LMFDB - Embedded newform 798.2.bj.a.601.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(559,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("798.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			601.3
Character	$\chi$	$=$	798.601
Dual form			798.2.bj.a.559.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.397289 + 0.229375i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.97350 - 1.76218i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.397289 + 0.229375i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.97350 - 1.76218i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.229375 - 0.397289i) q^{10} -5.18994 q^{11} -1.00000 q^{12} +(1.34597 - 2.33128i) q^{13} +(-0.828014 + 2.51285i) q^{14} +(0.397289 + 0.229375i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.111434 + 0.0643362i) q^{17} -1.00000i q^{18} +(1.63845 - 4.03924i) q^{19} +0.458750i q^{20} +(-2.51285 - 0.828014i) q^{21} +(4.49462 - 2.59497i) q^{22} +(0.769401 - 1.33264i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.39477 + 4.14787i) q^{25} +2.69193i q^{26} +1.00000 q^{27} +(-0.539342 - 2.59020i) q^{28} +(-0.521362 - 0.301008i) q^{29} -0.458750 q^{30} -6.44999 q^{31} +(0.866025 + 0.500000i) q^{32} +(2.59497 + 4.49462i) q^{33} +(0.0643362 - 0.111434i) q^{34} +(-0.379851 + 1.15277i) q^{35} +(0.500000 + 0.866025i) q^{36} +6.53699i q^{37} +(0.600682 + 4.31731i) q^{38} -2.69193 q^{39} +(-0.229375 - 0.397289i) q^{40} +(-3.36092 - 5.82128i) q^{41} +(2.59020 - 0.539342i) q^{42} +(-2.61236 - 4.52474i) q^{43} +(-2.59497 + 4.49462i) q^{44} -0.458750i q^{45} +1.53880i q^{46} +(-0.675186 - 0.389819i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.789435 - 6.95534i) q^{49} -4.78955i q^{50} +(0.111434 + 0.0643362i) q^{51} +(-1.34597 - 2.33128i) q^{52} +(-7.14293 - 4.12397i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.06191 - 1.19044i) q^{55} +(1.76218 + 1.97350i) q^{56} +(-4.31731 + 0.600682i) q^{57} +0.602017 q^{58} +(-2.12593 - 3.68222i) q^{59} +(0.397289 - 0.229375i) q^{60} +(-7.19028 - 4.15131i) q^{61} +(5.58585 - 3.22499i) q^{62} +(0.539342 + 2.59020i) q^{63} -1.00000 q^{64} +1.23492i q^{65} +(-4.49462 - 2.59497i) q^{66} +(-9.81323 - 5.66567i) q^{67} +0.128672i q^{68} -1.53880 q^{69} +(-0.247423 - 1.18825i) q^{70} +(-4.78110 + 2.76037i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(6.89899 - 3.98313i) q^{73} +(-3.26849 - 5.66120i) q^{74} +4.78955 q^{75} +(-2.67886 - 3.43856i) q^{76} +(-10.2424 + 9.14562i) q^{77} +(2.33128 - 1.34597i) q^{78} +(9.65974 - 5.57705i) q^{79} +(0.397289 + 0.229375i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.82128 + 3.36092i) q^{82} -1.11680i q^{83} +(-1.97350 + 1.76218i) q^{84} +(0.0295142 - 0.0511201i) q^{85} +(4.52474 + 2.61236i) q^{86} +0.602017i q^{87} -5.18994i q^{88} +(-2.75371 + 4.76957i) q^{89} +(0.229375 + 0.397289i) q^{90} +(-1.45187 - 6.97263i) q^{91} +(-0.769401 - 1.33264i) q^{92} +(3.22499 + 5.58585i) q^{93} +0.779638 q^{94} +(0.275563 + 1.98057i) q^{95} -1.00000i q^{96} +(0.264199 + 0.457606i) q^{97} +(2.79400 + 6.41822i) q^{98} +(2.59497 - 4.49462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9} + 2 q^{10} - 24 q^{12} + 10 q^{13} + 4 q^{14} - 12 q^{16} - 10 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{25} + 24 q^{27} + 12 q^{28} - 4 q^{30} - 36 q^{31} + 2 q^{34} - 16 q^{35} + 12 q^{36} + 12 q^{38} - 20 q^{39} - 2 q^{40} - 20 q^{41} - 8 q^{42} - 6 q^{43} - 12 q^{48} + 2 q^{49} - 10 q^{52} + 12 q^{53} - 30 q^{55} - 4 q^{56} + 2 q^{57} - 8 q^{58} + 8 q^{59} - 42 q^{61} - 12 q^{62} - 12 q^{63} - 24 q^{64} - 6 q^{66} + 6 q^{67} + 6 q^{70} - 24 q^{71} + 66 q^{73} - 12 q^{75} - 8 q^{76} + 16 q^{77} - 24 q^{78} + 30 q^{79} - 12 q^{81} - 6 q^{82} - 6 q^{84} - 2 q^{85} + 12 q^{86} - 8 q^{89} + 2 q^{90} - 66 q^{91} + 18 q^{93} + 20 q^{95} + 36 q^{97} - 32 q^{98}+O(q^{100}) $ 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9 + 2 * q^10 - 24 * q^12 + 10 * q^13 + 4 * q^14 - 12 * q^16 - 10 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^25 + 24 * q^27 + 12 * q^28 - 4 * q^30 - 36 * q^31 + 2 * q^34 - 16 * q^35 + 12 * q^36 + 12 * q^38 - 20 * q^39 - 2 * q^40 - 20 * q^41 - 8 * q^42 - 6 * q^43 - 12 * q^48 + 2 * q^49 - 10 * q^52 + 12 * q^53 - 30 * q^55 - 4 * q^56 + 2 * q^57 - 8 * q^58 + 8 * q^59 - 42 * q^61 - 12 * q^62 - 12 * q^63 - 24 * q^64 - 6 * q^66 + 6 * q^67 + 6 * q^70 - 24 * q^71 + 66 * q^73 - 12 * q^75 - 8 * q^76 + 16 * q^77 - 24 * q^78 + 30 * q^79 - 12 * q^81 - 6 * q^82 - 6 * q^84 - 2 * q^85 + 12 * q^86 - 8 * q^89 + 2 * q^90 - 66 * q^91 + 18 * q^93 + 20 * q^95 + 36 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.397289	+	0.229375i	−0.177673	+	0.102580i	−0.586199	−	0.810167i	$-0.699376\pi$
$5$	−0.397289	+	0.229375i	−0.177673	+	0.102580i	0.408526	+	0.912747i	$0.366043\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	1.97350	−	1.76218i	0.745914	−	0.666042i
$7$	1.97350	−	1.76218i	0.745914	−	0.666042i
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.229375	−	0.397289i	0.0725347	−	0.125634i
$11$	−5.18994			−1.56483			−0.782414	−	0.622759i	$-0.786012\pi$
$11$	−5.18994			−1.56483			−0.782414	+	0.622759i	$0.786012\pi$
$12$	−1.00000			−0.288675
$13$	1.34597	−	2.33128i	0.373304	−	0.646581i	−0.616768	−	0.787145i	$-0.711558\pi$
$13$	1.34597	−	2.33128i	0.373304	−	0.646581i	0.990072	+	0.140564i	$0.0448916\pi$
$14$	−0.828014	+	2.51285i	−0.221296	+	0.671586i
$15$	0.397289	+	0.229375i	0.102580	+	0.0592244i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.111434	+	0.0643362i	−0.0270266	+	0.0156038i	−0.513452	−	0.858118i	$-0.671634\pi$
$17$	−0.111434	+	0.0643362i	−0.0270266	+	0.0156038i	0.486426	+	0.873722i	$0.338300\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.63845	−	4.03924i	0.375886	−	0.926666i
$19$	1.63845	−	4.03924i	0.375886	−	0.926666i
$20$			0.458750i			0.102580i
$21$	−2.51285	−	0.828014i	−0.548348	−	0.180687i
$22$	4.49462	−	2.59497i	0.958257	−	0.553250i
$23$	0.769401	−	1.33264i	0.160431	−	0.277875i	−0.774592	−	0.632461i	$-0.782045\pi$
$23$	0.769401	−	1.33264i	0.160431	−	0.277875i	0.935023	+	0.354586i	$0.115378\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−2.39477	+	4.14787i	−0.478955	+	0.829574i
$26$			2.69193i			0.527931i
$27$	1.00000			0.192450
$28$	−0.539342	−	2.59020i	−0.101926	−	0.489501i
$29$	−0.521362	−	0.301008i	−0.0968144	−	0.0558958i	0.450811	−	0.892619i	$-0.351135\pi$
$29$	−0.521362	−	0.301008i	−0.0968144	−	0.0558958i	−0.547626	+	0.836724i	$0.684468\pi$
$30$	−0.458750			−0.0837559
$31$	−6.44999			−1.15845			−0.579226	−	0.815167i	$-0.696645\pi$
$31$	−6.44999			−1.15845			−0.579226	+	0.815167i	$0.696645\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.59497	+	4.49462i	0.451727	+	0.782414i
$34$	0.0643362	−	0.111434i	0.0110336	−	0.0191107i
$35$	−0.379851	+	1.15277i	−0.0642066	+	0.194853i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			6.53699i			1.07467i	0.843368	+	0.537337i	$0.180570\pi$
$37$			6.53699i			1.07467i	−0.843368	+	0.537337i	$0.819430\pi$
$38$	0.600682	+	4.31731i	0.0974434	+	0.700360i
$39$	−2.69193			−0.431054
$40$	−0.229375	−	0.397289i	−0.0362674	−	0.0628169i
$41$	−3.36092	−	5.82128i	−0.524887	−	0.909132i	−0.999580	−	0.0289801i	$-0.990774\pi$
$41$	−3.36092	−	5.82128i	−0.524887	−	0.909132i	0.474693	−	0.880152i	$-0.342559\pi$
$42$	2.59020	−	0.539342i	0.399676	−	0.0832222i
$43$	−2.61236	−	4.52474i	−0.398381	−	0.690016i	0.595145	−	0.803618i	$-0.297094\pi$
$43$	−2.61236	−	4.52474i	−0.398381	−	0.690016i	−0.993526	+	0.113602i	$0.963761\pi$
$44$	−2.59497	+	4.49462i	−0.391207	+	0.677590i
$45$		−	0.458750i		−	0.0683864i
$46$			1.53880i			0.226884i
$47$	−0.675186	−	0.389819i	−0.0984861	−	0.0568609i	0.449948	−	0.893055i	$-0.351443\pi$
$47$	−0.675186	−	0.389819i	−0.0984861	−	0.0568609i	−0.548434	+	0.836194i	$0.684776\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	0.789435	−	6.95534i	0.112776	−	0.993620i
$50$		−	4.78955i		−	0.677344i
$51$	0.111434	+	0.0643362i	0.0156038	+	0.00900887i
$52$	−1.34597	−	2.33128i	−0.186652	−	0.323291i
$53$	−7.14293	−	4.12397i	−0.981157	−	0.566471i	−0.0785378	−	0.996911i	$-0.525025\pi$
$53$	−7.14293	−	4.12397i	−0.981157	−	0.566471i	−0.902619	+	0.430440i	$0.858358\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	2.06191	−	1.19044i	0.278028	−	0.160519i
$56$	1.76218	+	1.97350i	0.235481	+	0.263721i
$57$	−4.31731	+	0.600682i	−0.571842	+	0.0795622i
$58$	0.602017			0.0790487
$59$	−2.12593	−	3.68222i	−0.276773	−	0.479385i	0.693808	−	0.720160i	$-0.255932\pi$
$59$	−2.12593	−	3.68222i	−0.276773	−	0.479385i	−0.970581	+	0.240775i	$0.922598\pi$
$60$	0.397289	−	0.229375i	0.0512898	−	0.0296122i
$61$	−7.19028	−	4.15131i	−0.920622	−	0.531521i	−0.0367883	−	0.999323i	$-0.511713\pi$
$61$	−7.19028	−	4.15131i	−0.920622	−	0.531521i	−0.883833	+	0.467802i	$0.845046\pi$
$62$	5.58585	−	3.22499i	0.709404	−	0.409575i
$63$	0.539342	+	2.59020i	0.0679507	+	0.326334i
$64$	−1.00000			−0.125000
$65$			1.23492i			0.153173i
$66$	−4.49462	−	2.59497i	−0.553250	−	0.319419i
$67$	−9.81323	−	5.66567i	−1.19888	−	0.692172i	−0.238572	−	0.971125i	$-0.576679\pi$
$67$	−9.81323	−	5.66567i	−1.19888	−	0.692172i	−0.960305	+	0.278953i	$0.910013\pi$
$68$			0.128672i			0.0156038i
$69$	−1.53880			−0.185250
$70$	−0.247423	−	1.18825i	−0.0295727	−	0.142023i
$71$	−4.78110	+	2.76037i	−0.567413	+	0.327596i	−0.756115	−	0.654438i	$-0.772905\pi$
$71$	−4.78110	+	2.76037i	−0.567413	+	0.327596i	0.188703	+	0.982034i	$0.439572\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	6.89899	−	3.98313i	0.807466	−	0.466191i	−0.0386092	−	0.999254i	$-0.512293\pi$
$73$	6.89899	−	3.98313i	0.807466	−	0.466191i	0.846075	+	0.533064i	$0.178959\pi$
$74$	−3.26849	−	5.66120i	−0.379955	−	0.658101i
$75$	4.78955			0.553049
$76$	−2.67886	−	3.43856i	−0.307286	−	0.394430i
$77$	−10.2424	+	9.14562i	−1.16723	+	1.04224i
$78$	2.33128	−	1.34597i	0.263966	−	0.152401i
$79$	9.65974	−	5.57705i	1.08681	−	0.627468i	0.154082	−	0.988058i	$-0.450758\pi$
$79$	9.65974	−	5.57705i	1.08681	−	0.627468i	0.932724	+	0.360591i	$0.117425\pi$
$80$	0.397289	+	0.229375i	0.0444183	+	0.0256449i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.82128	+	3.36092i	0.642853	+	0.371151i
$83$		−	1.11680i		−	0.122585i	−0.998120	−	0.0612925i	$-0.980478\pi$
$83$		−	1.11680i		−	0.122585i	0.998120	−	0.0612925i	$-0.0195222\pi$
$84$	−1.97350	+	1.76218i	−0.215327	+	0.192270i
$85$	0.0295142	−	0.0511201i	0.00320127	−	0.00554475i
$86$	4.52474	+	2.61236i	0.487915	+	0.281698i
$87$			0.602017i			0.0645430i
$88$		−	5.18994i		−	0.553250i
$89$	−2.75371	+	4.76957i	−0.291893	+	0.505574i	−0.974257	−	0.225439i	$-0.927618\pi$
$89$	−2.75371	+	4.76957i	−0.291893	+	0.505574i	0.682364	+	0.731012i	$0.260952\pi$
$90$	0.229375	+	0.397289i	0.0241782	+	0.0418779i
$91$	−1.45187	−	6.97263i	−0.152197	−	0.730930i
$92$	−0.769401	−	1.33264i	−0.0802156	−	0.138938i
$93$	3.22499	+	5.58585i	0.334416	+	0.579226i
$94$	0.779638			0.0804135
$95$	0.275563	+	1.98057i	0.0282721	+	0.203202i
$96$		−	1.00000i		−	0.102062i
$97$	0.264199	+	0.457606i	0.0268253	+	0.0464628i	0.879126	−	0.476589i	$-0.158127\pi$
$97$	0.264199	+	0.457606i	0.0268253	+	0.0464628i	−0.852301	+	0.523051i	$0.824794\pi$
$98$	2.79400	+	6.41822i	0.282237	+	0.648338i
$99$	2.59497	−	4.49462i	0.260805	−	0.451727i
$100$	2.39477	+	4.14787i	0.239477	+	0.414787i
$101$	8.53140	+	4.92560i	0.848906	+	0.490116i	0.860281	−	0.509819i	$-0.170288\pi$
$101$	8.53140	+	4.92560i	0.848906	+	0.490116i	−0.0113759	+	0.999935i	$0.503621\pi$
$102$	−0.128672			−0.0127405
$103$	−14.4350			−1.42233			−0.711163	−	0.703027i	$-0.751831\pi$
$103$	−14.4350			−1.42233			−0.711163	+	0.703027i	$0.751831\pi$
$104$	2.33128	+	1.34597i	0.228601	+	0.131983i
$105$	1.18825	−	0.247423i	0.115961	−	0.0241460i
$106$	8.24795			0.801111
$107$		−	7.63075i		−	0.737692i	−0.929490	−	0.368846i	$-0.879753\pi$
$107$		−	7.63075i		−	0.737692i	0.929490	−	0.368846i	$-0.120247\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−1.70978	+	0.987142i	−0.163767	+	0.0945510i	−0.579644	−	0.814870i	$-0.696808\pi$
$109$	−1.70978	+	0.987142i	−0.163767	+	0.0945510i	0.415876	+	0.909421i	$0.363475\pi$
$110$	−1.19044	+	2.06191i	−0.113504	+	0.196595i
$111$	5.66120	−	3.26849i	0.537337	−	0.310232i
$112$	−2.51285	−	0.828014i	−0.237442	−	0.0782400i
$113$			3.56351i			0.335227i	0.985853	+	0.167614i	$0.0536061\pi$
$113$			3.56351i			0.335227i	−0.985853	+	0.167614i	$0.946394\pi$
$114$	3.43856	−	2.67886i	0.322051	−	0.250898i
$115$			0.705925i			0.0658279i
$116$	−0.521362	+	0.301008i	−0.0484072	+	0.0279479i
$117$	1.34597	+	2.33128i	0.124435	+	0.215527i
$118$	3.68222	+	2.12593i	0.338976	+	0.195708i
$119$	−0.106542	+	0.323334i	−0.00976673	+	0.0296400i
$120$	−0.229375	+	0.397289i	−0.0209390	+	0.0362674i
$121$	15.9355			1.44868
$122$	8.30263			0.751684
$123$	−3.36092	+	5.82128i	−0.303044	+	0.524887i
$124$	−3.22499	+	5.58585i	−0.289613	+	0.501624i
$125$		−	4.49095i		−	0.401683i
$126$	−1.76218	−	1.97350i	−0.156988	−	0.175814i
$127$	11.1212	+	6.42083i	0.986847	+	0.569756i	0.904330	−	0.426833i	$-0.140371\pi$
$127$	11.1212	+	6.42083i	0.986847	+	0.569756i	0.0825166	+	0.996590i	$0.473704\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.61236	+	4.52474i	−0.230005	+	0.398381i
$130$	−0.617462	−	1.06947i	−0.0541550	−	0.0937992i
$131$	9.97528	−	5.75923i	0.871544	−	0.503186i	0.00368308	−	0.999993i	$-0.498828\pi$
$131$	9.97528	−	5.75923i	0.871544	−	0.503186i	0.867861	+	0.496807i	$0.165494\pi$
$132$	5.18994			0.451727
$133$	−3.88439	−	10.8587i	−0.336819	−	0.941569i
$134$	11.3313			0.978879
$135$	−0.397289	+	0.229375i	−0.0341932	+	0.0197415i
$136$	−0.0643362	−	0.111434i	−0.00551678	−	0.00955535i
$137$	−4.20501	+	7.28329i	−0.359258	+	0.622253i	−0.987837	−	0.155492i	$-0.950304\pi$
$137$	−4.20501	+	7.28329i	−0.359258	+	0.622253i	0.628579	+	0.777746i	$0.283637\pi$
$138$	1.33264	−	0.769401i	0.113442	−	0.0654958i
$139$	−7.30065	−	4.21504i	−0.619233	−	0.357515i	0.157337	−	0.987545i	$-0.449709\pi$
$139$	−7.30065	−	4.21504i	−0.619233	−	0.357515i	−0.776571	+	0.630030i	$0.783042\pi$
$140$	0.808400	+	0.905345i	0.0683223	+	0.0765156i
$141$			0.779638i			0.0656574i
$142$	2.76037	−	4.78110i	0.231645	−	0.401221i
$143$	−6.98549	+	12.0992i	−0.584156	+	1.01179i
$144$	1.00000			0.0833333
$145$	0.276175			0.0229351
$146$	−3.98313	+	6.89899i	−0.329647	+	0.570965i
$147$	−6.41822	+	2.79400i	−0.529366	+	0.230445i
$148$	5.66120	+	3.26849i	0.465347	+	0.268668i
$149$	5.52508	+	9.56971i	0.452632	+	0.783981i	0.998549	−	0.0538581i	$-0.0171519\pi$
$149$	5.52508	+	9.56971i	0.452632	+	0.783981i	−0.545917	+	0.837839i	$0.683819\pi$
$150$	−4.14787	+	2.39477i	−0.338672	+	0.195533i
$151$		−	8.74943i		−	0.712019i	−0.934482	−	0.356009i	$-0.884137\pi$
$151$		−	8.74943i		−	0.712019i	0.934482	−	0.356009i	$-0.115863\pi$
$152$	4.03924	+	1.63845i	0.327626	+	0.132896i
$153$		−	0.128672i		−	0.0104025i
$154$	4.29735	−	13.0415i	0.346290	−	1.05092i
$155$	2.56251	−	1.47947i	0.205826	−	0.118834i
$156$	−1.34597	+	2.33128i	−0.107764	+	0.186652i
$157$	−4.86447	+	2.80850i	−0.388227	+	0.224143i	−0.681392	−	0.731919i	$-0.738625\pi$
$157$	−4.86447	+	2.80850i	−0.388227	+	0.224143i	0.293165	+	0.956062i	$0.405292\pi$
$158$	−5.57705	+	9.65974i	−0.443687	+	0.768488i
$159$			8.24795i			0.654105i
$160$	−0.458750			−0.0362674
$161$	−0.829940	−	3.98580i	−0.0654085	−	0.314125i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	6.73415			0.527459			0.263730	−	0.964597i	$-0.415047\pi$
$163$	6.73415			0.527459			0.263730	+	0.964597i	$0.415047\pi$
$164$	−6.72184			−0.524887
$165$	−2.06191	−	1.19044i	−0.160519	−	0.0926759i
$166$	0.558401	+	0.967179i	0.0433403	+	0.0750676i
$167$	−0.685214	+	1.18683i	−0.0530234	+	0.0918393i	−0.891319	−	0.453377i	$-0.850219\pi$
$167$	−0.685214	+	1.18683i	−0.0530234	+	0.0918393i	0.838295	+	0.545216i	$0.183552\pi$
$168$	0.828014	−	2.51285i	0.0638827	−	0.193870i
$169$	2.87675	+	4.98268i	0.221289	+	0.383283i
$170$			0.0590284i			0.00452727i
$171$	2.67886	+	3.43856i	0.204858	+	0.262953i
$172$	−5.22472			−0.398381
$173$	−9.71511	−	16.8271i	−0.738626	−	1.27934i	−0.953114	−	0.302611i	$-0.902142\pi$
$173$	−9.71511	−	16.8271i	−0.738626	−	1.27934i	0.214488	−	0.976727i	$-0.431192\pi$
$174$	−0.301008	−	0.521362i	−0.0228194	−	0.0395243i
$175$	2.58320	+	12.4059i	0.195272	+	0.937795i
$176$	2.59497	+	4.49462i	0.195603	+	0.338795i
$177$	−2.12593	+	3.68222i	−0.159795	+	0.276773i
$178$		−	5.50743i		−	0.412799i
$179$		−	14.5273i		−	1.08582i	−0.839792	−	0.542909i	$-0.817323\pi$
$179$		−	14.5273i		−	1.08582i	0.839792	−	0.542909i	$-0.182677\pi$
$180$	−0.397289	−	0.229375i	−0.0296122	−	0.0170966i
$181$	−8.15416	+	14.1234i	−0.606094	+	1.04979i	0.385784	+	0.922589i	$0.373931\pi$
$181$	−8.15416	+	14.1234i	−0.606094	+	1.04979i	−0.991878	+	0.127196i	$0.959402\pi$
$182$	4.74367	+	5.31254i	0.351624	+	0.393791i
$183$			8.30263i			0.613748i
$184$	1.33264	+	0.769401i	0.0982437	+	0.0567210i
$185$	−1.49942	−	2.59707i	−0.110240	−	0.190941i
$186$	−5.58585	−	3.22499i	−0.409575	−	0.236468i
$187$	0.578334	−	0.333901i	0.0422920	−	0.0244173i
$188$	−0.675186	+	0.389819i	−0.0492430	+	0.0284305i
$189$	1.97350	−	1.76218i	0.143551	−	0.128180i
$190$	−1.22893	−	1.57744i	−0.0891558	−	0.114439i
$191$	22.6633			1.63986			0.819930	−	0.572464i	$-0.194013\pi$
$191$	22.6633			1.63986			0.819930	+	0.572464i	$0.194013\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	9.29634	−	5.36725i	0.669165	−	0.386343i	−0.126595	−	0.991955i	$-0.540405\pi$
$193$	9.29634	−	5.36725i	0.669165	−	0.386343i	0.795760	+	0.605612i	$0.207071\pi$
$194$	−0.457606	−	0.264199i	−0.0328542	−	0.0189684i
$195$	1.06947	−	0.617462i	0.0765867	−	0.0442173i
$196$	−5.62879	−	4.16134i	−0.402056	−	0.297239i
$197$	26.8877			1.91567			0.957835	−	0.287318i	$-0.0927637\pi$
$197$	26.8877			1.91567			0.957835	+	0.287318i	$0.0927637\pi$
$198$			5.18994i			0.368833i
$199$	20.5898	+	11.8875i	1.45957	+	0.842683i	0.998990	−	0.0449357i	$-0.0143083\pi$
$199$	20.5898	+	11.8875i	1.45957	+	0.842683i	0.460580	+	0.887618i	$0.347642\pi$
$200$	−4.14787	−	2.39477i	−0.293299	−	0.169336i
$201$			11.3313i			0.799251i
$202$	−9.85121			−0.693129
$203$	−1.55934	+	0.324693i	−0.109444	+	0.0227890i
$204$	0.111434	−	0.0643362i	0.00780191	−	0.00450443i
$205$	2.67051	+	1.54182i	0.186517	+	0.107685i
$206$	12.5011	−	7.21751i	0.870993	−	0.502868i
$207$	0.769401	+	1.33264i	0.0534771	+	0.0926250i
$208$	−2.69193			−0.186652
$209$	−8.50347	+	20.9634i	−0.588197	+	1.45007i
$210$	−0.905345	+	0.808400i	−0.0624747	+	0.0557849i
$211$	21.0917	−	12.1773i	1.45201	−	0.838321i	0.453418	−	0.891298i	$-0.350204\pi$
$211$	21.0917	−	12.1773i	1.45201	−	0.838321i	0.998596	+	0.0529771i	$0.0168710\pi$
$212$	−7.14293	+	4.12397i	−0.490579	+	0.283236i
$213$	4.78110	+	2.76037i	0.327596	+	0.189138i
$214$	3.81537	+	6.60842i	0.260814	+	0.451742i
$215$	2.07572	+	1.19842i	0.141563	+	0.0817315i
$216$			1.00000i			0.0680414i
$217$	−12.7291	+	11.3660i	−0.864106	+	0.771578i
$218$	0.987142	−	1.70978i	0.0668577	−	0.115801i
$219$	−6.89899	−	3.98313i	−0.466191	−	0.269155i
$220$		−	2.38089i		−	0.160519i
$221$			0.346377i			0.0232998i
$222$	−3.26849	+	5.66120i	−0.219367	+	0.379955i
$223$	10.8421	+	18.7790i	0.726039	+	1.25754i	0.958545	+	0.284941i	$0.0919740\pi$
$223$	10.8421	+	18.7790i	0.726039	+	1.25754i	−0.232506	+	0.972595i	$0.574693\pi$
$224$	2.59020	−	0.539342i	0.173065	−	0.0360363i
$225$	−2.39477	−	4.14787i	−0.159652	−	0.276525i
$226$	−1.78176	−	3.08609i	−0.118521	−	0.205284i
$227$	−15.3031			−1.01570			−0.507850	−	0.861445i	$-0.669560\pi$
$227$	−15.3031			−1.01570			−0.507850	+	0.861445i	$0.669560\pi$
$228$	−1.63845	+	4.03924i	−0.108509	+	0.267505i
$229$			9.40873i			0.621747i	0.950451	+	0.310873i	$0.100621\pi$
$229$			9.40873i			0.621747i	−0.950451	+	0.310873i	$0.899379\pi$
$230$	−0.352963	−	0.611349i	−0.0232737	−	0.0403112i
$231$	13.0415	+	4.29735i	0.858070	+	0.282745i
$232$	0.301008	−	0.521362i	0.0197622	−	0.0342291i
$233$	3.26580	+	5.65652i	0.213949	+	0.370571i	0.952947	−	0.303137i	$-0.0980339\pi$
$233$	3.26580	+	5.65652i	0.213949	+	0.370571i	−0.738998	+	0.673708i	$0.764701\pi$
$234$	−2.33128	−	1.34597i	−0.152401	−	0.0879885i
$235$	0.357659			0.0233311
$236$	−4.25186			−0.276773
$237$	−9.65974	−	5.57705i	−0.627468	−	0.362269i
$238$	−0.0693984	−	0.333286i	−0.00449843	−	0.0216038i
$239$	6.74778			0.436477			0.218239	−	0.975895i	$-0.429969\pi$
$239$	6.74778			0.436477			0.218239	+	0.975895i	$0.429969\pi$
$240$		−	0.458750i		−	0.0296122i
$241$	−8.28548	+	14.3509i	−0.533714	+	0.924421i	0.465510	+	0.885043i	$0.345871\pi$
$241$	−8.28548	+	14.3509i	−0.533714	+	0.924421i	−0.999224	+	0.0393779i	$0.987462\pi$
$242$	−13.8006	+	7.96776i	−0.887134	+	0.512187i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.19028	+	4.15131i	−0.460311	+	0.265761i
$245$	1.28175	+	2.94436i	0.0818878	+	0.188108i
$246$		−	6.72184i		−	0.428569i
$247$	−7.21131	−	9.25637i	−0.458845	−	0.588969i
$248$		−	6.44999i		−	0.409575i
$249$	−0.967179	+	0.558401i	−0.0612925	+	0.0353872i
$250$	2.24548	+	3.88928i	0.142016	+	0.245980i
$251$	22.4192	+	12.9437i	1.41509	+	0.817001i	0.995862	−	0.0908806i	$-0.0289682\pi$
$251$	22.4192	+	12.9437i	1.41509	+	0.817001i	0.419226	+	0.907882i	$0.362301\pi$
$252$	2.51285	+	0.828014i	0.158294	+	0.0521600i
$253$	−3.99315	+	6.91634i	−0.251047	+	0.434826i
$254$	−12.8417			−0.805757
$255$	−0.0590284			−0.00369650
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.58534	+	7.94205i	−0.286026	+	0.495411i	−0.972857	−	0.231405i	$-0.925668\pi$
$257$	−4.58534	+	7.94205i	−0.286026	+	0.495411i	0.686832	+	0.726817i	$0.259001\pi$
$258$		−	5.22472i		−	0.325277i
$259$	11.5194	+	12.9008i	0.715778	+	0.801615i
$260$	1.06947	+	0.617462i	0.0663260	+	0.0382933i
$261$	0.521362	−	0.301008i	0.0322715	−	0.0186319i
$262$	−5.75923	+	9.97528i	−0.355806	+	0.616275i
$263$	−9.94448	−	17.2243i	−0.613203	−	1.06210i	−0.990697	−	0.136086i	$-0.956548\pi$
$263$	−9.94448	−	17.2243i	−0.613203	−	1.06210i	0.377494	−	0.926012i	$-0.376786\pi$
$264$	−4.49462	+	2.59497i	−0.276625	+	0.159710i
$265$	3.78374			0.232434
$266$	8.79333	+	7.46172i	0.539154	+	0.457508i
$267$	5.50743			0.337049
$268$	−9.81323	+	5.66567i	−0.599438	+	0.346086i
$269$	−14.1964	−	24.5889i	−0.865571	−	1.49921i	−0.866479	−	0.499213i	$-0.833623\pi$
$269$	−14.1964	−	24.5889i	−0.865571	−	1.49921i	0.000908877	−	1.00000i	$-0.499711\pi$
$270$	0.229375	−	0.397289i	0.0139593	−	0.0241782i
$271$	14.6776	−	8.47409i	0.891598	−	0.514764i	0.0171332	−	0.999853i	$-0.494546\pi$
$271$	14.6776	−	8.47409i	0.891598	−	0.514764i	0.874465	+	0.485089i	$0.161213\pi$
$272$	0.111434	+	0.0643362i	0.00675665	+	0.00390095i
$273$	−5.31254	+	4.74367i	−0.321529	+	0.287100i
$274$		−	8.41002i		−	0.508068i
$275$	12.4287	−	21.5272i	0.749482	−	1.29814i
$276$	−0.769401	+	1.33264i	−0.0463125	+	0.0802156i
$277$	−18.7585			−1.12709			−0.563544	−	0.826086i	$-0.690562\pi$
$277$	−18.7585			−1.12709			−0.563544	+	0.826086i	$0.690562\pi$
$278$	8.43007			0.505602
$279$	3.22499	−	5.58585i	0.193075	−	0.334416i
$280$	−1.15277	−	0.379851i	−0.0688910	−	0.0227005i
$281$	11.9410	+	6.89411i	0.712338	+	0.411268i	0.811926	−	0.583760i	$-0.198419\pi$
$281$	11.9410	+	6.89411i	0.712338	+	0.411268i	−0.0995884	+	0.995029i	$0.531753\pi$
$282$	−0.389819	−	0.675186i	−0.0232134	−	0.0402068i
$283$	16.2636	−	9.38981i	0.966772	−	0.558166i	0.0685217	−	0.997650i	$-0.478172\pi$
$283$	16.2636	−	9.38981i	0.966772	−	0.558166i	0.898251	+	0.439483i	$0.144838\pi$
$284$			5.52074i			0.327596i
$285$	1.57744	−	1.22893i	0.0934394	−	0.0727954i
$286$		−	13.9710i		−	0.826121i
$287$	−16.8909	−	5.56578i	−0.997041	−	0.328537i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−8.49172	+	14.7081i	−0.499513	+	0.865182i
$290$	−0.239175	+	0.138088i	−0.0140448	+	0.00810878i
$291$	0.264199	−	0.457606i	0.0154876	−	0.0268253i
$292$		−	7.96627i		−	0.466191i
$293$	−2.13023			−0.124449			−0.0622246	−	0.998062i	$-0.519820\pi$
$293$	−2.13023			−0.124449			−0.0622246	+	0.998062i	$0.519820\pi$
$294$	4.16134	−	5.62879i	0.242694	−	0.328277i
$295$	1.68922	+	0.975271i	0.0983501	+	0.0567825i
$296$	−6.53699			−0.379955
$297$	−5.18994			−0.301151
$298$	−9.56971	−	5.52508i	−0.554359	−	0.320059i
$299$	−2.07118	−	3.58738i	−0.119779	−	0.207464i
$300$	2.39477	−	4.14787i	0.138262	−	0.239477i
$301$	−13.1289	−	4.32614i	−0.756738	−	0.249354i
$302$	4.37472	+	7.57723i	0.251737	+	0.436021i
$303$		−	9.85121i		−	0.565937i
$304$	−4.31731	+	0.600682i	−0.247615	+	0.0344515i
$305$	3.80883			0.218093
$306$	0.0643362	+	0.111434i	0.00367785	+	0.00637023i
$307$	−5.06811	−	8.77822i	−0.289252	−	0.500999i	0.684379	−	0.729126i	$-0.260073\pi$
$307$	−5.06811	−	8.77822i	−0.289252	−	0.500999i	−0.973631	+	0.228127i	$0.926740\pi$
$308$	2.79915	+	13.4430i	0.159497	+	0.765984i
$309$	7.21751	+	12.5011i	0.410590	+	0.711163i
$310$	−1.47947	+	2.56251i	−0.0840280	+	0.145541i
$311$		−	14.8729i		−	0.843367i	−0.906743	−	0.421683i	$-0.861439\pi$
$311$		−	14.8729i		−	0.843367i	0.906743	−	0.421683i	$-0.138561\pi$
$312$		−	2.69193i		−	0.152401i
$313$	−21.8542	−	12.6175i	−1.23527	−	0.713186i	−0.267150	−	0.963655i	$-0.586082\pi$
$313$	−21.8542	−	12.6175i	−1.23527	−	0.713186i	−0.968125	+	0.250469i	$0.919415\pi$
$314$	2.80850	−	4.86447i	0.158493	−	0.274518i
$315$	−0.808400	−	0.905345i	−0.0455482	−	0.0510104i
$316$		−	11.1541i		−	0.627468i
$317$	−11.4181	−	6.59222i	−0.641302	−	0.370256i	0.143814	−	0.989605i	$-0.454063\pi$
$317$	−11.4181	−	6.59222i	−0.641302	−	0.370256i	−0.785116	+	0.619349i	$0.787397\pi$
$318$	−4.12397	−	7.14293i	−0.231261	−	0.400556i
$319$	2.70584	+	1.56222i	0.151498	+	0.0874673i
$320$	0.397289	−	0.229375i	0.0222091	−	0.0128224i
$321$	−6.60842	+	3.81537i	−0.368846	+	0.212953i
$322$	2.71165	+	3.03683i	0.151114	+	0.169236i
$323$	0.0772911	+	0.555519i	0.00430059	+	0.0309099i
$324$	−1.00000			−0.0555556
$325$	6.44657	+	11.1658i	0.357591	+	0.619366i
$326$	−5.83195	+	3.36708i	−0.323002	+	0.186485i
$327$	1.70978	+	0.987142i	0.0945510	+	0.0545891i
$328$	5.82128	−	3.36092i	0.321427	−	0.185576i
$329$	−2.01941	+	0.420491i	−0.111334	+	0.0231824i
$330$	2.38089			0.131063
$331$		−	19.6647i		−	1.08087i	−0.841386	−	0.540435i	$-0.818260\pi$
$331$		−	19.6647i		−	1.08087i	0.841386	−	0.540435i	$-0.181740\pi$
$332$	−0.967179	−	0.558401i	−0.0530808	−	0.0306462i
$333$	−5.66120	−	3.26849i	−0.310232	−	0.179112i
$334$		−	1.37043i		−	0.0749865i
$335$	5.19825			0.284011
$336$	0.539342	+	2.59020i	0.0294235	+	0.141307i
$337$	2.00268	−	1.15625i	0.109093	−	0.0629848i	−0.444461	−	0.895798i	$-0.646605\pi$
$337$	2.00268	−	1.15625i	0.109093	−	0.0629848i	0.553554	+	0.832814i	$0.313271\pi$
$338$	−4.98268	−	2.87675i	−0.271022	−	0.156475i
$339$	3.08609	−	1.78176i	0.167614	−	0.0967718i
$340$	−0.0295142	−	0.0511201i	−0.00160063	−	0.00277238i
$341$	33.4751			1.81278
$342$	−4.03924	−	1.63845i	−0.218417	−	0.0885972i
$343$	−10.6986	−	15.1175i	−0.577671	−	0.816270i
$344$	4.52474	−	2.61236i	0.243958	−	0.140849i
$345$	0.611349	−	0.352963i	0.0329139	−	0.0190029i
$346$	16.8271	+	9.71511i	0.904629	+	0.522288i
$347$	6.20598	+	10.7491i	0.333154	+	0.577040i	0.983129	−	0.182916i	$-0.0585536\pi$
$347$	6.20598	+	10.7491i	0.333154	+	0.577040i	−0.649974	+	0.759956i	$0.725220\pi$
$348$	0.521362	+	0.301008i	0.0279479	+	0.0161357i
$349$		−	19.3223i		−	1.03430i	−0.855895	−	0.517149i	$-0.826993\pi$
$349$		−	19.3223i		−	1.03430i	0.855895	−	0.517149i	$-0.173007\pi$
$350$	−8.44005	−	9.45219i	−0.451140	−	0.505241i
$351$	1.34597	−	2.33128i	0.0718423	−	0.124435i
$352$	−4.49462	−	2.59497i	−0.239564	−	0.138312i
$353$		−	31.9136i		−	1.69859i	−0.527918	−	0.849295i	$-0.677027\pi$
$353$		−	31.9136i		−	1.69859i	0.527918	−	0.849295i	$-0.322973\pi$
$354$		−	4.25186i		−	0.225984i
$355$	1.26632	−	2.19333i	0.0672093	−	0.116410i
$356$	2.75371	+	4.76957i	0.145947	+	0.252787i
$357$	0.333286	−	0.0693984i	0.0176394	−	0.00367295i
$358$	7.26363	+	12.5810i	0.383895	+	0.664925i
$359$	−2.76491	−	4.78897i	−0.145927	−	0.252752i	0.783792	−	0.621024i	$-0.213283\pi$
$359$	−2.76491	−	4.78897i	−0.145927	−	0.252752i	−0.929718	+	0.368272i	$0.879950\pi$
$360$	0.458750			0.0241782
$361$	−13.6310	−	13.2362i	−0.717419	−	0.696642i
$362$		−	16.3083i		−	0.857146i
$363$	−7.96776	−	13.8006i	−0.418199	−	0.724342i
$364$	−6.76441	−	2.22896i	−0.354551	−	0.116829i
$365$	−1.82726	+	3.16491i	−0.0956433	+	0.165659i
$366$	−4.15131	−	7.19028i	−0.216993	−	0.375842i
$367$	29.4201	+	16.9857i	1.53571	+	0.886645i	0.999082	+	0.0428284i	$0.0136369\pi$
$367$	29.4201	+	16.9857i	1.53571	+	0.886645i	0.536632	+	0.843817i	$0.319696\pi$
$368$	−1.53880			−0.0802156
$369$	6.72184			0.349925
$370$	2.59707	+	1.49942i	0.135015	+	0.0779512i
$371$	−21.3638	+	4.44846i	−1.10915	+	0.230953i
$372$	6.44999			0.334416
$373$			6.12874i			0.317334i	0.987332	+	0.158667i	$0.0507197\pi$
$373$			6.12874i			0.317334i	−0.987332	+	0.158667i	$0.949280\pi$
$374$	−0.333901	+	0.578334i	−0.0172656	+	0.0299049i
$375$	−3.88928	+	2.24548i	−0.200842	+	0.115956i
$376$	0.389819	−	0.675186i	0.0201034	−	0.0348201i
$377$	−1.40347	+	0.810294i	−0.0722824	+	0.0417323i
$378$	−0.828014	+	2.51285i	−0.0425884	+	0.129247i
$379$			17.3441i			0.890908i	0.895305	+	0.445454i	$0.146958\pi$
$379$			17.3441i			0.890908i	−0.895305	+	0.445454i	$0.853042\pi$
$380$	1.85300	+	0.751639i	0.0950570	+	0.0385583i
$381$		−	12.8417i		−	0.657898i
$382$	−19.6270	+	11.3317i	−1.00420	+	0.579778i
$383$	−8.37792	−	14.5110i	−0.428092	−	0.741477i	0.568612	−	0.822606i	$-0.307481\pi$
$383$	−8.37792	−	14.5110i	−0.428092	−	0.741477i	−0.996704	+	0.0811291i	$0.974147\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	1.97141	−	5.98280i	0.100472	−	0.304912i
$386$	−5.36725	+	9.29634i	−0.273186	+	0.473171i
$387$	5.22472			0.265587
$388$	0.528398			0.0268253
$389$	12.3578	−	21.4043i	0.626565	−	1.08524i	−0.361671	−	0.932306i	$-0.617794\pi$
$389$	12.3578	−	21.4043i	0.626565	−	1.08524i	0.988236	−	0.152937i	$-0.0488731\pi$
$390$	−0.617462	+	1.06947i	−0.0312664	+	0.0541550i
$391$			0.198001i			0.0100134i
$392$	6.95534	+	0.789435i	0.351298	+	0.0398725i
$393$	−9.97528	−	5.75923i	−0.503186	−	0.290515i
$394$	−23.2854	+	13.4439i	−1.17310	+	0.677292i
$395$	−2.55847	+	4.43140i	−0.128731	+	0.222968i
$396$	−2.59497	−	4.49462i	−0.130402	−	0.225863i
$397$	14.7787	−	8.53249i	0.741722	−	0.428233i	−0.0809732	−	0.996716i	$-0.525803\pi$
$397$	14.7787	−	8.53249i	0.741722	−	0.428233i	0.822695	+	0.568483i	$0.192469\pi$
$398$	−23.7750			−1.19173
$399$	−7.46172	+	8.79333i	−0.373553	+	0.440217i
$400$	4.78955			0.239477
$401$	26.4081	−	15.2467i	1.31876	−	0.761385i	0.335229	−	0.942137i	$-0.391186\pi$
$401$	26.4081	−	15.2467i	1.31876	−	0.761385i	0.983529	+	0.180751i	$0.0578530\pi$
$402$	−5.66567	−	9.81323i	−0.282578	−	0.489439i
$403$	−8.68146	+	15.0367i	−0.432454	+	0.749033i
$404$	8.53140	−	4.92560i	0.424453	−	0.245058i
$405$	0.397289	+	0.229375i	0.0197415	+	0.0113977i
$406$	1.18808	−	1.06086i	0.0589635	−	0.0526497i
$407$		−	33.9266i		−	1.68168i
$408$	−0.0643362	+	0.111434i	−0.00318512	+	0.00551678i
$409$	−17.7488	+	30.7419i	−0.877624	+	1.52009i	−0.0236821	+	0.999720i	$0.507539\pi$
$409$	−17.7488	+	30.7419i	−0.877624	+	1.52009i	−0.853941	+	0.520369i	$0.825794\pi$
$410$	−3.08364			−0.152290
$411$	8.41002			0.414836
$412$	−7.21751	+	12.5011i	−0.355581	+	0.615885i
$413$	−10.6843	−	3.52060i	−0.525739	−	0.173238i
$414$	−1.33264	−	0.769401i	−0.0654958	−	0.0378140i
$415$	0.256166	+	0.443693i	0.0125747	+	0.0217800i
$416$	2.33128	−	1.34597i	0.114300	−	0.0659914i
$417$			8.43007i			0.412822i
$418$	−3.11750	−	22.4066i	−0.152482	−	1.09594i
$419$			6.08960i			0.297497i	0.988875	+	0.148748i	$0.0475244\pi$
$419$			6.08960i			0.297497i	−0.988875	+	0.148748i	$0.952476\pi$
$420$	0.379851	−	1.15277i	0.0185348	−	0.0562493i
$421$	6.48633	−	3.74489i	0.316125	−	0.182515i	−0.333539	−	0.942736i	$-0.608243\pi$
$421$	6.48633	−	3.74489i	0.316125	−	0.182515i	0.649664	+	0.760222i	$0.274910\pi$
$422$	−12.1773	+	21.0917i	−0.592782	+	1.02673i
$423$	0.675186	−	0.389819i	0.0328287	−	0.0189536i
$424$	4.12397	−	7.14293i	0.200278	−	0.346891i
$425$		−	0.616282i		−	0.0298941i
$426$	−5.52074			−0.267481
$427$	−21.5054	+	4.47795i	−1.04072	+	0.216703i
$428$	−6.60842	−	3.81537i	−0.319430	−	0.184423i
$429$	13.9710			0.674525
$430$	−2.39684			−0.115586
$431$	−9.26137	−	5.34705i	−0.446104	−	0.257558i	0.260079	−	0.965587i	$-0.416251\pi$
$431$	−9.26137	−	5.34705i	−0.446104	−	0.257558i	−0.706183	+	0.708029i	$0.749585\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	1.75223	−	3.03494i	0.0842066	−	0.145850i	−0.820846	−	0.571149i	$-0.806498\pi$
$433$	1.75223	−	3.03494i	0.0842066	−	0.145850i	0.905053	+	0.425299i	$0.139831\pi$
$434$	5.34068	−	16.2078i	0.256361	−	0.778000i
$435$	−0.138088	−	0.239175i	−0.00662079	−	0.0114675i
$436$			1.97428i			0.0945510i
$437$	−4.12224	−	5.29127i	−0.197193	−	0.253116i
$438$	7.96627			0.380643
$439$	−11.3465	−	19.6526i	−0.541537	−	0.937969i	−0.998816	−	0.0486462i	$-0.984509\pi$
$439$	−11.3465	−	19.6526i	−0.541537	−	0.937969i	0.457279	−	0.889323i	$-0.348824\pi$
$440$	1.19044	+	2.06191i	0.0567522	+	0.0982976i
$441$	5.62879	+	4.16134i	0.268037	+	0.198159i
$442$	−0.173189	−	0.299971i	−0.00823774	−	0.0142682i
$443$	2.19929	−	3.80928i	0.104491	−	0.180984i	−0.809039	−	0.587755i	$-0.800012\pi$
$443$	2.19929	−	3.80928i	0.104491	−	0.180984i	0.913530	+	0.406771i	$0.133345\pi$
$444$		−	6.53699i		−	0.310232i
$445$		−	2.52653i		−	0.119769i
$446$	−18.7790	−	10.8421i	−0.889212	−	0.513387i
$447$	5.52508	−	9.56971i	0.261327	−	0.452632i
$448$	−1.97350	+	1.76218i	−0.0932393	+	0.0832552i
$449$			32.4011i			1.52910i	0.644564	+	0.764550i	$0.277039\pi$
$449$			32.4011i			1.52910i	−0.644564	+	0.764550i	$0.722961\pi$
$450$	4.14787	+	2.39477i	0.195533	+	0.112891i
$451$	17.4430	+	30.2121i	0.821358	+	1.42263i
$452$	3.08609	+	1.78176i	0.145158	+	0.0838068i
$453$	−7.57723	+	4.37472i	−0.356009	+	0.205542i
$454$	13.2528	−	7.65153i	0.621987	−	0.359104i
$455$	2.17616	+	2.43713i	0.102020	+	0.114254i
$456$	−0.600682	−	4.31731i	−0.0281295	−	0.202177i
$457$	−1.30803			−0.0611870			−0.0305935	−	0.999532i	$-0.509740\pi$
$457$	−1.30803			−0.0611870			−0.0305935	+	0.999532i	$0.509740\pi$
$458$	−4.70437	−	8.14820i	−0.219821	−	0.380741i
$459$	−0.111434	+	0.0643362i	−0.00520127	+	0.00300296i
$460$	0.611349	+	0.352963i	0.0285043	+	0.0164570i
$461$	−1.35435	+	0.781933i	−0.0630782	+	0.0364182i	−0.531207	−	0.847242i	$-0.678262\pi$
$461$	−1.35435	+	0.781933i	−0.0630782	+	0.0364182i	0.468129	+	0.883660i	$0.344928\pi$
$462$	−13.4430	+	2.79915i	−0.625423	+	0.130228i
$463$	−29.0590			−1.35048			−0.675242	−	0.737596i	$-0.735961\pi$
$463$	−29.0590			−1.35048			−0.675242	+	0.737596i	$0.735961\pi$
$464$			0.602017i			0.0279479i
$465$	−2.56251	−	1.47947i	−0.118834	−	0.0686086i
$466$	−5.65652	−	3.26580i	−0.262033	−	0.151285i
$467$			9.48604i			0.438962i	0.975617	+	0.219481i	$0.0704364\pi$
$467$			9.48604i			0.438962i	−0.975617	+	0.219481i	$0.929564\pi$
$468$	2.69193			0.124435
$469$	−29.3504	+	6.11147i	−1.35527	+	0.282201i
$470$	−0.309742	+	0.178829i	−0.0142873	+	0.00824879i
$471$	4.86447	+	2.80850i	0.224143	+	0.129409i
$472$	3.68222	−	2.12593i	0.169488	−	0.0978540i
$473$	13.5580	+	23.4831i	0.623397	+	1.07976i
$474$	11.1541			0.512325
$475$	12.8305	+	16.4692i	0.588705	+	0.755657i
$476$	0.226744	+	0.253935i	0.0103928	+	0.0116391i
$477$	7.14293	−	4.12397i	0.327052	−	0.188824i
$478$	−5.84375	+	3.37389i	−0.267287	+	0.154318i
$479$	−21.7280	−	12.5447i	−0.992777	−	0.573180i	−0.0866739	−	0.996237i	$-0.527624\pi$
$479$	−21.7280	−	12.5447i	−0.992777	−	0.573180i	−0.906103	+	0.423057i	$0.860957\pi$
$480$	0.229375	+	0.397289i	0.0104695	+	0.0181337i
$481$	15.2396	+	8.79856i	0.694864	+	0.401180i
$482$		−	16.5710i		−	0.754786i
$483$	−3.03683	+	2.71165i	−0.138181	+	0.123384i
$484$	7.96776	−	13.8006i	0.362171	−	0.627299i
$485$	−0.209927	−	0.121201i	−0.00953228	−	0.00550346i
$486$		−	1.00000i		−	0.0453609i
$487$			22.8550i			1.03566i	0.855484	+	0.517829i	$0.173260\pi$
$487$			22.8550i			1.03566i	−0.855484	+	0.517829i	$0.826740\pi$
$488$	4.15131	−	7.19028i	0.187921	−	0.325489i
$489$	−3.36708	−	5.83195i	−0.152264	−	0.263730i
$490$	−2.58220	−	1.90902i	−0.116652	−	0.0862405i
$491$	−13.2416	−	22.9351i	−0.597585	−	1.03505i	−0.993176	−	0.116621i	$-0.962794\pi$
$491$	−13.2416	−	22.9351i	−0.597585	−	1.03505i	0.395591	−	0.918427i	$-0.370540\pi$
$492$	3.36092	+	5.82128i	0.151522	+	0.262444i
$493$	0.0774629			0.00348875
$494$	10.8734	+	4.41060i	0.489216	+	0.198442i
$495$			2.38089i			0.107013i
$496$	3.22499	+	5.58585i	0.144807	+	0.250812i
$497$	−4.57125	+	13.8728i	−0.205049	+	0.622279i
$498$	0.558401	−	0.967179i	0.0250225	−	0.0433403i
$499$	2.52699	+	4.37688i	0.113124	+	0.195936i	0.917028	−	0.398822i	$-0.130581\pi$
$499$	2.52699	+	4.37688i	0.113124	+	0.195936i	−0.803904	+	0.594759i	$0.797248\pi$
$500$	−3.88928	−	2.24548i	−0.173934	−	0.100421i
$501$	1.37043			0.0612262
$502$	−25.8875			−1.15541
$503$	8.18052	+	4.72303i	0.364751	+	0.210589i	0.671163	−	0.741310i	$-0.265795\pi$
$503$	8.18052	+	4.72303i	0.364751	+	0.210589i	−0.306412	+	0.951899i	$0.599128\pi$
$504$	−2.59020	+	0.539342i	−0.115376	+	0.0240242i
$505$	−4.51924			−0.201104
$506$		−	7.98630i		−	0.355034i
$507$	2.87675	−	4.98268i	0.127761	−	0.221289i
$508$	11.1212	−	6.42083i	0.493423	−	0.284878i
$509$	15.4530	−	26.7653i	0.684941	−	1.18635i	−0.288514	−	0.957476i	$-0.593161\pi$
$509$	15.4530	−	26.7653i	0.684941	−	1.18635i	0.973455	−	0.228878i	$-0.0735055\pi$
$510$	0.0511201	−	0.0295142i	0.00226364	−	0.00130691i
$511$	6.59618	−	20.0180i	0.291798	−	0.885544i
$512$		−	1.00000i		−	0.0441942i
$513$	1.63845	−	4.03924i	0.0723393	−	0.178337i
$514$		−	9.17069i		−	0.404502i
$515$	5.73488	−	3.31103i	0.252709	−	0.145902i
$516$	2.61236	+	4.52474i	0.115003	+	0.199190i
$517$	3.50418	+	2.02314i	0.154114	+	0.0889776i
$518$	−16.4264	−	5.41271i	−0.721736	−	0.237821i
$519$	−9.71511	+	16.8271i	−0.426446	+	0.738626i
$520$	−1.23492			−0.0541550
$521$	40.1147			1.75746			0.878729	−	0.477321i	$-0.158392\pi$
$521$	40.1147			1.75746			0.878729	+	0.477321i	$0.158392\pi$
$522$	−0.301008	+	0.521362i	−0.0131748	+	0.0228194i
$523$	−11.5422	+	19.9916i	−0.504704	+	0.874173i	0.495281	+	0.868733i	$0.335065\pi$
$523$	−11.5422	+	19.9916i	−0.504704	+	0.874173i	−0.999985	+	0.00544039i	$0.998268\pi$
$524$		−	11.5185i		−	0.503186i
$525$	9.45219	−	8.44005i	0.412527	−	0.368354i
$526$	17.2243	+	9.94448i	0.751017	+	0.433600i
$527$	0.718745	−	0.414968i	0.0313090	−	0.0180763i
$528$	2.59497	−	4.49462i	0.112932	−	0.195603i
$529$	10.3160	+	17.8679i	0.448524	+	0.776866i
$530$	−3.27682	+	1.89187i	−0.142336	+	0.0821777i
$531$	4.25186			0.184515
$532$	−11.3461	−	2.06537i	−0.491916	−	0.0895453i
$533$	−18.0947			−0.783770
$534$	−4.76957	+	2.75371i	−0.206400	+	0.119165i
$535$	1.75030	+	3.03161i	0.0756722	+	0.131068i
$536$	5.66567	−	9.81323i	0.244720	−	0.423867i
$537$	−12.5810	+	7.26363i	−0.542909	+	0.313449i
$538$	24.5889	+	14.1964i	1.06010	+	0.612051i
$539$	−4.09712	+	36.0978i	−0.176476	+	1.55484i
$540$			0.458750i			0.0197415i
$541$	12.8111	−	22.1894i	0.550790	−	0.953997i	−0.447427	−	0.894320i	$-0.647660\pi$
$541$	12.8111	−	22.1894i	0.550790	−	0.953997i	0.998218	−	0.0596767i	$-0.0190070\pi$
$542$	−8.47409	+	14.6776i	−0.363993	+	0.630455i
$543$	16.3083			0.699857
$544$	−0.128672			−0.00551678
$545$	0.452851	−	0.784361i	0.0193980	−	0.0335983i
$546$	2.22896	−	6.76441i	0.0953905	−	0.289490i
$547$	−13.1171	−	7.57318i	−0.560848	−	0.323806i	0.192638	−	0.981270i	$-0.438296\pi$
$547$	−13.1171	−	7.57318i	−0.560848	−	0.323806i	−0.753486	+	0.657464i	$0.771629\pi$
$548$	4.20501	+	7.28329i	0.179629	+	0.311127i
$549$	7.19028	−	4.15131i	0.306874	−	0.177174i
$550$			24.8575i			1.05993i
$551$	−2.07007	+	1.61272i	−0.0881880	+	0.0687041i
$552$		−	1.53880i		−	0.0654958i
$553$	9.23576	−	28.0286i	0.392744	−	1.19190i
$554$	16.2453	−	9.37923i	0.690197	−	0.398485i
$555$	−1.49942	+	2.59707i	−0.0636469	+	0.110240i
$556$	−7.30065	+	4.21504i	−0.309617	+	0.178757i
$557$	−19.0157	+	32.9361i	−0.805720	+	1.39555i	0.110085	+	0.993922i	$0.464888\pi$
$557$	−19.0157	+	32.9361i	−0.805720	+	1.39555i	−0.915804	+	0.401625i	$0.868446\pi$
$558$			6.44999i			0.273050i
$559$	−14.0646			−0.594868
$560$	1.18825	−	0.247423i	0.0502128	−	0.0104555i
$561$	−0.578334	−	0.333901i	−0.0244173	−	0.0140973i
$562$	−13.7882			−0.581621
$563$	−45.7455			−1.92794			−0.963971	−	0.266006i	$-0.914296\pi$
$563$	−45.7455			−1.92794			−0.963971	+	0.266006i	$0.914296\pi$
$564$	0.675186	+	0.389819i	0.0284305	+	0.0164143i
$565$	−0.817381	−	1.41575i	−0.0343875	−	0.0595609i
$566$	−9.38981	+	16.2636i	−0.394683	+	0.683611i
$567$	−2.51285	−	0.828014i	−0.105530	−	0.0347733i
$568$	−2.76037	−	4.78110i	−0.115823	−	0.200611i
$569$		−	4.17624i		−	0.175077i	−0.996161	−	0.0875386i	$-0.972100\pi$
$569$		−	4.17624i		−	0.175077i	0.996161	−	0.0875386i	$-0.0279001\pi$
$570$	−0.751639	+	1.85300i	−0.0314827	+	0.0776137i
$571$	15.4895			0.648215			0.324107	−	0.946020i	$-0.394936\pi$
$571$	15.4895			0.648215			0.324107	+	0.946020i	$0.394936\pi$
$572$	6.98549	+	12.0992i	0.292078	+	0.505894i
$573$	−11.3317	−	19.6270i	−0.473387	−	0.819930i
$574$	17.4109	−	3.62537i	0.726716	−	0.151320i
$575$	3.68508	+	6.38275i	0.153679	+	0.266179i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			27.8565i			1.15968i	0.814731	+	0.579840i	$0.196885\pi$
$577$			27.8565i			1.15968i	−0.814731	+	0.579840i	$0.803115\pi$
$578$		−	16.9834i		−	0.706418i
$579$	−9.29634	−	5.36725i	−0.386343	−	0.223055i
$580$	0.138088	−	0.239175i	0.00573377	−	0.00993118i
$581$	−1.96801	−	2.20401i	−0.0816467	−	0.0914379i
$582$			0.528398i			0.0219028i
$583$	37.0714	+	21.4032i	1.53534	+	0.886430i
$584$	3.98313	+	6.89899i	0.164823	+	0.285482i
$585$	−1.06947	−	0.617462i	−0.0442173	−	0.0255289i
$586$	1.84483	−	1.06511i	0.0762093	−	0.0439995i
$587$	−16.9957	+	9.81247i	−0.701488	+	0.405004i	−0.807901	−	0.589318i	$-0.799397\pi$
$587$	−16.9957	+	9.81247i	−0.701488	+	0.405004i	0.106414	+	0.994322i	$0.466063\pi$
$588$	−0.789435	+	6.95534i	−0.0325557	+	0.286834i
$589$	−10.5680	+	26.0531i	−0.435446	+	1.07350i
$590$	−1.95054			−0.0803026
$591$	−13.4439	−	23.2854i	−0.553006	−	0.957835i
$592$	5.66120	−	3.26849i	0.232674	−	0.134334i
$593$	9.08703	+	5.24640i	0.373160	+	0.215444i	0.674838	−	0.737966i	$-0.264214\pi$
$593$	9.08703	+	5.24640i	0.373160	+	0.215444i	−0.301678	+	0.953410i	$0.597547\pi$
$594$	4.49462	−	2.59497i	0.184417	−	0.106473i
$595$	−0.0318365	−	0.152895i	−0.00130517	−	0.00626809i
$596$	11.0502			0.452632
$597$		−	23.7750i		−	0.973046i
$598$	3.58738	+	2.07118i	0.146699	+	0.0846967i
$599$	−13.7858	−	7.95922i	−0.563271	−	0.325205i	0.191186	−	0.981554i	$-0.438767\pi$
$599$	−13.7858	−	7.95922i	−0.563271	−	0.325205i	−0.754457	+	0.656349i	$0.772100\pi$
$600$			4.78955i			0.195533i
$601$	5.48889			0.223896			0.111948	−	0.993714i	$-0.464291\pi$
$601$	5.48889			0.223896			0.111948	+	0.993714i	$0.464291\pi$
$602$	13.5330	−	2.81791i	0.551565	−	0.114849i
$603$	9.81323	−	5.66567i	0.399626	−	0.230724i
$604$	−7.57723	−	4.37472i	−0.308313	−	0.178005i
$605$	−6.33101	+	3.65521i	−0.257392	+	0.148605i
$606$	4.92560	+	8.53140i	0.200089	+	0.346564i
$607$	11.5222			0.467673			0.233836	−	0.972276i	$-0.424872\pi$
$607$	11.5222			0.467673			0.233836	+	0.972276i	$0.424872\pi$
$608$	3.43856	−	2.67886i	0.139452	−	0.108642i
$609$	1.06086	+	1.18808i	0.0429883	+	0.0481435i
$610$	−3.29854	+	1.90441i	−0.133554	+	0.0771075i
$611$	−1.81756	+	1.04937i	−0.0735304	+	0.0424528i
$612$	−0.111434	−	0.0643362i	−0.00450443	−	0.00260064i
$613$	−15.9010	−	27.5414i	−0.642236	−	1.11239i	−0.984933	−	0.172939i	$-0.944674\pi$
$613$	−15.9010	−	27.5414i	−0.642236	−	1.11239i	0.342697	−	0.939446i	$-0.388660\pi$
$614$	8.77822	+	5.06811i	0.354260	+	0.204532i
$615$		−	3.08364i		−	0.124344i
$616$	−9.14562	−	10.2424i	−0.368488	−	0.412677i
$617$	1.64908	−	2.85628i	0.0663893	−	0.114990i	−0.830920	−	0.556392i	$-0.812185\pi$
$617$	1.64908	−	2.85628i	0.0663893	−	0.114990i	0.897309	+	0.441402i	$0.145519\pi$
$618$	−12.5011	−	7.21751i	−0.502868	−	0.290331i
$619$		−	38.1143i		−	1.53194i	−0.642875	−	0.765971i	$-0.722259\pi$
$619$		−	38.1143i		−	1.53194i	0.642875	−	0.765971i	$-0.277741\pi$
$620$		−	2.95893i		−	0.118834i
$621$	0.769401	−	1.33264i	0.0308750	−	0.0534771i
$622$	7.43647	+	12.8803i	0.298175	+	0.516455i
$623$	2.97039	+	14.2653i	0.119006	+	0.571528i
$624$	1.34597	+	2.33128i	0.0538818	+	0.0933259i
$625$	−10.9438	−	18.9551i	−0.437750	−	0.758206i
$626$	25.2351			1.00860
$627$	22.4066	−	3.11750i	0.894834	−	0.124501i
$628$			5.61701i			0.224143i
$629$	−0.420565	−	0.728439i	−0.0167690	−	0.0290448i
$630$	1.15277	+	0.379851i	0.0459274	+	0.0151336i
$631$	0.698473	−	1.20979i	0.0278058	−	0.0481610i	−0.851788	−	0.523887i	$-0.824481\pi$
$631$	0.698473	−	1.20979i	0.0278058	−	0.0481610i	0.879593	+	0.475726i	$0.157815\pi$
$632$	5.57705	+	9.65974i	0.221843	+	0.384244i
$633$	−21.0917	−	12.1773i	−0.838321	−	0.484005i
$634$	13.1844			0.523621
$635$	−5.89111			−0.233781
$636$	7.14293	+	4.12397i	0.283236	+	0.163526i
$637$	−15.1523	−	11.2020i	−0.600356	−	0.443841i
$638$	−3.12443			−0.123697
$639$		−	5.52074i		−	0.218397i
$640$	−0.229375	+	0.397289i	−0.00906684	+	0.0157042i
$641$	29.8203	−	17.2167i	1.17783	−	0.680021i	0.222319	−	0.974974i	$-0.428638\pi$
$641$	29.8203	−	17.2167i	1.17783	−	0.680021i	0.955512	+	0.294954i	$0.0953042\pi$
$642$	3.81537	−	6.60842i	0.150581	−	0.260814i
$643$	−25.6155	+	14.7891i	−1.01018	+	0.583225i	−0.911243	−	0.411869i	$-0.864876\pi$
$643$	−25.6155	+	14.7891i	−1.01018	+	0.583225i	−0.0989328	+	0.995094i	$0.531543\pi$
$644$	−3.86677	−	1.27415i	−0.152372	−	0.0502085i
$645$		−	2.39684i		−	0.0943754i
$646$	−0.344695	−	0.442448i	−0.0135619	−	0.0174079i
$647$		−	20.6345i		−	0.811227i	−0.914045	−	0.405614i	$-0.867058\pi$
$647$		−	20.6345i		−	0.811227i	0.914045	−	0.405614i	$-0.132942\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	11.0335	+	19.1105i	0.433102	+	0.750154i
$650$	−11.1658	−	6.44657i	−0.437958	−	0.252855i
$651$	16.2078	+	5.34068i	0.635235	+	0.209318i
$652$	3.36708	−	5.83195i	0.131865	−	0.228397i
$653$	−43.5950			−1.70600			−0.853002	−	0.521907i	$-0.825221\pi$
$653$	−43.5950			−1.70600			−0.853002	+	0.521907i	$0.825221\pi$
$654$	−1.97428			−0.0772006
$655$	−2.64205	+	4.57616i	−0.103233	+	0.178805i
$656$	−3.36092	+	5.82128i	−0.131222	+	0.227283i
$657$			7.96627i			0.310794i
$658$	1.53862	−	1.37386i	0.0599816	−	0.0535588i
$659$	−16.4748	−	9.51174i	−0.641768	−	0.370525i	0.143527	−	0.989646i	$-0.454155\pi$
$659$	−16.4748	−	9.51174i	−0.641768	−	0.370525i	−0.785295	+	0.619122i	$0.787489\pi$
$660$	−2.06191	+	1.19044i	−0.0802597	+	0.0463379i
$661$	−8.48749	+	14.7008i	−0.330125	+	0.571793i	−0.982536	−	0.186072i	$-0.940424\pi$
$661$	−8.48749	+	14.7008i	−0.330125	+	0.571793i	0.652411	+	0.757865i	$0.273758\pi$
$662$	9.83236	+	17.0301i	0.382145	+	0.661895i
$663$	0.299971	−	0.173189i	0.0116499	−	0.00672609i
$664$	1.11680			0.0433403
$665$	4.03394	+	3.42306i	0.156430	+	0.132741i
$666$	6.53699			0.253303
$667$	−0.802273	+	0.463192i	−0.0310641	+	0.0179349i
$668$	0.685214	+	1.18683i	0.0265117	+	0.0459197i
$669$	10.8421	−	18.7790i	0.419179	−	0.726039i
$670$	−4.50182	+	2.59913i	−0.173920	+	0.100413i
$671$	37.3172	+	21.5451i	1.44061	+	0.831739i
$672$	−1.76218	−	1.97350i	−0.0679776	−	0.0761296i
$673$			17.7009i			0.682318i	0.940006	+	0.341159i	$0.110819\pi$
$673$			17.7009i			0.682318i	−0.940006	+	0.341159i	$0.889181\pi$
$674$	−1.15625	+	2.00268i	−0.0445370	+	0.0771403i
$675$	−2.39477	+	4.14787i	−0.0921749	+	0.159652i
$676$	5.75350			0.221289
$677$	−15.3950			−0.591679			−0.295840	−	0.955238i	$-0.595599\pi$
$677$	−15.3950			−0.591679			−0.295840	+	0.955238i	$0.595599\pi$
$678$	−1.78176	+	3.08609i	−0.0684280	+	0.118521i
$679$	1.32778	+	0.437521i	0.0509556	+	0.0167905i
$680$	0.0511201	+	0.0295142i	0.00196037	+	0.00113182i
$681$	7.65153	+	13.2528i	0.293207	+	0.507850i
$682$	−28.9903	+	16.7375i	−1.11009	+	0.640914i
$683$			32.8760i			1.25797i	0.777419	+	0.628983i	$0.216528\pi$
$683$			32.8760i			1.25797i	−0.777419	+	0.628983i	$0.783472\pi$
$684$	4.31731	−	0.600682i	0.165077	−	0.0229676i
$685$		−	3.85810i		−	0.147410i
$686$	16.8240	+	7.74285i	0.642345	+	0.295623i
$687$	8.14820	−	4.70437i	0.310873	−	0.179483i
$688$	−2.61236	+	4.52474i	−0.0995952	+	0.172504i
$689$	−19.2283	+	11.1015i	−0.732539	+	0.422932i
$690$	−0.352963	+	0.611349i	−0.0134371	+	0.0232737i
$691$			38.3582i			1.45921i	0.683866	+	0.729607i	$0.260297\pi$
$691$			38.3582i			1.45921i	−0.683866	+	0.729607i	$0.739703\pi$
$692$	−19.4302			−0.738626
$693$	−2.79915	−	13.4430i	−0.106331	−	0.510656i
$694$	−10.7491	−	6.20598i	−0.408029	−	0.235576i
$695$	3.86729			0.146695
$696$	−0.602017			−0.0228194
$697$	0.749038	+	0.432457i	0.0283718	+	0.0163805i
$698$	9.66115	+	16.7336i	0.365680	+	0.633376i
$699$	3.26580	−	5.65652i	0.123524	−	0.213949i
$700$	12.0354	+	3.96581i	0.454895	+	0.149894i
$701$	25.7550	+	44.6089i	0.972752	+	1.68486i	0.687164	+	0.726503i	$0.258856\pi$
$701$	25.7550	+	44.6089i	0.972752	+	1.68486i	0.285588	+	0.958352i	$0.407811\pi$
$702$			2.69193i			0.101600i
$703$	26.4045	+	10.7105i	0.995864	+	0.403955i
$704$	5.18994			0.195603
$705$	−0.178829	−	0.309742i	−0.00673511	−	0.0116655i
$706$	15.9568	+	27.6380i	0.600542	+	1.04017i
$707$	25.5165	−	5.31317i	0.959649	−	0.199822i
$708$	2.12593	+	3.68222i	0.0798974	+	0.138386i
$709$	−2.60715	+	4.51571i	−0.0979134	+	0.169591i	−0.910821	−	0.412802i	$-0.864550\pi$
$709$	−2.60715	+	4.51571i	−0.0979134	+	0.169591i	0.812907	+	0.582393i	$0.197883\pi$
$710$			2.53264i			0.0950483i
$711$			11.1541i			0.418312i
$712$	−4.76957	−	2.75371i	−0.178747	−	0.103200i
$713$	−4.96263	+	8.59552i	−0.185852	+	0.321905i
$714$	−0.253935	+	0.226744i	−0.00950329	+	0.00848568i
$715$		−	6.40918i		−	0.239690i
$716$	−12.5810	−	7.26363i	−0.470173	−	0.271454i
$717$	−3.37389	−	5.84375i	−0.126000	−	0.218239i
$718$	4.78897	+	2.76491i	0.178723	+	0.103186i
$719$	15.1307	−	8.73572i	0.564280	−	0.325787i	−0.190582	−	0.981671i	$-0.561037\pi$
$719$	15.1307	−	8.73572i	0.564280	−	0.325787i	0.754862	+	0.655884i	$0.227704\pi$
$720$	−0.397289	+	0.229375i	−0.0148061	+	0.00854830i
$721$	−28.4876	+	25.4371i	−1.06093	+	0.947329i
$722$	18.4229	+	4.64740i	0.685628	+	0.172958i
$723$	16.5710			0.616280
$724$	8.15416	+	14.1234i	0.303047	+	0.524893i
$725$	2.49709	−	1.44169i	0.0927395	−	0.0535432i
$726$	13.8006	+	7.96776i	0.512187	+	0.295711i
$727$	−3.83154	+	2.21214i	−0.142104	+	0.0820437i	−0.569366	−	0.822084i	$-0.692811\pi$
$727$	−3.83154	+	2.21214i	−0.142104	+	0.0820437i	0.427262	+	0.904128i	$0.359478\pi$
$728$	6.97263	−	1.45187i	0.258423	−	0.0538099i
$729$	1.00000			0.0370370
$730$		−	3.65453i		−	0.135260i
$731$	0.582209	+	0.336138i	0.0215338	+	0.0124325i
$732$	7.19028	+	4.15131i	0.265761	+	0.153437i
$733$		−	21.3710i		−	0.789357i	−0.918819	−	0.394679i	$-0.870856\pi$
$733$		−	21.3710i		−	0.789357i	0.918819	−	0.394679i	$-0.129144\pi$
$734$	−33.9713			−1.25391
$735$	1.90902	−	2.58220i	0.0704151	−	0.0952461i
$736$	1.33264	−	0.769401i	0.0491218	−	0.0283605i
$737$	50.9301	+	29.4045i	1.87603	+	1.08313i
$738$	−5.82128	+	3.36092i	−0.214284	+	0.123717i
$739$	19.0647	+	33.0210i	0.701307	+	1.21470i	0.968008	+	0.250920i	$0.0807330\pi$
$739$	19.0647	+	33.0210i	0.701307	+	1.21470i	−0.266701	+	0.963779i	$0.585934\pi$
$740$	−2.99884			−0.110240
$741$	−4.41060	+	10.8734i	−0.162027	+	0.399443i
$742$	16.2774	−	14.5344i	0.597560	−	0.533574i
$743$	26.5247	−	15.3140i	0.973096	−	0.561817i	0.0729175	−	0.997338i	$-0.476769\pi$
$743$	26.5247	−	15.3140i	0.973096	−	0.561817i	0.900179	+	0.435521i	$0.143436\pi$
$744$	−5.58585	+	3.22499i	−0.204787	+	0.118234i
$745$	−4.39010	−	2.53463i	−0.160841	−	0.0928616i
$746$	−3.06437	−	5.30765i	−0.112195	−	0.194327i
$747$	0.967179	+	0.558401i	0.0353872	+	0.0204308i
$748$		−	0.667802i		−	0.0244173i
$749$	−13.4468	−	15.0593i	−0.491334	−	0.550255i
$750$	2.24548	−	3.88928i	0.0819932	−	0.142016i
$751$	−33.5355	−	19.3617i	−1.22373	−	0.706519i	−0.258017	−	0.966140i	$-0.583069\pi$
$751$	−33.5355	−	19.3617i	−1.22373	−	0.706519i	−0.965711	+	0.259621i	$0.916402\pi$
$752$			0.779638i			0.0284305i
$753$		−	25.8875i		−	0.943392i
$754$	0.810294	−	1.40347i	0.0295092	−	0.0511114i
$755$	2.00690	+	3.47605i	0.0730386	+	0.126507i
$756$	−0.539342	−	2.59020i	−0.0196157	−	0.0942045i
$757$	13.7263	+	23.7747i	0.498893	+	0.864107i	0.999999	−	0.00127818i	$-0.000406857\pi$
$757$	13.7263	+	23.7747i	0.498893	+	0.864107i	−0.501107	+	0.865386i	$0.667074\pi$
$758$	−8.67206	−	15.0205i	−0.314984	−	0.545567i
$759$	7.98630			0.289884
$760$	−1.98057	+	0.275563i	−0.0718427	+	0.00999571i
$761$			33.0133i			1.19673i	0.801223	+	0.598365i	$0.204183\pi$
$761$			33.0133i			1.19673i	−0.801223	+	0.598365i	$0.795817\pi$
$762$	6.42083	+	11.1212i	0.232602	+	0.402879i
$763$	−1.63473	+	4.96107i	−0.0591814	+	0.179603i
$764$	11.3317	−	19.6270i	0.409965	−	0.710080i
$765$	0.0295142	+	0.0511201i	0.00106709	+	0.00184825i
$766$	14.5110	+	8.37792i	0.524303	+	0.302707i
$767$	−11.4457			−0.413281
$768$	1.00000			0.0360844
$769$	−27.7877	−	16.0433i	−1.00205	−	0.578535i	−0.0931968	−	0.995648i	$-0.529709\pi$
$769$	−27.7877	−	16.0433i	−1.00205	−	0.578535i	−0.908855	+	0.417113i	$0.863042\pi$
$770$	1.28411	+	6.16696i	0.0462762	+	0.222242i
$771$	9.17069			0.330274
$772$		−	10.7345i		−	0.386343i
$773$	12.4256	−	21.5217i	0.446916	−	0.774082i	−0.551267	−	0.834329i	$-0.685855\pi$
$773$	12.4256	−	21.5217i	0.446916	−	0.774082i	0.998184	+	0.0602469i	$0.0191888\pi$
$774$	−4.52474	+	2.61236i	−0.162638	+	0.0938993i
$775$	15.4463	−	26.7537i	0.554846	−	0.961022i
$776$	−0.457606	+	0.264199i	−0.0164271	+	0.00948419i
$777$	5.41271	−	16.4264i	0.194180	−	0.589295i
$778$			24.7156i			0.886097i
$779$	−29.0203	+	4.03769i	−1.03976	+	0.144665i
$780$		−	1.23492i		−	0.0442173i
$781$	24.8137	−	14.3262i	0.887903	−	0.512631i
$782$	−0.0990006	−	0.171474i	−0.00354026	−	0.00613190i
$783$	−0.521362	−	0.301008i	−0.0186319	−	0.0107572i
$784$	−6.41822	+	2.79400i	−0.229222	+	0.0997857i
$785$	1.28840	−	2.23158i	0.0459850	−	0.0796484i
$786$	11.5185			0.410850
$787$	33.0778			1.17910			0.589548	−	0.807733i	$-0.299306\pi$
$787$	33.0778			1.17910			0.589548	+	0.807733i	$0.299306\pi$
$788$	13.4439	−	23.2854i	0.478918	−	0.829510i
$789$	−9.94448	+	17.2243i	−0.354033	+	0.613203i
$790$		−	5.11695i		−	0.182053i
$791$	6.27956	+	7.03261i	0.223275	+	0.250051i
$792$	4.49462	+	2.59497i	0.159710	+	0.0922083i
$793$	−19.3558	+	11.1751i	−0.687343	+	0.396838i
$794$	−8.53249	+	14.7787i	−0.302807	+	0.524477i
$795$	−1.89187	−	3.27682i	−0.0670978	−	0.116217i
$796$	20.5898	−	11.8875i	0.729785	−	0.421341i
$797$	45.1430			1.59905			0.799524	−	0.600634i	$-0.205085\pi$
$797$	45.1430			1.59905			0.799524	+	0.600634i	$0.205085\pi$
$798$	2.06537	−	11.3461i	0.0731134	−	0.401648i
$799$	0.100318			0.00354899
$800$	−4.14787	+	2.39477i	−0.146649	+	0.0846681i
$801$	−2.75371	−	4.76957i	−0.0972977	−	0.168525i
$802$	−15.2467	+	26.4081i	−0.538381	+	0.932503i
$803$	−35.8054	+	20.6722i	−1.26354	+	0.729508i
$804$	9.81323	+	5.66567i	0.346086	+	0.199813i
$805$	1.24397	+	1.39315i	0.0438441	+	0.0491020i
$806$		−	17.3629i		−	0.611583i
$807$	−14.1964	+	24.5889i	−0.499737	+	0.865571i
$808$	−4.92560	+	8.53140i	−0.173282	+	0.300133i
$809$	47.8527			1.68241			0.841206	−	0.540714i	$-0.181846\pi$
$809$	47.8527			1.68241			0.841206	+	0.540714i	$0.181846\pi$
$810$	−0.458750			−0.0161188
$811$	5.23232	−	9.06265i	0.183732	−	0.318233i	−0.759417	−	0.650605i	$-0.774516\pi$
$811$	5.23232	−	9.06265i	0.183732	−	0.318233i	0.943148	+	0.332372i	$0.107849\pi$
$812$	−0.498478	+	1.51277i	−0.0174932	+	0.0530880i
$813$	−14.6776	−	8.47409i	−0.514764	−	0.297199i
$814$	16.9633	+	29.3813i	0.594563	+	1.02981i
$815$	−2.67540	+	1.54465i	−0.0937153	+	0.0541066i
$816$		−	0.128672i		−	0.00450443i
$817$	−22.5567	+	3.13839i	−0.789160	+	0.109798i
$818$		−	35.4977i		−	1.24115i
$819$	6.76441	+	2.22896i	0.236368	+	0.0778860i
$820$	2.67051	−	1.54182i	0.0932584	−	0.0538427i
$821$	1.99158	−	3.44952i	0.0695066	−	0.120389i	−0.829178	−	0.558985i	$-0.811191\pi$
$821$	1.99158	−	3.44952i	0.0695066	−	0.120389i	0.898684	+	0.438596i	$0.144524\pi$
$822$	−7.28329	+	4.20501i	−0.254034	+	0.146667i
$823$	−6.85089	+	11.8661i	−0.238807	+	0.413626i	−0.960372	−	0.278721i	$-0.910090\pi$
$823$	−6.85089	+	11.8661i	−0.238807	+	0.413626i	0.721565	+	0.692346i	$0.243423\pi$
$824$		−	14.4350i		−	0.502868i
$825$	−24.8575			−0.865427
$826$	11.0132	−	2.29321i	0.383197	−	0.0797909i
$827$	−34.4877	−	19.9115i	−1.19925	−	0.692390i	−0.238865	−	0.971053i	$-0.576775\pi$
$827$	−34.4877	−	19.9115i	−1.19925	−	0.692390i	−0.960389	+	0.278663i	$0.910109\pi$
$828$	1.53880			0.0534771
$829$	25.0184			0.868923			0.434462	−	0.900690i	$-0.356939\pi$
$829$	25.0184			0.868923			0.434462	+	0.900690i	$0.356939\pi$
$830$	−0.443693	−	0.256166i	−0.0154008	−	0.00889166i
$831$	9.37923	+	16.2453i	0.325362	+	0.563544i
$832$	−1.34597	+	2.33128i	−0.0466630	+	0.0808226i
$833$	0.359511	+	0.825848i	0.0124563	+	0.0286139i
$834$	−4.21504	−	7.30065i	−0.145955	−	0.252801i
$835$		−	0.628684i		−	0.0217565i
$836$	13.9031	+	17.8459i	0.480850	+	0.617215i
$837$	−6.44999			−0.222944
$838$	−3.04480	−	5.27375i	−0.105181	−	0.182179i
$839$	−20.8796	−	36.1646i	−0.720845	−	1.24854i	−0.960661	−	0.277722i	$-0.910421\pi$
$839$	−20.8796	−	36.1646i	−0.720845	−	1.24854i	0.239816	−	0.970818i	$-0.422913\pi$
$840$	0.247423	+	1.18825i	0.00853690	+	0.0409986i
$841$	−14.3188	−	24.8009i	−0.493751	−	0.855202i
$842$	−3.74489	+	6.48633i	−0.129057	+	0.223534i
$843$		−	13.7882i		−	0.474892i
$844$		−	24.3546i		−	0.838321i
$845$	−2.28580	−	1.31971i	−0.0786341	−	0.0453994i
$846$	−0.389819	+	0.675186i	−0.0134023	+	0.0232134i
$847$	31.4488	−	28.0813i	1.08059	−	0.964884i
$848$			8.24795i			0.283236i
$849$	−16.2636	−	9.38981i	−0.558166	−	0.322257i
$850$	0.308141	+	0.533716i	0.0105692	+	0.0183063i
$851$	8.71146	+	5.02956i	0.298625	+	0.172411i
$852$	4.78110	−	2.76037i	0.163798	−	0.0945688i
$853$	38.5714	−	22.2692i	1.32066	−	0.762484i	0.336827	−	0.941567i	$-0.390646\pi$
$853$	38.5714	−	22.2692i	1.32066	−	0.762484i	0.983834	+	0.179083i	$0.0573130\pi$
$854$	16.3853	−	14.6307i	0.560692	−	0.500653i
$855$	−1.85300	−	0.751639i	−0.0633713	−	0.0257055i
$856$	7.63075			0.260814
$857$	−4.96174	−	8.59399i	−0.169490	−	0.293565i	0.768751	−	0.639549i	$-0.220879\pi$
$857$	−4.96174	−	8.59399i	−0.169490	−	0.293565i	−0.938241	+	0.345983i	$0.887545\pi$
$858$	−12.0992	+	6.98549i	−0.413061	+	0.238481i
$859$	−47.7725	−	27.5815i	−1.62998	−	0.941068i	−0.984098	−	0.177629i	$-0.943157\pi$
$859$	−47.7725	−	27.5815i	−1.62998	−	0.941068i	−0.645880	−	0.763439i	$-0.723509\pi$
$860$	2.07572	−	1.19842i	0.0707816	−	0.0408658i
$861$	3.62537	+	17.4109i	0.123552	+	0.593361i
$862$	10.6941			0.364243
$863$			47.6689i			1.62267i	0.584583	+	0.811334i	$0.301258\pi$
$863$			47.6689i			1.62267i	−0.584583	+	0.811334i	$0.698742\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	7.71941	+	4.45681i	0.262468	+	0.151536i
$866$			3.50445i			0.119086i
$867$	16.9834			0.576788
$868$	3.47875	+	16.7067i	0.118076	+	0.567063i
$869$	−50.1335	+	28.9446i	−1.70066	+	0.981878i
$870$	0.239175	+	0.138088i	0.00810878	+	0.00468161i
$871$	−26.4165	+	15.2516i	−0.895090	+	0.516781i
$872$	−0.987142	−	1.70978i	−0.0334288	−	0.0579005i
$873$	−0.528398			−0.0178836
$874$	6.21560	+	2.52125i	0.210246	+	0.0852826i
$875$	−7.91387	−	8.86292i	−0.267538	−	0.299621i
$876$	−6.89899	+	3.98313i	−0.233095	+	0.134578i
$877$	26.2834	−	15.1747i	0.887526	−	0.512414i	0.0143938	−	0.999896i	$-0.495418\pi$
$877$	26.2834	−	15.1747i	0.887526	−	0.512414i	0.873133	+	0.487483i	$0.162085\pi$
$878$	19.6526	+	11.3465i	0.663245	+	0.382924i
$879$	1.06511	+	1.84483i	0.0359254	+	0.0622246i
$880$	−2.06191	−	1.19044i	−0.0695069	−	0.0401298i
$881$		−	33.3313i		−	1.12296i	−0.827490	−	0.561480i	$-0.810232\pi$
$881$		−	33.3313i		−	1.12296i	0.827490	−	0.561480i	$-0.189768\pi$
$882$	−6.95534	−	0.789435i	−0.234199	−	0.0265817i
$883$	5.70364	−	9.87899i	0.191943	−	0.332455i	−0.753951	−	0.656930i	$-0.771855\pi$
$883$	5.70364	−	9.87899i	0.191943	−	0.332455i	0.945894	+	0.324476i	$0.105188\pi$
$884$	0.299971	+	0.173189i	0.0100891	+	0.00582496i
$885$		−	1.95054i		−	0.0655668i
$886$			4.39858i			0.147773i
$887$	23.3126	−	40.3787i	0.782762	−	1.35578i	−0.147565	−	0.989052i	$-0.547144\pi$
$887$	23.3126	−	40.3787i	0.782762	−	1.35578i	0.930327	−	0.366731i	$-0.119523\pi$
$888$	3.26849	+	5.66120i	0.109683	+	0.189977i
$889$	33.2624	−	6.92604i	1.11558	−	0.232292i
$890$	1.26327	+	2.18804i	0.0423448	+	0.0733433i
$891$	2.59497	+	4.49462i	0.0869348	+	0.150576i
$892$	21.6841			0.726039
$893$	−2.68083	+	2.08854i	−0.0897107	+	0.0698904i
$894$			11.0502i			0.369572i
$895$	3.33219	+	5.77152i	0.111383	+	0.192921i
$896$	0.828014	−	2.51285i	0.0276620	−	0.0839483i
$897$	−2.07118	+	3.58738i	−0.0691545	+	0.119779i
$898$	−16.2005	−	28.0601i	−0.540619	−	0.936379i
$899$	3.36278	+	1.94150i	0.112155	+	0.0647527i
$900$	−4.78955			−0.159652
$901$	1.06128			0.0353565
$902$	−30.2121	−	17.4430i	−1.00595	−	0.580788i
$903$	2.81791	+	13.5330i	0.0937741	+	0.450351i
$904$	−3.56351			−0.118521
$905$		−	7.48144i		−	0.248691i
$906$	4.37472	−	7.57723i	0.145340	−	0.251737i
$907$	19.8902	−	11.4836i	0.660444	−	0.381308i	−0.132002	−	0.991249i	$-0.542141\pi$
$907$	19.8902	−	11.4836i	0.660444	−	0.381308i	0.792446	+	0.609942i	$0.208807\pi$
$908$	−7.65153	+	13.2528i	−0.253925	+	0.439811i
$909$	−8.53140	+	4.92560i	−0.282969	+	0.163372i
$910$	−3.10317	−	1.02253i	−0.102869	−	0.0338967i
$911$		−	32.8634i		−	1.08881i	−0.838822	−	0.544406i	$-0.816755\pi$
$911$		−	32.8634i		−	1.08881i	0.838822	−	0.544406i	$-0.183245\pi$
$912$	2.67886	+	3.43856i	0.0887060	+	0.113862i
$913$			5.79614i			0.191824i
$914$	1.13279	−	0.654014i	0.0374692	−	0.0216329i
$915$	−1.90441	−	3.29854i	−0.0629580	−	0.109046i
$916$	8.14820	+	4.70437i	0.269224	+	0.155437i
$917$	9.53744	−	28.9441i	0.314954	−	0.955819i
$918$	0.0643362	−	0.111434i	0.00212341	−	0.00367785i
$919$	13.2289			0.436380			0.218190	−	0.975906i	$-0.429985\pi$
$919$	13.2289			0.436380			0.218190	+	0.975906i	$0.429985\pi$
$920$	−0.705925			−0.0232737
$921$	−5.06811	+	8.77822i	−0.167000	+	0.289252i
$922$	0.781933	−	1.35435i	0.0257516	−	0.0446030i
$923$			14.8615i			0.489171i
$924$	10.2424	−	9.14562i	0.336949	−	0.300869i
$925$	−27.1146	−	15.6546i	−0.891522	−	0.514720i
$926$	25.1658	−	14.5295i	0.827000	−	0.477468i
$927$	7.21751	−	12.5011i	0.237054	−	0.410590i
$928$	−0.301008	−	0.521362i	−0.00988108	−	0.0171145i
$929$	−31.0783	+	17.9431i	−1.01965	+	0.588693i	−0.914002	−	0.405711i	$-0.867024\pi$
$929$	−31.0783	+	17.9431i	−1.01965	+	0.588693i	−0.105645	+	0.994404i	$0.533691\pi$
$930$	2.95893			0.0970272
$931$	−26.8009	−	14.5847i	−0.878363	−	0.477994i
$932$	6.53159			0.213949
$933$	−12.8803	+	7.43647i	−0.421683	+	0.243459i
$934$	−4.74302	−	8.21515i	−0.155196	−	0.268808i
$935$	−0.153177	+	0.265311i	−0.00500943	+	0.00867658i
$936$	−2.33128	+	1.34597i	−0.0762003	+	0.0439943i
$937$	19.4033	+	11.2025i	0.633879	+	0.365970i	0.782253	−	0.622961i	$-0.214070\pi$
$937$	19.4033	+	11.2025i	0.633879	+	0.365970i	−0.148374	+	0.988931i	$0.547404\pi$
$938$	22.3624	−	19.9679i	0.730160	−	0.651974i
$939$			25.2351i			0.823516i
$940$	0.178829	−	0.309742i	0.00583277	−	0.0101027i
$941$	−7.72208	+	13.3750i	−0.251732	+	0.436013i	−0.964003	−	0.265892i	$-0.914334\pi$
$941$	−7.72208	+	13.3750i	−0.251732	+	0.436013i	0.712270	+	0.701905i	$0.247667\pi$
$942$	−5.61701			−0.183012
$943$	−10.3436			−0.336833
$944$	−2.12593	+	3.68222i	−0.0691932	+	0.119846i
$945$	−0.379851	+	1.15277i	−0.0123566	+	0.0374995i
$946$	−23.4831	−	13.5580i	−0.763503	−	0.440808i
$947$	−27.9135	−	48.3476i	−0.907066	−	1.57108i	−0.818120	−	0.575048i	$-0.804983\pi$
$947$	−27.9135	−	48.3476i	−0.907066	−	1.57108i	−0.0889462	−	0.996036i	$-0.528350\pi$
$948$	−9.65974	+	5.57705i	−0.313734	+	0.181134i
$949$		−	21.4447i		−	0.696123i
$950$	−19.3461	−	7.84744i	−0.627672	−	0.254604i
$951$			13.1844i			0.427535i
$952$	−0.323334	−	0.106542i	−0.0104793	−	0.00345306i
$953$	−48.3776	+	27.9308i	−1.56710	+	0.904768i	−0.570600	+	0.821228i	$0.693289\pi$
$953$	−48.3776	+	27.9308i	−1.56710	+	0.904768i	−0.996504	+	0.0835396i	$0.973378\pi$
$954$	−4.12397	+	7.14293i	−0.133519	+	0.231261i
$955$	−9.00388	+	5.19839i	−0.291359	+	0.168216i
$956$	3.37389	−	5.84375i	0.109119	−	0.189000i
$957$		−	3.12443i		−	0.100999i
$958$	25.0893			0.810599
$959$	4.53587	+	21.7836i	0.146471	+	0.703429i
$960$	−0.397289	−	0.229375i	−0.0128224	−	0.00740304i
$961$	10.6023			0.342011
$962$	−17.5971			−0.567354
$963$	6.60842	+	3.81537i	0.212953	+	0.122949i
$964$	8.28548	+	14.3509i	0.266857	+	0.462210i
$965$	−2.46222	+	4.26470i	−0.0792618	+	0.137285i
$966$	1.27415	−	3.86677i	0.0409951	−	0.124411i
$967$	−19.9870	−	34.6185i	−0.642739	−	1.11326i	−0.984819	−	0.173586i	$-0.944465\pi$
$967$	−19.9870	−	34.6185i	−0.642739	−	1.11326i	0.342079	−	0.939671i	$-0.388869\pi$
$968$			15.9355i			0.512187i
$969$	0.442448	−	0.344695i	0.0142135	−	0.0110732i
$970$	0.242402			0.00778307
$971$	8.39950	+	14.5484i	0.269553	+	0.466879i	0.968746	−	0.248053i	$-0.0797908\pi$
$971$	8.39950	+	14.5484i	0.269553	+	0.466879i	−0.699194	+	0.714932i	$0.746457\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−21.8355	+	4.54669i	−0.700015	+	0.145760i
$974$	−11.4275	−	19.7930i	−0.366161	−	0.634209i
$975$	6.44657	−	11.1658i	0.206455	−	0.357591i
$976$			8.30263i			0.265761i
$977$			21.9399i			0.701918i	0.936391	+	0.350959i	$0.114144\pi$
$977$			21.9399i			0.701918i	−0.936391	+	0.350959i	$0.885856\pi$
$978$	5.83195	+	3.36708i	0.186485	+	0.107667i
$979$	14.2916	−	24.7538i	0.456762	−	0.791135i
$980$	3.19076	+	0.362153i	0.101925	+	0.0115686i
$981$		−	1.97428i		−	0.0630340i
$982$	22.9351	+	13.2416i	0.731889	+	0.422557i
$983$	3.58780	+	6.21424i	0.114433	+	0.198204i	0.917553	−	0.397614i	$-0.130162\pi$
$983$	3.58780	+	6.21424i	0.114433	+	0.198204i	−0.803120	+	0.595817i	$0.796828\pi$
$984$	−5.82128	−	3.36092i	−0.185576	−	0.107142i
$985$	−10.6822	+	6.16737i	−0.340363	+	0.196509i
$986$	−0.0670848	+	0.0387314i	−0.00213642	+	0.00123346i
$987$	1.37386	+	1.53862i	0.0437306	+	0.0489748i
$988$	−11.6219	+	1.61699i	−0.369742	+	0.0514434i
$989$	−8.03981			−0.255651
$990$	−1.19044	−	2.06191i	−0.0378348	−	0.0655317i
$991$	21.3103	−	12.3035i	0.676945	−	0.390834i	−0.121758	−	0.992560i	$-0.538853\pi$
$991$	21.3103	−	12.3035i	0.676945	−	0.390834i	0.798703	+	0.601725i	$0.205520\pi$
$992$	−5.58585	−	3.22499i	−0.177351	−	0.102394i
$993$	−17.0301	+	9.83236i	−0.540435	+	0.312020i
$994$	−2.97757	−	14.2998i	−0.0944427	−	0.453562i
$995$	−10.9068			−0.345768
$996$			1.11680i			0.0353872i
$997$	8.11759	+	4.68669i	0.257087	+	0.148429i	0.623005	−	0.782218i	$-0.285912\pi$
$997$	8.11759	+	4.68669i	0.257087	+	0.148429i	−0.365918	+	0.930647i	$0.619245\pi$
$998$	−4.37688	−	2.52699i	−0.138548	−	0.0799906i
$999$			6.53699i			0.206821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bj.a.601.3	yes	24
7.6	odd	2		798.2.bj.b.601.4	yes	24
19.8	odd	6		798.2.bj.b.559.4	yes	24
133.27	even	6	inner	798.2.bj.a.559.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bj.a.559.3	✓	24	133.27	even	6	inner
798.2.bj.a.601.3	yes	24	1.1	even	1	trivial
798.2.bj.b.559.4	yes	24	19.8	odd	6
798.2.bj.b.601.4	yes	24	7.6	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.397289 + 0.229375i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.97350 - 1.76218i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.397289 + 0.229375i) q^{5} +(0.866025 + 0.500000i) q^{6} +(1.97350 - 1.76218i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.229375 - 0.397289i) q^{10} -5.18994 q^{11} -1.00000 q^{12} +(1.34597 - 2.33128i) q^{13} +(-0.828014 + 2.51285i) q^{14} +(0.397289 + 0.229375i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.111434 + 0.0643362i) q^{17} -1.00000i q^{18} +(1.63845 - 4.03924i) q^{19} +0.458750i q^{20} +(-2.51285 - 0.828014i) q^{21} +(4.49462 - 2.59497i) q^{22} +(0.769401 - 1.33264i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.39477 + 4.14787i) q^{25} +2.69193i q^{26} +1.00000 q^{27} +(-0.539342 - 2.59020i) q^{28} +(-0.521362 - 0.301008i) q^{29} -0.458750 q^{30} -6.44999 q^{31} +(0.866025 + 0.500000i) q^{32} +(2.59497 + 4.49462i) q^{33} +(0.0643362 - 0.111434i) q^{34} +(-0.379851 + 1.15277i) q^{35} +(0.500000 + 0.866025i) q^{36} +6.53699i q^{37} +(0.600682 + 4.31731i) q^{38} -2.69193 q^{39} +(-0.229375 - 0.397289i) q^{40} +(-3.36092 - 5.82128i) q^{41} +(2.59020 - 0.539342i) q^{42} +(-2.61236 - 4.52474i) q^{43} +(-2.59497 + 4.49462i) q^{44} -0.458750i q^{45} +1.53880i q^{46} +(-0.675186 - 0.389819i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.789435 - 6.95534i) q^{49} -4.78955i q^{50} +(0.111434 + 0.0643362i) q^{51} +(-1.34597 - 2.33128i) q^{52} +(-7.14293 - 4.12397i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.06191 - 1.19044i) q^{55} +(1.76218 + 1.97350i) q^{56} +(-4.31731 + 0.600682i) q^{57} +0.602017 q^{58} +(-2.12593 - 3.68222i) q^{59} +(0.397289 - 0.229375i) q^{60} +(-7.19028 - 4.15131i) q^{61} +(5.58585 - 3.22499i) q^{62} +(0.539342 + 2.59020i) q^{63} -1.00000 q^{64} +1.23492i q^{65} +(-4.49462 - 2.59497i) q^{66} +(-9.81323 - 5.66567i) q^{67} +0.128672i q^{68} -1.53880 q^{69} +(-0.247423 - 1.18825i) q^{70} +(-4.78110 + 2.76037i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(6.89899 - 3.98313i) q^{73} +(-3.26849 - 5.66120i) q^{74} +4.78955 q^{75} +(-2.67886 - 3.43856i) q^{76} +(-10.2424 + 9.14562i) q^{77} +(2.33128 - 1.34597i) q^{78} +(9.65974 - 5.57705i) q^{79} +(0.397289 + 0.229375i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.82128 + 3.36092i) q^{82} -1.11680i q^{83} +(-1.97350 + 1.76218i) q^{84} +(0.0295142 - 0.0511201i) q^{85} +(4.52474 + 2.61236i) q^{86} +0.602017i q^{87} -5.18994i q^{88} +(-2.75371 + 4.76957i) q^{89} +(0.229375 + 0.397289i) q^{90} +(-1.45187 - 6.97263i) q^{91} +(-0.769401 - 1.33264i) q^{92} +(3.22499 + 5.58585i) q^{93} +0.779638 q^{94} +(0.275563 + 1.98057i) q^{95} -1.00000i q^{96} +(0.264199 + 0.457606i) q^{97} +(2.79400 + 6.41822i) q^{98} +(2.59497 - 4.49462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9} + 2 q^{10} - 24 q^{12} + 10 q^{13} + 4 q^{14} - 12 q^{16} - 10 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{25} + 24 q^{27} + 12 q^{28} - 4 q^{30} - 36 q^{31} + 2 q^{34} - 16 q^{35} + 12 q^{36} + 12 q^{38} - 20 q^{39} - 2 q^{40} - 20 q^{41} - 8 q^{42} - 6 q^{43} - 12 q^{48} + 2 q^{49} - 10 q^{52} + 12 q^{53} - 30 q^{55} - 4 q^{56} + 2 q^{57} - 8 q^{58} + 8 q^{59} - 42 q^{61} - 12 q^{62} - 12 q^{63} - 24 q^{64} - 6 q^{66} + 6 q^{67} + 6 q^{70} - 24 q^{71} + 66 q^{73} - 12 q^{75} - 8 q^{76} + 16 q^{77} - 24 q^{78} + 30 q^{79} - 12 q^{81} - 6 q^{82} - 6 q^{84} - 2 q^{85} + 12 q^{86} - 8 q^{89} + 2 q^{90} - 66 q^{91} + 18 q^{93} + 20 q^{95} + 36 q^{97} - 32 q^{98}+O(q^{100}) \) 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9 + 2 * q^10 - 24 * q^12 + 10 * q^13 + 4 * q^14 - 12 * q^16 - 10 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^25 + 24 * q^27 + 12 * q^28 - 4 * q^30 - 36 * q^31 + 2 * q^34 - 16 * q^35 + 12 * q^36 + 12 * q^38 - 20 * q^39 - 2 * q^40 - 20 * q^41 - 8 * q^42 - 6 * q^43 - 12 * q^48 + 2 * q^49 - 10 * q^52 + 12 * q^53 - 30 * q^55 - 4 * q^56 + 2 * q^57 - 8 * q^58 + 8 * q^59 - 42 * q^61 - 12 * q^62 - 12 * q^63 - 24 * q^64 - 6 * q^66 + 6 * q^67 + 6 * q^70 - 24 * q^71 + 66 * q^73 - 12 * q^75 - 8 * q^76 + 16 * q^77 - 24 * q^78 + 30 * q^79 - 12 * q^81 - 6 * q^82 - 6 * q^84 - 2 * q^85 + 12 * q^86 - 8 * q^89 + 2 * q^90 - 66 * q^91 + 18 * q^93 + 20 * q^95 + 36 * q^97 - 32 * q^98

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