LMFDB - Embedded newform 115.2.g.c.6.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.4
Character	$\chi$	$=$	115.6
Dual form			115.2.g.c.96.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.418214 - 0.915761i) q^{2} +(0.166345 + 0.0488434i) q^{3} +(0.646006 + 0.745531i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.114297 - 0.131906i) q^{6} +(-0.333337 + 2.31841i) q^{7} +(2.88481 - 0.847058i) q^{8} +(-2.49848 - 1.60567i) q^{9} +O(q^{10})$	\(q+(0.418214 - 0.915761i) q^{2} +(0.166345 + 0.0488434i) q^{3} +(0.646006 + 0.745531i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.114297 - 0.131906i) q^{6} +(-0.333337 + 2.31841i) q^{7} +(2.88481 - 0.847058i) q^{8} +(-2.49848 - 1.60567i) q^{9} +(-0.143274 - 0.996491i) q^{10} +(-2.29336 - 5.02176i) q^{11} +(0.0710458 + 0.155569i) q^{12} +(0.372780 + 2.59274i) q^{13} +(1.98370 + 1.27485i) q^{14} +(0.166345 - 0.0488434i) q^{15} +(0.149986 - 1.04318i) q^{16} +(-3.91110 + 4.51365i) q^{17} +(-2.51531 + 1.61649i) q^{18} +(-1.00845 - 1.16381i) q^{19} +(0.946519 + 0.277923i) q^{20} +(-0.168688 + 0.369375i) q^{21} -5.55785 q^{22} +(3.97944 - 2.67657i) q^{23} +0.521248 q^{24} +(0.415415 - 0.909632i) q^{25} +(2.53023 + 0.742944i) q^{26} +(-0.677779 - 0.782198i) q^{27} +(-1.94378 + 1.24919i) q^{28} +(-6.49455 + 7.49511i) q^{29} +(0.0248391 - 0.172760i) q^{30} +(-1.90061 + 0.558068i) q^{31} +(4.16605 + 2.67736i) q^{32} +(-0.136210 - 0.947363i) q^{33} +(2.49775 + 5.46930i) q^{34} +(0.973006 + 2.13059i) q^{35} +(-0.416952 - 2.89996i) q^{36} +(0.981146 + 0.630544i) q^{37} +(-1.48752 + 0.436775i) q^{38} +(-0.0646281 + 0.449498i) q^{39} +(1.96891 - 2.27224i) q^{40} +(9.20568 - 5.91613i) q^{41} +(0.267712 + 0.308956i) q^{42} +(-10.4979 - 3.08247i) q^{43} +(2.26235 - 4.95386i) q^{44} -2.96994 q^{45} +(-0.786839 - 4.76360i) q^{46} +5.54708 q^{47} +(0.0759017 - 0.166202i) q^{48} +(1.45254 + 0.426505i) q^{49} +(-0.659273 - 0.760842i) q^{50} +(-0.871054 + 0.559793i) q^{51} +(-1.69215 + 1.95285i) q^{52} +(0.548491 - 3.81484i) q^{53} +(-0.999763 + 0.293557i) q^{54} +(-4.64427 - 2.98469i) q^{55} +(1.00221 + 6.97053i) q^{56} +(-0.110906 - 0.242850i) q^{57} +(4.14762 + 9.08202i) q^{58} +(-1.36484 - 9.49267i) q^{59} +(0.143874 + 0.0924624i) q^{60} +(7.47655 - 2.19531i) q^{61} +(-0.283803 + 1.97389i) q^{62} +(4.55544 - 5.25726i) q^{63} +(5.96733 - 3.83497i) q^{64} +(1.71534 + 1.97961i) q^{65} +(-0.924523 - 0.271464i) q^{66} +(0.387241 - 0.847939i) q^{67} -5.89165 q^{68} +(0.792695 - 0.250865i) q^{69} +2.35803 q^{70} +(-1.24979 + 2.73667i) q^{71} +(-8.56773 - 2.51571i) q^{72} +(6.99192 + 8.06911i) q^{73} +(0.987757 - 0.634793i) q^{74} +(0.113532 - 0.131023i) q^{75} +(0.216193 - 1.50366i) q^{76} +(12.4070 - 3.64302i) q^{77} +(0.384605 + 0.247170i) q^{78} +(0.115762 + 0.805145i) q^{79} +(-0.437807 - 0.958664i) q^{80} +(3.62674 + 7.94145i) q^{81} +(-1.56782 - 10.9044i) q^{82} +(4.13661 + 2.65844i) q^{83} +(-0.384354 + 0.112857i) q^{84} +(-0.849963 + 5.91162i) q^{85} +(-7.21319 + 8.32447i) q^{86} +(-1.44643 + 0.929561i) q^{87} +(-10.8696 - 12.5442i) q^{88} +(-6.73344 - 1.97712i) q^{89} +(-1.24207 + 2.71976i) q^{90} -6.13530 q^{91} +(4.56621 + 1.23772i) q^{92} -0.343415 q^{93} +(2.31987 - 5.07980i) q^{94} +(-1.47756 - 0.433851i) q^{95} +(0.562232 + 0.648851i) q^{96} +(-5.84939 + 3.75918i) q^{97} +(0.998049 - 1.15181i) q^{98} +(-2.33340 + 16.2291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.418214	−	0.915761i	0.295722	−	0.647541i	−0.702200	−	0.711980i	$-0.747799\pi$
$2$	0.418214	−	0.915761i	0.295722	−	0.647541i	0.997922	+	0.0644392i	$0.0205259\pi$
$3$	0.166345	+	0.0488434i	0.0960395	+	0.0281997i	0.329399	−	0.944191i	$-0.393154\pi$
$3$	0.166345	+	0.0488434i	0.0960395	+	0.0281997i	−0.233360	+	0.972390i	$0.574972\pi$
$4$	0.646006	+	0.745531i	0.323003	+	0.372765i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	0.114297	−	0.131906i	0.0466615	−	0.0538502i
$7$	−0.333337	+	2.31841i	−0.125990	+	0.876276i	0.824576	+	0.565752i	$0.191414\pi$
$7$	−0.333337	+	2.31841i	−0.125990	+	0.876276i	−0.950565	+	0.310525i	$0.899495\pi$
$8$	2.88481	−	0.847058i	1.01994	−	0.299480i
$9$	−2.49848	−	1.60567i	−0.832825	−	0.535224i
$10$	−0.143274	−	0.996491i	−0.0453071	−	0.315118i
$11$	−2.29336	−	5.02176i	−0.691475	−	1.51412i	−0.850010	−	0.526766i	$-0.823404\pi$
$11$	−2.29336	−	5.02176i	−0.691475	−	1.51412i	0.158535	−	0.987353i	$-0.449323\pi$
$12$	0.0710458	+	0.155569i	0.0205092	+	0.0449088i
$13$	0.372780	+	2.59274i	0.103391	+	0.719097i	0.973905	+	0.226955i	$0.0728770\pi$
$13$	0.372780	+	2.59274i	0.103391	+	0.719097i	−0.870515	+	0.492142i	$0.836214\pi$
$14$	1.98370	+	1.27485i	0.530167	+	0.340718i
$15$	0.166345	−	0.0488434i	0.0429502	−	0.0126113i
$16$	0.149986	−	1.04318i	0.0374965	−	0.260794i
$17$	−3.91110	+	4.51365i	−0.948580	+	1.09472i	0.0468185	+	0.998903i	$0.485092\pi$
$17$	−3.91110	+	4.51365i	−0.948580	+	1.09472i	−0.995399	+	0.0958168i	$0.969454\pi$
$18$	−2.51531	+	1.61649i	−0.592864	+	0.381011i
$19$	−1.00845	−	1.16381i	−0.231353	−	0.266996i	0.628189	−	0.778061i	$-0.283797\pi$
$19$	−1.00845	−	1.16381i	−0.231353	−	0.266996i	−0.859542	+	0.511065i	$0.829251\pi$
$20$	0.946519	+	0.277923i	0.211648	+	0.0621455i
$21$	−0.168688	+	0.369375i	−0.0368107	+	0.0806043i
$22$	−5.55785			−1.18494
$23$	3.97944	−	2.67657i	0.829771	−	0.558103i
$23$	3.97944	−	2.67657i	0.829771	−	0.558103i
$24$	0.521248			0.106399
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	2.53023	+	0.742944i	0.496220	+	0.145703i
$27$	−0.677779	−	0.782198i	−0.130439	−	0.150534i
$28$	−1.94378	+	1.24919i	−0.367341	+	0.236075i
$29$	−6.49455	+	7.49511i	−1.20601	+	1.39181i	−0.308258	+	0.951303i	$0.599746\pi$
$29$	−6.49455	+	7.49511i	−1.20601	+	1.39181i	−0.897750	+	0.440505i	$0.854799\pi$
$30$	0.0248391	−	0.172760i	0.00453497	−	0.0315414i
$31$	−1.90061	+	0.558068i	−0.341359	+	0.100232i	−0.447919	−	0.894074i	$-0.647835\pi$
$31$	−1.90061	+	0.558068i	−0.341359	+	0.100232i	0.106560	+	0.994306i	$0.466016\pi$
$32$	4.16605	+	2.67736i	0.736461	+	0.473295i
$33$	−0.136210	−	0.947363i	−0.0237111	−	0.164915i
$34$	2.49775	+	5.46930i	0.428360	+	0.937978i
$35$	0.973006	+	2.13059i	0.164468	+	0.360135i
$36$	−0.416952	−	2.89996i	−0.0694920	−	0.483327i
$37$	0.981146	+	0.630544i	0.161299	+	0.103661i	0.618800	−	0.785548i	$-0.287619\pi$
$37$	0.981146	+	0.630544i	0.161299	+	0.103661i	−0.457501	+	0.889209i	$0.651255\pi$
$38$	−1.48752	+	0.436775i	−0.241307	+	0.0708542i
$39$	−0.0646281	+	0.449498i	−0.0103488	+	0.0719773i
$40$	1.96891	−	2.27224i	0.311311	−	0.359272i
$41$	9.20568	−	5.91613i	1.43769	−	0.923945i	0.437998	−	0.898976i	$-0.355688\pi$
$41$	9.20568	−	5.91613i	1.43769	−	0.923945i	0.999688	−	0.0249689i	$-0.00794866\pi$
$42$	0.267712	+	0.308956i	0.0413088	+	0.0476729i
$43$	−10.4979	−	3.08247i	−1.60092	−	0.470073i	−0.645118	−	0.764083i	$-0.723192\pi$
$43$	−10.4979	−	3.08247i	−1.60092	−	0.470073i	−0.955802	+	0.294010i	$0.905010\pi$
$44$	2.26235	−	4.95386i	0.341063	−	0.746823i
$45$	−2.96994			−0.442733
$46$	−0.786839	−	4.76360i	−0.116013	−	0.702354i
$47$	5.54708			0.809125			0.404562	−	0.914510i	$-0.367424\pi$
$47$	5.54708			0.809125			0.404562	+	0.914510i	$0.367424\pi$
$48$	0.0759017	−	0.166202i	0.0109555	−	0.0239891i
$49$	1.45254	+	0.426505i	0.207506	+	0.0609292i
$50$	−0.659273	−	0.760842i	−0.0932353	−	0.107599i
$51$	−0.871054	+	0.559793i	−0.121972	+	0.0783867i
$52$	−1.69215	+	1.95285i	−0.234659	+	0.270811i
$53$	0.548491	−	3.81484i	0.0753410	−	0.524008i	−0.916845	−	0.399243i	$-0.869273\pi$
$53$	0.548491	−	3.81484i	0.0753410	−	0.524008i	0.992186	−	0.124765i	$-0.0398178\pi$
$54$	−0.999763	+	0.293557i	−0.136051	+	0.0399481i
$55$	−4.64427	−	2.98469i	−0.626233	−	0.402456i
$56$	1.00221	+	6.97053i	0.133926	+	0.931477i
$57$	−0.110906	−	0.242850i	−0.0146898	−	0.0321663i
$58$	4.14762	+	9.08202i	0.544609	+	1.19253i
$59$	−1.36484	−	9.49267i	−0.177687	−	1.23584i	−0.862097	−	0.506743i	$-0.830849\pi$
$59$	−1.36484	−	9.49267i	−0.177687	−	1.23584i	0.684410	−	0.729097i	$-0.260060\pi$
$60$	0.143874	+	0.0924624i	0.0185741	+	0.0119368i
$61$	7.47655	−	2.19531i	0.957274	−	0.281081i	0.234462	−	0.972125i	$-0.424667\pi$
$61$	7.47655	−	2.19531i	0.957274	−	0.281081i	0.722812	+	0.691044i	$0.242849\pi$
$62$	−0.283803	+	1.97389i	−0.0360430	+	0.250685i
$63$	4.55544	−	5.25726i	0.573932	−	0.662352i
$64$	5.96733	−	3.83497i	0.745916	−	0.479371i
$65$	1.71534	+	1.97961i	0.212762	+	0.245541i
$66$	−0.924523	−	0.271464i	−0.113801	−	0.0334150i
$67$	0.387241	−	0.847939i	0.0473090	−	0.103592i	−0.884502	−	0.466537i	$-0.845501\pi$
$67$	0.387241	−	0.847939i	0.0473090	−	0.103592i	0.931811	+	0.362945i	$0.118229\pi$
$68$	−5.89165			−0.714468
$69$	0.792695	−	0.250865i	0.0954292	−	0.0302006i
$70$	2.35803			0.281839
$71$	−1.24979	+	2.73667i	−0.148323	+	0.324783i	−0.969181	−	0.246350i	$-0.920769\pi$
$71$	−1.24979	+	2.73667i	−0.148323	+	0.324783i	0.820858	+	0.571133i	$0.193496\pi$
$72$	−8.56773	−	2.51571i	−1.00972	−	0.296480i
$73$	6.99192	+	8.06911i	0.818343	+	0.944418i	0.999236	−	0.0390848i	$-0.0124442\pi$
$73$	6.99192	+	8.06911i	0.818343	+	0.944418i	−0.180893	+	0.983503i	$0.557899\pi$
$74$	0.987757	−	0.634793i	0.114824	−	0.0737932i
$75$	0.113532	−	0.131023i	0.0131095	−	0.0151292i
$76$	0.216193	−	1.50366i	0.0247990	−	0.172481i
$77$	12.4070	−	3.64302i	1.41391	−	0.415160i
$78$	0.384605	+	0.247170i	0.0435479	+	0.0279865i
$79$	0.115762	+	0.805145i	0.0130243	+	0.0905859i	0.995297	−	0.0968728i	$-0.0308840\pi$
$79$	0.115762	+	0.805145i	0.0130243	+	0.0905859i	−0.982272	+	0.187459i	$0.939975\pi$
$80$	−0.437807	−	0.958664i	−0.0489483	−	0.107182i
$81$	3.62674	+	7.94145i	0.402971	+	0.882383i
$82$	−1.56782	−	10.9044i	−0.173137	−	1.20419i
$83$	4.13661	+	2.65844i	0.454051	+	0.291801i	0.747608	−	0.664141i	$-0.231202\pi$
$83$	4.13661	+	2.65844i	0.454051	+	0.291801i	−0.293556	+	0.955942i	$0.594839\pi$
$84$	−0.384354	+	0.112857i	−0.0419365	+	0.0123137i
$85$	−0.849963	+	5.91162i	−0.0921914	+	0.641205i
$86$	−7.21319	+	8.32447i	−0.777819	+	0.897651i
$87$	−1.44643	+	0.929561i	−0.155073	+	0.0996594i
$88$	−10.8696	−	12.5442i	−1.15871	−	1.33722i
$89$	−6.73344	−	1.97712i	−0.713743	−	0.209574i	−0.0953513	−	0.995444i	$-0.530397\pi$
$89$	−6.73344	−	1.97712i	−0.713743	−	0.209574i	−0.618392	+	0.785870i	$0.712216\pi$
$90$	−1.24207	+	2.71976i	−0.130926	+	0.286688i
$91$	−6.13530			−0.643154
$92$	4.56621	+	1.23772i	0.476060	+	0.129041i
$93$	−0.343415			−0.0356105
$94$	2.31987	−	5.07980i	0.239276	−	0.523941i
$95$	−1.47756	−	0.433851i	−0.151595	−	0.0445122i
$96$	0.562232	+	0.648851i	0.0573826	+	0.0662230i
$97$	−5.84939	+	3.75918i	−0.593916	+	0.381687i	−0.802795	−	0.596255i	$-0.796655\pi$
$97$	−5.84939	+	3.75918i	−0.593916	+	0.381687i	0.208879	+	0.977941i	$0.433018\pi$
$98$	0.998049	−	1.15181i	0.100818	−	0.116350i
$99$	−2.33340	+	16.2291i	−0.234515	+	1.63109i
$100$	0.946519	−	0.277923i	0.0946519	−	0.0277923i
$101$	3.13919	+	2.01744i	0.312361	+	0.200742i	0.687423	−	0.726258i	$-0.258742\pi$
$101$	3.13919	+	2.01744i	0.312361	+	0.200742i	−0.375061	+	0.927000i	$0.622378\pi$
$102$	0.148349	+	1.03179i	0.0146888	+	0.102163i
$103$	1.03172	+	2.25916i	0.101659	+	0.222601i	0.953626	−	0.300993i	$-0.0973181\pi$
$103$	1.03172	+	2.25916i	0.101659	+	0.222601i	−0.851968	+	0.523594i	$0.824591\pi$
$104$	3.27160	+	7.16381i	0.320807	+	0.702469i
$105$	0.0577899	+	0.401938i	0.00563972	+	0.0392251i
$106$	−3.26409	−	2.09770i	−0.317037	−	0.203747i
$107$	7.83031	−	2.29919i	0.756984	−	0.222271i	0.119606	−	0.992821i	$-0.461837\pi$
$107$	7.83031	−	2.29919i	0.756984	−	0.222271i	0.637379	+	0.770551i	$0.280019\pi$
$108$	0.145304	−	1.01061i	0.0139819	−	0.0972460i
$109$	1.16648	−	1.34619i	0.111729	−	0.128942i	−0.697130	−	0.716944i	$-0.745540\pi$
$109$	1.16648	−	1.34619i	0.111729	−	0.128942i	0.808859	+	0.588003i	$0.200086\pi$
$110$	−4.67556	+	3.00480i	−0.445798	+	0.286497i
$111$	0.132411	+	0.152811i	0.0125679	+	0.0145041i
$112$	2.36851	+	0.695458i	0.223803	+	0.0657146i
$113$	−4.38993	+	9.61261i	−0.412970	+	0.904278i	0.582819	+	0.812602i	$0.301950\pi$
$113$	−4.38993	+	9.61261i	−0.412970	+	0.904278i	−0.995789	+	0.0916761i	$0.970778\pi$
$114$	−0.268775			−0.0251731
$115$	1.90066	−	4.40312i	0.177237	−	0.410593i
$116$	−9.78336			−0.908362
$117$	3.23171	−	7.07647i	0.298772	−	0.654219i
$118$	−9.26381	−	2.72010i	−0.852803	−	0.250406i
$119$	−9.16077	−	10.5721i	−0.839766	−	0.969142i
$120$	0.438502	−	0.281808i	0.0400296	−	0.0257254i
$121$	−12.7551	+	14.7202i	−1.15956	+	1.33820i
$122$	1.11642	−	7.76484i	0.101076	−	0.702996i
$123$	1.82029	−	0.534484i	0.164130	−	0.0481928i
$124$	−1.64386	−	1.05644i	−0.147623	−	0.0948716i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	−2.90924	−	6.37036i	−0.259176	−	0.567516i
$127$	−2.32299	−	5.08664i	−0.206132	−	0.451366i	0.778125	−	0.628110i	$-0.216171\pi$
$127$	−2.32299	−	5.08664i	−0.206132	−	0.451366i	−0.984257	+	0.176743i	$0.943444\pi$
$128$	0.393248	+	2.73510i	0.0347586	+	0.241751i
$129$	−1.59572	−	1.02551i	−0.140496	−	0.0902911i
$130$	2.53023	−	0.742944i	0.221916	−	0.0651605i
$131$	−0.241551	+	1.68003i	−0.0211044	+	0.146785i	−0.997649	−	0.0685308i	$-0.978169\pi$
$131$	−0.241551	+	1.68003i	−0.0211044	+	0.146785i	0.976545	+	0.215315i	$0.0690780\pi$
$132$	0.618295	−	0.713551i	0.0538157	−	0.0621066i
$133$	3.03434	−	1.95005i	0.263111	−	0.169091i
$134$	−0.614560	−	0.709240i	−0.0530899	−	0.0612690i
$135$	−0.993072	−	0.291592i	−0.0854700	−	0.0250963i
$136$	−7.45947	+	16.3340i	−0.639644	+	1.40062i
$137$	−11.4455			−0.977854			−0.488927	−	0.872325i	$-0.662612\pi$
$137$	−11.4455			−0.977854			−0.488927	+	0.872325i	$0.662612\pi$
$138$	0.101783	−	0.830834i	0.00866438	−	0.0707253i
$139$	17.9531			1.52276			0.761381	−	0.648304i	$-0.224521\pi$
$139$	17.9531			1.52276			0.761381	+	0.648304i	$0.224521\pi$
$140$	−0.959849	+	2.10178i	−0.0811221	+	0.177633i
$141$	0.922730	+	0.270938i	0.0777079	+	0.0228171i
$142$	1.98345	+	2.28902i	0.166448	+	0.192091i
$143$	12.1652	−	7.81811i	1.01731	−	0.653783i
$144$	−2.04974	+	2.36552i	−0.170811	+	0.197127i
$145$	−1.41140	+	9.81651i	−0.117210	+	0.815217i
$146$	10.3135	−	3.02832i	0.853551	−	0.250625i
$147$	0.220791	+	0.141894i	0.0182106	+	0.0117032i
$148$	0.163736	+	1.13881i	0.0134590	+	0.0936096i
$149$	−2.27380	−	4.97892i	−0.186277	−	0.407889i	0.793336	−	0.608784i	$-0.208342\pi$
$149$	−2.27380	−	4.97892i	−0.186277	−	0.407889i	−0.979613	+	0.200895i	$0.935615\pi$
$150$	−0.0725049	−	0.158764i	−0.00592000	−	0.0129630i
$151$	−0.858018	−	5.96764i	−0.0698245	−	0.485640i	−0.994488	−	0.104854i	$-0.966563\pi$
$151$	−0.858018	−	5.96764i	−0.0698245	−	0.485640i	0.924663	−	0.380786i	$-0.124347\pi$
$152$	−3.89499	−	2.50316i	−0.315926	−	0.203033i
$153$	17.0192	−	4.99729i	1.37592	−	0.404007i
$154$	1.85264	−	12.8854i	0.149290	−	1.03833i
$155$	−1.29718	+	1.49702i	−0.104192	+	0.120244i
$156$	−0.376865	+	0.242196i	−0.0301733	+	0.0193912i
$157$	−2.78158	−	3.21012i	−0.221994	−	0.256195i	0.633817	−	0.773483i	$-0.281487\pi$
$157$	−2.78158	−	3.21012i	−0.221994	−	0.256195i	−0.855812	+	0.517288i	$0.826942\pi$
$158$	0.785734	+	0.230712i	0.0625096	+	0.0183545i
$159$	0.277568	−	0.607790i	0.0220126	−	0.0482009i
$160$	4.95220			0.391506
$161$	4.87889	+	10.1182i	0.384510	+	0.797424i
$162$	8.78922			0.690546
$163$	2.95249	−	6.46505i	0.231257	−	0.506382i	−0.758056	−	0.652189i	$-0.773851\pi$
$163$	2.95249	−	6.46505i	0.231257	−	0.506382i	0.989313	+	0.145808i	$0.0465780\pi$
$164$	10.3576	+	3.04126i	0.808792	+	0.237483i
$165$	−0.626770	−	0.723331i	−0.0487940	−	0.0563113i
$166$	4.16448	−	2.67635i	0.323226	−	0.207725i
$167$	−3.55306	+	4.10045i	−0.274944	+	0.317302i	−0.876381	−	0.481618i	$-0.840049\pi$
$167$	−3.55306	+	4.10045i	−0.274944	+	0.317302i	0.601438	+	0.798920i	$0.294595\pi$
$168$	−0.173751	+	1.20847i	−0.0134052	+	0.0932353i
$169$	5.89006	−	1.72948i	0.453082	−	0.133037i
$170$	5.05817	+	3.25069i	0.387944	+	0.249316i
$171$	0.650882	+	4.52698i	0.0497742	+	0.346187i
$172$	−4.48365	−	9.81783i	−0.341875	−	0.748602i
$173$	−0.815415	−	1.78551i	−0.0619948	−	0.135750i	0.876099	−	0.482132i	$-0.160137\pi$
$173$	−0.815415	−	1.78551i	−0.0619948	−	0.135750i	−0.938094	+	0.346382i	$0.887410\pi$
$174$	0.246340	+	1.71334i	0.0186750	+	0.129888i
$175$	1.97043	+	1.26632i	0.148950	+	0.0957245i
$176$	−5.58256	+	1.63919i	−0.420801	+	0.123558i
$177$	0.236619	−	1.64572i	0.0177854	−	0.123700i
$178$	−4.62659	+	5.33937i	−0.346777	+	0.400202i
$179$	−13.2707	+	8.52855i	−0.991898	+	0.637454i	−0.932647	−	0.360789i	$-0.882507\pi$
$179$	−13.2707	+	8.52855i	−0.991898	+	0.637454i	−0.0592502	+	0.998243i	$0.518871\pi$
$180$	−1.91860	−	2.21418i	−0.143004	−	0.165036i
$181$	−8.32906	−	2.44563i	−0.619094	−	0.181783i	−0.0428789	−	0.999080i	$-0.513653\pi$
$181$	−8.32906	−	2.44563i	−0.619094	−	0.181783i	−0.576216	+	0.817298i	$0.695471\pi$
$182$	−2.56587	+	5.61847i	−0.190195	+	0.416469i
$183$	1.35092			0.0998625
$184$	9.21274	−	11.0922i	0.679173	−	0.817729i
$185$	1.16629			0.0857474
$186$	−0.143621	+	0.314486i	−0.0105308	+	0.0230592i
$187$	31.6360	+	9.28918i	2.31346	+	0.679292i
$188$	3.58345	+	4.13552i	0.261350	+	0.301614i
$189$	2.03938	−	1.31063i	0.148343	−	0.0953345i
$190$	−1.01524	+	1.17165i	−0.0736533	+	0.0850005i
$191$	2.76851	−	19.2554i	0.200322	−	1.39327i	−0.603007	−	0.797736i	$-0.706031\pi$
$191$	2.76851	−	19.2554i	0.200322	−	1.39327i	0.803329	−	0.595536i	$-0.203060\pi$
$192$	1.17995	−	0.346464i	0.0851555	−	0.0250039i
$193$	8.86653	+	5.69817i	0.638226	+	0.410163i	0.819347	−	0.573298i	$-0.194336\pi$
$193$	8.86653	+	5.69817i	0.638226	+	0.410163i	−0.181121	+	0.983461i	$0.557972\pi$
$194$	0.996210	+	6.92879i	0.0715237	+	0.497458i
$195$	0.188649	+	0.413083i	0.0135094	+	0.0295815i
$196$	0.620378	+	1.35844i	0.0443127	+	0.0970313i
$197$	−0.624137	−	4.34096i	−0.0444679	−	0.309281i	−0.999901	−	0.0140732i	$-0.995520\pi$
$197$	−0.624137	−	4.34096i	−0.0444679	−	0.309281i	0.955433	−	0.295208i	$-0.0953889\pi$
$198$	13.8862	+	8.92409i	0.986847	+	0.634208i
$199$	−14.8020	+	4.34625i	−1.04928	+	0.308097i	−0.760528	−	0.649305i	$-0.775060\pi$
$199$	−14.8020	+	4.34625i	−1.04928	+	0.308097i	−0.288756	+	0.957403i	$0.593242\pi$
$200$	0.427884	−	2.97600i	0.0302560	−	0.210435i
$201$	0.105832	−	0.122136i	0.00746480	−	0.00861484i
$202$	3.16034	−	2.03103i	0.222361	−	0.142903i
$203$	−15.2119	−	17.5554i	−1.06766	−	1.23215i
$204$	−0.980049	−	0.287768i	−0.0686172	−	0.0201478i
$205$	4.54581	−	9.95394i	0.317493	−	0.695213i
$206$	2.50033			0.174206
$207$	−14.2402	+	0.297659i	−0.989765	+	0.0206887i
$208$	2.76060			0.191413
$209$	−3.53164	+	7.73322i	−0.244289	+	0.534918i
$210$	0.392248	+	0.115174i	0.0270677	+	0.00794778i
$211$	−6.38360	−	7.36707i	−0.439465	−	0.507170i	0.492203	−	0.870481i	$-0.336192\pi$
$211$	−6.38360	−	7.36707i	−0.439465	−	0.507170i	−0.931668	+	0.363311i	$0.881646\pi$
$212$	3.19841	−	2.05549i	0.219667	−	0.141172i
$213$	−0.341565	+	0.394187i	−0.0234037	+	0.0270093i
$214$	1.16924	−	8.13224i	0.0799276	−	0.555909i
$215$	−10.4979	+	3.08247i	−0.715953	+	0.210223i
$216$	−2.61783	−	1.68238i	−0.178121	−	0.114471i
$217$	−0.660289	−	4.59241i	−0.0448233	−	0.311753i
$218$	−0.744951	−	1.63121i	−0.0504544	−	0.110480i
$219$	0.768951	+	1.68377i	0.0519609	+	0.113778i
$220$	−0.775048	−	5.39058i	−0.0522537	−	0.363433i
$221$	−13.1607	−	8.45787i	−0.885285	−	0.568938i
$222$	0.195314	−	0.0573494i	0.0131086	−	0.00384904i
$223$	−2.32808	+	16.1921i	−0.155900	+	1.08431i	0.750190	+	0.661222i	$0.229962\pi$
$223$	−2.32808	+	16.1921i	−0.155900	+	1.08431i	−0.906090	+	0.423085i	$0.860947\pi$
$224$	−7.59592	+	8.76616i	−0.507524	+	0.585714i
$225$	−2.49848	+	1.60567i	−0.166565	+	0.107045i
$226$	6.96692	+	8.04026i	0.463433	+	0.534830i
$227$	−16.7007	−	4.90376i	−1.10846	−	0.325474i	−0.324254	−	0.945970i	$-0.605113\pi$
$227$	−16.7007	−	4.90376i	−1.10846	−	0.325474i	−0.784210	+	0.620496i	$0.786931\pi$
$228$	0.109406	−	0.239566i	0.00724561	−	0.0158657i
$229$	16.2129			1.07138			0.535688	−	0.844416i	$-0.320052\pi$
$229$	16.2129			1.07138			0.535688	+	0.844416i	$0.320052\pi$
$230$	−3.23733	−	3.58200i	−0.213463	−	0.236190i
$231$	2.24178			0.147498
$232$	−12.3868	+	27.1233i	−0.813232	+	1.78073i
$233$	−24.6540	−	7.23907i	−1.61514	−	0.474247i	−0.655431	−	0.755255i	$-0.727513\pi$
$233$	−24.6540	−	7.23907i	−1.61514	−	0.474247i	−0.959705	+	0.281008i	$0.909331\pi$
$234$	−5.12880	−	5.91896i	−0.335280	−	0.386934i
$235$	4.66650	−	2.99898i	0.304409	−	0.195632i
$236$	6.19538	−	7.14985i	0.403285	−	0.465416i
$237$	−0.0200695	+	0.139586i	−0.00130365	+	0.00906711i
$238$	−13.5127	+	3.96768i	−0.875897	+	0.257186i
$239$	−17.7780	−	11.4252i	−1.14996	−	0.739036i	−0.180331	−	0.983606i	$-0.557717\pi$
$239$	−17.7780	−	11.4252i	−1.14996	−	0.739036i	−0.969632	+	0.244570i	$0.921353\pi$
$240$	−0.0260028	−	0.180853i	−0.00167847	−	0.0116740i
$241$	12.2004	+	26.7151i	0.785896	+	1.72087i	0.688040	+	0.725672i	$0.258471\pi$
$241$	12.2004	+	26.7151i	0.785896	+	1.72087i	0.0978559	+	0.995201i	$0.468802\pi$
$242$	8.14582	+	17.8369i	0.523633	+	1.14660i
$243$	0.657290	+	4.57155i	0.0421652	+	0.293265i
$244$	6.46657	+	4.15581i	0.413980	+	0.266049i
$245$	1.45254	−	0.426505i	0.0927994	−	0.0272484i
$246$	0.271809	−	1.89048i	0.0173299	−	0.120532i
$247$	2.64153	−	3.04849i	0.168076	−	0.193971i
$248$	−5.01018	+	3.21985i	−0.318147	+	0.204460i
$249$	0.558258	+	0.644264i	0.0353782	+	0.0408286i
$250$	−0.965958	−	0.283631i	−0.0610926	−	0.0179384i
$251$	5.35033	−	11.7156i	0.337710	−	0.739482i	−0.662242	−	0.749290i	$-0.730395\pi$
$251$	5.35033	−	11.7156i	0.337710	−	0.739482i	0.999952	+	0.00980817i	$0.00312209\pi$
$252$	6.86229			0.432284
$253$	−22.5674	−	13.8455i	−1.41880	−	0.870458i
$254$	−5.62965			−0.353236
$255$	−0.430131	+	0.941855i	−0.0269358	+	0.0589813i
$256$	16.2812	+	4.78061i	1.01758	+	0.298788i
$257$	−7.37033	−	8.50581i	−0.459748	−	0.530578i	0.477783	−	0.878478i	$-0.341440\pi$
$257$	−7.37033	−	8.50581i	−0.459748	−	0.530578i	−0.937532	+	0.347900i	$0.886895\pi$
$258$	−1.60648	+	1.03242i	−0.100015	+	0.0642756i
$259$	−1.78891	+	2.06452i	−0.111158	+	0.128283i
$260$	−0.367739	+	2.55768i	−0.0228062	+	0.158621i
$261$	28.2612	−	8.29823i	1.74932	−	0.513648i
$262$	1.43748	+	0.923814i	0.0888080	+	0.0570734i
$263$	3.08753	+	21.4742i	0.190385	+	1.32416i	0.830990	+	0.556287i	$0.187775\pi$
$263$	3.08753	+	21.4742i	0.190385	+	1.32416i	−0.640605	+	0.767871i	$0.721316\pi$
$264$	−1.19541	−	2.61759i	−0.0735725	−	0.161101i
$265$	−1.60104	−	3.50578i	−0.0983509	−	0.215358i
$266$	−0.516778	−	3.59427i	−0.0316857	−	0.220379i
$267$	−1.02351	−	0.657768i	−0.0626376	−	0.0402548i
$268$	0.882324	−	0.259074i	0.0538965	−	0.0158254i
$269$	−1.87251	+	13.0236i	−0.114169	+	0.794062i	0.849620	+	0.527395i	$0.176831\pi$
$269$	−1.87251	+	13.0236i	−0.114169	+	0.794062i	−0.963789	+	0.266667i	$0.914078\pi$
$270$	−0.682346	+	0.787469i	−0.0415262	+	0.0479238i
$271$	−1.75634	+	1.12873i	−0.106690	+	0.0685657i	−0.592898	−	0.805278i	$-0.702016\pi$
$271$	−1.75634	+	1.12873i	−0.106690	+	0.0685657i	0.486208	+	0.873843i	$0.338380\pi$
$272$	4.12192	+	4.75695i	0.249928	+	0.288432i
$273$	−1.02058	−	0.299669i	−0.0617682	−	0.0181368i
$274$	−4.78666	+	10.4813i	−0.289173	+	0.633200i
$275$	−5.52066			−0.332908
$276$	0.699113	+	0.428918i	0.0420817	+	0.0258178i
$277$	−23.6500			−1.42099			−0.710496	−	0.703702i	$-0.751529\pi$
$277$	−23.6500			−1.42099			−0.710496	+	0.703702i	$0.751529\pi$
$278$	7.50824	−	16.4408i	0.450315	−	0.986051i
$279$	5.64469	+	1.65743i	0.337939	+	0.0992278i
$280$	4.61167	+	5.32215i	0.275600	+	0.318059i
$281$	−12.7822	+	8.21465i	−0.762524	+	0.490045i	−0.863192	−	0.504875i	$-0.831538\pi$
$281$	−12.7822	+	8.21465i	−0.762524	+	0.490045i	0.100668	+	0.994920i	$0.467902\pi$
$282$	0.634013	−	0.731691i	0.0377550	−	0.0435715i
$283$	−4.49240	+	31.2453i	−0.267045	+	1.85734i	0.208995	+	0.977917i	$0.432981\pi$
$283$	−4.49240	+	31.2453i	−0.267045	+	1.85734i	−0.476041	+	0.879423i	$0.657928\pi$
$284$	−2.84764	+	0.836143i	−0.168977	+	0.0496160i
$285$	−0.224595	−	0.144338i	−0.0133038	−	0.00854986i
$286$	−2.07186	−	14.4101i	−0.122511	−	0.852086i
$287$	10.6474	+	23.3146i	0.628498	+	1.37622i
$288$	−6.10982	−	13.3786i	−0.360025	−	0.788344i
$289$	−2.65697	−	18.4797i	−0.156293	−	1.08704i
$290$	8.39931	+	5.39791i	0.493225	+	0.316976i
$291$	−1.15663	+	0.339617i	−0.0678029	+	0.0199087i
$292$	−1.49894	+	10.4254i	−0.0877191	+	0.610100i
$293$	17.9808	−	20.7510i	1.05045	−	1.21229i	0.0738404	−	0.997270i	$-0.476474\pi$
$293$	17.9808	−	20.7510i	1.05045	−	1.21229i	0.976611	−	0.215015i	$-0.0689801\pi$
$294$	0.222279	−	0.142850i	0.0129636	−	0.00833119i
$295$	−6.28030	−	7.24785i	−0.365653	−	0.421986i
$296$	3.36453	+	0.987915i	0.195559	+	0.0574214i
$297$	−2.37362	+	5.19751i	−0.137732	+	0.301590i
$298$	−5.51044			−0.319211
$299$	8.42311	+	9.31990i	0.487121	+	0.538984i
$300$	0.171024			0.00987406
$301$	10.6458	−	23.3110i	0.613613	−	1.34362i
$302$	−5.82377	−	1.71001i	−0.335120	−	0.0984002i
$303$	0.423651	+	0.488920i	0.0243381	+	0.0280877i
$304$	−1.36531	+	0.877432i	−0.0783059	+	0.0503242i
$305$	5.10280	−	5.88894i	0.292185	−	0.337200i
$306$	2.54135	−	17.6755i	0.145279	−	1.01044i
$307$	−6.82047	+	2.00267i	−0.389265	+	0.114298i	−0.470508	−	0.882396i	$-0.655929\pi$
$307$	−6.82047	+	2.00267i	−0.389265	+	0.114298i	0.0812430	+	0.996694i	$0.474111\pi$
$308$	10.7310	+	6.89637i	0.611453	+	0.392957i
$309$	0.0612773	+	0.426193i	0.00348594	+	0.0242453i
$310$	0.828417	+	1.81398i	0.0470509	+	0.103027i
$311$	−9.17611	−	20.0929i	−0.520329	−	1.13936i	−0.969315	−	0.245823i	$-0.920942\pi$
$311$	−9.17611	−	20.0929i	−0.520329	−	1.13936i	0.448985	−	0.893539i	$-0.351786\pi$
$312$	0.194311	+	1.35146i	0.0110007	+	0.0765115i
$313$	−4.18623	−	2.69033i	−0.236620	−	0.152066i	0.416958	−	0.908926i	$-0.363096\pi$
$313$	−4.18623	−	2.69033i	−0.236620	−	0.152066i	−0.653578	+	0.756859i	$0.726733\pi$
$314$	−4.10300	+	1.20475i	−0.231545	+	0.0679879i
$315$	0.989992	−	6.88555i	0.0557797	−	0.387957i
$316$	−0.525477	+	0.606433i	−0.0295604	+	0.0341145i
$317$	3.29592	−	2.11816i	0.185117	−	0.118968i	−0.444800	−	0.895630i	$-0.646725\pi$
$317$	3.29592	−	2.11816i	0.185117	−	0.118968i	0.629917	+	0.776662i	$0.283089\pi$
$318$	−0.440507	−	0.508373i	−0.0247024	−	0.0285081i
$319$	52.5331	+	15.4251i	2.94129	+	0.863640i
$320$	2.94669	−	6.45236i	0.164725	−	0.360698i
$321$	1.41483			0.0789684
$322$	11.3063	−	0.236331i	0.630073	−	0.0131702i
$323$	9.19716			0.511743
$324$	−3.57770	+	7.83407i	−0.198761	+	0.435226i
$325$	2.51330	+	0.737971i	0.139413	+	0.0409353i
$326$	−4.68567	−	5.40755i	−0.259515	−	0.299496i
$327$	0.259791	−	0.166958i	0.0143665	−	0.00923278i
$328$	21.5454	−	24.8647i	1.18964	−	1.37292i
$329$	−1.84905	+	12.8604i	−0.101941	+	0.709017i
$330$	−0.924523	+	0.271464i	−0.0508933	+	0.0149436i
$331$	−0.469341	−	0.301627i	−0.0257973	−	0.0165789i	0.527679	−	0.849444i	$-0.323063\pi$
$331$	−0.469341	−	0.301627i	−0.0257973	−	0.0165789i	−0.553476	+	0.832865i	$0.686699\pi$
$332$	0.690327	+	4.80133i	0.0378866	+	0.263507i
$333$	−1.43892	−	3.15080i	−0.0788524	−	0.172663i
$334$	2.26909	+	4.96862i	0.124159	+	0.271871i
$335$	−0.132663	−	0.922689i	−0.00724814	−	0.0504119i
$336$	0.360023	+	0.231372i	0.0196408	+	0.0126224i
$337$	1.55452	−	0.456448i	0.0846800	−	0.0248643i	−0.239118	−	0.970990i	$-0.576858\pi$
$337$	1.55452	−	0.456448i	0.0846800	−	0.0248643i	0.323798	+	0.946126i	$0.395040\pi$
$338$	0.879518	−	6.11718i	0.0478395	−	0.332731i
$339$	−1.19976	+	1.38459i	−0.0651618	+	0.0752008i
$340$	−4.95638	+	3.18527i	−0.268797	+	0.172745i
$341$	7.16127	+	8.26455i	0.387804	+	0.447550i
$342$	4.41784	+	1.29720i	0.238890	+	0.0701443i
$343$	−8.28404	+	18.1395i	−0.447296	+	0.979442i
$344$	−32.8956			−1.77361
$345$	0.531229	−	0.639604i	0.0286004	−	0.0344351i
$346$	−1.97612			−0.106237
$347$	0.902570	−	1.97635i	0.0484525	−	0.106096i	−0.883858	−	0.467756i	$-0.845063\pi$
$347$	0.902570	−	1.97635i	0.0484525	−	0.106096i	0.932310	+	0.361660i	$0.117790\pi$
$348$	−1.62742	−	0.477852i	−0.0872386	−	0.0256156i
$349$	−4.18036	−	4.82439i	−0.223770	−	0.258244i	0.632753	−	0.774354i	$-0.281925\pi$
$349$	−4.18036	−	4.82439i	−0.223770	−	0.258244i	−0.856522	+	0.516110i	$0.827380\pi$
$350$	1.98370	−	1.27485i	0.106033	−	0.0681435i
$351$	1.77538	−	2.04889i	0.0947626	−	0.109362i
$352$	3.89080	−	27.0611i	0.207380	−	1.44236i
$353$	−27.5665	+	8.09425i	−1.46722	+	0.430814i	−0.915193	−	0.403015i	$-0.867962\pi$
$353$	−27.5665	+	8.09425i	−1.46722	+	0.430814i	−0.552023	+	0.833829i	$0.686144\pi$
$354$	−1.40813	−	0.904952i	−0.0748414	−	0.0480976i
$355$	0.428160	+	2.97792i	0.0227244	+	0.158052i
$356$	−2.87584	−	6.29722i	−0.152419	−	0.333752i
$357$	−1.00747	−	2.20606i	−0.0533212	−	0.116757i
$358$	2.26013	+	15.7195i	0.119451	+	0.830803i
$359$	8.50186	+	5.46381i	0.448711	+	0.288369i	0.745415	−	0.666600i	$-0.232251\pi$
$359$	8.50186	+	5.46381i	0.448711	+	0.288369i	−0.296704	+	0.954969i	$0.595888\pi$
$360$	−8.56773	+	2.51571i	−0.451559	+	0.132590i
$361$	2.36649	−	16.4593i	0.124552	−	0.866280i
$362$	−5.72295	+	6.60463i	−0.300791	+	0.347132i
$363$	−2.84074	+	1.82563i	−0.149100	+	0.0958210i
$364$	−3.96344	−	4.57405i	−0.207741	−	0.239746i
$365$	10.2445	+	3.00805i	0.536220	+	0.157448i
$366$	0.564972	−	1.23712i	0.0295315	−	0.0646651i
$367$	14.0806			0.735003			0.367502	−	0.930023i	$-0.380213\pi$
$367$	14.0806			0.735003			0.367502	+	0.930023i	$0.380213\pi$
$368$	−2.19527	−	4.55271i	−0.114436	−	0.237326i
$369$	−32.4995			−1.69186
$370$	0.487759	−	1.06804i	0.0253574	−	0.0555250i
$371$	8.66152	+	2.54325i	0.449684	+	0.132039i
$372$	−0.221848	−	0.256026i	−0.0115023	−	0.0132743i
$373$	4.00882	−	2.57631i	0.207569	−	0.133396i	−0.432727	−	0.901525i	$-0.642448\pi$
$373$	4.00882	−	2.57631i	0.207569	−	0.133396i	0.640295	+	0.768129i	$0.278812\pi$
$374$	21.7373	−	25.0862i	1.12401	−	1.29718i
$375$	0.0246728	−	0.171603i	0.00127410	−	0.00886156i
$376$	16.0023	−	4.69869i	0.825255	−	0.242317i
$377$	−21.8539	−	14.0447i	−1.12553	−	0.723337i
$378$	−0.347327	−	2.41571i	−0.0178646	−	0.124251i
$379$	−2.66716	−	5.84027i	−0.137003	−	0.299994i	0.828678	−	0.559725i	$-0.189093\pi$
$379$	−2.66716	−	5.84027i	−0.137003	−	0.299994i	−0.965681	+	0.259731i	$0.916366\pi$
$380$	−0.631064	−	1.38184i	−0.0323729	−	0.0708868i
$381$	−0.137970	−	0.959601i	−0.00706841	−	0.0491619i
$382$	−16.4755	−	10.5882i	−0.842961	−	0.541738i
$383$	32.7810	−	9.62537i	1.67503	−	0.491833i	0.700044	−	0.714099i	$-0.253163\pi$
$383$	32.7810	−	9.62537i	1.67503	−	0.491833i	0.974986	+	0.222266i	$0.0713453\pi$
$384$	−0.0681767	+	0.474179i	−0.00347913	+	0.0241978i
$385$	8.46785	−	9.77241i	0.431561	−	0.498048i
$386$	8.92627	−	5.73656i	0.454335	−	0.291983i
$387$	21.2794	+	24.5577i	1.08169	+	1.24834i
$388$	−6.58133	−	1.93245i	−0.334116	−	0.0981054i
$389$	7.02935	−	15.3921i	0.356402	−	0.780412i	−0.643486	−	0.765458i	$-0.722513\pi$
$389$	7.02935	−	15.3921i	0.356402	−	0.780412i	0.999888	−	0.0149538i	$-0.00476013\pi$
$390$	0.457180			0.0231502
$391$	−3.48290	+	28.4301i	−0.176138	+	1.43777i
$392$	4.55158			0.229890
$393$	−0.122239	+	0.267666i	−0.00616615	+	0.0135020i
$394$	−4.23631	−	1.24389i	−0.213422	−	0.0626664i
$395$	0.532680	+	0.614745i	0.0268020	+	0.0309312i
$396$	−13.6067	+	8.74451i	−0.683763	+	0.439428i
$397$	−5.17394	+	5.97105i	−0.259673	+	0.299678i	−0.870583	−	0.492021i	$-0.836258\pi$
$397$	−5.17394	+	5.97105i	−0.259673	+	0.299678i	0.610910	+	0.791700i	$0.290804\pi$
$398$	−2.21026	+	15.3727i	−0.110791	+	0.770565i
$399$	0.599995	−	0.176174i	0.0300373	−	0.00881975i
$400$	−0.886600	−	0.569783i	−0.0443300	−	0.0284892i
$401$	3.27200	+	22.7572i	0.163396	+	1.13644i	0.892174	+	0.451692i	$0.149180\pi$
$401$	3.27200	+	22.7572i	0.163396	+	1.13644i	−0.728778	+	0.684750i	$0.759911\pi$
$402$	−0.0675875	−	0.147996i	−0.00337096	−	0.00738136i
$403$	−2.15544	−	4.71975i	−0.107370	−	0.235107i
$404$	0.523876	+	3.64364i	0.0260638	+	0.181278i
$405$	7.34448	+	4.72001i	0.364950	+	0.234539i
$406$	−22.4384	+	6.58851i	−1.11360	+	0.326982i
$407$	0.916321	−	6.37315i	0.0454203	−	0.315905i
$408$	−2.03865	+	2.35273i	−0.100928	+	0.116478i
$409$	1.60454	−	1.03117i	0.0793392	−	0.0509882i	−0.500370	−	0.865812i	$-0.666803\pi$
$409$	1.60454	−	1.03117i	0.0793392	−	0.0509882i	0.579709	+	0.814824i	$0.303166\pi$
$410$	−7.21431	−	8.32575i	−0.356289	−	0.411180i
$411$	−1.90390	−	0.559036i	−0.0939126	−	0.0275752i
$412$	−1.01777	+	2.22861i	−0.0501420	+	0.109796i
$413$	22.4628			1.10532
$414$	−5.68288	+	13.1651i	−0.279299	+	0.647031i
$415$	4.91719			0.241375
$416$	−5.38868	+	11.7996i	−0.264202	+	0.578522i
$417$	2.98642	+	0.876891i	0.146245	+	0.0429415i
$418$	5.60480	+	6.46828i	0.274140	+	0.316374i
$419$	14.4849	−	9.30890i	0.707635	−	0.454770i	−0.136681	−	0.990615i	$-0.543643\pi$
$419$	14.4849	−	9.30890i	0.707635	−	0.454770i	0.844316	+	0.535846i	$0.180007\pi$
$420$	−0.262324	+	0.302738i	−0.0128001	+	0.0147721i
$421$	−0.00351107	+	0.0244201i	−0.000171119	+	0.00119016i	−0.989907	−	0.141720i	$-0.954737\pi$
$421$	−0.00351107	+	0.0244201i	−0.000171119	+	0.00119016i	0.989736	+	0.142910i	$0.0456459\pi$
$422$	−9.41619	+	2.76484i	−0.458373	+	0.134590i
$423$	−13.8592	−	8.90679i	−0.673859	−	0.433063i
$424$	−1.64909	−	11.4697i	−0.0800870	−	0.557017i
$425$	2.48103	+	5.43270i	0.120348	+	0.263524i
$426$	0.218134	+	0.477647i	0.0105686	+	0.0231421i
$427$	2.59742	+	18.0655i	0.125698	+	0.874250i
$428$	6.77254	+	4.35245i	0.327363	+	0.210383i
$429$	2.40549	−	0.706316i	0.116138	−	0.0341012i
$430$	−1.56758	+	10.9027i	−0.0755953	+	0.525777i
$431$	−8.70411	+	10.0451i	−0.419262	+	0.483854i	−0.925612	−	0.378474i	$-0.876449\pi$
$431$	−8.70411	+	10.0451i	−0.419262	+	0.483854i	0.506350	+	0.862328i	$0.330994\pi$
$432$	−0.917628	+	0.589724i	−0.0441494	+	0.0283731i
$433$	−0.00244337	−	0.00281980i	−0.000117421	−	0.000135511i	0.755691	−	0.654928i	$-0.227301\pi$
$433$	−0.00244337	−	0.00281980i	−0.000117421	−	0.000135511i	−0.755808	+	0.654793i	$0.772756\pi$
$434$	−4.48169	−	1.31594i	−0.215128	−	0.0631673i
$435$	−0.714252	+	1.56399i	−0.0342457	+	0.0749877i
$436$	1.75718			0.0841537
$437$	−7.12807	−	1.93214i	−0.340982	−	0.0924266i
$438$	1.86352			0.0890422
$439$	−1.29625	+	2.83840i	−0.0618669	+	0.135470i	−0.938040	−	0.346527i	$-0.887361\pi$
$439$	−1.29625	+	2.83840i	−0.0618669	+	0.135470i	0.876173	+	0.481996i	$0.160088\pi$
$440$	−15.9261	−	4.67631i	−0.759245	−	0.222934i
$441$	−2.94431	−	3.39792i	−0.140205	−	0.161806i
$442$	−13.2494	+	8.51486i	−0.630209	+	0.405011i
$443$	1.39355	−	1.60824i	0.0662096	−	0.0764099i	−0.721679	−	0.692228i	$-0.756629\pi$
$443$	1.39355	−	1.60824i	0.0662096	−	0.0764099i	0.787888	+	0.615818i	$0.211175\pi$
$444$	−0.0283866	+	0.197433i	−0.00134717	+	0.00936976i
$445$	−6.73344	+	1.97712i	−0.319196	+	0.0937243i
$446$	13.8545	+	8.90375i	0.656030	+	0.421605i
$447$	−0.135048	−	0.939281i	−0.00638756	−	0.0444265i
$448$	6.90189	+	15.1130i	0.326084	+	0.714024i
$449$	−7.54113	−	16.5128i	−0.355888	−	0.779285i	−0.999898	−	0.0142687i	$-0.995458\pi$
$449$	−7.54113	−	16.5128i	−0.355888	−	0.779285i	0.644010	−	0.765017i	$-0.277269\pi$
$450$	0.425515	+	2.95952i	0.0200590	+	0.139513i
$451$	−50.8214	−	32.6609i	−2.39309	−	1.53794i
$452$	−10.0024	+	2.93697i	−0.470474	+	0.138144i
$453$	0.148753	−	1.03460i	0.00698901	−	0.0486097i
$454$	−11.4751	+	13.2430i	−0.538555	+	0.621525i
$455$	−5.16134	+	3.31699i	−0.241967	+	0.155503i
$456$	−0.525651	−	0.606633i	−0.0246159	−	0.0284082i
$457$	8.32816	+	2.44537i	0.389575	+	0.114389i	0.470653	−	0.882318i	$-0.344018\pi$
$457$	8.32816	+	2.44537i	0.389575	+	0.114389i	−0.0810785	+	0.996708i	$0.525836\pi$
$458$	6.78045	−	14.8471i	0.316829	−	0.693760i
$459$	6.18143			0.288524
$460$	4.51050	−	1.42744i	0.210303	−	0.0665550i
$461$	21.8795			1.01903			0.509515	−	0.860462i	$-0.329825\pi$
$461$	21.8795			1.01903			0.509515	+	0.860462i	$0.329825\pi$
$462$	0.937543	−	2.05293i	0.0436185	−	0.0955111i
$463$	−18.8495	−	5.53470i	−0.876009	−	0.257219i	−0.187340	−	0.982295i	$-0.559987\pi$
$463$	−18.8495	−	5.53470i	−0.876009	−	0.257219i	−0.688669	+	0.725076i	$0.741805\pi$
$464$	6.84463	+	7.89912i	0.317754	+	0.366708i
$465$	−0.288899	+	0.185664i	−0.0133974	+	0.00860997i
$466$	−16.9399	+	19.5497i	−0.784726	+	0.905622i
$467$	2.02700	−	14.0981i	0.0937982	−	0.652381i	−0.887631	−	0.460556i	$-0.847650\pi$
$467$	2.02700	−	14.0981i	0.0937982	−	0.652381i	0.981429	−	0.191825i	$-0.0614407\pi$
$468$	7.36343	−	2.16210i	0.340375	−	0.0999430i
$469$	1.83679	+	1.18043i	0.0848150	+	0.0545073i
$470$	−0.794751	−	5.52761i	−0.0366591	−	0.254970i
$471$	−0.305910	−	0.669850i	−0.0140956	−	0.0308650i
$472$	−11.9781	−	26.2285i	−0.551339	−	1.20726i
$473$	8.59613	+	59.7874i	0.395250	+	2.74903i
$474$	0.119434	+	0.0767558i	0.00548580	+	0.00352551i
$475$	−1.47756	+	0.433851i	−0.0677952	+	0.0199065i
$476$	1.96391	−	13.6593i	0.0900155	−	0.626072i
$477$	−7.49577	+	8.65058i	−0.343208	+	0.396083i
$478$	−17.8978	+	11.5022i	−0.818625	+	0.526099i
$479$	19.0904	+	22.0315i	0.872264	+	1.00665i	0.999890	+	0.0148235i	$0.00471865\pi$
$479$	19.0904	+	22.0315i	0.872264	+	1.00665i	−0.127627	+	0.991822i	$0.540736\pi$
$480$	0.823775	+	0.241882i	0.0376000	+	0.0110404i
$481$	−1.26909	+	2.77891i	−0.0578654	+	0.126708i
$482$	29.5671			1.34674
$483$	0.317374	+	1.92141i	0.0144410	+	0.0874273i
$484$	−19.2143			−0.873376
$485$	−2.88846	+	6.32484i	−0.131158	+	0.287196i
$486$	4.46134	+	1.30997i	0.202370	+	0.0594213i
$487$	11.4680	+	13.2348i	0.519665	+	0.599725i	0.953547	−	0.301244i	$-0.0974020\pi$
$487$	11.4680	+	13.2348i	0.519665	+	0.599725i	−0.433882	+	0.900970i	$0.642857\pi$
$488$	19.7089	−	12.6661i	0.892179	−	0.573369i
$489$	0.806908	−	0.931221i	0.0364896	−	0.0421113i
$490$	0.216897	−	1.50855i	0.00979840	−	0.0681494i
$491$	−24.0385	+	7.05834i	−1.08484	+	0.318538i	−0.774814	−	0.632189i	$-0.782157\pi$
$491$	−24.0385	+	7.05834i	−1.08484	+	0.318538i	−0.310028	+	0.950727i	$0.600338\pi$
$492$	1.57439	+	1.01180i	0.0709790	+	0.0456154i
$493$	−8.42947	−	58.6282i	−0.379644	−	2.64048i
$494$	−1.68696	−	3.69393i	−0.0759000	−	0.166198i
$495$	6.81116	+	14.9144i	0.306139	+	0.670351i
$496$	0.297099	+	2.06637i	0.0133401	+	0.0927827i
$497$	−5.92811	−	3.80977i	−0.265912	−	0.170891i
$498$	0.823463	−	0.241791i	0.0369003	−	0.0108349i
$499$	−0.919612	+	6.39604i	−0.0411675	+	0.286326i	0.958830	+	0.283981i	$0.0916554\pi$
$499$	−0.919612	+	6.39604i	−0.0411675	+	0.286326i	−0.999997	+	0.00234468i	$0.999254\pi$
$500$	0.646006	−	0.745531i	0.0288903	−	0.0333411i
$501$	−0.791314	+	0.508547i	−0.0353533	+	0.0227202i
$502$	−8.49111	−	9.79926i	−0.378977	−	0.437362i
$503$	−24.9062	−	7.31313i	−1.11051	−	0.326077i	−0.325493	−	0.945545i	$-0.605530\pi$
$503$	−24.9062	−	7.31313i	−1.11051	−	0.326077i	−0.785022	+	0.619468i	$0.787348\pi$
$504$	8.68840	−	19.0249i	0.387012	−	0.847438i
$505$	3.73157			0.166052
$506$	−22.1172	+	14.8760i	−0.983228	+	0.661318i
$507$	1.06426			0.0472653
$508$	2.29158	−	5.01786i	0.101672	−	0.222632i
$509$	13.2871	+	3.90144i	0.588939	+	0.172928i	0.562606	−	0.826725i	$-0.309799\pi$
$509$	13.2871	+	3.90144i	0.588939	+	0.172928i	0.0263332	+	0.999653i	$0.491617\pi$
$510$	0.682628	+	0.787794i	0.0302273	+	0.0348841i
$511$	−21.0382	+	13.5204i	−0.930674	+	0.598108i
$512$	7.56788	−	8.73380i	0.334456	−	0.385983i
$513$	−0.226826	+	1.57761i	−0.0100146	+	0.0696532i
$514$	−10.8717	+	3.19221i	−0.479529	+	0.140802i
$515$	2.08933	+	1.34273i	0.0920669	+	0.0591678i
$516$	−0.266298	−	1.85215i	−0.0117231	−	0.0815362i
$517$	−12.7215	−	27.8561i	−0.559489	−	1.22511i
$518$	1.14245	+	2.50163i	0.0501966	+	0.109915i
$519$	−0.0484301	−	0.336839i	−0.00212584	−	0.0147856i
$520$	6.62530	+	4.25782i	0.290538	+	0.186718i
$521$	11.1086	−	3.26177i	0.486676	−	0.142901i	−0.0291838	−	0.999574i	$-0.509291\pi$
$521$	11.1086	−	3.26177i	0.486676	−	0.142901i	0.515860	+	0.856673i	$0.327473\pi$
$522$	4.22003	−	29.3509i	0.184706	−	1.28466i
$523$	21.8807	−	25.2517i	0.956776	−	1.10418i	−0.0377078	−	0.999289i	$-0.512006\pi$
$523$	21.8807	−	25.2517i	0.956776	−	1.10418i	0.994484	−	0.104890i	$-0.0334489\pi$
$524$	−1.40856	+	0.905224i	−0.0615330	+	0.0395449i
$525$	0.265920	+	0.306888i	0.0116057	+	0.0133937i
$526$	20.9565	+	6.15339i	0.913748	+	0.268301i
$527$	4.91453	−	10.7613i	0.214080	−	0.468771i
$528$	−1.00870			−0.0438978
$529$	8.67195	−	21.3025i	0.377041	−	0.926196i
$530$	−3.88003			−0.168538
$531$	−11.8321	+	25.9087i	−0.513469	+	1.12434i
$532$	3.41402	+	1.00245i	0.148017	+	0.0434616i
$533$	18.7707	+	21.6625i	0.813049	+	0.938309i
$534$	−1.03040	+	0.662200i	−0.0445899	+	0.0286562i
$535$	5.34424	−	6.16758i	0.231052	−	0.266648i
$536$	0.398864	−	2.77416i	0.0172283	−	0.119825i
$537$	−2.62408	+	0.770499i	−0.113237	+	0.0332495i
$538$	11.1434	+	7.16142i	0.480425	+	0.308751i
$539$	−1.18940	−	8.27245i	−0.0512310	−	0.356320i
$540$	−0.424140	−	0.928736i	−0.0182521	−	0.0399664i
$541$	−5.62143	−	12.3092i	−0.241684	−	0.529214i	0.749453	−	0.662058i	$-0.230317\pi$
$541$	−5.62143	−	12.3092i	−0.241684	−	0.529214i	−0.991137	+	0.132843i	$0.957589\pi$
$542$	0.299123	+	2.08044i	0.0128484	+	0.0893627i
$543$	−1.26605	−	0.813639i	−0.0543313	−	0.0349166i
$544$	−28.3785	+	8.33268i	−1.21672	+	0.357261i
$545$	0.253501	−	1.76314i	0.0108588	−	0.0755244i
$546$	−0.701245	+	0.809280i	−0.0300105	+	0.0346340i
$547$	36.0600	−	23.1744i	1.54182	−	0.990865i	0.554484	−	0.832194i	$-0.312916\pi$
$547$	36.0600	−	23.1744i	1.54182	−	0.990865i	0.987332	−	0.158670i	$-0.0507207\pi$
$548$	−7.39385	−	8.53296i	−0.315850	−	0.364510i
$549$	−22.2049	−	6.51995i	−0.947683	−	0.278265i
$550$	−2.30882	+	5.05560i	−0.0984482	+	0.215572i
$551$	15.2723			0.650621
$552$	2.07428	−	1.39516i	0.0882871	−	0.0593818i
$553$	−1.90524			−0.0810192
$554$	−9.89077	+	21.6578i	−0.420218	+	0.920150i
$555$	0.194007	+	0.0569656i	0.00823514	+	0.00241805i
$556$	11.5978	+	13.3846i	0.491857	+	0.567633i
$557$	19.3809	−	12.4553i	0.821193	−	0.527749i	−0.0612750	−	0.998121i	$-0.519517\pi$
$557$	19.3809	−	12.4553i	0.821193	−	0.527749i	0.882468	+	0.470372i	$0.155880\pi$
$558$	3.87850	−	4.47603i	0.164190	−	0.189485i
$559$	4.07863	−	28.3675i	0.172508	−	1.19982i
$560$	2.36851	−	0.695458i	0.100088	−	0.0293885i
$561$	4.80879	+	3.09042i	0.203027	+	0.130478i
$562$	2.17694	+	15.1410i	0.0918287	+	0.638683i
$563$	2.56796	+	5.62306i	0.108227	+	0.236984i	0.955995	−	0.293384i	$-0.0947813\pi$
$563$	2.56796	+	5.62306i	0.108227	+	0.236984i	−0.847768	+	0.530367i	$0.822054\pi$
$564$	0.394097	+	0.862952i	0.0165945	+	0.0363368i
$565$	1.50392	+	10.4600i	0.0632705	+	0.440056i
$566$	26.7344	+	17.1812i	1.12373	+	0.722179i
$567$	−19.6205	+	5.76108i	−0.823982	+	0.241943i
$568$	−1.28731	+	8.95342i	−0.0540142	+	0.375677i
$569$	25.8728	−	29.8588i	1.08464	−	1.25175i	0.118719	−	0.992928i	$-0.462121\pi$
$569$	25.8728	−	29.8588i	1.08464	−	1.25175i	0.965926	−	0.258819i	$-0.0833333\pi$
$570$	−0.226108	+	0.145311i	−0.00947062	+	0.00608640i
$571$	25.8434	+	29.8249i	1.08151	+	1.24813i	0.967018	+	0.254707i	$0.0819792\pi$
$571$	25.8434	+	29.8249i	1.08151	+	1.24813i	0.114494	+	0.993424i	$0.463475\pi$
$572$	13.6874	+	4.01900i	0.572301	+	0.168043i
$573$	1.40103	−	3.06782i	0.0585287	−	0.128160i
$574$	25.8035			1.07702
$575$	−0.781572	−	4.73172i	−0.0325938	−	0.197326i
$576$	−21.0669			−0.877788
$577$	10.6926	−	23.4134i	0.445137	−	0.974714i	−0.545490	−	0.838118i	$-0.683656\pi$
$577$	10.6926	−	23.4134i	0.445137	−	0.974714i	0.990627	−	0.136597i	$-0.0436164\pi$
$578$	−18.0341	−	5.29530i	−0.750121	−	0.220255i
$579$	1.19659	+	1.38093i	0.0497285	+	0.0573897i
$580$	−8.23028	+	5.28928i	−0.341744	+	0.219625i
$581$	−7.54223	+	8.70419i	−0.312904	+	0.361111i
$582$	−0.172711	+	1.20123i	−0.00715909	+	0.0497926i
$583$	−20.4151	+	5.99441i	−0.845507	+	0.248263i
$584$	27.0054	+	17.3553i	1.11749	+	0.718168i
$585$	−1.10714	−	7.70030i	−0.0457744	−	0.318368i
$586$	−11.4831	−	25.1445i	−0.474363	−	1.03871i
$587$	−2.24564	−	4.91726i	−0.0926873	−	0.202957i	0.857610	−	0.514300i	$-0.171948\pi$
$587$	−2.24564	−	4.91726i	−0.0926873	−	0.202957i	−0.950297	+	0.311343i	$0.899221\pi$
$588$	0.0368462	+	0.256271i	0.00151951	+	0.0105684i
$589$	2.56614	+	1.64916i	0.105736	+	0.0679525i
$590$	−9.26381	+	2.72010i	−0.381385	+	0.111985i
$591$	0.108205	−	0.752584i	0.00445097	−	0.0309572i
$592$	0.804927	−	0.928935i	0.0330823	−	0.0381790i
$593$	−35.0520	+	22.5266i	−1.43941	+	0.925055i	−0.439777	+	0.898107i	$0.644942\pi$
$593$	−35.0520	+	22.5266i	−1.43941	+	0.925055i	−0.999637	+	0.0269478i	$0.991421\pi$
$594$	3.76700	+	4.34734i	0.154562	+	0.178374i
$595$	−13.4222	−	3.94112i	−0.550258	−	0.161570i
$596$	2.24305	−	4.91160i	0.0918790	−	0.201187i
$597$	−2.67452			−0.109461
$598$	12.0575	−	3.81584i	0.493067	−	0.156041i
$599$	36.4662			1.48997			0.744985	−	0.667081i	$-0.232457\pi$
$599$	36.4662			1.48997			0.744985	+	0.667081i	$0.232457\pi$
$600$	0.216534	−	0.474144i	0.00883998	−	0.0193569i
$601$	7.92166	+	2.32601i	0.323131	+	0.0948799i	0.439275	−	0.898352i	$-0.355235\pi$
$601$	7.92166	+	2.32601i	0.323131	+	0.0948799i	−0.116144	+	0.993232i	$0.537053\pi$
$602$	−16.8951	−	19.4980i	−0.688593	−	0.794679i
$603$	−2.32902	+	1.49677i	−0.0948452	+	0.0609533i
$604$	3.89478	−	4.49481i	0.158476	−	0.182891i
$605$	−2.77196	+	19.2794i	−0.112696	+	0.783818i
$606$	0.624911	−	0.183490i	0.0253853	−	0.00745379i
$607$	36.5256	+	23.4736i	1.48253	+	0.952763i	0.996907	+	0.0785947i	$0.0250433\pi$
$607$	36.5256	+	23.4736i	1.48253	+	0.952763i	0.485622	+	0.874169i	$0.338593\pi$
$608$	−1.08531	−	7.54847i	−0.0440150	−	0.306131i
$609$	−1.67296	−	3.66326i	−0.0677916	−	0.148443i
$610$	−3.25880	−	7.13578i	−0.131945	−	0.288919i
$611$	2.06784	+	14.3821i	0.0836559	+	0.581839i
$612$	14.7202	+	9.46007i	0.595027	+	0.382401i
$613$	−20.9615	+	6.15485i	−0.846626	+	0.248592i	−0.676145	−	0.736769i	$-0.736351\pi$
$613$	−20.9615	+	6.15485i	−0.846626	+	0.248592i	−0.170482	+	0.985361i	$0.554532\pi$
$614$	−1.01845	+	7.08347i	−0.0411012	+	0.285865i
$615$	1.24236	−	1.43376i	0.0500967	−	0.0578147i
$616$	32.7059	−	21.0188i	1.31776	−	0.846873i
$617$	25.0934	+	28.9593i	1.01022	+	1.16586i	0.986101	+	0.166149i	$0.0531331\pi$
$617$	25.0934	+	28.9593i	1.01022	+	1.16586i	0.0241207	+	0.999709i	$0.492321\pi$
$618$	0.415918	+	0.122124i	0.0167307	+	0.00491257i
$619$	4.27684	−	9.36498i	0.171901	−	0.376410i	−0.803999	−	0.594631i	$-0.797298\pi$
$619$	4.27684	−	9.36498i	0.171901	−	0.376410i	0.975899	+	0.218221i	$0.0700253\pi$
$620$	−1.95406			−0.0784770
$621$	−4.79079	−	1.29859i	−0.192248	−	0.0521107i
$622$	−22.2378			−0.891657
$623$	6.82827	−	14.9518i	0.273569	−	0.599032i
$624$	0.459213	+	0.134837i	0.0183832	+	0.00539780i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−4.21444	+	2.70846i	−0.168443	+	0.108252i
$627$	−0.965189	+	1.11389i	−0.0385459	+	0.0444844i
$628$	0.596322	−	4.14751i	0.0237958	−	0.165504i
$629$	−6.68341	+	1.96243i	−0.266485	+	0.0782471i
$630$	−5.89149	−	3.78623i	−0.234722	−	0.150847i
$631$	−1.53857	−	10.7010i	−0.0612497	−	0.426001i	−0.997257	−	0.0740198i	$-0.976417\pi$
$631$	−1.53857	−	10.7010i	−0.0612497	−	0.426001i	0.936007	−	0.351981i	$-0.114492\pi$
$632$	1.01596	+	2.22464i	0.0404126	+	0.0884913i
$633$	−0.702050	−	1.53727i	−0.0279040	−	0.0611012i
$634$	−0.561328	−	3.90412i	−0.0222932	−	0.155052i
$635$	−4.70427	−	3.02325i	−0.186683	−	0.119974i
$636$	0.632437	−	0.185700i	0.0250777	−	0.00736349i
$637$	−0.564338	+	3.92506i	−0.0223599	+	0.155516i
$638$	36.0958	−	41.6567i	1.42905	−	1.64921i
$639$	7.51677	−	4.83073i	0.297359	−	0.191101i
$640$	1.80953	+	2.08831i	0.0715279	+	0.0825476i
$641$	25.0557	+	7.35702i	0.989641	+	0.290585i	0.736199	−	0.676766i	$-0.236619\pi$
$641$	25.0557	+	7.35702i	0.989641	+	0.290585i	0.253442	+	0.967350i	$0.418437\pi$
$642$	0.591704	−	1.29565i	0.0233527	−	0.0511352i
$643$	−19.8689			−0.783554			−0.391777	−	0.920060i	$-0.628140\pi$
$643$	−19.8689			−0.783554			−0.391777	+	0.920060i	$0.628140\pi$
$644$	−4.39162	+	10.1738i	−0.173054	+	0.400903i
$645$	−1.89684			−0.0746880
$646$	3.84638	−	8.42240i	0.151334	−	0.331375i
$647$	−30.1304	−	8.84708i	−1.18455	−	0.347815i	−0.370622	−	0.928784i	$-0.620856\pi$
$647$	−30.1304	−	8.84708i	−1.18455	−	0.347815i	−0.813926	+	0.580969i	$0.802674\pi$
$648$	17.1893	+	19.8375i	0.675260	+	0.779292i
$649$	−44.5399	+	28.6240i	−1.74834	+	1.12359i
$650$	1.72690	−	1.99295i	0.0677347	−	0.0781700i
$651$	0.114473	−	0.796176i	0.00448655	−	0.0312046i
$652$	6.72722	−	1.97529i	0.263458	−	0.0773583i
$653$	−32.1725	−	20.6760i	−1.25901	−	0.809114i	−0.270858	−	0.962619i	$-0.587307\pi$
$653$	−32.1725	−	20.6760i	−1.25901	−	0.809114i	−0.988148	+	0.153506i	$0.950944\pi$
$654$	−0.0442450	−	0.307731i	−0.00173012	−	0.0120332i
$655$	0.705085	+	1.54392i	0.0275500	+	0.0603260i
$656$	−4.79084	−	10.4905i	−0.187051	−	0.409585i
$657$	−4.51280	−	31.3872i	−0.176061	−	1.22453i
$658$	11.0038	+	7.07169i	0.428971	+	0.275683i
$659$	−8.05355	+	2.36473i	−0.313722	+	0.0921170i	−0.434803	−	0.900526i	$-0.643182\pi$
$659$	−8.05355	+	2.36473i	−0.313722	+	0.0921170i	0.121081	+	0.992643i	$0.461364\pi$
$660$	0.134368	−	0.934553i	0.00523028	−	0.0363774i
$661$	−26.3826	+	30.4471i	−1.02616	+	1.18425i	−0.0434616	+	0.999055i	$0.513839\pi$
$661$	−26.3826	+	30.4471i	−1.02616	+	1.18425i	−0.982701	+	0.185200i	$0.940707\pi$
$662$	−0.472504	+	0.303660i	−0.0183644	+	0.0118021i
$663$	−1.77611	−	2.04974i	−0.0689784	−	0.0796053i
$664$	14.1852	+	4.16515i	0.550492	+	0.161639i
$665$	1.49837	−	3.28097i	0.0581043	−	0.127231i
$666$	−3.48716			−0.135125
$667$	−5.78352	+	47.2095i	−0.223939	+	1.82796i
$668$	−5.35230			−0.207087
$669$	−1.17814	+	2.57978i	−0.0455497	+	0.0997399i
$670$	−0.900445	−	0.264394i	−0.0347872	−	0.0102144i
$671$	−28.1708	−	32.5108i	−1.08752	−	1.25507i
$672$	−1.69171	+	1.08720i	−0.0652593	+	0.0419396i
$673$	17.6975	−	20.4240i	0.682187	−	0.787286i	−0.304044	−	0.952658i	$-0.598337\pi$
$673$	17.6975	−	20.4240i	0.682187	−	0.787286i	0.986231	+	0.165372i	$0.0528824\pi$
$674$	0.232124	−	1.61446i	0.00894110	−	0.0621867i
$675$	−0.993072	+	0.291592i	−0.0382234	+	0.0112234i
$676$	5.09439	+	3.27397i	0.195938	+	0.125922i
$677$	−5.24912	−	36.5084i	−0.201740	−	1.40313i	−0.799118	−	0.601174i	$-0.794700\pi$
$677$	−5.24912	−	36.5084i	−0.201740	−	1.40313i	0.597378	−	0.801960i	$-0.296209\pi$
$678$	0.766201	+	1.67775i	0.0294258	+	0.0644335i
$679$	−6.76549	−	14.8144i	−0.259636	−	0.568523i
$680$	2.55550	+	17.7739i	0.0979989	+	0.681597i
$681$	−2.53856	−	1.63144i	−0.0972780	−	0.0625168i
$682$	10.5633	−	3.10166i	0.404489	−	0.118769i
$683$	−5.91072	+	41.1100i	−0.226167	+	1.57303i	0.487866	+	0.872918i	$0.337775\pi$
$683$	−5.91072	+	41.1100i	−0.226167	+	1.57303i	−0.714034	+	0.700111i	$0.753134\pi$
$684$	−2.95453	+	3.40971i	−0.112969	+	0.130374i
$685$	−9.62856	+	6.18790i	−0.367888	+	0.236427i
$686$	13.1470	+	15.1724i	0.501953	+	0.579285i
$687$	2.69693	+	0.791891i	0.102894	+	0.0302125i
$688$	−4.79011	+	10.4889i	−0.182621	+	0.399884i
$689$	10.0954			0.384602
$690$	−0.363557	−	0.753971i	−0.0138404	−	0.0287032i
$691$	−30.9323			−1.17672			−0.588360	−	0.808599i	$-0.700226\pi$
$691$	−30.9323			−1.17672			−0.588360	+	0.808599i	$0.700226\pi$
$692$	0.804389	−	1.76137i	0.0305783	−	0.0669571i
$693$	−36.8480	−	10.8196i	−1.39974	−	0.411001i
$694$	−1.43240	−	1.65308i	−0.0543732	−	0.0627500i
$695$	15.1031	−	9.70618i	0.572894	−	0.368177i
$696$	−3.38527	+	3.90681i	−0.128318	+	0.148087i
$697$	−9.30099	+	64.6898i	−0.352300	+	2.45030i
$698$	−6.16628	+	1.81058i	−0.233397	+	0.0685316i
$699$	−3.74750	−	2.40837i	−0.141743	−	0.0910929i
$700$	0.328830	+	2.28706i	0.0124286	+	0.0864428i
$701$	−1.64153	−	3.59444i	−0.0619996	−	0.135760i	0.876096	−	0.482137i	$-0.160139\pi$
$701$	−1.64153	−	3.59444i	−0.0619996	−	0.135760i	−0.938096	+	0.346377i	$0.887412\pi$
$702$	−1.13381	−	2.48270i	−0.0427929	−	0.0937033i
$703$	−0.255600	−	1.77774i	−0.00964014	−	0.0670486i
$704$	−32.9435	−	21.1715i	−1.24161	−	0.797932i
$705$	0.922730	−	0.270938i	0.0347520	−	0.0102041i
$706$	−4.11629	+	28.6295i	−0.154919	+	1.07748i
$707$	−5.72365	+	6.60545i	−0.215260	+	0.248423i
$708$	1.37980	−	0.886741i	0.0518559	−	0.0333257i
$709$	10.1549	+	11.7194i	0.381376	+	0.440132i	0.913688	−	0.406417i	$-0.133222\pi$
$709$	10.1549	+	11.7194i	0.381376	+	0.440132i	−0.532312	+	0.846549i	$0.678677\pi$
$710$	2.90613	+	0.853315i	0.109065	+	0.0320244i
$711$	1.00357	−	2.19751i	0.0376368	−	0.0824131i
$712$	−21.0995			−0.790735
$713$	−6.06965	+	7.30791i	−0.227310	+	0.273683i
$714$	−2.44156			−0.0913733
$715$	6.00724	−	13.1540i	0.224658	−	0.491933i
$716$	−14.9312	−	4.38421i	−0.558007	−	0.163846i
$717$	−2.39924	−	2.76887i	−0.0896012	−	0.103405i
$718$	8.55914	−	5.50063i	0.319424	−	0.205282i
$719$	−22.2269	+	25.6513i	−0.828925	+	0.956631i	−0.999588	−	0.0286988i	$-0.990864\pi$
$719$	−22.2269	+	25.6513i	−0.828925	+	0.956631i	0.170663	+	0.985329i	$0.445409\pi$
$720$	−0.445450	+	3.09817i	−0.0166009	+	0.115462i
$721$	−5.58156	+	1.63889i	−0.207868	+	0.0610356i
$722$	−14.0831	−	9.05067i	−0.524119	−	0.336831i
$723$	0.724620	+	5.03985i	0.0269489	+	0.187434i
$724$	−3.55733	−	7.78947i	−0.132207	−	0.289493i
$725$	4.11986	+	9.02124i	0.153008	+	0.335040i
$726$	0.483807	+	3.36495i	0.0179557	+	0.124885i
$727$	−17.9890	−	11.5608i	−0.667175	−	0.428767i	0.162731	−	0.986670i	$-0.447970\pi$
$727$	−17.9890	−	11.5608i	−0.667175	−	0.428767i	−0.829906	+	0.557903i	$0.811606\pi$
$728$	−17.6992	+	5.19695i	−0.655976	+	0.192612i
$729$	3.61344	−	25.1320i	0.133831	−	0.930816i
$730$	7.03904	−	8.12348i	0.260526	−	0.300664i
$731$	54.9716	−	35.3281i	2.03320	−	1.30666i
$732$	0.872699	+	1.00715i	0.0322559	+	0.0372253i
$733$	33.1870	+	9.74457i	1.22579	+	0.359924i	0.829659	−	0.558271i	$-0.188535\pi$
$733$	33.1870	+	9.74457i	1.22579	+	0.359924i	0.396129	+	0.918195i	$0.370353\pi$
$734$	5.88872	−	12.8945i	0.217357	−	0.475945i
$735$	0.262455			0.00968081
$736$	23.7447	−	0.496327i	0.875242	−	0.0182949i
$737$	−5.14623			−0.189564
$738$	−13.5918	+	29.7618i	−0.500320	+	1.09555i
$739$	−24.2672	−	7.12548i	−0.892682	−	0.262115i	−0.196947	−	0.980414i	$-0.563103\pi$
$739$	−24.2672	−	7.12548i	−0.892682	−	0.262115i	−0.695734	+	0.718299i	$0.744921\pi$
$740$	0.753431	+	0.869506i	0.0276967	+	0.0319637i
$741$	0.588304	−	0.378080i	0.0216119	−	0.0138891i
$742$	5.95138	−	6.86826i	0.218482	−	0.252142i
$743$	0.807111	−	5.61358i	0.0296100	−	0.205942i	−0.969646	−	0.244514i	$-0.921372\pi$
$743$	0.807111	−	5.61358i	0.0296100	−	0.205942i	0.999256	+	0.0385715i	$0.0122807\pi$
$744$	−0.990688	+	0.290892i	−0.0363204	+	0.0106646i
$745$	−4.60465	−	2.95923i	−0.168701	−	0.108418i
$746$	−0.682741	−	4.74857i	−0.0249969	−	0.173857i
$747$	−6.06663	−	13.2841i	−0.221966	−	0.486039i
$748$	13.5117	+	29.5865i	0.494037	+	1.08179i
$749$	2.72032	+	18.9203i	0.0993984	+	0.691331i
$750$	−0.146829	−	0.0943613i	−0.00536144	−	0.00344559i
$751$	−0.217605	+	0.0638946i	−0.00794052	+	0.00233155i	−0.285700	−	0.958319i	$-0.592226\pi$
$751$	−0.217605	+	0.0638946i	−0.00794052	+	0.00233155i	0.277760	+	0.960651i	$0.410408\pi$
$752$	0.831985	−	5.78658i	0.0303394	−	0.211015i
$753$	1.46223	−	1.68751i	0.0532867	−	0.0614962i
$754$	−22.0012	+	14.1393i	−0.801236	+	0.514923i
$755$	−3.94816	−	4.55642i	−0.143688	−	0.165825i
$756$	2.29457	+	0.673747i	0.0834528	+	0.0245039i
$757$	2.79217	−	6.11400i	0.101483	−	0.222217i	−0.852079	−	0.523413i	$-0.824659\pi$
$757$	2.79217	−	6.11400i	0.101483	−	0.222217i	0.953562	+	0.301196i	$0.0973858\pi$
$758$	−6.46374			−0.234773
$759$	−3.07772	−	3.40540i	−0.111714	−	0.123608i
$760$	−4.62999			−0.167947
$761$	−11.0996	+	24.3047i	−0.402359	+	0.881044i	0.594666	+	0.803973i	$0.297284\pi$
$761$	−11.0996	+	24.3047i	−0.402359	+	0.881044i	−0.997026	+	0.0770713i	$0.975443\pi$
$762$	−0.936466	−	0.274971i	−0.0339246	−	0.00996116i
$763$	2.73219	+	3.15312i	0.0989120	+	0.114150i
$764$	16.1440	−	10.3751i	0.584068	−	0.375358i
$765$	11.6157	−	13.4053i	0.419968	−	0.484669i
$766$	4.89494	−	34.0450i	0.176861	−	1.23010i
$767$	24.1033	−	7.07735i	0.870318	−	0.255548i
$768$	2.47481	+	1.59046i	0.0893019	+	0.0573909i
$769$	−0.336021	−	2.33708i	−0.0121172	−	0.0842772i	0.982865	−	0.184324i	$-0.0590097\pi$
$769$	−0.336021	−	2.33708i	−0.0121172	−	0.0842772i	−0.994983	+	0.100047i	$0.968101\pi$
$770$	−5.40783	−	11.8415i	−0.194884	−	0.426738i
$771$	−0.810567	−	1.77489i	−0.0291919	−	0.0639212i
$772$	1.47967	+	10.2913i	0.0532544	+	0.370393i
$773$	28.2875	+	18.1793i	1.01743	+	0.653863i	0.939306	−	0.343080i	$-0.111470\pi$
$773$	28.2875	+	18.1793i	1.01743	+	0.653863i	0.0781249	+	0.996944i	$0.475107\pi$
$774$	31.3884	−	9.21645i	1.12823	−	0.331279i
$775$	−0.281904	+	1.96068i	−0.0101263	+	0.0704298i
$776$	−13.6902	+	15.7993i	−0.491448	+	0.567162i
$777$	−0.398415	+	0.256046i	−0.0142931	+	0.00918559i
$778$	−11.1557	−	12.8744i	−0.399953	−	0.461570i
$779$	−16.1687	−	4.74755i	−0.579303	−	0.170099i
$780$	−0.186098	+	0.407497i	−0.00666337	+	0.0145907i
$781$	16.6091			0.594321
$782$	24.5786	+	15.0794i	0.878929	+	0.539238i
$783$	10.2645			0.366825
$784$	0.662780	−	1.45129i	0.0236707	−	0.0518317i
$785$	−4.07554	−	1.19669i	−0.145462	−	0.0427115i
$786$	0.193996	+	0.223884i	0.00691962	+	0.00798567i
$787$	−21.2936	+	13.6846i	−0.759035	+	0.487802i	−0.862016	−	0.506881i	$-0.830798\pi$
$787$	−21.2936	+	13.6846i	−0.759035	+	0.487802i	0.102981	+	0.994683i	$0.467162\pi$
$788$	2.83313	−	3.26960i	0.100926	−	0.116475i
$789$	−0.535279	+	3.72294i	−0.0190564	+	0.132540i
$790$	0.785734	−	0.230712i	0.0279552	−	0.00820838i
$791$	−20.8226	−	13.3819i	−0.740368	−	0.475805i
$792$	7.01560	+	48.7946i	0.249289	+	1.73384i
$793$	8.47899	+	18.5664i	0.301098	+	0.659312i
$794$	3.30424	+	7.23528i	0.117263	+	0.256770i
$795$	−0.0950907	−	0.661370i	−0.00337252	−	0.0234564i
$796$	−12.8024	−	8.22762i	−0.453770	−	0.291620i
$797$	−35.6459	+	10.4666i	−1.26264	+	0.370745i	−0.843477	−	0.537165i	$-0.819495\pi$
$797$	−35.6459	+	10.4666i	−1.26264	+	0.370745i	−0.419164	+	0.907910i	$0.637677\pi$
$798$	0.0895927	−	0.623131i	0.00317155	−	0.0220586i
$799$	−21.6952	+	25.0376i	−0.767520	+	0.885765i
$800$	4.16605	−	2.67736i	0.147292	−	0.0946590i
$801$	13.6487	+	15.7515i	0.482254	+	0.556551i
$802$	22.2086	+	6.52103i	0.784213	+	0.230266i
$803$	24.4862	−	53.6172i	0.864098	−	1.89211i
$804$	0.159424			0.00562247
$805$	9.57468	+	5.87423i	0.337463	+	0.207039i
$806$	−5.22359			−0.183993
$807$	−0.947599	+	2.07495i	−0.0333571	+	0.0730418i
$808$	10.7649	+	3.16085i	0.378707	+	0.111198i
$809$	15.2135	+	17.5573i	0.534879	+	0.617283i	0.957293	−	0.289120i	$-0.0933626\pi$
$809$	15.2135	+	17.5573i	0.534879	+	0.617283i	−0.422414	+	0.906403i	$0.638817\pi$
$810$	7.39396	−	4.75181i	0.259797	−	0.166962i
$811$	21.0932	−	24.3428i	0.740681	−	0.854791i	−0.252950	−	0.967479i	$-0.581401\pi$
$811$	21.0932	−	24.3428i	0.740681	−	0.854791i	0.993630	+	0.112688i	$0.0359462\pi$
$812$	3.26115	−	22.6818i	0.114444	−	0.795976i
$813$	−0.347291	+	0.101974i	−0.0121800	+	0.00357638i
$814$	−5.45307	−	3.50447i	−0.191130	−	0.122832i
$815$	−1.01148	−	7.03498i	−0.0354305	−	0.246425i
$816$	0.453316	+	0.992624i	0.0158692	+	0.0347488i
$817$	6.99920	+	15.3261i	0.244871	+	0.536192i
$818$	−0.273268	−	1.90062i	−0.00955460	−	0.0664537i
$819$	15.3289	+	9.85128i	0.535635	+	0.344232i
$820$	10.3576	−	3.04126i	0.361703	−	0.106205i
$821$	3.85347	−	26.8015i	0.134487	−	0.935379i	−0.805117	−	0.593116i	$-0.797898\pi$
$821$	3.85347	−	26.8015i	0.134487	−	0.935379i	0.939604	−	0.342263i	$-0.111193\pi$
$822$	−1.30818	+	1.50972i	−0.0456281	+	0.0526577i
$823$	−2.03675	+	1.30894i	−0.0709966	+	0.0456267i	−0.575658	−	0.817691i	$-0.695254\pi$
$823$	−2.03675	+	1.30894i	−0.0709966	+	0.0456267i	0.504661	+	0.863318i	$0.331617\pi$
$824$	4.88996	+	5.64331i	0.170350	+	0.196594i
$825$	−0.918335	−	0.269648i	−0.0319723	−	0.00938792i
$826$	9.39428	−	20.5706i	0.326869	−	0.715743i
$827$	−12.1224			−0.421538			−0.210769	−	0.977536i	$-0.567597\pi$
$827$	−12.1224			−0.421538			−0.210769	+	0.977536i	$0.567597\pi$
$828$	−9.42119	−	10.4242i	−0.327409	−	0.362268i
$829$	39.5761			1.37454			0.687268	−	0.726404i	$-0.258810\pi$
$829$	39.5761			1.37454			0.687268	+	0.726404i	$0.258810\pi$
$830$	2.05644	−	4.50297i	0.0713801	−	0.156301i
$831$	−3.93407	−	1.15515i	−0.136471	−	0.0400716i
$832$	12.1676	+	14.0421i	0.421835	+	0.486823i
$833$	−7.60612	+	4.88816i	−0.263536	+	0.169365i
$834$	2.05198	−	2.36812i	0.0710544	−	0.0820011i
$835$	−0.772153	+	5.37044i	−0.0267215	+	0.185852i
$836$	−8.04681	+	2.36276i	−0.278305	+	0.0817177i
$837$	1.72471	+	1.10840i	0.0596147	+	0.0383121i
$838$	−2.46693	−	17.1579i	−0.0852186	−	0.592708i
$839$	10.3898	+	22.7505i	0.358695	+	0.785434i	0.999838	+	0.0180115i	$0.00573356\pi$
$839$	10.3898	+	22.7505i	0.358695	+	0.785434i	−0.641142	+	0.767422i	$0.721539\pi$
$840$	0.507178	+	1.11056i	0.0174993	+	0.0383181i
$841$	−9.87038	−	68.6500i	−0.340358	−	2.36724i
$842$	0.0208946	+	0.0134281i	0.000720074	+	0.000462764i
$843$	−2.52750	+	0.742140i	−0.0870516	+	0.0255607i
$844$	1.36853	−	9.51834i	0.0471068	−	0.327635i
$845$	4.02001	−	4.63934i	0.138293	−	0.159598i
$846$	−13.9526	+	8.96681i	−0.479701	+	0.308285i
$847$	−29.8757	−	34.4784i	−1.02654	−	1.18469i
$848$	−3.89728	−	1.14434i	−0.133833	−	0.0392969i
$849$	−2.27341	+	4.97808i	−0.0780234	+	0.170847i
$850$	6.01265			0.206232
$851$	5.59211	−	0.116890i	0.191695	−	0.00400693i
$852$	−0.514532			−0.0176276
$853$	11.9183	−	26.0975i	0.408076	−	0.893561i	−0.588311	−	0.808635i	$-0.700207\pi$
$853$	11.9183	−	26.0975i	0.408076	−	0.893561i	0.996387	−	0.0849270i	$-0.0270657\pi$
$854$	17.6299	+	5.17662i	0.603284	+	0.177140i
$855$	2.99503	+	3.45645i	0.102428	+	0.118208i
$856$	20.6414	−	13.2654i	0.705509	−	0.453403i
$857$	−18.0167	+	20.7924i	−0.615439	+	0.710255i	−0.974834	−	0.222931i	$-0.928438\pi$
$857$	−18.0167	+	20.7924i	−0.615439	+	0.710255i	0.359395	+	0.933185i	$0.382983\pi$
$858$	0.359194	−	2.49825i	0.0122627	−	0.0852887i
$859$	−33.6422	+	9.87823i	−1.14786	+	0.337041i	−0.799703	−	0.600396i	$-0.795009\pi$
$859$	−33.6422	+	9.87823i	−1.14786	+	0.337041i	−0.348154	+	0.937437i	$0.613191\pi$
$860$	−9.07981	−	5.83524i	−0.309619	−	0.198980i
$861$	0.632385	+	4.39833i	0.0215516	+	0.149895i
$862$	5.55871	+	12.1719i	0.189330	+	0.414576i
$863$	4.86784	+	10.6591i	0.165703	+	0.362840i	0.974209	−	0.225649i	$-0.0724503\pi$
$863$	4.86784	+	10.6591i	0.165703	+	0.362840i	−0.808505	+	0.588489i	$0.799723\pi$
$864$	−0.729436	−	5.07334i	−0.0248159	−	0.172598i
$865$	−1.65129	−	1.06122i	−0.0561455	−	0.0360825i
$866$	−0.00360412	+	0.00105826i	−0.000122473	+	3.59613e-5i
$867$	0.460634	−	3.20378i	0.0156440	−	0.108806i
$868$	2.99723	−	3.45899i	0.101733	−	0.117406i
$869$	3.77776	−	2.42782i	0.128152	−	0.0823582i
$870$	1.13353	+	1.30817i	0.0384304	+	0.0443510i
$871$	2.34284	+	0.687920i	0.0793842	+	0.0233093i
$872$	2.22478	−	4.87159i	0.0753405	−	0.164973i
$873$	20.6506			0.698916
$874$	−4.75044	+	5.71956i	−0.160686	+	0.193467i
$875$	2.34225			0.0791825
$876$	−0.758554	+	1.66100i	−0.0256292	+	0.0561200i
$877$	43.7141	+	12.8356i	1.47612	+	0.433428i	0.918083	−	0.396389i	$-0.129737\pi$
$877$	43.7141	+	12.8356i	1.47612	+	0.433428i	0.558037	+	0.829816i	$0.311555\pi$
$878$	2.05719	+	2.37412i	0.0694267	+	0.0801226i
$879$	4.00457	−	2.57358i	0.135071	−	0.0868048i
$880$	−3.81013	+	4.39713i	−0.128440	+	0.148227i
$881$	2.91424	−	20.2690i	0.0981831	−	0.682879i	−0.879976	−	0.475019i	$-0.842441\pi$
$881$	2.91424	−	20.2690i	0.0981831	−	0.682879i	0.978159	−	0.207860i	$-0.0666497\pi$
$882$	−4.34303	+	1.27523i	−0.146238	+	0.0429392i
$883$	34.2621	+	22.0189i	1.15301	+	0.740996i	0.970237	−	0.242159i	$-0.0778556\pi$
$883$	34.2621	+	22.0189i	1.15301	+	0.740996i	0.182775	+	0.983155i	$0.441492\pi$
$884$	−2.19629	−	15.2755i	−0.0738693	−	0.513772i
$885$	−0.690689	−	1.51240i	−0.0232172	−	0.0508387i
$886$	−0.889964	−	1.94875i	−0.0298989	−	0.0654695i
$887$	7.27891	+	50.6259i	0.244402	+	1.69985i	0.629520	+	0.776985i	$0.283252\pi$
$887$	7.27891	+	50.6259i	0.244402	+	1.69985i	−0.385118	+	0.922867i	$0.625839\pi$
$888$	0.511421	+	0.328670i	0.0171622	+	0.0110294i
$889$	12.5673	−	3.69008i	0.421492	−	0.123761i
$890$	−1.00545	+	6.99308i	−0.0337029	+	0.234409i
$891$	31.5627	−	36.4252i	1.05739	−	1.22029i
$892$	−13.5757	+	8.72457i	−0.454548	+	0.292120i
$893$	−5.59393	−	6.45574i	−0.187194	−	0.216033i
$894$	−0.916636	−	0.269149i	−0.0306569	−	0.00900167i
$895$	−6.55313	+	14.3493i	−0.219047	+	0.479646i
$896$	−6.47217			−0.216220
$897$	0.945930	+	1.96174i	0.0315837	+	0.0655004i
$898$	−18.2756			−0.609863
$899$	8.16080	−	17.8697i	0.272178	−	0.595987i
$900$	−2.81111	−	0.825416i	−0.0937036	−	0.0275139i
$901$	15.0736	+	17.3959i	0.502175	+	0.579541i
$902$	−51.1638	+	32.8810i	−1.70357	+	1.09482i
$903$	2.90947	−	3.35770i	0.0968209	−	0.111737i
$904$	−4.52170	+	31.4491i	−0.150389	+	1.04598i
$905$	−8.32906	+	2.44563i	−0.276867	+	0.0812956i
$906$	−0.885234	−	0.568905i	−0.0294099	−	0.0189006i
$907$	−2.95078	−	20.5231i	−0.0979790	−	0.681459i	−0.978317	−	0.207112i	$-0.933593\pi$
$907$	−2.95078	−	20.5231i	−0.0979790	−	0.681459i	0.880338	−	0.474347i	$-0.157316\pi$
$908$	−7.13284	−	15.6187i	−0.236711	−	0.518326i
$909$	−4.60385	−	10.0810i	−0.152700	−	0.334367i
$910$	0.879027	+	6.11377i	0.0291395	+	0.202670i
$911$	−13.6114	−	8.74752i	−0.450966	−	0.289818i	0.295376	−	0.955381i	$-0.404555\pi$
$911$	−13.6114	−	8.74752i	−0.450966	−	0.289818i	−0.746342	+	0.665563i	$0.768192\pi$
$912$	−0.269970	+	0.0792703i	−0.00893959	+	0.00262490i
$913$	3.86330	−	26.8698i	0.127856	−	0.889261i
$914$	5.72233	−	6.60392i	0.189278	−	0.218438i
$915$	1.13646	−	0.730360i	0.0375703	−	0.0241450i
$916$	10.4736	+	12.0872i	0.346058	+	0.399372i
$917$	−3.81447	−	1.12003i	−0.125965	−	0.0369867i
$918$	2.58516	−	5.66071i	0.0853230	−	0.186831i
$919$	−15.2671			−0.503617			−0.251808	−	0.967777i	$-0.581025\pi$
$919$	−15.2671			−0.503617			−0.251808	+	0.967777i	$0.581025\pi$
$920$	1.75335	−	14.3122i	0.0578061	−	0.471858i
$921$	−1.23237			−0.0406080
$922$	9.15032	−	20.0364i	0.301350	−	0.659864i
$923$	−7.56137	−	2.22022i	−0.248885	−	0.0730794i
$924$	1.44820	+	1.67131i	0.0476424	+	0.0549822i
$925$	0.981146	−	0.630544i	0.0322599	−	0.0207322i
$926$	−12.9516	+	14.9469i	−0.425615	+	0.491186i
$927$	1.04973	−	7.30105i	0.0344778	−	0.239798i
$928$	−47.1238	+	13.8368i	−1.54691	+	0.454215i
$929$	−10.4000	−	6.68369i	−0.341214	−	0.219285i	0.358799	−	0.933415i	$-0.383186\pi$
$929$	−10.4000	−	6.68369i	−0.341214	−	0.219285i	−0.700013	+	0.714130i	$0.746823\pi$
$930$	0.0492023	+	0.342210i	0.00161341	+	0.0112215i
$931$	−0.968440	−	2.12059i	−0.0317393	−	0.0694994i
$932$	−10.5297	−	23.0568i	−0.344911	−	0.755250i
$933$	−0.544998	−	3.79055i	−0.0178424	−	0.124097i
$934$	−12.0627	−	7.75226i	−0.394705	−	0.253662i
$935$	31.6360	−	9.28918i	1.03461	−	0.303789i
$936$	3.32872	−	23.1517i	0.108802	−	0.756738i
$937$	9.60187	−	11.0812i	0.313680	−	0.362006i	−0.576915	−	0.816805i	$-0.695743\pi$
$937$	9.60187	−	11.0812i	0.313680	−	0.362006i	0.890594	+	0.454799i	$0.150289\pi$
$938$	1.84916	−	1.18839i	0.0603773	−	0.0388022i
$939$	−0.564956	−	0.651994i	−0.0184366	−	0.0212770i
$940$	5.25042	+	1.54166i	0.171250	+	0.0502834i
$941$	−19.3451	+	42.3598i	−0.630631	+	1.38089i	0.276898	+	0.960899i	$0.410694\pi$
$941$	−19.3451	+	42.3598i	−0.630631	+	1.38089i	−0.907529	+	0.419990i	$0.862034\pi$
$942$	−0.741358			−0.0241548
$943$	20.7986	−	48.1826i	0.677294	−	1.56904i
$944$	−10.1072			−0.328962
$945$	1.00706	−	2.20515i	0.0327596	−	0.0717335i
$946$	58.3460	+	17.1319i	1.89699	+	0.557007i
$947$	−27.6541	−	31.9145i	−0.898637	−	1.03708i	−0.999112	−	0.0421430i	$-0.986581\pi$
$947$	−27.6541	−	31.9145i	−0.898637	−	1.03708i	0.100474	−	0.994940i	$-0.467964\pi$
$948$	−0.117031	+	0.0752112i	−0.00380099	+	0.00244275i
$949$	−18.3147	+	21.1363i	−0.594519	+	0.686112i
$950$	−0.220633	+	1.53454i	−0.00715828	+	0.0497869i
$951$	0.651719	−	0.191362i	0.0211334	−	0.00620534i
$952$	−35.3823	−	22.7388i	−1.14675	−	0.736969i
$953$	3.82271	+	26.5875i	0.123830	+	0.861254i	0.953154	+	0.302486i	$0.0978165\pi$
$953$	3.82271	+	26.5875i	0.123830	+	0.861254i	−0.829324	+	0.558768i	$0.811274\pi$
$954$	4.78703	+	10.4821i	0.154986	+	0.339371i
$955$	−8.08124	−	17.6954i	−0.261503	−	0.572611i
$956$	−2.96684	−	20.6348i	−0.0959543	−	0.667377i
$957$	7.98521	+	5.13179i	0.258125	+	0.165887i
$958$	28.1595	−	8.26837i	0.909792	−	0.267139i
$959$	3.81520	−	26.5353i	0.123199	−	0.856870i
$960$	0.805324	−	0.929393i	0.0259917	−	0.0299960i
$961$	−22.7780	+	14.6385i	−0.734774	+	0.472211i
$962$	2.01407	+	2.32436i	0.0649362	+	0.0749404i
$963$	−23.2556	−	6.82845i	−0.749400	−	0.220044i
$964$	−12.0354	+	26.3539i	−0.387635	+	0.848802i
$965$	10.5397			0.339284
$966$	1.89229	+	0.512923i	0.0608833	+	0.0165030i
$967$	28.2549			0.908618			0.454309	−	0.890844i	$-0.349886\pi$
$967$	28.2549			0.908618			0.454309	+	0.890844i	$0.349886\pi$
$968$	−24.3273	+	53.2694i	−0.781910	+	1.71214i
$969$	1.52990	+	0.449220i	0.0491476	+	0.0144310i
$970$	4.58405	+	5.29028i	0.147185	+	0.169861i
$971$	3.99248	−	2.56581i	0.128125	−	0.0823408i	−0.475009	−	0.879981i	$-0.657555\pi$
$971$	3.99248	−	2.56581i	0.128125	−	0.0823408i	0.603133	+	0.797640i	$0.293919\pi$
$972$	−2.98362	+	3.44328i	−0.0956996	+	0.110443i
$973$	−5.98444	+	41.6227i	−0.191852	+	1.33436i
$974$	16.9160	−	4.96698i	0.542023	−	0.159152i
$975$	0.382031	+	0.245516i	0.0122348	+	0.00786281i
$976$	−1.16872	−	8.12862i	−0.0374098	−	0.260191i
$977$	7.63271	+	16.7133i	0.244192	+	0.534706i	0.991551	−	0.129714i	$-0.0414059\pi$
$977$	7.63271	+	16.7133i	0.244192	+	0.534706i	−0.747359	+	0.664420i	$0.768679\pi$
$978$	−0.515316	−	1.12838i	−0.0164780	−	0.0360818i
$979$	5.51361	+	38.3480i	0.176216	+	1.22561i
$980$	1.25632	+	0.807389i	0.0401317	+	0.0257911i
$981$	−5.07597	+	1.49044i	−0.162063	+	0.0475860i
$982$	−3.58949	+	24.9654i	−0.114545	+	0.796679i
$983$	−29.9069	+	34.5144i	−0.953881	+	1.10084i	0.0409370	+	0.999162i	$0.486966\pi$
$983$	−29.9069	+	34.5144i	−0.953881	+	1.10084i	−0.994818	+	0.101675i	$0.967580\pi$
$984$	4.79845	−	3.08377i	0.152969	−	0.0983071i
$985$	−2.87196	−	3.31442i	−0.0915083	−	0.105606i
$986$	−57.2148	−	16.7998i	−1.82209	−	0.535014i
$987$	−0.935726	+	2.04895i	−0.0297845	+	0.0652189i
$988$	3.97918			0.126595
$989$	−50.0264	+	15.8319i	−1.59075	+	0.503426i
$990$	16.5065			0.524611
$991$	10.2332	−	22.4075i	0.325068	−	0.711799i	−0.674584	−	0.738198i	$-0.735677\pi$
$991$	10.2332	−	22.4075i	0.325068	−	0.711799i	0.999651	+	0.0263992i	$0.00840409\pi$
$992$	−9.41218	−	2.76367i	−0.298837	−	0.0877465i
$993$	−0.0633402	−	0.0730985i	−0.00201004	−	0.00231971i
$994$	−5.96805	+	3.83544i	−0.189295	+	0.121653i
$995$	−10.1024	+	11.6588i	−0.320269	+	0.369610i
$996$	−0.119681	+	0.832397i	−0.00379222	+	0.0263755i
$997$	9.79135	−	2.87500i	0.310095	−	0.0910521i	−0.122982	−	0.992409i	$-0.539246\pi$
$997$	9.79135	−	2.87500i	0.310095	−	0.0910521i	0.433077	+	0.901357i	$0.357428\pi$
$998$	5.47265	+	3.51706i	0.173234	+	0.111331i
$999$	−0.171789	−	1.19482i	−0.00543517	−	0.0378024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.6.4	✓	50
5.2	odd	4		575.2.p.d.374.7		100
5.3	odd	4		575.2.p.d.374.4		100
5.4	even	2		575.2.k.d.351.2		50
23.2	even	11		2645.2.a.y.1.16		25
23.4	even	11	inner	115.2.g.c.96.4	yes	50
23.21	odd	22		2645.2.a.x.1.16		25
115.4	even	22		575.2.k.d.326.2		50
115.27	odd	44		575.2.p.d.349.4		100
115.73	odd	44		575.2.p.d.349.7		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.6.4	✓	50	1.1	even	1	trivial
115.2.g.c.96.4	yes	50	23.4	even	11	inner
575.2.k.d.326.2		50	115.4	even	22
575.2.k.d.351.2		50	5.4	even	2
575.2.p.d.349.4		100	115.27	odd	44
575.2.p.d.349.7		100	115.73	odd	44
575.2.p.d.374.4		100	5.3	odd	4
575.2.p.d.374.7		100	5.2	odd	4
2645.2.a.x.1.16		25	23.21	odd	22
2645.2.a.y.1.16		25	23.2	even	11

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.418214 - 0.915761i) q^{2} +(0.166345 + 0.0488434i) q^{3} +(0.646006 + 0.745531i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.114297 - 0.131906i) q^{6} +(-0.333337 + 2.31841i) q^{7} +(2.88481 - 0.847058i) q^{8} +(-2.49848 - 1.60567i) q^{9} +O(q^{10})\)	\(q+(0.418214 - 0.915761i) q^{2} +(0.166345 + 0.0488434i) q^{3} +(0.646006 + 0.745531i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.114297 - 0.131906i) q^{6} +(-0.333337 + 2.31841i) q^{7} +(2.88481 - 0.847058i) q^{8} +(-2.49848 - 1.60567i) q^{9} +(-0.143274 - 0.996491i) q^{10} +(-2.29336 - 5.02176i) q^{11} +(0.0710458 + 0.155569i) q^{12} +(0.372780 + 2.59274i) q^{13} +(1.98370 + 1.27485i) q^{14} +(0.166345 - 0.0488434i) q^{15} +(0.149986 - 1.04318i) q^{16} +(-3.91110 + 4.51365i) q^{17} +(-2.51531 + 1.61649i) q^{18} +(-1.00845 - 1.16381i) q^{19} +(0.946519 + 0.277923i) q^{20} +(-0.168688 + 0.369375i) q^{21} -5.55785 q^{22} +(3.97944 - 2.67657i) q^{23} +0.521248 q^{24} +(0.415415 - 0.909632i) q^{25} +(2.53023 + 0.742944i) q^{26} +(-0.677779 - 0.782198i) q^{27} +(-1.94378 + 1.24919i) q^{28} +(-6.49455 + 7.49511i) q^{29} +(0.0248391 - 0.172760i) q^{30} +(-1.90061 + 0.558068i) q^{31} +(4.16605 + 2.67736i) q^{32} +(-0.136210 - 0.947363i) q^{33} +(2.49775 + 5.46930i) q^{34} +(0.973006 + 2.13059i) q^{35} +(-0.416952 - 2.89996i) q^{36} +(0.981146 + 0.630544i) q^{37} +(-1.48752 + 0.436775i) q^{38} +(-0.0646281 + 0.449498i) q^{39} +(1.96891 - 2.27224i) q^{40} +(9.20568 - 5.91613i) q^{41} +(0.267712 + 0.308956i) q^{42} +(-10.4979 - 3.08247i) q^{43} +(2.26235 - 4.95386i) q^{44} -2.96994 q^{45} +(-0.786839 - 4.76360i) q^{46} +5.54708 q^{47} +(0.0759017 - 0.166202i) q^{48} +(1.45254 + 0.426505i) q^{49} +(-0.659273 - 0.760842i) q^{50} +(-0.871054 + 0.559793i) q^{51} +(-1.69215 + 1.95285i) q^{52} +(0.548491 - 3.81484i) q^{53} +(-0.999763 + 0.293557i) q^{54} +(-4.64427 - 2.98469i) q^{55} +(1.00221 + 6.97053i) q^{56} +(-0.110906 - 0.242850i) q^{57} +(4.14762 + 9.08202i) q^{58} +(-1.36484 - 9.49267i) q^{59} +(0.143874 + 0.0924624i) q^{60} +(7.47655 - 2.19531i) q^{61} +(-0.283803 + 1.97389i) q^{62} +(4.55544 - 5.25726i) q^{63} +(5.96733 - 3.83497i) q^{64} +(1.71534 + 1.97961i) q^{65} +(-0.924523 - 0.271464i) q^{66} +(0.387241 - 0.847939i) q^{67} -5.89165 q^{68} +(0.792695 - 0.250865i) q^{69} +2.35803 q^{70} +(-1.24979 + 2.73667i) q^{71} +(-8.56773 - 2.51571i) q^{72} +(6.99192 + 8.06911i) q^{73} +(0.987757 - 0.634793i) q^{74} +(0.113532 - 0.131023i) q^{75} +(0.216193 - 1.50366i) q^{76} +(12.4070 - 3.64302i) q^{77} +(0.384605 + 0.247170i) q^{78} +(0.115762 + 0.805145i) q^{79} +(-0.437807 - 0.958664i) q^{80} +(3.62674 + 7.94145i) q^{81} +(-1.56782 - 10.9044i) q^{82} +(4.13661 + 2.65844i) q^{83} +(-0.384354 + 0.112857i) q^{84} +(-0.849963 + 5.91162i) q^{85} +(-7.21319 + 8.32447i) q^{86} +(-1.44643 + 0.929561i) q^{87} +(-10.8696 - 12.5442i) q^{88} +(-6.73344 - 1.97712i) q^{89} +(-1.24207 + 2.71976i) q^{90} -6.13530 q^{91} +(4.56621 + 1.23772i) q^{92} -0.343415 q^{93} +(2.31987 - 5.07980i) q^{94} +(-1.47756 - 0.433851i) q^{95} +(0.562232 + 0.648851i) q^{96} +(-5.84939 + 3.75918i) q^{97} +(0.998049 - 1.15181i) q^{98} +(-2.33340 + 16.2291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

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