LMFDB - Embedded newform 756.2.ba.a.71.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.10
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +O(q^{10})$	\(q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +(0.635018 + 3.60669i) q^{10} +(0.124825 + 0.216204i) q^{11} +(-0.0646102 + 0.111908i) q^{13} +(1.32880 + 0.484025i) q^{14} +(-3.75739 - 1.37188i) q^{16} -0.554691i q^{17} +3.58986i q^{19} +(3.33106 - 3.96573i) q^{20} +(0.120837 - 0.331737i) q^{22} +(-3.94814 + 6.83839i) q^{23} +(0.852871 + 1.47722i) q^{25} +(0.179977 - 0.0316879i) q^{26} +(-0.683091 - 1.87973i) q^{28} +(5.90477 - 3.40912i) q^{29} +(6.96683 + 4.02230i) q^{31} +(1.92804 + 5.31814i) q^{32} +(-0.601052 + 0.504084i) q^{34} +2.58954 q^{35} +9.96519 q^{37} +(3.88991 - 3.26234i) q^{38} +(-7.32434 - 0.00555133i) q^{40} +(-4.25964 - 2.45930i) q^{41} +(3.78791 - 2.18695i) q^{43} +(-0.469276 + 0.170534i) q^{44} +(10.9979 - 1.93636i) q^{46} +(2.41916 + 4.19011i) q^{47} +(0.500000 - 0.866025i) q^{49} +(0.825622 - 2.26660i) q^{50} +(-0.197893 - 0.166223i) q^{52} +9.00057i q^{53} -0.646482i q^{55} +(-1.41607 + 2.44842i) q^{56} +(-9.06010 - 3.30020i) q^{58} +(-3.71629 + 6.43680i) q^{59} +(6.42524 + 11.1288i) q^{61} +(-1.97273 - 11.2045i) q^{62} +(4.01050 - 6.92213i) q^{64} +(0.289791 - 0.167311i) q^{65} +(5.23554 + 3.02274i) q^{67} +(1.09243 + 0.193194i) q^{68} +(-2.35329 - 2.80598i) q^{70} +15.7820 q^{71} -14.1020 q^{73} +(-9.05602 - 10.7981i) q^{74} +(-7.07002 - 1.25032i) q^{76} +(-0.216204 - 0.124825i) q^{77} +(2.04035 - 1.17800i) q^{79} +(6.65009 + 7.94155i) q^{80} +(1.20616 + 6.85059i) q^{82} +(2.36518 + 4.09661i) q^{83} +(-0.718199 + 1.24396i) q^{85} +(-5.81205 - 2.11708i) q^{86} +(0.611249 + 0.353523i) q^{88} -7.82233i q^{89} -0.129220i q^{91} +(-12.0927 - 10.1574i) q^{92} +(2.34187 - 6.42918i) q^{94} +(4.64806 - 8.05067i) q^{95} +(-5.67078 - 9.82208i) q^{97} +(-1.39279 + 0.245224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.908765	−	1.08358i	−0.642594	−	0.766207i
$2$	−0.908765	−	1.08358i	−0.642594	−	0.766207i
$3$		0			0
$3$		0			0
$4$	−0.348292	+	1.96944i	−0.174146	+	0.984720i
$5$	−2.24261	−	1.29477i	−1.00293	−	0.579040i	−0.0938136	−	0.995590i	$-0.529906\pi$
$5$	−2.24261	−	1.29477i	−1.00293	−	0.579040i	−0.909113	+	0.416550i	$0.863239\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$	2.45056	−	1.41236i	0.866404	−	0.499343i
$9$		0			0
$10$	0.635018	+	3.60669i	0.200810	+	1.14054i
$11$	0.124825	+	0.216204i	0.0376363	+	0.0651879i	0.884230	−	0.467052i	$-0.154684\pi$
$11$	0.124825	+	0.216204i	0.0376363	+	0.0651879i	−0.846594	+	0.532240i	$0.821351\pi$
$12$		0			0
$13$	−0.0646102	+	0.111908i	−0.0179197	+	0.0310377i	−0.874846	−	0.484401i	$-0.839038\pi$
$13$	−0.0646102	+	0.111908i	−0.0179197	+	0.0310377i	0.856927	+	0.515439i	$0.172371\pi$
$14$	1.32880	+	0.484025i	0.355138	+	0.129361i
$15$		0			0
$16$	−3.75739	−	1.37188i	−0.939347	−	0.342970i
$17$		−	0.554691i		−	0.134532i	−0.997735	−	0.0672662i	$-0.978572\pi$
$17$		−	0.554691i		−	0.134532i	0.997735	−	0.0672662i	$-0.0214277\pi$
$18$		0			0
$19$			3.58986i			0.823571i	0.911281	+	0.411786i	$0.135095\pi$
$19$			3.58986i			0.823571i	−0.911281	+	0.411786i	$0.864905\pi$
$20$	3.33106	−	3.96573i	0.744847	−	0.886764i
$21$		0			0
$22$	0.120837	−	0.331737i	0.0257626	−	0.0707265i
$23$	−3.94814	+	6.83839i	−0.823245	+	1.42590i	0.0800083	+	0.996794i	$0.474505\pi$
$23$	−3.94814	+	6.83839i	−0.823245	+	1.42590i	−0.903253	+	0.429108i	$0.858828\pi$
$24$		0			0
$25$	0.852871	+	1.47722i	0.170574	+	0.295443i
$26$	0.179977	−	0.0316879i	0.0352964	−	0.00621451i
$27$		0			0
$28$	−0.683091	−	1.87973i	−0.129092	−	0.355236i
$29$	5.90477	−	3.40912i	1.09649	−	0.633058i	0.161192	−	0.986923i	$-0.448466\pi$
$29$	5.90477	−	3.40912i	1.09649	−	0.633058i	0.935296	+	0.353865i	$0.115133\pi$
$30$		0			0
$31$	6.96683	+	4.02230i	1.25128	+	0.722427i	0.971364	−	0.237597i	$-0.0763598\pi$
$31$	6.96683	+	4.02230i	1.25128	+	0.722427i	0.279917	+	0.960024i	$0.409693\pi$
$32$	1.92804	+	5.31814i	0.340833	+	0.940124i
$33$		0			0
$34$	−0.601052	+	0.504084i	−0.103080	+	0.0864497i
$35$	2.58954			0.437713
$36$		0			0
$37$	9.96519			1.63827			0.819134	−	0.573603i	$-0.194455\pi$
$37$	9.96519			1.63827			0.819134	+	0.573603i	$0.194455\pi$
$38$	3.88991	−	3.26234i	0.631026	−	0.529222i
$39$		0			0
$40$	−7.32434	−	0.00555133i	−1.15808	−	0.000877742i
$41$	−4.25964	−	2.45930i	−0.665244	−	0.384079i	0.129028	−	0.991641i	$-0.458814\pi$
$41$	−4.25964	−	2.45930i	−0.665244	−	0.384079i	−0.794272	+	0.607562i	$0.792148\pi$
$42$		0			0
$43$	3.78791	−	2.18695i	0.577651	−	0.333507i	−0.182549	−	0.983197i	$-0.558435\pi$
$43$	3.78791	−	2.18695i	0.577651	−	0.333507i	0.760199	+	0.649690i	$0.225101\pi$
$44$	−0.469276	+	0.170534i	−0.0707460	+	0.0257090i
$45$		0			0
$46$	10.9979	−	1.93636i	1.62155	−	0.285500i
$47$	2.41916	+	4.19011i	0.352871	+	0.611190i	0.986751	−	0.162241i	$-0.0518721\pi$
$47$	2.41916	+	4.19011i	0.352871	+	0.611190i	−0.633880	+	0.773431i	$0.718539\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	0.825622	−	2.26660i	0.116761	−	0.320545i
$51$		0			0
$52$	−0.197893	−	0.166223i	−0.0274429	−	0.0230509i
$53$			9.00057i			1.23632i	0.786051	+	0.618162i	$0.212122\pi$
$53$			9.00057i			1.23632i	−0.786051	+	0.618162i	$0.787878\pi$
$54$		0			0
$55$		−	0.646482i		−	0.0871715i
$56$	−1.41607	+	2.44842i	−0.189230	+	0.327184i
$57$		0			0
$58$	−9.06010	−	3.30020i	−1.18965	−	0.433338i
$59$	−3.71629	+	6.43680i	−0.483820	+	0.838001i	−0.999827	−	0.0185836i	$-0.994084\pi$
$59$	−3.71629	+	6.43680i	−0.483820	+	0.838001i	0.516007	+	0.856584i	$0.327418\pi$
$60$		0			0
$61$	6.42524	+	11.1288i	0.822667	+	1.42490i	0.903689	+	0.428189i	$0.140848\pi$
$61$	6.42524	+	11.1288i	0.822667	+	1.42490i	−0.0810220	+	0.996712i	$0.525818\pi$
$62$	−1.97273	−	11.2045i	−0.250537	−	1.42297i
$63$		0			0
$64$	4.01050	−	6.92213i	0.501312	−	0.865266i
$65$	0.289791	−	0.167311i	0.0359442	−	0.0207524i
$66$		0			0
$67$	5.23554	+	3.02274i	0.639623	+	0.369287i	0.784469	−	0.620167i	$-0.212935\pi$
$67$	5.23554	+	3.02274i	0.639623	+	0.369287i	−0.144846	+	0.989454i	$0.546269\pi$
$68$	1.09243	+	0.193194i	0.132477	+	0.0234282i
$69$		0			0
$70$	−2.35329	−	2.80598i	−0.281272	−	0.335379i
$71$	15.7820			1.87298			0.936489	−	0.350697i	$-0.114055\pi$
$71$	15.7820			1.87298			0.936489	+	0.350697i	$0.114055\pi$
$72$		0			0
$73$	−14.1020			−1.65051			−0.825256	−	0.564759i	$-0.808969\pi$
$73$	−14.1020			−1.65051			−0.825256	+	0.564759i	$0.808969\pi$
$74$	−9.05602	−	10.7981i	−1.05274	−	1.25525i
$75$		0			0
$76$	−7.07002	−	1.25032i	−0.810987	−	0.143421i
$77$	−0.216204	−	0.124825i	−0.0246387	−	0.0142252i
$78$		0			0
$79$	2.04035	−	1.17800i	0.229558	−	0.132535i	−0.380810	−	0.924653i	$-0.624355\pi$
$79$	2.04035	−	1.17800i	0.229558	−	0.132535i	0.610368	+	0.792118i	$0.291022\pi$
$80$	6.65009	+	7.94155i	0.743502	+	0.887892i
$81$		0			0
$82$	1.20616	+	6.85059i	0.133198	+	0.756521i
$83$	2.36518	+	4.09661i	0.259612	+	0.449662i	0.966138	−	0.258026i	$-0.0830719\pi$
$83$	2.36518	+	4.09661i	0.259612	+	0.449662i	−0.706526	+	0.707687i	$0.749739\pi$
$84$		0			0
$85$	−0.718199	+	1.24396i	−0.0778996	+	0.134926i
$86$	−5.81205	−	2.11708i	−0.626730	−	0.228290i
$87$		0			0
$88$	0.611249	+	0.353523i	0.0651594	+	0.0376856i
$89$		−	7.82233i		−	0.829165i	−0.910012	−	0.414582i	$-0.863928\pi$
$89$		−	7.82233i		−	0.829165i	0.910012	−	0.414582i	$-0.136072\pi$
$90$		0			0
$91$		−	0.129220i		−	0.0135460i
$92$	−12.0927	−	10.1574i	−1.26075	−	1.05898i
$93$		0			0
$94$	2.34187	−	6.42918i	0.241545	−	0.663119i
$95$	4.64806	−	8.05067i	0.476881	−	0.825981i
$96$		0			0
$97$	−5.67078	−	9.82208i	−0.575780	−	0.997281i	−0.995956	−	0.0898382i	$-0.971365\pi$
$97$	−5.67078	−	9.82208i	−0.575780	−	0.997281i	0.420176	−	0.907443i	$-0.361968\pi$
$98$	−1.39279	+	0.245224i	−0.140693	+	0.0247713i
$99$		0			0
$100$	−3.20634	+	1.16518i	−0.320634	+	0.116518i
$101$	3.16980	−	1.83009i	0.315407	−	0.182100i	−0.333936	−	0.942596i	$-0.608377\pi$
$101$	3.16980	−	1.83009i	0.315407	−	0.182100i	0.649344	+	0.760495i	$0.275044\pi$
$102$		0			0
$103$	−5.95960	−	3.44077i	−0.587216	−	0.339030i	0.176780	−	0.984250i	$-0.443432\pi$
$103$	−5.95960	−	3.44077i	−0.587216	−	0.339030i	−0.763996	+	0.645221i	$0.776765\pi$
$104$	−0.000277016		0.365490i	−2.71637e−5		0.0358393i
$105$		0			0
$106$	9.75284	−	8.17941i	0.947280	−	0.794454i
$107$	−7.43669			−0.718932			−0.359466	−	0.933158i	$-0.617041\pi$
$107$	−7.43669			−0.718932			−0.359466	+	0.933158i	$0.617041\pi$
$108$		0			0
$109$	−8.23684			−0.788947			−0.394473	−	0.918907i	$-0.629073\pi$
$109$	−8.23684			−0.788947			−0.394473	+	0.918907i	$0.629073\pi$
$110$	−0.700514	+	0.587500i	−0.0667914	+	0.0560159i
$111$		0			0
$112$	3.93993	−	0.690611i	0.372288	−	0.0652567i
$113$	7.42933	+	4.28933i	0.698893	+	0.403506i	0.806935	−	0.590640i	$-0.201125\pi$
$113$	7.42933	+	4.28933i	0.698893	+	0.403506i	−0.108042	+	0.994146i	$0.534458\pi$
$114$		0			0
$115$	17.7083	−	10.2239i	1.65131	−	0.953383i
$116$	4.65748	+	12.8165i	0.432436	+	1.18998i
$117$		0			0
$118$	10.3520	−	1.82265i	0.952981	−	0.167788i
$119$	0.277346	+	0.480377i	0.0254242	+	0.0440361i
$120$		0			0
$121$	5.46884	−	9.47230i	0.497167	−	0.861119i
$122$	6.21995	−	17.0758i	0.563128	−	1.54597i
$123$		0			0
$124$	−10.3482	+	12.3198i	−0.929294	+	1.10635i
$125$			8.53063i			0.763003i
$126$		0			0
$127$			4.71023i			0.417965i	0.977919	+	0.208982i	$0.0670152\pi$
$127$			4.71023i			0.417965i	−0.977919	+	0.208982i	$0.932985\pi$
$128$	−11.1453	+	1.94490i	−0.985113	+	0.171906i
$129$		0			0
$130$	−0.444647	−	0.161966i	−0.0389981	−	0.0142053i
$131$	−4.97136	+	8.61065i	−0.434350	+	0.752316i	−0.997242	−	0.0742144i	$-0.976355\pi$
$131$	−4.97136	+	8.61065i	−0.434350	+	0.752316i	0.562893	+	0.826530i	$0.309688\pi$
$132$		0			0
$133$	−1.79493	−	3.10891i	−0.155640	−	0.269577i
$134$	−1.48250	−	8.42009i	−0.128068	−	0.727385i
$135$		0			0
$136$	−0.783422	−	1.35930i	−0.0671779	−	0.116559i
$137$	−13.1903	+	7.61545i	−1.12693	+	0.650632i	−0.943160	−	0.332338i	$-0.892162\pi$
$137$	−13.1903	+	7.61545i	−1.12693	+	0.650632i	−0.183767	+	0.982970i	$0.558829\pi$
$138$		0			0
$139$	−1.53695	−	0.887356i	−0.130362	−	0.0752645i	0.433401	−	0.901201i	$-0.357313\pi$
$139$	−1.53695	−	0.887356i	−0.130362	−	0.0752645i	−0.563763	+	0.825937i	$0.690647\pi$
$140$	−0.901917	+	5.09995i	−0.0762259	+	0.431025i
$141$		0			0
$142$	−14.3421	−	17.1011i	−1.20356	−	1.43509i
$143$	−0.0322600			−0.00269771
$144$		0			0
$145$	−17.6561			−1.46626
$146$	12.8154	+	15.2806i	1.06061	+	1.26463i
$147$		0			0
$148$	−3.47079	+	19.6258i	−0.285297	+	1.61323i
$149$	14.3488	+	8.28427i	1.17550	+	0.678674i	0.954969	−	0.296706i	$-0.0958882\pi$
$149$	14.3488	+	8.28427i	1.17550	+	0.678674i	0.220529	+	0.975380i	$0.429222\pi$
$150$		0			0
$151$	−15.2363	+	8.79668i	−1.23991	+	0.715864i	−0.969076	−	0.246761i	$-0.920634\pi$
$151$	−15.2363	+	8.79668i	−1.23991	+	0.715864i	−0.270836	+	0.962625i	$0.587300\pi$
$152$	5.07017	+	8.79718i	0.411245	+	0.713546i
$153$		0			0
$154$	0.0612203	+	0.347711i	0.00493327	+	0.0280194i
$155$	−10.4159	−	18.0409i	−0.836628	−	1.44908i
$156$		0			0
$157$	1.12675	−	1.95160i	0.0899248	−	0.155754i	−0.817554	−	0.575851i	$-0.804671\pi$
$157$	1.12675	−	1.95160i	0.0899248	−	0.155754i	0.907479	+	0.420097i	$0.138004\pi$
$158$	−3.13066	−	1.14036i	−0.249062	−	0.0907223i
$159$		0			0
$160$	2.56194	−	14.4229i	0.202539	−	1.14023i
$161$		−	7.89629i		−	0.622315i
$162$		0			0
$163$			6.99511i			0.547899i	0.961744	+	0.273950i	$0.0883302\pi$
$163$			6.99511i			0.547899i	−0.961744	+	0.273950i	$0.911670\pi$
$164$	6.32705	−	7.53255i	0.494060	−	0.588193i
$165$		0			0
$166$	2.28961	−	6.28572i	0.177709	−	0.487867i
$167$	−5.40220	+	9.35689i	−0.418035	+	0.724058i	−0.995742	−	0.0921866i	$-0.970614\pi$
$167$	−5.40220	+	9.35689i	−0.418035	+	0.724058i	0.577707	+	0.816244i	$0.303948\pi$
$168$		0			0
$169$	6.49165	+	11.2439i	0.499358	+	0.864913i
$170$	2.00060	−	0.352239i	0.153439	−	0.0270155i
$171$		0			0
$172$	2.98777	+	8.22175i	0.227815	+	0.626903i
$173$	−4.01988	+	2.32088i	−0.305626	+	0.176453i	−0.644968	−	0.764210i	$-0.723129\pi$
$173$	−4.01988	+	2.32088i	−0.305626	+	0.176453i	0.339341	+	0.940663i	$0.389796\pi$
$174$		0			0
$175$	−1.47722	−	0.852871i	−0.111667	−	0.0644710i
$176$	−0.172412	−	0.983606i	−0.0129960	−	0.0741421i
$177$		0			0
$178$	−8.47612	+	7.10866i	−0.635312	+	0.532816i
$179$	−6.66668			−0.498291			−0.249145	−	0.968466i	$-0.580150\pi$
$179$	−6.66668			−0.498291			−0.249145	+	0.968466i	$0.580150\pi$
$180$		0			0
$181$	−7.61248			−0.565831			−0.282916	−	0.959145i	$-0.591302\pi$
$181$	−7.61248			−0.565831			−0.282916	+	0.959145i	$0.591302\pi$
$182$	−0.140021	+	0.117431i	−0.0103790	+	0.00870457i
$183$		0			0
$184$	−0.0169276	+	22.3341i	−0.00124792	+	1.64649i
$185$	−22.3481	−	12.9027i	−1.64306	−	0.948622i
$186$		0			0
$187$	0.119926	−	0.0692395i	0.00876988	−	0.00506329i
$188$	−9.09474	+	3.30501i	−0.663302	+	0.241043i
$189$		0			0
$190$	−12.9475	+	2.27963i	−0.939313	+	0.165382i
$191$	2.15506	+	3.73268i	0.155935	+	0.270087i	0.933399	−	0.358840i	$-0.116828\pi$
$191$	2.15506	+	3.73268i	0.155935	+	0.270087i	−0.777464	+	0.628927i	$0.783494\pi$
$192$		0			0
$193$	−0.690908	+	1.19669i	−0.0497327	+	0.0861395i	−0.889820	−	0.456312i	$-0.849170\pi$
$193$	−0.690908	+	1.19669i	−0.0497327	+	0.0861395i	0.840087	+	0.542451i	$0.182504\pi$
$194$	−5.48960	+	15.0707i	−0.394130	+	1.08201i
$195$		0			0
$196$	1.53144	+	1.28635i	0.109389	+	0.0918821i
$197$		−	9.26481i		−	0.660091i	−0.943965	−	0.330045i	$-0.892936\pi$
$197$		−	9.26481i		−	0.660091i	0.943965	−	0.330045i	$-0.107064\pi$
$198$		0			0
$199$		−	24.5989i		−	1.74377i	−0.489712	−	0.871884i	$-0.662898\pi$
$199$		−	24.5989i		−	1.74377i	0.489712	−	0.871884i	$-0.337102\pi$
$200$	4.17637	+	2.41545i	0.295314	+	0.170798i
$201$		0			0
$202$	−4.86365	−	1.77162i	−0.342205	−	0.124650i
$203$	−3.40912	+	5.90477i	−0.239273	+	0.414434i
$204$		0			0
$205$	6.36848	+	11.0305i	0.444794	+	0.770406i
$206$	1.68752	+	9.58456i	0.117575	+	0.667788i
$207$		0			0
$208$	0.396290	−	0.331845i	0.0274778	−	0.0230093i
$209$	−0.776142	+	0.448106i	−0.0536869	+	0.0309961i
$210$		0			0
$211$	8.98731	+	5.18882i	0.618712	+	0.357213i	0.776367	−	0.630281i	$-0.217060\pi$
$211$	8.98731	+	5.18882i	0.618712	+	0.357213i	−0.157655	+	0.987494i	$0.550394\pi$
$212$	−17.7261	−	3.13482i	−1.21743	−	0.215301i
$213$		0			0
$214$	6.75820	+	8.05824i	0.461981	+	0.550850i
$215$	−11.3264			−0.772455
$216$		0			0
$217$	−8.04461			−0.546104
$218$	7.48536	+	8.92528i	0.506972	+	0.604496i
$219$		0			0
$220$	1.27321	+	0.225164i	0.0858396	+	0.0151806i
$221$	0.0620745	+	0.0358387i	0.00417558	+	0.00241077i
$222$		0			0
$223$	−22.3502	+	12.9039i	−1.49668	+	0.864109i	−0.999993	−	0.00382012i	$-0.998784\pi$
$223$	−22.3502	+	12.9039i	−1.49668	+	0.864109i	−0.496688	+	0.867929i	$0.665451\pi$
$224$	−4.32881	−	3.64163i	−0.289230	−	0.243316i
$225$		0			0
$226$	−2.10369	−	11.9483i	−0.139935	−	0.794787i
$227$	−6.74196	−	11.6774i	−0.447480	−	0.775057i	0.550742	−	0.834676i	$-0.314345\pi$
$227$	−6.74196	−	11.6774i	−0.447480	−	0.775057i	−0.998221	+	0.0596183i	$0.981012\pi$
$228$		0			0
$229$	6.49974	−	11.2579i	0.429515	−	0.743941i	−0.567315	−	0.823501i	$-0.692018\pi$
$229$	6.49974	−	11.2579i	0.429515	−	0.743941i	0.996830	+	0.0795594i	$0.0253513\pi$
$230$	−27.1711	−	9.89725i	−1.79161	−	0.652605i
$231$		0			0
$232$	9.65510	−	16.6939i	0.633889	−	1.09601i
$233$			22.7845i			1.49266i	0.665575	+	0.746331i	$0.268186\pi$
$233$			22.7845i			1.49266i	−0.665575	+	0.746331i	$0.731814\pi$
$234$		0			0
$235$		−	12.5291i		−	0.817305i
$236$	−11.3825	−	9.56089i	−0.740941	−	0.622361i
$237$		0			0
$238$	0.268485	−	0.737076i	0.0174033	−	0.0477775i
$239$	10.1962	−	17.6603i	0.659537	−	1.14235i	−0.321198	−	0.947012i	$-0.604086\pi$
$239$	10.1962	−	17.6603i	0.659537	−	1.14235i	0.980736	−	0.195340i	$-0.0625810\pi$
$240$		0			0
$241$	3.27539	+	5.67314i	0.210986	+	0.365439i	0.952024	−	0.306025i	$-0.0989991\pi$
$241$	3.27539	+	5.67314i	0.210986	+	0.365439i	−0.741037	+	0.671464i	$0.765666\pi$
$242$	−15.2339	+	2.68218i	−0.979271	+	0.172417i
$243$		0			0
$244$	−24.1554	+	8.77804i	−1.54639	+	0.561956i
$245$	−2.24261	+	1.29477i	−0.143275	+	0.0827200i
$246$		0			0
$247$	−0.401735	−	0.231942i	−0.0255618	−	0.0147581i
$248$	22.7536	+	0.0172456i	1.44485	+	0.00109510i
$249$		0			0
$250$	9.24362	−	7.75234i	0.584618	−	0.490301i
$251$	18.3086			1.15563			0.577814	−	0.816169i	$-0.303906\pi$
$251$	18.3086			1.15563			0.577814	+	0.816169i	$0.303906\pi$
$252$		0			0
$253$	−1.97131			−0.123935
$254$	5.10391	−	4.28049i	0.320248	−	0.268582i
$255$		0			0
$256$	12.2359	+	10.3094i	0.764744	+	0.644335i
$257$	−13.8378	−	7.98924i	−0.863176	−	0.498355i	0.00189858	−	0.999998i	$-0.499396\pi$
$257$	−13.8378	−	7.98924i	−0.863176	−	0.498355i	−0.865075	+	0.501643i	$0.832729\pi$
$258$		0			0
$259$	−8.63011	+	4.98260i	−0.536249	+	0.309603i
$260$	0.228577	+	0.628999i	0.0141758	+	0.0390089i
$261$		0			0
$262$	13.8481	−	2.43819i	0.855540	−	0.150632i
$263$	1.92259	+	3.33002i	0.118552	+	0.205338i	0.919194	−	0.393805i	$-0.128841\pi$
$263$	1.92259	+	3.33002i	0.118552	+	0.205338i	−0.800642	+	0.599143i	$0.795508\pi$
$264$		0			0
$265$	11.6537	−	20.1848i	0.715881	−	1.23994i
$266$	−1.73758	+	4.77022i	−0.106538	+	0.292481i
$267$		0			0
$268$	−7.77660	+	9.25829i	−0.475032	+	0.565540i
$269$			3.59531i			0.219210i	0.993975	+	0.109605i	$0.0349585\pi$
$269$			3.59531i			0.219210i	−0.993975	+	0.109605i	$0.965041\pi$
$270$		0			0
$271$			4.24361i			0.257781i	0.991659	+	0.128891i	$0.0411416\pi$
$271$			4.24361i			0.257781i	−0.991659	+	0.128891i	$0.958858\pi$
$272$	−0.760969	+	2.08419i	−0.0461405	+	0.126373i
$273$		0			0
$274$	20.2389	+	7.37214i	1.22267	+	0.445367i
$275$	−0.212920	+	0.368788i	−0.0128395	+	0.0222387i
$276$		0			0
$277$	4.88987	+	8.46950i	0.293804	+	0.508883i	0.974706	−	0.223491i	$-0.0717454\pi$
$277$	4.88987	+	8.46950i	0.293804	+	0.508883i	−0.680902	+	0.732374i	$0.738412\pi$
$278$	0.435201	+	2.47180i	0.0261016	+	0.148249i
$279$		0			0
$280$	6.34584	−	3.65736i	0.379236	−	0.218569i
$281$	−20.3980	+	11.7768i	−1.21684	+	0.702544i	−0.964241	−	0.265027i	$-0.914619\pi$
$281$	−20.3980	+	11.7768i	−1.21684	+	0.702544i	−0.252600	+	0.967571i	$0.581286\pi$
$282$		0			0
$283$	4.19988	+	2.42480i	0.249657	+	0.144139i	0.619607	−	0.784912i	$-0.287292\pi$
$283$	4.19988	+	2.42480i	0.249657	+	0.144139i	−0.369950	+	0.929052i	$0.620625\pi$
$284$	−5.49673	+	31.0817i	−0.326171	+	1.84436i
$285$		0			0
$286$	0.0293167	+	0.0349563i	0.00173353	+	0.00206701i
$287$	4.91861			0.290336
$288$		0			0
$289$	16.6923			0.981901
$290$	16.0453	+	19.1318i	0.942212	+	1.12346i
$291$		0			0
$292$	4.91160	−	27.7730i	0.287430	−	1.62529i
$293$	16.8856	+	9.74890i	0.986467	+	0.569537i	0.904216	−	0.427075i	$-0.140456\pi$
$293$	16.8856	+	9.74890i	0.986467	+	0.569537i	0.0822504	+	0.996612i	$0.473789\pi$
$294$		0			0
$295$	16.6684	−	9.62350i	0.970471	−	0.560302i
$296$	24.4203	−	14.0744i	1.41940	−	0.818058i
$297$		0			0
$298$	−4.06300	−	23.0765i	−0.235363	−	1.33679i
$299$	−0.510181	−	0.883659i	−0.0295045	−	0.0511033i
$300$		0			0
$301$	−2.18695	+	3.78791i	−0.126054	+	0.218331i
$302$	23.3781	+	8.51563i	1.34526	+	0.490020i
$303$		0			0
$304$	4.92486	−	13.4885i	0.282460	−	0.773619i
$305$		−	33.2769i		−	1.90543i
$306$		0			0
$307$		−	6.21611i		−	0.354772i	−0.984141	−	0.177386i	$-0.943236\pi$
$307$		−	6.21611i		−	0.354772i	0.984141	−	0.177386i	$-0.0567642\pi$
$308$	0.321138	−	0.382325i	0.0182985	−	0.0217850i
$309$		0			0
$310$	−10.0832	+	27.6815i	−0.572685	+	1.57220i
$311$	11.2742	−	19.5275i	0.639303	−	1.10731i	−0.346283	−	0.938130i	$-0.612556\pi$
$311$	11.2742	−	19.5275i	0.639303	−	1.10731i	0.985586	−	0.169176i	$-0.0541105\pi$
$312$		0			0
$313$	−7.53213	−	13.0460i	−0.425741	−	0.737405i	0.570748	−	0.821125i	$-0.306653\pi$
$313$	−7.53213	−	13.0460i	−0.425741	−	0.737405i	−0.996489	+	0.0837201i	$0.973320\pi$
$314$	−3.13867	+	0.552614i	−0.177125	+	0.0311858i
$315$		0			0
$316$	1.60936	+	4.42864i	0.0905335	+	0.249130i
$317$	9.34442	−	5.39500i	0.524835	−	0.303013i	−0.214076	−	0.976817i	$-0.568674\pi$
$317$	9.34442	−	5.39500i	0.524835	−	0.303013i	0.738911	+	0.673804i	$0.235341\pi$
$318$		0			0
$319$	1.47413	+	0.851089i	0.0825354	+	0.0476518i
$320$	−17.9566	+	10.3310i	−1.00380	+	0.577519i
$321$		0			0
$322$	−8.55626	+	7.17587i	−0.476822	+	0.399896i
$323$	1.99127			0.110797
$324$		0			0
$325$	−0.220417			−0.0122265
$326$	7.57976	−	6.35691i	0.419804	−	0.352077i
$327$		0			0
$328$	−13.9119	−	0.0105443i	−0.768158	−	0.000582209i
$329$	−4.19011	−	2.41916i	−0.231008	−	0.133373i
$330$		0			0
$331$	−9.03466	+	5.21616i	−0.496590	+	0.286706i	−0.727304	−	0.686315i	$-0.759227\pi$
$331$	−9.03466	+	5.21616i	−0.496590	+	0.286706i	0.230714	+	0.973021i	$0.425894\pi$
$332$	−8.89181	+	3.23127i	−0.488001	+	0.177339i
$333$		0			0
$334$	15.0483	−	2.64950i	0.823405	−	0.144974i
$335$	−7.82753	−	13.5577i	−0.427663	−	0.740735i
$336$		0			0
$337$	15.0986	−	26.1516i	0.822475	−	1.42457i	−0.0813590	−	0.996685i	$-0.525926\pi$
$337$	15.0986	−	26.1516i	0.822475	−	1.42457i	0.903834	−	0.427883i	$-0.140741\pi$
$338$	6.28425	−	17.2523i	0.341818	−	0.938399i
$339$		0			0
$340$	−2.19976	−	1.84771i	−0.119299	−	0.100206i
$341$			2.00834i			0.108758i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	6.19375	−	10.7091i	0.333944	−	0.577398i
$345$		0			0
$346$	6.16799	+	2.24673i	0.331593	+	0.120785i
$347$	12.7498	−	22.0832i	0.684443	−	1.18549i	−0.289169	−	0.957278i	$-0.593379\pi$
$347$	12.7498	−	22.0832i	0.684443	−	1.18549i	0.973612	−	0.228212i	$-0.0732878\pi$
$348$		0			0
$349$	15.4421	+	26.7465i	0.826597	+	1.43171i	0.900692	+	0.434457i	$0.143060\pi$
$349$	15.4421	+	26.7465i	0.826597	+	1.43171i	−0.0740953	+	0.997251i	$0.523607\pi$
$350$	0.418288	+	2.37574i	0.0223585	+	0.126989i
$351$		0			0
$352$	−0.909134	+	1.08069i	−0.0484570	+	0.0576009i
$353$	30.2542	−	17.4672i	1.61027	−	0.929688i	0.620958	−	0.783843i	$-0.286744\pi$
$353$	30.2542	−	17.4672i	1.61027	−	0.929688i	0.989308	−	0.145844i	$-0.0465898\pi$
$354$		0			0
$355$	−35.3929	−	20.4341i	−1.87846	−	1.08453i
$356$	15.4056	+	2.72445i	0.816495	+	0.144396i
$357$		0			0
$358$	6.05844	+	7.22388i	0.320199	+	0.381794i
$359$	−5.92966			−0.312956			−0.156478	−	0.987681i	$-0.550014\pi$
$359$	−5.92966			−0.312956			−0.156478	+	0.987681i	$0.550014\pi$
$360$		0			0
$361$	6.11288			0.321730
$362$	6.91796	+	8.24873i	0.363600	+	0.433544i
$363$		0			0
$364$	0.254492	+	0.0450064i	0.0133390	+	0.00235898i
$365$	31.6253	+	18.2589i	1.65534	+	0.955712i
$366$		0			0
$367$	−26.1820	+	15.1162i	−1.36669	+	0.789059i	−0.990504	−	0.137485i	$-0.956098\pi$
$367$	−26.1820	+	15.1162i	−1.36669	+	0.789059i	−0.376187	+	0.926544i	$0.622765\pi$
$368$	24.2161	−	20.2781i	1.26235	−	1.05707i
$369$		0			0
$370$	6.32807	+	35.9414i	0.328981	+	1.86850i
$371$	−4.50029	−	7.79472i	−0.233643	−	0.404682i
$372$		0			0
$373$	2.54373	−	4.40588i	0.131710	−	0.228128i	−0.792626	−	0.609708i	$-0.791287\pi$
$373$	2.54373	−	4.40588i	0.131710	−	0.228128i	0.924336	+	0.381580i	$0.124620\pi$
$374$	−0.184011	−	0.0670273i	−0.00951501	−	0.00346590i
$375$		0			0
$376$	11.8462	+	6.85140i	0.610923	+	0.353334i
$377$			0.881056i			0.0453767i
$378$		0			0
$379$			18.6036i			0.955600i	0.878469	+	0.477800i	$0.158566\pi$
$379$			18.6036i			0.955600i	−0.878469	+	0.477800i	$0.841434\pi$
$380$	14.2364	+	11.9580i	0.730314	+	0.613435i
$381$		0			0
$382$	2.08621	−	5.72731i	0.106740	−	0.293035i
$383$	5.98305	−	10.3630i	0.305720	−	0.529522i	−0.671702	−	0.740822i	$-0.734436\pi$
$383$	5.98305	−	10.3630i	0.305720	−	0.529522i	0.977421	+	0.211300i	$0.0677696\pi$
$384$		0			0
$385$	0.323241	+	0.559869i	0.0164739	+	0.0285336i
$386$	1.92458	−	0.338854i	0.0979586	−	0.0172472i
$387$		0			0
$388$	21.3191	−	7.74731i	1.08231	−	0.393310i
$389$	16.3655	−	9.44864i	0.829765	−	0.479065i	−0.0240072	−	0.999712i	$-0.507642\pi$
$389$	16.3655	−	9.44864i	0.829765	−	0.479065i	0.853772	+	0.520647i	$0.174309\pi$
$390$		0			0
$391$	3.79319	+	2.19000i	0.191830	+	0.110753i
$392$	0.00214375	−	2.82843i	0.000108276	−	0.142857i
$393$		0			0
$394$	−10.0392	+	8.41954i	−0.505766	+	0.424170i
$395$	−6.10096			−0.306973
$396$		0			0
$397$	−26.3234			−1.32113			−0.660566	−	0.750768i	$-0.729684\pi$
$397$	−26.3234			−1.32113			−0.660566	+	0.750768i	$0.729684\pi$
$398$	−26.6549	+	22.3546i	−1.33609	+	1.12054i
$399$		0			0
$400$	−1.17801	−	6.72051i	−0.0589003	−	0.336025i
$401$	7.64521	+	4.41396i	0.381783	+	0.220423i	0.678594	−	0.734514i	$-0.262590\pi$
$401$	7.64521	+	4.41396i	0.381783	+	0.220423i	−0.296811	+	0.954936i	$0.595923\pi$
$402$		0			0
$403$	−0.900257	+	0.519764i	−0.0448450	+	0.0258913i
$404$	2.50023	+	6.88014i	0.124391	+	0.342300i
$405$		0			0
$406$	9.49638	−	1.67199i	0.471297	−	0.0829797i
$407$	1.24391	+	2.15451i	0.0616582	+	0.106795i
$408$		0			0
$409$	−11.4524	+	19.8361i	−0.566283	+	0.980831i	0.430646	+	0.902521i	$0.358286\pi$
$409$	−11.4524	+	19.8361i	−0.566283	+	0.980831i	−0.996929	+	0.0783100i	$0.975048\pi$
$410$	6.16501	−	16.9249i	0.304468	−	0.835862i
$411$		0			0
$412$	8.85207	−	10.5387i	0.436110	−	0.519203i
$413$		−	7.43258i		−	0.365733i
$414$		0			0
$415$		−	12.2495i		−	0.601304i
$416$	−0.719715	−	0.127843i	−0.0352869	−	0.00626801i
$417$		0			0
$418$	1.19089	+	0.433789i	0.0582483	+	0.0212173i
$419$	−5.10769	+	8.84679i	−0.249527	+	0.432194i	−0.963395	−	0.268087i	$-0.913609\pi$
$419$	−5.10769	+	8.84679i	−0.249527	+	0.432194i	0.713868	+	0.700281i	$0.246942\pi$
$420$		0			0
$421$	5.95328	+	10.3114i	0.290145	+	0.502546i	0.973844	−	0.227218i	$-0.0729630\pi$
$421$	5.95328	+	10.3114i	0.290145	+	0.502546i	−0.683699	+	0.729765i	$0.739630\pi$
$422$	−2.54485	−	14.4539i	−0.123881	−	0.703604i
$423$		0			0
$424$	12.7120	+	22.0565i	0.617350	+	1.07116i
$425$	0.819399	−	0.473080i	0.0397467	−	0.0229478i
$426$		0			0
$427$	−11.1288	−	6.42524i	−0.538562	−	0.310939i
$428$	2.59013	−	14.6461i	0.125199	−	0.707946i
$429$		0			0
$430$	10.2930	+	12.2731i	0.496375	+	0.591860i
$431$	−4.26567			−0.205470			−0.102735	−	0.994709i	$-0.532759\pi$
$431$	−4.26567			−0.205470			−0.102735	+	0.994709i	$0.532759\pi$
$432$		0			0
$433$	36.7838			1.76772			0.883858	−	0.467756i	$-0.154937\pi$
$433$	36.7838			1.76772			0.883858	+	0.467756i	$0.154937\pi$
$434$	7.31066	+	8.71698i	0.350923	+	0.418428i
$435$		0			0
$436$	2.86882	−	16.2220i	0.137392	−	0.776891i
$437$	−24.5489	−	14.1733i	−1.17433	−	0.678001i
$438$		0			0
$439$	13.2806	−	7.66755i	0.633848	−	0.365952i	−0.148393	−	0.988928i	$-0.547410\pi$
$439$	13.2806	−	7.66755i	0.633848	−	0.365952i	0.782241	+	0.622976i	$0.214077\pi$
$440$	−0.913062	−	1.58424i	−0.0435285	−	0.0755258i
$441$		0			0
$442$	−0.0175770	−	0.0998317i	−0.000836053	−	0.00474851i
$443$	5.27986	+	9.14498i	0.250854	+	0.434491i	0.963761	−	0.266767i	$-0.0859554\pi$
$443$	5.27986	+	9.14498i	0.250854	+	0.434491i	−0.712907	+	0.701258i	$0.752622\pi$
$444$		0			0
$445$	−10.1281	+	17.5424i	−0.480119	+	0.831591i
$446$	34.2935	+	12.4916i	1.62384	+	0.591496i
$447$		0			0
$448$	−0.0121269	+	7.99999i	−0.000572940	+	0.377964i
$449$			16.5280i			0.780006i	0.920813	+	0.390003i	$0.127526\pi$
$449$			16.5280i			0.780006i	−0.920813	+	0.390003i	$0.872474\pi$
$450$		0			0
$451$		−	1.22793i		−	0.0578212i
$452$	−11.0351	+	13.1377i	−0.519050	+	0.617945i
$453$		0			0
$454$	−6.52656	+	17.9175i	−0.306307	+	0.840909i
$455$	−0.167311	+	0.289791i	−0.00784366	+	0.0135856i
$456$		0			0
$457$	−5.27095	−	9.12955i	−0.246564	−	0.427062i	0.716006	−	0.698094i	$-0.245968\pi$
$457$	−5.27095	−	9.12955i	−0.246564	−	0.427062i	−0.962570	+	0.271032i	$0.912635\pi$
$458$	−18.1055	+	3.18778i	−0.846016	+	0.148955i
$459$		0			0
$460$	13.9677	+	38.4363i	0.651247	+	1.79210i
$461$	21.5838	−	12.4614i	1.00526	−	0.580387i	0.0954593	−	0.995433i	$-0.469568\pi$
$461$	21.5838	−	12.4614i	1.00526	−	0.580387i	0.909800	+	0.415046i	$0.136235\pi$
$462$		0			0
$463$	−27.8446	−	16.0761i	−1.29405	−	0.747119i	−0.314679	−	0.949198i	$-0.601897\pi$
$463$	−27.8446	−	16.0761i	−1.29405	−	0.747119i	−0.979369	+	0.202079i	$0.935230\pi$
$464$	−26.8634	+	4.70876i	−1.24710	+	0.218598i
$465$		0			0
$466$	24.6888	−	20.7058i	1.14369	−	0.959176i
$467$	−8.54957			−0.395627			−0.197813	−	0.980240i	$-0.563384\pi$
$467$	−8.54957			−0.395627			−0.197813	+	0.980240i	$0.563384\pi$
$468$		0			0
$469$	−6.04548			−0.279155
$470$	−13.5762	+	11.3860i	−0.626225	+	0.525195i
$471$		0			0
$472$	−0.0159336	+	21.0225i	−0.000733402	+	0.967639i
$473$	0.945654	+	0.545973i	0.0434812	+	0.0251039i
$474$		0			0
$475$	−5.30300	+	3.06169i	−0.243319	+	0.140480i
$476$	−1.04267	+	0.378904i	−0.0477907	+	0.0173671i
$477$		0			0
$478$	−28.4023	+	5.00070i	−1.29909	+	0.228727i
$479$	8.25859	+	14.3043i	0.377345	+	0.653580i	0.990675	−	0.136247i	$-0.0435039\pi$
$479$	8.25859	+	14.3043i	0.377345	+	0.653580i	−0.613330	+	0.789826i	$0.710171\pi$
$480$		0			0
$481$	−0.643853	+	1.11519i	−0.0293572	+	0.0508481i
$482$	3.17074	−	8.70470i	0.144423	−	0.396488i
$483$		0			0
$484$	16.7504	+	14.0697i	0.761381	+	0.639530i
$485$			29.3695i			1.33360i
$486$		0			0
$487$		−	7.93519i		−	0.359578i	−0.983705	−	0.179789i	$-0.942459\pi$
$487$		−	7.93519i		−	0.359578i	0.983705	−	0.179789i	$-0.0575415\pi$
$488$	31.4633	+	18.1972i	1.42428	+	0.823747i
$489$		0			0
$490$	3.44100	+	1.25341i	0.155448	+	0.0566231i
$491$	−1.83003	+	3.16970i	−0.0825880	+	0.143047i	−0.904361	−	0.426769i	$-0.859652\pi$
$491$	−1.83003	+	3.16970i	−0.0825880	+	0.143047i	0.821773	+	0.569815i	$0.192985\pi$
$492$		0			0
$493$	−1.89101	−	3.27532i	−0.0851668	−	0.147513i
$494$	0.113755	+	0.646093i	0.00511809	+	0.0290691i
$495$		0			0
$496$	−20.6590	−	24.6710i	−0.927615	−	1.10776i
$497$	−13.6676	+	7.89100i	−0.613076	+	0.353960i
$498$		0			0
$499$	−7.46689	−	4.31101i	−0.334264	−	0.192987i	0.323469	−	0.946239i	$-0.395151\pi$
$499$	−7.46689	−	4.31101i	−0.334264	−	0.192987i	−0.657733	+	0.753252i	$0.728484\pi$
$500$	−16.8006	−	2.97115i	−0.751344	−	0.132874i
$501$		0			0
$502$	−16.6382	−	19.8388i	−0.742599	−	0.885449i
$503$	−44.0191			−1.96271			−0.981357	−	0.192194i	$-0.938440\pi$
$503$	−44.0191			−1.96271			−0.981357	+	0.192194i	$0.938440\pi$
$504$		0			0
$505$	−9.47818			−0.421773
$506$	1.79146	+	2.13608i	0.0796402	+	0.0949602i
$507$		0			0
$508$	−9.27651	−	1.64053i	−0.411578	−	0.0727868i
$509$	−9.48279	−	5.47489i	−0.420317	−	0.242670i	0.274896	−	0.961474i	$-0.411357\pi$
$509$	−9.48279	−	5.47489i	−0.420317	−	0.242670i	−0.695213	+	0.718804i	$0.744690\pi$
$510$		0			0
$511$	12.2127	−	7.05099i	0.540257	−	0.311917i
$512$	0.0514499	−	22.6274i	0.00227379	−	0.999997i
$513$		0			0
$514$	3.91830	+	22.2547i	0.172829	+	0.981611i
$515$	8.91004	+	15.4326i	0.392623	+	0.680043i
$516$		0			0
$517$	−0.603945	+	1.04606i	−0.0265615	+	0.0460058i
$518$	13.2418	+	4.82340i	0.581811	+	0.211928i
$519$		0			0
$520$	0.473848	−	0.819295i	0.0207796	−	0.0359284i
$521$		−	6.26841i		−	0.274624i	−0.990528	−	0.137312i	$-0.956154\pi$
$521$		−	6.26841i		−	0.274624i	0.990528	−	0.137312i	$-0.0438463\pi$
$522$		0			0
$523$			18.7279i			0.818913i	0.912330	+	0.409456i	$0.134282\pi$
$523$			18.7279i			0.818913i	−0.912330	+	0.409456i	$0.865718\pi$
$524$	−15.2267	−	12.7898i	−0.665180	−	0.558725i
$525$		0			0
$526$	1.86116	−	5.10948i	0.0811505	−	0.222784i
$527$	2.23114	−	3.86444i	0.0971898	−	0.168338i
$528$		0			0
$529$	−19.6757	−	34.0793i	−0.855465	−	1.48171i
$530$	−32.4623	+	5.71552i	−1.41007	+	0.248267i
$531$		0			0
$532$	6.74798	−	2.45220i	0.292562	−	0.106316i
$533$	0.550433	−	0.317792i	0.0238419	−	0.0137651i
$534$		0			0
$535$	16.6776	+	9.62882i	0.721035	+	0.416290i
$536$	17.0992	+	0.0129600i	0.738573	+	0.000559786i
$537$		0			0
$538$	3.89580	−	3.26729i	0.167960	−	0.140863i
$539$	0.249651			0.0107532
$540$		0			0
$541$	24.7122			1.06246			0.531230	−	0.847228i	$-0.321730\pi$
$541$	24.7122			1.06246			0.531230	+	0.847228i	$0.321730\pi$
$542$	4.59830	−	3.85645i	0.197514	−	0.165649i
$543$		0			0
$544$	2.94993	−	1.06947i	0.126477	−	0.0458531i
$545$	18.4720	+	10.6648i	0.791255	+	0.456832i
$546$		0			0
$547$	23.9787	−	13.8441i	1.02525	−	0.591930i	0.109632	−	0.993972i	$-0.465033\pi$
$547$	23.9787	−	13.8441i	1.02525	−	0.591930i	0.915621	+	0.402042i	$0.131699\pi$
$548$	−10.4041	−	28.6300i	−0.444440	−	1.22301i
$549$		0			0
$550$	0.593105	−	0.104426i	0.0252901	−	0.00445274i
$551$	12.2383	+	21.1973i	0.521368	+	0.903036i
$552$		0			0
$553$	−1.17800	+	2.04035i	−0.0500936	+	0.0867646i
$554$	4.73364	−	12.9954i	0.201113	−	0.552120i
$555$		0			0
$556$	2.28290	−	2.71786i	0.0968165	−	0.115263i
$557$		−	43.5015i		−	1.84322i	−0.388119	−	0.921609i	$-0.626875\pi$
$557$		−	43.5015i		−	1.84322i	0.388119	−	0.921609i	$-0.373125\pi$
$558$		0			0
$559$			0.565197i			0.0239053i
$560$	−9.72992	−	3.55254i	−0.411164	−	0.150122i
$561$		0			0
$562$	31.2981	+	11.4005i	1.32023	+	0.480902i
$563$	0.525773	−	0.910665i	0.0221587	−	0.0383800i	−0.854733	−	0.519067i	$-0.826279\pi$
$563$	0.525773	−	0.910665i	0.0221587	−	0.0383800i	0.876892	+	0.480687i	$0.159613\pi$
$564$		0			0
$565$	−11.1074	−	19.2386i	−0.467292	−	0.809374i
$566$	−1.18924	−	6.75448i	−0.0499874	−	0.283912i
$567$		0			0
$568$	38.6747	−	22.2898i	1.62276	−	0.935259i
$569$	4.94731	−	2.85633i	0.207402	−	0.119744i	−0.392701	−	0.919666i	$-0.628459\pi$
$569$	4.94731	−	2.85633i	0.207402	−	0.119744i	0.600103	+	0.799922i	$0.295126\pi$
$570$		0			0
$571$	15.2710	+	8.81671i	0.639071	+	0.368968i	0.784257	−	0.620436i	$-0.213045\pi$
$571$	15.2710	+	8.81671i	0.639071	+	0.368968i	−0.145185	+	0.989404i	$0.546378\pi$
$572$	0.0112359	−	0.0635341i	0.000469795	−	0.00265649i
$573$		0			0
$574$	−4.46986	−	5.32971i	−0.186568	−	0.222458i
$575$	−13.4690			−0.561697
$576$		0			0
$577$	−18.3399			−0.763501			−0.381751	−	0.924265i	$-0.624679\pi$
$577$	−18.3399			−0.763501			−0.381751	+	0.924265i	$0.624679\pi$
$578$	−15.1694	−	18.0875i	−0.630964	−	0.752339i
$579$		0			0
$580$	6.14948	−	34.7727i	0.255343	−	1.44386i
$581$	−4.09661	−	2.36518i	−0.169956	−	0.0981243i
$582$		0			0
$583$	−1.94596	+	1.12350i	−0.0805933	+	0.0465306i
$584$	−34.5578	+	19.9170i	−1.43001	+	0.824172i
$585$		0			0
$586$	−4.78132	−	27.1563i	−0.197515	−	1.12182i
$587$	8.18823	+	14.1824i	0.337965	+	0.585372i	0.984050	−	0.177893i	$-0.0569282\pi$
$587$	8.18823	+	14.1824i	0.337965	+	0.585372i	−0.646085	+	0.763265i	$0.723595\pi$
$588$		0			0
$589$	−14.4395	+	25.0100i	−0.594970	+	1.03052i
$590$	−25.5755	−	9.31603i	−1.05293	−	0.383535i
$591$		0			0
$592$	−37.4431	−	13.6710i	−1.53890	−	0.561876i
$593$		−	2.86950i		−	0.117836i	−0.998263	−	0.0589181i	$-0.981235\pi$
$593$		−	2.86950i		−	0.117836i	0.998263	−	0.0589181i	$-0.0187651\pi$
$594$		0			0
$595$		−	1.43640i		−	0.0588866i
$596$	−21.3129	+	25.3737i	−0.873012	+	1.03935i
$597$		0			0
$598$	−0.493881	+	1.35586i	−0.0201963	+	0.0554453i
$599$	−0.530101	+	0.918163i	−0.0216594	+	0.0375151i	−0.876652	−	0.481125i	$-0.840228\pi$
$599$	−0.530101	+	0.918163i	−0.0216594	+	0.0375151i	0.854993	+	0.518640i	$0.173562\pi$
$600$		0			0
$601$	6.48648	+	11.2349i	0.264589	+	0.458282i	0.967456	−	0.253040i	$-0.0814303\pi$
$601$	6.48648	+	11.2349i	0.264589	+	0.458282i	−0.702867	+	0.711322i	$0.748097\pi$
$602$	6.09192	−	1.07258i	0.248288	−	0.0437153i
$603$		0			0
$604$	−12.0179	−	33.0708i	−0.489000	−	1.34563i
$605$	−24.5290	+	14.1618i	−0.997244	+	0.575759i
$606$		0			0
$607$	24.3945	+	14.0842i	0.990144	+	0.571660i	0.905317	−	0.424736i	$-0.139633\pi$
$607$	24.3945	+	14.0842i	0.990144	+	0.571660i	0.0848266	+	0.996396i	$0.472966\pi$
$608$	−19.0914	+	6.92141i	−0.774259	+	0.280700i
$609$		0			0
$610$	−36.0582	+	30.2409i	−1.45995	+	1.22442i
$611$	−0.625210			−0.0252933
$612$		0			0
$613$	−22.1934			−0.896381			−0.448191	−	0.893938i	$-0.647931\pi$
$613$	−22.1934			−0.896381			−0.448191	+	0.893938i	$0.647931\pi$
$614$	−6.73566	+	5.64899i	−0.271829	+	0.227975i
$615$		0			0
$616$	−0.706118		0.000535188i	−0.0284503		2.15633e-5i
$617$	−12.7221	−	7.34512i	−0.512173	−	0.295703i	0.221553	−	0.975148i	$-0.428887\pi$
$617$	−12.7221	−	7.34512i	−0.512173	−	0.295703i	−0.733726	+	0.679445i	$0.762221\pi$
$618$		0			0
$619$	−14.2161	+	8.20765i	−0.571392	+	0.329893i	−0.757705	−	0.652597i	$-0.773679\pi$
$619$	−14.2161	+	8.20765i	−0.571392	+	0.329893i	0.186313	+	0.982490i	$0.440346\pi$
$620$	39.1583	−	14.2301i	1.57264	−	0.571493i
$621$		0			0
$622$	−31.4053	+	5.52942i	−1.25924	+	0.221710i
$623$	3.91116	+	6.77433i	0.156697	+	0.271408i
$624$		0			0
$625$	15.3096	−	26.5170i	0.612383	−	1.06068i
$626$	−7.29148	+	20.0174i	−0.291426	+	0.800058i
$627$		0			0
$628$	3.45111	+	2.89880i	0.137714	+	0.115675i
$629$		−	5.52760i		−	0.220400i
$630$		0			0
$631$		−	12.7711i		−	0.508411i	−0.967150	−	0.254205i	$-0.918186\pi$
$631$		−	12.7711i		−	0.508411i	0.967150	−	0.254205i	$-0.0818139\pi$
$632$	3.33626	−	5.76846i	0.132709	−	0.229457i
$633$		0			0
$634$	−14.3378	−	5.22263i	−0.569427	−	0.207417i
$635$	6.09867	−	10.5632i	0.242018	−	0.419188i
$636$		0			0
$637$	0.0646102	+	0.111908i	0.00255995	+	0.00443396i
$638$	−0.417414	−	2.37078i	−0.0165256	−	0.0938600i
$639$		0			0
$640$	27.5127	+	10.0690i	1.08754	+	0.398010i
$641$	−13.2162	+	7.63040i	−0.522010	+	0.301383i	−0.737757	−	0.675067i	$-0.764115\pi$
$641$	−13.2162	+	7.63040i	−0.522010	+	0.301383i	0.215746	+	0.976449i	$0.430782\pi$
$642$		0			0
$643$	33.5137	+	19.3492i	1.32165	+	0.763057i	0.983992	−	0.178211i	$-0.0570311\pi$
$643$	33.5137	+	19.3492i	1.32165	+	0.763057i	0.337661	+	0.941268i	$0.390364\pi$
$644$	15.5513	+	2.75021i	0.612806	+	0.108373i
$645$		0			0
$646$	−1.80959	−	2.15770i	−0.0711975	−	0.0848934i
$647$	0.564326			0.0221860			0.0110930	−	0.999938i	$-0.496469\pi$
$647$	0.564326			0.0221860			0.0110930	+	0.999938i	$0.496469\pi$
$648$		0			0
$649$	−1.85555			−0.0728367
$650$	0.200307	+	0.238839i	0.00785669	+	0.00936804i
$651$		0			0
$652$	−13.7765	−	2.43634i	−0.539527	−	0.0954144i
$653$	3.90030	+	2.25184i	0.152631	+	0.0881214i	0.574370	−	0.818596i	$-0.305247\pi$
$653$	3.90030	+	2.25184i	0.152631	+	0.0881214i	−0.421740	+	0.906717i	$0.638580\pi$
$654$		0			0
$655$	22.2977	−	12.8736i	0.871241	−	0.503011i
$656$	12.6312	+	15.0843i	0.493167	+	0.588942i
$657$		0			0
$658$	1.18647	+	6.73877i	0.0462535	+	0.262705i
$659$	−7.02737	−	12.1718i	−0.273747	−	0.474144i	0.696071	−	0.717973i	$-0.254930\pi$
$659$	−7.02737	−	12.1718i	−0.273747	−	0.474144i	−0.969818	+	0.243829i	$0.921597\pi$
$660$		0			0
$661$	−17.4242	+	30.1797i	−0.677724	+	1.17385i	0.297940	+	0.954585i	$0.403700\pi$
$661$	−17.4242	+	30.1797i	−0.677724	+	1.17385i	−0.975665	+	0.219269i	$0.929633\pi$
$662$	13.8625	+	5.04951i	0.538782	+	0.196255i
$663$		0			0
$664$	11.5819	+	6.69852i	0.449465	+	0.259953i
$665$			9.29611i			0.360488i
$666$		0			0
$667$			53.8388i			2.08465i
$668$	−16.5463	−	13.8982i	−0.640195	−	0.537739i
$669$		0			0
$670$	−7.57744	+	20.8025i	−0.292742	+	0.803670i
$671$	−1.60406	+	2.77832i	−0.0619242	+	0.107256i
$672$		0			0
$673$	−9.76133	−	16.9071i	−0.376272	−	0.651722i	0.614245	−	0.789115i	$-0.289461\pi$
$673$	−9.76133	−	16.9071i	−0.376272	−	0.651722i	−0.990516	+	0.137394i	$0.956127\pi$
$674$	−42.0585	+	7.40509i	−1.62003	+	0.285233i
$675$		0			0
$676$	−24.4051	+	8.86877i	−0.938658	+	0.341107i
$677$	−7.35277	+	4.24512i	−0.282590	+	0.163153i	−0.634595	−	0.772845i	$-0.718833\pi$
$677$	−7.35277	+	4.24512i	−0.282590	+	0.163153i	0.352005	+	0.935998i	$0.385500\pi$
$678$		0			0
$679$	9.82208	+	5.67078i	0.376937	+	0.217625i
$680$	−0.00307927	+	4.06275i	−0.000118085	+	0.155799i
$681$		0			0
$682$	2.17620	−	1.82511i	0.0833310	−	0.0698871i
$683$	16.0399			0.613751			0.306876	−	0.951750i	$-0.400716\pi$
$683$	16.0399			0.613751			0.306876	+	0.951750i	$0.400716\pi$
$684$		0			0
$685$	39.4411			1.50697
$686$	1.08358	−	0.908765i	0.0413713	−	0.0346968i
$687$		0			0
$688$	−17.2329	+	3.02066i	−0.656997	+	0.115162i
$689$	−1.00724	−	0.581529i	−0.0383727	−	0.0221545i
$690$		0			0
$691$	17.7036	−	10.2212i	0.673476	−	0.388831i	−0.123917	−	0.992293i	$-0.539546\pi$
$691$	17.7036	−	10.2212i	0.673476	−	0.388831i	0.797392	+	0.603461i	$0.206212\pi$
$692$	−3.17074	−	8.72526i	−0.120534	−	0.331685i
$693$		0			0
$694$	−35.5155	+	6.25309i	−1.34815	+	0.237364i
$695$	2.29785	+	3.97999i	0.0871623	+	0.150970i
$696$		0			0
$697$	−1.36415	+	2.36279i	−0.0516710	+	0.0894969i
$698$	14.9487	−	41.0391i	0.565818	−	1.55335i
$699$		0			0
$700$	2.19418	−	2.61224i	0.0829322	−	0.0987334i
$701$			11.4242i			0.431488i	0.976450	+	0.215744i	$0.0692176\pi$
$701$			11.4242i			0.431488i	−0.976450	+	0.215744i	$0.930782\pi$
$702$		0			0
$703$			35.7737i			1.34923i
$704$	1.99720	+	0.00302748i	0.0752724	+	0.000114102i
$705$		0			0
$706$	−46.4211	−	16.9092i	−1.74708	−	0.636385i
$707$	−1.83009	+	3.16980i	−0.0688275	+	0.119213i
$708$		0			0
$709$	5.08955	+	8.81537i	0.191142	+	0.331068i	0.945629	−	0.325247i	$-0.105447\pi$
$709$	5.08955	+	8.81537i	0.191142	+	0.331068i	−0.754487	+	0.656315i	$0.772114\pi$
$710$	10.0218	+	56.9208i	0.376113	+	2.13620i
$711$		0			0
$712$	−11.0479	−	19.1691i	−0.414038	−	0.718392i
$713$	−55.0121	+	31.7613i	−2.06022	+	1.18947i
$714$		0			0
$715$	0.0723466	+	0.0417693i	0.00270561	+	0.00156208i
$716$	2.32195	−	13.1296i	0.0867752	−	0.490677i
$717$		0			0
$718$	5.38867	+	6.42526i	0.201103	+	0.239789i
$719$	25.4397			0.948741			0.474370	−	0.880325i	$-0.342676\pi$
$719$	25.4397			0.948741			0.474370	+	0.880325i	$0.342676\pi$
$720$		0			0
$721$	6.88155			0.256282
$722$	−5.55517	−	6.62379i	−0.206742	−	0.246512i
$723$		0			0
$724$	2.65136	−	14.9923i	0.0985371	−	0.557185i
$725$	10.0720	+	5.81508i	0.374065	+	0.215967i
$726$		0			0
$727$	−14.2142	+	8.20655i	−0.527174	+	0.304364i	−0.739865	−	0.672756i	$-0.765111\pi$
$727$	−14.2142	+	8.20655i	−0.527174	+	0.304364i	0.212691	+	0.977120i	$0.431777\pi$
$728$	−0.182505	−	0.316663i	−0.00676410	−	0.0117363i
$729$		0			0
$730$	−8.95501	−	50.8615i	−0.331440	−	1.88247i
$731$	−1.21308	−	2.10112i	−0.0448674	−	0.0777127i
$732$		0			0
$733$	−18.2362	+	31.5859i	−0.673568	+	1.16665i	0.303318	+	0.952889i	$0.401906\pi$
$733$	−18.2362	+	31.5859i	−0.673568	+	1.16665i	−0.976885	+	0.213764i	$0.931428\pi$
$734$	40.1729	+	14.6332i	1.48281	+	0.540123i
$735$		0			0
$736$	−43.9797	−	7.81211i	−1.62111	−	0.287958i
$737$			1.50926i			0.0555943i
$738$		0			0
$739$		−	43.0747i		−	1.58453i	−0.610177	−	0.792265i	$-0.708902\pi$
$739$		−	43.0747i		−	1.58453i	0.610177	−	0.792265i	$-0.291098\pi$
$740$	33.1946	−	39.5193i	1.22026	−	1.45276i
$741$		0			0
$742$	−4.35650	+	11.9600i	−0.159932	+	0.439065i
$743$	−21.0352	+	36.4340i	−0.771705	+	1.33663i	0.164922	+	0.986307i	$0.447263\pi$
$743$	−21.0352	+	36.4340i	−0.771705	+	1.33663i	−0.936628	+	0.350326i	$0.886071\pi$
$744$		0			0
$745$	−21.4525	−	37.1568i	−0.785959	−	1.36132i
$746$	−7.08578	+	1.24757i	−0.259429	+	0.0456767i
$747$		0			0
$748$	0.0945937	+	0.260303i	0.00345869	+	0.00951763i
$749$	6.44036	−	3.71834i	0.235326	−	0.135865i
$750$		0			0
$751$	−3.20236	−	1.84888i	−0.116856	−	0.0674667i	0.440433	−	0.897786i	$-0.354825\pi$
$751$	−3.20236	−	1.84888i	−0.116856	−	0.0674667i	−0.557289	+	0.830319i	$0.688158\pi$
$752$	−3.34140	−	19.0627i	−0.121848	−	0.695144i
$753$		0			0
$754$	0.954695	−	0.800673i	0.0347679	−	0.0291588i
$755$	45.5588			1.65805
$756$		0			0
$757$	12.8240			0.466097			0.233048	−	0.972465i	$-0.425130\pi$
$757$	12.8240			0.466097			0.233048	+	0.972465i	$0.425130\pi$
$758$	20.1584	−	16.9063i	0.732188	−	0.614063i
$759$		0			0
$760$	0.0199285	−	26.2934i	0.000722883	−	0.953761i
$761$	−30.7741	−	17.7674i	−1.11556	−	0.644069i	−0.175296	−	0.984516i	$-0.556088\pi$
$761$	−30.7741	−	17.7674i	−1.11556	−	0.644069i	−0.940264	+	0.340447i	$0.889422\pi$
$762$		0			0
$763$	7.13332	−	4.11842i	0.258243	−	0.149097i
$764$	−8.10188	+	2.94421i	−0.293116	+	0.106518i
$765$		0			0
$766$	−16.6663	+	2.93437i	−0.602177	+	0.106023i
$767$	−0.480221	−	0.831767i	−0.0173398	−	0.0300334i
$768$		0			0
$769$	−3.57085	+	6.18489i	−0.128768	+	0.223033i	−0.923200	−	0.384321i	$-0.874436\pi$
$769$	−3.57085	+	6.18489i	−0.128768	+	0.223033i	0.794431	+	0.607354i	$0.207769\pi$
$770$	0.312913	−	0.859047i	0.0112766	−	0.0309579i
$771$		0			0
$772$	−2.11617	−	1.77750i	−0.0761626	−	0.0639736i
$773$			39.5269i			1.42168i	0.703351	+	0.710842i	$0.251686\pi$
$773$			39.5269i			1.42168i	−0.703351	+	0.710842i	$0.748314\pi$
$774$		0			0
$775$			13.7220i			0.492910i
$776$	−27.7689	−	16.0604i	−0.996844	−	0.576536i
$777$		0			0
$778$	−25.1108	−	9.14676i	−0.900265	−	0.327927i
$779$	8.82857	−	15.2915i	0.316316	−	0.547876i
$780$		0			0
$781$	1.96999	+	3.41213i	0.0704919	+	0.122095i
$782$	−1.07408	−	6.10042i	−0.0384090	−	0.218151i
$783$		0			0
$784$	−3.06677	+	2.56805i	−0.109528	+	0.0917162i
$785$	−5.05375	+	2.91778i	−0.180376	+	0.104140i
$786$		0			0
$787$	−37.4865	−	21.6428i	−1.33625	−	0.771484i	−0.350000	−	0.936750i	$-0.613818\pi$
$787$	−37.4865	−	21.6428i	−1.33625	−	0.771484i	−0.986249	+	0.165266i	$0.947152\pi$
$788$	18.2465	+	3.22686i	0.650004	+	0.114952i
$789$		0			0
$790$	5.54434	+	6.61088i	0.197259	+	0.235204i
$791$	−8.57866			−0.305022
$792$		0			0
$793$	−1.66054			−0.0589676
$794$	23.9218	+	28.5235i	0.848952	+	1.01226i
$795$		0			0
$796$	48.4460	+	8.56758i	1.71712	+	0.303670i
$797$	8.31298	+	4.79950i	0.294461	+	0.170007i	0.639952	−	0.768415i	$-0.278954\pi$
$797$	8.31298	+	4.79950i	0.294461	+	0.170007i	−0.345491	+	0.938422i	$0.612288\pi$
$798$		0			0
$799$	2.32422	−	1.34189i	0.0822249	−	0.0474726i
$800$	−6.21168	+	7.38383i	−0.219616	+	0.261058i
$801$		0			0
$802$	−2.16482	−	12.2954i	−0.0764423	−	0.434167i
$803$	−1.76028	−	3.04890i	−0.0621191	−	0.107593i
$804$		0			0
$805$	−10.2239	+	17.7083i	−0.360345	+	0.624136i
$806$	1.38133	+	0.503158i	0.0486552	+	0.0177230i
$807$		0			0
$808$	5.18306	−	8.96163i	0.182339	−	0.315269i
$809$			29.1906i			1.02629i	0.858303	+	0.513144i	$0.171519\pi$
$809$			29.1906i			1.02629i	−0.858303	+	0.513144i	$0.828481\pi$
$810$		0			0
$811$		−	55.7718i		−	1.95841i	−0.202866	−	0.979207i	$-0.565026\pi$
$811$		−	55.7718i		−	1.95841i	0.202866	−	0.979207i	$-0.434974\pi$
$812$	−10.4417	−	8.77064i	−0.366433	−	0.307789i
$813$		0			0
$814$	1.20417	−	3.30582i	0.0422060	−	0.115869i
$815$	9.05708	−	15.6873i	0.317256	−	0.549503i
$816$		0			0
$817$	7.85085	+	13.5981i	0.274667	+	0.475736i
$818$	31.9015	−	5.61678i	1.11541	−	0.196386i
$819$		0			0
$820$	−23.9421	+	8.70050i	−0.836093	+	0.303835i
$821$	−1.49795	+	0.864842i	−0.0522788	+	0.0301832i	−0.525912	−	0.850539i	$-0.676276\pi$
$821$	−1.49795	+	0.864842i	−0.0522788	+	0.0301832i	0.473633	+	0.880722i	$0.342942\pi$
$822$		0			0
$823$	26.6424	+	15.3820i	0.928697	+	0.536184i	0.886399	−	0.462922i	$-0.153199\pi$
$823$	26.6424	+	15.3820i	0.928697	+	0.536184i	0.0422978	+	0.999105i	$0.486532\pi$
$824$	−19.4640	−	0.0147523i	−0.678059	−	0.000513921i
$825$		0			0
$826$	−8.05380	+	6.75447i	−0.280227	+	0.235018i
$827$	−18.2699			−0.635305			−0.317653	−	0.948207i	$-0.602895\pi$
$827$	−18.2699			−0.635305			−0.317653	+	0.948207i	$0.602895\pi$
$828$		0			0
$829$	33.8459			1.17552			0.587758	−	0.809037i	$-0.300011\pi$
$829$	33.8459			1.17552			0.587758	+	0.809037i	$0.300011\pi$
$830$	−13.2733	+	11.1319i	−0.460723	+	0.386394i
$831$		0			0
$832$	0.515524	+	0.896048i	0.0178726	+	0.0310649i
$833$	−0.480377	−	0.277346i	−0.0166441	−	0.00960946i
$834$		0			0
$835$	24.2301	−	13.9892i	0.838517	−	0.484118i
$836$	−0.612194	−	1.68464i	−0.0211732	−	0.0582644i
$837$		0			0
$838$	14.2279	−	2.50506i	0.491494	−	0.0865357i
$839$	−8.32917	−	14.4265i	−0.287555	−	0.498060i	0.685671	−	0.727912i	$-0.259509\pi$
$839$	−8.32917	−	14.4265i	−0.287555	−	0.498060i	−0.973226	+	0.229852i	$0.926176\pi$
$840$		0			0
$841$	8.74420	−	15.1454i	0.301524	−	0.522255i
$842$	5.76308	−	15.8215i	0.198609	−	0.545245i
$843$		0			0
$844$	−13.3493	+	15.8927i	−0.459501	+	0.547051i
$845$		−	33.6208i		−	1.15659i
$846$		0			0
$847$			10.9377i			0.375823i
$848$	12.3477	−	33.8186i	0.424021	−	1.16134i
$849$		0			0
$850$	−1.25726	−	0.457965i	−0.0431237	−	0.0157081i
$851$	−39.3440	+	68.1458i	−1.34870	+	2.33601i
$852$		0			0
$853$	−17.7026	−	30.6618i	−0.606126	−	1.04984i	−0.991872	−	0.127236i	$-0.959390\pi$
$853$	−17.7026	−	30.6618i	−0.606126	−	1.04984i	0.385747	−	0.922605i	$-0.373944\pi$
$854$	3.15124	+	17.8980i	0.107833	+	0.612457i
$855$		0			0
$856$	−18.2241	+	10.5033i	−0.622885	+	0.358994i
$857$	7.62418	−	4.40182i	0.260437	−	0.150363i	−0.364097	−	0.931361i	$-0.618622\pi$
$857$	7.62418	−	4.40182i	0.260437	−	0.150363i	0.624534	+	0.780998i	$0.285289\pi$
$858$		0			0
$859$	−22.0092	−	12.7070i	−0.750944	−	0.433558i	0.0750910	−	0.997177i	$-0.476075\pi$
$859$	−22.0092	−	12.7070i	−0.750944	−	0.433558i	−0.826035	+	0.563619i	$0.809409\pi$
$860$	3.94489	−	22.3067i	0.134520	−	0.760651i
$861$		0			0
$862$	3.87649	+	4.62219i	0.132034	+	0.157432i
$863$	−31.5520			−1.07404			−0.537021	−	0.843569i	$-0.680451\pi$
$863$	−31.5520			−1.07404			−0.537021	+	0.843569i	$0.680451\pi$
$864$		0			0
$865$	12.0200			0.408694
$866$	−33.4278	−	39.8582i	−1.13592	−	1.35444i
$867$		0			0
$868$	2.80187	−	15.8434i	0.0951016	−	0.537759i
$869$	0.509375	+	0.294088i	0.0172794	+	0.00997625i
$870$		0			0
$871$	−0.676539	+	0.390600i	−0.0229237	+	0.0132350i
$872$	−20.1849	+	11.6334i	−0.683547	+	0.393955i
$873$		0			0
$874$	6.95126	+	39.4809i	0.235130	+	1.33546i
$875$	−4.26531	−	7.38774i	−0.144194	−	0.249751i
$876$		0			0
$877$	17.1063	−	29.6290i	0.577639	−	1.00050i	−0.418110	−	0.908396i	$-0.637307\pi$
$877$	17.1063	−	29.6290i	0.577639	−	1.00050i	0.995749	−	0.0921044i	$-0.0293593\pi$
$878$	−20.3773	−	7.42257i	−0.687702	−	0.250500i
$879$		0			0
$880$	−0.886894	+	2.42908i	−0.0298972	+	0.0818843i
$881$		−	4.09172i		−	0.137854i	−0.997622	−	0.0689268i	$-0.978043\pi$
$881$		−	4.09172i		−	0.137854i	0.997622	−	0.0689268i	$-0.0219575\pi$
$882$		0			0
$883$			33.1247i			1.11474i	0.830266	+	0.557368i	$0.188189\pi$
$883$			33.1247i			1.11474i	−0.830266	+	0.557368i	$0.811811\pi$
$884$	−0.0922022	+	0.109770i	−0.00310110	+	0.00369195i
$885$		0			0
$886$	5.11117	−	14.0318i	0.171713	−	0.471407i
$887$	9.55299	−	16.5463i	0.320758	−	0.555569i	−0.659887	−	0.751365i	$-0.729396\pi$
$887$	9.55299	−	16.5463i	0.320758	−	0.555569i	0.980645	+	0.195796i	$0.0627290\pi$
$888$		0			0
$889$	−2.35511	−	4.07918i	−0.0789879	−	0.136811i
$890$	28.2127	−	4.96732i	0.945693	−	0.166505i
$891$		0			0
$892$	−17.6291	−	48.5117i	−0.590265	−	1.62429i
$893$	−15.0419	+	8.68446i	−0.503359	+	0.290614i
$894$		0			0
$895$	14.9508	+	8.63183i	0.499749	+	0.288530i
$896$	8.67965	−	7.25697i	0.289967	−	0.242438i
$897$		0			0
$898$	17.9095	−	15.0201i	0.597646	−	0.501227i
$899$	54.8501			1.82935
$900$		0			0
$901$	4.99254			0.166326
$902$	−1.33056	+	1.11590i	−0.0443030	+	0.0371555i
$903$		0			0
$904$	24.2641	+	0.0183905i	0.807012	+	0.000611658i
$905$	17.0718	+	9.85643i	0.567487	+	0.327639i
$906$		0			0
$907$	−14.4678	+	8.35301i	−0.480397	+	0.277357i	−0.720582	−	0.693370i	$-0.756125\pi$
$907$	−14.4678	+	8.35301i	−0.480397	+	0.277357i	0.240185	+	0.970727i	$0.422792\pi$
$908$	25.3461	−	9.21074i	0.841141	−	0.305669i
$909$		0			0
$910$	0.466058	−	0.0820573i	0.0154497	−	0.00272017i
$911$	23.3136	+	40.3803i	0.772414	+	1.33786i	0.936237	+	0.351370i	$0.114284\pi$
$911$	23.3136	+	40.3803i	0.772414	+	1.33786i	−0.163823	+	0.986490i	$0.552382\pi$
$912$		0			0
$913$	−0.590469	+	1.02272i	−0.0195417	+	0.0338472i
$914$	−5.10254	+	14.0081i	−0.168777	+	0.463347i
$915$		0			0
$916$	19.9079	+	16.7219i	0.657776	+	0.552506i
$917$		−	9.94272i		−	0.328337i
$918$		0			0
$919$		−	27.8829i		−	0.919771i	−0.887978	−	0.459885i	$-0.847890\pi$
$919$		−	27.8829i		−	0.919771i	0.887978	−	0.459885i	$-0.152110\pi$
$920$	28.9555	−	50.0647i	0.954635	−	1.65059i
$921$		0			0
$922$	−33.1176	−	12.0633i	−1.09067	−	0.397284i
$923$	−1.01968	+	1.76613i	−0.0335631	+	0.0581330i
$924$		0			0
$925$	8.49902	+	14.7207i	0.279446	+	0.484015i
$926$	7.88448	+	44.7812i	0.259100	+	1.47160i
$927$		0			0
$928$	29.5148	+	24.8295i	0.968872	+	0.815068i
$929$	19.5047	−	11.2610i	0.639929	−	0.369463i	−0.144658	−	0.989482i	$-0.546208\pi$
$929$	19.5047	−	11.2610i	0.639929	−	0.369463i	0.784587	+	0.620019i	$0.212875\pi$
$930$		0			0
$931$	3.10891	+	1.79493i	0.101891	+	0.0588265i
$932$	−44.8727	−	7.93565i	−1.46985	−	0.259941i
$933$		0			0
$934$	7.76955	+	9.26414i	0.254227	+	0.303132i
$935$	−0.358598			−0.0117274
$936$		0			0
$937$	−30.6374			−1.00088			−0.500440	−	0.865771i	$-0.666828\pi$
$937$	−30.6374			−1.00088			−0.500440	+	0.865771i	$0.666828\pi$
$938$	5.49393	+	6.55077i	0.179383	+	0.213890i
$939$		0			0
$940$	24.6752	+	4.36376i	0.804817	+	0.142330i
$941$	−14.0870	−	8.13315i	−0.459224	−	0.265133i	0.252494	−	0.967598i	$-0.418749\pi$
$941$	−14.0870	−	8.13315i	−0.459224	−	0.265133i	−0.711718	+	0.702465i	$0.752083\pi$
$942$		0			0
$943$	33.6354	−	19.4194i	1.09532	−	0.632382i
$944$	22.7941	−	19.0873i	0.741883	−	0.621237i
$945$		0			0
$946$	−0.267771	−	1.52085i	−0.00870599	−	0.0494472i
$947$	0.924500	+	1.60128i	0.0300422	+	0.0520347i	0.880656	−	0.473757i	$-0.157102\pi$
$947$	0.924500	+	1.60128i	0.0300422	+	0.0520347i	−0.850613	+	0.525792i	$0.823769\pi$
$948$		0			0
$949$	0.911132	−	1.57813i	0.0295766	−	0.0512282i
$950$	8.13677	+	2.96387i	0.263992	+	0.0961607i
$951$		0			0
$952$	1.35812	+	0.785481i	0.0440168	+	0.0254576i
$953$		−	58.7162i		−	1.90200i	−0.309186	−	0.951002i	$-0.600056\pi$
$953$		−	58.7162i		−	1.90200i	0.309186	−	0.951002i	$-0.399944\pi$
$954$		0			0
$955$		−	11.1613i		−	0.361170i
$956$	31.2297	+	26.2317i	1.01004	+	0.848395i
$957$		0			0
$958$	7.99473	−	21.9481i	0.258298	−	0.709110i
$959$	7.61545	−	13.1903i	0.245916	−	0.425938i
$960$		0			0
$961$	16.8579	+	29.1987i	0.543802	+	0.941892i
$962$	1.79351	−	0.315776i	0.0578249	−	0.0101810i
$963$		0			0
$964$	−12.3137	+	4.47478i	−0.396598	+	0.144123i
$965$	3.09888	−	1.78914i	0.0997564	−	0.0575944i
$966$		0			0
$967$	10.2999	+	5.94663i	0.331221	+	0.191231i	0.656383	−	0.754428i	$-0.272085\pi$
$967$	10.2999	+	5.94663i	0.331221	+	0.191231i	−0.325162	+	0.945658i	$0.605419\pi$
$968$	0.0234476	−	30.9364i	0.000753635	−	0.994334i
$969$		0			0
$970$	31.8242	−	26.6900i	1.02181	−	0.856963i
$971$	9.56549			0.306971			0.153486	−	0.988151i	$-0.450950\pi$
$971$	9.56549			0.306971			0.153486	+	0.988151i	$0.450950\pi$
$972$		0			0
$973$	1.77471			0.0568946
$974$	−8.59842	+	7.21123i	−0.275511	+	0.231063i
$975$		0			0
$976$	−8.87468	−	50.6300i	−0.284072	−	1.62063i
$977$	−31.6762	−	18.2882i	−1.01341	−	0.585093i	−0.101222	−	0.994864i	$-0.532275\pi$
$977$	−31.6762	−	18.2882i	−1.01341	−	0.585093i	−0.912188	+	0.409771i	$0.865608\pi$
$978$		0			0
$979$	1.69122	−	0.976424i	0.0540515	−	0.0312067i
$980$	−1.76889	−	4.86765i	−0.0565052	−	0.155491i
$981$		0			0
$982$	5.09769	−	0.897532i	0.162674	−	0.0286414i
$983$	14.3674	+	24.8851i	0.458250	+	0.793712i	0.998869	−	0.0475560i	$-0.0151432\pi$
$983$	14.3674	+	24.8851i	0.458250	+	0.793712i	−0.540619	+	0.841268i	$0.681810\pi$
$984$		0			0
$985$	−11.9958	+	20.7774i	−0.382219	+	0.662022i
$986$	−1.83059	+	5.02556i	−0.0582979	+	0.160046i
$987$		0			0
$988$	0.596717	−	0.710410i	0.0189841	−	0.0226011i
$989$			34.5376i			1.09823i
$990$		0			0
$991$			23.6126i			0.750078i	0.927009	+	0.375039i	$0.122371\pi$
$991$			23.6126i			0.750078i	−0.927009	+	0.375039i	$0.877629\pi$
$992$	−7.95884	+	44.8058i	−0.252694	+	1.42259i
$993$		0			0
$994$	20.9712	+	7.63888i	0.665165	+	0.242291i
$995$	−31.8500	+	55.1657i	−1.00971	+	1.74887i
$996$		0			0
$997$	−5.49998	−	9.52625i	−0.174186	−	0.301699i	0.765693	−	0.643206i	$-0.222396\pi$
$997$	−5.49998	−	9.52625i	−0.174186	−	0.301699i	−0.939879	+	0.341507i	$0.889063\pi$
$998$	2.11432	+	12.0087i	0.0669278	+	0.380128i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.10		72
3.2	odd	2		252.2.ba.a.239.27	yes	72
4.3	odd	2	inner	756.2.ba.a.71.22		72
9.2	odd	6	inner	756.2.ba.a.575.22		72
9.7	even	3		252.2.ba.a.155.15	✓	72
12.11	even	2		252.2.ba.a.239.15	yes	72
36.7	odd	6		252.2.ba.a.155.27	yes	72
36.11	even	6	inner	756.2.ba.a.575.10		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.15	✓	72	9.7	even	3
252.2.ba.a.155.27	yes	72	36.7	odd	6
252.2.ba.a.239.15	yes	72	12.11	even	2
252.2.ba.a.239.27	yes	72	3.2	odd	2
756.2.ba.a.71.10		72	1.1	even	1	trivial
756.2.ba.a.71.22		72	4.3	odd	2	inner
756.2.ba.a.575.10		72	36.11	even	6	inner
756.2.ba.a.575.22		72	9.2	odd	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.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +O(q^{10})\)	\(q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +(0.635018 + 3.60669i) q^{10} +(0.124825 + 0.216204i) q^{11} +(-0.0646102 + 0.111908i) q^{13} +(1.32880 + 0.484025i) q^{14} +(-3.75739 - 1.37188i) q^{16} -0.554691i q^{17} +3.58986i q^{19} +(3.33106 - 3.96573i) q^{20} +(0.120837 - 0.331737i) q^{22} +(-3.94814 + 6.83839i) q^{23} +(0.852871 + 1.47722i) q^{25} +(0.179977 - 0.0316879i) q^{26} +(-0.683091 - 1.87973i) q^{28} +(5.90477 - 3.40912i) q^{29} +(6.96683 + 4.02230i) q^{31} +(1.92804 + 5.31814i) q^{32} +(-0.601052 + 0.504084i) q^{34} +2.58954 q^{35} +9.96519 q^{37} +(3.88991 - 3.26234i) q^{38} +(-7.32434 - 0.00555133i) q^{40} +(-4.25964 - 2.45930i) q^{41} +(3.78791 - 2.18695i) q^{43} +(-0.469276 + 0.170534i) q^{44} +(10.9979 - 1.93636i) q^{46} +(2.41916 + 4.19011i) q^{47} +(0.500000 - 0.866025i) q^{49} +(0.825622 - 2.26660i) q^{50} +(-0.197893 - 0.166223i) q^{52} +9.00057i q^{53} -0.646482i q^{55} +(-1.41607 + 2.44842i) q^{56} +(-9.06010 - 3.30020i) q^{58} +(-3.71629 + 6.43680i) q^{59} +(6.42524 + 11.1288i) q^{61} +(-1.97273 - 11.2045i) q^{62} +(4.01050 - 6.92213i) q^{64} +(0.289791 - 0.167311i) q^{65} +(5.23554 + 3.02274i) q^{67} +(1.09243 + 0.193194i) q^{68} +(-2.35329 - 2.80598i) q^{70} +15.7820 q^{71} -14.1020 q^{73} +(-9.05602 - 10.7981i) q^{74} +(-7.07002 - 1.25032i) q^{76} +(-0.216204 - 0.124825i) q^{77} +(2.04035 - 1.17800i) q^{79} +(6.65009 + 7.94155i) q^{80} +(1.20616 + 6.85059i) q^{82} +(2.36518 + 4.09661i) q^{83} +(-0.718199 + 1.24396i) q^{85} +(-5.81205 - 2.11708i) q^{86} +(0.611249 + 0.353523i) q^{88} -7.82233i q^{89} -0.129220i q^{91} +(-12.0927 - 10.1574i) q^{92} +(2.34187 - 6.42918i) q^{94} +(4.64806 - 8.05067i) q^{95} +(-5.67078 - 9.82208i) q^{97} +(-1.39279 + 0.245224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Introduction

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