LMFDB - Embedded newform 80.2.s.b.27.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 3]))

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

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

chi := DirichletCharacter("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (of order $4$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.6
Root			$1.41303 - 0.0578659i$ of defining polynomial
Character	$\chi$	$=$	80.27
Dual form			80.2.s.b.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.567819 + 1.29521i) q^{2} +1.96251 q^{3} +(-1.35516 + 1.47090i) q^{4} +(-1.42182 - 1.72581i) q^{5} +(1.11435 + 2.54187i) q^{6} +(-1.60205 - 1.60205i) q^{7} +(-2.67461 - 0.920026i) q^{8} +0.851447 q^{9} +(1.42795 - 2.82151i) q^{10} +(0.754587 - 0.754587i) q^{11} +(-2.65952 + 2.88665i) q^{12} +5.94580i q^{13} +(1.16532 - 2.98467i) q^{14} +(-2.79034 - 3.38692i) q^{15} +(-0.327065 - 3.98661i) q^{16} +(1.95574 + 1.95574i) q^{17} +(0.483468 + 1.10281i) q^{18} +(0.780680 - 0.780680i) q^{19} +(4.46529 + 0.247399i) q^{20} +(-3.14404 - 3.14404i) q^{21} +(1.40582 + 0.548884i) q^{22} +(4.93121 - 4.93121i) q^{23} +(-5.24896 - 1.80556i) q^{24} +(-0.956833 + 4.90759i) q^{25} +(-7.70109 + 3.37614i) q^{26} -4.21656 q^{27} +(4.52748 - 0.185408i) q^{28} +(-1.44802 - 1.44802i) q^{29} +(2.80238 - 5.53725i) q^{30} -3.60859i q^{31} +(4.97780 - 2.68729i) q^{32} +(1.48089 - 1.48089i) q^{33} +(-1.42260 + 3.64361i) q^{34} +(-0.486998 + 5.04266i) q^{35} +(-1.15385 + 1.25239i) q^{36} +10.2364i q^{37} +(1.45443 + 0.567864i) q^{38} +11.6687i q^{39} +(2.21504 + 5.92398i) q^{40} -6.93334i q^{41} +(2.28696 - 5.85745i) q^{42} +9.91344i q^{43} +(0.0873298 + 2.13251i) q^{44} +(-1.21061 - 1.46944i) q^{45} +(9.18700 + 3.58694i) q^{46} +(0.104270 - 0.104270i) q^{47} +(-0.641868 - 7.82376i) q^{48} -1.86688i q^{49} +(-6.89970 + 1.54732i) q^{50} +(3.83816 + 3.83816i) q^{51} +(-8.74565 - 8.05753i) q^{52} -4.03213 q^{53} +(-2.39424 - 5.46135i) q^{54} +(-2.37516 - 0.229383i) q^{55} +(2.81093 + 5.75878i) q^{56} +(1.53209 - 1.53209i) q^{57} +(1.05328 - 2.69771i) q^{58} +(-3.46736 - 3.46736i) q^{59} +(8.76317 + 0.485523i) q^{60} +(0.680578 - 0.680578i) q^{61} +(4.67390 - 2.04902i) q^{62} +(-1.36406 - 1.36406i) q^{63} +(6.30711 + 4.92142i) q^{64} +(10.2613 - 8.45388i) q^{65} +(2.75894 + 1.07719i) q^{66} -9.04721i q^{67} +(-5.52703 + 0.226341i) q^{68} +(9.67754 - 9.67754i) q^{69} +(-6.80785 + 2.23255i) q^{70} -3.64007 q^{71} +(-2.27729 - 0.783353i) q^{72} +(-2.94030 - 2.94030i) q^{73} +(-13.2583 + 5.81242i) q^{74} +(-1.87779 + 9.63120i) q^{75} +(0.0903496 + 2.20625i) q^{76} -2.41777 q^{77} +(-15.1135 + 6.62570i) q^{78} +10.7140 q^{79} +(-6.41509 + 6.23270i) q^{80} -10.8294 q^{81} +(8.98016 - 3.93688i) q^{82} -4.23845 q^{83} +(8.88523 - 0.363865i) q^{84} +(0.594515 - 6.15595i) q^{85} +(-12.8400 + 5.62904i) q^{86} +(-2.84176 - 2.84176i) q^{87} +(-2.71247 + 1.32399i) q^{88} +0.0426256 q^{89} +(1.21583 - 2.40237i) q^{90} +(9.52546 - 9.52546i) q^{91} +(0.570698 + 13.9359i) q^{92} -7.08189i q^{93} +(0.194258 + 0.0758455i) q^{94} +(-2.45730 - 0.237315i) q^{95} +(9.76898 - 5.27383i) q^{96} +(-1.91173 - 1.91173i) q^{97} +(2.41802 - 1.06005i) q^{98} +(0.642491 - 0.642491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25}+ \cdots + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.567819	+	1.29521i	0.401509	+	0.915855i
$2$	0.567819	+	1.29521i	0.401509	+	0.915855i
$3$	1.96251			1.13306			0.566528	−	0.824043i	$-0.308286\pi$
$3$	1.96251			1.13306			0.566528	+	0.824043i	$0.308286\pi$
$4$	−1.35516	+	1.47090i	−0.677582	+	0.735448i
$5$	−1.42182	−	1.72581i	−0.635859	−	0.771805i
$5$	−1.42182	−	1.72581i	−0.635859	−	0.771805i
$6$	1.11435	+	2.54187i	0.454932	+	1.03772i
$7$	−1.60205	−	1.60205i	−0.605517	−	0.605517i	0.336254	−	0.941771i	$-0.390840\pi$
$7$	−1.60205	−	1.60205i	−0.605517	−	0.605517i	−0.941771	+	0.336254i	$0.890840\pi$
$8$	−2.67461	−	0.920026i	−0.945618	−	0.325278i
$9$	0.851447			0.283816
$10$	1.42795	−	2.82151i	0.451559	−	0.892241i
$11$	0.754587	−	0.754587i	0.227517	−	0.227517i	−0.584138	−	0.811654i	$-0.698567\pi$
$11$	0.754587	−	0.754587i	0.227517	−	0.227517i	0.811654	+	0.584138i	$0.198567\pi$
$12$	−2.65952	+	2.88665i	−0.767738	+	0.833303i
$13$			5.94580i			1.64907i	0.565812	+	0.824534i	$0.308563\pi$
$13$			5.94580i			1.64907i	−0.565812	+	0.824534i	$0.691437\pi$
$14$	1.16532	−	2.98467i	0.311446	−	0.797687i
$15$	−2.79034	−	3.38692i	−0.720464	−	0.874498i
$16$	−0.327065	−	3.98661i	−0.0817662	−	0.996652i
$17$	1.95574	+	1.95574i	0.474336	+	0.474336i	0.903315	−	0.428978i	$-0.141126\pi$
$17$	1.95574	+	1.95574i	0.474336	+	0.474336i	−0.428978	+	0.903315i	$0.641126\pi$
$18$	0.483468	+	1.10281i	0.113954	+	0.259934i
$19$	0.780680	−	0.780680i	0.179100	−	0.179100i	−0.611863	−	0.790964i	$-0.709580\pi$
$19$	0.780680	−	0.780680i	0.179100	−	0.179100i	0.790964	+	0.611863i	$0.209580\pi$
$20$	4.46529	+	0.247399i	0.998469	+	0.0553201i
$21$	−3.14404	−	3.14404i	−0.686085	−	0.686085i
$22$	1.40582	+	0.548884i	0.299722	+	0.117022i
$23$	4.93121	−	4.93121i	1.02823	−	1.02823i	0.0286378	−	0.999590i	$-0.490883\pi$
$23$	4.93121	−	4.93121i	1.02823	−	1.02823i	0.999590	−	0.0286378i	$-0.00911693\pi$
$24$	−5.24896	−	1.80556i	−1.07144	−	0.368558i
$25$	−0.956833	+	4.90759i	−0.191367	+	0.981519i
$26$	−7.70109	+	3.37614i	−1.51031	+	0.662115i
$27$	−4.21656			−0.811477
$28$	4.52748	−	0.185408i	0.855614	−	0.0350388i
$29$	−1.44802	−	1.44802i	−0.268891	−	0.268891i	0.559762	−	0.828653i	$-0.310892\pi$
$29$	−1.44802	−	1.44802i	−0.268891	−	0.268891i	−0.828653	+	0.559762i	$0.810892\pi$
$30$	2.80238	−	5.53725i	0.511642	−	1.01096i
$31$		−	3.60859i		−	0.648121i	−0.946036	−	0.324061i	$-0.894952\pi$
$31$		−	3.60859i		−	0.648121i	0.946036	−	0.324061i	$-0.105048\pi$
$32$	4.97780	−	2.68729i	0.879959	−	0.475050i
$33$	1.48089	−	1.48089i	0.257789	−	0.257789i
$34$	−1.42260	+	3.64361i	−0.243973	+	0.624874i
$35$	−0.486998	+	5.04266i	−0.0823177	+	0.852365i
$36$	−1.15385	+	1.25239i	−0.192308	+	0.208732i
$37$			10.2364i			1.68285i	0.540371	+	0.841427i	$0.318284\pi$
$37$			10.2364i			1.68285i	−0.540371	+	0.841427i	$0.681716\pi$
$38$	1.45443	+	0.567864i	0.235940	+	0.0921197i
$39$			11.6687i			1.86849i
$40$	2.21504	+	5.92398i	0.350229	+	0.936664i
$41$		−	6.93334i		−	1.08281i	−0.840763	−	0.541403i	$-0.817893\pi$
$41$		−	6.93334i		−	1.08281i	0.840763	−	0.541403i	$-0.182107\pi$
$42$	2.28696	−	5.85745i	0.352885	−	0.903823i
$43$			9.91344i			1.51179i	0.654695	+	0.755893i	$0.272797\pi$
$43$			9.91344i			1.51179i	−0.654695	+	0.755893i	$0.727203\pi$
$44$	0.0873298	+	2.13251i	0.0131655	+	0.321488i
$45$	−1.21061	−	1.46944i	−0.180467	−	0.219050i
$46$	9.18700	+	3.58694i	1.35455	+	0.528865i
$47$	0.104270	−	0.104270i	0.0152093	−	0.0152093i	−0.699461	−	0.714671i	$-0.746577\pi$
$47$	0.104270	−	0.104270i	0.0152093	−	0.0152093i	0.714671	+	0.699461i	$0.246577\pi$
$48$	−0.641868	−	7.82376i	−0.0926457	−	1.12926i
$49$		−	1.86688i		−	0.266698i
$50$	−6.89970	+	1.54732i	−0.975764	+	0.218824i
$51$	3.83816	+	3.83816i	0.537450	+	0.537450i
$52$	−8.74565	−	8.05753i	−1.21280	−	1.11738i
$53$	−4.03213			−0.553856			−0.276928	−	0.960891i	$-0.589316\pi$
$53$	−4.03213			−0.553856			−0.276928	+	0.960891i	$0.589316\pi$
$54$	−2.39424	−	5.46135i	−0.325815	−	0.743195i
$55$	−2.37516	−	0.229383i	−0.320267	−	0.0309300i
$56$	2.81093	+	5.75878i	0.375627	+	0.769550i
$57$	1.53209	−	1.53209i	0.202931	−	0.202931i
$58$	1.05328	−	2.69771i	0.138303	−	0.354227i
$59$	−3.46736	−	3.46736i	−0.451412	−	0.451412i	0.444411	−	0.895823i	$-0.353413\pi$
$59$	−3.46736	−	3.46736i	−0.451412	−	0.451412i	−0.895823	+	0.444411i	$0.853413\pi$
$60$	8.76317	+	0.485523i	1.13132	+	0.0626807i
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	−0.662194	−	0.749333i	$-0.730374\pi$
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	0.749333	+	0.662194i	$0.230374\pi$
$62$	4.67390	−	2.04902i	0.593585	−	0.260226i
$63$	−1.36406	−	1.36406i	−0.171855	−	0.171855i
$64$	6.30711	+	4.92142i	0.788388	+	0.615178i
$65$	10.2613	−	8.45388i	1.27276	−	1.04857i
$66$	2.75894	+	1.07719i	0.339602	+	0.132593i
$67$		−	9.04721i		−	1.10529i	−0.833416	−	0.552646i	$-0.813618\pi$
$67$		−	9.04721i		−	1.10529i	0.833416	−	0.552646i	$-0.186382\pi$
$68$	−5.52703	+	0.226341i	−0.670251	+	0.0274479i
$69$	9.67754	−	9.67754i	1.16504	−	1.16504i
$70$	−6.80785	+	2.23255i	−0.813694	+	0.266841i
$71$	−3.64007			−0.431997			−0.215998	−	0.976394i	$-0.569301\pi$
$71$	−3.64007			−0.431997			−0.215998	+	0.976394i	$0.569301\pi$
$72$	−2.27729	−	0.783353i	−0.268381	−	0.0923191i
$73$	−2.94030	−	2.94030i	−0.344136	−	0.344136i	0.513784	−	0.857920i	$-0.328243\pi$
$73$	−2.94030	−	2.94030i	−0.344136	−	0.344136i	−0.857920	+	0.513784i	$0.828243\pi$
$74$	−13.2583	+	5.81242i	−1.54125	+	0.675681i
$75$	−1.87779	+	9.63120i	−0.216829	+	1.11212i
$76$	0.0903496	+	2.20625i	0.0103638	+	0.253074i
$77$	−2.41777			−0.275530
$78$	−15.1135	+	6.62570i	−1.71126	+	0.750213i
$79$	10.7140			1.20542			0.602711	−	0.797960i	$-0.294087\pi$
$79$	10.7140			1.20542			0.602711	+	0.797960i	$0.294087\pi$
$80$	−6.41509	+	6.23270i	−0.717229	+	0.696838i
$81$	−10.8294			−1.20326
$82$	8.98016	−	3.93688i	0.991693	−	0.434756i
$83$	−4.23845			−0.465230			−0.232615	−	0.972569i	$-0.574728\pi$
$83$	−4.23845			−0.465230			−0.232615	+	0.972569i	$0.574728\pi$
$84$	8.88523	−	0.363865i	0.969458	−	0.0397009i
$85$	0.594515	−	6.15595i	0.0644842	−	0.667707i
$86$	−12.8400	+	5.62904i	−1.38458	+	0.606995i
$87$	−2.84176	−	2.84176i	−0.304668	−	0.304668i
$88$	−2.71247	+	1.32399i	−0.289150	+	0.141138i
$89$	0.0426256			0.00451831			0.00225915	−	0.999997i	$-0.499281\pi$
$89$	0.0426256			0.00451831			0.00225915	+	0.999997i	$0.499281\pi$
$90$	1.21583	−	2.40237i	0.128160	−	0.253232i
$91$	9.52546	−	9.52546i	0.998539	−	0.998539i
$92$	0.570698	+	13.9359i	0.0594993	+	1.45292i
$93$		−	7.08189i		−	0.734358i
$94$	0.194258	+	0.0758455i	0.0200362	+	0.00782287i
$95$	−2.45730	−	0.237315i	−0.252113	−	0.0243480i
$96$	9.76898	−	5.27383i	0.997042	−	0.538258i
$97$	−1.91173	−	1.91173i	−0.194106	−	0.194106i	0.603362	−	0.797468i	$-0.293828\pi$
$97$	−1.91173	−	1.91173i	−0.194106	−	0.194106i	−0.797468	+	0.603362i	$0.793828\pi$
$98$	2.41802	−	1.06005i	0.244257	−	0.107081i
$99$	0.642491	−	0.642491i	0.0645728	−	0.0645728i
$100$	−5.92189	−	8.05799i	−0.592189	−	0.805799i
$101$	4.96537	+	4.96537i	0.494073	+	0.494073i	0.909587	−	0.415514i	$-0.136398\pi$
$101$	4.96537	+	4.96537i	0.494073	+	0.494073i	−0.415514	+	0.909587i	$0.636398\pi$
$102$	−2.79186	+	7.15062i	−0.276435	+	0.708017i
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	−0.684984	−	0.728558i	$-0.740191\pi$
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	0.728558	+	0.684984i	$0.240191\pi$
$104$	5.47029	−	15.9027i	0.536406	−	1.55939i
$105$	−0.955739	+	9.89627i	−0.0932706	+	0.965777i
$106$	−2.28952	−	5.22248i	−0.222378	−	0.507252i
$107$	17.5924			1.70072			0.850359	−	0.526204i	$-0.176385\pi$
$107$	17.5924			1.70072			0.850359	+	0.526204i	$0.176385\pi$
$108$	5.71412	−	6.20211i	0.549842	−	0.596799i
$109$	0.345161	+	0.345161i	0.0330605	+	0.0330605i	0.723444	−	0.690383i	$-0.242558\pi$
$109$	0.345161	+	0.345161i	0.0330605	+	0.0330605i	−0.690383	+	0.723444i	$0.742558\pi$
$110$	−1.05156	−	3.20660i	−0.100263	−	0.305737i
$111$			20.0890i			1.90677i
$112$	−5.86276	+	6.91071i	−0.553979	+	0.653001i
$113$	−5.43662	+	5.43662i	−0.511435	+	0.511435i	−0.914966	−	0.403531i	$-0.867783\pi$
$113$	−5.43662	+	5.43662i	−0.511435	+	0.511435i	0.403531	+	0.914966i	$0.367783\pi$
$114$	2.85434	+	1.11444i	0.267334	+	0.104377i
$115$	−15.5216	−	1.49901i	−1.44740	−	0.139784i
$116$	4.09219	−	0.167582i	0.379950	−	0.0155596i
$117$			5.06253i			0.468031i
$118$	2.52214	−	6.45981i	0.232182	−	0.594673i
$119$		−	6.26638i		−	0.574438i
$120$	4.34704	+	11.6259i	0.396829	+	1.06129i
$121$			9.86120i			0.896472i
$122$	1.26794	+	0.495050i	0.114794	+	0.0448197i
$123$		−	13.6067i		−	1.22688i
$124$	5.30785	+	4.89023i	0.476659	+	0.439155i
$125$	9.83002	−	5.32642i	0.879223	−	0.476410i
$126$	0.992211	−	2.54129i	0.0883932	−	0.226396i
$127$	−6.27150	+	6.27150i	−0.556505	+	0.556505i	−0.928311	−	0.371805i	$-0.878739\pi$
$127$	−6.27150	+	6.27150i	−0.556505	+	0.556505i	0.371805	+	0.928311i	$0.378739\pi$
$128$	−2.79301	+	10.9635i	−0.246869	+	0.969049i
$129$			19.4552i			1.71294i
$130$	16.7762	+	8.49033i	1.47137	+	0.744651i
$131$	1.61521	+	1.61521i	0.141122	+	0.141122i	0.774138	−	0.633017i	$-0.218184\pi$
$131$	1.61521	+	1.61521i	0.141122	+	0.141122i	−0.633017	+	0.774138i	$0.718184\pi$
$132$	0.171386	+	4.18507i	0.0149172	+	0.364263i
$133$	−2.50138			−0.216897
$134$	11.7181	−	5.13718i	1.01229	−	0.443785i
$135$	5.99520	+	7.27697i	0.515985	+	0.626302i
$136$	−3.43152	−	7.03018i	−0.294250	−	0.602833i
$137$	6.83585	−	6.83585i	0.584026	−	0.584026i	−0.351981	−	0.936007i	$-0.614492\pi$
$137$	6.83585	−	6.83585i	0.584026	−	0.584026i	0.936007	+	0.351981i	$0.114492\pi$
$138$	18.0296	+	7.03941i	1.53478	+	0.599234i
$139$	−13.7427	−	13.7427i	−1.16564	−	1.16564i	−0.983220	−	0.182423i	$-0.941606\pi$
$139$	−13.7427	−	13.7427i	−1.16564	−	1.16564i	−0.182423	−	0.983220i	$-0.558394\pi$
$140$	−6.75726	−	7.54995i	−0.571093	−	0.638087i
$141$	0.204631	−	0.204631i	0.0172330	−	0.0172330i
$142$	−2.06690	−	4.71467i	−0.173450	−	0.395647i
$143$	4.48662	+	4.48662i	0.375190	+	0.375190i
$144$	−0.278479	−	3.39439i	−0.0232066	−	0.282865i
$145$	−0.440176	+	4.55784i	−0.0365547	+	0.378508i
$146$	2.13876	−	5.47788i	0.177005	−	0.453353i
$147$		−	3.66378i		−	0.302184i
$148$	−15.0567	−	13.8720i	−1.23765	−	1.14027i
$149$	−1.73811	+	1.73811i	−0.142391	+	0.142391i	−0.774709	−	0.632318i	$-0.782104\pi$
$149$	−1.73811	+	1.73811i	−0.142391	+	0.142391i	0.632318	+	0.774709i	$0.282104\pi$
$150$	−13.5407	+	3.03663i	−1.10560	+	0.247940i
$151$	5.83522			0.474864			0.237432	−	0.971404i	$-0.423694\pi$
$151$	5.83522			0.474864			0.237432	+	0.971404i	$0.423694\pi$
$152$	−2.80626	+	1.36977i	−0.227618	+	0.111103i
$153$	1.66521	+	1.66521i	0.134624	+	0.134624i
$154$	−1.37286	−	3.13153i	−0.110628	−	0.252346i
$155$	−6.22773	+	5.13078i	−0.500223	+	0.412114i
$156$	−17.1634	−	15.8130i	−1.37417	−	1.26605i
$157$	3.14732			0.251183			0.125592	−	0.992082i	$-0.459917\pi$
$157$	3.14732			0.251183			0.125592	+	0.992082i	$0.459917\pi$
$158$	6.08363	+	13.8770i	0.483987	+	1.10399i
$159$	−7.91310			−0.627550
$160$	−11.7153	−	4.76987i	−0.926176	−	0.377092i
$161$	−15.8001			−1.24522
$162$	−6.14913	−	14.0264i	−0.483121	−	1.10202i
$163$	7.82117			0.612601			0.306301	−	0.951935i	$-0.400909\pi$
$163$	7.82117			0.612601			0.306301	+	0.951935i	$0.400909\pi$
$164$	10.1982	+	9.39580i	0.796347	+	0.733689i
$165$	−4.66128	−	0.450167i	−0.362880	−	0.0350454i
$166$	−2.40667	−	5.48970i	−0.186794	−	0.426083i
$167$	−9.88460	−	9.88460i	−0.764893	−	0.764893i	0.212309	−	0.977203i	$-0.431902\pi$
$167$	−9.88460	−	9.88460i	−0.764893	−	0.764893i	−0.977203	+	0.212309i	$0.931902\pi$
$168$	5.51649	+	11.3017i	0.425606	+	0.871943i
$169$	−22.3525			−1.71942
$170$	8.31085	−	2.72544i	0.637413	−	0.209032i
$171$	0.664708	−	0.664708i	0.0508315	−	0.0508315i
$172$	−14.5816	−	13.4343i	−1.11184	−	1.02436i
$173$		−	3.49245i		−	0.265526i	−0.991148	−	0.132763i	$-0.957615\pi$
$173$		−	3.49245i		−	0.265526i	0.991148	−	0.132763i	$-0.0423849\pi$
$174$	2.06708	−	5.29429i	0.156705	−	0.401359i
$175$	9.39509	−	6.32931i	0.710202	−	0.478451i
$176$	−3.25504	−	2.76144i	−0.245358	−	0.208152i
$177$	−6.80473	−	6.80473i	−0.511475	−	0.511475i
$178$	0.0242036	+	0.0552094i	0.00181414	+	0.00413812i
$179$	−13.0809	+	13.0809i	−0.977713	+	0.977713i	−0.999757	−	0.0220444i	$-0.992982\pi$
$179$	−13.0809	+	13.0809i	−0.977713	+	0.977713i	0.0220444	+	0.999757i	$0.492982\pi$
$180$	3.80196	+	0.210647i	0.283381	+	0.0157007i
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.999903	+	0.0138952i	$0.00442312\pi$
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.0138952	+	0.999903i	$0.495577\pi$
$182$	17.7462	+	6.92878i	1.31544	+	0.513595i
$183$	1.33564	−	1.33564i	0.0987335	−	0.0987335i
$184$	−17.7259	+	8.65223i	−1.30677	+	0.637851i
$185$	17.6661	−	14.5544i	1.29884	−	1.07006i
$186$	9.17257	−	4.02123i	0.672565	−	0.294851i
$187$	2.95155			0.215839
$188$	0.0120674	+	0.294673i	0.000880102	+	0.0214912i
$189$	6.75513	+	6.75513i	0.491363	+	0.491363i
$190$	−1.08792	−	3.31748i	−0.0789264	−	0.240675i
$191$			2.92523i			0.211662i	0.994384	+	0.105831i	$0.0337503\pi$
$191$			2.92523i			0.211662i	−0.994384	+	0.105831i	$0.966250\pi$
$192$	12.3778	+	9.65835i	0.893288	+	0.697031i
$193$	0.0830702	−	0.0830702i	0.00597953	−	0.00597953i	−0.704111	−	0.710090i	$-0.748654\pi$
$193$	0.0830702	−	0.0830702i	0.00597953	−	0.00597953i	0.710090	+	0.704111i	$0.248654\pi$
$194$	1.39058	−	3.56161i	0.0998379	−	0.255709i
$195$	20.1379	−	16.5908i	1.44211	−	1.18809i
$196$	2.74599	+	2.52993i	0.196142	+	0.180710i
$197$			7.80487i			0.556074i	0.960570	+	0.278037i	$0.0896838\pi$
$197$			7.80487i			0.556074i	−0.960570	+	0.278037i	$0.910316\pi$
$198$	1.19698	+	0.467346i	0.0850659	+	0.0332128i
$199$			10.9740i			0.777924i	0.921254	+	0.388962i	$0.127166\pi$
$199$			10.9740i			0.777924i	−0.921254	+	0.388962i	$0.872834\pi$
$200$	7.07427	−	12.2456i	0.500226	−	0.865895i
$201$		−	17.7552i		−	1.25236i
$202$	−3.61179	+	9.25065i	−0.254125	+	0.650873i
$203$			4.63960i			0.325636i
$204$	−10.8469	+	0.444197i	−0.759432	+	0.0311000i
$205$	−11.9656	+	9.85799i	−0.835715	+	0.688512i
$206$	0.823871	+	0.321669i	0.0574018	+	0.0224118i
$207$	4.19866	−	4.19866i	0.291827	−	0.291827i
$208$	23.7036	−	1.94466i	1.64355	−	0.134838i
$209$		−	1.17818i		−	0.0814966i
$210$	−13.3605	+	4.38140i	−0.921961	+	0.302345i
$211$	−8.92204	−	8.92204i	−0.614218	−	0.614218i	0.329824	−	0.944042i	$-0.393011\pi$
$211$	−8.92204	−	8.92204i	−0.614218	−	0.614218i	−0.944042	+	0.329824i	$0.893011\pi$
$212$	5.46420	−	5.93085i	0.375283	−	0.407332i
$213$	−7.14367			−0.489477
$214$	9.98927	+	22.7859i	0.682853	+	1.55761i
$215$	17.1087	−	14.0952i	1.16680	−	0.961283i
$216$	11.2777	+	3.87934i	0.767347	+	0.263956i
$217$	−5.78113	+	5.78113i	−0.392449	+	0.392449i
$218$	−0.251069	+	0.643047i	−0.0170045	+	0.0435527i
$219$	−5.77037	−	5.77037i	−0.389926	−	0.389926i
$220$	3.55613	−	3.18276i	0.239754	−	0.214582i
$221$	−11.6284	+	11.6284i	−0.782213	+	0.782213i
$222$	−26.0196	+	11.4069i	−1.74632	+	0.765584i
$223$	−13.1678	−	13.1678i	−0.881784	−	0.881784i	0.111931	−	0.993716i	$-0.464296\pi$
$223$	−13.1678	−	13.1678i	−0.881784	−	0.881784i	−0.993716	+	0.111931i	$0.964296\pi$
$224$	−12.2798	−	3.66950i	−0.820481	−	0.245179i
$225$	−0.814693	+	4.17856i	−0.0543129	+	0.278570i
$226$	−10.1286	−	3.95458i	−0.673745	−	0.263055i
$227$			19.3432i			1.28385i	0.766766	+	0.641927i	$0.221865\pi$
$227$			19.3432i			1.28385i	−0.766766	+	0.641927i	$0.778135\pi$
$228$	0.177312	+	4.32979i	0.0117428	+	0.286747i
$229$	13.2143	−	13.2143i	0.873223	−	0.873223i	−0.119599	−	0.992822i	$-0.538161\pi$
$229$	13.2143	−	13.2143i	0.873223	−	0.873223i	0.992822	+	0.119599i	$0.0381610\pi$
$230$	−6.87193	−	20.9550i	−0.453122	−	1.38173i
$231$	−4.74490			−0.312191
$232$	2.54068	+	5.20511i	0.166804	+	0.341732i
$233$	20.6884	+	20.6884i	1.35534	+	1.35534i	0.879570	+	0.475769i	$0.157830\pi$
$233$	20.6884	+	20.6884i	1.35534	+	1.35534i	0.475769	+	0.879570i	$0.342170\pi$
$234$	−6.55707	+	2.87460i	−0.428649	+	0.187919i
$235$	−0.328204	−	0.0316965i	−0.0214096	−	0.00206765i
$236$	9.79896	−	0.401284i	0.637858	−	0.0261214i
$237$	21.0264			1.36581
$238$	8.11630	−	3.55817i	0.526102	−	0.230642i
$239$	14.1053			0.912395			0.456198	−	0.889878i	$-0.349211\pi$
$239$	14.1053			0.912395			0.456198	+	0.889878i	$0.349211\pi$
$240$	−12.5897	+	12.2317i	−0.812661	+	0.789556i
$241$	12.8011			0.824592			0.412296	−	0.911050i	$-0.364727\pi$
$241$	12.8011			0.824592			0.412296	+	0.911050i	$0.364727\pi$
$242$	−12.7724	+	5.59937i	−0.821039	+	0.359941i
$243$	−8.60310			−0.551889
$244$	0.0787646	+	1.92335i	0.00504238	+	0.123130i
$245$	−3.22189	+	2.65438i	−0.205839	+	0.169582i
$246$	17.6237	−	7.72617i	1.12364	−	0.492603i
$247$	4.64177	+	4.64177i	0.295349	+	0.295349i
$248$	−3.31999	+	9.65157i	−0.210820	+	0.612876i
$249$	−8.31800			−0.527132
$250$	12.4805	+	9.70754i	0.789338	+	0.613959i
$251$	−6.84118	+	6.84118i	−0.431812	+	0.431812i	−0.889244	−	0.457433i	$-0.848769\pi$
$251$	−6.84118	+	6.84118i	−0.431812	+	0.431812i	0.457433	+	0.889244i	$0.348769\pi$
$252$	3.85491	−	0.157865i	0.242837	−	0.00994457i
$253$		−	7.44205i		−	0.467878i
$254$	−11.6840	−	4.56186i	−0.733120	−	0.286237i
$255$	1.16674	−	12.0811i	0.0730642	−	0.756549i
$256$	−15.7861	+	2.60776i	−0.986629	+	0.162985i
$257$	−6.66524	−	6.66524i	−0.415766	−	0.415766i	0.467975	−	0.883742i	$-0.344984\pi$
$257$	−6.66524	−	6.66524i	−0.415766	−	0.415766i	−0.883742	+	0.467975i	$0.844984\pi$
$258$	−25.1987	+	11.0471i	−1.56880	+	0.687759i
$259$	16.3992	−	16.3992i	1.01900	−	1.01900i
$260$	−1.47098	+	26.5497i	−0.0912265	+	1.64654i
$261$	−1.23291	−	1.23291i	−0.0763154	−	0.0763154i
$262$	−1.17490	+	3.00919i	−0.0725854	+	0.185908i
$263$	−7.32015	+	7.32015i	−0.451380	+	0.451380i	−0.895812	−	0.444432i	$-0.853405\pi$
$263$	−7.32015	+	7.32015i	−0.451380	+	0.451380i	0.444432	+	0.895812i	$0.353405\pi$
$264$	−5.32325	+	2.59834i	−0.327623	+	0.159917i
$265$	5.73298	+	6.95869i	0.352174	+	0.427469i
$266$	−1.42033	−	3.23982i	−0.0870859	−	0.198646i
$267$	0.0836533			0.00511950
$268$	13.3075	+	12.2604i	0.812885	+	0.748926i
$269$	−15.9801	−	15.9801i	−0.974321	−	0.974321i	0.0253576	−	0.999678i	$-0.491928\pi$
$269$	−15.9801	−	15.9801i	−0.974321	−	0.974321i	−0.999678	+	0.0253576i	$0.991928\pi$
$270$	−6.02105	+	11.8971i	−0.366430	+	0.724033i
$271$		−	3.59684i		−	0.218492i	−0.994015	−	0.109246i	$-0.965156\pi$
$271$		−	3.59684i		−	0.218492i	0.994015	−	0.109246i	$-0.0348437\pi$
$272$	7.15711	−	8.43642i	0.433963	−	0.511533i
$273$	18.6938	−	18.6938i	1.13140	−	1.13140i
$274$	12.7354	+	4.97237i	0.769375	+	0.300392i
$275$	2.98119	+	4.42522i	0.179773	+	0.266851i
$276$	1.12000	+	27.3493i	0.0674161	+	1.64623i
$277$		−	20.9416i		−	1.25826i	−0.777300	−	0.629131i	$-0.783411\pi$
$277$		−	20.9416i		−	1.25826i	0.777300	−	0.629131i	$-0.216589\pi$
$278$	9.99640	−	25.6032i	0.599545	−	1.53558i
$279$		−	3.07252i		−	0.183947i
$280$	5.94191	−	13.0391i	0.355097	−	0.779236i
$281$		−	3.26699i		−	0.194892i	−0.995241	−	0.0974462i	$-0.968933\pi$
$281$		−	3.26699i		−	0.194892i	0.995241	−	0.0974462i	$-0.0310674\pi$
$282$	0.381234	+	0.148848i	0.0227022	+	0.00886375i
$283$		0	0.000151619i		0	9.01279e-6i	−1.00000		4.50640e-6i	$-0.999999\pi$
$283$		0	0.000151619i		0	9.01279e-6i	1.00000		4.50640e-6i	$-1.43443e-6\pi$
$284$	4.93289	−	5.35416i	0.292713	−	0.317711i
$285$	−4.82247	−	0.465733i	−0.285658	−	0.0275877i
$286$	−3.26355	+	8.35873i	−0.192978	+	0.494262i
$287$	−11.1075	+	11.1075i	−0.655657	+	0.655657i
$288$	4.23833	−	2.28809i	0.249746	−	0.134827i
$289$		−	9.35017i		−	0.550010i
$290$	−6.15332	+	2.01790i	−0.361335	+	0.118495i
$291$	−3.75178	−	3.75178i	−0.219933	−	0.219933i
$292$	8.30947	−	0.340287i	0.486275	−	0.0199138i
$293$	−11.0593			−0.646091			−0.323045	−	0.946384i	$-0.604707\pi$
$293$	−11.0593			−0.646091			−0.323045	+	0.946384i	$0.604707\pi$
$294$	4.74538	−	2.08036i	0.276756	−	0.121329i
$295$	−1.05402	+	10.9140i	−0.0613677	+	0.635436i
$296$	9.41775	−	27.3784i	0.547396	−	1.59134i
$297$	−3.18176	+	3.18176i	−0.184624	+	0.184624i
$298$	−3.23815	−	1.26429i	−0.187581	−	0.0732384i
$299$	29.3200	+	29.3200i	1.69562	+	1.69562i
$300$	−11.6218	−	15.8139i	−0.670983	−	0.913015i
$301$	15.8818	−	15.8818i	0.915413	−	0.915413i
$302$	3.31335	+	7.55787i	0.190662	+	0.434906i
$303$	9.74459	+	9.74459i	0.559812	+	0.559812i
$304$	−3.36760	−	2.85693i	−0.193145	−	0.163856i
$305$	−2.14221	−	0.206885i	−0.122663	−	0.0118462i
$306$	−1.21127	+	3.10234i	−0.0692435	+	0.177349i
$307$			15.1317i			0.863613i	0.901966	+	0.431806i	$0.142124\pi$
$307$			15.1317i			0.863613i	−0.901966	+	0.431806i	$0.857876\pi$
$308$	3.27647	−	3.55629i	0.186694	−	0.202638i
$309$	0.867862	−	0.867862i	0.0493709	−	0.0493709i
$310$	−10.1817	−	5.15290i	−0.578281	−	0.292665i
$311$	−27.1556			−1.53985			−0.769925	−	0.638134i	$-0.779707\pi$
$311$	−27.1556			−1.53985			−0.769925	+	0.638134i	$0.779707\pi$
$312$	10.7355	−	31.2092i	0.607778	−	1.76687i
$313$	−13.6695	−	13.6695i	−0.772646	−	0.772646i	0.205922	−	0.978568i	$-0.433981\pi$
$313$	−13.6695	−	13.6695i	−0.772646	−	0.772646i	−0.978568	+	0.205922i	$0.933981\pi$
$314$	1.78711	+	4.07645i	0.100852	+	0.230048i
$315$	−0.414653	+	4.29356i	−0.0233631	+	0.241915i
$316$	−14.5193	+	15.7592i	−0.816772	+	0.886525i
$317$	−25.8314			−1.45084			−0.725419	−	0.688307i	$-0.758354\pi$
$317$	−25.8314			−1.45084			−0.725419	+	0.688307i	$0.758354\pi$
$318$	−4.49321	−	10.2492i	−0.251967	−	0.574745i
$319$	−2.18532			−0.122354
$320$	−0.474158	−	17.8823i	−0.0265062	−	0.999649i
$321$	34.5252			1.92701
$322$	−8.97157	−	20.4645i	−0.499966	−	1.14044i
$323$	3.05361			0.169908
$324$	14.6756	−	15.9289i	0.815310	−	0.884938i
$325$	−29.1796	−	5.68914i	−1.61859	−	0.315576i
$326$	4.44101	+	10.1301i	0.245965	+	0.561054i
$327$	0.677383	+	0.677383i	0.0374594	+	0.0374594i
$328$	−6.37885	+	18.5440i	−0.352213	+	1.02392i
$329$	−0.334091			−0.0184190
$330$	−2.06370	−	6.29298i	−0.113603	−	0.346417i
$331$	−13.6207	+	13.6207i	−0.748659	+	0.748659i	−0.974227	−	0.225568i	$-0.927576\pi$
$331$	−13.6207	+	13.6207i	−0.748659	+	0.748659i	0.225568	+	0.974227i	$0.427576\pi$
$332$	5.74379	−	6.23431i	0.315231	−	0.342152i
$333$			8.71576i			0.477621i
$334$	7.19002	−	18.4153i	0.393420	−	1.00764i
$335$	−15.6138	+	12.8635i	−0.853071	+	0.702810i
$336$	−11.5057	+	13.5623i	−0.627689	+	0.739886i
$337$	16.0911	+	16.0911i	0.876536	+	0.876536i	0.993174	−	0.116638i	$-0.0372119\pi$
$337$	16.0911	+	16.0911i	0.876536	+	0.876536i	−0.116638	+	0.993174i	$0.537212\pi$
$338$	−12.6922	−	28.9513i	−0.690364	−	1.57474i
$339$	−10.6694	+	10.6694i	−0.579484	+	0.579484i
$340$	8.24909	+	9.21679i	0.447370	+	0.499850i
$341$	−2.72299	−	2.72299i	−0.147458	−	0.147458i
$342$	1.23837	+	0.483506i	0.0669636	+	0.0261450i
$343$	−14.2052	+	14.2052i	−0.767007	+	0.767007i
$344$	9.12062	−	26.5146i	0.491751	−	1.42957i
$345$	−30.4614	−	2.94183i	−1.63998	−	0.158383i
$346$	4.52347	−	1.98308i	0.243183	−	0.106611i
$347$	5.57562			0.299315			0.149658	−	0.988738i	$-0.452183\pi$
$347$	5.57562			0.299315			0.149658	+	0.988738i	$0.452183\pi$
$348$	8.03097	−	0.328882i	0.430505	−	0.0176299i
$349$	15.0811	+	15.0811i	0.807273	+	0.807273i	0.984220	−	0.176947i	$-0.0566222\pi$
$349$	15.0811	+	15.0811i	0.807273	+	0.807273i	−0.176947	+	0.984220i	$0.556622\pi$
$350$	13.5325	+	8.57476i	0.723344	+	0.458340i
$351$		−	25.0708i		−	1.33818i
$352$	1.72839	−	5.78398i	0.0921234	−	0.308287i
$353$	2.57880	−	2.57880i	0.137256	−	0.137256i	−0.635141	−	0.772397i	$-0.719058\pi$
$353$	2.57880	−	2.57880i	0.137256	−	0.137256i	0.772397	+	0.635141i	$0.219058\pi$
$354$	4.94973	−	12.6774i	0.263075	−	0.673798i
$355$	5.17554	+	6.28206i	0.274689	+	0.333417i
$356$	−0.0577647	+	0.0626979i	−0.00306152	+	0.00332298i
$357$		−	12.2978i		−	0.650870i
$358$	−24.3702	−	9.51500i	−1.28800	−	0.502883i
$359$		−	5.77227i		−	0.304649i	−0.988331	−	0.152324i	$-0.951324\pi$
$359$		−	5.77227i		−	0.304649i	0.988331	−	0.152324i	$-0.0486758\pi$
$360$	1.88599	+	5.04396i	0.0994004	+	0.265840i
$361$			17.7811i			0.935846i
$362$	−9.92115	+	25.4104i	−0.521444	+	1.33554i
$363$			19.3527i			1.01575i
$364$	1.10240	+	26.9195i	0.0577814	+	1.41096i
$365$	−0.893807	+	9.25499i	−0.0467840	+	0.484428i
$366$	2.48835	+	0.971540i	0.130068	+	0.0507832i
$367$	8.30496	−	8.30496i	0.433516	−	0.433516i	−0.456307	−	0.889822i	$-0.650828\pi$
$367$	8.30496	−	8.30496i	0.433516	−	0.433516i	0.889822	+	0.456307i	$0.150828\pi$
$368$	−21.2716	−	18.0460i	−1.10886	−	0.940710i
$369$		−	5.90337i		−	0.307317i
$370$	28.8822	+	14.6171i	1.50151	+	0.759908i
$371$	6.45967	+	6.45967i	0.335369	+	0.335369i
$372$	10.4167	+	9.59712i	0.540082	+	0.497587i
$373$	16.0484			0.830953			0.415477	−	0.909604i	$-0.363615\pi$
$373$	16.0484			0.830953			0.415477	+	0.909604i	$0.363615\pi$
$374$	1.67595	+	3.82289i	0.0866612	+	0.197677i
$375$	19.2915	−	10.4532i	0.996209	−	0.539799i
$376$	−0.374813	+	0.182951i	−0.0193295	+	0.00943496i
$377$	8.60964	−	8.60964i	0.443419	−	0.443419i
$378$	−4.91365	+	12.5850i	−0.252731	+	0.647304i
$379$	−8.91367	−	8.91367i	−0.457865	−	0.457865i	0.440089	−	0.897954i	$-0.354947\pi$
$379$	−8.91367	−	8.91367i	−0.457865	−	0.457865i	−0.897954	+	0.440089i	$0.854947\pi$
$380$	3.67910	−	3.29282i	0.188734	−	0.168918i
$381$	−12.3079	+	12.3079i	−0.630552	+	0.630552i
$382$	−3.78880	+	1.66100i	−0.193852	+	0.0849841i
$383$	−24.8928	−	24.8928i	−1.27196	−	1.27196i	−0.945057	−	0.326904i	$-0.893995\pi$
$383$	−24.8928	−	24.8928i	−1.27196	−	1.27196i	−0.326904	−	0.945057i	$-0.606005\pi$
$384$	−5.48131	+	21.5161i	−0.279717	+	1.09799i
$385$	3.43764	+	4.17261i	0.175199	+	0.212656i
$386$	0.154763	+	0.0604250i	0.00787721	+	0.00307555i
$387$			8.44078i			0.429069i
$388$	5.40265	−	0.221247i	0.274278	−	0.0112321i
$389$	−16.5819	+	16.5819i	−0.840738	+	0.840738i	−0.988955	−	0.148217i	$-0.952647\pi$
$389$	−16.5819	+	16.5819i	−0.840738	+	0.840738i	0.148217	+	0.988955i	$0.452647\pi$
$390$	32.9234	+	16.6624i	1.66714	+	0.843732i
$391$	19.2883			0.975452
$392$	−1.71758	+	4.99319i	−0.0867510	+	0.252194i
$393$	3.16987	+	3.16987i	0.159899	+	0.159899i
$394$	−10.1090	+	4.43176i	−0.509284	+	0.223269i
$395$	−15.2335	−	18.4904i	−0.766478	−	0.930351i
$396$	0.0743567	+	1.81572i	0.00373656	+	0.0912432i
$397$	−8.62531			−0.432892			−0.216446	−	0.976295i	$-0.569447\pi$
$397$	−8.62531			−0.432892			−0.216446	+	0.976295i	$0.569447\pi$
$398$	−14.2137	+	6.23123i	−0.712466	+	0.312343i
$399$	−4.90897			−0.245756
$400$	19.8776	+	2.20941i	0.993879	+	0.110471i
$401$	19.7107			0.984307			0.492153	−	0.870508i	$-0.336210\pi$
$401$	19.7107			0.984307			0.492153	+	0.870508i	$0.336210\pi$
$402$	22.9969	−	10.0818i	1.14698	−	0.502833i
$403$	21.4559			1.06880
$404$	−14.0324	+	0.574651i	−0.698139	+	0.0285900i
$405$	15.3975	+	18.6894i	0.765107	+	0.928686i
$406$	−6.00928	+	2.63445i	−0.298235	+	0.130746i
$407$	7.72426	+	7.72426i	0.382877	+	0.382877i
$408$	−6.73438	−	13.7968i	−0.333402	−	0.683043i
$409$	26.7930			1.32483			0.662414	−	0.749138i	$-0.269532\pi$
$409$	26.7930			1.32483			0.662414	+	0.749138i	$0.269532\pi$
$410$	−19.5625	−	9.90049i	−0.966124	−	0.488950i
$411$	13.4154	−	13.4154i	0.661734	−	0.661734i
$412$	0.0511790	+	1.24974i	0.00252141	+	0.0615703i
$413$			11.1098i			0.546675i
$414$	7.82225	+	3.05409i	0.384443	+	0.150100i
$415$	6.02633	+	7.31475i	0.295821	+	0.359067i
$416$	15.9781	+	29.5970i	0.783390	+	1.45111i
$417$	−26.9702	−	26.9702i	−1.32074	−	1.32074i
$418$	1.52600	−	0.668995i	0.0746391	−	0.0327216i
$419$	11.0752	−	11.0752i	0.541061	−	0.541061i	−0.382779	−	0.923840i	$-0.625033\pi$
$419$	11.0752	−	11.0752i	0.541061	−	0.541061i	0.923840	+	0.382779i	$0.125033\pi$
$420$	−13.2612	−	14.8169i	−0.647080	−	0.722989i
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	0.701158	−	0.713006i	$-0.252667\pi$
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	−0.713006	+	0.701158i	$0.752667\pi$
$422$	6.48985	−	16.6221i	0.315921	−	0.809149i
$423$	0.0887804	−	0.0887804i	0.00431665	−	0.00431665i
$424$	10.7844	+	3.70967i	0.523737	+	0.180157i
$425$	−11.4693	+	7.72666i	−0.556342	+	0.374798i
$426$	−4.05631	−	9.25259i	−0.196529	−	0.448290i
$427$	−2.18064			−0.105528
$428$	−23.8405	+	25.8765i	−1.15237	+	1.25079i
$429$	8.80505	+	8.80505i	0.425112	+	0.425112i
$430$	27.9709	+	14.1560i	1.34888	+	0.682661i
$431$		−	20.7024i		−	0.997200i	−0.866832	−	0.498600i	$-0.833848\pi$
$431$		−	20.7024i		−	0.997200i	0.866832	−	0.498600i	$-0.166152\pi$
$432$	1.37909	+	16.8098i	0.0663514	+	0.808760i
$433$	−5.68221	+	5.68221i	−0.273069	+	0.273069i	−0.830335	−	0.557265i	$-0.811851\pi$
$433$	−5.68221	+	5.68221i	−0.273069	+	0.273069i	0.557265	+	0.830335i	$0.311851\pi$
$434$	−10.7704	−	4.20517i	−0.516998	−	0.201855i
$435$	−0.863851	+	8.94480i	−0.0414185	+	0.428871i
$436$	−0.975446	+	0.0399462i	−0.0467154	+	0.00191307i
$437$		−	7.69939i		−	0.368312i
$438$	4.19735	−	10.7504i	0.200557	−	0.513674i
$439$		−	18.7902i		−	0.896808i	−0.893831	−	0.448404i	$-0.851993\pi$
$439$		−	18.7902i		−	0.896808i	0.893831	−	0.448404i	$-0.148007\pi$
$440$	6.14160	+	2.79872i	0.292789	+	0.133424i
$441$		−	1.58955i		−	0.0756930i
$442$	−21.6642	−	8.45848i	−1.03046	−	0.402329i
$443$		−	12.1641i		−	0.577934i	−0.957339	−	0.288967i	$-0.906688\pi$
$443$		−	12.1641i		−	0.577934i	0.957339	−	0.288967i	$-0.0933119\pi$
$444$	−29.5489	−	27.2239i	−1.40233	−	1.29199i
$445$	−0.0606062	−	0.0735637i	−0.00287301	−	0.00348725i
$446$	9.57824	−	24.5321i	0.453543	−	1.16163i
$447$	−3.41105	+	3.41105i	−0.161337	+	0.161337i
$448$	−2.21993	−	17.9886i	−0.104882	−	0.849884i
$449$			27.2708i			1.28699i	0.765452	+	0.643493i	$0.222516\pi$
$449$			27.2708i			1.28699i	−0.765452	+	0.643493i	$0.777484\pi$
$450$	−5.87473	+	1.31746i	−0.276937	+	0.0621057i
$451$	−5.23181	−	5.23181i	−0.246356	−	0.246356i
$452$	−0.629191	−	15.3642i	−0.0295946	−	0.722672i
$453$	11.4517			0.538047
$454$	−25.0536	+	10.9834i	−1.17582	+	0.515479i
$455$	−29.9826	−	2.89559i	−1.40561	−	0.135748i
$456$	−5.50732	+	2.68819i	−0.257904	+	0.125886i
$457$	19.7514	−	19.7514i	0.923933	−	0.923933i	−0.0733714	−	0.997305i	$-0.523376\pi$
$457$	19.7514	−	19.7514i	0.923933	−	0.923933i	0.997305	+	0.0733714i	$0.0233758\pi$
$458$	24.6186	+	9.61200i	1.15035	+	0.449139i
$459$	−8.24649	−	8.24649i	−0.384913	−	0.384913i
$460$	23.2392	−	20.7993i	1.08353	−	0.969771i
$461$	12.9262	−	12.9262i	0.602035	−	0.602035i	−0.338818	−	0.940852i	$-0.610027\pi$
$461$	12.9262	−	12.9262i	0.602035	−	0.602035i	0.940852	+	0.338818i	$0.110027\pi$
$462$	−2.69424	−	6.14566i	−0.125348	−	0.285922i
$463$	14.5647	+	14.5647i	0.676879	+	0.676879i	0.959293	−	0.282414i	$-0.0911351\pi$
$463$	14.5647	+	14.5647i	0.676879	+	0.676879i	−0.282414	+	0.959293i	$0.591135\pi$
$464$	−5.29909	+	6.24629i	−0.246004	+	0.289977i
$465$	−12.2220	+	10.0692i	−0.566781	+	0.466948i
$466$	−15.0486	+	38.5431i	−0.697114	+	1.78547i
$467$		−	42.3556i		−	1.95998i	−0.199040	−	0.979991i	$-0.563782\pi$
$467$		−	42.3556i		−	1.95998i	0.199040	−	0.979991i	$-0.436218\pi$
$468$	−7.44646	−	6.86056i	−0.344213	−	0.317130i
$469$	−14.4941	+	14.4941i	−0.669274	+	0.669274i
$470$	−0.145306	−	0.443092i	−0.00670248	−	0.0204383i
$471$	6.17665			0.284605
$472$	6.08378	+	12.4639i	0.280029	+	0.573698i
$473$	7.48056	+	7.48056i	0.343956	+	0.343956i
$474$	11.9392	+	27.2337i	0.548385	+	1.25088i
$475$	3.08428	+	4.57824i	0.141517	+	0.210064i
$476$	9.21718	+	8.49196i	0.422469	+	0.389229i
$477$	−3.43315			−0.157193
$478$	8.00925	+	18.2694i	0.366335	+	0.835622i
$479$	27.0905			1.23780			0.618899	−	0.785470i	$-0.287579\pi$
$479$	27.0905			1.23780			0.618899	+	0.785470i	$0.287579\pi$
$480$	−22.9914	−	9.36093i	−1.04941	−	0.427266i
$481$	−60.8636			−2.77514
$482$	7.26871	+	16.5802i	0.331081	+	0.755207i
$483$	−31.0078			−1.41090
$484$	−14.5048	−	13.3635i	−0.659308	−	0.607433i
$485$	−0.581136	+	6.01741i	−0.0263880	+	0.273236i
$486$	−4.88500	−	11.1429i	−0.221588	−	0.505450i
$487$	21.9674	+	21.9674i	0.995436	+	0.995436i	0.999990	−	0.00455390i	$-0.00144956\pi$
$487$	21.9674	+	21.9674i	0.995436	+	0.995436i	−0.00455390	+	0.999990i	$0.501450\pi$
$488$	−2.44643	+	1.19413i	−0.110745	+	0.0540559i
$489$	15.3491			0.694111
$490$	−5.26744	−	2.66583i	−0.237959	−	0.120430i
$491$	−6.11955	+	6.11955i	−0.276171	+	0.276171i	−0.831579	−	0.555407i	$-0.812562\pi$
$491$	−6.11955	+	6.11955i	−0.276171	+	0.276171i	0.555407	+	0.831579i	$0.312562\pi$
$492$	20.0141	+	18.4394i	0.902305	+	0.831311i
$493$		−	5.66390i		−	0.255089i
$494$	−3.37640	+	8.64777i	−0.151912	+	0.389082i
$495$	−2.02233	−	0.195308i	−0.0908968	−	0.00877842i
$496$	−14.3860	+	1.18024i	−0.645951	+	0.0529945i
$497$	5.83157	+	5.83157i	0.261581	+	0.261581i
$498$	−4.72312	−	10.7736i	−0.211648	−	0.482776i
$499$	15.4115	−	15.4115i	0.689914	−	0.689914i	−0.272298	−	0.962213i	$-0.587784\pi$
$499$	15.4115	−	15.4115i	0.689914	−	0.689914i	0.962213	+	0.272298i	$0.0877838\pi$
$500$	−5.48667	+	21.6771i	−0.245371	+	0.969429i
$501$	−19.3986	−	19.3986i	−0.866667	−	0.866667i
$502$	−12.7454	−	4.97625i	−0.568853	−	0.222101i
$503$	26.4312	−	26.4312i	1.17851	−	1.17851i	0.198387	−	0.980124i	$-0.436430\pi$
$503$	26.4312	−	26.4312i	1.17851	−	1.17851i	0.980124	−	0.198387i	$-0.0635704\pi$
$504$	2.39336	+	4.90330i	0.106609	+	0.218410i
$505$	1.50940	−	15.6292i	0.0671673	−	0.695488i
$506$	9.63905	−	4.22574i	0.428508	−	0.187857i
$507$	−43.8671			−1.94820
$508$	−0.725812	−	17.7236i	−0.0322027	−	0.786358i
$509$	−0.233714	−	0.233714i	−0.0103592	−	0.0103592i	0.701908	−	0.712267i	$-0.252332\pi$
$509$	−0.233714	−	0.233714i	−0.0103592	−	0.0103592i	−0.712267	+	0.701908i	$0.752332\pi$
$510$	16.3101	−	5.34870i	0.722225	−	0.236845i
$511$			9.42101i			0.416761i
$512$	−12.3412	−	18.9656i	−0.545410	−	0.838169i
$513$	−3.29178	+	3.29178i	−0.145336	+	0.145336i
$514$	4.84827	−	12.4176i	0.213848	−	0.547716i
$515$	−1.39195	−	0.134428i	−0.0613365	−	0.00592362i
$516$	−28.6166	−	26.3650i	−1.25978	−	1.16066i
$517$		−	0.157362i		−	0.00692075i
$518$	30.5523	+	11.9287i	1.34239	+	0.524118i
$519$		−	6.85397i		−	0.300856i
$520$	−35.2228	+	13.1702i	−1.54462	+	0.577551i
$521$		−	4.50147i		−	0.197213i	−0.995127	−	0.0986064i	$-0.968562\pi$
$521$		−	4.50147i		−	0.197213i	0.995127	−	0.0986064i	$-0.0314385\pi$
$522$	0.896816	−	2.29696i	0.0392526	−	0.100535i
$523$			12.6042i			0.551141i	0.961281	+	0.275571i	$0.0888668\pi$
$523$			12.6042i			0.551141i	−0.961281	+	0.275571i	$0.911133\pi$
$524$	−4.56468	+	0.186931i	−0.199409	+	0.00816613i
$525$	18.4380	−	12.4213i	0.804699	−	0.542111i
$526$	−13.6377	−	5.32465i	−0.594632	−	0.232166i
$527$	7.05746	−	7.05746i	0.307428	−	0.307428i
$528$	−6.38805	−	5.41936i	−0.278004	−	0.235847i
$529$		−	25.6336i		−	1.11450i
$530$	−5.75770	+	11.3767i	−0.250099	+	0.494173i
$531$	−2.95227	−	2.95227i	−0.128118	−	0.128118i
$532$	3.38977	−	3.67926i	0.146965	−	0.159516i
$533$	41.2242			1.78562
$534$	0.0474999	+	0.108349i	0.00205552	+	0.00468872i
$535$	−25.0132	−	30.3610i	−1.08142	−	1.31262i
$536$	−8.32367	+	24.1978i	−0.359528	+	1.04519i
$537$	−25.6714	+	25.6714i	−1.10780	+	1.10780i
$538$	11.6238	−	29.7714i	0.501139	−	1.28354i
$539$	−1.40873	−	1.40873i	−0.0606782	−	0.0606782i
$540$	−18.8281	−	1.04317i	−0.810234	−	0.0448909i
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	−0.322955	−	0.946414i	$-0.604676\pi$
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	0.946414	+	0.322955i	$0.104676\pi$
$542$	4.65868	−	2.04235i	0.200107	−	0.0877266i
$543$	26.7672	+	26.7672i	1.14869	+	1.14869i
$544$	14.9909	+	4.47964i	0.642730	+	0.192063i
$545$	0.104924	−	1.08644i	0.00449444	−	0.0465380i
$546$	34.8272	+	13.5978i	1.49047	+	0.581932i
$547$			30.2936i			1.29526i	0.761955	+	0.647630i	$0.224240\pi$
$547$			30.2936i			1.29526i	−0.761955	+	0.647630i	$0.775760\pi$
$548$	0.791125	+	19.3185i	0.0337952	+	0.825246i
$549$	0.579476	−	0.579476i	0.0247314	−	0.0247314i
$550$	−4.03883	+	6.37401i	−0.172216	+	0.271789i
$551$	−2.26088			−0.0963169
$552$	−34.7873	+	16.9801i	−1.48064	+	0.722721i
$553$	−17.1644	−	17.1644i	−0.729904	−	0.729904i
$554$	27.1239	−	11.8911i	1.15239	−	0.505203i
$555$	34.6699	−	28.5631i	1.47165	−	1.21244i
$556$	38.8378	−	1.59047i	1.64709	−	0.0674510i
$557$	−9.72758			−0.412171			−0.206085	−	0.978534i	$-0.566072\pi$
$557$	−9.72758			−0.412171			−0.206085	+	0.978534i	$0.566072\pi$
$558$	3.97958	−	1.74464i	0.168469	−	0.0738563i
$559$	−58.9433			−2.49304
$560$	20.2624	+	0.292193i	0.856242	+	0.0123474i
$561$	5.79245			0.244557
$562$	4.23146	−	1.85506i	0.178493	−	0.0782510i
$563$	−17.7853			−0.749562			−0.374781	−	0.927113i	$-0.622282\pi$
$563$	−17.7853			−0.749562			−0.374781	+	0.927113i	$0.622282\pi$
$564$	0.0236823	+	0.578299i	0.000997205	+	0.0243508i
$565$	17.1125	+	1.65265i	0.719928	+	0.0695276i
$566$	0.000196379	0	8.60919e-5i	8.25441e−6	0	3.61871e-6i
$567$	17.3492	+	17.3492i	0.728597	+	0.728597i
$568$	9.73578	+	3.34896i	0.408504	+	0.140519i
$569$	15.7897			0.661938			0.330969	−	0.943642i	$-0.392624\pi$
$569$	15.7897			0.661938			0.330969	+	0.943642i	$0.392624\pi$
$570$	−2.13506	−	6.51058i	−0.0894280	−	0.272698i
$571$	23.3108	−	23.3108i	0.975528	−	0.975528i	−0.0241793	−	0.999708i	$-0.507697\pi$
$571$	23.3108	−	23.3108i	0.975528	−	0.975528i	0.999708	+	0.0241793i	$0.00769727\pi$
$572$	−12.6795	+	0.519245i	−0.530155	+	0.0217107i
$573$			5.74079i			0.239825i
$574$	−20.6937	−	8.07958i	−0.863739	−	0.337235i
$575$	19.4820	+	28.9187i	0.812456	+	1.20599i
$576$	5.37017	+	4.19033i	0.223757	+	0.174597i
$577$	25.7383	+	25.7383i	1.07150	+	1.07150i	0.997239	+	0.0742597i	$0.0236594\pi$
$577$	25.7383	+	25.7383i	1.07150	+	1.07150i	0.0742597	+	0.997239i	$0.476341\pi$
$578$	12.1105	−	5.30920i	0.503729	−	0.220834i
$579$	0.163026	−	0.163026i	0.00677514	−	0.00677514i
$580$	−6.10759	−	6.82407i	−0.253604	−	0.283354i
$581$	6.79020	+	6.79020i	0.281705	+	0.281705i
$582$	2.72903	−	6.98969i	0.113122	−	0.289732i
$583$	−3.04260	+	3.04260i	−0.126011	+	0.126011i
$584$	5.15902	+	10.5693i	0.213482	+	0.437362i
$585$	8.73697	−	7.19803i	0.361229	−	0.297602i
$586$	−6.27967	−	14.3242i	−0.259411	−	0.591725i
$587$	23.1327			0.954790			0.477395	−	0.878689i	$-0.341581\pi$
$587$	23.1327			0.954790			0.477395	+	0.878689i	$0.341581\pi$
$588$	5.38904	+	4.96502i	0.222240	+	0.204754i
$589$	−2.81715	−	2.81715i	−0.116079	−	0.116079i
$590$	−14.7344	+	4.83197i	−0.606607	+	0.198929i
$591$			15.3171i			0.630063i
$592$	40.8085	−	3.34797i	1.67722	−	0.137601i
$593$	−25.5047	+	25.5047i	−1.04735	+	1.04735i	−0.0485322	+	0.998822i	$0.515454\pi$
$593$	−25.5047	+	25.5047i	−1.04735	+	1.04735i	−0.998822	+	0.0485322i	$0.984546\pi$
$594$	−5.92773	−	2.31440i	−0.243218	−	0.0949609i
$595$	−10.8146	+	8.90969i	−0.443354	+	0.365261i
$596$	−0.201154	−	4.91199i	−0.00823960	−	0.201203i
$597$			21.5365i			0.881432i
$598$	−21.3272	+	54.6241i	−0.872135	+	2.23374i
$599$			11.0699i			0.452304i	0.974092	+	0.226152i	$0.0726146\pi$
$599$			11.0699i			0.452304i	−0.974092	+	0.226152i	$0.927385\pi$
$600$	13.8833	−	24.0321i	0.566784	−	0.981107i
$601$			13.7579i			0.561197i	0.959825	+	0.280599i	$0.0905330\pi$
$601$			13.7579i			0.561197i	−0.959825	+	0.280599i	$0.909467\pi$
$602$	29.5884	+	11.5524i	1.20593	+	0.470839i
$603$		−	7.70322i		−	0.313700i
$604$	−7.90768	+	8.58300i	−0.321759	+	0.349237i
$605$	17.0185	−	14.0209i	0.691902	−	0.570030i
$606$	−7.08817	+	18.1545i	−0.287937	+	0.737476i
$607$	−18.4675	+	18.4675i	−0.749573	+	0.749573i	−0.974399	−	0.224826i	$-0.927819\pi$
$607$	−18.4675	+	18.4675i	−0.749573	+	0.749573i	0.224826	+	0.974399i	$0.427819\pi$
$608$	1.78815	−	5.98398i	0.0725193	−	0.242683i
$609$			9.10526i			0.368964i
$610$	−0.948426	−	2.89210i	−0.0384007	−	0.117098i
$611$	0.619968	+	0.619968i	0.0250812	+	0.0250812i
$612$	−4.70598	+	0.192718i	−0.190228	+	0.00779015i
$613$	−11.6810			−0.471790			−0.235895	−	0.971779i	$-0.575802\pi$
$613$	−11.6810			−0.471790			−0.235895	+	0.971779i	$0.575802\pi$
$614$	−19.5988	+	8.59208i	−0.790944	+	0.346748i
$615$	−23.4826	+	19.3464i	−0.946912	+	0.780122i
$616$	6.46660	+	2.22441i	0.260547	+	0.0896240i
$617$	−29.1000	+	29.1000i	−1.17152	+	1.17152i	−0.189677	+	0.981847i	$0.560744\pi$
$617$	−29.1000	+	29.1000i	−1.17152	+	1.17152i	−0.981847	+	0.189677i	$0.939256\pi$
$618$	1.61686	+	0.631279i	0.0650395	+	0.0253938i
$619$	4.23279	+	4.23279i	0.170130	+	0.170130i	0.787036	−	0.616906i	$-0.211614\pi$
$619$	4.23279	+	4.23279i	0.170130	+	0.170130i	−0.616906	+	0.787036i	$0.711614\pi$
$620$	0.892760	−	16.1134i	0.0358541	−	0.647129i
$621$	−20.7927	+	20.7927i	−0.834383	+	0.834383i
$622$	−15.4194	−	35.1723i	−0.618263	−	1.41028i
$623$	−0.0682883	−	0.0682883i	−0.00273591	−	0.00273591i
$624$	46.5185	−	3.81642i	1.86223	−	0.152779i
$625$	−23.1689	−	9.39149i	−0.926758	−	0.375660i
$626$	9.94314	−	25.4668i	0.397408	−	1.01786i
$627$		−	2.31220i		−	0.0923402i
$628$	−4.26513	+	4.62938i	−0.170197	+	0.184732i
$629$	−20.0197	+	20.0197i	−0.798239	+	0.798239i
$630$	−5.79653	+	1.90090i	−0.230939	+	0.0757336i
$631$	−1.33886			−0.0532991			−0.0266496	−	0.999645i	$-0.508484\pi$
$631$	−1.33886			−0.0532991			−0.0266496	+	0.999645i	$0.508484\pi$
$632$	−28.6559	−	9.85718i	−1.13987	−	0.392097i
$633$	−17.5096	−	17.5096i	−0.695944	−	0.695944i
$634$	−14.6676	−	33.4573i	−0.582524	−	1.32876i
$635$	19.7404	+	1.90644i	0.783373	+	0.0756548i
$636$	10.7235	−	11.6393i	0.425216	−	0.461530i
$637$	11.1001			0.439803
$638$	−1.24086	−	2.83045i	−0.0491263	−	0.112059i
$639$	−3.09933			−0.122608
$640$	22.8921	−	10.7680i	0.904891	−	0.425643i
$641$	24.5069			0.967965			0.483982	−	0.875078i	$-0.339190\pi$
$641$	24.5069			0.967965			0.483982	+	0.875078i	$0.339190\pi$
$642$	19.6041	+	44.7175i	0.773710	+	1.76486i
$643$	−10.8979			−0.429771			−0.214885	−	0.976639i	$-0.568938\pi$
$643$	−10.8979			−0.429771			−0.214885	+	0.976639i	$0.568938\pi$
$644$	21.4117	−	23.2402i	0.843738	−	0.915793i
$645$	33.5760	−	27.6619i	1.32205	−	1.08919i
$646$	1.73390	+	3.95509i	0.0682194	+	0.155611i
$647$	−11.6612	−	11.6612i	−0.458448	−	0.458448i	0.439698	−	0.898146i	$-0.355085\pi$
$647$	−11.6612	−	11.6612i	−0.458448	−	0.458448i	−0.898146	+	0.439698i	$0.855085\pi$
$648$	28.9644	+	9.96331i	1.13783	+	0.391396i
$649$	−5.23285			−0.205407
$650$	−9.20006	−	41.0242i	−0.360856	−	1.60910i
$651$	−11.3455	+	11.3455i	−0.444666	+	0.444666i
$652$	−10.5990	+	11.5041i	−0.415087	+	0.450536i
$653$		−	5.28393i		−	0.206776i	−0.994641	−	0.103388i	$-0.967032\pi$
$653$		−	5.28393i		−	0.206776i	0.994641	−	0.103388i	$-0.0329684\pi$
$654$	−0.492726	+	1.26199i	−0.0192671	+	0.0493476i
$655$	0.491000	−	5.08409i	0.0191849	−	0.198652i
$656$	−27.6405	+	2.26765i	−1.07918	+	0.0885369i
$657$	−2.50351	−	2.50351i	−0.0976713	−	0.0976713i
$658$	−0.189703	−	0.432720i	−0.00739540	−	0.0168692i
$659$	−16.2902	+	16.2902i	−0.634578	+	0.634578i	−0.949213	−	0.314635i	$-0.898118\pi$
$659$	−16.2902	+	16.2902i	−0.634578	+	0.634578i	0.314635	+	0.949213i	$0.398118\pi$
$660$	6.97895	−	6.24621i	0.271655	−	0.243133i
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	0.413114	−	0.910679i	$-0.364441\pi$
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	−0.910679	+	0.413114i	$0.864441\pi$
$662$	−25.3757	−	9.90761i	−0.986256	−	0.385070i
$663$	−22.8209	+	22.8209i	−0.886291	+	0.886291i
$664$	11.3362	+	3.89948i	0.439930	+	0.151329i
$665$	3.55652	+	4.31690i	0.137916	+	0.167402i
$666$	−11.2888	+	4.94897i	−0.437431	+	0.191769i
$667$	−14.2810			−0.552962
$668$	27.9344	−	1.14396i	1.08082	−	0.0442613i
$669$	−25.8420	−	25.8420i	−0.999111	−	0.999111i
$670$	−25.5268	−	12.9190i	−0.986188	−	0.499105i
$671$		−	1.02711i		−	0.0396512i
$672$	−24.0993	−	7.20144i	−0.929651	−	0.277802i
$673$	11.9553	−	11.9553i	0.460841	−	0.460841i	−0.438090	−	0.898931i	$-0.644345\pi$
$673$	11.9553	−	11.9553i	0.460841	−	0.460841i	0.898931	+	0.438090i	$0.144345\pi$
$674$	−11.7046	+	29.9782i	−0.450843	+	1.15472i
$675$	4.03454	−	20.6931i	0.155290	−	0.796480i
$676$	30.2913	−	32.8782i	1.16505	−	1.26455i
$677$		−	3.18699i		−	0.122486i	−0.998123	−	0.0612430i	$-0.980494\pi$
$677$		−	3.18699i		−	0.122486i	0.998123	−	0.0612430i	$-0.0195065\pi$
$678$	−19.8775	−	7.76090i	−0.763391	−	0.298056i
$679$			6.12535i			0.235069i
$680$	−7.25373	+	15.9178i	−0.278168	+	0.610420i
$681$			37.9613i			1.45468i
$682$	1.98069	−	5.07303i	0.0758447	−	0.194256i
$683$		−	35.1661i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$683$		−	35.1661i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$684$	0.0769279	+	1.87850i	0.00294141	+	0.0718264i
$685$	−21.5167	−	2.07799i	−0.822112	−	0.0793961i
$686$	−26.4647	−	10.3328i	−1.01043	−	0.394508i
$687$	25.9331	−	25.9331i	0.989410	−	0.989410i
$688$	39.5210	−	3.24234i	1.50672	−	0.123613i
$689$		−	23.9743i		−	0.913346i
$690$	−13.4862	−	41.1244i	−0.513412	−	1.56558i
$691$	2.90121	+	2.90121i	0.110367	+	0.110367i	0.760134	−	0.649767i	$-0.225133\pi$
$691$	2.90121	+	2.90121i	0.110367	+	0.110367i	−0.649767	+	0.760134i	$0.725133\pi$
$692$	5.13703	+	4.73284i	0.195280	+	0.179916i
$693$	−2.05860			−0.0781999
$694$	3.16594	+	7.22163i	0.120178	+	0.274129i
$695$	−4.17758	+	43.2571i	−0.158465	+	1.64083i
$696$	4.98611	+	10.2151i	0.188998	+	0.387202i
$697$	13.5598	−	13.5598i	0.513614	−	0.513614i
$698$	−10.9699	+	28.0966i	−0.415218	+	1.06347i
$699$	40.6011	+	40.6011i	1.53568	+	1.53568i
$700$	−3.42214	+	22.3964i	−0.129345	+	0.846506i
$701$	15.7397	−	15.7397i	0.594481	−	0.594481i	−0.344358	−	0.938839i	$-0.611903\pi$
$701$	15.7397	−	15.7397i	0.594481	−	0.594481i	0.938839	+	0.344358i	$0.111903\pi$
$702$	32.4721	−	14.2357i	1.22558	−	0.537291i
$703$	7.99136	+	7.99136i	0.301400	+	0.301400i
$704$	8.47290	−	1.04562i	0.319335	−	0.0394082i
$705$	−0.644103	−	0.0622047i	−0.0242583	−	0.00234276i
$706$	4.80440	+	1.87581i	0.180816	+	0.0705971i
$707$		−	15.9095i		−	0.598339i
$708$	19.2306	−	0.787524i	0.722729	−	0.0295970i
$709$	1.95755	−	1.95755i	0.0735172	−	0.0735172i	−0.669392	−	0.742909i	$-0.733445\pi$
$709$	1.95755	−	1.95755i	0.0735172	−	0.0735172i	0.742909	+	0.669392i	$0.233445\pi$
$710$	−5.19785	+	10.2705i	−0.195072	+	0.385445i
$711$	9.12243			0.342118
$712$	−0.114007	−	0.0392167i	−0.00427260	−	0.00146971i
$713$	−17.7947	−	17.7947i	−0.666416	−	0.666416i
$714$	15.9283	−	6.98294i	0.596103	−	0.261330i
$715$	1.36387	−	14.1222i	0.0510057	−	0.528142i
$716$	−1.51388	−	36.9674i	−0.0565762	−	1.38154i
$717$	27.6818			1.03379
$718$	7.47633	−	3.27760i	0.279014	−	0.122319i
$719$	0.0658604			0.00245618			0.00122809	−	0.999999i	$-0.499609\pi$
$719$	0.0658604			0.00245618			0.00122809	+	0.999999i	$0.499609\pi$
$720$	−5.46211	+	5.30682i	−0.203561	+	0.197773i
$721$	−1.41692			−0.0527687
$722$	−23.0303	+	10.0964i	−0.857100	+	0.375750i
$723$	25.1223			0.934309
$724$	−38.5454	+	1.57850i	−1.43253	+	0.0586644i
$725$	8.49181	−	5.72078i	0.315378	−	0.212465i
$726$	−25.0659	+	10.9888i	−0.930283	+	0.407834i
$727$	−16.2286	−	16.2286i	−0.601885	−	0.601885i	0.338927	−	0.940813i	$-0.389936\pi$
$727$	−16.2286	−	16.2286i	−0.601885	−	0.601885i	−0.940813	+	0.338927i	$0.889936\pi$
$728$	−34.2406	+	16.7132i	−1.26904	+	0.619434i
$729$	15.6045			0.577943
$730$	−12.4947	+	4.09749i	−0.462451	+	0.151655i
$731$	−19.3881	+	19.3881i	−0.717095	+	0.717095i
$732$	0.154576	+	3.77460i	0.00571330	+	0.139513i
$733$			0.669106i			0.0247140i	0.999924	+	0.0123570i	$0.00393345\pi$
$733$			0.669106i			0.0247140i	−0.999924	+	0.0123570i	$0.996067\pi$
$734$	15.4724	+	6.04100i	0.571098	+	0.222977i
$735$	−6.32298	+	5.20925i	−0.233227	+	0.192146i
$736$	11.2950	−	37.7981i	0.416338	−	1.39326i
$737$	−6.82691	−	6.82691i	−0.251472	−	0.251472i
$738$	7.64614	−	3.35205i	0.281458	−	0.123391i
$739$	−23.4183	+	23.4183i	−0.861454	+	0.861454i	−0.991507	−	0.130053i	$-0.958485\pi$
$739$	−23.4183	+	23.4183i	−0.861454	+	0.861454i	0.130053	+	0.991507i	$0.458485\pi$
$740$	−2.53247	+	45.7085i	−0.0930956	+	1.68028i
$741$	9.10952	+	9.10952i	0.334647	+	0.334647i
$742$	−4.69874	+	12.0346i	−0.172496	+	0.441804i
$743$	30.0968	−	30.0968i	1.10414	−	1.10414i	0.110238	−	0.993905i	$-0.464839\pi$
$743$	30.0968	−	30.0968i	1.10414	−	1.10414i	0.993905	−	0.110238i	$-0.0351614\pi$
$744$	−6.51552	+	18.9413i	−0.238871	+	0.694422i
$745$	5.47092	+	0.528358i	0.200439	+	0.0193575i
$746$	9.11257	+	20.7861i	0.333635	+	0.761033i
$747$	−3.60882			−0.132040
$748$	−3.99983	+	4.34142i	−0.146248	+	0.158738i
$749$	−28.1838	−	28.1838i	−1.02981	−	1.02981i
$750$	24.4932	+	19.0511i	0.894364	+	0.695650i
$751$			53.2724i			1.94394i	0.235107	+	0.971970i	$0.424456\pi$
$751$			53.2724i			1.94394i	−0.235107	+	0.971970i	$0.575544\pi$
$752$	−0.449786	−	0.381580i	−0.0164020	−	0.0139148i
$753$	−13.4259	+	13.4259i	−0.489267	+	0.489267i
$754$	16.0401	+	6.26262i	0.584144	+	0.228071i
$755$	−8.29666	−	10.0705i	−0.301946	−	0.366502i
$756$	−19.0904	+	0.781783i	−0.694311	+	0.0284332i
$757$		−	27.1717i		−	0.987574i	−0.869583	−	0.493787i	$-0.835612\pi$
$757$		−	27.1717i		−	0.987574i	0.869583	−	0.493787i	$-0.164388\pi$
$758$	6.48377	−	16.6065i	0.235501	−	0.603174i
$759$		−	14.6051i		−	0.530132i
$760$	6.35398	+	2.89550i	0.230483	+	0.105031i
$761$		−	12.9068i		−	0.467870i	−0.972252	−	0.233935i	$-0.924840\pi$
$761$		−	12.9068i		−	0.467870i	0.972252	−	0.233935i	$-0.0751604\pi$
$762$	−22.9300	−	8.95270i	−0.830666	−	0.324322i
$763$		−	1.10593i		−	0.0400374i
$764$	−4.30270	−	3.96416i	−0.155666	−	0.143418i
$765$	0.506198	−	5.24147i	0.0183016	−	0.189506i
$766$	18.1069	−	46.3761i	0.654229	−	1.67564i
$767$	20.6162	−	20.6162i	0.744409	−	0.744409i
$768$	−30.9803	+	5.11775i	−1.11791	+	0.184671i
$769$		−	34.4858i		−	1.24359i	−0.783180	−	0.621795i	$-0.786404\pi$
$769$		−	34.4858i		−	1.24359i	0.783180	−	0.621795i	$-0.213596\pi$
$770$	−3.45247	+	6.82177i	−0.124418	+	0.245840i
$771$	−13.0806	−	13.0806i	−0.471087	−	0.471087i
$772$	0.00961387	+	0.234761i	0.000346011	+	0.00844925i
$773$	26.6789			0.959574			0.479787	−	0.877385i	$-0.340714\pi$
$773$	26.6789			0.959574			0.479787	+	0.877385i	$0.340714\pi$
$774$	−10.9326	+	4.79283i	−0.392965	+	0.172275i
$775$	17.7095	+	3.45281i	0.636143	+	0.124029i
$776$	3.35429	+	6.87196i	0.120412	+	0.246689i
$777$	32.1836	−	32.1836i	1.15458	−	1.15458i
$778$	−30.8927	−	12.0616i	−1.10756	−	0.432431i
$779$	−5.41272	−	5.41272i	−0.193931	−	0.193931i
$780$	−2.88682	+	52.1041i	−0.103365	+	1.86562i
$781$	−2.74675	+	2.74675i	−0.0982864	+	0.0982864i
$782$	10.9523	+	24.9825i	0.391652	+	0.893373i
$783$	6.10566	+	6.10566i	0.218199	+	0.218199i
$784$	−7.44253	+	0.610593i	−0.265805	+	0.0218069i
$785$	−4.47493	−	5.43167i	−0.159717	−	0.193865i
$786$	−2.30575	+	5.90557i	−0.0822433	+	0.210645i
$787$		−	33.2611i		−	1.18563i	−0.805338	−	0.592815i	$-0.798016\pi$
$787$		−	33.2611i		−	1.18563i	0.805338	−	0.592815i	$-0.201984\pi$
$788$	−11.4802	−	10.5769i	−0.408963	−	0.376786i
$789$	−14.3659	+	14.3659i	−0.511439	+	0.511439i
$790$	15.2991	−	30.2298i	0.544319	−	1.07553i
$791$	17.4195			0.619365
$792$	−2.30952	+	1.12731i	−0.0820653	+	0.0400571i
$793$	4.04658	+	4.04658i	0.143698	+	0.143698i
$794$	−4.89762	−	11.1716i	−0.173810	−	0.396466i
$795$	11.2510	+	13.6565i	0.399033	+	0.484346i
$796$	−16.1416	−	14.8715i	−0.572122	−	0.527107i
$797$	15.9072			0.563461			0.281730	−	0.959494i	$-0.409092\pi$
$797$	15.9072			0.563461			0.281730	+	0.959494i	$0.409092\pi$
$798$	−2.78741	−	6.35818i	−0.0986732	−	0.225077i
$799$	0.407850			0.0144287
$800$	8.42521	+	27.0003i	0.297876	+	0.954605i
$801$	0.0362935			0.00128237
$802$	11.1921	+	25.5296i	0.395208	+	0.901483i
$803$	−4.43743			−0.156593
$804$	26.1161	+	24.0613i	0.921044	+	0.848575i
$805$	22.4649	+	27.2679i	0.791784	+	0.961067i
$806$	12.1831	+	27.7900i	0.429131	+	0.978863i
$807$	−31.3610	−	31.3610i	−1.10396	−	1.10396i
$808$	−8.71217	−	17.8487i	−0.306493	−	0.627915i
$809$	−12.4922			−0.439204			−0.219602	−	0.975590i	$-0.570476\pi$
$809$	−12.4922			−0.439204			−0.219602	+	0.975590i	$0.570476\pi$
$810$	−15.4639	+	30.5553i	−0.543345	+	1.07360i
$811$	−35.4886	+	35.4886i	−1.24617	+	1.24617i	−0.288777	+	0.957396i	$0.593249\pi$
$811$	−35.4886	+	35.4886i	−1.24617	+	1.24617i	−0.957396	+	0.288777i	$0.906751\pi$
$812$	−6.82436	−	6.28741i	−0.239488	−	0.220645i
$813$		−	7.05884i		−	0.247564i
$814$	−5.61859	+	14.3906i	−0.196932	+	0.504389i
$815$	−11.1203	−	13.4978i	−0.389528	−	0.472809i
$816$	14.0459	−	16.5566i	0.491705	−	0.579595i
$817$	7.73923	+	7.73923i	0.270761	+	0.270761i
$818$	15.2136	+	34.7027i	0.531930	+	1.21335i
$819$	8.11042	−	8.11042i	0.283401	−	0.283401i
$820$	1.71530	−	30.9593i	0.0599009	−	1.08115i
$821$	−15.9683	−	15.9683i	−0.557299	−	0.557299i	0.371239	−	0.928537i	$-0.378933\pi$
$821$	−15.9683	−	15.9683i	−0.557299	−	0.557299i	−0.928537	+	0.371239i	$0.878933\pi$
$822$	24.9934	+	9.75833i	0.871745	+	0.340361i
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	−0.975846	−	0.218462i	$-0.929896\pi$
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	0.218462	+	0.975846i	$0.429896\pi$
$824$	−1.58962	+	0.775914i	−0.0553771	+	0.0270302i
$825$	5.85062	+	8.68454i	0.203693	+	0.302357i
$826$	−14.3895	+	6.30833i	−0.500675	+	0.219495i
$827$	−39.2381			−1.36444			−0.682221	−	0.731146i	$-0.738986\pi$
$827$	−39.2381			−1.36444			−0.682221	+	0.731146i	$0.738986\pi$
$828$	0.485919	+	11.8657i	0.0168869	+	0.412360i
$829$	18.6072	+	18.6072i	0.646254	+	0.646254i	0.952086	−	0.305831i	$-0.0989344\pi$
$829$	18.6072	+	18.6072i	0.646254	+	0.646254i	−0.305831	+	0.952086i	$0.598934\pi$
$830$	−6.05231	+	11.9588i	−0.210079	+	0.415098i
$831$		−	41.0982i		−	1.42568i
$832$	−29.2618	+	37.5008i	−1.01447	+	1.30011i
$833$	3.65114	−	3.65114i	0.126504	−	0.126504i
$834$	19.6180	−	50.2465i	0.679317	−	1.73989i
$835$	−3.00477	+	31.1131i	−0.103984	+	1.07671i
$836$	1.73298	+	1.59663i	0.0599365	+	0.0552206i
$837$			15.2158i			0.525935i
$838$	20.6335	+	8.05608i	0.712774	+	0.278293i
$839$			12.5955i			0.434845i	0.976078	+	0.217422i	$0.0697649\pi$
$839$			12.5955i			0.434845i	−0.976078	+	0.217422i	$0.930235\pi$
$840$	11.6611	−	25.5894i	0.402345	−	0.882918i
$841$		−	24.8065i		−	0.855396i
$842$	0.176824	−	0.452889i	0.00609377	−	0.0156076i
$843$		−	6.41151i		−	0.220824i
$844$	25.2142	−	1.03256i	0.867909	−	0.0355423i
$845$	31.7814	+	38.5762i	1.09331	+	1.32706i
$846$	0.165401	+	0.0645785i	0.00568660	+	0.00222025i
$847$	15.7981	−	15.7981i	0.542829	−	0.542829i
$848$	1.31877	+	16.0745i	0.0452867	+	0.552002i
$849$		0	0.000297553i		0	1.02120e-5i
$850$	−16.5202	−	10.4679i	−0.566637	−	0.359044i
$851$	50.4778	+	50.4778i	1.73036	+	1.73036i
$852$	9.68085	−	10.5076i	0.331660	−	0.359984i
$853$	−43.6914			−1.49597			−0.747983	−	0.663718i	$-0.768978\pi$
$853$	−43.6914			−1.49597			−0.747983	+	0.663718i	$0.768978\pi$
$854$	−1.23821	−	2.82439i	−0.0423706	−	0.0966488i
$855$	−2.09226	−	0.202061i	−0.0715537	−	0.00691035i
$856$	−47.0527	−	16.1854i	−1.60823	−	0.553206i
$857$	−28.9373	+	28.9373i	−0.988478	+	0.988478i	−0.999934	−	0.0114561i	$-0.996353\pi$
$857$	−28.9373	+	28.9373i	−0.988478	+	0.988478i	0.0114561	+	0.999934i	$0.496353\pi$
$858$	−6.40475	+	16.4041i	−0.218655	+	0.560027i
$859$	28.1247	+	28.1247i	0.959602	+	0.959602i	0.999215	−	0.0396134i	$-0.0126126\pi$
$859$	28.1247	+	28.1247i	0.959602	+	0.959602i	−0.0396134	+	0.999215i	$0.512613\pi$
$860$	−2.45257	+	44.2664i	−0.0836321	+	1.50947i
$861$	−21.7987	+	21.7987i	−0.742896	+	0.742896i
$862$	26.8141	−	11.7552i	0.913291	−	0.400384i
$863$	−22.2144	−	22.2144i	−0.756186	−	0.756186i	0.219440	−	0.975626i	$-0.429577\pi$
$863$	−22.2144	−	22.2144i	−0.756186	−	0.756186i	−0.975626	+	0.219440i	$0.929577\pi$
$864$	−20.9892	+	11.3311i	−0.714066	+	0.385492i
$865$	−6.02730	+	4.96565i	−0.204934	+	0.168837i
$866$	−10.5861	−	4.13322i	−0.359732	−	0.140452i
$867$		−	18.3498i		−	0.623192i
$868$	−0.669061	−	16.3378i	−0.0227094	−	0.554541i
$869$	8.08466	−	8.08466i	0.274253	−	0.274253i
$870$	−12.0760	+	3.96016i	−0.409413	+	0.134262i
$871$	53.7929			1.82270
$872$	−0.605616	−	1.24073i	−0.0205087	−	0.0420164i
$873$	−1.62773	−	1.62773i	−0.0550904	−	0.0550904i
$874$	9.97237	−	4.37186i	0.337320	−	0.147880i
$875$	−24.2813	−	7.21497i	−0.820859	−	0.243911i
$876$	16.3074	−	0.667816i	0.550976	−	0.0225634i
$877$	−5.13889			−0.173528			−0.0867640	−	0.996229i	$-0.527653\pi$
$877$	−5.13889			−0.173528			−0.0867640	+	0.996229i	$0.527653\pi$
$878$	24.3374	−	10.6694i	0.821346	−	0.360076i
$879$	−21.7040			−0.732057
$880$	−0.137627	+	9.54386i	−0.00463941	+	0.321724i
$881$	−4.34528			−0.146396			−0.0731982	−	0.997317i	$-0.523321\pi$
$881$	−4.34528			−0.146396			−0.0731982	+	0.997317i	$0.523321\pi$
$882$	2.05881	−	0.902579i	0.0693239	−	0.0303914i
$883$	35.4317			1.19237			0.596186	−	0.802846i	$-0.296682\pi$
$883$	35.4317			1.19237			0.596186	+	0.802846i	$0.296682\pi$
$884$	−1.34578	−	32.8626i	−0.0452635	−	1.10529i
$885$	−2.06853	+	21.4188i	−0.0695330	+	0.719985i
$886$	15.7551	−	6.90701i	0.529304	−	0.232046i
$887$	37.4644	+	37.4644i	1.25793	+	1.25793i	0.952078	+	0.305855i	$0.0989422\pi$
$887$	37.4644	+	37.4644i	1.25793	+	1.25793i	0.305855	+	0.952078i	$0.401058\pi$
$888$	18.4824	−	53.7304i	0.620230	−	1.80307i
$889$	20.0945			0.673947
$890$	0.0608675	−	0.120269i	0.00204028	−	0.00403142i
$891$	−8.17171	+	8.17171i	−0.273763	+	0.273763i
$892$	37.2131	−	1.52394i	1.24599	−	0.0510253i
$893$		−	0.162803i		−	0.00544799i
$894$	−6.35491	−	2.48119i	−0.212540	−	0.0829833i
$895$	41.1739	+	3.97640i	1.37629	+	0.132916i
$896$	22.0386	−	13.0896i	0.736259	−	0.437292i
$897$	57.5407	+	57.5407i	1.92123	+	1.92123i
$898$	−35.3215	+	15.4849i	−1.17869	+	0.516736i
$899$	−5.22531	+	5.22531i	−0.174274	+	0.174274i
$900$	−5.04218	−	6.86095i	−0.168073	−	0.228698i
$901$	−7.88580	−	7.88580i	−0.262714	−	0.262714i
$902$	3.80560	−	9.74703i	0.126712	−	0.324541i
$903$	31.1682	−	31.1682i	1.03721	−	1.03721i
$904$	19.5427	−	9.53903i	0.649980	−	0.317263i
$905$	4.14613	−	42.9314i	0.137822	−	1.42709i
$906$	6.50248	+	14.8324i	0.216031	+	0.492773i
$907$	0.181405			0.00602345			0.00301173	−	0.999995i	$-0.499041\pi$
$907$	0.181405			0.00602345			0.00301173	+	0.999995i	$0.499041\pi$
$908$	−28.4518	−	26.2132i	−0.944208	−	0.869916i
$909$	4.22775	+	4.22775i	0.140226	+	0.140226i
$910$	−13.2743	−	40.4781i	−0.440039	−	1.34184i
$911$		−	23.4249i		−	0.776101i	−0.921638	−	0.388050i	$-0.873149\pi$
$911$		−	23.4249i		−	0.776101i	0.921638	−	0.388050i	$-0.126851\pi$
$912$	−6.60895	−	5.60676i	−0.218844	−	0.185658i
$913$	−3.19828	+	3.19828i	−0.105848	+	0.105848i
$914$	36.7976	+	14.3671i	1.21716	+	0.475222i
$915$	−4.20411	−	0.406015i	−0.138984	−	0.0134224i
$916$	1.52931	+	37.3443i	0.0505299	+	1.23389i
$917$		−	5.17529i		−	0.170903i
$918$	5.99846	−	15.3635i	0.197979	−	0.507071i
$919$		−	3.05885i		−	0.100902i	−0.998727	−	0.0504511i	$-0.983934\pi$
$919$		−	3.05885i		−	0.100902i	0.998727	−	0.0504511i	$-0.0160659\pi$
$920$	40.1352	+	18.2896i	1.32322	+	0.602989i
$921$			29.6962i			0.978522i
$922$	24.0820	+	9.40249i	0.793099	+	0.309654i
$923$		−	21.6431i		−	0.712392i
$924$	6.43011	−	6.97925i	0.211535	−	0.229600i
$925$	−50.2361	−	9.79453i	−1.65175	−	0.322042i
$926$	−10.5943	+	27.1345i	−0.348150	+	0.891696i
$927$	0.376527	−	0.376527i	0.0123668	−	0.0123668i
$928$	−11.0992	−	3.31670i	−0.364349	−	0.108876i
$929$		−	59.9772i		−	1.96779i	−0.178752	−	0.983894i	$-0.557206\pi$
$929$		−	59.9772i		−	1.96779i	0.178752	−	0.983894i	$-0.442794\pi$
$930$	−19.9817	−	10.1126i	−0.655224	−	0.331606i
$931$	−1.45744	−	1.45744i	−0.0477657	−	0.0477657i
$932$	−58.4665	+	2.39430i	−1.91513	+	0.0784280i
$933$	−53.2931			−1.74474
$934$	54.8596	−	24.0503i	1.79506	−	0.786950i
$935$	−4.19659	−	5.09381i	−0.137243	−	0.166586i
$936$	4.65766	−	13.5403i	0.152240	−	0.442579i
$937$	−23.7463	+	23.7463i	−0.775759	+	0.775759i	−0.979107	−	0.203347i	$-0.934818\pi$
$937$	−23.7463	+	23.7463i	−0.775759	+	0.775759i	0.203347	+	0.979107i	$0.434818\pi$
$938$	−27.0029	−	10.5429i	−0.881677	−	0.344239i
$939$	−26.8266	−	26.8266i	−0.875451	−	0.875451i
$940$	0.491392	−	0.439799i	0.0160274	−	0.0143447i
$941$	−35.2727	+	35.2727i	−1.14986	+	1.14986i	−0.163278	+	0.986580i	$0.552207\pi$
$941$	−35.2727	+	35.2727i	−1.14986	+	1.14986i	−0.986580	+	0.163278i	$0.947793\pi$
$942$	3.50722	+	8.00008i	0.114271	+	0.260657i
$943$	−34.1897	−	34.1897i	−1.11337	−	1.11337i
$944$	−12.6889	+	14.9570i	−0.412990	+	0.486810i
$945$	2.05346	−	21.2627i	0.0667989	−	0.691674i
$946$	−5.44133	+	13.9365i	−0.176913	+	0.453116i
$947$		−	19.9140i		−	0.647118i	−0.946208	−	0.323559i	$-0.895121\pi$
$947$		−	19.9140i		−	0.647118i	0.946208	−	0.323559i	$-0.104879\pi$
$948$	−28.4942	+	30.9276i	−0.925448	+	1.00448i
$949$	17.4824	−	17.4824i	0.567504	−	0.567504i
$950$	−4.17849	+	6.59442i	−0.135568	+	0.213951i
$951$	−50.6945			−1.64388
$952$	−5.76523	+	16.7601i	−0.186852	+	0.543199i
$953$	23.1060	+	23.1060i	0.748477	+	0.748477i	0.974193	−	0.225716i	$-0.0724722\pi$
$953$	23.1060	+	23.1060i	0.748477	+	0.748477i	−0.225716	+	0.974193i	$0.572472\pi$
$954$	−1.94941	−	4.44667i	−0.0631144	−	0.143966i
$955$	5.04838	−	4.15916i	0.163362	−	0.134587i
$956$	−19.1150	+	20.7474i	−0.618222	+	0.671019i
$957$	−4.28871			−0.138634
$958$	15.3825	+	35.0881i	0.496987	+	1.13364i
$959$	−21.9027			−0.707276
$960$	−0.930539	−	35.0941i	−0.0300330	−	1.13266i
$961$	17.9781			0.579939
$962$	−34.5595	−	78.8314i	−1.11424	−	2.54163i
$963$	14.9790			0.482690
$964$	−17.3476	+	18.8291i	−0.558728	+	0.606444i
$965$	−0.261475	−	0.0252521i	−0.00841717	−	0.000812894i
$966$	−17.6068	−	40.1617i	−0.566490	−	1.29218i
$967$	−41.7332	−	41.7332i	−1.34205	−	1.34205i	−0.894018	−	0.448030i	$-0.852126\pi$
$967$	−41.7332	−	41.7332i	−1.34205	−	1.34205i	−0.448030	−	0.894018i	$-0.647874\pi$
$968$	9.07255	−	26.3749i	0.291603	−	0.847721i
$969$	5.99275			0.192515
$970$	−8.12382	+	2.66410i	−0.260840	+	0.0855392i
$971$	33.5030	−	33.5030i	1.07516	−	1.07516i	0.0782268	−	0.996936i	$-0.475074\pi$
$971$	33.5030	−	33.5030i	1.07516	−	1.07516i	0.996936	−	0.0782268i	$-0.0249258\pi$
$972$	11.6586	−	12.6543i	0.373950	−	0.405885i
$973$			44.0330i			1.41163i
$974$	−15.9790	+	40.9259i	−0.511999	+	1.31135i
$975$	−57.2652	−	11.1650i	−1.83395	−	0.357566i
$976$	−2.93579	−	2.49060i	−0.0939723	−	0.0797223i
$977$	9.16848	+	9.16848i	0.293326	+	0.293326i	0.838393	−	0.545067i	$-0.183496\pi$
$977$	9.16848	+	9.16848i	0.293326	+	0.293326i	−0.545067	+	0.838393i	$0.683496\pi$
$978$	8.71552	+	19.8804i	0.278692	+	0.635706i
$979$	0.0321648	−	0.0321648i	0.00102799	−	0.00102799i
$980$	0.461865	−	8.33618i	0.0147537	−	0.266289i
$981$	0.293887	+	0.293887i	0.00938308	+	0.00938308i
$982$	−11.4009	−	4.45134i	−0.363818	−	0.142048i
$983$	−39.1183	+	39.1183i	−1.24768	+	1.24768i	−0.290936	+	0.956742i	$0.593967\pi$
$983$	−39.1183	+	39.1183i	−1.24768	+	1.24768i	−0.956742	+	0.290936i	$0.906033\pi$
$984$	−12.5186	+	36.3928i	−0.399077	+	1.16016i
$985$	13.4697	−	11.0972i	0.429181	−	0.353585i
$986$	7.33597	−	3.21607i	0.233625	−	0.102421i
$987$	−0.655657			−0.0208698
$988$	−13.1179	+	0.537201i	−0.417336	+	0.0170906i
$989$	48.8852	+	48.8852i	1.55446	+	1.55446i
$990$	−0.895350	−	2.73025i	−0.0284561	−	0.0867729i
$991$		−	12.9925i		−	0.412722i	−0.978476	−	0.206361i	$-0.933838\pi$
$991$		−	12.9925i		−	0.412722i	0.978476	−	0.206361i	$-0.0661621\pi$
$992$	−9.69732	−	17.9628i	−0.307890	−	0.570320i
$993$	−26.7307	+	26.7307i	−0.848273	+	0.848273i
$994$	−4.24186	+	10.8644i	−0.134544	+	0.344598i
$995$	18.9390	−	15.6031i	0.600406	−	0.494650i
$996$	11.2722	−	12.2349i	0.357175	−	0.387678i
$997$		−	8.89509i		−	0.281710i	−0.990030	−	0.140855i	$-0.955015\pi$
$997$		−	8.89509i		−	0.281710i	0.990030	−	0.140855i	$-0.0449852\pi$
$998$	28.7122	+	11.2103i	0.908868	+	0.354855i
$999$		−	43.1624i		−	1.36560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.s.b.27.6	yes	18
3.2	odd	2		720.2.z.g.667.4		18
4.3	odd	2		320.2.s.b.207.2		18
5.2	odd	4		400.2.j.d.43.1		18
5.3	odd	4		80.2.j.b.43.9	✓	18
5.4	even	2		400.2.s.d.107.4		18
8.3	odd	2		640.2.s.c.287.8		18
8.5	even	2		640.2.s.d.287.2		18
15.8	even	4		720.2.bd.g.523.1		18
16.3	odd	4		80.2.j.b.67.9	yes	18
16.5	even	4		640.2.j.c.607.2		18
16.11	odd	4		640.2.j.d.607.8		18
16.13	even	4		320.2.j.b.47.8		18
20.3	even	4		320.2.j.b.143.2		18
20.7	even	4		1600.2.j.d.143.8		18
20.19	odd	2		1600.2.s.d.207.8		18
40.3	even	4		640.2.j.c.543.8		18
40.13	odd	4		640.2.j.d.543.2		18
48.35	even	4		720.2.bd.g.307.1		18
80.3	even	4	inner	80.2.s.b.3.6	yes	18
80.13	odd	4		320.2.s.b.303.2		18
80.19	odd	4		400.2.j.d.307.1		18
80.29	even	4		1600.2.j.d.1007.2		18
80.43	even	4		640.2.s.d.223.2		18
80.53	odd	4		640.2.s.c.223.8		18
80.67	even	4		400.2.s.d.243.4		18
80.77	odd	4		1600.2.s.d.943.8		18
240.83	odd	4		720.2.z.g.163.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.9	✓	18	5.3	odd	4
80.2.j.b.67.9	yes	18	16.3	odd	4
80.2.s.b.3.6	yes	18	80.3	even	4	inner
80.2.s.b.27.6	yes	18	1.1	even	1	trivial
320.2.j.b.47.8		18	16.13	even	4
320.2.j.b.143.2		18	20.3	even	4
320.2.s.b.207.2		18	4.3	odd	2
320.2.s.b.303.2		18	80.13	odd	4
400.2.j.d.43.1		18	5.2	odd	4
400.2.j.d.307.1		18	80.19	odd	4
400.2.s.d.107.4		18	5.4	even	2
400.2.s.d.243.4		18	80.67	even	4
640.2.j.c.543.8		18	40.3	even	4
640.2.j.c.607.2		18	16.5	even	4
640.2.j.d.543.2		18	40.13	odd	4
640.2.j.d.607.8		18	16.11	odd	4
640.2.s.c.223.8		18	80.53	odd	4
640.2.s.c.287.8		18	8.3	odd	2
640.2.s.d.223.2		18	80.43	even	4
640.2.s.d.287.2		18	8.5	even	2
720.2.z.g.163.4		18	240.83	odd	4
720.2.z.g.667.4		18	3.2	odd	2
720.2.bd.g.307.1		18	48.35	even	4
720.2.bd.g.523.1		18	15.8	even	4
1600.2.j.d.143.8		18	20.7	even	4
1600.2.j.d.1007.2		18	80.29	even	4
1600.2.s.d.207.8		18	20.19	odd	2
1600.2.s.d.943.8		18	80.77	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.567819 + 1.29521i) q^{2} +1.96251 q^{3} +(-1.35516 + 1.47090i) q^{4} +(-1.42182 - 1.72581i) q^{5} +(1.11435 + 2.54187i) q^{6} +(-1.60205 - 1.60205i) q^{7} +(-2.67461 - 0.920026i) q^{8} +0.851447 q^{9} +(1.42795 - 2.82151i) q^{10} +(0.754587 - 0.754587i) q^{11} +(-2.65952 + 2.88665i) q^{12} +5.94580i q^{13} +(1.16532 - 2.98467i) q^{14} +(-2.79034 - 3.38692i) q^{15} +(-0.327065 - 3.98661i) q^{16} +(1.95574 + 1.95574i) q^{17} +(0.483468 + 1.10281i) q^{18} +(0.780680 - 0.780680i) q^{19} +(4.46529 + 0.247399i) q^{20} +(-3.14404 - 3.14404i) q^{21} +(1.40582 + 0.548884i) q^{22} +(4.93121 - 4.93121i) q^{23} +(-5.24896 - 1.80556i) q^{24} +(-0.956833 + 4.90759i) q^{25} +(-7.70109 + 3.37614i) q^{26} -4.21656 q^{27} +(4.52748 - 0.185408i) q^{28} +(-1.44802 - 1.44802i) q^{29} +(2.80238 - 5.53725i) q^{30} -3.60859i q^{31} +(4.97780 - 2.68729i) q^{32} +(1.48089 - 1.48089i) q^{33} +(-1.42260 + 3.64361i) q^{34} +(-0.486998 + 5.04266i) q^{35} +(-1.15385 + 1.25239i) q^{36} +10.2364i q^{37} +(1.45443 + 0.567864i) q^{38} +11.6687i q^{39} +(2.21504 + 5.92398i) q^{40} -6.93334i q^{41} +(2.28696 - 5.85745i) q^{42} +9.91344i q^{43} +(0.0873298 + 2.13251i) q^{44} +(-1.21061 - 1.46944i) q^{45} +(9.18700 + 3.58694i) q^{46} +(0.104270 - 0.104270i) q^{47} +(-0.641868 - 7.82376i) q^{48} -1.86688i q^{49} +(-6.89970 + 1.54732i) q^{50} +(3.83816 + 3.83816i) q^{51} +(-8.74565 - 8.05753i) q^{52} -4.03213 q^{53} +(-2.39424 - 5.46135i) q^{54} +(-2.37516 - 0.229383i) q^{55} +(2.81093 + 5.75878i) q^{56} +(1.53209 - 1.53209i) q^{57} +(1.05328 - 2.69771i) q^{58} +(-3.46736 - 3.46736i) q^{59} +(8.76317 + 0.485523i) q^{60} +(0.680578 - 0.680578i) q^{61} +(4.67390 - 2.04902i) q^{62} +(-1.36406 - 1.36406i) q^{63} +(6.30711 + 4.92142i) q^{64} +(10.2613 - 8.45388i) q^{65} +(2.75894 + 1.07719i) q^{66} -9.04721i q^{67} +(-5.52703 + 0.226341i) q^{68} +(9.67754 - 9.67754i) q^{69} +(-6.80785 + 2.23255i) q^{70} -3.64007 q^{71} +(-2.27729 - 0.783353i) q^{72} +(-2.94030 - 2.94030i) q^{73} +(-13.2583 + 5.81242i) q^{74} +(-1.87779 + 9.63120i) q^{75} +(0.0903496 + 2.20625i) q^{76} -2.41777 q^{77} +(-15.1135 + 6.62570i) q^{78} +10.7140 q^{79} +(-6.41509 + 6.23270i) q^{80} -10.8294 q^{81} +(8.98016 - 3.93688i) q^{82} -4.23845 q^{83} +(8.88523 - 0.363865i) q^{84} +(0.594515 - 6.15595i) q^{85} +(-12.8400 + 5.62904i) q^{86} +(-2.84176 - 2.84176i) q^{87} +(-2.71247 + 1.32399i) q^{88} +0.0426256 q^{89} +(1.21583 - 2.40237i) q^{90} +(9.52546 - 9.52546i) q^{91} +(0.570698 + 13.9359i) q^{92} -7.08189i q^{93} +(0.194258 + 0.0758455i) q^{94} +(-2.45730 - 0.237315i) q^{95} +(9.76898 - 5.27383i) q^{96} +(-1.91173 - 1.91173i) q^{97} +(2.41802 - 1.06005i) q^{98} +(0.642491 - 0.642491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25}+ \cdots + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

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