LMFDB - Embedded newform 77.2.n.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(17,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 27]))

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

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

chi := DirichletCharacter("77.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (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:	$0.614848095564$
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			17.6
Character	$\chi$	$=$	77.17
Dual form			77.2.n.a.68.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75157 + 1.57712i) q^{2} +(-0.821231 - 1.84451i) q^{3} +(0.371633 + 3.53585i) q^{4} +(-0.00617973 - 0.0290734i) q^{5} +(1.47058 - 4.52598i) q^{6} +(-2.21185 + 1.45180i) q^{7} +(-2.15474 + 2.96574i) q^{8} +(-0.720422 + 0.800109i) q^{9} +O(q^{10})$	\(q+(1.75157 + 1.57712i) q^{2} +(-0.821231 - 1.84451i) q^{3} +(0.371633 + 3.53585i) q^{4} +(-0.00617973 - 0.0290734i) q^{5} +(1.47058 - 4.52598i) q^{6} +(-2.21185 + 1.45180i) q^{7} +(-2.15474 + 2.96574i) q^{8} +(-0.720422 + 0.800109i) q^{9} +(0.0350280 - 0.0606703i) q^{10} +(-2.88224 - 1.64094i) q^{11} +(6.21673 - 3.58923i) q^{12} +(-1.27203 - 3.91491i) q^{13} +(-6.16388 - 0.945438i) q^{14} +(-0.0485512 + 0.0352745i) q^{15} +(-1.49625 + 0.318039i) q^{16} +(2.61126 + 2.90010i) q^{17} +(-2.52374 + 0.265256i) q^{18} +(-0.627828 + 5.97338i) q^{19} +(0.100502 - 0.0326552i) q^{20} +(4.49430 + 2.88753i) q^{21} +(-2.46049 - 7.41987i) q^{22} +(1.70992 + 2.96167i) q^{23} +(7.23989 + 1.53889i) q^{24} +(4.56692 - 2.03332i) q^{25} +(3.94624 - 8.86340i) q^{26} +(-3.69331 - 1.20003i) q^{27} +(-5.95532 - 7.28124i) q^{28} +(2.60417 + 3.58434i) q^{29} +(-0.140673 - 0.0147854i) q^{30} +(0.713914 - 3.35870i) q^{31} +(3.22707 + 1.86315i) q^{32} +(-0.659750 + 6.66393i) q^{33} +9.19801i q^{34} +(0.0558772 + 0.0553343i) q^{35} +(-3.09680 - 2.24995i) q^{36} +(-9.81531 - 4.37006i) q^{37} +(-10.5204 + 9.47265i) q^{38} +(-6.17648 + 5.56132i) q^{39} +(0.0995398 + 0.0443180i) q^{40} +(4.39238 + 3.19125i) q^{41} +(3.31809 + 12.1458i) q^{42} -4.40101i q^{43} +(4.73098 - 10.8010i) q^{44} +(0.0277139 + 0.0160006i) q^{45} +(-1.67587 + 7.88433i) q^{46} +(-1.98760 - 0.208905i) q^{47} +(1.81540 + 2.49868i) q^{48} +(2.78458 - 6.42231i) q^{49} +(11.2061 + 3.64108i) q^{50} +(3.20483 - 7.19816i) q^{51} +(13.3698 - 5.95262i) q^{52} +(-1.63050 - 0.346573i) q^{53} +(-4.57651 - 7.92674i) q^{54} +(-0.0298961 + 0.0939370i) q^{55} +(0.460310 - 9.68802i) q^{56} +(11.5336 - 3.74749i) q^{57} +(-1.09154 + 10.3853i) q^{58} +(3.96280 - 0.416507i) q^{59} +(-0.142769 - 0.158561i) q^{60} +(-8.45471 + 1.79710i) q^{61} +(6.54756 - 4.75708i) q^{62} +(0.431871 - 2.81563i) q^{63} +(3.65942 + 11.2626i) q^{64} +(-0.105959 + 0.0611753i) q^{65} +(-11.6654 + 10.6318i) q^{66} +(1.46468 - 2.53690i) q^{67} +(-9.28387 + 10.3108i) q^{68} +(4.05860 - 5.58618i) q^{69} +(0.0106041 + 0.185047i) q^{70} +(-0.813218 + 2.50283i) q^{71} +(-0.820598 - 3.86061i) q^{72} +(0.203196 + 1.93328i) q^{73} +(-10.3001 - 23.1344i) q^{74} +(-7.50099 - 6.75392i) q^{75} -21.3543 q^{76} +(8.75740 - 0.554911i) q^{77} -19.5894 q^{78} +(-8.27944 - 7.45484i) q^{79} +(0.0184929 + 0.0415357i) q^{80} +(1.15721 + 11.0101i) q^{81} +(2.66058 + 12.5170i) q^{82} +(2.78172 - 8.56125i) q^{83} +(-8.53965 + 16.9643i) q^{84} +(0.0681787 - 0.0938399i) q^{85} +(6.94093 - 7.70868i) q^{86} +(4.47274 - 7.74701i) q^{87} +(11.0771 - 5.01219i) q^{88} +(1.57470 - 0.909151i) q^{89} +(0.0233079 + 0.0717345i) q^{90} +(8.49719 + 6.81247i) q^{91} +(-9.83654 + 7.14667i) q^{92} +(-6.78146 + 1.44144i) q^{93} +(-3.15196 - 3.50060i) q^{94} +(0.177546 - 0.0186609i) q^{95} +(0.786437 - 7.48245i) q^{96} +(-10.7699 + 3.49934i) q^{97} +(15.0062 - 6.85752i) q^{98} +(3.38936 - 1.12394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	1.75157	+	1.57712i	1.23855	+	1.11519i	0.989168	+	0.146789i	$0.0468938\pi$
$2$	1.75157	+	1.57712i	1.23855	+	1.11519i	0.249381	+	0.968405i	$0.419773\pi$
$3$	−0.821231	−	1.84451i	−0.474138	−	1.06493i	−0.979394	−	0.201961i	$-0.935268\pi$
$3$	−0.821231	−	1.84451i	−0.474138	−	1.06493i	0.505256	−	0.862970i	$-0.331398\pi$
$4$	0.371633	+	3.53585i	0.185816	+	1.76792i
$5$	−0.00617973	−	0.0290734i	−0.00276366	−	0.0130020i	0.976744	−	0.214408i	$-0.0687822\pi$
$5$	−0.00617973	−	0.0290734i	−0.00276366	−	0.0130020i	−0.979508	+	0.201406i	$0.935449\pi$
$6$	1.47058	−	4.52598i	0.600362	−	1.84772i
$7$	−2.21185	+	1.45180i	−0.836002	+	0.548727i
$7$	−2.21185	+	1.45180i	−0.836002	+	0.548727i
$8$	−2.15474	+	2.96574i	−0.761815	+	1.04855i
$9$	−0.720422	+	0.800109i	−0.240141	+	0.266703i
$10$	0.0350280	−	0.0606703i	0.0110768	−	0.0191856i
$11$	−2.88224	−	1.64094i	−0.869029	−	0.494762i
$11$	−2.88224	−	1.64094i	−0.869029	−	0.494762i
$12$	6.21673	−	3.58923i	1.79461	−	1.03612i
$13$	−1.27203	−	3.91491i	−0.352798	−	1.08580i	−0.957275	−	0.289178i	$-0.906618\pi$
$13$	−1.27203	−	3.91491i	−0.352798	−	1.08580i	0.604477	−	0.796622i	$-0.293382\pi$
$14$	−6.16388	−	0.945438i	−1.64737	−	0.252679i
$15$	−0.0485512	+	0.0352745i	−0.0125359	+	0.00910785i
$16$	−1.49625	+	0.318039i	−0.374063	+	0.0795096i
$17$	2.61126	+	2.90010i	0.633323	+	0.703377i	0.971322	−	0.237770i	$-0.0764164\pi$
$17$	2.61126	+	2.90010i	0.633323	+	0.703377i	−0.337998	+	0.941147i	$0.609750\pi$
$18$	−2.52374	+	0.265256i	−0.594852	+	0.0625214i
$19$	−0.627828	+	5.97338i	−0.144034	+	1.37039i	0.648804	+	0.760956i	$0.275269\pi$
$19$	−0.627828	+	5.97338i	−0.144034	+	1.37039i	−0.792838	+	0.609433i	$0.791397\pi$
$20$	0.100502	−	0.0326552i	0.0224730	−	0.00730193i
$21$	4.49430	+	2.88753i	0.980736	+	0.630112i
$22$	−2.46049	−	7.41987i	−0.524579	−	1.58192i
$23$	1.70992	+	2.96167i	0.356543	+	0.617550i	0.987381	−	0.158364i	$-0.0506220\pi$
$23$	1.70992	+	2.96167i	0.356543	+	0.617550i	−0.630838	+	0.775915i	$0.717289\pi$
$24$	7.23989	+	1.53889i	1.47784	+	0.314124i
$25$	4.56692	−	2.03332i	0.913384	−	0.406665i
$26$	3.94624	−	8.86340i	0.773921	−	1.73826i
$27$	−3.69331	−	1.20003i	−0.710778	−	0.230946i
$28$	−5.95532	−	7.28124i	−1.12545	−	1.37602i
$29$	2.60417	+	3.58434i	0.483583	+	0.665595i	0.979189	−	0.202953i	$-0.0650538\pi$
$29$	2.60417	+	3.58434i	0.483583	+	0.665595i	−0.495605	+	0.868548i	$0.665054\pi$
$30$	−0.140673	−	0.0147854i	−0.0256833	−	0.00269943i
$31$	0.713914	−	3.35870i	0.128223	−	0.603241i	−0.866371	−	0.499401i	$-0.833554\pi$
$31$	0.713914	−	3.35870i	0.128223	−	0.603241i	0.994594	−	0.103840i	$-0.0331131\pi$
$32$	3.22707	+	1.86315i	0.570470	+	0.329361i
$33$	−0.659750	+	6.66393i	−0.114848	+	1.16004i
$34$			9.19801i			1.57745i
$35$	0.0558772	+	0.0553343i	0.00944498	+	0.00935320i
$36$	−3.09680	−	2.24995i	−0.516133	−	0.374992i
$37$	−9.81531	−	4.37006i	−1.61363	−	0.718433i	−0.616030	−	0.787723i	$-0.711260\pi$
$37$	−9.81531	−	4.37006i	−1.61363	−	0.718433i	−0.997597	+	0.0692903i	$0.977927\pi$
$38$	−10.5204	+	9.47265i	−1.70664	+	1.53667i
$39$	−6.17648	+	5.56132i	−0.989028	+	0.890525i
$40$	0.0995398	+	0.0443180i	0.0157386	+	0.00700728i
$41$	4.39238	+	3.19125i	0.685975	+	0.498390i	0.875334	−	0.483518i	$-0.160641\pi$
$41$	4.39238	+	3.19125i	0.685975	+	0.498390i	−0.189360	+	0.981908i	$0.560641\pi$
$42$	3.31809	+	12.1458i	0.511993	+	1.87414i
$43$		−	4.40101i		−	0.671147i	−0.942014	−	0.335574i	$-0.891070\pi$
$43$		−	4.40101i		−	0.671147i	0.942014	−	0.335574i	$-0.108930\pi$
$44$	4.73098	−	10.8010i	0.713221	−	1.62831i
$45$	0.0277139	+	0.0160006i	0.00413134	+	0.00238523i
$46$	−1.67587	+	7.88433i	−0.247093	+	1.16248i
$47$	−1.98760	−	0.208905i	−0.289921	−	0.0304720i	−0.0415485	−	0.999136i	$-0.513229\pi$
$47$	−1.98760	−	0.208905i	−0.289921	−	0.0304720i	−0.248373	+	0.968665i	$0.579896\pi$
$48$	1.81540	+	2.49868i	0.262030	+	0.360653i
$49$	2.78458	−	6.42231i	0.397797	−	0.917473i
$50$	11.2061	+	3.64108i	1.58478	+	0.514927i
$51$	3.20483	−	7.19816i	0.448765	−	1.00794i
$52$	13.3698	−	5.95262i	1.85406	−	0.825479i
$53$	−1.63050	−	0.346573i	−0.223966	−	0.0476055i	0.0945616	−	0.995519i	$-0.469855\pi$
$53$	−1.63050	−	0.346573i	−0.223966	−	0.0476055i	−0.318528	+	0.947914i	$0.603188\pi$
$54$	−4.57651	−	7.92674i	−0.622784	−	1.07869i
$55$	−0.0298961	+	0.0939370i	−0.00403119	+	0.0126665i
$56$	0.460310	−	9.68802i	0.0615115	−	1.29462i
$57$	11.5336	−	3.74749i	1.52766	−	0.496367i
$58$	−1.09154	+	10.3853i	−0.143327	+	1.36366i
$59$	3.96280	−	0.416507i	0.515913	−	0.0542246i	0.157005	−	0.987598i	$-0.449816\pi$
$59$	3.96280	−	0.416507i	0.515913	−	0.0542246i	0.358908	+	0.933373i	$0.383149\pi$
$60$	−0.142769	−	0.158561i	−0.0184314	−	0.0204701i
$61$	−8.45471	+	1.79710i	−1.08251	+	0.230096i	−0.714437	−	0.699699i	$-0.753317\pi$
$61$	−8.45471	+	1.79710i	−1.08251	+	0.230096i	−0.368078	+	0.929795i	$0.619984\pi$
$62$	6.54756	−	4.75708i	0.831541	−	0.604150i
$63$	0.431871	−	2.81563i	0.0544106	−	0.354736i
$64$	3.65942	+	11.2626i	0.457428	+	1.40782i
$65$	−0.105959	+	0.0611753i	−0.0131426	+	0.00758787i
$66$	−11.6654	+	10.6318i	−1.43592	+	1.30869i
$67$	1.46468	−	2.53690i	0.178939	−	0.309932i	−0.762578	−	0.646896i	$-0.776067\pi$
$67$	1.46468	−	2.53690i	0.178939	−	0.309932i	0.941517	+	0.336964i	$0.109400\pi$
$68$	−9.28387	+	10.3108i	−1.12584	+	1.25037i
$69$	4.05860	−	5.58618i	0.488598	−	0.672498i
$70$	0.0106041	+	0.185047i	0.00126743	+	0.0221174i
$71$	−0.813218	+	2.50283i	−0.0965112	+	0.297031i	−0.987645	−	0.156710i	$-0.949911\pi$
$71$	−0.813218	+	2.50283i	−0.0965112	+	0.297031i	0.891133	+	0.453741i	$0.149911\pi$
$72$	−0.820598	−	3.86061i	−0.0967084	−	0.454977i
$73$	0.203196	+	1.93328i	0.0237823	+	0.226273i	0.999957	+	0.00928671i	$0.00295610\pi$
$73$	0.203196	+	1.93328i	0.0237823	+	0.226273i	−0.976175	+	0.216987i	$0.930377\pi$
$74$	−10.3001	−	23.1344i	−1.19736	−	2.68932i
$75$	−7.50099	−	6.75392i	−0.866140	−	0.779876i
$76$	−21.3543			−2.44951
$77$	8.75740	−	0.554911i	0.997998	−	0.0632380i
$78$	−19.5894			−2.21807
$79$	−8.27944	−	7.45484i	−0.931510	−	0.838736i	0.0556530	−	0.998450i	$-0.482276\pi$
$79$	−8.27944	−	7.45484i	−0.931510	−	0.838736i	−0.987163	+	0.159715i	$0.948943\pi$
$80$	0.0184929	+	0.0415357i	0.00206757	+	0.00464384i
$81$	1.15721	+	11.0101i	0.128579	+	1.22335i
$82$	2.66058	+	12.5170i	0.293812	+	1.38228i
$83$	2.78172	−	8.56125i	0.305333	−	0.939720i	−0.674219	−	0.738531i	$-0.735520\pi$
$83$	2.78172	−	8.56125i	0.305333	−	0.939720i	0.979553	−	0.201188i	$-0.0644803\pi$
$84$	−8.53965	+	16.9643i	−0.931753	+	1.85095i
$85$	0.0681787	−	0.0938399i	0.00739502	−	0.0101784i
$86$	6.94093	−	7.70868i	0.748460	−	0.831249i
$87$	4.47274	−	7.74701i	0.479528	−	0.830566i
$88$	11.0771	−	5.01219i	1.18082	−	0.534301i
$89$	1.57470	−	0.909151i	0.166917	−	0.0963698i	−0.414214	−	0.910179i	$-0.635944\pi$
$89$	1.57470	−	0.909151i	0.166917	−	0.0963698i	0.581132	+	0.813810i	$0.302610\pi$
$90$	0.0233079	+	0.0717345i	0.00245687	+	0.00756148i
$91$	8.49719	+	6.81247i	0.890748	+	0.714141i
$92$	−9.83654	+	7.14667i	−1.02553	+	0.745092i
$93$	−6.78146	+	1.44144i	−0.703205	+	0.149471i
$94$	−3.15196	−	3.50060i	−0.325100	−	0.361060i
$95$	0.177546	−	0.0186609i	0.0182159	−	0.00191456i
$96$	0.786437	−	7.48245i	0.0802654	−	0.763674i
$97$	−10.7699	+	3.49934i	−1.09351	+	0.355304i	−0.799604	−	0.600528i	$-0.794957\pi$
$97$	−10.7699	+	3.49934i	−1.09351	+	0.355304i	−0.293911	+	0.955833i	$0.594957\pi$
$98$	15.0062	−	6.85752i	1.51585	−	0.692715i
$99$	3.38936	−	1.12394i	0.340644	−	0.112960i
$100$	8.88674	+	15.3923i	0.888674	+	1.53923i
$101$	−0.225301	−	0.0478893i	−0.0224183	−	0.00476516i	0.196689	−	0.980466i	$-0.436981\pi$
$101$	−0.225301	−	0.0478893i	−0.0224183	−	0.00476516i	−0.219107	+	0.975701i	$0.570314\pi$
$102$	16.9659	−	7.55369i	1.67987	−	0.747927i
$103$	2.14251	−	4.81216i	0.211108	−	0.474157i	−0.776693	−	0.629880i	$-0.783104\pi$
$103$	2.14251	−	4.81216i	0.211108	−	0.474157i	0.987801	+	0.155723i	$0.0497708\pi$
$104$	14.3515	+	4.66309i	1.40728	+	0.457253i
$105$	0.0561768	−	0.148509i	0.00548229	−	0.0144930i
$106$	−2.30935	−	3.17855i	−0.224304	−	0.308728i
$107$	−2.79838	−	0.294121i	−0.270529	−	0.0284338i	−0.0317075	−	0.999497i	$-0.510094\pi$
$107$	−2.79838	−	0.294121i	−0.270529	−	0.0284338i	−0.238822	+	0.971063i	$0.576761\pi$
$108$	2.87057	−	13.5050i	0.276220	−	1.29951i
$109$	6.87837	+	3.97123i	0.658829	+	0.380375i	0.791831	−	0.610741i	$-0.209128\pi$
$109$	6.87837	+	3.97123i	0.658829	+	0.380375i	−0.133002	+	0.991116i	$0.542462\pi$
$110$	−0.200516	+	0.117388i	−0.0191184	+	0.0111925i
$111$			21.6933i			2.05904i
$112$	2.84777	−	2.87571i	0.269089	−	0.271729i
$113$	−6.61822	−	4.80842i	−0.622590	−	0.452338i	0.231235	−	0.972898i	$-0.425723\pi$
$113$	−6.61822	−	4.80842i	−0.622590	−	0.452338i	−0.853825	+	0.520560i	$0.825723\pi$
$114$	26.1122	+	11.6259i	2.44563	+	1.08886i
$115$	0.0755388	−	0.0680154i	0.00704403	−	0.00634247i
$116$	−11.7059	+	10.5400i	−1.08686	+	0.978616i
$117$	4.04875	+	1.80262i	0.374308	+	0.166652i
$118$	7.59802	+	5.52028i	0.699454	+	0.508183i
$119$	−9.98607	−	2.62357i	−0.915421	−	0.240502i
$120$		−	0.219998i		−	0.0200830i
$121$	5.61464	+	9.45917i	0.510422	+	0.859924i
$122$	−17.6433	−	10.1864i	−1.59735	−	0.922230i
$123$	2.27915	−	10.7226i	0.205504	−	0.966821i
$124$	12.1412	+	1.27609i	1.09031	+	0.114596i
$125$	−0.174691	−	0.240442i	−0.0156249	−	0.0215058i
$126$	5.19705	−	4.25066i	0.462990	−	0.378679i
$127$	−8.06437	−	2.62027i	−0.715597	−	0.232512i	−0.0714839	−	0.997442i	$-0.522773\pi$
$127$	−8.06437	−	2.62027i	−0.715597	−	0.232512i	−0.644113	+	0.764930i	$0.722773\pi$
$128$	−8.32144	+	18.6903i	−0.735518	+	1.65200i
$129$	−8.11772	+	3.61424i	−0.714725	+	0.318216i
$130$	−0.282076	−	0.0599570i	−0.0247397	−	0.00525858i
$131$	11.0180	+	19.0837i	0.962645	+	1.66735i	0.715814	+	0.698292i	$0.246056\pi$
$131$	11.0180	+	19.0837i	0.962645	+	1.66735i	0.246831	+	0.969058i	$0.420611\pi$
$132$	−23.8078	+	0.143756i	−2.07220	+	0.0125123i
$133$	−7.28347	−	14.1237i	−0.631557	−	1.22468i
$134$	6.56650	−	2.13359i	0.567259	−	0.184314i
$135$	−0.0120652	+	0.114793i	−0.00103841	+	0.00987979i
$136$	−14.2275	+	1.49537i	−1.22000	+	0.128227i
$137$	4.25628	+	4.72708i	0.363639	+	0.403862i	0.897003	−	0.442024i	$-0.145739\pi$
$137$	4.25628	+	4.72708i	0.363639	+	0.403862i	−0.533365	+	0.845885i	$0.679073\pi$
$138$	15.9190	−	3.38370i	1.35512	−	0.288039i
$139$	16.2591	−	11.8129i	1.37908	−	1.00196i	0.382113	−	0.924115i	$-0.375196\pi$
$139$	16.2591	−	11.8129i	1.37908	−	1.00196i	0.996966	−	0.0778440i	$-0.0248036\pi$
$140$	−0.174888	+	0.218137i	−0.0147807	+	0.0184360i
$141$	1.24695	+	3.83772i	0.105012	+	0.323194i
$142$	−5.37168	+	3.10134i	−0.450781	+	0.260259i
$143$	−2.75783	+	13.3710i	−0.230621	+	1.11814i
$144$	0.823468	−	1.42629i	0.0686224	−	0.118857i
$145$	0.0881157	−	0.0978624i	0.00731761	−	0.00812703i
$146$	−2.69311	+	3.70674i	−0.222883	+	0.306772i
$147$	−14.1328	+	0.138004i	−1.16566	+	0.0113824i
$148$	11.8042	−	36.3295i	0.970296	−	2.98626i
$149$	2.81197	+	13.2293i	0.230366	+	1.08379i	0.929507	+	0.368803i	$0.120232\pi$
$149$	2.81197	+	13.2293i	0.230366	+	1.08379i	−0.699142	+	0.714983i	$0.746434\pi$
$150$	−2.48676	−	23.6600i	−0.203043	−	1.93183i
$151$	−0.225819	−	0.507198i	−0.0183769	−	0.0412752i	0.904124	−	0.427270i	$-0.140525\pi$
$151$	−0.225819	−	0.507198i	−0.0183769	−	0.0412752i	−0.922501	+	0.385995i	$0.873858\pi$
$152$	−16.3627	−	14.7330i	−1.32719	−	1.19501i
$153$	−4.20160			−0.339680
$154$	16.2144	+	12.8395i	1.30659	+	1.03464i
$155$	−0.102061			−0.00819770
$156$	−21.9594	−	19.7723i	−1.75816	−	1.58305i
$157$	−1.16593	−	2.61873i	−0.0930516	−	0.208997i	0.861023	−	0.508566i	$-0.169824\pi$
$157$	−1.16593	−	2.61873i	−0.0930516	−	0.208997i	−0.954075	+	0.299568i	$0.903157\pi$
$158$	−2.74484	−	26.1154i	−0.218368	−	2.07763i
$159$	0.699756	+	3.29209i	0.0554943	+	0.261080i
$160$	0.0342256	−	0.105335i	0.00270577	−	0.00832750i
$161$	−8.08183	−	4.06832i	−0.636937	−	0.320628i
$162$	−15.3374	+	21.1101i	−1.20502	+	1.65857i
$163$	4.81743	−	5.35030i	0.377330	−	0.419068i	−0.524329	−	0.851516i	$-0.675684\pi$
$163$	4.81743	−	5.35030i	0.377330	−	0.419068i	0.901659	+	0.432449i	$0.142350\pi$
$164$	−9.65143	+	16.7168i	−0.753650	+	1.30536i
$165$	0.197820	−	0.0220001i	0.0154003	−	0.00171271i
$166$	18.3745	−	10.6085i	1.42614	−	0.823383i
$167$	5.04207	+	15.5179i	0.390167	+	1.20081i	0.932662	+	0.360752i	$0.117480\pi$
$167$	5.04207	+	15.5179i	0.390167	+	1.20081i	−0.542494	+	0.840059i	$0.682520\pi$
$168$	−18.2477	+	7.10705i	−1.40784	+	0.548321i
$169$	−3.19123	+	2.31857i	−0.245479	+	0.178351i
$170$	0.267417	−	0.0568413i	0.0205100	−	0.00435952i
$171$	−4.32706	−	4.80569i	−0.330899	−	0.367500i
$172$	15.5613	−	1.63556i	1.18654	−	0.124710i
$173$	−0.695184	+	6.61423i	−0.0528539	+	0.502871i	0.935786	+	0.352568i	$0.114692\pi$
$173$	−0.695184	+	6.61423i	−0.0528539	+	0.502871i	−0.988640	+	0.150303i	$0.951975\pi$
$174$	20.0523	−	6.51539i	1.52016	−	0.493930i
$175$	−7.14938	+	11.1276i	−0.540442	+	0.841171i
$176$	4.83445	+	1.53860i	0.364410	+	0.115976i
$177$	−4.02263	−	6.96740i	−0.302359	−	0.523702i
$178$	4.19204	+	0.891045i	0.314207	+	0.0667867i
$179$	−15.4807	+	6.89247i	−1.15708	+	0.515167i	−0.893321	−	0.449420i	$-0.851631\pi$
$179$	−15.4807	+	6.89247i	−1.15708	+	0.515167i	−0.263764	+	0.964587i	$0.584964\pi$
$180$	−0.0462764	+	0.103938i	−0.00344924	+	0.00774711i
$181$	−11.1436	−	3.62077i	−0.828295	−	0.269129i	−0.135968	−	0.990713i	$-0.543415\pi$
$181$	−11.1436	−	3.62077i	−0.828295	−	0.269129i	−0.692327	+	0.721584i	$0.743415\pi$
$182$	4.13934	+	25.3337i	0.306829	+	1.87786i
$183$	10.2581	+	14.1190i	0.758297	+	1.04371i
$184$	−12.4680	−	1.31044i	−0.919151	−	0.0966066i
$185$	−0.0663962	+	0.312370i	−0.00488155	+	0.0229659i
$186$	−14.1516	−	8.17041i	−1.03764	−	0.599083i
$187$	−2.76740	−	12.6437i	−0.202372	−	0.924599i
$188$		−	7.10549i		−	0.518221i
$189$	9.91125	−	2.70764i	0.720938	−	0.196952i
$190$	0.340416	+	0.247326i	0.0246963	+	0.0179429i
$191$	5.64351	+	2.51265i	0.408350	+	0.181809i	0.600623	−	0.799532i	$-0.294919\pi$
$191$	5.64351	+	2.51265i	0.408350	+	0.181809i	−0.192273	+	0.981341i	$0.561586\pi$
$192$	17.7687	−	15.9990i	1.28235	−	1.15463i
$193$	11.2502	−	10.1297i	0.809805	−	0.729152i	−0.156186	−	0.987728i	$-0.549920\pi$
$193$	11.2502	−	10.1297i	0.809805	−	0.729152i	0.965991	+	0.258576i	$0.0832533\pi$
$194$	−24.3831	−	10.8561i	−1.75061	−	0.779420i
$195$	0.199855	+	0.145203i	0.0143119	+	0.0103982i
$196$	23.7432	+	7.45911i	1.69594	+	0.532793i
$197$		−	22.5384i		−	1.60579i	−0.596117	−	0.802897i	$-0.703291\pi$
$197$		−	22.5384i		−	1.60579i	0.596117	−	0.802897i	$-0.296709\pi$
$198$	7.70930	+	3.37678i	0.547876	+	0.239977i
$199$	16.8635	+	9.73617i	1.19543	+	0.690179i	0.959532	−	0.281600i	$-0.0908651\pi$
$199$	16.8635	+	9.73617i	1.19543	+	0.690179i	0.235893	+	0.971779i	$0.424198\pi$
$200$	−3.81020	+	17.9256i	−0.269422	+	1.26753i
$201$	−5.88219	−	0.618243i	−0.414898	−	0.0436075i
$202$	−0.319104	−	0.439210i	−0.0224521	−	0.0309027i
$203$	−10.9638	−	4.14730i	−0.769506	−	0.291083i
$204$	26.6426	+	8.65670i	1.86535	+	0.606091i
$205$	0.0656367	−	0.147422i	0.00458426	−	0.0102964i
$206$	11.3421	−	5.04985i	0.790244	−	0.351839i
$207$	−3.60152	−	0.765527i	−0.250323	−	0.0532078i
$208$	3.14837	+	5.45314i	0.218300	+	0.378107i
$209$	11.6115	−	16.1865i	0.803185	−	1.11964i
$210$	0.332614	−	0.171526i	0.0229525	−	0.0118364i
$211$	−6.06462	+	1.97051i	−0.417506	+	0.135656i	−0.510234	−	0.860036i	$-0.670441\pi$
$211$	−6.06462	+	1.97051i	−0.417506	+	0.135656i	0.0927283	+	0.995691i	$0.470441\pi$
$212$	0.619484	−	5.89399i	0.0425463	−	0.404801i
$213$	5.28434	−	0.555407i	0.362077	−	0.0380558i
$214$	−4.43769	−	4.92856i	−0.303354	−	0.336909i
$215$	−0.127952	+	0.0271970i	−0.00872626	+	0.00185482i
$216$	11.5171	−	8.36765i	0.783639	−	0.569347i
$217$	3.29708	+	8.46541i	0.223820	+	0.574670i
$218$	5.78485	+	17.8039i	0.391800	+	1.20584i
$219$	3.39909	−	1.96247i	0.229689	−	0.132611i
$220$	−0.343257	−	0.0707981i	−0.0231424	−	0.00477321i
$221$	8.03202	−	13.9119i	0.540292	−	0.935813i
$222$	−34.2130	+	37.9974i	−2.29623	+	2.55022i
$223$	−11.8544	+	16.3162i	−0.793831	+	1.09261i	0.199790	+	0.979839i	$0.435974\pi$
$223$	−11.8544	+	16.3162i	−0.793831	+	1.09261i	−0.993620	+	0.112776i	$0.964026\pi$
$224$	−9.84271	+	0.564034i	−0.657644	+	0.0376861i
$225$	−1.66323	+	5.11889i	−0.110882	+	0.341259i
$226$	−4.00883	−	18.8600i	−0.266663	−	1.25455i
$227$	−0.157350	−	1.49708i	−0.0104437	−	0.0993648i	0.988058	−	0.154080i	$-0.0492415\pi$
$227$	−0.157350	−	1.49708i	−0.0104437	−	0.0993648i	−0.998502	+	0.0547155i	$0.982575\pi$
$228$	17.5368	+	39.3883i	1.16140	+	2.60855i
$229$	−4.27258	−	3.84705i	−0.282340	−	0.254220i	0.515777	−	0.856723i	$-0.327503\pi$
$229$	−4.27258	−	3.84705i	−0.282340	−	0.254220i	−0.798117	+	0.602503i	$0.794170\pi$
$230$	0.239580			0.0157975
$231$	−8.21539	−	15.6974i	−0.540533	−	1.03282i
$232$	−16.2415			−1.06631
$233$	−5.12054	−	4.61055i	−0.335458	−	0.302047i	0.484136	−	0.874993i	$-0.339134\pi$
$233$	−5.12054	−	4.61055i	−0.335458	−	0.302047i	−0.819593	+	0.572945i	$0.805801\pi$
$234$	4.24873	+	9.54281i	0.277748	+	0.623833i
$235$	0.00620926	+	0.0590772i	0.000405048	+	0.00385377i
$236$	2.94541	+	13.8571i	0.191730	+	0.902019i
$237$	−6.95123	+	21.3937i	−0.451531	+	1.38967i
$238$	−13.3536	−	20.3446i	−0.865587	−	1.31875i
$239$	−6.48482	+	8.92559i	−0.419468	+	0.577348i	−0.965496	−	0.260419i	$-0.916139\pi$
$239$	−6.48482	+	8.92559i	−0.419468	+	0.577348i	0.546028	+	0.837767i	$0.316139\pi$
$240$	0.0614263	−	0.0682209i	0.00396505	−	0.00440364i
$241$	−8.41403	+	14.5735i	−0.541996	+	0.938764i	0.456794	+	0.889573i	$0.348998\pi$
$241$	−8.41403	+	14.5735i	−0.541996	+	0.938764i	−0.998789	+	0.0491912i	$0.984336\pi$
$242$	−5.08383	+	25.4234i	−0.326801	+	1.63428i
$243$	9.26870	−	5.35129i	0.594587	−	0.343285i
$244$	−9.49633	−	29.2267i	−0.607940	−	1.87105i
$245$	−0.203926	−	0.0412689i	−0.0130284	−	0.00263657i
$246$	20.9029	−	15.1868i	1.33272	−	0.968278i
$247$	24.1839	−	5.14044i	1.53878	−	0.327078i
$248$	8.42274	+	9.35441i	0.534845	+	0.594005i
$249$	−18.0758	+	1.89984i	−1.14551	+	0.120398i
$250$	0.0732220	−	0.696661i	0.00463097	−	0.0440607i
$251$	23.1263	−	7.51418i	1.45972	−	0.474291i	0.531734	−	0.846912i	$-0.321541\pi$
$251$	23.1263	−	7.51418i	1.45972	−	0.474291i	0.927984	+	0.372621i	$0.121541\pi$
$252$	10.1161	+	0.480651i	0.637256	+	0.0302782i
$253$	−0.0684857	−	11.3421i	−0.00430566	−	0.713073i
$254$	−9.99284	−	17.3081i	−0.627006	−	1.08601i
$255$	−0.229080	−	0.0486924i	−0.0143455	−	0.00304923i
$256$	−22.4158	+	9.98014i	−1.40098	+	0.623759i
$257$	5.31332	−	11.9339i	0.331436	−	0.744417i	−0.668564	−	0.743655i	$-0.733091\pi$
$257$	5.31332	−	11.9339i	0.331436	−	0.744417i	1.00000		0.000762346i	$-0.000242662\pi$
$258$	−19.9189	−	6.47204i	−1.24010	−	0.402931i
$259$	28.0544	−	4.58390i	1.74322	−	0.284830i
$260$	−0.255684	−	0.351919i	−0.0158569	−	0.0218251i
$261$	−4.74397	−	0.498611i	−0.293644	−	0.0308632i
$262$	−10.7985	+	50.8032i	−0.667137	+	3.13863i
$263$	−2.83734	−	1.63814i	−0.174958	−	0.101012i	0.409964	−	0.912102i	$-0.365541\pi$
$263$	−2.83734	−	1.63814i	−0.174958	−	0.101012i	−0.584922	+	0.811090i	$0.698875\pi$
$264$	−18.3419	−	16.3157i	−1.12887	−	1.00416i
$265$			0.0495458i			0.00304357i
$266$	9.51732	−	36.2257i	0.583544	−	2.22114i
$267$	−2.97013	−	2.15793i	−0.181769	−	0.132063i
$268$	9.51442	+	4.23609i	0.581186	+	0.258761i
$269$	20.4461	−	18.4098i	1.24662	−	1.12246i	0.258955	−	0.965889i	$-0.416622\pi$
$269$	20.4461	−	18.4098i	1.24662	−	1.12246i	0.987666	−	0.156573i	$-0.0500447\pi$
$270$	−0.202175	+	0.182040i	−0.0123040	+	0.0110786i
$271$	2.08800	+	0.929639i	0.126837	+	0.0564715i	0.469174	−	0.883106i	$-0.344552\pi$
$271$	2.08800	+	0.929639i	0.126837	+	0.0564715i	−0.342337	+	0.939577i	$0.611218\pi$
$272$	−4.82945	−	3.50880i	−0.292828	−	0.212752i
$273$	5.58755	−	21.2678i	0.338174	−	1.28719i
$274$			14.9925i			0.905730i
$275$	−16.4995	−	1.63351i	−0.994959	−	0.0985042i
$276$	21.2602	+	12.2746i	1.27971	+	0.738843i
$277$	−2.47579	+	11.6477i	−0.148756	+	0.699841i	0.839038	+	0.544073i	$0.183119\pi$
$277$	−2.47579	+	11.6477i	−0.148756	+	0.699841i	−0.987794	+	0.155768i	$0.950215\pi$
$278$	47.1094	+	4.95140i	2.82544	+	0.296965i
$279$	2.17301	+	2.99089i	0.130095	+	0.179060i
$280$	−0.284508	+	0.0464866i	−0.0170026	+	0.00277811i
$281$	−13.1094	−	4.25950i	−0.782040	−	0.254100i	−0.109329	−	0.994006i	$-0.534870\pi$
$281$	−13.1094	−	4.25950i	−0.782040	−	0.254100i	−0.672711	+	0.739905i	$0.734870\pi$
$282$	−3.86843	+	8.68863i	−0.230362	+	0.517400i
$283$	7.36001	−	3.27689i	0.437507	−	0.194791i	−0.176150	−	0.984363i	$-0.556364\pi$
$283$	7.36001	−	3.27689i	0.437507	−	0.194791i	0.613657	+	0.789573i	$0.289698\pi$
$284$	−9.15184	−	1.94528i	−0.543062	−	0.115431i
$285$	−0.180227	−	0.312162i	−0.0106757	−	0.0184909i
$286$	−25.9183	+	19.0709i	−1.53258	+	1.12769i
$287$	−14.3483	−	0.681738i	−0.846956	−	0.0402417i
$288$	−3.81557	+	1.23975i	−0.224835	+	0.0730532i
$289$	0.185095	−	1.76106i	0.0108879	−	0.103592i
$290$	0.308682	−	0.0324438i	0.0181264	−	0.00190516i
$291$	15.2991	+	16.9914i	0.896851	+	0.996054i
$292$	−6.76027	+	1.43694i	−0.395615	+	0.0840905i
$293$	−18.0983	+	13.1492i	−1.05732	+	0.768186i	−0.973590	−	0.228303i	$-0.926682\pi$
$293$	−18.0983	+	13.1492i	−1.05732	+	0.768186i	−0.0837268	+	0.996489i	$0.526682\pi$
$294$	−24.9723	−	22.0475i	−1.45642	−	1.28584i
$295$	−0.0365983	−	0.112638i	−0.00213084	−	0.00655804i
$296$	34.1099	−	19.6933i	1.98260	−	1.14465i
$297$	8.67584	+	9.51927i	0.503423	+	0.552364i
$298$	−15.9389	+	27.6069i	−0.923313	+	1.59923i
$299$	9.41959	−	10.4615i	0.544749	−	0.605005i
$300$	21.0932	−	29.0323i	1.21782	−	1.67618i
$301$	6.38936	+	9.73438i	0.368277	+	0.561080i
$302$	0.404375	−	1.24454i	0.0232692	−	0.0716152i
$303$	0.0966919	+	0.454900i	0.00555481	+	0.0261333i
$304$	−0.960377	−	9.13737i	−0.0550814	−	0.524064i
$305$	0.104496	+	0.234701i	0.00598341	+	0.0134390i
$306$	−7.35941	−	6.62645i	−0.420710	−	0.378809i
$307$	−1.94636			−0.111085			−0.0555423	−	0.998456i	$-0.517689\pi$
$307$	−1.94636			−0.111085			−0.0555423	+	0.998456i	$0.517689\pi$
$308$	5.21662	+	30.7586i	0.297244	+	1.75263i
$309$	−10.6356			−0.605038
$310$	−0.178767	−	0.160962i	−0.0101533	−	0.00914203i
$311$	−8.38741	−	18.8384i	−0.475606	−	1.06823i	−0.978942	−	0.204138i	$-0.934561\pi$
$311$	−8.38741	−	18.8384i	−0.475606	−	1.06823i	0.503336	−	0.864091i	$-0.332106\pi$
$312$	−3.18477	−	30.3010i	−0.180302	−	1.71546i
$313$	−1.02448	−	4.81982i	−0.0579072	−	0.272432i	0.939663	−	0.342102i	$-0.111139\pi$
$313$	−1.02448	−	4.81982i	−0.0579072	−	0.272432i	−0.997570	+	0.0696697i	$0.977805\pi$
$314$	2.08784	−	6.42571i	0.117824	−	0.362624i
$315$	−0.0845286	+	0.00484389i	−0.00476265	+	0.000272922i
$316$	23.2823	−	32.0453i	1.30973	−	1.80269i
$317$	−3.43595	+	3.81601i	−0.192982	+	0.214329i	−0.831869	−	0.554973i	$-0.812729\pi$
$317$	−3.43595	+	3.81601i	−0.192982	+	0.214329i	0.638886	+	0.769301i	$0.279395\pi$
$318$	−3.96636	+	6.86994i	−0.222423	+	0.385247i
$319$	−1.62418	−	14.6042i	−0.0909366	−	0.817680i
$320$	0.304826	−	0.175991i	0.0170403	−	0.00983822i
$321$	1.75560	+	5.40319i	0.0979881	+	0.301576i
$322$	−7.73967	−	19.8720i	−0.431315	−	1.10742i
$323$	−18.9628	+	13.7773i	−1.05512	+	0.766589i
$324$	−38.5001	+	8.18345i	−2.13889	+	0.454636i
$325$	−13.7695	−	15.2926i	−0.763797	−	0.848282i
$326$	16.8762	−	1.77376i	0.934684	−	0.0982392i
$327$	1.67626	−	15.9486i	0.0926974	−	0.881957i
$328$	−18.9289	+	6.15036i	−1.04517	+	0.339597i
$329$	4.69956	−	2.42352i	0.259095	−	0.133613i
$330$	0.381193	+	0.273451i	0.0209840	+	0.0150530i
$331$	7.67422	+	13.2921i	0.421813	+	0.730602i	0.996117	−	0.0880402i	$-0.0280604\pi$
$331$	7.67422	+	13.2921i	0.421813	+	0.730602i	−0.574304	+	0.818642i	$0.694727\pi$
$332$	31.3051	+	6.65410i	1.71809	+	0.365191i
$333$	10.5677	−	4.70503i	0.579105	−	0.257834i
$334$	−15.6421	+	35.1327i	−0.855897	+	1.92238i
$335$	−0.0828076	−	0.0269058i	−0.00452426	−	0.00147002i
$336$	−7.64296	−	2.89112i	−0.416958	−	0.157724i
$337$	3.54840	+	4.88396i	0.193294	+	0.266046i	0.894653	−	0.446762i	$-0.147423\pi$
$337$	3.54840	+	4.88396i	0.193294	+	0.266046i	−0.701359	+	0.712808i	$0.747423\pi$
$338$	−9.24634	−	0.971829i	−0.502935	−	0.0528606i
$339$	−3.43411	+	16.1562i	−0.186515	+	0.877486i
$340$	0.357141	+	0.206196i	0.0193687	+	0.0111825i
$341$	−7.56910	+	8.50910i	−0.409890	+	0.460794i
$342$		−	15.2418i		−	0.824183i
$343$	3.16481	+	18.2478i	0.170884	+	0.985291i
$344$	13.0522	+	9.48301i	0.703730	+	0.511290i
$345$	−0.187490	−	0.0834760i	−0.0100941	−	0.00449420i
$346$	−11.6491	+	10.4889i	−0.626261	+	0.563888i
$347$	22.2119	−	19.9997i	1.19240	−	1.07364i	0.196749	−	0.980454i	$-0.436962\pi$
$347$	22.2119	−	19.9997i	1.19240	−	1.07364i	0.995649	−	0.0931856i	$-0.0297050\pi$
$348$	29.0544	+	12.9359i	1.55748	+	0.693436i
$349$	0.428252	+	0.311143i	0.0229238	+	0.0166551i	0.599188	−	0.800608i	$-0.295490\pi$
$349$	0.428252	+	0.311143i	0.0229238	+	0.0166551i	−0.576264	+	0.817263i	$0.695490\pi$
$350$	−30.0723	+	8.21543i	−1.60743	+	0.439133i
$351$			15.9854i			0.853240i
$352$	−6.24388	−	10.6655i	−0.332800	−	0.568471i
$353$	−11.2172	−	6.47623i	−0.597029	−	0.344695i	0.170843	−	0.985298i	$-0.445351\pi$
$353$	−11.2172	−	6.47623i	−0.597029	−	0.344695i	−0.767872	+	0.640604i	$0.778684\pi$
$354$	3.94252	−	18.5481i	0.209542	−	0.985819i
$355$	0.0777911	+	0.00817617i	0.00412872	+	0.000433946i
$356$	3.79983	+	5.23002i	0.201391	+	0.277190i
$357$	3.36165	+	20.5740i	0.177917	+	1.08889i
$358$	−37.9859	−	12.3424i	−2.00762	−	0.652314i
$359$	−0.142270	+	0.319545i	−0.00750875	+	0.0168649i	−0.917261	−	0.398287i	$-0.869605\pi$
$359$	−0.142270	+	0.319545i	−0.00750875	+	0.0168649i	0.909752	+	0.415152i	$0.136272\pi$
$360$	−0.107170	+	0.0477151i	−0.00564835	+	0.00251481i
$361$	−16.7023	−	3.55019i	−0.879071	−	0.186852i
$362$	−13.8084	−	23.9168i	−0.725753	−	1.25704i
$363$	12.8367	−	18.1244i	0.673750	−	0.951286i
$364$	−20.9300	+	32.5765i	−1.09703	+	1.70747i
$365$	0.0549512	−	0.0178547i	0.00287628	−	0.000934560i
$366$	−4.29967	+	40.9087i	−0.224748	+	2.13833i
$367$	15.9688	−	1.67839i	0.833564	−	0.0876111i	0.321875	−	0.946782i	$-0.395687\pi$
$367$	15.9688	−	1.67839i	0.833564	−	0.0876111i	0.511689	+	0.859171i	$0.329020\pi$
$368$	−3.50040	−	3.88759i	−0.182471	−	0.202654i
$369$	−5.71772	+	1.21534i	−0.297652	+	0.0632680i
$370$	−0.608943	+	0.442423i	−0.0316575	+	0.0230005i
$371$	4.10958	−	1.60058i	0.213359	−	0.0830981i
$372$	−7.61694	−	23.4425i	−0.394920	−	1.21544i
$373$	2.07349	−	1.19713i	0.107361	−	0.0619851i	−0.445358	−	0.895353i	$-0.646924\pi$
$373$	2.07349	−	1.19713i	0.107361	−	0.0619851i	0.552719	+	0.833368i	$0.313590\pi$
$374$	15.0934	−	26.5109i	0.780460	−	1.37085i
$375$	−0.300037	+	0.519679i	−0.0154938	+	0.0268361i
$376$	4.90231	−	5.44457i	0.252818	−	0.280782i
$377$	10.7198	−	14.7545i	0.552096	−	0.759895i
$378$	21.6306	+	10.8886i	1.11256	+	0.560051i
$379$	−7.52711	+	23.1661i	−0.386642	+	1.18996i	0.548640	+	0.836058i	$0.315146\pi$
$379$	−7.52711	+	23.1661i	−0.386642	+	1.18996i	−0.935282	+	0.353903i	$0.884854\pi$
$380$	0.131964	+	0.620841i	0.00676960	+	0.0318485i
$381$	1.78958	+	17.0267i	0.0916829	+	0.872304i
$382$	5.92225	+	13.3016i	0.303009	+	0.680569i
$383$	14.3048	+	12.8801i	0.730942	+	0.658143i	0.948092	−	0.317995i	$-0.103010\pi$
$383$	14.3048	+	12.8801i	0.730942	+	0.658143i	−0.217150	+	0.976138i	$0.569676\pi$
$384$	41.3083			2.10800
$385$	−0.0702515	−	0.251178i	−0.00358035	−	0.0128012i
$386$	35.6813			1.81613
$387$	3.52129	+	3.17058i	0.178997	+	0.161170i
$388$	−16.3756	−	36.7802i	−0.831344	−	1.86723i
$389$	3.92931	+	37.3849i	0.199224	+	1.89549i	0.401031	+	0.916064i	$0.368652\pi$
$389$	3.92931	+	37.3849i	0.199224	+	1.89549i	−0.201808	+	0.979425i	$0.564682\pi$
$390$	0.121058	+	0.569531i	0.00612999	+	0.0288393i
$391$	−4.12408	+	12.6926i	−0.208564	+	0.641893i
$392$	13.0469	+	22.0967i	0.658967	+	1.11605i
$393$	26.1518	−	35.9949i	1.31919	−	1.81570i
$394$	35.5458	−	39.4776i	1.79077	−	1.98886i
$395$	−0.165573	+	0.286780i	−0.00833086	+	0.0144295i
$396$	5.23368	+	11.5666i	0.263002	+	0.581242i
$397$	6.98930	−	4.03527i	0.350783	−	0.202525i	−0.314247	−	0.949341i	$-0.601752\pi$
$397$	6.98930	−	4.03527i	0.350783	−	0.202525i	0.665030	+	0.746817i	$0.268419\pi$
$398$	14.1826	+	43.6495i	0.710909	+	2.18795i
$399$	−20.0700	+	25.0333i	−1.00476	+	1.25323i
$400$	−6.18660	+	4.49483i	−0.309330	+	0.224741i
$401$	−13.2371	+	2.81363i	−0.661029	+	0.140506i	−0.526197	−	0.850363i	$-0.676383\pi$
$401$	−13.2371	+	2.81363i	−0.661029	+	0.140506i	−0.134832	+	0.990869i	$0.543049\pi$
$402$	−9.32804	−	10.3598i	−0.465241	−	0.516702i
$403$	−14.0571	+	1.47746i	−0.700236	+	0.0735978i
$404$	0.0855999	−	0.814429i	0.00425875	−	0.0405193i
$405$	0.312950	−	0.101684i	0.0155506	−	0.00505270i
$406$	−12.6630	−	24.5555i	−0.628457	−	1.21867i
$407$	21.1191	+	28.7019i	1.04683	+	1.42270i
$408$	14.4423	+	25.0148i	0.715001	+	1.23842i
$409$	−26.5600	−	5.64550i	−1.31331	−	0.279152i	−0.502557	−	0.864544i	$-0.667607\pi$
$409$	−26.5600	−	5.64550i	−1.31331	−	0.279152i	−0.810751	+	0.585392i	$0.800941\pi$
$410$	0.347471	−	0.154704i	0.0171604	−	0.00764028i
$411$	5.22378	−	11.7328i	0.257670	−	0.578736i
$412$	17.8113	+	5.78724i	0.877500	+	0.285117i
$413$	−8.16045	+	6.67443i	−0.401549	+	0.328427i
$414$	−5.10100	−	7.02092i	−0.250700	−	0.345059i
$415$	−0.266095	−	0.0279677i	−0.0130621	−	0.00137288i
$416$	3.18913	−	15.0037i	0.156360	−	0.735615i
$417$	−35.1416	−	20.2890i	−1.72089	−	0.993557i
$418$	45.8665	−	10.0391i	2.24341	−	0.491027i
$419$		−	27.7723i		−	1.35676i	−0.734709	−	0.678382i	$-0.762681\pi$
$419$		−	27.7723i		−	1.35676i	0.734709	−	0.678382i	$-0.237319\pi$
$420$	0.545981	+	0.143442i	0.0266411	+	0.00699924i
$421$	10.4163	+	7.56787i	0.507659	+	0.368836i	0.811935	−	0.583748i	$-0.198415\pi$
$421$	10.4163	+	7.56787i	0.507659	+	0.368836i	−0.304276	+	0.952584i	$0.598415\pi$
$422$	−13.7304	−	6.11315i	−0.668384	−	0.297584i
$423$	1.59906	−	1.43980i	0.0777488	−	0.0700054i
$424$	4.54114	−	4.08886i	0.220537	−	0.198573i
$425$	17.8223	+	7.93498i	0.864506	+	0.384903i
$426$	10.1319	+	7.36122i	0.490890	+	0.356652i
$427$	16.0915	−	16.2494i	0.778724	−	0.786366i
$428$		−	10.0039i		−	0.483559i
$429$	26.9279	−	5.89386i	1.30009	−	0.284558i
$430$	−0.267010	−	0.154159i	−0.0128764	−	0.00743418i
$431$	1.25278	−	5.89386i	0.0603442	−	0.283897i	−0.937621	−	0.347659i	$-0.886977\pi$
$431$	1.25278	−	5.89386i	0.0603442	−	0.283897i	0.997965	+	0.0637622i	$0.0203099\pi$
$432$	5.90779	+	0.620933i	0.284238	+	0.0298747i
$433$	−14.5439	−	20.0180i	−0.698935	−	0.962002i	−0.999965	−	0.00838697i	$-0.997330\pi$
$433$	−14.5439	−	20.0180i	−0.698935	−	0.962002i	0.301030	−	0.953615i	$-0.402670\pi$
$434$	−7.57593	+	20.0277i	−0.363656	+	0.961359i
$435$	−0.252872	−	0.0821630i	−0.0121243	−	0.00393942i
$436$	−11.4854	+	25.7967i	−0.550053	+	1.23544i
$437$	−18.7647	+	8.35459i	−0.897638	+	0.399654i
$438$	9.04880	+	1.92338i	0.432369	+	0.0919028i
$439$	−16.0379	−	27.7785i	−0.765449	−	1.32580i	−0.940009	−	0.341150i	$-0.889184\pi$
$439$	−16.0379	−	27.7785i	−0.765449	−	1.32580i	0.174560	−	0.984647i	$-0.444150\pi$
$440$	−0.214175	−	0.291074i	−0.0102104	−	0.0138764i
$441$	3.13248	+	6.85474i	0.149166	+	0.326416i
$442$	36.0094	−	11.7002i	1.71279	−	0.556520i
$443$	−3.35343	+	31.9058i	−0.159326	+	1.51589i	0.564226	+	0.825621i	$0.309175\pi$
$443$	−3.35343	+	31.9058i	−0.159326	+	1.51589i	−0.723552	+	0.690270i	$0.757492\pi$
$444$	−76.7042	+	8.06194i	−3.64022	+	0.382603i
$445$	−0.0361633	−	0.0401634i	−0.00171430	−	0.00190393i
$446$	−46.4966	+	9.88315i	−2.20168	+	0.467981i
$447$	22.0924	−	16.0510i	1.04493	−	0.759188i
$448$	−24.4450	−	19.5984i	−1.15492	−	0.925935i
$449$	−2.27236	−	6.99359i	−0.107239	−	0.330048i	0.883010	−	0.469354i	$-0.155513\pi$
$449$	−2.27236	−	6.99359i	−0.107239	−	0.330048i	−0.990249	+	0.139305i	$0.955513\pi$
$450$	−10.9864	+	6.34299i	−0.517903	+	0.299011i
$451$	−7.42325	−	16.4056i	−0.349547	−	0.772509i
$452$	14.5423	−	25.1880i	0.684012	−	1.18474i
$453$	−0.750085	+	0.833054i	−0.0352421	+	0.0391403i
$454$	2.08547	−	2.87041i	0.0978761	−	0.134715i
$455$	0.145551	−	0.289141i	0.00682354	−	0.0135552i
$456$	−13.7378	+	42.2805i	−0.643330	+	1.97996i
$457$	2.50484	+	11.7843i	0.117171	+	0.551248i	0.997097	+	0.0761374i	$0.0242588\pi$
$457$	2.50484	+	11.7843i	0.117171	+	0.551248i	−0.879926	+	0.475111i	$0.842408\pi$
$458$	−1.41647	−	13.4768i	−0.0661871	−	0.629728i
$459$	−6.16399	−	13.8445i	−0.287710	−	0.646208i
$460$	0.268565	+	0.241817i	0.0125219	+	0.0112748i
$461$	−40.9735			−1.90833			−0.954163	−	0.299286i	$-0.903251\pi$
$461$	−40.9735			−1.90833			−0.954163	+	0.299286i	$0.903251\pi$
$462$	10.3669	−	40.4519i	0.482314	−	1.88199i
$463$	−10.2910			−0.478264			−0.239132	−	0.970987i	$-0.576863\pi$
$463$	−10.2910			−0.478264			−0.239132	+	0.970987i	$0.576863\pi$
$464$	−5.03646	−	4.53485i	−0.233812	−	0.210525i
$465$	0.0838153	+	0.188252i	0.00388684	+	0.00872999i
$466$	−1.69758	−	16.1514i	−0.0786391	−	0.748201i
$467$	−5.51819	−	25.9611i	−0.255352	−	1.20133i	−0.899668	−	0.436575i	$-0.856191\pi$
$467$	−5.51819	−	25.9611i	−0.255352	−	1.20133i	0.644316	−	0.764759i	$-0.277142\pi$
$468$	−4.86915	+	14.9857i	−0.225076	+	0.692714i
$469$	0.443405	+	7.73767i	0.0204745	+	0.357292i
$470$	−0.0822960	+	0.113271i	−0.00379603	+	0.00522479i
$471$	−3.87278	+	4.30116i	−0.178448	+	0.198187i
$472$	−7.30354	+	12.6501i	−0.336173	+	0.582268i
$473$	−7.22178	+	12.6848i	−0.332058	+	0.583246i
$474$	−45.9161	+	26.5097i	−2.10900	+	1.21763i
$475$	9.27858	+	28.5565i	0.425731	+	1.31026i
$476$	5.56540	−	36.2842i	0.255090	−	1.66308i
$477$	1.45194	−	1.05490i	0.0664799	−	0.0483005i
$478$	−25.4354	+	5.40646i	−1.16339	+	0.247286i
$479$	−14.0485	−	15.6024i	−0.641893	−	0.712894i	0.331135	−	0.943583i	$-0.392569\pi$
$479$	−14.0485	−	15.6024i	−0.641893	−	0.712894i	−0.973027	+	0.230689i	$0.925902\pi$
$480$	−0.222400	+	0.0233752i	−0.0101511	+	0.00106693i
$481$	−4.62300	+	43.9849i	−0.210791	+	2.00554i
$482$	−37.7220	+	12.2566i	−1.71819	+	0.558274i
$483$	−0.867027	+	18.2481i	−0.0394511	+	0.830316i
$484$	−31.3596	+	23.3678i	−1.42544	+	1.06217i
$485$	0.168293	+	0.291491i	0.00764177	+	0.0132359i
$486$	24.6744	+	5.24471i	1.11926	+	0.237905i
$487$	9.42195	−	4.19492i	0.426949	−	0.190090i	−0.182001	−	0.983298i	$-0.558257\pi$
$487$	9.42195	−	4.19492i	0.426949	−	0.190090i	0.608951	+	0.793208i	$0.291591\pi$
$488$	12.8879	−	28.9468i	0.583409	−	1.31036i
$489$	−13.8249	−	4.49199i	−0.625184	−	0.203135i
$490$	−0.292105	−	0.393902i	−0.0131960	−	0.0177947i
$491$	−21.1098	−	29.0552i	−0.952673	−	1.31124i	−0.950330	−	0.311244i	$-0.899254\pi$
$491$	−21.1098	−	29.0552i	−0.952673	−	1.31124i	−0.00234281	−	0.999997i	$-0.500746\pi$
$492$	38.7604	+	4.07388i	1.74745	+	0.183665i
$493$	−3.59476	+	16.9120i	−0.161900	+	0.761678i
$494$	50.4669	+	29.1371i	2.27061	+	1.31094i
$495$	−0.0536221	−	0.0915945i	−0.00241013	−	0.00411686i
$496$			5.25252i			0.235845i
$497$	−1.83488	−	6.71651i	−0.0823054	−	0.301277i
$498$	−34.6573	−	25.1800i	−1.55303	−	1.12834i
$499$	−18.8946	−	8.41242i	−0.845839	−	0.376592i	−0.0623928	−	0.998052i	$-0.519873\pi$
$499$	−18.8946	−	8.41242i	−0.845839	−	0.376592i	−0.783446	+	0.621460i	$0.786540\pi$
$500$	0.785245	−	0.707038i	0.0351172	−	0.0316197i
$501$	24.4823	−	22.0440i	1.09379	−	0.984852i
$502$	52.3581	+	23.3113i	2.33686	+	1.04044i
$503$	−22.3995	−	16.2742i	−0.998745	−	0.725631i	−0.0369261	−	0.999318i	$-0.511757\pi$
$503$	−22.3995	−	16.2742i	−0.998745	−	0.725631i	−0.961819	+	0.273687i	$0.911757\pi$
$504$	7.41986	+	7.34776i	0.330507	+	0.327295i
$505$			0.00684621i			0.000304652i
$506$	17.7680	−	19.9746i	0.789882	−	0.887977i
$507$	6.89737	+	3.98220i	0.306323	+	0.176856i
$508$	6.26790	−	29.4882i	0.278093	−	1.30833i
$509$	5.61666	+	0.590335i	0.248954	+	0.0261661i	0.228183	−	0.973618i	$-0.426721\pi$
$509$	5.61666	+	0.590335i	0.248954	+	0.0261661i	0.0207705	+	0.999784i	$0.493388\pi$
$510$	−0.324456	−	0.446575i	−0.0143671	−	0.0197747i
$511$	−3.25617	−	3.98113i	−0.144044	−	0.176115i
$512$	−16.0873	−	5.22709i	−0.710967	−	0.231007i
$513$	9.48700	−	21.3081i	0.418861	−	0.940778i
$514$	28.1279	−	12.5234i	1.24067	−	0.552382i
$515$	−0.153146	−	0.0325522i	−0.00674842	−	0.00143442i
$516$	−15.7962	−	27.3599i	−0.695390	−	1.20445i
$517$	5.38594	+	3.86365i	0.236874	+	0.169923i
$518$	56.3687	+	36.2163i	2.47670	+	1.59125i
$519$	12.7710	−	4.14954i	0.560583	−	0.182144i
$520$	0.0468831	−	0.446063i	0.00205596	−	0.0195612i
$521$	32.1815	−	3.38241i	1.40990	−	0.148186i	0.631216	−	0.775607i	$-0.282556\pi$
$521$	32.1815	−	3.38241i	1.40990	−	0.148186i	0.778680	+	0.627421i	$0.215889\pi$
$522$	−7.52303	−	8.35517i	−0.329274	−	0.365696i
$523$	−8.17887	+	1.73847i	−0.357637	+	0.0760181i	−0.383226	−	0.923654i	$-0.625187\pi$
$523$	−8.17887	+	1.73847i	−0.357637	+	0.0760181i	0.0255894	+	0.999673i	$0.491854\pi$
$524$	−63.3824	+	46.0500i	−2.76887	+	2.01170i
$525$	26.3964	+	4.04877i	1.15203	+	0.176703i
$526$	−2.38626	−	7.34415i	−0.104046	−	0.320220i
$527$	11.6048	−	6.70002i	0.505512	−	0.291858i
$528$	−1.13223	−	10.1808i	−0.0492741	−	0.443060i
$529$	5.65235	−	9.79016i	0.245754	−	0.425659i
$530$	−0.0781398	+	0.0867831i	−0.00339418	+	0.00376962i
$531$	−2.52164	+	3.47074i	−0.109430	+	0.150617i
$532$	47.2326	−	31.0021i	2.04779	−	1.34411i
$533$	6.90622	−	21.2551i	0.299141	−	0.920663i
$534$	−1.79908	−	8.46403i	−0.0778540	−	0.366274i
$535$	0.00874213	+	0.0831758i	0.000377955	+	0.00359600i
$536$	4.36779	+	9.81022i	0.188660	+	0.423737i
$537$	25.4265	+	22.8941i	1.09724	+	0.987955i
$538$	64.8473			2.79577
$539$	−18.5645	+	13.9413i	−0.799628	+	0.600496i
$540$	−0.410374			−0.0176597
$541$	14.3479	+	12.9189i	0.616863	+	0.555426i	0.917210	−	0.398404i	$-0.130436\pi$
$541$	14.3479	+	12.9189i	0.616863	+	0.555426i	−0.300347	+	0.953830i	$0.597102\pi$
$542$	2.19113	+	4.92137i	0.0941172	+	0.211391i
$543$	2.47289	+	23.5280i	0.106122	+	1.00968i
$544$	3.02340	+	14.2240i	0.129627	+	0.609848i
$545$	0.0729505	−	0.224519i	0.00312486	−	0.00961732i
$546$	43.3289	−	28.4399i	1.85431	−	1.21711i
$547$	0.357385	−	0.491898i	0.0152807	−	0.0210320i	−0.801308	−	0.598252i	$-0.795862\pi$
$547$	0.357385	−	0.491898i	0.0152807	−	0.0210320i	0.816589	+	0.577220i	$0.195862\pi$
$548$	−15.1325	+	16.8063i	−0.646426	+	0.717929i
$549$	4.65308	−	8.05937i	0.198589	−	0.343965i
$550$	−26.3239	−	28.8830i	−1.12245	−	1.23158i
$551$	−23.0456	+	13.3054i	−0.981776	+	0.566829i
$552$	7.82196	+	24.0735i	0.332925	+	1.02464i
$553$	29.1358	+	4.46895i	1.23898	+	0.190039i
$554$	−22.7063	+	16.4971i	−0.964700	+	0.700896i
$555$	0.630697	−	0.134059i	0.0267716	−	0.00569048i
$556$	47.8111	+	53.0996i	2.02764	+	2.25193i
$557$	−18.8529	+	1.98152i	−0.798823	+	0.0839596i	−0.495140	−	0.868813i	$-0.664883\pi$
$557$	−18.8529	+	1.98152i	−0.798823	+	0.0839596i	−0.303683	+	0.952773i	$0.598216\pi$
$558$	−0.910819	+	8.66587i	−0.0385581	+	0.366855i
$559$	−17.2295	+	5.59822i	−0.728732	+	0.236779i
$560$	−0.101205	−	0.0650230i	−0.00427669	−	0.00274772i
$561$	−21.0488	+	15.4879i	−0.888682	+	0.653900i
$562$	−16.2443	−	28.1359i	−0.685224	−	1.18684i
$563$	−0.360430	−	0.0766118i	−0.0151903	−	0.00322880i	0.200310	−	0.979733i	$-0.435805\pi$
$563$	−0.360430	−	0.0766118i	−0.0151903	−	0.00322880i	−0.215501	+	0.976504i	$0.569138\pi$
$564$	−13.1062	+	5.83524i	−0.551869	+	0.245708i
$565$	−0.0988981	+	0.222129i	−0.00416067	+	0.00934502i
$566$	18.0596	+	5.86794i	0.759104	+	0.246648i
$567$	−18.5440	−	22.6727i	−0.778776	−	0.952166i
$568$	−5.67047	−	7.80473i	−0.237928	−	0.327479i
$569$	12.3241	+	1.29532i	0.516653	+	0.0543024i	0.359267	−	0.933235i	$-0.383027\pi$
$569$	12.3241	+	1.29532i	0.516653	+	0.0543024i	0.157386	+	0.987537i	$0.449693\pi$
$570$	0.176637	−	0.831013i	0.00739852	−	0.0348073i
$571$	21.4388	+	12.3777i	0.897187	+	0.517991i	0.876286	−	0.481790i	$-0.160013\pi$
$571$	21.4388	+	12.3777i	0.897187	+	0.517991i	0.0209004	+	0.999782i	$0.493347\pi$
$572$	−48.3029	−	4.78214i	−2.01964	−	0.199951i
$573$		−	12.4730i		−	0.521067i
$574$	−24.0570	−	23.8232i	−1.00412	−	0.994362i
$575$	13.8311	+	10.0489i	0.576797	+	0.419067i
$576$	−11.6476	−	5.18585i	−0.485317	−	0.216077i
$577$	−20.9765	+	18.8873i	−0.873261	+	0.786288i	−0.978086	−	0.208203i	$-0.933239\pi$
$577$	−20.9765	+	18.8873i	−0.873261	+	0.786288i	0.104825	+	0.994491i	$0.466572\pi$
$578$	3.10161	−	2.79270i	0.129010	−	0.116161i
$579$	−27.9234	−	12.4323i	−1.16046	−	0.516668i
$580$	0.378773	+	0.275195i	0.0157277	+	0.0114268i
$581$	6.27644	+	22.9747i	0.260390	+	0.953152i
$582$			53.8903i			2.23383i
$583$	4.13079	+	3.67446i	0.171080	+	0.152180i
$584$	−6.17144	−	3.56308i	−0.255376	−	0.147441i
$585$	0.0273880	−	0.128851i	0.00113236	−	0.00532732i
$586$	−52.4385	−	5.51151i	−2.16622	−	0.227678i
$587$	0.846793	+	1.16551i	0.0349509	+	0.0481058i	0.826135	−	0.563473i	$-0.190535\pi$
$587$	0.846793	+	1.16551i	0.0349509	+	0.0481058i	−0.791184	+	0.611578i	$0.790535\pi$
$588$	−5.74018	−	49.9203i	−0.236721	−	2.05868i
$589$	19.6146	+	6.37317i	0.808206	+	0.262602i
$590$	0.113539	−	0.255014i	0.00467435	−	0.0104988i
$591$	−41.5724	+	18.5092i	−1.71006	+	0.761368i
$592$	16.0760	+	3.41707i	0.660721	+	0.140441i
$593$	11.9989	+	20.7826i	0.492734	+	0.853441i	0.999965	−	0.00836933i	$-0.00266407\pi$
$593$	11.9989	+	20.7826i	0.492734	+	0.853441i	−0.507231	+	0.861810i	$0.669331\pi$
$594$	0.183298	+	30.3566i	0.00752082	+	1.24554i
$595$	−0.0145648	+	0.306542i	−0.000597099	+	0.0125670i
$596$	−45.7318	+	14.8592i	−1.87325	+	0.608655i
$597$	4.10965	−	39.1007i	0.168197	−	1.60028i
$598$	32.9982	−	3.46825i	1.34940	−	0.141827i
$599$	0.240223	+	0.266795i	0.00981524	+	0.0109009i	0.748032	−	0.663662i	$-0.230999\pi$
$599$	0.240223	+	0.266795i	0.00981524	+	0.0109009i	−0.738217	+	0.674563i	$0.764332\pi$
$600$	36.1930	−	7.69307i	1.47757	−	0.314068i
$601$	7.01674	−	5.09796i	0.286219	−	0.207950i	−0.435406	−	0.900234i	$-0.643395\pi$
$601$	7.01674	−	5.09796i	0.286219	−	0.207950i	0.721625	+	0.692284i	$0.243395\pi$
$602$	−4.16088	+	27.1273i	−0.169585	+	1.10563i
$603$	0.974611	+	2.99954i	0.0396892	+	0.122151i
$604$	1.70945	−	0.986954i	0.0695567	−	0.0401586i
$605$	0.240313	−	0.221692i	0.00977011	−	0.00901304i
$606$	−0.548070	+	0.949285i	−0.0222638	+	0.0385621i
$607$	−16.6688	+	18.5126i	−0.676566	+	0.751403i	−0.979464	−	0.201620i	$-0.935379\pi$
$607$	−16.6688	+	18.5126i	−0.676566	+	0.751403i	0.302898	+	0.953023i	$0.402046\pi$
$608$	−13.1553	+	18.1068i	−0.533520	+	0.734327i
$609$	1.35404	+	23.6287i	0.0548684	+	0.957484i
$610$	−0.187121	+	0.575899i	−0.00757630	+	0.0233175i
$611$	1.71044	+	8.04701i	0.0691972	+	0.325547i
$612$	−1.56145	−	14.8562i	−0.0631180	−	0.600527i
$613$	4.23914	+	9.52126i	0.171217	+	0.384560i	0.978690	−	0.205345i	$-0.0658317\pi$
$613$	4.23914	+	9.52126i	0.171217	+	0.384560i	−0.807472	+	0.589905i	$0.799165\pi$
$614$	−3.40919	−	3.06965i	−0.137584	−	0.123881i
$615$	−0.325826			−0.0131386
$616$	−17.2242	+	27.1679i	−0.693982	+	1.09462i
$617$	48.2452			1.94228			0.971140	−	0.238511i	$-0.0766594\pi$
$617$	48.2452			1.94228			0.971140	+	0.238511i	$0.0766594\pi$
$618$	−18.6290	−	16.7737i	−0.749369	−	0.674735i
$619$	−1.04933	−	2.35683i	−0.0421760	−	0.0947289i	0.891229	−	0.453554i	$-0.149844\pi$
$619$	−1.04933	−	2.35683i	−0.0421760	−	0.0947289i	−0.933405	+	0.358825i	$0.883177\pi$
$620$	−0.0379290	−	0.360871i	−0.00152327	−	0.0144929i
$621$	−2.76118	−	12.9903i	−0.110802	−	0.521283i
$622$	15.0194	−	46.2248i	0.602222	−	1.85345i
$623$	−2.16309	+	4.29704i	−0.0866625	+	0.172157i
$624$	7.47286	−	10.2855i	0.299154	−	0.411750i
$625$	16.7194	−	18.5688i	0.668776	−	0.742751i
$626$	5.80699	−	10.0580i	0.232094	−	0.401998i
$627$	−39.3920	−	8.12474i	−1.57316	−	0.324471i
$628$	8.82613	−	5.09577i	0.352201	−	0.203343i
$629$	−12.9567	−	39.8767i	−0.516618	−	1.58999i
$630$	−0.155697	−	0.124828i	−0.00620314	−	0.00497325i
$631$	38.1253	−	27.6997i	1.51775	−	1.10271i	0.555155	−	0.831747i	$-0.312659\pi$
$631$	38.1253	−	27.6997i	1.51775	−	1.10271i	0.962591	−	0.270960i	$-0.0873411\pi$
$632$	39.9492	−	8.49146i	1.58909	−	0.337772i
$633$	8.61509	+	9.56803i	0.342419	+	0.380295i
$634$	−12.0366	+	1.26510i	−0.478036	+	0.0502436i
$635$	−0.0263445	+	0.250651i	−0.00104545	+	0.00994678i
$636$	−11.3803	+	3.69768i	−0.451258	+	0.146623i
$637$	−28.6849	−	2.73199i	−1.13654	−	0.108246i
$638$	20.1878	−	28.1419i	0.799242	−	1.11415i
$639$	−1.41668	−	2.45376i	−0.0560428	−	0.0970691i
$640$	0.594813	+	0.126431i	0.0235120	+	0.00499764i
$641$	16.3906	−	7.29754i	0.647388	−	0.288236i	−0.0566542	−	0.998394i	$-0.518043\pi$
$641$	16.3906	−	7.29754i	0.647388	−	0.288236i	0.704042	+	0.710158i	$0.251377\pi$
$642$	−5.44643	+	12.2329i	−0.214953	+	0.482793i
$643$	40.6310	+	13.2018i	1.60233	+	0.520629i	0.967682	−	0.252172i	$-0.0811450\pi$
$643$	40.6310	+	13.2018i	1.60233	+	0.520629i	0.634648	+	0.772801i	$0.281145\pi$
$644$	11.3815	−	30.0880i	0.448493	−	1.18563i
$645$	0.155244	+	0.213674i	0.00611271	+	0.00841342i
$646$	−54.9432	−	5.77477i	−2.16171	−	0.227205i
$647$	−4.05053	+	19.0563i	−0.159243	+	0.749179i	0.823958	+	0.566651i	$0.191761\pi$
$647$	−4.05053	+	19.0563i	−0.159243	+	0.749179i	−0.983201	+	0.182528i	$0.941572\pi$
$648$	−35.1467	−	20.2919i	−1.38069	−	0.797143i
$649$	−12.1052	−	5.30224i	−0.475171	−	0.208131i
$650$		−	48.5024i		−	1.90242i
$651$	12.9069	−	13.0336i	0.505862	−	0.510825i
$652$	20.7081	+	15.0453i	0.810994	+	0.589221i
$653$	18.8249	+	8.38141i	0.736677	+	0.327990i	0.740549	−	0.672003i	$-0.234566\pi$
$653$	18.8249	+	8.38141i	0.736677	+	0.327990i	−0.00387156	+	0.999993i	$0.501232\pi$
$654$	28.0889	−	25.2914i	1.09836	−	0.988971i
$655$	0.486739	−	0.438262i	0.0190185	−	0.0171243i
$656$	−7.58706	−	3.37798i	−0.296225	−	0.131888i
$657$	−1.69322	−	1.23020i	−0.0660589	−	0.0479946i
$658$	12.0538	+	3.16682i	0.469907	+	0.123455i
$659$		−	16.0855i		−	0.626603i	−0.949654	−	0.313302i	$-0.898565\pi$
$659$		−	16.0855i		−	0.626603i	0.949654	−	0.313302i	$-0.101435\pi$
$660$	0.151305	+	0.691285i	0.00588956	+	0.0269082i
$661$	−29.6782	−	17.1347i	−1.15435	−	0.666462i	−0.204404	−	0.978887i	$-0.565526\pi$
$661$	−29.6782	−	17.1347i	−1.15435	−	0.666462i	−0.949943	+	0.312424i	$0.898859\pi$
$662$	−7.52139	+	35.3853i	−0.292327	+	1.37529i
$663$	−32.2568	−	3.39032i	−1.25275	−	0.131669i
$664$	19.3966	+	26.6971i	0.752734	+	1.03605i
$665$	−0.365614	+	0.299036i	−0.0141779	+	0.0115961i
$666$	25.9305	+	8.42532i	1.00479	+	0.326475i
$667$	−6.16269	+	13.8416i	−0.238620	+	0.535950i
$668$	−52.9952	+	23.5950i	−2.05044	+	0.912917i
$669$	39.8307	+	8.46628i	1.53994	+	0.327325i
$670$	−0.102610	−	0.177725i	−0.00396416	−	0.00686613i
$671$	27.3175	+	8.69398i	1.05458	+	0.335627i
$672$	9.12350	+	17.6918i	0.351947	+	0.682477i
$673$	−41.2055	+	13.3885i	−1.58835	+	0.516087i	−0.964191	−	0.265207i	$-0.914560\pi$
$673$	−41.2055	+	13.3885i	−1.58835	+	0.516087i	−0.624162	+	0.781295i	$0.714560\pi$
$674$	−1.48732	+	14.1509i	−0.0572893	+	0.545071i
$675$	−19.3071	+	2.02926i	−0.743131	+	0.0781062i
$676$	−9.38406	−	10.4221i	−0.360925	−	0.400848i
$677$	24.7780	−	5.26672i	0.952296	−	0.202417i	0.294532	−	0.955641i	$-0.404836\pi$
$677$	24.7780	−	5.26672i	0.952296	−	0.202417i	0.657763	+	0.753225i	$0.271503\pi$
$678$	−31.4955	+	22.8828i	−1.20958	+	0.878808i
$679$	18.7410	−	23.3757i	0.719215	−	0.897076i
$680$	0.131398	+	0.404401i	0.00503887	+	0.0155081i
$681$	−2.63217	+	1.51968i	−0.100865	+	0.0582344i
$682$	−26.6777	+	2.96691i	−1.02154	+	0.113609i
$683$	−15.3101	+	26.5179i	−0.585826	+	1.01468i	0.408946	+	0.912559i	$0.365897\pi$
$683$	−15.3101	+	26.5179i	−0.585826	+	1.01468i	−0.994772	+	0.102122i	$0.967437\pi$
$684$	15.3841	−	17.0858i	0.588226	−	0.653291i
$685$	0.111129	−	0.152956i	0.00424604	−	0.00584417i
$686$	−23.2357	+	36.9537i	−0.887144	+	1.41090i
$687$	−3.58716	+	11.0401i	−0.136859	+	0.421208i
$688$	1.39969	+	6.58502i	0.0533627	+	0.251052i
$689$	0.717242	+	6.82411i	0.0273248	+	0.259978i
$690$	−0.196751	−	0.441910i	−0.00749017	−	0.0168232i
$691$	−18.4476	−	16.6103i	−0.701779	−	0.631885i	0.238955	−	0.971031i	$-0.423195\pi$
$691$	−18.4476	−	16.6103i	−0.701779	−	0.631885i	−0.940734	+	0.339146i	$0.889862\pi$
$692$	−23.6453			−0.898859
$693$	−5.86503	+	7.40665i	−0.222794	+	0.281355i
$694$	70.4477			2.67416
$695$	−0.443918	−	0.399706i	−0.0168388	−	0.0151617i
$696$	13.3380	+	29.9577i	0.505577	+	1.13555i
$697$	2.21471	+	21.0715i	0.0838880	+	0.798141i
$698$	0.259403	+	1.22040i	0.00981856	+	0.0461927i
$699$	−4.29909	+	13.2312i	−0.162606	+	0.500451i
$700$	−42.0026	−	21.1437i	−1.58755	−	0.799158i
$701$	11.3251	−	15.5877i	0.427744	−	0.588740i	−0.539689	−	0.841864i	$-0.681458\pi$
$701$	11.3251	−	15.5877i	0.427744	−	0.588740i	0.967434	+	0.253125i	$0.0814583\pi$
$702$	−25.2110	+	27.9997i	−0.951529	+	1.05678i
$703$	32.2663	−	55.8869i	1.21695	−	2.10782i
$704$	7.93381	−	38.4663i	0.299017	−	1.44975i
$705$	0.103870	−	0.0599691i	0.00391195	−	0.00225857i
$706$	−9.43385	−	29.0344i	−0.355048	−	1.09272i
$707$	0.567859	−	0.221168i	0.0213565	−	0.00831786i
$708$	23.1407	−	16.8127i	0.869681	−	0.631860i
$709$	−41.1567	+	8.74812i	−1.54567	+	0.328543i	−0.900281	−	0.435310i	$-0.856639\pi$
$709$	−41.1567	+	8.74812i	−1.54567	+	0.328543i	−0.645391	+	0.763853i	$0.723305\pi$
$710$	0.123362	+	0.137007i	0.00462969	+	0.00514179i
$711$	11.9294	−	1.25383i	0.447387	−	0.0470222i
$712$	−0.696749	+	6.62912i	−0.0261118	+	0.248437i
$713$	11.1681	−	3.62873i	0.418249	−	0.135897i
$714$	−26.5596	+	41.3386i	−0.993967	+	1.54706i
$715$	0.405784	−	0.00245019i	0.0151755	−	9.16320e-5i
$716$	−30.1239	−	52.1761i	−1.12578	−	1.94991i
$717$	21.7889	+	4.63137i	0.813722	+	0.172962i
$718$	−0.753158	+	0.335328i	−0.0281076	+	0.0125143i
$719$	20.4602	−	45.9543i	0.763036	−	1.71381i	0.0648467	−	0.997895i	$-0.479344\pi$
$719$	20.4602	−	45.9543i	0.763036	−	1.71381i	0.698190	−	0.715913i	$-0.253989\pi$
$720$	−0.0465558	−	0.0151269i	−0.00173503	−	0.000563746i
$721$	2.24735	+	13.7543i	0.0836959	+	0.512236i
$722$	−23.6563	−	32.5601i	−0.880396	−	1.21176i
$723$	33.7910	+	3.55157i	1.25670	+	0.132084i
$724$	8.66117	−	40.7476i	0.321890	−	1.51437i
$725$	19.1812	+	11.0743i	0.712371	+	0.411288i
$726$	51.0688	−	11.5013i	1.89534	−	0.426853i
$727$			2.86794i			0.106366i	0.998585	+	0.0531830i	$0.0169367\pi$
$727$			2.86794i			0.106366i	−0.998585	+	0.0531830i	$0.983063\pi$
$728$	−38.5132	+	10.5214i	−1.42740	+	0.389949i
$729$	9.38707	+	6.82011i	0.347669	+	0.252597i
$730$	0.124410	+	0.0553910i	0.00460463	+	0.00205011i
$731$	12.7633	−	11.4922i	0.472069	−	0.425053i
$732$	−46.1104	+	41.5180i	−1.70429	+	1.53455i
$733$	12.1677	+	5.41741i	0.449424	+	0.200096i	0.618952	−	0.785429i	$-0.287558\pi$
$733$	12.1677	+	5.41741i	0.449424	+	0.200096i	−0.169528	+	0.985525i	$0.554224\pi$
$734$	30.6175	+	22.2449i	1.13011	+	0.821075i
$735$	0.0913494	+	0.410036i	0.00336947	+	0.0151244i
$736$			12.7433i			0.469726i
$737$	−8.38447	+	4.90851i	−0.308846	+	0.180807i
$738$	−11.9317	−	6.88879i	−0.439213	−	0.253580i
$739$	−3.45510	+	16.2550i	−0.127098	+	0.597949i	0.867787	+	0.496936i	$0.165542\pi$
$739$	−3.45510	+	16.2550i	−0.127098	+	0.597949i	−0.994885	+	0.101013i	$0.967792\pi$
$740$	−1.12917	−	0.118680i	−0.0415090	−	0.00436277i
$741$	−29.3422	−	40.3860i	−1.07791	−	1.48362i
$742$	9.72253	+	3.67777i	0.356925	+	0.135015i
$743$	−12.3025	−	3.99731i	−0.451333	−	0.146647i	0.0745253	−	0.997219i	$-0.476256\pi$
$743$	−12.3025	−	3.99731i	−0.451333	−	0.146647i	−0.525858	+	0.850572i	$0.676256\pi$
$744$	10.3373	−	23.2180i	0.378984	−	0.851213i
$745$	0.367243	−	0.163507i	0.0134547	−	0.00599044i
$746$	5.51990	+	1.17329i	0.202098	+	0.0429572i
$747$	4.84593	+	8.39339i	0.177303	+	0.307098i
$748$	43.6777	−	14.4839i	1.59702	−	0.529584i
$749$	6.61660	−	3.41212i	0.241765	−	0.124676i
$750$	−1.34513	+	0.437060i	−0.0491173	+	0.0159592i
$751$	2.73645	−	26.0356i	0.0998546	−	0.950053i	−0.823814	−	0.566860i	$-0.808158\pi$
$751$	2.73645	−	26.0356i	0.0998546	−	0.950053i	0.923668	−	0.383193i	$-0.125175\pi$
$752$	3.04039	−	0.319558i	0.110872	−	0.0116531i
$753$	−32.8520	−	36.4859i	−1.19719	−	1.32962i
$754$	42.0461	−	8.93718i	1.53123	−	0.325473i
$755$	−0.0133505	+	0.00969967i	−0.000485873	+	0.000353007i
$756$	13.2572	+	34.0384i	0.482158	+	1.23797i
$757$	−10.5845	−	32.5757i	−0.384699	−	1.18398i	−0.936698	−	0.350138i	$-0.886135\pi$
$757$	−10.5845	−	32.5757i	−0.384699	−	1.18398i	0.551999	−	0.833845i	$-0.313865\pi$
$758$	−49.7200	+	28.7059i	−1.80591	+	1.04264i
$759$	−20.8645	+	9.44082i	−0.757332	+	0.342680i
$760$	−0.327222	+	0.566765i	−0.0118696	+	0.0205587i
$761$	9.15171	−	10.1640i	0.331749	−	0.368445i	−0.554074	−	0.832467i	$-0.686928\pi$
$761$	9.15171	−	10.1640i	0.331749	−	0.368445i	0.885823	+	0.464022i	$0.153594\pi$
$762$	−23.7186	+	32.6459i	−0.859235	+	1.18264i
$763$	−20.9794	+	1.20222i	−0.759504	+	0.0435232i
$764$	−6.78704	+	20.8884i	−0.245546	+	0.755714i
$765$	0.0259648	+	0.122155i	0.000938759	+	0.00441651i
$766$	4.74240	+	45.1209i	0.171350	+	1.63028i
$767$	−6.67140	−	14.9842i	−0.240890	−	0.541048i
$768$	36.8170	+	33.1502i	1.32852	+	1.19620i
$769$	5.33632			0.192433			0.0962163	−	0.995360i	$-0.469326\pi$
$769$	5.33632			0.192433			0.0962163	+	0.995360i	$0.469326\pi$
$770$	0.273088	−	0.550752i	0.00984140	−	0.0198477i
$771$	−26.3757			−0.949899
$772$	39.9980	+	36.0144i	1.43956	+	1.29618i
$773$	−15.0145	−	33.7232i	−0.540035	−	1.21294i	−0.953216	−	0.302290i	$-0.902249\pi$
$773$	−15.0145	−	33.7232i	−0.540035	−	1.21294i	0.413181	−	0.910649i	$-0.364418\pi$
$774$	1.16739	+	11.1070i	0.0419611	+	0.399233i
$775$	−3.56894	−	16.7905i	−0.128200	−	0.603134i
$776$	12.8281	−	39.4808i	0.460502	−	1.41728i
$777$	−31.4942	−	47.9824i	−1.12985	−	1.72136i
$778$	−52.0781	+	71.6794i	−1.86709	+	2.56983i
$779$	−21.8202	+	24.2338i	−0.781791	+	0.868267i
$780$	−0.439144	+	0.760620i	−0.0157239	+	0.0272346i
$781$	6.45088	−	5.87931i	0.230831	−	0.210378i
$782$	−27.2414	+	15.7279i	−0.974152	+	0.562427i
$783$	−5.31671	−	16.3632i	−0.190004	−	0.584772i
$784$	−2.12389	+	10.4950i	−0.0758534	+	0.374822i
$785$	−0.0689301	+	0.0500806i	−0.00246022	+	0.00178745i
$786$	102.575	−	21.8031i	3.65874	−	0.777689i
$787$	32.4638	+	36.0547i	1.15721	+	1.28521i	0.951864	+	0.306520i	$0.0991647\pi$
$787$	32.4638	+	36.0547i	1.15721	+	1.28521i	0.205344	+	0.978690i	$0.434169\pi$
$788$	79.6923	−	8.37600i	2.83892	−	0.298383i
$789$	−0.691460	+	6.57880i	−0.0246166	+	0.234212i
$790$	−0.742300	+	0.241188i	−0.0264099	+	0.00858108i
$791$	21.6194	+	1.02721i	0.768696	+	0.0365233i
$792$	−3.96986	+	12.4738i	−0.141063	+	0.443236i
$793$	17.7902	+	30.8135i	0.631747	+	1.09422i
$794$	18.6064	+	3.95491i	0.660316	+	0.140354i
$795$	0.0913880	−	0.0406885i	0.00324120	−	0.00144307i
$796$	−28.1586	+	63.2452i	−0.998054	+	2.24167i
$797$	43.2263	+	14.0451i	1.53115	+	0.497502i	0.948920	−	0.315518i	$-0.102178\pi$
$797$	43.2263	+	14.0451i	1.53115	+	0.497502i	0.582235	+	0.813020i	$0.302178\pi$
$798$	−74.6347	+	12.1948i	−2.64204	+	0.431691i
$799$	−4.58429	−	6.30974i	−0.162181	−	0.223223i
$800$	18.5261	+	1.94718i	0.654998	+	0.0688431i
$801$	−0.407025	+	1.91490i	−0.0143815	+	0.0676597i
$802$	−27.6232	−	15.9482i	−0.975408	−	0.563152i
$803$	2.58673	−	5.90561i	0.0912839	−	0.208404i
$804$		−	21.0283i		−	0.741611i
$805$	−0.0683361	+	0.260107i	−0.00240853	+	0.00916757i
$806$	−26.9522	−	19.5819i	−0.949352	−	0.689745i
$807$	−50.7480	−	22.5945i	−1.78642	−	0.795363i
$808$	0.627493	−	0.564997i	0.0220751	−	0.0198765i
$809$	−28.2693	+	25.4538i	−0.993896	+	0.894908i	−0.994462	−	0.105092i	$-0.966486\pi$
$809$	−28.2693	+	25.4538i	−0.993896	+	0.894908i	0.000566900		1.00000i	$0.499820\pi$
$810$	0.708523	+	0.315455i	0.0248950	+	0.0110839i
$811$	−28.1472	−	20.4501i	−0.988381	−	0.718101i	−0.0288150	−	0.999585i	$-0.509173\pi$
$811$	−28.1472	−	20.4501i	−0.988381	−	0.718101i	−0.959566	+	0.281484i	$0.909173\pi$
$812$	10.5897	−	40.3075i	0.371626	−	1.41452i
$813$		−	4.61480i		−	0.161848i
$814$	−8.27477	+	83.5808i	−0.290031	+	2.92951i
$815$	−0.185322	−	0.106995i	−0.00649153	−	0.00374789i
$816$	−2.50594	+	11.7895i	−0.0877255	+	0.412716i
$817$	26.2889	+	2.76307i	0.919732	+	0.0966678i
$818$	−37.6181	−	51.7769i	−1.31529	−	1.81034i
$819$	−11.5723	+	1.89083i	−0.404368	+	0.0660710i
$820$	0.545656	+	0.177294i	0.0190551	+	0.00619139i
$821$	−0.875046	+	1.96538i	−0.0305393	+	0.0685924i	−0.928171	−	0.372154i	$-0.878619\pi$
$821$	−0.875046	+	1.96538i	−0.0305393	+	0.0685924i	0.897632	+	0.440746i	$0.145286\pi$
$822$	27.6539	−	12.3123i	0.964540	−	0.429441i
$823$	12.5635	+	2.67045i	0.437935	+	0.0930859i	0.421603	−	0.906781i	$-0.361468\pi$
$823$	12.5635	+	2.67045i	0.437935	+	0.0930859i	0.0163322	+	0.999867i	$0.494801\pi$
$824$	9.65508	+	16.7231i	0.336351	+	0.582576i
$825$	10.5369	+	31.7751i	0.366848	+	1.10627i
$826$	−24.8200	−	1.17928i	−0.863599	−	0.0410325i
$827$	−32.2290	+	10.4718i	−1.12071	+	0.364141i	−0.810039	−	0.586376i	$-0.800554\pi$
$827$	−32.2290	+	10.4718i	−1.12071	+	0.364141i	−0.310672	+	0.950517i	$0.600554\pi$
$828$	1.36834	−	13.0189i	0.0475533	−	0.452439i
$829$	13.1585	−	1.38302i	0.457014	−	0.0480342i	0.126775	−	0.991931i	$-0.459537\pi$
$829$	13.1585	−	1.38302i	0.457014	−	0.0480342i	0.330239	+	0.943897i	$0.392871\pi$
$830$	−0.421976	−	0.468652i	−0.0146470	−	0.0162671i
$831$	23.5175	−	4.99880i	0.815813	−	0.173406i
$832$	39.4370	−	28.6526i	1.36723	−	0.993351i
$833$	25.8966	−	8.69478i	0.897264	−	0.301256i
$834$	−29.5548	−	90.9603i	−1.02340	−	3.14970i
$835$	0.419999	−	0.242487i	0.0145347	−	0.00839159i
$836$	61.5483	+	35.0411i	2.12869	+	1.21192i
$837$	−6.66725	+	11.5480i	−0.230454	+	0.399158i
$838$	43.8003	−	48.6452i	1.51306	−	1.68042i
$839$	−5.96676	+	8.21255i	−0.205996	+	0.283529i	−0.899497	−	0.436926i	$-0.856067\pi$
$839$	−5.96676	+	8.21255i	−0.205996	+	0.283529i	0.693502	+	0.720455i	$0.256067\pi$
$840$	0.319392	+	0.486603i	0.0110201	+	0.0167894i
$841$	2.89573	−	8.91215i	0.0998529	−	0.307316i
$842$	6.30941	+	29.6834i	0.217437	+	1.02296i
$843$	2.90913	+	27.6785i	0.100196	+	0.953298i
$844$	−9.22125	−	20.7113i	−0.317408	−	0.712911i
$845$	0.0871295	+	0.0784517i	0.00299735	+	0.00269882i
$846$	5.07160			0.174365
$847$	−26.1515	−	12.7710i	−0.898577	−	0.438816i
$848$	2.54986			0.0875627
$849$	−12.0885	−	10.8846i	−0.414877	−	0.373557i
$850$	18.7025	+	42.0066i	0.641492	+	1.44081i
$851$	−3.84073	−	36.5421i	−0.131659	−	1.25265i
$852$	3.92767	+	18.4782i	0.134560	+	0.633053i
$853$	−16.6829	+	51.3448i	−0.571213	+	1.75801i	0.0775145	+	0.996991i	$0.475302\pi$
$853$	−16.6829	+	51.3448i	−0.571213	+	1.75801i	−0.648727	+	0.761021i	$0.724698\pi$
$854$	53.8129	−	3.08373i	1.84144	−	0.105523i
$855$	−0.112977	+	0.155500i	−0.00386375	+	0.00531799i
$856$	6.90205	−	7.66551i	0.235907	−	0.262002i
$857$	−13.3649	+	23.1486i	−0.456535	+	0.790741i	−0.998775	−	0.0494823i	$-0.984243\pi$
$857$	−13.3649	+	23.1486i	−0.456535	+	0.790741i	0.542240	+	0.840223i	$0.317576\pi$
$858$	56.4615	+	32.1451i	1.92756	+	1.09741i
$859$	−5.85586	+	3.38088i	−0.199799	+	0.115354i	−0.596562	−	0.802567i	$-0.703467\pi$
$859$	−5.85586	+	3.38088i	−0.199799	+	0.115354i	0.396763	+	0.917921i	$0.370134\pi$
$860$	−0.143716	−	0.442312i	−0.00490067	−	0.0150827i
$861$	10.5258	+	27.0256i	0.358719	+	0.921030i
$862$	11.4897	−	8.34774i	0.391340	−	0.284325i
$863$	6.47038	−	1.37532i	0.220254	−	0.0468165i	−0.0964626	−	0.995337i	$-0.530753\pi$
$863$	6.47038	−	1.37532i	0.220254	−	0.0468165i	0.316717	+	0.948520i	$0.397419\pi$
$864$	−9.68273	−	10.7538i	−0.329413	−	0.365850i
$865$	0.196594	−	0.0206629i	0.00668440	−	0.000702559i
$866$	6.09609	−	58.0004i	0.207154	−	1.97093i
$867$	−3.40030	+	1.10483i	−0.115480	+	0.0375218i
$868$	−28.7071	+	14.8040i	−0.974382	+	0.502480i
$869$	11.6304	+	35.0727i	0.394535	+	1.18976i
$870$	−0.313342	−	0.542725i	−0.0106233	−	0.0184001i
$871$	−11.7949	−	2.50708i	−0.399654	−	0.0849490i
$872$	−26.5987	+	11.8425i	−0.900747	+	0.401038i
$873$	4.95899	−	11.1381i	0.167836	−	0.376967i
$874$	−46.0440	−	14.9606i	−1.55746	−	0.506050i
$875$	0.735464	+	0.278206i	0.0248632	+	0.00940508i
$876$	8.20219	+	11.2894i	0.277126	+	0.381432i
$877$	−21.4357	−	2.25299i	−0.723834	−	0.0760780i	−0.264555	−	0.964370i	$-0.585225\pi$
$877$	−21.4357	−	2.25299i	−0.723834	−	0.0760780i	−0.459278	+	0.888293i	$0.651892\pi$
$878$	15.7185	−	73.9499i	0.530475	−	2.49569i
$879$	39.1168	+	22.5841i	1.31938	+	0.761744i
$880$	0.0148566	−	0.150062i	0.000500816	−	0.00505858i
$881$			57.0407i			1.92175i	0.276982	+	0.960875i	$0.410666\pi$
$881$			57.0407i			1.92175i	−0.276982	+	0.960875i	$0.589334\pi$
$882$	−5.32400	+	16.9469i	−0.179269	+	0.570631i
$883$	34.8976	+	25.3546i	1.17440	+	0.853249i	0.991529	−	0.129888i	$-0.0414619\pi$
$883$	34.8976	+	25.3546i	1.17440	+	0.853249i	0.182868	+	0.983137i	$0.441462\pi$
$884$	52.1752	+	23.2299i	1.75484	+	0.781306i
$885$	−0.177707	+	0.160008i	−0.00597355	+	0.00537861i
$886$	−56.1932	+	50.5965i	−1.88785	+	1.69982i
$887$	33.0097	+	14.6969i	1.10836	+	0.493473i	0.877530	−	0.479522i	$-0.159190\pi$
$887$	33.0097	+	14.6969i	1.10836	+	0.493473i	0.230828	+	0.972995i	$0.425857\pi$
$888$	−64.3367	−	46.7433i	−2.15900	−	1.56860i
$889$	21.6413	−	5.91216i	0.725826	−	0.198288i
$890$		−	0.127383i		−	0.00426989i
$891$	14.7316	−	33.6328i	0.493527	−	1.12674i
$892$	−62.0971	−	35.8518i	−2.07917	−	1.20041i
$893$	2.49574	−	11.7415i	0.0835168	−	0.392916i
$894$	64.0108	+	6.72781i	2.14084	+	0.225012i
$895$	0.296054	+	0.407483i	0.00989600	+	0.0136207i
$896$	−8.72864	−	53.4211i	−0.291603	−	1.78467i
$897$	−27.0321	−	8.78325i	−0.902575	−	0.293264i
$898$	7.04956	−	15.8336i	0.235247	−	0.528373i
$899$	13.8979	−	6.18774i	0.463520	−	0.206373i
$900$	−18.7177	−	3.97857i	−0.623924	−	0.132619i
$901$	−3.25256	−	5.63360i	−0.108358	−	0.187682i
$902$	12.8713	−	40.4430i	0.428566	−	1.34660i
$903$	12.7081	−	19.7794i	0.422898	−	0.658218i
$904$	28.5211	−	9.26705i	0.948596	−	0.308218i
$905$	−0.0364035	+	0.346357i	−0.00121009	+	0.0115133i
$906$	−2.62766	+	0.276178i	−0.0872980	+	0.00917539i
$907$	13.1930	+	14.6523i	0.438065	+	0.486520i	0.921235	−	0.389006i	$-0.127182\pi$
$907$	13.1930	+	14.6523i	0.438065	+	0.486520i	−0.483170	+	0.875526i	$0.660515\pi$
$908$	5.23498	−	1.11273i	0.173729	−	0.0369272i
$909$	0.200629	−	0.145765i	0.00665443	−	0.00483473i
$910$	0.710955	−	0.276900i	0.0235679	−	0.00917914i
$911$	7.43263	+	22.8753i	0.246254	+	0.757892i	0.995428	+	0.0955186i	$0.0304509\pi$
$911$	7.43263	+	22.8753i	0.246254	+	0.757892i	−0.749173	+	0.662374i	$0.769549\pi$
$912$	−16.0653	+	9.27532i	−0.531976	+	0.307137i
$913$	−22.0661	+	20.1110i	−0.730281	+	0.665576i
$914$	−14.1980	+	24.5916i	−0.469627	+	0.813417i
$915$	0.347095	−	0.385488i	0.0114746	−	0.0127438i
$916$	12.0147	−	16.5369i	0.396978	−	0.546394i
$917$	−52.0757	−	26.2145i	−1.71969	−	0.865678i
$918$	11.0379	−	33.9711i	0.364304	−	1.12121i
$919$	−4.62482	−	21.7581i	−0.152559	−	0.717732i	−0.986218	−	0.165453i	$-0.947092\pi$
$919$	−4.62482	−	21.7581i	−0.152559	−	0.717732i	0.833659	−	0.552279i	$-0.186242\pi$
$920$	0.0389499	+	0.370584i	0.00128414	+	0.0122178i
$921$	1.59841	+	3.59009i	0.0526694	+	0.118297i
$922$	−71.7681	−	64.6203i	−2.36356	−	2.12816i
$923$	10.8328			0.356565
$924$	52.4507	−	34.8820i	1.72550	−	1.14753i
$925$	−53.7115			−1.76602
$926$	−18.0254	−	16.2302i	−0.592353	−	0.533357i
$927$	2.30674	+	5.18103i	0.0757634	+	0.170167i
$928$	1.72569	+	16.4189i	0.0566486	+	0.538976i
$929$	3.91022	+	18.3961i	0.128290	+	0.603557i	0.994576	+	0.104009i	$0.0331672\pi$
$929$	3.91022	+	18.3961i	0.128290	+	0.603557i	−0.866286	+	0.499548i	$0.833499\pi$
$930$	−0.150088	+	0.461924i	−0.00492159	+	0.0151471i
$931$	36.6147	+	20.6655i	1.20000	+	0.677284i
$932$	14.3993	−	19.8189i	0.471663	−	0.649189i
$933$	−27.8597	+	30.9414i	−0.912087	+	1.01298i
$934$	31.2783	−	54.1756i	1.02346	−	1.77268i
$935$	−0.350493	+	0.158592i	−0.0114624	+	0.00518652i
$936$	−14.0701	+	8.12338i	−0.459896	+	0.265521i
$937$	−4.97540	−	15.3127i	−0.162539	−	0.500244i	0.836307	−	0.548261i	$-0.184710\pi$
$937$	−4.97540	−	15.3127i	−0.162539	−	0.500244i	−0.998847	+	0.0480169i	$0.984710\pi$
$938$	−11.4266	+	14.2524i	−0.373092	+	0.465357i
$939$	−8.04888	+	5.84786i	−0.262665	+	0.190838i
$940$	−0.206580	+	0.0439100i	−0.00673791	+	0.00143219i
$941$	−16.2496	−	18.0470i	−0.529722	−	0.588316i	0.417587	−	0.908637i	$-0.362876\pi$
$941$	−16.2496	−	18.0470i	−0.529722	−	0.588316i	−0.947309	+	0.320321i	$0.896209\pi$
$942$	−13.5669	+	1.42594i	−0.442034	+	0.0464597i
$943$	−1.94081	+	18.4656i	−0.0632014	+	0.601321i
$944$	−5.79689	+	1.88352i	−0.188673	+	0.0613035i
$945$	−0.139969	−	0.271421i	−0.00455320	−	0.00882932i
$946$	−32.6549	+	10.8286i	−1.06170	+	0.352070i
$947$	9.87699	+	17.1074i	0.320959	+	0.555917i	0.980686	−	0.195588i	$-0.0626615\pi$
$947$	9.87699	+	17.1074i	0.320959	+	0.555917i	−0.659727	+	0.751505i	$0.729328\pi$
$948$	−78.2282	−	16.6279i	−2.54073	−	0.540049i
$949$	7.31014	−	3.25468i	0.237297	−	0.105652i
$950$	−28.7851	+	64.6523i	−0.933911	+	2.09760i
$951$	9.86040	+	3.20384i	0.319745	+	0.103892i
$952$	29.2982	−	23.9630i	0.949560	−	0.776645i
$953$	23.1036	+	31.7994i	0.748399	+	1.03008i	0.998091	+	0.0617579i	$0.0196707\pi$
$953$	23.1036	+	31.7994i	0.748399	+	1.03008i	−0.249692	+	0.968325i	$0.580329\pi$
$954$	4.20689	+	0.442162i	0.136203	+	0.0143155i
$955$	0.0381758	−	0.179603i	0.00123534	−	0.00581182i
$956$	−33.9695	−	19.6123i	−1.09865	−	0.634307i
$957$	−25.6039	+	14.9893i	−0.827656	+	0.484534i
$958$		−	49.4851i		−	1.59879i
$959$	−16.2770	−	4.27635i	−0.525612	−	0.138091i
$960$	−0.574951	−	0.417726i	−0.0185565	−	0.0134821i
$961$	17.5487	+	7.81319i	0.566087	+	0.252038i
$962$	−77.4671	+	69.7517i	−2.49764	+	2.24888i
$963$	2.25134	−	2.02712i	0.0725484	−	0.0653229i
$964$	−54.6567	−	24.3347i	−1.76037	−	0.783769i
$965$	−0.364027	−	0.264481i	−0.0117185	−	0.00851396i
$966$	−30.2981	+	30.5954i	−0.974826	+	0.984391i
$967$			11.1389i			0.358202i	0.983831	+	0.179101i	$0.0573190\pi$
$967$			11.1389i			0.358202i	−0.983831	+	0.179101i	$0.942681\pi$
$968$	−40.1515	−	3.73046i	−1.29052	−	0.119901i
$969$	40.9853	+	23.6629i	1.31664	+	0.760160i
$970$	−0.164941	+	0.775987i	−0.00529594	+	0.0249154i
$971$	−19.0938	−	2.00684i	−0.612749	−	0.0644025i	−0.206930	−	0.978356i	$-0.566347\pi$
$971$	−19.0938	−	2.00684i	−0.612749	−	0.0644025i	−0.405819	+	0.913953i	$0.633014\pi$
$972$	22.3659	+	30.7840i	0.717386	+	0.987397i
$973$	−18.8128	+	49.7333i	−0.603110	+	1.59438i
$974$	23.1191	+	7.51186i	0.740785	+	0.240696i
$975$	−16.8995	+	37.9569i	−0.541217	+	1.21559i
$976$	12.0788	−	5.37785i	0.386634	−	0.172141i
$977$	−10.2190	−	2.17212i	−0.326936	−	0.0694923i	0.0415199	−	0.999138i	$-0.486780\pi$
$977$	−10.2190	−	2.17212i	−0.326936	−	0.0694923i	−0.368456	+	0.929645i	$0.620113\pi$
$978$	−17.1309	−	29.6716i	−0.547787	−	0.948795i
$979$	−6.03052	+	0.0364133i	−0.192736	+	0.00116377i
$980$	0.0701349	−	0.736389i	0.00224038	−	0.0235231i
$981$	−8.13275	+	2.64249i	−0.259659	+	0.0843682i
$982$	8.84820	−	84.1850i	0.282357	−	2.68645i
$983$	19.4035	−	2.03939i	0.618874	−	0.0650463i	0.210097	−	0.977681i	$-0.432622\pi$
$983$	19.4035	−	2.03939i	0.618874	−	0.0650463i	0.408777	+	0.912634i	$0.365955\pi$
$984$	26.8894	+	29.8637i	0.857202	+	0.952019i
$985$	−0.655267	+	0.139281i	−0.0208785	+	0.00443787i
$986$	−32.9688	+	23.9532i	−1.04994	+	0.762826i
$987$	−8.32965	−	6.67815i	−0.265136	−	0.212568i
$988$	27.1633	+	83.6001i	0.864181	+	2.65967i
$989$	13.0343	−	7.52537i	0.414467	−	0.239293i
$990$	0.0505328	−	0.245003i	0.00160604	−	0.00778671i
$991$	11.7802	−	20.4039i	0.374210	−	0.648151i	−0.615998	−	0.787747i	$-0.711247\pi$
$991$	11.7802	−	20.4039i	0.374210	−	0.648151i	0.990208	+	0.139597i	$0.0445805\pi$
$992$	8.56161	−	9.50863i	0.271831	−	0.301899i
$993$	18.2152	−	25.0711i	0.578043	−	0.795608i
$994$	7.37885	−	14.6583i	0.234043	−	0.464933i
$995$	0.178851	−	0.550447i	0.00566996	−	0.0174503i
$996$	−13.4351	−	63.2072i	−0.425708	−	2.00280i
$997$	−4.84998	−	46.1445i	−0.153601	−	1.46141i	−0.751443	−	0.659798i	$-0.770642\pi$
$997$	−4.84998	−	46.1445i	−0.153601	−	1.46141i	0.597842	−	0.801614i	$-0.296025\pi$
$998$	−19.8279	−	44.5341i	−0.627640	−	1.40970i
$999$	31.0068	+	27.9186i	0.981011	+	0.883306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.17.6	✓	48
3.2	odd	2		693.2.cg.a.325.1		48
7.2	even	3		539.2.s.d.215.6		48
7.3	odd	6		539.2.m.a.391.2		48
7.4	even	3		539.2.m.a.391.1		48
7.5	odd	6	inner	77.2.n.a.61.6	yes	48
7.6	odd	2		539.2.s.d.325.6		48
11.2	odd	10	inner	77.2.n.a.24.6	yes	48
11.3	even	5		847.2.i.b.241.23		48
11.4	even	5		847.2.r.a.360.1		48
11.5	even	5		847.2.r.d.766.1		48
11.6	odd	10		847.2.r.a.766.6		48
11.7	odd	10		847.2.r.d.360.6		48
11.8	odd	10		847.2.i.b.241.2		48
11.9	even	5		847.2.r.c.717.1		48
11.10	odd	2		847.2.r.c.94.1		48
21.5	even	6		693.2.cg.a.523.1		48
33.2	even	10		693.2.cg.a.640.1		48
77.2	odd	30		539.2.s.d.68.6		48
77.5	odd	30		847.2.r.d.40.6		48
77.13	even	10		539.2.s.d.178.6		48
77.19	even	30		847.2.i.b.362.23		48
77.24	even	30		539.2.m.a.244.1		48
77.26	odd	30		847.2.r.a.481.6		48
77.40	even	30		847.2.r.d.481.1		48
77.46	odd	30		539.2.m.a.244.2		48
77.47	odd	30		847.2.i.b.362.2		48
77.54	even	6		847.2.r.c.215.1		48
77.61	even	30		847.2.r.a.40.1		48
77.68	even	30	inner	77.2.n.a.68.6	yes	48
77.75	odd	30		847.2.r.c.838.1		48
231.68	odd	30		693.2.cg.a.145.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.17.6	✓	48	1.1	even	1	trivial
77.2.n.a.24.6	yes	48	11.2	odd	10	inner
77.2.n.a.61.6	yes	48	7.5	odd	6	inner
77.2.n.a.68.6	yes	48	77.68	even	30	inner
539.2.m.a.244.1		48	77.24	even	30
539.2.m.a.244.2		48	77.46	odd	30
539.2.m.a.391.1		48	7.4	even	3
539.2.m.a.391.2		48	7.3	odd	6
539.2.s.d.68.6		48	77.2	odd	30
539.2.s.d.178.6		48	77.13	even	10
539.2.s.d.215.6		48	7.2	even	3
539.2.s.d.325.6		48	7.6	odd	2
693.2.cg.a.145.1		48	231.68	odd	30
693.2.cg.a.325.1		48	3.2	odd	2
693.2.cg.a.523.1		48	21.5	even	6
693.2.cg.a.640.1		48	33.2	even	10
847.2.i.b.241.2		48	11.8	odd	10
847.2.i.b.241.23		48	11.3	even	5
847.2.i.b.362.2		48	77.47	odd	30
847.2.i.b.362.23		48	77.19	even	30
847.2.r.a.40.1		48	77.61	even	30
847.2.r.a.360.1		48	11.4	even	5
847.2.r.a.481.6		48	77.26	odd	30
847.2.r.a.766.6		48	11.6	odd	10
847.2.r.c.94.1		48	11.10	odd	2
847.2.r.c.215.1		48	77.54	even	6
847.2.r.c.717.1		48	11.9	even	5
847.2.r.c.838.1		48	77.75	odd	30
847.2.r.d.40.6		48	77.5	odd	30
847.2.r.d.360.6		48	11.7	odd	10
847.2.r.d.481.1		48	77.40	even	30
847.2.r.d.766.1		48	11.5	even	5

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75157 + 1.57712i) q^{2} +(-0.821231 - 1.84451i) q^{3} +(0.371633 + 3.53585i) q^{4} +(-0.00617973 - 0.0290734i) q^{5} +(1.47058 - 4.52598i) q^{6} +(-2.21185 + 1.45180i) q^{7} +(-2.15474 + 2.96574i) q^{8} +(-0.720422 + 0.800109i) q^{9} +O(q^{10})\)	\(q+(1.75157 + 1.57712i) q^{2} +(-0.821231 - 1.84451i) q^{3} +(0.371633 + 3.53585i) q^{4} +(-0.00617973 - 0.0290734i) q^{5} +(1.47058 - 4.52598i) q^{6} +(-2.21185 + 1.45180i) q^{7} +(-2.15474 + 2.96574i) q^{8} +(-0.720422 + 0.800109i) q^{9} +(0.0350280 - 0.0606703i) q^{10} +(-2.88224 - 1.64094i) q^{11} +(6.21673 - 3.58923i) q^{12} +(-1.27203 - 3.91491i) q^{13} +(-6.16388 - 0.945438i) q^{14} +(-0.0485512 + 0.0352745i) q^{15} +(-1.49625 + 0.318039i) q^{16} +(2.61126 + 2.90010i) q^{17} +(-2.52374 + 0.265256i) q^{18} +(-0.627828 + 5.97338i) q^{19} +(0.100502 - 0.0326552i) q^{20} +(4.49430 + 2.88753i) q^{21} +(-2.46049 - 7.41987i) q^{22} +(1.70992 + 2.96167i) q^{23} +(7.23989 + 1.53889i) q^{24} +(4.56692 - 2.03332i) q^{25} +(3.94624 - 8.86340i) q^{26} +(-3.69331 - 1.20003i) q^{27} +(-5.95532 - 7.28124i) q^{28} +(2.60417 + 3.58434i) q^{29} +(-0.140673 - 0.0147854i) q^{30} +(0.713914 - 3.35870i) q^{31} +(3.22707 + 1.86315i) q^{32} +(-0.659750 + 6.66393i) q^{33} +9.19801i q^{34} +(0.0558772 + 0.0553343i) q^{35} +(-3.09680 - 2.24995i) q^{36} +(-9.81531 - 4.37006i) q^{37} +(-10.5204 + 9.47265i) q^{38} +(-6.17648 + 5.56132i) q^{39} +(0.0995398 + 0.0443180i) q^{40} +(4.39238 + 3.19125i) q^{41} +(3.31809 + 12.1458i) q^{42} -4.40101i q^{43} +(4.73098 - 10.8010i) q^{44} +(0.0277139 + 0.0160006i) q^{45} +(-1.67587 + 7.88433i) q^{46} +(-1.98760 - 0.208905i) q^{47} +(1.81540 + 2.49868i) q^{48} +(2.78458 - 6.42231i) q^{49} +(11.2061 + 3.64108i) q^{50} +(3.20483 - 7.19816i) q^{51} +(13.3698 - 5.95262i) q^{52} +(-1.63050 - 0.346573i) q^{53} +(-4.57651 - 7.92674i) q^{54} +(-0.0298961 + 0.0939370i) q^{55} +(0.460310 - 9.68802i) q^{56} +(11.5336 - 3.74749i) q^{57} +(-1.09154 + 10.3853i) q^{58} +(3.96280 - 0.416507i) q^{59} +(-0.142769 - 0.158561i) q^{60} +(-8.45471 + 1.79710i) q^{61} +(6.54756 - 4.75708i) q^{62} +(0.431871 - 2.81563i) q^{63} +(3.65942 + 11.2626i) q^{64} +(-0.105959 + 0.0611753i) q^{65} +(-11.6654 + 10.6318i) q^{66} +(1.46468 - 2.53690i) q^{67} +(-9.28387 + 10.3108i) q^{68} +(4.05860 - 5.58618i) q^{69} +(0.0106041 + 0.185047i) q^{70} +(-0.813218 + 2.50283i) q^{71} +(-0.820598 - 3.86061i) q^{72} +(0.203196 + 1.93328i) q^{73} +(-10.3001 - 23.1344i) q^{74} +(-7.50099 - 6.75392i) q^{75} -21.3543 q^{76} +(8.75740 - 0.554911i) q^{77} -19.5894 q^{78} +(-8.27944 - 7.45484i) q^{79} +(0.0184929 + 0.0415357i) q^{80} +(1.15721 + 11.0101i) q^{81} +(2.66058 + 12.5170i) q^{82} +(2.78172 - 8.56125i) q^{83} +(-8.53965 + 16.9643i) q^{84} +(0.0681787 - 0.0938399i) q^{85} +(6.94093 - 7.70868i) q^{86} +(4.47274 - 7.74701i) q^{87} +(11.0771 - 5.01219i) q^{88} +(1.57470 - 0.909151i) q^{89} +(0.0233079 + 0.0717345i) q^{90} +(8.49719 + 6.81247i) q^{91} +(-9.83654 + 7.14667i) q^{92} +(-6.78146 + 1.44144i) q^{93} +(-3.15196 - 3.50060i) q^{94} +(0.177546 - 0.0186609i) q^{95} +(0.786437 - 7.48245i) q^{96} +(-10.7699 + 3.49934i) q^{97} +(15.0062 - 6.85752i) q^{98} +(3.38936 - 1.12394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more