LMFDB - Embedded newform 273.2.bj.d.142.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (of order $6$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 310x^{10} + 807x^{8} - 1196x^{6} + 1273x^{4} - 688x^{2} + 256 $ x^16 - 11x^14 + 85x^12 - 310x^10 + 807x^8 - 1196x^6 + 1273x^4 - 688*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			142.8
Root			$1.39394 - 0.804793i$ of defining polynomial
Character	$\chi$	$=$	273.142
Dual form			273.2.bj.d.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.35955 + 1.36229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.71165 + 4.69671i) q^{4} +(-1.84188 - 1.06341i) q^{5} +2.72457i q^{6} +(-1.72383 - 2.00709i) q^{7} +9.32701i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(2.35955 + 1.36229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.71165 + 4.69671i) q^{4} +(-1.84188 - 1.06341i) q^{5} +2.72457i q^{6} +(-1.72383 - 2.00709i) q^{7} +9.32701i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.89733 - 5.01833i) q^{10} +(3.75349 - 2.16708i) q^{11} +(-2.71165 + 4.69671i) q^{12} +(-1.28348 - 3.36937i) q^{13} +(-1.33324 - 7.08417i) q^{14} -2.12682i q^{15} +(-7.28277 + 12.6141i) q^{16} +(0.109697 + 0.190001i) q^{17} +(-2.35955 + 1.36229i) q^{18} +(4.42238 + 2.55326i) q^{19} -11.5344i q^{20} +(0.876271 - 2.49643i) q^{21} +11.8087 q^{22} +(-0.0830193 + 0.143794i) q^{23} +(-8.07743 + 4.66351i) q^{24} +(-0.238325 - 0.412791i) q^{25} +(1.56161 - 9.69867i) q^{26} -1.00000 q^{27} +(4.75227 - 13.5389i) q^{28} +1.18984 q^{29} +(2.89733 - 5.01833i) q^{30} +(-5.78315 + 3.33890i) q^{31} +(-18.2132 + 10.5154i) q^{32} +(3.75349 + 2.16708i) q^{33} +0.597755i q^{34} +(1.04074 + 5.52995i) q^{35} -5.42329 q^{36} +(-8.92499 - 5.15285i) q^{37} +(6.95655 + 12.0491i) q^{38} +(2.27622 - 2.79622i) q^{39} +(9.91842 - 17.1792i) q^{40} +1.73537i q^{41} +(5.46845 - 4.69671i) q^{42} -3.96214 q^{43} +(20.3563 + 11.7527i) q^{44} +(1.84188 - 1.06341i) q^{45} +(-0.391776 + 0.226192i) q^{46} +(-2.30677 - 1.33182i) q^{47} -14.5655 q^{48} +(-1.05679 + 6.91977i) q^{49} -1.29867i q^{50} +(-0.109697 + 0.190001i) q^{51} +(12.3446 - 15.1647i) q^{52} +(5.75654 + 9.97062i) q^{53} +(-2.35955 - 1.36229i) q^{54} -9.21796 q^{55} +(18.7201 - 16.0782i) q^{56} +5.10653i q^{57} +(2.80748 + 1.62090i) q^{58} +(1.36077 - 0.785638i) q^{59} +(9.98904 - 5.76718i) q^{60} +(4.23787 - 7.34021i) q^{61} -18.1942 q^{62} +(2.60010 - 0.489341i) q^{63} -28.1689 q^{64} +(-1.21900 + 7.57084i) q^{65} +(5.90436 + 10.2267i) q^{66} +(-5.00979 + 2.89240i) q^{67} +(-0.594920 + 1.03043i) q^{68} -0.166039 q^{69} +(-5.07770 + 14.4660i) q^{70} -1.29867i q^{71} +(-8.07743 - 4.66351i) q^{72} +(-6.44293 + 3.71983i) q^{73} +(-14.0393 - 24.3168i) q^{74} +(0.238325 - 0.412791i) q^{75} +27.6942i q^{76} +(-10.8199 - 3.79790i) q^{77} +(9.18010 - 3.49694i) q^{78} +(8.46774 - 14.6665i) q^{79} +(26.8279 - 15.4891i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.36408 + 4.09470i) q^{82} -9.46848i q^{83} +(14.1011 - 2.65384i) q^{84} -0.466611i q^{85} +(-9.34886 - 5.39757i) q^{86} +(0.594920 + 1.03043i) q^{87} +(20.2124 + 35.0089i) q^{88} +(10.7794 + 6.22347i) q^{89} +5.79467 q^{90} +(-4.55011 + 8.38430i) q^{91} -0.900476 q^{92} +(-5.78315 - 3.33890i) q^{93} +(-3.62863 - 6.28497i) q^{94} +(-5.43032 - 9.40560i) q^{95} +(-18.2132 - 10.5154i) q^{96} -0.414075i q^{97} +(-11.9203 + 14.8879i) q^{98} +4.33416i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.35955	+	1.36229i	1.66845	+	0.963282i	0.968473	+	0.249120i	$0.0801412\pi$
$2$	2.35955	+	1.36229i	1.66845	+	0.963282i	0.699980	+	0.714162i	$0.253192\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.71165	+	4.69671i	1.35582	+	2.34836i
$5$	−1.84188	−	1.06341i	−0.823713	−	0.475571i	0.0279824	−	0.999608i	$-0.491092\pi$
$5$	−1.84188	−	1.06341i	−0.823713	−	0.475571i	−0.851695	+	0.524038i	$0.824425\pi$
$6$			2.72457i			1.11230i
$7$	−1.72383	−	2.00709i	−0.651548	−	0.758607i
$7$	−1.72383	−	2.00709i	−0.651548	−	0.758607i
$8$			9.32701i			3.29760i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.89733	−	5.01833i	−0.916217	−	1.58693i
$11$	3.75349	−	2.16708i	1.13172	−	0.653399i	0.187353	−	0.982293i	$-0.440009\pi$
$11$	3.75349	−	2.16708i	1.13172	−	0.653399i	0.944367	+	0.328894i	$0.106676\pi$
$12$	−2.71165	+	4.69671i	−0.782785	+	1.35582i
$13$	−1.28348	−	3.36937i	−0.355974	−	0.934496i
$13$	−1.28348	−	3.36937i	−0.355974	−	0.934496i
$14$	−1.33324	−	7.08417i	−0.356325	−	1.89333i
$15$		−	2.12682i		−	0.549142i
$16$	−7.28277	+	12.6141i	−1.82069	+	3.15353i
$17$	0.109697	+	0.190001i	0.0266055	+	0.0460820i	0.879022	−	0.476782i	$-0.158197\pi$
$17$	0.109697	+	0.190001i	0.0266055	+	0.0460820i	−0.852416	+	0.522864i	$0.824864\pi$
$18$	−2.35955	+	1.36229i	−0.556151	+	0.321094i
$19$	4.42238	+	2.55326i	1.01456	+	0.585759i	0.912525	−	0.409021i	$-0.134130\pi$
$19$	4.42238	+	2.55326i	1.01456	+	0.585759i	0.102039	+	0.994780i	$0.467463\pi$
$20$		−	11.5344i		−	2.57916i
$21$	0.876271	−	2.49643i	0.191218	−	0.544765i
$22$	11.8087			2.51763
$23$	−0.0830193	+	0.143794i	−0.0173107	+	0.0299831i	−0.874551	−	0.484934i	$-0.838844\pi$
$23$	−0.0830193	+	0.143794i	−0.0173107	+	0.0299831i	0.857240	+	0.514917i	$0.172177\pi$
$24$	−8.07743	+	4.66351i	−1.64880	+	0.951934i
$25$	−0.238325	−	0.412791i	−0.0476650	−	0.0825582i
$26$	1.56161	−	9.69867i	0.306257	−	1.90207i
$27$	−1.00000			−0.192450
$28$	4.75227	−	13.5389i	0.898095	−	2.55860i
$29$	1.18984			0.220948			0.110474	−	0.993879i	$-0.464763\pi$
$29$	1.18984			0.220948			0.110474	+	0.993879i	$0.464763\pi$
$30$	2.89733	−	5.01833i	0.528978	−	0.916217i
$31$	−5.78315	+	3.33890i	−1.03868	+	0.599685i	−0.919460	−	0.393183i	$-0.871374\pi$
$31$	−5.78315	+	3.33890i	−1.03868	+	0.599685i	−0.119224	+	0.992867i	$0.538041\pi$
$32$	−18.2132	+	10.5154i	−3.21967	+	1.85888i
$33$	3.75349	+	2.16708i	0.653399	+	0.377240i
$34$			0.597755i			0.102514i
$35$	1.04074	+	5.52995i	0.175917	+	0.934732i
$36$	−5.42329			−0.903882
$37$	−8.92499	−	5.15285i	−1.46726	−	0.847123i	−0.467931	−	0.883765i	$-0.655001\pi$
$37$	−8.92499	−	5.15285i	−1.46726	−	0.847123i	−0.999328	+	0.0366419i	$0.988334\pi$
$38$	6.95655	+	12.0491i	1.12850	+	1.95462i
$39$	2.27622	−	2.79622i	0.364487	−	0.447753i
$40$	9.91842	−	17.1792i	1.56824	−	2.71627i
$41$			1.73537i			0.271020i	0.990776	+	0.135510i	$0.0432673\pi$
$41$			1.73537i			0.271020i	−0.990776	+	0.135510i	$0.956733\pi$
$42$	5.46845	−	4.69671i	0.843800	−	0.724718i
$43$	−3.96214			−0.604220			−0.302110	−	0.953273i	$-0.597691\pi$
$43$	−3.96214			−0.604220			−0.302110	+	0.953273i	$0.597691\pi$
$44$	20.3563	+	11.7527i	3.06883	+	1.77179i
$45$	1.84188	−	1.06341i	0.274571	−	0.158524i
$46$	−0.391776	+	0.226192i	−0.0577643	+	0.0333502i
$47$	−2.30677	−	1.33182i	−0.336477	−	0.194265i	0.322236	−	0.946659i	$-0.395566\pi$
$47$	−2.30677	−	1.33182i	−0.336477	−	0.194265i	−0.658713	+	0.752394i	$0.728899\pi$
$48$	−14.5655			−2.10235
$49$	−1.05679	+	6.91977i	−0.150970	+	0.988538i
$50$		−	1.29867i		−	0.183659i
$51$	−0.109697	+	0.190001i	−0.0153607	+	0.0266055i
$52$	12.3446	−	15.1647i	1.71189	−	2.10297i
$53$	5.75654	+	9.97062i	0.790721	+	1.36957i	0.925521	+	0.378697i	$0.123628\pi$
$53$	5.75654	+	9.97062i	0.790721	+	1.36957i	−0.134799	+	0.990873i	$0.543039\pi$
$54$	−2.35955	−	1.36229i	−0.321094	−	0.185384i
$55$	−9.21796			−1.24295
$56$	18.7201	−	16.0782i	2.50158	−	2.14854i
$57$			5.10653i			0.676376i
$58$	2.80748	+	1.62090i	0.368641	+	0.212835i
$59$	1.36077	−	0.785638i	0.177157	−	0.102281i	−0.408799	−	0.912624i	$-0.634052\pi$
$59$	1.36077	−	0.785638i	0.177157	−	0.102281i	0.585956	+	0.810343i	$0.300719\pi$
$60$	9.98904	−	5.76718i	1.28958	−	0.744539i
$61$	4.23787	−	7.34021i	0.542604	−	0.939818i	−0.456149	−	0.889903i	$-0.650772\pi$
$61$	4.23787	−	7.34021i	0.542604	−	0.939818i	0.998753	−	0.0499148i	$-0.0158950\pi$
$62$	−18.1942			−2.31066
$63$	2.60010	−	0.489341i	0.327582	−	0.0616512i
$64$	−28.1689			−3.52112
$65$	−1.21900	+	7.57084i	−0.151198	+	0.939047i
$66$	5.90436	+	10.2267i	0.726777	+	1.25881i
$67$	−5.00979	+	2.89240i	−0.612043	+	0.353363i	−0.773765	−	0.633473i	$-0.781629\pi$
$67$	−5.00979	+	2.89240i	−0.612043	+	0.353363i	0.161721	+	0.986836i	$0.448295\pi$
$68$	−0.594920	+	1.03043i	−0.0721446	+	0.124958i
$69$	−0.166039			−0.0199887
$70$	−5.07770	+	14.4660i	−0.606901	+	1.72901i
$71$		−	1.29867i		−	0.154123i	−0.997026	−	0.0770617i	$-0.975446\pi$
$71$		−	1.29867i		−	0.154123i	0.997026	−	0.0770617i	$-0.0245538\pi$
$72$	−8.07743	−	4.66351i	−0.951934	−	0.549599i
$73$	−6.44293	+	3.71983i	−0.754088	+	0.435373i	−0.827169	−	0.561953i	$-0.810050\pi$
$73$	−6.44293	+	3.71983i	−0.754088	+	0.435373i	0.0730810	+	0.997326i	$0.476717\pi$
$74$	−14.0393	−	24.3168i	−1.63204	−	2.82677i
$75$	0.238325	−	0.412791i	0.0275194	−	0.0476650i
$76$			27.6942i			3.17674i
$77$	−10.8199	−	3.79790i	−1.23304	−	0.432810i
$78$	9.18010	−	3.49694i	1.03944	−	0.395951i
$79$	8.46774	−	14.6665i	0.952695	−	1.65012i	0.213137	−	0.977022i	$-0.431632\pi$
$79$	8.46774	−	14.6665i	0.952695	−	1.65012i	0.739558	−	0.673093i	$-0.235035\pi$
$80$	26.8279	−	15.4891i	2.99945	−	1.73174i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.36408	+	4.09470i	−0.261068	+	0.452184i
$83$		−	9.46848i		−	1.03930i	−0.854379	−	0.519650i	$-0.826062\pi$
$83$		−	9.46848i		−	1.03930i	0.854379	−	0.519650i	$-0.173938\pi$
$84$	14.1011	−	2.65384i	1.53856	−	0.289558i
$85$		−	0.466611i		−	0.0506111i
$86$	−9.34886	−	5.39757i	−1.00811	−	0.582035i
$87$	0.594920	+	1.03043i	0.0637821	+	0.110474i
$88$	20.2124	+	35.0089i	2.15465	+	3.73196i
$89$	10.7794	+	6.22347i	1.14261	+	0.659686i	0.947076	−	0.321011i	$-0.104023\pi$
$89$	10.7794	+	6.22347i	1.14261	+	0.659686i	0.195534	+	0.980697i	$0.437356\pi$
$90$	5.79467			0.610811
$91$	−4.55011	+	8.38430i	−0.476981	+	0.878913i
$92$	−0.900476			−0.0938812
$93$	−5.78315	−	3.33890i	−0.599685	−	0.346228i
$94$	−3.62863	−	6.28497i	−0.374264	−	0.648245i
$95$	−5.43032	−	9.40560i	−0.557140	−	0.964994i
$96$	−18.2132	−	10.5154i	−1.85888	−	1.07322i
$97$		−	0.414075i		−	0.0420429i	−0.999779	−	0.0210215i	$-0.993308\pi$
$97$		−	0.414075i		−	0.0420429i	0.999779	−	0.0210215i	$-0.00669184\pi$
$98$	−11.9203	+	14.8879i	−1.20413	+	1.50390i
$99$			4.33416i			0.435599i
$100$	1.29251	−	2.23869i	0.129251	−	0.223869i
$101$	5.72597	+	9.91768i	0.569756	+	0.986846i	0.996590	+	0.0825159i	$0.0262955\pi$
$101$	5.72597	+	9.91768i	0.569756	+	0.986846i	−0.426834	+	0.904330i	$0.640371\pi$
$102$	−0.517671	+	0.298878i	−0.0512571	+	0.0295933i
$103$	−4.66604	+	8.08182i	−0.459758	+	0.796325i	−0.998948	−	0.0458595i	$-0.985397\pi$
$103$	−4.66604	+	8.08182i	−0.459758	+	0.796325i	0.539189	+	0.842185i	$0.318731\pi$
$104$	31.4262	−	11.9711i	3.08159	−	1.17386i
$105$	−4.26871	+	3.66628i	−0.416583	+	0.357792i
$106$			31.3682i			3.04675i
$107$	3.04516	−	5.27437i	0.294387	−	0.509892i	−0.680455	−	0.732789i	$-0.738218\pi$
$107$	3.04516	−	5.27437i	0.294387	−	0.509892i	0.974842	+	0.222897i	$0.0715514\pi$
$108$	−2.71165	−	4.69671i	−0.260928	−	0.451941i
$109$	−8.31799	+	4.80239i	−0.796719	+	0.459986i	−0.842322	−	0.538974i	$-0.818812\pi$
$109$	−8.31799	+	4.80239i	−0.796719	+	0.459986i	0.0456039	+	0.998960i	$0.485479\pi$
$110$	−21.7502	−	12.5575i	−2.07380	−	1.19731i
$111$		−	10.3057i		−	0.978173i
$112$	37.8719	−	7.12751i	3.57856	−	0.673486i
$113$	18.6496			1.75440			0.877202	−	0.480122i	$-0.159408\pi$
$113$	18.6496			1.75440			0.877202	+	0.480122i	$0.159408\pi$
$114$	−6.95655	+	12.0491i	−0.651541	+	1.12850i
$115$	0.305823	−	0.176567i	0.0285181	−	0.0164649i
$116$	3.22642	+	5.58833i	0.299566	+	0.518864i
$117$	3.55970	+	0.573158i	0.329095	+	0.0529884i
$118$	4.28106			0.394103
$119$	0.192249	−	0.547702i	0.0176234	−	0.0502077i
$120$	19.8368			1.81085
$121$	3.89246	−	6.74194i	0.353860	−	0.612904i
$122$	19.9989	−	11.5464i	1.81062	−	1.04536i
$123$	−1.50288	+	0.867687i	−0.135510	+	0.0782367i
$124$	−31.3637	−	18.1078i	−2.81654	−	1.62613i
$125$			11.6478i			1.04181i
$126$	6.80170	+	2.38746i	0.605943	+	0.212692i
$127$	−9.30918			−0.826056			−0.413028	−	0.910718i	$-0.635529\pi$
$127$	−9.30918			−0.826056			−0.413028	+	0.910718i	$0.635529\pi$
$128$	−30.0395	−	17.3433i	−2.65514	−	1.53295i
$129$	−1.98107	−	3.43131i	−0.174423	−	0.302110i
$130$	−13.1899	+	16.2031i	−1.15683	+	1.42111i
$131$	−0.738325	+	1.27882i	−0.0645077	+	0.111731i	−0.896476	−	0.443093i	$-0.853881\pi$
$131$	−0.738325	+	1.27882i	−0.0645077	+	0.111731i	0.831968	+	0.554824i	$0.187214\pi$
$132$			23.5054i			2.04588i
$133$	−2.49883	−	13.2775i	−0.216676	−	1.15131i
$134$	−15.7611			−1.36155
$135$	1.84188	+	1.06341i	0.158524	+	0.0915236i
$136$	−1.77214	+	1.02315i	−0.151960	+	0.0877341i
$137$	−11.6340	+	6.71691i	−0.993963	+	0.573865i	−0.906456	−	0.422299i	$-0.861223\pi$
$137$	−11.6340	+	6.71691i	−0.993963	+	0.573865i	−0.0875062	+	0.996164i	$0.527890\pi$
$138$	−0.391776	−	0.226192i	−0.0333502	−	0.0192548i
$139$	−3.06166			−0.259687			−0.129843	−	0.991535i	$-0.541447\pi$
$139$	−3.06166			−0.259687			−0.129843	+	0.991535i	$0.541447\pi$
$140$	−23.1504	+	19.8833i	−1.95657	+	1.68045i
$141$		−	2.66363i		−	0.224318i
$142$	1.76916	−	3.06427i	0.148464	−	0.257148i
$143$	−12.1192	−	9.86550i	−1.01346	−	0.824995i
$144$	−7.28277	−	12.6141i	−0.606897	−	1.05118i
$145$	−2.19154	−	1.26529i	−0.181997	−	0.105076i
$146$	−20.2699			−1.67755
$147$	−6.52109	+	2.54468i	−0.537851	+	0.209881i
$148$		−	55.8908i		−	4.59420i
$149$	4.61354	+	2.66363i	0.377956	+	0.218213i	0.676929	−	0.736049i	$-0.263311\pi$
$149$	4.61354	+	2.66363i	0.377956	+	0.218213i	−0.298972	+	0.954262i	$0.596644\pi$
$150$	1.12468	−	0.649333i	0.0918296	−	0.0530179i
$151$	2.55180	−	1.47328i	0.207662	−	0.119894i	−0.392562	−	0.919725i	$-0.628411\pi$
$151$	2.55180	−	1.47328i	0.207662	−	0.119894i	0.600225	+	0.799832i	$0.295078\pi$
$152$	−23.8143	+	41.2476i	−1.93160	+	3.34562i
$153$	−0.219394			−0.0177370
$154$	−20.3563	−	23.7011i	−1.64036	−	1.90989i
$155$	14.2025			1.14077
$156$	19.3053	+	3.10840i	1.54566	+	0.248871i
$157$	7.80170	+	13.5129i	0.622643	+	1.07845i	0.988992	+	0.147972i	$0.0472745\pi$
$157$	7.80170	+	13.5129i	0.622643	+	1.07845i	−0.366348	+	0.930478i	$0.619392\pi$
$158$	39.9601	−	23.0710i	3.17905	−	1.83543i
$159$	−5.75654	+	9.97062i	−0.456523	+	0.790721i
$160$	44.7287			3.53611
$161$	0.431718	−	0.0812495i	0.0340241	−	0.00640336i
$162$		−	2.72457i		−	0.214063i
$163$	16.9222	+	9.77003i	1.32545	+	0.765248i	0.984592	−	0.174867i	$-0.0559496\pi$
$163$	16.9222	+	9.77003i	1.32545	+	0.765248i	0.340857	+	0.940115i	$0.389283\pi$
$164$	−8.15055	+	4.70572i	−0.636451	+	0.367455i
$165$	−4.60898	−	7.98299i	−0.358809	−	0.621475i
$166$	12.8988	−	22.3413i	1.00114	−	1.73402i
$167$			11.5623i			0.894721i	0.894354	+	0.447360i	$0.147636\pi$
$167$			11.5623i			0.894721i	−0.894354	+	0.447360i	$0.852364\pi$
$168$	23.2842	+	8.17299i	1.79642	+	0.630560i
$169$	−9.70534	+	8.64906i	−0.746565	+	0.665313i
$170$	0.635658	−	1.10099i	0.0487528	−	0.0844422i
$171$	−4.42238	+	2.55326i	−0.338188	+	0.195253i
$172$	−10.7439	−	18.6090i	−0.819216	−	1.41892i
$173$	2.47377	−	4.28470i	0.188077	−	0.325760i	−0.756532	−	0.653957i	$-0.773108\pi$
$173$	2.47377	−	4.28470i	0.188077	−	0.325760i	0.944609	+	0.328197i	$0.106441\pi$
$174$			3.24180i			0.245760i
$175$	−0.417674	+	1.18992i	−0.0315732	+	0.0899496i
$176$			63.1293i			4.75855i
$177$	1.36077	+	0.785638i	0.102281	+	0.0590522i
$178$	16.9563	+	29.3691i	1.27093	+	2.20131i
$179$	−3.24490	−	5.62034i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$179$	−3.24490	−	5.62034i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$180$	9.98904	+	5.76718i	0.744539	+	0.429860i
$181$	−5.15198			−0.382944			−0.191472	−	0.981498i	$-0.561326\pi$
$181$	−5.15198			−0.382944			−0.191472	+	0.981498i	$0.561326\pi$
$182$	−22.1580	+	13.5846i	−1.64246	+	1.00696i
$183$	8.47575			0.626545
$184$	−1.34117	−	0.774322i	−0.0988720	−	0.0570838i
$185$	10.9592	+	18.9818i	0.805734	+	1.39557i
$186$	−9.09708	−	15.7566i	−0.667030	−	1.15533i
$187$	0.823494	+	0.475445i	0.0602199	+	0.0347680i
$188$		−	14.4457i		−	1.05356i
$189$	1.72383	+	2.00709i	0.125390	+	0.145994i
$190$		−	29.5906i		−	2.14673i
$191$	2.59780	−	4.49952i	0.187970	−	0.325574i	−0.756603	−	0.653874i	$-0.773143\pi$
$191$	2.59780	−	4.49952i	0.187970	−	0.325574i	0.944573	+	0.328301i	$0.106476\pi$
$192$	−14.0845	−	24.3950i	−1.01646	−	1.76056i
$193$	7.77946	−	4.49147i	0.559978	−	0.323303i	−0.193159	−	0.981167i	$-0.561873\pi$
$193$	7.77946	−	4.49147i	0.559978	−	0.323303i	0.753137	+	0.657864i	$0.228540\pi$
$194$	0.564089	−	0.977030i	0.0404992	−	0.0701467i
$195$	−7.16604	+	2.72973i	−0.513171	+	0.195480i
$196$	−35.3658	+	13.8005i	−2.52613	+	0.985752i
$197$			3.36454i			0.239714i	0.992791	+	0.119857i	$0.0382436\pi$
$197$			3.36454i			0.239714i	−0.992791	+	0.119857i	$0.961756\pi$
$198$	−5.90436	+	10.2267i	−0.419605	+	0.726777i
$199$	2.30657	+	3.99509i	0.163508	+	0.283204i	0.936125	−	0.351669i	$-0.114386\pi$
$199$	2.30657	+	3.99509i	0.163508	+	0.283204i	−0.772616	+	0.634873i	$0.781052\pi$
$200$	3.85011	−	2.22286i	0.272244	−	0.157180i
$201$	−5.00979	−	2.89240i	−0.353363	−	0.204014i
$202$			31.2017i			2.19534i
$203$	−2.05109	−	2.38811i	−0.143958	−	0.167612i
$204$	−1.18984			−0.0833054
$205$	1.84541	−	3.19635i	0.128889	−	0.223242i
$206$	−22.0195	+	12.7130i	−1.53417	+	0.885754i
$207$	−0.0830193	−	0.143794i	−0.00577024	−	0.00999435i
$208$	51.8490	+	8.34834i	3.59508	+	0.578854i
$209$	22.1325			1.53094
$210$	−15.0667	+	2.83557i	−1.03970	+	0.195673i
$211$	−7.38453			−0.508372			−0.254186	−	0.967155i	$-0.581808\pi$
$211$	−7.38453			−0.508372			−0.254186	+	0.967155i	$0.581808\pi$
$212$	−31.2194	+	54.0736i	−2.14416	+	3.71379i
$213$	1.12468	−	0.649333i	0.0770617	−	0.0444916i
$214$	14.3704	−	8.29675i	0.982340	−	0.567154i
$215$	7.29777	+	4.21337i	0.497704	+	0.287350i
$216$		−	9.32701i		−	0.634623i
$217$	16.6707	+	5.85156i	1.13168	+	0.397230i
$218$	−26.1689			−1.77238
$219$	−6.44293	−	3.71983i	−0.435373	−	0.251363i
$220$	−24.9959	−	43.2941i	−1.68522	−	2.91889i
$221$	0.499390	−	0.613473i	0.0335926	−	0.0412667i
$222$	14.0393	−	24.3168i	0.942256	−	1.63204i
$223$		−	24.8041i		−	1.66100i	−0.557016	−	0.830502i	$-0.688054\pi$
$223$		−	24.8041i		−	1.66100i	0.557016	−	0.830502i	$-0.311946\pi$
$224$	52.5019	+	18.4287i	3.50793	+	1.23132i
$225$	0.476650			0.0317767
$226$	44.0046	+	25.4060i	2.92714	+	1.68998i
$227$	−12.7072	+	7.33650i	−0.843406	+	0.486941i	−0.858421	−	0.512947i	$-0.828554\pi$
$227$	−12.7072	+	7.33650i	−0.843406	+	0.486941i	0.0150146	+	0.999887i	$0.495221\pi$
$228$	−23.9839	+	13.8471i	−1.58837	+	0.917047i
$229$	8.39036	+	4.84418i	0.554451	+	0.320112i	0.750915	−	0.660399i	$-0.229613\pi$
$229$	8.39036	+	4.84418i	0.554451	+	0.320112i	−0.196464	+	0.980511i	$0.562946\pi$
$230$	0.962139			0.0634415
$231$	−2.12088	−	11.2693i	−0.139544	−	0.741463i
$232$			11.0976i			0.728596i
$233$	6.84270	−	11.8519i	0.448280	−	0.776444i	−0.549994	−	0.835169i	$-0.685370\pi$
$233$	6.84270	−	11.8519i	0.448280	−	0.776444i	0.998274	+	0.0587244i	$0.0187033\pi$
$234$	7.61849	+	6.20173i	0.498036	+	0.405420i
$235$	2.83253	+	4.90608i	0.184774	+	0.320038i
$236$	7.37983	+	4.26075i	0.480386	+	0.277351i
$237$	16.9355			1.10008
$238$	1.19975	−	1.03043i	0.0777680	−	0.0667929i
$239$		−	17.4015i		−	1.12561i	−0.826590	−	0.562804i	$-0.809723\pi$
$239$		−	17.4015i		−	1.12561i	0.826590	−	0.562804i	$-0.190277\pi$
$240$	26.8279	+	15.4891i	1.73174	+	0.999818i
$241$	10.0818	−	5.82071i	0.649423	−	0.374945i	−0.138812	−	0.990319i	$-0.544328\pi$
$241$	10.0818	−	5.82071i	0.649423	−	0.374945i	0.788235	+	0.615374i	$0.210995\pi$
$242$	18.3689	−	10.6053i	1.18080	−	0.681734i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	45.9665			2.94270
$245$	9.30502	−	11.6216i	0.594476	−	0.742474i
$246$	−4.72815			−0.301456
$247$	2.92684	−	18.1777i	0.186231	−	1.15662i
$248$	−31.1420	−	53.9395i	−1.97752	−	3.42516i
$249$	8.19994	−	4.73424i	0.519650	−	0.300020i
$250$	−15.8677	+	27.4836i	−1.00356	+	1.73822i
$251$	−19.2684			−1.21621			−0.608107	−	0.793855i	$-0.708071\pi$
$251$	−19.2684			−1.21621			−0.608107	+	0.793855i	$0.708071\pi$
$252$	9.34886	+	10.8850i	0.588923	+	0.685692i
$253$			0.719638i			0.0452432i
$254$	−21.9655	−	12.6818i	−1.37824	−	0.795725i
$255$	0.404097	−	0.233306i	0.0253056	−	0.0146102i
$256$	−19.0842	−	33.0548i	−1.19276	−	2.06592i
$257$	5.38229	−	9.32240i	0.335738	−	0.581515i	−0.647888	−	0.761735i	$-0.724348\pi$
$257$	5.38229	−	9.32240i	0.335738	−	0.581515i	0.983626	+	0.180220i	$0.0576810\pi$
$258$		−	10.7951i		−	0.672076i
$259$	5.04300	+	26.7959i	0.313357	+	1.66502i
$260$	−38.8635	+	14.8041i	−2.41021	+	0.918114i
$261$	−0.594920	+	1.03043i	−0.0368246	+	0.0637821i
$262$	−3.48423	+	2.01162i	−0.215256	+	0.124278i
$263$	−8.41887	−	14.5819i	−0.519130	−	0.899160i	−0.999753	−	0.0222322i	$-0.992923\pi$
$263$	−8.41887	−	14.5819i	−0.519130	−	0.899160i	0.480623	−	0.876927i	$-0.340411\pi$
$264$	−20.2124	+	35.0089i	−1.24399	+	2.15465i
$265$		−	24.4862i		−	1.50418i
$266$	12.1916	−	34.7331i	0.747518	−	2.12962i
$267$			12.4469i			0.761740i
$268$	−27.1696	−	15.6864i	−1.65965	−	0.958197i
$269$	9.27158	+	16.0589i	0.565298	+	0.979125i	0.997022	+	0.0771195i	$0.0245723\pi$
$269$	9.27158	+	16.0589i	0.565298	+	0.979125i	−0.431723	+	0.902006i	$0.642094\pi$
$270$	2.89733	+	5.01833i	0.176326	+	0.305406i
$271$	−10.2706	−	5.92975i	−0.623896	−	0.360207i	0.154488	−	0.987995i	$-0.450627\pi$
$271$	−10.2706	−	5.92975i	−0.623896	−	0.360207i	−0.778384	+	0.627788i	$0.783960\pi$
$272$	−3.19559			−0.193761
$273$	−9.53607	+	0.251639i	−0.577149	+	0.0152299i
$274$	−36.6014			−2.21117
$275$	−1.78910	−	1.03294i	−0.107887	−	0.0622885i
$276$	−0.450238	−	0.779835i	−0.0271012	−	0.0469406i
$277$	−4.39030	−	7.60423i	−0.263788	−	0.456894i	0.703458	−	0.710737i	$-0.251639\pi$
$277$	−4.39030	−	7.60423i	−0.263788	−	0.456894i	−0.967245	+	0.253843i	$0.918305\pi$
$278$	−7.22414	−	4.17086i	−0.433275	−	0.250152i
$279$		−	6.67780i		−	0.399790i
$280$	−51.5779	+	9.70698i	−3.08237	+	0.580103i
$281$			7.07210i			0.421886i	0.977498	+	0.210943i	$0.0676535\pi$
$281$			7.07210i			0.421886i	−0.977498	+	0.210943i	$0.932347\pi$
$282$	3.62863	−	6.28497i	0.216082	−	0.374264i
$283$	−0.541005	−	0.937048i	−0.0321594	−	0.0557017i	0.849498	−	0.527592i	$-0.176905\pi$
$283$	−0.541005	−	0.937048i	−0.0321594	−	0.0557017i	−0.881657	+	0.471891i	$0.843572\pi$
$284$	6.09946	−	3.52153i	0.361937	−	0.208964i
$285$	5.43032	−	9.40560i	0.321665	−	0.557140i
$286$	−15.1563	−	39.7880i	−0.896211	−	2.35271i
$287$	3.48305	−	2.99150i	0.205598	−	0.176582i
$288$		−	21.0308i		−	1.23925i
$289$	8.47593	−	14.6807i	0.498584	−	0.863573i
$290$	−3.44736	−	5.97100i	−0.202436	−	0.350629i
$291$	0.358599	−	0.207037i	0.0210215	−	0.0121368i
$292$	−34.9419	−	20.1737i	−2.04482	−	1.18058i
$293$		−	19.3446i		−	1.13012i	−0.825048	−	0.565062i	$-0.808852\pi$
$293$		−	19.3446i		−	1.13012i	0.825048	−	0.565062i	$-0.191148\pi$
$294$	−18.8534	−	2.87931i	−1.09955	−	0.167925i
$295$	−3.34182			−0.194568
$296$	48.0607	−	83.2435i	2.79347	−	4.83843i
$297$	−3.75349	+	2.16708i	−0.217800	+	0.125747i
$298$	7.25726	+	12.5699i	0.420402	+	0.728157i
$299$	0.591048	+	0.0951663i	0.0341812	+	0.00550361i
$300$	2.58501			0.149246
$301$	6.83007	+	7.95235i	0.393679	+	0.458366i
$302$	8.02812			0.461966
$303$	−5.72597	+	9.91768i	−0.328949	+	0.569756i
$304$	−64.4144	+	37.1896i	−3.69442	+	2.13297i
$305$	−15.6113	+	9.01318i	−0.893900	+	0.516093i
$306$	−0.517671	−	0.298878i	−0.0295933	−	0.0170857i
$307$		−	13.2794i		−	0.757895i	−0.925418	−	0.378947i	$-0.876286\pi$
$307$		−	13.2794i		−	0.757895i	0.925418	−	0.378947i	$-0.123714\pi$
$308$	−11.5022	−	61.1165i	−0.655396	−	3.48244i
$309$	−9.33208			−0.530883
$310$	33.5114	+	19.3478i	1.90332	+	1.09888i
$311$	1.32063	+	2.28739i	0.0748859	+	0.129706i	0.901037	−	0.433743i	$-0.142807\pi$
$311$	1.32063	+	2.28739i	0.0748859	+	0.129706i	−0.826151	+	0.563449i	$0.809474\pi$
$312$	26.0803	+	21.2303i	1.47651	+	1.20193i
$313$	3.46603	−	6.00333i	0.195911	−	0.339328i	−0.751288	−	0.659975i	$-0.770567\pi$
$313$	3.46603	−	6.00333i	0.195911	−	0.339328i	0.947199	+	0.320647i	$0.103900\pi$
$314$			42.5126i			2.39912i
$315$	−5.30944	−	1.86367i	−0.299153	−	0.105006i
$316$	91.8460			5.16674
$317$	−10.0418	−	5.79765i	−0.564005	−	0.325628i	0.190747	−	0.981639i	$-0.438909\pi$
$317$	−10.0418	−	5.79765i	−0.564005	−	0.325628i	−0.754751	+	0.656011i	$0.772242\pi$
$318$	−27.1657	+	15.6841i	−1.52338	+	0.879521i
$319$	4.46605	−	2.57848i	0.250051	−	0.144367i
$320$	51.8837	+	29.9551i	2.90039	+	1.67454i
$321$	6.09032			0.339928
$322$	1.12934	+	0.396411i	0.0629359	+	0.0220911i
$323$			1.12034i			0.0623375i
$324$	2.71165	−	4.69671i	0.150647	−	0.260928i
$325$	−1.08496	+	1.33282i	−0.0601828	+	0.0739313i
$326$	26.6192	+	46.1057i	1.47430	+	2.55356i
$327$	−8.31799	−	4.80239i	−0.459986	−	0.265573i
$328$	−16.1859			−0.893714
$329$	1.30342	+	6.92572i	0.0718601	+	0.381827i
$330$		−	25.1150i		−	1.38254i
$331$	7.00736	+	4.04570i	0.385159	+	0.222372i	0.680061	−	0.733156i	$-0.261953\pi$
$331$	7.00736	+	4.04570i	0.385159	+	0.222372i	−0.294901	+	0.955528i	$0.595287\pi$
$332$	44.4707	−	25.6752i	2.44065	−	1.40911i
$333$	8.92499	−	5.15285i	0.489087	−	0.282374i
$334$	−15.7512	+	27.2819i	−0.861868	+	1.49280i
$335$	12.3032			0.672197
$336$	25.1086	+	29.2343i	1.36978	+	1.59486i
$337$	31.7121			1.72747			0.863734	−	0.503948i	$-0.168120\pi$
$337$	31.7121			1.72747			0.863734	+	0.503948i	$0.168120\pi$
$338$	−34.6827	+	7.18643i	−1.88649	+	0.390890i
$339$	9.32478	+	16.1510i	0.506453	+	0.877202i
$340$	2.19154	−	1.26529i	0.118853	−	0.0686197i
$341$	−14.4713	+	25.0651i	−0.783666	+	1.35735i
$342$	−13.9131			−0.752334
$343$	15.7103	−	9.80746i	0.848277	−	0.529553i
$344$		−	36.9549i		−	1.99248i
$345$	0.305823	+	0.176567i	0.0164649	+	0.00950604i
$346$	11.6740	−	6.73997i	0.627597	−	0.362343i
$347$	−6.49928	−	11.2571i	−0.348900	−	0.604312i	0.637154	−	0.770736i	$-0.280111\pi$
$347$	−6.49928	−	11.2571i	−0.348900	−	0.604312i	−0.986054	+	0.166424i	$0.946778\pi$
$348$	−3.22642	+	5.58833i	−0.172955	+	0.299566i
$349$			15.0051i			0.803205i	0.915814	+	0.401602i	$0.131547\pi$
$349$			15.0051i			0.803205i	−0.915814	+	0.401602i	$0.868453\pi$
$350$	−2.60654	+	2.23869i	−0.139325	+	0.119663i
$351$	1.28348	+	3.36937i	0.0685072	+	0.179844i
$352$	−45.5754	+	78.9390i	−2.42918	+	4.20746i
$353$	4.22441	−	2.43896i	0.224843	−	0.129813i	−0.383348	−	0.923604i	$-0.625229\pi$
$353$	4.22441	−	2.43896i	0.224843	−	0.129813i	0.608191	+	0.793791i	$0.291896\pi$
$354$	2.14053	+	3.70750i	0.113768	+	0.197052i
$355$	−1.38101	+	2.39199i	−0.0732966	+	0.126953i
$356$			67.5034i			3.57767i
$357$	0.570448	−	0.107359i	0.0301913	−	0.00568202i
$358$		−	17.6820i		−	0.934520i
$359$	16.7449	+	9.66768i	0.883762	+	0.510240i	0.871897	−	0.489689i	$-0.162890\pi$
$359$	16.7449	+	9.66768i	0.883762	+	0.510240i	0.0118653	+	0.999930i	$0.496223\pi$
$360$	9.91842	+	17.1792i	0.522747	+	0.905424i
$361$	3.53831	+	6.12854i	0.186227	+	0.322555i
$362$	−12.1563	−	7.01847i	−0.638923	−	0.368883i
$363$	7.78493			0.408603
$364$	−51.7169	+	1.36471i	−2.71070	+	0.0715303i
$365$	15.8228			0.828203
$366$	19.9989	+	11.5464i	1.04536	+	0.603540i
$367$	−17.4987	−	30.3087i	−0.913426	−	1.58210i	−0.809189	−	0.587549i	$-0.800093\pi$
$367$	−17.4987	−	30.3087i	−0.913426	−	1.58210i	−0.104238	−	0.994552i	$-0.533240\pi$
$368$	−1.20922	−	2.09443i	−0.0630350	−	0.109180i
$369$	−1.50288	−	0.867687i	−0.0782367	−	0.0451700i
$370$			59.7181i			3.10459i
$371$	10.0886	−	28.7416i	0.523773	−	1.49219i
$372$		−	36.2157i		−	1.87770i
$373$	−1.00876	+	1.74722i	−0.0522315	+	0.0904676i	−0.890959	−	0.454084i	$-0.849967\pi$
$373$	−1.00876	+	1.74722i	−0.0522315	+	0.0904676i	0.838728	+	0.544551i	$0.183300\pi$
$374$	1.29538	+	2.24367i	0.0669827	+	0.116017i
$375$	−10.0873	+	5.82392i	−0.520907	+	0.300746i
$376$	12.4219	−	21.5153i	0.640609	−	1.10957i
$377$	−1.52714	−	4.00901i	−0.0786516	−	0.206475i
$378$	1.33324	+	7.08417i	0.0685747	+	0.364371i
$379$		−	4.29320i		−	0.220527i	−0.993902	−	0.110263i	$-0.964831\pi$
$379$		−	4.29320i		−	0.220527i	0.993902	−	0.110263i	$-0.0351694\pi$
$380$	29.4502	−	51.0093i	1.51077	−	2.61672i
$381$	−4.65459	−	8.06198i	−0.238462	−	0.413028i
$382$	12.2593	−	7.07789i	0.627238	−	0.362136i
$383$	27.7251	+	16.0071i	1.41668	+	0.817923i	0.996006	−	0.0892871i	$-0.0284589\pi$
$383$	27.7251	+	16.0071i	1.41668	+	0.817923i	0.420678	+	0.907210i	$0.361792\pi$
$384$		−	34.6866i		−	1.77009i
$385$	15.8902	+	18.5012i	0.809841	+	0.942911i
$386$	24.4747			1.24573
$387$	1.98107	−	3.43131i	0.100703	−	0.174423i
$388$	1.94479	−	1.12283i	0.0987318	−	0.0570028i
$389$	−4.44050	−	7.69117i	−0.225142	−	0.389958i	0.731220	−	0.682142i	$-0.238951\pi$
$389$	−4.44050	−	7.69117i	−0.225142	−	0.389958i	−0.956362	+	0.292184i	$0.905618\pi$
$390$	−20.6273	−	3.32126i	−1.04450	−	0.168178i
$391$	−0.0364279			−0.00184224
$392$	−64.5408	−	9.85671i	−3.25980	−	0.497839i
$393$	−1.47665			−0.0744871
$394$	−4.58347	+	7.93880i	−0.230912	+	0.399951i
$395$	−31.1931	+	18.0093i	−1.56949	+	0.906147i
$396$	−20.3563	+	11.7527i	−1.02294	+	0.590596i
$397$	17.8008	+	10.2773i	0.893395	+	0.515802i	0.875051	−	0.484030i	$-0.160827\pi$
$397$	17.8008	+	10.2773i	0.893395	+	0.515802i	0.0183433	+	0.999832i	$0.494161\pi$
$398$			12.5688i			0.630018i
$399$	10.2492	−	8.80281i	0.513104	−	0.440692i
$400$	6.94266			0.347133
$401$	−29.1190	−	16.8119i	−1.45413	−	0.839544i	−0.455421	−	0.890276i	$-0.650511\pi$
$401$	−29.1190	−	16.8119i	−1.45413	−	0.839544i	−0.998712	+	0.0507321i	$0.983845\pi$
$402$	−7.88056	−	13.6495i	−0.393047	−	0.680777i
$403$	18.6726	+	15.2002i	0.930147	+	0.757174i
$404$	−31.0536	+	53.7865i	−1.54498	+	2.67598i
$405$			2.12682i			0.105682i
$406$	−1.58635	−	8.42903i	−0.0787291	−	0.418326i
$407$	−44.6665			−2.21404
$408$	−1.77214	−	1.02315i	−0.0877341	−	0.0506533i
$409$	27.4075	−	15.8237i	1.35521	−	0.782432i	0.366239	−	0.930521i	$-0.380645\pi$
$409$	27.4075	−	15.8237i	1.35521	−	0.782432i	0.988974	+	0.148089i	$0.0473121\pi$
$410$	8.70868	−	5.02796i	0.430091	−	0.248313i
$411$	−11.6340	−	6.71691i	−0.573865	−	0.331321i
$412$	−50.6106			−2.49341
$413$	−3.92258	−	1.37686i	−0.193017	−	0.0677510i
$414$		−	0.452384i		−	0.0222335i
$415$	−10.0689	+	17.4398i	−0.494261	+	0.856085i
$416$	58.8067	+	47.8708i	2.88324	+	2.34706i
$417$	−1.53083	−	2.65148i	−0.0749651	−	0.129843i
$418$	52.2227	+	30.1508i	2.55430	+	1.47472i
$419$	−5.65930			−0.276475			−0.138237	−	0.990399i	$-0.544144\pi$
$419$	−5.65930			−0.276475			−0.138237	+	0.990399i	$0.544144\pi$
$420$	−28.7947	−	10.1072i	−1.40504	−	0.493182i
$421$			29.5137i			1.43841i	0.694799	+	0.719204i	$0.255493\pi$
$421$			29.5137i			1.43841i	−0.694799	+	0.719204i	$0.744507\pi$
$422$	−17.4242	−	10.0598i	−0.848195	−	0.489706i
$423$	2.30677	−	1.33182i	0.112159	−	0.0647551i
$424$	−92.9961	+	53.6913i	−4.51629	+	2.60748i
$425$	0.0522871	−	0.0905639i	0.00253630	−	0.00439300i
$426$	3.53831			0.171432
$427$	−22.0378	+	4.14753i	−1.06649	+	0.200713i
$428$	33.0296			1.59654
$429$	2.48416	−	15.4283i	0.119936	−	0.744886i
$430$	11.4796	+	19.8833i	0.553597	+	0.958858i
$431$	−13.1198	+	7.57473i	−0.631960	+	0.364862i	−0.781511	−	0.623892i	$-0.785551\pi$
$431$	−13.1198	+	7.57473i	−0.631960	+	0.364862i	0.149551	+	0.988754i	$0.452217\pi$
$432$	7.28277	−	12.6141i	0.350392	−	0.606897i
$433$	−38.0602			−1.82906			−0.914529	−	0.404519i	$-0.867439\pi$
$433$	−38.0602			−1.82906			−0.914529	+	0.404519i	$0.867439\pi$
$434$	31.3637	+	36.5173i	1.50551	+	1.75288i
$435$		−	2.53057i		−	0.121332i
$436$	−45.1109	−	26.0448i	−2.16042	−	1.24732i
$437$	−0.734286	+	0.423940i	−0.0351257	+	0.0202798i
$438$	−10.1349	−	17.5542i	−0.484266	−	0.838774i
$439$	7.90996	−	13.7005i	0.377522	−	0.653887i	−0.613179	−	0.789944i	$-0.710110\pi$
$439$	7.90996	−	13.7005i	0.377522	−	0.653887i	0.990701	+	0.136057i	$0.0434430\pi$
$440$		−	85.9760i		−	4.09875i
$441$	−5.46430	−	4.37509i	−0.260205	−	0.208338i
$442$	2.01406	−	0.767209i	0.0957991	−	0.0364924i
$443$	−4.64151	+	8.03933i	−0.220525	+	0.381960i	−0.954967	−	0.296711i	$-0.904110\pi$
$443$	−4.64151	+	8.03933i	−0.220525	+	0.381960i	0.734443	+	0.678671i	$0.237444\pi$
$444$	48.4029	−	27.9454i	2.29710	−	1.32623i
$445$	−13.2362	−	22.9257i	−0.627455	−	1.08678i
$446$	33.7903	−	58.5264i	1.60002	−	2.77131i
$447$			5.32726i			0.251971i
$448$	48.5586	+	56.5375i	2.29418	+	2.67114i
$449$			10.9156i			0.515137i	0.966260	+	0.257569i	$0.0829214\pi$
$449$			10.9156i			0.515137i	−0.966260	+	0.257569i	$0.917079\pi$
$450$	1.12468	+	0.649333i	0.0530179	+	0.0306099i
$451$	3.76069	+	6.51371i	0.177084	+	0.306719i
$452$	50.5710	+	87.5916i	2.37866	+	4.11996i
$453$	2.55180	+	1.47328i	0.119894	+	0.0692208i
$454$	−39.9777			−1.87624
$455$	17.2967	−	10.6042i	0.810881	−	0.497134i
$456$	−47.6286			−2.23042
$457$	−11.0613	−	6.38624i	−0.517425	−	0.298736i	0.218455	−	0.975847i	$-0.429898\pi$
$457$	−11.0613	−	6.38624i	−0.517425	−	0.298736i	−0.735881	+	0.677111i	$0.763232\pi$
$458$	13.1983	+	22.8601i	0.616717	+	1.06818i
$459$	−0.109697	−	0.190001i	−0.00512022	−	0.00886849i
$460$	1.65857	+	0.957574i	0.0773311	+	0.0446471i
$461$			17.8435i			0.831057i	0.909580	+	0.415528i	$0.136403\pi$
$461$			17.8435i			0.831057i	−0.909580	+	0.415528i	$0.863597\pi$
$462$	10.3476	−	29.4796i	0.481416	−	1.37152i
$463$			8.42495i			0.391541i	0.980650	+	0.195770i	$0.0627207\pi$
$463$			8.42495i			0.391541i	−0.980650	+	0.195770i	$0.937279\pi$
$464$	−8.66532	+	15.0088i	−0.402277	+	0.696765i
$465$	7.10123	+	12.2997i	0.329312	+	0.570385i
$466$	32.2914	−	18.6434i	1.49587	−	0.863640i
$467$	5.15757	−	8.93318i	0.238664	−	0.413378i	−0.721667	−	0.692240i	$-0.756624\pi$
$467$	5.15757	−	8.93318i	0.238664	−	0.413378i	0.960331	+	0.278862i	$0.0899572\pi$
$468$	6.96071	+	18.2731i	0.321759	+	0.844674i
$469$	14.4414	+	5.06906i	0.666840	+	0.234067i
$470$			15.4349i			0.711957i
$471$	−7.80170	+	13.5129i	−0.359483	+	0.622643i
$472$	7.32766	+	12.6919i	0.337283	+	0.584191i
$473$	−14.8719	+	8.58627i	−0.683808	+	0.394797i
$474$	39.9601	+	23.0710i	1.83543	+	1.05968i
$475$		−	2.43403i		−	0.111681i
$476$	3.09371	−	0.582237i	0.141800	−	0.0266868i
$477$	−11.5131			−0.527148
$478$	23.7058	−	41.0596i	1.08428	−	1.87802i
$479$	23.3424	−	13.4768i	1.06654	−	0.615769i	0.139308	−	0.990249i	$-0.455512\pi$
$479$	23.3424	−	13.4768i	1.06654	−	0.615769i	0.927235	+	0.374480i	$0.122179\pi$
$480$	22.3644	+	38.7362i	1.02079	+	1.76806i
$481$	−5.90679	+	36.6852i	−0.269326	+	1.67270i
$482$	31.7179			1.44471
$483$	0.286223	+	0.333254i	0.0130236	+	0.0151636i
$484$	42.2199			1.91909
$485$	−0.440331	+	0.762675i	−0.0199944	+	0.0346313i
$486$	2.35955	−	1.36229i	0.107031	−	0.0617946i
$487$	−24.6131	+	14.2104i	−1.11532	+	0.643933i	−0.940203	−	0.340614i	$-0.889365\pi$
$487$	−24.6131	+	14.2104i	−1.11532	+	0.643933i	−0.175121	+	0.984547i	$0.556032\pi$
$488$	68.4623	+	39.5267i	3.09914	+	1.78929i
$489$			19.5401i			0.883632i
$490$	37.7875	−	14.7455i	1.70707	−	0.666136i
$491$	−11.5946			−0.523255			−0.261627	−	0.965169i	$-0.584259\pi$
$491$	−11.5946			−0.523255			−0.261627	+	0.965169i	$0.584259\pi$
$492$	−8.15055	−	4.70572i	−0.367455	−	0.212150i
$493$	0.130522	+	0.226071i	0.00587841	+	0.0101817i
$494$	31.6693	−	38.9040i	1.42487	−	1.75038i
$495$	4.60898	−	7.98299i	0.207158	−	0.358809i
$496$		−	97.2658i		−	4.36736i
$497$	−2.60654	+	2.23869i	−0.116919	+	0.100419i
$498$	25.7976			1.15602
$499$	−13.7598	−	7.94425i	−0.615975	−	0.355633i	0.159325	−	0.987226i	$-0.449068\pi$
$499$	−13.7598	−	7.94425i	−0.615975	−	0.355633i	−0.775300	+	0.631593i	$0.782401\pi$
$500$	−54.7065	+	31.5848i	−2.44655	+	1.41252i
$501$	−10.0133	+	5.78117i	−0.447360	+	0.258284i
$502$	−45.4648	−	26.2491i	−2.02920	−	1.17156i
$503$	−1.11645			−0.0497801			−0.0248900	−	0.999690i	$-0.507924\pi$
$503$	−1.11645			−0.0497801			−0.0248900	+	0.999690i	$0.507924\pi$
$504$	4.56409	+	24.2512i	0.203301	+	1.08023i
$505$		−	24.3562i		−	1.08384i
$506$	−0.980353	+	1.69802i	−0.0435820	+	0.0754862i
$507$	−12.3430	−	4.08054i	−0.548171	−	0.181223i
$508$	−25.2432	−	43.7225i	−1.11999	−	1.93987i
$509$	−34.7012	−	20.0347i	−1.53810	−	0.888024i	−0.998950	−	0.0458167i	$-0.985411\pi$
$509$	−34.7012	−	20.0347i	−1.53810	−	0.888024i	−0.539153	−	0.842208i	$-0.681256\pi$
$510$	1.27132			0.0562948
$511$	18.5726	+	6.51915i	0.821602	+	0.288390i
$512$		−	34.6193i		−	1.52997i
$513$	−4.42238	−	2.55326i	−0.195253	−	0.112729i
$514$	25.3996	−	14.6644i	1.12033	−	0.646821i
$515$	17.1885	−	9.92381i	0.757418	−	0.437295i
$516$	10.7439	−	18.6090i	0.472975	−	0.819216i
$517$	−11.5446			−0.507731
$518$	−24.6045	+	70.0962i	−1.08106	+	3.07985i
$519$	4.94755			0.217173
$520$	−70.6133	−	11.3696i	−3.09660	−	0.498592i
$521$	−14.6466	−	25.3686i	−0.641678	−	1.11142i	−0.985058	−	0.172223i	$-0.944905\pi$
$521$	−14.6466	−	25.3686i	−0.641678	−	1.11142i	0.343380	−	0.939197i	$-0.388428\pi$
$522$	−2.80748	+	1.62090i	−0.122880	+	0.0709449i
$523$	−5.41997	+	9.38766i	−0.236999	+	0.410494i	−0.959852	−	0.280508i	$-0.909497\pi$
$523$	−5.41997	+	9.38766i	−0.236999	+	0.410494i	0.722853	+	0.691002i	$0.242830\pi$
$524$	−8.00831			−0.349844
$525$	−1.23934	+	0.233244i	−0.0540892	+	0.0101796i
$526$		−	45.8757i		−	2.00027i
$527$	−1.26879	−	0.732536i	−0.0552693	−	0.0319098i
$528$	−54.6716	+	31.5647i	−2.37928	+	1.37368i
$529$	11.4862	+	19.8947i	0.499401	+	0.864987i
$530$	33.3572	−	57.7764i	1.44895	−	2.50965i
$531$			1.57128i			0.0681876i
$532$	55.5847	−	47.7402i	2.40990	−	2.06980i
$533$	5.84712	−	2.22732i	0.253267	−	0.0964760i
$534$	−16.9563	+	29.3691i	−0.733770	+	1.27093i
$535$	−11.2176	+	6.47649i	−0.484980	+	0.280003i
$536$	−26.9775	−	46.7264i	−1.16525	−	2.01827i
$537$	3.24490	−	5.62034i	0.140028	−	0.242536i
$538$			50.5222i			2.17817i
$539$	11.0290	+	28.2634i	0.475054	+	1.21739i
$540$			11.5344i			0.496360i
$541$	18.1884	+	10.5011i	0.781981	+	0.451477i	0.837132	−	0.547001i	$-0.184231\pi$
$541$	18.1884	+	10.5011i	0.781981	+	0.451477i	−0.0551509	+	0.998478i	$0.517564\pi$
$542$	−16.1560	−	27.9831i	−0.693961	−	1.20198i
$543$	−2.57599	−	4.46174i	−0.110546	−	0.191472i
$544$	−3.99588	−	2.30702i	−0.171322	−	0.0989127i
$545$	20.4276			0.875023
$546$	−22.8436	−	12.3971i	−0.977617	−	0.530547i
$547$	0.897589			0.0383781			0.0191891	−	0.999816i	$-0.493892\pi$
$547$	0.897589			0.0383781			0.0191891	+	0.999816i	$0.493892\pi$
$548$	−63.0948	−	36.4278i	−2.69528	−	1.55612i
$549$	4.23787	+	7.34021i	0.180868	+	0.313273i
$550$	−2.81431	−	4.87453i	−0.120003	−	0.207851i
$551$	5.26192	+	3.03797i	0.224166	+	0.129422i
$552$		−	1.54864i		−	0.0659147i
$553$	−44.0340	+	8.28722i	−1.87252	+	0.352408i
$554$		−	23.9234i		−	1.01641i
$555$	−10.9592	+	18.9818i	−0.465191	+	0.805734i
$556$	−8.30215	−	14.3797i	−0.352089	−	0.609837i
$557$	−27.2035	+	15.7059i	−1.15265	+	0.665482i	−0.949531	−	0.313672i	$-0.898441\pi$
$557$	−27.2035	+	15.7059i	−1.15265	+	0.665482i	−0.203117	+	0.979154i	$0.565107\pi$
$558$	9.09708	−	15.7566i	0.385110	−	0.667030i
$559$	5.08534	+	13.3499i	0.215087	+	0.564642i
$560$	−77.3349	−	27.1453i	−3.26799	−	1.14710i
$561$			0.950889i			0.0401466i
$562$	−9.63422	+	16.6870i	−0.406395	+	0.703897i
$563$	18.2911	+	31.6811i	0.770877	+	1.33520i	0.937083	+	0.349107i	$0.113515\pi$
$563$	18.2911	+	31.6811i	0.770877	+	1.33520i	−0.166206	+	0.986091i	$0.553152\pi$
$564$	12.5103	−	7.22283i	0.526779	−	0.304136i
$565$	−34.3502	−	19.8321i	−1.44512	−	0.834343i
$566$		−	2.94801i		−	0.123914i
$567$	−0.876271	+	2.49643i	−0.0367999	+	0.104840i
$568$	12.1127			0.508237
$569$	−17.4808	+	30.2777i	−0.732834	+	1.26931i	0.222833	+	0.974857i	$0.428469\pi$
$569$	−17.4808	+	30.2777i	−0.732834	+	1.26931i	−0.955667	+	0.294449i	$0.904864\pi$
$570$	25.6262	−	14.7953i	1.07336	−	0.619707i
$571$	17.2667	+	29.9068i	0.722589	+	1.25156i	0.959959	+	0.280142i	$0.0903816\pi$
$571$	17.2667	+	29.9068i	0.722589	+	1.25156i	−0.237369	+	0.971420i	$0.576285\pi$
$572$	13.4723	−	83.6723i	0.563305	−	3.49852i
$573$	5.19559			0.217049
$574$	12.2937	−	2.31368i	0.513129	−	0.0965710i
$575$	0.0791423			0.00330046
$576$	14.0845	−	24.3950i	0.586853	−	1.01646i
$577$	−9.35380	+	5.40042i	−0.389404	+	0.224822i	−0.681902	−	0.731444i	$-0.738847\pi$
$577$	−9.35380	+	5.40042i	−0.389404	+	0.224822i	0.292498	+	0.956266i	$0.405513\pi$
$578$	39.9988	−	23.0933i	1.66373	−	0.960554i
$579$	7.77946	+	4.49147i	0.323303	+	0.186659i
$580$		−	13.7240i		−	0.569859i
$581$	−19.0041	+	16.3221i	−0.788421	+	0.677154i
$582$	1.12818			0.0467645
$583$	43.2142	+	24.9497i	1.78975	+	1.03331i
$584$	−34.6949	−	60.0933i	−1.43568	−	2.48668i
$585$	−5.94704	−	4.84111i	−0.245880	−	0.200155i
$586$	26.3529	−	45.6446i	1.08863	−	1.88556i
$587$		−	27.5429i		−	1.13682i	−0.822747	−	0.568408i	$-0.807559\pi$
$587$		−	27.5429i		−	1.13682i	0.822747	−	0.568408i	$-0.192441\pi$
$588$	−29.6345	−	23.7274i	−1.22211	−	0.978502i
$589$	−34.1004			−1.40508
$590$	−7.88518	−	4.55251i	−0.324628	−	0.187424i
$591$	−2.91378	+	1.68227i	−0.119857	+	0.0691994i
$592$	129.997	−	75.0540i	5.34286	−	3.08470i
$593$	0.131048	+	0.0756604i	0.00538148	+	0.00310700i	0.502688	−	0.864468i	$-0.332344\pi$
$593$	0.131048	+	0.0756604i	0.00538148	+	0.00310700i	−0.497307	+	0.867575i	$0.665678\pi$
$594$	−11.8087			−0.484518
$595$	−0.936529	+	0.804361i	−0.0383940	+	0.0329756i
$596$			28.8913i			1.18343i
$597$	−2.30657	+	3.99509i	−0.0944015	+	0.163508i
$598$	1.26496	+	1.02973i	0.0517282	+	0.0421087i
$599$	6.55509	+	11.3538i	0.267834	+	0.463902i	0.968302	−	0.249782i	$-0.0803589\pi$
$599$	6.55509	+	11.3538i	0.267834	+	0.463902i	−0.700468	+	0.713683i	$0.747026\pi$
$600$	3.85011	+	2.22286i	0.157180	+	0.0907479i
$601$	−16.2807			−0.664103			−0.332052	−	0.943261i	$-0.607741\pi$
$601$	−16.2807			−0.664103			−0.332052	+	0.943261i	$0.607741\pi$
$602$	5.28250	+	28.0685i	0.215299	+	1.14399i
$603$		−	5.78481i		−	0.235576i
$604$	13.8391	+	7.99004i	0.563107	+	0.325110i
$605$	−14.3389	+	8.27856i	−0.582958	+	0.336571i
$606$	−27.0214	+	15.6008i	−1.09767	+	0.633740i
$607$	−8.31315	+	14.3988i	−0.337420	+	0.584429i	−0.983947	−	0.178463i	$-0.942888\pi$
$607$	−8.31315	+	14.3988i	−0.337420	+	0.584429i	0.646526	+	0.762892i	$0.276221\pi$
$608$	−107.394			−4.35542
$609$	1.04262	−	2.97035i	0.0422492	−	0.120365i
$610$	−49.1141			−1.98857
$611$	−1.52668	+	9.48174i	−0.0617629	+	0.383590i
$612$	−0.594920	−	1.03043i	−0.0240482	−	0.0416527i
$613$	17.3314	−	10.0063i	0.700009	−	0.404150i	−0.107342	−	0.994222i	$-0.534234\pi$
$613$	17.3314	−	10.0063i	0.700009	−	0.404150i	0.807351	+	0.590072i	$0.200901\pi$
$614$	18.0903	−	31.3334i	0.730066	−	1.26451i
$615$	3.69082			0.148828
$616$	35.4230	−	100.917i	1.42723	−	4.06608i
$617$		−	3.72768i		−	0.150071i	−0.997181	−	0.0750354i	$-0.976093\pi$
$617$		−	3.72768i		−	0.150071i	0.997181	−	0.0750354i	$-0.0239070\pi$
$618$	−22.0195	−	12.7130i	−0.885754	−	0.511390i
$619$	−0.370348	+	0.213820i	−0.0148855	+	0.00859416i	−0.507424	−	0.861696i	$-0.669402\pi$
$619$	−0.370348	+	0.213820i	−0.0148855	+	0.00859416i	0.492539	+	0.870291i	$0.336069\pi$
$620$	38.5121	+	66.7049i	1.54668	+	2.67893i
$621$	0.0830193	−	0.143794i	0.00333145	−	0.00577024i
$622$			7.19629i			0.288545i
$623$	−6.09079	−	32.3633i	−0.244022	−	1.29661i
$624$	18.6946	+	49.0767i	0.748383	+	1.96464i
$625$	11.1948	−	19.3899i	0.447791	−	0.775597i
$626$	16.3565	−	9.44344i	0.653738	−	0.377436i
$627$	11.0662	+	19.1673i	0.441943	+	0.765468i
$628$	−42.3109	+	73.2846i	−1.68839	+	2.92437i
$629$		−	2.26101i		−	0.0901524i
$630$	−9.98904	−	11.6304i	−0.397973	−	0.463366i
$631$		−	18.1977i		−	0.724440i	−0.932093	−	0.362220i	$-0.882019\pi$
$631$		−	18.1977i		−	0.724440i	0.932093	−	0.362220i	$-0.117981\pi$
$632$	136.795	+	78.9787i	5.44142	+	3.14160i
$633$	−3.69227	−	6.39519i	−0.146754	−	0.254186i
$634$	−15.7961	−	27.3597i	−0.627344	−	1.08659i
$635$	17.1464	+	9.89946i	0.680433	+	0.392848i
$636$	−62.4388			−2.47586
$637$	24.6717	−	5.32068i	0.977526	−	0.210813i
$638$	14.0505			0.556264
$639$	1.12468	+	0.649333i	0.0444916	+	0.0256872i
$640$	36.8861	+	63.8885i	1.45805	+	2.52542i
$641$	−20.2646	−	35.0993i	−0.800402	−	1.38634i	−0.919352	−	0.393437i	$-0.871286\pi$
$641$	−20.2646	−	35.0993i	−0.800402	−	1.38634i	0.118950	−	0.992900i	$-0.462047\pi$
$642$	14.3704	+	8.29675i	0.567154	+	0.327447i
$643$		−	13.1230i		−	0.517519i	−0.965942	−	0.258759i	$-0.916686\pi$
$643$		−	13.1230i		−	0.517519i	0.965942	−	0.258759i	$-0.0833137\pi$
$644$	1.55227	+	1.80733i	0.0611681	+	0.0712189i
$645$			8.42674i			0.331803i
$646$	−1.52623	+	2.64350i	−0.0600486	+	0.104007i
$647$	−24.2508	−	42.0036i	−0.953396	−	1.65133i	−0.737997	−	0.674804i	$-0.764228\pi$
$647$	−24.2508	−	42.0036i	−0.953396	−	1.65133i	−0.215399	−	0.976526i	$-0.569105\pi$
$648$	8.07743	−	4.66351i	0.317311	−	0.183200i
$649$	3.40508	−	5.89777i	0.133661	−	0.231508i
$650$	−4.37569	+	1.66682i	−0.171629	+	0.0653779i
$651$	3.26772	+	17.3630i	0.128072	+	0.680509i
$652$			105.972i			4.15017i
$653$	−15.5978	+	27.0162i	−0.610389	+	1.05723i	0.380785	+	0.924663i	$0.375654\pi$
$653$	−15.5978	+	27.0162i	−0.610389	+	1.05723i	−0.991175	+	0.132562i	$0.957680\pi$
$654$	−13.0845	−	22.6630i	−0.511643	−	0.886192i
$655$	2.71981	−	1.57028i	0.106272	−	0.0613560i
$656$	−21.8902	−	12.6383i	−0.854669	−	0.493444i
$657$		−	7.43966i		−	0.290249i
$658$	−6.35932	+	18.1172i	−0.247912	+	0.706282i
$659$	39.0377			1.52069			0.760346	−	0.649519i	$-0.225030\pi$
$659$	39.0377			1.52069			0.760346	+	0.649519i	$0.225030\pi$
$660$	24.9959	−	43.2941i	0.972962	−	1.68522i
$661$	18.9240	−	10.9258i	0.736057	−	0.424962i	−0.0845772	−	0.996417i	$-0.526954\pi$
$661$	18.9240	−	10.9258i	0.736057	−	0.424962i	0.820634	+	0.571454i	$0.193621\pi$
$662$	11.0228	+	19.0921i	0.428413	+	0.742034i
$663$	0.780978	+	0.125747i	0.0303307	+	0.00488363i
$664$	88.3126			3.42719
$665$	−9.51687	+	27.1128i	−0.369048	+	1.05139i
$666$	28.0786			1.08802
$667$	−0.0987797	+	0.171091i	−0.00382476	+	0.00662469i
$668$	−54.3050	+	31.3530i	−2.10112	+	1.21308i
$669$	21.4810	−	12.4020i	0.830502	−	0.479491i
$670$	29.0301	+	16.7605i	1.12153	+	0.647515i
$671$		−	36.7352i		−	1.41815i
$672$	10.2912	+	54.6823i	0.396993	+	2.10942i
$673$	20.3611			0.784863			0.392431	−	0.919781i	$-0.371634\pi$
$673$	20.3611			0.784863			0.392431	+	0.919781i	$0.371634\pi$
$674$	74.8262	+	43.2009i	2.88220	+	1.66404i
$675$	0.238325	+	0.412791i	0.00917313	+	0.0158883i
$676$	−66.9396	−	22.1300i	−2.57460	−	0.851153i
$677$	−18.4454	+	31.9484i	−0.708914	+	1.22788i	0.256346	+	0.966585i	$0.417481\pi$
$677$	−18.4454	+	31.9484i	−0.708914	+	1.22788i	−0.965260	+	0.261290i	$0.915852\pi$
$678$			50.8121i			1.95143i
$679$	−0.831084	+	0.713797i	−0.0318941	+	0.0273930i
$680$	4.35209			0.166895
$681$	−12.7072	−	7.33650i	−0.486941	−	0.281135i
$682$	−68.2916	+	39.4282i	−2.61502	+	1.50978i
$683$	−34.5279	+	19.9347i	−1.32117	+	0.762780i	−0.983916	−	0.178633i	$-0.942833\pi$
$683$	−34.5279	+	19.9347i	−1.32117	+	0.762780i	−0.337257	+	0.941412i	$0.609499\pi$
$684$	−23.9839	−	13.8471i	−0.917047	−	0.529457i
$685$	28.5713			1.09165
$686$	50.4298	−	1.73924i	1.92542	−	0.0664047i
$687$			9.68836i			0.369634i
$688$	28.8553	−	49.9789i	1.10010	−	1.90543i
$689$	26.2063	−	32.1930i	0.998381	−	1.22646i
$690$	0.481069	+	0.833236i	0.0183140	+	0.0317208i
$691$	−26.5895	−	15.3515i	−1.01151	−	0.583998i	−0.0998793	−	0.995000i	$-0.531846\pi$
$691$	−26.5895	−	15.3515i	−1.01151	−	0.583998i	−0.911635	+	0.411002i	$0.865179\pi$
$692$	26.8320			1.02000
$693$	8.69903	−	7.47137i	0.330449	−	0.283814i
$694$		−	35.4155i		−	1.34436i
$695$	5.63921	+	3.25580i	0.213907	+	0.123499i
$696$	−9.61084	+	5.54882i	−0.364298	+	0.210328i
$697$	−0.329723	+	0.190365i	−0.0124891	+	0.00721061i
$698$	−20.4412	+	35.4053i	−0.773712	+	1.34011i
$699$	13.6854			0.517629
$700$	−6.72130	+	1.26495i	−0.254041	+	0.0478107i
$701$	−47.7195			−1.80234			−0.901170	−	0.433465i	$-0.857291\pi$
$701$	−47.7195			−1.80234			−0.901170	+	0.433465i	$0.857291\pi$
$702$	−1.56161	+	9.69867i	−0.0589391	+	0.366053i
$703$	−26.3132	−	45.5757i	−0.992420	−	1.71892i
$704$	−105.732	+	61.0443i	−3.98492	+	2.30069i
$705$	−2.83253	+	4.90608i	−0.106679	+	0.184774i
$706$	13.2903			0.500186
$707$	10.0350	−	28.5890i	0.377405	−	1.07520i
$708$			8.52149i			0.320257i
$709$	−24.8716	−	14.3596i	−0.934071	−	0.539286i	−0.0459741	−	0.998943i	$-0.514639\pi$
$709$	−24.8716	−	14.3596i	−0.934071	−	0.539286i	−0.888097	+	0.459657i	$0.847973\pi$
$710$	−6.51714	+	3.76267i	−0.244584	+	0.141211i
$711$	8.46774	+	14.6665i	0.317565	+	0.550039i
$712$	−58.0464	+	100.539i	−2.17538	+	3.76787i
$713$		−	1.10877i		−	0.0415239i
$714$	1.49225	+	0.523796i	0.0558462	+	0.0196026i
$715$	11.8311	+	31.0587i	0.442458	+	1.16153i
$716$	17.5981	−	30.4808i	0.657671	−	1.13912i
$717$	15.0701	−	8.70074i	0.562804	−	0.324935i
$718$	26.3403	+	45.6227i	0.983011	+	1.70262i
$719$	6.15587	−	10.6623i	0.229575	−	0.397636i	−0.728107	−	0.685463i	$-0.759600\pi$
$719$	6.15587	−	10.6623i	0.229575	−	0.397636i	0.957682	+	0.287828i	$0.0929330\pi$
$720$			30.9782i			1.15449i
$721$	24.2644	−	4.56657i	0.903653	−	0.170068i
$722$			19.2808i			0.717556i
$723$	10.0818	+	5.82071i	0.374945	+	0.216474i
$724$	−13.9703	−	24.1973i	−0.519204	−	0.899287i
$725$	−0.283568	−	0.491155i	−0.0105315	−	0.0182410i
$726$	18.3689	+	10.6053i	0.681734	+	0.393600i
$727$	32.7278			1.21381			0.606904	−	0.794776i	$-0.292411\pi$
$727$	32.7278			1.21381			0.606904	+	0.794776i	$0.292411\pi$
$728$	−78.2005	−	42.4389i	−2.89830	−	1.57289i
$729$	1.00000			0.0370370
$730$	37.3346	+	21.5552i	1.38182	+	0.797792i
$731$	−0.434635	−	0.752810i	−0.0160756	−	0.0278437i
$732$	22.9832	+	39.8081i	0.849485	+	1.47135i
$733$	5.42163	+	3.13018i	0.200253	+	0.115616i	0.596773	−	0.802410i	$-0.296449\pi$
$733$	5.42163	+	3.13018i	0.200253	+	0.115616i	−0.396521	+	0.918026i	$0.629783\pi$
$734$		−	95.3531i		−	3.51955i
$735$	14.7171	+	2.24760i	0.542848	+	0.0829041i
$736$		−	3.49193i		−	0.128714i
$737$	−12.5361	+	21.7132i	−0.461774	+	0.799817i
$738$	−2.36408	−	4.09470i	−0.0870228	−	0.150728i
$739$	−31.2786	+	18.0587i	−1.15060	+	0.664300i	−0.949034	−	0.315175i	$-0.897937\pi$
$739$	−31.2786	+	18.0587i	−1.15060	+	0.664300i	−0.201567	+	0.979475i	$0.564603\pi$
$740$	−59.4348	+	102.944i	−2.18487	+	3.78430i
$741$	17.2058	−	6.55414i	0.632071	−	0.240772i
$742$	62.9587	−	54.0736i	2.31129	−	1.98510i
$743$			15.3807i			0.564264i	0.959376	+	0.282132i	$0.0910416\pi$
$743$			15.3807i			0.564264i	−0.959376	+	0.282132i	$0.908958\pi$
$744$	31.1420	−	53.9395i	1.14172	−	1.97752i
$745$	−5.66506	−	9.81216i	−0.207552	−	0.359490i
$746$	−4.76042	+	2.74843i	−0.174291	+	0.100627i
$747$	8.19994	+	4.73424i	0.300020	+	0.173217i
$748$			5.15695i			0.188557i
$749$	−15.8355	+	2.98024i	−0.578615	+	0.108896i
$750$	−31.7354			−1.15881
$751$	4.11600	−	7.12912i	0.150195	−	0.260145i	−0.781104	−	0.624401i	$-0.785343\pi$
$751$	4.11600	−	7.12912i	0.150195	−	0.260145i	0.931299	+	0.364256i	$0.118677\pi$
$752$	33.5994	−	19.3986i	1.22524	−	0.707394i
$753$	−9.63422	−	16.6870i	−0.351091	−	0.608107i
$754$	1.85806	−	11.5399i	0.0676667	−	0.420257i
$755$	−6.26680			−0.228072
$756$	−4.75227	+	13.5389i	−0.172839	+	0.492404i
$757$	−3.48549			−0.126682			−0.0633411	−	0.997992i	$-0.520176\pi$
$757$	−3.48549			−0.126682			−0.0633411	+	0.997992i	$0.520176\pi$
$758$	5.84856	−	10.1300i	0.212429	−	0.367939i
$759$	−0.623225	+	0.359819i	−0.0226216	+	0.0130606i
$760$	87.7261	−	50.6487i	3.18216	−	1.83722i
$761$	31.5938	+	18.2407i	1.14527	+	0.661224i	0.947731	−	0.319070i	$-0.103371\pi$
$761$	31.5938	+	18.2407i	1.14527	+	0.661224i	0.197542	+	0.980294i	$0.436704\pi$
$762$		−	25.3635i		−	0.918824i
$763$	23.9776	+	8.41639i	0.868049	+	0.304694i
$764$	28.1772			1.01942
$765$	0.404097	+	0.233306i	0.0146102	+	0.00843518i
$766$	43.6124	+	75.5389i	1.57578	+	2.72933i
$767$	−4.39363	−	3.57657i	−0.158645	−	0.129143i
$768$	19.0842	−	33.0548i	0.688642	−	1.19276i
$769$		−	27.8970i		−	1.00599i	−0.864289	−	0.502995i	$-0.832231\pi$
$769$		−	27.8970i		−	1.00599i	0.864289	−	0.502995i	$-0.167769\pi$
$770$	12.2898	+	65.3016i	0.442894	+	2.35331i
$771$	10.7646			0.387677
$772$	42.1903	+	24.3586i	1.51846	+	0.876684i
$773$	46.0073	−	26.5623i	1.65477	−	0.955380i	0.679693	−	0.733496i	$-0.262113\pi$
$773$	46.0073	−	26.5623i	1.65477	−	0.955380i	0.975073	−	0.221883i	$-0.0712205\pi$
$774$	9.34886	−	5.39757i	0.336038	−	0.194012i
$775$	2.75654	+	1.59149i	0.0990177	+	0.0571679i
$776$	3.86208			0.138641
$777$	−20.6844	+	17.7653i	−0.742049	+	0.637327i
$778$		−	24.1969i		−	0.867501i
$779$	−4.43087	+	7.67449i	−0.158752	+	0.274967i
$780$	−32.2525	−	26.2547i	−1.15483	−	0.940070i
$781$	−2.81431	−	4.87453i	−0.100704	−	0.174425i
$782$	−0.0859535	−	0.0496252i	−0.00307369	−	0.00177460i
$783$	−1.18984			−0.0425214
$784$	−79.5904	−	63.7256i	−2.84252	−	2.27591i
$785$		−	33.1856i		−	1.18444i
$786$	−3.48423	−	2.01162i	−0.124278	−	0.0717521i
$787$	−17.8517	+	10.3067i	−0.636345	+	0.367394i	−0.783205	−	0.621763i	$-0.786417\pi$
$787$	−17.8517	+	10.3067i	−0.636345	+	0.367394i	0.146860	+	0.989157i	$0.453083\pi$
$788$	−15.8023	+	9.12345i	−0.562933	+	0.325010i
$789$	8.41887	−	14.5819i	0.299720	−	0.519130i
$790$	−98.1354			−3.49150
$791$	−32.1487	−	37.4313i	−1.14308	−	1.33090i
$792$	−40.4247			−1.43643
$793$	−30.1712	−	4.85794i	−1.07141	−	0.172510i
$794$	28.0012	+	48.4995i	0.993725	+	1.72118i
$795$	21.2057	−	12.2431i	0.752088	−	0.434218i
$796$	−12.5092	+	21.6666i	−0.443377	+	0.767951i
$797$	34.5400			1.22347			0.611734	−	0.791063i	$-0.290472\pi$
$797$	34.5400			1.22347			0.611734	+	0.791063i	$0.290472\pi$
$798$	36.1755	−	6.80825i	1.28060	−	0.241009i
$799$		−	0.584385i		−	0.0206741i
$800$	8.68133	+	5.01217i	0.306931	+	0.177207i
$801$	−10.7794	+	6.22347i	−0.380870	+	0.219895i
$802$	−45.8051	−	79.3368i	−1.61744	−	2.80148i
$803$	−16.1223	+	27.9247i	−0.568944	+	0.985441i
$804$		−	31.3727i		−	1.10643i
$805$	−0.881573	−	0.309441i	−0.0310714	−	0.0109064i
$806$	23.3519	+	61.3029i	0.822535	+	2.15930i
$807$	−9.27158	+	16.0589i	−0.326375	+	0.565298i
$808$	−92.5023	+	53.4062i	−3.25422	+	1.87882i
$809$	17.7211	+	30.6939i	0.623042	+	1.07914i	0.988916	+	0.148476i	$0.0474367\pi$
$809$	17.7211	+	30.6939i	0.623042	+	1.07914i	−0.365874	+	0.930664i	$0.619230\pi$
$810$	−2.89733	+	5.01833i	−0.101802	+	0.176326i
$811$		−	14.7885i		−	0.519293i	−0.965704	−	0.259647i	$-0.916394\pi$
$811$		−	14.7885i		−	0.519293i	0.965704	−	0.259647i	$-0.0836061\pi$
$812$	5.65444	−	16.1091i	0.198432	−	0.565317i
$813$		−	11.8595i		−	0.415931i
$814$	−105.393	−	60.8486i	−3.69402	−	2.13274i
$815$	−20.7791	−	35.9904i	−0.727859	−	1.26069i
$816$	−1.59780	−	2.76747i	−0.0559341	−	0.0968807i
$817$	−17.5221	−	10.1164i	−0.613020	−	0.353928i
$818$	86.2257			3.01481
$819$	−4.98596	−	8.13266i	−0.174224	−	0.284178i
$820$	20.0164			0.699004
$821$	11.1225	+	6.42160i	0.388179	+	0.224115i	0.681371	−	0.731938i	$-0.261384\pi$
$821$	11.1225	+	6.42160i	0.388179	+	0.224115i	−0.293192	+	0.956054i	$0.594717\pi$
$822$	−18.3007	−	31.6978i	−0.638311	−	1.10559i
$823$	15.9689	+	27.6590i	0.556641	+	0.964131i	0.997774	+	0.0666890i	$0.0212435\pi$
$823$	15.9689	+	27.6590i	0.556641	+	0.964131i	−0.441132	+	0.897442i	$0.645423\pi$
$824$	−75.3792	−	43.5202i	−2.62596	−	1.51610i
$825$		−	2.06588i		−	0.0719246i
$826$	−7.37983	−	8.59245i	−0.256777	−	0.298970i
$827$		−	4.87884i		−	0.169654i	−0.996396	−	0.0848269i	$-0.972966\pi$
$827$		−	4.87884i		−	0.169654i	0.996396	−	0.0848269i	$-0.0270337\pi$
$828$	0.450238	−	0.779835i	0.0156469	−	0.0271012i
$829$	−5.42944	−	9.40407i	−0.188572	−	0.326617i	0.756202	−	0.654338i	$-0.227053\pi$
$829$	−5.42944	−	9.40407i	−0.188572	−	0.326617i	−0.944774	+	0.327721i	$0.893719\pi$
$830$	−47.5159	+	27.4333i	−1.64930	+	0.952225i
$831$	4.39030	−	7.60423i	0.152298	−	0.263788i
$832$	36.1543	+	94.9116i	1.25343	+	3.29047i
$833$	−1.43069	+	0.558287i	−0.0495705	+	0.0193435i
$834$		−	8.34172i		−	0.288850i
$835$	12.2955	−	21.2964i	0.425503	−	0.736993i
$836$	60.0155	+	103.950i	2.07568	+	3.59518i
$837$	5.78315	−	3.33890i	0.199895	−	0.115409i
$838$	−13.3534	−	7.70959i	−0.461285	−	0.266323i
$839$			34.4032i			1.18773i	0.804565	+	0.593865i	$0.202399\pi$
$839$			34.4032i			1.18773i	−0.804565	+	0.593865i	$0.797601\pi$
$840$	−34.1954	−	39.8143i	−1.17985	−	1.37372i
$841$	−27.5843			−0.951182
$842$	−40.2061	+	69.6389i	−1.38559	+	2.39992i
$843$	−6.12462	+	3.53605i	−0.210943	+	0.121788i
$844$	−20.0242	−	34.6830i	−0.689263	−	1.19384i
$845$	27.0735	−	5.60977i	0.931358	−	0.192982i
$846$	7.25726			0.249510
$847$	−20.2416	+	3.80948i	−0.695510	+	0.130895i
$848$	−167.694			−5.75864
$849$	0.541005	−	0.937048i	0.0185672	−	0.0321594i
$850$	0.246748	−	0.142460i	0.00846339	−	0.00488634i
$851$	1.48189	−	0.855572i	0.0507987	−	0.0293286i
$852$	6.09946	+	3.52153i	0.208964	+	0.120646i
$853$			10.4452i			0.357638i	0.983882	+	0.178819i	$0.0572277\pi$
$853$			10.4452i			0.357638i	−0.983882	+	0.178819i	$0.942772\pi$
$854$	−57.6495	−	20.2355i	−1.97272	−	0.692446i
$855$	10.8606			0.371426
$856$	49.1941	+	28.4022i	1.68142	+	0.970768i
$857$	1.35487	+	2.34670i	0.0462814	+	0.0801618i	0.888238	−	0.459383i	$-0.151930\pi$
$857$	1.35487	+	2.34670i	0.0462814	+	0.0801618i	−0.841957	+	0.539545i	$0.818596\pi$
$858$	26.8793	−	33.0197i	0.917643	−	1.12728i
$859$	5.29538	−	9.17187i	0.180676	−	0.312940i	−0.761435	−	0.648241i	$-0.775505\pi$
$859$	5.29538	−	9.17187i	0.180676	−	0.312940i	0.942111	+	0.335301i	$0.108838\pi$
$860$			45.7007i			1.55838i
$861$	4.33223	+	1.52066i	0.147642	+	0.0518239i
$862$	−41.2758			−1.40586
$863$	−3.99249	−	2.30507i	−0.135906	−	0.0784654i	0.430505	−	0.902588i	$-0.358335\pi$
$863$	−3.99249	−	2.30507i	−0.135906	−	0.0784654i	−0.566411	+	0.824123i	$0.691669\pi$
$864$	18.2132	−	10.5154i	0.619626	−	0.357742i
$865$	−9.11277	+	5.26126i	−0.309844	+	0.178888i
$866$	−89.8050	−	51.8489i	−3.05170	−	1.76190i
$867$	16.9519			0.575716
$868$	17.7218	+	94.1646i	0.601518	+	3.19616i
$869$		−	73.4010i		−	2.48996i
$870$	3.44736	−	5.97100i	0.116876	−	0.202436i
$871$	16.1756	+	13.1675i	0.548088	+	0.446164i
$872$	−44.7920	−	77.5820i	−1.51685	−	2.62726i
$873$	0.358599	+	0.207037i	0.0121368	+	0.00700716i
$874$	−2.31011			−0.0781407
$875$	23.3782	−	20.0789i	0.790328	−	0.678792i
$876$		−	40.3474i		−	1.36321i
$877$	2.02823	+	1.17100i	0.0684885	+	0.0395419i	0.533853	−	0.845577i	$-0.320743\pi$
$877$	2.02823	+	1.17100i	0.0684885	+	0.0395419i	−0.465365	+	0.885119i	$0.654077\pi$
$878$	37.3279	−	21.5513i	1.25975	−	0.727320i
$879$	16.7529	−	9.67231i	0.565062	−	0.326239i
$880$	67.1323	−	116.276i	2.26303	−	3.91968i
$881$	44.2447			1.49064			0.745320	−	0.666706i	$-0.232297\pi$
$881$	44.2447			1.49064			0.745320	+	0.666706i	$0.232297\pi$
$882$	−6.93315	−	17.7672i	−0.233451	−	0.598252i
$883$	−12.7323			−0.428474			−0.214237	−	0.976782i	$-0.568727\pi$
$883$	−12.7323			−0.428474			−0.214237	+	0.976782i	$0.568727\pi$
$884$	4.23548	+	0.681965i	0.142454	+	0.0229370i
$885$	−1.67091	−	2.89410i	−0.0561670	−	0.0972841i
$886$	−21.9037	+	12.6461i	−0.735871	+	0.424855i
$887$	22.5720	−	39.0959i	0.757895	−	1.31271i	−0.186028	−	0.982544i	$-0.559561\pi$
$887$	22.5720	−	39.0959i	0.757895	−	1.31271i	0.943922	−	0.330167i	$-0.107105\pi$
$888$	96.1213			3.22562
$889$	16.0475	+	18.6843i	0.538215	+	0.626652i
$890$		−	72.1258i		−	2.41766i
$891$	−3.75349	−	2.16708i	−0.125747	−	0.0725999i
$892$	116.498	−	67.2599i	3.90063	−	2.25203i
$893$	−6.80095	−	11.7796i	−0.227585	−	0.394189i
$894$	−7.25726	+	12.5699i	−0.242719	+	0.420402i
$895$			13.8026i			0.461371i
$896$	16.9736	+	90.1889i	0.567048	+	3.01300i
$897$	0.213108	+	0.559446i	0.00711546	+	0.0186794i
$898$	−14.8701	+	25.7558i	−0.496222	+	0.859482i
$899$	−6.88102	+	3.97276i	−0.229495	+	0.132499i
$900$	1.29251	+	2.23869i	0.0430835	+	0.0746229i
$901$	−1.26295	+	2.18750i	−0.0420750	+	0.0728761i
$902$			20.4926i			0.682327i
$903$	−3.47191	+	9.89119i	−0.115538	+	0.329158i
$904$			173.945i			5.78531i
$905$	9.48931	+	5.47866i	0.315435	+	0.182117i
$906$	4.01406	+	6.95256i	0.133358	+	0.230983i
$907$	−6.83687	−	11.8418i	−0.227014	−	0.393200i	0.729907	−	0.683546i	$-0.239563\pi$
$907$	−6.83687	−	11.8418i	−0.227014	−	0.393200i	−0.956922	+	0.290345i	$0.906230\pi$
$908$	−68.9148	−	39.7880i	−2.28702	−	1.32041i
$909$	−11.4519			−0.379837
$910$	55.2584	−	1.45816i	1.83180	−	0.0483376i
$911$	33.1635			1.09876			0.549379	−	0.835574i	$-0.314865\pi$
$911$	33.1635			1.09876			0.549379	+	0.835574i	$0.314865\pi$
$912$	−64.4144	−	37.1896i	−2.13297	−	1.23147i
$913$	−20.5189	−	35.5398i	−0.679078	−	1.17620i
$914$	−17.3998	−	30.1373i	−0.575533	−	0.996853i
$915$	−15.6113	−	9.01318i	−0.516093	−	0.297967i
$916$			52.5428i			1.73606i
$917$	3.83944	−	0.722585i	0.126790	−	0.0238619i
$918$		−	0.597755i		−	0.0197289i
$919$	−1.02495	+	1.77527i	−0.0338100	+	0.0585607i	−0.882435	−	0.470434i	$-0.844097\pi$
$919$	−1.02495	+	1.77527i	−0.0338100	+	0.0585607i	0.848625	+	0.528994i	$0.177431\pi$
$920$	1.64684	+	2.85241i	0.0542948	+	0.0940413i
$921$	11.5003	−	6.63969i	0.378947	−	0.218785i
$922$	−24.3080	+	42.1027i	−0.800542	+	1.38658i
$923$	−4.37569	+	1.66682i	−0.144028	+	0.0548639i
$924$	47.1774	−	40.5194i	1.55202	−	1.33299i
$925$			4.91221i			0.161512i
$926$	−11.4772	+	19.8791i	−0.377164	+	0.653267i
$927$	−4.66604	−	8.08182i	−0.153253	−	0.265442i
$928$	−21.6708	+	12.5116i	−0.711379	+	0.410715i
$929$	17.5841	+	10.1522i	0.576916	+	0.333082i	0.759907	−	0.650032i	$-0.225245\pi$
$929$	17.5841	+	10.1522i	0.576916	+	0.333082i	−0.182991	+	0.983115i	$0.558578\pi$
$930$			38.6956i			1.26888i
$931$	−22.3415	+	27.9036i	−0.732214	+	0.914503i
$932$	74.2200			2.43116
$933$	−1.32063	+	2.28739i	−0.0432354	+	0.0748859i
$934$	24.3391	−	14.0522i	0.796400	−	0.459802i
$935$	−1.01118	−	1.75142i	−0.0330692	−	0.0572776i
$936$	−5.34585	+	33.2014i	−0.174735	+	1.08522i
$937$	−53.1013			−1.73474			−0.867372	−	0.497660i	$-0.834193\pi$
$937$	−53.1013			−1.73474			−0.867372	+	0.497660i	$0.834193\pi$
$938$	27.1696	+	31.6339i	0.887118	+	1.03288i
$939$	6.93205			0.226219
$940$	−15.3616	+	26.6071i	−0.501041	+	0.867829i
$941$	51.2205	−	29.5722i	1.66974	−	0.964026i	0.701967	−	0.712209i	$-0.252305\pi$
$941$	51.2205	−	29.5722i	1.66974	−	0.964026i	0.967775	−	0.251817i	$-0.0810280\pi$
$942$	−36.8170	+	21.2563i	−1.19956	+	0.692567i
$943$	−0.249536	−	0.144070i	−0.00812600	−	0.00469155i
$944$			22.8865i			0.744891i
$945$	−1.04074	−	5.52995i	−0.0338552	−	0.179889i
$946$	−46.7878			−1.52120
$947$	−5.90583	−	3.40973i	−0.191914	−	0.110801i	0.400964	−	0.916094i	$-0.368675\pi$
$947$	−5.90583	−	3.40973i	−0.191914	−	0.110801i	−0.592878	+	0.805292i	$0.702008\pi$
$948$	45.9230	+	79.5410i	1.49151	+	2.58337i
$949$	20.8029	+	16.9343i	0.675290	+	0.549711i
$950$	3.31584	−	5.74320i	0.107580	−	0.186334i
$951$		−	11.5953i		−	0.376003i
$952$	5.10842	+	1.79311i	0.165565	+	0.0581149i
$953$	−27.4700			−0.889842			−0.444921	−	0.895570i	$-0.646768\pi$
$953$	−27.4700			−0.889842			−0.444921	+	0.895570i	$0.646768\pi$
$954$	−27.1657	−	15.6841i	−0.879521	−	0.507792i
$955$	−9.56965	+	5.52504i	−0.309666	+	0.178786i
$956$	81.7297	−	47.1867i	2.64333	−	1.52613i
$957$	4.46605	+	2.57848i	0.144367	+	0.0833503i
$958$	73.4368			2.37264
$959$	33.5366	+	11.7717i	1.08295	+	0.380127i
$960$			59.9101i			1.93359i
$961$	6.79653	−	11.7719i	0.219243	−	0.379740i
$962$	−63.9131	+	78.5138i	−2.06064	+	2.53139i
$963$	3.04516	+	5.27437i	0.0981288	+	0.169964i
$964$	54.6764	+	31.5674i	1.76101	+	1.01672i
$965$	−19.1051			−0.615014
$966$	0.221370	+	1.17625i	0.00712247	+	0.0378451i
$967$		−	22.8660i		−	0.735320i	−0.929960	−	0.367660i	$-0.880159\pi$
$967$		−	22.8660i		−	0.735320i	0.929960	−	0.367660i	$-0.119841\pi$
$968$	62.8822	+	36.3051i	2.02111	+	1.16689i
$969$	−0.970245	+	0.560171i	−0.0311688	+	0.0179953i
$970$	−2.07796	+	1.19971i	−0.0667194	+	0.0385205i
$971$	22.3786	−	38.7608i	0.718162	−	1.24389i	−0.243565	−	0.969885i	$-0.578317\pi$
$971$	22.3786	−	38.7608i	0.718162	−	1.24389i	0.961727	−	0.274009i	$-0.0883499\pi$
$972$	5.42329			0.173952
$973$	5.27780	+	6.14502i	0.169198	+	0.197000i
$974$	−77.4343			−2.48115
$975$	−1.69673	−	0.273195i	−0.0543389	−	0.00874926i
$976$	61.7269	+	106.914i	1.97583	+	3.42224i
$977$	20.4587	−	11.8118i	0.654531	−	0.377894i	−0.135659	−	0.990756i	$-0.543315\pi$
$977$	20.4587	−	11.8118i	0.654531	−	0.377894i	0.790190	+	0.612862i	$0.209982\pi$
$978$	−26.6192	+	46.1057i	−0.851187	+	1.47430i
$979$	53.9470			1.72415
$980$	79.8151	+	12.1894i	2.54960	+	0.389377i
$981$		−	9.60478i		−	0.306657i
$982$	−27.3579	−	15.7951i	−0.873026	−	0.504042i
$983$	−4.67560	+	2.69946i	−0.149128	+	0.0860993i	−0.572707	−	0.819760i	$-0.694107\pi$
$983$	−4.67560	+	2.69946i	−0.149128	+	0.0860993i	0.423579	+	0.905859i	$0.360774\pi$
$984$	−8.09293	−	14.0174i	−0.257993	−	0.446857i
$985$	3.57788	−	6.19708i	0.114001	−	0.197455i
$986$			0.711233i			0.0226503i
$987$	−5.34614	+	4.59166i	−0.170169	+	0.146154i
$988$	93.3121	−	35.5450i	2.96865	−	1.13084i
$989$	0.328934	−	0.569731i	0.0104595	−	0.0181164i
$990$	21.7502	−	12.5575i	0.691268	−	0.399104i
$991$	−9.63537	−	16.6890i	−0.306078	−	0.530142i	0.671423	−	0.741074i	$-0.265683\pi$
$991$	−9.63537	−	16.6890i	−0.306078	−	0.530142i	−0.977501	+	0.210932i	$0.932350\pi$
$992$	70.2198	−	121.624i	2.22948	−	3.86158i
$993$			8.09140i			0.256773i
$994$	−9.19998	+	1.73144i	−0.291806	+	0.0549180i
$995$		−	9.81129i		−	0.311039i
$996$	44.4707	+	25.6752i	1.40911	+	0.813549i
$997$	−3.34642	−	5.79617i	−0.105982	−	0.183567i	0.808157	−	0.588967i	$-0.200465\pi$
$997$	−3.34642	−	5.79617i	−0.105982	−	0.183567i	−0.914139	+	0.405401i	$0.867132\pi$
$998$	−21.6447	−	37.4897i	−0.685150	−	1.18671i
$999$	8.92499	+	5.15285i	0.282374	+	0.163029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.d.142.8	yes	16
3.2	odd	2		819.2.dl.g.415.1		16
7.2	even	3		1911.2.c.j.883.1		8
7.4	even	3	inner	273.2.bj.d.25.1	✓	16
7.5	odd	6		1911.2.c.m.883.1		8
13.12	even	2	inner	273.2.bj.d.142.1	yes	16
21.11	odd	6		819.2.dl.g.298.8		16
39.38	odd	2		819.2.dl.g.415.8		16
91.12	odd	6		1911.2.c.m.883.8		8
91.25	even	6	inner	273.2.bj.d.25.8	yes	16
91.51	even	6		1911.2.c.j.883.8		8
273.116	odd	6		819.2.dl.g.298.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.d.25.1	✓	16	7.4	even	3	inner
273.2.bj.d.25.8	yes	16	91.25	even	6	inner
273.2.bj.d.142.1	yes	16	13.12	even	2	inner
273.2.bj.d.142.8	yes	16	1.1	even	1	trivial
819.2.dl.g.298.1		16	273.116	odd	6
819.2.dl.g.298.8		16	21.11	odd	6
819.2.dl.g.415.1		16	3.2	odd	2
819.2.dl.g.415.8		16	39.38	odd	2
1911.2.c.j.883.1		8	7.2	even	3
1911.2.c.j.883.8		8	91.51	even	6
1911.2.c.m.883.1		8	7.5	odd	6
1911.2.c.m.883.8		8	91.12	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.35955 + 1.36229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.71165 + 4.69671i) q^{4} +(-1.84188 - 1.06341i) q^{5} +2.72457i q^{6} +(-1.72383 - 2.00709i) q^{7} +9.32701i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.35955 + 1.36229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.71165 + 4.69671i) q^{4} +(-1.84188 - 1.06341i) q^{5} +2.72457i q^{6} +(-1.72383 - 2.00709i) q^{7} +9.32701i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.89733 - 5.01833i) q^{10} +(3.75349 - 2.16708i) q^{11} +(-2.71165 + 4.69671i) q^{12} +(-1.28348 - 3.36937i) q^{13} +(-1.33324 - 7.08417i) q^{14} -2.12682i q^{15} +(-7.28277 + 12.6141i) q^{16} +(0.109697 + 0.190001i) q^{17} +(-2.35955 + 1.36229i) q^{18} +(4.42238 + 2.55326i) q^{19} -11.5344i q^{20} +(0.876271 - 2.49643i) q^{21} +11.8087 q^{22} +(-0.0830193 + 0.143794i) q^{23} +(-8.07743 + 4.66351i) q^{24} +(-0.238325 - 0.412791i) q^{25} +(1.56161 - 9.69867i) q^{26} -1.00000 q^{27} +(4.75227 - 13.5389i) q^{28} +1.18984 q^{29} +(2.89733 - 5.01833i) q^{30} +(-5.78315 + 3.33890i) q^{31} +(-18.2132 + 10.5154i) q^{32} +(3.75349 + 2.16708i) q^{33} +0.597755i q^{34} +(1.04074 + 5.52995i) q^{35} -5.42329 q^{36} +(-8.92499 - 5.15285i) q^{37} +(6.95655 + 12.0491i) q^{38} +(2.27622 - 2.79622i) q^{39} +(9.91842 - 17.1792i) q^{40} +1.73537i q^{41} +(5.46845 - 4.69671i) q^{42} -3.96214 q^{43} +(20.3563 + 11.7527i) q^{44} +(1.84188 - 1.06341i) q^{45} +(-0.391776 + 0.226192i) q^{46} +(-2.30677 - 1.33182i) q^{47} -14.5655 q^{48} +(-1.05679 + 6.91977i) q^{49} -1.29867i q^{50} +(-0.109697 + 0.190001i) q^{51} +(12.3446 - 15.1647i) q^{52} +(5.75654 + 9.97062i) q^{53} +(-2.35955 - 1.36229i) q^{54} -9.21796 q^{55} +(18.7201 - 16.0782i) q^{56} +5.10653i q^{57} +(2.80748 + 1.62090i) q^{58} +(1.36077 - 0.785638i) q^{59} +(9.98904 - 5.76718i) q^{60} +(4.23787 - 7.34021i) q^{61} -18.1942 q^{62} +(2.60010 - 0.489341i) q^{63} -28.1689 q^{64} +(-1.21900 + 7.57084i) q^{65} +(5.90436 + 10.2267i) q^{66} +(-5.00979 + 2.89240i) q^{67} +(-0.594920 + 1.03043i) q^{68} -0.166039 q^{69} +(-5.07770 + 14.4660i) q^{70} -1.29867i q^{71} +(-8.07743 - 4.66351i) q^{72} +(-6.44293 + 3.71983i) q^{73} +(-14.0393 - 24.3168i) q^{74} +(0.238325 - 0.412791i) q^{75} +27.6942i q^{76} +(-10.8199 - 3.79790i) q^{77} +(9.18010 - 3.49694i) q^{78} +(8.46774 - 14.6665i) q^{79} +(26.8279 - 15.4891i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.36408 + 4.09470i) q^{82} -9.46848i q^{83} +(14.1011 - 2.65384i) q^{84} -0.466611i q^{85} +(-9.34886 - 5.39757i) q^{86} +(0.594920 + 1.03043i) q^{87} +(20.2124 + 35.0089i) q^{88} +(10.7794 + 6.22347i) q^{89} +5.79467 q^{90} +(-4.55011 + 8.38430i) q^{91} -0.900476 q^{92} +(-5.78315 - 3.33890i) q^{93} +(-3.62863 - 6.28497i) q^{94} +(-5.43032 - 9.40560i) q^{95} +(-18.2132 - 10.5154i) q^{96} -0.414075i q^{97} +(-11.9203 + 14.8879i) q^{98} +4.33416i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

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