LMFDB - Embedded newform 756.2.bq.a.25.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10, 12]))

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

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

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05320 - 1.37506i) q^{3} +(-1.13419 - 0.412813i) q^{5} +(2.58962 - 0.542074i) q^{7} +(-0.781555 + 2.89641i) q^{9} +O(q^{10})$	\(q+(-1.05320 - 1.37506i) q^{3} +(-1.13419 - 0.412813i) q^{5} +(2.58962 - 0.542074i) q^{7} +(-0.781555 + 2.89641i) q^{9} +(3.43712 - 1.25101i) q^{11} +(0.798016 + 4.52577i) q^{13} +(0.626889 + 1.99435i) q^{15} +2.09049 q^{17} +3.68079 q^{19} +(-3.47277 - 2.98997i) q^{21} +(-0.774983 - 4.39515i) q^{23} +(-2.71424 - 2.27752i) q^{25} +(4.80585 - 1.97580i) q^{27} +(1.70270 - 9.65650i) q^{29} +(-4.34781 + 3.64825i) q^{31} +(-5.34018 - 3.40868i) q^{33} +(-3.16091 - 0.454213i) q^{35} +(1.40343 - 2.43081i) q^{37} +(5.38272 - 5.86384i) q^{39} +(0.317136 + 1.79857i) q^{41} +(3.28251 + 2.75435i) q^{43} +(2.08211 - 2.96245i) q^{45} +(-0.960637 - 0.806070i) q^{47} +(6.41231 - 2.80754i) q^{49} +(-2.20170 - 2.87454i) q^{51} +(4.61726 - 7.99733i) q^{53} -4.41480 q^{55} +(-3.87660 - 5.06129i) q^{57} +(0.671747 + 3.80967i) q^{59} +(-0.359536 - 0.301687i) q^{61} +(-0.453867 + 7.92427i) q^{63} +(0.963192 - 5.46254i) q^{65} +(1.05889 + 0.385406i) q^{67} +(-5.22736 + 5.69460i) q^{69} +(-2.88571 - 4.99820i) q^{71} +(-0.450547 - 0.780371i) q^{73} +(-0.273085 + 6.13090i) q^{75} +(8.22272 - 5.10282i) q^{77} +(10.6917 - 3.89147i) q^{79} +(-7.77834 - 4.52740i) q^{81} +(-0.254323 + 1.44234i) q^{83} +(-2.37102 - 0.862982i) q^{85} +(-15.0715 + 7.82888i) q^{87} +0.152263 q^{89} +(4.51986 + 11.2875i) q^{91} +(9.59564 + 2.13616i) q^{93} +(-4.17473 - 1.51948i) q^{95} +(-11.4856 - 9.63760i) q^{97} +(0.937136 + 10.9330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−1.05320	−	1.37506i	−0.608063	−	0.793889i
$3$	−1.05320	−	1.37506i	−0.608063	−	0.793889i
$4$		0			0
$5$	−1.13419	−	0.412813i	−0.507227	−	0.184616i	0.0757147	−	0.997130i	$-0.475876\pi$
$5$	−1.13419	−	0.412813i	−0.507227	−	0.184616i	−0.582942	+	0.812514i	$0.698098\pi$
$6$		0			0
$7$	2.58962	−	0.542074i	0.978786	−	0.204885i
$7$	2.58962	−	0.542074i	0.978786	−	0.204885i
$8$		0			0
$9$	−0.781555	+	2.89641i	−0.260518	+	0.965469i
$10$		0			0
$11$	3.43712	−	1.25101i	1.03633	−	0.377194i	0.232843	−	0.972514i	$-0.425197\pi$
$11$	3.43712	−	1.25101i	1.03633	−	0.377194i	0.803489	+	0.595320i	$0.202975\pi$
$12$		0			0
$13$	0.798016	+	4.52577i	0.221330	+	1.25522i	0.869578	+	0.493795i	$0.164391\pi$
$13$	0.798016	+	4.52577i	0.221330	+	1.25522i	−0.648249	+	0.761429i	$0.724498\pi$
$14$		0			0
$15$	0.626889	+	1.99435i	0.161862	+	0.514940i
$16$		0			0
$17$	2.09049			0.507019			0.253509	−	0.967333i	$-0.418415\pi$
$17$	2.09049			0.507019			0.253509	+	0.967333i	$0.418415\pi$
$18$		0			0
$19$	3.68079			0.844432			0.422216	−	0.906495i	$-0.361252\pi$
$19$	3.68079			0.844432			0.422216	+	0.906495i	$0.361252\pi$
$20$		0			0
$21$	−3.47277	−	2.98997i	−0.757819	−	0.652464i
$22$		0			0
$23$	−0.774983	−	4.39515i	−0.161595	−	0.916452i	−0.952506	−	0.304520i	$-0.901504\pi$
$23$	−0.774983	−	4.39515i	−0.161595	−	0.916452i	0.790911	−	0.611932i	$-0.209607\pi$
$24$		0			0
$25$	−2.71424	−	2.27752i	−0.542848	−	0.455504i
$26$		0			0
$27$	4.80585	−	1.97580i	0.924886	−	0.380244i
$28$		0			0
$29$	1.70270	−	9.65650i	0.316184	−	1.79317i	−0.249319	−	0.968421i	$-0.580207\pi$
$29$	1.70270	−	9.65650i	0.316184	−	1.79317i	0.565503	−	0.824746i	$-0.308682\pi$
$30$		0			0
$31$	−4.34781	+	3.64825i	−0.780890	+	0.655245i	−0.943473	−	0.331450i	$-0.892462\pi$
$31$	−4.34781	+	3.64825i	−0.780890	+	0.655245i	0.162583	+	0.986695i	$0.448018\pi$
$32$		0			0
$33$	−5.34018	−	3.40868i	−0.929605	−	0.593374i
$34$		0			0
$35$	−3.16091	−	0.454213i	−0.534292	−	0.0767761i
$36$		0			0
$37$	1.40343	−	2.43081i	0.230722	−	0.399622i	−0.727299	−	0.686321i	$-0.759225\pi$
$37$	1.40343	−	2.43081i	0.230722	−	0.399622i	0.958021	+	0.286699i	$0.0925579\pi$
$38$		0			0
$39$	5.38272	−	5.86384i	0.861925	−	0.938966i
$40$		0			0
$41$	0.317136	+	1.79857i	0.0495283	+	0.280889i	0.999506	−	0.0314288i	$-0.0100057\pi$
$41$	0.317136	+	1.79857i	0.0495283	+	0.280889i	−0.949978	+	0.312318i	$0.898895\pi$
$42$		0			0
$43$	3.28251	+	2.75435i	0.500578	+	0.420035i	0.857799	−	0.513985i	$-0.171831\pi$
$43$	3.28251	+	2.75435i	0.500578	+	0.420035i	−0.357221	+	0.934020i	$0.616276\pi$
$44$		0			0
$45$	2.08211	−	2.96245i	0.310382	−	0.441616i
$46$		0			0
$47$	−0.960637	−	0.806070i	−0.140123	−	0.117577i	0.570032	−	0.821623i	$-0.306931\pi$
$47$	−0.960637	−	0.806070i	−0.140123	−	0.117577i	−0.710155	+	0.704045i	$0.751375\pi$
$48$		0			0
$49$	6.41231	−	2.80754i	0.916045	−	0.401077i
$50$		0			0
$51$	−2.20170	−	2.87454i	−0.308300	−	0.402517i
$52$		0			0
$53$	4.61726	−	7.99733i	0.634230	−	1.09852i	−0.352448	−	0.935831i	$-0.614651\pi$
$53$	4.61726	−	7.99733i	0.634230	−	1.09852i	0.986678	−	0.162687i	$-0.0520161\pi$
$54$		0			0
$55$	−4.41480			−0.595291
$56$		0			0
$57$	−3.87660	−	5.06129i	−0.513468	−	0.670385i
$58$		0			0
$59$	0.671747	+	3.80967i	0.0874540	+	0.495976i	0.996800	+	0.0799356i	$0.0254715\pi$
$59$	0.671747	+	3.80967i	0.0874540	+	0.495976i	−0.909346	+	0.416041i	$0.863417\pi$
$60$		0			0
$61$	−0.359536	−	0.301687i	−0.0460339	−	0.0386270i	0.619480	−	0.785012i	$-0.287343\pi$
$61$	−0.359536	−	0.301687i	−0.0460339	−	0.0386270i	−0.665514	+	0.746385i	$0.731788\pi$
$62$		0			0
$63$	−0.453867	+	7.92427i	−0.0571818	+	0.998364i
$64$		0			0
$65$	0.963192	−	5.46254i	0.119469	−	0.677544i
$66$		0			0
$67$	1.05889	+	0.385406i	0.129365	+	0.0470849i	0.405891	−	0.913921i	$-0.366961\pi$
$67$	1.05889	+	0.385406i	0.129365	+	0.0470849i	−0.276527	+	0.961006i	$0.589183\pi$
$68$		0			0
$69$	−5.22736	+	5.69460i	−0.629301	+	0.685549i
$70$		0			0
$71$	−2.88571	−	4.99820i	−0.342471	−	0.593177i	0.642420	−	0.766353i	$-0.277930\pi$
$71$	−2.88571	−	4.99820i	−0.342471	−	0.593177i	−0.984891	+	0.173176i	$0.944597\pi$
$72$		0			0
$73$	−0.450547	−	0.780371i	−0.0527326	−	0.0913355i	0.838454	−	0.544972i	$-0.183460\pi$
$73$	−0.450547	−	0.780371i	−0.0527326	−	0.0913355i	−0.891187	+	0.453637i	$0.850126\pi$
$74$		0			0
$75$	−0.273085	+	6.13090i	−0.0315332	+	0.707936i
$76$		0			0
$77$	8.22272	−	5.10282i	0.937066	−	0.581521i
$78$		0			0
$79$	10.6917	−	3.89147i	1.20291	−	0.437825i	0.338674	−	0.940904i	$-0.390022\pi$
$79$	10.6917	−	3.89147i	1.20291	−	0.437825i	0.864240	+	0.503079i	$0.167800\pi$
$80$		0			0
$81$	−7.77834	−	4.52740i	−0.864261	−	0.503045i
$82$		0			0
$83$	−0.254323	+	1.44234i	−0.0279156	+	0.158317i	−0.995579	−	0.0939277i	$-0.970058\pi$
$83$	−0.254323	+	1.44234i	−0.0279156	+	0.158317i	0.967663	+	0.252245i	$0.0811688\pi$
$84$		0			0
$85$	−2.37102	−	0.862982i	−0.257174	−	0.0936036i
$86$		0			0
$87$	−15.0715	+	7.82888i	−1.61584	+	0.839345i
$88$		0			0
$89$	0.152263			0.0161399			0.00806993	−	0.999967i	$-0.497431\pi$
$89$	0.152263			0.0161399			0.00806993	+	0.999967i	$0.497431\pi$
$90$		0			0
$91$	4.51986	+	11.2875i	0.473811	+	1.18325i
$92$		0			0
$93$	9.59564	+	2.13616i	0.995022	+	0.221510i
$94$		0			0
$95$	−4.17473	−	1.51948i	−0.428319	−	0.155895i
$96$		0			0
$97$	−11.4856	−	9.63760i	−1.16619	−	0.978550i	−0.166218	−	0.986089i	$-0.553156\pi$
$97$	−11.4856	−	9.63760i	−1.16619	−	0.978550i	−0.999972	+	0.00753946i	$0.997600\pi$
$98$		0			0
$99$	0.937136	+	10.9330i	0.0941857	+	1.09881i
$100$		0			0
$101$	−0.152049	+	0.862313i	−0.0151294	+	0.0858034i	−0.991438	−	0.130582i	$-0.958316\pi$
$101$	−0.152049	+	0.862313i	−0.0151294	+	0.0858034i	0.976308	+	0.216385i	$0.0694266\pi$
$102$		0			0
$103$	15.7412	+	5.72932i	1.55102	+	0.564527i	0.968658	−	0.248399i	$-0.0799044\pi$
$103$	15.7412	+	5.72932i	1.55102	+	0.564527i	0.582367	+	0.812926i	$0.302127\pi$
$104$		0			0
$105$	2.70449	+	4.82481i	0.263931	+	0.470853i
$106$		0			0
$107$	6.93104	+	12.0049i	0.670049	+	1.16056i	0.977890	+	0.209120i	$0.0670601\pi$
$107$	6.93104	+	12.0049i	0.670049	+	1.16056i	−0.307841	+	0.951438i	$0.599607\pi$
$108$		0			0
$109$	0.480502	−	0.832253i	0.0460237	−	0.0797154i	−0.842096	−	0.539328i	$-0.818678\pi$
$109$	0.480502	−	0.832253i	0.0460237	−	0.0797154i	0.888120	+	0.459612i	$0.152012\pi$
$110$		0			0
$111$	−4.82058	+	0.630327i	−0.457549	+	0.0598280i
$112$		0			0
$113$	−15.7652	+	13.2286i	−1.48306	+	1.24444i	−0.580228	+	0.814454i	$0.697036\pi$
$113$	−15.7652	+	13.2286i	−1.48306	+	1.24444i	−0.902836	+	0.429984i	$0.858519\pi$
$114$		0			0
$115$	−0.935393	+	5.30488i	−0.0872258	+	0.494682i
$116$		0			0
$117$	−13.7322	−	1.22576i	−1.26954	−	0.113322i
$118$		0			0
$119$	5.41359	−	1.13320i	0.496263	−	0.103880i
$120$		0			0
$121$	1.82231	−	1.52910i	0.165664	−	0.139009i
$122$		0			0
$123$	2.13912	−	2.33032i	0.192878	−	0.210118i
$124$		0			0
$125$	5.15575	+	8.93002i	0.461144	+	0.798725i
$126$		0			0
$127$	−5.14252	+	8.90711i	−0.456325	+	0.790378i	−0.998763	−	0.0497175i	$-0.984168\pi$
$127$	−5.14252	+	8.90711i	−0.456325	+	0.790378i	0.542438	+	0.840096i	$0.317501\pi$
$128$		0			0
$129$	0.330260	−	7.41451i	0.0290778	−	0.652811i
$130$		0			0
$131$	−2.91733	−	16.5450i	−0.254888	−	1.44554i	−0.796360	−	0.604823i	$-0.793244\pi$
$131$	−2.91733	−	16.5450i	−0.254888	−	1.44554i	0.541472	−	0.840719i	$-0.317867\pi$
$132$		0			0
$133$	9.53187	−	1.99526i	0.826518	−	0.173011i
$134$		0			0
$135$	−6.26640	+	0.257028i	−0.539326	+	0.0221215i
$136$		0			0
$137$	−4.35873	−	3.65741i	−0.372391	−	0.312473i	0.437315	−	0.899308i	$-0.355929\pi$
$137$	−4.35873	−	3.65741i	−0.372391	−	0.312473i	−0.809707	+	0.586835i	$0.800374\pi$
$138$		0			0
$139$	14.3057	+	5.20685i	1.21339	+	0.441639i	0.867880	−	0.496775i	$-0.165482\pi$
$139$	14.3057	+	5.20685i	1.21339	+	0.441639i	0.345514	+	0.938414i	$0.387705\pi$
$140$		0			0
$141$	−0.0966517	+	2.16988i	−0.00813954	+	0.182737i
$142$		0			0
$143$	8.40467	+	14.5573i	0.702834	+	1.21734i
$144$		0			0
$145$	−5.91752	+	10.2495i	−0.491424	+	0.851171i
$146$		0			0
$147$	−10.6139	−	5.86040i	−0.875423	−	0.483357i
$148$		0			0
$149$	10.2346	−	8.58788i	0.838454	−	0.703547i	−0.118761	−	0.992923i	$-0.537892\pi$
$149$	10.2346	−	8.58788i	0.838454	−	0.703547i	0.957215	+	0.289376i	$0.0934478\pi$
$150$		0			0
$151$	−16.9914	+	6.18438i	−1.38274	+	0.503277i	−0.923009	−	0.384779i	$-0.874278\pi$
$151$	−16.9914	+	6.18438i	−1.38274	+	0.503277i	−0.459734	+	0.888056i	$0.652055\pi$
$152$		0			0
$153$	−1.63383	+	6.05492i	−0.132088	+	0.489511i
$154$		0			0
$155$	6.43731	−	2.34299i	0.517057	−	0.188193i
$156$		0			0
$157$	1.76232	+	9.99462i	0.140648	+	0.797657i	0.970759	+	0.240058i	$0.0771664\pi$
$157$	1.76232	+	9.99462i	0.140648	+	0.797657i	−0.830110	+	0.557599i	$0.811723\pi$
$158$		0			0
$159$	−15.8597	+	2.07377i	−1.25775	+	0.164461i
$160$		0			0
$161$	−4.38941	−	10.9617i	−0.345934	−	0.863902i
$162$		0			0
$163$	9.70366	+	16.8072i	0.760049	+	1.31644i	0.942825	+	0.333290i	$0.108159\pi$
$163$	9.70366	+	16.8072i	0.760049	+	1.31644i	−0.182775	+	0.983155i	$0.558508\pi$
$164$		0			0
$165$	4.64965	+	6.07059i	0.361975	+	0.472595i
$166$		0			0
$167$	3.29134	−	2.76176i	0.254692	−	0.213712i	−0.506498	−	0.862241i	$-0.669060\pi$
$167$	3.29134	−	2.76176i	0.254692	−	0.213712i	0.761190	+	0.648530i	$0.224616\pi$
$168$		0			0
$169$	−7.62978	+	2.77701i	−0.586906	+	0.213616i
$170$		0			0
$171$	−2.87674	+	10.6611i	−0.219990	+	0.815273i
$172$		0			0
$173$	1.80500	−	10.2366i	0.137231	−	0.778278i	−0.836048	−	0.548656i	$-0.815140\pi$
$173$	1.80500	−	10.2366i	0.137231	−	0.778278i	0.973280	−	0.229622i	$-0.0737491\pi$
$174$		0			0
$175$	−8.26345	−	4.42660i	−0.624658	−	0.334619i
$176$		0			0
$177$	4.53102	−	4.93601i	0.340572	−	0.371014i
$178$		0			0
$179$	−7.93269			−0.592917			−0.296459	−	0.955046i	$-0.595806\pi$
$179$	−7.93269			−0.592917			−0.296459	+	0.955046i	$0.595806\pi$
$180$		0			0
$181$	−11.1402	+	19.2954i	−0.828045	+	1.43422i	0.0715251	+	0.997439i	$0.477213\pi$
$181$	−11.1402	+	19.2954i	−0.828045	+	1.43422i	−0.899570	+	0.436777i	$0.856120\pi$
$182$		0			0
$183$	−0.0361737	+	0.812118i	−0.00267404	+	0.0600335i
$184$		0			0
$185$	−2.59523	+	2.17765i	−0.190805	+	0.160104i
$186$		0			0
$187$	7.18528	−	2.61523i	0.525440	−	0.191244i
$188$		0			0
$189$	11.3743	−	7.72172i	0.827360	−	0.561672i
$190$		0			0
$191$	16.9913	−	6.18434i	1.22945	−	0.447483i	0.356041	−	0.934470i	$-0.384126\pi$
$191$	16.9913	−	6.18434i	1.22945	−	0.447483i	0.873409	+	0.486987i	$0.161904\pi$
$192$		0			0
$193$	5.14485	−	4.31704i	0.370335	−	0.310748i	−0.438559	−	0.898702i	$-0.644511\pi$
$193$	5.14485	−	4.31704i	0.370335	−	0.310748i	0.808894	+	0.587955i	$0.200067\pi$
$194$		0			0
$195$	−8.52572	+	4.42868i	−0.610539	+	0.317144i
$196$		0			0
$197$	−10.1631	+	17.6031i	−0.724094	+	1.25417i	0.235252	+	0.971935i	$0.424409\pi$
$197$	−10.1631	+	17.6031i	−0.724094	+	1.25417i	−0.959346	+	0.282233i	$0.908925\pi$
$198$		0			0
$199$	3.17142			0.224816			0.112408	−	0.993662i	$-0.464144\pi$
$199$	3.17142			0.224816			0.112408	+	0.993662i	$0.464144\pi$
$200$		0			0
$201$	−0.585269	−	1.86195i	−0.0412817	−	0.131332i
$202$		0			0
$203$	−0.825179	−	25.9297i	−0.0579162	−	1.81991i
$204$		0			0
$205$	0.382778	−	2.17084i	0.0267344	−	0.151618i
$206$		0			0
$207$	13.3358	+	1.19038i	0.926904	+	0.0827373i
$208$		0			0
$209$	12.6513	−	4.60471i	0.875112	−	0.318515i
$210$		0			0
$211$	18.6985	−	15.6899i	1.28725	−	1.08013i	0.295054	−	0.955480i	$-0.404662\pi$
$211$	18.6985	−	15.6899i	1.28725	−	1.08013i	0.992200	−	0.124654i	$-0.0397822\pi$
$212$		0			0
$213$	−3.83358	+	9.23209i	−0.262672	+	0.632573i
$214$		0			0
$215$	−2.58597	−	4.47904i	−0.176362	−	0.305468i
$216$		0			0
$217$	−9.28158	+	11.8044i	−0.630075	+	0.801337i
$218$		0			0
$219$	−0.598538	+	1.44141i	−0.0404455	+	0.0974016i
$220$		0			0
$221$	1.66825	+	9.46109i	0.112218	+	0.636422i
$222$		0			0
$223$	−20.6223	+	7.50591i	−1.38097	+	0.502633i	−0.922473	−	0.386062i	$-0.873835\pi$
$223$	−20.6223	+	7.50591i	−1.38097	+	0.502633i	−0.458499	+	0.888695i	$0.651613\pi$
$224$		0			0
$225$	8.71795	−	6.08154i	0.581196	−	0.405436i
$226$		0			0
$227$	−18.0231	+	6.55989i	−1.19624	+	0.435395i	−0.861910	−	0.507062i	$-0.830732\pi$
$227$	−18.0231	+	6.55989i	−1.19624	+	0.435395i	−0.334328	+	0.942457i	$0.608509\pi$
$228$		0			0
$229$	8.18031	−	6.86409i	0.540570	−	0.453592i	−0.331163	−	0.943574i	$-0.607441\pi$
$229$	8.18031	−	6.86409i	0.540570	−	0.453592i	0.871733	+	0.489982i	$0.162997\pi$
$230$		0			0
$231$	−15.6768	−	5.93242i	−1.03146	−	0.390325i
$232$		0			0
$233$	−9.50178	+	16.4576i	−0.622482	+	1.07817i	0.366540	+	0.930402i	$0.380542\pi$
$233$	−9.50178	+	16.4576i	−0.622482	+	1.07817i	−0.989022	+	0.147769i	$0.952791\pi$
$234$		0			0
$235$	0.756792	+	1.31080i	0.0493677	+	0.0855074i
$236$		0			0
$237$	−16.6115	−	10.6032i	−1.07903	−	0.688754i
$238$		0			0
$239$	−19.3313	−	7.03601i	−1.25044	−	0.455121i	−0.369887	−	0.929077i	$-0.620604\pi$
$239$	−19.3313	−	7.03601i	−1.25044	−	0.455121i	−0.880549	+	0.473955i	$0.842826\pi$
$240$		0			0
$241$	5.29735	+	4.44500i	0.341232	+	0.286328i	0.797258	−	0.603639i	$-0.206283\pi$
$241$	5.29735	+	4.44500i	0.341232	+	0.286328i	−0.456026	+	0.889967i	$0.650728\pi$
$242$		0			0
$243$	1.96670	+	15.4639i	0.126164	+	0.992009i
$244$		0			0
$245$	−8.43179	+	0.537206i	−0.538688	+	0.0343208i
$246$		0			0
$247$	2.93733	+	16.6584i	0.186898	+	1.05995i
$248$		0			0
$249$	2.25115	−	1.16936i	0.142661	−	0.0741050i
$250$		0			0
$251$	−9.23927	+	16.0029i	−0.583178	+	1.01009i	0.411922	+	0.911219i	$0.364858\pi$
$251$	−9.23927	+	16.0029i	−0.583178	+	1.01009i	−0.995100	+	0.0988743i	$0.968476\pi$
$252$		0			0
$253$	−8.16209	−	14.1372i	−0.513146	−	0.888796i
$254$		0			0
$255$	1.31051	+	4.16918i	0.0820671	+	0.261084i
$256$		0			0
$257$	−12.3817	+	10.3895i	−0.772350	+	0.648079i	−0.941310	−	0.337544i	$-0.890404\pi$
$257$	−12.3817	+	10.3895i	−0.772350	+	0.648079i	0.168960	+	0.985623i	$0.445959\pi$
$258$		0			0
$259$	2.31667	−	7.05564i	0.143951	−	0.438416i
$260$		0			0
$261$	26.6384	+	12.4788i	1.64888	+	0.772419i
$262$		0			0
$263$	−0.0361514	+	0.205025i	−0.00222919	+	0.0126424i	−0.985902	−	0.167323i	$-0.946488\pi$
$263$	−0.0361514	+	0.205025i	−0.00222919	+	0.0126424i	0.983673	+	0.179966i	$0.0575987\pi$
$264$		0			0
$265$	−8.53828	+	7.16446i	−0.524502	+	0.440110i
$266$		0			0
$267$	−0.160363	−	0.209370i	−0.00981405	−	0.0128132i
$268$		0			0
$269$	14.5609	−	25.2203i	0.887796	−	1.53771i	0.0453204	−	0.998973i	$-0.485569\pi$
$269$	14.5609	−	25.2203i	0.887796	−	1.53771i	0.842475	−	0.538735i	$-0.181098\pi$
$270$		0			0
$271$	−14.7517	−	25.5507i	−0.896100	−	1.55209i	−0.832437	−	0.554120i	$-0.813055\pi$
$271$	−14.7517	−	25.5507i	−0.896100	−	1.55209i	−0.0636638	−	0.997971i	$-0.520279\pi$
$272$		0			0
$273$	10.7606	−	18.1030i	0.651261	−	1.09564i
$274$		0			0
$275$	−12.1784	−	4.43257i	−0.734384	−	0.267294i
$276$		0			0
$277$	5.13594	−	29.1274i	0.308589	−	1.75009i	−0.297523	−	0.954715i	$-0.596160\pi$
$277$	5.13594	−	29.1274i	0.308589	−	1.75009i	0.606112	−	0.795380i	$-0.292728\pi$
$278$		0			0
$279$	−7.16875	−	15.4443i	−0.429182	−	0.924628i
$280$		0			0
$281$	15.4822	+	12.9911i	0.923592	+	0.774986i	0.974656	−	0.223710i	$-0.0718167\pi$
$281$	15.4822	+	12.9911i	0.923592	+	0.774986i	−0.0510637	+	0.998695i	$0.516261\pi$
$282$		0			0
$283$	−3.17060	−	1.15400i	−0.188472	−	0.0685983i	0.246060	−	0.969255i	$-0.420864\pi$
$283$	−3.17060	−	1.15400i	−0.188472	−	0.0685983i	−0.434532	+	0.900656i	$0.643086\pi$
$284$		0			0
$285$	2.30745	+	7.34080i	0.136681	+	0.434831i
$286$		0			0
$287$	1.79622	+	4.48570i	0.106027	+	0.264783i
$288$		0			0
$289$	−12.6298			−0.742932
$290$		0			0
$291$	−1.15559	+	25.9437i	−0.0677421	+	1.52084i
$292$		0			0
$293$	−15.0016	−	5.46015i	−0.876404	−	0.318985i	−0.135647	−	0.990757i	$-0.543311\pi$
$293$	−15.0016	−	5.46015i	−0.876404	−	0.318985i	−0.740758	+	0.671772i	$0.765533\pi$
$294$		0			0
$295$	0.810788	−	4.59821i	0.0472059	−	0.267718i
$296$		0			0
$297$	14.0466	−	12.8033i	0.815064	−	0.742920i
$298$		0			0
$299$	19.2730	−	7.01480i	1.11459	−	0.405676i
$300$		0			0
$301$	9.99354	+	5.35338i	0.576018	+	0.308564i
$302$		0			0
$303$	1.34587	−	0.699109i	0.0773180	−	0.0401628i
$304$		0			0
$305$	0.283244	+	0.490593i	0.0162185	+	0.0280913i
$306$		0			0
$307$	14.5172	+	25.1445i	0.828540	+	1.43507i	0.899183	+	0.437572i	$0.144162\pi$
$307$	14.5172	+	25.1445i	0.828540	+	1.43507i	−0.0706430	+	0.997502i	$0.522505\pi$
$308$		0			0
$309$	−8.70042	−	27.6791i	−0.494950	−	1.57461i
$310$		0			0
$311$	−14.8617	−	5.40921i	−0.842728	−	0.306728i	−0.115656	−	0.993289i	$-0.536897\pi$
$311$	−14.8617	−	5.40921i	−0.842728	−	0.306728i	−0.727072	+	0.686561i	$0.759119\pi$
$312$		0			0
$313$	1.85460	−	10.5180i	0.104828	−	0.594510i	−0.886461	−	0.462804i	$-0.846843\pi$
$313$	1.85460	−	10.5180i	0.104828	−	0.594510i	0.991289	−	0.131706i	$-0.0420455\pi$
$314$		0			0
$315$	3.78601	−	8.80029i	0.213318	−	0.495840i
$316$		0			0
$317$	26.3529	+	22.1127i	1.48013	+	1.24197i	0.906048	+	0.423175i	$0.139084\pi$
$317$	26.3529	+	22.1127i	1.48013	+	1.24197i	0.574080	+	0.818800i	$0.305360\pi$
$318$		0			0
$319$	−6.22799	−	35.3207i	−0.348701	−	1.97758i
$320$		0			0
$321$	9.20767	−	22.1741i	0.513922	−	1.23764i
$322$		0			0
$323$	7.69467			0.428143
$324$		0			0
$325$	8.14152	−	14.1015i	0.451610	−	0.782212i
$326$		0			0
$327$	−1.65046	+	0.215810i	−0.0912705	+	0.0119343i
$328$		0			0
$329$	−2.92464	−	1.56668i	−0.161241	−	0.0863740i
$330$		0			0
$331$	−6.55242	−	5.49813i	−0.360154	−	0.302205i	0.444698	−	0.895680i	$-0.353311\pi$
$331$	−6.55242	−	5.49813i	−0.360154	−	0.302205i	−0.804852	+	0.593476i	$0.797755\pi$
$332$		0			0
$333$	5.94375	+	5.96470i	0.325715	+	0.326864i
$334$		0			0
$335$	−1.04189	−	0.874251i	−0.0569246	−	0.0477654i
$336$		0			0
$337$	1.31587	+	7.46267i	0.0716800	+	0.406518i	0.999444	+	0.0333495i	$0.0106174\pi$
$337$	1.31587	+	7.46267i	0.0716800	+	0.406518i	−0.927764	+	0.373168i	$0.878271\pi$
$338$		0			0
$339$	34.7938	+	7.74573i	1.88974	+	0.420690i
$340$		0			0
$341$	−10.3800	+	17.9786i	−0.562107	+	0.973598i
$342$		0			0
$343$	15.0836	−	10.7464i	0.814437	−	0.580252i
$344$		0			0
$345$	8.27965	−	4.30086i	0.445761	−	0.231550i
$346$		0			0
$347$	1.03249	−	0.866364i	0.0554271	−	0.0465088i	−0.614653	−	0.788797i	$-0.710704\pi$
$347$	1.03249	−	0.866364i	0.0554271	−	0.0465088i	0.670080	+	0.742289i	$0.266260\pi$
$348$		0			0
$349$	−0.0242275	+	0.137401i	−0.00129687	+	0.00735490i	−0.985449	−	0.169970i	$-0.945633\pi$
$349$	−0.0242275	+	0.137401i	−0.00129687	+	0.00735490i	0.984152	+	0.177324i	$0.0567442\pi$
$350$		0			0
$351$	12.7772	+	20.1735i	0.681996	+	1.07678i
$352$		0			0
$353$	13.2229	+	11.0953i	0.703783	+	0.590544i	0.922847	−	0.385167i	$-0.125856\pi$
$353$	13.2229	+	11.0953i	0.703783	+	0.590544i	−0.219064	+	0.975710i	$0.570300\pi$
$354$		0			0
$355$	1.20964	+	6.86018i	0.0642008	+	0.364101i
$356$		0			0
$357$	−7.25979	−	6.25050i	−0.384229	−	0.330812i
$358$		0			0
$359$	6.02055			0.317753			0.158876	−	0.987298i	$-0.449213\pi$
$359$	6.02055			0.317753			0.158876	+	0.987298i	$0.449213\pi$
$360$		0			0
$361$	−5.45176			−0.286935
$362$		0			0
$363$	−4.02184	−	0.895333i	−0.211092	−	0.0469928i
$364$		0			0
$365$	0.188861	+	1.07108i	0.00988544	+	0.0560631i
$366$		0			0
$367$	10.0466	−	3.65666i	0.524428	−	0.190876i	−0.0662209	−	0.997805i	$-0.521094\pi$
$367$	10.0466	−	3.65666i	0.524428	−	0.190876i	0.590649	+	0.806929i	$0.298872\pi$
$368$		0			0
$369$	−5.45724	−	0.487124i	−0.284093	−	0.0253587i
$370$		0			0
$371$	7.62183	−	23.2130i	0.395706	−	1.20516i
$372$		0			0
$373$	−4.79052	−	1.74361i	−0.248044	−	0.0902805i	0.215006	−	0.976613i	$-0.431023\pi$
$373$	−4.79052	−	1.74361i	−0.248044	−	0.0902805i	−0.463050	+	0.886332i	$0.653245\pi$
$374$		0			0
$375$	6.84925	−	16.4945i	0.353694	−	0.851772i
$376$		0			0
$377$	45.0619			2.32081
$378$		0			0
$379$	27.8454			1.43032			0.715160	−	0.698960i	$-0.246354\pi$
$379$	27.8454			1.43032			0.715160	+	0.698960i	$0.246354\pi$
$380$		0			0
$381$	17.6639	−	2.30968i	0.904947	−	0.118329i
$382$		0			0
$383$	−5.21679	−	1.89876i	−0.266566	−	0.0970220i	0.205280	−	0.978703i	$-0.434190\pi$
$383$	−5.21679	−	1.89876i	−0.266566	−	0.0970220i	−0.471845	+	0.881681i	$0.656412\pi$
$384$		0			0
$385$	−11.4327	+	2.39315i	−0.582663	+	0.121966i
$386$		0			0
$387$	−10.5432	+	7.35481i	−0.535941	+	0.373866i
$388$		0			0
$389$	−34.0601	+	12.3969i	−1.72692	+	0.628546i	−0.998403	−	0.0564847i	$-0.982011\pi$
$389$	−34.0601	+	12.3969i	−1.72692	+	0.628546i	−0.728514	+	0.685031i	$0.759789\pi$
$390$		0			0
$391$	−1.62010	−	9.18803i	−0.0819318	−	0.464659i
$392$		0			0
$393$	−19.6778	+	21.4366i	−0.992612	+	1.08133i
$394$		0			0
$395$	−13.7330			−0.690980
$396$		0			0
$397$	−36.8052			−1.84720			−0.923599	−	0.383359i	$-0.874767\pi$
$397$	−36.8052			−1.84720			−0.923599	+	0.383359i	$0.874767\pi$
$398$		0			0
$399$	−12.7825	−	11.0054i	−0.639927	−	0.550962i
$400$		0			0
$401$	6.08020	+	34.4825i	0.303631	+	1.72197i	0.629881	+	0.776691i	$0.283103\pi$
$401$	6.08020	+	34.4825i	0.303631	+	1.72197i	−0.326251	+	0.945283i	$0.605785\pi$
$402$		0			0
$403$	−19.9808	−	16.7658i	−0.995312	−	0.835166i
$404$		0			0
$405$	6.95318	+	8.34595i	0.345506	+	0.414714i
$406$		0			0
$407$	1.78279	−	10.1107i	0.0883694	−	0.501168i
$408$		0			0
$409$	5.82546	−	4.88814i	0.288050	−	0.241703i	−0.487299	−	0.873235i	$-0.662018\pi$
$409$	5.82546	−	4.88814i	0.288050	−	0.241703i	0.775350	+	0.631532i	$0.217574\pi$
$410$		0			0
$411$	−0.438541	+	9.84546i	−0.0216316	+	0.485641i
$412$		0			0
$413$	3.80469	+	9.50147i	0.187217	+	0.467537i
$414$		0			0
$415$	0.883867	−	1.53090i	0.0433873	−	0.0751491i
$416$		0			0
$417$	−7.90700	−	25.1550i	−0.387208	−	1.23184i
$418$		0			0
$419$	4.98261	+	28.2578i	0.243416	+	1.38048i	0.824142	+	0.566383i	$0.191658\pi$
$419$	4.98261	+	28.2578i	0.243416	+	1.38048i	−0.580726	+	0.814099i	$0.697231\pi$
$420$		0			0
$421$	−13.7683	−	11.5530i	−0.671025	−	0.563057i	0.242344	−	0.970190i	$-0.422084\pi$
$421$	−13.7683	−	11.5530i	−0.671025	−	0.563057i	−0.913369	+	0.407134i	$0.866528\pi$
$422$		0			0
$423$	3.08550	−	2.15241i	0.150022	−	0.104654i
$424$		0			0
$425$	−5.67410	−	4.76113i	−0.275234	−	0.230949i
$426$		0			0
$427$	−1.09460	−	0.586360i	−0.0529714	−	0.0283760i
$428$		0			0
$429$	11.1653	−	26.8886i	0.539068	−	1.29819i
$430$		0			0
$431$	−2.14008	+	3.70673i	−0.103084	+	0.178547i	−0.912954	−	0.408063i	$-0.866204\pi$
$431$	−2.14008	+	3.70673i	−0.103084	+	0.178547i	0.809870	+	0.586610i	$0.199538\pi$
$432$		0			0
$433$	−37.9956			−1.82595			−0.912976	−	0.408012i	$-0.866222\pi$
$433$	−37.9956			−1.82595			−0.912976	+	0.408012i	$0.866222\pi$
$434$		0			0
$435$	20.3259	−	2.65776i	0.974551	−	0.127430i
$436$		0			0
$437$	−2.85255	−	16.1776i	−0.136456	−	0.773881i
$438$		0			0
$439$	15.6822	+	13.1589i	0.748469	+	0.628040i	0.935098	−	0.354390i	$-0.115312\pi$
$439$	15.6822	+	13.1589i	0.748469	+	0.628040i	−0.186628	+	0.982431i	$0.559756\pi$
$440$		0			0
$441$	3.12019	+	20.7669i	0.148581	+	0.988900i
$442$		0			0
$443$	−2.17900	+	12.3577i	−0.103528	+	0.587134i	0.888271	+	0.459320i	$0.151907\pi$
$443$	−2.17900	+	12.3577i	−0.103528	+	0.587134i	−0.991798	+	0.127813i	$0.959204\pi$
$444$		0			0
$445$	−0.172696	−	0.0628562i	−0.00818657	−	0.00297967i
$446$		0			0
$447$	−22.5879	−	5.02847i	−1.06837	−	0.237838i
$448$		0			0
$449$	−5.21674	−	9.03566i	−0.246193	−	0.426419i	0.716273	−	0.697820i	$-0.245846\pi$
$449$	−5.21674	−	9.03566i	−0.246193	−	0.426419i	−0.962466	+	0.271401i	$0.912513\pi$
$450$		0			0
$451$	3.34006	+	5.78516i	0.157277	+	0.272412i
$452$		0			0
$453$	26.3992	+	16.8508i	1.24034	+	0.791720i
$454$		0			0
$455$	−0.466791	−	14.6680i	−0.0218835	−	0.687648i
$456$		0			0
$457$	−14.3827	+	5.23487i	−0.672794	+	0.244877i	−0.655750	−	0.754978i	$-0.727648\pi$
$457$	−14.3827	+	5.23487i	−0.672794	+	0.244877i	−0.0170435	+	0.999855i	$0.505425\pi$
$458$		0			0
$459$	10.0466	−	4.13040i	0.468935	−	0.192791i
$460$		0			0
$461$	1.57802	−	8.94942i	0.0734959	−	0.416816i	−0.925755	−	0.378123i	$-0.876570\pi$
$461$	1.57802	−	8.94942i	0.0734959	−	0.416816i	0.999251	−	0.0386926i	$-0.0123193\pi$
$462$		0			0
$463$	15.6894	+	5.71047i	0.729148	+	0.265388i	0.679804	−	0.733394i	$-0.262065\pi$
$463$	15.6894	+	5.71047i	0.729148	+	0.265388i	0.0493440	+	0.998782i	$0.484287\pi$
$464$		0			0
$465$	−10.0015	−	6.38403i	−0.463808	−	0.296052i
$466$		0			0
$467$	−8.72724			−0.403848			−0.201924	−	0.979401i	$-0.564719\pi$
$467$	−8.72724			−0.403848			−0.201924	+	0.979401i	$0.564719\pi$
$468$		0			0
$469$	2.95106	+	0.424058i	0.136267	+	0.0195812i
$470$		0			0
$471$	11.8871	−	12.9496i	0.547728	−	0.596685i
$472$		0			0
$473$	14.7281	+	5.36060i	0.677200	+	0.246481i
$474$		0			0
$475$	−9.99056	−	8.38307i	−0.458398	−	0.384642i
$476$		0			0
$477$	19.5549	+	19.6238i	0.895357	+	0.898513i
$478$		0			0
$479$	0.739687	−	4.19497i	0.0337972	−	0.191673i	−0.963235	−	0.268661i	$-0.913419\pi$
$479$	0.739687	−	4.19497i	0.0337972	−	0.191673i	0.997032	+	0.0769873i	$0.0245301\pi$
$480$		0			0
$481$	12.1212	+	4.41177i	0.552681	+	0.201159i
$482$		0			0
$483$	−10.4500	+	17.5805i	−0.475492	+	0.799940i
$484$		0			0
$485$	9.04842	+	15.6723i	0.410868	+	0.711644i
$486$		0			0
$487$	1.82711	−	3.16465i	0.0827944	−	0.143404i	−0.821655	−	0.569985i	$-0.806949\pi$
$487$	1.82711	−	3.16465i	0.0827944	−	0.143404i	0.904449	+	0.426581i	$0.140282\pi$
$488$		0			0
$489$	12.8910	−	31.0444i	0.582952	−	1.40388i
$490$		0			0
$491$	11.6988	−	9.81645i	0.527959	−	0.443010i	−0.339437	−	0.940629i	$-0.610237\pi$
$491$	11.6988	−	9.81645i	0.527959	−	0.443010i	0.867396	+	0.497619i	$0.165792\pi$
$492$		0			0
$493$	3.55949	−	20.1868i	0.160311	−	0.909170i
$494$		0			0
$495$	3.45041	−	12.7871i	0.155084	−	0.574735i
$496$		0			0
$497$	−10.1823	−	11.3792i	−0.456738	−	0.510426i
$498$		0			0
$499$	3.23573	−	2.71510i	0.144851	−	0.121545i	−0.567483	−	0.823385i	$-0.692083\pi$
$499$	3.23573	−	2.71510i	0.144851	−	0.121545i	0.712334	+	0.701841i	$0.247638\pi$
$500$		0			0
$501$	−7.26401	−	1.61710i	−0.324532	−	0.0722466i
$502$		0			0
$503$	−0.531735	−	0.920993i	−0.0237089	−	0.0410650i	0.853928	−	0.520392i	$-0.174214\pi$
$503$	−0.531735	−	0.920993i	−0.0237089	−	0.0410650i	−0.877636	+	0.479327i	$0.840881\pi$
$504$		0			0
$505$	0.528427	−	0.915263i	0.0235147	−	0.0407287i
$506$		0			0
$507$	11.8542	+	7.56663i	0.526464	+	0.336046i
$508$		0			0
$509$	−1.60515	−	9.10327i	−0.0711471	−	0.403496i	−0.999495	−	0.0317824i	$-0.989882\pi$
$509$	−1.60515	−	9.10327i	−0.0711471	−	0.403496i	0.928348	−	0.371713i	$-0.121229\pi$
$510$		0			0
$511$	−1.58977	−	1.77664i	−0.0703272	−	0.0785938i
$512$		0			0
$513$	17.6893	−	7.27253i	0.781003	−	0.321090i
$514$		0			0
$515$	−15.4884	−	12.9963i	−0.682501	−	0.572687i
$516$		0			0
$517$	−4.31023	−	1.56880i	−0.189564	−	0.0689955i
$518$		0			0
$519$	−15.9770	+	8.29923i	−0.701311	+	0.364296i
$520$		0			0
$521$	10.3118	+	17.8605i	0.451767	+	0.782483i	0.998496	−	0.0548266i	$-0.0174606\pi$
$521$	10.3118	+	17.8605i	0.451767	+	0.782483i	−0.546729	+	0.837309i	$0.684127\pi$
$522$		0			0
$523$	3.43772	−	5.95431i	0.150321	−	0.260364i	−0.781024	−	0.624501i	$-0.785303\pi$
$523$	3.43772	−	5.95431i	0.150321	−	0.260364i	0.931346	+	0.364137i	$0.118636\pi$
$524$		0			0
$525$	2.61621	+	16.0248i	0.114181	+	0.699379i
$526$		0			0
$527$	−9.08907	+	7.62663i	−0.395926	+	0.332221i
$528$		0			0
$529$	2.89619	−	1.05413i	0.125921	−	0.0458316i
$530$		0			0
$531$	−11.5593	−	1.03181i	−0.501633	−	0.0447767i
$532$		0			0
$533$	−7.88683	+	2.87057i	−0.341616	+	0.124338i
$534$		0			0
$535$	−2.90536	−	16.4771i	−0.125610	−	0.712368i
$536$		0			0
$537$	8.35469	+	10.9079i	0.360531	+	0.470710i
$538$		0			0
$539$	18.5277	−	17.6717i	0.798043	−	0.761175i
$540$		0			0
$541$	−5.89634	−	10.2128i	−0.253503	−	0.439081i	0.710985	−	0.703208i	$-0.248250\pi$
$541$	−5.89634	−	10.2128i	−0.253503	−	0.439081i	−0.964488	+	0.264127i	$0.914916\pi$
$542$		0			0
$543$	38.2651	−	5.00345i	1.64211	−	0.214718i
$544$		0			0
$545$	−0.888547	+	0.745580i	−0.0380612	+	0.0319371i
$546$		0			0
$547$	−1.85783	+	0.676195i	−0.0794351	+	0.0289120i	−0.381432	−	0.924397i	$-0.624569\pi$
$547$	−1.85783	+	0.676195i	−0.0794351	+	0.0289120i	0.301997	+	0.953309i	$0.402347\pi$
$548$		0			0
$549$	1.15481	−	0.805579i	0.0492859	−	0.0343813i
$550$		0			0
$551$	6.26729	−	35.5436i	0.266996	−	1.51421i
$552$		0			0
$553$	25.5781	−	15.8732i	1.08769	−	0.674996i
$554$		0			0
$555$	5.72768	+	1.27508i	0.243126	+	0.0541243i
$556$		0			0
$557$	−38.6603			−1.63809			−0.819045	−	0.573729i	$-0.805496\pi$
$557$	−38.6603			−1.63809			−0.819045	+	0.573729i	$0.805496\pi$
$558$		0			0
$559$	−9.84609	+	17.0539i	−0.416445	+	0.721304i
$560$		0			0
$561$	−11.1636	−	7.12581i	−0.471328	−	0.300852i
$562$		0			0
$563$	−26.0488	+	21.8576i	−1.09783	+	0.921186i	−0.997277	−	0.0737458i	$-0.976505\pi$
$563$	−26.0488	+	21.8576i	−1.09783	+	0.921186i	−0.100550	+	0.994932i	$0.532060\pi$
$564$		0			0
$565$	23.3417	−	8.49569i	0.981993	−	0.357416i
$566$		0			0
$567$	−22.5972	−	7.50783i	−0.948992	−	0.315299i
$568$		0			0
$569$	−19.6300	+	7.14475i	−0.822934	+	0.299523i	−0.718955	−	0.695056i	$-0.755379\pi$
$569$	−19.6300	+	7.14475i	−0.822934	+	0.299523i	−0.103978	+	0.994580i	$0.533157\pi$
$570$		0			0
$571$	28.8385	−	24.1984i	1.20685	−	1.01267i	0.207446	−	0.978246i	$-0.433485\pi$
$571$	28.8385	−	24.1984i	1.20685	−	1.01267i	0.999407	−	0.0344239i	$-0.0109596\pi$
$572$		0			0
$573$	−26.3990	−	16.8507i	−1.10283	−	0.703948i
$574$		0			0
$575$	−7.90654	+	13.6945i	−0.329726	+	0.571101i
$576$		0			0
$577$	−24.9439			−1.03843			−0.519214	−	0.854644i	$-0.673775\pi$
$577$	−24.9439			−1.03843			−0.519214	+	0.854644i	$0.673775\pi$
$578$		0			0
$579$	−11.3547	−	2.52776i	−0.471886	−	0.105050i
$580$		0			0
$581$	0.123252	+	3.87298i	0.00511337	+	0.160678i
$582$		0			0
$583$	5.86535	−	33.2641i	0.242918	−	1.37766i
$584$		0			0
$585$	15.0689	+	7.05907i	0.623024	+	0.291857i
$586$		0			0
$587$	11.1778	−	4.06839i	0.461358	−	0.167920i	−0.100876	−	0.994899i	$-0.532164\pi$
$587$	11.1778	−	4.06839i	0.461358	−	0.167920i	0.562233	+	0.826979i	$0.309942\pi$
$588$		0			0
$589$	−16.0034	+	13.4284i	−0.659408	+	0.553309i
$590$		0			0
$591$	34.9090	−	4.56462i	1.43596	−	0.187763i
$592$		0			0
$593$	13.7146	+	23.7543i	0.563189	+	0.975472i	0.997216	+	0.0745723i	$0.0237591\pi$
$593$	13.7146	+	23.7543i	0.563189	+	0.975472i	−0.434026	+	0.900900i	$0.642908\pi$
$594$		0			0
$595$	−6.60786	−	0.949530i	−0.270896	−	0.0389269i
$596$		0			0
$597$	−3.34012	−	4.36087i	−0.136702	−	0.178479i
$598$		0			0
$599$	6.46850	+	36.6847i	0.264296	+	1.49890i	0.771033	+	0.636795i	$0.219740\pi$
$599$	6.46850	+	36.6847i	0.264296	+	1.49890i	−0.506737	+	0.862101i	$0.669149\pi$
$600$		0			0
$601$	0.664863	−	0.241990i	0.0271203	−	0.00987100i	−0.328424	−	0.944530i	$-0.606518\pi$
$601$	0.664863	−	0.241990i	0.0271203	−	0.00987100i	0.355545	+	0.934659i	$0.384295\pi$
$602$		0			0
$603$	−1.94388	+	2.76577i	−0.0791608	+	0.112631i
$604$		0			0
$605$	−2.69808	+	0.982021i	−0.109693	+	0.0399248i
$606$		0			0
$607$	−28.2702	+	23.7215i	−1.14745	+	0.962826i	−0.999657	−	0.0261919i	$-0.991662\pi$
$607$	−28.2702	+	23.7215i	−1.14745	+	0.962826i	−0.147795	+	0.989018i	$0.547217\pi$
$608$		0			0
$609$	−34.7857	+	28.4437i	−1.40959	+	1.15260i
$610$		0			0
$611$	2.88149	−	4.99088i	0.116572	−	0.201909i
$612$		0			0
$613$	−12.9228	−	22.3830i	−0.521948	−	0.904040i	−0.999674	−	0.0255314i	$-0.991872\pi$
$613$	−12.9228	−	22.3830i	−0.521948	−	0.904040i	0.477726	−	0.878509i	$-0.341461\pi$
$614$		0			0
$615$	−3.38817	+	1.75998i	−0.136624	+	0.0709693i
$616$		0			0
$617$	−3.05865	−	1.11326i	−0.123136	−	0.0448180i	0.279717	−	0.960082i	$-0.409759\pi$
$617$	−3.05865	−	1.11326i	−0.123136	−	0.0448180i	−0.402853	+	0.915264i	$0.631982\pi$
$618$		0			0
$619$	−11.7236	−	9.83728i	−0.471212	−	0.395394i	0.376024	−	0.926610i	$-0.377291\pi$
$619$	−11.7236	−	9.83728i	−0.471212	−	0.395394i	−0.847236	+	0.531216i	$0.821735\pi$
$620$		0			0
$621$	−12.4084	−	19.5912i	−0.497932	−	0.786168i
$622$		0			0
$623$	0.394304	−	0.0825378i	0.0157975	−	0.00330681i
$624$		0			0
$625$	0.915150	+	5.19007i	0.0366060	+	0.207603i
$626$		0			0
$627$	−19.6561	−	12.5466i	−0.784988	−	0.501064i
$628$		0			0
$629$	2.93385	−	5.08158i	0.116980	−	0.202616i
$630$		0			0
$631$	11.8242	+	20.4801i	0.470713	+	0.815298i	0.999439	−	0.0334941i	$-0.0106635\pi$
$631$	11.8242	+	20.4801i	0.470713	+	0.815298i	−0.528726	+	0.848792i	$0.677330\pi$
$632$		0			0
$633$	−41.2676	−	9.18690i	−1.64024	−	0.365146i
$634$		0			0
$635$	9.50959	−	7.97949i	0.377377	−	0.316656i
$636$		0			0
$637$	17.8234	+	26.7802i	0.706189	+	1.06107i
$638$		0			0
$639$	16.7322	−	4.45183i	0.661914	−	0.176112i
$640$		0			0
$641$	−6.73041	+	38.1701i	−0.265835	+	1.50763i	0.500811	+	0.865557i	$0.333035\pi$
$641$	−6.73041	+	38.1701i	−0.265835	+	1.50763i	−0.766646	+	0.642070i	$0.778076\pi$
$642$		0			0
$643$	−27.9529	+	23.4553i	−1.10236	+	0.924987i	−0.997581	−	0.0695088i	$-0.977857\pi$
$643$	−27.9529	+	23.4553i	−1.10236	+	0.924987i	−0.104775	+	0.994496i	$0.533412\pi$
$644$		0			0
$645$	−3.43539	+	8.27316i	−0.135268	+	0.325755i
$646$		0			0
$647$	−11.2213	+	19.4359i	−0.441155	+	0.764103i	−0.997775	−	0.0666638i	$-0.978765\pi$
$647$	−11.2213	+	19.4359i	−0.441155	+	0.764103i	0.556620	+	0.830767i	$0.312098\pi$
$648$		0			0
$649$	7.07481	+	12.2539i	0.277711	+	0.481009i
$650$		0			0
$651$	26.0071	+	0.330309i	1.01930	+	0.0129458i
$652$		0			0
$653$	−13.6063	−	4.95228i	−0.532455	−	0.193798i	0.0617794	−	0.998090i	$-0.480322\pi$
$653$	−13.6063	−	4.95228i	−0.532455	−	0.193798i	−0.594234	+	0.804292i	$0.702545\pi$
$654$		0			0
$655$	−3.52117	+	19.9695i	−0.137583	+	0.780275i
$656$		0			0
$657$	2.61240	−	0.695066i	0.101919	−	0.0271171i
$658$		0			0
$659$	18.5527	+	15.5675i	0.722709	+	0.606425i	0.928133	−	0.372248i	$-0.121413\pi$
$659$	18.5527	+	15.5675i	0.722709	+	0.606425i	−0.205424	+	0.978673i	$0.565857\pi$
$660$		0			0
$661$	−25.1760	−	9.16332i	−0.979234	−	0.356412i	−0.197691	−	0.980264i	$-0.563344\pi$
$661$	−25.1760	−	9.16332i	−0.979234	−	0.356412i	−0.781542	+	0.623852i	$0.785567\pi$
$662$		0			0
$663$	11.2525	−	12.2583i	0.437012	−	0.476074i
$664$		0			0
$665$	−11.6347	−	1.67187i	−0.451173	−	0.0648322i
$666$		0			0
$667$	−43.7613			−1.69445
$668$		0			0
$669$	32.0404	+	20.4516i	1.23875	+	0.790706i
$670$		0			0
$671$	−1.61318	−	0.587151i	−0.0622763	−	0.0226667i
$672$		0			0
$673$	−1.30563	+	7.40457i	−0.0503282	+	0.285425i	−0.999576	−	0.0291026i	$-0.990735\pi$
$673$	−1.30563	+	7.40457i	−0.0503282	+	0.285425i	0.949248	+	0.314528i	$0.101846\pi$
$674$		0			0
$675$	−17.5442	−	5.58260i	−0.675275	−	0.214875i
$676$		0			0
$677$	−20.5176	+	7.46779i	−0.788555	+	0.287011i	−0.704735	−	0.709470i	$-0.748934\pi$
$677$	−20.5176	+	7.46779i	−0.788555	+	0.287011i	−0.0838198	+	0.996481i	$0.526712\pi$
$678$		0			0
$679$	−34.9678	−	18.7317i	−1.34194	−	0.718856i
$680$		0			0
$681$	28.0021	+	17.8740i	1.07304	+	0.684932i
$682$		0			0
$683$	14.8198	+	25.6686i	0.567063	+	0.982182i	0.996854	+	0.0792539i	$0.0252538\pi$
$683$	14.8198	+	25.6686i	0.567063	+	0.982182i	−0.429791	+	0.902928i	$0.641413\pi$
$684$		0			0
$685$	3.43382	+	5.94755i	0.131199	+	0.227244i
$686$		0			0
$687$	−18.0540	−	4.01914i	−0.688802	−	0.153340i
$688$		0			0
$689$	39.8788	+	14.5147i	1.51926	+	0.552965i
$690$		0			0
$691$	0.464699	−	2.63544i	0.0176780	−	0.100257i	−0.974692	−	0.223551i	$-0.928235\pi$
$691$	0.464699	−	2.63544i	0.0176780	−	0.100257i	0.992370	+	0.123295i	$0.0393460\pi$
$692$		0			0
$693$	8.35335	+	27.8045i	0.317317	+	1.05620i
$694$		0			0
$695$	−14.0760	−	11.8112i	−0.533932	−	0.448023i
$696$		0			0
$697$	0.662970	+	3.75989i	0.0251118	+	0.142416i
$698$		0			0
$699$	32.6373	−	4.26757i	1.23446	−	0.161415i
$700$		0			0
$701$	−13.6977			−0.517355			−0.258677	−	0.965964i	$-0.583287\pi$
$701$	−13.6977			−0.517355			−0.258677	+	0.965964i	$0.583287\pi$
$702$		0			0
$703$	5.16572	−	8.94729i	0.194829	−	0.337454i
$704$		0			0
$705$	1.00538	−	2.42116i	0.0378646	−	0.0911863i
$706$		0			0
$707$	0.0736874	+	2.31549i	0.00277130	+	0.0870829i
$708$		0			0
$709$	−5.40259	−	4.53331i	−0.202899	−	0.170252i	0.535677	−	0.844423i	$-0.320057\pi$
$709$	−5.40259	−	4.53331i	−0.202899	−	0.170252i	−0.738575	+	0.674171i	$0.764501\pi$
$710$		0			0
$711$	2.91511	+	34.0090i	0.109325	+	1.27544i
$712$		0			0
$713$	19.4041	+	16.2820i	0.726688	+	0.609764i
$714$		0			0
$715$	−3.52308	−	19.9804i	−0.131756	−	0.747224i
$716$		0			0
$717$	10.6847	+	33.9919i	0.399028	+	1.26945i
$718$		0			0
$719$	−6.81434	+	11.8028i	−0.254132	+	0.440170i	−0.964659	−	0.263500i	$-0.915123\pi$
$719$	−6.81434	+	11.8028i	−0.254132	+	0.440170i	0.710527	+	0.703670i	$0.248456\pi$
$720$		0			0
$721$	43.8695	+	6.30391i	1.63378	+	0.234770i
$722$		0			0
$723$	0.532977	−	11.9656i	0.0198216	−	0.445006i
$724$		0			0
$725$	−26.6144	+	22.3321i	−0.988434	+	0.829395i
$726$		0			0
$727$	−3.28961	+	18.6563i	−0.122005	+	0.691923i	0.861037	+	0.508542i	$0.169815\pi$
$727$	−3.28961	+	18.6563i	−0.122005	+	0.691923i	−0.983042	+	0.183381i	$0.941296\pi$
$728$		0			0
$729$	19.1924	−	18.9908i	0.710829	−	0.703364i
$730$		0			0
$731$	6.86207	+	5.75796i	0.253803	+	0.212966i
$732$		0			0
$733$	5.13872	+	29.1431i	0.189803	+	1.07643i	0.919628	+	0.392791i	$0.128491\pi$
$733$	5.13872	+	29.1431i	0.189803	+	1.07643i	−0.729825	+	0.683634i	$0.760398\pi$
$734$		0			0
$735$	9.61902	+	11.0284i	0.354803	+	0.406789i
$736$		0			0
$737$	4.12170			0.151825
$738$		0			0
$739$	17.8461			0.656479			0.328240	−	0.944594i	$-0.393545\pi$
$739$	17.8461			0.656479			0.328240	+	0.944594i	$0.393545\pi$
$740$		0			0
$741$	19.8127	−	21.5836i	0.727837	−	0.792893i
$742$		0			0
$743$	−5.47527	−	31.0518i	−0.200868	−	1.13918i	−0.903810	−	0.427934i	$-0.859242\pi$
$743$	−5.47527	−	31.0518i	−0.200868	−	1.13918i	0.702942	−	0.711247i	$-0.251869\pi$
$744$		0			0
$745$	−15.1533	+	5.51533i	−0.555172	+	0.202066i
$746$		0			0
$747$	−3.97883	−	1.86389i	−0.145578	−	0.0681961i
$748$		0			0
$749$	24.4563	+	27.3311i	0.893615	+	0.998656i
$750$		0			0
$751$	−5.29396	−	1.92684i	−0.193179	−	0.0703115i	0.243619	−	0.969871i	$-0.421665\pi$
$751$	−5.29396	−	1.92684i	−0.193179	−	0.0703115i	−0.436798	+	0.899560i	$0.643888\pi$
$752$		0			0
$753$	31.7356	−	4.14967i	1.15651	−	0.151223i
$754$		0			0
$755$	21.8246			0.794277
$756$		0			0
$757$	6.73854			0.244916			0.122458	−	0.992474i	$-0.460922\pi$
$757$	6.73854			0.244916			0.122458	+	0.992474i	$0.460922\pi$
$758$		0			0
$759$	−10.8431	+	26.1125i	−0.393579	+	0.947825i
$760$		0			0
$761$	−28.3672	−	10.3248i	−1.02831	−	0.374274i	−0.227873	−	0.973691i	$-0.573177\pi$
$761$	−28.3672	−	10.3248i	−1.02831	−	0.374274i	−0.800437	+	0.599417i	$0.795399\pi$
$762$		0			0
$763$	0.793176	−	2.41569i	0.0287149	−	0.0874539i
$764$		0			0
$765$	4.35263	−	6.19298i	0.157370	−	0.223908i
$766$		0			0
$767$	−16.7056	+	6.08035i	−0.603205	+	0.219549i
$768$		0			0
$769$	5.51482	+	31.2761i	0.198869	+	1.12784i	0.906800	+	0.421562i	$0.138518\pi$
$769$	5.51482	+	31.2761i	0.198869	+	1.12784i	−0.707930	+	0.706282i	$0.750371\pi$
$770$		0			0
$771$	27.3265	+	6.08337i	0.984140	+	0.219087i
$772$		0			0
$773$	−42.2652			−1.52017			−0.760087	−	0.649822i	$-0.774844\pi$
$773$	−42.2652			−1.52017			−0.760087	+	0.649822i	$0.774844\pi$
$774$		0			0
$775$	20.1100			0.722371
$776$		0			0
$777$	−12.1418	+	4.24542i	−0.435585	+	0.152304i
$778$		0			0
$779$	1.16731	+	6.62015i	0.0418233	+	0.237192i
$780$		0			0
$781$	−16.1713	−	13.5694i	−0.578656	−	0.485550i
$782$		0			0
$783$	−10.8964	−	49.7719i	−0.389407	−	1.77870i
$784$		0			0
$785$	2.12709	−	12.0633i	0.0759192	−	0.430559i
$786$		0			0
$787$	4.67210	−	3.92036i	0.166542	−	0.139746i	−0.555707	−	0.831378i	$-0.687553\pi$
$787$	4.67210	−	3.92036i	0.166542	−	0.139746i	0.722250	+	0.691632i	$0.243108\pi$
$788$		0			0
$789$	0.319995	−	0.166221i	0.0113921	−	0.00591763i
$790$		0			0
$791$	−33.6551	+	42.8029i	−1.19664	+	1.52190i
$792$		0			0
$793$	1.07845	−	1.86793i	0.0382969	−	0.0663322i
$794$		0			0
$795$	18.8440	+	4.19501i	0.668328	+	0.148782i
$796$		0			0
$797$	5.31754	+	30.1573i	0.188357	+	1.06823i	0.921566	+	0.388222i	$0.126911\pi$
$797$	5.31754	+	30.1573i	0.188357	+	1.06823i	−0.733209	+	0.680003i	$0.761978\pi$
$798$		0			0
$799$	−2.00820	−	1.68508i	−0.0710451	−	0.0596140i
$800$		0			0
$801$	−0.119002	+	0.441016i	−0.00420473	+	0.0155825i
$802$		0			0
$803$	−2.52484	−	2.11859i	−0.0890997	−	0.0747635i
$804$		0			0
$805$	0.453319	+	14.2447i	0.0159774	+	0.502059i
$806$		0			0
$807$	−50.0148	+	6.53981i	−1.76060	+	0.230212i
$808$		0			0
$809$	25.6272	−	44.3876i	0.901005	−	1.56059i	0.0748122	−	0.997198i	$-0.476164\pi$
$809$	25.6272	−	44.3876i	0.901005	−	1.56059i	0.826192	−	0.563388i	$-0.190502\pi$
$810$		0			0
$811$	−10.3989			−0.365154			−0.182577	−	0.983192i	$-0.558444\pi$
$811$	−10.3989			−0.365154			−0.182577	+	0.983192i	$0.558444\pi$
$812$		0			0
$813$	−19.5972	+	47.1942i	−0.687302	+	1.65517i
$814$		0			0
$815$	−4.06759	−	23.0685i	−0.142482	−	0.808053i
$816$		0			0
$817$	12.0822	+	10.1382i	0.422704	+	0.354691i
$818$		0			0
$819$	−36.2256	+	4.26959i	−1.26583	+	0.149192i
$820$		0			0
$821$	−3.10643	+	17.6174i	−0.108415	+	0.614853i	0.881386	+	0.472397i	$0.156611\pi$
$821$	−3.10643	+	17.6174i	−0.108415	+	0.614853i	−0.989801	+	0.142456i	$0.954500\pi$
$822$		0			0
$823$	21.2975	+	7.75166i	0.742384	+	0.270206i	0.685397	−	0.728169i	$-0.259628\pi$
$823$	21.2975	+	7.75166i	0.742384	+	0.270206i	0.0569868	+	0.998375i	$0.481851\pi$
$824$		0			0
$825$	6.73120	+	21.4143i	0.234350	+	0.745551i
$826$		0			0
$827$	−18.8254	−	32.6066i	−0.654624	−	1.13384i	−0.981988	−	0.188943i	$-0.939494\pi$
$827$	−18.8254	−	32.6066i	−0.654624	−	1.13384i	0.327364	−	0.944898i	$-0.393840\pi$
$828$		0			0
$829$	18.2430	+	31.5979i	0.633607	+	1.09744i	0.986808	+	0.161892i	$0.0517597\pi$
$829$	18.2430	+	31.5979i	0.633607	+	1.09744i	−0.353201	+	0.935547i	$0.614907\pi$
$830$		0			0
$831$	−45.4609	+	23.6146i	−1.57702	+	0.819183i
$832$		0			0
$833$	13.4049	−	5.86913i	0.464452	−	0.203353i
$834$		0			0
$835$	−4.87311	+	1.77367i	−0.168641	+	0.0613803i
$836$		0			0
$837$	−13.6867	+	26.1234i	−0.473082	+	0.902955i
$838$		0			0
$839$	5.39830	−	30.6153i	0.186370	−	1.05696i	−0.737813	−	0.675005i	$-0.764141\pi$
$839$	5.39830	−	30.6153i	0.186370	−	1.05696i	0.924183	−	0.381951i	$-0.124748\pi$
$840$		0			0
$841$	−63.0978	−	22.9657i	−2.17579	−	0.791921i
$842$		0			0
$843$	1.55770	−	34.9711i	0.0536500	−	1.20447i
$844$		0			0
$845$	9.80004			0.337132
$846$		0			0
$847$	3.89021	−	4.94761i	0.133669	−	0.170002i
$848$		0			0
$849$	1.75244	+	5.57514i	0.0601437	+	0.191338i
$850$		0			0
$851$	−11.7714	−	4.28443i	−0.403518	−	0.146869i
$852$		0			0
$853$	20.3650	+	17.0883i	0.697284	+	0.585091i	0.921000	−	0.389563i	$-0.127374\pi$
$853$	20.3650	+	17.0883i	0.697284	+	0.585091i	−0.223715	+	0.974655i	$0.571819\pi$
$854$		0			0
$855$	7.66381	−	10.9042i	0.262097	−	0.372915i
$856$		0			0
$857$	3.30975	−	18.7705i	0.113059	−	0.641189i	−0.874634	−	0.484784i	$-0.838898\pi$
$857$	3.30975	−	18.7705i	0.113059	−	0.641189i	0.987693	−	0.156405i	$-0.0499906\pi$
$858$		0			0
$859$	45.0436	+	16.3945i	1.53687	+	0.559374i	0.965292	−	0.261174i	$-0.0841098\pi$
$859$	45.0436	+	16.3945i	1.53687	+	0.559374i	0.571577	+	0.820549i	$0.306332\pi$
$860$		0			0
$861$	4.27632	−	7.19423i	0.145737	−	0.245179i
$862$		0			0
$863$	−27.8559	−	48.2478i	−0.948226	−	1.64238i	−0.749160	−	0.662389i	$-0.769542\pi$
$863$	−27.8559	−	48.2478i	−0.948226	−	1.64238i	−0.199066	−	0.979986i	$-0.563791\pi$
$864$		0			0
$865$	−6.27304	+	10.8652i	−0.213290	+	0.369429i
$866$		0			0
$867$	13.3017	+	17.3667i	0.451750	+	0.589805i
$868$		0			0
$869$	31.8805	−	26.7510i	1.08147	−	0.907464i
$870$		0			0
$871$	−0.899246	+	5.09988i	−0.0304698	+	0.172803i
$872$		0			0
$873$	36.8911	−	25.7348i	1.24857	−	0.870990i
$874$		0			0
$875$	18.1922	+	20.3306i	0.615008	+	0.687299i
$876$		0			0
$877$	−20.8456	+	17.4916i	−0.703907	+	0.590648i	−0.922882	−	0.385082i	$-0.874173\pi$
$877$	−20.8456	+	17.4916i	−0.703907	+	0.590648i	0.218975	+	0.975730i	$0.429729\pi$
$878$		0			0
$879$	8.29166	+	26.3787i	0.279671	+	0.889731i
$880$		0			0
$881$	−2.70498	−	4.68516i	−0.0911331	−	0.157847i	0.816855	−	0.576843i	$-0.195716\pi$
$881$	−2.70498	−	4.68516i	−0.0911331	−	0.157847i	−0.907988	+	0.418996i	$0.862382\pi$
$882$		0			0
$883$	20.8606	−	36.1317i	0.702016	−	1.21593i	−0.265741	−	0.964044i	$-0.585617\pi$
$883$	20.8606	−	36.1317i	0.702016	−	1.21593i	0.967758	−	0.251884i	$-0.0810500\pi$
$884$		0			0
$885$	−7.17671	+	3.72794i	−0.241242	+	0.125313i
$886$		0			0
$887$	−0.771266	−	4.37407i	−0.0258966	−	0.146867i	0.969118	−	0.246598i	$-0.0793128\pi$
$887$	−0.771266	−	4.37407i	−0.0258966	−	0.146867i	−0.995014	+	0.0997314i	$0.968202\pi$
$888$		0			0
$889$	−8.48889	+	25.8537i	−0.284708	+	0.867105i
$890$		0			0
$891$	−32.3990	−	5.83044i	−1.08541	−	0.195327i
$892$		0			0
$893$	−3.53590	−	2.96698i	−0.118325	−	0.0992861i
$894$		0			0
$895$	8.99722	+	3.27472i	0.300744	+	0.109462i
$896$		0			0
$897$	−29.9440	−	19.1135i	−0.999801	−	0.638181i
$898$		0			0
$899$	27.8263	+	48.1965i	0.928058	+	1.60744i
$900$		0			0
$901$	9.65235	−	16.7184i	0.321567	−	0.556970i
$902$		0			0
$903$	−3.16396	−	19.3798i	−0.105290	−	0.644920i
$904$		0			0
$905$	20.6005	−	17.2859i	0.684785	−	0.574603i
$906$		0			0
$907$	−27.0345	+	9.83975i	−0.897666	+	0.326724i	−0.749317	−	0.662211i	$-0.769618\pi$
$907$	−27.0345	+	9.83975i	−0.897666	+	0.326724i	−0.148349	+	0.988935i	$0.547396\pi$
$908$		0			0
$909$	−2.37877	−	1.11434i	−0.0788990	−	0.0369604i
$910$		0			0
$911$	−18.7461	+	6.82302i	−0.621086	+	0.226057i	−0.633347	−	0.773868i	$-0.718319\pi$
$911$	−18.7461	+	6.82302i	−0.621086	+	0.226057i	0.0122611	+	0.999925i	$0.496097\pi$
$912$		0			0
$913$	0.930240	+	5.27566i	0.0307865	+	0.174599i
$914$		0			0
$915$	0.376281	−	0.906166i	0.0124395	−	0.0299569i
$916$		0			0
$917$	−16.5234	−	41.2639i	−0.545650	−	1.36265i
$918$		0			0
$919$	−19.2864	−	33.4051i	−0.636200	−	1.10193i	−0.986259	−	0.165204i	$-0.947172\pi$
$919$	−19.2864	−	33.4051i	−0.636200	−	1.10193i	0.350059	−	0.936728i	$-0.386162\pi$
$920$		0			0
$921$	19.2857	−	46.4441i	0.635484	−	1.53038i
$922$		0			0
$923$	20.3179	−	17.0487i	0.668770	−	0.561165i
$924$		0			0
$925$	−9.34544	+	3.40146i	−0.307276	+	0.111839i
$926$		0			0
$927$	−28.8970	+	41.1151i	−0.949103	+	1.35040i
$928$		0			0
$929$	8.88361	−	50.3815i	0.291462	−	1.65296i	−0.389783	−	0.920907i	$-0.627450\pi$
$929$	8.88361	−	50.3815i	0.291462	−	1.65296i	0.681245	−	0.732056i	$-0.261439\pi$
$930$		0			0
$931$	23.6024	−	10.3340i	0.773537	−	0.338682i
$932$		0			0
$933$	8.21430	+	26.1326i	0.268924	+	0.855543i
$934$		0			0
$935$	−9.22911			−0.301824
$936$		0			0
$937$	15.7092	−	27.2091i	0.513197	−	0.888883i	−0.486686	−	0.873577i	$-0.661794\pi$
$937$	15.7092	−	27.2091i	0.513197	−	0.888883i	0.999883	−	0.0153062i	$-0.00487230\pi$
$938$		0			0
$939$	−16.4160	+	8.52729i	−0.535717	+	0.278278i
$940$		0			0
$941$	21.1592	−	17.7547i	0.689769	−	0.578785i	−0.229073	−	0.973409i	$-0.573570\pi$
$941$	21.1592	−	17.7547i	0.689769	−	0.578785i	0.918843	+	0.394624i	$0.129125\pi$
$942$		0			0
$943$	7.65920	−	2.78772i	0.249418	−	0.0907806i
$944$		0			0
$945$	−16.0883	+	4.06246i	−0.523353	+	0.132152i
$946$		0			0
$947$	15.8697	−	5.77611i	0.515697	−	0.187698i	−0.0710438	−	0.997473i	$-0.522633\pi$
$947$	15.8697	−	5.77611i	0.515697	−	0.187698i	0.586741	+	0.809775i	$0.300411\pi$
$948$		0			0
$949$	3.17224	−	2.66182i	0.102975	−	0.0864064i
$950$		0			0
$951$	2.65142	−	59.5258i	0.0859783	−	1.93026i
$952$		0			0
$953$	−10.8675	+	18.8231i	−0.352034	+	0.609742i	−0.986606	−	0.163123i	$-0.947843\pi$
$953$	−10.8675	+	18.8231i	−0.352034	+	0.609742i	0.634571	+	0.772864i	$0.281177\pi$
$954$		0			0
$955$	−21.8244			−0.706222
$956$		0			0
$957$	−42.0086	+	45.7635i	−1.35795	+	1.47932i
$958$		0			0
$959$	−13.2701	−	7.10856i	−0.428512	−	0.229547i
$960$		0			0
$961$	0.210665	−	1.19474i	0.00679564	−	0.0385400i
$962$		0			0
$963$	−40.1881	+	10.6926i	−1.29504	+	0.344565i
$964$		0			0
$965$	−7.61739	+	2.77250i	−0.245213	+	0.0892501i
$966$		0			0
$967$	27.3313	−	22.9336i	0.878914	−	0.737496i	−0.0870416	−	0.996205i	$-0.527741\pi$
$967$	27.3313	−	22.9336i	0.878914	−	0.737496i	0.965955	+	0.258708i	$0.0832968\pi$
$968$		0			0
$969$	−8.10400	−	10.5806i	−0.260338	−	0.339898i
$970$		0			0
$971$	−5.92611	−	10.2643i	−0.190178	−	0.329398i	0.755131	−	0.655574i	$-0.227573\pi$
$971$	−5.92611	−	10.2643i	−0.190178	−	0.329398i	−0.945309	+	0.326176i	$0.894240\pi$
$972$		0			0
$973$	39.8689	+	5.72904i	1.27814	+	0.183664i
$974$		0			0
$975$	−27.9650	+	3.65664i	−0.895597	+	0.117106i
$976$		0			0
$977$	9.24038	+	52.4048i	0.295626	+	1.67658i	0.664647	+	0.747157i	$0.268582\pi$
$977$	9.24038	+	52.4048i	0.295626	+	1.67658i	−0.369022	+	0.929421i	$0.620307\pi$
$978$		0			0
$979$	0.523347	−	0.190483i	0.0167262	−	0.00608786i
$980$		0			0
$981$	2.03501	+	2.04218i	0.0649727	+	0.0652018i
$982$		0			0
$983$	42.9849	−	15.6452i	1.37101	−	0.499006i	0.451567	−	0.892237i	$-0.350865\pi$
$983$	42.9849	−	15.6452i	1.37101	−	0.499006i	0.919439	+	0.393232i	$0.128643\pi$
$984$		0			0
$985$	18.7938	−	15.7698i	0.598819	−	0.502469i
$986$		0			0
$987$	0.925943	+	5.67156i	0.0294731	+	0.180528i
$988$		0			0
$989$	9.56191	−	16.5617i	0.304051	−	0.526632i
$990$		0			0
$991$	11.9539	+	20.7047i	0.379727	+	0.657707i	0.991022	−	0.133696i	$-0.0426845\pi$
$991$	11.9539	+	20.7047i	0.379727	+	0.657707i	−0.611295	+	0.791403i	$0.709351\pi$
$992$		0			0
$993$	−0.659253	+	14.8006i	−0.0209207	+	0.469681i
$994$		0			0
$995$	−3.59700	−	1.30920i	−0.114033	−	0.0415045i
$996$		0			0
$997$	4.51248	+	3.78642i	0.142912	+	0.119917i	0.711441	−	0.702746i	$-0.248043\pi$
$997$	4.51248	+	3.78642i	0.142912	+	0.119917i	−0.568529	+	0.822663i	$0.692487\pi$
$998$		0			0
$999$	1.94186	−	14.4550i	0.0614378	−	0.457335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.9	yes	144
7.2	even	3		756.2.bp.a.457.24	yes	144
27.13	even	9		756.2.bp.a.445.24	✓	144
189.121	even	9	inner	756.2.bq.a.121.9	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.24	✓	144	27.13	even	9
756.2.bp.a.457.24	yes	144	7.2	even	3
756.2.bq.a.25.9	yes	144	1.1	even	1	trivial
756.2.bq.a.121.9	yes	144	189.121	even	9	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.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05320 - 1.37506i) q^{3} +(-1.13419 - 0.412813i) q^{5} +(2.58962 - 0.542074i) q^{7} +(-0.781555 + 2.89641i) q^{9} +O(q^{10})\)	\(q+(-1.05320 - 1.37506i) q^{3} +(-1.13419 - 0.412813i) q^{5} +(2.58962 - 0.542074i) q^{7} +(-0.781555 + 2.89641i) q^{9} +(3.43712 - 1.25101i) q^{11} +(0.798016 + 4.52577i) q^{13} +(0.626889 + 1.99435i) q^{15} +2.09049 q^{17} +3.68079 q^{19} +(-3.47277 - 2.98997i) q^{21} +(-0.774983 - 4.39515i) q^{23} +(-2.71424 - 2.27752i) q^{25} +(4.80585 - 1.97580i) q^{27} +(1.70270 - 9.65650i) q^{29} +(-4.34781 + 3.64825i) q^{31} +(-5.34018 - 3.40868i) q^{33} +(-3.16091 - 0.454213i) q^{35} +(1.40343 - 2.43081i) q^{37} +(5.38272 - 5.86384i) q^{39} +(0.317136 + 1.79857i) q^{41} +(3.28251 + 2.75435i) q^{43} +(2.08211 - 2.96245i) q^{45} +(-0.960637 - 0.806070i) q^{47} +(6.41231 - 2.80754i) q^{49} +(-2.20170 - 2.87454i) q^{51} +(4.61726 - 7.99733i) q^{53} -4.41480 q^{55} +(-3.87660 - 5.06129i) q^{57} +(0.671747 + 3.80967i) q^{59} +(-0.359536 - 0.301687i) q^{61} +(-0.453867 + 7.92427i) q^{63} +(0.963192 - 5.46254i) q^{65} +(1.05889 + 0.385406i) q^{67} +(-5.22736 + 5.69460i) q^{69} +(-2.88571 - 4.99820i) q^{71} +(-0.450547 - 0.780371i) q^{73} +(-0.273085 + 6.13090i) q^{75} +(8.22272 - 5.10282i) q^{77} +(10.6917 - 3.89147i) q^{79} +(-7.77834 - 4.52740i) q^{81} +(-0.254323 + 1.44234i) q^{83} +(-2.37102 - 0.862982i) q^{85} +(-15.0715 + 7.82888i) q^{87} +0.152263 q^{89} +(4.51986 + 11.2875i) q^{91} +(9.59564 + 2.13616i) q^{93} +(-4.17473 - 1.51948i) q^{95} +(-11.4856 - 9.63760i) q^{97} +(0.937136 + 10.9330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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