10855	−	0.640019i	0.170094	−	0.985428i	$-0.445593\pi$
$347$	20.6499	−	11.9222i	1.10855	−	0.640019i	0.938452	+	0.345408i	$0.112260\pi$
$348$		0			0
$349$		−	25.9993i		−	1.39171i	−0.718183	−	0.695854i	$-0.755026\pi$
$349$		−	25.9993i		−	1.39171i	0.718183	−	0.695854i	$-0.244974\pi$
$350$	−1.48466	−	13.6078i	−0.0793587	−	0.727365i
$351$		0			0
$352$	6.76926	−	3.65035i	0.360803	−	0.194564i
$353$	−22.2666	+	12.8556i	−1.18513	+	0.684237i	−0.957196	−	0.289439i	$-0.906531\pi$
$353$	−22.2666	+	12.8556i	−1.18513	+	0.684237i	−0.227936	+	0.973676i	$0.573198\pi$
$354$		0			0
$355$	9.19247	−	15.9218i	0.487886	−	0.845043i
$356$	−2.55108	−	5.91377i	−0.135207	−	0.313429i
$357$		0			0
$358$	−4.00055	−	19.3738i	−0.211436	−	1.02394i
$359$	25.2900	+	14.6012i	1.33475	+	0.770621i	0.986024	−	0.166603i	$-0.0532797\pi$
$359$	25.2900	+	14.6012i	1.33475	+	0.770621i	0.348730	+	0.937223i	$0.386613\pi$
$360$		0			0
$361$	−9.03623	−	15.6512i	−0.475591	−	0.823748i
$362$	13.7066	+	4.54175i	0.720405	+	0.238709i
$363$		0			0
$364$	−14.1809	−	12.8162i	−0.743282	−	0.671754i
$365$	−4.72637			−0.247389
$366$		0			0
$367$	13.2640	+	22.9739i	0.692374	+	1.19923i	0.971058	+	0.238844i	$0.0767683\pi$
$367$	13.2640	+	22.9739i	0.692374	+	1.19923i	−0.278684	+	0.960383i	$0.589898\pi$
$368$	−2.54420	+	10.7366i	−0.132626	+	0.559682i
$369$		0			0
$370$	−1.21478	−	5.88292i	−0.0631534	−	0.305838i
$371$	−23.8358	+	10.8925i	−1.23749	+	0.565509i
$372$		0			0
$373$	11.2352	−	19.4600i	0.581737	−	1.00760i	−0.413536	−	0.910488i	$-0.635706\pi$
$373$	11.2352	−	19.4600i	0.581737	−	1.00760i	0.995274	−	0.0971110i	$-0.0309602\pi$
$374$	−8.89943	−	10.0000i	−0.460178	−	0.517089i
$375$		0			0
$376$	−3.09058	−	35.3145i	−0.159385	−	1.82121i
$377$		−	21.2301i		−	1.09340i
$378$		0			0
$379$			16.3621i			0.840464i	0.907417	+	0.420232i	$0.138051\pi$
$379$			16.3621i			0.840464i	−0.907417	+	0.420232i	$0.861949\pi$
$380$	−14.0094	−	1.63721i	−0.718668	−	0.0839871i
$381$		0			0
$382$	21.9749	−	19.5564i	1.12434	−	1.00059i
$383$	−0.412929	+	0.715214i	−0.0210997	+	0.0365458i	−0.876382	−	0.481616i	$-0.840050\pi$
$383$	−0.412929	+	0.715214i	−0.0210997	+	0.0365458i	0.855283	+	0.518162i	$0.173383\pi$
$384$		0			0
$385$	−0.395025	+	4.14756i	−0.0201323	+	0.211379i
$386$	−32.1122	+	6.63095i	−1.63447	+	0.337506i
$387$		0			0
$388$	−1.47005	+	1.97470i	−0.0746306	+	0.100250i
$389$	0.0913436	+	0.158212i	0.00463130	+	0.00802165i	0.868332	−	0.495984i	$-0.165192\pi$
$389$	0.0913436	+	0.158212i	0.00463130	+	0.00802165i	−0.863700	+	0.504005i	$0.831859\pi$
$390$		0			0
$391$	19.2056			0.971270
$392$	18.0703	−	8.09095i	0.912689	−	0.408655i
$393$		0			0
$394$	−3.52124	+	10.6268i	−0.177398	+	0.535372i
$395$	−0.0581728	−	0.100758i	−0.00292699	−	0.00506970i
$396$		0			0
$397$	2.36094	+	1.36309i	0.118492	+	0.0684114i	0.558075	−	0.829791i	$-0.311540\pi$
$397$	2.36094	+	1.36309i	0.118492	+	0.0684114i	−0.439583	+	0.898202i	$0.644874\pi$
$398$	4.79414	−	0.989955i	0.240308	−	0.0496220i
$399$		0			0
$400$	10.0418	−	10.6445i	0.502091	−	0.532224i
$401$	−14.3573	+	24.8675i	−0.716967	+	1.24182i	0.245229	+	0.969465i	$0.421137\pi$
$401$	−14.3573	+	24.8675i	−0.716967	+	1.24182i	−0.962196	+	0.272358i	$0.912196\pi$
$402$		0			0
$403$	13.0769	−	7.54993i	0.651405	−	0.376089i
$404$	14.9991	+	1.75287i	0.746233	+	0.0872085i
$405$		0			0
$406$	20.1246	+	8.86487i	0.998769	+	0.439956i
$407$		−	4.98574i		−	0.247134i
$408$		0			0
$409$	4.02082	−	2.32142i	0.198817	−	0.114787i	−0.397287	−	0.917695i	$-0.630048\pi$
$409$	4.02082	−	2.32142i	0.198817	−	0.114787i	0.596103	+	0.802908i	$0.296715\pi$
$410$	6.23051	+	7.00104i	0.307703	+	0.345757i
$411$		0			0
$412$	13.9230	−	6.00611i	0.685939	−	0.295900i
$413$	−4.15051	+	1.89670i	−0.204233	+	0.0933303i
$414$		0			0
$415$	−3.13898	−	1.81229i	−0.154087	−	0.0889620i
$416$	0.593393	−	20.4254i	0.0290935	−	1.00144i
$417$		0			0
$418$	−11.1125	−	3.68219i	−0.543532	−	0.180102i
$419$	−22.5769			−1.10295			−0.551477	−	0.834190i	$-0.685936\pi$
$419$	−22.5769			−1.10295			−0.551477	+	0.834190i	$0.685936\pi$
$420$		0			0
$421$	28.1988			1.37432			0.687162	−	0.726504i	$-0.258856\pi$
$421$	28.1988			1.37432			0.687162	+	0.726504i	$0.258856\pi$
$422$	−4.02381	−	1.33331i	−0.195876	−	0.0649043i
$423$		0			0
$424$	−25.3916	−	11.8395i	−1.23312	−	0.574975i
$425$	−22.0588	−	12.7357i	−1.07001	−	0.617771i
$426$		0			0
$427$	3.95478	−	5.55657i	0.191385	−	0.268901i
$428$	7.76016	+	17.9892i	0.375101	+	0.869539i
$429$		0			0
$430$	−6.49603	−	7.29940i	−0.313266	−	0.352008i
$431$	−9.72135	+	5.61263i	−0.468261	+	0.270351i	−0.715512	−	0.698601i	$-0.753806\pi$
$431$	−9.72135	+	5.61263i	−0.468261	+	0.270351i	0.247250	+	0.968952i	$0.420473\pi$
$432$		0			0
$433$		−	7.61724i		−	0.366061i	−0.983107	−	0.183031i	$-0.941409\pi$
$433$		−	7.61724i		−	0.366061i	0.983107	−	0.183031i	$-0.0585907\pi$
$434$	1.69641	+	15.5485i	0.0814303	+	0.746353i
$435$		0			0
$436$	1.91401	−	16.3780i	0.0916644	−	0.784362i
$437$	14.5454	−	8.39778i	0.695800	−	0.401720i
$438$		0			0
$439$	6.62111	−	11.4681i	0.316008	−	0.547342i	−0.663643	−	0.748049i	$-0.730991\pi$
$439$	6.62111	−	11.4681i	0.316008	−	0.547342i	0.979651	+	0.200707i	$0.0643239\pi$
$440$	−3.64843	+	2.55480i	−0.173932	+	0.121796i
$441$		0			0
$442$	−34.8326	+	7.19269i	−1.65682	+	0.342121i
$443$	22.3598	+	12.9094i	1.06234	+	0.613345i	0.926080	−	0.377327i	$-0.123157\pi$
$443$	22.3598	+	12.9094i	1.06234	+	0.613345i	0.136265	+	0.990672i	$0.456490\pi$
$444$		0			0
$445$	1.86498	+	3.23023i	0.0884084	+	0.153128i
$446$	7.11553	−	21.4741i	0.336930	−	1.01683i
$447$		0			0
$448$	19.1141	+	9.09135i	0.903054	+	0.429526i
$449$	−16.1043			−0.760008			−0.380004	−	0.924985i	$-0.624077\pi$
$449$	−16.1043			−0.760008			−0.380004	+	0.924985i	$0.624077\pi$
$450$		0			0
$451$	3.88929	+	6.73644i	0.183139	+	0.317207i
$452$	−23.7477	−	17.6788i	−1.11700	−	0.831543i
$453$		0			0
$454$	35.7174	−	7.37538i	1.67630	−	0.346144i
$455$	9.01871	+	6.41888i	0.422803	+	0.300922i
$456$		0			0
$457$	−18.9212	+	32.7725i	−0.885097	+	1.53303i	−0.0394940	+	0.999220i	$0.512575\pi$
$457$	−18.9212	+	32.7725i	−0.885097	+	1.53303i	−0.845603	+	0.533813i	$0.820759\pi$
$458$	23.4053	−	20.8293i	1.09366	−	0.973290i
$459$		0			0
$460$	0.741732	−	6.34692i	0.0345834	−	0.295927i
$461$		−	30.8123i		−	1.43507i	−0.696522	−	0.717535i	$-0.745270\pi$
$461$		−	30.8123i		−	1.43507i	0.696522	−	0.717535i	$-0.254730\pi$
$462$		0			0
$463$		−	19.1361i		−	0.889328i	−0.895697	−	0.444664i	$-0.853323\pi$
$463$		−	19.1361i		−	0.889328i	0.895697	−	0.444664i	$-0.146677\pi$
$464$	6.74326	+	22.5211i	0.313048	+	1.04551i
$465$		0			0
$466$	−3.93035	−	4.41642i	−0.182070	−	0.204587i
$467$	−2.47520	+	4.28717i	−0.114538	+	0.198386i	−0.917595	−	0.397516i	$-0.869872\pi$
$467$	−2.47520	+	4.28717i	−0.114538	+	0.198386i	0.803057	+	0.595903i	$0.203206\pi$
$468$		0			0
$469$	−8.09688	−	17.7183i	−0.373879	−	0.818154i
$470$	4.15172	+	20.1059i	0.191504	+	0.927415i
$471$		0			0
$472$	−4.42142	−	2.06159i	−0.203512	−	0.0948926i
$473$	−4.05504	−	7.02353i	−0.186451	−	0.322942i
$474$		0			0
$475$	−22.2750			−1.02205
$476$	7.72661	−	36.0223i	0.354148	−	1.65108i
$477$		0			0
$478$	−25.4775	−	8.44206i	−1.16531	−	0.386131i
$479$	−0.929096	−	1.60924i	−0.0424515	−	0.0735281i	0.844019	−	0.536313i	$-0.180183\pi$
$479$	−0.929096	−	1.60924i	−0.0424515	−	0.0735281i	−0.886470	+	0.462785i	$0.846850\pi$
$480$		0			0
$481$	−11.4721	−	6.62343i	−0.523084	−	0.302003i
$482$	1.63484	+	7.91716i	0.0744648	+	0.360617i
$483$		0			0
$484$	16.8062	−	7.24986i	0.763919	−	0.329539i
$485$	0.712860	−	1.23471i	0.0323693	−	0.0560653i
$486$		0			0
$487$	−14.7172	+	8.49700i	−0.666902	+	0.385036i	−0.794902	−	0.606738i	$-0.792478\pi$
$487$	−14.7172	+	8.49700i	−0.666902	+	0.385036i	0.128000	+	0.991774i	$0.459144\pi$
$488$	7.26339	−	0.635663i	0.328798	−	0.0287751i
$489$		0			0
$490$	−9.85052	+	5.86883i	−0.445001	+	0.265127i
$491$		−	3.96363i		−	0.178876i	−0.995992	−	0.0894382i	$-0.971493\pi$
$491$		−	3.96363i		−	0.178876i	0.995992	−	0.0894382i	$-0.0285071\pi$
$492$		0			0
$493$	35.4376	−	20.4599i	1.59603	−	0.921467i
$494$	−23.2354	+	20.6782i	−1.04541	+	0.930354i
$495$		0			0
$496$	−11.4740	+	12.1626i	−0.515198	+	0.546118i
$497$	41.8062	+	3.98174i	1.87526	+	0.178605i
$498$		0			0
$499$	34.1897	+	19.7394i	1.53054	+	0.883658i	0.999337	+	0.0364142i	$0.0115936\pi$
$499$	34.1897	+	19.7394i	1.53054	+	0.883658i	0.531204	+	0.847244i	$0.321740\pi$
$500$	−11.9773	+	16.0889i	−0.535639	+	0.719515i
$501$		0			0
$502$	−4.12203	+	12.4400i	−0.183975	+	0.555222i
$503$	−13.9163			−0.620495			−0.310248	−	0.950656i	$-0.600412\pi$
$503$	−13.9163			−0.620495			−0.310248	+	0.950656i	$0.600412\pi$
$504$		0			0
$505$	−8.74563			−0.389175
$506$	1.66820	−	5.03450i	0.0741606	−	0.223811i
$507$		0			0
$508$	−16.6074	+	22.3084i	−0.736833	+	0.989776i
$509$	11.8138	+	6.82072i	0.523639	+	0.302323i	0.738422	−	0.674339i	$-0.235571\pi$
$509$	11.8138	+	6.82072i	0.523639	+	0.302323i	−0.214783	+	0.976662i	$0.568905\pi$
$510$		0			0
$511$	−4.48725	−	9.81937i	−0.198504	−	0.434383i
$512$	5.85819	+	21.8559i	0.258898	+	0.965905i
$513$		0			0
$514$	−14.3576	+	12.7774i	−0.633285	+	0.563586i
$515$	−7.60507	+	4.39079i	−0.335119	+	0.193481i
$516$		0			0
$517$			17.0396i			0.749400i
$518$	11.0689	−	8.10908i	0.486338	−	0.356293i
$519$		0			0
$520$	1.03173	+	11.7890i	0.0452441	+	0.516981i
$521$	−17.8279	+	10.2930i	−0.781056	+	0.450943i	−0.836804	−	0.547502i	$-0.815579\pi$
$521$	−17.8279	+	10.2930i	−0.781056	+	0.450943i	0.0557484	+	0.998445i	$0.482246\pi$
$522$		0			0
$523$	−21.0812	+	36.5137i	−0.921816	+	1.59663i	−0.125213	+	0.992130i	$0.539961\pi$
$523$	−21.0812	+	36.5137i	−0.921816	+	1.59663i	−0.796603	+	0.604502i	$0.793372\pi$
$524$	−12.1332	+	5.23400i	−0.530040	+	0.228648i
$525$		0			0
$526$	−0.334985	−	1.62226i	−0.0146060	−	0.0707339i
$527$	25.2049	+	14.5521i	1.09794	+	0.633898i
$528$		0			0
$529$	−7.69542	−	13.3289i	−0.334583	−	0.579515i
$530$	15.4017	+	5.10340i	0.669005	+	0.221677i
$531$		0			0
$532$	−9.89922	−	30.6600i	−0.429186	−	1.32928i
$533$	20.6673			0.895201
$534$		0			0
$535$	−5.67309	−	9.82608i	−0.245269	−	0.424819i
$536$	8.80081	−	18.8747i	0.380137	−	0.815265i
$537$		0			0
$538$	0.685299	+	3.31875i	0.0295453	+	0.143082i
$539$	−8.99190	+	3.11703i	−0.387309	+	0.134260i
$540$		0			0
$541$	8.99343	−	15.5771i	0.386658	−	0.669711i	−0.605340	−	0.795967i	$-0.706963\pi$
$541$	8.99343	−	15.5771i	0.386658	−	0.669711i	0.991998	+	0.126256i	$0.0402961\pi$
$542$	1.81341	+	2.03767i	0.0778926	+	0.0875256i
$543$		0			0
$544$	34.6662	−	18.6939i	1.48630	−	0.801493i
$545$			9.54960i			0.409060i
$546$		0			0
$547$		−	21.7465i		−	0.929815i	−0.885359	−	0.464907i	$-0.846088\pi$
$547$		−	21.7465i		−	0.929815i	0.885359	−	0.464907i	$-0.153912\pi$
$548$	3.00152	−	25.6836i	0.128218	−	1.09715i
$549$		0			0
$550$	−5.25452	+	4.67621i	−0.224054	+	0.199394i
$551$	17.8924	−	30.9906i	0.762242	−	1.32024i
$552$		0			0
$553$	0.154103	−	0.216519i	0.00655313	−	0.00920732i
$554$	10.0710	−	2.07958i	0.427875	−	0.0883530i
$555$		0			0
$556$	21.5562	+	16.0474i	0.914187	+	0.680561i
$557$	3.21602	+	5.57031i	0.136267	+	0.236021i	0.926081	−	0.377325i	$-0.123156\pi$
$557$	3.21602	+	5.57031i	0.136267	+	0.236021i	−0.789814	+	0.613347i	$0.789823\pi$
$558$		0			0
$559$	−21.5481			−0.911387
$560$	−11.6060	−	3.94463i	−0.490441	−	0.166691i
$561$		0			0
$562$	−7.72727	+	23.3203i	−0.325955	+	0.983708i
$563$	19.5471	+	33.8566i	0.823812	+	1.42688i	0.902824	+	0.430010i	$0.141490\pi$
$563$	19.5471	+	33.8566i	0.823812	+	1.42688i	−0.0790120	+	0.996874i	$0.525177\pi$
$564$		0			0
$565$	14.8486	+	8.57284i	0.624685	+	0.360662i
$566$	30.2510	−	6.24661i	1.27154	−	0.262565i
$567$		0			0
$568$	25.7517	+	36.7751i	1.08052	+	1.54305i
$569$	11.9781	−	20.7466i	0.502147	−	0.869744i	−0.497850	−	0.867263i	$-0.665877\pi$
$569$	11.9781	−	20.7466i	0.502147	−	0.869744i	0.999997	−	0.00248112i	$-0.000789766\pi$
$570$		0			0
$571$	8.26843	−	4.77378i	0.346023	−	0.199777i	−0.316909	−	0.948456i	$-0.602645\pi$
$571$	8.26843	−	4.77378i	0.346023	−	0.199777i	0.662932	+	0.748679i	$0.269312\pi$
$572$	−1.14010	+	9.75567i	−0.0476698	+	0.407905i
$573$		0			0
$574$	−8.62988	+	19.5912i	−0.360204	+	0.817720i
$575$		−	10.0916i		−	0.420850i
$576$		0			0
$577$	−35.4044	+	20.4408i	−1.47391	+	0.850960i	−0.999568	−	0.0293836i	$-0.990646\pi$
$577$	−35.4044	+	20.4408i	−1.47391	+	0.850960i	−0.474337	+	0.880343i	$0.657312\pi$
$578$	−29.5922	−	33.2518i	−1.23087	−	1.38309i
$579$		0			0
$580$	−5.39280	−	12.5013i	−0.223924	−	0.519088i
$581$	0.784998	−	8.24208i	0.0325672	−	0.341939i
$582$		0			0
$583$	11.6624	+	6.73330i	0.483008	+	0.278865i
$584$	4.87737	−	10.4603i	0.201827	−	0.432850i
$585$		0			0
$586$	32.1011	+	10.6368i	1.32608	+	0.439403i
$587$	−35.5124			−1.46575			−0.732876	−	0.680362i	$-0.761822\pi$
$587$	−35.5124			−1.46575			−0.732876	+	0.680362i	$0.761822\pi$
$588$		0			0
$589$	25.4519			1.04873
$590$	2.68188	+	0.888650i	0.110411	+	0.0365852i
$591$		0			0
$592$	14.2735	+	3.38234i	0.586638	+	0.139013i
$593$	25.9003	+	14.9535i	1.06360	+	0.614068i	0.926425	−	0.376479i	$-0.122865\pi$
$593$	25.9003	+	14.9535i	1.06360	+	0.614068i	0.137172	+	0.990547i	$0.456199\pi$
$594$		0			0
$595$	−2.02297	+	21.2402i	−0.0829338	+	0.870762i
$596$	−9.46757	+	4.08412i	−0.387807	+	0.167292i
$597$		0			0
$598$	−9.36817	−	10.5267i	−0.383093	−	0.430470i
$599$	−11.5183	+	6.65008i	−0.470624	+	0.271715i	−0.716501	−	0.697586i	$-0.754257\pi$
$599$	−11.5183	+	6.65008i	−0.470624	+	0.271715i	0.245877	+	0.969301i	$0.420924\pi$
$600$		0			0
$601$		−	10.0647i		−	0.410549i	−0.978704	−	0.205274i	$-0.934191\pi$
$601$		−	10.0647i		−	0.410549i	0.978704	−	0.205274i	$-0.0658087\pi$
$602$	8.99766	−	20.4261i	0.366717	−	0.832505i
$603$		0			0
$604$	43.5006	+	5.08369i	1.77001	+	0.206853i
$605$	−9.17993	+	5.30003i	−0.373217	+	0.215477i
$606$		0			0
$607$	−9.48193	+	16.4232i	−0.384860	+	0.666597i	−0.991750	−	0.128189i	$-0.959084\pi$
$607$	−9.48193	+	16.4232i	−0.384860	+	0.666597i	0.606890	+	0.794786i	$0.292417\pi$
$608$	18.0804	−	29.3158i	0.733258	−	1.18891i
$609$		0			0
$610$	−4.13532	+	0.853914i	−0.167434	+	0.0345740i
$611$	39.2079	+	22.6367i	1.58618	+	0.915783i
$612$		0			0
$613$	19.0294	+	32.9599i	0.768590	+	1.33124i	0.938328	+	0.345748i	$0.112375\pi$
$613$	19.0294	+	32.9599i	0.768590	+	1.33124i	−0.169738	+	0.985489i	$0.554292\pi$
$614$	−2.96128	+	8.93692i	−0.119508	+	0.360665i
$615$		0			0
$616$	−8.77164	−	5.15433i	−0.353419	−	0.207674i
$617$	38.5818			1.55325			0.776623	−	0.629966i	$-0.216931\pi$
$617$	38.5818			1.55325			0.776623	+	0.629966i	$0.216931\pi$
$618$		0			0
$619$	−7.02322	−	12.1646i	−0.282287	−	0.488936i	0.689661	−	0.724133i	$-0.257760\pi$
$619$	−7.02322	−	12.1646i	−0.282287	−	0.488936i	−0.971948	+	0.235197i	$0.924426\pi$
$620$	5.78248	−	7.76751i	0.232230	−	0.311951i
$621$		0			0
$622$	−16.3809	+	3.38254i	−0.656814	+	0.135627i
$623$	−4.94043	+	6.94143i	−0.197934	+	0.278103i
$624$		0			0
$625$	−3.33800	+	5.78159i	−0.133520	+	0.231263i
$626$	−33.5804	+	29.8846i	−1.34214	+	1.19443i
$627$		0			0
$628$	5.48852	+	0.641415i	0.219016	+	0.0255953i
$629$		−	25.5326i		−	1.01805i
$630$		0			0
$631$		−	6.55732i		−	0.261043i	−0.991445	−	0.130521i	$-0.958335\pi$
$631$		−	6.55732i		−	0.261043i	0.991445	−	0.130521i	$-0.0416651\pi$
$632$	0.283027	−	0.0247694i	0.0112582	−	0.000985274i
$633$		0			0
$634$	19.5672	+	21.9871i	0.777112	+	0.873218i
$635$	8.05327	−	13.9487i	0.319584	−	0.553536i
$636$		0			0
$637$	−4.77328	+	24.8312i	−0.189124	+	0.983846i
$638$	−2.28518	−	11.0666i	−0.0904712	−	0.438132i
$639$		0			0
$640$	−4.83897	−	12.1782i	−0.191277	−	0.481385i
$641$	7.84092	+	13.5809i	0.309698	+	0.536412i	0.978296	−	0.207211i	$-0.0664388\pi$
$641$	7.84092	+	13.5809i	0.309698	+	0.536412i	−0.668598	+	0.743624i	$0.733105\pi$
$642$		0			0
$643$	−12.6415			−0.498531			−0.249266	−	0.968435i	$-0.580189\pi$
$643$	−12.6415			−0.498531			−0.249266	+	0.968435i	$0.580189\pi$
$644$	13.8904	−	4.48481i	0.547358	−	0.176726i
$645$		0			0
$646$	−56.9088	−	18.8569i	−2.23905	−	0.741916i
$647$	10.5441	+	18.2630i	0.414533	+	0.717992i	0.995379	−	0.0960215i	$-0.0306117\pi$
$647$	10.5441	+	18.2630i	0.414533	+	0.717992i	−0.580847	+	0.814013i	$0.697278\pi$
$648$		0			0
$649$	2.03077	+	1.17246i	0.0797146	+	0.0460233i
$650$	3.77941	+	18.3028i	0.148240	+	0.717897i
$651$		0			0
$652$	−3.54868	−	8.22636i	−0.138977	−	0.322169i
$653$	−11.4096	+	19.7620i	−0.446491	+	0.773345i	−0.998155	−	0.0607216i	$-0.980660\pi$
$653$	−11.4096	+	19.7620i	−0.446491	+	0.773345i	0.551664	+	0.834067i	$0.313993\pi$
$654$		0			0
$655$	6.62740	−	3.82633i	0.258954	−	0.149507i
$656$	−21.9241	+	6.56451i	−0.855992	+	0.256301i
$657$		0			0
$658$	−37.8297	+	27.7142i	−1.47476	+	1.08041i
$659$		−	42.3133i		−	1.64829i	−0.566377	−	0.824146i	$-0.691656\pi$
$659$		−	42.3133i		−	1.64829i	0.566377	−	0.824146i	$-0.308344\pi$
$660$		0			0
$661$	−21.3277	+	12.3135i	−0.829550	+	0.478941i	−0.853699	−	0.520768i	$-0.825646\pi$
$661$	−21.3277	+	12.3135i	−0.829550	+	0.478941i	0.0241486	+	0.999708i	$0.492312\pi$
$662$	−28.4797	+	25.3452i	−1.10689	+	0.985070i
$663$		0			0
$664$	7.25020	−	5.07693i	0.281362	−	0.197023i
$665$	7.75530	+	16.9708i	0.300737	+	0.658099i
$666$		0			0
$667$	14.0402	+	8.10610i	0.543638	+	0.313869i
$668$	38.6641	+	28.7833i	1.49596	+	1.11366i
$669$		0			0
$670$	−3.79359	+	11.4488i	−0.146559	+	0.442304i
$671$	−3.50466			−0.135296
$672$		0			0
$673$	−4.89981			−0.188874			−0.0944368	−	0.995531i	$-0.530105\pi$
$673$	−4.89981			−0.188874			−0.0944368	+	0.995531i	$0.530105\pi$
$674$	−12.8366	+	38.7398i	−0.494447	+	1.49220i
$675$		0			0
$676$	0.0776173	+	0.0577818i	0.00298528	+	0.00222238i
$677$	19.7504	+	11.4029i	0.759068	+	0.438248i	0.828961	−	0.559307i	$-0.188933\pi$
$677$	19.7504	+	11.4029i	0.759068	+	0.438248i	−0.0698932	+	0.997554i	$0.522266\pi$
$678$		0			0
$679$	3.24199	+	0.308776i	0.124416	+	0.0118498i
$680$	−18.6841	+	13.0835i	−0.716501	+	0.501728i
$681$		0			0
$682$	6.00393	−	5.34314i	0.229902	−	0.204600i
$683$	−2.14422	+	1.23797i	−0.0820464	+	0.0473695i	−0.540462	−	0.841368i	$-0.681750\pi$
$683$	−2.14422	+	1.23797i	−0.0820464	+	0.0473695i	0.458416	+	0.888738i	$0.348417\pi$
$684$		0			0
$685$			14.9755i			0.572186i
$686$	−21.5451	−	14.8933i	−0.822595	−	0.568628i
$687$		0			0
$688$	22.8584	−	6.84426i	0.871469	−	0.260935i
$689$	30.9865	−	17.8901i	1.18049	−	0.681557i
$690$		0			0
$691$	3.19681	−	5.53704i	0.121612	−	0.210639i	−0.798791	−	0.601608i	$-0.794527\pi$
$691$	3.19681	−	5.53704i	0.121612	−	0.210639i	0.920404	+	0.390969i	$0.127860\pi$
$692$	4.60928	+	10.6850i	0.175219	+	0.406182i
$693$		0			0
$694$	−6.81932	−	33.0245i	−0.258858	−	1.25359i
$695$	−13.4783	−	7.78172i	−0.511262	−	0.295177i
$696$		0			0
$697$	19.9175	+	34.4982i	0.754430	+	1.30671i
$698$	−34.9023	−	11.5650i	−1.32107	−	0.437742i
$699$		0			0
$700$	−18.9280	−	4.05995i	−0.715410	−	0.153452i
$701$	9.89742			0.373820			0.186910	−	0.982377i	$-0.440153\pi$
$701$	9.89742			0.373820			0.186910	+	0.982377i	$0.440153\pi$
$702$		0			0
$703$	−11.1643	−	19.3371i	−0.421069	−	0.729312i
$704$	−1.88925	−	10.7110i	−0.0712036	−	0.403688i
$705$		0			0
$706$	7.35320	+	35.6100i	0.276741	+	1.34020i
$707$	−8.30316	−	18.1697i	−0.312273	−	0.683341i
$708$		0			0
$709$	−17.3541	+	30.0582i	−0.651747	+	1.12886i	0.330952	+	0.943647i	$0.392630\pi$
$709$	−17.3541	+	30.0582i	−0.651747	+	1.12886i	−0.982699	+	0.185211i	$0.940703\pi$
$710$	−17.2850	−	19.4227i	−0.648696	−	0.728920i
$711$		0			0
$712$	−9.07364	+	0.794089i	−0.340049	+	0.0297597i
$713$			11.5309i			0.431836i
$714$		0			0
$715$		−	5.68830i		−	0.212731i
$716$	−27.7876	−	3.24740i	−1.03847	−	0.121361i
$717$		0			0
$718$	30.8507	−	27.4553i	1.15134	−	1.02462i
$719$	−2.29538	+	3.97572i	−0.0856034	+	0.148269i	−0.905648	−	0.424030i	$-0.860615\pi$
$719$	−2.29538	+	3.97572i	−0.0856034	+	0.148269i	0.820045	+	0.572299i	$0.193948\pi$
$720$		0			0
$721$	−16.3425	−	11.6314i	−0.608626	−	0.433178i
$722$	−25.0302	+	5.16857i	−0.931529	+	0.192354i
$723$		0			0
$724$	12.1940	−	16.3800i	0.453187	−	0.608759i
$725$	−10.7507	−	18.6207i	−0.399270	−	0.691556i
$726$		0			0
$727$	5.14301			0.190744			0.0953718	−	0.995442i	$-0.469596\pi$
$727$	5.14301			0.190744			0.0953718	+	0.995442i	$0.469596\pi$
$728$	−23.5130	+	13.3360i	−0.871448	+	0.494266i
$729$		0			0
$730$	−2.10239	+	6.34484i	−0.0778129	+	0.234833i
$731$	−20.7664	−	35.9684i	−0.768071	−	1.33034i
$732$		0			0
$733$	11.0631	+	6.38726i	0.408624	+	0.235919i	0.690198	−	0.723620i	$-0.257523\pi$
$733$	11.0631	+	6.38726i	0.408624	+	0.235919i	−0.281575	+	0.959539i	$0.590857\pi$
$734$	36.7410	−	7.58676i	1.35614	−	0.280032i
$735$		0			0
$736$	13.2814	+	8.19128i	0.489560	+	0.301935i
$737$	−5.00518	+	8.66922i	−0.184368	+	0.319335i
$738$		0			0
$739$	15.7546	−	9.09590i	0.579541	−	0.334598i	−0.181410	−	0.983408i	$-0.558066\pi$
$739$	15.7546	−	9.09590i	0.579541	−	0.334598i	0.760951	+	0.648810i	$0.224733\pi$
$740$	−8.43780	−	0.986083i	−0.310180	−	0.0362491i
$741$		0			0
$742$	4.01976	+	36.8433i	0.147570	+	1.35256i
$743$			18.5365i			0.680039i	0.940418	+	0.340019i	$0.110434\pi$
$743$			18.5365i			0.680039i	−0.940418	+	0.340019i	$0.889566\pi$
$744$		0			0
$745$	5.17140	−	2.98571i	0.189465	−	0.109388i
$746$	−21.1261	−	23.7388i	−0.773481	−	0.869138i
$747$		0			0
$748$	−17.3830	+	7.49869i	−0.635587	+	0.274179i
$749$	15.0283	−	21.1152i	0.549123	−	0.771533i
$750$		0			0
$751$	−10.5927	−	6.11570i	−0.386533	−	0.223165i	0.294124	−	0.955767i	$-0.404972\pi$
$751$	−10.5927	−	6.11570i	−0.386533	−	0.223165i	−0.680657	+	0.732602i	$0.738306\pi$
$752$	−48.7822	−	11.5597i	−1.77890	−	0.421540i
$753$		0			0
$754$	−28.5000	−	9.44359i	−1.03791	−	0.343915i
$755$	−25.3642			−0.923097
$756$		0			0
$757$	−0.220216			−0.00800389			−0.00400194	−	0.999992i	$-0.501274\pi$
$757$	−0.220216			−0.00800389			−0.00400194	+	0.999992i	$0.501274\pi$
$758$	21.9651	+	7.27821i	0.797807	+	0.264356i
$759$		0			0
$760$	−8.42954	+	18.0785i	−0.305771	+	0.655775i
$761$	38.1299	+	22.0143i	1.38221	+	0.798018i	0.992421	−	0.122888i	$-0.0392155\pi$
$761$	38.1299	+	22.0143i	1.38221	+	0.798018i	0.389786	+	0.920905i	$0.372549\pi$
$762$		0			0
$763$	−19.8400	+	9.06646i	−0.718256	+	0.328228i
$764$	−16.4783	−	38.1990i	−0.596163	−	1.38199i
$765$		0			0
$766$	0.776450	+	0.872474i	0.0280543	+	0.0315238i
$767$	5.39566	−	3.11518i	0.194826	−	0.112483i
$768$		0			0
$769$		−	37.8753i		−	1.36582i	−0.730503	−	0.682909i	$-0.760714\pi$
$769$		−	37.8753i		−	1.36582i	0.730503	−	0.682909i	$-0.239286\pi$
$770$	5.39212	+	2.37522i	0.194318	+	0.0855969i
$771$		0			0
$772$	−5.38259	+	46.0582i	−0.193724	+	1.65767i
$773$	2.36114	−	1.36320i	0.0849241	−	0.0490310i	−0.456937	−	0.889499i	$-0.651053\pi$
$773$	2.36114	−	1.36320i	0.0849241	−	0.0490310i	0.541861	+	0.840468i	$0.317720\pi$
$774$		0			0
$775$	7.64640	−	13.2440i	0.274667	−	0.475737i
$776$	1.99700	+	2.85184i	0.0716880	+	0.102375i
$777$		0			0
$778$	0.253021	−	0.0522469i	0.00907123	−	0.00187314i
$779$	30.1691	+	17.4181i	1.08092	+	0.624069i
$780$		0			0
$781$	−10.7899	−	18.6886i	−0.386092	−	0.668732i
$782$	8.54307	−	25.7823i	0.305500	−	0.921974i
$783$		0			0
$784$	−2.82352	−	27.8573i	−0.100840	−	0.994903i
$785$	−3.20023			−0.114221
$786$		0			0
$787$	−18.0195	−	31.2107i	−0.642326	−	1.11254i	−0.984912	−	0.173055i	$-0.944636\pi$
$787$	−18.0195	−	31.2107i	−0.642326	−	1.11254i	0.342586	−	0.939486i	$-0.388697\pi$
$788$	12.6995	+	9.45409i	0.452402	+	0.336788i
$789$		0			0
$790$	−0.161138	+	0.0332738i	−0.00573303	+	0.00118383i
$791$	−3.71334	+	38.9882i	−0.132031	+	1.38626i
$792$		0			0
$793$	−4.65586	+	8.06418i	−0.165334	+	0.286367i
$794$	2.88005	−	2.56308i	0.102209	−	0.0909602i
$795$		0			0
$796$	0.803584	−	6.87618i	0.0284823	−	0.243720i
$797$			41.5025i			1.47009i	0.678017	+	0.735046i	$0.262840\pi$
$797$			41.5025i			1.47009i	−0.678017	+	0.735046i	$0.737160\pi$
$798$		0			0
$799$			87.2619i			3.08710i
$800$	−9.82272	−	18.2154i	−0.347286	−	0.644012i
$801$		0			0
$802$	26.9966	+	30.3353i	0.953283	+	1.07118i
$803$	−2.77384	+	4.80444i	−0.0978868	+	0.169545i
$804$		0			0
$805$	−7.68856	+	3.51351i	−0.270986	+	0.123835i
$806$	−4.31843	−	20.9132i	−0.152110	−	0.736637i
$807$		0			0
$808$	9.02503	−	19.3556i	0.317500	−	0.680928i
$809$	−6.58994	−	11.4141i	−0.231690	−	0.401299i	0.726616	−	0.687044i	$-0.241092\pi$
$809$	−6.58994	−	11.4141i	−0.231690	−	0.401299i	−0.958306	+	0.285746i	$0.907759\pi$
$810$		0			0
$811$	−1.44850			−0.0508636			−0.0254318	−	0.999677i	$-0.508096\pi$
$811$	−1.44850			−0.0508636			−0.0254318	+	0.999677i	$0.508096\pi$
$812$	20.8524	−	23.0727i	0.731775	−	0.809695i
$813$		0			0
$814$	−6.69303	−	2.21776i	−0.234591	−	0.0777325i
$815$	2.59428	+	4.49342i	0.0908735	+	0.157398i
$816$		0			0
$817$	−31.4548	−	18.1604i	−1.10046	−	0.635353i
$818$	−1.32781	−	6.43031i	−0.0464259	−	0.224830i
$819$		0			0
$820$	12.1699	−	5.24985i	0.424992	−	0.183333i
$821$	2.74548	−	4.75532i	0.0958181	−	0.165962i	−0.814132	−	0.580680i	$-0.802787\pi$
$821$	2.74548	−	4.75532i	0.0958181	−	0.165962i	0.909950	+	0.414719i	$0.136120\pi$
$822$		0			0
$823$	−16.2490	+	9.38136i	−0.566404	+	0.327014i	−0.755712	−	0.654904i	$-0.772709\pi$
$823$	−16.2490	+	9.38136i	−0.566404	+	0.327014i	0.189308	+	0.981918i	$0.439376\pi$
$824$	−1.86956	−	21.3624i	−0.0651290	−	0.744196i
$825$		0			0
$826$	0.699957	+	6.41549i	0.0243546	+	0.223223i
$827$			47.3905i			1.64793i	0.566641	+	0.823965i	$0.308243\pi$
$827$			47.3905i			1.64793i	−0.566641	+	0.823965i	$0.691757\pi$
$828$		0			0
$829$	41.6495	−	24.0463i	1.44655	−	0.835164i	0.448272	−	0.893897i	$-0.352039\pi$
$829$	41.6495	−	24.0463i	1.44655	−	0.835164i	0.998274	+	0.0587332i	$0.0187061\pi$
$830$	−3.82918	+	3.40774i	−0.132913	+	0.118284i
$831$		0			0
$832$	−27.1558	−	9.88224i	−0.941458	−	0.342605i
$833$	−46.0487	+	15.9627i	−1.59549	+	0.553075i
$834$		0			0
$835$	−24.1753	−	13.9576i	−0.836621	−	0.483023i
$836$	−9.88620	+	13.2800i	−0.341921	+	0.459297i
$837$		0			0
$838$	−10.0427	+	30.3080i	−0.346919	+	1.04697i
$839$	−17.7789			−0.613796			−0.306898	−	0.951742i	$-0.599291\pi$
$839$	−17.7789			−0.613796			−0.306898	+	0.951742i	$0.599291\pi$
$840$		0			0
$841$	5.54191			0.191100
$842$	12.5434	−	37.8550i	0.432275	−	1.30457i
$843$		0			0
$844$	−3.57976	+	4.80863i	−0.123220	+	0.165520i
$845$	−0.0485313	−	0.0280196i	−0.00166953	−	0.000963903i
$846$		0			0
$847$	−19.7267	−	14.0401i	−0.677817	−	0.482423i
$848$	−27.1884	+	28.8201i	−0.933654	+	0.989688i
$849$		0			0
$850$	−26.9091	+	23.9475i	−0.922974	+	0.821392i
$851$	8.76060	−	5.05794i	0.300310	−	0.173384i
$852$		0			0
$853$			44.7018i			1.53056i	0.643698	+	0.765280i	$0.277399\pi$
$853$			44.7018i			1.53056i	−0.643698	+	0.765280i	$0.722601\pi$
$854$	−5.70017	−	7.78072i	−0.195056	−	0.266251i
$855$		0			0
$856$	27.6012	−	2.41555i	0.943389	−	0.0825617i
$857$	3.75104	−	2.16566i	0.128133	−	0.0739777i	−0.434563	−	0.900641i	$-0.643097\pi$
$857$	3.75104	−	2.16566i	0.128133	−	0.0739777i	0.562696	+	0.826664i	$0.309764\pi$
$858$		0			0
$859$	11.0825	−	19.1955i	0.378131	−	0.654943i	−0.612659	−	0.790347i	$-0.709900\pi$
$859$	11.0825	−	19.1955i	0.378131	−	0.654943i	0.990790	+	0.135405i	$0.0432334\pi$
$860$	−12.6885	+	5.47358i	−0.432676	+	0.186647i
$861$		0			0
$862$	3.21033	+	15.5469i	0.109344	+	0.529530i
$863$	−22.7287	−	13.1224i	−0.773695	−	0.446693i	0.0604962	−	0.998168i	$-0.480732\pi$
$863$	−22.7287	−	13.1224i	−0.773695	−	0.446693i	−0.834191	+	0.551475i	$0.814065\pi$
$864$		0			0
$865$	−3.36963	−	5.83637i	−0.114571	−	0.198443i
$866$	−10.2257	−	3.38831i	−0.347482	−	0.115139i
$867$		0			0
$868$	21.6275	+	4.63899i	0.734085	+	0.157458i
$869$	−0.136563			−0.00463260
$870$		0			0
$871$	13.2985	+	23.0337i	0.450603	+	0.780467i
$872$	−21.1350	−	9.85470i	−0.715720	−	0.333722i
$873$		0			0
$874$	−4.80338	−	23.2617i	−0.162477	−	0.786840i
$875$	26.4141	+	2.51576i	0.892961	+	0.0850481i
$876$		0			0
$877$	−4.84358	+	8.38932i	−0.163556	+	0.283287i	−0.936142	−	0.351623i	$-0.885630\pi$
$877$	−4.84358	+	8.38932i	−0.163556	+	0.283287i	0.772586	+	0.634911i	$0.218963\pi$
$878$	−12.4500	−	13.9897i	−0.420166	−	0.472128i
$879$		0			0
$880$	1.80676	+	6.03421i	0.0609059	+	0.203413i
$881$			25.0989i			0.845605i	0.906222	+	0.422802i	$0.138954\pi$
$881$			25.0989i			0.845605i	−0.906222	+	0.422802i	$0.861046\pi$
$882$		0			0
$883$		−	24.4711i		−	0.823517i	−0.911293	−	0.411758i	$-0.864915\pi$
$883$		−	24.4711i		−	0.823517i	0.911293	−	0.411758i	$-0.135085\pi$
$884$	−5.83857	+	49.9600i	−0.196372	+	1.68034i
$885$		0			0
$886$	27.2762	−	24.2742i	0.916361	−	0.815507i
$887$	10.9768	−	19.0124i	0.368566	−	0.638375i	−0.620776	−	0.783988i	$-0.713182\pi$
$887$	10.9768	−	19.0124i	0.368566	−	0.638375i	0.989342	+	0.145614i	$0.0465156\pi$
$888$		0			0
$889$	36.6252	+	3.48829i	1.22837	+	0.116993i
$890$	5.16596	−	1.06673i	0.173163	−	0.0357570i
$891$		0			0
$892$	−25.6625	−	19.1043i	−0.859243	−	0.639659i
$893$	38.1558	+	66.0878i	1.27683	+	2.21154i
$894$		0			0
$895$	16.2023			0.541584
$896$	20.7069	−	21.6154i	0.691769	−	0.722119i
$897$		0			0
$898$	−7.16353	+	21.6190i	−0.239050	+	0.721435i
$899$	12.2839	+	21.2764i	0.409692	+	0.709608i
$900$		0			0
$901$	59.7247	+	34.4821i	1.98972	+	1.14877i
$902$	10.7733	−	2.22461i	0.358711	−	0.0740713i
$903$		0			0
$904$	−34.2962	+	24.0158i	−1.14067	+	0.798755i
$905$	−5.91313	+	10.2418i	−0.196559	+	0.340451i
$906$		0			0
$907$	45.7123	−	26.3920i	1.51785	−	0.876332i	0.518072	−	0.855337i	$-0.326650\pi$
$907$	45.7123	−	26.3920i	1.51785	−	0.876332i	0.999780	−	0.0209953i	$-0.00668352\pi$
$908$	5.98687	−	51.2290i	0.198681	−	1.70009i
$909$		0			0
$910$	12.6287	−	9.25178i	0.418636	−	0.306693i
$911$		−	26.5062i		−	0.878191i	−0.898440	−	0.439096i	$-0.855299\pi$
$911$		−	26.5062i		−	0.878191i	0.898440	−	0.439096i	$-0.144701\pi$
$912$		0			0
$913$	−3.68446	+	2.12722i	−0.121938	+	0.0704008i
$914$	35.5784	+	39.9784i	1.17683	+	1.32237i
$915$		0			0
$916$	−17.5509	−	40.6854i	−0.579896	−	1.34428i
$917$	14.2416	+	10.1362i	0.470299	+	0.334726i
$918$		0			0
$919$	−0.689059	−	0.397829i	−0.0227300	−	0.0131232i	0.488592	−	0.872512i	$-0.337511\pi$
$919$	−0.689059	−	0.397829i	−0.0227300	−	0.0131232i	−0.511322	+	0.859389i	$0.670844\pi$
$920$	−8.19040	−	3.81897i	−0.270029	−	0.125908i
$921$		0			0
$922$	−41.3635	−	13.7060i	−1.36223	−	0.451382i
$923$	−57.3364			−1.88725
$924$		0			0
$925$	−13.4161			−0.441119
$926$	−25.6889	−	8.51213i	−0.844191	−	0.279726i
$927$		0			0
$928$	33.2326	+	0.965467i	1.09092	+	0.0316930i
$929$	0.0371415	+	0.0214437i	0.00121857	+	0.000703544i	0.500609	−	0.865673i	$-0.333109\pi$
$929$	0.0371415	+	0.0214437i	0.00121857	+	0.000703544i	−0.499391	+	0.866377i	$0.666443\pi$
$930$		0			0
$931$	−27.8951	+	32.2244i	−0.914226	+	1.05611i
$932$	−7.67707	+	3.31173i	−0.251471	+	0.108479i
$933$		0			0
$934$	4.65423	+	5.22982i	0.152291	+	0.171125i
$935$	9.49500	−	5.48194i	0.310520	−	0.179279i
$936$		0			0
$937$			9.01798i			0.294604i	0.989092	+	0.147302i	$0.0470590\pi$
$937$			9.01798i			0.294604i	−0.989092	+	0.147302i	$0.952941\pi$
$938$	−27.3873	+	2.98807i	−0.894227	+	0.0975640i
$939$		0			0
$940$	28.8376	+	3.37010i	0.940579	+	0.109921i
$941$	37.5521	−	21.6807i	1.22416	−	0.706771i	0.258361	−	0.966048i	$-0.416818\pi$
$941$	37.5521	−	21.6807i	1.22416	−	0.706771i	0.965803	+	0.259277i	$0.0834843\pi$
$942$		0			0
$943$	−7.89122	+	13.6680i	−0.256974	+	0.445091i
$944$	−4.73430	+	5.01843i	−0.154088	+	0.163336i
$945$		0			0
$946$	−11.2324	+	2.31941i	−0.365197	+	0.0754105i
$947$	−15.5511	−	8.97845i	−0.505344	−	0.291761i	0.225574	−	0.974226i	$-0.427574\pi$
$947$	−15.5511	−	8.97845i	−0.505344	−	0.291761i	−0.730918	+	0.682466i	$0.760908\pi$
$948$		0			0
$949$	7.36997	+	12.7652i	0.239239	+	0.414375i
$950$	−9.90840	+	29.9028i	−0.321471	+	0.970174i
$951$		0			0
$952$	−44.9207	−	26.3960i	−1.45589	−	0.855498i
$953$	19.8477			0.642930			0.321465	−	0.946921i	$-0.395825\pi$
$953$	19.8477			0.642930			0.321465	+	0.946921i	$0.395825\pi$
$954$		0			0
$955$	12.0465	+	20.8651i	0.389816	+	0.675180i
$956$	−22.6659	+	30.4467i	−0.733066	+	0.984716i
$957$		0			0
$958$	−2.57359	+	0.531427i	−0.0831488	+	0.0171696i
$959$	−31.1128	+	14.2179i	−1.00468	+	0.459119i
$960$		0			0
$961$	6.76306	−	11.7140i	0.218163	−	0.377870i
$962$	−13.9946	+	12.4543i	−0.451203	+	0.401544i
$963$		0			0
$964$	11.3555	+	1.32706i	0.365736	+	0.0427417i
$965$		−	26.8555i		−	0.864508i
$966$		0			0
$967$			44.4334i			1.42888i	0.699695	+	0.714442i	$0.253319\pi$
$967$			44.4334i			1.42888i	−0.699695	+	0.714442i	$0.746681\pi$
$968$	−2.25670	−	25.7862i	−0.0725331	−	0.828799i
$969$		0			0
$970$	−1.34042	−	1.50619i	−0.0430384	−	0.0483610i
$971$	−4.23520	+	7.33558i	−0.135914	+	0.235410i	−0.925946	−	0.377655i	$-0.876730\pi$
$971$	−4.23520	+	7.33558i	−0.135914	+	0.235410i	0.790032	+	0.613065i	$0.210064\pi$
$972$		0			0
$973$	3.37067	−	35.3902i	0.108059	−	1.13456i
$974$	4.86014	+	23.5366i	0.155729	+	0.754161i
$975$		0			0
$976$	2.37757	−	10.0334i	0.0761043	−	0.321161i
$977$	−17.7710	−	30.7804i	−0.568546	−	0.984751i	−0.996710	−	0.0810496i	$-0.974173\pi$
$977$	−17.7710	−	30.7804i	−0.568546	−	0.984751i	0.428164	−	0.903701i	$-0.359161\pi$
$978$		0			0
$979$	4.37812			0.139925
$980$	3.49680	+	15.8343i	0.111701	+	0.505807i
$981$		0			0
$982$	−5.32092	−	1.76311i	−0.169798	−	0.0562631i
$983$	−6.48843	−	11.2383i	−0.206949	−	0.358446i	0.743803	−	0.668399i	$-0.233020\pi$
$983$	−6.48843	−	11.2383i	−0.206949	−	0.358446i	−0.950752	+	0.309953i	$0.899687\pi$
$984$		0			0
$985$	−7.94056	−	4.58448i	−0.253007	−	0.146074i
$986$	−11.7027	−	56.6736i	−0.372690	−	1.80486i
$987$		0			0
$988$	17.4235	+	40.3902i	0.554315	+	1.28498i
$989$	8.22752	−	14.2505i	0.261620	−	0.453139i
$990$		0			0
$991$	28.3992	−	16.3963i	0.902129	−	0.520845i	0.0242389	−	0.999706i	$-0.492284\pi$
$991$	28.3992	−	16.3963i	0.902129	−	0.520845i	0.877890	+	0.478862i	$0.158950\pi$
$992$	11.2237	+	20.8133i	0.356351	+	0.660823i
$993$		0			0
$994$	23.9415	−	54.3509i	0.759378	−	1.72391i
$995$			4.00934i			0.127105i
$996$		0			0
$997$	28.1732	−	16.2658i	0.892255	−	0.515144i	0.0175757	−	0.999846i	$-0.494405\pi$
$997$	28.1732	−	16.2658i	0.892255	−	0.515144i	0.874679	+	0.484702i	$0.161072\pi$
$998$	41.7072	−	37.1169i	1.32022	−	1.17492i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.d.271.10	yes	32
3.2	odd	2	inner	756.2.bf.d.271.7	yes	32
4.3	odd	2		756.2.bf.a.271.13	yes	32
7.3	odd	6		756.2.bf.a.703.13	yes	32
12.11	even	2		756.2.bf.a.271.4	✓	32
21.17	even	6		756.2.bf.a.703.4	yes	32
28.3	even	6	inner	756.2.bf.d.703.10	yes	32
84.59	odd	6	inner	756.2.bf.d.703.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.a.271.4	✓	32	12.11	even	2
756.2.bf.a.271.13	yes	32	4.3	odd	2
756.2.bf.a.703.4	yes	32	21.17	even	6
756.2.bf.a.703.13	yes	32	7.3	odd	6
756.2.bf.d.271.7	yes	32	3.2	odd	2	inner
756.2.bf.d.271.10	yes	32	1.1	even	1	trivial
756.2.bf.d.703.7	yes	32	84.59	odd	6	inner
756.2.bf.d.703.10	yes	32	28.3	even	6	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.444821 - 1.34244i) q^{2} +(-1.60427 - 1.19429i) q^{4} +(1.00309 + 0.579135i) q^{5} +(-0.250854 + 2.63383i) q^{7} +(-2.31687 + 1.62238i) q^{8} +O(q^{10})\)	\(q+(0.444821 - 1.34244i) q^{2} +(-1.60427 - 1.19429i) q^{4} +(1.00309 + 0.579135i) q^{5} +(-0.250854 + 2.63383i) q^{7} +(-2.31687 + 1.62238i) q^{8} +(1.22365 - 1.08897i) q^{10} +(1.17740 - 0.679774i) q^{11} -3.61225i q^{13} +(3.42417 + 1.50834i) q^{14} +(1.14735 + 3.83192i) q^{16} +(6.02963 - 3.48121i) q^{17} +(3.04436 - 5.27298i) q^{19} +(-0.917574 - 2.12707i) q^{20} +(-0.388819 - 1.88297i) q^{22} +(2.38891 + 1.37924i) q^{23} +(-1.82920 - 3.16828i) q^{25} +(-4.84922 - 1.60681i) q^{26} +(3.54799 - 3.92578i) q^{28} +5.87724 q^{29} +(2.09009 + 3.62014i) q^{31} +(5.65447 + 0.164272i) q^{32} +(-1.99119 - 9.64291i) q^{34} +(-1.77697 + 2.49670i) q^{35} +(1.83360 - 3.17589i) q^{37} +(-5.72445 - 6.43239i) q^{38} +(-3.26361 + 0.285618i) q^{40} +5.72144i q^{41} -5.96527i q^{43} +(-2.70072 - 0.315619i) q^{44} +(2.91417 - 2.59344i) q^{46} +(-6.26664 + 10.8541i) q^{47} +(-6.87415 - 1.32141i) q^{49} +(-5.06688 + 1.04627i) q^{50} +(-4.31407 + 5.79502i) q^{52} +(4.95261 + 8.57816i) q^{53} +1.57472 q^{55} +(-3.69189 - 6.50922i) q^{56} +(2.61432 - 7.88981i) q^{58} +(0.862393 + 1.49371i) q^{59} +(-2.23245 - 1.28891i) q^{61} +(5.78952 - 1.19549i) q^{62} +(2.73575 - 7.51769i) q^{64} +(2.09198 - 3.62342i) q^{65} +(-6.37655 + 3.68150i) q^{67} +(-13.8307 - 1.61632i) q^{68} +(2.56122 + 3.49606i) q^{70} -15.8728i q^{71} +(-3.53385 + 2.04027i) q^{73} +(-3.44780 - 3.87420i) q^{74} +(-11.1814 + 4.82344i) q^{76} +(1.49505 + 3.27161i) q^{77} +(-0.0869902 - 0.0502238i) q^{79} +(-1.06830 + 4.50824i) q^{80} +(7.68067 + 2.54502i) q^{82} -3.12931 q^{83} +8.06436 q^{85} +(-8.00800 - 2.65348i) q^{86} +(-1.62503 + 3.48514i) q^{88} +(2.78884 + 1.61014i) q^{89} +(9.51407 + 0.906147i) q^{91} +(-2.18524 - 5.06571i) q^{92} +(11.7835 + 13.2407i) q^{94} +(6.10754 - 3.52619i) q^{95} -1.23090i q^{97} +(-4.83168 + 8.64031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{7}+O(q^{10}) \) 32 * q + 2 * q^7	\( 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) \) 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

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