LMFDB - Embedded newform 108.3.j.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(7,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("108.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	108.31
Dual form			108.3.j.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90734 + 0.601703i) q^{2} +(-2.99807 - 0.107643i) q^{3} +(3.27591 - 2.29531i) q^{4} +(-0.755508 + 4.28470i) q^{5} +(5.78311 - 1.59863i) q^{6} +(-6.44162 - 7.67682i) q^{7} +(-4.86718 + 6.34906i) q^{8} +(8.97683 + 0.645444i) q^{9} +O(q^{10})$	\(q+(-1.90734 + 0.601703i) q^{2} +(-2.99807 - 0.107643i) q^{3} +(3.27591 - 2.29531i) q^{4} +(-0.755508 + 4.28470i) q^{5} +(5.78311 - 1.59863i) q^{6} +(-6.44162 - 7.67682i) q^{7} +(-4.86718 + 6.34906i) q^{8} +(8.97683 + 0.645444i) q^{9} +(-1.13710 - 8.62697i) q^{10} +(16.5915 - 2.92553i) q^{11} +(-10.0685 + 6.52886i) q^{12} +(7.70282 - 2.80360i) q^{13} +(16.9055 + 10.7664i) q^{14} +(2.72628 - 12.7645i) q^{15} +(5.46314 - 15.0384i) q^{16} +(13.2638 - 22.9735i) q^{17} +(-17.5102 + 4.17030i) q^{18} +(10.2637 - 5.92574i) q^{19} +(7.35972 + 15.7704i) q^{20} +(18.4861 + 23.7090i) q^{21} +(-29.8854 + 15.5631i) q^{22} +(-14.3578 + 17.1110i) q^{23} +(15.2756 - 18.5110i) q^{24} +(5.70448 + 2.07626i) q^{25} +(-13.0050 + 9.98223i) q^{26} +(-26.8437 - 2.90138i) q^{27} +(-38.7228 - 10.3631i) q^{28} +(-29.1256 - 10.6009i) q^{29} +(2.48048 + 25.9867i) q^{30} +(12.9259 - 15.4045i) q^{31} +(-1.37140 + 31.9706i) q^{32} +(-50.0574 + 6.98497i) q^{33} +(-11.4753 + 51.7992i) q^{34} +(37.7596 - 21.8005i) q^{35} +(30.8887 - 18.4902i) q^{36} +(20.1962 - 34.9808i) q^{37} +(-16.0108 + 17.4781i) q^{38} +(-23.3954 + 7.57622i) q^{39} +(-23.5266 - 25.6512i) q^{40} +(-34.1160 + 12.4172i) q^{41} +(-49.5250 - 34.0981i) q^{42} +(25.3466 - 4.46929i) q^{43} +(47.6372 - 47.6664i) q^{44} +(-9.54759 + 37.9753i) q^{45} +(17.0895 - 41.2756i) q^{46} +(-12.9992 - 15.4919i) q^{47} +(-17.9976 + 44.4981i) q^{48} +(-8.93040 + 50.6468i) q^{49} +(-12.1297 - 0.527738i) q^{50} +(-42.2386 + 67.4484i) q^{51} +(18.7986 - 26.8647i) q^{52} +46.7045 q^{53} +(52.9458 - 10.6180i) q^{54} +73.2998i q^{55} +(80.0931 - 3.53372i) q^{56} +(-31.4091 + 16.6610i) q^{57} +(61.9311 + 2.69449i) q^{58} +(36.4280 + 6.42325i) q^{59} +(-20.3674 - 48.0729i) q^{60} +(48.7491 - 40.9054i) q^{61} +(-15.3852 + 37.1592i) q^{62} +(-52.8703 - 73.0712i) q^{63} +(-16.6211 - 61.8040i) q^{64} +(6.19303 + 35.1224i) q^{65} +(91.2737 - 43.4424i) q^{66} +(25.9527 + 71.3043i) q^{67} +(-9.28040 - 105.704i) q^{68} +(44.8875 - 49.7543i) q^{69} +(-58.9030 + 64.3010i) q^{70} +(-17.4692 - 10.0858i) q^{71} +(-47.7898 + 53.8529i) q^{72} +(-50.2648 - 87.0613i) q^{73} +(-17.4729 + 78.8724i) q^{74} +(-16.8789 - 6.83883i) q^{75} +(20.0215 - 42.9705i) q^{76} +(-129.335 - 108.525i) q^{77} +(40.0643 - 28.5275i) q^{78} +(-29.7876 + 81.8406i) q^{79} +(60.3076 + 34.7695i) q^{80} +(80.1668 + 11.5881i) q^{81} +(57.5993 - 44.2115i) q^{82} +(25.2237 - 69.3017i) q^{83} +(114.978 + 35.2374i) q^{84} +(88.4137 + 74.1879i) q^{85} +(-45.6555 + 23.7756i) q^{86} +(86.1795 + 34.9173i) q^{87} +(-62.1795 + 119.580i) q^{88} +(-37.6081 - 65.1392i) q^{89} +(-4.63935 - 78.1768i) q^{90} +(-71.1414 - 41.0735i) q^{91} +(-7.75992 + 89.0095i) q^{92} +(-40.4110 + 44.7924i) q^{93} +(34.1155 + 21.7266i) q^{94} +(17.6357 + 48.4537i) q^{95} +(7.55298 - 95.7024i) q^{96} +(12.6145 + 71.5405i) q^{97} +(-13.4410 - 101.974i) q^{98} +(150.827 - 15.5531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−1.90734	+	0.601703i	−0.953671	+	0.300851i
$2$	−1.90734	+	0.601703i	−0.953671	+	0.300851i
$3$	−2.99807	−	0.107643i	−0.999356	−	0.0358811i
$3$	−2.99807	−	0.107643i	−0.999356	−	0.0358811i
$4$	3.27591	−	2.29531i	0.818977	−	0.573827i
$5$	−0.755508	+	4.28470i	−0.151102	+	0.856939i	0.811162	+	0.584821i	$0.198835\pi$
$5$	−0.755508	+	4.28470i	−0.151102	+	0.856939i	−0.962264	+	0.272118i	$0.912276\pi$
$6$	5.78311	−	1.59863i	0.963852	−	0.266439i
$7$	−6.44162	−	7.67682i	−0.920232	−	1.09669i	−0.995038	−	0.0994912i	$-0.968278\pi$
$7$	−6.44162	−	7.67682i	−0.920232	−	1.09669i	0.0748069	−	0.997198i	$-0.476166\pi$
$8$	−4.86718	+	6.34906i	−0.608398	+	0.793632i
$9$	8.97683	+	0.645444i	0.997425	+	0.0717160i
$10$	−1.13710	−	8.62697i	−0.113710	−	0.862697i
$11$	16.5915	−	2.92553i	1.50832	−	0.265957i	0.642489	−	0.766295i	$-0.277902\pi$
$11$	16.5915	−	2.92553i	1.50832	−	0.265957i	0.865830	+	0.500338i	$0.166791\pi$
$12$	−10.0685	+	6.52886i	−0.839039	+	0.544071i
$13$	7.70282	−	2.80360i	0.592525	−	0.215661i	−0.0283148	−	0.999599i	$-0.509014\pi$
$13$	7.70282	−	2.80360i	0.592525	−	0.215661i	0.620840	+	0.783938i	$0.286792\pi$
$14$	16.9055	+	10.7664i	1.20754	+	0.769028i
$15$	2.72628	−	12.7645i	0.181752	−	0.850966i
$16$	5.46314	−	15.0384i	0.341446	−	0.939901i
$17$	13.2638	−	22.9735i	0.780222	−	1.35138i	−0.151590	−	0.988443i	$-0.548439\pi$
$17$	13.2638	−	22.9735i	0.780222	−	1.35138i	0.931812	−	0.362941i	$-0.118227\pi$
$18$	−17.5102	+	4.17030i	−0.972791	+	0.231683i
$19$	10.2637	−	5.92574i	0.540194	−	0.311881i	−0.204964	−	0.978770i	$-0.565708\pi$
$19$	10.2637	−	5.92574i	0.540194	−	0.311881i	0.745158	+	0.666888i	$0.232374\pi$
$20$	7.35972	+	15.7704i	0.367986	+	0.788519i
$21$	18.4861	+	23.7090i	0.880289	+	1.12900i
$22$	−29.8854	+	15.5631i	−1.35843	+	0.707416i
$23$	−14.3578	+	17.1110i	−0.624252	+	0.743955i	−0.981795	−	0.189942i	$-0.939170\pi$
$23$	−14.3578	+	17.1110i	−0.624252	+	0.743955i	0.357543	+	0.933897i	$0.383615\pi$
$24$	15.2756	−	18.5110i	0.636482	−	0.771291i
$25$	5.70448	+	2.07626i	0.228179	+	0.0830505i
$26$	−13.0050	+	9.98223i	−0.500192	+	0.383932i
$27$	−26.8437	−	2.90138i	−0.994210	−	0.107459i
$28$	−38.7228	−	10.3631i	−1.38296	−	0.370110i
$29$	−29.1256	−	10.6009i	−1.00433	−	0.365547i	−0.213078	−	0.977035i	$-0.568349\pi$
$29$	−29.1256	−	10.6009i	−1.00433	−	0.365547i	−0.791254	+	0.611488i	$0.790571\pi$
$30$	2.48048	+	25.9867i	0.0826825	+	0.866222i
$31$	12.9259	−	15.4045i	0.416965	−	0.496920i	−0.516150	−	0.856498i	$-0.672635\pi$
$31$	12.9259	−	15.4045i	0.416965	−	0.496920i	0.933115	+	0.359579i	$0.117080\pi$
$32$	−1.37140	+	31.9706i	−0.0428564	+	0.999081i
$33$	−50.0574	+	6.98497i	−1.51689	+	0.211666i
$34$	−11.4753	+	51.7992i	−0.337509	+	1.52351i
$35$	37.7596	−	21.8005i	1.07884	−	0.622871i
$36$	30.8887	−	18.4902i	0.858021	−	0.513615i
$37$	20.1962	−	34.9808i	0.545842	−	0.945426i	−0.452711	−	0.891657i	$-0.649543\pi$
$37$	20.1962	−	34.9808i	0.545842	−	0.945426i	0.998553	−	0.0537690i	$-0.0171235\pi$
$38$	−16.0108	+	17.4781i	−0.421338	+	0.459950i
$39$	−23.3954	+	7.57622i	−0.599881	+	0.194262i
$40$	−23.5266	−	25.6512i	−0.588165	−	0.641279i
$41$	−34.1160	+	12.4172i	−0.832096	+	0.302858i	−0.722719	−	0.691142i	$-0.757108\pi$
$41$	−34.1160	+	12.4172i	−0.832096	+	0.302858i	−0.109377	+	0.994000i	$0.534886\pi$
$42$	−49.5250	−	34.0981i	−1.17917	−	0.811860i
$43$	25.3466	−	4.46929i	0.589456	−	0.103937i	0.129039	−	0.991640i	$-0.458811\pi$
$43$	25.3466	−	4.46929i	0.589456	−	0.103937i	0.460417	+	0.887703i	$0.347700\pi$
$44$	47.6372	−	47.6664i	1.08266	−	1.08333i
$45$	−9.54759	+	37.9753i	−0.212169	+	0.843896i
$46$	17.0895	−	41.2756i	0.371511	−	0.897295i
$47$	−12.9992	−	15.4919i	−0.276579	−	0.329614i	0.609817	−	0.792543i	$-0.291243\pi$
$47$	−12.9992	−	15.4919i	−0.276579	−	0.329614i	−0.886396	+	0.462928i	$0.846799\pi$
$48$	−17.9976	+	44.4981i	−0.374951	+	0.927045i
$49$	−8.93040	+	50.6468i	−0.182253	+	1.03361i
$50$	−12.1297	−	0.527738i	−0.242594	−	0.0105548i
$51$	−42.2386	+	67.4484i	−0.828209	+	1.32252i
$52$	18.7986	−	26.8647i	0.361512	−	0.516628i
$53$	46.7045			0.881217			0.440609	−	0.897699i	$-0.354763\pi$
$53$	46.7045			0.881217			0.440609	+	0.897699i	$0.354763\pi$
$54$	52.9458	−	10.6180i	0.980478	−	0.196629i
$55$			73.2998i			1.33272i
$56$	80.0931	−	3.53372i	1.43023	−	0.0631021i
$57$	−31.4091	+	16.6610i	−0.551037	+	0.292298i
$58$	61.9311	+	2.69449i	1.06778	+	0.0464568i
$59$	36.4280	+	6.42325i	0.617424	+	0.108869i	0.473608	−	0.880736i	$-0.342951\pi$
$59$	36.4280	+	6.42325i	0.617424	+	0.108869i	0.143817	+	0.989604i	$0.454062\pi$
$60$	−20.3674	−	48.0729i	−0.339456	−	0.801215i
$61$	48.7491	−	40.9054i	0.799166	−	0.670580i	−0.148830	−	0.988863i	$-0.547551\pi$
$61$	48.7491	−	40.9054i	0.799166	−	0.670580i	0.947996	+	0.318283i	$0.103106\pi$
$62$	−15.3852	+	37.1592i	−0.248149	+	0.599342i
$63$	−52.8703	−	73.0712i	−0.839212	−	1.15986i
$64$	−16.6211	−	61.8040i	−0.259704	−	0.965688i
$65$	6.19303	+	35.1224i	0.0952773	+	0.540344i
$66$	91.2737	−	43.4424i	1.38293	−	0.658218i
$67$	25.9527	+	71.3043i	0.387353	+	1.06424i	0.968188	+	0.250223i	$0.0805038\pi$
$67$	25.9527	+	71.3043i	0.387353	+	1.06424i	−0.580835	+	0.814021i	$0.697274\pi$
$68$	−9.28040	−	105.704i	−0.136477	−	1.55446i
$69$	44.8875	−	49.7543i	0.650544	−	0.721077i
$70$	−58.9030	+	64.3010i	−0.841471	+	0.918586i
$71$	−17.4692	−	10.0858i	−0.246045	−	0.142054i	0.371907	−	0.928270i	$-0.378704\pi$
$71$	−17.4692	−	10.0858i	−0.246045	−	0.142054i	−0.617952	+	0.786216i	$0.712037\pi$
$72$	−47.7898	+	53.8529i	−0.663747	+	0.747957i
$73$	−50.2648	−	87.0613i	−0.688560	−	1.19262i	−0.972304	−	0.233720i	$-0.924910\pi$
$73$	−50.2648	−	87.0613i	−0.688560	−	1.19262i	0.283744	−	0.958900i	$-0.408423\pi$
$74$	−17.4729	+	78.8724i	−0.236121	+	1.06584i
$75$	−16.8789	−	6.83883i	−0.225053	−	0.0911844i
$76$	20.0215	−	42.9705i	0.263441	−	0.565401i
$77$	−129.335	−	108.525i	−1.67967	−	1.40941i
$78$	40.0643	−	28.5275i	0.513645	−	0.365737i
$79$	−29.7876	+	81.8406i	−0.377058	+	1.03596i	0.595512	+	0.803346i	$0.296949\pi$
$79$	−29.7876	+	81.8406i	−0.377058	+	1.03596i	−0.972570	+	0.232611i	$0.925273\pi$
$80$	60.3076	+	34.7695i	0.753845	+	0.434619i
$81$	80.1668	+	11.5881i	0.989714	+	0.143063i
$82$	57.5993	−	44.2115i	0.702431	−	0.539165i
$83$	25.2237	−	69.3017i	0.303900	−	0.834960i	−0.689912	−	0.723893i	$-0.742351\pi$
$83$	25.2237	−	69.3017i	0.303900	−	0.834960i	0.993813	−	0.111067i	$-0.0354268\pi$
$84$	114.978	+	35.2374i	1.36879	+	0.419493i
$85$	88.4137	+	74.1879i	1.04016	+	0.872799i
$86$	−45.6555	+	23.7756i	−0.530878	+	0.276461i
$87$	86.1795	+	34.9173i	0.990569	+	0.401348i
$88$	−62.1795	+	119.580i	−0.706586	+	1.35886i
$89$	−37.6081	−	65.1392i	−0.422563	−	0.731901i	0.573626	−	0.819117i	$-0.305536\pi$
$89$	−37.6081	−	65.1392i	−0.422563	−	0.731901i	−0.996189	+	0.0872163i	$0.972203\pi$
$90$	−4.63935	−	78.1768i	−0.0515483	−	0.868631i
$91$	−71.1414	−	41.0735i	−0.781774	−	0.451357i
$92$	−7.75992	+	89.0095i	−0.0843470	+	0.967494i
$93$	−40.4110	+	44.7924i	−0.434527	+	0.481639i
$94$	34.1155	+	21.7266i	0.362930	+	0.231134i
$95$	17.6357	+	48.4537i	0.185639	+	0.510039i
$96$	7.55298	−	95.7024i	0.0786769	−	0.996900i
$97$	12.6145	+	71.5405i	0.130047	+	0.737531i	0.978182	+	0.207751i	$0.0666144\pi$
$97$	12.6145	+	71.5405i	0.130047	+	0.737531i	−0.848135	+	0.529780i	$0.822274\pi$
$98$	−13.4410	−	101.974i	−0.137153	−	1.04055i
$99$	150.827	−	15.5531i	1.52351	−	0.157102i
$100$	23.4530	−	6.29190i	0.234530	−	0.0629190i
$101$	40.3702	−	33.8746i	0.399705	−	0.335392i	−0.420675	−	0.907211i	$-0.638207\pi$
$101$	40.3702	−	33.8746i	0.399705	−	0.335392i	0.820379	+	0.571820i	$0.193762\pi$
$102$	39.9796	−	154.062i	0.391957	−	1.51042i
$103$	42.8748	+	7.55998i	0.416260	+	0.0733979i	0.377856	−	0.925864i	$-0.376661\pi$
$103$	42.8748	+	7.55998i	0.416260	+	0.0733979i	0.0384042	+	0.999262i	$0.487773\pi$
$104$	−19.6908	+	62.5513i	−0.189335	+	0.601455i
$105$	−115.552	+	61.2948i	−1.10050	+	0.583760i
$106$	−89.0815	+	28.1022i	−0.840391	+	0.265115i
$107$		−	70.5658i		−	0.659493i	−0.944069	−	0.329747i	$-0.893037\pi$
$107$		−	70.5658i		−	0.659493i	0.944069	−	0.329747i	$-0.106963\pi$
$108$	−94.5969	+	52.1098i	−0.875897	+	0.482498i
$109$	−89.3232			−0.819479			−0.409739	−	0.912203i	$-0.634380\pi$
$109$	−89.3232			−0.819479			−0.409739	+	0.912203i	$0.634380\pi$
$110$	−44.1047	−	139.808i	−0.400952	−	1.27098i
$111$	−64.3149	+	102.701i	−0.579413	+	0.925232i
$112$	−150.639	+	54.9323i	−1.34499	+	0.490467i
$113$	−13.7107	+	77.7573i	−0.121334	+	0.688118i	0.862084	+	0.506765i	$0.169159\pi$
$113$	−13.7107	+	77.7573i	−0.121334	+	0.688118i	−0.983418	+	0.181353i	$0.941952\pi$
$114$	49.8829	−	50.6771i	0.437570	−	0.444536i
$115$	−62.4678	−	74.4463i	−0.543199	−	0.647359i
$116$	−119.745	+	32.1248i	−1.03228	+	0.276938i
$117$	70.9565	−	20.1957i	0.606465	−	0.172613i
$118$	−73.3456	+	9.66753i	−0.621573	+	0.0819282i
$119$	−261.804	+	46.1631i	−2.20003	+	0.387925i
$120$	67.7731	+	79.4364i	0.564776	+	0.661970i
$121$	153.017	−	55.6935i	1.26460	−	0.460277i
$122$	−68.3684	+	107.353i	−0.560397	+	0.879943i
$123$	103.619	−	33.5552i	0.842427	−	0.272807i
$124$	6.98604	−	80.1327i	0.0563390	−	0.646231i
$125$	−67.5909	+	117.071i	−0.540727	+	0.936567i
$126$	144.809	+	107.560i	1.14928	+	0.853647i
$127$	−82.1426	+	47.4250i	−0.646792	+	0.373425i	−0.787226	−	0.616665i	$-0.788483\pi$
$127$	−82.1426	+	47.4250i	−0.646792	+	0.373425i	0.140434	+	0.990090i	$0.455150\pi$
$128$	68.8897	+	107.881i	0.538201	+	0.842816i
$129$	−76.4720	+	10.6708i	−0.592806	+	0.0827198i
$130$	−32.9455	−	63.2641i	−0.253427	−	0.486647i
$131$	−7.26521	+	8.65835i	−0.0554597	+	0.0660942i	−0.793061	−	0.609142i	$-0.791514\pi$
$131$	−7.26521	+	8.65835i	−0.0554597	+	0.0660942i	0.737601	+	0.675236i	$0.235958\pi$
$132$	−147.951	+	137.779i	−1.12084	+	1.04378i
$133$	−111.606	−	40.6211i	−0.839140	−	0.305422i
$134$	−92.4046	−	120.386i	−0.689587	−	0.898403i
$135$	32.7121	−	112.825i	0.242312	−	0.835740i
$136$	81.3031	+	196.029i	0.597817	+	1.44139i
$137$	147.499	+	53.6854i	1.07664	+	0.391864i	0.818655	−	0.574286i	$-0.194720\pi$
$137$	147.499	+	53.6854i	1.07664	+	0.391864i	0.257982	+	0.966150i	$0.416942\pi$
$138$	−55.6786	+	121.907i	−0.403468	+	0.883387i
$139$	113.198	−	134.904i	0.814376	−	0.970535i	−0.185551	−	0.982635i	$-0.559407\pi$
$139$	113.198	−	134.904i	0.814376	−	0.970535i	0.999927	+	0.0120996i	$0.00385153\pi$
$140$	73.6580	−	158.086i	0.526129	−	1.12919i
$141$	37.3049	+	47.8449i	0.264574	+	0.339326i
$142$	39.3884	+	8.72588i	0.277383	+	0.0614498i
$143$	119.599	−	69.0507i	0.836359	−	0.482872i
$144$	58.7481	−	131.471i	0.407973	−	0.912994i
$145$	67.4261	−	116.785i	0.465008	−	0.805417i
$146$	148.257	+	135.811i	1.01546	+	0.930213i
$147$	32.2257	−	150.881i	0.219223	−	1.02640i
$148$	−14.1309	−	160.950i	−0.0954788	−	1.08750i
$149$	−92.5431	+	33.6829i	−0.621094	+	0.226060i	−0.633351	−	0.773865i	$-0.718321\pi$
$149$	−92.5431	+	33.6829i	−0.621094	+	0.226060i	0.0122562	+	0.999925i	$0.496099\pi$
$150$	36.3089	+	2.88787i	0.242059	+	0.0192525i
$151$	−0.769516	+	0.135686i	−0.00509613	+	0.000898586i	−0.176196	−	0.984355i	$-0.556379\pi$
$151$	−0.769516	+	0.135686i	−0.00509613	+	0.000898586i	0.171100	+	0.985254i	$0.445268\pi$
$152$	−12.3324	+	94.0064i	−0.0811339	+	0.618463i
$153$	133.895	−	197.668i	0.875129	−	1.29195i
$154$	311.986	+	129.173i	2.02588	+	0.838785i
$155$	56.2380	+	67.0219i	0.362826	+	0.432399i
$156$	−59.2513	+	78.5186i	−0.379816	+	0.503324i
$157$	−30.8928	+	175.202i	−0.196769	+	1.11593i	0.713107	+	0.701055i	$0.247287\pi$
$157$	−30.8928	+	175.202i	−0.196769	+	1.11593i	−0.909876	+	0.414879i	$0.863824\pi$
$158$	7.57130	−	174.021i	0.0479196	−	1.10140i
$159$	−140.023	−	5.02743i	−0.880650	−	0.0316191i
$160$	−135.948	−	30.0301i	−0.849676	−	0.187688i
$161$	223.845			1.39034
$162$	−159.878	+	26.1342i	−0.986902	+	0.161322i
$163$			268.797i			1.64906i	0.565818	+	0.824530i	$0.308561\pi$
$163$			268.797i			1.64906i	−0.565818	+	0.824530i	$0.691439\pi$
$164$	−83.2594	+	118.984i	−0.507679	+	0.725513i
$165$	7.89024	−	219.758i	0.0478196	−	1.33187i
$166$	−6.41129	+	147.359i	−0.0386222	+	0.887706i
$167$	−21.3074	−	3.75708i	−0.127589	−	0.0224975i	0.109489	−	0.993988i	$-0.465079\pi$
$167$	−21.3074	−	3.75708i	−0.127589	−	0.0224975i	−0.237078	+	0.971491i	$0.576190\pi$
$168$	−240.505	+	1.97282i	−1.43158	+	0.0117430i
$169$	−77.9882	+	65.4399i	−0.461469	+	0.387218i
$170$	−213.274	−	88.3029i	−1.25455	−	0.519429i
$171$	95.9601	−	46.5697i	0.561170	−	0.272338i
$172$	72.7748	−	72.8192i	0.423109	−	0.423368i
$173$	−20.3403	−	115.356i	−0.117574	−	0.666796i	−0.985443	−	0.170003i	$-0.945622\pi$
$173$	−20.3403	−	115.356i	−0.117574	−	0.666796i	0.867869	−	0.496792i	$-0.165489\pi$
$174$	−185.384	−	14.7447i	−1.06542	−	0.0847399i
$175$	−20.8070	−	57.1668i	−0.118897	−	0.326668i
$176$	46.6463	−	265.493i	0.265036	−	1.50848i
$177$	−108.522	−	23.1786i	−0.613121	−	0.130952i
$178$	110.926	+	101.614i	0.623180	+	0.570864i
$179$	−17.3998	−	10.0458i	−0.0972054	−	0.0561216i	0.450609	−	0.892721i	$-0.351207\pi$
$179$	−17.3998	−	10.0458i	−0.0972054	−	0.0561216i	−0.547815	+	0.836600i	$0.684540\pi$
$180$	55.8880	+	146.318i	0.310489	+	0.812880i
$181$	96.6241	+	167.358i	0.533835	+	0.924629i	0.999219	+	0.0395201i	$0.0125829\pi$
$181$	96.6241	+	167.358i	0.533835	+	0.924629i	−0.465384	+	0.885109i	$0.654084\pi$
$182$	160.405	+	35.5352i	0.881346	+	0.195249i
$183$	−150.556	+	117.390i	−0.822713	+	0.641473i
$184$	−38.7564	−	174.441i	−0.210633	−	0.948047i
$185$	134.624	+	112.963i	0.727695	+	0.610609i
$186$	50.1258	−	109.750i	0.269494	−	0.590053i
$187$	152.856	−	419.969i	0.817413	−	2.24582i
$188$	−78.1428	−	20.9127i	−0.415653	−	0.111238i
$189$	150.643	+	224.764i	0.797054	+	1.18923i
$190$	−62.7921	−	81.8064i	−0.330485	−	0.430560i
$191$	87.6196	−	240.733i	0.458741	−	1.26038i	−0.467682	−	0.883897i	$-0.654911\pi$
$191$	87.6196	−	240.733i	0.458741	−	1.26038i	0.926423	−	0.376484i	$-0.122867\pi$
$192$	43.1783	+	187.082i	0.224887	+	0.974385i
$193$	−217.111	−	182.178i	−1.12493	−	0.943928i	−0.126087	−	0.992019i	$-0.540242\pi$
$193$	−217.111	−	182.178i	−1.12493	−	0.943928i	−0.998843	+	0.0480909i	$0.984686\pi$
$194$	−67.1064	−	128.862i	−0.345909	−	0.664237i
$195$	−14.7864	−	105.966i	−0.0758278	−	0.543415i
$196$	86.9948	+	186.412i	0.443851	+	0.951083i
$197$	142.022	+	245.990i	0.720925	+	1.24868i	0.960630	+	0.277832i	$0.0896160\pi$
$197$	142.022	+	245.990i	0.720925	+	1.24868i	−0.239705	+	0.970846i	$0.577051\pi$
$198$	−278.321	+	120.418i	−1.40566	+	0.608173i
$199$	−118.652	−	68.5039i	−0.596242	−	0.344241i	0.171320	−	0.985216i	$-0.445197\pi$
$199$	−118.652	−	68.5039i	−0.596242	−	0.344241i	−0.767562	+	0.640975i	$0.778530\pi$
$200$	−40.9471	+	26.1126i	−0.204735	+	0.130563i
$201$	−70.1324	−	216.569i	−0.348917	−	1.07746i
$202$	−56.6173	+	88.9013i	−0.280283	+	0.440105i
$203$	106.235	+	291.879i	0.523326	+	1.43783i
$204$	16.4450	+	317.905i	0.0806127	+	1.55836i
$205$	−27.4290	−	155.558i	−0.133800	−	0.758818i
$206$	−86.3258	+	11.3784i	−0.419057	+	0.0552350i
$207$	−139.932	+	144.335i	−0.675998	+	0.697270i
$208$	−0.0801338	−	131.155i	−0.000385259	−	0.630552i
$209$	152.954	−	128.344i	0.731838	−	0.614085i
$210$	183.517	−	186.438i	0.873889	−	0.887802i
$211$	181.862	+	32.0671i	0.861903	+	0.151977i	0.587091	−	0.809521i	$-0.300273\pi$
$211$	181.862	+	32.0671i	0.861903	+	0.151977i	0.274813	+	0.961498i	$0.411384\pi$
$212$	153.000	−	107.201i	0.721696	−	0.505666i
$213$	51.2881	+	32.1185i	0.240789	+	0.150791i
$214$	42.4596	+	134.593i	0.198409	+	0.628940i
$215$			111.979i			0.520833i
$216$	149.074	−	156.310i	0.690158	−	0.723659i
$217$	−201.522			−0.928671
$218$	170.370	−	53.7460i	0.781513	−	0.246541i
$219$	141.326	+	266.426i	0.645324	+	1.21656i
$220$	168.246	+	240.123i	0.764753	+	1.09147i
$221$	37.7599	−	214.147i	0.170859	−	0.968992i
$222$	60.8752	−	234.584i	0.274212	−	1.05668i
$223$	−140.359	−	167.273i	−0.629413	−	0.750105i	0.353245	−	0.935531i	$-0.385078\pi$
$223$	−140.359	−	167.273i	−0.629413	−	0.750105i	−0.982658	+	0.185426i	$0.940634\pi$
$224$	254.267	−	195.414i	1.13512	−	0.872386i
$225$	49.8681	+	22.3202i	0.221636	+	0.0992008i
$226$	−20.6358	−	156.560i	−0.0913088	−	0.692741i
$227$	−298.580	+	52.6476i	−1.31533	+	0.231928i	−0.786916	−	0.617060i	$-0.788324\pi$
$227$	−298.580	+	52.6476i	−1.31533	+	0.231928i	−0.528412	+	0.848988i	$0.677212\pi$
$228$	−64.6513	+	126.673i	−0.283558	+	0.555585i
$229$	−291.207	+	105.991i	−1.27164	+	0.462841i	−0.887660	−	0.460499i	$-0.847671\pi$
$229$	−291.207	+	105.991i	−1.27164	+	0.462841i	−0.383985	+	0.923340i	$0.625448\pi$
$230$	163.942	+	104.407i	0.712792	+	0.453945i
$231$	376.073	+	339.287i	1.62802	+	1.46878i
$232$	209.065	−	133.324i	0.901143	−	0.574672i
$233$	−21.7586	+	37.6870i	−0.0933845	+	0.161747i	−0.908933	−	0.416942i	$-0.863102\pi$
$233$	−21.7586	+	37.6870i	−0.0933845	+	0.161747i	0.815549	+	0.578688i	$0.196435\pi$
$234$	−123.186	+	81.2148i	−0.526438	+	0.347072i
$235$	76.1989	−	43.9935i	0.324251	−	0.187206i
$236$	134.078	−	62.5716i	0.568128	−	0.265134i
$237$	98.1147	−	242.157i	0.413986	−	1.02176i
$238$	471.573	−	245.577i	1.98140	−	1.03184i
$239$	−214.161	+	255.227i	−0.896069	+	1.06789i	0.101260	+	0.994860i	$0.467713\pi$
$239$	−214.161	+	255.227i	−0.896069	+	1.06789i	−0.997329	+	0.0730337i	$0.976732\pi$
$240$	−177.064	−	110.733i	−0.737765	−	0.461388i
$241$	325.919	+	118.625i	1.35236	+	0.492219i	0.913684	−	0.406426i	$-0.133225\pi$
$241$	325.919	+	118.625i	1.35236	+	0.492219i	0.438677	+	0.898645i	$0.355447\pi$
$242$	−258.344	+	198.297i	−1.06754	+	0.819409i
$243$	−239.098	−	43.3713i	−0.983943	−	0.178483i
$244$	65.8073	−	245.896i	0.269702	−	1.00777i
$245$	−210.259	−	76.5281i	−0.858201	−	0.312360i
$246$	−177.446	+	126.349i	−0.721324	+	0.513613i
$247$	62.4460	−	74.4202i	0.252818	−	0.301296i
$248$	34.8913	+	157.044i	0.140691	+	0.633242i
$249$	−83.0823	+	205.056i	−0.333664	+	0.823518i
$250$	58.4770	−	263.964i	0.233908	−	1.05585i
$251$	−12.1468	+	7.01295i	−0.0483935	+	0.0279400i	−0.524002	−	0.851717i	$-0.675561\pi$
$251$	−12.1468	+	7.01295i	−0.0483935	+	0.0279400i	0.475608	+	0.879657i	$0.342228\pi$
$252$	−340.919	−	118.021i	−1.35285	−	0.468337i
$253$	−188.159	+	325.901i	−0.743711	+	1.28815i
$254$	128.138	−	139.881i	0.504481	−	0.550713i
$255$	−257.084	−	231.938i	−1.00817	−	0.909559i
$256$	−196.308	−	164.314i	−0.766829	−	0.641851i
$257$	−159.478	+	58.0452i	−0.620537	+	0.225857i	−0.633107	−	0.774064i	$-0.718221\pi$
$257$	−159.478	+	58.0452i	−0.620537	+	0.225857i	0.0125705	+	0.999921i	$0.495999\pi$
$258$	139.438	−	66.3664i	0.540456	−	0.257234i
$259$	−398.637	+	70.2905i	−1.53914	+	0.271392i
$260$	100.904	+	100.843i	0.388094	+	0.387857i
$261$	−254.613	−	113.961i	−0.975530	−	0.436632i
$262$	8.64750	−	20.8859i	0.0330057	−	0.0797173i
$263$	208.683	+	248.699i	0.793473	+	0.945624i	0.999458	−	0.0329313i	$-0.0104843\pi$
$263$	208.683	+	248.699i	0.793473	+	0.945624i	−0.205985	+	0.978555i	$0.566040\pi$
$264$	199.290	−	351.814i	0.754888	−	1.33263i
$265$	−35.2856	+	200.115i	−0.133153	+	0.755150i
$266$	237.312	+	10.3250i	0.892151	+	0.0388156i
$267$	105.740	+	199.340i	0.396030	+	0.746592i
$268$	248.684	+	174.017i	0.927924	+	0.649317i
$269$	−281.085			−1.04493			−0.522463	−	0.852662i	$-0.674987\pi$
$269$	−281.085			−1.04493			−0.522463	+	0.852662i	$0.674987\pi$
$270$	5.49387	+	234.879i	0.0203477	+	0.869921i
$271$		−	270.921i		−	0.999709i	−0.866109	−	0.499855i	$-0.833387\pi$
$271$		−	270.921i		−	0.999709i	0.866109	−	0.499855i	$-0.166613\pi$
$272$	−273.024	−	324.974i	−1.00376	−	1.19476i
$273$	208.865	+	130.799i	0.765075	+	0.479117i
$274$	−313.634	−	13.6456i	−1.14465	−	0.0498014i
$275$	100.720	+	17.7597i	0.366255	+	0.0645807i
$276$	32.8461	−	266.021i	0.119007	−	0.963845i
$277$	80.9996	−	67.9667i	0.292417	−	0.245367i	−0.484763	−	0.874646i	$-0.661094\pi$
$277$	80.9996	−	67.9667i	0.292417	−	0.245367i	0.777180	+	0.629279i	$0.216650\pi$
$278$	−134.735	+	325.420i	−0.484659	+	1.17058i
$279$	125.976	−	129.941i	0.451529	−	0.465737i
$280$	−45.3701	+	345.845i	−0.162036	+	1.23516i
$281$	14.7191	+	83.4761i	0.0523811	+	0.297068i	0.999733	−	0.0231277i	$-0.00736245\pi$
$281$	14.7191	+	83.4761i	0.0523811	+	0.297068i	−0.947351	+	0.320196i	$0.896251\pi$
$282$	−99.9417	−	68.8102i	−0.354403	−	0.244008i
$283$	110.305	+	303.060i	0.389770	+	1.07088i	0.967105	+	0.254376i	$0.0818702\pi$
$283$	110.305	+	303.060i	0.389770	+	1.07088i	−0.577336	+	0.816507i	$0.695908\pi$
$284$	−80.3775	+	7.05686i	−0.283019	+	0.0248481i
$285$	−47.6574	−	147.166i	−0.167219	−	0.516372i
$286$	−186.569	+	203.667i	−0.652339	+	0.712121i
$287$	315.087	+	181.915i	1.09786	+	0.633851i
$288$	−32.9461	+	286.109i	−0.114396	+	0.993435i
$289$	−207.355	−	359.150i	−0.717493	−	1.24273i
$290$	−58.3345	+	263.320i	−0.201153	+	0.908001i
$291$	−30.1183	−	215.841i	−0.103499	−	0.741722i
$292$	−364.495	−	169.831i	−1.24827	−	0.581614i
$293$	157.814	+	132.422i	0.538615	+	0.451952i	0.871064	−	0.491170i	$-0.163430\pi$
$293$	157.814	+	132.422i	0.538615	+	0.451952i	−0.332449	+	0.943121i	$0.607875\pi$
$294$	29.3202	+	307.173i	0.0997286	+	1.04480i
$295$	−55.0433	+	151.230i	−0.186588	+	0.512645i
$296$	123.797	+	298.484i	0.418232	+	1.00839i
$297$	−453.865	+	30.3936i	−1.52816	+	0.102335i
$298$	156.244	−	119.928i	0.524309	−	0.402444i
$299$	−62.6233	+	172.056i	−0.209443	+	0.575439i
$300$	−70.9910	+	16.3390i	−0.236637	+	0.0544633i
$301$	−197.583	−	165.792i	−0.656423	−	0.550804i
$302$	1.38609	−	0.721821i	0.00458969	−	0.00239013i
$303$	−124.679	+	97.2127i	−0.411481	+	0.320834i
$304$	−33.0419	−	186.723i	−0.108691	−	0.614220i
$305$	138.437	+	239.780i	0.453891	+	0.786163i
$306$	−136.445	+	457.586i	−0.445900	+	1.49538i
$307$	194.400	+	112.237i	0.633225	+	0.365593i	0.782000	−	0.623278i	$-0.214200\pi$
$307$	194.400	+	112.237i	0.633225	+	0.365593i	−0.148775	+	0.988871i	$0.547533\pi$
$308$	−672.787	−	58.6542i	−2.18437	−	0.190436i
$309$	−127.728	−	27.2805i	−0.413359	−	0.0882865i
$310$	−147.592	−	93.9950i	−0.476104	−	0.303210i
$311$	−76.8272	−	211.081i	−0.247033	−	0.678717i	−0.999791	−	0.0204207i	$-0.993499\pi$
$311$	−76.8272	−	211.081i	−0.247033	−	0.678717i	0.752759	−	0.658297i	$-0.228723\pi$
$312$	65.7677	−	185.413i	0.210794	−	0.594274i
$313$	−69.3890	−	393.525i	−0.221690	−	1.25727i	−0.868912	−	0.494966i	$-0.835181\pi$
$313$	−69.3890	−	393.525i	−0.221690	−	1.25727i	0.647222	−	0.762301i	$-0.275931\pi$
$314$	−46.4963	−	352.758i	−0.148077	−	1.12343i
$315$	353.032	−	171.328i	1.12074	−	0.543897i
$316$	90.2681	+	336.474i	0.285658	+	1.06479i
$317$	11.8267	−	9.92380i	0.0373083	−	0.0313054i	−0.623943	−	0.781470i	$-0.714470\pi$
$317$	11.8267	−	9.92380i	0.0373083	−	0.0313054i	0.661251	+	0.750165i	$0.270026\pi$
$318$	270.097	−	74.6634i	0.849363	−	0.234791i
$319$	−514.251	−	90.6763i	−1.61207	−	0.284252i
$320$	277.369	−	24.5228i	0.866778	−	0.0766338i
$321$	−7.59594	+	211.561i	−0.0236634	+	0.659069i
$322$	−426.950	+	134.688i	−1.32593	+	0.418287i
$323$		−	314.391i		−	0.973346i
$324$	289.217	−	146.046i	0.892646	−	0.450759i
$325$	49.7616			0.153113
$326$	−161.736	−	512.688i	−0.496122	−	1.57266i
$327$	267.797	+	9.61505i	0.818951	+	0.0294038i
$328$	87.2111	−	277.041i	0.265887	−	0.844637i
$329$	−35.1923	+	199.585i	−0.106967	+	0.606643i
$330$	117.180	+	423.901i	0.355090	+	1.28455i
$331$	178.560	+	212.799i	0.539455	+	0.642898i	0.965065	−	0.262009i	$-0.0843850\pi$
$331$	178.560	+	212.799i	0.539455	+	0.642898i	−0.425610	+	0.904907i	$0.639941\pi$
$332$	−76.4379	−	284.922i	−0.230235	−	0.858199i
$333$	203.875	−	300.981i	0.612239	−	0.903846i
$334$	42.9012	−	5.65472i	0.128447	−	0.0169303i
$335$	−325.125	+	57.3283i	−0.970522	+	0.171129i
$336$	457.538	−	148.475i	1.36172	−	0.441891i
$337$	524.664	−	190.962i	1.55687	−	0.566653i	0.586850	−	0.809696i	$-0.300368\pi$
$337$	524.664	−	190.962i	1.55687	−	0.566653i	0.970015	+	0.243043i	$0.0781457\pi$
$338$	109.375	−	171.742i	0.323594	−	0.508112i
$339$	49.4757	−	231.646i	0.145946	−	0.683321i
$340$	459.919	+	40.0961i	1.35270	+	0.117930i
$341$	169.394	−	293.399i	0.496757	−	0.860408i
$342$	−155.008	+	146.564i	−0.453238	+	0.428549i
$343$	21.0731	−	12.1666i	0.0614376	−	0.0354710i
$344$	−94.9908	+	182.680i	−0.276136	+	0.531046i
$345$	179.269	+	229.919i	0.519621	+	0.666433i
$346$	108.206	+	207.784i	0.312733	+	0.600531i
$347$	288.093	−	343.336i	0.830241	−	0.989442i	−0.169752	−	0.985487i	$-0.554297\pi$
$347$	288.093	−	343.336i	0.830241	−	0.989442i	0.999992	−	0.00395526i	$-0.00125900\pi$
$348$	362.462	−	83.4226i	1.04156	−	0.239720i
$349$	479.457	+	174.508i	1.37380	+	0.500023i	0.920294	−	0.391228i	$-0.127950\pi$
$349$	479.457	+	174.508i	1.37380	+	0.500023i	0.453509	+	0.891252i	$0.350172\pi$
$350$	74.0836	+	96.5170i	0.211667	+	0.275763i
$351$	−214.906	+	52.9100i	−0.612268	+	0.150741i
$352$	70.7773	+	534.452i	0.201072	+	1.51833i
$353$	−194.831	−	70.9126i	−0.551928	−	0.200885i	0.0509748	−	0.998700i	$-0.483767\pi$
$353$	−194.831	−	70.9126i	−0.551928	−	0.200885i	−0.602903	+	0.797814i	$0.705989\pi$
$354$	220.936	−	21.0888i	0.624113	−	0.0595727i
$355$	56.4128	−	67.2302i	0.158909	−	0.189381i
$356$	−272.715	−	127.068i	−0.766054	−	0.356932i
$357$	789.875	−	110.219i	2.21254	−	0.308736i
$358$	39.2319	+	8.69121i	0.109586	+	0.0242771i
$359$	52.8592	−	30.5183i	0.147240	−	0.0850091i	−0.424570	−	0.905395i	$-0.639575\pi$
$359$	52.8592	−	30.5183i	0.147240	−	0.0850091i	0.571810	+	0.820386i	$0.306241\pi$
$360$	−194.638	−	245.451i	−0.540660	−	0.681809i
$361$	−110.271	+	190.995i	−0.305460	+	0.529073i
$362$	−284.995	−	261.070i	−0.787279	−	0.721187i
$363$	−464.749	+	150.502i	−1.28030	+	0.414605i
$364$	−327.329	+	28.7383i	−0.899255	+	0.0789515i
$365$	411.007	−	149.594i	1.12605	−	0.409847i
$366$	216.529	−	314.492i	0.591609	−	0.859269i
$367$	258.395	−	45.5620i	0.704073	−	0.124147i	0.189862	−	0.981811i	$-0.439196\pi$
$367$	258.395	−	45.5620i	0.704073	−	0.124147i	0.514211	+	0.857664i	$0.328085\pi$
$368$	178.883	+	309.398i	0.486096	+	0.840756i
$369$	−314.268	+	89.4470i	−0.851674	+	0.242404i
$370$	−324.743	−	134.455i	−0.877684	−	0.363392i
$371$	−300.853	−	358.542i	−0.810924	−	0.966421i
$372$	−29.5704	+	239.491i	−0.0794902	+	0.643794i
$373$	−96.1685	+	545.399i	−0.257824	+	1.46219i	0.530893	+	0.847439i	$0.321857\pi$
$373$	−96.1685	+	545.399i	−0.257824	+	1.46219i	−0.788717	+	0.614756i	$0.789254\pi$
$374$	−38.8525	+	892.999i	−0.103884	+	2.38770i
$375$	215.244	−	343.711i	0.573984	−	0.916562i
$376$	161.628	−	7.13105i	0.429863	−	0.0189656i
$377$	−254.070			−0.673926
$378$	−422.569	−	338.059i	−1.11791	−	0.894335i
$379$			61.8712i			0.163249i	0.996663	+	0.0816243i	$0.0260107\pi$
$379$			61.8712i			0.163249i	−0.996663	+	0.0816243i	$0.973989\pi$
$380$	168.989	+	118.251i	0.444708	+	0.311186i
$381$	251.374	−	133.341i	0.659774	−	0.349977i
$382$	−22.2709	+	511.881i	−0.0583007	+	1.34000i
$383$	−356.264	−	62.8189i	−0.930193	−	0.164018i	−0.312034	−	0.950071i	$-0.601010\pi$
$383$	−356.264	−	62.8189i	−0.930193	−	0.164018i	−0.618159	+	0.786053i	$0.712121\pi$
$384$	−194.924	−	330.849i	−0.507613	−	0.861585i
$385$	562.710	−	472.170i	1.46158	−	1.22641i
$386$	523.723	+	216.839i	1.35680	+	0.561760i
$387$	230.417	−	23.7602i	0.595392	−	0.0613959i
$388$	205.531	+	205.406i	0.529720	+	0.529397i
$389$	−51.9683	−	294.727i	−0.133595	−	0.757653i	−0.975828	−	0.218540i	$-0.929871\pi$
$389$	−51.9683	−	294.727i	−0.133595	−	0.757653i	0.842233	−	0.539113i	$-0.181241\pi$
$390$	91.9628	+	193.216i	0.235802	+	0.495426i
$391$	202.661	+	556.805i	0.518313	+	1.42405i
$392$	−278.094	−	303.207i	−0.709423	−	0.773487i
$393$	22.7136	−	25.1763i	0.0577955	−	0.0640617i
$394$	−418.898	−	383.731i	−1.06319	−	0.973937i
$395$	−328.158	−	189.462i	−0.830778	−	0.479650i
$396$	458.397	−	397.145i	1.15757	−	1.00289i
$397$	197.081	+	341.354i	0.496425	+	0.859833i	0.999991	−	0.00412318i	$-0.00131245\pi$
$397$	197.081	+	341.354i	0.496425	+	0.859833i	−0.503567	+	0.863956i	$0.667979\pi$
$398$	267.529	+	59.2670i	0.672184	+	0.148912i
$399$	330.229	+	133.799i	0.827641	+	0.335335i
$400$	62.3881	−	74.4435i	0.155970	−	0.186109i
$401$	−33.5438	−	28.1466i	−0.0836503	−	0.0701909i	0.600004	−	0.799997i	$-0.295166\pi$
$401$	−33.5438	−	28.1466i	−0.0836503	−	0.0701909i	−0.683654	+	0.729806i	$0.739610\pi$
$402$	264.077	+	370.872i	0.656907	+	0.922567i
$403$	56.3780	−	154.897i	0.139896	−	0.384360i
$404$	54.4963	−	203.632i	0.134892	−	0.504039i
$405$	−110.218	+	334.736i	−0.272143	+	0.826507i
$406$	−378.251	−	492.791i	−0.931654	−	1.21377i
$407$	232.747	−	639.468i	0.571861	−	1.57117i
$408$	−222.651	−	596.459i	−0.545713	−	1.46191i
$409$	−318.044	−	266.870i	−0.777613	−	0.652495i	0.165033	−	0.986288i	$-0.447227\pi$
$409$	−318.044	−	266.870i	−0.777613	−	0.652495i	−0.942646	+	0.333793i	$0.891671\pi$
$410$	145.916	+	280.198i	0.355893	+	0.683409i
$411$	−436.434	−	176.830i	−1.06188	−	0.430243i
$412$	157.806	−	73.6450i	0.383025	−	0.178750i
$413$	−185.346	−	321.028i	−0.448778	−	0.777307i
$414$	180.051	−	359.493i	0.434905	−	0.868342i
$415$	277.880	+	160.434i	0.669590	+	0.386588i
$416$	79.0690	+	250.109i	0.190070	+	0.601223i
$417$	−353.897	+	392.267i	−0.848675	+	0.940689i
$418$	−214.511	+	336.828i	−0.513184	+	0.805809i
$419$	−21.7249	−	59.6886i	−0.0518493	−	0.142455i	0.911065	−	0.412264i	$-0.135262\pi$
$419$	−21.7249	−	59.6886i	−0.0518493	−	0.142455i	−0.962914	+	0.269809i	$0.913039\pi$
$420$	−237.849	+	466.024i	−0.566306	+	1.10958i
$421$	108.764	+	616.830i	0.258346	+	1.46515i	0.787335	+	0.616525i	$0.211460\pi$
$421$	108.764	+	616.830i	0.258346	+	1.46515i	−0.528989	+	0.848629i	$0.677429\pi$
$422$	−366.167	+	48.2637i	−0.867695	+	0.114369i
$423$	−106.693	−	147.458i	−0.252228	−	0.348601i
$424$	−227.319	+	296.530i	−0.536131	+	0.699362i
$425$	123.362	−	103.513i	0.290264	−	0.243560i
$426$	−117.150	−	30.4007i	−0.274999	−	0.0713631i
$427$	−628.047	−	110.742i	−1.47084	−	0.259348i
$428$	−161.970	−	231.167i	−0.378435	−	0.540110i
$429$	−366.000	+	194.145i	−0.853147	+	0.452552i
$430$	−67.3782	−	213.583i	−0.156693	−	0.496704i
$431$		−	127.048i		−	0.294775i	−0.989079	−	0.147388i	$-0.952914\pi$
$431$		−	127.048i		−	0.294775i	0.989079	−	0.147388i	$-0.0470865\pi$
$432$	−190.283	+	387.836i	−0.440469	+	0.897768i
$433$	587.542			1.35691			0.678454	−	0.734642i	$-0.262650\pi$
$433$	587.542			1.35691			0.678454	+	0.734642i	$0.262650\pi$
$434$	384.371	−	121.256i	0.885647	−	0.279392i
$435$	−214.719	+	342.873i	−0.493607	+	0.788213i
$436$	−292.615	+	205.024i	−0.671134	+	0.470239i
$437$	−45.9688	+	260.702i	−0.105192	+	0.596573i
$438$	−429.866	−	423.130i	−0.981430	−	0.966050i
$439$	277.190	+	330.342i	0.631412	+	0.752488i	0.982988	−	0.183672i	$-0.0587984\pi$
$439$	277.190	+	330.342i	0.631412	+	0.752488i	−0.351576	+	0.936159i	$0.614354\pi$
$440$	−465.385	−	356.764i	−1.05769	−	0.810826i
$441$	−112.856	+	448.884i	−0.255910	+	1.01788i
$442$	56.8319	+	431.172i	0.128579	+	0.975503i
$443$	774.476	−	136.561i	1.74825	−	0.308264i	0.794145	−	0.607729i	$-0.207919\pi$
$443$	774.476	−	136.561i	1.74825	−	0.308264i	0.954107	+	0.299465i	$0.0968081\pi$
$444$	25.0401	+	484.060i	0.0563965	+	1.09023i
$445$	307.515	−	111.926i	0.691045	−	0.251520i
$446$	368.362	+	234.593i	0.825923	+	0.525994i
$447$	281.076	−	91.0220i	0.628806	−	0.203629i
$448$	−367.392	+	525.715i	−0.820072	+	1.17347i
$449$	−242.525	+	420.066i	−0.540145	+	0.935559i	0.458750	+	0.888566i	$0.348297\pi$
$449$	−242.525	+	420.066i	−0.540145	+	0.935559i	−0.998895	+	0.0469939i	$0.985036\pi$
$450$	−108.546	−	12.5665i	−0.241212	−	0.0279254i
$451$	−529.708	+	305.827i	−1.17452	+	0.678109i
$452$	133.562	+	286.196i	0.295491	+	0.633177i
$453$	2.32167	−	0.323964i	0.00512509	−	0.000715152i
$454$	537.815	−	280.073i	1.18461	−	0.616901i
$455$	229.735	−	273.788i	0.504913	−	0.601732i
$456$	47.0924	−	280.510i	0.103273	−	0.615154i
$457$	−813.496	−	296.088i	−1.78008	−	0.647896i	−0.999746	−	0.0225304i	$-0.992828\pi$
$457$	−813.496	−	296.088i	−1.78008	−	0.647896i	−0.780332	−	0.625365i	$-0.784950\pi$
$458$	491.656	−	377.380i	1.07348	−	0.823974i
$459$	−422.703	+	578.210i	−0.920922	+	1.25972i
$460$	−375.516	−	100.496i	−0.816339	−	0.218470i
$461$	−652.111	−	237.349i	−1.41456	−	0.514857i	−0.482094	−	0.876120i	$-0.660124\pi$
$461$	−652.111	−	237.349i	−1.41456	−	0.514857i	−0.932464	+	0.361263i	$0.882346\pi$
$462$	−921.450	−	420.852i	−1.99448	−	0.910936i
$463$	438.512	−	522.598i	0.947111	−	1.12872i	−0.0444414	−	0.999012i	$-0.514151\pi$
$463$	438.512	−	522.598i	0.947111	−	1.12872i	0.991552	−	0.129710i	$-0.0414048\pi$
$464$	−318.537	+	380.089i	−0.686503	+	0.819158i
$465$	−161.391	−	206.990i	−0.347077	−	0.445139i
$466$	18.8247	−	84.9742i	0.0403964	−	0.182348i
$467$	−388.222	+	224.140i	−0.831310	+	0.479957i	−0.854301	−	0.519779i	$-0.826014\pi$
$467$	−388.222	+	224.140i	−0.831310	+	0.479957i	0.0229910	+	0.999736i	$0.492681\pi$
$468$	186.092	−	229.026i	0.397631	−	0.489372i
$469$	380.214	−	658.549i	0.810690	−	1.40416i
$470$	−118.866	+	129.760i	−0.252907	+	0.276085i
$471$	111.478	−	521.941i	0.236684	−	1.10816i
$472$	−218.083	+	200.021i	−0.462041	+	0.423773i
$473$	407.463	−	148.305i	0.861445	−	0.313540i
$474$	−41.4315	+	520.913i	−0.0874083	+	1.09897i
$475$	70.8524	−	12.4932i	0.149163	−	0.0263015i
$476$	−751.687	+	752.146i	−1.57917	+	1.58014i
$477$	419.258	+	30.1452i	0.878948	+	0.0631974i
$478$	254.907	−	615.665i	0.533278	−	1.28800i
$479$	370.059	+	441.020i	0.772567	+	0.920709i	0.998572	−	0.0534168i	$-0.0170112\pi$
$479$	370.059	+	441.020i	0.772567	+	0.920709i	−0.226006	+	0.974126i	$0.572567\pi$
$480$	404.349	+	104.666i	0.842395	+	0.218054i
$481$	57.4954	−	326.073i	0.119533	−	0.677905i
$482$	−693.015	−	30.1517i	−1.43779	−	0.0625553i
$483$	−671.104	−	24.0955i	−1.38945	−	0.0498871i
$484$	373.434	−	533.666i	0.771559	−	1.10262i
$485$	−316.060			−0.651670
$486$	482.139	−	61.1422i	0.992055	−	0.125807i
$487$		−	109.976i		−	0.225824i	−0.993605	−	0.112912i	$-0.963982\pi$
$487$		−	109.976i		−	0.225824i	0.993605	−	0.112912i	$-0.0360178\pi$
$488$	22.4397	+	508.605i	0.0459830	+	1.04222i
$489$	28.9342	−	805.872i	0.0591702	−	1.64800i
$490$	447.083	+	19.4517i	0.912415	+	0.0396973i
$491$	382.906	+	67.5166i	0.779849	+	0.137508i	0.549381	−	0.835572i	$-0.314863\pi$
$491$	382.906	+	67.5166i	0.779849	+	0.137508i	0.230467	+	0.973080i	$0.425975\pi$
$492$	262.425	−	347.760i	0.533385	−	0.706830i
$493$	−629.855	+	528.511i	−1.27760	+	1.07203i
$494$	−74.3269	+	179.519i	−0.150459	+	0.363398i
$495$	−47.3109	+	658.000i	−0.0955777	+	1.32929i
$496$	−161.043	−	278.542i	−0.324684	−	0.561577i
$497$	35.1026	+	199.077i	0.0706290	+	0.400557i
$498$	35.0837	−	441.103i	0.0704492	−	0.885748i
$499$	−36.1272	−	99.2586i	−0.0723992	−	0.198915i	0.898215	−	0.439557i	$-0.144864\pi$
$499$	−36.1272	−	99.2586i	−0.0723992	−	0.198915i	−0.970614	+	0.240642i	$0.922642\pi$
$500$	47.2920	+	538.655i	0.0945840	+	1.07731i
$501$	63.4767	+	13.5576i	0.126700	+	0.0270610i
$502$	18.9484	−	20.6848i	0.0377457	−	0.0412049i
$503$	417.548	+	241.072i	0.830116	+	0.479268i	0.853892	−	0.520449i	$-0.174236\pi$
$503$	417.548	+	241.072i	0.830116	+	0.479268i	−0.0237762	+	0.999717i	$0.507569\pi$
$504$	721.263	+	19.9741i	1.43108	+	0.0396312i
$505$	114.642	+	198.566i	0.227015	+	0.393201i
$506$	162.788	−	734.820i	0.321715	−	1.45221i
$507$	240.858	−	187.798i	0.475065	−	0.370411i
$508$	−160.236	+	343.902i	−0.315426	+	0.676973i
$509$	−466.979	−	391.842i	−0.917443	−	0.769826i	0.0560770	−	0.998426i	$-0.482141\pi$
$509$	−466.979	−	391.842i	−0.917443	−	0.769826i	−0.973520	+	0.228600i	$0.926585\pi$
$510$	629.906	+	287.696i	1.23511	+	0.564109i
$511$	−344.567	+	946.690i	−0.674299	+	1.85262i
$512$	473.295	+	195.283i	0.924405	+	0.381413i
$513$	−292.708	+	129.290i	−0.570580	+	0.252027i
$514$	269.253	−	206.670i	0.523839	−	0.402083i
$515$	−64.7845	+	177.994i	−0.125795	+	0.345619i
$516$	−226.022	+	210.483i	−0.438028	+	0.407913i
$517$	−260.999	−	219.004i	−0.504833	−	0.423605i
$518$	718.043	−	373.929i	1.38618	−	0.721871i
$519$	48.5644	+	348.034i	0.0935730	+	0.670585i
$520$	−253.137	−	131.627i	−0.486801	−	0.253129i
$521$	−96.1278	−	166.498i	−0.184506	−	0.319575i	0.758904	−	0.651203i	$-0.225735\pi$
$521$	−96.1278	−	166.498i	−0.184506	−	0.319575i	−0.943410	+	0.331628i	$0.892402\pi$
$522$	554.205	+	64.1611i	1.06170	+	0.122914i
$523$	261.108	+	150.751i	0.499250	+	0.288242i	0.728404	−	0.685148i	$-0.240262\pi$
$523$	261.108	+	150.751i	0.499250	+	0.288242i	−0.229154	+	0.973390i	$0.573596\pi$
$524$	−3.92661	+	45.0398i	−0.00749353	+	0.0859539i
$525$	56.2272	+	173.630i	0.107100	+	0.330723i
$526$	−547.673	−	348.789i	−1.04120	−	0.663097i
$527$	−182.449	−	501.276i	−0.346204	−	0.951188i
$528$	−168.427	+	790.944i	−0.318991	+	1.49800i
$529$	5.22135	+	29.6117i	0.00987022	+	0.0559768i
$530$	−53.1078	−	402.919i	−0.100203	−	0.760224i
$531$	322.862	+	81.1726i	0.608027	+	0.152867i
$532$	−458.848	+	123.098i	−0.862496	+	0.231387i
$533$	−227.976	+	191.295i	−0.427723	+	0.358902i
$534$	−321.626	−	316.585i	−0.602295	−	0.592857i
$535$	302.353	+	53.3130i	0.565146	+	0.0996504i
$536$	−579.032	−	182.276i	−1.08028	−	0.340068i
$537$	51.0843	+	31.9908i	0.0951291	+	0.0595733i
$538$	536.126	−	169.130i	0.996517	−	0.314368i
$539$			866.433i			1.60748i
$540$	−151.806	−	444.688i	−0.281122	−	0.823497i
$541$	−53.7516			−0.0993561			−0.0496780	−	0.998765i	$-0.515820\pi$
$541$	−53.7516			−0.0993561			−0.0496780	+	0.998765i	$0.515820\pi$
$542$	163.014	+	516.739i	0.300764	+	0.953394i
$543$	−271.671	−	512.151i	−0.500314	−	0.943188i
$544$	716.287	+	455.557i	1.31670	+	0.837421i
$545$	67.4844	−	382.723i	0.123825	−	0.702244i
$546$	−477.080	−	123.804i	−0.873773	−	0.226746i
$547$	−309.469	−	368.810i	−0.565756	−	0.674242i	0.404998	−	0.914318i	$-0.367272\pi$
$547$	−309.469	−	368.810i	−0.565756	−	0.674242i	−0.970754	+	0.240076i	$0.922828\pi$
$548$	606.418	−	162.688i	1.10660	−	0.296876i
$549$	464.015	−	335.736i	0.845200	−	0.611540i
$550$	−202.794	+	26.7298i	−0.368716	+	0.0485997i
$551$	−361.754	+	63.7870i	−0.656541	+	0.115766i
$552$	97.4171	+	527.157i	0.176480	+	0.954994i
$553$	820.156	−	298.512i	1.48310	−	0.539806i
$554$	−113.598	+	178.373i	−0.205051	+	0.321974i
$555$	−391.451	−	353.161i	−0.705317	−	0.636326i
$556$	61.1799	−	701.759i	0.110036	−	1.26216i
$557$	220.981	−	382.751i	0.396735	−	0.687165i	−0.596586	−	0.802549i	$-0.703477\pi$
$557$	220.981	−	382.751i	0.396735	−	0.687165i	0.993321	+	0.115384i	$0.0368100\pi$
$558$	−162.095	+	323.642i	−0.290492	+	0.580003i
$559$	182.710	−	105.488i	0.326852	−	0.188708i
$560$	−121.559	−	686.943i	−0.217070	−	1.22668i
$561$	−503.480	+	1242.64i	−0.897469	+	2.21505i
$562$	−78.3021	−	150.361i	−0.139328	−	0.267546i
$563$	−539.434	+	642.872i	−0.958142	+	1.14187i	0.0316719	+	0.999498i	$0.489917\pi$
$563$	−539.434	+	642.872i	−0.958142	+	1.14187i	−0.989813	+	0.142370i	$0.954528\pi$
$564$	232.026	+	71.1093i	0.411394	+	0.126080i
$565$	−322.808	−	117.492i	−0.571341	−	0.207951i
$566$	−392.741	−	511.668i	−0.693889	−	0.904008i
$567$	−427.444	−	690.073i	−0.753870	−	1.21706i
$568$	149.061	−	61.8232i	0.262432	−	0.108844i
$569$	1001.95	+	364.680i	1.76090	+	0.640914i	0.999969	−	0.00792419i	$-0.00252237\pi$
$569$	1001.95	+	364.680i	1.76090	+	0.640914i	0.760927	+	0.648838i	$0.224745\pi$
$570$	179.449	+	252.020i	0.314823	+	0.442141i
$571$	−421.903	+	502.804i	−0.738884	+	0.880567i	−0.996319	−	0.0857285i	$-0.972678\pi$
$571$	−421.903	+	502.804i	−0.738884	+	0.880567i	0.257435	+	0.966296i	$0.417123\pi$
$572$	233.304	−	500.721i	0.407874	−	0.875387i
$573$	−288.603	+	712.302i	−0.503670	+	1.24311i
$574$	−710.437	−	157.386i	−1.23770	−	0.274192i
$575$	−117.431	+	67.7987i	−0.204227	+	0.117911i
$576$	−109.313	−	565.532i	−0.189780	−	0.981827i
$577$	−117.795	+	204.027i	−0.204151	+	0.353600i	−0.949862	−	0.312670i	$-0.898777\pi$
$577$	−117.795	+	204.027i	−0.204151	+	0.353600i	0.745711	+	0.666270i	$0.232110\pi$
$578$	611.599	+	560.256i	1.05813	+	0.969300i
$579$	631.305	+	569.553i	1.09034	+	0.983684i
$580$	−47.1767	−	537.342i	−0.0813392	−	0.926451i
$581$	−694.498	+	252.777i	−1.19535	+	0.435072i
$582$	187.318	+	393.561i	0.321853	+	0.676221i
$583$	774.898	−	136.635i	1.32916	−	0.234366i
$584$	797.405	+	104.609i	1.36542	+	0.179124i
$585$	32.9242	+	319.285i	0.0562806	+	0.545786i
$586$	−380.684	−	157.616i	−0.649632	−	0.268970i
$587$	294.660	+	351.162i	0.501976	+	0.598232i	0.956221	−	0.292645i	$-0.0945354\pi$
$587$	294.660	+	351.162i	0.501976	+	0.598232i	−0.454245	+	0.890877i	$0.650091\pi$
$588$	−240.750	−	568.241i	−0.409439	−	0.966396i
$589$	41.3844	−	234.703i	0.0702622	−	0.398477i
$590$	13.9907	−	321.568i	0.0237131	−	0.545030i
$591$	−399.313	−	752.781i	−0.675657	−	1.27374i
$592$	−415.721	−	494.823i	−0.702232	−	0.835850i
$593$	530.547			0.894683			0.447342	−	0.894363i	$-0.352371\pi$
$593$	530.547			0.894683			0.447342	+	0.894363i	$0.352371\pi$
$594$	847.387	−	331.063i	1.42658	−	0.557345i
$595$		−	1156.63i		−	1.94391i
$596$	−225.850	+	322.757i	−0.378943	+	0.541538i
$597$	348.353	+	218.151i	0.583507	+	0.365413i
$598$	15.9174	−	365.851i	0.0266177	−	0.611790i
$599$	367.257	+	64.7574i	0.613118	+	0.108109i	0.471579	−	0.881824i	$-0.343684\pi$
$599$	367.257	+	64.7574i	0.613118	+	0.108109i	0.141538	+	0.989933i	$0.454795\pi$
$600$	125.573	−	73.8795i	0.209288	−	0.123133i
$601$	−335.573	+	281.579i	−0.558358	+	0.468518i	−0.877759	−	0.479102i	$-0.840962\pi$
$601$	−335.573	+	281.579i	−0.558358	+	0.468518i	0.319402	+	0.947619i	$0.396518\pi$
$602$	476.616	+	197.336i	0.791722	+	0.327800i
$603$	186.949	+	656.837i	0.310032	+	1.08928i
$604$	−2.20942	+	2.21077i	−0.00365798	+	0.00366022i
$605$	123.024	+	697.706i	0.203346	+	1.15323i
$606$	179.312	−	260.438i	0.295894	−	0.429765i
$607$	−56.8614	−	156.226i	−0.0936762	−	0.257373i	0.884001	−	0.467484i	$-0.154840\pi$
$607$	−56.8614	−	156.226i	−0.0936762	−	0.257373i	−0.977677	+	0.210111i	$0.932617\pi$
$608$	175.374	+	336.263i	0.288444	+	0.553064i
$609$	−287.082	−	886.509i	−0.471399	−	1.45568i
$610$	−408.322	−	374.044i	−0.669381	−	0.613187i
$611$	−143.564	−	82.8865i	−0.234965	−	0.135657i
$612$	−15.0828	−	954.873i	−0.0246451	−	1.56025i
$613$	−95.7272	−	165.804i	−0.156162	−	0.270480i	0.777320	−	0.629106i	$-0.216579\pi$
$613$	−95.7272	−	165.804i	−0.156162	−	0.270480i	−0.933481	+	0.358626i	$0.883245\pi$
$614$	−438.321	−	97.1032i	−0.713878	−	0.158149i
$615$	65.4893	+	469.325i	0.106487	+	0.763131i
$616$	1318.53	−	292.945i	2.14047	−	0.475559i
$617$	216.274	+	181.476i	0.350526	+	0.294126i	0.801001	−	0.598663i	$-0.204301\pi$
$617$	216.274	+	181.476i	0.350526	+	0.294126i	−0.450475	+	0.892789i	$0.648745\pi$
$618$	260.035	−	24.8209i	0.420769	−	0.0401632i
$619$	22.1636	−	60.8940i	0.0358055	−	0.0983748i	−0.920502	−	0.390739i	$-0.872220\pi$
$619$	22.1636	−	60.8940i	0.0358055	−	0.0983748i	0.956307	+	0.292364i	$0.0944418\pi$
$620$	338.066	+	90.4739i	0.545268	+	0.145926i
$621$	435.061	−	417.663i	0.700582	−	0.672566i
$622$	273.544	+	356.377i	0.439781	+	0.572953i
$623$	−257.805	+	708.313i	−0.413812	+	1.13694i
$624$	−13.8777	+	393.219i	−0.0222399	+	0.630159i
$625$	−334.289	−	280.502i	−0.534862	−	0.448803i
$626$	369.133	+	708.834i	0.589670	+	1.13232i
$627$	−472.382	+	368.319i	−0.753401	+	0.587430i
$628$	300.940	+	644.853i	0.479203	+	1.02684i
$629$	−535.754	−	927.954i	−0.851756	−	1.47528i
$630$	−570.264	+	539.201i	−0.905182	+	0.855874i
$631$	−310.209	−	179.099i	−0.491615	−	0.283834i	0.233629	−	0.972326i	$-0.424940\pi$
$631$	−310.209	−	179.099i	−0.491615	−	0.283834i	−0.725244	+	0.688492i	$0.758273\pi$
$632$	−374.629	−	587.456i	−0.592768	−	0.929519i
$633$	−541.782	−	115.716i	−0.855895	−	0.182805i
$634$	−16.5864	+	26.0443i	−0.0261616	+	0.0410793i
$635$	−141.143	−	387.786i	−0.222272	−	0.610686i
$636$	−470.243	+	304.927i	−0.739376	+	0.479445i
$637$	73.2040	+	415.161i	0.114920	+	0.651744i
$638$	1035.41	−	136.476i	1.62290	−	0.213912i
$639$	−150.308	−	101.814i	−0.235224	−	0.159334i
$640$	−514.282	+	213.667i	−0.803566	+	0.333855i
$641$	−575.070	+	482.541i	−0.897146	+	0.752795i	−0.969630	−	0.244575i	$-0.921352\pi$
$641$	−575.070	+	482.541i	−0.897146	+	0.752795i	0.0724847	+	0.997370i	$0.476907\pi$
$642$	−112.809	−	408.090i	−0.175715	−	0.635654i
$643$	−899.318	−	158.574i	−1.39863	−	0.246616i	−0.577049	−	0.816709i	$-0.695796\pi$
$643$	−899.318	−	158.574i	−1.39863	−	0.246616i	−0.821580	+	0.570093i	$0.806907\pi$
$644$	733.297	−	513.794i	1.13866	−	0.797816i
$645$	12.0538	−	335.721i	0.0186881	−	0.520498i
$646$	189.170	+	599.651i	0.292833	+	0.928252i
$647$		−	457.889i		−	0.707710i	−0.935300	−	0.353855i	$-0.884871\pi$
$647$		−	457.889i		−	0.707710i	0.935300	−	0.353855i	$-0.115129\pi$
$648$	−463.760	+	452.582i	−0.715679	+	0.698430i
$649$	623.187			0.960227
$650$	−94.9125	+	29.9417i	−0.146019	+	0.0460642i
$651$	604.175	+	21.6925i	0.928073	+	0.0333218i
$652$	616.971	+	880.554i	0.946275	+	1.35054i
$653$	44.8800	−	254.527i	0.0687289	−	0.389781i	−0.930967	−	0.365104i	$-0.881033\pi$
$653$	44.8800	−	254.527i	0.0687289	−	0.389781i	0.999695	−	0.0246765i	$-0.00785556\pi$
$654$	−516.566	+	142.795i	−0.789856	+	0.218341i
$655$	−31.6095	−	37.6707i	−0.0482587	−	0.0575125i
$656$	0.354914	+	580.887i	0.000541028	+	0.885498i
$657$	−395.026	−	813.977i	−0.601257	−	1.23893i
$658$	−52.9674	−	401.853i	−0.0804976	−	0.610719i
$659$	773.092	−	136.317i	1.17313	−	0.206854i	0.447078	−	0.894495i	$-0.352465\pi$
$659$	773.092	−	136.317i	1.17313	−	0.206854i	0.726051	+	0.687640i	$0.241353\pi$
$660$	−478.564	−	738.017i	−0.725097	−	1.11821i
$661$	871.348	−	317.145i	1.31823	−	0.479795i	0.415337	−	0.909668i	$-0.363664\pi$
$661$	871.348	−	317.145i	1.31823	−	0.479795i	0.902890	+	0.429872i	$0.141441\pi$
$662$	−468.616	−	298.441i	−0.707880	−	0.450817i
$663$	−136.258	+	637.964i	−0.205518	+	0.962238i
$664$	317.232	+	497.451i	0.477758	+	0.749173i
$665$	258.368	−	447.507i	0.388524	−	0.672943i
$666$	−207.759	+	696.746i	−0.311951	+	1.04616i
$667$	599.571	−	346.162i	0.898907	−	0.518984i
$668$	−78.4248	+	36.5993i	−0.117402	+	0.0547893i
$669$	402.800	+	516.606i	0.602093	+	0.772206i
$670$	585.630	−	304.973i	0.874074	−	0.455184i
$671$	689.152	−	821.299i	1.02705	−	1.22399i
$672$	−783.344	+	558.496i	−1.16569	+	0.831095i
$673$	−435.450	−	158.491i	−0.647029	−	0.235499i	−0.00240244	−	0.999997i	$-0.500765\pi$
$673$	−435.450	−	158.491i	−0.647029	−	0.235499i	−0.644626	+	0.764498i	$0.722987\pi$
$674$	−885.811	+	679.921i	−1.31426	+	1.00879i
$675$	−147.105	−	72.2854i	−0.217934	−	0.107089i
$676$	−105.278	+	393.382i	−0.155736	+	0.581926i
$677$	1255.40	+	456.930i	1.85436	+	0.674933i	0.982806	+	0.184642i	$0.0591126\pi$
$677$	1255.40	+	456.930i	1.85436	+	0.674933i	0.871559	+	0.490291i	$0.163110\pi$
$678$	45.0149	+	471.598i	0.0663937	+	0.695572i
$679$	467.946	−	557.676i	0.689169	−	0.821320i
$680$	−901.349	+	200.258i	−1.32551	+	0.294497i
$681$	900.829	−	125.701i	1.32280	−	0.184583i
$682$	−146.553	+	661.537i	−0.214888	+	0.969996i
$683$	−608.347	+	351.229i	−0.890698	+	0.514245i	−0.874171	−	0.485619i	$-0.838594\pi$
$683$	−608.347	+	351.229i	−0.890698	+	0.514245i	−0.0165271	+	0.999863i	$0.505261\pi$
$684$	207.464	−	372.816i	0.303311	−	0.545052i
$685$	−341.462	+	591.430i	−0.498485	+	0.863402i
$686$	−32.8730	+	35.8855i	−0.0479198	+	0.0523113i
$687$	884.467	−	286.420i	1.28743	−	0.416915i
$688$	71.2609	−	405.589i	0.103577	−	0.589520i
$689$	359.757	−	130.941i	0.522143	−	0.190045i
$690$	−480.271	−	330.668i	−0.696045	−	0.479229i
$691$	−57.8084	+	10.1932i	−0.0836590	+	0.0147513i	−0.215321	−	0.976543i	$-0.569080\pi$
$691$	−57.8084	+	10.1932i	−0.0836590	+	0.0147513i	0.131662	+	0.991295i	$0.457969\pi$
$692$	−331.410	−	331.207i	−0.478916	−	0.478623i
$693$	−1090.97	−	1057.69i	−1.57427	−	1.52625i
$694$	−342.906	+	828.207i	−0.494101	+	1.19338i
$695$	492.502	+	586.941i	0.708636	+	0.844520i
$696$	−641.143	+	377.210i	−0.921183	+	0.541968i
$697$	−167.240	+	948.463i	−0.239942	+	1.36078i
$698$	−1019.49	−	44.3559i	−1.46059	−	0.0635472i
$699$	69.2905	−	110.646i	0.0991280	−	0.158292i
$700$	−199.377	−	139.515i	−0.284825	−	0.199307i
$701$	−50.6411			−0.0722413			−0.0361206	−	0.999347i	$-0.511500\pi$
$701$	−50.6411			−0.0722413			−0.0361206	+	0.999347i	$0.511500\pi$
$702$	378.064	−	230.227i	0.538552	−	0.327959i
$703$		−	478.709i		−	0.680951i
$704$	−456.578	−	976.797i	−0.648548	−	1.38750i
$705$	−233.185	+	123.693i	−0.330759	+	0.175451i
$706$	414.277	+	18.0243i	0.586795	+	0.0255302i
$707$	−520.099	−	91.7074i	−0.735641	−	0.129713i
$708$	−408.711	+	173.161i	−0.577275	+	0.244578i
$709$	−541.957	+	454.756i	−0.764397	+	0.641405i	−0.939267	−	0.343186i	$-0.888494\pi$
$709$	−541.957	+	454.756i	−0.764397	+	0.641405i	0.174870	+	0.984591i	$0.444049\pi$
$710$	−67.1459	+	162.175i	−0.0945718	+	0.228415i
$711$	−320.221	+	715.443i	−0.450381	+	1.00625i
$712$	596.618	+	78.2681i	0.837947	+	0.109927i
$713$	77.9982	+	442.350i	0.109394	+	0.620406i
$714$	−1440.24	+	685.495i	−2.01715	+	0.960077i
$715$	205.503	+	564.615i	0.287417	+	0.789672i
$716$	−80.0581	+	7.02882i	−0.111813	+	0.00981679i
$717$	669.541	−	742.134i	0.933809	−	1.03505i
$718$	−82.4576	+	90.0143i	−0.114843	+	0.125368i
$719$	−1042.00	−	601.598i	−1.44923	−	0.836715i	−0.450798	−	0.892626i	$-0.648860\pi$
$719$	−1042.00	−	601.598i	−1.44923	−	0.836715i	−0.998436	+	0.0559107i	$0.982194\pi$
$720$	518.929	+	351.045i	0.720735	+	0.487563i
$721$	−218.147	−	377.841i	−0.302561	−	0.524051i
$722$	95.4024	−	430.644i	0.132136	−	0.596459i
$723$	−964.358	−	390.728i	−1.33383	−	0.540426i
$724$	700.669	+	326.467i	0.967775	+	0.450921i
$725$	−144.136	−	120.945i	−0.198809	−	0.166821i
$726$	795.878	−	566.699i	1.09625	−	0.780577i
$727$	−74.9737	+	205.989i	−0.103128	+	0.283341i	−0.980516	−	0.196441i	$-0.937062\pi$
$727$	−74.9737	+	205.989i	−0.103128	+	0.283341i	0.877388	+	0.479781i	$0.159284\pi$
$728$	607.036	−	251.769i	0.833841	−	0.345836i
$729$	712.164	+	155.767i	0.976905	+	0.213673i
$730$	−693.919	+	532.631i	−0.950574	+	0.729632i
$731$	233.516	−	641.581i	0.319448	−	0.877676i
$732$	−223.764	+	730.131i	−0.305688	+	0.997446i
$733$	18.6768	+	15.6717i	0.0254799	+	0.0213802i	0.655439	−	0.755248i	$-0.272484\pi$
$733$	18.6768	+	15.6717i	0.0254799	+	0.0213802i	−0.629959	+	0.776629i	$0.716928\pi$
$734$	−465.433	+	242.379i	−0.634104	+	0.330217i
$735$	622.134	+	252.069i	0.846440	+	0.342952i
$736$	−527.357	−	482.494i	−0.716518	−	0.655562i
$737$	639.196	+	1107.12i	0.867295	+	1.50220i
$738$	545.595	−	359.702i	0.739289	−	0.487401i
$739$	223.668	+	129.135i	0.302664	+	0.174743i	0.643639	−	0.765329i	$-0.277424\pi$
$739$	223.668	+	129.135i	0.302664	+	0.174743i	−0.340975	+	0.940072i	$0.610757\pi$
$740$	700.298	+	61.0526i	0.946349	+	0.0825035i
$741$	−195.228	+	216.395i	−0.263466	+	0.292031i
$742$	789.565	+	502.839i	1.06410	+	0.677680i
$743$	118.080	+	324.422i	0.158923	+	0.436638i	0.993441	−	0.114342i	$-0.0364761\pi$
$743$	118.080	+	324.422i	0.158923	+	0.436638i	−0.834518	+	0.550980i	$0.814254\pi$
$744$	−87.7018	−	474.584i	−0.117879	−	0.637882i
$745$	−74.4041	−	421.967i	−0.0998713	−	0.566398i
$746$	−144.742	−	1098.13i	−0.194024	−	1.47202i
$747$	271.159	−	605.828i	0.362998	−	0.811015i
$748$	−463.215	−	1726.63i	−0.619271	−	2.30833i
$749$	−541.721	+	454.558i	−0.723259	+	0.606886i
$750$	−203.732	+	785.087i	−0.271643	+	1.04678i
$751$	−461.870	−	81.4402i	−0.615007	−	0.108442i	−0.142538	−	0.989789i	$-0.545526\pi$
$751$	−461.870	−	81.4402i	−0.615007	−	0.108442i	−0.472470	+	0.881347i	$0.656637\pi$
$752$	−303.990	+	110.854i	−0.404242	+	0.147412i
$753$	37.1718	−	19.7178i	0.0493649	−	0.0261856i
$754$	484.598	−	152.875i	0.642703	−	0.202752i
$755$		−	3.39966i		−	0.00450285i
$756$	1009.39	+	390.532i	1.33518	+	0.516577i
$757$	−653.653			−0.863479			−0.431739	−	0.901998i	$-0.642100\pi$
$757$	−653.653			−0.863479			−0.431739	+	0.901998i	$0.642100\pi$
$758$	−37.2281	−	118.010i	−0.0491136	−	0.155685i
$759$	599.194	−	956.819i	0.789452	−	1.26063i
$760$	−393.472	−	123.863i	−0.517726	−	0.162978i
$761$	114.654	−	650.234i	0.150662	−	0.854446i	−0.811983	−	0.583681i	$-0.801612\pi$
$761$	114.654	−	650.234i	0.150662	−	0.854446i	0.962645	−	0.270766i	$-0.0872769\pi$
$762$	−399.224	+	405.580i	−0.523916	+	0.532257i
$763$	575.386	+	685.719i	0.754110	+	0.898714i
$764$	−265.522	−	989.732i	−0.347542	−	1.29546i
$765$	745.790	+	723.038i	0.974889	+	0.945148i
$766$	717.316	−	94.5479i	0.936443	−	0.123431i
$767$	298.607	−	52.6525i	0.389318	−	0.0686473i
$768$	570.858	+	513.755i	0.743305	+	0.668952i
$769$	−1263.92	+	460.030i	−1.64359	+	0.598219i	−0.987662	−	0.156602i	$-0.949946\pi$
$769$	−1263.92	+	460.030i	−1.64359	+	0.598219i	−0.655931	+	0.754821i	$0.727724\pi$
$770$	−789.174	+	1239.17i	−1.02490	+	1.60932i
$771$	484.374	−	156.857i	0.628241	−	0.203446i
$772$	−1129.39	−	98.4613i	−1.46294	−	0.127541i
$773$	−116.766	+	202.245i	−0.151056	+	0.261637i	−0.931616	−	0.363444i	$-0.881601\pi$
$773$	−116.766	+	202.245i	−0.151056	+	0.261637i	0.780560	+	0.625081i	$0.214934\pi$
$774$	−425.187	+	183.961i	−0.549337	+	0.237676i
$775$	105.720	−	61.0372i	0.136412	−	0.0787577i
$776$	−515.612	−	268.110i	−0.664449	−	0.345503i
$777$	1202.71	−	167.825i	1.54789	−	0.215991i
$778$	276.460	+	530.876i	0.355346	+	0.682360i
$779$	−276.574	+	329.609i	−0.355038	+	0.423117i
$780$	−291.663	−	313.195i	−0.373927	−	0.401532i
$781$	−319.346	−	116.233i	−0.408894	−	0.148825i
$782$	−721.574	−	940.077i	−0.922729	−	1.20214i
$783$	751.081	+	369.070i	0.959235	+	0.471354i
$784$	712.860	+	410.989i	0.909260	+	0.524221i
$785$	−727.346	−	264.732i	−0.926556	−	0.337239i
$786$	−28.1740	+	61.6866i	−0.0358448	+	0.0784817i
$787$	−393.189	+	468.584i	−0.499604	+	0.595405i	−0.955633	−	0.294560i	$-0.904827\pi$
$787$	−393.189	+	468.584i	−0.499604	+	0.595405i	0.456029	+	0.889965i	$0.349271\pi$
$788$	1029.87	+	479.855i	1.30695	+	0.608953i
$789$	−598.876	−	768.080i	−0.759032	−	0.973486i
$790$	739.908	+	163.915i	0.936593	+	0.207488i
$791$	685.248	−	395.628i	0.866306	−	0.500162i
$792$	−635.357	+	1033.31i	−0.802218	+	1.30469i
$793$	260.824	−	451.760i	0.328908	−	0.569685i
$794$	−581.294	−	532.494i	−0.732108	−	0.670648i
$795$	127.330	−	596.159i	0.160163	−	0.749886i
$796$	−545.931	+	47.9308i	−0.685843	+	0.0602146i
$797$	494.327	−	179.920i	0.620234	−	0.225747i	−0.0127409	−	0.999919i	$-0.504056\pi$
$797$	494.327	−	179.920i	0.620234	−	0.225747i	0.632975	+	0.774172i	$0.281833\pi$
$798$	−710.366	−	56.5000i	−0.890183	−	0.0708020i
$799$	−528.321	+	93.1573i	−0.661228	+	0.116592i
$800$	−74.2025	+	179.528i	−0.0927531	+	0.224411i
$801$	−295.558	−	609.017i	−0.368986	−	0.760321i
$802$	80.9153	+	33.5017i	0.100892	+	0.0417727i
$803$	−1088.67	−	1297.43i	−1.35575	−	1.61572i
$804$	−726.839	−	548.484i	−0.904029	−	0.682194i
$805$	−169.117	+	959.109i	−0.210083	+	1.19144i
$806$	−14.3300	+	329.365i	−0.0177791	+	0.408641i
$807$	842.713	+	30.2570i	1.04425	+	0.0374931i
$808$	18.5828	+	421.186i	0.0229985	+	0.521270i
$809$	544.887			0.673531			0.336766	−	0.941588i	$-0.390667\pi$
$809$	544.887			0.673531			0.336766	+	0.941588i	$0.390667\pi$
$810$	8.81214	−	704.774i	0.0108792	−	0.870091i
$811$			770.624i			0.950214i	0.879928	+	0.475107i	$0.157591\pi$
$811$			770.624i			0.950214i	−0.879928	+	0.475107i	$0.842409\pi$
$812$	1017.97	+	712.326i	1.25366	+	0.877249i
$813$	−29.1629	+	812.240i	−0.0358707	+	0.999065i
$814$	−59.1590	+	1359.73i	−0.0726769	+	1.67043i
$815$	−1151.71	−	203.078i	−1.41315	−	0.249176i
$816$	783.563	+	1003.68i	0.960249	+	1.23000i
$817$	233.666	−	196.069i	0.286005	−	0.239986i
$818$	767.195	+	317.645i	0.937891	+	0.388319i
$819$	−612.113	−	414.627i	−0.747391	−	0.506261i
$820$	−446.908	−	446.635i	−0.545009	−	0.544677i
$821$	11.4448	+	64.9068i	0.0139401	+	0.0790582i	0.990984	−	0.133979i	$-0.0427755\pi$
$821$	11.4448	+	64.9068i	0.0139401	+	0.0790582i	−0.977044	+	0.213037i	$0.931664\pi$
$822$	938.828	+	74.6710i	1.14213	+	0.0908406i
$823$	−408.452	−	1122.21i	−0.496297	−	1.36356i	−0.894828	−	0.446410i	$-0.852702\pi$
$823$	−408.452	−	1122.21i	−0.496297	−	1.36356i	0.398531	−	0.917155i	$-0.369520\pi$
$824$	−256.678	+	235.419i	−0.311503	+	0.285702i
$825$	−300.054	−	64.0866i	−0.363702	−	0.0776807i
$826$	546.681	+	500.787i	0.661841	+	0.606280i
$827$	−956.879	−	552.455i	−1.15705	−	0.668022i	−0.206454	−	0.978456i	$-0.566192\pi$
$827$	−956.879	−	552.455i	−1.15705	−	0.668022i	−0.950595	+	0.310434i	$0.899526\pi$
$828$	−127.110	+	794.014i	−0.153515	+	0.958954i
$829$	281.510	+	487.590i	0.339578	+	0.588167i	0.984353	−	0.176205i	$-0.0563823\pi$
$829$	281.510	+	487.590i	0.339578	+	0.588167i	−0.644775	+	0.764372i	$0.723049\pi$
$830$	−626.545	−	138.801i	−0.754874	−	0.167231i
$831$	−250.158	+	195.050i	−0.301033	+	0.234717i
$832$	−301.303	−	429.467i	−0.362143	−	0.516186i
$833$	1045.09	+	876.931i	1.25460	+	1.05274i
$834$	438.975	−	961.129i	0.526349	−	1.15243i
$835$	32.1959	−	88.4574i	0.0385579	−	0.105937i
$836$	206.475	−	771.519i	0.246980	−	0.922869i
$837$	−391.673	+	376.010i	−0.467949	+	0.449236i
$838$	77.3515	+	100.775i	0.0923049	+	0.120256i
$839$	−341.688	+	938.779i	−0.407256	+	1.11893i	0.551371	+	0.834260i	$0.314105\pi$
$839$	−341.688	+	938.779i	−0.407256	+	1.11893i	−0.958627	+	0.284666i	$0.908117\pi$
$840$	173.250	−	1031.98i	0.206251	−	1.22855i
$841$	91.6803	+	76.9289i	0.109013	+	0.0914731i
$842$	−578.598	−	1111.06i	−0.687171	−	1.31955i
$843$	−35.1432	−	251.851i	−0.0416882	−	0.298756i
$844$	669.366	−	312.379i	0.793087	−	0.370118i
$845$	−221.469	−	383.596i	−0.262094	−	0.453960i
$846$	292.225	+	217.056i	0.345420	+	0.256567i
$847$	−1413.22	−	815.925i	−1.66850	−	0.963312i
$848$	255.153	−	702.362i	0.300888	−	0.828257i
$849$	−298.079	−	920.468i	−0.351094	−	1.08418i
$850$	−173.010	+	271.662i	−0.203541	+	0.319603i
$851$	308.582	+	847.823i	0.362611	+	0.996266i
$852$	241.737	−	12.5048i	0.283729	−	0.0146771i
$853$	23.3839	+	132.617i	0.0274137	+	0.155471i	0.995442	−	0.0953710i	$-0.0304037\pi$
$853$	23.3839	+	132.617i	0.0274137	+	0.155471i	−0.968028	+	0.250842i	$0.919293\pi$
$854$	1264.53	−	166.676i	1.48072	−	0.195170i
$855$	127.039	+	446.344i	0.148583	+	0.522039i
$856$	448.026	+	343.456i	0.523395	+	0.401234i
$857$	219.310	−	184.023i	0.255904	−	0.214729i	−0.505806	−	0.862647i	$-0.668805\pi$
$857$	219.310	−	184.023i	0.255904	−	0.214729i	0.761710	+	0.647918i	$0.224360\pi$
$858$	581.270	−	590.524i	0.677471	−	0.688256i
$859$	−1032.05	−	181.978i	−1.20145	−	0.211848i	−0.463126	−	0.886292i	$-0.653272\pi$
$859$	−1032.05	−	181.978i	−1.20145	−	0.211848i	−0.738326	+	0.674444i	$0.764383\pi$
$860$	257.026	+	366.833i	0.298868	+	0.426550i
$861$	−925.069	−	579.312i	−1.07441	−	0.672836i
$862$	76.4452	+	242.324i	0.0886836	+	0.281119i
$863$			1607.61i			1.86282i	0.363973	+	0.931409i	$0.381420\pi$
$863$			1607.61i			1.86282i	−0.363973	+	0.931409i	$0.618580\pi$
$864$	129.572	−	854.229i	0.149968	−	0.988691i
$865$	509.631			0.589169
$866$	−1120.64	+	353.525i	−1.29404	+	0.408228i
$867$	583.005	+	1099.08i	0.672440	+	1.26768i
$868$	−660.166	+	462.554i	−0.760560	+	0.532896i
$869$	−254.793	+	1445.00i	−0.293203	+	1.66283i
$870$	203.235	−	783.173i	0.233604	−	0.900198i
$871$	399.817	+	476.484i	0.459032	+	0.547054i
$872$	434.752	−	567.118i	0.498569	−	0.650365i
$873$	67.0630	+	650.349i	0.0768190	+	0.744959i
$874$	−69.1870	−	524.908i	−0.0791613	−	0.600581i
$875$	1334.13	−	235.243i	1.52472	−	0.268849i
$876$	1074.50	+	548.402i	1.22660	+	0.626029i
$877$	1014.63	−	369.294i	1.15693	−	0.421087i	0.308929	−	0.951085i	$-0.400030\pi$
$877$	1014.63	−	369.294i	1.15693	−	0.421087i	0.847999	+	0.529998i	$0.177807\pi$
$878$	−727.464	−	463.289i	−0.828546	−	0.527664i
$879$	−458.883	−	413.997i	−0.522052	−	0.470987i
$880$	1102.31	+	400.447i	1.25263	+	0.455053i
$881$	152.141	−	263.516i	0.172691	−	0.299110i	−0.766668	−	0.642043i	$-0.778087\pi$
$881$	152.141	−	263.516i	0.172691	−	0.299110i	0.939360	+	0.342933i	$0.111420\pi$
$882$	−54.8389	−	924.080i	−0.0621756	−	1.04771i
$883$	960.150	−	554.343i	1.08737	−	0.627795i	0.154497	−	0.987993i	$-0.450624\pi$
$883$	960.150	−	554.343i	1.08737	−	0.627795i	0.932876	+	0.360198i	$0.117291\pi$
$884$	−367.836	−	788.197i	−0.416104	−	0.891626i
$885$	181.303	−	447.474i	0.204862	−	0.505620i
$886$	−1395.02	+	726.473i	−1.57452	+	0.819947i
$887$	−215.519	+	256.845i	−0.242975	+	0.289566i	−0.873725	−	0.486419i	$-0.838303\pi$
$887$	−215.519	+	256.845i	−0.242975	+	0.289566i	0.630750	+	0.775986i	$0.282747\pi$
$888$	−339.021	−	908.202i	−0.381780	−	1.02275i
$889$	893.205	+	325.100i	1.00473	+	0.365692i
$890$	−519.190	+	398.514i	−0.583359	+	0.447769i
$891$	1363.99	−	42.2667i	1.53085	−	0.0474374i
$892$	−843.747	−	225.805i	−0.945905	−	0.253145i
$893$	−225.221	−	81.9736i	−0.252207	−	0.0917958i
$894$	−481.340	+	342.734i	−0.538412	+	0.383372i
$895$	56.1887	−	66.9631i	0.0627807	−	0.0748191i
$896$	384.418	−	1223.78i	0.429038	−	1.36583i
$897$	206.270	−	509.095i	0.229955	−	0.567553i
$898$	209.824	−	947.138i	0.233657	−	1.05472i
$899$	−539.776	+	311.640i	−0.600419	+	0.346652i
$900$	214.595	−	41.3437i	0.238439	−	0.0459374i
$901$	619.478	−	1072.97i	0.687545	−	1.19086i
$902$	826.317	−	902.044i	0.916095	−	1.00005i
$903$	574.522	+	518.324i	0.636237	+	0.574003i
$904$	−426.953	−	465.509i	−0.472293	−	0.514944i
$905$	−790.078	+	287.565i	−0.873014	+	0.317751i
$906$	−4.23328	+	2.01486i	−0.00467250	+	0.00222391i
$907$	187.688	−	33.0945i	0.206933	−	0.0364878i	−0.0692208	−	0.997601i	$-0.522051\pi$
$907$	187.688	−	33.0945i	0.206933	−	0.0364878i	0.276154	+	0.961114i	$0.410940\pi$
$908$	−857.276	+	857.800i	−0.944137	+	0.944714i
$909$	384.260	−	278.030i	0.422728	−	0.305863i
$910$	−273.445	+	660.440i	−0.300489	+	0.725758i
$911$	−358.732	−	427.520i	−0.393778	−	0.469287i	0.532334	−	0.846534i	$-0.321315\pi$
$911$	−358.732	−	427.520i	−0.393778	−	0.469287i	−0.926112	+	0.377248i	$0.876871\pi$
$912$	78.9624	+	563.364i	0.0865816	+	0.617724i
$913$	215.756	−	1223.61i	0.236315	−	1.34021i
$914$	1729.77	+	75.2588i	1.89253	+	0.0823400i
$915$	−389.232	−	733.777i	−0.425391	−	0.801942i
$916$	−710.685	+	1015.62i	−0.775857	+	1.10876i
$917$	113.268			0.123521
$918$	458.329	−	1357.19i	0.499269	−	1.47842i
$919$			1133.08i			1.23295i	0.787376	+	0.616473i	$0.211439\pi$
$919$			1133.08i			1.23295i	−0.787376	+	0.616473i	$0.788561\pi$
$920$	776.706	−	34.2683i	0.844246	−	0.0372482i
$921$	−570.743	−	357.420i	−0.619700	−	0.388078i
$922$	1386.61	+	60.3286i	1.50392	+	0.0654323i
$923$	−162.839	−	28.7128i	−0.176423	−	0.0311082i
$924$	2010.75	+	248.270i	2.17613	+	0.268691i
$925$	187.838	−	157.615i	0.203068	−	0.170394i
$926$	−521.944	+	1260.63i	−0.563654	+	1.36137i
$927$	380.000	+	95.5380i	0.409925	+	0.103061i
$928$	378.859	−	916.626i	0.408253	−	0.987743i
$929$	−2.83827	−	16.0966i	−0.00305519	−	0.0173269i	0.983242	−	0.182305i	$-0.0583558\pi$
$929$	−2.83827	−	16.0966i	−0.00305519	−	0.0173269i	−0.986297	+	0.164978i	$0.947245\pi$
$930$	432.374	+	297.691i	0.464918	+	0.320098i
$931$	208.461	+	572.742i	0.223911	+	0.615190i
$932$	15.2241	+	173.402i	0.0163348	+	0.186053i
$933$	207.612	+	641.105i	0.222521	+	0.687144i
$934$	605.606	−	661.106i	0.648400	−	0.707822i
$935$	1683.96	+	972.232i	1.80102	+	1.03982i
$936$	−217.135	+	548.803i	−0.231981	+	0.586328i
$937$	−208.069	−	360.386i	−0.222059	−	0.384617i	0.733374	−	0.679825i	$-0.237944\pi$
$937$	−208.069	−	360.386i	−0.222059	−	0.384617i	−0.955433	+	0.295208i	$0.904611\pi$
$938$	−328.946	+	1484.85i	−0.350689	+	1.58300i
$939$	165.673	+	1187.28i	0.176435	+	1.26441i
$940$	148.642	−	319.018i	0.158130	−	0.339381i
$941$	−248.379	−	208.415i	−0.263952	−	0.221482i	0.501200	−	0.865331i	$-0.332892\pi$
$941$	−248.379	−	208.415i	−0.263952	−	0.221482i	−0.765153	+	0.643849i	$0.777336\pi$
$942$	101.427	+	1062.60i	0.107672	+	1.12802i
$943$	277.360	−	762.040i	0.294125	−	0.808102i
$944$	295.607	−	512.729i	0.313143	−	0.543145i
$945$	−1076.86	+	475.650i	−1.13953	+	0.503333i
$946$	−687.937	+	528.040i	−0.727206	+	0.558181i
$947$	−505.822	+	1389.74i	−0.534131	+	1.46751i	0.319980	+	0.947424i	$0.396324\pi$
$947$	−505.822	+	1389.74i	−0.534131	+	1.46751i	−0.854112	+	0.520090i	$0.825899\pi$
$948$	−234.411	−	1018.49i	−0.247269	−	1.07435i
$949$	−631.266	−	529.695i	−0.665191	−	0.558161i
$950$	−127.623	+	66.4609i	−0.134340	+	0.0699589i
$951$	−36.5256	+	28.4792i	−0.0384075	+	0.0299465i
$952$	981.155	−	1886.89i	1.03063	−	1.98203i
$953$	−711.138	−	1231.73i	−0.746210	−	1.29247i	−0.949627	−	0.313382i	$-0.898538\pi$
$953$	−711.138	−	1231.73i	−0.746210	−	1.29247i	0.203417	−	0.979092i	$-0.434795\pi$
$954$	−817.807	+	194.772i	−0.857240	+	0.204163i
$955$	965.270	+	557.299i	1.01075	+	0.583559i
$956$	−115.747	+	1327.66i	−0.121074	+	1.38877i
$957$	1532.00	+	327.210i	1.60083	+	0.341912i
$958$	−971.193	−	618.510i	−1.01377	−	0.645626i
$959$	−538.002	−	1478.15i	−0.561003	−	1.54134i
$960$	−834.211	+	43.6641i	−0.868969	+	0.0454835i
$961$	96.6563	+	548.165i	0.100579	+	0.570411i
$962$	86.5354	+	656.527i	0.0899537	+	0.682460i
$963$	45.5463	−	633.457i	0.0472962	−	0.657795i
$964$	1339.96	−	359.480i	1.39000	−	0.372904i
$965$	944.607	−	792.620i	0.978868	−	0.821368i
$966$	1294.52	−	357.847i	1.34009	−	0.370442i
$967$	1199.62	+	211.526i	1.24056	+	0.218745i	0.755156	−	0.655545i	$-0.227561\pi$
$967$	1199.62	+	211.526i	1.24056	+	0.218745i	0.485405	+	0.874289i	$0.338672\pi$
$968$	−391.158	+	1242.58i	−0.404089	+	1.28366i
$969$	−33.8421	+	942.565i	−0.0349247	+	0.972719i
$970$	602.834	−	190.174i	0.621478	−	0.196056i
$971$		−	203.866i		−	0.209955i	−0.994475	−	0.104977i	$-0.966523\pi$
$971$		−	203.866i		−	0.209955i	0.994475	−	0.104977i	$-0.0334770\pi$
$972$	−882.814	+	406.723i	−0.908245	+	0.418440i
$973$	−1764.82			−1.81379
$974$	66.1730	+	209.762i	0.0679394	+	0.215362i
$975$	−149.189	−	5.35651i	−0.153014	−	0.00549386i
$976$	−348.829	−	956.582i	−0.357407	−	0.980104i
$977$	−65.5958	+	372.012i	−0.0671400	+	0.380770i	0.932660	+	0.360757i	$0.117482\pi$
$977$	−65.5958	+	372.012i	−0.0671400	+	0.380770i	−0.999800	+	0.0200126i	$0.993629\pi$
$978$	429.708	+	1554.48i	0.439374	+	1.58945i
$979$	−814.542	−	970.733i	−0.832014	−	0.991556i
$980$	−864.445	+	231.910i	−0.882087	+	0.236643i
$981$	−801.839	−	57.6531i	−0.817369	−	0.0587698i
$982$	−770.957	+	101.618i	−0.785089	+	0.103481i
$983$	−215.781	+	38.0481i	−0.219513	+	0.0387061i	−0.282323	−	0.959319i	$-0.591105\pi$
$983$	−215.781	+	38.0481i	−0.219513	+	0.0387061i	0.0628098	+	0.998026i	$0.479994\pi$
$984$	−291.286	+	821.200i	−0.296023	+	0.834553i
$985$	−1161.29	+	422.675i	−1.17897	+	0.429112i
$986$	883.342	−	1387.04i	0.895884	−	1.40673i
$987$	126.993	−	594.583i	0.128666	−	0.602414i
$988$	33.7500	−	387.126i	0.0341599	−	0.391828i
$989$	−287.448	+	497.874i	−0.290645	+	0.503412i
$990$	−305.682	−	1283.50i	−0.308770	−	1.29646i
$991$	−1357.24	+	783.603i	−1.36957	+	0.790720i	−0.990873	−	0.134802i	$-0.956960\pi$
$991$	−1357.24	+	783.603i	−1.36957	+	0.790720i	−0.378694	+	0.925522i	$0.623627\pi$
$992$	474.765	+	434.375i	0.478594	+	0.437878i
$993$	−512.428	−	657.207i	−0.516040	−	0.661840i
$994$	−186.738	−	358.586i	−0.187865	−	0.360751i
$995$	383.161	−	456.633i	0.385086	−	0.458928i
$996$	198.496	+	862.444i	0.199293	+	0.865907i
$997$	136.762	+	49.7773i	0.137174	+	0.0499271i	0.409695	−	0.912223i	$-0.365635\pi$
$997$	136.762	+	49.7773i	0.137174	+	0.0499271i	−0.272521	+	0.962150i	$0.587857\pi$
$998$	128.631	+	167.582i	0.128889	+	0.167918i
$999$	−643.631	+	880.415i	−0.644275	+	0.881296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.31.4	yes	204
3.2	odd	2		324.3.j.a.307.31		204
4.3	odd	2	inner	108.3.j.a.31.12	yes	204
12.11	even	2		324.3.j.a.307.23		204
27.7	even	9	inner	108.3.j.a.7.12	yes	204
27.20	odd	18		324.3.j.a.19.23		204
108.7	odd	18	inner	108.3.j.a.7.4	✓	204
108.47	even	18		324.3.j.a.19.31		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.4	✓	204	108.7	odd	18	inner
108.3.j.a.7.12	yes	204	27.7	even	9	inner
108.3.j.a.31.4	yes	204	1.1	even	1	trivial
108.3.j.a.31.12	yes	204	4.3	odd	2	inner
324.3.j.a.19.23		204	27.20	odd	18
324.3.j.a.19.31		204	108.47	even	18
324.3.j.a.307.23		204	12.11	even	2
324.3.j.a.307.31		204	3.2	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90734 + 0.601703i) q^{2} +(-2.99807 - 0.107643i) q^{3} +(3.27591 - 2.29531i) q^{4} +(-0.755508 + 4.28470i) q^{5} +(5.78311 - 1.59863i) q^{6} +(-6.44162 - 7.67682i) q^{7} +(-4.86718 + 6.34906i) q^{8} +(8.97683 + 0.645444i) q^{9} +O(q^{10})\)	\(q+(-1.90734 + 0.601703i) q^{2} +(-2.99807 - 0.107643i) q^{3} +(3.27591 - 2.29531i) q^{4} +(-0.755508 + 4.28470i) q^{5} +(5.78311 - 1.59863i) q^{6} +(-6.44162 - 7.67682i) q^{7} +(-4.86718 + 6.34906i) q^{8} +(8.97683 + 0.645444i) q^{9} +(-1.13710 - 8.62697i) q^{10} +(16.5915 - 2.92553i) q^{11} +(-10.0685 + 6.52886i) q^{12} +(7.70282 - 2.80360i) q^{13} +(16.9055 + 10.7664i) q^{14} +(2.72628 - 12.7645i) q^{15} +(5.46314 - 15.0384i) q^{16} +(13.2638 - 22.9735i) q^{17} +(-17.5102 + 4.17030i) q^{18} +(10.2637 - 5.92574i) q^{19} +(7.35972 + 15.7704i) q^{20} +(18.4861 + 23.7090i) q^{21} +(-29.8854 + 15.5631i) q^{22} +(-14.3578 + 17.1110i) q^{23} +(15.2756 - 18.5110i) q^{24} +(5.70448 + 2.07626i) q^{25} +(-13.0050 + 9.98223i) q^{26} +(-26.8437 - 2.90138i) q^{27} +(-38.7228 - 10.3631i) q^{28} +(-29.1256 - 10.6009i) q^{29} +(2.48048 + 25.9867i) q^{30} +(12.9259 - 15.4045i) q^{31} +(-1.37140 + 31.9706i) q^{32} +(-50.0574 + 6.98497i) q^{33} +(-11.4753 + 51.7992i) q^{34} +(37.7596 - 21.8005i) q^{35} +(30.8887 - 18.4902i) q^{36} +(20.1962 - 34.9808i) q^{37} +(-16.0108 + 17.4781i) q^{38} +(-23.3954 + 7.57622i) q^{39} +(-23.5266 - 25.6512i) q^{40} +(-34.1160 + 12.4172i) q^{41} +(-49.5250 - 34.0981i) q^{42} +(25.3466 - 4.46929i) q^{43} +(47.6372 - 47.6664i) q^{44} +(-9.54759 + 37.9753i) q^{45} +(17.0895 - 41.2756i) q^{46} +(-12.9992 - 15.4919i) q^{47} +(-17.9976 + 44.4981i) q^{48} +(-8.93040 + 50.6468i) q^{49} +(-12.1297 - 0.527738i) q^{50} +(-42.2386 + 67.4484i) q^{51} +(18.7986 - 26.8647i) q^{52} +46.7045 q^{53} +(52.9458 - 10.6180i) q^{54} +73.2998i q^{55} +(80.0931 - 3.53372i) q^{56} +(-31.4091 + 16.6610i) q^{57} +(61.9311 + 2.69449i) q^{58} +(36.4280 + 6.42325i) q^{59} +(-20.3674 - 48.0729i) q^{60} +(48.7491 - 40.9054i) q^{61} +(-15.3852 + 37.1592i) q^{62} +(-52.8703 - 73.0712i) q^{63} +(-16.6211 - 61.8040i) q^{64} +(6.19303 + 35.1224i) q^{65} +(91.2737 - 43.4424i) q^{66} +(25.9527 + 71.3043i) q^{67} +(-9.28040 - 105.704i) q^{68} +(44.8875 - 49.7543i) q^{69} +(-58.9030 + 64.3010i) q^{70} +(-17.4692 - 10.0858i) q^{71} +(-47.7898 + 53.8529i) q^{72} +(-50.2648 - 87.0613i) q^{73} +(-17.4729 + 78.8724i) q^{74} +(-16.8789 - 6.83883i) q^{75} +(20.0215 - 42.9705i) q^{76} +(-129.335 - 108.525i) q^{77} +(40.0643 - 28.5275i) q^{78} +(-29.7876 + 81.8406i) q^{79} +(60.3076 + 34.7695i) q^{80} +(80.1668 + 11.5881i) q^{81} +(57.5993 - 44.2115i) q^{82} +(25.2237 - 69.3017i) q^{83} +(114.978 + 35.2374i) q^{84} +(88.4137 + 74.1879i) q^{85} +(-45.6555 + 23.7756i) q^{86} +(86.1795 + 34.9173i) q^{87} +(-62.1795 + 119.580i) q^{88} +(-37.6081 - 65.1392i) q^{89} +(-4.63935 - 78.1768i) q^{90} +(-71.1414 - 41.0735i) q^{91} +(-7.75992 + 89.0095i) q^{92} +(-40.4110 + 44.7924i) q^{93} +(34.1155 + 21.7266i) q^{94} +(17.6357 + 48.4537i) q^{95} +(7.55298 - 95.7024i) q^{96} +(12.6145 + 71.5405i) q^{97} +(-13.4410 - 101.974i) q^{98} +(150.827 - 15.5531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more