LMFDB - Embedded newform 756.2.ck.a.605.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, 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 $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			605.9
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573178 + 1.63446i) q^{3} +(-0.0962103 - 0.545636i) q^{5} +(2.05240 + 1.66962i) q^{7} +(-2.34293 - 1.87368i) q^{9} +O(q^{10})$	\(q+(-0.573178 + 1.63446i) q^{3} +(-0.0962103 - 0.545636i) q^{5} +(2.05240 + 1.66962i) q^{7} +(-2.34293 - 1.87368i) q^{9} +(4.15140 + 0.732003i) q^{11} +(0.321641 + 0.383316i) q^{13} +(0.946967 + 0.155495i) q^{15} -0.634761 q^{17} +3.87297i q^{19} +(-3.90533 + 2.39759i) q^{21} +(0.0380538 + 0.0453508i) q^{23} +(4.41000 - 1.60511i) q^{25} +(4.40537 - 2.75548i) q^{27} +(0.935412 - 1.11478i) q^{29} +(-1.96410 + 5.39632i) q^{31} +(-3.57592 + 6.36573i) q^{33} +(0.713543 - 1.28050i) q^{35} +(-4.65406 + 8.06107i) q^{37} +(-0.810873 + 0.306001i) q^{39} +(-3.38733 + 2.84230i) q^{41} +(-2.15999 + 0.786173i) q^{43} +(-0.796931 + 1.45866i) q^{45} +(-1.12989 + 0.411247i) q^{47} +(1.42472 + 6.85348i) q^{49} +(0.363831 - 1.03749i) q^{51} +(1.86398 + 1.07617i) q^{53} -2.33558i q^{55} +(-6.33022 - 2.21990i) q^{57} +(6.19145 - 5.19525i) q^{59} +(1.28793 + 3.53855i) q^{61} +(-1.68031 - 7.75735i) q^{63} +(0.178206 - 0.212378i) q^{65} +(0.512180 + 2.90472i) q^{67} +(-0.0959358 + 0.0362035i) q^{69} +(4.37928 - 2.52838i) q^{71} +(-9.70247 + 5.60172i) q^{73} +(0.0957728 + 8.12799i) q^{75} +(7.29817 + 8.43363i) q^{77} +(1.31483 - 7.45679i) q^{79} +(1.97867 + 8.77980i) q^{81} +(-8.98967 - 7.54323i) q^{83} +(0.0610706 + 0.346349i) q^{85} +(1.28591 + 2.16786i) q^{87} -12.2440 q^{89} +(0.0201431 + 1.32374i) q^{91} +(-7.69431 - 6.30331i) q^{93} +(2.11323 - 0.372620i) q^{95} +(-0.237892 - 0.653602i) q^{97} +(-8.35491 - 9.49341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.573178	+	1.63446i	−0.330925	+	0.943657i
$3$	−0.573178	+	1.63446i	−0.330925	+	0.943657i
$4$		0			0
$5$	−0.0962103	−	0.545636i	−0.0430266	−	0.244016i	0.955707	−	0.294318i	$-0.0950926\pi$
$5$	−0.0962103	−	0.545636i	−0.0430266	−	0.244016i	−0.998734	+	0.0503025i	$0.983981\pi$
$6$		0			0
$7$	2.05240	+	1.66962i	0.775736	+	0.631058i
$7$	2.05240	+	1.66962i	0.775736	+	0.631058i
$8$		0			0
$9$	−2.34293	−	1.87368i	−0.780978	−	0.624559i
$10$		0			0
$11$	4.15140	+	0.732003i	1.25169	+	0.220707i	0.759920	−	0.650016i	$-0.225238\pi$
$11$	4.15140	+	0.732003i	1.25169	+	0.220707i	0.491773	+	0.870724i	$0.336349\pi$
$12$		0			0
$13$	0.321641	+	0.383316i	0.0892070	+	0.106313i	0.808801	−	0.588082i	$-0.200117\pi$
$13$	0.321641	+	0.383316i	0.0892070	+	0.106313i	−0.719594	+	0.694395i	$0.755672\pi$
$14$		0			0
$15$	0.946967	+	0.155495i	0.244506	+	0.0401485i
$16$		0			0
$17$	−0.634761			−0.153952			−0.0769761	−	0.997033i	$-0.524527\pi$
$17$	−0.634761			−0.153952			−0.0769761	+	0.997033i	$0.524527\pi$
$18$		0			0
$19$			3.87297i			0.888520i	0.895898	+	0.444260i	$0.146533\pi$
$19$			3.87297i			0.888520i	−0.895898	+	0.444260i	$0.853467\pi$
$20$		0			0
$21$	−3.90533	+	2.39759i	−0.852212	+	0.523196i
$22$		0			0
$23$	0.0380538	+	0.0453508i	0.00793477	+	0.00945630i	0.769997	−	0.638047i	$-0.220258\pi$
$23$	0.0380538	+	0.0453508i	0.00793477	+	0.00945630i	−0.762062	+	0.647504i	$0.775813\pi$
$24$		0			0
$25$	4.41000	−	1.60511i	0.882000	−	0.321022i
$26$		0			0
$27$	4.40537	−	2.75548i	0.847814	−	0.530293i
$28$		0			0
$29$	0.935412	−	1.11478i	0.173702	−	0.207009i	−0.672169	−	0.740398i	$-0.734637\pi$
$29$	0.935412	−	1.11478i	0.173702	−	0.207009i	0.845870	+	0.533388i	$0.179082\pi$
$30$		0			0
$31$	−1.96410	+	5.39632i	−0.352763	+	0.969208i	0.628715	+	0.777635i	$0.283581\pi$
$31$	−1.96410	+	5.39632i	−0.352763	+	0.969208i	−0.981478	+	0.191573i	$0.938641\pi$
$32$		0			0
$33$	−3.57592	+	6.36573i	−0.622488	+	1.10813i
$34$		0			0
$35$	0.713543	−	1.28050i	0.120611	−	0.216444i
$36$		0			0
$37$	−4.65406	+	8.06107i	−0.765122	+	1.32523i	0.175059	+	0.984558i	$0.443988\pi$
$37$	−4.65406	+	8.06107i	−0.765122	+	1.32523i	−0.940182	+	0.340673i	$0.889345\pi$
$38$		0			0
$39$	−0.810873	+	0.306001i	−0.129844	+	0.0489993i
$40$		0			0
$41$	−3.38733	+	2.84230i	−0.529012	+	0.443893i	−0.867760	−	0.496984i	$-0.834441\pi$
$41$	−3.38733	+	2.84230i	−0.529012	+	0.443893i	0.338748	+	0.940877i	$0.389996\pi$
$42$		0			0
$43$	−2.15999	+	0.786173i	−0.329396	+	0.119890i	−0.501424	−	0.865202i	$-0.667190\pi$
$43$	−2.15999	+	0.786173i	−0.329396	+	0.119890i	0.172028	+	0.985092i	$0.444968\pi$
$44$		0			0
$45$	−0.796931	+	1.45866i	−0.118799	+	0.217444i
$46$		0			0
$47$	−1.12989	+	0.411247i	−0.164812	+	0.0599866i	−0.423108	−	0.906079i	$-0.639061\pi$
$47$	−1.12989	+	0.411247i	−0.164812	+	0.0599866i	0.258297	+	0.966066i	$0.416839\pi$
$48$		0			0
$49$	1.42472	+	6.85348i	0.203532	+	0.979068i
$50$		0			0
$51$	0.363831	−	1.03749i	0.0509466	−	0.145278i
$52$		0			0
$53$	1.86398	+	1.07617i	0.256037	+	0.147823i	0.622526	−	0.782599i	$-0.286107\pi$
$53$	1.86398	+	1.07617i	0.256037	+	0.147823i	−0.366488	+	0.930423i	$0.619440\pi$
$54$		0			0
$55$		−	2.33558i		−	0.314929i
$56$		0			0
$57$	−6.33022	−	2.21990i	−0.838459	−	0.294033i
$58$		0			0
$59$	6.19145	−	5.19525i	0.806058	−	0.676363i	−0.143605	−	0.989635i	$-0.545870\pi$
$59$	6.19145	−	5.19525i	0.806058	−	0.676363i	0.949664	+	0.313272i	$0.101425\pi$
$60$		0			0
$61$	1.28793	+	3.53855i	0.164902	+	0.453065i	0.994430	−	0.105400i	$-0.0336124\pi$
$61$	1.28793	+	3.53855i	0.164902	+	0.453065i	−0.829528	+	0.558466i	$0.811390\pi$
$62$		0			0
$63$	−1.68031	−	7.75735i	−0.211700	−	0.977335i
$64$		0			0
$65$	0.178206	−	0.212378i	0.0221037	−	0.0263422i
$66$		0			0
$67$	0.512180	+	2.90472i	0.0625728	+	0.354868i	0.999978	+	0.00662750i	$0.00210961\pi$
$67$	0.512180	+	2.90472i	0.0625728	+	0.354868i	−0.937405	+	0.348240i	$0.886779\pi$
$68$		0			0
$69$	−0.0959358	+	0.0362035i	−0.0115493	+	0.00435838i
$70$		0			0
$71$	4.37928	−	2.52838i	0.519724	−	0.300063i	−0.217098	−	0.976150i	$-0.569659\pi$
$71$	4.37928	−	2.52838i	0.519724	−	0.300063i	0.736822	+	0.676087i	$0.236326\pi$
$72$		0			0
$73$	−9.70247	+	5.60172i	−1.13559	+	0.655632i	−0.945334	−	0.326103i	$-0.894264\pi$
$73$	−9.70247	+	5.60172i	−1.13559	+	0.655632i	−0.190254	+	0.981735i	$0.560931\pi$
$74$		0			0
$75$	0.0957728	+	8.12799i	0.0110589	+	0.938540i
$76$		0			0
$77$	7.29817	+	8.43363i	0.831704	+	0.961101i
$78$		0			0
$79$	1.31483	−	7.45679i	0.147930	−	0.838954i	−0.817037	−	0.576585i	$-0.804385\pi$
$79$	1.31483	−	7.45679i	0.147930	−	0.838954i	0.964968	−	0.262369i	$-0.0845038\pi$
$80$		0			0
$81$	1.97867	+	8.77980i	0.219852	+	0.975533i
$82$		0			0
$83$	−8.98967	−	7.54323i	−0.986745	−	0.827977i	−0.00165153	−	0.999999i	$-0.500526\pi$
$83$	−8.98967	−	7.54323i	−0.986745	−	0.827977i	−0.985093	+	0.172021i	$0.944970\pi$
$84$		0			0
$85$	0.0610706	+	0.346349i	0.00662404	+	0.0375668i
$86$		0			0
$87$	1.28591	+	2.16786i	0.137864	+	0.232419i
$88$		0			0
$89$	−12.2440			−1.29786			−0.648930	−	0.760848i	$-0.724783\pi$
$89$	−12.2440			−1.29786			−0.648930	+	0.760848i	$0.724783\pi$
$90$		0			0
$91$	0.0201431	+	1.32374i	0.00211157	+	0.138765i
$92$		0			0
$93$	−7.69431	−	6.30331i	−0.797862	−	0.653622i
$94$		0			0
$95$	2.11323	−	0.372620i	0.216813	−	0.0382300i
$96$		0			0
$97$	−0.237892	−	0.653602i	−0.0241542	−	0.0663632i	0.927029	−	0.374988i	$-0.122353\pi$
$97$	−0.237892	−	0.653602i	−0.0241542	−	0.0663632i	−0.951184	+	0.308625i	$0.900131\pi$
$98$		0			0
$99$	−8.35491	−	9.49341i	−0.839700	−	0.954124i
$100$		0			0
$101$	14.9463	+	12.5414i	1.48721	+	1.24792i	0.898043	+	0.439907i	$0.144989\pi$
$101$	14.9463	+	12.5414i	1.48721	+	1.24792i	0.589168	+	0.808011i	$0.299456\pi$
$102$		0			0
$103$	10.0086	−	1.76479i	0.986180	−	0.173890i	0.342776	−	0.939417i	$-0.388633\pi$
$103$	10.0086	−	1.76479i	0.986180	−	0.173890i	0.643404	+	0.765527i	$0.277522\pi$
$104$		0			0
$105$	1.68394	+	1.90021i	0.164336	+	0.185442i
$106$		0			0
$107$	10.0981	−	5.83016i	0.976223	−	0.563622i	0.0750950	−	0.997176i	$-0.476074\pi$
$107$	10.0981	−	5.83016i	0.976223	−	0.563622i	0.901128	+	0.433554i	$0.142741\pi$
$108$		0			0
$109$	7.58999	−	13.1462i	0.726989	−	1.25918i	−0.231161	−	0.972916i	$-0.574252\pi$
$109$	7.58999	−	13.1462i	0.726989	−	1.25918i	0.958150	−	0.286266i	$-0.0924142\pi$
$110$		0			0
$111$	−10.5079	−	12.2273i	−0.997366	−	1.16056i
$112$		0			0
$113$	4.91686	−	13.5090i	0.462539	−	1.27082i	−0.461030	−	0.887384i	$-0.652520\pi$
$113$	4.91686	−	13.5090i	0.462539	−	1.27082i	0.923569	−	0.383431i	$-0.125258\pi$
$114$		0			0
$115$	0.0210839	−	0.0251268i	0.00196608	−	0.00234308i
$116$		0			0
$117$	−0.0353715	−	1.50073i	−0.00327009	−	0.138743i
$118$		0			0
$119$	−1.30279	−	1.05981i	−0.119426	−	0.0971527i
$120$		0			0
$121$	6.36164	+	2.31545i	0.578331	+	0.210495i
$122$		0			0
$123$	−2.70410	−	7.16561i	−0.243820	−	0.646101i
$124$		0			0
$125$	−2.68523	−	4.65095i	−0.240174	−	0.415993i
$126$		0			0
$127$	−3.46904	+	6.00855i	−0.307827	+	0.533173i	−0.977887	−	0.209135i	$-0.932935\pi$
$127$	−3.46904	+	6.00855i	−0.307827	+	0.533173i	0.670059	+	0.742307i	$0.266269\pi$
$128$		0			0
$129$	−0.0469089	−	3.98104i	−0.00413010	−	0.350511i
$130$		0			0
$131$	11.6409	−	9.76784i	1.01707	−	0.853420i	0.0278105	−	0.999613i	$-0.491147\pi$
$131$	11.6409	−	9.76784i	1.01707	−	0.853420i	0.989256	+	0.146193i	$0.0467021\pi$
$132$		0			0
$133$	−6.46640	+	7.94890i	−0.560708	+	0.689257i
$134$		0			0
$135$	−1.92733	−	2.13862i	−0.165878	−	0.184063i
$136$		0			0
$137$	0.0437366	+	0.120165i	0.00373667	+	0.0102664i	0.941547	−	0.336882i	$-0.109372\pi$
$137$	0.0437366	+	0.120165i	0.00373667	+	0.0102664i	−0.937810	+	0.347148i	$0.887150\pi$
$138$		0			0
$139$	0.0959082	−	0.0169112i	0.00813482	−	0.00143439i	−0.169579	−	0.985517i	$-0.554241\pi$
$139$	0.0959082	−	0.0169112i	0.00813482	−	0.00143439i	0.177714	+	0.984082i	$0.443130\pi$
$140$		0			0
$141$	−0.0245381	−	2.08248i	−0.00206648	−	0.175377i
$142$		0			0
$143$	1.05467	+	1.82674i	0.0881958	+	0.152760i
$144$		0			0
$145$	−0.698260	−	0.403141i	−0.0579874	−	0.0334790i
$146$		0			0
$147$	−12.0184	−	1.59961i	−0.991259	−	0.131933i
$148$		0			0
$149$	6.80797	−	18.7047i	0.557731	−	1.53235i	−0.265190	−	0.964196i	$-0.585435\pi$
$149$	6.80797	−	18.7047i	0.557731	−	1.53235i	0.822921	−	0.568156i	$-0.192343\pi$
$150$		0			0
$151$	1.05185	−	5.96535i	0.0855986	−	0.485454i	−0.911627	−	0.411018i	$-0.865173\pi$
$151$	1.05185	−	5.96535i	0.0855986	−	0.485454i	0.997226	−	0.0744357i	$-0.0237155\pi$
$152$		0			0
$153$	1.48720	+	1.18934i	0.120233	+	0.0961522i
$154$		0			0
$155$	3.13339	+	0.552502i	0.251680	+	0.0443780i
$156$		0			0
$157$	6.10649	+	7.27743i	0.487351	+	0.580802i	0.952542	−	0.304408i	$-0.0984587\pi$
$157$	6.10649	+	7.27743i	0.487351	+	0.580802i	−0.465191	+	0.885211i	$0.654014\pi$
$158$		0			0
$159$	−2.82735	+	2.42977i	−0.224224	+	0.192693i
$160$		0			0
$161$	0.00238316	+	0.156614i	0.000187819	+	0.0123429i
$162$		0			0
$163$	3.38072	+	5.85558i	0.264799	+	0.458644i	0.967511	−	0.252830i	$-0.0813612\pi$
$163$	3.38072	+	5.85558i	0.264799	+	0.458644i	−0.702712	+	0.711474i	$0.748028\pi$
$164$		0			0
$165$	3.81741	+	1.33870i	0.297185	+	0.104218i
$166$		0			0
$167$	8.41037	+	3.06112i	0.650814	+	0.236877i	0.646265	−	0.763113i	$-0.276330\pi$
$167$	8.41037	+	3.06112i	0.650814	+	0.236877i	0.00454856	+	0.999990i	$0.498552\pi$
$168$		0			0
$169$	2.21395	−	12.5559i	0.170304	−	0.965840i
$170$		0			0
$171$	7.25670	−	9.07411i	0.554933	−	0.693915i
$172$		0			0
$173$	−11.0188	−	9.24588i	−0.837744	−	0.702951i	0.119311	−	0.992857i	$-0.461931\pi$
$173$	−11.0188	−	9.24588i	−0.837744	−	0.702951i	−0.957055	+	0.289906i	$0.906376\pi$
$174$		0			0
$175$	11.7310	+	4.06870i	0.886782	+	0.307565i
$176$		0			0
$177$	4.94263	+	13.0975i	0.371510	+	0.984468i
$178$		0			0
$179$		−	21.7169i		−	1.62320i	−0.584214	−	0.811600i	$-0.698597\pi$
$179$		−	21.7169i		−	1.62320i	0.584214	−	0.811600i	$-0.301403\pi$
$180$		0			0
$181$	−1.00514	−	0.580317i	−0.0747114	−	0.0431346i	0.462179	−	0.886787i	$-0.347068\pi$
$181$	−1.00514	−	0.580317i	−0.0747114	−	0.0431346i	−0.536890	+	0.843652i	$0.680401\pi$
$182$		0			0
$183$	−6.52184	+	0.0768474i	−0.482109	+	0.00568072i
$184$		0			0
$185$	4.84618	+	1.76386i	0.356298	+	0.129682i
$186$		0			0
$187$	−2.63515	−	0.464647i	−0.192701	−	0.0339784i
$188$		0			0
$189$	13.6422	+	1.69994i	0.992326	+	0.123652i
$190$		0			0
$191$	−10.4123	−	1.83597i	−0.753406	−	0.132846i	−0.216261	−	0.976336i	$-0.569386\pi$
$191$	−10.4123	−	1.83597i	−0.753406	−	0.132846i	−0.537145	+	0.843490i	$0.680497\pi$
$192$		0			0
$193$	2.42583	+	0.882930i	0.174615	+	0.0635547i	0.427848	−	0.903851i	$-0.359272\pi$
$193$	2.42583	+	0.882930i	0.174615	+	0.0635547i	−0.253233	+	0.967405i	$0.581494\pi$
$194$		0			0
$195$	0.244979	+	0.413001i	0.0175433	+	0.0295756i
$196$		0			0
$197$	−19.8716	−	11.4729i	−1.41580	−	0.817410i	−0.419869	−	0.907585i	$-0.637924\pi$
$197$	−19.8716	−	11.4729i	−1.41580	−	0.817410i	−0.995926	+	0.0901747i	$0.971257\pi$
$198$		0			0
$199$			19.0252i			1.34866i	0.738431	+	0.674329i	$0.235567\pi$
$199$			19.0252i			1.34866i	−0.738431	+	0.674329i	$0.764433\pi$
$200$		0			0
$201$	−5.04122	−	0.827783i	−0.355581	−	0.0583873i
$202$		0			0
$203$	3.78110	−	0.726195i	0.265381	−	0.0509689i
$204$		0			0
$205$	1.87676	+	1.57479i	0.131079	+	0.109988i
$206$		0			0
$207$	−0.00418486	−	0.177554i	−0.000290868	−	0.0123409i
$208$		0			0
$209$	−2.83503	+	16.0782i	−0.196103	+	1.11215i
$210$		0			0
$211$	−0.106878	−	0.0389005i	−0.00735779	−	0.00267802i	0.338339	−	0.941024i	$-0.390135\pi$
$211$	−0.106878	−	0.0389005i	−0.00735779	−	0.00267802i	−0.345696	+	0.938346i	$0.612357\pi$
$212$		0			0
$213$	1.62243	+	8.60697i	0.111167	+	0.589740i
$214$		0			0
$215$	0.636778	+	1.10293i	0.0434279	+	0.0752193i
$216$		0			0
$217$	−13.0410	+	7.79613i	−0.885277	+	0.529236i
$218$		0			0
$219$	−3.59456	−	19.0691i	−0.242898	−	1.28857i
$220$		0			0
$221$	−0.204165	−	0.243314i	−0.0137336	−	0.0163671i
$222$		0			0
$223$	−14.3012	−	2.52169i	−0.957682	−	0.168865i	−0.327101	−	0.944989i	$-0.606072\pi$
$223$	−14.3012	−	2.52169i	−0.957682	−	0.168865i	−0.630580	+	0.776124i	$0.717183\pi$
$224$		0			0
$225$	−13.3398	−	4.50225i	−0.889320	−	0.300150i
$226$		0			0
$227$	−2.13748	+	12.1223i	−0.141870	+	0.804582i	0.827958	+	0.560790i	$0.189503\pi$
$227$	−2.13748	+	12.1223i	−0.141870	+	0.804582i	−0.969828	+	0.243792i	$0.921609\pi$
$228$		0			0
$229$	6.16134	−	16.9281i	0.407153	−	1.11864i	−0.551527	−	0.834157i	$-0.685955\pi$
$229$	6.16134	−	16.9281i	0.407153	−	1.11864i	0.958680	−	0.284487i	$-0.0918231\pi$
$230$		0			0
$231$	−17.9676	+	7.09461i	−1.18218	+	0.466791i
$232$		0			0
$233$	−9.89657	−	5.71379i	−0.648346	−	0.374323i	0.139476	−	0.990225i	$-0.455458\pi$
$233$	−9.89657	−	5.71379i	−0.648346	−	0.374323i	−0.787822	+	0.615903i	$0.788791\pi$
$234$		0			0
$235$	0.333099	+	0.576944i	0.0217290	+	0.0376356i
$236$		0			0
$237$	11.4342	+	6.42311i	0.742731	+	0.417226i
$238$		0			0
$239$	−0.643294	+	0.113430i	−0.0416112	+	0.00733718i	−0.194415	−	0.980919i	$-0.562281\pi$
$239$	−0.643294	+	0.113430i	−0.0416112	+	0.00733718i	0.152804	+	0.988257i	$0.451170\pi$
$240$		0			0
$241$	−6.67035	−	18.3266i	−0.429675	−	1.18052i	−0.946011	−	0.324136i	$-0.894927\pi$
$241$	−6.67035	−	18.3266i	−0.429675	−	1.18052i	0.516336	−	0.856386i	$-0.327296\pi$
$242$		0			0
$243$	−15.4844	−	1.79833i	−0.993323	−	0.115363i
$244$		0			0
$245$	3.60243	−	1.43676i	0.230151	−	0.0917910i
$246$		0			0
$247$	−1.48457	+	1.24570i	−0.0944611	+	0.0792623i
$248$		0			0
$249$	17.4818	−	10.3697i	1.10786	−	0.657151i
$250$		0			0
$251$	8.03105	−	13.9102i	0.506916	−	0.878004i	−0.493052	−	0.870000i	$-0.664119\pi$
$251$	8.03105	−	13.9102i	0.506916	−	0.878004i	0.999968	−	0.00800396i	$-0.00254777\pi$
$252$		0			0
$253$	0.124780	+	0.216125i	0.00784483	+	0.0135876i
$254$		0			0
$255$	−0.601098	−	0.0987019i	−0.0376422	−	0.00618095i
$256$		0			0
$257$	−20.3727	−	7.41506i	−1.27081	−	0.462539i	−0.383431	−	0.923570i	$-0.625257\pi$
$257$	−20.3727	−	7.41506i	−1.27081	−	0.462539i	−0.887384	+	0.461031i	$0.847480\pi$
$258$		0			0
$259$	−23.0109	+	8.77405i	−1.42983	+	0.545193i
$260$		0			0
$261$	−4.28034	+	0.859196i	−0.264947	+	0.0531829i
$262$		0			0
$263$	−3.05565	+	3.64158i	−0.188420	+	0.224550i	−0.851982	−	0.523571i	$-0.824599\pi$
$263$	−3.05565	+	3.64158i	−0.188420	+	0.224550i	0.663562	+	0.748121i	$0.269044\pi$
$264$		0			0
$265$	0.407863	−	1.12059i	0.0250548	−	0.0688375i
$266$		0			0
$267$	7.01799	−	20.0123i	0.429494	−	1.22474i
$268$		0			0
$269$	−4.02474	+	6.97105i	−0.245393	+	0.425033i	−0.962242	−	0.272196i	$-0.912250\pi$
$269$	−4.02474	+	6.97105i	−0.245393	+	0.425033i	0.716849	+	0.697228i	$0.245584\pi$
$270$		0			0
$271$	−4.48964	+	2.59210i	−0.272726	+	0.157459i	−0.630126	−	0.776493i	$-0.716997\pi$
$271$	−4.48964	+	2.59210i	−0.272726	+	0.157459i	0.357400	+	0.933952i	$0.383663\pi$
$272$		0			0
$273$	−2.17515	−	0.725815i	−0.131646	−	0.0439283i
$274$		0			0
$275$	19.4826	−	3.43531i	1.17485	−	0.207157i
$276$		0			0
$277$	5.66410	+	4.75274i	0.340323	+	0.285565i	0.796890	−	0.604124i	$-0.206477\pi$
$277$	5.66410	+	4.75274i	0.340323	+	0.285565i	−0.456568	+	0.889689i	$0.650921\pi$
$278$		0			0
$279$	14.7127	−	8.96313i	0.880828	−	0.536609i
$280$		0			0
$281$	9.61797	+	26.4251i	0.573760	+	1.57639i	0.798514	+	0.601976i	$0.205620\pi$
$281$	9.61797	+	26.4251i	0.573760	+	1.57639i	−0.224754	+	0.974416i	$0.572158\pi$
$282$		0			0
$283$	14.1402	−	2.49330i	0.840548	−	0.148211i	0.263233	−	0.964732i	$-0.415211\pi$
$283$	14.1402	−	2.49330i	0.840548	−	0.148211i	0.577316	+	0.816521i	$0.304100\pi$
$284$		0			0
$285$	−0.602226	+	3.66758i	−0.0356728	+	0.217248i
$286$		0			0
$287$	−11.6977	+	0.178002i	−0.690496	+	0.0105071i
$288$		0			0
$289$	−16.5971			−0.976299
$290$		0			0
$291$	1.20464	−	0.0141944i	0.0706174	−	0.000832090i
$292$		0			0
$293$	5.28738	+	29.9862i	0.308892	+	1.75181i	0.604595	+	0.796533i	$0.293335\pi$
$293$	5.28738	+	29.9862i	0.308892	+	1.75181i	−0.295703	+	0.955280i	$0.595554\pi$
$294$		0			0
$295$	−3.43039	−	2.87844i	−0.199725	−	0.167589i
$296$		0			0
$297$	20.3055	−	8.21436i	1.17824	−	0.476646i
$298$		0			0
$299$	−0.00514404	+	0.0291733i	−0.000297488	+	0.00168714i
$300$		0			0
$301$	−5.74579	−	1.99283i	−0.331182	−	0.114865i
$302$		0			0
$303$	−29.0654	+	17.2407i	−1.66976	+	0.990450i
$304$		0			0
$305$	1.80685	−	1.04319i	0.103460	−	0.0597326i
$306$		0			0
$307$	11.2817	−	6.51348i	0.643879	−	0.371744i	−0.142228	−	0.989834i	$-0.545427\pi$
$307$	11.2817	−	6.51348i	0.643879	−	0.371744i	0.786107	+	0.618090i	$0.212093\pi$
$308$		0			0
$309$	−2.85225	+	17.3703i	−0.162259	+	0.988160i
$310$		0			0
$311$	5.36781	+	30.4424i	0.304381	+	1.72623i	0.626406	+	0.779497i	$0.284525\pi$
$311$	5.36781	+	30.4424i	0.304381	+	1.72623i	−0.322025	+	0.946731i	$0.604364\pi$
$312$		0			0
$313$	13.8278	−	16.4793i	0.781592	−	0.931465i	−0.217412	−	0.976080i	$-0.569762\pi$
$313$	13.8278	−	16.4793i	0.781592	−	0.931465i	0.999004	+	0.0446148i	$0.0142061\pi$
$314$		0			0
$315$	−4.07103	+	1.66318i	−0.229376	+	0.0937094i
$316$		0			0
$317$	6.44736	+	17.7140i	0.362120	+	0.994916i	0.978279	+	0.207294i	$0.0664657\pi$
$317$	6.44736	+	17.7140i	0.362120	+	0.994916i	−0.616159	+	0.787622i	$0.711312\pi$
$318$		0			0
$319$	4.69929	−	3.94317i	0.263110	−	0.220775i
$320$		0			0
$321$	3.74114	+	19.8467i	0.208810	+	1.10774i
$322$		0			0
$323$		−	2.45841i		−	0.136790i
$324$		0			0
$325$	2.03370	+	1.17416i	0.112809	+	0.0651305i
$326$		0			0
$327$	17.1366	+	19.9407i	0.947657	+	1.10272i
$328$		0			0
$329$	−3.00562	−	1.04245i	−0.165705	−	0.0574720i
$330$		0			0
$331$	29.9532	−	10.9021i	1.64638	−	0.599232i	0.658240	−	0.752808i	$-0.271301\pi$
$331$	29.9532	−	10.9021i	1.64638	−	0.599232i	0.988137	+	0.153576i	$0.0490790\pi$
$332$		0			0
$333$	26.0080	−	10.1663i	1.42523	−	0.557112i
$334$		0			0
$335$	1.53564	−	0.558928i	0.0839011	−	0.0305375i
$336$		0			0
$337$	−11.8444	+	9.93861i	−0.645204	+	0.541391i	−0.905611	−	0.424108i	$-0.860588\pi$
$337$	−11.8444	+	9.93861i	−0.645204	+	0.541391i	0.260407	+	0.965499i	$0.416143\pi$
$338$		0			0
$339$	19.2616	+	15.7795i	1.04615	+	0.857023i
$340$		0			0
$341$	−12.1039	+	20.9645i	−0.655462	+	1.13529i
$342$		0			0
$343$	−8.51861	+	16.4449i	−0.459962	+	0.887939i
$344$		0			0
$345$	0.0289839	+	0.0488629i	0.00156044	+	0.00263069i
$346$		0			0
$347$	2.37448	−	6.52382i	0.127469	−	0.350217i	−0.859499	−	0.511138i	$-0.829224\pi$
$347$	2.37448	−	6.52382i	0.127469	−	0.350217i	0.986967	+	0.160921i	$0.0514464\pi$
$348$		0			0
$349$	16.9744	−	20.2294i	0.908621	−	1.08285i	−0.0876135	−	0.996155i	$-0.527924\pi$
$349$	16.9744	−	20.2294i	0.908621	−	1.08285i	0.996235	−	0.0866979i	$-0.0276315\pi$
$350$		0			0
$351$	2.47317	+	0.802375i	0.132008	+	0.0428276i
$352$		0			0
$353$	−26.6523	+	9.70066i	−1.41856	+	0.516314i	−0.933630	−	0.358238i	$-0.883377\pi$
$353$	−26.6523	+	9.70066i	−1.41856	+	0.516314i	−0.484931	+	0.874552i	$0.661155\pi$
$354$		0			0
$355$	−1.80090	−	2.14623i	−0.0955821	−	0.113910i
$356$		0			0
$357$	2.47895	−	1.52189i	0.131200	−	0.0805472i
$358$		0			0
$359$		−	21.8568i		−	1.15356i	−0.816900	−	0.576779i	$-0.804309\pi$
$359$		−	21.8568i		−	1.15356i	0.816900	−	0.576779i	$-0.195691\pi$
$360$		0			0
$361$	4.00010			0.210531
$362$		0			0
$363$	−7.43087	+	9.07070i	−0.390019	+	0.476088i
$364$		0			0
$365$	3.98998	+	4.75507i	0.208845	+	0.248892i
$366$		0			0
$367$	−2.29250	−	0.404230i	−0.119668	−	0.0211007i	0.113494	−	0.993539i	$-0.463796\pi$
$367$	−2.29250	−	0.404230i	−0.119668	−	0.0211007i	−0.233161	+	0.972438i	$0.574907\pi$
$368$		0			0
$369$	13.2618	−	0.312574i	0.690384	−	0.0162719i
$370$		0			0
$371$	2.02884	+	5.32088i	0.105332	+	0.276246i
$372$		0			0
$373$	4.27168	+	24.2259i	0.221179	+	1.25437i	0.869856	+	0.493306i	$0.164212\pi$
$373$	4.27168	+	24.2259i	0.221179	+	1.25437i	−0.648676	+	0.761064i	$0.724677\pi$
$374$		0			0
$375$	9.14091	−	1.72308i	0.472035	−	0.0889793i
$376$		0			0
$377$	0.728180			0.0375032
$378$		0			0
$379$	−26.3042			−1.35115			−0.675577	−	0.737289i	$-0.736105\pi$
$379$	−26.3042			−1.35115			−0.675577	+	0.737289i	$0.736105\pi$
$380$		0			0
$381$	−7.83237	−	9.11398i	−0.401265	−	0.466924i
$382$		0			0
$383$	0.938875	+	5.32463i	0.0479743	+	0.272076i	0.999354	−	0.0359456i	$-0.0114443\pi$
$383$	0.938875	+	5.32463i	0.0479743	+	0.272076i	−0.951379	+	0.308021i	$0.900333\pi$
$384$		0			0
$385$	3.89953	−	4.79355i	0.198738	−	0.244302i
$386$		0			0
$387$	6.53375	+	2.20518i	0.332129	+	0.112095i
$388$		0			0
$389$	17.0349	+	3.00370i	0.863701	+	0.152294i	0.587913	−	0.808924i	$-0.299950\pi$
$389$	17.0349	+	3.00370i	0.863701	+	0.152294i	0.275789	+	0.961218i	$0.411061\pi$
$390$		0			0
$391$	−0.0241551	−	0.0287869i	−0.00122158	−	0.00145582i
$392$		0			0
$393$	9.29288	+	24.6253i	0.468764	+	1.24218i
$394$		0			0
$395$	−4.19519			−0.211083
$396$		0			0
$397$		−	35.6021i		−	1.78682i	−0.449244	−	0.893409i	$-0.648307\pi$
$397$		−	35.6021i		−	1.78682i	0.449244	−	0.893409i	$-0.351693\pi$
$398$		0			0
$399$	−9.28578	−	15.1252i	−0.464870	−	0.757208i
$400$		0			0
$401$	−14.5463	−	17.3356i	−0.726407	−	0.865698i	0.268829	−	0.963188i	$-0.413363\pi$
$401$	−14.5463	−	17.3356i	−0.726407	−	0.865698i	−0.995237	+	0.0974895i	$0.968919\pi$
$402$		0			0
$403$	−2.70023	+	0.982805i	−0.134508	+	0.0489570i
$404$		0			0
$405$	4.60020	−	1.92434i	0.228586	−	0.0956213i
$406$		0			0
$407$	−25.2216	+	30.0579i	−1.25019	+	1.48991i
$408$		0			0
$409$	5.24708	−	14.4162i	0.259452	−	0.712837i	−0.739750	−	0.672882i	$-0.765056\pi$
$409$	5.24708	−	14.4162i	0.259452	−	0.712837i	0.999201	−	0.0399554i	$-0.0127216\pi$
$410$		0			0
$411$	−0.221475	+	0.00260965i	−0.0109245	+	0.000128725i
$412$		0			0
$413$	21.3815	−	0.325358i	1.05211	−	0.0160098i
$414$		0			0
$415$	−3.25096	+	5.63082i	−0.159583	+	0.276406i
$416$		0			0
$417$	−0.0273318	+	0.166451i	−0.00133844	+	0.00815116i
$418$		0			0
$419$	9.50477	−	7.97545i	0.464338	−	0.389626i	−0.380386	−	0.924828i	$-0.624209\pi$
$419$	9.50477	−	7.97545i	0.464338	−	0.389626i	0.844724	+	0.535202i	$0.179764\pi$
$420$		0			0
$421$	−23.2648	+	8.46771i	−1.13386	+	0.412691i	−0.839692	−	0.543063i	$-0.817264\pi$
$421$	−23.2648	+	8.46771i	−1.13386	+	0.412691i	−0.294167	+	0.955754i	$0.595042\pi$
$422$		0			0
$423$	3.41781	+	1.15353i	0.166179	+	0.0560865i
$424$		0			0
$425$	−2.79930	+	1.01886i	−0.135786	+	0.0494220i
$426$		0			0
$427$	−3.26470	+	9.41289i	−0.157990	+	0.455522i
$428$		0			0
$429$	−3.59025	+	0.676768i	−0.173339	+	0.0326747i
$430$		0			0
$431$	−3.52219	−	2.03354i	−0.169658	−	0.0979520i	0.412767	−	0.910837i	$-0.364562\pi$
$431$	−3.52219	−	2.03354i	−0.169658	−	0.0979520i	−0.582424	+	0.812885i	$0.697896\pi$
$432$		0			0
$433$		−	15.1591i		−	0.728499i	−0.931301	−	0.364249i	$-0.881326\pi$
$433$		−	15.1591i		−	0.728499i	0.931301	−	0.364249i	$-0.118674\pi$
$434$		0			0
$435$	1.05915	−	0.910209i	0.0507822	−	0.0436412i
$436$		0			0
$437$	−0.175642	+	0.147381i	−0.00840211	+	0.00705021i
$438$		0			0
$439$	1.75309	+	4.81657i	0.0836703	+	0.229882i	0.974472	−	0.224511i	$-0.0720784\pi$
$439$	1.75309	+	4.81657i	0.0836703	+	0.229882i	−0.890801	+	0.454393i	$0.849856\pi$
$440$		0			0
$441$	9.50317	−	18.7267i	0.452532	−	0.891748i
$442$		0			0
$443$	22.7817	−	27.1502i	1.08239	−	1.28995i	0.127876	−	0.991790i	$-0.459184\pi$
$443$	22.7817	−	27.1502i	1.08239	−	1.28995i	0.954517	−	0.298155i	$-0.0963714\pi$
$444$		0			0
$445$	1.17800	+	6.68076i	0.0558425	+	0.316698i
$446$		0			0
$447$	26.6700	+	21.8485i	1.26145	+	1.03340i
$448$		0			0
$449$	−30.4940	+	17.6057i	−1.43910	+	0.830866i	−0.997787	−	0.0664866i	$-0.978821\pi$
$449$	−30.4940	+	17.6057i	−1.43910	+	0.830866i	−0.441315	+	0.897352i	$0.645488\pi$
$450$		0			0
$451$	−16.1427	+	9.32000i	−0.760131	+	0.438862i
$452$		0			0
$453$	9.14725	+	5.13843i	0.429775	+	0.241424i
$454$		0			0
$455$	0.720341	−	0.138348i	0.0337701	−	0.00648586i
$456$		0			0
$457$	3.27561	−	18.5769i	0.153226	−	0.868991i	−0.807163	−	0.590329i	$-0.798998\pi$
$457$	3.27561	−	18.5769i	0.153226	−	0.868991i	0.960389	−	0.278662i	$-0.0898908\pi$
$458$		0			0
$459$	−2.79636	+	1.74907i	−0.130523	+	0.0816398i
$460$		0			0
$461$	−28.9553	−	24.2964i	−1.34858	−	1.13159i	−0.979331	−	0.202265i	$-0.935170\pi$
$461$	−28.9553	−	24.2964i	−1.34858	−	1.13159i	−0.369252	−	0.929329i	$-0.620386\pi$
$462$		0			0
$463$	−1.15887	−	6.57229i	−0.0538574	−	0.305440i	0.945965	−	0.324268i	$-0.105118\pi$
$463$	−1.15887	−	6.57229i	−0.0538574	−	0.305440i	−0.999823	+	0.0188273i	$0.994007\pi$
$464$		0			0
$465$	−2.69904	+	4.80473i	−0.125165	+	0.222814i
$466$		0			0
$467$	−14.7392			−0.682050			−0.341025	−	0.940054i	$-0.610774\pi$
$467$	−14.7392			−0.682050			−0.341025	+	0.940054i	$0.610774\pi$
$468$		0			0
$469$	−3.79858	+	6.81681i	−0.175402	+	0.314771i
$470$		0			0
$471$	−15.3948	+	5.80956i	−0.709355	+	0.267690i
$472$		0			0
$473$	−9.54247	+	1.68259i	−0.438763	+	0.0773658i
$474$		0			0
$475$	6.21654	+	17.0798i	0.285234	+	0.783675i
$476$		0			0
$477$	−2.35079	−	6.01389i	−0.107635	−	0.275357i
$478$		0			0
$479$	23.1775	+	19.4482i	1.05901	+	0.888612i	0.994012	−	0.109274i	$-0.0348526\pi$
$479$	23.1775	+	19.4482i	1.05901	+	0.888612i	0.0649944	+	0.997886i	$0.479297\pi$
$480$		0			0
$481$	−4.58687	+	0.808789i	−0.209143	+	0.0368776i
$482$		0			0
$483$	−0.257345	−	0.0858724i	−0.0117096	−	0.00390733i
$484$		0			0
$485$	−0.333741	+	0.192686i	−0.0151544	+	0.00874940i
$486$		0			0
$487$	−10.1186	+	17.5260i	−0.458519	+	0.794177i	−0.998883	−	0.0472537i	$-0.984953\pi$
$487$	−10.1186	+	17.5260i	−0.458519	+	0.794177i	0.540364	+	0.841431i	$0.318286\pi$
$488$		0			0
$489$	−11.5085	+	2.16937i	−0.520432	+	0.0981022i
$490$		0			0
$491$	−3.07553	+	8.44994i	−0.138797	+	0.381340i	−0.989543	−	0.144235i	$-0.953928\pi$
$491$	−3.07553	+	8.44994i	−0.138797	+	0.381340i	0.850747	+	0.525576i	$0.176150\pi$
$492$		0			0
$493$	−0.593763	+	0.707619i	−0.0267417	+	0.0318696i
$494$		0			0
$495$	−4.37612	+	5.47210i	−0.196692	+	0.245953i
$496$		0			0
$497$	13.2095	+	2.12249i	0.592526	+	0.0952065i
$498$		0			0
$499$	40.8211	+	14.8576i	1.82740	+	0.665120i	0.993586	+	0.113075i	$0.0360702\pi$
$499$	40.8211	+	14.8576i	1.82740	+	0.665120i	0.833815	+	0.552044i	$0.186152\pi$
$500$		0			0
$501$	−9.82393	+	11.9919i	−0.438901	+	0.535757i
$502$		0			0
$503$	4.11258	+	7.12321i	0.183371	+	0.317608i	0.943026	−	0.332718i	$-0.107966\pi$
$503$	4.11258	+	7.12321i	0.183371	+	0.317608i	−0.759655	+	0.650326i	$0.774632\pi$
$504$		0			0
$505$	5.40506	−	9.36184i	0.240522	−	0.416597i
$506$		0			0
$507$	19.2532	+	10.8154i	0.855064	+	0.480329i
$508$		0			0
$509$	−14.5922	+	12.2443i	−0.646790	+	0.542721i	−0.906095	−	0.423074i	$-0.860951\pi$
$509$	−14.5922	+	12.2443i	−0.646790	+	0.542721i	0.259305	+	0.965795i	$0.416506\pi$
$510$		0			0
$511$	−29.2661	−	4.70245i	−1.29466	−	0.208024i
$512$		0			0
$513$	10.6719	+	17.0619i	0.471176	+	0.753300i
$514$		0			0
$515$	−1.92587	−	5.29128i	−0.0848639	−	0.233162i
$516$		0			0
$517$	−4.99166	+	0.880165i	−0.219533	+	0.0387096i
$518$		0			0
$519$	21.4278	−	12.7103i	0.940575	−	0.557920i
$520$		0			0
$521$	1.31024	+	2.26940i	0.0574027	+	0.0994244i	0.893299	−	0.449463i	$-0.148385\pi$
$521$	1.31024	+	2.26940i	0.0574027	+	0.0994244i	−0.835896	+	0.548888i	$0.815051\pi$
$522$		0			0
$523$	11.2694	+	6.50639i	0.492776	+	0.284505i	0.725726	−	0.687984i	$-0.241504\pi$
$523$	11.2694	+	6.50639i	0.492776	+	0.284505i	−0.232949	+	0.972489i	$0.574838\pi$
$524$		0			0
$525$	−13.3741	+	16.8418i	−0.583694	+	0.735038i
$526$		0			0
$527$	1.24674	−	3.42538i	0.0543086	−	0.149212i
$528$		0			0
$529$	3.99330	−	22.6471i	0.173622	−	0.984658i
$530$		0			0
$531$	−24.2404	+	0.571331i	−1.05194	+	0.0247937i
$532$		0			0
$533$	−2.17900	−	0.384217i	−0.0943831	−	0.0166423i
$534$		0			0
$535$	−4.15269	−	4.94898i	−0.179536	−	0.213963i
$536$		0			0
$537$	35.4955	+	12.4477i	1.53174	+	0.537157i
$538$		0			0
$539$	0.897829	+	29.4944i	0.0386722	+	1.27041i
$540$		0			0
$541$	3.26613	+	5.65710i	0.140422	+	0.243218i	0.927655	−	0.373437i	$-0.121821\pi$
$541$	3.26613	+	5.65710i	0.140422	+	0.243218i	−0.787234	+	0.616655i	$0.788487\pi$
$542$		0			0
$543$	1.52463	−	1.31024i	0.0654281	−	0.0562276i
$544$		0			0
$545$	−7.90330	−	2.87657i	−0.338540	−	0.123219i
$546$		0			0
$547$	4.30486	−	24.4141i	0.184063	−	1.04387i	−0.743091	−	0.669190i	$-0.766641\pi$
$547$	4.30486	−	24.4141i	0.184063	−	1.04387i	0.927154	−	0.374681i	$-0.122248\pi$
$548$		0			0
$549$	3.61258	−	10.7038i	0.154181	−	0.456825i
$550$		0			0
$551$	4.31751	+	3.62282i	0.183932	+	0.154337i
$552$		0			0
$553$	15.1486	−	13.1091i	0.644183	−	0.557454i
$554$		0			0
$555$	−5.66069	+	6.90988i	−0.240283	+	0.293308i
$556$		0			0
$557$			39.4427i			1.67124i	0.549308	+	0.835620i	$0.314891\pi$
$557$			39.4427i			1.67124i	−0.549308	+	0.835620i	$0.685109\pi$
$558$		0			0
$559$	−0.996094	−	0.575095i	−0.0421303	−	0.0243239i
$560$		0			0
$561$	2.26986	−	4.04072i	0.0958334	−	0.170599i
$562$		0			0
$563$	−2.37268	−	0.863585i	−0.0999965	−	0.0363958i	0.291537	−	0.956559i	$-0.405833\pi$
$563$	−2.37268	−	0.863585i	−0.0999965	−	0.0363958i	−0.391534	+	0.920164i	$0.628055\pi$
$564$		0			0
$565$	−7.84403	−	1.38311i	−0.330001	−	0.0581880i
$566$		0			0
$567$	−10.5979	+	21.3233i	−0.445071	+	0.895496i
$568$		0			0
$569$	−32.9897	−	5.81697i	−1.38300	−	0.243860i	−0.567859	−	0.823126i	$-0.692228\pi$
$569$	−32.9897	−	5.81697i	−1.38300	−	0.243860i	−0.815139	+	0.579266i	$0.803339\pi$
$570$		0			0
$571$	7.98320	+	2.90565i	0.334087	+	0.121598i	0.503616	−	0.863928i	$-0.332003\pi$
$571$	7.98320	+	2.90565i	0.334087	+	0.121598i	−0.169530	+	0.985525i	$0.554225\pi$
$572$		0			0
$573$	8.96891	−	15.9661i	0.374682	−	0.666995i
$574$		0			0
$575$	0.240610	+	0.138917i	0.0100341	+	0.00579322i
$576$		0			0
$577$		−	16.3727i		−	0.681606i	−0.940135	−	0.340803i	$-0.889301\pi$
$577$		−	16.3727i		−	0.681606i	0.940135	−	0.340803i	$-0.110699\pi$
$578$		0			0
$579$	−2.83355	+	3.45885i	−0.117758	+	0.143745i
$580$		0			0
$581$	−5.85610	−	30.4911i	−0.242952	−	1.26498i
$582$		0			0
$583$	6.95036	+	5.83205i	0.287855	+	0.241539i
$584$		0			0
$585$	−0.815452	+	0.163686i	−0.0337148	+	0.00676759i
$586$		0			0
$587$	−5.51445	+	31.2740i	−0.227606	+	1.29082i	0.630035	+	0.776567i	$0.283041\pi$
$587$	−5.51445	+	31.2740i	−0.227606	+	1.29082i	−0.857641	+	0.514249i	$0.828071\pi$
$588$		0			0
$589$	−20.8998	−	7.60691i	−0.861162	−	0.313437i
$590$		0			0
$591$	30.1420	−	25.9034i	1.23988	−	1.06552i
$592$		0			0
$593$	−15.2689	−	26.4465i	−0.627019	−	1.08603i	−0.988147	−	0.153513i	$-0.950941\pi$
$593$	−15.2689	−	26.4465i	−0.627019	−	1.08603i	0.361127	−	0.932517i	$-0.382392\pi$
$594$		0			0
$595$	−0.452930	+	0.812812i	−0.0185683	+	0.0333220i
$596$		0			0
$597$	−31.0959	−	10.9048i	−1.27267	−	0.446304i
$598$		0			0
$599$	−6.67755	−	7.95800i	−0.272837	−	0.325155i	0.612175	−	0.790722i	$-0.290295\pi$
$599$	−6.67755	−	7.95800i	−0.272837	−	0.325155i	−0.885012	+	0.465567i	$0.845850\pi$
$600$		0			0
$601$	−0.660314	−	0.116431i	−0.0269348	−	0.00474933i	0.160165	−	0.987090i	$-0.448798\pi$
$601$	−0.660314	−	0.116431i	−0.0269348	−	0.00474933i	−0.187099	+	0.982341i	$0.559909\pi$
$602$		0			0
$603$	4.24250	−	7.76522i	0.172768	−	0.316224i
$604$		0			0
$605$	0.651336	−	3.69391i	0.0264806	−	0.150179i
$606$		0			0
$607$	−1.11798	+	3.07164i	−0.0453776	+	0.124674i	−0.960311	−	0.278930i	$-0.910020\pi$
$607$	−1.11798	+	3.07164i	−0.0453776	+	0.124674i	0.914934	+	0.403604i	$0.132243\pi$
$608$		0			0
$609$	−0.980308	+	6.59631i	−0.0397241	+	0.267296i
$610$		0			0
$611$	−0.521057	−	0.300832i	−0.0210797	−	0.0121704i
$612$		0			0
$613$	−17.2368	−	29.8550i	−0.696187	−	1.20583i	−0.969779	−	0.243985i	$-0.921545\pi$
$613$	−17.2368	−	29.8550i	−0.696187	−	1.20583i	0.273592	−	0.961846i	$-0.411788\pi$
$614$		0			0
$615$	−3.64965	+	2.16486i	−0.147168	+	0.0872955i
$616$		0			0
$617$	37.9055	−	6.68375i	1.52602	−	0.269078i	0.653222	−	0.757166i	$-0.273417\pi$
$617$	37.9055	−	6.68375i	1.52602	−	0.269078i	0.872794	+	0.488089i	$0.162306\pi$
$618$		0			0
$619$	−12.1028	−	33.2522i	−0.486453	−	1.33652i	−0.903872	−	0.427804i	$-0.859287\pi$
$619$	−12.1028	−	33.2522i	−0.486453	−	1.33652i	0.417419	−	0.908714i	$-0.362935\pi$
$620$		0			0
$621$	0.292605	+	0.0949304i	0.0117418	+	0.00380943i
$622$		0			0
$623$	−25.1296	−	20.4428i	−1.00680	−	0.819025i
$624$		0			0
$625$	15.6960	−	13.1705i	0.627838	−	0.526819i
$626$		0			0
$627$	−24.6543	−	13.8494i	−0.984598	−	0.553093i
$628$		0			0
$629$	2.95422	−	5.11685i	0.117792	−	0.204022i
$630$		0			0
$631$	−12.0125	−	20.8062i	−0.478208	−	0.828281i	0.521480	−	0.853264i	$-0.325380\pi$
$631$	−12.0125	−	20.8062i	−0.478208	−	0.828281i	−0.999688	+	0.0249829i	$0.992047\pi$
$632$		0			0
$633$	0.124842	−	0.152391i	0.00496201	−	0.00605701i
$634$		0			0
$635$	3.61224	+	1.31475i	0.143347	+	0.0521742i
$636$		0			0
$637$	−2.16880	+	2.75048i	−0.0859310	+	0.108978i
$638$		0			0
$639$	−14.9977	−	2.28153i	−0.593300	−	0.0902560i
$640$		0			0
$641$	−8.90313	+	10.6103i	−0.351653	+	0.419083i	−0.912655	−	0.408731i	$-0.865971\pi$
$641$	−8.90313	+	10.6103i	−0.351653	+	0.419083i	0.561002	+	0.827814i	$0.310416\pi$
$642$		0			0
$643$	1.97788	−	5.43418i	0.0780000	−	0.214303i	−0.894563	−	0.446941i	$-0.852513\pi$
$643$	1.97788	−	5.43418i	0.0780000	−	0.214303i	0.972563	+	0.232638i	$0.0747356\pi$
$644$		0			0
$645$	−2.16769	+	0.408613i	−0.0853526	+	0.0160891i
$646$		0			0
$647$	−4.57324	+	7.92108i	−0.179793	+	0.311410i	−0.941809	−	0.336147i	$-0.890876\pi$
$647$	−4.57324	+	7.92108i	−0.179793	+	0.311410i	0.762017	+	0.647557i	$0.224209\pi$
$648$		0			0
$649$	29.5061	−	17.0354i	1.15822	−	0.668696i
$650$		0			0
$651$	−5.26769	−	25.7835i	−0.206457	−	1.01054i
$652$		0			0
$653$	−1.55734	+	0.274601i	−0.0609433	+	0.0107460i	−0.204037	−	0.978963i	$-0.565406\pi$
$653$	−1.55734	+	0.274601i	−0.0609433	+	0.0107460i	0.143093	+	0.989709i	$0.454295\pi$
$654$		0			0
$655$	−6.44966	−	5.41190i	−0.252009	−	0.211461i
$656$		0			0
$657$	33.2280	+	5.05483i	1.29635	+	0.197208i
$658$		0			0
$659$	−3.88785	−	10.6818i	−0.151449	−	0.416103i	0.840647	−	0.541583i	$-0.182175\pi$
$659$	−3.88785	−	10.6818i	−0.151449	−	0.416103i	−0.992096	+	0.125481i	$0.959953\pi$
$660$		0			0
$661$	−26.9919	+	4.75940i	−1.04986	+	0.185119i	−0.671854	−	0.740683i	$-0.734502\pi$
$661$	−26.9919	+	4.75940i	−1.04986	+	0.185119i	−0.378008	+	0.925802i	$0.623391\pi$
$662$		0			0
$663$	0.514711	−	0.194237i	0.0199897	−	0.00754355i
$664$		0			0
$665$	4.95934	+	2.76353i	0.192315	+	0.107165i
$666$		0			0
$667$	0.0861522			0.00333583
$668$		0			0
$669$	12.3188	−	21.9294i	0.476271	−	0.847842i
$670$		0			0
$671$	2.75647	+	15.6327i	0.106412	+	0.603494i
$672$		0			0
$673$	30.5814	+	25.6609i	1.17883	+	0.989154i	0.999986	+	0.00527559i	$0.00167928\pi$
$673$	30.5814	+	25.6609i	1.17883	+	0.989154i	0.178841	+	0.983878i	$0.442765\pi$
$674$		0			0
$675$	15.0048	−	19.2228i	0.577537	−	0.739886i
$676$		0			0
$677$	−0.621865	+	3.52677i	−0.0239002	+	0.135545i	−0.994423	−	0.105464i	$-0.966367\pi$
$677$	−0.621865	+	3.52677i	−0.0239002	+	0.135545i	0.970523	+	0.241009i	$0.0774783\pi$
$678$		0			0
$679$	0.603018	−	1.73864i	0.0231417	−	0.0667231i
$680$		0			0
$681$	−18.5882	−	10.4418i	−0.712302	−	0.400132i
$682$		0			0
$683$	−6.44543	+	3.72127i	−0.246627	+	0.142390i	−0.618219	−	0.786006i	$-0.712146\pi$
$683$	−6.44543	+	3.72127i	−0.246627	+	0.142390i	0.371592	+	0.928396i	$0.378812\pi$
$684$		0			0
$685$	0.0613587	−	0.0354254i	0.00234439	−	0.00135354i
$686$		0			0
$687$	24.1369	+	19.7733i	0.920879	+	0.754400i
$688$		0			0
$689$	0.187018	+	1.06063i	0.00712483	+	0.0404069i
$690$		0			0
$691$	16.2167	−	19.3264i	0.616914	−	0.735209i	−0.363623	−	0.931546i	$-0.618460\pi$
$691$	16.2167	−	19.3264i	0.616914	−	0.735209i	0.980536	+	0.196337i	$0.0629047\pi$
$692$		0			0
$693$	−1.29724	−	33.4338i	−0.0492780	−	1.27005i
$694$		0			0
$695$	−0.0184547	−	0.0507039i	−0.000700027	−	0.00192331i
$696$		0			0
$697$	2.15014	−	1.80418i	0.0814425	−	0.0683384i
$698$		0			0
$699$	15.0115	−	12.9006i	0.567786	−	0.487944i
$700$		0			0
$701$		−	26.7157i		−	1.00904i	−0.863401	−	0.504518i	$-0.831670\pi$
$701$		−	26.7157i		−	1.00904i	0.863401	−	0.504518i	$-0.168330\pi$
$702$		0			0
$703$	−31.2203	−	18.0250i	−1.17749	−	0.679827i
$704$		0			0
$705$	−1.13392	+	0.213745i	−0.0427058	+	0.00805011i
$706$		0			0
$707$	9.73638	+	50.6947i	0.366174	+	1.90657i
$708$		0			0
$709$	−24.9988	+	9.09883i	−0.938850	+	0.341714i	−0.765712	−	0.643184i	$-0.777613\pi$
$709$	−24.9988	+	9.09883i	−0.938850	+	0.341714i	−0.173139	+	0.984897i	$0.555391\pi$
$710$		0			0
$711$	−17.0522	+	15.0072i	−0.639506	+	0.562813i
$712$		0			0
$713$	−0.319469	+	0.116277i	−0.0119642	+	0.00435462i
$714$		0			0
$715$	0.895265	−	0.751216i	0.0334810	−	0.0280939i
$716$		0			0
$717$	0.183325	−	1.11646i	0.00684640	−	0.0416948i
$718$		0			0
$719$	13.5495	−	23.4684i	0.505311	−	0.875225i	−0.494670	−	0.869081i	$-0.664711\pi$
$719$	13.5495	−	23.4684i	0.505311	−	0.875225i	0.999981	−	0.00614379i	$-0.00195564\pi$
$720$		0			0
$721$	23.4883	+	13.0886i	0.874750	+	0.487444i
$722$		0			0
$723$	33.7775	−	0.398003i	1.25620	−	0.0148019i
$724$		0			0
$725$	2.33582	−	6.41762i	0.0867503	−	0.238344i
$726$		0			0
$727$	−18.8028	+	22.4084i	−0.697359	+	0.831080i	−0.992225	−	0.124459i	$-0.960281\pi$
$727$	−18.8028	+	22.4084i	−0.697359	+	0.831080i	0.294866	+	0.955539i	$0.404725\pi$
$728$		0			0
$729$	11.8146	−	24.2779i	0.437578	−	0.899180i
$730$		0			0
$731$	1.37108	−	0.499032i	0.0507112	−	0.0184574i
$732$		0			0
$733$	−14.5245	−	17.3096i	−0.536473	−	0.639344i	0.427920	−	0.903817i	$-0.359247\pi$
$733$	−14.5245	−	17.3096i	−0.536473	−	0.639344i	−0.964393	+	0.264473i	$0.914802\pi$
$734$		0			0
$735$	0.283489	+	6.71155i	0.0104566	+	0.247559i
$736$		0			0
$737$			12.4336i			0.457996i
$738$		0			0
$739$	−28.0070			−1.03025			−0.515127	−	0.857114i	$-0.672255\pi$
$739$	−28.0070			−1.03025			−0.515127	+	0.857114i	$0.672255\pi$
$740$		0			0
$741$	−1.18513	−	3.14049i	−0.0435369	−	0.115369i
$742$		0			0
$743$	11.9061	+	14.1891i	0.436791	+	0.520547i	0.938869	−	0.344275i	$-0.111875\pi$
$743$	11.9061	+	14.1891i	0.436791	+	0.520547i	−0.502078	+	0.864822i	$0.667431\pi$
$744$		0			0
$745$	−10.8610	−	1.91508i	−0.397915	−	0.0701632i
$746$		0			0
$747$	6.92862	+	34.5170i	0.253505	+	1.26291i
$748$		0			0
$749$	30.4596	+	4.89422i	1.11297	+	0.178831i
$750$		0			0
$751$	5.90033	+	33.4624i	0.215306	+	1.22106i	0.880375	+	0.474279i	$0.157291\pi$
$751$	5.90033	+	33.4624i	0.215306	+	1.22106i	−0.665068	+	0.746782i	$0.731598\pi$
$752$		0			0
$753$	18.1325	+	21.0995i	0.660783	+	0.768908i
$754$		0			0
$755$	−3.35611			−0.122141
$756$		0			0
$757$	27.8065			1.01064			0.505322	−	0.862931i	$-0.331374\pi$
$757$	27.8065			1.01064			0.505322	+	0.862931i	$0.331374\pi$
$758$		0			0
$759$	−0.424769	+	0.0800696i	−0.0154181	+	0.00290634i
$760$		0			0
$761$	−7.09933	−	40.2623i	−0.257351	−	1.45951i	−0.789966	−	0.613150i	$-0.789902\pi$
$761$	−7.09933	−	40.2623i	−0.257351	−	1.45951i	0.532616	−	0.846357i	$-0.321209\pi$
$762$		0			0
$763$	37.5270	−	14.3090i	1.35857	−	0.518020i
$764$		0			0
$765$	0.505861	−	0.925898i	0.0182894	−	0.0334759i
$766$		0			0
$767$	3.98284	+	0.702283i	0.143812	+	0.0253580i
$768$		0			0
$769$	−32.0054	−	38.1425i	−1.15414	−	1.37545i	−0.914497	−	0.404593i	$-0.867413\pi$
$769$	−32.0054	−	38.1425i	−1.15414	−	1.37545i	−0.239646	−	0.970860i	$-0.577031\pi$
$770$		0			0
$771$	23.7968	−	29.0483i	0.857022	−	1.04615i
$772$		0			0
$773$	−9.51135			−0.342099			−0.171050	−	0.985262i	$-0.554716\pi$
$773$	−9.51135			−0.342099			−0.171050	+	0.985262i	$0.554716\pi$
$774$		0			0
$775$			26.9504i			0.968087i
$776$		0			0
$777$	−1.15147	−	42.6396i	−0.0413088	−	1.52969i
$778$		0			0
$779$	−11.0082	−	13.1190i	−0.394408	−	0.470038i
$780$		0			0
$781$	20.0309	−	7.29065i	0.716761	−	0.260880i
$782$		0			0
$783$	1.04908	−	7.48853i	0.0374910	−	0.267618i
$784$		0			0
$785$	3.38332	−	4.03209i	0.120756	−	0.143911i
$786$		0			0
$787$	−2.46486	+	6.77214i	−0.0878626	+	0.241401i	−0.975840	−	0.218487i	$-0.929888\pi$
$787$	−2.46486	+	6.77214i	−0.0878626	+	0.241401i	0.887977	+	0.459887i	$0.152110\pi$
$788$		0			0
$789$	−4.20060	−	7.08162i	−0.149545	−	0.252113i
$790$		0			0
$791$	32.6462	−	19.5165i	1.16077	−	0.693928i
$792$		0			0
$793$	−0.942135	+	1.63183i	−0.0334562	+	0.0579478i
$794$		0			0
$795$	1.59779	+	1.30894i	0.0566677	+	0.0464232i
$796$		0			0
$797$	−9.88313	+	8.29293i	−0.350078	+	0.293751i	−0.800822	−	0.598903i	$-0.795603\pi$
$797$	−9.88313	+	8.29293i	−0.350078	+	0.293751i	0.450743	+	0.892654i	$0.351159\pi$
$798$		0			0
$799$	0.717212	−	0.261044i	0.0253731	−	0.00923506i
$800$		0			0
$801$	28.6868	+	22.9413i	1.01360	+	0.810590i
$802$		0			0
$803$	−44.3793	+	16.1527i	−1.56611	+	0.570017i
$804$		0			0
$805$	0.0852248	−	0.0163682i	0.00300378	−	0.000576903i
$806$		0			0
$807$	−9.08703	−	10.5739i	−0.319879	−	0.372220i
$808$		0			0
$809$	−6.22539	−	3.59423i	−0.218873	−	0.126366i	0.386555	−	0.922266i	$-0.373665\pi$
$809$	−6.22539	−	3.59423i	−0.218873	−	0.126366i	−0.605428	+	0.795900i	$0.706998\pi$
$810$		0			0
$811$		−	8.78622i		−	0.308526i	−0.988030	−	0.154263i	$-0.950700\pi$
$811$		−	8.78622i		−	0.308526i	0.988030	−	0.154263i	$-0.0493003\pi$
$812$		0			0
$813$	−1.66332	−	8.82389i	−0.0583351	−	0.309467i
$814$		0			0
$815$	2.86975	−	2.40801i	0.100523	−	0.0843489i
$816$		0			0
$817$	−3.04483	−	8.36559i	−0.106525	−	0.292675i
$818$		0			0
$819$	2.43306	−	3.13917i	0.0850181	−	0.109692i
$820$		0			0
$821$	36.4342	−	43.4205i	1.27156	−	1.51539i	0.522979	−	0.852346i	$-0.324821\pi$
$821$	36.4342	−	43.4205i	1.27156	−	1.51539i	0.748582	−	0.663042i	$-0.230735\pi$
$822$		0			0
$823$	−5.82074	−	33.0111i	−0.202898	−	1.15069i	−0.900713	−	0.434415i	$-0.856955\pi$
$823$	−5.82074	−	33.0111i	−0.202898	−	1.15069i	0.697814	−	0.716279i	$-0.254156\pi$
$824$		0			0
$825$	−5.55213	+	33.8126i	−0.193300	+	1.17720i
$826$		0			0
$827$	16.4277	−	9.48453i	0.571247	−	0.329809i	−0.186400	−	0.982474i	$-0.559682\pi$
$827$	16.4277	−	9.48453i	0.571247	−	0.329809i	0.757647	+	0.652664i	$0.226349\pi$
$828$		0			0
$829$	2.80253	−	1.61804i	0.0973360	−	0.0561969i	−0.450542	−	0.892755i	$-0.648769\pi$
$829$	2.80253	−	1.61804i	0.0973360	−	0.0561969i	0.547878	+	0.836558i	$0.315436\pi$
$830$		0			0
$831$	−11.0147	+	6.53359i	−0.382096	+	0.226648i
$832$		0			0
$833$	−0.904360	−	4.35032i	−0.0313342	−	0.150730i
$834$		0			0
$835$	0.861095	−	4.88351i	0.0297994	−	0.169001i
$836$		0			0
$837$	6.21689	+	29.1849i	0.214887	+	1.00878i
$838$		0			0
$839$	−29.0176	−	24.3487i	−1.00180	−	0.840610i	−0.0145673	−	0.999894i	$-0.504637\pi$
$839$	−29.0176	−	24.3487i	−1.00180	−	0.840610i	−0.987233	+	0.159284i	$0.949082\pi$
$840$		0			0
$841$	4.66806	+	26.4739i	0.160967	+	0.912892i
$842$		0			0
$843$	−48.7037	+	0.573879i	−1.67744	+	0.0197655i
$844$		0			0
$845$	−7.06397			−0.243008
$846$		0			0
$847$	9.19074	+	15.3738i	0.315797	+	0.528249i
$848$		0			0
$849$	−4.02966	+	24.5408i	−0.138298	+	0.842236i
$850$		0			0
$851$	−0.542681	+	0.0956892i	−0.0186028	+	0.00328018i
$852$		0			0
$853$	7.23977	+	19.8911i	0.247885	+	0.681059i	0.999763	+	0.0217566i	$0.00692587\pi$
$853$	7.23977	+	19.8911i	0.247885	+	0.681059i	−0.751878	+	0.659302i	$0.770852\pi$
$854$		0			0
$855$	−5.64933	−	3.08649i	−0.193203	−	0.105556i
$856$		0			0
$857$	4.37999	+	3.67525i	0.149618	+	0.125544i	0.714524	−	0.699611i	$-0.246643\pi$
$857$	4.37999	+	3.67525i	0.149618	+	0.125544i	−0.564906	+	0.825155i	$0.691088\pi$
$858$		0			0
$859$	31.9605	−	5.63550i	1.09048	−	0.192281i	0.400634	−	0.916238i	$-0.368790\pi$
$859$	31.9605	−	5.63550i	1.09048	−	0.192281i	0.689844	+	0.723958i	$0.257679\pi$
$860$		0			0
$861$	6.41395	−	19.2215i	0.218587	−	0.655068i
$862$		0			0
$863$	−30.0304	+	17.3381i	−1.02225	+	0.590195i	−0.914754	−	0.404010i	$-0.867616\pi$
$863$	−30.0304	+	17.3381i	−1.02225	+	0.590195i	−0.107494	+	0.994206i	$0.534283\pi$
$864$		0			0
$865$	−3.98476	+	6.90180i	−0.135486	+	0.234668i
$866$		0			0
$867$	9.51309	−	27.1273i	0.323081	−	0.921291i
$868$		0			0
$869$	10.9168	−	29.9936i	0.370326	−	1.01746i
$870$		0			0
$871$	−0.948688	+	1.13060i	−0.0321451	+	0.0383090i
$872$		0			0
$873$	−0.667275	+	1.97708i	−0.0225838	+	0.0669139i
$874$		0			0
$875$	2.25416	−	14.0289i	0.0762044	−	0.474265i
$876$		0			0
$877$	29.3723	+	10.6906i	0.991831	+	0.360997i	0.786429	−	0.617681i	$-0.211928\pi$
$877$	29.3723	+	10.6906i	0.991831	+	0.360997i	0.205402	+	0.978678i	$0.434150\pi$
$878$		0			0
$879$	−52.0419	−	8.54543i	−1.75533	−	0.288230i
$880$		0			0
$881$	−13.4190	−	23.2423i	−0.452096	−	0.783054i	0.546420	−	0.837512i	$-0.315990\pi$
$881$	−13.4190	−	23.2423i	−0.452096	−	0.783054i	−0.998516	+	0.0544575i	$0.982657\pi$
$882$		0			0
$883$	6.51565	−	11.2854i	0.219269	−	0.379785i	−0.735316	−	0.677725i	$-0.762966\pi$
$883$	6.51565	−	11.2854i	0.219269	−	0.379785i	0.954585	+	0.297940i	$0.0962994\pi$
$884$		0			0
$885$	6.67093	−	3.95699i	0.224241	−	0.133013i
$886$		0			0
$887$	−28.5874	+	23.9877i	−0.959871	+	0.805427i	−0.980932	−	0.194351i	$-0.937740\pi$
$887$	−28.5874	+	23.9877i	−0.959871	+	0.805427i	0.0210612	+	0.999778i	$0.493296\pi$
$888$		0			0
$889$	−17.1519	+	6.53999i	−0.575256	+	0.219344i
$890$		0			0
$891$	1.78741	+	37.8968i	0.0598803	+	1.26959i
$892$		0			0
$893$	−1.59275	−	4.37604i	−0.0532993	−	0.146439i
$894$		0			0
$895$	−11.8495	+	2.08939i	−0.396086	+	0.0698407i
$896$		0			0
$897$	−0.0447342	−	0.0251293i	−0.00149363	−	0.000839041i
$898$		0			0
$899$	4.17847	+	7.23733i	0.139360	+	0.241378i
$900$		0			0
$901$	−1.18318	−	0.683111i	−0.0394175	−	0.0227577i
$902$		0			0
$903$	6.55056	−	8.24903i	0.217989	−	0.274511i
$904$		0			0
$905$	−0.219937	+	0.604272i	−0.00731096	+	0.0200867i
$906$		0			0
$907$	−3.86002	+	21.8913i	−0.128170	+	0.726888i	0.851205	+	0.524834i	$0.175873\pi$
$907$	−3.86002	+	21.8913i	−0.128170	+	0.726888i	−0.979374	+	0.202054i	$0.935238\pi$
$908$		0			0
$909$	−11.5196	−	57.3882i	−0.382080	−	1.90345i
$910$		0			0
$911$	31.6495	+	5.58066i	1.04859	+	0.184895i	0.671291	−	0.741194i	$-0.265740\pi$
$911$	31.6495	+	5.58066i	1.04859	+	0.184895i	0.377304	+	0.926090i	$0.376851\pi$
$912$		0			0
$913$	−31.7980	−	37.8954i	−1.05236	−	1.25415i
$914$		0			0
$915$	0.669399	+	3.55116i	0.0221297	+	0.117398i
$916$		0			0
$917$	40.2003	−	0.611721i	1.32753	−	0.0202008i
$918$		0			0
$919$	24.2898	+	42.0712i	0.801248	+	1.38780i	0.918795	+	0.394735i	$0.129164\pi$
$919$	24.2898	+	42.0712i	0.801248	+	1.38780i	−0.117547	+	0.993067i	$0.537503\pi$
$920$		0			0
$921$	4.17962	+	22.1728i	0.137723	+	0.730620i
$922$		0			0
$923$	2.37772	+	0.865419i	0.0782636	+	0.0284856i
$924$		0			0
$925$	−7.58551	+	43.0196i	−0.249410	+	1.41447i
$926$		0			0
$927$	−26.7562	−	14.6182i	−0.878789	−	0.480123i
$928$		0			0
$929$	12.8746	+	10.8030i	0.422401	+	0.354436i	0.829076	−	0.559137i	$-0.188867\pi$
$929$	12.8746	+	10.8030i	0.422401	+	0.354436i	−0.406675	+	0.913573i	$0.633312\pi$
$930$		0			0
$931$	−26.5433	+	5.51792i	−0.869922	+	0.180842i
$932$		0			0
$933$	−52.8336	−	8.67542i	−1.72969	−	0.284021i
$934$		0			0
$935$			1.48253i			0.0484840i
$936$		0			0
$937$	37.6065	+	21.7121i	1.22855	+	0.709304i	0.966727	−	0.255811i	$-0.0823426\pi$
$937$	37.6065	+	21.7121i	1.22855	+	0.709304i	0.261824	+	0.965116i	$0.415676\pi$
$938$		0			0
$939$	19.0090	+	32.0466i	0.620336	+	1.04580i
$940$		0			0
$941$	−19.5994	−	7.13359i	−0.638922	−	0.232549i	0.00218805	−	0.999998i	$-0.499304\pi$
$941$	−19.5994	−	7.13359i	−0.638922	−	0.232549i	−0.641110	+	0.767449i	$0.721526\pi$
$942$		0			0
$943$	−0.257802	−	0.0454574i	−0.00839518	−	0.00148030i
$944$		0			0
$945$	−0.384975	−	7.60724i	−0.0125232	−	0.247463i
$946$		0			0
$947$	56.3197	+	9.93068i	1.83014	+	0.322704i	0.979254	−	0.202639i	$-0.0649517\pi$
$947$	56.3197	+	9.93068i	1.83014	+	0.322704i	0.850891	+	0.525343i	$0.176063\pi$
$948$		0			0
$949$	−5.26794	−	1.91737i	−0.171004	−	0.0622405i
$950$		0			0
$951$	−32.6483	+	0.384697i	−1.05869	+	0.0124747i
$952$		0			0
$953$	13.8015	+	7.96833i	0.447076	+	0.258119i	0.706595	−	0.707619i	$-0.250231\pi$
$953$	13.8015	+	7.96833i	0.447076	+	0.258119i	−0.259518	+	0.965738i	$0.583564\pi$
$954$		0			0
$955$			5.85795i			0.189559i
$956$		0			0
$957$	3.75143	+	9.94095i	0.121267	+	0.321345i
$958$		0			0
$959$	−0.110866	+	0.319652i	−0.00358004	+	0.0103221i
$960$		0			0
$961$	−1.51524	−	1.27144i	−0.0488787	−	0.0410141i
$962$		0			0
$963$	−34.5831	−	5.26096i	−1.11442	−	0.169532i
$964$		0			0
$965$	0.248368	−	1.40857i	0.00799526	−	0.0453434i
$966$		0			0
$967$	−4.50777	−	1.64069i	−0.144960	−	0.0527611i	0.268521	−	0.963274i	$-0.413465\pi$
$967$	−4.50777	−	1.64069i	−0.144960	−	0.0527611i	−0.413481	+	0.910513i	$0.635687\pi$
$968$		0			0
$969$	4.01818	+	1.40911i	0.129083	+	0.0452671i
$970$		0			0
$971$	−16.9136	−	29.2952i	−0.542783	−	0.940128i	−0.998743	−	0.0501276i	$-0.984037\pi$
$971$	−16.9136	−	29.2952i	−0.542783	−	0.940128i	0.455960	−	0.890000i	$-0.349296\pi$
$972$		0			0
$973$	0.225078	+	0.125422i	0.00721566	+	0.00402084i
$974$		0			0
$975$	−3.08479	+	2.65100i	−0.0987923	+	0.0849001i
$976$		0			0
$977$	14.7099	+	17.5305i	0.470611	+	0.560852i	0.948177	−	0.317744i	$-0.102925\pi$
$977$	14.7099	+	17.5305i	0.470611	+	0.560852i	−0.477566	+	0.878596i	$0.658481\pi$
$978$		0			0
$979$	−50.8296	−	8.96264i	−1.62452	−	0.286447i
$980$		0			0
$981$	−42.4146	+	16.5796i	−1.35420	+	0.529346i
$982$		0			0
$983$	9.64572	−	54.7036i	0.307651	−	1.74477i	−0.303108	−	0.952956i	$-0.598024\pi$
$983$	9.64572	−	54.7036i	0.307651	−	1.74477i	0.610758	−	0.791817i	$-0.290865\pi$
$984$		0			0
$985$	−4.34817	+	11.9465i	−0.138544	+	0.380647i
$986$		0			0
$987$	3.42660	−	4.31507i	0.109070	−	0.137350i
$988$		0			0
$989$	−0.117850	−	0.0680405i	−0.00374740	−	0.00216356i
$990$		0			0
$991$	25.1595	+	43.5775i	0.799217	+	1.38428i	0.920127	+	0.391620i	$0.128085\pi$
$991$	25.1595	+	43.5775i	0.799217	+	1.38428i	−0.120910	+	0.992663i	$0.538581\pi$
$992$		0			0
$993$	0.650499	+	55.2062i	0.0206430	+	1.75192i
$994$		0			0
$995$	10.3808	−	1.83042i	0.329094	−	0.0580281i
$996$		0			0
$997$	11.0908	+	30.4717i	0.351249	+	0.965049i	0.981970	+	0.189039i	$0.0605373\pi$
$997$	11.0908	+	30.4717i	0.351249	+	0.965049i	−0.630720	+	0.776010i	$0.717241\pi$
$998$		0			0
$999$	1.70928	+	48.3362i	0.0540792	+	1.52929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.9	yes	144
7.5	odd	6		756.2.ca.a.173.18	✓	144
27.5	odd	18		756.2.ca.a.437.18	yes	144
189.5	even	18	inner	756.2.ck.a.5.9	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.18	✓	144	7.5	odd	6
756.2.ca.a.437.18	yes	144	27.5	odd	18
756.2.ck.a.5.9	yes	144	189.5	even	18	inner
756.2.ck.a.605.9	yes	144	1.1	even	1	trivial

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.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573178 + 1.63446i) q^{3} +(-0.0962103 - 0.545636i) q^{5} +(2.05240 + 1.66962i) q^{7} +(-2.34293 - 1.87368i) q^{9} +O(q^{10})\)	\(q+(-0.573178 + 1.63446i) q^{3} +(-0.0962103 - 0.545636i) q^{5} +(2.05240 + 1.66962i) q^{7} +(-2.34293 - 1.87368i) q^{9} +(4.15140 + 0.732003i) q^{11} +(0.321641 + 0.383316i) q^{13} +(0.946967 + 0.155495i) q^{15} -0.634761 q^{17} +3.87297i q^{19} +(-3.90533 + 2.39759i) q^{21} +(0.0380538 + 0.0453508i) q^{23} +(4.41000 - 1.60511i) q^{25} +(4.40537 - 2.75548i) q^{27} +(0.935412 - 1.11478i) q^{29} +(-1.96410 + 5.39632i) q^{31} +(-3.57592 + 6.36573i) q^{33} +(0.713543 - 1.28050i) q^{35} +(-4.65406 + 8.06107i) q^{37} +(-0.810873 + 0.306001i) q^{39} +(-3.38733 + 2.84230i) q^{41} +(-2.15999 + 0.786173i) q^{43} +(-0.796931 + 1.45866i) q^{45} +(-1.12989 + 0.411247i) q^{47} +(1.42472 + 6.85348i) q^{49} +(0.363831 - 1.03749i) q^{51} +(1.86398 + 1.07617i) q^{53} -2.33558i q^{55} +(-6.33022 - 2.21990i) q^{57} +(6.19145 - 5.19525i) q^{59} +(1.28793 + 3.53855i) q^{61} +(-1.68031 - 7.75735i) q^{63} +(0.178206 - 0.212378i) q^{65} +(0.512180 + 2.90472i) q^{67} +(-0.0959358 + 0.0362035i) q^{69} +(4.37928 - 2.52838i) q^{71} +(-9.70247 + 5.60172i) q^{73} +(0.0957728 + 8.12799i) q^{75} +(7.29817 + 8.43363i) q^{77} +(1.31483 - 7.45679i) q^{79} +(1.97867 + 8.77980i) q^{81} +(-8.98967 - 7.54323i) q^{83} +(0.0610706 + 0.346349i) q^{85} +(1.28591 + 2.16786i) q^{87} -12.2440 q^{89} +(0.0201431 + 1.32374i) q^{91} +(-7.69431 - 6.30331i) q^{93} +(2.11323 - 0.372620i) q^{95} +(-0.237892 - 0.653602i) q^{97} +(-8.35491 - 9.49341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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