LMFDB - Embedded newform 507.2.m.b.40.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.16
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38165 + 0.587024i) q^{2} +(0.120537 - 0.992709i) q^{3} +(3.55674 + 1.86672i) q^{4} +(-1.58170 + 2.29149i) q^{5} +(0.869820 - 2.29353i) q^{6} +(2.70346 + 2.39506i) q^{7} +(3.70302 + 3.28059i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(2.38165 + 0.587024i) q^{2} +(0.120537 - 0.992709i) q^{3} +(3.55674 + 1.86672i) q^{4} +(-1.58170 + 2.29149i) q^{5} +(0.869820 - 2.29353i) q^{6} +(2.70346 + 2.39506i) q^{7} +(3.70302 + 3.28059i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-5.11221 + 4.52903i) q^{10} +(-2.78452 + 0.686322i) q^{11} +(2.28183 - 3.30580i) q^{12} +(2.66025 - 2.43374i) q^{13} +(5.03274 + 7.29118i) q^{14} +(2.08413 + 1.84638i) q^{15} +(2.32985 + 3.37537i) q^{16} +(-5.27260 - 4.67112i) q^{17} +(-2.17196 - 1.13993i) q^{18} +2.65939 q^{19} +(-9.90328 + 5.19764i) q^{20} +(2.70346 - 2.39506i) q^{21} -7.03463 q^{22} +4.78657 q^{23} +(3.70302 - 3.28059i) q^{24} +(-0.976121 - 2.57382i) q^{25} +(7.76444 - 4.23469i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(5.14461 + 13.5652i) q^{28} +(-2.37767 - 0.586044i) q^{29} +(3.87980 + 5.62086i) q^{30} +(2.09435 - 5.52235i) q^{31} +(0.0588734 + 0.155236i) q^{32} +(0.345681 + 2.84694i) q^{33} +(-9.81543 - 14.2201i) q^{34} +(-9.76431 + 2.40669i) q^{35} +(-3.00666 - 2.66366i) q^{36} +(2.06916 - 5.45593i) q^{37} +(6.33375 + 1.56113i) q^{38} +(-2.09534 - 2.93421i) q^{39} +(-13.3745 + 3.29652i) q^{40} +(0.283872 - 2.33790i) q^{41} +(7.84465 - 4.11719i) q^{42} +(2.80796 + 7.40398i) q^{43} +(-11.1850 - 2.75685i) q^{44} +(2.08413 - 1.84638i) q^{45} +(11.3999 + 2.80983i) q^{46} +(-3.03607 + 1.59345i) q^{47} +(3.63160 - 1.90601i) q^{48} +(0.728643 + 6.00092i) q^{49} +(-0.813884 - 6.70294i) q^{50} +(-5.27260 + 4.67112i) q^{51} +(14.0049 - 3.69025i) q^{52} +(0.354671 + 0.314211i) q^{53} +(-1.39342 + 2.01872i) q^{54} +(2.83157 - 7.46624i) q^{55} +(2.15377 + 17.7379i) q^{56} +(0.320555 - 2.64000i) q^{57} +(-5.31876 - 2.79150i) q^{58} +(3.05944 - 4.43237i) q^{59} +(3.96604 + 10.4576i) q^{60} +(-8.53181 + 7.55852i) q^{61} +(8.22976 - 11.9229i) q^{62} +(-2.05173 - 2.97244i) q^{63} +(-0.939646 - 7.73868i) q^{64} +(1.36917 + 9.94537i) q^{65} +(-0.847931 + 6.98334i) q^{66} +(-13.8525 + 7.27036i) q^{67} +(-10.0336 - 26.4565i) q^{68} +(0.576957 - 4.75167i) q^{69} -24.6679 q^{70} +(0.444934 - 3.66436i) q^{71} +(-2.81032 - 4.07145i) q^{72} +(-6.02299 + 1.48453i) q^{73} +(8.13078 - 11.7795i) q^{74} +(-2.67271 + 0.658764i) q^{75} +(9.45879 + 4.96435i) q^{76} +(-9.17161 - 4.81363i) q^{77} +(-3.26791 - 8.21826i) q^{78} +(-9.45285 + 4.96124i) q^{79} -11.4198 q^{80} +(0.885456 + 0.464723i) q^{81} +(2.04848 - 5.40141i) q^{82} +(-2.01170 - 16.5678i) q^{83} +(14.0864 - 3.47199i) q^{84} +(19.0435 - 4.69380i) q^{85} +(2.34126 + 19.2820i) q^{86} +(-0.868368 + 2.28970i) q^{87} +(-12.5627 - 6.59340i) q^{88} +8.66543 q^{89} +(6.04753 - 3.17399i) q^{90} +(13.0208 - 0.208077i) q^{91} +(17.0246 + 8.93520i) q^{92} +(-5.22964 - 2.74473i) q^{93} +(-8.16625 + 2.01280i) q^{94} +(-4.20637 + 6.09397i) q^{95} +(0.161201 - 0.0397325i) q^{96} +(1.69426 + 2.45456i) q^{97} +(-1.78731 + 14.7198i) q^{98} +2.86785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

Coefficient data

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

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

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

$2$	2.38165	+	0.587024i	1.68408	+	0.415089i	0.961193	−	0.275877i	$-0.0889683\pi$
$2$	2.38165	+	0.587024i	1.68408	+	0.415089i	0.722887	+	0.690966i	$0.242814\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	3.55674	+	1.86672i	1.77837	+	0.933362i
$5$	−1.58170	+	2.29149i	−0.707358	+	1.02479i	0.290337	+	0.956925i	$0.406233\pi$
$5$	−1.58170	+	2.29149i	−0.707358	+	1.02479i	−0.997695	+	0.0678605i	$0.978383\pi$
$6$	0.869820	−	2.29353i	0.355102	−	0.936328i
$7$	2.70346	+	2.39506i	1.02181	+	0.905246i	0.995534	−	0.0944083i	$-0.0300959\pi$
$7$	2.70346	+	2.39506i	1.02181	+	0.905246i	0.0262783	+	0.999655i	$0.491634\pi$
$8$	3.70302	+	3.28059i	1.30922	+	1.15986i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−5.11221	+	4.52903i	−1.61662	+	1.43220i
$11$	−2.78452	+	0.686322i	−0.839563	+	0.206934i	−0.635575	−	0.772039i	$-0.719237\pi$
$11$	−2.78452	+	0.686322i	−0.839563	+	0.206934i	−0.203989	+	0.978973i	$0.565391\pi$
$12$	2.28183	−	3.30580i	0.658708	−	0.954303i
$13$	2.66025	−	2.43374i	0.737820	−	0.674998i
$13$	2.66025	−	2.43374i	0.737820	−	0.674998i
$14$	5.03274	+	7.29118i	1.34506	+	1.94865i
$15$	2.08413	+	1.84638i	0.538120	+	0.476732i
$16$	2.32985	+	3.37537i	0.582463	+	0.843843i
$17$	−5.27260	−	4.67112i	−1.27879	−	1.13291i	−0.984156	−	0.177303i	$-0.943263\pi$
$17$	−5.27260	−	4.67112i	−1.27879	−	1.13291i	−0.294637	−	0.955609i	$-0.595199\pi$
$18$	−2.17196	−	1.13993i	−0.511936	−	0.268685i
$19$	2.65939			0.610107			0.305054	−	0.952335i	$-0.401326\pi$
$19$	2.65939			0.610107			0.305054	+	0.952335i	$0.401326\pi$
$20$	−9.90328	+	5.19764i	−2.21444	+	1.16223i
$21$	2.70346	−	2.39506i	0.589943	−	0.522644i
$22$	−7.03463			−1.49979
$23$	4.78657			0.998068			0.499034	−	0.866582i	$-0.333688\pi$
$23$	4.78657			0.998068			0.499034	+	0.866582i	$0.333688\pi$
$24$	3.70302	−	3.28059i	0.755876	−	0.669648i
$25$	−0.976121	−	2.57382i	−0.195224	−	0.514764i
$26$	7.76444	−	4.23469i	1.52273	−	0.830490i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	5.14461	+	13.5652i	0.972240	+	2.56358i
$29$	−2.37767	−	0.586044i	−0.441523	−	0.108826i	0.0122862	−	0.999925i	$-0.496089\pi$
$29$	−2.37767	−	0.586044i	−0.441523	−	0.108826i	−0.453809	+	0.891099i	$0.649935\pi$
$30$	3.87980	+	5.62086i	0.708351	+	1.02622i
$31$	2.09435	−	5.52235i	0.376157	−	0.991844i	−0.604586	−	0.796540i	$-0.706661\pi$
$31$	2.09435	−	5.52235i	0.376157	−	0.991844i	0.980743	−	0.195304i	$-0.0625693\pi$
$32$	0.0588734	+	0.155236i	0.0104074	+	0.0274422i
$33$	0.345681	+	2.84694i	0.0601754	+	0.495589i
$34$	−9.81543	−	14.2201i	−1.68333	−	2.43873i
$35$	−9.76431	+	2.40669i	−1.65047	+	0.406804i
$36$	−3.00666	−	2.66366i	−0.501109	−	0.443944i
$37$	2.06916	−	5.45593i	0.340168	−	0.896949i	−0.650358	−	0.759627i	$-0.725381\pi$
$37$	2.06916	−	5.45593i	0.340168	−	0.896949i	0.990526	−	0.137322i	$-0.0438495\pi$
$38$	6.33375	+	1.56113i	1.02747	+	0.253248i
$39$	−2.09534	−	2.93421i	−0.335523	−	0.469849i
$40$	−13.3745	+	3.29652i	−2.11470	+	0.521226i
$41$	0.283872	−	2.33790i	0.0443334	−	0.365118i	−0.953612	−	0.301040i	$-0.902666\pi$
$41$	0.283872	−	2.33790i	0.0443334	−	0.365118i	0.997945	−	0.0640781i	$-0.0204107\pi$
$42$	7.84465	−	4.11719i	1.21046	−	0.635296i
$43$	2.80796	+	7.40398i	0.428210	+	1.12910i	0.959451	+	0.281876i	$0.0909566\pi$
$43$	2.80796	+	7.40398i	0.428210	+	1.12910i	−0.531241	+	0.847221i	$0.678274\pi$
$44$	−11.1850	−	2.75685i	−1.68620	−	0.415611i
$45$	2.08413	−	1.84638i	0.310684	−	0.275242i
$46$	11.3999	+	2.80983i	1.68083	+	0.414287i
$47$	−3.03607	+	1.59345i	−0.442856	+	0.232429i	−0.671386	−	0.741108i	$-0.734301\pi$
$47$	−3.03607	+	1.59345i	−0.442856	+	0.232429i	0.228529	+	0.973537i	$0.426608\pi$
$48$	3.63160	−	1.90601i	0.524176	−	0.275109i
$49$	0.728643	+	6.00092i	0.104092	+	0.857274i
$50$	−0.813884	−	6.70294i	−0.115101	−	0.947939i
$51$	−5.27260	+	4.67112i	−0.738312	+	0.654087i
$52$	14.0049	−	3.69025i	1.94214	−	0.511745i
$53$	0.354671	+	0.314211i	0.0487178	+	0.0431602i	0.687130	−	0.726534i	$-0.258870\pi$
$53$	0.354671	+	0.314211i	0.0487178	+	0.0431602i	−0.638413	+	0.769694i	$0.720409\pi$
$54$	−1.39342	+	2.01872i	−0.189621	+	0.274713i
$55$	2.83157	−	7.46624i	0.381809	−	1.00675i
$56$	2.15377	+	17.7379i	0.287810	+	2.37033i
$57$	0.320555	−	2.64000i	0.0424585	−	0.349677i
$58$	−5.31876	−	2.79150i	−0.698388	−	0.366542i
$59$	3.05944	−	4.43237i	0.398306	−	0.577045i	−0.571598	−	0.820534i	$-0.693676\pi$
$59$	3.05944	−	4.43237i	0.398306	−	0.577045i	0.969904	+	0.243488i	$0.0782918\pi$
$60$	3.96604	+	10.4576i	0.512013	+	1.35007i
$61$	−8.53181	+	7.55852i	−1.09239	+	0.967770i	−0.999610	−	0.0279172i	$-0.991113\pi$
$61$	−8.53181	+	7.55852i	−1.09239	+	0.967770i	−0.0927760	+	0.995687i	$0.529574\pi$
$62$	8.22976	−	11.9229i	1.04518	−	1.51421i
$63$	−2.05173	−	2.97244i	−0.258493	−	0.374492i
$64$	−0.939646	−	7.73868i	−0.117456	−	0.967335i
$65$	1.36917	+	9.94537i	0.169825	+	1.23357i
$66$	−0.847931	+	6.98334i	−0.104373	+	0.859589i
$67$	−13.8525	+	7.27036i	−1.69235	+	0.888215i	−0.709297	+	0.704910i	$0.750988\pi$
$67$	−13.8525	+	7.27036i	−1.69235	+	0.888215i	−0.983056	+	0.183306i	$0.941320\pi$
$68$	−10.0336	−	26.4565i	−1.21675	−	3.20832i
$69$	0.576957	−	4.75167i	0.0694575	−	0.572034i
$70$	−24.6679			−2.94838
$71$	0.444934	−	3.66436i	0.0528040	−	0.434880i	−0.942201	−	0.335050i	$-0.891247\pi$
$71$	0.444934	−	3.66436i	0.0528040	−	0.434880i	0.995004	−	0.0998302i	$-0.0318300\pi$
$72$	−2.81032	−	4.07145i	−0.331200	−	0.479825i
$73$	−6.02299	+	1.48453i	−0.704938	+	0.173752i	−0.575459	−	0.817831i	$-0.695177\pi$
$73$	−6.02299	+	1.48453i	−0.704938	+	0.173752i	−0.129479	+	0.991582i	$0.541330\pi$
$74$	8.13078	−	11.7795i	0.945184	−	1.36934i
$75$	−2.67271	+	0.658764i	−0.308618	+	0.0760675i
$76$	9.45879	+	4.96435i	1.08500	+	0.569451i
$77$	−9.17161	−	4.81363i	−1.04520	−	0.548564i
$78$	−3.26791	−	8.21826i	−0.370018	−	0.930535i
$79$	−9.45285	+	4.96124i	−1.06353	+	0.558183i	−0.903350	−	0.428905i	$-0.858900\pi$
$79$	−9.45285	+	4.96124i	−1.06353	+	0.558183i	−0.160179	+	0.987088i	$0.551207\pi$
$80$	−11.4198			−1.27677
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	2.04848	−	5.40141i	0.226217	−	0.596486i
$83$	−2.01170	−	16.5678i	−0.220812	−	1.81855i	−0.508761	−	0.860908i	$-0.669896\pi$
$83$	−2.01170	−	16.5678i	−0.220812	−	1.81855i	0.287949	−	0.957646i	$-0.407027\pi$
$84$	14.0864	−	3.47199i	1.53695	−	0.378825i
$85$	19.0435	−	4.69380i	2.06556	−	0.509114i
$86$	2.34126	+	19.2820i	0.252465	+	2.07923i
$87$	−0.868368	+	2.28970i	−0.0930988	+	0.245481i
$88$	−12.5627	−	6.59340i	−1.33918	−	0.702858i
$89$	8.66543			0.918534			0.459267	−	0.888298i	$-0.348112\pi$
$89$	8.66543			0.918534			0.459267	+	0.888298i	$0.348112\pi$
$90$	6.04753	−	3.17399i	0.637466	−	0.334568i
$91$	13.0208	−	0.208077i	1.36495	−	0.0218124i
$92$	17.0246	+	8.93520i	1.77494	+	0.931559i
$93$	−5.22964	−	2.74473i	−0.542289	−	0.284615i
$94$	−8.16625	+	2.01280i	−0.842284	+	0.207604i
$95$	−4.20637	+	6.09397i	−0.431564	+	0.625229i
$96$	0.161201	−	0.0397325i	0.0164525	−	0.00405518i
$97$	1.69426	+	2.45456i	0.172026	+	0.249223i	0.899508	−	0.436904i	$-0.143925\pi$
$97$	1.69426	+	2.45456i	0.172026	+	0.249223i	−0.727482	+	0.686127i	$0.759310\pi$
$98$	−1.78731	+	14.7198i	−0.180545	+	1.48693i
$99$	2.86785			0.288230
$100$	1.33280	−	10.9766i	0.133280	−	1.09766i
$101$	4.13166	+	10.8943i	0.411115	+	1.08402i	0.967450	+	0.253064i	$0.0814382\pi$
$101$	4.13166	+	10.8943i	0.411115	+	1.08402i	−0.556334	+	0.830959i	$0.687793\pi$
$102$	−15.2995	+	8.02982i	−1.51488	+	0.795071i
$103$	0.548693	−	4.51889i	0.0540643	−	0.445260i	−0.940391	−	0.340096i	$-0.889540\pi$
$103$	0.548693	−	4.51889i	0.0540643	−	0.445260i	0.994455	−	0.105163i	$-0.0335366\pi$
$104$	17.8351	−	0.285011i	1.74887	−	0.0279476i
$105$	1.21218	+	9.98321i	0.118297	+	0.974262i
$106$	0.660252	+	0.956541i	0.0641294	+	0.0929075i
$107$	−10.7616	+	15.5908i	−1.04036	+	1.50722i	−0.189461	+	0.981888i	$0.560674\pi$
$107$	−10.7616	+	15.5908i	−1.04036	+	1.50722i	−0.850898	+	0.525331i	$0.823941\pi$
$108$	−3.00666	+	2.66366i	−0.289316	+	0.256311i
$109$	2.64783	+	6.98176i	0.253616	+	0.668732i	0.999995	+	0.00320976i	$0.00102170\pi$
$109$	2.64783	+	6.98176i	0.253616	+	0.668732i	−0.746378	+	0.665522i	$0.768209\pi$
$110$	11.1267	−	16.1198i	1.06089	−	1.53696i
$111$	−5.16674	−	2.71171i	−0.490405	−	0.257385i
$112$	−1.78555	+	14.7053i	−0.168718	+	1.38952i
$113$	1.76907	+	14.5696i	0.166420	+	1.37059i	0.801431	+	0.598087i	$0.204072\pi$
$113$	1.76907	+	14.5696i	0.166420	+	1.37059i	−0.635011	+	0.772503i	$0.719005\pi$
$114$	2.31319	−	6.09939i	0.216651	−	0.571260i
$115$	−7.57092	+	10.9684i	−0.705992	+	1.02281i
$116$	−7.36280	−	6.52287i	−0.683618	−	0.605633i
$117$	−3.16538	+	1.72638i	−0.292639	+	0.159604i
$118$	9.88843	−	8.76038i	0.910303	−	0.806458i
$119$	−3.06668	−	25.2564i	−0.281122	−	2.31525i
$120$	1.66037	+	13.6743i	0.151570	+	1.24829i
$121$	−2.45752	+	1.28981i	−0.223411	+	0.117255i
$122$	−24.7568	+	12.9934i	−2.24138	+	1.17637i
$123$	−2.28663	−	0.563605i	−0.206179	−	0.0508185i
$124$	17.7578	−	15.7320i	1.59470	−	1.41278i
$125$	−6.07548	−	1.49747i	−0.543408	−	0.133938i
$126$	−3.14160	−	8.28373i	−0.279876	−	0.737973i
$127$	12.5355	−	6.57913i	1.11234	−	0.583804i	0.194564	−	0.980890i	$-0.437671\pi$
$127$	12.5355	−	6.57913i	1.11234	−	0.583804i	0.917781	+	0.397086i	$0.129979\pi$
$128$	2.34491	−	19.3121i	0.207263	−	1.70696i
$129$	7.68846	−	1.89503i	0.676931	−	0.166849i
$130$	−2.57728	+	24.4901i	−0.226042	+	2.14793i
$131$	11.5763	+	2.85329i	1.01142	+	0.249293i	0.710003	−	0.704199i	$-0.248693\pi$
$131$	11.5763	+	2.85329i	1.01142	+	0.249293i	0.301419	+	0.953492i	$0.402540\pi$
$132$	−4.08495	+	10.7711i	−0.355549	+	0.937507i
$133$	7.18957	+	6.36940i	0.623415	+	0.552297i
$134$	−37.2597	+	9.18369i	−3.21875	+	0.793350i
$135$	−1.58170	−	2.29149i	−0.136131	−	0.197220i
$136$	−4.20053	−	34.5945i	−0.360193	−	2.96645i
$137$	1.85238	+	4.88432i	0.158259	+	0.417296i	0.990569	−	0.137015i	$-0.0437510\pi$
$137$	1.85238	+	4.88432i	0.158259	+	0.417296i	−0.832309	+	0.554311i	$0.812982\pi$
$138$	4.16345	−	10.9781i	0.354417	−	0.934520i
$139$	−2.91106	−	4.21740i	−0.246913	−	0.357715i	0.679857	−	0.733345i	$-0.262042\pi$
$139$	−2.91106	−	4.21740i	−0.246913	−	0.357715i	−0.926770	+	0.375630i	$0.877426\pi$
$140$	−39.2218	−	9.66730i	−3.31484	−	0.817036i
$141$	1.21588	+	3.20600i	0.102395	+	0.269994i
$142$	3.21074	−	8.46604i	0.269440	−	0.710454i
$143$	−5.73717	+	8.60257i	−0.479766	+	0.719383i
$144$	−1.45437	−	3.83486i	−0.121198	−	0.319572i
$145$	5.10368	−	4.52147i	0.423838	−	0.375487i
$146$	−15.2161			−1.25929
$147$	6.04499			0.498583
$148$	17.5442	−	15.5428i	1.44212	−	1.27761i
$149$	−1.05924	+	0.555930i	−0.0867761	+	0.0455436i	−0.507553	−	0.861621i	$-0.669450\pi$
$149$	−1.05924	+	0.555930i	−0.0867761	+	0.0455436i	0.420777	+	0.907164i	$0.361758\pi$
$150$	−6.75217			−0.551312
$151$	18.5192	+	9.71963i	1.50707	+	0.790972i	0.997582	−	0.0695040i	$-0.0221417\pi$
$151$	18.5192	+	9.71963i	1.50707	+	0.790972i	0.509490	+	0.860476i	$0.329834\pi$
$152$	9.84780	+	8.72439i	0.798762	+	0.707641i
$153$	4.00152	+	5.79720i	0.323504	+	0.468676i
$154$	−19.0178	−	16.8483i	−1.53250	−	1.35768i
$155$	9.34177	+	13.5339i	0.750349	+	1.08707i
$156$	−1.97523	−	14.3476i	−0.158145	−	1.14873i
$157$	3.82014	−	5.53443i	0.304881	−	0.441696i	−0.640358	−	0.768077i	$-0.721214\pi$
$157$	3.82014	−	5.53443i	0.304881	−	0.441696i	0.945238	+	0.326381i	$0.105829\pi$
$158$	−25.4257	+	6.26688i	−2.02276	+	0.498566i
$159$	0.354671	−	0.314211i	0.0281272	−	0.0249186i
$160$	−0.448843	−	0.110630i	−0.0354841	−	0.00874605i
$161$	12.9403	+	11.4641i	1.01984	+	0.903498i
$162$	1.83604	+	1.62659i	0.144253	+	0.127797i
$163$	−3.50715	+	9.24760i	−0.274701	+	0.724328i	0.724677	+	0.689088i	$0.241989\pi$
$163$	−3.50715	+	9.24760i	−0.274701	+	0.724328i	−0.999379	+	0.0352398i	$0.988780\pi$
$164$	5.37387	−	7.78539i	0.419628	−	0.607937i
$165$	−7.07050	−	3.71088i	−0.550438	−	0.288892i
$166$	4.93454	−	40.6396i	0.382995	−	3.15425i
$167$	−17.8158	−	4.39120i	−1.37863	−	0.339801i	−0.520774	−	0.853694i	$-0.674357\pi$
$167$	−17.8158	−	4.39120i	−1.37863	−	0.339801i	−0.857854	+	0.513893i	$0.828203\pi$
$168$	17.8682			1.37856
$169$	1.15382	−	12.9487i	0.0887555	−	0.996053i
$170$	48.1103			3.68989
$171$	−2.58212	−	0.636435i	−0.197459	−	0.0486694i
$172$	−3.83399	+	31.5757i	−0.292339	+	2.40763i
$173$	16.7307	+	8.78094i	1.27201	+	0.667603i	0.959338	−	0.282258i	$-0.0910835\pi$
$173$	16.7307	+	8.78094i	1.27201	+	0.667603i	0.312672	+	0.949861i	$0.398776\pi$
$174$	−3.41226	+	4.94350i	−0.258682	+	0.374766i
$175$	3.52554	−	9.29608i	0.266506	−	0.702718i
$176$	−8.80410	−	7.79976i	−0.663634	−	0.587929i
$177$	−4.03128	−	3.57140i	−0.303009	−	0.268443i
$178$	20.6380	+	5.08681i	1.54688	+	0.381273i
$179$	13.1568	−	11.6559i	0.983385	−	0.871203i	−0.00829069	−	0.999966i	$-0.502639\pi$
$179$	13.1568	−	11.6559i	0.983385	−	0.871203i	0.991675	+	0.128763i	$0.0411006\pi$
$180$	10.8594	−	2.67660i	0.809411	−	0.199502i
$181$	9.64201	−	13.9689i	0.716685	−	1.03830i	−0.280239	−	0.959930i	$-0.590414\pi$
$181$	9.64201	−	13.9689i	0.716685	−	1.03830i	0.996925	−	0.0783675i	$-0.0249708\pi$
$182$	31.1332	+	7.14796i	2.30774	+	0.529842i
$183$	6.47502	+	9.38068i	0.478647	+	0.693440i
$184$	17.7248	+	15.7028i	1.30669	+	1.15762i
$185$	9.22941	+	13.3711i	0.678560	+	0.983064i
$186$	−10.8440	−	9.60690i	−0.795117	−	0.704412i
$187$	17.8875	+	9.38810i	1.30807	+	0.686526i
$188$	−13.7731			−1.00450
$189$	−3.19808	+	1.67848i	−0.232626	+	0.122091i
$190$	−13.5954	+	12.0445i	−0.986314	+	0.873798i
$191$	−2.65241			−0.191921			−0.0959607	−	0.995385i	$-0.530592\pi$
$191$	−2.65241			−0.191921			−0.0959607	+	0.995385i	$0.530592\pi$
$192$	−7.79552			−0.562593
$193$	14.9642	−	13.2571i	1.07715	−	0.954269i	0.0780585	−	0.996949i	$-0.475128\pi$
$193$	14.9642	−	13.2571i	1.07715	−	0.954269i	0.999089	+	0.0426795i	$0.0135894\pi$
$194$	2.59425	+	6.84048i	0.186257	+	0.491118i
$195$	10.0379	−	0.160409i	0.718829	−	0.0114871i
$196$	−8.61046	+	22.7039i	−0.615033	+	1.62171i
$197$	0.421759	+	1.11209i	0.0300491	+	0.0792329i	0.949201	−	0.314670i	$-0.101894\pi$
$197$	0.421759	+	1.11209i	0.0300491	+	0.0792329i	−0.919152	+	0.393903i	$0.871125\pi$
$198$	6.83021	+	1.68350i	0.485402	+	0.119641i
$199$	−15.4600	−	22.3977i	−1.09593	−	1.58773i	−0.764948	−	0.644092i	$-0.777235\pi$
$199$	−15.4600	−	22.3977i	−1.09593	−	1.58773i	−0.330982	−	0.943637i	$-0.607380\pi$
$200$	4.82905	−	12.7332i	0.341465	−	0.900370i
$201$	5.54761	+	14.6279i	0.391298	+	1.03177i
$202$	3.44496	+	28.3718i	0.242386	+	1.99623i
$203$	−5.02434	−	7.27901i	−0.352639	−	0.510886i
$204$	−27.4730	+	6.77148i	−1.92349	+	0.474098i
$205$	4.90826	+	4.34834i	0.342808	+	0.303701i
$206$	3.95949	−	10.4403i	0.275871	−	0.727411i
$207$	−4.64748	−	1.14550i	−0.323022	−	0.0796178i
$208$	14.4128	+	3.30907i	0.999345	+	0.229443i
$209$	−7.40513	+	1.82520i	−0.512223	+	0.126252i
$210$	−2.97339	+	24.4881i	−0.205184	+	1.68984i
$211$	−15.8856	+	8.33743i	−1.09361	+	0.573972i	−0.912329	−	0.409458i	$-0.865718\pi$
$211$	−15.8856	+	8.33743i	−1.09361	+	0.573972i	−0.181284	+	0.983431i	$0.558025\pi$
$212$	0.674929	+	1.77964i	0.0463543	+	0.122226i
$213$	−3.58401	−	0.883380i	−0.245573	−	0.0605282i
$214$	−34.7824	+	30.8145i	−2.37768	+	2.10644i
$215$	−21.4075	−	5.27647i	−1.45998	−	0.359852i
$216$	−4.38052	+	2.29907i	−0.298056	+	0.156432i
$217$	18.8883	−	9.91337i	1.28222	−	0.672963i
$218$	2.20775	+	18.1825i	0.149528	+	1.23147i
$219$	0.747719	+	6.15802i	0.0505262	+	0.416121i
$220$	24.0086	−	21.2698i	1.61866	−	1.43401i
$221$	−25.3947	+	0.405816i	−1.70823	+	0.0272982i
$222$	−10.7135	−	9.49135i	−0.719045	−	0.637018i
$223$	5.80179	−	8.40534i	0.388517	−	0.562863i	−0.579110	−	0.815249i	$-0.696600\pi$
$223$	5.80179	−	8.40534i	0.388517	−	0.562863i	0.967627	+	0.252386i	$0.0812152\pi$
$224$	−0.212638	+	0.560681i	−0.0142075	+	0.0374621i
$225$	0.331801	+	2.73263i	0.0221201	+	0.182175i
$226$	−4.33939	+	35.7381i	−0.288652	+	2.37726i
$227$	13.8200	+	7.25331i	0.917267	+	0.481419i	0.856159	−	0.516712i	$-0.172844\pi$
$227$	13.8200	+	7.25331i	0.917267	+	0.481419i	0.0611082	+	0.998131i	$0.480537\pi$
$228$	6.06829	−	8.79143i	0.401882	−	0.582227i
$229$	−1.74279	−	4.59535i	−0.115167	−	0.303669i	0.865023	−	0.501733i	$-0.167304\pi$
$229$	−1.74279	−	4.59535i	−0.115167	−	0.303669i	−0.980189	+	0.198064i	$0.936535\pi$
$230$	−24.4700	+	21.6785i	−1.61350	+	1.42944i
$231$	−5.88405	+	8.52452i	−0.387142	+	0.560872i
$232$	−6.88201	−	9.97031i	−0.451826	−	0.654583i
$233$	0.387817	+	3.19396i	0.0254067	+	0.209243i	0.999884	−	0.0152438i	$-0.00485243\pi$
$233$	0.387817	+	3.19396i	0.0254067	+	0.209243i	−0.974477	+	0.224487i	$0.927929\pi$
$234$	−8.55224	+	2.25348i	−0.559078	+	0.147315i
$235$	1.15078	−	9.47749i	0.0750683	−	0.618243i
$236$	19.1557	−	10.0537i	1.24693	−	0.654438i
$237$	3.78565	+	9.98194i	0.245904	+	0.648397i
$238$	7.52233	−	61.9520i	0.487601	−	4.01575i
$239$	7.59980			0.491590			0.245795	−	0.969322i	$-0.420951\pi$
$239$	7.59980			0.491590			0.245795	+	0.969322i	$0.420951\pi$
$240$	−1.37650	+	11.3365i	−0.0888527	+	0.731768i
$241$	−8.34146	−	12.0847i	−0.537320	−	0.778443i	0.456467	−	0.889741i	$-0.349115\pi$
$241$	−8.34146	−	12.0847i	−0.537320	−	0.778443i	−0.993787	+	0.111297i	$0.964499\pi$
$242$	−6.61010	+	1.62924i	−0.424914	+	0.104732i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	−44.4551	+	10.9572i	−2.84595	+	0.701463i
$245$	−14.9035	−	7.82198i	−0.952152	−	0.499728i
$246$	−5.11511	−	2.68462i	−0.326127	−	0.171165i
$247$	7.07465	−	6.47227i	0.450149	−	0.411821i
$248$	25.8720	−	13.5787i	1.64287	−	0.862247i
$249$	−16.6895			−1.05765
$250$	−13.5906	−	7.13291i	−0.859546	−	0.451125i
$251$	−0.800011	+	2.10946i	−0.0504962	+	0.133148i	−0.957891	−	0.287131i	$-0.907298\pi$
$251$	−0.800011	+	2.10946i	−0.0504962	+	0.133148i	0.907395	+	0.420279i	$0.138068\pi$
$252$	−1.74875	−	14.4022i	−0.110161	−	0.907255i
$253$	−13.3283	+	3.28513i	−0.837942	+	0.206534i
$254$	33.7172	−	8.31056i	2.11561	−	0.521451i
$255$	−2.36414	−	19.4704i	−0.148048	−	1.21928i
$256$	11.3927	−	30.0401i	0.712045	−	1.87751i
$257$	−23.8697	−	12.5278i	−1.48895	−	0.781461i	−0.492885	−	0.870095i	$-0.664058\pi$
$257$	−23.8697	−	12.5278i	−1.48895	−	0.781461i	−0.996064	+	0.0886341i	$0.971750\pi$
$258$	19.4236			1.20926
$259$	18.6612	−	9.79413i	1.15955	−	0.608578i
$260$	−13.6955	+	37.9290i	−0.849356	+	2.35226i
$261$	2.16833	+	1.13803i	0.134216	+	0.0704422i
$262$	25.8956	+	13.5911i	1.59984	+	0.839660i
$263$	−7.58890	+	1.87050i	−0.467952	+	0.115340i	−0.466239	−	0.884659i	$-0.654391\pi$
$263$	−7.58890	+	1.87050i	−0.467952	+	0.115340i	−0.00171268	+	0.999999i	$0.500545\pi$
$264$	−8.05958	+	11.6763i	−0.496033	+	0.718628i
$265$	−1.28099	+	0.315737i	−0.0786909	+	0.0193956i
$266$	13.3840	+	19.3901i	0.820628	+	1.18889i
$267$	1.04450	−	8.60225i	0.0639225	−	0.526449i
$268$	−62.8416			−3.83866
$269$	−2.96257	+	24.3990i	−0.180631	+	1.48763i	0.567110	+	0.823642i	$0.308061\pi$
$269$	−2.96257	+	24.3990i	−0.180631	+	1.48763i	−0.747741	+	0.663990i	$0.768862\pi$
$270$	−2.42190	−	6.38602i	−0.147392	−	0.388641i
$271$	2.30081	−	1.20756i	0.139764	−	0.0733539i	−0.393392	−	0.919371i	$-0.628698\pi$
$271$	2.30081	−	1.20756i	0.139764	−	0.0733539i	0.533156	+	0.846017i	$0.321006\pi$
$272$	3.48238	−	28.6800i	0.211151	−	1.73898i
$273$	1.36293	−	12.9510i	0.0824880	−	0.783828i
$274$	1.54450	+	12.7201i	0.0933069	+	0.768451i
$275$	4.48449	+	6.49691i	0.270425	+	0.391778i
$276$	10.9221	−	15.8234i	0.657436	−	0.952460i
$277$	−21.3595	+	18.9228i	−1.28337	+	1.13696i	−0.300273	+	0.953853i	$0.597078\pi$
$277$	−21.3595	+	18.9228i	−1.28337	+	1.13696i	−0.983093	+	0.183109i	$0.941384\pi$
$278$	−4.45741	−	11.7532i	−0.267338	−	0.704912i
$279$	−3.35508	+	4.86067i	−0.200863	+	0.291001i
$280$	−44.0528	−	23.1207i	−2.63266	−	1.38173i
$281$	−1.47304	+	12.1316i	−0.0878741	+	0.723708i	0.880472	+	0.474098i	$0.157226\pi$
$281$	−1.47304	+	12.1316i	−0.0878741	+	0.723708i	−0.968346	+	0.249610i	$0.919697\pi$
$282$	1.01379	+	8.34932i	0.0603704	+	0.497195i
$283$	−2.72798	+	7.19309i	−0.162162	+	0.427585i	−0.991327	−	0.131418i	$-0.958047\pi$
$283$	−2.72798	+	7.19309i	−0.162162	+	0.427585i	0.829165	+	0.559003i	$0.188816\pi$
$284$	8.42287	−	12.2026i	0.499805	−	0.724093i
$285$	5.54252	+	4.91024i	0.328311	+	0.290858i
$286$	−18.7138	+	17.1205i	−1.10657	+	1.01235i
$287$	6.36683	−	5.64052i	0.375822	−	0.332949i
$288$	−0.0200121	−	0.164815i	−0.00117923	−	0.00971181i
$289$	3.93186	+	32.3818i	0.231286	+	1.90481i
$290$	14.8094	−	7.77257i	0.869637	−	0.456421i
$291$	2.64089	−	1.38605i	0.154812	−	0.0812514i
$292$	−24.1935	−	5.96315i	−1.41582	−	0.348967i
$293$	−19.2560	+	17.0593i	−1.12495	+	0.996615i	−0.124956	+	0.992162i	$0.539879\pi$
$293$	−19.2560	+	17.0593i	−1.12495	+	0.996615i	−0.999990	+	0.00445252i	$0.998583\pi$
$294$	14.3971	+	3.54856i	0.839653	+	0.206956i
$295$	5.31760	+	14.0214i	0.309603	+	0.816355i
$296$	25.5608	−	13.4154i	1.48569	−	0.779752i
$297$	0.345681	−	2.84694i	0.0200585	−	0.165196i
$298$	−2.84907	+	0.702234i	−0.165042	+	0.0406793i
$299$	12.7335	−	11.6493i	0.736394	−	0.673694i
$300$	−10.7359	−	2.64616i	−0.619836	−	0.152776i
$301$	−10.1417	+	26.7416i	−0.584561	+	1.54136i
$302$	38.4006	+	34.0200i	2.20971	+	1.95763i
$303$	11.3129	−	2.78837i	0.649908	−	0.160188i
$304$	6.19600	+	8.97645i	0.355365	+	0.514835i
$305$	−3.82551	−	31.5059i	−0.219048	−	1.80402i
$306$	6.12712	+	16.1559i	0.350264	+	0.923570i
$307$	−2.50590	+	6.60752i	−0.143019	+	0.377111i	−0.987317	−	0.158764i	$-0.949249\pi$
$307$	−2.50590	+	6.60752i	−0.143019	+	0.377111i	0.844297	+	0.535875i	$0.180018\pi$
$308$	−23.6353	−	34.2417i	−1.34675	−	1.95110i
$309$	−4.41981	−	1.08938i	−0.251434	−	0.0619729i
$310$	14.3041	+	37.7168i	0.812419	+	2.14217i
$311$	−1.69771	+	4.47648i	−0.0962680	+	0.253838i	−0.974496	−	0.224404i	$-0.927957\pi$
$311$	−1.69771	+	4.47648i	−0.0962680	+	0.253838i	0.878228	+	0.478242i	$0.158726\pi$
$312$	1.86685	−	17.7394i	0.105689	−	1.00429i
$313$	5.08916	+	13.4190i	0.287656	+	0.758488i	0.998480	+	0.0551172i	$0.0175533\pi$
$313$	5.08916	+	13.4190i	0.287656	+	0.758488i	−0.710823	+	0.703370i	$0.751678\pi$
$314$	12.3471	−	10.9386i	0.696787	−	0.617299i
$315$	10.0565			0.566622
$316$	−42.8826			−2.41234
$317$	10.6744	−	9.45671i	0.599535	−	0.531142i	−0.307854	−	0.951434i	$-0.599611\pi$
$317$	10.6744	−	9.45671i	0.599535	−	0.531142i	0.907389	+	0.420292i	$0.138072\pi$
$318$	1.02915	−	0.540140i	0.0577119	−	0.0302896i
$319$	7.02289			0.393206
$320$	19.2193	+	10.0871i	1.07439	+	0.563886i
$321$	14.1800	+	12.5624i	0.791448	+	0.701162i
$322$	24.0895	+	34.8997i	1.34246	+	1.94489i
$323$	−14.0219	−	12.4223i	−0.780201	−	0.691198i
$324$	2.28183	+	3.30580i	0.126768	+	0.183656i
$325$	−8.86073	−	4.47137i	−0.491505	−	0.248027i
$326$	−13.7814	+	19.9658i	−0.763279	+	1.10580i
$327$	7.25002	−	1.78697i	0.400927	−	0.0988196i
$328$	8.72087	−	7.72601i	0.481529	−	0.426598i
$329$	−12.0243	−	2.96373i	−0.662921	−	0.163395i
$330$	−14.6611	−	12.9886i	−0.807065	−	0.714998i
$331$	−15.3521	−	13.6008i	−0.843828	−	0.747566i	0.125825	−	0.992052i	$-0.459842\pi$
$331$	−15.3521	−	13.6008i	−0.843828	−	0.747566i	−0.969653	+	0.244486i	$0.921381\pi$
$332$	23.7724	−	62.6828i	1.30468	−	3.44016i
$333$	−3.31472	+	4.80221i	−0.181646	+	0.263159i
$334$	−39.8533	−	20.9166i	−2.18067	−	1.14451i
$335$	5.25058	−	43.2424i	0.286870	−	2.36258i
$336$	14.3829	+	3.54506i	0.784650	+	0.193399i
$337$	6.69909			0.364923			0.182461	−	0.983213i	$-0.441594\pi$
$337$	6.69909			0.364923			0.182461	+	0.983213i	$0.441594\pi$
$338$	10.3492	−	30.1619i	0.562922	−	1.64059i
$339$	14.6766			0.797122
$340$	76.4948	+	18.8543i	4.14852	+	1.02252i
$341$	−2.04165	+	16.8145i	−0.110561	+	0.910555i
$342$	−5.77610	−	3.03153i	−0.312336	−	0.163926i
$343$	1.95941	−	2.83870i	0.105798	−	0.153275i
$344$	−13.8915	+	36.6289i	−0.748979	+	1.97490i
$345$	9.97582	+	8.83781i	0.537080	+	0.475812i
$346$	34.6920	+	30.7344i	1.86505	+	1.65229i
$347$	−25.8726	−	6.37702i	−1.38891	−	0.342337i	−0.527204	−	0.849738i	$-0.676760\pi$
$347$	−25.8726	−	6.37702i	−1.38891	−	0.342337i	−0.861710	+	0.507402i	$0.830606\pi$
$348$	−7.36280	+	6.52287i	−0.394687	+	0.349662i
$349$	2.49561	−	0.615112i	0.133587	−	0.0329262i	−0.171955	−	0.985105i	$-0.555008\pi$
$349$	2.49561	−	0.615112i	0.133587	−	0.0329262i	0.305542	+	0.952179i	$0.401162\pi$
$350$	13.8536	−	20.0704i	0.740507	−	1.07281i
$351$	1.33225	+	3.35039i	0.0711102	+	0.178831i
$352$	−0.270476	−	0.391852i	−0.0144164	−	0.0208858i
$353$	13.2917	+	11.7754i	0.707446	+	0.626743i	0.938129	−	0.346286i	$-0.112557\pi$
$353$	13.2917	+	11.7754i	0.707446	+	0.626743i	−0.230683	+	0.973029i	$0.574096\pi$
$354$	−7.50459	−	10.8723i	−0.398864	−	0.577855i
$355$	7.69309	+	6.81549i	0.408307	+	0.361728i
$356$	30.8207	+	16.1760i	1.63349	+	0.857324i
$357$	−25.4419			−1.34653
$358$	38.1772	−	20.0369i	2.01773	−	1.05898i
$359$	18.4316	−	16.3290i	0.972784	−	0.861811i	−0.0176438	−	0.999844i	$-0.505616\pi$
$359$	18.4316	−	16.3290i	0.972784	−	0.861811i	0.990428	+	0.138033i	$0.0440780\pi$
$360$	13.7748			0.725995
$361$	−11.9276			−0.627769
$362$	31.1639	−	27.6088i	1.63794	−	1.45109i
$363$	0.984182	+	2.59507i	0.0516561	+	0.136206i
$364$	46.7001	+	23.5662i	2.44775	+	1.23520i
$365$	6.12478	−	16.1497i	0.320586	−	0.845315i
$366$	9.91454	+	26.1425i	0.518241	+	1.36649i
$367$	−15.0801	−	3.71691i	−0.787176	−	0.194021i	−0.174816	−	0.984601i	$-0.555933\pi$
$367$	−15.0801	−	3.71691i	−0.787176	−	0.194021i	−0.612359	+	0.790580i	$0.709779\pi$
$368$	11.1520	+	16.1565i	0.581338	+	0.842213i
$369$	−0.835118	+	2.20203i	−0.0434745	+	0.114633i
$370$	14.1321	+	37.2632i	0.734691	+	1.93722i
$371$	0.206286	+	1.69891i	0.0107098	+	0.0882032i
$372$	−13.4768	−	19.5246i	−0.698742	−	1.01230i
$373$	−17.8719	+	4.40503i	−0.925371	+	0.228084i	−0.673082	−	0.739568i	$-0.735030\pi$
$373$	−17.8719	+	4.40503i	−0.925371	+	0.228084i	−0.252290	+	0.967652i	$0.581184\pi$
$374$	37.0908	+	32.8596i	1.91792	+	1.69913i
$375$	−2.21887	+	5.85069i	−0.114582	+	0.302128i
$376$	−16.4701	−	4.05952i	−0.849381	−	0.209354i
$377$	−7.75148	+	4.22762i	−0.399221	+	0.217733i
$378$	−8.60201	+	2.12020i	−0.442439	+	0.109052i
$379$	−0.523032	+	4.30755i	−0.0268663	+	0.221264i	−0.999958	−	0.00915376i	$-0.997086\pi$
$379$	−0.523032	+	4.30755i	−0.0268663	+	0.221264i	0.973092	+	0.230418i	$0.0740093\pi$
$380$	−26.3367	+	13.8226i	−1.35105	+	0.709084i
$381$	−5.02018	−	13.2371i	−0.257191	−	0.678158i
$382$	−6.31710	−	1.55703i	−0.323211	−	0.0796643i
$383$	2.45158	−	2.17191i	0.125270	−	0.110980i	−0.598162	−	0.801375i	$-0.704102\pi$
$383$	2.45158	−	2.17191i	0.125270	−	0.110980i	0.723432	+	0.690396i	$0.242564\pi$
$384$	−18.8886	−	4.65562i	−0.963905	−	0.237581i
$385$	25.5371	−	13.4029i	1.30149	−	0.683076i
$386$	43.4218	−	22.7895i	2.21011	−	1.15995i
$387$	−0.954477	−	7.86082i	−0.0485188	−	0.399588i
$388$	1.44407	+	11.8930i	0.0733115	+	0.603774i
$389$	−12.4631	+	11.0414i	−0.631906	+	0.559820i	−0.917104	−	0.398649i	$-0.869479\pi$
$389$	−12.4631	+	11.0414i	−0.631906	+	0.559820i	0.285198	+	0.958469i	$0.407941\pi$
$390$	24.0009	+	5.51045i	1.21533	+	0.279032i
$391$	−25.2377	−	22.3586i	−1.27632	−	1.13072i
$392$	−16.9884	+	24.6119i	−0.858043	+	1.24309i
$393$	4.22785	−	11.1479i	0.213267	−	0.562339i
$394$	0.351660	+	2.89618i	0.0177164	+	0.145908i
$395$	3.58296	−	29.5083i	0.180278	−	1.48472i
$396$	10.2002	+	5.35348i	0.512580	+	0.269023i
$397$	−18.8601	+	27.3236i	−0.946564	+	1.37133i	−0.0181300	+	0.999836i	$0.505771\pi$
$397$	−18.8601	+	27.3236i	−0.946564	+	1.37133i	−0.928434	+	0.371498i	$0.878844\pi$
$398$	−23.6723	−	62.4188i	−1.18659	−	3.12877i
$399$	7.18957	−	6.36940i	0.359929	−	0.318869i
$400$	6.41338	−	9.29139i	0.320669	−	0.464569i
$401$	9.95824	+	14.4270i	0.497291	+	0.720450i	0.988605	−	0.150532i	$-0.0480987\pi$
$401$	9.95824	+	14.4270i	0.497291	+	0.720450i	−0.491314	+	0.870982i	$0.663483\pi$
$402$	4.62557	+	38.0950i	0.230702	+	1.90001i
$403$	−7.86847	−	19.7879i	−0.391957	−	0.985707i
$404$	−5.64137	+	46.4609i	−0.280669	+	2.31151i
$405$	−2.46543	+	1.29396i	−0.122508	+	0.0642974i
$406$	−7.69326	−	20.2855i	−0.381810	−	1.00675i
$407$	−2.01709	+	16.6122i	−0.0999835	+	0.823438i
$408$	−34.8486			−1.72526
$409$	1.71876	−	14.1552i	0.0849870	−	0.699931i	−0.886482	−	0.462764i	$-0.846858\pi$
$409$	1.71876	−	14.1552i	0.0849870	−	0.699931i	0.971469	−	0.237168i	$-0.0762191\pi$
$410$	9.13718	+	13.2375i	0.451253	+	0.653753i
$411$	5.07199	−	1.25013i	0.250183	−	0.0616645i
$412$	10.3871	−	15.0483i	0.511735	−	0.741376i
$413$	18.8869	−	4.65519i	0.929361	−	0.229067i
$414$	−10.3962	−	5.45636i	−0.510947	−	0.268166i
$415$	41.1469	+	21.5955i	2.01982	+	1.06008i
$416$	0.534423	+	0.269685i	0.0262022	+	0.0132224i
$417$	−4.53754	+	2.38148i	−0.222204	+	0.116622i
$418$	−18.7079			−0.915031
$419$	0.415497	+	0.218070i	0.0202984	+	0.0106534i	0.474842	−	0.880071i	$-0.342505\pi$
$419$	0.415497	+	0.218070i	0.0202984	+	0.0106534i	−0.454543	+	0.890725i	$0.650198\pi$
$420$	−14.3245	+	37.7705i	−0.698963	+	1.84301i
$421$	3.14374	+	25.8911i	0.153217	+	1.26185i	0.843030	+	0.537866i	$0.180769\pi$
$421$	3.14374	+	25.8911i	0.153217	+	1.26185i	−0.689814	+	0.723987i	$0.742308\pi$
$422$	−42.7283	+	10.5316i	−2.07998	+	0.512669i
$423$	3.32919	−	0.820571i	0.161871	−	0.0398975i
$424$	0.282556	+	2.32706i	0.0137221	+	0.113012i
$425$	−6.87591	+	18.1303i	−0.333531	+	0.879448i
$426$	−8.01730	−	4.20780i	−0.388439	−	0.203869i
$427$	−41.1685			−1.99228
$428$	−67.3798	+	35.3636i	−3.25693	+	1.70937i
$429$	7.84831	+	6.73227i	0.378920	+	0.325037i
$430$	−47.8877	−	25.1334i	−2.30935	−	1.21204i
$431$	6.05017	+	3.17537i	0.291426	+	0.152952i	0.604101	−	0.796908i	$-0.293533\pi$
$431$	6.05017	+	3.17537i	0.291426	+	0.152952i	−0.312674	+	0.949860i	$0.601225\pi$
$432$	−3.98221	+	0.981526i	−0.191594	+	0.0472237i
$433$	17.9934	−	26.0679i	0.864705	−	1.25274i	−0.101466	−	0.994839i	$-0.532353\pi$
$433$	17.9934	−	26.0679i	0.864705	−	1.25274i	0.966171	−	0.257903i	$-0.0830314\pi$
$434$	50.8048	−	12.5223i	2.43871	−	0.601087i
$435$	−3.87332	−	5.61147i	−0.185711	−	0.269050i
$436$	−3.61535	+	29.7751i	−0.173144	+	1.42597i
$437$	12.7294			0.608929
$438$	−1.83410	+	15.1052i	−0.0876367	+	0.721753i
$439$	0.625014	+	1.64803i	0.0298303	+	0.0786561i	0.949104	−	0.314963i	$-0.101992\pi$
$439$	0.625014	+	1.64803i	0.0298303	+	0.0786561i	−0.919274	+	0.393619i	$0.871223\pi$
$440$	34.9791	−	18.3584i	1.66756	−	0.875204i
$441$	0.728643	−	6.00092i	0.0346973	−	0.285758i
$442$	−60.7195	−	13.9408i	−2.88813	−	0.663095i
$443$	−2.37067	−	19.5243i	−0.112634	−	0.927626i	−0.934012	−	0.357241i	$-0.883717\pi$
$443$	−2.37067	−	19.5243i	−0.112634	−	0.927626i	0.821378	−	0.570384i	$-0.193206\pi$
$444$	−13.3148	−	19.2898i	−0.631890	−	0.915451i
$445$	−13.7061	+	19.8567i	−0.649732	+	0.941300i
$446$	18.7520	−	16.6128i	0.887931	−	0.786638i
$447$	0.424200	+	1.11852i	0.0200640	+	0.0529044i
$448$	15.9943	−	23.1717i	0.755659	−	1.09476i
$449$	−3.16696	−	1.66215i	−0.149458	−	0.0784417i	0.388336	−	0.921518i	$-0.373050\pi$
$449$	−3.16696	−	1.66215i	−0.149458	−	0.0784417i	−0.537794	+	0.843076i	$0.680742\pi$
$450$	−0.813884	+	6.70294i	−0.0383669	+	0.315980i
$451$	0.814103	+	6.70474i	0.0383346	+	0.315714i
$452$	−20.9052	+	55.1226i	−0.983300	+	2.59275i
$453$	11.8810	−	17.2126i	0.558218	−	0.808719i
$454$	28.6566	+	25.3875i	1.34492	+	1.19150i
$455$	−20.1182	+	30.1662i	−0.943157	+	1.41421i
$456$	9.84780	−	8.72439i	0.461165	−	0.408557i
$457$	−2.47246	−	20.3625i	−0.115657	−	0.952520i	−0.928832	−	0.370501i	$-0.879186\pi$
$457$	−2.47246	−	20.3625i	−0.115657	−	0.952520i	0.813175	−	0.582019i	$-0.197737\pi$
$458$	−1.45313	−	11.9676i	−0.0679001	−	0.559208i
$459$	6.23726	−	3.27357i	0.291130	−	0.152797i
$460$	−47.4027	+	24.8789i	−2.21016	+	1.15998i
$461$	27.0364	+	6.66388i	1.25921	+	0.310368i	0.811787	−	0.583954i	$-0.198495\pi$
$461$	27.0364	+	6.66388i	1.25921	+	0.310368i	0.447425	+	0.894322i	$0.352341\pi$
$462$	−19.0178	+	16.8483i	−0.884790	+	0.783855i
$463$	16.0408	+	3.95369i	0.745477	+	0.183744i	0.593717	−	0.804674i	$-0.297660\pi$
$463$	16.0408	+	3.95369i	0.745477	+	0.183744i	0.151760	+	0.988417i	$0.451506\pi$
$464$	−3.56151	−	9.39093i	−0.165339	−	0.435963i
$465$	14.5612	−	7.64233i	0.675261	−	0.354404i
$466$	−0.951287	+	7.83455i	−0.0440675	+	0.362929i
$467$	13.5796	−	3.34707i	0.628390	−	0.154884i	0.0877556	−	0.996142i	$-0.472031\pi$
$467$	13.5796	−	3.34707i	0.628390	−	0.154884i	0.540634	+	0.841258i	$0.318184\pi$
$468$	−14.4811	+	0.231413i	−0.669390	+	0.0106971i
$469$	−54.8626	−	13.5224i	−2.53332	−	0.624407i
$470$	8.30425	−	21.8965i	0.383047	−	1.01001i
$471$	−5.03361	−	4.45939i	−0.231937	−	0.205478i
$472$	25.8700	−	6.37638i	1.19076	−	0.293496i
$473$	−12.9003	−	18.6893i	−0.593157	−	0.859337i
$474$	3.15646	+	25.9957i	0.144981	+	1.19402i
$475$	−2.59589	−	6.84480i	−0.119108	−	0.314061i
$476$	36.2392	−	95.5550i	1.66102	−	4.37976i
$477$	−0.269169	−	0.389959i	−0.0123244	−	0.0178550i
$478$	18.1001	+	4.46127i	0.827878	+	0.204054i
$479$	−2.64267	−	6.96816i	−0.120747	−	0.318383i	0.860992	−	0.508619i	$-0.169844\pi$
$479$	−2.64267	−	6.96816i	−0.120747	−	0.318383i	−0.981738	+	0.190236i	$0.939075\pi$
$480$	−0.163925	+	0.432235i	−0.00748213	+	0.0197287i
$481$	−7.77383	−	19.5499i	−0.354456	−	0.891400i
$482$	−12.7724	−	33.6781i	−0.581768	−	1.53400i
$483$	12.9403	−	11.4641i	0.588804	−	0.521635i
$484$	−11.1485			−0.506750
$485$	−8.30442			−0.377084
$486$	1.83604	−	1.62659i	0.0832846	−	0.0737837i
$487$	28.2339	−	14.8183i	1.27940	−	0.671481i	0.318381	−	0.947963i	$-0.396861\pi$
$487$	28.2339	−	14.8183i	1.27940	−	0.671481i	0.961019	+	0.276481i	$0.0891684\pi$
$488$	−56.3899			−2.55265
$489$	8.75744	+	4.59626i	0.396025	+	0.207850i
$490$	−30.9033	−	27.3779i	−1.39607	−	1.23681i
$491$	−12.5605	−	18.1970i	−0.566845	−	0.821217i	0.429811	−	0.902919i	$-0.358580\pi$
$491$	−12.5605	−	18.1970i	−0.566845	−	0.821217i	−0.996657	+	0.0817013i	$0.973965\pi$
$492$	−7.08088	−	6.27311i	−0.319231	−	0.282814i
$493$	9.79904	+	14.1964i	0.441327	+	0.639372i
$494$	20.6487	−	11.2617i	0.929029	−	0.506688i
$495$	−4.53608	+	6.57165i	−0.203882	+	0.295374i
$496$	23.5195	−	5.79704i	1.05606	−	0.260295i
$497$	9.97922	−	8.84081i	0.447629	−	0.396565i
$498$	−39.7485	−	9.79713i	−1.78117	−	0.439020i
$499$	32.5195	+	28.8098i	1.45577	+	1.28970i	0.882479	+	0.470353i	$0.155873\pi$
$499$	32.5195	+	28.8098i	1.45577	+	1.28970i	0.573294	+	0.819350i	$0.305665\pi$
$500$	−18.8136	−	16.6674i	−0.841369	−	0.745388i
$501$	−6.50664	+	17.1566i	−0.290695	+	0.766501i
$502$	−3.14365	+	4.55436i	−0.140308	+	0.203271i
$503$	−2.27007	−	1.19142i	−0.101217	−	0.0531229i	0.413355	−	0.910570i	$-0.364357\pi$
$503$	−2.27007	−	1.19142i	−0.101217	−	0.0531229i	−0.514572	+	0.857447i	$0.672049\pi$
$504$	2.15377	−	17.7379i	0.0959366	−	0.790109i
$505$	−31.4992	−	7.76385i	−1.40170	−	0.345487i
$506$	−33.6717			−1.49689
$507$	−12.7152	−	2.70620i	−0.564702	−	0.120187i
$508$	56.8670			2.52306
$509$	−27.4263	−	6.75998i	−1.21565	−	0.299631i	−0.421204	−	0.906966i	$-0.638392\pi$
$509$	−27.4263	−	6.75998i	−1.21565	−	0.299631i	−0.794446	+	0.607335i	$0.792238\pi$
$510$	5.79905	−	47.7595i	0.256786	−	2.11483i
$511$	−19.8385	−	10.4120i	−0.877602	−	0.460601i
$512$	22.6656	−	32.8368i	1.00169	−	1.45120i
$513$	−0.943034	+	2.48658i	−0.0416360	+	0.109785i
$514$	−49.4951	−	43.8488i	−2.18313	−	1.93409i
$515$	9.48712	+	8.40486i	0.418053	+	0.370362i
$516$	30.8834	+	7.61207i	1.35957	+	0.335103i
$517$	7.36037	−	6.52072i	0.323709	−	0.286781i
$518$	50.1937	−	12.3716i	2.20539	−	0.543579i
$519$	10.7336	−	15.5503i	0.471152	−	0.682582i
$520$	−27.5566	+	41.3196i	−1.20844	+	1.81199i
$521$	21.8465	+	31.6502i	0.957114	+	1.38662i	0.921981	+	0.387236i	$0.126570\pi$
$521$	21.8465	+	31.6502i	0.957114	+	1.38662i	0.0351328	+	0.999383i	$0.488815\pi$
$522$	4.49616	+	3.98325i	0.196792	+	0.174342i
$523$	−6.54692	−	9.48484i	−0.286277	−	0.414743i	0.653291	−	0.757107i	$-0.273388\pi$
$523$	−6.54692	−	9.48484i	−0.286277	−	0.414743i	−0.939567	+	0.342364i	$0.888772\pi$
$524$	35.8475	+	31.7581i	1.56600	+	1.38736i
$525$	−8.80334	−	4.62035i	−0.384209	−	0.201649i
$526$	−19.1721			−0.835944
$527$	−36.8382	+	19.3342i	−1.60470	+	0.842211i
$528$	−8.80410	+	7.79976i	−0.383149	+	0.339441i
$529$	−0.0887677			−0.00385947
$530$	−3.23622			−0.140573
$531$	−4.03128	+	3.57140i	−0.174942	+	0.154986i
$532$	13.6815	+	36.0753i	0.593170	+	1.56406i
$533$	−4.93466	−	6.91025i	−0.213744	−	0.299316i
$534$	7.53736	−	19.8744i	0.326174	−	0.860049i
$535$	−18.7046	−	49.3200i	−0.808670	−	2.13229i
$536$	−75.1472	−	18.5221i	−3.24586	−	0.800034i
$537$	−9.98504	−	14.4658i	−0.430886	−	0.624246i
$538$	−21.3786	+	56.3707i	−0.921697	+	2.43031i
$539$	−6.14748	−	16.2096i	−0.264791	−	0.698196i
$540$	−1.34813	−	11.1028i	−0.0580142	−	0.477790i
$541$	−21.6628	−	31.3840i	−0.931356	−	1.34930i	−0.937004	−	0.349318i	$-0.886413\pi$
$541$	−21.6628	−	31.3840i	−0.931356	−	1.34930i	0.00564787	−	0.999984i	$-0.498202\pi$
$542$	6.18858	−	1.52535i	0.265822	−	0.0655194i
$543$	−12.7048	−	11.2555i	−0.545215	−	0.483019i
$544$	0.414711	−	1.09350i	0.0177806	−	0.0468836i
$545$	−20.1867	−	4.97558i	−0.864704	−	0.213130i
$546$	10.8485	−	30.0446i	0.464274	−	1.28579i
$547$	40.8024	−	10.0569i	1.74458	−	0.430001i	0.767188	−	0.641422i	$-0.221655\pi$
$547$	40.8024	−	10.0569i	1.74458	−	0.430001i	0.977395	+	0.211421i	$0.0678092\pi$
$548$	−2.52924	+	20.8302i	−0.108044	+	0.889821i
$549$	10.0928	−	5.29709i	0.430749	−	0.226074i
$550$	6.86665	+	18.1059i	0.292795	+	0.772036i
$551$	−6.32317	−	1.55852i	−0.269376	−	0.0663953i
$552$	17.7248	−	15.7028i	0.754416	−	0.668354i
$553$	−37.4379	−	9.22760i	−1.59202	−	0.392398i
$554$	−61.9789	+	32.5290i	−2.63323	+	1.38203i
$555$	14.3861	−	7.55041i	0.610656	−	0.320497i
$556$	−2.48118	−	20.4343i	−0.105225	−	0.866609i
$557$	2.97842	+	24.5295i	0.126200	+	1.03935i	0.908919	+	0.416973i	$0.136909\pi$
$557$	2.97842	+	24.5295i	0.126200	+	1.03935i	−0.782719	+	0.622375i	$0.786168\pi$
$558$	−10.8440	+	9.60690i	−0.459061	+	0.406693i
$559$	25.4892	+	12.8626i	1.07808	+	0.544029i
$560$	−30.8729	−	27.3510i	−1.30462	−	1.15579i
$561$	11.4758	−	16.6255i	0.484507	−	0.701929i
$562$	−10.6298	+	28.0284i	−0.448390	+	1.18231i
$563$	−0.00368946	−	0.0303854i	−0.000155492	−	0.00128059i	0.992631	−	0.121177i	$-0.0386668\pi$
$563$	−0.00368946	−	0.0303854i	−0.000155492	−	0.00128059i	−0.992786	+	0.119896i	$0.961744\pi$
$564$	−1.66016	+	13.6726i	−0.0699053	+	0.575722i
$565$	−36.1841	−	18.9909i	−1.52228	−	0.798953i
$566$	−10.7196	+	15.5300i	−0.450579	+	0.652776i
$567$	1.28076	+	3.37708i	0.0537867	+	0.141824i
$568$	13.6689	−	12.1096i	0.573533	−	0.508106i
$569$	14.0293	−	20.3249i	0.588138	−	0.852065i	−0.410061	−	0.912058i	$-0.634493\pi$
$569$	14.0293	−	20.3249i	0.588138	−	0.852065i	0.998199	+	0.0599935i	$0.0191080\pi$
$570$	10.3179	+	14.9481i	0.432170	+	0.626106i
$571$	0.619129	+	5.09898i	0.0259097	+	0.213386i	0.999914	−	0.0131456i	$-0.00418449\pi$
$571$	0.619129	+	5.09898i	0.0259097	+	0.213386i	−0.974004	+	0.226531i	$0.927261\pi$
$572$	−36.4643	+	19.8874i	−1.52465	+	0.831536i
$573$	−0.319712	+	2.63307i	−0.0133562	+	0.109998i
$574$	18.4747	−	9.69626i	0.771118	−	0.404714i
$575$	−4.67227	−	12.3198i	−0.194847	−	0.513769i
$576$	−0.939646	+	7.73868i	−0.0391519	+	0.322445i
$577$	26.3998			1.09904			0.549520	−	0.835481i	$-0.314811\pi$
$577$	26.3998			1.09904			0.549520	+	0.835481i	$0.314811\pi$
$578$	−9.64458	+	79.4302i	−0.401161	+	3.30386i
$579$	−11.3567	−	16.4531i	−0.471970	−	0.683766i
$580$	26.5928	−	6.55454i	1.10421	−	0.272162i
$581$	34.2423	−	49.6085i	1.42061	−	2.05811i
$582$	7.10331	−	1.75081i	0.294442	−	0.0725734i
$583$	−1.20324	−	0.631507i	−0.0498330	−	0.0261544i
$584$	−27.1734	−	14.2617i	−1.12444	−	0.590154i
$585$	1.05070	−	9.98404i	0.0434409	−	0.412789i
$586$	−55.8752	+	29.3256i	−2.30818	+	1.21143i
$587$	2.05640			0.0848767			0.0424383	−	0.999099i	$-0.486487\pi$
$587$	2.05640			0.0848767			0.0424383	+	0.999099i	$0.486487\pi$
$588$	21.5005	+	11.2843i	0.886666	+	0.465358i
$589$	5.56971	−	14.6861i	0.229496	−	0.605131i
$590$	4.43379	+	36.5155i	0.182536	+	1.50332i
$591$	1.15482	−	0.284637i	0.0475028	−	0.0117084i
$592$	23.2366	−	5.72732i	0.955020	−	0.235391i
$593$	−1.24792	−	10.2775i	−0.0512459	−	0.422048i	−0.995643	−	0.0932420i	$-0.970277\pi$
$593$	−1.24792	−	10.2775i	−0.0512459	−	0.422048i	0.944398	−	0.328806i	$-0.106646\pi$
$594$	2.49451	−	6.57749i	0.102351	−	0.269878i
$595$	62.7252	+	32.9207i	2.57148	+	1.34962i
$596$	−4.80520			−0.196829
$597$	−24.0979	+	12.6475i	−0.986260	+	0.517629i
$598$	37.1650	−	20.2696i	1.51979	−	0.828886i
$599$	−15.6730	−	8.22585i	−0.640383	−	0.336099i	0.113083	−	0.993586i	$-0.463927\pi$
$599$	−15.6730	−	8.22585i	−0.640383	−	0.336099i	−0.753466	+	0.657486i	$0.771620\pi$
$600$	−12.0582	−	6.32865i	−0.492276	−	0.258366i
$601$	−21.1077	+	5.20259i	−0.861002	+	0.212218i	−0.645007	−	0.764176i	$-0.723146\pi$
$601$	−21.1077	+	5.20259i	−0.861002	+	0.212218i	−0.215995	+	0.976394i	$0.569300\pi$
$602$	−39.8520	+	57.7356i	−1.62425	+	2.35313i
$603$	15.1899	−	3.74397i	0.618580	−	0.152466i
$604$	47.7242	+	69.1405i	1.94187	+	2.81329i
$605$	0.931486	−	7.67147i	0.0378703	−	0.311890i
$606$	28.5801			1.16099
$607$	0.106915	−	0.880523i	0.00433954	−	0.0357393i	−0.990378	−	0.138387i	$-0.955808\pi$
$607$	0.106915	−	0.880523i	0.00433954	−	0.0357393i	0.994718	+	0.102647i	$0.0327314\pi$
$608$	0.156568	+	0.412835i	0.00634966	+	0.0167427i
$609$	−7.83155	+	4.11032i	−0.317351	+	0.166558i
$610$	9.38368	−	77.2816i	0.379934	−	3.12904i
$611$	−4.19865	+	11.6280i	−0.169859	+	0.470418i
$612$	3.41061	+	28.0889i	0.137866	+	1.13543i
$613$	2.85983	+	4.14317i	0.115507	+	0.167341i	0.876473	−	0.481451i	$-0.159890\pi$
$613$	2.85983	+	4.14317i	0.115507	+	0.167341i	−0.760966	+	0.648792i	$0.775275\pi$
$614$	−9.84695	+	14.2658i	−0.397390	+	0.575719i
$615$	4.90826	−	4.34834i	0.197920	−	0.175342i
$616$	−18.1711	−	47.9133i	−0.732135	−	1.93048i
$617$	19.9920	−	28.9634i	0.804847	−	1.16602i	−0.178439	−	0.983951i	$-0.557105\pi$
$617$	19.9920	−	28.9634i	0.804847	−	1.16602i	0.983285	−	0.182071i	$-0.0582800\pi$
$618$	−9.88693	−	5.18906i	−0.397711	−	0.208735i
$619$	−0.930394	+	7.66249i	−0.0373957	+	0.307981i	0.961995	+	0.273068i	$0.0880385\pi$
$619$	−0.930394	+	7.66249i	−0.0373957	+	0.307981i	−0.999390	+	0.0349131i	$0.988885\pi$
$620$	7.96226	+	65.5751i	0.319772	+	2.63356i
$621$	−1.69734	+	4.47552i	−0.0681119	+	0.179596i
$622$	−6.67114	+	9.66481i	−0.267488	+	0.387524i
$623$	23.4266	+	20.7542i	0.938569	+	0.831499i
$624$	5.02221	−	13.9088i	0.201049	−	0.556798i
$625$	23.3432	−	20.6802i	0.933727	−	0.827210i
$626$	4.24332	+	34.9469i	0.169597	+	1.39676i
$627$	0.919303	+	7.57114i	0.0367134	+	0.302362i
$628$	23.9185	−	12.5534i	0.954453	−	0.500936i
$629$	−36.3952	+	19.1016i	−1.45117	+	0.761633i
$630$	23.9511	+	5.90343i	0.954236	+	0.235198i
$631$	−4.71866	+	4.18037i	−0.187847	+	0.166418i	−0.751805	−	0.659386i	$-0.770816\pi$
$631$	−4.71866	+	4.18037i	−0.187847	+	0.166418i	0.563958	+	0.825804i	$0.309278\pi$
$632$	−51.2799	−	12.6394i	−2.03981	−	0.502767i
$633$	6.36184	+	16.7748i	0.252860	+	0.666738i
$634$	30.9741	−	16.2564i	1.23014	−	0.645626i
$635$	−4.75138	+	39.1312i	−0.188553	+	1.55287i
$636$	1.84802	−	0.455496i	0.0732787	−	0.0180616i
$637$	16.5430	+	14.1906i	0.655459	+	0.562252i
$638$	16.7261	+	4.12260i	0.662191	+	0.163215i
$639$	−1.30894	+	3.45140i	−0.0517810	+	0.136535i
$640$	40.5444	+	35.9192i	1.60266	+	1.41983i
$641$	28.5747	−	7.04302i	1.12863	−	0.278183i	0.369571	−	0.929203i	$-0.379505\pi$
$641$	28.5747	−	7.04302i	1.12863	−	0.278183i	0.759061	+	0.651020i	$0.225659\pi$
$642$	26.3973	+	38.2431i	1.04182	+	1.50933i
$643$	0.0262717	+	0.216367i	0.00103606	+	0.00853269i	0.993218	−	0.116269i	$-0.0370935\pi$
$643$	0.0262717	+	0.216367i	0.00103606	+	0.00853269i	−0.992182	+	0.124802i	$0.960170\pi$
$644$	24.6250	+	64.9308i	0.970362	+	2.55863i
$645$	−7.81839	+	20.6154i	−0.307849	+	0.811730i
$646$	−26.1031	−	37.8169i	−1.02701	−	1.48788i
$647$	−41.3949	−	10.2029i	−1.62740	−	0.401118i	−0.683132	−	0.730295i	$-0.739383\pi$
$647$	−41.3949	−	10.2029i	−1.62740	−	0.401118i	−0.944268	+	0.329177i	$0.893229\pi$
$648$	1.75430	+	4.62570i	0.0689153	+	0.181715i
$649$	−5.47704	+	14.4418i	−0.214993	+	0.566889i
$650$	−18.4783	−	15.8507i	−0.724780	−	0.621715i
$651$	−7.56435	−	19.9455i	−0.296470	−	0.781728i
$652$	−29.7368	+	26.3445i	−1.16458	+	1.03173i
$653$	31.9058			1.24857			0.624285	−	0.781197i	$-0.285390\pi$
$653$	31.9058			1.24857			0.624285	+	0.781197i	$0.285390\pi$
$654$	18.3160			0.716212
$655$	−24.8485	+	22.0138i	−0.970910	+	0.860151i
$656$	8.55265	−	4.48878i	0.333925	−	0.175257i
$657$	6.20325			0.242012
$658$	−26.8979	−	14.1171i	−1.04859	−	0.550342i
$659$	20.1437	+	17.8458i	0.784689	+	0.695173i	0.957070	−	0.289857i	$-0.0936077\pi$
$659$	20.1437	+	17.8458i	0.784689	+	0.695173i	−0.172381	+	0.985030i	$0.555146\pi$
$660$	−18.2208	−	26.3973i	−0.709242	−	1.02751i
$661$	−14.9526	−	13.2469i	−0.581590	−	0.515244i	0.320239	−	0.947337i	$-0.396237\pi$
$661$	−14.9526	−	13.2469i	−0.581590	−	0.515244i	−0.901829	+	0.432093i	$0.857775\pi$
$662$	−28.5793	−	41.4043i	−1.11077	−	1.60922i
$663$	−2.65814	+	25.2585i	−0.103233	+	0.980957i
$664$	46.9029	−	67.9505i	1.82018	−	2.63699i
$665$	−25.9672	+	6.40033i	−1.00696	+	0.248194i
$666$	−10.7135	+	9.49135i	−0.415141	+	0.367782i
$667$	−11.3809	−	2.80514i	−0.440670	−	0.108615i
$668$	−55.1691	−	48.8756i	−2.13456	−	1.89105i
$669$	−7.64473	−	6.77264i	−0.295562	−	0.261845i
$670$	37.8894	−	99.9060i	1.46379	−	3.85971i
$671$	18.5694	−	26.9024i	0.716863	−	1.03856i
$672$	0.530962	+	0.278670i	0.0204823	+	0.0107499i
$673$	−1.82126	+	14.9995i	−0.0702046	+	0.578187i	0.914580	+	0.404406i	$0.132522\pi$
$673$	−1.82126	+	14.9995i	−0.0702046	+	0.578187i	−0.984784	+	0.173781i	$0.944402\pi$
$674$	15.9549	+	3.93253i	0.614559	+	0.151475i
$675$	2.75270			0.105951
$676$	28.2755	−	43.9013i	1.08752	−	1.68851i
$677$	39.2220			1.50742			0.753711	−	0.657206i	$-0.228262\pi$
$677$	39.2220			1.50742			0.753711	+	0.657206i	$0.228262\pi$
$678$	34.9545	+	8.61550i	1.34242	+	0.330876i
$679$	−1.29845	+	10.6937i	−0.0498298	+	0.410385i
$680$	85.9169	+	45.0927i	3.29476	+	1.72922i
$681$	8.86625	−	12.8450i	0.339755	−	0.492220i
$682$	−14.7330	+	38.8477i	−0.564155	+	1.48755i
$683$	−4.03449	−	3.57424i	−0.154375	−	0.136765i	0.582400	−	0.812903i	$-0.302114\pi$
$683$	−4.03449	−	3.57424i	−0.154375	−	0.136765i	−0.736775	+	0.676138i	$0.763652\pi$
$684$	−7.99588	−	7.08374i	−0.305730	−	0.270853i
$685$	−14.1223	−	3.48083i	−0.539585	−	0.132996i
$686$	6.33302	−	5.61057i	0.241796	−	0.214212i
$687$	−4.77192	+	1.17617i	−0.182060	+	0.0448737i
$688$	−18.4491	+	26.7281i	−0.703364	+	1.01900i
$689$	1.70822	−	0.0272980i	0.0650780	−	0.00103997i
$690$	18.5709	+	26.9046i	0.706982	+	1.02424i
$691$	−26.3233	−	23.3204i	−1.00139	−	0.887151i	−0.00777103	−	0.999970i	$-0.502474\pi$
$691$	−26.3233	−	23.3204i	−1.00139	−	0.887151i	−0.993616	+	0.112819i	$0.964012\pi$
$692$	43.1152	+	62.4631i	1.63899	+	2.37449i
$693$	7.75312	+	6.86867i	0.294517	+	0.260919i
$694$	−57.8760	−	30.3757i	−2.19694	−	1.15304i
$695$	14.2685			0.541237
$696$	−10.7271	+	5.63004i	−0.406612	+	0.213406i
$697$	−12.4173	+	11.0008i	−0.470340	+	0.416685i
$698$	6.30474			0.238638
$699$	3.21742			0.121694
$700$	29.8926	−	26.4826i	1.12984	−	1.00095i
$701$	8.02601	+	21.1628i	0.303138	+	0.799309i	0.996869	+	0.0790748i	$0.0251966\pi$
$701$	8.02601	+	21.1628i	0.303138	+	0.799309i	−0.693731	+	0.720235i	$0.744034\pi$
$702$	1.20619	+	8.76152i	0.0455248	+	0.330682i
$703$	5.50272	−	14.5095i	0.207539	−	0.547235i
$704$	7.92769	+	20.9036i	0.298786	+	0.787834i
$705$	−9.26968	−	2.28477i	−0.349116	−	0.0860494i
$706$	24.7437	+	35.8475i	0.931242	+	1.34914i
$707$	−14.9227	+	39.3478i	−0.561225	+	1.47983i
$708$	−7.67140	−	20.2278i	−0.288309	−	0.760208i
$709$	0.0519749	+	0.428052i	0.00195196	+	0.0160758i	0.993652	−	0.112495i	$-0.0358842\pi$
$709$	0.0519749	+	0.428052i	0.00195196	+	0.0160758i	−0.991700	+	0.128571i	$0.958961\pi$
$710$	14.3214	+	20.7481i	0.537472	+	0.778663i
$711$	10.3655	−	2.55486i	0.388736	−	0.0958147i
$712$	32.0883	+	28.4277i	1.20256	+	1.06537i
$713$	10.0248	−	26.4331i	0.375430	−	0.989928i
$714$	−60.5936	−	14.9350i	−2.26766	−	0.558927i
$715$	−10.6382	−	26.7534i	−0.397847	−	1.00052i
$716$	68.5537	−	16.8970i	2.56197	−	0.631469i
$717$	0.916055	−	7.54439i	0.0342107	−	0.281751i
$718$	53.4832	−	28.0701i	1.99597	−	1.04757i
$719$	11.9782	+	31.5840i	0.446712	+	1.17788i	0.949581	+	0.313521i	$0.101509\pi$
$719$	11.9782	+	31.5840i	0.446712	+	1.17788i	−0.502869	+	0.864363i	$0.667722\pi$
$720$	11.0879	+	2.73293i	0.413222	+	0.101850i
$721$	12.3064	−	10.9025i	0.458313	−	0.406030i
$722$	−28.4074	−	7.00180i	−1.05721	−	0.260580i
$723$	−13.0020	+	6.82399i	−0.483551	+	0.253787i
$724$	60.3702	−	31.6847i	2.24364	−	1.17755i
$725$	0.812526	+	6.69175i	0.0301764	+	0.248525i
$726$	0.820605	+	6.75829i	0.0304555	+	0.250824i
$727$	20.8661	−	18.4857i	0.773880	−	0.685598i	−0.180705	−	0.983537i	$-0.557838\pi$
$727$	20.8661	−	18.4857i	0.773880	−	0.685598i	0.954585	+	0.297939i	$0.0962993\pi$
$728$	48.8990	+	41.9455i	1.81232	+	1.55460i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	24.0673	−	34.8676i	0.890772	−	1.29051i
$731$	19.7796	−	52.1545i	0.731575	−	1.92901i
$732$	5.51884	+	45.4518i	0.203982	+	1.67995i
$733$	0.314232	−	2.58793i	0.0116064	−	0.0955875i	−0.985754	−	0.168191i	$-0.946208\pi$
$733$	0.314232	−	2.58793i	0.0116064	−	0.0955875i	0.997361	+	0.0726031i	$0.0231307\pi$
$734$	−33.7336	−	17.7048i	−1.24513	−	0.653495i
$735$	−9.56137	+	13.8520i	−0.352676	+	0.510940i
$736$	0.281802	+	0.743050i	0.0103873	+	0.0273892i
$737$	33.5827	−	29.7517i	1.23704	−	1.09592i
$738$	−3.28160	+	4.75422i	−0.120797	+	0.175005i
$739$	3.84865	+	5.57573i	0.141575	+	0.205107i	0.887357	−	0.461084i	$-0.152539\pi$
$739$	3.84865	+	5.57573i	0.141575	+	0.205107i	−0.745782	+	0.666190i	$0.767924\pi$
$740$	7.86649	+	64.7864i	0.289178	+	2.38159i
$741$	−5.57233	−	7.80321i	−0.204705	−	0.286658i
$742$	−0.506003	+	4.16731i	−0.0185760	+	0.152987i
$743$	5.38401	−	2.82575i	0.197520	−	0.103667i	−0.363063	−	0.931764i	$-0.618269\pi$
$743$	5.38401	−	2.82575i	0.197520	−	0.103667i	0.560584	+	0.828098i	$0.310577\pi$
$744$	−10.3611	−	27.3201i	−0.379858	−	1.00160i
$745$	0.401487	−	3.30654i	0.0147094	−	0.121142i
$746$	−45.1504			−1.65307
$747$	−2.01170	+	16.5678i	−0.0736041	+	0.606185i
$748$	46.0964	+	66.7821i	1.68545	+	2.44180i
$749$	−66.4343	+	16.3746i	−2.42746	+	0.598314i
$750$	−8.71907	+	12.6318i	−0.318375	+	0.461246i
$751$	−36.9526	+	9.10799i	−1.34842	+	0.332355i	−0.846421	−	0.532514i	$-0.821247\pi$
$751$	−36.9526	+	9.10799i	−1.34842	+	0.332355i	−0.501997	+	0.864869i	$0.667401\pi$
$752$	−12.4521	−	6.53536i	−0.454081	−	0.238320i
$753$	1.99764	+	1.04844i	0.0727982	+	0.0382075i
$754$	−20.9430	+	5.51840i	−0.762699	+	0.200968i
$755$	−51.5643	+	27.0630i	−1.87662	+	0.984924i
$756$	−14.5080			−0.527651
$757$	5.53709	+	2.90609i	0.201249	+	0.105624i	0.562337	−	0.826908i	$-0.309902\pi$
$757$	5.53709	+	2.90609i	0.201249	+	0.105624i	−0.361088	+	0.932532i	$0.617595\pi$
$758$	−3.77431	+	9.95205i	−0.137089	+	0.361475i
$759$	1.65463	+	13.6271i	0.0600591	+	0.494632i
$760$	−35.5681	+	8.76675i	−1.29019	+	0.318003i
$761$	−5.09862	+	1.25670i	−0.184825	+	0.0455552i	−0.330642	−	0.943756i	$-0.607265\pi$
$761$	−5.09862	+	1.25670i	−0.184825	+	0.0455552i	0.145817	+	0.989312i	$0.453419\pi$
$762$	−4.18580	−	34.4731i	−0.151635	−	1.24883i
$763$	−9.56341	+	25.2166i	−0.346219	+	0.912903i
$764$	−9.43393	−	4.95131i	−0.341308	−	0.179132i
$765$	−19.6134			−0.709125
$766$	7.11378	−	3.73360i	0.257031	−	0.134900i
$767$	−2.64836	−	19.2371i	−0.0956267	−	0.694611i
$768$	−28.4479	−	14.9306i	−1.02652	−	0.538762i
$769$	33.2058	+	17.4278i	1.19743	+	0.628461i	0.941100	−	0.338128i	$-0.109794\pi$
$769$	33.2058	+	17.4278i	1.19743	+	0.628461i	0.256332	+	0.966589i	$0.417486\pi$
$770$	68.6883	−	16.9301i	2.47535	−	0.610120i
$771$	−15.3136	+	22.1856i	−0.551506	+	0.798994i
$772$	77.9713	−	19.2182i	2.80625	−	0.691678i
$773$	−5.10831	−	7.40066i	−0.183733	−	0.266183i	0.720284	−	0.693679i	$-0.244011\pi$
$773$	−5.10831	−	7.40066i	−0.183733	−	0.266183i	−0.904017	+	0.427496i	$0.859396\pi$
$774$	2.34126	−	19.2820i	0.0841549	−	0.693078i
$775$	−16.2579			−0.584000
$776$	−1.77853	+	14.6475i	−0.0638454	+	0.525814i
$777$	−7.47337	−	19.7056i	−0.268106	−	0.706936i
$778$	−36.1644	+	18.9805i	−1.29655	+	0.680484i
$779$	0.754928	−	6.21739i	0.0270481	−	0.222761i
$780$	36.0017	+	18.1674i	1.28907	+	0.650499i
$781$	1.27600	+	10.5088i	0.0456590	+	0.376036i
$782$	−46.9822	−	68.0655i	−1.68008	−	2.43402i
$783$	1.39110	−	2.01535i	0.0497137	−	0.0720227i
$784$	−18.5577	+	16.4407i	−0.662775	+	0.587168i
$785$	6.63977	+	17.5076i	0.236984	+	0.624874i
$786$	16.6134	−	24.0686i	0.592579	−	0.858499i
$787$	−1.34328	−	0.705006i	−0.0478826	−	0.0251307i	0.440612	−	0.897698i	$-0.354761\pi$
$787$	−1.34328	−	0.705006i	−0.0478826	−	0.0251307i	−0.488495	+	0.872567i	$0.662454\pi$
$788$	−0.575870	+	4.74272i	−0.0205145	+	0.168952i
$789$	0.942117	+	7.75903i	0.0335403	+	0.276229i
$790$	25.8554	−	68.1751i	0.919895	−	2.42556i
$791$	−30.1123	+	43.6253i	−1.07067	+	1.55114i
$792$	10.6197	+	9.40825i	0.377355	+	0.334307i
$793$	−4.30124	+	40.8717i	−0.152741	+	1.45140i
$794$	−60.9579	+	54.0040i	−2.16331	+	1.91653i
$795$	0.159028	+	1.30971i	0.00564014	+	0.0464507i
$796$	−13.1770	−	108.522i	−0.467046	−	3.84647i
$797$	34.5731	−	18.1454i	1.22464	−	0.642742i	0.276631	−	0.960976i	$-0.410782\pi$
$797$	34.5731	−	18.1454i	1.22464	−	0.642742i	0.948012	+	0.318234i	$0.103090\pi$
$798$	20.8620	−	10.9492i	0.738507	−	0.387599i
$799$	23.4512	+	5.78020i	0.829644	+	0.204489i
$800$	0.342083	−	0.303059i	0.0120945	−	0.0107148i
$801$	−8.41363	−	2.07377i	−0.297281	−	0.0732732i
$802$	15.2480	+	40.2058i	0.538427	+	1.41972i
$803$	15.7523	−	8.26742i	0.555885	−	0.291751i
$804$	−7.57471	+	62.3834i	−0.267140	+	2.20009i
$805$	−46.7375	+	11.5198i	−1.64728	+	0.406018i
$806$	−7.12396	−	51.7469i	−0.250931	−	1.82271i
$807$	23.8640	+	5.88194i	0.840052	+	0.207054i
$808$	−20.4401	+	53.8961i	−0.719080	+	1.89606i
$809$	12.1199	+	10.7373i	0.426113	+	0.377503i	0.848749	−	0.528797i	$-0.177357\pi$
$809$	12.1199	+	10.7373i	0.426113	+	0.377503i	−0.422636	+	0.906300i	$0.638895\pi$
$810$	−6.63139	+	1.63449i	−0.233003	+	0.0574301i
$811$	6.55330	+	9.49409i	0.230117	+	0.333383i	0.920985	−	0.389599i	$-0.127386\pi$
$811$	6.55330	+	9.49409i	0.230117	+	0.333383i	−0.690867	+	0.722982i	$0.742771\pi$
$812$	−4.28239	−	35.2686i	−0.150282	−	1.23769i
$813$	−0.921421	−	2.42959i	−0.0323157	−	0.0852094i
$814$	−14.5558	+	38.3804i	−0.510180	+	1.34523i
$815$	−15.6435	−	22.6635i	−0.547968	−	0.793869i
$816$	−28.0511	−	6.91399i	−0.981987	−	0.242038i
$817$	7.46747	+	19.6901i	0.261254	+	0.688870i
$818$	12.4029	−	32.7039i	0.433658	−	1.14346i
$819$	−12.6922	−	2.91405i	−0.443503	−	0.101825i
$820$	9.34029	+	24.6283i	0.326177	+	0.860058i
$821$	26.4074	−	23.3949i	0.921623	−	0.816487i	−0.0617485	−	0.998092i	$-0.519668\pi$
$821$	26.4074	−	23.3949i	0.921623	−	0.816487i	0.983372	+	0.181605i	$0.0581292\pi$
$822$	12.8136			0.446924
$823$	52.7708			1.83947			0.919737	−	0.392536i	$-0.128402\pi$
$823$	52.7708			1.83947			0.919737	+	0.392536i	$0.128402\pi$
$824$	16.8565	−	14.9335i	0.587223	−	0.520234i
$825$	6.99008	−	3.66868i	0.243363	−	0.127727i
$826$	47.7146			1.66020
$827$	−5.22738	−	2.74354i	−0.181774	−	0.0954022i	0.371382	−	0.928480i	$-0.378884\pi$
$827$	−5.22738	−	2.74354i	−0.181774	−	0.0954022i	−0.553155	+	0.833078i	$0.686576\pi$
$828$	−14.3916	−	12.7498i	−0.500141	−	0.443087i
$829$	30.4168	+	44.0664i	1.05642	+	1.53049i	0.831036	+	0.556219i	$0.187748\pi$
$829$	30.4168	+	44.0664i	1.05642	+	1.53049i	0.225385	+	0.974270i	$0.427636\pi$
$830$	85.3203	+	75.5872i	2.96151	+	2.62367i
$831$	16.2103	+	23.4846i	0.562328	+	0.814672i
$832$	−21.3336	−	18.3000i	−0.739611	−	0.634437i
$833$	24.1891	−	35.0440i	0.838104	−	1.21420i
$834$	−12.2048	+	3.00822i	−0.422618	+	0.104166i
$835$	38.2417	−	33.8792i	1.32341	−	1.17244i
$836$	−29.7453	−	7.33156i	−1.02876	−	0.253567i
$837$	4.42082	+	3.91651i	0.152806	+	0.135374i
$838$	0.861556	+	0.763272i	0.0297620	+	0.0263668i
$839$	5.30729	−	13.9942i	0.183228	−	0.483133i	−0.811658	−	0.584132i	$-0.801435\pi$
$839$	5.30729	−	13.9942i	0.183228	−	0.483133i	0.994886	+	0.101000i	$0.0322041\pi$
$840$	−28.2621	+	40.9447i	−0.975135	+	1.41273i
$841$	−20.3683	−	10.6901i	−0.702357	−	0.368625i
$842$	−7.71137	+	63.5089i	−0.265751	+	2.18866i
$843$	11.8655	+	2.92460i	0.408671	+	0.100728i
$844$	−72.0649			−2.48057
$845$	27.8468	+	23.1249i	0.957959	+	0.795522i
$846$	8.41065			0.289164
$847$	−9.73298	−	2.39896i	−0.334429	−	0.0824293i
$848$	−0.234249	+	1.92921i	−0.00804414	+	0.0662494i
$849$	6.81182	+	3.57512i	0.233781	+	0.122698i
$850$	−27.0189	+	39.1437i	−0.926741	+	1.34262i
$851$	9.90418	−	26.1152i	0.339511	−	0.895217i
$852$	−11.0984	−	9.83232i	−0.380225	−	0.336850i
$853$	−15.4727	−	13.7076i	−0.529775	−	0.469340i	0.355324	−	0.934743i	$-0.384371\pi$
$853$	−15.4727	−	13.7076i	−0.529775	−	0.469340i	−0.885099	+	0.465404i	$0.845909\pi$
$854$	−98.0489	−	24.1669i	−3.35517	−	0.826974i
$855$	5.54252	−	4.91024i	0.189550	−	0.167927i
$856$	−90.9973	+	22.4288i	−3.11022	+	0.766601i
$857$	13.5407	−	19.6171i	0.462542	−	0.670108i	−0.520421	−	0.853910i	$-0.674225\pi$
$857$	13.5407	−	19.6171i	0.462542	−	0.670108i	0.982963	+	0.183802i	$0.0588404\pi$
$858$	14.7399	+	20.6410i	0.503213	+	0.704674i
$859$	15.8788	+	23.0043i	0.541776	+	0.784898i	0.994273	−	0.106868i	$-0.0340821\pi$
$859$	15.8788	+	23.0043i	0.541776	+	0.784898i	−0.452497	+	0.891766i	$0.649467\pi$
$860$	−66.2912	−	58.7289i	−2.26051	−	2.00264i
$861$	−4.83196	−	7.00030i	−0.164673	−	0.238570i
$862$	12.5454	+	11.1142i	0.427296	+	0.378552i
$863$	−7.65695	−	4.01868i	−0.260646	−	0.136797i	0.329339	−	0.944212i	$-0.393174\pi$
$863$	−7.65695	−	4.01868i	−0.260646	−	0.136797i	−0.589985	+	0.807414i	$0.700866\pi$
$864$	−0.166025			−0.00564830
$865$	−46.5844	+	24.4494i	−1.58392	+	0.831304i
$866$	58.1563	−	51.5220i	1.97623	−	1.75079i
$867$	32.6197			1.10782
$868$	85.6865			2.90839
$869$	22.9166	−	20.3023i	0.777393	−	0.688710i
$870$	−5.93082	−	15.6383i	−0.201074	−	0.530188i
$871$	−19.1569	+	53.0543i	−0.649108	+	1.79768i
$872$	−13.0993	+	34.5401i	−0.443599	+	1.16967i
$873$	−1.05762	−	2.78870i	−0.0357949	−	0.0943833i
$874$	30.3169	+	7.47245i	1.02548	+	0.252759i
$875$	−12.8383	−	18.5995i	−0.434014	−	0.628777i
$876$	−8.83588	+	23.2983i	−0.298537	+	0.787176i
$877$	−5.48194	−	14.4547i	−0.185112	−	0.488101i	0.810048	−	0.586363i	$-0.199441\pi$
$877$	−5.48194	−	14.4547i	−0.185112	−	0.488101i	−0.995161	+	0.0982625i	$0.968672\pi$
$878$	0.521134	+	4.29192i	0.0175874	+	0.144845i
$879$	14.6139	+	21.1718i	0.492913	+	0.714108i
$880$	31.7985	−	7.83763i	1.07193	−	0.264206i
$881$	2.59009	+	2.29462i	0.0872624	+	0.0773078i	0.705626	−	0.708584i	$-0.250666\pi$
$881$	2.59009	+	2.29462i	0.0872624	+	0.0773078i	−0.618364	+	0.785892i	$0.712204\pi$
$882$	5.25806	−	13.8644i	0.177048	−	0.466837i
$883$	−25.2064	−	6.21283i	−0.848264	−	0.209078i	−0.208856	−	0.977946i	$-0.566974\pi$
$883$	−25.2064	−	6.21283i	−0.848264	−	0.209078i	−0.639407	+	0.768868i	$0.720820\pi$
$884$	−91.0800	−	45.9615i	−3.06335	−	1.54585i
$885$	14.5601	−	3.58874i	0.489432	−	0.120634i
$886$	5.81509	−	47.8916i	0.195362	−	1.60895i
$887$	−3.03038	+	1.59046i	−0.101750	+	0.0534025i	−0.514830	−	0.857292i	$-0.672145\pi$
$887$	−3.03038	+	1.59046i	−0.101750	+	0.0534025i	0.413080	+	0.910695i	$0.364453\pi$
$888$	−10.2365	−	26.9915i	−0.343515	−	0.905775i
$889$	49.6466	+	12.2368i	1.66509	+	0.410409i
$890$	−44.2995	+	39.2460i	−1.48492	+	1.31553i
$891$	−2.78452	−	0.686322i	−0.0932848	−	0.0229926i
$892$	36.3259	−	19.0653i	1.21628	−	0.638354i
$893$	−8.07411	+	4.23762i	−0.270190	+	0.141807i
$894$	0.353696	+	2.91295i	0.0118294	+	0.0974235i
$895$	5.89926	+	48.5848i	0.197191	+	1.62401i
$896$	52.5928	−	46.5932i	1.75700	−	1.55657i
$897$	−10.0295	−	14.0448i	−0.334874	−	0.468941i
$898$	−6.56687	−	5.81774i	−0.219139	−	0.194140i
$899$	−8.21603	+	11.9030i	−0.274020	+	0.396986i
$900$	−3.92093	+	10.3386i	−0.130698	+	0.344621i
$901$	−0.402322	−	3.31342i	−0.0134033	−	0.110386i
$902$	−1.99693	+	16.4462i	−0.0664906	+	0.547600i
$903$	25.3242	+	13.2911i	0.842735	+	0.442302i
$904$	−41.2459	+	59.7550i	−1.37182	+	1.98742i
$905$	16.7587	+	44.1891i	0.557079	+	1.46890i
$906$	38.4006	−	34.0200i	1.27577	−	1.13024i
$907$	0.0129950	−	0.0188265i	0.000431492	−	0.000625125i	−0.822768	−	0.568377i	$-0.807571\pi$
$907$	0.0129950	−	0.0188265i	0.000431492	−	0.000625125i	0.823200	+	0.567752i	$0.192187\pi$
$908$	35.6144	+	51.5963i	1.18190	+	1.71228i
$909$	−1.40443	−	11.5665i	−0.0465819	−	0.383636i
$910$	−65.6228	+	60.0354i	−2.17538	+	1.99015i
$911$	−4.73951	+	39.0333i	−0.157027	+	1.29323i	0.674719	+	0.738075i	$0.264265\pi$
$911$	−4.73951	+	39.0333i	−0.157027	+	1.29323i	−0.831745	+	0.555157i	$0.812658\pi$
$912$	9.65785	−	5.06883i	0.319803	−	0.167846i
$913$	16.9725	+	44.7527i	0.561706	+	1.48110i
$914$	6.06476	−	49.9478i	0.200605	−	1.65213i
$915$	−31.7373			−1.04920
$916$	2.37960	−	19.5978i	0.0786243	−	0.647529i
$917$	24.4622	+	35.4396i	0.807812	+	1.17032i
$918$	16.7766	−	4.13507i	0.553711	−	0.136478i
$919$	12.5454	−	18.1751i	0.413833	−	0.599541i	−0.559530	−	0.828810i	$-0.689018\pi$
$919$	12.5454	−	18.1751i	0.413833	−	0.599541i	0.973363	+	0.229269i	$0.0736336\pi$
$920$	−64.0180	+	15.7790i	−2.11061	+	0.520219i
$921$	6.25729	+	3.28408i	0.206185	+	0.108214i
$922$	60.4794	+	31.7420i	1.99178	+	1.04537i
$923$	−7.73447	−	10.8310i	−0.254583	−	0.356505i
$924$	−36.8410	+	19.3356i	−1.21198	+	0.636096i
$925$	−16.0623			−0.528126
$926$	35.8825	+	18.8326i	1.17917	+	0.618878i
$927$	−1.61419	+	4.25627i	−0.0530170	+	0.139794i
$928$	−0.0490064	−	0.403604i	−0.00160871	−	0.0132489i
$929$	−30.5004	+	7.51766i	−1.00068	+	0.246646i	−0.705436	−	0.708774i	$-0.749249\pi$
$929$	−30.5004	+	7.51766i	−1.00068	+	0.246646i	−0.295249	+	0.955420i	$0.595402\pi$
$930$	39.1660	−	9.65355i	1.28430	−	0.316552i
$931$	1.93775	+	15.9588i	0.0635072	+	0.523029i
$932$	−4.58287	+	12.0840i	−0.150117	+	0.395826i
$933$	4.23921	+	2.22491i	0.138785	+	0.0728402i
$934$	34.3067			1.12255
$935$	−49.8055	+	26.1399i	−1.62881	+	0.854867i
$936$	−17.3850	−	3.99148i	−0.568247	−	0.130466i
$937$	5.84752	+	3.06901i	0.191030	+	0.100260i	0.557527	−	0.830159i	$-0.311750\pi$
$937$	5.84752	+	3.06901i	0.191030	+	0.100260i	−0.366496	+	0.930419i	$0.619443\pi$
$938$	−122.726	−	64.4113i	−4.00713	−	2.10310i
$939$	13.9346	−	3.43457i	0.454739	−	0.112083i
$940$	21.7849	−	31.5608i	0.710544	−	1.02940i
$941$	−36.0806	+	8.89306i	−1.17619	+	0.289905i	−0.778519	−	0.627622i	$-0.784029\pi$
$941$	−36.0806	+	8.89306i	−1.17619	+	0.289905i	−0.397674	+	0.917527i	$0.630182\pi$
$942$	−9.37053	−	13.5756i	−0.305309	−	0.442316i
$943$	1.35877	−	11.1905i	0.0442477	−	0.364413i
$944$	22.0889			0.718934
$945$	1.21218	−	9.98321i	0.0394323	−	0.324754i
$946$	−19.7529	−	52.0842i	−0.642224	−	1.69340i
$947$	27.5229	−	14.4451i	0.894373	−	0.469403i	0.0460847	−	0.998938i	$-0.485326\pi$
$947$	27.5229	−	14.4451i	0.894373	−	0.469403i	0.848289	+	0.529534i	$0.177633\pi$
$948$	−5.16893	+	42.5700i	−0.167879	+	1.38261i
$949$	−12.4097	+	18.6076i	−0.402835	+	0.604029i
$950$	−2.16444	−	17.8258i	−0.0702237	−	0.578344i
$951$	−8.10110	−	11.7365i	−0.262696	−	0.380581i
$952$	71.4998	−	103.585i	2.31732	−	3.35722i
$953$	11.9582	−	10.5941i	0.387365	−	0.343176i	−0.446856	−	0.894606i	$-0.647456\pi$
$953$	11.9582	−	10.5941i	0.387365	−	0.343176i	0.834221	+	0.551431i	$0.185918\pi$
$954$	−0.412152	−	1.08675i	−0.0133439	−	0.0351850i
$955$	4.19531	−	6.07796i	0.135757	−	0.196678i
$956$	27.0306	+	14.1867i	0.874231	+	0.458832i
$957$	0.846515	−	6.97168i	0.0273640	−	0.225362i
$958$	−2.20345	−	18.1470i	−0.0711901	−	0.586303i
$959$	−6.69040	+	17.6411i	−0.216044	+	0.569662i
$960$	12.3302	−	17.8634i	0.397955	−	0.576537i
$961$	−2.90622	−	2.57469i	−0.0937491	−	0.0830545i
$962$	−7.03828	−	51.1245i	−0.226923	−	1.64832i
$963$	14.1800	−	12.5624i	0.456943	−	0.404816i
$964$	−7.10966	−	58.5533i	−0.228987	−	1.88588i
$965$	6.70967	+	55.2591i	0.215992	+	1.77885i
$966$	37.5489	−	19.7072i	1.20812	−	0.634069i
$967$	−30.7498	+	16.1387i	−0.988847	+	0.518987i	−0.879950	−	0.475066i	$-0.842424\pi$
$967$	−30.7498	+	16.1387i	−0.988847	+	0.518987i	−0.108897	+	0.994053i	$0.534732\pi$
$968$	−13.3316	−	3.28594i	−0.428494	−	0.105614i
$969$	−14.0219	+	12.4223i	−0.450449	+	0.399063i
$970$	−19.7782	−	4.87489i	−0.635040	−	0.156523i
$971$	−1.76350	−	4.64997i	−0.0565935	−	0.149225i	0.903738	−	0.428086i	$-0.140812\pi$
$971$	−1.76350	−	4.64997i	−0.0565935	−	0.149225i	−0.960331	+	0.278862i	$0.910043\pi$
$972$	3.55674	−	1.86672i	0.114083	−	0.0598752i
$973$	2.23097	−	18.3737i	0.0715217	−	0.589034i
$974$	75.9420	−	18.7180i	2.43334	−	0.599764i
$975$	−5.50681	+	8.25716i	−0.176359	+	0.264441i
$976$	−45.3907	−	11.1878i	−1.45292	−	0.358113i
$977$	4.29084	−	11.3140i	0.137276	−	0.361968i	−0.848695	−	0.528882i	$-0.822611\pi$
$977$	4.29084	−	11.3140i	0.137276	−	0.361968i	0.985971	+	0.166915i	$0.0533805\pi$
$978$	18.1590	+	16.0875i	0.580662	+	0.514421i
$979$	−24.1290	+	5.94727i	−0.771167	+	0.190076i
$980$	−38.4066	−	55.6416i	−1.22685	−	1.77740i
$981$	−0.900047	−	7.41255i	−0.0287363	−	0.236665i
$982$	−19.2325	−	50.7121i	−0.613735	−	1.61829i
$983$	13.5034	−	35.6055i	0.430691	−	1.13564i	−0.527511	−	0.849548i	$-0.676875\pi$
$983$	13.5034	−	35.6055i	0.430691	−	1.13564i	0.958202	−	0.286091i	$-0.0923561\pi$
$984$	−6.61850	−	9.58855i	−0.210990	−	0.305672i
$985$	−3.21543	−	0.792533i	−0.102452	−	0.0252522i
$986$	15.0043	+	39.5630i	0.477834	+	1.25994i
$987$	−4.39149	+	11.5794i	−0.139783	+	0.368576i
$988$	37.2447	−	9.81382i	1.18491	−	0.312219i
$989$	13.4405	+	35.4397i	0.427383	+	1.12692i
$990$	−14.6611	+	12.9886i	−0.465959	+	0.412804i
$991$	−46.9679			−1.49198			−0.745992	−	0.665955i	$-0.768024\pi$
$991$	−46.9679			−1.49198			−0.745992	+	0.665955i	$0.768024\pi$
$992$	0.980572			0.0311332
$993$	−15.3521	+	13.6008i	−0.487184	+	0.431608i
$994$	28.9568	−	15.1977i	0.918453	−	0.482041i
$995$	75.7771			2.40230
$996$	−59.3603	−	31.1547i	−1.88090	−	0.987174i
$997$	−14.9047	−	13.2044i	−0.472036	−	0.418188i	0.393276	−	0.919420i	$-0.371342\pi$
$997$	−14.9047	−	13.2044i	−0.472036	−	0.418188i	−0.865313	+	0.501233i	$0.832880\pi$
$998$	60.5380	+	87.7045i	1.91630	+	2.77624i
$999$	4.36765	+	3.86940i	0.138186	+	0.122422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.16	✓	204
169.131	even	13	inner	507.2.m.b.469.16	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.16	✓	204	1.1	even	1	trivial
507.2.m.b.469.16	yes	204	169.131	even	13	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.38165 + 0.587024i) q^{2} +(0.120537 - 0.992709i) q^{3} +(3.55674 + 1.86672i) q^{4} +(-1.58170 + 2.29149i) q^{5} +(0.869820 - 2.29353i) q^{6} +(2.70346 + 2.39506i) q^{7} +(3.70302 + 3.28059i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(2.38165 + 0.587024i) q^{2} +(0.120537 - 0.992709i) q^{3} +(3.55674 + 1.86672i) q^{4} +(-1.58170 + 2.29149i) q^{5} +(0.869820 - 2.29353i) q^{6} +(2.70346 + 2.39506i) q^{7} +(3.70302 + 3.28059i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-5.11221 + 4.52903i) q^{10} +(-2.78452 + 0.686322i) q^{11} +(2.28183 - 3.30580i) q^{12} +(2.66025 - 2.43374i) q^{13} +(5.03274 + 7.29118i) q^{14} +(2.08413 + 1.84638i) q^{15} +(2.32985 + 3.37537i) q^{16} +(-5.27260 - 4.67112i) q^{17} +(-2.17196 - 1.13993i) q^{18} +2.65939 q^{19} +(-9.90328 + 5.19764i) q^{20} +(2.70346 - 2.39506i) q^{21} -7.03463 q^{22} +4.78657 q^{23} +(3.70302 - 3.28059i) q^{24} +(-0.976121 - 2.57382i) q^{25} +(7.76444 - 4.23469i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(5.14461 + 13.5652i) q^{28} +(-2.37767 - 0.586044i) q^{29} +(3.87980 + 5.62086i) q^{30} +(2.09435 - 5.52235i) q^{31} +(0.0588734 + 0.155236i) q^{32} +(0.345681 + 2.84694i) q^{33} +(-9.81543 - 14.2201i) q^{34} +(-9.76431 + 2.40669i) q^{35} +(-3.00666 - 2.66366i) q^{36} +(2.06916 - 5.45593i) q^{37} +(6.33375 + 1.56113i) q^{38} +(-2.09534 - 2.93421i) q^{39} +(-13.3745 + 3.29652i) q^{40} +(0.283872 - 2.33790i) q^{41} +(7.84465 - 4.11719i) q^{42} +(2.80796 + 7.40398i) q^{43} +(-11.1850 - 2.75685i) q^{44} +(2.08413 - 1.84638i) q^{45} +(11.3999 + 2.80983i) q^{46} +(-3.03607 + 1.59345i) q^{47} +(3.63160 - 1.90601i) q^{48} +(0.728643 + 6.00092i) q^{49} +(-0.813884 - 6.70294i) q^{50} +(-5.27260 + 4.67112i) q^{51} +(14.0049 - 3.69025i) q^{52} +(0.354671 + 0.314211i) q^{53} +(-1.39342 + 2.01872i) q^{54} +(2.83157 - 7.46624i) q^{55} +(2.15377 + 17.7379i) q^{56} +(0.320555 - 2.64000i) q^{57} +(-5.31876 - 2.79150i) q^{58} +(3.05944 - 4.43237i) q^{59} +(3.96604 + 10.4576i) q^{60} +(-8.53181 + 7.55852i) q^{61} +(8.22976 - 11.9229i) q^{62} +(-2.05173 - 2.97244i) q^{63} +(-0.939646 - 7.73868i) q^{64} +(1.36917 + 9.94537i) q^{65} +(-0.847931 + 6.98334i) q^{66} +(-13.8525 + 7.27036i) q^{67} +(-10.0336 - 26.4565i) q^{68} +(0.576957 - 4.75167i) q^{69} -24.6679 q^{70} +(0.444934 - 3.66436i) q^{71} +(-2.81032 - 4.07145i) q^{72} +(-6.02299 + 1.48453i) q^{73} +(8.13078 - 11.7795i) q^{74} +(-2.67271 + 0.658764i) q^{75} +(9.45879 + 4.96435i) q^{76} +(-9.17161 - 4.81363i) q^{77} +(-3.26791 - 8.21826i) q^{78} +(-9.45285 + 4.96124i) q^{79} -11.4198 q^{80} +(0.885456 + 0.464723i) q^{81} +(2.04848 - 5.40141i) q^{82} +(-2.01170 - 16.5678i) q^{83} +(14.0864 - 3.47199i) q^{84} +(19.0435 - 4.69380i) q^{85} +(2.34126 + 19.2820i) q^{86} +(-0.868368 + 2.28970i) q^{87} +(-12.5627 - 6.59340i) q^{88} +8.66543 q^{89} +(6.04753 - 3.17399i) q^{90} +(13.0208 - 0.208077i) q^{91} +(17.0246 + 8.93520i) q^{92} +(-5.22964 - 2.74473i) q^{93} +(-8.16625 + 2.01280i) q^{94} +(-4.20637 + 6.09397i) q^{95} +(0.161201 - 0.0397325i) q^{96} +(1.69426 + 2.45456i) q^{97} +(-1.78731 + 14.7198i) q^{98} +2.86785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

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