LMFDB - Embedded newform 93.2.m.b.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	93.10
Dual form			93.2.m.b.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75230 - 1.27312i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.831686 + 2.55967i) q^{4} +(-1.24535 - 2.15701i) q^{5} +(-1.08298 + 1.87578i) q^{6} +(-1.22375 - 0.260117i) q^{7} +(0.462763 - 1.42424i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-1.75230 - 1.27312i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.831686 + 2.55967i) q^{4} +(-1.24535 - 2.15701i) q^{5} +(-1.08298 + 1.87578i) q^{6} +(-1.22375 - 0.260117i) q^{7} +(0.462763 - 1.42424i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.563906 + 5.36520i) q^{10} +(-0.461187 + 0.512200i) q^{11} +(2.45871 - 1.09469i) q^{12} +(-4.28011 - 1.90563i) q^{13} +(1.81322 + 2.01379i) q^{14} +(-2.01502 + 1.46399i) q^{15} +(1.73064 - 1.25738i) q^{16} +(0.123953 + 0.137663i) q^{17} +(1.97871 + 0.880976i) q^{18} +(7.04525 - 3.13675i) q^{19} +(4.48548 - 4.98163i) q^{20} +(-0.130775 + 1.24424i) q^{21} +(1.46023 - 0.310381i) q^{22} +(2.57997 - 7.94032i) q^{23} +(-1.46481 - 0.311355i) q^{24} +(-0.601785 + 1.04232i) q^{25} +(5.07394 + 8.78833i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.351966 - 3.34874i) q^{28} +(3.57810 + 2.59964i) q^{29} +5.39476 q^{30} +(-5.18900 - 2.01847i) q^{31} -7.62847 q^{32} +(0.557601 + 0.405121i) q^{33} +(-0.0419402 - 0.399034i) q^{34} +(0.962926 + 2.96358i) q^{35} +(-1.34570 - 2.33082i) q^{36} +(-0.974224 + 1.68741i) q^{37} +(-16.3389 - 3.47293i) q^{38} +(-1.44779 + 4.45585i) q^{39} +(-3.64839 + 0.775490i) q^{40} +(-0.893843 + 8.50435i) q^{41} +(1.81322 - 2.01379i) q^{42} +(9.84954 - 4.38530i) q^{43} +(-1.69462 - 0.754495i) q^{44} +(1.66660 + 1.85095i) q^{45} +(-14.6299 + 10.6292i) q^{46} +(-3.76465 + 2.73518i) q^{47} +(-1.43140 - 1.58973i) q^{48} +(-4.96491 - 2.21052i) q^{49} +(2.38151 - 1.06032i) q^{50} +(0.123953 - 0.137663i) q^{51} +(1.31806 - 12.5405i) q^{52} +(8.21925 - 1.74706i) q^{53} +(0.669319 - 2.05995i) q^{54} +(1.67916 + 0.356916i) q^{55} +(-0.936776 + 1.62254i) q^{56} +(-3.85599 - 6.67878i) q^{57} +(-2.96025 - 9.11071i) q^{58} +(-0.604971 - 5.75592i) q^{59} +(-5.42320 - 3.94019i) q^{60} -3.09888 q^{61} +(6.52293 + 10.1432i) q^{62} +1.25109 q^{63} +(9.90609 + 7.19719i) q^{64} +(1.21978 + 11.6054i) q^{65} +(-0.461317 - 1.41979i) q^{66} +(5.04480 + 8.73786i) q^{67} +(-0.249283 + 0.431771i) q^{68} +(-8.16650 - 1.73584i) q^{69} +(2.08566 - 6.41900i) q^{70} +(9.19163 - 1.95374i) q^{71} +(-0.156535 + 1.48933i) q^{72} +(-7.51632 + 8.34771i) q^{73} +(3.85540 - 1.71654i) q^{74} +(1.09952 + 0.489536i) q^{75} +(13.8885 + 15.4247i) q^{76} +(0.697610 - 0.506844i) q^{77} +(8.20981 - 5.96478i) q^{78} +(-0.141156 - 0.156769i) q^{79} +(-4.86743 - 2.16712i) q^{80} +(0.913545 - 0.406737i) q^{81} +(12.3933 - 13.7642i) q^{82} +(0.756688 - 7.19941i) q^{83} +(-3.29360 + 0.700077i) q^{84} +(0.142577 - 0.438806i) q^{85} +(-22.8424 - 4.85530i) q^{86} +(2.21139 - 3.83024i) q^{87} +(0.516074 + 0.893867i) q^{88} +(-0.741825 - 2.28310i) q^{89} +(-0.563906 - 5.36520i) q^{90} +(4.74211 + 3.44535i) q^{91} +22.4703 q^{92} +(-1.46502 + 5.37157i) q^{93} +10.0790 q^{94} +(-15.5398 - 11.2903i) q^{95} +(0.797392 + 7.58668i) q^{96} +(-1.13746 - 3.50073i) q^{97} +(5.88575 + 10.1944i) q^{98} +(0.344616 - 0.596893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−1.75230	−	1.27312i	−1.23906	−	0.900232i	−0.241528	−	0.970394i	$-0.577649\pi$
$2$	−1.75230	−	1.27312i	−1.23906	−	0.900232i	−0.997536	+	0.0701615i	$0.977649\pi$
$3$	−0.104528	−	0.994522i	−0.0603495	−	0.574187i
$3$	−0.104528	−	0.994522i	−0.0603495	−	0.574187i
$4$	0.831686	+	2.55967i	0.415843	+	1.27983i
$5$	−1.24535	−	2.15701i	−0.556937	−	0.964643i	−0.997750	−	0.0670439i	$-0.978643\pi$
$5$	−1.24535	−	2.15701i	−0.556937	−	0.964643i	0.440813	−	0.897599i	$-0.354690\pi$
$6$	−1.08298	+	1.87578i	−0.442125	+	0.765783i
$7$	−1.22375	−	0.260117i	−0.462535	−	0.0983149i	−0.0292508	−	0.999572i	$-0.509312\pi$
$7$	−1.22375	−	0.260117i	−0.462535	−	0.0983149i	−0.433284	+	0.901257i	$0.642645\pi$
$8$	0.462763	−	1.42424i	0.163611	−	0.503544i
$9$	−0.978148	+	0.207912i	−0.326049	+	0.0693039i
$10$	−0.563906	+	5.36520i	−0.178323	+	1.69663i
$11$	−0.461187	+	0.512200i	−0.139053	+	0.154434i	−0.808649	−	0.588292i	$-0.799801\pi$
$11$	−0.461187	+	0.512200i	−0.139053	+	0.154434i	0.669596	+	0.742726i	$0.266467\pi$
$12$	2.45871	−	1.09469i	0.709769	−	0.316009i
$13$	−4.28011	−	1.90563i	−1.18709	−	0.528526i	−0.284352	−	0.958720i	$-0.591778\pi$
$13$	−4.28011	−	1.90563i	−1.18709	−	0.528526i	−0.902736	+	0.430194i	$0.858445\pi$
$14$	1.81322	+	2.01379i	0.484604	+	0.538208i
$15$	−2.01502	+	1.46399i	−0.520275	+	0.378002i
$16$	1.73064	−	1.25738i	0.432660	−	0.314346i
$17$	0.123953	+	0.137663i	0.0300629	+	0.0333883i	0.757989	−	0.652268i	$-0.226182\pi$
$17$	0.123953	+	0.137663i	0.0300629	+	0.0333883i	−0.727926	+	0.685656i	$0.759515\pi$
$18$	1.97871	+	0.880976i	0.466385	+	0.207648i
$19$	7.04525	−	3.13675i	1.61629	−	0.719619i	0.618484	−	0.785797i	$-0.287747\pi$
$19$	7.04525	−	3.13675i	1.61629	−	0.719619i	0.997808	+	0.0661780i	$0.0210805\pi$
$20$	4.48548	−	4.98163i	1.00298	−	1.11393i
$21$	−0.130775	+	1.24424i	−0.0285374	+	0.271515i
$22$	1.46023	−	0.310381i	0.311322	−	0.0661735i
$23$	2.57997	−	7.94032i	0.537960	−	1.65567i	−0.199204	−	0.979958i	$-0.563836\pi$
$23$	2.57997	−	7.94032i	0.537960	−	1.65567i	0.737164	−	0.675714i	$-0.236164\pi$
$24$	−1.46481	−	0.311355i	−0.299003	−	0.0635550i
$25$	−0.601785	+	1.04232i	−0.120357	+	0.208465i
$26$	5.07394	+	8.78833i	0.995082	+	1.72353i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.351966	−	3.34874i	−0.0665154	−	0.632852i
$29$	3.57810	+	2.59964i	0.664437	+	0.482742i	0.868158	−	0.496287i	$-0.165304\pi$
$29$	3.57810	+	2.59964i	0.664437	+	0.482742i	−0.203722	+	0.979029i	$0.565304\pi$
$30$	5.39476			0.984943
$31$	−5.18900	−	2.01847i	−0.931973	−	0.362529i
$31$	−5.18900	−	2.01847i	−0.931973	−	0.362529i
$32$	−7.62847			−1.34853
$33$	0.557601	+	0.405121i	0.0970658	+	0.0705225i
$34$	−0.0419402	−	0.399034i	−0.00719269	−	0.0684338i
$35$	0.962926	+	2.96358i	0.162764	+	0.500936i
$36$	−1.34570	−	2.33082i	−0.224283	−	0.388469i
$37$	−0.974224	+	1.68741i	−0.160161	+	0.277408i	−0.934926	−	0.354842i	$-0.884535\pi$
$37$	−0.974224	+	1.68741i	−0.160161	+	0.277408i	0.774765	+	0.632249i	$0.217868\pi$
$38$	−16.3389	−	3.47293i	−2.65051	−	0.563384i
$39$	−1.44779	+	4.45585i	−0.231833	+	0.713508i
$40$	−3.64839	+	0.775490i	−0.576862	+	0.122616i
$41$	−0.893843	+	8.50435i	−0.139595	+	1.32816i	0.670523	+	0.741889i	$0.266070\pi$
$41$	−0.893843	+	8.50435i	−0.139595	+	1.32816i	−0.810118	+	0.586267i	$0.800597\pi$
$42$	1.81322	−	2.01379i	0.279786	−	0.310734i
$43$	9.84954	−	4.38530i	1.50204	−	0.668752i	0.519445	−	0.854504i	$-0.326139\pi$
$43$	9.84954	−	4.38530i	1.50204	−	0.668752i	0.982597	+	0.185752i	$0.0594721\pi$
$44$	−1.69462	−	0.754495i	−0.255474	−	0.113744i
$45$	1.66660	+	1.85095i	0.248442	+	0.275923i
$46$	−14.6299	+	10.6292i	−2.15706	+	1.56719i
$47$	−3.76465	+	2.73518i	−0.549131	+	0.398967i	−0.827465	−	0.561518i	$-0.810218\pi$
$47$	−3.76465	+	2.73518i	−0.549131	+	0.398967i	0.278334	+	0.960484i	$0.410218\pi$
$48$	−1.43140	−	1.58973i	−0.206604	−	0.229457i
$49$	−4.96491	−	2.21052i	−0.709272	−	0.315788i
$50$	2.38151	−	1.06032i	0.336797	−	0.149952i
$51$	0.123953	−	0.137663i	0.0173569	−	0.0192767i
$52$	1.31806	−	12.5405i	0.182783	−	1.73906i
$53$	8.21925	−	1.74706i	1.12900	−	0.239977i	0.394706	−	0.918807i	$-0.370846\pi$
$53$	8.21925	−	1.74706i	1.12900	−	0.239977i	0.734295	+	0.678831i	$0.237513\pi$
$54$	0.669319	−	2.05995i	0.0910828	−	0.280324i
$55$	1.67916	+	0.356916i	0.226417	+	0.0481265i
$56$	−0.936776	+	1.62254i	−0.125182	+	0.216822i
$57$	−3.85599	−	6.67878i	−0.510739	−	0.884626i
$58$	−2.96025	−	9.11071i	−0.388700	−	1.19630i
$59$	−0.604971	−	5.75592i	−0.0787606	−	0.749357i	−0.960624	−	0.277852i	$-0.910378\pi$
$59$	−0.604971	−	5.75592i	−0.0787606	−	0.749357i	0.881863	−	0.471505i	$-0.156289\pi$
$60$	−5.42320	−	3.94019i	−0.700132	−	0.508676i
$61$	−3.09888			−0.396771			−0.198386	−	0.980124i	$-0.563570\pi$
$61$	−3.09888			−0.396771			−0.198386	+	0.980124i	$0.563570\pi$
$62$	6.52293	+	10.1432i	0.828413	+	1.28819i
$63$	1.25109			0.157623
$64$	9.90609	+	7.19719i	1.23826	+	0.899649i
$65$	1.21978	+	11.6054i	0.151295	+	1.43947i
$66$	−0.461317	−	1.41979i	−0.0567841	−	0.174764i
$67$	5.04480	+	8.73786i	0.616321	+	1.06750i	0.990151	+	0.140002i	$0.0447109\pi$
$67$	5.04480	+	8.73786i	0.616321	+	1.06750i	−0.373830	+	0.927497i	$0.621956\pi$
$68$	−0.249283	+	0.431771i	−0.0302300	+	0.0523599i
$69$	−8.16650	−	1.73584i	−0.983132	−	0.208971i
$70$	2.08566	−	6.41900i	0.249284	−	0.767218i
$71$	9.19163	−	1.95374i	1.09085	−	0.231867i	0.372835	−	0.927898i	$-0.378386\pi$
$71$	9.19163	−	1.95374i	1.09085	−	0.231867i	0.718011	+	0.696031i	$0.245053\pi$
$72$	−0.156535	+	1.48933i	−0.0184478	+	0.175519i
$73$	−7.51632	+	8.34771i	−0.879718	+	0.977026i	−0.999876	−	0.0157287i	$-0.994993\pi$
$73$	−7.51632	+	8.34771i	−0.879718	+	0.977026i	0.120158	+	0.992755i	$0.461660\pi$
$74$	3.85540	−	1.71654i	0.448182	−	0.199543i
$75$	1.09952	+	0.489536i	0.126961	+	0.0565268i
$76$	13.8885	+	15.4247i	1.59312	+	1.76934i
$77$	0.697610	−	0.506844i	0.0795001	−	0.0577602i
$78$	8.20981	−	5.96478i	0.929578	−	0.675378i
$79$	−0.141156	−	0.156769i	−0.0158812	−	0.0176379i	0.735152	−	0.677902i	$-0.237111\pi$
$79$	−0.141156	−	0.156769i	−0.0158812	−	0.0176379i	−0.751033	+	0.660265i	$0.770444\pi$
$80$	−4.86743	−	2.16712i	−0.544195	−	0.242291i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	12.3933	−	13.7642i	1.36862	−	1.52000i
$83$	0.756688	−	7.19941i	0.0830573	−	0.790238i	−0.871135	−	0.491044i	$-0.836616\pi$
$83$	0.756688	−	7.19941i	0.0830573	−	0.790238i	0.954192	−	0.299194i	$-0.0967178\pi$
$84$	−3.29360	+	0.700077i	−0.359361	+	0.0763846i
$85$	0.142577	−	0.438806i	0.0154646	−	0.0475952i
$86$	−22.8424	−	4.85530i	−2.46316	−	0.523560i
$87$	2.21139	−	3.83024i	0.237086	−	0.410645i
$88$	0.516074	+	0.893867i	0.0550137	+	0.0952865i
$89$	−0.741825	−	2.28310i	−0.0786333	−	0.242008i	0.904011	−	0.427510i	$-0.140609\pi$
$89$	−0.741825	−	2.28310i	−0.0786333	−	0.242008i	−0.982644	+	0.185501i	$0.940609\pi$
$90$	−0.563906	−	5.36520i	−0.0594409	−	0.565542i
$91$	4.74211	+	3.44535i	0.497108	+	0.361170i
$92$	22.4703			2.34269
$93$	−1.46502	+	5.37157i	−0.151915	+	0.557005i
$94$	10.0790			1.03957
$95$	−15.5398	−	11.2903i	−1.59435	−	1.15836i
$96$	0.797392	+	7.58668i	0.0813835	+	0.774312i
$97$	−1.13746	−	3.50073i	−0.115491	−	0.355445i	0.876558	−	0.481296i	$-0.159834\pi$
$97$	−1.13746	−	3.50073i	−0.115491	−	0.355445i	−0.992049	+	0.125851i	$0.959834\pi$
$98$	5.88575	+	10.1944i	0.594551	+	1.02979i
$99$	0.344616	−	0.596893i	0.0346352	−	0.0599900i
$100$	−3.16850	−	0.673485i	−0.316850	−	0.0673485i
$101$	−1.97950	+	6.09228i	−0.196968	+	0.606205i	0.802980	+	0.596006i	$0.203247\pi$
$101$	−1.97950	+	6.09228i	−0.196968	+	0.606205i	−0.999948	+	0.0101991i	$0.996753\pi$
$102$	−0.392465	+	0.0834209i	−0.0388598	+	0.00825990i
$103$	−0.512153	+	4.87281i	−0.0504639	+	0.480132i	0.939881	+	0.341504i	$0.110936\pi$
$103$	−0.512153	+	4.87281i	−0.0504639	+	0.480132i	−0.990344	+	0.138629i	$0.955731\pi$
$104$	−4.69474	+	5.21404i	−0.460357	+	0.511279i
$105$	2.84669	−	1.26743i	0.277809	−	0.123688i
$106$	−16.6268	−	7.40273i	−1.61494	−	0.719017i
$107$	2.13088	+	2.36658i	0.205999	+	0.228786i	0.837288	−	0.546763i	$-0.184140\pi$
$107$	2.13088	+	2.36658i	0.205999	+	0.228786i	−0.631288	+	0.775548i	$0.717473\pi$
$108$	−2.17738	+	1.58196i	−0.209519	+	0.152224i
$109$	1.19547	−	0.868557i	0.114505	−	0.0831927i	−0.529059	−	0.848585i	$-0.677455\pi$
$109$	1.19547	−	0.868557i	0.114505	−	0.0831927i	0.643564	+	0.765392i	$0.277455\pi$
$110$	−2.48799	−	2.76319i	−0.237220	−	0.263460i
$111$	1.78000	+	0.792505i	0.168950	+	0.0752213i
$112$	−2.44494	+	1.08856i	−0.231025	+	0.102859i
$113$	4.75744	−	5.28367i	0.447542	−	0.497046i	−0.476586	−	0.879128i	$-0.658126\pi$
$113$	4.75744	−	5.28367i	0.447542	−	0.497046i	0.924129	+	0.382082i	$0.124793\pi$
$114$	−1.74603	+	16.6124i	−0.163531	+	1.55589i
$115$	−20.3403	+	4.32346i	−1.89674	+	0.403165i
$116$	−3.67836	+	11.3208i	−0.341527	+	1.05111i
$117$	4.58278	+	0.974100i	0.423678	+	0.0900556i
$118$	−6.26789	+	10.8563i	−0.577006	+	0.999404i
$119$	−0.115879	−	0.200708i	−0.0106226	−	0.0183989i
$120$	1.15260	+	3.54735i	0.105218	+	0.323827i
$121$	1.10016	+	10.4673i	0.100014	+	0.951573i
$122$	5.43018	+	3.94525i	0.491625	+	0.357187i
$123$	8.55120			0.771035
$124$	0.850997	−	14.9609i	0.0764218	−	1.34353i
$125$	−9.45575			−0.845748
$126$	−2.19229	−	1.59279i	−0.195305	−	0.141897i
$127$	0.391138	+	3.72143i	0.0347079	+	0.330223i	0.998074	+	0.0620338i	$0.0197587\pi$
$127$	0.391138	+	3.72143i	0.0347079	+	0.330223i	−0.963366	+	0.268189i	$0.913575\pi$
$128$	−3.48089	−	10.7131i	−0.307670	−	0.946912i
$129$	−5.39083	−	9.33720i	−0.474637	−	0.822095i
$130$	12.6377	−	21.8891i	1.10840	−	1.91980i
$131$	18.4580	+	3.92336i	1.61268	+	0.342786i	0.924033	−	0.382312i	$-0.124872\pi$
$131$	18.4580	+	3.92336i	1.61268	+	0.342786i	0.688646	+	0.725097i	$0.258205\pi$
$132$	−0.573225	+	1.76421i	−0.0498929	+	0.153554i
$133$	−9.43757	+	2.00602i	−0.818341	+	0.173944i
$134$	2.28434	−	21.7340i	0.197337	−	1.87753i
$135$	1.66660	−	1.85095i	0.143438	−	0.159304i
$136$	0.253426	−	0.112833i	0.0217311	−	0.00967532i
$137$	−15.1348	−	6.73846i	−1.29306	−	0.575706i	−0.359169	−	0.933273i	$-0.616940\pi$
$137$	−15.1348	−	6.73846i	−1.29306	−	0.575706i	−0.933888	+	0.357567i	$0.883606\pi$
$138$	12.1002	+	13.4387i	1.03004	+	1.14398i
$139$	7.21648	−	5.24308i	0.612094	−	0.444712i	−0.238057	−	0.971251i	$-0.576511\pi$
$139$	7.21648	−	5.24308i	0.612094	−	0.444712i	0.850151	+	0.526539i	$0.176511\pi$
$140$	−6.78493	+	4.92954i	−0.573431	+	0.416622i
$141$	3.11371	+	3.45812i	0.262221	+	0.291226i
$142$	−18.5939	−	8.27852i	−1.56036	−	0.694718i
$143$	2.94999	−	1.31342i	0.246691	−	0.109834i
$144$	−1.43140	+	1.58973i	−0.119283	+	0.132477i
$145$	1.15146	−	10.9555i	0.0956239	−	0.909801i
$146$	23.7985	−	5.05853i	1.96958	−	0.418647i
$147$	−1.67944	+	5.16877i	−0.138517	+	0.426313i
$148$	−5.12945	−	1.09030i	−0.421638	−	0.0896219i
$149$	9.39257	−	16.2684i	0.769470	−	1.33276i	−0.168381	−	0.985722i	$-0.553854\pi$
$149$	9.39257	−	16.2684i	0.769470	−	1.33276i	0.937851	−	0.347038i	$-0.112813\pi$
$150$	−1.30344	−	2.25763i	−0.106426	−	0.184335i
$151$	−0.762723	−	2.34742i	−0.0620695	−	0.191030i	0.915213	−	0.402970i	$-0.132022\pi$
$151$	−0.762723	−	2.34742i	−0.0620695	−	0.191030i	−0.977283	+	0.211939i	$0.932022\pi$
$152$	−1.20719	−	11.4857i	−0.0979164	−	0.931612i
$153$	−0.149866	−	0.108884i	−0.0121159	−	0.00880274i
$154$	−1.86770			−0.150503
$155$	2.10826	+	13.7064i	0.169339	+	1.10093i
$156$	−12.6096			−1.00958
$157$	−1.13574	−	0.825167i	−0.0906423	−	0.0658555i	0.541541	−	0.840674i	$-0.317841\pi$
$157$	−1.13574	−	0.825167i	−0.0906423	−	0.0658555i	−0.632183	+	0.774819i	$0.717841\pi$
$158$	0.0477609	+	0.454415i	0.00379965	+	0.0361513i
$159$	−2.59663	−	7.99161i	−0.205926	−	0.633776i
$160$	9.50010	+	16.4547i	0.751049	+	1.30085i
$161$	−5.22265	+	9.04590i	−0.411603	+	0.712917i
$162$	−2.11863	−	0.450329i	−0.166455	−	0.0353812i
$163$	−2.52550	+	7.77269i	−0.197812	+	0.608804i	0.802120	+	0.597163i	$0.203705\pi$
$163$	−2.52550	+	7.77269i	−0.197812	+	0.608804i	−0.999932	+	0.0116407i	$0.996295\pi$
$164$	−22.5117	+	4.78501i	−1.75787	+	0.373647i
$165$	0.179441	−	1.70727i	0.0139694	−	0.132910i
$166$	−10.4917	+	11.6522i	−0.814311	+	0.904384i
$167$	−3.70935	+	1.65151i	−0.287038	+	0.127798i	−0.545205	−	0.838303i	$-0.683548\pi$
$167$	−3.70935	+	1.65151i	−0.287038	+	0.127798i	0.258167	+	0.966100i	$0.416882\pi$
$168$	1.71158	+	0.762042i	0.132051	+	0.0587928i
$169$	5.98922	+	6.65170i	0.460709	+	0.511669i
$170$	−0.808490	+	0.587402i	−0.0620083	+	0.0450517i
$171$	−6.23913	+	4.53299i	−0.477118	+	0.346647i
$172$	19.4166	+	21.5644i	1.48051	+	1.64427i
$173$	16.6701	+	7.42200i	1.26740	+	0.564285i	0.926670	−	0.375875i	$-0.122658\pi$
$173$	16.6701	+	7.42200i	1.26740	+	0.564285i	0.340734	+	0.940160i	$0.389325\pi$
$174$	−8.75137	+	3.89636i	−0.663440	+	0.295382i
$175$	1.00756	−	1.11901i	0.0761646	−	0.0845893i
$176$	−0.154117	+	1.46632i	−0.0116170	+	0.110528i
$177$	−5.66115	+	1.20331i	−0.425518	+	0.0904467i
$178$	−1.60677	+	4.94512i	−0.120432	+	0.370652i
$179$	−4.93883	−	1.04978i	−0.369145	−	0.0784643i	0.0196039	−	0.999808i	$-0.493759\pi$
$179$	−4.93883	−	1.04978i	−0.369145	−	0.0784643i	−0.388749	+	0.921344i	$0.627093\pi$
$180$	−3.35172	+	5.80535i	−0.249823	+	0.432706i
$181$	−12.9996	−	22.5159i	−0.966250	−	1.67359i	−0.706218	−	0.707994i	$-0.749600\pi$
$181$	−12.9996	−	22.5159i	−0.966250	−	1.67359i	−0.260032	−	0.965600i	$-0.583733\pi$
$182$	−3.92326	−	12.0746i	−0.290812	−	0.895026i
$183$	0.323922	+	3.08191i	0.0239450	+	0.227821i
$184$	−10.1150	−	7.34898i	−0.745687	−	0.541774i
$185$	4.85299			0.356799
$186$	9.40580	−	7.54745i	0.689667	−	0.553406i
$187$	−0.127676			−0.00933663
$188$	−10.1322	−	7.36144i	−0.738963	−	0.536888i
$189$	−0.130775	−	1.24424i	−0.00951247	−	0.0905051i
$190$	12.8564	+	39.5680i	0.932704	+	2.87057i
$191$	−4.54288	−	7.86850i	−0.328711	−	0.569345i	0.653545	−	0.756888i	$-0.273281\pi$
$191$	−4.54288	−	7.86850i	−0.328711	−	0.569345i	−0.982256	+	0.187543i	$0.939948\pi$
$192$	6.12230	−	10.6041i	0.441839	−	0.765287i
$193$	21.9047	+	4.65598i	1.57673	+	0.335145i	0.911439	−	0.411436i	$-0.134973\pi$
$193$	21.9047	+	4.65598i	1.57673	+	0.335145i	0.665295	+	0.746581i	$0.268306\pi$
$194$	−2.46369	+	7.58245i	−0.176882	+	0.544388i
$195$	11.4143	−	2.42619i	0.817396	−	0.173743i
$196$	1.52895	−	14.5470i	0.109211	−	1.03907i
$197$	0.902627	−	1.00247i	0.0643095	−	0.0714229i	−0.710132	−	0.704069i	$-0.751365\pi$
$197$	0.902627	−	1.00247i	0.0643095	−	0.0714229i	0.774441	+	0.632646i	$0.218031\pi$
$198$	−1.36379	+	0.607197i	−0.0969202	+	0.0431516i
$199$	6.35147	+	2.82785i	0.450243	+	0.200461i	0.619315	−	0.785142i	$-0.287410\pi$
$199$	6.35147	+	2.82785i	0.450243	+	0.200461i	−0.169072	+	0.985604i	$0.554077\pi$
$200$	1.20603	+	1.33943i	0.0852793	+	0.0947123i
$201$	8.16267	−	5.93052i	0.575750	−	0.418307i
$202$	11.2249	−	8.15537i	0.789781	−	0.573810i
$203$	−3.70250	−	4.11205i	−0.259865	−	0.288609i
$204$	0.455462	+	0.202785i	0.0318887	+	0.0141978i
$205$	19.4571	−	8.66285i	1.35894	−	0.605040i
$206$	7.10112	−	7.88659i	0.494759	−	0.549485i
$207$	−0.872703	+	8.30321i	−0.0606570	+	0.577113i
$208$	−9.80343	+	2.08378i	−0.679745	+	0.144484i
$209$	−1.64253	+	5.05520i	−0.113616	+	0.349676i
$210$	−6.60185	−	1.40327i	−0.455571	−	0.0968346i
$211$	−6.77621	+	11.7367i	−0.466494	+	0.807991i	−0.999268	−	0.0382669i	$-0.987816\pi$
$211$	−6.77621	+	11.7367i	−0.466494	+	0.807991i	0.532774	+	0.846258i	$0.321150\pi$
$212$	11.3077	+	19.5856i	0.776618	+	1.34514i
$213$	−2.90383	−	8.93706i	−0.198967	−	0.612357i
$214$	−0.720996	−	6.85982i	−0.0492862	−	0.468927i
$215$	−21.7252	−	15.7843i	−1.48165	−	1.07648i
$216$	1.49753			0.101894
$217$	5.82502	+	3.81986i	0.395428	+	0.259309i
$218$	−3.20059			−0.216772
$219$	9.08765	+	6.60257i	0.614087	+	0.446160i
$220$	0.482946	+	4.59492i	0.0325602	+	0.309790i
$221$	−0.268196	−	0.825422i	−0.0180408	−	0.0555239i
$222$	−2.11013	−	3.65486i	−0.141623	−	0.245298i
$223$	10.7814	−	18.6740i	0.721977	−	1.25050i	−0.238230	−	0.971209i	$-0.576567\pi$
$223$	10.7814	−	18.6740i	0.721977	−	1.25050i	0.960206	−	0.279291i	$-0.0900996\pi$
$224$	9.33536	+	1.98429i	0.623745	+	0.132581i
$225$	0.371924	−	1.14466i	0.0247949	−	0.0763109i
$226$	−15.0632	+	3.20179i	−1.00199	+	0.212980i
$227$	0.305622	−	2.90780i	0.0202848	−	0.192997i	−0.979687	−	0.200534i	$-0.935732\pi$
$227$	0.305622	−	2.90780i	0.0202848	−	0.192997i	0.999972	+	0.00753657i	$0.00239899\pi$
$228$	13.8885	−	15.4247i	0.919787	−	1.02153i
$229$	8.63007	−	3.84235i	0.570291	−	0.253910i	−0.101270	−	0.994859i	$-0.532291\pi$
$229$	8.63007	−	3.84235i	0.570291	−	0.253910i	0.671561	+	0.740949i	$0.265624\pi$
$230$	41.1466	+	18.3196i	2.71313	+	1.20796i
$231$	−0.576987	−	0.640809i	−0.0379630	−	0.0421621i
$232$	5.35832	−	3.89305i	0.351791	−	0.255591i
$233$	−18.2871	+	13.2864i	−1.19803	+	0.870419i	−0.994089	−	0.108564i	$-0.965375\pi$
$233$	−18.2871	+	13.2864i	−1.19803	+	0.870419i	−0.203940	+	0.978983i	$0.565375\pi$
$234$	−6.79026	−	7.54135i	−0.443893	−	0.492993i
$235$	10.5881	+	4.71412i	0.690691	+	0.307516i
$236$	14.2301	−	6.33565i	0.926300	−	0.412415i
$237$	−0.141156	+	0.156769i	−0.00916904	+	0.0101832i
$238$	−0.0524711	+	0.499229i	−0.00340120	+	0.0323602i
$239$	−17.1580	+	3.64705i	−1.10986	+	0.235908i	−0.726144	−	0.687543i	$-0.758689\pi$
$239$	−17.1580	+	3.64705i	−1.10986	+	0.235908i	−0.383717	+	0.923451i	$0.625356\pi$
$240$	−1.64646	+	5.06729i	−0.106279	+	0.327092i
$241$	2.16494	+	0.460172i	0.139456	+	0.0296423i	0.277111	−	0.960838i	$-0.410623\pi$
$241$	2.16494	+	0.460172i	0.139456	+	0.0296423i	−0.137655	+	0.990480i	$0.543956\pi$
$242$	11.3983	−	19.7425i	0.732713	−	1.26910i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.57730	−	7.93211i	−0.164995	−	0.507802i
$245$	1.41493	+	13.4622i	0.0903969	+	0.860069i
$246$	−14.9843	−	10.8867i	−0.955362	−	0.694111i
$247$	−36.1319			−2.29902
$248$	−5.27607	+	6.45630i	−0.335031	+	0.409976i
$249$	−7.23906			−0.458757
$250$	16.5693	+	12.0383i	1.04794	+	0.761370i
$251$	−1.47171	−	14.0024i	−0.0928934	−	0.883822i	−0.937395	−	0.348268i	$-0.886770\pi$
$251$	−1.47171	−	14.0024i	−0.0928934	−	0.883822i	0.844501	−	0.535553i	$-0.179897\pi$
$252$	1.04052	+	3.20238i	0.0655464	+	0.201731i
$253$	2.87718	+	4.98343i	0.180887	+	0.313305i
$254$	4.05244	−	7.01902i	0.254272	−	0.440413i
$255$	−0.451305	−	0.0959279i	−0.0282618	−	0.00600724i
$256$	0.0280942	−	0.0864650i	0.00175589	−	0.00540406i
$257$	12.5168	−	2.66052i	0.780775	−	0.165959i	0.199753	−	0.979846i	$-0.435986\pi$
$257$	12.5168	−	2.66052i	0.780775	−	0.165959i	0.581023	+	0.813887i	$0.302653\pi$
$258$	−2.44102	+	23.2248i	−0.151971	+	1.44591i
$259$	1.63113	−	1.81156i	0.101354	−	0.112565i
$260$	−28.6915	+	12.7743i	−1.77937	+	0.792226i
$261$	−4.04041	−	1.79891i	−0.250095	−	0.111349i
$262$	−27.3490	−	30.3741i	−1.68963	−	1.87652i
$263$	−12.8086	+	9.30601i	−0.789813	+	0.573833i	−0.907908	−	0.419169i	$-0.862321\pi$
$263$	−12.8086	+	9.30601i	−0.789813	+	0.573833i	0.118095	+	0.993002i	$0.462321\pi$
$264$	0.835025	−	0.606681i	0.0513923	−	0.0373387i
$265$	−14.0042	−	15.5533i	−0.860274	−	0.955431i
$266$	19.0914	+	8.50002i	1.17057	+	0.521170i
$267$	−2.19305	+	0.976411i	−0.134213	+	0.0597554i
$268$	−18.1703	+	20.1802i	−1.10993	+	1.23270i
$269$	−1.60316	+	15.2530i	−0.0977463	+	0.929994i	0.830247	+	0.557396i	$0.188200\pi$
$269$	−1.60316	+	15.2530i	−0.0977463	+	0.929994i	−0.927993	+	0.372598i	$0.878467\pi$
$270$	−5.27687	+	1.12163i	−0.321140	+	0.0682604i
$271$	9.71042	−	29.8856i	0.589866	−	1.81542i	0.0110853	−	0.999939i	$-0.496471\pi$
$271$	9.71042	−	29.8856i	0.589866	−	1.81542i	0.578781	−	0.815483i	$-0.303529\pi$
$272$	0.387613	+	0.0823897i	0.0235025	+	0.00499561i
$273$	2.93079	−	5.07627i	0.177379	−	0.307230i
$274$	17.9419	+	31.0763i	1.08391	+	1.87739i
$275$	−0.256342	−	0.788939i	−0.0154580	−	0.0475748i
$276$	−2.34879	−	22.3472i	−0.141380	−	1.34514i
$277$	−0.0735319	−	0.0534241i	−0.00441810	−	0.00320994i	0.585574	−	0.810619i	$-0.300869\pi$
$277$	−0.0735319	−	0.0534241i	−0.00441810	−	0.00320994i	−0.589992	+	0.807409i	$0.700869\pi$
$278$	−19.3205			−1.15877
$279$	5.49528	+	0.895510i	0.328994	+	0.0536128i
$280$	4.66645			0.278874
$281$	0.313108	+	0.227486i	0.0186784	+	0.0135707i	0.597085	−	0.802178i	$-0.296325\pi$
$281$	0.313108	+	0.227486i	0.0186784	+	0.0135707i	−0.578407	+	0.815748i	$0.696325\pi$
$282$	−1.05354	−	10.0238i	−0.0627376	−	0.596908i
$283$	0.244162	+	0.751455i	0.0145140	+	0.0446693i	0.958051	−	0.286597i	$-0.0925241\pi$
$283$	0.244162	+	0.751455i	0.0145140	+	0.0446693i	−0.943537	+	0.331266i	$0.892524\pi$
$284$	12.6455	+	21.9026i	0.750372	+	1.29968i
$285$	−9.60411	+	16.6348i	−0.568899	+	0.985361i
$286$	−6.84141	−	1.45419i	−0.404541	−	0.0859879i
$287$	3.30597	−	10.1747i	0.195145	−	0.600595i
$288$	7.46177	−	1.58605i	0.439689	−	0.0934587i
$289$	1.77340	−	16.8727i	0.104317	−	0.992514i
$290$	−15.9653	+	17.7313i	−0.937516	+	1.04122i
$291$	−3.36265	+	1.49715i	−0.197122	+	0.0877645i
$292$	−27.6186	−	12.2966i	−1.61626	−	0.719603i
$293$	5.58804	+	6.20615i	0.326457	+	0.362567i	0.883923	−	0.467633i	$-0.154893\pi$
$293$	5.58804	+	6.20615i	0.326457	+	0.362567i	−0.557466	+	0.830200i	$0.688226\pi$
$294$	9.52335	−	6.91912i	0.555413	−	0.403531i
$295$	−11.6622	+	8.47305i	−0.678997	+	0.493320i
$296$	1.95243	+	2.16840i	0.113483	+	0.126035i
$297$	−0.629645	−	0.280336i	−0.0365357	−	0.0162668i
$298$	−37.1703	+	16.5493i	−2.15322	+	0.958673i
$299$	−26.1738	+	29.0690i	−1.51367	+	1.68110i
$300$	−0.338597	+	3.22154i	−0.0195489	+	0.185996i
$301$	−13.1941	+	2.80449i	−0.760495	+	0.161648i
$302$	−1.65203	+	5.08442i	−0.0950636	+	0.292576i
$303$	6.26582	+	1.33184i	0.359962	+	0.0765123i
$304$	8.24870	−	14.2872i	0.473095	−	0.819425i
$305$	3.85919	+	6.68431i	0.220977	+	0.382743i
$306$	0.123988	+	0.381595i	0.00708790	+	0.0218143i
$307$	−0.227405	−	2.16362i	−0.0129787	−	0.123484i	0.986114	−	0.166069i	$-0.0531074\pi$
$307$	−0.227405	−	2.16362i	−0.0129787	−	0.123484i	−0.999093	+	0.0425847i	$0.986441\pi$
$308$	1.87754	+	1.36412i	0.106983	+	0.0777277i
$309$	4.89965			0.278731
$310$	13.7556	−	26.7018i	0.781267	−	1.51656i
$311$	4.80773			0.272622			0.136311	−	0.990666i	$-0.456475\pi$
$311$	4.80773			0.272622			0.136311	+	0.990666i	$0.456475\pi$
$312$	5.67621	+	4.12401i	0.321352	+	0.233476i
$313$	−1.73935	−	16.5488i	−0.0983140	−	0.935395i	−0.926843	−	0.375449i	$-0.877488\pi$
$313$	−1.73935	−	16.5488i	−0.0983140	−	0.935395i	0.828529	−	0.559946i	$-0.189178\pi$
$314$	0.939629	+	2.89188i	0.0530263	+	0.163198i
$315$	−1.55805	−	2.69862i	−0.0877860	−	0.152050i
$316$	0.283880	−	0.491694i	0.0159695	−	0.0276599i
$317$	−2.21033	−	0.469821i	−0.124145	−	0.0263878i	0.145420	−	0.989370i	$-0.453547\pi$
$317$	−2.21033	−	0.469821i	−0.124145	−	0.0263878i	−0.269565	+	0.962982i	$0.586880\pi$
$318$	−5.62421	+	17.3095i	−0.315390	+	0.970670i
$319$	−2.98171	+	0.633782i	−0.166944	+	0.0354850i
$320$	3.18786	−	30.3305i	0.178207	−	1.69553i
$321$	2.13088	−	2.36658i	0.118934	−	0.132089i
$322$	20.6682	−	9.20207i	1.15179	−	0.512811i
$323$	1.30509	+	0.581065i	0.0726174	+	0.0323313i
$324$	1.80089	+	2.00010i	0.100050	+	0.111116i
$325$	4.56199	−	3.31448i	0.253053	−	0.183854i
$326$	14.3210	−	10.4048i	0.793167	−	0.576269i
$327$	−0.988759	−	1.09813i	−0.0546785	−	0.0607266i
$328$	11.6986	+	5.20855i	0.645946	+	0.287594i
$329$	5.31847	−	2.36793i	0.293217	−	0.130548i
$330$	−2.48799	+	2.76319i	−0.136959	+	0.152109i
$331$	−2.05879	+	19.5881i	−0.113161	+	1.07666i	0.779646	+	0.626220i	$0.215399\pi$
$331$	−2.05879	+	19.5881i	−0.113161	+	1.07666i	−0.892808	+	0.450438i	$0.851268\pi$
$332$	19.0574	−	4.05078i	1.04591	−	0.222315i
$333$	0.602103	−	1.85308i	0.0329951	−	0.101548i
$334$	8.60247	+	1.82851i	0.470706	+	0.100052i
$335$	12.5651	−	21.7634i	0.686504	−	1.18906i
$336$	1.33816	+	2.31776i	0.0730027	+	0.126444i
$337$	7.22786	+	22.2451i	0.393727	+	1.21177i	0.929949	+	0.367689i	$0.119851\pi$
$337$	7.22786	+	22.2451i	0.393727	+	1.21177i	−0.536222	+	0.844077i	$0.680149\pi$
$338$	−2.02649	−	19.2808i	−0.110227	−	1.04874i
$339$	−5.75202	−	4.17909i	−0.312407	−	0.226977i
$340$	1.24178			0.0673448
$341$	3.42696	−	1.72691i	0.185580	−	0.0935176i
$342$	16.7039			0.903242
$343$	12.5859	+	9.14420i	0.679575	+	0.493740i
$344$	−1.68771	−	16.0575i	−0.0909950	−	0.865760i
$345$	6.42592	+	19.7769i	0.345960	+	1.06475i
$346$	−19.7619	−	34.2286i	−1.06241	−	1.84014i
$347$	−5.41453	+	9.37825i	−0.290667	+	0.503451i	−0.973968	−	0.226687i	$-0.927211\pi$
$347$	−5.41453	+	9.37825i	−0.290667	+	0.503451i	0.683300	+	0.730137i	$0.260544\pi$
$348$	11.6433	+	2.47486i	0.624147	+	0.132667i
$349$	−4.39226	+	13.5180i	−0.235112	+	0.723601i	0.761994	+	0.647584i	$0.224220\pi$
$349$	−4.39226	+	13.5180i	−0.235112	+	0.723601i	−0.997107	+	0.0760171i	$0.975780\pi$
$350$	−3.19019	+	0.678096i	−0.170523	+	0.0362457i
$351$	0.489733	−	4.65950i	0.0261400	−	0.248706i
$352$	3.51815	−	3.90730i	0.187518	−	0.208260i
$353$	9.41579	−	4.19218i	0.501152	−	0.223127i	−0.140561	−	0.990072i	$-0.544891\pi$
$353$	9.41579	−	4.19218i	0.501152	−	0.223127i	0.641713	+	0.766945i	$0.278224\pi$
$354$	11.4520	+	5.09876i	0.608667	+	0.270996i
$355$	−15.6610	−	17.3933i	−0.831201	−	0.923142i
$356$	5.22702	−	3.79765i	0.277032	−	0.201275i
$357$	−0.187496	+	0.136224i	−0.00992335	+	0.00720973i
$358$	7.31782	+	8.12726i	0.386759	+	0.429539i
$359$	2.86736	+	1.27663i	0.151334	+	0.0673781i	0.481006	−	0.876717i	$-0.340272\pi$
$359$	2.86736	+	1.27663i	0.151334	+	0.0673781i	−0.329672	+	0.944095i	$0.606938\pi$
$360$	3.40743	−	1.51709i	0.179587	−	0.0799575i
$361$	27.0829	−	30.0786i	1.42542	−	1.58309i
$362$	−5.88633	+	56.0047i	−0.309378	+	2.94354i
$363$	10.2950	−	2.18826i	0.540345	−	0.114854i
$364$	−4.87499	+	15.0037i	−0.255519	+	0.786406i
$365$	27.3665	+	5.81693i	1.43243	+	0.304472i
$366$	3.35603	−	5.81282i	0.175423	−	0.303841i
$367$	13.4930	+	23.3705i	0.704326	+	1.21993i	0.966934	+	0.255026i	$0.0820842\pi$
$367$	13.4930	+	23.3705i	0.704326	+	1.21993i	−0.262608	+	0.964903i	$0.584583\pi$
$368$	−5.51903	−	16.9858i	−0.287699	−	0.885448i
$369$	−0.893843	−	8.50435i	−0.0465316	−	0.442719i
$370$	−8.50390	−	6.17845i	−0.442097	−	0.321202i
$371$	−10.5128			−0.545796
$372$	−14.9679	+	0.717501i	−0.776047	+	0.0372007i
$373$	24.5340			1.27032			0.635162	−	0.772379i	$-0.280933\pi$
$373$	24.5340			1.27032			0.635162	+	0.772379i	$0.280933\pi$
$374$	0.223728	+	0.162548i	0.0115687	+	0.00840513i
$375$	0.988395	+	9.40395i	0.0510405	+	0.485618i
$376$	2.15340	+	6.62750i	0.111053	+	0.341787i
$377$	−10.3607	−	17.9453i	−0.533604	−	0.924229i
$378$	−1.35491	+	2.34677i	−0.0696890	+	0.120705i
$379$	35.4055	+	7.52567i	1.81866	+	0.386568i	0.985936	−	0.167124i	$-0.0534479\pi$
$379$	35.4055	+	7.52567i	1.81866	+	0.386568i	0.832722	+	0.553691i	$0.186781\pi$
$380$	15.9752	−	49.1667i	0.819511	−	2.52220i
$381$	3.66016	−	0.777990i	0.187515	−	0.0398576i
$382$	−2.05706	+	19.5716i	−0.105248	+	1.00137i
$383$	−22.5875	+	25.0859i	−1.15417	+	1.28183i	−0.200929	+	0.979606i	$0.564396\pi$
$383$	−22.5875	+	25.0859i	−1.15417	+	1.28183i	−0.953237	+	0.302225i	$0.902271\pi$
$384$	−10.2905	+	4.58165i	−0.525137	+	0.233806i
$385$	−1.96203	−	0.873553i	−0.0999944	−	0.0445204i
$386$	−32.4560	−	36.0460i	−1.65196	−	1.83469i
$387$	−8.72255	+	6.33731i	−0.443392	+	0.322143i
$388$	8.01469	−	5.82302i	0.406884	−	0.295619i
$389$	−2.28719	−	2.54018i	−0.115965	−	0.128792i	0.682367	−	0.731010i	$-0.260951\pi$
$389$	−2.28719	−	2.54018i	−0.115965	−	0.128792i	−0.798332	+	0.602217i	$0.794284\pi$
$390$	−23.0901	−	10.2804i	−1.16921	−	0.520568i
$391$	1.41289	−	0.629057i	0.0714527	−	0.0318128i
$392$	−5.44588	+	6.04826i	−0.275059	+	0.305483i
$393$	1.97249	−	18.7670i	0.0994988	−	0.946667i
$394$	−2.85794	+	0.607473i	−0.143981	+	0.0306041i
$395$	−0.162364	+	0.499706i	−0.00816943	+	0.0251429i
$396$	1.81446	+	0.385675i	0.0911800	+	0.0193809i
$397$	−17.1076	+	29.6312i	−0.858604	+	1.48715i	0.0146573	+	0.999893i	$0.495334\pi$
$397$	−17.1076	+	29.6312i	−0.858604	+	1.48715i	−0.873261	+	0.487253i	$0.837999\pi$
$398$	−7.52947	−	13.0414i	−0.377418	−	0.653708i
$399$	2.98152	+	9.17619i	0.149263	+	0.459384i
$400$	0.269126	+	2.56056i	0.0134563	+	0.128028i
$401$	30.2216	+	21.9573i	1.50919	+	1.09649i	0.966533	+	0.256543i	$0.0825834\pi$
$401$	30.2216	+	21.9573i	1.50919	+	1.09649i	0.542662	+	0.839951i	$0.317417\pi$
$402$	−21.8537			−1.08996
$403$	18.3630	+	18.5276i	0.914728	+	0.922925i
$404$	−17.2405			−0.857749
$405$	−2.01502	−	1.46399i	−0.100127	−	0.0727465i
$406$	1.25277	+	11.9193i	0.0621737	+	0.591544i
$407$	−0.414989	−	1.27721i	−0.0205703	−	0.0633087i
$408$	−0.138705	−	0.240244i	−0.00686691	−	0.0118938i
$409$	−12.9241	+	22.3851i	−0.639053	+	1.10687i	0.346587	+	0.938018i	$0.387340\pi$
$409$	−12.9241	+	22.3851i	−0.639053	+	1.10687i	−0.985641	+	0.168855i	$0.945993\pi$
$410$	−45.1235	−	9.59130i	−2.22849	−	0.473681i
$411$	−5.11953	+	15.7563i	−0.252528	+	0.777200i
$412$	−12.8987	+	2.74171i	−0.635474	+	0.135074i
$413$	−0.756875	+	7.20119i	−0.0372434	+	0.354347i
$414$	12.1002	−	13.4387i	0.594694	−	0.660474i
$415$	−16.4715	+	7.33359i	−0.808555	+	0.359992i
$416$	32.6507	+	14.5370i	1.60083	+	0.712736i
$417$	−5.96868	−	6.62889i	−0.292288	−	0.324618i
$418$	9.31410	−	6.76709i	0.455567	−	0.330989i
$419$	3.64364	−	2.64726i	0.178003	−	0.129327i	−0.495216	−	0.868770i	$-0.664911\pi$
$419$	3.64364	−	2.64726i	0.178003	−	0.129327i	0.673219	+	0.739443i	$0.264911\pi$
$420$	5.61175	+	6.23248i	0.273825	+	0.304114i
$421$	−22.9040	−	10.1975i	−1.11627	−	0.496996i	−0.236137	−	0.971720i	$-0.575881\pi$
$421$	−22.9040	−	10.1975i	−1.11627	−	0.496996i	−0.880135	+	0.474724i	$0.842548\pi$
$422$	26.8163	−	11.9394i	1.30539	−	0.581199i
$423$	3.11371	−	3.45812i	0.151394	−	0.168140i
$424$	1.31534	−	12.5146i	0.0638787	−	0.607765i
$425$	−0.218083	+	0.0463549i	−0.0105786	+	0.00224854i
$426$	−6.28958	+	19.3573i	−0.304731	+	0.937866i
$427$	3.79227	+	0.806072i	0.183521	+	0.0390085i
$428$	−4.28543	+	7.42258i	−0.207144	+	0.358784i
$429$	−1.61458	−	2.79654i	−0.0779528	−	0.135018i
$430$	17.9738	+	55.3177i	0.866774	+	2.66766i
$431$	1.64204	+	15.6230i	0.0790942	+	0.752531i	0.960144	+	0.279507i	$0.0901710\pi$
$431$	1.64204	+	15.6230i	0.0790942	+	0.752531i	−0.881049	+	0.473024i	$0.843162\pi$
$432$	1.73064	+	1.25738i	0.0832654	+	0.0604959i
$433$	−12.4368			−0.597672			−0.298836	−	0.954304i	$-0.596598\pi$
$433$	−12.4368			−0.597672			−0.298836	+	0.954304i	$0.596598\pi$
$434$	−5.34404	−	14.1095i	−0.256522	−	0.677278i
$435$	−11.0158			−0.528167
$436$	3.21747	+	2.33763i	0.154089	+	0.111952i
$437$	−6.73027	−	64.0343i	−0.321953	−	3.06317i
$438$	−7.51843	−	23.1394i	−0.359245	−	1.10564i
$439$	3.12797	+	5.41781i	0.149290	+	0.258578i	0.930965	−	0.365108i	$-0.118968\pi$
$439$	3.12797	+	5.41781i	0.149290	+	0.258578i	−0.781675	+	0.623686i	$0.785635\pi$
$440$	1.28538	−	2.22635i	0.0612783	−	0.106137i
$441$	5.31600	+	1.12995i	0.253143	+	0.0538072i
$442$	−0.580902	+	1.78783i	−0.0276307	+	0.0850386i
$443$	9.01553	−	1.91631i	0.428341	−	0.0910466i	0.0113036	−	0.999936i	$-0.496402\pi$
$443$	9.01553	−	1.91631i	0.428341	−	0.0910466i	0.417037	+	0.908889i	$0.363069\pi$
$444$	−0.548151	+	5.21531i	−0.0260141	+	0.247508i
$445$	−4.00084	+	4.44338i	−0.189658	+	0.210636i
$446$	−42.6665	+	18.9963i	−2.02032	+	0.899503i
$447$	−17.1611	−	7.64061i	−0.811691	−	0.361388i
$448$	−10.2505	−	11.3843i	−0.484290	−	0.537859i
$449$	11.3223	−	8.22617i	0.534335	−	0.388217i	−0.287642	−	0.957738i	$-0.592871\pi$
$449$	11.3223	−	8.22617i	0.534335	−	0.388217i	0.821977	+	0.569521i	$0.192871\pi$
$450$	−2.10902	+	1.53229i	−0.0994200	+	0.0722329i
$451$	−3.94370	−	4.37992i	−0.185701	−	0.206242i
$452$	17.4811	+	7.78311i	0.822244	+	0.366087i
$453$	−2.25483	+	1.00392i	−0.105941	+	0.0471681i
$454$	−4.23752	+	4.70624i	−0.198877	+	0.220875i
$455$	1.52605	−	14.5194i	0.0715425	−	0.680681i
$456$	−11.2966	+	2.40116i	−0.529011	+	0.112445i
$457$	1.38079	−	4.24964i	0.0645907	−	0.198790i	−0.913553	−	0.406720i	$-0.866673\pi$
$457$	1.38079	−	4.24964i	0.0645907	−	0.198790i	0.978144	+	0.207930i	$0.0666726\pi$
$458$	−20.0142	−	4.25416i	−0.935204	−	0.198784i
$459$	−0.0926222	+	0.160426i	−0.00432323	+	0.00748806i
$460$	−27.9834	−	48.4686i	−1.30473	−	2.25986i
$461$	−0.926958	−	2.85288i	−0.0431727	−	0.132872i	0.927147	−	0.374698i	$-0.122254\pi$
$461$	−0.926958	−	2.85288i	−0.0431727	−	0.132872i	−0.970320	+	0.241826i	$0.922254\pi$
$462$	0.195227	+	1.85746i	0.00908280	+	0.0864171i
$463$	−21.4066	−	15.5528i	−0.994847	−	0.722799i	−0.0338700	−	0.999426i	$-0.510783\pi$
$463$	−21.4066	−	15.5528i	−0.994847	−	0.722799i	−0.960977	+	0.276627i	$0.910783\pi$
$464$	9.46115			0.439223
$465$	13.4110	−	3.52942i	0.621918	−	0.163673i
$466$	48.9597			2.26801
$467$	18.1164	+	13.1623i	0.838326	+	0.609080i	0.921903	−	0.387422i	$-0.126634\pi$
$467$	18.1164	+	13.1623i	0.838326	+	0.609080i	−0.0835763	+	0.996501i	$0.526634\pi$
$468$	1.31806	+	12.5405i	0.0609275	+	0.579687i
$469$	−3.90073	−	12.0052i	−0.180119	−	0.554350i
$470$	−12.5519	−	21.7405i	−0.578975	−	1.00281i
$471$	−0.701929	+	1.21578i	−0.0323432	+	0.0560200i
$472$	−8.47776	−	1.80200i	−0.390220	−	0.0829439i
$473$	−2.29633	+	7.06737i	−0.105585	+	0.324958i
$474$	0.446933	−	0.0949985i	0.0205283	−	0.00436343i
$475$	−0.970225	+	9.23108i	−0.0445170	+	0.423551i
$476$	0.417371	−	0.463538i	0.0191302	−	0.0212462i
$477$	−7.67641	+	3.41776i	−0.351479	+	0.156488i
$478$	34.7092	+	15.4535i	1.58756	+	0.706827i
$479$	−1.36314	−	1.51392i	−0.0622833	−	0.0691726i	0.711198	−	0.702992i	$-0.248153\pi$
$479$	−1.36314	−	1.51392i	−0.0622833	−	0.0691726i	−0.773481	+	0.633819i	$0.781486\pi$
$480$	15.3715	−	11.1680i	0.701609	−	0.509749i
$481$	7.38535	−	5.36577i	0.336743	−	0.244658i
$482$	−3.20777	−	3.56258i	−0.146110	−	0.162271i
$483$	9.54226	+	4.24849i	0.434188	+	0.193313i
$484$	−25.8778	+	11.5216i	−1.17626	+	0.523707i
$485$	−6.13457	+	6.81312i	−0.278556	+	0.309368i
$486$	−0.226405	+	2.15410i	−0.0102699	+	0.0977118i
$487$	−2.13739	+	0.454316i	−0.0968544	+	0.0205870i	−0.256084	−	0.966655i	$-0.582432\pi$
$487$	−2.13739	+	0.454316i	−0.0968544	+	0.0205870i	0.159230	+	0.987242i	$0.449099\pi$
$488$	−1.43405	+	4.41355i	−0.0649164	+	0.199792i
$489$	7.99409	+	1.69920i	0.361505	+	0.0768403i
$490$	14.6596	−	25.3912i	0.662254	−	1.14706i
$491$	−13.4192	−	23.2427i	−0.605600	−	1.04893i	−0.991956	−	0.126580i	$-0.959600\pi$
$491$	−13.4192	−	23.2427i	−0.605600	−	1.04893i	0.386357	−	0.922349i	$-0.373733\pi$
$492$	7.11191	+	21.8882i	0.320630	+	0.986797i
$493$	0.0856396	+	0.814807i	0.00385701	+	0.0366970i
$494$	63.3140	+	46.0003i	2.84863	+	2.06965i
$495$	−1.71667			−0.0771585
$496$	−11.5183	+	3.03132i	−0.517186	+	0.136110i
$497$	−11.7565			−0.527351
$498$	12.6850	+	9.21620i	0.568429	+	0.412988i
$499$	−0.397276	−	3.77983i	−0.0177845	−	0.169208i	0.982024	−	0.188754i	$-0.0604448\pi$
$499$	−0.397276	−	3.77983i	−0.0177845	−	0.169208i	−0.999809	+	0.0195453i	$0.993778\pi$
$500$	−7.86422	−	24.2036i	−0.351699	−	1.08242i
$501$	2.03020	+	3.51640i	0.0907024	+	0.157101i
$502$	−15.2478	+	26.4100i	−0.680544	+	1.17874i
$503$	0.733018	+	0.155808i	0.0326837	+	0.00694713i	0.224225	−	0.974538i	$-0.428015\pi$
$503$	0.733018	+	0.155808i	0.0326837	+	0.00694713i	−0.191541	+	0.981485i	$0.561348\pi$
$504$	0.578959	−	1.78185i	0.0257889	−	0.0793701i
$505$	15.6063	−	3.31721i	0.694470	−	0.147614i
$506$	1.30282	−	12.3955i	0.0579172	−	0.551046i
$507$	5.98922	−	6.65170i	0.265990	−	0.295412i
$508$	−9.20031	+	4.09624i	−0.408198	+	0.181741i
$509$	−30.1558	−	13.4262i	−1.33663	−	0.595107i	−0.391014	−	0.920385i	$-0.627876\pi$
$509$	−30.1558	−	13.4262i	−1.33663	−	0.595107i	−0.945619	+	0.325277i	$0.894542\pi$
$510$	0.668695	+	0.742661i	0.0296103	+	0.0328856i
$511$	11.3695	−	8.26042i	0.502957	−	0.365420i
$512$	−18.3855	+	13.3578i	−0.812532	+	0.590339i
$513$	5.16033	+	5.73112i	0.227834	+	0.253035i
$514$	−25.3203	−	11.2733i	−1.11683	−	0.497246i
$515$	11.1485	−	4.96363i	0.491261	−	0.218724i
$516$	19.4166	−	21.5644i	0.854770	−	0.949318i
$517$	0.335249	−	3.18968i	0.0147442	−	0.140282i
$518$	−5.16456	+	1.09776i	−0.226918	+	0.0482329i
$519$	5.63885	−	17.3546i	0.247518	−	0.761782i
$520$	17.0933	+	3.63330i	0.749591	+	0.159331i
$521$	−17.4154	+	30.1643i	−0.762981	+	1.32152i	0.178326	+	0.983971i	$0.442932\pi$
$521$	−17.4154	+	30.1643i	−0.762981	+	1.32152i	−0.941307	+	0.337551i	$0.890402\pi$
$522$	4.78978	+	8.29615i	0.209643	+	0.363113i
$523$	−3.06621	−	9.43681i	−0.134076	−	0.412643i	0.861369	−	0.507979i	$-0.169607\pi$
$523$	−3.06621	−	9.43681i	−0.134076	−	0.412643i	−0.995445	+	0.0953363i	$0.969607\pi$
$524$	5.30874	+	50.5093i	0.231913	+	2.20651i
$525$	−1.21820	−	0.885074i	−0.0531666	−	0.0386278i
$526$	34.2922			1.49521
$527$	−0.365321	−	0.964531i	−0.0159136	−	0.0420156i
$528$	1.47440			0.0641649
$529$	−37.7851	−	27.4525i	−1.64283	−	1.19359i
$530$	4.73843	+	45.0831i	0.205824	+	1.95829i
$531$	1.78847	+	5.50436i	0.0776132	+	0.238869i
$532$	−12.9838	−	22.4887i	−0.562921	−	0.975007i
$533$	20.0319	−	34.6962i	0.867677	−	1.50286i
$534$	5.08598	+	1.08106i	0.220092	+	0.0467820i
$535$	2.45104	−	7.54353i	0.105968	−	0.326135i
$536$	14.7793	−	3.14145i	0.638370	−	0.135690i
$537$	−0.527782	+	5.02151i	−0.0227755	+	0.216694i
$538$	22.2282	−	24.6869i	0.958325	−	1.06433i
$539$	3.42198	−	1.52356i	0.147395	−	0.0656244i
$540$	6.12390	+	2.72654i	0.263531	+	0.117331i
$541$	8.98294	+	9.97657i	0.386207	+	0.428926i	0.904630	−	0.426198i	$-0.140147\pi$
$541$	8.98294	+	9.97657i	0.386207	+	0.428926i	−0.518423	+	0.855124i	$0.673481\pi$
$542$	−55.0636	+	40.0060i	−2.36518	+	1.71841i
$543$	−21.0337	+	15.2819i	−0.902644	+	0.655809i
$544$	−0.945569	−	1.05016i	−0.0405409	−	0.0450253i
$545$	−3.36226	−	1.49697i	−0.144023	−	0.0641233i
$546$	−11.5983	+	5.16391i	−0.496362	+	0.220995i
$547$	−18.7054	+	20.7744i	−0.799785	+	0.888251i	−0.995725	−	0.0923650i	$-0.970557\pi$
$547$	−18.7054	+	20.7744i	−0.799785	+	0.888251i	0.195941	+	0.980616i	$0.437224\pi$
$548$	4.66079	−	44.3444i	0.199099	−	1.89430i
$549$	3.03117	−	0.644294i	0.129367	−	0.0274978i
$550$	−0.555227	+	1.70881i	−0.0236750	+	0.0728640i
$551$	33.3631	+	7.09154i	1.42131	+	0.302110i
$552$	−6.25141	+	10.8278i	−0.266078	+	0.460860i
$553$	0.131961	+	0.228564i	0.00561156	+	0.00971951i
$554$	0.0608347	+	0.187230i	0.00258462	+	0.00795464i
$555$	−0.507276	−	4.82641i	−0.0215327	−	0.204870i
$556$	19.4224	+	14.1112i	0.823692	+	0.598448i
$557$	32.3729			1.37169			0.685843	−	0.727750i	$-0.259434\pi$
$557$	32.3729			1.37169			0.685843	+	0.727750i	$0.259434\pi$
$558$	−8.48928	−	8.56535i	−0.359380	−	0.362600i
$559$	−50.5139			−2.13651
$560$	5.39283	+	3.91812i	0.227889	+	0.165571i
$561$	0.0133458	+	0.126977i	0.000563461	+	0.00536097i
$562$	−0.259042	−	0.797248i	−0.0109270	−	0.0336299i
$563$	10.8902	+	18.8623i	0.458966	+	0.794952i	0.998907	−	0.0467509i	$-0.0148867\pi$
$563$	10.8902	+	18.8623i	0.458966	+	0.794952i	−0.539941	+	0.841703i	$0.681553\pi$
$564$	−6.26202	+	10.8461i	−0.263678	+	0.456704i
$565$	−17.3216	−	3.68182i	−0.728725	−	0.154895i
$566$	0.528847	−	1.62762i	0.0222291	−	0.0684141i
$567$	−1.22375	+	0.260117i	−0.0513928	+	0.0109239i
$568$	1.47095	−	13.9952i	0.0617199	−	0.587225i
$569$	−3.05758	+	3.39579i	−0.128181	+	0.142359i	−0.803818	−	0.594875i	$-0.797202\pi$
$569$	−3.05758	+	3.39579i	−0.128181	+	0.142359i	0.675638	+	0.737234i	$0.263868\pi$
$570$	38.0074	−	16.9220i	1.59196	−	0.708784i
$571$	−9.43387	−	4.20023i	−0.394795	−	0.175774i	0.199730	−	0.979851i	$-0.435993\pi$
$571$	−9.43387	−	4.20023i	−0.394795	−	0.175774i	−0.594525	+	0.804077i	$0.702660\pi$
$572$	5.81539	+	6.45864i	0.243153	+	0.270049i
$573$	−7.35053	+	5.34047i	−0.307073	+	0.223102i
$574$	−18.7467	+	13.6203i	−0.782472	+	0.568499i
$575$	6.72379	+	7.46753i	0.280402	+	0.311417i
$576$	−11.1860	−	4.98033i	−0.466083	−	0.207514i
$577$	12.6666	−	5.63955i	0.527319	−	0.234778i	−0.125769	−	0.992060i	$-0.540140\pi$
$577$	12.6666	−	5.63955i	0.527319	−	0.234778i	0.653088	+	0.757282i	$0.273473\pi$
$578$	−24.5886	+	27.3084i	−1.02275	+	1.13588i
$579$	2.34082	−	22.2714i	0.0972810	−	0.925566i
$580$	29.0000	−	6.16413i	1.20416	−	0.255952i
$581$	−2.79869	+	8.61347i	−0.116109	+	0.357347i
$582$	7.79843	+	1.65761i	0.323255	+	0.0687101i
$583$	−2.89577	+	5.01562i	−0.119930	+	0.207726i
$584$	8.41086	+	14.5680i	0.348044	+	0.602830i
$585$	−3.60602	−	11.0982i	−0.149090	−	0.458853i
$586$	−1.89075	−	17.9893i	−0.0781062	−	0.743131i
$587$	−15.7332	−	11.4308i	−0.649377	−	0.471800i	0.213682	−	0.976903i	$-0.431454\pi$
$587$	−15.7332	−	11.4308i	−0.649377	−	0.471800i	−0.863059	+	0.505103i	$0.831454\pi$
$588$	−14.6271			−0.603211
$589$	−42.8893	+	2.05595i	−1.76722	+	0.0847138i
$590$	31.2228			1.28542
$591$	−1.09133	−	0.792895i	−0.0448912	−	0.0326154i
$592$	0.435685	+	4.14526i	0.0179065	+	0.170369i
$593$	−10.3100	−	31.7308i	−0.423380	−	1.30303i	−0.904537	−	0.426395i	$-0.859783\pi$
$593$	−10.3100	−	31.7308i	−0.423380	−	1.30303i	0.481157	−	0.876634i	$-0.340217\pi$
$594$	0.746426	+	1.29285i	0.0306262	+	0.0530462i
$595$	−0.288619	+	0.499903i	−0.0118322	+	0.0204940i
$596$	49.4534	+	10.5116i	2.02569	+	0.430574i
$597$	2.14845	−	6.61226i	0.0879304	−	0.270622i
$598$	82.8727	−	17.6151i	3.38892	−	0.720337i
$599$	2.14245	−	20.3841i	0.0875382	−	0.832870i	−0.859367	−	0.511359i	$-0.829142\pi$
$599$	2.14245	−	20.3841i	0.0875382	−	0.832870i	0.946906	−	0.321512i	$-0.104191\pi$
$600$	1.20603	−	1.33943i	0.0492360	−	0.0546822i
$601$	−1.60495	+	0.714572i	−0.0654675	+	0.0291480i	−0.439209	−	0.898385i	$-0.644741\pi$
$601$	−1.60495	+	0.714572i	−0.0654675	+	0.0291480i	0.373742	+	0.927533i	$0.378075\pi$
$602$	26.6905	+	11.8834i	1.08782	+	0.484330i
$603$	−6.75127	−	7.49804i	−0.274933	−	0.305344i
$604$	5.37427	−	3.90464i	0.218676	−	0.158877i
$605$	21.2080	−	15.4085i	0.862226	−	0.626444i
$606$	−9.28401	−	10.3109i	−0.377137	−	0.418853i
$607$	20.4982	+	9.12639i	0.831996	+	0.370429i	0.778117	−	0.628119i	$-0.216175\pi$
$607$	20.4982	+	9.12639i	0.831996	+	0.370429i	0.0538789	+	0.998547i	$0.482841\pi$
$608$	−53.7445	+	23.9286i	−2.17963	+	0.970432i
$609$	−3.70250	+	4.11205i	−0.150033	+	0.166629i
$610$	1.74748	−	16.6261i	0.0707533	−	0.673173i
$611$	21.3253	−	4.53284i	0.862731	−	0.183379i
$612$	0.154065	−	0.474164i	0.00622772	−	0.0191669i
$613$	−0.793338	−	0.168629i	−0.0320426	−	0.00681087i	0.191862	−	0.981422i	$-0.438547\pi$
$613$	−0.793338	−	0.168629i	−0.0320426	−	0.00681087i	−0.223905	+	0.974611i	$0.571881\pi$
$614$	−2.35606	+	4.08082i	−0.0950830	+	0.164689i
$615$	−10.6492	−	18.4450i	−0.429418	−	0.743774i
$616$	−0.399038	−	1.22811i	−0.0160777	−	0.0494820i
$617$	3.73792	+	35.5639i	0.150483	+	1.43175i	0.765602	+	0.643314i	$0.222441\pi$
$617$	3.73792	+	35.5639i	0.150483	+	1.43175i	−0.615119	+	0.788434i	$0.710892\pi$
$618$	−8.58566	−	6.23785i	−0.345366	−	0.250923i
$619$	11.5430			0.463954			0.231977	−	0.972721i	$-0.425481\pi$
$619$	11.5430			0.463954			0.231977	+	0.972721i	$0.425481\pi$
$620$	−33.3305	+	16.7959i	−1.33858	+	0.674539i
$621$	8.34895			0.335032
$622$	−8.42459	−	6.12083i	−0.337795	−	0.245423i
$623$	0.313938	+	2.98692i	0.0125776	+	0.119668i
$624$	3.09710	+	9.53191i	0.123983	+	0.381582i
$625$	14.7846	+	25.6077i	0.591385	+	1.02431i
$626$	−18.0208	+	31.2129i	−0.720256	+	1.24752i
$627$	5.19920	+	1.10512i	0.207636	+	0.0441344i
$628$	1.16757	−	3.59341i	0.0465911	−	0.143393i
$629$	−0.353052	+	0.0750435i	−0.0140771	+	0.00299218i
$630$	−0.705498	+	6.71237i	−0.0281077	+	0.267427i
$631$	7.75094	−	8.60829i	0.308560	−	0.342691i	−0.568842	−	0.822447i	$-0.692608\pi$
$631$	7.75094	−	8.60829i	0.308560	−	0.342691i	0.877402	+	0.479756i	$0.159275\pi$
$632$	−0.288598	+	0.128492i	−0.0114798	+	0.00511114i
$633$	12.3808	+	5.51227i	0.492091	+	0.219093i
$634$	3.27503	+	3.63729i	0.130068	+	0.144455i
$635$	7.54004	−	5.47816i	0.299217	−	0.217394i
$636$	18.2963	−	13.2930i	0.725495	−	0.527103i
$637$	17.0379	+	18.9225i	0.675067	+	0.749738i
$638$	6.03173	+	2.68550i	0.238798	+	0.106320i
$639$	−8.58457	+	3.82210i	−0.339600	+	0.151200i
$640$	−18.7733	+	20.8498i	−0.742079	+	0.824162i
$641$	0.174892	−	1.66398i	0.00690781	−	0.0657234i	−0.990525	−	0.137333i	$-0.956147\pi$
$641$	0.174892	−	1.66398i	0.00690781	−	0.0657234i	0.997433	+	0.0716097i	$0.0228136\pi$
$642$	−6.74687	+	1.43409i	−0.266278	+	0.0565991i
$643$	8.03529	−	24.7301i	0.316881	−	0.975259i	−0.658092	−	0.752937i	$-0.728636\pi$
$643$	8.03529	−	24.7301i	0.316881	−	0.975259i	0.974973	−	0.222322i	$-0.0713636\pi$
$644$	−27.4981	−	5.84490i	−1.08358	−	0.230321i
$645$	−13.4269	+	23.2561i	−0.528685	+	0.915709i
$646$	−1.54715	−	2.67974i	−0.0608718	−	0.105433i
$647$	−0.0674850	−	0.207698i	−0.00265311	−	0.00816543i	0.949721	−	0.313097i	$-0.101366\pi$
$647$	−0.0674850	−	0.207698i	−0.00265311	−	0.00816543i	−0.952374	+	0.304931i	$0.901366\pi$
$648$	−0.156535	−	1.48933i	−0.00614927	−	0.0585064i
$649$	3.22718	+	2.34469i	0.126678	+	0.0920370i
$650$	−12.2137			−0.479061
$651$	3.19005	−	6.19240i	0.125028	−	0.242699i
$652$	−21.9959			−0.861426
$653$	−20.7560	−	15.0801i	−0.812245	−	0.590130i	0.102236	−	0.994760i	$-0.467400\pi$
$653$	−20.7560	−	15.0801i	−0.812245	−	0.590130i	−0.914481	+	0.404630i	$0.867400\pi$
$654$	0.334553	+	3.18306i	0.0130821	+	0.124468i
$655$	−14.5239	−	44.6999i	−0.567495	−	1.74657i
$656$	9.14631	+	15.8419i	0.357103	+	0.618521i
$657$	5.61648	−	9.72803i	0.219120	−	0.379526i
$658$	−12.3342	−	2.62172i	−0.480838	−	0.102205i
$659$	6.92458	−	21.3117i	0.269743	−	0.830185i	−0.720819	−	0.693123i	$-0.756234\pi$
$659$	6.92458	−	21.3117i	0.269743	−	0.830185i	0.990563	−	0.137062i	$-0.0437658\pi$
$660$	4.51927	−	0.960600i	0.175912	−	0.0373913i
$661$	−3.78534	+	36.0151i	−0.147233	+	1.40082i	0.632426	+	0.774620i	$0.282059\pi$
$661$	−3.78534	+	36.0151i	−0.147233	+	1.40082i	−0.779659	+	0.626204i	$0.784608\pi$
$662$	28.5456	−	31.7031i	1.10946	−	1.23218i
$663$	−0.792866	+	0.353007i	−0.0307924	+	0.0137096i
$664$	−9.90350	−	4.40932i	−0.384331	−	0.171115i
$665$	16.0801	+	17.8587i	0.623558	+	0.692531i
$666$	−3.41427	+	2.48061i	−0.132300	+	0.0961217i
$667$	29.8734	−	21.7043i	1.15670	−	0.840393i
$668$	−7.31233	−	8.12117i	−0.282923	−	0.314217i
$669$	−19.6986	−	8.77039i	−0.761593	−	0.339083i
$670$	−49.7252	+	22.1391i	−1.92105	+	0.855307i
$671$	1.42916	−	1.58725i	0.0551723	−	0.0612750i
$672$	0.997611	−	9.49163i	0.0384837	−	0.366148i
$673$	−13.4180	+	2.85209i	−0.517228	+	0.109940i	−0.459127	−	0.888371i	$-0.651838\pi$
$673$	−13.4180	+	2.85209i	−0.517228	+	0.109940i	−0.0581006	+	0.998311i	$0.518504\pi$
$674$	15.6553	−	48.1820i	0.603018	−	1.85590i
$675$	−1.17727	−	0.250236i	−0.0453131	−	0.00963160i
$676$	−12.0450	+	20.8625i	−0.463269	+	0.802405i
$677$	−6.59786	−	11.4278i	−0.253577	−	0.439207i	0.710931	−	0.703261i	$-0.248274\pi$
$677$	−6.59786	−	11.4278i	−0.253577	−	0.439207i	−0.964508	+	0.264054i	$0.914940\pi$
$678$	4.75878	+	14.6460i	0.182760	+	0.562477i
$679$	0.481367	+	4.57990i	0.0184732	+	0.175760i
$680$	−0.558985	−	0.406126i	−0.0214361	−	0.0155742i
$681$	−2.92382			−0.112041
$682$	−8.20363	−	1.33686i	−0.314133	−	0.0511912i
$683$	43.1032			1.64930			0.824649	−	0.565645i	$-0.191373\pi$
$683$	43.1032			1.64930			0.824649	+	0.565645i	$0.191373\pi$
$684$	−16.7920	−	12.2001i	−0.642056	−	0.466481i
$685$	4.31323	+	41.0377i	0.164800	+	1.56797i
$686$	−10.4126	−	32.0468i	−0.397556	−	1.22355i
$687$	−4.72339	−	8.18115i	−0.180209	−	0.312131i
$688$	11.5320	−	19.9740i	0.439654	−	0.761502i
$689$	−38.5085	−	8.18524i	−1.46706	−	0.311833i
$690$	13.9183	−	42.8361i	0.529860	−	1.63074i
$691$	17.2607	−	3.66887i	0.656626	−	0.139570i	0.132463	−	0.991188i	$-0.457711\pi$
$691$	17.2607	−	3.66887i	0.656626	−	0.139570i	0.524163	+	0.851618i	$0.324378\pi$
$692$	−5.13357	+	48.8427i	−0.195149	+	1.85672i
$693$	−0.576987	+	0.640809i	−0.0219179	+	0.0243423i
$694$	21.4275	−	9.54015i	0.813378	−	0.362139i
$695$	−20.2964	−	9.03653i	−0.769886	−	0.342775i
$696$	−4.43182	−	4.92204i	−0.167988	−	0.186569i
$697$	−1.28153	+	0.931088i	−0.0485415	+	0.0352675i
$698$	24.9066	−	18.0957i	0.942728	−	0.684932i
$699$	15.1251	+	16.7981i	0.572084	+	0.635364i
$700$	3.70227	+	1.64836i	0.139933	+	0.0623021i
$701$	−6.20929	+	2.76455i	−0.234522	+	0.104416i	−0.520633	−	0.853781i	$-0.674304\pi$
$701$	−6.20929	+	2.76455i	−0.234522	+	0.104416i	0.286111	+	0.958196i	$0.407637\pi$
$702$	−6.79026	+	7.54135i	−0.256282	+	0.284630i
$703$	−1.57069	+	14.9441i	−0.0592396	+	0.563627i
$704$	−8.25495	+	1.75464i	−0.311120	+	0.0661306i
$705$	3.58154	−	11.0229i	0.134889	−	0.415145i
$706$	−21.8364	−	4.64148i	−0.821825	−	0.174684i
$707$	4.00713	−	6.94055i	0.150704	−	0.261026i
$708$	−7.78839	−	13.4899i	−0.292706	−	0.506981i
$709$	9.99372	+	30.7575i	0.375322	+	1.15512i	0.943261	+	0.332052i	$0.107741\pi$
$709$	9.99372	+	30.7575i	0.375322	+	1.15512i	−0.567939	+	0.823070i	$0.692259\pi$
$710$	5.29901	+	50.4167i	0.198868	+	1.89211i
$711$	0.170665	+	0.123995i	0.00640044	+	0.00465019i
$712$	−3.59497			−0.134727
$713$	−29.4148	+	35.9948i	−1.10159	+	1.34801i
$714$	0.501979			0.0187861
$715$	−6.50682	−	4.72748i	−0.243341	−	0.176798i
$716$	−1.42047	−	13.5149i	−0.0530854	−	0.505074i
$717$	5.42058	+	16.6828i	0.202435	+	0.623031i
$718$	−3.39918	−	5.88755i	−0.126856	−	0.219721i
$719$	−4.52554	+	7.83847i	−0.168774	+	0.292326i	−0.937989	−	0.346665i	$-0.887314\pi$
$719$	−4.52554	+	7.83847i	−0.168774	+	0.292326i	0.769215	+	0.638990i	$0.220648\pi$
$720$	5.21164	+	1.10777i	0.194226	+	0.0412841i
$721$	1.89425	−	5.82990i	0.0705455	−	0.217117i
$722$	−85.7511	+	18.2270i	−3.19133	+	0.678337i
$723$	0.231353	−	2.20118i	0.00860412	−	0.0818627i
$724$	46.8217	−	52.0007i	1.74011	−	1.93259i
$725$	−4.86292	+	2.16511i	−0.180604	+	0.0804102i
$726$	−20.8258	−	9.27224i	−0.772918	−	0.344125i
$727$	24.3735	+	27.0695i	0.903964	+	1.00395i	0.999963	+	0.00857232i	$0.00272869\pi$
$727$	24.3735	+	27.0695i	0.903964	+	1.00395i	−0.0959993	+	0.995381i	$0.530605\pi$
$728$	7.10147	−	5.15952i	0.263198	−	0.191224i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−40.5487	−	45.0339i	−1.50077	−	1.66678i
$731$	1.82457	+	0.812352i	0.0674843	+	0.0300459i
$732$	−7.61926	+	3.39231i	−0.281616	+	0.125383i
$733$	7.68396	−	8.53391i	0.283814	−	0.315207i	−0.584334	−	0.811513i	$-0.698644\pi$
$733$	7.68396	−	8.53391i	0.283814	−	0.315207i	0.868147	+	0.496306i	$0.165311\pi$
$734$	6.10974	−	58.1303i	0.225514	−	2.14563i
$735$	13.2406	−	2.81437i	0.488385	−	0.103809i
$736$	−19.6812	+	60.5725i	−0.725458	+	2.23273i
$737$	−6.80212	−	1.44584i	−0.250559	−	0.0532581i
$738$	−9.26078	+	16.0401i	−0.340894	+	0.590446i
$739$	0.304647	+	0.527664i	0.0112066	+	0.0194104i	0.871574	−	0.490263i	$-0.163099\pi$
$739$	0.304647	+	0.527664i	0.0112066	+	0.0194104i	−0.860368	+	0.509674i	$0.829766\pi$
$740$	4.03617	+	12.4220i	0.148372	+	0.456644i
$741$	3.77681	+	35.9340i	0.138745	+	1.32007i
$742$	18.4215	+	13.3840i	0.676276	+	0.491343i
$743$	3.71890			0.136433			0.0682167	−	0.997671i	$-0.478269\pi$
$743$	3.71890			0.136433			0.0682167	+	0.997671i	$0.478269\pi$
$744$	6.97243	+	4.57230i	0.255622	+	0.167629i
$745$	−46.7881			−1.71418
$746$	−42.9910	−	31.2348i	−1.57401	−	1.14359i
$747$	0.756688	+	7.19941i	0.0276858	+	0.263413i
$748$	−0.106187	−	0.326809i	−0.00388257	−	0.0119493i
$749$	−1.99208	−	3.45038i	−0.0727890	−	0.126074i
$750$	10.2404	−	17.7369i	0.373927	−	0.647660i
$751$	0.652422	+	0.138677i	0.0238072	+	0.00506038i	0.219800	−	0.975545i	$-0.429460\pi$
$751$	0.652422	+	0.138677i	0.0238072	+	0.00506038i	−0.195993	+	0.980605i	$0.562793\pi$
$752$	−3.07608	+	9.46721i	−0.112173	+	0.345234i
$753$	−13.7718	+	2.92729i	−0.501873	+	0.106676i
$754$	−4.69143	+	44.6360i	−0.170852	+	1.62555i
$755$	−4.11355	+	4.56856i	−0.149707	+	0.166267i
$756$	3.07607	−	1.36956i	0.111876	−	0.0498103i
$757$	36.8836	+	16.4216i	1.34056	+	0.596854i	0.946640	−	0.322292i	$-0.104453\pi$
$757$	36.8836	+	16.4216i	1.34056	+	0.596854i	0.393917	+	0.919146i	$0.371120\pi$
$758$	−52.4600	−	58.2627i	−1.90543	−	2.11620i
$759$	4.65538	−	3.38233i	0.168980	−	0.122771i
$760$	−23.2713	+	16.9076i	−0.844140	+	0.613304i
$761$	−1.78656	−	1.98417i	−0.0647626	−	0.0719261i	0.709893	−	0.704310i	$-0.248743\pi$
$761$	−1.78656	−	1.98417i	−0.0647626	−	0.0719261i	−0.774655	+	0.632384i	$0.782077\pi$
$762$	−7.40417	−	3.29655i	−0.268225	−	0.119421i
$763$	−1.68888	+	0.751939i	−0.0611416	+	0.0272220i
$764$	16.3625	−	18.1724i	0.591974	−	0.657454i
$765$	−0.0482281	+	0.458860i	−0.00174369	+	0.0165901i
$766$	71.5174	−	15.2015i	2.58403	−	0.549252i
$767$	−8.37929	+	25.7888i	−0.302559	+	0.931180i
$768$	−0.0889280	−	0.0189022i	−0.00320891	−	0.000682075i
$769$	−0.923465	+	1.59949i	−0.0333010	+	0.0576790i	−0.882196	−	0.470883i	$-0.843935\pi$
$769$	−0.923465	+	1.59949i	−0.0333010	+	0.0576790i	0.848895	+	0.528562i	$0.177269\pi$
$770$	2.32593	+	4.02863i	0.0838208	+	0.145182i
$771$	−3.95431	−	12.1701i	−0.142411	−	0.438296i
$772$	6.30005	+	59.9410i	0.226744	+	2.15732i
$773$	−6.32767	−	4.59732i	−0.227590	−	0.165354i	0.468146	−	0.883651i	$-0.344922\pi$
$773$	−6.32767	−	4.59732i	−0.227590	−	0.165354i	−0.695737	+	0.718297i	$0.744922\pi$
$774$	23.3527			0.839395
$775$	5.22657	−	4.19393i	0.187744	−	0.150650i
$776$	−5.51224			−0.197878
$777$	−1.97213	−	1.43284i	−0.0707498	−	0.0514028i
$778$	0.773886	+	7.36303i	0.0277452	+	0.263978i
$779$	20.3787	+	62.7191i	0.730141	+	2.24714i
$780$	15.7034	+	27.1990i	0.562271	+	0.973881i
$781$	−3.23835	+	5.60899i	−0.115877	+	0.200705i
$782$	−3.27667	−	0.696477i	−0.117173	−	0.0249060i
$783$	−1.36671	+	4.20631i	−0.0488423	+	0.150321i
$784$	−11.3719	+	2.41718i	−0.406140	+	0.0863278i
$785$	−0.365492	+	3.47743i	−0.0130450	+	0.124115i
$786$	−27.3490	+	30.3741i	−0.975506	+	1.08341i
$787$	−23.7713	+	10.5837i	−0.847357	+	0.377267i	−0.784028	−	0.620725i	$-0.786838\pi$
$787$	−23.7713	+	10.5837i	−0.847357	+	0.377267i	−0.0633284	+	0.997993i	$0.520172\pi$
$788$	3.31669	+	1.47668i	0.118152	+	0.0526047i
$789$	10.5939	+	11.7657i	0.377153	+	0.418870i
$790$	0.920696	−	0.668925i	0.0327569	−	0.0237993i
$791$	−7.19631	+	5.22842i	−0.255871	+	0.185901i
$792$	−0.690642	−	0.767036i	−0.0245409	−	0.0272554i
$793$	13.2636	+	5.90532i	0.471003	+	0.209704i
$794$	67.7016	−	30.1427i	2.40264	−	1.06972i
$795$	−14.0042	+	15.5533i	−0.496679	+	0.551618i
$796$	−1.95594	+	18.6095i	−0.0693265	+	0.659597i
$797$	35.6187	−	7.57098i	1.26168	−	0.268178i	0.471944	−	0.881628i	$-0.343552\pi$
$797$	35.6187	−	7.57098i	1.26168	−	0.268178i	0.789733	+	0.613451i	$0.210219\pi$
$798$	6.45787	−	19.8753i	0.228606	−	0.703577i
$799$	−0.843172	−	0.179222i	−0.0298293	−	0.00634041i
$800$	4.59070	−	7.95132i	0.162306	−	0.281122i
$801$	1.20030	+	2.07898i	0.0424105	+	0.0734571i
$802$	−25.0031	−	76.9515i	−0.882889	−	2.71725i
$803$	−0.809272	−	7.69971i	−0.0285586	−	0.271717i
$804$	21.9689	+	15.9614i	0.774785	+	0.562914i
$805$	26.0161			0.916947
$806$	−8.58971	−	55.8443i	−0.302559	−	1.96703i
$807$	15.3371			0.539890
$808$	7.76082	+	5.63857i	0.273025	+	0.198364i
$809$	4.32480	+	41.1477i	0.152052	+	1.44668i	0.758562	+	0.651601i	$0.225902\pi$
$809$	4.32480	+	41.1477i	0.152052	+	1.44668i	−0.606510	+	0.795076i	$0.707431\pi$
$810$	1.66707	+	5.13072i	0.0585749	+	0.180275i
$811$	−27.4699	−	47.5793i	−0.964598	−	1.67073i	−0.710690	−	0.703505i	$-0.751617\pi$
$811$	−27.4699	−	47.5793i	−0.964598	−	1.67073i	−0.253908	−	0.967228i	$-0.581716\pi$
$812$	7.44615	−	12.8971i	0.261309	−	0.452600i
$813$	−30.7369	−	6.53333i	−1.07799	−	0.229134i
$814$	−0.898851	+	2.76638i	−0.0315047	+	0.0969616i
$815$	19.9109	−	4.23218i	0.697447	−	0.148247i
$816$	0.0414218	−	0.394102i	0.00145005	−	0.0137963i
$817$	55.6369	−	61.7911i	1.94649	−	2.16180i
$818$	51.1458	−	22.7716i	1.78827	−	0.796189i
$819$	−5.35481	−	2.38412i	−0.187112	−	0.0833078i
$820$	38.3562	+	42.5989i	1.33946	+	1.48762i
$821$	12.6697	−	9.20507i	0.442175	−	0.321259i	−0.344324	−	0.938851i	$-0.611892\pi$
$821$	12.6697	−	9.20507i	0.442175	−	0.321259i	0.786499	+	0.617592i	$0.211892\pi$
$822$	29.0306	−	21.0920i	1.01256	−	0.735667i
$823$	5.91372	+	6.56785i	0.206139	+	0.228941i	0.837345	−	0.546674i	$-0.184106\pi$
$823$	5.91372	+	6.56785i	0.206139	+	0.228941i	−0.631206	+	0.775615i	$0.717440\pi$
$824$	6.70304	+	2.98438i	0.233511	+	0.103966i
$825$	−0.757822	+	0.337404i	−0.0263840	+	0.0117469i
$826$	10.4943	−	11.6551i	0.365142	−	0.405531i
$827$	2.03173	−	19.3306i	0.0706500	−	0.672190i	−0.900685	−	0.434474i	$-0.856934\pi$
$827$	2.03173	−	19.3306i	0.0706500	−	0.672190i	0.971335	−	0.237717i	$-0.0763989\pi$
$828$	−21.9793	+	4.67184i	−0.763833	+	0.162358i
$829$	4.79366	−	14.7534i	0.166491	−	0.512405i	−0.832652	−	0.553796i	$-0.813179\pi$
$829$	4.79366	−	14.7534i	0.166491	−	0.512405i	0.999143	+	0.0413906i	$0.0131788\pi$
$830$	38.1996	+	8.11957i	1.32593	+	0.281834i
$831$	−0.0454452	+	0.0787134i	−0.00157648	+	0.00273054i
$832$	−28.6840	−	49.6821i	−0.994437	−	1.72242i
$833$	−0.311106	−	0.957486i	−0.0107792	−	0.0331749i
$834$	2.01954	+	19.2147i	0.0699311	+	0.665350i
$835$	8.18175	+	5.94439i	0.283141	+	0.205714i
$836$	−14.3057			−0.494773
$837$	0.316192	−	5.55878i	0.0109292	−	0.192140i
$838$	−9.75502			−0.336982
$839$	21.6779	+	15.7499i	0.748404	+	0.543748i	0.895332	−	0.445400i	$-0.146938\pi$
$839$	21.6779	+	15.7499i	0.748404	+	0.543748i	−0.146928	+	0.989147i	$0.546938\pi$
$840$	−0.487777	−	4.64089i	−0.0168299	−	0.160126i
$841$	−2.91683	−	8.97707i	−0.100580	−	0.309554i
$842$	27.1520	+	47.0286i	0.935720	+	1.62071i
$843$	0.193511	−	0.335171i	0.00666488	−	0.0115439i
$844$	−35.6778	−	7.58356i	−1.22808	−	0.261037i
$845$	6.88910	−	21.2025i	0.236992	−	0.729387i
$846$	−9.85876	+	2.09554i	−0.338951	+	0.0720463i
$847$	1.37640	−	13.0956i	0.0472936	−	0.449969i
$848$	12.0278	−	13.3583i	0.413038	−	0.458725i
$849$	0.721816	−	0.321373i	0.0247727	−	0.0110295i
$850$	0.441162	+	0.196418i	0.0151317	+	0.00673708i
$851$	10.8851	+	12.0891i	0.373136	+	0.414409i
$852$	20.4608	−	14.8657i	0.700976	−	0.509289i
$853$	1.25415	−	0.911196i	0.0429414	−	0.0311988i	−0.566108	−	0.824331i	$-0.691551\pi$
$853$	1.25415	−	0.911196i	0.0429414	−	0.0311988i	0.609049	+	0.793133i	$0.291551\pi$
$854$	−5.61897	−	6.24050i	−0.192277	−	0.213545i
$855$	17.5476	+	7.81269i	0.600115	+	0.267188i
$856$	4.35666	−	1.93971i	0.148908	−	0.0662979i
$857$	21.7680	−	24.1758i	0.743579	−	0.825829i	−0.246082	−	0.969249i	$-0.579143\pi$
$857$	21.7680	−	24.1758i	0.743579	−	0.825829i	0.989662	+	0.143420i	$0.0458101\pi$
$858$	−0.731098	+	6.95594i	−0.0249593	+	0.237472i
$859$	−16.3786	+	3.48138i	−0.558831	+	0.118783i	−0.478664	−	0.877998i	$-0.658879\pi$
$859$	−16.3786	+	3.48138i	−0.558831	+	0.118783i	−0.0801672	+	0.996781i	$0.525545\pi$
$860$	22.3340	−	68.7370i	0.761583	−	2.34391i
$861$	−10.4646	−	2.22431i	−0.356631	−	0.0758043i
$862$	17.0126	−	29.4666i	0.579450	−	1.00364i
$863$	11.8471	+	20.5198i	0.403280	+	0.698502i	0.994120	−	0.108287i	$-0.0345366\pi$
$863$	11.8471	+	20.5198i	0.403280	+	0.698502i	−0.590839	+	0.806789i	$0.701203\pi$
$864$	−2.35733	−	7.25510i	−0.0801978	−	0.246824i
$865$	−4.75076	−	45.2005i	−0.161531	−	1.53686i
$866$	21.7929	+	15.8335i	0.740554	+	0.538044i
$867$	−16.9657			−0.576185
$868$	−4.93298	+	18.0870i	−0.167436	+	0.613914i
$869$	0.145396			0.00493222
$870$	19.3030	+	14.0244i	0.654432	+	0.475473i
$871$	−4.94121	−	47.0125i	−0.167427	−	1.59296i
$872$	−0.683815	−	2.10456i	−0.0231569	−	0.0712696i
$873$	1.84044	+	3.18774i	0.0622895	+	0.107889i
$874$	−69.7299	+	120.776i	−2.35865	+	4.08530i
$875$	11.5715	+	2.45960i	0.391188	+	0.0831497i
$876$	−9.34230	+	28.7526i	−0.315647	+	0.971462i
$877$	−55.4628	+	11.7890i	−1.87285	+	0.398086i	−0.996500	−	0.0835937i	$-0.973360\pi$
$877$	−55.4628	+	11.7890i	−1.87285	+	0.398086i	−0.876347	+	0.481680i	$0.840027\pi$
$878$	1.41638	−	13.4759i	0.0478004	−	0.454790i
$879$	5.58804	−	6.20615i	0.188480	−	0.209328i
$880$	3.35479	−	1.49365i	0.113090	−	0.0503509i
$881$	−42.5807	−	18.9582i	−1.43458	−	0.638717i	−0.465408	−	0.885096i	$-0.654092\pi$
$881$	−42.5807	−	18.9582i	−1.43458	−	0.638717i	−0.969173	+	0.246379i	$0.920759\pi$
$882$	−7.87667	−	8.74793i	−0.265221	−	0.294558i
$883$	−1.44338	+	1.04868i	−0.0485738	+	0.0352909i	−0.611807	−	0.791007i	$-0.709557\pi$
$883$	−1.44338	+	1.04868i	−0.0485738	+	0.0352909i	0.563233	+	0.826298i	$0.309557\pi$
$884$	1.88975	−	1.37298i	0.0635592	−	0.0461785i
$885$	9.64566	+	10.7126i	0.324235	+	0.360100i
$886$	−18.2376	−	8.11991i	−0.612704	−	0.272794i
$887$	−33.7605	+	15.0312i	−1.13357	+	0.504697i	−0.885774	−	0.464116i	$-0.846372\pi$
$887$	−33.7605	+	15.0312i	−1.13357	+	0.504697i	−0.247793	+	0.968813i	$0.579705\pi$
$888$	1.95243	−	2.16840i	0.0655193	−	0.0727666i
$889$	0.489350	−	4.65585i	0.0164123	−	0.156152i
$890$	12.6676	−	2.69259i	0.424620	−	0.0902558i
$891$	−0.212985	+	0.655499i	−0.00713525	+	0.0219600i
$892$	56.7659	+	12.0660i	1.90066	+	0.403998i
$893$	−17.9433	+	31.0788i	−0.600451	+	1.04001i
$894$	20.3440	+	35.2368i	0.680404	+	1.17849i
$895$	3.88618	+	11.9604i	0.129901	+	0.399793i
$896$	1.47310	+	14.0156i	0.0492128	+	0.468229i
$897$	31.6457	+	22.9919i	1.05662	+	0.767678i
$898$	−30.3131			−1.01156
$899$	−13.3195	−	20.7119i	−0.444229	−	0.690779i
$900$	3.23928			0.107976
$901$	1.25930	+	0.914938i	0.0419535	+	0.0304810i
$902$	1.33438	+	12.6957i	0.0444298	+	0.422722i
$903$	4.16829	+	12.8287i	0.138712	+	0.426912i
$904$	−5.32364	−	9.22082i	−0.177062	−	0.306680i
$905$	−32.3780	+	56.0803i	−1.07628	+	1.86417i
$906$	5.22926	+	1.11151i	0.173730	+	0.0369275i
$907$	1.96742	−	6.05510i	0.0653271	−	0.201056i	−0.913065	−	0.407814i	$-0.866291\pi$
$907$	1.96742	−	6.05510i	0.0653271	−	0.201056i	0.978392	+	0.206758i	$0.0662912\pi$
$908$	7.69718	−	1.63609i	0.255440	−	0.0542954i
$909$	0.669589	−	6.37072i	0.0222089	−	0.211303i
$910$	−21.1591	+	23.4995i	−0.701417	+	0.779002i
$911$	−1.39633	+	0.621686i	−0.0462625	+	0.0205974i	−0.429737	−	0.902954i	$-0.641394\pi$
$911$	−1.39633	+	0.621686i	−0.0462625	+	0.0205974i	0.383475	+	0.923551i	$0.374727\pi$
$912$	−15.0711	−	6.71009i	−0.499055	−	0.222193i
$913$	3.33856	+	3.70785i	0.110490	+	0.122712i
$914$	−7.82987	+	5.68873i	−0.258989	+	0.188167i
$915$	6.24430	−	4.53675i	0.206430	−	0.149980i
$916$	17.0127	+	18.8945i	0.562114	+	0.624291i
$917$	−21.5675	−	9.60245i	−0.712220	−	0.317101i
$918$	0.366544	−	0.163196i	0.0120978	−	0.00538627i
$919$	−12.0987	+	13.4370i	−0.399099	+	0.443244i	−0.908879	−	0.417061i	$-0.863060\pi$
$919$	−12.0987	+	13.4370i	−0.399099	+	0.443244i	0.509780	+	0.860305i	$0.329727\pi$
$920$	−3.25509	+	30.9702i	−0.107317	+	1.02106i
$921$	−2.12800	+	0.452319i	−0.0701198	+	0.0149044i
$922$	−2.00776	+	6.17924i	−0.0661219	+	0.203502i
$923$	−43.0643	−	9.15360i	−1.41748	−	0.301294i
$924$	1.16039	−	2.00985i	0.0381739	−	0.0661191i
$925$	−1.17255	−	2.03091i	−0.0385531	−	0.0667760i
$926$	17.7102	+	54.5063i	0.581992	+	1.79119i
$927$	−0.512153	−	4.87281i	−0.0168213	−	0.160044i
$928$	−27.2954	−	19.8313i	−0.896016	−	0.650994i
$929$	−23.0644			−0.756719			−0.378359	−	0.925659i	$-0.623512\pi$
$929$	−23.0644			−0.756719			−0.378359	+	0.925659i	$0.623512\pi$
$930$	−27.9934	−	10.8892i	−0.917940	−	0.357070i
$931$	−41.9129			−1.37364
$932$	−49.2178	−	35.7589i	−1.61218	−	1.17132i
$933$	−0.502545	−	4.78140i	−0.0164526	−	0.156536i
$934$	−14.9881	−	46.1287i	−0.490426	−	1.50938i
$935$	0.159002	+	0.275399i	0.00519991	+	0.00900651i
$936$	3.50809	−	6.07619i	0.114666	−	0.198607i
$937$	−14.4905	−	3.08006i	−0.473386	−	0.100621i	−0.0349600	−	0.999389i	$-0.511130\pi$
$937$	−14.4905	−	3.08006i	−0.473386	−	0.100621i	−0.438426	+	0.898768i	$0.644464\pi$
$938$	−8.44884	+	26.0029i	−0.275864	+	0.849023i
$939$	−16.2764	+	3.45965i	−0.531159	+	0.112901i
$940$	−3.26062	+	31.0227i	−0.106350	+	1.01185i
$941$	−23.7439	+	26.3703i	−0.774029	+	0.859646i	−0.993246	−	0.116030i	$-0.962983\pi$
$941$	−23.7439	+	26.3703i	−0.774029	+	0.859646i	0.219217	+	0.975676i	$0.429650\pi$
$942$	2.77782	−	1.23677i	0.0905063	−	0.0402960i
$943$	65.2212	+	29.0383i	2.12389	+	0.945619i
$944$	−8.28438	−	9.20074i	−0.269634	−	0.299458i
$945$	−2.52097	+	1.83159i	−0.0820072	+	0.0595817i
$946$	13.0215	−	9.46066i	0.423365	−	0.307593i
$947$	−9.72655	−	10.8024i	−0.316070	−	0.351032i	0.564086	−	0.825716i	$-0.309229\pi$
$947$	−9.72655	−	10.8024i	−0.316070	−	0.351032i	−0.880156	+	0.474685i	$0.842562\pi$
$948$	−0.518674	−	0.230928i	−0.0168457	−	0.00750021i
$949$	48.0783	−	21.4058i	1.56069	−	0.694863i
$950$	13.4524	−	14.9404i	0.436454	−	0.484731i
$951$	−0.236204	+	2.24733i	−0.00765945	+	0.0728748i
$952$	−0.339481	+	0.0721589i	−0.0110026	+	0.00233868i
$953$	−7.32055	+	22.5303i	−0.237136	+	0.729829i	0.759695	+	0.650279i	$0.225348\pi$
$953$	−7.32055	+	22.5303i	−0.237136	+	0.729829i	−0.996831	+	0.0795496i	$0.974652\pi$
$954$	17.8026	+	3.78406i	0.576380	+	0.122513i
$955$	−11.3149	+	19.5980i	−0.366143	+	0.634178i
$956$	−23.6053	−	40.8857i	−0.763451	−	1.32234i
$957$	0.941983	+	2.89913i	0.0304500	+	0.0937154i
$958$	0.461226	+	4.38827i	0.0149015	+	0.141779i
$959$	16.7685	+	12.1830i	0.541484	+	0.393411i
$960$	−30.4976			−0.984305
$961$	22.8515	+	20.9477i	0.737146	+	0.675733i
$962$	−19.7726			−0.637495
$963$	−2.57635	−	1.87183i	−0.0830217	−	0.0603188i
$964$	0.622662	+	5.92424i	0.0200546	+	0.190807i
$965$	−17.2360	−	53.0469i	−0.554846	−	1.70764i
$966$	−11.3121	−	19.5931i	−0.363960	−	0.630397i
$967$	16.7411	−	28.9965i	0.538358	−	0.932464i	−0.460634	−	0.887590i	$-0.652378\pi$
$967$	16.7411	−	28.9965i	0.538358	−	0.932464i	0.998993	−	0.0448738i	$-0.0142886\pi$
$968$	15.4170	+	3.27699i	0.495523	+	0.105327i
$969$	0.441463	−	1.35868i	0.0141818	−	0.0436472i
$970$	19.4235	−	4.12860i	0.623652	−	0.132561i
$971$	−0.388432	+	3.69568i	−0.0124654	+	0.118600i	−0.998985	−	0.0450425i	$-0.985658\pi$
$971$	−0.388432	+	3.69568i	−0.0124654	+	0.118600i	0.986520	+	0.163642i	$0.0523243\pi$
$972$	1.80089	−	2.00010i	0.0577637	−	0.0641531i
$973$	−10.1950	+	4.53911i	−0.326837	+	0.145517i
$974$	4.32375	+	1.92506i	0.138542	+	0.0616828i
$975$	−3.77318	−	4.19054i	−0.120838	−	0.134205i
$976$	−5.36305	+	3.89648i	−0.171667	+	0.124723i
$977$	−26.8413	+	19.5013i	−0.858729	+	0.623903i	−0.927539	−	0.373727i	$-0.878080\pi$
$977$	−26.8413	+	19.5013i	−0.858729	+	0.623903i	0.0688100	+	0.997630i	$0.478080\pi$
$978$	−11.8448	−	13.1549i	−0.378754	−	0.420649i
$979$	1.51152	+	0.672974i	0.0483085	+	0.0215083i
$980$	−33.2820	+	14.8181i	−1.06315	+	0.473347i
$981$	−0.988759	+	1.09813i	−0.0315687	+	0.0350605i
$982$	−6.07634	+	57.8125i	−0.193904	+	1.84487i
$983$	14.4544	−	3.07237i	0.461023	−	0.0979934i	0.0284554	−	0.999595i	$-0.490941\pi$
$983$	14.4544	−	3.07237i	0.461023	−	0.0979934i	0.432567	+	0.901602i	$0.357608\pi$
$984$	3.95718	−	12.1789i	0.126150	−	0.388250i
$985$	−3.28642	−	0.698549i	−0.104714	−	0.0222576i
$986$	0.887281	−	1.53682i	0.0282568	−	0.0489422i
$987$	−2.91089	−	5.04182i	−0.0926548	−	0.160483i
$988$	−30.0504	−	92.4857i	−0.956031	−	2.94236i
$989$	−9.40919	−	89.5225i	−0.299195	−	2.84665i
$990$	3.00812	+	2.18553i	0.0956043	+	0.0694606i
$991$	21.5787			0.685470			0.342735	−	0.939432i	$-0.388647\pi$
$991$	21.5787			0.685470			0.342735	+	0.939432i	$0.388647\pi$
$992$	39.5841	+	15.3979i	1.25680	+	0.488882i
$993$	19.6960			0.625033
$994$	20.6009	+	14.9674i	0.653421	+	0.474738i
$995$	−1.81009	−	17.2218i	−0.0573836	−	0.545968i
$996$	−6.02063	−	18.5296i	−0.190771	−	0.587133i
$997$	−2.07645	−	3.59651i	−0.0657618	−	0.113903i	0.831270	−	0.555869i	$-0.187614\pi$
$997$	−2.07645	−	3.59651i	−0.0657618	−	0.113903i	−0.897032	+	0.441966i	$0.854281\pi$
$998$	−4.11603	+	7.12918i	−0.130291	+	0.225670i
$999$	−1.90587	−	0.405105i	−0.0602990	−	0.0128170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.10.1	✓	24
3.2	odd	2		279.2.y.d.10.3		24
31.11	odd	30		2883.2.a.s.1.9		12
31.20	even	15		2883.2.a.t.1.9		12
31.28	even	15	inner	93.2.m.b.28.1	yes	24
93.11	even	30		8649.2.a.bl.1.4		12
93.20	odd	30		8649.2.a.bk.1.4		12
93.59	odd	30		279.2.y.d.28.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.10.1	✓	24	1.1	even	1	trivial
93.2.m.b.28.1	yes	24	31.28	even	15	inner
279.2.y.d.10.3		24	3.2	odd	2
279.2.y.d.28.3		24	93.59	odd	30
2883.2.a.s.1.9		12	31.11	odd	30
2883.2.a.t.1.9		12	31.20	even	15
8649.2.a.bk.1.4		12	93.20	odd	30
8649.2.a.bl.1.4		12	93.11	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75230 - 1.27312i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.831686 + 2.55967i) q^{4} +(-1.24535 - 2.15701i) q^{5} +(-1.08298 + 1.87578i) q^{6} +(-1.22375 - 0.260117i) q^{7} +(0.462763 - 1.42424i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-1.75230 - 1.27312i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.831686 + 2.55967i) q^{4} +(-1.24535 - 2.15701i) q^{5} +(-1.08298 + 1.87578i) q^{6} +(-1.22375 - 0.260117i) q^{7} +(0.462763 - 1.42424i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.563906 + 5.36520i) q^{10} +(-0.461187 + 0.512200i) q^{11} +(2.45871 - 1.09469i) q^{12} +(-4.28011 - 1.90563i) q^{13} +(1.81322 + 2.01379i) q^{14} +(-2.01502 + 1.46399i) q^{15} +(1.73064 - 1.25738i) q^{16} +(0.123953 + 0.137663i) q^{17} +(1.97871 + 0.880976i) q^{18} +(7.04525 - 3.13675i) q^{19} +(4.48548 - 4.98163i) q^{20} +(-0.130775 + 1.24424i) q^{21} +(1.46023 - 0.310381i) q^{22} +(2.57997 - 7.94032i) q^{23} +(-1.46481 - 0.311355i) q^{24} +(-0.601785 + 1.04232i) q^{25} +(5.07394 + 8.78833i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.351966 - 3.34874i) q^{28} +(3.57810 + 2.59964i) q^{29} +5.39476 q^{30} +(-5.18900 - 2.01847i) q^{31} -7.62847 q^{32} +(0.557601 + 0.405121i) q^{33} +(-0.0419402 - 0.399034i) q^{34} +(0.962926 + 2.96358i) q^{35} +(-1.34570 - 2.33082i) q^{36} +(-0.974224 + 1.68741i) q^{37} +(-16.3389 - 3.47293i) q^{38} +(-1.44779 + 4.45585i) q^{39} +(-3.64839 + 0.775490i) q^{40} +(-0.893843 + 8.50435i) q^{41} +(1.81322 - 2.01379i) q^{42} +(9.84954 - 4.38530i) q^{43} +(-1.69462 - 0.754495i) q^{44} +(1.66660 + 1.85095i) q^{45} +(-14.6299 + 10.6292i) q^{46} +(-3.76465 + 2.73518i) q^{47} +(-1.43140 - 1.58973i) q^{48} +(-4.96491 - 2.21052i) q^{49} +(2.38151 - 1.06032i) q^{50} +(0.123953 - 0.137663i) q^{51} +(1.31806 - 12.5405i) q^{52} +(8.21925 - 1.74706i) q^{53} +(0.669319 - 2.05995i) q^{54} +(1.67916 + 0.356916i) q^{55} +(-0.936776 + 1.62254i) q^{56} +(-3.85599 - 6.67878i) q^{57} +(-2.96025 - 9.11071i) q^{58} +(-0.604971 - 5.75592i) q^{59} +(-5.42320 - 3.94019i) q^{60} -3.09888 q^{61} +(6.52293 + 10.1432i) q^{62} +1.25109 q^{63} +(9.90609 + 7.19719i) q^{64} +(1.21978 + 11.6054i) q^{65} +(-0.461317 - 1.41979i) q^{66} +(5.04480 + 8.73786i) q^{67} +(-0.249283 + 0.431771i) q^{68} +(-8.16650 - 1.73584i) q^{69} +(2.08566 - 6.41900i) q^{70} +(9.19163 - 1.95374i) q^{71} +(-0.156535 + 1.48933i) q^{72} +(-7.51632 + 8.34771i) q^{73} +(3.85540 - 1.71654i) q^{74} +(1.09952 + 0.489536i) q^{75} +(13.8885 + 15.4247i) q^{76} +(0.697610 - 0.506844i) q^{77} +(8.20981 - 5.96478i) q^{78} +(-0.141156 - 0.156769i) q^{79} +(-4.86743 - 2.16712i) q^{80} +(0.913545 - 0.406737i) q^{81} +(12.3933 - 13.7642i) q^{82} +(0.756688 - 7.19941i) q^{83} +(-3.29360 + 0.700077i) q^{84} +(0.142577 - 0.438806i) q^{85} +(-22.8424 - 4.85530i) q^{86} +(2.21139 - 3.83024i) q^{87} +(0.516074 + 0.893867i) q^{88} +(-0.741825 - 2.28310i) q^{89} +(-0.563906 - 5.36520i) q^{90} +(4.74211 + 3.44535i) q^{91} +22.4703 q^{92} +(-1.46502 + 5.37157i) q^{93} +10.0790 q^{94} +(-15.5398 - 11.2903i) q^{95} +(0.797392 + 7.58668i) q^{96} +(-1.13746 - 3.50073i) q^{97} +(5.88575 + 10.1944i) q^{98} +(0.344616 - 0.596893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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