LMFDB - Embedded newform 23.3.d.a.11.3

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			11.3
Character	$\chi$	$=$	23.11
Dual form			23.3.d.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20995 - 0.777587i) q^{2} +(-0.238691 + 1.66013i) q^{3} +(-0.802326 + 1.75685i) q^{4} +(-2.65558 - 9.04406i) q^{5} +(1.00209 + 2.19428i) q^{6} +(-5.31379 + 4.60443i) q^{7} +(1.21408 + 8.44409i) q^{8} +(5.93637 + 1.74307i) q^{9} +O(q^{10})$	\(q+(1.20995 - 0.777587i) q^{2} +(-0.238691 + 1.66013i) q^{3} +(-0.802326 + 1.75685i) q^{4} +(-2.65558 - 9.04406i) q^{5} +(1.00209 + 2.19428i) q^{6} +(-5.31379 + 4.60443i) q^{7} +(1.21408 + 8.44409i) q^{8} +(5.93637 + 1.74307i) q^{9} +(-10.2457 - 8.87791i) q^{10} +(1.86461 - 2.90139i) q^{11} +(-2.72510 - 1.75131i) q^{12} +(7.08824 - 8.18027i) q^{13} +(-2.84907 + 9.70305i) q^{14} +(15.6482 - 2.24987i) q^{15} +(2.97583 + 3.43429i) q^{16} +(-8.16077 + 3.72690i) q^{17} +(8.53809 - 2.50701i) q^{18} +(-3.35280 - 1.53117i) q^{19} +(18.0197 + 2.59084i) q^{20} +(-6.37561 - 9.92064i) q^{21} -4.96042i q^{22} +(22.4639 + 4.93692i) q^{23} -14.3081 q^{24} +(-53.7117 + 34.5184i) q^{25} +(2.21554 - 15.4094i) q^{26} +(-10.5813 + 23.1699i) q^{27} +(-3.82589 - 13.0298i) q^{28} +(-10.2313 - 22.4035i) q^{29} +(17.1841 - 14.8901i) q^{30} +(-1.70705 - 11.8728i) q^{31} +(-26.4704 - 7.77241i) q^{32} +(4.37162 + 3.78803i) q^{33} +(-6.97612 + 10.8551i) q^{34} +(55.7539 + 35.8309i) q^{35} +(-7.82522 + 9.03079i) q^{36} +(-3.28873 + 11.2004i) q^{37} +(-5.24734 + 0.754453i) q^{38} +(11.8884 + 13.7200i) q^{39} +(73.1448 - 33.4041i) q^{40} +(25.6809 - 7.54059i) q^{41} +(-15.4283 - 7.04587i) q^{42} +(-16.9933 - 2.44327i) q^{43} +(3.60127 + 5.60369i) q^{44} -58.3178i q^{45} +(31.0190 - 11.4942i) q^{46} -40.2594 q^{47} +(-6.41168 + 4.12054i) q^{48} +(0.0622113 - 0.432689i) q^{49} +(-38.1473 + 83.5309i) q^{50} +(-4.23924 - 14.4375i) q^{51} +(8.68441 + 19.0162i) q^{52} +(-12.2941 + 10.6529i) q^{53} +(5.21372 + 36.2622i) q^{54} +(-31.1919 - 9.15878i) q^{55} +(-45.3315 - 39.2800i) q^{56} +(3.34224 - 5.20062i) q^{57} +(-29.8000 - 19.1513i) q^{58} +(37.3160 - 43.0650i) q^{59} +(-8.60228 + 29.2967i) q^{60} +(100.863 - 14.5019i) q^{61} +(-11.2975 - 13.0381i) q^{62} +(-39.5705 + 18.0712i) q^{63} +(-55.5121 + 16.2998i) q^{64} +(-92.8062 - 42.3832i) q^{65} +(8.23496 + 1.18401i) q^{66} +(64.9484 + 101.062i) q^{67} -17.3274i q^{68} +(-13.5579 + 36.1147i) q^{69} +95.3210 q^{70} +(79.3329 - 50.9841i) q^{71} +(-7.51147 + 52.2434i) q^{72} +(4.06137 - 8.89315i) q^{73} +(4.73008 + 16.1092i) q^{74} +(-44.4846 - 97.4078i) q^{75} +(5.38008 - 4.66187i) q^{76} +(3.45108 + 24.0028i) q^{77} +(25.0529 + 7.35618i) q^{78} +(-63.5192 - 55.0397i) q^{79} +(23.1574 - 36.0336i) q^{80} +(10.9040 + 7.00759i) q^{81} +(25.2091 - 29.0928i) q^{82} +(-7.26126 + 24.7296i) q^{83} +(22.5444 - 3.24139i) q^{84} +(55.3778 + 63.9094i) q^{85} +(-22.4609 + 10.2576i) q^{86} +(39.6349 - 11.6379i) q^{87} +(26.7633 + 12.2224i) q^{88} +(-53.1052 - 7.63538i) q^{89} +(-45.3471 - 70.5615i) q^{90} +76.1055i q^{91} +(-26.6968 + 35.5047i) q^{92} +20.1178 q^{93} +(-48.7118 + 31.3052i) q^{94} +(-4.94441 + 34.3891i) q^{95} +(19.2215 - 42.0892i) q^{96} +(-5.80052 - 19.7548i) q^{97} +(-0.261181 - 0.571906i) q^{98} +(16.1263 - 13.9735i) 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 $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	1.20995	−	0.777587i	0.604974	−	0.388793i	−0.201995	−	0.979386i	$-0.564743\pi$
$2$	1.20995	−	0.777587i	0.604974	−	0.388793i	0.806969	+	0.590593i	$0.201106\pi$
$3$	−0.238691	+	1.66013i	−0.0795637	+	0.553378i	0.910581	+	0.413330i	$0.135635\pi$
$3$	−0.238691	+	1.66013i	−0.0795637	+	0.553378i	−0.990145	+	0.140047i	$0.955275\pi$
$4$	−0.802326	+	1.75685i	−0.200582	+	0.439212i
$5$	−2.65558	−	9.04406i	−0.531115	−	1.80881i	−0.585988	−	0.810319i	$-0.699294\pi$
$5$	−2.65558	−	9.04406i	−0.531115	−	1.80881i	0.0548730	−	0.998493i	$-0.482525\pi$
$6$	1.00209	+	2.19428i	0.167016	+	0.365713i
$7$	−5.31379	+	4.60443i	−0.759113	+	0.657775i	−0.945839	−	0.324637i	$-0.894758\pi$
$7$	−5.31379	+	4.60443i	−0.759113	+	0.657775i	0.186726	+	0.982412i	$0.440212\pi$
$8$	1.21408	+	8.44409i	0.151760	+	1.05551i
$9$	5.93637	+	1.74307i	0.659596	+	0.193675i
$10$	−10.2457	−	8.87791i	−1.02457	−	0.887791i
$11$	1.86461	−	2.90139i	0.169510	−	0.263762i	−0.746097	−	0.665837i	$-0.768075\pi$
$11$	1.86461	−	2.90139i	0.169510	−	0.263762i	0.915607	+	0.402075i	$0.131711\pi$
$12$	−2.72510	−	1.75131i	−0.227091	−	0.145943i
$13$	7.08824	−	8.18027i	0.545249	−	0.629251i	−0.414520	−	0.910040i	$-0.636051\pi$
$13$	7.08824	−	8.18027i	0.545249	−	0.629251i	0.959770	+	0.280789i	$0.0905960\pi$
$14$	−2.84907	+	9.70305i	−0.203505	+	0.693075i
$15$	15.6482	−	2.24987i	1.04321	−	0.149992i
$16$	2.97583	+	3.43429i	0.185989	+	0.214643i
$17$	−8.16077	+	3.72690i	−0.480045	+	0.219229i	−0.640715	−	0.767779i	$-0.721362\pi$
$17$	−8.16077	+	3.72690i	−0.480045	+	0.219229i	0.160670	+	0.987008i	$0.448635\pi$
$18$	8.53809	−	2.50701i	0.474338	−	0.139278i
$19$	−3.35280	−	1.53117i	−0.176463	−	0.0805881i	0.325225	−	0.945637i	$-0.394560\pi$
$19$	−3.35280	−	1.53117i	−0.176463	−	0.0805881i	−0.501688	+	0.865049i	$0.667287\pi$
$20$	18.0197	+	2.59084i	0.900985	+	0.129542i
$21$	−6.37561	−	9.92064i	−0.303600	−	0.472411i
$22$		−	4.96042i		−	0.225474i
$23$	22.4639	+	4.93692i	0.976691	+	0.214649i
$23$	22.4639	+	4.93692i	0.976691	+	0.214649i
$24$	−14.3081			−0.596171
$25$	−53.7117	+	34.5184i	−2.14847	+	1.38074i
$26$	2.21554	−	15.4094i	0.0852131	−	0.592670i
$27$	−10.5813	+	23.1699i	−0.391901	+	0.858143i
$28$	−3.82589	−	13.0298i	−0.136639	−	0.465349i
$29$	−10.2313	−	22.4035i	−0.352805	−	0.772534i	−0.999948	−	0.0101664i	$-0.996764\pi$
$29$	−10.2313	−	22.4035i	−0.352805	−	0.772534i	0.647144	−	0.762368i	$-0.275963\pi$
$30$	17.1841	−	14.8901i	0.572802	−	0.496336i
$31$	−1.70705	−	11.8728i	−0.0550660	−	0.382992i	−0.998654	−	0.0518701i	$-0.983482\pi$
$31$	−1.70705	−	11.8728i	−0.0550660	−	0.382992i	0.943588	−	0.331122i	$-0.107427\pi$
$32$	−26.4704	−	7.77241i	−0.827199	−	0.242888i
$33$	4.37162	+	3.78803i	0.132473	+	0.114789i
$34$	−6.97612	+	10.8551i	−0.205180	+	0.319266i
$35$	55.7539	+	35.8309i	1.59297	+	1.02374i
$36$	−7.82522	+	9.03079i	−0.217367	+	0.250855i
$37$	−3.28873	+	11.2004i	−0.0888847	+	0.302713i	−0.991922	−	0.126848i	$-0.959514\pi$
$37$	−3.28873	+	11.2004i	−0.0888847	+	0.302713i	0.903037	+	0.429562i	$0.141332\pi$
$38$	−5.24734	+	0.754453i	−0.138088	+	0.0198540i
$39$	11.8884	+	13.7200i	0.304832	+	0.351794i
$40$	73.1448	−	33.4041i	1.82862	−	0.835103i
$41$	25.6809	−	7.54059i	0.626363	−	0.183917i	0.0468793	−	0.998901i	$-0.485072\pi$
$41$	25.6809	−	7.54059i	0.626363	−	0.183917i	0.579484	+	0.814984i	$0.303254\pi$
$42$	−15.4283	−	7.04587i	−0.367341	−	0.167759i
$43$	−16.9933	−	2.44327i	−0.395194	−	0.0568203i	−0.0581466	−	0.998308i	$-0.518519\pi$
$43$	−16.9933	−	2.44327i	−0.395194	−	0.0568203i	−0.337047	+	0.941488i	$0.609428\pi$
$44$	3.60127	+	5.60369i	0.0818471	+	0.127357i
$45$		−	58.3178i		−	1.29595i
$46$	31.0190	−	11.4942i	0.674327	−	0.249874i
$47$	−40.2594			−0.856583			−0.428292	−	0.903641i	$-0.640884\pi$
$47$	−40.2594			−0.856583			−0.428292	+	0.903641i	$0.640884\pi$
$48$	−6.41168	+	4.12054i	−0.133577	+	0.0858445i
$49$	0.0622113	−	0.432689i	0.00126962	−	0.00883039i
$50$	−38.1473	+	83.5309i	−0.762946	+	1.67062i
$51$	−4.23924	−	14.4375i	−0.0831224	−	0.283089i
$52$	8.68441	+	19.0162i	0.167008	+	0.365696i
$53$	−12.2941	+	10.6529i	−0.231965	+	0.200999i	−0.763086	−	0.646297i	$-0.776317\pi$
$53$	−12.2941	+	10.6529i	−0.231965	+	0.200999i	0.531121	+	0.847296i	$0.321771\pi$
$54$	5.21372	+	36.2622i	0.0965504	+	0.671523i
$55$	−31.1919	−	9.15878i	−0.567126	−	0.166523i
$56$	−45.3315	−	39.2800i	−0.809492	−	0.701429i
$57$	3.34224	−	5.20062i	0.0586357	−	0.0912390i
$58$	−29.8000	−	19.1513i	−0.513794	−	0.330195i
$59$	37.3160	−	43.0650i	0.632475	−	0.729915i	−0.345551	−	0.938400i	$-0.612308\pi$
$59$	37.3160	−	43.0650i	0.632475	−	0.729915i	0.978025	+	0.208485i	$0.0668534\pi$
$60$	−8.60228	+	29.2967i	−0.143371	+	0.488278i
$61$	100.863	−	14.5019i	1.65349	−	0.237737i	0.748492	−	0.663144i	$-0.230778\pi$
$61$	100.863	−	14.5019i	1.65349	−	0.237737i	0.905002	+	0.425407i	$0.139869\pi$
$62$	−11.2975	−	13.0381i	−0.182218	−	0.210291i
$63$	−39.5705	+	18.0712i	−0.628103	+	0.286845i
$64$	−55.5121	+	16.2998i	−0.867376	+	0.254685i
$65$	−92.8062	−	42.3832i	−1.42779	−	0.652049i
$66$	8.23496	+	1.18401i	0.124772	+	0.0179395i
$67$	64.9484	+	101.062i	0.969380	+	1.50838i	0.857385	+	0.514676i	$0.172088\pi$
$67$	64.9484	+	101.062i	0.969380	+	1.50838i	0.111995	+	0.993709i	$0.464276\pi$
$68$		−	17.3274i		−	0.254815i
$69$	−13.5579	+	36.1147i	−0.196491	+	0.523401i
$70$	95.3210			1.36173
$71$	79.3329	−	50.9841i	1.11736	−	0.718086i	0.154479	−	0.987996i	$-0.450630\pi$
$71$	79.3329	−	50.9841i	1.11736	−	0.718086i	0.962886	+	0.269910i	$0.0869938\pi$
$72$	−7.51147	+	52.2434i	−0.104326	+	0.725603i
$73$	4.06137	−	8.89315i	0.0556352	−	0.121824i	−0.879773	−	0.475395i	$-0.842305\pi$
$73$	4.06137	−	8.89315i	0.0556352	−	0.121824i	0.935408	+	0.353571i	$0.115033\pi$
$74$	4.73008	+	16.1092i	0.0639200	+	0.217692i
$75$	−44.4846	−	97.4078i	−0.593128	−	1.29877i
$76$	5.38008	−	4.66187i	0.0707906	−	0.0613404i
$77$	3.45108	+	24.0028i	0.0448193	+	0.311725i
$78$	25.0529	+	7.35618i	0.321191	+	0.0943101i
$79$	−63.5192	−	55.0397i	−0.804040	−	0.696705i	0.152501	−	0.988303i	$-0.451267\pi$
$79$	−63.5192	−	55.0397i	−0.804040	−	0.696705i	−0.956541	+	0.291599i	$0.905813\pi$
$80$	23.1574	−	36.0336i	0.289467	−	0.450420i
$81$	10.9040	+	7.00759i	0.134617	+	0.0865134i
$82$	25.2091	−	29.0928i	0.307428	−	0.354791i
$83$	−7.26126	+	24.7296i	−0.0874851	+	0.297947i	−0.991600	−	0.129343i	$-0.958713\pi$
$83$	−7.26126	+	24.7296i	−0.0874851	+	0.297947i	0.904115	+	0.427289i	$0.140531\pi$
$84$	22.5444	−	3.24139i	0.268385	−	0.0385880i
$85$	55.3778	+	63.9094i	0.651504	+	0.751876i
$86$	−22.4609	+	10.2576i	−0.261173	+	0.119274i
$87$	39.6349	−	11.6379i	0.455574	−	0.133769i
$88$	26.7633	+	12.2224i	0.304129	+	0.138891i
$89$	−53.1052	−	7.63538i	−0.596688	−	0.0857908i	−0.162648	−	0.986684i	$-0.552003\pi$
$89$	−53.1052	−	7.63538i	−0.596688	−	0.0857908i	−0.434040	+	0.900893i	$0.642912\pi$
$90$	−45.3471	−	70.5615i	−0.503857	−	0.784016i
$91$			76.1055i			0.836325i
$92$	−26.6968	+	35.5047i	−0.290183	+	0.385920i
$93$	20.1178			0.216321
$94$	−48.7118	+	31.3052i	−0.518211	+	0.333034i
$95$	−4.94441	+	34.3891i	−0.0520464	+	0.361991i
$96$	19.2215	−	42.0892i	0.200224	−	0.438429i
$97$	−5.80052	−	19.7548i	−0.0597992	−	0.203657i	0.924175	−	0.381970i	$-0.124754\pi$
$97$	−5.80052	−	19.7548i	−0.0597992	−	0.203657i	−0.983974	+	0.178313i	$0.942936\pi$
$98$	−0.261181	−	0.571906i	−0.00266511	−	0.00583578i
$99$	16.1263	−	13.9735i	0.162892	−	0.141147i
$100$	−17.5493	−	122.058i	−0.175493	−	1.22058i
$101$	−9.06536	−	2.66183i	−0.0897561	−	0.0263548i	0.236546	−	0.971620i	$-0.423985\pi$
$101$	−9.06536	−	2.66183i	−0.0897561	−	0.0263548i	−0.326302	+	0.945265i	$0.605803\pi$
$102$	−16.3557	−	14.1723i	−0.160350	−	0.138944i
$103$	−72.7900	+	113.263i	−0.706699	+	1.09964i	0.283363	+	0.959013i	$0.408550\pi$
$103$	−72.7900	+	113.263i	−0.706699	+	1.09964i	−0.990062	+	0.140632i	$0.955087\pi$
$104$	77.6806	+	49.9223i	0.746929	+	0.480022i
$105$	−72.7920	+	84.0064i	−0.693257	+	0.800061i
$106$	−6.59169	+	22.4492i	−0.0621858	+	0.211785i
$107$	−118.240	+	17.0003i	−1.10504	+	0.158881i	−0.670601	−	0.741818i	$-0.733964\pi$
$107$	−118.240	+	17.0003i	−1.10504	+	0.158881i	−0.434443	+	0.900699i	$0.643055\pi$
$108$	−32.2163	−	37.1796i	−0.298299	−	0.344255i
$109$	51.2604	−	23.4099i	0.470279	−	0.214769i	−0.166156	−	0.986099i	$-0.553136\pi$
$109$	51.2604	−	23.4099i	0.470279	−	0.214769i	0.636435	+	0.771330i	$0.280408\pi$
$110$	−44.8624	+	13.1728i	−0.407840	+	0.119753i
$111$	−17.8092	−	8.13317i	−0.160443	−	0.0732718i
$112$	−31.6259	−	4.54711i	−0.282374	−	0.0405992i
$113$	−4.27948	−	6.65900i	−0.0378715	−	0.0589292i	0.821802	−	0.569774i	$-0.192969\pi$
$113$	−4.27948	−	6.65900i	−0.0378715	−	0.0589292i	−0.859673	+	0.510844i	$0.829333\pi$
$114$		−	8.89136i		−	0.0779944i
$115$	−15.0048	−	216.275i	−0.130476	−	1.88066i
$116$	47.5684			0.410073
$117$	56.3372	−	36.2057i	0.481515	−	0.309451i
$118$	11.6637	−	81.1228i	0.0988449	−	0.687481i
$119$	26.2044	−	57.3796i	0.220205	−	0.482182i
$120$	37.9963	+	129.403i	0.316636	+	1.07836i
$121$	45.3239	+	99.2456i	0.374578	+	0.820211i
$122$	110.763	−	95.9764i	0.907891	−	0.786692i
$123$	6.38858	+	44.4336i	0.0519397	+	0.361248i
$124$	22.2283	+	6.52681i	0.179260	+	0.0526355i
$125$	276.732	+	239.790i	2.21386	+	1.91832i
$126$	−33.8263	+	52.6347i	−0.268463	+	0.417736i
$127$	−76.3448	−	49.0638i	−0.601140	−	0.386329i	0.204385	−	0.978890i	$-0.434480\pi$
$127$	−76.3448	−	49.0638i	−0.601140	−	0.386329i	−0.805525	+	0.592561i	$0.798117\pi$
$128$	17.7727	−	20.5107i	0.138849	−	0.160240i
$129$	8.11232	−	27.6280i	0.0628862	−	0.214171i
$130$	−145.247	+	20.8834i	−1.11729	+	0.160642i
$131$	−42.2285	−	48.7343i	−0.322355	−	0.372017i	0.571324	−	0.820725i	$-0.306430\pi$
$131$	−42.2285	−	48.7343i	−0.322355	−	0.372017i	−0.893679	+	0.448707i	$0.851885\pi$
$132$	−10.1625	+	4.64104i	−0.0769884	+	0.0351594i
$133$	24.8663	−	7.30140i	0.186964	−	0.0548977i
$134$	157.169	+	71.7765i	1.17290	+	0.535645i
$135$	237.649	+	34.1688i	1.76036	+	0.253102i
$136$	−41.3780	−	64.3855i	−0.304250	−	0.473423i
$137$		−	139.490i		−	1.01818i	−0.860714	−	0.509088i	$-0.829983\pi$
$137$		−	139.490i		−	1.01818i	0.860714	−	0.509088i	$-0.170017\pi$
$138$	11.6779	+	54.2393i	0.0846228	+	0.393038i
$139$	−228.447			−1.64351			−0.821753	−	0.569843i	$-0.807004\pi$
$139$	−228.447			−1.64351			−0.821753	+	0.569843i	$0.807004\pi$
$140$	−107.682	+	69.2032i	−0.769159	+	0.494308i
$141$	9.60956	−	66.8360i	0.0681529	−	0.474014i
$142$	56.3441	−	123.376i	0.396789	−	0.868848i
$143$	−10.5173	−	35.8187i	−0.0735477	−	0.250481i
$144$	11.6794	+	25.5743i	0.0811069	+	0.177599i
$145$	−175.449	+	152.027i	−1.20999	+	1.04846i
$146$	−2.00115	−	13.9183i	−0.0137065	−	0.0953309i
$147$	0.703472	+	0.206558i	0.00478553	+	0.00140516i
$148$	−17.0388	−	14.7642i	−0.115127	−	0.0997580i
$149$	97.4478	−	151.632i	0.654012	−	1.01766i	−0.342918	−	0.939365i	$-0.611415\pi$
$149$	97.4478	−	151.632i	0.654012	−	1.01766i	0.996930	−	0.0782976i	$-0.0249484\pi$
$150$	−129.567	−	83.2677i	−0.863780	−	0.555118i
$151$	−96.3101	+	111.148i	−0.637815	+	0.736078i	−0.978987	−	0.203923i	$-0.934631\pi$
$151$	−96.3101	+	111.148i	−0.637815	+	0.736078i	0.341172	+	0.940001i	$0.389176\pi$
$152$	8.85881	−	30.1703i	0.0582816	−	0.198489i
$153$	−54.9416	+	7.89940i	−0.359095	+	0.0516301i
$154$	22.8399	+	26.3586i	0.148311	+	0.171160i
$155$	−102.845	+	46.9677i	−0.663515	+	0.303017i
$156$	−33.6423	+	9.87828i	−0.215656	+	0.0633223i
$157$	49.6966	+	22.6957i	0.316539	+	0.144559i	0.567348	−	0.823478i	$-0.307969\pi$
$157$	49.6966	+	22.6957i	0.316539	+	0.144559i	−0.250809	+	0.968037i	$0.580697\pi$
$158$	−119.653	−	17.2035i	−0.757297	−	0.108883i
$159$	−14.7508	−	22.9527i	−0.0927722	−	0.144356i
$160$			260.040i			1.62525i
$161$	−142.100	+	77.1996i	−0.882610	+	0.479501i
$162$	18.6423			0.115076
$163$	197.534	−	126.947i	1.21186	−	0.778818i	0.230894	−	0.972979i	$-0.425835\pi$
$163$	197.534	−	126.947i	1.21186	−	0.778818i	0.980970	+	0.194161i	$0.0621985\pi$
$164$	−7.35677	+	51.1675i	−0.0448583	+	0.311997i
$165$	22.6500	−	49.5966i	0.137273	−	0.300586i
$166$	10.4436	+	35.5678i	0.0629135	+	0.214264i
$167$	36.4522	+	79.8192i	0.218277	+	0.477959i	0.986817	−	0.161843i	$-0.0517437\pi$
$167$	36.4522	+	79.8192i	0.218277	+	0.477959i	−0.768540	+	0.639802i	$0.779016\pi$
$168$	76.0303	−	65.8806i	0.452561	−	0.392147i
$169$	7.37761	+	51.3124i	0.0436545	+	0.303624i
$170$	116.699	+	34.2660i	0.686467	+	0.201565i
$171$	−17.2345	−	14.9338i	−0.100787	−	0.0873322i
$172$	17.9267	−	27.8944i	0.104225	−	0.162177i
$173$	−147.410	−	94.7344i	−0.852079	−	0.547598i	0.0401437	−	0.999194i	$-0.487218\pi$
$173$	−147.410	−	94.7344i	−0.852079	−	0.547598i	−0.892222	+	0.451596i	$0.850855\pi$
$174$	38.9068	−	44.9008i	0.223602	−	0.258051i
$175$	126.475	−	430.735i	0.722716	−	2.46134i
$176$	15.5130	−	2.23043i	0.0881418	−	0.0126729i
$177$	62.5866	+	72.2288i	0.353596	+	0.408072i
$178$	−70.1917	+	32.0555i	−0.394336	+	0.180087i
$179$	109.799	−	32.2399i	0.613403	−	0.180111i	0.0397497	−	0.999210i	$-0.487344\pi$
$179$	109.799	−	32.2399i	0.613403	−	0.180111i	0.573653	+	0.819098i	$0.305526\pi$
$180$	102.456	+	46.7899i	0.569197	+	0.259944i
$181$	−122.981	−	17.6821i	−0.679455	−	0.0976910i	−0.206058	−	0.978540i	$-0.566064\pi$
$181$	−122.981	−	17.6821i	−0.679455	−	0.0976910i	−0.473398	+	0.880849i	$0.656973\pi$
$182$	59.1786	+	92.0838i	0.325157	+	0.505955i
$183$			170.908i			0.933922i
$184$	−14.4149	+	195.681i	−0.0783419	+	1.06348i
$185$	110.031			0.594760
$186$	24.3415	−	15.6434i	0.130868	−	0.0841040i
$187$	−4.40346	+	30.6267i	−0.0235479	+	0.163779i
$188$	32.3012	−	70.7297i	0.171815	−	0.376222i
$189$	−50.4570	−	171.841i	−0.266968	−	0.909210i
$190$	20.7580	+	45.4538i	0.109253	+	0.239230i
$191$	−198.872	+	172.323i	−1.04121	+	0.902216i	−0.995311	−	0.0967295i	$-0.969162\pi$
$191$	−198.872	+	172.323i	−1.04121	+	0.902216i	−0.0459025	+	0.998946i	$0.514616\pi$
$192$	−13.8096	−	96.0481i	−0.0719252	−	0.500250i
$193$	274.740	+	80.6709i	1.42352	+	0.417984i	0.900694	−	0.434453i	$-0.143058\pi$
$193$	274.740	+	80.6709i	1.42352	+	0.417984i	0.522829	+	0.852438i	$0.324877\pi$
$194$	−22.3794	−	19.3918i	−0.115358	−	0.0999579i
$195$	92.5138	−	143.954i	0.474430	−	0.738227i
$196$	0.710256	+	0.456454i	0.00362375	+	0.00232885i
$197$	12.8238	−	14.7994i	0.0650952	−	0.0751239i	−0.722268	−	0.691613i	$-0.756900\pi$
$197$	12.8238	−	14.7994i	0.0650952	−	0.0751239i	0.787363	+	0.616489i	$0.211446\pi$
$198$	8.64638	−	29.4469i	0.0436686	−	0.148722i
$199$	90.5632	−	13.0210i	0.455091	−	0.0654323i	0.0890424	−	0.996028i	$-0.471619\pi$
$199$	90.5632	−	13.0210i	0.455091	−	0.0654323i	0.366049	+	0.930596i	$0.380710\pi$
$200$	−356.686	−	411.638i	−1.78343	−	2.05819i
$201$	−183.279	+	83.7005i	−0.911834	+	0.416421i
$202$	−13.0384	+	3.82843i	−0.0645467	+	0.0189526i
$203$	157.522	+	71.9381i	0.775973	+	0.354375i
$204$	28.7658	+	4.13590i	0.141009	+	0.0202740i
$205$	−136.395	−	212.235i	−0.665342	−	1.03529i
$206$			193.643i			0.940016i
$207$	124.749	+	68.4636i	0.602650	+	0.330742i
$208$	49.1868			0.236475
$209$	−10.6942	+	6.87274i	−0.0511684	+	0.0328839i
$210$	−22.7523	+	158.245i	−0.108344	+	0.753550i
$211$	−11.6030	+	25.4070i	−0.0549905	+	0.120412i	−0.935133	−	0.354298i	$-0.884720\pi$
$211$	−11.6030	+	25.4070i	−0.0549905	+	0.120412i	0.880142	+	0.474710i	$0.157447\pi$
$212$	−8.85168	−	30.1461i	−0.0417532	−	0.142198i
$213$	65.7044	+	143.873i	0.308471	+	0.675458i
$214$	−129.845	+	112.511i	−0.606751	+	0.525753i
$215$	23.0300	+	160.177i	0.107116	+	0.745010i
$216$	−208.495	−	61.2196i	−0.965254	−	0.283424i
$217$	63.7382	+	55.2294i	0.293724	+	0.254514i
$218$	43.8193	−	68.1842i	0.201006	−	0.312771i
$219$	13.7944	+	8.86513i	0.0629882	+	0.0404800i
$220$	41.1167	−	47.4512i	0.186894	−	0.215687i
$221$	−27.3585	+	93.1744i	−0.123794	+	0.421604i
$222$	−27.8724	+	4.00745i	−0.125551	+	0.0180516i
$223$	30.0318	+	34.6586i	0.134672	+	0.155420i	0.819080	−	0.573680i	$-0.194485\pi$
$223$	30.0318	+	34.6586i	0.134672	+	0.155420i	−0.684408	+	0.729099i	$0.739939\pi$
$224$	176.446	−	80.5800i	0.787704	−	0.359732i
$225$	−379.020	+	111.290i	−1.68453	+	0.494624i
$226$	−10.3559	−	4.72938i	−0.0458226	−	0.0209265i
$227$	−231.195	−	33.2408i	−1.01848	−	0.146435i	−0.387203	−	0.921994i	$-0.626559\pi$
$227$	−231.195	−	33.2408i	−1.01848	−	0.146435i	−0.631275	+	0.775559i	$0.717468\pi$
$228$	6.45514	+	10.0444i	0.0283120	+	0.0440544i
$229$		−	300.027i		−	1.31016i	−0.755558	−	0.655081i	$-0.772634\pi$
$229$		−	300.027i		−	1.31016i	0.755558	−	0.655081i	$-0.227366\pi$
$230$	−186.328	−	250.014i	−0.810121	−	1.08702i
$231$	−40.6716			−0.176068
$232$	176.756	−	113.594i	0.761877	−	0.489629i
$233$	32.2976	−	224.635i	0.138616	−	0.964098i	−0.795201	−	0.606346i	$-0.792635\pi$
$233$	32.2976	−	224.635i	0.138616	−	0.964098i	0.933817	−	0.357751i	$-0.116456\pi$
$234$	40.0120	−	87.6141i	0.170992	−	0.374419i
$235$	106.912	+	364.109i	0.454944	+	1.54940i
$236$	45.7190	+	100.111i	0.193725	+	0.424198i
$237$	106.535	−	92.3128i	0.449513	−	0.389505i
$238$	−12.9117	−	89.8025i	−0.0542506	−	0.377322i
$239$	−184.645	−	54.2168i	−0.772575	−	0.226848i	−0.128396	−	0.991723i	$-0.540983\pi$
$239$	−184.645	−	54.2168i	−0.772575	−	0.226848i	−0.644179	+	0.764875i	$0.722801\pi$
$240$	54.2931	+	47.0453i	0.226221	+	0.196022i
$241$	−86.1924	+	134.118i	−0.357645	+	0.556506i	−0.972726	−	0.231958i	$-0.925487\pi$
$241$	−86.1924	+	134.118i	−0.357645	+	0.556506i	0.615081	+	0.788464i	$0.289123\pi$
$242$	132.012	+	84.8387i	0.545503	+	0.350573i
$243$	−164.360	+	189.681i	−0.676378	+	0.780582i
$244$	−55.4474	+	188.837i	−0.227244	+	0.773920i
$245$	−4.07848	+	0.586396i	−0.0166468	+	0.00239345i
$246$	42.2808	+	48.7946i	0.171873	+	0.198352i
$247$	−36.2909	+	16.5735i	−0.146927	+	0.0670992i
$248$	98.1822	−	28.8289i	0.395896	−	0.116246i
$249$	−39.3212	−	17.9574i	−0.157916	−	0.0721180i
$250$	521.288	+	74.9500i	2.08515	+	0.299800i
$251$	90.6894	+	141.115i	0.361312	+	0.562213i	0.973554	−	0.228458i	$-0.0733683\pi$
$251$	90.6894	+	141.115i	0.361312	+	0.562213i	−0.612242	+	0.790671i	$0.709732\pi$
$252$		−	84.0184i		−	0.333406i
$253$	56.2103	−	55.9710i	0.222175	−	0.221229i
$254$	−130.525			−0.513876
$255$	−119.316	+	76.6800i	−0.467907	+	0.300706i
$256$	38.4900	−	267.704i	0.150352	−	1.04572i
$257$	76.7282	−	168.011i	0.298553	−	0.653740i	−0.699597	−	0.714538i	$-0.746637\pi$
$257$	76.7282	−	168.011i	0.298553	−	0.653740i	0.998150	+	0.0607974i	$0.0193644\pi$
$258$	−11.6677	−	39.7365i	−0.0452236	−	0.154017i
$259$	−34.0958	−	74.6593i	−0.131644	−	0.288260i
$260$	148.922	−	129.041i	0.572776	−	0.496313i
$261$	−21.6860	−	150.829i	−0.0830881	−	0.577890i
$262$	−88.9894	−	26.1296i	−0.339654	−	0.0997315i
$263$	108.730	+	94.2152i	0.413423	+	0.358233i	0.836600	−	0.547814i	$-0.184540\pi$
$263$	108.730	+	94.2152i	0.413423	+	0.358233i	−0.423177	+	0.906047i	$0.639085\pi$
$264$	−26.6790	+	41.5133i	−0.101057	+	0.157247i
$265$	128.994	+	82.8993i	0.486769	+	0.312827i
$266$	24.4094	−	28.1700i	0.0917648	−	0.105902i
$267$	25.3515	−	86.3392i	0.0949494	−	0.323368i
$268$	−229.660	+	33.0201i	−0.856941	+	0.123209i
$269$	202.445	+	233.634i	0.752582	+	0.868526i	0.994816	−	0.101692i	$-0.0324256\pi$
$269$	202.445	+	233.634i	0.752582	+	0.868526i	−0.242234	+	0.970218i	$0.577880\pi$
$270$	314.112	−	143.450i	1.16338	−	0.531298i
$271$	465.819	−	136.777i	1.71889	−	0.504712i	0.734186	−	0.678948i	$-0.237564\pi$
$271$	465.819	−	136.777i	1.71889	−	0.504712i	0.984704	+	0.174236i	$0.0557457\pi$
$272$	−37.0843	−	16.9358i	−0.136339	−	0.0622641i
$273$	−126.345	−	18.1657i	−0.462803	−	0.0665411i
$274$	−108.466	−	168.776i	−0.395860	−	0.615971i
$275$			220.202i			0.800733i
$276$	−52.5702	−	52.7949i	−0.190472	−	0.191286i
$277$	56.0790			0.202451			0.101226	−	0.994864i	$-0.467724\pi$
$277$	56.0790			0.202451			0.101226	+	0.994864i	$0.467724\pi$
$278$	−276.410	+	177.638i	−0.994279	+	0.638984i
$279$	10.5615	−	73.4566i	0.0378547	−	0.263285i
$280$	−234.870	+	514.293i	−0.838820	+	1.83676i
$281$	−6.05768	−	20.6306i	−0.0215576	−	0.0734183i	0.948012	−	0.318235i	$-0.103090\pi$
$281$	−6.05768	−	20.6306i	−0.0215576	−	0.0734183i	−0.969569	+	0.244817i	$0.921272\pi$
$282$	−40.3437	−	88.3404i	−0.143063	−	0.313264i
$283$	228.285	−	197.810i	0.806660	−	0.698975i	−0.150476	−	0.988614i	$-0.548081\pi$
$283$	228.285	−	197.810i	0.806660	−	0.698975i	0.957136	+	0.289639i	$0.0935352\pi$
$284$	25.9206	+	180.282i	0.0912697	+	0.634795i
$285$	−55.9103	−	16.4168i	−0.196177	−	0.0576026i
$286$	−40.5776	−	35.1607i	−0.141880	−	0.122939i
$287$	−101.743	+	158.315i	−0.354505	+	0.551620i
$288$	−143.590	−	92.2797i	−0.498577	−	0.320416i
$289$	−136.546	+	157.583i	−0.472479	+	0.545270i
$290$	−94.0695	+	320.371i	−0.324378	+	1.10473i
$291$	34.1801	−	4.91435i	0.117457	−	0.0168878i
$292$	12.3654	+	14.2704i	0.0423472	+	0.0488713i
$293$	−214.803	+	98.0973i	−0.733116	+	0.334803i	−0.746751	−	0.665104i	$-0.768387\pi$
$293$	−214.803	+	98.0973i	−0.733116	+	0.334803i	0.0136345	+	0.999907i	$0.495660\pi$
$294$	1.01178	−	0.297086i	0.00344144	−	0.00101050i
$295$	−488.578	−	223.126i	−1.65620	−	0.756359i
$296$	−98.5699	−	14.1722i	−0.333007	−	0.0478791i
$297$	47.4947	+	73.9032i	0.159915	+	0.248832i
$298$		−	259.241i		−	0.869935i
$299$	199.615	−	148.767i	0.667608	−	0.497547i
$300$	206.822			0.689406
$301$	101.549	−	65.2615i	0.337372	−	0.216816i
$302$	−30.1032	+	209.373i	−0.0996796	+	0.693287i
$303$	6.58282	−	14.4144i	0.0217255	−	0.0475721i
$304$	−4.71887	−	16.0710i	−0.0155226	−	0.0528652i
$305$	−399.006	−	873.702i	−1.30822	−	2.86460i
$306$	−60.3340	+	52.2797i	−0.197170	+	0.170849i
$307$	−28.1909	−	196.072i	−0.0918271	−	0.638671i	−0.982808	−	0.184631i	$-0.940891\pi$
$307$	−28.1909	−	196.072i	−0.0918271	−	0.638671i	0.890981	−	0.454041i	$-0.150018\pi$
$308$	−44.9382	−	13.1950i	−0.145903	−	0.0428411i
$309$	−170.658	−	147.876i	−0.552291	−	0.478563i
$310$	−87.9155	+	136.799i	−0.283598	+	0.441288i
$311$	131.934	+	84.7891i	0.424227	+	0.272634i	0.735286	−	0.677756i	$-0.237048\pi$
$311$	131.934	+	84.7891i	0.424227	+	0.272634i	−0.311060	+	0.950390i	$0.600684\pi$
$312$	−101.419	+	117.044i	−0.325062	+	0.375141i
$313$	−3.11069	+	10.5941i	−0.00993832	+	0.0338468i	−0.964313	−	0.264765i	$-0.914706\pi$
$313$	−3.11069	+	10.5941i	−0.00993832	+	0.0338468i	0.954375	+	0.298612i	$0.0965237\pi$
$314$	77.7782	−	11.1828i	0.247701	−	0.0356141i
$315$	268.520	+	309.888i	0.852444	+	0.983773i
$316$	147.659	−	67.4338i	0.467277	−	0.213398i
$317$	−272.168	+	79.9158i	−0.858575	+	0.252100i	−0.681249	−	0.732052i	$-0.738563\pi$
$317$	−272.168	+	79.9158i	−0.858575	+	0.252100i	−0.177326	+	0.984152i	$0.556745\pi$
$318$	−35.6954	−	16.3015i	−0.112250	−	0.0512627i
$319$	−84.0786	−	12.0887i	−0.263569	−	0.0378955i
$320$	294.833	+	458.769i	0.921354	+	1.43365i
$321$		−	200.351i		−	0.624148i
$322$	−111.905	+	203.903i	−0.347530	+	0.633238i
$323$	33.0680			0.102378
$324$	−21.0598	+	13.5343i	−0.0649995	+	0.0417727i
$325$	−98.3516	+	684.051i	−0.302620	+	2.10477i
$326$	140.293	−	307.199i	0.430347	−	0.942329i
$327$	26.6281	+	90.6869i	0.0814314	+	0.277330i
$328$	94.8520	+	207.697i	0.289183	+	0.633222i
$329$	213.930	−	185.372i	0.650244	−	0.563439i
$330$	−11.1603	−	77.6217i	−0.0338191	−	0.235217i
$331$	428.650	+	125.863i	1.29501	+	0.380250i	0.855415	−	0.517944i	$-0.173302\pi$
$331$	428.650	+	125.863i	1.29501	+	0.380250i	0.439599	+	0.898194i	$0.355121\pi$
$332$	−37.6202	−	32.5981i	−0.113314	−	0.0981871i
$333$	−39.0463	+	60.7572i	−0.117256	+	0.182454i
$334$	106.172	+	68.2324i	0.317879	+	0.204289i
$335$	741.533	−	855.775i	2.21353	−	2.55455i
$336$	15.0976	−	51.4178i	0.0449334	−	0.153029i
$337$	380.687	−	54.7345i	1.12964	−	0.162417i	0.447947	−	0.894060i	$-0.352155\pi$
$337$	380.687	−	54.7345i	1.12964	−	0.162417i	0.681688	+	0.731643i	$0.261246\pi$
$338$	48.8263	+	56.3486i	0.144457	+	0.166712i
$339$	12.0763	−	5.51506i	0.0356233	−	0.0162686i
$340$	−156.710	+	46.0143i	−0.460913	+	0.135336i
$341$	−37.6304	−	17.1852i	−0.110353	−	0.0503966i
$342$	−32.4652	−	4.66779i	−0.0949275	−	0.0136485i
$343$	−184.603	−	287.249i	−0.538202	−	0.837459i
$344$		−	146.460i		−	0.425754i
$345$	362.627	+	26.7131i	1.05109	+	0.0774292i
$346$	−252.022			−0.728388
$347$	−81.9624	+	52.6740i	−0.236203	+	0.151798i	−0.653388	−	0.757023i	$-0.726653\pi$
$347$	−81.9624	+	52.6740i	−0.236203	+	0.151798i	0.417185	+	0.908821i	$0.363017\pi$
$348$	−11.3542	+	78.9699i	−0.0326269	+	0.226925i
$349$	−224.813	+	492.271i	−0.644162	+	1.41052i	0.252409	+	0.967621i	$0.418777\pi$
$349$	−224.813	+	492.271i	−0.644162	+	1.41052i	−0.896572	+	0.442898i	$0.853950\pi$
$350$	−181.905	−	619.513i	−0.519729	−	1.77004i
$351$	114.533	+	250.792i	0.326304	+	0.714506i
$352$	−71.9076	+	62.3083i	−0.204283	+	0.177012i
$353$	82.8382	+	576.152i	0.234669	+	1.63216i	0.677478	+	0.735543i	$0.263073\pi$
$353$	82.8382	+	576.152i	0.234669	+	1.63216i	−0.442809	+	0.896616i	$0.646018\pi$
$354$	131.891	+	38.7266i	0.372572	+	0.109397i
$355$	−671.778	−	582.099i	−1.89233	−	1.63972i
$356$	56.0219	−	87.1718i	0.157365	−	0.244865i
$357$	89.0030	+	57.1988i	0.249308	+	0.160221i
$358$	107.782	−	124.387i	0.301067	−	0.347450i
$359$	−107.203	+	365.101i	−0.298616	+	1.01699i	0.664361	+	0.747411i	$0.268704\pi$
$359$	−107.203	+	365.101i	−0.298616	+	1.01699i	−0.962978	+	0.269582i	$0.913115\pi$
$360$	492.440	−	70.8022i	1.36789	−	0.196673i
$361$	−227.508	−	262.558i	−0.630216	−	0.727308i
$362$	−162.551	+	74.2343i	−0.449035	+	0.205067i
$363$	−175.579	+	51.5547i	−0.483690	+	0.142024i
$364$	−133.706	−	61.0615i	−0.367324	−	0.167751i
$365$	−91.2155	−	13.1148i	−0.249905	−	0.0359310i
$366$	132.896	+	206.790i	0.363103	+	0.564999i
$367$		−	234.739i		−	0.639616i	−0.947482	−	0.319808i	$-0.896382\pi$
$367$		−	234.739i		−	0.639616i	0.947482	−	0.319808i	$-0.103618\pi$
$368$	49.8939	+	91.8390i	0.135581	+	0.249562i
$369$	165.595			0.448767
$370$	133.131	−	85.5583i	0.359814	−	0.231239i
$371$	16.2778	−	113.215i	0.0438756	−	0.305161i
$372$	−16.1411	+	35.3440i	−0.0433899	+	0.0950107i
$373$	26.7558	+	91.1217i	0.0717313	+	0.244294i	0.987552	−	0.157293i	$-0.0502768\pi$
$373$	26.7558	+	91.1217i	0.0717313	+	0.244294i	−0.915821	+	0.401587i	$0.868459\pi$
$374$	18.4870	+	40.4808i	0.0494304	+	0.108237i
$375$	−464.136	+	402.176i	−1.23770	+	1.07247i
$376$	−48.8780	−	339.954i	−0.129995	−	0.904133i
$377$	−255.789	−	75.1064i	−0.678485	−	0.199221i
$378$	−194.671	−	168.684i	−0.515004	−	0.446253i
$379$	−28.9146	+	44.9921i	−0.0762919	+	0.118713i	−0.877303	−	0.479937i	$-0.840659\pi$
$379$	−28.9146	+	44.9921i	−0.0762919	+	0.118713i	0.801011	+	0.598650i	$0.204296\pi$
$380$	−56.4495	−	36.2779i	−0.148551	−	0.0954681i
$381$	99.6753	−	115.031i	0.261615	−	0.301920i
$382$	−106.628	+	363.142i	−0.279131	+	0.950634i
$383$	−364.781	+	52.4476i	−0.952431	+	0.136939i	−0.600977	−	0.799266i	$-0.705222\pi$
$383$	−364.781	+	52.4476i	−0.952431	+	0.136939i	−0.351454	+	0.936205i	$0.614313\pi$
$384$	29.8084	+	34.4007i	0.0776260	+	0.0895852i
$385$	207.918	−	94.9531i	0.540048	−	0.246631i
$386$	395.150	−	116.026i	1.02370	−	0.300587i
$387$	−96.6199	−	44.1248i	−0.249664	−	0.114018i
$388$	39.3601	+	5.65912i	0.101443	+	0.0145854i
$389$	290.357	+	451.804i	0.746419	+	1.16145i	0.981868	+	0.189564i	$0.0607073\pi$
$389$	290.357	+	451.804i	0.746419	+	1.16145i	−0.235450	+	0.971887i	$0.575656\pi$
$390$		−	246.115i		−	0.631063i
$391$	−201.722	+	43.4316i	−0.515913	+	0.111078i
$392$	3.72920			0.00951325
$393$	90.9850	−	58.4725i	0.231514	−	0.148785i
$394$	4.00826	−	27.8781i	0.0101733	−	0.0707566i
$395$	−329.102	+	720.633i	−0.833170	+	1.82439i
$396$	11.6108	+	39.5429i	0.0293203	+	0.0998557i
$397$	−85.2523	−	186.676i	−0.214741	−	0.470218i	0.771352	−	0.636408i	$-0.219581\pi$
$397$	−85.2523	−	186.676i	−0.214741	−	0.470218i	−0.986094	+	0.166191i	$0.946853\pi$
$398$	99.4518	−	86.1755i	0.249879	−	0.216521i
$399$	6.18593	+	43.0241i	0.0155036	+	0.107830i
$400$	−278.383	−	81.7406i	−0.695957	−	0.204352i
$401$	184.588	+	159.946i	0.460318	+	0.398868i	0.853913	−	0.520416i	$-0.174223\pi$
$401$	184.588	+	159.946i	0.460318	+	0.398868i	−0.393595	+	0.919284i	$0.628769\pi$
$402$	−156.673	+	243.788i	−0.389734	+	0.606438i
$403$	−109.222	−	70.1929i	−0.271023	−	0.174176i
$404$	11.9498	−	13.7908i	0.0295787	−	0.0341357i
$405$	34.4206	−	117.226i	0.0849891	−	0.289446i
$406$	246.532	−	35.4460i	0.607222	−	0.0873053i
$407$	26.3645	+	30.4262i	0.0647776	+	0.0747573i
$408$	116.765	−	53.3248i	0.286189	−	0.130698i
$409$	53.9847	−	15.8513i	0.131992	−	0.0387564i	−0.215069	−	0.976599i	$-0.568998\pi$
$409$	53.9847	−	15.8513i	0.131992	−	0.0387564i	0.347061	+	0.937842i	$0.387180\pi$
$410$	−330.062	−	150.734i	−0.805030	−	0.367645i
$411$	231.572	+	33.2951i	0.563436	+	0.0810099i
$412$	−140.585	−	218.755i	−0.341227	−	0.530959i
$413$			400.657i			0.970114i
$414$	204.176	−	14.1653i	0.493178	−	0.0342158i
$415$	242.939			0.585395
$416$	−251.209	+	161.442i	−0.603867	+	0.388082i
$417$	54.5284	−	379.253i	0.130763	−	0.909480i
$418$	−7.59527	+	16.6313i	−0.0181705	+	0.0397878i
$419$	−101.053	−	344.156i	−0.241178	−	0.821376i	−0.987746	−	0.156067i	$-0.950118\pi$
$419$	−101.053	−	344.156i	−0.241178	−	0.821376i	0.746569	−	0.665308i	$-0.231700\pi$
$420$	−89.1837	−	195.285i	−0.212342	−	0.464964i
$421$	298.067	−	258.276i	0.707997	−	0.613483i	−0.224579	−	0.974456i	$-0.572101\pi$
$421$	298.067	−	258.276i	0.707997	−	0.613483i	0.932576	+	0.360973i	$0.117555\pi$
$422$	5.71713	+	39.7635i	0.0135477	+	0.0942264i
$423$	−238.995	−	70.1752i	−0.564999	−	0.165899i
$424$	−104.880	−	90.8793i	−0.247359	−	0.214338i
$425$	309.682	−	481.874i	0.728663	−	1.13382i
$426$	191.372	+	122.988i	0.449231	+	0.288703i
$427$	−469.193	+	541.477i	−1.09881	+	1.26810i
$428$	64.9998	−	221.369i	0.151869	−	0.517217i
$429$	61.9742	−	8.91055i	0.144462	−	0.0207705i
$430$	152.417	+	175.898i	0.354457	+	0.409066i
$431$	642.388	−	293.369i	1.49046	−	0.680670i	0.507024	−	0.861932i	$-0.330746\pi$
$431$	642.388	−	293.369i	1.49046	−	0.680670i	0.983435	+	0.181263i	$0.0580184\pi$
$432$	−111.060	+	32.6102i	−0.257084	+	0.0754866i
$433$	559.026	+	255.299i	1.29105	+	0.589604i	0.938206	−	0.346077i	$-0.112486\pi$
$433$	559.026	+	255.299i	1.29105	+	0.589604i	0.352847	+	0.935681i	$0.385214\pi$
$434$	120.066	+	17.2628i	0.276649	+	0.0397761i
$435$	−210.507	−	327.556i	−0.483925	−	0.753001i
$436$			108.839i			0.249631i
$437$	−67.7577	−	50.9487i	−0.155052	−	0.116587i
$438$	23.5839			0.0538446
$439$	−682.574	+	438.664i	−1.55484	+	0.999234i	−0.570840	+	0.821061i	$0.693382\pi$
$439$	−682.574	+	438.664i	−1.55484	+	0.999234i	−0.983999	+	0.178173i	$0.942981\pi$
$440$	39.4681	−	274.507i	0.0897003	−	0.623879i
$441$	1.12352	−	2.46016i	0.00254766	−	0.00557860i
$442$	39.3488	+	134.010i	0.0890245	+	0.303190i
$443$	139.121	+	304.633i	0.314044	+	0.687660i	0.999169	−	0.0407658i	$-0.0129798\pi$
$443$	139.121	+	304.633i	0.314044	+	0.687660i	−0.685125	+	0.728425i	$0.740252\pi$
$444$	28.5775	−	24.7626i	0.0643638	−	0.0557715i
$445$	71.9701	+	500.563i	0.161731	+	1.12486i
$446$	63.2870	+	18.5827i	0.141899	+	0.0416653i
$447$	228.469	+	197.970i	0.511116	+	0.442885i
$448$	219.928	−	342.215i	0.490912	−	0.763873i
$449$	317.934	+	204.324i	0.708093	+	0.455063i	0.844477	−	0.535593i	$-0.179912\pi$
$449$	317.934	+	204.324i	0.708093	+	0.455063i	−0.136384	+	0.990656i	$0.543548\pi$
$450$	−372.057	+	429.377i	−0.826794	+	0.954171i
$451$	26.0066	−	88.5704i	0.0576643	−	0.196387i
$452$	15.1324	−	2.17571i	0.0334788	−	0.00481352i
$453$	−161.532	−	186.418i	−0.356582	−	0.411518i
$454$	−305.581	+	139.554i	−0.673086	+	0.307388i
$455$	688.303	−	202.104i	1.51275	−	0.444185i
$456$	47.9723	+	21.9082i	0.105202	+	0.0480443i
$457$	476.928	+	68.5718i	1.04361	+	0.150048i	0.642736	−	0.766088i	$-0.277799\pi$
$457$	476.928	+	68.5718i	1.04361	+	0.150048i	0.400869	+	0.916135i	$0.368708\pi$
$458$	−233.297	−	363.017i	−0.509382	−	0.792614i
$459$		−	228.519i		−	0.497863i
$460$	392.002	+	147.162i	0.852178	+	0.319918i
$461$	−834.211			−1.80957			−0.904784	−	0.425870i	$-0.859968\pi$
$461$	−834.211			−1.80957			−0.904784	+	0.425870i	$0.859968\pi$
$462$	−49.2105	+	31.6257i	−0.106516	+	0.0684539i
$463$	61.3035	−	426.375i	0.132405	−	0.920896i	−0.810002	−	0.586427i	$-0.800534\pi$
$463$	61.3035	−	426.375i	0.132405	−	0.920896i	0.942407	−	0.334469i	$-0.108557\pi$
$464$	46.4934	−	101.806i	0.100201	−	0.219410i
$465$	−53.4244	−	181.947i	−0.114891	−	0.391284i
$466$	−135.595	−	296.911i	−0.290975	−	0.637147i
$467$	−74.9962	+	64.9846i	−0.160591	+	0.139153i	−0.731450	−	0.681895i	$-0.761156\pi$
$467$	−74.9962	+	64.9846i	−0.160591	+	0.139153i	0.570858	+	0.821049i	$0.306611\pi$
$468$	18.4072	+	128.025i	0.0393316	+	0.273557i
$469$	−810.454	−	237.971i	−1.72805	−	0.507400i
$470$	412.484	+	357.419i	0.877625	+	0.760467i
$471$	−49.5400	+	77.0858i	−0.105181	+	0.163664i
$472$	408.949	+	262.816i	0.866417	+	0.556813i
$473$	−38.7748	+	44.7485i	−0.0819763	+	0.0946056i
$474$	57.1202	−	194.534i	0.120507	−	0.410408i
$475$	232.938	−	33.4915i	0.490396	−	0.0705084i
$476$	79.7828	+	92.0743i	0.167611	+	0.193433i
$477$	−91.5514	+	41.8101i	−0.191932	+	0.0876522i
$478$	−265.570	+	77.9783i	−0.555585	+	0.163134i
$479$	−536.105	−	244.831i	−1.11922	−	0.511129i	−0.232108	−	0.972690i	$-0.574562\pi$
$479$	−536.105	−	244.831i	−1.11922	−	0.511129i	−0.887108	+	0.461561i	$0.847290\pi$
$480$	−431.701	−	62.0693i	−0.899377	−	0.129311i
$481$	68.3109	+	106.294i	0.142019	+	0.220985i
$482$			229.298i			0.475722i
$483$	−94.2436	−	254.332i	−0.195121	−	0.526568i
$484$	−210.724			−0.435380
$485$	−163.260	+	104.921i	−0.336618	+	0.216331i
$486$	−51.3732	+	357.309i	−0.105706	+	0.735203i
$487$	229.023	−	501.490i	0.470273	−	1.02975i	−0.514751	−	0.857340i	$-0.672116\pi$
$487$	229.023	−	501.490i	0.470273	−	1.02975i	0.985024	−	0.172415i	$-0.0551570\pi$
$488$	244.911	+	834.091i	0.501867	+	1.70920i
$489$	163.600	+	358.234i	0.334560	+	0.732584i
$490$	−4.47877	+	3.88088i	−0.00914035	+	0.00792016i
$491$	−106.403	−	740.049i	−0.216707	−	1.50723i	−0.750079	−	0.661348i	$-0.769985\pi$
$491$	−106.403	−	740.049i	−0.216707	−	1.50723i	0.533373	−	0.845880i	$-0.320924\pi$
$492$	−83.1888	−	24.4264i	−0.169083	−	0.0496472i
$493$	166.991	+	144.699i	0.338724	+	0.293506i
$494$	−31.0228	+	48.2724i	−0.0627991	+	0.0977174i
$495$	−169.202	−	108.740i	−0.341823	−	0.219676i
$496$	35.6946	−	41.1938i	0.0719650	−	0.0830520i
$497$	−186.806	+	636.202i	−0.375866	+	1.28008i
$498$	−61.5401	+	8.84812i	−0.123574	+	0.0177673i
$499$	−204.862	−	236.424i	−0.410546	−	0.473795i	0.512388	−	0.858754i	$-0.328761\pi$
$499$	−204.862	−	236.424i	−0.410546	−	0.473795i	−0.922934	+	0.384959i	$0.874216\pi$
$500$	−643.303	+	293.787i	−1.28661	+	0.587574i
$501$	−141.211	+	41.4634i	−0.281859	+	0.0827613i
$502$	219.459	+	100.224i	0.437169	+	0.199648i
$503$	−678.263	−	97.5195i	−1.34844	−	0.193876i	−0.570023	−	0.821629i	$-0.693066\pi$
$503$	−678.263	−	97.5195i	−1.34844	−	0.193876i	−0.778412	+	0.627753i	$0.783975\pi$
$504$	−200.637	−	312.197i	−0.398089	−	0.619438i
$505$			89.0564i			0.176349i
$506$	24.4892	−	111.430i	0.0483976	−	0.220218i
$507$	−86.9464			−0.171492
$508$	147.451	−	94.7611i	0.290258	−	0.186538i
$509$	51.8602	−	360.695i	0.101886	−	0.708635i	−0.873289	−	0.487202i	$-0.838017\pi$
$509$	51.8602	−	360.695i	0.101886	−	0.708635i	0.975176	−	0.221433i	$-0.0710734\pi$
$510$	−84.7413	+	185.558i	−0.166159	+	0.363838i
$511$	19.3666	+	65.9566i	0.0378994	+	0.129074i
$512$	−116.495	−	255.089i	−0.227530	−	0.498220i
$513$	70.9542	−	61.4821i	0.138312	−	0.119848i
$514$	−37.8062	−	262.948i	−0.0735529	−	0.511571i
$515$	1217.66	+	357.537i	2.36439	+	0.694247i
$516$	42.0295	+	36.4188i	0.0814526	+	0.0705790i
$517$	−75.0680	+	116.808i	−0.145199	+	0.225934i
$518$	−99.3082	−	63.8215i	−0.191715	−	0.123208i
$519$	192.457	−	222.107i	0.370823	−	0.427953i
$520$	245.214	−	835.121i	0.471565	−	1.60600i
$521$	−573.666	+	82.4807i	−1.10109	+	0.158312i	−0.668813	−	0.743430i	$-0.733197\pi$
$521$	−573.666	+	82.4807i	−1.10109	+	0.158312i	−0.432273	+	0.901743i	$0.642288\pi$
$522$	−143.522	−	165.633i	−0.274946	−	0.317305i
$523$	302.809	−	138.288i	0.578986	−	0.264414i	−0.104323	−	0.994543i	$-0.533268\pi$
$523$	302.809	−	138.288i	0.578986	−	0.264414i	0.683309	+	0.730130i	$0.260540\pi$
$524$	119.500	−	35.0883i	0.228053	−	0.0669624i
$525$	684.889	+	312.778i	1.30455	+	0.595768i
$526$	204.818	+	29.4484i	0.389389	+	0.0559856i
$527$	58.1794	+	90.5289i	0.110397	+	0.171782i
$528$			26.2860i			0.0497840i
$529$	480.254	+	221.805i	0.907852	+	0.419291i
$530$	220.537			0.416108
$531$	296.587	−	190.605i	0.558544	−	0.358955i
$532$	−7.12341	+	49.5444i	−0.0133899	+	0.0931286i
$533$	120.348	−	263.526i	0.225794	−	0.494420i
$534$	−36.4622	−	124.179i	−0.0682813	−	0.232545i
$535$	467.746	+	1024.22i	0.874292	+	1.91443i
$536$	−774.522	+	671.127i	−1.44500	+	1.25210i
$537$	27.3145	+	189.977i	0.0508650	+	0.353774i
$538$	426.618	+	125.266i	0.792970	+	0.232837i
$539$	−1.13940	−	0.987294i	−0.00211391	−	0.00183171i
$540$	−250.702	+	390.099i	−0.464262	+	0.722406i
$541$	−624.605	−	401.410i	−1.15454	−	0.741977i	−0.184001	−	0.982926i	$-0.558905\pi$
$541$	−624.605	−	401.410i	−1.15454	−	0.741977i	−0.970538	+	0.240949i	$0.922541\pi$
$542$	457.261	−	527.708i	0.843656	−	0.973630i
$543$	58.7092	−	199.945i	0.108120	−	0.368223i
$544$	244.986	−	35.2236i	0.450341	−	0.0647493i
$545$	−347.846	−	401.436i	−0.638250	−	0.736580i
$546$	−166.997	+	76.2649i	−0.305855	+	0.139679i
$547$	−337.619	+	99.1339i	−0.617219	+	0.181232i	−0.575372	−	0.817892i	$-0.695143\pi$
$547$	−337.619	+	99.1339i	−0.617219	+	0.181232i	−0.0418476	+	0.999124i	$0.513324\pi$
$548$	245.063	+	111.917i	0.447196	+	0.204227i
$549$	624.039	+	89.7232i	1.13668	+	0.163430i
$550$	171.226	+	266.432i	0.311320	+	0.484423i
$551$			90.7805i			0.164756i
$552$	−321.416	−	70.6380i	−0.582275	−	0.127967i
$553$	590.954			1.06863
$554$	67.8526	−	43.6062i	0.122478	−	0.0787116i
$555$	−26.2633	+	182.665i	−0.0473213	+	0.329127i
$556$	183.289	−	401.348i	0.329657	−	0.721848i
$557$	−202.349	−	689.139i	−0.363284	−	1.23723i	−0.915086	−	0.403258i	$-0.867878\pi$
$557$	−202.349	−	689.139i	−0.363284	−	1.23723i	0.551802	−	0.833975i	$-0.313940\pi$
$558$	−44.3400	−	97.0911i	−0.0794624	−	0.173998i
$559$	−140.439	+	121.691i	−0.251233	+	0.217695i
$560$	42.8605	+	298.102i	0.0765367	+	0.532324i
$561$	−49.7934	−	14.6207i	−0.0887583	−	0.0260618i
$562$	−23.3715	−	20.2515i	−0.0415863	−	0.0360348i
$563$	460.442	−	716.462i	0.817837	−	1.27258i	−0.141393	−	0.989954i	$-0.545158\pi$
$563$	460.442	−	716.462i	0.817837	−	1.27258i	0.959230	−	0.282626i	$-0.0912056\pi$
$564$	109.711	+	70.5068i	0.194523	+	0.125012i
$565$	−48.8600	+	56.3874i	−0.0864778	+	0.0998007i
$566$	122.398	−	416.851i	0.216252	−	0.736486i
$567$	−90.2076	+	12.9699i	−0.159096	+	0.0228746i
$568$	526.831	+	607.995i	0.927519	+	1.07041i
$569$	−403.104	+	184.091i	−0.708442	+	0.323535i	−0.736845	−	0.676062i	$-0.763685\pi$
$569$	−403.104	+	184.091i	−0.708442	+	0.323535i	0.0284027	+	0.999597i	$0.490958\pi$
$570$	−80.4141	+	23.6117i	−0.141077	+	0.0414240i
$571$	172.582	+	78.8157i	0.302246	+	0.138031i	0.560765	−	0.827975i	$-0.310507\pi$
$571$	172.582	+	78.8157i	0.302246	+	0.138031i	−0.258519	+	0.966006i	$0.583234\pi$
$572$	71.3664	+	10.2609i	0.124766	+	0.0179387i
$573$	−238.611	−	371.286i	−0.416424	−	0.647968i
$574$			270.667i			0.471545i
$575$	−1376.99	+	510.247i	−2.39476	+	0.887387i
$576$	−357.952			−0.621444
$577$	441.473	−	283.717i	0.765117	−	0.491711i	−0.0989467	−	0.995093i	$-0.531547\pi$
$577$	441.473	−	283.717i	0.765117	−	0.491711i	0.864064	+	0.503382i	$0.167911\pi$
$578$	−42.6797	+	296.844i	−0.0738403	+	0.513571i
$579$	−199.503	+	436.850i	−0.344564	+	0.754490i
$580$	−126.322	−	430.212i	−0.217796	−	0.741745i
$581$	−75.2807	−	164.842i	−0.129571	−	0.283721i
$582$	37.5348	−	32.5241i	0.0644928	−	0.0558833i
$583$	7.98452	+	55.5336i	0.0136956	+	0.0952548i
$584$	80.0254	+	23.4976i	0.137030	+	0.0402356i
$585$	−477.055	−	413.370i	−0.815478	−	0.706616i
$586$	−183.621	+	285.721i	−0.313347	+	0.487578i
$587$	−489.004	−	314.264i	−0.833057	−	0.535373i	0.0531909	−	0.998584i	$-0.483061\pi$
$587$	−489.004	−	314.264i	−0.833057	−	0.535373i	−0.886248	+	0.463211i	$0.846697\pi$
$588$	−0.927306	+	1.07017i	−0.00157705	+	0.00182001i
$589$	−12.4559	+	42.4208i	−0.0211475	+	0.0720218i
$590$	−764.654	+	109.941i	−1.29602	+	0.186340i
$591$	21.5081	+	24.8216i	0.0363927	+	0.0419994i
$592$	−48.2521	+	22.0360i	−0.0815070	+	0.0372230i
$593$	−307.461	+	90.2786i	−0.518483	+	0.152240i	−0.530496	−	0.847687i	$-0.677994\pi$
$593$	−307.461	+	90.2786i	−0.518483	+	0.152240i	0.0120128	+	0.999928i	$0.496176\pi$
$594$	114.932	+	52.4878i	0.193489	+	0.0883633i
$595$	−588.533	−	84.6182i	−0.989130	−	0.142215i
$596$	188.209	+	292.859i	0.315787	+	0.491375i
$597$			153.455i			0.257044i
$598$	125.845	−	335.218i	0.210443	−	0.560565i
$599$	672.475			1.12266			0.561331	−	0.827591i	$-0.310289\pi$
$599$	672.475			1.12266			0.561331	+	0.827591i	$0.310289\pi$
$600$	768.512	−	493.893i	1.28085	−	0.823155i
$601$	−167.241	+	1163.19i	−0.278272	+	1.93542i	0.0689094	+	0.997623i	$0.478048\pi$
$601$	−167.241	+	1163.19i	−0.278272	+	1.93542i	−0.347181	+	0.937798i	$0.612861\pi$
$602$	72.1224	−	157.926i	0.119805	−	0.262336i
$603$	209.400	+	713.150i	0.347263	+	1.18267i
$604$	−117.998	−	258.379i	−0.195361	−	0.427780i
$605$	777.222	−	673.467i	1.28466	−	1.11317i
$606$	−3.24354	−	22.5593i	−0.00535238	−	0.0372266i
$607$	48.0575	+	14.1109i	0.0791721	+	0.0232470i	0.321079	−	0.947053i	$-0.395955\pi$
$607$	48.0575	+	14.1109i	0.0791721	+	0.0232470i	−0.241907	+	0.970300i	$0.577773\pi$
$608$	76.8491	+	66.5901i	0.126397	+	0.109523i
$609$	−157.026	+	244.337i	−0.257842	+	0.401211i
$610$	−1162.16	−	746.872i	−1.90517	−	1.22438i
$611$	−285.368	+	329.333i	−0.467051	+	0.539006i
$612$	30.2030	−	102.862i	0.0493513	−	0.168075i
$613$	−996.018	+	143.206i	−1.62482	+	0.233615i	−0.893712	−	0.448642i	$-0.851908\pi$
$613$	−996.018	+	143.206i	−1.62482	+	0.233615i	−0.731113	+	0.682256i	$0.760999\pi$
$614$	−186.573	−	215.316i	−0.303864	−	0.350678i
$615$	384.895	−	175.775i	0.625845	−	0.285814i
$616$	−198.492	+	58.2825i	−0.322227	+	0.0946145i
$617$	314.534	+	143.643i	0.509779	+	0.232808i	0.653662	−	0.756786i	$-0.273232\pi$
$617$	314.534	+	143.643i	0.509779	+	0.232808i	−0.143883	+	0.989595i	$0.545959\pi$
$618$	−321.474	−	46.2209i	−0.520184	−	0.0747912i
$619$	406.709	+	632.852i	0.657042	+	1.02238i	0.996648	+	0.0818099i	$0.0260700\pi$
$619$	406.709	+	632.852i	0.657042	+	1.02238i	−0.339606	+	0.940568i	$0.610294\pi$
$620$		−	218.366i		−	0.352204i
$621$	−352.085	+	468.246i	−0.566965	+	0.754020i
$622$	225.565			0.362644
$623$	317.347	−	203.946i	0.509385	−	0.327362i
$624$	−11.7405	+	81.6567i	−0.0188148	+	0.130860i
$625$	770.713	−	1687.63i	1.23314	−	2.70020i
$626$	4.47401	+	15.2371i	0.00714699	+	0.0243404i
$627$	−8.85705	−	19.3942i	−0.0141261	−	0.0309318i
$628$	−79.7458	+	69.1001i	−0.126984	+	0.110032i
$629$	−14.9041	−	103.661i	−0.0236950	−	0.164802i
$630$	565.860	+	166.152i	0.898191	+	0.263733i
$631$	459.044	+	397.764i	0.727486	+	0.630370i	0.937765	−	0.347271i	$-0.112892\pi$
$631$	459.044	+	397.764i	0.727486	+	0.630370i	−0.210279	+	0.977641i	$0.567437\pi$
$632$	387.643	−	603.184i	0.613359	−	0.954405i
$633$	−39.4095	−	25.3270i	−0.0622583	−	0.0400110i
$634$	−267.168	+	308.329i	−0.421401	+	0.486323i
$635$	−240.997	+	820.760i	−0.379523	+	1.29254i
$636$	52.1593	−	7.49938i	0.0820115	−	0.0117915i
$637$	−3.09854	−	3.57591i	−0.00486428	−	0.00561367i
$638$	−111.131	+	50.7517i	−0.174186	+	0.0795482i
$639$	559.818	−	164.377i	0.876085	−	0.257242i
$640$	−232.697	−	106.269i	−0.363589	−	0.166046i
$641$	774.559	+	111.365i	1.20836	+	0.173736i	0.716907	−	0.697168i	$-0.245557\pi$
$641$	774.559	+	111.365i	1.20836	+	0.173736i	0.491453	+	0.870904i	$0.336466\pi$
$642$	−155.791	−	242.415i	−0.242664	−	0.377593i
$643$			703.523i			1.09413i	0.837091	+	0.547063i	$0.184254\pi$
$643$			703.523i			1.09413i	−0.837091	+	0.547063i	$0.815746\pi$
$644$	−21.6174	−	311.588i	−0.0335674	−	0.483832i
$645$	−271.412			−0.420794
$646$	40.0105	−	25.7132i	0.0619358	−	0.0398037i
$647$	−9.02989	+	62.8042i	−0.0139565	+	0.0970699i	−0.995609	−	0.0936087i	$-0.970160\pi$
$647$	−9.02989	+	62.8042i	−0.0139565	+	0.0970699i	0.981653	+	0.190679i	$0.0610688\pi$
$648$	−45.9344	+	100.582i	−0.0708864	+	0.155220i
$649$	−55.3684	−	188.567i	−0.0853134	−	0.290551i
$650$	412.908	+	904.143i	0.635243	+	1.39099i
$651$	−106.902	+	92.6311i	−0.164212	+	0.142290i
$652$	64.5407	+	448.890i	0.0989888	+	0.688482i
$653$	−188.572	−	55.3698i	−0.288778	−	0.0847929i	0.134135	−	0.990963i	$-0.457174\pi$
$653$	−188.572	−	55.3698i	−0.288778	−	0.0847929i	−0.422913	+	0.906170i	$0.638993\pi$
$654$	102.736	+	89.0208i	0.157088	+	0.136117i
$655$	−328.615	+	511.335i	−0.501702	+	0.780664i
$656$	102.318	+	65.7561i	0.155973	+	0.100238i
$657$	39.6112	−	45.7138i	0.0602910	−	0.0695795i
$658$	114.702	−	390.639i	0.174319	−	0.593677i
$659$	783.363	−	112.631i	1.18871	−	0.170911i	0.480555	−	0.876964i	$-0.340435\pi$
$659$	783.363	−	112.631i	1.18871	−	0.170911i	0.708159	+	0.706053i	$0.249526\pi$
$660$	68.9611	+	79.5853i	0.104487	+	0.120584i
$661$	−429.835	+	196.299i	−0.650280	+	0.296973i	−0.713111	−	0.701051i	$-0.752714\pi$
$661$	−429.835	+	196.299i	−0.650280	+	0.296973i	0.0628310	+	0.998024i	$0.479987\pi$
$662$	616.513	−	181.025i	0.931289	−	0.273451i
$663$	−148.152	−	67.6586i	−0.223457	−	0.102049i
$664$	−217.635	−	31.2911i	−0.327763	−	0.0471252i
$665$	−132.069	−	205.503i	−0.198599	−	0.309027i
$666$			103.875i			0.155968i
$667$	−119.231	−	553.781i	−0.178758	−	0.830257i
$668$	−169.477			−0.253708
$669$	−64.7061	+	41.5841i	−0.0967207	+	0.0621586i
$670$	231.778	−	1612.05i	0.345937	−	2.40604i
$671$	145.994	−	319.683i	0.217577	−	0.476428i
$672$	91.6575	+	312.157i	0.136395	+	0.464519i
$673$	−216.195	−	473.402i	−0.321241	−	0.703420i	0.678266	−	0.734817i	$-0.262732\pi$
$673$	−216.195	−	473.402i	−0.321241	−	0.703420i	−0.999507	+	0.0313965i	$0.990005\pi$
$674$	418.051	−	362.243i	0.620253	−	0.537453i
$675$	−231.446	−	1609.74i	−0.342883	−	2.38480i
$676$	−96.0674	−	28.2079i	−0.142111	−	0.0417277i
$677$	615.886	+	533.668i	0.909729	+	0.788284i	0.977831	−	0.209394i	$-0.0671491\pi$
$677$	615.886	+	533.668i	0.909729	+	0.788284i	−0.0681028	+	0.997678i	$0.521695\pi$
$678$	10.3233	−	16.0633i	0.0152261	−	0.0236922i
$679$	121.782	+	78.2647i	0.179355	+	0.115265i
$680$	−472.424	+	545.206i	−0.694741	+	0.801774i
$681$	110.368	−	375.879i	0.162068	−	0.551952i
$682$	−58.8939	+	8.46766i	−0.0863547	+	0.0124159i
$683$	−530.908	−	612.700i	−0.777317	−	0.897072i	0.219595	−	0.975591i	$-0.429526\pi$
$683$	−530.908	−	612.700i	−0.777317	−	0.897072i	−0.996913	+	0.0785191i	$0.974981\pi$
$684$	40.0641	−	18.2967i	0.0585733	−	0.0267495i
$685$	−1261.56	+	370.427i	−1.84169	+	0.540769i
$686$	−446.721	−	204.011i	−0.651197	−	0.297392i
$687$	498.085	+	71.6138i	0.725015	+	0.104241i
$688$	−42.1783	−	65.6308i	−0.0613057	−	0.0953936i
$689$			176.080i			0.255559i
$690$	459.532	−	249.653i	0.665989	−	0.361816i
$691$	−122.282			−0.176964			−0.0884820	−	0.996078i	$-0.528202\pi$
$691$	−122.282			−0.176964			−0.0884820	+	0.996078i	$0.528202\pi$
$692$	284.705	−	182.969i	0.411423	−	0.264405i
$693$	−21.3518	+	148.505i	−0.0308107	+	0.214293i
$694$	−58.2117	+	127.466i	−0.0838785	+	0.183668i
$695$	606.660	+	2066.09i	0.872892	+	2.97280i
$696$	146.391	+	320.552i	0.210332	+	0.460563i
$697$	−181.473	+	157.247i	−0.260363	+	0.225605i
$698$	110.772	+	770.434i	0.158699	+	1.10377i
$699$	365.214	+	107.237i	0.522481	+	0.153414i
$700$	655.262	+	567.788i	0.936089	+	0.811125i
$701$	−450.428	+	700.880i	−0.642551	+	0.999828i	0.355329	+	0.934741i	$0.384369\pi$
$701$	−450.428	+	700.880i	−0.642551	+	0.999828i	−0.997880	+	0.0650870i	$0.979268\pi$
$702$	333.591	+	214.386i	0.475201	+	0.305393i
$703$	28.1762	−	32.5171i	0.0400800	−	0.0462548i
$704$	−56.2162	+	191.455i	−0.0798525	+	0.271953i
$705$	−629.988	+	90.5786i	−0.893600	+	0.128480i
$706$	548.238	+	632.700i	0.776541	+	0.896176i
$707$	60.4277	−	27.5964i	0.0854705	−	0.0390331i
$708$	−177.110	+	52.0042i	−0.250155	+	0.0734522i
$709$	−97.1132	−	44.3501i	−0.136972	−	0.0625530i	0.345750	−	0.938327i	$-0.387625\pi$
$709$	−97.1132	−	44.3501i	−0.136972	−	0.0625530i	−0.482722	+	0.875774i	$0.660352\pi$
$710$	−1265.45	−	181.944i	−1.78232	−	0.256259i
$711$	−281.135	−	437.454i	−0.395408	−	0.615266i
$712$		−	457.695i		−	0.642830i
$713$	20.2680	−	275.136i	0.0284264	−	0.385885i
$714$	152.166			0.213118
$715$	−296.017	+	190.239i	−0.414010	+	0.266068i
$716$	−31.4540	+	218.767i	−0.0439302	+	0.305541i
$717$	134.080	−	293.595i	0.187002	−	0.409477i
$718$	154.187	+	525.112i	0.214745	+	0.731354i
$719$	−435.881	−	954.446i	−0.606232	−	1.32746i	−0.925121	−	0.379671i	$-0.876037\pi$
$719$	−435.881	−	954.446i	−0.606232	−	1.32746i	0.318889	−	0.947792i	$-0.396690\pi$
$720$	200.280	−	173.544i	0.278167	−	0.241033i
$721$	−134.722	−	937.014i	−0.186855	−	1.29960i
$722$	−479.435	−	140.775i	−0.664037	−	0.194979i
$723$	−202.080	−	175.104i	−0.279503	−	0.242190i
$724$	129.736	−	201.873i	0.179193	−	0.278830i
$725$	1322.87	+	850.160i	1.82466	+	1.17263i
$726$	−172.354	+	198.907i	−0.237402	+	0.273976i
$727$	136.866	−	466.123i	0.188262	−	0.641160i	−0.810223	−	0.586122i	$-0.800654\pi$
$727$	136.866	−	466.123i	0.188262	−	0.641160i	0.998484	−	0.0550378i	$-0.0175279\pi$
$728$	−642.642	+	92.3980i	−0.882750	+	0.126920i
$729$	−199.273	−	229.973i	−0.273351	−	0.315463i
$730$	−120.564	+	55.0597i	−0.165156	+	0.0754243i
$731$	147.784	−	43.3934i	0.202167	−	0.0593617i
$732$	−300.259	−	137.124i	−0.410190	−	0.187327i
$733$	−328.395	−	47.2161i	−0.448015	−	0.0644148i	−0.0853850	−	0.996348i	$-0.527212\pi$
$733$	−328.395	−	47.2161i	−0.448015	−	0.0644148i	−0.362630	+	0.931933i	$0.618121\pi$
$734$	−182.530	−	284.022i	−0.248678	−	0.386951i
$735$		−	6.91078i		−	0.00940242i
$736$	−556.256	−	305.281i	−0.755783	−	0.414784i
$737$	414.322			0.562174
$738$	200.361	−	128.764i	0.271492	−	0.174478i
$739$	−5.30378	+	36.8886i	−0.00717696	+	0.0499169i	−0.993095	−	0.117311i	$-0.962573\pi$
$739$	−5.30378	+	36.8886i	−0.00717696	+	0.0499169i	0.985918	+	0.167228i	$0.0534816\pi$
$740$	−88.2804	+	193.307i	−0.119298	+	0.261226i
$741$	−18.8519	−	64.2037i	−0.0254412	−	0.0866446i
$742$	−68.3390	−	149.642i	−0.0921011	−	0.201673i
$743$	14.3871	−	12.4665i	0.0193635	−	0.0167786i	−0.645125	−	0.764077i	$-0.723195\pi$
$743$	14.3871	−	12.4665i	0.0193635	−	0.0167786i	0.664489	+	0.747298i	$0.268649\pi$
$744$	24.4246	+	169.877i	0.0328287	+	0.228329i
$745$	−1630.15	−	478.655i	−2.18812	−	0.642489i
$746$	103.228	+	89.4477i	0.138376	+	0.119903i
$747$	−86.2110	+	134.147i	−0.115410	+	0.179581i
$748$	−50.2735	−	32.3088i	−0.0672106	−	0.0431936i
$749$	550.025	−	634.762i	0.734345	−	0.847480i
$750$	−248.854	+	847.518i	−0.331805	+	1.13002i
$751$	458.946	−	65.9865i	0.611113	−	0.0878649i	0.170193	−	0.985411i	$-0.445561\pi$
$751$	458.946	−	65.9865i	0.611113	−	0.0878649i	0.440921	+	0.897546i	$0.354652\pi$
$752$	−119.805	−	138.262i	−0.159315	−	0.183860i
$753$	−255.917	+	116.873i	−0.339863	+	0.155210i
$754$	−367.893	+	108.023i	−0.487922	+	0.143267i
$755$	1260.99	+	575.873i	1.67018	+	0.762746i
$756$	342.381	+	49.2270i	0.452885	+	0.0651151i
$757$	145.322	+	226.125i	0.191971	+	0.298712i	0.923874	−	0.382696i	$-0.125004\pi$
$757$	145.322	+	226.125i	0.191971	+	0.298712i	−0.731904	+	0.681408i	$0.761368\pi$
$758$			76.9217i			0.101480i
$759$	79.5025	+	106.676i	0.104746	+	0.140549i
$760$	−296.388			−0.389984
$761$	−192.842	+	123.932i	−0.253407	+	0.162855i	−0.661177	−	0.750230i	$-0.729943\pi$
$761$	−192.842	+	123.932i	−0.253407	+	0.162855i	0.407770	+	0.913085i	$0.366306\pi$
$762$	31.1551	−	216.688i	0.0408859	−	0.284368i
$763$	−164.598	+	360.420i	−0.215725	+	0.472372i
$764$	−143.186	−	487.647i	−0.187416	−	0.638282i
$765$	217.344	+	475.918i	0.284110	+	0.622114i
$766$	−400.584	+	347.108i	−0.522955	+	0.453143i
$767$	−87.7781	−	610.510i	−0.114443	−	0.795971i
$768$	435.237	+	127.797i	0.566714	+	0.166402i
$769$	161.239	+	139.715i	0.209674	+	0.181684i	0.753366	−	0.657601i	$-0.228429\pi$
$769$	161.239	+	139.715i	0.209674	+	0.181684i	−0.543692	+	0.839285i	$0.682974\pi$
$770$	177.736	−	276.563i	0.230826	−	0.359173i
$771$	260.607	+	167.482i	0.338011	+	0.217227i
$772$	−362.158	+	417.952i	−0.469116	+	0.541389i
$773$	348.139	−	1185.65i	0.450374	−	1.53383i	−0.351410	−	0.936222i	$-0.614298\pi$
$773$	348.139	−	1185.65i	0.450374	−	1.53383i	0.801785	−	0.597613i	$-0.203884\pi$
$774$	−151.216	+	21.7416i	−0.195369	+	0.0280899i
$775$	501.517	+	578.782i	0.647119	+	0.746815i
$776$	159.769	−	72.9640i	0.205888	−	0.0940257i
$777$	132.083	−	38.7830i	0.169991	−	0.0499138i
$778$	702.634	+	320.882i	0.903128	+	0.412445i
$779$	−97.6489	−	14.0398i	−0.125352	−	0.0180228i
$780$	178.680	+	278.031i	0.229076	+	0.356450i
$781$		−	325.241i		−	0.416441i
$782$	−210.301	+	209.406i	−0.268928	+	0.267783i
$783$	627.347			0.801209
$784$	1.67111	−	1.07396i	0.00213152	−	0.00136984i
$785$	73.2881	−	509.730i	0.0933606	−	0.649337i
$786$	64.6197	−	141.497i	0.0822133	−	0.180022i
$787$	−355.004	−	1209.03i	−0.451085	−	1.53625i	−0.800528	−	0.599295i	$-0.795447\pi$
$787$	−355.004	−	1209.03i	−0.451085	−	1.53625i	0.349443	−	0.936957i	$-0.386371\pi$
$788$	15.7115	+	34.4033i	0.0199384	+	0.0436591i
$789$	−182.363	+	158.018i	−0.231132	+	0.200277i
$790$	162.158	+	1127.83i	0.205263	+	1.42764i
$791$	53.4012	+	15.6800i	0.0675110	+	0.0198230i
$792$	137.572	+	119.207i	0.173703	+	0.150514i
$793$	596.313	−	927.881i	0.751971	−	1.17009i
$794$	−248.308	−	159.578i	−0.312730	−	0.200980i
$795$	−168.414	+	194.360i	−0.211841	+	0.244477i
$796$	−49.7852	+	169.553i	−0.0625443	+	0.213006i
$797$	879.504	−	126.454i	1.10352	−	0.158662i	0.433606	−	0.901102i	$-0.357241\pi$
$797$	879.504	−	126.454i	1.10352	−	0.158662i	0.669912	+	0.742440i	$0.266332\pi$
$798$	40.9396	+	47.2469i	0.0513028	+	0.0592066i
$799$	328.548	−	150.043i	0.411198	−	0.187788i
$800$	1690.06	−	496.246i	2.11257	−	0.620308i
$801$	−301.943	−	137.893i	−0.376958	−	0.172151i
$802$	347.713	+	49.9936i	0.433558	+	0.0623362i
$803$	−18.2296	−	28.3658i	−0.0227019	−	0.0353248i
$804$		−	389.148i		−	0.484015i
$805$	1075.56	+	1080.15i	1.33609	+	1.34181i
$806$	−186.734			−0.231680
$807$	−436.184	+	280.319i	−0.540501	+	0.347359i
$808$	11.4707	−	79.7804i	0.0141964	−	0.0987381i
$809$	−328.317	+	718.915i	−0.405831	+	0.888646i	0.590815	+	0.806807i	$0.298806\pi$
$809$	−328.317	+	718.915i	−0.405831	+	0.888646i	−0.996646	+	0.0818386i	$0.973921\pi$
$810$	−49.5061	−	168.602i	−0.0611186	−	0.208151i
$811$	89.6814	+	196.375i	0.110581	+	0.242139i	0.956830	−	0.290649i	$-0.0938713\pi$
$811$	89.6814	+	196.375i	0.110581	+	0.242139i	−0.846248	+	0.532789i	$0.821144\pi$
$812$	−252.769	+	219.025i	−0.311292	+	0.269736i
$813$	115.881	+	805.969i	0.142535	+	0.991352i
$814$	55.5587	+	16.3135i	0.0682539	+	0.0200412i
$815$	−1672.69	−	1449.39i	−2.05237	−	1.77839i
$816$	36.9674	−	57.5224i	0.0453032	−	0.0704932i
$817$	53.2342	+	34.2116i	0.0651582	+	0.0418746i
$818$	52.9929	−	61.1571i	0.0647836	−	0.0747642i
$819$	−132.658	+	451.790i	−0.161975	+	0.551637i
$820$	482.298	−	69.3440i	0.588168	−	0.0845659i
$821$	−743.236	−	857.740i	−0.905281	−	1.04475i	−0.998792	−	0.0491319i	$-0.984355\pi$
$821$	−743.236	−	857.740i	−0.905281	−	1.04475i	0.0935111	−	0.995618i	$-0.470191\pi$
$822$	306.080	−	139.782i	0.372361	−	0.170051i
$823$	−636.705	+	186.954i	−0.773640	+	0.227161i	−0.644643	−	0.764484i	$-0.722994\pi$
$823$	−636.705	+	186.954i	−0.773640	+	0.227161i	−0.128997	+	0.991645i	$0.541176\pi$
$824$	−1044.78	−	477.134i	−1.26794	−	0.579047i
$825$	−365.564	−	52.5601i	−0.443108	−	0.0637093i
$826$	311.546	+	484.774i	0.377174	+	0.586894i
$827$			1168.85i			1.41336i	0.707531	+	0.706682i	$0.249809\pi$
$827$			1168.85i			1.41336i	−0.707531	+	0.706682i	$0.750191\pi$
$828$	−220.369	+	164.234i	−0.266146	+	0.198350i
$829$	543.466			0.655568			0.327784	−	0.944753i	$-0.393698\pi$
$829$	543.466			0.655568			0.327784	+	0.944753i	$0.393698\pi$
$830$	293.943	−	188.906i	0.354149	−	0.227597i
$831$	−13.3856	+	93.0986i	−0.0161078	+	0.112032i
$832$	−260.146	+	569.641i	−0.312676	+	0.684664i
$833$	1.10490	+	3.76293i	0.00132641	+	0.00451732i
$834$	−228.926	−	501.277i	−0.274491	−	0.601052i
$835$	625.088	−	541.642i	0.748609	−	0.648673i
$836$	−3.49414	−	24.3022i	−0.00417959	−	0.0290697i
$837$	293.153	+	86.0775i	0.350243	+	0.102841i
$838$	−389.881	−	337.834i	−0.465252	−	0.403143i
$839$	−809.674	+	1259.88i	−0.965047	+	1.50164i	−0.103083	+	0.994673i	$0.532871\pi$
$839$	−809.674	+	1259.88i	−0.965047	+	1.50164i	−0.861964	+	0.506970i	$0.830766\pi$
$840$	−797.733	−	512.672i	−0.949682	−	0.610324i
$841$	153.501	−	177.150i	0.182522	−	0.210642i
$842$	159.813	−	544.274i	0.189802	−	0.646406i
$843$	35.6954	−	5.13222i	0.0423433	−	0.00608804i
$844$	−35.3269	−	40.7694i	−0.0418566	−	0.0483050i
$845$	444.481	−	202.988i	0.526013	−	0.240222i
$846$	−343.738	+	100.931i	−0.406310	+	0.119303i
$847$	−697.811	−	318.680i	−0.823862	−	0.376245i
$848$	−73.1705	−	10.5203i	−0.0862860	−	0.0124060i
$849$	273.901	+	426.199i	0.322616	+	0.502001i
$850$		−	823.847i		−	0.969232i
$851$	−129.173	+	235.368i	−0.151790	+	0.276579i
$852$	−305.479			−0.358543
$853$	−73.3327	+	47.1281i	−0.0859704	+	0.0552498i	−0.582920	−	0.812530i	$-0.698090\pi$
$853$	−73.3327	+	47.1281i	−0.0859704	+	0.0552498i	0.496949	+	0.867780i	$0.334453\pi$
$854$	−146.653	+	1020.00i	−0.171725	+	1.19438i
$855$	−89.2946	+	195.528i	−0.104438	+	0.228688i
$856$	−287.104	−	977.787i	−0.335402	−	1.14227i
$857$	375.542	+	822.322i	0.438205	+	0.959536i	0.991924	+	0.126832i	$0.0404810\pi$
$857$	375.542	+	822.322i	0.438205	+	0.959536i	−0.553719	+	0.832704i	$0.686792\pi$
$858$	68.0569	−	58.9716i	0.0793204	−	0.0687315i
$859$	−35.7053	−	248.336i	−0.0415661	−	0.289099i	−0.999993	−	0.00376028i	$-0.998803\pi$
$859$	−35.7053	−	248.336i	−0.0415661	−	0.289099i	0.958427	−	0.285339i	$-0.0921060\pi$
$860$	−299.885	−	88.0540i	−0.348703	−	0.102388i
$861$	−238.539	−	206.695i	−0.277048	−	0.240064i
$862$	549.136	−	854.473i	0.637049	−	0.991268i
$863$	−1257.56	−	808.183i	−1.45719	−	0.936481i	−0.998862	−	0.0476999i	$-0.984811\pi$
$863$	−1257.56	−	808.183i	−1.45719	−	0.936481i	−0.458332	−	0.888781i	$-0.651553\pi$
$864$	460.177	−	531.073i	0.532612	−	0.614667i
$865$	−465.327	+	1584.76i	−0.537950	+	1.83209i
$866$	874.909	−	125.793i	1.01029	−	0.145257i
$867$	−229.016	−	264.299i	−0.264148	−	0.304843i
$868$	−148.169	+	67.6663i	−0.170701	+	0.0779566i
$869$	−278.130	+	81.6662i	−0.320057	+	0.0939772i
$870$	−509.406	−	232.638i	−0.585524	−	0.267400i
$871$	1287.08	+	185.055i	1.47771	+	0.212462i
$872$	259.909	+	404.426i	0.298061	+	0.463792i
$873$		−	127.382i		−	0.145913i
$874$	−121.600	−	8.95774i	−0.139131	−	0.0102491i
$875$	−2574.59			−2.94239
$876$	−26.6423	+	17.1220i	−0.0304136	+	0.0195456i
$877$	−210.751	+	1465.80i	−0.240309	+	1.67138i	0.410284	+	0.911958i	$0.365429\pi$
$877$	−210.751	+	1465.80i	−0.240309	+	1.67138i	−0.650593	+	0.759426i	$0.725480\pi$
$878$	−484.781	+	1061.52i	−0.552142	+	1.20902i
$879$	−111.583	−	380.017i	−0.126943	−	0.432328i
$880$	−61.3680	−	134.377i	−0.0697363	−	0.152701i
$881$	−727.420	+	630.313i	−0.825676	+	0.715452i	−0.961358	−	0.275300i	$-0.911223\pi$
$881$	−727.420	+	630.313i	−0.825676	+	0.715452i	0.135682	+	0.990752i	$0.456677\pi$
$882$	−0.553590	−	3.85030i	−0.000627653	−	0.00436542i
$883$	1522.70	+	447.106i	1.72446	+	0.506348i	0.985829	−	0.167756i	$-0.0536522\pi$
$883$	1522.70	+	447.106i	1.72446	+	0.506348i	0.738636	+	0.674105i	$0.235470\pi$
$884$	−141.743	−	122.821i	−0.160343	−	0.138938i
$885$	487.038	−	757.846i	0.550326	−	0.856323i
$886$	405.208	+	260.412i	0.457346	+	0.293918i
$887$	514.928	−	594.258i	0.580527	−	0.669964i	−0.387191	−	0.922000i	$-0.626554\pi$
$887$	514.928	−	594.258i	0.580527	−	0.669964i	0.967718	+	0.252035i	$0.0810999\pi$
$888$	47.0555	−	160.256i	0.0529905	−	0.180469i
$889$	631.591	−	90.8091i	0.710451	−	0.102147i
$890$	476.311	+	549.693i	0.535181	+	0.617632i
$891$	40.6634	−	18.5704i	0.0456380	−	0.0208422i
$892$	−84.9852	+	24.9539i	−0.0952748	+	0.0279752i
$893$	134.982	+	61.6442i	0.151156	+	0.0690304i
$894$	430.374	+	61.8785i	0.481403	+	0.0692153i
$895$	−583.160	−	907.415i	−0.651575	−	1.01387i
$896$			190.823i			0.212972i
$897$	199.326	+	366.897i	0.222214	+	0.409026i
$898$	543.562			0.605303
$899$	−248.526	+	159.718i	−0.276447	+	0.177662i
$900$	108.577	−	755.173i	0.120642	−	0.839081i
$901$	60.6272	−	132.755i	0.0672888	−	0.147342i
$902$	−37.4045	−	127.388i	−0.0414684	−	0.141228i
$903$	84.1040	+	184.162i	0.0931384	+	0.203945i
$904$	51.0336	−	44.2209i	0.0564531	−	0.0489169i
$905$	166.669	+	1159.21i	0.184165	+	1.28089i
$906$	−340.401	−	99.9507i	−0.375718	−	0.110321i
$907$	−387.117	−	335.439i	−0.426810	−	0.369833i	0.414805	−	0.909910i	$-0.363850\pi$
$907$	−387.117	−	335.439i	−0.426810	−	0.369833i	−0.841616	+	0.540077i	$0.818395\pi$
$908$	243.892	−	379.504i	0.268604	−	0.417956i
$909$	−49.1756	−	31.6032i	−0.0540985	−	0.0347670i
$910$	675.658	−	779.751i	0.742481	−	0.856869i
$911$	−54.4412	+	185.410i	−0.0597599	+	0.203523i	−0.983961	−	0.178382i	$-0.942914\pi$
$911$	−54.4412	+	185.410i	−0.0597599	+	0.203523i	0.924201	+	0.381905i	$0.124732\pi$
$912$	27.8064	−	3.99795i	0.0304894	−	0.00438372i
$913$	58.2107	+	67.1787i	0.0637576	+	0.0735802i
$914$	630.378	−	287.884i	0.689692	−	0.314972i
$915$	1545.70	−	453.859i	1.68929	−	0.496020i
$916$	527.103	+	240.720i	0.575439	+	0.262794i
$917$	448.787	+	64.5258i	0.489408	+	0.0703662i
$918$	−177.693	−	276.496i	−0.193566	−	0.301194i
$919$		−	238.225i		−	0.259222i	−0.991565	−	0.129611i	$-0.958627\pi$
$919$		−	238.225i		−	0.259222i	0.991565	−	0.129611i	$-0.0413729\pi$
$920$	1808.03	−	389.277i	1.96525	−	0.423127i
$921$	332.235			0.360733
$922$	−1009.35	+	648.671i	−1.09474	+	0.703548i
$923$	145.267	−	1010.35i	0.157385	−	1.09464i
$924$	32.6319	−	71.4539i	0.0353159	−	0.0773310i
$925$	−209.976	−	715.114i	−0.227001	−	0.773096i
$926$	−257.369	−	563.560i	−0.277937	−	0.608596i
$927$	−629.535	+	545.495i	−0.679110	+	0.588452i
$928$	96.6983	+	672.551i	0.104201	+	0.724732i
$929$	−322.629	−	94.7324i	−0.347286	−	0.101972i	0.103437	−	0.994636i	$-0.467016\pi$
$929$	−322.629	−	94.7324i	−0.347286	−	0.101972i	−0.450724	+	0.892663i	$0.648834\pi$
$930$	−206.120	−	178.604i	−0.221635	−	0.192048i
$931$	−0.871105	+	1.35547i	−0.000935666	+	0.00145592i
$932$	368.736	+	236.972i	0.395640	+	0.254262i
$933$	−172.253	+	198.790i	−0.184623	+	0.213066i
$934$	−40.2104	+	136.944i	−0.0430518	+	0.146621i
$935$	288.684	−	41.5065i	0.308753	−	0.0443919i
$936$	374.122	+	431.760i	0.399703	+	0.461282i
$937$	−251.126	+	114.686i	−0.268011	+	0.122397i	−0.544888	−	0.838509i	$-0.683428\pi$
$937$	−251.126	+	114.686i	−0.268011	+	0.122397i	0.276877	+	0.960905i	$0.410701\pi$
$938$	−1165.65	+	342.266i	−1.24270	+	0.364889i
$939$	−16.8450	−	7.69287i	−0.0179393	−	0.00819262i
$940$	−725.462	−	104.306i	−0.771768	−	0.110964i
$941$	83.1863	+	129.440i	0.0884020	+	0.137556i	0.882638	−	0.470053i	$-0.155765\pi$
$941$	83.1863	+	129.440i	0.0884020	+	0.137556i	−0.794236	+	0.607609i	$0.792129\pi$
$942$			131.791i			0.139906i
$943$	614.120	−	42.6065i	0.651241	−	0.0451819i
$944$	258.944			0.274305
$945$	−1420.15	+	912.672i	−1.50280	+	0.965791i
$946$	−12.1197	+	84.2941i	−0.0128115	+	0.0891058i
$947$	−192.262	+	420.995i	−0.203022	+	0.444556i	−0.983567	−	0.180543i	$-0.942214\pi$
$947$	−192.262	+	420.995i	−0.203022	+	0.444556i	0.780545	+	0.625100i	$0.214942\pi$
$948$	76.7041	+	261.230i	0.0809115	+	0.275559i
$949$	−43.9604	−	96.2599i	−0.0463229	−	0.101433i
$950$	255.801	−	221.653i	0.269264	−	0.233319i
$951$	−67.7068	−	470.911i	−0.0711954	−	0.495175i
$952$	516.333	+	151.609i	0.542366	+	0.159253i
$953$	230.913	+	200.087i	0.242301	+	0.209955i	0.767542	−	0.640998i	$-0.221479\pi$
$953$	230.913	+	200.087i	0.242301	+	0.209955i	−0.525241	+	0.850953i	$0.676025\pi$
$954$	−78.2614	+	121.777i	−0.0820351	+	0.127649i
$955$	2086.62	+	1340.99i	2.18494	+	1.40418i
$956$	243.397	−	280.895i	0.254599	−	0.293823i
$957$	40.1376	−	136.696i	0.0419411	−	0.142838i
$958$	−839.036	+	120.635i	−0.875820	+	0.125924i
$959$	642.273	+	741.222i	0.669732	+	0.772911i
$960$	−831.992	+	379.958i	−0.866659	+	0.395790i
$961$	784.024	−	230.210i	0.815842	−	0.239553i
$962$	165.305	+	75.4924i	0.171835	+	0.0784744i
$963$	−731.547	−	105.181i	−0.759654	−	0.109222i
$964$	−166.471	−	259.033i	−0.172687	−	0.268707i
$965$		−	2698.99i		−	2.79689i
$966$	−311.795	−	234.446i	−0.322769	−	0.242698i
$967$	−961.177			−0.993978			−0.496989	−	0.867757i	$-0.665561\pi$
$967$	−961.177			−0.993978			−0.496989	+	0.867757i	$0.665561\pi$
$968$	−783.012	+	503.211i	−0.808897	+	0.519846i
$969$	−7.89303	+	54.8972i	−0.00814554	+	0.0566535i
$970$	−115.951	+	253.897i	−0.119537	+	0.261750i
$971$	−290.097	−	987.980i	−0.298761	−	1.01749i	−0.962896	−	0.269874i	$-0.913018\pi$
$971$	−290.097	−	987.980i	−0.298761	−	1.01749i	0.664134	−	0.747613i	$-0.268800\pi$
$972$	−201.371	−	440.942i	−0.207172	−	0.453644i
$973$	1213.92	−	1051.87i	1.24761	−	1.08106i
$974$	−112.846	−	784.863i	−0.115859	−	0.805814i
$975$	−1112.14	−	326.554i	−1.14066	−	0.334927i
$976$	349.955	+	303.238i	0.358561	+	0.310695i
$977$	−630.361	+	980.861i	−0.645201	+	1.00395i	0.352476	+	0.935821i	$0.385340\pi$
$977$	−630.361	+	980.861i	−0.645201	+	1.00395i	−0.997676	+	0.0681309i	$0.978296\pi$
$978$	476.505	+	306.231i	0.487224	+	0.313120i
$979$	−121.174	+	139.842i	−0.123773	+	0.142841i
$980$	2.24206	−	7.63575i	0.00228781	−	0.00779158i
$981$	345.106	−	49.6188i	0.351790	−	0.0505798i
$982$	−704.194	−	812.684i	−0.717102	−	0.827580i
$983$	967.009	−	441.618i	0.983732	−	0.449255i	0.142421	−	0.989806i	$-0.454511\pi$
$983$	967.009	−	441.618i	0.983732	−	0.449255i	0.841311	+	0.540551i	$0.181784\pi$
$984$	−367.445	+	107.892i	−0.373419	+	0.109646i
$985$	−167.901	−	76.6779i	−0.170458	−	0.0778456i
$986$	314.566	+	45.2278i	0.319033	+	0.0458700i
$987$	256.678	+	399.399i	0.260059	+	0.404660i
$988$		−	77.0550i		−	0.0779909i
$989$	−369.674	−	138.780i	−0.373786	−	0.140324i
$990$	−289.281			−0.292203
$991$	314.928	−	202.392i	0.317788	−	0.204230i	−0.372016	−	0.928227i	$-0.621333\pi$
$991$	314.928	−	202.392i	0.317788	−	0.204230i	0.689804	+	0.723996i	$0.257697\pi$
$992$	−47.0938	+	327.544i	−0.0474736	+	0.330186i
$993$	−311.264	+	681.573i	−0.313458	+	0.686378i
$994$	268.677	+	915.029i	0.270298	+	0.920552i
$995$	−358.260	−	784.481i	−0.360061	−	0.788423i
$996$	63.0969	−	54.6737i	0.0633503	−	0.0548933i
$997$	−137.279	−	954.794i	−0.137692	−	0.957667i	−0.935140	−	0.354279i	$-0.884726\pi$
$997$	−137.279	−	954.794i	−0.137692	−	0.957667i	0.797448	−	0.603388i	$-0.206183\pi$
$998$	−431.713	−	126.762i	−0.432578	−	0.127016i
$999$	−224.712	−	194.714i	−0.224937	−	0.194909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.11.3	✓	30
3.2	odd	2		207.3.j.a.172.1		30
4.3	odd	2		368.3.p.a.241.2		30
23.5	odd	22		529.3.b.b.528.20		30
23.18	even	11		529.3.b.b.528.19		30
23.21	odd	22	inner	23.3.d.a.21.3	yes	30
69.44	even	22		207.3.j.a.136.1		30
92.67	even	22		368.3.p.a.113.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.11.3	✓	30	1.1	even	1	trivial
23.3.d.a.21.3	yes	30	23.21	odd	22	inner
207.3.j.a.136.1		30	69.44	even	22
207.3.j.a.172.1		30	3.2	odd	2
368.3.p.a.113.2		30	92.67	even	22
368.3.p.a.241.2		30	4.3	odd	2
529.3.b.b.528.19		30	23.18	even	11
529.3.b.b.528.20		30	23.5	odd	22

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)

\(f(q)\)	\(=\)	\(q+(1.20995 - 0.777587i) q^{2} +(-0.238691 + 1.66013i) q^{3} +(-0.802326 + 1.75685i) q^{4} +(-2.65558 - 9.04406i) q^{5} +(1.00209 + 2.19428i) q^{6} +(-5.31379 + 4.60443i) q^{7} +(1.21408 + 8.44409i) q^{8} +(5.93637 + 1.74307i) q^{9} +O(q^{10})\)	\(q+(1.20995 - 0.777587i) q^{2} +(-0.238691 + 1.66013i) q^{3} +(-0.802326 + 1.75685i) q^{4} +(-2.65558 - 9.04406i) q^{5} +(1.00209 + 2.19428i) q^{6} +(-5.31379 + 4.60443i) q^{7} +(1.21408 + 8.44409i) q^{8} +(5.93637 + 1.74307i) q^{9} +(-10.2457 - 8.87791i) q^{10} +(1.86461 - 2.90139i) q^{11} +(-2.72510 - 1.75131i) q^{12} +(7.08824 - 8.18027i) q^{13} +(-2.84907 + 9.70305i) q^{14} +(15.6482 - 2.24987i) q^{15} +(2.97583 + 3.43429i) q^{16} +(-8.16077 + 3.72690i) q^{17} +(8.53809 - 2.50701i) q^{18} +(-3.35280 - 1.53117i) q^{19} +(18.0197 + 2.59084i) q^{20} +(-6.37561 - 9.92064i) q^{21} -4.96042i q^{22} +(22.4639 + 4.93692i) q^{23} -14.3081 q^{24} +(-53.7117 + 34.5184i) q^{25} +(2.21554 - 15.4094i) q^{26} +(-10.5813 + 23.1699i) q^{27} +(-3.82589 - 13.0298i) q^{28} +(-10.2313 - 22.4035i) q^{29} +(17.1841 - 14.8901i) q^{30} +(-1.70705 - 11.8728i) q^{31} +(-26.4704 - 7.77241i) q^{32} +(4.37162 + 3.78803i) q^{33} +(-6.97612 + 10.8551i) q^{34} +(55.7539 + 35.8309i) q^{35} +(-7.82522 + 9.03079i) q^{36} +(-3.28873 + 11.2004i) q^{37} +(-5.24734 + 0.754453i) q^{38} +(11.8884 + 13.7200i) q^{39} +(73.1448 - 33.4041i) q^{40} +(25.6809 - 7.54059i) q^{41} +(-15.4283 - 7.04587i) q^{42} +(-16.9933 - 2.44327i) q^{43} +(3.60127 + 5.60369i) q^{44} -58.3178i q^{45} +(31.0190 - 11.4942i) q^{46} -40.2594 q^{47} +(-6.41168 + 4.12054i) q^{48} +(0.0622113 - 0.432689i) q^{49} +(-38.1473 + 83.5309i) q^{50} +(-4.23924 - 14.4375i) q^{51} +(8.68441 + 19.0162i) q^{52} +(-12.2941 + 10.6529i) q^{53} +(5.21372 + 36.2622i) q^{54} +(-31.1919 - 9.15878i) q^{55} +(-45.3315 - 39.2800i) q^{56} +(3.34224 - 5.20062i) q^{57} +(-29.8000 - 19.1513i) q^{58} +(37.3160 - 43.0650i) q^{59} +(-8.60228 + 29.2967i) q^{60} +(100.863 - 14.5019i) q^{61} +(-11.2975 - 13.0381i) q^{62} +(-39.5705 + 18.0712i) q^{63} +(-55.5121 + 16.2998i) q^{64} +(-92.8062 - 42.3832i) q^{65} +(8.23496 + 1.18401i) q^{66} +(64.9484 + 101.062i) q^{67} -17.3274i q^{68} +(-13.5579 + 36.1147i) q^{69} +95.3210 q^{70} +(79.3329 - 50.9841i) q^{71} +(-7.51147 + 52.2434i) q^{72} +(4.06137 - 8.89315i) q^{73} +(4.73008 + 16.1092i) q^{74} +(-44.4846 - 97.4078i) q^{75} +(5.38008 - 4.66187i) q^{76} +(3.45108 + 24.0028i) q^{77} +(25.0529 + 7.35618i) q^{78} +(-63.5192 - 55.0397i) q^{79} +(23.1574 - 36.0336i) q^{80} +(10.9040 + 7.00759i) q^{81} +(25.2091 - 29.0928i) q^{82} +(-7.26126 + 24.7296i) q^{83} +(22.5444 - 3.24139i) q^{84} +(55.3778 + 63.9094i) q^{85} +(-22.4609 + 10.2576i) q^{86} +(39.6349 - 11.6379i) q^{87} +(26.7633 + 12.2224i) q^{88} +(-53.1052 - 7.63538i) q^{89} +(-45.3471 - 70.5615i) q^{90} +76.1055i q^{91} +(-26.6968 + 35.5047i) q^{92} +20.1178 q^{93} +(-48.7118 + 31.3052i) q^{94} +(-4.94441 + 34.3891i) q^{95} +(19.2215 - 42.0892i) q^{96} +(-5.80052 - 19.7548i) q^{97} +(-0.261181 - 0.571906i) q^{98} +(16.1263 - 13.9735i) 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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