LMFDB - Embedded newform 62.3.h.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,3,Mod(3,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(30))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("62.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	62.h (of order $30$, 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:	$1.68937763903$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	62.11
Dual form			62.3.h.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.437016 + 1.34500i) q^{2} +(-0.426688 + 0.384192i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(2.75524 + 4.77222i) q^{5} +(-0.703206 - 0.405996i) q^{6} +(0.186434 + 1.77380i) q^{7} +(-2.28825 - 1.66251i) q^{8} +(-0.906297 + 8.62284i) q^{9} +O(q^{10})$	\(q+(0.437016 + 1.34500i) q^{2} +(-0.426688 + 0.384192i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(2.75524 + 4.77222i) q^{5} +(-0.703206 - 0.405996i) q^{6} +(0.186434 + 1.77380i) q^{7} +(-2.28825 - 1.66251i) q^{8} +(-0.906297 + 8.62284i) q^{9} +(-5.21454 + 5.79133i) q^{10} +(7.06408 - 15.8662i) q^{11} +(0.238751 - 1.12324i) q^{12} +(-1.57884 - 7.42786i) q^{13} +(-2.30429 + 1.02593i) q^{14} +(-3.00908 - 0.977708i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-4.04394 - 9.08285i) q^{17} +(-11.9938 + 2.54935i) q^{18} +(21.8719 + 4.64901i) q^{19} +(-10.0682 - 4.48263i) q^{20} +(-0.761030 - 0.685234i) q^{21} +(24.4271 + 2.56739i) q^{22} +(14.1916 - 19.5331i) q^{23} +(1.61509 - 0.169753i) q^{24} +(-2.68273 + 4.64662i) q^{25} +(9.30047 - 5.36963i) q^{26} +(-5.96349 - 8.20804i) q^{27} +(-2.38689 - 2.65091i) q^{28} +(-31.0533 + 10.0898i) q^{29} -4.47447i q^{30} +(-30.5047 + 5.51936i) q^{31} +5.65685 q^{32} +(3.08149 + 9.48386i) q^{33} +(10.4491 - 9.40844i) q^{34} +(-7.95131 + 5.77697i) q^{35} +(-8.67033 - 15.0175i) q^{36} +(29.5776 + 17.0767i) q^{37} +(3.30545 + 31.4493i) q^{38} +(3.52739 + 2.56280i) q^{39} +(1.62918 - 15.5006i) q^{40} +(-27.5480 + 30.5952i) q^{41} +(0.589056 - 1.32304i) q^{42} +(-4.74031 + 22.3014i) q^{43} +(7.22189 + 33.9763i) q^{44} +(-43.6472 + 19.4330i) q^{45} +(32.4739 + 10.5514i) q^{46} +(6.56908 - 20.2175i) q^{47} +(0.934136 + 2.09810i) q^{48} +(44.8176 - 9.52628i) q^{49} +(-7.42209 - 1.57761i) q^{50} +(5.21506 + 2.32189i) q^{51} +(11.2866 + 10.1625i) q^{52} +(-64.5709 - 6.78668i) q^{53} +(8.43365 - 11.6079i) q^{54} +(95.1801 - 10.0038i) q^{55} +(2.52236 - 4.36885i) q^{56} +(-11.1186 + 6.41931i) q^{57} +(-27.1416 - 37.3572i) q^{58} +(-14.9883 - 16.6462i) q^{59} +(6.01815 - 1.95542i) q^{60} +78.4335i q^{61} +(-20.7546 - 38.6167i) q^{62} -15.4642 q^{63} +(2.47214 + 7.60845i) q^{64} +(31.0973 - 28.0001i) q^{65} +(-11.4091 + 8.28920i) q^{66} +(-12.3922 - 21.4639i) q^{67} +(17.2208 + 9.94242i) q^{68} +(1.44905 + 13.7868i) q^{69} +(-11.2449 - 8.16987i) q^{70} +(11.3091 - 107.599i) q^{71} +(16.4094 - 18.2244i) q^{72} +(31.6472 - 71.0808i) q^{73} +(-10.0422 + 47.2446i) q^{74} +(-0.640505 - 3.01334i) q^{75} +(-40.8547 + 18.1897i) q^{76} +(29.4605 + 9.57229i) q^{77} +(-1.90543 + 5.86432i) q^{78} +(-0.245637 - 0.551709i) q^{79} +(21.5603 - 4.58278i) q^{80} +(-70.6298 - 15.0128i) q^{81} +(-53.1894 - 23.6814i) q^{82} +(-95.5098 - 85.9974i) q^{83} +(2.03691 + 0.214088i) q^{84} +(32.2033 - 44.3241i) q^{85} +(-32.0669 + 3.37037i) q^{86} +(9.37365 - 16.2356i) q^{87} +(-42.5420 + 24.5616i) q^{88} +(47.7655 + 65.7436i) q^{89} +(-45.2118 - 50.2128i) q^{90} +(12.8812 - 4.18536i) q^{91} +48.2884i q^{92} +(10.8955 - 14.0747i) q^{93} +30.0633 q^{94} +(38.0762 + 117.187i) q^{95} +(-2.41371 + 2.17332i) q^{96} +(86.3662 - 62.7487i) q^{97} +(32.3988 + 56.1164i) q^{98} +(130.409 + 75.2918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{3} - 24 q^{4} + 6 q^{5} + 18 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 6 * q^3 - 24 * q^4 + 6 * q^5 + 18 * q^7 - 44 * q^9	\( 48 q + 6 q^{3} - 24 q^{4} + 6 q^{5} + 18 q^{7} - 44 q^{9} + 16 q^{10} - 4 q^{11} + 12 q^{12} + 48 q^{13} - 24 q^{14} - 70 q^{15} - 48 q^{16} + 70 q^{17} + 16 q^{18} + 38 q^{19} + 12 q^{20} - 24 q^{21} - 52 q^{22} - 50 q^{23} - 242 q^{25} - 168 q^{26} - 270 q^{27} - 64 q^{28} - 40 q^{29} - 26 q^{31} + 126 q^{33} + 112 q^{34} + 300 q^{35} + 152 q^{36} + 504 q^{37} + 264 q^{38} + 122 q^{39} - 48 q^{40} + 46 q^{41} + 432 q^{42} + 100 q^{43} + 12 q^{44} - 36 q^{45} - 160 q^{46} - 336 q^{47} + 64 q^{48} + 68 q^{49} + 128 q^{50} - 518 q^{51} - 24 q^{52} - 314 q^{53} - 418 q^{55} - 8 q^{56} - 66 q^{57} + 40 q^{58} - 170 q^{59} + 140 q^{60} + 16 q^{62} + 604 q^{63} - 96 q^{64} + 788 q^{65} - 360 q^{66} - 30 q^{67} + 60 q^{68} + 288 q^{69} - 48 q^{70} - 66 q^{71} + 32 q^{72} + 346 q^{73} + 176 q^{74} + 930 q^{75} - 264 q^{76} - 1100 q^{77} - 1144 q^{78} + 62 q^{79} - 216 q^{80} - 460 q^{81} - 384 q^{82} - 1146 q^{83} - 68 q^{84} - 220 q^{85} - 484 q^{86} - 572 q^{87} - 24 q^{88} - 430 q^{89} - 704 q^{90} - 440 q^{91} - 440 q^{93} + 862 q^{95} + 814 q^{97} + 792 q^{98} + 942 q^{99}+O(q^{100}) \) 48 * q + 6 * q^3 - 24 * q^4 + 6 * q^5 + 18 * q^7 - 44 * q^9 + 16 * q^10 - 4 * q^11 + 12 * q^12 + 48 * q^13 - 24 * q^14 - 70 * q^15 - 48 * q^16 + 70 * q^17 + 16 * q^18 + 38 * q^19 + 12 * q^20 - 24 * q^21 - 52 * q^22 - 50 * q^23 - 242 * q^25 - 168 * q^26 - 270 * q^27 - 64 * q^28 - 40 * q^29 - 26 * q^31 + 126 * q^33 + 112 * q^34 + 300 * q^35 + 152 * q^36 + 504 * q^37 + 264 * q^38 + 122 * q^39 - 48 * q^40 + 46 * q^41 + 432 * q^42 + 100 * q^43 + 12 * q^44 - 36 * q^45 - 160 * q^46 - 336 * q^47 + 64 * q^48 + 68 * q^49 + 128 * q^50 - 518 * q^51 - 24 * q^52 - 314 * q^53 - 418 * q^55 - 8 * q^56 - 66 * q^57 + 40 * q^58 - 170 * q^59 + 140 * q^60 + 16 * q^62 + 604 * q^63 - 96 * q^64 + 788 * q^65 - 360 * q^66 - 30 * q^67 + 60 * q^68 + 288 * q^69 - 48 * q^70 - 66 * q^71 + 32 * q^72 + 346 * q^73 + 176 * q^74 + 930 * q^75 - 264 * q^76 - 1100 * q^77 - 1144 * q^78 + 62 * q^79 - 216 * q^80 - 460 * q^81 - 384 * q^82 - 1146 * q^83 - 68 * q^84 - 220 * q^85 - 484 * q^86 - 572 * q^87 - 24 * q^88 - 430 * q^89 - 704 * q^90 - 440 * q^91 - 440 * q^93 + 862 * q^95 + 814 * q^97 + 792 * q^98 + 942 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

Coefficient data

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

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

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

$2$	0.437016	+	1.34500i	0.218508	+	0.672499i
$2$	0.437016	+	1.34500i	0.218508	+	0.672499i
$3$	−0.426688	+	0.384192i	−0.142229	+	0.128064i	−0.737174	−	0.675702i	$-0.763840\pi$
$3$	−0.426688	+	0.384192i	−0.142229	+	0.128064i	0.594945	+	0.803766i	$0.297174\pi$
$4$	−1.61803	+	1.17557i	−0.404508	+	0.293893i
$5$	2.75524	+	4.77222i	0.551049	+	0.954444i	0.998199	+	0.0599855i	$0.0191054\pi$
$5$	2.75524	+	4.77222i	0.551049	+	0.954444i	−0.447151	+	0.894459i	$0.647561\pi$
$6$	−0.703206	−	0.405996i	−0.117201	−	0.0676660i
$7$	0.186434	+	1.77380i	0.0266335	+	0.253401i	0.999735	+	0.0230236i	$0.00732928\pi$
$7$	0.186434	+	1.77380i	0.0266335	+	0.253401i	−0.973101	+	0.230377i	$0.926004\pi$
$8$	−2.28825	−	1.66251i	−0.286031	−	0.207813i
$9$	−0.906297	+	8.62284i	−0.100700	+	0.958093i
$10$	−5.21454	+	5.79133i	−0.521454	+	0.579133i
$11$	7.06408	−	15.8662i	0.642189	−	1.44238i	−0.239665	−	0.970856i	$-0.577038\pi$
$11$	7.06408	−	15.8662i	0.642189	−	1.44238i	0.881853	−	0.471524i	$-0.156296\pi$
$12$	0.238751	−	1.12324i	0.0198959	−	0.0936031i
$13$	−1.57884	−	7.42786i	−0.121449	−	0.571374i	−0.996222	−	0.0868406i	$-0.972323\pi$
$13$	−1.57884	−	7.42786i	−0.121449	−	0.571374i	0.874773	−	0.484533i	$-0.161010\pi$
$14$	−2.30429	+	1.02593i	−0.164592	+	0.0732810i
$15$	−3.00908	−	0.977708i	−0.200605	−	0.0651805i
$16$	1.23607	−	3.80423i	0.0772542	−	0.237764i
$17$	−4.04394	−	9.08285i	−0.237879	−	0.534285i	0.754674	−	0.656100i	$-0.227795\pi$
$17$	−4.04394	−	9.08285i	−0.237879	−	0.534285i	−0.992553	+	0.121815i	$0.961129\pi$
$18$	−11.9938	+	2.54935i	−0.666320	+	0.141631i
$19$	21.8719	+	4.64901i	1.15115	+	0.244685i	0.743681	−	0.668534i	$-0.233078\pi$
$19$	21.8719	+	4.64901i	1.15115	+	0.244685i	0.407469	+	0.913219i	$0.366411\pi$
$20$	−10.0682	−	4.48263i	−0.503408	−	0.224132i
$21$	−0.761030	−	0.685234i	−0.0362395	−	0.0326302i
$22$	24.4271	+	2.56739i	1.11032	+	0.116699i
$23$	14.1916	−	19.5331i	0.617027	−	0.849264i	−0.380106	−	0.924943i	$-0.624112\pi$
$23$	14.1916	−	19.5331i	0.617027	−	0.849264i	0.997132	+	0.0756788i	$0.0241124\pi$
$24$	1.61509	−	0.169753i	0.0672953	−	0.00707303i
$25$	−2.68273	+	4.64662i	−0.107309	+	0.185865i
$26$	9.30047	−	5.36963i	0.357710	−	0.206524i
$27$	−5.96349	−	8.20804i	−0.220870	−	0.304001i
$28$	−2.38689	−	2.65091i	−0.0852460	−	0.0946753i
$29$	−31.0533	+	10.0898i	−1.07080	+	0.347925i	−0.790801	−	0.612074i	$-0.790336\pi$
$29$	−31.0533	+	10.0898i	−1.07080	+	0.347925i	−0.280003	+	0.959999i	$0.590336\pi$
$30$		−	4.47447i		−	0.149149i
$31$	−30.5047	+	5.51936i	−0.984023	+	0.178044i
$31$	−30.5047	+	5.51936i	−0.984023	+	0.178044i
$32$	5.65685			0.176777
$33$	3.08149	+	9.48386i	0.0933786	+	0.287390i
$34$	10.4491	−	9.40844i	0.307328	−	0.276719i
$35$	−7.95131	+	5.77697i	−0.227180	+	0.165056i
$36$	−8.67033	−	15.0175i	−0.240843	−	0.417152i
$37$	29.5776	+	17.0767i	0.799396	+	0.461531i	0.843260	−	0.537506i	$-0.180633\pi$
$37$	29.5776	+	17.0767i	0.799396	+	0.461531i	−0.0438640	+	0.999038i	$0.513967\pi$
$38$	3.30545	+	31.4493i	0.0869856	+	0.827613i
$39$	3.52739	+	2.56280i	0.0904459	+	0.0657128i
$40$	1.62918	−	15.5006i	0.0407295	−	0.387516i
$41$	−27.5480	+	30.5952i	−0.671903	+	0.746224i	−0.978643	−	0.205570i	$-0.934095\pi$
$41$	−27.5480	+	30.5952i	−0.671903	+	0.746224i	0.306739	+	0.951794i	$0.400762\pi$
$42$	0.589056	−	1.32304i	0.0140251	−	0.0315010i
$43$	−4.74031	+	22.3014i	−0.110240	+	0.518637i	0.888027	+	0.459791i	$0.152076\pi$
$43$	−4.74031	+	22.3014i	−0.110240	+	0.518637i	−0.998267	+	0.0588464i	$0.981258\pi$
$44$	7.22189	+	33.9763i	0.164134	+	0.772189i
$45$	−43.6472	+	19.4330i	−0.969937	+	0.431844i
$46$	32.4739	+	10.5514i	0.705954	+	0.229378i
$47$	6.56908	−	20.2175i	0.139768	−	0.430161i	−0.856533	−	0.516091i	$-0.827386\pi$
$47$	6.56908	−	20.2175i	0.139768	−	0.430161i	0.996301	+	0.0859309i	$0.0273864\pi$
$48$	0.934136	+	2.09810i	0.0194612	+	0.0437105i
$49$	44.8176	−	9.52628i	0.914645	−	0.194414i
$50$	−7.42209	−	1.57761i	−0.148442	−	0.0315523i
$51$	5.21506	+	2.32189i	0.102256	+	0.0455273i
$52$	11.2866	+	10.1625i	0.217050	+	0.195432i
$53$	−64.5709	−	6.78668i	−1.21832	−	0.128050i	−0.526534	−	0.850154i	$-0.676509\pi$
$53$	−64.5709	−	6.78668i	−1.21832	−	0.128050i	−0.691785	+	0.722104i	$0.743175\pi$
$54$	8.43365	−	11.6079i	0.156179	−	0.214961i
$55$	95.1801	−	10.0038i	1.73055	−	0.181888i
$56$	2.52236	−	4.36885i	0.0450421	−	0.0780151i
$57$	−11.1186	+	6.41931i	−0.195063	+	0.112619i
$58$	−27.1416	−	37.3572i	−0.467959	−	0.644090i
$59$	−14.9883	−	16.6462i	−0.254040	−	0.282139i	0.602613	−	0.798034i	$-0.294126\pi$
$59$	−14.9883	−	16.6462i	−0.254040	−	0.282139i	−0.856652	+	0.515894i	$0.827460\pi$
$60$	6.01815	−	1.95542i	0.100303	−	0.0325903i
$61$			78.4335i			1.28580i	0.765952	+	0.642898i	$0.222268\pi$
$61$			78.4335i			1.28580i	−0.765952	+	0.642898i	$0.777732\pi$
$62$	−20.7546	−	38.6167i	−0.334751	−	0.622850i
$63$	−15.4642			−0.245463
$64$	2.47214	+	7.60845i	0.0386271	+	0.118882i
$65$	31.0973	−	28.0001i	0.478420	−	0.430771i
$66$	−11.4091	+	8.28920i	−0.172865	+	0.125594i
$67$	−12.3922	−	21.4639i	−0.184958	−	0.320356i	0.758605	−	0.651551i	$-0.225881\pi$
$67$	−12.3922	−	21.4639i	−0.184958	−	0.320356i	−0.943562	+	0.331195i	$0.892548\pi$
$68$	17.2208	+	9.94242i	0.253247	+	0.146212i
$69$	1.44905	+	13.7868i	0.0210008	+	0.199809i
$70$	−11.2449	−	8.16987i	−0.160641	−	0.116712i
$71$	11.3091	−	107.599i	0.159283	−	1.51548i	−0.564489	−	0.825441i	$-0.690927\pi$
$71$	11.3091	−	107.599i	0.159283	−	1.51548i	0.723772	−	0.690039i	$-0.242407\pi$
$72$	16.4094	−	18.2244i	0.227908	−	0.253117i
$73$	31.6472	−	71.0808i	0.433524	−	0.973710i	−0.556244	−	0.831019i	$-0.687758\pi$
$73$	31.6472	−	71.0808i	0.433524	−	0.973710i	0.989767	−	0.142691i	$-0.0455755\pi$
$74$	−10.0422	+	47.2446i	−0.135705	+	0.638441i
$75$	−0.640505	−	3.01334i	−0.00854006	−	0.0401778i
$76$	−40.8547	+	18.1897i	−0.537561	+	0.239338i
$77$	29.4605	+	9.57229i	0.382604	+	0.124315i
$78$	−1.90543	+	5.86432i	−0.0244286	+	0.0751835i
$79$	−0.245637	−	0.551709i	−0.00310933	−	0.00698366i	0.911984	−	0.410226i	$-0.134550\pi$
$79$	−0.245637	−	0.551709i	−0.00310933	−	0.00698366i	−0.915093	+	0.403242i	$0.867883\pi$
$80$	21.5603	−	4.58278i	0.269503	−	0.0572847i
$81$	−70.6298	−	15.0128i	−0.871973	−	0.185344i
$82$	−53.1894	−	23.6814i	−0.648651	−	0.288798i
$83$	−95.5098	−	85.9974i	−1.15072	−	1.03611i	−0.998861	−	0.0477117i	$-0.984807\pi$
$83$	−95.5098	−	85.9974i	−1.15072	−	1.03611i	−0.151860	−	0.988402i	$-0.548526\pi$
$84$	2.03691	+	0.214088i	0.0242490	+	0.00254867i
$85$	32.2033	−	44.3241i	0.378862	−	0.521459i
$86$	−32.0669	+	3.37037i	−0.372871	+	0.0391903i
$87$	9.37365	−	16.2356i	0.107743	−	0.186616i
$88$	−42.5420	+	24.5616i	−0.483432	+	0.279109i
$89$	47.7655	+	65.7436i	0.536691	+	0.738692i	0.988132	−	0.153609i	$-0.0490897\pi$
$89$	47.7655	+	65.7436i	0.536691	+	0.738692i	−0.451441	+	0.892301i	$0.649090\pi$
$90$	−45.2118	−	50.2128i	−0.502353	−	0.557920i
$91$	12.8812	−	4.18536i	0.141552	−	0.0459930i
$92$			48.2884i			0.524874i
$93$	10.8955	−	14.0747i	0.117156	−	0.151341i
$94$	30.0633			0.319823
$95$	38.0762	+	117.187i	0.400802	+	1.23354i
$96$	−2.41371	+	2.17332i	−0.0251428	+	0.0226387i
$97$	86.3662	−	62.7487i	0.890373	−	0.646894i	−0.0456024	−	0.998960i	$-0.514521\pi$
$97$	86.3662	−	62.7487i	0.890373	−	0.646894i	0.935975	+	0.352066i	$0.114521\pi$
$98$	32.3988	+	56.1164i	0.330600	+	0.572616i
$99$	130.409	+	75.2918i	1.31727	+	0.760524i
$100$	−1.12169	−	10.6721i	−0.0112169	−	0.106721i
$101$	52.3283	+	38.0187i	0.518102	+	0.376423i	0.815888	−	0.578210i	$-0.196248\pi$
$101$	52.3283	+	38.0187i	0.518102	+	0.376423i	−0.297787	+	0.954632i	$0.596248\pi$
$102$	−0.843876	+	8.02894i	−0.00827329	+	0.0787151i
$103$	−66.6971	+	74.0747i	−0.647545	+	0.719171i	−0.974128	−	0.225997i	$-0.927436\pi$
$103$	−66.6971	+	74.0747i	−0.647545	+	0.719171i	0.326583	+	0.945168i	$0.394103\pi$
$104$	−8.73610	+	19.6216i	−0.0840009	+	0.188669i
$105$	1.17327	−	5.51979i	0.0111740	−	0.0525694i
$106$	−19.0905	−	89.8136i	−0.180099	−	0.847298i
$107$	−30.2592	+	13.4722i	−0.282796	+	0.125909i	−0.543233	−	0.839582i	$-0.682800\pi$
$107$	−30.2592	+	13.4722i	−0.282796	+	0.125909i	0.260437	+	0.965491i	$0.416133\pi$
$108$	19.2983	+	6.27038i	0.178688	+	0.0580591i
$109$	−65.9685	+	203.030i	−0.605215	+	1.86266i	−0.109913	+	0.993941i	$0.535057\pi$
$109$	−65.9685	+	203.030i	−0.605215	+	1.86266i	−0.495303	+	0.868720i	$0.664943\pi$
$110$	55.0504	+	123.645i	0.500458	+	1.12405i
$111$	−19.1811	+	4.07708i	−0.172803	+	0.0367304i
$112$	6.97840	+	1.48330i	0.0623071	+	0.0132438i
$113$	−168.601	−	75.0660i	−1.49204	−	0.664301i	−0.511265	−	0.859423i	$-0.670823\pi$
$113$	−168.601	−	75.0660i	−1.49204	−	0.664301i	−0.980779	+	0.195122i	$0.937490\pi$
$114$	−13.4929	−	12.1491i	−0.118359	−	0.106571i
$115$	132.318	+	13.9071i	1.15059	+	0.120932i
$116$	38.3840	−	52.8311i	0.330897	−	0.455440i
$117$	65.4801	−	6.88223i	0.559659	−	0.0588225i
$118$	15.8390	−	27.4339i	0.134229	−	0.232491i
$119$	15.3573	−	8.86652i	0.129053	−	0.0745086i
$120$	5.26006	+	7.23985i	0.0438338	+	0.0603321i
$121$	−120.869	−	134.239i	−0.998921	−	1.10941i
$122$	−105.493	+	34.2767i	−0.864695	+	0.280957i
$123$		−	23.6383i		−	0.192181i
$124$	42.8692	−	44.7909i	0.345720	−	0.361217i
$125$	108.196			0.865567
$126$	−6.75810	−	20.7993i	−0.0536357	−	0.165074i
$127$	−120.226	+	108.252i	−0.946660	+	0.852376i	−0.989178	−	0.146719i	$-0.953129\pi$
$127$	−120.226	+	108.252i	−0.946660	+	0.852376i	0.0425185	+	0.999096i	$0.486462\pi$
$128$	−9.15298	+	6.65003i	−0.0715077	+	0.0519534i
$129$	−6.54538	−	11.3369i	−0.0507393	−	0.0878831i
$130$	51.2501	+	29.5893i	0.394231	+	0.227610i
$131$	24.3969	+	232.121i	0.186236	+	1.77191i	0.544952	+	0.838467i	$0.316548\pi$
$131$	24.3969	+	232.121i	0.186236	+	1.77191i	−0.358716	+	0.933447i	$0.616785\pi$
$132$	−16.1349	−	11.7227i	−0.122234	−	0.0888083i
$133$	−4.16876	+	39.6631i	−0.0313441	+	0.298219i
$134$	23.4533	−	26.0475i	0.175024	−	0.194384i
$135$	22.7397	−	51.0742i	0.168442	−	0.378328i
$136$	−5.84677	+	27.5069i	−0.0429909	+	0.202256i
$137$	−45.0127	−	211.768i	−0.328560	−	1.54575i	−0.763809	−	0.645442i	$-0.776673\pi$
$137$	−45.0127	−	211.768i	−0.328560	−	1.54575i	0.435249	−	0.900310i	$-0.356660\pi$
$138$	−17.9100	+	7.97404i	−0.129782	+	0.0577829i
$139$	−83.9292	−	27.2703i	−0.603807	−	0.196189i	−0.00886954	−	0.999961i	$-0.502823\pi$
$139$	−83.9292	−	27.2703i	−0.603807	−	0.196189i	−0.594938	+	0.803772i	$0.702823\pi$
$140$	6.07426	−	18.6947i	0.0433876	−	0.133533i
$141$	4.96446	+	11.1504i	0.0352090	+	0.0790806i
$142$	149.663	−	31.8118i	1.05396	−	0.224027i
$143$	−129.005	−	27.4208i	−0.902131	−	0.191754i
$144$	31.6830	+	14.1062i	0.220021	+	0.0979595i
$145$	−133.710	−	120.393i	−0.922140	−	0.830299i
$146$	109.434	+	11.5020i	0.749547	+	0.0787806i
$147$	−15.4632	+	21.2833i	−0.105192	+	0.144784i
$148$	−67.9325	+	7.13999i	−0.459003	+	0.0482432i
$149$	39.9702	−	69.2304i	0.268256	−	0.464633i	−0.700155	−	0.713990i	$-0.746886\pi$
$149$	39.9702	−	69.2304i	0.268256	−	0.464633i	0.968412	+	0.249357i	$0.0802193\pi$
$150$	3.77302	−	2.17835i	0.0251535	−	0.0145224i
$151$	13.9135	+	19.1502i	0.0921421	+	0.126823i	0.852599	−	0.522566i	$-0.175025\pi$
$151$	13.9135	+	19.1502i	0.0921421	+	0.126823i	−0.760457	+	0.649388i	$0.775025\pi$
$152$	−42.3192	−	47.0002i	−0.278416	−	0.309212i
$153$	81.9849	−	26.6385i	0.535849	−	0.174108i
$154$			43.8075i			0.284464i
$155$	−110.387	−	130.368i	−0.712177	−	0.841084i
$156$	−8.72019			−0.0558987
$157$	31.5116	+	96.9826i	0.200711	+	0.617724i	0.999862	+	0.0165943i	$0.00528236\pi$
$157$	31.5116	+	96.9826i	0.200711	+	0.617724i	−0.799152	+	0.601129i	$0.794718\pi$
$158$	0.634700	−	0.571487i	0.00401709	−	0.00361700i
$159$	30.1590	−	21.9118i	0.189679	−	0.137810i
$160$	15.5860	+	26.9958i	0.0974125	+	0.168723i
$161$	37.2937	+	21.5315i	0.231638	+	0.133736i
$162$	−10.6741	−	101.558i	−0.0658898	−	0.626899i
$163$	−176.943	−	128.556i	−1.08554	−	0.788689i	−0.106897	−	0.994270i	$-0.534092\pi$
$163$	−176.943	−	128.556i	−1.08554	−	0.788689i	−0.978640	+	0.205581i	$0.934092\pi$
$164$	8.60685	−	81.8887i	0.0524808	−	0.499321i
$165$	−36.7688	+	40.8359i	−0.222841	+	0.247490i
$166$	73.9270	−	166.043i	0.445343	−	1.00026i
$167$	−13.5364	+	63.6839i	−0.0810565	+	0.381341i	−0.999912	−	0.0132530i	$-0.995781\pi$
$167$	−13.5364	+	63.6839i	−0.0810565	+	0.381341i	0.918856	+	0.394594i	$0.129115\pi$
$168$	0.602216	+	2.83320i	0.00358462	+	0.0168643i
$169$	101.709	−	45.2837i	0.601828	−	0.267951i
$170$	73.6891	+	23.9430i	0.433465	+	0.140841i
$171$	−59.9101	+	184.384i	−0.350351	+	1.07827i
$172$	−18.5469	−	41.6570i	−0.107831	−	0.242192i
$173$	323.474	−	68.7565i	1.86979	−	0.397437i	0.873754	−	0.486368i	$-0.161679\pi$
$173$	323.474	−	68.7565i	1.86979	−	0.397437i	0.996038	+	0.0889313i	$0.0283452\pi$
$174$	25.9333	+	5.51230i	0.149042	+	0.0316799i
$175$	−8.74235	−	3.89234i	−0.0499563	−	0.0222420i
$176$	−51.6268	−	46.4850i	−0.293334	−	0.264119i
$177$	12.7907	+	1.34435i	0.0722637	+	0.00759522i
$178$	−67.5506	+	92.9754i	−0.379498	+	0.522334i
$179$	321.946	−	33.8379i	1.79858	−	0.189038i	0.854654	−	0.519198i	$-0.173769\pi$
$179$	321.946	−	33.8379i	1.79858	−	0.189038i	0.943925	+	0.330160i	$0.107103\pi$
$180$	47.7778	−	82.7535i	0.265432	−	0.459742i
$181$	−46.7255	+	26.9770i	−0.258152	+	0.149044i	−0.623491	−	0.781830i	$-0.714286\pi$
$181$	−46.7255	+	26.9770i	−0.258152	+	0.149044i	0.365339	+	0.930874i	$0.380953\pi$
$182$	11.2586	+	15.4961i	0.0618604	+	0.0851435i
$183$	−30.1335	−	33.4666i	−0.164664	−	0.182878i
$184$	−64.9478	+	21.1028i	−0.352977	+	0.114689i
$185$			188.201i			1.01730i
$186$	23.6919	+	8.50354i	0.127376	+	0.0457180i
$187$	−172.677			−0.923405
$188$	13.1382	+	40.4351i	0.0698838	+	0.215080i
$189$	13.4477	−	12.1083i	0.0711516	−	0.0640652i
$190$	−140.976	+	102.425i	−0.741977	+	0.539078i
$191$	−103.031	−	178.456i	−0.539431	−	0.934322i	−0.998935	−	0.0461463i	$-0.985306\pi$
$191$	−103.031	−	178.456i	−0.539431	−	0.934322i	0.459503	−	0.888176i	$-0.348027\pi$
$192$	−3.97793	−	2.29666i	−0.0207184	−	0.0119618i
$193$	−3.56128	−	33.8833i	−0.0184522	−	0.175561i	0.981414	−	0.191901i	$-0.0614653\pi$
$193$	−3.56128	−	33.8833i	−0.0184522	−	0.175561i	−0.999866	+	0.0163400i	$0.994799\pi$
$194$	122.140	+	88.7400i	0.629589	+	0.457423i
$195$	−2.51143	+	23.8946i	−0.0128791	+	0.122537i
$196$	−61.3176	+	68.1001i	−0.312845	+	0.347449i
$197$	−52.4360	+	117.773i	−0.266173	+	0.597833i	−0.996344	−	0.0854305i	$-0.972773\pi$
$197$	−52.4360	+	117.773i	−0.266173	+	0.597833i	0.730172	+	0.683264i	$0.239440\pi$
$198$	−44.2763	+	208.304i	−0.223618	+	1.05204i
$199$	38.5241	+	181.241i	0.193588	+	0.910761i	0.962474	+	0.271375i	$0.0874783\pi$
$199$	38.5241	+	181.241i	0.193588	+	0.910761i	−0.768885	+	0.639387i	$0.779188\pi$
$200$	13.8638	−	6.17255i	0.0693189	−	0.0308628i
$201$	13.5338	+	4.39741i	0.0673325	+	0.0218776i
$202$	−28.2668	+	86.9961i	−0.139934	+	0.430674i
$203$	−23.6868	−	53.2014i	−0.116684	−	0.262076i
$204$	−11.1677	+	2.37377i	−0.0547436	+	0.0116361i
$205$	−221.908	−	47.1681i	−1.08248	−	0.230088i
$206$	−128.778	−	57.3356i	−0.625135	−	0.278328i
$207$	155.569	+	140.075i	0.751540	+	0.676690i
$208$	−30.2088	−	3.17507i	−0.145235	−	0.0152648i
$209$	228.267	−	314.182i	1.09218	−	1.50326i
$210$	7.93684	−	0.834195i	0.0377945	−	0.00397236i
$211$	−59.9996	+	103.922i	−0.284358	+	0.492523i	−0.972453	−	0.233098i	$-0.925114\pi$
$211$	−59.9996	+	103.922i	−0.284358	+	0.492523i	0.688095	+	0.725621i	$0.258447\pi$
$212$	112.456	−	64.9266i	0.530453	−	0.306257i
$213$	36.5132	+	50.2561i	0.171423	+	0.235944i
$214$	−31.3439	−	34.8109i	−0.146467	−	0.162668i
$215$	−119.488	+	38.8240i	−0.555758	+	0.180577i
$216$			28.6964i			0.132853i
$217$	−15.4774	−	53.0804i	−0.0713244	−	0.244610i
$218$	−301.904			−1.38488
$219$	13.8052	+	42.4879i	0.0630373	+	0.194009i
$220$	−142.244	+	128.077i	−0.646566	+	0.582170i
$221$	−61.0814	+	44.3782i	−0.276386	+	0.200806i
$222$	−13.8661	−	24.0168i	−0.0624600	−	0.108184i
$223$	311.331	+	179.747i	1.39610	+	0.806040i	0.993982	−	0.109547i	$-0.0349400\pi$
$223$	311.331	+	179.747i	1.39610	+	0.806040i	0.402120	+	0.915587i	$0.368273\pi$
$224$	1.05463	+	10.0342i	0.00470818	+	0.0447953i
$225$	−37.6357	−	27.3439i	−0.167270	−	0.121529i
$226$	27.2822	−	259.573i	0.120718	−	1.14855i
$227$	0.196750	−	0.218513i	0.000866740	−	0.000962612i	−0.742711	−	0.669612i	$-0.766461\pi$
$227$	0.196750	−	0.218513i	0.000866740	−	0.000962612i	0.743578	+	0.668649i	$0.233127\pi$
$228$	10.4439	−	23.4573i	0.0458065	−	0.102883i
$229$	−73.2814	+	344.762i	−0.320006	+	1.50551i	0.464602	+	0.885519i	$0.346197\pi$
$229$	−73.2814	+	344.762i	−0.320006	+	1.50551i	−0.784609	+	0.619991i	$0.787136\pi$
$230$	39.1198	+	184.044i	0.170086	+	0.800193i
$231$	−16.2480	+	7.23408i	−0.0703377	+	0.0313164i
$232$	87.8320	+	28.5384i	0.378586	+	0.123010i
$233$	105.963	−	326.120i	0.454775	−	1.39965i	−0.416623	−	0.909079i	$-0.636787\pi$
$233$	105.963	−	326.120i	0.454775	−	1.39965i	0.871399	−	0.490575i	$-0.163213\pi$
$234$	37.8724	+	85.0629i	0.161848	+	0.363517i
$235$	114.582	−	24.3552i	0.487583	−	0.103639i
$236$	43.8204	+	9.31432i	0.185680	+	0.0394675i
$237$	0.316772	+	0.141036i	0.00133659	+	0.000595089i
$238$	18.6368	+	16.7807i	0.0783059	+	0.0705070i
$239$	−16.5102	−	1.73529i	−0.0690803	−	0.00726064i	0.0699252	−	0.997552i	$-0.477724\pi$
$239$	−16.5102	−	1.73529i	−0.0690803	−	0.00726064i	−0.139006	+	0.990292i	$0.544391\pi$
$240$	−7.43884	+	10.2387i	−0.0309952	+	0.0426612i
$241$	160.500	−	16.8692i	0.665974	−	0.0699967i	0.234492	−	0.972118i	$-0.424657\pi$
$241$	160.500	−	16.8692i	0.665974	−	0.0699967i	0.431482	+	0.902121i	$0.357991\pi$
$242$	127.729	−	221.234i	0.527807	−	0.914189i
$243$	114.983	−	66.3852i	0.473179	−	0.273190i
$244$	−92.2041	−	126.908i	−0.377886	−	0.520115i
$245$	168.945	+	187.632i	0.689571	+	0.765846i
$246$	31.7935	−	10.3303i	0.129242	−	0.0419932i
$247$		−	169.801i		−	0.687454i
$248$	78.9782	+	38.0846i	0.318461	+	0.153567i
$249$	73.7924			0.296355
$250$	47.2833	+	145.523i	0.189133	+	0.582093i
$251$	−14.1257	+	12.7188i	−0.0562777	+	0.0506726i	−0.696790	−	0.717276i	$-0.745389\pi$
$251$	−14.1257	+	12.7188i	−0.0562777	+	0.0506726i	0.640512	+	0.767948i	$0.278722\pi$
$252$	25.0216	−	18.1792i	0.0992920	−	0.0721399i
$253$	−209.665	−	363.150i	−0.828714	−	1.43537i
$254$	−198.139	−	114.396i	−0.780074	−	0.450376i
$255$	3.28816	+	31.2848i	0.0128948	+	0.122685i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	−40.0679	+	381.221i	−0.155906	+	1.48335i	0.584612	+	0.811313i	$0.301247\pi$
$257$	−40.0679	+	381.221i	−0.155906	+	1.48335i	−0.740518	+	0.672036i	$0.765420\pi$
$258$	12.3877	−	13.7579i	0.0480143	−	0.0533253i
$259$	−24.7764	+	55.6486i	−0.0956616	+	0.214860i
$260$	−17.4003	+	81.8622i	−0.0669244	+	0.314855i
$261$	−58.8595	−	276.912i	−0.225515	−	1.06097i
$262$	−301.540	+	134.254i	−1.15092	+	0.512421i
$263$	−187.778	−	61.0129i	−0.713986	−	0.231988i	−0.0705721	−	0.997507i	$-0.522482\pi$
$263$	−187.778	−	61.0129i	−0.713986	−	0.231988i	−0.643414	+	0.765519i	$0.722482\pi$
$264$	8.71578	−	26.8244i	0.0330143	−	0.101608i
$265$	−145.521	−	326.846i	−0.549136	−	1.23338i
$266$	−55.1686	+	11.7265i	−0.207401	+	0.0440844i
$267$	−45.6391	−	9.70089i	−0.170933	−	0.0363329i
$268$	45.2832	+	20.1614i	0.168967	+	0.0752291i
$269$	66.0590	+	59.4798i	0.245572	+	0.221114i	0.782720	−	0.622374i	$-0.213832\pi$
$269$	66.0590	+	59.4798i	0.245572	+	0.221114i	−0.537148	+	0.843488i	$0.680498\pi$
$270$	78.6323	+	8.26459i	0.291231	+	0.0306096i
$271$	164.769	−	226.786i	0.608005	−	0.836847i	−0.388406	−	0.921488i	$-0.626974\pi$
$271$	164.769	−	226.786i	0.608005	−	0.836847i	0.996412	+	0.0846408i	$0.0269743\pi$
$272$	−39.5518	+	4.15706i	−0.145411	+	0.0152833i
$273$	−3.88828	+	6.73470i	−0.0142428	+	0.0246692i
$274$	265.156	−	153.088i	0.967723	−	0.558715i
$275$	54.7731	+	75.3887i	0.199175	+	0.274141i
$276$	−18.5520	−	20.6041i	−0.0672174	−	0.0746525i
$277$	−248.558	+	80.7615i	−0.897322	+	0.291558i	−0.721131	−	0.692798i	$-0.756378\pi$
$277$	−248.558	+	80.7615i	−0.897322	+	0.291558i	−0.176191	+	0.984356i	$0.556378\pi$
$278$		−	124.802i		−	0.448928i
$279$	−19.9463	−	268.039i	−0.0714920	−	0.960714i
$280$	27.7988			0.0992815
$281$	96.9514	+	298.386i	0.345023	+	1.06187i	0.961572	+	0.274554i	$0.0885303\pi$
$281$	96.9514	+	298.386i	0.345023	+	1.06187i	−0.616549	+	0.787317i	$0.711470\pi$
$282$	−12.8277	+	11.5501i	−0.0454882	+	0.0409577i
$283$	223.966	−	162.721i	0.791399	−	0.574985i	−0.116979	−	0.993134i	$-0.537321\pi$
$283$	223.966	−	162.721i	0.791399	−	0.574985i	0.908378	+	0.418149i	$0.137321\pi$
$284$	108.192	+	187.394i	0.380957	+	0.659836i
$285$	−61.2687	−	35.3735i	−0.214978	−	0.124118i
$286$	−19.4962	−	185.494i	−0.0681686	−	0.648581i
$287$	−59.4058	−	43.1608i	−0.206989	−	0.150386i
$288$	−5.12679	+	48.7781i	−0.0178013	+	0.169369i
$289$	127.234	−	141.308i	0.440256	−	0.488954i
$290$	103.495	−	232.454i	0.356880	−	0.801565i
$291$	−12.7439	+	59.9553i	−0.0437934	+	0.206032i
$292$	32.3543	+	152.215i	0.110802	+	0.521283i
$293$	−107.218	+	47.7366i	−0.365932	+	0.162923i	−0.581462	−	0.813574i	$-0.697519\pi$
$293$	−107.218	+	47.7366i	−0.365932	+	0.162923i	0.215529	+	0.976497i	$0.430852\pi$
$294$	−35.3836	−	11.4968i	−0.120353	−	0.0391049i
$295$	38.1430	−	117.392i	0.129298	−	0.397939i
$296$	−39.2908	−	88.2487i	−0.132739	−	0.298137i
$297$	−172.357	+	36.6355i	−0.580325	+	0.123352i
$298$	110.582	+	23.5050i	0.371081	+	0.0788758i
$299$	−167.495	−	74.5737i	−0.560185	−	0.249410i
$300$	4.57875	+	4.12273i	0.0152625	+	0.0137424i
$301$	−40.4421	−	4.25063i	−0.134359	−	0.0141217i
$302$	−19.6766	+	27.0825i	−0.0651543	+	0.0896772i
$303$	−36.9343	+	3.88195i	−0.121895	+	0.0128117i
$304$	44.7210	−	77.4590i	0.147109	−	0.254799i
$305$	−374.302	+	216.103i	−1.22722	+	0.708536i
$306$	71.6575	+	98.6280i	0.234175	+	0.322314i
$307$	33.9312	+	37.6844i	0.110525	+	0.122750i	0.795869	−	0.605469i	$-0.207015\pi$
$307$	33.9312	+	37.6844i	0.110525	+	0.122750i	−0.685344	+	0.728220i	$0.740348\pi$
$308$	−58.9209	+	19.1446i	−0.191302	+	0.0621577i
$309$		−	57.2312i		−	0.185214i
$310$	127.103	−	205.444i	0.410011	−	0.662722i
$311$	−24.4687			−0.0786776			−0.0393388	−	0.999226i	$-0.512525\pi$
$311$	−24.4687			−0.0786776			−0.0393388	+	0.999226i	$0.512525\pi$
$312$	−3.81086	−	11.7286i	−0.0122143	−	0.0375918i
$313$	−43.7221	+	39.3676i	−0.139687	+	0.125775i	−0.736012	−	0.676968i	$-0.763294\pi$
$313$	−43.7221	+	39.3676i	−0.139687	+	0.125775i	0.596325	+	0.802743i	$0.296627\pi$
$314$	−116.670	+	84.7659i	−0.371561	+	0.269955i
$315$	−42.6076	−	73.7985i	−0.135262	−	0.234281i
$316$	1.04602	+	0.603921i	0.00331020	+	0.00191114i
$317$	45.8213	+	435.961i	0.144547	+	1.37527i	0.790766	+	0.612119i	$0.209682\pi$
$317$	45.8213	+	435.961i	0.144547	+	1.37527i	−0.646219	+	0.763152i	$0.723651\pi$
$318$	42.6513	+	30.9880i	0.134124	+	0.0974464i
$319$	−59.2759	+	563.973i	−0.185818	+	1.76794i
$320$	−29.4979	+	32.7607i	−0.0921809	+	0.102377i
$321$	7.73529	−	17.3738i	0.0240975	−	0.0541239i
$322$	−12.6619	+	59.5695i	−0.0393226	+	0.184998i
$323$	−46.2224	−	217.459i	−0.143103	−	0.673248i
$324$	131.930	−	58.7390i	0.407191	−	0.181293i
$325$	38.7500	+	12.5906i	0.119231	+	0.0387404i
$326$	95.5811	−	294.168i	0.293194	−	0.902357i
$327$	−49.8545	−	111.975i	−0.152460	−	0.342431i
$328$	113.901	−	24.2105i	0.347260	−	0.0738125i
$329$	37.0867	+	7.88301i	0.112725	+	0.0239605i
$330$	−70.9927	−	31.6080i	−0.215130	−	0.0957818i
$331$	12.6602	+	11.3993i	0.0382482	+	0.0344389i	0.688033	−	0.725679i	$-0.258474\pi$
$331$	12.6602	+	11.3993i	0.0382482	+	0.0344389i	−0.649785	+	0.760118i	$0.725141\pi$
$332$	255.634	+	26.8682i	0.769983	+	0.0809284i
$333$	−174.055	+	239.567i	−0.522689	+	0.719420i
$334$	−91.5703	+	9.62443i	−0.274163	+	0.0288156i
$335$	68.2869	−	118.276i	0.203841	−	0.353064i
$336$	−3.54747	+	2.04813i	−0.0105579	+	0.00609563i
$337$	234.141	+	322.267i	0.694780	+	0.956283i	0.999992	+	0.00399855i	$0.00127278\pi$
$337$	234.141	+	322.267i	0.694780	+	0.956283i	−0.305212	+	0.952285i	$0.598727\pi$
$338$	105.355	+	117.008i	0.311701	+	0.346179i
$339$	100.780	−	32.7453i	0.297285	−	0.0965939i
$340$			109.575i			0.322280i
$341$	−127.916	+	522.982i	−0.375121	+	1.53367i
$342$	−274.178			−0.801690
$343$	52.2599	+	160.839i	0.152361	+	0.468919i
$344$	47.9232	−	43.1503i	0.139312	−	0.125437i
$345$	−61.8013	+	44.9013i	−0.179134	+	0.130149i
$346$	233.841	+	405.024i	0.675840	+	1.17059i
$347$	−232.781	−	134.396i	−0.670837	−	0.387308i	0.125557	−	0.992086i	$-0.459928\pi$
$347$	−232.781	−	134.396i	−0.670837	−	0.387308i	−0.796394	+	0.604778i	$0.793262\pi$
$348$	3.91925	+	37.2892i	0.0112622	+	0.107153i
$349$	−35.8885	−	26.0746i	−0.102833	−	0.0747122i	0.535181	−	0.844738i	$-0.320244\pi$
$349$	−35.8885	−	26.0746i	−0.102833	−	0.0747122i	−0.638013	+	0.770025i	$0.720244\pi$
$350$	1.41465	−	13.4594i	0.00404184	−	0.0384556i
$351$	−51.5527	+	57.2551i	−0.146874	+	0.163120i
$352$	39.9604	−	89.7526i	0.113524	−	0.254979i
$353$	−21.2898	+	100.160i	−0.0603109	+	0.283741i	−0.997960	−	0.0638429i	$-0.979664\pi$
$353$	−21.2898	+	100.160i	−0.0603109	+	0.283741i	0.937649	+	0.347584i	$0.112998\pi$
$354$	3.78158	+	17.7909i	0.0106824	+	0.0502569i
$355$	544.646	−	242.492i	1.53421	−	0.683076i
$356$	−154.572	−	50.2236i	−0.434192	−	0.141078i
$357$	−3.14632	+	9.68337i	−0.00881321	+	0.0271243i
$358$	186.207	+	418.228i	0.520132	+	1.16824i
$359$	−262.393	+	55.7733i	−0.730899	+	0.155357i	−0.558305	−	0.829636i	$-0.688548\pi$
$359$	−262.393	+	55.7733i	−0.730899	+	0.155357i	−0.172594	+	0.984993i	$0.555215\pi$
$360$	132.183	+	28.0963i	0.367175	+	0.0780454i
$361$	126.975	+	56.5331i	0.351732	+	0.156601i
$362$	−56.7037	−	51.0563i	−0.156640	−	0.141039i
$363$	103.147	+	10.8412i	0.284152	+	0.0298656i
$364$	−15.9221	+	21.9148i	−0.0437419	+	0.0602056i
$365$	426.409	−	44.8174i	1.16824	−	0.122787i
$366$	31.8437	−	55.1549i	0.0870046	−	0.150696i
$367$	403.000	−	232.672i	1.09809	−	0.633984i	0.162373	−	0.986730i	$-0.448085\pi$
$367$	403.000	−	232.672i	1.09809	−	0.633984i	0.935719	+	0.352746i	$0.114752\pi$
$368$	−56.7665	−	78.1323i	−0.154257	−	0.212316i
$369$	−238.851	−	265.270i	−0.647292	−	0.718890i
$370$	−253.130	+	82.2470i	−0.684136	+	0.222289i
$371$		−	115.801i		−	0.312133i
$372$	−1.08349	+	35.5818i	−0.00291260	+	0.0956499i
$373$	40.1576			0.107661			0.0538306	−	0.998550i	$-0.482857\pi$
$373$	40.1576			0.107661			0.0538306	+	0.998550i	$0.482857\pi$
$374$	−75.4625	−	232.250i	−0.201771	−	0.620989i
$375$	−46.1659	+	41.5679i	−0.123109	+	0.110848i
$376$	−48.6435	+	35.3416i	−0.129371	+	0.0939935i
$377$	123.974	+	214.729i	0.328844	+	0.569574i
$378$	22.1625	+	12.7955i	0.0586309	+	0.0338506i
$379$	−28.8048	−	274.059i	−0.0760020	−	0.723111i	−0.964474	−	0.264179i	$-0.914899\pi$
$379$	−28.8048	−	274.059i	−0.0760020	−	0.723111i	0.888472	−	0.458932i	$-0.151768\pi$
$380$	−199.370	−	144.851i	−0.524657	−	0.381186i
$381$	9.70947	−	92.3795i	0.0254842	−	0.242466i
$382$	194.996	−	216.565i	0.510460	−	0.566924i
$383$	−106.694	+	239.638i	−0.278574	+	0.625687i	−0.997596	−	0.0693004i	$-0.977923\pi$
$383$	−106.694	+	239.638i	−0.278574	+	0.625687i	0.719022	+	0.694987i	$0.244590\pi$
$384$	1.35058	−	6.35399i	0.00351714	−	0.0165468i
$385$	35.4897	+	166.966i	0.0921810	+	0.433678i
$386$	44.0166	−	19.5974i	0.114033	−	0.0507706i
$387$	−188.005	−	61.0866i	−0.485802	−	0.157846i
$388$	−65.9779	+	203.059i	−0.170046	+	0.523348i
$389$	−189.542	−	425.718i	−0.487254	−	1.09439i	−0.975162	−	0.221495i	$-0.928906\pi$
$389$	−189.542	−	425.718i	−0.487254	−	1.09439i	0.487908	−	0.872895i	$-0.337760\pi$
$390$	−33.2357	+	7.06447i	−0.0852198	+	0.0181140i
$391$	−234.806	−	49.9096i	−0.600527	−	0.127646i
$392$	−118.391	−	52.7112i	−0.302018	−	0.134467i
$393$	−99.5887	−	89.6701i	−0.253406	−	0.228168i
$394$	−181.320	−	19.0575i	−0.460203	−	0.0483693i
$395$	1.95609	−	2.69233i	0.00495213	−	0.00681602i
$396$	−299.518	+	31.4806i	−0.756357	+	0.0794964i
$397$	−52.0211	+	90.1032i	−0.131036	+	0.226960i	−0.924076	−	0.382209i	$-0.875164\pi$
$397$	−52.0211	+	90.1032i	−0.131036	+	0.226960i	0.793040	+	0.609169i	$0.208497\pi$
$398$	−226.934	+	131.020i	−0.570185	+	0.329196i
$399$	−13.4595	−	18.5254i	−0.0337330	−	0.0464295i
$400$	14.3608	+	15.9492i	0.0359019	+	0.0398731i
$401$	2.33150	−	0.757549i	0.00581421	−	0.00188915i	−0.306108	−	0.951997i	$-0.599027\pi$
$401$	2.33150	−	0.757549i	0.00581421	−	0.00188915i	0.311923	+	0.950107i	$0.399027\pi$
$402$			20.1247i			0.0500614i
$403$	89.1591	+	217.870i	0.221238	+	0.540621i
$404$	−129.363			−0.320204
$405$	−122.958	−	378.425i	−0.303599	−	0.934383i
$406$	61.2042	−	55.1085i	0.150749	−	0.135735i
$407$	479.880	−	348.653i	1.17907	−	0.856642i
$408$	−8.07317	−	13.9831i	−0.0197872	−	0.0342724i
$409$	−494.758	−	285.649i	−1.20968	−	0.698408i	−0.246989	−	0.969018i	$-0.579441\pi$
$409$	−494.758	−	285.649i	−1.20968	−	0.698408i	−0.962689	+	0.270611i	$0.912774\pi$
$410$	−33.5366	−	319.079i	−0.0817966	−	0.778243i
$411$	100.566	+	73.0654i	0.244686	+	0.177775i
$412$	20.8382	−	198.262i	0.0505782	−	0.481220i
$413$	26.7328	−	29.6898i	0.0647284	−	0.0718881i
$414$	−120.414	+	270.454i	−0.290855	+	0.653272i
$415$	147.246	−	692.738i	0.354810	−	1.66925i
$416$	−8.93126	−	42.0183i	−0.0214694	−	0.101006i
$417$	46.2886	−	20.6090i	0.111004	−	0.0494221i
$418$	522.330	+	169.715i	1.24959	+	0.406017i
$419$	−208.260	+	640.958i	−0.497040	+	1.52973i	0.316712	+	0.948522i	$0.397421\pi$
$419$	−208.260	+	640.958i	−0.497040	+	1.52973i	−0.813753	+	0.581211i	$0.802579\pi$
$420$	4.59052	+	10.3105i	0.0109298	+	0.0245487i
$421$	486.948	−	103.504i	1.15665	−	0.245853i	0.410644	−	0.911796i	$-0.365304\pi$
$421$	486.948	−	103.504i	1.15665	−	0.245853i	0.746002	+	0.665943i	$0.231971\pi$
$422$	−165.996	−	35.2836i	−0.393356	−	0.0836103i
$423$	168.379	+	74.9672i	0.398059	+	0.177227i
$424$	136.471	+	122.879i	0.321866	+	0.289809i
$425$	53.0534	+	5.57613i	0.124831	+	0.0131203i
$426$	−51.6374	+	71.0728i	−0.121215	+	0.166838i
$427$	−139.126	+	14.6227i	−0.325821	+	0.0342452i
$428$	33.1228	−	57.3703i	0.0773897	−	0.134043i
$429$	65.5796	−	37.8624i	0.152866	−	0.0882573i
$430$	−104.436	−	143.744i	−0.242875	−	0.334289i
$431$	380.355	+	422.427i	0.882493	+	0.980108i	0.999916	−	0.0129740i	$-0.00412987\pi$
$431$	380.355	+	422.427i	0.882493	+	0.980108i	−0.117423	+	0.993082i	$0.537463\pi$
$432$	−38.5965	+	12.5408i	−0.0893438	+	0.0290295i
$433$		−	472.634i		−	1.09153i	−0.837937	−	0.545767i	$-0.816239\pi$
$433$		−	472.634i		−	1.09153i	0.837937	−	0.545767i	$-0.183761\pi$
$434$	64.6291	−	44.0140i	0.148915	−	0.101415i
$435$	103.307			0.237487
$436$	−131.937	−	406.060i	−0.302608	−	0.931331i
$437$	401.207	−	361.248i	0.918093	−	0.826654i
$438$	−51.1131	+	37.1358i	−0.116697	+	0.0847850i
$439$	−272.561	−	472.089i	−0.620867	−	1.07537i	−0.989325	−	0.145729i	$-0.953447\pi$
$439$	−272.561	−	472.089i	−0.620867	−	1.07537i	0.368457	−	0.929645i	$-0.379886\pi$
$440$	−234.427	−	135.346i	−0.532789	−	0.307606i
$441$	41.5255	+	395.089i	0.0941621	+	0.895892i
$442$	−86.3821	−	62.7603i	−0.195435	−	0.141992i
$443$	53.5001	−	509.019i	0.120768	−	1.14903i	−0.751409	−	0.659836i	$-0.770626\pi$
$443$	53.5001	−	509.019i	0.120768	−	1.14903i	0.872177	−	0.489191i	$-0.162708\pi$
$444$	26.2428	−	29.1456i	0.0591055	−	0.0656433i
$445$	−182.137	+	409.087i	−0.409297	+	0.919297i
$446$	−105.702	+	497.291i	−0.237001	+	1.11500i
$447$	9.54293	+	44.8960i	0.0213488	+	0.100438i
$448$	−13.0350	+	5.80356i	−0.0290960	+	0.0129544i
$449$	−280.654	−	91.1900i	−0.625064	−	0.203096i	−0.0206768	−	0.999786i	$-0.506582\pi$
$449$	−280.654	−	91.1900i	−0.625064	−	0.203096i	−0.604387	+	0.796691i	$0.706582\pi$
$450$	20.3301	−	62.5697i	0.0451780	−	0.139044i
$451$	290.827	+	653.208i	0.644850	+	1.44836i
$452$	361.047	−	76.7430i	0.798778	−	0.169785i
$453$	−13.2941	−	2.82574i	−0.0293467	−	0.00623784i
$454$	0.379882	+	0.169134i	0.000836745	+	0.000372543i
$455$	55.4643	+	49.9403i	0.121900	+	0.109759i
$456$	36.1142	+	3.79575i	0.0791978	+	0.00832402i
$457$	−326.719	+	449.689i	−0.714920	+	0.984003i	0.284757	+	0.958600i	$0.408087\pi$
$457$	−326.719	+	449.689i	−0.714920	+	0.984003i	−0.999677	+	0.0254035i	$0.991913\pi$
$458$	−495.729	+	52.1032i	−1.08238	+	0.113762i
$459$	−50.4363	+	87.3583i	−0.109883	+	0.190323i
$460$	−230.443	+	133.046i	−0.500963	+	0.289231i
$461$	−228.195	−	314.084i	−0.495000	−	0.681309i	0.486300	−	0.873792i	$-0.338346\pi$
$461$	−228.195	−	314.084i	−0.495000	−	0.681309i	−0.981300	+	0.192482i	$0.938346\pi$
$462$	−16.8305	−	18.6921i	−0.0364296	−	0.0404591i
$463$	720.192	−	234.005i	1.55549	−	0.505410i	0.599892	−	0.800081i	$-0.295210\pi$
$463$	720.192	−	234.005i	1.55549	−	0.505410i	0.955599	+	0.294672i	$0.0952102\pi$
$464$			130.606i			0.281478i
$465$	97.1873	+	13.2165i	0.209005	+	0.0284226i
$466$	484.937			1.04064
$467$	−121.868	−	375.071i	−0.260960	−	0.803151i	−0.992597	−	0.121457i	$-0.961243\pi$
$467$	−121.868	−	375.071i	−0.260960	−	0.803151i	0.731637	−	0.681694i	$-0.238757\pi$
$468$	−97.8585	+	88.1121i	−0.209099	+	0.188274i
$469$	35.7624	−	25.9829i	0.0762524	−	0.0554006i
$470$	82.8318	+	143.469i	0.176238	+	0.305253i
$471$	−50.7055	−	29.2748i	−0.107655	−	0.0621546i
$472$	6.62250	+	63.0089i	0.0140307	+	0.133493i
$473$	320.352	+	232.749i	0.677277	+	0.492070i
$474$	−0.0512586	+	0.487693i	−0.000108141	+	0.00102889i
$475$	−80.2784	+	89.1582i	−0.169007	+	0.187702i
$476$	−14.4254	+	32.3999i	−0.0303054	+	0.0680670i
$477$	117.041	−	550.634i	0.245369	−	1.15437i
$478$	−4.88126	−	22.9645i	−0.0102118	−	0.0480429i
$479$	−317.760	+	141.476i	−0.663381	+	0.295356i	−0.710671	−	0.703525i	$-0.751608\pi$
$479$	−317.760	+	141.476i	−0.663381	+	0.295356i	0.0472893	+	0.998881i	$0.484942\pi$
$480$	−17.0219	−	5.53075i	−0.0354623	−	0.0115224i
$481$	80.1446	−	246.660i	0.166621	−	0.512806i
$482$	92.8300	+	208.500i	0.192593	+	0.432572i
$483$	−24.1850	+	5.14068i	−0.0500724	+	0.0106432i
$484$	353.379	+	75.1129i	0.730121	+	0.155192i
$485$	537.410	+	239.270i	1.10806	+	0.493341i
$486$	139.537	+	125.640i	0.287113	+	0.258518i
$487$	−582.754	−	61.2500i	−1.19662	−	0.125770i	−0.514814	−	0.857302i	$-0.672139\pi$
$487$	−582.754	−	61.2500i	−1.19662	−	0.125770i	−0.681807	+	0.731532i	$0.738806\pi$
$488$	130.396	−	179.475i	0.267206	−	0.367777i
$489$	124.889	−	13.1264i	0.255398	−	0.0268434i
$490$	−178.533	+	309.229i	−0.364354	+	0.631079i
$491$	−562.376	+	324.688i	−1.14537	+	0.661278i	−0.947754	−	0.319002i	$-0.896652\pi$
$491$	−562.376	+	324.688i	−1.14537	+	0.661278i	−0.197614	+	0.980280i	$0.563319\pi$
$492$	27.7885	+	38.2476i	0.0564807	+	0.0777390i
$493$	217.222	+	241.250i	0.440613	+	0.489351i
$494$	228.382	−	74.2058i	0.462312	−	0.150214i
$495$			829.789i			1.67634i
$496$	−16.7090	+	122.869i	−0.0336874	+	0.247720i
$497$	192.968			0.388266
$498$	32.2485	+	99.2505i	0.0647559	+	0.199298i
$499$	−593.927	+	534.774i	−1.19023	+	1.07169i	−0.194362	+	0.980930i	$0.562264\pi$
$499$	−593.927	+	534.774i	−1.19023	+	1.07169i	−0.995873	+	0.0907626i	$0.971070\pi$
$500$	−175.065	+	127.192i	−0.350129	+	0.254384i
$501$	−18.6910	−	32.3737i	−0.0373074	−	0.0646182i
$502$	−23.2799	−	13.4407i	−0.0463744	−	0.0267743i
$503$	−34.7673	−	330.789i	−0.0691199	−	0.657632i	−0.973151	−	0.230166i	$-0.926073\pi$
$503$	−34.7673	−	330.789i	−0.0691199	−	0.657632i	0.904032	−	0.427466i	$-0.140594\pi$
$504$	35.3859	+	25.7093i	0.0702100	+	0.0510106i
$505$	−37.2566	+	354.473i	−0.0737754	+	0.701926i
$506$	396.809	−	440.700i	0.784207	−	0.870950i
$507$	−26.0003	+	58.3977i	−0.0512827	+	0.115183i
$508$	67.2718	−	316.489i	0.132425	−	0.623010i
$509$	124.068	+	583.696i	0.243749	+	1.14675i	0.914348	+	0.404930i	$0.132704\pi$
$509$	124.068	+	583.696i	0.243749	+	1.14675i	−0.670599	+	0.741820i	$0.733963\pi$
$510$	−40.6410	+	18.0945i	−0.0796881	+	0.0354794i
$511$	131.984	+	42.8841i	0.258285	+	0.0839219i
$512$	6.99226	−	21.5200i	0.0136568	−	0.0420312i
$513$	−92.2734	−	207.249i	−0.179870	−	0.403995i
$514$	−530.251	+	112.708i	−1.03162	+	0.219277i
$515$	−537.267	−	114.200i	−1.04324	−	0.221747i
$516$	23.9180	+	10.6490i	0.0463527	+	0.0206376i
$517$	−274.371	−	247.044i	−0.530698	−	0.477842i
$518$	−85.6749	−	9.00480i	−0.165396	−	0.0173838i
$519$	−111.607	+	153.614i	−0.215042	+	0.295980i
$520$	−117.709	+	12.3717i	−0.226363	+	0.0237917i
$521$	−113.521	+	196.625i	−0.217892	+	0.377399i	−0.954163	−	0.299287i	$-0.903251\pi$
$521$	−113.521	+	196.625i	−0.217892	+	0.377399i	0.736272	+	0.676686i	$0.236585\pi$
$522$	346.723	−	200.181i	0.664221	−	0.383488i
$523$	323.450	+	445.191i	0.618451	+	0.851225i	0.997239	−	0.0742586i	$-0.0236590\pi$
$523$	323.450	+	445.191i	0.618451	+	0.851225i	−0.378788	+	0.925484i	$0.623659\pi$
$524$	−312.349	−	346.899i	−0.596086	−	0.662021i
$525$	5.22566	−	1.69792i	0.00995364	−	0.00323413i
$526$		−	279.225i		−	0.530846i
$527$	173.491	+	254.750i	0.329205	+	0.483396i
$528$	39.8877			0.0755449
$529$	−16.6693	−	51.3029i	−0.0315110	−	0.0969809i
$530$	376.011	−	338.562i	0.709455	−	0.638796i
$531$	157.122	−	114.156i	0.295898	−	0.214982i
$532$	−39.8816	−	69.0770i	−0.0749655	−	0.129844i
$533$	270.751	+	156.318i	0.507975	+	0.293279i
$534$	−6.89735	−	65.6239i	−0.0129164	−	0.122891i
$535$	−147.664	−	107.284i	−0.276007	−	0.200531i
$536$	−7.32752	+	69.7167i	−0.0136707	+	0.130068i
$537$	−124.370	+	138.127i	−0.231602	+	0.257220i
$538$	−51.1313	+	114.843i	−0.0950395	+	0.213462i
$539$	165.449	−	778.378i	0.306956	−	1.44412i
$540$	23.2477	+	109.372i	0.0430513	+	0.202541i
$541$	165.947	−	73.8843i	0.306741	−	0.136570i	−0.247593	−	0.968864i	$-0.579640\pi$
$541$	165.947	−	73.8843i	0.306741	−	0.136570i	0.554334	+	0.832294i	$0.312973\pi$
$542$	377.033	+	122.505i	0.695633	+	0.226025i
$543$	9.57288	−	29.4623i	0.0176296	−	0.0542583i
$544$	−22.8760	−	51.3804i	−0.0420515	−	0.0944492i
$545$	−1150.66	+	244.581i	−2.11131	+	0.448773i
$546$	−10.7574	−	2.28655i	−0.0197022	−	0.00418783i
$547$	243.285	+	108.317i	0.444762	+	0.198021i	0.616883	−	0.787055i	$-0.288395\pi$
$547$	243.285	+	108.317i	0.444762	+	0.198021i	−0.172121	+	0.985076i	$0.555062\pi$
$548$	321.780	+	289.732i	0.587190	+	0.528709i
$549$	−676.319	−	71.0840i	−1.23191	−	0.129479i
$550$	−77.4609	+	106.616i	−0.140838	+	0.193847i
$551$	−726.102	+	76.3164i	−1.31779	+	0.138505i
$552$	19.6049	−	33.9567i	0.0355162	−	0.0615158i
$553$	0.932829	−	0.538569i	0.00168685	−	0.000973905i
$554$	−217.248	−	299.016i	−0.392144	−	0.539740i
$555$	−72.3054	−	80.3033i	−0.130280	−	0.144691i
$556$	167.858	−	54.5405i	0.301904	−	0.0980944i
$557$		−	293.655i		−	0.527209i	−0.964631	−	0.263604i	$-0.915089\pi$
$557$		−	293.655i		−	0.527209i	0.964631	−	0.263604i	$-0.0849113\pi$
$558$	351.795	−	143.965i	0.630457	−	0.258002i
$559$	173.136			0.309724
$560$	12.1485	+	37.3893i	0.0216938	+	0.0667666i
$561$	73.6791	−	66.3410i	0.131335	−	0.118255i
$562$	−358.959	+	260.799i	−0.638716	+	0.464055i
$563$	306.480	+	530.840i	0.544370	+	0.942877i	0.998646	+	0.0520160i	$0.0165647\pi$
$563$	306.480	+	530.840i	0.544370	+	0.942877i	−0.454276	+	0.890861i	$0.650102\pi$
$564$	−21.1407	−	12.2056i	−0.0374835	−	0.0216411i
$565$	−106.305	−	1011.43i	−0.188151	−	1.79013i
$566$	316.736	+	230.122i	0.559604	+	0.406576i
$567$	13.4620	−	128.082i	0.0237425	−	0.225895i
$568$	−204.762	+	227.412i	−0.360497	+	0.400372i
$569$	143.932	−	323.276i	0.252956	−	0.568148i	−0.741778	−	0.670646i	$-0.766017\pi$
$569$	143.932	−	323.276i	0.252956	−	0.568148i	0.994733	+	0.102498i	$0.0326837\pi$
$570$	20.8019	−	97.8651i	0.0364945	−	0.171693i
$571$	−116.220	−	546.773i	−0.203538	−	0.957571i	−0.954727	−	0.297484i	$-0.903853\pi$
$571$	−116.220	−	546.773i	−0.203538	−	0.957571i	0.751189	−	0.660087i	$-0.229481\pi$
$572$	240.969	−	107.286i	0.421275	−	0.187564i
$573$	112.523	+	36.5611i	0.196376	+	0.0638064i
$574$	32.0899	−	98.7625i	0.0559057	−	0.172060i
$575$	52.6906	+	118.345i	0.0916358	+	0.205817i
$576$	−67.8469	+	14.4213i	−0.117790	+	0.0250370i
$577$	1053.53	+	223.934i	1.82587	+	0.388100i	0.987579	−	0.157125i	$-0.0502226\pi$
$577$	1053.53	+	223.934i	1.82587	+	0.388100i	0.838290	+	0.545225i	$0.183556\pi$
$578$	245.662	+	109.376i	0.425021	+	0.189231i
$579$	14.5372	+	13.0894i	0.0251075	+	0.0226069i
$580$	357.879	+	37.6146i	0.617032	+	0.0648527i
$581$	134.736	−	185.449i	0.231904	−	0.319189i
$582$	−86.2089	+	9.06092i	−0.148125	+	0.0155686i
$583$	−563.812	+	976.552i	−0.967088	+	1.67505i
$584$	−190.589	+	110.037i	−0.326351	+	0.188419i
$585$	213.257	+	293.523i	0.364542	+	0.501749i
$586$	−111.062	−	123.346i	−0.189525	−	0.210489i
$587$	724.108	−	235.277i	1.23357	−	0.400813i	0.381566	−	0.924341i	$-0.375385\pi$
$587$	724.108	−	235.277i	1.23357	−	0.400813i	0.852008	+	0.523529i	$0.175385\pi$
$588$		−	52.6152i		−	0.0894816i
$589$	−692.854	−	21.0978i	−1.17632	−	0.0358197i
$590$	174.561			0.295866
$591$	−22.8736	−	70.3978i	−0.0387033	−	0.119116i
$592$	101.523	−	91.4121i	0.171492	−	0.154412i
$593$	319.759	−	232.319i	0.539223	−	0.391768i	−0.284573	−	0.958654i	$-0.591852\pi$
$593$	319.759	−	232.319i	0.539223	−	0.391768i	0.823796	+	0.566886i	$0.191852\pi$
$594$	−124.597	−	215.809i	−0.209760	−	0.363315i
$595$	84.6260	+	48.8588i	0.142229	+	0.0821157i
$596$	16.7121	+	159.005i	0.0280404	+	0.266787i
$597$	−86.0692	−	62.5329i	−0.144170	−	0.104745i
$598$	27.1033	−	257.870i	0.0453232	−	0.431221i
$599$	153.319	−	170.278i	0.255958	−	0.284270i	−0.601447	−	0.798913i	$-0.705409\pi$
$599$	153.319	−	170.278i	0.255958	−	0.284270i	0.857405	+	0.514643i	$0.172075\pi$
$600$	−3.54407	+	7.96010i	−0.00590678	+	0.0132668i
$601$	141.620	−	666.268i	0.235640	−	1.10860i	−0.688111	−	0.725605i	$-0.741560\pi$
$601$	141.620	−	666.268i	0.235640	−	1.10860i	0.923751	−	0.382993i	$-0.125107\pi$
$602$	−11.9567	−	56.2521i	−0.0198617	−	0.0934419i
$603$	196.310	−	87.4030i	0.325556	−	0.144947i
$604$	−45.0249	−	14.6295i	−0.0745445	−	0.0242210i
$605$	307.594	−	946.677i	0.508420	−	1.56476i
$606$	−21.3621	−	47.9801i	−0.0352510	−	0.0791750i
$607$	−841.002	+	178.761i	−1.38551	+	0.294498i	−0.839535	−	0.543306i	$-0.817172\pi$
$607$	−841.002	+	178.761i	−1.38551	+	0.294498i	−0.545971	+	0.837804i	$0.683839\pi$
$608$	123.726	+	26.2988i	0.203497	+	0.0432546i
$609$	30.5464	+	13.6001i	0.0501583	+	0.0223319i
$610$	−454.234	−	408.994i	−0.744646	−	0.670483i
$611$	−160.545	−	16.8739i	−0.262757	−	0.0276169i
$612$	−101.339	+	139.481i	−0.165587	+	0.227910i
$613$	−173.635	+	18.2497i	−0.283254	+	0.0297712i	−0.245090	−	0.969500i	$-0.578818\pi$
$613$	−173.635	+	18.2497i	−0.283254	+	0.0297712i	−0.0381637	+	0.999271i	$0.512151\pi$
$614$	−35.8569	+	62.1060i	−0.0583989	+	0.101150i
$615$	112.807	−	65.1293i	0.183426	−	0.105901i
$616$	−51.4988	−	70.8820i	−0.0836019	−	0.115068i
$617$	283.680	+	315.059i	0.459773	+	0.510630i	0.927797	−	0.373086i	$-0.121700\pi$
$617$	283.680	+	315.059i	0.459773	+	0.510630i	−0.468023	+	0.883716i	$0.655034\pi$
$618$	76.9758	−	25.0110i	0.124556	−	0.0404708i
$619$		−	504.161i		−	0.814477i	−0.913322	−	0.407239i	$-0.866492\pi$
$619$		−	504.161i		−	0.814477i	0.913322	−	0.407239i	$-0.133508\pi$
$620$	331.867	+	81.1715i	0.535270	+	0.130922i
$621$	−244.960			−0.394460
$622$	−10.6932	−	32.9104i	−0.0171917	−	0.0529106i
$623$	−107.711	+	96.9835i	−0.172891	+	0.155672i
$624$	14.1096	−	10.2512i	0.0226115	−	0.0164282i
$625$	365.174	+	632.500i	0.584279	+	1.01200i
$626$	−72.0565	−	41.6019i	−0.115106	−	0.0664566i
$627$	23.3075	+	221.756i	0.0371730	+	0.353677i
$628$	−164.997	−	119.877i	−0.262734	−	0.190887i
$629$	35.4944	−	337.706i	0.0564298	−	0.536894i
$630$	80.6386	−	89.5582i	0.127998	−	0.142156i
$631$	148.407	−	333.327i	0.235193	−	0.528251i	−0.756934	−	0.653492i	$-0.773303\pi$
$631$	148.407	−	333.327i	0.235193	−	0.528251i	0.992126	+	0.125240i	$0.0399702\pi$
$632$	−0.355144	+	1.67082i	−0.000561936	+	0.00264370i
$633$	−14.3250	−	67.3938i	−0.0226303	−	0.106467i
$634$	−566.341	+	252.151i	−0.893283	+	0.397715i
$635$	−847.853	−	275.484i	−1.33520	−	0.433833i
$636$	−23.0394	+	70.9081i	−0.0362255	+	0.111491i
$637$	−141.520	−	317.858i	−0.222166	−	0.498993i
$638$	−784.446	+	166.739i	−1.22954	+	0.261347i
$639$	917.560	+	195.033i	1.43593	+	0.305216i
$640$	−56.9541	−	25.3576i	−0.0889908	−	0.0396213i
$641$	377.729	+	340.108i	0.589280	+	0.530590i	0.908932	−	0.416945i	$-0.136899\pi$
$641$	377.729	+	340.108i	0.589280	+	0.530590i	−0.319652	+	0.947535i	$0.603566\pi$
$642$	26.7481	+	2.81134i	0.0416637	+	0.00437903i
$643$	−317.304	+	436.732i	−0.493475	+	0.679210i	−0.981024	−	0.193886i	$-0.937891\pi$
$643$	−317.304	+	436.732i	−0.493475	+	0.679210i	0.487550	+	0.873095i	$0.337891\pi$
$644$	−85.6542	+	9.00262i	−0.133003	+	0.0139792i
$645$	36.0682	−	62.4720i	0.0559197	−	0.0968557i
$646$	272.282	−	157.202i	0.421489	−	0.243347i
$647$	−709.532	−	976.587i	−1.09665	−	1.50941i	−0.839752	−	0.542970i	$-0.817300\pi$
$647$	−709.532	−	976.587i	−1.09665	−	1.50941i	−0.256897	−	0.966439i	$-0.582700\pi$
$648$	136.659	+	151.776i	0.210894	+	0.234222i
$649$	−369.991	+	120.217i	−0.570093	+	0.185235i
$650$			57.6210i			0.0886477i
$651$	26.9970	+	16.7025i	0.0414701	+	0.0256566i
$652$	437.426			0.670899
$653$	−92.3679	−	284.279i	−0.141452	−	0.435343i	0.855086	−	0.518486i	$-0.173504\pi$
$653$	−92.3679	−	284.279i	−0.141452	−	0.435343i	−0.996538	+	0.0831429i	$0.973504\pi$
$654$	128.819	−	115.989i	0.196971	−	0.177353i
$655$	−1040.51	+	755.976i	−1.58857	+	1.15416i
$656$	82.3398	+	142.617i	0.125518	+	0.217403i
$657$	584.237	+	337.309i	0.889249	+	0.513408i
$658$	5.60484	+	53.3265i	0.00851799	+	0.0810433i
$659$	571.281	+	415.060i	0.866891	+	0.629833i	0.929751	−	0.368189i	$-0.120022\pi$
$659$	571.281	+	415.060i	0.866891	+	0.629833i	−0.0628597	+	0.998022i	$0.520022\pi$
$660$	11.4877	−	109.298i	0.0174056	−	0.165603i
$661$	47.8936	−	53.1913i	0.0724563	−	0.0804709i	−0.705827	−	0.708385i	$-0.749424\pi$
$661$	47.8936	−	53.1913i	0.0724563	−	0.0804709i	0.778283	+	0.627914i	$0.216091\pi$
$662$	−9.79928	+	22.0095i	−0.0148025	+	0.0332470i
$663$	9.01295	−	42.4026i	0.0135942	−	0.0639556i
$664$	75.5785	+	355.569i	0.113823	+	0.535496i
$665$	−200.767	+	89.3873i	−0.301906	+	0.134417i
$666$	−398.282	−	129.410i	−0.598020	−	0.194309i
$667$	−243.611	+	749.758i	−0.365234	+	1.12407i
$668$	−52.9625	−	118.956i	−0.0792852	−	0.178077i
$669$	−201.898	+	42.9148i	−0.301791	+	0.0641477i
$670$	188.924	+	40.1570i	0.281976	+	0.0599358i
$671$	1244.44	+	554.060i	1.85460	+	0.825723i
$672$	−4.30503	−	3.87627i	−0.00640630	−	0.00576826i
$673$	−70.8326	−	7.44481i	−0.105249	−	0.0110621i	0.0517575	−	0.998660i	$-0.483518\pi$
$673$	−70.8326	−	7.44481i	−0.105249	−	0.0110621i	−0.157007	+	0.987598i	$0.550184\pi$
$674$	−331.125	+	455.755i	−0.491284	+	0.676194i
$675$	54.1381	−	5.69014i	0.0802045	−	0.00842983i
$676$	−111.334	+	192.837i	−0.164696	+	0.285261i
$677$	99.6314	−	57.5222i	0.147166	−	0.0849663i	−0.424609	−	0.905377i	$-0.639588\pi$
$677$	99.6314	−	57.5222i	0.147166	−	0.0849663i	0.571775	+	0.820411i	$0.306255\pi$
$678$	88.0847	+	121.238i	0.129918	+	0.178817i
$679$	127.405	+	141.498i	0.187637	+	0.208392i
$680$	−147.378	+	47.8861i	−0.216733	+	0.0704207i
$681$			0.168827i			0.000247910i
$682$	−759.311	+	56.5045i	−1.11336	+	0.0828511i
$683$	378.552			0.554249			0.277124	−	0.960834i	$-0.410619\pi$
$683$	378.552			0.554249			0.277124	+	0.960834i	$0.410619\pi$
$684$	−119.820	−	368.768i	−0.175176	−	0.539135i
$685$	886.583	−	798.283i	1.29428	−	1.16538i
$686$	−193.490	+	140.579i	−0.282056	+	0.204925i
$687$	−101.186	−	175.260i	−0.147287	−	0.255109i
$688$	78.9802	+	45.5992i	0.114797	+	0.0662780i
$689$	51.5366	+	490.338i	0.0747992	+	0.711667i
$690$	−87.4002	−	63.5000i	−0.126667	−	0.0920289i
$691$	−69.9689	+	665.709i	−0.101257	+	0.963400i	0.819451	+	0.573149i	$0.194278\pi$
$691$	−69.9689	+	665.709i	−0.101257	+	0.963400i	−0.920709	+	0.390251i	$0.872388\pi$
$692$	−442.564	+	491.517i	−0.639543	+	0.710285i
$693$	−109.240	+	245.358i	−0.157634	+	0.354051i
$694$	79.0333	−	371.822i	0.113881	−	0.535767i
$695$	−101.106	−	475.665i	−0.145476	−	0.684410i
$696$	−48.4411	+	21.5674i	−0.0695992	+	0.0309876i
$697$	389.294	+	126.489i	0.558528	+	0.181477i
$698$	19.3863	−	59.6650i	0.0277741	−	0.0854799i
$699$	80.0794	+	179.861i	0.114563	+	0.257312i
$700$	18.7211	−	3.97930i	0.0267445	−	0.00568472i
$701$	450.651	+	95.7888i	0.642869	+	0.136646i	0.517799	−	0.855502i	$-0.326751\pi$
$701$	450.651	+	95.7888i	0.642869	+	0.136646i	0.125069	+	0.992148i	$0.460085\pi$
$702$	−99.5373	−	44.3169i	−0.141791	−	0.0631294i
$703$	567.529	+	511.005i	0.807296	+	0.726892i
$704$	138.180	+	14.5233i	0.196279	+	0.0206297i
$705$	−39.5337	+	54.4135i	−0.0560762	+	0.0771823i
$706$	−144.019	+	15.1371i	−0.203994	+	0.0214406i
$707$	−57.6820	+	99.9081i	−0.0815869	+	0.141313i
$708$	−22.2761	+	12.8611i	−0.0314635	+	0.0181654i
$709$	−523.029	−	719.887i	−0.737699	−	1.01536i	−0.998748	−	0.0500298i	$-0.984068\pi$
$709$	−523.029	−	719.887i	−0.737699	−	1.01536i	0.261049	−	0.965326i	$-0.415932\pi$
$710$	564.170	+	626.574i	0.794605	+	0.882499i
$711$	4.97992	−	1.61807i	0.00700411	−	0.00227577i
$712$		−	229.848i		−	0.322820i
$713$	−325.101	+	674.179i	−0.455962	+	0.945553i
$714$	−14.3991			−0.0201668
$715$	−224.581	−	691.190i	−0.314100	−	0.966699i
$716$	−481.140	+	433.221i	−0.671984	+	0.605057i
$717$	7.71139	−	5.60265i	0.0107551	−	0.00781402i
$718$	−189.685	−	328.544i	−0.264185	−	0.457582i
$719$	379.205	+	218.934i	0.527406	+	0.304498i	0.739960	−	0.672651i	$-0.234845\pi$
$719$	379.205	+	218.934i	0.527406	+	0.304498i	−0.212553	+	0.977149i	$0.568178\pi$
$720$	19.9765	+	190.064i	0.0277452	+	0.263978i
$721$	−143.829	−	104.498i	−0.199485	−	0.144934i
$722$	−20.5466	+	195.487i	−0.0284578	+	0.270758i
$723$	−62.0023	+	68.8605i	−0.0857570	+	0.0952428i
$724$	43.8901	−	98.5787i	0.0606217	−	0.136158i
$725$	36.4240	−	171.361i	0.0502399	−	0.236360i
$726$	30.4956	+	143.470i	0.0420049	+	0.197618i
$727$	284.053	−	126.469i	0.390720	−	0.173960i	−0.201968	−	0.979392i	$-0.564734\pi$
$727$	284.053	−	126.469i	0.390720	−	0.173960i	0.592688	+	0.805432i	$0.298067\pi$
$728$	−36.4336	−	11.8380i	−0.0500461	−	0.0162610i
$729$	177.264	−	545.561i	0.243160	−	0.748370i
$730$	246.627	+	553.933i	0.337845	+	0.758813i
$731$	221.730	−	47.1301i	0.303324	−	0.0644735i
$732$	88.0994	+	18.7261i	0.120354	+	0.0255821i
$733$	−571.237	−	254.331i	−0.779314	−	0.346973i	−0.0217751	−	0.999763i	$-0.506932\pi$
$733$	−571.237	−	254.331i	−0.779314	−	0.346973i	−0.757539	+	0.652790i	$0.773598\pi$
$734$	489.060	+	440.352i	0.666295	+	0.599935i
$735$	−144.174	−	15.1532i	−0.196154	−	0.0206167i
$736$	80.2799	−	110.496i	0.109076	−	0.150130i
$737$	−428.089	+	44.9939i	−0.580853	+	0.0610501i
$738$	252.406	−	437.181i	0.342014	−	0.592386i
$739$	20.7858	−	12.0007i	0.0281270	−	0.0162391i	−0.485871	−	0.874031i	$-0.661497\pi$
$739$	20.7858	−	12.0007i	0.0281270	−	0.0162391i	0.513998	+	0.857792i	$0.328164\pi$
$740$	−221.244	−	304.516i	−0.298978	−	0.411508i
$741$	65.2362	+	72.4521i	0.0880380	+	0.0977761i
$742$	155.753	−	50.6071i	0.209909	−	0.0682036i
$743$			306.668i			0.412743i	0.978474	+	0.206372i	$0.0661655\pi$
$743$			306.668i			0.412743i	−0.978474	+	0.206372i	$0.933834\pi$
$744$	−48.3309	+	14.0925i	−0.0649608	+	0.0189415i
$745$	440.510			0.591289
$746$	17.5495	+	54.0119i	0.0235248	+	0.0724020i
$747$	828.102	−	745.627i	1.10857	−	0.998161i
$748$	279.397	−	202.994i	0.373525	−	0.271382i
$749$	−29.5385	−	51.1621i	−0.0394372	−	0.0683072i
$750$	−76.0840	−	43.9271i	−0.101445	−	0.0585695i
$751$	−79.5680	−	757.039i	−0.105949	−	1.00804i	−0.910318	−	0.413910i	$-0.864163\pi$
$751$	−79.5680	−	757.039i	−0.105949	−	1.00804i	0.804368	−	0.594131i	$-0.202504\pi$
$752$	−68.7923	−	49.9805i	−0.0914791	−	0.0664635i
$753$	1.14080	−	10.8539i	0.00151500	−	0.0144143i
$754$	−234.632	+	260.585i	−0.311183	+	0.345603i
$755$	−53.0542	+	119.162i	−0.0702704	+	0.157830i
$756$	−7.52457	+	35.4003i	−0.00995314	+	0.0468258i
$757$	227.294	+	1069.34i	0.300257	+	1.41260i	0.826823	+	0.562462i	$0.190146\pi$
$757$	227.294	+	1069.34i	0.300257	+	1.41260i	−0.526567	+	0.850134i	$0.676521\pi$
$758$	356.020	−	158.511i	0.469684	−	0.209117i
$759$	228.980	+	74.4002i	0.301687	+	0.0980240i
$760$	107.696	−	331.454i	0.141705	−	0.436123i
$761$	104.265	+	234.184i	0.137011	+	0.307732i	0.969000	−	0.247060i	$-0.0794645\pi$
$761$	104.265	+	234.184i	0.137011	+	0.307732i	−0.831989	+	0.554792i	$0.812798\pi$
$762$	128.493	−	27.3121i	0.168626	−	0.0358426i
$763$	−372.434	−	79.1634i	−0.488119	−	0.103753i
$764$	376.495	+	167.627i	0.492795	+	0.219406i
$765$	353.013	+	317.855i	0.461455	+	0.415496i
$766$	−368.939	−	38.7771i	−0.481644	−	0.0506228i
$767$	−99.9816	+	137.613i	−0.130354	+	0.179417i
$768$	9.13632	−	0.960266i	0.0118962	−	0.00125035i
$769$	−377.065	+	653.095i	−0.490331	+	0.849279i	−0.999938	−	0.0111286i	$-0.996458\pi$
$769$	−377.065	+	653.095i	−0.490331	+	0.849279i	0.509607	+	0.860407i	$0.329791\pi$
$770$	−209.059	+	120.700i	−0.271505	+	0.156754i
$771$	−129.365	−	178.056i	−0.167789	−	0.230942i
$772$	45.5945	+	50.6378i	0.0590602	+	0.0655930i
$773$	296.127	−	96.2174i	0.383087	−	0.124473i	−0.111141	−	0.993805i	$-0.535451\pi$
$773$	296.127	−	96.2174i	0.383087	−	0.124473i	0.494229	+	0.869332i	$0.335451\pi$
$774$		−	279.562i		−	0.361192i
$775$	56.1894	−	156.551i	0.0725025	−	0.202001i
$776$	−301.947			−0.389107
$777$	−10.8080	−	33.2635i	−0.0139099	−	0.0428101i
$778$	489.756	−	440.978i	0.629507	−	0.566810i
$779$	−744.764	+	541.103i	−0.956051	+	0.694612i
$780$	−24.0262	−	41.6147i	−0.0308029	−	0.0533521i
$781$	−1627.30	−	939.520i	−2.08361	−	1.20297i
$782$	−35.4858	−	337.625i	−0.0453783	−	0.431745i
$783$	268.004	+	194.716i	0.342278	+	0.248680i
$784$	19.1575	−	182.271i	0.0244356	−	0.232489i
$785$	−376.000	+	417.591i	−0.478981	+	0.531963i
$786$	77.0841	−	173.134i	0.0980714	−	0.220272i
$787$	69.1170	−	325.170i	0.0878234	−	0.413177i	−0.912171	−	0.409810i	$-0.865595\pi$
$787$	69.1170	−	325.170i	0.0878234	−	0.413177i	0.999994	−	0.00336666i	$-0.00107164\pi$
$788$	−53.6074	−	252.203i	−0.0680297	−	0.320055i
$789$	103.563	−	46.1094i	0.131259	−	0.0584403i
$790$	4.47601	+	1.45435i	0.00566584	+	0.00184094i
$791$	101.719	−	313.060i	0.128596	−	0.395777i
$792$	−173.235	−	389.093i	−0.218731	−	0.491279i
$793$	582.593	−	123.834i	0.734669	−	0.156159i
$794$	−143.923	−	30.5917i	−0.181263	−	0.0385286i
$795$	187.663	+	83.5531i	0.236055	+	0.105098i
$796$	−275.395	−	247.967i	−0.345974	−	0.311516i
$797$	−187.764	−	19.7348i	−0.235589	−	0.0247614i	−0.0140016	−	0.999902i	$-0.504457\pi$
$797$	−187.764	−	19.7348i	−0.235589	−	0.0247614i	−0.221587	+	0.975141i	$0.571124\pi$
$798$	19.0346	−	26.1989i	0.0238529	−	0.0328306i
$799$	−210.198	+	22.0927i	−0.263076	+	0.0276504i
$800$	−15.1758	+	26.2853i	−0.0189697	+	0.0328566i
$801$	−610.186	+	352.291i	−0.761780	+	0.439814i
$802$	2.03780	+	2.80480i	0.00254090	+	0.00349725i
$803$	−904.223	−	1004.24i	−1.12606	−	1.25061i
$804$	−27.0676	+	8.79481i	−0.0336662	+	0.0109388i
$805$			237.298i			0.294780i
$806$	−254.071	+	215.131i	−0.315225	+	0.266913i
$807$	−51.0382			−0.0632443
$808$	−56.5335	−	173.992i	−0.0699672	−	0.215337i
$809$	−39.1950	+	35.2914i	−0.0484488	+	0.0436235i	−0.692999	−	0.720938i	$-0.743711\pi$
$809$	−39.1950	+	35.2914i	−0.0484488	+	0.0436235i	0.644551	+	0.764562i	$0.277044\pi$
$810$	455.246	−	330.756i	0.562032	−	0.408340i
$811$	−301.619	−	522.419i	−0.371910	−	0.644167i	0.617950	−	0.786218i	$-0.287964\pi$
$811$	−301.619	−	522.419i	−0.371910	−	0.644167i	−0.989859	+	0.142051i	$0.954630\pi$
$812$	100.868	+	58.2362i	0.124222	+	0.0717195i
$813$	16.8240	+	160.070i	0.0206937	+	0.196888i
$814$	678.653	+	493.070i	0.833726	+	0.605737i
$815$	125.979	−	1198.61i	0.154576	−	1.47069i
$816$	15.2792	−	16.9692i	0.0187245	−	0.0207956i
$817$	−207.359	+	465.735i	−0.253805	+	0.570056i
$818$	167.979	−	790.281i	0.205354	−	0.966114i
$819$	24.4155	+	114.866i	0.0298113	+	0.140251i
$820$	414.505	−	184.549i	0.505494	−	0.225060i
$821$	−78.9004	−	25.6363i	−0.0961028	−	0.0312257i	0.260571	−	0.965455i	$-0.416089\pi$
$821$	−78.9004	−	25.6363i	−0.0961028	−	0.0312257i	−0.356674	+	0.934229i	$0.616089\pi$
$822$	−54.3238	+	167.192i	−0.0660874	+	0.203396i
$823$	−421.833	−	947.452i	−0.512555	−	1.15122i	−0.965672	−	0.259766i	$-0.916355\pi$
$823$	−421.833	−	947.452i	−0.512555	−	1.15122i	0.453117	−	0.891451i	$-0.350312\pi$
$824$	275.769	−	58.6165i	0.334671	−	0.0711366i
$825$	−52.3347	−	11.1241i	−0.0634360	−	0.0134837i
$826$	51.6153	+	22.9806i	0.0624883	+	0.0278216i
$827$	−393.886	−	354.657i	−0.476283	−	0.428847i	0.395702	−	0.918379i	$-0.370501\pi$
$827$	−393.886	−	354.657i	−0.476283	−	0.428847i	−0.871986	+	0.489531i	$0.837168\pi$
$828$	−416.383	−	43.7636i	−0.502878	−	0.0528546i
$829$	379.587	−	522.457i	0.457886	−	0.630226i	−0.516183	−	0.856478i	$-0.672647\pi$
$829$	379.587	−	522.457i	0.457886	−	0.630226i	0.974069	+	0.226253i	$0.0726475\pi$
$830$	996.079	−	104.692i	1.20010	−	0.126135i
$831$	75.0290	−	129.954i	0.0902875	−	0.156383i
$832$	52.6114	−	30.3752i	0.0632348	−	0.0365086i
$833$	−267.766	−	368.548i	−0.321447	−	0.442434i
$834$	47.9479	+	53.2515i	0.0574915	+	0.0638508i
$835$	−341.210	+	110.866i	−0.408635	+	0.132773i
$836$			776.700i			0.929067i
$837$	227.218	+	217.469i	0.271467	+	0.259820i
$838$	−953.100			−1.13735
$839$	−51.5074	−	158.524i	−0.0613915	−	0.188944i	0.915657	−	0.401960i	$-0.131671\pi$
$839$	−51.5074	−	158.524i	−0.0613915	−	0.188944i	−0.977049	+	0.213017i	$0.931671\pi$
$840$	−11.8614	+	10.6801i	−0.0141207	+	0.0127144i
$841$	182.121	−	132.318i	0.216552	−	0.157334i
$842$	352.017	+	609.711i	0.418072	+	0.724122i
$843$	−156.005	−	90.0697i	−0.185060	−	0.106844i
$844$	−25.0867	−	238.684i	−0.0297235	−	0.282801i
$845$	496.337	+	360.610i	0.587380	+	0.426757i
$846$	−27.2463	+	259.231i	−0.0322060	+	0.306420i
$847$	215.580	−	239.426i	0.254522	−	0.282675i
$848$	−105.632	+	237.254i	−0.124566	+	0.279780i
$849$	−33.0476	+	155.477i	−0.0389254	+	0.183129i
$850$	15.6853	+	73.7935i	0.0184533	+	0.0868158i
$851$	753.314	−	335.397i	0.885211	−	0.394121i
$852$	−118.159	−	38.3922i	−0.138684	−	0.0450613i
$853$	−148.034	+	455.603i	−0.173546	+	0.534118i	−0.999564	−	0.0295248i	$-0.990601\pi$
$853$	−148.034	+	455.603i	−0.173546	+	0.534118i	0.826019	+	0.563643i	$0.190601\pi$
$854$	−80.4676	−	180.733i	−0.0942244	−	0.211631i
$855$	−1044.99	+	222.119i	−1.22221	+	0.259789i
$856$	91.6381	+	19.4783i	0.107054	+	0.0227550i
$857$	−1484.89	−	661.115i	−1.73266	−	0.771429i	−0.995399	−	0.0958200i	$-0.969453\pi$
$857$	−1484.89	−	661.115i	−1.73266	−	0.771429i	−0.737260	−	0.675609i	$-0.763881\pi$
$858$	79.5841	+	71.6579i	0.0927554	+	0.0835173i
$859$	707.683	+	74.3805i	0.823845	+	0.0865896i	0.507063	−	0.861909i	$-0.330731\pi$
$859$	707.683	+	74.3805i	0.823845	+	0.0865896i	0.316782	+	0.948498i	$0.397398\pi$
$860$	147.695	−	203.285i	0.171739	−	0.236378i
$861$	41.9297	−	4.40699i	0.0486989	−	0.00511846i
$862$	−401.941	+	696.183i	−0.466289	+	0.807637i
$863$	−164.921	+	95.2174i	−0.191102	+	0.110333i	−0.592499	−	0.805572i	$-0.701858\pi$
$863$	−164.921	+	95.2174i	−0.191102	+	0.110333i	0.401396	+	0.915905i	$0.368525\pi$
$864$	−33.7346	−	46.4317i	−0.0390447	−	0.0537404i
$865$	1219.37	+	1354.25i	1.40968	+	1.56561i
$866$	635.691	−	206.549i	0.734054	−	0.238509i
$867$			109.177i			0.125925i
$868$	87.4427	+	67.6911i	0.100740	+	0.0779851i
$869$	−10.4887			−0.0120699
$870$	45.1467	+	138.947i	0.0518927	+	0.159709i
$871$	−139.865	+	125.935i	−0.160580	+	0.144587i
$872$	488.491	−	354.910i	0.560196	−	0.407006i
$873$	462.798	+	801.590i	0.530124	+	0.918202i
$874$	661.211	+	381.750i	0.756535	+	0.436785i
$875$	20.1714	+	191.918i	0.0230531	+	0.219335i
$876$	−72.2848	−	52.5180i	−0.0825169	−	0.0599520i
$877$	−35.1240	+	334.182i	−0.0400501	+	0.381052i	0.956076	+	0.293118i	$0.0946929\pi$
$877$	−35.1240	+	334.182i	−0.0400501	+	0.381052i	−0.996126	+	0.0879334i	$0.971974\pi$
$878$	515.845	−	572.904i	0.587523	−	0.652510i
$879$	27.4087	−	61.5609i	0.0311817	−	0.0700352i
$880$	79.5923	−	374.452i	0.0904457	−	0.425514i
$881$	−45.6621	−	214.823i	−0.0518299	−	0.243840i	0.944605	−	0.328210i	$-0.106446\pi$
$881$	−45.6621	−	214.823i	−0.0518299	−	0.243840i	−0.996434	+	0.0843701i	$0.973112\pi$
$882$	−513.246	+	228.512i	−0.581911	+	0.259084i
$883$	1550.40	+	503.755i	1.75583	+	0.570504i	0.996755	−	0.0804974i	$-0.0256509\pi$
$883$	1550.40	+	503.755i	1.75583	+	0.570504i	0.759076	+	0.651002i	$0.225651\pi$
$884$	46.6620	−	143.611i	0.0527851	−	0.162456i
$885$	28.8259	+	64.7440i	0.0325716	+	0.0731570i
$886$	708.009	−	150.492i	0.799108	−	0.169856i
$887$	538.987	+	114.565i	0.607652	+	0.129160i	0.501454	−	0.865185i	$-0.332799\pi$
$887$	538.987	+	114.565i	0.607652	+	0.129160i	0.106198	+	0.994345i	$0.466132\pi$
$888$	50.6693	+	22.5594i	0.0570600	+	0.0254048i
$889$	−214.432	−	193.075i	−0.241205	−	0.217182i
$890$	−629.818	−	66.1965i	−0.707660	−	0.0743781i
$891$	−737.130	+	1014.57i	−0.827307	+	1.13869i
$892$	−715.049	+	75.1547i	−0.801624	+	0.0842541i
$893$	237.670	−	411.656i	0.266147	−	0.460981i
$894$	−56.2145	+	32.4555i	−0.0628798	+	0.0363037i
$895$	1048.52	+	1443.16i	1.17153	+	1.61247i
$896$	−13.5023	−	14.9958i	−0.0150695	−	0.0167364i
$897$	100.119	−	32.5305i	0.111615	−	0.0362659i
$898$		−	417.330i		−	0.464733i
$899$	891.583	−	479.182i	0.991749	−	0.533017i
$900$	93.0406			0.103378
$901$	199.479	+	613.933i	0.221397	+	0.681390i
$902$	−751.467	+	676.624i	−0.833112	+	0.750138i
$903$	18.8892	−	13.7238i	0.0209183	−	0.0151980i
$904$	261.003	+	452.070i	0.288720	+	0.500077i
$905$	−257.480	−	148.656i	−0.284508	−	0.164261i
$906$	−2.00911	−	19.1154i	−0.00221756	−	0.0210986i
$907$	−1275.05	−	926.381i	−1.40579	−	1.02137i	−0.993917	−	0.110128i	$-0.964874\pi$
$907$	−1275.05	−	926.381i	−1.40579	−	1.02137i	−0.411876	−	0.911240i	$-0.635126\pi$
$908$	−0.0614707	+	0.584855i	−6.76990e−5	+	0.000644113i
$909$	−375.254	+	416.762i	−0.412821	+	0.458484i
$910$	−42.9308	+	96.4241i	−0.0471767	+	0.105961i
$911$	−222.714	+	1047.79i	−0.244472	+	1.15015i	0.669005	+	0.743258i	$0.266721\pi$
$911$	−222.714	+	1047.79i	−0.244472	+	1.15015i	−0.913476	+	0.406892i	$0.866613\pi$
$912$	10.6772	+	50.2323i	0.0117075	+	0.0550792i
$913$	−2039.14	+	907.883i	−2.23345	+	0.994396i
$914$	−747.612	−	242.914i	−0.817956	−	0.265770i
$915$	76.6851	−	236.012i	0.0838088	−	0.257937i
$916$	−286.720	−	643.984i	−0.313013	−	0.703039i
$917$	−407.188	+	86.5506i	−0.444044	+	0.0943845i
$918$	−139.538	−	29.6598i	−0.152002	−	0.0323091i
$919$	1214.10	+	540.550i	1.32110	+	0.588194i	0.941518	−	0.336963i	$-0.109400\pi$
$919$	1214.10	+	540.550i	1.32110	+	0.588194i	0.379587	+	0.925156i	$0.376066\pi$
$920$	−279.654	−	251.802i	−0.303972	−	0.273698i
$921$	−28.9560	−	3.04340i	−0.0314398	−	0.00330446i
$922$	322.717	−	444.181i	0.350018	−	0.481758i
$923$	−817.085	+	85.8791i	−0.885250	+	0.0930435i
$924$	17.7857	−	30.8057i	0.0192486	−	0.0333395i
$925$	−158.698	+	91.6241i	−0.171565	+	0.0990530i
$926$	629.471	+	866.392i	0.679774	+	0.935629i
$927$	−578.286	−	642.252i	−0.623826	−	0.692829i
$928$	−175.664	+	57.0767i	−0.189293	+	0.0615051i
$929$		−	915.506i		−	0.985475i	−0.870178	−	0.492737i	$-0.835996\pi$
$929$		−	915.506i		−	0.985475i	0.870178	−	0.492737i	$-0.164004\pi$
$930$	24.6962	+	136.492i	0.0265551	+	0.146766i
$931$	1024.53			1.10046
$932$	211.925	+	652.239i	0.227388	+	0.699827i
$933$	10.4405	−	9.40068i	0.0111903	−	0.0100758i
$934$	451.212	−	327.825i	0.483096	−	0.350990i
$935$	−475.767	−	824.052i	−0.508841	−	0.881339i
$936$	−161.276	−	93.1129i	−0.172304	−	0.0994796i
$937$	64.5702	+	614.345i	0.0689116	+	0.655651i	0.973394	+	0.229139i	$0.0735910\pi$
$937$	64.5702	+	614.345i	0.0689116	+	0.655651i	−0.904482	+	0.426512i	$0.859742\pi$
$938$	50.5756	+	36.7453i	0.0539186	+	0.0391741i
$939$	3.53101	−	33.5953i	0.00376040	−	0.0357778i
$940$	−156.766	+	174.107i	−0.166773	+	0.185220i
$941$	−175.611	+	394.429i	−0.186622	+	0.419159i	−0.982491	−	0.186309i	$-0.940347\pi$
$941$	−175.611	+	394.429i	−0.186622	+	0.419159i	0.795869	+	0.605468i	$0.207014\pi$
$942$	17.2154	−	80.9923i	0.0182754	−	0.0859791i
$943$	206.667	+	972.293i	0.219159	+	1.03106i
$944$	−81.8526	+	36.4431i	−0.0867083	+	0.0386050i
$945$	94.8351	+	30.8138i	0.100355	+	0.0326072i
$946$	−173.048	+	532.588i	−0.182926	+	0.562989i
$947$	713.808	+	1603.24i	0.753757	+	1.69297i	0.720435	+	0.693522i	$0.243942\pi$
$947$	713.808	+	1603.24i	0.753757	+	1.69297i	0.0333221	+	0.999445i	$0.489391\pi$
$948$	−0.678346	+	0.144187i	−0.000715555	+	0.000152096i
$949$	−577.944	−	122.846i	−0.609003	−	0.129448i
$950$	−155.001	−	69.0107i	−0.163158	−	0.0726428i
$951$	−187.044	−	168.415i	−0.196681	−	0.177093i
$952$	−49.8819	−	5.24279i	−0.0523969	−	0.00550714i
$953$	370.152	−	509.470i	0.388407	−	0.534596i	−0.569380	−	0.822074i	$-0.692817\pi$
$953$	370.152	−	509.470i	0.388407	−	0.534596i	0.957787	+	0.287478i	$0.0928168\pi$
$954$	791.749	−	83.2162i	0.829926	−	0.0872287i
$955$	567.753	−	983.377i	0.594506	−	1.02971i
$956$	28.7540	−	16.6011i	0.0300774	−	0.0173652i
$957$	−191.381	−	263.414i	−0.199980	−	0.275249i
$958$	−329.150	−	365.559i	−0.343581	−	0.381585i
$959$	367.243	−	119.325i	0.382944	−	0.124426i
$960$		−	25.3114i		−	0.0263661i
$961$	900.073	−	336.733i	0.936601	−	0.350399i
$962$	366.781			0.381269
$963$	−88.7452	−	273.130i	−0.0921549	−	0.283624i
$964$	−239.863	+	215.974i	−0.248821	+	0.224039i
$965$	151.886	−	110.352i	0.157395	−	0.114354i
$966$	−17.4834	−	30.2822i	−0.0180988	−	0.0313480i
$967$	273.041	+	157.640i	0.282359	+	0.163020i	0.634491	−	0.772931i	$-0.281210\pi$
$967$	273.041	+	157.640i	0.282359	+	0.163020i	−0.352132	+	0.935950i	$0.614543\pi$
$968$	53.4054	+	508.119i	0.0551709	+	0.524916i
$969$	103.269	+	75.0290i	0.106572	+	0.0774293i
$970$	−86.9612	+	827.380i	−0.0896507	+	0.852969i
$971$	1071.86	−	1190.42i	1.10387	−	1.22597i	0.131801	−	0.991276i	$-0.457924\pi$
$971$	1071.86	−	1190.42i	1.10387	−	1.22597i	0.972069	−	0.234695i	$-0.0754093\pi$
$972$	−108.005	+	242.584i	−0.111116	+	0.249572i
$973$	32.7248	−	153.958i	0.0336329	−	0.158230i
$974$	−172.292	−	810.570i	−0.176891	−	0.832208i
$975$	−21.3714	+	9.51515i	−0.0219194	+	0.00975913i
$976$	298.379	+	96.9491i	0.305716	+	0.0993331i
$977$	−42.5042	+	130.814i	−0.0435048	+	0.133894i	−0.970450	−	0.241303i	$-0.922425\pi$
$977$	−42.5042	+	130.814i	−0.0435048	+	0.133894i	0.926945	+	0.375197i	$0.122425\pi$
$978$	72.2337	+	162.240i	0.0738586	+	0.165889i
$979$	1380.52	−	293.438i	1.41013	−	0.299733i
$980$	−493.934	−	104.989i	−0.504014	−	0.107131i
$981$	−1690.91	−	752.841i	−1.72366	−	0.767422i
$982$	−682.471	−	614.500i	−0.694981	−	0.625764i
$983$	70.5437	+	7.41445i	0.0717637	+	0.00754267i	0.140342	−	0.990103i	$-0.455180\pi$
$983$	70.5437	+	7.41445i	0.0717637	+	0.00754267i	−0.0685785	+	0.997646i	$0.521846\pi$
$984$	−39.2989	+	54.0903i	−0.0399379	+	0.0549698i
$985$	−706.513	+	74.2575i	−0.717272	+	0.0753884i
$986$	−229.551	+	397.593i	−0.232810	+	0.403239i
$987$	−18.8530	+	10.8848i	−0.0191013	+	0.0110282i
$988$	199.613	+	274.744i	0.202038	+	0.278081i
$989$	368.342	+	409.086i	0.372439	+	0.413636i
$990$	−1116.06	+	362.631i	−1.12734	+	0.366294i
$991$		−	1592.72i		−	1.60718i	−0.595182	−	0.803591i	$-0.702920\pi$
$991$		−	1592.72i		−	1.60718i	0.595182	−	0.803591i	$-0.297080\pi$
$992$	−172.561	+	31.2222i	−0.173952	+	0.0314740i
$993$	−9.78144			−0.00985039
$994$	84.3301	+	259.541i	0.0848392	+	0.261108i
$995$	−758.781	+	683.210i	−0.762594	+	0.686643i
$996$	−119.399	+	86.7482i	−0.119878	+	0.0870965i
$997$	936.652	+	1622.33i	0.939471	+	1.62721i	0.766461	+	0.642291i	$0.222016\pi$
$997$	936.652	+	1622.33i	0.939471	+	1.62721i	0.173009	+	0.984920i	$0.444651\pi$
$998$	−978.826	−	565.125i	−0.980787	−	0.566258i
$999$	−36.2201	−	344.611i	−0.0362563	−	0.344956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.3.h.a.11.5	✓	48
31.17	odd	30	inner	62.3.h.a.17.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.3.h.a.11.5	✓	48	1.1	even	1	trivial
62.3.h.a.17.5	yes	48	31.17	odd	30	inner

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	62.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.437016 + 1.34500i) q^{2} +(-0.426688 + 0.384192i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(2.75524 + 4.77222i) q^{5} +(-0.703206 - 0.405996i) q^{6} +(0.186434 + 1.77380i) q^{7} +(-2.28825 - 1.66251i) q^{8} +(-0.906297 + 8.62284i) q^{9} +O(q^{10})\)	\(q+(0.437016 + 1.34500i) q^{2} +(-0.426688 + 0.384192i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(2.75524 + 4.77222i) q^{5} +(-0.703206 - 0.405996i) q^{6} +(0.186434 + 1.77380i) q^{7} +(-2.28825 - 1.66251i) q^{8} +(-0.906297 + 8.62284i) q^{9} +(-5.21454 + 5.79133i) q^{10} +(7.06408 - 15.8662i) q^{11} +(0.238751 - 1.12324i) q^{12} +(-1.57884 - 7.42786i) q^{13} +(-2.30429 + 1.02593i) q^{14} +(-3.00908 - 0.977708i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-4.04394 - 9.08285i) q^{17} +(-11.9938 + 2.54935i) q^{18} +(21.8719 + 4.64901i) q^{19} +(-10.0682 - 4.48263i) q^{20} +(-0.761030 - 0.685234i) q^{21} +(24.4271 + 2.56739i) q^{22} +(14.1916 - 19.5331i) q^{23} +(1.61509 - 0.169753i) q^{24} +(-2.68273 + 4.64662i) q^{25} +(9.30047 - 5.36963i) q^{26} +(-5.96349 - 8.20804i) q^{27} +(-2.38689 - 2.65091i) q^{28} +(-31.0533 + 10.0898i) q^{29} -4.47447i q^{30} +(-30.5047 + 5.51936i) q^{31} +5.65685 q^{32} +(3.08149 + 9.48386i) q^{33} +(10.4491 - 9.40844i) q^{34} +(-7.95131 + 5.77697i) q^{35} +(-8.67033 - 15.0175i) q^{36} +(29.5776 + 17.0767i) q^{37} +(3.30545 + 31.4493i) q^{38} +(3.52739 + 2.56280i) q^{39} +(1.62918 - 15.5006i) q^{40} +(-27.5480 + 30.5952i) q^{41} +(0.589056 - 1.32304i) q^{42} +(-4.74031 + 22.3014i) q^{43} +(7.22189 + 33.9763i) q^{44} +(-43.6472 + 19.4330i) q^{45} +(32.4739 + 10.5514i) q^{46} +(6.56908 - 20.2175i) q^{47} +(0.934136 + 2.09810i) q^{48} +(44.8176 - 9.52628i) q^{49} +(-7.42209 - 1.57761i) q^{50} +(5.21506 + 2.32189i) q^{51} +(11.2866 + 10.1625i) q^{52} +(-64.5709 - 6.78668i) q^{53} +(8.43365 - 11.6079i) q^{54} +(95.1801 - 10.0038i) q^{55} +(2.52236 - 4.36885i) q^{56} +(-11.1186 + 6.41931i) q^{57} +(-27.1416 - 37.3572i) q^{58} +(-14.9883 - 16.6462i) q^{59} +(6.01815 - 1.95542i) q^{60} +78.4335i q^{61} +(-20.7546 - 38.6167i) q^{62} -15.4642 q^{63} +(2.47214 + 7.60845i) q^{64} +(31.0973 - 28.0001i) q^{65} +(-11.4091 + 8.28920i) q^{66} +(-12.3922 - 21.4639i) q^{67} +(17.2208 + 9.94242i) q^{68} +(1.44905 + 13.7868i) q^{69} +(-11.2449 - 8.16987i) q^{70} +(11.3091 - 107.599i) q^{71} +(16.4094 - 18.2244i) q^{72} +(31.6472 - 71.0808i) q^{73} +(-10.0422 + 47.2446i) q^{74} +(-0.640505 - 3.01334i) q^{75} +(-40.8547 + 18.1897i) q^{76} +(29.4605 + 9.57229i) q^{77} +(-1.90543 + 5.86432i) q^{78} +(-0.245637 - 0.551709i) q^{79} +(21.5603 - 4.58278i) q^{80} +(-70.6298 - 15.0128i) q^{81} +(-53.1894 - 23.6814i) q^{82} +(-95.5098 - 85.9974i) q^{83} +(2.03691 + 0.214088i) q^{84} +(32.2033 - 44.3241i) q^{85} +(-32.0669 + 3.37037i) q^{86} +(9.37365 - 16.2356i) q^{87} +(-42.5420 + 24.5616i) q^{88} +(47.7655 + 65.7436i) q^{89} +(-45.2118 - 50.2128i) q^{90} +(12.8812 - 4.18536i) q^{91} +48.2884i q^{92} +(10.8955 - 14.0747i) q^{93} +30.0633 q^{94} +(38.0762 + 117.187i) q^{95} +(-2.41371 + 2.17332i) q^{96} +(86.3662 - 62.7487i) q^{97} +(32.3988 + 56.1164i) q^{98} +(130.409 + 75.2918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{3} - 24 q^{4} + 6 q^{5} + 18 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 6 * q^3 - 24 * q^4 + 6 * q^5 + 18 * q^7 - 44 * q^9	\( 48 q + 6 q^{3} - 24 q^{4} + 6 q^{5} + 18 q^{7} - 44 q^{9} + 16 q^{10} - 4 q^{11} + 12 q^{12} + 48 q^{13} - 24 q^{14} - 70 q^{15} - 48 q^{16} + 70 q^{17} + 16 q^{18} + 38 q^{19} + 12 q^{20} - 24 q^{21} - 52 q^{22} - 50 q^{23} - 242 q^{25} - 168 q^{26} - 270 q^{27} - 64 q^{28} - 40 q^{29} - 26 q^{31} + 126 q^{33} + 112 q^{34} + 300 q^{35} + 152 q^{36} + 504 q^{37} + 264 q^{38} + 122 q^{39} - 48 q^{40} + 46 q^{41} + 432 q^{42} + 100 q^{43} + 12 q^{44} - 36 q^{45} - 160 q^{46} - 336 q^{47} + 64 q^{48} + 68 q^{49} + 128 q^{50} - 518 q^{51} - 24 q^{52} - 314 q^{53} - 418 q^{55} - 8 q^{56} - 66 q^{57} + 40 q^{58} - 170 q^{59} + 140 q^{60} + 16 q^{62} + 604 q^{63} - 96 q^{64} + 788 q^{65} - 360 q^{66} - 30 q^{67} + 60 q^{68} + 288 q^{69} - 48 q^{70} - 66 q^{71} + 32 q^{72} + 346 q^{73} + 176 q^{74} + 930 q^{75} - 264 q^{76} - 1100 q^{77} - 1144 q^{78} + 62 q^{79} - 216 q^{80} - 460 q^{81} - 384 q^{82} - 1146 q^{83} - 68 q^{84} - 220 q^{85} - 484 q^{86} - 572 q^{87} - 24 q^{88} - 430 q^{89} - 704 q^{90} - 440 q^{91} - 440 q^{93} + 862 q^{95} + 814 q^{97} + 792 q^{98} + 942 q^{99}+O(q^{100}) \) 48 * q + 6 * q^3 - 24 * q^4 + 6 * q^5 + 18 * q^7 - 44 * q^9 + 16 * q^10 - 4 * q^11 + 12 * q^12 + 48 * q^13 - 24 * q^14 - 70 * q^15 - 48 * q^16 + 70 * q^17 + 16 * q^18 + 38 * q^19 + 12 * q^20 - 24 * q^21 - 52 * q^22 - 50 * q^23 - 242 * q^25 - 168 * q^26 - 270 * q^27 - 64 * q^28 - 40 * q^29 - 26 * q^31 + 126 * q^33 + 112 * q^34 + 300 * q^35 + 152 * q^36 + 504 * q^37 + 264 * q^38 + 122 * q^39 - 48 * q^40 + 46 * q^41 + 432 * q^42 + 100 * q^43 + 12 * q^44 - 36 * q^45 - 160 * q^46 - 336 * q^47 + 64 * q^48 + 68 * q^49 + 128 * q^50 - 518 * q^51 - 24 * q^52 - 314 * q^53 - 418 * q^55 - 8 * q^56 - 66 * q^57 + 40 * q^58 - 170 * q^59 + 140 * q^60 + 16 * q^62 + 604 * q^63 - 96 * q^64 + 788 * q^65 - 360 * q^66 - 30 * q^67 + 60 * q^68 + 288 * q^69 - 48 * q^70 - 66 * q^71 + 32 * q^72 + 346 * q^73 + 176 * q^74 + 930 * q^75 - 264 * q^76 - 1100 * q^77 - 1144 * q^78 + 62 * q^79 - 216 * q^80 - 460 * q^81 - 384 * q^82 - 1146 * q^83 - 68 * q^84 - 220 * q^85 - 484 * q^86 - 572 * q^87 - 24 * q^88 - 430 * q^89 - 704 * q^90 - 440 * q^91 - 440 * q^93 + 862 * q^95 + 814 * q^97 + 792 * q^98 + 942 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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