LMFDB - Embedded newform 243.2.i.a.4.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			4.8
Character	$\chi$	$=$	243.4
Dual form			243.2.i.a.61.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.53351 - 0.0595072i) q^{2} +(-1.14640 + 1.29838i) q^{3} +(0.354129 + 0.0275251i) q^{4} +(0.161696 + 0.200471i) q^{5} +(1.83527 - 1.92285i) q^{6} +(-4.41863 + 2.00851i) q^{7} +(2.50715 + 0.293044i) q^{8} +(-0.371555 - 2.97690i) q^{9} +(-0.236033 - 0.317047i) q^{10} +(-0.0477295 - 2.46092i) q^{11} +(-0.441709 + 0.428237i) q^{12} +(3.14616 + 1.00877i) q^{13} +(6.89553 - 2.81713i) q^{14} +(-0.445654 - 0.0198776i) q^{15} +(-4.52917 - 0.708350i) q^{16} +(-1.07248 - 3.58234i) q^{17} +(0.392637 + 4.58722i) q^{18} +(-3.11473 + 0.738204i) q^{19} +(0.0517431 + 0.0754433i) q^{20} +(2.45769 - 8.03958i) q^{21} +(-0.0732488 + 3.77669i) q^{22} +(6.63084 - 4.73944i) q^{23} +(-3.25467 + 2.91928i) q^{24} +(1.04448 - 4.82184i) q^{25} +(-4.76464 - 1.73419i) q^{26} +(4.29108 + 2.93029i) q^{27} +(-1.62005 + 0.589649i) q^{28} +(-0.888872 - 6.50770i) q^{29} +(0.682232 + 0.0570021i) q^{30} +(-5.20773 - 5.10770i) q^{31} +(1.94957 + 0.382883i) q^{32} +(3.24992 + 2.75922i) q^{33} +(1.43149 + 5.55738i) q^{34} +(-1.11712 - 0.561039i) q^{35} +(-0.0496391 - 1.06443i) q^{36} +(0.121679 + 0.0800296i) q^{37} +(4.82040 - 0.946696i) q^{38} +(-4.91651 + 2.92844i) q^{39} +(0.346649 + 0.549996i) q^{40} +(-3.91017 + 7.42328i) q^{41} +(-4.24731 + 12.1825i) q^{42} +(-2.89571 + 8.46304i) q^{43} +(0.0508346 - 0.872797i) q^{44} +(0.536704 - 0.555838i) q^{45} +(-10.4505 + 6.87340i) q^{46} +(-3.28669 + 3.22356i) q^{47} +(6.11192 - 5.06851i) q^{48} +(10.8875 - 12.4757i) q^{49} +(-1.88865 + 7.33219i) q^{50} +(5.88071 + 2.71429i) q^{51} +(1.08638 + 0.443834i) q^{52} +(-0.394644 - 0.331146i) q^{53} +(-6.40605 - 4.74898i) q^{54} +(0.485626 - 0.407489i) q^{55} +(-11.6668 + 3.74080i) q^{56} +(2.61224 - 4.89036i) q^{57} +(0.975841 + 10.0325i) q^{58} +(-5.18606 + 2.86155i) q^{59} +(-0.157272 - 0.0193059i) q^{60} +(-2.10417 + 0.163549i) q^{61} +(7.68216 + 8.14261i) q^{62} +(7.62091 + 12.4075i) q^{63} +(5.95442 + 1.41122i) q^{64} +(0.306490 + 0.793828i) q^{65} +(-4.81959 - 4.42468i) q^{66} +(1.20024 - 8.78728i) q^{67} +(-0.281193 - 1.29813i) q^{68} +(-1.44799 + 14.0426i) q^{69} +(1.67973 + 0.926837i) q^{70} +(1.80912 - 4.19400i) q^{71} +(-0.0591827 - 7.57243i) q^{72} +(0.0487264 - 0.0654510i) q^{73} +(-0.181834 - 0.129967i) q^{74} +(5.06317 + 6.88386i) q^{75} +(-1.12333 + 0.175686i) q^{76} +(5.15369 + 10.7780i) q^{77} +(7.71378 - 4.19822i) q^{78} +(0.906458 - 1.43819i) q^{79} +(-0.590344 - 1.02251i) q^{80} +(-8.72389 + 2.21217i) q^{81} +(6.43803 - 11.1510i) q^{82} +(-4.93529 - 9.36941i) q^{83} +(1.09163 - 2.77940i) q^{84} +(0.544740 - 0.794251i) q^{85} +(4.94422 - 12.8058i) q^{86} +(9.46843 + 6.30630i) q^{87} +(0.601494 - 6.18389i) q^{88} +(-6.19275 - 14.3564i) q^{89} +(-0.856118 + 0.820446i) q^{90} +(-15.9278 + 1.86170i) q^{91} +(2.47862 - 1.49586i) q^{92} +(12.6018 - 0.906136i) q^{93} +(5.23199 - 4.74778i) q^{94} +(-0.651627 - 0.505049i) q^{95} +(-2.73210 + 2.09234i) q^{96} +(-10.1384 + 12.5697i) q^{97} +(-17.4385 + 18.4837i) q^{98} +(-7.30819 + 1.05645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{81}\right)$

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 $

$2$	−1.53351	−	0.0595072i	−1.08436	−	0.0420779i	−0.509607	−	0.860407i	$-0.670209\pi$
$2$	−1.53351	−	0.0595072i	−1.08436	−	0.0420779i	−0.574749	+	0.818330i	$0.694900\pi$
$3$	−1.14640	+	1.29838i	−0.661872	+	0.749617i
$3$	−1.14640	+	1.29838i	−0.661872	+	0.749617i
$4$	0.354129	+	0.0275251i	0.177064	+	0.0137625i
$5$	0.161696	+	0.200471i	0.0723125	+	0.0896534i	0.813229	−	0.581943i	$-0.197707\pi$
$5$	0.161696	+	0.200471i	0.0723125	+	0.0896534i	−0.740917	+	0.671597i	$0.765609\pi$
$6$	1.83527	−	1.92285i	0.749247	−	0.785002i
$7$	−4.41863	+	2.00851i	−1.67008	+	0.759146i	−0.670228	+	0.742155i	$0.733804\pi$
$7$	−4.41863	+	2.00851i	−1.67008	+	0.759146i	−0.999856	+	0.0169910i	$0.994591\pi$
$8$	2.50715	+	0.293044i	0.886413	+	0.103607i
$9$	−0.371555	−	2.97690i	−0.123852	−	0.992301i
$10$	−0.236033	−	0.317047i	−0.0746401	−	0.100259i
$11$	−0.0477295	−	2.46092i	−0.0143910	−	0.741996i	−0.935627	−	0.352991i	$-0.885165\pi$
$11$	−0.0477295	−	2.46092i	−0.0143910	−	0.741996i	0.921236	−	0.389005i	$-0.127181\pi$
$12$	−0.441709	+	0.428237i	−0.127511	+	0.123621i
$13$	3.14616	+	1.00877i	0.872587	+	0.279784i	0.707687	−	0.706526i	$-0.249739\pi$
$13$	3.14616	+	1.00877i	0.872587	+	0.279784i	0.164900	+	0.986310i	$0.447270\pi$
$14$	6.89553	−	2.81713i	1.84291	−	0.752911i
$15$	−0.445654	−	0.0198776i	−0.115067	−	0.00513237i
$16$	−4.52917	−	0.708350i	−1.13229	−	0.177087i
$17$	−1.07248	−	3.58234i	−0.260115	−	0.868845i	−0.983885	−	0.178804i	$-0.942777\pi$
$17$	−1.07248	−	3.58234i	−0.260115	−	0.868845i	0.723770	−	0.690042i	$-0.242408\pi$
$18$	0.392637	+	4.58722i	0.0925455	+	1.08122i
$19$	−3.11473	+	0.738204i	−0.714568	+	0.169356i	−0.571791	−	0.820399i	$-0.693751\pi$
$19$	−3.11473	+	0.738204i	−0.714568	+	0.169356i	−0.142777	+	0.989755i	$0.545603\pi$
$20$	0.0517431	+	0.0754433i	0.0115701	+	0.0168696i
$21$	2.45769	−	8.03958i	0.536312	−	1.75438i
$22$	−0.0732488	+	3.77669i	−0.0156167	+	0.805193i
$23$	6.63084	−	4.73944i	1.38263	−	0.988241i	0.384755	−	0.923019i	$-0.374286\pi$
$23$	6.63084	−	4.73944i	1.38263	−	0.988241i	0.997871	−	0.0652226i	$-0.0207757\pi$
$24$	−3.25467	+	2.91928i	−0.664357	+	0.595896i
$25$	1.04448	−	4.82184i	0.208895	−	0.964368i
$26$	−4.76464	−	1.73419i	−0.934422	−	0.340102i
$27$	4.29108	+	2.93029i	0.825820	+	0.563934i
$28$	−1.62005	+	0.589649i	−0.306160	+	0.111433i
$29$	−0.888872	−	6.50770i	−0.165059	−	1.20845i	−0.867767	−	0.496971i	$-0.834446\pi$
$29$	−0.888872	−	6.50770i	−0.165059	−	1.20845i	0.702708	−	0.711478i	$-0.251974\pi$
$30$	0.682232	+	0.0570021i	0.124558	+	0.0104071i
$31$	−5.20773	−	5.10770i	−0.935335	−	0.917370i	0.0613999	−	0.998113i	$-0.480443\pi$
$31$	−5.20773	−	5.10770i	−0.935335	−	0.917370i	−0.996735	+	0.0807431i	$0.974271\pi$
$32$	1.94957	+	0.382883i	0.344638	+	0.0676848i
$33$	3.24992	+	2.75922i	0.565738	+	0.480318i
$34$	1.43149	+	5.55738i	0.245498	+	0.953083i
$35$	−1.11712	−	0.561039i	−0.188828	−	0.0948330i
$36$	−0.0496391	−	1.06443i	−0.00827318	−	0.177406i
$37$	0.121679	+	0.0800296i	0.0200039	+	0.0131568i	0.559472	−	0.828850i	$-0.311004\pi$
$37$	0.121679	+	0.0800296i	0.0200039	+	0.0131568i	−0.539468	+	0.842006i	$0.681374\pi$
$38$	4.82040	−	0.946696i	0.781972	−	0.153574i
$39$	−4.91651	+	2.92844i	−0.787271	+	0.468925i
$40$	0.346649	+	0.549996i	0.0548100	+	0.0869620i
$41$	−3.91017	+	7.42328i	−0.610666	+	1.15932i	0.363095	+	0.931752i	$0.381720\pi$
$41$	−3.91017	+	7.42328i	−0.610666	+	1.15932i	−0.973762	+	0.227570i	$0.926922\pi$
$42$	−4.24731	+	12.1825i	−0.655374	+	1.87981i
$43$	−2.89571	+	8.46304i	−0.441592	+	1.29060i	0.471146	+	0.882055i	$0.343841\pi$
$43$	−2.89571	+	8.46304i	−0.441592	+	1.29060i	−0.912738	+	0.408546i	$0.866036\pi$
$44$	0.0508346	−	0.872797i	0.00766361	−	0.131579i
$45$	0.536704	−	0.555838i	0.0800071	−	0.0828595i
$46$	−10.4505	+	6.87340i	−1.54084	+	1.01343i
$47$	−3.28669	+	3.22356i	−0.479412	+	0.470204i	−0.899275	−	0.437383i	$-0.855905\pi$
$47$	−3.28669	+	3.22356i	−0.479412	+	0.470204i	0.419863	+	0.907588i	$0.362078\pi$
$48$	6.11192	−	5.06851i	0.882180	−	0.731577i
$49$	10.8875	−	12.4757i	1.55536	−	1.78224i
$50$	−1.88865	+	7.33219i	−0.267095	+	1.03693i
$51$	5.88071	+	2.71429i	0.823464	+	0.380077i
$52$	1.08638	+	0.443834i	0.150654	+	0.0615487i
$53$	−0.394644	−	0.331146i	−0.0542085	−	0.0454863i	0.615281	−	0.788308i	$-0.289043\pi$
$53$	−0.394644	−	0.331146i	−0.0542085	−	0.0454863i	−0.669489	+	0.742822i	$0.733487\pi$
$54$	−6.40605	−	4.74898i	−0.871753	−	0.646254i
$55$	0.485626	−	0.407489i	0.0654818	−	0.0549458i
$56$	−11.6668	+	3.74080i	−1.55904	+	0.499885i
$57$	2.61224	−	4.89036i	0.346000	−	0.647744i
$58$	0.975841	+	10.0325i	0.128134	+	1.31733i
$59$	−5.18606	+	2.86155i	−0.675167	+	0.372542i	−0.783343	−	0.621590i	$-0.786487\pi$
$59$	−5.18606	+	2.86155i	−0.675167	+	0.372542i	0.108175	+	0.994132i	$0.465499\pi$
$60$	−0.157272	−	0.0193059i	−0.0203037	−	0.00249238i
$61$	−2.10417	+	0.163549i	−0.269412	+	0.0209403i	−0.211488	−	0.977381i	$-0.567831\pi$
$61$	−2.10417	+	0.163549i	−0.269412	+	0.0209403i	−0.0579239	+	0.998321i	$0.518448\pi$
$62$	7.68216	+	8.14261i	0.975635	+	1.03411i
$63$	7.62091	+	12.4075i	0.960144	+	1.56320i
$64$	5.95442	+	1.41122i	0.744302	+	0.176403i
$65$	0.306490	+	0.793828i	0.0380154	+	0.0984623i
$66$	−4.81959	−	4.42468i	−0.593250	−	0.544641i
$67$	1.20024	−	8.78728i	0.146632	−	1.07354i	−0.759489	−	0.650520i	$-0.774551\pi$
$67$	1.20024	−	8.78728i	0.146632	−	1.07354i	0.906122	−	0.423017i	$-0.139029\pi$
$68$	−0.281193	−	1.29813i	−0.0340996	−	0.157421i
$69$	−1.44799	+	14.0426i	−0.174318	+	1.69053i
$70$	1.67973	+	0.926837i	0.200766	+	0.110778i
$71$	1.80912	−	4.19400i	0.214703	−	0.497737i	−0.776496	−	0.630123i	$-0.783005\pi$
$71$	1.80912	−	4.19400i	0.214703	−	0.497737i	0.991198	+	0.132386i	$0.0422638\pi$
$72$	−0.0591827	−	7.57243i	−0.00697475	−	0.892420i
$73$	0.0487264	−	0.0654510i	0.00570300	−	0.00766046i	−0.799263	−	0.600982i	$-0.794776\pi$
$73$	0.0487264	−	0.0654510i	0.00570300	−	0.00766046i	0.804966	+	0.593322i	$0.202184\pi$
$74$	−0.181834	−	0.129967i	−0.0211378	−	0.0151084i
$75$	5.06317	+	6.88386i	0.584645	+	0.794879i
$76$	−1.12333	+	0.175686i	−0.128855	+	0.0201526i
$77$	5.15369	+	10.7780i	0.587317	+	1.22827i
$78$	7.71378	−	4.19822i	0.873414	−	0.475355i
$79$	0.906458	−	1.43819i	0.101984	−	0.161809i	−0.791117	−	0.611665i	$-0.790500\pi$
$79$	0.906458	−	1.43819i	0.101984	−	0.161809i	0.893101	+	0.449856i	$0.148525\pi$
$80$	−0.590344	−	1.02251i	−0.0660024	−	0.114320i
$81$	−8.72389	+	2.21217i	−0.969321	+	0.245797i
$82$	6.43803	−	11.1510i	0.710962	−	1.23142i
$83$	−4.93529	−	9.36941i	−0.541718	−	1.02843i	−0.990851	−	0.134961i	$-0.956909\pi$
$83$	−4.93529	−	9.36941i	−0.541718	−	1.02843i	0.449133	−	0.893465i	$-0.351733\pi$
$84$	1.09163	−	2.77940i	0.119106	−	0.303257i
$85$	0.544740	−	0.794251i	0.0590854	−	0.0861486i
$86$	4.94422	−	12.8058i	0.533149	−	1.38089i
$87$	9.46843	+	6.30630i	1.01512	+	0.676107i
$88$	0.601494	−	6.18389i	0.0641194	−	0.659205i
$89$	−6.19275	−	14.3564i	−0.656430	−	1.52178i	−0.842190	−	0.539182i	$-0.818734\pi$
$89$	−6.19275	−	14.3564i	−0.656430	−	1.52178i	0.185759	−	0.982595i	$-0.440526\pi$
$90$	−0.856118	+	0.820446i	−0.0902428	+	0.0864826i
$91$	−15.9278	+	1.86170i	−1.66969	+	0.195159i
$92$	2.47862	−	1.49586i	0.258414	−	0.155954i
$93$	12.6018	−	0.906136i	1.30675	−	0.0939619i
$94$	5.23199	−	4.74778i	0.539639	−	0.489696i
$95$	−0.651627	−	0.505049i	−0.0668555	−	0.0518169i
$96$	−2.73210	+	2.09234i	−0.278844	+	0.213548i
$97$	−10.1384	+	12.5697i	−1.02940	+	1.27626i	−0.0690057	+	0.997616i	$0.521983\pi$
$97$	−10.1384	+	12.5697i	−1.02940	+	1.27626i	−0.960395	+	0.278641i	$0.910116\pi$
$98$	−17.4385	+	18.4837i	−1.76155	+	1.86714i
$99$	−7.30819	+	1.05645i	−0.734500	+	0.106178i
$100$	0.502600	−	1.67880i	0.0502600	−	0.167880i
$101$	4.59586	−	9.61143i	0.457305	−	0.956373i	−0.536360	−	0.843989i	$-0.680201\pi$
$101$	4.59586	−	9.61143i	0.457305	−	0.956373i	0.993665	−	0.112383i	$-0.0358484\pi$
$102$	−8.85661	−	4.51234i	−0.876936	−	0.446789i
$103$	−15.5970	−	9.41281i	−1.53681	−	0.927472i	−0.996282	−	0.0861486i	$-0.972544\pi$
$103$	−15.5970	−	9.41281i	−1.53681	−	0.927472i	−0.540532	−	0.841324i	$-0.681777\pi$
$104$	7.59228	+	3.45112i	0.744485	+	0.338410i
$105$	2.00910	−	0.807270i	0.196068	−	0.0787814i
$106$	0.585485	+	0.531299i	0.0568673	+	0.0516044i
$107$	−0.335161	−	1.90079i	−0.0324012	−	0.183756i	0.964312	−	0.264769i	$-0.0852957\pi$
$107$	−0.335161	−	1.90079i	−0.0324012	−	0.183756i	−0.996713	+	0.0810126i	$0.974185\pi$
$108$	1.43894	+	1.15581i	0.138462	+	0.111218i
$109$	−0.806093	+	4.57158i	−0.0772097	+	0.437878i	0.921558	+	0.388241i	$0.126917\pi$
$109$	−0.806093	+	4.57158i	−0.0772097	+	0.437878i	−0.998767	+	0.0496363i	$0.984194\pi$
$110$	−0.768961	+	0.595990i	−0.0733176	+	0.0568254i
$111$	−0.243401	+	0.0662396i	−0.0231026	+	0.00628718i
$112$	21.4354	−	5.96696i	2.02546	−	0.563825i
$113$	−0.450001	−	1.31518i	−0.0423325	−	0.123722i	0.922957	−	0.384902i	$-0.125765\pi$
$113$	−0.450001	−	1.31518i	−0.0423325	−	0.123722i	−0.965290	+	0.261180i	$0.915888\pi$
$114$	−4.29692	+	7.34397i	−0.402443	+	0.687826i
$115$	2.02230	+	0.562945i	0.188580	+	0.0524949i
$116$	−0.135650	−	2.32903i	−0.0125948	−	0.216245i
$117$	1.83405	−	9.74062i	0.169558	−	0.900520i
$118$	8.12316	−	4.07961i	0.747798	−	0.375558i
$119$	11.9341	+	13.6749i	1.09399	+	1.25358i
$120$	−1.11150	−	0.180433i	−0.101465	−	0.0164712i
$121$	4.93787	−	0.191612i	0.448898	−	0.0174193i
$122$	3.23650	−	0.125591i	0.293019	−	0.0113705i
$123$	−5.15560	−	13.5869i	−0.464865	−	1.22509i
$124$	−1.70362	−	1.95213i	−0.152989	−	0.175306i
$125$	2.28632	−	1.14823i	0.204495	−	0.102701i
$126$	−10.9484	−	19.4806i	−0.975362	−	1.73547i
$127$	−0.0485922	−	0.834296i	−0.00431186	−	0.0740318i	0.995466	−	0.0951208i	$-0.0303237\pi$
$127$	−0.0485922	−	0.834296i	−0.00431186	−	0.0740318i	−0.999778	+	0.0210889i	$0.993287\pi$
$128$	−12.8753	−	3.58407i	−1.13802	−	0.316790i
$129$	−7.66857	−	13.4617i	−0.675180	−	1.18524i
$130$	−0.422767	−	1.23558i	−0.0370791	−	0.108368i
$131$	0.998800	−	0.278035i	0.0872655	−	0.0242920i	−0.224265	−	0.974528i	$-0.571998\pi$
$131$	0.998800	−	0.278035i	0.0872655	−	0.0242920i	0.311530	+	0.950236i	$0.399158\pi$
$132$	1.07494	+	1.06657i	0.0935616	+	0.0928332i
$133$	12.2801	−	9.51782i	1.06482	−	0.825300i
$134$	−2.36348	+	13.4040i	−0.204174	+	1.15793i
$135$	0.106411	+	1.33405i	0.00915844	+	0.114817i
$136$	−1.63909	−	9.29577i	−0.140551	−	0.797105i
$137$	−1.54511	−	1.40211i	−0.132007	−	0.119790i	0.603330	−	0.797492i	$-0.293840\pi$
$137$	−1.54511	−	1.40211i	−0.132007	−	0.119790i	−0.735337	+	0.677702i	$0.762976\pi$
$138$	3.05615	−	21.4483i	0.260157	−	1.82580i
$139$	8.69713	+	3.95333i	0.737681	+	0.335317i	0.747166	−	0.664638i	$-0.231414\pi$
$139$	8.69713	+	3.95333i	0.737681	+	0.335317i	−0.00948484	+	0.999955i	$0.503019\pi$
$140$	−0.380162	−	0.229429i	−0.0321296	−	0.0193903i
$141$	−0.417547	−	7.96282i	−0.0351638	−	0.670591i
$142$	−3.02387	+	6.32390i	−0.253758	+	0.530690i
$143$	2.33235	−	7.79059i	0.195041	−	0.651482i
$144$	−0.425849	+	13.7461i	−0.0354874	+	1.14551i
$145$	1.16088	−	1.23046i	0.0964057	−	0.102184i
$146$	−0.0786173	+	0.0974702i	−0.00650642	+	0.00806669i
$147$	3.71674	+	28.4381i	0.306552	+	2.34553i
$148$	0.0408873	+	0.0316900i	0.00336091	+	0.00260490i
$149$	2.93950	−	2.66745i	0.240813	−	0.218526i	−0.542659	−	0.839953i	$-0.682582\pi$
$149$	2.93950	−	2.66745i	0.240813	−	0.218526i	0.783472	+	0.621427i	$0.213447\pi$
$150$	−7.35479	−	10.8578i	−0.600516	−	0.886533i
$151$	12.1105	−	7.30875i	0.985542	−	0.594778i	0.0702336	−	0.997531i	$-0.477626\pi$
$151$	12.1105	−	7.30875i	0.985542	−	0.594778i	0.915309	+	0.402753i	$0.131947\pi$
$152$	−8.02543	+	0.938039i	−0.650949	+	0.0760850i
$153$	−10.2658	+	4.52371i	−0.829940	+	0.365721i
$154$	−7.26187	−	16.8349i	−0.585178	−	1.35659i
$155$	0.181880	−	1.86989i	0.0146090	−	0.150193i
$156$	−1.82168	+	0.901717i	−0.145851	+	0.0721951i
$157$	−2.03160	+	5.26198i	−0.162139	+	0.419952i	−0.990015	−	0.140960i	$-0.954981\pi$
$157$	−2.03160	+	5.26198i	−0.162139	+	0.419952i	0.827876	+	0.560911i	$0.189549\pi$
$158$	−1.47565	+	2.15154i	−0.117396	+	0.171168i
$159$	0.882369	−	0.132772i	0.0699764	−	0.0105295i
$160$	0.238480	+	0.452743i	0.0188535	+	0.0357925i
$161$	−19.7800	+	34.2599i	−1.55888	+	2.70006i
$162$	13.5098	−	2.87325i	1.06143	−	0.225744i
$163$	5.33048	+	9.23266i	0.417515	+	0.723158i	0.995689	−	0.0927559i	$-0.0295676\pi$
$163$	5.33048	+	9.23266i	0.417515	+	0.723158i	−0.578173	+	0.815914i	$0.696234\pi$
$164$	−1.58903	+	2.52117i	−0.124082	+	0.196870i
$165$	−0.0276464	+	1.09767i	−0.00215227	+	0.0854533i
$166$	7.01077	+	14.6618i	0.544141	+	1.13797i
$167$	0.415654	−	0.0650071i	0.0321643	−	0.00503040i	−0.138416	−	0.990374i	$-0.544201\pi$
$167$	0.415654	−	0.0650071i	0.0321643	−	0.00503040i	0.170580	+	0.985344i	$0.445436\pi$
$168$	8.51776	−	19.4363i	0.657160	−	1.49954i
$169$	−1.69550	−	1.21187i	−0.130423	−	0.0932208i
$170$	−0.882629	+	1.18558i	−0.0676945	+	0.0909295i
$171$	3.35486	+	8.99796i	0.256552	+	0.688091i
$172$	−1.25840	+	2.91730i	−0.0959521	+	0.222442i
$173$	−5.06314	−	2.79372i	−0.384943	−	0.212403i	0.278823	−	0.960342i	$-0.410056\pi$
$173$	−5.06314	−	2.79372i	−0.384943	−	0.212403i	−0.663767	+	0.747940i	$0.731043\pi$
$174$	−14.1447	−	10.2342i	−1.07230	−	0.775855i
$175$	5.06957	+	23.4037i	0.383224	+	1.76916i
$176$	−1.52702	+	11.1797i	−0.115103	+	0.842705i
$177$	2.22991	−	10.0139i	0.167611	−	0.752692i
$178$	8.64234	+	22.3842i	0.647771	+	1.67777i
$179$	6.43630	+	1.52543i	0.481071	+	0.114016i	0.463994	−	0.885838i	$-0.346416\pi$
$179$	6.43630	+	1.52543i	0.481071	+	0.114016i	0.0170770	+	0.999854i	$0.494564\pi$
$180$	0.205362	−	0.182065i	0.0153068	−	0.0135704i
$181$	−7.35741	−	7.79839i	−0.546872	−	0.579650i	0.393703	−	0.919238i	$-0.371194\pi$
$181$	−7.35741	−	7.79839i	−0.546872	−	0.579650i	−0.940574	+	0.339588i	$0.889712\pi$
$182$	24.5363	−	1.90711i	1.81875	−	0.141364i
$183$	2.19986	−	2.91950i	0.162619	−	0.215815i
$184$	18.0134	−	9.93937i	1.32797	−	0.732740i
$185$	0.00363136	+	0.0373336i	0.000266983	+	0.00274482i
$186$	−19.3790	+	0.639670i	−1.42093	+	0.0469029i
$187$	−8.76467	+	2.81028i	−0.640936	+	0.205508i
$188$	−1.25264	+	1.05109i	−0.0913580	+	0.0766585i
$189$	−24.8462	−	4.32915i	−1.80730	−	0.314900i
$190$	0.969223	+	0.813275i	0.0703148	+	0.0590011i
$191$	−7.35828	−	3.00619i	−0.532427	−	0.217520i	0.0960108	−	0.995380i	$-0.469392\pi$
$191$	−7.35828	−	3.00619i	−0.532427	−	0.217520i	−0.628438	+	0.777860i	$0.716305\pi$
$192$	−8.65841	+	6.11325i	−0.624867	+	0.441186i
$193$	−2.15006	+	8.34703i	−0.154765	+	0.600833i	0.843231	+	0.537551i	$0.180650\pi$
$193$	−2.15006	+	8.34703i	−0.154765	+	0.600833i	−0.997996	+	0.0632816i	$0.979843\pi$
$194$	16.2954	−	18.6724i	1.16994	−	1.34060i
$195$	−1.38205	−	0.512102i	−0.0989703	−	0.0366724i
$196$	4.19897	−	4.11832i	0.299926	−	0.294165i
$197$	13.5993	−	8.94438i	0.968908	−	0.637261i	0.0367543	−	0.999324i	$-0.488298\pi$
$197$	13.5993	−	8.94438i	0.968908	−	0.637261i	0.932153	+	0.362064i	$0.117928\pi$
$198$	11.2701	−	1.18520i	0.800928	−	0.0842282i
$199$	−0.0235860	+	0.404956i	−0.00167197	+	0.0287066i	−0.999041	−	0.0437855i	$-0.986058\pi$
$199$	−0.0235860	+	0.404956i	−0.00167197	+	0.0287066i	0.997369	+	0.0724921i	$0.0230952\pi$
$200$	4.03167	−	11.7830i	0.285082	−	0.833185i
$201$	10.0332	+	11.6321i	0.707690	+	0.820462i
$202$	−7.61975	+	14.4657i	−0.536124	+	1.01781i
$203$	16.9984	+	26.9698i	1.19305	+	1.89291i
$204$	2.00782	+	1.12308i	0.140575	+	0.0786311i
$205$	−2.12041	+	0.416435i	−0.148096	+	0.0290851i
$206$	23.3580	+	15.3628i	1.62743	+	1.07038i
$207$	−16.5726	−	17.9784i	−1.15187	−	1.24958i
$208$	−13.5349	−	6.79749i	−0.938478	−	0.471321i
$209$	1.96533	+	7.62987i	0.135945	+	0.527769i
$210$	−3.12902	+	1.11840i	−0.215923	+	0.0771770i
$211$	−22.3244	−	4.38437i	−1.53688	−	0.301833i	−0.648596	−	0.761133i	$-0.724643\pi$
$211$	−22.3244	−	4.38437i	−1.53688	−	0.301833i	−0.888281	+	0.459300i	$0.848100\pi$
$212$	−0.130640	−	0.128131i	−0.00897239	−	0.00880005i
$213$	3.37143	+	7.15690i	0.231006	+	0.490383i
$214$	0.400862	+	2.93483i	0.0274023	+	0.200621i
$215$	−2.16482	+	0.787930i	−0.147639	+	0.0537364i
$216$	9.89971	+	8.60416i	0.673590	+	0.585439i
$217$	33.2699	+	12.1092i	2.25851	+	0.822029i
$218$	1.50819	−	6.96260i	0.102148	−	0.471567i
$219$	0.0291201	+	0.138298i	0.00196776	+	0.00934531i
$220$	0.183190	−	0.130937i	0.0123507	−	0.00882774i
$221$	0.239576	−	12.3525i	0.0161157	−	0.830919i
$222$	0.377200	−	0.0870950i	0.0253160	−	0.00584543i
$223$	15.5598	+	22.6867i	1.04196	+	1.51921i	0.842051	+	0.539398i	$0.181348\pi$
$223$	15.5598	+	22.6867i	1.04196	+	1.51921i	0.199907	+	0.979815i	$0.435936\pi$
$224$	−9.38345	+	2.22392i	−0.626958	+	0.148592i
$225$	−14.7422	−	1.31772i	−0.982815	−	0.0878482i
$226$	0.611819	+	2.04362i	0.0406976	+	0.135939i
$227$	−15.3549	−	2.40147i	−1.01914	−	0.159391i	−0.377190	−	0.926136i	$-0.623110\pi$
$227$	−15.3549	−	2.40147i	−1.01914	−	0.159391i	−0.641952	+	0.766745i	$0.721875\pi$
$228$	1.05968	−	1.65991i	0.0701789	−	0.109931i
$229$	−6.90799	+	2.82223i	−0.456493	+	0.186498i	−0.594770	−	0.803896i	$-0.702757\pi$
$229$	−6.90799	+	2.82223i	−0.456493	+	0.186498i	0.138277	+	0.990394i	$0.455843\pi$
$230$	−3.06772	−	0.983624i	−0.202279	−	0.0648583i
$231$	−19.9021	−	5.66446i	−1.30946	−	0.372694i
$232$	−0.321497	−	16.5763i	−0.0211073	−	1.08829i
$233$	8.24207	+	11.0710i	0.539956	+	0.725286i	0.985444	−	0.170001i	$-0.0543772\pi$
$233$	8.24207	+	11.0710i	0.539956	+	0.725286i	−0.445488	+	0.895288i	$0.646970\pi$
$234$	−3.39217	+	14.8282i	−0.221753	+	0.969350i
$235$	−1.17767	−	0.137650i	−0.0768229	−	0.00897931i
$236$	−1.91530	+	0.870609i	−0.124675	+	0.0566718i
$237$	0.828155	+	2.82566i	0.0537944	+	0.183546i
$238$	−17.4873	−	21.6808i	−1.13353	−	1.40536i
$239$	−25.5710	−	1.98753i	−1.65405	−	0.128563i	−0.783747	−	0.621080i	$-0.786694\pi$
$239$	−25.5710	−	1.98753i	−1.65405	−	0.128563i	−0.870303	+	0.492517i	$0.836077\pi$
$240$	2.00436	+	0.405708i	0.129381	+	0.0261883i
$241$	−12.0327	−	0.466925i	−0.775097	−	0.0300773i	−0.351808	−	0.936072i	$-0.614433\pi$
$241$	−12.0327	−	0.466925i	−0.775097	−	0.0300773i	−0.423289	+	0.905995i	$0.639124\pi$
$242$	−7.58369			−0.487498
$243$	7.12881	−	13.8629i	0.457313	−	0.889306i
$244$	−0.749649			−0.0479914
$245$	4.26147	+	0.165365i	0.272256	+	0.0105648i
$246$	7.09765	+	21.1424i	0.452530	+	1.34799i
$247$	−10.5441	−	0.819553i	−0.670906	−	0.0521469i
$248$	−11.5598	−	14.3319i	−0.734047	−	0.910076i
$249$	17.8228	+	4.33320i	1.12947	+	0.274605i
$250$	−3.57443	+	1.62478i	−0.226067	+	0.102760i
$251$	24.4098	+	2.85310i	1.54074	+	0.180086i	0.843647	−	0.536899i	$-0.180404\pi$
$251$	24.4098	+	2.85310i	1.54074	+	0.180086i	0.697089	+	0.716985i	$0.254478\pi$
$252$	2.35726	+	4.60363i	0.148494	+	0.290002i
$253$	−11.9799	−	16.0918i	−0.753168	−	1.01168i
$254$	0.0248701	+	1.28229i	0.00156049	+	0.0804583i
$255$	0.406748	+	1.61780i	0.0254715	+	0.101311i
$256$	7.87677	+	2.52558i	0.492298	+	0.157849i
$257$	−16.8810	+	6.89664i	−1.05301	+	0.430201i	−0.837577	−	0.546319i	$-0.816029\pi$
$257$	−16.8810	+	6.89664i	−1.05301	+	0.430201i	−0.215430	+	0.976519i	$0.569115\pi$
$258$	10.9588	+	21.1000i	0.682263	+	1.31363i
$259$	−0.698395	−	0.109227i	−0.0433962	−	0.00678704i
$260$	0.0866866	+	0.289554i	0.00537608	+	0.0179573i
$261$	−19.0425	+	5.06406i	−1.17870	+	0.313457i
$262$	−1.54822	+	0.366934i	−0.0956491	+	0.0226692i
$263$	3.30188	+	4.81425i	0.203602	+	0.296860i	0.913009	−	0.407940i	$-0.133753\pi$
$263$	3.30188	+	4.81425i	0.203602	+	0.296860i	−0.709406	+	0.704800i	$0.751037\pi$
$264$	7.33947	+	7.87015i	0.451713	+	0.484374i
$265$	0.00257293	−	0.132660i	0.000158054	−	0.00814921i
$266$	−19.3981	+	13.8649i	−1.18937	+	0.850113i
$267$	25.7394	+	8.41761i	1.57522	+	0.515149i
$268$	0.666908	−	3.07879i	0.0407379	−	0.188067i
$269$	−1.32469	−	0.482147i	−0.0807677	−	0.0293970i	0.301320	−	0.953523i	$-0.402573\pi$
$269$	−1.32469	−	0.482147i	−0.0807677	−	0.0293970i	−0.382088	+	0.924126i	$0.624795\pi$
$270$	−0.0837974	−	2.05212i	−0.00509975	−	0.124888i
$271$	−0.647129	+	0.235536i	−0.0393103	+	0.0143078i	−0.361600	−	0.932333i	$-0.617770\pi$
$271$	−0.647129	+	0.235536i	−0.0393103	+	0.0143078i	0.322290	+	0.946641i	$0.395547\pi$
$272$	2.31991	+	16.9847i	0.140665	+	1.02985i
$273$	15.8424	−	22.8145i	0.958826	−	1.38080i
$274$	2.28600	+	2.24210i	0.138102	+	0.135450i
$275$	−11.9160	−	2.34023i	−0.718563	−	0.141121i
$276$	−0.899299	+	4.93303i	−0.0541315	+	0.296933i
$277$	3.41157	+	13.2445i	0.204981	+	0.795787i	0.985361	+	0.170481i	$0.0545320\pi$
$277$	3.41157	+	13.2445i	0.204981	+	0.795787i	−0.780380	+	0.625306i	$0.784974\pi$
$278$	−13.1019	−	6.58002i	−0.785799	−	0.394643i
$279$	−13.2702	+	17.4007i	−0.794464	+	1.04175i
$280$	−2.63639	−	1.73398i	−0.157554	−	0.103625i
$281$	21.5268	−	4.22773i	1.28418	−	0.252205i	0.496365	−	0.868114i	$-0.334668\pi$
$281$	21.5268	−	4.22773i	1.28418	−	0.252205i	0.787818	+	0.615909i	$0.211211\pi$
$282$	0.166467	+	12.2359i	0.00991299	+	0.728639i
$283$	2.64732	+	4.20025i	0.157367	+	0.249679i	0.915408	−	0.402527i	$-0.131868\pi$
$283$	2.64732	+	4.20025i	0.157367	+	0.249679i	−0.758041	+	0.652207i	$0.773843\pi$
$284$	0.756100	−	1.43542i	0.0448663	−	0.0851766i
$285$	1.40276	−	0.267070i	0.0830926	−	0.0158199i
$286$	−4.04028	+	11.8082i	−0.238907	+	0.698231i
$287$	2.36785	−	40.6543i	0.139769	−	2.39975i
$288$	0.415432	−	5.94594i	0.0244796	−	0.350368i
$289$	2.52034	−	1.65766i	0.148256	−	0.0975092i
$290$	−1.85344	+	1.81784i	−0.108838	+	0.106747i
$291$	−4.69751	−	27.5733i	−0.275373	−	1.61638i
$292$	0.0190570	−	0.0218369i	0.00111523	−	0.00127791i
$293$	4.59130	−	17.8245i	0.268227	−	1.04132i	−0.682399	−	0.730980i	$-0.739063\pi$
$293$	4.59130	−	17.8245i	0.268227	−	1.04132i	0.950626	−	0.310340i	$-0.100443\pi$
$294$	−4.00739	−	43.8313i	−0.233716	−	2.55629i
$295$	−1.41222	−	0.576956i	−0.0822227	−	0.0335917i
$296$	0.281616	+	0.236304i	0.0163686	+	0.0137349i
$297$	7.00640	−	10.6999i	0.406552	−	0.620870i
$298$	−4.66649	+	3.91565i	−0.270322	+	0.226827i
$299$	25.6427	−	8.22200i	1.48295	−	0.475490i
$300$	1.60354	+	2.57713i	0.0925802	+	0.148791i
$301$	−4.20304	−	43.2111i	−0.242259	−	2.49065i
$302$	−19.0066	+	10.4874i	−1.09371	+	0.603481i
$303$	7.21056	+	16.9856i	0.414236	+	0.975800i
$304$	14.6300	−	1.13714i	0.839091	−	0.0652193i
$305$	−0.373022	−	0.395380i	−0.0213592	−	0.0226394i
$306$	16.0119	−	6.32628i	0.915339	−	0.361649i
$307$	20.6042	+	4.88327i	1.17594	+	0.278703i	0.771723	−	0.635959i	$-0.219395\pi$
$307$	20.6042	+	4.88327i	1.17594	+	0.278703i	0.404219	+	0.914662i	$0.367543\pi$
$308$	1.52840	+	3.95866i	0.0870889	+	0.225566i
$309$	30.1016	−	9.45990i	1.71242	−	0.538155i
$310$	−0.390187	+	2.85668i	−0.0221611	+	0.162248i
$311$	−1.05169	−	4.85513i	−0.0596357	−	0.275309i	0.937773	−	0.347248i	$-0.112884\pi$
$311$	−1.05169	−	4.85513i	−0.0596357	−	0.275309i	−0.997409	+	0.0719389i	$0.977081\pi$
$312$	−13.1846	+	5.90129i	−0.746431	+	0.334095i
$313$	3.85923	+	2.12943i	0.218136	+	0.120363i	0.588418	−	0.808557i	$-0.299751\pi$
$313$	3.85923	+	2.12943i	0.218136	+	0.120363i	−0.370281	+	0.928920i	$0.620739\pi$
$314$	3.42861	−	7.94841i	0.193488	−	0.448555i
$315$	−1.25509	+	3.53402i	−0.0707161	+	0.199119i
$316$	0.360589	−	0.484355i	0.0202847	−	0.0272471i
$317$	7.50858	+	5.36681i	0.421724	+	0.301430i	0.772483	−	0.635036i	$-0.219015\pi$
$317$	7.50858	+	5.36681i	0.421724	+	0.301430i	−0.350759	+	0.936466i	$0.614076\pi$
$318$	−1.36102	+	0.151100i	−0.0763224	+	0.00847327i
$319$	−15.9725	+	2.49805i	−0.894288	+	0.139864i
$320$	0.679894	+	1.42188i	0.0380072	+	0.0794854i
$321$	2.85217	+	1.74389i	0.159192	+	0.0973346i
$322$	32.3715	−	51.3609i	1.80399	−	2.86223i
$323$	5.98499	+	10.3663i	0.333014	+	0.576797i
$324$	−3.15027	+	0.543267i	−0.175015	+	0.0301815i
$325$	8.15023	−	14.1166i	0.452094	−	0.783049i
$326$	−7.62494	−	14.4756i	−0.422306	−	0.801729i
$327$	−5.01152	−	6.28745i	−0.277138	−	0.347697i
$328$	−11.9788	+	17.4655i	−0.661416	+	0.964368i
$329$	8.04808	−	20.8450i	0.443705	−	1.14922i
$330$	0.107715	−	1.68164i	0.00592952	−	0.0925713i
$331$	3.10459	−	31.9180i	0.170644	−	1.75437i	−0.384967	−	0.922930i	$-0.625787\pi$
$331$	3.10459	−	31.9180i	0.170644	−	1.75437i	0.555611	−	0.831442i	$-0.312484\pi$
$332$	−1.48983	−	3.45382i	−0.0817652	−	0.189553i
$333$	0.193030	−	0.391962i	0.0105780	−	0.0214794i
$334$	−0.641279	+	0.0749547i	−0.0350892	+	0.00410134i
$335$	1.95567	−	1.18025i	0.106850	−	0.0644841i
$336$	−16.8261	+	34.6717i	−0.917941	+	1.89150i
$337$	−20.7458	+	18.8258i	−1.13010	+	1.02551i	−0.130679	+	0.991425i	$0.541716\pi$
$337$	−20.7458	+	18.8258i	−1.13010	+	1.02551i	−0.999419	+	0.0340845i	$0.989148\pi$
$338$	2.52795	+	1.95931i	0.137502	+	0.106572i
$339$	2.22347	+	0.923444i	0.120762	+	0.0501546i
$340$	0.214770	−	0.266273i	0.0116475	−	0.0144407i
$341$	−12.3211	+	13.0596i	−0.667224	+	0.707216i
$342$	−4.60927	−	13.9981i	−0.249241	−	0.756931i
$343$	−13.3058	+	44.4445i	−0.718446	+	2.39978i
$344$	−9.74004	+	20.3696i	−0.525148	+	1.09825i
$345$	−3.04927	+	1.98034i	−0.164167	+	0.106618i
$346$	7.59813	+	4.58550i	0.408478	+	0.246518i
$347$	−8.55028	−	3.88658i	−0.459003	−	0.208643i	0.170944	−	0.985281i	$-0.445318\pi$
$347$	−8.55028	−	3.88658i	−0.459003	−	0.208643i	−0.629947	+	0.776638i	$0.716923\pi$
$348$	3.17946	+	2.49386i	0.170437	+	0.133685i
$349$	15.3705	+	13.9480i	0.822766	+	0.746620i	0.970162	−	0.242457i	$-0.0779535\pi$
$349$	15.3705	+	13.9480i	0.822766	+	0.746620i	−0.147396	+	0.989078i	$0.547089\pi$
$350$	−6.38155	−	36.1916i	−0.341108	−	1.93452i
$351$	10.5444	+	13.5479i	0.562820	+	0.723133i
$352$	0.849193	−	4.81601i	0.0452621	−	0.256694i
$353$	−23.4541	+	18.1783i	−1.24833	+	0.967532i	−0.999999	−	0.00114274i	$-0.999636\pi$
$353$	−23.4541	+	18.1783i	−1.24833	+	0.967532i	−0.248334	+	0.968674i	$0.579883\pi$
$354$	−4.01550	+	15.2238i	−0.213421	+	0.809133i
$355$	1.13330	−	0.315477i	0.0601495	−	0.0167438i
$356$	−1.79787	−	5.25447i	−0.0952869	−	0.278487i
$357$	−31.4364	−	0.181974i	−1.66379	−	0.00963108i
$358$	−9.77936	−	2.72227i	−0.516855	−	0.143876i
$359$	0.860696	+	14.7776i	0.0454258	+	0.779931i	0.941705	+	0.336440i	$0.109223\pi$
$359$	0.860696	+	14.7776i	0.0454258	+	0.779931i	−0.896279	+	0.443491i	$0.853740\pi$
$360$	1.50849	−	1.23629i	0.0795041	−	0.0651584i
$361$	−7.82243	+	3.92857i	−0.411707	+	0.206767i
$362$	10.8186	+	12.3967i	0.568613	+	0.651558i
$363$	−5.41197	+	6.63088i	−0.284055	+	0.348031i
$364$	−5.69174	+	0.220866i	−0.298328	+	0.0115765i
$365$	0.0209999		0.000814891i	0.00109918		4.26534e-5i
$366$	−3.54725	+	4.34617i	−0.185418	+	0.227178i
$367$	−3.60571	−	4.13168i	−0.188216	−	0.215672i	0.651571	−	0.758588i	$-0.274110\pi$
$367$	−3.60571	−	4.13168i	−0.188216	−	0.215672i	−0.839787	+	0.542916i	$0.817320\pi$
$368$	−33.3894	+	16.7688i	−1.74054	+	0.874133i
$369$	23.5512	+	8.88204i	1.22603	+	0.462381i
$370$	−0.00334711	−	0.0574676i	−0.000174008	−	0.00298760i
$371$	2.40889	+	0.670561i	0.125064	+	0.0348138i
$372$	4.48761	+	0.0259772i	0.232672	+	0.00134685i
$373$	−3.16866	−	9.26076i	−0.164067	−	0.479504i	0.833234	−	0.552920i	$-0.186486\pi$
$373$	−3.16866	−	9.26076i	−0.164067	−	0.479504i	−0.997301	+	0.0734160i	$0.976610\pi$
$374$	13.6079	−	3.78803i	0.703650	−	0.195874i
$375$	−1.13019	+	4.28483i	−0.0583628	+	0.221268i
$376$	−9.18487	+	7.11881i	−0.473674	+	0.367125i
$377$	3.76827	−	21.3709i	0.194076	−	1.10066i
$378$	37.8443	+	8.11733i	1.94650	+	0.417511i
$379$	0.900675	+	5.10798i	0.0462646	+	0.262380i	0.999163	−	0.0409108i	$-0.0130259\pi$
$379$	0.900675	+	5.10798i	0.0462646	+	0.262380i	−0.952898	+	0.303290i	$0.901915\pi$
$380$	−0.216858	−	0.196788i	−0.0111246	−	0.0100950i
$381$	1.13894	+	0.893343i	0.0583494	+	0.0457673i
$382$	11.1051	+	5.04790i	0.568187	+	0.258273i
$383$	1.61425	+	0.974203i	0.0824842	+	0.0497795i	0.557342	−	0.830283i	$-0.311821\pi$
$383$	1.61425	+	0.974203i	0.0824842	+	0.0497795i	−0.474857	+	0.880063i	$0.657500\pi$
$384$	19.4136	−	12.6082i	0.990697	−	0.643407i
$385$	−1.32735	+	2.77593i	−0.0676482	+	0.141474i
$386$	3.79385	−	12.6723i	0.193102	−	0.645004i
$387$	26.2696	+	5.47576i	1.33536	+	0.278349i
$388$	−3.93629	+	4.17222i	−0.199835	+	0.211812i
$389$	13.7165	−	17.0058i	0.695454	−	0.862228i	−0.300341	−	0.953832i	$-0.597101\pi$
$389$	13.7165	−	17.0058i	0.695454	−	0.862228i	0.995796	+	0.0916039i	$0.0291994\pi$
$390$	2.08891	+	0.867556i	0.105776	+	0.0439304i
$391$	−24.0897	−	18.6710i	−1.21827	−	0.944231i
$392$	30.9525	−	28.0879i	1.56334	−	1.41865i
$393$	−0.784026	+	1.61555i	−0.0395489	+	0.0814940i
$394$	−21.3869	+	12.9070i	−1.07746	+	0.650248i
$395$	0.434886	−	0.0508309i	0.0218815	−	0.00255758i
$396$	−2.61712	+	0.172963i	−0.131515	+	0.00869170i
$397$	−11.4834	−	26.6216i	−0.576336	−	1.33610i	−0.918114	−	0.396317i	$-0.870288\pi$
$397$	−11.4834	−	26.6216i	−0.576336	−	1.33610i	0.341777	−	0.939781i	$-0.388971\pi$
$398$	0.0602672	−	0.619601i	0.00302092	−	0.0310578i
$399$	−1.72019	+	26.8554i	−0.0861170	+	1.34445i
$400$	−8.14616	+	21.0991i	−0.407308	+	1.05495i
$401$	−20.2293	+	29.4950i	−1.01020	+	1.47291i	−0.133992	+	0.990982i	$0.542780\pi$
$401$	−20.2293	+	29.4950i	−1.01020	+	1.47291i	−0.876210	+	0.481929i	$0.839936\pi$
$402$	−14.6939	−	18.4349i	−0.732865	−	0.919451i
$403$	−11.2318	−	21.3230i	−0.559496	−	1.06218i
$404$	1.89208	−	3.27718i	0.0941346	−	0.163046i
$405$	−1.85409	−	1.39119i	−0.0921306	−	0.0691288i
$406$	−24.4623	−	42.3700i	−1.21404	−	2.10279i
$407$	0.191139	−	0.303263i	0.00947440	−	0.0150322i
$408$	13.9484	+	8.52846i	0.690551	+	0.422222i
$409$	9.23741	+	19.3184i	0.456761	+	0.955234i	0.993748	+	0.111644i	$0.0356116\pi$
$409$	9.23741	+	19.3184i	0.456761	+	0.955234i	−0.536988	+	0.843590i	$0.680438\pi$
$410$	3.27646	−	0.512428i	0.161813	−	0.0253070i
$411$	3.59177	−	0.398756i	0.177169	−	0.0196692i
$412$	−5.26424	−	3.76266i	−0.259351	−	0.185373i
$413$	17.1678	−	23.0604i	0.844773	−	1.13473i
$414$	24.3444	+	28.5563i	1.19646	+	1.40346i
$415$	1.08028	−	2.50438i	0.0530290	−	0.122935i
$416$	5.74741	+	3.17129i	0.281790	+	0.155485i
$417$	−15.1032	+	6.76005i	−0.739609	+	0.331041i
$418$	−2.55982	−	11.8174i	−0.125205	−	0.578010i
$419$	3.54436	−	25.9493i	0.173153	−	1.26771i	−0.674945	−	0.737868i	$-0.735833\pi$
$419$	3.54436	−	25.9493i	0.173153	−	1.26771i	0.848098	−	0.529839i	$-0.177748\pi$
$420$	0.733701	−	0.230577i	0.0358009	−	0.0112510i
$421$	−10.0097	−	25.9258i	−0.487843	−	1.26354i	−0.930315	−	0.366762i	$-0.880466\pi$
$421$	−10.0097	−	25.9258i	−0.487843	−	1.26354i	0.442472	−	0.896782i	$-0.354102\pi$
$422$	33.9738	+	8.05195i	1.65382	+	0.391963i
$423$	10.8174	+	8.58641i	0.525960	+	0.417486i
$424$	−0.892393	−	0.945881i	−0.0433384	−	0.0459360i
$425$	−18.3937	+	1.42967i	−0.892223	+	0.0693491i
$426$	−4.74423	−	11.1758i	−0.229859	−	0.541470i
$427$	8.96906	−	4.94892i	0.434043	−	0.239495i
$428$	−0.0663706	−	0.682350i	−0.00320815	−	0.0329826i
$429$	7.44131	+	11.9594i	0.359270	+	0.577403i
$430$	3.36666	−	1.07948i	0.162355	−	0.0520570i
$431$	6.80566	−	5.71062i	0.327817	−	0.275071i	−0.463993	−	0.885839i	$-0.653584\pi$
$431$	6.80566	−	5.71062i	0.327817	−	0.275071i	0.791810	+	0.610768i	$0.209139\pi$
$432$	−17.3594	−	16.3114i	−0.835204	−	0.784781i
$433$	17.4935	+	14.6788i	0.840682	+	0.705416i	0.957717	−	0.287712i	$-0.0928946\pi$
$433$	17.4935	+	14.6788i	0.840682	+	0.705416i	−0.117035	+	0.993128i	$0.537339\pi$
$434$	−50.2991	−	20.5495i	−2.41443	−	0.986405i
$435$	0.266772	+	2.91785i	0.0127907	+	0.139900i
$436$	−0.411293	+	1.59674i	−0.0196974	+	0.0764699i
$437$	−17.1546	+	19.6570i	−0.820616	+	0.940321i
$438$	−0.0364263	−	0.213814i	−0.00174052	−	0.0102164i
$439$	−1.75819	+	1.72442i	−0.0839140	+	0.0823023i	−0.740964	−	0.671545i	$-0.765631\pi$
$439$	−1.75819	+	1.72442i	−0.0839140	+	0.0823023i	0.657050	+	0.753847i	$0.271804\pi$
$440$	1.33695	−	0.879327i	0.0637367	−	0.0419203i
$441$	−41.1842	−	27.7756i	−1.96115	−	1.32265i
$442$	−1.10246	+	18.9284i	−0.0524385	+	0.900334i
$443$	3.14573	−	9.19374i	0.149458	−	0.436808i	−0.845867	−	0.533395i	$-0.820916\pi$
$443$	3.14573	−	9.19374i	0.149458	−	0.436808i	0.995325	+	0.0965871i	$0.0307926\pi$
$444$	−0.0880185	+	0.0167577i	−0.00417717	+	0.000795286i
$445$	1.87671	−	3.56284i	0.0889644	−	0.168895i
$446$	−22.5110	−	35.7162i	−1.06593	−	1.69121i
$447$	0.0935267	+	6.87453i	0.00442366	+	0.325154i
$448$	−29.1448	+	5.72385i	−1.37696	+	0.270427i
$449$	15.5258	+	10.2115i	0.732706	+	0.481909i	0.860217	−	0.509929i	$-0.170328\pi$
$449$	15.5258	+	10.2115i	0.732706	+	0.481909i	−0.127510	+	0.991837i	$0.540699\pi$
$450$	22.5289	+	2.89801i	1.06202	+	0.136614i
$451$	18.4547	+	9.26832i	0.869000	+	0.436428i
$452$	−0.123158	−	0.478129i	−0.00579286	−	0.0224893i
$453$	−4.39397	+	24.1028i	−0.206447	+	1.13245i
$454$	23.4040	+	4.59640i	1.09841	+	0.215720i
$455$	−2.94868	−	2.89204i	−0.138236	−	0.135581i
$456$	7.98239	−	11.4954i	0.373810	−	0.538321i
$457$	−0.223092	−	1.63332i	−0.0104358	−	0.0764036i	0.984846	−	0.173432i	$-0.0554858\pi$
$457$	−0.223092	−	1.63332i	−0.0104358	−	0.0764036i	−0.995282	+	0.0970289i	$0.969066\pi$
$458$	10.7614	−	3.91684i	0.502848	−	0.183022i
$459$	5.89518	−	18.5148i	0.275163	−	0.864197i
$460$	0.700659	+	0.255019i	0.0326684	+	0.0118903i
$461$	3.63862	−	16.7977i	0.169467	−	0.782348i	−0.810903	−	0.585181i	$-0.801023\pi$
$461$	3.63862	−	16.7977i	0.169467	−	0.782348i	0.980370	−	0.197167i	$-0.0631740\pi$
$462$	30.1830	+	9.87082i	1.40424	+	0.459232i
$463$	10.8692	−	7.76882i	0.505134	−	0.361048i	−0.300194	−	0.953878i	$-0.597051\pi$
$463$	10.8692	−	7.76882i	0.505134	−	0.361048i	0.805327	+	0.592831i	$0.201990\pi$
$464$	−0.583868	+	30.1041i	−0.0271054	+	1.39755i
$465$	2.21931	+	2.37978i	0.102918	+	0.110360i
$466$	−11.9805	−	17.4680i	−0.554986	−	0.809189i
$467$	−11.0340	+	2.61511i	−0.510594	+	0.121013i	−0.477834	−	0.878450i	$-0.658578\pi$
$467$	−11.0340	+	2.61511i	−0.510594	+	0.121013i	−0.0327600	+	0.999463i	$0.510430\pi$
$468$	0.917601	−	3.39895i	0.0424161	−	0.157117i
$469$	12.3460	+	41.2384i	0.570084	+	1.90421i
$470$	1.79778	+	0.281168i	0.0829256	+	0.0129693i
$471$	−4.50300	−	8.67009i	−0.207487	−	0.399497i
$472$	−13.8408	+	5.65459i	−0.637075	+	0.260274i
$473$	20.9651	+	6.72218i	0.963975	+	0.309086i
$474$	−1.10184	−	4.38246i	−0.0506091	−	0.201293i
$475$	0.306242	+	15.7898i	0.0140513	+	0.724484i
$476$	3.84980	+	5.17117i	0.176455	+	0.237020i
$477$	−0.839156	+	1.29786i	−0.0384223	+	0.0594247i
$478$	39.0951	+	4.56956i	1.78817	+	0.209007i
$479$	2.38925	−	1.08605i	0.109168	−	0.0496228i	−0.358482	−	0.933536i	$-0.616706\pi$
$479$	2.38925	−	1.08605i	0.109168	−	0.0496228i	0.467650	+	0.883914i	$0.345101\pi$
$480$	−0.861223	−	0.209386i	−0.0393093	−	0.00955712i
$481$	0.302090	+	0.374533i	0.0137741	+	0.0170772i
$482$	18.4245	+	1.43207i	0.839215	+	0.0652289i
$483$	−21.8066	−	64.9573i	−0.992233	−	2.95566i
$484$	1.75392	+	0.0680600i	0.0797235	+	0.00309364i
$485$	−4.15920			−0.188859
$486$	−11.7570	+	20.8347i	−0.533310	+	0.945081i
$487$	−36.5440			−1.65597			−0.827983	−	0.560753i	$-0.810512\pi$
$487$	−36.5440			−1.65597			−0.827983	+	0.560753i	$0.810512\pi$
$488$	−5.32341	−	0.206573i	−0.240979	−	0.00935110i
$489$	−18.0983	−	3.66332i	−0.818433	−	0.165661i
$490$	−6.52517	−	0.507177i	−0.294777	−	0.0229119i
$491$	10.0038	+	12.4028i	0.451466	+	0.559730i	0.952044	−	0.305962i	$-0.0989779\pi$
$491$	10.0038	+	12.4028i	0.451466	+	0.559730i	−0.500578	+	0.865691i	$0.666879\pi$
$492$	−1.45177	−	4.95341i	−0.0654506	−	0.223317i
$493$	−22.3595	+	10.1636i	−1.00702	+	0.457747i
$494$	16.1207	+	1.88424i	0.725306	+	0.0847761i
$495$	−1.39349	−	1.29426i	−0.0626328	−	0.0581725i
$496$	19.9686	+	26.8225i	0.896619	+	1.20437i
$497$	0.429897	+	22.1654i	0.0192835	+	0.994253i
$498$	−27.0736	−	7.70559i	−1.21320	−	0.345296i
$499$	23.3422	+	7.48436i	1.04494	+	0.335046i	0.777734	−	0.628594i	$-0.216369\pi$
$499$	23.3422	+	7.48436i	1.04494	+	0.335046i	0.267205	+	0.963640i	$0.413900\pi$
$500$	0.841257	−	0.343691i	0.0376222	−	0.0153703i
$501$	−0.392100	+	0.614199i	−0.0175178	+	0.0274404i
$502$	−37.2630	−	5.82782i	−1.66313	−	0.260108i
$503$	0.427783	+	1.42890i	0.0190739	+	0.0637113i	0.966997	−	0.254789i	$-0.0820060\pi$
$503$	0.427783	+	1.42890i	0.0190739	+	0.0637113i	−0.947923	+	0.318500i	$0.896821\pi$
$504$	15.4708	+	33.3409i	0.689126	+	1.48512i
$505$	2.66994	−	0.632788i	0.118811	−	0.0281587i
$506$	17.4137	+	25.3898i	0.774133	+	1.12871i
$507$	3.51718	−	0.812112i	0.156203	−	0.0360672i
$508$	0.00575615	−	0.296786i	0.000255388	−	0.0131677i
$509$	−11.9952	+	8.57366i	−0.531679	+	0.380021i	−0.815411	−	0.578883i	$-0.803489\pi$
$509$	−11.9952	+	8.57366i	−0.531679	+	0.380021i	0.283732	+	0.958903i	$0.408427\pi$
$510$	−0.527481	−	2.50512i	−0.0233573	−	0.110929i
$511$	−0.0838449	+	0.387071i	−0.00370908	+	0.0171230i
$512$	13.1888	+	4.80033i	0.582868	+	0.212147i
$513$	−15.5287	−	5.95936i	−0.685610	−	0.263112i
$514$	26.2976	−	9.57154i	1.15994	−	0.422182i
$515$	−0.634963	−	4.64875i	−0.0279798	−	0.204848i
$516$	−2.34513	−	4.97826i	−0.103238	−	0.219155i
$517$	8.08979	+	7.93441i	0.355789	+	0.348955i
$518$	1.06450	+	0.209060i	0.0467713	+	0.00918558i
$519$	9.43166	−	3.37114i	0.414004	−	0.147977i
$520$	0.535790	+	2.08006i	0.0234959	+	0.0912169i
$521$	−1.97203	−	0.990393i	−0.0863964	−	0.0433899i	0.405076	−	0.914283i	$-0.367245\pi$
$521$	−1.97203	−	0.990393i	−0.0863964	−	0.0433899i	−0.491473	+	0.870893i	$0.663541\pi$
$522$	29.5032	−	6.63262i	1.29132	−	0.290302i
$523$	14.0792	+	9.26003i	0.615640	+	0.404913i	0.818674	−	0.574259i	$-0.194710\pi$
$523$	14.0792	+	9.26003i	0.615640	+	0.404913i	−0.203034	+	0.979172i	$0.565080\pi$
$524$	0.361357	−	0.0709681i	0.0157859	−	0.00310026i
$525$	−36.1986	−	20.2477i	−1.57984	−	0.883684i
$526$	−4.77698	−	7.57920i	−0.208286	−	0.330469i
$527$	−12.7123	+	24.1338i	−0.553758	+	1.05128i
$528$	−12.7649	−	14.7990i	−0.555522	−	0.644046i
$529$	14.0599	−	41.0915i	0.611299	−	1.78659i
$530$	−0.0118398	+	0.203282i	−0.000514288	+	0.00882999i
$531$	10.4455	+	14.3752i	0.453294	+	0.623829i
$532$	4.61073	−	3.03252i	0.199900	−	0.131477i
$533$	−19.7904	+	19.4103i	−0.857219	+	0.840754i
$534$	−38.9707	−	14.4402i	−1.68643	−	0.624887i
$535$	0.326860	−	0.374540i	0.0141314	−	0.0161928i
$536$	5.58424	−	21.6793i	0.241202	−	0.936405i
$537$	−9.35912	+	6.60798i	−0.403876	+	0.285155i
$538$	2.00273	+	0.818206i	0.0863439	+	0.0352754i
$539$	−31.2213	−	26.1978i	−1.34480	−	1.12842i
$540$	0.000963456		0.475356i	4.14605e−5		0.0204561i
$541$	−0.419795	+	0.352250i	−0.0180484	+	0.0151444i	−0.651767	−	0.758419i	$-0.725972\pi$
$541$	−0.419795	+	0.352250i	−0.0180484	+	0.0151444i	0.633719	+	0.773563i	$0.281528\pi$
$542$	1.00639	−	0.322687i	0.0432284	−	0.0138606i
$543$	18.5597	−	0.612629i	0.796475	−	0.0262904i
$544$	−0.719262	−	7.39466i	−0.0308381	−	0.317043i
$545$	−1.04681	+	0.577606i	−0.0448405	+	0.0247419i
$546$	−25.6521	+	34.0436i	−1.09781	+	1.45693i
$547$	46.4618	−	3.61130i	1.98656	−	0.154408i	0.986601	−	0.163154i	$-0.0521667\pi$
$547$	46.4618	−	3.61130i	1.98656	−	0.154408i	0.999962	+	0.00874599i	$0.00278397\pi$
$548$	−0.508573	−	0.539056i	−0.0217252	−	0.0230273i
$549$	1.26869	+	6.20314i	0.0541462	+	0.264744i
$550$	18.1341	+	4.29786i	0.773240	+	0.183261i
$551$	7.57261	+	19.6135i	0.322604	+	0.835565i
$552$	−7.74544	+	34.7826i	−0.329668	+	1.48045i
$553$	−1.11667	+	8.17547i	−0.0474856	+	0.347656i
$554$	−4.44354	−	20.5136i	−0.188788	−	0.871541i
$555$	−0.0526360	−	0.0380842i	−0.00223427	−	0.00161658i
$556$	2.97109	+	1.63938i	0.126002	+	0.0695250i
$557$	14.8687	−	34.4696i	0.630009	−	1.46052i	−0.241626	−	0.970369i	$-0.577681\pi$
$557$	14.8687	−	34.4696i	0.630009	−	1.46052i	0.871635	−	0.490155i	$-0.163060\pi$
$558$	21.3854	−	25.8945i	0.905317	−	1.09620i
$559$	−17.6477	+	23.7049i	−0.746417	+	1.00261i
$560$	4.66222	+	3.33236i	0.197015	+	0.140818i
$561$	6.39898	−	14.6015i	0.270165	−	0.616477i
$562$	−33.2632	+	5.20227i	−1.40312	+	0.219445i
$563$	6.20030	+	12.9668i	0.261311	+	0.546486i	0.990449	−	0.137881i	$-0.0440291\pi$
$563$	6.20030	+	12.9668i	0.261311	+	0.546486i	−0.729137	+	0.684367i	$0.760079\pi$
$564$	0.0713118	−	2.83136i	0.00300277	−	0.119222i
$565$	0.190892	−	0.302871i	0.00803089	−	0.0127419i
$566$	−3.80974	−	6.59867i	−0.160135	−	0.277363i
$567$	34.1045	−	27.2968i	1.43225	−	1.14636i
$568$	5.76476	−	9.98486i	0.241884	−	0.418956i
$569$	13.8758	+	26.3425i	0.581703	+	1.10434i	0.982165	+	0.188023i	$0.0602079\pi$
$569$	13.8758	+	26.3425i	0.581703	+	1.10434i	−0.400461	+	0.916314i	$0.631150\pi$
$570$	−2.16705	+	0.326081i	−0.0907676	+	0.0136580i
$571$	−3.16268	+	4.61130i	−0.132354	+	0.192977i	−0.885188	−	0.465234i	$-0.845970\pi$
$571$	−3.16268	+	4.61130i	−0.132354	+	0.192977i	0.752834	+	0.658211i	$0.228686\pi$
$572$	1.04039	−	2.69467i	0.0435008	−	0.112670i
$573$	12.3387	−	6.10753i	0.515455	−	0.255146i
$574$	−6.05034	+	62.2030i	−0.252536	+	2.59630i
$575$	−15.9271	−	36.9231i	−0.664204	−	1.53980i
$576$	1.98868	−	18.2501i	0.0828615	−	0.760420i
$577$	−14.6304	+	1.71005i	−0.609072	+	0.0711904i	−0.415038	−	0.909804i	$-0.636232\pi$
$577$	−14.6304	+	1.71005i	−0.609072	+	0.0711904i	−0.194035	+	0.980995i	$0.562157\pi$
$578$	−3.96362	+	2.39206i	−0.164865	+	0.0994964i
$579$	−8.37277	−	12.3606i	−0.347960	−	0.513688i
$580$	0.444969	−	0.403788i	0.0184763	−	0.0167664i
$581$	40.6258	+	31.4873i	1.68544	+	1.30632i
$582$	5.56287	+	42.5635i	0.230588	+	1.76431i
$583$	−0.796087	+	0.986993i	−0.0329705	+	0.0408771i
$584$	0.141345	−	0.149817i	0.00584889	−	0.00619946i
$585$	2.24927	−	1.20734i	0.0929959	−	0.0499174i
$586$	−8.10150	+	27.0609i	−0.334670	+	1.11787i
$587$	6.66370	−	13.9359i	0.275040	−	0.575198i	−0.717578	−	0.696478i	$-0.754749\pi$
$587$	6.66370	−	13.9359i	0.275040	−	0.575198i	0.992618	+	0.121280i	$0.0386999\pi$
$588$	0.533445	+	10.1731i	0.0219989	+	0.419530i
$589$	19.9912	+	12.0647i	0.823722	+	0.497119i
$590$	2.13132	+	0.968805i	0.0877452	+	0.0398851i
$591$	−3.97698	+	27.9107i	−0.163591	+	1.14809i
$592$	−0.494417	−	0.448659i	−0.0203204	−	0.0184398i
$593$	4.12932	+	23.4185i	0.169571	+	0.961684i	0.944226	+	0.329300i	$0.106813\pi$
$593$	4.12932	+	23.4185i	0.169571	+	0.961684i	−0.774655	+	0.632384i	$0.782076\pi$
$594$	−11.3811	+	15.9915i	−0.466972	+	0.656137i
$595$	−0.811741	+	4.60361i	−0.0332782	+	0.188730i
$596$	1.11438	−	0.863712i	0.0456469	−	0.0353790i
$597$	−0.498746	−	0.494863i	−0.0204123	−	0.0202534i
$598$	−39.8126	+	11.0826i	−1.62806	+	0.453201i
$599$	−13.1557	−	38.4490i	−0.537527	−	1.57098i	−0.796210	−	0.605020i	$-0.793165\pi$
$599$	−13.1557	−	38.4490i	−0.537527	−	1.57098i	0.258683	−	0.965962i	$-0.416712\pi$
$600$	10.6769	+	18.7426i	0.435882	+	0.765164i
$601$	29.0036	+	8.07371i	1.18308	+	0.329334i	0.803205	−	0.595703i	$-0.203127\pi$
$601$	29.0036	+	8.07371i	1.18308	+	0.329334i	0.379878	+	0.925037i	$0.375966\pi$
$602$	3.87404	+	66.5148i	0.157894	+	2.71094i
$603$	−26.6048	−	0.308022i	−1.08343	−	0.0125436i
$604$	4.48987	−	2.25490i	0.182690	−	0.0917504i
$605$	0.836845	+	0.958918i	0.0340226	+	0.0389856i
$606$	−10.0467	−	26.4767i	−0.408120	−	1.07554i
$607$	−26.6942	+	1.03585i	−1.08348	+	0.0420440i	−0.574323	−	0.818629i	$-0.694735\pi$
$607$	−26.6942	+	1.03585i	−1.08348	+	0.0420440i	−0.509159	+	0.860673i	$0.670043\pi$
$608$	−6.35503	+	0.246604i	−0.257730	+	0.0100011i
$609$	−54.5037	−	8.84774i	−2.20860	−	0.358529i
$610$	0.548506	+	0.628518i	0.0222083	+	0.0254479i
$611$	−13.5923	+	6.82629i	−0.549884	+	0.276162i
$612$	−3.75993	+	1.31941i	−0.151986	+	0.0533340i
$613$	−0.879467	−	15.0999i	−0.0355213	−	0.609878i	−0.968356	−	0.249573i	$-0.919710\pi$
$613$	−0.879467	−	15.0999i	−0.0355213	−	0.609878i	0.932835	−	0.360305i	$-0.117327\pi$
$614$	−31.3061	−	8.71465i	−1.26341	−	0.351695i
$615$	1.89014	−	3.23049i	0.0762178	−	0.130266i
$616$	9.76265	+	28.5324i	0.393348	+	1.14960i
$617$	0.0560813	−	0.0156113i	0.00225775	−	0.000628487i	−0.267044	−	0.963684i	$-0.586047\pi$
$617$	0.0560813	−	0.0156113i	0.00225775	−	0.000628487i	0.269301	+	0.963056i	$0.413207\pi$
$618$	−46.7241	+	12.7156i	−1.87952	+	0.511496i
$619$	−23.8497	+	18.4849i	−0.958601	+	0.742972i	−0.966412	−	0.256998i	$-0.917267\pi$
$619$	−23.8497	+	18.4849i	−0.958601	+	0.742972i	0.00781093	+	0.999969i	$0.497514\pi$
$620$	0.115878	−	0.657176i	0.00465377	−	0.0263928i
$621$	42.3414	−	0.907065i	1.69910	−	0.0363992i
$622$	1.32386	+	7.50798i	0.0530819	+	0.301043i
$623$	56.1985	+	50.9974i	2.25154	+	2.04317i
$624$	24.3421	−	9.78079i	0.974462	−	0.391545i
$625$	−21.8573	−	9.93534i	−0.874290	−	0.397414i
$626$	−5.79145	−	3.49516i	−0.231473	−	0.139695i
$627$	−12.1595	−	6.19511i	−0.485603	−	0.247409i
$628$	−0.864285	+	1.80750i	−0.0344887	+	0.0721270i
$629$	0.156195	−	0.521727i	0.00622789	−	0.0208026i
$630$	2.13499	−	5.34477i	0.0850600	−	0.212941i
$631$	8.39067	−	8.89359i	0.334027	−	0.354048i	−0.538490	−	0.842632i	$-0.681005\pi$
$631$	8.39067	−	8.89359i	0.334027	−	0.354048i	0.872517	+	0.488584i	$0.162486\pi$
$632$	2.69408	−	3.34014i	0.107165	−	0.132864i
$633$	31.2852	−	23.9593i	1.24347	−	0.952295i
$634$	−11.1951	−	8.67687i	−0.444615	−	0.344603i
$635$	0.159395	−	0.144643i	0.00632541	−	0.00574000i
$636$	0.316127	−	0.0227311i	0.0125352	−	0.000901348i
$637$	46.8389	−	28.2674i	1.85582	−	1.12000i
$638$	24.6427	−	2.88031i	0.975612	−	0.114033i
$639$	−13.1573	−	3.82726i	−0.520496	−	0.151404i
$640$	−1.36337	−	3.16065i	−0.0538919	−	0.124936i
$641$	−4.44842	+	45.7337i	−0.175702	+	1.80637i	0.330336	+	0.943863i	$0.392838\pi$
$641$	−4.44842	+	45.7337i	−0.175702	+	1.80637i	−0.506038	+	0.862511i	$0.668891\pi$
$642$	−4.27005	−	2.84400i	−0.168526	−	0.112244i
$643$	11.1525	−	28.8857i	0.439811	−	1.13914i	−0.518920	−	0.854823i	$-0.673666\pi$
$643$	11.1525	−	28.8857i	0.439811	−	1.13914i	0.958731	−	0.284316i	$-0.0917665\pi$
$644$	−7.94767	+	11.5880i	−0.313182	+	0.456630i
$645$	1.45871	−	3.71403i	0.0574367	−	0.146240i
$646$	−8.56118	−	16.2530i	−0.336835	−	0.639466i
$647$	19.7219	−	34.1594i	0.775349	−	1.34294i	−0.159249	−	0.987238i	$-0.550907\pi$
$647$	19.7219	−	34.1594i	0.775349	−	1.34294i	0.934598	−	0.355705i	$-0.115759\pi$
$648$	−22.5204	+	2.98976i	−0.884685	+	0.117449i
$649$	7.28957	+	12.6259i	0.286141	+	0.495610i
$650$	−13.3385	+	21.1630i	−0.523180	+	0.830081i
$651$	−53.8628	+	29.3148i	−2.11105	+	1.14894i
$652$	1.63355	+	3.41627i	0.0639746	+	0.133792i
$653$	−13.6379	+	2.13293i	−0.533693	+	0.0834680i	−0.415623	−	0.909537i	$-0.636436\pi$
$653$	−13.6379	+	2.13293i	−0.533693	+	0.0834680i	−0.118070	+	0.993005i	$0.537671\pi$
$654$	7.31108	+	9.94009i	0.285886	+	0.388688i
$655$	0.217240	+	0.155274i	0.00848825	+	0.00606704i
$656$	22.9681	−	30.8515i	0.896754	−	1.20455i
$657$	−0.212946	−	0.120735i	−0.00830780	−	0.00471033i
$658$	−13.5822	+	31.4872i	−0.529491	+	1.22750i
$659$	−30.2961	−	16.7167i	−1.18017	−	0.651190i	−0.233174	−	0.972435i	$-0.574911\pi$
$659$	−30.2961	−	16.7167i	−1.18017	−	0.651190i	−0.946996	+	0.321245i	$0.895899\pi$
$660$	−0.0400037	+	0.387955i	−0.00155714	+	0.0151011i
$661$	4.61618	+	21.3106i	0.179548	+	0.828888i	0.974883	+	0.222717i	$0.0714927\pi$
$661$	4.61618	+	21.3106i	0.179548	+	0.828888i	−0.795335	+	0.606171i	$0.792705\pi$
$662$	−6.66028	+	48.7619i	−0.258859	+	1.89518i
$663$	15.7635	+	14.4719i	0.612205	+	0.562042i
$664$	−9.62787	−	24.9368i	−0.373634	−	0.967736i
$665$	3.89369	+	0.922822i	0.150991	+	0.0357855i
$666$	−0.319338	+	0.589592i	−0.0123741	+	0.0228462i
$667$	−36.7368	−	38.9387i	−1.42245	−	1.50771i
$668$	0.148984	−	0.0115800i	0.00576438	−	0.000448043i
$669$	−47.2935	−	5.80550i	−1.82847	−	0.224454i
$670$	−3.06927	+	1.69355i	−0.118576	+	0.0654277i
$671$	0.502913	+	5.17039i	0.0194147	+	0.199601i
$672$	7.86966	−	14.7327i	0.303579	−	0.568327i
$673$	−1.79599	+	0.575862i	−0.0692304	+	0.0221978i	−0.339739	−	0.940520i	$-0.610339\pi$
$673$	−1.79599	+	0.575862i	−0.0692304	+	0.0221978i	0.270509	+	0.962717i	$0.412808\pi$
$674$	32.9342	−	27.6351i	1.26858	−	1.06446i
$675$	18.6113	−	17.6303i	0.716350	−	0.678591i
$676$	−0.567068	−	0.475827i	−0.0218103	−	0.0183010i
$677$	−13.7723	−	5.62659i	−0.529311	−	0.216247i	0.0977591	−	0.995210i	$-0.468833\pi$
$677$	−13.7723	−	5.62659i	−0.529311	−	0.216247i	−0.627070	+	0.778963i	$0.715746\pi$
$678$	−3.35477	−	1.54842i	−0.128839	−	0.0594668i
$679$	19.5516	−	75.9038i	0.750320	−	2.91292i
$680$	1.59850	−	1.83168i	0.0612996	−	0.0702416i
$681$	20.7208	−	17.1834i	0.794024	−	0.658470i
$682$	19.6717	−	19.2938i	0.753267	−	0.738799i
$683$	−16.5246	+	10.8684i	−0.632297	+	0.415868i	−0.824797	−	0.565429i	$-0.808711\pi$
$683$	−16.5246	+	10.8684i	−0.632297	+	0.415868i	0.192500	+	0.981297i	$0.438340\pi$
$684$	0.940382	+	3.27878i	0.0359564	+	0.125367i
$685$	0.0312455	−	0.536464i	0.00119383	−	0.0204972i
$686$	23.0494	−	67.3643i	0.880028	−	2.57198i
$687$	4.25498	−	12.2046i	0.162338	−	0.465633i
$688$	19.1100	−	36.2794i	0.728561	−	1.38314i
$689$	−0.907560	−	1.43994i	−0.0345753	−	0.0548574i
$690$	4.79393	−	2.85543i	0.182502	−	0.108704i
$691$	15.0021	−	2.94631i	0.570706	−	0.112083i	0.100969	−	0.994890i	$-0.467806\pi$
$691$	15.0021	−	2.94631i	0.570706	−	0.112083i	0.469737	+	0.882807i	$0.344349\pi$
$692$	−1.71611	−	1.12870i	−0.0652366	−	0.0429068i
$693$	30.1702	−	19.3467i	1.14607	−	0.734919i
$694$	12.8807	+	6.46892i	0.488944	+	0.245557i
$695$	0.613759	+	2.38276i	0.0232812	+	0.0903832i
$696$	21.8908	+	18.5855i	0.829768	+	0.704483i
$697$	30.7863	+	6.04623i	1.16611	+	0.229017i
$698$	−22.7409	−	22.3041i	−0.860755	−	0.844222i
$699$	−23.8230	−	1.99047i	−0.901069	−	0.0752864i
$700$	1.15109	+	8.42748i	0.0435072	+	0.318529i
$701$	−31.4104	+	11.4324i	−1.18635	+	0.431798i	−0.858442	−	0.512911i	$-0.828567\pi$
$701$	−31.4104	+	11.4324i	−1.18635	+	0.431798i	−0.327912	+	0.944708i	$0.606345\pi$
$702$	−15.3638	−	21.4033i	−0.579869	−	0.807815i
$703$	−0.438076	−	0.159447i	−0.0165223	−	0.00601364i
$704$	3.18871	−	14.7207i	0.120179	−	0.554808i
$705$	1.52880	−	1.37126i	0.0575780	−	0.0516446i
$706$	37.0488	−	26.4809i	1.39435	−	0.996621i
$707$	−1.00272	+	51.7001i	−0.0377113	+	1.94438i
$708$	1.06531	−	3.48484i	0.0400368	−	0.130968i
$709$	−0.189853	−	0.276812i	−0.00713008	−	0.0103959i	0.821094	−	0.570794i	$-0.193364\pi$
$709$	−0.189853	−	0.276812i	−0.00713008	−	0.0103959i	−0.828224	+	0.560398i	$0.810648\pi$
$710$	−1.75671	+	0.416347i	−0.0659280	+	0.0156252i
$711$	−4.61816	−	2.16407i	−0.173194	−	0.0811589i
$712$	−11.3191	−	37.8085i	−0.424202	−	1.41693i
$713$	−58.7392	−	9.18665i	−2.19980	−	0.344043i
$714$	48.1972	+	2.14975i	1.80373	+	0.0804523i
$715$	1.93892	−	0.792136i	0.0725115	−	0.0296242i
$716$	2.23729	+	0.717358i	0.0836114	+	0.0268089i
$717$	31.8950	−	30.9222i	1.19114	−	1.15481i
$718$	−0.440514	−	22.7128i	−0.0164398	−	0.847634i
$719$	−14.0265	−	18.8408i	−0.523099	−	0.702644i	0.459543	−	0.888156i	$-0.348013\pi$
$719$	−14.0265	−	18.8408i	−0.523099	−	0.702644i	−0.982642	+	0.185511i	$0.940606\pi$
$720$	−2.82455	+	2.13731i	−0.105265	+	0.0796530i
$721$	87.8229	+	10.2650i	3.27070	+	0.382289i
$722$	12.2296	−	5.55902i	0.455137	−	0.206885i
$723$	14.4005	−	15.0877i	0.535561	−	0.561118i
$724$	−2.39082	−	2.96415i	−0.0888540	−	0.110162i
$725$	−32.3075	−	2.51114i	−1.19987	−	0.0932612i
$726$	8.69390	−	9.84647i	0.322661	−	0.365437i
$727$	−18.0993	−	0.702336i	−0.671266	−	0.0260482i	−0.299110	−	0.954218i	$-0.596690\pi$
$727$	−18.0993	−	0.702336i	−0.671266	−	0.0260482i	−0.372156	+	0.928170i	$0.621381\pi$
$728$	−40.4791			−1.50025
$729$	9.82682	+	25.1482i	0.363956	+	0.931416i
$730$	−0.0322520			−0.00119370
$731$	33.4231	+	1.29697i	1.23620	+	0.0479701i
$732$	0.859394	−	0.973326i	0.0317641	−	0.0359752i
$733$	35.3050	+	2.74412i	1.30402	+	0.101357i	0.710635	−	0.703561i	$-0.248408\pi$
$733$	35.3050	+	2.74412i	1.30402	+	0.101357i	0.593386	+	0.804918i	$0.297791\pi$
$734$	5.28353	+	6.55055i	0.195019	+	0.241785i
$735$	−5.10004	+	5.34342i	−0.188118	+	0.197095i
$736$	14.7419	−	6.70103i	0.543395	−	0.247003i
$737$	−21.6821	−	2.53427i	−0.798670	−	0.0933511i
$738$	−35.5875	−	15.0222i	−1.30999	−	0.552974i
$739$	−1.91420	−	2.57122i	−0.0704150	−	0.0945838i	0.765520	−	0.643412i	$-0.222482\pi$
$739$	−1.91420	−	2.57122i	−0.0704150	−	0.0945838i	−0.835935	+	0.548828i	$0.815074\pi$
$740$	0.000258358		0.0133209i	9.49742e−6		0.000489684i
$741$	13.1518	−	12.7507i	0.483144	−	0.468408i
$742$	−3.65416	−	1.17166i	−0.134148	−	0.0430130i
$743$	−4.98703	+	2.03742i	−0.182956	+	0.0747459i	−0.467827	−	0.883820i	$-0.654963\pi$
$743$	−4.98703	+	2.03742i	−0.182956	+	0.0747459i	0.284871	+	0.958566i	$0.408049\pi$
$744$	31.8602	+	1.42107i	1.16805	+	0.0520989i
$745$	1.01005	+	0.157969i	0.0370054	+	0.00578755i
$746$	4.30809	+	14.3900i	0.157730	+	0.526856i
$747$	−26.0581	+	18.1731i	−0.953416	+	0.664920i
$748$	−3.18117	+	0.753952i	−0.116315	+	0.0275672i
$749$	5.29871	+	7.72571i	0.193611	+	0.282291i
$750$	1.98814	−	6.50358i	0.0725965	−	0.237477i
$751$	0.883685	−	45.5626i	0.0322461	−	1.66260i	−0.539362	−	0.842074i	$-0.681334\pi$
$751$	0.883685	−	45.5626i	0.0322461	−	1.66260i	0.571608	−	0.820527i	$-0.306320\pi$
$752$	17.1694	−	12.2719i	0.626102	−	0.447511i
$753$	−31.6877	+	28.4223i	−1.15476	+	1.03577i
$754$	−7.05040	+	32.5483i	−0.256760	+	1.18534i
$755$	3.42342	+	1.24602i	0.124591	+	0.0453474i
$756$	−8.67960	−	2.21697i	−0.315674	−	0.0806305i
$757$	42.5488	−	15.4865i	1.54646	−	0.562866i	0.578877	−	0.815415i	$-0.303491\pi$
$757$	42.5488	−	15.4865i	1.54646	−	0.562866i	0.967584	+	0.252549i	$0.0812690\pi$
$758$	−1.07723	−	7.88675i	−0.0391269	−	0.286460i
$759$	34.6268	+	2.89315i	1.25687	+	0.105015i
$760$	−1.48573	−	1.45719i	−0.0538930	−	0.0528579i
$761$	15.0945	+	2.96447i	0.547176	+	0.107462i	0.458658	−	0.888613i	$-0.348330\pi$
$761$	15.0945	+	2.96447i	0.547176	+	0.107462i	0.0885178	+	0.996075i	$0.471787\pi$
$762$	−1.69341	−	1.43773i	−0.0613458	−	0.0520833i
$763$	−5.62025	−	21.8191i	−0.203467	−	0.789906i
$764$	−2.52303	−	1.26712i	−0.0912802	−	0.0458426i
$765$	−2.56681	−	1.32653i	−0.0928031	−	0.0479608i
$766$	−2.41749	−	1.59001i	−0.0873476	−	0.0574494i
$767$	−19.2028	+	3.77131i	−0.693373	+	0.136174i
$768$	−12.3090	+	7.33168i	−0.444164	+	0.264559i
$769$	2.99998	+	4.75979i	0.108182	+	0.171643i	0.895713	−	0.444632i	$-0.146666\pi$
$769$	2.99998	+	4.75979i	0.108182	+	0.171643i	−0.787531	+	0.616275i	$0.788641\pi$
$770$	2.20070	−	4.17792i	0.0793077	−	0.150562i
$771$	10.3979	−	29.8241i	0.374470	−	1.07409i
$772$	−0.991150	+	2.89674i	−0.0356723	+	0.104256i
$773$	−0.385059	+	6.61120i	−0.0138496	+	0.237788i	0.984278	+	0.176625i	$0.0565180\pi$
$773$	−0.385059	+	6.61120i	−0.0138496	+	0.237788i	−0.998128	+	0.0611632i	$0.980519\pi$
$774$	−39.9588	−	9.96037i	−1.43629	−	0.358018i
$775$	−30.0679	+	19.7759i	−1.08007	+	0.710373i
$776$	−29.1021	+	28.5431i	−1.04470	+	1.02464i
$777$	0.942455	−	0.781561i	0.0338104	−	0.0280384i
$778$	−22.0464	+	25.2623i	−0.790401	+	0.905699i
$779$	6.69923	−	26.0080i	0.240025	−	0.931834i
$780$	−0.475326	−	0.219391i	−0.0170194	−	0.00785546i
$781$	−10.4075	−	4.25192i	−0.372408	−	0.152146i
$782$	35.8308	+	30.0656i	1.28131	+	1.07515i
$783$	15.2552	−	30.5297i	0.545176	−	1.09104i
$784$	−58.1484	+	48.7923i	−2.07673	+	1.74258i
$785$	−1.38338	+	0.443562i	−0.0493748	+	0.0158314i
$786$	1.29845	−	2.43082i	0.0463142	−	0.0867043i
$787$	1.00667	+	10.3495i	0.0358839	+	0.368918i	0.996002	+	0.0893254i	$0.0284711\pi$
$787$	1.00667	+	10.3495i	0.0358839	+	0.368918i	−0.960119	+	0.279593i	$0.909800\pi$
$788$	5.06209	−	2.79314i	0.180329	−	0.0995015i
$789$	−10.0360	−	1.23196i	−0.357290	−	0.0438591i
$790$	−0.669928	+	0.0520709i	−0.0238350	+	0.00185260i
$791$	4.62994	+	4.90745i	0.164622	+	0.174489i
$792$	−18.6323	+	0.507073i	−0.662071	+	0.0180180i
$793$	−6.78504	−	1.60808i	−0.240944	−	0.0571047i
$794$	16.0258	+	41.5078i	0.568734	+	1.47306i
$795$	0.169292	+	0.155421i	0.00600418	+	0.00551221i
$796$	−0.0194989	+	0.142757i	−0.000691120	+	0.00505990i
$797$	−3.19429	−	14.7465i	−0.113148	−	0.522347i	−0.998365	−	0.0571688i	$-0.981793\pi$
$797$	−3.19429	−	14.7465i	−0.113148	−	0.522347i	0.885217	−	0.465178i	$-0.154010\pi$
$798$	4.23601	−	41.0807i	0.149953	−	1.45424i
$799$	15.0728	+	8.31682i	0.533237	+	0.294228i
$800$	3.88248	−	9.00060i	0.137266	−	0.318219i
$801$	−40.4367	+	23.7694i	−1.42876	+	0.839851i
$802$	32.7770	−	44.0272i	1.15740	−	1.55465i
$803$	−0.163395	−	0.116788i	−0.00576610	−	0.00412136i
$804$	3.23289	+	4.39541i	0.114015	+	0.155014i
$805$	−10.0665	+	1.57437i	−0.354796	+	0.0554891i
$806$	15.9552	+	33.3675i	0.561998	+	1.17532i
$807$	2.14462	−	1.16721i	0.0754943	−	0.0410878i
$808$	14.3391	−	22.7505i	0.504448	−	0.800361i
$809$	13.9004	+	24.0762i	0.488713	+	0.846475i	0.999916	−	0.0129849i	$-0.00413334\pi$
$809$	13.9004	+	24.0762i	0.488713	+	0.846475i	−0.511203	+	0.859460i	$0.670800\pi$
$810$	2.76048	+	2.24374i	0.0969935	+	0.0788369i
$811$	14.3220	−	24.8064i	0.502913	−	0.871071i	−0.497081	−	0.867704i	$-0.665595\pi$
$811$	14.3220	−	24.8064i	0.502913	−	0.871071i	0.999994	−	0.00336726i	$-0.00107183\pi$
$812$	5.27727	+	10.0187i	0.185196	+	0.351586i
$813$	0.436052	−	1.11023i	0.0152930	−	0.0389375i
$814$	−0.311160	+	0.453682i	−0.0109061	+	0.0159016i
$815$	−0.988967	+	2.56149i	−0.0346420	+	0.0897251i
$816$	−24.7121	−	16.4591i	−0.865096	−	0.576184i
$817$	2.77191	−	28.4977i	0.0969768	−	0.997008i
$818$	−13.0161	−	30.1747i	−0.455097	−	1.05503i
$819$	11.4602	+	46.7239i	0.400450	+	1.63266i
$820$	−0.762361	+	0.0891072i	−0.0266228	+	0.00311176i
$821$	−14.6809	+	8.85998i	−0.512368	+	0.309216i	−0.749210	−	0.662333i	$-0.769567\pi$
$821$	−14.6809	+	8.85998i	−0.512368	+	0.309216i	0.236842	+	0.971548i	$0.423888\pi$
$822$	−5.53174	+	0.397761i	−0.192942	+	0.0138735i
$823$	−14.1920	+	12.8785i	−0.494702	+	0.448918i	−0.880764	−	0.473555i	$-0.842971\pi$
$823$	−14.1920	+	12.8785i	−0.494702	+	0.448918i	0.386063	+	0.922473i	$0.373835\pi$
$824$	−36.3456	−	28.1700i	−1.26616	−	0.981348i
$825$	16.6990	−	12.7886i	0.581383	−	0.445243i
$826$	−27.6993	+	34.3417i	−0.963781	+	1.19490i
$827$	−28.5434	+	30.2542i	−0.992551	+	1.05204i	0.00609257	+	0.999981i	$0.498061\pi$
$827$	−28.5434	+	30.2542i	−0.992551	+	1.05204i	−0.998644	+	0.0520615i	$0.983421\pi$
$828$	−5.37397	−	6.82283i	−0.186758	−	0.237110i
$829$	3.50096	−	11.6940i	0.121593	−	0.406150i	−0.875421	−	0.483360i	$-0.839416\pi$
$829$	3.50096	−	11.6940i	0.121593	−	0.406150i	0.997015	+	0.0772102i	$0.0246013\pi$
$830$	−1.80565	+	3.77620i	−0.0626751	+	0.131074i
$831$	−21.1074	−	10.7540i	−0.732207	−	0.373051i
$832$	17.3099	+	10.4466i	0.600114	+	0.362171i
$833$	−56.3688	−	25.6227i	−1.95306	−	0.887776i
$834$	23.5633	−	9.46787i	0.815929	−	0.327845i
$835$	0.0802415	+	0.0728153i	0.00277687	+	0.00251988i
$836$	0.485966	+	2.75605i	0.0168075	+	0.0953200i
$837$	−7.37975	−	37.1777i	−0.255082	−	1.28505i
$838$	−6.97949	+	39.5827i	−0.241103	+	1.36736i
$839$	36.4457	−	28.2475i	1.25824	−	0.975212i	0.258286	−	0.966069i	$-0.416842\pi$
$839$	36.4457	−	28.2475i	1.25824	−	0.975212i	0.999958	−	0.00914387i	$-0.00291063\pi$
$840$	5.27369	−	1.43519i	0.181960	−	0.0495189i
$841$	−13.6223	+	3.79202i	−0.469733	+	0.130759i
$842$	13.8072	+	40.3531i	0.475828	+	1.39066i
$843$	−19.1891	+	32.7965i	−0.660907	+	1.12957i
$844$	−7.78504	−	2.16711i	−0.267972	−	0.0745951i
$845$	−0.0312099	−	0.535853i	−0.00107365	−	0.0184339i
$846$	−16.0777	−	13.8111i	−0.552761	−	0.474834i
$847$	−21.4338	+	10.7644i	−0.736473	+	0.369871i
$848$	1.55284	+	1.77936i	0.0533248	+	0.0611035i
$849$	−8.48838	−	1.37794i	−0.291320	−	0.0472908i
$850$	28.2919	−	1.09786i	0.970406	−	0.0376562i
$851$	1.18613	−	0.0460273i	0.0406600	−	0.00157779i
$852$	0.996925	+	2.62726i	0.0341541	+	0.0900085i
$853$	5.45264	+	6.24803i	0.186695	+	0.213928i	0.839152	−	0.543897i	$-0.183052\pi$
$853$	5.45264	+	6.24803i	0.186695	+	0.213928i	−0.652457	+	0.757826i	$0.726262\pi$
$854$	−14.0486	+	7.05549i	−0.480735	+	0.241434i
$855$	−1.26137	+	2.12748i	−0.0431378	+	0.0727584i
$856$	−0.283284	−	4.86379i	−0.00968243	−	0.166241i
$857$	−1.94338	−	0.540977i	−0.0663846	−	0.0184794i	0.234821	−	0.972039i	$-0.424550\pi$
$857$	−1.94338	−	0.540977i	−0.0663846	−	0.0184794i	−0.301206	+	0.953559i	$0.597389\pi$
$858$	−10.6997	−	18.7826i	−0.365281	−	0.641228i
$859$	7.06379	+	20.6447i	0.241013	+	0.704388i	0.998661	+	0.0517248i	$0.0164719\pi$
$859$	7.06379	+	20.6447i	0.241013	+	0.704388i	−0.757648	+	0.652663i	$0.773652\pi$
$860$	−0.788313	+	0.219442i	−0.0268812	+	0.00748290i
$861$	50.0701	+	49.6803i	1.70638	+	1.69310i
$862$	−10.7764	+	8.35232i	−0.367045	+	0.284481i
$863$	−1.24976	+	7.08777i	−0.0425425	+	0.241270i	−0.998662	−	0.0517052i	$-0.983534\pi$
$863$	−1.24976	+	7.08777i	−0.0425425	+	0.241270i	0.956120	+	0.292976i	$0.0946455\pi$
$864$	7.24381	+	7.35579i	0.246439	+	0.250249i
$865$	−0.258627	−	1.46675i	−0.00879358	−	0.0498709i
$866$	−25.9529	−	23.5510i	−0.881916	−	0.800296i
$867$	−0.737051	+	5.17268i	−0.0250316	+	0.175673i
$868$	11.4485	+	5.20399i	0.388588	+	0.176635i
$869$	−3.58254	−	2.16208i	−0.121529	−	0.0733434i
$870$	−0.235465	−	4.49043i	−0.00798300	−	0.152240i
$871$	12.6405	−	26.4354i	0.428308	−	0.895729i
$872$	−3.36067	+	11.2254i	−0.113807	+	0.380141i
$873$	41.1857	+	25.5108i	1.39392	+	0.863409i
$874$	27.4765	−	29.1234i	0.929406	−	0.985113i
$875$	−7.79616	+	9.66572i	−0.263558	+	0.326761i
$876$	0.00650562	+	0.0497768i	0.000219805	+	0.00168180i
$877$	−0.912795	−	0.707470i	−0.0308229	−	0.0238896i	0.597073	−	0.802187i	$-0.296330\pi$
$877$	−0.912795	−	0.707470i	−0.0308229	−	0.0238896i	−0.627896	+	0.778298i	$0.716083\pi$
$878$	2.79882	−	2.53980i	0.0944557	−	0.0857140i
$879$	17.8795	+	26.3952i	0.603059	+	0.890287i
$880$	−2.48813	+	1.50159i	−0.0838748	+	0.0506187i
$881$	45.3380	−	5.29925i	1.52748	−	0.178536i	0.689517	−	0.724269i	$-0.257823\pi$
$881$	45.3380	−	5.29925i	1.52748	−	0.178536i	0.837959	+	0.545733i	$0.183749\pi$
$882$	61.5035	+	45.0449i	2.07093	+	1.51674i
$883$	−14.9295	−	34.6104i	−0.502416	−	1.16473i	−0.961117	−	0.276141i	$-0.910944\pi$
$883$	−14.9295	−	34.6104i	−0.502416	−	1.16473i	0.458701	−	0.888591i	$-0.348315\pi$
$884$	0.424844	−	4.36778i	0.0142891	−	0.146904i
$885$	2.36807	−	1.17217i	0.0796017	−	0.0394022i
$886$	−5.37110	+	13.9115i	−0.180446	+	0.467366i
$887$	5.41608	−	7.89684i	0.181854	−	0.265150i	−0.723022	−	0.690825i	$-0.757247\pi$
$887$	5.41608	−	7.89684i	0.181854	−	0.265150i	0.904876	+	0.425675i	$0.139963\pi$
$888$	−0.629655	+	0.0947456i	−0.0211298	+	0.00317945i
$889$	1.89041	+	3.58885i	0.0634022	+	0.120366i
$890$	−3.08996	+	5.35197i	−0.103576	+	0.179399i
$891$	5.86036	+	21.3632i	0.196329	+	0.715695i
$892$	4.88570	+	8.46229i	0.163585	+	0.283338i
$893$	7.85749	−	12.4668i	0.262941	−	0.417184i
$894$	0.265660	−	10.5477i	0.00888500	−	0.352769i
$895$	0.734916	+	1.53695i	0.0245655	+	0.0513745i
$896$	64.0896	−	10.0234i	2.14108	−	0.334859i
$897$	−18.7214	+	42.7195i	−0.625090	+	1.42636i
$898$	−23.2013	−	16.5833i	−0.774237	−	0.553391i
$899$	−28.6104	+	38.4304i	−0.954209	+	1.28173i
$900$	−5.18437	−	0.872424i	−0.172812	−	0.0290808i
$901$	−0.763028	+	1.76890i	−0.0254201	+	0.0589305i
$902$	−27.7490	−	15.3113i	−0.923941	−	0.509809i
$903$	60.9225	+	44.0799i	2.02738	+	1.46689i
$904$	−0.742817	−	3.42922i	−0.0247057	−	0.114054i
$905$	0.373693	−	2.73591i	0.0124220	−	0.0909449i
$906$	8.17249	−	36.7004i	0.271513	−	1.21929i
$907$	5.80588	+	15.0376i	0.192781	+	0.499316i	0.995247	−	0.0973823i	$-0.0310470\pi$
$907$	5.80588	+	15.0376i	0.192781	+	0.499316i	−0.802466	+	0.596698i	$0.796479\pi$
$908$	−5.37152	−	1.27307i	−0.178260	−	0.0422484i
$909$	−30.3199	−	10.1102i	−1.00565	−	0.335336i
$910$	4.34973	+	4.61045i	0.144192	+	0.152835i
$911$	30.4321	−	2.36537i	1.00826	−	0.0783683i	0.437275	−	0.899328i	$-0.355944\pi$
$911$	30.4321	−	2.36537i	1.00826	−	0.0783683i	0.570987	+	0.820959i	$0.306561\pi$
$912$	−15.2954	+	20.2989i	−0.506481	+	0.672164i
$913$	−22.8218	+	12.5925i	−0.755292	+	0.416753i
$914$	0.244920	+	2.51799i	0.00810122	+	0.0832878i
$915$	0.940983	−	0.0310604i	0.0311079	−	0.00102683i
$916$	−2.52400	+	0.809288i	−0.0833953	+	0.0267396i
$917$	−3.85489	+	3.23463i	−0.127300	+	0.106817i
$918$	−10.1421	+	28.0419i	−0.334739	+	0.925519i
$919$	−32.2210	−	27.0367i	−1.06287	−	0.891857i	−0.0684860	−	0.997652i	$-0.521817\pi$
$919$	−32.2210	−	27.0367i	−1.06287	−	0.891857i	−0.994388	+	0.105795i	$0.966261\pi$
$920$	4.90525	+	2.00401i	0.161721	+	0.0660704i
$921$	−29.9608	+	21.1538i	−0.987243	+	0.697040i
$922$	−6.57944	+	25.5430i	−0.216682	+	0.841213i
$923$	9.92257	−	11.3700i	0.326605	−	0.374248i
$924$	−6.89198	−	2.55375i	−0.226730	−	0.0840123i
$925$	0.512981	−	0.503128i	0.0168667	−	0.0165428i
$926$	−17.1303	+	11.2668i	−0.562937	+	0.370249i
$927$	−22.2259	+	49.9280i	−0.729994	+	1.63985i
$928$	0.758768	−	13.0275i	0.0249078	−	0.427650i
$929$	−7.06936	+	20.6610i	−0.231938	+	0.677865i	0.767389	+	0.641182i	$0.221556\pi$
$929$	−7.06936	+	20.6610i	−0.231938	+	0.677865i	−0.999327	+	0.0366826i	$0.988321\pi$
$930$	−3.26173	−	3.78149i	−0.106956	−	0.124000i
$931$	−24.7020	+	46.8955i	−0.809575	+	1.53694i
$932$	2.61402	+	4.14743i	0.0856251	+	0.135854i
$933$	7.50943	+	4.20041i	0.245848	+	0.137515i
$934$	17.0764	−	3.35370i	0.558757	−	0.109736i
$935$	−1.98059	−	1.30265i	−0.0647722	−	0.0426013i
$936$	7.45268	−	23.8838i	0.243599	−	0.780665i
$937$	−23.0399	−	11.5711i	−0.752679	−	0.378010i	0.0307204	−	0.999528i	$-0.490220\pi$
$937$	−23.0399	−	11.5711i	−0.752679	−	0.378010i	−0.783400	+	0.621518i	$0.786516\pi$
$938$	−16.4787	−	63.9742i	−0.538048	−	2.08883i
$939$	−7.18900	+	2.56955i	−0.234604	+	0.0838542i
$940$	−0.413259	−	0.0811614i	−0.0134790	−	0.00264719i
$941$	33.7537	+	33.1054i	1.10034	+	1.07921i	0.996413	+	0.0846215i	$0.0269681\pi$
$941$	33.7537	+	33.1054i	1.10034	+	1.07921i	0.103927	+	0.994585i	$0.466859\pi$
$942$	6.38947	+	13.5636i	0.208180	+	0.441927i
$943$	9.25446	+	67.7546i	0.301367	+	2.20639i
$944$	25.5155	−	9.28689i	0.830460	−	0.302263i
$945$	−3.14966	−	5.68096i	−0.102458	−	0.184802i
$946$	−31.7502	−	11.5561i	−1.03229	−	0.375722i
$947$	5.18527	−	23.9379i	0.168499	−	0.777877i	−0.812360	−	0.583156i	$-0.801818\pi$
$947$	5.18527	−	23.9379i	0.168499	−	0.777877i	0.980859	−	0.194721i	$-0.0623800\pi$
$948$	0.215497	+	1.02344i	0.00699902	+	0.0332399i
$949$	0.219326	−	0.156765i	0.00711963	−	0.00508881i
$950$	0.469979	−	24.2320i	0.0152481	−	0.786190i
$951$	−15.5759	+	3.59646i	−0.505084	+	0.116623i
$952$	25.9132	+	37.7824i	0.839852	+	1.22453i
$953$	−54.1828	+	12.8416i	−1.75515	+	0.415979i	−0.977196	−	0.212337i	$-0.931893\pi$
$953$	−54.1828	+	12.8416i	−1.75515	+	0.415979i	−0.777958	+	0.628316i	$0.783744\pi$
$954$	1.36409	−	1.94034i	0.0441639	−	0.0628208i
$955$	−0.587148	−	1.96121i	−0.0189997	−	0.0634633i
$956$	−9.00072	−	1.40769i	−0.291104	−	0.0455278i
$957$	15.0674	−	23.6021i	0.487060	−	0.762946i
$958$	−3.72857	+	1.52329i	−0.120465	+	0.0492152i
$959$	9.64340	+	3.09203i	0.311402	+	0.0998469i
$960$	−2.62556	−	0.747277i	−0.0847395	−	0.0241182i
$961$	0.430662	+	22.2048i	0.0138923	+	0.716285i
$962$	−0.440971	−	0.592326i	−0.0142175	−	0.0190974i
$963$	−5.53394	+	1.70399i	−0.178329	+	0.0549103i
$964$	−4.24828	−	0.496553i	−0.136828	−	0.0159929i
$965$	−2.02099	+	0.918655i	−0.0650581	+	0.0295725i
$966$	29.5752	+	100.910i	0.951566	+	3.24674i
$967$	5.50549	+	6.82574i	0.177045	+	0.219501i	0.859111	−	0.511789i	$-0.171017\pi$
$967$	5.50549	+	6.82574i	0.177045	+	0.219501i	−0.682066	+	0.731290i	$0.738918\pi$
$968$	12.4362	+	0.966615i	0.399713	+	0.0310682i
$969$	−20.3205	−	4.11313i	−0.652789	−	0.132133i
$970$	6.37817	+	0.247502i	0.204791	+	0.00794682i
$971$	−15.5580			−0.499280			−0.249640	−	0.968339i	$-0.580312\pi$
$971$	−15.5580			−0.499280			−0.249640	+	0.968339i	$0.580312\pi$
$972$	2.90609	−	4.71303i	0.0932129	−	0.151171i
$973$	−46.3697			−1.48654
$974$	56.0406	+	2.17463i	1.79566	+	0.0696797i
$975$	8.98528	+	26.7653i	0.287759	+	0.857175i
$976$	9.64600	+	0.749747i	0.308761	+	0.0239988i
$977$	−34.8032	−	43.1493i	−1.11345	−	1.38047i	−0.916491	−	0.400056i	$-0.868991\pi$
$977$	−34.8032	−	43.1493i	−1.11345	−	1.38047i	−0.196964	−	0.980411i	$-0.563108\pi$
$978$	27.5359	+	6.69472i	0.880502	+	0.214074i
$979$	−35.0344	+	15.9251i	−1.11971	+	0.508968i
$980$	1.50456	+	0.175858i	0.0480613	+	0.00561757i
$981$	13.9086	+	0.701064i	0.444069	+	0.0223832i
$982$	−14.6029	−	19.6151i	−0.465997	−	0.625943i
$983$	−0.992401	−	51.1679i	−0.0316527	−	1.63200i	−0.593551	−	0.804797i	$-0.702274\pi$
$983$	−0.992401	−	51.1679i	−0.0316527	−	1.63200i	0.561898	−	0.827207i	$-0.310071\pi$
$984$	−8.94432	−	35.5752i	−0.285134	−	1.13410i
$985$	3.99203	+	1.27999i	0.127197	+	0.0407840i
$986$	34.8933	−	14.2555i	1.11123	−	0.453987i
$987$	17.8384	+	34.3461i	0.567803	+	1.09325i
$988$	−3.71141	−	0.580454i	−0.118076	−	0.0184667i
$989$	20.9091	+	69.8411i	0.664869	+	2.22082i
$990$	2.05992	+	2.06768i	0.0654684	+	0.0657152i
$991$	38.0028	−	9.00684i	1.20720	−	0.286112i	0.422717	−	0.906262i	$-0.361076\pi$
$991$	38.0028	−	9.00684i	1.20720	−	0.286112i	0.784483	+	0.620150i	$0.212928\pi$
$992$	−8.19717	−	11.9518i	−0.260260	−	0.379469i
$993$	37.8825	+	40.6216i	1.20216	+	1.28909i
$994$	0.659748	−	34.0164i	0.0209259	−	1.07894i
$995$	−0.0849957	+	0.0607513i	−0.00269454	+	0.00192594i
$996$	6.19229	+	2.02508i	0.196210	+	0.0641672i
$997$	−2.71122	+	12.5164i	−0.0858652	+	0.396398i	−0.999959	−	0.00910591i	$-0.997101\pi$
$997$	−2.71122	+	12.5164i	−0.0858652	+	0.396398i	0.914093	+	0.405504i	$0.132904\pi$
$998$	−35.3501	−	12.8664i	−1.11899	−	0.407278i
$999$	0.287626	+	0.699969i	0.00910007	+	0.0221460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.4.8	✓	1404
3.2	odd	2		729.2.i.a.64.19		1404
243.61	even	81	inner	243.2.i.a.61.8	yes	1404
243.182	odd	162		729.2.i.a.262.19		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.8	✓	1404	1.1	even	1	trivial
243.2.i.a.61.8	yes	1404	243.61	even	81	inner
729.2.i.a.64.19		1404	3.2	odd	2
729.2.i.a.262.19		1404	243.182	odd	162

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53351 - 0.0595072i) q^{2} +(-1.14640 + 1.29838i) q^{3} +(0.354129 + 0.0275251i) q^{4} +(0.161696 + 0.200471i) q^{5} +(1.83527 - 1.92285i) q^{6} +(-4.41863 + 2.00851i) q^{7} +(2.50715 + 0.293044i) q^{8} +(-0.371555 - 2.97690i) q^{9} +(-0.236033 - 0.317047i) q^{10} +(-0.0477295 - 2.46092i) q^{11} +(-0.441709 + 0.428237i) q^{12} +(3.14616 + 1.00877i) q^{13} +(6.89553 - 2.81713i) q^{14} +(-0.445654 - 0.0198776i) q^{15} +(-4.52917 - 0.708350i) q^{16} +(-1.07248 - 3.58234i) q^{17} +(0.392637 + 4.58722i) q^{18} +(-3.11473 + 0.738204i) q^{19} +(0.0517431 + 0.0754433i) q^{20} +(2.45769 - 8.03958i) q^{21} +(-0.0732488 + 3.77669i) q^{22} +(6.63084 - 4.73944i) q^{23} +(-3.25467 + 2.91928i) q^{24} +(1.04448 - 4.82184i) q^{25} +(-4.76464 - 1.73419i) q^{26} +(4.29108 + 2.93029i) q^{27} +(-1.62005 + 0.589649i) q^{28} +(-0.888872 - 6.50770i) q^{29} +(0.682232 + 0.0570021i) q^{30} +(-5.20773 - 5.10770i) q^{31} +(1.94957 + 0.382883i) q^{32} +(3.24992 + 2.75922i) q^{33} +(1.43149 + 5.55738i) q^{34} +(-1.11712 - 0.561039i) q^{35} +(-0.0496391 - 1.06443i) q^{36} +(0.121679 + 0.0800296i) q^{37} +(4.82040 - 0.946696i) q^{38} +(-4.91651 + 2.92844i) q^{39} +(0.346649 + 0.549996i) q^{40} +(-3.91017 + 7.42328i) q^{41} +(-4.24731 + 12.1825i) q^{42} +(-2.89571 + 8.46304i) q^{43} +(0.0508346 - 0.872797i) q^{44} +(0.536704 - 0.555838i) q^{45} +(-10.4505 + 6.87340i) q^{46} +(-3.28669 + 3.22356i) q^{47} +(6.11192 - 5.06851i) q^{48} +(10.8875 - 12.4757i) q^{49} +(-1.88865 + 7.33219i) q^{50} +(5.88071 + 2.71429i) q^{51} +(1.08638 + 0.443834i) q^{52} +(-0.394644 - 0.331146i) q^{53} +(-6.40605 - 4.74898i) q^{54} +(0.485626 - 0.407489i) q^{55} +(-11.6668 + 3.74080i) q^{56} +(2.61224 - 4.89036i) q^{57} +(0.975841 + 10.0325i) q^{58} +(-5.18606 + 2.86155i) q^{59} +(-0.157272 - 0.0193059i) q^{60} +(-2.10417 + 0.163549i) q^{61} +(7.68216 + 8.14261i) q^{62} +(7.62091 + 12.4075i) q^{63} +(5.95442 + 1.41122i) q^{64} +(0.306490 + 0.793828i) q^{65} +(-4.81959 - 4.42468i) q^{66} +(1.20024 - 8.78728i) q^{67} +(-0.281193 - 1.29813i) q^{68} +(-1.44799 + 14.0426i) q^{69} +(1.67973 + 0.926837i) q^{70} +(1.80912 - 4.19400i) q^{71} +(-0.0591827 - 7.57243i) q^{72} +(0.0487264 - 0.0654510i) q^{73} +(-0.181834 - 0.129967i) q^{74} +(5.06317 + 6.88386i) q^{75} +(-1.12333 + 0.175686i) q^{76} +(5.15369 + 10.7780i) q^{77} +(7.71378 - 4.19822i) q^{78} +(0.906458 - 1.43819i) q^{79} +(-0.590344 - 1.02251i) q^{80} +(-8.72389 + 2.21217i) q^{81} +(6.43803 - 11.1510i) q^{82} +(-4.93529 - 9.36941i) q^{83} +(1.09163 - 2.77940i) q^{84} +(0.544740 - 0.794251i) q^{85} +(4.94422 - 12.8058i) q^{86} +(9.46843 + 6.30630i) q^{87} +(0.601494 - 6.18389i) q^{88} +(-6.19275 - 14.3564i) q^{89} +(-0.856118 + 0.820446i) q^{90} +(-15.9278 + 1.86170i) q^{91} +(2.47862 - 1.49586i) q^{92} +(12.6018 - 0.906136i) q^{93} +(5.23199 - 4.74778i) q^{94} +(-0.651627 - 0.505049i) q^{95} +(-2.73210 + 2.09234i) q^{96} +(-10.1384 + 12.5697i) q^{97} +(-17.4385 + 18.4837i) q^{98} +(-7.30819 + 1.05645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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