LMFDB - Embedded newform 209.2.j.b.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(23,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.j (of order $9$, degree $6$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			177.2
Character	$\chi$	$=$	209.177
Dual form			209.2.j.b.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28771 + 1.08051i) q^{2} +(-1.02863 - 0.374390i) q^{3} +(0.143380 - 0.813151i) q^{4} +(-0.0882338 - 0.500399i) q^{5} +(1.72910 - 0.629342i) q^{6} +(0.0395283 - 0.0684651i) q^{7} +(-0.986992 - 1.70952i) q^{8} +(-1.38023 - 1.15815i) q^{9} +O(q^{10})$	\(q+(-1.28771 + 1.08051i) q^{2} +(-1.02863 - 0.374390i) q^{3} +(0.143380 - 0.813151i) q^{4} +(-0.0882338 - 0.500399i) q^{5} +(1.72910 - 0.629342i) q^{6} +(0.0395283 - 0.0684651i) q^{7} +(-0.986992 - 1.70952i) q^{8} +(-1.38023 - 1.15815i) q^{9} +(0.654306 + 0.549028i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.451921 + 0.782749i) q^{12} +(3.43796 - 1.25131i) q^{13} +(0.0230766 + 0.130874i) q^{14} +(-0.0965845 + 0.547758i) q^{15} +(4.66991 + 1.69971i) q^{16} +(2.75007 - 2.30758i) q^{17} +3.02872 q^{18} +(-1.99861 - 3.87370i) q^{19} -0.419550 q^{20} +(-0.0662926 + 0.0556261i) q^{21} +(1.57960 + 0.574929i) q^{22} +(0.963469 - 5.46411i) q^{23} +(0.375220 + 2.12798i) q^{24} +(4.45585 - 1.62180i) q^{25} +(-3.07502 + 5.32609i) q^{26} +(2.62810 + 4.55201i) q^{27} +(-0.0500048 - 0.0419590i) q^{28} +(-3.09472 - 2.59678i) q^{29} +(-0.467487 - 0.809711i) q^{30} +(-3.24816 + 5.62598i) q^{31} +(-4.14016 + 1.50689i) q^{32} +(0.190083 + 1.07801i) q^{33} +(-1.04791 + 5.94298i) q^{34} +(-0.0377476 - 0.0137390i) q^{35} +(-1.13965 + 0.956276i) q^{36} -1.71356 q^{37} +(6.75921 + 2.82866i) q^{38} -4.00486 q^{39} +(-0.768355 + 0.644727i) q^{40} +(-10.3928 - 3.78266i) q^{41} +(0.0252606 - 0.143260i) q^{42} +(-0.804230 - 4.56102i) q^{43} +(-0.775899 + 0.282404i) q^{44} +(-0.457753 + 0.792851i) q^{45} +(4.66337 + 8.07720i) q^{46} +(-5.30916 - 4.45491i) q^{47} +(-4.16725 - 3.49674i) q^{48} +(3.49688 + 6.05677i) q^{49} +(-3.98545 + 6.90300i) q^{50} +(-3.69274 + 1.34405i) q^{51} +(-0.524572 - 2.97499i) q^{52} +(0.538388 - 3.05335i) q^{53} +(-8.30273 - 3.02195i) q^{54} +(-0.389241 + 0.326612i) q^{55} -0.156057 q^{56} +(0.605555 + 4.73286i) q^{57} +6.79094 q^{58} +(-3.17254 + 2.66208i) q^{59} +(0.431561 + 0.157075i) q^{60} +(1.54866 - 8.78290i) q^{61} +(-1.89627 - 10.7543i) q^{62} +(-0.133851 + 0.0487177i) q^{63} +(-1.26653 + 2.19370i) q^{64} +(-0.929500 - 1.60994i) q^{65} +(-1.40958 - 1.18278i) q^{66} +(2.26925 + 1.90412i) q^{67} +(-1.48211 - 2.56709i) q^{68} +(-3.03676 + 5.25982i) q^{69} +(0.0634529 - 0.0230950i) q^{70} +(2.22726 + 12.6314i) q^{71} +(-0.617604 + 3.50261i) q^{72} +(8.63359 + 3.14237i) q^{73} +(2.20656 - 1.85152i) q^{74} -5.19060 q^{75} +(-3.43646 + 1.06976i) q^{76} -0.0790567 q^{77} +(5.15708 - 4.32730i) q^{78} +(-7.78094 - 2.83203i) q^{79} +(0.438488 - 2.48679i) q^{80} +(-0.0604992 - 0.343108i) q^{81} +(17.4701 - 6.35858i) q^{82} +(1.38214 - 2.39394i) q^{83} +(0.0357273 + 0.0618816i) q^{84} +(-1.39736 - 1.17253i) q^{85} +(5.96385 + 5.00427i) q^{86} +(2.21111 + 3.82975i) q^{87} +(-0.986992 + 1.70952i) q^{88} +(3.37004 - 1.22659i) q^{89} +(-0.267235 - 1.51557i) q^{90} +(0.0502254 - 0.284843i) q^{91} +(-4.30500 - 1.56689i) q^{92} +(5.44746 - 4.57096i) q^{93} +11.6502 q^{94} +(-1.76205 + 1.34189i) q^{95} +4.82285 q^{96} +(11.7344 - 9.84632i) q^{97} +(-11.0474 - 4.02091i) q^{98} +(-0.312872 + 1.77438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8}+O(q^{10}) $ 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8	\( 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8} - 15 q^{10} - 21 q^{11} - 30 q^{12} - 18 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{18} - 6 q^{19} + 30 q^{20} + 9 q^{21} + 6 q^{22} + 15 q^{23} + 3 q^{24} - 6 q^{26} - 24 q^{27} - 9 q^{28} - 15 q^{29} + 30 q^{30} - 54 q^{31} + 42 q^{32} - 45 q^{34} - 12 q^{35} + 6 q^{36} + 114 q^{37} - 60 q^{38} - 48 q^{40} + 15 q^{41} + 84 q^{42} - 6 q^{43} + 3 q^{44} + 3 q^{45} - 15 q^{46} - 42 q^{47} + 12 q^{48} - 21 q^{49} - 33 q^{50} + 93 q^{51} + 3 q^{52} + 48 q^{54} + 3 q^{55} + 114 q^{56} - 15 q^{57} + 60 q^{58} - 33 q^{59} - 81 q^{60} + 63 q^{61} - 24 q^{62} + 87 q^{63} + 15 q^{64} + 24 q^{65} - 15 q^{66} - 51 q^{67} + 48 q^{68} - 54 q^{69} - 84 q^{70} + 9 q^{71} - 51 q^{72} - 27 q^{73} - 33 q^{74} + 54 q^{75} - 60 q^{76} + 12 q^{77} - 87 q^{78} + 24 q^{79} + 120 q^{80} - 36 q^{81} + 111 q^{82} - 12 q^{83} + 48 q^{84} + 39 q^{85} - 60 q^{86} - 75 q^{87} - 15 q^{88} - 21 q^{89} - 63 q^{90} - 3 q^{91} + 6 q^{92} - 72 q^{93} + 84 q^{94} - 72 q^{95} - 6 q^{96} - 18 q^{97} - 120 q^{98}+O(q^{100}) \) 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8 - 15 * q^10 - 21 * q^11 - 30 * q^12 - 18 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^18 - 6 * q^19 + 30 * q^20 + 9 * q^21 + 6 * q^22 + 15 * q^23 + 3 * q^24 - 6 * q^26 - 24 * q^27 - 9 * q^28 - 15 * q^29 + 30 * q^30 - 54 * q^31 + 42 * q^32 - 45 * q^34 - 12 * q^35 + 6 * q^36 + 114 * q^37 - 60 * q^38 - 48 * q^40 + 15 * q^41 + 84 * q^42 - 6 * q^43 + 3 * q^44 + 3 * q^45 - 15 * q^46 - 42 * q^47 + 12 * q^48 - 21 * q^49 - 33 * q^50 + 93 * q^51 + 3 * q^52 + 48 * q^54 + 3 * q^55 + 114 * q^56 - 15 * q^57 + 60 * q^58 - 33 * q^59 - 81 * q^60 + 63 * q^61 - 24 * q^62 + 87 * q^63 + 15 * q^64 + 24 * q^65 - 15 * q^66 - 51 * q^67 + 48 * q^68 - 54 * q^69 - 84 * q^70 + 9 * q^71 - 51 * q^72 - 27 * q^73 - 33 * q^74 + 54 * q^75 - 60 * q^76 + 12 * q^77 - 87 * q^78 + 24 * q^79 + 120 * q^80 - 36 * q^81 + 111 * q^82 - 12 * q^83 + 48 * q^84 + 39 * q^85 - 60 * q^86 - 75 * q^87 - 15 * q^88 - 21 * q^89 - 63 * q^90 - 3 * q^91 + 6 * q^92 - 72 * q^93 + 84 * q^94 - 72 * q^95 - 6 * q^96 - 18 * q^97 - 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−1.28771	+	1.08051i	−0.910545	+	0.764038i	−0.972223	−	0.234058i	$-0.924799\pi$
$2$	−1.28771	+	1.08051i	−0.910545	+	0.764038i	0.0616773	+	0.998096i	$0.480355\pi$
$3$	−1.02863	−	0.374390i	−0.593879	−	0.216154i	0.0275559	−	0.999620i	$-0.491228\pi$
$3$	−1.02863	−	0.374390i	−0.593879	−	0.216154i	−0.621434	+	0.783466i	$0.713450\pi$
$4$	0.143380	−	0.813151i	0.0716902	−	0.406575i
$5$	−0.0882338	−	0.500399i	−0.0394593	−	0.223785i	0.958701	−	0.284416i	$-0.0917998\pi$
$5$	−0.0882338	−	0.500399i	−0.0394593	−	0.223785i	−0.998160	+	0.0606312i	$0.980689\pi$
$6$	1.72910	−	0.629342i	0.705903	−	0.256928i
$7$	0.0395283	−	0.0684651i	0.0149403	−	0.0258774i	−0.858459	−	0.512883i	$-0.828578\pi$
$7$	0.0395283	−	0.0684651i	0.0149403	−	0.0258774i	0.873399	+	0.487006i	$0.161911\pi$
$8$	−0.986992	−	1.70952i	−0.348954	−	0.604407i
$9$	−1.38023	−	1.15815i	−0.460075	−	0.386049i
$10$	0.654306	+	0.549028i	0.206910	+	0.173618i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−0.451921	+	0.782749i	−0.130458	+	0.225960i
$13$	3.43796	−	1.25131i	0.953518	−	0.347052i	0.182028	−	0.983293i	$-0.441734\pi$
$13$	3.43796	−	1.25131i	0.953518	−	0.347052i	0.771490	+	0.636241i	$0.219512\pi$
$14$	0.0230766	+	0.130874i	0.00616747	+	0.0349775i
$15$	−0.0965845	+	0.547758i	−0.0249380	+	0.141430i
$16$	4.66991	+	1.69971i	1.16748	+	0.424927i
$17$	2.75007	−	2.30758i	0.666991	−	0.559672i	−0.245182	−	0.969477i	$-0.578848\pi$
$17$	2.75007	−	2.30758i	0.666991	−	0.559672i	0.912173	+	0.409805i	$0.134403\pi$
$18$	3.02872			0.713876
$19$	−1.99861	−	3.87370i	−0.458513	−	0.888688i
$19$	−1.99861	−	3.87370i	−0.458513	−	0.888688i
$20$	−0.419550			−0.0938143
$21$	−0.0662926	+	0.0556261i	−0.0144662	+	0.0121386i
$22$	1.57960	+	0.574929i	0.336773	+	0.122575i
$23$	0.963469	−	5.46411i	0.200897	−	1.13934i	−0.702869	−	0.711319i	$-0.748098\pi$
$23$	0.963469	−	5.46411i	0.200897	−	1.13934i	0.903766	−	0.428026i	$-0.140791\pi$
$24$	0.375220	+	2.12798i	0.0765915	+	0.434372i
$25$	4.45585	−	1.62180i	0.891170	−	0.324359i
$26$	−3.07502	+	5.32609i	−0.603060	+	1.04453i
$27$	2.62810	+	4.55201i	0.505779	+	0.876035i
$28$	−0.0500048	−	0.0419590i	−0.00945003	−	0.00792951i
$29$	−3.09472	−	2.59678i	−0.574675	−	0.482210i	0.308518	−	0.951218i	$-0.400167\pi$
$29$	−3.09472	−	2.59678i	−0.574675	−	0.482210i	−0.883194	+	0.469009i	$0.844611\pi$
$30$	−0.467487	−	0.809711i	−0.0853511	−	0.147832i
$31$	−3.24816	+	5.62598i	−0.583387	+	1.01046i	0.411687	+	0.911325i	$0.364940\pi$
$31$	−3.24816	+	5.62598i	−0.583387	+	1.01046i	−0.995074	+	0.0991313i	$0.968394\pi$
$32$	−4.14016	+	1.50689i	−0.731883	+	0.266384i
$33$	0.190083	+	1.07801i	0.0330892	+	0.187658i
$34$	−1.04791	+	5.94298i	−0.179715	+	1.01921i
$35$	−0.0377476	−	0.0137390i	−0.00638050	−	0.00232231i
$36$	−1.13965	+	0.956276i	−0.189941	+	0.159379i
$37$	−1.71356			−0.281707			−0.140854	−	0.990030i	$-0.544985\pi$
$37$	−1.71356			−0.281707			−0.140854	+	0.990030i	$0.544985\pi$
$38$	6.75921	+	2.82866i	1.09649	+	0.458869i
$39$	−4.00486			−0.641291
$40$	−0.768355	+	0.644727i	−0.121488	+	0.101940i
$41$	−10.3928	−	3.78266i	−1.62308	−	0.590753i	−0.639114	−	0.769112i	$-0.720699\pi$
$41$	−10.3928	−	3.78266i	−1.62308	−	0.590753i	−0.983965	+	0.178360i	$0.942921\pi$
$42$	0.0252606	−	0.143260i	0.00389780	−	0.0221055i
$43$	−0.804230	−	4.56102i	−0.122644	−	0.695549i	−0.982679	−	0.185314i	$-0.940670\pi$
$43$	−0.804230	−	4.56102i	−0.122644	−	0.695549i	0.860035	−	0.510234i	$-0.170441\pi$
$44$	−0.775899	+	0.282404i	−0.116971	+	0.0425740i
$45$	−0.457753	+	0.792851i	−0.0682377	+	0.118191i
$46$	4.66337	+	8.07720i	0.687577	+	1.19092i
$47$	−5.30916	−	4.45491i	−0.774420	−	0.649816i	0.167416	−	0.985886i	$-0.446458\pi$
$47$	−5.30916	−	4.45491i	−0.774420	−	0.649816i	−0.941837	+	0.336070i	$0.890902\pi$
$48$	−4.16725	−	3.49674i	−0.601491	−	0.504710i
$49$	3.49688	+	6.05677i	0.499554	+	0.865252i
$50$	−3.98545	+	6.90300i	−0.563628	+	0.976232i
$51$	−3.69274	+	1.34405i	−0.517087	+	0.188204i
$52$	−0.524572	−	2.97499i	−0.0727450	−	0.412557i
$53$	0.538388	−	3.05335i	0.0739532	−	0.419410i	−0.925245	−	0.379370i	$-0.876141\pi$
$53$	0.538388	−	3.05335i	0.0739532	−	0.419410i	0.999198	−	0.0400392i	$-0.0127483\pi$
$54$	−8.30273	−	3.02195i	−1.12986	−	0.411235i
$55$	−0.389241	+	0.326612i	−0.0524852	+	0.0440403i
$56$	−0.156057			−0.0208539
$57$	0.605555	+	4.73286i	0.0802077	+	0.626882i
$58$	6.79094			0.891694
$59$	−3.17254	+	2.66208i	−0.413030	+	0.346573i	−0.825504	−	0.564396i	$-0.809109\pi$
$59$	−3.17254	+	2.66208i	−0.413030	+	0.346573i	0.412474	+	0.910969i	$0.364665\pi$
$60$	0.431561	+	0.157075i	0.0557143	+	0.0202784i
$61$	1.54866	−	8.78290i	0.198286	−	1.12453i	−0.709375	−	0.704831i	$-0.751023\pi$
$61$	1.54866	−	8.78290i	0.198286	−	1.12453i	0.907661	−	0.419704i	$-0.137866\pi$
$62$	−1.89627	−	10.7543i	−0.240827	−	1.36580i
$63$	−0.133851	+	0.0487177i	−0.0168636	+	0.00613785i
$64$	−1.26653	+	2.19370i	−0.158317	+	0.274213i
$65$	−0.929500	−	1.60994i	−0.115290	−	0.199689i
$66$	−1.40958	−	1.18278i	−0.173507	−	0.145590i
$67$	2.26925	+	1.90412i	0.277233	+	0.232626i	0.770793	−	0.637086i	$-0.219860\pi$
$67$	2.26925	+	1.90412i	0.277233	+	0.232626i	−0.493560	+	0.869712i	$0.664305\pi$
$68$	−1.48211	−	2.56709i	−0.179732	−	0.311305i
$69$	−3.03676	+	5.25982i	−0.365583	+	0.633208i
$70$	0.0634529	−	0.0230950i	0.00758407	−	0.00276038i
$71$	2.22726	+	12.6314i	0.264327	+	1.49907i	0.770945	+	0.636901i	$0.219784\pi$
$71$	2.22726	+	12.6314i	0.264327	+	1.49907i	−0.506619	+	0.862170i	$0.669105\pi$
$72$	−0.617604	+	3.50261i	−0.0727853	+	0.412786i
$73$	8.63359	+	3.14237i	1.01049	+	0.367787i	0.793619	−	0.608415i	$-0.208194\pi$
$73$	8.63359	+	3.14237i	1.01049	+	0.367787i	0.216866	+	0.976201i	$0.430416\pi$
$74$	2.20656	−	1.85152i	0.256507	−	0.215235i
$75$	−5.19060			−0.599358
$76$	−3.43646	+	1.06976i	−0.394189	+	0.122710i
$77$	−0.0790567			−0.00900934
$78$	5.15708	−	4.32730i	0.583924	−	0.489971i
$79$	−7.78094	−	2.83203i	−0.875424	−	0.318628i	−0.135062	−	0.990837i	$-0.543123\pi$
$79$	−7.78094	−	2.83203i	−0.875424	−	0.318628i	−0.740362	+	0.672209i	$0.765346\pi$
$80$	0.438488	−	2.48679i	0.0490245	−	0.278032i
$81$	−0.0604992	−	0.343108i	−0.00672214	−	0.0381231i
$82$	17.4701	−	6.35858i	1.92924	−	0.702188i
$83$	1.38214	−	2.39394i	0.151710	−	0.262769i	−0.780146	−	0.625597i	$-0.784855\pi$
$83$	1.38214	−	2.39394i	0.151710	−	0.262769i	0.931856	+	0.362828i	$0.118189\pi$
$84$	0.0357273	+	0.0618816i	0.00389817	+	0.00675183i
$85$	−1.39736	−	1.17253i	−0.151565	−	0.127178i
$86$	5.96385	+	5.00427i	0.643099	+	0.539624i
$87$	2.21111	+	3.82975i	0.237056	+	0.410592i
$88$	−0.986992	+	1.70952i	−0.105214	+	0.182235i
$89$	3.37004	−	1.22659i	0.357223	−	0.130019i	−0.157173	−	0.987571i	$-0.550238\pi$
$89$	3.37004	−	1.22659i	0.357223	−	0.130019i	0.514397	+	0.857552i	$0.328016\pi$
$90$	−0.267235	−	1.51557i	−0.0281691	−	0.159755i
$91$	0.0502254	−	0.284843i	0.00526506	−	0.0298596i
$92$	−4.30500	−	1.56689i	−0.448827	−	0.163360i
$93$	5.44746	−	4.57096i	0.564876	−	0.473987i
$94$	11.6502			1.20163
$95$	−1.76205	+	1.34189i	−0.180782	+	0.137675i
$96$	4.82285			0.492230
$97$	11.7344	−	9.84632i	1.19145	−	0.999742i	0.191613	−	0.981471i	$-0.438628\pi$
$97$	11.7344	−	9.84632i	1.19145	−	0.999742i	0.999833	−	0.0182713i	$-0.00581624\pi$
$98$	−11.0474	−	4.02091i	−1.11595	−	0.406173i
$99$	−0.312872	+	1.77438i	−0.0314448	+	0.178332i
$100$	−0.679884	−	3.85581i	−0.0679884	−	0.385581i
$101$	10.1379	−	3.68988i	1.00876	−	0.367157i	0.215801	−	0.976437i	$-0.430764\pi$
$101$	10.1379	−	3.68988i	1.00876	−	0.367157i	0.792955	+	0.609280i	$0.208541\pi$
$102$	3.30290	−	5.72079i	0.327036	−	0.566443i
$103$	1.53787	+	2.66367i	0.151531	+	0.262460i	0.931791	−	0.362996i	$-0.118246\pi$
$103$	1.53787	+	2.66367i	0.151531	+	0.262460i	−0.780259	+	0.625456i	$0.784913\pi$
$104$	−5.53239	−	4.64222i	−0.542495	−	0.455207i
$105$	0.0336845	+	0.0282646i	0.00328727	+	0.00275834i
$106$	2.60590	+	4.51355i	0.253107	+	0.438395i
$107$	−6.91680	+	11.9803i	−0.668673	+	1.15818i	0.309603	+	0.950866i	$0.399804\pi$
$107$	−6.91680	+	11.9803i	−0.668673	+	1.15818i	−0.978275	+	0.207309i	$0.933529\pi$
$108$	4.07829	−	1.48438i	0.392434	−	0.142834i
$109$	−0.569584	−	3.23027i	−0.0545563	−	0.309404i	0.945303	−	0.326194i	$-0.105766\pi$
$109$	−0.569584	−	3.23027i	−0.0545563	−	0.309404i	−0.999859	+	0.0167903i	$0.994655\pi$
$110$	0.148319	−	0.841160i	0.0141417	−	0.0802015i
$111$	1.76261	+	0.641538i	0.167300	+	0.0608921i
$112$	0.300965	−	0.252539i	0.0284385	−	0.0238627i
$113$	13.7861			1.29688			0.648441	−	0.761265i	$-0.275421\pi$
$113$	13.7861			1.29688			0.648441	+	0.761265i	$0.275421\pi$
$114$	−5.89369	−	5.44021i	−0.551995	−	0.509523i
$115$	−2.81924			−0.262896
$116$	−2.55529	+	2.14415i	−0.237253	+	0.199079i
$117$	−6.19437	−	2.25457i	−0.572669	−	0.208435i
$118$	1.20889	−	6.85595i	0.111287	−	0.631141i
$119$	−0.0492832	−	0.279499i	−0.00451778	−	0.0256216i
$120$	1.03173	−	0.375519i	0.0941837	−	0.0342801i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	7.49582	+	12.9831i	0.678639	+	1.17544i
$123$	9.27411	+	7.78190i	0.836218	+	0.701671i
$124$	4.10905	+	3.44790i	0.369004	+	0.309631i
$125$	−2.47500	−	4.28682i	−0.221370	−	0.383425i
$126$	0.119720	−	0.207361i	0.0106655	−	0.0184732i
$127$	5.32325	−	1.93751i	0.472362	−	0.171926i	−0.0948598	−	0.995491i	$-0.530240\pi$
$127$	5.32325	−	1.93751i	0.472362	−	0.171926i	0.567222	+	0.823565i	$0.308018\pi$
$128$	−2.26954	−	12.8712i	−0.200601	−	1.13766i
$129$	−0.880345	+	4.99269i	−0.0775101	+	0.439581i
$130$	2.93649	+	1.06879i	0.257547	+	0.0937394i
$131$	2.49979	−	2.09757i	0.218407	−	0.183266i	−0.527019	−	0.849853i	$-0.676690\pi$
$131$	2.49979	−	2.09757i	0.218407	−	0.183266i	0.745426	+	0.666588i	$0.232246\pi$
$132$	0.903841			0.0786693
$133$	−0.344215	−	0.0162857i	−0.0298472	−	0.00141215i
$134$	−4.97955			−0.430168
$135$	2.04593	−	1.71674i	0.176086	−	0.147754i
$136$	−6.65916	−	2.42374i	−0.571018	−	0.207834i
$137$	−1.81987	+	10.3210i	−0.155482	+	0.881784i	0.802861	+	0.596166i	$0.203310\pi$
$137$	−1.81987	+	10.3210i	−0.155482	+	0.881784i	−0.958344	+	0.285618i	$0.907801\pi$
$138$	−1.77285	−	10.0544i	−0.150915	−	0.855884i
$139$	−15.3848	+	5.59961i	−1.30492	+	0.474953i	−0.898597	−	0.438775i	$-0.855412\pi$
$139$	−15.3848	+	5.59961i	−1.30492	+	0.474953i	−0.406326	+	0.913728i	$0.633190\pi$
$140$	−0.0165841	+	0.0287246i	−0.00140161	+	0.00242767i
$141$	3.79327	+	6.57014i	0.319451	+	0.553306i
$142$	−16.5165	−	13.8589i	−1.38603	−	1.16302i
$143$	−2.80265	−	2.35170i	−0.234369	−	0.196659i
$144$	−4.47702	−	7.75443i	−0.373085	−	0.646202i
$145$	−1.02637	+	1.77772i	−0.0852350	+	0.147631i
$146$	−14.5129	+	5.28226i	−1.20110	+	0.437163i
$147$	−1.32939	−	7.53935i	−0.109646	−	0.621835i
$148$	−0.245690	+	1.39338i	−0.0201956	+	0.114535i
$149$	16.4155	+	5.97475i	1.34481	+	0.489470i	0.911324	−	0.411691i	$-0.135062\pi$
$149$	16.4155	+	5.97475i	1.34481	+	0.489470i	0.433485	+	0.901161i	$0.357284\pi$
$150$	6.68396	−	5.60851i	0.545743	−	0.457933i
$151$	−3.64299			−0.296463			−0.148231	−	0.988953i	$-0.547358\pi$
$151$	−3.64299			−0.296463			−0.148231	+	0.988953i	$0.547358\pi$
$152$	−4.64955	+	7.23998i	−0.377128	+	0.587240i
$153$	−6.46824			−0.522927
$154$	0.101802	−	0.0854218i	0.00820342	−	0.00688348i
$155$	3.10183	+	1.12897i	0.249145	+	0.0906814i
$156$	−0.574218	+	3.25655i	−0.0459743	+	0.260733i
$157$	1.84085	+	10.4400i	0.146916	+	0.833201i	0.965809	+	0.259255i	$0.0834771\pi$
$157$	1.84085	+	10.4400i	0.146916	+	0.833201i	−0.818893	+	0.573946i	$0.805412\pi$
$158$	13.0796	−	4.76059i	1.04056	−	0.378732i
$159$	−1.69694	+	2.93919i	−0.134576	+	0.233093i
$160$	1.11935	+	1.93877i	0.0884923	+	0.153273i
$161$	−0.336016	−	0.281951i	−0.0264818	−	0.0222209i
$162$	0.448638	+	0.376452i	0.0352483	+	0.0295769i
$163$	−9.92608	−	17.1925i	−0.777471	−	1.34662i	−0.933395	−	0.358850i	$-0.883169\pi$
$163$	−9.92608	−	17.1925i	−0.777471	−	1.34662i	0.155925	−	0.987769i	$-0.450164\pi$
$164$	−4.56600	+	7.90854i	−0.356544	+	0.617553i
$165$	0.522664	−	0.190234i	0.0406894	−	0.0148097i
$166$	0.806893	+	4.57612i	0.0626270	+	0.355176i
$167$	1.13151	−	6.41710i	0.0875588	−	0.496570i	−0.909216	−	0.416324i	$-0.863318\pi$
$167$	1.13151	−	6.41710i	0.0875588	−	0.496570i	0.996775	−	0.0802464i	$-0.0255707\pi$
$168$	0.160524	+	0.0584260i	0.0123847	+	0.00450766i
$169$	0.295196	−	0.247699i	0.0227074	−	0.0190538i
$170$	3.06632			0.235176
$171$	−1.72778	+	7.66127i	−0.132126	+	0.585872i
$172$	−3.82411			−0.291585
$173$	2.89064	−	2.42553i	0.219771	−	0.184410i	−0.526255	−	0.850327i	$-0.676404\pi$
$173$	2.89064	−	2.42553i	0.219771	−	0.184410i	0.746026	+	0.665917i	$0.231960\pi$
$174$	−6.98535	−	2.54246i	−0.529558	−	0.192743i
$175$	0.0650959	−	0.369177i	0.00492079	−	0.0279072i
$176$	−0.862965	−	4.89412i	−0.0650484	−	0.368908i
$177$	4.26002	−	1.55052i	0.320203	−	0.116544i
$178$	−3.01427	+	5.22086i	−0.225929	+	0.391320i
$179$	−1.56220	−	2.70580i	−0.116764	−	0.202241i	0.801720	−	0.597700i	$-0.203919\pi$
$179$	−1.56220	−	2.70580i	−0.116764	−	0.202241i	−0.918483	+	0.395459i	$0.870585\pi$
$180$	0.579074	+	0.485901i	0.0431617	+	0.0362169i
$181$	−9.35055	−	7.84604i	−0.695021	−	0.583192i	0.225332	−	0.974282i	$-0.427653\pi$
$181$	−9.35055	−	7.84604i	−0.695021	−	0.583192i	−0.920352	+	0.391091i	$0.872098\pi$
$182$	0.243101	+	0.421063i	0.0180198	+	0.0312112i
$183$	−4.88122	+	8.45453i	−0.360831	+	0.624977i
$184$	−10.2919	+	3.74596i	−0.758732	+	0.276156i
$185$	0.151194	+	0.857461i	0.0111160	+	0.0630418i
$186$	−2.07574	+	11.7721i	−0.152201	+	0.863173i
$187$	−3.37346	−	1.22784i	−0.246692	−	0.0897886i
$188$	−4.38375	+	3.67840i	−0.319717	+	0.268275i
$189$	0.415538			0.0302260
$190$	0.819065	−	3.63188i	0.0594212	−	0.263484i
$191$	1.89191			0.136894			0.0684469	−	0.997655i	$-0.478196\pi$
$191$	1.89191			0.136894			0.0684469	+	0.997655i	$0.478196\pi$
$192$	2.12409	−	1.78232i	0.153293	−	0.128628i
$193$	0.908430	+	0.330642i	0.0653902	+	0.0238001i	0.374508	−	0.927224i	$-0.377812\pi$
$193$	0.908430	+	0.330642i	0.0653902	+	0.0238001i	−0.309118	+	0.951024i	$0.600034\pi$
$194$	−4.47135	+	25.3583i	−0.321025	+	1.82062i
$195$	0.353364	+	2.00403i	0.0253049	+	0.143511i
$196$	5.42645	−	1.97506i	0.387603	−	0.141076i
$197$	−9.85573	+	17.0706i	−0.702192	+	1.21623i	0.265504	+	0.964110i	$0.414462\pi$
$197$	−9.85573	+	17.0706i	−0.702192	+	1.21623i	−0.967695	+	0.252122i	$0.918872\pi$
$198$	−1.51436	−	2.62295i	−0.107621	−	0.186405i
$199$	16.9708	+	14.2402i	1.20303	+	1.00946i	0.999538	+	0.0303803i	$0.00967185\pi$
$199$	16.9708	+	14.2402i	1.20303	+	1.00946i	0.203487	+	0.979078i	$0.434773\pi$
$200$	−7.17038	−	6.01666i	−0.507023	−	0.425442i
$201$	−1.62133	−	2.80822i	−0.114360	−	0.198076i
$202$	−9.06763	+	15.7056i	−0.637996	+	1.10504i
$203$	−0.300118	+	0.109234i	−0.0210641	+	0.00766672i
$204$	0.563446	+	3.19546i	0.0394491	+	0.223727i
$205$	−0.975845	+	5.53429i	−0.0681559	+	0.386532i
$206$	−4.85846	−	1.76834i	−0.338505	−	0.123206i
$207$	−7.65804	+	6.42586i	−0.532271	+	0.446628i
$208$	18.1818			1.26068
$209$	−2.35542	+	3.66770i	−0.162928	+	0.253700i
$210$	−0.0739160			−0.00510069
$211$	9.01894	−	7.56779i	0.620890	−	0.520988i	−0.277193	−	0.960814i	$-0.589404\pi$
$211$	9.01894	−	7.56779i	0.620890	−	0.520988i	0.898083	+	0.439826i	$0.144960\pi$
$212$	−2.40564	−	0.875581i	−0.165220	−	0.0601351i
$213$	2.43805	−	13.8269i	0.167053	−	0.947402i
$214$	−4.03802	−	22.9007i	−0.276033	−	1.56546i
$215$	−2.21137	+	0.804871i	−0.150814	+	0.0548918i
$216$	5.18784	−	8.98560i	0.352988	−	0.611392i
$217$	0.256789	+	0.444772i	0.0174320	+	0.0301931i
$218$	4.22381	+	3.54420i	0.286072	+	0.240043i
$219$	−7.70428	−	6.46466i	−0.520607	−	0.436841i
$220$	0.209775	+	0.363341i	0.0141430	+	0.0244965i
$221$	6.56712	−	11.3746i	0.441752	−	0.765138i
$222$	−2.96292	+	1.07841i	−0.198858	+	0.0723784i
$223$	3.50378	+	19.8709i	0.234630	+	1.33066i	0.843390	+	0.537301i	$0.180556\pi$
$223$	3.50378	+	19.8709i	0.234630	+	1.33066i	−0.608760	+	0.793354i	$0.708333\pi$
$224$	−0.0604839	+	0.343021i	−0.00404125	+	0.0229191i
$225$	−8.02836	−	2.92208i	−0.535224	−	0.194806i
$226$	−17.7524	+	14.8960i	−1.18087	+	0.990868i
$227$	23.7410			1.57574			0.787872	−	0.615839i	$-0.211183\pi$
$227$	23.7410			1.57574			0.787872	+	0.615839i	$0.211183\pi$
$228$	3.93535	+	0.186191i	0.260625	+	0.0123308i
$229$	−2.98452			−0.197222			−0.0986112	−	0.995126i	$-0.531440\pi$
$229$	−2.98452			−0.197222			−0.0986112	+	0.995126i	$0.531440\pi$
$230$	3.63035	−	3.04623i	0.239378	−	0.200862i
$231$	0.0813199	+	0.0295980i	0.00535046	+	0.00194741i
$232$	−1.38478	+	7.85349i	−0.0909154	+	0.515607i
$233$	−1.78767	−	10.1384i	−0.117114	−	0.664189i	−0.985682	−	0.168617i	$-0.946070\pi$
$233$	−1.78767	−	10.1384i	−0.117114	−	0.664189i	0.868567	−	0.495571i	$-0.165041\pi$
$234$	10.4126	−	3.78988i	0.680693	−	0.247752i
$235$	−1.76079	+	3.04977i	−0.114861	+	0.198945i
$236$	1.70979	+	2.96145i	0.111298	+	0.192774i
$237$	6.94341	+	5.82621i	0.451023	+	0.378453i
$238$	0.365465	+	0.306661i	0.0236896	+	0.0198779i
$239$	10.1316	+	17.5484i	0.655356	+	1.13511i	0.981804	+	0.189895i	$0.0608148\pi$
$239$	10.1316	+	17.5484i	0.655356	+	1.13511i	−0.326448	+	0.945215i	$0.605852\pi$
$240$	−1.38207	+	2.39382i	−0.0892122	+	0.154520i
$241$	16.4409	−	5.98401i	1.05905	−	0.385464i	0.246981	−	0.969020i	$-0.420562\pi$
$241$	16.4409	−	5.98401i	1.05905	−	0.385464i	0.812073	+	0.583557i	$0.198339\pi$
$242$	−0.291899	−	1.65544i	−0.0187640	−	0.106416i
$243$	2.67197	−	15.1535i	0.171407	−	0.972097i
$244$	−6.91977	−	2.51859i	−0.442993	−	0.161236i
$245$	2.72225	−	2.28424i	0.173918	−	0.145935i
$246$	−20.3508			−1.29752
$247$	−11.7184	−	10.8167i	−0.745622	−	0.688252i
$248$	12.8236			0.814302
$249$	−2.31798	+	1.94501i	−0.146896	+	0.123260i
$250$	7.81903	+	2.84589i	0.494519	+	0.179990i
$251$	3.57926	−	20.2990i	0.225921	−	1.28126i	−0.634996	−	0.772515i	$-0.718998\pi$
$251$	3.57926	−	20.2990i	0.225921	−	1.28126i	0.860917	−	0.508746i	$-0.169891\pi$
$252$	0.0204232	+	0.115826i	0.00128654	+	0.00729635i
$253$	−5.21379	+	1.89766i	−0.327788	+	0.119305i
$254$	−4.76128	+	8.24678i	−0.298749	+	0.517449i
$255$	0.998383	+	1.72925i	0.0625212	+	0.108290i
$256$	12.9491	+	10.8656i	0.809320	+	0.679100i
$257$	3.89491	+	3.26822i	0.242958	+	0.203866i	0.756133	−	0.654418i	$-0.227086\pi$
$257$	3.89491	+	3.26822i	0.242958	+	0.203866i	−0.513175	+	0.858284i	$0.671531\pi$
$258$	−4.26104	−	7.38033i	−0.265281	−	0.459479i
$259$	−0.0677341	+	0.117319i	−0.00420879	+	0.00728984i
$260$	−1.44240	+	0.524990i	−0.0894537	+	0.0325585i
$261$	1.26396	+	7.16828i	0.0782373	+	0.443706i
$262$	−0.952537	+	5.40211i	−0.0588479	+	0.333743i
$263$	15.1106	+	5.49981i	0.931760	+	0.339133i	0.762907	−	0.646508i	$-0.223771\pi$
$263$	15.1106	+	5.49981i	0.931760	+	0.339133i	0.168853	+	0.985641i	$0.445994\pi$
$264$	1.65527	−	1.38894i	0.101875	−	0.0854834i
$265$	−1.57540			−0.0967757
$266$	0.460844	−	0.350958i	0.0282562	−	0.0215186i
$267$	−3.92574			−0.240251
$268$	1.87371	−	1.57223i	0.114455	−	0.0960390i
$269$	2.03165	+	0.739461i	0.123872	+	0.0450857i	0.403212	−	0.915106i	$-0.367894\pi$
$269$	2.03165	+	0.739461i	0.123872	+	0.0450857i	−0.279340	+	0.960192i	$0.590116\pi$
$270$	−0.779597	+	4.42131i	−0.0474448	+	0.269073i
$271$	−1.19083	−	6.75354i	−0.0723379	−	0.410248i	−0.999377	−	0.0352846i	$-0.988766\pi$
$271$	−1.19083	−	6.75354i	−0.0723379	−	0.410248i	0.927039	−	0.374964i	$-0.122345\pi$
$272$	16.7648	−	6.10190i	1.01652	−	0.369982i
$273$	−0.158305	+	0.274193i	−0.00958108	+	0.0165949i
$274$	−8.80854	−	15.2568i	−0.532143	−	0.921699i
$275$	−3.63244	−	3.04798i	−0.219044	−	0.183800i
$276$	3.84161	+	3.22350i	0.231238	+	0.194032i
$277$	−13.3046	−	23.0442i	−0.799394	−	1.38459i	−0.920011	−	0.391892i	$-0.871821\pi$
$277$	−13.3046	−	23.0442i	−0.799394	−	1.38459i	0.120617	−	0.992699i	$-0.461513\pi$
$278$	13.7607	−	23.8341i	0.825309	−	1.42948i
$279$	10.9989	−	4.00328i	0.658488	−	0.239670i
$280$	0.0137695	+	0.0780905i	0.000822883	+	0.00466680i
$281$	−2.30194	+	13.0549i	−0.137322	+	0.778792i	0.835892	+	0.548893i	$0.184951\pi$
$281$	−2.30194	+	13.0549i	−0.137322	+	0.778792i	−0.973215	+	0.229899i	$0.926160\pi$
$282$	−11.9837	−	4.36173i	−0.713622	−	0.259737i
$283$	6.69872	−	5.62090i	0.398198	−	0.334128i	−0.421599	−	0.906782i	$-0.638531\pi$
$283$	6.69872	−	5.62090i	0.398198	−	0.334128i	0.819797	+	0.572655i	$0.194086\pi$
$284$	10.5906			0.628435
$285$	2.31488	−	0.720616i	0.137122	−	0.0426856i
$286$	6.15003			0.363659
$287$	−0.669789	+	0.562020i	−0.0395364	+	0.0331750i
$288$	7.45955	+	2.71506i	0.439558	+	0.159986i
$289$	−0.714068	+	4.04968i	−0.0420040	+	0.238216i
$290$	−0.599190	−	3.39818i	−0.0351857	−	0.199548i
$291$	−15.7567	+	5.73496i	−0.923673	+	0.336189i
$292$	3.79311	−	6.56986i	0.221975	−	0.384472i
$293$	4.52848	+	7.84357i	0.264557	+	0.458226i	0.967447	−	0.253072i	$-0.0814410\pi$
$293$	4.52848	+	7.84357i	0.264557	+	0.458226i	−0.702891	+	0.711298i	$0.748108\pi$
$294$	9.85824	+	8.27204i	0.574944	+	0.482435i
$295$	1.61203	+	1.35265i	0.0938558	+	0.0787544i
$296$	1.69127	+	2.92936i	0.0983029	+	0.170266i
$297$	2.62810	−	4.55201i	0.152498	−	0.264134i
$298$	−27.5941	+	10.0434i	−1.59848	+	0.581800i
$299$	−3.52495	−	19.9910i	−0.203853	−	1.15611i
$300$	−0.744230	+	4.22074i	−0.0429681	+	0.243684i
$301$	−0.344060	−	0.125228i	−0.0198313	−	0.00721801i
$302$	4.69110	−	3.93630i	0.269943	−	0.226509i
$303$	−11.8096			−0.678441
$304$	−2.74919	−	21.4869i	−0.157677	−	1.23236i
$305$	−4.53159			−0.259478
$306$	8.32919	−	6.98902i	0.476148	−	0.399536i
$307$	−11.1702	−	4.06563i	−0.637519	−	0.232038i	0.00298175	−	0.999996i	$-0.499051\pi$
$307$	−11.1702	−	4.06563i	−0.637519	−	0.232038i	−0.640501	+	0.767958i	$0.721273\pi$
$308$	−0.0113352	+	0.0642850i	−0.000645882	+	0.00366298i
$309$	−0.584646	−	3.31569i	−0.0332594	−	0.188623i
$310$	−5.21412	+	1.89778i	−0.296142	+	0.107787i
$311$	−15.1392	+	26.2219i	−0.858466	+	1.48691i	0.0149257	+	0.999889i	$0.495249\pi$
$311$	−15.1392	+	26.2219i	−0.858466	+	1.48691i	−0.873392	+	0.487018i	$0.838085\pi$
$312$	3.95276	+	6.84639i	0.223781	+	0.387600i
$313$	−13.3789	−	11.2263i	−0.756222	−	0.634546i	0.180918	−	0.983498i	$-0.442093\pi$
$313$	−13.3789	−	11.2263i	−0.756222	−	0.634546i	−0.937140	+	0.348953i	$0.886537\pi$
$314$	−13.6510	−	11.4546i	−0.770371	−	0.646418i
$315$	0.0361884	+	0.0626801i	0.00203898	+	0.00353163i
$316$	−3.41850	+	5.92102i	−0.192306	+	0.333083i
$317$	−13.9303	+	5.07021i	−0.782404	+	0.284772i	−0.702175	−	0.712005i	$-0.747787\pi$
$317$	−13.9303	+	5.07021i	−0.782404	+	0.284772i	−0.0802290	+	0.996776i	$0.525565\pi$
$318$	−0.990673	−	5.61838i	−0.0555542	−	0.315063i
$319$	−0.701516	+	3.97850i	−0.0392774	+	0.222753i
$320$	1.20948	+	0.440213i	0.0676118	+	0.0246087i
$321$	11.6001	−	9.73364i	0.647455	−	0.543279i
$322$	0.737342			0.0410905
$323$	−14.4352	−	6.04099i	−0.803197	−	0.336129i
$324$	−0.287673			−0.0159818
$325$	13.2897	−	11.1513i	0.737177	−	0.618565i
$326$	31.3586	+	11.4136i	1.73679	+	0.632140i
$327$	−0.623491	+	3.53599i	−0.0344791	+	0.195541i
$328$	3.79105	+	21.5001i	0.209326	+	1.18715i
$329$	−0.514868	+	0.187397i	−0.0283856	+	0.0103315i
$330$	−0.467487	+	0.809711i	−0.0257343	+	0.0445731i
$331$	−14.5581	−	25.2153i	−0.800184	−	1.38596i	−0.919495	−	0.393102i	$-0.871402\pi$
$331$	−14.5581	−	25.2153i	−0.800184	−	1.38596i	0.119311	−	0.992857i	$-0.461931\pi$
$332$	−1.74846	−	1.46714i	−0.0959594	−	0.0805195i
$333$	2.36510	+	1.98455i	0.129606	+	0.108753i
$334$	5.47672	+	9.48595i	0.299673	+	0.519048i
$335$	0.752597	−	1.30354i	0.0411188	−	0.0712198i
$336$	−0.404129	+	0.147091i	−0.0220470	+	0.00802446i
$337$	6.22261	+	35.2902i	0.338967	+	1.92238i	0.383868	+	0.923388i	$0.374592\pi$
$337$	6.22261	+	35.2902i	0.338967	+	1.92238i	−0.0449005	+	0.998991i	$0.514297\pi$
$338$	−0.112484	+	0.637926i	−0.00611830	+	0.0346986i
$339$	−14.1807	−	5.16136i	−0.770191	−	0.280327i
$340$	−1.15379	+	0.968148i	−0.0625733	+	0.0525052i
$341$	6.49633			0.351796
$342$	−6.05323	−	11.7323i	−0.327321	−	0.634412i
$343$	1.10630			0.0597345
$344$	−7.00338	+	5.87654i	−0.377597	+	0.316842i
$345$	2.89995	+	1.05550i	0.156128	+	0.0568260i
$346$	−1.10147	+	6.24674i	−0.0592154	+	0.335827i
$347$	−2.48137	−	14.0725i	−0.133207	−	0.755454i	−0.976092	−	0.217360i	$-0.930256\pi$
$347$	−2.48137	−	14.0725i	−0.133207	−	0.755454i	0.842885	−	0.538094i	$-0.180856\pi$
$348$	3.43119	−	1.24885i	0.183931	−	0.0669455i
$349$	10.8839	−	18.8515i	0.582602	−	1.00910i	−0.412568	−	0.910927i	$-0.635368\pi$
$349$	10.8839	−	18.8515i	0.582602	−	1.00910i	0.995170	−	0.0981690i	$-0.0312986\pi$
$350$	0.315076	+	0.545728i	0.0168415	+	0.0291704i
$351$	14.7313	+	12.3610i	0.786299	+	0.659784i
$352$	3.37509	+	2.83203i	0.179893	+	0.150948i
$353$	−5.59818	−	9.69634i	−0.297961	−	0.516084i	0.677708	−	0.735331i	$-0.262973\pi$
$353$	−5.59818	−	9.69634i	−0.297961	−	0.516084i	−0.975669	+	0.219247i	$0.929640\pi$
$354$	−3.81030	+	6.59963i	−0.202515	+	0.350766i
$355$	6.12422	−	2.22903i	0.325040	−	0.118305i
$356$	−0.514208	−	2.91622i	−0.0272530	−	0.154559i
$357$	−0.0539475	+	0.305952i	−0.00285521	+	0.0161927i
$358$	4.93530	+	1.79630i	0.260839	+	0.0949376i
$359$	3.03699	−	2.54834i	0.160286	−	0.134496i	−0.559117	−	0.829089i	$-0.688860\pi$
$359$	3.03699	−	2.54834i	0.160286	−	0.134496i	0.719403	+	0.694593i	$0.244415\pi$
$360$	1.80719			0.0952474
$361$	−11.0111	+	15.4841i	−0.579531	+	0.814950i
$362$	20.5185			1.07843
$363$	0.838545	−	0.703623i	0.0440122	−	0.0369306i
$364$	−0.224419	−	0.0816817i	−0.0117627	−	0.00428128i
$365$	0.810663	−	4.59750i	0.0424321	−	0.240644i
$366$	−2.84965	−	16.1612i	−0.148954	−	0.844758i
$367$	−2.21219	+	0.805171i	−0.115475	+	0.0420296i	−0.399112	−	0.916902i	$-0.630681\pi$
$367$	−2.21219	+	0.805171i	−0.115475	+	0.0420296i	0.283636	+	0.958932i	$0.408459\pi$
$368$	13.7867	−	23.8793i	0.718682	−	1.24479i
$369$	9.96350	+	17.2573i	0.518679	+	0.898379i
$370$	−1.12119	−	0.940791i	−0.0582880	−	0.0489094i
$371$	−0.187766	−	0.157555i	−0.00974834	−	0.00817982i
$372$	−2.93582	−	5.08500i	−0.152215	−	0.263645i
$373$	4.42425	−	7.66303i	0.229079	−	0.396777i	−0.728456	−	0.685092i	$-0.759762\pi$
$373$	4.42425	−	7.66303i	0.229079	−	0.396777i	0.957535	+	0.288316i	$0.0930952\pi$
$374$	5.67073	−	2.06398i	0.293226	−	0.106726i
$375$	0.940908	+	5.33615i	0.0485883	+	0.275558i
$376$	−2.37567	+	13.4731i	−0.122516	+	0.694821i
$377$	−13.8889	−	5.05515i	−0.715315	−	0.260353i
$378$	−0.535091	+	0.448995i	−0.0275221	+	0.0230938i
$379$	19.4443			0.998788			0.499394	−	0.866375i	$-0.333556\pi$
$379$	19.4443			0.998788			0.499394	+	0.866375i	$0.333556\pi$
$380$	0.838519	+	1.62521i	0.0430151	+	0.0833716i
$381$	−6.20103			−0.317688
$382$	−2.43622	+	2.04423i	−0.124648	+	0.104592i
$383$	29.4829	+	10.7309i	1.50651	+	0.548324i	0.957736	−	0.287649i	$-0.0928735\pi$
$383$	29.4829	+	10.7309i	1.50651	+	0.548324i	0.548771	+	0.835972i	$0.315096\pi$
$384$	−2.48434	+	14.0894i	−0.126778	+	0.718995i
$385$	0.00697547	+	0.0395598i	0.000355503	+	0.00201616i
$386$	−1.52705	+	0.555802i	−0.0777250	+	0.0282896i
$387$	−4.17231	+	7.22665i	−0.212090	+	0.367351i
$388$	−6.32406	−	10.9536i	−0.321055	−	0.556084i
$389$	21.4528	+	18.0010i	1.08770	+	0.912687i	0.996537	−	0.0831488i	$-0.0264977\pi$
$389$	21.4528	+	18.0010i	1.08770	+	0.912687i	0.0911612	+	0.995836i	$0.470942\pi$
$390$	−2.62041	−	2.19878i	−0.132689	−	0.111340i
$391$	−9.95928	−	17.2500i	−0.503662	−	0.872369i
$392$	6.90277	−	11.9560i	0.348643	−	0.603867i
$393$	−3.35666	+	1.22172i	−0.169321	+	0.0616278i
$394$	−5.75376	−	32.6312i	−0.289870	−	1.64394i
$395$	−0.730602	+	4.14345i	−0.0367606	+	0.208480i
$396$	1.39798	+	0.508824i	0.0702512	+	0.0255694i
$397$	−14.9259	+	12.5243i	−0.749111	+	0.628579i	−0.935268	−	0.353941i	$-0.884841\pi$
$397$	−14.9259	+	12.5243i	−0.749111	+	0.628579i	0.186157	+	0.982520i	$0.440397\pi$
$398$	−37.2400			−1.86667
$399$	0.347972	+	0.145623i	0.0174204	+	0.00729025i
$400$	23.5650			1.17825
$401$	−22.5145	+	18.8919i	−1.12432	+	0.943418i	−0.998815	−	0.0486744i	$-0.984500\pi$
$401$	−22.5145	+	18.8919i	−1.12432	+	0.943418i	−0.125507	+	0.992093i	$0.540056\pi$
$402$	5.12211	+	1.86430i	0.255468	+	0.0929826i
$403$	−4.12718	+	23.4064i	−0.205589	+	1.16595i
$404$	−1.54686	−	8.77268i	−0.0769591	−	0.436457i
$405$	−0.166353	+	0.0605475i	−0.00826614	+	0.00300863i
$406$	0.268435	−	0.464942i	0.0133222	−	0.0230747i
$407$	0.856778	+	1.48398i	0.0424689	+	0.0735583i
$408$	5.94238	+	4.98625i	0.294192	+	0.246856i
$409$	25.2932	+	21.2235i	1.25067	+	1.04944i	0.996612	+	0.0822472i	$0.0262097\pi$
$409$	25.2932	+	21.2235i	1.25067	+	1.04944i	0.254057	+	0.967189i	$0.418235\pi$
$410$	−4.72327	−	8.18095i	−0.233266	−	0.404028i
$411$	5.73606	−	9.93514i	0.282939	−	0.490065i
$412$	2.38647	−	0.868604i	0.117573	−	0.0427930i
$413$	0.0568542	+	0.322436i	0.00279761	+	0.0158660i
$414$	2.91808	−	16.5492i	0.143416	−	0.813351i
$415$	−1.31988	−	0.480396i	−0.0647902	−	0.0235817i
$416$	−12.3481	+	10.3613i	−0.605415	+	0.508003i
$417$	17.9217			0.877629
$418$	−0.929916	−	7.26797i	−0.0454837	−	0.355488i
$419$	21.9296			1.07133			0.535664	−	0.844431i	$-0.320061\pi$
$419$	21.9296			1.07133			0.535664	+	0.844431i	$0.320061\pi$
$420$	0.0278131	−	0.0233379i	0.00135714	−	0.00113878i
$421$	−26.2322	−	9.54773i	−1.27848	−	0.465328i	−0.388549	−	0.921428i	$-0.627024\pi$
$421$	−26.2322	−	9.54773i	−1.27848	−	0.465328i	−0.889928	+	0.456100i	$0.849246\pi$
$422$	−3.43664	+	19.4902i	−0.167293	+	0.948767i
$423$	2.16839	+	12.2976i	0.105431	+	0.597928i
$424$	−5.75115	+	2.09325i	−0.279300	+	0.101657i
$425$	8.51148	−	14.7423i	0.412867	−	0.715107i
$426$	11.8006	+	20.4393i	0.571742	+	0.990287i
$427$	−0.540106	−	0.453203i	−0.0261376	−	0.0219320i
$428$	8.75002	+	7.34214i	0.422948	+	0.354896i
$429$	2.00243	+	3.46831i	0.0966782	+	0.167452i
$430$	1.97791	−	3.42585i	0.0953835	−	0.165209i
$431$	−20.1143	+	7.32100i	−0.968871	+	0.352640i	−0.777504	−	0.628878i	$-0.783514\pi$
$431$	−20.1143	+	7.32100i	−0.968871	+	0.352640i	−0.191368	+	0.981518i	$0.561292\pi$
$432$	4.53592	+	25.7245i	0.218235	+	1.23767i
$433$	6.20737	−	35.2038i	0.298307	−	1.69178i	−0.355140	−	0.934813i	$-0.615567\pi$
$433$	6.20737	−	35.2038i	0.298307	−	1.69178i	0.653448	−	0.756972i	$-0.273322\pi$
$434$	−0.811250	−	0.295271i	−0.0389413	−	0.0141735i
$435$	1.72131	−	1.44435i	0.0825304	−	0.0692512i
$436$	−2.70836			−0.129707
$437$	−23.0919	+	7.18844i	−1.10464	+	0.343870i
$438$	16.9060			0.807800
$439$	−2.94649	+	2.47240i	−0.140629	+	0.118001i	−0.710388	−	0.703810i	$-0.751481\pi$
$439$	−2.94649	+	2.47240i	−0.140629	+	0.118001i	0.569760	+	0.821811i	$0.307036\pi$
$440$	0.942527	+	0.343052i	0.0449332	+	0.0163544i
$441$	2.18815	−	12.4096i	0.104197	−	0.590933i
$442$	3.83387	+	21.7430i	0.182359	+	1.03421i
$443$	−1.75163	+	0.637541i	−0.0832224	+	0.0302905i	−0.383296	−	0.923626i	$-0.625211\pi$
$443$	−1.75163	+	0.637541i	−0.0832224	+	0.0302905i	0.300073	+	0.953916i	$0.402989\pi$
$444$	0.774392	−	1.34129i	0.0367510	−	0.0636546i
$445$	−0.911137	−	1.57814i	−0.0431920	−	0.0748108i
$446$	−25.9826	−	21.8020i	−1.23031	−	1.03236i
$447$	−14.6485	−	12.2916i	−0.692852	−	0.581372i
$448$	0.100128	+	0.173427i	0.00473060	+	0.00819364i
$449$	7.09625	−	12.2911i	0.334893	−	0.580051i	−0.648572	−	0.761154i	$-0.724633\pi$
$449$	7.09625	−	12.2911i	0.334893	−	0.580051i	0.983464	+	0.181103i	$0.0579666\pi$
$450$	13.4955	−	4.91196i	0.636185	−	0.231552i
$451$	1.92051	+	10.8917i	0.0904332	+	0.512872i
$452$	1.97665	−	11.2101i	0.0929738	−	0.527281i
$453$	3.74728	+	1.36390i	0.176063	+	0.0640816i
$454$	−30.5714	+	25.6525i	−1.43479	+	1.20393i
$455$	−0.146966			−0.00688989
$456$	7.49323	−	5.70650i	0.350903	−	0.267231i
$457$	−23.3764			−1.09350			−0.546752	−	0.837295i	$-0.684136\pi$
$457$	−23.3764			−1.09350			−0.546752	+	0.837295i	$0.684136\pi$
$458$	3.84318	−	3.22481i	0.179580	−	0.150685i
$459$	17.7316	+	6.45379i	0.827642	+	0.301237i
$460$	−0.404224	+	2.29247i	−0.0188470	+	0.106887i
$461$	−0.753641	−	4.27411i	−0.0351006	−	0.199065i	0.962215	−	0.272292i	$-0.0877815\pi$
$461$	−0.753641	−	4.27411i	−0.0351006	−	0.199065i	−0.997315	+	0.0732264i	$0.976670\pi$
$462$	−0.136697	+	0.0497537i	−0.00635973	+	0.00231475i
$463$	−8.93852	+	15.4820i	−0.415408	+	0.719508i	−0.995471	−	0.0950633i	$-0.969695\pi$
$463$	−8.93852	+	15.4820i	−0.415408	+	0.719508i	0.580063	+	0.814572i	$0.303028\pi$
$464$	−10.0383	−	17.3869i	−0.466017	−	0.807164i
$465$	−2.76795	−	2.32259i	−0.128361	−	0.107707i
$466$	13.2567	+	11.1237i	0.614104	+	0.515294i
$467$	10.4233	+	18.0536i	0.482331	+	0.835422i	0.999794	−	0.0202838i	$-0.00645696\pi$
$467$	10.4233	+	18.0536i	0.482331	+	0.835422i	−0.517463	+	0.855705i	$0.673124\pi$
$468$	−2.72145	+	4.71369i	−0.125799	+	0.217891i
$469$	0.220066	−	0.0800973i	0.0101617	−	0.00369855i
$470$	−1.02794	−	5.82976i	−0.0474155	−	0.268907i
$471$	2.01507	−	11.4281i	0.0928497	−	0.526577i
$472$	7.68215	+	2.79608i	0.353600	+	0.128700i
$473$	−3.54784	+	2.97699i	−0.163130	+	0.136882i
$474$	−15.2364			−0.699829
$475$	−15.1879	−	14.0193i	−0.696867	−	0.643249i
$476$	−0.234341			−0.0107410
$477$	−4.27932	+	3.59078i	−0.195937	+	0.164410i
$478$	−32.0077	−	11.6499i	−1.46400	−	0.532852i
$479$	−0.382530	+	2.16943i	−0.0174782	+	0.0991240i	−0.992299	−	0.123866i	$-0.960471\pi$
$479$	−0.382530	+	2.16943i	−0.0174782	+	0.0991240i	0.974821	+	0.222990i	$0.0715818\pi$
$480$	−0.425538	−	2.41334i	−0.0194231	−	0.110154i
$481$	−5.89114	+	2.14420i	−0.268613	+	0.0977671i
$482$	−14.7053	+	25.4703i	−0.669807	+	1.16014i
$483$	0.240076	+	0.415824i	0.0109238	+	0.0189206i
$484$	0.632519	+	0.530746i	0.0287509	+	0.0241248i
$485$	−5.96245	−	5.00309i	−0.270741	−	0.227179i
$486$	12.9328	+	22.4003i	0.586645	+	1.01610i
$487$	10.1402	−	17.5633i	0.459494	−	0.795867i	−0.539440	−	0.842024i	$-0.681364\pi$
$487$	10.1402	−	17.5633i	0.459494	−	0.795867i	0.998934	+	0.0461569i	$0.0146974\pi$
$488$	−16.5431	+	6.02118i	−0.748869	+	0.272566i
$489$	3.77355	+	21.4009i	0.170646	+	0.967781i
$490$	−1.03731	+	5.88286i	−0.0468608	+	0.265761i
$491$	−18.9165	−	6.88504i	−0.853689	−	0.310717i	−0.122145	−	0.992512i	$-0.538977\pi$
$491$	−18.9165	−	6.88504i	−0.853689	−	0.310717i	−0.731543	+	0.681795i	$0.761200\pi$
$492$	7.65759	−	6.42548i	0.345231	−	0.289683i
$493$	−14.5030			−0.653182
$494$	26.7774	+	1.26691i	1.20477	+	0.0570009i
$495$	0.915505			0.0411489
$496$	−24.7312	+	20.7519i	−1.11046	+	0.931789i
$497$	0.952850	+	0.346809i	0.0427412	+	0.0155565i
$498$	0.883259	−	5.00921i	0.0395798	−	0.224468i
$499$	4.58442	+	25.9995i	0.205227	+	1.16390i	0.897082	+	0.441863i	$0.145682\pi$
$499$	4.58442	+	25.9995i	0.205227	+	1.16390i	−0.691856	+	0.722036i	$0.743207\pi$
$500$	−3.84070	+	1.39790i	−0.171761	+	0.0625159i
$501$	−3.56640	+	6.17719i	−0.159335	+	0.275976i
$502$	17.3243	+	30.0066i	0.773221	+	1.33926i
$503$	−6.41404	−	5.38202i	−0.285988	−	0.239973i	0.488496	−	0.872566i	$-0.337546\pi$
$503$	−6.41404	−	5.38202i	−0.285988	−	0.239973i	−0.774484	+	0.632594i	$0.781990\pi$
$504$	0.215393	+	0.180736i	0.00959438	+	0.00805064i
$505$	−2.74092	−	4.74740i	−0.121969	−	0.211257i
$506$	4.66337	−	8.07720i	0.207312	−	0.359075i
$507$	−0.396383	+	0.144272i	−0.0176040	+	0.00640732i
$508$	−0.812234	−	4.60641i	−0.0360371	−	0.204376i
$509$	6.56127	−	37.2108i	0.290823	−	1.64934i	−0.392887	−	0.919587i	$-0.628524\pi$
$509$	6.56127	−	37.2108i	0.290823	−	1.64934i	0.683710	−	0.729754i	$-0.260365\pi$
$510$	−3.15410	−	1.14800i	−0.139666	−	0.0508343i
$511$	0.556414	−	0.466887i	0.0246143	−	0.0206539i
$512$	−2.27556			−0.100567
$513$	12.3806	−	19.2782i	0.546615	−	0.851153i
$514$	−8.54685			−0.376985
$515$	1.19721	−	1.00458i	0.0527552	−	0.0442669i
$516$	3.93358	+	1.43171i	0.173166	+	0.0630274i
$517$	−1.20349	+	6.82532i	−0.0529294	+	0.300177i
$518$	−0.0395430	−	0.224260i	−0.00173742	−	0.00985340i
$519$	−3.88148	+	1.41274i	−0.170378	+	0.0620126i
$520$	−1.83482	+	3.17800i	−0.0804621	+	0.139364i
$521$	−10.2425	−	17.7405i	−0.448732	−	0.777227i	0.549572	−	0.835447i	$-0.314791\pi$
$521$	−10.2425	−	17.7405i	−0.448732	−	0.777227i	−0.998304	+	0.0582197i	$0.981458\pi$
$522$	−9.37303	−	7.86491i	−0.410247	−	0.344238i
$523$	−23.2068	−	19.4728i	−1.01476	−	0.851487i	−0.0258018	−	0.999667i	$-0.508214\pi$
$523$	−23.2068	−	19.4728i	−1.01476	−	0.851487i	−0.988960	+	0.148181i	$0.952658\pi$
$524$	−1.34722	−	2.33345i	−0.0588536	−	0.101937i
$525$	−0.205176	+	0.355375i	−0.00895460	+	0.0155098i
$526$	−25.4006	+	9.24508i	−1.10752	+	0.403105i
$527$	4.04975	+	22.9673i	0.176410	+	1.00047i
$528$	−0.944639	+	5.35731i	−0.0411101	+	0.233147i
$529$	−7.31525	−	2.66253i	−0.318054	−	0.115762i
$530$	2.02865	−	1.70224i	0.0881187	−	0.0739404i
$531$	7.46191			0.323819
$532$	−0.0625964	+	0.277564i	−0.00271390	+	0.0120339i
$533$	−40.4632			−1.75266
$534$	5.05520	−	4.24181i	0.218760	−	0.183561i
$535$	6.60520	+	2.40410i	0.285568	+	0.103938i
$536$	1.01541	−	5.75868i	0.0438591	−	0.248737i
$537$	0.593893	+	3.36813i	0.0256284	+	0.145346i
$538$	−3.41517	+	1.24302i	−0.147238	+	0.0535903i
$539$	3.49688	−	6.05677i	0.150621	−	0.260883i
$540$	−1.10262	−	1.90980i	−0.0474493	−	0.0821846i
$541$	34.0178	+	28.5443i	1.46254	+	1.22722i	0.922740	+	0.385424i	$0.125945\pi$
$541$	34.0178	+	28.5443i	1.46254	+	1.22722i	0.539800	+	0.841793i	$0.318500\pi$
$542$	8.83073	+	7.40986i	0.379312	+	0.318281i
$543$	6.68075	+	11.5714i	0.286699	+	0.496577i
$544$	−7.90844	+	13.6978i	−0.339072	+	0.587290i
$545$	−1.56617	+	0.570038i	−0.0670872	+	0.0244177i
$546$	−0.0924185	−	0.524131i	−0.00395515	−	0.0224307i
$547$	7.54188	−	42.7721i	0.322468	−	1.82881i	−0.204436	−	0.978880i	$-0.565536\pi$
$547$	7.54188	−	42.7721i	0.322468	−	1.82881i	0.526904	−	0.849925i	$-0.323353\pi$
$548$	8.13161	+	2.95966i	0.347365	+	0.126431i
$549$	−12.3094	+	10.3288i	−0.525352	+	0.440823i
$550$	7.97090			0.339880
$551$	−3.87399	+	17.1780i	−0.165038	+	0.731806i
$552$	11.9890			0.510287
$553$	−0.501463	+	0.420777i	−0.0213244	+	0.0178933i
$554$	42.0319	+	15.2984i	1.78576	+	0.649965i
$555$	0.165503	−	0.938614i	0.00702521	−	0.0398419i
$556$	2.34745	+	13.3130i	0.0995540	+	0.564599i
$557$	−41.8871	+	15.2456i	−1.77481	+	0.645979i	−0.774908	+	0.632074i	$0.782204\pi$
$557$	−41.8871	+	15.2456i	−1.77481	+	0.645979i	−0.999903	+	0.0139045i	$0.995574\pi$
$558$	−9.83777	+	17.0395i	−0.416466	+	0.721340i
$559$	−8.47218	−	14.6742i	−0.358335	−	0.620654i
$560$	−0.152926	−	0.128320i	−0.00646228	−	0.00542250i
$561$	3.01035	+	2.52598i	0.127097	+	0.106647i
$562$	−11.1418	−	19.2982i	−0.469989	−	0.814045i
$563$	3.86065	−	6.68685i	0.162707	−	0.281817i	−0.773132	−	0.634246i	$-0.781311\pi$
$563$	3.86065	−	6.68685i	0.162707	−	0.281817i	0.935839	+	0.352429i	$0.114644\pi$
$564$	5.88640	−	2.14247i	0.247862	−	0.0902144i
$565$	−1.21640	−	6.89852i	−0.0511741	−	0.290223i
$566$	−2.55253	+	14.4761i	−0.107291	+	0.608477i
$567$	−0.0258824	−	0.00942041i	−0.00108696	−	0.000395620i
$568$	19.3954	−	16.2746i	0.813811	−	0.682868i
$569$	−11.1299			−0.466589			−0.233294	−	0.972406i	$-0.574951\pi$
$569$	−11.1299			−0.466589			−0.233294	+	0.972406i	$0.574951\pi$
$570$	−2.20225	+	3.42920i	−0.0922422	+	0.143634i
$571$	9.06319			0.379283			0.189641	−	0.981853i	$-0.439267\pi$
$571$	9.06319			0.379283			0.189641	+	0.981853i	$0.439267\pi$
$572$	−2.31413	+	1.94179i	−0.0967588	+	0.0811903i
$573$	−1.94607	−	0.708312i	−0.0812983	−	0.0295902i
$574$	0.255221	−	1.44743i	0.0106527	−	0.0604147i
$575$	−4.56859	−	25.9098i	−0.190524	−	1.08051i
$576$	4.28873	−	1.56097i	0.178697	−	0.0650404i
$577$	15.4464	−	26.7539i	0.643042	−	1.11378i	−0.341708	−	0.939806i	$-0.611006\pi$
$577$	15.4464	−	26.7539i	0.643042	−	1.11378i	0.984750	−	0.173975i	$-0.0556611\pi$
$578$	−3.45622	−	5.98636i	−0.143760	−	0.249000i
$579$	−0.810648	−	0.680214i	−0.0336894	−	0.0282687i
$580$	1.29839	+	1.08948i	0.0539128	+	0.0452382i
$581$	−0.109268	−	0.189257i	−0.00453319	−	0.00785171i
$582$	14.0933	−	24.4102i	0.584184	−	1.01184i
$583$	−2.91347	+	1.06042i	−0.120664	+	0.0439180i
$584$	−3.14934	−	17.8608i	−0.130321	−	0.739085i
$585$	−0.581629	+	3.29858i	−0.0240474	+	0.136380i
$586$	−14.3064	−	5.20712i	−0.590993	−	0.215104i
$587$	30.3547	−	25.4707i	1.25287	−	1.05129i	0.256471	−	0.966552i	$-0.417440\pi$
$587$	30.3547	−	25.4707i	1.25287	−	1.05129i	0.996404	−	0.0847346i	$-0.0270043\pi$
$588$	−6.32124			−0.260683
$589$	28.2852	+	1.33824i	1.16547	+	0.0551414i
$590$	−3.53737			−0.145631
$591$	16.5290	−	13.8694i	0.679910	−	0.570512i
$592$	−8.00216	−	2.91255i	−0.328887	−	0.119705i
$593$	−4.00705	+	22.7251i	−0.164550	+	0.933207i	0.784978	+	0.619524i	$0.212674\pi$
$593$	−4.00705	+	22.7251i	−0.164550	+	0.933207i	−0.949528	+	0.313684i	$0.898437\pi$
$594$	1.53428	+	8.70135i	0.0629524	+	0.357021i
$595$	−0.135512	+	0.0493225i	−0.00555547	+	0.00202202i
$596$	7.21203	−	12.4916i	0.295416	−	0.511676i
$597$	−12.1252	−	21.0015i	−0.496252	−	0.859534i
$598$	26.1396	+	21.9337i	1.06893	+	0.896937i
$599$	13.6380	+	11.4436i	0.557232	+	0.467573i	0.877381	−	0.479794i	$-0.159289\pi$
$599$	13.6380	+	11.4436i	0.557232	+	0.467573i	−0.320149	+	0.947367i	$0.603733\pi$
$600$	5.12308	+	8.87343i	0.209149	+	0.362256i
$601$	1.78137	−	3.08542i	0.0726636	−	0.125857i	−0.827404	−	0.561607i	$-0.810183\pi$
$601$	1.78137	−	3.08542i	0.0726636	−	0.125857i	0.900068	+	0.435750i	$0.143517\pi$
$602$	0.578359	−	0.210505i	0.0235721	−	0.00857956i
$603$	−0.926818	−	5.25624i	−0.0377429	−	0.214051i
$604$	−0.522334	+	2.96230i	−0.0212535	+	0.120534i
$605$	0.477475	+	0.173787i	0.0194121	+	0.00706543i
$606$	15.2072	−	12.7604i	0.617752	−	0.518355i
$607$	3.06484			0.124398			0.0621990	−	0.998064i	$-0.480189\pi$
$607$	3.06484			0.124398			0.0621990	+	0.998064i	$0.480189\pi$
$608$	14.1118	+	13.0260i	0.572310	+	0.528275i
$609$	0.349606			0.0141667
$610$	5.83536	−	4.89645i	0.236267	−	0.198251i
$611$	−23.8272	−	8.67238i	−0.963944	−	0.350847i
$612$	−0.927419	+	5.25966i	−0.0374887	+	0.212609i
$613$	3.40038	+	19.2845i	0.137340	+	0.778893i	0.973202	+	0.229953i	$0.0738574\pi$
$613$	3.40038	+	19.2845i	0.137340	+	0.778893i	−0.835862	+	0.548940i	$0.815032\pi$
$614$	18.7769	−	6.83425i	0.757776	−	0.275808i
$615$	3.07576	−	5.32738i	0.124027	−	0.214821i
$616$	0.0780283	+	0.135149i	0.00314385	+	0.00544531i
$617$	14.2274	+	11.9382i	0.572772	+	0.480613i	0.882564	−	0.470191i	$-0.155815\pi$
$617$	14.2274	+	11.9382i	0.572772	+	0.480613i	−0.309792	+	0.950804i	$0.600260\pi$
$618$	4.33550	+	3.63792i	0.174400	+	0.146339i
$619$	5.91046	+	10.2372i	0.237561	+	0.411468i	0.960014	−	0.279952i	$-0.0903186\pi$
$619$	5.91046	+	10.2372i	0.237561	+	0.411468i	−0.722453	+	0.691420i	$0.756985\pi$
$620$	1.36277	−	2.36038i	0.0547301	−	0.0947953i
$621$	27.4048	−	9.97452i	1.09972	−	0.400264i
$622$	−8.83825	−	50.1242i	−0.354381	−	2.00980i
$623$	0.0492332	−	0.279215i	0.00197249	−	0.0111865i
$624$	−18.7023	−	6.80710i	−0.748693	−	0.272502i
$625$	16.2355	−	13.6232i	0.649419	−	0.544927i
$626$	29.3582			1.17339
$627$	3.79600	−	2.89085i	0.151597	−	0.115450i
$628$	8.75322			0.349292
$629$	−4.71241	+	3.95418i	−0.187896	+	0.157663i
$630$	−0.114327	−	0.0416115i	−0.00455489	−	0.00165784i
$631$	5.35593	−	30.3750i	0.213216	−	1.20921i	−0.670759	−	0.741675i	$-0.734031\pi$
$631$	5.35593	−	30.3750i	0.213216	−	1.20921i	0.883975	−	0.467534i	$-0.154857\pi$
$632$	2.83831	+	16.0969i	0.112902	+	0.640299i
$633$	−12.1104	+	4.40784i	−0.481347	+	0.175196i
$634$	12.4597	−	21.5808i	0.494838	−	0.857084i
$635$	−1.43922	−	2.49280i	−0.0571135	−	0.0989236i
$636$	2.14670	+	1.80129i	0.0851221	+	0.0714259i
$637$	19.6010	+	16.4472i	0.776621	+	0.651663i
$638$	−3.39547	−	5.88113i	−0.134428	−	0.232836i
$639$	11.5549	−	20.0137i	0.457105	−	0.791729i
$640$	−6.24048	+	2.27135i	−0.246677	+	0.0897830i
$641$	−4.19198	−	23.7739i	−0.165573	−	0.939012i	−0.948472	−	0.316862i	$-0.897371\pi$
$641$	−4.19198	−	23.7739i	−0.165573	−	0.939012i	0.782898	−	0.622149i	$-0.213740\pi$
$642$	−4.42019	+	25.0681i	−0.174451	+	0.989360i
$643$	5.88633	+	2.14245i	0.232134	+	0.0844900i	0.455468	−	0.890252i	$-0.349472\pi$
$643$	5.88633	+	2.14245i	0.232134	+	0.0844900i	−0.223334	+	0.974742i	$0.571694\pi$
$644$	−0.277447	+	0.232806i	−0.0109329	+	0.00917382i
$645$	2.57601			0.101430
$646$	25.1157	−	7.81844i	0.988163	−	0.307612i
$647$	29.4783			1.15891			0.579455	−	0.815004i	$-0.303265\pi$
$647$	29.4783			1.15891			0.579455	+	0.815004i	$0.303265\pi$
$648$	−0.526838	+	0.442070i	−0.0206962	+	0.0173661i
$649$	3.89170	+	1.41646i	0.152763	+	0.0556010i
$650$	−5.06399	+	28.7193i	−0.198626	+	1.12646i
$651$	−0.0976223	−	0.553644i	−0.00382612	−	0.0216990i
$652$	−15.4033	+	5.60634i	−0.603239	+	0.219561i
$653$	−8.65600	+	14.9926i	−0.338735	+	0.586707i	−0.984195	−	0.177087i	$-0.943332\pi$
$653$	−8.65600	+	14.9926i	−0.338735	+	0.586707i	0.645460	+	0.763794i	$0.276666\pi$
$654$	−3.01782	−	5.22701i	−0.118006	−	0.204392i
$655$	−1.27019	−	1.06581i	−0.0496303	−	0.0416448i
$656$	−42.1039	−	35.3294i	−1.64388	−	1.37938i
$657$	−8.27698	−	14.3361i	−0.322916	−	0.559306i
$658$	0.460514	−	0.797634i	0.0179527	−	0.0310950i
$659$	34.8982	−	12.7019i	1.35944	−	0.494796i	0.443560	−	0.896245i	$-0.353715\pi$
$659$	34.8982	−	12.7019i	1.35944	−	0.494796i	0.915881	+	0.401449i	$0.131493\pi$
$660$	−0.0797493	−	0.452281i	−0.00310424	−	0.0176050i
$661$	0.468468	−	2.65681i	0.0182213	−	0.103338i	−0.974341	−	0.225078i	$-0.927736\pi$
$661$	0.468468	−	2.65681i	0.0182213	−	0.103338i	0.992562	+	0.121740i	$0.0388474\pi$
$662$	45.9920	+	16.7397i	1.78753	+	0.650608i
$663$	−11.0137	+	9.24155i	−0.427735	+	0.358912i
$664$	−5.45666			−0.211759
$665$	0.0222221	+	0.173682i	0.000861734	+	0.00673508i
$666$	−5.18988			−0.201104
$667$	−17.1707	+	14.4080i	−0.664854	+	0.557879i
$668$	−5.05584	−	1.84017i	−0.195616	−	0.0711985i
$669$	3.83539	−	21.7516i	0.148285	−	0.840964i
$670$	0.439365	+	2.49176i	0.0169741	+	0.0962652i
$671$	−8.38054	+	3.05027i	−0.323527	+	0.117754i
$672$	0.190639	−	0.330197i	0.00735406	−	0.0127376i
$673$	12.8194	+	22.2038i	0.494151	+	0.855895i	0.999977	−	0.00674080i	$-0.00214568\pi$
$673$	12.8194	+	22.2038i	0.494151	+	0.855895i	−0.505826	+	0.862635i	$0.668812\pi$
$674$	−46.1444	−	38.7198i	−1.77742	−	1.49143i
$675$	19.0929	+	16.0208i	0.734885	+	0.616642i
$676$	−0.159091	−	0.275554i	−0.00611889	−	0.0105982i
$677$	0.164744	−	0.285344i	0.00633161	−	0.0109667i	−0.862842	−	0.505473i	$-0.831318\pi$
$677$	0.164744	−	0.285344i	0.00633161	−	0.0109667i	0.869174	+	0.494507i	$0.164651\pi$
$678$	23.8375	−	8.67614i	0.915474	−	0.333205i
$679$	−0.210288	−	1.19260i	−0.00807012	−	0.0457679i
$680$	−0.625271	+	3.54609i	−0.0239781	+	0.135986i
$681$	−24.4206	−	8.88839i	−0.935801	−	0.340604i
$682$	−8.36536	+	7.01937i	−0.320326	+	0.268785i
$683$	−21.8760			−0.837061			−0.418531	−	0.908203i	$-0.637455\pi$
$683$	−21.8760			−0.837061			−0.418531	+	0.908203i	$0.637455\pi$
$684$	5.98204	+	2.50342i	0.228729	+	0.0957206i
$685$	5.32520			0.203465
$686$	−1.42459	+	1.19537i	−0.0543910	+	0.0456395i
$687$	3.06996	+	1.11737i	0.117126	+	0.0426304i
$688$	3.99672	−	22.6665i	0.152373	−	0.864153i
$689$	−1.96975	−	11.1710i	−0.0750413	−	0.425580i
$690$	−4.87476	+	1.77427i	−0.185579	+	0.0675452i
$691$	10.5965	−	18.3536i	0.403109	−	0.698205i	−0.590991	−	0.806678i	$-0.701263\pi$
$691$	10.5965	−	18.3536i	0.403109	−	0.698205i	0.994099	+	0.108474i	$0.0345963\pi$
$692$	−1.55786	−	2.69830i	−0.0592210	−	0.102574i
$693$	0.109116	+	0.0915593i	0.00414498	+	0.00347805i
$694$	18.4008	+	15.4401i	0.698487	+	0.586100i
$695$	4.15950	+	7.20446i	0.157779	+	0.273281i
$696$	4.36469	−	7.55987i	0.165443	−	0.286556i
$697$	−37.3097	+	13.5796i	−1.41321	+	0.514365i
$698$	6.35400	+	36.0353i	0.240503	+	1.36396i
$699$	−1.95686	+	11.0979i	−0.0740154	+	0.419762i
$700$	−0.290863	−	0.105866i	−0.0109936	−	0.00400134i
$701$	23.1314	−	19.4096i	0.873662	−	0.733090i	−0.0912038	−	0.995832i	$-0.529071\pi$
$701$	23.1314	−	19.4096i	0.873662	−	0.733090i	0.964866	+	0.262743i	$0.0846270\pi$
$702$	−32.3259			−1.22006
$703$	3.42474	+	6.63780i	0.129166	+	0.250350i
$704$	2.53307			0.0954686
$705$	2.95300	−	2.47786i	0.111216	−	0.0933215i
$706$	17.6858	+	6.43712i	0.665615	+	0.242264i
$707$	0.148105	−	0.839945i	0.00557006	−	0.0315894i
$708$	−0.650004	−	3.68635i	−0.0244286	−	0.138542i
$709$	−35.5784	+	12.9495i	−1.33617	+	0.486328i	−0.908606	−	0.417655i	$-0.862852\pi$
$709$	−35.5784	+	12.9495i	−1.33617	+	0.486328i	−0.427569	+	0.903983i	$0.640630\pi$
$710$	−5.47769	+	9.48763i	−0.205574	+	0.356065i
$711$	7.45955	+	12.9203i	0.279755	+	0.484550i
$712$	−5.42309	−	4.55051i	−0.203239	−	0.170538i
$713$	27.6115	+	23.1688i	1.03406	+	0.867677i
$714$	−0.261116	−	0.452267i	−0.00977203	−	0.0169256i
$715$	−0.929500	+	1.60994i	−0.0347613	+	0.0602084i
$716$	−2.42421	+	0.882341i	−0.0905971	+	0.0329746i
$717$	−3.85167	−	21.8439i	−0.143843	−	0.815776i
$718$	−1.15724	+	6.56302i	−0.0431877	+	0.244930i
$719$	35.8699	+	13.0556i	1.33772	+	0.486891i	0.909094	−	0.416591i	$-0.136775\pi$
$719$	35.8699	+	13.0556i	1.33772	+	0.486891i	0.428627	+	0.903482i	$0.358998\pi$
$720$	−3.48528	+	2.92450i	−0.129889	+	0.108990i
$721$	0.243158			0.00905569
$722$	−2.55168	−	31.8365i	−0.0949636	−	1.18483i
$723$	−19.1519			−0.712269
$724$	−7.72070	+	6.47844i	−0.286937	+	0.240769i
$725$	−18.0011	−	6.55185i	−0.668542	−	0.243330i
$726$	−0.319525	+	1.81212i	−0.0118587	+	0.0672540i
$727$	3.88485	+	22.0321i	0.144081	+	0.817125i	0.968100	+	0.250563i	$0.0806158\pi$
$727$	3.88485	+	22.0321i	0.144081	+	0.817125i	−0.824019	+	0.566562i	$0.808273\pi$
$728$	−0.536516	+	0.195276i	−0.0198846	+	0.00723741i
$729$	−8.94438	+	15.4921i	−0.331273	+	0.573782i
$730$	3.92376	+	6.79616i	0.145225	+	0.251537i
$731$	−12.7366	−	10.6873i	−0.471081	−	0.395284i
$732$	6.17493	+	5.18139i	0.228232	+	0.191510i
$733$	16.7424	+	28.9986i	0.618394	+	1.07109i	0.989779	+	0.142611i	$0.0455497\pi$
$733$	16.7424	+	28.9986i	0.618394	+	1.07109i	−0.371385	+	0.928479i	$0.621117\pi$
$734$	1.97865	−	3.42712i	0.0730333	−	0.126497i
$735$	−3.65538	+	1.33045i	−0.134831	+	0.0490744i
$736$	4.24491	+	24.0741i	0.156470	+	0.887383i
$737$	0.514397	−	2.91729i	0.0189480	−	0.107460i
$738$	−31.4768	−	11.4566i	−1.15868	−	0.421724i
$739$	−6.66509	+	5.59268i	−0.245179	+	0.205730i	−0.757093	−	0.653307i	$-0.773381\pi$
$739$	−6.66509	+	5.59268i	−0.245179	+	0.205730i	0.511914	+	0.859037i	$0.328937\pi$
$740$	0.718924			0.0264282
$741$	8.00417	+	15.5136i	0.294040	+	0.569907i
$742$	0.412027			0.0151260
$743$	−24.2044	+	20.3099i	−0.887974	+	0.745099i	−0.967803	−	0.251710i	$-0.919007\pi$
$743$	−24.2044	+	20.3099i	−0.887974	+	0.745099i	0.0798284	+	0.996809i	$0.474563\pi$
$744$	−13.1908	−	4.80104i	−0.483597	−	0.176015i
$745$	1.54135	−	8.74146i	0.0564709	−	0.320262i
$746$	2.58287	+	14.6482i	0.0945656	+	0.536308i
$747$	−4.68021	+	1.70346i	−0.171240	+	0.0623262i
$748$	−1.48211	+	2.56709i	−0.0541912	+	0.0938620i
$749$	0.546820	+	0.947119i	0.0199804	+	0.0346070i
$750$	−6.97740	−	5.85473i	−0.254779	−	0.213785i
$751$	23.4801	+	19.7022i	0.856803	+	0.718943i	0.961277	−	0.275585i	$-0.0888715\pi$
$751$	23.4801	+	19.7022i	0.856803	+	0.718943i	−0.104474	+	0.994528i	$0.533316\pi$
$752$	−17.2213	−	29.8281i	−0.627994	−	1.08772i
$753$	−11.2815	+	19.5401i	−0.411119	+	0.712080i
$754$	23.3470	−	8.49761i	0.850247	−	0.309465i
$755$	0.321435	+	1.82295i	0.0116982	+	0.0663439i
$756$	0.0595801	−	0.337895i	0.00216691	−	0.0122891i
$757$	39.8723	+	14.5123i	1.44919	+	0.527460i	0.942364	−	0.334591i	$-0.108598\pi$
$757$	39.8723	+	14.5123i	1.44919	+	0.527460i	0.506822	+	0.862051i	$0.330820\pi$
$758$	−25.0386	+	21.0098i	−0.909442	+	0.763112i
$759$	6.07352			0.220455
$760$	4.03312	+	1.68782i	0.146297	+	0.0612236i
$761$	−33.9440			−1.23047			−0.615234	−	0.788344i	$-0.710939\pi$
$761$	−33.9440			−1.23047			−0.615234	+	0.788344i	$0.710939\pi$
$762$	7.98510	−	6.70030i	0.289270	−	0.242726i
$763$	−0.243676	−	0.0886906i	−0.00882165	−	0.00321082i
$764$	0.271263	−	1.53841i	0.00981394	−	0.0556576i
$765$	0.570717	+	3.23670i	0.0206343	+	0.117023i
$766$	−49.5602	+	18.0384i	−1.79068	+	0.651756i
$767$	−7.57597	+	13.1220i	−0.273553	+	0.473807i
$768$	−9.25185	−	16.0247i	−0.333848	−	0.578241i
$769$	−36.9320	−	30.9896i	−1.33180	−	1.11752i	−0.983653	−	0.180076i	$-0.942366\pi$
$769$	−36.9320	−	30.9896i	−1.33180	−	1.11752i	−0.348150	−	0.937439i	$-0.613190\pi$
$770$	−0.0517273	−	0.0434043i	−0.00186412	−	0.00156418i
$771$	−2.78282	−	4.81999i	−0.100221	−	0.173588i
$772$	0.399112	−	0.691283i	0.0143644	−	0.0248798i
$773$	−4.30725	+	1.56771i	−0.154921	+	0.0563867i	−0.418317	−	0.908301i	$-0.637380\pi$
$773$	−4.30725	+	1.56771i	−0.154921	+	0.0563867i	0.263396	+	0.964688i	$0.415158\pi$
$774$	−2.43579	−	13.8140i	−0.0875526	−	0.496535i
$775$	−5.34913	+	30.3364i	−0.192146	+	1.08972i
$776$	−28.4142	−	10.3419i	−1.02001	−	0.371254i
$777$	0.113596	−	0.0953185i	0.00407524	−	0.00341953i
$778$	−47.0752			−1.68773
$779$	6.11825	+	47.8186i	0.219209	+	1.71328i
$780$	1.68024			0.0601623
$781$	9.82549	−	8.24456i	0.351584	−	0.295014i
$782$	31.4634	+	11.4518i	1.12513	+	0.409514i
$783$	3.68732	−	20.9118i	0.131774	−	0.747327i
$784$	6.03536	+	34.2282i	0.215549	+	1.22244i
$785$	5.06173	−	1.84232i	0.180661	−	0.0657552i
$786$	3.00230	−	5.20014i	0.107088	−	0.185483i
$787$	−9.43247	−	16.3375i	−0.336231	−	0.582370i	0.647489	−	0.762075i	$-0.275819\pi$
$787$	−9.43247	−	16.3375i	−0.336231	−	0.582370i	−0.983721	+	0.179705i	$0.942486\pi$
$788$	12.4679	+	10.4618i	0.444150	+	0.372686i
$789$	−13.4841	−	11.3145i	−0.480048	−	0.402808i
$790$	−3.53625	−	6.12497i	−0.125814	−	0.217917i
$791$	0.544940	−	0.943863i	0.0193758	−	0.0335599i
$792$	3.34215	−	1.21644i	0.118758	−	0.0432244i
$793$	−5.66593	−	32.1331i	−0.201203	−	1.14108i
$794$	5.68749	−	32.2553i	0.201841	−	1.14470i
$795$	1.62050	+	0.589812i	0.0574730	+	0.0209185i
$796$	14.0127	−	11.7580i	0.496666	−	0.416752i
$797$	29.7563			1.05402			0.527012	−	0.849858i	$-0.323312\pi$
$797$	29.7563			1.05402			0.527012	+	0.849858i	$0.323312\pi$
$798$	−0.605433	+	0.188469i	−0.0214321	+	0.00667174i
$799$	−24.8807			−0.880215
$800$	−16.0040	+	13.4290i	−0.565828	+	0.474786i
$801$	−6.07199	−	2.21002i	−0.214543	−	0.0780873i
$802$	8.57910	−	48.6545i	0.302939	−	1.71805i
$803$	−1.59542	−	9.04809i	−0.0563013	−	0.319300i
$804$	−2.51597	+	0.915739i	−0.0887315	+	0.0322956i
$805$	−0.111440	+	0.193020i	−0.00392774	+	0.00680305i
$806$	−19.9763	−	34.6000i	−0.703636	−	1.21873i
$807$	−1.81297	−	1.52126i	−0.0638194	−	0.0535509i
$808$	−16.3139	−	13.6890i	−0.573922	−	0.481578i
$809$	14.0962	+	24.4153i	0.495595	+	0.858395i	0.999987	−	0.00507920i	$-0.00161677\pi$
$809$	14.0962	+	24.4153i	0.495595	+	0.858395i	−0.504392	+	0.863475i	$0.668283\pi$
$810$	0.148791	−	0.257714i	0.00522799	−	0.00905514i
$811$	34.7503	−	12.6481i	1.22025	−	0.444134i	0.350001	−	0.936750i	$-0.386181\pi$
$811$	34.7503	−	12.6481i	1.22025	−	0.444134i	0.870247	+	0.492616i	$0.163959\pi$
$812$	0.0457926	+	0.259703i	0.00160701	+	0.00911379i
$813$	−1.30354	+	7.39272i	−0.0457170	+	0.259274i
$814$	−2.70674	−	0.985174i	−0.0948713	−	0.0345303i
$815$	−7.72727	+	6.48395i	−0.270675	+	0.227123i
$816$	−19.5293			−0.683661
$817$	−16.0607	+	12.2311i	−0.561892	+	0.427910i
$818$	−55.5025			−1.94060
$819$	−0.399212	+	0.334979i	−0.0139496	+	0.0117051i
$820$	4.36029	+	1.58702i	0.152268	+	0.0554211i
$821$	−7.56966	+	42.9297i	−0.264183	+	1.49826i	0.507169	+	0.861846i	$0.330692\pi$
$821$	−7.56966	+	42.9297i	−0.264183	+	1.49826i	−0.771352	+	0.636409i	$0.780419\pi$
$822$	3.34870	+	18.9914i	0.116799	+	0.662402i
$823$	14.0016	−	5.09617i	0.488065	−	0.177641i	−0.0862531	−	0.996273i	$-0.527489\pi$
$823$	14.0016	−	5.09617i	0.488065	−	0.177641i	0.574318	+	0.818632i	$0.305267\pi$
$824$	3.03574	−	5.25805i	0.105755	−	0.183173i
$825$	2.59530	+	4.49519i	0.0903567	+	0.156502i
$826$	−0.421608	−	0.353771i	−0.0146696	−	0.0123093i
$827$	−20.2486	−	16.9906i	−0.704112	−	0.590820i	0.218828	−	0.975763i	$-0.429777\pi$
$827$	−20.2486	−	16.9906i	−0.704112	−	0.590820i	−0.922940	+	0.384943i	$0.874221\pi$
$828$	4.12718	+	7.14849i	0.143429	+	0.248427i
$829$	−7.97549	+	13.8140i	−0.277000	+	0.479779i	−0.970638	−	0.240546i	$-0.922674\pi$
$829$	−7.97549	+	13.8140i	−0.277000	+	0.479779i	0.693638	+	0.720324i	$0.256007\pi$
$830$	2.21869	−	0.807536i	0.0770117	−	0.0280300i
$831$	5.05794	+	28.6850i	0.175458	+	0.995071i
$832$	−1.60928	+	9.12669i	−0.0557918	+	0.316411i
$833$	23.5932	+	8.58721i	0.817455	+	0.297529i
$834$	−23.0779	+	19.3646i	−0.799121	+	0.670542i
$835$	−3.31095			−0.114580
$836$	2.64467	+	2.44118i	0.0914679	+	0.0844301i
$837$	−34.1461			−1.18026
$838$	−28.2388	+	23.6952i	−0.975493	+	0.818536i
$839$	29.8003	+	10.8464i	1.02882	+	0.374460i	0.800631	−	0.599157i	$-0.204498\pi$
$839$	29.8003	+	10.8464i	1.02882	+	0.374460i	0.228189	+	0.973617i	$0.426720\pi$
$840$	0.0150726	−	0.0854812i	0.000520056	−	0.00294938i
$841$	−2.20176	−	12.4868i	−0.0759229	−	0.430580i
$842$	44.0958	−	16.0495i	1.51964	−	0.553104i
$843$	7.25547	−	12.5668i	0.249892	−	0.432825i
$844$	−4.86062	−	8.41883i	−0.167309	−	0.289788i
$845$	−0.149994	−	0.125860i	−0.00515996	−	0.00432972i
$846$	−16.0799	−	13.4927i	−0.552840	−	0.463888i
$847$	0.0395283	+	0.0684651i	0.00135821	+	0.00235249i
$848$	7.70403	−	13.3438i	0.264557	−	0.458227i
$849$	−8.99490	+	3.27388i	−0.308704	+	0.112359i
$850$	4.96899	+	28.1805i	0.170435	+	0.966584i
$851$	−1.65096	+	9.36306i	−0.0565942	+	0.320961i
$852$	−10.8938	−	3.96501i	−0.373214	−	0.135839i
$853$	10.5358	−	8.84060i	0.360740	−	0.302696i	−0.444346	−	0.895855i	$-0.646564\pi$
$853$	10.5358	−	8.84060i	0.360740	−	0.302696i	0.805085	+	0.593159i	$0.202119\pi$
$854$	1.18519			0.0405563
$855$	3.98614	+	0.188594i	0.136323	+	0.00644978i
$856$	27.3073			0.933345
$857$	−36.4416	+	30.5782i	−1.24482	+	1.04453i	−0.247692	+	0.968839i	$0.579672\pi$
$857$	−36.4416	+	30.5782i	−1.24482	+	1.04453i	−0.997131	+	0.0756916i	$0.975884\pi$
$858$	−6.32610	−	2.30251i	−0.215969	−	0.0786064i
$859$	6.57407	−	37.2834i	0.224304	−	1.27209i	−0.639706	−	0.768620i	$-0.720944\pi$
$859$	6.57407	−	37.2834i	0.224304	−	1.27209i	0.864010	−	0.503474i	$-0.167945\pi$
$860$	0.337415	+	1.91358i	0.0115058	+	0.0652524i
$861$	0.899379	−	0.327347i	0.0306507	−	0.0111560i
$862$	17.9908	−	31.1611i	0.612771	−	1.06135i
$863$	2.02337	+	3.50459i	0.0688765	+	0.119298i	0.898407	−	0.439164i	$-0.144725\pi$
$863$	2.02337	+	3.50459i	0.0688765	+	0.119298i	−0.829531	+	0.558461i	$0.811392\pi$
$864$	−17.7402	−	14.8858i	−0.603532	−	0.506424i
$865$	−1.46878	−	1.23246i	−0.0499402	−	0.0419048i
$866$	30.0449	+	52.0392i	1.02097	+	1.76837i
$867$	2.25067	−	3.89827i	0.0764367	−	0.132392i
$868$	0.398485	−	0.145037i	0.0135255	−	0.00492286i
$869$	1.43786	+	8.15451i	0.0487760	+	0.276623i
$870$	−0.655900	+	3.71979i	−0.0222371	+	0.126113i
$871$	10.1842	+	3.70676i	0.345080	+	0.125599i
$872$	−4.96004	+	4.16197i	−0.167968	+	0.140942i
$873$	−27.5996			−0.934104
$874$	21.9684	−	34.2077i	0.743091	−	1.15709i
$875$	−0.391330			−0.0132294
$876$	−6.36139	+	5.33784i	−0.214931	+	0.180349i
$877$	24.6178	+	8.96014i	0.831283	+	0.302562i	0.722385	−	0.691491i	$-0.243046\pi$
$877$	24.6178	+	8.96014i	0.831283	+	0.302562i	0.108898	+	0.994053i	$0.465268\pi$
$878$	1.12275	−	6.36745i	0.0378911	−	0.214891i
$879$	−1.72157	−	9.76353i	−0.0580672	−	0.329316i
$880$	−2.37287	+	0.863653i	−0.0799893	+	0.0291137i
$881$	−5.27475	+	9.13613i	−0.177711	+	0.307804i	−0.941096	−	0.338139i	$-0.890202\pi$
$881$	−5.27475	+	9.13613i	−0.177711	+	0.307804i	0.763385	+	0.645943i	$0.223536\pi$
$882$	10.5910	+	18.3442i	0.356619	+	0.617682i
$883$	0.231877	+	0.194568i	0.00780329	+	0.00654774i	0.646681	−	0.762761i	$-0.276157\pi$
$883$	0.231877	+	0.194568i	0.00780329	+	0.00654774i	−0.638878	+	0.769308i	$0.720601\pi$
$884$	−8.30766	−	6.97095i	−0.279417	−	0.234459i
$885$	−1.15176	−	1.99490i	−0.0387159	−	0.0670578i
$886$	1.56671	−	2.71362i	0.0526347	−	0.0911660i
$887$	35.0392	−	12.7532i	1.17650	−	0.428212i	0.321537	−	0.946897i	$-0.395801\pi$
$887$	35.0392	−	12.7532i	1.17650	−	0.428212i	0.854965	+	0.518685i	$0.173578\pi$
$888$	−0.642961	−	3.64641i	−0.0215764	−	0.122366i
$889$	0.0777679	−	0.441043i	0.00260825	−	0.0147921i
$890$	2.87847	+	1.04768i	0.0964866	+	0.0351182i
$891$	−0.266891	+	0.223948i	−0.00894118	+	0.00750254i
$892$	16.6604			0.557832
$893$	−6.64604	+	29.4697i	−0.222401	+	0.986167i
$894$	32.1442			1.07506
$895$	−1.21614	+	1.02046i	−0.0406511	+	0.0341103i
$896$	−0.970939	−	0.353393i	−0.0324368	−	0.0118060i
$897$	−3.85856	+	21.8830i	−0.128834	+	0.730651i
$898$	4.14278	+	23.4949i	0.138246	+	0.784034i
$899$	24.6616	−	8.97609i	0.822510	−	0.299369i
$900$	−3.52720	+	6.10930i	−0.117573	+	0.203643i
$901$	−5.56526	−	9.63931i	−0.185406	−	0.321132i
$902$	−14.2417	−	11.9502i	−0.474197	−	0.397899i
$903$	0.307026	+	0.257625i	0.0102172	+	0.00857324i
$904$	−13.6067	−	23.5675i	−0.452553	−	0.783845i
$905$	−3.10111	+	5.37129i	−0.103084	+	0.178548i
$906$	−6.29911	+	2.29269i	−0.209274	+	0.0761695i
$907$	−3.05691	−	17.3366i	−0.101503	−	0.575652i	−0.992560	−	0.121760i	$-0.961146\pi$
$907$	−3.05691	−	17.3366i	−0.101503	−	0.575652i	0.891057	−	0.453892i	$-0.149965\pi$
$908$	3.40399	−	19.3050i	0.112965	−	0.640659i
$909$	−18.2660	−	6.64827i	−0.605844	−	0.220509i
$910$	0.189249	−	0.158799i	0.00627356	−	0.00526414i
$911$	−57.8952			−1.91815			−0.959076	−	0.283148i	$-0.908621\pi$
$911$	−57.8952			−1.91815			−0.959076	+	0.283148i	$0.908621\pi$
$912$	−5.21659	+	23.1313i	−0.172739	+	0.765954i
$913$	−2.76429			−0.0914845
$914$	30.1020	−	25.2586i	0.995685	−	0.835479i
$915$	4.66132	+	1.69658i	0.154099	+	0.0560873i
$916$	−0.427921	+	2.42686i	−0.0141389	+	0.0801858i
$917$	−0.0447979	−	0.254062i	−0.00147936	−	0.00838985i
$918$	−29.8065	+	10.8487i	−0.983762	+	0.358060i
$919$	6.43588	−	11.1473i	0.212300	−	0.367714i	−0.740134	−	0.672459i	$-0.765238\pi$
$919$	6.43588	−	11.1473i	0.212300	−	0.367714i	0.952434	+	0.304745i	$0.0985713\pi$
$920$	2.78257	+	4.81955i	0.0917386	+	0.158896i
$921$	9.96788	+	8.36405i	0.328453	+	0.275605i
$922$	5.58870	+	4.68948i	0.184054	+	0.154440i
$923$	23.4631	+	40.6392i	0.772297	+	1.33766i
$924$	0.0357273	−	0.0618816i	0.00117534	−	0.00203575i
$925$	−7.63535	+	2.77904i	−0.251049	+	0.0913743i
$926$	−5.21829	−	29.5944i	−0.171484	−	0.972533i
$927$	0.962314	−	5.45755i	0.0316065	−	0.179250i
$928$	16.7257	+	6.08765i	0.549048	+	0.199837i
$929$	14.5264	−	12.1891i	0.476597	−	0.399912i	−0.372597	−	0.927993i	$-0.621533\pi$
$929$	14.5264	−	12.1891i	0.476597	−	0.399912i	0.849194	+	0.528081i	$0.177088\pi$
$930$	6.07390			0.199171
$931$	16.4732	−	25.6510i	0.539887	−	0.840677i
$932$	−8.50037			−0.278439
$933$	25.3898	−	21.3046i	0.831226	−	0.697481i
$934$	−32.9293	−	11.9853i	−1.07748	−	0.392170i
$935$	−0.316756	+	1.79641i	−0.0103590	+	0.0587490i
$936$	2.25957	+	12.8146i	0.0738562	+	0.418859i
$937$	44.1896	−	16.0837i	1.44361	−	0.525432i	0.502812	−	0.864396i	$-0.332299\pi$
$937$	44.1896	−	16.0837i	1.44361	−	0.525432i	0.940799	+	0.338964i	$0.110076\pi$
$938$	−0.196834	+	0.340926i	−0.00642684	+	0.0111316i
$939$	9.55894	+	16.5566i	0.311944	+	0.540304i
$940$	2.22746	+	1.86906i	0.0726517	+	0.0609620i
$941$	14.0418	+	11.7825i	0.457750	+	0.384098i	0.842302	−	0.539006i	$-0.181200\pi$
$941$	14.0418	+	11.7825i	0.457750	+	0.384098i	−0.384553	+	0.923103i	$0.625644\pi$
$942$	9.75334	+	16.8933i	0.317781	+	0.550413i
$943$	−30.6820	+	53.1428i	−0.999143	+	1.73057i
$944$	−19.3403	+	7.03928i	−0.629472	+	0.229109i
$945$	−0.0366645	−	0.207935i	−0.00119270	−	0.00676412i
$946$	1.35190	−	7.66698i	0.0439539	−	0.249275i
$947$	41.2603	+	15.0175i	1.34078	+	0.488004i	0.910058	−	0.414480i	$-0.136037\pi$
$947$	41.2603	+	15.0175i	1.34078	+	0.488004i	0.430722	+	0.902484i	$0.358259\pi$
$948$	5.73314	−	4.81067i	0.186204	−	0.156243i
$949$	33.6140			1.09116
$950$	34.7055	+	1.64201i	1.12600	+	0.0532737i
$951$	16.2273			0.526207
$952$	−0.429167	+	0.360114i	−0.0139094	+	0.0116714i
$953$	33.9596	+	12.3603i	1.10006	+	0.400389i	0.827338	−	0.561704i	$-0.189854\pi$
$953$	33.9596	+	12.3603i	1.10006	+	0.400389i	0.272721	+	0.962093i	$0.412076\pi$
$954$	1.63062	−	9.24773i	0.0527934	−	0.299406i
$955$	−0.166930	−	0.946709i	−0.00540174	−	0.0306348i
$956$	15.7221	−	5.72239i	0.508491	−	0.185075i
$957$	2.21111	−	3.82975i	0.0714750	−	0.123798i
$958$	−1.85152	−	3.20692i	−0.0598198	−	0.103611i
$959$	0.634693	+	0.532571i	0.0204953	+	0.0171976i
$960$	−1.07929	−	0.905631i	−0.0348339	−	0.0292291i
$961$	−5.60113	−	9.70145i	−0.180682	−	0.312950i
$962$	5.26922	−	9.12655i	0.169886	−	0.294252i
$963$	23.4217	−	8.52478i	0.754752	−	0.274707i
$964$	−2.50859	−	14.2269i	−0.0807964	−	0.458219i
$965$	0.0852983	−	0.483751i	0.00274585	−	0.0155725i
$966$	−0.758450	−	0.276053i	−0.0244027	−	0.00888187i
$967$	−24.9725	+	20.9544i	−0.803061	+	0.673848i	−0.948941	−	0.315454i	$-0.897843\pi$
$967$	−24.9725	+	20.9544i	−0.803061	+	0.673848i	0.145880	+	0.989302i	$0.453399\pi$
$968$	1.97398			0.0634462
$969$	12.5868	+	11.6183i	0.404346	+	0.373234i
$970$	13.0838			0.420095
$971$	19.1399	−	16.0603i	0.614229	−	0.515399i	−0.281755	−	0.959486i	$-0.590916\pi$
$971$	19.1399	−	16.0603i	0.614229	−	0.515399i	0.895983	+	0.444087i	$0.146472\pi$
$972$	−11.9390	−	4.34543i	−0.382942	−	0.139380i
$973$	−0.224758	+	1.27467i	−0.00720541	+	0.0408639i
$974$	5.91980	+	33.5729i	0.189683	+	1.07574i
$975$	−17.8451	+	6.49507i	−0.571499	+	0.208009i
$976$	22.1605	−	38.3831i	0.709340	−	1.22861i
$977$	−11.3026	−	19.5768i	−0.361604	−	0.626316i	0.626621	−	0.779324i	$-0.284437\pi$
$977$	−11.3026	−	19.5768i	−0.361604	−	0.626316i	−0.988225	+	0.153008i	$0.951104\pi$
$978$	−27.9832	−	23.4807i	−0.894803	−	0.750829i
$979$	−2.74728	−	2.30524i	−0.0878035	−	0.0736758i
$980$	−1.46712	−	2.54112i	−0.0468653	−	0.0811730i
$981$	−2.95497	+	5.11817i	−0.0943451	+	0.163410i
$982$	31.7982	−	11.5736i	1.01472	−	0.369329i
$983$	−7.23829	−	41.0504i	−0.230865	−	1.30930i	−0.851149	−	0.524925i	$-0.824093\pi$
$983$	−7.23829	−	41.0504i	−0.230865	−	1.30930i	0.620283	−	0.784378i	$-0.287018\pi$
$984$	4.14985	−	23.5350i	0.132292	−	0.750267i
$985$	9.41173	+	3.42559i	0.299883	+	0.109148i
$986$	18.6756	−	15.6707i	0.594752	−	0.499056i
$987$	0.599767			0.0190908
$988$	−10.4758	+	7.97789i	−0.333280	+	0.253811i
$989$	−25.6967			−0.817109
$990$	−1.17890	+	0.989215i	−0.0374679	+	0.0314393i
$991$	19.8330	+	7.21862i	0.630015	+	0.229307i	0.637238	−	0.770667i	$-0.280077\pi$
$991$	19.8330	+	7.21862i	0.630015	+	0.229307i	−0.00722256	+	0.999974i	$0.502299\pi$
$992$	4.97014	−	28.1871i	0.157802	−	0.894941i
$993$	5.53448	+	31.3876i	0.175631	+	0.996055i
$994$	−1.60172	+	0.582979i	−0.0508035	+	0.0184910i
$995$	5.62836	−	9.74861i	0.178431	−	0.309052i
$996$	1.24924	+	2.16374i	0.0395836	+	0.0685608i
$997$	−0.511447	−	0.429155i	−0.0161977	−	0.0135915i	0.634653	−	0.772797i	$-0.281143\pi$
$997$	−0.511447	−	0.429155i	−0.0161977	−	0.0135915i	−0.650851	+	0.759206i	$0.725588\pi$
$998$	−33.9962	−	28.5262i	−1.07613	−	0.902982i
$999$	−4.50341	−	7.80013i	−0.142481	−	0.246785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.j.b.177.2	yes	42
19.4	even	9		3971.2.a.t.1.5		21
19.15	odd	18		3971.2.a.s.1.17		21
19.16	even	9	inner	209.2.j.b.111.2	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.j.b.111.2	✓	42	19.16	even	9	inner
209.2.j.b.177.2	yes	42	1.1	even	1	trivial
3971.2.a.s.1.17		21	19.15	odd	18
3971.2.a.t.1.5		21	19.4	even	9

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28771 + 1.08051i) q^{2} +(-1.02863 - 0.374390i) q^{3} +(0.143380 - 0.813151i) q^{4} +(-0.0882338 - 0.500399i) q^{5} +(1.72910 - 0.629342i) q^{6} +(0.0395283 - 0.0684651i) q^{7} +(-0.986992 - 1.70952i) q^{8} +(-1.38023 - 1.15815i) q^{9} +O(q^{10})\)	\(q+(-1.28771 + 1.08051i) q^{2} +(-1.02863 - 0.374390i) q^{3} +(0.143380 - 0.813151i) q^{4} +(-0.0882338 - 0.500399i) q^{5} +(1.72910 - 0.629342i) q^{6} +(0.0395283 - 0.0684651i) q^{7} +(-0.986992 - 1.70952i) q^{8} +(-1.38023 - 1.15815i) q^{9} +(0.654306 + 0.549028i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.451921 + 0.782749i) q^{12} +(3.43796 - 1.25131i) q^{13} +(0.0230766 + 0.130874i) q^{14} +(-0.0965845 + 0.547758i) q^{15} +(4.66991 + 1.69971i) q^{16} +(2.75007 - 2.30758i) q^{17} +3.02872 q^{18} +(-1.99861 - 3.87370i) q^{19} -0.419550 q^{20} +(-0.0662926 + 0.0556261i) q^{21} +(1.57960 + 0.574929i) q^{22} +(0.963469 - 5.46411i) q^{23} +(0.375220 + 2.12798i) q^{24} +(4.45585 - 1.62180i) q^{25} +(-3.07502 + 5.32609i) q^{26} +(2.62810 + 4.55201i) q^{27} +(-0.0500048 - 0.0419590i) q^{28} +(-3.09472 - 2.59678i) q^{29} +(-0.467487 - 0.809711i) q^{30} +(-3.24816 + 5.62598i) q^{31} +(-4.14016 + 1.50689i) q^{32} +(0.190083 + 1.07801i) q^{33} +(-1.04791 + 5.94298i) q^{34} +(-0.0377476 - 0.0137390i) q^{35} +(-1.13965 + 0.956276i) q^{36} -1.71356 q^{37} +(6.75921 + 2.82866i) q^{38} -4.00486 q^{39} +(-0.768355 + 0.644727i) q^{40} +(-10.3928 - 3.78266i) q^{41} +(0.0252606 - 0.143260i) q^{42} +(-0.804230 - 4.56102i) q^{43} +(-0.775899 + 0.282404i) q^{44} +(-0.457753 + 0.792851i) q^{45} +(4.66337 + 8.07720i) q^{46} +(-5.30916 - 4.45491i) q^{47} +(-4.16725 - 3.49674i) q^{48} +(3.49688 + 6.05677i) q^{49} +(-3.98545 + 6.90300i) q^{50} +(-3.69274 + 1.34405i) q^{51} +(-0.524572 - 2.97499i) q^{52} +(0.538388 - 3.05335i) q^{53} +(-8.30273 - 3.02195i) q^{54} +(-0.389241 + 0.326612i) q^{55} -0.156057 q^{56} +(0.605555 + 4.73286i) q^{57} +6.79094 q^{58} +(-3.17254 + 2.66208i) q^{59} +(0.431561 + 0.157075i) q^{60} +(1.54866 - 8.78290i) q^{61} +(-1.89627 - 10.7543i) q^{62} +(-0.133851 + 0.0487177i) q^{63} +(-1.26653 + 2.19370i) q^{64} +(-0.929500 - 1.60994i) q^{65} +(-1.40958 - 1.18278i) q^{66} +(2.26925 + 1.90412i) q^{67} +(-1.48211 - 2.56709i) q^{68} +(-3.03676 + 5.25982i) q^{69} +(0.0634529 - 0.0230950i) q^{70} +(2.22726 + 12.6314i) q^{71} +(-0.617604 + 3.50261i) q^{72} +(8.63359 + 3.14237i) q^{73} +(2.20656 - 1.85152i) q^{74} -5.19060 q^{75} +(-3.43646 + 1.06976i) q^{76} -0.0790567 q^{77} +(5.15708 - 4.32730i) q^{78} +(-7.78094 - 2.83203i) q^{79} +(0.438488 - 2.48679i) q^{80} +(-0.0604992 - 0.343108i) q^{81} +(17.4701 - 6.35858i) q^{82} +(1.38214 - 2.39394i) q^{83} +(0.0357273 + 0.0618816i) q^{84} +(-1.39736 - 1.17253i) q^{85} +(5.96385 + 5.00427i) q^{86} +(2.21111 + 3.82975i) q^{87} +(-0.986992 + 1.70952i) q^{88} +(3.37004 - 1.22659i) q^{89} +(-0.267235 - 1.51557i) q^{90} +(0.0502254 - 0.284843i) q^{91} +(-4.30500 - 1.56689i) q^{92} +(5.44746 - 4.57096i) q^{93} +11.6502 q^{94} +(-1.76205 + 1.34189i) q^{95} +4.82285 q^{96} +(11.7344 - 9.84632i) q^{97} +(-11.0474 - 4.02091i) q^{98} +(-0.312872 + 1.77438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8}+O(q^{10}) \) 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8	\( 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8} - 15 q^{10} - 21 q^{11} - 30 q^{12} - 18 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{18} - 6 q^{19} + 30 q^{20} + 9 q^{21} + 6 q^{22} + 15 q^{23} + 3 q^{24} - 6 q^{26} - 24 q^{27} - 9 q^{28} - 15 q^{29} + 30 q^{30} - 54 q^{31} + 42 q^{32} - 45 q^{34} - 12 q^{35} + 6 q^{36} + 114 q^{37} - 60 q^{38} - 48 q^{40} + 15 q^{41} + 84 q^{42} - 6 q^{43} + 3 q^{44} + 3 q^{45} - 15 q^{46} - 42 q^{47} + 12 q^{48} - 21 q^{49} - 33 q^{50} + 93 q^{51} + 3 q^{52} + 48 q^{54} + 3 q^{55} + 114 q^{56} - 15 q^{57} + 60 q^{58} - 33 q^{59} - 81 q^{60} + 63 q^{61} - 24 q^{62} + 87 q^{63} + 15 q^{64} + 24 q^{65} - 15 q^{66} - 51 q^{67} + 48 q^{68} - 54 q^{69} - 84 q^{70} + 9 q^{71} - 51 q^{72} - 27 q^{73} - 33 q^{74} + 54 q^{75} - 60 q^{76} + 12 q^{77} - 87 q^{78} + 24 q^{79} + 120 q^{80} - 36 q^{81} + 111 q^{82} - 12 q^{83} + 48 q^{84} + 39 q^{85} - 60 q^{86} - 75 q^{87} - 15 q^{88} - 21 q^{89} - 63 q^{90} - 3 q^{91} + 6 q^{92} - 72 q^{93} + 84 q^{94} - 72 q^{95} - 6 q^{96} - 18 q^{97} - 120 q^{98}+O(q^{100}) \) 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8 - 15 * q^10 - 21 * q^11 - 30 * q^12 - 18 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^18 - 6 * q^19 + 30 * q^20 + 9 * q^21 + 6 * q^22 + 15 * q^23 + 3 * q^24 - 6 * q^26 - 24 * q^27 - 9 * q^28 - 15 * q^29 + 30 * q^30 - 54 * q^31 + 42 * q^32 - 45 * q^34 - 12 * q^35 + 6 * q^36 + 114 * q^37 - 60 * q^38 - 48 * q^40 + 15 * q^41 + 84 * q^42 - 6 * q^43 + 3 * q^44 + 3 * q^45 - 15 * q^46 - 42 * q^47 + 12 * q^48 - 21 * q^49 - 33 * q^50 + 93 * q^51 + 3 * q^52 + 48 * q^54 + 3 * q^55 + 114 * q^56 - 15 * q^57 + 60 * q^58 - 33 * q^59 - 81 * q^60 + 63 * q^61 - 24 * q^62 + 87 * q^63 + 15 * q^64 + 24 * q^65 - 15 * q^66 - 51 * q^67 + 48 * q^68 - 54 * q^69 - 84 * q^70 + 9 * q^71 - 51 * q^72 - 27 * q^73 - 33 * q^74 + 54 * q^75 - 60 * q^76 + 12 * q^77 - 87 * q^78 + 24 * q^79 + 120 * q^80 - 36 * q^81 + 111 * q^82 - 12 * q^83 + 48 * q^84 + 39 * q^85 - 60 * q^86 - 75 * q^87 - 15 * q^88 - 21 * q^89 - 63 * q^90 - 3 * q^91 + 6 * q^92 - 72 * q^93 + 84 * q^94 - 72 * q^95 - 6 * q^96 - 18 * q^97 - 120 * q^98

Introduction

L-functions

Modular forms

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Database

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