LMFDB - Embedded newform 483.2.q.e.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	483.127
Dual form			483.2.q.e.232.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.539950 + 0.347005i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.659696 + 1.44453i) q^{4} +(-3.99137 + 1.17197i) q^{5} +(0.266630 + 0.583838i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.327744 - 2.27951i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.539950 + 0.347005i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.659696 + 1.44453i) q^{4} +(-3.99137 + 1.17197i) q^{5} +(0.266630 + 0.583838i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.327744 - 2.27951i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(1.74846 - 2.01783i) q^{10} +(2.64767 + 1.70155i) q^{11} +(1.33595 + 0.858560i) q^{12} +(1.00830 - 1.16364i) q^{13} +(-0.615841 - 0.180827i) q^{14} +(0.592012 + 4.11753i) q^{15} +(-1.11193 - 1.28323i) q^{16} +(-3.23133 - 7.07562i) q^{17} +(0.615841 - 0.180827i) q^{18} +(2.46258 - 5.39229i) q^{19} +(0.940139 - 6.53881i) q^{20} +(0.841254 - 0.540641i) q^{21} -2.02005 q^{22} +(-4.22974 + 2.26039i) q^{23} -2.30295 q^{24} +(10.3512 - 6.65233i) q^{25} +(-0.140643 + 0.978190i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.52371 + 0.447403i) q^{28} +(-2.19983 - 4.81696i) q^{29} +(-1.74846 - 2.01783i) q^{30} +(0.226234 + 1.57349i) q^{31} +(5.46500 + 1.60467i) q^{32} +(2.06104 - 2.37856i) q^{33} +(4.20003 + 2.69919i) q^{34} +(-3.49951 - 2.24900i) q^{35} +(1.03995 - 1.20016i) q^{36} +(-5.90669 - 1.73436i) q^{37} +(0.541482 + 3.76609i) q^{38} +(-1.00830 - 1.16364i) q^{39} +(3.97966 + 8.71425i) q^{40} +(4.93959 - 1.45040i) q^{41} +(-0.266630 + 0.583838i) q^{42} +(-0.288256 + 2.00486i) q^{43} +(-4.20461 + 2.70214i) q^{44} +4.15987 q^{45} +(1.49948 - 2.68823i) q^{46} -8.72097 q^{47} +(-1.42841 + 0.917986i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-3.28076 + 7.18386i) q^{50} +(-7.46347 + 2.19147i) q^{51} +(1.01574 + 2.22417i) q^{52} +(1.01111 + 1.16688i) q^{53} +(-0.0913433 - 0.635307i) q^{54} +(-12.5620 - 3.68853i) q^{55} +(1.50811 - 1.74045i) q^{56} +(-4.98694 - 3.20491i) q^{57} +(2.85931 + 1.83756i) q^{58} +(6.35867 - 7.33830i) q^{59} +(-6.33846 - 1.86114i) q^{60} +(0.829081 + 5.76639i) q^{61} +(-0.668163 - 0.771101i) q^{62} +(-0.415415 - 0.909632i) q^{63} +(-0.249291 + 0.0731985i) q^{64} +(-2.66074 + 5.82620i) q^{65} +(-0.287484 + 1.99949i) q^{66} +(-2.65525 + 1.70643i) q^{67} +12.3527 q^{68} +(1.63542 + 4.50837i) q^{69} +2.66997 q^{70} +(3.81452 - 2.45144i) q^{71} +(-0.327744 + 2.27951i) q^{72} +(3.25978 - 7.13793i) q^{73} +(3.79115 - 1.11318i) q^{74} +(-5.11149 - 11.1926i) q^{75} +(6.16479 + 7.11455i) q^{76} +(0.447906 + 3.11525i) q^{77} +(0.948218 + 0.278422i) q^{78} +(5.29648 - 6.11247i) q^{79} +(5.94202 + 3.81871i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-2.16384 + 2.49720i) q^{82} +(-6.43249 - 1.88875i) q^{83} +(0.226002 + 1.57188i) q^{84} +(21.1898 + 24.4544i) q^{85} +(-0.540053 - 1.18255i) q^{86} +(-5.08100 + 1.49191i) q^{87} +(3.01094 - 6.59305i) q^{88} +(1.95326 - 13.5852i) q^{89} +(-2.24612 + 1.44350i) q^{90} +1.53971 q^{91} +(-0.474861 - 7.60116i) q^{92} +1.58967 q^{93} +(4.70889 - 3.02622i) q^{94} +(-3.50944 + 24.4087i) q^{95} +(2.36609 - 5.18100i) q^{96} +(-5.43057 + 1.59456i) q^{97} +(-0.266630 - 0.583838i) q^{98} +(-2.06104 - 2.37856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	−0.539950	+	0.347005i	−0.381802	+	0.245369i	−0.717438	−	0.696622i	$-0.754685\pi$
$2$	−0.539950	+	0.347005i	−0.381802	+	0.245369i	0.335636	+	0.941992i	$0.391049\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	−0.659696	+	1.44453i	−0.329848	+	0.722267i
$5$	−3.99137	+	1.17197i	−1.78499	+	0.524122i	−0.995925	−	0.0901831i	$-0.971255\pi$
$5$	−3.99137	+	1.17197i	−1.78499	+	0.524122i	−0.789069	+	0.614305i	$0.789437\pi$
$6$	0.266630	+	0.583838i	0.108851	+	0.238351i
$7$	0.654861	+	0.755750i	0.247514	+	0.285646i
$7$	0.654861	+	0.755750i	0.247514	+	0.285646i
$8$	−0.327744	−	2.27951i	−0.115875	−	0.805927i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	1.74846	−	2.01783i	0.552911	−	0.638094i
$11$	2.64767	+	1.70155i	0.798302	+	0.513037i	0.875061	−	0.484012i	$-0.160821\pi$
$11$	2.64767	+	1.70155i	0.798302	+	0.513037i	−0.0767595	+	0.997050i	$0.524457\pi$
$12$	1.33595	+	0.858560i	0.385654	+	0.247845i
$13$	1.00830	−	1.16364i	0.279651	−	0.322735i	−0.598495	−	0.801126i	$-0.704234\pi$
$13$	1.00830	−	1.16364i	0.279651	−	0.322735i	0.878147	+	0.478391i	$0.158780\pi$
$14$	−0.615841	−	0.180827i	−0.164590	−	0.0483281i
$15$	0.592012	+	4.11753i	0.152857	+	1.06314i
$16$	−1.11193	−	1.28323i	−0.277982	−	0.320808i
$17$	−3.23133	−	7.07562i	−0.783712	−	1.71609i	−0.693832	−	0.720137i	$-0.744079\pi$
$17$	−3.23133	−	7.07562i	−0.783712	−	1.71609i	−0.0898800	−	0.995953i	$-0.528648\pi$
$18$	0.615841	−	0.180827i	0.145155	−	0.0426214i
$19$	2.46258	−	5.39229i	0.564954	−	1.23708i	−0.384487	−	0.923130i	$-0.625622\pi$
$19$	2.46258	−	5.39229i	0.564954	−	1.23708i	0.949441	−	0.313946i	$-0.101651\pi$
$20$	0.940139	−	6.53881i	0.210221	−	1.46212i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	−2.02005			−0.430677
$23$	−4.22974	+	2.26039i	−0.881961	+	0.471323i
$23$	−4.22974	+	2.26039i	−0.881961	+	0.471323i
$24$	−2.30295			−0.470087
$25$	10.3512	−	6.65233i	2.07025	−	1.33047i
$26$	−0.140643	+	0.978190i	−0.0275823	+	0.191839i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−1.52371	+	0.447403i	−0.287955	+	0.0845512i
$29$	−2.19983	−	4.81696i	−0.408498	−	0.894486i	−0.996337	−	0.0855086i	$-0.972748\pi$
$29$	−2.19983	−	4.81696i	−0.408498	−	0.894486i	0.587839	−	0.808978i	$-0.299979\pi$
$30$	−1.74846	−	2.01783i	−0.319224	−	0.368404i
$31$	0.226234	+	1.57349i	0.0406328	+	0.282607i	1.00000		0.000446281i	$0.000142056\pi$
$31$	0.226234	+	1.57349i	0.0406328	+	0.282607i	−0.959367	+	0.282161i	$0.908949\pi$
$32$	5.46500	+	1.60467i	0.966084	+	0.283668i
$33$	2.06104	−	2.37856i	0.358780	−	0.414054i
$34$	4.20003	+	2.69919i	0.720299	+	0.462908i
$35$	−3.49951	−	2.24900i	−0.591525	−	0.380150i
$36$	1.03995	−	1.20016i	0.173324	−	0.200027i
$37$	−5.90669	−	1.73436i	−0.971053	−	0.285127i	−0.242527	−	0.970145i	$-0.577976\pi$
$37$	−5.90669	−	1.73436i	−0.971053	−	0.285127i	−0.728526	+	0.685018i	$0.759794\pi$
$38$	0.541482	+	3.76609i	0.0878401	+	0.610941i
$39$	−1.00830	−	1.16364i	−0.161457	−	0.186331i
$40$	3.97966	+	8.71425i	0.629240	+	1.37784i
$41$	4.93959	−	1.45040i	0.771435	−	0.226514i	0.127752	−	0.991806i	$-0.459224\pi$
$41$	4.93959	−	1.45040i	0.771435	−	0.226514i	0.643683	+	0.765292i	$0.277406\pi$
$42$	−0.266630	+	0.583838i	−0.0411419	+	0.0900882i
$43$	−0.288256	+	2.00486i	−0.0439586	+	0.305739i	0.955966	+	0.293477i	$0.0948123\pi$
$43$	−0.288256	+	2.00486i	−0.0439586	+	0.305739i	−0.999925	+	0.0122620i	$0.996097\pi$
$44$	−4.20461	+	2.70214i	−0.633868	+	0.407362i
$45$	4.15987			0.620117
$46$	1.49948	−	2.68823i	0.221086	−	0.396358i
$47$	−8.72097			−1.27208			−0.636042	−	0.771654i	$-0.719430\pi$
$47$	−8.72097			−1.27208			−0.636042	+	0.771654i	$0.719430\pi$
$48$	−1.42841	+	0.917986i	−0.206174	+	0.132500i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	−3.28076	+	7.18386i	−0.463969	+	1.01595i
$51$	−7.46347	+	2.19147i	−1.04509	+	0.306867i
$52$	1.01574	+	2.22417i	0.140858	+	0.308437i
$53$	1.01111	+	1.16688i	0.138886	+	0.160283i	0.820931	−	0.571027i	$-0.193455\pi$
$53$	1.01111	+	1.16688i	0.138886	+	0.160283i	−0.682045	+	0.731310i	$0.738909\pi$
$54$	−0.0913433	−	0.635307i	−0.0124303	−	0.0864543i
$55$	−12.5620	−	3.68853i	−1.69386	−	0.497362i
$56$	1.50811	−	1.74045i	0.201530	−	0.232578i
$57$	−4.98694	−	3.20491i	−0.660537	−	0.424501i
$58$	2.85931	+	1.83756i	0.375445	+	0.241284i
$59$	6.35867	−	7.33830i	0.827828	−	0.955365i	−0.171728	−	0.985144i	$-0.554935\pi$
$59$	6.35867	−	7.33830i	0.827828	−	0.955365i	0.999556	+	0.0297795i	$0.00948050\pi$
$60$	−6.33846	−	1.86114i	−0.818292	−	0.240272i
$61$	0.829081	+	5.76639i	0.106153	+	0.738310i	0.971483	+	0.237108i	$0.0761996\pi$
$61$	0.829081	+	5.76639i	0.106153	+	0.738310i	−0.865330	+	0.501202i	$0.832891\pi$
$62$	−0.668163	−	0.771101i	−0.0848568	−	0.0979300i
$63$	−0.415415	−	0.909632i	−0.0523374	−	0.114603i
$64$	−0.249291	+	0.0731985i	−0.0311614	+	0.00914981i
$65$	−2.66074	+	5.82620i	−0.330024	+	0.722651i
$66$	−0.287484	+	1.99949i	−0.0353868	+	0.246121i
$67$	−2.65525	+	1.70643i	−0.324391	+	0.208473i	−0.692692	−	0.721233i	$-0.743576\pi$
$67$	−2.65525	+	1.70643i	−0.324391	+	0.208473i	0.368302	+	0.929706i	$0.379939\pi$
$68$	12.3527			1.49798
$69$	1.63542	+	4.50837i	0.196882	+	0.542744i
$70$	2.66997			0.319123
$71$	3.81452	−	2.45144i	0.452700	−	0.290933i	−0.294353	−	0.955697i	$-0.595104\pi$
$71$	3.81452	−	2.45144i	0.452700	−	0.290933i	0.747054	+	0.664764i	$0.231468\pi$
$72$	−0.327744	+	2.27951i	−0.0386250	+	0.268642i
$73$	3.25978	−	7.13793i	0.381529	−	0.835432i	−0.617285	−	0.786740i	$-0.711767\pi$
$73$	3.25978	−	7.13793i	0.381529	−	0.835432i	0.998814	−	0.0486921i	$-0.0155053\pi$
$74$	3.79115	−	1.11318i	0.440712	−	0.129405i
$75$	−5.11149	−	11.1926i	−0.590224	−	1.29241i
$76$	6.16479	+	7.11455i	0.707150	+	0.816095i
$77$	0.447906	+	3.11525i	0.0510436	+	0.355016i
$78$	0.948218	+	0.278422i	0.107365	+	0.0315251i
$79$	5.29648	−	6.11247i	0.595901	−	0.687706i	−0.375045	−	0.927007i	$-0.622373\pi$
$79$	5.29648	−	6.11247i	0.595901	−	0.687706i	0.970946	+	0.239301i	$0.0769181\pi$
$80$	5.94202	+	3.81871i	0.664338	+	0.426944i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−2.16384	+	2.49720i	−0.238956	+	0.275770i
$83$	−6.43249	−	1.88875i	−0.706058	−	0.207317i	−0.0910592	−	0.995845i	$-0.529025\pi$
$83$	−6.43249	−	1.88875i	−0.706058	−	0.207317i	−0.614999	+	0.788528i	$0.710843\pi$
$84$	0.226002	+	1.57188i	0.0246588	+	0.171506i
$85$	21.1898	+	24.4544i	2.29836	+	2.65245i
$86$	−0.540053	−	1.18255i	−0.0582355	−	0.127518i
$87$	−5.08100	+	1.49191i	−0.544740	+	0.159950i
$88$	3.01094	−	6.59305i	0.320968	−	0.702821i
$89$	1.95326	−	13.5852i	0.207045	−	1.44003i	−0.575686	−	0.817671i	$-0.695265\pi$
$89$	1.95326	−	13.5852i	0.207045	−	1.44003i	0.782731	−	0.622360i	$-0.213826\pi$
$90$	−2.24612	+	1.44350i	−0.236762	+	0.152158i
$91$	1.53971			0.161406
$92$	−0.474861	−	7.60116i	−0.0495077	−	0.792476i
$93$	1.58967			0.164841
$94$	4.70889	−	3.02622i	0.485685	−	0.312131i
$95$	−3.50944	+	24.4087i	−0.360061	+	2.50428i
$96$	2.36609	−	5.18100i	0.241488	−	0.528784i
$97$	−5.43057	+	1.59456i	−0.551391	+	0.161903i	−0.545548	−	0.838080i	$-0.683678\pi$
$97$	−5.43057	+	1.59456i	−0.551391	+	0.161903i	−0.00584357	+	0.999983i	$0.501860\pi$
$98$	−0.266630	−	0.583838i	−0.0269337	−	0.0589765i
$99$	−2.06104	−	2.37856i	−0.207142	−	0.239054i
$100$	2.78085	+	19.3412i	0.278085	+	1.93412i
$101$	−14.1566	−	4.15676i	−1.40864	−	0.413614i	−0.512997	−	0.858390i	$-0.671465\pi$
$101$	−14.1566	−	4.15676i	−1.40864	−	0.413614i	−0.895641	+	0.444777i	$0.853283\pi$
$102$	3.26945	−	3.77314i	0.323723	−	0.373597i
$103$	−11.6213	−	7.46853i	−1.14508	−	0.735896i	−0.176423	−	0.984314i	$-0.556453\pi$
$103$	−11.6213	−	7.46853i	−1.14508	−	0.735896i	−0.968653	+	0.248419i	$0.920089\pi$
$104$	−2.98298	−	1.91705i	−0.292506	−	0.187982i
$105$	−2.72414	+	3.14382i	−0.265849	+	0.306806i
$106$	−0.950860	−	0.279198i	−0.0923557	−	0.0271181i
$107$	2.20114	+	15.3092i	0.212792	+	1.48000i	0.763775	+	0.645483i	$0.223344\pi$
$107$	2.20114	+	15.3092i	0.212792	+	1.48000i	−0.550983	+	0.834516i	$0.685747\pi$
$108$	−1.03995	−	1.20016i	−0.100069	−	0.115486i
$109$	−3.77260	−	8.26084i	−0.361350	−	0.791245i	−0.999768	−	0.0215554i	$-0.993138\pi$
$109$	−3.77260	−	8.26084i	−0.361350	−	0.791245i	0.638418	−	0.769690i	$-0.279589\pi$
$110$	8.06278	−	2.36745i	0.768756	−	0.225727i
$111$	−2.55732	+	5.59974i	−0.242730	+	0.531504i
$112$	0.241645	−	1.68068i	0.0228333	−	0.158809i
$113$	−10.4217	+	6.69763i	−0.980392	+	0.630060i	−0.929569	−	0.368648i	$-0.879821\pi$
$113$	−10.4217	+	6.69763i	−0.980392	+	0.630060i	−0.0508231	+	0.998708i	$0.516184\pi$
$114$	3.80482			0.356354
$115$	14.2333	−	13.9792i	1.32726	−	1.30356i
$116$	8.40948			0.780800
$117$	−1.29529	+	0.832432i	−0.119750	+	0.0769584i
$118$	−0.886940	+	6.16880i	−0.0816494	+	0.567884i
$119$	3.23133	−	7.07562i	0.296215	−	0.648621i
$120$	9.19191	−	2.69899i	0.839103	−	0.246383i
$121$	−0.454704	−	0.995663i	−0.0413367	−	0.0905148i
$122$	−2.44863	−	2.82587i	−0.221688	−	0.255842i
$123$	−0.732655	−	5.09573i	−0.0660613	−	0.459466i
$124$	−2.42220	−	0.711223i	−0.217520	−	0.0638697i
$125$	−19.8986	+	22.9642i	−1.77978	+	2.05398i
$126$	0.539950	+	0.347005i	0.0481026	+	0.0309136i
$127$	−2.89067	−	1.85772i	−0.256506	−	0.164846i	0.406068	−	0.913843i	$-0.366900\pi$
$127$	−2.89067	−	1.85772i	−0.256506	−	0.164846i	−0.662574	+	0.748997i	$0.730536\pi$
$128$	−7.35059	+	8.48304i	−0.649707	+	0.749802i
$129$	1.94343	+	0.570644i	0.171110	+	0.0502424i
$130$	−0.585055	−	4.06915i	−0.0513127	−	0.356888i
$131$	7.80933	+	9.01245i	0.682305	+	0.787422i	0.986249	−	0.165268i	$-0.0528490\pi$
$131$	7.80933	+	9.01245i	0.682305	+	0.787422i	−0.303944	+	0.952690i	$0.598304\pi$
$132$	2.07625	+	4.54636i	0.180715	+	0.395710i
$133$	5.68787	−	1.67011i	0.493201	−	0.144817i
$134$	0.841565	−	1.84277i	0.0727001	−	0.159191i
$135$	0.592012	−	4.11753i	0.0509522	−	0.354381i
$136$	−15.0699	+	9.68482i	−1.29223	+	0.830467i
$137$	−4.91662			−0.420055			−0.210028	−	0.977695i	$-0.567355\pi$
$137$	−4.91662			−0.420055			−0.210028	+	0.977695i	$0.567355\pi$
$138$	−2.44747	−	1.86679i	−0.208343	−	0.158912i
$139$	−0.812643			−0.0689275			−0.0344637	−	0.999406i	$-0.510972\pi$
$139$	−0.812643			−0.0689275			−0.0344637	+	0.999406i	$0.510972\pi$
$140$	5.55736	−	3.57150i	0.469683	−	0.301847i
$141$	−1.24112	+	8.63221i	−0.104521	+	0.726963i
$142$	−1.20899	+	2.64731i	−0.101456	+	0.222158i
$143$	4.64963	−	1.36525i	0.388821	−	0.114168i
$144$	0.705358	+	1.54452i	0.0587798	+	0.128710i
$145$	14.4257	+	16.6481i	1.19799	+	1.38255i
$146$	0.716776	+	4.98529i	0.0593208	+	0.412585i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	6.40196	−	7.38826i	0.526238	−	0.607311i
$149$	−8.87854	−	5.70589i	−0.727358	−	0.467445i	0.123831	−	0.992303i	$-0.460482\pi$
$149$	−8.87854	−	5.70589i	−0.727358	−	0.467445i	−0.851190	+	0.524858i	$0.824118\pi$
$150$	6.64383	+	4.26973i	0.542467	+	0.348622i
$151$	−9.89748	+	11.4223i	−0.805445	+	0.929533i	−0.998667	−	0.0516219i	$-0.983561\pi$
$151$	−9.89748	+	11.4223i	−0.805445	+	0.929533i	0.193222	+	0.981155i	$0.438106\pi$
$152$	−13.0989	−	3.84617i	−1.06246	−	0.311966i
$153$	1.10700	+	7.69938i	0.0894959	+	0.622458i
$154$	−1.32285	−	1.52666i	−0.106599	−	0.123021i
$155$	−2.74707	−	6.01524i	−0.220650	−	0.483155i
$156$	2.34608	−	0.688872i	0.187837	−	0.0551539i
$157$	−1.65593	+	3.62598i	−0.132158	+	0.289385i	−0.964129	−	0.265434i	$-0.914485\pi$
$157$	−1.65593	+	3.62598i	−0.132158	+	0.289385i	0.831972	+	0.554818i	$0.187212\pi$
$158$	−0.738780	+	5.13833i	−0.0587742	+	0.408784i
$159$	1.29890	−	0.834751i	0.103009	−	0.0662001i
$160$	−23.6934			−1.87313
$161$	−4.47817	−	1.71638i	−0.352929	−	0.135270i
$162$	−0.641840			−0.0504277
$163$	2.15539	−	1.38519i	0.168824	−	0.108496i	−0.453501	−	0.891256i	$-0.649825\pi$
$163$	2.15539	−	1.38519i	0.168824	−	0.108496i	0.622324	+	0.782760i	$0.286189\pi$
$164$	−1.16349	+	8.09223i	−0.0908531	+	0.631897i
$165$	−5.43874	+	11.9092i	−0.423406	+	0.927129i
$166$	4.12863	−	1.21228i	0.320444	−	0.0940908i
$167$	−1.80633	−	3.95532i	−0.139778	−	0.306072i	0.826777	−	0.562530i	$-0.190172\pi$
$167$	−1.80633	−	3.95532i	−0.139778	−	0.306072i	−0.966555	+	0.256458i	$0.917444\pi$
$168$	−1.50811	−	1.74045i	−0.116353	−	0.134279i
$169$	1.51270	+	10.5211i	0.116362	+	0.809315i
$170$	−19.9272	−	5.85116i	−1.52835	−	0.448764i
$171$	−3.88201	+	4.48008i	−0.296865	+	0.342600i
$172$	−2.70593	−	1.73900i	−0.206325	−	0.132597i
$173$	13.9795	+	8.98409i	1.06284	+	0.683048i	0.950532	−	0.310625i	$-0.100538\pi$
$173$	13.9795	+	8.98409i	1.06284	+	0.683048i	0.112311	+	0.993673i	$0.464175\pi$
$174$	2.22578	−	2.56869i	0.168736	−	0.194732i
$175$	11.8061	+	3.46659i	0.892459	+	0.262049i
$176$	−0.760526	−	5.28958i	−0.0573268	−	0.398717i
$177$	−6.35867	−	7.33830i	−0.477947	−	0.551580i
$178$	3.65948	+	8.01313i	0.274289	+	0.600610i
$179$	11.0028	−	3.23072i	0.822388	−	0.241475i	0.156644	−	0.987655i	$-0.449932\pi$
$179$	11.0028	−	3.23072i	0.822388	−	0.241475i	0.665744	+	0.746180i	$0.268114\pi$
$180$	−2.74425	+	6.00908i	−0.204545	+	0.447890i
$181$	1.10185	−	7.66356i	0.0819002	−	0.569628i	−0.907010	−	0.421110i	$-0.861641\pi$
$181$	1.10185	−	7.66356i	0.0819002	−	0.569628i	0.988910	−	0.148518i	$-0.0474503\pi$
$182$	−0.831368	+	0.534288i	−0.0616251	+	0.0396041i
$183$	5.82568			0.430647
$184$	6.53883	+	8.90088i	0.482049	+	0.656182i
$185$	25.6084			1.88277
$186$	−0.858342	+	0.551623i	−0.0629367	+	0.0404470i
$187$	3.48406	−	24.2322i	0.254780	−	1.77203i
$188$	5.75319	−	12.5977i	0.419595	−	0.918784i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	−6.57501	−	14.3973i	−0.477001	−	1.04449i
$191$	0.566532	+	0.653812i	0.0409928	+	0.0473082i	0.775876	−	0.630886i	$-0.217308\pi$
$191$	0.566532	+	0.653812i	0.0409928	+	0.0473082i	−0.734883	+	0.678194i	$0.762763\pi$
$192$	0.0369756	+	0.257171i	0.00266848	+	0.0185597i
$193$	−19.6790	−	5.77828i	−1.41653	−	0.415929i	−0.518200	−	0.855260i	$-0.673398\pi$
$193$	−19.6790	−	5.77828i	−1.41653	−	0.415929i	−0.898326	+	0.439330i	$0.855216\pi$
$194$	2.37892	−	2.74542i	0.170796	−	0.197109i
$195$	5.38824	+	3.46281i	0.385860	+	0.247977i
$196$	−1.33595	−	0.858560i	−0.0954247	−	0.0613257i
$197$	15.4699	−	17.8532i	1.10218	−	1.27199i	0.142837	−	0.989746i	$-0.454377\pi$
$197$	15.4699	−	17.8532i	1.10218	−	1.27199i	0.959344	−	0.282239i	$-0.0910772\pi$
$198$	1.93823	+	0.569115i	0.137744	+	0.0404453i
$199$	−2.07357	−	14.4220i	−0.146992	−	1.02235i	−0.921108	−	0.389306i	$-0.872715\pi$
$199$	−2.07357	−	14.4220i	−0.146992	−	1.02235i	0.774117	−	0.633043i	$-0.218194\pi$
$200$	−18.5566	−	21.4155i	−1.31215	−	1.51430i
$201$	1.31118	+	2.87107i	0.0924832	+	0.202510i
$202$	9.08629	−	2.66798i	0.639309	−	0.187718i
$203$	2.19983	−	4.81696i	0.154398	−	0.338084i
$204$	1.75797	−	12.2269i	0.123082	−	0.856056i
$205$	−18.0159	+	11.5781i	−1.25829	+	0.808651i
$206$	8.86651			0.617759
$207$	4.69523	−	0.977170i	0.326341	−	0.0679180i
$208$	−2.61437			−0.181274
$209$	15.6954	−	10.0868i	1.08567	−	0.697718i
$210$	0.379977	−	2.64279i	0.0262209	−	0.182370i
$211$	−1.77276	+	3.88180i	−0.122042	+	0.267234i	−0.960786	−	0.277292i	$-0.910563\pi$
$211$	−1.77276	+	3.88180i	−0.122042	+	0.267234i	0.838744	+	0.544526i	$0.183290\pi$
$212$	−2.35262	+	0.690792i	−0.161579	+	0.0474438i
$213$	−1.88363	−	4.12457i	−0.129064	−	0.282611i
$214$	−6.50088	−	7.50241i	−0.444391	−	0.512855i
$215$	−1.19911	−	8.33997i	−0.0817784	−	0.568782i
$216$	2.20966	+	0.648815i	0.150348	+	0.0441463i
$217$	−1.04101	+	1.20139i	−0.0706685	+	0.0815558i
$218$	4.90357	+	3.15133i	0.332111	+	0.213435i
$219$	−6.60136	−	4.24244i	−0.446079	−	0.286677i
$220$	13.6153	−	15.7129i	0.917944	−	1.05936i
$221$	−11.4916	−	3.37424i	−0.773008	−	0.226976i
$222$	−0.562314	−	3.91098i	−0.0377400	−	0.262488i
$223$	−12.9249	−	14.9161i	−0.865516	−	0.998859i	−0.999968	−	0.00793915i	$-0.997473\pi$
$223$	−12.9249	−	14.9161i	−0.865516	−	0.998859i	0.134452	−	0.990920i	$-0.457073\pi$
$224$	2.36609	+	5.18100i	0.158091	+	0.346170i
$225$	−11.8061	+	3.46659i	−0.787074	+	0.231106i
$226$	3.30309	−	7.23277i	0.219719	−	0.481117i
$227$	−4.17978	+	29.0710i	−0.277422	+	1.92951i	0.0826319	+	0.996580i	$0.473667\pi$
$227$	−4.17978	+	29.0710i	−0.277422	+	1.92951i	−0.360054	+	0.932932i	$0.617242\pi$
$228$	7.91948	−	5.08954i	0.524480	−	0.337063i
$229$	−19.6715			−1.29993			−0.649963	−	0.759965i	$-0.725216\pi$
$229$	−19.6715			−1.29993			−0.649963	+	0.759965i	$0.725216\pi$
$230$	−2.83445	+	12.4871i	−0.186898	+	0.823373i
$231$	3.14729			0.207076
$232$	−10.2593	+	6.59326i	−0.673556	+	0.432868i
$233$	2.41093	−	16.7684i	0.157945	−	1.09853i	−0.744467	−	0.667660i	$-0.767296\pi$
$233$	2.41093	−	16.7684i	0.157945	−	1.09853i	0.902412	−	0.430874i	$-0.141795\pi$
$234$	0.410534	−	0.898943i	0.0268374	−	0.0587657i
$235$	34.8086	−	10.2207i	2.27066	−	0.666727i
$236$	6.40562	+	14.0264i	0.416971	+	0.913038i
$237$	−5.29648	−	6.11247i	−0.344043	−	0.397047i
$238$	0.710519	+	4.94177i	0.0460561	+	0.320327i
$239$	21.2218	+	6.23127i	1.37272	+	0.403067i	0.883230	−	0.468940i	$-0.155364\pi$
$239$	21.2218	+	6.23127i	1.37272	+	0.403067i	0.489492	+	0.872008i	$0.337182\pi$
$240$	4.62548	−	5.33808i	0.298573	−	0.344572i
$241$	5.04111	+	3.23972i	0.324726	+	0.208689i	0.692839	−	0.721092i	$-0.256360\pi$
$241$	5.04111	+	3.23972i	0.324726	+	0.208689i	−0.368113	+	0.929781i	$0.619996\pi$
$242$	0.591017	+	0.379824i	0.0379920	+	0.0244160i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−8.87668	−	2.60643i	−0.568271	−	0.166860i
$245$	−0.592012	−	4.11753i	−0.0378222	−	0.263059i
$246$	2.16384	+	2.49720i	0.137961	+	0.159216i
$247$	−3.79166	−	8.30258i	−0.241258	−	0.528281i
$248$	3.51263	−	1.03140i	0.223052	−	0.0654941i
$249$	−2.78496	+	6.09822i	−0.176490	+	0.386459i
$250$	2.77555	−	19.3044i	0.175541	−	1.22092i
$251$	1.95236	−	1.25471i	0.123232	−	0.0791965i	−0.477573	−	0.878592i	$-0.658483\pi$
$251$	1.95236	−	1.25471i	0.123232	−	0.0791965i	0.600805	+	0.799396i	$0.294847\pi$
$252$	1.58804			0.100037
$253$	−15.0451	−	1.21237i	−0.945877	−	0.0762209i
$254$	2.20546			0.138383
$255$	27.2211	−	17.4939i	1.70465	−	1.09551i
$256$	1.09925	−	7.64545i	0.0687031	−	0.477841i
$257$	1.29223	−	2.82959i	0.0806072	−	0.176505i	−0.865037	−	0.501708i	$-0.832705\pi$
$257$	1.29223	−	2.82959i	0.0806072	−	0.176505i	0.945644	+	0.325203i	$0.105433\pi$
$258$	−1.24737	+	0.366262i	−0.0776580	+	0.0228025i
$259$	−2.55732	−	5.59974i	−0.158904	−	0.347951i
$260$	−6.66087	−	7.68705i	−0.413089	−	0.476731i
$261$	0.753628	+	5.24160i	0.0466484	+	0.324447i
$262$	−7.34401	−	2.15640i	−0.453715	−	0.133223i
$263$	4.56474	−	5.26799i	0.281474	−	0.324838i	−0.597353	−	0.801978i	$-0.703781\pi$
$263$	4.56474	−	5.26799i	0.281474	−	0.324838i	0.878827	+	0.477140i	$0.158326\pi$
$264$	−6.09744	−	3.91859i	−0.375271	−	0.241172i
$265$	−5.40325	−	3.47246i	−0.331919	−	0.213311i
$266$	−2.49163	+	2.87549i	−0.152772	+	0.176308i
$267$	−13.1690	−	3.86676i	−0.805928	−	0.236642i
$268$	−0.713331	−	4.96132i	−0.0435736	−	0.303061i
$269$	6.79698	+	7.84413i	0.414419	+	0.478265i	0.924129	−	0.382081i	$-0.124793\pi$
$269$	6.79698	+	7.84413i	0.414419	+	0.478265i	−0.509710	+	0.860347i	$0.670247\pi$
$270$	1.10915	+	2.42869i	0.0675005	+	0.147805i
$271$	22.9223	−	6.73060i	1.39243	−	0.408855i	0.502354	−	0.864662i	$-0.332468\pi$
$271$	22.9223	−	6.73060i	1.39243	−	0.408855i	0.890078	+	0.455807i	$0.150649\pi$
$272$	−5.48666	+	12.0141i	−0.332678	+	0.728463i
$273$	0.219124	−	1.52404i	0.0132620	−	0.0922392i
$274$	2.65473	−	1.70609i	0.160378	−	0.103069i
$275$	38.7259			2.33526
$276$	−7.59137	−	0.611730i	−0.456947	−	0.0368218i
$277$	16.4313			0.987261			0.493630	−	0.869672i	$-0.335670\pi$
$277$	16.4313			0.987261			0.493630	+	0.869672i	$0.335670\pi$
$278$	0.438787	−	0.281991i	0.0263167	−	0.0169127i
$279$	0.226234	−	1.57349i	0.0135443	−	0.0942023i
$280$	−3.97966	+	8.71425i	−0.237830	+	0.520776i
$281$	4.70363	−	1.38111i	0.280595	−	0.0823901i	−0.138407	−	0.990375i	$-0.544198\pi$
$281$	4.70363	−	1.38111i	0.280595	−	0.0823901i	0.419002	+	0.907985i	$0.362380\pi$
$282$	−2.32527	−	5.09164i	−0.138468	−	0.303202i
$283$	−0.902457	−	1.04149i	−0.0536455	−	0.0619102i	0.728293	−	0.685266i	$-0.240314\pi$
$283$	−0.902457	−	1.04149i	−0.0536455	−	0.0619102i	−0.781938	+	0.623356i	$0.785769\pi$
$284$	1.02477	+	7.12741i	0.0608088	+	0.422934i
$285$	23.6608	+	6.94744i	1.40154	+	0.411531i
$286$	−2.03682	+	2.35061i	−0.120439	+	0.138995i
$287$	4.33088	+	2.78329i	0.255644	+	0.164292i
$288$	−4.79154	−	3.07934i	−0.282344	−	0.181452i
$289$	−28.4903	+	32.8795i	−1.67590	+	1.93409i
$290$	−13.5661	−	3.98337i	−0.796630	−	0.233912i
$291$	0.805479	+	5.60223i	0.0472180	+	0.328408i
$292$	8.16051	+	9.41774i	0.477558	+	0.551131i
$293$	10.3186	+	22.5947i	0.602821	+	1.31999i	0.927377	+	0.374128i	$0.122058\pi$
$293$	10.3186	+	22.5947i	0.602821	+	1.31999i	−0.324555	+	0.945867i	$0.605215\pi$
$294$	−0.615841	+	0.180827i	−0.0359166	+	0.0105461i
$295$	−16.7795	+	36.7420i	−0.976941	+	2.13920i
$296$	−2.01761	+	14.0328i	−0.117271	+	0.815638i
$297$	−2.64767	+	1.70155i	−0.153633	+	0.0987341i
$298$	6.77394			0.392404
$299$	−1.63456	+	7.20102i	−0.0945292	+	0.416446i
$300$	19.5401			1.12815
$301$	−1.70394	+	1.09506i	−0.0982136	+	0.0631180i
$302$	1.38055	−	9.60194i	0.0794418	−	0.552530i
$303$	−6.12915	+	13.4210i	−0.352111	+	0.771015i
$304$	−9.65777	+	2.83578i	−0.553911	+	0.162643i
$305$	−10.0672	−	22.0441i	−0.576447	−	1.26224i
$306$	−3.26945	−	3.77314i	−0.186902	−	0.215696i
$307$	−2.80686	−	19.5221i	−0.160196	−	1.11419i	−0.898263	−	0.439459i	$-0.855170\pi$
$307$	−2.80686	−	19.5221i	−0.160196	−	1.11419i	0.738067	−	0.674727i	$-0.235739\pi$
$308$	−4.79557	−	1.40811i	−0.273253	−	0.0802343i
$309$	−9.04638	+	10.4401i	−0.514631	+	0.593916i
$310$	3.57059	+	2.29468i	0.202796	+	0.130329i
$311$	−13.7746	−	8.85239i	−0.781085	−	0.501973i	0.0883084	−	0.996093i	$-0.471854\pi$
$311$	−13.7746	−	8.85239i	−0.781085	−	0.501973i	−0.869394	+	0.494120i	$0.835490\pi$
$312$	−2.32206	+	2.67980i	−0.131461	+	0.151714i
$313$	−9.35624	−	2.74724i	−0.528846	−	0.155283i	0.00639973	−	0.999980i	$-0.497963\pi$
$313$	−9.35624	−	2.74724i	−0.528846	−	0.155283i	−0.535246	+	0.844696i	$0.679781\pi$
$314$	−0.364113	−	2.53246i	−0.0205481	−	0.142915i
$315$	2.72414	+	3.14382i	0.153488	+	0.177134i
$316$	5.33559	+	11.6833i	0.300151	+	0.657238i
$317$	7.33192	−	2.15285i	0.411802	−	0.120916i	−0.0692683	−	0.997598i	$-0.522066\pi$
$317$	7.33192	−	2.15285i	0.411802	−	0.120916i	0.481070	+	0.876682i	$0.340248\pi$
$318$	−0.411677	+	0.901448i	−0.0230857	+	0.0505507i
$319$	2.37189	−	16.4968i	0.132800	−	0.923645i
$320$	0.909226	−	0.584324i	0.0508273	−	0.0326647i
$321$	15.4667			0.863265
$322$	3.01358	−	0.627186i	0.167940	−	0.0349517i
$323$	−46.1112			−2.56570
$324$	−1.33595	+	0.858560i	−0.0742192	+	0.0476978i
$325$	2.69622	−	18.7526i	0.149559	−	1.04021i
$326$	−0.683139	+	1.49586i	−0.0378355	+	0.0828483i
$327$	−8.71366	+	2.55856i	−0.481866	+	0.141489i
$328$	−4.92511	−	10.7845i	−0.271944	−	0.595473i
$329$	−5.71102	−	6.59087i	−0.314859	−	0.363367i
$330$	−1.19590	−	8.31764i	−0.0658319	−	0.457871i
$331$	−2.05183	−	0.602472i	−0.112779	−	0.0331149i	0.224856	−	0.974392i	$-0.427809\pi$
$331$	−2.05183	−	0.602472i	−0.112779	−	0.0331149i	−0.337635	+	0.941277i	$0.609627\pi$
$332$	6.97186	−	8.04595i	0.382630	−	0.441579i
$333$	5.17880	+	3.32821i	0.283796	+	0.182385i
$334$	2.34784	+	1.50887i	0.128468	+	0.0825615i
$335$	8.59820	−	9.92286i	0.469770	−	0.542144i
$336$	−1.62918	−	0.478371i	−0.0888791	−	0.0260973i
$337$	−1.26405	−	8.79169i	−0.0688574	−	0.478914i	−0.994849	−	0.101369i	$-0.967678\pi$
$337$	−1.26405	−	8.79169i	−0.0688574	−	0.478914i	0.925991	−	0.377544i	$-0.123231\pi$
$338$	−4.46765	−	5.15595i	−0.243008	−	0.280447i
$339$	5.14629	+	11.2688i	0.279508	+	0.612038i
$340$	−49.3040	+	14.4770i	−2.67389	+	0.785124i
$341$	−2.07838	+	4.55102i	−0.112551	+	0.246452i
$342$	0.541482	−	3.76609i	0.0292800	−	0.203647i
$343$	−0.841254	+	0.540641i	−0.0454234	+	0.0291919i
$344$	4.66457			0.251497
$345$	−11.8113	−	16.0779i	−0.635897	−	0.865604i
$346$	−10.6658			−0.573395
$347$	26.2383	−	16.8623i	1.40855	−	0.905217i	0.408573	−	0.912726i	$-0.366026\pi$
$347$	26.2383	−	16.8623i	1.40855	−	0.905217i	0.999972	+	0.00750858i	$0.00239008\pi$
$348$	1.19679	−	8.32388i	0.0641549	−	0.446207i
$349$	10.7496	−	23.5383i	0.575411	−	1.25997i	−0.368455	−	0.929646i	$-0.620113\pi$
$349$	10.7496	−	23.5383i	0.575411	−	1.25997i	0.943866	−	0.330329i	$-0.107160\pi$
$350$	−7.57763	+	2.22499i	−0.405042	+	0.118931i
$351$	0.639620	+	1.40057i	0.0341404	+	0.0747570i
$352$	11.7391	+	13.5476i	0.625694	+	0.722090i
$353$	−1.92170	−	13.3658i	−0.102282	−	0.711387i	−0.974845	−	0.222885i	$-0.928453\pi$
$353$	−1.92170	−	13.3658i	−0.102282	−	0.711387i	0.872563	−	0.488502i	$-0.162457\pi$
$354$	5.97979	+	1.75582i	0.317822	+	0.0933210i
$355$	−12.3521	+	14.2551i	−0.655583	+	0.756584i
$356$	18.3358	+	11.7837i	0.971793	+	0.624534i
$357$	−6.54373	−	4.20540i	−0.346331	−	0.222573i
$358$	−4.81989	+	5.56245i	−0.254739	+	0.293985i
$359$	11.6134	+	3.41000i	0.612931	+	0.179973i	0.573440	−	0.819247i	$-0.305608\pi$
$359$	11.6134	+	3.41000i	0.612931	+	0.179973i	0.0394902	+	0.999220i	$0.487427\pi$
$360$	−1.36337	−	9.48246i	−0.0718560	−	0.499769i
$361$	−10.5702	−	12.1986i	−0.556325	−	0.642033i
$362$	2.06435	+	4.52029i	0.108500	+	0.237581i
$363$	−1.05024	+	0.308378i	−0.0551233	+	0.0161857i
$364$	−1.01574	+	2.22417i	−0.0532394	+	0.116578i
$365$	−4.64555	+	32.3105i	−0.243159	+	1.69121i
$366$	−3.14558	+	2.02154i	−0.164422	+	0.105668i
$367$	16.2865			0.850150			0.425075	−	0.905158i	$-0.360248\pi$
$367$	16.2865			0.850150			0.425075	+	0.905158i	$0.360248\pi$
$368$	7.60376	+	2.91435i	0.396373	+	0.151921i
$369$	−5.14813			−0.268001
$370$	−13.8272	+	8.88623i	−0.718844	+	0.461973i
$371$	−0.219735	+	1.52829i	−0.0114081	+	0.0793448i
$372$	−1.04870	+	2.29633i	−0.0543725	+	0.119059i
$373$	−5.79129	+	1.70048i	−0.299861	+	0.0880473i	−0.428202	−	0.903683i	$-0.640853\pi$
$373$	−5.79129	+	1.70048i	−0.299861	+	0.0880473i	0.128341	+	0.991730i	$0.459035\pi$
$374$	6.52746	+	14.2931i	0.337527	+	0.739080i
$375$	19.8986	+	22.9642i	1.02756	+	1.18586i
$376$	2.85824	+	19.8795i	0.147403	+	1.02521i
$377$	−7.82328	−	2.29712i	−0.402919	−	0.118308i
$378$	0.420316	−	0.485070i	0.0216187	−	0.0249493i
$379$	−16.2976	−	10.4738i	−0.837151	−	0.538004i	0.0503918	−	0.998730i	$-0.483953\pi$
$379$	−16.2976	−	10.4738i	−0.837151	−	0.538004i	−0.887543	+	0.460725i	$0.847589\pi$
$380$	−32.9440	−	21.1718i	−1.68999	−	1.08609i
$381$	−2.25020	+	2.59687i	−0.115281	+	0.133042i
$382$	−0.532775	−	0.156437i	−0.0272591	−	0.00800400i
$383$	−4.23083	−	29.4261i	−0.216185	−	1.50360i	−0.751941	−	0.659230i	$-0.770882\pi$
$383$	−4.23083	−	29.4261i	−0.216185	−	1.50360i	0.535756	−	0.844373i	$-0.320027\pi$
$384$	7.35059	+	8.48304i	0.375108	+	0.432898i
$385$	−5.43874	−	11.9092i	−0.277184	−	0.606949i
$386$	12.6308	−	3.70873i	0.642889	−	0.188769i
$387$	0.841415	−	1.84244i	0.0427715	−	0.0936565i
$388$	1.27913	−	8.89657i	0.0649382	−	0.451655i
$389$	−19.8310	+	12.7446i	−1.00547	+	0.646179i	−0.936218	−	0.351420i	$-0.885699\pi$
$389$	−19.8310	+	12.7446i	−1.00547	+	0.646179i	−0.0692562	+	0.997599i	$0.522063\pi$
$390$	−4.11099			−0.208168
$391$	29.6613	+	22.6240i	1.50004	+	1.14414i
$392$	2.30295			0.116316
$393$	10.0321	−	6.44724i	0.506053	−	0.325220i
$394$	−2.15781	+	15.0079i	−0.108709	+	0.756089i
$395$	−13.9766	+	30.6044i	−0.703238	+	1.53988i
$396$	4.79557	−	1.40811i	0.240986	−	0.0707600i
$397$	15.8055	+	34.6092i	0.793255	+	1.73699i	0.667090	+	0.744977i	$0.267540\pi$
$397$	15.8055	+	34.6092i	0.793255	+	1.73699i	0.126165	+	0.992009i	$0.459733\pi$
$398$	6.12413	+	7.06763i	0.306975	+	0.354268i
$399$	−0.843641	−	5.86765i	−0.0422349	−	0.293750i
$400$	−20.0463	−	5.88613i	−1.00232	−	0.294306i
$401$	−7.82346	+	9.02875i	−0.390685	+	0.450874i	−0.916685	−	0.399610i	$-0.869146\pi$
$401$	−7.82346	+	9.02875i	−0.390685	+	0.450874i	0.526000	+	0.850484i	$0.323691\pi$
$402$	−1.70425	−	1.09525i	−0.0850001	−	0.0546262i
$403$	2.05908	+	1.32329i	0.102570	+	0.0659179i
$404$	15.3437	−	17.7075i	0.763376	−	0.880983i
$405$	−3.99137	−	1.17197i	−0.198333	−	0.0582357i
$406$	0.483709	+	3.36427i	0.0240061	+	0.166966i
$407$	−12.6878	−	14.6425i	−0.628913	−	0.725804i
$408$	7.44158	+	16.2948i	0.368413	+	0.806712i
$409$	−20.9382	+	6.14802i	−1.03533	+	0.304000i	−0.754876	−	0.655868i	$-0.772303\pi$
$409$	−20.9382	+	6.14802i	−1.03533	+	0.304000i	−0.280453	+	0.959868i	$0.590485\pi$
$410$	5.71003	−	12.5032i	0.281998	−	0.617490i
$411$	−0.699708	+	4.86658i	−0.0345141	+	0.240051i
$412$	18.4550	−	11.8603i	0.909214	−	0.584317i
$413$	9.70996			0.477796
$414$	−2.19610	+	2.15689i	−0.107933	+	0.106005i
$415$	27.8880			1.36897
$416$	7.37760	−	4.74129i	0.361716	−	0.232461i
$417$	−0.115651	+	0.804371i	−0.00566346	+	0.0393902i
$418$	−4.97454	+	10.8927i	−0.243313	+	0.532780i
$419$	31.6405	−	9.29048i	1.54574	−	0.453870i	0.605914	−	0.795530i	$-0.292807\pi$
$419$	31.6405	−	9.29048i	1.54574	−	0.453870i	0.939823	+	0.341660i	$0.110989\pi$
$420$	−2.74425	−	6.00908i	−0.133906	−	0.293213i
$421$	13.7735	+	15.8955i	0.671281	+	0.774699i	0.984576	−	0.174956i	$-0.0559784\pi$
$421$	13.7735	+	15.8955i	0.671281	+	0.774699i	−0.313295	+	0.949656i	$0.601433\pi$
$422$	−0.389802	−	2.71113i	−0.0189753	−	0.131976i
$423$	8.36771	+	2.45698i	0.406852	+	0.119463i
$424$	2.32853	−	2.68726i	0.113083	−	0.130505i
$425$	−80.5176	−	51.7455i	−3.90568	−	2.51003i
$426$	2.44831	+	1.57343i	0.118621	+	0.0762331i
$427$	−3.81501	+	4.40276i	−0.184621	+	0.213064i
$428$	−23.5668	−	6.91983i	−1.13914	−	0.334483i
$429$	−0.689647	−	4.79660i	−0.0332964	−	0.231582i
$430$	3.54147	+	4.08707i	0.170785	+	0.197096i
$431$	0.0558165	+	0.122221i	0.00268859	+	0.00588718i	0.910972	−	0.412469i	$-0.135334\pi$
$431$	0.0558165	+	0.122221i	0.00268859	+	0.00588718i	−0.908283	+	0.418356i	$0.862606\pi$
$432$	1.62918	−	0.478371i	0.0783840	−	0.0230156i
$433$	−7.07778	+	15.4982i	−0.340137	+	0.744795i	−0.999978	−	0.00660961i	$-0.997896\pi$
$433$	−7.07778	+	15.4982i	−0.340137	+	0.744795i	0.659842	+	0.751405i	$0.270623\pi$
$434$	0.145206	−	1.00993i	0.00697010	−	0.0484781i
$435$	18.5316	−	11.9096i	0.888524	−	0.571020i
$436$	14.4218			0.690681
$437$	1.77261	+	28.3743i	0.0847953	+	1.35733i
$438$	5.03655			0.240656
$439$	4.49863	−	2.89109i	0.214708	−	0.137984i	−0.428867	−	0.903368i	$-0.641087\pi$
$439$	4.49863	−	2.89109i	0.214708	−	0.137984i	0.643575	+	0.765383i	$0.277451\pi$
$440$	−4.29092	+	29.8440i	−0.204562	+	1.42276i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	7.37576	−	2.16572i	0.350829	−	0.103013i
$443$	2.70444	+	5.92191i	0.128492	+	0.281358i	0.962934	−	0.269738i	$-0.0869370\pi$
$443$	2.70444	+	5.92191i	0.128492	+	0.281358i	−0.834442	+	0.551096i	$0.814210\pi$
$444$	−6.40196	−	7.38826i	−0.303824	−	0.350631i
$445$	8.12532	+	56.5128i	0.385177	+	2.67896i
$446$	12.1548	+	3.56897i	0.575546	+	0.168995i
$447$	−6.91136	+	7.97614i	−0.326896	+	0.377258i
$448$	−0.218571	−	0.140467i	−0.0103265	−	0.00663644i
$449$	16.2476	+	10.4417i	0.766773	+	0.492775i	0.864620	−	0.502427i	$-0.167559\pi$
$449$	16.2476	+	10.4417i	0.766773	+	0.492775i	−0.0978472	+	0.995201i	$0.531196\pi$
$450$	5.17179	−	5.96856i	0.243800	−	0.281361i
$451$	15.5463	+	4.56481i	0.732048	+	0.214949i
$452$	−2.79978	−	19.4729i	−0.131691	−	0.915929i
$453$	9.89748	+	11.4223i	0.465024	+	0.536666i
$454$	−7.83091	−	17.1473i	−0.367523	−	0.804763i
$455$	−6.14556	+	1.80450i	−0.288108	+	0.0845963i
$456$	−5.67119	+	12.4182i	−0.265578	+	0.581534i
$457$	1.05224	−	7.31847i	0.0492215	−	0.342343i	−0.950298	−	0.311342i	$-0.899221\pi$
$457$	1.05224	−	7.31847i	0.0492215	−	0.342343i	0.999519	−	0.0310010i	$-0.00986950\pi$
$458$	10.6216	−	6.82609i	0.496315	−	0.318962i
$459$	7.77855			0.363072
$460$	10.8037	+	29.7825i	0.503725	+	1.38862i
$461$	−9.72792			−0.453074			−0.226537	−	0.974003i	$-0.572740\pi$
$461$	−9.72792			−0.453074			−0.226537	+	0.974003i	$0.572740\pi$
$462$	−1.69938	+	1.09212i	−0.0790622	+	0.0508102i
$463$	4.42520	−	30.7779i	0.205656	−	1.43037i	−0.581464	−	0.813572i	$-0.697520\pi$
$463$	4.42520	−	30.7779i	0.205656	−	1.43037i	0.787121	−	0.616799i	$-0.211571\pi$
$464$	−3.73522	+	8.17900i	−0.173403	+	0.379701i
$465$	−6.34496	+	1.86305i	−0.294240	+	0.0863968i
$466$	4.51693	+	9.89070i	0.209243	+	0.458178i
$467$	7.23789	+	8.35297i	0.334930	+	0.386529i	0.898085	−	0.439822i	$-0.144958\pi$
$467$	7.23789	+	8.35297i	0.334930	+	0.386529i	−0.563156	+	0.826351i	$0.690413\pi$
$468$	−0.347978	−	2.42024i	−0.0160853	−	0.111876i
$469$	−3.02845	−	0.889234i	−0.139841	−	0.0410610i
$470$	−15.2483	+	17.5974i	−0.703350	+	0.811709i
$471$	3.35341	+	2.15510i	0.154517	+	0.0993020i
$472$	−18.8117	−	12.0896i	−0.865879	−	0.556467i
$473$	−4.17459	+	4.81773i	−0.191948	+	0.221519i
$474$	4.98089	+	1.46252i	0.228780	+	0.0671758i
$475$	−10.3806	−	72.1988i	−0.476295	−	3.31271i
$476$	8.08927	+	9.33552i	0.370771	+	0.427893i
$477$	−0.641402	−	1.40448i	−0.0293678	−	0.0643065i
$478$	−13.6210	+	3.99948i	−0.623009	+	0.182932i
$479$	−10.8692	+	23.8002i	−0.496627	+	1.08746i	0.480924	+	0.876762i	$0.340301\pi$
$479$	−10.8692	+	23.8002i	−0.496627	+	1.08746i	−0.977551	+	0.210699i	$0.932426\pi$
$480$	−3.37193	+	23.4523i	−0.153907	+	1.07045i
$481$	−7.97387	+	5.12449i	−0.363577	+	0.233657i
$482$	−3.84614			−0.175187
$483$	−2.33622	+	4.18832i	−0.106302	+	0.190575i
$484$	1.73824			0.0790107
$485$	19.8066	−	12.7290i	0.899373	−	0.577992i
$486$	−0.0913433	+	0.635307i	−0.00414342	+	0.0288181i
$487$	−7.80883	+	17.0990i	−0.353852	+	0.774828i	0.646081	+	0.763269i	$0.276407\pi$
$487$	−7.80883	+	17.0990i	−0.353852	+	0.774828i	−0.999933	+	0.0115592i	$0.996321\pi$
$488$	12.8728	−	3.77979i	0.582724	−	0.171103i
$489$	−1.06434	−	2.33059i	−0.0481313	−	0.105393i
$490$	1.74846	+	2.01783i	0.0789873	+	0.0911563i
$491$	3.20361	+	22.2816i	0.144577	+	1.00555i	0.924909	+	0.380189i	$0.124141\pi$
$491$	3.20361	+	22.2816i	0.144577	+	1.00555i	−0.780332	+	0.625365i	$0.784950\pi$
$492$	7.84428	+	2.30329i	0.353648	+	0.103840i
$493$	−26.9746	+	31.1303i	−1.21487	+	1.40204i
$494$	4.92834	+	3.16725i	0.221737	+	0.142502i
$495$	11.0140	+	7.07824i	0.495041	+	0.318143i
$496$	1.76760	−	2.03992i	0.0793675	−	0.0915949i
$497$	4.35066	+	1.27747i	0.195154	+	0.0573023i
$498$	−0.612371	−	4.25913i	−0.0274410	−	0.190856i
$499$	0.689230	+	0.795414i	0.0308542	+	0.0356076i	0.770967	−	0.636875i	$-0.219773\pi$
$499$	0.689230	+	0.795414i	0.0308542	+	0.0356076i	−0.740113	+	0.672483i	$0.765228\pi$
$500$	−20.0455	−	43.8935i	−0.896462	−	1.96298i
$501$	−4.17213	+	1.22505i	−0.186397	+	0.0547311i
$502$	−0.618789	+	1.35496i	−0.0276179	+	0.0604748i
$503$	0.991789	−	6.89804i	0.0442217	−	0.307568i	−0.955691	−	0.294371i	$-0.904890\pi$
$503$	0.991789	−	6.89804i	0.0442217	−	0.307568i	0.999913	−	0.0131975i	$-0.00420102\pi$
$504$	−1.93736	+	1.24507i	−0.0862970	+	0.0554597i
$505$	61.3760			2.73119
$506$	8.54430	−	4.56610i	0.379840	−	0.202988i
$507$	10.6293			0.472063
$508$	4.59051	−	2.95014i	0.203671	−	0.130891i
$509$	−5.10470	+	35.5040i	−0.226262	+	1.57369i	0.487389	+	0.873185i	$0.337949\pi$
$509$	−5.10470	+	35.5040i	−0.226262	+	1.57369i	−0.713651	+	0.700502i	$0.752960\pi$
$510$	−8.62755	+	18.8917i	−0.382034	+	0.836539i
$511$	7.52919	−	2.21077i	0.333072	−	0.0977987i
$512$	−7.26632	−	15.9110i	−0.321129	−	0.703175i
$513$	3.88201	+	4.48008i	0.171395	+	0.197800i
$514$	0.284142	+	1.97625i	0.0125329	+	0.0871686i
$515$	55.1376	+	16.1899i	2.42965	+	0.713411i
$516$	−2.10639	+	2.43090i	−0.0927286	+	0.107015i
$517$	−23.0902	−	14.8392i	−1.01551	−	0.652627i
$518$	3.32396	+	2.13618i	0.146046	+	0.0938583i
$519$	10.8821	−	12.5587i	0.477673	−	0.551264i
$520$	14.1529	+	4.15567i	0.620646	+	0.182238i
$521$	1.80475	+	12.5523i	0.0790676	+	0.549927i	0.990397	+	0.138250i	$0.0441478\pi$
$521$	1.80475	+	12.5523i	0.0790676	+	0.549927i	−0.911330	+	0.411677i	$0.864943\pi$
$522$	−2.22578	−	2.56869i	−0.0974198	−	0.112428i
$523$	7.50457	+	16.4327i	0.328152	+	0.718553i	0.999750	−	0.0223632i	$-0.00711901\pi$
$523$	7.50457	+	16.4327i	0.328152	+	0.718553i	−0.671598	+	0.740916i	$0.734392\pi$
$524$	−18.1706	+	5.33536i	−0.793785	+	0.233076i
$525$	5.11149	−	11.1926i	0.223084	−	0.488485i
$526$	−0.636714	+	4.42844i	−0.0277620	+	0.193089i
$527$	10.4024	−	6.68520i	0.453135	−	0.291212i
$528$	−5.34397			−0.232566
$529$	12.7813	−	19.1217i	0.555709	−	0.831377i
$530$	4.12245			0.179068
$531$	−8.16854	+	5.24960i	−0.354484	+	0.227813i
$532$	−1.33974	+	9.31808i	−0.0580850	+	0.403990i
$533$	3.29285	−	7.21033i	0.142629	−	0.312314i
$534$	8.45237	−	2.48184i	0.365770	−	0.107400i
$535$	−26.7275	−	58.5251i	−1.15553	−	2.53026i
$536$	4.76005	+	5.49339i	0.205603	+	0.237279i
$537$	−1.63197	−	11.3506i	−0.0704247	−	0.489814i
$538$	−6.39198	−	1.87685i	−0.275578	−	0.0809170i
$539$	−2.06104	+	2.37856i	−0.0887751	+	0.102452i
$540$	5.55736	+	3.57150i	0.239151	+	0.153693i
$541$	20.3770	+	13.0955i	0.876074	+	0.563019i	0.899605	−	0.436704i	$-0.143854\pi$
$541$	20.3770	+	13.0955i	0.876074	+	0.563019i	−0.0235309	+	0.999723i	$0.507491\pi$
$542$	−10.0414	+	11.5883i	−0.431313	+	0.497762i
$543$	−7.42875	−	2.18128i	−0.318798	−	0.0936076i
$544$	−6.30517	−	43.8534i	−0.270332	−	1.88020i
$545$	24.7393	+	28.5507i	1.05972	+	1.22298i
$546$	0.410534	+	0.898943i	0.0175692	+	0.0384712i
$547$	22.2093	−	6.52125i	0.949603	−	0.278829i	0.229981	−	0.973195i	$-0.426133\pi$
$547$	22.2093	−	6.52125i	0.949603	−	0.278829i	0.719622	+	0.694366i	$0.244315\pi$
$548$	3.24348	−	7.10223i	0.138555	−	0.303392i
$549$	0.829081	−	5.76639i	0.0353843	−	0.246103i
$550$	−20.9101	+	13.4381i	−0.891608	+	0.573002i
$551$	−31.3917			−1.33733
$552$	9.74086	−	5.20555i	0.414599	−	0.221563i
$553$	8.08795			0.343935
$554$	−8.87208	+	5.70174i	−0.376938	+	0.242244i
$555$	3.64445	−	25.3477i	0.154698	−	1.07595i
$556$	0.536098	−	1.17389i	0.0227356	−	0.0497840i
$557$	−29.5355	+	8.67241i	−1.25146	+	0.367462i	−0.839310	−	0.543654i	$-0.817041\pi$
$557$	−29.5355	+	8.67241i	−1.25146	+	0.367462i	−0.412151	+	0.911116i	$0.635222\pi$
$558$	0.423853	+	0.928110i	0.0179431	+	0.0392900i
$559$	2.04229	+	2.35692i	0.0863795	+	0.0996873i
$560$	1.00521	+	6.99140i	0.0424780	+	0.295441i
$561$	−23.4897	−	6.89719i	−0.991735	−	0.291200i
$562$	−2.06047	+	2.37791i	−0.0869158	+	0.100306i
$563$	28.8023	+	18.5101i	1.21387	+	0.780108i	0.981303	−	0.192472i	$-0.0616503\pi$
$563$	28.8023	+	18.5101i	1.21387	+	0.780108i	0.232570	+	0.972580i	$0.425287\pi$
$564$	−11.6507	−	7.48748i	−0.490585	−	0.315280i
$565$	33.7475	−	38.9466i	1.41977	−	1.63850i
$566$	0.848684	+	0.249196i	0.0356729	+	0.0104745i
$567$	0.142315	+	0.989821i	0.00597666	+	0.0415686i
$568$	−6.83827	−	7.89178i	−0.286927	−	0.331132i
$569$	−16.5415	−	36.2207i	−0.693454	−	1.51845i	−0.847732	−	0.530425i	$-0.822032\pi$
$569$	−16.5415	−	36.2207i	−0.693454	−	1.51845i	0.154278	−	0.988027i	$-0.450695\pi$
$570$	−15.1864	+	4.45914i	−0.636090	+	0.186773i
$571$	−3.51590	+	7.69875i	−0.147136	+	0.322183i	−0.968822	−	0.247758i	$-0.920306\pi$
$571$	−3.51590	+	7.69875i	−0.147136	+	0.322183i	0.821686	+	0.569940i	$0.193034\pi$
$572$	−1.09519	+	7.61720i	−0.0457921	+	0.318491i
$573$	0.727783	−	0.467718i	0.0304036	−	0.0195392i
$574$	−3.30427			−0.137918
$575$	−28.7461	+	51.5354i	−1.19880	+	2.14917i
$576$	0.259816			0.0108256
$577$	−38.0002	+	24.4213i	−1.58197	+	1.01667i	−0.606899	+	0.794779i	$0.707587\pi$
$577$	−38.0002	+	24.4213i	−1.58197	+	1.01667i	−0.975071	+	0.221892i	$0.928777\pi$
$578$	3.97397	−	27.6396i	0.165295	−	1.14965i
$579$	−8.52008	+	18.6564i	−0.354082	+	0.775332i
$580$	−33.5653	+	9.85567i	−1.39372	+	0.409234i
$581$	−2.78496	−	6.09822i	−0.115540	−	0.252997i
$582$	−2.37892	−	2.74542i	−0.0986093	−	0.113801i
$583$	0.691568	+	4.80996i	0.0286418	+	0.199208i
$584$	−17.3393	−	5.09129i	−0.717507	−	0.210679i
$585$	4.19439	−	4.84058i	0.173417	−	0.200134i
$586$	−13.4120	−	8.61938i	−0.554045	−	0.356063i
$587$	−19.0503	−	12.2429i	−0.786289	−	0.505317i	0.0848265	−	0.996396i	$-0.472966\pi$
$587$	−19.0503	−	12.2429i	−0.786289	−	0.505317i	−0.871115	+	0.491079i	$0.836603\pi$
$588$	−1.03995	+	1.20016i	−0.0428867	+	0.0494938i
$589$	9.04183	+	2.65492i	0.372562	+	0.109394i
$590$	−3.68956	−	25.6614i	−0.151897	−	1.05646i
$591$	−15.4699	−	17.8532i	−0.636345	−	0.734381i
$592$	4.34222	+	9.50814i	0.178464	+	0.390782i
$593$	24.4674	−	7.18428i	1.00476	−	0.295023i	0.262350	−	0.964973i	$-0.415503\pi$
$593$	24.4674	−	7.18428i	1.00476	−	0.295023i	0.742407	+	0.669950i	$0.233684\pi$
$594$	0.839161	−	1.83751i	0.0344312	−	0.0753938i
$595$	−4.60499	+	32.0284i	−0.188786	+	1.31304i
$596$	14.0995	−	9.06119i	0.577538	−	0.371161i
$597$	−14.5703			−0.596323
$598$	−1.61621	−	4.45539i	−0.0660916	−	0.182195i
$599$	−9.47618			−0.387186			−0.193593	−	0.981082i	$-0.562014\pi$
$599$	−9.47618			−0.387186			−0.193593	+	0.981082i	$0.562014\pi$
$600$	−23.8384	+	15.3200i	−0.973197	+	0.625436i
$601$	4.43695	−	30.8596i	0.180987	−	1.25879i	−0.673449	−	0.739234i	$-0.735188\pi$
$601$	4.43695	−	30.8596i	0.180987	−	1.25879i	0.854436	−	0.519557i	$-0.173903\pi$
$602$	0.540053	−	1.18255i	0.0220109	−	0.0481972i
$603$	3.02845	−	0.889234i	0.123328	−	0.0362124i
$604$	−9.97056	−	21.8325i	−0.405696	−	0.888351i
$605$	2.98178	+	3.44116i	0.121227	+	0.139903i
$606$	−1.34771	−	9.37350i	−0.0547468	−	0.380772i
$607$	1.19874	+	0.351980i	0.0486552	+	0.0142864i	0.305970	−	0.952041i	$-0.401019\pi$
$607$	1.19874	+	0.351980i	0.0486552	+	0.0142864i	−0.257314	+	0.966328i	$0.582838\pi$
$608$	22.1108	−	25.5172i	0.896712	−	1.03486i
$609$	−4.45486	−	2.86296i	−0.180520	−	0.116013i
$610$	13.0852	+	8.40935i	0.529804	+	0.340485i
$611$	−8.79334	+	10.1481i	−0.355740	+	0.410546i
$612$	−11.8523	−	3.48015i	−0.479101	−	0.140677i
$613$	6.37078	+	44.3097i	0.257313	+	1.78965i	0.551779	+	0.833991i	$0.313949\pi$
$613$	6.37078	+	44.3097i	0.257313	+	1.78965i	−0.294466	+	0.955662i	$0.595142\pi$
$614$	8.28983	+	9.56698i	0.334550	+	0.386092i
$615$	8.89635	+	19.4803i	0.358735	+	0.785521i
$616$	6.95444	−	2.04201i	0.280203	−	0.0822749i
$617$	17.1900	−	37.6408i	0.692043	−	1.51536i	−0.157316	−	0.987548i	$-0.550284\pi$
$617$	17.1900	−	37.6408i	0.692043	−	1.51536i	0.849359	−	0.527815i	$-0.176989\pi$
$618$	1.26184	−	8.77626i	0.0507585	−	0.353033i
$619$	−24.6554	+	15.8451i	−0.990984	+	0.636867i	−0.932405	−	0.361416i	$-0.882293\pi$
$619$	−24.6554	+	15.8451i	−0.990984	+	0.636867i	−0.0585791	+	0.998283i	$0.518657\pi$
$620$	10.5014			0.421748
$621$	−0.299023	−	4.78650i	−0.0119994	−	0.192076i
$622$	10.5094			0.421389
$623$	11.5461	−	7.42026i	0.462587	−	0.297286i
$624$	−0.372064	+	2.58776i	−0.0148945	+	0.103593i
$625$	26.9517	−	59.0160i	1.07807	−	2.36064i
$626$	6.00521	−	1.76329i	0.240016	−	0.0704752i
$627$	−7.75044	−	16.9711i	−0.309523	−	0.677760i
$628$	−4.14544	−	4.78409i	−0.165421	−	0.190906i
$629$	6.81477	+	47.3977i	0.271723	+	1.88987i
$630$	−2.56182	−	0.752218i	−0.102065	−	0.0299691i
$631$	29.2974	−	33.8110i	1.16631	−	1.34599i	0.239306	−	0.970944i	$-0.423080\pi$
$631$	29.2974	−	33.8110i	1.16631	−	1.34599i	0.927005	−	0.375050i	$-0.122375\pi$
$632$	−15.6693	−	10.0700i	−0.623291	−	0.400565i
$633$	3.59000	+	2.30715i	0.142690	+	0.0917011i
$634$	−3.21182	+	3.70664i	−0.127558	+	0.147210i
$635$	13.7149	+	4.02707i	0.544260	+	0.159809i
$636$	0.348948	+	2.42698i	0.0138367	+	0.0962362i
$637$	1.00830	+	1.16364i	0.0399502	+	0.0461050i
$638$	4.44378	+	9.73052i	0.175931	+	0.385235i
$639$	−4.35066	+	1.27747i	−0.172109	+	0.0505359i
$640$	19.3970	−	42.4736i	0.766736	−	1.67892i
$641$	−2.78186	+	19.3483i	−0.109877	+	0.764211i	0.858156	+	0.513389i	$0.171610\pi$
$641$	−2.78186	+	19.3483i	−0.109877	+	0.764211i	−0.968033	+	0.250823i	$0.919299\pi$
$642$	−8.35122	+	5.36701i	−0.329596	+	0.211819i
$643$	−12.2596			−0.483472			−0.241736	−	0.970342i	$-0.577717\pi$
$643$	−12.2596			−0.483472			−0.241736	+	0.970342i	$0.577717\pi$
$644$	5.43361	−	5.33658i	0.214114	−	0.210291i
$645$	−8.42574			−0.331763
$646$	24.8977	−	16.0008i	0.979588	−	0.629543i
$647$	1.95274	−	13.5816i	0.0767703	−	0.533949i	−0.914752	−	0.404015i	$-0.867614\pi$
$647$	1.95274	−	13.5816i	0.0767703	−	0.533949i	0.991523	−	0.129934i	$-0.0414766\pi$
$648$	0.956679	−	2.09484i	0.0375819	−	0.0822929i
$649$	29.3221	−	8.60976i	1.15099	−	0.337963i
$650$	5.05143	+	11.0611i	0.198133	+	0.433851i
$651$	1.04101	+	1.20139i	0.0408005	+	0.0470863i
$652$	0.579045	+	4.02734i	0.0226771	+	0.157723i
$653$	19.4963	+	5.72464i	0.762951	+	0.224023i	0.639984	−	0.768388i	$-0.278941\pi$
$653$	19.4963	+	5.72464i	0.762951	+	0.224023i	0.122967	+	0.992411i	$0.460759\pi$
$654$	3.81711	−	4.40517i	0.149261	−	0.172256i
$655$	−41.7323	−	26.8197i	−1.63061	−	1.04793i
$656$	−7.35367	−	4.72591i	−0.287112	−	0.184516i
$657$	−5.13873	+	5.93041i	−0.200481	+	0.231367i
$658$	5.37073	+	1.57699i	0.209373	+	0.0614774i
$659$	0.0818992	+	0.569621i	0.00319034	+	0.0221893i	0.991354	−	0.131211i	$-0.0418866\pi$
$659$	0.0818992	+	0.569621i	0.00319034	+	0.0221893i	−0.988164	+	0.153401i	$0.950978\pi$
$660$	−13.6153	−	15.7129i	−0.529975	−	0.611624i
$661$	16.5515	+	36.2428i	0.643780	+	1.40968i	0.896894	+	0.442246i	$0.145818\pi$
$661$	16.5515	+	36.2428i	0.643780	+	1.40968i	−0.253114	+	0.967437i	$0.581455\pi$
$662$	1.31695	−	0.386691i	0.0511846	−	0.0150292i
$663$	−4.97532	+	10.8944i	−0.193225	+	0.423104i
$664$	−2.19721	+	15.2819i	−0.0852683	+	0.593054i
$665$	−20.7451	+	13.3320i	−0.804459	+	0.516994i
$666$	−3.95120			−0.153106
$667$	20.1929	+	15.4020i	0.781871	+	0.596367i
$668$	6.90522			0.267171
$669$	−16.6037	+	10.6706i	−0.641937	+	0.412548i
$670$	−1.19932	+	8.34146i	−0.0463338	+	0.322259i
$671$	−7.61668	+	16.6782i	−0.294039	+	0.643855i
$672$	5.46500	−	1.60467i	0.210817	−	0.0619014i
$673$	4.79569	+	10.5011i	0.184860	+	0.404788i	0.979260	−	0.202608i	$-0.0649416\pi$
$673$	4.79569	+	10.5011i	0.184860	+	0.404788i	−0.794400	+	0.607395i	$0.792214\pi$
$674$	3.73328	+	4.30844i	0.143801	+	0.165955i
$675$	1.75112	+	12.1793i	0.0674006	+	0.468781i
$676$	−16.1960	−	4.75557i	−0.622923	−	0.182907i
$677$	−0.805274	+	0.929335i	−0.0309492	+	0.0357173i	−0.771013	−	0.636819i	$-0.780250\pi$
$677$	−0.805274	+	0.929335i	−0.0309492	+	0.0357173i	0.740064	+	0.672537i	$0.234795\pi$
$678$	−6.68907	−	4.29880i	−0.256892	−	0.165095i
$679$	−4.76136	−	3.05994i	−0.182724	−	0.117430i
$680$	48.7991	−	56.3172i	1.87136	−	2.15966i
$681$	28.1803	+	8.27448i	1.07987	+	0.317079i
$682$	−0.457004	−	3.17853i	−0.0174996	−	0.121712i
$683$	−12.7818	−	14.7510i	−0.489084	−	0.564433i	0.456537	−	0.889705i	$-0.349090\pi$
$683$	−12.7818	−	14.7510i	−0.489084	−	0.564433i	−0.945621	+	0.325272i	$0.894544\pi$
$684$	−3.91067	−	8.56318i	−0.149528	−	0.327422i
$685$	19.6241	−	5.76214i	0.749796	−	0.220160i
$686$	0.266630	−	0.583838i	0.0101800	−	0.0222910i
$687$	−2.79954	+	19.4712i	−0.106809	+	0.742874i
$688$	2.89323	−	1.85936i	0.110303	−	0.0708875i
$689$	2.37732			0.0905688
$690$	11.9566	+	4.58269i	0.455180	+	0.174460i
$691$	−30.1627			−1.14744			−0.573722	−	0.819050i	$-0.694501\pi$
$691$	−30.1627			−1.14744			−0.573722	+	0.819050i	$0.694501\pi$
$692$	−22.2001	+	14.2671i	−0.843920	+	0.542354i
$693$	0.447906	−	3.11525i	0.0170145	−	0.118339i
$694$	−8.31606	+	18.2096i	−0.315673	+	0.691228i
$695$	3.24356	−	0.952394i	0.123035	−	0.0361264i
$696$	5.06609	+	11.0932i	0.192030	+	0.420487i
$697$	−26.2239	−	30.2640i	−0.993301	−	1.14633i
$698$	2.36366	+	16.4396i	0.0894660	+	0.622250i
$699$	−16.2546	−	4.77278i	−0.614805	−	0.180523i
$700$	−12.7961	+	14.7674i	−0.483645	+	0.558157i
$701$	16.2760	+	10.4599i	0.614735	+	0.395066i	0.810630	−	0.585559i	$-0.199125\pi$
$701$	16.2760	+	10.4599i	0.614735	+	0.395066i	−0.195895	+	0.980625i	$0.562761\pi$
$702$	−0.831368	−	0.534288i	−0.0313780	−	0.0201654i
$703$	−23.8978	+	27.5796i	−0.901324	+	1.04018i
$704$	−0.784591	−	0.230377i	−0.0295704	−	0.00868265i
$705$	−5.16292	−	35.9089i	−0.194447	−	1.35241i
$706$	5.67560	+	6.55000i	0.213604	+	0.246512i
$707$	−6.12915	−	13.4210i	−0.230511	−	0.504748i
$708$	14.7952	−	4.34427i	0.556038	−	0.163267i
$709$	−3.07481	+	6.73290i	−0.115477	+	0.252859i	−0.958541	−	0.284953i	$-0.908022\pi$
$709$	−3.07481	+	6.73290i	−0.115477	+	0.252859i	0.843064	+	0.537813i	$0.180749\pi$
$710$	1.72294	−	11.9833i	0.0646608	−	0.449725i
$711$	−6.80402	+	4.37268i	−0.255171	+	0.163988i
$712$	−31.6078			−1.18455
$713$	−4.51360	−	6.14407i	−0.169036	−	0.230097i
$714$	4.99258			0.186843
$715$	−16.9583	+	10.8985i	−0.634206	+	0.407579i
$716$	−2.59163	+	18.0252i	−0.0968539	+	0.673634i
$717$	9.18802	−	20.1190i	0.343133	−	0.751356i
$718$	−7.45393	+	2.18867i	−0.278178	+	0.0816805i
$719$	−6.01390	−	13.1686i	−0.224281	−	0.491106i	0.763721	−	0.645546i	$-0.223370\pi$
$719$	−6.01390	−	13.1686i	−0.224281	−	0.491106i	−0.988002	+	0.154440i	$0.950643\pi$
$720$	−4.62548	−	5.33808i	−0.172381	−	0.198939i
$721$	−1.96597	−	13.6736i	−0.0732164	−	0.509232i
$722$	9.94034	+	2.91875i	0.369941	+	0.108625i
$723$	3.92417	−	4.52873i	0.145941	−	0.168425i
$724$	10.3434	+	6.64729i	0.384409	+	0.247045i
$725$	−54.8150	−	35.2274i	−2.03578	−	1.30831i
$726$	0.460068	−	0.530947i	0.0170747	−	0.0197053i
$727$	2.95182	+	0.866733i	0.109477	+	0.0321453i	0.336012	−	0.941858i	$-0.390922\pi$
$727$	2.95182	+	0.866733i	0.109477	+	0.0321453i	−0.226535	+	0.974003i	$0.572740\pi$
$728$	−0.504631	−	3.50979i	−0.0187029	−	0.130081i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−8.70353	−	19.0581i	−0.322132	−	0.705371i
$731$	15.1171	−	4.43878i	0.559126	−	0.164174i
$732$	−3.84318	+	8.41540i	−0.142048	+	0.311042i
$733$	1.67615	−	11.6578i	0.0619098	−	0.430592i	−0.935168	−	0.354204i	$-0.884752\pi$
$733$	1.67615	−	11.6578i	0.0619098	−	0.430592i	0.997078	−	0.0763887i	$-0.0243390\pi$
$734$	−8.79391	+	5.65150i	−0.324589	+	0.208601i
$735$	−4.15987			−0.153439
$736$	−26.7427	+	5.56568i	−0.985747	+	0.205154i
$737$	−9.93380			−0.365916
$738$	2.77973	−	1.78643i	0.102323	−	0.0657592i
$739$	0.734955	−	5.11173i	0.0270358	−	0.188038i	−0.971828	−	0.235690i	$-0.924265\pi$
$739$	0.734955	−	5.11173i	0.0270358	−	0.188038i	0.998864	+	0.0476524i	$0.0151740\pi$
$740$	−16.8938	+	36.9922i	−0.621027	+	1.35986i
$741$	−8.75768	+	2.57149i	−0.321722	+	0.0944660i
$742$	−0.411677	−	0.901448i	−0.0151132	−	0.0330932i
$743$	−1.12020	−	1.29278i	−0.0410962	−	0.0474275i	0.734829	−	0.678252i	$-0.237262\pi$
$743$	−1.12020	−	1.29278i	−0.0410962	−	0.0474275i	−0.775926	+	0.630825i	$0.782717\pi$
$744$	−0.521004	−	3.62366i	−0.0191009	−	0.132850i
$745$	42.1247	+	12.3689i	1.54333	+	0.453162i
$746$	2.53693	−	2.92778i	0.0928837	−	0.107193i
$747$	5.63981	+	3.62449i	0.206350	+	0.132613i
$748$	32.7057	+	21.0187i	1.19584	+	0.768520i
$749$	−10.1285	+	11.6889i	−0.370088	+	0.427104i
$750$	−18.7129	−	5.49460i	−0.683298	−	0.200635i
$751$	6.89273	+	47.9400i	0.251519	+	1.74936i	0.589101	+	0.808060i	$0.299482\pi$
$751$	6.89273	+	47.9400i	0.251519	+	1.74936i	−0.337581	+	0.941296i	$0.609609\pi$
$752$	9.69709	+	11.1910i	0.353616	+	0.408095i
$753$	−0.964087	−	2.11106i	−0.0351333	−	0.0769311i
$754$	5.02129	−	1.47438i	0.182865	−	0.0536939i
$755$	26.1179	−	57.1901i	0.950526	−	2.08136i
$756$	0.226002	−	1.57188i	0.00821961	−	0.0571686i
$757$	33.4605	−	21.5038i	1.21614	−	0.781567i	0.234466	−	0.972124i	$-0.424666\pi$
$757$	33.4605	−	21.5038i	1.21614	−	0.781567i	0.981676	+	0.190557i	$0.0610294\pi$
$758$	12.4344			0.451636
$759$	−3.34117	+	14.7194i	−0.121277	+	0.534281i
$760$	56.7900			2.05999
$761$	−28.9845	+	18.6272i	−1.05069	+	0.675237i	−0.947608	−	0.319436i	$-0.896507\pi$
$761$	−28.9845	+	18.6272i	−1.05069	+	0.675237i	−0.103081	+	0.994673i	$0.532870\pi$
$762$	0.313869	−	2.18301i	0.0113703	−	0.0790820i
$763$	3.77260	−	8.26084i	0.136577	−	0.299063i
$764$	−1.31819	+	0.387056i	−0.0476905	+	0.0140032i
$765$	−13.4419	−	29.4337i	−0.485993	−	1.06418i
$766$	12.4954	+	14.4205i	0.451478	+	0.521034i
$767$	−2.12769	−	14.7984i	−0.0768263	−	0.534338i
$768$	−7.41119	−	2.17612i	−0.267428	−	0.0785240i
$769$	−3.58921	+	4.14216i	−0.129430	+	0.149370i	−0.816765	−	0.576970i	$-0.804235\pi$
$769$	−3.58921	+	4.14216i	−0.129430	+	0.149370i	0.687335	+	0.726340i	$0.258780\pi$
$770$	7.06920	+	4.54310i	0.254756	+	0.163722i
$771$	−2.61689	−	1.68177i	−0.0942449	−	0.0605675i
$772$	21.3291	−	24.6151i	0.767650	−	0.885916i
$773$	−32.6737	−	9.59385i	−1.17519	−	0.345067i	−0.364872	−	0.931058i	$-0.618887\pi$
$773$	−32.6737	−	9.59385i	−1.17519	−	0.345067i	−0.810318	+	0.585991i	$0.800705\pi$
$774$	0.185014	+	1.28680i	0.00665019	+	0.0462531i
$775$	12.8092	+	14.7826i	0.460119	+	0.531006i
$776$	5.41465	+	11.8564i	0.194374	+	0.425621i
$777$	−5.90669	+	1.73436i	−0.211901	+	0.0622198i
$778$	6.28532	−	13.7629i	0.225340	−	0.493425i
$779$	4.34317	−	30.2074i	0.155610	−	1.08229i
$780$	−8.55675	+	5.49909i	−0.306381	+	0.196899i
$781$	14.2708			0.510651
$782$	−23.8662	−	1.92320i	−0.853454	−	0.0687733i
$783$	5.29550			0.189246
$784$	1.42841	−	0.917986i	0.0510148	−	0.0327852i
$785$	2.35988	−	16.4133i	0.0842277	−	0.585816i
$786$	−3.17961	+	6.96237i	−0.113413	+	0.248340i
$787$	−17.5400	+	5.15021i	−0.625234	+	0.183585i	−0.578977	−	0.815344i	$-0.696548\pi$
$787$	−17.5400	+	5.15021i	−0.625234	+	0.183585i	−0.0462577	+	0.998930i	$0.514730\pi$
$788$	15.5841	+	34.1244i	0.555160	+	1.21563i
$789$	−4.56474	−	5.26799i	−0.162509	−	0.187546i
$790$	−3.07323	−	21.3748i	−0.109341	−	0.760481i
$791$	−11.8865	−	3.49019i	−0.422635	−	0.124097i
$792$	−4.74646	+	5.47770i	−0.168658	+	0.194642i
$793$	7.54595	+	4.84949i	0.267964	+	0.172210i
$794$	−20.5437	−	13.2027i	−0.729070	−	0.468545i
$795$	−4.20608	+	4.85407i	−0.149174	+	0.172156i
$796$	22.2010	+	6.51880i	0.786894	+	0.231053i
$797$	−5.30984	−	36.9308i	−0.188084	−	1.30815i	−0.836962	−	0.547262i	$-0.815670\pi$
$797$	−5.30984	−	36.9308i	−0.188084	−	1.30815i	0.648877	−	0.760893i	$-0.275239\pi$
$798$	2.49163	+	2.87549i	0.0882027	+	0.101791i
$799$	28.1803	+	61.7063i	0.996948	+	2.18301i
$800$	67.2443	−	19.7447i	2.37744	−	0.698080i
$801$	−5.70154	+	12.4846i	−0.201454	+	0.441123i
$802$	1.09126	−	7.58985i	0.0385336	−	0.268007i
$803$	20.7764	−	13.3522i	0.733183	−	0.471188i
$804$	−5.01234			−0.176772
$805$	19.8856	+	1.60243i	0.700875	+	0.0564781i
$806$	−1.57099			−0.0553358
$807$	8.73160	−	5.61146i	0.307367	−	0.197533i
$808$	−4.83563	+	33.6325i	−0.170117	+	1.18319i
$809$	−1.79063	+	3.92092i	−0.0629551	+	0.137852i	−0.938494	−	0.345295i	$-0.887779\pi$
$809$	−1.79063	+	3.92092i	−0.0629551	+	0.137852i	0.875539	+	0.483147i	$0.160506\pi$
$810$	2.56182	−	0.752218i	0.0900131	−	0.0264302i
$811$	−7.60695	−	16.6569i	−0.267116	−	0.584903i	0.727779	−	0.685811i	$-0.240552\pi$
$811$	−7.60695	−	16.6569i	−0.267116	−	0.584903i	−0.994896	+	0.100908i	$0.967825\pi$
$812$	5.50704	+	6.35546i	0.193259	+	0.223033i
$813$	−3.39991	−	23.6469i	−0.119240	−	0.829332i
$814$	11.9318	+	3.50350i	0.418210	+	0.122798i
$815$	−6.97957	+	8.05486i	−0.244484	+	0.282149i
$816$	11.1110	+	7.14060i	0.388963	+	0.249971i
$817$	10.1010	+	6.49149i	0.353388	+	0.227108i
$818$	9.17220	−	10.5853i	0.320698	−	0.370106i
$819$	−1.47734	−	0.433787i	−0.0516226	−	0.0151578i
$820$	−4.83996	−	33.6626i	−0.169019	−	1.17555i
$821$	−12.2464	−	14.1331i	−0.427402	−	0.493248i	0.500676	−	0.865635i	$-0.333085\pi$
$821$	−12.2464	−	14.1331i	−0.427402	−	0.493248i	−0.928078	+	0.372387i	$0.878539\pi$
$822$	−1.31092	−	2.87051i	−0.0457235	−	0.100121i
$823$	22.2523	−	6.53387i	0.775667	−	0.227756i	0.130142	−	0.991495i	$-0.458457\pi$
$823$	22.2523	−	6.53387i	0.775667	−	0.227756i	0.645525	+	0.763739i	$0.276639\pi$
$824$	−13.2158	+	28.9385i	−0.460393	+	1.00812i
$825$	5.51127	−	38.3317i	0.191878	−	1.33454i
$826$	−5.24289	+	3.36940i	−0.182424	+	0.117236i
$827$	−31.6945			−1.10213			−0.551063	−	0.834464i	$-0.685778\pi$
$827$	−31.6945			−1.10213			−0.551063	+	0.834464i	$0.685778\pi$
$828$	−1.68587	+	7.42705i	−0.0585880	+	0.258108i
$829$	−10.3162			−0.358295			−0.179147	−	0.983822i	$-0.557334\pi$
$829$	−10.3162			−0.358295			−0.179147	+	0.983822i	$0.557334\pi$
$830$	−15.0581	+	9.67727i	−0.522675	+	0.335903i
$831$	2.33842	−	16.2640i	0.0811188	−	0.564194i
$832$	−0.166183	+	0.363891i	−0.00576137	+	0.0126156i
$833$	7.46347	−	2.19147i	0.258594	−	0.0759300i
$834$	−0.216675	−	0.474452i	−0.00750284	−	0.0164289i
$835$	11.8453	+	13.6702i	0.409922	+	0.473075i
$836$	4.21654	+	29.3267i	0.145832	+	1.01428i
$837$	−1.52528	−	0.447862i	−0.0527213	−	0.0154804i
$838$	−13.8604	+	15.9958i	−0.478800	+	0.552565i
$839$	−26.5633	−	17.0712i	−0.917067	−	0.589363i	−0.00526144	−	0.999986i	$-0.501675\pi$
$839$	−26.5633	−	17.0712i	−0.917067	−	0.589363i	−0.911805	+	0.410623i	$0.865311\pi$
$840$	8.05918	+	5.17932i	0.278068	+	0.178704i
$841$	0.627143	−	0.723761i	0.0216256	−	0.0249573i
$842$	−12.9528	−	3.80329i	−0.446384	−	0.131070i
$843$	−0.697656	−	4.85230i	−0.0240285	−	0.167122i
$844$	−4.43791	−	5.12162i	−0.152759	−	0.176293i
$845$	−18.3682	−	40.2207i	−0.631885	−	1.38363i
$846$	−5.37073	+	1.57699i	−0.184650	+	0.0542180i
$847$	0.454704	−	0.995663i	0.0156238	−	0.0342114i
$848$	0.373101	−	2.59497i	0.0128123	−	0.0891117i
$849$	−1.15932	+	0.745052i	−0.0397879	+	0.0255701i
$850$	61.4314			2.10708
$851$	28.9040	−	6.01551i	0.990818	−	0.206209i
$852$	7.20071			0.246692
$853$	−0.110159	+	0.0707950i	−0.00377178	+	0.00242397i	−0.542525	−	0.840039i	$-0.682532\pi$
$853$	−0.110159	+	0.0707950i	−0.00377178	+	0.00242397i	0.538754	+	0.842463i	$0.318895\pi$
$854$	0.532137	−	3.70110i	0.0182094	−	0.126649i
$855$	10.2440	−	22.4312i	0.350338	−	0.767132i
$856$	34.1761	−	10.0350i	1.16811	−	0.342989i
$857$	−15.1165	−	33.1005i	−0.516369	−	1.13069i	−0.970796	−	0.239907i	$-0.922883\pi$
$857$	−15.1165	−	33.1005i	−0.516369	−	1.13069i	0.454427	−	0.890784i	$-0.349844\pi$
$858$	2.03682	+	2.35061i	0.0695358	+	0.0802486i
$859$	−4.39578	−	30.5734i	−0.149982	−	1.04315i	−0.916244	−	0.400621i	$-0.868794\pi$
$859$	−4.39578	−	30.5734i	−0.149982	−	1.04315i	0.766262	−	0.642529i	$-0.222115\pi$
$860$	12.8384	+	3.76970i	0.437786	+	0.128546i
$861$	3.37131	−	3.89070i	0.114894	−	0.132595i
$862$	−0.0725494	−	0.0466247i	−0.00247104	−	0.00158804i
$863$	−37.6382	−	24.1886i	−1.28122	−	0.823389i	−0.290181	−	0.956972i	$-0.593716\pi$
$863$	−37.6382	−	24.1886i	−1.28122	−	0.823389i	−0.991038	+	0.133582i	$0.957352\pi$
$864$	−3.72990	+	4.30453i	−0.126894	+	0.146443i
$865$	−66.3265	−	19.4752i	−2.25517	−	0.662177i
$866$	−1.55629	−	10.8243i	−0.0528850	−	0.367824i
$867$	28.4903	+	32.8795i	0.967581	+	1.11665i
$868$	−1.04870	−	2.29633i	−0.0355952	−	0.0779426i
$869$	24.4240	−	7.17153i	0.828528	−	0.243278i
$870$	−5.87348	+	12.8611i	−0.199130	+	0.436033i
$871$	−0.691622	+	4.81034i	−0.0234347	+	0.162992i
$872$	−17.5942	+	11.3071i	−0.595815	+	0.382907i
$873$	5.65984			0.191556
$874$	−10.8031	−	14.7056i	−0.365422	−	0.497425i
$875$	−30.3859			−1.02723
$876$	10.4832	−	6.73717i	0.354196	−	0.227628i
$877$	4.75995	−	33.1062i	0.160732	−	1.11792i	−0.736526	−	0.676410i	$-0.763535\pi$
$877$	4.75995	−	33.1062i	0.160732	−	1.11792i	0.897258	−	0.441507i	$-0.145556\pi$
$878$	−1.42581	+	3.12209i	−0.0481188	+	0.105365i
$879$	23.8332	−	6.99806i	0.803873	−	0.236039i
$880$	9.23477	+	20.2213i	0.311304	+	0.681661i
$881$	11.2353	+	12.9663i	0.378528	+	0.436844i	0.912762	−	0.408492i	$-0.133945\pi$
$881$	11.2353	+	12.9663i	0.378528	+	0.436844i	−0.534234	+	0.845337i	$0.679400\pi$
$882$	0.0913433	+	0.635307i	0.00307569	+	0.0213919i
$883$	9.82134	+	2.88381i	0.330514	+	0.0970478i	0.442780	−	0.896631i	$-0.353992\pi$
$883$	9.82134	+	2.88381i	0.330514	+	0.0970478i	−0.112265	+	0.993678i	$0.535811\pi$
$884$	12.4552	−	14.3740i	0.418912	−	0.483451i
$885$	33.9801	+	21.8377i	1.14223	+	0.734065i
$886$	−3.51519	−	2.25908i	−0.118095	−	0.0758952i
$887$	−4.63577	+	5.34996i	−0.155654	+	0.179634i	−0.828220	−	0.560403i	$-0.810646\pi$
$887$	−4.63577	+	5.34996i	−0.155654	+	0.179634i	0.672566	+	0.740037i	$0.265192\pi$
$888$	13.6028	+	3.99414i	0.456480	+	0.134035i
$889$	−0.489015	−	3.40117i	−0.0164010	−	0.114072i
$890$	−23.9975	−	27.6946i	−0.804397	−	0.928324i
$891$	1.30743	+	2.86287i	0.0438006	+	0.0959099i
$892$	30.0734	−	8.83035i	1.00693	−	0.295662i
$893$	−21.4761	+	47.0260i	−0.718669	+	1.57367i
$894$	0.964032	−	6.70499i	0.0322421	−	0.224248i
$895$	−40.1300	+	25.7900i	−1.34140	+	0.862063i
$896$	−11.2247			−0.374990
$897$	6.89510	+	2.64274i	0.230221	+	0.0882384i
$898$	−12.3962			−0.413667
$899$	7.08175	−	4.55117i	0.236190	−	0.151790i
$900$	2.78085	−	19.3412i	0.0926950	−	0.644708i
$901$	4.98918	−	10.9248i	0.166214	−	0.363957i
$902$	−9.97825	+	2.92988i	−0.332239	+	0.0975543i
$903$	0.841415	+	1.84244i	0.0280005	+	0.0613126i
$904$	18.6829	+	21.5613i	0.621385	+	0.717117i
$905$	4.58357	+	31.8795i	0.152363	+	1.05971i
$906$	−9.30773	−	2.73300i	−0.309229	−	0.0907977i
$907$	33.0450	−	38.1359i	1.09724	−	1.26628i	0.135959	−	0.990715i	$-0.456589\pi$
$907$	33.0450	−	38.1359i	1.09724	−	1.26628i	0.961282	−	0.275568i	$-0.0888659\pi$
$908$	−39.2367	−	25.2159i	−1.30212	−	0.836819i
$909$	12.4121	+	7.97677i	0.411683	+	0.264573i
$910$	2.69213	−	3.10688i	0.0892431	−	0.102992i
$911$	−11.4345	−	3.35748i	−0.378843	−	0.111238i	0.0867665	−	0.996229i	$-0.472347\pi$
$911$	−11.4345	−	3.35748i	−0.378843	−	0.111238i	−0.465609	+	0.884990i	$0.654165\pi$
$912$	1.43247	+	9.96304i	0.0474338	+	0.329909i
$913$	−13.8173	−	15.9460i	−0.457286	−	0.527736i
$914$	1.97139	+	4.31674i	0.0652077	+	0.142785i
$915$	−23.2525	+	6.82754i	−0.768702	+	0.225711i
$916$	12.9772	−	28.4161i	0.428779	−	0.938894i
$917$	−1.69713	+	11.8038i	−0.0560442	+	0.389796i
$918$	−4.20003	+	2.69919i	−0.138622	+	0.0890867i
$919$	−40.5310			−1.33700			−0.668498	−	0.743714i	$-0.733062\pi$
$919$	−40.5310			−1.33700			−0.668498	+	0.743714i	$0.733062\pi$
$920$	−36.5305	−	27.8634i	−1.20437	−	0.918628i
$921$	−19.7229			−0.649891
$922$	5.25259	−	3.37564i	0.172985	−	0.111171i
$923$	0.993581	−	6.91051i	0.0327041	−	0.227462i
$924$	−2.07625	+	4.54636i	−0.0683038	+	0.149564i
$925$	−72.6790	+	21.3405i	−2.38967	+	0.701671i
$926$	8.29070	+	18.1541i	0.272449	+	0.596581i
$927$	9.04638	+	10.4401i	0.297122	+	0.342897i
$928$	−4.29245	−	29.8547i	−0.140907	−	0.980027i
$929$	30.1946	+	8.86592i	0.990651	+	0.290881i	0.736614	−	0.676313i	$-0.236423\pi$
$929$	30.1946	+	8.86592i	0.990651	+	0.290881i	0.254037	+	0.967195i	$0.418242\pi$
$930$	2.77947	−	3.20768i	0.0911425	−	0.105184i
$931$	4.98694	+	3.20491i	0.163441	+	0.105037i
$932$	22.6320	+	14.5447i	0.741336	+	0.476428i
$933$	−10.7226	+	12.3746i	−0.351043	+	0.405125i
$934$	−6.80662	−	1.99860i	−0.222719	−	0.0653963i
$935$	14.4932	+	100.803i	0.473980	+	3.29660i
$936$	2.32206	+	2.67980i	0.0758988	+	0.0875919i
$937$	21.4167	+	46.8960i	0.699653	+	1.53203i	0.840392	+	0.541980i	$0.182325\pi$
$937$	21.4167	+	46.8960i	0.699653	+	1.53203i	−0.140738	+	0.990047i	$0.544948\pi$
$938$	1.94378	−	0.570745i	0.0634667	−	0.0186355i
$939$	−4.05081	+	8.87004i	−0.132193	+	0.289463i
$940$	−8.19893	+	57.0248i	−0.267420	+	1.85994i
$941$	−13.6135	+	8.74887i	−0.443788	+	0.285205i	−0.743389	−	0.668860i	$-0.766783\pi$
$941$	−13.6135	+	8.74887i	−0.443788	+	0.285205i	0.299601	+	0.954065i	$0.403146\pi$
$942$	−2.55850			−0.0833606
$943$	−17.6147	+	17.3002i	−0.573614	+	0.563371i
$944$	−16.4871			−0.536610
$945$	3.49951	−	2.24900i	0.113839	−	0.0731599i
$946$	0.582292	−	4.04993i	0.0189320	−	0.131675i
$947$	3.25994	−	7.13828i	0.105934	−	0.231963i	−0.849241	−	0.528006i	$-0.822940\pi$
$947$	3.25994	−	7.13828i	0.105934	−	0.231963i	0.955175	+	0.296043i	$0.0956671\pi$
$948$	12.3237	−	3.61857i	0.400256	−	0.117526i
$949$	−5.01913	−	10.9904i	−0.162928	−	0.356762i
$950$	30.6583	+	35.3816i	0.994687	+	1.14793i
$951$	−1.08749	−	7.56368i	−0.0352644	−	0.245269i
$952$	−17.1880	−	5.04684i	−0.557065	−	0.163569i
$953$	−9.25055	+	10.6757i	−0.299655	+	0.345820i	−0.885531	−	0.464581i	$-0.846205\pi$
$953$	−9.25055	+	10.6757i	−0.299655	+	0.345820i	0.585876	+	0.810401i	$0.300750\pi$
$954$	0.833685	+	0.535777i	0.0269915	+	0.0173464i
$955$	−3.02749	−	1.94565i	−0.0979671	−	0.0629597i
$956$	−23.0012	+	26.5448i	−0.743912	+	0.858520i
$957$	−15.9914	−	4.69549i	−0.516927	−	0.151784i
$958$	−2.38997	−	16.6226i	−0.0772164	−	0.537052i
$959$	−3.21970	−	3.71574i	−0.103970	−	0.119987i
$960$	−0.448980	−	0.983130i	−0.0144908	−	0.0317304i
$961$	27.3196	−	8.02176i	0.881277	−	0.258766i
$962$	2.52727	−	5.53394i	0.0814823	−	0.178421i
$963$	2.20114	−	15.3092i	0.0709306	−	0.493333i
$964$	−8.00549	+	5.14481i	−0.257839	+	0.165703i
$965$	85.3181			2.74649
$966$	−0.191925	−	3.07217i	−0.00617508	−	0.0988453i
$967$	13.4899			0.433805			0.216903	−	0.976193i	$-0.430405\pi$
$967$	13.4899			0.433805			0.216903	+	0.976193i	$0.430405\pi$
$968$	−2.12059	+	1.36282i	−0.0681585	+	0.0438028i
$969$	−6.56231	+	45.6418i	−0.210812	+	1.46623i
$970$	−6.27758	+	13.7460i	−0.201561	+	0.441357i
$971$	−42.3435	+	12.4332i	−1.35887	+	0.399000i	−0.878364	−	0.477993i	$-0.841364\pi$
$971$	−42.3435	+	12.4332i	−1.35887	+	0.399000i	−0.480504	+	0.876993i	$0.659546\pi$
$972$	0.659696	+	1.44453i	0.0211598	+	0.0463334i
$973$	−0.532168	−	0.614155i	−0.0170605	−	0.0196889i
$974$	−1.71704	−	11.9423i	−0.0550176	−	0.382656i
$975$	−18.1780	−	5.33755i	−0.582163	−	0.170938i
$976$	6.47774	−	7.47571i	0.207347	−	0.239292i
$977$	7.45231	+	4.78931i	0.238420	+	0.153223i	0.654395	−	0.756153i	$-0.272923\pi$
$977$	7.45231	+	4.78931i	0.238420	+	0.153223i	−0.415975	+	0.909376i	$0.636560\pi$
$978$	1.38342	+	0.889069i	0.0442368	+	0.0284293i
$979$	28.2876	−	32.6456i	0.904074	−	1.04336i
$980$	6.33846	+	1.86114i	0.202475	+	0.0594519i
$981$	1.29244	+	8.98908i	0.0412643	+	0.286999i
$982$	−9.46160	−	10.9193i	−0.301932	−	0.348448i
$983$	−9.76635	−	21.3853i	−0.311498	−	0.682086i	0.687530	−	0.726156i	$-0.258695\pi$
$983$	−9.76635	−	21.3853i	−0.311498	−	0.682086i	−0.999028	+	0.0440699i	$0.985968\pi$
$984$	−11.3756	+	3.34019i	−0.362642	+	0.106481i
$985$	−40.8225	+	89.3888i	−1.30071	+	2.84816i
$986$	3.76255	−	26.1691i	0.119824	−	0.833395i
$987$	−7.33655	+	4.71491i	−0.233525	+	0.150077i
$988$	14.4947			0.461138
$989$	−3.31252	−	9.13161i	−0.105332	−	0.290368i
$990$	−8.40317			−0.267070
$991$	35.4981	−	22.8133i	1.12763	−	0.724687i	0.162570	−	0.986697i	$-0.448022\pi$
$991$	35.4981	−	22.8133i	1.12763	−	0.724687i	0.965065	+	0.262010i	$0.0843854\pi$
$992$	−1.28856	+	8.96214i	−0.0409119	+	0.284548i
$993$	−0.888346	+	1.94521i	−0.0281908	+	0.0617293i
$994$	−2.79243	+	0.819930i	−0.0885704	+	0.0260066i
$995$	25.1786	+	55.1334i	0.798215	+	1.74785i
$996$	−6.97186	−	8.04595i	−0.220912	−	0.254946i
$997$	−4.33275	−	30.1349i	−0.137220	−	0.954383i	−0.935809	−	0.352507i	$-0.885329\pi$
$997$	−4.33275	−	30.1349i	−0.137220	−	0.954383i	0.798589	−	0.601876i	$-0.205580\pi$
$998$	−0.648162	−	0.190318i	−0.0205172	−	0.00602440i
$999$	4.03136	−	4.65243i	0.127546	−	0.147196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.e.127.3	✓	60
23.2	even	11	inner	483.2.q.e.232.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.e.127.3	✓	60	1.1	even	1	trivial
483.2.q.e.232.3	yes	60	23.2	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.539950 + 0.347005i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.659696 + 1.44453i) q^{4} +(-3.99137 + 1.17197i) q^{5} +(0.266630 + 0.583838i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.327744 - 2.27951i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.539950 + 0.347005i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.659696 + 1.44453i) q^{4} +(-3.99137 + 1.17197i) q^{5} +(0.266630 + 0.583838i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.327744 - 2.27951i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(1.74846 - 2.01783i) q^{10} +(2.64767 + 1.70155i) q^{11} +(1.33595 + 0.858560i) q^{12} +(1.00830 - 1.16364i) q^{13} +(-0.615841 - 0.180827i) q^{14} +(0.592012 + 4.11753i) q^{15} +(-1.11193 - 1.28323i) q^{16} +(-3.23133 - 7.07562i) q^{17} +(0.615841 - 0.180827i) q^{18} +(2.46258 - 5.39229i) q^{19} +(0.940139 - 6.53881i) q^{20} +(0.841254 - 0.540641i) q^{21} -2.02005 q^{22} +(-4.22974 + 2.26039i) q^{23} -2.30295 q^{24} +(10.3512 - 6.65233i) q^{25} +(-0.140643 + 0.978190i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.52371 + 0.447403i) q^{28} +(-2.19983 - 4.81696i) q^{29} +(-1.74846 - 2.01783i) q^{30} +(0.226234 + 1.57349i) q^{31} +(5.46500 + 1.60467i) q^{32} +(2.06104 - 2.37856i) q^{33} +(4.20003 + 2.69919i) q^{34} +(-3.49951 - 2.24900i) q^{35} +(1.03995 - 1.20016i) q^{36} +(-5.90669 - 1.73436i) q^{37} +(0.541482 + 3.76609i) q^{38} +(-1.00830 - 1.16364i) q^{39} +(3.97966 + 8.71425i) q^{40} +(4.93959 - 1.45040i) q^{41} +(-0.266630 + 0.583838i) q^{42} +(-0.288256 + 2.00486i) q^{43} +(-4.20461 + 2.70214i) q^{44} +4.15987 q^{45} +(1.49948 - 2.68823i) q^{46} -8.72097 q^{47} +(-1.42841 + 0.917986i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-3.28076 + 7.18386i) q^{50} +(-7.46347 + 2.19147i) q^{51} +(1.01574 + 2.22417i) q^{52} +(1.01111 + 1.16688i) q^{53} +(-0.0913433 - 0.635307i) q^{54} +(-12.5620 - 3.68853i) q^{55} +(1.50811 - 1.74045i) q^{56} +(-4.98694 - 3.20491i) q^{57} +(2.85931 + 1.83756i) q^{58} +(6.35867 - 7.33830i) q^{59} +(-6.33846 - 1.86114i) q^{60} +(0.829081 + 5.76639i) q^{61} +(-0.668163 - 0.771101i) q^{62} +(-0.415415 - 0.909632i) q^{63} +(-0.249291 + 0.0731985i) q^{64} +(-2.66074 + 5.82620i) q^{65} +(-0.287484 + 1.99949i) q^{66} +(-2.65525 + 1.70643i) q^{67} +12.3527 q^{68} +(1.63542 + 4.50837i) q^{69} +2.66997 q^{70} +(3.81452 - 2.45144i) q^{71} +(-0.327744 + 2.27951i) q^{72} +(3.25978 - 7.13793i) q^{73} +(3.79115 - 1.11318i) q^{74} +(-5.11149 - 11.1926i) q^{75} +(6.16479 + 7.11455i) q^{76} +(0.447906 + 3.11525i) q^{77} +(0.948218 + 0.278422i) q^{78} +(5.29648 - 6.11247i) q^{79} +(5.94202 + 3.81871i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-2.16384 + 2.49720i) q^{82} +(-6.43249 - 1.88875i) q^{83} +(0.226002 + 1.57188i) q^{84} +(21.1898 + 24.4544i) q^{85} +(-0.540053 - 1.18255i) q^{86} +(-5.08100 + 1.49191i) q^{87} +(3.01094 - 6.59305i) q^{88} +(1.95326 - 13.5852i) q^{89} +(-2.24612 + 1.44350i) q^{90} +1.53971 q^{91} +(-0.474861 - 7.60116i) q^{92} +1.58967 q^{93} +(4.70889 - 3.02622i) q^{94} +(-3.50944 + 24.4087i) q^{95} +(2.36609 - 5.18100i) q^{96} +(-5.43057 + 1.59456i) q^{97} +(-0.266630 - 0.583838i) q^{98} +(-2.06104 - 2.37856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Introduction

L-functions

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