LMFDB - Embedded newform 847.2.f.u.729.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 $ x^12 - x^11 + 7x^10 - 15x^9 + 59x^8 + 118x^7 + 266x^6 + 324x^5 + 1036x^4 + 376x^3 + 136x^2 + 48x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.2
Root			$0.112275 - 0.345546i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.u.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10296 - 0.801344i) q^{2} +(0.112275 + 0.345546i) q^{3} +(-0.0436753 + 0.134419i) q^{4} +(-2.54139 - 1.84643i) q^{5} +(0.400735 + 0.291151i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.902127 + 2.77646i) q^{8} +(2.32025 - 1.68576i) q^{9} +O(q^{10})$	\(q+(1.10296 - 0.801344i) q^{2} +(0.112275 + 0.345546i) q^{3} +(-0.0436753 + 0.134419i) q^{4} +(-2.54139 - 1.84643i) q^{5} +(0.400735 + 0.291151i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.902127 + 2.77646i) q^{8} +(2.32025 - 1.68576i) q^{9} -4.28267 q^{10} -0.0513514 q^{12} +(3.86549 - 2.80844i) q^{13} +(0.421292 + 1.29660i) q^{14} +(0.352692 - 1.08548i) q^{15} +(2.99122 + 2.17325i) q^{16} +(3.86549 + 2.80844i) q^{17} +(1.20826 - 3.71865i) q^{18} +(-2.16600 - 6.66627i) q^{19} +(0.359191 - 0.260967i) q^{20} -0.363328 q^{21} +5.14134 q^{23} +(-0.858108 + 0.623452i) q^{24} +(1.50429 + 4.62974i) q^{25} +(2.01293 - 6.19518i) q^{26} +(1.72483 + 1.25316i) q^{27} +(-0.114343 - 0.0830753i) q^{28} +(2.16600 - 6.66627i) q^{29} +(-0.480835 - 1.47986i) q^{30} +(2.94213 - 2.13758i) q^{31} -0.797984 q^{32} +6.51399 q^{34} +(2.54139 - 1.84643i) q^{35} +(0.125260 + 0.385512i) q^{36} +(-3.04938 + 9.38502i) q^{37} +(-7.73098 - 5.61689i) q^{38} +(1.40444 + 1.02039i) q^{39} +(2.83388 - 8.72180i) q^{40} +(-0.995650 - 3.06430i) q^{41} +(-0.400735 + 0.291151i) q^{42} +4.28267 q^{43} -9.00933 q^{45} +(5.67067 - 4.11998i) q^{46} +(-0.240418 - 0.739929i) q^{47} +(-0.415119 + 1.27760i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(5.36918 + 3.90094i) q^{50} +(-0.536449 + 1.65102i) q^{51} +(0.208681 + 0.642253i) q^{52} +(-1.84672 + 1.34172i) q^{53} +2.90663 q^{54} -2.91934 q^{56} +(2.06031 - 1.49691i) q^{57} +(-2.95297 - 9.08831i) q^{58} +(-0.112275 + 0.345546i) q^{59} +(0.130504 + 0.0948168i) q^{60} +(-2.60665 - 1.89384i) q^{61} +(1.53210 - 4.71532i) q^{62} +(0.886258 + 2.72762i) q^{63} +(-6.86258 + 4.98596i) q^{64} -15.0093 q^{65} -6.59465 q^{67} +(-0.546333 + 0.396934i) q^{68} +(0.577241 + 1.77657i) q^{69} +(1.32342 - 4.07306i) q^{70} +(12.2647 + 8.91082i) q^{71} +(6.77362 + 4.92132i) q^{72} +(-0.995650 + 3.06430i) q^{73} +(4.15730 + 12.7949i) q^{74} +(-1.43089 + 1.03960i) q^{75} +0.990671 q^{76} +2.36672 q^{78} +(3.00738 - 2.18499i) q^{79} +(-3.58912 - 11.0462i) q^{80} +(2.41941 - 7.44616i) q^{81} +(-3.55371 - 2.58192i) q^{82} +(-1.25884 - 0.914603i) q^{83} +(0.0158685 - 0.0488381i) q^{84} +(-4.63814 - 14.2747i) q^{85} +(4.72360 - 3.43189i) q^{86} +2.54669 q^{87} -5.58532 q^{89} +(-9.93689 + 7.21957i) q^{90} +(1.47649 + 4.54416i) q^{91} +(-0.224549 + 0.691091i) q^{92} +(1.06896 + 0.776644i) q^{93} +(-0.858108 - 0.623452i) q^{94} +(-6.80414 + 20.9410i) q^{95} +(-0.0895933 - 0.275740i) q^{96} +(-4.97599 + 3.61527i) q^{97} -1.36333 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9	$ 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9} + 16 q^{10} + 8 q^{12} + 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} + 8 q^{17} - 18 q^{18} + 14 q^{20} + 4 q^{21} + 28 q^{23} + 20 q^{24} - 2 q^{25} + 12 q^{26} + 19 q^{27} + 8 q^{28} - 8 q^{30} + 13 q^{31} - 136 q^{32} - 48 q^{34} + q^{35} - 18 q^{36} + 17 q^{37} - 16 q^{38} - 20 q^{39} - 36 q^{40} + 16 q^{41} - 12 q^{42} - 16 q^{43} - 24 q^{45} - 4 q^{47} - 36 q^{48} - 3 q^{49} + 22 q^{50} - 20 q^{51} + 10 q^{53} - 32 q^{54} + 24 q^{56} + 16 q^{57} + 16 q^{58} - q^{59} + 30 q^{60} - 16 q^{61} + 4 q^{62} + 4 q^{63} - 34 q^{64} - 96 q^{65} - 12 q^{67} + 7 q^{69} + 4 q^{70} - 5 q^{71} + 2 q^{72} + 16 q^{73} - 32 q^{74} - 20 q^{75} + 96 q^{76} + 112 q^{78} + 28 q^{79} + 56 q^{80} - 15 q^{81} - 28 q^{82} + 8 q^{83} + 2 q^{84} + 24 q^{85} - 12 q^{86} + 64 q^{87} - 84 q^{89} - 20 q^{90} - 8 q^{91} - 2 q^{92} - 17 q^{93} + 20 q^{94} + 24 q^{95} + 20 q^{96} + 11 q^{97} - 8 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9 + 16 * q^10 + 8 * q^12 + 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 + 8 * q^17 - 18 * q^18 + 14 * q^20 + 4 * q^21 + 28 * q^23 + 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 + 8 * q^28 - 8 * q^30 + 13 * q^31 - 136 * q^32 - 48 * q^34 + q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 - 20 * q^39 - 36 * q^40 + 16 * q^41 - 12 * q^42 - 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 + 22 * q^50 - 20 * q^51 + 10 * q^53 - 32 * q^54 + 24 * q^56 + 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^63 - 34 * q^64 - 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 + 2 * q^72 + 16 * q^73 - 32 * q^74 - 20 * q^75 + 96 * q^76 + 112 * q^78 + 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 + 8 * q^83 + 2 * q^84 + 24 * q^85 - 12 * q^86 + 64 * q^87 - 84 * q^89 - 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 + 20 * q^94 + 24 * q^95 + 20 * q^96 + 11 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.10296	−	0.801344i	0.779907	−	0.566636i	−0.125044	−	0.992151i	$-0.539907\pi$
$2$	1.10296	−	0.801344i	0.779907	−	0.566636i	0.904951	+	0.425515i	$0.139907\pi$
$3$	0.112275	+	0.345546i	0.0648218	+	0.199501i	0.978222	−	0.207562i	$-0.0665529\pi$
$3$	0.112275	+	0.345546i	0.0648218	+	0.199501i	−0.913400	+	0.407063i	$0.866553\pi$
$4$	−0.0436753	+	0.134419i	−0.0218376	+	0.0672093i
$5$	−2.54139	−	1.84643i	−1.13655	−	0.825749i	−0.149912	−	0.988699i	$-0.547899\pi$
$5$	−2.54139	−	1.84643i	−1.13655	−	0.825749i	−0.986634	+	0.162950i	$0.947899\pi$
$6$	0.400735	+	0.291151i	0.163599	+	0.118862i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.902127	+	2.77646i	0.318950	+	0.981627i
$9$	2.32025	−	1.68576i	0.773418	−	0.561921i
$10$	−4.28267			−1.35430
$11$		0			0
$11$		0			0
$12$	−0.0513514			−0.0148239
$13$	3.86549	−	2.80844i	1.07209	−	0.778922i	0.0958065	−	0.995400i	$-0.469457\pi$
$13$	3.86549	−	2.80844i	1.07209	−	0.778922i	0.976287	+	0.216478i	$0.0694570\pi$
$14$	0.421292	+	1.29660i	0.112595	+	0.346532i
$15$	0.352692	−	1.08548i	0.0910647	−	0.280268i
$16$	2.99122	+	2.17325i	0.747805	+	0.543312i
$17$	3.86549	+	2.80844i	0.937519	+	0.681147i	0.947822	−	0.318800i	$-0.103280\pi$
$17$	3.86549	+	2.80844i	0.937519	+	0.681147i	−0.0103032	+	0.999947i	$0.503280\pi$
$18$	1.20826	−	3.71865i	0.284790	−	0.876493i
$19$	−2.16600	−	6.66627i	−0.496915	−	1.52935i	−0.813951	−	0.580933i	$-0.802688\pi$
$19$	−2.16600	−	6.66627i	−0.496915	−	1.52935i	0.317036	−	0.948413i	$-0.397312\pi$
$20$	0.359191	−	0.260967i	0.0803175	−	0.0583541i
$21$	−0.363328			−0.0792847
$22$		0			0
$23$	5.14134			1.07204			0.536021	−	0.844204i	$-0.319927\pi$
$23$	5.14134			1.07204			0.536021	+	0.844204i	$0.319927\pi$
$24$	−0.858108	+	0.623452i	−0.175161	+	0.127262i
$25$	1.50429	+	4.62974i	0.300858	+	0.925947i
$26$	2.01293	−	6.19518i	0.394769	−	1.21497i
$27$	1.72483	+	1.25316i	0.331944	+	0.241171i
$28$	−0.114343	−	0.0830753i	−0.0216089	−	0.0156998i
$29$	2.16600	−	6.66627i	0.402216	−	1.23789i	−0.520981	−	0.853568i	$-0.674434\pi$
$29$	2.16600	−	6.66627i	0.402216	−	1.23789i	0.923197	−	0.384326i	$-0.125566\pi$
$30$	−0.480835	−	1.47986i	−0.0877881	−	0.270184i
$31$	2.94213	−	2.13758i	0.528422	−	0.383921i	−0.291345	−	0.956618i	$-0.594103\pi$
$31$	2.94213	−	2.13758i	0.528422	−	0.383921i	0.819767	+	0.572697i	$0.194103\pi$
$32$	−0.797984			−0.141065
$33$		0			0
$34$	6.51399			1.11714
$35$	2.54139	−	1.84643i	0.429574	−	0.312104i
$36$	0.125260	+	0.385512i	0.0208767	+	0.0642519i
$37$	−3.04938	+	9.38502i	−0.501315	+	1.54289i	0.305565	+	0.952171i	$0.401155\pi$
$37$	−3.04938	+	9.38502i	−0.501315	+	1.54289i	−0.806879	+	0.590716i	$0.798845\pi$
$38$	−7.73098	−	5.61689i	−1.25413	−	0.911179i
$39$	1.40444	+	1.02039i	0.224891	+	0.163393i
$40$	2.83388	−	8.72180i	0.448076	−	1.37904i
$41$	−0.995650	−	3.06430i	−0.155494	−	0.478563i	0.842716	−	0.538358i	$-0.180955\pi$
$41$	−0.995650	−	3.06430i	−0.155494	−	0.478563i	−0.998211	+	0.0597953i	$0.980955\pi$
$42$	−0.400735	+	0.291151i	−0.0618347	+	0.0449256i
$43$	4.28267			0.653101			0.326551	−	0.945180i	$-0.394114\pi$
$43$	4.28267			0.653101			0.326551	+	0.945180i	$0.394114\pi$
$44$		0			0
$45$	−9.00933			−1.34303
$46$	5.67067	−	4.11998i	0.836094	−	0.607458i
$47$	−0.240418	−	0.739929i	−0.0350685	−	0.107930i	0.931990	−	0.362484i	$-0.118071\pi$
$47$	−0.240418	−	0.739929i	−0.0350685	−	0.107930i	−0.967059	+	0.254554i	$0.918071\pi$
$48$	−0.415119	+	1.27760i	−0.0599172	+	0.184406i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	5.36918	+	3.90094i	0.759317	+	0.551676i
$51$	−0.536449	+	1.65102i	−0.0751179	+	0.231189i
$52$	0.208681	+	0.642253i	0.0289388	+	0.0890645i
$53$	−1.84672	+	1.34172i	−0.253667	+	0.184300i	−0.707350	−	0.706863i	$-0.750110\pi$
$53$	−1.84672	+	1.34172i	−0.253667	+	0.184300i	0.453684	+	0.891163i	$0.350110\pi$
$54$	2.90663			0.395542
$55$		0			0
$56$	−2.91934			−0.390114
$57$	2.06031	−	1.49691i	0.272895	−	0.198270i
$58$	−2.95297	−	9.08831i	−0.387744	−	1.19335i
$59$	−0.112275	+	0.345546i	−0.0146169	+	0.0449862i	−0.958099	−	0.286437i	$-0.907529\pi$
$59$	−0.112275	+	0.345546i	−0.0146169	+	0.0449862i	0.943482	+	0.331424i	$0.107529\pi$
$60$	0.130504	+	0.0948168i	0.0168480	+	0.0122408i
$61$	−2.60665	−	1.89384i	−0.333747	−	0.242481i	0.408272	−	0.912860i	$-0.366132\pi$
$61$	−2.60665	−	1.89384i	−0.333747	−	0.242481i	−0.742019	+	0.670379i	$0.766132\pi$
$62$	1.53210	−	4.71532i	0.194577	−	0.598846i
$63$	0.886258	+	2.72762i	0.111658	+	0.343648i
$64$	−6.86258	+	4.98596i	−0.857823	+	0.623245i
$65$	−15.0093			−1.86168
$66$		0			0
$67$	−6.59465			−0.805665			−0.402832	−	0.915274i	$-0.631974\pi$
$67$	−6.59465			−0.805665			−0.402832	+	0.915274i	$0.631974\pi$
$68$	−0.546333	+	0.396934i	−0.0662526	+	0.0481354i
$69$	0.577241	+	1.77657i	0.0694917	+	0.213873i
$70$	1.32342	−	4.07306i	0.158179	−	0.486824i
$71$	12.2647	+	8.91082i	1.45555	+	1.05752i	0.984494	+	0.175417i	$0.0561274\pi$
$71$	12.2647	+	8.91082i	1.45555	+	1.05752i	0.471057	+	0.882103i	$0.343873\pi$
$72$	6.77362	+	4.92132i	0.798279	+	0.579984i
$73$	−0.995650	+	3.06430i	−0.116532	+	0.358649i	−0.992263	−	0.124150i	$-0.960380\pi$
$73$	−0.995650	+	3.06430i	−0.116532	+	0.358649i	0.875731	+	0.482799i	$0.160380\pi$
$74$	4.15730	+	12.7949i	0.483277	+	1.48737i
$75$	−1.43089	+	1.03960i	−0.165225	+	0.120043i
$76$	0.990671			0.113638
$77$		0			0
$78$	2.36672			0.267978
$79$	3.00738	−	2.18499i	0.338357	−	0.245831i	−0.405611	−	0.914046i	$-0.632941\pi$
$79$	3.00738	−	2.18499i	0.338357	−	0.245831i	0.743968	+	0.668215i	$0.232941\pi$
$80$	−3.58912	−	11.0462i	−0.401275	−	1.23500i
$81$	2.41941	−	7.44616i	0.268823	−	0.827351i
$82$	−3.55371	−	2.58192i	−0.392442	−	0.285126i
$83$	−1.25884	−	0.914603i	−0.138176	−	0.100391i	0.516550	−	0.856257i	$-0.327216\pi$
$83$	−1.25884	−	0.914603i	−0.138176	−	0.100391i	−0.654726	+	0.755866i	$0.727216\pi$
$84$	0.0158685	−	0.0488381i	0.00173139	−	0.00532867i
$85$	−4.63814	−	14.2747i	−0.503077	−	1.54831i
$86$	4.72360	−	3.43189i	0.509359	−	0.370071i
$87$	2.54669			0.273034
$88$		0			0
$89$	−5.58532			−0.592043			−0.296021	−	0.955181i	$-0.595660\pi$
$89$	−5.58532			−0.592043			−0.296021	+	0.955181i	$0.595660\pi$
$90$	−9.93689	+	7.21957i	−1.04744	+	0.761010i
$91$	1.47649	+	4.54416i	0.154778	+	0.476357i
$92$	−0.224549	+	0.691091i	−0.0234109	+	0.0720513i
$93$	1.06896	+	0.776644i	0.110846	+	0.0805342i
$94$	−0.858108	−	0.623452i	−0.0885071	−	0.0643042i
$95$	−6.80414	+	20.9410i	−0.698090	+	2.14850i
$96$	−0.0895933	−	0.275740i	−0.00914408	−	0.0281426i
$97$	−4.97599	+	3.61527i	−0.505235	+	0.367075i	−0.811013	−	0.585028i	$-0.801084\pi$
$97$	−4.97599	+	3.61527i	−0.505235	+	0.367075i	0.305778	+	0.952103i	$0.401084\pi$
$98$	−1.36333			−0.137717
$99$		0			0
$100$	−0.688023			−0.0688023
$101$	8.73469	−	6.34612i	0.869134	−	0.631463i	−0.0612206	−	0.998124i	$-0.519499\pi$
$101$	8.73469	−	6.34612i	0.869134	−	0.631463i	0.930354	+	0.366662i	$0.119499\pi$
$102$	0.731356	+	2.25088i	0.0724150	+	0.222871i
$103$	−4.09159	+	12.5926i	−0.403156	+	1.24079i	0.519269	+	0.854611i	$0.326204\pi$
$103$	−4.09159	+	12.5926i	−0.403156	+	1.24079i	−0.922425	+	0.386176i	$0.873796\pi$
$104$	11.2847	+	8.19881i	1.10656	+	0.803959i
$105$	0.923360	+	0.670861i	0.0901107	+	0.0654693i
$106$	−0.961671	+	2.95972i	−0.0934057	+	0.287473i
$107$	4.33200	+	13.3325i	0.418791	+	1.28890i	0.908816	+	0.417197i	$0.136987\pi$
$107$	4.33200	+	13.3325i	0.418791	+	1.28890i	−0.490026	+	0.871708i	$0.663013\pi$
$108$	−0.243781	+	0.177117i	−0.0234578	+	0.0170431i
$109$	−15.5747			−1.49178			−0.745892	−	0.666067i	$-0.767976\pi$
$109$	−15.5747			−1.49178			−0.745892	+	0.666067i	$0.767976\pi$
$110$		0			0
$111$	−3.58532			−0.340304
$112$	−2.99122	+	2.17325i	−0.282644	+	0.205353i
$113$	1.27686	+	3.92977i	0.120117	+	0.369682i	0.992980	−	0.118284i	$-0.0377392\pi$
$113$	1.27686	+	3.92977i	0.120117	+	0.369682i	−0.872863	+	0.487965i	$0.837739\pi$
$114$	1.07290	−	3.30204i	0.100486	−	0.309264i
$115$	−13.0662	−	9.49312i	−1.21843	−	0.885238i
$116$	0.801470	+	0.582302i	0.0744146	+	0.0540654i
$117$	4.23455	−	13.0326i	0.391484	−	1.20486i
$118$	0.153067	+	0.471092i	0.0140910	+	0.0433676i
$119$	−3.86549	+	2.80844i	−0.354349	+	0.257450i
$120$	3.33195			0.304164
$121$		0			0
$122$	−4.39263			−0.397690
$123$	0.947068	−	0.688085i	0.0853943	−	0.0620426i
$124$	0.158833	+	0.488836i	0.0142636	+	0.0438988i
$125$	−0.128143	+	0.394384i	−0.0114615	+	0.0352748i
$126$	3.16327	+	2.29825i	0.281806	+	0.204744i
$127$	−17.8135	−	12.9422i	−1.58069	−	1.14844i	−0.915899	−	0.401408i	$-0.868521\pi$
$127$	−17.8135	−	12.9422i	−1.58069	−	1.14844i	−0.664791	−	0.747030i	$-0.731479\pi$
$128$	−3.08047	+	9.48073i	−0.272278	+	0.837986i
$129$	0.480835	+	1.47986i	0.0423352	+	0.130294i
$130$	−16.5546	+	12.0276i	−1.45194	+	1.05489i
$131$	15.0093			1.31137			0.655686	−	0.755034i	$-0.272380\pi$
$131$	15.0093			1.31137			0.655686	+	0.755034i	$0.272380\pi$
$132$		0			0
$133$	7.00933			0.607786
$134$	−7.27361	+	5.28458i	−0.628344	+	0.456519i
$135$	−2.06960	−	6.36956i	−0.178122	−	0.548204i
$136$	−4.31037	+	13.2660i	−0.369611	+	1.13755i
$137$	8.65434	+	6.28775i	0.739390	+	0.537198i	0.892520	−	0.451008i	$-0.148935\pi$
$137$	8.65434	+	6.28775i	0.739390	+	0.537198i	−0.153130	+	0.988206i	$0.548935\pi$
$138$	2.06031	+	1.49691i	0.175385	+	0.127425i
$139$	1.26780	−	3.90190i	0.107534	−	0.330955i	−0.882783	−	0.469781i	$-0.844333\pi$
$139$	1.26780	−	3.90190i	0.107534	−	0.330955i	0.990317	+	0.138826i	$0.0443329\pi$
$140$	0.137199	+	0.422254i	0.0115954	+	0.0356870i
$141$	0.228687	−	0.166151i	0.0192589	−	0.0139924i
$142$	20.6680			1.73442
$143$		0			0
$144$	10.6040			0.883665
$145$	−17.8135	+	12.9422i	−1.47933	+	1.07479i
$146$	1.35740	+	4.17764i	0.112339	+	0.345744i
$147$	0.112275	−	0.345546i	0.00926025	−	0.0285001i
$148$	−1.12834	−	0.819786i	−0.0927489	−	0.0673860i
$149$	−11.3413	−	8.23996i	−0.929118	−	0.675044i	0.0166586	−	0.999861i	$-0.494697\pi$
$149$	−11.3413	−	8.23996i	−0.929118	−	0.675044i	−0.945777	+	0.324817i	$0.894697\pi$
$150$	−0.745130	+	2.29327i	−0.0608396	+	0.187245i
$151$	−2.11039	−	6.49511i	−0.171741	−	0.528564i	0.827729	−	0.561129i	$-0.189633\pi$
$151$	−2.11039	−	6.49511i	−0.171741	−	0.528564i	−0.999470	+	0.0325642i	$0.989633\pi$
$152$	16.5546	−	12.0276i	1.34276	−	0.975570i
$153$	13.7033			1.10785
$154$		0			0
$155$	−11.4240			−0.917598
$156$	−0.198498	+	0.144217i	−0.0158926	+	0.0115466i
$157$	−7.24418	−	22.2953i	−0.578149	−	1.77936i	−0.625198	−	0.780466i	$-0.714982\pi$
$157$	−7.24418	−	22.2953i	−0.578149	−	1.77936i	0.0470494	−	0.998893i	$-0.485018\pi$
$158$	1.56608	−	4.81990i	0.124591	−	0.383450i
$159$	−0.670966	−	0.487485i	−0.0532110	−	0.0386601i
$160$	2.02799	+	1.47342i	0.160327	+	0.116484i
$161$	−1.58876	+	4.88970i	−0.125212	+	0.385362i
$162$	−3.29844	−	10.1516i	−0.259150	−	0.797582i
$163$	0.801470	−	0.582302i	0.0627760	−	0.0456094i	−0.555955	−	0.831213i	$-0.687647\pi$
$163$	0.801470	−	0.582302i	0.0627760	−	0.0456094i	0.618731	+	0.785603i	$0.287647\pi$
$164$	0.455384			0.0355595
$165$		0			0
$166$	−2.12136			−0.164649
$167$	−0.457373	+	0.332301i	−0.0353926	+	0.0257142i	−0.605341	−	0.795966i	$-0.706963\pi$
$167$	−0.457373	+	0.332301i	−0.0353926	+	0.0257142i	0.569948	+	0.821681i	$0.306963\pi$
$168$	−0.327768	−	1.00877i	−0.0252879	−	0.0778280i
$169$	3.03744	−	9.34828i	0.233649	−	0.719098i
$170$	−16.5546	−	12.0276i	−1.26968	−	0.922478i
$171$	−16.2634	−	11.8161i	−1.24370	−	0.903598i
$172$	−0.187047	+	0.575671i	−0.0142622	+	0.0438945i
$173$	−5.32765	−	16.3968i	−0.405054	−	1.24663i	−0.920850	−	0.389917i	$-0.872504\pi$
$173$	−5.32765	−	16.3968i	−0.405054	−	1.24663i	0.515796	−	0.856711i	$-0.327496\pi$
$174$	2.80888	−	2.04077i	0.212941	−	0.154711i
$175$	−4.86799			−0.367986
$176$		0			0
$177$	−0.132007			−0.00992228
$178$	−6.16036	+	4.47576i	−0.461739	+	0.335473i
$179$	3.49848	+	10.7672i	0.261488	+	0.804778i	0.992482	+	0.122394i	$0.0390571\pi$
$179$	3.49848	+	10.7672i	0.261488	+	0.804778i	−0.730993	+	0.682385i	$0.760943\pi$
$180$	0.393485	−	1.21102i	0.0293286	−	0.0902642i
$181$	−12.0360	−	8.74467i	−0.894629	−	0.649986i	0.0424516	−	0.999099i	$-0.486483\pi$
$181$	−12.0360	−	8.74467i	−0.894629	−	0.649986i	−0.937081	+	0.349112i	$0.886483\pi$
$182$	5.26993	+	3.82883i	0.390633	+	0.283812i
$183$	0.361748	−	1.11335i	0.0267412	−	0.0823009i
$184$	4.63814	+	14.2747i	0.341928	+	1.05235i
$185$	25.0785	−	18.2206i	1.84381	−	1.33960i
$186$	1.80137			0.132083
$187$		0			0
$188$	0.109961			0.00801970
$189$	−1.72483	+	1.25316i	−0.125463	+	0.0911542i
$190$	9.27628	+	28.5494i	0.672972	+	2.07119i
$191$	1.18951	−	3.66094i	0.0860699	−	0.264896i	−0.898754	−	0.438454i	$-0.855526\pi$
$191$	1.18951	−	3.66094i	0.0860699	−	0.264896i	0.984824	+	0.173558i	$0.0555263\pi$
$192$	−2.49337	−	1.81154i	−0.179943	−	0.130737i
$193$	2.06031	+	1.49691i	0.148305	+	0.107750i	0.659463	−	0.751737i	$-0.270784\pi$
$193$	2.06031	+	1.49691i	0.148305	+	0.107750i	−0.511159	+	0.859486i	$0.670784\pi$
$194$	−2.59122	+	7.97497i	−0.186039	+	0.572569i
$195$	−1.68517	−	5.18641i	−0.120677	−	0.371406i
$196$	0.114343	−	0.0830753i	0.00816738	−	0.00593395i
$197$	−10.5467			−0.751420			−0.375710	−	0.926737i	$-0.622601\pi$
$197$	−10.5467			−0.751420			−0.375710	+	0.926737i	$0.622601\pi$
$198$		0			0
$199$	11.6846			0.828302			0.414151	−	0.910208i	$-0.364079\pi$
$199$	11.6846			0.828302			0.414151	+	0.910208i	$0.364079\pi$
$200$	−11.4972	+	8.35322i	−0.812976	+	0.590662i
$201$	−0.740412	−	2.27875i	−0.0522246	−	0.160731i
$202$	4.54854	−	13.9990i	0.320034	−	0.984965i
$203$	5.67067	+	4.11998i	0.398003	+	0.289166i
$204$	−0.198498	−	0.144217i	−0.0138977	−	0.0100972i
$205$	−3.12767	+	9.62599i	−0.218446	+	0.672308i
$206$	5.57817	+	17.1679i	0.388650	+	1.19614i
$207$	11.9292	−	8.66708i	0.829137	−	0.602404i
$208$	17.6660			1.22492
$209$		0			0
$210$	1.55602			0.107375
$211$	−8.98982	+	6.53149i	−0.618885	+	0.449646i	−0.852532	−	0.522675i	$-0.824934\pi$
$211$	−8.98982	+	6.53149i	−0.618885	+	0.449646i	0.233647	+	0.972322i	$0.424934\pi$
$212$	−0.0996963	−	0.306834i	−0.00684717	−	0.0210734i
$213$	−1.70208	+	5.23847i	−0.116625	+	0.358934i
$214$	15.4620	+	11.2338i	1.05696	+	0.767925i
$215$	−10.8840	−	7.90766i	−0.742280	−	0.539298i
$216$	−1.92334	+	5.91944i	−0.130867	+	0.402767i
$217$	1.12379	+	3.45868i	0.0762881	+	0.234791i
$218$	−17.1782	+	12.4807i	−1.16345	+	0.845298i
$219$	−1.17064			−0.0791046
$220$		0			0
$221$	22.8294			1.53567
$222$	−3.95445	+	2.87308i	−0.265405	+	0.192828i
$223$	8.66505	+	26.6683i	0.580255	+	1.78584i	0.617544	+	0.786537i	$0.288128\pi$
$223$	8.66505	+	26.6683i	0.580255	+	1.78584i	−0.0372888	+	0.999305i	$0.511872\pi$
$224$	0.246591	−	0.758928i	0.0164760	−	0.0507080i
$225$	11.2950	+	8.20629i	0.752999	+	0.547086i
$226$	4.55742	+	3.31116i	0.303155	+	0.220255i
$227$	−7.11027	+	21.8832i	−0.471925	+	1.45244i	0.378134	+	0.925751i	$0.376566\pi$
$227$	−7.11027	+	21.8832i	−0.471925	+	1.45244i	−0.850060	+	0.526686i	$0.823434\pi$
$228$	0.111227	+	0.342322i	0.00736620	+	0.0226708i
$229$	−10.8603	+	7.89043i	−0.717666	+	0.521415i	−0.885638	−	0.464377i	$-0.846278\pi$
$229$	−10.8603	+	7.89043i	−0.717666	+	0.521415i	0.167972	+	0.985792i	$0.446278\pi$
$230$	−22.0187			−1.45187
$231$		0			0
$232$	20.4626			1.34344
$233$	2.86178	−	2.07921i	0.187482	−	0.136213i	−0.490085	−	0.871674i	$-0.663034\pi$
$233$	2.86178	−	2.07921i	0.187482	−	0.136213i	0.677567	+	0.735461i	$0.263034\pi$
$234$	−5.77308	−	17.7677i	−0.377398	−	1.16151i
$235$	−0.755233	+	2.32437i	−0.0492659	+	0.151625i
$236$	−0.0415442	−	0.0301836i	−0.00270429	−	0.00196478i
$237$	1.09267	+	0.793869i	0.0709763	+	0.0515673i
$238$	−2.01293	+	6.19518i	−0.130479	+	0.401574i
$239$	6.80414	+	20.9410i	0.440123	+	1.35456i	0.887744	+	0.460337i	$0.152271\pi$
$239$	6.80414	+	20.9410i	0.440123	+	1.35456i	−0.447621	+	0.894223i	$0.647729\pi$
$240$	3.41399	−	2.48041i	0.220372	−	0.160110i
$241$	−0.315366			−0.0203145			−0.0101573	−	0.999948i	$-0.503233\pi$
$241$	−0.315366			−0.0203145			−0.0101573	+	0.999948i	$0.503233\pi$
$242$		0			0
$243$	9.24065			0.592788
$244$	0.368413	−	0.267668i	0.0235852	−	0.0171357i
$245$	0.970726	+	2.98759i	0.0620174	+	0.190870i
$246$	0.493181	−	1.51786i	0.0314441	−	0.0967749i
$247$	−27.0945	−	19.6853i	−1.72398	−	1.25255i
$248$	8.58909	+	6.24034i	0.545408	+	0.396262i
$249$	0.174701	−	0.537675i	0.0110712	−	0.0340737i
$250$	0.174701	+	0.537675i	0.0110491	+	0.0340055i
$251$	−15.0849	+	10.9598i	−0.952152	+	0.691779i	−0.951315	−	0.308220i	$-0.900267\pi$
$251$	−15.0849	+	10.9598i	−0.952152	+	0.691779i	−0.000837449		1.00000i	$0.500267\pi$
$252$	−0.405351			−0.0255347
$253$		0			0
$254$	−30.0187			−1.88354
$255$	4.41182	−	3.20538i	0.276279	−	0.200728i
$256$	−1.04285	−	3.20956i	−0.0651780	−	0.200597i
$257$	−2.64107	+	8.12838i	−0.164746	+	0.507035i	−0.999017	−	0.0443186i	$-0.985888\pi$
$257$	−2.64107	+	8.12838i	−0.164746	+	0.507035i	0.834272	+	0.551353i	$0.185888\pi$
$258$	1.71622	+	1.24690i	0.106847	+	0.0776289i
$259$	−7.98337	−	5.80026i	−0.496063	−	0.360411i
$260$	0.655536	−	2.01753i	0.0406546	−	0.125122i
$261$	−6.21208	−	19.1188i	−0.384518	−	1.18342i
$262$	16.5546	−	12.0276i	1.02275	−	0.743070i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	7.17064			0.440489
$266$	7.73098	−	5.61689i	0.474017	−	0.344393i
$267$	−0.627090	−	1.92998i	−0.0383773	−	0.118113i
$268$	0.288023	−	0.886444i	0.0175938	−	0.0541482i
$269$	−6.11295	−	4.44131i	−0.372713	−	0.270792i	0.385622	−	0.922657i	$-0.373987\pi$
$269$	−6.11295	−	4.44131i	−0.372713	−	0.270792i	−0.758335	+	0.651865i	$0.773987\pi$
$270$	−7.38688	−	5.36688i	−0.449551	−	0.326618i
$271$	4.33200	−	13.3325i	0.263150	−	0.809894i	−0.728963	−	0.684553i	$-0.759998\pi$
$271$	4.33200	−	13.3325i	0.263150	−	0.809894i	0.992114	−	0.125341i	$-0.0400025\pi$
$272$	5.45909	+	16.8013i	0.331006	+	1.01873i
$273$	−1.40444	+	1.02039i	−0.0850007	+	0.0617566i
$274$	14.5840			0.881052
$275$		0			0
$276$	−0.264015			−0.0158918
$277$	4.86920	−	3.53768i	0.292562	−	0.212558i	−0.431816	−	0.901962i	$-0.642127\pi$
$277$	4.86920	−	3.53768i	0.292562	−	0.212558i	0.724378	+	0.689403i	$0.242127\pi$
$278$	−1.72843	−	5.31957i	−0.103665	−	0.319047i
$279$	3.22303	−	9.91947i	0.192958	−	0.593863i
$280$	7.41920	+	5.39037i	0.443382	+	0.322136i
$281$	16.7208	+	12.1484i	0.997479	+	0.724711i	0.961546	−	0.274643i	$-0.0885597\pi$
$281$	16.7208	+	12.1484i	0.997479	+	0.724711i	0.0359331	+	0.999354i	$0.488560\pi$
$282$	0.119087	−	0.366513i	0.00709155	−	0.0218256i
$283$	3.06420	+	9.43063i	0.182148	+	0.560593i	0.999888	−	0.0149950i	$-0.00477324\pi$
$283$	3.06420	+	9.43063i	0.182148	+	0.560593i	−0.817740	+	0.575588i	$0.804773\pi$
$284$	−1.73344	+	1.25942i	−0.102861	+	0.0747329i
$285$	−8.00000			−0.473879
$286$		0			0
$287$	3.22199			0.190188
$288$	−1.85153	+	1.34521i	−0.109102	+	0.0792674i
$289$	1.80137	+	5.54405i	0.105963	+	0.326121i
$290$	−9.27628	+	28.5494i	−0.544722	+	1.67648i
$291$	−1.80792	−	1.31353i	−0.105982	−	0.0770005i
$292$	−0.368413	−	0.267668i	−0.0215598	−	0.0156641i
$293$	−8.28062	+	25.4851i	−0.483759	+	1.48886i	0.350011	+	0.936746i	$0.386178\pi$
$293$	−8.28062	+	25.4851i	−0.483759	+	1.48886i	−0.833770	+	0.552112i	$0.813822\pi$
$294$	−0.153067	−	0.471092i	−0.00892706	−	0.0274747i
$295$	0.923360	−	0.670861i	0.0537601	−	0.0390590i
$296$	−28.8081			−1.67443
$297$		0			0
$298$	−19.1120			−1.10713
$299$	19.8738	−	14.4391i	1.14933	−	0.835037i
$300$	−0.0772475	−	0.237743i	−0.00445989	−	0.0137261i
$301$	−1.32342	+	4.07306i	−0.0762806	+	0.234767i
$302$	−7.53248	−	5.47267i	−0.433446	−	0.314917i
$303$	3.17356	+	2.30572i	0.182316	+	0.132460i
$304$	8.00847	−	24.6475i	0.459317	−	1.41363i
$305$	3.12767	+	9.62599i	0.179090	+	0.551182i
$306$	15.1141	−	10.9811i	0.864017	−	0.627745i
$307$	11.8973			0.679015			0.339507	−	0.940603i	$-0.389740\pi$
$307$	11.8973			0.679015			0.339507	+	0.940603i	$0.389740\pi$
$308$		0			0
$309$	−4.81070			−0.273671
$310$	−12.6002	+	9.15456i	−0.715642	+	0.519944i
$311$	−6.56372	−	20.2011i	−0.372195	−	1.14550i	−0.945352	−	0.326052i	$-0.894282\pi$
$311$	−6.56372	−	20.2011i	−0.372195	−	1.14550i	0.573157	−	0.819445i	$-0.305718\pi$
$312$	−1.56608	+	4.81990i	−0.0886618	+	0.272873i
$313$	10.2724	+	7.46332i	0.580629	+	0.421852i	0.838951	−	0.544207i	$-0.183170\pi$
$313$	10.2724	+	7.46332i	0.580629	+	0.421852i	−0.258322	+	0.966059i	$0.583170\pi$
$314$	−25.8562	−	18.7856i	−1.45915	−	1.06014i
$315$	2.78404	−	8.56838i	0.156863	−	0.482774i
$316$	0.162355	+	0.499678i	0.00913320	+	0.0281091i
$317$	9.60141	−	6.97583i	0.539269	−	0.391802i	−0.284545	−	0.958663i	$-0.591842\pi$
$317$	9.60141	−	6.97583i	0.539269	−	0.391802i	0.823813	+	0.566861i	$0.191842\pi$
$318$	−1.13069			−0.0634059
$319$		0			0
$320$	26.6468			1.48960
$321$	−4.12063	+	2.99381i	−0.229991	+	0.167098i
$322$	2.16600	+	6.66627i	0.120707	+	0.371497i
$323$	10.3492	−	31.8515i	0.575843	−	1.77226i
$324$	0.895235	+	0.650426i	0.0497353	+	0.0361348i
$325$	18.8172	+	13.6715i	1.04379	+	0.758357i
$326$	0.417361	−	1.28451i	0.0231155	−	0.0711422i
$327$	−1.74864	−	5.38176i	−0.0967000	−	0.297612i
$328$	7.60970	−	5.52877i	0.420175	−	0.305275i
$329$	0.778008			0.0428930
$330$		0			0
$331$	−11.8867			−0.653349			−0.326675	−	0.945137i	$-0.605928\pi$
$331$	−11.8867			−0.653349			−0.326675	+	0.945137i	$0.605928\pi$
$332$	0.177920	−	0.129266i	0.00976463	−	0.00709442i
$333$	8.74559	+	26.9162i	0.479255	+	1.47500i
$334$	−0.238175	+	0.733027i	−0.0130323	+	0.0401094i
$335$	16.7596	+	12.1766i	0.915675	+	0.665277i
$336$	−1.08679	−	0.789603i	−0.0592895	−	0.0430764i
$337$	0.306134	−	0.942184i	0.0166762	−	0.0513241i	−0.942372	−	0.334567i	$-0.891410\pi$
$337$	0.306134	−	0.942184i	0.0166762	−	0.0513241i	0.959048	+	0.283242i	$0.0914101\pi$
$338$	−4.14103	−	12.7448i	−0.225242	−	0.693224i
$339$	−1.21456	+	0.882427i	−0.0659657	+	0.0479269i
$340$	2.12136			0.115047
$341$		0			0
$342$	−27.4066			−1.48198
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	3.86351	+	11.8907i	0.208307	+	0.641102i
$345$	1.81331	−	5.58079i	0.0976253	−	0.300460i
$346$	−19.0157	−	13.8157i	−1.02229	−	0.742736i
$347$	12.2884	+	8.92805i	0.659676	+	0.479283i	0.866553	−	0.499084i	$-0.166330\pi$
$347$	12.2884	+	8.92805i	0.659676	+	0.479283i	−0.206878	+	0.978367i	$0.566330\pi$
$348$	−0.111227	+	0.342322i	−0.00596241	+	0.0183504i
$349$	−9.17882	−	28.2495i	−0.491331	−	1.51216i	−0.822597	−	0.568624i	$-0.807476\pi$
$349$	−9.17882	−	28.2495i	−0.491331	−	1.51216i	0.331266	−	0.943537i	$-0.392524\pi$
$350$	−5.36918	+	3.90094i	−0.286995	+	0.208514i
$351$	10.1867			0.543728
$352$		0			0
$353$	−6.71601			−0.357457			−0.178729	−	0.983898i	$-0.557198\pi$
$353$	−6.71601			−0.357457			−0.178729	+	0.983898i	$0.557198\pi$
$354$	−0.145598	+	0.105783i	−0.00773846	+	0.00562232i
$355$	−14.7162	−	45.2918i	−0.781055	−	2.40384i
$356$	0.243940	−	0.750771i	0.0129288	−	0.0397908i
$357$	−1.40444	−	1.02039i	−0.0743309	−	0.0540046i
$358$	12.4869	+	9.07226i	0.659953	+	0.479484i
$359$	5.48072	−	16.8679i	0.289261	−	0.890255i	−0.695828	−	0.718209i	$-0.744962\pi$
$359$	5.48072	−	16.8679i	0.289261	−	0.890255i	0.985089	−	0.172046i	$-0.0550378\pi$
$360$	−8.12756	−	25.0141i	−0.428360	−	1.31836i
$361$	−24.3762	+	17.7104i	−1.28296	+	0.932125i
$362$	−20.2827			−1.06603
$363$		0			0
$364$	−0.675305			−0.0353956
$365$	8.18835	−	5.94919i	0.428598	−	0.311395i
$366$	−0.493181	−	1.51786i	−0.0257790	−	0.0793396i
$367$	−2.50283	+	7.70290i	−0.130646	+	0.402088i	−0.994887	−	0.100990i	$-0.967799\pi$
$367$	−2.50283	+	7.70290i	−0.130646	+	0.402088i	0.864241	+	0.503078i	$0.167799\pi$
$368$	15.3789	+	11.1734i	0.801679	+	0.582454i
$369$	−7.47584	−	5.43152i	−0.389177	−	0.282754i
$370$	13.0595	−	40.1930i	0.678930	−	2.08953i
$371$	−0.705385	−	2.17095i	−0.0366217	−	0.112710i
$372$	−0.151082	+	0.109768i	−0.00783326	+	0.00569120i
$373$	0.565344			0.0292724			0.0146362	−	0.999893i	$-0.495341\pi$
$373$	0.565344			0.0292724			0.0146362	+	0.999893i	$0.495341\pi$
$374$		0			0
$375$	−0.150665			−0.00778030
$376$	1.83750	−	1.33502i	0.0947617	−	0.0688484i
$377$	−10.3492	−	31.8515i	−0.533010	−	1.64043i
$378$	−0.898197	+	2.76437i	−0.0461983	+	0.142184i
$379$	18.2320	+	13.2464i	0.936517	+	0.680419i	0.947580	−	0.319519i	$-0.103521\pi$
$379$	18.2320	+	13.2464i	0.936517	+	0.680419i	−0.0110628	+	0.999939i	$0.503521\pi$
$380$	−2.51769	−	1.82921i	−0.129155	−	0.0938363i
$381$	2.47214	−	7.60845i	0.126651	−	0.389793i
$382$	−1.62169	−	4.99106i	−0.0829730	−	0.255365i
$383$	−17.3059	+	12.5735i	−0.884292	+	0.642476i	−0.934383	−	0.356269i	$-0.884049\pi$
$383$	−17.3059	+	12.5735i	−0.884292	+	0.642476i	0.0500914	+	0.998745i	$0.484049\pi$
$384$	−3.62188			−0.184828
$385$		0			0
$386$	3.47197			0.176719
$387$	9.93689	−	7.21957i	0.505121	−	0.366992i
$388$	−0.268632	−	0.826764i	−0.0136377	−	0.0419726i
$389$	3.29990	−	10.1560i	0.167311	−	0.514932i	−0.831888	−	0.554944i	$-0.812740\pi$
$389$	3.29990	−	10.1560i	0.167311	−	0.514932i	0.999199	+	0.0400122i	$0.0127397\pi$
$390$	−6.01476	−	4.36998i	−0.304569	−	0.221283i
$391$	19.8738	+	14.4391i	1.00506	+	0.730219i
$392$	0.902127	−	2.77646i	0.0455643	−	0.140232i
$393$	1.68517	+	5.18641i	0.0850054	+	0.261620i
$394$	−11.6325	+	8.45153i	−0.586038	+	0.425782i
$395$	−11.6774			−0.587553
$396$		0			0
$397$	−23.9160			−1.20031			−0.600154	−	0.799885i	$-0.704894\pi$
$397$	−23.9160			−1.20031			−0.600154	+	0.799885i	$0.704894\pi$
$398$	12.8876	−	9.36341i	0.645999	−	0.469346i
$399$	0.786970	+	2.42204i	0.0393978	+	0.121254i
$400$	−5.56190	+	17.1178i	−0.278095	+	0.855888i
$401$	−9.43210	−	6.85282i	−0.471017	−	0.342214i	0.326821	−	0.945086i	$-0.394023\pi$
$401$	−9.43210	−	6.85282i	−0.471017	−	0.342214i	−0.797837	+	0.602873i	$0.794023\pi$
$402$	−2.64271	−	1.92004i	−0.131806	−	0.0957628i
$403$	5.36949	−	16.5256i	0.267474	−	0.823199i
$404$	0.471547	+	1.45127i	0.0234603	+	0.0722035i
$405$	−19.8975	+	14.4564i	−0.988714	+	0.718343i
$406$	9.55602			0.474257
$407$		0			0
$408$	−5.06794			−0.250900
$409$	−26.5482	+	19.2884i	−1.31272	+	0.953748i	−0.312729	+	0.949842i	$0.601243\pi$
$409$	−26.5482	+	19.2884i	−1.31272	+	0.953748i	−0.999992	+	0.00390587i	$0.998757\pi$
$410$	4.26404	+	13.1234i	0.210586	+	0.648117i
$411$	−1.20104	+	3.69642i	−0.0592430	+	0.182331i
$412$	−1.51398	−	1.09997i	−0.0745884	−	0.0541917i
$413$	−0.293939	−	0.213559i	−0.0144638	−	0.0105086i
$414$	6.21208	−	19.1188i	0.305307	−	0.939638i
$415$	1.51047	+	4.64873i	0.0741458	+	0.228197i
$416$	−3.08460	+	2.24109i	−0.151235	+	0.109879i
$417$	1.49063			0.0729964
$418$		0			0
$419$	10.7967			0.527452			0.263726	−	0.964598i	$-0.415049\pi$
$419$	10.7967			0.527452			0.263726	+	0.964598i	$0.415049\pi$
$420$	−0.130504	+	0.0948168i	−0.00636795	+	0.00462659i
$421$	−0.355982	−	1.09560i	−0.0173495	−	0.0533963i	0.942007	−	0.335593i	$-0.108937\pi$
$421$	−0.355982	−	1.09560i	−0.0173495	−	0.0533963i	−0.959356	+	0.282197i	$0.908937\pi$
$422$	−4.68141	+	14.4079i	−0.227887	+	0.701365i
$423$	−1.80518	−	1.31154i	−0.0877707	−	0.0637691i
$424$	−5.39121	−	3.91695i	−0.261820	−	0.190224i
$425$	−7.18752	+	22.1209i	−0.348646	+	1.07302i
$426$	2.32050	+	7.14175i	0.112428	+	0.346019i
$427$	2.60665	−	1.89384i	0.126144	−	0.0916493i
$428$	−1.98134			−0.0957718
$429$		0			0
$430$	−18.3413			−0.884495
$431$	25.8562	−	18.7856i	1.24545	−	0.904873i	0.247501	−	0.968888i	$-0.420391\pi$
$431$	25.8562	−	18.7856i	1.24545	−	0.904873i	0.997949	+	0.0640148i	$0.0203905\pi$
$432$	2.43591	+	7.49697i	0.117198	+	0.360698i
$433$	−1.36998	+	4.21635i	−0.0658369	+	0.202625i	−0.978563	−	0.205946i	$-0.933973\pi$
$433$	−1.36998	+	4.21635i	−0.0658369	+	0.202625i	0.912726	+	0.408571i	$0.133973\pi$
$434$	4.01109	+	2.91423i	0.192538	+	0.139887i
$435$	−6.47214	−	4.70228i	−0.310315	−	0.225457i
$436$	0.680228	−	2.09353i	0.0325770	−	0.100262i
$437$	−11.1361	−	34.2735i	−0.532714	−	1.63952i
$438$	−1.29116	+	0.938086i	−0.0616942	+	0.0448235i
$439$	−27.4720			−1.31117			−0.655583	−	0.755123i	$-0.727577\pi$
$439$	−27.4720			−1.31117			−0.655583	+	0.755123i	$0.727577\pi$
$440$		0			0
$441$	−2.86799			−0.136571
$442$	25.1798	−	18.2942i	1.19768	−	0.870165i
$443$	−2.40747	−	7.40942i	−0.114382	−	0.352032i	0.877435	−	0.479695i	$-0.159253\pi$
$443$	−2.40747	−	7.40942i	−0.114382	−	0.352032i	−0.991818	+	0.127662i	$0.959253\pi$
$444$	0.156590	−	0.481934i	0.00743142	−	0.0228716i
$445$	14.1945	+	10.3129i	0.672884	+	0.488879i
$446$	30.9277	+	22.4703i	1.46447	+	1.06400i
$447$	1.57394	−	4.84409i	0.0744448	−	0.229117i
$448$	−2.62127	−	8.06745i	−0.123844	−	0.381151i
$449$	−16.5934	+	12.0558i	−0.783092	+	0.568950i	−0.905905	−	0.423480i	$-0.860808\pi$
$449$	−16.5934	+	12.0558i	−0.783092	+	0.568950i	0.122813	+	0.992430i	$0.460808\pi$
$450$	19.0339			0.897268
$451$		0			0
$452$	−0.584002			−0.0274691
$453$	2.00741	−	1.45847i	0.0943165	−	0.0685249i
$454$	9.69364	+	29.8339i	0.454945	+	1.40018i
$455$	4.63814	−	14.2747i	0.217439	−	0.669209i
$456$	6.01476	+	4.36998i	0.281667	+	0.204643i
$457$	6.92951	+	5.03458i	0.324149	+	0.235508i	0.737944	−	0.674862i	$-0.235797\pi$
$457$	6.92951	+	5.03458i	0.324149	+	0.235508i	−0.413795	+	0.910370i	$0.635797\pi$
$458$	−5.65542	+	17.4056i	−0.264261	+	0.813310i
$459$	3.14788	+	9.68817i	0.146930	+	0.452205i
$460$	1.84672	−	1.34172i	0.0861038	−	0.0625581i
$461$	9.66598			0.450189			0.225095	−	0.974337i	$-0.427731\pi$
$461$	9.66598			0.450189			0.225095	+	0.974337i	$0.427731\pi$
$462$		0			0
$463$	11.4240			0.530919			0.265459	−	0.964122i	$-0.414476\pi$
$463$	11.4240			0.530919			0.265459	+	0.964122i	$0.414476\pi$
$464$	20.9664	−	15.2330i	0.973343	−	0.707175i
$465$	−1.28263	−	3.94752i	−0.0594804	−	0.183062i
$466$	1.49026	−	4.58655i	0.0690349	−	0.212468i
$467$	−14.7408	−	10.7098i	−0.682124	−	0.495592i	0.191937	−	0.981407i	$-0.438523\pi$
$467$	−14.7408	−	10.7098i	−0.682124	−	0.495592i	−0.874062	+	0.485815i	$0.838523\pi$
$468$	1.56688	+	1.13840i	0.0724290	+	0.0526228i
$469$	2.03786	−	6.27188i	0.0940996	−	0.289609i
$470$	1.02963	+	3.16888i	0.0474933	+	0.146169i
$471$	6.89071	−	5.00639i	0.317507	−	0.230682i
$472$	−1.06068			−0.0488218
$473$		0			0
$474$	1.84132			0.0845749
$475$	27.6048	−	20.0560i	1.26659	−	0.920234i
$476$	−0.208681	−	0.642253i	−0.00956487	−	0.0294376i
$477$	−2.02304	+	6.22627i	−0.0926285	+	0.285081i
$478$	24.2856	+	17.6445i	1.11080	+	0.807042i
$479$	−2.80888	−	2.04077i	−0.128341	−	0.0932453i	0.521763	−	0.853091i	$-0.325275\pi$
$479$	−2.80888	−	2.04077i	−0.128341	−	0.0932453i	−0.650104	+	0.759845i	$0.725275\pi$
$480$	−0.281443	+	0.866192i	−0.0128460	+	0.0395361i
$481$	14.5699	+	44.8417i	0.664333	+	2.04461i
$482$	−0.347835	+	0.252717i	−0.0158434	+	0.0115109i
$483$	−1.86799			−0.0849966
$484$		0			0
$485$	19.3213			0.877335
$486$	10.1920	−	7.40494i	0.462320	−	0.335895i
$487$	−8.48602	−	26.1173i	−0.384538	−	1.18349i	−0.936815	−	0.349826i	$-0.886241\pi$
$487$	−8.48602	−	26.1173i	−0.384538	−	1.18349i	0.552277	−	0.833661i	$-0.313759\pi$
$488$	2.90665	−	8.94574i	0.131578	−	0.404954i
$489$	0.291197	+	0.211567i	0.0131684	+	0.00956738i
$490$	3.46475	+	2.51729i	0.156522	+	0.113720i
$491$	−1.93569	+	5.95743i	−0.0873563	+	0.268855i	−0.985186	−	0.171487i	$-0.945143\pi$
$491$	−1.93569	+	5.95743i	−0.0873563	+	0.268855i	0.897830	+	0.440342i	$0.145143\pi$
$492$	0.0511280	+	0.157356i	0.00230503	+	0.00709415i
$493$	27.0945	−	19.6853i	1.22027	−	0.886581i
$494$	−45.6587			−2.05428
$495$		0			0
$496$	13.4461			0.603746
$497$	−12.2647	+	8.91082i	−0.550147	+	0.399705i
$498$	−0.238175	−	0.733027i	−0.0106729	−	0.0328477i
$499$	−6.38678	+	19.6565i	−0.285911	+	0.879945i	0.700213	+	0.713934i	$0.253089\pi$
$499$	−6.38678	+	19.6565i	−0.285911	+	0.879945i	−0.986124	+	0.166010i	$0.946911\pi$
$500$	−0.0474158	−	0.0344496i	−0.00212050	−	0.00154063i
$501$	−0.166177	−	0.120734i	−0.00742422	−	0.00539401i
$502$	−7.85540	+	24.1764i	−0.350604	+	1.07905i
$503$	6.80414	+	20.9410i	0.303382	+	0.933712i	0.980276	+	0.197633i	$0.0633253\pi$
$503$	6.80414	+	20.9410i	0.303382	+	0.933712i	−0.676895	+	0.736080i	$0.736675\pi$
$504$	−6.77362	+	4.92132i	−0.301721	+	0.219213i
$505$	−33.9160			−1.50924
$506$		0			0
$507$	3.57128			0.158606
$508$	2.51769	−	1.82921i	0.111704	−	0.0811579i
$509$	6.62038	+	20.3754i	0.293443	+	0.903126i	0.983740	+	0.179599i	$0.0574801\pi$
$509$	6.62038	+	20.3754i	0.293443	+	0.903126i	−0.690297	+	0.723527i	$0.742520\pi$
$510$	2.29743	−	7.07078i	0.101732	−	0.313099i
$511$	−2.60665	−	1.89384i	−0.115311	−	0.0837785i
$512$	−19.8517	−	14.4231i	−0.877332	−	0.637419i
$513$	4.61793	−	14.2125i	0.203887	−	0.627499i
$514$	3.60065	+	11.0817i	0.158818	+	0.488791i
$515$	33.6497	−	24.4479i	1.48278	−	1.07731i
$516$	−0.219921			−0.00968149
$517$		0			0
$518$	−13.4533			−0.591105
$519$	5.06769	−	3.68190i	0.222447	−	0.161617i
$520$	−13.5403	−	41.6728i	−0.593782	−	1.82747i
$521$	4.30932	−	13.2627i	0.188795	−	0.581051i	−0.811198	−	0.584771i	$-0.801184\pi$
$521$	4.30932	−	13.2627i	0.188795	−	0.581051i	0.999993	+	0.00372050i	$0.00118427\pi$
$522$	−22.1724	−	16.1092i	−0.970459	−	0.705080i
$523$	14.9517	+	10.8630i	0.653792	+	0.475007i	0.864561	−	0.502529i	$-0.167597\pi$
$523$	14.9517	+	10.8630i	0.653792	+	0.475007i	−0.210769	+	0.977536i	$0.567597\pi$
$524$	−0.655536	+	2.01753i	−0.0286372	+	0.0881364i
$525$	−0.546552	−	1.68211i	−0.0238535	−	0.0734135i
$526$	17.6473	−	12.8215i	0.769458	−	0.559044i
$527$	17.3760			0.756912
$528$		0			0
$529$	3.43334			0.149276
$530$	7.90890	−	5.74615i	0.343541	−	0.249597i
$531$	0.322003	+	0.991022i	0.0139737	+	0.0430067i
$532$	−0.306134	+	0.942184i	−0.0132726	+	0.0408489i
$533$	−12.4546	−	9.04878i	−0.539468	−	0.391946i
$534$	−2.23823	−	1.62617i	−0.0968578	−	0.0703713i
$535$	13.6083	−	41.8820i	0.588337	−	1.81072i
$536$	−5.94921	−	18.3098i	−0.256967	−	0.790862i
$537$	−3.32777	+	2.41777i	−0.143604	+	0.104334i
$538$	−10.3013			−0.444122
$539$		0			0
$540$	0.946578			0.0407342
$541$	−30.3004	+	22.0145i	−1.30271	+	0.946477i	−0.999978	−	0.00659687i	$-0.997900\pi$
$541$	−30.3004	+	22.0145i	−1.30271	+	0.946477i	−0.302736	+	0.953074i	$0.597900\pi$
$542$	−5.90594	−	18.1766i	−0.253682	−	0.780753i
$543$	1.67035	−	5.14079i	0.0716814	−	0.220613i
$544$	−3.08460	−	2.24109i	−0.132251	−	0.0960860i
$545$	39.5814	+	28.7576i	1.69548	+	1.23184i
$546$	−0.731356	+	2.25088i	−0.0312991	+	0.0963289i
$547$	−5.29367	−	16.2923i	−0.226341	−	0.696606i	−0.998153	−	0.0607551i	$-0.980649\pi$
$547$	−5.29367	−	16.2923i	−0.226341	−	0.696606i	0.771812	−	0.635851i	$-0.219351\pi$
$548$	−1.22317	+	0.888686i	−0.0522513	+	0.0379628i
$549$	−9.24065			−0.394381
$550$		0			0
$551$	−49.1307			−2.09304
$552$	−4.41182	+	3.20538i	−0.187780	+	0.136430i
$553$	1.14872	+	3.53539i	0.0488484	+	0.150340i
$554$	2.53561	−	7.80380i	0.107728	−	0.331552i
$555$	9.11171	+	6.62005i	0.386771	+	0.281005i
$556$	0.469117	+	0.340833i	0.0198950	+	0.0144545i
$557$	7.59111	−	23.3630i	0.321646	−	0.989923i	−0.651286	−	0.758832i	$-0.725770\pi$
$557$	7.59111	−	23.3630i	0.321646	−	0.989923i	0.972932	−	0.231091i	$-0.0742296\pi$
$558$	−4.39405	−	13.5235i	−0.186015	−	0.572495i
$559$	16.5546	−	12.0276i	0.700186	−	0.508715i
$560$	11.6146			0.490807
$561$		0			0
$562$	28.1773			1.18859
$563$	12.1428	−	8.82226i	0.511758	−	0.371814i	−0.301732	−	0.953393i	$-0.597565\pi$
$563$	12.1428	−	8.82226i	0.511758	−	0.371814i	0.813490	+	0.581579i	$0.197565\pi$
$564$	0.0123458	+	0.0379964i	0.000519851	+	0.00159994i
$565$	4.01105	−	12.3447i	0.168746	−	0.519347i
$566$	10.9369	+	7.94609i	0.459710	+	0.333999i
$567$	6.33408	+	4.60198i	0.266007	+	0.193265i
$568$	−13.6762	+	42.0911i	−0.573842	+	1.76610i
$569$	3.73994	+	11.5104i	0.156786	+	0.482539i	0.998338	−	0.0576384i	$-0.0183571\pi$
$569$	3.73994	+	11.5104i	0.156786	+	0.482539i	−0.841551	+	0.540178i	$0.818357\pi$
$570$	−8.82365	+	6.41075i	−0.369582	+	0.268517i
$571$	38.9439			1.62975			0.814877	−	0.579634i	$-0.196805\pi$
$571$	38.9439			1.62975			0.814877	+	0.579634i	$0.196805\pi$
$572$		0			0
$573$	1.39857			0.0584262
$574$	3.55371	−	2.58192i	0.148329	−	0.107767i
$575$	7.73407	+	23.8030i	0.322533	+	0.992655i
$576$	−7.51779	+	23.1374i	−0.313241	+	0.964058i
$577$	−30.8645	−	22.4244i	−1.28491	−	0.933540i	−0.285218	−	0.958463i	$-0.592066\pi$
$577$	−30.8645	−	22.4244i	−1.28491	−	0.933540i	−0.999689	+	0.0249227i	$0.992066\pi$
$578$	6.42953	+	4.67132i	0.267433	+	0.194301i
$579$	−0.285928	+	0.879997i	−0.0118828	+	0.0365714i
$580$	−0.961671	−	2.95972i	−0.0399312	−	0.122896i
$581$	1.25884	−	0.914603i	0.0522256	−	0.0379441i
$582$	−3.04664			−0.126287
$583$		0			0
$584$	−9.40610			−0.389227
$585$	−34.8255	+	25.3022i	−1.43986	+	1.04612i
$586$	11.2892	+	34.7446i	0.466353	+	1.43529i
$587$	−10.7528	+	33.0936i	−0.443814	+	1.36592i	0.439965	+	0.898015i	$0.354991\pi$
$587$	−10.7528	+	33.0936i	−0.443814	+	1.36592i	−0.883779	+	0.467904i	$0.845009\pi$
$588$	0.0415442	+	0.0301836i	0.00171325	+	0.00124475i
$589$	−20.6224	−	14.9830i	−0.849729	−	0.617364i
$590$	0.480835	−	1.47986i	0.0197957	−	0.0609248i
$591$	−1.18413	−	3.64436i	−0.0487084	−	0.149909i
$592$	−29.5173	+	21.4456i	−1.21316	+	0.881409i
$593$	−18.5913			−0.763452			−0.381726	−	0.924276i	$-0.624670\pi$
$593$	−18.5913			−0.763452			−0.381726	+	0.924276i	$0.624670\pi$
$594$		0			0
$595$	15.0093			0.615322
$596$	1.60294	−	1.16460i	0.0656590	−	0.0477040i
$597$	1.31189	+	4.03757i	0.0536920	+	0.165247i
$598$	10.3492	−	31.8515i	0.423209	−	1.30250i
$599$	−19.9569	−	14.4995i	−0.815416	−	0.592434i	0.0999801	−	0.994989i	$-0.468122\pi$
$599$	−19.9569	−	14.4995i	−0.815416	−	0.592434i	−0.915396	+	0.402555i	$0.868122\pi$
$600$	−4.17726	−	3.03496i	−0.170536	−	0.123902i
$601$	−9.31025	+	28.6540i	−0.379773	+	1.16882i	0.560428	+	0.828203i	$0.310637\pi$
$601$	−9.31025	+	28.6540i	−0.379773	+	1.16882i	−0.940201	+	0.340619i	$0.889363\pi$
$602$	1.80425	+	5.55292i	0.0735359	+	0.226320i
$603$	−15.3013	+	11.1170i	−0.623116	+	0.452720i
$604$	0.965235			0.0392749
$605$		0			0
$606$	5.34797			0.217247
$607$	11.0501	−	8.02839i	0.448511	−	0.325862i	−0.340497	−	0.940246i	$-0.610595\pi$
$607$	11.0501	−	8.02839i	0.448511	−	0.325862i	0.789008	+	0.614383i	$0.210595\pi$
$608$	1.72843	+	5.31957i	0.0700973	+	0.215737i
$609$	−0.786970	+	2.42204i	−0.0318896	+	0.0981461i
$610$	11.1634	+	8.11069i	0.451993	+	0.328392i
$611$	−3.00738	−	2.18499i	−0.121666	−	0.0883953i
$612$	−0.598495	+	1.84198i	−0.0241927	+	0.0744575i
$613$	−13.9144	−	42.8242i	−0.561998	−	1.72965i	−0.676707	−	0.736252i	$-0.736594\pi$
$613$	−13.9144	−	42.8242i	−0.561998	−	1.72965i	0.114709	−	0.993399i	$-0.463406\pi$
$614$	13.1222	−	9.53383i	0.529569	−	0.384754i
$615$	−3.67738			−0.148286
$616$		0			0
$617$	−8.26401			−0.332697			−0.166348	−	0.986067i	$-0.553198\pi$
$617$	−8.26401			−0.332697			−0.166348	+	0.986067i	$0.553198\pi$
$618$	−5.30599	+	3.85503i	−0.213438	+	0.155072i
$619$	13.3032	+	40.9430i	0.534700	+	1.64564i	0.744296	+	0.667850i	$0.232785\pi$
$619$	13.3032	+	40.9430i	0.534700	+	1.64564i	−0.209595	+	0.977788i	$0.567215\pi$
$620$	0.498947	−	1.53560i	0.0200382	−	0.0616712i
$621$	8.86793	+	6.44293i	0.355858	+	0.258546i
$622$	−23.4275	−	17.0211i	−0.939357	−	0.682483i
$623$	1.72596	−	5.31196i	0.0691491	−	0.212819i
$624$	1.98344	+	6.10440i	0.0794012	+	0.244372i
$625$	20.7453	−	15.0723i	0.829812	−	0.602894i
$626$	17.3107			0.691873
$627$		0			0
$628$	3.31330			0.132215
$629$	−38.1446	+	27.7137i	−1.52093	+	1.10502i
$630$	−3.79555	−	11.6815i	−0.151219	−	0.465403i
$631$	0.320955	−	0.987799i	0.0127770	−	0.0393237i	−0.944465	−	0.328613i	$-0.893419\pi$
$631$	0.320955	−	0.987799i	0.0127770	−	0.0393237i	0.957242	+	0.289289i	$0.0934189\pi$
$632$	8.77958	+	6.37874i	0.349233	+	0.253733i
$633$	−3.26626	−	2.37307i	−0.129822	−	0.0943212i
$634$	4.99989	−	15.3881i	0.198571	−	0.611138i
$635$	21.3741	+	65.7827i	0.848205	+	2.61051i
$636$	0.0948317	−	0.0688993i	0.00376032	−	0.00273203i
$637$	−4.77801			−0.189312
$638$		0			0
$639$	43.4787			1.71999
$640$	25.3342	−	18.4064i	1.00142	−	0.727576i
$641$	10.3957	+	31.9948i	0.410607	+	1.26372i	0.916122	+	0.400900i	$0.131302\pi$
$641$	10.3957	+	31.9948i	0.410607	+	1.26372i	−0.505515	+	0.862818i	$0.668698\pi$
$642$	−2.14580	+	6.60408i	−0.0846878	+	0.260642i
$643$	17.0147	+	12.3619i	0.670996	+	0.487507i	0.870358	−	0.492419i	$-0.163887\pi$
$643$	17.0147	+	12.3619i	0.670996	+	0.487507i	−0.199363	+	0.979926i	$0.563887\pi$
$644$	−0.587877	−	0.427118i	−0.0231656	−	0.0168308i
$645$	1.51047	−	4.64873i	0.0594745	−	0.183044i
$646$	−14.1093	−	43.4240i	−0.555124	−	1.70850i
$647$	−20.4115	+	14.8298i	−0.802459	+	0.583021i	−0.911634	−	0.411002i	$-0.865179\pi$
$647$	−20.4115	+	14.8298i	−0.802459	+	0.583021i	0.109176	+	0.994022i	$0.465179\pi$
$648$	22.8566			0.897892
$649$		0			0
$650$	31.7101			1.24377
$651$	−1.06896	+	0.776644i	−0.0418958	+	0.0304391i
$652$	0.0432678	+	0.133165i	0.00169450	+	0.00521513i
$653$	6.37772	−	19.6286i	0.249580	−	0.768127i	−0.745270	−	0.666763i	$-0.767679\pi$
$653$	6.37772	−	19.6286i	0.249580	−	0.768127i	0.994849	−	0.101364i	$-0.0323207\pi$
$654$	−6.24132	−	4.53458i	−0.244055	−	0.177316i
$655$	−38.1446	−	27.7137i	−1.49043	−	1.08286i
$656$	3.68127	−	11.3298i	0.143729	−	0.442354i
$657$	2.85552	+	8.78838i	0.111404	+	0.342867i
$658$	0.858108	−	0.623452i	0.0334525	−	0.0243047i
$659$	−18.5067			−0.720920			−0.360460	−	0.932775i	$-0.617380\pi$
$659$	−18.5067			−0.720920			−0.360460	+	0.932775i	$0.617380\pi$
$660$		0			0
$661$	16.8001			0.653446			0.326723	−	0.945120i	$-0.394056\pi$
$661$	16.8001			0.653446			0.326723	+	0.945120i	$0.394056\pi$
$662$	−13.1104	+	9.52530i	−0.509552	+	0.370211i
$663$	2.56316	+	7.88859i	0.0995448	+	0.306367i
$664$	1.40372	−	4.32022i	0.0544750	−	0.167657i
$665$	−17.8135	−	12.9422i	−0.690777	−	0.501879i
$666$	31.2151	+	22.6791i	1.20956	+	0.878798i
$667$	11.1361	−	34.2735i	0.431193	−	1.32708i
$668$	−0.0246916	−	0.0759928i	−0.000955345	−	0.00294025i
$669$	−8.24225	+	5.98834i	−0.318664	+	0.231523i
$670$	28.2427			1.09111
$671$		0			0
$672$	0.289930			0.0111843
$673$	−14.2031	+	10.3192i	−0.547490	+	0.397775i	−0.826859	−	0.562409i	$-0.809875\pi$
$673$	−14.2031	+	10.3192i	−0.547490	+	0.397775i	0.279369	+	0.960184i	$0.409875\pi$
$674$	−0.417361	−	1.28451i	−0.0160762	−	0.0494773i
$675$	−3.20716	+	9.87063i	−0.123444	+	0.379921i
$676$	1.12392	+	0.816577i	0.0432278	+	0.0314068i
$677$	2.95074	+	2.14384i	0.113406	+	0.0823945i	0.643043	−	0.765830i	$-0.277672\pi$
$677$	2.95074	+	2.14384i	0.113406	+	0.0823945i	−0.529637	+	0.848225i	$0.677672\pi$
$678$	−0.632475	+	1.94656i	−0.0242900	+	0.0747570i
$679$	−1.90066	−	5.84963i	−0.0729406	−	0.224488i
$680$	35.4490	−	25.7552i	1.35941	−	0.987668i
$681$	−8.35994			−0.320354
$682$		0			0
$683$	27.4720			1.05119			0.525593	−	0.850736i	$-0.323844\pi$
$683$	27.4720			1.05119			0.525593	+	0.850736i	$0.323844\pi$
$684$	2.29861	−	1.67004i	0.0878895	−	0.0638555i
$685$	−10.3842	−	31.9593i	−0.396760	−	1.22110i
$686$	0.421292	−	1.29660i	0.0160850	−	0.0495045i
$687$	−3.94584	−	2.86682i	−0.150543	−	0.109376i
$688$	12.8104	+	9.30731i	0.488393	+	0.354838i
$689$	−3.37033	+	10.3728i	−0.128399	+	0.395173i
$690$	−2.47214	−	7.60845i	−0.0941126	−	0.289649i
$691$	4.81904	−	3.50124i	0.183325	−	0.133193i	−0.492338	−	0.870404i	$-0.663858\pi$
$691$	4.81904	−	3.50124i	0.183325	−	0.133193i	0.675663	+	0.737211i	$0.263858\pi$
$692$	2.43673			0.0926304
$693$		0			0
$694$	20.7080			0.786065
$695$	−10.4266	+	7.57536i	−0.395503	+	0.287350i
$696$	2.29743	+	7.07078i	0.0870840	+	0.268017i
$697$	4.75723	−	14.6412i	0.180193	−	0.554576i
$698$	−32.7614	−	23.8026i	−1.24004	−	0.900940i
$699$	1.03977	+	0.755435i	0.0393276	+	0.0285732i
$700$	0.212611	−	0.654349i	0.00803593	−	0.0247321i
$701$	2.27723	+	7.00859i	0.0860097	+	0.264711i	0.984807	−	0.173655i	$-0.0555576\pi$
$701$	2.27723	+	7.00859i	0.0860097	+	0.264711i	−0.898797	+	0.438365i	$0.855558\pi$
$702$	11.2355	−	8.16309i	0.424058	−	0.308096i
$703$	69.1680			2.60872
$704$		0			0
$705$	−0.887968			−0.0334428
$706$	−7.40746	+	5.38184i	−0.278783	+	0.202548i
$707$	3.33635	+	10.2682i	0.125476	+	0.386177i
$708$	0.00576546	−	0.0177443i	0.000216679	−	0.000666870i
$709$	28.0858	+	20.4056i	1.05479	+	0.766347i	0.973117	−	0.230313i	$-0.0739749\pi$
$709$	28.0858	+	20.4056i	1.05479	+	0.766347i	0.0816692	+	0.996659i	$0.473975\pi$
$710$	−52.5257	−	38.1621i	−1.97125	−	1.43220i
$711$	3.29451	−	10.1395i	0.123554	−	0.380260i
$712$	−5.03867	−	15.5074i	−0.188832	−	0.581165i
$713$	15.1265	−	10.9900i	0.566491	−	0.411580i
$714$	−2.36672			−0.0885722
$715$		0			0
$716$	−1.60011			−0.0597989
$717$	−6.47214	+	4.70228i	−0.241706	+	0.175610i
$718$	−7.47202	−	22.9965i	−0.278853	−	0.858222i
$719$	−1.25523	+	3.86319i	−0.0468121	+	0.144073i	−0.971730	−	0.236093i	$-0.924133\pi$
$719$	−1.25523	+	3.86319i	−0.0468121	+	0.144073i	0.924918	+	0.380166i	$0.124133\pi$
$720$	−26.9489	−	19.5795i	−1.00433	−	0.729685i
$721$	−10.7119	−	7.78266i	−0.398932	−	0.289841i
$722$	−12.6938	+	39.0675i	−0.472415	+	1.45394i
$723$	−0.0354076	−	0.108973i	−0.00131682	−	0.00405277i
$724$	1.70112	−	1.23594i	0.0632217	−	0.0459333i
$725$	34.1214			1.26724
$726$		0			0
$727$	−30.5433			−1.13279			−0.566394	−	0.824135i	$-0.691662\pi$
$727$	−30.5433			−1.13279			−0.566394	+	0.824135i	$0.691662\pi$
$728$	−11.2847	+	8.19881i	−0.418239	+	0.303868i
$729$	−6.22072	−	19.1454i	−0.230397	−	0.709090i
$730$	4.26404	−	13.1234i	0.157819	−	0.485718i
$731$	16.5546	+	12.0276i	0.612295	+	0.444858i
$732$	0.133855	+	0.0972513i	0.00494742	+	0.00359451i
$733$	−9.52822	+	29.3249i	−0.351933	+	1.08314i	0.605834	+	0.795591i	$0.292840\pi$
$733$	−9.52822	+	29.3249i	−0.351933	+	1.08314i	−0.957767	+	0.287547i	$0.907160\pi$
$734$	3.41217	+	10.5016i	0.125946	+	0.387621i
$735$	−0.923360	+	0.670861i	−0.0340587	+	0.0247451i
$736$	−4.10270			−0.151228
$737$		0			0
$738$	−12.5980			−0.463740
$739$	−17.9796	+	13.0630i	−0.661392	+	0.480529i	−0.867133	−	0.498077i	$-0.834040\pi$
$739$	−17.9796	+	13.0630i	−0.661392	+	0.480529i	0.205741	+	0.978607i	$0.434040\pi$
$740$	1.35388	+	4.16680i	0.0497695	+	0.153175i
$741$	3.76015	−	11.5725i	0.138132	−	0.425128i
$742$	−2.51769	−	1.82921i	−0.0924272	−	0.0671523i
$743$	25.2004	+	18.3091i	0.924511	+	0.671697i	0.944643	−	0.328101i	$-0.106409\pi$
$743$	25.2004	+	18.3091i	0.924511	+	0.671697i	−0.0201316	+	0.999797i	$0.506409\pi$
$744$	−1.19199	+	3.66855i	−0.0437003	+	0.134496i
$745$	13.6083	+	41.8820i	0.498569	+	1.53444i
$746$	0.623550	−	0.453036i	0.0228298	−	0.0165868i
$747$	−4.46264			−0.163280
$748$		0			0
$749$	−14.0187			−0.512231
$750$	−0.166177	+	0.120734i	−0.00606791	+	0.00440860i
$751$	3.70491	+	11.4026i	0.135194	+	0.416085i	0.995620	−	0.0934905i	$-0.0298025\pi$
$751$	3.70491	+	11.4026i	0.135194	+	0.416085i	−0.860426	+	0.509575i	$0.829802\pi$
$752$	0.888909	−	2.73578i	0.0324152	−	0.0997636i
$753$	−5.48078	−	3.98202i	−0.199731	−	0.145113i
$754$	−36.9387	−	26.8375i	−1.34523	−	0.977365i
$755$	−6.62944	+	20.4033i	−0.241270	+	0.742553i
$756$	−0.0931160	−	0.286582i	−0.00338660	−	0.0104229i
$757$	9.26592	−	6.73209i	0.336776	−	0.244682i	−0.406524	−	0.913640i	$-0.633259\pi$
$757$	9.26592	−	6.73209i	0.336776	−	0.244682i	0.743300	+	0.668958i	$0.233259\pi$
$758$	30.7240			1.11595
$759$		0			0
$760$	−64.2800			−2.33168
$761$	−6.38318	+	4.63765i	−0.231390	+	0.168115i	−0.697439	−	0.716644i	$-0.745677\pi$
$761$	−6.38318	+	4.63765i	−0.231390	+	0.168115i	0.466049	+	0.884759i	$0.345677\pi$
$762$	−3.37033	−	10.3728i	−0.122094	−	0.375768i
$763$	4.81284	−	14.8124i	0.174236	−	0.536245i
$764$	0.440146	+	0.319785i	0.0159239	+	0.0115694i
$765$	−34.8255	−	25.3022i	−1.25912	−	0.914802i
$766$	−9.01198	+	27.7360i	−0.325616	+	1.00214i
$767$	0.536449	+	1.65102i	0.0193700	+	0.0596149i
$768$	0.991963	−	0.720703i	0.0357944	−	0.0260061i
$769$	−48.8153			−1.76033			−0.880163	−	0.474672i	$-0.842567\pi$
$769$	−48.8153			−1.76033			−0.880163	+	0.474672i	$0.842567\pi$
$770$		0			0
$771$	−3.10525			−0.111833
$772$	−0.291197	+	0.211567i	−0.0104804	+	0.00761445i
$773$	−0.987642	−	3.03965i	−0.0355230	−	0.109329i	0.931723	−	0.363170i	$-0.118306\pi$
$773$	−0.987642	−	3.03965i	−0.0355230	−	0.109329i	−0.967246	+	0.253842i	$0.918306\pi$
$774$	5.17459	−	15.9257i	0.185997	−	0.572439i
$775$	14.3223	+	10.4057i	0.514471	+	0.373785i
$776$	−14.5266	−	10.5542i	−0.521476	−	0.378874i
$777$	1.10792	−	3.40984i	0.0397466	−	0.122327i
$778$	−4.49884	−	13.8460i	−0.161291	−	0.496404i
$779$	−18.2708	+	13.2745i	−0.654621	+	0.475610i
$780$	0.770750			0.0275973
$781$		0			0
$782$	33.4906			1.19762
$783$	12.0899	−	8.78383i	0.432058	−	0.313908i
$784$	−1.14254	−	3.51639i	−0.0408052	−	0.125585i
$785$	−22.7564	+	70.0370i	−0.812211	+	2.49973i
$786$	6.01476	+	4.36998i	0.214539	+	0.155872i
$787$	34.3681	+	24.9699i	1.22509	+	0.890080i	0.996512	−	0.0834455i	$-0.0265925\pi$
$787$	34.3681	+	24.9699i	1.22509	+	0.890080i	0.228578	+	0.973526i	$0.426592\pi$
$788$	0.460629	−	1.41767i	0.0164092	−	0.0505024i
$789$	1.79639	+	5.52873i	0.0639533	+	0.196828i
$790$	−12.8796	+	9.35760i	−0.458237	+	0.332928i
$791$	−4.13201			−0.146917
$792$		0			0
$793$	−15.3947			−0.546682
$794$	−26.3782	+	19.1649i	−0.936129	+	0.680137i
$795$	0.805081	+	2.47778i	0.0285533	+	0.0878779i
$796$	−0.510329	+	1.57063i	−0.0180881	+	0.0556696i
$797$	23.3471	+	16.9627i	0.826998	+	0.600850i	0.918709	−	0.394936i	$-0.129233\pi$
$797$	23.3471	+	16.9627i	0.826998	+	0.600850i	−0.0917101	+	0.995786i	$0.529233\pi$
$798$	2.80888	+	2.04077i	0.0994334	+	0.0722426i
$799$	1.14872	−	3.53539i	0.0406387	−	0.125073i
$800$	−1.20040	−	3.69445i	−0.0424406	−	0.130619i
$801$	−12.9594	+	9.41553i	−0.457897	+	0.332681i
$802$	−15.8947			−0.561260
$803$		0			0
$804$	0.338644			0.0119431
$805$	13.0662	−	9.49312i	0.460522	−	0.334589i
$806$	−7.32038	−	22.5298i	−0.257849	−	0.793579i
$807$	0.848349	−	2.61095i	0.0298633	−	0.0919097i
$808$	25.4996	+	18.5265i	0.897071	+	0.651760i
$809$	23.8282	+	17.3122i	0.837756	+	0.608665i	0.921743	−	0.387802i	$-0.126765\pi$
$809$	23.8282	+	17.3122i	0.837756	+	0.608665i	−0.0839869	+	0.996467i	$0.526765\pi$
$810$	−10.3615	+	31.8895i	−0.364067	+	1.12048i
$811$	−0.766764	−	2.35986i	−0.0269247	−	0.0828657i	0.936691	−	0.350156i	$-0.113872\pi$
$811$	−0.766764	−	2.35986i	−0.0269247	−	0.0828657i	−0.963616	+	0.267291i	$0.913872\pi$
$812$	−0.801470	+	0.582302i	−0.0281261	+	0.0204348i
$813$	5.09337			0.178632
$814$		0			0
$815$	−3.11203			−0.109010
$816$	−5.19271	+	3.77273i	−0.181781	+	0.132072i
$817$	−9.27628	−	28.5494i	−0.324536	−	0.998818i
$818$	−13.8248	+	42.5484i	−0.483373	+	1.48767i
$819$	11.0862	+	8.05459i	0.387383	+	0.281450i
$820$	−1.15731	−	0.840835i	−0.0404150	−	0.0293632i
$821$	−4.33200	+	13.3325i	−0.151188	+	0.465309i	−0.997755	−	0.0669738i	$-0.978666\pi$
$821$	−4.33200	+	13.3325i	−0.151188	+	0.465309i	0.846567	+	0.532283i	$0.178666\pi$
$822$	1.63741	+	5.03944i	0.0571113	+	0.175771i
$823$	34.6205	−	25.1533i	1.20679	−	0.876787i	0.211859	−	0.977300i	$-0.432048\pi$
$823$	34.6205	−	25.1533i	1.20679	−	0.876787i	0.994936	+	0.100513i	$0.0320484\pi$
$824$	−38.6540			−1.34658
$825$		0			0
$826$	−0.495336			−0.0172349
$827$	−7.41920	+	5.39037i	−0.257991	+	0.187441i	−0.709261	−	0.704946i	$-0.750971\pi$
$827$	−7.41920	+	5.39037i	−0.257991	+	0.187441i	0.451270	+	0.892388i	$0.350971\pi$
$828$	0.644005	+	1.98204i	0.0223807	+	0.0688808i
$829$	9.02246	−	27.7683i	0.313363	−	0.964433i	−0.663060	−	0.748566i	$-0.730743\pi$
$829$	9.02246	−	27.7683i	0.313363	−	0.964433i	0.976423	−	0.215866i	$-0.0692575\pi$
$830$	5.39121	+	3.91695i	0.187132	+	0.135959i
$831$	1.76912	+	1.28534i	0.0613700	+	0.0445879i
$832$	−12.5245	+	38.5463i	−0.434208	+	1.33635i
$833$	−1.47649	−	4.54416i	−0.0511572	−	0.157446i
$834$	1.64410	−	1.19451i	0.0569304	−	0.0413624i
$835$	1.77594			0.0614588
$836$		0			0
$837$	7.75341			0.267997
$838$	11.9082	−	8.65185i	0.411363	−	0.298873i
$839$	6.09771	+	18.7668i	0.210516	+	0.647902i	0.999442	+	0.0334134i	$0.0106378\pi$
$839$	6.09771	+	18.7668i	0.210516	+	0.647902i	−0.788925	+	0.614489i	$0.789362\pi$
$840$	−1.02963	+	3.16888i	−0.0355256	+	0.109337i
$841$	−16.2861	−	11.8325i	−0.561589	−	0.408018i
$842$	−1.27059	−	0.923135i	−0.0437873	−	0.0318133i
$843$	−2.32050	+	7.14175i	−0.0799222	+	0.245975i
$844$	−0.485321	−	1.49366i	−0.0167054	−	0.0514140i
$845$	−24.9803	+	18.1492i	−0.859348	+	0.624353i
$846$	−3.04202			−0.104587
$847$		0			0
$848$	−8.43984			−0.289825
$849$	−2.91468	+	2.11764i	−0.100032	+	0.0726773i
$850$	9.79895	+	30.1581i	0.336101	+	1.03441i
$851$	−15.6779	+	48.2515i	−0.537431	+	1.65404i
$852$	−0.629809	−	0.457583i	−0.0215769	−	0.0156765i
$853$	−22.9378	−	16.6653i	−0.785375	−	0.570609i	0.121212	−	0.992627i	$-0.461322\pi$
$853$	−22.9378	−	16.6653i	−0.785375	−	0.570609i	−0.906587	+	0.422018i	$0.861322\pi$
$854$	1.35740	−	4.17764i	0.0464492	−	0.142956i
$855$	19.5142	+	60.0586i	0.667372	+	2.05396i
$856$	−33.1092	+	24.0553i	−1.13165	+	0.822192i
$857$	−13.2033			−0.451017			−0.225509	−	0.974241i	$-0.572404\pi$
$857$	−13.2033			−0.451017			−0.225509	+	0.974241i	$0.572404\pi$
$858$		0			0
$859$	−20.8260			−0.710573			−0.355286	−	0.934757i	$-0.615617\pi$
$859$	−20.8260			−0.710573			−0.355286	+	0.934757i	$0.615617\pi$
$860$	1.53830	−	1.11764i	0.0524555	−	0.0381111i
$861$	0.361748	+	1.11335i	0.0123283	+	0.0379427i
$862$	13.4645	−	41.4395i	0.458603	−	1.41143i
$863$	−28.2702	−	20.5395i	−0.962330	−	0.699174i	−0.00863946	−	0.999963i	$-0.502750\pi$
$863$	−28.2702	−	20.5395i	−0.962330	−	0.699174i	−0.953691	+	0.300789i	$0.902750\pi$
$864$	−1.37639	−	1.00000i	−0.0468256	−	0.0340208i
$865$	−16.7360	+	51.5080i	−0.569039	+	1.75132i
$866$	1.86773	+	5.74827i	0.0634680	+	0.195334i
$867$	−1.71347	+	1.24491i	−0.0581926	+	0.0422794i
$868$	−0.513993			−0.0174461
$869$		0			0
$870$	−10.9066			−0.369769
$871$	−25.4915	+	18.5207i	−0.863748	+	0.627550i
$872$	−14.0503	−	43.2425i	−0.475804	−	1.46437i
$873$	−5.45108	+	16.7767i	−0.184491	+	0.567805i
$874$	−39.7476	−	28.8783i	−1.34448	−	0.976823i
$875$	−0.335483	−	0.243743i	−0.0113414	−	0.00824000i
$876$	0.0511280	−	0.157356i	0.00172746	−	0.00531656i
$877$	8.18317	+	25.1852i	0.276326	+	0.850444i	0.988865	+	0.148812i	$0.0475450\pi$
$877$	8.18317	+	25.1852i	0.276326	+	0.850444i	−0.712539	+	0.701632i	$0.752455\pi$
$878$	−30.3004	+	22.0145i	−1.02259	+	0.742954i
$879$	−9.73599			−0.328387
$880$		0			0
$881$	17.2627			0.581595			0.290798	−	0.956785i	$-0.406079\pi$
$881$	17.2627			0.581595			0.290798	+	0.956785i	$0.406079\pi$
$882$	−3.16327	+	2.29825i	−0.106513	+	0.0773861i
$883$	−13.7830	−	42.4196i	−0.463834	−	1.42753i	−0.860443	−	0.509547i	$-0.829813\pi$
$883$	−13.7830	−	42.4196i	−0.463834	−	1.42753i	0.396609	−	0.917988i	$-0.370187\pi$
$884$	−0.997078	+	3.06869i	−0.0335354	+	0.103211i
$885$	0.335483	+	0.243743i	0.0112771	+	0.00819332i
$886$	−8.59283	−	6.24305i	−0.288682	−	0.209739i
$887$	−9.51445	+	29.2825i	−0.319464	+	0.983209i	0.654414	+	0.756137i	$0.272915\pi$
$887$	−9.51445	+	29.2825i	−0.319464	+	0.983209i	−0.973878	+	0.227072i	$0.927085\pi$
$888$	−3.23441	−	9.95450i	−0.108540	−	0.334051i
$889$	17.8135	−	12.9422i	0.597445	−	0.434069i
$890$	23.9201			0.801803
$891$		0			0
$892$	−3.96316			−0.132697
$893$	−4.41182	+	3.20538i	−0.147636	+	0.107264i
$894$	−2.14580	−	6.60408i	−0.0717661	−	0.220873i
$895$	10.9899	−	33.8234i	0.367351	−	1.13059i
$896$	−8.06479	−	5.85941i	−0.269426	−	0.195749i
$897$	7.22071	+	5.24615i	0.241092	+	0.175164i
$898$	−8.64094	+	26.5941i	−0.288352	+	0.887456i
$899$	−7.87704	−	24.2430i	−0.262714	−	0.808550i
$900$	−1.59639	+	1.15984i	−0.0532130	+	0.0386615i
$901$	−10.9066			−0.363352
$902$		0			0
$903$	−1.55602			−0.0517810
$904$	−9.75897	+	7.09031i	−0.324579	+	0.235820i
$905$	14.4418	+	44.4473i	0.480062	+	1.47748i
$906$	1.04535	−	3.21726i	0.0347294	−	0.106886i
$907$	−19.2385	−	13.9776i	−0.638804	−	0.464118i	0.220635	−	0.975356i	$-0.429187\pi$
$907$	−19.2385	−	13.9776i	−0.638804	−	0.464118i	−0.859439	+	0.511238i	$0.829187\pi$
$908$	−2.63096	−	1.91151i	−0.0873116	−	0.0634356i
$909$	9.56864	−	29.4492i	0.317372	−	0.976769i
$910$	−6.32330	−	19.4611i	−0.209615	−	0.645130i
$911$	−39.6645	+	28.8179i	−1.31414	+	0.954781i	−0.314157	+	0.949371i	$0.601722\pi$
$911$	−39.6645	+	28.8179i	−1.31414	+	0.954781i	−0.999985	+	0.00540957i	$0.998278\pi$
$912$	9.41600			0.311795
$913$		0			0
$914$	11.6774			0.386253
$915$	−2.97506	+	2.16151i	−0.0983524	+	0.0714572i
$916$	−0.586297	−	1.80444i	−0.0193718	−	0.0596203i
$917$	−4.63814	+	14.2747i	−0.153165	+	0.471393i
$918$	11.2355	+	8.16309i	0.370828	+	0.269422i
$919$	−32.3607	−	23.5114i	−1.06748	−	0.775570i	−0.0920227	−	0.995757i	$-0.529333\pi$
$919$	−32.3607	−	23.5114i	−1.06748	−	0.775570i	−0.975458	+	0.220187i	$0.929333\pi$
$920$	14.5699	−	44.8417i	0.480357	−	1.47839i
$921$	1.33576	+	4.11106i	0.0440149	+	0.135464i
$922$	10.6611	−	7.74577i	0.351106	−	0.255093i
$923$	72.4346			2.38421
$924$		0			0
$925$	−48.0373			−1.57946
$926$	12.6002	−	9.15456i	0.414067	−	0.300838i
$927$	11.7346	+	36.1155i	0.385416	+	1.18619i
$928$	−1.72843	+	5.31957i	−0.0567386	+	0.174624i
$929$	45.7774	+	33.2592i	1.50191	+	1.09120i	0.969614	+	0.244641i	$0.0786702\pi$
$929$	45.7774	+	33.2592i	1.50191	+	1.09120i	0.532295	+	0.846559i	$0.321330\pi$
$930$	−4.57800	−	3.32611i	−0.150119	−	0.109067i
$931$	−2.16600	+	6.66627i	−0.0709878	+	0.218478i
$932$	0.154495	+	0.475487i	0.00506065	+	0.0155751i
$933$	6.24345	−	4.53613i	0.204401	−	0.148506i
$934$	−24.8408			−0.812814
$935$		0			0
$936$	40.0046			1.30759
$937$	13.6039	−	9.88380i	0.444419	−	0.322890i	−0.342969	−	0.939347i	$-0.611433\pi$
$937$	13.6039	−	9.88380i	0.444419	−	0.322890i	0.787389	+	0.616457i	$0.211433\pi$
$938$	−2.77827	−	8.55064i	−0.0907137	−	0.279188i
$939$	−1.42559	+	4.38752i	−0.0465224	+	0.143181i
$940$	−0.279453	−	0.203035i	−0.00911476	−	0.00662226i
$941$	−5.87290	−	4.26691i	−0.191451	−	0.139097i	0.487931	−	0.872882i	$-0.337752\pi$
$941$	−5.87290	−	4.26691i	−0.191451	−	0.139097i	−0.679382	+	0.733785i	$0.737752\pi$
$942$	3.58830	−	11.0437i	0.116913	−	0.359822i
$943$	−5.11897	−	15.7546i	−0.166697	−	0.513040i
$944$	−1.08679	+	0.789603i	−0.0353722	+	0.0256994i
$945$	6.69735			0.217865
$946$		0			0
$947$	−25.6040			−0.832017			−0.416009	−	0.909361i	$-0.636571\pi$
$947$	−25.6040			−0.832017			−0.416009	+	0.909361i	$0.636571\pi$
$948$	−0.154433	+	0.112202i	−0.00501576	+	0.00364416i
$949$	4.75723	+	14.6412i	0.154426	+	0.475275i
$950$	14.3750	−	44.2418i	0.466388	−	1.43539i
$951$	3.48846	+	2.53452i	0.113121	+	0.0821873i
$952$	−11.2847	−	8.19881i	−0.365739	−	0.265725i
$953$	2.20927	−	6.79943i	0.0715653	−	0.220255i	−0.908876	−	0.417066i	$-0.863058\pi$
$953$	2.20927	−	6.79943i	0.0715653	−	0.220255i	0.980442	+	0.196811i	$0.0630584\pi$
$954$	2.75806	+	8.48845i	0.0892956	+	0.274824i
$955$	−9.78268	+	7.10753i	−0.316560	+	0.229994i
$956$	−3.11203			−0.100650
$957$		0			0
$958$	−4.73344			−0.152930
$959$	−8.65434	+	6.28775i	−0.279463	+	0.203042i
$960$	2.99175	+	9.20767i	0.0965584	+	0.297176i
$961$	−5.49266	+	16.9047i	−0.177183	+	0.545312i
$962$	52.0036	+	37.7829i	1.67666	+	1.21817i
$963$	32.5269	+	23.6321i	1.04816	+	0.761535i
$964$	0.0137737	−	0.0423911i	0.000443621	−	0.00136533i
$965$	−2.47214	−	7.60845i	−0.0795809	−	0.244925i
$966$	−2.06031	+	1.49691i	−0.0662895	+	0.0481621i
$967$	15.9600			0.513241			0.256620	−	0.966512i	$-0.417391\pi$
$967$	15.9600			0.513241			0.256620	+	0.966512i	$0.417391\pi$
$968$		0			0
$969$	12.1681			0.390895
$970$	21.3105	−	15.4830i	0.684240	−	0.497130i
$971$	−9.41819	−	28.9862i	−0.302244	−	0.930212i	−0.980691	−	0.195563i	$-0.937347\pi$
$971$	−9.41819	−	28.9862i	−0.302244	−	0.930212i	0.678447	−	0.734649i	$-0.262653\pi$
$972$	−0.403588	+	1.24212i	−0.0129451	+	0.0398409i
$973$	3.31916	+	2.41151i	0.106407	+	0.0773094i
$974$	−30.2886	−	22.0060i	−0.970510	−	0.705117i
$975$	−2.61143	+	8.03715i	−0.0836327	+	0.257395i
$976$	−3.68127	−	11.3298i	−0.117835	−	0.362658i
$977$	−3.34286	+	2.42873i	−0.106948	+	0.0777021i	−0.639974	−	0.768397i	$-0.721055\pi$
$977$	−3.34286	+	2.42873i	−0.106948	+	0.0777021i	0.533026	+	0.846099i	$0.321055\pi$
$978$	0.490715			0.0156913
$979$		0			0
$980$	−0.443984			−0.0141826
$981$	−36.1372	+	26.2552i	−1.15377	+	0.838265i
$982$	2.63898	+	8.12194i	0.0842131	+	0.259181i
$983$	−7.73303	+	23.7998i	−0.246645	+	0.759096i	0.748716	+	0.662891i	$0.230671\pi$
$983$	−7.73303	+	23.7998i	−0.246645	+	0.759096i	−0.995362	+	0.0962053i	$0.969329\pi$
$984$	2.76482	+	2.00876i	0.0881392	+	0.0640369i
$985$	26.8033	+	19.4737i	0.854024	+	0.620485i
$986$	14.1093	−	43.4240i	0.449332	−	1.38290i
$987$	0.0873505	+	0.268837i	0.00278040	+	0.00855718i
$988$	3.82943	−	2.78224i	0.121830	−	0.0885150i
$989$	22.0187			0.700153
$990$		0			0
$991$	−27.5747			−0.875938			−0.437969	−	0.898990i	$-0.644302\pi$
$991$	−27.5747			−0.875938			−0.437969	+	0.898990i	$0.644302\pi$
$992$	−2.34777	+	1.70576i	−0.0745418	+	0.0541578i
$993$	−1.33457	−	4.10738i	−0.0423513	−	0.130344i
$994$	−6.38678	+	19.6565i	−0.202576	+	0.623466i
$995$	−29.6953	−	21.5749i	−0.941403	−	0.683969i
$996$	0.0646434	+	0.0469662i	0.00204830	+	0.00148818i
$997$	7.31895	−	22.5254i	0.231794	−	0.713387i	−0.765737	−	0.643154i	$-0.777626\pi$
$997$	7.31895	−	22.5254i	0.231794	−	0.713387i	0.997531	−	0.0702335i	$-0.0223744\pi$
$998$	8.70727	+	26.7982i	0.275624	+	0.848283i
$999$	−17.0206	+	12.3662i	−0.538508	+	0.391249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.u.729.2		12
11.2	odd	10		847.2.a.j.1.2	yes	3
11.3	even	5	inner	847.2.f.u.148.2		12
11.4	even	5	inner	847.2.f.u.323.2		12
11.5	even	5	inner	847.2.f.u.372.2		12
11.6	odd	10		847.2.f.t.372.2		12
11.7	odd	10		847.2.f.t.323.2		12
11.8	odd	10		847.2.f.t.148.2		12
11.9	even	5		847.2.a.i.1.2	✓	3
11.10	odd	2		847.2.f.t.729.2		12
33.2	even	10		7623.2.a.bz.1.2		3
33.20	odd	10		7623.2.a.ce.1.2		3
77.13	even	10		5929.2.a.y.1.2		3
77.20	odd	10		5929.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.2	✓	3	11.9	even	5
847.2.a.j.1.2	yes	3	11.2	odd	10
847.2.f.t.148.2		12	11.8	odd	10
847.2.f.t.323.2		12	11.7	odd	10
847.2.f.t.372.2		12	11.6	odd	10
847.2.f.t.729.2		12	11.10	odd	2
847.2.f.u.148.2		12	11.3	even	5	inner
847.2.f.u.323.2		12	11.4	even	5	inner
847.2.f.u.372.2		12	11.5	even	5	inner
847.2.f.u.729.2		12	1.1	even	1	trivial
5929.2.a.t.1.2		3	77.20	odd	10
5929.2.a.y.1.2		3	77.13	even	10
7623.2.a.bz.1.2		3	33.2	even	10
7623.2.a.ce.1.2		3	33.20	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10296 - 0.801344i) q^{2} +(0.112275 + 0.345546i) q^{3} +(-0.0436753 + 0.134419i) q^{4} +(-2.54139 - 1.84643i) q^{5} +(0.400735 + 0.291151i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.902127 + 2.77646i) q^{8} +(2.32025 - 1.68576i) q^{9} +O(q^{10})\)	\(q+(1.10296 - 0.801344i) q^{2} +(0.112275 + 0.345546i) q^{3} +(-0.0436753 + 0.134419i) q^{4} +(-2.54139 - 1.84643i) q^{5} +(0.400735 + 0.291151i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.902127 + 2.77646i) q^{8} +(2.32025 - 1.68576i) q^{9} -4.28267 q^{10} -0.0513514 q^{12} +(3.86549 - 2.80844i) q^{13} +(0.421292 + 1.29660i) q^{14} +(0.352692 - 1.08548i) q^{15} +(2.99122 + 2.17325i) q^{16} +(3.86549 + 2.80844i) q^{17} +(1.20826 - 3.71865i) q^{18} +(-2.16600 - 6.66627i) q^{19} +(0.359191 - 0.260967i) q^{20} -0.363328 q^{21} +5.14134 q^{23} +(-0.858108 + 0.623452i) q^{24} +(1.50429 + 4.62974i) q^{25} +(2.01293 - 6.19518i) q^{26} +(1.72483 + 1.25316i) q^{27} +(-0.114343 - 0.0830753i) q^{28} +(2.16600 - 6.66627i) q^{29} +(-0.480835 - 1.47986i) q^{30} +(2.94213 - 2.13758i) q^{31} -0.797984 q^{32} +6.51399 q^{34} +(2.54139 - 1.84643i) q^{35} +(0.125260 + 0.385512i) q^{36} +(-3.04938 + 9.38502i) q^{37} +(-7.73098 - 5.61689i) q^{38} +(1.40444 + 1.02039i) q^{39} +(2.83388 - 8.72180i) q^{40} +(-0.995650 - 3.06430i) q^{41} +(-0.400735 + 0.291151i) q^{42} +4.28267 q^{43} -9.00933 q^{45} +(5.67067 - 4.11998i) q^{46} +(-0.240418 - 0.739929i) q^{47} +(-0.415119 + 1.27760i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(5.36918 + 3.90094i) q^{50} +(-0.536449 + 1.65102i) q^{51} +(0.208681 + 0.642253i) q^{52} +(-1.84672 + 1.34172i) q^{53} +2.90663 q^{54} -2.91934 q^{56} +(2.06031 - 1.49691i) q^{57} +(-2.95297 - 9.08831i) q^{58} +(-0.112275 + 0.345546i) q^{59} +(0.130504 + 0.0948168i) q^{60} +(-2.60665 - 1.89384i) q^{61} +(1.53210 - 4.71532i) q^{62} +(0.886258 + 2.72762i) q^{63} +(-6.86258 + 4.98596i) q^{64} -15.0093 q^{65} -6.59465 q^{67} +(-0.546333 + 0.396934i) q^{68} +(0.577241 + 1.77657i) q^{69} +(1.32342 - 4.07306i) q^{70} +(12.2647 + 8.91082i) q^{71} +(6.77362 + 4.92132i) q^{72} +(-0.995650 + 3.06430i) q^{73} +(4.15730 + 12.7949i) q^{74} +(-1.43089 + 1.03960i) q^{75} +0.990671 q^{76} +2.36672 q^{78} +(3.00738 - 2.18499i) q^{79} +(-3.58912 - 11.0462i) q^{80} +(2.41941 - 7.44616i) q^{81} +(-3.55371 - 2.58192i) q^{82} +(-1.25884 - 0.914603i) q^{83} +(0.0158685 - 0.0488381i) q^{84} +(-4.63814 - 14.2747i) q^{85} +(4.72360 - 3.43189i) q^{86} +2.54669 q^{87} -5.58532 q^{89} +(-9.93689 + 7.21957i) q^{90} +(1.47649 + 4.54416i) q^{91} +(-0.224549 + 0.691091i) q^{92} +(1.06896 + 0.776644i) q^{93} +(-0.858108 - 0.623452i) q^{94} +(-6.80414 + 20.9410i) q^{95} +(-0.0895933 - 0.275740i) q^{96} +(-4.97599 + 3.61527i) q^{97} -1.36333 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9	\( 12 q + 2 q^{2} + q^{3} - 8 q^{4} - q^{5} + 12 q^{6} + 3 q^{7} + 6 q^{8} - 4 q^{9} + 16 q^{10} + 8 q^{12} + 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} + 8 q^{17} - 18 q^{18} + 14 q^{20} + 4 q^{21} + 28 q^{23} + 20 q^{24} - 2 q^{25} + 12 q^{26} + 19 q^{27} + 8 q^{28} - 8 q^{30} + 13 q^{31} - 136 q^{32} - 48 q^{34} + q^{35} - 18 q^{36} + 17 q^{37} - 16 q^{38} - 20 q^{39} - 36 q^{40} + 16 q^{41} - 12 q^{42} - 16 q^{43} - 24 q^{45} - 4 q^{47} - 36 q^{48} - 3 q^{49} + 22 q^{50} - 20 q^{51} + 10 q^{53} - 32 q^{54} + 24 q^{56} + 16 q^{57} + 16 q^{58} - q^{59} + 30 q^{60} - 16 q^{61} + 4 q^{62} + 4 q^{63} - 34 q^{64} - 96 q^{65} - 12 q^{67} + 7 q^{69} + 4 q^{70} - 5 q^{71} + 2 q^{72} + 16 q^{73} - 32 q^{74} - 20 q^{75} + 96 q^{76} + 112 q^{78} + 28 q^{79} + 56 q^{80} - 15 q^{81} - 28 q^{82} + 8 q^{83} + 2 q^{84} + 24 q^{85} - 12 q^{86} + 64 q^{87} - 84 q^{89} - 20 q^{90} - 8 q^{91} - 2 q^{92} - 17 q^{93} + 20 q^{94} + 24 q^{95} + 20 q^{96} + 11 q^{97} - 8 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 8 * q^4 - q^5 + 12 * q^6 + 3 * q^7 + 6 * q^8 - 4 * q^9 + 16 * q^10 + 8 * q^12 + 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 + 8 * q^17 - 18 * q^18 + 14 * q^20 + 4 * q^21 + 28 * q^23 + 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 + 8 * q^28 - 8 * q^30 + 13 * q^31 - 136 * q^32 - 48 * q^34 + q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 - 20 * q^39 - 36 * q^40 + 16 * q^41 - 12 * q^42 - 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 + 22 * q^50 - 20 * q^51 + 10 * q^53 - 32 * q^54 + 24 * q^56 + 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 - 16 * q^61 + 4 * q^62 + 4 * q^63 - 34 * q^64 - 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 + 2 * q^72 + 16 * q^73 - 32 * q^74 - 20 * q^75 + 96 * q^76 + 112 * q^78 + 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 + 8 * q^83 + 2 * q^84 + 24 * q^85 - 12 * q^86 + 64 * q^87 - 84 * q^89 - 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 + 20 * q^94 + 24 * q^95 + 20 * q^96 + 11 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more