LMFDB - Embedded newform 129.2.m.b.40.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [129,2,Mod(10,129)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(129, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("129.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 129 = 3 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	129.m (of order $21$, degree $12$, 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:	$1.03007018607$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			40.1
Character	$\chi$	$=$	129.40
Dual form			129.2.m.b.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26929 - 1.09283i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.70841 + 3.39624i) q^{4} +(-1.86451 - 0.575125i) q^{5} +(-1.25936 + 2.18128i) q^{6} +(-1.60016 - 2.77155i) q^{7} +(-1.31371 - 5.75575i) q^{8} +(-0.988831 - 0.149042i) q^{9} +O(q^{10})$	\(q+(-2.26929 - 1.09283i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.70841 + 3.39624i) q^{4} +(-1.86451 - 0.575125i) q^{5} +(-1.25936 + 2.18128i) q^{6} +(-1.60016 - 2.77155i) q^{7} +(-1.31371 - 5.75575i) q^{8} +(-0.988831 - 0.149042i) q^{9} +(3.60259 + 3.34272i) q^{10} +(-2.48708 + 3.11871i) q^{11} +(3.58914 - 2.44704i) q^{12} +(-2.72351 + 2.52705i) q^{13} +(0.602376 + 8.03815i) q^{14} +(-0.712852 + 1.81632i) q^{15} +(-1.37563 + 6.02703i) q^{16} +(4.46660 - 1.37776i) q^{17} +(2.08106 + 1.41885i) q^{18} +(-7.13439 + 1.07534i) q^{19} +(-3.09659 - 7.88999i) q^{20} +(-2.88338 + 1.38856i) q^{21} +(9.05213 - 4.35928i) q^{22} +(-0.951682 - 2.42485i) q^{23} +(-5.83783 + 0.879911i) q^{24} +(-0.985569 - 0.671950i) q^{25} +(8.94208 - 2.75827i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(5.07897 - 12.9410i) q^{28} +(-0.319731 - 4.26651i) q^{29} +(3.60259 - 3.34272i) q^{30} +(7.19970 - 4.90867i) q^{31} +(2.34636 - 2.94225i) q^{32} +(2.92412 + 2.71319i) q^{33} +(-11.6417 - 1.75470i) q^{34} +(1.38952 + 6.08787i) q^{35} +(-2.17198 - 3.76197i) q^{36} +(2.24583 - 3.88990i) q^{37} +(17.3652 + 5.35644i) q^{38} +(2.31646 + 2.90474i) q^{39} +(-0.860846 + 11.4872i) q^{40} +(-1.16952 - 0.563212i) q^{41} +8.06069 q^{42} +(-5.29434 - 3.86911i) q^{43} -17.3279 q^{44} +(1.75797 + 0.846592i) q^{45} +(-0.490308 + 6.54271i) q^{46} +(-6.13115 - 7.68822i) q^{47} +(5.90738 + 1.82219i) q^{48} +(-1.62099 + 2.80765i) q^{49} +(1.50221 + 2.60191i) q^{50} +(-1.04012 - 4.55707i) q^{51} +(-15.9589 - 2.40541i) q^{52} +(3.07918 + 2.85706i) q^{53} +(1.57040 - 1.96922i) q^{54} +(6.43084 - 4.38447i) q^{55} +(-13.8502 + 12.8511i) q^{56} +(0.539176 + 7.19480i) q^{57} +(-3.93702 + 10.0314i) q^{58} +(-0.611439 + 2.67889i) q^{59} +(-8.09934 + 2.49832i) q^{60} +(9.71505 + 6.62361i) q^{61} +(-21.7026 + 3.27113i) q^{62} +(1.16920 + 2.97909i) q^{63} +(2.59967 - 1.25194i) q^{64} +(6.53138 - 3.14535i) q^{65} +(-3.67062 - 9.35259i) q^{66} +(6.66613 - 1.00476i) q^{67} +(16.7766 + 11.4381i) q^{68} +(-2.48919 + 0.767812i) q^{69} +(3.49980 - 15.3336i) q^{70} +(0.305881 - 0.779372i) q^{71} +(0.441189 + 5.88726i) q^{72} +(-8.12328 + 7.53730i) q^{73} +(-9.34745 + 6.37298i) q^{74} +(-0.743723 + 0.932599i) q^{75} +(-22.9750 - 21.3177i) q^{76} +(12.6234 + 1.90267i) q^{77} +(-2.08231 - 9.12320i) q^{78} +(-4.16288 - 7.21033i) q^{79} +(6.03117 - 10.4463i) q^{80} +(0.955573 + 0.294755i) q^{81} +(2.03849 + 2.55618i) q^{82} +(1.03147 - 13.7640i) q^{83} +(-12.5253 - 6.03185i) q^{84} -9.12040 q^{85} +(7.78609 + 14.5659i) q^{86} -4.27848 q^{87} +(21.2178 + 10.2179i) q^{88} +(-0.598638 + 7.98826i) q^{89} +(-3.06415 - 3.84232i) q^{90} +(11.3619 + 3.50468i) q^{91} +(5.65781 - 9.79962i) q^{92} +(-4.35691 - 7.54640i) q^{93} +(5.51142 + 24.1471i) q^{94} +(13.9206 + 2.09819i) q^{95} +(-2.75868 - 2.55968i) q^{96} +(-4.84029 + 6.06953i) q^{97} +(6.74679 - 4.59988i) q^{98} +(2.92412 - 2.71319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + q^{5} - q^{6} - 16 q^{7} - 14 q^{8} + 4 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + q^5 - q^6 - 16 * q^7 - 14 * q^8 + 4 * q^9	\( 48 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + q^{5} - q^{6} - 16 q^{7} - 14 q^{8} + 4 q^{9} - 2 q^{10} - 15 q^{11} - 6 q^{12} - 3 q^{13} + 60 q^{14} - 6 q^{15} - 38 q^{16} + 3 q^{17} - q^{18} + 9 q^{19} - 61 q^{20} - 3 q^{21} + 16 q^{22} - 2 q^{23} - 7 q^{24} - 25 q^{25} - 15 q^{26} - 8 q^{27} - 39 q^{28} - 52 q^{29} - 2 q^{30} + 6 q^{31} + 20 q^{32} + 11 q^{33} - 62 q^{34} + 50 q^{35} - 27 q^{36} + 5 q^{37} + 52 q^{38} - 15 q^{39} + 154 q^{40} - 23 q^{41} + 48 q^{42} - 31 q^{43} - 30 q^{44} + 12 q^{45} + 18 q^{46} - 6 q^{47} + 103 q^{48} - 48 q^{49} + 29 q^{50} - 6 q^{51} + 8 q^{52} + 61 q^{53} + 2 q^{54} - 41 q^{55} - 21 q^{56} - 12 q^{57} - 57 q^{58} - 28 q^{59} - 40 q^{60} + 71 q^{61} - 61 q^{62} - 2 q^{63} - 90 q^{64} - 37 q^{65} + 6 q^{66} - 48 q^{67} - 57 q^{68} - 2 q^{69} + 117 q^{70} - 6 q^{71} - 7 q^{73} + 102 q^{74} - 34 q^{75} + 39 q^{76} + 33 q^{77} - 12 q^{78} + 30 q^{79} + 80 q^{80} + 4 q^{81} - 38 q^{82} + 71 q^{83} - 41 q^{84} + 44 q^{85} + 55 q^{86} - 8 q^{87} + 112 q^{88} + 32 q^{89} - 10 q^{90} + 117 q^{91} - 11 q^{92} - 15 q^{93} - 2 q^{94} + 25 q^{95} + 60 q^{96} - 17 q^{97} - 23 q^{98} + 11 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + q^5 - q^6 - 16 * q^7 - 14 * q^8 + 4 * q^9 - 2 * q^10 - 15 * q^11 - 6 * q^12 - 3 * q^13 + 60 * q^14 - 6 * q^15 - 38 * q^16 + 3 * q^17 - q^18 + 9 * q^19 - 61 * q^20 - 3 * q^21 + 16 * q^22 - 2 * q^23 - 7 * q^24 - 25 * q^25 - 15 * q^26 - 8 * q^27 - 39 * q^28 - 52 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 + 11 * q^33 - 62 * q^34 + 50 * q^35 - 27 * q^36 + 5 * q^37 + 52 * q^38 - 15 * q^39 + 154 * q^40 - 23 * q^41 + 48 * q^42 - 31 * q^43 - 30 * q^44 + 12 * q^45 + 18 * q^46 - 6 * q^47 + 103 * q^48 - 48 * q^49 + 29 * q^50 - 6 * q^51 + 8 * q^52 + 61 * q^53 + 2 * q^54 - 41 * q^55 - 21 * q^56 - 12 * q^57 - 57 * q^58 - 28 * q^59 - 40 * q^60 + 71 * q^61 - 61 * q^62 - 2 * q^63 - 90 * q^64 - 37 * q^65 + 6 * q^66 - 48 * q^67 - 57 * q^68 - 2 * q^69 + 117 * q^70 - 6 * q^71 - 7 * q^73 + 102 * q^74 - 34 * q^75 + 39 * q^76 + 33 * q^77 - 12 * q^78 + 30 * q^79 + 80 * q^80 + 4 * q^81 - 38 * q^82 + 71 * q^83 - 41 * q^84 + 44 * q^85 + 55 * q^86 - 8 * q^87 + 112 * q^88 + 32 * q^89 - 10 * q^90 + 117 * q^91 - 11 * q^92 - 15 * q^93 - 2 * q^94 + 25 * q^95 + 60 * q^96 - 17 * q^97 - 23 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/129\mathbb{Z}\right)^\times$.

$n$	$44$	$46$
$\chi(n)$	$1$	$e\left(\frac{11}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.26929	−	1.09283i	−1.60463	−	0.772749i	−0.604907	−	0.796296i	$-0.706790\pi$
$2$	−2.26929	−	1.09283i	−1.60463	−	0.772749i	−0.999723	+	0.0235473i	$0.992504\pi$
$3$	0.0747301	−	0.997204i	0.0431454	−	0.575736i
$3$	0.0747301	−	0.997204i	0.0431454	−	0.575736i
$4$	2.70841	+	3.39624i	1.35421	+	1.69812i
$5$	−1.86451	−	0.575125i	−0.833834	−	0.257204i	−0.151696	−	0.988427i	$-0.548473\pi$
$5$	−1.86451	−	0.575125i	−0.833834	−	0.257204i	−0.682138	+	0.731224i	$0.738950\pi$
$6$	−1.25936	+	2.18128i	−0.514132	+	0.890502i
$7$	−1.60016	−	2.77155i	−0.604802	−	1.04755i	−0.992083	−	0.125586i	$-0.959919\pi$
$7$	−1.60016	−	2.77155i	−0.604802	−	1.04755i	0.387281	−	0.921962i	$-0.373414\pi$
$8$	−1.31371	−	5.75575i	−0.464467	−	2.03496i
$9$	−0.988831	−	0.149042i	−0.329610	−	0.0496808i
$10$	3.60259	+	3.34272i	1.13924	+	1.05706i
$11$	−2.48708	+	3.11871i	−0.749884	+	0.940325i	−0.999608	−	0.0279921i	$-0.991089\pi$
$11$	−2.48708	+	3.11871i	−0.749884	+	0.940325i	0.249724	+	0.968317i	$0.419660\pi$
$12$	3.58914	−	2.44704i	1.03610	−	0.706399i
$13$	−2.72351	+	2.52705i	−0.755366	+	0.700878i	−0.960631	−	0.277829i	$-0.910385\pi$
$13$	−2.72351	+	2.52705i	−0.755366	+	0.700878i	0.205264	+	0.978707i	$0.434195\pi$
$14$	0.602376	+	8.03815i	0.160992	+	2.14829i
$15$	−0.712852	+	1.81632i	−0.184057	+	0.468971i
$16$	−1.37563	+	6.02703i	−0.343908	+	1.50676i
$17$	4.46660	−	1.37776i	1.08331	−	0.334157i	0.298827	−	0.954307i	$-0.403405\pi$
$17$	4.46660	−	1.37776i	1.08331	−	0.334157i	0.784483	+	0.620151i	$0.212929\pi$
$18$	2.08106	+	1.41885i	0.490512	+	0.334425i
$19$	−7.13439	+	1.07534i	−1.63674	+	0.246699i	−0.902028	−	0.431678i	$-0.857922\pi$
$19$	−7.13439	+	1.07534i	−1.63674	+	0.246699i	−0.734714	+	0.678377i	$0.762684\pi$
$20$	−3.09659	−	7.88999i	−0.692420	−	1.76426i
$21$	−2.88338	+	1.38856i	−0.629205	+	0.303009i
$22$	9.05213	−	4.35928i	1.92992	−	0.929401i
$23$	−0.951682	−	2.42485i	−0.198439	−	0.505615i	0.796668	−	0.604418i	$-0.206594\pi$
$23$	−0.951682	−	2.42485i	−0.198439	−	0.505615i	−0.995107	+	0.0988022i	$0.968499\pi$
$24$	−5.83783	+	0.879911i	−1.19164	+	0.179611i
$25$	−0.985569	−	0.671950i	−0.197114	−	0.134390i
$26$	8.94208	−	2.75827i	1.75369	−	0.540940i
$27$	−0.222521	+	0.974928i	−0.0428242	+	0.187625i
$28$	5.07897	−	12.9410i	0.959836	−	2.44562i
$29$	−0.319731	−	4.26651i	−0.0593726	−	0.792272i	−0.944832	−	0.327555i	$-0.893775\pi$
$29$	−0.319731	−	4.26651i	−0.0593726	−	0.792272i	0.885459	−	0.464717i	$-0.153844\pi$
$30$	3.60259	−	3.34272i	0.657741	−	0.610294i
$31$	7.19970	−	4.90867i	1.29310	−	0.881624i	0.295818	−	0.955244i	$-0.404408\pi$
$31$	7.19970	−	4.90867i	1.29310	−	0.881624i	0.997286	+	0.0736204i	$0.0234553\pi$
$32$	2.34636	−	2.94225i	0.414783	−	0.520121i
$33$	2.92412	+	2.71319i	0.509025	+	0.472306i
$34$	−11.6417	−	1.75470i	−1.99653	−	0.300928i
$35$	1.38952	+	6.08787i	0.234871	+	1.02904i
$36$	−2.17198	−	3.76197i	−0.361996	−	0.626996i
$37$	2.24583	−	3.88990i	0.369213	−	0.639495i	−0.620230	−	0.784420i	$-0.712961\pi$
$37$	2.24583	−	3.88990i	0.369213	−	0.639495i	0.989443	+	0.144925i	$0.0462940\pi$
$38$	17.3652	+	5.35644i	2.81700	+	0.868930i
$39$	2.31646	+	2.90474i	0.370930	+	0.465131i
$40$	−0.860846	+	11.4872i	−0.136112	+	1.81628i
$41$	−1.16952	−	0.563212i	−0.182649	−	0.0879589i	0.340325	−	0.940308i	$-0.389463\pi$
$41$	−1.16952	−	0.563212i	−0.182649	−	0.0879589i	−0.522973	+	0.852349i	$0.675177\pi$
$42$	8.06069			1.24379
$43$	−5.29434	−	3.86911i	−0.807379	−	0.590034i
$43$	−5.29434	−	3.86911i	−0.807379	−	0.590034i
$44$	−17.3279			−2.61228
$45$	1.75797	+	0.846592i	0.262062	+	0.126202i
$46$	−0.490308	+	6.54271i	−0.0722920	+	0.964669i
$47$	−6.13115	−	7.68822i	−0.894320	−	1.12144i	−0.992002	−	0.126224i	$-0.959714\pi$
$47$	−6.13115	−	7.68822i	−0.894320	−	1.12144i	0.0976814	−	0.995218i	$-0.468857\pi$
$48$	5.90738	+	1.82219i	0.852657	+	0.263010i
$49$	−1.62099	+	2.80765i	−0.231571	+	0.401092i
$50$	1.50221	+	2.60191i	0.212445	+	0.367966i
$51$	−1.04012	−	4.55707i	−0.145646	−	0.638117i
$52$	−15.9589	−	2.40541i	−2.21310	−	0.333570i
$53$	3.07918	+	2.85706i	0.422958	+	0.392448i	0.862733	−	0.505661i	$-0.168751\pi$
$53$	3.07918	+	2.85706i	0.422958	+	0.392448i	−0.439775	+	0.898108i	$0.644942\pi$
$54$	1.57040	−	1.96922i	0.213704	−	0.267976i
$55$	6.43084	−	4.38447i	0.867134	−	0.591202i
$56$	−13.8502	+	12.8511i	−1.85081	+	1.71730i
$57$	0.539176	+	7.19480i	0.0714156	+	0.952975i
$58$	−3.93702	+	10.0314i	−0.516956	+	1.31718i
$59$	−0.611439	+	2.67889i	−0.0796026	+	0.348762i	−0.999007	−	0.0445517i	$-0.985814\pi$
$59$	−0.611439	+	2.67889i	−0.0796026	+	0.348762i	0.919405	+	0.393313i	$0.128671\pi$
$60$	−8.09934	+	2.49832i	−1.04562	+	0.322531i
$61$	9.71505	+	6.62361i	1.24388	+	0.848066i	0.992786	−	0.119896i	$-0.0382560\pi$
$61$	9.71505	+	6.62361i	1.24388	+	0.848066i	0.251098	+	0.967962i	$0.419208\pi$
$62$	−21.7026	+	3.27113i	−2.75623	+	0.415435i
$63$	1.16920	+	2.97909i	0.147306	+	0.375329i
$64$	2.59967	−	1.25194i	0.324959	−	0.156492i
$65$	6.53138	−	3.14535i	0.810118	−	0.390132i
$66$	−3.67062	−	9.35259i	−0.451822	−	1.15122i
$67$	6.66613	−	1.00476i	0.814398	−	0.122751i	0.271380	−	0.962472i	$-0.412520\pi$
$67$	6.66613	−	1.00476i	0.814398	−	0.122751i	0.543017	+	0.839721i	$0.317282\pi$
$68$	16.7766	+	11.4381i	2.03446	+	1.38707i
$69$	−2.48919	+	0.767812i	−0.299663	+	0.0924337i
$70$	3.49980	−	15.3336i	0.418307	−	1.83272i
$71$	0.305881	−	0.779372i	0.0363014	−	0.0924944i	−0.911574	−	0.411137i	$-0.865132\pi$
$71$	0.305881	−	0.779372i	0.0363014	−	0.0924944i	0.947875	+	0.318643i	$0.103227\pi$
$72$	0.441189	+	5.88726i	0.0519946	+	0.693820i
$73$	−8.12328	+	7.53730i	−0.950758	+	0.882174i	−0.993140	−	0.116927i	$-0.962696\pi$
$73$	−8.12328	+	7.53730i	−0.950758	+	0.882174i	0.0423828	+	0.999101i	$0.486505\pi$
$74$	−9.34745	+	6.37298i	−1.08662	+	0.740844i
$75$	−0.743723	+	0.932599i	−0.0858777	+	0.107687i
$76$	−22.9750	−	21.3177i	−2.63541	−	2.44530i
$77$	12.6234	+	1.90267i	1.43857	+	0.216829i
$78$	−2.08231	−	9.12320i	−0.235775	−	1.03300i
$79$	−4.16288	−	7.21033i	−0.468361	−	0.811225i	0.530985	−	0.847381i	$-0.321822\pi$
$79$	−4.16288	−	7.21033i	−0.468361	−	0.811225i	−0.999346	+	0.0361561i	$0.988489\pi$
$80$	6.03117	−	10.4463i	0.674306	−	1.16793i
$81$	0.955573	+	0.294755i	0.106175	+	0.0327506i
$82$	2.03849	+	2.55618i	0.225113	+	0.282283i
$83$	1.03147	−	13.7640i	0.113218	−	1.51079i	−0.594383	−	0.804182i	$-0.702604\pi$
$83$	1.03147	−	13.7640i	0.113218	−	1.51079i	0.707602	−	0.706612i	$-0.249777\pi$
$84$	−12.5253	−	6.03185i	−1.36662	−	0.658129i
$85$	−9.12040			−0.989246
$86$	7.78609	+	14.5659i	0.839596	+	1.57069i
$87$	−4.27848			−0.458701
$88$	21.2178	+	10.2179i	2.26182	+	1.08924i
$89$	−0.598638	+	7.98826i	−0.0634555	+	0.846754i	0.871138	+	0.491038i	$0.163382\pi$
$89$	−0.598638	+	7.98826i	−0.0634555	+	0.846754i	−0.934594	+	0.355717i	$0.884237\pi$
$90$	−3.06415	−	3.84232i	−0.322990	−	0.405016i
$91$	11.3619	+	3.50468i	1.19105	+	0.367390i
$92$	5.65781	−	9.79962i	0.589868	−	1.02168i
$93$	−4.35691	−	7.54640i	−0.451791	−	0.782525i
$94$	5.51142	+	24.1471i	0.568460	+	2.49058i
$95$	13.9206	+	2.09819i	1.42822	+	0.215270i
$96$	−2.75868	−	2.55968i	−0.281556	−	0.261246i
$97$	−4.84029	+	6.06953i	−0.491457	+	0.616267i	−0.964278	−	0.264891i	$-0.914664\pi$
$97$	−4.84029	+	6.06953i	−0.491457	+	0.616267i	0.472822	+	0.881158i	$0.343235\pi$
$98$	6.74679	−	4.59988i	0.681529	−	0.464658i
$99$	2.92412	−	2.71319i	0.293886	−	0.272686i
$100$	−0.387224	−	5.16715i	−0.0387224	−	0.516715i
$101$	−1.10005	+	2.80288i	−0.109459	+	0.278897i	−0.975099	−	0.221770i	$-0.928817\pi$
$101$	−1.10005	+	2.80288i	−0.109459	+	0.278897i	0.865640	+	0.500667i	$0.166912\pi$
$102$	−2.61978	+	11.4780i	−0.259396	+	1.13649i
$103$	0.269709	−	0.0831942i	0.0265752	−	0.00819737i	−0.281439	−	0.959579i	$-0.590812\pi$
$103$	0.269709	−	0.0831942i	0.0265752	−	0.00819737i	0.308014	+	0.951382i	$0.400336\pi$
$104$	18.1230	+	12.3560i	1.77710	+	1.21161i
$105$	6.17469	−	0.930684i	0.602588	−	0.0908255i
$106$	−3.86526	−	9.84853i	−0.375427	−	0.956574i
$107$	−14.9821	+	7.21499i	−1.44837	+	0.697499i	−0.982312	−	0.187254i	$-0.940041\pi$
$107$	−14.9821	+	7.21499i	−1.44837	+	0.697499i	−0.466060	+	0.884753i	$0.654327\pi$
$108$	−3.91377	+	1.88477i	−0.376602	+	0.181362i
$109$	−2.58039	−	6.57472i	−0.247156	−	0.629744i	0.752425	−	0.658678i	$-0.228884\pi$
$109$	−2.58039	−	6.57472i	−0.247156	−	0.629744i	−0.999581	+	0.0289337i	$0.990789\pi$
$110$	−19.3849	+	2.92181i	−1.84828	+	0.278583i
$111$	−3.71119	−	2.53025i	−0.352251	−	0.240160i
$112$	18.9055	−	5.83156i	1.78640	−	0.551031i
$113$	2.68348	−	11.7571i	0.252440	−	1.10601i	−0.676692	−	0.736266i	$-0.736587\pi$
$113$	2.68348	−	11.7571i	0.252440	−	1.10601i	0.929133	−	0.369747i	$-0.120556\pi$
$114$	6.63916	−	16.9163i	0.621815	−	1.58436i
$115$	0.379830	+	5.06848i	0.0354194	+	0.472639i
$116$	13.6241	−	12.6414i	1.26497	−	1.17372i
$117$	3.06973	−	2.09291i	0.283797	−	0.193489i
$118$	4.31511	−	5.41097i	0.397238	−	0.498120i
$119$	−10.9658	−	10.1748i	−1.00523	−	0.932720i
$120$	11.3907	+	1.71688i	1.03983	+	0.156729i
$121$	−1.09300	−	4.78876i	−0.0993639	−	0.435342i
$122$	−14.8078	−	25.6478i	−1.34063	−	2.32204i
$123$	−0.649035	+	1.12416i	−0.0585216	+	0.101362i
$124$	36.1708	+	11.1572i	3.24823	+	1.00195i
$125$	7.53390	+	9.44721i	0.673852	+	0.844984i
$126$	0.602376	−	8.03815i	0.0536639	−	0.716095i
$127$	−9.46555	−	4.55837i	−0.839932	−	0.404490i	−0.0361013	−	0.999348i	$-0.511494\pi$
$127$	−9.46555	−	4.55837i	−0.839932	−	0.404490i	−0.803831	+	0.594858i	$0.797208\pi$
$128$	−14.7941			−1.30763
$129$	−4.25394	+	4.99039i	−0.374538	+	0.439380i
$130$	−18.2589			−1.60141
$131$	−0.879150	−	0.423376i	−0.0768117	−	0.0369906i	0.395084	−	0.918645i	$-0.370716\pi$
$131$	−0.879150	−	0.423376i	−0.0768117	−	0.0369906i	−0.471895	+	0.881655i	$0.656430\pi$
$132$	−1.29492	+	17.2795i	−0.112708	+	1.50398i
$133$	14.3965	+	18.0526i	1.24833	+	1.56536i
$134$	−16.2254	−	5.00488i	−1.40166	−	0.432356i
$135$	0.975597	−	1.68978i	0.0839661	−	0.145433i
$136$	−13.7979	−	23.8986i	−1.18316	−	2.04929i
$137$	0.646220	+	2.83128i	0.0552103	+	0.241892i	0.995002	−	0.0998559i	$-0.0318382\pi$
$137$	0.646220	+	2.83128i	0.0552103	+	0.241892i	−0.939792	+	0.341748i	$0.888981\pi$
$138$	6.48777	+	0.977874i	0.552276	+	0.0832422i
$139$	10.3884	+	9.63905i	0.881135	+	0.817573i	0.984193	−	0.177102i	$-0.0566722\pi$
$139$	10.3884	+	9.63905i	0.881135	+	0.817573i	−0.103058	+	0.994675i	$0.532863\pi$
$140$	−16.9125	+	21.2076i	−1.42937	+	1.79237i
$141$	−8.12490	+	5.53947i	−0.684240	+	0.466507i
$142$	−1.54585	+	1.43434i	−0.129725	+	0.120367i
$143$	−1.10752	−	14.7788i	−0.0926154	−	1.23587i
$144$	2.25855	−	5.75469i	0.188212	−	0.479558i
$145$	−1.85764	+	8.13884i	−0.154268	+	0.675894i
$146$	26.6711	−	8.22693i	2.20731	−	0.680866i
$147$	2.67866	+	1.82628i	0.220932	+	0.150629i
$148$	19.2937	−	2.90805i	1.58593	−	0.239040i
$149$	−1.70429	−	4.34247i	−0.139621	−	0.355749i	0.843911	−	0.536484i	$-0.180248\pi$
$149$	−1.70429	−	4.34247i	−0.139621	−	0.355749i	−0.983532	+	0.180735i	$0.942152\pi$
$150$	2.70690	−	1.30357i	0.221017	−	0.106436i
$151$	−6.51168	+	3.13586i	−0.529913	+	0.255193i	−0.679654	−	0.733532i	$-0.737870\pi$
$151$	−6.51168	+	3.13586i	−0.529913	+	0.255193i	0.149741	+	0.988725i	$0.452156\pi$
$152$	15.5619	+	39.6511i	1.26224	+	3.21613i
$153$	−4.62206	+	0.696663i	−0.373671	+	0.0563218i
$154$	−26.5668	−	18.1129i	−2.14081	−	1.45958i
$155$	−16.2470	+	5.01154i	−1.30499	+	0.402536i
$156$	−3.59129	+	15.7345i	−0.287533	+	1.25977i
$157$	−2.01078	+	5.12337i	−0.160477	+	0.408890i	−0.988384	−	0.151976i	$-0.951436\pi$
$157$	−2.01078	+	5.12337i	−0.160477	+	0.408890i	0.827907	+	0.560866i	$0.189532\pi$
$158$	1.56711	+	20.9116i	0.124673	+	1.66364i
$159$	3.07918	−	2.85706i	0.244195	−	0.226580i
$160$	−6.06698	+	4.13639i	−0.479637	+	0.327011i
$161$	−5.19774	+	6.51777i	−0.409640	+	0.513672i
$162$	−1.84635	−	1.71317i	−0.145063	−	0.134599i
$163$	9.30501	+	1.40250i	0.728825	+	0.109853i	0.502965	−	0.864307i	$-0.332243\pi$
$163$	9.30501	+	1.40250i	0.728825	+	0.109853i	0.225860	+	0.974160i	$0.427481\pi$
$164$	−1.25474	−	5.49738i	−0.0979789	−	0.429274i
$165$	−3.89163	−	6.74051i	−0.302963	−	0.524748i
$166$	−17.3824	+	30.1072i	−1.34914	+	2.33677i
$167$	0.432924	+	0.133540i	0.0335007	+	0.0103336i	0.311460	−	0.950259i	$-0.399182\pi$
$167$	0.432924	+	0.133540i	0.0335007	+	0.0103336i	−0.277960	+	0.960593i	$0.589658\pi$
$168$	11.7801	+	14.7718i	0.908858	+	1.13967i
$169$	0.0600455	−	0.801251i	0.00461888	−	0.0616347i
$170$	20.6968	+	9.96706i	1.58737	+	0.764439i
$171$	7.21498			0.551743
$172$	−1.19881	−	28.4600i	−0.0914088	−	2.17005i
$173$	15.8129			1.20223			0.601116	−	0.799161i	$-0.294723\pi$
$173$	15.8129			1.20223			0.601116	+	0.799161i	$0.294723\pi$
$174$	9.70910	+	4.67566i	0.736045	+	0.354461i
$175$	−0.285279	+	3.80678i	−0.0215650	+	0.287765i
$176$	−15.3752	−	19.2799i	−1.15895	−	1.45328i
$177$	2.62570	+	0.809923i	0.197360	+	0.0608775i
$178$	10.0883	−	17.4735i	0.756151	−	1.30969i
$179$	−11.0781	−	19.1878i	−0.828016	−	1.43417i	−0.899593	−	0.436730i	$-0.856136\pi$
$179$	−11.0781	−	19.1878i	−0.828016	−	1.43417i	0.0715769	−	0.997435i	$-0.477197\pi$
$180$	1.88607	+	8.26339i	0.140579	+	0.615917i
$181$	−6.03241	−	0.909239i	−0.448385	−	0.0675832i	−0.0790316	−	0.996872i	$-0.525183\pi$
$181$	−6.03241	−	0.909239i	−0.448385	−	0.0675832i	−0.369354	+	0.929289i	$0.620421\pi$
$182$	−21.9534	−	20.3698i	−1.62729	−	1.50991i
$183$	7.33109	−	9.19290i	0.541930	−	0.679559i
$184$	−12.7066	+	8.66319i	−0.936740	+	0.638659i
$185$	−6.42455	+	5.96111i	−0.472343	+	0.438270i
$186$	1.64015	+	21.8863i	0.120262	+	1.60478i
$187$	−6.81197	+	17.3566i	−0.498141	+	1.26924i
$188$	9.50536	−	41.6457i	0.693250	−	3.03733i
$189$	3.05813	−	0.943308i	0.222446	−	0.0686156i
$190$	−29.2969	−	19.9743i	−2.12542	−	1.44909i
$191$	21.8415	−	3.29208i	1.58039	−	0.238206i	0.700598	−	0.713556i	$-0.252917\pi$
$191$	21.8415	−	3.29208i	1.58039	−	0.238206i	0.879797	+	0.475350i	$0.157679\pi$
$192$	−1.05416	−	2.68596i	−0.0760776	−	0.193843i
$193$	6.24354	−	3.00673i	0.449420	−	0.216429i	−0.195462	−	0.980711i	$-0.562621\pi$
$193$	6.24354	−	3.00673i	0.449420	−	0.216429i	0.644882	+	0.764282i	$0.276906\pi$
$194$	17.6170	−	8.48389i	1.26483	−	0.609108i
$195$	−2.64846	−	6.74817i	−0.189660	−	0.483246i
$196$	−13.9258	+	2.09897i	−0.994697	+	0.149926i
$197$	6.94342	+	4.73394i	0.494698	+	0.337279i	0.784834	−	0.619706i	$-0.212748\pi$
$197$	6.94342	+	4.73394i	0.494698	+	0.337279i	−0.290136	+	0.956985i	$0.593701\pi$
$198$	−9.60075	+	2.96144i	−0.682295	+	0.210460i
$199$	−0.777379	+	3.40592i	−0.0551069	+	0.241439i	−0.994979	−	0.100089i	$-0.968087\pi$
$199$	−0.777379	+	3.40592i	−0.0551069	+	0.241439i	0.939872	+	0.341528i	$0.110944\pi$
$200$	−2.57282	+	6.55544i	−0.181926	+	0.463539i
$201$	−0.503788	−	6.72258i	−0.0355344	−	0.474174i
$202$	5.55942	−	5.15838i	0.391159	−	0.362943i
$203$	−11.3132	+	7.71324i	−0.794034	+	0.541363i
$204$	12.6598	−	15.8749i	0.886365	−	1.11147i
$205$	1.85667	+	1.72273i	0.129675	+	0.120321i
$206$	−0.702965	−	0.105955i	−0.0489779	−	0.00738223i
$207$	0.579648	+	2.53960i	0.0402883	+	0.176515i
$208$	−11.4841	−	19.8910i	−0.796277	−	1.37919i
$209$	14.3902	−	24.9245i	0.995389	−	1.72406i
$210$	−15.0292	−	4.63590i	−1.03712	−	0.319908i
$211$	−10.3603	−	12.9915i	−0.713235	−	0.894368i	0.284699	−	0.958617i	$-0.408106\pi$
$211$	−10.3603	−	12.9915i	−0.713235	−	0.894368i	−0.997934	+	0.0642486i	$0.979535\pi$
$212$	−1.36358	+	18.1957i	−0.0936512	+	1.24969i
$213$	−0.754334	−	0.363268i	−0.0516861	−	0.0248907i
$214$	41.8834			2.86309
$215$	7.64612	+	10.2589i	0.521461	+	0.699651i
$216$	5.90377			0.401700
$217$	−25.1253	−	12.0997i	−1.70562	−	0.821381i
$218$	−1.32942	+	17.7399i	−0.0900397	+	1.20150i
$219$	6.90917	+	8.66383i	0.466878	+	0.585447i
$220$	32.3081	+	9.96572i	2.17821	+	0.671888i
$221$	−8.68316	+	15.0397i	−0.584092	+	1.01168i
$222$	5.65663	+	9.79757i	0.379648	+	0.657570i
$223$	0.972493	+	4.26077i	0.0651230	+	0.285322i	0.996995	−	0.0774645i	$-0.0246825\pi$
$223$	0.972493	+	4.26077i	0.0651230	+	0.285322i	−0.931872	+	0.362787i	$0.881825\pi$
$224$	−11.9091	−	1.79501i	−0.795713	−	0.119934i
$225$	0.874412	+	0.811336i	0.0582942	+	0.0540891i
$226$	−18.9381	+	23.7476i	−1.25974	+	1.57967i
$227$	−6.30585	+	4.29925i	−0.418534	+	0.285352i	−0.754219	−	0.656623i	$-0.771984\pi$
$227$	−6.30585	+	4.29925i	−0.418534	+	0.285352i	0.335685	+	0.941974i	$0.391032\pi$
$228$	−22.9750	+	21.3177i	−1.52155	+	1.41180i
$229$	−1.06622	−	14.2278i	−0.0704580	−	0.940197i	−0.914674	−	0.404193i	$-0.867552\pi$
$229$	−1.06622	−	14.2278i	−0.0704580	−	0.940197i	0.844216	−	0.536004i	$-0.180067\pi$
$230$	4.67706	−	11.9169i	0.308396	−	0.785780i
$231$	2.84069	−	12.4459i	0.186904	−	0.818879i
$232$	−24.1369	+	7.44526i	−1.58467	+	0.488805i
$233$	−6.59120	−	4.49381i	−0.431804	−	0.294399i	0.327846	−	0.944731i	$-0.393677\pi$
$233$	−6.59120	−	4.49381i	−0.431804	−	0.294399i	−0.759650	+	0.650332i	$0.774630\pi$
$234$	−9.25330	+	1.39471i	−0.604907	+	0.0911751i
$235$	7.00990	+	17.8609i	0.457275	+	1.16512i
$236$	−10.7542	+	5.17894i	−0.700037	+	0.337120i
$237$	−7.50126	+	3.61241i	−0.487259	+	0.234652i
$238$	13.7652	+	35.0733i	0.892268	+	2.27346i
$239$	2.56212	−	0.386178i	0.165730	−	0.0249798i	−0.0656530	−	0.997843i	$-0.520913\pi$
$239$	2.56212	−	0.386178i	0.165730	−	0.0249798i	0.231383	+	0.972863i	$0.425675\pi$
$240$	−9.96638	−	6.79496i	−0.643327	−	0.438613i
$241$	14.3851	−	4.43720i	0.926623	−	0.285825i	0.205520	−	0.978653i	$-0.434112\pi$
$241$	14.3851	−	4.43720i	0.926623	−	0.285825i	0.721103	+	0.692828i	$0.243635\pi$
$242$	−2.75297	+	12.0615i	−0.176968	+	0.775345i
$243$	0.365341	−	0.930874i	0.0234366	−	0.0597156i
$244$	3.81698	+	50.9341i	0.244357	+	3.26072i
$245$	4.63711	−	4.30260i	0.296254	−	0.274883i
$246$	2.70137	−	1.84176i	0.172233	−	0.117426i
$247$	16.7132	−	20.9577i	1.06343	−	1.33350i
$248$	−37.7114	−	34.9911i	−2.39468	−	2.22194i
$249$	−13.6484	−	2.05717i	−0.864933	−	0.130368i
$250$	−6.77238	−	29.6717i	−0.428323	−	1.87661i
$251$	11.0931	+	19.2139i	0.700192	+	1.21277i	0.968399	+	0.249407i	$0.0802357\pi$
$251$	11.0931	+	19.2139i	0.700192	+	1.21277i	−0.268207	+	0.963361i	$0.586431\pi$
$252$	−6.95100	+	12.0395i	−0.437872	+	0.758417i
$253$	9.92929	+	3.06278i	0.624249	+	0.192555i
$254$	16.4985	+	20.6885i	1.03521	+	1.29811i
$255$	−0.681568	+	9.09490i	−0.0426815	+	0.569544i
$256$	28.3728	+	13.6636i	1.77330	+	0.853976i
$257$	−14.7956			−0.922927			−0.461463	−	0.887159i	$-0.652675\pi$
$257$	−14.7956			−0.922927			−0.461463	+	0.887159i	$0.652675\pi$
$258$	15.1071	−	6.67581i	0.940525	−	0.415618i
$259$	−14.3747			−0.893202
$260$	28.3720	+	13.6632i	1.75956	+	0.847359i
$261$	−0.319731	+	4.26651i	−0.0197909	+	0.264091i
$262$	1.53237	+	1.92153i	0.0946699	+	0.118712i
$263$	−3.05638	−	0.942767i	−0.188464	−	0.0581335i	0.199086	−	0.979982i	$-0.436203\pi$
$263$	−3.05638	−	0.942767i	−0.188464	−	0.0581335i	−0.387551	+	0.921848i	$0.626679\pi$
$264$	11.7750	−	20.3949i	0.724700	−	1.25522i
$265$	−4.09799	−	7.09793i	−0.251738	−	0.436022i
$266$	−12.9413	−	56.6996i	−0.793482	−	3.47647i
$267$	7.92119	+	1.19393i	0.484769	+	0.0730672i
$268$	21.4670	+	19.9185i	1.31131	+	1.21672i
$269$	−6.69049	+	8.38961i	−0.407927	+	0.511524i	−0.942777	−	0.333423i	$-0.891796\pi$
$269$	−6.69049	+	8.38961i	−0.407927	+	0.511524i	0.534851	+	0.844946i	$0.320368\pi$
$270$	−4.06056	+	2.76844i	−0.247118	+	0.168482i
$271$	14.0364	−	13.0239i	0.852649	−	0.791143i	−0.126991	−	0.991904i	$-0.540532\pi$
$271$	14.0364	−	13.0239i	0.852649	−	0.791143i	0.979640	+	0.200761i	$0.0643415\pi$
$272$	2.15943	+	28.8156i	0.130935	+	1.74720i
$273$	4.34395	−	11.0682i	0.262908	−	0.669879i
$274$	1.62765	−	7.13120i	0.0983299	−	0.430811i
$275$	4.54681	−	1.40250i	0.274183	−	0.0845742i
$276$	−9.34941	−	6.37432i	−0.562768	−	0.383689i
$277$	11.0587	−	1.66683i	0.664454	−	0.100150i	0.191849	−	0.981425i	$-0.438552\pi$
$277$	11.0587	−	1.66683i	0.664454	−	0.100150i	0.472605	+	0.881274i	$0.343314\pi$
$278$	−13.0405	−	33.2266i	−0.782116	−	1.99280i
$279$	−7.85089	+	3.78079i	−0.470020	+	0.226350i
$280$	33.2148	−	15.9954i	1.98496	−	0.955909i
$281$	−1.53604	−	3.91378i	−0.0916327	−	0.233476i	0.877708	−	0.479195i	$-0.159071\pi$
$281$	−1.53604	−	3.91378i	−0.0916327	−	0.233476i	−0.969341	+	0.245719i	$0.920976\pi$
$282$	24.4915	−	3.69149i	1.45845	−	0.219825i
$283$	−23.0316	−	15.7027i	−1.36909	−	0.933429i	−0.999992	−	0.00403751i	$-0.998715\pi$
$283$	−23.0316	−	15.7027i	−1.36909	−	0.933429i	−0.369096	−	0.929391i	$-0.620333\pi$
$284$	3.47539	−	1.07201i	0.206226	−	0.0636124i
$285$	3.13261	−	13.7249i	0.185560	−	0.812991i
$286$	−13.6375	+	34.7477i	−0.806401	+	2.05468i
$287$	0.310446	+	4.14261i	0.0183250	+	0.244531i
$288$	−2.75868	+	2.55968i	−0.162557	+	0.150830i
$289$	4.00621	−	2.73139i	0.235660	−	0.160670i
$290$	13.1099	−	16.4393i	0.769840	−	0.965349i
$291$	5.69084	+	5.28033i	0.333603	+	0.309538i
$292$	−47.5997	−	7.17449i	−2.78556	−	0.419855i
$293$	−4.70568	−	20.6169i	−0.274909	−	1.20445i	−0.904140	−	0.427236i	$-0.859487\pi$
$293$	−4.70568	−	20.6169i	−0.274909	−	1.20445i	0.629231	−	0.777218i	$-0.283370\pi$
$294$	−4.08283	−	7.07167i	−0.238116	−	0.412428i
$295$	2.68073	−	4.64316i	0.156078	−	0.270335i
$296$	−25.3396	−	7.81625i	−1.47284	−	0.454310i
$297$	−2.48708	−	3.11871i	−0.144315	−	0.180966i
$298$	−0.878054	+	11.7168i	−0.0508643	+	0.678737i
$299$	8.71963	+	4.19915i	0.504269	+	0.242843i
$300$	−5.18164			−0.299162
$301$	−2.25167	+	20.8647i	−0.129784	+	1.20262i
$302$	18.2039			1.04751
$303$	2.71284	+	1.30643i	0.155849	+	0.0750527i
$304$	3.33320	−	44.4785i	0.191172	−	2.55102i
$305$	−14.3044	−	17.9371i	−0.819067	−	1.02708i
$306$	11.2501	+	3.47020i	0.643126	+	0.198378i
$307$	−6.75069	+	11.6925i	−0.385282	+	0.667329i	−0.991808	−	0.127735i	$-0.959229\pi$
$307$	−6.75069	+	11.6925i	−0.385282	+	0.667329i	0.606526	+	0.795064i	$0.292563\pi$
$308$	27.7274	+	48.0252i	1.57991	+	2.73649i
$309$	−0.0628062	−	0.275172i	−0.00357292	−	0.0156540i
$310$	42.3459	+	6.38262i	2.40509	+	0.362509i
$311$	7.96959	+	7.39470i	0.451914	+	0.419315i	0.873011	−	0.487701i	$-0.162164\pi$
$311$	7.96959	+	7.39470i	0.451914	+	0.419315i	−0.421097	+	0.907016i	$0.638355\pi$
$312$	13.6758	−	17.1489i	0.774240	−	0.970867i
$313$	−2.68235	+	1.82880i	−0.151615	+	0.103370i	−0.636752	−	0.771069i	$-0.719722\pi$
$313$	−2.68235	+	1.82880i	−0.151615	+	0.103370i	0.485136	+	0.874439i	$0.338770\pi$
$314$	10.1620	−	9.42898i	0.573476	−	0.532108i
$315$	−0.466647	−	6.22697i	−0.0262926	−	0.350850i
$316$	13.2132	−	33.6667i	0.743300	−	1.89390i
$317$	2.52572	−	11.0659i	0.141859	−	0.621524i	−0.853144	−	0.521676i	$-0.825307\pi$
$317$	2.52572	−	11.0659i	0.141859	−	0.621524i	0.995003	−	0.0998481i	$-0.0318357\pi$
$318$	−10.1098	+	3.11847i	−0.566932	+	0.174875i
$319$	14.1012	+	9.61403i	0.789516	+	0.538283i
$320$	−5.56713	+	0.839110i	−0.311212	+	0.0469077i
$321$	6.07520	+	15.4794i	0.339085	+	0.863973i
$322$	18.9180	−	9.11043i	1.05426	−	0.507705i
$323$	−30.3849	+	14.6326i	−1.69066	+	0.814180i
$324$	1.58702	+	4.04367i	0.0881680	+	0.224649i
$325$	4.38226	−	0.660519i	0.243084	−	0.0366390i
$326$	−19.5831	−	13.3515i	−1.08461	−	0.739471i
$327$	−6.74917	+	2.08184i	−0.373230	+	0.115126i
$328$	−1.70529	+	7.47137i	−0.0941589	+	0.412537i
$329$	−11.4975	+	29.2951i	−0.633877	+	1.61509i
$330$	1.46500	+	19.5491i	0.0806455	+	1.07614i
$331$	18.3456	−	17.0222i	1.00836	−	0.935626i	0.0104355	−	0.999946i	$-0.496678\pi$
$331$	18.3456	−	17.0222i	1.00836	−	0.935626i	0.997929	+	0.0643197i	$0.0204878\pi$
$332$	49.5394	−	33.7754i	2.71883	−	1.85367i
$333$	−2.80051	+	3.51173i	−0.153467	+	0.192441i
$334$	−0.836494	−	0.776153i	−0.0457709	−	0.0424692i
$335$	−13.0069	−	1.96048i	−0.710644	−	0.107112i
$336$	−4.40245	−	19.2884i	−0.240173	−	1.05227i
$337$	−0.490147	−	0.848959i	−0.0267000	−	0.0462457i	0.852367	−	0.522945i	$-0.175167\pi$
$337$	−0.490147	−	0.848959i	−0.0267000	−	0.0462457i	−0.879067	+	0.476699i	$0.841833\pi$
$338$	−1.01189	+	1.75265i	−0.0550398	+	0.0953317i
$339$	−11.5237	−	3.55458i	−0.625880	−	0.193058i
$340$	−24.7018	−	30.9751i	−1.33964	−	1.67986i
$341$	−2.59756	+	34.6620i	−0.140666	+	1.87705i
$342$	−16.3729	−	7.88476i	−0.885343	−	0.426359i
$343$	−12.0268			−0.649386
$344$	−15.3144	+	35.5558i	−0.825696	+	1.91704i
$345$	5.08270			0.273643
$346$	−35.8841	−	17.2808i	−1.92914	−	0.929024i
$347$	−0.469896	+	6.27033i	−0.0252254	+	0.336609i	0.970286	+	0.241962i	$0.0777911\pi$
$347$	−0.469896	+	6.27033i	−0.0252254	+	0.336609i	−0.995511	+	0.0946464i	$0.969828\pi$
$348$	−11.5879	−	14.5307i	−0.621175	−	0.778929i
$349$	−20.1334	−	6.21033i	−1.07772	−	0.332432i	−0.295439	−	0.955362i	$-0.595466\pi$
$349$	−20.1334	−	6.21033i	−1.07772	−	0.332432i	−0.782278	+	0.622930i	$0.785942\pi$
$350$	4.80755	−	8.32692i	0.256974	−	0.445093i
$351$	−1.85765	−	3.21755i	−0.0991542	−	0.171740i
$352$	3.34040	+	14.6352i	0.178044	+	0.780061i
$353$	7.31398	+	1.10241i	0.389284	+	0.0586751i	0.340768	−	0.940147i	$-0.389313\pi$
$353$	7.31398	+	1.10241i	0.389284	+	0.0586751i	0.0485157	+	0.998822i	$0.484551\pi$
$354$	−5.07337	−	4.70740i	−0.269647	−	0.250196i
$355$	−1.01855	+	1.27723i	−0.0540592	+	0.0677881i
$356$	−28.7514	+	19.6024i	−1.52382	+	1.03892i
$357$	−10.9658	+	10.1748i	−0.580371	+	0.538506i
$358$	4.17033	+	55.6492i	0.220409	+	2.94115i
$359$	−4.51917	+	11.5147i	−0.238513	+	0.607721i	−0.999140	−	0.0414683i	$-0.986796\pi$
$359$	−4.51917	+	11.5147i	−0.238513	+	0.607721i	0.760627	+	0.649189i	$0.224892\pi$
$360$	2.56331	−	11.2306i	0.135098	−	0.591904i
$361$	31.5873	−	9.74340i	1.66249	−	0.512810i
$362$	12.6956	+	8.65573i	0.667267	+	0.454935i
$363$	−4.85705	+	0.732082i	−0.254929	+	0.0384243i
$364$	18.8699	+	48.0798i	0.989053	+	2.52007i
$365$	19.4808	−	9.38146i	1.01967	−	0.491048i
$366$	−26.6827	+	12.8497i	−1.39473	+	0.671664i
$367$	−3.25035	−	8.28176i	−0.169667	−	0.432304i	0.820597	−	0.571507i	$-0.193641\pi$
$367$	−3.25035	−	8.28176i	−0.169667	−	0.432304i	−0.990264	+	0.139203i	$0.955546\pi$
$368$	15.9238	−	2.40013i	0.830085	−	0.125115i
$369$	1.07252	+	0.731229i	0.0558330	+	0.0380663i
$370$	21.0937	−	6.50653i	1.09661	−	0.338259i
$371$	2.99132	−	13.1058i	0.155302	−	0.680422i
$372$	13.8291	−	35.2359i	0.717003	−	1.82689i
$373$	−2.30653	−	30.7784i	−0.119427	−	1.59365i	−0.659286	−	0.751892i	$-0.729141\pi$
$373$	−2.30653	−	30.7784i	−0.119427	−	1.59365i	0.539859	−	0.841756i	$-0.318478\pi$
$374$	34.4262	−	31.9428i	1.78014	−	1.65173i
$375$	9.98380	−	6.80684i	0.515561	−	0.351504i
$376$	−36.1969	+	45.3895i	−1.86671	+	2.34078i
$377$	11.6525	+	10.8119i	0.600134	+	0.556843i
$378$	−7.97066	−	1.20138i	−0.409966	−	0.0617925i
$379$	0.322955	+	1.41496i	0.0165891	+	0.0726816i	0.982545	−	0.186026i	$-0.0595607\pi$
$379$	0.322955	+	1.41496i	0.0165891	+	0.0726816i	−0.965956	+	0.258707i	$0.916704\pi$
$380$	30.5767	+	52.9604i	1.56855	+	2.71681i
$381$	−5.25299	+	9.09844i	−0.269119	+	0.466127i
$382$	−53.1623	−	16.3984i	−2.72002	−	0.839016i
$383$	−5.12040	−	6.42078i	−0.261640	−	0.328086i	0.633608	−	0.773654i	$-0.281573\pi$
$383$	−5.12040	−	6.42078i	−0.261640	−	0.328086i	−0.895248	+	0.445568i	$0.853002\pi$
$384$	−1.10557	+	14.7528i	−0.0564182	+	0.752848i
$385$	−22.4421	−	10.8076i	−1.14376	−	0.550804i
$386$	−17.4542			−0.888397
$387$	4.65854	+	4.61497i	0.236807	+	0.234592i
$388$	−33.7231			−1.71203
$389$	−5.29144	−	2.54822i	−0.268287	−	0.129200i	0.294904	−	0.955527i	$-0.404712\pi$
$389$	−5.29144	−	2.54822i	−0.268287	−	0.129200i	−0.563191	+	0.826327i	$0.690427\pi$
$390$	−1.36449	+	18.2079i	−0.0690937	+	0.921991i
$391$	−7.59165	−	9.51962i	−0.383926	−	0.481428i
$392$	18.2896	+	5.64160i	0.923765	+	0.284944i
$393$	−0.487891	+	0.845053i	−0.0246109	+	0.0426273i
$394$	−10.5832	−	18.3307i	−0.533175	−	0.923486i
$395$	3.61490	+	15.8379i	0.181885	+	0.796891i
$396$	17.1344	+	2.58259i	0.861035	+	0.129780i
$397$	−12.8592	−	11.9316i	−0.645386	−	0.598831i	0.288032	−	0.957621i	$-0.406999\pi$
$397$	−12.8592	−	11.9316i	−0.645386	−	0.598831i	−0.933418	+	0.358790i	$0.883189\pi$
$398$	5.48619	−	6.87947i	0.274998	−	0.344837i
$399$	19.0780	−	13.0072i	0.955094	−	0.651172i
$400$	5.40564	−	5.01571i	0.270282	−	0.250785i
$401$	−1.39771	−	18.6511i	−0.0697982	−	0.931392i	−0.916683	−	0.399615i	$-0.869144\pi$
$401$	−1.39771	−	18.6511i	−0.0697982	−	0.931392i	0.846885	−	0.531776i	$-0.178475\pi$
$402$	−6.20341	+	15.8060i	−0.309398	+	0.788333i
$403$	−7.20401	+	31.5628i	−0.358857	+	1.57226i
$404$	−12.4987	+	3.85533i	−0.621832	+	0.191810i
$405$	−1.61215	−	1.09915i	−0.0801085	−	0.0546171i
$406$	34.1023	−	5.14009i	1.69247	−	0.255099i
$407$	6.54587	+	16.6786i	0.324467	+	0.826727i
$408$	−24.8629	+	11.9734i	−1.23090	+	0.592769i
$409$	6.01921	−	2.89870i	0.297631	−	0.143331i	−0.279109	−	0.960260i	$-0.590039\pi$
$409$	6.01921	−	2.89870i	0.297631	−	0.143331i	0.576740	+	0.816928i	$0.304325\pi$
$410$	−2.33065	−	5.93841i	−0.115103	−	0.293277i
$411$	2.87165	−	0.432832i	0.141648	−	0.0213500i
$412$	1.01303	+	0.690672i	0.0499084	+	0.0340270i
$413$	8.40307	−	2.59200i	0.413488	−	0.127544i
$414$	1.45997	−	6.39655i	0.0717537	−	0.314373i
$415$	−9.83919	+	25.0698i	−0.482987	+	1.23063i
$416$	1.04486	+	13.9426i	0.0512283	+	0.683594i
$417$	10.3884	−	9.63905i	0.508723	−	0.472026i
$418$	−59.8938	+	40.8349i	−2.92950	+	1.99730i
$419$	−16.8615	+	21.1436i	−0.823737	+	1.03293i	0.175091	+	0.984552i	$0.443978\pi$
$419$	−16.8615	+	21.1436i	−0.823737	+	1.03293i	−0.998829	+	0.0483820i	$0.984594\pi$
$420$	19.8844	+	18.4500i	0.970260	+	0.900270i
$421$	−28.0376	−	4.22599i	−1.36647	−	0.205962i	−0.575491	−	0.817808i	$-0.695189\pi$
$421$	−28.0376	−	4.22599i	−1.36647	−	0.205962i	−0.790977	+	0.611846i	$0.790427\pi$
$422$	9.31312	+	40.8035i	0.453356	+	1.98628i
$423$	4.91680	+	8.51615i	0.239063	+	0.414069i
$424$	12.3994	−	21.4763i	0.602167	−	1.04298i
$425$	−5.32793	−	1.64345i	−0.258443	−	0.0797190i
$426$	1.31481	+	1.64872i	0.0637028	+	0.0798808i
$427$	2.81208	−	37.5245i	0.136086	−	1.81594i
$428$	−65.0814	−	31.3416i	−3.14583	−	1.51495i
$429$	−14.8203			−0.715529
$430$	−6.14000	−	31.6363i	−0.296097	−	1.52564i
$431$	−14.7401			−0.710008			−0.355004	−	0.934865i	$-0.615520\pi$
$431$	−14.7401			−0.710008			−0.355004	+	0.934865i	$0.615520\pi$
$432$	−5.56982	−	2.68228i	−0.267978	−	0.129051i
$433$	−1.47338	+	19.6609i	−0.0708060	+	0.944840i	0.842797	+	0.538232i	$0.180908\pi$
$433$	−1.47338	+	19.6609i	−0.0708060	+	0.944840i	−0.913603	+	0.406608i	$0.866711\pi$
$434$	43.7936	+	54.9154i	2.10216	+	2.63602i
$435$	7.97726	+	2.46066i	0.382480	+	0.117980i
$436$	15.3406	−	26.5707i	0.734681	−	1.27250i
$437$	9.39720	+	16.2764i	0.449529	+	0.778607i
$438$	−6.21080	−	27.2113i	−0.296763	−	1.30021i
$439$	−21.3148	−	3.21269i	−1.01730	−	0.153333i	−0.380838	−	0.924642i	$-0.624364\pi$
$439$	−21.3148	−	3.21269i	−1.01730	−	0.153333i	−0.636461	+	0.771309i	$0.719603\pi$
$440$	−33.6842	−	31.2543i	−1.60583	−	1.48999i
$441$	2.02135	−	2.53469i	0.0962546	−	0.120699i
$442$	36.1404	−	24.6401i	1.71903	−	1.17201i
$443$	−25.9634	+	24.0905i	−1.23356	+	1.14457i	−0.249187	+	0.968455i	$0.580163\pi$
$443$	−25.9634	+	24.0905i	−1.23356	+	1.14457i	−0.984369	+	0.176118i	$0.943646\pi$
$444$	−1.45810	−	19.4570i	−0.0691985	−	0.923390i
$445$	5.71041	−	14.5499i	0.270700	−	0.689731i
$446$	2.44944	−	10.7317i	0.115984	−	0.508160i
$447$	−4.45769	+	1.37501i	−0.210841	+	0.0650359i
$448$	−7.62969	−	5.20183i	−0.360469	−	0.245763i
$449$	35.7920	−	5.39478i	1.68913	−	0.254595i	0.767048	−	0.641589i	$-0.221725\pi$
$449$	35.7920	−	5.39478i	1.68913	−	0.254595i	0.922082	+	0.386994i	$0.126487\pi$
$450$	−1.09764	−	2.79674i	−0.0517433	−	0.131840i
$451$	4.66519	−	2.24664i	0.219675	−	0.105790i
$452$	47.1978	−	22.7293i	2.22000	−	1.06909i
$453$	2.64047	+	6.72782i	0.124060	+	0.316101i
$454$	19.0082	−	2.86502i	0.892097	−	0.134462i
$455$	−19.1687	−	13.0690i	−0.898643	−	0.612685i
$456$	40.7031	−	12.5553i	1.90610	−	0.587954i
$457$	−1.73505	+	7.60175i	−0.0811622	+	0.355595i	−0.999159	−	0.0409918i	$-0.986948\pi$
$457$	−1.73505	+	7.60175i	−0.0811622	+	0.355595i	0.917997	+	0.396587i	$0.129805\pi$
$458$	−13.1290	+	33.4521i	−0.613477	+	1.56311i
$459$	0.349308	+	4.66119i	0.0163043	+	0.217566i
$460$	−16.1851	+	15.0175i	−0.754632	+	0.700196i
$461$	27.4798	−	18.7354i	1.27986	−	0.872596i	0.283598	−	0.958943i	$-0.408472\pi$
$461$	27.4798	−	18.7354i	1.27986	−	0.872596i	0.996265	+	0.0863476i	$0.0275196\pi$
$462$	−20.0476	+	25.1389i	−0.932699	+	1.16957i
$463$	19.4230	+	18.0219i	0.902665	+	0.837550i	0.987301	−	0.158861i	$-0.0507823\pi$
$463$	19.4230	+	18.0219i	0.902665	+	0.837550i	−0.0846362	+	0.996412i	$0.526973\pi$
$464$	26.1543	+	3.94212i	1.21418	+	0.183008i
$465$	3.78338	+	16.5761i	0.175450	+	0.768698i
$466$	10.0464	+	17.4008i	0.465389	+	0.806078i
$467$	1.30392	−	2.25846i	0.0603384	−	0.104509i	−0.834278	−	0.551344i	$-0.814115\pi$
$467$	1.30392	−	2.25846i	0.0603384	−	0.104509i	0.894617	+	0.446834i	$0.147449\pi$
$468$	15.4221	+	4.75709i	0.712887	+	0.219897i
$469$	−13.4516	−	16.8678i	−0.621137	−	0.778881i
$470$	3.61151	−	48.1923i	0.166587	−	2.22294i
$471$	4.95878	+	2.38802i	0.228489	+	0.110034i
$472$	16.2223			0.746690
$473$	25.2341	−	6.88867i	1.16026	−	0.316741i
$474$	20.9703			0.963197
$475$	7.75401	+	3.73413i	0.355778	+	0.171334i
$476$	4.85608	−	64.7999i	0.222578	−	2.97010i
$477$	−2.61897	−	3.28408i	−0.119914	−	0.150368i
$478$	−6.23623	−	1.92362i	−0.285238	−	0.0879844i
$479$	−10.6948	+	18.5239i	−0.488656	+	0.846378i	−0.999915	−	0.0130492i	$-0.995846\pi$
$479$	−10.6948	+	18.5239i	−0.488656	+	0.846378i	0.511258	+	0.859427i	$0.329180\pi$
$480$	3.67144	+	6.35913i	0.167578	+	0.290253i
$481$	3.71341	+	16.2695i	0.169317	+	0.741826i
$482$	−37.4930	−	5.65115i	−1.70776	−	0.257403i
$483$	6.11111	+	5.67028i	0.278065	+	0.258007i
$484$	13.3035	−	16.6820i	0.604703	−	0.758274i
$485$	12.5155	−	8.53292i	0.568299	−	0.387460i
$486$	−1.84635	+	1.71317i	−0.0837523	+	0.0777108i
$487$	0.499898	+	6.67067i	0.0226525	+	0.302277i	0.997010	+	0.0772718i	$0.0246209\pi$
$487$	0.499898	+	6.67067i	0.0226525	+	0.302277i	−0.974358	+	0.225005i	$0.927760\pi$
$488$	25.3610	−	64.6189i	1.14804	−	2.92516i
$489$	2.09395	−	9.17418i	0.0946916	−	0.414871i
$490$	−15.2250	+	4.69628i	−0.687793	+	0.212156i
$491$	5.82335	+	3.97030i	0.262804	+	0.179177i	0.687553	−	0.726135i	$-0.258685\pi$
$491$	5.82335	+	3.97030i	0.262804	+	0.179177i	−0.424748	+	0.905311i	$0.639637\pi$
$492$	−5.57578	+	0.840414i	−0.251376	+	0.0378888i
$493$	−7.30636	−	18.6163i	−0.329062	−	0.838436i
$494$	−60.8302	+	29.2943i	−2.73688	+	1.31801i
$495$	−7.01248	+	3.37703i	−0.315188	+	0.151786i
$496$	19.6806	+	50.1454i	0.883685	+	2.25159i
$497$	−2.64953	+	0.399352i	−0.118847	+	0.0179134i
$498$	28.7241	+	19.5837i	1.28716	+	0.877568i
$499$	36.9651	−	11.4022i	1.65478	−	0.510434i	0.679931	−	0.733277i	$-0.262010\pi$
$499$	36.9651	−	11.4022i	1.65478	−	0.510434i	0.974854	+	0.222843i	$0.0715337\pi$
$500$	−11.6801	+	51.1739i	−0.522350	+	2.28856i
$501$	0.165519	−	0.421734i	0.00739483	−	0.0188417i
$502$	−4.17599	−	55.7247i	−0.186384	−	2.48712i
$503$	−10.2948	+	9.55213i	−0.459020	+	0.425909i	−0.875486	−	0.483243i	$-0.839459\pi$
$503$	−10.2948	+	9.55213i	−0.459020	+	0.425909i	0.416466	+	0.909151i	$0.363268\pi$
$504$	15.6109	−	10.6433i	0.695363	−	0.474091i
$505$	3.66306	−	4.59334i	0.163004	−	0.204401i
$506$	−19.1853	−	17.8014i	−0.852892	−	0.791368i
$507$	−0.794524	−	0.119755i	−0.0352860	−	0.00531851i
$508$	−10.1553	−	44.4932i	−0.450568	−	1.97407i
$509$	−17.1779	−	29.7531i	−0.761399	−	1.31878i	−0.942130	−	0.335249i	$-0.891180\pi$
$509$	−17.1779	−	29.7531i	−0.761399	−	1.31878i	0.180731	−	0.983533i	$-0.442154\pi$
$510$	11.4859	−	19.8941i	0.508603	−	0.880926i
$511$	33.8885	+	10.4532i	1.49914	+	0.462423i
$512$	−31.0061	−	38.8804i	−1.37029	−	1.71829i
$513$	0.539176	−	7.19480i	0.0238052	−	0.317658i
$514$	33.5756	+	16.1691i	1.48096	+	0.713191i
$515$	−0.550722			−0.0242677
$516$	−28.4700	−	0.931354i	−1.25332	−	0.0410006i
$517$	39.2260			1.72516
$518$	32.6204	+	15.7092i	1.43326	+	0.690221i
$519$	1.18170	−	15.7687i	0.0518709	−	0.692169i
$520$	−26.6842	−	33.4609i	−1.17018	−	1.46736i
$521$	2.67243	+	0.824335i	0.117081	+	0.0361148i	0.352742	−	0.935721i	$-0.385249\pi$
$521$	2.67243	+	0.824335i	0.117081	+	0.0361148i	−0.235661	+	0.971835i	$0.575725\pi$
$522$	5.38815	−	9.33254i	0.235833	−	0.408474i
$523$	−5.16914	−	8.95321i	−0.226031	−	0.391496i	0.730598	−	0.682808i	$-0.239242\pi$
$523$	−5.16914	−	8.95321i	−0.226031	−	0.391496i	−0.956628	+	0.291312i	$0.905908\pi$
$524$	−0.943212	−	4.13248i	−0.0412044	−	0.180528i
$525$	3.77482	+	0.568962i	0.164746	+	0.0248315i
$526$	5.90552	+	5.47952i	0.257493	+	0.238918i
$527$	25.3952	−	31.8446i	1.10623	−	1.38717i
$528$	−20.3750	+	13.8914i	−0.886709	+	0.604548i
$529$	11.8860	−	11.0286i	0.516783	−	0.479505i
$530$	1.54268	+	20.5857i	0.0670099	+	0.894185i
$531$	1.00388	−	2.55784i	0.0435646	−	0.111001i
$532$	−22.3194	+	97.7879i	−0.967670	+	4.23964i
$533$	4.60847	−	1.42152i	0.199615	−	0.0615731i
$534$	−16.6707	−	11.3659i	−0.721412	−	0.491850i
$535$	32.0837	−	4.83584i	1.38710	−	0.209072i
$536$	−14.5405	−	37.0486i	−0.628054	−	1.60026i
$537$	−19.9620	+	9.61321i	−0.861425	+	0.414841i
$538$	24.3511	−	11.7269i	1.04985	−	0.505581i
$539$	−4.72467	−	12.0383i	−0.203506	−	0.518524i
$540$	8.38123	−	1.26327i	0.360671	−	0.0543624i
$541$	12.5459	+	8.55363i	0.539389	+	0.367749i	0.802160	−	0.597109i	$-0.203684\pi$
$541$	12.5459	+	8.55363i	0.539389	+	0.367749i	−0.262771	+	0.964858i	$0.584636\pi$
$542$	−46.0855	+	14.2155i	−1.97954	+	0.610607i
$543$	−1.35750	+	5.94759i	−0.0582558	+	0.255236i
$544$	6.42655	−	16.3746i	0.275536	−	0.702054i
$545$	1.02987	+	13.7427i	0.0441148	+	0.588672i
$546$	−21.9534	+	20.3698i	−0.939518	+	0.871745i
$547$	14.7679	−	10.0686i	0.631429	−	0.430501i	−0.204859	−	0.978791i	$-0.565674\pi$
$547$	14.7679	−	10.0686i	0.631429	−	0.430501i	0.836288	+	0.548291i	$0.184721\pi$
$548$	−7.86546	+	9.86298i	−0.335996	+	0.421326i
$549$	−8.61934	−	7.99758i	−0.367865	−	0.341328i
$550$	−11.8507	−	1.78621i	−0.505316	−	0.0761642i
$551$	6.86903	+	30.0952i	0.292630	+	1.28210i
$552$	7.68940	+	13.3184i	0.327283	+	0.566870i
$553$	−13.3225	+	23.0753i	−0.566531	+	0.981261i
$554$	−26.9170	−	8.30279i	−1.14359	−	0.352752i
$555$	5.46434	+	6.85206i	0.231948	+	0.290854i
$556$	−4.60040	+	61.3881i	−0.195100	+	2.60344i
$557$	−3.80749	−	1.83359i	−0.161328	−	0.0776916i	0.351477	−	0.936196i	$-0.385680\pi$
$557$	−3.80749	−	1.83359i	−0.161328	−	0.0776916i	−0.512805	+	0.858505i	$0.671394\pi$
$558$	21.9477			0.929120
$559$	24.1966	−	2.84149i	1.02341	−	0.120182i
$560$	−38.6033			−1.63129
$561$	16.7990	+	8.08998i	0.709255	+	0.341559i
$562$	−0.791372	+	10.5601i	−0.0333820	+	0.445452i
$563$	21.1353	+	26.5028i	0.890747	+	1.11696i	0.992511	+	0.122152i	$0.0389797\pi$
$563$	21.1353	+	26.5028i	0.890747	+	1.11696i	−0.101765	+	0.994808i	$0.532449\pi$
$564$	−40.8189	−	12.5910i	−1.71879	−	0.530176i
$565$	−11.7652	+	20.3778i	−0.494964	+	0.857302i
$566$	35.1050	+	60.8037i	1.47557	+	2.55577i
$567$	−0.712136	−	3.12007i	−0.0299069	−	0.131031i
$568$	−4.88771	−	0.736703i	−0.205084	−	0.0309114i
$569$	−22.4287	−	20.8108i	−0.940260	−	0.872433i	0.0517417	−	0.998661i	$-0.483523\pi$
$569$	−22.4287	−	20.8108i	−0.940260	−	0.872433i	−0.992001	+	0.126227i	$0.959713\pi$
$570$	−22.1078	+	27.7223i	−0.925993	+	1.16116i
$571$	−16.0514	+	10.9436i	−0.671728	+	0.457977i	−0.850543	−	0.525906i	$-0.823726\pi$
$571$	−16.0514	+	10.9436i	−0.671728	+	0.457977i	0.178814	+	0.983883i	$0.442774\pi$
$572$	47.1928	−	43.7885i	1.97323	−	1.83089i
$573$	−1.65065	−	22.0264i	−0.0689570	−	0.920167i
$574$	3.82269	−	9.74005i	0.159556	−	0.406542i
$575$	−0.691426	+	3.02934i	−0.0288345	+	0.126332i
$576$	−2.75723	+	0.850492i	−0.114885	+	0.0354372i
$577$	11.0652	+	7.54413i	0.460651	+	0.314066i	0.771315	−	0.636453i	$-0.219599\pi$
$577$	11.0652	+	7.54413i	0.460651	+	0.314066i	−0.310665	+	0.950520i	$0.600552\pi$
$578$	−12.0762	+	1.82020i	−0.502304	+	0.0757101i
$579$	−2.53174	−	6.45077i	−0.105216	−	0.268085i
$580$	−32.6727	+	15.7343i	−1.35666	+	0.653333i
$581$	−39.7981	+	19.1657i	−1.65110	+	0.795129i
$582$	−7.14365	−	18.2017i	−0.296114	−	0.754486i
$583$	−16.5685	+	2.49730i	−0.686198	+	0.103428i
$584$	54.0544	+	36.8537i	2.23679	+	1.52502i
$585$	−6.92722	+	2.13676i	−0.286405	+	0.0883443i
$586$	−11.8523	+	51.9283i	−0.489614	+	2.14514i
$587$	17.2706	−	44.0049i	0.712835	−	1.81627i	0.151937	−	0.988390i	$-0.451449\pi$
$587$	17.2706	−	44.0049i	0.712835	−	1.81627i	0.560899	−	0.827884i	$-0.310456\pi$
$588$	1.05243	+	14.0437i	0.0434014	+	0.579151i
$589$	−46.0870	+	42.7625i	−1.89898	+	1.76200i
$590$	−11.1575	+	7.60708i	−0.459349	+	0.313179i
$591$	5.23959	−	6.57024i	0.215528	−	0.270263i
$592$	20.3551	+	18.8868i	0.836590	+	0.776242i
$593$	24.1971	+	3.64713i	0.993657	+	0.149770i	0.625692	−	0.780070i	$-0.284817\pi$
$593$	24.1971	+	3.64713i	0.993657	+	0.149770i	0.367965	+	0.929840i	$0.380055\pi$
$594$	2.23569	+	9.79521i	0.0917316	+	0.401902i
$595$	14.5941	+	25.2776i	0.598298	+	1.03628i
$596$	10.1321	−	17.5494i	0.415028	−	0.718850i
$597$	3.33830	+	1.02973i	0.136628	+	0.0421440i
$598$	−15.1984	−	19.0582i	−0.621508	−	0.779347i
$599$	2.74541	−	36.6350i	0.112175	−	1.49687i	−0.602900	−	0.797817i	$-0.705988\pi$
$599$	2.74541	−	36.6350i	0.112175	−	1.49687i	0.715074	−	0.699048i	$-0.246393\pi$
$600$	6.34484	+	3.05551i	0.259027	+	0.124741i
$601$	−0.143221			−0.00584210			−0.00292105	−	0.999996i	$-0.500930\pi$
$601$	−0.143221			−0.00584210			−0.00292105	+	0.999996i	$0.500930\pi$
$602$	27.9113	−	44.8873i	1.13758	−	1.82947i
$603$	−6.74143			−0.274532
$604$	−28.2865	−	13.6220i	−1.15096	−	0.554273i
$605$	−0.716220	+	9.55729i	−0.0291185	+	0.388559i
$606$	−4.72850	−	5.92936i	−0.192082	−	0.240864i
$607$	3.65968	+	1.12886i	0.148542	+	0.0458191i	0.368134	−	0.929773i	$-0.379997\pi$
$607$	3.65968	+	1.12886i	0.148542	+	0.0458191i	−0.219593	+	0.975592i	$0.570473\pi$
$608$	−13.5760	+	23.5143i	−0.550579	+	0.953630i
$609$	6.84623	+	11.8580i	0.277423	+	0.480511i
$610$	12.8585	+	56.3368i	0.520626	+	2.28101i
$611$	36.1268	+	5.44524i	1.46153	+	0.220291i
$612$	−14.8845	−	13.8108i	−0.601669	−	0.558267i
$613$	4.39635	−	5.51285i	0.177567	−	0.222662i	−0.685081	−	0.728467i	$-0.740233\pi$
$613$	4.39635	−	5.51285i	0.177567	−	0.222662i	0.862648	+	0.505805i	$0.168805\pi$
$614$	28.0973	−	19.1564i	1.13391	−	0.773089i
$615$	1.85667	−	1.72273i	0.0748680	−	0.0694673i
$616$	−5.63220	−	75.1565i	−0.226928	−	3.02814i
$617$	−11.6256	+	29.6215i	−0.468029	+	1.19252i	0.480830	+	0.876814i	$0.340336\pi$
$617$	−11.6256	+	29.6215i	−0.468029	+	1.19252i	−0.948858	+	0.315703i	$0.897760\pi$
$618$	−0.158191	+	0.693081i	−0.00636339	+	0.0278798i
$619$	−16.6157	+	5.12527i	−0.667842	+	0.206002i	−0.610094	−	0.792329i	$-0.708868\pi$
$619$	−16.6157	+	5.12527i	−0.667842	+	0.206002i	−0.0577481	+	0.998331i	$0.518392\pi$
$620$	−61.0240	−	41.6054i	−2.45078	−	1.67091i
$621$	2.57582	−	0.388242i	0.103364	−	0.0155796i
$622$	−10.0041	−	25.4901i	−0.401129	−	1.02206i
$623$	23.0978	−	11.1233i	0.925393	−	0.445646i
$624$	−20.6936	+	9.96550i	−0.828406	+	0.398939i
$625$	−6.43473	−	16.3954i	−0.257389	−	0.655817i
$626$	8.08559	−	1.21871i	0.323165	−	0.0487093i
$627$	−23.7794	−	16.2126i	−0.949660	−	0.647467i
$628$	−22.8462	+	7.04713i	−0.911663	+	0.281211i
$629$	4.67188	−	20.4688i	0.186280	−	0.816146i
$630$	−5.74607	+	14.6408i	−0.228929	+	0.583302i
$631$	−2.01340	−	26.8669i	−0.0801521	−	1.06956i	−0.881758	−	0.471703i	$-0.843640\pi$
$631$	−2.01340	−	26.8669i	−0.0801521	−	1.06956i	0.801606	−	0.597853i	$-0.203979\pi$
$632$	−36.0320	+	33.4328i	−1.43328	+	1.32988i
$633$	−13.7294	+	9.36051i	−0.545693	+	0.372047i
$634$	−17.8248	+	22.3516i	−0.707912	+	0.887694i
$635$	15.0270	+	13.9430i	0.596327	+	0.553311i
$636$	18.0430	+	2.71954i	0.715450	+	0.107837i
$637$	−2.68026	−	11.7430i	−0.106196	−	0.465274i
$638$	−21.4932	−	37.2273i	−0.850923	−	1.47384i
$639$	−0.418624	+	0.725078i	−0.0165605	+	0.0286836i
$640$	27.5838	+	8.50846i	1.09034	+	0.336327i
$641$	−18.7738	−	23.5416i	−0.741521	−	0.929838i	0.257818	−	0.966194i	$-0.416997\pi$
$641$	−18.7738	−	23.5416i	−0.741521	−	0.929838i	−0.999339	+	0.0363555i	$0.988425\pi$
$642$	3.12995	−	41.7663i	0.123529	−	1.64838i
$643$	−24.4157	−	11.7580i	−0.962861	−	0.463690i	−0.114684	−	0.993402i	$-0.536586\pi$
$643$	−24.4157	−	11.7580i	−0.962861	−	0.463690i	−0.848177	+	0.529712i	$0.822300\pi$
$644$	−36.2135			−1.42701
$645$	10.8016	−	6.85809i	0.425313	−	0.270037i
$646$	84.9431			3.34204
$647$	11.3230	+	5.45287i	0.445153	+	0.214374i	0.643012	−	0.765856i	$-0.277685\pi$
$647$	11.3230	+	5.45287i	0.445153	+	0.214374i	−0.197859	+	0.980230i	$0.563399\pi$
$648$	0.441189	−	5.88726i	0.0173315	−	0.231273i
$649$	−6.83396	−	8.56952i	−0.268257	−	0.336383i
$650$	−10.6665	−	3.29016i	−0.418373	−	0.129051i
$651$	−13.9435	+	24.1508i	−0.546488	+	0.946545i
$652$	20.4386	+	35.4006i	0.800436	+	1.38640i
$653$	−5.10415	−	22.3627i	−0.199741	−	0.875121i	−0.971091	−	0.238710i	$-0.923275\pi$
$653$	−5.10415	−	22.3627i	−0.199741	−	0.875121i	0.771350	−	0.636411i	$-0.219582\pi$
$654$	17.5909	+	2.65141i	0.687860	+	0.103678i
$655$	1.39569	+	1.29501i	0.0545341	+	0.0506002i
$656$	5.00333	−	6.27397i	0.195347	−	0.244958i
$657$	9.15592	−	6.24240i	0.357207	−	0.243539i
$658$	58.1058	−	53.9143i	2.26520	−	2.10180i
$659$	3.11922	+	41.6231i	0.121508	+	1.62141i	0.641423	+	0.767188i	$0.278344\pi$
$659$	3.11922	+	41.6231i	0.121508	+	1.62141i	−0.519915	+	0.854218i	$0.674036\pi$
$660$	12.3522	−	31.4730i	0.480810	−	1.22508i
$661$	2.94707	−	12.9120i	0.114628	−	0.502218i	−0.884720	−	0.466122i	$-0.845651\pi$
$661$	2.94707	−	12.9120i	0.114628	−	0.502218i	0.999348	−	0.0360956i	$-0.0114921\pi$
$662$	−60.2339	+	18.5797i	−2.34106	+	0.722120i
$663$	14.3487	+	9.78280i	0.557258	+	0.379932i
$664$	−80.5771	+	12.1450i	−3.12700	+	0.471319i
$665$	−16.4599	−	41.9390i	−0.638286	−	1.62633i
$666$	10.1929	−	4.90864i	0.394967	−	0.190206i
$667$	−10.0414	+	4.83566i	−0.388803	+	0.187238i
$668$	0.719005	+	1.83200i	0.0278191	+	0.0708820i
$669$	4.32153	−	0.651366i	0.167080	−	0.0251833i
$670$	27.3740	+	18.6633i	1.05755	+	0.721025i
$671$	−44.8192	+	13.8249i	−1.73023	+	0.533704i
$672$	−2.67997	+	11.7417i	−0.103382	+	0.452946i
$673$	−3.55704	+	9.06318i	−0.137114	+	0.349360i	−0.982894	−	0.184171i	$-0.941040\pi$
$673$	−3.55704	+	9.06318i	−0.137114	+	0.349360i	0.845781	+	0.533531i	$0.179135\pi$
$674$	0.184515	+	2.46218i	0.00710725	+	0.0948397i
$675$	0.874412	−	0.811336i	0.0336561	−	0.0312283i
$676$	2.88387	−	1.96619i	0.110918	−	0.0756227i
$677$	−13.7876	+	17.2891i	−0.529899	+	0.664473i	−0.972678	−	0.232158i	$-0.925421\pi$
$677$	−13.7876	+	17.2891i	−0.529899	+	0.664473i	0.442779	+	0.896631i	$0.353993\pi$
$678$	22.2660	+	20.6598i	0.855119	+	0.793435i
$679$	24.5672	+	3.70291i	0.942803	+	0.142105i
$680$	11.9816	+	52.4947i	0.459472	+	2.01308i
$681$	3.81600	+	6.60950i	0.146229	+	0.253277i
$682$	43.7744	−	75.8195i	1.67621	−	2.90328i
$683$	9.40213	+	2.90017i	0.359763	+	0.110972i	0.469367	−	0.883003i	$-0.344482\pi$
$683$	9.40213	+	2.90017i	0.359763	+	0.110972i	−0.109604	+	0.993975i	$0.534958\pi$
$684$	19.5411	+	24.5038i	0.747174	+	0.936926i
$685$	0.423454	−	5.65060i	0.0161793	−	0.215898i
$686$	27.2923	+	13.1433i	1.04202	+	0.501813i
$687$	−14.2677			−0.544345
$688$	30.6023	−	26.5867i	1.16670	−	1.01361i
$689$	−15.6061			−0.594546
$690$	−11.5341	−	5.55453i	−0.439096	−	0.211457i
$691$	0.411524	−	5.49140i	0.0156551	−	0.208903i	−0.983891	−	0.178770i	$-0.942788\pi$
$691$	0.411524	−	5.49140i	0.0156551	−	0.208903i	0.999546	−	0.0301323i	$-0.00959288\pi$
$692$	42.8278	+	53.7044i	1.62807	+	2.04154i
$693$	−12.1988	−	3.76283i	−0.463394	−	0.142938i
$694$	7.91875	−	13.7157i	0.300592	−	0.520640i
$695$	−13.8257	−	23.9467i	−0.524437	−	0.908351i
$696$	5.62069	+	24.6258i	0.213052	+	0.933440i
$697$	−5.99976	−	0.904318i	−0.227257	−	0.0342535i
$698$	38.9017	+	36.0955i	1.47245	+	1.36623i
$699$	−4.97380	+	6.23695i	−0.188126	+	0.235903i
$700$	−13.7014	+	9.34145i	−0.517864	+	0.353074i
$701$	16.6392	−	15.4390i	0.628455	−	0.583121i	−0.300286	−	0.953849i	$-0.597082\pi$
$701$	16.6392	−	15.4390i	0.628455	−	0.583121i	0.928742	+	0.370728i	$0.120892\pi$
$702$	0.699311	+	9.33165i	0.0263938	+	0.352201i
$703$	−11.8397	+	30.1671i	−0.446543	+	1.13777i
$704$	−2.56119	+	11.2213i	−0.0965283	+	0.422918i
$705$	18.3348	−	5.65555i	0.690530	−	0.213000i
$706$	−15.3928	−	10.4946i	−0.579315	−	0.394971i
$707$	9.52859	−	1.43620i	0.358359	−	0.0540140i
$708$	4.36080	+	11.1111i	0.163889	+	0.417582i
$709$	−12.4624	+	6.00158i	−0.468036	+	0.225394i	−0.653010	−	0.757349i	$-0.726494\pi$
$709$	−12.4624	+	6.00158i	−0.468036	+	0.225394i	0.184974	+	0.982743i	$0.440780\pi$
$710$	3.70719	−	1.78529i	0.139128	−	0.0670006i
$711$	3.04174	+	7.75024i	0.114074	+	0.290657i
$712$	46.7649	−	7.04867i	1.75259	−	0.264160i
$713$	−18.7546	−	12.7867i	−0.702366	−	0.478865i
$714$	36.0039	−	11.1057i	1.34741	−	0.415621i
$715$	−6.43468	+	28.1922i	−0.240644	+	1.05433i
$716$	35.1624	−	89.5924i	1.31408	−	3.34822i
$717$	−0.193630	−	2.58382i	−0.00723126	−	0.0964945i
$718$	22.8389	−	21.1914i	0.852341	−	0.790857i
$719$	9.47147	−	6.45754i	0.353226	−	0.240826i	−0.373687	−	0.927555i	$-0.621907\pi$
$719$	9.47147	−	6.45754i	0.353226	−	0.240826i	0.726913	+	0.686729i	$0.240954\pi$
$720$	−7.52075	+	9.43072i	−0.280282	+	0.351462i
$721$	−0.662153	−	0.614388i	−0.0246599	−	0.0228810i
$722$	−82.3287	−	12.4090i	−3.06396	−	0.461817i
$723$	−3.34980	−	14.6764i	−0.124580	−	0.545822i
$724$	−13.2502	−	22.9501i	−0.492441	−	0.852934i
$725$	−2.55177	+	4.41979i	−0.0947702	+	0.164147i
$726$	11.8221	+	3.64663i	0.438759	+	0.135339i
$727$	11.6368	+	14.5921i	0.431586	+	0.541192i	0.949304	−	0.314360i	$-0.101790\pi$
$727$	11.6368	+	14.5921i	0.431586	+	0.541192i	−0.517718	+	0.855551i	$0.673218\pi$
$728$	5.24580	−	70.0003i	0.194422	−	2.59438i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	−54.4600			−2.01565
$731$	−28.9784	−	9.98742i	−1.07180	−	0.369398i
$732$	51.0769			1.88786
$733$	−31.7079	−	15.2697i	−1.17116	−	0.563999i	−0.255834	−	0.966721i	$-0.582350\pi$
$733$	−31.7079	−	15.2697i	−1.17116	−	0.563999i	−0.915323	+	0.402721i	$0.868064\pi$
$734$	−1.67459	+	22.3458i	−0.0618101	+	0.824798i
$735$	−3.94404	−	4.94567i	−0.145478	−	0.182424i
$736$	−9.36749	−	2.88949i	−0.345290	−	0.106508i
$737$	−13.4457	+	23.2886i	−0.495278	+	0.857847i
$738$	−1.63474	−	2.83145i	−0.0601756	−	0.104227i
$739$	6.76225	+	29.6273i	0.248753	+	1.08986i	0.932792	+	0.360414i	$0.117365\pi$
$739$	6.76225	+	29.6273i	0.248753	+	1.08986i	−0.684039	+	0.729445i	$0.739778\pi$
$740$	−37.6457	−	5.67418i	−1.38388	−	0.208587i
$741$	−19.6501	−	18.2326i	−0.721864	−	0.669792i
$742$	−21.1107	+	26.4719i	−0.774997	+	0.971816i
$743$	29.1331	−	19.8626i	1.06879	−	0.728689i	0.104765	−	0.994497i	$-0.466591\pi$
$743$	29.1331	−	19.8626i	1.06879	−	0.728689i	0.964026	+	0.265808i	$0.0856386\pi$
$744$	−37.7114	+	34.9911i	−1.38257	+	1.28284i
$745$	0.680208	+	9.07675i	0.0249209	+	0.332546i
$746$	−28.4015	+	72.3658i	−1.03985	+	2.64950i
$747$	−3.07136	+	13.4565i	−0.112375	+	0.492348i
$748$	−77.3969	+	23.8738i	−2.82991	+	0.872911i
$749$	43.9703	+	29.9785i	1.60664	+	1.09539i
$750$	−30.0949	+	4.53607i	−1.09891	+	0.165634i
$751$	−13.9711	−	35.5979i	−0.509814	−	1.29899i	−0.921754	−	0.387774i	$-0.873244\pi$
$751$	−13.9711	−	35.5979i	−0.509814	−	1.29899i	0.411940	−	0.911211i	$-0.364851\pi$
$752$	54.7714	−	26.3765i	1.99731	−	0.961852i
$753$	19.9891	−	9.62626i	0.728444	−	0.350800i
$754$	−14.6272	−	37.2696i	−0.532693	−	1.35728i
$755$	13.9446	−	2.10181i	0.507496	−	0.0764927i
$756$	11.4864	+	7.83128i	0.417755	+	0.284821i
$757$	−42.1842	+	13.0121i	−1.53321	+	0.472933i	−0.942572	−	0.334002i	$-0.891601\pi$
$757$	−42.1842	+	13.0121i	−1.53321	+	0.472933i	−0.590640	+	0.806935i	$0.701125\pi$
$758$	0.813434	−	3.56389i	0.0295452	−	0.129446i
$759$	3.79623	−	9.67265i	0.137795	−	0.351095i
$760$	−6.21098	−	82.8798i	−0.225296	−	3.00637i
$761$	−5.94423	+	5.51544i	−0.215478	+	0.199935i	−0.780526	−	0.625124i	$-0.785048\pi$
$761$	−5.94423	+	5.51544i	−0.215478	+	0.199935i	0.565047	+	0.825059i	$0.308858\pi$
$762$	21.8636	−	14.9064i	0.792035	−	0.540000i
$763$	−14.0932	+	17.6723i	−0.510207	+	0.639779i
$764$	70.3364	+	65.2627i	2.54468	+	2.36112i
$765$	9.01853	+	1.35932i	0.326066	+	0.0491465i
$766$	4.60283	+	20.1663i	0.166307	+	0.728639i
$767$	−5.10442	−	8.84112i	−0.184310	−	0.319234i
$768$	15.7457	−	27.2724i	0.568174	−	0.984107i
$769$	51.5584	+	15.9037i	1.85924	+	0.573501i	0.997848	+	0.0655646i	$0.0208848\pi$
$769$	51.5584	+	15.9037i	1.85924	+	0.573501i	0.861395	+	0.507936i	$0.169591\pi$
$770$	39.1168	+	49.0509i	1.40967	+	1.76767i
$771$	−1.10568	+	14.7543i	−0.0398201	+	0.531362i
$772$	27.1216	+	13.0611i	0.976129	+	0.470079i
$773$	−9.74093			−0.350357			−0.175178	−	0.984537i	$-0.556050\pi$
$773$	−9.74093			−0.350357			−0.175178	+	0.984537i	$0.556050\pi$
$774$	−5.52819	−	15.5637i	−0.198707	−	0.559426i
$775$	−10.3942			−0.373370
$776$	41.2934	+	19.8858i	1.48235	+	0.713860i
$777$	−1.07423	+	14.3345i	−0.0385376	+	0.514249i
$778$	9.22303	+	11.5653i	0.330662	+	0.414637i
$779$	8.94947	+	2.76054i	0.320648	+	0.0989068i
$780$	15.7453	−	27.2716i	0.563772	−	0.976481i
$781$	1.66988	+	2.89232i	0.0597530	+	0.103495i
$782$	6.82429	+	29.8992i	0.244036	+	1.06919i
$783$	4.23069	+	0.637674i	0.151193	+	0.0227886i
$784$	−14.6919	−	13.6321i	−0.524710	−	0.486860i
$785$	6.69569	−	8.39613i	0.238979	−	0.299671i
$786$	2.03067	−	1.38449i	0.0724315	−	0.0493830i
$787$	−36.4322	+	33.8041i	−1.29867	+	1.20499i	−0.333680	+	0.942687i	$0.608290\pi$
$787$	−36.4322	+	33.8041i	−1.29867	+	1.20499i	−0.964987	+	0.262299i	$0.915519\pi$
$788$	2.72803	+	36.4030i	0.0971819	+	1.29680i
$789$	−1.16853	+	2.97738i	−0.0416009	+	0.105997i
$790$	9.10491	−	39.8912i	0.323938	−	1.41927i
$791$	−36.8793	+	11.3758i	−1.31128	+	0.404475i
$792$	−19.4579	−	13.2662i	−0.691406	−	0.471393i
$793$	−43.1972	+	6.51094i	−1.53398	+	0.231210i
$794$	16.1421	+	41.1293i	0.572860	+	1.45962i
$795$	−7.38433	+	3.55610i	−0.261895	+	0.126122i
$796$	−13.6728	+	6.58446i	−0.484619	+	0.233380i
$797$	11.2983	+	28.7877i	0.400207	+	1.01971i	0.978932	+	0.204188i	$0.0654555\pi$
$797$	11.2983	+	28.7877i	0.400207	+	1.01971i	−0.578724	+	0.815523i	$0.696449\pi$
$798$	−57.5081	+	8.66795i	−2.03577	+	0.306842i
$799$	−37.9779	−	25.8929i	−1.34356	−	0.916026i
$800$	−4.28955	+	1.32315i	−0.151658	+	0.0467804i
$801$	1.78254	−	7.80982i	0.0629830	−	0.275946i
$802$	−17.2107	+	43.8522i	−0.607732	+	1.54848i
$803$	−3.30334	−	44.0800i	−0.116572	−	1.55555i
$804$	21.4670	−	19.9185i	0.757084	−	0.702471i
$805$	13.4398	−	9.16308i	0.473690	−	0.322956i
$806$	50.8409	−	63.7524i	1.79079	−	2.24558i
$807$	7.86617	+	7.29874i	0.276902	+	0.256928i
$808$	17.5778	+	2.64943i	0.618386	+	0.0932067i
$809$	−6.38145	−	27.9590i	−0.224360	−	0.982985i	−0.954154	−	0.299318i	$-0.903241\pi$
$809$	−6.38145	−	27.9590i	−0.224360	−	0.982985i	0.729794	−	0.683668i	$-0.239616\pi$
$810$	2.45726	+	4.25609i	0.0863392	+	0.149544i
$811$	18.1879	−	31.5024i	0.638664	−	1.10620i	−0.347062	−	0.937842i	$-0.612821\pi$
$811$	18.1879	−	31.5024i	0.638664	−	1.10620i	0.985726	−	0.168357i	$-0.0538461\pi$
$812$	−56.8369	−	17.5319i	−1.99458	−	0.615248i
$813$	−11.9385	−	14.9704i	−0.418701	−	0.525035i
$814$	3.37244	−	45.0021i	0.118204	−	1.57732i
$815$	−16.5427	−	7.96653i	−0.579464	−	0.279055i
$816$	28.8964			1.01158
$817$	41.9325	+	21.9105i	1.46703	+	0.766553i
$818$	−16.8271			−0.588347
$819$	−10.7126	−	5.15894i	−0.374330	−	0.180268i
$820$	−0.822204	+	10.9716i	−0.0287126	+	0.383143i
$821$	−26.7118	−	33.4956i	−0.932249	−	1.16900i	−0.985372	−	0.170415i	$-0.945489\pi$
$821$	−26.7118	−	33.4956i	−0.932249	−	1.16900i	0.0531235	−	0.998588i	$-0.483082\pi$
$822$	−6.98962	−	2.15601i	−0.243791	−	0.0751996i
$823$	26.8706	−	46.5412i	0.936650	−	1.62232i	0.164984	−	0.986296i	$-0.447243\pi$
$823$	26.8706	−	46.5412i	0.936650	−	1.62232i	0.771665	−	0.636029i	$-0.219424\pi$
$824$	−0.833165	−	1.44308i	−0.0290247	−	0.0502722i
$825$	−1.05880	−	4.63890i	−0.0368627	−	0.161506i
$826$	−21.9016	−	3.30114i	−0.762055	−	0.114861i
$827$	−8.90111	−	8.25902i	−0.309522	−	0.287194i	0.510081	−	0.860126i	$-0.329615\pi$
$827$	−8.90111	−	8.25902i	−0.309522	−	0.287194i	−0.819603	+	0.572932i	$0.805806\pi$
$828$	−7.05518	+	8.84691i	−0.245184	+	0.307452i
$829$	−1.35318	+	0.922583i	−0.0469979	+	0.0320426i	−0.586591	−	0.809883i	$-0.699530\pi$
$829$	−1.35318	+	0.922583i	−0.0469979	+	0.0320426i	0.539593	+	0.841926i	$0.318578\pi$
$830$	49.7251	−	46.1381i	1.72598	−	1.60148i
$831$	−0.835753	−	11.1524i	−0.0289920	−	0.386871i
$832$	−3.91653	+	9.97917i	−0.135781	+	0.345965i
$833$	−3.37206	+	14.7740i	−0.116835	+	0.511888i
$834$	−34.1082	+	10.5210i	−1.18107	+	0.364312i
$835$	−0.730390	−	0.497971i	−0.0252762	−	0.0172330i
$836$	123.624	−	18.6333i	4.27563	−	0.644448i
$837$	3.18352	+	8.11147i	0.110039	+	0.280374i
$838$	61.3700	−	29.5542i	2.11999	−	1.02093i
$839$	−7.68508	+	3.70094i	−0.265318	+	0.127771i	−0.561814	−	0.827264i	$-0.689896\pi$
$839$	−7.68508	+	3.70094i	−0.265318	+	0.127771i	0.296495	+	0.955034i	$0.404182\pi$
$840$	−13.4685	−	34.3173i	−0.464709	−	1.18406i
$841$	10.5752	−	1.59395i	0.364661	−	0.0549638i
$842$	59.0071	+	40.2304i	2.03352	+	1.38643i
$843$	−4.01762	+	1.23927i	−0.138374	+	0.0426828i
$844$	16.0620	−	70.3724i	0.552878	−	2.42232i
$845$	−0.572775	+	1.45941i	−0.0197041	+	0.0502051i
$846$	−1.85092	−	24.6988i	−0.0636360	−	0.849164i
$847$	−11.5233	+	10.6921i	−0.395946	+	0.367384i
$848$	−21.4554	+	14.6281i	−0.736783	+	0.502330i
$849$	−17.3799	+	21.7938i	−0.596478	+	0.747960i
$850$	10.2946	+	9.55199i	0.353102	+	0.327631i
$851$	−11.5697	−	1.74386i	−0.396605	−	0.0597786i
$852$	−0.809301	−	3.54578i	−0.0277262	−	0.121476i
$853$	26.9313	+	46.6463i	0.922109	+	1.59714i	0.796146	+	0.605105i	$0.206869\pi$
$853$	26.9313	+	46.6463i	0.922109	+	1.59714i	0.125963	+	0.992035i	$0.459798\pi$
$854$	−47.3894	+	82.0809i	−1.62163	+	2.80875i
$855$	−13.4524	−	4.14951i	−0.460062	−	0.141910i
$856$	61.2098	+	76.7546i	2.09211	+	2.62342i
$857$	0.584141	−	7.79482i	0.0199539	−	0.266266i	−0.978300	−	0.207194i	$-0.933567\pi$
$857$	0.584141	−	7.79482i	0.0199539	−	0.266266i	0.998254	−	0.0590719i	$-0.0188141\pi$
$858$	33.6314	+	16.1961i	1.14816	+	0.552924i
$859$	−34.9555			−1.19267			−0.596333	−	0.802737i	$-0.703376\pi$
$859$	−34.9555			−1.19267			−0.596333	+	0.802737i	$0.703376\pi$
$860$	−14.1328	+	53.7533i	−0.481926	+	1.83297i
$861$	4.15423			0.141576
$862$	33.4496	+	16.1085i	1.13930	+	0.548658i
$863$	3.00873	−	40.1487i	0.102418	−	1.36668i	−0.675058	−	0.737765i	$-0.735881\pi$
$863$	3.00873	−	40.1487i	0.102418	−	1.36668i	0.777476	−	0.628912i	$-0.216499\pi$
$864$	2.34636	+	2.94225i	0.0798249	+	0.100097i
$865$	−29.4833	−	9.09439i	−1.00246	−	0.309219i
$866$	24.8295	−	43.0060i	0.843742	−	1.46140i
$867$	−2.42437	−	4.19913i	−0.0823359	−	0.142610i
$868$	−26.9561	−	118.102i	−0.914950	−	4.00866i
$869$	32.8403	+	4.94988i	1.11403	+	0.167913i
$870$	−15.4136	−	14.3018i	−0.522571	−	0.484875i
$871$	−15.6162	+	19.5821i	−0.529135	+	0.663515i
$872$	−34.4526	+	23.4894i	−1.16671	+	0.795450i
$873$	5.69084	−	5.28033i	0.192606	−	0.178712i
$874$	−3.53756	−	47.2055i	−0.119660	−	1.59675i
$875$	14.1280	−	35.9976i	0.477614	−	1.21694i
$876$	−10.7116	+	46.9304i	−0.361910	+	1.58563i
$877$	16.9088	−	5.21566i	0.570968	−	0.176120i	0.00419056	−	0.999991i	$-0.498666\pi$
$877$	16.9088	−	5.21566i	0.570968	−	0.176120i	0.566778	+	0.823871i	$0.308190\pi$
$878$	44.8585	+	30.5840i	1.51390	+	1.03216i
$879$	−20.9109	+	3.15182i	−0.705309	+	0.106308i
$880$	17.5789	+	44.7903i	0.592584	+	1.50988i
$881$	−43.0575	+	20.7354i	−1.45064	+	0.698593i	−0.982707	−	0.185169i	$-0.940717\pi$
$881$	−43.0575	+	20.7354i	−1.45064	+	0.698593i	−0.467936	+	0.883762i	$0.655002\pi$
$882$	−7.35701	+	3.54295i	−0.247723	+	0.119297i
$883$	−7.20281	−	18.3525i	−0.242394	−	0.617609i	0.756963	−	0.653457i	$-0.226682\pi$
$883$	−7.20281	−	18.3525i	−0.242394	−	0.617609i	−0.999357	+	0.0358478i	$0.988587\pi$
$884$	−74.5959	+	11.2435i	−2.50893	+	0.378161i
$885$	−4.42984	−	3.02022i	−0.148908	−	0.101523i
$886$	85.2452	−	26.2947i	2.86387	−	0.883386i
$887$	0.836091	−	3.66315i	0.0280732	−	0.122997i	−0.958950	−	0.283576i	$-0.908479\pi$
$887$	0.836091	−	3.66315i	0.0280732	−	0.122997i	0.987023	+	0.160579i	$0.0513363\pi$
$888$	−9.68802	+	24.6847i	−0.325109	+	0.828364i
$889$	2.51260	+	33.5284i	0.0842700	+	1.12450i
$890$	−28.8592	+	26.7774i	−0.967362	+	0.897580i
$891$	−3.29584	+	2.24707i	−0.110415	+	0.0752796i
$892$	−11.8367	+	14.8427i	−0.396322	+	0.496972i
$893$	52.0095	+	48.2577i	1.74043	+	1.61488i
$894$	11.6184	+	1.75120i	0.388579	+	0.0585688i
$895$	9.61981	+	42.1472i	0.321555	+	1.40882i
$896$	23.6729	+	41.0026i	0.790856	+	1.36980i
$897$	4.83903	−	8.38144i	0.161570	−	0.279848i
$898$	−87.1181	−	26.8724i	−2.90717	−	0.896742i
$899$	−23.2449	−	29.1482i	−0.775261	−	0.972146i
$900$	−0.387224	+	5.16715i	−0.0129075	+	0.172238i
$901$	17.6898	+	8.51897i	0.589333	+	0.283808i
$902$	−13.0419			−0.434246
$903$	20.6381	+	3.80460i	0.686793	+	0.126609i
$904$	−71.1961			−2.36795
$905$	10.7245	+	5.16467i	0.356496	+	0.171679i
$906$	1.36038	−	18.1530i	0.0451955	−	0.603092i
$907$	23.0545	+	28.9094i	0.765511	+	0.959920i	0.999925	−	0.0122168i	$-0.00388882\pi$
$907$	23.0545	+	28.9094i	0.765511	+	0.959920i	−0.234415	+	0.972137i	$0.575317\pi$
$908$	−31.6801	−	9.77203i	−1.05134	−	0.324296i
$909$	1.50551	−	2.60762i	0.0499347	−	0.0864894i
$910$	29.2171	+	50.6055i	0.968538	+	1.67756i
$911$	−2.74925	−	12.0452i	−0.0910866	−	0.399077i	0.908746	−	0.417349i	$-0.137041\pi$
$911$	−2.74925	−	12.0452i	−0.0910866	−	0.399077i	−0.999833	+	0.0182721i	$0.994183\pi$
$912$	−44.1050	−	6.64776i	−1.46046	−	0.220129i
$913$	40.3605	+	37.4490i	1.33574	+	1.23938i
$914$	12.2448	−	15.3545i	0.405021	−	0.507880i
$915$	−18.9560	+	12.9239i	−0.626664	+	0.427253i
$916$	45.4331	−	42.1558i	1.50115	−	1.39287i
$917$	0.233368	+	3.11408i	0.00770648	+	0.102836i
$918$	4.30122	−	10.9593i	0.141961	−	0.361712i
$919$	10.2482	−	44.9002i	0.338056	−	1.48112i	−0.465050	−	0.885285i	$-0.653964\pi$
$919$	10.2482	−	44.9002i	0.338056	−	1.48112i	0.803106	−	0.595836i	$-0.203179\pi$
$920$	28.6739	−	8.84473i	0.945351	−	0.291602i
$921$	11.1554	+	7.60560i	0.367582	+	0.250613i
$922$	−82.8343	+	12.4853i	−2.72800	+	0.411180i
$923$	1.13644	+	2.89561i	0.0374064	+	0.0953100i
$924$	49.9630	−	24.0609i	1.64366	−	0.791546i
$925$	−4.82724	+	2.32468i	−0.158719	+	0.0764349i
$926$	−24.3815	−	62.1231i	−0.801226	−	2.04149i
$927$	−0.279096	+	0.0420670i	−0.00916672	+	0.00138166i
$928$	−13.3033	−	9.07007i	−0.436704	−	0.297740i
$929$	−9.04169	+	2.78899i	−0.296648	+	0.0915038i	−0.439507	−	0.898239i	$-0.644847\pi$
$929$	−9.04169	+	2.78899i	−0.296648	+	0.0915038i	0.142859	+	0.989743i	$0.454371\pi$
$930$	9.52929	−	41.7505i	0.312478	−	1.36905i
$931$	8.54565	−	21.7740i	0.280072	−	0.713613i
$932$	−2.58964	−	34.5564i	−0.0848266	−	1.13193i
$933$	7.96959	−	7.39470i	0.260913	−	0.242091i
$934$	−5.42710	+	3.70013i	−0.177580	+	0.121072i
$935$	22.6832	−	28.4438i	0.741820	−	0.930213i
$936$	−16.0790	−	14.9191i	−0.525558	−	0.487646i
$937$	22.7176	+	3.42413i	0.742153	+	0.111862i	0.509226	−	0.860633i	$-0.329932\pi$
$937$	22.7176	+	3.42413i	0.742153	+	0.111862i	0.232927	+	0.972494i	$0.425170\pi$
$938$	12.0919	+	52.9781i	0.394815	+	1.72980i
$939$	1.62323	+	2.81152i	0.0529721	+	0.0917503i
$940$	−41.6743	+	72.1820i	−1.35927	+	2.35432i
$941$	9.88943	+	3.05049i	0.322386	+	0.0994430i	0.451724	−	0.892158i	$-0.350809\pi$
$941$	9.88943	+	3.05049i	0.322386	+	0.0994430i	−0.129338	+	0.991601i	$0.541285\pi$
$942$	−8.64320	−	10.8382i	−0.281611	−	0.353129i
$943$	−0.252690	+	3.37191i	−0.00822871	+	0.109804i
$944$	−15.3046	−	7.37033i	−0.498124	−	0.239884i
$945$	−6.24443			−0.203131
$946$	−64.7916	−	11.9442i	−2.10656	−	0.388340i
$947$	12.9650			0.421305			0.210653	−	0.977561i	$-0.432441\pi$
$947$	12.9650			0.421305			0.210653	+	0.977561i	$0.432441\pi$
$948$	−32.5851	−	15.6922i	−1.05832	−	0.509658i
$949$	3.07671	−	41.0559i	0.0998743	−	1.33273i
$950$	−13.5153	−	16.9477i	−0.438495	−	0.549855i
$951$	−10.8462	−	3.34562i	−0.351713	−	0.108489i
$952$	−44.1575	+	76.4830i	−1.43115	+	2.47883i
$953$	−26.5638	−	46.0098i	−0.860486	−	1.49040i	−0.871461	−	0.490465i	$-0.836827\pi$
$953$	−26.5638	−	46.0098i	−0.860486	−	1.49040i	0.0109754	−	0.999940i	$-0.496506\pi$
$954$	2.35424	+	10.3146i	0.0762215	+	0.333948i
$955$	−42.6170	−	6.42348i	−1.37905	−	0.207859i
$956$	8.25084	+	7.65566i	0.266851	+	0.247602i
$957$	10.6409	−	13.3433i	0.343973	−	0.431328i
$958$	44.5130	−	30.3485i	1.43815	−	0.980514i
$959$	6.81297	−	6.32151i	0.220002	−	0.204132i
$960$	0.420732	+	5.61427i	0.0135791	+	0.181200i
$961$	16.4151	−	41.8249i	0.529518	−	1.34919i
$962$	9.35305	−	40.9784i	0.301554	−	1.32120i
$963$	15.8901	−	4.90144i	0.512050	−	0.157947i
$964$	54.0304	+	36.8373i	1.74020	+	1.18645i
$965$	−13.3704	+	2.01526i	−0.430408	+	0.0648735i
$966$	−7.67121	−	19.5459i	−0.246817	−	0.628880i
$967$	1.77063	−	0.852691i	0.0569396	−	0.0274207i	−0.405197	−	0.914229i	$-0.632797\pi$
$967$	1.77063	−	0.852691i	0.0569396	−	0.0274207i	0.462137	+	0.886809i	$0.347083\pi$
$968$	−26.1270	+	12.5821i	−0.839753	+	0.404404i
$969$	12.3210	+	31.3934i	0.395808	+	1.00850i
$970$	−37.7263	+	5.68633i	−1.21132	+	0.182577i
$971$	10.0371	+	6.84320i	0.322107	+	0.219609i	0.713568	−	0.700586i	$-0.247078\pi$
$971$	10.0371	+	6.84320i	0.322107	+	0.219609i	−0.391461	+	0.920195i	$0.628030\pi$
$972$	4.15096	−	1.28040i	0.133142	−	0.0410689i
$973$	10.0920	−	44.2160i	0.323535	−	1.41750i
$974$	6.15551	−	15.6840i	0.197235	−	0.502547i
$975$	−0.331186	−	4.41937i	−0.0106064	−	0.141533i
$976$	−53.2850	+	49.4413i	−1.70561	+	1.58258i
$977$	−4.08394	+	2.78438i	−0.130657	+	0.0890802i	−0.626885	−	0.779112i	$-0.715670\pi$
$977$	−4.08394	+	2.78438i	−0.130657	+	0.0890802i	0.496228	+	0.868192i	$0.334718\pi$
$978$	−14.7776	+	18.5305i	−0.472536	+	0.592541i
$979$	−23.4242	−	21.7345i	−0.748640	−	0.694636i
$980$	27.1719	+	4.09550i	0.867973	+	0.130826i
$981$	1.57166	+	6.88588i	0.0501791	+	0.219849i
$982$	−8.87601	−	15.3737i	−0.283245	−	0.490594i
$983$	−11.0166	+	19.0813i	−0.351375	+	0.608599i	−0.986491	−	0.163818i	$-0.947619\pi$
$983$	−11.0166	+	19.0813i	−0.351375	+	0.608599i	0.635116	+	0.772417i	$0.280952\pi$
$984$	7.32304	+	2.25886i	0.233450	+	0.0720098i
$985$	−10.2235	−	12.8198i	−0.325746	−	0.408473i
$986$	−3.76425	+	50.2304i	−0.119878	+	1.59966i
$987$	28.3540	+	13.6546i	0.902518	+	0.434630i
$988$	116.443			3.70456
$989$	−4.34347	+	16.5201i	−0.138114	+	0.525309i
$990$	19.6039			0.623052
$991$	−15.6471	−	7.53523i	−0.497045	−	0.239364i	0.168528	−	0.985697i	$-0.446099\pi$
$991$	−15.6471	−	7.53523i	−0.497045	−	0.239364i	−0.665573	+	0.746332i	$0.731813\pi$
$992$	2.45059	−	32.7008i	0.0778063	−	1.03825i
$993$	−15.6037	−	19.5664i	−0.495167	−	0.620920i
$994$	6.44896	+	1.98924i	0.204549	+	0.0630949i
$995$	3.40826	−	5.90327i	0.108049	−	0.187146i
$996$	−29.9789	−	51.9249i	−0.949917	−	1.64530i
$997$	11.4449	+	50.1434i	0.362463	+	1.58806i	0.746921	+	0.664913i	$0.231532\pi$
$997$	11.4449	+	50.1434i	0.362463	+	1.58806i	−0.384457	+	0.923143i	$0.625611\pi$
$998$	−96.3452	−	14.5217i	−3.04975	−	0.459676i
$999$	3.29263	+	3.05511i	0.104174	+	0.0966594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	129.2.m.b.40.1	✓	48
3.2	odd	2		387.2.y.d.298.4		48
43.10	even	21		5547.2.a.bb.1.23		24
43.14	even	21	inner	129.2.m.b.100.1	yes	48
43.33	odd	42		5547.2.a.ba.1.2		24
129.14	odd	42		387.2.y.d.100.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.2.m.b.40.1	✓	48	1.1	even	1	trivial
129.2.m.b.100.1	yes	48	43.14	even	21	inner
387.2.y.d.100.4		48	129.14	odd	42
387.2.y.d.298.4		48	3.2	odd	2
5547.2.a.ba.1.2		24	43.33	odd	42
5547.2.a.bb.1.23		24	43.10	even	21

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:	\( N \)	\(=\)	\( 129 = 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	129.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26929 - 1.09283i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.70841 + 3.39624i) q^{4} +(-1.86451 - 0.575125i) q^{5} +(-1.25936 + 2.18128i) q^{6} +(-1.60016 - 2.77155i) q^{7} +(-1.31371 - 5.75575i) q^{8} +(-0.988831 - 0.149042i) q^{9} +O(q^{10})\)	\(q+(-2.26929 - 1.09283i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.70841 + 3.39624i) q^{4} +(-1.86451 - 0.575125i) q^{5} +(-1.25936 + 2.18128i) q^{6} +(-1.60016 - 2.77155i) q^{7} +(-1.31371 - 5.75575i) q^{8} +(-0.988831 - 0.149042i) q^{9} +(3.60259 + 3.34272i) q^{10} +(-2.48708 + 3.11871i) q^{11} +(3.58914 - 2.44704i) q^{12} +(-2.72351 + 2.52705i) q^{13} +(0.602376 + 8.03815i) q^{14} +(-0.712852 + 1.81632i) q^{15} +(-1.37563 + 6.02703i) q^{16} +(4.46660 - 1.37776i) q^{17} +(2.08106 + 1.41885i) q^{18} +(-7.13439 + 1.07534i) q^{19} +(-3.09659 - 7.88999i) q^{20} +(-2.88338 + 1.38856i) q^{21} +(9.05213 - 4.35928i) q^{22} +(-0.951682 - 2.42485i) q^{23} +(-5.83783 + 0.879911i) q^{24} +(-0.985569 - 0.671950i) q^{25} +(8.94208 - 2.75827i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(5.07897 - 12.9410i) q^{28} +(-0.319731 - 4.26651i) q^{29} +(3.60259 - 3.34272i) q^{30} +(7.19970 - 4.90867i) q^{31} +(2.34636 - 2.94225i) q^{32} +(2.92412 + 2.71319i) q^{33} +(-11.6417 - 1.75470i) q^{34} +(1.38952 + 6.08787i) q^{35} +(-2.17198 - 3.76197i) q^{36} +(2.24583 - 3.88990i) q^{37} +(17.3652 + 5.35644i) q^{38} +(2.31646 + 2.90474i) q^{39} +(-0.860846 + 11.4872i) q^{40} +(-1.16952 - 0.563212i) q^{41} +8.06069 q^{42} +(-5.29434 - 3.86911i) q^{43} -17.3279 q^{44} +(1.75797 + 0.846592i) q^{45} +(-0.490308 + 6.54271i) q^{46} +(-6.13115 - 7.68822i) q^{47} +(5.90738 + 1.82219i) q^{48} +(-1.62099 + 2.80765i) q^{49} +(1.50221 + 2.60191i) q^{50} +(-1.04012 - 4.55707i) q^{51} +(-15.9589 - 2.40541i) q^{52} +(3.07918 + 2.85706i) q^{53} +(1.57040 - 1.96922i) q^{54} +(6.43084 - 4.38447i) q^{55} +(-13.8502 + 12.8511i) q^{56} +(0.539176 + 7.19480i) q^{57} +(-3.93702 + 10.0314i) q^{58} +(-0.611439 + 2.67889i) q^{59} +(-8.09934 + 2.49832i) q^{60} +(9.71505 + 6.62361i) q^{61} +(-21.7026 + 3.27113i) q^{62} +(1.16920 + 2.97909i) q^{63} +(2.59967 - 1.25194i) q^{64} +(6.53138 - 3.14535i) q^{65} +(-3.67062 - 9.35259i) q^{66} +(6.66613 - 1.00476i) q^{67} +(16.7766 + 11.4381i) q^{68} +(-2.48919 + 0.767812i) q^{69} +(3.49980 - 15.3336i) q^{70} +(0.305881 - 0.779372i) q^{71} +(0.441189 + 5.88726i) q^{72} +(-8.12328 + 7.53730i) q^{73} +(-9.34745 + 6.37298i) q^{74} +(-0.743723 + 0.932599i) q^{75} +(-22.9750 - 21.3177i) q^{76} +(12.6234 + 1.90267i) q^{77} +(-2.08231 - 9.12320i) q^{78} +(-4.16288 - 7.21033i) q^{79} +(6.03117 - 10.4463i) q^{80} +(0.955573 + 0.294755i) q^{81} +(2.03849 + 2.55618i) q^{82} +(1.03147 - 13.7640i) q^{83} +(-12.5253 - 6.03185i) q^{84} -9.12040 q^{85} +(7.78609 + 14.5659i) q^{86} -4.27848 q^{87} +(21.2178 + 10.2179i) q^{88} +(-0.598638 + 7.98826i) q^{89} +(-3.06415 - 3.84232i) q^{90} +(11.3619 + 3.50468i) q^{91} +(5.65781 - 9.79962i) q^{92} +(-4.35691 - 7.54640i) q^{93} +(5.51142 + 24.1471i) q^{94} +(13.9206 + 2.09819i) q^{95} +(-2.75868 - 2.55968i) q^{96} +(-4.84029 + 6.06953i) q^{97} +(6.74679 - 4.59988i) q^{98} +(2.92412 - 2.71319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + q^{5} - q^{6} - 16 q^{7} - 14 q^{8} + 4 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + q^5 - q^6 - 16 * q^7 - 14 * q^8 + 4 * q^9	\( 48 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + q^{5} - q^{6} - 16 q^{7} - 14 q^{8} + 4 q^{9} - 2 q^{10} - 15 q^{11} - 6 q^{12} - 3 q^{13} + 60 q^{14} - 6 q^{15} - 38 q^{16} + 3 q^{17} - q^{18} + 9 q^{19} - 61 q^{20} - 3 q^{21} + 16 q^{22} - 2 q^{23} - 7 q^{24} - 25 q^{25} - 15 q^{26} - 8 q^{27} - 39 q^{28} - 52 q^{29} - 2 q^{30} + 6 q^{31} + 20 q^{32} + 11 q^{33} - 62 q^{34} + 50 q^{35} - 27 q^{36} + 5 q^{37} + 52 q^{38} - 15 q^{39} + 154 q^{40} - 23 q^{41} + 48 q^{42} - 31 q^{43} - 30 q^{44} + 12 q^{45} + 18 q^{46} - 6 q^{47} + 103 q^{48} - 48 q^{49} + 29 q^{50} - 6 q^{51} + 8 q^{52} + 61 q^{53} + 2 q^{54} - 41 q^{55} - 21 q^{56} - 12 q^{57} - 57 q^{58} - 28 q^{59} - 40 q^{60} + 71 q^{61} - 61 q^{62} - 2 q^{63} - 90 q^{64} - 37 q^{65} + 6 q^{66} - 48 q^{67} - 57 q^{68} - 2 q^{69} + 117 q^{70} - 6 q^{71} - 7 q^{73} + 102 q^{74} - 34 q^{75} + 39 q^{76} + 33 q^{77} - 12 q^{78} + 30 q^{79} + 80 q^{80} + 4 q^{81} - 38 q^{82} + 71 q^{83} - 41 q^{84} + 44 q^{85} + 55 q^{86} - 8 q^{87} + 112 q^{88} + 32 q^{89} - 10 q^{90} + 117 q^{91} - 11 q^{92} - 15 q^{93} - 2 q^{94} + 25 q^{95} + 60 q^{96} - 17 q^{97} - 23 q^{98} + 11 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + q^5 - q^6 - 16 * q^7 - 14 * q^8 + 4 * q^9 - 2 * q^10 - 15 * q^11 - 6 * q^12 - 3 * q^13 + 60 * q^14 - 6 * q^15 - 38 * q^16 + 3 * q^17 - q^18 + 9 * q^19 - 61 * q^20 - 3 * q^21 + 16 * q^22 - 2 * q^23 - 7 * q^24 - 25 * q^25 - 15 * q^26 - 8 * q^27 - 39 * q^28 - 52 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 + 11 * q^33 - 62 * q^34 + 50 * q^35 - 27 * q^36 + 5 * q^37 + 52 * q^38 - 15 * q^39 + 154 * q^40 - 23 * q^41 + 48 * q^42 - 31 * q^43 - 30 * q^44 + 12 * q^45 + 18 * q^46 - 6 * q^47 + 103 * q^48 - 48 * q^49 + 29 * q^50 - 6 * q^51 + 8 * q^52 + 61 * q^53 + 2 * q^54 - 41 * q^55 - 21 * q^56 - 12 * q^57 - 57 * q^58 - 28 * q^59 - 40 * q^60 + 71 * q^61 - 61 * q^62 - 2 * q^63 - 90 * q^64 - 37 * q^65 + 6 * q^66 - 48 * q^67 - 57 * q^68 - 2 * q^69 + 117 * q^70 - 6 * q^71 - 7 * q^73 + 102 * q^74 - 34 * q^75 + 39 * q^76 + 33 * q^77 - 12 * q^78 + 30 * q^79 + 80 * q^80 + 4 * q^81 - 38 * q^82 + 71 * q^83 - 41 * q^84 + 44 * q^85 + 55 * q^86 - 8 * q^87 + 112 * q^88 + 32 * q^89 - 10 * q^90 + 117 * q^91 - 11 * q^92 - 15 * q^93 - 2 * q^94 + 25 * q^95 + 60 * q^96 - 17 * q^97 - 23 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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