LMFDB - Embedded newform 441.2.h.h.214.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			214.12
Character	$\chi$	$=$	441.214
Dual form			441.2.h.h.373.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17631 q^{2} +(0.507459 - 1.65605i) q^{3} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-2.48497 - 1.68075i) q^{9} +O(q^{10})$	\(q+2.17631 q^{2} +(0.507459 - 1.65605i) q^{3} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-2.48497 - 1.68075i) q^{9} +(1.38010 - 2.39040i) q^{10} +(2.73867 + 4.74351i) q^{11} +(1.38857 - 4.53149i) q^{12} +(-2.37268 - 4.10960i) q^{13} +(-1.49715 - 1.60755i) q^{15} -1.98516 q^{16} +(-2.40822 + 4.17116i) q^{17} +(-5.40807 - 3.65783i) q^{18} +(2.69059 + 4.66025i) q^{19} +(1.73523 - 3.00550i) q^{20} +(5.96019 + 10.3233i) q^{22} +(2.58816 - 4.48282i) q^{23} +(0.813193 - 2.65378i) q^{24} +(1.69572 + 2.93707i) q^{25} +(-5.16368 - 8.94376i) q^{26} +(-4.04442 + 3.26231i) q^{27} +(2.01656 - 3.49278i) q^{29} +(-3.25826 - 3.49853i) q^{30} +1.46419 q^{31} -7.52529 q^{32} +(9.24522 - 2.12822i) q^{33} +(-5.24103 + 9.07773i) q^{34} +(-6.79970 - 4.59908i) q^{36} +(-0.959170 - 1.66133i) q^{37} +(5.85557 + 10.1421i) q^{38} +(-8.00971 + 1.84381i) q^{39} +(1.01621 - 1.76012i) q^{40} +(1.94808 + 3.37418i) q^{41} +(-1.66016 + 2.87549i) q^{43} +(7.49389 + 12.9798i) q^{44} +(-3.42192 + 1.66358i) q^{45} +(5.63263 - 9.75600i) q^{46} -3.15546 q^{47} +(-1.00739 + 3.28752i) q^{48} +(3.69042 + 6.39199i) q^{50} +(5.68555 + 6.10481i) q^{51} +(-6.49243 - 11.2452i) q^{52} +(3.57149 - 6.18601i) q^{53} +(-8.80191 + 7.09981i) q^{54} +6.94684 q^{55} +(9.08294 - 2.09086i) q^{57} +(4.38866 - 7.60138i) q^{58} -0.308683 q^{59} +(-4.09669 - 4.39879i) q^{60} -10.3429 q^{61} +3.18652 q^{62} -12.4070 q^{64} -6.01848 q^{65} +(20.1205 - 4.63167i) q^{66} +4.47310 q^{67} +(-6.58968 + 11.4137i) q^{68} +(-6.11037 - 6.56095i) q^{69} -1.96688 q^{71} +(-3.98212 - 2.69337i) q^{72} +(-5.27515 + 9.13683i) q^{73} +(-2.08745 - 3.61557i) q^{74} +(5.72444 - 1.31775i) q^{75} +(7.36235 + 12.7520i) q^{76} +(-17.4316 + 4.01270i) q^{78} -9.01643 q^{79} +(-1.25888 + 2.18044i) q^{80} +(3.35017 + 8.35323i) q^{81} +(4.23963 + 7.34326i) q^{82} +(5.08023 - 8.79921i) q^{83} +(3.05432 + 5.29023i) q^{85} +(-3.61303 + 6.25796i) q^{86} +(-4.76089 - 5.11196i) q^{87} +(4.38866 + 7.60138i) q^{88} +(2.59776 + 4.49945i) q^{89} +(-7.44716 + 3.62047i) q^{90} +(7.08205 - 12.2665i) q^{92} +(0.743014 - 2.42476i) q^{93} -6.86726 q^{94} +6.82490 q^{95} +(-3.81877 + 12.4622i) q^{96} +(2.48521 - 4.30451i) q^{97} +(1.16714 - 16.3905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.17631			1.53888			0.769442	−	0.638717i	$-0.220534\pi$
$2$	2.17631			1.53888			0.769442	+	0.638717i	$0.220534\pi$
$3$	0.507459	−	1.65605i	0.292981	−	0.956118i
$3$	0.507459	−	1.65605i	0.292981	−	0.956118i
$4$	2.73633			1.36816
$5$	0.634145	−	1.09837i	0.283598	−	0.491206i	−0.688670	−	0.725075i	$-0.741805\pi$
$5$	0.634145	−	1.09837i	0.283598	−	0.491206i	0.972268	+	0.233868i	$0.0751385\pi$
$6$	1.10439	−	3.60407i	0.450864	−	1.47136i
$7$		0			0
$7$		0			0
$8$	1.60248			0.566563
$9$	−2.48497	−	1.68075i	−0.828324	−	0.560250i
$10$	1.38010	−	2.39040i	0.436425	−	0.755910i
$11$	2.73867	+	4.74351i	0.825739	+	1.43022i	0.901353	+	0.433084i	$0.142575\pi$
$11$	2.73867	+	4.74351i	0.825739	+	1.43022i	−0.0756148	+	0.997137i	$0.524092\pi$
$12$	1.38857	−	4.53149i	0.400847	−	1.30813i
$13$	−2.37268	−	4.10960i	−0.658062	−	1.13980i	−0.981117	−	0.193417i	$-0.938043\pi$
$13$	−2.37268	−	4.10960i	−0.658062	−	1.13980i	0.323054	−	0.946380i	$-0.395290\pi$
$14$		0			0
$15$	−1.49715	−	1.60755i	−0.386562	−	0.415068i
$16$	−1.98516			−0.496290
$17$	−2.40822	+	4.17116i	−0.584079	+	1.01165i	0.410911	+	0.911676i	$0.365211\pi$
$17$	−2.40822	+	4.17116i	−0.584079	+	1.01165i	−0.994990	+	0.0999785i	$0.968123\pi$
$18$	−5.40807	−	3.65783i	−1.27469	−	0.862159i
$19$	2.69059	+	4.66025i	0.617265	+	1.06913i	0.989983	+	0.141189i	$0.0450925\pi$
$19$	2.69059	+	4.66025i	0.617265	+	1.06913i	−0.372718	+	0.927945i	$0.621574\pi$
$20$	1.73523	−	3.00550i	0.388009	−	0.672051i
$21$		0			0
$22$	5.96019	+	10.3233i	1.27072	+	2.20095i
$23$	2.58816	−	4.48282i	0.539668	−	0.934732i	−0.459254	−	0.888305i	$-0.651883\pi$
$23$	2.58816	−	4.48282i	0.539668	−	0.934732i	0.998922	−	0.0464269i	$-0.0147835\pi$
$24$	0.813193	−	2.65378i	0.165992	−	0.541701i
$25$	1.69572	+	2.93707i	0.339144	+	0.587415i
$26$	−5.16368	−	8.94376i	−1.01268	−	1.75402i
$27$	−4.04442	+	3.26231i	−0.778348	+	0.627833i
$28$		0			0
$29$	2.01656	−	3.49278i	0.374466	−	0.648594i	−0.615781	−	0.787917i	$-0.711159\pi$
$29$	2.01656	−	3.49278i	0.374466	−	0.648594i	0.990247	+	0.139324i	$0.0444928\pi$
$30$	−3.25826	−	3.49853i	−0.594875	−	0.638741i
$31$	1.46419			0.262976			0.131488	−	0.991318i	$-0.458025\pi$
$31$	1.46419			0.262976			0.131488	+	0.991318i	$0.458025\pi$
$32$	−7.52529			−1.33030
$33$	9.24522	−	2.12822i	1.60939	−	0.370476i
$34$	−5.24103	+	9.07773i	−0.898830	+	1.55682i
$35$		0			0
$36$	−6.79970	−	4.59908i	−1.13328	−	0.766514i
$37$	−0.959170	−	1.66133i	−0.157687	−	0.273121i	0.776347	−	0.630305i	$-0.217070\pi$
$37$	−0.959170	−	1.66133i	−0.157687	−	0.273121i	−0.934034	+	0.357184i	$0.883737\pi$
$38$	5.85557	+	10.1421i	0.949899	+	1.64527i
$39$	−8.00971	+	1.84381i	−1.28258	+	0.295246i
$40$	1.01621	−	1.76012i	0.160676	−	0.278299i
$41$	1.94808	+	3.37418i	0.304239	+	0.526958i	0.977092	−	0.212819i	$-0.0682644\pi$
$41$	1.94808	+	3.37418i	0.304239	+	0.526958i	−0.672852	+	0.739777i	$0.734931\pi$
$42$		0			0
$43$	−1.66016	+	2.87549i	−0.253173	+	0.438508i	−0.964398	−	0.264457i	$-0.914807\pi$
$43$	−1.66016	+	2.87549i	−0.253173	+	0.438508i	0.711225	+	0.702964i	$0.248141\pi$
$44$	7.49389	+	12.9798i	1.12975	+	1.95678i
$45$	−3.42192	+	1.66358i	−0.510109	+	0.247992i
$46$	5.63263	−	9.75600i	0.830486	−	1.43844i
$47$	−3.15546			−0.460271			−0.230135	−	0.973159i	$-0.573917\pi$
$47$	−3.15546			−0.460271			−0.230135	+	0.973159i	$0.573917\pi$
$48$	−1.00739	+	3.28752i	−0.145404	+	0.474512i
$49$		0			0
$50$	3.69042	+	6.39199i	0.521904	+	0.903964i
$51$	5.68555	+	6.10481i	0.796137	+	0.854844i
$52$	−6.49243	−	11.2452i	−0.900338	−	1.55943i
$53$	3.57149	−	6.18601i	0.490582	−	0.849714i	−0.509359	−	0.860554i	$-0.670117\pi$
$53$	3.57149	−	6.18601i	0.490582	−	0.849714i	0.999941	+	0.0108405i	$0.00345071\pi$
$54$	−8.80191	+	7.09981i	−1.19779	+	0.966162i
$55$	6.94684			0.936712
$56$		0			0
$57$	9.08294	−	2.09086i	1.20307	−	0.276942i
$58$	4.38866	−	7.60138i	0.576259	−	0.998111i
$59$	−0.308683			−0.0401871			−0.0200935	−	0.999798i	$-0.506396\pi$
$59$	−0.308683			−0.0401871			−0.0200935	+	0.999798i	$0.506396\pi$
$60$	−4.09669	−	4.39879i	−0.528881	−	0.567881i
$61$	−10.3429			−1.32427			−0.662134	−	0.749385i	$-0.730349\pi$
$61$	−10.3429			−1.32427			−0.662134	+	0.749385i	$0.730349\pi$
$62$	3.18652			0.404689
$63$		0			0
$64$	−12.4070			−1.55088
$65$	−6.01848			−0.746501
$66$	20.1205	−	4.63167i	2.47666	−	0.570119i
$67$	4.47310			0.546476			0.273238	−	0.961946i	$-0.411905\pi$
$67$	4.47310			0.546476			0.273238	+	0.961946i	$0.411905\pi$
$68$	−6.58968	+	11.4137i	−0.799116	+	1.38411i
$69$	−6.11037	−	6.56095i	−0.735602	−	0.789845i
$70$		0			0
$71$	−1.96688			−0.233426			−0.116713	−	0.993166i	$-0.537236\pi$
$71$	−1.96688			−0.233426			−0.116713	+	0.993166i	$0.537236\pi$
$72$	−3.98212	−	2.69337i	−0.469297	−	0.317417i
$73$	−5.27515	+	9.13683i	−0.617409	+	1.06938i	0.372547	+	0.928013i	$0.378484\pi$
$73$	−5.27515	+	9.13683i	−0.617409	+	1.06938i	−0.989957	+	0.141371i	$0.954849\pi$
$74$	−2.08745	−	3.61557i	−0.242662	−	0.420302i
$75$	5.72444	−	1.31775i	0.661001	−	0.152160i
$76$	7.36235	+	12.7520i	0.844520	+	1.46275i
$77$		0			0
$78$	−17.4316	+	4.01270i	−1.97374	+	0.454349i
$79$	−9.01643			−1.01443			−0.507214	−	0.861820i	$-0.669325\pi$
$79$	−9.01643			−1.01443			−0.507214	+	0.861820i	$0.669325\pi$
$80$	−1.25888	+	2.18044i	−0.140747	+	0.243781i
$81$	3.35017	+	8.35323i	0.372241	+	0.928136i
$82$	4.23963	+	7.34326i	0.468189	+	0.810927i
$83$	5.08023	−	8.79921i	0.557627	−	0.965839i	−0.440066	−	0.897965i	$-0.645045\pi$
$83$	5.08023	−	8.79921i	0.557627	−	0.965839i	0.997694	−	0.0678739i	$-0.0216216\pi$
$84$		0			0
$85$	3.05432	+	5.29023i	0.331287	+	0.573806i
$86$	−3.61303	+	6.25796i	−0.389603	+	0.674813i
$87$	−4.76089	−	5.11196i	−0.510421	−	0.548059i
$88$	4.38866	+	7.60138i	0.467833	+	0.810310i
$89$	2.59776	+	4.49945i	0.275362	+	0.476941i	0.970226	−	0.242200i	$-0.0778690\pi$
$89$	2.59776	+	4.49945i	0.275362	+	0.476941i	−0.694864	+	0.719141i	$0.744536\pi$
$90$	−7.44716	+	3.62047i	−0.784999	+	0.381631i
$91$		0			0
$92$	7.08205	−	12.2665i	0.738354	−	1.27887i
$93$	0.743014	−	2.42476i	0.0770469	−	0.251436i
$94$	−6.86726			−0.708303
$95$	6.82490			0.700220
$96$	−3.81877	+	12.4622i	−0.389752	+	1.27192i
$97$	2.48521	−	4.30451i	0.252335	−	0.437057i	−0.711833	−	0.702348i	$-0.752135\pi$
$97$	2.48521	−	4.30451i	0.252335	−	0.437057i	0.964168	+	0.265291i	$0.0854682\pi$
$98$		0			0
$99$	1.16714	−	16.3905i	0.117302	−	1.64731i
$100$	4.64005	+	8.03680i	0.464005	+	0.803680i
$101$	0.00266904	+	0.00462292i	0.000265580	+	0.000459997i	0.866158	−	0.499770i	$-0.166582\pi$
$101$	0.00266904	+	0.00462292i	0.000265580	+	0.000459997i	−0.865893	+	0.500230i	$0.833249\pi$
$102$	12.3735	+	13.2860i	1.22516	+	1.31551i
$103$	6.51741	−	11.2885i	0.642180	−	1.11229i	−0.342765	−	0.939421i	$-0.611364\pi$
$103$	6.51741	−	11.2885i	0.642180	−	1.11229i	0.984945	−	0.172867i	$-0.0553030\pi$
$104$	−3.80217	−	6.58555i	−0.372834	−	0.645767i
$105$		0			0
$106$	7.77268	−	13.4627i	0.754950	−	1.30761i
$107$	−4.71081	−	8.15936i	−0.455411	−	0.788795i	0.543301	−	0.839538i	$-0.317174\pi$
$107$	−4.71081	−	8.15936i	−0.455411	−	0.788795i	−0.998712	+	0.0507430i	$0.983841\pi$
$108$	−11.0669	+	8.92677i	−1.06491	+	0.858979i
$109$	−8.44513	+	14.6274i	−0.808896	+	1.40105i	0.104732	+	0.994500i	$0.466601\pi$
$109$	−8.44513	+	14.6274i	−0.808896	+	1.40105i	−0.913629	+	0.406549i	$0.866732\pi$
$110$	15.1185			1.44149
$111$	−3.23798	+	0.745372i	−0.307335	+	0.0707476i
$112$		0			0
$113$	−3.07313	−	5.32281i	−0.289095	−	0.500728i	0.684499	−	0.729014i	$-0.260021\pi$
$113$	−3.07313	−	5.32281i	−0.289095	−	0.500728i	−0.973594	+	0.228286i	$0.926688\pi$
$114$	19.7673	−	4.55037i	1.85138	−	0.426181i
$115$	−3.28253	−	5.68551i	−0.306098	−	0.530176i
$116$	5.51797	−	9.55741i	0.512331	−	0.887383i
$117$	−1.01117	+	14.2001i	−0.0934823	+	1.31280i
$118$	−0.671790			−0.0618432
$119$		0			0
$120$	−2.39915	−	2.57607i	−0.219012	−	0.235162i
$121$	−9.50058	+	16.4555i	−0.863689	+	1.49595i
$122$	−22.5093			−2.03790
$123$	6.57636	−	1.51386i	0.592970	−	0.136500i
$124$	4.00649			0.359794
$125$	10.6428			0.951919
$126$		0			0
$127$	−13.9305			−1.23613			−0.618065	−	0.786127i	$-0.712083\pi$
$127$	−13.9305			−1.23613			−0.618065	+	0.786127i	$0.712083\pi$
$128$	−11.9510			−1.05633
$129$	3.91947	+	4.20850i	0.345090	+	0.370538i
$130$	−13.0981			−1.14878
$131$	−0.0895778	+	0.155153i	−0.00782645	+	0.0135558i	−0.869912	−	0.493207i	$-0.835825\pi$
$131$	−0.0895778	+	0.155153i	−0.00782645	+	0.0135558i	0.862086	+	0.506763i	$0.169158\pi$
$132$	25.2980	−	5.82351i	2.20191	−	0.506872i
$133$		0			0
$134$	9.73486			0.840964
$135$	1.01849	+	6.51105i	0.0876574	+	0.560382i
$136$	−3.85913	+	6.68420i	−0.330917	+	0.573166i
$137$	−1.57603	−	2.72977i	−0.134649	−	0.233220i	0.790814	−	0.612056i	$-0.209657\pi$
$137$	−1.57603	−	2.72977i	−0.134649	−	0.233220i	−0.925463	+	0.378837i	$0.876324\pi$
$138$	−13.2981	−	14.2787i	−1.13201	−	1.21548i
$139$	−9.42857	−	16.3308i	−0.799721	−	1.38516i	−0.919798	−	0.392392i	$-0.871648\pi$
$139$	−9.42857	−	16.3308i	−0.799721	−	1.38516i	0.120077	−	0.992765i	$-0.461686\pi$
$140$		0			0
$141$	−1.60126	+	5.22558i	−0.134851	+	0.440073i
$142$	−4.28054			−0.359215
$143$	12.9959	−	22.5096i	1.08677	−	1.88235i
$144$	4.93307	+	3.33656i	0.411089	+	0.278046i
$145$	−2.55758	−	4.42986i	−0.212396	−	0.367880i
$146$	−11.4804	+	19.8846i	−0.950122	+	1.64566i
$147$		0			0
$148$	−2.62461	−	4.54595i	−0.215741	−	0.373675i
$149$	10.6370	−	18.4238i	0.871418	−	1.50934i	0.0108879	−	0.999941i	$-0.496534\pi$
$149$	10.6370	−	18.4238i	0.871418	−	1.50934i	0.860530	−	0.509400i	$-0.170132\pi$
$150$	12.4582	−	2.86783i	1.01720	−	0.234157i
$151$	−3.18281	−	5.51278i	−0.259013	−	0.448624i	0.706965	−	0.707249i	$-0.250064\pi$
$151$	−3.18281	−	5.51278i	−0.259013	−	0.448624i	−0.965978	+	0.258625i	$0.916731\pi$
$152$	4.31163	+	7.46796i	0.349719	+	0.605731i
$153$	12.9950	−	6.31759i	1.05059	−	0.510747i
$154$		0			0
$155$	0.928506	−	1.60822i	0.0745794	−	0.129175i
$156$	−21.9172	+	5.04527i	−1.75478	+	0.403945i
$157$	−1.39595			−0.111409			−0.0557045	−	0.998447i	$-0.517740\pi$
$157$	−1.39595			−0.111409			−0.0557045	+	0.998447i	$0.517740\pi$
$158$	−19.6226			−1.56109
$159$	−8.43193	−	9.05370i	−0.668695	−	0.718005i
$160$	−4.77212	+	8.26556i	−0.377269	+	0.653450i
$161$		0			0
$162$	7.29101	+	18.1792i	0.572836	+	1.42829i
$163$	9.53086	+	16.5079i	0.746515	+	1.29300i	0.949484	+	0.313816i	$0.101608\pi$
$163$	9.53086	+	16.5079i	0.746515	+	1.29300i	−0.202969	+	0.979185i	$0.565059\pi$
$164$	5.33059	+	9.23286i	0.416249	+	0.720965i
$165$	3.52523	−	11.5043i	0.274439	−	0.895607i
$166$	11.0562	−	19.1498i	0.858124	−	1.48631i
$167$	−0.872003	−	1.51035i	−0.0674776	−	0.116875i	0.830313	−	0.557298i	$-0.188162\pi$
$167$	−0.872003	−	1.51035i	−0.0674776	−	0.116875i	−0.897790	+	0.440423i	$0.854828\pi$
$168$		0			0
$169$	−4.75919	+	8.24317i	−0.366092	+	0.634090i
$170$	6.64715	+	11.5132i	0.509813	+	0.883022i
$171$	1.14665	−	16.1028i	0.0876867	−	1.23141i
$172$	−4.54276	+	7.86828i	−0.346382	+	0.599951i
$173$	10.0759			0.766056			0.383028	−	0.923737i	$-0.374881\pi$
$173$	10.0759			0.766056			0.383028	+	0.923737i	$0.374881\pi$
$174$	−10.3612	−	11.1252i	−0.785478	−	0.843400i
$175$		0			0
$176$	−5.43669	−	9.41662i	−0.409806	−	0.709805i
$177$	−0.156644	+	0.511193i	−0.0117741	+	0.0384236i
$178$	5.65353	+	9.79221i	0.423750	+	0.733957i
$179$	9.27118	−	16.0582i	0.692961	−	1.20024i	−0.277902	−	0.960609i	$-0.589639\pi$
$179$	9.27118	−	16.0582i	0.692961	−	1.20024i	0.970863	−	0.239634i	$-0.0770275\pi$
$180$	−9.36349	+	4.55211i	−0.697914	+	0.339294i
$181$	8.80982			0.654829			0.327414	−	0.944881i	$-0.393823\pi$
$181$	8.80982			0.654829			0.327414	+	0.944881i	$0.393823\pi$
$182$		0			0
$183$	−5.24858	+	17.1283i	−0.387986	+	1.26616i
$184$	4.14747	−	7.18363i	0.305756	−	0.529584i
$185$	−2.43301			−0.178879
$186$	1.61703	−	5.27703i	0.118566	−	0.386930i
$187$	−26.3812			−1.92919
$188$	−8.63437			−0.629726
$189$		0			0
$190$	14.8531			1.07756
$191$	4.90939			0.355231			0.177615	−	0.984100i	$-0.443162\pi$
$191$	4.90939			0.355231			0.177615	+	0.984100i	$0.443162\pi$
$192$	−6.29606	+	20.5466i	−0.454379	+	1.48283i
$193$	−9.76760			−0.703087			−0.351544	−	0.936171i	$-0.614343\pi$
$193$	−9.76760			−0.703087			−0.351544	+	0.936171i	$0.614343\pi$
$194$	5.40859	−	9.36796i	0.388314	−	0.672580i
$195$	−3.05413	+	9.96688i	−0.218711	+	0.713743i
$196$		0			0
$197$	3.31445			0.236145			0.118073	−	0.993005i	$-0.462328\pi$
$197$	3.31445			0.236145			0.118073	+	0.993005i	$0.462328\pi$
$198$	2.54006	−	35.6708i	0.180514	−	2.53501i
$199$	5.54432	−	9.60304i	0.393026	−	0.680742i	−0.599821	−	0.800134i	$-0.704761\pi$
$199$	5.54432	−	9.60304i	0.393026	−	0.680742i	0.992847	+	0.119393i	$0.0380948\pi$
$200$	2.71736	+	4.70661i	0.192146	+	0.332807i
$201$	2.26991	−	7.40766i	0.160107	−	0.522496i
$202$	0.00580866	+	0.0100609i	0.000408696	+	0.000707883i
$203$		0			0
$204$	15.5575	+	16.7048i	1.08925	+	1.16957i
$205$	4.94146			0.345127
$206$	14.1839	−	24.5673i	0.988240	−	1.71168i
$207$	−13.9660	+	6.78963i	−0.970703	+	0.471912i
$208$	4.71014	+	8.15821i	0.326590	+	0.565670i
$209$	−14.7373	+	25.5257i	−1.01940	+	1.76565i
$210$		0			0
$211$	−3.66118	−	6.34135i	−0.252046	−	0.436557i	0.712043	−	0.702136i	$-0.247770\pi$
$211$	−3.66118	−	6.34135i	−0.252046	−	0.436557i	−0.964089	+	0.265579i	$0.914437\pi$
$212$	9.77278	−	16.9270i	0.671198	−	1.16255i
$213$	−0.998111	+	3.25724i	−0.0683894	+	0.223183i
$214$	−10.2522	−	17.7573i	−0.700825	−	1.21386i
$215$	2.10557	+	3.64695i	0.143599	+	0.248720i
$216$	−6.48110	+	5.22780i	−0.440983	+	0.355707i
$217$		0			0
$218$	−18.3792	+	31.8337i	−1.24480	+	2.15605i
$219$	12.4541	+	13.3724i	0.841569	+	0.903626i
$220$	19.0088			1.28158
$221$	22.8557			1.53744
$222$	−7.04685	+	1.62216i	−0.472954	+	0.108872i
$223$	−2.02765	+	3.51199i	−0.135782	+	0.235181i	−0.925896	−	0.377779i	$-0.876688\pi$
$223$	−2.02765	+	3.51199i	−0.135782	+	0.235181i	0.790114	+	0.612960i	$0.210021\pi$
$224$		0			0
$225$	0.722667	−	10.1486i	0.0481778	−	0.676575i
$226$	−6.68808	−	11.5841i	−0.444884	−	0.770562i
$227$	0.667087	+	1.15543i	0.0442761	+	0.0766884i	0.887314	−	0.461165i	$-0.152569\pi$
$227$	0.667087	+	1.15543i	0.0442761	+	0.0766884i	−0.843038	+	0.537854i	$0.819235\pi$
$228$	24.8539	−	5.72129i	1.64599	−	0.378902i
$229$	−7.99832	+	13.8535i	−0.528544	+	0.915465i	0.470902	+	0.882185i	$0.343928\pi$
$229$	−7.99832	+	13.8535i	−0.528544	+	0.915465i	−0.999446	+	0.0332795i	$0.989405\pi$
$230$	−7.14381	−	12.3734i	−0.471049	−	0.815880i
$231$		0			0
$232$	3.23150	−	5.59712i	0.212158	−	0.367469i
$233$	−4.06542	−	7.04151i	−0.266334	−	0.461305i	0.701578	−	0.712593i	$-0.252479\pi$
$233$	−4.06542	−	7.04151i	−0.266334	−	0.461305i	−0.967912	+	0.251288i	$0.919146\pi$
$234$	−2.20061	+	30.9038i	−0.143858	+	2.02025i
$235$	−2.00102	+	3.46586i	−0.130532	+	0.226088i
$236$	−0.844658			−0.0549825
$237$	−4.57547	+	14.9316i	−0.297208	+	0.969913i
$238$		0			0
$239$	11.0509	+	19.1407i	0.714823	+	1.23811i	0.963028	+	0.269403i	$0.0868262\pi$
$239$	11.0509	+	19.1407i	0.714823	+	1.23811i	−0.248204	+	0.968708i	$0.579840\pi$
$240$	2.97208	+	3.19124i	0.191847	+	0.205994i
$241$	13.7973	+	23.8977i	0.888765	+	1.53939i	0.841336	+	0.540512i	$0.181770\pi$
$241$	13.7973	+	23.8977i	0.888765	+	1.53939i	0.0474292	+	0.998875i	$0.484897\pi$
$242$	−20.6762	+	35.8122i	−1.32912	+	2.30210i
$243$	15.5334	−	1.30911i	0.996467	−	0.0839796i
$244$	−28.3015			−1.81182
$245$		0			0
$246$	14.3122	−	3.29462i	0.912513	−	0.210057i
$247$	12.7678	−	22.1145i	0.812397	−	1.40711i
$248$	2.34633			0.148992
$249$	−11.9939	−	12.8783i	−0.760082	−	0.816131i
$250$	23.1620			1.46489
$251$	16.5610			1.04532			0.522661	−	0.852541i	$-0.324939\pi$
$251$	16.5610			1.04532			0.522661	+	0.852541i	$0.324939\pi$
$252$		0			0
$253$	28.3524			1.78250
$254$	−30.3171			−1.90226
$255$	10.3108	−	2.37351i	0.645688	−	0.148635i
$256$	−1.19503			−0.0746896
$257$	1.03287	−	1.78898i	0.0644285	−	0.111593i	−0.832012	−	0.554758i	$-0.812811\pi$
$257$	1.03287	−	1.78898i	0.0644285	−	0.111593i	0.896440	+	0.443164i	$0.146144\pi$
$258$	8.53000	+	9.15900i	0.531054	+	0.570214i
$259$		0			0
$260$	−16.4686			−1.02134
$261$	−10.8816	+	5.29014i	−0.673553	+	0.327451i
$262$	−0.194949	+	0.337662i	−0.0120440	+	0.0208608i
$263$	−5.06482	−	8.77252i	−0.312310	−	0.540937i	0.666552	−	0.745458i	$-0.267769\pi$
$263$	−5.06482	−	8.77252i	−0.312310	−	0.540937i	−0.978862	+	0.204522i	$0.934436\pi$
$264$	14.8153	−	3.41043i	0.911819	−	0.209898i
$265$	−4.52969	−	7.84565i	−0.278257	−	0.481954i
$266$		0			0
$267$	8.76955	−	2.01872i	0.536688	−	0.123544i
$268$	12.2399			0.747670
$269$	−7.54972	+	13.0765i	−0.460315	+	0.797289i	−0.998976	−	0.0452336i	$-0.985597\pi$
$269$	−7.54972	+	13.0765i	−0.460315	+	0.797289i	0.538662	+	0.842522i	$0.318930\pi$
$270$	2.21654	+	14.1701i	0.134895	+	0.862363i
$271$	−14.4026	−	24.9459i	−0.874893	−	1.51536i	−0.856877	−	0.515521i	$-0.827598\pi$
$271$	−14.4026	−	24.9459i	−0.874893	−	1.51536i	−0.0180156	−	0.999838i	$-0.505735\pi$
$272$	4.78070	−	8.28041i	0.289872	−	0.502074i
$273$		0			0
$274$	−3.42993	−	5.94082i	−0.207210	−	0.358898i
$275$	−9.28802	+	16.0873i	−0.560089	+	0.970102i
$276$	−16.7200	−	17.9529i	−1.00642	−	1.08064i
$277$	1.34982	+	2.33795i	0.0811026	+	0.140474i	0.903724	−	0.428116i	$-0.140823\pi$
$277$	1.34982	+	2.33795i	0.0811026	+	0.140474i	−0.822621	+	0.568590i	$0.807489\pi$
$278$	−20.5195	−	35.5408i	−1.23068	−	2.13160i
$279$	−3.63846	−	2.46093i	−0.217829	−	0.147332i
$280$		0			0
$281$	−2.46312	+	4.26626i	−0.146938	+	0.254503i	−0.930094	−	0.367321i	$-0.880275\pi$
$281$	−2.46312	+	4.26626i	−0.146938	+	0.254503i	0.783157	+	0.621825i	$0.213608\pi$
$282$	−3.48485	+	11.3725i	−0.207520	+	0.677222i
$283$	−3.58157			−0.212903			−0.106451	−	0.994318i	$-0.533949\pi$
$283$	−3.58157			−0.212903			−0.106451	+	0.994318i	$0.533949\pi$
$284$	−5.38203			−0.319365
$285$	3.46336	−	11.3024i	0.205152	−	0.669493i
$286$	28.2832	−	48.9879i	1.67242	−	2.89672i
$287$		0			0
$288$	18.7001	+	12.6481i	1.10192	+	0.745298i
$289$	−3.09903	−	5.36768i	−0.182296	−	0.315746i
$290$	−5.56609	−	9.64075i	−0.326852	−	0.566125i
$291$	−5.86732	−	6.29998i	−0.343949	−	0.369312i
$292$	−14.4345	+	25.0014i	−0.844718	+	1.46309i
$293$	−12.1955	−	21.1232i	−0.712469	−	1.23403i	−0.963928	−	0.266164i	$-0.914244\pi$
$293$	−12.1955	−	21.1232i	−0.712469	−	1.23403i	0.251459	−	0.967868i	$-0.419090\pi$
$294$		0			0
$295$	−0.195750	+	0.339048i	−0.0113970	+	0.0197401i
$296$	−1.53705	−	2.66225i	−0.0893394	−	0.154740i
$297$	−26.5511	−	10.2503i	−1.54065	−	0.594784i
$298$	23.1494	−	40.0960i	1.34101	−	2.32270i
$299$	−24.5634			−1.42054
$300$	15.6639	−	3.60579i	0.904358	−	0.208180i
$301$		0			0
$302$	−6.92678	−	11.9975i	−0.398591	−	0.690380i
$303$	0.00901018	−	0.00207412i	0.000517622	−	0.000119155i
$304$	−5.34126	−	9.25134i	−0.306342	−	0.530600i
$305$	−6.55887	+	11.3603i	−0.375560	+	0.650489i
$306$	28.2812	−	13.7491i	1.61673	−	0.785981i
$307$	23.9025			1.36419			0.682094	−	0.731265i	$-0.261070\pi$
$307$	23.9025			1.36419			0.682094	+	0.731265i	$0.261070\pi$
$308$		0			0
$309$	−15.3869	−	16.5216i	−0.875332	−	0.939879i
$310$	2.02072	−	3.49998i	0.114769	−	0.198786i
$311$	12.9416			0.733853			0.366926	−	0.930250i	$-0.380410\pi$
$311$	12.9416			0.733853			0.366926	+	0.930250i	$0.380410\pi$
$312$	−12.8354	+	2.95467i	−0.726663	+	0.167275i
$313$	26.8681			1.51867			0.759336	−	0.650698i	$-0.225524\pi$
$313$	26.8681			1.51867			0.759336	+	0.650698i	$0.225524\pi$
$314$	−3.03802			−0.171446
$315$		0			0
$316$	−24.6719			−1.38790
$317$	8.31169			0.466831			0.233415	−	0.972377i	$-0.425010\pi$
$317$	8.31169			0.466831			0.233415	+	0.972377i	$0.425010\pi$
$318$	−18.3505	−	19.7037i	−1.02904	−	1.10493i
$319$	22.0907			1.23684
$320$	−7.86786	+	13.6275i	−0.439827	+	0.761803i
$321$	−15.9028	+	3.66078i	−0.887608	+	0.204325i
$322$		0			0
$323$	−25.9182			−1.44212
$324$	9.16716	+	22.8572i	0.509287	+	1.26984i
$325$	8.04680	−	13.9375i	0.446356	−	0.773111i
$326$	20.7421	+	35.9264i	1.14880	+	1.98978i
$327$	19.9381	+	21.4083i	1.10258	+	1.18388i
$328$	3.12177	+	5.40706i	0.172371	+	0.298555i
$329$		0			0
$330$	7.67201	−	25.0369i	0.422330	−	1.37824i
$331$	12.3978			0.681443			0.340722	−	0.940164i	$-0.389329\pi$
$331$	12.3978			0.681443			0.340722	+	0.940164i	$0.389329\pi$
$332$	13.9012	−	24.0775i	0.762926	−	1.32143i
$333$	−0.408770	+	5.74049i	−0.0224005	+	0.314577i
$334$	−1.89775	−	3.28700i	−0.103840	−	0.179857i
$335$	2.83659	−	4.91312i	0.154980	−	0.268433i
$336$		0			0
$337$	−12.9588	−	22.4454i	−0.705913	−	1.22268i	−0.966361	−	0.257189i	$-0.917204\pi$
$337$	−12.9588	−	22.4454i	−0.705913	−	1.22268i	0.260448	−	0.965488i	$-0.416130\pi$
$338$	−10.3575	+	17.9397i	−0.563373	+	0.975791i
$339$	−10.3743	+	2.38813i	−0.563455	+	0.129705i
$340$	8.35762	+	14.4758i	0.453256	+	0.785062i
$341$	4.00992	+	6.94538i	0.217149	+	0.376113i
$342$	2.49547	−	35.0447i	0.134940	−	1.89500i
$343$		0			0
$344$	−2.66038	+	4.60792i	−0.143438	+	0.248442i
$345$	−11.0812	+	2.55086i	−0.596592	+	0.137334i
$346$	21.9283			1.17887
$347$	−16.8483			−0.904464			−0.452232	−	0.891900i	$-0.649372\pi$
$347$	−16.8483			−0.904464			−0.452232	+	0.891900i	$0.649372\pi$
$348$	−13.0274	−	13.9880i	−0.698340	−	0.749835i
$349$	−15.5503	+	26.9340i	−0.832390	+	1.44174i	0.0637477	+	0.997966i	$0.479695\pi$
$349$	−15.5503	+	26.9340i	−0.832390	+	1.44174i	−0.896138	+	0.443776i	$0.853639\pi$
$350$		0			0
$351$	23.0029	+	8.88050i	1.22780	+	0.474006i
$352$	−20.6092	−	35.6963i	−1.09848	−	1.90262i
$353$	1.32969	+	2.30309i	0.0707722	+	0.122581i	0.899240	−	0.437456i	$-0.144120\pi$
$353$	1.32969	+	2.30309i	0.0707722	+	0.122581i	−0.828468	+	0.560037i	$0.810787\pi$
$354$	−0.340905	+	1.11251i	−0.0181189	+	0.0591294i
$355$	−1.24729	+	2.16036i	−0.0661991	+	0.114660i
$356$	7.10833	+	12.3120i	0.376741	+	0.652534i
$357$		0			0
$358$	20.1770	−	34.9476i	1.06639	−	1.84704i
$359$	16.2715	+	28.1830i	0.858775	+	1.48744i	0.873098	+	0.487545i	$0.162107\pi$
$359$	16.2715	+	28.1830i	0.858775	+	1.48744i	−0.0143230	+	0.999897i	$0.504559\pi$
$360$	−5.48356	+	2.66586i	−0.289009	+	0.140503i
$361$	−4.97859	+	8.62318i	−0.262031	+	0.453852i
$362$	19.1729			1.00771
$363$	22.4299	+	24.0839i	1.17726	+	1.26407i
$364$		0			0
$365$	6.69042	+	11.5881i	0.350192	+	0.606551i
$366$	−11.4225	+	37.2764i	−0.597065	+	1.94847i
$367$	7.07678	+	12.2573i	0.369405	+	0.639828i	0.989473	−	0.144720i	$-0.0462283\pi$
$367$	7.07678	+	12.2573i	0.369405	+	0.639828i	−0.620068	+	0.784548i	$0.712895\pi$
$368$	−5.13790	+	8.89911i	−0.267832	+	0.463898i
$369$	0.830215	−	11.6590i	0.0432193	−	0.606942i
$370$	−5.29499			−0.275273
$371$		0			0
$372$	2.03313	−	6.63494i	0.105413	−	0.344005i
$373$	−1.33814	+	2.31773i	−0.0692863	+	0.120007i	−0.898587	−	0.438795i	$-0.855406\pi$
$373$	−1.33814	+	2.31773i	−0.0692863	+	0.120007i	0.829301	+	0.558802i	$0.188739\pi$
$374$	−57.4137			−2.96879
$375$	5.40077	−	17.6249i	0.278894	−	0.910147i
$376$	−5.05656			−0.260772
$377$	−19.1386			−0.985687
$378$		0			0
$379$	−0.312929			−0.0160741			−0.00803705	−	0.999968i	$-0.502558\pi$
$379$	−0.312929			−0.0160741			−0.00803705	+	0.999968i	$0.502558\pi$
$380$	18.6752			0.958017
$381$	−7.06914	+	23.0695i	−0.362163	+	1.18189i
$382$	10.6844			0.546659
$383$	−4.49440	+	7.78453i	−0.229653	+	0.397771i	−0.957705	−	0.287751i	$-0.907093\pi$
$383$	−4.49440	+	7.78453i	−0.229653	+	0.397771i	0.728052	+	0.685522i	$0.240426\pi$
$384$	−6.06465	+	19.7914i	−0.309485	+	1.00998i
$385$		0			0
$386$	−21.2573			−1.08197
$387$	8.95843	−	4.35519i	0.455383	−	0.221387i
$388$	6.80036	−	11.7786i	0.345236	−	0.597966i
$389$	13.4934	+	23.3713i	0.684144	+	1.18497i	0.973705	+	0.227813i	$0.0731575\pi$
$389$	13.4934	+	23.3713i	0.684144	+	1.18497i	−0.289560	+	0.957160i	$0.593509\pi$
$390$	−6.64674	+	21.6910i	−0.336571	+	1.09837i
$391$	12.4657	+	21.5912i	0.630417	+	1.09191i
$392$		0			0
$393$	0.211484	+	0.227079i	0.0106680	+	0.0114546i
$394$	7.21328			0.363400
$395$	−5.71772	+	9.90339i	−0.287690	+	0.498293i
$396$	3.19368	−	44.8498i	0.160488	−	2.25379i
$397$	14.7503	+	25.5482i	0.740295	+	1.28223i	0.952361	+	0.304973i	$0.0986475\pi$
$397$	14.7503	+	25.5482i	0.740295	+	1.28223i	−0.212066	+	0.977255i	$0.568019\pi$
$398$	12.0662	−	20.8992i	0.604822	−	1.04758i
$399$		0			0
$400$	−3.36628	−	5.83056i	−0.168314	−	0.291528i
$401$	17.1392	−	29.6860i	0.855891	−	1.48245i	−0.0199251	−	0.999801i	$-0.506343\pi$
$401$	17.1392	−	29.6860i	0.855891	−	1.48245i	0.875816	−	0.482645i	$-0.160324\pi$
$402$	4.94004	−	16.1214i	0.246387	−	0.804061i
$403$	−3.47404	−	6.01721i	−0.173054	−	0.299739i
$404$	0.00730338	+	0.0126498i	0.000363357	+	0.000629352i
$405$	11.2994	+	1.61743i	0.561473	+	0.0803706i
$406$		0			0
$407$	5.25369	−	9.09966i	0.260416	−	0.451054i
$408$	9.11099	+	9.78284i	0.451061	+	0.484323i
$409$	−10.9845			−0.543149			−0.271574	−	0.962417i	$-0.587544\pi$
$409$	−10.9845			−0.543149			−0.271574	+	0.962417i	$0.587544\pi$
$410$	10.7542			0.531110
$411$	−5.32038	+	1.22474i	−0.262435	+	0.0604117i
$412$	17.8338	−	30.8890i	0.878608	−	1.52179i
$413$		0			0
$414$	−30.3943	+	14.7764i	−1.49380	+	0.726218i
$415$	−6.44320	−	11.1599i	−0.316284	−	0.547820i
$416$	17.8551	+	30.9259i	0.875417	+	1.51627i
$417$	−31.8291	+	7.32695i	−1.55868	+	0.358802i
$418$	−32.0729	+	55.5519i	−1.56874	+	2.71713i
$419$	3.33207	+	5.77132i	0.162782	+	0.281947i	0.935866	−	0.352357i	$-0.114620\pi$
$419$	3.33207	+	5.77132i	0.162782	+	0.281947i	−0.773083	+	0.634305i	$0.781286\pi$
$420$		0			0
$421$	−17.0430	+	29.5193i	−0.830625	+	1.43868i	0.0669186	+	0.997758i	$0.478683\pi$
$421$	−17.0430	+	29.5193i	−0.830625	+	1.43868i	−0.897543	+	0.440926i	$0.854650\pi$
$422$	−7.96787	−	13.8008i	−0.387870	−	0.671810i
$423$	7.84122	+	5.30353i	0.381253	+	0.257867i
$424$	5.72325	−	9.91297i	0.277946	−	0.481416i
$425$	−16.3347			−0.792348
$426$	−2.17220	+	7.08877i	−0.105243	+	0.343452i
$427$		0			0
$428$	−12.8903	−	22.3267i	−0.623077	−	1.07920i
$429$	−30.6821	−	32.9446i	−1.48134	−	1.59058i
$430$	4.58237	+	7.93690i	0.220982	+	0.382751i
$431$	−1.12969	+	1.95669i	−0.0544155	+	0.0942504i	−0.891950	−	0.452134i	$-0.850663\pi$
$431$	−1.12969	+	1.95669i	−0.0544155	+	0.0942504i	0.837535	+	0.546384i	$0.183996\pi$
$432$	8.02881	−	6.47622i	0.386287	−	0.311587i
$433$	−34.3904			−1.65270			−0.826348	−	0.563160i	$-0.809585\pi$
$433$	−34.3904			−1.65270			−0.826348	+	0.563160i	$0.809585\pi$
$434$		0			0
$435$	−8.63392	+	1.98750i	−0.413965	+	0.0952933i
$436$	−23.1086	+	40.0254i	−1.10670	+	1.91687i
$437$	27.8547			1.33247
$438$	27.1039	+	29.1026i	1.29508	+	1.39058i
$439$	−5.99139			−0.285953			−0.142977	−	0.989726i	$-0.545667\pi$
$439$	−5.99139			−0.285953			−0.142977	+	0.989726i	$0.545667\pi$
$440$	11.1322			0.530706
$441$		0			0
$442$	49.7411			2.36594
$443$	−39.4380			−1.87376			−0.936879	−	0.349654i	$-0.886299\pi$
$443$	−39.4380			−1.87376			−0.936879	+	0.349654i	$0.886299\pi$
$444$	−8.86018	+	2.03958i	−0.420486	+	0.0967944i
$445$	6.58942			0.312369
$446$	−4.41280	+	7.64319i	−0.208952	+	0.361916i
$447$	−25.1129	−	26.9647i	−1.18780	−	1.27539i
$448$		0			0
$449$	2.45092			0.115666			0.0578330	−	0.998326i	$-0.481581\pi$
$449$	2.45092			0.115666			0.0578330	+	0.998326i	$0.481581\pi$
$450$	1.57275	−	22.0866i	0.0741400	−	1.04117i
$451$	−10.6703	+	18.4815i	−0.502444	+	0.870259i
$452$	−8.40909	−	14.5650i	−0.395530	−	0.685078i
$453$	−10.7446	+	2.47336i	−0.504824	+	0.116209i
$454$	1.45179	+	2.51457i	0.0681358	+	0.118015i
$455$		0			0
$456$	14.5552	−	3.35057i	0.681612	−	0.156905i
$457$	11.0212			0.515548			0.257774	−	0.966205i	$-0.417011\pi$
$457$	11.0212			0.515548			0.257774	+	0.966205i	$0.417011\pi$
$458$	−17.4068	+	30.1495i	−0.813368	+	1.40879i
$459$	−3.86779	−	24.7263i	−0.180533	−	1.15412i
$460$	−8.98208	−	15.5574i	−0.418792	−	0.725369i
$461$	−14.6540	+	25.3814i	−0.682503	+	1.18213i	0.291711	+	0.956506i	$0.405775\pi$
$461$	−14.6540	+	25.3814i	−0.682503	+	1.18213i	−0.974215	+	0.225624i	$0.927558\pi$
$462$		0			0
$463$	0.593566	+	1.02809i	0.0275853	+	0.0477792i	0.879489	−	0.475920i	$-0.157885\pi$
$463$	0.593566	+	1.02809i	0.0275853	+	0.0477792i	−0.851903	+	0.523699i	$0.824552\pi$
$464$	−4.00319	+	6.93374i	−0.185844	+	0.321891i
$465$	−2.19211	−	2.35375i	−0.101656	−	0.109153i
$466$	−8.84761	−	15.3245i	−0.409858	−	0.709894i
$467$	11.0573	+	19.1519i	0.511673	+	0.886243i	0.999908	+	0.0135313i	$0.00430729\pi$
$467$	11.0573	+	19.1519i	0.511673	+	0.886243i	−0.488236	+	0.872712i	$0.662359\pi$
$468$	−2.76688	+	38.8562i	−0.127899	+	1.79613i
$469$		0			0
$470$	−4.35483	+	7.54280i	−0.200874	+	0.347923i
$471$	−0.708387	+	2.31176i	−0.0326408	+	0.106520i
$472$	−0.494658			−0.0227685
$473$	−18.1865			−0.836218
$474$	−9.95764	+	32.4958i	−0.457369	+	1.49258i
$475$	−9.12499	+	15.8050i	−0.418683	+	0.725181i
$476$		0			0
$477$	−19.2722	+	9.36927i	−0.882413	+	0.428990i
$478$	24.0502	+	41.6562i	1.10003	+	1.90531i
$479$	−12.5714	−	21.7743i	−0.574402	−	0.994894i	−0.996106	−	0.0881606i	$-0.971901\pi$
$479$	−12.5714	−	21.7743i	−0.574402	−	0.994894i	0.421704	−	0.906734i	$-0.361432\pi$
$480$	11.2665	+	12.0973i	0.514242	+	0.552163i
$481$	−4.55160	+	7.88361i	−0.207535	+	0.359462i
$482$	30.0273	+	52.0088i	1.36771	+	2.36894i
$483$		0			0
$484$	−25.9967	+	45.0276i	−1.18167	+	2.04671i
$485$	−3.15197	−	5.45937i	−0.143123	−	0.247897i
$486$	33.8055	−	2.84904i	1.53345	−	0.129235i
$487$	−6.78904	+	11.7590i	−0.307641	+	0.532849i	−0.977846	−	0.209327i	$-0.932873\pi$
$487$	−6.78904	+	11.7590i	−0.307641	+	0.532849i	0.670205	+	0.742176i	$0.266206\pi$
$488$	−16.5743			−0.750281
$489$	32.1744	−	7.40644i	1.45498	−	0.334931i
$490$		0			0
$491$	7.25177	+	12.5604i	0.327268	+	0.566844i	0.981969	−	0.189044i	$-0.0605387\pi$
$491$	7.25177	+	12.5604i	0.327268	+	0.566844i	−0.654701	+	0.755888i	$0.727205\pi$
$492$	17.9951	−	4.14241i	0.811281	−	0.186754i
$493$	9.71263	+	16.8228i	0.437435	+	0.757659i
$494$	27.7868	−	48.1281i	1.25019	−	2.16538i
$495$	−17.2627	−	11.6759i	−0.775901	−	0.524792i
$496$	−2.90664			−0.130512
$497$		0			0
$498$	−26.1024	−	28.0272i	−1.16968	−	1.25593i
$499$	−6.99574	+	12.1170i	−0.313172	+	0.542431i	−0.979047	−	0.203633i	$-0.934725\pi$
$499$	−6.99574	+	12.1170i	−0.313172	+	0.542431i	0.665875	+	0.746063i	$0.268058\pi$
$500$	29.1221			1.30238
$501$	−2.94372	+	0.677635i	−0.131516	+	0.0302745i
$502$	36.0419			1.60863
$503$	−28.4011			−1.26634			−0.633171	−	0.774012i	$-0.718247\pi$
$503$	−28.4011			−1.26634			−0.633171	+	0.774012i	$0.718247\pi$
$504$		0			0
$505$	0.00677023			0.000301271
$506$	61.7036			2.74306
$507$	11.2360	+	12.0645i	0.499007	+	0.535803i
$508$	−38.1184			−1.69123
$509$	−1.72997	+	2.99639i	−0.0766794	+	0.132813i	−0.901815	−	0.432122i	$-0.857765\pi$
$509$	−1.72997	+	2.99639i	−0.0766794	+	0.132813i	0.825136	+	0.564934i	$0.191098\pi$
$510$	22.4395	−	5.16550i	0.993639	−	0.228732i
$511$		0			0
$512$	21.3013			0.941392
$513$	−26.0851	−	10.0704i	−1.15168	−	0.444619i
$514$	2.24784	−	3.89337i	0.0991480	−	0.171729i
$515$	−8.26597	−	14.3171i	−0.364242	−	0.630886i
$516$	10.7250	+	11.5158i	0.472141	+	0.506956i
$517$	−8.64174	−	14.9679i	−0.380063	−	0.658289i
$518$		0			0
$519$	5.11310	−	16.6861i	0.224440	−	0.732440i
$520$	−9.64451			−0.422940
$521$	3.56797	−	6.17991i	0.156316	−	0.270747i	−0.777222	−	0.629227i	$-0.783372\pi$
$521$	3.56797	−	6.17991i	0.156316	−	0.270747i	0.933537	+	0.358480i	$0.116705\pi$
$522$	−23.6817	+	11.5130i	−1.03652	+	0.503910i
$523$	−6.53235	−	11.3144i	−0.285640	−	0.494743i	0.687124	−	0.726540i	$-0.258873\pi$
$523$	−6.53235	−	11.3144i	−0.285640	−	0.494743i	−0.972764	+	0.231797i	$0.925539\pi$
$524$	−0.245114	+	0.424551i	−0.0107079	+	0.0185466i
$525$		0			0
$526$	−11.0226	−	19.0917i	−0.480609	−	0.832439i
$527$	−3.52608	+	6.10735i	−0.153598	+	0.266040i
$528$	−18.3532	+	4.22486i	−0.798723	+	0.183863i
$529$	−1.89710	−	3.28587i	−0.0824825	−	0.142864i
$530$	−9.85801	−	17.0746i	−0.428205	−	0.741672i
$531$	0.767068	+	0.518818i	0.0332879	+	0.0225148i
$532$		0			0
$533$	9.24434	−	16.0117i	0.400417	−	0.693542i
$534$	19.0853	−	4.39337i	0.825900	−	0.190120i
$535$	−11.9493			−0.516615
$536$	7.16806			0.309613
$537$	−21.8883	−	23.5024i	−0.944550	−	1.01420i
$538$	−16.4305	+	28.4585i	−0.708371	+	1.22693i
$539$		0			0
$540$	2.78691	+	17.8164i	0.119930	+	0.766695i
$541$	−2.46788	−	4.27450i	−0.106103	−	0.183775i	0.808086	−	0.589065i	$-0.200504\pi$
$541$	−2.46788	−	4.27450i	−0.106103	−	0.183775i	−0.914188	+	0.405290i	$0.867171\pi$
$542$	−31.3444	−	54.2901i	−1.34636	−	2.33196i
$543$	4.47062	−	14.5895i	0.191853	−	0.626094i
$544$	18.1225	−	31.3892i	0.776997	−	1.34580i
$545$	10.7109	+	18.5518i	0.458803	+	0.794670i
$546$		0			0
$547$	0.559964	−	0.969887i	0.0239423	−	0.0414694i	−0.853806	−	0.520591i	$-0.825712\pi$
$547$	0.559964	−	0.969887i	0.0239423	−	0.0414694i	0.877748	+	0.479122i	$0.159045\pi$
$548$	−4.31254	−	7.46954i	−0.184223	−	0.319083i
$549$	25.7017	+	17.3838i	1.09692	+	0.741921i
$550$	−20.2136	+	35.0110i	−0.861912	+	1.49288i
$551$	21.7030			0.924578
$552$	−9.79175	−	10.5138i	−0.416764	−	0.447497i
$553$		0			0
$554$	2.93762	+	5.08811i	0.124808	+	0.216173i
$555$	−1.23465	+	4.02918i	−0.0524081	+	0.171029i
$556$	−25.7997	−	44.6863i	−1.09415	−	1.89512i
$557$	5.47832	−	9.48873i	0.232124	−	0.402050i	−0.726309	−	0.687368i	$-0.758766\pi$
$557$	5.47832	−	9.48873i	0.232124	−	0.402050i	0.958433	+	0.285318i	$0.0920992\pi$
$558$	−7.91842	−	5.35575i	−0.335213	−	0.226727i
$559$	15.7561			0.666413
$560$		0			0
$561$	−13.3874	+	43.6885i	−0.565215	+	1.84453i
$562$	−5.36052	+	9.28470i	−0.226120	+	0.391651i
$563$	4.76096			0.200650			0.100325	−	0.994955i	$-0.468012\pi$
$563$	4.76096			0.200650			0.100325	+	0.994955i	$0.468012\pi$
$564$	−4.38159	+	14.2989i	−0.184498	+	0.602093i
$565$	−7.79523			−0.327948
$566$	−7.79462			−0.327632
$567$		0			0
$568$	−3.15189			−0.132250
$569$	3.49976			0.146718			0.0733588	−	0.997306i	$-0.476628\pi$
$569$	3.49976			0.146718			0.0733588	+	0.997306i	$0.476628\pi$
$570$	7.53734	−	24.5974i	0.315704	−	1.03027i
$571$	7.06101			0.295494			0.147747	−	0.989025i	$-0.452798\pi$
$571$	7.06101			0.295494			0.147747	+	0.989025i	$0.452798\pi$
$572$	35.5612	−	61.5937i	1.48689	−	2.57536i
$573$	2.49131	−	8.13017i	0.104076	−	0.339643i
$574$		0			0
$575$	17.5552			0.732101
$576$	30.8312	+	20.8531i	1.28463	+	0.868881i
$577$	6.44149	−	11.1570i	0.268163	−	0.464472i	−0.700225	−	0.713923i	$-0.746917\pi$
$577$	6.44149	−	11.1570i	0.268163	−	0.464472i	0.968387	+	0.249451i	$0.0802502\pi$
$578$	−6.74445	−	11.6817i	−0.280532	−	0.485896i
$579$	−4.95665	+	16.1756i	−0.205991	+	0.672235i
$580$	−6.99838	−	12.1216i	−0.290592	−	0.503320i
$581$		0			0
$582$	−12.7691	−	13.7107i	−0.529297	−	0.568328i
$583$	39.1245			1.62037
$584$	−8.45333	+	14.6416i	−0.349801	+	0.605874i
$585$	14.9558	+	10.1156i	0.618345	+	0.418227i
$586$	−26.5412	−	45.9707i	−1.09641	−	1.89903i
$587$	19.5044	−	33.7826i	0.805034	−	1.39436i	−0.111235	−	0.993794i	$-0.535481\pi$
$587$	19.5044	−	33.7826i	0.805034	−	1.39436i	0.916268	−	0.400565i	$-0.131186\pi$
$588$		0			0
$589$	3.93953	+	6.82347i	0.162326	+	0.281156i
$590$	−0.426012	+	0.737874i	−0.0175386	+	0.0303778i
$591$	1.68195	−	5.48889i	0.0691861	−	0.225783i
$592$	1.90411	+	3.29801i	0.0782583	+	0.135547i
$593$	20.1513	+	34.9031i	0.827515	+	1.43330i	0.899982	+	0.435927i	$0.143579\pi$
$593$	20.1513	+	34.9031i	0.827515	+	1.43330i	−0.0724676	+	0.997371i	$0.523087\pi$
$594$	−57.7835	−	22.3079i	−2.37089	−	0.915304i
$595$		0			0
$596$	29.1064	−	50.4137i	1.19224	−	2.06503i
$597$	−13.0896	−	14.0548i	−0.535720	−	0.575224i
$598$	−53.4577			−2.18605
$599$	−12.7821			−0.522261			−0.261130	−	0.965304i	$-0.584095\pi$
$599$	−12.7821			−0.522261			−0.261130	+	0.965304i	$0.584095\pi$
$600$	9.17330	−	2.11166i	0.374499	−	0.0862084i
$601$	4.86311	−	8.42316i	0.198371	−	0.343588i	−0.749630	−	0.661858i	$-0.769768\pi$
$601$	4.86311	−	8.42316i	0.198371	−	0.343588i	0.948000	+	0.318270i	$0.103102\pi$
$602$		0			0
$603$	−11.1155	−	7.51816i	−0.452659	−	0.306163i
$604$	−8.70921	−	15.0848i	−0.354373	−	0.613792i
$605$	12.0495	+	20.8703i	0.489881	+	0.848499i
$606$	0.0196090	−	0.00451392i	0.000796560	−	0.000183365i
$607$	20.7437	−	35.9291i	0.841959	−	1.45832i	−0.0462763	−	0.998929i	$-0.514735\pi$
$607$	20.7437	−	35.9291i	0.841959	−	1.45832i	0.888236	−	0.459388i	$-0.151931\pi$
$608$	−20.2475	−	35.0697i	−0.821145	−	1.42226i
$609$		0			0
$610$	−14.2742	+	24.7236i	−0.577943	+	1.00103i
$611$	7.48688	+	12.9677i	0.302887	+	0.524615i
$612$	35.5587	−	17.2870i	1.43737	−	0.698786i
$613$	−7.64783	+	13.2464i	−0.308893	+	0.535018i	−0.978120	−	0.208039i	$-0.933292\pi$
$613$	−7.64783	+	13.2464i	−0.308893	+	0.535018i	0.669228	+	0.743057i	$0.266625\pi$
$614$	52.0193			2.09933
$615$	2.50759	−	8.18329i	0.101116	−	0.329982i
$616$		0			0
$617$	−2.66563	−	4.61700i	−0.107314	−	0.185873i	0.807367	−	0.590049i	$-0.200892\pi$
$617$	−2.66563	−	4.61700i	−0.107314	−	0.185873i	−0.914681	+	0.404176i	$0.867558\pi$
$618$	−33.4867	−	35.9561i	−1.34703	−	1.44637i
$619$	−6.34205	−	10.9847i	−0.254908	−	0.441514i	0.709962	−	0.704240i	$-0.248712\pi$
$619$	−6.34205	−	10.9847i	−0.254908	−	0.441514i	−0.964871	+	0.262726i	$0.915379\pi$
$620$	2.54070	−	4.40062i	0.102037	−	0.176733i
$621$	4.15678	+	26.5738i	0.166806	+	1.06637i
$622$	28.1650			1.12931
$623$		0			0
$624$	15.9006	−	3.66026i	0.636532	−	0.146528i
$625$	−1.72954	+	2.99566i	−0.0691817	+	0.119826i
$626$	58.4733			2.33706
$627$	34.7932	+	37.3588i	1.38951	+	1.49197i
$628$	−3.81978			−0.152426
$629$	9.23957			0.368406
$630$		0			0
$631$	0.123764			0.00492698			0.00246349	−	0.999997i	$-0.499216\pi$
$631$	0.123764			0.00492698			0.00246349	+	0.999997i	$0.499216\pi$
$632$	−14.4487			−0.574737
$633$	−12.3595	+	2.84511i	−0.491245	+	0.113083i
$634$	18.0888			0.718399
$635$	−8.83394	+	15.3008i	−0.350564	+	0.607195i
$636$	−23.0725	−	24.7739i	−0.914885	−	0.982349i
$637$		0			0
$638$	48.0763			1.90336
$639$	4.88764	+	3.30583i	0.193352	+	0.130777i
$640$	−7.57868	+	13.1267i	−0.299573	+	0.518876i
$641$	−2.96588	−	5.13706i	−0.117145	−	0.202902i	0.801490	−	0.598008i	$-0.204041\pi$
$641$	−2.96588	−	5.13706i	−0.117145	−	0.202902i	−0.918635	+	0.395107i	$0.870708\pi$
$642$	−34.6095	+	7.96699i	−1.36593	+	0.314432i
$643$	23.4140	+	40.5542i	0.923358	+	1.59930i	0.794180	+	0.607682i	$0.207900\pi$
$643$	23.4140	+	40.5542i	0.923358	+	1.59930i	0.129178	+	0.991621i	$0.458766\pi$
$644$		0			0
$645$	7.10801	−	1.63624i	0.279877	−	0.0644269i
$646$	−56.4060			−2.21926
$647$	−19.5701	+	33.8964i	−0.769379	+	1.33260i	0.168521	+	0.985698i	$0.446101\pi$
$647$	−19.5701	+	33.8964i	−0.769379	+	1.33260i	−0.937900	+	0.346905i	$0.887233\pi$
$648$	5.36858	+	13.3859i	0.210898	+	0.525847i
$649$	−0.845379	−	1.46424i	−0.0331840	−	0.0574764i
$650$	17.5123	−	30.3322i	0.686890	−	1.18973i
$651$		0			0
$652$	26.0796	+	45.1711i	1.02135	+	1.76904i
$653$	−21.6640	+	37.5232i	−0.847779	+	1.46840i	0.0354068	+	0.999373i	$0.488727\pi$
$653$	−21.6640	+	37.5232i	−0.847779	+	1.46840i	−0.883186	+	0.469023i	$0.844606\pi$
$654$	43.3914	+	46.5911i	1.69674	+	1.82186i
$655$	0.113611	+	0.196779i	0.00443913	+	0.00768881i
$656$	−3.86726	−	6.69828i	−0.150991	−	0.261524i
$657$	28.4653	−	13.8386i	1.11054	−	0.539893i
$658$		0			0
$659$	3.43895	−	5.95643i	0.133962	−	0.232030i	−0.791238	−	0.611508i	$-0.790563\pi$
$659$	3.43895	−	5.95643i	0.133962	−	0.232030i	0.925201	+	0.379478i	$0.123897\pi$
$660$	9.64620	−	31.4795i	0.375478	−	1.22534i
$661$	−38.7671			−1.50786			−0.753932	−	0.656952i	$-0.771845\pi$
$661$	−38.7671			−1.50786			−0.753932	+	0.656952i	$0.771845\pi$
$662$	26.9814			1.04866
$663$	11.5983	−	37.8501i	0.450441	−	1.46997i
$664$	8.14097	−	14.1006i	0.315931	−	0.547209i
$665$		0			0
$666$	−0.889611	+	12.4931i	−0.0344717	+	0.484097i
$667$	−10.4383	−	18.0797i	−0.404174	−	0.700050i
$668$	−2.38609	−	4.13282i	−0.0923205	−	0.159904i
$669$	4.78707	+	5.14007i	0.185079	+	0.198727i
$670$	6.17331	−	10.6925i	0.238496	−	0.413087i
$671$	−28.3257	−	49.0615i	−1.09350	−	1.89400i
$672$		0			0
$673$	17.9897	−	31.1591i	0.693452	−	1.20109i	−0.277248	−	0.960798i	$-0.589422\pi$
$673$	17.9897	−	31.1591i	0.693452	−	1.20109i	0.970700	−	0.240295i	$-0.0772443\pi$
$674$	−28.2025	−	48.8481i	−1.08632	−	1.88156i
$675$	−16.4399	−	6.34678i	−0.632771	−	0.244288i
$676$	−13.0227	+	22.5560i	−0.500874	+	0.867539i
$677$	−4.46658			−0.171664			−0.0858322	−	0.996310i	$-0.527355\pi$
$677$	−4.46658			−0.171664			−0.0858322	+	0.996310i	$0.527355\pi$
$678$	−22.5777	+	5.19731i	−0.867092	+	0.199602i
$679$		0			0
$680$	4.89449	+	8.47750i	0.187695	+	0.325097i
$681$	2.25196	−	0.518394i	0.0862953	−	0.0198649i
$682$	8.72682	+	15.1153i	0.334167	+	0.578795i
$683$	13.3356	−	23.0980i	0.510274	−	0.883821i	−0.489655	−	0.871916i	$-0.662877\pi$
$683$	13.3356	−	23.0980i	0.510274	−	0.883821i	0.999929	−	0.0119046i	$-0.00378945\pi$
$684$	3.13762	−	44.0625i	0.119970	−	1.68477i
$685$	−3.99773			−0.152745
$686$		0			0
$687$	18.8832	+	20.2757i	0.720439	+	0.773565i
$688$	3.29569	−	5.70831i	0.125647	−	0.217627i
$689$	−33.8960			−1.29134
$690$	−24.1162	+	5.55146i	−0.918086	+	0.211340i
$691$	41.0440			1.56139			0.780694	−	0.624913i	$-0.214866\pi$
$691$	41.0440			1.56139			0.780694	+	0.624913i	$0.214866\pi$
$692$	27.5709			1.04809
$693$		0			0
$694$	−36.6671			−1.39187
$695$	−23.9163			−0.907197
$696$	−7.62923	−	8.19182i	−0.289185	−	0.310510i
$697$	−18.7656			−0.710799
$698$	−33.8424	+	58.6167i	−1.28095	+	2.21867i
$699$	−13.7241	+	3.15924i	−0.519093	+	0.119493i
$700$		0			0
$701$	9.63355			0.363854			0.181927	−	0.983312i	$-0.441767\pi$
$701$	9.63355			0.363854			0.181927	+	0.983312i	$0.441767\pi$
$702$	50.0615	+	19.3267i	1.88945	+	0.729441i
$703$	5.16148	−	8.93994i	0.194669	−	0.337176i
$704$	−33.9788	−	58.8529i	−1.28062	−	2.21810i
$705$	4.72419	+	5.07256i	0.177923	+	0.191044i
$706$	2.89382	+	5.01224i	0.108910	+	0.188638i
$707$		0			0
$708$	−0.428629	+	1.39879i	−0.0161089	+	0.0525698i
$709$	−10.1426			−0.380914			−0.190457	−	0.981696i	$-0.560997\pi$
$709$	−10.1426			−0.380914			−0.190457	+	0.981696i	$0.560997\pi$
$710$	−2.71448	+	4.70162i	−0.101873	+	0.176449i
$711$	22.4056	+	15.1544i	0.840275	+	0.568333i
$712$	4.16286	+	7.21029i	0.156010	+	0.270217i
$713$	3.78954	−	6.56368i	0.141919	−	0.245812i
$714$		0			0
$715$	−16.4826	−	28.5487i	−0.616415	−	1.06766i
$716$	25.3690	−	43.9404i	0.948085	−	1.64213i
$717$	37.3058	−	8.58767i	1.39321	−	0.320712i
$718$	35.4118	+	61.3350i	1.32156	+	2.28900i
$719$	−20.6844	−	35.8264i	−0.771397	−	1.33610i	−0.936797	−	0.349873i	$-0.886225\pi$
$719$	−20.6844	−	35.8264i	−0.771397	−	1.33610i	0.165400	−	0.986227i	$-0.447109\pi$
$720$	6.79305	−	3.30248i	0.253162	−	0.123076i
$721$		0			0
$722$	−10.8350	+	18.7667i	−0.403236	+	0.698425i
$723$	46.5773	−	10.7219i	1.73223	−	0.398753i
$724$	24.1066			0.895914
$725$	13.6781			0.507991
$726$	48.8144	+	52.4140i	1.81167	+	1.94526i
$727$	4.86372	−	8.42422i	0.180386	−	0.312437i	−0.761626	−	0.648016i	$-0.775599\pi$
$727$	4.86372	−	8.42422i	0.180386	−	0.312437i	0.942012	+	0.335580i	$0.108932\pi$
$728$		0			0
$729$	5.71460	−	26.3883i	0.211652	−	0.977345i
$730$	14.5604	+	25.2194i	0.538906	+	0.933412i
$731$	−7.99607	−	13.8496i	−0.295745	−	0.512246i
$732$	−14.3618	+	46.8685i	−0.530829	+	1.73231i
$733$	14.4554	−	25.0375i	0.533922	−	0.924780i	−0.465292	−	0.885157i	$-0.654051\pi$
$733$	14.4554	−	25.0375i	0.533922	−	0.924780i	0.999215	−	0.0396234i	$-0.0126158\pi$
$734$	15.4013	+	26.6758i	0.568471	+	0.984621i
$735$		0			0
$736$	−19.4766	+	33.7345i	−0.717918	+	1.24347i
$737$	12.2503	+	21.2182i	0.451247	+	0.781582i
$738$	1.80681	−	25.3735i	0.0665095	−	0.934013i
$739$	6.67467	−	11.5609i	0.245532	−	0.425273i	−0.716749	−	0.697331i	$-0.754371\pi$
$739$	6.67467	−	11.5609i	0.245532	−	0.425273i	0.962281	+	0.272058i	$0.0877041\pi$
$740$	−6.65752			−0.244735
$741$	−30.1435	−	32.3663i	−1.10735	−	1.18901i
$742$		0			0
$743$	19.9100	+	34.4851i	0.730425	+	1.26513i	0.956702	+	0.291071i	$0.0940115\pi$
$743$	19.9100	+	34.4851i	0.730425	+	1.26513i	−0.226276	+	0.974063i	$0.572655\pi$
$744$	1.19067	−	3.88563i	0.0436519	−	0.142454i
$745$	−13.4908	−	23.3668i	−0.494265	−	0.856092i
$746$	−2.91221	+	5.04410i	−0.106624	+	0.184678i
$747$	−27.4135	+	13.3272i	−1.00301	+	0.487617i
$748$	−72.1877			−2.63944
$749$		0			0
$750$	11.7538	−	38.3573i	0.429186	−	1.40061i
$751$	19.2173	−	33.2853i	0.701248	−	1.21460i	−0.266780	−	0.963757i	$-0.585960\pi$
$751$	19.2173	−	33.2853i	0.701248	−	1.21460i	0.968029	−	0.250840i	$-0.0807069\pi$
$752$	6.26409			0.228428
$753$	8.40402	−	27.4258i	0.306260	−	0.999451i
$754$	−41.6515			−1.51686
$755$	−8.07344			−0.293823
$756$		0			0
$757$	−5.66698			−0.205970			−0.102985	−	0.994683i	$-0.532839\pi$
$757$	−5.66698			−0.205970			−0.102985	+	0.994683i	$0.532839\pi$
$758$	−0.681032			−0.0247362
$759$	14.3877	−	46.9528i	0.522239	−	1.70428i
$760$	10.9368			0.396719
$761$	26.1661	−	45.3210i	0.948519	−	1.64288i	0.199973	−	0.979801i	$-0.435915\pi$
$761$	26.1661	−	45.3210i	0.948519	−	1.64288i	0.748546	−	0.663082i	$-0.230752\pi$
$762$	−15.3846	+	50.2064i	−0.557327	+	1.81879i
$763$		0			0
$764$	13.4337			0.486014
$765$	1.30166	−	18.2796i	0.0470616	−	0.660901i
$766$	−9.78121	+	16.9416i	−0.353410	+	0.612123i
$767$	0.732404	+	1.26856i	0.0264456	+	0.0458051i
$768$	−0.606430	+	1.97903i	−0.0218826	+	0.0714120i
$769$	−1.17360	−	2.03274i	−0.0423212	−	0.0733025i	0.844089	−	0.536203i	$-0.180142\pi$
$769$	−1.17360	−	2.03274i	−0.0423212	−	0.0733025i	−0.886410	+	0.462901i	$0.846809\pi$
$770$		0			0
$771$	−2.43849	−	2.61831i	−0.0878201	−	0.0942960i
$772$	−26.7274			−0.961939
$773$	18.1814	−	31.4912i	0.653941	−	1.13266i	−0.328217	−	0.944602i	$-0.606448\pi$
$773$	18.1814	−	31.4912i	0.653941	−	1.13266i	0.982158	−	0.188057i	$-0.0602189\pi$
$774$	19.4963	−	9.47824i	0.700781	−	0.340688i
$775$	2.48285	+	4.30042i	0.0891866	+	0.154476i
$776$	3.98251	−	6.89790i	0.142964	−	0.247620i
$777$		0			0
$778$	29.3659	+	50.8633i	1.05282	+	1.82354i
$779$	−10.4830	+	18.1571i	−0.375592	+	0.650545i
$780$	−8.35711	+	27.2727i	−0.299232	+	0.976518i
$781$	−5.38663	−	9.32991i	−0.192749	−	0.333851i
$782$	27.1292	+	46.9892i	0.970139	+	1.68033i
$783$	3.23875	+	20.7049i	0.115744	+	0.739934i
$784$		0			0
$785$	−0.885235	+	1.53327i	−0.0315954	+	0.0547248i
$786$	0.460255	+	0.494194i	0.0164167	+	0.0176273i
$787$	31.7692			1.13245			0.566224	−	0.824251i	$-0.308404\pi$
$787$	31.7692			1.13245			0.566224	+	0.824251i	$0.308404\pi$
$788$	9.06944			0.323085
$789$	−17.0979	+	3.93587i	−0.608700	+	0.140121i
$790$	−12.4435	+	21.5528i	−0.442721	+	0.766816i
$791$		0			0
$792$	1.87032	−	26.2655i	0.0664589	−	0.933302i
$793$	24.5403	+	42.5050i	0.871451	+	1.50940i
$794$	32.1012	+	55.6009i	1.13923	+	1.97320i
$795$	−15.2914	+	3.52003i	−0.542329	+	0.124842i
$796$	15.1711	−	26.2771i	0.537725	−	0.931367i
$797$	7.45306	+	12.9091i	0.264001	+	0.457263i	0.967301	−	0.253630i	$-0.0816245\pi$
$797$	7.45306	+	12.9091i	0.264001	+	0.457263i	−0.703301	+	0.710893i	$0.748291\pi$
$798$		0			0
$799$	7.59903	−	13.1619i	0.268834	−	0.465635i
$800$	−12.7608	−	22.1023i	−0.451162	−	0.781436i
$801$	1.10709	−	15.5472i	0.0391171	−	0.549333i
$802$	37.3002	−	64.6059i	1.31712	−	2.28131i
$803$	−57.7875			−2.03928
$804$	6.21123	−	20.2698i	0.219053	−	0.714860i
$805$		0			0
$806$	−7.56059	−	13.0953i	−0.266311	−	0.461263i
$807$	17.8241	+	19.1385i	0.627438	+	0.673706i
$808$	0.00427709	+	0.00740814i	0.000150467	+	0.000260617i
$809$	−23.9018	+	41.3992i	−0.840344	+	1.45552i	0.0492597	+	0.998786i	$0.484314\pi$
$809$	−23.9018	+	41.3992i	−0.840344	+	1.45552i	−0.889604	+	0.456733i	$0.849020\pi$
$810$	24.5911	+	3.52003i	0.864042	+	0.123681i
$811$	32.1131			1.12764			0.563821	−	0.825897i	$-0.309331\pi$
$811$	32.1131			1.12764			0.563821	+	0.825897i	$0.309331\pi$
$812$		0			0
$813$	−48.6203	+	11.1922i	−1.70519	+	0.392529i
$814$	11.4337	−	19.8037i	0.400750	−	0.694119i
$815$	24.1758			0.846841
$816$	−11.2867	−	12.1190i	−0.395115	−	0.424251i
$817$	−17.8673			−0.625098
$818$	−23.9057			−0.835843
$819$		0			0
$820$	13.5215			0.472190
$821$	47.1070			1.64405			0.822023	−	0.569455i	$-0.192846\pi$
$821$	47.1070			1.64405			0.822023	+	0.569455i	$0.192846\pi$
$822$	−11.5788	+	2.66540i	−0.403857	+	0.0929667i
$823$	33.7910			1.17788			0.588941	−	0.808176i	$-0.299545\pi$
$823$	33.7910			1.17788			0.588941	+	0.808176i	$0.299545\pi$
$824$	10.4440	−	18.0896i	0.363835	−	0.630181i
$825$	21.9281	+	23.5450i	0.763437	+	0.819733i
$826$		0			0
$827$	2.98023			0.103633			0.0518164	−	0.998657i	$-0.483499\pi$
$827$	2.98023			0.103633			0.0518164	+	0.998657i	$0.483499\pi$
$828$	−38.2155	+	18.5787i	−1.32808	+	0.645653i
$829$	3.03978	−	5.26506i	0.105576	−	0.182863i	−0.808397	−	0.588637i	$-0.799665\pi$
$829$	3.03978	−	5.26506i	0.105576	−	0.182863i	0.913973	+	0.405774i	$0.132998\pi$
$830$	−14.0224	−	24.2875i	−0.486725	−	0.843032i
$831$	4.55673	−	1.04894i	0.158071	−	0.0363875i
$832$	29.4379	+	50.9880i	1.02058	+	1.76769i
$833$		0			0
$834$	−69.2700	+	15.9457i	−2.39862	+	0.552155i
$835$	−2.21190			−0.0765461
$836$	−40.3260	+	69.8467i	−1.39471	+	2.41570i
$837$	−5.92178	+	4.77664i	−0.204687	+	0.165105i
$838$	7.25163	+	12.5602i	0.250503	+	0.433885i
$839$	−1.85858	+	3.21915i	−0.0641653	+	0.111138i	−0.896323	−	0.443401i	$-0.853772\pi$
$839$	−1.85858	+	3.21915i	−0.0641653	+	0.111138i	0.832158	+	0.554538i	$0.187105\pi$
$840$		0			0
$841$	6.36697	+	11.0279i	0.219551	+	0.380273i
$842$	−37.0909	+	64.2433i	−1.27824	+	2.21397i
$843$	5.81518	+	6.24399i	0.200285	+	0.215055i
$844$	−10.0182	−	17.3520i	−0.344841	−	0.597281i
$845$	6.03604	+	10.4547i	0.207646	+	0.359653i
$846$	17.0649	+	11.5421i	0.586705	+	0.396827i
$847$		0			0
$848$	−7.08999	+	12.2802i	−0.243471	+	0.421705i
$849$	−1.81750	+	5.93125i	−0.0623765	+	0.203560i
$850$	−35.5493			−1.21933
$851$	−9.92993			−0.340394
$852$	−2.73116	+	8.91289i	−0.0935680	+	0.305351i
$853$	0.553861	−	0.959315i	0.0189638	−	0.0328463i	−0.856388	−	0.516333i	$-0.827297\pi$
$853$	0.553861	−	0.959315i	0.0189638	−	0.0328463i	0.875352	+	0.483487i	$0.160630\pi$
$854$		0			0
$855$	−16.9597	−	11.4709i	−0.580009	−	0.392298i
$856$	−7.54899	−	13.0752i	−0.258019	−	0.446902i
$857$	−19.2597	−	33.3589i	−0.657900	−	1.13952i	−0.981158	−	0.193206i	$-0.938111\pi$
$857$	−19.2597	−	33.3589i	−0.657900	−	1.13952i	0.323258	−	0.946311i	$-0.395222\pi$
$858$	−66.7737	−	71.6976i	−2.27962	−	2.44772i
$859$	−17.4437	+	30.2134i	−0.595171	+	1.03087i	0.398352	+	0.917233i	$0.369582\pi$
$859$	−17.4437	+	30.2134i	−0.595171	+	1.03087i	−0.993523	+	0.113634i	$0.963751\pi$
$860$	5.76153	+	9.97926i	0.196467	+	0.340290i
$861$		0			0
$862$	−2.45857	+	4.25836i	−0.0837391	+	0.145040i
$863$	−1.07924	−	1.86931i	−0.0367379	−	0.0636319i	0.847072	−	0.531478i	$-0.178363\pi$
$863$	−1.07924	−	1.86931i	−0.0367379	−	0.0636319i	−0.883810	+	0.467847i	$0.845030\pi$
$864$	30.4354	−	24.5499i	1.03543	−	0.835203i
$865$	6.38957	−	11.0671i	0.217252	−	0.376291i
$866$	−74.8441			−2.54331
$867$	−10.4617	+	2.40826i	−0.355299	+	0.0817888i
$868$		0			0
$869$	−24.6930	−	42.7695i	−0.837652	−	1.45086i
$870$	−18.7901	+	4.32542i	−0.637044	+	0.146645i
$871$	−10.6132	−	18.3826i	−0.359615	−	0.622872i
$872$	−13.5332	+	23.4401i	−0.458291	+	0.793783i
$873$	−13.4105	+	6.51957i	−0.453876	+	0.220654i
$874$	60.6205			2.05052
$875$		0			0
$876$	34.0785	+	36.5914i	1.15140	+	1.23631i
$877$	−9.43950	+	16.3497i	−0.318749	+	0.552090i	−0.980227	−	0.197875i	$-0.936596\pi$
$877$	−9.43950	+	16.3497i	−0.318749	+	0.552090i	0.661478	+	0.749965i	$0.269929\pi$
$878$	−13.0391			−0.440049
$879$	−41.1697	+	9.47714i	−1.38862	+	0.319656i
$880$	−13.7906			−0.464881
$881$	18.7203			0.630704			0.315352	−	0.948975i	$-0.397877\pi$
$881$	18.7203			0.630704			0.315352	+	0.948975i	$0.397877\pi$
$882$		0			0
$883$	−13.3717			−0.449993			−0.224996	−	0.974360i	$-0.572237\pi$
$883$	−13.3717			−0.449993			−0.224996	+	0.974360i	$0.572237\pi$
$884$	62.5407			2.10347
$885$	0.462144	+	0.496223i	0.0155348	+	0.0166804i
$886$	−85.8294			−2.88350
$887$	20.6284	−	35.7294i	0.692633	−	1.19968i	−0.278339	−	0.960483i	$-0.589784\pi$
$887$	20.6284	−	35.7294i	0.692633	−	1.19968i	0.970972	−	0.239193i	$-0.0768829\pi$
$888$	−5.18880	+	1.19445i	−0.174125	+	0.0400830i
$889$		0			0
$890$	14.3406			0.480699
$891$	−30.4486	+	38.7682i	−1.02007	+	1.29878i
$892$	−5.54832	+	9.60997i	−0.185772	+	0.321766i
$893$	−8.49006	−	14.7052i	−0.284109	−	0.492091i
$894$	−54.6534	−	58.6836i	−1.82788	−	1.96267i
$895$	−11.7585	−	20.3664i	−0.393045	−	0.680774i
$896$		0			0
$897$	−12.4649	+	40.6782i	−0.416192	+	1.35820i
$898$	5.33396			0.177996
$899$	2.95262	−	5.11408i	0.0984753	−	0.170564i
$900$	1.97745	−	27.7700i	0.0659151	−	0.925666i
$901$	17.2019	+	29.7945i	0.573078	+	0.992599i
$902$	−23.2219	+	40.2215i	−0.773204	+	1.33923i
$903$		0			0
$904$	−4.92463	−	8.52971i	−0.163791	−	0.283694i
$905$	5.58670	−	9.67645i	0.185708	−	0.321656i
$906$	−23.3835	+	5.38281i	−0.776865	+	0.178832i
$907$	−1.84519	−	3.19595i	−0.0612684	−	0.106120i	0.833764	−	0.552121i	$-0.186181\pi$
$907$	−1.84519	−	3.19595i	−0.0612684	−	0.106120i	−0.895033	+	0.446001i	$0.852848\pi$
$908$	1.82537	+	3.16163i	0.0605770	+	0.104922i
$909$	0.00113747	−	0.0159738i	3.77274e−5	−	0.000529818i
$910$		0			0
$911$	−3.43831	+	5.95533i	−0.113916	+	0.197309i	−0.917346	−	0.398091i	$-0.869673\pi$
$911$	−3.43831	+	5.95533i	−0.113916	+	0.197309i	0.803430	+	0.595400i	$0.203006\pi$
$912$	−18.0311	+	4.15070i	−0.597069	+	0.137443i
$913$	55.6522			1.84182
$914$	23.9855			0.793369
$915$	15.4848	+	16.6267i	0.511912	+	0.549661i
$916$	−21.8860	+	37.9077i	−0.723135	+	1.25251i
$917$		0			0
$918$	−8.41751	−	53.8120i	−0.277819	−	1.77606i
$919$	−18.6473	−	32.2981i	−0.615119	−	1.06542i	−0.990364	−	0.138491i	$-0.955775\pi$
$919$	−18.6473	−	32.2981i	−0.615119	−	1.06542i	0.375245	−	0.926926i	$-0.377559\pi$
$920$	−5.26019	−	9.11092i	−0.173423	−	0.300378i
$921$	12.1295	−	39.5836i	0.399681	−	1.30432i
$922$	−31.8916	+	55.2378i	−1.05029	+	1.81916i
$923$	4.66677	+	8.08309i	0.153609	+	0.266058i
$924$		0			0
$925$	3.25297	−	5.63431i	0.106957	−	0.185255i
$926$	1.29178	+	2.23743i	0.0424506	+	0.0735267i
$927$	−35.1687	+	17.0974i	−1.15509	+	0.561554i
$928$	−15.1752	+	26.2842i	−0.498150	+	0.862821i
$929$	17.9787			0.589861			0.294930	−	0.955519i	$-0.404704\pi$
$929$	17.9787			0.589861			0.294930	+	0.955519i	$0.404704\pi$
$930$	−4.77070	−	5.12250i	−0.156438	−	0.167973i
$931$		0			0
$932$	−11.1243	−	19.2679i	−0.364389	−	0.631141i
$933$	6.56734	−	21.4319i	0.215005	−	0.701650i
$934$	24.0642	+	41.6804i	0.787405	+	1.36383i
$935$	−16.7295	+	28.9764i	−0.547113	+	0.947628i
$936$	−1.62037	+	22.7554i	−0.0529636	+	0.743784i
$937$	−34.7312			−1.13462			−0.567310	−	0.823504i	$-0.692016\pi$
$937$	−34.7312			−1.13462			−0.567310	+	0.823504i	$0.692016\pi$
$938$		0			0
$939$	13.6344	−	44.4947i	0.444943	−	1.45203i
$940$	−5.47544	+	9.48374i	−0.178589	+	0.309326i
$941$	−43.3025			−1.41162			−0.705810	−	0.708401i	$-0.749417\pi$
$941$	−43.3025			−1.41162			−0.705810	+	0.708401i	$0.749417\pi$
$942$	−1.54167	+	5.03110i	−0.0502304	+	0.163922i
$943$	20.1678			0.656752
$944$	0.612785			0.0199444
$945$		0			0
$946$	−39.5796			−1.28684
$947$	38.2591			1.24325			0.621626	−	0.783314i	$-0.286472\pi$
$947$	38.2591			1.24325			0.621626	+	0.783314i	$0.286472\pi$
$948$	−12.5200	+	40.8578i	−0.406630	+	1.32700i
$949$	50.0649			1.62518
$950$	−19.8588	+	34.3965i	−0.644305	+	1.11597i
$951$	4.21784	−	13.7645i	0.136773	−	0.446345i
$952$		0			0
$953$	−47.8757			−1.55085			−0.775423	−	0.631442i	$-0.782463\pi$
$953$	−47.8757			−1.55085			−0.775423	+	0.631442i	$0.782463\pi$
$954$	−41.9423	+	20.3905i	−1.35793	+	0.660165i
$955$	3.11326	−	5.39233i	0.100743	−	0.174492i
$956$	30.2389	+	52.3753i	0.977996	+	1.69394i
$957$	11.2101	−	36.5832i	0.362372	−	1.18257i
$958$	−27.3593	−	47.3877i	−0.883939	−	1.53103i
$959$		0			0
$960$	18.5752	+	19.9450i	0.599512	+	0.643721i
$961$	−28.8562			−0.930844
$962$	−9.90570	+	17.1572i	−0.319373	+	0.553170i
$963$	−2.00761	+	28.1935i	−0.0646943	+	0.908522i
$964$	37.7541	+	65.3920i	1.21598	+	2.10613i
$965$	−6.19407	+	10.7284i	−0.199394	+	0.345361i
$966$		0			0
$967$	15.5575	+	26.9463i	0.500294	+	0.866535i	1.00000		0.000339469i	$0.000108056\pi$
$967$	15.5575	+	26.9463i	0.500294	+	0.866535i	−0.499706	+	0.866195i	$0.666559\pi$
$968$	−15.2245	+	26.3696i	−0.489334	+	0.847551i
$969$	−13.1524	+	42.9216i	−0.422516	+	1.37884i
$970$	−6.85966	−	11.8813i	−0.220250	−	0.381485i
$971$	15.1312	+	26.2080i	0.485583	+	0.841055i	0.999863	−	0.0165676i	$-0.00527387\pi$
$971$	15.1312	+	26.2080i	0.485583	+	0.841055i	−0.514279	+	0.857623i	$0.671941\pi$
$972$	42.5045	−	3.58216i	1.36333	−	0.114898i
$973$		0			0
$974$	−14.7751	+	25.5911i	−0.473423	+	0.819993i
$975$	−18.9976	−	20.3985i	−0.608412	−	0.653276i
$976$	20.5323			0.657221
$977$	38.2201			1.22277			0.611385	−	0.791333i	$-0.290613\pi$
$977$	38.2201			1.22277			0.611385	+	0.791333i	$0.290613\pi$
$978$	70.0215	−	16.1187i	2.23904	−	0.515420i
$979$	−14.2288	+	24.6450i	−0.454754	+	0.787657i
$980$		0			0
$981$	45.5709	−	22.1545i	1.45497	−	0.707339i
$982$	15.7821	+	27.3354i	0.503627	+	0.872308i
$983$	18.6964	+	32.3832i	0.596324	+	1.03286i	0.993359	+	0.115059i	$0.0367058\pi$
$983$	18.6964	+	32.3832i	0.596324	+	1.03286i	−0.397035	+	0.917803i	$0.629961\pi$
$984$	10.5385	−	2.42593i	0.335955	−	0.0773357i
$985$	2.10184	−	3.64050i	0.0669703	−	0.115996i
$986$	21.1377	+	36.6116i	0.673162	+	1.16595i
$987$		0			0
$988$	34.9370	−	60.5126i	1.11149	−	1.92516i
$989$	8.59353	+	14.8844i	0.273258	+	0.473297i
$990$	−37.5690	−	25.4104i	−1.19402	−	0.807595i
$991$	11.9299	−	20.6631i	0.378965	−	0.656386i	−0.611947	−	0.790899i	$-0.709613\pi$
$991$	11.9299	−	20.6631i	0.378965	−	0.656386i	0.990912	+	0.134512i	$0.0429468\pi$
$992$	−11.0184			−0.349835
$993$	6.29136	−	20.5313i	0.199650	−	0.651540i
$994$		0			0
$995$	−7.03180	−	12.1794i	−0.222923	−	0.386114i
$996$	−32.8192	−	35.2393i	−1.03992	−	1.11660i
$997$	−25.8413	−	44.7585i	−0.818403	−	1.41751i	−0.906859	−	0.421435i	$-0.861527\pi$
$997$	−25.8413	−	44.7585i	−0.818403	−	1.41751i	0.0884560	−	0.996080i	$-0.471807\pi$
$998$	−15.2249	+	26.3703i	−0.481936	+	0.834738i
$999$	9.29907	+	3.59000i	0.294210	+	0.113583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.h.214.12		24
3.2	odd	2		1323.2.h.h.802.1		24
7.2	even	3		441.2.g.h.79.2		24
7.3	odd	6		441.2.f.h.295.2	yes	24
7.4	even	3		441.2.f.h.295.1	yes	24
7.5	odd	6		441.2.g.h.79.1		24
7.6	odd	2	inner	441.2.h.h.214.11		24
9.4	even	3		441.2.g.h.67.2		24
9.5	odd	6		1323.2.g.h.361.12		24
21.2	odd	6		1323.2.g.h.667.12		24
21.5	even	6		1323.2.g.h.667.11		24
21.11	odd	6		1323.2.f.h.883.11		24
21.17	even	6		1323.2.f.h.883.12		24
21.20	even	2		1323.2.h.h.802.2		24
63.4	even	3		441.2.f.h.148.1	✓	24
63.5	even	6		1323.2.h.h.226.2		24
63.11	odd	6		3969.2.a.bi.1.2		12
63.13	odd	6		441.2.g.h.67.1		24
63.23	odd	6		1323.2.h.h.226.1		24
63.25	even	3		3969.2.a.bh.1.11		12
63.31	odd	6		441.2.f.h.148.2	yes	24
63.32	odd	6		1323.2.f.h.442.11		24
63.38	even	6		3969.2.a.bi.1.1		12
63.40	odd	6	inner	441.2.h.h.373.11		24
63.41	even	6		1323.2.g.h.361.11		24
63.52	odd	6		3969.2.a.bh.1.12		12
63.58	even	3	inner	441.2.h.h.373.12		24
63.59	even	6		1323.2.f.h.442.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.1	✓	24	63.4	even	3
441.2.f.h.148.2	yes	24	63.31	odd	6
441.2.f.h.295.1	yes	24	7.4	even	3
441.2.f.h.295.2	yes	24	7.3	odd	6
441.2.g.h.67.1		24	63.13	odd	6
441.2.g.h.67.2		24	9.4	even	3
441.2.g.h.79.1		24	7.5	odd	6
441.2.g.h.79.2		24	7.2	even	3
441.2.h.h.214.11		24	7.6	odd	2	inner
441.2.h.h.214.12		24	1.1	even	1	trivial
441.2.h.h.373.11		24	63.40	odd	6	inner
441.2.h.h.373.12		24	63.58	even	3	inner
1323.2.f.h.442.11		24	63.32	odd	6
1323.2.f.h.442.12		24	63.59	even	6
1323.2.f.h.883.11		24	21.11	odd	6
1323.2.f.h.883.12		24	21.17	even	6
1323.2.g.h.361.11		24	63.41	even	6
1323.2.g.h.361.12		24	9.5	odd	6
1323.2.g.h.667.11		24	21.5	even	6
1323.2.g.h.667.12		24	21.2	odd	6
1323.2.h.h.226.1		24	63.23	odd	6
1323.2.h.h.226.2		24	63.5	even	6
1323.2.h.h.802.1		24	3.2	odd	2
1323.2.h.h.802.2		24	21.20	even	2
3969.2.a.bh.1.11		12	63.25	even	3
3969.2.a.bh.1.12		12	63.52	odd	6
3969.2.a.bi.1.1		12	63.38	even	6
3969.2.a.bi.1.2		12	63.11	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.17631 q^{2} +(0.507459 - 1.65605i) q^{3} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-2.48497 - 1.68075i) q^{9} +O(q^{10})\)	\(q+2.17631 q^{2} +(0.507459 - 1.65605i) q^{3} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} +(1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-2.48497 - 1.68075i) q^{9} +(1.38010 - 2.39040i) q^{10} +(2.73867 + 4.74351i) q^{11} +(1.38857 - 4.53149i) q^{12} +(-2.37268 - 4.10960i) q^{13} +(-1.49715 - 1.60755i) q^{15} -1.98516 q^{16} +(-2.40822 + 4.17116i) q^{17} +(-5.40807 - 3.65783i) q^{18} +(2.69059 + 4.66025i) q^{19} +(1.73523 - 3.00550i) q^{20} +(5.96019 + 10.3233i) q^{22} +(2.58816 - 4.48282i) q^{23} +(0.813193 - 2.65378i) q^{24} +(1.69572 + 2.93707i) q^{25} +(-5.16368 - 8.94376i) q^{26} +(-4.04442 + 3.26231i) q^{27} +(2.01656 - 3.49278i) q^{29} +(-3.25826 - 3.49853i) q^{30} +1.46419 q^{31} -7.52529 q^{32} +(9.24522 - 2.12822i) q^{33} +(-5.24103 + 9.07773i) q^{34} +(-6.79970 - 4.59908i) q^{36} +(-0.959170 - 1.66133i) q^{37} +(5.85557 + 10.1421i) q^{38} +(-8.00971 + 1.84381i) q^{39} +(1.01621 - 1.76012i) q^{40} +(1.94808 + 3.37418i) q^{41} +(-1.66016 + 2.87549i) q^{43} +(7.49389 + 12.9798i) q^{44} +(-3.42192 + 1.66358i) q^{45} +(5.63263 - 9.75600i) q^{46} -3.15546 q^{47} +(-1.00739 + 3.28752i) q^{48} +(3.69042 + 6.39199i) q^{50} +(5.68555 + 6.10481i) q^{51} +(-6.49243 - 11.2452i) q^{52} +(3.57149 - 6.18601i) q^{53} +(-8.80191 + 7.09981i) q^{54} +6.94684 q^{55} +(9.08294 - 2.09086i) q^{57} +(4.38866 - 7.60138i) q^{58} -0.308683 q^{59} +(-4.09669 - 4.39879i) q^{60} -10.3429 q^{61} +3.18652 q^{62} -12.4070 q^{64} -6.01848 q^{65} +(20.1205 - 4.63167i) q^{66} +4.47310 q^{67} +(-6.58968 + 11.4137i) q^{68} +(-6.11037 - 6.56095i) q^{69} -1.96688 q^{71} +(-3.98212 - 2.69337i) q^{72} +(-5.27515 + 9.13683i) q^{73} +(-2.08745 - 3.61557i) q^{74} +(5.72444 - 1.31775i) q^{75} +(7.36235 + 12.7520i) q^{76} +(-17.4316 + 4.01270i) q^{78} -9.01643 q^{79} +(-1.25888 + 2.18044i) q^{80} +(3.35017 + 8.35323i) q^{81} +(4.23963 + 7.34326i) q^{82} +(5.08023 - 8.79921i) q^{83} +(3.05432 + 5.29023i) q^{85} +(-3.61303 + 6.25796i) q^{86} +(-4.76089 - 5.11196i) q^{87} +(4.38866 + 7.60138i) q^{88} +(2.59776 + 4.49945i) q^{89} +(-7.44716 + 3.62047i) q^{90} +(7.08205 - 12.2665i) q^{92} +(0.743014 - 2.42476i) q^{93} -6.86726 q^{94} +6.82490 q^{95} +(-3.81877 + 12.4622i) q^{96} +(2.48521 - 4.30451i) q^{97} +(1.16714 - 16.3905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more