LMFDB - Embedded newform 23.3.d.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,3,Mod(5,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, 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:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	23.17
Dual form			23.3.d.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55977 + 3.41542i) q^{2} +(0.201951 + 0.0592983i) q^{3} +(-6.61275 - 7.63152i) q^{4} +(2.90325 + 4.51755i) q^{5} +(-0.517526 + 0.597257i) q^{6} +(7.13192 + 1.02541i) q^{7} +(21.9686 - 6.45058i) q^{8} +(-7.53401 - 4.84182i) q^{9} +O(q^{10})$	\(q+(-1.55977 + 3.41542i) q^{2} +(0.201951 + 0.0592983i) q^{3} +(-6.61275 - 7.63152i) q^{4} +(2.90325 + 4.51755i) q^{5} +(-0.517526 + 0.597257i) q^{6} +(7.13192 + 1.02541i) q^{7} +(21.9686 - 6.45058i) q^{8} +(-7.53401 - 4.84182i) q^{9} +(-19.9577 + 2.86949i) q^{10} +(5.58711 - 2.55155i) q^{11} +(-0.882918 - 1.93332i) q^{12} +(-1.22480 - 8.51866i) q^{13} +(-14.6264 + 22.7590i) q^{14} +(0.318433 + 1.08448i) q^{15} +(-6.48624 + 45.1128i) q^{16} +(-13.2210 - 11.4560i) q^{17} +(28.2881 - 18.1797i) q^{18} +(-2.09304 + 1.81363i) q^{19} +(15.2773 - 52.0296i) q^{20} +(1.37950 + 0.629994i) q^{21} +23.0621i q^{22} +(1.58473 + 22.9453i) q^{23} +4.81911 q^{24} +(-1.59400 + 3.49038i) q^{25} +(31.0052 + 9.10394i) q^{26} +(-2.47489 - 2.85618i) q^{27} +(-39.3361 - 61.2081i) q^{28} +(-4.81519 + 5.55702i) q^{29} +(-4.20065 - 0.603962i) q^{30} +(-8.51070 + 2.49897i) q^{31} +(-66.9163 - 43.0045i) q^{32} +(1.27963 - 0.183983i) q^{33} +(59.7487 - 27.2863i) q^{34} +(16.0734 + 35.1958i) q^{35} +(12.8701 + 89.5137i) q^{36} +(11.8833 - 18.4907i) q^{37} +(-2.92964 - 9.97743i) q^{38} +(0.257792 - 1.79299i) q^{39} +(92.9213 + 80.5168i) q^{40} +(-54.4615 + 35.0003i) q^{41} +(-4.30339 + 3.72891i) q^{42} +(7.49361 - 25.5209i) q^{43} +(-56.4183 - 25.7654i) q^{44} -48.0923i q^{45} +(-80.8397 - 30.3769i) q^{46} +49.7210 q^{47} +(-3.98502 + 8.72598i) q^{48} +(2.79758 + 0.821444i) q^{49} +(-9.43483 - 10.8884i) q^{50} +(-1.99067 - 3.09754i) q^{51} +(-56.9111 + 65.6789i) q^{52} +(-61.2431 - 8.80543i) q^{53} +(13.6153 - 3.99781i) q^{54} +(27.7475 + 17.8323i) q^{55} +(163.293 - 23.4780i) q^{56} +(-0.530237 + 0.242151i) q^{57} +(-11.4690 - 25.1135i) q^{58} +(-1.09158 - 7.59212i) q^{59} +(6.17054 - 9.60155i) q^{60} +(-7.78445 - 26.5114i) q^{61} +(4.73971 - 32.9654i) q^{62} +(-48.7671 - 42.2569i) q^{63} +(97.8859 - 62.9075i) q^{64} +(34.9276 - 30.2649i) q^{65} +(-1.36754 + 4.65743i) q^{66} +(81.5437 + 37.2398i) q^{67} +176.652i q^{68} +(-1.04058 + 4.72782i) q^{69} -145.279 q^{70} +(23.9561 - 52.4566i) q^{71} +(-196.745 - 57.7694i) q^{72} +(79.6614 + 91.9342i) q^{73} +(44.6183 + 69.4275i) q^{74} +(-0.528885 + 0.610366i) q^{75} +(27.6814 + 3.97999i) q^{76} +(42.4632 - 12.4683i) q^{77} +(5.72169 + 3.67711i) q^{78} +(-84.6615 + 12.1725i) q^{79} +(-222.631 + 101.672i) q^{80} +(33.1525 + 72.5939i) q^{81} +(-34.5932 - 240.601i) q^{82} +(-80.7470 + 125.645i) q^{83} +(-4.31444 - 14.6936i) q^{84} +(13.3694 - 92.9861i) q^{85} +(75.4762 + 65.4005i) q^{86} +(-1.30196 + 0.836716i) q^{87} +(106.282 - 92.0941i) q^{88} +(-2.59531 + 8.83880i) q^{89} +(164.255 + 75.0129i) q^{90} -62.0103i q^{91} +(164.628 - 163.826i) q^{92} -1.86693 q^{93} +(-77.5532 + 169.818i) q^{94} +(-14.2698 - 4.18998i) q^{95} +(-10.9638 - 12.6528i) q^{96} +(78.1151 + 121.550i) q^{97} +(-7.16915 + 8.27364i) q^{98} +(-54.4475 - 7.82837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{7}{22}\right)$

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 $

$2$	−1.55977	+	3.41542i	−0.779884	+	1.70771i	−0.0763124	+	0.997084i	$0.524315\pi$
$2$	−1.55977	+	3.41542i	−0.779884	+	1.70771i	−0.703572	+	0.710624i	$0.748413\pi$
$3$	0.201951	+	0.0592983i	0.0673172	+	0.0197661i	0.315218	−	0.949019i	$-0.397922\pi$
$3$	0.201951	+	0.0592983i	0.0673172	+	0.0197661i	−0.247901	+	0.968785i	$0.579741\pi$
$4$	−6.61275	−	7.63152i	−1.65319	−	1.90788i
$5$	2.90325	+	4.51755i	0.580651	+	0.903510i	0.999991	−	0.00431923i	$-0.00137486\pi$
$5$	2.90325	+	4.51755i	0.580651	+	0.903510i	−0.419340	+	0.907829i	$0.637738\pi$
$6$	−0.517526	+	0.597257i	−0.0862543	+	0.0995428i
$7$	7.13192	+	1.02541i	1.01885	+	0.146488i	0.631442	−	0.775423i	$-0.282463\pi$
$7$	7.13192	+	1.02541i	1.01885	+	0.146488i	0.387403	+	0.921911i	$0.373372\pi$
$8$	21.9686	−	6.45058i	2.74608	−	0.806322i
$9$	−7.53401	−	4.84182i	−0.837113	−	0.537980i
$10$	−19.9577	+	2.86949i	−1.99577	+	0.286949i
$11$	5.58711	−	2.55155i	0.507919	−	0.231959i	−0.144937	−	0.989441i	$-0.546298\pi$
$11$	5.58711	−	2.55155i	0.507919	−	0.231959i	0.652856	+	0.757482i	$0.273571\pi$
$12$	−0.882918	−	1.93332i	−0.0735765	−	0.161110i
$13$	−1.22480	−	8.51866i	−0.0942153	−	0.655282i	−0.981130	−	0.193349i	$-0.938065\pi$
$13$	−1.22480	−	8.51866i	−0.0942153	−	0.655282i	0.886915	−	0.461933i	$-0.152844\pi$
$14$	−14.6264	+	22.7590i	−1.04474	+	1.62565i
$15$	0.318433	+	1.08448i	0.0212289	+	0.0722989i
$16$	−6.48624	+	45.1128i	−0.405390	+	2.81955i
$17$	−13.2210	−	11.4560i	−0.777703	−	0.673884i	0.172675	−	0.984979i	$-0.444759\pi$
$17$	−13.2210	−	11.4560i	−0.777703	−	0.673884i	−0.950379	+	0.311095i	$0.899304\pi$
$18$	28.2881	−	18.1797i	1.57156	−	1.00998i
$19$	−2.09304	+	1.81363i	−0.110160	+	0.0954540i	−0.708199	−	0.706013i	$-0.750492\pi$
$19$	−2.09304	+	1.81363i	−0.110160	+	0.0954540i	0.598039	+	0.801467i	$0.295947\pi$
$20$	15.2773	−	52.0296i	0.763864	−	2.60148i
$21$	1.37950	+	0.629994i	0.0656903	+	0.0299997i
$22$			23.0621i			1.04828i
$23$	1.58473	+	22.9453i	0.0689013	+	0.997623i
$23$	1.58473	+	22.9453i	0.0689013	+	0.997623i
$24$	4.81911			0.200796
$25$	−1.59400	+	3.49038i	−0.0637602	+	0.139615i
$26$	31.0052	+	9.10394i	1.19251	+	0.350152i
$27$	−2.47489	−	2.85618i	−0.0916627	−	0.105784i
$28$	−39.3361	−	61.2081i	−1.40486	−	2.18601i
$29$	−4.81519	+	5.55702i	−0.166041	+	0.191621i	−0.832672	−	0.553766i	$-0.813190\pi$
$29$	−4.81519	+	5.55702i	−0.166041	+	0.191621i	0.666631	+	0.745388i	$0.267736\pi$
$30$	−4.20065	−	0.603962i	−0.140022	−	0.0201321i
$31$	−8.51070	+	2.49897i	−0.274539	+	0.0806119i	−0.416104	−	0.909317i	$-0.636605\pi$
$31$	−8.51070	+	2.49897i	−0.274539	+	0.0806119i	0.141565	+	0.989929i	$0.454787\pi$
$32$	−66.9163	−	43.0045i	−2.09113	−	1.34389i
$33$	1.27963	−	0.183983i	0.0387766	−	0.00557523i
$34$	59.7487	−	27.2863i	1.75732	−	0.802539i
$35$	16.0734	+	35.1958i	0.459240	+	1.00559i
$36$	12.8701	+	89.5137i	0.357503	+	2.48649i
$37$	11.8833	−	18.4907i	0.321169	−	0.499749i	−0.642703	−	0.766116i	$-0.722187\pi$
$37$	11.8833	−	18.4907i	0.321169	−	0.499749i	0.963872	+	0.266367i	$0.0858233\pi$
$38$	−2.92964	−	9.97743i	−0.0770957	−	0.262564i
$39$	0.257792	−	1.79299i	0.00661006	−	0.0459740i
$40$	92.9213	+	80.5168i	2.32303	+	2.01292i
$41$	−54.4615	+	35.0003i	−1.32833	+	0.853666i	−0.995987	−	0.0894925i	$-0.971475\pi$
$41$	−54.4615	+	35.0003i	−1.32833	+	0.853666i	−0.332343	+	0.943159i	$0.607839\pi$
$42$	−4.30339	+	3.72891i	−0.102462	+	0.0887835i
$43$	7.49361	−	25.5209i	0.174270	−	0.593509i	−0.825314	−	0.564674i	$-0.809002\pi$
$43$	7.49361	−	25.5209i	0.174270	−	0.593509i	0.999584	−	0.0288354i	$-0.00917987\pi$
$44$	−56.4183	−	25.7654i	−1.28223	−	0.585577i
$45$		−	48.0923i		−	1.06872i
$46$	−80.8397	−	30.3769i	−1.75738	−	0.660367i
$47$	49.7210			1.05789			0.528947	−	0.848655i	$-0.322587\pi$
$47$	49.7210			1.05789			0.528947	+	0.848655i	$0.322587\pi$
$48$	−3.98502	+	8.72598i	−0.0830212	+	0.181791i
$49$	2.79758	+	0.821444i	0.0570935	+	0.0167642i
$50$	−9.43483	−	10.8884i	−0.188697	−	0.217768i
$51$	−1.99067	−	3.09754i	−0.0390327	−	0.0607361i
$52$	−56.9111	+	65.6789i	−1.09444	+	1.26305i
$53$	−61.2431	−	8.80543i	−1.15553	−	0.166140i	−0.462211	−	0.886770i	$-0.652944\pi$
$53$	−61.2431	−	8.80543i	−1.15553	−	0.166140i	−0.693320	+	0.720630i	$0.743853\pi$
$54$	13.6153	−	3.99781i	0.252135	−	0.0740336i
$55$	27.7475	+	17.8323i	0.504501	+	0.324223i
$56$	163.293	−	23.4780i	2.91595	−	0.419250i
$57$	−0.530237	+	0.242151i	−0.00930240	+	0.00424826i
$58$	−11.4690	−	25.1135i	−0.197741	−	0.432992i
$59$	−1.09158	−	7.59212i	−0.0185014	−	0.128680i	0.978477	−	0.206354i	$-0.0661598\pi$
$59$	−1.09158	−	7.59212i	−0.0185014	−	0.128680i	−0.996979	+	0.0776738i	$0.975251\pi$
$60$	6.17054	−	9.60155i	0.102842	−	0.160026i
$61$	−7.78445	−	26.5114i	−0.127614	−	0.434613i	0.870754	−	0.491718i	$-0.163631\pi$
$61$	−7.78445	−	26.5114i	−0.127614	−	0.434613i	−0.998368	+	0.0571055i	$0.981813\pi$
$62$	4.73971	−	32.9654i	0.0764469	−	0.531700i
$63$	−48.7671	−	42.2569i	−0.774081	−	0.670745i
$64$	97.8859	−	62.9075i	1.52947	−	0.982929i
$65$	34.9276	−	30.2649i	0.537348	−	0.465614i
$66$	−1.36754	+	4.65743i	−0.0207204	+	0.0705671i
$67$	81.5437	+	37.2398i	1.21707	+	0.555817i	0.917301	−	0.398194i	$-0.130363\pi$
$67$	81.5437	+	37.2398i	1.21707	+	0.555817i	0.299769	+	0.954012i	$0.403090\pi$
$68$			176.652i			2.59782i
$69$	−1.04058	+	4.72782i	−0.0150809	+	0.0685191i
$70$	−145.279			−2.07542
$71$	23.9561	−	52.4566i	0.337410	−	0.738825i	−0.662538	−	0.749028i	$-0.730521\pi$
$71$	23.9561	−	52.4566i	0.337410	−	0.738825i	0.999948	+	0.0102034i	$0.00324790\pi$
$72$	−196.745	−	57.7694i	−2.73256	−	0.802353i
$73$	79.6614	+	91.9342i	1.09125	+	1.25937i	0.963541	+	0.267561i	$0.0862176\pi$
$73$	79.6614	+	91.9342i	1.09125	+	1.25937i	0.127711	+	0.991811i	$0.459237\pi$
$74$	44.6183	+	69.4275i	0.602950	+	0.938209i
$75$	−0.528885	+	0.610366i	−0.00705180	+	0.00813821i
$76$	27.6814	+	3.97999i	0.364229	+	0.0523683i
$77$	42.4632	−	12.4683i	0.551470	−	0.161926i
$78$	5.72169	+	3.67711i	0.0733551	+	0.0471424i
$79$	−84.6615	+	12.1725i	−1.07166	+	0.154082i	−0.655491	−	0.755203i	$-0.727538\pi$
$79$	−84.6615	+	12.1725i	−1.07166	+	0.154082i	−0.416174	+	0.909285i	$0.636629\pi$
$80$	−222.631	+	101.672i	−2.78288	+	1.27090i
$81$	33.1525	+	72.5939i	0.409291	+	0.896222i
$82$	−34.5932	−	240.601i	−0.421869	−	2.93416i
$83$	−80.7470	+	125.645i	−0.972855	+	1.51379i	−0.119255	+	0.992864i	$0.538051\pi$
$83$	−80.7470	+	125.645i	−0.972855	+	1.51379i	−0.853600	+	0.520928i	$0.825586\pi$
$84$	−4.31444	−	14.6936i	−0.0513624	−	0.174924i
$85$	13.3694	−	92.9861i	0.157287	−	1.09395i
$86$	75.4762	+	65.4005i	0.877630	+	0.760471i
$87$	−1.30196	+	0.836716i	−0.0149650	+	0.00961743i
$88$	106.282	−	92.0941i	1.20775	−	1.04652i
$89$	−2.59531	+	8.83880i	−0.0291607	+	0.0993123i	−0.972788	−	0.231699i	$-0.925572\pi$
$89$	−2.59531	+	8.83880i	−0.0291607	+	0.0993123i	0.943627	+	0.331011i	$0.107390\pi$
$90$	164.255	+	75.0129i	1.82506	+	0.833476i
$91$		−	62.0103i		−	0.681432i
$92$	164.628	−	163.826i	1.78944	−	1.78071i
$93$	−1.86693			−0.0200745
$94$	−77.5532	+	169.818i	−0.825034	+	1.80657i
$95$	−14.2698	−	4.18998i	−0.150208	−	0.0441050i
$96$	−10.9638	−	12.6528i	−0.114206	−	0.131800i
$97$	78.1151	+	121.550i	0.805311	+	1.25309i	0.964038	+	0.265765i	$0.0856246\pi$
$97$	78.1151	+	121.550i	0.805311	+	1.25309i	−0.158727	+	0.987322i	$0.550739\pi$
$98$	−7.16915	+	8.27364i	−0.0731546	+	0.0844249i
$99$	−54.4475	−	7.82837i	−0.549974	−	0.0790744i
$100$	37.1777	−	10.9163i	0.371777	−	0.109163i
$101$	−5.94494	−	3.82058i	−0.0588608	−	0.0378275i	0.510879	−	0.859652i	$-0.329320\pi$
$101$	−5.94494	−	3.82058i	−0.0588608	−	0.0378275i	−0.569740	+	0.821825i	$0.692956\pi$
$102$	13.6844	−	1.96752i	0.134161	−	0.0192894i
$103$	14.4528	−	6.60036i	0.140318	−	0.0640812i	−0.344018	−	0.938963i	$-0.611788\pi$
$103$	14.4528	−	6.60036i	0.140318	−	0.0640812i	0.484337	+	0.874882i	$0.339061\pi$
$104$	−81.8575	−	179.243i	−0.787091	−	1.72349i
$105$	1.15899	+	8.06097i	0.0110380	+	0.0767712i
$106$	125.599	−	195.436i	1.18490	−	1.84374i
$107$	−48.9869	−	166.834i	−0.457822	−	1.55920i	−0.788243	−	0.615364i	$-0.789009\pi$
$107$	−48.9869	−	166.834i	−0.457822	−	1.55920i	0.330421	−	0.943833i	$-0.392809\pi$
$108$	−5.43114	+	37.7744i	−0.0502883	+	0.349763i
$109$	−112.513	−	97.4934i	−1.03223	−	0.894435i	−0.0377454	−	0.999287i	$-0.512018\pi$
$109$	−112.513	−	97.4934i	−1.03223	−	0.894435i	−0.994488	+	0.104852i	$0.966563\pi$
$110$	−104.184	+	66.9552i	−0.947130	+	0.608683i
$111$	3.49631	−	3.02957i	0.0314983	−	0.0272934i
$112$	−92.5187	+	315.090i	−0.826060	+	2.81330i
$113$	−6.87849	−	3.14130i	−0.0608716	−	0.0277991i	0.384747	−	0.923022i	$-0.374289\pi$
$113$	−6.87849	−	3.14130i	−0.0608716	−	0.0277991i	−0.445618	+	0.895223i	$0.647016\pi$
$114$		−	2.18868i		−	0.0191989i
$115$	−99.0559	+	73.7752i	−0.861355	+	0.641524i
$116$	74.2501			0.640087
$117$	−32.0182	+	70.1100i	−0.273659	+	0.599231i
$118$	27.6329	+	8.11375i	0.234177	+	0.0687606i
$119$	−82.5436	−	95.2604i	−0.693643	−	0.800507i
$120$	13.9911	+	21.7706i	0.116592	+	0.181421i
$121$	−54.5328	+	62.9342i	−0.450684	+	0.520117i
$122$	102.689	+	14.7645i	0.841716	+	0.121021i
$123$	−13.0740	+	3.83889i	−0.106293	+	0.0312105i
$124$	75.3500	+	48.4245i	0.607662	+	0.390520i
$125$	112.488	−	16.1734i	0.899906	−	0.129387i
$126$	220.390	−	100.649i	1.74913	−	0.798801i
$127$	39.1578	+	85.7436i	0.308329	+	0.675146i	0.998839	−	0.0481767i	$-0.0153411\pi$
$127$	39.1578	+	85.7436i	0.308329	+	0.675146i	−0.690510	+	0.723323i	$0.742614\pi$
$128$	16.8949	+	117.507i	0.131991	+	0.918020i
$129$	3.02669	−	4.70962i	0.0234627	−	0.0365087i
$130$	48.8884	+	166.499i	0.376064	+	1.28076i
$131$	18.3191	−	127.412i	0.139841	−	0.972613i	−0.792201	−	0.610261i	$-0.791065\pi$
$131$	18.3191	−	127.412i	0.139841	−	0.972613i	0.932041	−	0.362352i	$-0.118026\pi$
$132$	−9.86592	−	8.54887i	−0.0747418	−	0.0647641i
$133$	−16.7871	+	10.7884i	−0.126219	+	0.0811158i
$134$	−254.379	+	220.420i	−1.89835	+	1.64493i
$135$	5.71769	−	19.4727i	0.0423533	−	0.144242i
$136$	−364.344	−	166.391i	−2.67900	−	1.22346i
$137$			6.37218i			0.0465123i	0.999730	+	0.0232561i	$0.00740332\pi$
$137$			6.37218i			0.0465123i	−0.999730	+	0.0232561i	$0.992597\pi$
$138$	−14.5244	−	10.9283i	−0.105249	−	0.0791907i
$139$	165.424			1.19010			0.595050	−	0.803688i	$-0.297132\pi$
$139$	165.424			1.19010			0.595050	+	0.803688i	$0.297132\pi$
$140$	162.308	−	355.405i	1.15934	−	2.53861i
$141$	10.0412	+	2.94837i	0.0712144	+	0.0209104i
$142$	141.795	+	163.640i	0.998557	+	1.15240i
$143$	−28.5789	−	44.4696i	−0.199852	−	0.310976i
$144$	267.295	−	308.475i	1.85622	−	2.14219i
$145$	−39.0838	−	5.61940i	−0.269544	−	0.0387545i
$146$	−438.247	+	128.681i	−3.00169	+	0.881376i
$147$	0.516265	+	0.331784i	0.00351201	+	0.00225703i
$148$	−219.693	+	31.5871i	−1.48441	+	0.213426i
$149$	53.5299	−	24.4463i	0.359261	−	0.164069i	−0.227604	−	0.973754i	$-0.573089\pi$
$149$	53.5299	−	24.4463i	0.359261	−	0.164069i	0.586865	+	0.809685i	$0.300362\pi$
$150$	−1.25972	−	2.75839i	−0.00839811	−	0.0183893i
$151$	36.5727	+	254.369i	0.242203	+	1.68456i	0.641015	+	0.767528i	$0.278514\pi$
$151$	36.5727	+	254.369i	0.242203	+	1.68456i	−0.398812	+	0.917033i	$0.630577\pi$
$152$	−34.2822	+	53.3442i	−0.225541	+	0.350949i
$153$	44.1389	+	150.323i	0.288490	+	0.982505i
$154$	−23.6482	+	164.477i	−0.153560	+	1.06803i
$155$	−35.9979	−	31.1924i	−0.232245	−	0.201241i
$156$	−15.3879	+	9.88921i	−0.0986405	+	0.0633924i
$157$	189.264	−	163.998i	1.20550	−	1.04457i	0.207707	−	0.978191i	$-0.433400\pi$
$157$	189.264	−	163.998i	1.20550	−	1.04457i	0.997794	−	0.0663813i	$-0.0211454\pi$
$158$	90.4782	−	308.141i	0.572647	−	1.95026i
$159$	−11.8460	−	5.40988i	−0.0745031	−	0.0340244i
$160$		−	427.151i		−	2.66969i
$161$	−12.2263	+	165.269i	−0.0759399	+	1.02652i
$162$	−299.649			−1.84968
$163$	25.0572	−	54.8675i	0.153725	−	0.336611i	−0.817064	−	0.576548i	$-0.804400\pi$
$163$	25.0572	−	54.8675i	0.153725	−	0.336611i	0.970788	+	0.239937i	$0.0771268\pi$
$164$	627.246	+	184.176i	3.82467	+	1.12302i
$165$	4.54623	+	5.24663i	0.0275529	+	0.0317978i
$166$	−303.183	−	471.761i	−1.82640	−	2.84194i
$167$	33.4475	−	38.6005i	0.200284	−	0.231140i	−0.646719	−	0.762729i	$-0.723859\pi$
$167$	33.4475	−	38.6005i	0.200284	−	0.231140i	0.847003	+	0.531588i	$0.178405\pi$
$168$	34.3695	+	4.94158i	0.204580	+	0.0294142i
$169$	91.0868	−	26.7455i	0.538975	−	0.158257i
$170$	296.733	+	190.699i	1.74549	+	1.12176i
$171$	24.5502	−	3.52979i	0.143568	−	0.0206420i
$172$	−244.317	+	111.576i	−1.42045	+	0.648696i
$173$	24.5129	+	53.6757i	0.141693	+	0.310264i	0.967152	−	0.254197i	$-0.0818112\pi$
$173$	24.5129	+	53.6757i	0.141693	+	0.310264i	−0.825460	+	0.564461i	$0.809084\pi$
$174$	−0.826984	−	5.75180i	−0.00475278	−	0.0330563i
$175$	−14.9474	+	23.2586i	−0.0854137	+	0.132906i
$176$	78.8681	+	268.600i	0.448114	+	1.52614i
$177$	0.229753	−	1.59797i	0.00129804	−	0.00902808i
$178$	−26.1401	−	22.6505i	−0.146854	−	0.127250i
$179$	−29.5773	+	19.0082i	−0.165236	+	0.106191i	−0.620645	−	0.784091i	$-0.713129\pi$
$179$	−29.5773	+	19.0082i	−0.165236	+	0.106191i	0.455409	+	0.890282i	$0.349493\pi$
$180$	−367.017	+	318.022i	−2.03898	+	1.76679i
$181$	21.4601	−	73.0864i	0.118564	−	0.403792i	−0.878729	−	0.477321i	$-0.841608\pi$
$181$	21.4601	−	73.0864i	0.118564	−	0.403792i	0.997293	+	0.0735287i	$0.0234261\pi$
$182$	211.791	+	96.7217i	1.16369	+	0.531438i
$183$		−	5.81562i		−	0.0317793i
$184$	182.825	+	493.856i	0.993614	+	2.68400i
$185$	118.033			0.638015
$186$	2.91198	−	6.37635i	0.0156558	−	0.0342815i
$187$	−103.098	−	30.2722i	−0.551324	−	0.161883i
$188$	−328.792	−	379.447i	−1.74890	−	2.01833i
$189$	−14.7220	−	22.9078i	−0.0778940	−	0.121205i
$190$	36.5680	−	42.2018i	0.192463	−	0.222115i
$191$	−71.4061	−	10.2666i	−0.373854	−	0.0537521i	−0.0471729	−	0.998887i	$-0.515021\pi$
$191$	−71.4061	−	10.2666i	−0.373854	−	0.0537521i	−0.326681	+	0.945135i	$0.605930\pi$
$192$	23.4985	−	6.89979i	0.122388	−	0.0359364i
$193$	−157.229	−	101.045i	−0.814660	−	0.523550i	0.0657094	−	0.997839i	$-0.479069\pi$
$193$	−157.229	−	101.045i	−0.814660	−	0.523550i	−0.880369	+	0.474289i	$0.842705\pi$
$194$	−536.984	+	77.2066i	−2.76796	+	0.397972i
$195$	8.84834	−	4.04090i	0.0453761	−	0.0207226i
$196$	−12.2308	−	26.7818i	−0.0624022	−	0.136642i
$197$	−9.38975	−	65.3072i	−0.0476637	−	0.331508i	−0.999676	−	0.0254490i	$-0.991898\pi$
$197$	−9.38975	−	65.3072i	−0.0476637	−	0.331508i	0.952012	−	0.306059i	$-0.0990106\pi$
$198$	111.663	−	173.750i	0.563952	−	0.877527i
$199$	−11.6894	−	39.8103i	−0.0587405	−	0.200052i	0.924895	−	0.380223i	$-0.124153\pi$
$199$	−11.6894	−	39.8103i	−0.0587405	−	0.200052i	−0.983635	+	0.180172i	$0.942335\pi$
$200$	−12.5031	+	86.9612i	−0.0625157	+	0.434806i
$201$	14.2596	+	12.3560i	0.0709434	+	0.0614728i
$202$	22.3216	−	14.3452i	0.110503	−	0.0710159i
$203$	−40.0397	+	34.6946i	−0.197240	+	0.170910i
$204$	−10.4751	+	35.6751i	−0.0513488	+	0.174878i
$205$	−316.231	−	144.418i	−1.54259	−	0.704478i
$206$			59.6573i			0.289598i
$207$	99.1578	−	180.543i	0.479023	−	0.872191i
$208$	392.245			1.88579
$209$	−7.06647	+	15.4734i	−0.0338108	+	0.0740354i
$210$	−29.3393	−	8.61481i	−0.139711	−	0.0410229i
$211$	7.85260	+	9.06238i	0.0372161	+	0.0429497i	0.774052	−	0.633121i	$-0.218227\pi$
$211$	7.85260	+	9.06238i	0.0372161	+	0.0429497i	−0.736836	+	0.676071i	$0.763681\pi$
$212$	337.787	+	525.606i	1.59333	+	2.47927i
$213$	7.94856	−	9.17313i	0.0373172	−	0.0430663i
$214$	646.216	+	92.9119i	3.01970	+	0.434168i
$215$	137.048	−	40.2409i	0.637432	−	0.187167i
$216$	−72.7940	−	46.7819i	−0.337009	−	0.216583i
$217$	−63.2601	+	9.09543i	−0.291521	+	0.0419144i
$218$	508.476	−	232.213i	2.33246	−	1.06520i
$219$	10.6362	+	23.2900i	0.0485671	+	0.106347i
$220$	−47.4003	−	329.676i	−0.215456	−	1.49853i
$221$	−81.3970	+	126.656i	−0.368312	+	0.573105i
$222$	4.89381	+	16.6668i	0.0220442	+	0.0750756i
$223$	−41.9922	+	292.062i	−0.188306	+	1.30969i	0.648088	+	0.761565i	$0.275569\pi$
$223$	−41.9922	+	292.062i	−0.188306	+	1.30969i	−0.836394	+	0.548129i	$0.815340\pi$
$224$	−433.144	−	375.321i	−1.93368	−	1.67554i
$225$	28.9090	−	18.5787i	0.128485	−	0.0825721i
$226$	21.4577	−	18.5932i	0.0949456	−	0.0822709i
$227$	−60.6506	+	206.557i	−0.267183	+	0.909942i	0.711174	+	0.703016i	$0.248164\pi$
$227$	−60.6506	+	206.557i	−0.267183	+	0.909942i	−0.978357	+	0.206926i	$0.933654\pi$
$228$	5.35430	+	2.44523i	0.0234838	+	0.0107247i
$229$		−	302.640i		−	1.32157i	−0.750573	−	0.660787i	$-0.770223\pi$
$229$		−	302.640i		−	1.32157i	0.750573	−	0.660787i	$-0.229777\pi$
$230$	−97.4689	−	453.389i	−0.423778	−	1.97126i
$231$	9.31485			0.0403240
$232$	−69.9371	+	153.141i	−0.301453	+	0.660090i
$233$	−91.8981	−	26.9837i	−0.394412	−	0.115810i	0.0785115	−	0.996913i	$-0.474983\pi$
$233$	−91.8981	−	26.9837i	−0.394412	−	0.115810i	−0.472924	+	0.881103i	$0.656801\pi$
$234$	−189.514	−	218.711i	−0.809888	−	0.934661i
$235$	144.353	+	224.617i	0.614267	+	0.955817i
$236$	−50.7211	+	58.5352i	−0.214920	+	0.248031i
$237$	−17.8193	−	2.56203i	−0.0751870	−	0.0108103i
$238$	454.103	−	133.337i	1.90799	−	0.560238i
$239$	−162.853	−	104.659i	−0.681392	−	0.437904i	0.153624	−	0.988129i	$-0.450905\pi$
$239$	−162.853	−	104.659i	−0.681392	−	0.437904i	−0.835016	+	0.550225i	$0.814542\pi$
$240$	−50.9896	+	7.33119i	−0.212456	+	0.0305466i
$241$	−345.877	+	157.957i	−1.43517	+	0.655422i	−0.972881	−	0.231305i	$-0.925700\pi$
$241$	−345.877	+	157.957i	−1.43517	+	0.655422i	−0.462293	+	0.886727i	$0.652973\pi$
$242$	−129.888	−	284.415i	−0.536727	−	1.17527i
$243$	7.23112	+	50.2935i	0.0297577	+	0.206969i
$244$	−150.846	+	234.720i	−0.618220	+	0.961968i
$245$	4.41117	+	15.0231i	0.0180048	+	0.0613187i
$246$	7.28109	−	50.6411i	0.0295979	−	0.205858i
$247$	18.0132	+	15.6085i	0.0729280	+	0.0631925i
$248$	−170.849	+	109.798i	−0.688906	+	0.442733i
$249$	−23.7575	+	20.5860i	−0.0954116	+	0.0826746i
$250$	−120.217	+	409.421i	−0.480868	+	1.63768i
$251$	315.690	+	144.171i	1.25773	+	0.574386i	0.929015	−	0.370042i	$-0.120657\pi$
$251$	315.690	+	144.171i	1.25773	+	0.574386i	0.328716	+	0.944429i	$0.393384\pi$
$252$			651.601i			2.58572i
$253$	67.4002	+	124.155i	0.266404	+	0.490730i
$254$	−353.927			−1.39341
$255$	8.21388	−	17.9859i	0.0322113	−	0.0705329i
$256$	18.8900	+	5.54660i	0.0737890	+	0.0216664i
$257$	108.463	+	125.173i	0.422034	+	0.487053i	0.926455	−	0.376404i	$-0.122840\pi$
$257$	108.463	+	125.173i	0.422034	+	0.487053i	−0.504421	+	0.863458i	$0.668294\pi$
$258$	11.3644	+	17.6833i	0.0440480	+	0.0685401i
$259$	103.711	−	119.689i	0.400429	−	0.462119i
$260$	−461.935	−	66.4162i	−1.77667	−	0.255447i
$261$	63.1837	−	18.5524i	0.242083	−	0.0710821i
$262$	406.592	+	261.301i	1.55188	+	0.997333i
$263$	258.491	−	37.1655i	0.982857	−	0.141314i	0.367893	−	0.929868i	$-0.380079\pi$
$263$	258.491	−	37.1655i	0.982857	−	0.141314i	0.614965	+	0.788555i	$0.289170\pi$
$264$	26.9249	−	12.2962i	0.101988	−	0.0465764i
$265$	−138.025	−	302.233i	−0.520850	−	1.14050i
$266$	−10.6629	−	74.1622i	−0.0400862	−	0.278805i
$267$	−1.04825	+	1.63111i	−0.00392603	+	0.00610903i
$268$	−255.032	−	868.560i	−0.951612	−	3.24089i
$269$	−36.3956	+	253.137i	−0.135299	+	0.941028i	0.803191	+	0.595722i	$0.203134\pi$
$269$	−36.3956	+	253.137i	−0.135299	+	0.941028i	−0.938490	+	0.345306i	$0.887775\pi$
$270$	57.5890	+	49.9011i	0.213293	+	0.184819i
$271$	308.338	−	198.157i	1.13778	−	0.731206i	0.170609	−	0.985339i	$-0.445426\pi$
$271$	308.338	−	198.157i	1.13778	−	0.731206i	0.967169	+	0.254133i	$0.0817901\pi$
$272$	602.568	−	522.128i	2.21532	−	1.91959i
$273$	3.67711	−	12.5231i	0.0134693	−	0.0458721i
$274$	−21.7636	−	9.93912i	−0.0794294	−	0.0362742i
$275$			23.5683i			0.0857030i
$276$	42.9615	−	23.3226i	0.155658	−	0.0845023i
$277$	−235.729			−0.851008			−0.425504	−	0.904957i	$-0.639903\pi$
$277$	−235.729			−0.851008			−0.425504	+	0.904957i	$0.639903\pi$
$278$	−258.023	+	564.992i	−0.928141	+	2.03234i
$279$	76.2193	+	22.3800i	0.273187	+	0.0802151i
$280$	580.144	+	669.522i	2.07194	+	2.39115i
$281$	−178.504	−	277.758i	−0.635247	−	0.988463i	−0.998390	−	0.0567295i	$-0.981933\pi$
$281$	−178.504	−	277.758i	−0.635247	−	0.988463i	0.363143	−	0.931733i	$-0.381704\pi$
$282$	−25.7319	+	29.6962i	−0.0912479	+	0.105306i
$283$	−42.3825	−	6.09369i	−0.149762	−	0.0215325i	0.0670262	−	0.997751i	$-0.478649\pi$
$283$	−42.3825	−	6.09369i	−0.149762	−	0.0215325i	−0.216788	+	0.976219i	$0.569558\pi$
$284$	−558.739	+	164.061i	−1.96739	+	0.577678i
$285$	−2.63334	−	1.69234i	−0.00923979	−	0.00593805i
$286$	196.458	−	28.2465i	0.686918	−	0.0987639i
$287$	−424.305	+	193.774i	−1.47841	+	0.675169i
$288$	295.929	+	647.993i	1.02753	+	2.24998i
$289$	2.42422	+	16.8608i	0.00838830	+	0.0583419i
$290$	80.1543	−	124.723i	0.276394	−	0.430078i
$291$	8.56778	+	29.1792i	0.0294426	+	0.100272i
$292$	174.816	−	1215.87i	0.598686	−	4.16396i
$293$	226.450	+	196.220i	0.772866	+	0.669692i	0.949212	−	0.314636i	$-0.101883\pi$
$293$	226.450	+	196.220i	0.772866	+	0.669692i	−0.176347	+	0.984328i	$0.556428\pi$
$294$	−1.93843	+	1.24576i	−0.00659331	+	0.00423726i
$295$	31.1287	−	26.9731i	0.105521	−	0.0914344i
$296$	141.783	−	482.870i	0.478998	−	1.63132i
$297$	−21.1152	−	9.64298i	−0.0710949	−	0.0324679i
$298$			220.957i			0.741467i
$299$	193.523	−	41.6032i	0.647233	−	0.139141i
$300$	8.15540			0.0271847
$301$	79.6133	−	174.329i	0.264496	−	0.579166i
$302$	−925.820	−	271.845i	−3.06563	−	0.900150i
$303$	−0.974035	−	1.12410i	−0.00321464	−	0.00370989i
$304$	−68.2418	−	106.186i	−0.224480	−	0.349297i
$305$	97.1663	−	112.136i	0.318578	−	0.367659i
$306$	−582.263	−	83.7168i	−1.90282	−	0.273584i
$307$	−453.384	+	133.126i	−1.47682	+	0.433634i	−0.918310	−	0.395863i	$-0.870446\pi$
$307$	−453.384	+	133.126i	−1.47682	+	0.433634i	−0.558512	+	0.829497i	$0.688627\pi$
$308$	−375.950	−	241.609i	−1.22062	−	0.784444i
$309$	3.31015	−	0.475928i	0.0107125	−	0.00154022i
$310$	162.683	−	74.2950i	0.524785	−	0.239661i
$311$	−30.8496	−	67.5513i	−0.0991950	−	0.217207i	0.853528	−	0.521047i	$-0.174458\pi$
$311$	−30.8496	−	67.5513i	−0.0991950	−	0.217207i	−0.952723	+	0.303840i	$0.901731\pi$
$312$	−5.90244	−	41.0524i	−0.0189181	−	0.131578i
$313$	134.926	−	209.950i	0.431075	−	0.670765i	−0.555972	−	0.831201i	$-0.687654\pi$
$313$	134.926	−	209.950i	0.431075	−	0.670765i	0.987046	+	0.160436i	$0.0512900\pi$
$314$	264.914	+	902.213i	0.843674	+	2.87329i
$315$	49.3145	−	342.990i	0.156554	−	1.08886i
$316$	652.740	+	565.602i	2.06563	+	1.78988i
$317$	229.808	−	147.689i	0.724947	−	0.465895i	−0.125407	−	0.992105i	$-0.540024\pi$
$317$	229.808	−	147.689i	0.724947	−	0.465895i	0.850355	+	0.526210i	$0.176387\pi$
$318$	36.9540	−	32.0208i	0.116208	−	0.100694i
$319$	−12.7240	+	43.3338i	−0.0398870	+	0.135843i
$320$	568.375	+	259.568i	1.77617	+	0.811151i
$321$		−	36.5972i		−	0.114010i
$322$	−545.393	−	299.540i	−1.69377	−	0.930248i
$323$	48.4489			0.149997
$324$	334.773	−	733.050i	1.03325	−	2.26250i
$325$	31.6857	+	9.30377i	0.0974946	+	0.0286270i
$326$	148.312	+	171.161i	0.454945	+	0.525035i
$327$	−16.9411	−	26.3608i	−0.0518075	−	0.0806141i
$328$	−970.674	+	1120.22i	−2.95937	+	3.41530i
$329$	354.606	+	50.9846i	1.07783	+	0.154969i
$330$	−25.0105	+	7.34375i	−0.0757894	+	0.0222538i
$331$	7.82299	+	5.02753i	0.0236344	+	0.0151889i	0.552405	−	0.833576i	$-0.313710\pi$
$331$	7.82299	+	5.02753i	0.0236344	+	0.0151889i	−0.528770	+	0.848765i	$0.677347\pi$
$332$	1492.82	−	214.635i	4.49644	−	0.646491i
$333$	−179.057	+	81.7727i	−0.537709	+	0.245564i
$334$	79.6663	+	174.445i	0.238522	+	0.522290i
$335$	68.5095	+	476.494i	0.204506	+	1.42237i
$336$	−37.3686	+	58.1466i	−0.111216	+	0.173055i
$337$	−50.3315	−	171.413i	−0.149352	−	0.508645i	0.850498	−	0.525978i	$-0.176301\pi$
$337$	−50.3315	−	171.413i	−0.149352	−	0.508645i	−0.999850	+	0.0173330i	$0.994482\pi$
$338$	−50.7273	+	352.816i	−0.150081	+	1.04383i
$339$	−1.20285	−	1.04227i	−0.00354822	−	0.00307455i
$340$	−798.033	+	512.865i	−2.34716	+	1.50843i
$341$	−41.1740	+	35.6775i	−0.120745	+	0.104626i
$342$	−26.2369	+	89.3548i	−0.0767162	+	0.261271i
$343$	−302.043	−	137.938i	−0.880591	−	0.402152i
$344$		−	608.998i		−	1.77034i
$345$	−24.3792	+	9.02517i	−0.0706644	+	0.0261599i
$346$	−221.559			−0.640345
$347$	19.9887	−	43.7692i	0.0576044	−	0.126136i	−0.878641	−	0.477483i	$-0.841549\pi$
$347$	19.9887	−	43.7692i	0.0576044	−	0.126136i	0.936245	+	0.351347i	$0.114276\pi$
$348$	14.9949	+	4.40290i	0.0430888	+	0.0126520i
$349$	−123.309	−	142.307i	−0.353322	−	0.407755i	0.551069	−	0.834459i	$-0.314220\pi$
$349$	−123.309	−	142.307i	−0.353322	−	0.407755i	−0.904391	+	0.426704i	$0.859674\pi$
$350$	−56.1233	−	87.3296i	−0.160352	−	0.249513i
$351$	−21.2996	+	24.5810i	−0.0606826	+	0.0700314i
$352$	−483.597	−	69.5307i	−1.37385	−	0.197530i
$353$	0.447413	−	0.131372i	0.00126746	−	0.000372159i	−0.281099	−	0.959679i	$-0.590699\pi$
$353$	0.447413	−	0.131372i	0.00126746	−	0.000372159i	0.282366	+	0.959307i	$0.408881\pi$
$354$	5.09937	+	3.27717i	0.0144050	+	0.00925753i
$355$	306.526	−	44.0718i	0.863453	−	0.124146i
$356$	84.6155	−	38.6426i	0.237684	−	0.108547i
$357$	−11.0210	−	24.1327i	−0.0308712	−	0.0675985i
$358$	−18.7871	−	130.667i	−0.0524779	−	0.364992i
$359$	329.821	−	513.212i	0.918722	−	1.42956i	0.0157429	−	0.999876i	$-0.494989\pi$
$359$	329.821	−	513.212i	0.918722	−	1.42956i	0.902979	−	0.429684i	$-0.141375\pi$
$360$	−310.223	−	1056.52i	−0.861731	−	2.93479i
$361$	−50.2841	+	349.734i	−0.139291	+	0.968791i
$362$	216.148	+	187.293i	0.597093	+	0.517384i
$363$	−14.7449	+	9.47595i	−0.0406194	+	0.0261045i
$364$	−473.233	+	410.059i	−1.30009	+	1.12653i
$365$	−184.040	+	626.783i	−0.504219	+	1.71721i
$366$	19.8628	+	9.07102i	0.0542698	+	0.0247842i
$367$			442.760i			1.20643i	0.797578	+	0.603215i	$0.206114\pi$
$367$			442.760i			1.20643i	−0.797578	+	0.603215i	$0.793886\pi$
$368$	−1045.41	−	77.3375i	−2.84078	−	0.210156i
$369$	579.779			1.57122
$370$	−184.104	+	403.131i	−0.497578	+	1.08954i
$371$	−427.752	−	125.599i	−1.15297	−	0.338542i
$372$	12.3456	+	14.2475i	0.0331870	+	0.0382998i
$373$	−73.8945	−	114.982i	−0.198109	−	0.308263i	0.727959	−	0.685621i	$-0.240469\pi$
$373$	−73.8945	−	114.982i	−0.198109	−	0.308263i	−0.926068	+	0.377358i	$0.876833\pi$
$374$	264.200	−	304.903i	0.706418	−	0.815250i
$375$	23.6762	+	3.40413i	0.0631366	+	0.00907767i
$376$	1092.30	−	320.729i	2.90506	−	0.853003i
$377$	53.2360	+	34.2127i	0.141210	+	0.0907499i
$378$	101.203	−	14.5507i	0.267732	−	0.0384940i
$379$	132.119	−	60.3367i	0.348599	−	0.159200i	−0.233418	−	0.972376i	$-0.574991\pi$
$379$	132.119	−	60.3367i	0.348599	−	0.159200i	0.582017	+	0.813177i	$0.302264\pi$
$380$	62.3864	+	136.607i	0.164175	+	0.359493i
$381$	2.82352	+	19.6380i	0.00741082	+	0.0515434i
$382$	146.442	−	227.868i	0.383356	−	0.596513i
$383$	179.155	+	610.148i	0.467769	+	1.59307i	0.768819	+	0.639466i	$0.220845\pi$
$383$	179.155	+	610.148i	0.467769	+	1.59307i	−0.301050	+	0.953608i	$0.597337\pi$
$384$	−3.55599	+	24.7325i	−0.00926039	+	0.0644074i
$385$	179.608	+	155.631i	0.466513	+	0.404236i
$386$	590.353	−	379.397i	1.52941	−	0.982893i
$387$	−180.024	+	155.992i	−0.465180	+	0.403080i
$388$	411.052	−	1399.91i	1.05941	−	3.60802i
$389$	−239.895	−	109.557i	−0.616698	−	0.281636i	0.0824705	−	0.996594i	$-0.473719\pi$
$389$	−239.895	−	109.557i	−0.616698	−	0.281636i	−0.699168	+	0.714957i	$0.746446\pi$
$390$			36.5236i			0.0936503i
$391$	241.911	−	321.514i	0.618698	−	0.822287i
$392$	66.7579			0.170301
$393$	11.2549	−	24.6448i	0.0286384	−	0.0627094i
$394$	237.697	+	69.7941i	0.603292	+	0.177142i
$395$	−300.784	−	347.123i	−0.761477	−	0.878792i
$396$	300.305	+	467.284i	0.758346	+	1.18001i
$397$	−219.695	+	253.542i	−0.553388	+	0.638644i	−0.961669	−	0.274212i	$-0.911583\pi$
$397$	−219.695	+	253.542i	−0.553388	+	0.638644i	0.408281	+	0.912856i	$0.366128\pi$
$398$	154.202	+	22.1708i	0.387441	+	0.0557056i
$399$	−4.02991	+	1.18329i	−0.0101000	+	0.00296563i
$400$	−147.122	−	94.5495i	−0.367805	−	0.236374i
$401$	−458.785	+	65.9633i	−1.14410	+	0.164497i	−0.688192	−	0.725529i	$-0.741595\pi$
$401$	−458.785	+	65.9633i	−1.14410	+	0.164497i	−0.455910	+	0.890026i	$0.650686\pi$
$402$	−64.4427	+	29.4300i	−0.160305	+	0.0732089i
$403$	31.7118	+	69.4391i	0.0786892	+	0.172305i
$404$	10.1556	+	70.6334i	0.0251375	+	0.174835i
$405$	−231.697	+	360.527i	−0.572090	+	0.890190i
$406$	−56.0439	−	190.868i	−0.138039	−	0.470118i
$407$	19.2131	−	133.630i	0.0472067	−	0.328330i
$408$	−63.7132	−	55.2078i	−0.156160	−	0.135313i
$409$	100.048	−	64.2969i	0.244616	−	0.157205i	−0.412588	−	0.910918i	$-0.635375\pi$
$409$	100.048	−	64.2969i	0.244616	−	0.157205i	0.657204	+	0.753712i	$0.271739\pi$
$410$	986.495	−	854.803i	2.40609	−	2.08489i
$411$	−0.377859	+	1.28687i	−0.000919366	+	0.00313107i
$412$	−145.943	−	66.6501i	−0.354231	−	0.161772i
$413$		−	55.2657i		−	0.133815i
$414$	461.968	+	620.271i	1.11586	+	1.49824i
$415$	−802.035			−1.93262
$416$	−284.382	+	622.710i	−0.683610	+	1.49690i
$417$	33.4076	+	9.80936i	0.0801142	+	0.0235237i
$418$	−41.8261	−	48.2699i	−0.100062	−	0.115478i
$419$	−44.5928	−	69.3877i	−0.106427	−	0.165603i	0.783955	−	0.620817i	$-0.213199\pi$
$419$	−44.5928	−	69.3877i	−0.106427	−	0.165603i	−0.890382	+	0.455214i	$0.849563\pi$
$420$	53.8533	−	62.1501i	0.128222	−	0.147976i
$421$	745.817	+	107.232i	1.77154	+	0.254709i	0.949286	−	0.314415i	$-0.101808\pi$
$421$	745.817	+	107.232i	1.77154	+	0.254709i	0.822252	+	0.569124i	$0.192718\pi$
$422$	−43.2000	+	12.6847i	−0.102370	+	0.0300585i
$423$	−374.599	−	240.740i	−0.885576	−	0.569125i
$424$	−1402.23	+	201.610i	−3.30714	+	0.475495i
$425$	61.0602	−	27.8852i	0.143671	−	0.0656123i
$426$	18.9321	+	41.4556i	0.0444416	+	0.0973136i
$427$	−28.3328	−	197.059i	−0.0663533	−	0.461497i
$428$	−949.259	+	1477.08i	−2.21790	+	3.45111i
$429$	−3.13457	−	10.6754i	−0.00730669	−	0.0248843i
$430$	−76.3235	+	530.842i	−0.177497	+	1.23452i
$431$	−358.964	−	311.044i	−0.832863	−	0.721680i	0.130045	−	0.991508i	$-0.458488\pi$
$431$	−358.964	−	311.044i	−0.832863	−	0.721680i	−0.962909	+	0.269828i	$0.913033\pi$
$432$	144.903	−	93.1235i	0.335424	−	0.215564i
$433$	270.073	−	234.020i	0.623726	−	0.540462i	−0.284642	−	0.958634i	$-0.591875\pi$
$433$	270.073	−	234.020i	0.623726	−	0.540462i	0.908368	+	0.418172i	$0.137329\pi$
$434$	67.6064	−	230.246i	0.155775	−	0.530521i
$435$	−7.55981	−	3.45245i	−0.0173789	−	0.00793667i
$436$			1503.35i			3.44805i
$437$	−44.9312	−	45.1513i	−0.102817	−	0.103321i
$438$	−96.1351			−0.219487
$439$	50.9331	−	111.528i	0.116021	−	0.254050i	−0.842709	−	0.538370i	$-0.819040\pi$
$439$	50.9331	−	111.528i	0.116021	−	0.254050i	0.958730	+	0.284320i	$0.0917677\pi$
$440$	724.604	+	212.763i	1.64683	+	0.483552i
$441$	−17.0997	−	19.7341i	−0.0387749	−	0.0447486i
$442$	−305.623	−	475.559i	−0.691455	−	1.07593i
$443$	278.582	−	321.501i	0.628854	−	0.725736i	−0.348509	−	0.937305i	$-0.613312\pi$
$443$	278.582	−	321.501i	0.628854	−	0.725736i	0.977363	+	0.211570i	$0.0678575\pi$
$444$	−46.2404	−	6.64837i	−0.104145	−	0.0149738i
$445$	−47.4645	+	13.9368i	−0.106662	+	0.0313188i
$446$	−932.015	−	598.970i	−2.08972	−	1.34298i
$447$	12.2601	−	1.76273i	0.0274274	−	0.00394347i
$448$	762.620	−	348.277i	1.70228	−	0.777404i
$449$	−218.215	−	477.824i	−0.486002	−	1.06420i	−0.980769	−	0.195171i	$-0.937474\pi$
$449$	−218.215	−	477.824i	−0.486002	−	1.06420i	0.494767	−	0.869026i	$-0.335253\pi$
$450$	18.3626	+	127.715i	0.0408058	+	0.283811i
$451$	−214.978	+	334.512i	−0.476669	+	0.741711i
$452$	21.5128	+	73.2660i	0.0475948	+	0.162093i
$453$	−7.69772	+	53.5388i	−0.0169928	+	0.118187i
$454$	−610.877	−	529.328i	−1.34554	−	1.16592i
$455$	280.135	−	180.032i	0.615681	−	0.395674i
$456$	−10.0866	+	8.74006i	−0.0221197	+	0.0191668i
$457$	2.93649	−	10.0008i	0.00642557	−	0.0218835i	−0.956218	−	0.292656i	$-0.905461\pi$
$457$	2.93649	−	10.0008i	0.00642557	−	0.0218835i	0.962643	+	0.270772i	$0.0872791\pi$
$458$	1033.64	+	472.049i	2.25686	+	1.03067i
$459$			66.1139i			0.144039i
$460$	1218.05	+	268.090i	2.64793	+	0.582803i
$461$	222.730			0.483145			0.241572	−	0.970383i	$-0.422337\pi$
$461$	222.730			0.483145			0.241572	+	0.970383i	$0.422337\pi$
$462$	−14.5290	+	31.8141i	−0.0314481	+	0.0688617i
$463$	205.304	+	60.2827i	0.443421	+	0.130200i	0.495818	−	0.868426i	$-0.334868\pi$
$463$	205.304	+	60.2827i	0.443421	+	0.130200i	−0.0523976	+	0.998626i	$0.516686\pi$
$464$	−219.460	−	253.271i	−0.472975	−	0.545842i
$465$	−5.42018	−	8.43396i	−0.0116563	−	0.0181376i
$466$	235.500	−	271.782i	0.505365	−	0.583223i
$467$	−687.579	−	98.8589i	−1.47233	−	0.211689i	−0.641032	−	0.767514i	$-0.721493\pi$
$467$	−687.579	−	98.8589i	−1.47233	−	0.211689i	−0.831299	+	0.555825i	$0.812402\pi$
$468$	746.774	−	219.273i	1.59567	−	0.468531i
$469$	543.377	+	349.207i	1.15859	+	0.744578i
$470$	−992.318	+	142.674i	−2.11131	+	0.303561i
$471$	47.9469	−	21.8966i	0.101798	−	0.0464896i
$472$	−72.9542	−	159.747i	−0.154564	−	0.338448i
$473$	−23.2501	−	161.708i	−0.0491547	−	0.341878i
$474$	36.5444	−	56.8642i	0.0770979	−	0.119967i
$475$	−2.99394	−	10.1964i	−0.00630303	−	0.0214662i
$476$	−181.141	+	1259.87i	−0.380549	+	2.64678i
$477$	418.772	+	362.868i	0.877929	+	0.760730i
$478$	611.466	−	392.966i	1.27922	−	0.822104i
$479$	−518.969	+	449.689i	−1.08344	+	0.938809i	−0.998342	−	0.0575636i	$-0.981667\pi$
$479$	−518.969	+	449.689i	−1.08344	+	0.938809i	−0.0851012	+	0.996372i	$0.527121\pi$
$480$	25.3293	−	86.2637i	0.0527694	−	0.179716i
$481$	−172.071	−	78.5821i	−0.357735	−	0.163372i
$482$		−	1427.69i		−	2.96201i
$483$	−12.2693	+	32.6514i	−0.0254023	+	0.0676012i
$484$	840.895			1.73739
$485$	−322.318	+	705.778i	−0.664573	+	1.45521i
$486$	−183.052	−	53.7490i	−0.376651	−	0.110595i
$487$	−60.0284	−	69.2765i	−0.123262	−	0.142252i	0.690764	−	0.723080i	$-0.257274\pi$
$487$	−60.0284	−	69.2765i	−0.123262	−	0.142252i	−0.814026	+	0.580828i	$0.802729\pi$
$488$	−342.027	−	532.205i	−0.700876	−	1.09058i
$489$	8.31388	−	9.59473i	0.0170018	−	0.0196211i
$490$	−58.1905	−	8.36652i	−0.118756	−	0.0170745i
$491$	662.787	−	194.612i	1.34987	−	0.396358i	0.474690	−	0.880153i	$-0.342560\pi$
$491$	662.787	−	194.612i	1.34987	−	0.396358i	0.875182	+	0.483795i	$0.160742\pi$
$492$	115.752	+	74.3892i	0.235268	+	0.151198i
$493$	127.323	−	18.3062i	0.258261	−	0.0371323i
$494$	−81.4061	+	37.1769i	−0.164790	+	0.0752569i
$495$	−122.710	−	268.697i	−0.247899	−	0.542822i
$496$	−57.5330	−	400.151i	−0.115994	−	0.806755i
$497$	224.643	−	349.551i	0.451997	−	0.703322i
$498$	−33.2535	−	113.251i	−0.0667741	−	0.227412i
$499$	−88.0938	+	612.706i	−0.176541	+	1.22787i	0.688152	+	0.725566i	$0.258422\pi$
$499$	−88.0938	+	612.706i	−0.176541	+	1.22787i	−0.864693	+	0.502301i	$0.832487\pi$
$500$	−867.284	−	751.506i	−1.73457	−	1.50301i
$501$	9.04371	−	5.81204i	0.0180513	−	0.0116009i
$502$	−984.808	+	853.341i	−1.96177	+	1.69988i
$503$	190.947	−	650.305i	0.379616	−	1.29285i	−0.519247	−	0.854624i	$-0.673788\pi$
$503$	190.947	−	650.305i	0.379616	−	1.29285i	0.898863	−	0.438230i	$-0.144394\pi$
$504$	−1343.93	−	613.751i	−2.66652	−	1.21776i
$505$		−	37.9487i		−	0.0751459i
$506$	−529.168	+	36.5472i	−1.04579	+	0.0722277i
$507$	19.9811			0.0394104
$508$	395.413	−	865.834i	0.778372	−	1.70440i
$509$	618.088	+	181.487i	1.21432	+	0.356556i	0.825311	−	0.564679i	$-0.191000\pi$
$509$	618.088	+	181.487i	1.21432	+	0.356556i	0.389007	+	0.921235i	$0.372818\pi$
$510$	48.6176	+	56.1076i	0.0953285	+	0.110015i
$511$	473.868	+	737.353i	0.927334	+	1.44296i
$512$	−359.375	+	414.741i	−0.701904	+	0.810040i
$513$	10.3601	+	1.48955i	0.0201951	+	0.00290362i
$514$	−596.694	+	175.205i	−1.16088	+	0.340866i
$515$	71.7775	+	46.1286i	0.139374	+	0.0895701i
$516$	−55.9563	+	8.04531i	−0.108443	+	0.0155917i
$517$	277.797	−	126.865i	0.537324	−	0.245388i
$518$	247.022	+	540.903i	0.476877	+	1.04421i
$519$	1.76753	+	12.2935i	0.00340565	+	0.0236868i
$520$	572.086	−	890.182i	1.10016	−	1.71189i
$521$	−135.416	−	461.184i	−0.259915	−	0.885189i	−0.981272	−	0.192626i	$-0.938300\pi$
$521$	−135.416	−	461.184i	−0.259915	−	0.885189i	0.721357	−	0.692563i	$-0.243519\pi$
$522$	−35.1878	+	244.736i	−0.0674095	+	0.468843i
$523$	313.190	+	271.380i	0.598833	+	0.518892i	0.900690	−	0.434461i	$-0.143061\pi$
$523$	313.190	+	271.380i	0.598833	+	0.518892i	−0.301858	+	0.953353i	$0.597607\pi$
$524$	−1093.49	+	702.743i	−2.08681	+	1.34111i
$525$	−4.39784	+	3.81075i	−0.00837684	+	0.00725858i
$526$	−276.251	+	940.825i	−0.525193	+	1.78864i
$527$	141.148	+	64.4601i	0.267833	+	0.122315i
$528$			58.9209i			0.111593i
$529$	−523.977	+	72.7243i	−0.990505	+	0.137475i
$530$	1247.54			2.35385
$531$	−28.5357	+	62.4844i	−0.0537395	+	0.117673i
$532$	193.341	+	56.7699i	0.363422	+	0.106710i
$533$	364.860	+	421.071i	0.684541	+	0.790002i
$534$	−3.93589	−	6.12437i	−0.00737059	−	0.0114689i
$535$	611.460	−	705.663i	1.14292	−	1.31900i
$536$	2031.62	+	292.103i	3.79034	+	0.544969i
$537$	−7.10033	+	2.08484i	−0.0132222	+	0.00388239i
$538$	−807.798	−	519.140i	−1.50148	−	0.964945i
$539$	17.7263	−	2.54866i	0.0328875	−	0.00472850i
$540$	−186.416	+	85.1332i	−0.345214	+	0.157654i
$541$	89.0805	+	195.059i	0.164659	+	0.360553i	0.973918	−	0.226899i	$-0.0728586\pi$
$541$	89.0805	+	195.059i	0.164659	+	0.360553i	−0.809259	+	0.587451i	$0.800131\pi$
$542$	195.852	+	1362.18i	0.361351	+	2.51325i
$543$	8.66780	−	13.4874i	0.0159628	−	0.0248386i
$544$	392.037	+	1335.16i	0.720656	+	2.45433i
$545$	113.777	−	791.333i	0.208764	−	1.45199i
$546$	37.0361	+	32.0919i	0.0678316	+	0.0587765i
$547$	−786.407	+	505.393i	−1.43767	+	0.923936i	−0.437984	+	0.898983i	$0.644307\pi$
$547$	−786.407	+	505.393i	−1.43767	+	0.923936i	−0.999689	+	0.0249529i	$0.992056\pi$
$548$	48.6294	−	42.1376i	0.0887398	−	0.0768935i
$549$	−69.7152	+	237.428i	−0.126986	+	0.432474i
$550$	−80.4956	−	36.7611i	−0.146356	−	0.0668384i
$551$		−	20.3640i		−	0.0369582i
$552$	7.63698	+	110.576i	0.0138351	+	0.200319i
$553$	−616.281			−1.11443
$554$	367.683	−	805.113i	0.663687	−	1.45327i
$555$	23.8369	+	6.99914i	0.0429494	+	0.0126111i
$556$	−1093.91	−	1262.44i	−1.96746	−	2.27057i
$557$	−296.576	−	461.481i	−0.532453	−	0.828512i	0.465962	−	0.884805i	$-0.345708\pi$
$557$	−296.576	−	461.481i	−0.532453	−	0.828512i	−0.998414	+	0.0562924i	$0.982072\pi$
$558$	−195.321	+	225.413i	−0.350038	+	0.403966i
$559$	−226.582	−	32.5776i	−0.405335	−	0.0582783i
$560$	−1692.04	+	496.827i	−3.02150	+	0.887192i
$561$	−19.0256	−	12.2270i	−0.0339137	−	0.0217950i
$562$	1227.08	−	176.428i	2.18342	−	0.313929i
$563$	607.935	−	277.634i	1.07981	−	0.493134i	0.205580	−	0.978640i	$-0.434092\pi$
$563$	607.935	−	277.634i	1.07981	−	0.493134i	0.874233	+	0.485506i	$0.161365\pi$
$564$	−43.8996	−	96.1267i	−0.0778361	−	0.170437i
$565$	−5.77902	−	40.1939i	−0.0102283	−	0.0711397i
$566$	86.9194	−	135.249i	0.153568	−	0.238956i
$567$	162.002	+	551.729i	0.285718	+	0.973067i
$568$	187.908	−	1306.93i	0.330824	−	2.30093i
$569$	53.7943	+	46.6130i	0.0945418	+	0.0819209i	0.700849	−	0.713309i	$-0.252805\pi$
$569$	53.7943	+	46.6130i	0.0945418	+	0.0819209i	−0.606308	+	0.795230i	$0.707350\pi$
$570$	9.88746	−	6.35429i	0.0173464	−	0.0111479i
$571$	143.358	−	124.221i	0.251065	−	0.217549i	−0.520231	−	0.854026i	$-0.674154\pi$
$571$	143.358	−	124.221i	0.251065	−	0.217549i	0.771296	+	0.636476i	$0.219609\pi$
$572$	−150.386	+	512.166i	−0.262912	+	0.895395i
$573$	−13.8118	−	6.30762i	−0.0241043	−	0.0110081i
$574$		−	1751.42i		−	3.05125i
$575$	−82.6141	−	31.0437i	−0.143677	−	0.0539890i
$576$	−1042.06			−1.80913
$577$	181.273	−	396.932i	0.314164	−	0.687923i	−0.685011	−	0.728533i	$-0.740203\pi$
$577$	181.273	−	396.932i	0.314164	−	0.687923i	0.999175	+	0.0406093i	$0.0129299\pi$
$578$	−61.3679	−	18.0192i	−0.106173	−	0.0311752i
$579$	−25.7609	−	29.7297i	−0.0444921	−	0.0513466i
$580$	215.567	+	335.429i	0.371667	+	0.578325i
$581$	−704.719	+	813.289i	−1.21294	+	1.39981i
$582$	−113.023	−	16.2502i	−0.194197	−	0.0279214i
$583$	−364.639	+	107.068i	−0.625454	+	0.183650i
$584$	2343.08	+	1505.81i	4.01213	+	2.57844i
$585$	−409.682	+	58.9034i	−0.700311	+	0.100690i
$586$	−1023.38	+	467.362i	−1.74638	+	0.797547i
$587$	112.554	+	246.459i	0.191744	+	0.419861i	0.980948	−	0.194270i	$-0.0622338\pi$
$587$	112.554	+	246.459i	0.191744	+	0.419861i	−0.789204	+	0.614131i	$0.789507\pi$
$588$	−0.881920	−	6.13389i	−0.00149986	−	0.0104318i
$589$	13.2810	−	20.6657i	0.0225484	−	0.0350860i
$590$	43.5710	+	148.389i	0.0738491	+	0.251507i
$591$	1.97633	−	13.7457i	0.00334404	−	0.0232583i
$592$	757.090	+	656.022i	1.27887	+	1.10815i
$593$	−158.194	+	101.665i	−0.266768	+	0.171442i	−0.667186	−	0.744891i	$-0.732501\pi$
$593$	−158.194	+	101.665i	−0.266768	+	0.171442i	0.400418	+	0.916333i	$0.368865\pi$
$594$	65.8696	−	57.0763i	0.110892	−	0.0960880i
$595$	190.699	−	649.460i	0.320502	−	1.09153i
$596$	−540.542	−	246.857i	−0.906949	−	0.414190i
$597$		−	8.73291i		−	0.0146280i
$598$	−159.758	+	725.852i	−0.267154	+	1.21380i
$599$	−780.771			−1.30346			−0.651729	−	0.758452i	$-0.725956\pi$
$599$	−780.771			−1.30346			−0.651729	+	0.758452i	$0.725956\pi$
$600$	−7.68168	+	16.8205i	−0.0128028	+	0.0280342i
$601$	−353.591	−	103.824i	−0.588339	−	0.172752i	−0.0260043	−	0.999662i	$-0.508278\pi$
$601$	−353.591	−	103.824i	−0.588339	−	0.172752i	−0.562334	+	0.826910i	$0.690097\pi$
$602$	471.227	+	543.825i	0.782769	+	0.903364i
$603$	−434.043	−	675.385i	−0.719807	−	1.12004i
$604$	1699.37	−	1961.18i	2.81353	−	3.24699i
$605$	−442.631	−	63.6407i	−0.731621	−	0.105191i
$606$	5.35853	−	1.57340i	0.00884245	−	0.00259638i
$607$	118.609	+	76.2252i	0.195401	+	0.125577i	0.634683	−	0.772773i	$-0.281131\pi$
$607$	118.609	+	76.2252i	0.195401	+	0.125577i	−0.439282	+	0.898349i	$0.644767\pi$
$608$	218.052	−	31.3512i	0.358639	−	0.0515645i
$609$	−10.1434	+	4.63234i	−0.0166559	+	0.00760647i
$610$	231.434	+	506.769i	0.379400	+	0.830770i
$611$	−60.8982	−	423.556i	−0.0996698	−	0.693218i
$612$	855.315	−	1330.90i	1.39757	−	2.17467i
$613$	−186.826	−	636.272i	−0.304774	−	1.03796i	−0.959409	−	0.282019i	$-0.908996\pi$
$613$	−186.826	−	636.272i	−0.304774	−	1.03796i	0.654635	−	0.755945i	$-0.272822\pi$
$614$	252.495	−	1756.14i	0.411230	−	2.86016i
$615$	−55.2996	−	47.9174i	−0.0899181	−	0.0779145i
$616$	852.431	−	547.824i	1.38382	−	0.889325i
$617$	135.404	−	117.328i	0.219455	−	0.190159i	−0.538194	−	0.842821i	$-0.680893\pi$
$617$	135.404	−	117.328i	0.219455	−	0.190159i	0.757649	+	0.652662i	$0.226348\pi$
$618$	−3.53757	+	12.0479i	−0.00572423	+	0.0194949i
$619$	724.058	+	330.666i	1.16972	+	0.534194i	0.903026	−	0.429586i	$-0.141341\pi$
$619$	724.058	+	330.666i	1.16972	+	0.534194i	0.266697	+	0.963780i	$0.414068\pi$
$620$			480.986i			0.775784i
$621$	61.6140	−	61.3135i	0.0992173	−	0.0987336i
$622$	278.834			0.448286
$623$	−27.5729	+	60.3763i	−0.0442583	+	0.0969122i
$624$	79.2145	+	23.2595i	0.126946	+	0.0372748i
$625$	462.466	+	533.714i	0.739945	+	0.853942i
$626$	506.611	+	788.302i	0.809283	+	1.25927i
$627$	−2.34463	+	2.70585i	−0.00373944	+	0.00431555i
$628$	−2503.11	−	359.892i	−3.98584	−	0.573077i
$629$	−368.938	+	108.330i	−0.586547	+	0.172226i
$630$	1094.54	+	703.415i	1.73736	+	1.11653i
$631$	293.872	−	42.2524i	0.465724	−	0.0669611i	0.0945416	−	0.995521i	$-0.469861\pi$
$631$	293.872	−	42.2524i	0.465724	−	0.0669611i	0.371183	+	0.928560i	$0.378952\pi$
$632$	−1781.38	+	813.529i	−2.81864	+	1.28723i
$633$	1.04846	+	2.29581i	0.00165633	+	0.00362687i
$634$	145.971	+	1015.25i	0.230238	+	1.60134i
$635$	−273.666	+	425.833i	−0.430970	+	0.670602i
$636$	37.0489	+	126.177i	0.0582530	+	0.198392i
$637$	3.57113	−	24.8378i	0.00560617	−	0.0389918i
$638$	−128.157	−	111.048i	−0.200873	−	0.174057i
$639$	−434.471	+	279.217i	−0.679923	+	0.436960i
$640$	−481.791	+	417.475i	−0.752799	+	0.652304i
$641$	62.9473	−	214.379i	0.0982017	−	0.334444i	−0.895708	−	0.444643i	$-0.853331\pi$
$641$	62.9473	−	214.379i	0.0982017	−	0.334444i	0.993910	+	0.110199i	$0.0351487\pi$
$642$	124.995	+	57.0832i	0.194696	+	0.0889147i
$643$			701.835i			1.09150i	0.837948	+	0.545750i	$0.183755\pi$
$643$			701.835i			1.09150i	−0.837948	+	0.545750i	$0.816245\pi$
$644$	1342.10	−	999.578i	2.08401	−	1.55214i
$645$	30.0632			0.0466096
$646$	−75.5690	+	165.473i	−0.116980	+	0.256150i
$647$	472.075	+	138.614i	0.729638	+	0.214241i	0.625392	−	0.780311i	$-0.284939\pi$
$647$	472.075	+	138.614i	0.729638	+	0.214241i	0.104245	+	0.994552i	$0.466757\pi$
$648$	1196.59	+	1380.94i	1.84659	+	2.13108i
$649$	−25.4705	−	39.6328i	−0.0392457	−	0.0610675i
$650$	−81.1986	+	93.7082i	−0.124921	+	0.144167i
$651$	−13.3148	−	1.91438i	−0.0204529	−	0.00294068i
$652$	−584.419	+	171.601i	−0.896349	+	0.263192i
$653$	507.801	+	326.344i	0.777643	+	0.499761i	0.868251	−	0.496126i	$-0.165245\pi$
$653$	507.801	+	326.344i	0.777643	+	0.499761i	−0.0906077	+	0.995887i	$0.528881\pi$
$654$	116.457	−	16.7440i	0.178069	−	0.0256025i
$655$	628.777	−	287.153i	0.959964	−	0.438401i
$656$	−1225.71	−	2683.93i	−1.86846	−	4.09136i
$657$	−155.042	−	1078.34i	−0.235984	−	1.64131i
$658$	−727.237	+	1131.60i	−1.10522	+	1.71976i
$659$	165.607	+	564.005i	0.251300	+	0.855850i	0.984432	+	0.175764i	$0.0562394\pi$
$659$	165.607	+	564.005i	0.251300	+	0.855850i	−0.733132	+	0.680086i	$0.761942\pi$
$660$	9.97668	−	69.3893i	0.0151162	−	0.105135i
$661$	−759.240	−	657.885i	−1.14862	−	0.995287i	−0.999980	−	0.00639633i	$-0.997964\pi$
$661$	−759.240	−	657.885i	−1.14862	−	0.995287i	−0.148643	−	0.988891i	$-0.547491\pi$
$662$	−29.3732	+	18.8770i	−0.0443704	+	0.0285151i
$663$	−23.9487	+	20.7517i	−0.0361218	+	0.0312997i
$664$	−963.421	+	3281.11i	−1.45093	+	4.94143i
$665$	−97.4742	−	44.5150i	−0.146578	−	0.0669398i
$666$		−	739.101i		−	1.10976i
$667$	−135.138	−	101.680i	−0.202606	−	0.152443i
$668$	−515.760			−0.772096
$669$	−25.7992	+	56.4923i	−0.0385638	+	0.0844428i
$670$	−1734.29	−	509.232i	−2.58849	−	0.760048i
$671$	−111.138	−	128.260i	−0.165630	−	0.191147i
$672$	−65.2181	−	101.481i	−0.0970508	−	0.151014i
$673$	−618.562	+	713.859i	−0.919111	+	1.06071i	0.0788497	+	0.996887i	$0.474875\pi$
$673$	−618.562	+	713.859i	−0.919111	+	1.06071i	−0.997961	+	0.0638246i	$0.979670\pi$
$674$	663.954	+	95.4621i	0.985095	+	0.141635i
$675$	13.9141	−	4.08556i	0.0206136	−	0.00605268i
$676$	−806.443	−	518.269i	−1.19296	−	0.766671i
$677$	−402.105	+	57.8139i	−0.593951	+	0.0853972i	−0.432734	−	0.901522i	$-0.642451\pi$
$677$	−402.105	+	57.8139i	−0.593951	+	0.0853972i	−0.161217	+	0.986919i	$0.551542\pi$
$678$	5.43596	−	2.48252i	0.00801764	−	0.00366154i
$679$	432.472	+	946.981i	0.636925	+	1.39467i
$680$	−306.107	−	2129.02i	−0.450157	−	3.13091i
$681$	−24.4969	+	38.1180i	−0.0359720	+	0.0559735i
$682$	−57.6315	−	196.275i	−0.0845037	−	0.287793i
$683$	30.1142	−	209.449i	0.0440911	−	0.306661i	−0.955828	−	0.293927i	$-0.905038\pi$
$683$	30.1142	−	209.449i	0.0440911	−	0.306661i	0.999919	−	0.0127333i	$-0.00405326\pi$
$684$	−189.282	−	164.014i	−0.276728	−	0.239786i
$685$	−28.7866	+	18.5000i	−0.0420243	+	0.0270074i
$686$	942.233	−	816.449i	1.37352	−	1.19016i
$687$	17.9461	−	61.1187i	0.0261224	−	0.0889646i
$688$	1102.71	+	503.593i	1.60278	+	0.731966i
$689$			532.494i			0.772851i
$690$	7.20122	−	97.3424i	0.0104365	−	0.141076i
$691$	803.388			1.16265			0.581323	−	0.813673i	$-0.302535\pi$
$691$	803.388			1.16265			0.581323	+	0.813673i	$0.302535\pi$
$692$	247.530	−	542.014i	0.357702	−	0.783258i
$693$	−380.287	−	111.662i	−0.548755	−	0.161129i
$694$	118.312	+	136.540i	0.170479	+	0.196743i
$695$	480.268	+	747.311i	0.691033	+	1.07527i
$696$	−23.2049	+	26.7799i	−0.0333404	+	0.0384768i
$697$	1121.00	+	161.175i	1.60832	+	0.231241i
$698$	678.370	−	199.187i	0.971877	−	0.285369i
$699$	−16.9589	−	10.8988i	−0.0242616	−	0.0155920i
$700$	276.342	−	39.7319i	0.394774	−	0.0567599i
$701$	−58.3170	+	26.6325i	−0.0831911	+	0.0379921i	−0.456576	−	0.889684i	$-0.650924\pi$
$701$	−58.3170	+	26.6325i	−0.0831911	+	0.0379921i	0.373385	+	0.927677i	$0.378197\pi$
$702$	−50.7320	−	111.088i	−0.0722679	−	0.158245i
$703$	8.66315	+	60.2535i	0.0123231	+	0.0857091i
$704$	386.388	−	601.231i	0.548847	−	0.854022i
$705$	15.8328	+	53.9216i	0.0224579	+	0.0764846i
$706$	−0.249169	+	1.73301i	−0.000352931	+	0.00245469i
$707$	−38.4811	−	33.3441i	−0.0544287	−	0.0471628i
$708$	−13.7142	+	8.81360i	−0.0193704	+	0.0124486i
$709$	430.388	−	372.933i	0.607035	−	0.525999i	−0.296210	−	0.955123i	$-0.595723\pi$
$709$	430.388	−	372.933i	0.607035	−	0.525999i	0.903246	+	0.429124i	$0.141178\pi$
$710$	−327.586	+	1115.66i	−0.461389	+	1.57135i
$711$	696.778	+	318.208i	0.979997	+	0.447550i
$712$			210.918i			0.296233i
$713$	−70.8268	−	191.321i	−0.0993363	−	0.268332i
$714$	99.6133			0.139514
$715$	117.922	−	258.213i	0.164926	−	0.361137i
$716$	340.648	+	100.023i	0.475766	+	0.139697i
$717$	−26.6822	−	30.7929i	−0.0372137	−	0.0429469i
$718$	1238.39	+	1926.97i	1.72477	+	2.68380i
$719$	−333.449	+	384.821i	−0.463768	+	0.535217i	−0.938668	−	0.344823i	$-0.887939\pi$
$719$	−333.449	+	384.821i	−0.463768	+	0.535217i	0.474899	+	0.880040i	$0.342484\pi$
$720$	2169.58	+	311.938i	3.01330	+	0.433248i
$721$	109.844	−	32.2531i	0.152350	−	0.0447339i
$722$	−1116.05	−	717.244i	−1.54578	−	0.993413i
$723$	−79.2169	+	11.3897i	−0.109567	+	0.0157534i
$724$	−699.671	+	319.529i	−0.966396	+	0.441338i
$725$	−11.7207	−	25.6648i	−0.0161665	−	0.0353997i
$726$	−9.36573	−	65.1401i	−0.0129005	−	0.0897247i
$727$	278.336	−	433.099i	0.382855	−	0.595734i	−0.595327	−	0.803484i	$-0.702977\pi$
$727$	278.336	−	433.099i	0.382855	−	0.595734i	0.978182	+	0.207749i	$0.0666138\pi$
$728$	−400.002	−	1362.28i	−0.549454	−	1.87127i
$729$	100.696	−	700.356i	0.138129	−	0.960708i
$730$	−1853.66	−	1606.21i	−2.53927	−	2.20029i
$731$	−391.441	+	251.564i	−0.535487	+	0.344136i
$732$	−44.3820	+	38.4572i	−0.0606311	+	0.0525372i
$733$	83.6377	−	284.844i	0.114103	−	0.388600i	−0.882562	−	0.470195i	$-0.844183\pi$
$733$	83.6377	−	284.844i	0.114103	−	0.388600i	0.996666	+	0.0815956i	$0.0260016\pi$
$734$	−1512.21	−	690.603i	−2.06023	−	0.940876i
$735$			3.29551i			0.00448368i
$736$	880.709	−	1603.57i	1.19662	−	2.17876i
$737$	550.613			0.747100
$738$	−904.321	+	1980.19i	−1.22537	+	2.68318i
$739$	−687.659	−	201.915i	−0.930526	−	0.273227i	−0.218869	−	0.975754i	$-0.570237\pi$
$739$	−687.659	−	201.915i	−0.930526	−	0.273227i	−0.711657	+	0.702527i	$0.752055\pi$
$740$	−780.521	−	900.769i	−1.05476	−	1.21726i
$741$	2.71224	+	4.22032i	0.00366024	+	0.00569544i
$742$	1096.17	−	1265.04i	1.47731	−	1.70491i
$743$	−155.534	−	22.3624i	−0.209332	−	0.0300974i	0.0368510	−	0.999321i	$-0.488267\pi$
$743$	−155.534	−	22.3624i	−0.209332	−	0.0300974i	−0.246183	+	0.969223i	$0.579176\pi$
$744$	−41.0140	+	12.0428i	−0.0551263	+	0.0161866i
$745$	265.848	+	170.850i	0.356843	+	0.229329i
$746$	507.970	−	73.0351i	0.680925	−	0.0979023i
$747$	1216.70	−	555.647i	1.62878	−	0.743838i
$748$	450.735	+	986.973i	0.602587	+	1.31948i
$749$	−178.296	−	1240.08i	−0.238046	−	1.65565i
$750$	−48.5559	+	75.5545i	−0.0647413	+	0.100739i
$751$	−340.061	−	1158.14i	−0.452811	−	1.54213i	−0.797442	−	0.603395i	$-0.793814\pi$
$751$	−340.061	−	1158.14i	−0.452811	−	1.54213i	0.344631	−	0.938738i	$-0.388004\pi$
$752$	−322.503	+	2243.05i	−0.428860	+	2.98279i
$753$	55.2051	+	47.8355i	0.0733135	+	0.0635265i
$754$	−199.887	+	128.459i	−0.265101	+	0.170370i
$755$	−1042.94	+	903.716i	−1.38138	+	1.19697i
$756$	−77.4688	+	263.835i	−0.102472	+	0.348987i
$757$	619.289	+	282.820i	0.818083	+	0.373606i	0.780086	−	0.625672i	$-0.215175\pi$
$757$	619.289	+	282.820i	0.818083	+	0.373606i	0.0379969	+	0.999278i	$0.487902\pi$
$758$			545.352i			0.719462i
$759$	6.24941	+	29.0699i	0.00823374	+	0.0383003i
$760$	−340.515			−0.448046
$761$	−481.514	+	1054.37i	−0.632738	+	1.38550i	0.273144	+	0.961973i	$0.411936\pi$
$761$	−481.514	+	1054.37i	−0.632738	+	1.38550i	−0.905882	+	0.423530i	$0.860791\pi$
$762$	−71.4761	−	20.9873i	−0.0938006	−	0.0275424i
$763$	−702.465	−	810.688i	−0.920662	−	1.06250i
$764$	393.840	+	612.828i	0.515498	+	0.802130i
$765$	−550.947	+	635.826i	−0.720192	+	0.831145i
$766$	−2363.35	−	339.798i	−3.08531	−	0.443601i
$767$	−63.3378	+	18.5977i	−0.0825786	+	0.0242473i
$768$	3.48596	+	2.24029i	0.00453901	+	0.00291704i
$769$	−854.613	+	122.875i	−1.11133	+	0.159785i	−0.673439	−	0.739243i	$-0.735184\pi$
$769$	−854.613	+	122.875i	−1.11133	+	0.159785i	−0.437892	+	0.899028i	$0.644275\pi$
$770$	−811.690	+	370.687i	−1.05414	+	0.481411i
$771$	14.4817	+	31.7105i	0.0187830	+	0.0411290i
$772$	268.590	+	1868.09i	0.347915	+	2.41980i
$773$	644.466	−	1002.81i	0.833720	−	1.29729i	−0.118831	−	0.992915i	$-0.537915\pi$
$773$	644.466	−	1002.81i	0.833720	−	1.29729i	0.952551	−	0.304380i	$-0.0984491\pi$
$774$	−251.981	−	858.170i	−0.325557	−	1.10875i
$775$	4.84374	−	33.6890i	0.00624999	−	0.0434696i
$776$	2500.15	+	2166.39i	3.22184	+	2.79174i
$777$	28.0419	−	18.0215i	0.0360900	−	0.0231936i
$778$	748.363	−	648.460i	0.961906	−	0.833496i
$779$	50.5125	−	172.030i	0.0648428	−	0.220834i
$780$	−89.3500	−	40.8048i	−0.114551	−	0.0523138i
$781$		−	354.206i		−	0.453528i
$782$	720.780	+	1327.71i	0.921713	+	1.69784i
$783$	27.7889			0.0354903
$784$	−55.2034	+	120.879i	−0.0704126	+	0.154182i
$785$	1290.35	+	378.881i	1.64376	+	0.482650i
$786$	66.6172	+	76.8804i	0.0847547	+	0.0978122i
$787$	−1.42325	−	2.21462i	−0.00180845	−	0.00281400i	0.840348	−	0.542047i	$-0.182351\pi$
$787$	−1.42325	−	2.21462i	−0.00180845	−	0.00281400i	−0.842157	+	0.539233i	$0.818714\pi$
$788$	−436.301	+	503.518i	−0.553681	+	0.638982i
$789$	54.4066	+	7.82248i	0.0689564	+	0.00991443i
$790$	1654.72	−	485.870i	2.09458	−	0.615025i
$791$	−45.8357	−	29.4568i	−0.0579465	−	0.0372400i
$792$	−1246.63	+	179.239i	−1.57403	+	0.226312i
$793$	−216.307	+	98.7842i	−0.272771	+	0.124570i
$794$	−523.277	−	1145.82i	−0.659039	−	1.44309i
$795$	−9.95249	−	69.2211i	−0.0125189	−	0.0870706i
$796$	−226.514	+	352.463i	−0.284566	+	0.442793i
$797$	−110.447	−	376.147i	−0.138578	−	0.471954i	0.860733	−	0.509056i	$-0.170005\pi$
$797$	−110.447	−	376.147i	−0.138578	−	0.471954i	−0.999311	+	0.0371023i	$0.988187\pi$
$798$	2.24430	−	15.6095i	0.00281241	−	0.0195607i
$799$	−657.359	−	569.605i	−0.822727	−	0.712897i
$800$	256.767	−	165.014i	0.320959	−	0.206268i
$801$	62.3489	−	54.0256i	0.0778388	−	0.0674477i
$802$	490.306	−	1669.83i	0.611354	−	2.08208i
$803$	679.651	+	310.386i	0.846390	+	0.386533i
$804$		−	190.530i		−	0.236977i
$805$	−782.108	+	424.585i	−0.971563	+	0.527435i
$806$	−286.626			−0.355616
$807$	−22.3607	+	48.9631i	−0.0277084	+	0.0606730i
$808$	−155.247	−	45.5847i	−0.192138	−	0.0564167i
$809$	542.157	+	625.683i	0.670157	+	0.773403i	0.984401	−	0.175940i	$-0.0562963\pi$
$809$	542.157	+	625.683i	0.670157	+	0.773403i	−0.314244	+	0.949342i	$0.601751\pi$
$810$	−869.956	−	1353.68i	−1.07402	−	1.67121i
$811$	918.424	−	1059.92i	1.13246	−	1.30693i	0.186568	−	0.982442i	$-0.440263\pi$
$811$	918.424	−	1059.92i	1.13246	−	1.30693i	0.945891	−	0.324485i	$-0.105191\pi$
$812$	529.545	+	76.1371i	0.652150	+	0.0937649i
$813$	74.0197	−	21.7341i	0.0910451	−	0.0267332i
$814$	426.435	+	274.053i	0.523876	+	0.336675i
$815$	320.614	−	46.0974i	0.393392	−	0.0565612i
$816$	152.651	−	69.7133i	0.187072	−	0.0854329i
$817$	30.6010	+	67.0068i	0.0374553	+	0.0820156i
$818$	63.5491	+	441.994i	0.0776884	+	0.540335i
$819$	−300.243	+	467.187i	−0.366597	+	0.570435i
$820$	989.029	+	3368.32i	1.20613	+	4.10771i
$821$	4.61742	−	32.1149i	0.00562414	−	0.0391168i	−0.986816	−	0.161845i	$-0.948255\pi$
$821$	4.61742	−	32.1149i	0.00562414	−	0.0391168i	0.992440	+	0.122729i	$0.0391645\pi$
$822$	−3.80583	−	3.29777i	−0.00462996	−	0.00401188i
$823$	−355.190	+	228.267i	−0.431580	+	0.277360i	−0.738342	−	0.674427i	$-0.764391\pi$
$823$	−355.190	+	228.267i	−0.431580	+	0.277360i	0.306762	+	0.951786i	$0.400754\pi$
$824$	274.932	−	238.230i	0.333655	−	0.289114i
$825$	−1.39756	+	4.75966i	−0.00169401	+	0.00576928i
$826$	188.755	+	86.2017i	0.228517	+	0.104360i
$827$			277.705i			0.335798i	0.985804	+	0.167899i	$0.0536982\pi$
$827$			277.705i			0.335798i	−0.985804	+	0.167899i	$0.946302\pi$
$828$	−2033.53	+	437.164i	−2.45595	+	0.527976i
$829$	−1275.77			−1.53893			−0.769466	−	0.638688i	$-0.779477\pi$
$829$	−1275.77			−1.53893			−0.769466	+	0.638688i	$0.779477\pi$
$830$	1250.99	−	2739.28i	1.50722	−	3.30034i
$831$	−47.6058	−	13.9783i	−0.0572874	−	0.0168211i
$832$	−655.778	−	756.808i	−0.788195	−	0.909625i
$833$	−27.5762	−	42.9094i	−0.0331047	−	0.0515119i
$834$	−85.6112	+	98.8006i	−0.102651	+	0.118466i
$835$	271.486	+	39.0338i	0.325133	+	0.0467471i
$836$	164.814	−	48.3939i	0.197146	−	0.0578874i
$837$	28.2006	+	18.1234i	0.0336924	+	0.0216528i
$838$	306.542	−	44.0741i	0.365802	−	0.0525944i
$839$	121.753	−	55.6029i	0.145117	−	0.0662728i	−0.341533	−	0.939870i	$-0.610946\pi$
$839$	121.753	−	55.6029i	0.145117	−	0.0662728i	0.486650	+	0.873597i	$0.338219\pi$
$840$	77.4594	+	169.612i	0.0922136	+	0.201920i
$841$	111.992	+	778.924i	0.133166	+	0.926187i
$842$	−1529.55	+	2380.02i	−1.81656	+	2.82663i
$843$	−19.5786	−	66.6786i	−0.0232249	−	0.0790969i
$844$	17.2325	−	119.854i	0.0204176	−	0.142008i
$845$	385.272	+	333.840i	0.455943	+	0.395077i
$846$	1406.51	−	903.912i	1.66255	−	1.06845i
$847$	−453.457	+	392.922i	−0.535368	+	0.463899i
$848$	794.476	−	2705.74i	0.936882	−	3.19073i
$849$	−8.19787	−	3.74384i	−0.00965591	−	0.00440971i
$850$			252.040i			0.296518i
$851$	443.107	+	243.363i	0.520690	+	0.285972i
$852$	−122.567			−0.143858
$853$	221.635	−	485.313i	0.259830	−	0.568948i	−0.734090	−	0.679052i	$-0.762391\pi$
$853$	221.635	−	485.313i	0.259830	−	0.568948i	0.993920	+	0.110104i	$0.0351184\pi$
$854$	717.232	+	210.598i	0.839850	+	0.246602i
$855$	87.2214	+	100.659i	0.102013	+	0.117730i
$856$	−2152.35	−	3349.13i	−2.51443	−	3.91253i
$857$	−446.707	+	515.528i	−0.521245	+	0.601549i	−0.953942	−	0.299990i	$-0.903017\pi$
$857$	−446.707	+	515.528i	−0.521245	+	0.601549i	0.432697	+	0.901539i	$0.357562\pi$
$858$	41.3500	+	5.94524i	0.0481935	+	0.00692918i
$859$	−1532.83	+	450.078i	−1.78443	+	0.523956i	−0.995853	−	0.0909781i	$-0.971001\pi$
$859$	−1532.83	+	450.078i	−1.78443	+	0.523956i	−0.788578	+	0.614934i	$0.789182\pi$
$860$	−1213.36	−	779.780i	−1.41089	−	0.906721i
$861$	−97.1795	+	13.9723i	−0.112868	+	0.0162280i
$862$	1622.25	−	740.855i	1.88196	−	0.859460i
$863$	115.631	+	253.197i	0.133988	+	0.293392i	0.964719	−	0.263282i	$-0.0848048\pi$
$863$	115.631	+	253.197i	0.133988	+	0.293392i	−0.830732	+	0.556673i	$0.812078\pi$
$864$	42.7822	+	297.557i	0.0495164	+	0.344394i
$865$	−171.316	+	266.572i	−0.198053	+	0.308176i
$866$	378.024	+	1287.43i	0.436517	+	1.48664i
$867$	−0.510243	+	3.54882i	−0.000588516	+	0.00409322i
$868$	487.735	+	422.625i	0.561907	+	0.486895i
$869$	−441.954	+	284.027i	−0.508578	+	0.326843i
$870$	23.5831	−	20.4349i	0.0271070	−	0.0234884i
$871$	217.358	−	740.255i	0.249550	−	0.849891i
$872$	−3100.66	−	1416.02i	−3.55580	−	1.62388i
$873$		−	1293.97i		−	1.48222i
$874$	224.293	−	83.0330i	0.256628	−	0.0950035i
$875$	818.841			0.935819
$876$	107.404	−	235.181i	0.122607	−	0.268472i
$877$	1303.00	+	382.595i	1.48575	+	0.436255i	0.921181	−	0.389134i	$-0.127226\pi$
$877$	1303.00	+	382.595i	1.48575	+	0.436255i	0.564566	+	0.825388i	$0.309044\pi$
$878$	301.470	+	347.915i	0.343360	+	0.396259i
$879$	34.0963	+	53.0549i	0.0387899	+	0.0603583i
$880$	−984.441	+	1136.10i	−1.11868	+	1.29103i
$881$	−1127.92	−	162.170i	−1.28027	−	0.184075i	−0.531589	−	0.847002i	$-0.678405\pi$
$881$	−1127.92	−	162.170i	−1.28027	−	0.184075i	−0.748684	+	0.662927i	$0.769314\pi$
$882$	94.0719	−	27.6220i	0.106658	−	0.0313175i
$883$	−243.632	−	156.573i	−0.275914	−	0.177319i	0.395365	−	0.918524i	$-0.370618\pi$
$883$	−243.632	−	156.573i	−0.275914	−	0.177319i	−0.671279	+	0.741205i	$0.734255\pi$
$884$	1504.84	−	216.363i	1.70230	−	0.244754i
$885$	7.88594	−	3.60139i	0.00891067	−	0.00406936i
$886$	663.536	+	1452.94i	0.748912	+	1.63989i
$887$	−31.2951	−	217.662i	−0.0352820	−	0.245391i	0.964546	−	0.263913i	$-0.0850132\pi$
$887$	−31.2951	−	217.662i	−0.0352820	−	0.245391i	−0.999828	+	0.0185215i	$0.994104\pi$
$888$	57.2667	−	89.1087i	0.0644895	−	0.100348i
$889$	191.347	+	651.669i	0.215239	+	0.733036i
$890$	26.4336	−	183.849i	0.0297006	−	0.206572i
$891$	370.454	+	321.000i	0.415773	+	0.360269i
$892$	2506.56	−	1610.87i	2.81004	−	1.80591i
$893$	−104.068	+	90.1753i	−0.116537	+	0.100980i
$894$	−13.1024	+	44.6227i	−0.0146559	+	0.0499135i
$895$	−171.741	−	78.4313i	−0.191889	−	0.0876328i
$896$			855.371i			0.954655i
$897$	41.5492	+	3.07374i	0.0463202	+	0.00342669i
$898$	1972.33			2.19636
$899$	27.0938	−	59.3271i	0.0301377	−	0.0659924i
$900$	−332.952	−	97.7635i	−0.369947	−	0.108626i
$901$	708.817	+	818.019i	0.786701	+	0.907901i
$902$	−807.182	−	1256.00i	−0.894880	−	1.39246i
$903$	26.4154	−	30.4850i	0.0292530	−	0.0337597i
$904$	−171.374	−	24.6399i	−0.189573	−	0.0272565i
$905$	392.476	−	115.241i	0.433675	−	0.127338i
$906$	−170.851	−	109.799i	−0.188577	−	0.121191i
$907$	−713.813	+	102.631i	−0.787005	+	0.113154i	−0.524088	−	0.851664i	$-0.675594\pi$
$907$	−713.813	+	102.631i	−0.787005	+	0.113154i	−0.262917	+	0.964818i	$0.584684\pi$
$908$	1977.41	−	903.053i	2.17776	−	0.994551i
$909$	26.2907	+	57.5686i	0.0289227	+	0.0633318i
$910$	177.938	+	1237.58i	0.195536	+	1.35998i
$911$	−164.951	+	256.669i	−0.181066	+	0.281745i	−0.919908	−	0.392135i	$-0.871737\pi$
$911$	−164.951	+	256.669i	−0.181066	+	0.281745i	0.738842	+	0.673879i	$0.235373\pi$
$912$	−7.48487	−	25.4911i	−0.00820709	−	0.0279508i
$913$	−130.554	+	908.021i	−0.142994	+	0.994546i
$914$	29.5765	+	25.6282i	0.0323594	+	0.0280396i
$915$	26.2723	−	16.8842i	0.0287129	−	0.0184527i
$916$	−2309.61	+	2001.29i	−2.52140	+	2.18481i
$917$	261.301	−	889.909i	0.284952	−	0.970457i
$918$	−225.806	−	103.122i	−0.245976	−	0.112334i
$919$			532.608i			0.579552i	0.957094	+	0.289776i	$0.0935808\pi$
$919$			532.608i			0.579552i	−0.957094	+	0.289776i	$0.906419\pi$
$920$	−1700.23	+	2259.71i	−1.84808	+	2.45621i
$921$	−99.4557			−0.107987
$922$	−347.407	+	760.715i	−0.376797	+	0.825070i
$923$	−476.201	−	139.825i	−0.515928	−	0.151490i
$924$	−61.5968	−	71.0864i	−0.0666632	−	0.0769334i
$925$	45.5977	+	70.9514i	0.0492948	+	0.0767042i
$926$	−526.117	+	607.171i	−0.568161	+	0.655692i
$927$	−140.845	−	20.2505i	−0.151936	−	0.0218452i
$928$	561.191	−	164.781i	0.604732	−	0.177565i
$929$	956.072	+	614.430i	1.02914	+	0.661389i	0.942278	−	0.334831i	$-0.108679\pi$
$929$	956.072	+	614.430i	1.02914	+	0.661389i	0.0868631	+	0.996220i	$0.472316\pi$
$930$	37.2597	−	5.35714i	0.0400642	−	0.00576036i
$931$	−7.34523	+	3.35445i	−0.00788961	+	0.00360307i
$932$	401.772	+	879.758i	0.431086	+	0.943947i
$933$	−2.22445	−	15.4714i	−0.00238419	−	0.0165824i
$934$	1410.11	−	2194.17i	1.50975	−	2.34922i
$935$	−162.562	−	553.636i	−0.173863	−	0.592124i
$936$	−251.146	+	1746.76i	−0.268318	+	1.86619i
$937$	160.112	+	138.738i	0.170878	+	0.148066i	0.736101	−	0.676871i	$-0.236665\pi$
$937$	160.112	+	138.738i	0.170878	+	0.148066i	−0.565224	+	0.824938i	$0.691210\pi$
$938$	−2040.23	+	1311.18i	−2.17508	+	1.39784i
$939$	39.6982	−	34.3987i	0.0422771	−	0.0366333i
$940$	759.602	−	2586.97i	0.808087	−	2.75209i
$941$	−1117.51	−	510.348i	−1.18757	−	0.542347i	−0.279089	−	0.960265i	$-0.590032\pi$
$941$	−1117.51	−	510.348i	−1.18757	−	0.542347i	−0.908484	+	0.417919i	$0.862760\pi$
$942$			197.912i			0.210098i
$943$	−889.401	−	1194.17i	−0.943161	−	1.26635i
$944$	349.582			0.370320
$945$	60.7456	−	133.014i	0.0642811	−	0.140756i
$946$	588.566	+	172.819i	0.622163	+	0.182684i
$947$	−929.308	−	1072.48i	−0.981318	−	1.13250i	−0.991176	−	0.132550i	$-0.957684\pi$
$947$	−929.308	−	1072.48i	−0.981318	−	1.13250i	0.00985850	−	0.999951i	$-0.496862\pi$
$948$	98.2825	+	152.931i	0.103674	+	0.161319i
$949$	685.587	−	791.210i	0.722431	−	0.833730i
$950$	39.4949	+	5.67851i	0.0415736	+	0.00597738i
$951$	55.1678	−	16.1987i	0.0580103	−	0.0170334i
$952$	−2427.85	−	1560.29i	−2.55027	−	1.63896i
$953$	418.896	−	60.2282i	0.439555	−	0.0631985i	0.0810153	−	0.996713i	$-0.474184\pi$
$953$	418.896	−	60.2282i	0.439555	−	0.0631985i	0.358540	+	0.933514i	$0.383275\pi$
$954$	−1892.53	+	864.291i	−1.98379	+	0.905966i
$955$	−160.930	−	352.387i	−0.168513	−	0.368992i
$956$	278.196	+	1934.90i	0.291000	+	2.02395i
$957$	−5.13925	+	7.99682i	−0.00537016	+	0.00835614i
$958$	−726.405	−	2473.91i	−0.758251	−	2.58237i
$959$	−6.53413	+	45.4458i	−0.00681348	+	0.0473888i
$960$	99.3923	+	86.1239i	0.103534	+	0.0897124i
$961$	−742.257	+	477.020i	−0.772380	+	0.496379i
$962$	536.781	−	465.123i	0.557984	−	0.483496i
$963$	−438.712	+	1494.12i	−0.455568	+	1.55152i
$964$	3492.65	+	1595.04i	3.62308	+	1.65460i
$965$		−	1003.65i		−	1.04005i
$966$	−92.3807	−	92.8334i	−0.0956322	−	0.0961008i
$967$	−1598.46			−1.65301			−0.826506	−	0.562928i	$-0.809675\pi$
$967$	−1598.46			−1.65301			−0.826506	+	0.562928i	$0.809675\pi$
$968$	−792.049	+	1734.35i	−0.818233	+	1.79168i
$969$	9.78432	+	2.87294i	0.0100973	+	0.00296485i
$970$	−1907.78	−	2201.70i	−1.96679	−	2.26979i
$971$	−356.315	−	554.436i	−0.366956	−	0.570995i	0.607849	−	0.794053i	$-0.292033\pi$
$971$	−356.315	−	554.436i	−0.366956	−	0.570995i	−0.974805	+	0.223057i	$0.928396\pi$
$972$	335.998	−	387.763i	0.345677	−	0.398933i
$973$	1179.79	+	169.628i	1.21253	+	0.174335i
$974$	330.239	−	96.9668i	0.339054	−	0.0995552i
$975$	5.84728	+	3.75782i	0.00599721	+	0.00385417i
$976$	1246.50	−	179.219i	1.27715	−	0.183626i
$977$	484.287	−	221.166i	0.495688	−	0.226373i	−0.151854	−	0.988403i	$-0.548524\pi$
$977$	484.287	−	221.166i	0.495688	−	0.226373i	0.647542	+	0.762030i	$0.275797\pi$
$978$	19.8023	+	43.3609i	0.0202477	+	0.0443363i
$979$	8.05236	+	56.0054i	0.00822508	+	0.0572067i
$980$	85.4789	−	133.008i	0.0872234	−	0.135722i
$981$	375.632	+	1279.29i	0.382908	+	1.30406i
$982$	−369.114	+	2567.24i	−0.375880	+	2.61430i
$983$	−278.764	−	241.550i	−0.283585	−	0.245728i	0.501439	−	0.865193i	$-0.332804\pi$
$983$	−278.764	−	241.550i	−0.283585	−	0.245728i	−0.785024	+	0.619465i	$0.787350\pi$
$984$	−262.456	+	168.670i	−0.266724	+	0.171413i
$985$	267.768	−	232.022i	0.271845	−	0.235555i
$986$	−136.070	+	463.414i	−0.138003	+	0.469993i
$987$	68.5899	+	31.3240i	0.0694933	+	0.0317365i
$988$		−	240.684i		−	0.243607i
$989$	597.461	+	131.500i	0.604106	+	0.132962i
$990$	1109.11			1.12031
$991$	401.182	−	878.467i	0.404826	−	0.886445i	−0.591932	−	0.805988i	$-0.701635\pi$
$991$	401.182	−	878.467i	0.404826	−	0.886445i	0.996758	−	0.0804572i	$-0.0256380\pi$
$992$	676.972	+	198.777i	0.682431	+	0.200380i
$993$	1.28174	+	1.47921i	0.00129078	+	0.00148964i
$994$	843.471	+	1312.47i	0.848563	+	1.32039i
$995$	145.908	−	168.387i	0.146641	−	0.169233i
$996$	314.205	+	45.1758i	0.315466	+	0.0453572i
$997$	1497.61	−	439.739i	1.50212	−	0.441062i	0.575734	−	0.817637i	$-0.304716\pi$
$997$	1497.61	−	439.739i	1.50212	−	0.441062i	0.926386	+	0.376575i	$0.122898\pi$
$998$	−1955.24	−	1256.56i	−1.95916	−	1.25907i
$999$	−82.2226	+	11.8218i	−0.0823049	+	0.0118337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.17.1	✓	30
3.2	odd	2		207.3.j.a.109.3		30
4.3	odd	2		368.3.p.a.17.2		30
23.2	even	11		529.3.b.b.528.2		30
23.19	odd	22	inner	23.3.d.a.19.1	yes	30
23.21	odd	22		529.3.b.b.528.1		30
69.65	even	22		207.3.j.a.19.3		30
92.19	even	22		368.3.p.a.65.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.17.1	✓	30	1.1	even	1	trivial
23.3.d.a.19.1	yes	30	23.19	odd	22	inner
207.3.j.a.19.3		30	69.65	even	22
207.3.j.a.109.3		30	3.2	odd	2
368.3.p.a.17.2		30	4.3	odd	2
368.3.p.a.65.2		30	92.19	even	22
529.3.b.b.528.1		30	23.21	odd	22
529.3.b.b.528.2		30	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55977 + 3.41542i) q^{2} +(0.201951 + 0.0592983i) q^{3} +(-6.61275 - 7.63152i) q^{4} +(2.90325 + 4.51755i) q^{5} +(-0.517526 + 0.597257i) q^{6} +(7.13192 + 1.02541i) q^{7} +(21.9686 - 6.45058i) q^{8} +(-7.53401 - 4.84182i) q^{9} +O(q^{10})\)	\(q+(-1.55977 + 3.41542i) q^{2} +(0.201951 + 0.0592983i) q^{3} +(-6.61275 - 7.63152i) q^{4} +(2.90325 + 4.51755i) q^{5} +(-0.517526 + 0.597257i) q^{6} +(7.13192 + 1.02541i) q^{7} +(21.9686 - 6.45058i) q^{8} +(-7.53401 - 4.84182i) q^{9} +(-19.9577 + 2.86949i) q^{10} +(5.58711 - 2.55155i) q^{11} +(-0.882918 - 1.93332i) q^{12} +(-1.22480 - 8.51866i) q^{13} +(-14.6264 + 22.7590i) q^{14} +(0.318433 + 1.08448i) q^{15} +(-6.48624 + 45.1128i) q^{16} +(-13.2210 - 11.4560i) q^{17} +(28.2881 - 18.1797i) q^{18} +(-2.09304 + 1.81363i) q^{19} +(15.2773 - 52.0296i) q^{20} +(1.37950 + 0.629994i) q^{21} +23.0621i q^{22} +(1.58473 + 22.9453i) q^{23} +4.81911 q^{24} +(-1.59400 + 3.49038i) q^{25} +(31.0052 + 9.10394i) q^{26} +(-2.47489 - 2.85618i) q^{27} +(-39.3361 - 61.2081i) q^{28} +(-4.81519 + 5.55702i) q^{29} +(-4.20065 - 0.603962i) q^{30} +(-8.51070 + 2.49897i) q^{31} +(-66.9163 - 43.0045i) q^{32} +(1.27963 - 0.183983i) q^{33} +(59.7487 - 27.2863i) q^{34} +(16.0734 + 35.1958i) q^{35} +(12.8701 + 89.5137i) q^{36} +(11.8833 - 18.4907i) q^{37} +(-2.92964 - 9.97743i) q^{38} +(0.257792 - 1.79299i) q^{39} +(92.9213 + 80.5168i) q^{40} +(-54.4615 + 35.0003i) q^{41} +(-4.30339 + 3.72891i) q^{42} +(7.49361 - 25.5209i) q^{43} +(-56.4183 - 25.7654i) q^{44} -48.0923i q^{45} +(-80.8397 - 30.3769i) q^{46} +49.7210 q^{47} +(-3.98502 + 8.72598i) q^{48} +(2.79758 + 0.821444i) q^{49} +(-9.43483 - 10.8884i) q^{50} +(-1.99067 - 3.09754i) q^{51} +(-56.9111 + 65.6789i) q^{52} +(-61.2431 - 8.80543i) q^{53} +(13.6153 - 3.99781i) q^{54} +(27.7475 + 17.8323i) q^{55} +(163.293 - 23.4780i) q^{56} +(-0.530237 + 0.242151i) q^{57} +(-11.4690 - 25.1135i) q^{58} +(-1.09158 - 7.59212i) q^{59} +(6.17054 - 9.60155i) q^{60} +(-7.78445 - 26.5114i) q^{61} +(4.73971 - 32.9654i) q^{62} +(-48.7671 - 42.2569i) q^{63} +(97.8859 - 62.9075i) q^{64} +(34.9276 - 30.2649i) q^{65} +(-1.36754 + 4.65743i) q^{66} +(81.5437 + 37.2398i) q^{67} +176.652i q^{68} +(-1.04058 + 4.72782i) q^{69} -145.279 q^{70} +(23.9561 - 52.4566i) q^{71} +(-196.745 - 57.7694i) q^{72} +(79.6614 + 91.9342i) q^{73} +(44.6183 + 69.4275i) q^{74} +(-0.528885 + 0.610366i) q^{75} +(27.6814 + 3.97999i) q^{76} +(42.4632 - 12.4683i) q^{77} +(5.72169 + 3.67711i) q^{78} +(-84.6615 + 12.1725i) q^{79} +(-222.631 + 101.672i) q^{80} +(33.1525 + 72.5939i) q^{81} +(-34.5932 - 240.601i) q^{82} +(-80.7470 + 125.645i) q^{83} +(-4.31444 - 14.6936i) q^{84} +(13.3694 - 92.9861i) q^{85} +(75.4762 + 65.4005i) q^{86} +(-1.30196 + 0.836716i) q^{87} +(106.282 - 92.0941i) q^{88} +(-2.59531 + 8.83880i) q^{89} +(164.255 + 75.0129i) q^{90} -62.0103i q^{91} +(164.628 - 163.826i) q^{92} -1.86693 q^{93} +(-77.5532 + 169.818i) q^{94} +(-14.2698 - 4.18998i) q^{95} +(-10.9638 - 12.6528i) q^{96} +(78.1151 + 121.550i) q^{97} +(-7.16915 + 8.27364i) q^{98} +(-54.4475 - 7.82837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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