LMFDB - Embedded newform 117.2.x.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(2,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("117.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0488315 + 0.0488315i) q^{2} +(0.804456 - 1.53390i) q^{3} +1.99523i q^{4} +(2.57746 + 0.690628i) q^{5} +(0.0356199 + 0.114186i) q^{6} +(-2.39973 - 0.643006i) q^{7} +(-0.195093 - 0.195093i) q^{8} +(-1.70570 - 2.46791i) q^{9} +O(q^{10})$	\(q+(-0.0488315 + 0.0488315i) q^{2} +(0.804456 - 1.53390i) q^{3} +1.99523i q^{4} +(2.57746 + 0.690628i) q^{5} +(0.0356199 + 0.114186i) q^{6} +(-2.39973 - 0.643006i) q^{7} +(-0.195093 - 0.195093i) q^{8} +(-1.70570 - 2.46791i) q^{9} +(-0.159586 + 0.0921368i) q^{10} +(2.15356 + 2.15356i) q^{11} +(3.06049 + 1.60508i) q^{12} +(0.168629 - 3.60161i) q^{13} +(0.148582 - 0.0857836i) q^{14} +(3.13281 - 3.39798i) q^{15} -3.97141 q^{16} +(0.757582 - 1.31217i) q^{17} +(0.203804 + 0.0372199i) q^{18} +(-5.08773 + 1.36325i) q^{19} +(-1.37796 + 5.14262i) q^{20} +(-2.91679 + 3.16368i) q^{21} -0.210324 q^{22} +(-3.08618 + 5.34542i) q^{23} +(-0.456198 + 0.142310i) q^{24} +(1.83620 + 1.06013i) q^{25} +(0.167638 + 0.184106i) q^{26} +(-5.15769 + 0.631049i) q^{27} +(1.28295 - 4.78802i) q^{28} -7.77733i q^{29} +(0.0129491 + 0.318909i) q^{30} +(-1.87394 + 6.99365i) q^{31} +(0.584117 - 0.584117i) q^{32} +(5.03580 - 1.57091i) q^{33} +(0.0270814 + 0.101069i) q^{34} +(-5.74113 - 3.31464i) q^{35} +(4.92405 - 3.40327i) q^{36} +(1.73614 + 0.465197i) q^{37} +(0.181872 - 0.315012i) q^{38} +(-5.38885 - 3.15599i) q^{39} +(-0.368108 - 0.637582i) q^{40} +(1.53837 + 5.74127i) q^{41} +(-0.0120562 - 0.296918i) q^{42} +(1.25711 - 0.725794i) q^{43} +(-4.29686 + 4.29686i) q^{44} +(-2.69196 - 7.53894i) q^{45} +(-0.110322 - 0.411728i) q^{46} +(11.0834 - 2.96979i) q^{47} +(-3.19482 + 6.09175i) q^{48} +(-0.716926 - 0.413918i) q^{49} +(-0.141432 + 0.0378966i) q^{50} +(-1.40330 - 2.21764i) q^{51} +(7.18604 + 0.336454i) q^{52} -9.11286i q^{53} +(0.221043 - 0.282673i) q^{54} +(4.06341 + 7.03803i) q^{55} +(0.342725 + 0.593618i) q^{56} +(-2.00176 + 8.90076i) q^{57} +(0.379779 + 0.379779i) q^{58} +(0.606620 + 0.606620i) q^{59} +(6.77976 + 6.25067i) q^{60} +(2.75095 + 4.76479i) q^{61} +(-0.250003 - 0.433018i) q^{62} +(2.50634 + 7.01910i) q^{63} -7.88577i q^{64} +(2.92200 - 9.16653i) q^{65} +(-0.169196 + 0.322616i) q^{66} +(4.21706 - 1.12996i) q^{67} +(2.61808 + 1.51155i) q^{68} +(5.71664 + 9.03404i) q^{69} +(0.442207 - 0.118489i) q^{70} +(0.849841 + 3.17165i) q^{71} +(-0.148702 + 0.814244i) q^{72} +(0.551749 - 0.551749i) q^{73} +(-0.107495 + 0.0620621i) q^{74} +(3.10327 - 1.96371i) q^{75} +(-2.72001 - 10.1512i) q^{76} +(-3.78322 - 6.55273i) q^{77} +(0.417258 - 0.109034i) q^{78} +(6.40258 - 11.0896i) q^{79} +(-10.2361 - 2.74277i) q^{80} +(-3.18117 + 8.41904i) q^{81} +(-0.355476 - 0.205234i) q^{82} +(-0.813378 - 3.03557i) q^{83} +(-6.31227 - 5.81966i) q^{84} +(2.85886 - 2.85886i) q^{85} +(-0.0259451 + 0.0968284i) q^{86} +(-11.9296 - 6.25652i) q^{87} -0.840292i q^{88} +(-3.38089 + 12.6176i) q^{89} +(0.499591 + 0.236685i) q^{90} +(-2.72052 + 8.53446i) q^{91} +(-10.6653 - 6.15764i) q^{92} +(9.22005 + 8.50052i) q^{93} +(-0.396201 + 0.686240i) q^{94} -14.0549 q^{95} +(-0.426081 - 1.36587i) q^{96} +(-0.745264 + 2.78136i) q^{97} +(0.0552209 - 0.0147964i) q^{98} +(1.64147 - 8.98814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.0488315	+	0.0488315i	−0.0345291	+	0.0345291i	−0.724161	−	0.689631i	$-0.757773\pi$
$2$	−0.0488315	+	0.0488315i	−0.0345291	+	0.0345291i	0.689631	+	0.724161i	$0.257773\pi$
$3$	0.804456	−	1.53390i	0.464453	−	0.885598i
$3$	0.804456	−	1.53390i	0.464453	−	0.885598i
$4$			1.99523i			0.997615i
$5$	2.57746	+	0.690628i	1.15267	+	0.308858i	0.784036	−	0.620715i	$-0.213158\pi$
$5$	2.57746	+	0.690628i	1.15267	+	0.308858i	0.368638	+	0.929573i	$0.379824\pi$
$6$	0.0356199	+	0.114186i	0.0145418	+	0.0466161i
$7$	−2.39973	−	0.643006i	−0.907013	−	0.243033i	−0.224987	−	0.974362i	$-0.572234\pi$
$7$	−2.39973	−	0.643006i	−0.907013	−	0.243033i	−0.682026	+	0.731328i	$0.738901\pi$
$8$	−0.195093	−	0.195093i	−0.0689759	−	0.0689759i
$9$	−1.70570	−	2.46791i	−0.568567	−	0.822637i
$10$	−0.159586	+	0.0921368i	−0.0504654	+	0.0291362i
$11$	2.15356	+	2.15356i	0.649324	+	0.649324i	0.952830	−	0.303506i	$-0.0981571\pi$
$11$	2.15356	+	2.15356i	0.649324	+	0.649324i	−0.303506	+	0.952830i	$0.598157\pi$
$12$	3.06049	+	1.60508i	0.883486	+	0.463345i
$13$	0.168629	−	3.60161i	0.0467693	−	0.998906i
$13$	0.168629	−	3.60161i	0.0467693	−	0.998906i
$14$	0.148582	−	0.0857836i	0.0397101	−	0.0229266i
$15$	3.13281	−	3.39798i	0.808887	−	0.877356i
$16$	−3.97141			−0.992852
$17$	0.757582	−	1.31217i	0.183741	−	0.318248i	−0.759411	−	0.650611i	$-0.774513\pi$
$17$	0.757582	−	1.31217i	0.183741	−	0.318248i	0.943151	+	0.332363i	$0.107846\pi$
$18$	0.203804	+	0.0372199i	0.0480370	+	0.00877281i
$19$	−5.08773	+	1.36325i	−1.16721	+	0.312752i	−0.789841	−	0.613312i	$-0.789837\pi$
$19$	−5.08773	+	1.36325i	−1.16721	+	0.312752i	−0.377366	+	0.926064i	$0.623170\pi$
$20$	−1.37796	+	5.14262i	−0.308122	+	1.14993i
$21$	−2.91679	+	3.16368i	−0.636495	+	0.690371i
$22$	−0.210324			−0.0448412
$23$	−3.08618	+	5.34542i	−0.643513	+	1.11460i	0.341130	+	0.940016i	$0.389190\pi$
$23$	−3.08618	+	5.34542i	−0.643513	+	1.11460i	−0.984643	+	0.174581i	$0.944143\pi$
$24$	−0.456198	+	0.142310i	−0.0931210	+	0.0290488i
$25$	1.83620	+	1.06013i	0.367239	+	0.212026i
$26$	0.167638	+	0.184106i	0.0328764	+	0.0361062i
$27$	−5.15769	+	0.631049i	−0.992598	+	0.121445i
$28$	1.28295	−	4.78802i	0.242454	−	0.904850i
$29$		−	7.77733i		−	1.44421i	−0.691781	−	0.722107i	$-0.743174\pi$
$29$		−	7.77733i		−	1.44421i	0.691781	−	0.722107i	$-0.256826\pi$
$30$	0.0129491	+	0.318909i	0.00236416	+	0.0582245i
$31$	−1.87394	+	6.99365i	−0.336570	+	1.25610i	0.565587	+	0.824689i	$0.308650\pi$
$31$	−1.87394	+	6.99365i	−0.336570	+	1.25610i	−0.902157	+	0.431408i	$0.858017\pi$
$32$	0.584117	−	0.584117i	0.103258	−	0.103258i
$33$	5.03580	−	1.57091i	0.876620	−	0.273460i
$34$	0.0270814	+	0.101069i	0.00464442	+	0.0173332i
$35$	−5.74113	−	3.31464i	−0.970428	−	0.560277i
$36$	4.92405	−	3.40327i	0.820675	−	0.567211i
$37$	1.73614	+	0.465197i	0.285420	+	0.0764780i	0.398689	−	0.917086i	$-0.369465\pi$
$37$	1.73614	+	0.465197i	0.285420	+	0.0764780i	−0.113269	+	0.993564i	$0.536132\pi$
$38$	0.181872	−	0.315012i	0.0295036	−	0.0511017i
$39$	−5.38885	−	3.15599i	−0.862907	−	0.505363i
$40$	−0.368108	−	0.637582i	−0.0582030	−	0.100811i
$41$	1.53837	+	5.74127i	0.240253	+	0.896635i	0.975710	+	0.219065i	$0.0703006\pi$
$41$	1.53837	+	5.74127i	0.240253	+	0.896635i	−0.735458	+	0.677571i	$0.763033\pi$
$42$	−0.0120562	−	0.296918i	−0.00186031	−	0.0458155i
$43$	1.25711	−	0.725794i	0.191708	−	0.110683i	−0.401074	−	0.916046i	$-0.631363\pi$
$43$	1.25711	−	0.725794i	0.191708	−	0.110683i	0.592782	+	0.805363i	$0.298030\pi$
$44$	−4.29686	+	4.29686i	−0.647776	+	0.647776i
$45$	−2.69196	−	7.53894i	−0.401294	−	1.12384i
$46$	−0.110322	−	0.411728i	−0.0162661	−	0.0607060i
$47$	11.0834	−	2.96979i	1.61668	−	0.433189i	0.666659	−	0.745363i	$-0.267724\pi$
$47$	11.0834	−	2.96979i	1.61668	−	0.433189i	0.950025	+	0.312174i	$0.101057\pi$
$48$	−3.19482	+	6.09175i	−0.461133	+	0.879268i
$49$	−0.716926	−	0.413918i	−0.102418	−	0.0591311i
$50$	−0.141432	+	0.0378966i	−0.0200015	+	0.00535939i
$51$	−1.40330	−	2.21764i	−0.196501	−	0.310532i
$52$	7.18604	+	0.336454i	0.996524	+	0.0466577i
$53$		−	9.11286i		−	1.25175i	−0.779924	−	0.625874i	$-0.784742\pi$
$53$		−	9.11286i		−	1.25175i	0.779924	−	0.625874i	$-0.215258\pi$
$54$	0.221043	−	0.282673i	0.0300801	−	0.0384669i
$55$	4.06341	+	7.03803i	0.547910	+	0.949008i
$56$	0.342725	+	0.593618i	0.0457986	+	0.0793255i
$57$	−2.00176	+	8.90076i	−0.265140	+	1.17893i
$58$	0.379779	+	0.379779i	0.0498674	+	0.0498674i
$59$	0.606620	+	0.606620i	0.0789752	+	0.0789752i	0.745491	−	0.666516i	$-0.232215\pi$
$59$	0.606620	+	0.606620i	0.0789752	+	0.0789752i	−0.666516	+	0.745491i	$0.732215\pi$
$60$	6.77976	+	6.25067i	0.875264	+	0.806958i
$61$	2.75095	+	4.76479i	0.352223	+	0.610069i	0.986639	−	0.162924i	$-0.0520924\pi$
$61$	2.75095	+	4.76479i	0.352223	+	0.610069i	−0.634415	+	0.772992i	$0.718759\pi$
$62$	−0.250003	−	0.433018i	−0.0317504	−	0.0549934i
$63$	2.50634	+	7.01910i	0.315769	+	0.884323i
$64$		−	7.88577i		−	0.985721i
$65$	2.92200	−	9.16653i	0.362430	−	1.13697i
$66$	−0.169196	+	0.322616i	−0.0208266	+	0.0397112i
$67$	4.21706	−	1.12996i	0.515196	−	0.138046i	0.00815218	−	0.999967i	$-0.497405\pi$
$67$	4.21706	−	1.12996i	0.515196	−	0.138046i	0.507043	+	0.861921i	$0.330738\pi$
$68$	2.61808	+	1.51155i	0.317489	+	0.183302i
$69$	5.71664	+	9.03404i	0.688203	+	1.08757i
$70$	0.442207	−	0.118489i	0.0528539	−	0.0141622i
$71$	0.849841	+	3.17165i	0.100858	+	0.376406i	0.997842	−	0.0656559i	$-0.0209140\pi$
$71$	0.849841	+	3.17165i	0.100858	+	0.376406i	−0.896985	+	0.442061i	$0.854247\pi$
$72$	−0.148702	+	0.814244i	−0.0175247	+	0.0959595i
$73$	0.551749	−	0.551749i	0.0645773	−	0.0645773i	−0.674081	−	0.738658i	$-0.735460\pi$
$73$	0.551749	−	0.551749i	0.0645773	−	0.0645773i	0.738658	+	0.674081i	$0.235460\pi$
$74$	−0.107495	+	0.0620621i	−0.0124960	+	0.00721457i
$75$	3.10327	−	1.96371i	0.358335	−	0.226750i
$76$	−2.72001	−	10.1512i	−0.312006	−	1.16442i
$77$	−3.78322	−	6.55273i	−0.431138	−	0.746753i
$78$	0.417258	−	0.109034i	0.0472452	−	0.0123456i
$79$	6.40258	−	11.0896i	0.720347	−	1.24768i	−0.240514	−	0.970646i	$-0.577316\pi$
$79$	6.40258	−	11.0896i	0.720347	−	1.24768i	0.960861	−	0.277032i	$-0.0893508\pi$
$80$	−10.2361	−	2.74277i	−1.14444	−	0.306650i
$81$	−3.18117	+	8.41904i	−0.353463	+	0.935448i
$82$	−0.355476	−	0.205234i	−0.0392557	−	0.0226643i
$83$	−0.813378	−	3.03557i	−0.0892798	−	0.333197i	0.906810	−	0.421539i	$-0.138510\pi$
$83$	−0.813378	−	3.03557i	−0.0892798	−	0.333197i	−0.996090	+	0.0883420i	$0.971843\pi$
$84$	−6.31227	−	5.81966i	−0.688725	−	0.634977i
$85$	2.85886	−	2.85886i	0.310087	−	0.310087i
$86$	−0.0259451	+	0.0968284i	−0.00279773	+	0.0104413i
$87$	−11.9296	−	6.25652i	−1.27899	−	0.670769i
$88$		−	0.840292i		−	0.0895754i
$89$	−3.38089	+	12.6176i	−0.358373	+	1.33747i	0.517813	+	0.855494i	$0.326746\pi$
$89$	−3.38089	+	12.6176i	−0.358373	+	1.33747i	−0.876186	+	0.481973i	$0.839920\pi$
$90$	0.499591	+	0.236685i	0.0526615	+	0.0249488i
$91$	−2.72052	+	8.53446i	−0.285188	+	0.894654i
$92$	−10.6653	−	6.15764i	−1.11194	−	0.641978i
$93$	9.22005	+	8.50052i	0.956075	+	0.881463i
$94$	−0.396201	+	0.686240i	−0.0408650	+	0.0707803i
$95$	−14.0549			−1.44200
$96$	−0.426081	−	1.36587i	−0.0434867	−	0.139404i
$97$	−0.745264	+	2.78136i	−0.0756701	+	0.282405i	−0.993384	−	0.114836i	$-0.963366\pi$
$97$	−0.745264	+	2.78136i	−0.0756701	+	0.282405i	0.917714	+	0.397241i	$0.130032\pi$
$98$	0.0552209	−	0.0147964i	0.00557815	−	0.00149466i
$99$	1.64147	−	8.98814i	0.164974	−	0.903342i
$100$	−2.11520	+	3.66363i	−0.211520	+	0.366363i
$101$	7.01693			0.698211			0.349105	−	0.937083i	$-0.386486\pi$
$101$	7.01693			0.698211			0.349105	+	0.937083i	$0.386486\pi$
$102$	0.176816	+	0.0397655i	0.0175074	+	0.00393738i
$103$	3.56398	−	2.05766i	0.351169	−	0.202748i	−0.314031	−	0.949413i	$-0.601680\pi$
$103$	3.56398	−	2.05766i	0.351169	−	0.202748i	0.665200	+	0.746665i	$0.268346\pi$
$104$	−0.735548	+	0.669751i	−0.0721264	+	0.0656745i
$105$	−9.70281	+	6.13983i	−0.946898	+	0.599186i
$106$	0.444995	+	0.444995i	0.0432217	+	0.0432217i
$107$	3.71622	−	2.14556i	0.359260	−	0.207419i	−0.309496	−	0.950901i	$-0.600160\pi$
$107$	3.71622	−	2.14556i	0.359260	−	0.207419i	0.668756	+	0.743482i	$0.266827\pi$
$108$	−1.25909	−	10.2908i	−0.121156	−	0.990231i
$109$	5.48305	+	5.48305i	0.525181	+	0.525181i	0.919132	−	0.393950i	$-0.128892\pi$
$109$	5.48305	+	5.48305i	0.525181	+	0.525181i	−0.393950	+	0.919132i	$0.628892\pi$
$110$	−0.542101	−	0.145255i	−0.0516873	−	0.0138496i
$111$	2.11021	−	2.28884i	0.200293	−	0.217247i
$112$	9.53031	+	2.55364i	0.900530	+	0.241296i
$113$			7.85837i			0.739253i	0.929180	+	0.369627i	$0.120514\pi$
$113$			7.85837i			0.739253i	−0.929180	+	0.369627i	$0.879486\pi$
$114$	−0.336889	−	0.532387i	−0.0315525	−	0.0498626i
$115$	−11.6462	+	11.6462i	−1.08601	+	1.08601i
$116$	15.5176			1.44077
$117$	−9.17607	+	5.72710i	−0.848328	+	0.529471i
$118$	−0.0592444			−0.00545389
$119$	−2.66173	+	2.66173i	−0.244000	+	0.244000i
$120$	−1.27411	+	0.0517345i	−0.116310	+	0.00472269i
$121$		−	1.72432i		−	0.156756i
$122$	−0.367005	−	0.0983387i	−0.0332271	−	0.00890317i
$123$	10.0441	+	2.25889i	0.905644	+	0.203678i
$124$	−13.9539	−	3.73895i	−1.25310	−	0.335767i
$125$	−5.43359	−	5.43359i	−0.485995	−	0.485995i
$126$	−0.465142	−	0.220365i	−0.0414381	−	0.0196317i
$127$	−5.60433	+	3.23566i	−0.497304	+	0.287119i	−0.727600	−	0.686002i	$-0.759364\pi$
$127$	−5.60433	+	3.23566i	−0.497304	+	0.287119i	0.230295	+	0.973121i	$0.426031\pi$
$128$	1.55331	+	1.55331i	0.137294	+	0.137294i
$129$	−0.102004	−	2.51215i	−0.00898097	−	0.221183i
$130$	0.304930	+	0.590302i	0.0267441	+	0.0517729i
$131$	−3.71544	+	2.14511i	−0.324619	+	0.187419i	−0.653450	−	0.756970i	$-0.726679\pi$
$131$	−3.71544	+	2.14511i	−0.324619	+	0.187419i	0.328831	+	0.944389i	$0.393346\pi$
$132$	3.13432	+	10.0476i	0.272807	+	0.874530i
$133$	13.0858			1.13468
$134$	−0.150748	+	0.261103i	−0.0130226	+	0.0225559i
$135$	−13.7296	−	1.93554i	−1.18165	−	0.166585i
$136$	−0.403795	+	0.108196i	−0.0346251	+	0.00927777i
$137$	−2.85894	+	10.6697i	−0.244256	+	0.911575i	0.729500	+	0.683981i	$0.239753\pi$
$137$	−2.85894	+	10.6697i	−0.244256	+	0.911575i	−0.973756	+	0.227595i	$0.926914\pi$
$138$	−0.720299	−	0.161994i	−0.0613159	−	0.0137898i
$139$	−22.9561			−1.94711			−0.973554	−	0.228458i	$-0.926632\pi$
$139$	−22.9561			−1.94711			−0.973554	+	0.228458i	$0.926632\pi$
$140$	6.61348	−	11.4549i	0.558941	−	0.968114i
$141$	4.36076	−	19.3899i	0.367242	−	1.63293i
$142$	−0.196376	−	0.113377i	−0.0164795	−	0.00951443i
$143$	8.11944	−	7.39314i	0.678982	−	0.618245i
$144$	6.77403	+	9.80108i	0.564503	+	0.816757i
$145$	5.37124	−	20.0457i	0.446057	−	1.66471i
$146$			0.0538855i			0.00445960i
$147$	−1.21164	+	0.766715i	−0.0999347	+	0.0632376i
$148$	−0.928176	+	3.46400i	−0.0762956	+	0.284739i
$149$	12.8211	−	12.8211i	1.05034	−	1.05034i	0.0516804	−	0.998664i	$-0.483542\pi$
$149$	12.8211	−	12.8211i	1.05034	−	1.05034i	0.998664	−	0.0516804i	$-0.0164577\pi$
$150$	−0.0556462	+	0.247429i	−0.00454350	+	0.0202025i
$151$	−1.12628	−	4.20335i	−0.0916557	−	0.342064i	0.904836	−	0.425761i	$-0.139994\pi$
$151$	−1.12628	−	4.20335i	−0.0916557	−	0.342064i	−0.996491	+	0.0836977i	$0.973327\pi$
$152$	1.25854	+	0.726621i	0.102081	+	0.0589368i
$153$	−4.53053	+	0.368525i	−0.366271	+	0.0297935i
$154$	0.504720	+	0.135239i	0.0406715	+	0.0108979i
$155$	−9.66001	+	16.7316i	−0.775911	+	1.34392i
$156$	6.29694	−	10.7520i	0.504158	−	0.860849i
$157$	7.99329	+	13.8448i	0.637934	+	1.10493i	0.985885	+	0.167422i	$0.0535442\pi$
$157$	7.99329	+	13.8448i	0.637934	+	1.10493i	−0.347951	+	0.937513i	$0.613122\pi$
$158$	0.228874	+	0.854170i	0.0182083	+	0.0679541i
$159$	−13.9782	−	7.33090i	−1.10855	−	0.581378i
$160$	1.90894	−	1.10213i	0.150915	−	0.0871309i
$161$	10.8431	−	10.8431i	0.854559	−	0.854559i
$162$	−0.255773	−	0.566456i	−0.0200954	−	0.0445050i
$163$	−0.954155	−	3.56095i	−0.0747352	−	0.278915i	0.918438	−	0.395565i	$-0.129451\pi$
$163$	−0.954155	−	3.56095i	−0.0747352	−	0.278915i	−0.993173	+	0.116650i	$0.962785\pi$
$164$	−11.4552	+	3.06940i	−0.894497	+	0.239680i
$165$	14.0645	−	0.571078i	1.09492	−	0.0444584i
$166$	0.187950	+	0.108513i	0.0145877	+	0.00842224i
$167$	11.3397	−	3.03845i	0.877489	−	0.235123i	0.208166	−	0.978094i	$-0.433251\pi$
$167$	11.3397	−	3.03845i	0.877489	−	0.235123i	0.669324	+	0.742971i	$0.266584\pi$
$168$	1.18626	−	0.0481671i	0.0915218	−	0.00371618i
$169$	−12.9431	−	1.21467i	−0.995625	−	0.0934362i
$170$			0.279205i			0.0214140i
$171$	12.0425	+	10.2308i	0.920916	+	0.782367i
$172$	1.44813	+	2.50823i	0.110419	+	0.191251i
$173$	11.9669	+	20.7272i	0.909825	+	1.57586i	0.814306	+	0.580435i	$0.197118\pi$
$173$	11.9669	+	20.7272i	0.909825	+	1.57586i	0.0955183	+	0.995428i	$0.469549\pi$
$174$	0.888059	−	0.277028i	0.0673236	−	0.0210014i
$175$	−3.72471	−	3.72471i	−0.281561	−	0.281561i
$176$	−8.55268	−	8.55268i	−0.644683	−	0.644683i
$177$	1.41849	−	0.442495i	0.106621	−	0.0332600i
$178$	−0.451045	−	0.781233i	−0.0338072	−	0.0585559i
$179$	10.4999	+	18.1864i	0.784802	+	1.35932i	0.929118	+	0.369785i	$0.120569\pi$
$179$	10.4999	+	18.1864i	0.784802	+	1.35932i	−0.144316	+	0.989532i	$0.546098\pi$
$180$	15.0419	−	5.37109i	1.12116	−	0.400337i
$181$			1.43702i			0.106813i	0.998573	+	0.0534065i	$0.0170079\pi$
$181$			1.43702i			0.106813i	−0.998573	+	0.0534065i	$0.982992\pi$
$182$	−0.283904	−	0.549598i	−0.0210443	−	0.0407389i
$183$	9.52173	−	0.386623i	0.703867	−	0.0285800i
$184$	1.64495	−	0.440762i	0.121267	−	0.0324934i
$185$	4.15355	+	2.39805i	0.305375	+	0.176308i
$186$	−0.865323	+	0.0351358i	−0.0634486	+	0.00257628i
$187$	4.45735	−	1.19434i	0.325953	−	0.0873389i
$188$	5.92543	+	22.1140i	0.432156	+	1.61283i
$189$	12.7828	+	1.80208i	0.929815	+	0.131082i
$190$	0.686324	−	0.686324i	0.0497911	−	0.0497911i
$191$	9.75031	−	5.62934i	0.705507	−	0.407325i	−0.103888	−	0.994589i	$-0.533128\pi$
$191$	9.75031	−	5.62934i	0.705507	−	0.407325i	0.809395	+	0.587264i	$0.199795\pi$
$192$	−12.0960	−	6.34376i	−0.872953	−	0.457821i
$193$	1.91899	+	7.16175i	0.138132	+	0.515514i	0.999965	+	0.00832337i	$0.00264944\pi$
$193$	1.91899	+	7.16175i	0.138132	+	0.515514i	−0.861834	+	0.507191i	$0.830684\pi$
$194$	−0.0994259	−	0.172211i	−0.00713836	−	0.0123640i
$195$	−11.7099	−	11.8561i	−0.838565	−	0.849035i
$196$	0.825861	−	1.43043i	0.0589901	−	0.102174i
$197$	−18.9257	−	5.07113i	−1.34840	−	0.361303i	−0.488856	−	0.872364i	$-0.662586\pi$
$197$	−18.9257	−	5.07113i	−1.34840	−	0.361303i	−0.859544	+	0.511062i	$0.829252\pi$
$198$	0.358749	+	0.519060i	0.0254952	+	0.0368880i
$199$	−18.7031	−	10.7982i	−1.32583	−	0.765466i	−0.341174	−	0.940000i	$-0.610825\pi$
$199$	−18.7031	−	10.7982i	−1.32583	−	0.765466i	−0.984651	+	0.174535i	$0.944158\pi$
$200$	−0.151406	−	0.565053i	−0.0107060	−	0.0399553i
$201$	1.65920	−	7.37755i	0.117031	−	0.520372i
$202$	−0.342648	+	0.342648i	−0.0241086	+	0.0241086i
$203$	−5.00087	+	18.6635i	−0.350992	+	1.30992i
$204$	4.42470	−	2.79990i	0.309791	−	0.196032i
$205$			15.8603i			1.10773i
$206$	−0.0735557	+	0.274514i	−0.00512487	+	0.0191263i
$207$	18.4561	−	1.50127i	1.28279	−	0.104345i
$208$	−0.669695	+	14.3034i	−0.0464350	+	0.991766i
$209$	−13.8926	−	8.02091i	−0.960973	−	0.554818i
$210$	0.173986	−	0.773621i	0.0120062	−	0.0533849i
$211$	2.64283	−	4.57751i	0.181940	−	0.315129i	−0.760601	−	0.649219i	$-0.775096\pi$
$211$	2.64283	−	4.57751i	0.181940	−	0.315129i	0.942541	+	0.334090i	$0.108429\pi$
$212$	18.1823			1.24876
$213$	5.54865	+	1.24788i	0.380188	+	0.0855034i
$214$	−0.0766977	+	0.286240i	−0.00524294	+	0.0195669i
$215$	3.74141	−	1.00251i	0.255162	−	0.0683704i
$216$	1.12934	+	0.883117i	0.0768422	+	0.0600885i
$217$	8.99391	−	15.5779i	0.610547	−	1.05750i
$218$	−0.535492			−0.0362681
$219$	−0.402470	−	1.29019i	−0.0271964	−	0.0871827i
$220$	−14.0425	+	8.10744i	−0.946745	+	0.546604i
$221$	−4.59817	−	2.94978i	−0.309306	−	0.198424i
$222$	0.00872231	+	0.214812i	0.000585403	+	0.0144173i
$223$	−17.1866	−	17.1866i	−1.15090	−	1.15090i	−0.986372	−	0.164530i	$-0.947389\pi$
$223$	−17.1866	−	17.1866i	−1.15090	−	1.15090i	−0.164530	−	0.986372i	$-0.552611\pi$
$224$	−1.77731	+	1.02613i	−0.118752	+	0.0685613i
$225$	−0.515699	−	6.33983i	−0.0343799	−	0.422655i
$226$	−0.383736	−	0.383736i	−0.0255258	−	0.0255258i
$227$	−8.77546	−	2.35138i	−0.582448	−	0.156066i	−0.0444484	−	0.999012i	$-0.514153\pi$
$227$	−8.77546	−	2.35138i	−0.582448	−	0.156066i	−0.537999	+	0.842945i	$0.680820\pi$
$228$	−17.7591	−	3.99398i	−1.17612	−	0.264508i
$229$	−8.49524	−	2.27629i	−0.561382	−	0.150422i	−0.0330406	−	0.999454i	$-0.510519\pi$
$229$	−8.49524	−	2.27629i	−0.561382	−	0.150422i	−0.528341	+	0.849032i	$0.677186\pi$
$230$		−	1.13740i		−	0.0749981i
$231$	−13.0947	+	0.531700i	−0.861566	+	0.0349833i
$232$	−1.51730	+	1.51730i	−0.0996159	+	0.0996159i
$233$	−15.0989			−0.989160			−0.494580	−	0.869132i	$-0.664678\pi$
$233$	−15.0989			−0.989160			−0.494580	+	0.869132i	$0.664678\pi$
$234$	0.168419	−	0.727745i	0.0110099	−	0.0475742i
$235$	30.6181			1.99730
$236$	−1.21035	+	1.21035i	−0.0787869	+	0.0787869i
$237$	−11.8597	−	18.7420i	−0.770373	−	1.21743i
$238$		−	0.259952i		−	0.0168502i
$239$	−3.36090	−	0.900550i	−0.217398	−	0.0582518i	0.148476	−	0.988916i	$-0.452563\pi$
$239$	−3.36090	−	0.900550i	−0.217398	−	0.0582518i	−0.365874	+	0.930664i	$0.619230\pi$
$240$	−12.4417	+	13.4948i	−0.803105	+	0.871084i
$241$	18.0220	+	4.82899i	1.16090	+	0.311063i	0.787326	−	0.616537i	$-0.211465\pi$
$241$	18.0220	+	4.82899i	1.16090	+	0.311063i	0.373576	+	0.927600i	$0.378132\pi$
$242$	0.0842012	+	0.0842012i	0.00541266	+	0.00541266i
$243$	10.3549	+	11.6523i	0.664264	+	0.747498i
$244$	−9.50685	+	5.48878i	−0.608614	+	0.351383i
$245$	−1.56198	−	1.56198i	−0.0997915	−	0.0997915i
$246$	−0.600773	+	0.380163i	−0.0383039	+	0.0242383i
$247$	4.05197	+	18.5539i	0.257820	+	1.18056i
$248$	1.73001	−	0.998820i	0.109856	−	0.0634251i
$249$	−5.31058	−	1.19434i	−0.336545	−	0.0756882i
$250$	0.530661			0.0335619
$251$	4.80452	−	8.32168i	0.303259	−	0.525260i	−0.673613	−	0.739084i	$-0.735259\pi$
$251$	4.80452	−	8.32168i	0.303259	−	0.525260i	0.976872	+	0.213824i	$0.0685920\pi$
$252$	−14.0047	+	5.00073i	−0.882215	+	0.315016i
$253$	−18.1580	+	4.86542i	−1.14158	+	0.305886i
$254$	0.115666	−	0.431671i	0.00725752	−	0.0270854i
$255$	−2.08538	−	6.68503i	−0.130591	−	0.418633i
$256$	15.6198			0.976240
$257$	6.82540	−	11.8219i	0.425757	−	0.737432i	−0.570734	−	0.821135i	$-0.693341\pi$
$257$	6.82540	−	11.8219i	0.425757	−	0.737432i	0.996491	+	0.0837028i	$0.0266746\pi$
$258$	0.127653	+	0.117691i	0.00794735	+	0.00732714i
$259$	−3.86714	−	2.23270i	−0.240293	−	0.138733i
$260$	18.2893	+	5.83007i	1.13426	+	0.361566i
$261$	−19.1938	+	13.2658i	−1.18806	+	0.821132i
$262$	0.0766815	−	0.286179i	0.00473740	−	0.0176802i
$263$		−	21.5743i		−	1.33033i	−0.746697	−	0.665165i	$-0.768361\pi$
$263$		−	21.5743i		−	1.33033i	0.746697	−	0.665165i	$-0.231639\pi$
$264$	−1.28892	−	0.675978i	−0.0793278	−	0.0416036i
$265$	6.29360	−	23.4880i	0.386612	−	1.44286i
$266$	−0.638999	+	0.638999i	−0.0391795	+	0.0391795i
$267$	16.6344	+	15.3363i	1.01801	+	0.938565i
$268$	2.25453	+	8.41400i	0.137717	+	0.513967i
$269$	4.14355	+	2.39228i	0.252637	+	0.145860i	0.620971	−	0.783834i	$-0.286738\pi$
$269$	4.14355	+	2.39228i	0.252637	+	0.145860i	−0.368334	+	0.929693i	$0.620072\pi$
$270$	0.764951	−	0.575920i	0.0465534	−	0.0350494i
$271$	−25.9261	−	6.94689i	−1.57490	−	0.421993i	−0.637558	−	0.770402i	$-0.720055\pi$
$271$	−25.9261	−	6.94689i	−1.57490	−	0.421993i	−0.937343	+	0.348409i	$0.886722\pi$
$272$	−3.00867	+	5.21116i	−0.182427	+	0.315973i
$273$	10.9025	+	11.0386i	0.659847	+	0.668086i
$274$	−0.381412	−	0.660625i	−0.0230419	−	0.0399098i
$275$	1.67131	+	6.23742i	0.100784	+	0.376131i
$276$	−18.0250	+	11.4060i	−1.08498	+	0.686562i
$277$	−5.84498	+	3.37460i	−0.351191	+	0.202760i	−0.665210	−	0.746657i	$-0.731658\pi$
$277$	−5.84498	+	3.37460i	−0.351191	+	0.202760i	0.314019	+	0.949417i	$0.398325\pi$
$278$	1.12098	−	1.12098i	0.0672319	−	0.0672319i
$279$	20.4561	−	7.30435i	1.22467	−	0.437300i
$280$	0.473391	+	1.76672i	0.0282905	+	0.105582i
$281$	−24.9941	+	6.69716i	−1.49102	+	0.399519i	−0.910083	−	0.414426i	$-0.863982\pi$
$281$	−24.9941	+	6.69716i	−1.49102	+	0.399519i	−0.580942	+	0.813945i	$0.697316\pi$
$282$	0.733898	+	1.15978i	0.0437030	+	0.0690641i
$283$	−12.7667	−	7.37086i	−0.758902	−	0.438152i	0.0699994	−	0.997547i	$-0.477700\pi$
$283$	−12.7667	−	7.37086i	−0.758902	−	0.438152i	−0.828901	+	0.559395i	$0.811034\pi$
$284$	−6.32817	+	1.69563i	−0.375508	+	0.100617i
$285$	−11.3066	+	21.5589i	−0.669743	+	1.27704i
$286$	−0.0354667	+	0.757503i	−0.00209719	+	0.0447921i
$287$		−	14.7667i		−	0.871649i
$288$	−2.43788	−	0.445220i	−0.143653	−	0.0262348i
$289$	7.35214	+	12.7343i	0.432479	+	0.749075i
$290$	0.716578	+	1.24115i	0.0420789	+	0.0728829i
$291$	3.66680	+	3.38064i	0.214952	+	0.198177i
$292$	1.10087	+	1.10087i	0.0644233	+	0.0644233i
$293$	−11.9906	−	11.9906i	−0.700501	−	0.700501i	0.264017	−	0.964518i	$-0.414952\pi$
$293$	−11.9906	−	11.9906i	−0.700501	−	0.700501i	−0.964518	+	0.264017i	$0.914952\pi$
$294$	0.0217266	−	0.0966063i	0.00126712	−	0.00563420i
$295$	1.14459	+	1.98249i	0.0666405	+	0.115425i
$296$	−0.247952	−	0.429466i	−0.0144119	−	0.0249622i
$297$	−12.4664	−	9.74842i	−0.723375	−	0.565660i
$298$			1.25215i			0.0725349i
$299$	18.7317	+	12.0166i	1.08328	+	0.694937i
$300$	3.91806	+	6.19174i	0.226210	+	0.357480i
$301$	−3.48342	+	0.933380i	−0.200781	+	0.0537991i
$302$	0.260254	+	0.150258i	0.0149759	+	0.00864637i
$303$	5.64481	−	10.7633i	0.324286	−	0.618334i
$304$	20.2055	−	5.41404i	1.15886	−	0.310517i
$305$	3.79977	+	14.1809i	0.217574	+	0.811997i
$306$	0.203237	−	0.239228i	0.0116183	−	0.0136758i
$307$	2.71788	−	2.71788i	0.155118	−	0.155118i	−0.625282	−	0.780399i	$-0.715016\pi$
$307$	2.71788	−	2.71788i	0.155118	−	0.155118i	0.780399	+	0.625282i	$0.215016\pi$
$308$	13.0742	−	7.54840i	0.744972	−	0.430110i
$309$	−0.289187	−	7.12209i	−0.0164513	−	0.405162i
$310$	−0.345318	−	1.28874i	−0.0196128	−	0.0731958i
$311$	−2.89624	−	5.01644i	−0.164231	−	0.284456i	0.772151	−	0.635439i	$-0.219181\pi$
$311$	−2.89624	−	5.01644i	−0.164231	−	0.284456i	−0.936382	+	0.350983i	$0.885848\pi$
$312$	0.435615	+	1.66704i	0.0246619	+	0.0943777i
$313$	1.55795	−	2.69845i	0.0880607	−	0.152526i	−0.818631	−	0.574320i	$-0.805266\pi$
$313$	1.55795	−	2.69845i	0.0880607	−	0.152526i	0.906691	+	0.421795i	$0.138600\pi$
$314$	−1.06639	−	0.285738i	−0.0601797	−	0.0161251i
$315$	1.61241	+	19.8224i	0.0908488	+	1.11686i
$316$	22.1263	+	12.7746i	1.24470	+	0.718629i
$317$	−4.56569	−	17.0394i	−0.256435	−	0.957027i	−0.967287	−	0.253685i	$-0.918357\pi$
$317$	−4.56569	−	17.0394i	−0.256435	−	0.957027i	0.710852	−	0.703341i	$-0.248309\pi$
$318$	1.04056	−	0.324599i	0.0583515	−	0.0182026i
$319$	16.7490	−	16.7490i	0.937763	−	0.937763i
$320$	5.44613	−	20.3252i	0.304448	−	1.13622i
$321$	−0.301540	−	7.42632i	−0.0168303	−	0.414497i
$322$			1.05897i			0.0590143i
$323$	−2.06555	+	7.70875i	−0.114930	+	0.428926i
$324$	−16.7979	−	6.34717i	−0.933218	−	0.352620i
$325$	4.12780	−	6.43448i	0.228969	−	0.356921i
$326$	0.220480	+	0.127294i	0.0122112	+	0.00705017i
$327$	12.8213	−	3.99958i	0.709021	−	0.221177i
$328$	0.819958	−	1.42021i	0.0452746	−	0.0784179i
$329$	−28.5068			−1.57163
$330$	−0.658903	+	0.714677i	−0.0362714	+	0.0393417i
$331$	2.92960	−	10.9334i	0.161026	−	0.600956i	−0.837488	−	0.546455i	$-0.815977\pi$
$331$	2.92960	−	10.9334i	0.161026	−	0.600956i	0.998514	−	0.0545002i	$-0.0173565\pi$
$332$	6.05666	−	1.62288i	0.332402	−	0.0890669i
$333$	−1.81327	−	5.07813i	−0.0993666	−	0.278280i
$334$	−0.405361	+	0.702106i	−0.0221804	+	0.0384175i
$335$	11.6497			0.636489
$336$	11.5837	−	12.5643i	0.631945	−	0.685436i
$337$	15.9475	−	9.20731i	0.868717	−	0.501554i	0.00179550	−	0.999998i	$-0.499428\pi$
$337$	15.9475	−	9.20731i	0.868717	−	0.501554i	0.866922	+	0.498444i	$0.166095\pi$
$338$	0.691347	−	0.572719i	0.0376043	−	0.0311518i
$339$	12.0540	+	6.32171i	0.654681	+	0.343348i
$340$	5.70408	+	5.70408i	0.309347	+	0.309347i
$341$	−19.0969	+	11.0256i	−1.03416	+	0.597071i
$342$	−1.08764	+	0.0884716i	−0.0588129	+	0.00478400i
$343$	13.7514	+	13.7514i	0.742503	+	0.742503i
$344$	−0.386852	−	0.103657i	−0.0208576	−	0.00558879i
$345$	8.49525	+	27.2329i	0.457369	+	1.46617i
$346$	−1.59650	−	0.427782i	−0.0858286	−	0.0229977i
$347$		−	1.22520i		−	0.0657723i	−0.999459	−	0.0328861i	$-0.989530\pi$
$347$		−	1.22520i		−	0.0657723i	0.999459	−	0.0328861i	$-0.0104699\pi$
$348$	12.4832	−	23.8024i	0.669170	−	1.27594i
$349$	6.73689	−	6.73689i	0.360617	−	0.360617i	−0.503423	−	0.864040i	$-0.667926\pi$
$349$	6.73689	−	6.73689i	0.360617	−	0.360617i	0.864040	+	0.503423i	$0.167926\pi$
$350$	0.363766			0.0194441
$351$	1.40305	+	18.6824i	0.0748895	+	0.997192i
$352$	2.51587			0.134096
$353$	−12.8088	+	12.8088i	−0.681746	+	0.681746i	−0.960393	−	0.278647i	$-0.910114\pi$
$353$	−12.8088	+	12.8088i	−0.681746	+	0.681746i	0.278647	+	0.960393i	$0.410114\pi$
$354$	−0.0476595	+	0.0908750i	−0.00253307	+	0.00482995i
$355$			8.76172i			0.465024i
$356$	−25.1751	−	6.74565i	−1.33428	−	0.357519i
$357$	1.94158	+	6.22406i	0.102759	+	0.329412i
$358$	−1.40080	−	0.375343i	−0.0740345	−	0.0198375i
$359$	10.4633	+	10.4633i	0.552233	+	0.552233i	0.927085	−	0.374851i	$-0.122306\pi$
$359$	10.4633	+	10.4633i	0.552233	+	0.552233i	−0.374851	+	0.927085i	$0.622306\pi$
$360$	−0.945613	+	1.99598i	−0.0498382	+	0.105197i
$361$	7.57210	−	4.37175i	0.398532	−	0.230092i
$362$	−0.0701720	−	0.0701720i	−0.00368816	−	0.00368816i
$363$	−2.64494	−	1.38714i	−0.138823	−	0.0728060i
$364$	−17.0282	−	5.42806i	−0.892521	−	0.284508i
$365$	1.80316	−	1.04106i	0.0943818	−	0.0544914i
$366$	−0.446081	+	0.483840i	−0.0233170	+	0.0252907i
$367$	0.757181			0.0395245			0.0197623	−	0.999805i	$-0.493709\pi$
$367$	0.757181			0.0395245			0.0197623	+	0.999805i	$0.493709\pi$
$368$	12.2565	−	21.2288i	0.638913	−	1.10663i
$369$	11.5449	−	13.5894i	0.601006	−	0.707438i
$370$	−0.319925	+	0.0857236i	−0.0166321	+	0.00445656i
$371$	−5.85962	+	21.8684i	−0.304217	+	1.13535i
$372$	−16.9605	+	18.3961i	−0.879361	+	0.953795i
$373$	22.3838			1.15899			0.579494	−	0.814977i	$-0.303250\pi$
$373$	22.3838			1.15899			0.579494	+	0.814977i	$0.303250\pi$
$374$	−0.159337	+	0.275981i	−0.00823914	+	0.0142706i
$375$	−12.7057	+	3.96350i	−0.656118	+	0.204674i
$376$	−2.74169	−	1.58291i	−0.141392	−	0.0816326i
$377$	−28.0109	−	1.31148i	−1.44263	−	0.0675448i
$378$	−0.712204	+	0.536207i	−0.0366318	+	0.0275795i
$379$	−5.60828	+	20.9304i	−0.288078	+	1.07512i	0.658483	+	0.752596i	$0.271199\pi$
$379$	−5.60828	+	20.9304i	−0.288078	+	1.07512i	−0.946561	+	0.322526i	$0.895468\pi$
$380$		−	28.0428i		−	1.43857i
$381$	0.454745	+	11.1994i	0.0232973	+	0.573765i
$382$	−0.201233	+	0.751012i	−0.0102960	+	0.0384251i
$383$	−8.28987	+	8.28987i	−0.423593	+	0.423593i	−0.886439	−	0.462846i	$-0.846828\pi$
$383$	−8.28987	+	8.28987i	−0.423593	+	0.423593i	0.462846	+	0.886439i	$0.346828\pi$
$384$	3.63219	−	1.13305i	0.185354	−	0.0578208i
$385$	−5.22559	−	19.5022i	−0.266321	−	0.993923i
$386$	−0.443427	−	0.256012i	−0.0225698	−	0.0130307i
$387$	−3.93545	−	1.86445i	−0.200050	−	0.0947755i
$388$	−5.54946	−	1.48697i	−0.281731	−	0.0754896i
$389$	5.55179	−	9.61598i	0.281487	−	0.487550i	−0.690264	−	0.723557i	$-0.742506\pi$
$389$	5.55179	−	9.61598i	0.281487	−	0.487550i	0.971751	+	0.236008i	$0.0758391\pi$
$390$	1.15077	+	0.00713984i	0.0582713	+	0.000361540i
$391$	4.67607	+	8.09918i	0.236479	+	0.409593i
$392$	0.0591150	+	0.220620i	0.00298576	+	0.0111430i
$393$	0.301477	+	7.42475i	0.0152075	+	0.374529i
$394$	1.17180	−	0.676540i	0.0590345	−	0.0340836i
$395$	24.1612	−	24.1612i	1.21568	−	1.21568i
$396$	17.9334	+	3.27511i	0.901188	+	0.164580i
$397$	−4.35209	−	16.2422i	−0.218425	−	0.815174i	−0.984933	−	0.172939i	$-0.944674\pi$
$397$	−4.35209	−	16.2422i	−0.218425	−	0.815174i	0.766507	−	0.642236i	$-0.221993\pi$
$398$	1.44059	−	0.386006i	0.0722104	−	0.0193487i
$399$	10.5269	−	20.0723i	0.527006	−	1.00487i
$400$	−7.29228	−	4.21020i	−0.364614	−	0.210510i
$401$	14.2769	−	3.82550i	0.712957	−	0.191036i	0.115930	−	0.993257i	$-0.463015\pi$
$401$	14.2769	−	3.82550i	0.712957	−	0.191036i	0.597027	+	0.802221i	$0.296349\pi$
$402$	0.279236	+	0.441278i	0.0139270	+	0.0220090i
$403$	24.8724	+	7.92853i	1.23898	+	0.394948i
$404$			14.0004i			0.696546i
$405$	−14.0138	+	19.5027i	−0.696349	+	0.969097i
$406$	−0.667167	−	1.15557i	−0.0331110	−	0.0573499i
$407$	2.73706	+	4.74072i	0.135671	+	0.234989i
$408$	−0.158873	+	0.706420i	−0.00786536	+	0.0349730i
$409$	5.49716	+	5.49716i	0.271817	+	0.271817i	0.829831	−	0.558014i	$-0.188437\pi$
$409$	5.49716	+	5.49716i	0.271817	+	0.271817i	−0.558014	+	0.829831i	$0.688437\pi$
$410$	−0.774484	−	0.774484i	−0.0382490	−	0.0382490i
$411$	14.0664	+	12.9686i	0.693844	+	0.639696i
$412$	4.10552	+	7.11096i	0.202264	+	0.350332i
$413$	−1.06566	−	1.84578i	−0.0524379	−	0.0908251i
$414$	−0.827931	+	0.974550i	−0.0406906	+	0.0478965i
$415$		−	8.38579i		−	0.411642i
$416$	−2.00526	−	2.20226i	−0.0983159	−	0.107975i
$417$	−18.4671	+	35.2123i	−0.904340	+	1.72435i
$418$	1.07007	−	0.286725i	0.0523389	−	0.0140242i
$419$	33.4591	+	19.3176i	1.63458	+	0.943727i	0.982654	+	0.185447i	$0.0593732\pi$
$419$	33.4591	+	19.3176i	1.63458	+	0.943727i	0.651929	+	0.758280i	$0.273960\pi$
$420$	−12.2504	−	19.3594i	−0.597758	−	0.944640i
$421$	−21.1545	+	5.66833i	−1.03101	+	0.276258i	−0.734382	−	0.678736i	$-0.762528\pi$
$421$	−21.1545	+	5.66833i	−1.03101	+	0.276258i	−0.296625	+	0.954994i	$0.595861\pi$
$422$	0.0944736	+	0.352580i	0.00459890	+	0.0171633i
$423$	−26.2342	−	22.2873i	−1.27555	−	1.08365i
$424$	−1.77786	+	1.77786i	−0.0863404	+	0.0863404i
$425$	2.78214	−	1.60627i	0.134953	−	0.0779154i
$426$	−0.331885	+	0.210013i	−0.0160799	+	0.0101752i
$427$	−3.53776	−	13.2031i	−0.171204	−	0.638942i
$428$	4.28089	+	7.41471i	0.206924	+	0.358404i
$429$	−4.80860	−	18.4019i	−0.232161	−	0.888451i
$430$	−0.133745	+	0.231653i	−0.00644974	+	0.0111713i
$431$	−6.12425	−	1.64099i	−0.294995	−	0.0790436i	0.108286	−	0.994120i	$-0.465464\pi$
$431$	−6.12425	−	1.64099i	−0.294995	−	0.0790436i	−0.403281	+	0.915076i	$0.632130\pi$
$432$	20.4833	−	2.50615i	0.985503	−	0.120577i
$433$	−15.1663	−	8.75626i	−0.728846	−	0.420799i	0.0891542	−	0.996018i	$-0.471584\pi$
$433$	−15.1663	−	8.75626i	−0.728846	−	0.420799i	−0.818000	+	0.575219i	$0.804917\pi$
$434$	0.321507	+	1.19988i	0.0154328	+	0.0575961i
$435$	−26.4272	−	24.3649i	−1.26709	−	1.16821i
$436$	−10.9400	+	10.9400i	−0.523929	+	0.523929i
$437$	8.41449	−	31.4033i	0.402520	−	1.50222i
$438$	0.0826550	+	0.0433485i	0.00394941	+	0.00207127i
$439$			19.2364i			0.918101i	0.888410	+	0.459051i	$0.151810\pi$
$439$			19.2364i			0.918101i	−0.888410	+	0.459051i	$0.848190\pi$
$440$	0.580329	−	2.16582i	0.0276661	−	0.103251i
$441$	0.201350	+	2.47533i	0.00958809	+	0.117873i
$442$	0.368578	−	0.0804934i	0.0175315	−	0.00382868i
$443$	10.3181	+	5.95715i	0.490227	+	0.283033i	0.724669	−	0.689097i	$-0.241993\pi$
$443$	10.3181	+	5.95715i	0.490227	+	0.283033i	−0.234442	+	0.972130i	$0.575326\pi$
$444$	4.56676	+	4.21037i	0.216729	+	0.199815i
$445$	−17.4282	+	30.1865i	−0.826175	+	1.43098i
$446$	1.67850			0.0794793
$447$	−9.35227	−	29.9803i	−0.442347	−	1.41802i
$448$	−5.07060	+	18.9237i	−0.239563	+	0.894062i
$449$	2.87999	−	0.771691i	0.135915	−	0.0364183i	−0.190220	−	0.981741i	$-0.560920\pi$
$449$	2.87999	−	0.771691i	0.135915	−	0.0364183i	0.326135	+	0.945323i	$0.394254\pi$
$450$	0.334766	+	0.284401i	0.0157810	+	0.0134068i
$451$	−9.05122	+	15.6772i	−0.426205	+	0.738209i
$452$	−15.6793			−0.737491
$453$	−7.35356	−	1.65380i	−0.345501	−	0.0777024i
$454$	0.543341	−	0.313698i	0.0255002	−	0.0147226i
$455$	−12.9062	+	20.1183i	−0.605050	+	0.943162i
$456$	2.12701	−	1.34595i	0.0996063	−	0.0630298i
$457$	−5.03165	−	5.03165i	−0.235371	−	0.235371i	0.579559	−	0.814930i	$-0.303225\pi$
$457$	−5.03165	−	5.03165i	−0.235371	−	0.235371i	−0.814930	+	0.579559i	$0.803225\pi$
$458$	0.525991	−	0.303681i	0.0245779	−	0.0141901i
$459$	−3.07933	+	7.24584i	−0.143731	+	0.338207i
$460$	−23.2368	−	23.2368i	−1.08342	−	1.08342i
$461$	14.5266	+	3.89238i	0.676570	+	0.181286i	0.580712	−	0.814109i	$-0.302774\pi$
$461$	14.5266	+	3.89238i	0.676570	+	0.181286i	0.0958574	+	0.995395i	$0.469441\pi$
$462$	0.613469	−	0.665397i	0.0285412	−	0.0309571i
$463$	−31.9383	−	8.55785i	−1.48430	−	0.397717i	−0.576492	−	0.817103i	$-0.695579\pi$
$463$	−31.9383	−	8.55785i	−1.48430	−	0.397717i	−0.907808	+	0.419386i	$0.862245\pi$
$464$			30.8870i			1.43389i
$465$	17.8936	+	28.2774i	0.829796	+	1.31133i
$466$	0.737301	−	0.737301i	0.0341548	−	0.0341548i
$467$	−17.4914			−0.809406			−0.404703	−	0.914448i	$-0.632625\pi$
$467$	−17.4914			−0.809406			−0.404703	+	0.914448i	$0.632625\pi$
$468$	−11.4269	−	18.3084i	−0.528208	−	0.846305i
$469$	−10.8464			−0.500839
$470$	−1.49513	+	1.49513i	−0.0689651	+	0.0689651i
$471$	27.6668	−	1.12339i	1.27482	−	0.0517631i
$472$		−	0.236695i		−	0.0108948i
$473$	4.27032	+	1.14423i	0.196349	+	0.0526117i
$474$	1.49433	+	0.336072i	0.0686369	+	0.0154363i
$475$	−10.7873	−	2.89045i	−0.494955	−	0.132623i
$476$	−5.31076	−	5.31076i	−0.243418	−	0.243418i
$477$	−22.4897	+	15.5438i	−1.02973	+	0.711702i
$478$	0.208093	−	0.120143i	0.00951796	−	0.00549520i
$479$	−3.79749	−	3.79749i	−0.173512	−	0.173512i	0.615009	−	0.788520i	$-0.289153\pi$
$479$	−3.79749	−	3.79749i	−0.173512	−	0.173512i	−0.788520	+	0.615009i	$0.789153\pi$
$480$	−0.154895	−	3.81474i	−0.00706995	−	0.174118i
$481$	1.96822	−	6.17445i	0.0897432	−	0.281531i
$482$	−1.11585	+	0.644237i	−0.0508256	+	0.0293442i
$483$	−7.90946	−	25.3551i	−0.359893	−	1.15370i
$484$	3.44042			0.156383
$485$	−3.84177	+	6.65415i	−0.174446	+	0.302149i
$486$	−1.07465	−	0.0633585i	−0.0487469	−	0.00287400i
$487$	28.6358	−	7.67295i	1.29761	−	0.347694i	0.457066	−	0.889433i	$-0.348900\pi$
$487$	28.6358	−	7.67295i	1.29761	−	0.347694i	0.840547	+	0.541738i	$0.182234\pi$
$488$	0.392886	−	1.46627i	0.0177851	−	0.0663749i
$489$	−6.22973	−	1.40105i	−0.281718	−	0.0633578i
$490$	0.152548			0.00689143
$491$	−11.9131	+	20.6341i	−0.537631	+	0.931204i	0.461400	+	0.887192i	$0.347347\pi$
$491$	−11.9131	+	20.6341i	−0.537631	+	0.931204i	−0.999031	+	0.0440116i	$0.985986\pi$
$492$	−4.50702	+	20.0403i	−0.203192	+	0.903485i
$493$	−10.2052	−	5.89196i	−0.459618	−	0.265361i
$494$	−1.10388	−	0.708152i	−0.0496659	−	0.0318613i
$495$	10.4383	−	22.0329i	0.469166	−	0.990306i
$496$	7.44219	−	27.7746i	0.334164	−	1.24712i
$497$		−	8.15756i		−	0.365916i
$498$	0.317645	−	0.201003i	0.0142340	−	0.00900714i
$499$	−4.12436	+	15.3923i	−0.184632	+	0.689054i	0.810078	+	0.586323i	$0.199425\pi$
$499$	−4.12436	+	15.3923i	−0.184632	+	0.689054i	−0.994709	+	0.102732i	$0.967242\pi$
$500$	10.8413	−	10.8413i	0.484836	−	0.484836i
$501$	4.46158	−	19.8382i	0.199329	−	0.886306i
$502$	0.171748	+	0.640973i	0.00766549	+	0.0286080i
$503$	−16.3090	−	9.41599i	−0.727182	−	0.419838i	0.0902087	−	0.995923i	$-0.471247\pi$
$503$	−16.3090	−	9.41599i	−0.727182	−	0.419838i	−0.817390	+	0.576084i	$0.804580\pi$
$504$	0.880409	−	1.85835i	0.0392165	−	0.0827775i
$505$	18.0858	+	4.84609i	0.804810	+	0.215648i
$506$	0.649097	−	1.12427i	0.0288559	−	0.0499798i
$507$	−12.2754	+	18.8763i	−0.545168	+	0.838327i
$508$	−6.45590	−	11.1819i	−0.286434	−	0.496118i
$509$	6.63911	+	24.7775i	0.294273	+	1.09824i	0.941793	+	0.336194i	$0.109140\pi$
$509$	6.63911	+	24.7775i	0.294273	+	1.09824i	−0.647520	+	0.762049i	$0.724194\pi$
$510$	0.428272	+	0.224608i	0.0189642	+	0.00994581i
$511$	−1.67883	+	0.969271i	−0.0742669	+	0.0428780i
$512$	−3.86936	+	3.86936i	−0.171003	+	0.171003i
$513$	25.3807	−	10.2419i	1.12058	−	0.452189i
$514$	0.243989	+	0.910578i	0.0107619	+	0.0401639i
$515$	10.6071	−	2.84216i	0.467404	−	0.125241i
$516$	5.01233	−	0.203522i	0.220655	−	0.00895956i
$517$	30.2645	+	17.4732i	1.33103	+	0.768471i
$518$	0.297865	−	0.0798126i	0.0130874	−	0.00350676i
$519$	41.4203	−	1.68184i	1.81815	−	0.0738247i
$520$	−2.35839	+	1.21826i	−0.103422	+	0.0534244i
$521$		−	0.0536058i		−	0.00234851i	−0.999999	−	0.00117426i	$-0.999626\pi$
$521$		−	0.0536058i		−	0.00234851i	0.999999	−	0.00117426i	$-0.000373777\pi$
$522$	0.289471	−	1.58505i	0.0126698	−	0.0693758i
$523$	−7.40582	−	12.8273i	−0.323834	−	0.560897i	0.657442	−	0.753505i	$-0.271639\pi$
$523$	−7.40582	−	12.8273i	−0.323834	−	0.560897i	−0.981276	+	0.192608i	$0.938305\pi$
$524$	−4.27998	−	7.41315i	−0.186972	−	0.323845i
$525$	−8.70969	+	2.71697i	−0.380122	+	0.118578i
$526$	1.05351	+	1.05351i	0.0459351	+	0.0459351i
$527$	7.75719	+	7.75719i	0.337909	+	0.337909i
$528$	−19.9992	+	6.23871i	−0.870355	+	0.271505i
$529$	−7.54899	−	13.0752i	−0.328217	−	0.568489i
$530$	0.839630	+	1.45428i	0.0364712	+	0.0631700i
$531$	0.462372	−	2.53180i	0.0200652	−	0.109871i
$532$			26.1091i			1.13197i
$533$	20.9372	−	4.57245i	0.906891	−	0.198055i
$534$	−1.56118	+	0.0633906i	−0.0675588	+	0.00274318i
$535$	11.0602	−	2.96357i	0.478173	−	0.128126i
$536$	−1.04317	−	0.602273i	−0.0450579	−	0.0260142i
$537$	36.3429	−	1.47568i	1.56831	−	0.0636801i
$538$	−0.319155	+	0.0855173i	−0.0137597	+	0.00368691i
$539$	−0.652549	−	2.43535i	−0.0281073	−	0.104898i
$540$	3.86185	−	27.3936i	0.166188	−	1.17883i
$541$	−6.00591	+	6.00591i	−0.258214	+	0.258214i	−0.824328	−	0.566113i	$-0.808447\pi$
$541$	−6.00591	+	6.00591i	−0.258214	+	0.258214i	0.566113	+	0.824328i	$0.308447\pi$
$542$	1.60524	−	0.926786i	0.0689510	−	0.0398089i
$543$	2.20425	+	1.15602i	0.0945933	+	0.0496096i
$544$	−0.323944	−	1.20898i	−0.0138890	−	0.0518344i
$545$	10.3456	+	17.9191i	0.443156	+	0.767569i
$546$	−1.07142	−	0.00664752i	−0.0458524	−	0.000284488i
$547$	−8.68966	+	15.0509i	−0.371543	+	0.643532i	−0.989803	−	0.142442i	$-0.954505\pi$
$547$	−8.68966	+	15.0509i	−0.371543	+	0.643532i	0.618260	+	0.785974i	$0.287838\pi$
$548$	−21.2885	−	5.70425i	−0.909402	−	0.243673i
$549$	7.06677	−	14.9164i	0.301603	−	0.636617i
$550$	−0.386196	−	0.222970i	−0.0164674	−	0.00950748i
$551$	10.6025	+	39.5690i	0.451681	+	1.68570i
$552$	0.647203	−	2.87776i	0.0275468	−	0.122486i
$553$	−22.4952	+	22.4952i	−0.956591	+	0.956591i
$554$	0.120633	−	0.450207i	0.00512518	−	0.0191274i
$555$	7.01972	−	4.44200i	0.297971	−	0.188553i
$556$		−	45.8026i		−	1.94246i
$557$	1.51385	−	5.64977i	0.0641440	−	0.239389i	−0.926409	−	0.376518i	$-0.877121\pi$
$557$	1.51385	−	5.64977i	0.0641440	−	0.239389i	0.990553	+	0.137130i	$0.0437878\pi$
$558$	−0.642220	+	1.35558i	−0.0271873	+	0.0573865i
$559$	−2.40204	−	4.65001i	−0.101595	−	0.196675i
$560$	22.8004	+	13.1638i	0.963491	+	0.556272i
$561$	1.75374	−	7.79792i	0.0740428	−	0.329228i
$562$	0.893469	−	1.54753i	0.0376887	−	0.0652788i
$563$	−20.1043			−0.847296			−0.423648	−	0.905827i	$-0.639251\pi$
$563$	−20.1043			−0.847296			−0.423648	+	0.905827i	$0.639251\pi$
$564$	38.6874	+	8.70072i	1.62903	+	0.366366i
$565$	−5.42721	+	20.2546i	−0.228324	+	0.852118i
$566$	0.983348	−	0.263487i	0.0413332	−	0.0110752i
$567$	13.0474	−	18.1579i	0.547941	−	0.762560i
$568$	0.452969	−	0.784566i	0.0190062	−	0.0329196i
$569$	−27.7031			−1.16137			−0.580687	−	0.814127i	$-0.697216\pi$
$569$	−27.7031			−1.16137			−0.580687	+	0.814127i	$0.697216\pi$
$570$	−0.500635	−	1.60487i	−0.0209693	−	0.0672206i
$571$	−12.3582	+	7.13501i	−0.517174	+	0.298591i	−0.735778	−	0.677223i	$-0.763183\pi$
$571$	−12.3582	+	7.13501i	−0.517174	+	0.298591i	0.218603	+	0.975814i	$0.429850\pi$
$572$	14.7510	+	16.2002i	0.616771	+	0.677363i
$573$	−0.791157	−	19.4846i	−0.0330510	−	0.813979i
$574$	0.721080	+	0.721080i	0.0300973	+	0.0300973i
$575$	−11.3337	+	6.54349i	−0.472646	+	0.272882i
$576$	−19.4614	+	13.4508i	−0.810891	+	0.560449i
$577$	5.31921	+	5.31921i	0.221442	+	0.221442i	0.809105	−	0.587664i	$-0.199952\pi$
$577$	5.31921	+	5.31921i	0.221442	+	0.221442i	−0.587664	+	0.809105i	$0.699952\pi$
$578$	−0.980851	−	0.262818i	−0.0407980	−	0.0109318i
$579$	12.5292	+	2.81778i	0.520694	+	0.117103i
$580$	39.9959	+	10.7169i	1.66074	+	0.444994i
$581$			7.80755i			0.323912i
$582$	−0.344138	+	0.0139735i	−0.0142650	+	0.000579219i
$583$	19.6251	−	19.6251i	0.812790	−	0.812790i
$584$	−0.215285			−0.00890856
$585$	−27.6062	+	8.42411i	−1.14138	+	0.348294i
$586$	1.17104			0.0483753
$587$	18.8700	−	18.8700i	0.778849	−	0.778849i	−0.200786	−	0.979635i	$-0.564350\pi$
$587$	18.8700	−	18.8700i	0.778849	−	0.778849i	0.979635	+	0.200786i	$0.0643496\pi$
$588$	−1.52977	−	2.41751i	−0.0630868	−	0.0996964i
$589$		−	38.1365i		−	1.57139i
$590$	−0.152700	−	0.0409158i	−0.00628655	−	0.00168448i
$591$	−23.0035	+	24.9506i	−0.946237	+	1.02633i
$592$	−6.89492	−	1.84749i	−0.283380	−	0.0759313i
$593$	30.8664	+	30.8664i	1.26753	+	1.26753i	0.947359	+	0.320173i	$0.103741\pi$
$593$	30.8664	+	30.8664i	1.26753	+	1.26753i	0.320173	+	0.947359i	$0.396259\pi$
$594$	1.08478	−	0.132725i	0.0445093	−	0.00544576i
$595$	−8.69875	+	5.02223i	−0.356614	+	0.205891i
$596$	25.5810	+	25.5810i	1.04784	+	1.04784i
$597$	−31.6092	+	20.0019i	−1.29368	+	0.818625i
$598$	−1.50148	+	0.327908i	−0.0614003	+	0.0134091i
$599$	15.8006	−	9.12248i	0.645595	−	0.372735i	−0.141171	−	0.989985i	$-0.545087\pi$
$599$	15.8006	−	9.12248i	0.645595	−	0.372735i	0.786767	+	0.617251i	$0.211754\pi$
$600$	−0.988535	−	0.222320i	−0.0403568	−	0.00907616i
$601$	−23.8112			−0.971281			−0.485641	−	0.874159i	$-0.661414\pi$
$601$	−23.8112			−0.971281			−0.485641	+	0.874159i	$0.661414\pi$
$602$	0.124522	−	0.215679i	0.00507516	−	0.00879043i
$603$	−9.98167	−	8.47995i	−0.406485	−	0.345330i
$604$	8.38665	−	2.24720i	0.341248	−	0.0914371i
$605$	1.19086	−	4.44436i	0.0484155	−	0.180689i
$606$	0.249942	+	0.801232i	0.0101532	+	0.0325478i
$607$	9.56599			0.388272			0.194136	−	0.980975i	$-0.437810\pi$
$607$	9.56599			0.388272			0.194136	+	0.980975i	$0.437810\pi$
$608$	−2.17553	+	3.76813i	−0.0882294	+	0.152818i
$609$	24.6050	+	22.6848i	0.997044	+	0.919234i
$610$	−0.878025	−	0.506928i	−0.0355502	−	0.0205249i
$611$	−8.82704	−	40.4189i	−0.357104	−	1.63517i
$612$	−0.735293	−	9.03945i	−0.0297225	−	0.365398i
$613$	−6.31167	+	23.5555i	−0.254926	+	0.951396i	0.713206	+	0.700955i	$0.247243\pi$
$613$	−6.31167	+	23.5555i	−0.254926	+	0.951396i	−0.968132	+	0.250442i	$0.919424\pi$
$614$			0.265437i			0.0107121i
$615$	24.3281	+	12.7589i	0.981005	+	0.514490i
$616$	−0.540313	+	2.01647i	−0.0217698	+	0.0812461i
$617$	34.0275	−	34.0275i	1.36989	−	1.36989i	0.509312	−	0.860582i	$-0.329900\pi$
$617$	34.0275	−	34.0275i	1.36989	−	1.36989i	0.860582	−	0.509312i	$-0.170100\pi$
$618$	0.361904	+	0.333661i	0.0145579	+	0.0134218i
$619$	2.46596	+	9.20307i	0.0991152	+	0.369903i	0.997611	−	0.0690788i	$-0.0220060\pi$
$619$	2.46596	+	9.20307i	0.0991152	+	0.369903i	−0.898496	+	0.438982i	$0.855339\pi$
$620$	−33.3835	−	19.2740i	−1.34071	−	0.774061i
$621$	12.5443	−	29.5175i	0.503387	−	1.18450i
$622$	0.386388	+	0.103532i	0.0154928	+	0.00415127i
$623$	16.2264	−	28.1050i	0.650098	−	1.12600i
$624$	21.4013	+	12.5337i	0.856739	+	0.501751i
$625$	−15.5529	−	26.9384i	−0.622116	−	1.07754i
$626$	0.0556924	+	0.207847i	0.00222592	+	0.00830723i
$627$	−23.4793	+	14.8574i	−0.937672	+	0.593349i
$628$	−27.6236	+	15.9485i	−1.10230	+	0.636413i
$629$	1.92569	−	1.92569i	0.0767822	−	0.0767822i
$630$	−1.04669	−	0.889221i	−0.0417013	−	0.0354274i
$631$	−4.48760	−	16.7479i	−0.178648	−	0.666725i	−0.995901	−	0.0904459i	$-0.971171\pi$
$631$	−4.48760	−	16.7479i	−0.178648	−	0.666725i	0.817253	−	0.576279i	$-0.195496\pi$
$632$	−3.41261	+	0.914406i	−0.135746	+	0.0363731i
$633$	−4.89541	−	7.73624i	−0.194575	−	0.307488i
$634$	1.05501	+	0.609110i	0.0418998	+	0.0241908i
$635$	−16.6796	+	4.46928i	−0.661909	+	0.177358i
$636$	14.6268	−	27.8898i	0.579992	−	1.10590i
$637$	−1.61166	+	2.51229i	−0.0638564	+	0.0995405i
$638$			1.63576i			0.0647602i
$639$	6.37777	−	7.50722i	0.252301	−	0.296981i
$640$	2.93083	+	5.07634i	0.115851	+	0.200660i
$641$	−7.16362	−	12.4077i	−0.282946	−	0.490077i	0.689163	−	0.724606i	$-0.257978\pi$
$641$	−7.16362	−	12.4077i	−0.282946	−	0.490077i	−0.972109	+	0.234530i	$0.924645\pi$
$642$	0.377363	+	0.347914i	0.0148933	+	0.0137311i
$643$	−17.4514	−	17.4514i	−0.688215	−	0.688215i	0.273622	−	0.961837i	$-0.411778\pi$
$643$	−17.4514	−	17.4514i	−0.688215	−	0.688215i	−0.961837	+	0.273622i	$0.911778\pi$
$644$	21.6346	+	21.6346i	0.852521	+	0.852521i
$645$	1.47205	−	6.54542i	0.0579620	−	0.257726i
$646$	−0.275566	−	0.477294i	−0.0108420	−	0.0187789i
$647$	−11.3450	−	19.6501i	−0.446017	−	0.772524i	0.552106	−	0.833774i	$-0.313824\pi$
$647$	−11.3450	−	19.6501i	−0.446017	−	0.772524i	−0.998122	+	0.0612504i	$0.980491\pi$
$648$	2.26312	−	1.02187i	0.0889038	−	0.0401429i
$649$			2.61279i			0.102561i
$650$	0.112639	+	0.515773i	0.00441807	+	0.0202303i
$651$	−16.6598	−	26.3275i	−0.652948	−	1.03186i
$652$	7.10493	−	1.90376i	0.278250	−	0.0745570i
$653$	0.217598	+	0.125630i	0.00851528	+	0.00491630i	0.504252	−	0.863557i	$-0.331768\pi$
$653$	0.217598	+	0.125630i	0.00851528	+	0.00491630i	−0.495736	+	0.868473i	$0.665102\pi$
$654$	−0.430780	+	0.821391i	−0.0168448	+	0.0321189i
$655$	−11.0578	+	2.96294i	−0.432066	+	0.115772i
$656$	−6.10949	−	22.8009i	−0.238535	−	0.890226i
$657$	−2.30279	−	0.420549i	−0.0898402	−	0.0164072i
$658$	1.39203	−	1.39203i	0.0542671	−	0.0542671i
$659$	23.3048	−	13.4550i	0.907824	−	0.524133i	0.0280939	−	0.999605i	$-0.491056\pi$
$659$	23.3048	−	13.4550i	0.907824	−	0.524133i	0.879731	+	0.475473i	$0.157723\pi$
$660$	1.13943	+	28.0619i	0.0443524	+	1.09231i
$661$	8.97289	+	33.4873i	0.349005	+	1.30250i	0.887863	+	0.460108i	$0.152189\pi$
$661$	8.97289	+	33.4873i	0.349005	+	1.30250i	−0.538858	+	0.842397i	$0.681144\pi$
$662$	0.390839	+	0.676953i	0.0151904	+	0.0263105i
$663$	−8.22370	+	4.68017i	−0.319382	+	0.181763i
$664$	−0.433534	+	0.750903i	−0.0168244	+	0.0291407i
$665$	33.7280	+	9.03740i	1.30792	+	0.350455i
$666$	0.336518	+	0.159428i	0.0130398	+	0.00617771i
$667$	41.5731	+	24.0022i	1.60972	+	0.929370i
$668$	6.06242	+	22.6252i	0.234562	+	0.875397i
$669$	−40.1885	+	12.5367i	−1.55378	+	0.484696i
$670$	−0.568871	+	0.568871i	−0.0219774	+	0.0219774i
$671$	−4.33693	+	16.1856i	−0.167425	+	0.624839i
$672$	0.144214	+	3.55170i	0.00556318	+	0.137010i
$673$		−	20.4388i		−	0.787860i	−0.919141	−	0.393930i	$-0.871115\pi$
$673$		−	20.4388i		−	0.787860i	0.919141	−	0.393930i	$-0.128885\pi$
$674$	−0.329135	+	1.22835i	−0.0126778	+	0.0473143i
$675$	−10.1395	−	4.30908i	−0.390270	−	0.165857i
$676$	2.42355	−	25.8245i	0.0932134	−	0.993251i
$677$	−11.4569	−	6.61467i	−0.440326	−	0.254222i	0.263410	−	0.964684i	$-0.415153\pi$
$677$	−11.4569	−	6.61467i	−0.440326	−	0.254222i	−0.703736	+	0.710462i	$0.748486\pi$
$678$	−0.897312	+	0.279914i	−0.0344611	+	0.0107500i
$679$	3.57687	−	6.19531i	0.137268	−	0.237754i
$680$	−1.11549			−0.0427770
$681$	−10.6662	+	11.5691i	−0.408732	+	0.443329i
$682$	0.394135	−	1.47093i	0.0150922	−	0.0563248i
$683$	13.5168	−	3.62181i	0.517205	−	0.138585i	0.00923131	−	0.999957i	$-0.497062\pi$
$683$	13.5168	−	3.62181i	0.517205	−	0.138585i	0.507973	+	0.861373i	$0.330395\pi$
$684$	−20.4128	+	24.0277i	−0.780501	+	0.918720i
$685$	−14.7376	+	25.5263i	−0.563095	+	0.975309i
$686$	−1.34300			−0.0512760
$687$	−10.3257	+	11.1997i	−0.393948	+	0.427294i
$688$	−4.99251	+	2.88242i	−0.190338	+	0.109891i
$689$	−32.8209	−	1.53669i	−1.25038	−	0.0585433i
$690$	−1.74466	−	0.914991i	−0.0664182	−	0.0348331i
$691$	29.2304	+	29.2304i	1.11198	+	1.11198i	0.992883	+	0.119094i	$0.0379988\pi$
$691$	29.2304	+	29.2304i	1.11198	+	1.11198i	0.119094	+	0.992883i	$0.462001\pi$
$692$	−41.3556	+	23.8767i	−1.57211	+	0.907655i
$693$	−9.71851	+	20.5136i	−0.369176	+	0.779249i
$694$	0.0598285	+	0.0598285i	0.00227106	+	0.00227106i
$695$	−59.1683	−	15.8541i	−2.24438	−	0.601380i
$696$	1.10679	+	3.54800i	0.0419527	+	0.134487i
$697$	8.69896	+	2.33088i	0.329497	+	0.0882884i
$698$			0.657945i			0.0249036i
$699$	−12.1464	+	23.1602i	−0.459418	+	0.875998i
$700$	7.43165	−	7.43165i	0.280890	−	0.280890i
$701$	23.7308			0.896298			0.448149	−	0.893959i	$-0.352083\pi$
$701$	23.7308			0.896298			0.448149	+	0.893959i	$0.352083\pi$
$702$	−0.980803	−	0.843776i	−0.0370180	−	0.0318463i
$703$	−9.46720			−0.357062
$704$	16.9825	−	16.9825i	0.640053	−	0.640053i
$705$	24.6309	−	46.9651i	0.927653	−	1.76881i
$706$		−	1.25095i		−	0.0470802i
$707$	−16.8387	−	4.51193i	−0.633286	−	0.169689i
$708$	0.882881	+	2.83022i	0.0331807	+	0.106366i
$709$	37.0075	+	9.91612i	1.38984	+	0.372408i	0.874687	−	0.484688i	$-0.161067\pi$
$709$	37.0075	+	9.91612i	1.38984	+	0.372408i	0.515157	+	0.857096i	$0.327734\pi$
$710$	−0.427848	−	0.427848i	−0.0160569	−	0.0160569i
$711$	−38.2890	+	3.11453i	−1.43595	+	0.116804i
$712$	3.12121	−	1.80203i	0.116972	−	0.0675339i
$713$	−31.6006	−	31.6006i	−1.18345	−	1.18345i
$714$	−0.398741	−	0.209120i	−0.0149225	−	0.00782613i
$715$	26.0334	−	13.4480i	0.973595	−	0.502926i
$716$	−36.2861	+	20.9498i	−1.35607	+	0.782930i
$717$	−4.08505	+	4.43083i	−0.152559	+	0.165472i
$718$	−1.02188			−0.0381363
$719$	−21.1677	+	36.6636i	−0.789423	+	1.36732i	0.136898	+	0.990585i	$0.456287\pi$
$719$	−21.1677	+	36.6636i	−0.789423	+	1.36732i	−0.926321	+	0.376735i	$0.877047\pi$
$720$	10.6909	+	29.9402i	0.398426	+	1.11581i
$721$	−9.87568	+	2.64618i	−0.367790	+	0.0985489i
$722$	−0.156278	+	0.583237i	−0.00581606	+	0.0217058i
$723$	21.9051	−	23.7593i	0.814660	−	0.883618i
$724$	−2.86719			−0.106558
$725$	8.24497	−	14.2807i	0.306210	−	0.530372i
$726$	0.196892	−	0.0614201i	0.00730737	−	0.00227951i
$727$	25.4774	+	14.7094i	0.944904	+	0.545541i	0.891494	−	0.453032i	$-0.149658\pi$
$727$	25.4774	+	14.7094i	0.944904	+	0.545541i	0.0534100	+	0.998573i	$0.482991\pi$
$728$	2.19577	−	1.13426i	0.0813806	−	0.0420385i
$729$	26.2036	−	6.50951i	0.970502	−	0.241093i
$730$	−0.0372148	+	0.138888i	−0.00137738	+	0.00514046i
$731$		−	2.19939i		−	0.0813475i
$732$	0.771402	+	18.9981i	0.0285119	+	0.702188i
$733$	−1.96355	+	7.32806i	−0.0725253	+	0.270668i	−0.992661	−	0.120932i	$-0.961412\pi$
$733$	−1.96355	+	7.32806i	−0.0725253	+	0.270668i	0.920135	+	0.391600i	$0.128078\pi$
$734$	−0.0369743	+	0.0369743i	−0.00136475	+	0.00136475i
$735$	−3.65248	+	1.13938i	−0.134724	+	0.0420267i
$736$	1.31966	+	4.92503i	0.0486433	+	0.181539i
$737$	11.5151	+	6.64827i	0.424166	+	0.244892i
$738$	0.0998360	+	1.22735i	0.00367501	+	0.0451794i
$739$	−6.96809	−	1.86709i	−0.256325	−	0.0686822i	0.128368	−	0.991727i	$-0.459026\pi$
$739$	−6.96809	−	1.86709i	−0.256325	−	0.0686822i	−0.384693	+	0.923044i	$0.625693\pi$
$740$	−4.78467	+	8.28729i	−0.175888	+	0.304647i
$741$	31.7195	+	8.71049i	1.16524	+	0.319988i
$742$	−0.781734	−	1.35400i	−0.0286984	−	0.0497070i
$743$	−11.3257	−	42.2680i	−0.415499	−	1.55066i	−0.783834	−	0.620971i	$-0.786739\pi$
$743$	−11.3257	−	42.2680i	−0.415499	−	1.55066i	0.368335	−	0.929693i	$-0.379928\pi$
$744$	−0.140376	−	3.45717i	−0.00514642	−	0.126746i
$745$	41.9004	−	24.1912i	1.53511	−	0.886297i
$746$	−1.09303	+	1.09303i	−0.0400188	+	0.0400188i
$747$	−6.10413	+	7.18511i	−0.223338	+	0.262890i
$748$	2.38299	+	8.89343i	0.0871307	+	0.325176i
$749$	−10.2975	+	2.75921i	−0.376264	+	0.100820i
$750$	0.426893	−	0.813981i	0.0155879	−	0.0297224i
$751$	−13.1592	−	7.59749i	−0.480187	−	0.277236i	0.240307	−	0.970697i	$-0.422752\pi$
$751$	−13.1592	−	7.59749i	−0.480187	−	0.277236i	−0.720495	+	0.693461i	$0.756085\pi$
$752$	−44.0168	+	11.7943i	−1.60513	+	0.430093i
$753$	−8.89960	−	14.0641i	−0.324319	−	0.512524i
$754$	1.43186	−	1.30377i	0.0521451	−	0.0474806i
$755$		−	11.6118i		−	0.422597i
$756$	−3.59556	+	25.5047i	−0.130769	+	0.927598i
$757$	−23.4618	−	40.6370i	−0.852732	−	1.47698i	−0.878733	−	0.477314i	$-0.841610\pi$
$757$	−23.4618	−	40.6370i	−0.852732	−	1.47698i	0.0260003	−	0.999662i	$-0.491723\pi$
$758$	−0.748202	−	1.29592i	−0.0271759	−	0.0470701i
$759$	−7.14424	+	31.7666i	−0.259319	+	1.15305i
$760$	2.74202	+	2.74202i	0.0994636	+	0.0994636i
$761$	−16.1286	−	16.1286i	−0.584660	−	0.584660i	0.351520	−	0.936180i	$-0.385665\pi$
$761$	−16.1286	−	16.1286i	−0.584660	−	0.584660i	−0.936180	+	0.351520i	$0.885665\pi$
$762$	−0.569092	−	0.524680i	−0.0206160	−	0.0190072i
$763$	−9.63222	−	16.6835i	−0.348710	−	0.603983i
$764$	11.2318	+	19.4541i	0.406354	+	0.703825i
$765$	−11.9318	−	2.17905i	−0.431394	−	0.0787837i
$766$		−	0.809614i		−	0.0292526i
$767$	2.28710	−	2.08251i	0.0825824	−	0.0751952i
$768$	12.5655	−	23.9593i	0.453418	−	0.864556i
$769$	−32.6213	+	8.74085i	−1.17635	+	0.315203i	−0.793479	−	0.608598i	$-0.791732\pi$
$769$	−32.6213	+	8.74085i	−1.17635	+	0.315203i	−0.382874	+	0.923800i	$0.625066\pi$
$770$	1.20750	+	0.697148i	0.0435151	+	0.0251235i
$771$	−12.6429	−	19.9797i	−0.455324	−	0.719552i
$772$	−14.2894	+	3.82882i	−0.514285	+	0.137802i
$773$	11.9731	+	44.6843i	0.430643	+	1.60718i	0.751283	+	0.659981i	$0.229435\pi$
$773$	11.9731	+	44.6843i	0.430643	+	1.60718i	−0.320640	+	0.947201i	$0.603898\pi$
$774$	0.283218	−	0.101130i	0.0101801	−	0.00363505i
$775$	−10.8551	+	10.8551i	−0.389926	+	0.389926i
$776$	0.688021	−	0.397229i	0.0246985	−	0.0142597i
$777$	−6.53568	+	4.13571i	−0.234466	+	0.148368i
$778$	0.198461	+	0.740666i	0.00711516	+	0.0265542i
$779$	−15.6536	−	27.1129i	−0.560849	−	0.971419i
$780$	23.6557	−	23.3640i	0.847011	−	0.836565i
$781$	−5.00016	+	8.66054i	−0.178920	+	0.309898i
$782$	−0.623835	−	0.167156i	−0.0223083	−	0.00597749i
$783$	4.90788	+	40.1131i	0.175393	+	1.43352i
$784$	2.84721	+	1.64384i	0.101686	+	0.0587084i
$785$	11.0408	+	41.2048i	0.394062	+	1.47066i
$786$	−0.377284	−	0.347841i	−0.0134573	−	0.0124071i
$787$	−5.36969	+	5.36969i	−0.191409	+	0.191409i	−0.796305	−	0.604896i	$-0.793215\pi$
$787$	−5.36969	+	5.36969i	−0.191409	+	0.191409i	0.604896	+	0.796305i	$0.293215\pi$
$788$	10.1181	−	37.7611i	0.360441	−	1.34519i
$789$	−33.0929	−	17.3556i	−1.17814	−	0.617875i
$790$			2.35966i			0.0839528i
$791$	5.05298	−	18.8580i	0.179663	−	0.670512i
$792$	−2.07377	+	1.43329i	−0.0736881	+	0.0509296i
$793$	17.6248	−	9.10436i	0.625874	−	0.323305i
$794$	1.00565	+	0.580614i	0.0356893	+	0.0206052i
$795$	−30.9654	−	28.5488i	−1.09823	−	1.01252i
$796$	21.5449	−	37.3169i	0.763640	−	1.32266i
$797$	37.6269			1.33281			0.666407	−	0.745588i	$-0.267831\pi$
$797$	37.6269			1.33281			0.666407	+	0.745588i	$0.267831\pi$
$798$	0.466114	+	1.49421i	0.0165003	+	0.0528943i
$799$	4.49972	−	16.7932i	0.159189	−	0.594101i
$800$	1.69179	−	0.453314i	0.0598138	−	0.0160271i
$801$	36.9060	−	13.1782i	1.30401	−	0.465629i
$802$	−0.510360	+	0.883970i	−0.0180214	+	0.0312141i
$803$	2.37645			0.0838632
$804$	14.7199	+	3.31048i	0.519131	+	0.116752i
$805$	35.4363	−	20.4591i	1.24896	−	0.721090i
$806$	−1.60172	+	0.827393i	−0.0564181	+	0.0291437i
$807$	7.00282	−	4.43131i	0.246511	−	0.155990i
$808$	−1.36896	−	1.36896i	−0.0481597	−	0.0481597i
$809$	19.7137	−	11.3817i	0.693096	−	0.400159i	−0.111675	−	0.993745i	$-0.535621\pi$
$809$	19.7137	−	11.3817i	0.693096	−	0.400159i	0.804771	+	0.593586i	$0.202288\pi$
$810$	−0.268034	−	1.63666i	−0.00941776	−	0.0575064i
$811$	10.9550	+	10.9550i	0.384681	+	0.384681i	0.872785	−	0.488104i	$-0.162312\pi$
$811$	10.9550	+	10.9550i	0.384681	+	0.384681i	−0.488104	+	0.872785i	$0.662312\pi$
$812$	−37.2380	−	9.97789i	−1.30680	−	0.350155i
$813$	−31.5123	+	34.1796i	−1.10518	+	1.19873i
$814$	−0.365152	−	0.0978421i	−0.0127986	−	0.00342936i
$815$		−	9.83718i		−	0.344581i
$816$	5.57307	+	8.80715i	0.195096	+	0.308312i
$817$	−5.40641	+	5.40641i	−0.189146	+	0.189146i
$818$	−0.536869			−0.0187712
$819$	25.7027	−	7.84323i	0.898124	−	0.274065i
$820$	−31.6450			−1.10509
$821$	33.5782	−	33.5782i	1.17189	−	1.17189i	0.190129	−	0.981759i	$-0.439109\pi$
$821$	33.5782	−	33.5782i	1.17189	−	1.17189i	0.981759	−	0.190129i	$-0.0608905\pi$
$822$	−1.32016	+	0.0536043i	−0.0460460	+	0.00186966i
$823$		−	12.2673i		−	0.427612i	−0.976876	−	0.213806i	$-0.931414\pi$
$823$		−	12.2673i		−	0.427612i	0.976876	−	0.213806i	$-0.0685861\pi$
$824$	−1.09674	−	0.293872i	−0.0382069	−	0.0102375i
$825$	10.9121	+	2.45410i	0.379910	+	0.0854410i
$826$	0.142171	+	0.0380945i	0.00494675	+	0.00132548i
$827$	6.58424	+	6.58424i	0.228957	+	0.228957i	0.812257	−	0.583300i	$-0.198239\pi$
$827$	6.58424	+	6.58424i	0.228957	+	0.228957i	−0.583300	+	0.812257i	$0.698239\pi$
$828$	2.99538	+	36.8242i	0.104097	+	1.27973i
$829$	28.6973	−	16.5684i	0.996698	−	0.575444i	0.0894284	−	0.995993i	$-0.471496\pi$
$829$	28.6973	−	16.5684i	0.996698	−	0.575444i	0.907270	+	0.420549i	$0.138163\pi$
$830$	0.409491	+	0.409491i	0.0142136	+	0.0142136i
$831$	0.474272	+	11.6803i	0.0164523	+	0.405187i
$832$	−28.4014	−	1.32977i	−0.984643	−	0.0461015i
$833$	−1.08626	+	0.627153i	−0.0376367	+	0.0217296i
$834$	−0.817692	−	2.62125i	−0.0283144	−	0.0907665i
$835$	31.3259			1.08408
$836$	16.0036	−	27.7190i	0.553495	−	0.958681i
$837$	5.25188	−	37.2536i	0.181532	−	1.28767i
$838$	−2.57717	+	0.690550i	−0.0890268	+	0.0238546i
$839$	2.06249	−	7.69732i	0.0712051	−	0.265741i	−0.921141	−	0.389229i	$-0.872741\pi$
$839$	2.06249	−	7.69732i	0.0712051	−	0.265741i	0.992346	+	0.123488i	$0.0394081\pi$
$840$	3.09079	+	0.695114i	0.106643	+	0.0239837i
$841$	−31.4869			−1.08575
$842$	0.756214	−	1.30980i	0.0260608	−	0.0451387i
$843$	−9.83391	+	43.7261i	−0.338698	+	1.50601i
$844$	9.13319	+	5.27305i	0.314378	+	0.181506i
$845$	−32.5215	−	12.0696i	−1.11877	−	0.415208i
$846$	2.36938	−	0.192732i	0.0814610	−	0.00662625i
$847$	−1.10875	+	4.13790i	−0.0380970	+	0.142180i
$848$			36.1909i			1.24280i
$849$	−21.5764	+	13.6533i	−0.740501	+	0.468581i
$850$	−0.0574195	+	0.214293i	−0.00196947	+	0.00735018i
$851$	−7.84471	+	7.84471i	−0.268913	+	0.268913i
$852$	−2.48981	+	11.0708i	−0.0852995	+	0.379281i
$853$	11.0414	+	41.2070i	0.378050	+	1.41090i	0.848837	+	0.528654i	$0.177303\pi$
$853$	11.0414	+	41.2070i	0.378050	+	1.41090i	−0.470788	+	0.882247i	$0.656030\pi$
$854$	0.817481	+	0.471973i	0.0279736	+	0.0161506i
$855$	23.9735	+	34.6863i	0.819876	+	1.18625i
$856$	−1.14359	−	0.306425i	−0.0390872	−	0.0104734i
$857$	2.75969	−	4.77993i	0.0942693	−	0.163279i	−0.815034	−	0.579413i	$-0.803282\pi$
$857$	2.75969	−	4.77993i	0.0942693	−	0.163279i	0.909303	+	0.416134i	$0.136615\pi$
$858$	1.13340	+	0.663780i	0.0386937	+	0.0226611i
$859$	3.49427	+	6.05226i	0.119223	+	0.206500i	0.919460	−	0.393184i	$-0.128626\pi$
$859$	3.49427	+	6.05226i	0.119223	+	0.206500i	−0.800237	+	0.599684i	$0.795293\pi$
$860$	2.00023	+	7.46497i	0.0682074	+	0.254553i
$861$	−22.6506	−	11.8791i	−0.771931	−	0.404840i
$862$	0.379189	−	0.218925i	0.0129152	−	0.00745661i
$863$	−15.2638	+	15.2638i	−0.519587	+	0.519587i	−0.917446	−	0.397859i	$-0.869753\pi$
$863$	−15.2638	+	15.2638i	−0.519587	+	0.519587i	0.397859	+	0.917446i	$0.369753\pi$
$864$	−2.64409	+	3.38130i	−0.0899537	+	0.115034i
$865$	16.5293	+	61.6882i	0.562014	+	2.09746i
$866$	1.16818	−	0.313012i	0.0396962	−	0.0106366i
$867$	25.4476	−	1.03328i	0.864245	−	0.0350921i
$868$	31.0815	+	17.9449i	1.05498	+	0.609091i
$869$	37.6705	−	10.0938i	1.27789	−	0.342408i
$870$	2.48026	−	0.100709i	0.0840886	−	0.00341436i
$871$	−3.35854	−	15.3787i	−0.113800	−	0.521088i
$872$		−	2.13941i		−	0.0724497i
$873$	8.13535	−	2.90493i	0.275340	−	0.0983169i
$874$	1.12258	+	1.94436i	0.0379718	+	0.0657691i
$875$	9.54532	+	16.5330i	0.322691	+	0.558917i
$876$	2.57422	−	0.803021i	0.0869748	−	0.0271316i
$877$	−2.56911	−	2.56911i	−0.0867526	−	0.0867526i	0.662399	−	0.749151i	$-0.269538\pi$
$877$	−2.56911	−	2.56911i	−0.0867526	−	0.0867526i	−0.749151	+	0.662399i	$0.769538\pi$
$878$	−0.939341	−	0.939341i	−0.0317012	−	0.0317012i
$879$	−28.0384	+	8.74650i	−0.945711	+	0.295012i
$880$	−16.1375	−	27.9509i	−0.543994	−	0.942225i
$881$	2.80287	+	4.85471i	0.0944310	+	0.163559i	0.909371	−	0.415986i	$-0.136563\pi$
$881$	2.80287	+	4.85471i	0.0944310	+	0.163559i	−0.814940	+	0.579545i	$0.803230\pi$
$882$	−0.130706	−	0.111042i	−0.00440111	−	0.00373898i
$883$		−	34.2767i		−	1.15350i	−0.816920	−	0.576751i	$-0.804320\pi$
$883$		−	34.2767i		−	1.15350i	0.816920	−	0.576751i	$-0.195680\pi$
$884$	5.88550	−	9.17441i	0.197951	−	0.308569i
$885$	3.96171	−	0.160862i	0.133171	−	0.00540733i
$886$	−0.794745	+	0.212951i	−0.0267000	+	0.00715424i
$887$	17.2725	+	9.97231i	0.579955	+	0.334837i	0.761116	−	0.648616i	$-0.224652\pi$
$887$	17.2725	+	9.97231i	0.579955	+	0.334837i	−0.181160	+	0.983454i	$0.557985\pi$
$888$	−0.858225	+	0.0348476i	−0.0288002	+	0.00116941i
$889$	15.5294	−	4.16110i	0.520841	−	0.139559i
$890$	−0.623008	−	2.32510i	−0.0208833	−	0.0779375i
$891$	−24.9818	+	11.2801i	−0.836921	+	0.377897i
$892$	34.2913	−	34.2913i	1.14816	−	1.14816i
$893$	−52.3409	+	30.2191i	−1.75152	+	1.01124i
$894$	1.92067	+	1.00730i	0.0642368	+	0.0336891i
$895$	14.5031	+	54.1263i	0.484785	+	1.80924i
$896$	−2.72873	−	4.72631i	−0.0911606	−	0.157895i
$897$	33.5011	−	19.0657i	1.11857	−	0.636585i
$898$	−0.102951	+	0.178317i	−0.00343553	+	0.00595052i
$899$	54.3919	+	14.5743i	1.81407	+	0.486079i
$900$	12.6494	−	1.02894i	0.421647	−	0.0342979i
$901$	−11.9576	−	6.90374i	−0.398366	−	0.229997i
$902$	−0.323555	−	1.20752i	−0.0107732	−	0.0402062i
$903$	−1.37055	+	6.09408i	−0.0456090	+	0.202798i
$904$	1.53312	−	1.53312i	0.0509907	−	0.0509907i
$905$	−0.992447	+	3.70386i	−0.0329900	+	0.123121i
$906$	0.439844	−	0.278328i	0.0146128	−	0.00924683i
$907$		−	0.193305i		−	0.00641859i	−0.999995	−	0.00320929i	$-0.998978\pi$
$907$		−	0.193305i		−	0.00641859i	0.999995	−	0.00320929i	$-0.00102155\pi$
$908$	4.69154	−	17.5091i	0.155694	−	0.581059i
$909$	−11.9688	−	17.3172i	−0.396980	−	0.574374i
$910$	−0.352182	−	1.61264i	−0.0116747	−	0.0534584i
$911$	50.8660	+	29.3675i	1.68526	+	0.972988i	0.958060	+	0.286567i	$0.0925142\pi$
$911$	50.8660	+	29.3675i	1.68526	+	0.972988i	0.727205	+	0.686421i	$0.240819\pi$
$912$	7.94982	−	35.3485i	0.263245	−	1.17051i
$913$	4.78563	−	8.28895i	0.158381	−	0.274324i
$914$	0.491407			0.0162543
$915$	24.8089	+	5.57947i	0.820156	+	0.184451i
$916$	4.54173	−	16.9500i	0.150063	−	0.560043i
$917$	10.2954	−	2.75863i	0.339983	−	0.0910981i
$918$	−0.203457	−	0.504194i	−0.00671509	−	0.0166409i
$919$	1.01215	−	1.75309i	0.0333876	−	0.0578290i	−0.848849	−	0.528636i	$-0.822704\pi$
$919$	1.01215	−	1.75309i	0.0333876	−	0.0578290i	0.882236	+	0.470807i	$0.156037\pi$
$920$	4.54419			0.149817
$921$	−1.98254	−	6.35537i	−0.0653270	−	0.209417i
$922$	−0.899426	+	0.519284i	−0.0296210	+	0.0171017i
$923$	11.5663	−	2.52596i	0.380711	−	0.0831430i
$924$	−1.06086	−	26.1269i	−0.0348999	−	0.859512i
$925$	2.69472	+	2.69472i	0.0886020	+	0.0886020i
$926$	1.97749	−	1.14170i	0.0649844	−	0.0375188i
$927$	−11.1572	−	5.28582i	−0.366451	−	0.173609i
$928$	−4.54287	−	4.54287i	−0.149127	−	0.149127i
$929$	−24.9610	−	6.68829i	−0.818945	−	0.219436i	−0.175060	−	0.984558i	$-0.556012\pi$
$929$	−24.9610	−	6.68829i	−0.818945	−	0.219436i	−0.643885	+	0.765122i	$0.722679\pi$
$930$	−2.25460	−	0.507055i	−0.0739312	−	0.0166270i
$931$	4.21181	+	1.12855i	0.138036	+	0.0369867i
$932$		−	30.1257i		−	0.986801i
$933$	−10.0246	+	0.407042i	−0.328191	+	0.0133260i
$934$	0.854133	−	0.854133i	0.0279481	−	0.0279481i
$935$	12.3135			0.402693
$936$	2.90751	+	0.672871i	0.0950349	+	0.0219935i
$937$	−48.9912			−1.60047			−0.800237	−	0.599684i	$-0.795293\pi$
$937$	−48.9912			−1.60047			−0.800237	+	0.599684i	$0.795293\pi$
$938$	0.529645	−	0.529645i	0.0172935	−	0.0172935i
$939$	−2.88585	−	4.56053i	−0.0941763	−	0.148827i
$940$			61.0901i			1.99254i
$941$	−13.8154	−	3.70184i	−0.450371	−	0.120676i	0.0265022	−	0.999649i	$-0.491563\pi$
$941$	−13.8154	−	3.70184i	−0.450371	−	0.120676i	−0.476873	+	0.878972i	$0.658230\pi$
$942$	−1.29615	+	1.40587i	−0.0422310	+	0.0458057i
$943$	−35.4372	−	9.49536i	−1.15399	−	0.309211i
$944$	−2.40914	−	2.40914i	−0.0784107	−	0.0784107i
$945$	31.7027	+	13.4730i	1.03129	+	0.438276i
$946$	−0.264401	+	0.152652i	−0.00859640	+	0.00496314i
$947$	−23.2929	−	23.2929i	−0.756917	−	0.756917i	0.218843	−	0.975760i	$-0.429772\pi$
$947$	−23.2929	−	23.2929i	−0.756917	−	0.756917i	−0.975760	+	0.218843i	$0.929772\pi$
$948$	37.3947	−	23.6629i	1.21452	−	0.768536i
$949$	−1.89414	−	2.08022i	−0.0614864	−	0.0675269i
$950$	0.667906	−	0.385616i	0.0216697	−	0.0125110i
$951$	−29.8096	−	6.70412i	−0.966643	−	0.217396i
$952$	1.03857			0.0336602
$953$	3.71729	−	6.43853i	0.120415	−	0.208564i	−0.799517	−	0.600644i	$-0.794911\pi$
$953$	3.71729	−	6.43853i	0.120415	−	0.208564i	0.919931	+	0.392080i	$0.128244\pi$
$954$	0.339180	−	1.85724i	0.0109814	−	0.0601303i
$955$	29.0188	−	7.77556i	0.939026	−	0.251611i
$956$	1.79681	−	6.70577i	0.0581128	−	0.216880i
$957$	−12.2174	−	39.1651i	−0.394934	−	1.26603i
$958$	0.370875			0.0119824
$959$	13.7214	−	23.7661i	0.443086	−	0.767448i
$960$	−26.7957	−	24.7046i	−0.864828	−	0.797337i
$961$	−18.5527	−	10.7114i	−0.598473	−	0.345528i
$962$	0.205396	+	0.397619i	0.00662225	+	0.0128198i
$963$	−11.6338	−	5.51161i	−0.374894	−	0.177609i
$964$	−9.63495	+	35.9581i	−0.310321	+	1.15813i
$965$			19.7844i			0.636883i
$966$	1.62436	+	0.851898i	0.0522629	+	0.0274094i
$967$	−6.03626	+	22.5276i	−0.194113	+	0.724440i	0.798382	+	0.602152i	$0.205690\pi$
$967$	−6.03626	+	22.5276i	−0.194113	+	0.724440i	−0.992495	+	0.122288i	$0.960977\pi$
$968$	−0.336403	+	0.336403i	−0.0108124	+	0.0108124i
$969$	10.1628	+	9.36971i	0.326477	+	0.300998i
$970$	−0.137333	−	0.512532i	−0.00440948	−	0.0164564i
$971$	−14.4605	−	8.34875i	−0.464058	−	0.267924i	0.249691	−	0.968326i	$-0.419671\pi$
$971$	−14.4605	−	8.34875i	−0.464058	−	0.267924i	−0.713749	+	0.700401i	$0.753004\pi$
$972$	−23.2491	+	20.6603i	−0.745716	+	0.662680i
$973$	55.0884	+	14.7609i	1.76605	+	0.473212i
$974$	−1.02365	+	1.77301i	−0.0327999	+	0.0568110i
$975$	−6.54923	−	11.5079i	−0.209743	−	0.368548i
$976$	−10.9252	−	18.9229i	−0.349706	−	0.605708i
$977$	9.98072	+	37.2486i	0.319312	+	1.19169i	0.919908	+	0.392135i	$0.128263\pi$
$977$	9.98072	+	37.2486i	0.319312	+	1.19169i	−0.600596	+	0.799553i	$0.705070\pi$
$978$	0.372623	−	0.235792i	0.0119152	−	0.00753978i
$979$	−34.4539	+	19.8919i	−1.10115	+	0.635749i
$980$	3.11652	−	3.11652i	0.0995536	−	0.0995536i
$981$	4.17924	−	22.8841i	0.133433	−	0.730634i
$982$	−0.425860	−	1.58933i	−0.0135897	−	0.0507176i
$983$	−54.6271	+	14.6373i	−1.74234	+	0.466857i	−0.982964	−	0.183800i	$-0.941160\pi$
$983$	−54.6271	+	14.6373i	−1.74234	+	0.466857i	−0.759372	+	0.650657i	$0.774494\pi$
$984$	−1.51884	−	2.40023i	−0.0484188	−	0.0765165i
$985$	−45.2779	−	26.1412i	−1.44268	−	0.832929i
$986$	0.786048	−	0.210621i	0.0250329	−	0.00670754i
$987$	−22.9325	+	43.7266i	−0.729949	+	1.39183i
$988$	−37.0193	+	8.08461i	−1.17774	+	0.257206i
$989$			8.95972i			0.284902i
$990$	0.566184	+	1.58562i	0.0179945	+	0.0503943i
$991$	−0.778818	−	1.34895i	−0.0247400	−	0.0428509i	0.853390	−	0.521272i	$-0.174542\pi$
$991$	−0.778818	−	1.34895i	−0.0247400	−	0.0428509i	−0.878130	+	0.478422i	$0.841209\pi$
$992$	2.99050	+	5.17971i	0.0949486	+	0.164456i
$993$	−14.4141	−	13.2892i	−0.457416	−	0.421719i
$994$	0.398346	+	0.398346i	0.0126348	+	0.0126348i
$995$	−40.7488	−	40.7488i	−1.29182	−	1.29182i
$996$	2.38298	−	10.5958i	0.0755077	−	0.335742i
$997$	2.09843	+	3.63459i	0.0664580	+	0.115109i	0.897340	−	0.441340i	$-0.145497\pi$
$997$	2.09843	+	3.63459i	0.0664580	+	0.115109i	−0.830882	+	0.556449i	$0.812164\pi$
$998$	−0.550231	−	0.953029i	−0.0174173	−	0.0301676i
$999$	−9.24804	−	1.30375i	−0.292595	−	0.0412490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.6	✓	48
3.2	odd	2		351.2.ba.a.89.7		48
9.4	even	3		351.2.bf.a.206.6		48
9.5	odd	6		117.2.bc.a.50.7	yes	48
13.6	odd	12		117.2.bc.a.110.7	yes	48
39.32	even	12		351.2.bf.a.305.6		48
117.32	even	12	inner	117.2.x.a.32.6	yes	48
117.58	odd	12		351.2.ba.a.71.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.6	✓	48	1.1	even	1	trivial
117.2.x.a.32.6	yes	48	117.32	even	12	inner
117.2.bc.a.50.7	yes	48	9.5	odd	6
117.2.bc.a.110.7	yes	48	13.6	odd	12
351.2.ba.a.71.7		48	117.58	odd	12
351.2.ba.a.89.7		48	3.2	odd	2
351.2.bf.a.206.6		48	9.4	even	3
351.2.bf.a.305.6		48	39.32	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0488315 + 0.0488315i) q^{2} +(0.804456 - 1.53390i) q^{3} +1.99523i q^{4} +(2.57746 + 0.690628i) q^{5} +(0.0356199 + 0.114186i) q^{6} +(-2.39973 - 0.643006i) q^{7} +(-0.195093 - 0.195093i) q^{8} +(-1.70570 - 2.46791i) q^{9} +O(q^{10})\)	\(q+(-0.0488315 + 0.0488315i) q^{2} +(0.804456 - 1.53390i) q^{3} +1.99523i q^{4} +(2.57746 + 0.690628i) q^{5} +(0.0356199 + 0.114186i) q^{6} +(-2.39973 - 0.643006i) q^{7} +(-0.195093 - 0.195093i) q^{8} +(-1.70570 - 2.46791i) q^{9} +(-0.159586 + 0.0921368i) q^{10} +(2.15356 + 2.15356i) q^{11} +(3.06049 + 1.60508i) q^{12} +(0.168629 - 3.60161i) q^{13} +(0.148582 - 0.0857836i) q^{14} +(3.13281 - 3.39798i) q^{15} -3.97141 q^{16} +(0.757582 - 1.31217i) q^{17} +(0.203804 + 0.0372199i) q^{18} +(-5.08773 + 1.36325i) q^{19} +(-1.37796 + 5.14262i) q^{20} +(-2.91679 + 3.16368i) q^{21} -0.210324 q^{22} +(-3.08618 + 5.34542i) q^{23} +(-0.456198 + 0.142310i) q^{24} +(1.83620 + 1.06013i) q^{25} +(0.167638 + 0.184106i) q^{26} +(-5.15769 + 0.631049i) q^{27} +(1.28295 - 4.78802i) q^{28} -7.77733i q^{29} +(0.0129491 + 0.318909i) q^{30} +(-1.87394 + 6.99365i) q^{31} +(0.584117 - 0.584117i) q^{32} +(5.03580 - 1.57091i) q^{33} +(0.0270814 + 0.101069i) q^{34} +(-5.74113 - 3.31464i) q^{35} +(4.92405 - 3.40327i) q^{36} +(1.73614 + 0.465197i) q^{37} +(0.181872 - 0.315012i) q^{38} +(-5.38885 - 3.15599i) q^{39} +(-0.368108 - 0.637582i) q^{40} +(1.53837 + 5.74127i) q^{41} +(-0.0120562 - 0.296918i) q^{42} +(1.25711 - 0.725794i) q^{43} +(-4.29686 + 4.29686i) q^{44} +(-2.69196 - 7.53894i) q^{45} +(-0.110322 - 0.411728i) q^{46} +(11.0834 - 2.96979i) q^{47} +(-3.19482 + 6.09175i) q^{48} +(-0.716926 - 0.413918i) q^{49} +(-0.141432 + 0.0378966i) q^{50} +(-1.40330 - 2.21764i) q^{51} +(7.18604 + 0.336454i) q^{52} -9.11286i q^{53} +(0.221043 - 0.282673i) q^{54} +(4.06341 + 7.03803i) q^{55} +(0.342725 + 0.593618i) q^{56} +(-2.00176 + 8.90076i) q^{57} +(0.379779 + 0.379779i) q^{58} +(0.606620 + 0.606620i) q^{59} +(6.77976 + 6.25067i) q^{60} +(2.75095 + 4.76479i) q^{61} +(-0.250003 - 0.433018i) q^{62} +(2.50634 + 7.01910i) q^{63} -7.88577i q^{64} +(2.92200 - 9.16653i) q^{65} +(-0.169196 + 0.322616i) q^{66} +(4.21706 - 1.12996i) q^{67} +(2.61808 + 1.51155i) q^{68} +(5.71664 + 9.03404i) q^{69} +(0.442207 - 0.118489i) q^{70} +(0.849841 + 3.17165i) q^{71} +(-0.148702 + 0.814244i) q^{72} +(0.551749 - 0.551749i) q^{73} +(-0.107495 + 0.0620621i) q^{74} +(3.10327 - 1.96371i) q^{75} +(-2.72001 - 10.1512i) q^{76} +(-3.78322 - 6.55273i) q^{77} +(0.417258 - 0.109034i) q^{78} +(6.40258 - 11.0896i) q^{79} +(-10.2361 - 2.74277i) q^{80} +(-3.18117 + 8.41904i) q^{81} +(-0.355476 - 0.205234i) q^{82} +(-0.813378 - 3.03557i) q^{83} +(-6.31227 - 5.81966i) q^{84} +(2.85886 - 2.85886i) q^{85} +(-0.0259451 + 0.0968284i) q^{86} +(-11.9296 - 6.25652i) q^{87} -0.840292i q^{88} +(-3.38089 + 12.6176i) q^{89} +(0.499591 + 0.236685i) q^{90} +(-2.72052 + 8.53446i) q^{91} +(-10.6653 - 6.15764i) q^{92} +(9.22005 + 8.50052i) q^{93} +(-0.396201 + 0.686240i) q^{94} -14.0549 q^{95} +(-0.426081 - 1.36587i) q^{96} +(-0.745264 + 2.78136i) q^{97} +(0.0552209 - 0.0147964i) q^{98} +(1.64147 - 8.98814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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