LMFDB - Embedded newform 483.2.q.d.127.2

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			127.2
Character	$\chi$	$=$	483.127
Dual form			483.2.q.d.232.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49352 + 0.959824i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.478496 - 1.04776i) q^{4} +(1.94954 - 0.572436i) q^{5} +(0.737505 + 1.61491i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.214292 - 1.49043i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-1.49352 + 0.959824i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.478496 - 1.04776i) q^{4} +(1.94954 - 0.572436i) q^{5} +(0.737505 + 1.61491i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.214292 - 1.49043i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.36223 + 2.72616i) q^{10} +(2.43863 + 1.56722i) q^{11} +(-0.968999 - 0.622738i) q^{12} +(0.544730 - 0.628652i) q^{13} +(1.70343 + 0.500173i) q^{14} +(-0.289161 - 2.01116i) q^{15} +(3.25920 + 3.76132i) q^{16} +(-2.83980 - 6.21829i) q^{17} +(1.70343 - 0.500173i) q^{18} +(-0.350095 + 0.766601i) q^{19} +(0.333071 - 2.31656i) q^{20} +(-0.841254 + 0.540641i) q^{21} -5.14639 q^{22} +(0.989578 - 4.69263i) q^{23} -1.50576 q^{24} +(-0.733252 + 0.471233i) q^{25} +(-0.210168 + 1.46175i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.10519 + 0.324514i) q^{28} +(-2.77652 - 6.07973i) q^{29} +(2.36223 + 2.72616i) q^{30} +(0.335445 + 2.33307i) q^{31} +(-5.58835 - 1.64089i) q^{32} +(1.89832 - 2.19077i) q^{33} +(10.2097 + 6.56140i) q^{34} +(-1.70929 - 1.09850i) q^{35} +(-0.754302 + 0.870511i) q^{36} +(5.84870 + 1.71733i) q^{37} +(-0.212930 - 1.48096i) q^{38} +(-0.544730 - 0.628652i) q^{39} +(-1.27095 - 2.78298i) q^{40} +(6.71491 - 1.97168i) q^{41} +(0.737505 - 1.61491i) q^{42} +(1.34798 - 9.37541i) q^{43} +(2.80894 - 1.80520i) q^{44} -2.03184 q^{45} +(3.02614 + 7.95833i) q^{46} +10.2178 q^{47} +(4.18687 - 2.69074i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.642823 - 1.40759i) q^{50} +(-6.55914 + 1.92594i) q^{51} +(-0.398026 - 0.871555i) q^{52} +(-3.61565 - 4.17268i) q^{53} +(-0.252658 - 1.75727i) q^{54} +(5.65134 + 1.65938i) q^{55} +(-0.986061 + 1.13798i) q^{56} +(0.708974 + 0.455630i) q^{57} +(9.98225 + 6.41520i) q^{58} +(7.73530 - 8.92701i) q^{59} +(-2.24558 - 0.659361i) q^{60} +(0.885704 + 6.16021i) q^{61} +(-2.74033 - 3.16251i) q^{62} +(0.415415 + 0.909632i) q^{63} +(0.370572 - 0.108810i) q^{64} +(0.702109 - 1.53740i) q^{65} +(-0.732408 + 5.09401i) q^{66} +(0.886508 - 0.569724i) q^{67} -7.87411 q^{68} +(-4.50403 - 1.64734i) q^{69} +3.60722 q^{70} +(-4.86289 + 3.12519i) q^{71} +(-0.214292 + 1.49043i) q^{72} +(-3.95488 + 8.65998i) q^{73} +(-10.3835 + 3.04886i) q^{74} +(0.362083 + 0.792852i) q^{75} +(0.635695 + 0.733631i) q^{76} +(-0.412544 - 2.86931i) q^{77} +(1.41696 + 0.416057i) q^{78} +(5.94152 - 6.85688i) q^{79} +(8.50706 + 5.46715i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-8.13637 + 9.38987i) q^{82} +(5.41309 + 1.58943i) q^{83} +(0.163925 + 1.14013i) q^{84} +(-9.09586 - 10.4972i) q^{85} +(6.98551 + 15.2961i) q^{86} +(-6.41299 + 1.88302i) q^{87} +(1.81325 - 3.97046i) q^{88} +(-2.12312 + 14.7666i) q^{89} +(3.03459 - 1.95021i) q^{90} -0.831826 q^{91} +(-4.44324 - 3.28224i) q^{92} +2.35706 q^{93} +(-15.2605 + 9.80733i) q^{94} +(-0.243693 + 1.69492i) q^{95} +(-2.41949 + 5.29795i) q^{96} +(-9.12433 + 2.67915i) q^{97} +(-0.737505 - 1.61491i) q^{98} +(-1.89832 - 2.19077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * 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 $

$2$	−1.49352	+	0.959824i	−1.05607	+	0.678698i	−0.948911	−	0.315543i	$-0.897813\pi$
$2$	−1.49352	+	0.959824i	−1.05607	+	0.678698i	−0.107164	+	0.994241i	$0.534177\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.478496	−	1.04776i	0.239248	−	0.523880i
$5$	1.94954	−	0.572436i	0.871860	−	0.256001i	0.184954	−	0.982747i	$-0.440786\pi$
$5$	1.94954	−	0.572436i	0.871860	−	0.256001i	0.686906	+	0.726746i	$0.258968\pi$
$6$	0.737505	+	1.61491i	0.301085	+	0.659285i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.214292	−	1.49043i	−0.0757635	−	0.526947i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−2.36223	+	2.72616i	−0.747002	+	0.862086i
$11$	2.43863	+	1.56722i	0.735276	+	0.472533i	0.853920	−	0.520404i	$-0.174218\pi$
$11$	2.43863	+	1.56722i	0.735276	+	0.472533i	−0.118644	+	0.992937i	$0.537855\pi$
$12$	−0.968999	−	0.622738i	−0.279726	−	0.179769i
$13$	0.544730	−	0.628652i	0.151081	−	0.174357i	−0.675164	−	0.737668i	$-0.735927\pi$
$13$	0.544730	−	0.628652i	0.151081	−	0.174357i	0.826245	+	0.563311i	$0.190473\pi$
$14$	1.70343	+	0.500173i	0.455261	+	0.133677i
$15$	−0.289161	−	2.01116i	−0.0746611	−	0.519279i
$16$	3.25920	+	3.76132i	0.814801	+	0.940330i
$17$	−2.83980	−	6.21829i	−0.688752	−	1.50816i	−0.853097	−	0.521753i	$-0.825278\pi$
$17$	−2.83980	−	6.21829i	−0.688752	−	1.50816i	0.164345	−	0.986403i	$-0.447449\pi$
$18$	1.70343	−	0.500173i	0.401503	−	0.117892i
$19$	−0.350095	+	0.766601i	−0.0803173	+	0.175870i	−0.945530	−	0.325534i	$-0.894456\pi$
$19$	−0.350095	+	0.766601i	−0.0803173	+	0.175870i	0.865213	+	0.501404i	$0.167183\pi$
$20$	0.333071	−	2.31656i	0.0744769	−	0.517998i
$21$	−0.841254	+	0.540641i	−0.183577	+	0.117977i
$22$	−5.14639			−1.09721
$23$	0.989578	−	4.69263i	0.206341	−	0.978480i
$23$	0.989578	−	4.69263i	0.206341	−	0.978480i
$24$	−1.50576			−0.307361
$25$	−0.733252	+	0.471233i	−0.146650	+	0.0942465i
$26$	−0.210168	+	1.46175i	−0.0412172	+	0.286672i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−1.10519	+	0.324514i	−0.208862	+	0.0613274i
$29$	−2.77652	−	6.07973i	−0.515587	−	1.12898i	−0.971084	−	0.238740i	$-0.923266\pi$
$29$	−2.77652	−	6.07973i	−0.515587	−	1.12898i	0.455497	−	0.890237i	$-0.349462\pi$
$30$	2.36223	+	2.72616i	0.431282	+	0.497726i
$31$	0.335445	+	2.33307i	0.0602477	+	0.419032i	0.997517	+	0.0704257i	$0.0224358\pi$
$31$	0.335445	+	2.33307i	0.0602477	+	0.419032i	−0.937269	+	0.348606i	$0.886655\pi$
$32$	−5.58835	−	1.64089i	−0.987890	−	0.290071i
$33$	1.89832	−	2.19077i	0.330455	−	0.381365i
$34$	10.2097	+	6.56140i	1.75096	+	1.12527i
$35$	−1.70929	−	1.09850i	−0.288923	−	0.185680i
$36$	−0.754302	+	0.870511i	−0.125717	+	0.145085i
$37$	5.84870	+	1.71733i	0.961520	+	0.282328i	0.724576	−	0.689195i	$-0.242036\pi$
$37$	5.84870	+	1.71733i	0.961520	+	0.282328i	0.236945	+	0.971523i	$0.423854\pi$
$38$	−0.212930	−	1.48096i	−0.0345418	−	0.240243i
$39$	−0.544730	−	0.628652i	−0.0872266	−	0.100665i
$40$	−1.27095	−	2.78298i	−0.200954	−	0.440028i
$41$	6.71491	−	1.97168i	1.04869	−	0.307924i	0.288404	−	0.957509i	$-0.406875\pi$
$41$	6.71491	−	1.97168i	1.04869	−	0.307924i	0.760289	+	0.649585i	$0.225057\pi$
$42$	0.737505	−	1.61491i	0.113800	−	0.249186i
$43$	1.34798	−	9.37541i	0.205565	−	1.42974i	−0.581842	−	0.813302i	$-0.697668\pi$
$43$	1.34798	−	9.37541i	0.205565	−	1.42974i	0.787407	−	0.616434i	$-0.211423\pi$
$44$	2.80894	−	1.80520i	0.423464	−	0.272144i
$45$	−2.03184			−0.302889
$46$	3.02614	+	7.95833i	0.446181	+	1.17339i
$47$	10.2178			1.49043			0.745213	−	0.666827i	$-0.232348\pi$
$47$	10.2178			1.49043			0.745213	+	0.666827i	$0.232348\pi$
$48$	4.18687	−	2.69074i	0.604323	−	0.388375i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	0.642823	−	1.40759i	0.0909089	−	0.199063i
$51$	−6.55914	+	1.92594i	−0.918463	+	0.269685i
$52$	−0.398026	−	0.871555i	−0.0551962	−	0.120863i
$53$	−3.61565	−	4.17268i	−0.496648	−	0.573162i	0.450982	−	0.892533i	$-0.351074\pi$
$53$	−3.61565	−	4.17268i	−0.496648	−	0.573162i	−0.947630	+	0.319371i	$0.896528\pi$
$54$	−0.252658	−	1.75727i	−0.0343824	−	0.239135i
$55$	5.65134	+	1.65938i	0.762027	+	0.223751i
$56$	−0.986061	+	1.13798i	−0.131768	+	0.152068i
$57$	0.708974	+	0.455630i	0.0939059	+	0.0603497i
$58$	9.98225	+	6.41520i	1.31073	+	0.842357i
$59$	7.73530	−	8.92701i	1.00705	−	1.16220i	0.0203260	−	0.999793i	$-0.493530\pi$
$59$	7.73530	−	8.92701i	1.00705	−	1.16220i	0.986724	−	0.162405i	$-0.0519250\pi$
$60$	−2.24558	−	0.659361i	−0.289903	−	0.0851231i
$61$	0.885704	+	6.16021i	0.113403	+	0.788734i	0.964568	+	0.263835i	$0.0849876\pi$
$61$	0.885704	+	6.16021i	0.113403	+	0.788734i	−0.851165	+	0.524898i	$0.824103\pi$
$62$	−2.74033	−	3.16251i	−0.348022	−	0.401639i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	0.370572	−	0.108810i	0.0463216	−	0.0136012i
$65$	0.702109	−	1.53740i	0.0870859	−	0.190692i
$66$	−0.732408	+	5.09401i	−0.0901532	+	0.627029i
$67$	0.886508	−	0.569724i	0.108304	−	0.0696029i	−0.485367	−	0.874310i	$-0.661314\pi$
$67$	0.886508	−	0.569724i	0.108304	−	0.0696029i	0.593672	+	0.804707i	$0.297678\pi$
$68$	−7.87411			−0.954876
$69$	−4.50403	−	1.64734i	−0.542221	−	0.198316i
$70$	3.60722			0.431145
$71$	−4.86289	+	3.12519i	−0.577119	+	0.370892i	−0.796400	−	0.604770i	$-0.793265\pi$
$71$	−4.86289	+	3.12519i	−0.577119	+	0.370892i	0.219281	+	0.975662i	$0.429629\pi$
$72$	−0.214292	+	1.49043i	−0.0252545	+	0.175649i
$73$	−3.95488	+	8.65998i	−0.462884	+	1.01357i	0.523937	+	0.851757i	$0.324463\pi$
$73$	−3.95488	+	8.65998i	−0.462884	+	1.01357i	−0.986821	+	0.161817i	$0.948265\pi$
$74$	−10.3835	+	3.04886i	−1.20705	+	0.354423i
$75$	0.362083	+	0.792852i	0.0418098	+	0.0915507i
$76$	0.635695	+	0.733631i	0.0729192	+	0.0841533i
$77$	−0.412544	−	2.86931i	−0.0470137	−	0.326988i
$78$	1.41696	+	0.416057i	0.160439	+	0.0471091i
$79$	5.94152	−	6.85688i	0.668473	−	0.771459i	−0.315664	−	0.948871i	$-0.602227\pi$
$79$	5.94152	−	6.85688i	0.668473	−	0.771459i	0.984137	+	0.177412i	$0.0567726\pi$
$80$	8.50706	+	5.46715i	0.951118	+	0.611246i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−8.13637	+	9.38987i	−0.898511	+	1.03694i
$83$	5.41309	+	1.58943i	0.594164	+	0.174462i	0.564970	−	0.825111i	$-0.308888\pi$
$83$	5.41309	+	1.58943i	0.594164	+	0.174462i	0.0291942	+	0.999574i	$0.490706\pi$
$84$	0.163925	+	1.14013i	0.0178857	+	0.124398i
$85$	−9.09586	−	10.4972i	−0.986585	−	1.13858i
$86$	6.98551	+	15.2961i	0.753267	+	1.64942i
$87$	−6.41299	+	1.88302i	−0.687544	+	0.201881i
$88$	1.81325	−	3.97046i	0.193293	−	0.423252i
$89$	−2.12312	+	14.7666i	−0.225050	+	1.56526i	0.493478	+	0.869758i	$0.335725\pi$
$89$	−2.12312	+	14.7666i	−0.225050	+	1.56526i	−0.718528	+	0.695498i	$0.755184\pi$
$90$	3.03459	−	1.95021i	0.319874	−	0.205570i
$91$	−0.831826			−0.0871991
$92$	−4.44324	−	3.28224i	−0.463240	−	0.342198i
$93$	2.35706			0.244416
$94$	−15.2605	+	9.80733i	−1.57400	+	1.01155i
$95$	−0.243693	+	1.69492i	−0.0250024	+	0.173896i
$96$	−2.41949	+	5.29795i	−0.246938	+	0.540719i
$97$	−9.12433	+	2.67915i	−0.926436	+	0.272026i	−0.709944	−	0.704258i	$-0.751280\pi$
$97$	−9.12433	+	2.67915i	−0.926436	+	0.272026i	−0.216492	+	0.976284i	$0.569462\pi$
$98$	−0.737505	−	1.61491i	−0.0744993	−	0.163131i
$99$	−1.89832	−	2.19077i	−0.190788	−	0.220181i
$100$	0.142880	+	0.993756i	0.0142880	+	0.0993756i
$101$	−13.7501	−	4.03740i	−1.36819	−	0.401736i	−0.486546	−	0.873655i	$-0.661743\pi$
$101$	−13.7501	−	4.03740i	−1.36819	−	0.401736i	−0.881642	+	0.471919i	$0.843562\pi$
$102$	7.94761	−	9.17204i	0.786931	−	0.908167i
$103$	1.39945	+	0.899370i	0.137892	+	0.0886175i	0.607768	−	0.794115i	$-0.292065\pi$
$103$	1.39945	+	0.899370i	0.137892	+	0.0886175i	−0.469876	+	0.882732i	$0.655701\pi$
$104$	−1.05369	−	0.677168i	−0.103323	−	0.0664018i
$105$	−1.33057	+	1.53556i	−0.129851	+	0.149856i
$106$	9.40507	+	2.76158i	0.913501	+	0.268228i
$107$	1.21136	+	8.42521i	0.117107	+	0.814496i	0.960715	+	0.277537i	$0.0895180\pi$
$107$	1.21136	+	8.42521i	0.117107	+	0.814496i	−0.843608	+	0.536959i	$0.819573\pi$
$108$	0.754302	+	0.870511i	0.0725827	+	0.0837650i
$109$	−4.49511	−	9.84292i	−0.430554	−	0.942781i	−0.993237	−	0.116108i	$-0.962958\pi$
$109$	−4.49511	−	9.84292i	−0.430554	−	0.942781i	0.562683	−	0.826673i	$-0.309769\pi$
$110$	−10.0331	+	2.94598i	−0.956617	+	0.280888i
$111$	2.53221	−	5.54477i	0.240347	−	0.526286i
$112$	0.708293	−	4.92628i	0.0669274	−	0.465490i
$113$	−4.05028	+	2.60296i	−0.381018	+	0.244866i	−0.717105	−	0.696966i	$-0.754533\pi$
$113$	−4.05028	+	2.60296i	−0.381018	+	0.244866i	0.336086	+	0.941831i	$0.390897\pi$
$114$	−1.49619			−0.140131
$115$	−0.757007	−	9.71492i	−0.0705913	−	0.905921i
$116$	−7.69866			−0.714802
$117$	−0.699777	+	0.449719i	−0.0646944	+	0.0415765i
$118$	−2.98443	+	20.7572i	−0.274739	+	1.91085i
$119$	−2.83980	+	6.21829i	−0.260324	+	0.570029i
$120$	−2.93553	+	0.861950i	−0.267976	+	0.0786849i
$121$	−1.07879	−	2.36222i	−0.0980718	−	0.214747i
$122$	−7.23553	−	8.35025i	−0.655074	−	0.755996i
$123$	−0.995976	−	6.92717i	−0.0898041	−	0.624601i
$124$	2.60501	+	0.764899i	0.233937	+	0.0686900i
$125$	−7.81262	+	9.01624i	−0.698782	+	0.806437i
$126$	−1.49352	−	0.959824i	−0.133053	−	0.0855079i
$127$	5.00298	+	3.21522i	0.443943	+	0.285305i	0.743453	−	0.668788i	$-0.233187\pi$
$127$	5.00298	+	3.21522i	0.443943	+	0.285305i	−0.299510	+	0.954093i	$0.596823\pi$
$128$	7.17916	−	8.28519i	0.634554	−	0.732315i
$129$	−9.08814	−	2.66852i	−0.800166	−	0.234950i
$130$	0.427027	+	2.97004i	0.0374528	+	0.260490i
$131$	−6.40469	−	7.39141i	−0.559581	−	0.645790i	0.403508	−	0.914976i	$-0.367791\pi$
$131$	−6.40469	−	7.39141i	−0.559581	−	0.645790i	−0.963088	+	0.269186i	$0.913245\pi$
$132$	−1.38707	−	3.03726i	−0.120729	−	0.264360i
$133$	0.808622	−	0.237433i	0.0701164	−	0.0205880i
$134$	−0.777178	+	1.70178i	−0.0671380	+	0.147012i
$135$	−0.289161	+	2.01116i	−0.0248870	+	0.173093i
$136$	−8.65938	+	5.56505i	−0.742536	+	0.477199i
$137$	−18.6281			−1.59151			−0.795753	−	0.605622i	$-0.792925\pi$
$137$	−18.6281			−1.59151			−0.795753	+	0.605622i	$0.792925\pi$
$138$	8.30799	−	1.86275i	0.707223	−	0.158568i
$139$	0.985794			0.0836140			0.0418070	−	0.999126i	$-0.486689\pi$
$139$	0.985794			0.0836140			0.0418070	+	0.999126i	$0.486689\pi$
$140$	−1.96885	+	1.26530i	−0.166398	+	0.106938i
$141$	1.45415	−	10.1138i	0.122462	−	0.851739i
$142$	4.26317	−	9.33505i	0.357758	−	0.783380i
$143$	2.31363	−	0.679344i	0.193476	−	0.0568096i
$144$	−2.06750	−	4.52719i	−0.172291	−	0.377265i
$145$	−8.89319	−	10.2633i	−0.738539	−	0.852319i
$146$	−2.40538	−	16.7298i	−0.199071	−	1.38457i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	4.59793	−	5.30630i	0.377948	−	0.436175i
$149$	14.5521	+	9.35205i	1.19215	+	0.766150i	0.977581	−	0.210558i	$-0.0675282\pi$
$149$	14.5521	+	9.35205i	1.19215	+	0.766150i	0.214571	+	0.976708i	$0.431165\pi$
$150$	−1.30178	−	0.836601i	−0.106290	−	0.0683081i
$151$	−3.05970	+	3.53109i	−0.248995	+	0.287356i	−0.866464	−	0.499240i	$-0.833613\pi$
$151$	−3.05970	+	3.53109i	−0.248995	+	0.287356i	0.617469	+	0.786595i	$0.288158\pi$
$152$	1.21759	+	0.357516i	0.0987594	+	0.0289984i
$153$	0.972871	+	6.76646i	0.0786519	+	0.547036i
$154$	3.37017	+	3.88938i	0.271576	+	0.313415i
$155$	1.98950	+	4.35639i	0.159800	+	0.349913i
$156$	−0.919328	+	0.269939i	−0.0736052	+	0.0216124i
$157$	1.28676	−	2.81761i	0.102695	−	0.224870i	−0.851309	−	0.524664i	$-0.824191\pi$
$157$	1.28676	−	2.81761i	0.102695	−	0.224870i	0.954004	+	0.299794i	$0.0969181\pi$
$158$	−2.29235	+	15.9437i	−0.182370	+	1.26841i
$159$	−4.64477	+	2.98501i	−0.368354	+	0.236727i
$160$	−11.8340			−0.935560
$161$	−4.19449	+	2.32514i	−0.330572	+	0.183247i
$162$	−1.77535			−0.139484
$163$	2.40576	−	1.54609i	0.188434	−	0.121099i	−0.443023	−	0.896510i	$-0.646094\pi$
$163$	2.40576	−	1.54609i	0.188434	−	0.121099i	0.631456	+	0.775411i	$0.282458\pi$
$164$	1.14722	−	7.97906i	0.0895825	−	0.623060i
$165$	2.44676	−	5.35766i	0.190480	−	0.417094i
$166$	−9.61011	+	2.82178i	−0.745889	+	0.219013i
$167$	10.2954	+	22.5438i	0.796684	+	1.74449i	0.656442	+	0.754376i	$0.272061\pi$
$167$	10.2954	+	22.5438i	0.796684	+	1.74449i	0.140241	+	0.990117i	$0.455212\pi$
$168$	0.986061	+	1.13798i	0.0760763	+	0.0877967i
$169$	1.75162	+	12.1828i	0.134740	+	0.937137i
$170$	23.6603	+	6.94728i	1.81466	+	0.532832i
$171$	0.551890	−	0.636915i	0.0422041	−	0.0487061i
$172$	−9.17818	−	5.89846i	−0.699829	−	0.449753i
$173$	11.3544	+	7.29702i	0.863258	+	0.554782i	0.895684	−	0.444692i	$-0.146687\pi$
$173$	11.3544	+	7.29702i	0.863258	+	0.554782i	−0.0324254	+	0.999474i	$0.510323\pi$
$174$	7.77052	−	8.96766i	0.589082	−	0.679837i
$175$	0.836312	+	0.245563i	0.0632192	+	0.0185628i
$176$	2.05321	+	14.2804i	0.154766	+	1.07642i
$177$	−7.73530	−	8.92701i	−0.581421	−	0.670995i
$178$	−11.0024	−	24.0920i	−0.824667	−	1.80577i
$179$	8.97000	−	2.63383i	0.670449	−	0.196862i	0.0712461	−	0.997459i	$-0.477302\pi$
$179$	8.97000	−	2.63383i	0.670449	−	0.196862i	0.599203	+	0.800597i	$0.295484\pi$
$180$	−0.972229	+	2.12888i	−0.0724656	+	0.158678i
$181$	−2.50032	+	17.3901i	−0.185848	+	1.29260i	0.656772	+	0.754089i	$0.271921\pi$
$181$	−2.50032	+	17.3901i	−0.185848	+	1.29260i	−0.842620	+	0.538509i	$0.818988\pi$
$182$	1.24235	−	0.798407i	0.0920888	−	0.0591818i
$183$	6.22355			0.460058
$184$	−7.20609	−	0.469308i	−0.531240	−	0.0345978i
$185$	12.3853			0.910587
$186$	−3.52031	+	2.26236i	−0.258121	+	0.165885i
$187$	2.82017	−	19.6147i	0.206231	−	1.43437i
$188$	4.88920	−	10.7059i	0.356582	−	0.780805i
$189$	0.959493	−	0.281733i	0.0697928	−	0.0204930i
$190$	−1.26287	−	2.76530i	−0.0916182	−	0.200616i
$191$	4.76888	+	5.50358i	0.345064	+	0.398225i	0.901580	−	0.432612i	$-0.142408\pi$
$191$	4.76888	+	5.50358i	0.345064	+	0.398225i	−0.556516	+	0.830837i	$0.687862\pi$
$192$	−0.0549644	−	0.382286i	−0.00396671	−	0.0275891i
$193$	21.8533	+	6.41672i	1.57304	+	0.461886i	0.947884	−	0.318616i	$-0.103218\pi$
$193$	21.8533	+	6.41672i	1.57304	+	0.461886i	0.625154	+	0.780502i	$0.285036\pi$
$194$	11.0558	−	12.7591i	0.793762	−	0.916050i
$195$	−1.42184	−	0.913758i	−0.101820	−	0.0654356i
$196$	0.968999	+	0.622738i	0.0692142	+	0.0444813i
$197$	−12.0158	+	13.8669i	−0.856088	+	0.987979i	−0.999999	−	0.00161203i	$-0.999487\pi$
$197$	−12.0158	+	13.8669i	−0.856088	+	0.987979i	0.143910	+	0.989591i	$0.454032\pi$
$198$	4.93793	+	1.44991i	0.350923	+	0.103040i
$199$	1.68482	+	11.7182i	0.119434	+	0.830679i	0.958182	+	0.286160i	$0.0923788\pi$
$199$	1.68482	+	11.7182i	0.119434	+	0.830679i	−0.838748	+	0.544519i	$0.816712\pi$
$200$	0.859469	+	0.991880i	0.0607737	+	0.0701365i
$201$	−0.437762	−	0.958565i	−0.0308773	−	0.0676119i
$202$	24.4112	−	7.16778i	1.71757	−	0.504323i
$203$	−2.77652	+	6.07973i	−0.194873	+	0.426713i
$204$	−1.12060	+	7.79396i	−0.0784579	+	0.545686i
$205$	11.9623	−	7.68772i	0.835485	−	0.536934i
$206$	−2.95333			−0.205768
$207$	−2.27156	+	4.22374i	−0.157884	+	0.293571i
$208$	4.13995			0.287054
$209$	−2.05518	+	1.32079i	−0.142160	+	0.0913606i
$210$	0.513361	−	3.57050i	0.0354253	−	0.246388i
$211$	−3.15631	+	6.91135i	−0.217289	+	0.475797i	−0.986616	−	0.163058i	$-0.947864\pi$
$211$	−3.15631	+	6.91135i	−0.217289	+	0.475797i	0.769327	+	0.638855i	$0.220592\pi$
$212$	−6.10205	+	1.79172i	−0.419090	+	0.123056i
$213$	2.40132	+	5.25816i	0.164536	+	0.360283i
$214$	−9.89591	−	11.4205i	−0.676470	−	0.780688i
$215$	−2.73888	−	19.0493i	−0.186790	−	1.29915i
$216$	1.44476	+	0.424221i	0.0983037	+	0.0288646i
$217$	1.54355	−	1.78135i	0.104783	−	0.120926i
$218$	16.1610	+	10.3860i	1.09456	+	0.703431i
$219$	8.00899	+	5.14707i	0.541198	+	0.347807i
$220$	4.44278	−	5.12724i	0.299532	−	0.345679i
$221$	−5.45606	−	1.60204i	−0.367014	−	0.107765i
$222$	1.54011	+	10.7117i	0.103365	+	0.718920i
$223$	−9.96391	−	11.4990i	−0.667233	−	0.770028i	0.316708	−	0.948523i	$-0.397422\pi$
$223$	−9.96391	−	11.4990i	−0.667233	−	0.770028i	−0.983941	+	0.178496i	$0.942877\pi$
$224$	2.41949	+	5.29795i	0.161659	+	0.353984i
$225$	0.836312	−	0.245563i	0.0557541	−	0.0163709i
$226$	3.55077	−	7.77511i	0.236194	−	0.517193i
$227$	1.48599	−	10.3353i	0.0986285	−	0.685976i	−0.879182	−	0.476486i	$-0.841910\pi$
$227$	1.48599	−	10.3353i	0.0986285	−	0.685976i	0.977811	−	0.209491i	$-0.0671805\pi$
$228$	0.816633	−	0.524818i	0.0540828	−	0.0347569i
$229$	0.843004			0.0557073			0.0278536	−	0.999612i	$-0.491133\pi$
$229$	0.843004			0.0557073			0.0278536	+	0.999612i	$0.491133\pi$
$230$	10.4552	+	13.7828i	0.689397	+	0.908811i
$231$	−2.89881			−0.190728
$232$	−8.46643	+	5.44105i	−0.555848	+	0.357222i
$233$	4.20095	−	29.2182i	0.275213	−	1.91415i	−0.114890	−	0.993378i	$-0.536651\pi$
$233$	4.20095	−	29.2182i	0.275213	−	1.91415i	0.390103	−	0.920771i	$-0.372439\pi$
$234$	0.613476	−	1.34333i	0.0401042	−	0.0878159i
$235$	19.9201	−	5.84906i	1.29944	−	0.381551i
$236$	−5.65206	−	12.3763i	−0.367918	−	0.805627i
$237$	−5.94152	−	6.85688i	−0.385943	−	0.445402i
$238$	−1.72718	−	12.0128i	−0.111957	−	0.778675i
$239$	−4.18585	−	1.22908i	−0.270760	−	0.0795024i	0.143534	−	0.989645i	$-0.454153\pi$
$239$	−4.18585	−	1.22908i	−0.270760	−	0.0795024i	−0.414294	+	0.910143i	$0.635972\pi$
$240$	6.62219	−	7.64241i	0.427460	−	0.493315i
$241$	−7.20170	−	4.62825i	−0.463902	−	0.298132i	0.287733	−	0.957711i	$-0.407098\pi$
$241$	−7.20170	−	4.62825i	−0.463902	−	0.298132i	−0.751635	+	0.659579i	$0.770735\pi$
$242$	3.87851	+	2.49256i	0.249320	+	0.160228i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	6.87823	+	2.01963i	0.440333	+	0.129294i
$245$	0.289161	+	2.01116i	0.0184738	+	0.128488i
$246$	8.13637	+	9.38987i	0.518756	+	0.598676i
$247$	0.291218	+	0.637678i	0.0185298	+	0.0405745i
$248$	3.40540	−	0.999914i	0.216243	−	0.0634946i
$249$	2.34361	−	5.13180i	0.148520	−	0.325214i
$250$	3.01426	−	20.9646i	0.190639	−	1.32592i
$251$	−8.84435	+	5.68392i	−0.558250	+	0.358766i	−0.789139	−	0.614214i	$-0.789473\pi$
$251$	−8.84435	+	5.68392i	−0.558250	+	0.358766i	0.230889	+	0.972980i	$0.425837\pi$
$252$	1.15185			0.0725598
$253$	9.76758	−	9.89272i	0.614082	−	0.621950i
$254$	−10.5581			−0.662473
$255$	−11.6848	+	7.50937i	−0.731731	+	0.470255i
$256$	−2.87979	+	20.0294i	−0.179987	+	1.25184i
$257$	−6.86056	+	15.0225i	−0.427950	+	0.937080i	0.565705	+	0.824608i	$0.308604\pi$
$257$	−6.86056	+	15.0225i	−0.427950	+	0.937080i	−0.993655	+	0.112472i	$0.964123\pi$
$258$	16.1346	−	4.73754i	1.00450	−	0.294946i
$259$	−2.53221	−	5.54477i	−0.157344	−	0.344535i
$260$	−1.27488	−	1.47128i	−0.0790644	−	0.0912452i
$261$	0.951193	+	6.61569i	0.0588774	+	0.409501i
$262$	16.6600	+	4.89181i	1.02926	+	0.302217i
$263$	9.26430	−	10.6916i	0.571261	−	0.659270i	−0.394442	−	0.918921i	$-0.629062\pi$
$263$	9.26430	−	10.6916i	0.571261	−	0.659270i	0.965703	+	0.259651i	$0.0836074\pi$
$264$	−3.67199	−	2.35985i	−0.225995	−	0.145238i
$265$	−9.43744	−	6.06508i	−0.579737	−	0.372575i
$266$	−0.979795	+	1.13074i	−0.0600751	+	0.0693304i
$267$	14.3141	+	4.20301i	0.876012	+	0.257220i
$268$	−0.172744	−	1.20146i	−0.0105520	−	0.0733908i
$269$	−4.73251	−	5.46161i	−0.288546	−	0.333000i	0.592907	−	0.805271i	$-0.297980\pi$
$269$	−4.73251	−	5.46161i	−0.288546	−	0.333000i	−0.881454	+	0.472270i	$0.843435\pi$
$270$	−1.49849	−	3.28124i	−0.0911954	−	0.199690i
$271$	−6.76506	+	1.98640i	−0.410948	+	0.120665i	−0.480671	−	0.876901i	$-0.659607\pi$
$271$	−6.76506	+	1.98640i	−0.410948	+	0.120665i	0.0697227	+	0.997566i	$0.477789\pi$
$272$	14.1335	−	30.9480i	0.856969	−	1.87650i
$273$	−0.118381	+	0.823359i	−0.00716476	+	0.0498320i
$274$	27.8213	−	17.8797i	1.68075	−	1.08015i
$275$	−2.52666			−0.152363
$276$	−3.88118	+	3.93090i	−0.233619	+	0.236612i
$277$	0.626626			0.0376503			0.0188252	−	0.999823i	$-0.494007\pi$
$277$	0.626626			0.0376503			0.0188252	+	0.999823i	$0.494007\pi$
$278$	−1.47230	+	0.946189i	−0.0883026	+	0.0567486i
$279$	0.335445	−	2.33307i	0.0200826	−	0.139677i
$280$	−1.27095	+	2.78298i	−0.0759535	+	0.166315i
$281$	10.4943	−	3.08139i	0.626035	−	0.183821i	0.0466988	−	0.998909i	$-0.485130\pi$
$281$	10.4943	−	3.08139i	0.626035	−	0.183821i	0.579337	+	0.815088i	$0.303312\pi$
$282$	7.53571	+	16.5009i	0.448745	+	0.982615i
$283$	15.6365	+	18.0454i	0.929491	+	1.07269i	0.997185	+	0.0749833i	$0.0238903\pi$
$283$	15.6365	+	18.0454i	0.929491	+	1.07269i	−0.0676941	+	0.997706i	$0.521564\pi$
$284$	0.947577	+	6.59054i	0.0562283	+	0.391077i
$285$	1.64299	+	0.482426i	0.0973224	+	0.0285764i
$286$	−2.80339	+	3.23529i	−0.165768	+	0.191307i
$287$	−5.88743	−	3.78362i	−0.347524	−	0.223340i
$288$	4.89969	+	3.14884i	0.288717	+	0.185547i
$289$	−19.4700	+	22.4696i	−1.14529	+	1.32174i
$290$	23.1331	+	6.79248i	1.35842	+	0.398868i
$291$	1.35335	+	9.41274i	0.0793347	+	0.551785i
$292$	7.18119	+	8.28753i	0.420247	+	0.484991i
$293$	−4.29349	−	9.40143i	−0.250828	−	0.549237i	0.741774	−	0.670650i	$-0.233985\pi$
$293$	−4.29349	−	9.40143i	−0.250828	−	0.549237i	−0.992602	+	0.121413i	$0.961258\pi$
$294$	−1.70343	+	0.500173i	−0.0993461	+	0.0291707i
$295$	9.97012	−	21.8315i	0.580483	−	1.27108i
$296$	1.30624	−	9.08509i	0.0759236	−	0.528060i
$297$	−2.43863	+	1.56722i	−0.141504	+	0.0909391i
$298$	−30.7101			−1.77899
$299$	−2.41098	−	3.17832i	−0.139430	−	0.183807i
$300$	1.00397			0.0579645
$301$	−7.96820	+	5.12085i	−0.459279	+	0.295161i
$302$	1.18049	−	8.21051i	0.0679297	−	0.472462i
$303$	−5.95315	+	13.0356i	−0.342000	+	0.748875i
$304$	−4.02446	+	1.18169i	−0.230819	+	0.0677745i
$305$	5.25304	+	11.5025i	0.300788	+	0.658634i
$306$	−7.94761	−	9.17204i	−0.454335	−	0.524330i
$307$	3.25843	+	22.6629i	0.185968	+	1.29344i	0.842318	+	0.538982i	$0.181191\pi$
$307$	3.25843	+	22.6629i	0.185968	+	1.29344i	−0.656349	+	0.754457i	$0.727900\pi$
$308$	−3.20375	−	0.940705i	−0.182550	−	0.0536016i
$309$	1.08938	−	1.25721i	0.0619725	−	0.0715201i
$310$	−7.15271	−	4.59677i	−0.406247	−	0.261079i
$311$	14.4345	+	9.27647i	0.818504	+	0.526021i	0.881606	−	0.471987i	$-0.156463\pi$
$311$	14.4345	+	9.27647i	0.818504	+	0.526021i	−0.0631018	+	0.998007i	$0.520099\pi$
$312$	−0.820232	+	0.946598i	−0.0464365	+	0.0535905i
$313$	20.3202	+	5.96654i	1.14856	+	0.337249i	0.799978	−	0.600029i	$-0.204844\pi$
$313$	20.3202	+	5.96654i	1.14856	+	0.337249i	0.348585	+	0.937277i	$0.386662\pi$
$314$	0.782616	+	5.44321i	0.0441656	+	0.307178i
$315$	1.33057	+	1.53556i	0.0749693	+	0.0865192i
$316$	−4.34137	−	9.50628i	−0.244221	−	0.534770i
$317$	−6.57427	+	1.93038i	−0.369248	+	0.108421i	−0.461092	−	0.887352i	$-0.652542\pi$
$317$	−6.57427	+	1.93038i	−0.369248	+	0.108421i	0.0918438	+	0.995773i	$0.470724\pi$
$318$	4.07195	−	8.91633i	0.228344	−	0.500003i
$319$	2.75733	−	19.1776i	0.154381	−	1.07374i
$320$	0.660158	−	0.424258i	0.0369040	−	0.0237167i
$321$	8.51185			0.475085
$322$	4.03280	−	7.49861i	0.224739	−	0.417881i
$323$	5.76114			0.320558
$324$	0.968999	−	0.622738i	0.0538333	−	0.0345965i
$325$	−0.103183	+	0.717655i	−0.00572358	+	0.0398083i
$326$	−2.10907	+	4.61821i	−0.116810	+	0.255779i
$327$	−10.3825	+	3.04856i	−0.574151	+	0.168586i
$328$	−4.37760	−	9.58560i	−0.241712	−	0.529276i
$329$	−6.69126	−	7.72213i	−0.368901	−	0.425735i
$330$	1.48814	+	10.3502i	0.0819192	+	0.569761i
$331$	20.3511	+	5.97562i	1.11860	+	0.328450i	0.788216	−	0.615398i	$-0.211005\pi$
$331$	20.3511	+	5.97562i	1.11860	+	0.328450i	0.330380	+	0.943848i	$0.392823\pi$
$332$	4.25548	−	4.91109i	0.233550	−	0.269531i
$333$	−5.12796	−	3.29554i	−0.281010	−	0.180594i
$334$	−37.0145	−	23.7878i	−2.02534	−	1.30161i
$335$	1.40215	−	1.61817i	0.0766076	−	0.0884099i
$336$	−4.77534	−	1.40217i	−0.260516	−	0.0764944i
$337$	−1.72133	−	11.9721i	−0.0937667	−	0.652162i	−0.981452	−	0.191710i	$-0.938597\pi$
$337$	−1.72133	−	11.9721i	−0.0937667	−	0.652162i	0.887685	−	0.460452i	$-0.152313\pi$
$338$	−14.3094	−	16.5139i	−0.778329	−	0.898240i
$339$	2.00005	+	4.37949i	0.108628	+	0.237861i
$340$	−15.3509	+	4.50742i	−0.832518	+	0.244449i
$341$	−2.83840	+	6.21522i	−0.153708	+	0.336573i
$342$	−0.212930	+	1.48096i	−0.0115139	+	0.0800811i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	−14.2623			−0.768969
$345$	−9.72377	−	0.633276i	−0.523510	−	0.0340944i
$346$	−23.9618			−1.28820
$347$	−17.9296	+	11.5227i	−0.962513	+	0.618569i	−0.924692	−	0.380715i	$-0.875678\pi$
$347$	−17.9296	+	11.5227i	−0.962513	+	0.618569i	−0.0378203	+	0.999285i	$0.512041\pi$
$348$	−1.09563	+	7.62029i	−0.0587321	+	0.408491i
$349$	0.643455	−	1.40897i	0.0344434	−	0.0754205i	−0.891628	−	0.452768i	$-0.850437\pi$
$349$	0.643455	−	1.40897i	0.0344434	−	0.0754205i	0.926072	+	0.377348i	$0.123164\pi$
$350$	−1.48474	+	0.435960i	−0.0793628	+	0.0233030i
$351$	0.345553	+	0.756656i	0.0184443	+	0.0403873i
$352$	−11.0563	−	12.7597i	−0.589304	−	0.680093i
$353$	−3.36215	−	23.3843i	−0.178949	−	1.24462i	−0.859200	−	0.511640i	$-0.829038\pi$
$353$	−3.36215	−	23.3843i	−0.178949	−	1.24462i	0.680251	−	0.732980i	$-0.261871\pi$
$354$	20.1212	+	5.90810i	1.06943	+	0.314012i
$355$	−7.69142	+	8.87638i	−0.408218	+	0.471109i
$356$	14.4560	+	9.29028i	0.766164	+	0.492384i
$357$	5.75085	+	3.69585i	0.304367	+	0.195605i
$358$	−10.8688	+	12.5433i	−0.574435	+	0.662933i
$359$	5.13218	+	1.50694i	0.270866	+	0.0795335i	0.414345	−	0.910120i	$-0.364011\pi$
$359$	5.13218	+	1.50694i	0.270866	+	0.0795335i	−0.143479	+	0.989653i	$0.545829\pi$
$360$	0.435407	+	3.02832i	0.0229479	+	0.159606i
$361$	11.9772	+	13.8225i	0.630381	+	0.727499i
$362$	−12.9572	−	28.3723i	−0.681015	−	1.49122i
$363$	−2.49170	+	0.731630i	−0.130781	+	0.0384006i
$364$	−0.398026	+	0.871555i	−0.0208622	+	0.0456819i
$365$	−2.75290	+	19.1469i	−0.144094	+	1.00219i
$366$	−9.29498	+	5.97352i	−0.485856	+	0.312241i
$367$	−25.1939			−1.31511			−0.657556	−	0.753405i	$-0.728410\pi$
$367$	−25.1939			−1.31511			−0.657556	+	0.753405i	$0.728410\pi$
$368$	20.8757	−	11.5721i	1.08822	−	0.603237i
$369$	−6.99840			−0.364322
$370$	−18.4977	+	11.8877i	−0.961648	+	0.618014i
$371$	−0.785756	+	5.46505i	−0.0407944	+	0.283731i
$372$	1.12784	−	2.46964i	0.0584760	−	0.128045i
$373$	−18.5187	+	5.43757i	−0.958860	+	0.281547i	−0.723471	−	0.690354i	$-0.757455\pi$
$373$	−18.5187	+	5.43757i	−0.958860	+	0.281547i	−0.235389	+	0.971901i	$0.575636\pi$
$374$	14.6147	+	32.0017i	0.755708	+	1.65477i
$375$	7.81262	+	9.01624i	0.403442	+	0.465597i
$376$	−2.18960	−	15.2290i	−0.112920	−	0.785375i
$377$	−5.33449	−	1.56635i	−0.274740	−	0.0806710i
$378$	−1.16260	+	1.34172i	−0.0597979	+	0.0690104i
$379$	26.0422	+	16.7363i	1.33770	+	0.859686i	0.996763	−	0.0804013i	$-0.0256202\pi$
$379$	26.0422	+	16.7363i	1.33770	+	0.859686i	0.340935	+	0.940087i	$0.389257\pi$
$380$	1.65927	+	1.06635i	0.0851187	+	0.0547024i
$381$	3.89450	−	4.49449i	0.199521	−	0.230260i
$382$	−12.4049	−	3.64240i	−0.634688	−	0.186361i
$383$	−0.0702126	−	0.488339i	−0.00358770	−	0.0249530i	0.987949	−	0.154780i	$-0.0494669\pi$
$383$	−0.0702126	−	0.488339i	−0.00358770	−	0.0249530i	−0.991537	+	0.129827i	$0.958558\pi$
$384$	−7.17916	−	8.28519i	−0.366360	−	0.422802i
$385$	−2.44676	−	5.35766i	−0.124699	−	0.273052i
$386$	−38.7972	+	11.3919i	−1.97473	+	0.579832i
$387$	−3.93473	+	8.61587i	−0.200014	+	0.437969i
$388$	−1.55886	+	10.8421i	−0.0791389	+	0.550423i
$389$	25.9846	−	16.6993i	1.31747	−	0.846686i	0.322472	−	0.946579i	$-0.395486\pi$
$389$	25.9846	−	16.6993i	1.31747	−	0.846686i	0.994998	+	0.0998927i	$0.0318499\pi$
$390$	3.00058			0.151940
$391$	−31.9903	+	7.17262i	−1.61782	+	0.362735i
$392$	1.50576			0.0760522
$393$	−8.22766	+	5.28759i	−0.415030	+	0.266724i
$394$	4.63592	−	32.2435i	0.233554	−	1.62441i
$395$	7.65809	−	16.7689i	0.385320	−	0.843734i
$396$	−3.20375	+	0.940705i	−0.160994	+	0.0472722i
$397$	1.40014	+	3.06589i	0.0702712	+	0.153873i	0.941508	−	0.336990i	$-0.109409\pi$
$397$	1.40014	+	3.06589i	0.0702712	+	0.153873i	−0.871237	+	0.490863i	$0.836682\pi$
$398$	−13.7637	−	15.8841i	−0.689911	−	0.796200i
$399$	−0.119937	−	0.834181i	−0.00600437	−	0.0417613i
$400$	−4.16227	−	1.22215i	−0.208114	−	0.0611077i
$401$	−17.4131	+	20.0958i	−0.869569	+	1.00354i	0.130358	+	0.991467i	$0.458387\pi$
$401$	−17.4131	+	20.0958i	−0.869569	+	1.00354i	−0.999927	+	0.0120695i	$0.996158\pi$
$402$	1.57386	+	1.01146i	0.0784969	+	0.0504469i
$403$	1.64942	+	1.06002i	0.0821633	+	0.0528031i
$404$	−10.8096	+	12.4750i	−0.537798	+	0.620652i
$405$	1.94954	+	0.572436i	0.0968733	+	0.0284446i
$406$	−1.68870	−	11.7451i	−0.0838086	−	0.582902i
$407$	11.5714	+	13.3541i	0.573573	+	0.661939i
$408$	4.27604	+	9.36323i	0.211696	+	0.463549i
$409$	8.19497	−	2.40626i	0.405215	−	0.118982i	−0.0727722	−	0.997349i	$-0.523185\pi$
$409$	8.19497	−	2.40626i	0.405215	−	0.118982i	0.477987	+	0.878367i	$0.341366\pi$
$410$	−10.4871	+	22.9635i	−0.517919	+	1.13408i
$411$	−2.65105	+	18.4385i	−0.130767	+	0.909504i
$412$	1.61195	−	1.03594i	0.0794153	−	0.0510371i
$413$	−11.8121			−0.581237
$414$	−0.661444	−	8.48853i	−0.0325082	−	0.417188i
$415$	11.4629			0.562691
$416$	−4.07569	+	2.61929i	−0.199827	+	0.128421i
$417$	0.140293	−	0.975760i	0.00687018	−	0.0477832i
$418$	1.80172	−	3.94523i	0.0881252	−	0.192967i
$419$	−20.7611	+	6.09602i	−1.01425	+	0.297810i	−0.746290	−	0.665621i	$-0.768167\pi$
$419$	−20.7611	+	6.09602i	−1.01425	+	0.297810i	−0.267958	+	0.963431i	$0.586349\pi$
$420$	0.972229	+	2.12888i	0.0474399	+	0.103879i
$421$	3.44048	+	3.97053i	0.167679	+	0.193512i	0.833370	−	0.552716i	$-0.186409\pi$
$421$	3.44048	+	3.97053i	0.167679	+	0.193512i	−0.665691	+	0.746228i	$0.731863\pi$
$422$	−1.91969	−	13.3517i	−0.0934488	−	0.649951i
$423$	−9.80395	−	2.87870i	−0.476684	−	0.139967i
$424$	−5.44429	+	6.28305i	−0.264398	+	0.305132i
$425$	5.01255	+	3.22137i	0.243144	+	0.156259i
$426$	−8.63332	−	5.54830i	−0.418286	−	0.268816i
$427$	4.07556	−	4.70345i	0.197230	−	0.227616i
$428$	9.40723	+	2.76221i	0.454716	+	0.133517i
$429$	−0.343165	−	2.38676i	−0.0165681	−	0.115234i
$430$	22.3746	+	25.8216i	1.07900	+	1.24523i
$431$	−11.6551	−	25.5210i	−0.561405	−	1.22931i	−0.951249	−	0.308424i	$-0.900198\pi$
$431$	−11.6551	−	25.5210i	−0.561405	−	1.22931i	0.389844	−	0.920881i	$-0.372529\pi$
$432$	−4.77534	+	1.40217i	−0.229754	+	0.0674618i
$433$	11.2893	−	24.7202i	0.542530	−	1.18797i	−0.417654	−	0.908606i	$-0.637148\pi$
$433$	11.2893	−	24.7202i	0.542530	−	1.18797i	0.960184	−	0.279369i	$-0.0901251\pi$
$434$	−0.595530	+	4.14200i	−0.0285864	+	0.198823i
$435$	−11.4245	+	7.34205i	−0.547761	+	0.352024i
$436$	−12.4639			−0.596913
$437$	3.25092	+	2.40148i	0.155513	+	0.114878i
$438$	−16.9018			−0.807601
$439$	8.04988	−	5.17334i	0.384200	−	0.246910i	−0.334257	−	0.942482i	$-0.608485\pi$
$439$	8.04988	−	5.17334i	0.384200	−	0.246910i	0.718457	+	0.695572i	$0.244849\pi$
$440$	1.26216	−	8.77853i	0.0601712	−	0.418500i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	9.68639	−	2.84418i	0.460735	−	0.135284i
$443$	−5.87852	−	12.8722i	−0.279297	−	0.611575i	0.717046	−	0.697026i	$-0.245494\pi$
$443$	−5.87852	−	12.8722i	−0.279297	−	0.611575i	−0.996342	+	0.0854517i	$0.972767\pi$
$444$	−4.59793	−	5.30630i	−0.218208	−	0.251826i
$445$	4.31384	+	30.0034i	0.204495	+	1.42230i
$446$	25.9182	+	7.61028i	1.22726	+	0.360357i
$447$	11.3278	−	13.0730i	0.535788	−	0.618333i
$448$	−0.324906	−	0.208805i	−0.0153504	−	0.00986509i
$449$	26.4799	+	17.0176i	1.24966	+	0.803109i	0.986834	−	0.161734i	$-0.0517086\pi$
$449$	26.4799	+	17.0176i	1.24966	+	0.803109i	0.262828	+	0.964843i	$0.415345\pi$
$450$	−1.01335	+	1.16946i	−0.0477696	+	0.0551291i
$451$	19.4653	+	5.71552i	0.916584	+	0.269133i
$452$	0.789232	+	5.48923i	0.0371223	+	0.258192i
$453$	3.05970	+	3.53109i	0.143757	+	0.165905i
$454$	7.70070	+	16.8622i	0.361412	+	0.791381i
$455$	−1.62168	+	0.476167i	−0.0760254	+	0.0223231i
$456$	0.527158	−	1.15431i	0.0246864	−	0.0540557i
$457$	5.40581	−	37.5982i	0.252873	−	1.75877i	−0.327906	−	0.944710i	$-0.606343\pi$
$457$	5.40581	−	37.5982i	0.252873	−	1.75877i	0.580779	−	0.814061i	$-0.302748\pi$
$458$	−1.25904	+	0.809136i	−0.0588311	+	0.0378084i
$459$	6.83605			0.319079
$460$	−10.5411	−	3.85539i	−0.491483	−	0.179759i
$461$	−24.9657			−1.16277			−0.581385	−	0.813628i	$-0.697489\pi$
$461$	−24.9657			−1.16277			−0.581385	+	0.813628i	$0.697489\pi$
$462$	4.32942	−	2.78235i	0.201423	−	0.129447i
$463$	2.94488	−	20.4821i	0.136860	−	0.951884i	−0.799456	−	0.600725i	$-0.794879\pi$
$463$	2.94488	−	20.4821i	0.136860	−	0.951884i	0.936316	−	0.351159i	$-0.114212\pi$
$464$	13.8186	−	30.2585i	0.641511	−	1.40471i
$465$	4.59518	−	1.34927i	0.213096	−	0.0625707i
$466$	21.7702	+	47.6700i	1.00848	+	2.20827i
$467$	−0.861439	−	0.994154i	−0.0398626	−	0.0460040i	0.735468	−	0.677559i	$-0.236962\pi$
$467$	−0.861439	−	0.994154i	−0.0398626	−	0.0460040i	−0.775331	+	0.631555i	$0.782417\pi$
$468$	0.136358	+	0.948387i	0.00630313	+	0.0438392i
$469$	−1.01111	−	0.296888i	−0.0466886	−	0.0137090i
$470$	−24.1369	+	27.8554i	−1.11335	+	1.28488i
$471$	−2.60581	−	1.67465i	−0.120069	−	0.0771638i
$472$	−14.9627	−	9.61595i	−0.688714	−	0.442610i
$473$	17.9805	−	20.7506i	0.826745	−	0.954114i
$474$	15.4551	+	4.53804i	0.709878	+	0.208439i
$475$	−0.104539	−	0.727088i	−0.00479660	−	0.0333611i
$476$	5.15644	+	5.95085i	0.236345	+	0.272757i
$477$	2.29361	+	5.02231i	0.105017	+	0.229956i
$478$	7.43133	−	2.18204i	0.339901	−	0.0998040i
$479$	−3.90280	+	8.54594i	−0.178323	+	0.390474i	−0.977595	−	0.210497i	$-0.932492\pi$
$479$	−3.90280	+	8.54594i	−0.178323	+	0.390474i	0.799271	+	0.600971i	$0.205219\pi$
$480$	−1.68415	+	11.7136i	−0.0768708	+	0.534648i
$481$	4.26557	−	2.74131i	0.194493	−	0.124993i
$482$	15.1982			0.692257
$483$	1.70454	+	4.48269i	0.0775592	+	0.203970i
$484$	−2.99124			−0.135965
$485$	−16.2546	+	10.4462i	−0.738083	+	0.474337i
$486$	−0.252658	+	1.75727i	−0.0114608	+	0.0797116i
$487$	−8.03471	+	17.5936i	−0.364088	+	0.797241i	0.635594	+	0.772023i	$0.280755\pi$
$487$	−8.03471	+	17.5936i	−0.364088	+	0.797241i	−0.999682	+	0.0252175i	$0.991972\pi$
$488$	8.99156	−	2.64016i	0.407029	−	0.119514i
$489$	−1.18798	−	2.60130i	−0.0537221	−	0.117635i
$490$	−2.36223	−	2.72616i	−0.106715	−	0.123155i
$491$	0.167724	+	1.16655i	0.00756929	+	0.0526456i	0.993256	−	0.115942i	$-0.0369886\pi$
$491$	0.167724	+	1.16655i	0.00756929	+	0.0526456i	−0.985687	+	0.168587i	$0.946079\pi$
$492$	−7.73458	−	2.27108i	−0.348702	−	0.102388i
$493$	−29.9207	+	34.5304i	−1.34756	+	1.55517i
$494$	−1.04700	−	0.672865i	−0.0471067	−	0.0302736i
$495$	−4.95492	−	3.18433i	−0.222707	−	0.143125i
$496$	−7.68214	+	8.86566i	−0.344938	+	0.398080i
$497$	5.54638	+	1.62856i	0.248789	+	0.0730511i
$498$	1.42540	+	9.91388i	0.0638737	+	0.444251i
$499$	−8.46989	−	9.77478i	−0.379165	−	0.437579i	0.533805	−	0.845608i	$-0.320762\pi$
$499$	−8.46989	−	9.77478i	−0.379165	−	0.437579i	−0.912969	+	0.408029i	$0.866216\pi$
$500$	5.70856	+	12.5000i	0.255294	+	0.559017i
$501$	23.7796	−	6.98231i	1.06239	−	0.311946i
$502$	7.75361	−	16.9780i	0.346060	−	0.757767i
$503$	−1.50337	+	10.4562i	−0.0670319	+	0.466217i	0.928465	+	0.371420i	$0.121129\pi$
$503$	−1.50337	+	10.4562i	−0.0670319	+	0.466217i	−0.995497	+	0.0947964i	$0.969780\pi$
$504$	1.26672	−	0.814074i	0.0564244	−	0.0362617i
$505$	−29.1175			−1.29571
$506$	−5.09276	+	24.1501i	−0.226401	+	1.07360i
$507$	12.3081			0.546620
$508$	5.76269	−	3.70346i	0.255678	−	0.164314i
$509$	−4.54420	+	31.6056i	−0.201418	+	1.40089i	0.598663	+	0.801001i	$0.295699\pi$
$509$	−4.54420	+	31.6056i	−0.201418	+	1.40089i	−0.800081	+	0.599892i	$0.795210\pi$
$510$	10.2438	−	22.4307i	0.453602	−	0.993250i
$511$	9.13467	−	2.68218i	0.404094	−	0.118653i
$512$	−5.81537	−	12.7339i	−0.257006	−	0.562764i
$513$	−0.551890	−	0.636915i	−0.0243665	−	0.0281205i
$514$	−4.17263	−	29.0213i	−0.184047	−	1.28008i
$515$	3.24311	+	0.952262i	0.142908	+	0.0419617i
$516$	−7.14461	+	8.24532i	−0.314524	+	0.362980i
$517$	24.9176	+	16.0136i	1.09587	+	0.704276i
$518$	9.10389	+	5.85072i	0.400002	+	0.257066i
$519$	8.83865	−	10.2003i	0.387974	−	0.447745i
$520$	−2.44185	−	0.716992i	−0.107082	−	0.0314422i
$521$	−4.78759	−	33.2984i	−0.209748	−	1.45883i	−0.773978	−	0.633213i	$-0.781736\pi$
$521$	−4.78759	−	33.2984i	−0.209748	−	1.45883i	0.564230	−	0.825618i	$-0.309173\pi$
$522$	−7.77052	−	8.96766i	−0.340107	−	0.392504i
$523$	0.0767083	+	0.167968i	0.00335422	+	0.00734472i	0.911302	−	0.411739i	$-0.135079\pi$
$523$	0.0767083	+	0.167968i	0.00335422	+	0.00734472i	−0.907947	+	0.419084i	$0.862351\pi$
$524$	−10.8090	+	3.17382i	−0.472195	+	0.138649i
$525$	0.362083	−	0.792852i	0.0158026	−	0.0346029i
$526$	−3.57434	+	24.8601i	−0.155849	+	1.08395i
$527$	13.5551	−	8.71133i	0.590469	−	0.379472i
$528$	14.4272			0.627864
$529$	−21.0415	−	9.28744i	−0.914846	−	0.403802i
$530$	19.9164			0.865112
$531$	−9.93700	+	6.38612i	−0.431229	+	0.277134i
$532$	0.138150	−	0.960852i	0.00598955	−	0.0416582i
$533$	2.41832	−	5.29538i	0.104749	−	0.229368i
$534$	−25.4126	+	7.46180i	−1.09971	+	0.322904i
$535$	7.18449	+	15.7318i	0.310613	+	0.680147i
$536$	−1.03911	−	1.19919i	−0.0448825	−	0.0517972i
$537$	−1.33046	−	9.25353i	−0.0574134	−	0.399319i
$538$	12.3103	+	3.61462i	0.530734	+	0.155837i
$539$	−1.89832	+	2.19077i	−0.0817663	+	0.0943634i
$540$	1.96885	+	1.26530i	0.0847259	+	0.0544500i
$541$	−0.206016	−	0.132399i	−0.00885734	−	0.00569226i	0.536205	−	0.844088i	$-0.319858\pi$
$541$	−0.206016	−	0.132399i	−0.00885734	−	0.00569226i	−0.545062	+	0.838396i	$0.683494\pi$
$542$	8.19712	−	9.45998i	0.352097	−	0.406341i
$543$	16.8573	+	4.94975i	0.723416	+	0.212414i
$544$	5.66627	+	39.4098i	0.242939	+	1.68968i
$545$	−14.3978	−	16.6160i	−0.616735	−	0.711751i
$546$	−0.613476	−	1.34333i	−0.0262543	−	0.0574890i
$547$	31.2587	−	9.17838i	1.33653	−	0.392439i	0.466097	−	0.884734i	$-0.345660\pi$
$547$	31.2587	−	9.17838i	1.33653	−	0.392439i	0.870429	+	0.492294i	$0.163842\pi$
$548$	−8.91347	+	19.5178i	−0.380765	+	0.833758i
$549$	0.885704	−	6.16021i	0.0378009	−	0.262911i
$550$	3.77360	−	2.42515i	0.160907	−	0.103409i
$551$	5.63277			0.239964
$552$	−1.49006	+	7.06595i	−0.0634214	+	0.300747i
$553$	−9.07295			−0.385821
$554$	−0.935876	+	0.601451i	−0.0397616	+	0.0255532i
$555$	1.76262	−	12.2593i	0.0748188	−	0.520377i
$556$	0.471699	−	1.03288i	0.0200045	−	0.0438037i
$557$	41.6147	−	12.2192i	1.76327	−	0.517743i	0.770466	−	0.637481i	$-0.220024\pi$
$557$	41.6147	−	12.2192i	1.76327	−	0.517743i	0.992806	+	0.119738i	$0.0382054\pi$
$558$	1.73834	+	3.80644i	0.0735900	+	0.161140i
$559$	−5.15958	−	5.95448i	−0.218227	−	0.251848i
$560$	−1.43914	−	10.0094i	−0.0608147	−	0.422976i
$561$	−19.0137	−	5.58293i	−0.802759	−	0.235711i
$562$	−12.7158	+	14.6748i	−0.536382	+	0.619017i
$563$	−5.94278	−	3.81919i	−0.250458	−	0.160960i	0.409388	−	0.912360i	$-0.365742\pi$
$563$	−5.94278	−	3.81919i	−0.250458	−	0.160960i	−0.659846	+	0.751401i	$0.729379\pi$
$564$	−9.90108	−	6.36304i	−0.416911	−	0.267932i
$565$	−6.40615	+	7.39309i	−0.269509	+	0.311030i
$566$	−40.6737	−	11.9429i	−1.70964	−	0.501997i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	5.69996	+	6.57811i	0.239165	+	0.276011i
$569$	16.3491	+	35.7996i	0.685391	+	1.50080i	0.856828	+	0.515602i	$0.172432\pi$
$569$	16.3491	+	35.7996i	0.685391	+	1.50080i	−0.171437	+	0.985195i	$0.554841\pi$
$570$	−2.91688	+	0.856472i	−0.122175	+	0.0358737i
$571$	7.10240	−	15.5521i	0.297226	−	0.650835i	−0.700818	−	0.713340i	$-0.747182\pi$
$571$	7.10240	−	15.5521i	0.297226	−	0.650835i	0.998045	+	0.0625050i	$0.0199089\pi$
$572$	0.395275	−	2.74920i	0.0165273	−	0.114950i
$573$	6.12624	−	3.93710i	0.255927	−	0.164475i
$574$	12.4246			0.518592
$575$	1.48571	+	3.90720i	0.0619583	+	0.162941i
$576$	−0.386217			−0.0160924
$577$	1.52466	−	0.979841i	0.0634725	−	0.0407913i	−0.508520	−	0.861050i	$-0.669807\pi$
$577$	1.52466	−	0.979841i	0.0634725	−	0.0407913i	0.571992	+	0.820259i	$0.306171\pi$
$578$	7.51191	−	52.2465i	0.312454	−	2.17317i
$579$	9.46146	−	20.7177i	0.393205	−	0.860999i
$580$	−15.0088	+	4.40699i	−0.623207	+	0.182990i
$581$	−2.34361	−	5.13180i	−0.0972295	−	0.212903i
$582$	−11.0558	−	12.7591i	−0.458279	−	0.528882i
$583$	−2.27776	−	15.8422i	−0.0943351	−	0.656115i
$584$	13.7546	+	4.03871i	0.569169	+	0.167123i
$585$	−1.10681	+	1.27732i	−0.0457608	+	0.0528108i
$586$	15.4361	+	9.92019i	0.637660	+	0.409799i
$587$	21.6870	+	13.9374i	0.895120	+	0.575259i	0.905339	−	0.424689i	$-0.139617\pi$
$587$	21.6870	+	13.9374i	0.895120	+	0.575259i	−0.0102192	+	0.999948i	$0.503253\pi$
$588$	0.754302	−	0.870511i	0.0311069	−	0.0358993i
$589$	−1.90597	−	0.559643i	−0.0785341	−	0.0230597i
$590$	6.06389	+	42.1753i	0.249646	+	1.73633i
$591$	12.0158	+	13.8669i	0.494263	+	0.570410i
$592$	12.6027	+	27.5960i	0.517966	+	1.13419i
$593$	−45.6875	+	13.4151i	−1.87616	+	0.550891i	−0.878893	+	0.477018i	$0.841718\pi$
$593$	−45.6875	+	13.4151i	−1.87616	+	0.550891i	−0.997268	+	0.0738723i	$0.976464\pi$
$594$	2.13789	−	4.68132i	0.0877186	−	0.192077i
$595$	−1.97672	+	13.7484i	−0.0810376	+	0.563629i
$596$	16.7618	−	10.7722i	0.686591	−	0.441245i
$597$	11.8387			0.484524
$598$	6.65145	+	2.43275i	0.271998	+	0.0994826i
$599$	−19.1385			−0.781978			−0.390989	−	0.920395i	$-0.627867\pi$
$599$	−19.1385			−0.781978			−0.390989	+	0.920395i	$0.627867\pi$
$600$	1.10410	−	0.709562i	0.0450747	−	0.0289677i
$601$	−2.98718	+	20.7763i	−0.121849	+	0.847482i	0.833609	+	0.552355i	$0.186271\pi$
$601$	−2.98718	+	20.7763i	−0.121849	+	0.847482i	−0.955458	+	0.295126i	$0.904638\pi$
$602$	6.98551	−	15.2961i	0.284708	−	0.623424i
$603$	−1.01111	+	0.296888i	−0.0411755	+	0.0120902i
$604$	2.23568	+	4.89545i	0.0909684	+	0.199193i
$605$	−3.45536	−	3.98770i	−0.140480	−	0.162123i
$606$	−3.62074	−	25.1828i	−0.147083	−	1.02298i
$607$	6.25635	+	1.83703i	0.253937	+	0.0745627i	0.406224	−	0.913774i	$-0.366845\pi$
$607$	6.25635	+	1.83703i	0.253937	+	0.0745627i	−0.152286	+	0.988336i	$0.548664\pi$
$608$	3.21436	−	3.70957i	0.130359	−	0.150443i
$609$	5.62271	+	3.61349i	0.227844	+	0.146426i
$610$	−18.8859	−	12.1372i	−0.764669	−	0.491423i
$611$	5.56597	−	6.42347i	0.225175	−	0.259866i
$612$	7.55515	+	2.21839i	0.305399	+	0.0896732i
$613$	−1.02755	−	7.14680i	−0.0415026	−	0.288657i	−0.999994	−	0.00353449i	$-0.998875\pi$
$613$	−1.02755	−	7.14680i	−0.0415026	−	0.288657i	0.958491	−	0.285122i	$-0.0920342\pi$
$614$	−26.6189	−	30.7198i	−1.07425	−	1.23975i
$615$	−5.90705	−	12.9346i	−0.238195	−	0.521575i
$616$	−4.18810	+	1.22974i	−0.168743	+	0.0495475i
$617$	19.3144	−	42.2925i	0.777567	−	1.70263i	0.0683300	−	0.997663i	$-0.478233\pi$
$617$	19.3144	−	42.2925i	0.777567	−	1.70263i	0.709237	−	0.704971i	$-0.249040\pi$
$618$	−0.420303	+	2.92327i	−0.0169071	+	0.117591i
$619$	10.7068	−	6.88085i	0.430343	−	0.276565i	−0.307486	−	0.951553i	$-0.599488\pi$
$619$	10.7068	−	6.88085i	0.430343	−	0.276565i	0.737829	+	0.674988i	$0.235851\pi$
$620$	5.51642			0.221545
$621$	3.85748	+	2.84954i	0.154795	+	0.114348i
$622$	−30.4619			−1.22141
$623$	12.5502	−	8.06552i	0.502813	−	0.323138i
$624$	0.589176	−	4.09781i	0.0235859	−	0.164044i
$625$	−8.25936	+	18.0855i	−0.330374	+	0.723419i
$626$	−36.0753	+	10.5927i	−1.44186	+	0.423368i
$627$	1.01486	+	2.22223i	0.0405295	+	0.0887473i
$628$	−2.33647	−	2.69643i	−0.0932354	−	0.107599i
$629$	−5.93024	−	41.2458i	−0.236454	−	1.64458i
$630$	−3.46110	−	1.01627i	−0.137894	−	0.0404892i
$631$	20.5362	−	23.7001i	0.817534	−	0.943484i	−0.181671	−	0.983359i	$-0.558150\pi$
$631$	20.5362	−	23.7001i	0.817534	−	0.943484i	0.999205	+	0.0398749i	$0.0126959\pi$
$632$	−11.4929	−	7.38605i	−0.457164	−	0.293801i
$633$	6.39181	+	4.10777i	0.254052	+	0.163269i
$634$	7.96596	−	9.19320i	0.316368	−	0.365109i
$635$	11.5940	+	3.40431i	0.460095	+	0.135096i
$636$	0.905074	+	6.29493i	0.0358885	+	0.249610i
$637$	0.544730	+	0.628652i	0.0215830	+	0.0249081i
$638$	14.2891	+	31.2887i	0.565709	+	1.23873i
$639$	5.54638	−	1.62856i	0.219411	−	0.0644250i
$640$	9.25330	−	20.2619i	0.365769	−	0.800922i
$641$	−0.875999	+	6.09271i	−0.0345999	+	0.240647i	−0.999781	−	0.0209357i	$-0.993335\pi$
$641$	−0.875999	+	6.09271i	−0.0345999	+	0.240647i	0.965181	+	0.261583i	$0.0842446\pi$
$642$	−12.7126	+	8.16988i	−0.501725	+	0.322439i
$643$	21.0568			0.830399			0.415199	−	0.909730i	$-0.363712\pi$
$643$	21.0568			0.830399			0.415199	+	0.909730i	$0.363712\pi$
$644$	0.429147	+	5.50739i	0.0169108	+	0.217022i
$645$	−19.2452			−0.757780
$646$	−8.60435	+	5.52968i	−0.338534	+	0.217562i
$647$	−6.46903	+	44.9931i	−0.254324	+	1.76886i	0.317279	+	0.948332i	$0.397231\pi$
$647$	−6.46903	+	44.9931i	−0.254324	+	1.76886i	−0.571603	+	0.820530i	$0.693678\pi$
$648$	0.625514	−	1.36968i	0.0245725	−	0.0538063i
$649$	32.8541	−	9.64684i	1.28964	−	0.378672i
$650$	−0.534717	−	1.17087i	−0.0209733	−	0.0459252i
$651$	−1.54355	−	1.78135i	−0.0604964	−	0.0698165i
$652$	−0.468783	−	3.26046i	−0.0183590	−	0.127689i
$653$	−41.4399	−	12.1678i	−1.62167	−	0.476164i	−0.660201	−	0.751089i	$-0.729529\pi$
$653$	−41.4399	−	12.1678i	−1.62167	−	0.476164i	−0.961466	+	0.274924i	$0.911347\pi$
$654$	12.5803	−	14.5184i	0.491928	−	0.567715i
$655$	−16.7173	−	10.7436i	−0.653199	−	0.419785i
$656$	29.3014	+	18.8309i	1.14403	+	0.735221i
$657$	6.23448	−	7.19497i	0.243230	−	0.280702i
$658$	17.4054	+	5.11069i	0.678533	+	0.199235i
$659$	−1.91917	−	13.3481i	−0.0747601	−	0.519968i	−0.992448	−	0.122666i	$-0.960856\pi$
$659$	−1.91917	−	13.3481i	−0.0747601	−	0.519968i	0.917688	−	0.397302i	$-0.130053\pi$
$660$	−4.44278	−	5.12724i	−0.172935	−	0.199578i
$661$	−4.00227	−	8.76376i	−0.155670	−	0.340871i	0.815687	−	0.578493i	$-0.196359\pi$
$661$	−4.00227	−	8.76376i	−0.155670	−	0.340871i	−0.971358	+	0.237623i	$0.923632\pi$
$662$	−36.1302	+	10.6088i	−1.40424	+	0.412322i
$663$	−2.36222	+	5.17253i	−0.0917409	+	0.200885i
$664$	1.20895	−	8.40844i	0.0469164	−	0.326311i
$665$	1.44052	−	0.925768i	0.0558611	−	0.0358997i
$666$	10.8218			0.419337
$667$	−31.2775	+	7.01280i	−1.21107	+	0.271537i
$668$	28.5469			1.10451
$669$	−12.7999	+	8.22602i	−0.494874	+	0.318036i
$670$	−0.540977	+	3.76258i	−0.0208998	+	0.145361i
$671$	−7.49446	+	16.4106i	−0.289321	+	0.633524i
$672$	5.58835	−	1.64089i	0.215575	−	0.0632986i
$673$	−2.24573	−	4.91746i	−0.0865665	−	0.189554i	0.861398	−	0.507931i	$-0.169590\pi$
$673$	−2.24573	−	4.91746i	−0.0865665	−	0.189554i	−0.947964	+	0.318377i	$0.896862\pi$
$674$	14.0619	+	16.2283i	0.541646	+	0.625093i
$675$	−0.124044	−	0.862747i	−0.00477447	−	0.0332071i
$676$	13.6028	+	3.99414i	0.523184	+	0.153621i
$677$	−4.73430	+	5.46368i	−0.181954	+	0.209986i	−0.839398	−	0.543517i	$-0.817092\pi$
$677$	−4.73430	+	5.46368i	−0.181954	+	0.209986i	0.657444	+	0.753504i	$0.271638\pi$
$678$	−7.19065	−	4.62115i	−0.276155	−	0.177474i
$679$	7.99993	+	5.14124i	0.307009	+	0.197303i
$680$	−13.6962	+	15.8062i	−0.525224	+	0.606140i
$681$	−10.0186	−	2.94173i	−0.383914	−	0.112727i
$682$	−1.72633	−	12.0069i	−0.0661046	−	0.459767i
$683$	0.233613	+	0.269604i	0.00893897	+	0.0103161i	0.760201	−	0.649687i	$-0.225100\pi$
$683$	0.233613	+	0.269604i	0.00893897	+	0.0103161i	−0.751262	+	0.660004i	$0.770555\pi$
$684$	−0.403257	−	0.883010i	−0.0154189	−	0.0337627i
$685$	−36.3162	+	10.6634i	−1.38757	+	0.407427i
$686$	−0.737505	+	1.61491i	−0.0281581	+	0.0616576i
$687$	0.119972	−	0.834423i	0.00457722	−	0.0318352i
$688$	39.6573	−	25.4862i	1.51192	−	0.971651i
$689$	−4.59272			−0.174969
$690$	15.1304	−	8.38730i	0.576006	−	0.319299i
$691$	20.6719			0.786395			0.393198	−	0.919454i	$-0.371369\pi$
$691$	20.6719			0.786395			0.393198	+	0.919454i	$0.371369\pi$
$692$	13.0786	−	8.40508i	0.497173	−	0.319513i
$693$	−0.412544	+	2.86931i	−0.0156712	+	0.108996i
$694$	15.7184	−	34.4186i	0.596664	−	1.30651i
$695$	1.92184	−	0.564304i	0.0728997	−	0.0214053i
$696$	4.18076	+	9.15460i	0.158471	+	0.347004i
$697$	−31.3294	−	36.1561i	−1.18669	−	1.36951i
$698$	0.391353	+	2.72192i	0.0148129	+	0.103026i
$699$	−28.3230	−	8.31637i	−1.07127	−	0.314554i
$700$	0.657464	−	0.758753i	0.0248498	−	0.0286782i
$701$	−40.2634	−	25.8757i	−1.52073	−	0.977311i	−0.991681	−	0.128717i	$-0.958914\pi$
$701$	−40.2634	−	25.8757i	−1.52073	−	0.977311i	−0.529044	−	0.848594i	$-0.677449\pi$
$702$	−1.24235	−	0.798407i	−0.0468893	−	0.0301339i
$703$	−3.36411	+	3.88239i	−0.126880	+	0.146427i
$704$	1.07422	+	0.315419i	0.0404862	+	0.0118878i
$705$	−2.95460	−	20.5497i	−0.111277	−	0.773947i
$706$	27.4662	+	31.6977i	1.03371	+	1.19296i
$707$	5.95315	+	13.0356i	0.223891	+	0.490253i
$708$	−13.0547	+	3.83320i	−0.490625	+	0.144061i
$709$	−11.1298	+	24.3708i	−0.417988	+	0.915266i	0.577137	+	0.816647i	$0.304170\pi$
$709$	−11.1298	+	24.3708i	−0.417988	+	0.915266i	−0.995125	+	0.0986191i	$0.968557\pi$
$710$	2.96750	−	20.6394i	0.111368	−	0.774584i
$711$	−7.63265	+	4.90521i	−0.286247	+	0.183960i
$712$	22.4636			0.841858
$713$	11.2802	+	0.734639i	0.422446	+	0.0275124i
$714$	−12.1363			−0.454191
$715$	4.12163	−	2.64881i	0.154140	−	0.0990600i
$716$	1.53249	−	10.6587i	0.0572718	−	0.398334i
$717$	−1.81228	+	3.96833i	−0.0676807	+	0.148200i
$718$	−9.11139	+	2.67535i	−0.340034	+	0.0998430i
$719$	13.1110	+	28.7090i	0.488956	+	1.07066i	0.979903	+	0.199475i	$0.0639237\pi$
$719$	13.1110	+	28.7090i	0.488956	+	1.07066i	−0.490947	+	0.871190i	$0.663349\pi$
$720$	−6.62219	−	7.64241i	−0.246794	−	0.284816i
$721$	−0.236744	−	1.64659i	−0.00881682	−	0.0613223i
$722$	−31.1553	−	9.14803i	−1.15948	−	0.340455i
$723$	−5.60605	+	6.46973i	−0.208491	+	0.240612i
$724$	17.0243	+	10.9409i	0.632703	+	0.406614i
$725$	4.90086	+	3.14959i	0.182013	+	0.116973i
$726$	3.01916	−	3.48430i	0.112052	−	0.129314i
$727$	−9.19190	−	2.69899i	−0.340909	−	0.100100i	0.106797	−	0.994281i	$-0.465941\pi$
$727$	−9.19190	−	2.69899i	−0.340909	−	0.100100i	−0.447706	+	0.894181i	$0.647759\pi$
$728$	0.178253	+	1.23978i	0.00660651	+	0.0459493i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−14.2661	−	31.2384i	−0.528013	−	1.15619i
$731$	−62.1269	+	18.2421i	−2.29785	+	0.674709i
$732$	2.97795	−	6.52080i	0.110068	−	0.241016i
$733$	0.473813	−	3.29544i	0.0175007	−	0.121720i	−0.979198	−	0.202906i	$-0.934962\pi$
$733$	0.473813	−	3.29544i	0.0175007	−	0.121720i	0.996699	+	0.0811856i	$0.0258707\pi$
$734$	37.6275	−	24.1817i	1.38886	−	0.892564i
$735$	2.03184			0.0749456
$736$	−13.2302	+	24.6003i	−0.487671	+	0.906777i
$737$	3.05475			0.112523
$738$	10.4522	−	6.71723i	0.384751	−	0.247265i
$739$	−6.01881	+	41.8617i	−0.221405	+	1.53991i	0.511324	+	0.859388i	$0.329155\pi$
$739$	−6.01881	+	41.8617i	−0.221405	+	1.53991i	−0.732729	+	0.680520i	$0.761754\pi$
$740$	5.92633	−	12.9769i	0.217856	−	0.477039i
$741$	0.672632	−	0.197503i	0.0247098	−	0.00725544i
$742$	−4.07195	−	8.91633i	−0.149486	−	0.327329i
$743$	16.8306	+	19.4236i	0.617455	+	0.712581i	0.975222	−	0.221230i	$-0.0710071\pi$
$743$	16.8306	+	19.4236i	0.617455	+	0.712581i	−0.357766	+	0.933811i	$0.616462\pi$
$744$	−0.505098	−	3.51304i	−0.0185178	−	0.128794i
$745$	33.7233	+	9.90205i	1.23553	+	0.362783i
$746$	22.4388	−	25.8958i	0.821543	−	0.948111i
$747$	−4.74603	−	3.05009i	−0.173648	−	0.111597i
$748$	−19.2021	−	12.3404i	−0.702097	−	0.451210i
$749$	5.57408	−	6.43283i	0.203672	−	0.235050i
$750$	−20.3223	−	5.96716i	−0.742065	−	0.217890i
$751$	1.70865	+	11.8839i	0.0623496	+	0.433651i	0.996956	+	0.0779670i	$0.0248429\pi$
$751$	1.70865	+	11.8839i	0.0623496	+	0.433651i	−0.934606	+	0.355684i	$0.884248\pi$
$752$	33.3020	+	38.4326i	1.21440	+	1.40149i
$753$	4.36738	+	9.56323i	0.159156	+	0.348503i
$754$	9.47056	−	2.78081i	0.344897	−	0.101271i
$755$	−3.94369	+	8.63547i	−0.143525	+	0.314277i
$756$	0.163925	−	1.14013i	0.00596191	−	0.0414660i
$757$	9.07919	−	5.83484i	0.329989	−	0.212071i	−0.365146	−	0.930950i	$-0.618981\pi$
$757$	9.07919	−	5.83484i	0.329989	−	0.212071i	0.695135	+	0.718879i	$0.255345\pi$
$758$	−54.9583			−1.99618
$759$	−8.40195	−	11.0760i	−0.304972	−	0.402035i
$760$	2.57839			0.0935280
$761$	15.7109	−	10.0968i	0.569518	−	0.366007i	−0.223967	−	0.974597i	$-0.571901\pi$
$761$	15.7109	−	10.0968i	0.569518	−	0.366007i	0.793485	+	0.608590i	$0.208264\pi$
$762$	−1.50257	+	10.4506i	−0.0544324	+	0.378586i
$763$	−4.49511	+	9.84292i	−0.162734	+	0.356338i
$764$	8.04832	−	2.36320i	0.291178	−	0.0854976i
$765$	5.77002	+	12.6346i	0.208615	+	0.456804i
$766$	0.573583	+	0.661951i	0.0207244	+	0.0239172i
$767$	−1.39833	−	9.72563i	−0.0504909	−	0.351172i
$768$	19.4157	+	5.70095i	0.700602	+	0.205715i
$769$	19.4761	−	22.4766i	0.702325	−	0.810526i	−0.286740	−	0.958008i	$-0.592572\pi$
$769$	19.4761	−	22.4766i	0.702325	−	0.810526i	0.989065	+	0.147482i	$0.0471170\pi$
$770$	8.79669	+	5.65329i	0.317011	+	0.203731i
$771$	13.8933	+	8.92866i	0.500354	+	0.321558i
$772$	17.1799	−	19.8267i	0.618319	−	0.713578i
$773$	24.0653	+	7.06620i	0.865568	+	0.254154i	0.684229	−	0.729267i	$-0.260139\pi$
$773$	24.0653	+	7.06620i	0.865568	+	0.254154i	0.181339	+	0.983421i	$0.441957\pi$
$774$	−2.39313	−	16.6446i	−0.0860193	−	0.598277i
$775$	−1.34538	−	1.55266i	−0.0483276	−	0.0557730i
$776$	5.94835	+	13.0251i	0.213533	+	0.467573i
$777$	−5.84870	+	1.71733i	−0.209821	+	0.0616090i
$778$	−22.7800	+	49.8812i	−0.816702	+	1.78833i
$779$	−0.839368	+	5.83793i	−0.0300735	+	0.209166i
$780$	−1.63774	+	1.05251i	−0.0586406	+	0.0376860i
$781$	−16.7567			−0.599601
$782$	40.8935	−	41.4175i	1.46235	−	1.48109i
$783$	6.68372			0.238857
$784$	−4.18687	+	2.69074i	−0.149531	+	0.0960978i
$785$	0.895686	−	6.22963i	0.0319684	−	0.222345i
$786$	7.21297	−	15.7942i	0.257278	−	0.563361i
$787$	49.8775	−	14.6454i	1.77794	−	0.522051i	0.782956	−	0.622077i	$-0.213711\pi$
$787$	49.8775	−	14.6454i	1.77794	−	0.522051i	0.994985	+	0.100027i	$0.0318928\pi$
$788$	8.77973	+	19.2249i	0.312765	+	0.684860i
$789$	−9.26430	−	10.6916i	−0.329818	−	0.380630i
$790$	4.65770	+	32.3950i	0.165713	+	1.15256i
$791$	4.61955	+	1.35642i	0.164252	+	0.0482288i
$792$	−2.85841	+	3.29878i	−0.101569	+	0.117217i
$793$	4.35510	+	2.79885i	0.154654	+	0.0993901i
$794$	−5.03385	−	3.23506i	−0.178645	−	0.114808i
$795$	−7.34643	+	8.47823i	−0.260551	+	0.300692i
$796$	13.0840	+	3.84181i	0.463751	+	0.136169i
$797$	1.17967	+	8.20478i	0.0417860	+	0.290628i	0.999990	+	0.00454119i	$0.00144551\pi$
$797$	1.17967	+	8.20478i	0.0417860	+	0.290628i	−0.958204	+	0.286087i	$0.907645\pi$
$798$	0.979795	+	1.13074i	0.0346844	+	0.0400279i
$799$	−29.0166	−	63.5375i	−1.02653	−	2.24779i
$800$	4.87091	−	1.43023i	0.172213	−	0.0505662i
$801$	6.19735	−	13.5703i	0.218973	−	0.479483i
$802$	6.71832	−	46.7269i	0.237232	−	1.64998i
$803$	−23.2166	+	14.9204i	−0.819294	+	0.526529i
$804$	−1.21381			−0.0428079
$805$	−6.84631	+	6.93403i	−0.241301	+	0.244392i
$806$	−3.48086			−0.122608
$807$	−6.07953	+	3.90708i	−0.214010	+	0.137536i
$808$	−3.07093	+	21.3588i	−0.108035	+	0.751399i
$809$	−2.84734	+	6.23480i	−0.100107	+	0.219204i	−0.953058	−	0.302787i	$-0.902083\pi$
$809$	−2.84734	+	6.23480i	−0.100107	+	0.219204i	0.852951	+	0.521990i	$0.174810\pi$
$810$	−3.46110	+	1.01627i	−0.121611	+	0.0357081i
$811$	2.87511	+	6.29562i	0.100959	+	0.221069i	0.953371	−	0.301802i	$-0.0975881\pi$
$811$	2.87511	+	6.29562i	0.100959	+	0.221069i	−0.852412	+	0.522871i	$0.824861\pi$
$812$	5.04155	+	5.81826i	0.176924	+	0.204181i
$813$	1.00341	+	6.97889i	0.0351912	+	0.244760i
$814$	−30.0997	−	8.83806i	−1.05499	−	0.309774i
$815$	3.80508	−	4.39130i	0.133286	−	0.153821i
$816$	−28.6216	−	18.3940i	−1.00196	−	0.643919i
$817$	6.71527	+	4.31564i	0.234938	+	0.150985i
$818$	−9.92973	+	11.4595i	−0.347185	+	0.400673i
$819$	0.798131	+	0.234352i	0.0278890	+	0.00818894i
$820$	−2.33096	−	16.2122i	−0.0814007	−	0.566154i
$821$	−37.3885	−	43.1486i	−1.30487	−	1.50590i	−0.717443	−	0.696617i	$-0.754688\pi$
$821$	−37.3885	−	43.1486i	−1.30487	−	1.50590i	−0.587423	−	0.809280i	$-0.699858\pi$
$822$	−13.7383	−	30.0827i	−0.479179	−	1.04926i
$823$	0.944736	−	0.277399i	0.0329314	−	0.00966954i	−0.265225	−	0.964186i	$-0.585446\pi$
$823$	0.944736	−	0.277399i	0.0329314	−	0.00966954i	0.298157	+	0.954517i	$0.403628\pi$
$824$	1.04056	−	2.27851i	0.0362496	−	0.0793755i
$825$	−0.359581	+	2.50094i	−0.0125190	+	0.0870715i
$826$	17.6416	−	11.3376i	0.613830	−	0.394484i
$827$	−29.8214			−1.03699			−0.518496	−	0.855080i	$-0.673508\pi$
$827$	−29.8214			−1.03699			−0.518496	+	0.855080i	$0.673508\pi$
$828$	3.33854	+	4.40110i	0.116022	+	0.152949i
$829$	4.49762			0.156209			0.0781044	−	0.996945i	$-0.475113\pi$
$829$	4.49762			0.156209			0.0781044	+	0.996945i	$0.475113\pi$
$830$	−17.1200	+	11.0023i	−0.594243	+	0.381897i
$831$	0.0891782	−	0.620248i	0.00309356	−	0.0215162i
$832$	0.133458	−	0.292233i	0.00462684	−	0.0101314i
$833$	6.55914	−	1.92594i	0.227261	−	0.0667298i
$834$	0.727028	+	1.59197i	0.0251749	+	0.0551254i
$835$	32.9762	+	38.0566i	1.14119	+	1.31700i
$836$	0.400470	+	2.78533i	0.0138505	+	0.0963326i
$837$	−2.26158	−	0.664061i	−0.0781718	−	0.0229533i
$838$	25.1560	−	29.0315i	0.868999	−	1.00288i
$839$	3.60512	+	2.31687i	0.124462	+	0.0799872i	0.601391	−	0.798955i	$-0.294614\pi$
$839$	3.60512	+	2.31687i	0.124462	+	0.0799872i	−0.476928	+	0.878942i	$0.658250\pi$
$840$	2.57378	+	1.65407i	0.0888039	+	0.0570708i
$841$	−10.2631	+	11.8442i	−0.353900	+	0.408422i
$842$	−8.94943	−	2.62779i	−0.308418	−	0.0905596i
$843$	−1.55654	−	10.8260i	−0.0536101	−	0.372866i
$844$	5.73116	+	6.61411i	0.197275	+	0.227667i
$845$	10.3887	+	22.7481i	0.357383	+	0.782559i
$846$	17.4054	−	5.11069i	0.598410	−	0.175709i
$847$	−1.07879	+	2.36222i	−0.0370677	+	0.0811668i
$848$	3.91066	−	27.1992i	0.134293	−	0.934026i
$849$	20.0871	−	12.9092i	0.689386	−	0.443041i
$850$	−10.5783			−0.362831
$851$	13.8465	−	25.7463i	0.474653	−	0.882572i
$852$	6.65831			0.228110
$853$	−31.2629	+	20.0914i	−1.07042	+	0.687917i	−0.952325	−	0.305085i	$-0.901315\pi$
$853$	−31.2629	+	20.0914i	−1.07042	+	0.687917i	−0.118095	+	0.993002i	$0.537679\pi$
$854$	−1.57243	+	10.9365i	−0.0538075	+	0.374239i
$855$	0.711337	−	1.55761i	0.0243272	−	0.0532692i
$856$	12.2976	−	3.61090i	0.420324	−	0.123418i
$857$	−15.5161	−	33.9756i	−0.530021	−	1.16058i	−0.965504	−	0.260387i	$-0.916150\pi$
$857$	−15.5161	−	33.9756i	−0.530021	−	1.16058i	0.435484	−	0.900197i	$-0.356577\pi$
$858$	2.80339	+	3.23529i	0.0957063	+	0.110451i
$859$	−0.565870	−	3.93571i	−0.0193072	−	0.134285i	0.977888	−	0.209129i	$-0.0670630\pi$
$859$	−0.565870	−	3.93571i	−0.0193072	−	0.134285i	−0.997195	+	0.0748447i	$0.976154\pi$
$860$	−21.2697	−	6.24535i	−0.725291	−	0.212965i
$861$	−4.58298	+	5.28904i	−0.156187	+	0.180250i
$862$	41.9027	+	26.9293i	1.42721	+	0.917214i
$863$	1.64761	+	1.05885i	0.0560853	+	0.0360438i	0.568383	−	0.822764i	$-0.307569\pi$
$863$	1.64761	+	1.05885i	0.0560853	+	0.0360438i	−0.512298	+	0.858808i	$0.671206\pi$
$864$	3.81409	−	4.40169i	0.129758	−	0.149749i
$865$	26.3129	+	7.72616i	0.894665	+	0.262697i
$866$	6.86623	+	47.7557i	0.233324	+	1.62280i
$867$	19.4700	+	22.4696i	0.661236	+	0.763107i
$868$	−1.12784	−	2.46964i	−0.0382815	−	0.0838249i
$869$	25.2354	−	7.40978i	0.856052	−	0.251360i
$870$	10.0155	−	21.9309i	0.339558	−	0.743528i
$871$	0.124749	−	0.867651i	0.00422697	−	0.0293992i
$872$	−13.7069	+	8.80891i	−0.464175	+	0.298307i
$873$	9.50954			0.321849
$874$	−7.16030	−	0.466326i	−0.242201	−	0.0157737i
$875$	11.9302			0.403314
$876$	9.22517	−	5.92865i	0.311689	−	0.200311i
$877$	−2.03384	+	14.1456i	−0.0686778	+	0.477664i	0.926237	+	0.376942i	$0.123024\pi$
$877$	−2.03384	+	14.1456i	−0.0686778	+	0.477664i	−0.994915	+	0.100722i	$0.967885\pi$
$878$	−7.05712	+	15.4529i	−0.238166	+	0.521511i
$879$	−9.91676	+	2.91182i	−0.334484	+	0.0982134i
$880$	12.1774	+	26.6648i	0.410500	+	0.898870i
$881$	−6.94740	−	8.01773i	−0.234064	−	0.270124i	0.626551	−	0.779380i	$-0.284466\pi$
$881$	−6.94740	−	8.01773i	−0.234064	−	0.270124i	−0.860615	+	0.509256i	$0.829921\pi$
$882$	0.252658	+	1.75727i	0.00850744	+	0.0591705i
$883$	−54.2517	−	15.9297i	−1.82571	−	0.536078i	−0.826091	−	0.563536i	$-0.809441\pi$
$883$	−54.2517	−	15.9297i	−1.82571	−	0.536078i	−0.999623	+	0.0274579i	$0.991259\pi$
$884$	−4.28926	+	4.95007i	−0.144264	+	0.166489i
$885$	−20.1904	−	12.9756i	−0.678693	−	0.436170i
$886$	21.1347	+	13.5824i	0.710033	+	0.456310i
$887$	8.24680	−	9.51732i	0.276900	−	0.319560i	−0.600216	−	0.799838i	$-0.704919\pi$
$887$	8.24680	−	9.51732i	0.276900	−	0.319560i	0.877116	+	0.480278i	$0.159464\pi$
$888$	−8.80672	−	2.58589i	−0.295534	−	0.0867767i
$889$	−0.846355	−	5.88653i	−0.0283858	−	0.197428i
$890$	−35.2408	−	40.6700i	−1.18127	−	1.36326i
$891$	1.20421	+	2.63685i	0.0403425	+	0.0883378i
$892$	−16.8159	+	4.93758i	−0.563036	+	0.165322i
$893$	−3.57721	+	7.83301i	−0.119707	+	0.262122i
$894$	−4.37050	+	30.3975i	−0.146171	+	1.01664i
$895$	15.9797	−	10.2695i	0.534141	−	0.343271i
$896$	−10.9629			−0.366244
$897$	−3.48908	+	1.93411i	−0.116497	+	0.0645782i
$898$	−55.8820			−1.86481
$899$	13.2531	−	8.51723i	0.442014	−	0.284065i
$900$	0.142880	−	0.993756i	0.00476268	−	0.0331252i
$901$	−15.6792	+	34.3327i	−0.522351	+	1.14379i
$902$	−34.5576	+	10.1470i	−1.15064	+	0.337859i
$903$	3.93473	+	8.61587i	0.130940	+	0.286718i
$904$	4.74747	+	5.47887i	0.157898	+	0.182224i
$905$	5.08026	+	35.3340i	0.168874	+	1.17454i
$906$	−7.95894	−	2.33695i	−0.264418	−	0.0776401i
$907$	16.9153	−	19.5212i	0.561662	−	0.648192i	−0.401898	−	0.915684i	$-0.631649\pi$
$907$	16.9153	−	19.5212i	0.561662	−	0.648192i	0.963560	+	0.267492i	$0.0861949\pi$
$908$	−10.1179	−	6.50235i	−0.335773	−	0.215788i
$909$	12.0557	+	7.74771i	0.399862	+	0.256975i
$910$	1.96496	−	2.26769i	0.0651379	−	0.0751731i
$911$	9.21192	+	2.70486i	0.305204	+	0.0896161i	0.430749	−	0.902472i	$-0.358250\pi$
$911$	9.21192	+	2.70486i	0.305204	+	0.0896161i	−0.125544	+	0.992088i	$0.540068\pi$
$912$	0.596920	+	4.15167i	0.0197660	+	0.137476i
$913$	10.7096	+	12.3595i	0.354435	+	0.409040i
$914$	28.0140	+	61.3422i	0.926622	+	2.02902i
$915$	12.1331	−	3.56259i	0.401106	−	0.117775i
$916$	0.403374	−	0.883266i	0.0133279	−	0.0291839i
$917$	−1.39187	+	9.68069i	−0.0459637	+	0.319684i
$918$	−10.2097	+	6.56140i	−0.336972	+	0.216559i
$919$	42.2755			1.39454			0.697270	−	0.716808i	$-0.254398\pi$
$919$	42.2755			1.39454			0.697270	+	0.716808i	$0.254398\pi$
$920$	−14.3172	+	3.21009i	−0.472024	+	0.105834i
$921$	22.8959			0.754446
$922$	37.2867	−	23.9627i	1.22797	−	0.789170i
$923$	−0.684307	+	4.75946i	−0.0225242	+	0.156659i
$924$	−1.38707	+	3.03726i	−0.0456313	+	0.0999185i
$925$	−5.09783	+	1.49686i	−0.167616	+	0.0492164i
$926$	15.2610	+	33.4169i	0.501507	+	1.09815i
$927$	−1.08938	−	1.25721i	−0.0357799	−	0.0412921i
$928$	5.54001	+	38.5316i	0.181860	+	1.26486i
$929$	−15.4966	−	4.55023i	−0.508428	−	0.149288i	0.0174501	−	0.999848i	$-0.494445\pi$
$929$	−15.4966	−	4.55023i	−0.508428	−	0.149288i	−0.525879	+	0.850560i	$0.676263\pi$
$930$	−5.56791	+	6.42572i	−0.182579	+	0.210708i
$931$	−0.708974	−	0.455630i	−0.0232357	−	0.0149327i
$932$	−28.6036	−	18.3824i	−0.936941	−	0.602135i
$933$	11.2363	−	12.9674i	0.367860	−	0.424533i
$934$	2.24079	+	0.657954i	0.0733207	+	0.0215289i
$935$	−5.73014	−	39.8540i	−0.187395	−	1.30336i
$936$	0.820232	+	0.946598i	0.0268101	+	0.0309405i
$937$	15.8625	+	34.7340i	0.518205	+	1.13471i	0.970115	+	0.242647i	$0.0780157\pi$
$937$	15.8625	+	34.7340i	0.518205	+	1.13471i	−0.451910	+	0.892064i	$0.649257\pi$
$938$	1.79507	−	0.527079i	0.0586110	−	0.0172097i
$939$	8.79766	−	19.2642i	0.287101	−	0.628663i
$940$	3.40326	−	23.6702i	0.111002	−	0.772038i
$941$	−14.3073	+	9.19474i	−0.466404	+	0.299740i	−0.752655	−	0.658415i	$-0.771227\pi$
$941$	−14.3073	+	9.19474i	−0.466404	+	0.299740i	0.286251	+	0.958155i	$0.407591\pi$
$942$	5.49918			0.179173
$943$	−2.60741	−	33.4617i	−0.0849088	−	1.08966i
$944$	58.7883			1.91340
$945$	1.70929	−	1.09850i	0.0556033	−	0.0357341i
$946$	−6.93723	+	48.2495i	−0.225549	+	1.56873i
$947$	8.56243	−	18.7491i	0.278241	−	0.609264i	−0.717985	−	0.696059i	$-0.754935\pi$
$947$	8.56243	−	18.7491i	0.278241	−	0.609264i	0.996226	+	0.0867950i	$0.0276625\pi$
$948$	−10.0274	+	2.94430i	−0.325673	+	0.0956264i
$949$	3.28977	+	7.20359i	0.106790	+	0.233839i
$950$	0.854008	+	0.985577i	0.0277077	+	0.0319763i
$951$	0.975116	+	6.78208i	0.0316203	+	0.219924i
$952$	9.87647	+	2.89999i	0.320098	+	0.0939893i
$953$	20.2348	−	23.3522i	0.655469	−	0.756452i	−0.326561	−	0.945176i	$-0.605890\pi$
$953$	20.2348	−	23.3522i	0.655469	−	0.756452i	0.982030	+	0.188725i	$0.0604353\pi$
$954$	−8.24607	−	5.29943i	−0.266976	−	0.171575i
$955$	12.4476	+	7.99956i	0.402794	+	0.258860i
$956$	−3.29069	+	3.79766i	−0.106429	+	0.122825i
$957$	−18.5900	−	5.45853i	−0.600930	−	0.176449i
$958$	−2.37371	−	16.5095i	−0.0766910	−	0.533397i
$959$	12.1988	+	14.0782i	0.393920	+	0.454608i
$960$	−0.325989	−	0.713817i	−0.0105213	−	0.0230383i
$961$	24.4136	−	7.16848i	0.787535	−	0.231241i
$962$	−3.73951	+	8.18839i	−0.120567	+	0.264004i
$963$	1.21136	−	8.42521i	0.0390356	−	0.271499i
$964$	−8.29528	+	5.33106i	−0.267173	+	0.171702i
$965$	46.2771			1.48971
$966$	−6.84835	−	5.05892i	−0.220342	−	0.162768i
$967$	−22.1305			−0.711670			−0.355835	−	0.934549i	$-0.615804\pi$
$967$	−22.1305			−0.711670			−0.355835	+	0.934549i	$0.615804\pi$
$968$	−3.28955	+	2.11407i	−0.105730	+	0.0679486i
$969$	0.819896	−	5.70250i	0.0263388	−	0.183191i
$970$	14.2500	−	31.2031i	0.457539	−	1.00187i
$971$	46.0723	−	13.5280i	1.47853	−	0.434136i	0.559669	−	0.828716i	$-0.310928\pi$
$971$	46.0723	−	13.5280i	1.47853	−	0.434136i	0.918861	+	0.394581i	$0.129110\pi$
$972$	−0.478496	−	1.04776i	−0.0153478	−	0.0336069i
$973$	−0.645558	−	0.745013i	−0.0206956	−	0.0238840i
$974$	−4.88676	−	33.9882i	−0.156582	−	1.08905i
$975$	0.695666	+	0.204266i	0.0222791	+	0.00654175i
$976$	−20.2838	+	23.4088i	−0.649270	+	0.749297i
$977$	1.71609	+	1.10286i	0.0549024	+	0.0352837i	0.567804	−	0.823164i	$-0.307793\pi$
$977$	1.71609	+	1.10286i	0.0549024	+	0.0352837i	−0.512902	+	0.858447i	$0.671429\pi$
$978$	4.27105	+	2.74484i	0.136573	+	0.0877703i
$979$	−28.3199	+	32.6830i	−0.905109	+	1.04455i
$980$	2.24558	+	0.659361i	0.0717323	+	0.0210625i
$981$	1.53996	+	10.7106i	0.0491670	+	0.341964i
$982$	−1.37018	−	1.58127i	−0.0437242	−	0.0504604i
$983$	−6.69994	−	14.6708i	−0.213695	−	0.467927i	0.772181	−	0.635402i	$-0.219166\pi$
$983$	−6.69994	−	14.6708i	−0.213695	−	0.467927i	−0.985876	+	0.167476i	$0.946438\pi$
$984$	−10.1110	+	2.96887i	−0.322328	+	0.0946440i
$985$	−15.4873	+	33.9124i	−0.493465	+	1.08054i
$986$	11.5440	−	80.2903i	0.367636	−	2.55696i
$987$	−8.59580	+	5.52418i	−0.273607	+	0.175837i
$988$	0.807481			0.0256894
$989$	−42.6613	−	15.6033i	−1.35655	−	0.496155i
$990$	10.4567			0.332334
$991$	35.3352	−	22.7086i	1.12246	−	0.721362i	0.158488	−	0.987361i	$-0.449338\pi$
$991$	35.3352	−	22.7086i	1.12246	−	0.721362i	0.963973	+	0.265999i	$0.0857019\pi$
$992$	1.95372	−	13.5884i	0.0620308	−	0.431433i
$993$	8.81106	−	19.2935i	0.279610	−	0.612261i
$994$	−9.84674	+	2.89126i	−0.312320	+	0.0917053i
$995$	9.99252	+	21.8806i	0.316784	+	0.693660i
$996$	−4.25548	−	4.91109i	−0.134840	−	0.155614i
$997$	4.22060	+	29.3549i	0.133668	+	0.929680i	0.940716	+	0.339195i	$0.110155\pi$
$997$	4.22060	+	29.3549i	0.133668	+	0.929680i	−0.807048	+	0.590485i	$0.798936\pi$
$998$	22.0320	+	6.46918i	0.697410	+	0.204778i
$999$	−3.99178	+	4.60676i	−0.126294	+	0.145751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.127.2	✓	60
23.2	even	11	inner	483.2.q.d.232.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.127.2	✓	60	1.1	even	1	trivial
483.2.q.d.232.2	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)

\(f(q)\)	\(=\)	\(q+(-1.49352 + 0.959824i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.478496 - 1.04776i) q^{4} +(1.94954 - 0.572436i) q^{5} +(0.737505 + 1.61491i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.214292 - 1.49043i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-1.49352 + 0.959824i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.478496 - 1.04776i) q^{4} +(1.94954 - 0.572436i) q^{5} +(0.737505 + 1.61491i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.214292 - 1.49043i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.36223 + 2.72616i) q^{10} +(2.43863 + 1.56722i) q^{11} +(-0.968999 - 0.622738i) q^{12} +(0.544730 - 0.628652i) q^{13} +(1.70343 + 0.500173i) q^{14} +(-0.289161 - 2.01116i) q^{15} +(3.25920 + 3.76132i) q^{16} +(-2.83980 - 6.21829i) q^{17} +(1.70343 - 0.500173i) q^{18} +(-0.350095 + 0.766601i) q^{19} +(0.333071 - 2.31656i) q^{20} +(-0.841254 + 0.540641i) q^{21} -5.14639 q^{22} +(0.989578 - 4.69263i) q^{23} -1.50576 q^{24} +(-0.733252 + 0.471233i) q^{25} +(-0.210168 + 1.46175i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-1.10519 + 0.324514i) q^{28} +(-2.77652 - 6.07973i) q^{29} +(2.36223 + 2.72616i) q^{30} +(0.335445 + 2.33307i) q^{31} +(-5.58835 - 1.64089i) q^{32} +(1.89832 - 2.19077i) q^{33} +(10.2097 + 6.56140i) q^{34} +(-1.70929 - 1.09850i) q^{35} +(-0.754302 + 0.870511i) q^{36} +(5.84870 + 1.71733i) q^{37} +(-0.212930 - 1.48096i) q^{38} +(-0.544730 - 0.628652i) q^{39} +(-1.27095 - 2.78298i) q^{40} +(6.71491 - 1.97168i) q^{41} +(0.737505 - 1.61491i) q^{42} +(1.34798 - 9.37541i) q^{43} +(2.80894 - 1.80520i) q^{44} -2.03184 q^{45} +(3.02614 + 7.95833i) q^{46} +10.2178 q^{47} +(4.18687 - 2.69074i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.642823 - 1.40759i) q^{50} +(-6.55914 + 1.92594i) q^{51} +(-0.398026 - 0.871555i) q^{52} +(-3.61565 - 4.17268i) q^{53} +(-0.252658 - 1.75727i) q^{54} +(5.65134 + 1.65938i) q^{55} +(-0.986061 + 1.13798i) q^{56} +(0.708974 + 0.455630i) q^{57} +(9.98225 + 6.41520i) q^{58} +(7.73530 - 8.92701i) q^{59} +(-2.24558 - 0.659361i) q^{60} +(0.885704 + 6.16021i) q^{61} +(-2.74033 - 3.16251i) q^{62} +(0.415415 + 0.909632i) q^{63} +(0.370572 - 0.108810i) q^{64} +(0.702109 - 1.53740i) q^{65} +(-0.732408 + 5.09401i) q^{66} +(0.886508 - 0.569724i) q^{67} -7.87411 q^{68} +(-4.50403 - 1.64734i) q^{69} +3.60722 q^{70} +(-4.86289 + 3.12519i) q^{71} +(-0.214292 + 1.49043i) q^{72} +(-3.95488 + 8.65998i) q^{73} +(-10.3835 + 3.04886i) q^{74} +(0.362083 + 0.792852i) q^{75} +(0.635695 + 0.733631i) q^{76} +(-0.412544 - 2.86931i) q^{77} +(1.41696 + 0.416057i) q^{78} +(5.94152 - 6.85688i) q^{79} +(8.50706 + 5.46715i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-8.13637 + 9.38987i) q^{82} +(5.41309 + 1.58943i) q^{83} +(0.163925 + 1.14013i) q^{84} +(-9.09586 - 10.4972i) q^{85} +(6.98551 + 15.2961i) q^{86} +(-6.41299 + 1.88302i) q^{87} +(1.81325 - 3.97046i) q^{88} +(-2.12312 + 14.7666i) q^{89} +(3.03459 - 1.95021i) q^{90} -0.831826 q^{91} +(-4.44324 - 3.28224i) q^{92} +2.35706 q^{93} +(-15.2605 + 9.80733i) q^{94} +(-0.243693 + 1.69492i) q^{95} +(-2.41949 + 5.29795i) q^{96} +(-9.12433 + 2.67915i) q^{97} +(-0.737505 - 1.61491i) q^{98} +(-1.89832 - 2.19077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

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