LMFDB - Embedded newform 400.2.s.d.243.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.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:	$3.19401608085$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.4
Root			$1.41303 + 0.0578659i$ of defining polynomial
Character	$\chi$	$=$	400.243
Dual form			400.2.s.d.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.567819 + 1.29521i) q^{2} -1.96251 q^{3} +(-1.35516 - 1.47090i) q^{4} +(1.11435 - 2.54187i) q^{6} +(1.60205 - 1.60205i) q^{7} +(2.67461 - 0.920026i) q^{8} +0.851447 q^{9} +O(q^{10})$	\(q+(-0.567819 + 1.29521i) q^{2} -1.96251 q^{3} +(-1.35516 - 1.47090i) q^{4} +(1.11435 - 2.54187i) q^{6} +(1.60205 - 1.60205i) q^{7} +(2.67461 - 0.920026i) q^{8} +0.851447 q^{9} +(0.754587 + 0.754587i) q^{11} +(2.65952 + 2.88665i) q^{12} +5.94580i q^{13} +(1.16532 + 2.98467i) q^{14} +(-0.327065 + 3.98661i) q^{16} +(-1.95574 + 1.95574i) q^{17} +(-0.483468 + 1.10281i) q^{18} +(0.780680 + 0.780680i) q^{19} +(-3.14404 + 3.14404i) q^{21} +(-1.40582 + 0.548884i) q^{22} +(-4.93121 - 4.93121i) q^{23} +(-5.24896 + 1.80556i) q^{24} +(-7.70109 - 3.37614i) q^{26} +4.21656 q^{27} +(-4.52748 - 0.185408i) q^{28} +(-1.44802 + 1.44802i) q^{29} +3.60859i q^{31} +(-4.97780 - 2.68729i) q^{32} +(-1.48089 - 1.48089i) q^{33} +(-1.42260 - 3.64361i) q^{34} +(-1.15385 - 1.25239i) q^{36} +10.2364i q^{37} +(-1.45443 + 0.567864i) q^{38} -11.6687i q^{39} +6.93334i q^{41} +(-2.28696 - 5.85745i) q^{42} +9.91344i q^{43} +(0.0873298 - 2.13251i) q^{44} +(9.18700 - 3.58694i) q^{46} +(-0.104270 - 0.104270i) q^{47} +(0.641868 - 7.82376i) q^{48} +1.86688i q^{49} +(3.83816 - 3.83816i) q^{51} +(8.74565 - 8.05753i) q^{52} +4.03213 q^{53} +(-2.39424 + 5.46135i) q^{54} +(2.81093 - 5.75878i) q^{56} +(-1.53209 - 1.53209i) q^{57} +(-1.05328 - 2.69771i) q^{58} +(-3.46736 + 3.46736i) q^{59} +(0.680578 + 0.680578i) q^{61} +(-4.67390 - 2.04902i) q^{62} +(1.36406 - 1.36406i) q^{63} +(6.30711 - 4.92142i) q^{64} +(2.75894 - 1.07719i) q^{66} -9.04721i q^{67} +(5.52703 + 0.226341i) q^{68} +(9.67754 + 9.67754i) q^{69} -3.64007 q^{71} +(2.27729 - 0.783353i) q^{72} +(2.94030 - 2.94030i) q^{73} +(-13.2583 - 5.81242i) q^{74} +(0.0903496 - 2.20625i) q^{76} +2.41777 q^{77} +(15.1135 + 6.62570i) q^{78} +10.7140 q^{79} -10.8294 q^{81} +(-8.98016 - 3.93688i) q^{82} +4.23845 q^{83} +(8.88523 + 0.363865i) q^{84} +(-12.8400 - 5.62904i) q^{86} +(2.84176 - 2.84176i) q^{87} +(2.71247 + 1.32399i) q^{88} +0.0426256 q^{89} +(9.52546 + 9.52546i) q^{91} +(-0.570698 + 13.9359i) q^{92} -7.08189i q^{93} +(0.194258 - 0.0758455i) q^{94} +(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} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} + 6 q^{17} + 24 q^{18} - 2 q^{19} - 16 q^{21} - 12 q^{22} + 2 q^{23} - 4 q^{24} - 16 q^{26} + 24 q^{27} - 40 q^{28} + 14 q^{29} - 20 q^{32} + 8 q^{33} + 28 q^{34} - 4 q^{36} - 24 q^{38} - 8 q^{42} - 44 q^{44} + 12 q^{46} - 38 q^{47} - 4 q^{48} + 8 q^{51} - 8 q^{52} - 12 q^{53} + 4 q^{54} + 20 q^{56} + 24 q^{57} - 20 q^{58} + 10 q^{59} + 14 q^{61} + 40 q^{62} + 6 q^{63} + 16 q^{64} + 4 q^{66} + 60 q^{68} - 32 q^{69} + 24 q^{71} + 68 q^{72} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 44 q^{77} + 36 q^{78} - 16 q^{79} + 2 q^{81} - 48 q^{82} - 40 q^{83} + 24 q^{84} - 36 q^{86} - 24 q^{87} + 8 q^{88} + 12 q^{89} + 8 q^{92} - 28 q^{94} - 40 q^{96} - 18 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 + 6 * q^17 + 24 * q^18 - 2 * q^19 - 16 * q^21 - 12 * q^22 + 2 * q^23 - 4 * q^24 - 16 * q^26 + 24 * q^27 - 40 * q^28 + 14 * q^29 - 20 * q^32 + 8 * q^33 + 28 * q^34 - 4 * q^36 - 24 * q^38 - 8 * q^42 - 44 * q^44 + 12 * q^46 - 38 * q^47 - 4 * q^48 + 8 * q^51 - 8 * q^52 - 12 * q^53 + 4 * q^54 + 20 * q^56 + 24 * q^57 - 20 * q^58 + 10 * q^59 + 14 * q^61 + 40 * q^62 + 6 * q^63 + 16 * q^64 + 4 * q^66 + 60 * q^68 - 32 * q^69 + 24 * q^71 + 68 * q^72 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 44 * q^77 + 36 * q^78 - 16 * q^79 + 2 * q^81 - 48 * q^82 - 40 * q^83 + 24 * q^84 - 36 * q^86 - 24 * q^87 + 8 * q^88 + 12 * q^89 + 8 * q^92 - 28 * q^94 - 40 * q^96 - 18 * q^97 + 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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	$-0.691714\pi$
$3$	−1.96251			−1.13306			−0.566528	+	0.824043i	$0.691714\pi$
$4$	−1.35516	−	1.47090i	−0.677582	−	0.735448i
$5$		0			0
$5$		0			0
$6$	1.11435	−	2.54187i	0.454932	−	1.03772i
$7$	1.60205	−	1.60205i	0.605517	−	0.605517i	−0.336254	−	0.941771i	$-0.609160\pi$
$7$	1.60205	−	1.60205i	0.605517	−	0.605517i	0.941771	+	0.336254i	$0.109160\pi$
$8$	2.67461	−	0.920026i	0.945618	−	0.325278i
$9$	0.851447			0.283816
$10$		0			0
$11$	0.754587	+	0.754587i	0.227517	+	0.227517i	0.811654	−	0.584138i	$-0.198567\pi$
$11$	0.754587	+	0.754587i	0.227517	+	0.227517i	−0.584138	+	0.811654i	$0.698567\pi$
$12$	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
$15$		0			0
$16$	−0.327065	+	3.98661i	−0.0817662	+	0.996652i
$17$	−1.95574	+	1.95574i	−0.474336	+	0.474336i	−0.903315	−	0.428978i	$-0.858874\pi$
$17$	−1.95574	+	1.95574i	−0.474336	+	0.474336i	0.428978	+	0.903315i	$0.358874\pi$
$18$	−0.483468	+	1.10281i	−0.113954	+	0.259934i
$19$	0.780680	+	0.780680i	0.179100	+	0.179100i	0.790964	−	0.611863i	$-0.209580\pi$
$19$	0.780680	+	0.780680i	0.179100	+	0.179100i	−0.611863	+	0.790964i	$0.709580\pi$
$20$		0			0
$21$	−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	−0.999590	−	0.0286378i	$-0.990883\pi$
$23$	−4.93121	−	4.93121i	−1.02823	−	1.02823i	−0.0286378	−	0.999590i	$-0.509117\pi$
$24$	−5.24896	+	1.80556i	−1.07144	+	0.368558i
$25$		0			0
$26$	−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	−0.828653	−	0.559762i	$-0.810892\pi$
$29$	−1.44802	+	1.44802i	−0.268891	+	0.268891i	0.559762	+	0.828653i	$0.310892\pi$
$30$		0			0
$31$			3.60859i			0.648121i	0.946036	+	0.324061i	$0.105048\pi$
$31$			3.60859i			0.648121i	−0.946036	+	0.324061i	$0.894952\pi$
$32$	−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			0
$36$	−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
$40$		0			0
$41$			6.93334i			1.08281i	0.840763	+	0.541403i	$0.182107\pi$
$41$			6.93334i			1.08281i	−0.840763	+	0.541403i	$0.817893\pi$
$42$	−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
$45$		0			0
$46$	9.18700	−	3.58694i	1.35455	−	0.528865i
$47$	−0.104270	−	0.104270i	−0.0152093	−	0.0152093i	0.699461	−	0.714671i	$-0.253423\pi$
$47$	−0.104270	−	0.104270i	−0.0152093	−	0.0152093i	−0.714671	+	0.699461i	$0.753423\pi$
$48$	0.641868	−	7.82376i	0.0926457	−	1.12926i
$49$			1.86688i			0.266698i
$50$		0			0
$51$	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	$-0.410684\pi$
$53$	4.03213			0.553856			0.276928	+	0.960891i	$0.410684\pi$
$54$	−2.39424	+	5.46135i	−0.325815	+	0.743195i
$55$		0			0
$56$	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	−0.895823	−	0.444411i	$-0.853413\pi$
$59$	−3.46736	+	3.46736i	−0.451412	+	0.451412i	0.444411	+	0.895823i	$0.353413\pi$
$60$		0			0
$61$	0.680578	+	0.680578i	0.0871391	+	0.0871391i	0.749333	−	0.662194i	$-0.230374\pi$
$61$	0.680578	+	0.680578i	0.0871391	+	0.0871391i	−0.662194	+	0.749333i	$0.730374\pi$
$62$	−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
$65$		0			0
$66$	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
$70$		0			0
$71$	−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	$-0.671757\pi$
$73$	2.94030	−	2.94030i	0.344136	−	0.344136i	0.857920	+	0.513784i	$0.171757\pi$
$74$	−13.2583	−	5.81242i	−1.54125	−	0.675681i
$75$		0			0
$76$	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	$0.294087\pi$
$80$		0			0
$81$	−10.8294			−1.20326
$82$	−8.98016	−	3.93688i	−0.991693	−	0.434756i
$83$	4.23845			0.465230			0.232615	−	0.972569i	$-0.425272\pi$
$83$	4.23845			0.465230			0.232615	+	0.972569i	$0.425272\pi$
$84$	8.88523	+	0.363865i	0.969458	+	0.0397009i
$85$		0			0
$86$	−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	$0.499281\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	9.76898	+	5.27383i	0.997042	+	0.538258i
$97$	1.91173	−	1.91173i	0.194106	−	0.194106i	−0.603362	−	0.797468i	$-0.706172\pi$
$97$	1.91173	−	1.91173i	0.194106	−	0.194106i	0.797468	+	0.603362i	$0.206172\pi$
$98$	−2.41802	−	1.06005i	−0.244257	−	0.107081i
$99$	0.642491	+	0.642491i	0.0645728	+	0.0645728i
$100$		0			0
$101$	4.96537	−	4.96537i	0.494073	−	0.494073i	−0.415514	−	0.909587i	$-0.636398\pi$
$101$	4.96537	−	4.96537i	0.494073	−	0.494073i	0.909587	+	0.415514i	$0.136398\pi$
$102$	2.79186	+	7.15062i	0.276435	+	0.708017i
$103$	−0.442220	−	0.442220i	−0.0435733	−	0.0435733i	0.684984	−	0.728558i	$-0.259809\pi$
$103$	−0.442220	−	0.442220i	−0.0435733	−	0.0435733i	−0.728558	+	0.684984i	$0.759809\pi$
$104$	5.47029	+	15.9027i	0.536406	+	1.55939i
$105$		0			0
$106$	−2.28952	+	5.22248i	−0.222378	+	0.507252i
$107$	−17.5924			−1.70072			−0.850359	−	0.526204i	$-0.823615\pi$
$107$	−17.5924			−1.70072			−0.850359	+	0.526204i	$0.823615\pi$
$108$	−5.71412	−	6.20211i	−0.549842	−	0.596799i
$109$	0.345161	−	0.345161i	0.0330605	−	0.0330605i	−0.690383	−	0.723444i	$-0.742558\pi$
$109$	0.345161	−	0.345161i	0.0330605	−	0.0330605i	0.723444	+	0.690383i	$0.242558\pi$
$110$		0			0
$111$		−	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	$-0.132217\pi$
$113$	5.43662	+	5.43662i	0.511435	+	0.511435i	−0.403531	+	0.914966i	$0.632217\pi$
$114$	2.85434	−	1.11444i	0.267334	−	0.104377i
$115$		0			0
$116$	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
$120$		0			0
$121$		−	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
$125$		0			0
$126$	0.992211	+	2.54129i	0.0883932	+	0.226396i
$127$	6.27150	+	6.27150i	0.556505	+	0.556505i	0.928311	−	0.371805i	$-0.121261\pi$
$127$	6.27150	+	6.27150i	0.556505	+	0.556505i	−0.371805	+	0.928311i	$0.621261\pi$
$128$	2.79301	+	10.9635i	0.246869	+	0.969049i
$129$		−	19.4552i		−	1.71294i
$130$		0			0
$131$	1.61521	−	1.61521i	0.141122	−	0.141122i	−0.633017	−	0.774138i	$-0.718184\pi$
$131$	1.61521	−	1.61521i	0.141122	−	0.141122i	0.774138	+	0.633017i	$0.218184\pi$
$132$	−0.171386	+	4.18507i	−0.0149172	+	0.364263i
$133$	2.50138			0.216897
$134$	11.7181	+	5.13718i	1.01229	+	0.443785i
$135$		0			0
$136$	−3.43152	+	7.03018i	−0.294250	+	0.602833i
$137$	−6.83585	−	6.83585i	−0.584026	−	0.584026i	0.351981	−	0.936007i	$-0.385508\pi$
$137$	−6.83585	−	6.83585i	−0.584026	−	0.584026i	−0.936007	+	0.351981i	$0.885508\pi$
$138$	−18.0296	+	7.03941i	−1.53478	+	0.599234i
$139$	−13.7427	+	13.7427i	−1.16564	+	1.16564i	−0.182423	+	0.983220i	$0.558394\pi$
$139$	−13.7427	+	13.7427i	−1.16564	+	1.16564i	−0.983220	+	0.182423i	$0.941606\pi$
$140$		0			0
$141$	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			0
$146$	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	0.632318	−	0.774709i	$-0.282104\pi$
$149$	−1.73811	−	1.73811i	−0.142391	−	0.142391i	−0.774709	+	0.632318i	$0.782104\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−17.1634	+	15.8130i	−1.37417	+	1.26605i
$157$	−3.14732			−0.251183			−0.125592	−	0.992082i	$-0.540083\pi$
$157$	−3.14732			−0.251183			−0.125592	+	0.992082i	$0.540083\pi$
$158$	−6.08363	+	13.8770i	−0.483987	+	1.10399i
$159$	−7.91310			−0.627550
$160$		0			0
$161$	−15.8001			−1.24522
$162$	6.14913	−	14.0264i	0.483121	−	1.10202i
$163$	−7.82117			−0.612601			−0.306301	−	0.951935i	$-0.599091\pi$
$163$	−7.82117			−0.612601			−0.306301	+	0.951935i	$0.599091\pi$
$164$	10.1982	−	9.39580i	0.796347	−	0.733689i
$165$		0			0
$166$	−2.40667	+	5.48970i	−0.186794	+	0.426083i
$167$	9.88460	−	9.88460i	0.764893	−	0.764893i	−0.212309	−	0.977203i	$-0.568098\pi$
$167$	9.88460	−	9.88460i	0.764893	−	0.764893i	0.977203	+	0.212309i	$0.0680985\pi$
$168$	−5.51649	+	11.3017i	−0.425606	+	0.871943i
$169$	−22.3525			−1.71942
$170$		0			0
$171$	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
$175$		0			0
$176$	−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	0.0220444	−	0.999757i	$-0.492982\pi$
$179$	−13.0809	−	13.0809i	−0.977713	−	0.977713i	−0.999757	+	0.0220444i	$0.992982\pi$
$180$		0			0
$181$	13.6393	−	13.6393i	1.01380	−	1.01380i	0.0138952	−	0.999903i	$-0.495577\pi$
$181$	13.6393	−	13.6393i	1.01380	−	1.01380i	0.999903	−	0.0138952i	$-0.00442312\pi$
$182$	−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
$185$		0			0
$186$	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
$190$		0			0
$191$		−	2.92523i		−	0.211662i	−0.994384	−	0.105831i	$-0.966250\pi$
$191$		−	2.92523i		−	0.211662i	0.994384	−	0.105831i	$-0.0337503\pi$
$192$	−12.3778	+	9.65835i	−0.893288	+	0.697031i
$193$	−0.0830702	−	0.0830702i	−0.00597953	−	0.00597953i	0.704111	−	0.710090i	$-0.251346\pi$
$193$	−0.0830702	−	0.0830702i	−0.00597953	−	0.00597953i	−0.710090	+	0.704111i	$0.751346\pi$
$194$	1.39058	+	3.56161i	0.0998379	+	0.255709i
$195$		0			0
$196$	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	$-0.872834\pi$
$199$		−	10.9740i		−	0.777924i	0.921254	−	0.388962i	$-0.127166\pi$
$200$		0			0
$201$			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
$205$		0			0
$206$	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
$210$		0			0
$211$	−8.92204	+	8.92204i	−0.614218	+	0.614218i	−0.944042	−	0.329824i	$-0.893011\pi$
$211$	−8.92204	+	8.92204i	−0.614218	+	0.614218i	0.329824	+	0.944042i	$0.393011\pi$
$212$	−5.46420	−	5.93085i	−0.375283	−	0.407332i
$213$	7.14367			0.489477
$214$	9.98927	−	22.7859i	0.682853	−	1.55761i
$215$		0			0
$216$	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
$220$		0			0
$221$	−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	$-0.535704\pi$
$223$	13.1678	−	13.1678i	0.881784	−	0.881784i	0.993716	+	0.111931i	$0.0357037\pi$
$224$	−12.2798	+	3.66950i	−0.820481	+	0.245179i
$225$		0			0
$226$	−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	0.992822	−	0.119599i	$-0.0381610\pi$
$229$	13.2143	+	13.2143i	0.873223	+	0.873223i	−0.119599	+	0.992822i	$0.538161\pi$
$230$		0			0
$231$	−4.74490			−0.312191
$232$	−2.54068	+	5.20511i	−0.166804	+	0.341732i
$233$	−20.6884	+	20.6884i	−1.35534	+	1.35534i	−0.475769	+	0.879570i	$0.657830\pi$
$233$	−20.6884	+	20.6884i	−1.35534	+	1.35534i	−0.879570	+	0.475769i	$0.842170\pi$
$234$	−6.55707	−	2.87460i	−0.428649	−	0.187919i
$235$		0			0
$236$	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	$0.349211\pi$
$240$		0			0
$241$	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
$245$		0			0
$246$	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
$250$		0			0
$251$	−6.84118	−	6.84118i	−0.431812	−	0.431812i	0.457433	−	0.889244i	$-0.348769\pi$
$251$	−6.84118	−	6.84118i	−0.431812	−	0.431812i	−0.889244	+	0.457433i	$0.848769\pi$
$252$	−3.85491	−	0.157865i	−0.242837	−	0.00994457i
$253$		−	7.44205i		−	0.467878i
$254$	−11.6840	+	4.56186i	−0.733120	+	0.286237i
$255$		0			0
$256$	−15.7861	−	2.60776i	−0.986629	−	0.162985i
$257$	6.66524	−	6.66524i	0.415766	−	0.415766i	−0.467975	−	0.883742i	$-0.655016\pi$
$257$	6.66524	−	6.66524i	0.415766	−	0.415766i	0.883742	+	0.467975i	$0.155016\pi$
$258$	25.1987	+	11.0471i	1.56880	+	0.687759i
$259$	16.3992	+	16.3992i	1.01900	+	1.01900i
$260$		0			0
$261$	−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	$-0.146595\pi$
$263$	7.32015	+	7.32015i	0.451380	+	0.451380i	−0.444432	+	0.895812i	$0.646595\pi$
$264$	−5.32325	−	2.59834i	−0.327623	−	0.159917i
$265$		0			0
$266$	−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	−0.999678	−	0.0253576i	$-0.991928\pi$
$269$	−15.9801	+	15.9801i	−0.974321	+	0.974321i	0.0253576	+	0.999678i	$0.491928\pi$
$270$		0			0
$271$			3.59684i			0.218492i	0.994015	+	0.109246i	$0.0348437\pi$
$271$			3.59684i			0.218492i	−0.994015	+	0.109246i	$0.965156\pi$
$272$	−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
$275$		0			0
$276$	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
$280$		0			0
$281$			3.26699i			0.194892i	0.995241	+	0.0974462i	$0.0310674\pi$
$281$			3.26699i			0.194892i	−0.995241	+	0.0974462i	$0.968933\pi$
$282$	−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
$285$		0			0
$286$	−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
$290$		0			0
$291$	−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	$-0.395293\pi$
$293$	11.0593			0.646091			0.323045	+	0.946384i	$0.395293\pi$
$294$	4.74538	+	2.08036i	0.276756	+	0.121329i
$295$		0			0
$296$	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
$300$		0			0
$301$	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
$305$		0			0
$306$	−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
$310$		0			0
$311$	−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	$-0.566019\pi$
$313$	13.6695	−	13.6695i	0.772646	−	0.772646i	0.978568	+	0.205922i	$0.0660194\pi$
$314$	1.78711	−	4.07645i	0.100852	−	0.230048i
$315$		0			0
$316$	−14.5193	−	15.7592i	−0.816772	−	0.886525i
$317$	25.8314			1.45084			0.725419	−	0.688307i	$-0.241646\pi$
$317$	25.8314			1.45084			0.725419	+	0.688307i	$0.241646\pi$
$318$	4.49321	−	10.2492i	0.251967	−	0.574745i
$319$	−2.18532			−0.122354
$320$		0			0
$321$	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
$325$		0			0
$326$	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
$330$		0			0
$331$	−13.6207	−	13.6207i	−0.748659	−	0.748659i	0.225568	−	0.974227i	$-0.427576\pi$
$331$	−13.6207	−	13.6207i	−0.748659	−	0.748659i	−0.974227	+	0.225568i	$0.927576\pi$
$332$	−5.74379	−	6.23431i	−0.315231	−	0.342152i
$333$			8.71576i			0.477621i
$334$	7.19002	+	18.4153i	0.393420	+	1.00764i
$335$		0			0
$336$	−11.5057	−	13.5623i	−0.627689	−	0.739886i
$337$	−16.0911	+	16.0911i	−0.876536	+	0.876536i	−0.993174	−	0.116638i	$-0.962788\pi$
$337$	−16.0911	+	16.0911i	−0.876536	+	0.876536i	0.116638	+	0.993174i	$0.462788\pi$
$338$	12.6922	−	28.9513i	0.690364	−	1.57474i
$339$	−10.6694	−	10.6694i	−0.579484	−	0.579484i
$340$		0			0
$341$	−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
$345$		0			0
$346$	4.52347	+	1.98308i	0.243183	+	0.106611i
$347$	−5.57562			−0.299315			−0.149658	−	0.988738i	$-0.547817\pi$
$347$	−5.57562			−0.299315			−0.149658	+	0.988738i	$0.547817\pi$
$348$	−8.03097	−	0.328882i	−0.430505	−	0.0176299i
$349$	15.0811	−	15.0811i	0.807273	−	0.807273i	−0.176947	−	0.984220i	$-0.556622\pi$
$349$	15.0811	−	15.0811i	0.807273	−	0.807273i	0.984220	+	0.176947i	$0.0566222\pi$
$350$		0			0
$351$			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	$-0.280942\pi$
$353$	−2.57880	−	2.57880i	−0.137256	−	0.137256i	−0.772397	+	0.635141i	$0.780942\pi$
$354$	4.94973	+	12.6774i	0.263075	+	0.673798i
$355$		0			0
$356$	−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	$0.0486758\pi$
$359$			5.77227i			0.304649i	−0.988331	+	0.152324i	$0.951324\pi$
$360$		0			0
$361$		−	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			0
$366$	2.48835	−	0.971540i	0.130068	−	0.0507832i
$367$	−8.30496	−	8.30496i	−0.433516	−	0.433516i	0.456307	−	0.889822i	$-0.349172\pi$
$367$	−8.30496	−	8.30496i	−0.433516	−	0.433516i	−0.889822	+	0.456307i	$0.849172\pi$
$368$	21.2716	−	18.0460i	1.10886	−	0.940710i
$369$			5.90337i			0.307317i
$370$		0			0
$371$	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	$-0.636385\pi$
$373$	−16.0484			−0.830953			−0.415477	+	0.909604i	$0.636385\pi$
$374$	1.67595	−	3.82289i	0.0866612	−	0.197677i
$375$		0			0
$376$	−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	−0.897954	−	0.440089i	$-0.854947\pi$
$379$	−8.91367	+	8.91367i	−0.457865	+	0.457865i	0.440089	+	0.897954i	$0.354947\pi$
$380$		0			0
$381$	−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	0.326904	−	0.945057i	$-0.393995\pi$
$383$	24.8928	−	24.8928i	1.27196	−	1.27196i	0.945057	−	0.326904i	$-0.106005\pi$
$384$	−5.48131	−	21.5161i	−0.279717	−	1.09799i
$385$		0			0
$386$	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	0.148217	−	0.988955i	$-0.452647\pi$
$389$	−16.5819	−	16.5819i	−0.840738	−	0.840738i	−0.988955	+	0.148217i	$0.952647\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	0.0743567	−	1.81572i	0.00373656	−	0.0912432i
$397$	8.62531			0.432892			0.216446	−	0.976295i	$-0.430553\pi$
$397$	8.62531			0.432892			0.216446	+	0.976295i	$0.430553\pi$
$398$	14.2137	+	6.23123i	0.712466	+	0.312343i
$399$	−4.90897			−0.245756
$400$		0			0
$401$	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
$405$		0			0
$406$	−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	$0.269532\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	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	0.923840	−	0.382779i	$-0.125033\pi$
$419$	11.0752	+	11.0752i	0.541061	+	0.541061i	−0.382779	+	0.923840i	$0.625033\pi$
$420$		0			0
$421$	−0.243092	+	0.243092i	−0.0118476	+	0.0118476i	−0.713006	−	0.701158i	$-0.752667\pi$
$421$	−0.243092	+	0.243092i	−0.0118476	+	0.0118476i	0.701158	+	0.713006i	$0.252667\pi$
$422$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$			20.7024i			0.997200i	0.866832	+	0.498600i	$0.166152\pi$
$431$			20.7024i			0.997200i	−0.866832	+	0.498600i	$0.833848\pi$
$432$	−1.37909	+	16.8098i	−0.0663514	+	0.808760i
$433$	5.68221	+	5.68221i	0.273069	+	0.273069i	0.830335	−	0.557265i	$-0.188149\pi$
$433$	5.68221	+	5.68221i	0.273069	+	0.273069i	−0.557265	+	0.830335i	$0.688149\pi$
$434$	−10.7704	+	4.20517i	−0.516998	+	0.201855i
$435$		0			0
$436$	−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	$0.148007\pi$
$439$			18.7902i			0.896808i	−0.893831	+	0.448404i	$0.851993\pi$
$440$		0			0
$441$			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			0
$446$	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	$-0.777484\pi$
$449$		−	27.2708i		−	1.28699i	0.765452	−	0.643493i	$-0.222516\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	−5.50732	−	2.68819i	−0.257904	−	0.125886i
$457$	−19.7514	−	19.7514i	−0.923933	−	0.923933i	0.0733714	−	0.997305i	$-0.476624\pi$
$457$	−19.7514	−	19.7514i	−0.923933	−	0.923933i	−0.997305	+	0.0733714i	$0.976624\pi$
$458$	−24.6186	+	9.61200i	−1.15035	+	0.449139i
$459$	−8.24649	+	8.24649i	−0.384913	+	0.384913i
$460$		0			0
$461$	12.9262	+	12.9262i	0.602035	+	0.602035i	0.940852	−	0.338818i	$-0.110027\pi$
$461$	12.9262	+	12.9262i	0.602035	+	0.602035i	−0.338818	+	0.940852i	$0.610027\pi$
$462$	2.69424	−	6.14566i	0.125348	−	0.285922i
$463$	−14.5647	+	14.5647i	−0.676879	+	0.676879i	−0.959293	−	0.282414i	$-0.908865\pi$
$463$	−14.5647	+	14.5647i	−0.676879	+	0.676879i	0.282414	+	0.959293i	$0.408865\pi$
$464$	−5.29909	−	6.24629i	−0.246004	−	0.289977i
$465$		0			0
$466$	−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			0
$471$	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
$475$		0			0
$476$	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	$0.287579\pi$
$480$		0			0
$481$	−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			0
$486$	−4.88500	+	11.1429i	−0.221588	+	0.505450i
$487$	−21.9674	+	21.9674i	−0.995436	+	0.995436i	−0.999990	−	0.00455390i	$-0.998550\pi$
$487$	−21.9674	+	21.9674i	−0.995436	+	0.995436i	0.00455390	+	0.999990i	$0.498550\pi$
$488$	2.44643	+	1.19413i	0.110745	+	0.0540559i
$489$	15.3491			0.694111
$490$		0			0
$491$	−6.11955	−	6.11955i	−0.276171	−	0.276171i	0.555407	−	0.831579i	$-0.312562\pi$
$491$	−6.11955	−	6.11955i	−0.276171	−	0.276171i	−0.831579	+	0.555407i	$0.812562\pi$
$492$	−20.0141	+	18.4394i	−0.902305	+	0.831311i
$493$		−	5.66390i		−	0.255089i
$494$	−3.37640	−	8.64777i	−0.151912	−	0.389082i
$495$		0			0
$496$	−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	0.962213	−	0.272298i	$-0.0877838\pi$
$499$	15.4115	+	15.4115i	0.689914	+	0.689914i	−0.272298	+	0.962213i	$0.587784\pi$
$500$		0			0
$501$	−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	−0.980124	−	0.198387i	$-0.936430\pi$
$503$	−26.4312	−	26.4312i	−1.17851	−	1.17851i	−0.198387	−	0.980124i	$-0.563570\pi$
$504$	2.39336	−	4.90330i	0.106609	−	0.218410i
$505$		0			0
$506$	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	−0.712267	−	0.701908i	$-0.752332\pi$
$509$	−0.233714	+	0.233714i	−0.0103592	+	0.0103592i	0.701908	+	0.712267i	$0.252332\pi$
$510$		0			0
$511$		−	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
$515$		0			0
$516$	−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
$520$		0			0
$521$			4.50147i			0.197213i	0.995127	+	0.0986064i	$0.0314385\pi$
$521$			4.50147i			0.197213i	−0.995127	+	0.0986064i	$0.968562\pi$
$522$	−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
$525$		0			0
$526$	−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
$530$		0			0
$531$	−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
$535$		0			0
$536$	−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
$540$		0			0
$541$	14.5013	+	14.5013i	0.623459	+	0.623459i	0.946414	−	0.322955i	$-0.104676\pi$
$541$	14.5013	+	14.5013i	0.623459	+	0.623459i	−0.322955	+	0.946414i	$0.604676\pi$
$542$	−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			0
$546$	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
$550$		0			0
$551$	−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
$555$		0			0
$556$	38.8378	+	1.59047i	1.64709	+	0.0674510i
$557$	9.72758			0.412171			0.206085	−	0.978534i	$-0.433928\pi$
$557$	9.72758			0.412171			0.206085	+	0.978534i	$0.433928\pi$
$558$	−3.97958	−	1.74464i	−0.168469	−	0.0738563i
$559$	−58.9433			−2.49304
$560$		0			0
$561$	5.79245			0.244557
$562$	−4.23146	−	1.85506i	−0.178493	−	0.0782510i
$563$	17.7853			0.749562			0.374781	−	0.927113i	$-0.377718\pi$
$563$	17.7853			0.749562			0.374781	+	0.927113i	$0.377718\pi$
$564$	0.0236823	−	0.578299i	0.000997205	−	0.0243508i
$565$		0			0
$566$	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	$0.392624\pi$
$570$		0			0
$571$	23.3108	+	23.3108i	0.975528	+	0.975528i	0.999708	−	0.0241793i	$-0.00769727\pi$
$571$	23.3108	+	23.3108i	0.975528	+	0.975528i	−0.0241793	+	0.999708i	$0.507697\pi$
$572$	12.6795	+	0.519245i	0.530155	+	0.0217107i
$573$			5.74079i			0.239825i
$574$	−20.6937	+	8.07958i	−0.863739	+	0.337235i
$575$		0			0
$576$	5.37017	−	4.19033i	0.223757	−	0.174597i
$577$	−25.7383	+	25.7383i	−1.07150	+	1.07150i	−0.0742597	+	0.997239i	$0.523659\pi$
$577$	−25.7383	+	25.7383i	−1.07150	+	1.07150i	−0.997239	+	0.0742597i	$0.976341\pi$
$578$	−12.1105	−	5.30920i	−0.503729	−	0.220834i
$579$	0.163026	+	0.163026i	0.00677514	+	0.00677514i
$580$		0			0
$581$	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
$585$		0			0
$586$	−6.27967	+	14.3242i	−0.259411	+	0.591725i
$587$	−23.1327			−0.954790			−0.477395	−	0.878689i	$-0.658419\pi$
$587$	−23.1327			−0.954790			−0.477395	+	0.878689i	$0.658419\pi$
$588$	−5.38904	+	4.96502i	−0.222240	+	0.204754i
$589$	−2.81715	+	2.81715i	−0.116079	+	0.116079i
$590$		0			0
$591$		−	15.3171i		−	0.630063i
$592$	−40.8085	−	3.34797i	−1.67722	−	0.137601i
$593$	25.5047	+	25.5047i	1.04735	+	1.04735i	0.998822	+	0.0485322i	$0.0154543\pi$
$593$	25.5047	+	25.5047i	1.04735	+	1.04735i	0.0485322	+	0.998822i	$0.484546\pi$
$594$	−5.92773	+	2.31440i	−0.243218	+	0.0949609i
$595$		0			0
$596$	−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	$-0.927385\pi$
$599$		−	11.0699i		−	0.452304i	0.974092	−	0.226152i	$-0.0726146\pi$
$600$		0			0
$601$		−	13.7579i		−	0.561197i	−0.959825	−	0.280599i	$-0.909467\pi$
$601$		−	13.7579i		−	0.561197i	0.959825	−	0.280599i	$-0.0905330\pi$
$602$	−29.5884	+	11.5524i	−1.20593	+	0.470839i
$603$		−	7.70322i		−	0.313700i
$604$	−7.90768	−	8.58300i	−0.321759	−	0.349237i
$605$		0			0
$606$	−7.08817	−	18.1545i	−0.287937	−	0.737476i
$607$	18.4675	+	18.4675i	0.749573	+	0.749573i	0.974399	−	0.224826i	$-0.0721813\pi$
$607$	18.4675	+	18.4675i	0.749573	+	0.749573i	−0.224826	+	0.974399i	$0.572181\pi$
$608$	−1.78815	−	5.98398i	−0.0725193	−	0.242683i
$609$		−	9.10526i		−	0.368964i
$610$		0			0
$611$	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	$-0.424198\pi$
$613$	11.6810			0.471790			0.235895	+	0.971779i	$0.424198\pi$
$614$	−19.5988	−	8.59208i	−0.790944	−	0.346748i
$615$		0			0
$616$	6.46660	−	2.22441i	0.260547	−	0.0896240i
$617$	29.1000	+	29.1000i	1.17152	+	1.17152i	0.981847	+	0.189677i	$0.0607441\pi$
$617$	29.1000	+	29.1000i	1.17152	+	1.17152i	0.189677	+	0.981847i	$0.439256\pi$
$618$	−1.61686	+	0.631279i	−0.0650395	+	0.0253938i
$619$	4.23279	−	4.23279i	0.170130	−	0.170130i	−0.616906	−	0.787036i	$-0.711614\pi$
$619$	4.23279	−	4.23279i	0.170130	−	0.170130i	0.787036	+	0.616906i	$0.211614\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	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
$630$		0			0
$631$	−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
$635$		0			0
$636$	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
$640$		0			0
$641$	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	$-0.431062\pi$
$643$	10.8979			0.429771			0.214885	+	0.976639i	$0.431062\pi$
$644$	21.4117	+	23.2402i	0.843738	+	0.915793i
$645$		0			0
$646$	1.73390	−	3.95509i	0.0682194	−	0.155611i
$647$	11.6612	−	11.6612i	0.458448	−	0.458448i	−0.439698	−	0.898146i	$-0.644915\pi$
$647$	11.6612	−	11.6612i	0.458448	−	0.458448i	0.898146	+	0.439698i	$0.144915\pi$
$648$	−28.9644	+	9.96331i	−1.13783	+	0.391396i
$649$	−5.23285			−0.205407
$650$		0			0
$651$	−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			0
$656$	−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	0.314635	−	0.949213i	$-0.398118\pi$
$659$	−16.2902	−	16.2902i	−0.634578	−	0.634578i	−0.949213	+	0.314635i	$0.898118\pi$
$660$		0			0
$661$	−12.7924	+	12.7924i	−0.497566	+	0.497566i	−0.910679	−	0.413114i	$-0.864441\pi$
$661$	−12.7924	+	12.7924i	−0.497566	+	0.497566i	0.413114	+	0.910679i	$0.364441\pi$
$662$	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
$665$		0			0
$666$	−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
$670$		0			0
$671$			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	$-0.355655\pi$
$673$	−11.9553	−	11.9553i	−0.460841	−	0.460841i	−0.898931	+	0.438090i	$0.855655\pi$
$674$	−11.7046	−	29.9782i	−0.450843	−	1.15472i
$675$		0			0
$676$	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
$680$		0			0
$681$		−	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
$685$		0			0
$686$	−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
$690$		0			0
$691$	2.90121	−	2.90121i	0.110367	−	0.110367i	−0.649767	−	0.760134i	$-0.725133\pi$
$691$	2.90121	−	2.90121i	0.110367	−	0.110367i	0.760134	+	0.649767i	$0.225133\pi$
$692$	−5.13703	+	4.73284i	−0.195280	+	0.179916i
$693$	2.05860			0.0781999
$694$	3.16594	−	7.22163i	0.120178	−	0.274129i
$695$		0			0
$696$	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
$700$		0			0
$701$	15.7397	+	15.7397i	0.594481	+	0.594481i	0.938839	−	0.344358i	$-0.111903\pi$
$701$	15.7397	+	15.7397i	0.594481	+	0.594481i	−0.344358	+	0.938839i	$0.611903\pi$
$702$	−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			0
$706$	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	0.742909	−	0.669392i	$-0.233445\pi$
$709$	1.95755	+	1.95755i	0.0735172	+	0.0735172i	−0.669392	+	0.742909i	$0.733445\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	−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	$0.499609\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	−25.0659	−	10.9888i	−0.930283	−	0.407834i
$727$	16.2286	−	16.2286i	0.601885	−	0.601885i	−0.338927	−	0.940813i	$-0.610064\pi$
$727$	16.2286	−	16.2286i	0.601885	−	0.601885i	0.940813	+	0.338927i	$0.110064\pi$
$728$	34.2406	+	16.7132i	1.26904	+	0.619434i
$729$	15.6045			0.577943
$730$		0			0
$731$	−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
$735$		0			0
$736$	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	0.130053	−	0.991507i	$-0.458485\pi$
$739$	−23.4183	−	23.4183i	−0.861454	−	0.861454i	−0.991507	+	0.130053i	$0.958485\pi$
$740$		0			0
$741$	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	−0.993905	−	0.110238i	$-0.964839\pi$
$743$	−30.0968	−	30.0968i	−1.10414	−	1.10414i	−0.110238	−	0.993905i	$-0.535161\pi$
$744$	−6.51552	−	18.9413i	−0.238871	−	0.694422i
$745$		0			0
$746$	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
$750$		0			0
$751$		−	53.2724i		−	1.94394i	−0.235107	−	0.971970i	$-0.575544\pi$
$751$		−	53.2724i		−	1.94394i	0.235107	−	0.971970i	$-0.424456\pi$
$752$	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
$755$		0			0
$756$	−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
$760$		0			0
$761$			12.9068i			0.467870i	0.972252	+	0.233935i	$0.0751604\pi$
$761$			12.9068i			0.467870i	−0.972252	+	0.233935i	$0.924840\pi$
$762$	22.9300	−	8.95270i	0.830666	−	0.324322i
$763$		−	1.10593i		−	0.0400374i
$764$	−4.30270	+	3.96416i	−0.155666	+	0.143418i
$765$		0			0
$766$	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	$0.213596\pi$
$769$			34.4858i			1.24359i	−0.783180	+	0.621795i	$0.786404\pi$
$770$		0			0
$771$	−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	$-0.659286\pi$
$773$	−26.6789			−0.959574			−0.479787	+	0.877385i	$0.659286\pi$
$774$	−10.9326	−	4.79283i	−0.392965	−	0.172275i
$775$		0			0
$776$	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
$780$		0			0
$781$	−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
$785$		0			0
$786$	−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
$790$		0			0
$791$	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
$795$		0			0
$796$	−16.1416	+	14.8715i	−0.572122	+	0.527107i
$797$	−15.9072			−0.563461			−0.281730	−	0.959494i	$-0.590908\pi$
$797$	−15.9072			−0.563461			−0.281730	+	0.959494i	$0.590908\pi$
$798$	2.78741	−	6.35818i	0.0986732	−	0.225077i
$799$	0.407850			0.0144287
$800$		0			0
$801$	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
$805$		0			0
$806$	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	$0.570476\pi$
$810$		0			0
$811$	−35.4886	−	35.4886i	−1.24617	−	1.24617i	−0.957396	−	0.288777i	$-0.906751\pi$
$811$	−35.4886	−	35.4886i	−1.24617	−	1.24617i	−0.288777	−	0.957396i	$-0.593249\pi$
$812$	6.82436	−	6.28741i	0.239488	−	0.220645i
$813$		−	7.05884i		−	0.247564i
$814$	−5.61859	−	14.3906i	−0.196932	−	0.504389i
$815$		0			0
$816$	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
$820$		0			0
$821$	−15.9683	+	15.9683i	−0.557299	+	0.557299i	−0.928537	−	0.371239i	$-0.878933\pi$
$821$	−15.9683	+	15.9683i	−0.557299	+	0.557299i	0.371239	+	0.928537i	$0.378933\pi$
$822$	−24.9934	+	9.75833i	−0.871745	+	0.340361i
$823$	21.7278	+	21.7278i	0.757384	+	0.757384i	0.975846	−	0.218462i	$-0.0701039\pi$
$823$	21.7278	+	21.7278i	0.757384	+	0.757384i	−0.218462	+	0.975846i	$0.570104\pi$
$824$	−1.58962	−	0.775914i	−0.0553771	−	0.0270302i
$825$		0			0
$826$	−14.3895	−	6.30833i	−0.500675	−	0.219495i
$827$	39.2381			1.36444			0.682221	−	0.731146i	$-0.261014\pi$
$827$	39.2381			1.36444			0.682221	+	0.731146i	$0.261014\pi$
$828$	−0.485919	+	11.8657i	−0.0168869	+	0.412360i
$829$	18.6072	−	18.6072i	0.646254	−	0.646254i	−0.305831	−	0.952086i	$-0.598934\pi$
$829$	18.6072	−	18.6072i	0.646254	−	0.646254i	0.952086	+	0.305831i	$0.0989344\pi$
$830$		0			0
$831$			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
$835$		0			0
$836$	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	$-0.930235\pi$
$839$		−	12.5955i		−	0.434845i	0.976078	−	0.217422i	$-0.0697649\pi$
$840$		0			0
$841$			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
$845$		0			0
$846$	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
$850$		0			0
$851$	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	$-0.231022\pi$
$853$	43.6914			1.49597			0.747983	+	0.663718i	$0.231022\pi$
$854$	−1.23821	+	2.82439i	−0.0423706	+	0.0966488i
$855$		0			0
$856$	−47.0527	+	16.1854i	−1.60823	+	0.553206i
$857$	28.9373	+	28.9373i	0.988478	+	0.988478i	0.999934	−	0.0114561i	$-0.00364668\pi$
$857$	28.9373	+	28.9373i	0.988478	+	0.988478i	−0.0114561	+	0.999934i	$0.503647\pi$
$858$	6.40475	+	16.4041i	0.218655	+	0.560027i
$859$	28.1247	−	28.1247i	0.959602	−	0.959602i	−0.0396134	−	0.999215i	$-0.512613\pi$
$859$	28.1247	−	28.1247i	0.959602	−	0.959602i	0.999215	+	0.0396134i	$0.0126126\pi$
$860$		0			0
$861$	−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	$-0.570423\pi$
$863$	22.2144	−	22.2144i	0.756186	−	0.756186i	0.975626	+	0.219440i	$0.0704229\pi$
$864$	−20.9892	−	11.3311i	−0.714066	−	0.385492i
$865$		0			0
$866$	−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
$870$		0			0
$871$	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
$875$		0			0
$876$	16.3074	+	0.667816i	0.550976	+	0.0225634i
$877$	5.13889			0.173528			0.0867640	−	0.996229i	$-0.472347\pi$
$877$	5.13889			0.173528			0.0867640	+	0.996229i	$0.472347\pi$
$878$	−24.3374	−	10.6694i	−0.821346	−	0.360076i
$879$	−21.7040			−0.732057
$880$		0			0
$881$	−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	$-0.703318\pi$
$883$	−35.4317			−1.19237			−0.596186	+	0.802846i	$0.703318\pi$
$884$	−1.34578	+	32.8626i	−0.0452635	+	1.10529i
$885$		0			0
$886$	15.7551	+	6.90701i	0.529304	+	0.232046i
$887$	−37.4644	+	37.4644i	−1.25793	+	1.25793i	−0.305855	+	0.952078i	$0.598942\pi$
$887$	−37.4644	+	37.4644i	−1.25793	+	1.25793i	−0.952078	+	0.305855i	$0.901058\pi$
$888$	−18.4824	−	53.7304i	−0.620230	−	1.80307i
$889$	20.0945			0.673947
$890$		0			0
$891$	−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
$895$		0			0
$896$	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
$900$		0			0
$901$	−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
$905$		0			0
$906$	6.50248	−	14.8324i	0.216031	−	0.492773i
$907$	−0.181405			−0.00602345			−0.00301173	−	0.999995i	$-0.500959\pi$
$907$	−0.181405			−0.00602345			−0.00301173	+	0.999995i	$0.500959\pi$
$908$	28.4518	−	26.2132i	0.944208	−	0.869916i
$909$	4.22775	−	4.22775i	0.140226	−	0.140226i
$910$		0			0
$911$			23.4249i			0.776101i	0.921638	+	0.388050i	$0.126851\pi$
$911$			23.4249i			0.776101i	−0.921638	+	0.388050i	$0.873149\pi$
$912$	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
$915$		0			0
$916$	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	$0.0160659\pi$
$919$			3.05885i			0.100902i	−0.998727	+	0.0504511i	$0.983934\pi$
$920$		0			0
$921$		−	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
$925$		0			0
$926$	−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	$0.442794\pi$
$929$			59.9772i			1.96779i	−0.178752	+	0.983894i	$0.557206\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	4.65766	+	13.5403i	0.152240	+	0.442579i
$937$	23.7463	+	23.7463i	0.775759	+	0.775759i	0.979107	−	0.203347i	$-0.0651821\pi$
$937$	23.7463	+	23.7463i	0.775759	+	0.775759i	−0.203347	+	0.979107i	$0.565182\pi$
$938$	27.0029	−	10.5429i	0.881677	−	0.344239i
$939$	−26.8266	+	26.8266i	−0.875451	+	0.875451i
$940$		0			0
$941$	−35.2727	−	35.2727i	−1.14986	−	1.14986i	−0.986580	−	0.163278i	$-0.947793\pi$
$941$	−35.2727	−	35.2727i	−1.14986	−	1.14986i	−0.163278	−	0.986580i	$-0.552207\pi$
$942$	−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
$945$		0			0
$946$	−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
$950$		0			0
$951$	−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	$-0.927528\pi$
$953$	−23.1060	+	23.1060i	−0.748477	+	0.748477i	0.225716	+	0.974193i	$0.427528\pi$
$954$	−1.94941	+	4.44667i	−0.0631144	+	0.143966i
$955$		0			0
$956$	−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			0
$961$	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			0
$966$	−17.6068	+	40.1617i	−0.566490	+	1.29218i
$967$	41.7332	−	41.7332i	1.34205	−	1.34205i	0.448030	−	0.894018i	$-0.352126\pi$
$967$	41.7332	−	41.7332i	1.34205	−	1.34205i	0.894018	−	0.448030i	$-0.147874\pi$
$968$	−9.07255	−	26.3749i	−0.291603	−	0.847721i
$969$	5.99275			0.192515
$970$		0			0
$971$	33.5030	+	33.5030i	1.07516	+	1.07516i	0.996936	+	0.0782268i	$0.0249258\pi$
$971$	33.5030	+	33.5030i	1.07516	+	1.07516i	0.0782268	+	0.996936i	$0.475074\pi$
$972$	−11.6586	−	12.6543i	−0.373950	−	0.405885i
$973$			44.0330i			1.41163i
$974$	−15.9790	−	40.9259i	−0.511999	−	1.31135i
$975$		0			0
$976$	−2.93579	+	2.49060i	−0.0939723	+	0.0797223i
$977$	−9.16848	+	9.16848i	−0.293326	+	0.293326i	−0.838393	−	0.545067i	$-0.816504\pi$
$977$	−9.16848	+	9.16848i	−0.293326	+	0.293326i	0.545067	+	0.838393i	$0.316504\pi$
$978$	−8.71552	+	19.8804i	−0.278692	+	0.635706i
$979$	0.0321648	+	0.0321648i	0.00102799	+	0.00102799i
$980$		0			0
$981$	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	0.956742	+	0.290936i	$0.0939668\pi$
$983$	39.1183	+	39.1183i	1.24768	+	1.24768i	0.290936	+	0.956742i	$0.406033\pi$
$984$	−12.5186	−	36.3928i	−0.399077	−	1.16016i
$985$		0			0
$986$	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			0
$991$			12.9925i			0.412722i	0.978476	+	0.206361i	$0.0661621\pi$
$991$			12.9925i			0.412722i	−0.978476	+	0.206361i	$0.933838\pi$
$992$	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
$995$		0			0
$996$	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	400.2.s.d.243.4		18
4.3	odd	2		1600.2.s.d.943.8		18
5.2	odd	4		400.2.j.d.307.1		18
5.3	odd	4		80.2.j.b.67.9	yes	18
5.4	even	2		80.2.s.b.3.6	yes	18
15.8	even	4		720.2.bd.g.307.1		18
15.14	odd	2		720.2.z.g.163.4		18
16.5	even	4		1600.2.j.d.143.8		18
16.11	odd	4		400.2.j.d.43.1		18
20.3	even	4		320.2.j.b.47.8		18
20.7	even	4		1600.2.j.d.1007.2		18
20.19	odd	2		320.2.s.b.303.2		18
40.3	even	4		640.2.j.c.607.2		18
40.13	odd	4		640.2.j.d.607.8		18
40.19	odd	2		640.2.s.c.223.8		18
40.29	even	2		640.2.s.d.223.2		18
80.3	even	4		640.2.s.d.287.2		18
80.13	odd	4		640.2.s.c.287.8		18
80.19	odd	4		640.2.j.d.543.2		18
80.27	even	4	inner	400.2.s.d.107.4		18
80.29	even	4		640.2.j.c.543.8		18
80.37	odd	4		1600.2.s.d.207.8		18
80.43	even	4		80.2.s.b.27.6	yes	18
80.53	odd	4		320.2.s.b.207.2		18
80.59	odd	4		80.2.j.b.43.9	✓	18
80.69	even	4		320.2.j.b.143.2		18
240.59	even	4		720.2.bd.g.523.1		18
240.203	odd	4		720.2.z.g.667.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.9	✓	18	80.59	odd	4
80.2.j.b.67.9	yes	18	5.3	odd	4
80.2.s.b.3.6	yes	18	5.4	even	2
80.2.s.b.27.6	yes	18	80.43	even	4
320.2.j.b.47.8		18	20.3	even	4
320.2.j.b.143.2		18	80.69	even	4
320.2.s.b.207.2		18	80.53	odd	4
320.2.s.b.303.2		18	20.19	odd	2
400.2.j.d.43.1		18	16.11	odd	4
400.2.j.d.307.1		18	5.2	odd	4
400.2.s.d.107.4		18	80.27	even	4	inner
400.2.s.d.243.4		18	1.1	even	1	trivial
640.2.j.c.543.8		18	80.29	even	4
640.2.j.c.607.2		18	40.3	even	4
640.2.j.d.543.2		18	80.19	odd	4
640.2.j.d.607.8		18	40.13	odd	4
640.2.s.c.223.8		18	40.19	odd	2
640.2.s.c.287.8		18	80.13	odd	4
640.2.s.d.223.2		18	40.29	even	2
640.2.s.d.287.2		18	80.3	even	4
720.2.z.g.163.4		18	15.14	odd	2
720.2.z.g.667.4		18	240.203	odd	4
720.2.bd.g.307.1		18	15.8	even	4
720.2.bd.g.523.1		18	240.59	even	4
1600.2.j.d.143.8		18	16.5	even	4
1600.2.j.d.1007.2		18	20.7	even	4
1600.2.s.d.207.8		18	80.37	odd	4
1600.2.s.d.943.8		18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.567819 + 1.29521i) q^{2} -1.96251 q^{3} +(-1.35516 - 1.47090i) q^{4} +(1.11435 - 2.54187i) q^{6} +(1.60205 - 1.60205i) q^{7} +(2.67461 - 0.920026i) q^{8} +0.851447 q^{9} +O(q^{10})\)	\(q+(-0.567819 + 1.29521i) q^{2} -1.96251 q^{3} +(-1.35516 - 1.47090i) q^{4} +(1.11435 - 2.54187i) q^{6} +(1.60205 - 1.60205i) q^{7} +(2.67461 - 0.920026i) q^{8} +0.851447 q^{9} +(0.754587 + 0.754587i) q^{11} +(2.65952 + 2.88665i) q^{12} +5.94580i q^{13} +(1.16532 + 2.98467i) q^{14} +(-0.327065 + 3.98661i) q^{16} +(-1.95574 + 1.95574i) q^{17} +(-0.483468 + 1.10281i) q^{18} +(0.780680 + 0.780680i) q^{19} +(-3.14404 + 3.14404i) q^{21} +(-1.40582 + 0.548884i) q^{22} +(-4.93121 - 4.93121i) q^{23} +(-5.24896 + 1.80556i) q^{24} +(-7.70109 - 3.37614i) q^{26} +4.21656 q^{27} +(-4.52748 - 0.185408i) q^{28} +(-1.44802 + 1.44802i) q^{29} +3.60859i q^{31} +(-4.97780 - 2.68729i) q^{32} +(-1.48089 - 1.48089i) q^{33} +(-1.42260 - 3.64361i) q^{34} +(-1.15385 - 1.25239i) q^{36} +10.2364i q^{37} +(-1.45443 + 0.567864i) q^{38} -11.6687i q^{39} +6.93334i q^{41} +(-2.28696 - 5.85745i) q^{42} +9.91344i q^{43} +(0.0873298 - 2.13251i) q^{44} +(9.18700 - 3.58694i) q^{46} +(-0.104270 - 0.104270i) q^{47} +(0.641868 - 7.82376i) q^{48} +1.86688i q^{49} +(3.83816 - 3.83816i) q^{51} +(8.74565 - 8.05753i) q^{52} +4.03213 q^{53} +(-2.39424 + 5.46135i) q^{54} +(2.81093 - 5.75878i) q^{56} +(-1.53209 - 1.53209i) q^{57} +(-1.05328 - 2.69771i) q^{58} +(-3.46736 + 3.46736i) q^{59} +(0.680578 + 0.680578i) q^{61} +(-4.67390 - 2.04902i) q^{62} +(1.36406 - 1.36406i) q^{63} +(6.30711 - 4.92142i) q^{64} +(2.75894 - 1.07719i) q^{66} -9.04721i q^{67} +(5.52703 + 0.226341i) q^{68} +(9.67754 + 9.67754i) q^{69} -3.64007 q^{71} +(2.27729 - 0.783353i) q^{72} +(2.94030 - 2.94030i) q^{73} +(-13.2583 - 5.81242i) q^{74} +(0.0903496 - 2.20625i) q^{76} +2.41777 q^{77} +(15.1135 + 6.62570i) q^{78} +10.7140 q^{79} -10.8294 q^{81} +(-8.98016 - 3.93688i) q^{82} +4.23845 q^{83} +(8.88523 + 0.363865i) q^{84} +(-12.8400 - 5.62904i) q^{86} +(2.84176 - 2.84176i) q^{87} +(2.71247 + 1.32399i) q^{88} +0.0426256 q^{89} +(9.52546 + 9.52546i) q^{91} +(-0.570698 + 13.9359i) q^{92} -7.08189i q^{93} +(0.194258 - 0.0758455i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} + 6 q^{17} + 24 q^{18} - 2 q^{19} - 16 q^{21} - 12 q^{22} + 2 q^{23} - 4 q^{24} - 16 q^{26} + 24 q^{27} - 40 q^{28} + 14 q^{29} - 20 q^{32} + 8 q^{33} + 28 q^{34} - 4 q^{36} - 24 q^{38} - 8 q^{42} - 44 q^{44} + 12 q^{46} - 38 q^{47} - 4 q^{48} + 8 q^{51} - 8 q^{52} - 12 q^{53} + 4 q^{54} + 20 q^{56} + 24 q^{57} - 20 q^{58} + 10 q^{59} + 14 q^{61} + 40 q^{62} + 6 q^{63} + 16 q^{64} + 4 q^{66} + 60 q^{68} - 32 q^{69} + 24 q^{71} + 68 q^{72} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 44 q^{77} + 36 q^{78} - 16 q^{79} + 2 q^{81} - 48 q^{82} - 40 q^{83} + 24 q^{84} - 36 q^{86} - 24 q^{87} + 8 q^{88} + 12 q^{89} + 8 q^{92} - 28 q^{94} - 40 q^{96} - 18 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 + 6 * q^17 + 24 * q^18 - 2 * q^19 - 16 * q^21 - 12 * q^22 + 2 * q^23 - 4 * q^24 - 16 * q^26 + 24 * q^27 - 40 * q^28 + 14 * q^29 - 20 * q^32 + 8 * q^33 + 28 * q^34 - 4 * q^36 - 24 * q^38 - 8 * q^42 - 44 * q^44 + 12 * q^46 - 38 * q^47 - 4 * q^48 + 8 * q^51 - 8 * q^52 - 12 * q^53 + 4 * q^54 + 20 * q^56 + 24 * q^57 - 20 * q^58 + 10 * q^59 + 14 * q^61 + 40 * q^62 + 6 * q^63 + 16 * q^64 + 4 * q^66 + 60 * q^68 - 32 * q^69 + 24 * q^71 + 68 * q^72 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 44 * q^77 + 36 * q^78 - 16 * q^79 + 2 * q^81 - 48 * q^82 - 40 * q^83 + 24 * q^84 - 36 * q^86 - 24 * q^87 + 8 * q^88 + 12 * q^89 + 8 * q^92 - 28 * q^94 - 40 * q^96 - 18 * q^97 + 56 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

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