LMFDB - Embedded newform 804.2.j.a.499.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.11
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.727656 + 1.21265i) q^{2} -1.00000 q^{3} +(-0.941033 - 1.76478i) q^{4} -4.20985i q^{5} +(0.727656 - 1.21265i) q^{6} +(2.11068 - 3.65581i) q^{7} +(2.82481 + 0.143013i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.727656 + 1.21265i) q^{2} -1.00000 q^{3} +(-0.941033 - 1.76478i) q^{4} -4.20985i q^{5} +(0.727656 - 1.21265i) q^{6} +(2.11068 - 3.65581i) q^{7} +(2.82481 + 0.143013i) q^{8} +1.00000 q^{9} +(5.10506 + 3.06332i) q^{10} +(1.49147 - 2.58331i) q^{11} +(0.941033 + 1.76478i) q^{12} +(-3.05775 + 1.76539i) q^{13} +(2.89736 + 5.21969i) q^{14} +4.20985i q^{15} +(-2.22891 + 3.32144i) q^{16} +(-1.44760 - 2.50731i) q^{17} +(-0.727656 + 1.21265i) q^{18} +(3.47527 - 2.00645i) q^{19} +(-7.42946 + 3.96160i) q^{20} +(-2.11068 + 3.65581i) q^{21} +(2.04736 + 3.68839i) q^{22} +(5.23155 - 3.02044i) q^{23} +(-2.82481 - 0.143013i) q^{24} -12.7228 q^{25} +(0.0841897 - 4.99257i) q^{26} -1.00000 q^{27} +(-8.43793 - 0.284659i) q^{28} +(-1.32803 + 2.30022i) q^{29} +(-5.10506 - 3.06332i) q^{30} +(-3.03263 + 5.25267i) q^{31} +(-2.40585 - 5.11975i) q^{32} +(-1.49147 + 2.58331i) q^{33} +(4.09384 + 0.0690344i) q^{34} +(-15.3904 - 8.88565i) q^{35} +(-0.941033 - 1.76478i) q^{36} +(1.97775 + 3.42556i) q^{37} +(-0.0956854 + 5.67428i) q^{38} +(3.05775 - 1.76539i) q^{39} +(0.602061 - 11.8920i) q^{40} +(6.43182 + 3.71341i) q^{41} +(-2.89736 - 5.21969i) q^{42} +0.320226 q^{43} +(-5.96250 - 0.201148i) q^{44} -4.20985i q^{45} +(-0.144041 + 8.54187i) q^{46} +(2.22823 + 1.28647i) q^{47} +(2.22891 - 3.32144i) q^{48} +(-5.40996 - 9.37033i) q^{49} +(9.25782 - 15.4283i) q^{50} +(1.44760 + 2.50731i) q^{51} +(5.99297 + 3.73497i) q^{52} -6.08222i q^{53} +(0.727656 - 1.21265i) q^{54} +(-10.8753 - 6.27887i) q^{55} +(6.48510 - 10.0251i) q^{56} +(-3.47527 + 2.00645i) q^{57} +(-1.82301 - 3.28420i) q^{58} -2.14957i q^{59} +(7.42946 - 3.96160i) q^{60} +(-8.48738 + 4.90019i) q^{61} +(-4.16293 - 7.49965i) q^{62} +(2.11068 - 3.65581i) q^{63} +(7.95909 + 0.807967i) q^{64} +(7.43202 + 12.8726i) q^{65} +(-2.04736 - 3.68839i) q^{66} +(7.30425 - 3.69430i) q^{67} +(-3.06262 + 4.91415i) q^{68} +(-5.23155 + 3.02044i) q^{69} +(21.9741 - 12.1974i) q^{70} +(1.59389 + 0.920230i) q^{71} +(2.82481 + 0.143013i) q^{72} +(6.17242 + 10.6909i) q^{73} +(-5.59312 - 0.0943167i) q^{74} +12.7228 q^{75} +(-6.81128 - 4.24496i) q^{76} +(-6.29605 - 10.9051i) q^{77} +(-0.0841897 + 4.99257i) q^{78} +(-4.23762 + 7.33977i) q^{79} +(13.9827 + 9.38338i) q^{80} +1.00000 q^{81} +(-9.18322 + 5.09745i) q^{82} +(7.09780 - 4.09792i) q^{83} +(8.43793 + 0.284659i) q^{84} +(-10.5554 + 6.09416i) q^{85} +(-0.233014 + 0.388321i) q^{86} +(1.32803 - 2.30022i) q^{87} +(4.58257 - 7.08405i) q^{88} +15.2237 q^{89} +(5.10506 + 3.06332i) q^{90} +14.9047i q^{91} +(-10.2535 - 6.39021i) q^{92} +(3.03263 - 5.25267i) q^{93} +(-3.18143 + 1.76596i) q^{94} +(-8.44683 - 14.6303i) q^{95} +(2.40585 + 5.11975i) q^{96} +(-3.09505 + 1.78693i) q^{97} +(15.2995 + 0.257995i) q^{98} +(1.49147 - 2.58331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.727656	+	1.21265i	−0.514531	+	0.857472i
$2$	−0.727656	+	1.21265i	−0.514531	+	0.857472i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.941033	−	1.76478i	−0.470516	−	0.882391i
$5$		−	4.20985i		−	1.88270i	−0.337432	−	0.941350i	$-0.609558\pi$
$5$		−	4.20985i		−	1.88270i	0.337432	−	0.941350i	$-0.390442\pi$
$6$	0.727656	−	1.21265i	0.297064	−	0.495062i
$7$	2.11068	−	3.65581i	0.797763	−	1.38177i	−0.123307	−	0.992369i	$-0.539350\pi$
$7$	2.11068	−	3.65581i	0.797763	−	1.38177i	0.921070	−	0.389397i	$-0.127317\pi$
$8$	2.82481	+	0.143013i	0.998721	+	0.0505626i
$9$	1.00000			0.333333
$10$	5.10506	+	3.06332i	1.61436	+	0.968707i
$11$	1.49147	−	2.58331i	0.449696	−	0.778896i	−0.548670	−	0.836039i	$-0.684866\pi$
$11$	1.49147	−	2.58331i	0.449696	−	0.778896i	0.998366	+	0.0571427i	$0.0181990\pi$
$12$	0.941033	+	1.76478i	0.271653	+	0.509449i
$13$	−3.05775	+	1.76539i	−0.848066	+	0.489631i	−0.859998	−	0.510297i	$-0.829535\pi$
$13$	−3.05775	+	1.76539i	−0.848066	+	0.489631i	0.0119316	+	0.999929i	$0.496202\pi$
$14$	2.89736	+	5.21969i	0.774352	+	1.39502i
$15$			4.20985i			1.08698i
$16$	−2.22891	+	3.32144i	−0.557229	+	0.830359i
$17$	−1.44760	−	2.50731i	−0.351094	−	0.608112i	0.635348	−	0.772226i	$-0.280857\pi$
$17$	−1.44760	−	2.50731i	−0.351094	−	0.608112i	−0.986441	+	0.164114i	$0.947523\pi$
$18$	−0.727656	+	1.21265i	−0.171510	+	0.285824i
$19$	3.47527	−	2.00645i	0.797281	−	0.460310i	−0.0452385	−	0.998976i	$-0.514405\pi$
$19$	3.47527	−	2.00645i	0.797281	−	0.460310i	0.842520	+	0.538666i	$0.181071\pi$
$20$	−7.42946	+	3.96160i	−1.66128	+	0.885841i
$21$	−2.11068	+	3.65581i	−0.460589	+	0.797763i
$22$	2.04736	+	3.68839i	0.436499	+	0.786368i
$23$	5.23155	−	3.02044i	1.09085	−	0.629804i	0.157050	−	0.987591i	$-0.449802\pi$
$23$	5.23155	−	3.02044i	1.09085	−	0.629804i	0.933803	+	0.357786i	$0.116468\pi$
$24$	−2.82481	−	0.143013i	−0.576612	−	0.0291923i
$25$	−12.7228			−2.54456
$26$	0.0841897	−	4.99257i	0.0165110	−	0.979124i
$27$	−1.00000			−0.192450
$28$	−8.43793	−	0.284659i	−1.59462	−	0.0537954i
$29$	−1.32803	+	2.30022i	−0.246609	+	0.427140i	−0.962583	−	0.270988i	$-0.912650\pi$
$29$	−1.32803	+	2.30022i	−0.246609	+	0.427140i	0.715974	+	0.698127i	$0.245983\pi$
$30$	−5.10506	−	3.06332i	−0.932053	−	0.559283i
$31$	−3.03263	+	5.25267i	−0.544677	+	0.943408i	0.453951	+	0.891027i	$0.350014\pi$
$31$	−3.03263	+	5.25267i	−0.544677	+	0.943408i	−0.998627	+	0.0523807i	$0.983319\pi$
$32$	−2.40585	−	5.11975i	−0.425299	−	0.905053i
$33$	−1.49147	+	2.58331i	−0.259632	+	0.449696i
$34$	4.09384	+	0.0690344i	0.702087	+	0.0118393i
$35$	−15.3904	−	8.88565i	−2.60145	−	1.50195i
$36$	−0.941033	−	1.76478i	−0.156839	−	0.294130i
$37$	1.97775	+	3.42556i	0.325139	+	0.563158i	0.981541	−	0.191254i	$-0.0612554\pi$
$37$	1.97775	+	3.42556i	0.325139	+	0.563158i	−0.656401	+	0.754412i	$0.727922\pi$
$38$	−0.0956854	+	5.67428i	−0.0155222	+	0.920490i
$39$	3.05775	−	1.76539i	0.489631	−	0.282689i
$40$	0.602061	−	11.8920i	0.0951943	−	1.88029i
$41$	6.43182	+	3.71341i	1.00448	+	0.579938i	0.909571	−	0.415548i	$-0.136410\pi$
$41$	6.43182	+	3.71341i	1.00448	+	0.579938i	0.0949101	+	0.995486i	$0.469744\pi$
$42$	−2.89736	−	5.21969i	−0.447072	−	0.805415i
$43$	0.320226			0.0488340			0.0244170	−	0.999702i	$-0.492227\pi$
$43$	0.320226			0.0488340			0.0244170	+	0.999702i	$0.492227\pi$
$44$	−5.96250	−	0.201148i	−0.898881	−	0.0303243i
$45$		−	4.20985i		−	0.627567i
$46$	−0.144041	+	8.54187i	−0.0212378	+	1.25943i
$47$	2.22823	+	1.28647i	0.325021	+	0.187651i	0.653629	−	0.756816i	$-0.273246\pi$
$47$	2.22823	+	1.28647i	0.325021	+	0.187651i	−0.328607	+	0.944467i	$0.606579\pi$
$48$	2.22891	−	3.32144i	0.321716	−	0.479408i
$49$	−5.40996	−	9.37033i	−0.772851	−	1.33862i
$50$	9.25782	−	15.4283i	1.30925	−	2.18189i
$51$	1.44760	+	2.50731i	0.202704	+	0.351094i
$52$	5.99297	+	3.73497i	0.831076	+	0.517947i
$53$		−	6.08222i		−	0.835458i	−0.908572	−	0.417729i	$-0.862826\pi$
$53$		−	6.08222i		−	0.835458i	0.908572	−	0.417729i	$-0.137174\pi$
$54$	0.727656	−	1.21265i	0.0990215	−	0.165021i
$55$	−10.8753	−	6.27887i	−1.46643	−	0.846643i
$56$	6.48510	−	10.0251i	0.866608	−	1.33966i
$57$	−3.47527	+	2.00645i	−0.460310	+	0.265760i
$58$	−1.82301	−	3.28420i	−0.239372	−	0.431237i
$59$		−	2.14957i		−	0.279850i	−0.990162	−	0.139925i	$-0.955314\pi$
$59$		−	2.14957i		−	0.279850i	0.990162	−	0.139925i	$-0.0446862\pi$
$60$	7.42946	−	3.96160i	0.959139	−	0.511441i
$61$	−8.48738	+	4.90019i	−1.08670	+	0.627405i	−0.932695	−	0.360666i	$-0.882550\pi$
$61$	−8.48738	+	4.90019i	−1.08670	+	0.627405i	−0.154002	+	0.988071i	$0.549216\pi$
$62$	−4.16293	−	7.49965i	−0.528693	−	0.952457i
$63$	2.11068	−	3.65581i	0.265921	−	0.460589i
$64$	7.95909	+	0.807967i	0.994887	+	0.100996i
$65$	7.43202	+	12.8726i	0.921829	+	1.59665i
$66$	−2.04736	−	3.68839i	−0.252013	−	0.454010i
$67$	7.30425	−	3.69430i	0.892357	−	0.451331i
$67$	7.30425	−	3.69430i	0.892357	−	0.451331i
$68$	−3.06262	+	4.91415i	−0.371397	+	0.595929i
$69$	−5.23155	+	3.02044i	−0.629804	+	0.363618i
$70$	21.9741	−	12.1974i	2.62640	−	1.45787i
$71$	1.59389	+	0.920230i	0.189159	+	0.109211i	0.591589	−	0.806240i	$-0.298501\pi$
$71$	1.59389	+	0.920230i	0.189159	+	0.109211i	−0.402430	+	0.915451i	$0.631834\pi$
$72$	2.82481	+	0.143013i	0.332907	+	0.0168542i
$73$	6.17242	+	10.6909i	0.722427	+	1.25128i	0.960024	+	0.279916i	$0.0903067\pi$
$73$	6.17242	+	10.6909i	0.722427	+	1.25128i	−0.237598	+	0.971364i	$0.576360\pi$
$74$	−5.59312	−	0.0943167i	−0.650186	−	0.0109641i
$75$	12.7228			1.46910
$76$	−6.81128	−	4.24496i	−0.781308	−	0.486930i
$77$	−6.29605	−	10.9051i	−0.717502	−	1.24275i
$78$	−0.0841897	+	4.99257i	−0.00953261	+	0.565297i
$79$	−4.23762	+	7.33977i	−0.476769	+	0.825789i	−0.999646	−	0.0266199i	$-0.991526\pi$
$79$	−4.23762	+	7.33977i	−0.476769	+	0.825789i	0.522876	+	0.852409i	$0.324859\pi$
$80$	13.9827	+	9.38338i	1.56332	+	1.04909i
$81$	1.00000			0.111111
$82$	−9.18322	+	5.09745i	−1.01412	+	0.562919i
$83$	7.09780	−	4.09792i	0.779084	−	0.449805i	−0.0570212	−	0.998373i	$-0.518160\pi$
$83$	7.09780	−	4.09792i	0.779084	−	0.449805i	0.836106	+	0.548568i	$0.184827\pi$
$84$	8.43793	+	0.284659i	0.920654	+	0.0310588i
$85$	−10.5554	+	6.09416i	−1.14489	+	0.661004i
$86$	−0.233014	+	0.388321i	−0.0251266	+	0.0418738i
$87$	1.32803	−	2.30022i	0.142380	−	0.246609i
$88$	4.58257	−	7.08405i	0.488504	−	0.755162i
$89$	15.2237			1.61371			0.806857	−	0.590747i	$-0.201167\pi$
$89$	15.2237			1.61371			0.806857	+	0.590747i	$0.201167\pi$
$90$	5.10506	+	3.06332i	0.538121	+	0.322902i
$91$			14.9047i			1.56244i
$92$	−10.2535	−	6.39021i	−1.06900	−	0.666226i
$93$	3.03263	−	5.25267i	0.314469	−	0.544677i
$94$	−3.18143	+	1.76596i	−0.328139	+	0.182144i
$95$	−8.44683	−	14.6303i	−0.866626	−	1.50104i
$96$	2.40585	+	5.11975i	0.245546	+	0.522533i
$97$	−3.09505	+	1.78693i	−0.314255	+	0.181435i	−0.648829	−	0.760934i	$-0.724741\pi$
$97$	−3.09505	+	1.78693i	−0.314255	+	0.181435i	0.334574	+	0.942369i	$0.391408\pi$
$98$	15.2995	+	0.257995i	1.54548	+	0.0260615i
$99$	1.49147	−	2.58331i	0.149899	−	0.259632i
$100$	11.9726	+	22.4530i	1.19726	+	2.24530i
$101$	−16.3618	−	9.44651i	−1.62806	−	0.939963i	−0.984670	−	0.174427i	$-0.944193\pi$
$101$	−16.3618	−	9.44651i	−1.62806	−	0.939963i	−0.643393	−	0.765536i	$-0.722474\pi$
$102$	−4.09384	−	0.0690344i	−0.405350	−	0.00683542i
$103$	−4.51699	−	2.60789i	−0.445072	−	0.256963i	0.260674	−	0.965427i	$-0.416055\pi$
$103$	−4.51699	−	2.60789i	−0.445072	−	0.256963i	−0.705747	+	0.708464i	$0.749388\pi$
$104$	−8.89003	+	4.54960i	−0.871739	+	0.446125i
$105$	15.3904	+	8.88565i	1.50195	+	0.867150i
$106$	7.37560	+	4.42577i	0.716381	+	0.429869i
$107$			9.10239i			0.879962i	0.898007	+	0.439981i	$0.145015\pi$
$107$			9.10239i			0.879962i	−0.898007	+	0.439981i	$0.854985\pi$
$108$	0.941033	+	1.76478i	0.0905509	+	0.169816i
$109$		−	11.3230i		−	1.08454i	−0.840203	−	0.542271i	$-0.817565\pi$
$109$		−	11.3230i		−	1.08454i	0.840203	−	0.542271i	$-0.182435\pi$
$110$	15.5276	−	8.61908i	1.48049	−	0.821797i
$111$	−1.97775	−	3.42556i	−0.187719	−	0.325139i
$112$	7.43801	+	15.1590i	0.702826	+	1.43239i
$113$	−13.3276	−	7.69467i	−1.25375	−	0.723853i	−0.281898	−	0.959444i	$-0.590964\pi$
$113$	−13.3276	−	7.69467i	−1.25375	−	0.723853i	−0.971852	+	0.235591i	$0.924297\pi$
$114$	0.0956854	−	5.67428i	0.00896176	−	0.531445i
$115$	−12.7156	−	22.0240i	−1.18573	−	2.05375i
$116$	5.30911	+	0.179106i	0.492938	+	0.0166296i
$117$	−3.05775	+	1.76539i	−0.282689	+	0.163210i
$118$	2.60667	+	1.56415i	0.239964	+	0.143991i
$119$	−12.2217			−1.12036
$120$	−0.602061	+	11.8920i	−0.0549604	+	1.08559i
$121$	1.05102	+	1.82042i	0.0955471	+	0.165492i
$122$	0.233685	−	13.8579i	0.0211569	−	1.25463i
$123$	−6.43182	−	3.71341i	−0.579938	−	0.334827i
$124$	12.1236	+	0.408998i	1.08873	+	0.0367291i
$125$			32.5118i			2.90794i
$126$	2.89736	+	5.21969i	0.258117	+	0.465007i
$127$	13.3176	+	7.68893i	1.18175	+	0.682282i	0.956418	−	0.292001i	$-0.0943210\pi$
$127$	13.3176	+	7.68893i	1.18175	+	0.682282i	0.225329	+	0.974283i	$0.427654\pi$
$128$	−6.77126	+	9.06366i	−0.598501	+	0.801122i
$129$	−0.320226			−0.0281943
$130$	−21.0179	−	0.354426i	−1.84340	−	0.0310852i
$131$		−	21.3772i		−	1.86774i	−0.357617	−	0.933868i	$-0.616411\pi$
$131$		−	21.3772i		−	1.86774i	0.357617	−	0.933868i	$-0.383589\pi$
$132$	5.96250	+	0.201148i	0.518969	+	0.0175077i
$133$		−	16.9399i		−	1.46887i
$134$	−0.835096	+	11.5457i	−0.0721413	+	0.997394i
$135$			4.20985i			0.362326i
$136$	−3.73061	−	7.28970i	−0.319897	−	0.625086i
$137$			1.32789i			0.113449i	0.998390	+	0.0567245i	$0.0180657\pi$
$137$			1.32789i			0.113449i	−0.998390	+	0.0567245i	$0.981934\pi$
$138$	0.144041	−	8.54187i	0.0122616	−	0.727132i
$139$	−3.74623			−0.317751			−0.158875	−	0.987299i	$-0.550787\pi$
$139$	−3.74623			−0.317751			−0.158875	+	0.987299i	$0.550787\pi$
$140$	−1.19837	+	35.5224i	−0.101281	+	3.00219i
$141$	−2.22823	−	1.28647i	−0.187651	−	0.108340i
$142$	−2.27572	+	1.26321i	−0.190974	+	0.106006i
$143$			10.5321i			0.880741i
$144$	−2.22891	+	3.32144i	−0.185743	+	0.276786i
$145$	9.68356	+	5.59081i	0.804176	+	0.464291i
$146$	−17.4558	−	0.294356i	−1.44465	−	0.0243611i
$147$	5.40996	+	9.37033i	0.446206	+	0.772851i
$148$	4.18424	−	6.71385i	0.343942	−	0.551875i
$149$	−8.25723			−0.676458			−0.338229	−	0.941064i	$-0.609828\pi$
$149$	−8.25723			−0.676458			−0.338229	+	0.941064i	$0.609828\pi$
$150$	−9.25782	+	15.4283i	−0.755898	+	1.25971i
$151$	0.928470	−	0.536052i	0.0755578	−	0.0436233i	−0.461745	−	0.887013i	$-0.652777\pi$
$151$	0.928470	−	0.536052i	0.0755578	−	0.0436233i	0.537303	+	0.843389i	$0.319443\pi$
$152$	10.1039	−	5.17082i	0.819536	−	0.419409i
$153$	−1.44760	−	2.50731i	−0.117031	−	0.202704i
$154$	17.8054	+	0.300252i	1.43480	+	0.0241950i
$155$	22.1129	+	12.7669i	1.77615	+	1.02546i
$156$	−5.99297	−	3.73497i	−0.479822	−	0.299037i
$157$	−3.89226	−	6.74159i	−0.310636	−	0.538037i	0.667864	−	0.744283i	$-0.267209\pi$
$157$	−3.89226	−	6.74159i	−0.310636	−	0.538037i	−0.978500	+	0.206246i	$0.933875\pi$
$158$	−5.81703	−	10.4796i	−0.462778	−	0.833710i
$159$			6.08222i			0.482352i
$160$	−21.5534	+	10.1283i	−1.70394	+	0.800710i
$161$		−	25.5007i		−	2.00974i
$162$	−0.727656	+	1.21265i	−0.0571701	+	0.0952747i
$163$	−4.74776	−	2.74112i	−0.371873	−	0.214701i	0.302403	−	0.953180i	$-0.402211\pi$
$163$	−4.74776	−	2.74112i	−0.371873	−	0.214701i	−0.674276	+	0.738479i	$0.735544\pi$
$164$	0.500812	−	14.8452i	0.0391068	−	1.15922i
$165$	10.8753	+	6.27887i	0.846643	+	0.488809i
$166$	−0.195425	+	11.5890i	−0.0151680	+	0.899481i
$167$	4.58272	+	2.64583i	0.354621	+	0.204741i	0.666719	−	0.745309i	$-0.267698\pi$
$167$	4.58272	+	2.64583i	0.354621	+	0.204741i	−0.312098	+	0.950050i	$0.601032\pi$
$168$	−6.48510	+	10.0251i	−0.500337	+	0.773454i
$169$	−0.266789	+	0.462092i	−0.0205222	+	0.0355456i
$170$	0.290624	−	17.2344i	0.0222898	−	1.32182i
$171$	3.47527	−	2.00645i	0.265760	−	0.153437i
$172$	−0.301343	−	0.565129i	−0.0229772	−	0.0430907i
$173$	−11.5724	−	20.0439i	−0.879830	−	1.52391i	−0.851527	−	0.524311i	$-0.824323\pi$
$173$	−11.5724	−	20.0439i	−0.879830	−	1.52391i	−0.0283034	−	0.999599i	$-0.509010\pi$
$174$	1.82301	+	3.28420i	0.138202	+	0.248975i
$175$	−26.8538	+	46.5121i	−2.02996	+	3.51599i
$176$	5.25592	+	10.7118i	0.396180	+	0.807432i
$177$			2.14957i			0.161571i
$178$	−11.0776	+	18.4610i	−0.830305	+	1.38371i
$179$	−17.6635			−1.32023			−0.660117	−	0.751163i	$-0.729493\pi$
$179$	−17.6635			−1.32023			−0.660117	+	0.751163i	$0.729493\pi$
$180$	−7.42946	+	3.96160i	−0.553759	+	0.295280i
$181$	−10.9891	+	19.0336i	−0.816810	+	1.41476i	0.0912104	+	0.995832i	$0.470926\pi$
$181$	−10.9891	+	19.0336i	−0.816810	+	1.41476i	−0.908021	+	0.418925i	$0.862407\pi$
$182$	−18.0742	−	10.8455i	−1.33975	−	0.803923i
$183$	8.48738	−	4.90019i	0.627405	−	0.362232i
$184$	15.2101	−	7.78398i	1.12130	−	0.573842i
$185$	14.4211	−	8.32600i	1.06026	−	0.612140i
$186$	4.16293	+	7.49965i	0.305241	+	0.549901i
$187$	−8.63620			−0.631542
$188$	0.173501	−	5.14296i	0.0126538	−	0.375089i
$189$	−2.11068	+	3.65581i	−0.153530	+	0.265921i
$190$	23.8878	+	0.402821i	1.73301	+	0.0292237i
$191$	12.5653	+	21.7638i	0.909195	+	1.57477i	0.815185	+	0.579200i	$0.196635\pi$
$191$	12.5653	+	21.7638i	0.909195	+	1.57477i	0.0940094	+	0.995571i	$0.470032\pi$
$192$	−7.95909	−	0.807967i	−0.574398	−	0.0583100i
$193$	23.4013			1.68446			0.842232	−	0.539115i	$-0.181241\pi$
$193$	23.4013			1.68446			0.842232	+	0.539115i	$0.181241\pi$
$194$	0.0852168	−	5.05348i	0.00611821	−	0.362818i
$195$	−7.43202	−	12.8726i	−0.532218	−	0.921829i
$196$	−11.4456	+	18.3652i	−0.817545	+	1.31180i
$197$	18.7133	+	10.8042i	1.33327	+	0.769764i	0.985799	−	0.167927i	$-0.0537072\pi$
$197$	18.7133	+	10.8042i	1.33327	+	0.769764i	0.347471	+	0.937691i	$0.387041\pi$
$198$	2.04736	+	3.68839i	0.145500	+	0.262123i
$199$	−8.33084	+	4.80982i	−0.590558	+	0.340959i	−0.765318	−	0.643652i	$-0.777418\pi$
$199$	−8.33084	+	4.80982i	−0.590558	+	0.340959i	0.174760	+	0.984611i	$0.444085\pi$
$200$	−35.9395	−	1.81952i	−2.54130	−	0.128660i
$201$	−7.30425	+	3.69430i	−0.515202	+	0.260576i
$202$	23.3611	−	12.9673i	1.64368	−	0.912379i
$203$	5.60611	+	9.71006i	0.393472	+	0.681513i
$204$	3.06262	−	4.91415i	0.214426	−	0.344060i
$205$	15.6329	−	27.0770i	1.09185	−	1.89114i
$206$	6.44927	−	3.57988i	0.449342	−	0.249422i
$207$	5.23155	−	3.02044i	0.363618	−	0.209935i
$208$	0.951821	−	14.0910i	0.0659969	−	0.977036i
$209$		−	11.9702i		−	0.827999i
$210$	−21.9741	+	12.1974i	−1.51636	+	0.841703i
$211$	−0.588121	+	0.339552i	−0.0404879	+	0.0233757i	−0.520107	−	0.854101i	$-0.674108\pi$
$211$	−0.588121	+	0.339552i	−0.0404879	+	0.0233757i	0.479619	+	0.877477i	$0.340775\pi$
$212$	−10.7338	+	5.72357i	−0.737200	+	0.393097i
$213$	−1.59389	−	0.920230i	−0.109211	−	0.0630531i
$214$	−11.0380	−	6.62341i	−0.754542	−	0.452767i
$215$		−	1.34810i		−	0.0919397i
$216$	−2.82481	−	0.143013i	−0.192204	−	0.00973078i
$217$	12.8018	+	22.1734i	0.869046	+	1.50523i
$218$	13.7308	+	8.23922i	0.929965	+	0.558030i
$219$	−6.17242	−	10.6909i	−0.417093	−	0.722427i
$220$	−0.846804	+	25.1012i	−0.0570915	+	1.69232i
$221$	8.85277	+	5.11115i	0.595501	+	0.343813i
$222$	5.59312	+	0.0943167i	0.375385	+	0.00633012i
$223$		−	21.5026i		−	1.43992i	−0.694014	−	0.719962i	$-0.744159\pi$
$223$		−	21.5026i		−	1.43992i	0.694014	−	0.719962i	$-0.255841\pi$
$224$	−23.7948	−	2.01084i	−1.58986	−	0.134355i
$225$	−12.7228			−0.848187
$226$	19.0288	−	10.5626i	1.26578	−	0.702611i
$227$	18.5127	+	10.6883i	1.22873	+	0.709408i	0.966765	−	0.255668i	$-0.0822955\pi$
$227$	18.5127	+	10.6883i	1.22873	+	0.709408i	0.261967	+	0.965077i	$0.415629\pi$
$228$	6.81128	+	4.24496i	0.451088	+	0.281129i
$229$	6.38410	−	3.68586i	0.421873	−	0.243568i	−0.274005	−	0.961728i	$-0.588349\pi$
$229$	6.38410	−	3.68586i	0.421873	−	0.243568i	0.695878	+	0.718160i	$0.255015\pi$
$230$	35.9599	+	0.606392i	2.37113	+	0.0399843i
$231$	6.29605	+	10.9051i	0.414250	+	0.717502i
$232$	−4.08040	+	6.30775i	−0.267891	+	0.414124i
$233$	9.37212	+	5.41100i	0.613988	+	0.354486i	0.774525	−	0.632544i	$-0.217989\pi$
$233$	9.37212	+	5.41100i	0.613988	+	0.354486i	−0.160537	+	0.987030i	$0.551322\pi$
$234$	0.0841897	−	4.99257i	0.00550365	−	0.326375i
$235$	5.41585	−	9.38052i	0.353291	−	0.611918i
$236$	−3.79352	+	2.02281i	−0.246937	+	0.131674i
$237$	4.23762	−	7.33977i	0.275263	−	0.476769i
$238$	8.89317	−	14.8206i	0.576459	−	0.960676i
$239$	−2.89158	+	5.00837i	−0.187041	+	0.323965i	−0.944262	−	0.329194i	$-0.893223\pi$
$239$	−2.89158	+	5.00837i	−0.187041	+	0.323965i	0.757221	+	0.653158i	$0.226556\pi$
$240$	−13.9827	−	9.38338i	−0.902582	−	0.605695i
$241$	23.2961			1.50064			0.750318	−	0.661077i	$-0.229900\pi$
$241$	23.2961			1.50064			0.750318	+	0.661077i	$0.229900\pi$
$242$	−2.97231	−	0.0501220i	−0.191067	−	0.00322196i
$243$	−1.00000			−0.0641500
$244$	16.6347	+	10.3671i	1.06493	+	0.663688i
$245$	−39.4476	+	22.7751i	−2.52022	+	1.45505i
$246$	9.18322	−	5.09745i	0.585500	−	0.325001i
$247$	−7.08433	+	12.2704i	−0.450765	+	0.780748i
$248$	−9.31780	+	14.4041i	−0.591681	+	0.914661i
$249$	−7.09780	+	4.09792i	−0.449805	+	0.259695i
$250$	−39.4254	−	23.6574i	−2.49348	−	1.49623i
$251$	7.86623	+	13.6247i	0.496512	+	0.859984i	0.999992	−	0.00402320i	$-0.00128063\pi$
$251$	7.86623	+	13.6247i	0.496512	+	0.859984i	−0.503480	+	0.864007i	$0.667947\pi$
$252$	−8.43793	−	0.284659i	−0.531540	−	0.0179318i
$253$		−	18.0196i		−	1.13288i
$254$	−19.0146	+	10.5547i	−1.19308	+	0.662260i
$255$	10.5554	−	6.09416i	0.661004	−	0.381631i
$256$	−6.06388	−	14.8064i	−0.378993	−	0.925400i
$257$	0.878207	−	1.52110i	0.0547810	−	0.0948835i	−0.837334	−	0.546691i	$-0.815887\pi$
$257$	0.878207	−	1.52110i	0.0547810	−	0.0948835i	0.892115	+	0.451807i	$0.149221\pi$
$258$	0.233014	−	0.388321i	0.0145068	−	0.0241758i
$259$	16.6976			1.03754
$260$	15.7236	−	25.2295i	0.975138	−	1.56467i
$261$	−1.32803	+	2.30022i	−0.0822031	+	0.142380i
$262$	25.9231	+	15.5553i	1.60153	+	0.961008i
$263$		−	13.1413i		−	0.810325i	−0.914245	−	0.405162i	$-0.867215\pi$
$263$		−	13.1413i		−	0.810325i	0.914245	−	0.405162i	$-0.132785\pi$
$264$	−4.58257	+	7.08405i	−0.282038	+	0.435993i
$265$	−25.6052			−1.57292
$266$	20.5421	+	12.3264i	1.25952	+	0.755781i
$267$	−15.2237			−0.931678
$268$	−13.3932	−	9.41396i	−0.818119	−	0.575049i
$269$	−4.38757			−0.267515			−0.133758	−	0.991014i	$-0.542704\pi$
$269$	−4.38757			−0.267515			−0.133758	+	0.991014i	$0.542704\pi$
$270$	−5.10506	−	3.06332i	−0.310684	−	0.186428i
$271$	−9.96942			−0.605599			−0.302800	−	0.953054i	$-0.597921\pi$
$271$	−9.96942			−0.605599			−0.302800	+	0.953054i	$0.597921\pi$
$272$	11.5544	+	0.780480i	0.700591	+	0.0473235i
$273$		−	14.9047i		−	0.902075i
$274$	−1.61026	−	0.966246i	−0.0972794	−	0.0583730i
$275$	−18.9757	+	32.8669i	−1.14428	+	1.98195i
$276$	10.2535	+	6.39021i	0.617186	+	0.384646i
$277$	16.7737			1.00783			0.503916	−	0.863753i	$-0.331892\pi$
$277$	16.7737			1.00783			0.503916	+	0.863753i	$0.331892\pi$
$278$	2.72597	−	4.54286i	0.163493	−	0.272462i
$279$	−3.03263	+	5.25267i	−0.181559	+	0.314469i
$280$	−42.2042	−	27.3013i	−2.52218	−	1.63156i
$281$	−18.3619	+	10.6012i	−1.09538	+	0.632416i	−0.935003	−	0.354640i	$-0.884603\pi$
$281$	−18.3619	+	10.6012i	−1.09538	+	0.632416i	−0.160374	+	0.987056i	$0.551270\pi$
$282$	3.18143	−	1.76596i	0.189451	−	0.105161i
$283$		−	9.55127i		−	0.567764i	−0.958859	−	0.283882i	$-0.908378\pi$
$283$		−	9.55127i		−	0.567764i	0.958859	−	0.283882i	$-0.0916224\pi$
$284$	0.124107	−	3.67883i	0.00736442	−	0.218298i
$285$	8.44683	+	14.6303i	0.500347	+	0.866626i
$286$	−12.7718	−	7.66377i	−0.755211	−	0.453168i
$287$	27.1511	−	15.6757i	1.60268	−	0.925305i
$288$	−2.40585	−	5.11975i	−0.141766	−	0.301684i
$289$	4.30893	−	7.46329i	0.253467	−	0.439017i
$290$	−13.8260	+	7.67457i	−0.811890	+	0.450666i
$291$	3.09505	−	1.78693i	0.181435	−	0.104752i
$292$	13.0587	−	20.9535i	0.764205	−	1.22621i
$293$	−11.6905			−0.682965			−0.341483	−	0.939888i	$-0.610929\pi$
$293$	−11.6905			−0.682965			−0.341483	+	0.939888i	$0.610929\pi$
$294$	−15.2995	−	0.257995i	−0.892285	−	0.0150466i
$295$	−9.04935			−0.526874
$296$	5.09686	+	9.95939i	0.296249	+	0.578878i
$297$	−1.49147	+	2.58331i	−0.0865440	+	0.149899i
$298$	6.00842	−	10.0131i	0.348059	−	0.580044i
$299$	−10.6645	+	18.4715i	−0.616744	+	1.06823i
$300$	−11.9726	−	22.4530i	−0.691237	−	1.29632i
$301$	0.675895	−	1.17068i	0.0389579	−	0.0674771i
$302$	−0.0255638	+	1.51597i	−0.00147103	+	0.0872342i
$303$	16.3618	+	9.44651i	0.939963	+	0.542688i
$304$	−1.08179	+	16.0151i	−0.0620448	+	0.918528i
$305$	20.6290	+	35.7305i	1.18122	+	2.04593i
$306$	4.09384	+	0.0690344i	0.234029	+	0.00394643i
$307$	19.8605	−	11.4665i	1.13350	−	0.654425i	0.188685	−	0.982038i	$-0.439577\pi$
$307$	19.8605	−	11.4665i	1.13350	−	0.654425i	0.944812	+	0.327612i	$0.106244\pi$
$308$	−13.3203	+	21.3732i	−0.758995	+	1.21785i
$309$	4.51699	+	2.60789i	0.256963	+	0.148357i
$310$	−31.5724	+	17.5253i	−1.79319	+	0.995370i
$311$	17.3718			0.985066			0.492533	−	0.870294i	$-0.336071\pi$
$311$	17.3718			0.985066			0.492533	+	0.870294i	$0.336071\pi$
$312$	8.89003	−	4.54960i	0.503299	−	0.257570i
$313$		−	10.9531i		−	0.619107i	−0.950882	−	0.309554i	$-0.899820\pi$
$313$		−	10.9531i		−	0.619107i	0.950882	−	0.309554i	$-0.100180\pi$
$314$	11.0074	+	0.185618i	0.621183	+	0.0104750i
$315$	−15.3904	−	8.88565i	−0.867150	−	0.500649i
$316$	16.9408	+	0.571509i	0.952997	+	0.0321499i
$317$	11.5481	+	20.0019i	0.648607	+	1.12342i	0.983456	+	0.181149i	$0.0579816\pi$
$317$	11.5481	+	20.0019i	0.648607	+	1.12342i	−0.334848	+	0.942272i	$0.608685\pi$
$318$	−7.37560	−	4.42577i	−0.413603	−	0.248185i
$319$	3.96145	+	6.86143i	0.221798	+	0.384166i
$320$	3.40142	−	33.5066i	0.190145	−	1.87307i
$321$		−	9.10239i		−	0.508046i
$322$	30.9234	+	18.5558i	1.72329	+	1.03407i
$323$	−10.0616	−	5.80905i	−0.559841	−	0.323224i
$324$	−0.941033	−	1.76478i	−0.0522796	−	0.0980435i
$325$	38.9031	−	22.4607i	2.15796	−	1.24590i
$326$	6.77875	−	3.76277i	0.375440	−	0.208401i
$327$			11.3230i			0.626161i
$328$	17.6376	+	11.4095i	0.973873	+	0.629985i
$329$	9.40619	−	5.43067i	0.518580	−	0.299402i
$330$	−15.5276	+	8.61908i	−0.854764	+	0.474465i
$331$	6.40189	−	11.0884i	0.351880	−	0.609473i	−0.634699	−	0.772759i	$-0.718876\pi$
$331$	6.40189	−	11.0884i	0.351880	−	0.609473i	0.986579	+	0.163286i	$0.0522093\pi$
$332$	−13.9112	−	8.66980i	−0.763476	−	0.475817i
$333$	1.97775	+	3.42556i	0.108380	+	0.187719i
$334$	−6.54311	+	3.63197i	−0.358023	+	0.198732i
$335$	−15.5524	−	30.7498i	−0.849721	−	1.68004i
$336$	−7.43801	−	15.1590i	−0.405777	−	0.826990i
$337$	−3.83421	+	2.21368i	−0.208863	+	0.120587i	−0.600783	−	0.799412i	$-0.705144\pi$
$337$	−3.83421	+	2.21368i	−0.208863	+	0.120587i	0.391920	+	0.919999i	$0.371811\pi$
$338$	−0.366225	−	0.659766i	−0.0199200	−	0.0358865i
$339$	13.3276	+	7.69467i	0.723853	+	0.417917i
$340$	20.6878	+	12.8932i	1.12195	+	0.699230i
$341$	9.04617	+	15.6684i	0.489878	+	0.848493i
$342$	−0.0956854	+	5.67428i	−0.00517407	+	0.306830i
$343$	−16.1253			−0.870683
$344$	0.904577	+	0.0457964i	0.0487715	+	0.00246917i
$345$	12.7156	+	22.0240i	0.684583	+	1.18573i
$346$	32.7269	+	0.551874i	1.75941	+	0.0296689i
$347$	−1.97658	+	3.42354i	−0.106109	+	0.183785i	−0.914191	−	0.405285i	$-0.867172\pi$
$347$	−1.97658	+	3.42354i	−0.106109	+	0.183785i	0.808082	+	0.589070i	$0.200506\pi$
$348$	−5.30911	−	0.179106i	−0.284598	−	0.00960108i
$349$	10.5125			0.562723			0.281362	−	0.959602i	$-0.409214\pi$
$349$	10.5125			0.562723			0.281362	+	0.959602i	$0.409214\pi$
$350$	−36.8625	−	66.4090i	−1.97039	−	3.54971i
$351$	3.05775	−	1.76539i	0.163210	−	0.0942296i
$352$	−16.8142	−	1.42092i	−0.896198	−	0.0757352i
$353$	6.81039	−	3.93198i	0.362481	−	0.209278i	−0.307688	−	0.951487i	$-0.599555\pi$
$353$	6.81039	−	3.93198i	0.362481	−	0.209278i	0.670168	+	0.742209i	$0.266222\pi$
$354$	−2.60667	−	1.56415i	−0.138543	−	0.0831335i
$355$	3.87403	−	6.71001i	0.205612	−	0.356130i
$356$	−14.3260	−	26.8666i	−0.759279	−	1.42393i
$357$	12.2217			0.646839
$358$	12.8530	−	21.4196i	0.679300	−	1.13206i
$359$		−	4.97327i		−	0.262479i	−0.991351	−	0.131240i	$-0.958104\pi$
$359$		−	4.97327i		−	0.262479i	0.991351	−	0.131240i	$-0.0418957\pi$
$360$	0.602061	−	11.8920i	0.0317314	−	0.626764i
$361$	−1.44834	+	2.50861i	−0.0762287	+	0.132032i
$362$	−15.0848	−	27.1758i	−0.792841	−	1.42833i
$363$	−1.05102	−	1.82042i	−0.0551641	−	0.0955471i
$364$	26.3036	−	14.0258i	1.37868	−	0.735153i
$365$	45.0072	−	25.9849i	2.35579	−	1.36011i
$366$	−0.233685	+	13.8579i	−0.0122149	+	0.724362i
$367$	−0.579609	+	1.00391i	−0.0302554	+	0.0524038i	−0.880757	−	0.473569i	$-0.842965\pi$
$367$	−0.579609	+	1.00391i	−0.0302554	+	0.0524038i	0.850501	+	0.525973i	$0.176299\pi$
$368$	−1.62849	+	24.1085i	−0.0848907	+	1.25674i
$369$	6.43182	+	3.71341i	0.334827	+	0.193313i
$370$	−0.397059	+	23.5461i	−0.0206421	+	1.22411i
$371$	−22.2354	−	12.8376i	−1.15441	−	0.666497i
$372$	−12.1236	−	0.408998i	−0.628581	−	0.0212055i
$373$	−8.22450	−	4.74842i	−0.425848	−	0.245864i	0.271728	−	0.962374i	$-0.412405\pi$
$373$	−8.22450	−	4.74842i	−0.425848	−	0.245864i	−0.697576	+	0.716510i	$0.745738\pi$
$374$	6.28419	−	10.4727i	0.324947	−	0.541529i
$375$		−	32.5118i		−	1.67890i
$376$	6.11035	+	3.95270i	0.315117	+	0.203845i
$377$		−	9.37798i		−	0.482991i
$378$	−2.89736	−	5.21969i	−0.149024	−	0.268472i
$379$	8.98302	+	15.5590i	0.461427	+	0.799214i	0.999032	−	0.0439821i	$-0.0140045\pi$
$379$	8.98302	+	15.5590i	0.461427	+	0.799214i	−0.537606	+	0.843196i	$0.680671\pi$
$380$	−17.8706	+	28.6744i	−0.916743	+	1.47097i
$381$	−13.3176	−	7.68893i	−0.682282	−	0.393916i
$382$	−35.5350	−	0.599227i	−1.81813	−	0.0306591i
$383$	−16.1208	−	27.9221i	−0.823736	−	1.42675i	−0.902881	−	0.429890i	$-0.858552\pi$
$383$	−16.1208	−	27.9221i	−0.823736	−	1.42675i	0.0791448	−	0.996863i	$-0.474781\pi$
$384$	6.77126	−	9.06366i	0.345545	−	0.462528i
$385$	−45.9087	+	26.5054i	−2.33972	+	1.35084i
$386$	−17.0281	+	28.3776i	−0.866709	+	1.44438i
$387$	0.320226			0.0162780
$388$	6.06608	+	3.78053i	0.307959	+	0.191927i
$389$	−2.44386	−	4.23289i	−0.123909	−	0.214616i	0.797397	−	0.603455i	$-0.206210\pi$
$389$	−2.44386	−	4.23289i	−0.123909	−	0.214616i	−0.921306	+	0.388839i	$0.872876\pi$
$390$	21.0179	+	0.354426i	1.06429	+	0.0179470i
$391$	−15.1463	−	8.74474i	−0.765983	−	0.442241i
$392$	−13.9420	−	27.2431i	−0.704179	−	1.37598i
$393$			21.3772i			1.07834i
$394$	−26.7185	+	14.8310i	−1.34606	+	0.747175i
$395$	30.8993	+	17.8397i	1.55471	+	0.897614i
$396$	−5.96250	−	0.201148i	−0.299627	−	0.0101081i
$397$	−33.5318			−1.68292			−0.841458	−	0.540323i	$-0.818302\pi$
$397$	−33.5318			−1.68292			−0.841458	+	0.540323i	$0.818302\pi$
$398$	0.229375	−	13.6023i	0.0114975	−	0.681821i
$399$			16.9399i			0.848055i
$400$	28.3580	−	42.2580i	1.41790	−	2.11290i
$401$			2.67250i			0.133458i	0.997771	+	0.0667292i	$0.0212564\pi$
$401$			2.67250i			0.133458i	−0.997771	+	0.0667292i	$0.978744\pi$
$402$	0.835096	−	11.5457i	0.0416508	−	0.575846i
$403$		−	21.4151i		−	1.06676i
$404$	−1.27401	+	37.7646i	−0.0633843	+	1.87886i
$405$		−	4.20985i		−	0.209189i
$406$	−15.8542	−	0.267349i	−0.786831	−	0.0132683i
$407$	11.7990			0.584856
$408$	3.73061	+	7.28970i	0.184693	+	0.360894i
$409$	−23.1035	−	13.3388i	−1.14240	−	0.659562i	−0.195373	−	0.980729i	$-0.562592\pi$
$409$	−23.1035	−	13.3388i	−1.14240	−	0.659562i	−0.947023	+	0.321167i	$0.895925\pi$
$410$	21.4595	+	38.6599i	1.05981	+	1.90928i
$411$		−	1.32789i		−	0.0654999i
$412$	−0.351714	+	10.4256i	−0.0173277	+	0.513633i
$413$	−7.85841	−	4.53706i	−0.386687	−	0.223254i
$414$	−0.144041	+	8.54187i	−0.00707925	+	0.419810i
$415$	−17.2516	−	29.8806i	−0.846847	−	1.46678i
$416$	16.3949	+	11.4076i	0.803824	+	0.559306i
$417$	3.74623			0.183454
$418$	14.5157	+	8.71022i	0.709986	+	0.426031i
$419$	−17.6225	+	10.1743i	−0.860914	+	0.497049i	−0.864318	−	0.502945i	$-0.832250\pi$
$419$	−17.6225	+	10.1743i	−0.860914	+	0.497049i	0.00340393	+	0.999994i	$0.498916\pi$
$420$	1.19837	−	35.5224i	0.0584744	−	1.73331i
$421$	−0.295100	−	0.511128i	−0.0143823	−	0.0249109i	0.858745	−	0.512404i	$-0.171245\pi$
$421$	−0.295100	−	0.511128i	−0.0143823	−	0.0249109i	−0.873127	+	0.487493i	$0.837912\pi$
$422$	0.0161929	−	0.960261i	0.000788257	−	0.0467448i
$423$	2.22823	+	1.28647i	0.108340	+	0.0625504i
$424$	0.869835	−	17.1811i	0.0422429	−	0.834389i
$425$	18.4175	+	31.9000i	0.893379	+	1.54738i
$426$	2.27572	−	1.26321i	0.110259	−	0.0612028i
$427$			41.3710i			2.00208i
$428$	16.0637	−	8.56565i	0.776470	−	0.414036i
$429$		−	10.5321i		−	0.508496i
$430$	1.63477	+	0.980954i	0.0788357	+	0.0473058i
$431$	−0.606067	−	0.349913i	−0.0291932	−	0.0168547i	0.485332	−	0.874330i	$-0.338699\pi$
$431$	−0.606067	−	0.349913i	−0.0291932	−	0.0168547i	−0.514526	+	0.857475i	$0.672032\pi$
$432$	2.22891	−	3.32144i	0.107239	−	0.159803i
$433$	−6.18249	−	3.56946i	−0.297111	−	0.171537i	0.344033	−	0.938958i	$-0.388207\pi$
$433$	−6.18249	−	3.56946i	−0.297111	−	0.171537i	−0.641145	+	0.767420i	$0.721540\pi$
$434$	−36.2039	−	0.610507i	−1.73784	−	0.0293053i
$435$	−9.68356	−	5.59081i	−0.464291	−	0.268059i
$436$	−19.9826	+	10.6553i	−0.956991	+	0.510295i
$437$	12.1207	−	20.9936i	0.579811	−	1.00426i
$438$	17.4558	+	0.294356i	0.834068	+	0.0140649i
$439$	−6.06655	+	3.50252i	−0.289541	+	0.167166i	−0.637735	−	0.770256i	$-0.720128\pi$
$439$	−6.06655	+	3.50252i	−0.289541	+	0.167166i	0.348194	+	0.937422i	$0.386795\pi$
$440$	−29.8228	−	19.2919i	−1.42174	−	0.919706i
$441$	−5.40996	−	9.37033i	−0.257617	−	0.446206i
$442$	−12.6398	+	7.01614i	−0.601214	+	0.333724i
$443$	10.5952	−	18.3514i	0.503391	−	0.871899i	−0.496601	−	0.867979i	$-0.665419\pi$
$443$	10.5952	−	18.3514i	0.503391	−	0.871899i	0.999992	−	0.00392049i	$-0.00124793\pi$
$444$	−4.18424	+	6.71385i	−0.198575	+	0.318625i
$445$		−	64.0896i		−	3.03814i
$446$	26.0752	+	15.6465i	1.23469	+	0.740885i
$447$	8.25723			0.390553
$448$	19.7529	−	27.3916i	0.933237	−	1.29413i
$449$	5.33241	−	9.23601i	0.251652	−	0.435874i	−0.712329	−	0.701846i	$-0.752359\pi$
$449$	5.33241	−	9.23601i	0.251652	−	0.435874i	0.963981	+	0.265972i	$0.0856928\pi$
$450$	9.25782	−	15.4283i	0.436418	−	0.727296i
$451$	19.1858	−	11.0769i	0.903422	−	0.521591i
$452$	−1.03775	+	30.7612i	−0.0488115	+	1.44688i
$453$	−0.928470	+	0.536052i	−0.0436233	+	0.0251859i
$454$	−26.4321	+	14.6720i	−1.24052	+	0.688590i
$455$	62.7466			2.94160
$456$	−10.1039	+	5.17082i	−0.473159	+	0.242146i
$457$	15.4705	−	26.7957i	0.723679	−	1.25345i	−0.235836	−	0.971793i	$-0.575783\pi$
$457$	15.4705	−	26.7957i	0.723679	−	1.25345i	0.959515	−	0.281657i	$-0.0908839\pi$
$458$	−0.175775	+	10.4237i	−0.00821342	+	0.487068i
$459$	1.44760	+	2.50731i	0.0675680	+	0.117031i
$460$	−26.9018	+	43.1655i	−1.25430	+	2.01260i
$461$	1.61417			0.0751794			0.0375897	−	0.999293i	$-0.488032\pi$
$461$	1.61417			0.0751794			0.0375897	+	0.999293i	$0.488032\pi$
$462$	−17.8054	−	0.300252i	−0.828382	−	0.0139690i
$463$	15.0314	+	26.0352i	0.698570	+	1.20996i	0.968962	+	0.247209i	$0.0795134\pi$
$463$	15.0314	+	26.0352i	0.698570	+	1.20996i	−0.270392	+	0.962750i	$0.587153\pi$
$464$	−4.67996	−	9.53796i	−0.217262	−	0.442789i
$465$	−22.1129	−	12.7669i	−1.02546	−	0.592051i
$466$	−13.3813	+	7.42774i	−0.619878	+	0.344084i
$467$	27.1159	−	15.6554i	1.25478	−	0.724445i	0.282722	−	0.959202i	$-0.408763\pi$
$467$	27.1159	−	15.6554i	1.25478	−	0.724445i	0.972054	+	0.234756i	$0.0754292\pi$
$468$	5.99297	+	3.73497i	0.277025	+	0.172649i
$469$	1.91130	−	34.5005i	0.0882555	−	1.59308i
$470$	7.43440	+	13.3933i	0.342923	+	0.617787i
$471$	3.89226	+	6.74159i	0.179346	+	0.310636i
$472$	0.307416	−	6.07212i	0.0141500	−	0.279492i
$473$	0.477608	−	0.827241i	0.0219604	−	0.0380366i
$474$	5.81703	+	10.4796i	0.267185	+	0.481343i
$475$	−44.2151	+	25.5276i	−2.02873	+	1.17129i
$476$	11.5010	+	21.5686i	0.527147	+	0.988594i
$477$		−	6.08222i		−	0.278486i
$478$	−3.96932	−	7.15085i	−0.181552	−	0.327072i
$479$	6.77296	−	3.91037i	0.309464	−	0.178669i	−0.337222	−	0.941425i	$-0.609487\pi$
$479$	6.77296	−	3.91037i	0.309464	−	0.178669i	0.646687	+	0.762756i	$0.276154\pi$
$480$	21.5534	−	10.1283i	0.983772	−	0.462290i
$481$	−12.0949	−	6.98299i	−0.551480	−	0.318397i
$482$	−16.9516	+	28.2500i	−0.772124	+	1.28675i
$483$			25.5007i			1.16032i
$484$	2.22360	−	3.56789i	0.101073	−	0.162177i
$485$	7.52269	+	13.0297i	0.341588	+	0.591647i
$486$	0.727656	−	1.21265i	0.0330072	−	0.0550069i
$487$	9.13588	+	15.8238i	0.413986	+	0.717045i	0.995321	−	0.0966192i	$-0.0308029\pi$
$487$	9.13588	+	15.8238i	0.413986	+	0.717045i	−0.581335	+	0.813664i	$0.697470\pi$
$488$	−24.6760	+	12.6283i	−1.11703	+	0.571656i
$489$	4.74776	+	2.74112i	0.214701	+	0.123958i
$490$	1.08612	−	64.4085i	0.0490660	−	2.90968i
$491$		−	7.07454i		−	0.319270i	−0.987176	−	0.159635i	$-0.948968\pi$
$491$		−	7.07454i		−	0.319270i	0.987176	−	0.159635i	$-0.0510317\pi$
$492$	−0.500812	+	14.8452i	−0.0225783	+	0.669273i
$493$	7.68981			0.346332
$494$	−9.72474	−	17.5194i	−0.437537	−	0.788237i
$495$	−10.8753	−	6.27887i	−0.488809	−	0.282214i
$496$	−10.6869	−	21.7804i	−0.479858	−	0.977971i
$497$	6.72837	−	3.88463i	0.301809	−	0.174249i
$498$	0.195425	−	11.5890i	0.00875722	−	0.519316i
$499$	−13.1374	−	22.7546i	−0.588110	−	1.01864i	−0.994480	−	0.104928i	$-0.966539\pi$
$499$	−13.1374	−	22.7546i	−0.588110	−	1.01864i	0.406370	−	0.913709i	$-0.366794\pi$
$500$	57.3762	−	30.5947i	2.56594	−	1.36823i
$501$	−4.58272	−	2.64583i	−0.204741	−	0.118207i
$502$	−22.2459	−	0.375132i	−0.992882	−	0.0167430i
$503$	15.9903	−	27.6960i	0.712973	−	1.23490i	−0.250764	−	0.968048i	$-0.580682\pi$
$503$	15.9903	−	27.6960i	0.712973	−	1.23490i	0.963736	−	0.266857i	$-0.0859850\pi$
$504$	6.48510	−	10.0251i	0.288869	−	0.446554i
$505$	−39.7683	+	68.8808i	−1.76967	+	3.06516i
$506$	21.8514	+	13.1121i	0.971414	+	0.582902i
$507$	0.266789	−	0.462092i	0.0118485	−	0.0205222i
$508$	1.03697	−	30.7382i	0.0460082	−	1.36379i
$509$	−10.0313			−0.444630			−0.222315	−	0.974975i	$-0.571361\pi$
$509$	−10.0313			−0.444630			−0.222315	+	0.974975i	$0.571361\pi$
$510$	−0.290624	+	17.2344i	−0.0128691	+	0.763153i
$511$	52.1121			2.30530
$512$	22.3674	+	3.42061i	0.988508	+	0.151171i
$513$	−3.47527	+	2.00645i	−0.153437	+	0.0885868i
$514$	1.20553	+	2.17179i	0.0531734	+	0.0957937i
$515$	−10.9788	+	19.0158i	−0.483784	+	0.837938i
$516$	0.301343	+	0.565129i	0.0132659	+	0.0248784i
$517$	6.64670	−	3.83747i	0.292322	−	0.168772i
$518$	−12.1501	+	20.2483i	−0.533844	+	0.889659i
$519$	11.5724	+	20.0439i	0.507970	+	0.879830i
$520$	19.1531	+	37.4256i	0.839919	+	1.64122i
$521$			17.9011i			0.784263i	0.919909	+	0.392131i	$0.128262\pi$
$521$			17.9011i			0.784263i	−0.919909	+	0.392131i	$0.871738\pi$
$522$	−1.82301	−	3.28420i	−0.0797908	−	0.143746i
$523$	−31.7420	+	18.3262i	−1.38798	+	0.801350i	−0.993087	−	0.117378i	$-0.962551\pi$
$523$	−31.7420	+	18.3262i	−1.38798	+	0.801350i	−0.394891	+	0.918728i	$0.629218\pi$
$524$	−37.7261	+	20.1167i	−1.64807	+	0.878801i
$525$	26.8538	−	46.5121i	1.17200	−	2.02996i
$526$	15.9357	+	9.56232i	0.694831	+	0.416937i
$527$	17.5601			0.764930
$528$	−5.25592	−	10.7118i	−0.228735	−	0.466171i
$529$	6.74606	−	11.6845i	0.293307	−	0.508023i
$530$	18.6318	−	31.0501i	0.809314	−	1.34873i
$531$		−	2.14957i		−	0.0932833i
$532$	−29.8952	+	15.9410i	−1.29612	+	0.691130i
$533$	−26.2225			−1.13582
$534$	11.0776	−	18.4610i	0.479377	−	0.798888i
$535$	38.3197			1.65670
$536$	21.1615	−	9.39110i	0.914036	−	0.405634i
$537$	17.6635			0.762237
$538$	3.19264	−	5.32058i	0.137645	−	0.229387i
$539$	−32.2752			−1.39019
$540$	7.42946	−	3.96160i	0.319713	−	0.170480i
$541$		−	30.9797i		−	1.33192i	−0.745987	−	0.665961i	$-0.768022\pi$
$541$		−	30.9797i		−	1.33192i	0.745987	−	0.665961i	$-0.231978\pi$
$542$	7.25431	−	12.0894i	0.311599	−	0.519284i
$543$	10.9891	−	19.0336i	0.471586	−	0.816810i
$544$	−9.35411	+	13.4436i	−0.401054	+	0.576388i
$545$	−47.6679			−2.04187
$546$	18.0742	+	10.8455i	0.773504	+	0.464145i
$547$	2.97710	−	5.15649i	0.127292	−	0.220476i	−0.795335	−	0.606171i	$-0.792705\pi$
$547$	2.97710	−	5.15649i	0.127292	−	0.220476i	0.922626	+	0.385695i	$0.126038\pi$
$548$	2.34343	−	1.24959i	0.100106	−	0.0533797i
$549$	−8.48738	+	4.90019i	−0.362232	+	0.209135i
$550$	−26.0482	−	46.9267i	−1.11070	−	2.00096i
$551$			10.6585i			0.454067i
$552$	−15.2101	+	7.78398i	−0.647384	+	0.331308i
$553$	17.8885	+	30.9838i	0.760698	+	1.31757i
$554$	−12.2055	+	20.3405i	−0.518560	+	0.864187i
$555$	−14.4211	+	8.32600i	−0.612140	+	0.353419i
$556$	3.52532	+	6.61128i	0.149507	+	0.280381i
$557$	8.78267	−	15.2120i	0.372134	−	0.644554i	−0.617760	−	0.786367i	$-0.711960\pi$
$557$	8.78267	−	15.2120i	0.372134	−	0.644554i	0.989894	+	0.141812i	$0.0452930\pi$
$558$	−4.16293	−	7.49965i	−0.176231	−	0.317486i
$559$	−0.979169	+	0.565324i	−0.0414144	+	0.0239106i
$560$	63.8170	−	31.3129i	2.69676	−	1.32321i
$561$	8.63620			0.364621
$562$	0.505562	−	29.9805i	0.0213258	−	1.26465i
$563$	−30.8262			−1.29917			−0.649584	−	0.760290i	$-0.725057\pi$
$563$	−30.8262			−1.29917			−0.649584	+	0.760290i	$0.725057\pi$
$564$	−0.173501	+	5.14296i	−0.00730570	+	0.216558i
$565$	−32.3934	+	56.1069i	−1.36280	+	2.36044i
$566$	11.5823	+	6.95004i	0.486842	+	0.292132i
$567$	2.11068	−	3.65581i	0.0886403	−	0.153530i
$568$	4.37082	+	2.82742i	0.183395	+	0.118636i
$569$	−11.3813	+	19.7131i	−0.477131	+	0.826415i	−0.999656	−	0.0262087i	$-0.991657\pi$
$569$	−11.3813	+	19.7131i	−0.477131	+	0.826415i	0.522526	+	0.852624i	$0.324990\pi$
$570$	−23.8878	−	0.402821i	−1.00055	−	0.0168723i
$571$	25.8089	+	14.9008i	1.08007	+	0.623578i	0.930915	−	0.365236i	$-0.119012\pi$
$571$	25.8089	+	14.9008i	1.08007	+	0.623578i	0.149154	+	0.988814i	$0.452345\pi$
$572$	18.5869	−	9.91108i	0.777158	−	0.414403i
$573$	−12.5653	−	21.7638i	−0.524924	−	0.909195i
$574$	−0.747557	+	44.3312i	−0.0312024	+	1.85035i
$575$	−66.5599	+	38.4284i	−2.77574	+	1.60257i
$576$	7.95909	+	0.807967i	0.331629	+	0.0336653i
$577$	−14.6654	−	8.46708i	−0.610529	−	0.352489i	0.162644	−	0.986685i	$-0.447998\pi$
$577$	−14.6654	−	8.46708i	−0.610529	−	0.352489i	−0.773172	+	0.634196i	$0.781331\pi$
$578$	5.91492	+	10.6559i	0.246028	+	0.443228i
$579$	−23.4013			−0.972526
$580$	0.754008	−	22.3505i	0.0313085	−	0.928055i
$581$		−	34.5976i		−	1.43535i
$582$	−0.0852168	+	5.05348i	−0.00353235	+	0.209473i
$583$	−15.7122	−	9.07147i	−0.650735	−	0.375702i
$584$	15.9070	+	31.0826i	0.658235	+	1.28621i
$585$	7.43202	+	12.8726i	0.307276	+	0.532218i
$586$	8.50665	−	14.1764i	0.351406	−	0.585623i
$587$	−9.69460	−	16.7915i	−0.400139	−	0.693061i	0.593603	−	0.804758i	$-0.297705\pi$
$587$	−9.69460	−	16.7915i	−0.400139	−	0.693061i	−0.993742	+	0.111697i	$0.964371\pi$
$588$	11.4456	−	18.3652i	0.472010	−	0.757368i
$589$			24.3392i			1.00288i
$590$	6.58482	−	10.9737i	0.271093	−	0.451779i
$591$	−18.7133	−	10.8042i	−0.769764	−	0.444423i
$592$	−15.7860	−	1.06631i	−0.648800	−	0.0438252i
$593$	−6.04930	+	3.49257i	−0.248415	+	0.143423i	−0.619038	−	0.785361i	$-0.712477\pi$
$593$	−6.04930	+	3.49257i	−0.248415	+	0.143423i	0.370623	+	0.928783i	$0.379144\pi$
$594$	−2.04736	−	3.68839i	−0.0840043	−	0.151337i
$595$			51.4513i			2.10930i
$596$	7.77032	+	14.5722i	0.318285	+	0.596901i
$597$	8.33084	−	4.80982i	0.340959	−	0.196853i
$598$	−14.6393	−	26.3732i	−0.598645	−	1.07848i
$599$	2.15082	−	3.72532i	0.0878800	−	0.152213i	−0.818735	−	0.574172i	$-0.805324\pi$
$599$	2.15082	−	3.72532i	0.0878800	−	0.152213i	0.906615	+	0.421959i	$0.138657\pi$
$600$	35.9395	+	1.81952i	1.46722	+	0.0742817i
$601$	12.9532	+	22.4357i	0.528373	+	0.915169i	0.999453	+	0.0330786i	$0.0105312\pi$
$601$	12.9532	+	22.4357i	0.528373	+	0.915169i	−0.471079	+	0.882091i	$0.656136\pi$
$602$	0.927809	+	1.67148i	0.0378147	+	0.0681244i
$603$	7.30425	−	3.69430i	0.297452	−	0.150444i
$604$	−1.81974	−	1.13410i	−0.0740440	−	0.0461461i
$605$	7.66367	−	4.42462i	0.311573	−	0.179887i
$606$	−23.3611	+	12.9673i	−0.948979	+	0.526762i
$607$	−34.5048	−	19.9213i	−1.40050	−	0.808582i	−0.406061	−	0.913846i	$-0.633098\pi$
$607$	−34.5048	−	19.9213i	−1.40050	−	0.808582i	−0.994444	+	0.105264i	$0.966431\pi$
$608$	−18.6335	−	12.9653i	−0.755688	−	0.525812i
$609$	−5.60611	−	9.71006i	−0.227171	−	0.393472i
$610$	−58.3394	−	0.983778i	−2.36210	−	0.0398320i
$611$	−9.08450			−0.367520
$612$	−3.06262	+	4.91415i	−0.123799	+	0.198643i
$613$	18.4064	+	31.8809i	0.743429	+	1.28766i	0.950925	+	0.309421i	$0.100135\pi$
$613$	18.4064	+	31.8809i	0.743429	+	1.28766i	−0.207496	+	0.978236i	$0.566531\pi$
$614$	−0.546824	+	32.4274i	−0.0220680	+	1.30866i
$615$	−15.6329	+	27.0770i	−0.630379	+	1.09185i
$616$	−16.2256	−	31.7052i	−0.653747	−	1.27744i
$617$	4.51489			0.181762			0.0908812	−	0.995862i	$-0.471032\pi$
$617$	4.51489			0.181762			0.0908812	+	0.995862i	$0.471032\pi$
$618$	−6.44927	+	3.57988i	−0.259428	+	0.144004i
$619$	10.2851	−	5.93809i	0.413392	−	0.238672i	−0.278854	−	0.960333i	$-0.589955\pi$
$619$	10.2851	−	5.93809i	0.413392	−	0.238672i	0.692246	+	0.721661i	$0.256621\pi$
$620$	1.72182	−	51.0386i	0.0691498	−	2.04976i
$621$	−5.23155	+	3.02044i	−0.209935	+	0.121206i
$622$	−12.6407	+	21.0659i	−0.506846	+	0.844666i
$623$	32.1325	−	55.6551i	1.28736	−	2.22977i
$624$	−0.951821	+	14.0910i	−0.0381033	+	0.564092i
$625$	73.2556			2.93022
$626$	13.2823	+	7.97011i	0.530867	+	0.318550i
$627$			11.9702i			0.478045i
$628$	−8.23469	+	13.2130i	−0.328600	+	0.527258i
$629$	5.72595	−	9.91764i	0.228309	−	0.395442i
$630$	21.9741	−	12.1974i	0.875468	−	0.485958i
$631$	6.37659	+	11.0446i	0.253848	+	0.439678i	0.964582	−	0.263783i	$-0.0849703\pi$
$631$	6.37659	+	11.0446i	0.253848	+	0.439678i	−0.710734	+	0.703461i	$0.751637\pi$
$632$	−13.0201	+	20.1274i	−0.517914	+	0.800626i
$633$	0.588121	−	0.339552i	0.0233757	−	0.0134960i
$634$	−32.6584	−	0.550718i	−1.29703	−	0.0218718i
$635$	32.3692	−	56.0651i	1.28453	−	2.22487i
$636$	10.7338	−	5.72357i	0.425623	−	0.226954i
$637$	33.0846	+	19.1014i	1.31086	+	0.756825i
$638$	−11.2031	−	0.188917i	−0.443534	−	0.00747931i
$639$	1.59389	+	0.920230i	0.0630531	+	0.0364037i
$640$	38.1566	+	28.5060i	1.50827	+	1.12680i
$641$	34.8413	+	20.1157i	1.37615	+	0.794521i	0.991694	−	0.128622i	$-0.0410555\pi$
$641$	34.8413	+	20.1157i	1.37615	+	0.794521i	0.384457	+	0.923143i	$0.374389\pi$
$642$	11.0380	+	6.62341i	0.435635	+	0.261405i
$643$		−	37.9584i		−	1.49693i	−0.663172	−	0.748467i	$-0.730790\pi$
$643$		−	37.9584i		−	1.49693i	0.663172	−	0.748467i	$-0.269210\pi$
$644$	−45.0032	+	23.9970i	−1.77338	+	0.945615i
$645$			1.34810i			0.0530814i
$646$	14.3657	−	7.97415i	0.565211	−	0.313739i
$647$	−13.3485	−	23.1203i	−0.524783	−	0.908951i	−0.999584	−	0.0288576i	$-0.990813\pi$
$647$	−13.3485	−	23.1203i	−0.524783	−	0.908951i	0.474800	−	0.880094i	$-0.342520\pi$
$648$	2.82481	+	0.143013i	0.110969	+	0.00561807i
$649$	−5.55300	−	3.20602i	−0.217974	−	0.125847i
$650$	−1.07113	+	63.5195i	−0.0420131	+	2.49144i
$651$	−12.8018	−	22.1734i	−0.501744	−	0.869046i
$652$	−0.369683	+	10.9582i	−0.0144779	+	0.429158i
$653$	6.30017	−	3.63741i	0.246545	−	0.142343i	−0.371636	−	0.928378i	$-0.621203\pi$
$653$	6.30017	−	3.63741i	0.246545	−	0.142343i	0.618181	+	0.786036i	$0.287870\pi$
$654$	−13.7308	−	8.23922i	−0.536915	−	0.322179i
$655$	−89.9948			−3.51639
$656$	−26.6698	+	13.0860i	−1.04128	+	0.510922i
$657$	6.17242	+	10.6909i	0.240809	+	0.417093i
$658$	−0.258983	+	15.3581i	−0.0100962	+	0.598719i
$659$	16.6457	+	9.61042i	0.648426	+	0.374369i	0.787853	−	0.615863i	$-0.211193\pi$
$659$	16.6457	+	9.61042i	0.648426	+	0.374369i	−0.139427	+	0.990232i	$0.544526\pi$
$660$	0.846804	−	25.1012i	0.0329618	−	0.977063i
$661$			26.8261i			1.04342i	0.853124	+	0.521708i	$0.174705\pi$
$661$			26.8261i			1.04342i	−0.853124	+	0.521708i	$0.825295\pi$
$662$	8.78796	+	15.8318i	0.341554	+	0.615320i
$663$	−8.85277	−	5.11115i	−0.343813	−	0.198500i
$664$	20.6360	−	10.5608i	0.800831	−	0.409837i
$665$	−71.3143			−2.76545
$666$	−5.59312	−	0.0943167i	−0.216729	−	0.00365470i
$667$			16.0449i			0.621262i
$668$	0.356832	−	10.5773i	0.0138062	−	0.409248i
$669$			21.5026i			0.831340i
$670$	48.6055	+	3.51562i	1.87779	+	0.135820i
$671$			29.2340i			1.12857i
$672$	23.7948	+	2.01084i	0.917906	+	0.0775697i
$673$		−	11.3512i		−	0.437556i	−0.975775	−	0.218778i	$-0.929793\pi$
$673$		−	11.3512i		−	0.437556i	0.975775	−	0.218778i	$-0.0702071\pi$
$674$	0.105568	−	6.26034i	0.00406633	−	0.241139i
$675$	12.7228			0.489701
$676$	1.06655	+	0.0359807i	0.0410211	+	0.00138387i
$677$	−9.68685	−	5.59270i	−0.372296	−	0.214945i	0.302165	−	0.953256i	$-0.402291\pi$
$677$	−9.68685	−	5.59270i	−0.372296	−	0.214945i	−0.674461	+	0.738311i	$0.735624\pi$
$678$	−19.0288	+	10.5626i	−0.730797	+	0.405653i
$679$			15.0865i			0.578969i
$680$	−30.6885	+	15.7053i	−1.17685	+	0.602270i
$681$	−18.5127	−	10.6883i	−0.709408	−	0.409577i
$682$	−25.5828	−	0.431403i	−0.979616	−	0.0165193i
$683$	17.2049	+	29.7997i	0.658326	+	1.14025i	0.981049	+	0.193760i	$0.0620683\pi$
$683$	17.2049	+	29.7997i	0.658326	+	1.14025i	−0.322723	+	0.946493i	$0.604598\pi$
$684$	−6.81128	−	4.24496i	−0.260436	−	0.162310i
$685$	5.59020			0.213591
$686$	11.7337	−	19.5543i	0.447993	−	0.746586i
$687$	−6.38410	+	3.68586i	−0.243568	+	0.140624i
$688$	−0.713756	+	1.06361i	−0.0272117	+	0.0405497i
$689$	10.7375	+	18.5979i	0.409066	+	0.708524i
$690$	−35.9599	−	0.606392i	−1.36897	−	0.0230850i
$691$	17.5703	+	10.1442i	0.668405	+	0.385904i	0.795472	−	0.605990i	$-0.207223\pi$
$691$	17.5703	+	10.1442i	0.668405	+	0.385904i	−0.127067	+	0.991894i	$0.540556\pi$
$692$	−24.4832	+	39.2847i	−0.930711	+	1.49338i
$693$	−6.29605	−	10.9051i	−0.239167	−	0.414250i
$694$	−2.71328	−	4.88806i	−0.102995	−	0.185548i
$695$			15.7710i			0.598229i
$696$	4.08040	−	6.30775i	0.154667	−	0.239095i
$697$		−	21.5021i		−	0.814449i
$698$	−7.64951	+	12.7480i	−0.289538	+	0.482519i
$699$	−9.37212	−	5.41100i	−0.354486	−	0.204663i
$700$	107.354	+	3.62165i	4.05760	+	0.136886i
$701$	−28.5572	−	16.4875i	−1.07859	−	0.622725i	−0.148076	−	0.988976i	$-0.547308\pi$
$701$	−28.5572	−	16.4875i	−1.07859	−	0.622725i	−0.930516	+	0.366251i	$0.880641\pi$
$702$	−0.0841897	+	4.99257i	−0.00317754	+	0.188432i
$703$	13.7464	+	7.93648i	0.518455	+	0.299330i
$704$	13.9580	−	19.3557i	0.526062	−	0.729496i
$705$	−5.41585	+	9.38052i	−0.203973	+	0.353291i
$706$	−0.187512	+	11.1197i	−0.00705711	+	0.418497i
$707$	−69.0693	+	39.8772i	−2.59762	+	1.49974i
$708$	3.79352	−	2.02281i	0.142569	−	0.0760220i
$709$	1.17011	+	2.02670i	0.0439446	+	0.0761142i	0.887161	−	0.461460i	$-0.152674\pi$
$709$	1.17011	+	2.02670i	0.0439446	+	0.0761142i	−0.843217	+	0.537574i	$0.819341\pi$
$710$	5.31792	+	9.58041i	0.199578	+	0.359546i
$711$	−4.23762	+	7.33977i	−0.158923	+	0.275263i
$712$	43.0042	+	2.17719i	1.61165	+	0.0815936i
$713$			36.6395i			1.37216i
$714$	−8.89317	+	14.8206i	−0.332818	+	0.554646i
$715$	44.3386			1.65817
$716$	16.6219	+	31.1723i	0.621191	+	1.16496i
$717$	2.89158	−	5.00837i	0.107988	−	0.187041i
$718$	6.03083	+	3.61883i	0.225068	+	0.135054i
$719$	−42.2160	+	24.3734i	−1.57439	+	0.908975i	−0.578769	+	0.815491i	$0.696467\pi$
$719$	−42.2160	+	24.3734i	−1.57439	+	0.908975i	−0.995621	+	0.0934834i	$0.970200\pi$
$720$	13.9827	+	9.38338i	0.521106	+	0.349698i
$721$	−19.0679	+	11.0088i	−0.710125	+	0.409991i
$722$	−1.98816	−	3.58174i	−0.0739917	−	0.133298i
$723$	−23.2961			−0.866393
$724$	43.9312	+	1.48205i	1.63269	+	0.0550798i
$725$	16.8963	−	29.2652i	0.627512	−	1.08688i
$726$	2.97231	+	0.0501220i	0.110313	+	0.00186020i
$727$	−15.4475	−	26.7559i	−0.572916	−	0.992320i	−0.996265	−	0.0863531i	$-0.972479\pi$
$727$	−15.4475	−	26.7559i	−0.572916	−	0.992320i	0.423348	−	0.905967i	$-0.360855\pi$
$728$	−2.13156	+	42.1030i	−0.0790010	+	1.56044i
$729$	1.00000			0.0370370
$730$	−1.23919	+	73.4860i	−0.0458646	+	2.71984i
$731$	−0.463558	−	0.802905i	−0.0171453	−	0.0296965i
$732$	−16.6347	−	10.3671i	−0.614835	−	0.383180i
$733$	−2.83939	−	1.63932i	−0.104875	−	0.0605497i	0.446645	−	0.894711i	$-0.352619\pi$
$733$	−2.83939	−	1.63932i	−0.104875	−	0.0605497i	−0.551520	+	0.834162i	$0.685952\pi$
$734$	−0.795637	−	1.43337i	−0.0293675	−	0.0529065i
$735$	39.4476	−	22.7751i	1.45505	−	0.840072i
$736$	−28.0502	−	19.5175i	−1.03394	−	0.719425i
$737$	1.35058	−	24.3791i	0.0497493	−	0.898015i
$738$	−9.18322	+	5.09745i	−0.338039	+	0.187640i
$739$	12.3252	+	21.3478i	0.453389	+	0.785292i	0.998594	−	0.0530103i	$-0.0168816\pi$
$739$	12.3252	+	21.3478i	0.453389	+	0.785292i	−0.545205	+	0.838303i	$0.683548\pi$
$740$	−28.2643	−	17.6150i	−1.03902	−	0.647540i
$741$	7.08433	−	12.2704i	0.260249	−	0.450765i
$742$	31.7473	−	17.6224i	1.16548	−	0.646938i
$743$	10.3289	−	5.96339i	0.378930	−	0.218775i	−0.298423	−	0.954434i	$-0.596460\pi$
$743$	10.3289	−	5.96339i	0.378930	−	0.218775i	0.677353	+	0.735658i	$0.263127\pi$
$744$	9.31780	−	14.4041i	0.341607	−	0.528080i
$745$			34.7617i			1.27357i
$746$	11.7428	−	6.51821i	0.429933	−	0.238649i
$747$	7.09780	−	4.09792i	0.259695	−	0.149935i
$748$	8.12695	+	15.2410i	0.297151	+	0.557267i
$749$	33.2766	+	19.2123i	1.21590	+	0.702001i
$750$	39.4254	+	23.6574i	1.43961	+	0.863846i
$751$			10.1344i			0.369810i	0.982756	+	0.184905i	$0.0591978\pi$
$751$			10.1344i			0.369810i	−0.982756	+	0.184905i	$0.940802\pi$
$752$	−9.23948	+	4.53350i	−0.336929	+	0.165320i
$753$	−7.86623	−	13.6247i	−0.286661	−	0.496512i
$754$	11.3722	+	6.82395i	0.414151	+	0.248513i
$755$	−2.25670	−	3.90871i	−0.0821296	−	0.142253i
$756$	8.43793	+	0.284659i	0.306885	+	0.0103529i
$757$	29.9330	+	17.2818i	1.08793	+	0.628119i	0.933026	−	0.359810i	$-0.117158\pi$
$757$	29.9330	+	17.2818i	1.08793	+	0.628119i	0.154908	+	0.987929i	$0.450492\pi$
$758$	−25.4042	−	0.428391i	−0.922722	−	0.0155599i
$759$			18.0196i			0.654070i
$760$	−21.7684	−	42.5359i	−0.789621	−	1.54294i
$761$	−42.3656			−1.53575			−0.767875	−	0.640599i	$-0.778686\pi$
$761$	−42.3656			−1.53575			−0.767875	+	0.640599i	$0.778686\pi$
$762$	19.0146	−	10.5547i	0.688827	−	0.382356i
$763$	−41.3946	−	23.8992i	−1.49858	−	0.865208i
$764$	26.5839	−	42.6555i	0.961773	−	1.54322i
$765$	−10.5554	+	6.09416i	−0.381631	+	0.220335i
$766$	45.5901	+	0.768786i	1.64724	+	0.0277774i
$767$	3.79483	+	6.57284i	0.137023	+	0.237331i
$768$	6.06388	+	14.8064i	0.218812	+	0.534280i
$769$	−4.69198	−	2.70892i	−0.169197	−	0.0976861i	0.413010	−	0.910726i	$-0.364477\pi$
$769$	−4.69198	−	2.70892i	−0.169197	−	0.0976861i	−0.582207	+	0.813040i	$0.697811\pi$
$770$	1.26402	−	74.9579i	0.0455520	−	2.70130i
$771$	−0.878207	+	1.52110i	−0.0316278	+	0.0547810i
$772$	−22.0214	−	41.2983i	−0.792568	−	1.48636i
$773$	6.60532	−	11.4407i	0.237577	−	0.411495i	−0.722442	−	0.691432i	$-0.756980\pi$
$773$	6.60532	−	11.4407i	0.237577	−	0.411495i	0.960018	+	0.279937i	$0.0903135\pi$
$774$	−0.233014	+	0.388321i	−0.00837552	+	0.0139579i
$775$	38.5836	−	66.8287i	1.38596	−	2.40056i
$776$	−8.99848	+	4.60510i	−0.323027	+	0.165313i
$777$	−16.6976			−0.599022
$778$	6.91129	+	0.116545i	0.247782	+	0.00417834i
$779$	29.8030			1.06781
$780$	−15.7236	+	25.2295i	−0.562996	+	0.903360i
$781$	4.75447	−	2.74500i	0.170128	−	0.0982237i
$782$	21.6256	−	12.0040i	0.773331	−	0.429263i
$783$	1.32803	−	2.30022i	0.0474600	−	0.0822031i
$784$	43.1813	+	2.91681i	1.54219	+	0.104172i
$785$	−28.3810	+	16.3858i	−1.01296	+	0.584834i
$786$	−25.9231	−	15.5553i	−0.924645	−	0.554838i
$787$	−16.4224	−	28.4444i	−0.585394	−	1.01393i	−0.994826	−	0.101591i	$-0.967607\pi$
$787$	−16.4224	−	28.4444i	−0.585394	−	1.01393i	0.409432	−	0.912340i	$-0.365727\pi$
$788$	1.45711	−	43.1920i	0.0519074	−	1.53865i
$789$			13.1413i			0.467841i
$790$	−44.1174	+	24.4888i	−1.56963	+	0.871273i
$791$	−56.2605	+	32.4820i	−2.00039	+	1.15493i
$792$	4.58257	−	7.08405i	0.162835	−	0.251721i
$793$	17.3015	−	29.9671i	0.614394	−	1.06416i
$794$	24.3997	−	40.6623i	0.865911	−	1.44305i
$795$	25.6052			0.908124
$796$	16.3279	+	10.1759i	0.578726	+	0.360676i
$797$	−17.3066	+	29.9759i	−0.613031	+	1.06180i	0.377696	+	0.925930i	$0.376717\pi$
$797$	−17.3066	+	29.9759i	−0.613031	+	1.06180i	−0.990727	+	0.135871i	$0.956617\pi$
$798$	−20.5421	−	12.3264i	−0.727183	−	0.436350i
$799$		−	7.44916i		−	0.263532i
$800$	30.6092	+	65.1376i	1.08220	+	2.30296i
$801$	15.2237			0.537904
$802$	−3.24081	−	1.94466i	−0.114437	−	0.0686684i
$803$	36.8240			1.29949
$804$	13.3932	+	9.41396i	0.472341	+	0.332005i
$805$	−107.354			−3.78373
$806$	25.9690	+	15.5828i	0.914719	+	0.548882i
$807$	4.38757			0.154450
$808$	−44.8681	−	29.0245i	−1.57845	−	1.02108i
$809$		−	22.9494i		−	0.806858i	−0.915011	−	0.403429i	$-0.867818\pi$
$809$		−	22.9494i		−	0.806858i	0.915011	−	0.403429i	$-0.132182\pi$
$810$	5.10506	+	3.06332i	0.179374	+	0.107634i
$811$	17.3520	−	30.0546i	0.609312	−	1.05536i	−0.382042	−	0.924145i	$-0.624779\pi$
$811$	17.3520	−	30.0546i	0.609312	−	1.05536i	0.991354	−	0.131215i	$-0.0418878\pi$
$812$	11.8606	−	19.0310i	0.416226	−	0.667859i
$813$	9.96942			0.349643
$814$	−8.58563	+	14.3081i	−0.300926	+	0.501497i
$815$	−11.5397	+	19.9873i	−0.404218	+	0.700126i
$816$	−11.5544	−	0.780480i	−0.404486	−	0.0273223i
$817$	1.11287	−	0.642516i	0.0389344	−	0.0224788i
$818$	32.9867	−	18.3104i	1.15335	−	0.640207i
$819$			14.9047i			0.520813i
$820$	−62.4960	−	2.10834i	−2.18246	−	0.0736264i
$821$	18.4352	+	31.9307i	0.643392	+	1.11439i	0.984670	+	0.174425i	$0.0558068\pi$
$821$	18.4352	+	31.9307i	0.643392	+	1.11439i	−0.341278	+	0.939962i	$0.610860\pi$
$822$	1.61026	+	0.966246i	0.0561643	+	0.0337017i
$823$	36.5880	−	21.1241i	1.27538	−	0.736339i	0.299383	−	0.954133i	$-0.403219\pi$
$823$	36.5880	−	21.1241i	1.27538	−	0.736339i	0.975995	+	0.217794i	$0.0698860\pi$
$824$	−12.3867	−	8.01277i	−0.431510	−	0.279138i
$825$	18.9757	−	32.8669i	0.660649	−	1.14428i
$826$	11.2201	−	6.22808i	0.390396	−	0.216702i
$827$	9.50662	−	5.48865i	0.330578	−	0.190859i	−0.325520	−	0.945535i	$-0.605539\pi$
$827$	9.50662	−	5.48865i	0.330578	−	0.190859i	0.656098	+	0.754676i	$0.272206\pi$
$828$	−10.2535	−	6.39021i	−0.356333	−	0.222075i
$829$	39.2684			1.36385			0.681924	−	0.731423i	$-0.261143\pi$
$829$	39.2684			1.36385			0.681924	+	0.731423i	$0.261143\pi$
$830$	48.7879	+	0.822711i	1.69345	+	0.0285567i
$831$	−16.7737			−0.581872
$832$	−25.7633	+	11.5804i	−0.893181	+	0.401477i
$833$	−15.6629	+	27.1289i	−0.542686	+	0.939961i
$834$	−2.72597	+	4.54286i	−0.0943924	+	0.157306i
$835$	11.1385	−	19.2925i	0.385465	−	0.667645i
$836$	−21.1249	+	11.2644i	−0.730619	+	0.389587i
$837$	3.03263	−	5.25267i	0.104823	−	0.181559i
$838$	0.485204	−	28.7733i	0.0167611	−	0.993957i
$839$	−27.2610	−	15.7391i	−0.941153	−	0.543375i	−0.0508316	−	0.998707i	$-0.516187\pi$
$839$	−27.2610	−	15.7391i	−0.941153	−	0.543375i	−0.890322	+	0.455332i	$0.849521\pi$
$840$	42.2042	+	27.3013i	1.45618	+	0.941984i
$841$	10.9727	+	19.0052i	0.378368	+	0.655352i
$842$	0.834550	+	0.0140730i	0.0287605	+	0.000484988i
$843$	18.3619	−	10.6012i	0.632416	−	0.365126i
$844$	1.15268	+	0.718376i	0.0396768	+	0.0247275i
$845$	1.94534	+	1.12314i	0.0669216	+	0.0386372i
$846$	−3.18143	+	1.76596i	−0.109380	+	0.0607148i
$847$	8.87346			0.304896
$848$	20.2017	+	13.5568i	0.693730	+	0.465541i
$849$			9.55127i			0.327799i
$850$	−52.0851	−	0.878311i	−1.78650	−	0.0301258i
$851$	20.6933	+	11.9473i	0.709359	+	0.409548i
$852$	−0.124107	+	3.67883i	−0.00425185	+	0.126035i
$853$	−4.85956	−	8.41701i	−0.166388	−	0.288193i	0.770759	−	0.637127i	$-0.219877\pi$
$853$	−4.85956	−	8.41701i	−0.166388	−	0.288193i	−0.937147	+	0.348934i	$0.886544\pi$
$854$	−50.1685	−	30.1038i	−1.71673	−	1.03013i
$855$	−8.44683	−	14.6303i	−0.288875	−	0.500347i
$856$	−1.30176	+	25.7125i	−0.0444932	+	0.878836i
$857$		−	36.7528i		−	1.25545i	−0.778434	−	0.627727i	$-0.783986\pi$
$857$		−	36.7528i		−	1.25545i	0.778434	−	0.627727i	$-0.216014\pi$
$858$	12.7718	+	7.66377i	0.436021	+	0.261637i
$859$	15.6471	+	9.03383i	0.533871	+	0.308230i	0.742591	−	0.669745i	$-0.233597\pi$
$859$	15.6471	+	9.03383i	0.533871	+	0.308230i	−0.208721	+	0.977975i	$0.566930\pi$
$860$	−2.37910	+	1.26861i	−0.0811268	+	0.0432591i
$861$	−27.1511	+	15.6757i	−0.925305	+	0.534225i
$862$	0.865329	−	0.480330i	0.0294732	−	0.0163601i
$863$		−	7.86747i		−	0.267812i	−0.990994	−	0.133906i	$-0.957248\pi$
$863$		−	7.86747i		−	0.267812i	0.990994	−	0.133906i	$-0.0427520\pi$
$864$	2.40585	+	5.11975i	0.0818488	+	0.174178i
$865$	−84.3818	+	48.7178i	−2.86907	+	1.65646i
$866$	8.82723	−	4.89985i	0.299961	−	0.166504i
$867$	−4.30893	+	7.46329i	−0.146339	+	0.253467i
$868$	27.0843	−	43.4584i	0.919303	−	1.47507i
$869$	12.6406	+	21.8941i	0.428802	+	0.742708i
$870$	13.8260	−	7.67457i	0.468745	−	0.260192i
$871$	−15.8127	+	24.1911i	−0.535792	+	0.819684i
$872$	1.61933	−	31.9852i	0.0548373	−	1.08316i
$873$	−3.09505	+	1.78693i	−0.104752	+	0.0604783i
$874$	16.6382	+	29.9743i	0.562796	+	1.01390i
$875$	118.857	+	68.6221i	4.01810	+	2.31985i
$876$	−13.0587	+	20.9535i	−0.441214	+	0.707953i
$877$	17.2982	+	29.9614i	0.584120	+	1.01173i	0.994985	+	0.100029i	$0.0318935\pi$
$877$	17.2982	+	29.9614i	0.584120	+	1.01173i	−0.410865	+	0.911696i	$0.634773\pi$
$878$	0.167032	−	9.90523i	0.00563705	−	0.334285i
$879$	11.6905			0.394310
$880$	45.0950	−	22.1266i	1.52015	−	0.745889i
$881$	8.85706	+	15.3409i	0.298402	+	0.516847i	0.975771	−	0.218796i	$-0.0702131\pi$
$881$	8.85706	+	15.3409i	0.298402	+	0.516847i	−0.677369	+	0.735644i	$0.736880\pi$
$882$	15.2995	+	0.257995i	0.515161	+	0.00868716i
$883$	−10.0522	+	17.4109i	−0.338282	+	0.585922i	−0.984110	−	0.177561i	$-0.943179\pi$
$883$	−10.0522	+	17.4109i	−0.338282	+	0.585922i	0.645828	+	0.763483i	$0.276513\pi$
$884$	0.689318	−	20.4330i	0.0231843	−	0.687235i
$885$	9.04935			0.304191
$886$	14.5441	+	26.2017i	0.488619	+	0.880263i
$887$	2.36817	−	1.36727i	0.0795155	−	0.0459083i	−0.459715	−	0.888066i	$-0.652048\pi$
$887$	2.36817	−	1.36727i	0.0795155	−	0.0459083i	0.539231	+	0.842158i	$0.318715\pi$
$888$	−5.09686	−	9.95939i	−0.171039	−	0.334215i
$889$	56.2185	−	32.4578i	1.88551	−	1.08860i
$890$	77.7182	+	46.6352i	2.60512	+	1.56322i
$891$	1.49147	−	2.58331i	0.0499662	−	0.0865440i
$892$	−37.9475	+	20.2347i	−1.27058	+	0.677508i
$893$	10.3249			0.345511
$894$	−6.00842	+	10.0131i	−0.200952	+	0.334889i
$895$			74.3607i			2.48560i
$896$	18.8430	+	43.8850i	0.629501	+	1.46609i
$897$	10.6645	−	18.4715i	0.356077	−	0.616744i
$898$	7.31987	+	13.1870i	0.244267	+	0.440055i
$899$	−8.05486	−	13.9514i	−0.268645	−	0.465306i
$900$	11.9726	+	22.4530i	0.399086	+	0.748432i
$901$	−15.2500	+	8.80460i	−0.508052	+	0.293324i
$902$	−0.528246	+	31.3258i	−0.0175887	+	1.04303i
$903$	−0.675895	+	1.17068i	−0.0224924	+	0.0389579i
$904$	−36.5474	−	23.6420i	−1.21555	−	0.786320i
$905$	80.1285	+	46.2622i	2.66356	+	1.53781i
$906$	0.0255638	−	1.51597i	0.000849300	−	0.0503647i
$907$	−2.42986	−	1.40288i	−0.0806823	−	0.0465819i	0.459116	−	0.888376i	$-0.348166\pi$
$907$	−2.42986	−	1.40288i	−0.0806823	−	0.0465819i	−0.539798	+	0.841794i	$0.681500\pi$
$908$	1.44149	−	42.7290i	0.0478374	−	1.41801i
$909$	−16.3618	−	9.44651i	−0.542688	−	0.313321i
$910$	−45.6579	+	76.0895i	−1.51355	+	2.52234i
$911$		−	21.2119i		−	0.702781i	−0.936229	−	0.351391i	$-0.885709\pi$
$911$		−	21.2119i		−	0.702781i	0.936229	−	0.351391i	$-0.114291\pi$
$912$	1.08179	−	16.0151i	0.0358216	−	0.530312i
$913$		−	24.4477i		−	0.809101i
$914$	21.2365	+	38.2583i	0.702443	+	1.26547i
$915$	−20.6290	−	35.7305i	−0.681975	−	1.18122i
$916$	−12.5124	−	7.79802i	−0.413421	−	0.257654i
$917$	−78.1510	−	45.1205i	−2.58077	−	1.49001i
$918$	−4.09384	−	0.0690344i	−0.135117	−	0.00227847i
$919$	−8.47287	−	14.6754i	−0.279494	−	0.484098i	0.691765	−	0.722123i	$-0.256833\pi$
$919$	−8.47287	−	14.6754i	−0.279494	−	0.484098i	−0.971259	+	0.238024i	$0.923500\pi$
$920$	−32.7693	−	64.0321i	−1.08037	−	2.11108i
$921$	−19.8605	+	11.4665i	−0.654425	+	0.377833i
$922$	−1.17456	+	1.95742i	−0.0386821	+	0.0644642i
$923$	−6.49826			−0.213893
$924$	13.3203	−	21.3732i	0.438206	−	0.703127i
$925$	−25.1625	−	43.5827i	−0.827337	−	1.43299i
$926$	−42.5093	−	0.716834i	−1.39694	−	0.0235566i
$927$	−4.51699	−	2.60789i	−0.148357	−	0.0856542i
$928$	14.9716	+	1.26521i	0.491467	+	0.0415325i
$929$			10.0504i			0.329742i	0.986315	+	0.164871i	$0.0527209\pi$
$929$			10.0504i			0.329742i	−0.986315	+	0.164871i	$0.947279\pi$
$930$	31.5724	−	17.5253i	1.03530	−	0.574677i
$931$	−37.6021	−	21.7096i	−1.23236	−	0.711503i
$932$	0.729758	−	21.6317i	0.0239040	−	0.708569i
$933$	−17.3718			−0.568728
$934$	−0.746590	+	44.2739i	−0.0244292	+	1.44868i
$935$			36.3571i			1.18900i
$936$	−8.89003	+	4.54960i	−0.290580	+	0.148708i
$937$			28.0289i			0.915666i	0.889038	+	0.457833i	$0.151374\pi$
$937$			28.0289i			0.915666i	−0.889038	+	0.457833i	$0.848626\pi$
$938$	40.4462	+	27.4222i	1.32061	+	0.895367i
$939$			10.9531i			0.357442i
$940$	−21.6511	−	0.730411i	−0.706180	−	0.0238234i
$941$		−	4.04714i		−	0.131933i	−0.997822	−	0.0659665i	$-0.978987\pi$
$941$		−	4.04714i		−	0.131933i	0.997822	−	0.0659665i	$-0.0210131\pi$
$942$	−11.0074	−	0.185618i	−0.358640	−	0.00604775i
$943$	44.8645			1.46099
$944$	7.13966	+	4.79120i	0.232376	+	0.155940i
$945$	15.3904	+	8.88565i	0.500649	+	0.289050i
$946$	0.655618	+	1.18112i	0.0213160	+	0.0384015i
$947$		−	33.8197i		−	1.09899i	−0.835496	−	0.549496i	$-0.814820\pi$
$947$		−	33.8197i		−	1.09899i	0.835496	−	0.549496i	$-0.185180\pi$
$948$	−16.9408	−	0.571509i	−0.550213	−	0.0185618i
$949$	−37.7474	−	21.7935i	−1.22533	−	0.707446i
$950$	1.21739	−	72.1927i	0.0394972	−	2.34224i
$951$	−11.5481	−	20.0019i	−0.374474	−	0.648607i
$952$	−34.5239	−	1.74785i	−1.11892	−	0.0566482i
$953$	−46.6893			−1.51241			−0.756207	−	0.654332i	$-0.772950\pi$
$953$	−46.6893			−1.51241			−0.756207	+	0.654332i	$0.772950\pi$
$954$	7.37560	+	4.42577i	0.238794	+	0.143290i
$955$	91.6221	−	52.8981i	2.96482	−	1.71174i
$956$	11.5598	+	0.389975i	0.373869	+	0.0126127i
$957$	−3.96145	−	6.86143i	−0.128055	−	0.221798i
$958$	−0.186481	+	11.0586i	−0.00602494	+	0.357288i
$959$	4.85450	+	2.80275i	0.156760	+	0.0905055i
$960$	−3.40142	+	33.5066i	−0.109780	+	1.08142i
$961$	−2.89370	−	5.01204i	−0.0933452	−	0.161679i
$962$	17.2688	−	9.58564i	0.556770	−	0.309053i
$963$			9.10239i			0.293321i
$964$	−21.9224	−	41.1126i	−0.706074	−	1.32415i
$965$		−	98.5160i		−	3.17134i
$966$	−30.9234	−	18.5558i	−0.994944	−	0.597022i
$967$	8.51646	+	4.91698i	0.273871	+	0.158119i	0.630645	−	0.776071i	$-0.282790\pi$
$967$	8.51646	+	4.91698i	0.273871	+	0.158119i	−0.356775	+	0.934190i	$0.616124\pi$
$968$	2.70858	+	5.29264i	0.0870571	+	0.170112i
$969$	10.0616	+	5.80905i	0.323224	+	0.186614i
$970$	−21.2744	−	0.358749i	−0.683078	−	0.0115187i
$971$	−42.1808	−	24.3531i	−1.35365	−	0.781528i	−0.364887	−	0.931052i	$-0.618893\pi$
$971$	−42.1808	−	24.3531i	−1.35365	−	0.781528i	−0.988758	+	0.149524i	$0.952226\pi$
$972$	0.941033	+	1.76478i	0.0301836	+	0.0566054i
$973$	−7.90709	+	13.6955i	−0.253490	+	0.439057i
$974$	−25.8365	−	0.435681i	−0.827854	−	0.0139601i
$975$	−38.9031	+	22.4607i	−1.24590	+	0.719319i
$976$	2.64197	−	39.1124i	0.0845673	−	1.25196i
$977$	13.4514	+	23.2984i	0.430347	+	0.745383i	0.996903	−	0.0786404i	$-0.0250579\pi$
$977$	13.4514	+	23.2984i	0.430347	+	0.745383i	−0.566556	+	0.824023i	$0.691725\pi$
$978$	−6.77875	+	3.76277i	−0.216761	+	0.120320i
$979$	22.7058	−	39.3276i	0.725680	−	1.25692i
$980$	77.3146	+	48.1844i	2.46972	+	1.53919i
$981$		−	11.3230i		−	0.361514i
$982$	8.57893	+	5.14783i	0.273765	+	0.164274i
$983$	−1.60720			−0.0512618			−0.0256309	−	0.999671i	$-0.508159\pi$
$983$	−1.60720			−0.0512618			−0.0256309	+	0.999671i	$0.508159\pi$
$984$	−17.6376	−	11.4095i	−0.562266	−	0.363722i
$985$	45.4838	−	78.7803i	1.44923	−	2.51015i
$986$	−5.59554	+	9.32504i	−0.178198	+	0.296970i
$987$	−9.40619	+	5.43067i	−0.299402	+	0.172860i
$988$	28.3212	+	0.955432i	0.901017	+	0.0303963i
$989$	1.67528	−	0.967221i	0.0532707	−	0.0307558i
$990$	15.5276	−	8.61908i	0.493498	−	0.273932i
$991$	0.326579			0.0103741			0.00518705	−	0.999987i	$-0.498349\pi$
$991$	0.326579			0.0103741			0.00518705	+	0.999987i	$0.498349\pi$
$992$	34.1884	+	2.88917i	1.08548	+	0.0917313i
$993$	−6.40189	+	11.0884i	−0.203158	+	0.351880i
$994$	−0.185254	+	10.9858i	−0.00587590	+	0.348449i
$995$	20.2486	+	35.0716i	0.641923	+	1.11184i
$996$	13.9112	+	8.66980i	0.440793	+	0.274713i
$997$	−56.0453			−1.77497			−0.887486	−	0.460834i	$-0.847550\pi$
$997$	−56.0453			−1.77497			−0.887486	+	0.460834i	$0.847550\pi$
$998$	37.1529	+	0.626508i	1.17605	+	0.0198318i
$999$	−1.97775	−	3.42556i	−0.0625731	−	0.108380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.11	✓	68
4.3	odd	2		804.2.j.b.499.2	yes	68
67.38	odd	6		804.2.j.b.775.2	yes	68
268.239	even	6	inner	804.2.j.a.775.11	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.11	✓	68	1.1	even	1	trivial
804.2.j.a.775.11	yes	68	268.239	even	6	inner
804.2.j.b.499.2	yes	68	4.3	odd	2
804.2.j.b.775.2	yes	68	67.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.727656 + 1.21265i) q^{2} -1.00000 q^{3} +(-0.941033 - 1.76478i) q^{4} -4.20985i q^{5} +(0.727656 - 1.21265i) q^{6} +(2.11068 - 3.65581i) q^{7} +(2.82481 + 0.143013i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.727656 + 1.21265i) q^{2} -1.00000 q^{3} +(-0.941033 - 1.76478i) q^{4} -4.20985i q^{5} +(0.727656 - 1.21265i) q^{6} +(2.11068 - 3.65581i) q^{7} +(2.82481 + 0.143013i) q^{8} +1.00000 q^{9} +(5.10506 + 3.06332i) q^{10} +(1.49147 - 2.58331i) q^{11} +(0.941033 + 1.76478i) q^{12} +(-3.05775 + 1.76539i) q^{13} +(2.89736 + 5.21969i) q^{14} +4.20985i q^{15} +(-2.22891 + 3.32144i) q^{16} +(-1.44760 - 2.50731i) q^{17} +(-0.727656 + 1.21265i) q^{18} +(3.47527 - 2.00645i) q^{19} +(-7.42946 + 3.96160i) q^{20} +(-2.11068 + 3.65581i) q^{21} +(2.04736 + 3.68839i) q^{22} +(5.23155 - 3.02044i) q^{23} +(-2.82481 - 0.143013i) q^{24} -12.7228 q^{25} +(0.0841897 - 4.99257i) q^{26} -1.00000 q^{27} +(-8.43793 - 0.284659i) q^{28} +(-1.32803 + 2.30022i) q^{29} +(-5.10506 - 3.06332i) q^{30} +(-3.03263 + 5.25267i) q^{31} +(-2.40585 - 5.11975i) q^{32} +(-1.49147 + 2.58331i) q^{33} +(4.09384 + 0.0690344i) q^{34} +(-15.3904 - 8.88565i) q^{35} +(-0.941033 - 1.76478i) q^{36} +(1.97775 + 3.42556i) q^{37} +(-0.0956854 + 5.67428i) q^{38} +(3.05775 - 1.76539i) q^{39} +(0.602061 - 11.8920i) q^{40} +(6.43182 + 3.71341i) q^{41} +(-2.89736 - 5.21969i) q^{42} +0.320226 q^{43} +(-5.96250 - 0.201148i) q^{44} -4.20985i q^{45} +(-0.144041 + 8.54187i) q^{46} +(2.22823 + 1.28647i) q^{47} +(2.22891 - 3.32144i) q^{48} +(-5.40996 - 9.37033i) q^{49} +(9.25782 - 15.4283i) q^{50} +(1.44760 + 2.50731i) q^{51} +(5.99297 + 3.73497i) q^{52} -6.08222i q^{53} +(0.727656 - 1.21265i) q^{54} +(-10.8753 - 6.27887i) q^{55} +(6.48510 - 10.0251i) q^{56} +(-3.47527 + 2.00645i) q^{57} +(-1.82301 - 3.28420i) q^{58} -2.14957i q^{59} +(7.42946 - 3.96160i) q^{60} +(-8.48738 + 4.90019i) q^{61} +(-4.16293 - 7.49965i) q^{62} +(2.11068 - 3.65581i) q^{63} +(7.95909 + 0.807967i) q^{64} +(7.43202 + 12.8726i) q^{65} +(-2.04736 - 3.68839i) q^{66} +(7.30425 - 3.69430i) q^{67} +(-3.06262 + 4.91415i) q^{68} +(-5.23155 + 3.02044i) q^{69} +(21.9741 - 12.1974i) q^{70} +(1.59389 + 0.920230i) q^{71} +(2.82481 + 0.143013i) q^{72} +(6.17242 + 10.6909i) q^{73} +(-5.59312 - 0.0943167i) q^{74} +12.7228 q^{75} +(-6.81128 - 4.24496i) q^{76} +(-6.29605 - 10.9051i) q^{77} +(-0.0841897 + 4.99257i) q^{78} +(-4.23762 + 7.33977i) q^{79} +(13.9827 + 9.38338i) q^{80} +1.00000 q^{81} +(-9.18322 + 5.09745i) q^{82} +(7.09780 - 4.09792i) q^{83} +(8.43793 + 0.284659i) q^{84} +(-10.5554 + 6.09416i) q^{85} +(-0.233014 + 0.388321i) q^{86} +(1.32803 - 2.30022i) q^{87} +(4.58257 - 7.08405i) q^{88} +15.2237 q^{89} +(5.10506 + 3.06332i) q^{90} +14.9047i q^{91} +(-10.2535 - 6.39021i) q^{92} +(3.03263 - 5.25267i) q^{93} +(-3.18143 + 1.76596i) q^{94} +(-8.44683 - 14.6303i) q^{95} +(2.40585 + 5.11975i) q^{96} +(-3.09505 + 1.78693i) q^{97} +(15.2995 + 0.257995i) q^{98} +(1.49147 - 2.58331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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