LMFDB - Embedded newform 675.2.h.b.541.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(136,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("675.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			541.5
Character	$\chi$	$=$	675.541
Dual form			675.2.h.b.136.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.324639 - 0.235864i) q^{2} +(-0.568275 - 1.74897i) q^{4} +(-0.0534510 - 2.23543i) q^{5} -3.13164 q^{7} +(-0.476037 + 1.46509i) q^{8} +O(q^{10})$	\(q+(-0.324639 - 0.235864i) q^{2} +(-0.568275 - 1.74897i) q^{4} +(-0.0534510 - 2.23543i) q^{5} -3.13164 q^{7} +(-0.476037 + 1.46509i) q^{8} +(-0.509905 + 0.738315i) q^{10} +(0.141918 + 0.103109i) q^{11} +(-1.01620 + 0.738315i) q^{13} +(1.01665 + 0.738642i) q^{14} +(-2.47543 + 1.79850i) q^{16} +(2.01248 - 6.19378i) q^{17} +(-1.51903 + 4.67511i) q^{19} +(-3.87933 + 1.36382i) q^{20} +(-0.0217523 - 0.0669467i) q^{22} +(-2.48048 - 1.80217i) q^{23} +(-4.99429 + 0.238972i) q^{25} +0.504041 q^{26} +(1.77964 + 5.47716i) q^{28} +(3.10215 + 9.54744i) q^{29} +(-1.54075 + 4.74193i) q^{31} +4.30880 q^{32} +(-2.11422 + 1.53607i) q^{34} +(0.167389 + 7.00057i) q^{35} +(1.72263 - 1.25156i) q^{37} +(1.59583 - 1.15944i) q^{38} +(3.30055 + 0.985837i) q^{40} +(2.44679 - 1.77770i) q^{41} -6.72677 q^{43} +(0.0996870 - 0.306805i) q^{44} +(0.380192 + 1.17011i) q^{46} +(-3.99722 - 12.3022i) q^{47} +2.80719 q^{49} +(1.67770 + 1.10039i) q^{50} +(1.86877 + 1.35774i) q^{52} +(1.37726 + 4.23878i) q^{53} +(0.222908 - 0.322759i) q^{55} +(1.49078 - 4.58815i) q^{56} +(1.24482 - 3.83116i) q^{58} +(-10.5820 + 7.68825i) q^{59} +(-4.64423 - 3.37423i) q^{61} +(1.61864 - 1.17601i) q^{62} +(3.55205 + 2.58071i) q^{64} +(1.70477 + 2.23219i) q^{65} +(-2.19581 + 6.75799i) q^{67} -11.9764 q^{68} +(1.59684 - 2.31214i) q^{70} +(-1.96259 - 6.04023i) q^{71} +(-3.56527 - 2.59032i) q^{73} -0.854431 q^{74} +9.03986 q^{76} +(-0.444437 - 0.322902i) q^{77} +(-3.71597 - 11.4366i) q^{79} +(4.15274 + 5.43751i) q^{80} -1.21362 q^{82} +(2.31402 - 7.12182i) q^{83} +(-13.9533 - 4.16770i) q^{85} +(2.18377 + 1.58660i) q^{86} +(-0.218623 + 0.158839i) q^{88} +(-6.44977 - 4.68603i) q^{89} +(3.18239 - 2.31214i) q^{91} +(-1.74236 + 5.36242i) q^{92} +(-1.60399 + 4.93656i) q^{94} +(10.5321 + 3.14580i) q^{95} +(-4.86404 - 14.9700i) q^{97} +(-0.911325 - 0.662116i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 16 q^{4} + 20 q^{7}+O(q^{10}) $ 40 * q - 16 * q^4 + 20 * q^7	$ 40 q - 16 q^{4} + 20 q^{7} + 20 q^{10} - 8 q^{13} - 12 q^{16} + 2 q^{19} - 8 q^{22} - 30 q^{28} - 2 q^{31} - 6 q^{34} + 2 q^{37} - 50 q^{40} + 40 q^{43} - 36 q^{46} - 28 q^{49} - 30 q^{52} - 30 q^{55} - 52 q^{58} - 28 q^{61} + 46 q^{64} - 10 q^{67} + 60 q^{70} - 46 q^{73} + 260 q^{76} - 42 q^{79} + 136 q^{82} + 100 q^{85} - 68 q^{88} - 56 q^{91} + 182 q^{94} - 58 q^{97}+O(q^{100}) $ 40 * q - 16 * q^4 + 20 * q^7 + 20 * q^10 - 8 * q^13 - 12 * q^16 + 2 * q^19 - 8 * q^22 - 30 * q^28 - 2 * q^31 - 6 * q^34 + 2 * q^37 - 50 * q^40 + 40 * q^43 - 36 * q^46 - 28 * q^49 - 30 * q^52 - 30 * q^55 - 52 * q^58 - 28 * q^61 + 46 * q^64 - 10 * q^67 + 60 * q^70 - 46 * q^73 + 260 * q^76 - 42 * q^79 + 136 * q^82 + 100 * q^85 - 68 * q^88 - 56 * q^91 + 182 * q^94 - 58 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.324639	−	0.235864i	−0.229554	−	0.166781i	0.467063	−	0.884224i	$-0.345312\pi$
$2$	−0.324639	−	0.235864i	−0.229554	−	0.166781i	−0.696617	+	0.717443i	$0.745312\pi$
$3$		0			0
$3$		0			0
$4$	−0.568275	−	1.74897i	−0.284138	−	0.874486i
$5$	−0.0534510	−	2.23543i	−0.0239040	−	0.999714i
$5$	−0.0534510	−	2.23543i	−0.0239040	−	0.999714i
$6$		0			0
$7$	−3.13164			−1.18365			−0.591825	−	0.806066i	$-0.701592\pi$
$7$	−3.13164			−1.18365			−0.591825	+	0.806066i	$0.701592\pi$
$8$	−0.476037	+	1.46509i	−0.168305	+	0.517988i
$9$		0			0
$10$	−0.509905	+	0.738315i	−0.161246	+	0.233476i
$11$	0.141918	+	0.103109i	0.0427899	+	0.0310887i	0.608975	−	0.793190i	$-0.291581\pi$
$11$	0.141918	+	0.103109i	0.0427899	+	0.0310887i	−0.566185	+	0.824278i	$0.691581\pi$
$12$		0			0
$13$	−1.01620	+	0.738315i	−0.281844	+	0.204772i	−0.719721	−	0.694263i	$-0.755730\pi$
$13$	−1.01620	+	0.738315i	−0.281844	+	0.204772i	0.437877	+	0.899035i	$0.355730\pi$
$14$	1.01665	+	0.738642i	0.271712	+	0.197410i
$15$		0			0
$16$	−2.47543	+	1.79850i	−0.618856	+	0.449625i
$17$	2.01248	−	6.19378i	0.488099	−	1.50221i	−0.339344	−	0.940662i	$-0.610205\pi$
$17$	2.01248	−	6.19378i	0.488099	−	1.50221i	0.827442	−	0.561551i	$-0.189795\pi$
$18$		0			0
$19$	−1.51903	+	4.67511i	−0.348490	+	1.07254i	0.611198	+	0.791478i	$0.290688\pi$
$19$	−1.51903	+	4.67511i	−0.348490	+	1.07254i	−0.959689	+	0.281066i	$0.909312\pi$
$20$	−3.87933	+	1.36382i	−0.867444	+	0.304960i
$21$		0			0
$22$	−0.0217523	−	0.0669467i	−0.00463761	−	0.0142731i
$23$	−2.48048	−	1.80217i	−0.517216	−	0.375779i	0.298338	−	0.954460i	$-0.403568\pi$
$23$	−2.48048	−	1.80217i	−0.517216	−	0.375779i	−0.815554	+	0.578681i	$0.803568\pi$
$24$		0			0
$25$	−4.99429	+	0.238972i	−0.998857	+	0.0477943i
$26$	0.504041			0.0988506
$27$		0			0
$28$	1.77964	+	5.47716i	0.336320	+	1.03509i
$29$	3.10215	+	9.54744i	0.576055	+	1.77292i	0.632558	+	0.774513i	$0.282005\pi$
$29$	3.10215	+	9.54744i	0.576055	+	1.77292i	−0.0565032	+	0.998402i	$0.517995\pi$
$30$		0			0
$31$	−1.54075	+	4.74193i	−0.276726	+	0.851676i	0.712031	+	0.702148i	$0.247776\pi$
$31$	−1.54075	+	4.74193i	−0.276726	+	0.851676i	−0.988757	+	0.149528i	$0.952224\pi$
$32$	4.30880			0.761695
$33$		0			0
$34$	−2.11422	+	1.53607i	−0.362586	+	0.263434i
$35$	0.167389	+	7.00057i	0.0282940	+	1.18331i
$36$		0			0
$37$	1.72263	−	1.25156i	0.283198	−	0.205756i	−0.437113	−	0.899407i	$-0.643999\pi$
$37$	1.72263	−	1.25156i	0.283198	−	0.205756i	0.720311	+	0.693651i	$0.243999\pi$
$38$	1.59583	−	1.15944i	0.258877	−	0.188085i
$39$		0			0
$40$	3.30055	+	0.985837i	0.521863	+	0.155875i
$41$	2.44679	−	1.77770i	0.382125	−	0.277630i	−0.380096	−	0.924947i	$-0.624109\pi$
$41$	2.44679	−	1.77770i	0.382125	−	0.277630i	0.762221	+	0.647317i	$0.224109\pi$
$42$		0			0
$43$	−6.72677			−1.02582			−0.512912	−	0.858441i	$-0.671433\pi$
$43$	−6.72677			−1.02582			−0.512912	+	0.858441i	$0.671433\pi$
$44$	0.0996870	−	0.306805i	0.0150284	−	0.0462526i
$45$		0			0
$46$	0.380192	+	1.17011i	0.0560563	+	0.172524i
$47$	−3.99722	−	12.3022i	−0.583054	−	1.79446i	−0.606949	−	0.794741i	$-0.707607\pi$
$47$	−3.99722	−	12.3022i	−0.583054	−	1.79446i	0.0238953	−	0.999714i	$-0.492393\pi$
$48$		0			0
$49$	2.80719			0.401028
$50$	1.67770	+	1.10039i	0.237263	+	0.155619i
$51$		0			0
$52$	1.86877	+	1.35774i	0.259152	+	0.188285i
$53$	1.37726	+	4.23878i	0.189182	+	0.582241i	0.999995	−	0.00306302i	$-0.000974991\pi$
$53$	1.37726	+	4.23878i	0.189182	+	0.582241i	−0.810814	+	0.585304i	$0.800975\pi$
$54$		0			0
$55$	0.222908	−	0.322759i	0.0300569	−	0.0435208i
$56$	1.49078	−	4.58815i	0.199214	−	0.613117i
$57$		0			0
$58$	1.24482	−	3.83116i	0.163453	−	0.503056i
$59$	−10.5820	+	7.68825i	−1.37766	+	1.00093i	−0.380560	+	0.924756i	$0.624269\pi$
$59$	−10.5820	+	7.68825i	−1.37766	+	1.00093i	−0.997095	+	0.0761692i	$0.975731\pi$
$60$		0			0
$61$	−4.64423	−	3.37423i	−0.594632	−	0.432026i	0.249337	−	0.968417i	$-0.419787\pi$
$61$	−4.64423	−	3.37423i	−0.594632	−	0.432026i	−0.843970	+	0.536391i	$0.819787\pi$
$62$	1.61864	−	1.17601i	0.205567	−	0.149353i
$63$		0			0
$64$	3.55205	+	2.58071i	0.444006	+	0.322589i
$65$	1.70477	+	2.23219i	0.211450	+	0.276869i
$66$		0			0
$67$	−2.19581	+	6.75799i	−0.268260	+	0.825620i	0.722664	+	0.691199i	$0.242917\pi$
$67$	−2.19581	+	6.75799i	−0.268260	+	0.825620i	−0.990924	+	0.134421i	$0.957083\pi$
$68$	−11.9764			−1.45235
$69$		0			0
$70$	1.59684	−	2.31214i	0.190859	−	0.276353i
$71$	−1.96259	−	6.04023i	−0.232916	−	0.716843i	−0.997391	−	0.0721891i	$-0.977001\pi$
$71$	−1.96259	−	6.04023i	−0.232916	−	0.716843i	0.764475	−	0.644654i	$-0.222999\pi$
$72$		0			0
$73$	−3.56527	−	2.59032i	−0.417283	−	0.303174i	0.359261	−	0.933237i	$-0.383029\pi$
$73$	−3.56527	−	2.59032i	−0.417283	−	0.303174i	−0.776544	+	0.630063i	$0.783029\pi$
$74$	−0.854431			−0.0993256
$75$		0			0
$76$	9.03986			1.03694
$77$	−0.444437	−	0.322902i	−0.0506482	−	0.0367981i
$78$		0			0
$79$	−3.71597	−	11.4366i	−0.418079	−	1.28672i	−0.909468	−	0.415775i	$-0.863510\pi$
$79$	−3.71597	−	11.4366i	−0.418079	−	1.28672i	0.491388	−	0.870941i	$-0.336490\pi$
$80$	4.15274	+	5.43751i	0.464290	+	0.607932i
$81$		0			0
$82$	−1.21362			−0.134022
$83$	2.31402	−	7.12182i	0.253997	−	0.781721i	−0.740029	−	0.672575i	$-0.765188\pi$
$83$	2.31402	−	7.12182i	0.253997	−	0.781721i	0.994026	−	0.109146i	$-0.0348117\pi$
$84$		0			0
$85$	−13.9533	−	4.16770i	−1.51345	−	0.452050i
$86$	2.18377	+	1.58660i	0.235482	+	0.171088i
$87$		0			0
$88$	−0.218623	+	0.158839i	−0.0233053	+	0.0169323i
$89$	−6.44977	−	4.68603i	−0.683674	−	0.496718i	0.190901	−	0.981609i	$-0.438859\pi$
$89$	−6.44977	−	4.68603i	−0.683674	−	0.496718i	−0.874575	+	0.484891i	$0.838859\pi$
$90$		0			0
$91$	3.18239	−	2.31214i	0.333605	−	0.242378i
$92$	−1.74236	+	5.36242i	−0.181653	+	0.559071i
$93$		0			0
$94$	−1.60399	+	4.93656i	−0.165439	+	0.509167i
$95$	10.5321	+	3.14580i	1.08057	+	0.322753i
$96$		0			0
$97$	−4.86404	−	14.9700i	−0.493869	−	1.51997i	−0.818712	−	0.574204i	$-0.805312\pi$
$97$	−4.86404	−	14.9700i	−0.493869	−	1.51997i	0.324844	−	0.945768i	$-0.394688\pi$
$98$	−0.911325	−	0.662116i	−0.0920577	−	0.0668838i
$99$		0			0
$100$	3.25608	+	8.59906i	0.325608	+	0.859906i
$101$	9.11217			0.906695			0.453347	−	0.891334i	$-0.350230\pi$
$101$	9.11217			0.906695			0.453347	+	0.891334i	$0.350230\pi$
$102$		0			0
$103$	4.30180	+	13.2396i	0.423869	+	1.30454i	0.904073	+	0.427378i	$0.140563\pi$
$103$	4.30180	+	13.2396i	0.423869	+	1.30454i	−0.480204	+	0.877157i	$0.659437\pi$
$104$	−0.597949	−	1.84030i	−0.0586337	−	0.180456i
$105$		0			0
$106$	0.552663	−	1.70092i	0.0536793	−	0.165208i
$107$	−8.60833			−0.832199			−0.416099	−	0.909319i	$-0.636603\pi$
$107$	−8.60833			−0.832199			−0.416099	+	0.909319i	$0.636603\pi$
$108$		0			0
$109$	13.8766	−	10.0819i	1.32913	−	0.965672i	0.329363	−	0.944203i	$-0.393166\pi$
$109$	13.8766	−	10.0819i	1.32913	−	0.965672i	0.999770	−	0.0214683i	$-0.00683409\pi$
$110$	−0.148492	+	0.0522041i	−0.0141581	+	0.00497746i
$111$		0			0
$112$	7.75215	−	5.63227i	0.732509	−	0.532199i
$113$	−5.32174	+	3.86647i	−0.500627	+	0.363727i	−0.809256	−	0.587456i	$-0.800130\pi$
$113$	−5.32174	+	3.86647i	−0.500627	+	0.363727i	0.308630	+	0.951182i	$0.400130\pi$
$114$		0			0
$115$	−3.89605	+	5.64126i	−0.363308	+	0.526051i
$116$	14.9353	−	10.8512i	1.38671	−	1.00750i
$117$		0			0
$118$	5.24870			0.483182
$119$	−6.30238	+	19.3967i	−0.577738	+	1.77809i
$120$		0			0
$121$	−3.38968	−	10.4324i	−0.308153	−	0.948396i
$122$	0.711838	+	2.19081i	0.0644468	+	0.198347i
$123$		0			0
$124$	9.16908			0.823407
$125$	0.801153	+	11.1516i	0.0716573	+	0.997429i
$126$		0			0
$127$	1.30173	+	0.945765i	0.115510	+	0.0839231i	0.644041	−	0.764991i	$-0.277257\pi$
$127$	1.30173	+	0.945765i	0.115510	+	0.0839231i	−0.528530	+	0.848914i	$0.677257\pi$
$128$	−3.20742	−	9.87142i	−0.283499	−	0.872519i
$129$		0			0
$130$	−0.0269415	−	1.12675i	−0.00236292	−	0.0988223i
$131$	−0.0696286	+	0.214295i	−0.00608348	+	0.0187230i	−0.954052	−	0.299641i	$-0.903133\pi$
$131$	−0.0696286	+	0.214295i	−0.00608348	+	0.0187230i	0.947969	+	0.318364i	$0.103133\pi$
$132$		0			0
$133$	4.75708	−	14.6408i	0.412491	−	1.26952i
$134$	2.30681	−	1.67600i	0.199278	−	0.144784i
$135$		0			0
$136$	8.11645	+	5.89694i	0.695980	+	0.505659i
$137$	−0.555072	+	0.403283i	−0.0474230	+	0.0344548i	−0.611244	−	0.791442i	$-0.709331\pi$
$137$	−0.555072	+	0.403283i	−0.0474230	+	0.0344548i	0.563821	+	0.825897i	$0.309331\pi$
$138$		0			0
$139$	−7.19761	−	5.22937i	−0.610493	−	0.443549i	0.239095	−	0.970996i	$-0.423149\pi$
$139$	−7.19761	−	5.22937i	−0.610493	−	0.443549i	−0.849588	+	0.527447i	$0.823149\pi$
$140$	12.1487	−	4.27101i	1.02675	−	0.360966i
$141$		0			0
$142$	−0.787539	+	2.42380i	−0.0660888	+	0.203401i
$143$	−0.220345			−0.0184261
$144$		0			0
$145$	21.1768	−	7.44496i	1.75864	−	0.618270i
$146$	0.546462	+	1.68184i	0.0452255	+	0.139190i
$147$		0			0
$148$	−3.16787	−	2.30160i	−0.260398	−	0.189190i
$149$	−1.04284			−0.0854331			−0.0427166	−	0.999087i	$-0.513601\pi$
$149$	−1.04284			−0.0854331			−0.0427166	+	0.999087i	$0.513601\pi$
$150$		0			0
$151$	4.99662			0.406619			0.203310	−	0.979115i	$-0.434830\pi$
$151$	4.99662			0.406619			0.203310	+	0.979115i	$0.434830\pi$
$152$	−6.12635	−	4.45105i	−0.496912	−	0.361028i
$153$		0			0
$154$	0.0681205	+	0.209653i	0.00548930	+	0.0168943i
$155$	10.6826	+	3.19077i	0.858048	+	0.256289i
$156$		0			0
$157$	9.16799			0.731685			0.365843	−	0.930677i	$-0.380781\pi$
$157$	9.16799			0.731685			0.365843	+	0.930677i	$0.380781\pi$
$158$	−1.49113	+	4.58922i	−0.118628	+	0.365099i
$159$		0			0
$160$	−0.230309	−	9.63202i	−0.0182076	−	0.761478i
$161$	7.76798	+	5.64377i	0.612203	+	0.444791i
$162$		0			0
$163$	1.60388	−	1.16529i	0.125626	−	0.0912725i	−0.523198	−	0.852211i	$-0.675261\pi$
$163$	1.60388	−	1.16529i	0.125626	−	0.0912725i	0.648824	+	0.760939i	$0.275261\pi$
$164$	−4.49960	−	3.26915i	−0.351359	−	0.255278i
$165$		0			0
$166$	−2.43100	+	1.76623i	−0.188682	+	0.137086i
$167$	4.21231	−	12.9642i	0.325959	−	1.00320i	−0.645047	−	0.764143i	$-0.723162\pi$
$167$	4.21231	−	12.9642i	0.325959	−	1.00320i	0.971006	−	0.239055i	$-0.0768376\pi$
$168$		0			0
$169$	−3.52966	+	10.8632i	−0.271512	+	0.835629i
$170$	3.54679	+	4.64409i	0.272026	+	0.356185i
$171$		0			0
$172$	3.82266	+	11.7649i	0.291475	+	0.897068i
$173$	−8.39092	−	6.09636i	−0.637950	−	0.463498i	0.221195	−	0.975230i	$-0.429004\pi$
$173$	−8.39092	−	6.09636i	−0.637950	−	0.463498i	−0.859145	+	0.511732i	$0.829004\pi$
$174$		0			0
$175$	15.6403	−	0.748374i	1.18230	−	0.0565718i
$176$	−0.536750			−0.0404590
$177$		0			0
$178$	0.988580	+	3.04254i	0.0740972	+	0.228048i
$179$	−2.04101	−	6.28158i	−0.152552	−	0.469507i	0.845352	−	0.534209i	$-0.179390\pi$
$179$	−2.04101	−	6.28158i	−0.152552	−	0.469507i	−0.997905	+	0.0647016i	$0.979390\pi$
$180$		0			0
$181$	−3.22720	+	9.93230i	−0.239876	+	0.738262i	0.756561	+	0.653923i	$0.226878\pi$
$181$	−3.22720	+	9.93230i	−0.239876	+	0.738262i	−0.996437	+	0.0843390i	$0.973122\pi$
$182$	−1.57848			−0.117004
$183$		0			0
$184$	3.82115	−	2.77623i	0.281699	−	0.204666i
$185$	−2.88986	−	3.78392i	−0.212466	−	0.278199i
$186$		0			0
$187$	0.924245	−	0.671503i	0.0675875	−	0.0491052i
$188$	−19.2446	+	13.9820i	−1.40356	+	1.01974i
$189$		0			0
$190$	−2.67714	−	3.50539i	−0.194220	−	0.254307i
$191$	2.10095	−	1.52643i	0.152019	−	0.110448i	−0.509176	−	0.860663i	$-0.670050\pi$
$191$	2.10095	−	1.52643i	0.152019	−	0.110448i	0.661195	+	0.750214i	$0.270050\pi$
$192$		0			0
$193$	−7.65936			−0.551333			−0.275666	−	0.961253i	$-0.588899\pi$
$193$	−7.65936			−0.551333			−0.275666	+	0.961253i	$0.588899\pi$
$194$	−1.95182	+	6.00709i	−0.140133	+	0.431284i
$195$		0			0
$196$	−1.59526	−	4.90970i	−0.113947	−	0.350693i
$197$	−6.87038	−	21.1449i	−0.489494	−	1.50651i	−0.825364	−	0.564600i	$-0.809030\pi$
$197$	−6.87038	−	21.1449i	−0.489494	−	1.50651i	0.335870	−	0.941908i	$-0.390970\pi$
$198$		0			0
$199$	−3.65875			−0.259362			−0.129681	−	0.991556i	$-0.541395\pi$
$199$	−3.65875			−0.259362			−0.129681	+	0.991556i	$0.541395\pi$
$200$	2.02735	−	7.43085i	0.143355	−	0.525440i
$201$		0			0
$202$	−2.95817	−	2.14923i	−0.208136	−	0.151220i
$203$	−9.71483	−	29.8992i	−0.681848	−	2.09851i
$204$		0			0
$205$	−4.10470	−	5.37461i	−0.286685	−	0.375379i
$206$	1.72621	−	5.31273i	0.120271	−	0.370155i
$207$		0			0
$208$	1.18767	−	3.65529i	0.0823504	−	0.253448i
$209$	−0.697626	+	0.506855i	−0.0482558	+	0.0350599i
$210$		0			0
$211$	2.20221	+	1.60000i	0.151607	+	0.110149i	0.661003	−	0.750384i	$-0.270131\pi$
$211$	2.20221	+	1.60000i	0.151607	+	0.110149i	−0.509396	+	0.860532i	$0.670131\pi$
$212$	6.63084	−	4.81759i	0.455408	−	0.330873i
$213$		0			0
$214$	2.79460	+	2.03040i	0.191035	+	0.138795i
$215$	0.359552	+	15.0372i	0.0245213	+	1.02553i
$216$		0			0
$217$	4.82507	−	14.8500i	0.327547	−	1.00809i
$218$	−6.88283			−0.466164
$219$		0			0
$220$	−0.691169	−	0.206444i	−0.0465986	−	0.0139185i
$221$	2.52787	+	7.77998i	0.170043	+	0.523338i
$222$		0			0
$223$	2.10622	+	1.53026i	0.141043	+	0.102474i	0.656069	−	0.754701i	$-0.272218\pi$
$223$	2.10622	+	1.53026i	0.141043	+	0.102474i	−0.515026	+	0.857174i	$0.672218\pi$
$224$	−13.4936			−0.901581
$225$		0			0
$226$	2.63960			0.175584
$227$	−3.75854	−	2.73074i	−0.249463	−	0.181246i	0.456026	−	0.889967i	$-0.349273\pi$
$227$	−3.75854	−	2.73074i	−0.249463	−	0.181246i	−0.705489	+	0.708721i	$0.749273\pi$
$228$		0			0
$229$	1.29616	+	3.98918i	0.0856529	+	0.263612i	0.984705	−	0.174229i	$-0.0557432\pi$
$229$	1.29616	+	3.98918i	0.0856529	+	0.263612i	−0.899052	+	0.437841i	$0.855743\pi$
$230$	2.59538	−	0.912437i	0.171134	−	0.0601643i
$231$		0			0
$232$	−15.4646			−1.01530
$233$	−2.60538	+	8.01852i	−0.170684	+	0.525311i	−0.999410	−	0.0343433i	$-0.989066\pi$
$233$	−2.60538	+	8.01852i	−0.170684	+	0.525311i	0.828726	+	0.559654i	$0.189066\pi$
$234$		0			0
$235$	−27.2870	+	9.59305i	−1.78001	+	0.625782i
$236$	19.4600	+	14.1385i	1.26674	+	0.920340i
$237$		0			0
$238$	6.62099	−	4.81043i	0.429175	−	0.311814i
$239$	23.8601	+	17.3354i	1.54338	+	1.12133i	0.948171	+	0.317760i	$0.102931\pi$
$239$	23.8601	+	17.3354i	1.54338	+	1.12133i	0.595209	+	0.803571i	$0.297069\pi$
$240$		0			0
$241$	−10.1173	+	7.35063i	−0.651711	+	0.473496i	−0.863854	−	0.503743i	$-0.831956\pi$
$241$	−10.1173	+	7.35063i	−0.651711	+	0.473496i	0.212143	+	0.977239i	$0.431956\pi$
$242$	−1.36020	+	4.18625i	−0.0874367	+	0.269103i
$243$		0			0
$244$	−3.26223	+	10.0401i	−0.208843	+	0.642752i
$245$	−0.150047	−	6.27528i	−0.00958616	−	0.400913i
$246$		0			0
$247$	−1.90805	−	5.87238i	−0.121406	−	0.373651i
$248$	−6.21392	−	4.51467i	−0.394584	−	0.286682i
$249$		0			0
$250$	2.37018	−	3.80921i	0.149903	−	0.240915i
$251$	18.3321			1.15711			0.578557	−	0.815642i	$-0.303616\pi$
$251$	18.3321			1.15711			0.578557	+	0.815642i	$0.303616\pi$
$252$		0			0
$253$	−0.166204	−	0.511522i	−0.0104491	−	0.0321591i
$254$	−0.199522	−	0.614064i	−0.0125191	−	0.0385298i
$255$		0			0
$256$	1.42646	−	4.39020i	0.0891539	−	0.274387i
$257$	18.1308			1.13097			0.565485	−	0.824758i	$-0.308689\pi$
$257$	18.1308			1.13097			0.565485	+	0.824758i	$0.308689\pi$
$258$		0			0
$259$	−5.39466	+	3.91945i	−0.335208	+	0.243543i
$260$	2.93525	−	4.25009i	0.182037	−	0.263579i
$261$		0			0
$262$	0.0731486	−	0.0531456i	0.00451914	−	0.00328334i
$263$	−20.1547	+	14.6433i	−1.24279	+	0.902942i	−0.997781	−	0.0665782i	$-0.978792\pi$
$263$	−20.1547	+	14.6433i	−1.24279	+	0.902942i	−0.245012	+	0.969520i	$0.578792\pi$
$264$		0			0
$265$	9.40188	−	3.30534i	0.577553	−	0.203046i
$266$	−4.99756	+	3.63094i	−0.306420	+	0.222627i
$267$		0			0
$268$	13.0674			0.798216
$269$	8.18599	−	25.1939i	0.499109	−	1.53610i	−0.311345	−	0.950297i	$-0.600780\pi$
$269$	8.18599	−	25.1939i	0.499109	−	1.53610i	0.810454	−	0.585802i	$-0.199220\pi$
$270$		0			0
$271$	−9.65344	−	29.7102i	−0.586404	−	1.80477i	−0.593556	−	0.804793i	$-0.702276\pi$
$271$	−9.65344	−	29.7102i	−0.586404	−	1.80477i	0.00715116	−	0.999974i	$-0.497724\pi$
$272$	6.15778	+	18.9517i	0.373370	+	1.14912i
$273$		0			0
$274$	0.275318			0.0166326
$275$	−0.733419	−	0.481044i	−0.0442268	−	0.0290080i
$276$		0			0
$277$	14.5525	+	10.5730i	0.874378	+	0.635273i	0.931758	−	0.363080i	$-0.118275\pi$
$277$	14.5525	+	10.5730i	0.874378	+	0.635273i	−0.0573804	+	0.998352i	$0.518275\pi$
$278$	1.10320	+	3.39531i	0.0661658	+	0.203637i
$279$		0			0
$280$	−10.3362	−	3.08729i	−0.617704	−	0.184501i
$281$	−0.0748846	+	0.230471i	−0.00446724	+	0.0137488i	−0.953265	−	0.302135i	$-0.902301\pi$
$281$	−0.0748846	+	0.230471i	−0.00446724	+	0.0137488i	0.948798	+	0.315883i	$0.102301\pi$
$282$		0			0
$283$	−1.41024	+	4.34029i	−0.0838303	+	0.258003i	−0.984182	−	0.177159i	$-0.943309\pi$
$283$	−1.41024	+	4.34029i	−0.0838303	+	0.258003i	0.900352	+	0.435163i	$0.143309\pi$
$284$	−9.44889	+	6.86502i	−0.560689	+	0.407364i
$285$		0			0
$286$	0.0715325	+	0.0519714i	0.00422980	+	0.00307313i
$287$	−7.66248	+	5.56712i	−0.452302	+	0.328617i
$288$		0			0
$289$	−20.5596	−	14.9374i	−1.20939	−	0.878671i
$290$	−8.63082	−	2.57792i	−0.506819	−	0.151381i
$291$		0			0
$292$	−2.50434	+	7.70757i	−0.146555	+	0.451051i
$293$	−3.13176			−0.182960			−0.0914798	−	0.995807i	$-0.529160\pi$
$293$	−3.13176			−0.182960			−0.0914798	+	0.995807i	$0.529160\pi$
$294$		0			0
$295$	17.7522	+	23.2443i	1.03357	+	1.35334i
$296$	1.01362	+	3.11960i	0.0589154	+	0.181323i
$297$		0			0
$298$	0.338548	+	0.245969i	0.0196116	+	0.0142486i
$299$	3.85124			0.222723
$300$		0			0
$301$	21.0659			1.21422
$302$	−1.62210	−	1.17852i	−0.0933412	−	0.0678164i
$303$		0			0
$304$	−4.64793	−	14.3049i	−0.266577	−	0.820440i
$305$	−7.29461	+	10.5622i	−0.417688	+	0.604790i
$306$		0			0
$307$	−14.6864			−0.838198			−0.419099	−	0.907940i	$-0.637654\pi$
$307$	−14.6864			−0.838198			−0.419099	+	0.907940i	$0.637654\pi$
$308$	−0.312184	+	0.960804i	−0.0177883	+	0.0547469i
$309$		0			0
$310$	−2.71540	−	3.55549i	−0.154225	−	0.201938i
$311$	−25.0978	−	18.2346i	−1.42317	−	1.03399i	−0.991239	−	0.132083i	$-0.957833\pi$
$311$	−25.0978	−	18.2346i	−1.42317	−	1.03399i	−0.431928	−	0.901908i	$-0.642167\pi$
$312$		0			0
$313$	−19.3072	+	14.0275i	−1.09131	+	0.792883i	−0.979620	−	0.200860i	$-0.935626\pi$
$313$	−19.3072	+	14.0275i	−1.09131	+	0.792883i	−0.111690	+	0.993743i	$0.535626\pi$
$314$	−2.97629	−	2.16240i	−0.167962	−	0.122031i
$315$		0			0
$316$	−17.8906	+	12.9983i	−1.00642	+	0.731209i
$317$	7.38013	−	22.7137i	0.414509	−	1.27573i	−0.498180	−	0.867074i	$-0.665998\pi$
$317$	7.38013	−	22.7137i	0.414509	−	1.27573i	0.912689	−	0.408654i	$-0.134002\pi$
$318$		0			0
$319$	−0.544180	+	1.67481i	−0.0304682	+	0.0937716i
$320$	5.57914	−	8.07829i	0.311883	−	0.451590i
$321$		0			0
$322$	−1.19063	−	3.66437i	−0.0663511	−	0.204208i
$323$	25.8996	+	18.8171i	1.44109	+	1.04701i
$324$		0			0
$325$	4.89877	−	3.93020i	0.271735	−	0.218008i
$326$	−0.795532			−0.0440605
$327$		0			0
$328$	1.43973	+	4.43103i	0.0794957	+	0.244663i
$329$	12.5179	+	38.5260i	0.690132	+	2.12401i
$330$		0			0
$331$	−6.71235	+	20.6585i	−0.368944	+	1.13549i	0.578530	+	0.815661i	$0.303627\pi$
$331$	−6.71235	+	20.6585i	−0.368944	+	1.13549i	−0.947474	+	0.319832i	$0.896373\pi$
$332$	−13.7709			−0.755774
$333$		0			0
$334$	−4.42526	+	3.21514i	−0.242140	+	0.175925i
$335$	15.2244	+	4.54735i	0.831797	+	0.248448i
$336$		0			0
$337$	−22.4177	+	16.2874i	−1.22117	+	0.887231i	−0.996197	−	0.0871338i	$-0.972229\pi$
$337$	−22.4177	+	16.2874i	−1.22117	+	0.887231i	−0.224973	+	0.974365i	$0.572229\pi$
$338$	3.70810	−	2.69409i	0.201694	−	0.146539i
$339$		0			0
$340$	0.640150	+	26.7724i	0.0347170	+	1.45194i
$341$	−0.707598	+	0.514100i	−0.0383186	+	0.0278401i
$342$		0			0
$343$	13.1304			0.708974
$344$	3.20220	−	9.85534i	0.172651	−	0.531365i
$345$		0			0
$346$	1.28611	+	3.95823i	0.0691416	+	0.212796i
$347$	0.306225	+	0.942464i	0.0164390	+	0.0505941i	0.958940	−	0.283611i	$-0.0915323\pi$
$347$	0.306225	+	0.942464i	0.0164390	+	0.0505941i	−0.942501	+	0.334205i	$0.891532\pi$
$348$		0			0
$349$	18.0840			0.968016			0.484008	−	0.875064i	$-0.339181\pi$
$349$	18.0840			0.968016			0.484008	+	0.875064i	$0.339181\pi$
$350$	−5.25397	−	3.44604i	−0.280837	−	0.184199i
$351$		0			0
$352$	0.611496	+	0.444278i	0.0325929	+	0.0236801i
$353$	2.59159	+	7.97609i	0.137936	+	0.424524i	0.996035	−	0.0889601i	$-0.0283544\pi$
$353$	2.59159	+	7.97609i	0.137936	+	0.424524i	−0.858099	+	0.513485i	$0.828354\pi$
$354$		0			0
$355$	−13.3976	+	4.71008i	−0.711070	+	0.249985i
$356$	−4.53049	+	13.9434i	−0.240116	+	0.739000i
$357$		0			0
$358$	−0.819008	+	2.52065i	−0.0432859	+	0.133220i
$359$	−7.48904	+	5.44111i	−0.395256	+	0.287171i	−0.767606	−	0.640922i	$-0.778552\pi$
$359$	−7.48904	+	5.44111i	−0.395256	+	0.287171i	0.372350	+	0.928093i	$0.378552\pi$
$360$		0			0
$361$	−4.17784	−	3.03538i	−0.219886	−	0.159757i
$362$	3.39035	−	2.46323i	0.178193	−	0.129465i
$363$		0			0
$364$	−5.85234	−	4.25197i	−0.306746	−	0.222864i
$365$	−5.59991	+	8.10836i	−0.293113	+	0.424411i
$366$		0			0
$367$	−7.69876	+	23.6944i	−0.401872	+	1.23684i	0.521607	+	0.853186i	$0.325333\pi$
$367$	−7.69876	+	23.6944i	−0.401872	+	1.23684i	−0.923479	+	0.383649i	$0.874667\pi$
$368$	9.38146			0.489042
$369$		0			0
$370$	0.0456701	+	1.91002i	0.00237428	+	0.0992972i
$371$	−4.31310	−	13.2744i	−0.223925	−	0.689170i
$372$		0			0
$373$	−21.1042	−	15.3331i	−1.09273	−	0.793916i	−0.112873	−	0.993609i	$-0.536005\pi$
$373$	−21.1042	−	15.3331i	−1.09273	−	0.793916i	−0.979858	+	0.199694i	$0.936005\pi$
$374$	−0.458429			−0.0237048
$375$		0			0
$376$	19.9266			1.02764
$377$	−10.2014	−	7.41177i	−0.525400	−	0.381726i
$378$		0			0
$379$	6.22659	+	19.1635i	0.319839	+	0.984362i	0.973717	+	0.227762i	$0.0731408\pi$
$379$	6.22659	+	19.1635i	0.319839	+	0.984362i	−0.653878	+	0.756600i	$0.726859\pi$
$380$	−0.483189	−	20.2080i	−0.0247871	−	1.03665i
$381$		0			0
$382$	−1.04208			−0.0533174
$383$	9.65090	−	29.7024i	0.493138	−	1.51772i	−0.326701	−	0.945128i	$-0.605937\pi$
$383$	9.65090	−	29.7024i	0.493138	−	1.51772i	0.819839	−	0.572595i	$-0.194063\pi$
$384$		0			0
$385$	−0.698069	+	1.01077i	−0.0355769	+	0.0515134i
$386$	2.48653	+	1.80657i	0.126561	+	0.0919519i
$387$		0			0
$388$	−23.4180	+	17.0141i	−1.18887	+	0.863762i
$389$	−7.25901	−	5.27398i	−0.368046	−	0.267401i	0.388354	−	0.921510i	$-0.373044\pi$
$389$	−7.25901	−	5.27398i	−0.368046	−	0.267401i	−0.756400	+	0.654109i	$0.773044\pi$
$390$		0			0
$391$	−16.1542	+	11.7367i	−0.816953	+	0.593551i
$392$	−1.33633	+	4.11280i	−0.0674948	+	0.207728i
$393$		0			0
$394$	−2.75692	+	8.48492i	−0.138892	+	0.427464i
$395$	−25.3670	+	8.91808i	−1.27635	+	0.448717i
$396$		0			0
$397$	5.37728	+	16.5496i	0.269878	+	0.830599i	0.990529	+	0.137302i	$0.0438429\pi$
$397$	5.37728	+	16.5496i	0.269878	+	0.830599i	−0.720651	+	0.693298i	$0.756157\pi$
$398$	1.18777	+	0.862966i	0.0595376	+	0.0432566i
$399$		0			0
$400$	11.9332	−	9.57379i	0.596660	−	0.478689i
$401$	−28.6798			−1.43220			−0.716100	−	0.697998i	$-0.754074\pi$
$401$	−28.6798			−1.43220			−0.716100	+	0.697998i	$0.754074\pi$
$402$		0			0
$403$	−1.93533	−	5.95632i	−0.0964055	−	0.296706i
$404$	−5.17822	−	15.9369i	−0.257626	−	0.792892i
$405$		0			0
$406$	−3.89833	+	11.9978i	−0.193471	+	0.595442i
$407$	0.373520			0.0185147
$408$		0			0
$409$	−20.3664	+	14.7971i	−1.00705	+	0.731668i	−0.963589	−	0.267387i	$-0.913840\pi$
$409$	−20.3664	+	14.7971i	−1.00705	+	0.731668i	−0.0434655	+	0.999055i	$0.513840\pi$
$410$	0.0648691	+	2.71296i	0.00320366	+	0.133984i
$411$		0			0
$412$	20.7111	−	15.0475i	1.02036	−	0.741335i
$413$	33.1390	−	24.0769i	1.63066	−	1.18475i
$414$		0			0
$415$	−16.0440	−	4.79216i	−0.787569	−	0.235238i
$416$	−4.37861	+	3.18125i	−0.214679	+	0.155974i
$417$		0			0
$418$	0.346025			0.0169247
$419$	−8.15376	+	25.0947i	−0.398337	+	1.22596i	0.527995	+	0.849248i	$0.322944\pi$
$419$	−8.15376	+	25.0947i	−0.398337	+	1.22596i	−0.926332	+	0.376708i	$0.877056\pi$
$420$		0			0
$421$	−8.18115	−	25.1790i	−0.398725	−	1.22715i	−0.926023	−	0.377468i	$-0.876795\pi$
$421$	−8.18115	−	25.1790i	−0.398725	−	1.22715i	0.527298	−	0.849681i	$-0.323205\pi$
$422$	−0.337541	−	1.03885i	−0.0164313	−	0.0505702i
$423$		0			0
$424$	−6.86583			−0.333434
$425$	−8.57077	+	31.4144i	−0.415744	+	1.52382i
$426$		0			0
$427$	14.5441	+	10.5669i	0.703837	+	0.511367i
$428$	4.89190	+	15.0557i	0.236459	+	0.727746i
$429$		0			0
$430$	3.43002	−	4.96648i	0.165410	−	0.239505i
$431$	11.9805	−	36.8721i	0.577078	−	1.77606i	−0.0519119	−	0.998652i	$-0.516532\pi$
$431$	11.9805	−	36.8721i	0.577078	−	1.77606i	0.628990	−	0.777413i	$-0.283468\pi$
$432$		0			0
$433$	5.40678	−	16.6404i	0.259833	−	0.799684i	−0.733006	−	0.680223i	$-0.761883\pi$
$433$	5.40678	−	16.6404i	0.259833	−	0.799684i	0.992839	−	0.119462i	$-0.0381169\pi$
$434$	−5.06900	+	3.68284i	−0.243320	+	0.176782i
$435$		0			0
$436$	−25.5187	−	18.5404i	−1.22212	−	0.887924i
$437$	12.1933	−	8.85895i	0.583284	−	0.423781i
$438$		0			0
$439$	24.8777	+	18.0747i	1.18735	+	0.862660i	0.992982	−	0.118269i	$-0.0377346\pi$
$439$	24.8777	+	18.0747i	1.18735	+	0.862660i	0.194367	+	0.980929i	$0.437735\pi$
$440$	0.366759	+	0.480226i	0.0174845	+	0.0228939i
$441$		0			0
$442$	1.01437	−	3.12192i	0.0482488	−	0.148495i
$443$	10.7047			0.508594			0.254297	−	0.967126i	$-0.418156\pi$
$443$	10.7047			0.508594			0.254297	+	0.967126i	$0.418156\pi$
$444$		0			0
$445$	−10.1305	+	14.6685i	−0.480234	+	0.695352i
$446$	−0.322829	−	0.993564i	−0.0152864	−	0.0470466i
$447$		0			0
$448$	−11.1237	−	8.08187i	−0.525548	−	0.381833i
$449$	20.9945			0.990793			0.495396	−	0.868667i	$-0.335023\pi$
$449$	20.9945			0.990793			0.495396	+	0.868667i	$0.335023\pi$
$450$		0			0
$451$	0.530541			0.0249822
$452$	9.78655	+	7.11035i	0.460321	+	0.334443i
$453$		0			0
$454$	0.576086	+	1.77301i	0.0270370	+	0.0832115i
$455$	−5.33872	−	6.99041i	−0.250283	−	0.327716i
$456$		0			0
$457$	18.4640			0.863710			0.431855	−	0.901943i	$-0.357859\pi$
$457$	18.4640			0.863710			0.431855	+	0.901943i	$0.357859\pi$
$458$	0.520119	−	1.60076i	0.0243036	−	0.0747987i
$459$		0			0
$460$	12.0804	+	3.60829i	0.563253	+	0.168237i
$461$	−25.0480	−	18.1984i	−1.16660	−	0.847584i	−0.176002	−	0.984390i	$-0.556316\pi$
$461$	−25.0480	−	18.1984i	−1.16660	−	0.847584i	−0.990598	+	0.136806i	$0.956316\pi$
$462$		0			0
$463$	−2.90467	+	2.11036i	−0.134991	+	0.0980769i	−0.653232	−	0.757158i	$-0.726587\pi$
$463$	−2.90467	+	2.11036i	−0.134991	+	0.0980769i	0.518240	+	0.855235i	$0.326587\pi$
$464$	−24.8502	−	18.0548i	−1.15364	−	0.838171i
$465$		0			0
$466$	2.73709	−	1.98861i	0.126793	−	0.0921206i
$467$	−4.23143	+	13.0230i	−0.195807	+	0.602633i	0.804159	+	0.594414i	$0.202616\pi$
$467$	−4.23143	+	13.0230i	−0.195807	+	0.602633i	−0.999966	+	0.00821867i	$0.997384\pi$
$468$		0			0
$469$	6.87648	−	21.1636i	0.317526	−	0.977246i
$470$	11.1211	+	3.32173i	0.512977	+	0.153220i
$471$		0			0
$472$	−6.22659	−	19.1635i	−0.286602	−	0.882070i
$473$	−0.954650	−	0.693594i	−0.0438949	−	0.0318915i
$474$		0			0
$475$	6.46927	−	23.7118i	0.296831	−	1.08797i
$476$	37.5058			1.71908
$477$		0			0
$478$	−3.65712	−	11.2555i	−0.167273	−	0.514813i
$479$	−1.69985	−	5.23160i	−0.0776681	−	0.239038i	0.904683	−	0.426086i	$-0.140108\pi$
$479$	−1.69985	−	5.23160i	−0.0776681	−	0.239038i	−0.982351	+	0.187048i	$0.940108\pi$
$480$		0			0
$481$	−0.826493	+	2.54368i	−0.0376848	+	0.115982i
$482$	5.01821			0.228573
$483$		0			0
$484$	−16.3196	+	11.8569i	−0.741801	+	0.538950i
$485$	−33.2043	+	11.6734i	−1.50773	+	0.530061i
$486$		0			0
$487$	3.70715	−	2.69340i	0.167987	−	0.122050i	−0.500615	−	0.865670i	$-0.666893\pi$
$487$	3.70715	−	2.69340i	0.167987	−	0.122050i	0.668602	+	0.743620i	$0.266893\pi$
$488$	7.15438	−	5.19796i	0.323864	−	0.235301i
$489$		0			0
$490$	−1.43140	+	2.07259i	−0.0646642	+	0.0936302i
$491$	−12.3926	+	9.00377i	−0.559272	+	0.406335i	−0.831192	−	0.555985i	$-0.812341\pi$
$491$	−12.3926	+	9.00377i	−0.559272	+	0.406335i	0.271921	+	0.962320i	$0.412341\pi$
$492$		0			0
$493$	65.3778			2.94447
$494$	−0.765656	+	2.35645i	−0.0344485	+	0.106022i
$495$		0			0
$496$	−4.71437	−	14.5093i	−0.211681	−	0.651489i
$497$	6.14613	+	18.9158i	0.275692	+	0.848491i
$498$		0			0
$499$	10.5414			0.471899			0.235950	−	0.971765i	$-0.424180\pi$
$499$	10.5414			0.471899			0.235950	+	0.971765i	$0.424180\pi$
$500$	19.0486	−	7.73837i	0.851877	−	0.346071i
$501$		0			0
$502$	−5.95132	−	4.32389i	−0.265620	−	0.192985i
$503$	6.81885	+	20.9863i	0.304038	+	0.935732i	0.980035	+	0.198827i	$0.0637132\pi$
$503$	6.81885	+	20.9863i	0.304038	+	0.935732i	−0.675997	+	0.736904i	$0.736287\pi$
$504$		0			0
$505$	−0.487054	−	20.3696i	−0.0216736	−	0.906436i
$506$	−0.0666935	+	0.205261i	−0.00296489	+	0.00912498i
$507$		0			0
$508$	0.914373	−	2.81415i	0.0405687	−	0.124858i
$509$	17.5225	−	12.7308i	0.776670	−	0.564284i	−0.127308	−	0.991863i	$-0.540634\pi$
$509$	17.5225	−	12.7308i	0.776670	−	0.564284i	0.903978	+	0.427580i	$0.140634\pi$
$510$		0			0
$511$	11.1652	+	8.11196i	0.493917	+	0.358852i
$512$	−18.2928	+	13.2905i	−0.808437	+	0.587364i
$513$		0			0
$514$	−5.88598	−	4.27641i	−0.259619	−	0.188624i
$515$	29.3662	−	10.3240i	1.29403	−	0.454932i
$516$		0			0
$517$	0.701193	−	2.15805i	0.0308384	−	0.0949109i
$518$	2.67577			0.117567
$519$		0			0
$520$	−4.08189	+	1.43504i	−0.179003	+	0.0629305i
$521$	2.31133	+	7.11355i	0.101261	+	0.311650i	0.988835	−	0.149016i	$-0.0476106\pi$
$521$	2.31133	+	7.11355i	0.101261	+	0.311650i	−0.887573	+	0.460666i	$0.847611\pi$
$522$		0			0
$523$	−18.4737	−	13.4220i	−0.807800	−	0.586901i	0.105392	−	0.994431i	$-0.466390\pi$
$523$	−18.4737	−	13.4220i	−0.807800	−	0.586901i	−0.913192	+	0.407530i	$0.866390\pi$
$524$	0.414364			0.0181016
$525$		0			0
$526$	9.99682			0.435882
$527$	26.2698	+	19.0861i	1.14433	+	0.831404i
$528$		0			0
$529$	−4.20244	−	12.9338i	−0.182715	−	0.562339i
$530$	−3.83183	−	1.14452i	−0.166444	−	0.0497149i
$531$		0			0
$532$	−28.3096			−1.22738
$533$	−1.17394	+	3.61301i	−0.0508488	+	0.156497i
$534$		0			0
$535$	0.460124	+	19.2433i	0.0198929	+	0.831961i
$536$	−8.85580	−	6.43411i	−0.382512	−	0.277911i
$537$		0			0
$538$	−8.59983	+	6.24814i	−0.370765	+	0.269376i
$539$	0.398391	+	0.289448i	0.0171599	+	0.0124674i
$540$		0			0
$541$	23.9780	−	17.4210i	1.03089	−	0.748989i	0.0624069	−	0.998051i	$-0.480122\pi$
$541$	23.9780	−	17.4210i	1.03089	−	0.748989i	0.968487	+	0.249062i	$0.0801224\pi$
$542$	−3.87369	+	11.9220i	−0.166389	+	0.512094i
$543$		0			0
$544$	8.67138	−	26.6878i	0.371782	−	1.14423i
$545$	−23.2791	−	30.4812i	−0.997167	−	1.30567i
$546$		0			0
$547$	0.800897	+	2.46491i	0.0342439	+	0.105392i	0.966717	−	0.255846i	$-0.0823541\pi$
$547$	0.800897	+	2.46491i	0.0342439	+	0.105392i	−0.932474	+	0.361238i	$0.882354\pi$
$548$	1.02076	+	0.741629i	0.0436049	+	0.0316808i
$549$		0			0
$550$	0.124636	+	0.329153i	0.00531448	+	0.0140351i
$551$	−49.3476			−2.10228
$552$		0			0
$553$	11.6371	+	35.8153i	0.494860	+	1.52302i
$554$	−2.23052	−	6.86484i	−0.0947658	−	0.291659i
$555$		0			0
$556$	−5.05579	+	15.5601i	−0.214413	+	0.659897i
$557$	−25.5493			−1.08256			−0.541279	−	0.840843i	$-0.682060\pi$
$557$	−25.5493			−1.08256			−0.541279	+	0.840843i	$0.682060\pi$
$558$		0			0
$559$	6.83577	−	4.96648i	0.289122	−	0.210060i
$560$	−13.0049	−	17.0283i	−0.549557	−	0.719578i
$561$		0			0
$562$	0.0786703	−	0.0571573i	0.00331851	−	0.00241104i
$563$	9.91710	−	7.20519i	0.417956	−	0.303663i	−0.358859	−	0.933392i	$-0.616834\pi$
$563$	9.91710	−	7.20519i	0.417956	−	0.303663i	0.776815	+	0.629729i	$0.216834\pi$
$564$		0			0
$565$	8.92767	+	11.6897i	0.375590	+	0.491789i
$566$	1.48154	−	1.07640i	0.0622737	−	0.0452445i
$567$		0			0
$568$	9.78375			0.410517
$569$	7.16546	−	22.0530i	0.300392	−	0.924510i	−0.680965	−	0.732316i	$-0.738440\pi$
$569$	7.16546	−	22.0530i	0.300392	−	0.924510i	0.981357	−	0.192194i	$-0.0615604\pi$
$570$		0			0
$571$	−3.76709	−	11.5939i	−0.157648	−	0.485190i	0.840772	−	0.541390i	$-0.182102\pi$
$571$	−3.76709	−	11.5939i	−0.157648	−	0.485190i	−0.998420	+	0.0561996i	$0.982102\pi$
$572$	0.125216	+	0.385377i	0.00523556	+	0.0161134i
$573$		0			0
$574$	3.80062			0.158635
$575$	12.8189	+	8.40781i	0.534585	+	0.350630i
$576$		0			0
$577$	−28.1943	−	20.4844i	−1.17374	−	0.852775i	−0.182292	−	0.983244i	$-0.558352\pi$
$577$	−28.1943	−	20.4844i	−1.17374	−	0.852775i	−0.991452	+	0.130469i	$0.958352\pi$
$578$	3.15124	+	9.69853i	0.131074	+	0.403406i
$579$		0			0
$580$	−25.0553	−	32.8069i	−1.04036	−	1.36223i
$581$	−7.24668	+	22.3030i	−0.300643	+	0.925284i
$582$		0			0
$583$	−0.241600	+	0.743568i	−0.0100060	+	0.0307954i
$584$	5.49226	−	3.99036i	0.227271	−	0.165122i
$585$		0			0
$586$	1.01669	+	0.738670i	0.0419992	+	0.0305142i
$587$	22.7267	−	16.5119i	0.938030	−	0.681519i	−0.00991559	−	0.999951i	$-0.503156\pi$
$587$	22.7267	−	16.5119i	0.938030	−	0.681519i	0.947946	+	0.318432i	$0.103156\pi$
$588$		0			0
$589$	−19.8286	−	14.4063i	−0.817023	−	0.593602i
$590$	−0.280548	−	11.7331i	−0.0115500	−	0.483044i
$591$		0			0
$592$	−2.01330	+	6.19630i	−0.0827461	+	0.254666i
$593$	31.6055			1.29788			0.648942	−	0.760838i	$-0.275212\pi$
$593$	31.6055			1.29788			0.648942	+	0.760838i	$0.275212\pi$
$594$		0			0
$595$	43.6969	+	13.0517i	1.79140	+	0.535069i
$596$	0.592623	+	1.82391i	0.0242748	+	0.0747101i
$597$		0			0
$598$	−1.25026	−	0.908370i	−0.0511271	−	0.0371460i
$599$	24.9591			1.01980			0.509901	−	0.860233i	$-0.329682\pi$
$599$	24.9591			1.01980			0.509901	+	0.860233i	$0.329682\pi$
$600$		0			0
$601$	42.6024			1.73779			0.868894	−	0.494999i	$-0.164832\pi$
$601$	42.6024			1.73779			0.868894	+	0.494999i	$0.164832\pi$
$602$	−6.83880	−	4.96868i	−0.278729	−	0.202508i
$603$		0			0
$604$	−2.83946	−	8.73894i	−0.115536	−	0.355583i
$605$	−23.1396	+	8.13500i	−0.940759	+	0.330735i
$606$		0			0
$607$	46.1529			1.87329			0.936644	−	0.350282i	$-0.113914\pi$
$607$	46.1529			1.87329			0.936644	+	0.350282i	$0.113914\pi$
$608$	−6.54522	+	20.1441i	−0.265444	+	0.816951i
$609$		0			0
$610$	4.85936	−	1.70836i	0.196750	−	0.0691697i
$611$	13.1448	+	9.55029i	0.531784	+	0.386363i
$612$		0			0
$613$	−18.6262	+	13.5327i	−0.752305	+	0.546581i	−0.896540	−	0.442962i	$-0.853928\pi$
$613$	−18.6262	+	13.5327i	−0.752305	+	0.546581i	0.144236	+	0.989543i	$0.453928\pi$
$614$	4.76778	+	3.46400i	0.192412	+	0.139796i
$615$		0			0
$616$	0.684650	−	0.497427i	0.0275853	−	0.0200419i
$617$	−9.84125	+	30.2882i	−0.396194	+	1.21936i	0.531834	+	0.846848i	$0.321503\pi$
$617$	−9.84125	+	30.2882i	−0.396194	+	1.21936i	−0.928028	+	0.372510i	$0.878497\pi$
$618$		0			0
$619$	1.72587	−	5.31167i	0.0693684	−	0.213494i	−0.910363	−	0.413811i	$-0.864197\pi$
$619$	1.72587	−	5.31167i	0.0693684	−	0.213494i	0.979731	+	0.200317i	$0.0641973\pi$
$620$	−0.490096	−	20.4968i	−0.0196827	−	0.823172i
$621$		0			0
$622$	3.84684	+	11.8393i	0.154244	+	0.474715i
$623$	20.1984	+	14.6750i	0.809231	+	0.587941i
$624$		0			0
$625$	24.8858	−	2.38699i	0.995431	−	0.0954794i
$626$	9.57647			0.382753
$627$		0			0
$628$	−5.20994	−	16.0346i	−0.207899	−	0.639848i
$629$	−4.28515	−	13.1883i	−0.170860	−	0.525853i
$630$		0			0
$631$	−13.2312	+	40.7213i	−0.526724	+	1.62109i	0.234156	+	0.972199i	$0.424767\pi$
$631$	−13.2312	+	40.7213i	−0.526724	+	1.62109i	−0.760880	+	0.648892i	$0.775233\pi$
$632$	18.5246			0.736868
$633$		0			0
$634$	−7.75322	+	5.63304i	−0.307920	+	0.223717i
$635$	2.04461	−	2.96049i	0.0811379	−	0.117483i
$636$		0			0
$637$	−2.85268	+	2.07259i	−0.113027	+	0.0821191i
$638$	0.571691	−	0.415358i	0.0226334	−	0.0164442i
$639$		0			0
$640$	−21.8954	+	7.69760i	−0.865493	+	0.304274i
$641$	−29.3345	+	21.3127i	−1.15864	+	0.841803i	−0.989606	−	0.143807i	$-0.954066\pi$
$641$	−29.3345	+	21.3127i	−1.15864	+	0.841803i	−0.169037	+	0.985610i	$0.554066\pi$
$642$		0			0
$643$	27.7259			1.09340			0.546702	−	0.837327i	$-0.315883\pi$
$643$	27.7259			1.09340			0.546702	+	0.837327i	$0.315883\pi$
$644$	5.45644	−	16.7932i	0.215014	−	0.661744i
$645$		0			0
$646$	−3.96972	−	12.2176i	−0.156187	−	0.480693i
$647$	3.36057	+	10.3428i	0.132118	+	0.406616i	0.995131	−	0.0985657i	$-0.0314255\pi$
$647$	3.36057	+	10.3428i	0.132118	+	0.406616i	−0.863013	+	0.505182i	$0.831425\pi$
$648$		0			0
$649$	−2.29450			−0.0900671
$650$	−2.51732	+	0.120451i	−0.0987376	+	0.00472450i
$651$		0			0
$652$	−2.94950	−	2.14294i	−0.115511	−	0.0839240i
$653$	−5.90091	−	18.1611i	−0.230921	−	0.710700i	−0.997636	−	0.0687138i	$-0.978110\pi$
$653$	−5.90091	−	18.1611i	−0.230921	−	0.710700i	0.766716	−	0.641987i	$-0.221890\pi$
$654$		0			0
$655$	0.482763	+	0.144196i	0.0188631	+	0.00563419i
$656$	−2.85966	+	8.80112i	−0.111651	+	0.343626i
$657$		0			0
$658$	5.02311	−	15.4596i	0.195821	−	0.602676i
$659$	9.74450	−	7.07980i	0.379592	−	0.275790i	−0.381585	−	0.924334i	$-0.624622\pi$
$659$	9.74450	−	7.07980i	0.379592	−	0.275790i	0.761177	+	0.648544i	$0.224622\pi$
$660$		0			0
$661$	5.61964	+	4.08291i	0.218579	+	0.158807i	0.691687	−	0.722198i	$-0.256868\pi$
$661$	5.61964	+	4.08291i	0.218579	+	0.158807i	−0.473108	+	0.881004i	$0.656868\pi$
$662$	7.05169	−	5.12335i	0.274072	−	0.199125i
$663$		0			0
$664$	9.33256	+	6.78050i	0.362174	+	0.263135i
$665$	−32.9827	−	9.85154i	−1.27901	−	0.382026i
$666$		0			0
$667$	9.51133	−	29.2729i	0.368280	−	1.13345i
$668$	−25.0677			−0.969899
$669$		0			0
$670$	−3.86987	−	5.06713i	−0.149506	−	0.195760i
$671$	−0.311185	−	0.957727i	−0.0120131	−	0.0369727i
$672$		0			0
$673$	14.7483	+	10.7153i	0.568506	+	0.413044i	0.834562	−	0.550914i	$-0.185721\pi$
$673$	14.7483	+	10.7153i	0.568506	+	0.413044i	−0.266056	+	0.963958i	$0.585721\pi$
$674$	11.1193			0.428298
$675$		0			0
$676$	21.0052			0.807893
$677$	−5.70512	−	4.14501i	−0.219265	−	0.159306i	0.472731	−	0.881207i	$-0.343268\pi$
$677$	−5.70512	−	4.14501i	−0.219265	−	0.159306i	−0.691996	+	0.721901i	$0.743268\pi$
$678$		0			0
$679$	15.2324	+	46.8807i	0.584568	+	1.79911i
$680$	12.7484	−	18.4589i	0.488878	−	0.707868i
$681$		0			0
$682$	0.350972			0.0134394
$683$	1.08197	−	3.32996i	0.0414004	−	0.127417i	−0.928220	−	0.372032i	$-0.878661\pi$
$683$	1.08197	−	3.32996i	0.0414004	−	0.127417i	0.969620	+	0.244614i	$0.0786613\pi$
$684$		0			0
$685$	0.931180	+	1.21927i	0.0355786	+	0.0465858i
$686$	−4.26263	−	3.09698i	−0.162748	−	0.118243i
$687$		0			0
$688$	16.6516	−	12.0981i	0.634837	−	0.461236i
$689$	−4.52913	−	3.29061i	−0.172546	−	0.125362i
$690$		0			0
$691$	−21.6033	+	15.6957i	−0.821829	+	0.597093i	−0.917236	−	0.398345i	$-0.869585\pi$
$691$	−21.6033	+	15.6957i	−0.821829	+	0.597093i	0.0954071	+	0.995438i	$0.469585\pi$
$692$	−5.89401	+	18.1399i	−0.224057	+	0.689576i
$693$		0			0
$694$	0.122881	−	0.378188i	0.00466449	−	0.0143558i
$695$	−11.3052	+	16.3693i	−0.428829	+	0.620921i
$696$		0			0
$697$	−6.08655	−	18.7325i	−0.230545	−	0.709544i
$698$	−5.87078	−	4.26537i	−0.222212	−	0.161447i
$699$		0			0
$700$	−10.1969	−	26.9292i	−0.385406	−	1.01783i
$701$	−43.9763			−1.66096			−0.830481	−	0.557046i	$-0.811935\pi$
$701$	−43.9763			−1.66096			−0.830481	+	0.557046i	$0.811935\pi$
$702$		0			0
$703$	3.23446	+	9.95464i	0.121990	+	0.375446i
$704$	0.238003	+	0.732499i	0.00897009	+	0.0276071i
$705$		0			0
$706$	1.03994	−	3.20061i	0.0391387	−	0.120457i
$707$	−28.5361			−1.07321
$708$		0			0
$709$	35.6607	−	25.9090i	1.33927	−	0.973034i	0.339796	−	0.940499i	$-0.389642\pi$
$709$	35.6607	−	25.9090i	1.33927	−	0.973034i	0.999471	−	0.0325351i	$-0.0103581\pi$
$710$	5.46032	+	1.63093i	0.204922	+	0.0612079i
$711$		0			0
$712$	9.93580	−	7.21878i	0.372360	−	0.270535i
$713$	12.3676	−	8.98557i	0.463170	−	0.336512i
$714$		0			0
$715$	0.0117776	+	0.492565i	0.000440458	+	0.0184209i
$716$	−9.82645	+	7.13934i	−0.367232	+	0.266809i
$717$		0			0
$718$	3.71460			0.138627
$719$	11.1780	−	34.4024i	0.416869	−	1.28299i	−0.493699	−	0.869633i	$-0.664355\pi$
$719$	11.1780	−	34.4024i	0.416869	−	1.28299i	0.910568	−	0.413359i	$-0.135645\pi$
$720$		0			0
$721$	−13.4717	−	41.4617i	−0.501713	−	1.54411i
$722$	0.640353	+	1.97080i	0.0238315	+	0.0733458i
$723$		0			0
$724$	19.2052			0.713757
$725$	−17.7746	−	46.9413i	−0.660132	−	1.74336i
$726$		0			0
$727$	−4.74881	−	3.45021i	−0.176124	−	0.127961i	0.496231	−	0.868191i	$-0.334717\pi$
$727$	−4.74881	−	3.45021i	−0.176124	−	0.127961i	−0.672355	+	0.740229i	$0.734717\pi$
$728$	1.87256	+	5.76315i	0.0694018	+	0.213597i
$729$		0			0
$730$	3.73042	−	1.31147i	0.138069	−	0.0485398i
$731$	−13.5375	+	41.6642i	−0.500703	+	1.54101i
$732$		0			0
$733$	12.8049	−	39.4096i	0.472962	−	1.45563i	−0.375726	−	0.926731i	$-0.622606\pi$
$733$	12.8049	−	39.4096i	0.472962	−	1.45563i	0.848687	−	0.528895i	$-0.177394\pi$
$734$	8.08797	−	5.87625i	0.298532	−	0.216896i
$735$		0			0
$736$	−10.6879	−	7.76521i	−0.393961	−	0.286229i
$737$	−1.00844	+	0.732673i	−0.0371463	+	0.0269883i
$738$		0			0
$739$	17.9365	+	13.0317i	0.659807	+	0.479378i	0.866598	−	0.499008i	$-0.166302\pi$
$739$	17.9365	+	13.0317i	0.659807	+	0.479378i	−0.206791	+	0.978385i	$0.566302\pi$
$740$	−4.97573	+	7.20458i	−0.182911	+	0.264846i
$741$		0			0
$742$	−1.73074	+	5.32668i	−0.0635376	+	0.195549i
$743$	−17.9829			−0.659730			−0.329865	−	0.944028i	$-0.607003\pi$
$743$	−17.9829			−0.659730			−0.329865	+	0.944028i	$0.607003\pi$
$744$		0			0
$745$	0.0557410	+	2.33120i	0.00204219	+	0.0854087i
$746$	3.23471	+	9.95542i	0.118431	+	0.364494i
$747$		0			0
$748$	−1.69967	−	1.23488i	−0.0621459	−	0.0451517i
$749$	26.9582			0.985032
$750$		0			0
$751$	48.4856			1.76926			0.884632	−	0.466290i	$-0.154410\pi$
$751$	48.4856			1.76926			0.884632	+	0.466290i	$0.154410\pi$
$752$	32.0203	+	23.2641i	1.16766	+	0.848354i
$753$		0			0
$754$	1.56361	+	4.81230i	0.0569434	+	0.175254i
$755$	−0.267074	−	11.1696i	−0.00971982	−	0.406503i
$756$		0			0
$757$	24.0272			0.873285			0.436643	−	0.899635i	$-0.356167\pi$
$757$	24.0272			0.873285			0.436643	+	0.899635i	$0.356167\pi$
$758$	2.49858	−	7.68984i	0.0907526	−	0.279308i
$759$		0			0
$760$	−9.62255	+	13.9329i	−0.349047	+	0.505400i
$761$	30.3963	+	22.0842i	1.10186	+	0.800551i	0.981363	−	0.192163i	$-0.0615501\pi$
$761$	30.3963	+	22.0842i	1.10186	+	0.800551i	0.120500	+	0.992713i	$0.461550\pi$
$762$		0			0
$763$	−43.4564	+	31.5729i	−1.57323	+	1.14302i
$764$	−3.86360	−	2.80707i	−0.139780	−	0.101556i
$765$		0			0
$766$	−10.1388	+	7.36626i	−0.366329	+	0.266154i
$767$	5.07708	−	15.6256i	0.183323	−	0.564209i
$768$		0			0
$769$	10.9434	−	33.6804i	0.394629	−	1.21454i	−0.534620	−	0.845092i	$-0.679545\pi$
$769$	10.9434	−	33.6804i	0.394629	−	1.21454i	0.929250	−	0.369452i	$-0.120455\pi$
$770$	0.465024	−	0.163485i	0.0167583	−	0.00589158i
$771$		0			0
$772$	4.35263	+	13.3960i	0.156654	+	0.482133i
$773$	31.6828	+	23.0189i	1.13955	+	0.827932i	0.987057	−	0.160372i	$-0.0512695\pi$
$773$	31.6828	+	23.0189i	1.13955	+	0.827932i	0.152494	+	0.988304i	$0.451270\pi$
$774$		0			0
$775$	6.56175	−	24.0508i	0.235705	−	0.863929i
$776$	24.2479			0.870448
$777$		0			0
$778$	1.11262	+	3.42428i	0.0398892	+	0.122766i
$779$	4.59417	+	14.1394i	0.164603	+	0.506597i
$780$		0			0
$781$	0.344278	−	1.05958i	0.0123192	−	0.0379147i
$782$	8.01255			0.286528
$783$		0			0
$784$	−6.94900	+	5.04874i	−0.248179	+	0.180312i
$785$	−0.490038	−	20.4944i	−0.0174902	−	0.731476i
$786$		0			0
$787$	−22.5240	+	16.3646i	−0.802894	+	0.583336i	−0.911762	−	0.410720i	$-0.865277\pi$
$787$	−22.5240	+	16.3646i	−0.802894	+	0.583336i	0.108868	+	0.994056i	$0.465277\pi$
$788$	−33.0775	+	24.0322i	−1.17834	+	0.856112i
$789$		0			0
$790$	10.3386	+	3.08801i	0.367830	+	0.109867i
$791$	16.6658	−	12.1084i	0.592567	−	0.430525i
$792$		0			0
$793$	7.21072			0.256060
$794$	2.15777	−	6.64095i	0.0765765	−	0.235678i
$795$		0			0
$796$	2.07917	+	6.39904i	0.0736944	+	0.226808i
$797$	13.4033	+	41.2510i	0.474768	+	1.46119i	0.846270	+	0.532754i	$0.178843\pi$
$797$	13.4033	+	41.2510i	0.474768	+	1.46119i	−0.371502	+	0.928432i	$0.621157\pi$
$798$		0			0
$799$	−84.2413			−2.98024
$800$	−21.5194	+	1.02968i	−0.760825	+	0.0364047i
$801$		0			0
$802$	9.31057	+	6.76453i	0.328768	+	0.238864i
$803$	−0.238889	−	0.735226i	−0.00843022	−	0.0259456i
$804$		0			0
$805$	12.2010	−	17.6664i	0.430030	−	0.622660i
$806$	−0.776600	+	2.39013i	−0.0273546	+	0.0841887i
$807$		0			0
$808$	−4.33773	+	13.3502i	−0.152601	+	0.469657i
$809$	24.3361	−	17.6812i	0.855610	−	0.621637i	−0.0710771	−	0.997471i	$-0.522644\pi$
$809$	24.3361	−	17.6812i	0.855610	−	0.621637i	0.926687	+	0.375834i	$0.122644\pi$
$810$		0			0
$811$	9.15958	+	6.65482i	0.321636	+	0.233682i	0.736873	−	0.676031i	$-0.236301\pi$
$811$	9.15958	+	6.65482i	0.321636	+	0.233682i	−0.415237	+	0.909713i	$0.636301\pi$
$812$	−46.7721	+	33.9819i	−1.64138	+	1.19253i
$813$		0			0
$814$	−0.121259	−	0.0880999i	−0.00425013	−	0.00308790i
$815$	−2.69065	−	3.52308i	−0.0942493	−	0.123408i
$816$		0			0
$817$	10.2182	−	31.4484i	0.357490	−	1.10024i
$818$	10.1018			0.353202
$819$		0			0
$820$	−7.06744	+	10.2333i	−0.246806	+	0.357361i
$821$	2.61215	+	8.03936i	0.0911646	+	0.280576i	0.986235	−	0.165349i	$-0.0528750\pi$
$821$	2.61215	+	8.03936i	0.0911646	+	0.280576i	−0.895071	+	0.445924i	$0.852875\pi$
$822$		0			0
$823$	−38.6008	−	28.0451i	−1.34554	−	0.977592i	−0.999221	−	0.0394752i	$-0.987431\pi$
$823$	−38.6008	−	28.0451i	−1.34554	−	0.977592i	−0.346319	−	0.938117i	$-0.612569\pi$
$824$	−21.4450			−0.747073
$825$		0			0
$826$	−16.4371			−0.571919
$827$	−25.6273	−	18.6193i	−0.891149	−	0.647458i	0.0450282	−	0.998986i	$-0.485662\pi$
$827$	−25.6273	−	18.6193i	−0.891149	−	0.647458i	−0.936177	+	0.351528i	$0.885662\pi$
$828$		0			0
$829$	9.23512	+	28.4228i	0.320749	+	0.987164i	0.973323	+	0.229439i	$0.0736891\pi$
$829$	9.23512	+	28.4228i	0.320749	+	0.987164i	−0.652574	+	0.757725i	$0.726311\pi$
$830$	4.07821	+	5.33993i	0.141557	+	0.185352i
$831$		0			0
$832$	−5.51498			−0.191197
$833$	5.64943	−	17.3871i	0.195741	−	0.602429i
$834$		0			0
$835$	−29.2056	−	8.72338i	−1.01070	−	0.301885i
$836$	1.28292	+	0.932095i	0.0443707	+	0.0322372i
$837$		0			0
$838$	8.56596	−	6.22354i	0.295906	−	0.214988i
$839$	3.45865	+	2.51285i	0.119406	+	0.0867533i	0.645885	−	0.763434i	$-0.276488\pi$
$839$	3.45865	+	2.51285i	0.119406	+	0.0867533i	−0.526480	+	0.850188i	$0.676488\pi$
$840$		0			0
$841$	−58.0688	+	42.1894i	−2.00237	+	1.45481i
$842$	−3.28290	+	10.1037i	−0.113136	+	0.348197i
$843$		0			0
$844$	1.54689	−	4.76085i	0.0532463	−	0.163875i
$845$	24.4725	+	7.30966i	0.841881	+	0.251460i
$846$		0			0
$847$	10.6153	+	32.6704i	0.364745	+	1.12257i
$848$	−11.0328	−	8.01578i	−0.378867	−	0.275263i
$849$		0			0
$850$	10.1919	−	8.17682i	0.349581	−	0.280463i
$851$	−6.52848			−0.223793
$852$		0			0
$853$	−9.35118	−	28.7800i	−0.320178	−	0.985407i	−0.973570	−	0.228387i	$-0.926655\pi$
$853$	−9.35118	−	28.7800i	−0.320178	−	0.985407i	0.653392	−	0.757020i	$-0.273345\pi$
$854$	−2.22922	−	6.86084i	−0.0762825	−	0.234773i
$855$		0			0
$856$	4.09789	−	12.6120i	0.140063	−	0.431069i
$857$	44.1250			1.50728			0.753641	−	0.657287i	$-0.228296\pi$
$857$	44.1250			1.50728			0.753641	+	0.657287i	$0.228296\pi$
$858$		0			0
$859$	18.1105	−	13.1580i	0.617921	−	0.448946i	−0.234274	−	0.972171i	$-0.575271\pi$
$859$	18.1105	−	13.1580i	0.617921	−	0.448946i	0.852195	+	0.523225i	$0.175271\pi$
$860$	26.0954	−	9.17413i	0.889844	−	0.312835i
$861$		0			0
$862$	−12.5861	+	9.14435i	−0.428685	+	0.311458i
$863$	−26.0788	+	18.9474i	−0.887733	+	0.644975i	−0.935286	−	0.353893i	$-0.884858\pi$
$863$	−26.0788	+	18.9474i	−0.887733	+	0.644975i	0.0475533	+	0.998869i	$0.484858\pi$
$864$		0			0
$865$	−13.1795	+	19.0832i	−0.448116	+	0.648847i
$866$	−5.68011	+	4.12684i	−0.193018	+	0.140236i
$867$		0			0
$868$	−28.7143			−0.974626
$869$	0.651856	−	2.00621i	0.0221127	−	0.0680559i
$870$		0			0
$871$	−2.75814	−	8.48869i	−0.0934561	−	0.287628i
$872$	8.16517	+	25.1298i	0.276507	+	0.851002i
$873$		0			0
$874$	−6.04792			−0.204574
$875$	−2.50893	−	34.9228i	−0.0848172	−	1.18061i
$876$		0			0
$877$	−23.0634	−	16.7565i	−0.778796	−	0.565828i	0.125822	−	0.992053i	$-0.459843\pi$
$877$	−23.0634	−	16.7565i	−0.778796	−	0.565828i	−0.904617	+	0.426225i	$0.859843\pi$
$878$	−3.81310	−	11.7355i	−0.128686	−	0.396055i
$879$		0			0
$880$	0.0286898	+	1.19987i	0.000967133	+	0.0404475i
$881$	−13.8943	+	42.7623i	−0.468111	+	1.44070i	0.386916	+	0.922115i	$0.373540\pi$
$881$	−13.8943	+	42.7623i	−0.468111	+	1.44070i	−0.855027	+	0.518583i	$0.826460\pi$
$882$		0			0
$883$	−12.2121	+	37.5850i	−0.410970	+	1.26484i	0.504836	+	0.863215i	$0.331553\pi$
$883$	−12.2121	+	37.5850i	−0.410970	+	1.26484i	−0.915806	+	0.401620i	$0.868447\pi$
$884$	12.1704	−	8.84235i	0.409336	−	0.297400i
$885$		0			0
$886$	−3.47515	−	2.52485i	−0.116750	−	0.0848239i
$887$	−19.9546	+	14.4979i	−0.670011	+	0.486791i	−0.870029	−	0.493001i	$-0.835900\pi$
$887$	−19.9546	+	14.4979i	−0.670011	+	0.486791i	0.200018	+	0.979792i	$0.435900\pi$
$888$		0			0
$889$	−4.07657	−	2.96180i	−0.136724	−	0.0993356i
$890$	6.74853	−	2.37253i	0.226211	−	0.0795273i
$891$		0			0
$892$	1.47947	−	4.55333i	0.0495362	−	0.152457i
$893$	63.5858			2.12782
$894$		0			0
$895$	−13.9329	+	4.89829i	−0.465727	+	0.163732i
$896$	10.0445	+	30.9138i	0.335563	+	1.03276i
$897$		0			0
$898$	−6.81564	−	4.95185i	−0.227441	−	0.165245i
$899$	−50.0530			−1.66936
$900$		0			0
$901$	29.0258			0.966990
$902$	−0.172234	−	0.125136i	−0.00573478	−	0.00416656i
$903$		0			0
$904$	−3.13139	−	9.63742i	−0.104148	−	0.320536i
$905$	22.3754	+	6.68328i	0.743785	+	0.222160i
$906$		0			0
$907$	−2.08739			−0.0693106			−0.0346553	−	0.999399i	$-0.511033\pi$
$907$	−2.08739			−0.0693106			−0.0346553	+	0.999399i	$0.511033\pi$
$908$	−2.64010	+	8.12539i	−0.0876148	+	0.269651i
$909$		0			0
$910$	0.0843711	+	3.52857i	0.00279687	+	0.116971i
$911$	−21.2023	−	15.4044i	−0.702464	−	0.510370i	0.178269	−	0.983982i	$-0.442950\pi$
$911$	−21.2023	−	15.4044i	−0.702464	−	0.510370i	−0.880734	+	0.473611i	$0.842950\pi$
$912$		0			0
$913$	1.06273	−	0.772117i	0.0351712	−	0.0255533i
$914$	−5.99414	−	4.35500i	−0.198268	−	0.144050i
$915$		0			0
$916$	6.24039	−	4.53391i	0.206188	−	0.149804i
$917$	0.218052	−	0.671095i	0.00720071	−	0.0221615i
$918$		0			0
$919$	2.15025	−	6.61779i	0.0709303	−	0.218301i	−0.909307	−	0.416126i	$-0.863388\pi$
$919$	2.15025	−	6.61779i	0.0709303	−	0.218301i	0.980237	+	0.197825i	$0.0633877\pi$
$920$	−6.41031	−	8.39352i	−0.211342	−	0.276726i
$921$		0			0
$922$	3.83919	+	11.8158i	0.126437	+	0.389133i
$923$	6.45398	+	4.68909i	0.212435	+	0.154343i
$924$		0			0
$925$	−8.30421	+	6.66232i	−0.273041	+	0.219056i
$926$	1.44073			0.0473452
$927$		0			0
$928$	13.3665	+	41.1380i	0.438778	+	1.35042i
$929$	−14.2008	−	43.7057i	−0.465915	−	1.43394i	−0.857828	−	0.513936i	$-0.828187\pi$
$929$	−14.2008	−	43.7057i	−0.465915	−	1.43394i	0.391914	−	0.920002i	$-0.371813\pi$
$930$		0			0
$931$	−4.26422	+	13.1239i	−0.139754	+	0.430120i
$932$	15.5047			0.507875
$933$		0			0
$934$	4.44535	−	3.22973i	0.145456	−	0.105680i
$935$	−1.55050	−	2.03019i	−0.0507068	−	0.0663944i
$936$		0			0
$937$	−7.99113	+	5.80589i	−0.261059	+	0.189670i	−0.710614	−	0.703582i	$-0.751583\pi$
$937$	−7.99113	+	5.80589i	−0.261059	+	0.189670i	0.449555	+	0.893253i	$0.351583\pi$
$938$	−7.22411	+	5.24863i	−0.235876	+	0.171374i
$939$		0			0
$940$	32.2845	+	42.2726i	1.05300	+	1.37878i
$941$	−8.80946	+	6.40044i	−0.287180	+	0.208649i	−0.722043	−	0.691848i	$-0.756797\pi$
$941$	−8.80946	+	6.40044i	−0.287180	+	0.208649i	0.434863	+	0.900497i	$0.356797\pi$
$942$		0			0
$943$	−9.27294			−0.301969
$944$	12.3675	−	38.0634i	0.402529	−	1.23886i
$945$		0			0
$946$	0.146323	+	0.450335i	0.00475736	+	0.0146417i
$947$	−5.19354	−	15.9841i	−0.168767	−	0.519413i	0.830527	−	0.556979i	$-0.188040\pi$
$947$	−5.19354	−	15.9841i	−0.168767	−	0.519413i	−0.999294	+	0.0375662i	$0.988040\pi$
$948$		0			0
$949$	5.53551			0.179690
$950$	−7.69295	+	6.17192i	−0.249592	+	0.200243i
$951$		0			0
$952$	−25.4178	−	18.4671i	−0.823796	−	0.598523i
$953$	−4.21199	−	12.9632i	−0.136440	−	0.419918i	0.859371	−	0.511352i	$-0.170855\pi$
$953$	−4.21199	−	12.9632i	−0.136440	−	0.419918i	−0.995811	+	0.0914335i	$0.970855\pi$
$954$		0			0
$955$	−3.52452	−	4.61493i	−0.114051	−	0.149336i
$956$	16.7600	−	51.5818i	0.542056	−	1.66828i
$957$		0			0
$958$	−0.682109	+	2.09931i	−0.0220379	+	0.0678258i
$959$	1.73829	−	1.26294i	0.0561322	−	0.0407824i
$960$		0			0
$961$	4.96750	+	3.60910i	0.160242	+	0.116423i
$962$	0.868275	−	0.630839i	0.0279943	−	0.0203391i
$963$		0			0
$964$	18.6054	+	13.5176i	0.599241	+	0.435374i
$965$	0.409400	+	17.1220i	0.0131791	+	0.551175i
$966$		0			0
$967$	3.78631	−	11.6531i	0.121760	−	0.374738i	−0.871537	−	0.490329i	$-0.836876\pi$
$967$	3.78631	−	11.6531i	0.121760	−	0.374738i	0.993297	+	0.115592i	$0.0368765\pi$
$968$	16.8980			0.543122
$969$		0			0
$970$	13.5328	+	4.04208i	0.434511	+	0.129783i
$971$	−10.3855	−	31.9633i	−0.333287	−	1.02575i	−0.967560	−	0.252643i	$-0.918700\pi$
$971$	−10.3855	−	31.9633i	−0.333287	−	1.02575i	0.634272	−	0.773110i	$-0.281300\pi$
$972$		0			0
$973$	22.5403	+	16.3765i	0.722610	+	0.525007i
$974$	−1.83876			−0.0589177
$975$		0			0
$976$	17.5650			0.562242
$977$	4.23117	+	3.07413i	0.135367	+	0.0983500i	0.653408	−	0.757006i	$-0.273339\pi$
$977$	4.23117	+	3.07413i	0.135367	+	0.0983500i	−0.518041	+	0.855356i	$0.673339\pi$
$978$		0			0
$979$	−0.432164	−	1.33006i	−0.0138120	−	0.0425090i
$980$	−10.8900	+	3.82852i	−0.347869	+	0.122297i
$981$		0			0
$982$	6.14680			0.196152
$983$	−1.72718	+	5.31573i	−0.0550886	+	0.169545i	−0.974815	−	0.223014i	$-0.928410\pi$
$983$	−1.72718	+	5.31573i	−0.0550886	+	0.169545i	0.919727	+	0.392560i	$0.128410\pi$
$984$		0			0
$985$	−46.9006	+	16.4885i	−1.49438	+	0.525366i
$986$	−21.2242	−	15.4203i	−0.675916	−	0.491081i
$987$		0			0
$988$	−9.18633	+	6.67426i	−0.292256	+	0.212337i
$989$	16.6856	+	12.1228i	0.530572	+	0.385483i
$990$		0			0
$991$	−3.39886	+	2.46942i	−0.107968	+	0.0784436i	−0.640459	−	0.767992i	$-0.721256\pi$
$991$	−3.39886	+	2.46942i	−0.107968	+	0.0784436i	0.532491	+	0.846436i	$0.321256\pi$
$992$	−6.63877	+	20.4320i	−0.210781	+	0.648718i
$993$		0			0
$994$	2.46629	−	7.59047i	0.0782261	−	0.240755i
$995$	0.195563	+	8.17887i	0.00619978	+	0.259287i
$996$		0			0
$997$	2.87931	+	8.86160i	0.0911886	+	0.280650i	0.986242	−	0.165310i	$-0.0528625\pi$
$997$	2.87931	+	8.86160i	0.0911886	+	0.280650i	−0.895053	+	0.445960i	$0.852862\pi$
$998$	−3.42216	−	2.48634i	−0.108327	−	0.0787039i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.h.b.541.5	yes	40
3.2	odd	2	inner	675.2.h.b.541.6	yes	40
25.11	even	5	inner	675.2.h.b.136.5	✓	40
75.11	odd	10	inner	675.2.h.b.136.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.h.b.136.5	✓	40	25.11	even	5	inner
675.2.h.b.136.6	yes	40	75.11	odd	10	inner
675.2.h.b.541.5	yes	40	1.1	even	1	trivial
675.2.h.b.541.6	yes	40	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.324639 - 0.235864i) q^{2} +(-0.568275 - 1.74897i) q^{4} +(-0.0534510 - 2.23543i) q^{5} -3.13164 q^{7} +(-0.476037 + 1.46509i) q^{8} +O(q^{10})\)	\(q+(-0.324639 - 0.235864i) q^{2} +(-0.568275 - 1.74897i) q^{4} +(-0.0534510 - 2.23543i) q^{5} -3.13164 q^{7} +(-0.476037 + 1.46509i) q^{8} +(-0.509905 + 0.738315i) q^{10} +(0.141918 + 0.103109i) q^{11} +(-1.01620 + 0.738315i) q^{13} +(1.01665 + 0.738642i) q^{14} +(-2.47543 + 1.79850i) q^{16} +(2.01248 - 6.19378i) q^{17} +(-1.51903 + 4.67511i) q^{19} +(-3.87933 + 1.36382i) q^{20} +(-0.0217523 - 0.0669467i) q^{22} +(-2.48048 - 1.80217i) q^{23} +(-4.99429 + 0.238972i) q^{25} +0.504041 q^{26} +(1.77964 + 5.47716i) q^{28} +(3.10215 + 9.54744i) q^{29} +(-1.54075 + 4.74193i) q^{31} +4.30880 q^{32} +(-2.11422 + 1.53607i) q^{34} +(0.167389 + 7.00057i) q^{35} +(1.72263 - 1.25156i) q^{37} +(1.59583 - 1.15944i) q^{38} +(3.30055 + 0.985837i) q^{40} +(2.44679 - 1.77770i) q^{41} -6.72677 q^{43} +(0.0996870 - 0.306805i) q^{44} +(0.380192 + 1.17011i) q^{46} +(-3.99722 - 12.3022i) q^{47} +2.80719 q^{49} +(1.67770 + 1.10039i) q^{50} +(1.86877 + 1.35774i) q^{52} +(1.37726 + 4.23878i) q^{53} +(0.222908 - 0.322759i) q^{55} +(1.49078 - 4.58815i) q^{56} +(1.24482 - 3.83116i) q^{58} +(-10.5820 + 7.68825i) q^{59} +(-4.64423 - 3.37423i) q^{61} +(1.61864 - 1.17601i) q^{62} +(3.55205 + 2.58071i) q^{64} +(1.70477 + 2.23219i) q^{65} +(-2.19581 + 6.75799i) q^{67} -11.9764 q^{68} +(1.59684 - 2.31214i) q^{70} +(-1.96259 - 6.04023i) q^{71} +(-3.56527 - 2.59032i) q^{73} -0.854431 q^{74} +9.03986 q^{76} +(-0.444437 - 0.322902i) q^{77} +(-3.71597 - 11.4366i) q^{79} +(4.15274 + 5.43751i) q^{80} -1.21362 q^{82} +(2.31402 - 7.12182i) q^{83} +(-13.9533 - 4.16770i) q^{85} +(2.18377 + 1.58660i) q^{86} +(-0.218623 + 0.158839i) q^{88} +(-6.44977 - 4.68603i) q^{89} +(3.18239 - 2.31214i) q^{91} +(-1.74236 + 5.36242i) q^{92} +(-1.60399 + 4.93656i) q^{94} +(10.5321 + 3.14580i) q^{95} +(-4.86404 - 14.9700i) q^{97} +(-0.911325 - 0.662116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 16 q^{4} + 20 q^{7}+O(q^{10}) \) 40 * q - 16 * q^4 + 20 * q^7	\( 40 q - 16 q^{4} + 20 q^{7} + 20 q^{10} - 8 q^{13} - 12 q^{16} + 2 q^{19} - 8 q^{22} - 30 q^{28} - 2 q^{31} - 6 q^{34} + 2 q^{37} - 50 q^{40} + 40 q^{43} - 36 q^{46} - 28 q^{49} - 30 q^{52} - 30 q^{55} - 52 q^{58} - 28 q^{61} + 46 q^{64} - 10 q^{67} + 60 q^{70} - 46 q^{73} + 260 q^{76} - 42 q^{79} + 136 q^{82} + 100 q^{85} - 68 q^{88} - 56 q^{91} + 182 q^{94} - 58 q^{97}+O(q^{100}) \) 40 * q - 16 * q^4 + 20 * q^7 + 20 * q^10 - 8 * q^13 - 12 * q^16 + 2 * q^19 - 8 * q^22 - 30 * q^28 - 2 * q^31 - 6 * q^34 + 2 * q^37 - 50 * q^40 + 40 * q^43 - 36 * q^46 - 28 * q^49 - 30 * q^52 - 30 * q^55 - 52 * q^58 - 28 * q^61 + 46 * q^64 - 10 * q^67 + 60 * q^70 - 46 * q^73 + 260 * q^76 - 42 * q^79 + 136 * q^82 + 100 * q^85 - 68 * q^88 - 56 * q^91 + 182 * q^94 - 58 * q^97

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