LMFDB - Embedded newform 784.2.x.o.165.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.6
Character	$\chi$	$=$	784.165
Dual form			784.2.x.o.765.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.478757 + 1.33071i) q^{2} +(-0.659252 - 2.46036i) q^{3} +(-1.54158 - 1.27417i) q^{4} +(0.502490 - 1.87532i) q^{5} +(3.58965 + 0.300642i) q^{6} +(2.43360 - 1.44138i) q^{8} +(-3.02070 + 1.74400i) q^{9} +O(q^{10})$	\(q+(-0.478757 + 1.33071i) q^{2} +(-0.659252 - 2.46036i) q^{3} +(-1.54158 - 1.27417i) q^{4} +(0.502490 - 1.87532i) q^{5} +(3.58965 + 0.300642i) q^{6} +(2.43360 - 1.44138i) q^{8} +(-3.02070 + 1.74400i) q^{9} +(2.25494 + 1.56649i) q^{10} +(5.11917 - 1.37168i) q^{11} +(-2.11864 + 4.63286i) q^{12} +(3.61173 - 3.61173i) q^{13} -4.94523 q^{15} +(0.752959 + 3.92849i) q^{16} +(0.294815 - 0.510634i) q^{17} +(-0.874580 - 4.85462i) q^{18} +(-0.514822 - 0.137946i) q^{19} +(-3.16411 + 2.25070i) q^{20} +(-0.625532 + 7.46884i) q^{22} +(-0.378033 + 0.218258i) q^{23} +(-5.15068 - 5.03731i) q^{24} +(1.06581 + 0.615344i) q^{25} +(3.07703 + 6.53532i) q^{26} +(0.878939 + 0.878939i) q^{27} +(2.68976 - 2.68976i) q^{29} +(2.36756 - 6.58067i) q^{30} +(-3.94118 + 6.82633i) q^{31} +(-5.58817 - 0.878822i) q^{32} +(-6.74965 - 11.6907i) q^{33} +(0.538362 + 0.636783i) q^{34} +(6.87881 + 1.16037i) q^{36} +(0.779365 - 2.90863i) q^{37} +(0.430041 - 0.619036i) q^{38} +(-11.2672 - 6.50513i) q^{39} +(-1.48019 - 5.28806i) q^{40} +2.95135i q^{41} +(-7.67329 - 7.67329i) q^{43} +(-9.63939 - 4.40816i) q^{44} +(1.75268 + 6.54110i) q^{45} +(-0.109452 - 0.607545i) q^{46} +(-2.01771 - 3.49478i) q^{47} +(9.16913 - 4.44242i) q^{48} +(-1.32911 + 1.12368i) q^{50} +(-1.45070 - 0.388715i) q^{51} +(-10.1698 + 0.965811i) q^{52} +(-0.912017 + 0.244374i) q^{53} +(-1.59041 + 0.748816i) q^{54} -10.2893i q^{55} +1.35759i q^{57} +(2.29155 + 4.86703i) q^{58} +(0.0281166 - 0.00753382i) q^{59} +(7.62348 + 6.30108i) q^{60} +(1.97795 + 0.529990i) q^{61} +(-7.19700 - 8.51273i) q^{62} +(3.84483 - 7.01550i) q^{64} +(-4.95829 - 8.58801i) q^{65} +(18.7884 - 3.38481i) q^{66} +(1.67413 + 6.24795i) q^{67} +(-1.10512 + 0.411540i) q^{68} +(0.786212 + 0.786212i) q^{69} +2.05630i q^{71} +(-4.83740 + 8.59818i) q^{72} +(6.85664 + 3.95868i) q^{73} +(3.49742 + 2.42964i) q^{74} +(0.811334 - 3.02794i) q^{75} +(0.617873 + 0.868628i) q^{76} +(14.0507 - 11.8790i) q^{78} +(-6.53028 - 11.3108i) q^{79} +(7.74553 + 0.561989i) q^{80} +(-3.64893 + 6.32013i) q^{81} +(-3.92739 - 1.41298i) q^{82} +(-10.1551 + 10.1551i) q^{83} +(-0.809460 - 0.809460i) q^{85} +(13.8846 - 6.53729i) q^{86} +(-8.39101 - 4.84455i) q^{87} +(10.4809 - 10.7168i) q^{88} +(-3.35262 + 1.93564i) q^{89} +(-9.54343 - 0.799284i) q^{90} +(0.860868 + 0.145218i) q^{92} +(19.3935 + 5.19647i) q^{93} +(5.61654 - 1.01184i) q^{94} +(-0.517385 + 0.896137i) q^{95} +(1.52179 + 14.3283i) q^{96} +12.0556 q^{97} +(-13.0712 + 13.0712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.478757	+	1.33071i	−0.338532	+	0.940955i
$2$	−0.478757	+	1.33071i	−0.338532	+	0.940955i
$3$	−0.659252	−	2.46036i	−0.380619	−	1.42049i	−0.844958	−	0.534833i	$-0.820374\pi$
$3$	−0.659252	−	2.46036i	−0.380619	−	1.42049i	0.464338	−	0.885658i	$-0.346292\pi$
$4$	−1.54158	−	1.27417i	−0.770792	−	0.637087i
$5$	0.502490	−	1.87532i	0.224720	−	0.838668i	−0.757796	−	0.652491i	$-0.773724\pi$
$5$	0.502490	−	1.87532i	0.224720	−	0.838668i	0.982516	−	0.186176i	$-0.0596095\pi$
$6$	3.58965	+	0.300642i	1.46547	+	0.122736i
$7$		0			0
$7$		0			0
$8$	2.43360	−	1.44138i	0.860408	−	0.509606i
$9$	−3.02070	+	1.74400i	−1.00690	+	0.581333i
$10$	2.25494	+	1.56649i	0.713073	+	0.495368i
$11$	5.11917	−	1.37168i	1.54349	−	0.413576i	0.616097	−	0.787670i	$-0.288713\pi$
$11$	5.11917	−	1.37168i	1.54349	−	0.413576i	0.927391	+	0.374094i	$0.122046\pi$
$12$	−2.11864	+	4.63286i	−0.611598	+	1.33739i
$13$	3.61173	−	3.61173i	1.00171	−	1.00171i	0.00171617	−	0.999999i	$-0.499454\pi$
$13$	3.61173	−	3.61173i	1.00171	−	1.00171i	0.999999	−	0.00171617i	$-0.000546274\pi$
$14$		0			0
$15$	−4.94523			−1.27685
$16$	0.752959	+	3.92849i	0.188240	+	0.982123i
$17$	0.294815	−	0.510634i	0.0715031	−	0.123847i	−0.828057	−	0.560644i	$-0.810554\pi$
$17$	0.294815	−	0.510634i	0.0715031	−	0.123847i	0.899560	+	0.436797i	$0.143887\pi$
$18$	−0.874580	−	4.85462i	−0.206140	−	1.14425i
$19$	−0.514822	−	0.137946i	−0.118108	−	0.0316470i	0.199281	−	0.979942i	$-0.436139\pi$
$19$	−0.514822	−	0.137946i	−0.118108	−	0.0316470i	−0.317389	+	0.948295i	$0.602806\pi$
$20$	−3.16411	+	2.25070i	−0.707517	+	0.503272i
$21$		0			0
$22$	−0.625532	+	7.46884i	−0.133364	+	1.59236i
$23$	−0.378033	+	0.218258i	−0.0788254	+	0.0455098i	−0.538895	−	0.842373i	$-0.681158\pi$
$23$	−0.378033	+	0.218258i	−0.0788254	+	0.0455098i	0.460069	+	0.887883i	$0.347825\pi$
$24$	−5.15068	−	5.03731i	−1.05138	−	1.02824i
$25$	1.06581	+	0.615344i	0.213161	+	0.123069i
$26$	3.07703	+	6.53532i	0.603455	+	1.28168i
$27$	0.878939	+	0.878939i	0.169152	+	0.169152i
$28$		0			0
$29$	2.68976	−	2.68976i	0.499476	−	0.499476i	−0.411799	−	0.911275i	$-0.635099\pi$
$29$	2.68976	−	2.68976i	0.499476	−	0.499476i	0.911275	+	0.411799i	$0.135099\pi$
$30$	2.36756	−	6.58067i	0.432256	−	1.20146i
$31$	−3.94118	+	6.82633i	−0.707857	+	1.22605i	0.257793	+	0.966200i	$0.417005\pi$
$31$	−3.94118	+	6.82633i	−0.707857	+	1.22605i	−0.965650	+	0.259845i	$0.916329\pi$
$32$	−5.58817	−	0.878822i	−0.987859	−	0.155355i
$33$	−6.74965	−	11.6907i	−1.17496	−	2.03510i
$34$	0.538362	+	0.636783i	0.0923284	+	0.109207i
$35$		0			0
$36$	6.87881	+	1.16037i	1.14647	+	0.193395i
$37$	0.779365	−	2.90863i	0.128127	−	0.478176i	−0.871805	−	0.489853i	$-0.837050\pi$
$37$	0.779365	−	2.90863i	0.128127	−	0.478176i	0.999932	+	0.0116774i	$0.00371712\pi$
$38$	0.430041	−	0.619036i	0.0697618	−	0.100421i
$39$	−11.2672	−	6.50513i	−1.80420	−	1.04165i
$40$	−1.48019	−	5.28806i	−0.234038	−	0.836115i
$41$			2.95135i			0.460923i	0.973081	+	0.230461i	$0.0740235\pi$
$41$			2.95135i			0.460923i	−0.973081	+	0.230461i	$0.925976\pi$
$42$		0			0
$43$	−7.67329	−	7.67329i	−1.17017	−	1.17017i	−0.982170	−	0.187996i	$-0.939801\pi$
$43$	−7.67329	−	7.67329i	−1.17017	−	1.17017i	−0.187996	−	0.982170i	$-0.560199\pi$
$44$	−9.63939	−	4.40816i	−1.45319	−	0.664555i
$45$	1.75268	+	6.54110i	0.261275	+	0.975090i
$46$	−0.109452	−	0.607545i	−0.0161378	−	0.0895777i
$47$	−2.01771	−	3.49478i	−0.294314	−	0.509766i	0.680511	−	0.732738i	$-0.261758\pi$
$47$	−2.01771	−	3.49478i	−0.294314	−	0.509766i	−0.974825	+	0.222971i	$0.928424\pi$
$48$	9.16913	−	4.44242i	1.32345	−	0.641208i
$49$		0			0
$50$	−1.32911	+	1.12368i	−0.187964	+	0.158912i
$51$	−1.45070	−	0.388715i	−0.203139	−	0.0544310i
$52$	−10.1698	+	0.965811i	−1.41029	+	0.133934i
$53$	−0.912017	+	0.244374i	−0.125275	+	0.0335674i	−0.320912	−	0.947109i	$-0.603989\pi$
$53$	−0.912017	+	0.244374i	−0.125275	+	0.0335674i	0.195637	+	0.980676i	$0.437323\pi$
$54$	−1.59041	+	0.748816i	−0.216428	+	0.101901i
$55$		−	10.2893i		−	1.38741i
$56$		0			0
$57$			1.35759i			0.179817i
$58$	2.29155	+	4.86703i	0.300895	+	0.639073i
$59$	0.0281166	−	0.00753382i	0.00366047	−	0.000980820i	−0.256988	−	0.966415i	$-0.582730\pi$
$59$	0.0281166	−	0.00753382i	0.00366047	−	0.000980820i	0.260649	+	0.965434i	$0.416064\pi$
$60$	7.62348	+	6.30108i	0.984188	+	0.813466i
$61$	1.97795	+	0.529990i	0.253251	+	0.0678583i	0.383211	−	0.923661i	$-0.374818\pi$
$61$	1.97795	+	0.529990i	0.253251	+	0.0678583i	−0.129960	+	0.991519i	$0.541485\pi$
$62$	−7.19700	−	8.51273i	−0.914020	−	1.08112i
$63$		0			0
$64$	3.84483	−	7.01550i	0.480604	−	0.876938i
$65$	−4.95829	−	8.58801i	−0.615000	−	1.06521i
$66$	18.7884	−	3.38481i	2.31270	−	0.416641i
$67$	1.67413	+	6.24795i	0.204528	+	0.763309i	0.989593	+	0.143895i	$0.0459629\pi$
$67$	1.67413	+	6.24795i	0.204528	+	0.763309i	−0.785065	+	0.619414i	$0.787370\pi$
$68$	−1.10512	+	0.411540i	−0.134015	+	0.0499066i
$69$	0.786212	+	0.786212i	0.0946488	+	0.0946488i
$70$		0			0
$71$			2.05630i			0.244037i	0.992528	+	0.122019i	$0.0389368\pi$
$71$			2.05630i			0.244037i	−0.992528	+	0.122019i	$0.961063\pi$
$72$	−4.83740	+	8.59818i	−0.570093	+	1.01330i
$73$	6.85664	+	3.95868i	0.802509	+	0.463329i	0.844348	−	0.535796i	$-0.179988\pi$
$73$	6.85664	+	3.95868i	0.802509	+	0.463329i	−0.0418389	+	0.999124i	$0.513322\pi$
$74$	3.49742	+	2.42964i	0.406567	+	0.282439i
$75$	0.811334	−	3.02794i	0.0936847	−	0.349636i
$76$	0.617873	+	0.868628i	0.0708749	+	0.0996384i
$77$		0			0
$78$	14.0507	−	11.8790i	1.59093	−	1.34504i
$79$	−6.53028	−	11.3108i	−0.734714	−	1.27256i	−0.954849	−	0.297092i	$-0.903983\pi$
$79$	−6.53028	−	11.3108i	−0.734714	−	1.27256i	0.220135	−	0.975469i	$-0.429350\pi$
$80$	7.74553	+	0.561989i	0.865976	+	0.0628323i
$81$	−3.64893	+	6.32013i	−0.405437	+	0.702237i
$82$	−3.92739	−	1.41298i	−0.433708	−	0.156037i
$83$	−10.1551	+	10.1551i	−1.11467	+	1.11467i	−0.122161	+	0.992510i	$0.538982\pi$
$83$	−10.1551	+	10.1551i	−1.11467	+	1.11467i	−0.992510	+	0.122161i	$0.961018\pi$
$84$		0			0
$85$	−0.809460	−	0.809460i	−0.0877983	−	0.0877983i
$86$	13.8846	−	6.53729i	1.49721	−	0.704934i
$87$	−8.39101	−	4.84455i	−0.899611	−	0.519391i
$88$	10.4809	−	10.7168i	1.11727	−	1.14241i
$89$	−3.35262	+	1.93564i	−0.355377	+	0.205177i	−0.667051	−	0.745012i	$-0.732444\pi$
$89$	−3.35262	+	1.93564i	−0.355377	+	0.205177i	0.311674	+	0.950189i	$0.399110\pi$
$90$	−9.54343	−	0.799284i	−1.00597	−	0.0842519i
$91$		0			0
$92$	0.860868	+	0.145218i	0.0897517	+	0.0151400i
$93$	19.3935	+	5.19647i	2.01101	+	0.538849i
$94$	5.61654	−	1.01184i	0.579302	−	0.104364i
$95$	−0.517385	+	0.896137i	−0.0530826	+	0.0919418i
$96$	1.52179	+	14.3283i	0.155318	+	1.46238i
$97$	12.0556			1.22406			0.612029	−	0.790836i	$-0.290354\pi$
$97$	12.0556			1.22406			0.612029	+	0.790836i	$0.290354\pi$
$98$		0			0
$99$	−13.0712	+	13.0712i	−1.31371	+	1.31371i
$100$	−0.858975	−	2.30663i	−0.0858975	−	0.230663i
$101$	−2.59366	+	0.694969i	−0.258079	+	0.0691520i	−0.385539	−	0.922692i	$-0.625984\pi$
$101$	−2.59366	+	0.694969i	−0.258079	+	0.0691520i	0.127460	+	0.991844i	$0.459318\pi$
$102$	1.21180	−	1.74437i	0.119986	−	0.172718i
$103$	0.0773103	−	0.0446351i	0.00761761	−	0.00439803i	−0.496186	−	0.868216i	$-0.665267\pi$
$103$	0.0773103	−	0.0446351i	0.00761761	−	0.00439803i	0.503804	+	0.863818i	$0.331933\pi$
$104$	3.58363	−	13.9954i	0.351404	−	1.37236i
$105$		0			0
$106$	0.111443	−	1.33063i	0.0108243	−	0.129242i
$107$	−3.77279	+	14.0802i	−0.364729	+	1.36119i	0.503059	+	0.864252i	$0.332208\pi$
$107$	−3.77279	+	14.0802i	−0.364729	+	1.36119i	−0.867788	+	0.496935i	$0.834459\pi$
$108$	−0.235036	−	2.47488i	−0.0226164	−	0.238145i
$109$	1.79098	+	6.68404i	0.171545	+	0.640215i	0.997114	+	0.0759141i	$0.0241875\pi$
$109$	1.79098	+	6.68404i	0.171545	+	0.640215i	−0.825569	+	0.564301i	$0.809146\pi$
$110$	13.6921	+	4.92609i	1.30549	+	0.469684i
$111$	−7.67008			−0.728012
$112$		0			0
$113$	7.51142			0.706615			0.353307	−	0.935507i	$-0.385057\pi$
$113$	7.51142			0.706615			0.353307	+	0.935507i	$0.385057\pi$
$114$	−1.80656	−	0.649955i	−0.169200	−	0.0608739i
$115$	0.219344	+	0.818604i	0.0204540	+	0.0763353i
$116$	−7.57371	+	0.719266i	−0.703201	+	0.0667822i
$117$	−4.61109	+	17.2088i	−0.426295	+	1.59095i
$118$	−0.00343568	+	0.0410219i	−0.000316280	+	0.00377638i
$119$		0			0
$120$	−12.0347	+	7.12797i	−1.09861	+	0.650691i
$121$	14.7981	−	8.54370i	1.34528	−	0.776700i
$122$	−1.65222	+	2.37834i	−0.149585	+	0.215325i
$123$	7.26138	−	1.94568i	0.654737	−	0.175436i
$124$	14.7736	−	5.50160i	1.32671	−	0.494059i
$125$	8.55366	−	8.55366i	0.765063	−	0.765063i
$126$		0			0
$127$	4.25202			0.377306			0.188653	−	0.982044i	$-0.439588\pi$
$127$	4.25202			0.377306			0.188653	+	0.982044i	$0.439588\pi$
$128$	7.49486	+	8.47508i	0.662459	+	0.749099i
$129$	−13.8204	+	23.9377i	−1.21682	+	2.10760i
$130$	13.8020	−	2.48648i	1.21051	−	0.218079i
$131$	4.89071	+	1.31046i	0.427304	+	0.114496i	0.466060	−	0.884753i	$-0.345673\pi$
$131$	4.89071	+	1.31046i	0.427304	+	0.114496i	−0.0387565	+	0.999249i	$0.512340\pi$
$132$	−4.49089	+	26.6225i	−0.390882	+	2.31719i
$133$		0			0
$134$	−9.11572	−	0.763463i	−0.787479	−	0.0659531i
$135$	2.08995	−	1.20663i	0.179874	−	0.103850i
$136$	−0.0185573	−	1.66762i	−0.00159128	−	0.142997i
$137$	−0.241507	−	0.139434i	−0.0206333	−	0.0119127i	0.489648	−	0.871920i	$-0.337125\pi$
$137$	−0.241507	−	0.139434i	−0.0206333	−	0.0119127i	−0.510281	+	0.860008i	$0.670459\pi$
$138$	−1.42263	+	0.669816i	−0.121102	+	0.0570186i
$139$	12.1095	+	12.1095i	1.02712	+	1.02712i	0.999622	+	0.0274943i	$0.00875280\pi$
$139$	12.1095	+	12.1095i	1.02712	+	1.02712i	0.0274943	+	0.999622i	$0.491247\pi$
$140$		0			0
$141$	−7.26825	+	7.26825i	−0.612097	+	0.612097i
$142$	−2.73634	−	0.984466i	−0.229628	−	0.0826145i
$143$	13.5349	−	23.4432i	1.13185	−	1.96042i
$144$	−9.12575	−	10.5536i	−0.760479	−	0.879468i
$145$	−3.69258	−	6.39573i	−0.306652	−	0.531136i
$146$	−8.55052	+	7.22896i	−0.707646	+	0.598273i
$147$		0			0
$148$	−4.90756	+	3.49085i	−0.403399	+	0.286946i
$149$	−5.67786	+	21.1901i	−0.465149	+	1.73596i	0.191247	+	0.981542i	$0.438747\pi$
$149$	−5.67786	+	21.1901i	−0.465149	+	1.73596i	−0.656396	+	0.754417i	$0.727920\pi$
$150$	3.64088	+	2.52930i	0.297277	+	0.206516i
$151$	−8.08773	−	4.66946i	−0.658170	−	0.379995i	0.133409	−	0.991061i	$-0.457408\pi$
$151$	−8.08773	−	4.66946i	−0.658170	−	0.379995i	−0.791580	+	0.611066i	$0.790741\pi$
$152$	−1.45170	+	0.406349i	−0.117749	+	0.0329593i
$153$			2.05663i			0.166269i
$154$		0			0
$155$	10.8211	+	10.8211i	0.869174	+	0.869174i
$156$	9.08069	+	24.3846i	0.727037	+	1.95233i
$157$	−3.02179	−	11.2775i	−0.241165	−	0.900040i	−0.975272	−	0.221007i	$-0.929066\pi$
$157$	−3.02179	−	11.2775i	−0.241165	−	0.900040i	0.734107	−	0.679034i	$-0.237601\pi$
$158$	18.1778	−	3.27480i	1.44615	−	0.260529i
$159$	1.20250	+	2.08279i	0.0953643	+	0.165176i
$160$	−4.45607	+	10.0380i	−0.352283	+	0.793574i
$161$		0			0
$162$	−6.66332	−	7.88148i	−0.523520	−	0.619228i
$163$	−14.2860	−	3.82793i	−1.11897	−	0.299826i	−0.348502	−	0.937308i	$-0.613310\pi$
$163$	−14.2860	−	3.82793i	−1.11897	−	0.299826i	−0.770466	+	0.637482i	$0.779976\pi$
$164$	3.76053	−	4.54975i	0.293648	−	0.355275i
$165$	−25.3155	+	6.78326i	−1.97081	+	0.528076i
$166$	−8.65171	−	18.3754i	−0.671503	−	1.42621i
$167$		−	0.426814i		−	0.0330279i	−0.999864	−	0.0165139i	$-0.994743\pi$
$167$		−	0.426814i		−	0.0330279i	0.999864	−	0.0165139i	$-0.00525679\pi$
$168$		0			0
$169$		−	13.0892i		−	1.00686i
$170$	1.46469	−	0.689623i	0.112337	−	0.0528917i
$171$	1.79570	−	0.481156i	0.137320	−	0.0367949i
$172$	2.05191	+	21.6061i	0.156457	+	1.64745i
$173$	4.06740	+	1.08986i	0.309239	+	0.0828603i	0.410101	−	0.912040i	$-0.365493\pi$
$173$	4.06740	+	1.08986i	0.309239	+	0.0828603i	−0.100862	+	0.994900i	$0.532160\pi$
$174$	10.4640	−	8.84665i	0.793271	−	0.670663i
$175$		0			0
$176$	9.24315	+	19.0778i	0.696729	+	1.43804i
$177$	−0.0370719	−	0.0642104i	−0.00278649	−	0.00482635i
$178$	−0.970683	−	5.38807i	−0.0727557	−	0.403853i
$179$	3.63660	+	13.5720i	0.271812	+	1.01442i	0.957948	+	0.286943i	$0.0926392\pi$
$179$	3.63660	+	13.5720i	0.271812	+	1.01442i	−0.686135	+	0.727474i	$0.740694\pi$
$180$	5.63260	−	12.3169i	0.419829	−	0.918046i
$181$	−10.0681	−	10.0681i	−0.748356	−	0.748356i	0.225814	−	0.974170i	$-0.427496\pi$
$181$	−10.0681	−	10.0681i	−0.748356	−	0.748356i	−0.974170	+	0.225814i	$0.927496\pi$
$182$		0			0
$183$		−	5.21587i		−	0.385568i
$184$	−0.605390	+	1.07604i	−0.0446299	+	0.0793269i
$185$	−5.06298	−	2.92311i	−0.372238	−	0.214911i
$186$	−16.1998	+	23.3193i	−1.18782	+	1.70985i
$187$	0.808782	−	3.01842i	0.0591440	−	0.220728i
$188$	−1.34249	+	7.95842i	−0.0979110	+	0.580427i
$189$		0			0
$190$	−0.944798	−	1.11752i	−0.0685429	−	0.0810736i
$191$	−4.82250	−	8.35282i	−0.348944	−	0.604389i	0.637118	−	0.770766i	$-0.280126\pi$
$191$	−4.82250	−	8.35282i	−0.348944	−	0.604389i	−0.986062	+	0.166377i	$0.946793\pi$
$192$	−19.7954	−	4.83470i	−1.42861	−	0.348915i
$193$	9.77970	−	16.9389i	0.703959	−	1.21929i	−0.263108	−	0.964767i	$-0.584747\pi$
$193$	9.77970	−	16.9389i	0.703959	−	1.21929i	0.967066	−	0.254525i	$-0.0819193\pi$
$194$	−5.77169	+	16.0425i	−0.414383	+	1.15178i
$195$	−17.8609	+	17.8609i	−1.27904	+	1.27904i
$196$		0			0
$197$	−8.33252	−	8.33252i	−0.593668	−	0.593668i	0.344953	−	0.938620i	$-0.387895\pi$
$197$	−8.33252	−	8.33252i	−0.593668	−	0.593668i	−0.938620	+	0.344953i	$0.887895\pi$
$198$	−11.1361	−	23.6520i	−0.791408	−	1.68087i
$199$	−2.34374	−	1.35316i	−0.166144	−	0.0959230i	0.414623	−	0.909993i	$-0.363914\pi$
$199$	−2.34374	−	1.35316i	−0.166144	−	0.0959230i	−0.580766	+	0.814070i	$0.697247\pi$
$200$	3.48070	−	0.0387332i	0.246122	−	0.00273885i
$201$	14.2686	−	8.23795i	1.00643	−	0.581060i
$202$	0.316930	−	3.78413i	0.0222991	−	0.266251i
$203$		0			0
$204$	1.74109	+	2.44769i	0.121901	+	0.171372i
$205$	5.53471	+	1.48302i	0.386561	+	0.103579i
$206$	0.0223836	+	0.124247i	0.00155954	+	0.00865670i
$207$	0.761282	−	1.31858i	0.0529128	−	0.0916476i
$208$	16.9082	+	11.4692i	1.17237	+	0.795245i
$209$	−2.82468			−0.195387
$210$		0			0
$211$	11.9853	−	11.9853i	0.825100	−	0.825100i	−0.161734	−	0.986834i	$-0.551709\pi$
$211$	11.9853	−	11.9853i	0.825100	−	0.825100i	0.986834	+	0.161734i	$0.0517087\pi$
$212$	1.71733	+	0.785345i	0.117946	+	0.0539377i
$213$	5.05923	−	1.35562i	0.346653	−	0.0928854i
$214$	−16.9305	−	11.7615i	−1.15734	−	0.803999i
$215$	−18.2456	+	10.5341i	−1.24434	+	0.718420i
$216$	3.40587	+	0.872100i	0.231740	+	0.0593389i
$217$		0			0
$218$	−9.75197	−	0.816750i	−0.660487	−	0.0553173i
$219$	5.21954	−	19.4796i	0.352704	−	1.31631i
$220$	−13.1104	+	15.8619i	−0.883903	+	1.06941i
$221$	−0.779483	−	2.90907i	−0.0524337	−	0.195685i
$222$	3.67210	−	10.2067i	0.246455	−	0.685026i
$223$	−2.50874			−0.167998			−0.0839988	−	0.996466i	$-0.526769\pi$
$223$	−2.50874			−0.167998			−0.0839988	+	0.996466i	$0.526769\pi$
$224$		0			0
$225$	−4.29264			−0.286176
$226$	−3.59614	+	9.99552i	−0.239212	+	0.664892i
$227$	−4.90519	−	18.3064i	−0.325569	−	1.21504i	−0.913739	−	0.406303i	$-0.866818\pi$
$227$	−4.90519	−	18.3064i	−0.325569	−	1.21504i	0.588170	−	0.808738i	$-0.299849\pi$
$228$	1.72981	−	2.09284i	0.114559	−	0.138602i
$229$	6.72559	−	25.1003i	0.444440	−	1.65867i	−0.272972	−	0.962022i	$-0.588007\pi$
$229$	6.72559	−	25.1003i	0.444440	−	1.65867i	0.717412	−	0.696650i	$-0.245327\pi$
$230$	−1.19434	−	0.100029i	−0.0787524	−	0.00659569i
$231$		0			0
$232$	2.66883	−	10.4228i	0.175217	−	0.684289i
$233$	−12.2405	+	7.06704i	−0.801900	+	0.462977i	−0.844135	−	0.536130i	$-0.819886\pi$
$233$	−12.2405	+	7.06704i	−0.801900	+	0.462977i	0.0422348	+	0.999108i	$0.486552\pi$
$234$	−20.6924	−	14.3749i	−1.35270	−	0.939714i
$235$	−7.56771	+	2.02776i	−0.493663	+	0.132277i
$236$	−0.0529435	−	0.0242114i	−0.00344633	−	0.00157603i
$237$	−23.5235	+	23.5235i	−1.52802	+	1.52802i
$238$		0			0
$239$	−2.15987			−0.139710			−0.0698550	−	0.997557i	$-0.522254\pi$
$239$	−2.15987			−0.139710			−0.0698550	+	0.997557i	$0.522254\pi$
$240$	−3.72356	−	19.4273i	−0.240355	−	1.25403i
$241$	−4.85611	+	8.41103i	−0.312809	+	0.541802i	−0.978969	−	0.204007i	$-0.934603\pi$
$241$	−4.85611	+	8.41103i	−0.312809	+	0.541802i	0.666160	+	0.745809i	$0.267937\pi$
$242$	4.28449	+	23.7824i	0.275418	+	1.52879i
$243$	21.5573	+	5.77627i	1.38290	+	0.370548i
$244$	−2.37388	−	3.33728i	−0.151972	−	0.213647i
$245$		0			0
$246$	−0.887298	+	10.5943i	−0.0565720	+	0.675468i
$247$	−2.35762	+	1.36117i	−0.150012	+	0.0866094i
$248$	0.248080	+	22.2933i	0.0157531	+	1.41563i
$249$	31.6801	+	18.2905i	2.00765	+	1.15912i
$250$	7.28733	+	15.4776i	0.460891	+	0.978888i
$251$	10.1748	+	10.1748i	0.642228	+	0.642228i	0.951103	−	0.308875i	$-0.0999525\pi$
$251$	10.1748	+	10.1748i	0.642228	+	0.642228i	−0.308875	+	0.951103i	$0.599952\pi$
$252$		0			0
$253$	−1.63584	+	1.63584i	−0.102844	+	0.102844i
$254$	−2.03568	+	5.65821i	−0.127730	+	0.355028i
$255$	−1.45793	+	2.52520i	−0.0912990	+	0.158134i
$256$	−14.8661	+	5.91599i	−0.929132	+	0.369749i
$257$	13.2555	+	22.9591i	0.826853	+	1.43215i	0.900495	+	0.434867i	$0.143205\pi$
$257$	13.2555	+	22.9591i	0.826853	+	1.43215i	−0.0736418	+	0.997285i	$0.523462\pi$
$258$	−25.2375	−	29.8514i	−1.57122	−	1.85847i
$259$		0			0
$260$	−3.29900	+	19.5569i	−0.204595	+	1.21286i
$261$	−3.43401	+	12.8159i	−0.212560	+	0.793283i
$262$	−4.08531	+	5.88073i	−0.252391	+	0.363313i
$263$	17.9812	+	10.3814i	1.10877	+	0.640146i	0.938509	−	0.345254i	$-0.112207\pi$
$263$	17.9812	+	10.3814i	1.10877	+	0.640146i	0.170256	+	0.985400i	$0.445540\pi$
$264$	−33.2768	−	18.7218i	−2.04804	−	1.15225i
$265$			1.83312i			0.112607i
$266$		0			0
$267$	6.97259	+	6.97259i	0.426716	+	0.426716i
$268$	5.38016	−	11.7649i	0.328646	−	0.718654i
$269$	6.47880	+	24.1792i	0.395019	+	1.47423i	0.821747	+	0.569852i	$0.193000\pi$
$269$	6.47880	+	24.1792i	0.395019	+	1.47423i	−0.426728	+	0.904380i	$0.640334\pi$
$270$	0.605101	+	3.35880i	0.0368253	+	0.204410i
$271$	−2.82072	−	4.88563i	−0.171347	−	0.296781i	0.767544	−	0.640996i	$-0.221478\pi$
$271$	−2.82072	−	4.88563i	−0.171347	−	0.296781i	−0.938891	+	0.344215i	$0.888145\pi$
$272$	2.22801	+	0.773691i	0.135093	+	0.0469119i
$273$		0			0
$274$	0.301170	−	0.254621i	0.0181943	−	0.0153822i
$275$	6.30010	+	1.68811i	0.379910	+	0.101797i
$276$	−0.210240	−	2.21378i	−0.0126550	−	0.133254i
$277$	18.4760	−	4.95063i	1.11012	−	0.297455i	0.343239	−	0.939248i	$-0.388476\pi$
$277$	18.4760	−	4.95063i	1.11012	−	0.297455i	0.766878	+	0.641793i	$0.221809\pi$
$278$	−21.9118	+	10.3168i	−1.31418	+	0.618758i
$279$		−	27.4937i		−	1.64600i
$280$		0			0
$281$			20.6400i			1.23128i	0.788029	+	0.615639i	$0.211102\pi$
$281$			20.6400i			1.23128i	−0.788029	+	0.615639i	$0.788898\pi$
$282$	−6.19221	−	13.1517i	−0.368741	−	0.783170i
$283$	22.9351	−	6.14544i	1.36335	−	0.365309i	0.498305	−	0.867002i	$-0.333956\pi$
$283$	22.9351	−	6.14544i	1.36335	−	0.365309i	0.865046	+	0.501693i	$0.167289\pi$
$284$	2.62008	−	3.16995i	0.155473	−	0.188102i
$285$	2.54591	+	0.682175i	0.150807	+	0.0404085i
$286$	24.7162	+	29.2347i	1.46150	+	1.72868i
$287$		0			0
$288$	18.4128	−	7.09112i	1.08499	−	0.417848i
$289$	8.32617	+	14.4213i	0.489775	+	0.848315i
$290$	10.2787	−	1.85175i	0.603587	−	0.108739i
$291$	−7.94766	−	29.6611i	−0.465900	−	1.73876i
$292$	−5.52603	−	14.8392i	−0.323386	−	0.868398i
$293$	−20.5268	−	20.5268i	−1.19919	−	1.19919i	−0.974410	−	0.224778i	$-0.927834\pi$
$293$	−20.5268	−	20.5268i	−1.19919	−	1.19919i	−0.224778	−	0.974410i	$-0.572166\pi$
$294$		0			0
$295$		−	0.0565132i		−	0.00329033i
$296$	−2.29578	−	8.20181i	−0.133440	−	0.476720i
$297$	5.70506	+	3.29382i	0.331041	+	0.191127i
$298$	−25.4795	−	17.7005i	−1.47599	−	1.02536i
$299$	−0.577067	+	2.15364i	−0.0333726	+	0.124548i
$300$	−5.10886	+	3.63404i	−0.294960	+	0.209811i
$301$		0			0
$302$	10.0858	−	8.52690i	0.580370	−	0.490668i
$303$	3.41975	+	5.92318i	0.196460	+	0.340278i
$304$	0.154280	−	2.12634i	0.00884857	−	0.121954i
$305$	1.98780	−	3.44297i	0.113821	−	0.197144i
$306$	−2.73678	−	0.984625i	−0.156451	−	0.0562873i
$307$	6.03127	−	6.03127i	0.344223	−	0.344223i	−0.513730	−	0.857952i	$-0.671737\pi$
$307$	6.03127	−	6.03127i	0.344223	−	0.344223i	0.857952	+	0.513730i	$0.171737\pi$
$308$		0			0
$309$	−0.160786	−	0.160786i	−0.00914677	−	0.00914677i
$310$	−19.5805	+	9.21911i	−1.11210	+	0.523610i
$311$	13.8721	+	8.00907i	0.786616	+	0.454153i	0.838770	−	0.544486i	$-0.183275\pi$
$311$	13.8721	+	8.00907i	0.786616	+	0.454153i	−0.0521541	+	0.998639i	$0.516609\pi$
$312$	−36.7963	+	0.409469i	−2.08318	+	0.0231816i
$313$	−15.3757	+	8.87715i	−0.869085	+	0.501766i	−0.867044	−	0.498232i	$-0.833983\pi$
$313$	−15.3757	+	8.87715i	−0.869085	+	0.501766i	−0.00204070	+	0.999998i	$0.500650\pi$
$314$	16.4538	+	1.37804i	0.928539	+	0.0777673i
$315$		0			0
$316$	−4.34493	+	25.7572i	−0.244421	+	1.44896i
$317$	15.0144	+	4.02311i	0.843295	+	0.225960i	0.654505	−	0.756057i	$-0.272877\pi$
$317$	15.0144	+	4.02311i	0.843295	+	0.225960i	0.188790	+	0.982018i	$0.439544\pi$
$318$	−3.34729	+	0.603028i	−0.187707	+	0.0338161i
$319$	10.0799	−	17.4588i	0.564364	−	0.977506i
$320$	−11.2243	−	10.7355i	−0.627458	−	0.600133i
$321$	37.1297			2.07238
$322$		0			0
$323$	−0.222217	+	0.222217i	−0.0123645	+	0.0123645i
$324$	13.6781	−	5.09364i	0.759894	−	0.282980i
$325$	6.07187	−	1.62695i	0.336807	−	0.0902471i
$326$	11.9334	−	17.1779i	0.660930	−	0.951397i
$327$	15.2645	−	8.81294i	0.844126	−	0.487356i
$328$	4.25402	+	7.18240i	0.234889	+	0.396582i
$329$		0			0
$330$	3.09340	−	36.9351i	0.170286	−	2.03321i
$331$	3.93399	−	14.6818i	0.216232	−	0.806987i	−0.769498	−	0.638649i	$-0.779493\pi$
$331$	3.93399	−	14.6818i	0.216232	−	0.806987i	0.985729	−	0.168338i	$-0.0538399\pi$
$332$	28.5944	−	2.71558i	1.56932	−	0.149037i
$333$	2.71842	+	10.1453i	0.148969	+	0.555959i
$334$	0.567966	+	0.204340i	0.0310777	+	0.0111810i
$335$	12.5581			0.686124
$336$		0			0
$337$	18.9202			1.03065			0.515325	−	0.856995i	$-0.327671\pi$
$337$	18.9202			1.03065			0.515325	+	0.856995i	$0.327671\pi$
$338$	17.4180	+	6.26657i	0.947414	+	0.340856i
$339$	−4.95192	−	18.4808i	−0.268951	−	1.00374i
$340$	0.216457	+	2.27924i	0.0117390	+	0.123609i
$341$	−10.8121	+	40.3512i	−0.585506	+	2.18514i
$342$	−0.219423	+	2.61991i	−0.0118651	+	0.141669i
$343$		0			0
$344$	−29.7339	−	7.61359i	−1.60314	−	0.410497i
$345$	1.86946	−	1.07933i	0.100648	−	0.0581094i
$346$	−3.39758	+	4.89076i	−0.182655	+	0.262929i
$347$	5.92600	−	1.58787i	0.318125	−	0.0852412i	−0.0962234	−	0.995360i	$-0.530676\pi$
$347$	5.92600	−	1.58787i	0.318125	−	0.0852412i	0.414348	+	0.910119i	$0.364010\pi$
$348$	6.76264	+	18.1599i	0.362516	+	0.973473i
$349$	2.94202	−	2.94202i	0.157483	−	0.157483i	−0.623968	−	0.781450i	$-0.714480\pi$
$349$	2.94202	−	2.94202i	0.157483	−	0.157483i	0.781450	+	0.623968i	$0.214480\pi$
$350$		0			0
$351$	6.34899			0.338884
$352$	−29.8123	+	3.16633i	−1.58900	+	0.168766i
$353$	13.0287	−	22.5663i	0.693446	−	1.20108i	−0.277256	−	0.960796i	$-0.589425\pi$
$353$	13.0287	−	22.5663i	0.693446	−	1.20108i	0.970702	−	0.240288i	$-0.0772418\pi$
$354$	0.103194	−	0.0185908i	0.00548469	−	0.000988089i
$355$	3.85621	+	1.03327i	0.204666	+	0.0548402i
$356$	7.63469	+	1.28788i	0.404638	+	0.0682574i
$357$		0			0
$358$	−19.8014	−	1.65842i	−1.04654	−	0.0876500i
$359$	−25.7055	+	14.8411i	−1.35668	+	0.783282i	−0.989175	−	0.146739i	$-0.953122\pi$
$359$	−25.7055	+	14.8411i	−1.35668	+	0.783282i	−0.367508	+	0.930020i	$0.619789\pi$
$360$	13.6936	+	13.3922i	0.721714	+	0.705829i
$361$	−16.2085	−	9.35796i	−0.853077	−	0.492524i
$362$	18.2179	−	8.57756i	0.957512	−	0.450827i
$363$	−30.7763	−	30.7763i	−1.61534	−	1.61534i
$364$		0			0
$365$	10.8692	−	10.8692i	0.568919	−	0.568919i
$366$	6.94082	+	2.49713i	0.362802	+	0.130527i
$367$	−2.21998	+	3.84511i	−0.115882	+	0.200713i	−0.918132	−	0.396275i	$-0.870303\pi$
$367$	−2.21998	+	3.84511i	−0.115882	+	0.200713i	0.802250	+	0.596988i	$0.203636\pi$
$368$	−1.14207	−	1.32076i	−0.0595343	−	0.0688494i
$369$	−5.14714	−	8.91512i	−0.267950	−	0.464102i
$370$	6.31375	−	5.33790i	0.328236	−	0.277504i
$371$		0			0
$372$	−23.2755	−	32.7215i	−1.20678	−	1.69653i
$373$	4.73679	−	17.6779i	0.245261	−	0.915328i	−0.727990	−	0.685587i	$-0.759545\pi$
$373$	4.73679	−	17.6779i	0.245261	−	0.915328i	0.973252	−	0.229741i	$-0.0737879\pi$
$374$	3.62943	+	2.52134i	0.187673	+	0.130376i
$375$	−26.6841	−	15.4061i	−1.37796	−	0.795567i
$376$	−9.94763	−	5.59661i	−0.513010	−	0.288623i
$377$		−	19.4294i		−	1.00066i
$378$		0			0
$379$	1.71717	+	1.71717i	0.0882050	+	0.0882050i	0.749833	−	0.661628i	$-0.230134\pi$
$379$	1.71717	+	1.71717i	0.0882050	+	0.0882050i	−0.661628	+	0.749833i	$0.730134\pi$
$380$	1.93943	−	0.722232i	0.0994906	−	0.0370497i
$381$	−2.80315	−	10.4615i	−0.143610	−	0.535960i
$382$	13.4240	−	2.41839i	0.686832	−	0.123735i
$383$	−5.88728	−	10.1971i	−0.300826	−	0.521046i	0.675497	−	0.737363i	$-0.263929\pi$
$383$	−5.88728	−	10.1971i	−0.300826	−	0.521046i	−0.976323	+	0.216316i	$0.930596\pi$
$384$	15.9108	−	24.0273i	0.811943	−	1.22614i
$385$		0			0
$386$	17.8587	+	21.1236i	0.908986	+	1.07516i
$387$	36.5609	+	9.79646i	1.85849	+	0.497982i
$388$	−18.5847	−	15.3609i	−0.943493	−	0.779831i
$389$	−15.0984	+	4.04561i	−0.765520	+	0.205120i	−0.620391	−	0.784292i	$-0.713026\pi$
$389$	−15.0984	+	4.04561i	−0.765520	+	0.205120i	−0.145128	+	0.989413i	$0.546360\pi$
$390$	−15.2166	−	32.3186i	−0.770524	−	1.63652i
$391$			0.257382i			0.0130164i
$392$		0			0
$393$		−	12.8969i		−	0.650560i
$394$	15.0774	−	7.09892i	0.759590	−	0.357639i
$395$	−24.4927	+	6.56280i	−1.23236	+	0.330210i
$396$	36.8055	−	3.49537i	1.84954	−	0.175649i
$397$	−3.12318	−	0.836855i	−0.156748	−	0.0420005i	0.179592	−	0.983741i	$-0.442522\pi$
$397$	−3.12318	−	0.836855i	−0.156748	−	0.0420005i	−0.336340	+	0.941741i	$0.609189\pi$
$398$	2.92275	−	2.47101i	0.146504	−	0.123861i
$399$		0			0
$400$	−1.61486	+	4.65034i	−0.0807432	+	0.232517i
$401$	−2.37385	−	4.11163i	−0.118544	−	0.205325i	0.800647	−	0.599137i	$-0.204489\pi$
$401$	−2.37385	−	4.11163i	−0.118544	−	0.205325i	−0.919191	+	0.393812i	$0.871156\pi$
$402$	4.13117	+	22.9313i	0.206044	+	1.14371i
$403$	10.4204	+	38.8894i	0.519076	+	1.93722i
$404$	4.88386	+	2.23342i	0.242981	+	0.111117i
$405$	10.0187	+	10.0187i	0.497834	+	0.497834i
$406$		0			0
$407$		−	15.9588i		−	0.791048i
$408$	−4.09072	+	1.14504i	−0.202521	+	0.0566880i
$409$	−2.68361	−	1.54938i	−0.132696	−	0.0766121i	0.432182	−	0.901786i	$-0.357744\pi$
$409$	−2.68361	−	1.54938i	−0.132696	−	0.0766121i	−0.564879	+	0.825174i	$0.691077\pi$
$410$	−4.62325	+	6.65509i	−0.228326	+	0.328672i
$411$	−0.183845	+	0.686118i	−0.00906839	+	0.0338437i
$412$	−0.176053	−	0.0296980i	−0.00867352	−	0.00146312i
$413$		0			0
$414$	1.39018	+	1.64433i	0.0683236	+	0.0808142i
$415$	13.9413	+	24.1470i	0.684349	+	1.18533i
$416$	−23.3571	+	17.0089i	−1.14517	+	0.833931i
$417$	21.8106	−	37.7770i	1.06807	−	1.84995i
$418$	1.35233	−	3.75883i	0.0661448	−	0.183850i
$419$	−2.62329	+	2.62329i	−0.128156	+	0.128156i	−0.768276	−	0.640119i	$-0.778885\pi$
$419$	−2.62329	+	2.62329i	−0.128156	+	0.128156i	0.640119	+	0.768276i	$0.278885\pi$
$420$		0			0
$421$	−3.44059	−	3.44059i	−0.167684	−	0.167684i	0.618276	−	0.785961i	$-0.287831\pi$
$421$	−3.44059	−	3.44059i	−0.167684	−	0.167684i	−0.785961	+	0.618276i	$0.787831\pi$
$422$	10.2109	+	21.6870i	0.497059	+	1.05571i
$423$	12.1898	+	7.03778i	0.592688	+	0.342189i
$424$	−1.86725	+	1.90927i	−0.0906816	+	0.0927226i
$425$	0.628432	−	0.362825i	0.0304834	−	0.0175996i
$426$	−0.618208	+	7.38139i	−0.0299523	+	0.357629i
$427$		0			0
$428$	23.7567	−	16.8987i	1.14832	−	0.816828i
$429$	−66.6018	−	17.8459i	−3.21556	−	0.861608i
$430$	−5.28264	−	29.3229i	−0.254752	−	1.41408i
$431$	11.3945	−	19.7358i	0.548853	−	0.950642i	−0.449500	−	0.893280i	$-0.648398\pi$
$431$	11.3945	−	19.7358i	0.548853	−	0.950642i	0.998353	−	0.0573616i	$-0.0182688\pi$
$432$	−2.79110	+	4.11471i	−0.134287	+	0.197969i
$433$	16.6448			0.799899			0.399950	−	0.916537i	$-0.369028\pi$
$433$	16.6448			0.799899			0.399950	+	0.916537i	$0.369028\pi$
$434$		0			0
$435$	−13.3015	+	13.3015i	−0.637757	+	0.637757i
$436$	5.75568	−	12.5860i	0.275647	−	0.602762i
$437$	0.224727	−	0.0602155i	0.0107502	−	0.00288050i
$438$	23.4228	+	16.2717i	1.11918	+	0.777491i
$439$	−26.7406	+	15.4387i	−1.27626	+	0.736847i	−0.976158	−	0.217061i	$-0.930353\pi$
$439$	−26.7406	+	15.4387i	−1.27626	+	0.736847i	−0.300099	+	0.953908i	$0.597020\pi$
$440$	−14.8309	−	25.0401i	−0.707033	−	1.19374i
$441$		0			0
$442$	4.24431	+	0.355471i	0.201881	+	0.0169080i
$443$	3.68200	−	13.7414i	0.174937	−	0.652874i	−0.821625	−	0.570028i	$-0.806932\pi$
$443$	3.68200	−	13.7414i	0.174937	−	0.652874i	0.996562	−	0.0828461i	$-0.0264010\pi$
$444$	11.8241	+	9.77302i	0.561145	+	0.463807i
$445$	1.94528	+	7.25987i	0.0922149	+	0.344151i
$446$	1.20108	−	3.33841i	0.0568726	−	0.158078i
$447$	55.8784			2.64296
$448$		0			0
$449$	14.7633			0.696725			0.348363	−	0.937360i	$-0.386738\pi$
$449$	14.7633			0.696725			0.348363	+	0.937360i	$0.386738\pi$
$450$	2.05513	−	5.71226i	0.0968798	−	0.269278i
$451$	4.04830	+	15.1084i	0.190627	+	0.711429i
$452$	−11.5795	−	9.57085i	−0.544653	−	0.450175i
$453$	−6.15670	+	22.9771i	−0.289267	+	1.07956i
$454$	26.7090	+	2.23694i	1.25351	+	0.104985i
$455$		0			0
$456$	1.95680	+	3.30383i	0.0916358	+	0.154716i
$457$	1.80328	−	1.04112i	0.0843539	−	0.0487017i	−0.457230	−	0.889349i	$-0.651158\pi$
$457$	1.80328	−	1.04112i	0.0843539	−	0.0487017i	0.541584	+	0.840647i	$0.317825\pi$
$458$	30.1813	+	20.9667i	1.41028	+	0.979712i
$459$	0.707941	−	0.189692i	0.0330439	−	0.00885407i
$460$	0.704907	−	1.54143i	0.0328665	−	0.0718696i
$461$	−10.5211	+	10.5211i	−0.490015	+	0.490015i	−0.908311	−	0.418296i	$-0.862628\pi$
$461$	−10.5211	+	10.5211i	−0.490015	+	0.490015i	0.418296	+	0.908311i	$0.362628\pi$
$462$		0			0
$463$	26.5483			1.23380			0.616902	−	0.787040i	$-0.288387\pi$
$463$	26.5483			1.23380			0.616902	+	0.787040i	$0.288387\pi$
$464$	12.5920	+	8.54142i	0.584568	+	0.396525i
$465$	19.4901	−	33.7578i	0.903830	−	1.56548i
$466$	−3.54398	−	19.6719i	−0.164172	−	0.911285i
$467$	9.34512	+	2.50402i	0.432440	+	0.115872i	0.468472	−	0.883479i	$-0.344805\pi$
$467$	9.34512	+	2.50402i	0.432440	+	0.115872i	−0.0360311	+	0.999351i	$0.511472\pi$
$468$	29.0354	−	20.6535i	1.34216	−	0.954708i
$469$		0			0
$470$	0.924729	−	11.0412i	0.0426546	−	0.509294i
$471$	−25.7546	+	14.8694i	−1.18671	+	0.685146i
$472$	0.0575655	−	0.0588611i	0.00264967	−	0.00270930i
$473$	−49.8062	−	28.7556i	−2.29009	−	1.32218i
$474$	−20.0409	−	42.5650i	−0.920511	−	1.95508i
$475$	−0.463816	−	0.463816i	−0.0212813	−	0.0212813i
$476$		0			0
$477$	2.32874	−	2.32874i	0.106626	−	0.106626i
$478$	1.03405	−	2.87416i	0.0472964	−	0.131461i
$479$	−1.94642	+	3.37130i	−0.0889342	+	0.154039i	−0.907061	−	0.420999i	$-0.861679\pi$
$479$	−1.94642	+	3.37130i	−0.0889342	+	0.154039i	0.818127	+	0.575038i	$0.195013\pi$
$480$	27.6348	+	4.34598i	1.26135	+	0.198366i
$481$	−7.69033	−	13.3200i	−0.350649	−	0.607342i
$482$	−8.86775	−	10.4889i	−0.403915	−	0.477757i
$483$		0			0
$484$	−33.6987	−	5.68456i	−1.53176	−	0.258389i
$485$	6.05780	−	22.6080i	0.275070	−	1.02658i
$486$	−18.0073	+	25.9212i	−0.816827	+	1.17581i
$487$	2.49944	+	1.44305i	0.113260	+	0.0653909i	0.555560	−	0.831476i	$-0.312504\pi$
$487$	2.49944	+	1.44305i	0.113260	+	0.0653909i	−0.442300	+	0.896867i	$0.645837\pi$
$488$	5.57746	−	1.56120i	0.252480	−	0.0706721i
$489$			37.6724i			1.70360i
$490$		0			0
$491$	10.1200	+	10.1200i	0.456710	+	0.456710i	0.897574	−	0.440864i	$-0.145328\pi$
$491$	10.1200	+	10.1200i	0.456710	+	0.456710i	−0.440864	+	0.897574i	$0.645328\pi$
$492$	−13.6732	−	6.25284i	−0.616434	−	0.281900i
$493$	−0.580503	−	2.16647i	−0.0261445	−	0.0975727i
$494$	−0.682601	−	3.78899i	−0.0307117	−	0.170475i
$495$	17.9446	+	31.0809i	0.806549	+	1.39698i
$496$	−29.7847	−	10.3430i	−1.33737	−	0.464413i
$497$		0			0
$498$	−39.5065	+	33.4004i	−1.77033	+	1.49671i
$499$	18.5268	+	4.96424i	0.829373	+	0.222230i	0.648440	−	0.761265i	$-0.275422\pi$
$499$	18.5268	+	4.96424i	0.829373	+	0.222230i	0.180933	+	0.983495i	$0.442088\pi$
$500$	−24.0850	+	2.28733i	−1.07712	+	0.102292i
$501$	−1.05012	+	0.281378i	−0.0469158	+	0.0125710i
$502$	−18.4110	+	8.66846i	−0.821722	+	0.386892i
$503$			25.3179i			1.12887i	0.825477	+	0.564436i	$0.190906\pi$
$503$			25.3179i			1.12887i	−0.825477	+	0.564436i	$0.809094\pi$
$504$		0			0
$505$			5.21315i			0.231982i
$506$	−1.39366	−	2.96000i	−0.0619557	−	0.131588i
$507$	−32.2043	+	8.62911i	−1.43024	+	0.383232i
$508$	−6.55484	−	5.41782i	−0.290824	−	0.240377i
$509$	−2.13611	−	0.572369i	−0.0946814	−	0.0253698i	0.211167	−	0.977450i	$-0.432274\pi$
$509$	−2.13611	−	0.572369i	−0.0946814	−	0.0253698i	−0.305849	+	0.952080i	$0.598940\pi$
$510$	−2.66232	−	3.14904i	−0.117890	−	0.139442i
$511$		0			0
$512$	−0.755222	−	22.6148i	−0.0333764	−	0.999443i
$513$	−0.331251	−	0.573743i	−0.0146251	−	0.0253314i
$514$	−36.8981	+	6.64734i	−1.62751	+	0.293202i
$515$	−0.0448574	−	0.167410i	−0.00197665	−	0.00737697i
$516$	51.8062	−	19.2923i	2.28064	−	0.849298i
$517$	−15.1227	−	15.1227i	−0.665097	−	0.665097i
$518$		0			0
$519$		−	10.7258i		−	0.470809i
$520$	−24.4451	−	13.7530i	−1.07199	−	0.603109i
$521$	−8.90915	−	5.14370i	−0.390317	−	0.225349i	0.291981	−	0.956424i	$-0.405686\pi$
$521$	−8.90915	−	5.14370i	−0.390317	−	0.225349i	−0.682297	+	0.731075i	$0.739019\pi$
$522$	−15.4102	−	10.7054i	−0.674485	−	0.468561i
$523$	−1.69016	+	6.30777i	−0.0739056	+	0.275819i	−0.992983	−	0.118258i	$-0.962269\pi$
$523$	−1.69016	+	6.30777i	−0.0739056	+	0.275819i	0.919077	+	0.394077i	$0.128936\pi$
$524$	−5.86969	−	8.25181i	−0.256418	−	0.360482i
$525$		0			0
$526$	−22.4233	+	18.9575i	−0.977701	+	0.826588i
$527$	2.32384	+	4.02501i	0.101228	+	0.175332i
$528$	40.8448	−	35.3186i	1.77754	−	1.53704i
$529$	−11.4047	+	19.7536i	−0.495858	+	0.858851i
$530$	−2.43935	−	0.877617i	−0.105959	−	0.0381213i
$531$	−0.0717927	+	0.0717927i	−0.00311554	+	0.00311554i
$532$		0			0
$533$	10.6595	+	10.6595i	0.461713	+	0.461713i
$534$	−12.6167	+	5.94033i	−0.545977	+	0.257063i
$535$	24.5091	+	14.1503i	1.05962	+	0.611773i
$536$	13.0799	+	12.7920i	0.564964	+	0.552529i
$537$	30.9946	−	17.8947i	1.33751	−	0.772214i
$538$	−35.2773	−	2.95456i	−1.52091	−	0.127380i
$539$		0			0
$540$	−4.75929	−	0.802834i	−0.204807	−	0.0345485i
$541$	6.53469	+	1.75097i	0.280948	+	0.0752799i	0.396542	−	0.918017i	$-0.370210\pi$
$541$	6.53469	+	1.75097i	0.280948	+	0.0752799i	−0.115593	+	0.993297i	$0.536877\pi$
$542$	7.85180	−	1.41453i	0.337264	−	0.0607594i
$543$	−18.1338	+	31.4086i	−0.778195	+	1.34787i
$544$	−2.09623	+	2.59442i	−0.0898753	+	0.111235i
$545$	13.4346			0.575477
$546$		0			0
$547$	−1.78581	+	1.78581i	−0.0763555	+	0.0763555i	−0.744253	−	0.667898i	$-0.767194\pi$
$547$	−1.78581	+	1.78581i	−0.0763555	+	0.0763555i	0.667898	+	0.744253i	$0.267194\pi$
$548$	0.194640	+	0.522672i	0.00831461	+	0.0223274i
$549$	−6.89909	+	1.84860i	−0.294446	+	0.0788965i
$550$	−5.26260	+	7.57542i	−0.224398	+	0.323017i
$551$	−1.75579	+	1.01370i	−0.0747991	+	0.0431853i
$552$	3.04656	+	0.780095i	0.129670	+	0.0332030i
$553$		0			0
$554$	−2.25766	+	26.9564i	−0.0959188	+	1.14527i
$555$	−3.85414	+	14.3838i	−0.163599	+	0.610560i
$556$	−3.23820	−	34.0975i	−0.137330	−	1.44606i
$557$	−0.902940	−	3.36982i	−0.0382588	−	0.142784i	0.944155	−	0.329503i	$-0.106881\pi$
$557$	−0.902940	−	3.36982i	−0.0382588	−	0.142784i	−0.982413	+	0.186719i	$0.940215\pi$
$558$	36.5861	+	13.1628i	1.54882	+	0.557225i
$559$	−55.4278			−2.34435
$560$		0			0
$561$	−7.95959			−0.336054
$562$	−27.4658	−	9.88153i	−1.15858	−	0.416827i
$563$	10.3077	+	38.4688i	0.434417	+	1.62127i	0.742458	+	0.669893i	$0.233660\pi$
$563$	10.3077	+	38.4688i	0.434417	+	1.62127i	−0.308041	+	0.951373i	$0.599673\pi$
$564$	20.4656	−	1.94360i	0.861758	−	0.0818402i
$565$	3.77441	−	14.0863i	0.158791	−	0.592615i
$566$	−2.80253	+	33.4622i	−0.117799	+	1.40652i
$567$		0			0
$568$	2.96391	+	5.00420i	0.124363	+	0.209972i
$569$	39.1325	−	22.5931i	1.64052	−	0.947153i	0.659868	−	0.751381i	$-0.270612\pi$
$569$	39.1325	−	22.5931i	1.64052	−	0.947153i	0.980649	−	0.195772i	$-0.0627213\pi$
$570$	−2.12665	+	3.06128i	−0.0890756	+	0.128223i
$571$	−24.0429	+	6.44226i	−1.00616	+	0.269600i	−0.724025	−	0.689774i	$-0.757710\pi$
$571$	−24.0429	+	6.44226i	−1.00616	+	0.269600i	−0.282137	+	0.959374i	$0.591043\pi$
$572$	−50.7360	+	18.8938i	−2.12138	+	0.789989i
$573$	−17.3717	+	17.3717i	−0.725714	+	0.725714i
$574$		0			0
$575$	−0.537214			−0.0224034
$576$	0.620954	+	27.8971i	0.0258731	+	1.16238i
$577$	5.46579	−	9.46703i	0.227544	−	0.394118i	−0.729536	−	0.683943i	$-0.760264\pi$
$577$	5.46579	−	9.46703i	0.227544	−	0.394118i	0.957080	+	0.289825i	$0.0935971\pi$
$578$	−23.1769	+	4.17540i	−0.964030	+	0.173674i
$579$	−48.1232	−	12.8946i	−1.99993	−	0.535881i
$580$	−2.45686	+	14.5645i	−0.102016	+	0.604760i
$581$		0			0
$582$	43.2753	+	3.62441i	1.79382	+	0.150236i
$583$	−4.33357	+	2.50199i	−0.179478	+	0.103622i
$584$	22.3923	−	0.249181i	0.926600	−	0.0103112i
$585$	29.9550	+	17.2945i	1.23848	+	0.715040i
$586$	37.1426	−	17.4879i	1.53435	−	0.722418i
$587$	7.44744	+	7.44744i	0.307389	+	0.307389i	0.843896	−	0.536507i	$-0.180256\pi$
$587$	7.44744	+	7.44744i	0.307389	+	0.307389i	−0.536507	+	0.843896i	$0.680256\pi$
$588$		0			0
$589$	2.97067	−	2.97067i	0.122404	−	0.122404i
$590$	0.0752028	+	0.0270561i	0.00309605	+	0.00111388i
$591$	−15.0078	+	25.9943i	−0.617338	+	1.06926i
$592$	12.0134	+	0.871649i	0.493746	+	0.0358245i
$593$	−12.6447	−	21.9013i	−0.519256	−	0.899377i	−0.999750	−	0.0223792i	$-0.992876\pi$
$593$	−12.6447	−	21.9013i	−0.519256	−	0.899377i	0.480494	−	0.876998i	$-0.340457\pi$
$594$	−7.11446	+	6.01485i	−0.291910	+	0.246792i
$595$		0			0
$596$	35.7528	−	25.4317i	1.46449	−	1.04172i
$597$	−1.78415	+	6.65853i	−0.0730203	+	0.272516i
$598$	−2.58960	−	1.79898i	−0.105897	−	0.0735658i
$599$	−15.4613	−	8.92656i	−0.631730	−	0.364729i	0.149692	−	0.988733i	$-0.452172\pi$
$599$	−15.4613	−	8.92656i	−0.631730	−	0.364729i	−0.781422	+	0.624003i	$0.785505\pi$
$600$	−2.38995	−	8.53824i	−0.0975695	−	0.348572i
$601$		−	15.3921i		−	0.627855i	−0.949447	−	0.313928i	$-0.898355\pi$
$601$		−	15.3921i		−	0.627855i	0.949447	−	0.313928i	$-0.101645\pi$
$602$		0			0
$603$	−15.9535	−	15.9535i	−0.649676	−	0.649676i
$604$	6.51822	+	17.5035i	0.265222	+	0.712209i
$605$	−8.58625	−	32.0443i	−0.349081	−	1.30279i
$606$	−9.51928	+	1.71494i	−0.386694	+	0.0696645i
$607$	15.1434	+	26.2292i	0.614652	+	1.06461i	0.990445	+	0.137905i	$0.0440370\pi$
$607$	15.1434	+	26.2292i	0.614652	+	1.06461i	−0.375793	+	0.926704i	$0.622630\pi$
$608$	2.75568	+	1.22330i	0.111758	+	0.0496115i
$609$		0			0
$610$	3.62992	+	4.29353i	0.146971	+	0.173840i
$611$	−19.9097	−	5.33478i	−0.805459	−	0.215822i
$612$	2.62050	−	3.17046i	0.105928	−	0.128158i
$613$	−14.7741	+	3.95872i	−0.596722	+	0.159891i	−0.544523	−	0.838746i	$-0.683289\pi$
$613$	−14.7741	+	3.95872i	−0.596722	+	0.159891i	−0.0521982	+	0.998637i	$0.516623\pi$
$614$	5.13836	+	10.9134i	0.207367	+	0.440428i
$615$		−	14.5951i		−	0.588531i
$616$		0			0
$617$			39.3266i			1.58323i	0.611020	+	0.791615i	$0.290759\pi$
$617$			39.3266i			1.58323i	−0.611020	+	0.791615i	$0.709241\pi$
$618$	0.290936	−	0.136982i	0.0117032	−	0.00551022i
$619$	−5.19162	+	1.39109i	−0.208669	+	0.0559127i	−0.361639	−	0.932318i	$-0.617783\pi$
$619$	−5.19162	+	1.39109i	−0.208669	+	0.0559127i	0.152970	+	0.988231i	$0.451116\pi$
$620$	−2.89367	−	30.4697i	−0.116213	−	1.22369i
$621$	−0.524103	−	0.140433i	−0.0210315	−	0.00563538i
$622$	−17.2991	+	14.6254i	−0.693632	+	0.586424i
$623$		0			0
$624$	17.0716	−	49.1613i	0.683411	−	1.96803i
$625$	−8.66598	−	15.0099i	−0.346639	−	0.600397i
$626$	−4.45171	−	24.7106i	−0.177926	−	0.987633i
$627$	1.86217	+	6.94973i	0.0743681	+	0.277545i
$628$	−9.71112	+	21.2355i	−0.387516	+	0.847387i
$629$	−1.25548	−	1.25548i	−0.0500592	−	0.0500592i
$630$		0			0
$631$			7.48252i			0.297875i	0.988847	+	0.148937i	$0.0475853\pi$
$631$			7.48252i			0.297875i	−0.988847	+	0.148937i	$0.952415\pi$
$632$	−32.1952	−	18.1133i	−1.28066	−	0.720508i
$633$	−37.3894	−	21.5868i	−1.48610	−	0.857998i
$634$	−12.5419	+	18.0538i	−0.498101	+	0.717008i
$635$	2.13660	−	7.97389i	0.0847883	−	0.316434i
$636$	0.800084	−	4.74298i	0.0317254	−	0.188072i
$637$		0			0
$638$	18.4068	+	21.7719i	0.728734	+	0.861958i
$639$	−3.58618	−	6.21144i	−0.141867	−	0.245721i
$640$	19.6596	−	9.79660i	0.777113	−	0.387245i
$641$	−4.73385	+	8.19927i	−0.186976	+	0.323852i	−0.944241	−	0.329256i	$-0.893202\pi$
$641$	−4.73385	+	8.19927i	−0.186976	+	0.323852i	0.757265	+	0.653108i	$0.226535\pi$
$642$	−17.7761	+	49.4089i	−0.701567	+	1.95001i
$643$	20.6140	−	20.6140i	0.812939	−	0.812939i	−0.172135	−	0.985073i	$-0.555066\pi$
$643$	20.6140	−	20.6140i	0.812939	−	0.812939i	0.985073	+	0.172135i	$0.0550665\pi$
$644$		0			0
$645$	37.9462	+	37.9462i	1.49413	+	1.49413i
$646$	−0.189319	−	0.402095i	−0.00744865	−	0.0158202i
$647$	−30.2216	−	17.4485i	−1.18813	−	0.685970i	−0.230252	−	0.973131i	$-0.573955\pi$
$647$	−30.2216	−	17.4485i	−1.18813	−	0.685970i	−0.957882	+	0.287161i	$0.907288\pi$
$648$	0.229684	+	20.6402i	0.00902284	+	0.810823i
$649$	0.133600	−	0.0771338i	0.00524425	−	0.00302777i
$650$	−0.741946	+	8.85882i	−0.0291015	+	0.347471i
$651$		0			0
$652$	17.1456	+	24.1040i	0.671475	+	0.943984i
$653$	−38.5399	−	10.3267i	−1.50818	−	0.404117i	−0.592353	−	0.805679i	$-0.701801\pi$
$653$	−38.5399	−	10.3267i	−1.50818	−	0.404117i	−0.915832	+	0.401562i	$0.868467\pi$
$654$	4.41951	+	24.5318i	0.172816	+	0.959270i
$655$	4.91507	−	8.51315i	0.192048	−	0.332636i
$656$	−11.5943	+	2.22224i	−0.452683	+	0.0867640i
$657$	−27.6157			−1.07739
$658$		0			0
$659$	−6.66795	+	6.66795i	−0.259746	+	0.259746i	−0.824951	−	0.565205i	$-0.808797\pi$
$659$	−6.66795	+	6.66795i	−0.259746	+	0.259746i	0.565205	+	0.824951i	$0.308797\pi$
$660$	47.6690	+	21.7994i	1.85551	+	0.848539i
$661$	2.42421	−	0.649564i	0.0942907	−	0.0252651i	−0.211365	−	0.977407i	$-0.567791\pi$
$661$	2.42421	−	0.649564i	0.0942907	−	0.0252651i	0.305656	+	0.952142i	$0.401124\pi$
$662$	17.6539	+	12.2640i	0.686137	+	0.476655i
$663$	−6.64349	+	3.83562i	−0.258012	+	0.148963i
$664$	−10.0761	+	39.3510i	−0.391030	+	1.52711i
$665$		0			0
$666$	−14.8019	−	1.23969i	−0.573563	−	0.0480372i
$667$	−0.429758	+	1.60388i	−0.0166403	+	0.0621024i
$668$	−0.543836	+	0.657970i	−0.0210416	+	0.0254576i
$669$	1.65389	+	6.17241i	0.0639432	+	0.238639i
$670$	−6.01229	+	16.7112i	−0.232275	+	0.645612i
$671$	10.8524			0.418954
$672$		0			0
$673$	−36.8448			−1.42026			−0.710131	−	0.704070i	$-0.751364\pi$
$673$	−36.8448			−1.42026			−0.710131	+	0.704070i	$0.751364\pi$
$674$	−9.05818	+	25.1773i	−0.348908	+	0.969794i
$675$	0.395930	+	1.47763i	0.0152393	+	0.0568740i
$676$	−16.6780	+	20.1782i	−0.641461	+	0.776083i
$677$	4.52660	−	16.8935i	0.173971	−	0.649270i	−0.822753	−	0.568399i	$-0.807563\pi$
$677$	4.52660	−	16.8935i	0.173971	−	0.649270i	0.996725	−	0.0808713i	$-0.0257703\pi$
$678$	26.9634	+	2.25824i	1.03552	+	0.0867274i
$679$		0			0
$680$	−3.13665	−	0.803162i	−0.120285	−	0.0307999i
$681$	−41.8067	+	24.1371i	−1.60204	+	0.924936i
$682$	−48.5194	−	33.7061i	−1.85790	−	1.29068i
$683$	32.1132	−	8.60472i	1.22878	−	0.329250i	0.414675	−	0.909970i	$-0.363895\pi$
$683$	32.1132	−	8.60472i	1.22878	−	0.329250i	0.814104	+	0.580719i	$0.197229\pi$
$684$	−3.38129	−	1.54629i	−0.129287	−	0.0591239i
$685$	−0.382838	+	0.382838i	−0.0146275	+	0.0146275i
$686$		0			0
$687$	−66.1896			−2.52529
$688$	24.3668	−	35.9221i	0.928975	−	1.36952i
$689$	−2.41135	+	4.17658i	−0.0918650	+	0.159115i
$690$	0.541264	+	3.00445i	0.0206056	+	0.114377i
$691$	14.3466	+	3.84416i	0.545771	+	0.146239i	0.521161	−	0.853458i	$-0.325499\pi$
$691$	14.3466	+	3.84416i	0.545771	+	0.146239i	0.0246098	+	0.999697i	$0.492166\pi$
$692$	−4.88157	−	6.86269i	−0.185570	−	0.260880i
$693$		0			0
$694$	−0.724122	+	8.64600i	−0.0274873	+	0.328198i
$695$	28.7941	−	16.6243i	1.09222	−	0.630595i
$696$	−27.4032	+	0.304943i	−1.03872	+	0.0115588i
$697$	1.50706	+	0.870101i	0.0570839	+	0.0329574i
$698$	2.50647	+	5.32349i	0.0948711	+	0.201497i
$699$	25.4571	+	25.4571i	0.962874	+	0.962874i
$700$		0			0
$701$	−21.3787	+	21.3787i	−0.807464	+	0.807464i	−0.984249	−	0.176785i	$-0.943430\pi$
$701$	−21.3787	+	21.3787i	−0.807464	+	0.807464i	0.176785	+	0.984249i	$0.443430\pi$
$702$	−3.03962	+	8.44867i	−0.114723	+	0.318874i
$703$	−0.802467	+	1.38991i	−0.0302656	+	0.0524216i
$704$	10.0594	−	41.1874i	0.379126	−	1.55231i
$705$	9.97805	+	17.2825i	0.375795	+	0.650897i
$706$	23.7917	+	28.1412i	0.895412	+	1.05911i
$707$		0			0
$708$	−0.0246658	+	0.146222i	−0.000926998	+	0.00549535i
$709$	3.57430	−	13.3395i	0.134236	−	0.500974i	−0.865764	−	0.500452i	$-0.833167\pi$
$709$	3.57430	−	13.3395i	0.134236	−	0.500974i	1.00000		0.000522056i	$-0.000166175\pi$
$710$	−3.22117	+	4.63681i	−0.120888	+	0.174017i
$711$	39.4520	+	22.7776i	1.47956	+	0.854227i
$712$	−5.36895	+	9.54298i	−0.201210	+	0.357638i
$713$		−	3.44077i		−	0.128858i
$714$		0			0
$715$	−37.1623	−	37.1623i	−1.38979	−	1.38979i
$716$	11.6869	−	25.5560i	0.436762	−	0.955073i
$717$	1.42390	+	5.31405i	0.0531764	+	0.198457i
$718$	−7.44249	−	41.3118i	−0.277751	−	1.54174i
$719$	−22.1881	−	38.4309i	−0.827477	−	1.43323i	−0.900011	−	0.435866i	$-0.856442\pi$
$719$	−22.1881	−	38.4309i	−0.827477	−	1.43323i	0.0725344	−	0.997366i	$-0.476891\pi$
$720$	−24.3770	+	11.8106i	−0.908476	+	0.440155i
$721$		0			0
$722$	20.2127	−	17.0886i	0.752238	−	0.635972i
$723$	23.8956	+	6.40280i	0.888686	+	0.238123i
$724$	2.69230	+	28.3493i	0.100059	+	1.05360i
$725$	4.52189	−	1.21164i	0.167939	−	0.0449991i
$726$	55.6887	−	26.2200i	2.06680	−	0.973116i
$727$		−	1.44539i		−	0.0536067i	−0.999641	−	0.0268033i	$-0.991467\pi$
$727$		−	1.44539i		−	0.0536067i	0.999641	−	0.0268033i	$-0.00853279\pi$
$728$		0			0
$729$		−	34.9533i		−	1.29457i
$730$	9.26004	+	19.6674i	0.342729	+	0.727924i
$731$	−6.18045	+	1.65605i	−0.228592	+	0.0612511i
$732$	−6.64593	+	8.04070i	−0.245641	+	0.297193i
$733$	39.4186	+	10.5622i	1.45596	+	0.390123i	0.898093	−	0.439807i	$-0.144953\pi$
$733$	39.4186	+	10.5622i	1.45596	+	0.390123i	0.557868	+	0.829930i	$0.311620\pi$
$734$	−4.05390	−	4.79502i	−0.149632	−	0.176987i
$735$		0			0
$736$	2.30432	−	0.887437i	0.0849385	−	0.0327114i
$737$	17.1404	+	29.6880i	0.631373	+	1.09357i
$738$	14.3277	−	2.58119i	0.527409	−	0.0950148i
$739$	2.92937	+	10.9326i	0.107759	+	0.402161i	0.998644	−	0.0520685i	$-0.0165814\pi$
$739$	2.92937	+	10.9326i	0.107759	+	0.402161i	−0.890885	+	0.454229i	$0.849915\pi$
$740$	4.08045	+	10.9573i	0.150000	+	0.402800i
$741$	4.90325	+	4.90325i	0.180125	+	0.180125i
$742$		0			0
$743$			9.66874i			0.354712i	0.984147	+	0.177356i	$0.0567544\pi$
$743$			9.66874i			0.354712i	−0.984147	+	0.177356i	$0.943246\pi$
$744$	54.6861	−	15.3073i	2.00489	−	0.561192i
$745$	36.8851	+	21.2956i	1.35136	+	0.780210i
$746$	21.2564	+	14.7667i	0.778253	+	0.540648i
$747$	12.9650	−	48.3861i	0.474365	−	1.77036i
$748$	−5.09279	+	3.62261i	−0.186211	+	0.132456i
$749$		0			0
$750$	33.2763	−	28.1331i	1.21508	−	1.02728i
$751$	25.8756	+	44.8178i	0.944213	+	1.63542i	0.757319	+	0.653045i	$0.226509\pi$
$751$	25.8756	+	44.8178i	0.944213	+	1.63542i	0.186893	+	0.982380i	$0.440158\pi$
$752$	12.2100	−	10.5580i	0.445252	−	0.385011i
$753$	18.3259	−	31.7415i	0.667834	−	1.15672i
$754$	25.8549	+	9.30196i	0.941580	+	0.338757i
$755$	−12.8207	+	12.8207i	−0.466594	+	0.466594i
$756$		0			0
$757$	−28.2783	−	28.2783i	−1.02779	−	1.02779i	−0.999603	−	0.0281911i	$-0.991025\pi$
$757$	−28.2783	−	28.2783i	−1.02779	−	1.02779i	−0.0281911	−	0.999603i	$-0.508975\pi$
$758$	−3.10716	+	1.46295i	−0.112857	+	0.0531367i
$759$	5.10318	+	2.94632i	0.185234	+	0.106945i
$760$	0.0325671	+	2.92659i	0.00118133	+	0.106159i
$761$	−4.94191	+	2.85321i	−0.179144	+	0.103429i	−0.586891	−	0.809666i	$-0.699648\pi$
$761$	−4.94191	+	2.85321i	−0.179144	+	0.103429i	0.407746	+	0.913095i	$0.366315\pi$
$762$	15.2633	+	1.27833i	0.552930	+	0.0463092i
$763$		0			0
$764$	−3.20866	+	19.0213i	−0.116085	+	0.688166i
$765$	3.85683	+	1.03343i	0.139444	+	0.0373639i
$766$	16.3879	−	2.95235i	0.592120	−	0.106673i
$767$	0.0743395	−	0.128760i	0.00268425	−	0.00464925i
$768$	24.3560	+	32.6759i	0.878871	+	1.17909i
$769$	−39.6503			−1.42983			−0.714914	−	0.699212i	$-0.753534\pi$
$769$	−39.6503			−1.42983			−0.714914	+	0.699212i	$0.753534\pi$
$770$		0			0
$771$	47.7491	−	47.7491i	1.71964	−	1.71964i
$772$	−36.6594	+	13.6517i	−1.31940	+	0.491337i
$773$	21.4445	−	5.74604i	0.771305	−	0.206671i	0.148357	−	0.988934i	$-0.452601\pi$
$773$	21.4445	−	5.74604i	0.771305	−	0.206671i	0.622948	+	0.782263i	$0.285935\pi$
$774$	−30.5400	+	43.9619i	−1.09774	+	1.58018i
$775$	−8.40108	+	4.85037i	−0.301776	+	0.174230i
$776$	29.3384	−	17.3767i	1.05319	−	0.623786i
$777$		0			0
$778$	1.84494	−	22.0285i	0.0661442	−	0.789759i
$779$	0.407126	−	1.51942i	0.0145868	−	0.0544387i
$780$	50.2918	−	4.77615i	1.80074	−	0.171014i
$781$	2.82057	+	10.5265i	0.100928	+	0.376669i
$782$	−0.342502	−	0.123224i	−0.0122478	−	0.00440647i
$783$	4.72827			0.168975
$784$		0			0
$785$	−22.6673			−0.809029
$786$	17.1620	+	6.17446i	0.612148	+	0.220236i
$787$	5.05004	+	18.8470i	0.180014	+	0.671823i	0.995643	+	0.0932471i	$0.0297246\pi$
$787$	5.05004	+	18.8470i	0.180014	+	0.671823i	−0.815629	+	0.578576i	$0.803609\pi$
$788$	2.22819	+	23.4624i	0.0793761	+	0.835812i
$789$	13.6880	−	51.0841i	0.487304	−	1.81864i
$790$	2.99286	−	35.7347i	0.106481	−	1.27138i
$791$		0			0
$792$	−12.9695	+	50.6509i	−0.460853	+	1.79980i
$793$	9.05801	−	5.22965i	0.321659	−	0.185710i
$794$	2.60886	−	3.75541i	0.0925849	−	0.133274i
$795$	4.51013	−	1.20849i	0.159958	−	0.0428606i
$796$	1.88891	+	5.07235i	0.0669508	+	0.179785i
$797$	2.54421	−	2.54421i	0.0901206	−	0.0901206i	−0.660609	−	0.750730i	$-0.729702\pi$
$797$	2.54421	−	2.54421i	0.0901206	−	0.0901206i	0.750730	+	0.660609i	$0.229702\pi$
$798$		0			0
$799$	−2.37941			−0.0841774
$800$	−5.41514	−	4.37530i	−0.191454	−	0.154690i
$801$	6.75150	−	11.6939i	0.238553	−	0.413185i
$802$	6.60789	−	1.19044i	0.233333	−	0.0420358i
$803$	40.5303	+	10.8601i	1.43028	+	0.383244i
$804$	−32.4928	−	5.48113i	−1.14593	−	0.193305i
$805$		0			0
$806$	−56.7394	−	4.75205i	−1.99856	−	0.167384i
$807$	55.2185	−	31.8804i	1.94378	−	1.12224i
$808$	−5.31022	+	5.42973i	−0.186813	+	0.191017i
$809$	19.3519	+	11.1728i	0.680378	+	0.392816i	0.799997	−	0.600004i	$-0.204834\pi$
$809$	19.3519	+	11.1728i	0.680378	+	0.392816i	−0.119620	+	0.992820i	$0.538168\pi$
$810$	−18.1285	+	8.53548i	−0.636972	+	0.299906i
$811$	−31.7484	−	31.7484i	−1.11484	−	1.11484i	−0.992487	−	0.122349i	$-0.960957\pi$
$811$	−31.7484	−	31.7484i	−1.11484	−	1.11484i	−0.122349	−	0.992487i	$-0.539043\pi$
$812$		0			0
$813$	−10.1609	+	10.1609i	−0.356357	+	0.356357i
$814$	21.2366	+	7.64039i	0.744341	+	0.267795i
$815$	−14.3572	+	24.8673i	−0.502909	+	0.871065i
$816$	0.434742	−	5.99176i	0.0152190	−	0.209754i
$817$	2.89188	+	5.00888i	0.101174	+	0.175238i
$818$	3.34658	−	2.82933i	0.117010	−	0.0989253i
$819$		0			0
$820$	−6.64259	−	9.33839i	−0.231969	−	0.326111i
$821$	−12.5890	+	46.9829i	−0.439361	+	1.63972i	0.291050	+	0.956708i	$0.405995\pi$
$821$	−12.5890	+	46.9829i	−0.439361	+	1.63972i	−0.730411	+	0.683008i	$0.760671\pi$
$822$	−0.825007	−	0.573128i	−0.0287754	−	0.0199901i
$823$	16.7248	+	9.65608i	0.582991	+	0.336590i	0.762321	−	0.647199i	$-0.224060\pi$
$823$	16.7248	+	9.65608i	0.582991	+	0.336590i	−0.179330	+	0.983789i	$0.557393\pi$
$824$	0.123806	−	0.220058i	0.00431299	−	0.00766608i
$825$		−	16.6134i		−	0.578405i
$826$		0			0
$827$	14.4794	+	14.4794i	0.503498	+	0.503498i	0.912523	−	0.409025i	$-0.134131\pi$
$827$	14.4794	+	14.4794i	0.503498	+	0.503498i	−0.409025	+	0.912523i	$0.634131\pi$
$828$	−2.85368	+	1.06269i	−0.0991722	+	0.0369312i
$829$	−0.369998	−	1.38085i	−0.0128505	−	0.0479589i	0.959203	−	0.282719i	$-0.0912363\pi$
$829$	−0.369998	−	1.38085i	−0.0128505	−	0.0479589i	−0.972053	+	0.234760i	$0.924570\pi$
$830$	−38.8071	+	6.99126i	−1.34701	+	0.242670i
$831$	−24.3607	−	42.1940i	−0.845064	−	1.46369i
$832$	−11.4516	−	39.2246i	−0.397013	−	1.35987i
$833$		0			0
$834$	39.8284	+	47.1096i	1.37914	+	1.63127i
$835$	−0.800412	−	0.214470i	−0.0276994	−	0.00742203i
$836$	4.35448	+	3.59913i	0.150603	+	0.124479i
$837$	−9.46399	+	2.53587i	−0.327123	+	0.0876524i
$838$	−2.23492	−	4.74676i	−0.0772042	−	0.163974i
$839$			41.9512i			1.44832i	0.689634	+	0.724158i	$0.257772\pi$
$839$			41.9512i			1.44832i	−0.689634	+	0.724158i	$0.742228\pi$
$840$		0			0
$841$			14.5304i			0.501048i
$842$	6.22564	−	2.93123i	0.214550	−	0.101017i
$843$	50.7818	−	13.6069i	1.74902	−	0.468648i
$844$	−33.7476	+	3.20497i	−1.16164	+	0.110320i
$845$	−24.5465	−	6.57721i	−0.844425	−	0.226263i
$846$	−15.2012	+	12.8517i	−0.522628	+	0.441851i
$847$		0			0
$848$	−1.64673	−	3.39885i	−0.0565491	−	0.116717i
$849$	−30.2400	−	52.3773i	−1.03784	−	1.79758i
$850$	0.181949	+	1.00997i	0.00624081	+	0.0346415i
$851$	0.340204	+	1.26966i	0.0116621	+	0.0435234i
$852$	−9.52652	−	4.35655i	−0.326373	−	0.149253i
$853$	34.5722	+	34.5722i	1.18373	+	1.18373i	0.978770	+	0.204960i	$0.0657064\pi$
$853$	34.5722	+	34.5722i	1.18373	+	1.18373i	0.204960	+	0.978770i	$0.434294\pi$
$854$		0			0
$855$		−	3.60928i		−	0.123435i
$856$	11.1135	+	39.7037i	0.379853	+	1.35704i
$857$	−7.21992	−	4.16842i	−0.246628	−	0.142391i	0.371591	−	0.928396i	$-0.378812\pi$
$857$	−7.21992	−	4.16842i	−0.246628	−	0.142391i	−0.618219	+	0.786006i	$0.712146\pi$
$858$	55.6338	−	80.0838i	1.89931	−	2.73402i
$859$	3.38053	−	12.6163i	0.115342	−	0.430463i	−0.883970	−	0.467543i	$-0.845139\pi$
$859$	3.38053	−	12.6163i	0.115342	−	0.430463i	0.999312	+	0.0370807i	$0.0118059\pi$
$860$	41.5494	+	7.00888i	1.41682	+	0.239001i
$861$		0			0
$862$	20.8075	+	24.6114i	0.708706	+	0.838269i
$863$	−24.7192	−	42.8148i	−0.841450	−	1.45743i	−0.888669	−	0.458549i	$-0.848369\pi$
$863$	−24.7192	−	42.8148i	−0.841450	−	1.45743i	0.0472194	−	0.998885i	$-0.484964\pi$
$864$	−4.13923	−	5.68409i	−0.140820	−	0.193377i
$865$	4.08766	−	7.08003i	0.138985	−	0.240728i
$866$	−7.96883	+	22.1494i	−0.270792	+	0.752669i
$867$	29.9927	−	29.9927i	1.01861	−	1.01861i
$868$		0			0
$869$	−48.9443	−	48.9443i	−1.66032	−	1.66032i
$870$	−11.3322	−	24.0686i	−0.384199	−	0.816002i
$871$	28.6125	+	16.5194i	0.969497	+	0.559739i
$872$	13.9928	+	13.6848i	0.473856	+	0.463426i
$873$	−36.4162	+	21.0249i	−1.23250	+	0.711585i
$874$	−0.0274603	+	0.327876i	−0.000928860	+	0.0110906i
$875$		0			0
$876$	−32.8667	+	23.3788i	−1.11046	+	0.789897i
$877$	51.9644	+	13.9238i	1.75471	+	0.470174i	0.985622	−	0.168966i	$-0.0540428\pi$
$877$	51.9644	+	13.9238i	1.75471	+	0.470174i	0.769091	+	0.639140i	$0.220709\pi$
$878$	−7.74218	−	42.9753i	−0.261286	−	1.45035i
$879$	−36.9710	+	64.0357i	−1.24700	+	2.15987i
$880$	40.4215	−	7.74744i	1.36261	−	0.261166i
$881$	−26.2319			−0.883776			−0.441888	−	0.897070i	$-0.645691\pi$
$881$	−26.2319			−0.883776			−0.441888	+	0.897070i	$0.645691\pi$
$882$		0			0
$883$	−12.8278	+	12.8278i	−0.431688	+	0.431688i	−0.889202	−	0.457514i	$-0.848740\pi$
$883$	−12.8278	+	12.8278i	−0.431688	+	0.431688i	0.457514	+	0.889202i	$0.348740\pi$
$884$	−2.50502	+	5.47777i	−0.0842530	+	0.184237i
$885$	−0.139043	+	0.0372565i	−0.00467388	+	0.00125236i
$886$	16.5231	+	11.4785i	0.555103	+	0.385627i
$887$	46.3646	−	26.7686i	1.55677	−	0.898801i	0.559207	−	0.829028i	$-0.311106\pi$
$887$	46.3646	−	26.7686i	1.55677	−	0.898801i	0.997563	−	0.0697733i	$-0.0222276\pi$
$888$	−18.6659	+	11.0555i	−0.626387	+	0.370999i
$889$		0			0
$890$	−10.5921	−	0.887113i	−0.355048	−	0.0297361i
$891$	−10.0103	+	37.3590i	−0.335358	+	1.25157i
$892$	3.86743	+	3.19657i	0.129491	+	0.107029i
$893$	0.556671	+	2.07752i	0.0186283	+	0.0695217i
$894$	−26.7522	+	74.3580i	−0.894727	+	2.48690i
$895$	27.2791			0.911841
$896$		0			0
$897$	5.67918			0.189622
$898$	−7.06805	+	19.6457i	−0.235864	+	0.655587i
$899$	7.76035	+	28.9620i	0.258822	+	0.965937i
$900$	6.61746	+	5.46957i	0.220582	+	0.182319i
$901$	−0.144090	+	0.537752i	−0.00480034	+	0.0179151i
$902$	−22.0431	−	1.84616i	−0.733956	−	0.0614705i
$903$		0			0
$904$	18.2798	−	10.8268i	0.607977	−	0.360095i
$905$	−23.9400	+	13.8218i	−0.795793	+	0.459451i
$906$	−27.6283	−	19.1932i	−0.917890	−	0.637653i
$907$	−36.3248	+	9.73321i	−1.20615	+	0.323186i	−0.805249	−	0.592937i	$-0.797968\pi$
$907$	−36.3248	+	9.73321i	−1.20615	+	0.323186i	−0.400897	+	0.916123i	$0.631302\pi$
$908$	−15.7638	+	34.4710i	−0.523141	+	1.14396i
$909$	6.62263	−	6.62263i	0.219659	−	0.219659i
$910$		0			0
$911$	18.6202			0.616914			0.308457	−	0.951238i	$-0.400187\pi$
$911$	18.6202			0.616914			0.308457	+	0.951238i	$0.400187\pi$
$912$	−5.33328	+	1.02221i	−0.176602	+	0.0338487i
$913$	−38.0563	+	65.9155i	−1.25948	+	2.18148i
$914$	0.522102	+	2.89809i	0.0172696	+	0.0958603i
$915$	−9.78142	−	2.62092i	−0.323364	−	0.0866450i
$916$	−42.3502	+	30.1246i	−1.39929	+	0.995344i
$917$		0			0
$918$	−0.0865062	+	1.03288i	−0.00285513	+	0.0340902i
$919$	15.5605	−	8.98389i	0.513295	−	0.296351i	−0.220892	−	0.975298i	$-0.570897\pi$
$919$	15.5605	−	8.98389i	0.513295	−	0.296351i	0.734187	+	0.678947i	$0.237563\pi$
$920$	1.71372	+	1.67600i	0.0564996	+	0.0552560i
$921$	−18.8152	−	10.8630i	−0.619983	−	0.357947i
$922$	−8.96347	−	19.0376i	−0.295196	−	0.626968i
$923$	7.42679	+	7.42679i	0.244456	+	0.244456i
$924$		0			0
$925$	2.62046	−	2.62046i	0.0861602	−	0.0861602i
$926$	−12.7102	+	35.3281i	−0.417683	+	1.16095i
$927$	−0.155687	+	0.269658i	−0.00511344	+	0.00885674i
$928$	−17.3947	+	12.6670i	−0.571008	+	0.415815i
$929$	13.1258	+	22.7345i	0.430642	+	0.745894i	0.996929	−	0.0783141i	$-0.0249537\pi$
$929$	13.1258	+	22.7345i	0.430642	+	0.745894i	−0.566286	+	0.824209i	$0.691620\pi$
$930$	35.5908	+	42.0974i	1.16707	+	1.38043i
$931$		0			0
$932$	27.8744	+	4.70207i	0.913055	+	0.154021i
$933$	10.5600	−	39.4104i	0.345719	−	1.29024i
$934$	−7.80616	+	11.2368i	−0.255425	+	0.367680i
$935$	−5.25408	−	3.03345i	−0.171827	−	0.0992043i
$936$	13.5829	+	48.5257i	0.443972	+	1.58611i
$937$			47.7798i			1.56090i	0.625219	+	0.780449i	$0.285010\pi$
$937$			47.7798i			1.56090i	−0.625219	+	0.780449i	$0.714990\pi$
$938$		0			0
$939$	31.9775	+	31.9775i	1.04355	+	1.04355i
$940$	14.2500	+	6.51661i	0.464783	+	0.212549i
$941$	−11.2069	−	41.8248i	−0.365335	−	1.36345i	−0.866966	−	0.498368i	$-0.833933\pi$
$941$	−11.2069	−	41.8248i	−0.365335	−	1.36345i	0.501630	−	0.865082i	$-0.332734\pi$
$942$	−7.45670	−	41.3907i	−0.242952	−	1.34858i
$943$	−0.644154	−	1.11571i	−0.0209765	−	0.0363324i
$944$	0.0507672	+	0.104783i	0.00165233	+	0.00341040i
$945$		0			0
$946$	62.1105	−	52.5107i	2.01939	−	1.70727i
$947$	−18.0234	−	4.82935i	−0.585681	−	0.156933i	−0.0462023	−	0.998932i	$-0.514712\pi$
$947$	−18.0234	−	4.82935i	−0.585681	−	0.156933i	−0.539478	+	0.841999i	$0.681379\pi$
$948$	66.2365	−	6.29040i	2.15126	−	0.204303i
$949$	39.0620	−	10.4666i	1.26801	−	0.339762i
$950$	0.839260	−	0.395150i	0.0272292	−	0.0128204i
$951$		−	39.5932i		−	1.28390i
$952$		0			0
$953$		−	33.1972i		−	1.07536i	−0.843148	−	0.537681i	$-0.819300\pi$
$953$		−	33.1972i		−	1.07536i	0.843148	−	0.537681i	$-0.180700\pi$
$954$	1.98398	+	4.21377i	0.0642336	+	0.136426i
$955$	−18.0875	+	4.84652i	−0.585296	+	0.156830i
$956$	3.32961	+	2.75204i	0.107687	+	0.0890075i
$957$	−49.6002	−	13.2903i	−1.60335	−	0.429615i
$958$	−3.55436	−	4.20416i	−0.114836	−	0.135830i
$959$		0			0
$960$	−19.0136	+	34.6933i	−0.613661	+	1.11972i
$961$	−15.5659	−	26.9609i	−0.502124	−	0.869705i
$962$	21.4069	−	3.85655i	0.690187	−	0.124340i
$963$	−13.1595	−	49.1118i	−0.424058	−	1.58261i
$964$	18.2032	−	6.77877i	0.586286	−	0.218329i
$965$	−26.8517	−	26.8517i	−0.864387	−	0.864387i
$966$		0			0
$967$		−	13.2736i		−	0.426850i	−0.976959	−	0.213425i	$-0.931538\pi$
$967$		−	13.2736i		−	0.426850i	0.976959	−	0.213425i	$-0.0684619\pi$
$968$	23.6980	−	42.1217i	0.761683	−	1.35384i
$969$	0.693232	+	0.400238i	0.0222698	+	0.0128575i
$970$	27.1845	+	18.8849i	0.872842	+	0.606358i
$971$	−11.0202	+	41.1279i	−0.353655	+	1.31986i	0.528514	+	0.848925i	$0.322750\pi$
$971$	−11.0202	+	41.1279i	−0.353655	+	1.31986i	−0.882169	+	0.470934i	$0.843917\pi$
$972$	−25.8725	−	36.3724i	−0.829860	−	1.16665i
$973$		0			0
$974$	−3.11691	+	2.63516i	−0.0998722	+	0.0844359i
$975$	−8.00579	−	13.8664i	−0.256390	−	0.444081i
$976$	−0.592746	+	8.16942i	−0.0189733	+	0.261497i
$977$	−24.4001	+	42.2622i	−0.780628	+	1.35209i	0.150949	+	0.988542i	$0.451767\pi$
$977$	−24.4001	+	42.2622i	−0.780628	+	1.35209i	−0.931577	+	0.363545i	$0.881566\pi$
$978$	−50.1310	−	18.0359i	−1.60301	−	0.576725i
$979$	−14.5076	+	14.5076i	−0.463664	+	0.463664i
$980$		0			0
$981$	−17.0670	−	17.0670i	−0.544907	−	0.544907i
$982$	−18.3118	+	8.62179i	−0.584355	+	0.275132i
$983$	−45.9141	−	26.5085i	−1.46443	−	0.845491i	−0.465222	−	0.885194i	$-0.654025\pi$
$983$	−45.9141	−	26.5085i	−1.46443	−	0.845491i	−0.999212	+	0.0397033i	$0.987359\pi$
$984$	14.8668	−	15.2014i	0.473938	−	0.484604i
$985$	−19.8131	+	11.4391i	−0.631299	+	0.364481i
$986$	3.16086	+	0.264729i	0.100662	+	0.00843069i
$987$		0			0
$988$	5.36885	+	0.905659i	0.170806	+	0.0288128i
$989$	4.57551	+	1.22601i	0.145493	+	0.0389847i
$990$	−49.9508	+	8.99884i	−1.58754	+	0.286002i
$991$	6.92839	−	12.0003i	0.220088	−	0.381203i	−0.734747	−	0.678341i	$-0.762699\pi$
$991$	6.92839	−	12.0003i	0.220088	−	0.381203i	0.954834	+	0.297139i	$0.0960324\pi$
$992$	28.0231	−	34.6831i	0.889736	−	1.10119i
$993$	−38.7162			−1.22862
$994$		0			0
$995$	−3.71531	+	3.71531i	−0.117783	+	0.117783i
$996$	−25.5322	−	68.5624i	−0.809020	−	2.17248i
$997$	−25.8704	+	6.93196i	−0.819325	+	0.219537i	−0.644051	−	0.764982i	$-0.722748\pi$
$997$	−25.8704	+	6.93196i	−0.819325	+	0.219537i	−0.175273	+	0.984520i	$0.556081\pi$
$998$	−15.4758	+	22.2772i	−0.489878	+	0.705171i
$999$	3.24152	−	1.87149i	0.102557	−	0.0592114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.165.6		48
7.2	even	3	inner	784.2.x.o.373.11		48
7.3	odd	6		784.2.m.j.197.3		24
7.4	even	3		784.2.m.k.197.3		24
7.5	odd	6		112.2.w.c.37.11	✓	48
7.6	odd	2		112.2.w.c.53.6	yes	48
16.13	even	4	inner	784.2.x.o.557.11		48
28.19	even	6		448.2.ba.c.177.11		48
28.27	even	2		448.2.ba.c.305.2		48
56.5	odd	6		896.2.ba.f.737.11		48
56.13	odd	2		896.2.ba.f.865.2		48
56.19	even	6		896.2.ba.e.737.2		48
56.27	even	2		896.2.ba.e.865.11		48
112.5	odd	12		896.2.ba.f.289.2		48
112.13	odd	4		112.2.w.c.109.11	yes	48
112.19	even	12		448.2.ba.c.401.2		48
112.27	even	4		896.2.ba.e.417.2		48
112.45	odd	12		784.2.m.j.589.3		24
112.61	odd	12		112.2.w.c.93.6	yes	48
112.69	odd	4		896.2.ba.f.417.11		48
112.75	even	12		896.2.ba.e.289.11		48
112.83	even	4		448.2.ba.c.81.11		48
112.93	even	12	inner	784.2.x.o.765.6		48
112.109	even	12		784.2.m.k.589.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.11	✓	48	7.5	odd	6
112.2.w.c.53.6	yes	48	7.6	odd	2
112.2.w.c.93.6	yes	48	112.61	odd	12
112.2.w.c.109.11	yes	48	112.13	odd	4
448.2.ba.c.81.11		48	112.83	even	4
448.2.ba.c.177.11		48	28.19	even	6
448.2.ba.c.305.2		48	28.27	even	2
448.2.ba.c.401.2		48	112.19	even	12
784.2.m.j.197.3		24	7.3	odd	6
784.2.m.j.589.3		24	112.45	odd	12
784.2.m.k.197.3		24	7.4	even	3
784.2.m.k.589.3		24	112.109	even	12
784.2.x.o.165.6		48	1.1	even	1	trivial
784.2.x.o.373.11		48	7.2	even	3	inner
784.2.x.o.557.11		48	16.13	even	4	inner
784.2.x.o.765.6		48	112.93	even	12	inner
896.2.ba.e.289.11		48	112.75	even	12
896.2.ba.e.417.2		48	112.27	even	4
896.2.ba.e.737.2		48	56.19	even	6
896.2.ba.e.865.11		48	56.27	even	2
896.2.ba.f.289.2		48	112.5	odd	12
896.2.ba.f.417.11		48	112.69	odd	4
896.2.ba.f.737.11		48	56.5	odd	6
896.2.ba.f.865.2		48	56.13	odd	2

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.478757 + 1.33071i) q^{2} +(-0.659252 - 2.46036i) q^{3} +(-1.54158 - 1.27417i) q^{4} +(0.502490 - 1.87532i) q^{5} +(3.58965 + 0.300642i) q^{6} +(2.43360 - 1.44138i) q^{8} +(-3.02070 + 1.74400i) q^{9} +O(q^{10})\)	\(q+(-0.478757 + 1.33071i) q^{2} +(-0.659252 - 2.46036i) q^{3} +(-1.54158 - 1.27417i) q^{4} +(0.502490 - 1.87532i) q^{5} +(3.58965 + 0.300642i) q^{6} +(2.43360 - 1.44138i) q^{8} +(-3.02070 + 1.74400i) q^{9} +(2.25494 + 1.56649i) q^{10} +(5.11917 - 1.37168i) q^{11} +(-2.11864 + 4.63286i) q^{12} +(3.61173 - 3.61173i) q^{13} -4.94523 q^{15} +(0.752959 + 3.92849i) q^{16} +(0.294815 - 0.510634i) q^{17} +(-0.874580 - 4.85462i) q^{18} +(-0.514822 - 0.137946i) q^{19} +(-3.16411 + 2.25070i) q^{20} +(-0.625532 + 7.46884i) q^{22} +(-0.378033 + 0.218258i) q^{23} +(-5.15068 - 5.03731i) q^{24} +(1.06581 + 0.615344i) q^{25} +(3.07703 + 6.53532i) q^{26} +(0.878939 + 0.878939i) q^{27} +(2.68976 - 2.68976i) q^{29} +(2.36756 - 6.58067i) q^{30} +(-3.94118 + 6.82633i) q^{31} +(-5.58817 - 0.878822i) q^{32} +(-6.74965 - 11.6907i) q^{33} +(0.538362 + 0.636783i) q^{34} +(6.87881 + 1.16037i) q^{36} +(0.779365 - 2.90863i) q^{37} +(0.430041 - 0.619036i) q^{38} +(-11.2672 - 6.50513i) q^{39} +(-1.48019 - 5.28806i) q^{40} +2.95135i q^{41} +(-7.67329 - 7.67329i) q^{43} +(-9.63939 - 4.40816i) q^{44} +(1.75268 + 6.54110i) q^{45} +(-0.109452 - 0.607545i) q^{46} +(-2.01771 - 3.49478i) q^{47} +(9.16913 - 4.44242i) q^{48} +(-1.32911 + 1.12368i) q^{50} +(-1.45070 - 0.388715i) q^{51} +(-10.1698 + 0.965811i) q^{52} +(-0.912017 + 0.244374i) q^{53} +(-1.59041 + 0.748816i) q^{54} -10.2893i q^{55} +1.35759i q^{57} +(2.29155 + 4.86703i) q^{58} +(0.0281166 - 0.00753382i) q^{59} +(7.62348 + 6.30108i) q^{60} +(1.97795 + 0.529990i) q^{61} +(-7.19700 - 8.51273i) q^{62} +(3.84483 - 7.01550i) q^{64} +(-4.95829 - 8.58801i) q^{65} +(18.7884 - 3.38481i) q^{66} +(1.67413 + 6.24795i) q^{67} +(-1.10512 + 0.411540i) q^{68} +(0.786212 + 0.786212i) q^{69} +2.05630i q^{71} +(-4.83740 + 8.59818i) q^{72} +(6.85664 + 3.95868i) q^{73} +(3.49742 + 2.42964i) q^{74} +(0.811334 - 3.02794i) q^{75} +(0.617873 + 0.868628i) q^{76} +(14.0507 - 11.8790i) q^{78} +(-6.53028 - 11.3108i) q^{79} +(7.74553 + 0.561989i) q^{80} +(-3.64893 + 6.32013i) q^{81} +(-3.92739 - 1.41298i) q^{82} +(-10.1551 + 10.1551i) q^{83} +(-0.809460 - 0.809460i) q^{85} +(13.8846 - 6.53729i) q^{86} +(-8.39101 - 4.84455i) q^{87} +(10.4809 - 10.7168i) q^{88} +(-3.35262 + 1.93564i) q^{89} +(-9.54343 - 0.799284i) q^{90} +(0.860868 + 0.145218i) q^{92} +(19.3935 + 5.19647i) q^{93} +(5.61654 - 1.01184i) q^{94} +(-0.517385 + 0.896137i) q^{95} +(1.52179 + 14.3283i) q^{96} +12.0556 q^{97} +(-13.0712 + 13.0712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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