LMFDB - Embedded newform 403.2.f.c.94.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.12
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.137984 + 0.238996i) q^{2} +(-0.732250 - 1.26829i) q^{3} +(0.961921 - 1.66610i) q^{4} -1.37475 q^{5} +(0.202078 - 0.350009i) q^{6} +(0.239780 - 0.415311i) q^{7} +1.08286 q^{8} +(0.427621 - 0.740662i) q^{9} +O(q^{10})$	\(q+(0.137984 + 0.238996i) q^{2} +(-0.732250 - 1.26829i) q^{3} +(0.961921 - 1.66610i) q^{4} -1.37475 q^{5} +(0.202078 - 0.350009i) q^{6} +(0.239780 - 0.415311i) q^{7} +1.08286 q^{8} +(0.427621 - 0.740662i) q^{9} +(-0.189694 - 0.328559i) q^{10} +(0.323908 + 0.561024i) q^{11} -2.81746 q^{12} +(-3.42483 - 1.12717i) q^{13} +0.132343 q^{14} +(1.00666 + 1.74359i) q^{15} +(-1.77442 - 3.07339i) q^{16} +(1.17485 - 2.03489i) q^{17} +0.236020 q^{18} +(-0.704293 + 1.21987i) q^{19} +(-1.32240 + 2.29047i) q^{20} -0.702315 q^{21} +(-0.0893882 + 0.154825i) q^{22} +(-0.994005 - 1.72167i) q^{23} +(-0.792921 - 1.37338i) q^{24} -3.11006 q^{25} +(-0.203185 - 0.974052i) q^{26} -5.64600 q^{27} +(-0.461299 - 0.798993i) q^{28} +(-0.107161 - 0.185608i) q^{29} +(-0.277806 + 0.481175i) q^{30} +1.00000 q^{31} +(1.57254 - 2.72372i) q^{32} +(0.474362 - 0.821620i) q^{33} +0.648441 q^{34} +(-0.329638 + 0.570949i) q^{35} +(-0.822676 - 1.42492i) q^{36} +(-3.54620 - 6.14220i) q^{37} -0.388725 q^{38} +(1.07825 + 5.16906i) q^{39} -1.48866 q^{40} +(5.27418 + 9.13515i) q^{41} +(-0.0969084 - 0.167850i) q^{42} +(4.55483 - 7.88920i) q^{43} +1.24629 q^{44} +(-0.587873 + 1.01823i) q^{45} +(0.274314 - 0.475126i) q^{46} +8.99844 q^{47} +(-2.59864 + 4.50098i) q^{48} +(3.38501 + 5.86301i) q^{49} +(-0.429139 - 0.743291i) q^{50} -3.44112 q^{51} +(-5.17239 + 4.62186i) q^{52} +11.1521 q^{53} +(-0.779058 - 1.34937i) q^{54} +(-0.445292 - 0.771268i) q^{55} +(0.259647 - 0.449722i) q^{56} +2.06287 q^{57} +(0.0295730 - 0.0512220i) q^{58} +(0.838771 - 1.45279i) q^{59} +3.87331 q^{60} +(0.454325 - 0.786914i) q^{61} +(0.137984 + 0.238996i) q^{62} +(-0.205070 - 0.355192i) q^{63} -6.22976 q^{64} +(4.70829 + 1.54957i) q^{65} +0.261818 q^{66} +(-2.20119 - 3.81257i) q^{67} +(-2.26022 - 3.91481i) q^{68} +(-1.45572 + 2.52138i) q^{69} -0.181939 q^{70} +(2.48188 - 4.29873i) q^{71} +(0.463052 - 0.802030i) q^{72} +6.35196 q^{73} +(0.978638 - 1.69505i) q^{74} +(2.27734 + 3.94447i) q^{75} +(1.35495 + 2.34684i) q^{76} +0.310666 q^{77} +(-1.08660 + 0.970947i) q^{78} -2.73779 q^{79} +(2.43939 + 4.22515i) q^{80} +(2.85142 + 4.93880i) q^{81} +(-1.45551 + 2.52101i) q^{82} +6.40312 q^{83} +(-0.675571 + 1.17012i) q^{84} +(-1.61512 + 2.79747i) q^{85} +2.51398 q^{86} +(-0.156937 + 0.271823i) q^{87} +(0.350745 + 0.607509i) q^{88} +(2.40022 + 4.15730i) q^{89} -0.324468 q^{90} +(-1.28933 + 1.15210i) q^{91} -3.82462 q^{92} +(-0.732250 - 1.26829i) q^{93} +(1.24164 + 2.15059i) q^{94} +(0.968228 - 1.67702i) q^{95} -4.60597 q^{96} +(-5.40800 + 9.36693i) q^{97} +(-0.934156 + 1.61801i) q^{98} +0.554039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.137984	+	0.238996i	0.0975695	+	0.168995i	0.910678	−	0.413117i	$-0.135560\pi$
$2$	0.137984	+	0.238996i	0.0975695	+	0.168995i	−0.813109	+	0.582112i	$0.802226\pi$
$3$	−0.732250	−	1.26829i	−0.422764	−	0.732250i	0.573444	−	0.819245i	$-0.305607\pi$
$3$	−0.732250	−	1.26829i	−0.422764	−	0.732250i	−0.996209	+	0.0869950i	$0.972274\pi$
$4$	0.961921	−	1.66610i	0.480960	−	0.833048i
$5$	−1.37475			−0.614807			−0.307404	−	0.951579i	$-0.599460\pi$
$5$	−1.37475			−0.614807			−0.307404	+	0.951579i	$0.599460\pi$
$6$	0.202078	−	0.350009i	0.0824979	−	0.142890i
$7$	0.239780	−	0.415311i	0.0906283	−	0.156973i	−0.817147	−	0.576429i	$-0.804446\pi$
$7$	0.239780	−	0.415311i	0.0906283	−	0.156973i	0.907776	+	0.419456i	$0.137779\pi$
$8$	1.08286			0.382847
$9$	0.427621	−	0.740662i	0.142540	−	0.246887i
$10$	−0.189694	−	0.328559i	−0.0599864	−	0.103900i
$11$	0.323908	+	0.561024i	0.0976618	+	0.169155i	0.910716	−	0.413032i	$-0.135530\pi$
$11$	0.323908	+	0.561024i	0.0976618	+	0.169155i	−0.813055	+	0.582187i	$0.802197\pi$
$12$	−2.81746			−0.813332
$13$	−3.42483	−	1.12717i	−0.949878	−	0.312620i
$13$	−3.42483	−	1.12717i	−0.949878	−	0.312620i
$14$	0.132343			0.0353702
$15$	1.00666	+	1.74359i	0.259919	+	0.450192i
$16$	−1.77442	−	3.07339i	−0.443606	−	0.768348i
$17$	1.17485	−	2.03489i	0.284942	−	0.493534i	−0.687653	−	0.726040i	$-0.741359\pi$
$17$	1.17485	−	2.03489i	0.284942	−	0.493534i	0.972595	+	0.232505i	$0.0746922\pi$
$18$	0.236020			0.0556304
$19$	−0.704293	+	1.21987i	−0.161576	+	0.279858i	−0.935434	−	0.353501i	$-0.884991\pi$
$19$	−0.704293	+	1.21987i	−0.161576	+	0.279858i	0.773858	+	0.633359i	$0.218324\pi$
$20$	−1.32240	+	2.29047i	−0.295698	+	0.512164i
$21$	−0.702315			−0.153258
$22$	−0.0893882	+	0.154825i	−0.0190576	+	0.0330088i
$23$	−0.994005	−	1.72167i	−0.207264	−	0.358992i	0.743587	−	0.668639i	$-0.233123\pi$
$23$	−0.994005	−	1.72167i	−0.207264	−	0.358992i	−0.950852	+	0.309646i	$0.899789\pi$
$24$	−0.792921	−	1.37338i	−0.161854	−	0.280340i
$25$	−3.11006			−0.622012
$26$	−0.203185	−	0.974052i	−0.0398478	−	0.191027i
$27$	−5.64600			−1.08657
$28$	−0.461299	−	0.798993i	−0.0871773	−	0.150995i
$29$	−0.107161	−	0.185608i	−0.0198993	−	0.0344666i	0.855904	−	0.517134i	$-0.173001\pi$
$29$	−0.107161	−	0.185608i	−0.0198993	−	0.0344666i	−0.875804	+	0.482668i	$0.839668\pi$
$30$	−0.277806	+	0.481175i	−0.0507203	+	0.0878501i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	1.57254	−	2.72372i	0.277989	−	0.481490i
$33$	0.474362	−	0.821620i	0.0825759	−	0.143026i
$34$	0.648441			0.111207
$35$	−0.329638	+	0.570949i	−0.0557189	+	0.0965080i
$36$	−0.822676	−	1.42492i	−0.137113	−	0.237486i
$37$	−3.54620	−	6.14220i	−0.582991	−	1.00977i	−0.995123	−	0.0986462i	$-0.968549\pi$
$37$	−3.54620	−	6.14220i	−0.582991	−	1.00977i	0.412131	−	0.911125i	$-0.364785\pi$
$38$	−0.388725			−0.0630596
$39$	1.07825	+	5.16906i	0.172659	+	0.827713i
$40$	−1.48866			−0.235377
$41$	5.27418	+	9.13515i	0.823689	+	1.42667i	0.902917	+	0.429814i	$0.141421\pi$
$41$	5.27418	+	9.13515i	0.823689	+	1.42667i	−0.0792284	+	0.996856i	$0.525246\pi$
$42$	−0.0969084	−	0.167850i	−0.0149533	−	0.0258998i
$43$	4.55483	−	7.88920i	0.694606	−	1.20309i	−0.275708	−	0.961241i	$-0.588912\pi$
$43$	4.55483	−	7.88920i	0.694606	−	1.20309i	0.970313	−	0.241851i	$-0.0777544\pi$
$44$	1.24629			0.187886
$45$	−0.587873	+	1.01823i	−0.0876349	+	0.151788i
$46$	0.274314	−	0.475126i	0.0404454	−	0.0700535i
$47$	8.99844			1.31256			0.656279	−	0.754519i	$-0.272130\pi$
$47$	8.99844			1.31256			0.656279	+	0.754519i	$0.272130\pi$
$48$	−2.59864	+	4.50098i	−0.375082	+	0.649661i
$49$	3.38501	+	5.86301i	0.483573	+	0.837573i
$50$	−0.429139	−	0.743291i	−0.0606894	−	0.105117i
$51$	−3.44112			−0.481854
$52$	−5.17239	+	4.62186i	−0.717281	+	0.640936i
$53$	11.1521			1.53185			0.765926	−	0.642929i	$-0.222281\pi$
$53$	11.1521			1.53185			0.765926	+	0.642929i	$0.222281\pi$
$54$	−0.779058	−	1.34937i	−0.106016	−	0.183626i
$55$	−0.445292	−	0.771268i	−0.0600432	−	0.103998i
$56$	0.259647	−	0.449722i	0.0346968	−	0.0600966i
$57$	2.06287			0.273234
$58$	0.0295730	−	0.0512220i	0.00388313	−	0.00672578i
$59$	0.838771	−	1.45279i	0.109199	−	0.189138i	−0.806247	−	0.591579i	$-0.798505\pi$
$59$	0.838771	−	1.45279i	0.109199	−	0.189138i	0.915446	+	0.402441i	$0.131838\pi$
$60$	3.87331			0.500042
$61$	0.454325	−	0.786914i	0.0581704	−	0.100754i	−0.835474	−	0.549530i	$-0.814807\pi$
$61$	0.454325	−	0.786914i	0.0581704	−	0.100754i	0.893644	+	0.448776i	$0.148140\pi$
$62$	0.137984	+	0.238996i	0.0175240	+	0.0303525i
$63$	−0.205070	−	0.355192i	−0.0258364	−	0.0447500i
$64$	−6.22976			−0.778719
$65$	4.70829	+	1.54957i	0.583992	+	0.192201i
$66$	0.261818			0.0322276
$67$	−2.20119	−	3.81257i	−0.268918	−	0.465780i	0.699665	−	0.714471i	$-0.253333\pi$
$67$	−2.20119	−	3.81257i	−0.268918	−	0.465780i	−0.968583	+	0.248692i	$0.919999\pi$
$68$	−2.26022	−	3.91481i	−0.274092	−	0.474741i
$69$	−1.45572	+	2.52138i	−0.175248	+	0.303539i
$70$	−0.181939			−0.0217459
$71$	2.48188	−	4.29873i	0.294544	−	0.510166i	−0.680334	−	0.732902i	$-0.738165\pi$
$71$	2.48188	−	4.29873i	0.294544	−	0.510166i	0.974879	+	0.222736i	$0.0714988\pi$
$72$	0.463052	−	0.802030i	0.0545712	−	0.0945201i
$73$	6.35196			0.743440			0.371720	−	0.928345i	$-0.378768\pi$
$73$	6.35196			0.743440			0.371720	+	0.928345i	$0.378768\pi$
$74$	0.978638	−	1.69505i	0.113764	−	0.197046i
$75$	2.27734	+	3.94447i	0.262965	+	0.455468i
$76$	1.35495	+	2.34684i	0.155423	+	0.269201i
$77$	0.310666			0.0354037
$78$	−1.08660	+	0.970947i	−0.123033	+	0.109938i
$79$	−2.73779			−0.308025			−0.154012	−	0.988069i	$-0.549220\pi$
$79$	−2.73779			−0.308025			−0.154012	+	0.988069i	$0.549220\pi$
$80$	2.43939	+	4.22515i	0.272732	+	0.472386i
$81$	2.85142	+	4.93880i	0.316824	+	0.548755i
$82$	−1.45551	+	2.52101i	−0.160734	+	0.278399i
$83$	6.40312			0.702834			0.351417	−	0.936219i	$-0.385700\pi$
$83$	6.40312			0.702834			0.351417	+	0.936219i	$0.385700\pi$
$84$	−0.675571	+	1.17012i	−0.0737109	+	0.127671i
$85$	−1.61512	+	2.79747i	−0.175185	+	0.303428i
$86$	2.51398			0.271089
$87$	−0.156937	+	0.271823i	−0.0168254	+	0.0291425i
$88$	0.350745	+	0.607509i	0.0373896	+	0.0647606i
$89$	2.40022	+	4.15730i	0.254423	+	0.440673i	0.964739	−	0.263210i	$-0.0847812\pi$
$89$	2.40022	+	4.15730i	0.254423	+	0.440673i	−0.710316	+	0.703883i	$0.751448\pi$
$90$	−0.324468			−0.0342020
$91$	−1.28933	+	1.15210i	−0.135159	+	0.120773i
$92$	−3.82462			−0.398744
$93$	−0.732250	−	1.26829i	−0.0759307	−	0.131516i
$94$	1.24164	+	2.15059i	0.128066	+	0.221816i
$95$	0.968228	−	1.67702i	0.0993381	−	0.172059i
$96$	−4.60597			−0.470095
$97$	−5.40800	+	9.36693i	−0.549099	+	0.951068i	0.449237	+	0.893412i	$0.351696\pi$
$97$	−5.40800	+	9.36693i	−0.549099	+	0.951068i	−0.998337	+	0.0576552i	$0.981638\pi$
$98$	−0.934156	+	1.61801i	−0.0943640	+	0.163443i
$99$	0.554039			0.0556830
$100$	−2.99163	+	5.18166i	−0.299163	+	0.518166i
$101$	3.55301	+	6.15399i	0.353538	+	0.612345i	0.986867	−	0.161538i	$-0.0516453\pi$
$101$	3.55301	+	6.15399i	0.353538	+	0.612345i	−0.633329	+	0.773883i	$0.718312\pi$
$102$	−0.474821	−	0.822413i	−0.0470142	−	0.0814311i
$103$	5.08609			0.501147			0.250573	−	0.968098i	$-0.419381\pi$
$103$	5.08609			0.501147			0.250573	+	0.968098i	$0.419381\pi$
$104$	−3.70860	−	1.22056i	−0.363658	−	0.119686i
$105$	0.965508			0.0942239
$106$	1.53881	+	2.66529i	0.149462	+	0.258876i
$107$	−0.960487	−	1.66361i	−0.0928538	−	0.160828i	0.815857	−	0.578254i	$-0.196266\pi$
$107$	−0.960487	−	1.66361i	−0.0928538	−	0.160828i	−0.908711	+	0.417426i	$0.862932\pi$
$108$	−5.43100	+	9.40677i	−0.522599	+	0.905167i
$109$	9.77610			0.936380			0.468190	−	0.883628i	$-0.344906\pi$
$109$	9.77610			0.936380			0.468190	+	0.883628i	$0.344906\pi$
$110$	0.122887	−	0.212846i	0.0117168	−	0.0202940i
$111$	−5.19340	+	8.99524i	−0.492936	+	0.853790i
$112$	−1.70189			−0.160813
$113$	−3.66644	+	6.35045i	−0.344909	+	0.597400i	−0.985337	−	0.170618i	$-0.945424\pi$
$113$	−3.66644	+	6.35045i	−0.344909	+	0.597400i	0.640428	+	0.768018i	$0.278757\pi$
$114$	0.284644	+	0.493018i	0.0266593	+	0.0461753i
$115$	1.36651	+	2.36686i	0.127428	+	0.220711i
$116$	−0.412322			−0.0382831
$117$	−2.29938	+	2.05464i	−0.212578	+	0.189952i
$118$	0.462948			0.0426179
$119$	−0.563410	−	0.975854i	−0.0516477	−	0.0894564i
$120$	1.09007	+	1.88805i	0.0995092	+	0.172355i
$121$	5.29017	−	9.16284i	0.480924	−	0.832985i
$122$	0.250759			0.0227026
$123$	7.72403	−	13.3784i	0.696453	−	1.20629i
$124$	0.961921	−	1.66610i	0.0863830	−	0.149620i
$125$	11.1493			0.997225
$126$	0.0565928	−	0.0980217i	0.00504169	−	0.00873246i
$127$	−10.0770	−	17.4539i	−0.894190	−	1.54878i	−0.834804	−	0.550548i	$-0.814419\pi$
$127$	−10.0770	−	17.4539i	−0.894190	−	1.54878i	−0.0593868	−	0.998235i	$-0.518915\pi$
$128$	−4.00469	−	6.93633i	−0.353968	−	0.613090i
$129$	−13.3411			−1.17462
$130$	0.279328	+	1.33908i	0.0244987	+	0.117445i
$131$	−0.445880			−0.0389567			−0.0194784	−	0.999810i	$-0.506201\pi$
$131$	−0.445880			−0.0389567			−0.0194784	+	0.999810i	$0.506201\pi$
$132$	−0.912598	−	1.58067i	−0.0794315	−	0.137579i
$133$	0.337751	+	0.585002i	0.0292867	+	0.0507261i
$134$	0.607458	−	1.05215i	0.0524764	−	0.0908918i
$135$	7.76184			0.668033
$136$	1.27219	−	2.20350i	0.109089	−	0.188948i
$137$	−10.0058	+	17.3305i	−0.854851	+	1.48065i	0.0219326	+	0.999759i	$0.493018\pi$
$137$	−10.0058	+	17.3305i	−0.854851	+	1.48065i	−0.876783	+	0.480886i	$0.840315\pi$
$138$	−0.803465			−0.0683955
$139$	−5.05253	+	8.75123i	−0.428550	+	0.742270i	−0.996745	−	0.0806243i	$-0.974309\pi$
$139$	−5.05253	+	8.75123i	−0.428550	+	0.742270i	0.568195	+	0.822894i	$0.307642\pi$
$140$	0.634171	+	1.09842i	0.0535972	+	0.0928331i
$141$	−6.58910	−	11.4127i	−0.554903	−	0.961119i
$142$	1.36984			0.114954
$143$	−0.476961	−	2.28651i	−0.0398855	−	0.191208i
$144$	−3.03513			−0.252927
$145$	0.147320	+	0.255165i	0.0122342	+	0.0211903i
$146$	0.876469	+	1.51809i	0.0725371	+	0.125638i
$147$	4.95735	−	8.58637i	0.408875	−	0.708192i
$148$	−13.6446			−1.12158
$149$	−1.49818	+	2.59492i	−0.122736	+	0.212584i	−0.920846	−	0.389928i	$-0.872500\pi$
$149$	−1.49818	+	2.59492i	−0.122736	+	0.212584i	0.798110	+	0.602512i	$0.205833\pi$
$150$	−0.628474	+	1.08855i	−0.0513147	+	0.0888796i
$151$	17.5705			1.42987			0.714935	−	0.699191i	$-0.246456\pi$
$151$	17.5705			1.42987			0.714935	+	0.699191i	$0.246456\pi$
$152$	−0.762648	+	1.32095i	−0.0618589	+	0.107143i
$153$	−1.00478	−	1.74033i	−0.0812316	−	0.140697i
$154$	0.0428670	+	0.0742478i	0.00345432	+	0.00598306i
$155$	−1.37475			−0.110423
$156$	9.64935	+	3.17575i	0.772566	+	0.254264i
$157$	−3.11059			−0.248252			−0.124126	−	0.992266i	$-0.539613\pi$
$157$	−3.11059			−0.248252			−0.124126	+	0.992266i	$0.539613\pi$
$158$	−0.377771	−	0.654319i	−0.0300539	−	0.0520548i
$159$	−8.16609	−	14.1441i	−0.647613	−	1.12170i
$160$	−2.16185	+	3.74444i	−0.170909	+	0.296024i
$161$	−0.953370			−0.0751361
$162$	−0.786901	+	1.36295i	−0.0618247	+	0.107084i
$163$	4.83855	−	8.38061i	0.378984	−	0.656420i	−0.611931	−	0.790911i	$-0.709607\pi$
$163$	4.83855	−	8.38061i	0.378984	−	0.656420i	0.990915	+	0.134492i	$0.0429401\pi$
$164$	20.2934			1.58465
$165$	−0.652130	+	1.12952i	−0.0507682	+	0.0879332i
$166$	0.883530	+	1.53032i	0.0685752	+	0.118776i
$167$	−4.83260	−	8.37032i	−0.373958	−	0.647714i	0.616212	−	0.787580i	$-0.288666\pi$
$167$	−4.83260	−	8.37032i	−0.373958	−	0.647714i	−0.990171	+	0.139866i	$0.955333\pi$
$168$	−0.760506			−0.0586743
$169$	10.4590	+	7.72073i	0.804537	+	0.593902i
$170$	−0.891445			−0.0683707
$171$	0.602342	+	1.04329i	0.0460622	+	0.0797821i
$172$	−8.76278	−	15.1776i	−0.668156	−	1.15728i
$173$	4.89966	−	8.48645i	0.372514	−	0.645213i	−0.617438	−	0.786620i	$-0.711829\pi$
$173$	4.89966	−	8.48645i	0.372514	−	0.645213i	0.989952	+	0.141407i	$0.0451625\pi$
$174$	−0.0866194			−0.00656660
$175$	−0.745730	+	1.29164i	−0.0563719	+	0.0976390i
$176$	1.14950	−	1.99099i	0.0866468	−	0.150077i
$177$	−2.45676			−0.184661
$178$	−0.662385	+	1.14728i	−0.0496478	+	0.0859926i
$179$	−10.9139	−	18.9035i	−0.815745	−	1.41291i	−0.908792	−	0.417250i	$-0.862994\pi$
$179$	−10.9139	−	18.9035i	−0.815745	−	1.41291i	0.0930473	−	0.995662i	$-0.470339\pi$
$180$	1.13097	+	1.95890i	0.0842978	+	0.146008i
$181$	−16.4629			−1.22368			−0.611840	−	0.790982i	$-0.709570\pi$
$181$	−16.4629			−1.22368			−0.611840	+	0.790982i	$0.709570\pi$
$182$	−0.453254	−	0.149173i	−0.0335974	−	0.0110574i
$183$	−1.33072			−0.0983694
$184$	−1.07636	−	1.86432i	−0.0793506	−	0.137439i
$185$	4.87514	+	8.44399i	0.358427	+	0.620814i
$186$	0.202078	−	0.350009i	0.0148171	−	0.0256639i
$187$	1.52217			0.111312
$188$	8.65578	−	14.9923i	0.631288	−	1.09342i
$189$	−1.35380	+	2.34485i	−0.0984743	+	0.170562i
$190$	0.534400			0.0387695
$191$	1.19567	−	2.07097i	0.0865159	−	0.149850i	−0.819520	−	0.573050i	$-0.805760\pi$
$191$	1.19567	−	2.07097i	0.0865159	−	0.149850i	0.906036	+	0.423200i	$0.139093\pi$
$192$	4.56174	+	7.90116i	0.329215	+	0.570217i
$193$	4.89518	+	8.47870i	0.352363	+	0.610310i	0.986663	−	0.162777i	$-0.0520450\pi$
$193$	4.89518	+	8.47870i	0.352363	+	0.610310i	−0.634300	+	0.773087i	$0.718712\pi$
$194$	−2.98487			−0.214301
$195$	−1.48233	−	7.10617i	−0.106152	−	0.508884i
$196$	13.0244			0.930318
$197$	−9.78152	−	16.9421i	−0.696904	−	1.20707i	−0.969535	−	0.244954i	$-0.921227\pi$
$197$	−9.78152	−	16.9421i	−0.696904	−	1.20707i	0.272630	−	0.962119i	$-0.412106\pi$
$198$	0.0764486	+	0.132413i	0.00543297	+	0.00941017i
$199$	3.41590	−	5.91651i	0.242147	−	0.419411i	−0.719179	−	0.694825i	$-0.755482\pi$
$199$	3.41590	−	5.91651i	0.242147	−	0.419411i	0.961326	+	0.275415i	$0.0888151\pi$
$200$	−3.36775			−0.238136
$201$	−3.22364	+	5.58350i	−0.227378	+	0.393830i
$202$	−0.980518	+	1.69831i	−0.0689890	+	0.119492i
$203$	−0.102780			−0.00721376
$204$	−3.31009	+	5.73324i	−0.231753	+	0.401407i
$205$	−7.25068	−	12.5586i	−0.506410	−	0.877127i
$206$	0.701799	+	1.21555i	0.0488967	+	0.0846915i
$207$	−1.70023			−0.118174
$208$	2.61288	+	12.5259i	0.181171	+	0.868518i
$209$	−0.912504			−0.0631192
$210$	0.133225	+	0.230752i	0.00919338	+	0.0159234i
$211$	11.3270	+	19.6189i	0.779781	+	1.35062i	0.932068	+	0.362285i	$0.118003\pi$
$211$	11.3270	+	19.6189i	0.779781	+	1.35062i	−0.152286	+	0.988336i	$0.548664\pi$
$212$	10.7274	−	18.5804i	0.736760	−	1.27611i
$213$	−7.26941			−0.498092
$214$	0.265064	−	0.459104i	0.0181194	−	0.0313837i
$215$	−6.26176	+	10.8457i	−0.427048	+	0.739670i
$216$	−6.11380			−0.415992
$217$	0.239780	−	0.415311i	0.0162773	−	0.0281932i
$218$	1.34895	+	2.33644i	0.0913622	+	0.158244i
$219$	−4.65122	−	8.05614i	−0.314300	−	0.544384i
$220$	−1.71334			−0.115514
$221$	−6.31732	+	5.64493i	−0.424949	+	0.379719i
$222$	−2.86643			−0.192382
$223$	−4.19008	−	7.25744i	−0.280589	−	0.485994i	0.690941	−	0.722911i	$-0.257196\pi$
$223$	−4.19008	−	7.25744i	−0.280589	−	0.485994i	−0.971530	+	0.236917i	$0.923863\pi$
$224$	−0.754128	−	1.30619i	−0.0503873	−	0.0872733i
$225$	−1.32993	+	2.30350i	−0.0886619	+	0.153567i
$226$	−2.02364			−0.134611
$227$	−7.33695	+	12.7080i	−0.486970	+	0.843457i	−0.999888	−	0.0149806i	$-0.995231\pi$
$227$	−7.33695	+	12.7080i	−0.486970	+	0.843457i	0.512918	+	0.858438i	$0.328565\pi$
$228$	1.98432	−	3.43694i	0.131415	−	0.227617i
$229$	−0.0186783			−0.00123430			−0.000617150	−	1.00000i	$-0.500196\pi$
$229$	−0.0186783			−0.00123430			−0.000617150		1.00000i	$0.500196\pi$
$230$	−0.377113	+	0.653179i	−0.0248661	+	0.0430694i
$231$	−0.227485	−	0.394016i	−0.0149674	−	0.0259243i
$232$	−0.116040	−	0.200987i	−0.00761840	−	0.0131954i
$233$	27.1749			1.78029			0.890144	−	0.455680i	$-0.150604\pi$
$233$	27.1749			1.78029			0.890144	+	0.455680i	$0.150604\pi$
$234$	−0.808329	−	0.266034i	−0.0528421	−	0.0173912i
$235$	−12.3706			−0.806969
$236$	−1.61366	−	2.79495i	−0.105040	−	0.181935i
$237$	2.00474	+	3.47232i	0.130222	+	0.225551i
$238$	0.155483	−	0.269305i	0.0100785	−	0.0174564i
$239$	17.4218			1.12692			0.563460	−	0.826144i	$-0.309470\pi$
$239$	17.4218			1.12692			0.563460	+	0.826144i	$0.309470\pi$
$240$	3.57249	−	6.18773i	0.230603	−	0.399416i
$241$	−2.27037	+	3.93240i	−0.146248	+	0.253308i	−0.929838	−	0.367970i	$-0.880053\pi$
$241$	−2.27037	+	3.93240i	−0.146248	+	0.253308i	0.783590	+	0.621278i	$0.213386\pi$
$242$	2.91984			0.187694
$243$	−4.29310	+	7.43587i	−0.275403	+	0.477011i
$244$	−0.874049	−	1.51390i	−0.0559553	−	0.0969174i
$245$	−4.65355	−	8.06018i	−0.297304	−	0.514946i
$246$	4.26318			0.271810
$247$	3.78709	−	3.38400i	0.240967	−	0.215319i
$248$	1.08286			0.0687614
$249$	−4.68868	−	8.12104i	−0.297133	−	0.514650i
$250$	1.53843	+	2.66464i	0.0972987	+	0.168526i
$251$	−0.0336012	+	0.0581989i	−0.00212089	+	0.00367348i	−0.867084	−	0.498162i	$-0.834008\pi$
$251$	−0.0336012	+	0.0581989i	−0.00212089	+	0.00367348i	0.864963	+	0.501836i	$0.167342\pi$
$252$	−0.789044			−0.0497051
$253$	0.643932	−	1.11532i	0.0404836	−	0.0701197i
$254$	2.78094	−	4.81672i	0.174491	−	0.302228i
$255$	4.73069			0.296247
$256$	−5.12459	+	8.87605i	−0.320287	+	0.554753i
$257$	−7.08588	−	12.2731i	−0.442005	−	0.765576i	0.555833	−	0.831294i	$-0.312399\pi$
$257$	−7.08588	−	12.2731i	−0.442005	−	0.765576i	−0.997838	+	0.0657184i	$0.979066\pi$
$258$	−1.84086	−	3.18846i	−0.114607	−	0.198505i
$259$	−3.40123			−0.211342
$260$	7.11074	−	6.35390i	0.440990	−	0.394052i
$261$	−0.183297			−0.0113458
$262$	−0.0615244	−	0.106563i	−0.00380099	−	0.00658351i
$263$	13.4574	+	23.3090i	0.829821	+	1.43729i	0.898179	+	0.439631i	$0.144891\pi$
$263$	13.4574	+	23.3090i	0.829821	+	1.43729i	−0.0683581	+	0.997661i	$0.521776\pi$
$264$	0.513666	−	0.889696i	0.0316140	−	0.0547570i
$265$	−15.3313			−0.941794
$266$	−0.0932085	+	0.161442i	−0.00571498	+	0.00989864i
$267$	3.51512	−	6.08837i	0.215122	−	0.372602i
$268$	−8.46947			−0.517355
$269$	−9.86989	+	17.0952i	−0.601778	+	1.04231i	0.390774	+	0.920487i	$0.372207\pi$
$269$	−9.86989	+	17.0952i	−0.601778	+	1.04231i	−0.992552	+	0.121823i	$0.961126\pi$
$270$	1.07101	+	1.85505i	0.0651796	+	0.112894i
$271$	−7.77504	−	13.4668i	−0.472300	−	0.818047i	0.527198	−	0.849743i	$-0.323243\pi$
$271$	−7.77504	−	13.4668i	−0.472300	−	0.818047i	−0.999498	+	0.0316952i	$0.989909\pi$
$272$	−8.33871			−0.505608
$273$	2.40531	+	0.791627i	0.145576	+	0.0479114i
$274$	−5.52255			−0.333630
$275$	−1.00737	−	1.74482i	−0.0607468	−	0.105217i
$276$	2.80057	+	4.85074i	0.168575	+	0.291980i
$277$	−6.63492	+	11.4920i	−0.398654	+	0.690489i	−0.993560	−	0.113307i	$-0.963856\pi$
$277$	−6.63492	+	11.4920i	−0.398654	+	0.690489i	0.594906	+	0.803795i	$0.297189\pi$
$278$	−2.78867			−0.167254
$279$	0.427621	−	0.740662i	0.0256010	−	0.0443423i
$280$	−0.356950	+	0.618256i	−0.0213318	+	0.0369478i
$281$	−25.0215			−1.49266			−0.746329	−	0.665577i	$-0.768185\pi$
$281$	−25.0215			−1.49266			−0.746329	+	0.665577i	$0.768185\pi$
$282$	1.81838	−	3.14953i	0.108283	−	0.187552i
$283$	−12.6915	−	21.9823i	−0.754431	−	1.30671i	−0.945657	−	0.325166i	$-0.894580\pi$
$283$	−12.6915	−	21.9823i	−0.754431	−	1.30671i	0.191226	−	0.981546i	$-0.438754\pi$
$284$	−4.77473	−	8.27008i	−0.283328	−	0.490739i
$285$	−2.83594			−0.167986
$286$	0.480654	−	0.429494i	0.0284216	−	0.0253965i
$287$	5.05857			0.298598
$288$	−1.34490	−	2.32944i	−0.0792492	−	0.137264i
$289$	5.73947	+	9.94105i	0.337616	+	0.584768i
$290$	−0.0406556	+	0.0704175i	−0.00238738	+	0.00413506i
$291$	15.8400			0.928558
$292$	6.11008	−	10.5830i	0.357565	−	0.619321i
$293$	−1.87637	+	3.24996i	−0.109618	+	0.189865i	−0.915616	−	0.402055i	$-0.868296\pi$
$293$	−1.87637	+	3.24996i	−0.109618	+	0.189865i	0.805997	+	0.591919i	$0.201630\pi$
$294$	2.73614			0.159575
$295$	−1.15310	+	1.99723i	−0.0671361	+	0.116283i
$296$	−3.84002	−	6.65111i	−0.223197	−	0.386588i
$297$	−1.82878	−	3.16754i	−0.106117	−	0.183799i
$298$	−0.826900			−0.0479010
$299$	1.46370	+	7.01684i	0.0846477	+	0.405794i
$300$	8.76249			0.505902
$301$	−2.18432	−	3.78335i	−0.125902	−	0.218068i
$302$	2.42446	+	4.19928i	0.139512	+	0.241641i
$303$	5.20338	−	9.01251i	0.298926	−	0.517755i
$304$	4.99886			0.286704
$305$	−0.624584	+	1.08181i	−0.0357636	+	0.0619443i
$306$	0.277287	−	0.480276i	0.0158515	−	0.0274555i
$307$	−10.6024			−0.605109			−0.302554	−	0.953132i	$-0.597839\pi$
$307$	−10.6024			−0.605109			−0.302554	+	0.953132i	$0.597839\pi$
$308$	0.298836	−	0.517600i	0.0170278	−	0.0294930i
$309$	−3.72428	−	6.45065i	−0.211867	−	0.366965i
$310$	−0.189694	−	0.328559i	−0.0107739	−	0.0186609i
$311$	10.2239			0.579744			0.289872	−	0.957065i	$-0.406387\pi$
$311$	10.2239			0.579744			0.289872	+	0.957065i	$0.406387\pi$
$312$	1.16759	+	5.59735i	0.0661020	+	0.316888i
$313$	1.39017			0.0785773			0.0392886	−	0.999228i	$-0.487491\pi$
$313$	1.39017			0.0785773			0.0392886	+	0.999228i	$0.487491\pi$
$314$	−0.429212	−	0.743417i	−0.0242218	−	0.0419535i
$315$	0.281920	+	0.488300i	0.0158844	+	0.0275126i
$316$	−2.63353	+	4.56141i	−0.148148	+	0.256600i
$317$	−11.8851			−0.667536			−0.333768	−	0.942655i	$-0.608320\pi$
$317$	−11.8851			−0.667536			−0.333768	+	0.942655i	$0.608320\pi$
$318$	2.25358	−	3.90332i	0.126375	−	0.218887i
$319$	0.0694205	−	0.120240i	0.00388680	−	0.00673214i
$320$	8.56436			0.478762
$321$	−1.40663	+	2.43636i	−0.0785106	+	0.135984i
$322$	−0.131550	−	0.227851i	−0.00733099	−	0.0126977i
$323$	1.65487	+	2.86633i	0.0920796	+	0.159487i
$324$	10.9713			0.609519
$325$	10.6514	+	3.50556i	0.590836	+	0.194453i
$326$	2.67057			0.147909
$327$	−7.15854	−	12.3990i	−0.395868	−	0.685664i
$328$	5.71118	+	9.89205i	0.315347	+	0.546197i
$329$	2.15765	−	3.73715i	0.118955	−	0.206036i
$330$	−0.359934			−0.0198137
$331$	−12.0601	+	20.8888i	−0.662885	+	1.14815i	0.316969	+	0.948436i	$0.397335\pi$
$331$	−12.0601	+	20.8888i	−0.662885	+	1.14815i	−0.979854	+	0.199714i	$0.935999\pi$
$332$	6.15930	−	10.6682i	0.338035	−	0.585494i
$333$	−6.06572			−0.332399
$334$	1.33365	−	2.30994i	0.0729738	−	0.126394i
$335$	3.02608	+	5.24133i	0.165333	+	0.286365i
$336$	1.24621	+	2.15849i	0.0679861	+	0.117755i
$337$	−13.1114			−0.714224			−0.357112	−	0.934062i	$-0.616239\pi$
$337$	−13.1114			−0.714224			−0.357112	+	0.934062i	$0.616239\pi$
$338$	−0.402045	+	3.56499i	−0.0218684	+	0.193910i
$339$	10.7390			0.583262
$340$	3.10724	+	5.38189i	0.168514	+	0.291874i
$341$	0.323908	+	0.561024i	0.0175406	+	0.0303812i
$342$	−0.166227	+	0.287914i	−0.00898854	+	0.0155686i
$343$	6.60355			0.356558
$344$	4.93223	−	8.54287i	0.265928	−	0.460601i
$345$	2.00125	−	3.46627i	0.107744	−	0.186618i
$346$	2.70430			0.145384
$347$	−4.77787	+	8.27552i	−0.256490	+	0.444253i	−0.965299	−	0.261147i	$-0.915899\pi$
$347$	−4.77787	+	8.27552i	−0.256490	+	0.444253i	0.708809	+	0.705400i	$0.249233\pi$
$348$	0.301922	+	0.522945i	0.0161847	+	0.0280328i
$349$	3.85898	+	6.68394i	0.206566	+	0.357783i	0.950631	−	0.310325i	$-0.100438\pi$
$349$	3.85898	+	6.68394i	0.206566	+	0.357783i	−0.744064	+	0.668108i	$0.767104\pi$
$350$	−0.411596			−0.0220007
$351$	19.3366	+	6.36399i	1.03211	+	0.339685i
$352$	2.03743			0.108595
$353$	13.3043	+	23.0437i	0.708117	+	1.22649i	0.965555	+	0.260200i	$0.0837884\pi$
$353$	13.3043	+	23.0437i	0.708117	+	1.22649i	−0.257438	+	0.966295i	$0.582878\pi$
$354$	−0.338994	−	0.587154i	−0.0180173	−	0.0312069i
$355$	−3.41196	+	5.90969i	−0.181088	+	0.313654i
$356$	9.23529			0.489469
$357$	−0.825113	+	1.42914i	−0.0436696	+	0.0756380i
$358$	3.01190	−	5.21676i	0.159184	−	0.275714i
$359$	10.9463			0.577723			0.288862	−	0.957371i	$-0.406723\pi$
$359$	10.9463			0.577723			0.288862	+	0.957371i	$0.406723\pi$
$360$	−0.636581	+	1.10259i	−0.0335508	+	0.0581117i
$361$	8.50794	+	14.7362i	0.447786	+	0.775589i
$362$	−2.27162	−	3.93457i	−0.119394	−	0.206796i
$363$	−15.4949			−0.813271
$364$	0.679273	+	3.25638i	0.0356036	+	0.170681i
$365$	−8.73235			−0.457072
$366$	−0.183618	−	0.318036i	−0.00959786	−	0.0166240i
$367$	4.82355	+	8.35463i	0.251787	+	0.436108i	0.964018	−	0.265837i	$-0.0856483\pi$
$367$	4.82355	+	8.35463i	0.251787	+	0.436108i	−0.712231	+	0.701945i	$0.752315\pi$
$368$	−3.52757	+	6.10994i	−0.183888	+	0.318503i
$369$	9.02141			0.469636
$370$	−1.34538	+	2.33027i	−0.0699432	+	0.121145i
$371$	2.67404	−	4.63157i	0.138829	−	0.240459i
$372$	−2.81746			−0.146079
$373$	−11.0055	+	19.0621i	−0.569842	+	0.986996i	0.426739	+	0.904375i	$0.359662\pi$
$373$	−11.0055	+	19.0621i	−0.569842	+	0.986996i	−0.996581	+	0.0826208i	$0.973671\pi$
$374$	0.210035	+	0.363791i	0.0108606	+	0.0188112i
$375$	−8.16408	−	14.1406i	−0.421591	−	0.730217i
$376$	9.74401			0.502509
$377$	0.157797	+	0.756466i	0.00812696	+	0.0389600i
$378$	−0.747210			−0.0384324
$379$	−10.9266	−	18.9255i	−0.561264	−	0.972138i	−0.997387	−	0.0722504i	$-0.976982\pi$
$379$	−10.9266	−	18.9255i	−0.561264	−	0.972138i	0.436123	−	0.899887i	$-0.356351\pi$
$380$	−1.86272	−	3.22632i	−0.0955553	−	0.165507i
$381$	−14.7578	+	25.5612i	−0.756064	+	1.30954i
$382$	0.659936			0.0337653
$383$	−5.62338	+	9.73998i	−0.287341	+	0.497690i	−0.973174	−	0.230069i	$-0.926105\pi$
$383$	−5.62338	+	9.73998i	−0.287341	+	0.497690i	0.685833	+	0.727759i	$0.259438\pi$
$384$	−5.86486	+	10.1582i	−0.299290	+	0.518386i
$385$	−0.427088			−0.0217664
$386$	−1.35091	+	2.33985i	−0.0687597	+	0.119095i
$387$	−3.89549	−	6.74718i	−0.198019	−	0.342979i
$388$	10.4041	+	18.0205i	0.528190	+	0.914852i
$389$	−3.48614			−0.176754			−0.0883771	−	0.996087i	$-0.528168\pi$
$389$	−3.48614			−0.176754			−0.0883771	+	0.996087i	$0.528168\pi$
$390$	1.49381	−	1.33481i	0.0756418	−	0.0675907i
$391$	−4.67122			−0.236234
$392$	3.66548	+	6.34880i	0.185135	+	0.320663i
$393$	0.326496	+	0.565507i	0.0164695	+	0.0285261i
$394$	2.69939	−	4.67548i	0.135993	−	0.235547i
$395$	3.76377			0.189376
$396$	0.532942	−	0.923082i	0.0267813	−	0.0463866i
$397$	−0.602457	+	1.04349i	−0.0302364	+	0.0523710i	−0.880748	−	0.473586i	$-0.842959\pi$
$397$	−0.602457	+	1.04349i	−0.0302364	+	0.0523710i	0.850511	+	0.525957i	$0.176293\pi$
$398$	1.88536			0.0945046
$399$	0.494636	−	0.856734i	0.0247628	−	0.0428904i
$400$	5.51857	+	9.55844i	0.275928	+	0.477922i
$401$	16.1824	+	28.0287i	0.808108	+	1.39968i	0.914173	+	0.405325i	$0.132842\pi$
$401$	16.1824	+	28.0287i	0.808108	+	1.39968i	−0.106065	+	0.994359i	$0.533825\pi$
$402$	−1.77924			−0.0887406
$403$	−3.42483	−	1.12717i	−0.170603	−	0.0561482i
$404$	13.6709			0.680150
$405$	−3.91999	−	6.78961i	−0.194786	−	0.337379i
$406$	−0.0141820	−	0.0245640i	−0.000703843	−	0.00121909i
$407$	2.29728	−	3.97901i	0.113872	−	0.197232i
$408$	−3.72624			−0.184476
$409$	4.56787	−	7.91178i	0.225867	−	0.391213i	−0.730712	−	0.682685i	$-0.760812\pi$
$409$	4.56787	−	7.91178i	0.225867	−	0.391213i	0.956579	+	0.291473i	$0.0941453\pi$
$410$	2.00096	−	3.46576i	0.0988203	−	0.171162i
$411$	29.3069			1.44560
$412$	4.89241	−	8.47391i	0.241032	−	0.417479i
$413$	−0.402241	−	0.696702i	−0.0197930	−	0.0342825i
$414$	−0.234605	−	0.406348i	−0.0115302	−	0.0199709i
$415$	−8.80270			−0.432107
$416$	−8.45578	+	7.55578i	−0.414579	+	0.370452i
$417$	14.7988			0.724702
$418$	−0.125911	−	0.218084i	−0.00615851	−	0.0106669i
$419$	7.60307	+	13.1689i	0.371434	+	0.643343i	0.989786	−	0.142558i	$-0.0455328\pi$
$419$	7.60307	+	13.1689i	0.371434	+	0.643343i	−0.618352	+	0.785901i	$0.712199\pi$
$420$	0.928742	−	1.60863i	0.0453180	−	0.0784930i
$421$	26.3139			1.28246			0.641231	−	0.767348i	$-0.278424\pi$
$421$	26.3139			1.28246			0.641231	+	0.767348i	$0.278424\pi$
$422$	−3.12589	+	5.41420i	−0.152166	+	0.263559i
$423$	3.84792	−	6.66480i	0.187092	−	0.324054i
$424$	12.0761			0.586466
$425$	−3.65385	+	6.32865i	−0.177238	+	0.306984i
$426$	−1.00306	−	1.73736i	−0.0485986	−	0.0841752i
$427$	−0.217876	−	0.377372i	−0.0105438	−	0.0182623i
$428$	−3.69565			−0.178636
$429$	−2.55072	+	2.27923i	−0.123150	+	0.110042i
$430$	−3.45609			−0.166668
$431$	9.92141	+	17.1844i	0.477898	+	0.827743i	0.999679	−	0.0253362i	$-0.00806563\pi$
$431$	9.92141	+	17.1844i	0.477898	+	0.827743i	−0.521781	+	0.853079i	$0.674732\pi$
$432$	10.0184	+	17.3524i	0.482010	+	0.834867i
$433$	−1.00617	+	1.74273i	−0.0483534	+	0.0837505i	−0.889189	−	0.457540i	$-0.848731\pi$
$433$	−1.00617	+	1.74273i	−0.0483534	+	0.0837505i	0.840836	+	0.541290i	$0.182064\pi$
$434$	0.132343			0.00635268
$435$	0.215750	−	0.373689i	0.0103444	−	0.0179170i
$436$	9.40383	−	16.2879i	0.450362	−	0.780049i
$437$	2.80028			0.133956
$438$	1.28359	−	2.22324i	0.0613322	−	0.106231i
$439$	−4.33545	−	7.50922i	−0.206920	−	0.358396i	0.743823	−	0.668377i	$-0.233011\pi$
$439$	−4.33545	−	7.50922i	−0.206920	−	0.358396i	−0.950743	+	0.309981i	$0.899677\pi$
$440$	−0.482187	−	0.835173i	−0.0229874	−	0.0398153i
$441$	5.79001			0.275715
$442$	−2.22080	−	0.730902i	−0.105633	−	0.0347655i
$443$	−2.48474			−0.118054			−0.0590269	−	0.998256i	$-0.518800\pi$
$443$	−2.48474			−0.118054			−0.0590269	+	0.998256i	$0.518800\pi$
$444$	9.99129	+	17.3054i	0.474165	+	0.821279i
$445$	−3.29970	−	5.71526i	−0.156421	−	0.270929i
$446$	1.15633	−	2.00282i	0.0547538	−	0.0948364i
$447$	4.38816			0.207553
$448$	−1.49377	+	2.58729i	−0.0705740	+	0.122238i
$449$	−5.30980	+	9.19685i	−0.250585	+	0.434026i	−0.963687	−	0.267034i	$-0.913956\pi$
$449$	−5.30980	+	9.19685i	−0.250585	+	0.434026i	0.713102	+	0.701060i	$0.247290\pi$
$450$	−0.734036			−0.0346028
$451$	−3.41669	+	5.91789i	−0.160886	+	0.278663i
$452$	7.05364	+	12.2173i	0.331775	+	0.574652i
$453$	−12.8660	−	22.2846i	−0.604498	−	1.04702i
$454$	−4.04953			−0.190054
$455$	1.77251	−	1.58385i	0.0830965	−	0.0742520i
$456$	2.23380			0.104607
$457$	−16.8487	−	29.1829i	−0.788150	−	1.36512i	−0.927099	−	0.374817i	$-0.877706\pi$
$457$	−16.8487	−	29.1829i	−0.788150	−	1.36512i	0.138949	−	0.990300i	$-0.455628\pi$
$458$	−0.00257732	−	0.00446404i	−0.000120430	−	0.000208591i
$459$	−6.63318	+	11.4890i	−0.309611	+	0.536261i
$460$	5.25789			0.245151
$461$	3.51343	−	6.08543i	0.163637	−	0.283427i	−0.772534	−	0.634974i	$-0.781011\pi$
$461$	3.51343	−	6.08543i	0.163637	−	0.283427i	0.936170	+	0.351547i	$0.114344\pi$
$462$	0.0627787	−	0.108736i	0.00292073	−	0.00505885i
$463$	−1.42217			−0.0660939			−0.0330469	−	0.999454i	$-0.510521\pi$
$463$	−1.42217			−0.0660939			−0.0330469	+	0.999454i	$0.510521\pi$
$464$	−0.380298	+	0.658696i	−0.0176549	+	0.0305792i
$465$	1.00666	+	1.74359i	0.0466828	+	0.0808569i
$466$	3.74971	+	6.49468i	0.173702	+	0.300860i
$467$	−15.9194			−0.736663			−0.368331	−	0.929695i	$-0.620071\pi$
$467$	−15.9194			−0.736663			−0.368331	+	0.929695i	$0.620071\pi$
$468$	1.21141	+	5.80739i	0.0559974	+	0.268447i
$469$	−2.11120			−0.0974863
$470$	−1.70695	−	2.95652i	−0.0787356	−	0.136374i
$471$	2.27773	+	3.94514i	0.104952	+	0.181782i
$472$	0.908268	−	1.57317i	0.0418064	−	0.0724109i
$473$	5.90138			0.271346
$474$	−0.553245	+	0.958249i	−0.0254114	+	0.0440138i
$475$	2.19040	−	3.79388i	0.100502	−	0.174075i
$476$	−2.16782			−0.0993619
$477$	4.76886	−	8.25990i	0.218351	−	0.378195i
$478$	2.40393	+	4.16372i	0.109953	+	0.190444i
$479$	−5.10313	−	8.83888i	−0.233168	−	0.403859i	0.725571	−	0.688148i	$-0.241576\pi$
$479$	−5.10313	−	8.83888i	−0.233168	−	0.403859i	−0.958739	+	0.284289i	$0.908243\pi$
$480$	6.33206			0.289018
$481$	5.22186	+	25.0332i	0.238096	+	1.14141i
$482$	−1.25310			−0.0570773
$483$	0.698105	+	1.20915i	0.0317649	+	0.0550184i
$484$	−10.1774	−	17.6279i	−0.462611	−	0.801266i
$485$	7.43465	−	12.8772i	0.337590	−	0.584723i
$486$	−2.36952			−0.107484
$487$	9.28076	−	16.0748i	0.420551	−	0.728416i	−0.575442	−	0.817843i	$-0.695170\pi$
$487$	9.28076	−	16.0748i	0.420551	−	0.728416i	0.995993	+	0.0894261i	$0.0285033\pi$
$488$	0.491969	−	0.852115i	0.0222704	−	0.0385734i
$489$	−14.1721			−0.640884
$490$	1.28423	−	2.22435i	0.0580156	−	0.100486i
$491$	−6.57495	−	11.3881i	−0.296723	−	0.513940i	0.678661	−	0.734452i	$-0.262561\pi$
$491$	−6.57495	−	11.3881i	−0.296723	−	0.513940i	−0.975384	+	0.220512i	$0.929227\pi$
$492$	−14.8598	−	25.7380i	−0.669932	−	1.16036i
$493$	−0.503591			−0.0226806
$494$	1.33132	+	0.438159i	0.0598989	+	0.0197137i
$495$	−0.761665			−0.0342343
$496$	−1.77442	−	3.07339i	−0.0796740	−	0.137999i
$497$	−1.19021	−	2.06150i	−0.0533881	−	0.0924709i
$498$	1.29393	−	2.24115i	0.0579823	−	0.100428i
$499$	−2.18061			−0.0976175			−0.0488088	−	0.998808i	$-0.515542\pi$
$499$	−2.18061			−0.0976175			−0.0488088	+	0.998808i	$0.515542\pi$
$500$	10.7248	−	18.5758i	0.479626	−	0.830736i
$501$	−7.07734	+	12.2583i	−0.316192	+	0.547661i
$502$	−0.0185457			−0.000827736
$503$	−0.314336	+	0.544446i	−0.0140156	+	0.0242757i	−0.872948	−	0.487813i	$-0.837795\pi$
$503$	−0.314336	+	0.544446i	−0.0140156	+	0.0242757i	0.858933	+	0.512089i	$0.171128\pi$
$504$	−0.222061	−	0.384621i	−0.00989140	−	0.0171324i
$505$	−4.88450	−	8.46020i	−0.217357	−	0.376474i
$506$	0.355409			0.0157999
$507$	2.13356	−	18.9186i	0.0947546	−	0.840203i
$508$	−38.7732			−1.72028
$509$	−11.1164	−	19.2541i	−0.492725	−	0.853425i	0.507240	−	0.861805i	$-0.330666\pi$
$509$	−11.1164	−	19.2541i	−0.492725	−	0.853425i	−0.999965	+	0.00838010i	$0.997332\pi$
$510$	0.652760	+	1.13061i	0.0289047	+	0.0500644i
$511$	1.52307	−	2.63804i	0.0673767	−	0.116700i
$512$	−18.8472			−0.832937
$513$	3.97644	−	6.88740i	0.175564	−	0.304086i
$514$	1.95548	−	3.38699i	0.0862525	−	0.149394i
$515$	−6.99210			−0.308109
$516$	−12.8331	+	22.2275i	−0.564945	+	0.978513i
$517$	2.91466	+	5.04834i	0.128187	+	0.222026i
$518$	−0.469316	−	0.812879i	−0.0206206	−	0.0357158i
$519$	−14.3511			−0.629943
$520$	5.09840	+	1.67797i	0.223580	+	0.0735837i
$521$	−13.1236			−0.574954			−0.287477	−	0.957788i	$-0.592816\pi$
$521$	−13.1236			−0.574954			−0.287477	+	0.957788i	$0.592816\pi$
$522$	−0.0252921	−	0.0438073i	−0.00110701	−	0.00191739i
$523$	−10.9185	−	18.9114i	−0.477434	−	0.826939i	0.522232	−	0.852803i	$-0.325100\pi$
$523$	−10.9185	−	18.9114i	−0.477434	−	0.826939i	−0.999665	+	0.0258644i	$0.991766\pi$
$524$	−0.428902	+	0.742879i	−0.0187367	+	0.0324528i
$525$	2.18424			0.0953282
$526$	−3.71382	+	6.43253i	−0.161930	+	0.280472i
$527$	1.17485	−	2.03489i	0.0511771	−	0.0886414i
$528$	−3.36688			−0.146525
$529$	9.52391	−	16.4959i	0.414083	−	0.717213i
$530$	−2.11548	−	3.66411i	−0.0918904	−	0.159159i
$531$	−0.717353	−	1.24249i	−0.0311305	−	0.0539195i
$532$	1.29956			0.0563430
$533$	−7.76636	−	37.2313i	−0.336398	−	1.61267i
$534$	1.94012			0.0839574
$535$	1.32043	+	2.28705i	0.0570872	+	0.0988779i
$536$	−2.38357	−	4.12846i	−0.102955	−	0.178322i
$537$	−15.9834	+	27.6841i	−0.689736	+	1.19466i
$538$	−5.44755			−0.234861
$539$	−2.19286	+	3.79815i	−0.0944532	+	0.163598i
$540$	7.46627	−	12.9320i	0.321297	−	0.556503i
$541$	−1.20030			−0.0516048			−0.0258024	−	0.999667i	$-0.508214\pi$
$541$	−1.20030			−0.0516048			−0.0258024	+	0.999667i	$0.508214\pi$
$542$	2.14566	−	3.71640i	0.0921642	−	0.159633i
$543$	12.0550	+	20.8798i	0.517328	+	0.896039i
$544$	−3.69499	−	6.39991i	−0.158421	−	0.274394i
$545$	−13.4397			−0.575693
$546$	0.142700	+	0.684091i	0.00610699	+	0.0292764i
$547$	44.5664			1.90552			0.952761	−	0.303720i	$-0.0982286\pi$
$547$	44.5664			1.90552			0.952761	+	0.303720i	$0.0982286\pi$
$548$	19.2495	+	33.3411i	0.822299	+	1.42426i
$549$	−0.388558	−	0.673002i	−0.0165833	−	0.0287230i
$550$	0.278003	−	0.481515i	0.0118541	−	0.0205319i
$551$	0.301891			0.0128610
$552$	−1.57633	+	2.73029i	−0.0670933	+	0.116209i
$553$	−0.656466	+	1.13703i	−0.0279158	+	0.0483516i
$554$	−3.66206			−0.155586
$555$	7.13963	−	12.3662i	0.303061	−	0.524916i
$556$	9.72026	+	16.8360i	0.412231	+	0.714005i
$557$	−1.34798	−	2.33476i	−0.0571156	−	0.0989272i	0.836054	−	0.548647i	$-0.184857\pi$
$557$	−1.34798	−	2.33476i	−0.0571156	−	0.0989272i	−0.893169	+	0.449720i	$0.851524\pi$
$558$	0.236020			0.00999152
$559$	−24.4920	+	21.8852i	−1.03590	+	0.925643i
$560$	2.33967			0.0988690
$561$	−1.11461	−	1.93055i	−0.0470587	−	0.0815081i
$562$	−3.45257	−	5.98003i	−0.145638	−	0.252252i
$563$	21.1399	−	36.6155i	0.890942	−	1.54316i	0.0521946	−	0.998637i	$-0.483378\pi$
$563$	21.1399	−	36.6155i	0.890942	−	1.54316i	0.838748	−	0.544520i	$-0.183288\pi$
$564$	−25.3528			−1.06754
$565$	5.04043	−	8.73029i	0.212053	−	0.367286i
$566$	3.50245	−	6.06642i	0.147219	−	0.254991i
$567$	2.73485			0.114853
$568$	2.68751	−	4.65491i	0.112766	−	0.195316i
$569$	−11.8065	−	20.4495i	−0.494956	−	0.857289i	0.505027	−	0.863103i	$-0.331482\pi$
$569$	−11.8065	−	20.4495i	−0.494956	−	0.857289i	−0.999983	+	0.00581474i	$0.998149\pi$
$570$	−0.391314	−	0.677776i	−0.0163904	−	0.0283889i
$571$	−8.36986			−0.350268			−0.175134	−	0.984545i	$-0.556036\pi$
$571$	−8.36986			−0.350268			−0.175134	+	0.984545i	$0.556036\pi$
$572$	−4.26835	−	1.40478i	−0.178469	−	0.0587369i
$573$	−3.50213			−0.146303
$574$	0.698003	+	1.20898i	0.0291341	+	0.0504617i
$575$	3.09142	+	5.35449i	0.128921	+	0.223298i
$576$	−2.66398	+	4.61414i	−0.110999	+	0.192256i
$577$	−1.70007			−0.0707748			−0.0353874	−	0.999374i	$-0.511267\pi$
$577$	−1.70007			−0.0707748			−0.0353874	+	0.999374i	$0.511267\pi$
$578$	−1.58391	+	2.74342i	−0.0658820	+	0.114111i
$579$	7.16899	−	12.4170i	0.297933	−	0.516035i
$580$	0.566839			0.0235367
$581$	1.53534	−	2.65929i	0.0636967	−	0.110326i
$582$	2.18567	+	3.78569i	0.0905990	+	0.156922i
$583$	3.61223	+	6.25657i	0.149603	+	0.259121i
$584$	6.87825			0.284624
$585$	3.16108	−	2.82462i	0.130694	−	0.116784i
$586$	−1.03563			−0.0427817
$587$	24.1149	+	41.7683i	0.995330	+	1.72396i	0.581260	+	0.813718i	$0.302560\pi$
$587$	24.1149	+	41.7683i	0.995330	+	1.72396i	0.414071	+	0.910245i	$0.364107\pi$
$588$	−9.53715	−	16.5188i	−0.393305	−	0.681225i
$589$	−0.704293	+	1.21987i	−0.0290199	+	0.0502639i
$590$	−0.636439			−0.0262018
$591$	−14.3250	+	24.8117i	−0.589253	+	1.02062i
$592$	−12.5849	+	21.7977i	−0.517237	+	0.895881i
$593$	−37.2527			−1.52978			−0.764892	−	0.644159i	$-0.777208\pi$
$593$	−37.2527			−1.52978			−0.764892	+	0.644159i	$0.777208\pi$
$594$	0.504686	−	0.874142i	0.0207075	−	0.0358665i
$595$	0.774547	+	1.34156i	0.0317534	+	0.0549984i
$596$	2.88226	+	4.99222i	0.118062	+	0.204489i
$597$	−10.0052			−0.409484
$598$	−1.47503	+	1.31803i	−0.0603183	+	0.0538982i
$599$	−7.28226			−0.297545			−0.148772	−	0.988871i	$-0.547532\pi$
$599$	−7.28226			−0.297545			−0.148772	+	0.988871i	$0.547532\pi$
$600$	2.46603	+	4.27129i	0.100675	+	0.174375i
$601$	4.10696	+	7.11347i	0.167527	+	0.290165i	0.937550	−	0.347852i	$-0.113089\pi$
$601$	4.10696	+	7.11347i	0.167527	+	0.290165i	−0.770023	+	0.638016i	$0.779755\pi$
$602$	0.602802	−	1.04408i	0.0245684	−	0.0425537i
$603$	−3.76510			−0.153327
$604$	16.9015	−	29.2742i	0.687711	−	1.19115i
$605$	−7.27266	+	12.5966i	−0.295676	+	0.512125i
$606$	2.87193			0.116664
$607$	12.3260	−	21.3492i	0.500296	−	0.866539i	−0.499704	−	0.866196i	$-0.666558\pi$
$607$	12.3260	−	21.3492i	0.500296	−	0.866539i	1.00000		0.000342098i	$-0.000108893\pi$
$608$	2.21506	+	3.83660i	0.0898325	+	0.155595i
$609$	0.0752608	+	0.130356i	0.00304972	+	0.00528227i
$610$	−0.344731			−0.0139577
$611$	−30.8182	−	10.1427i	−1.24677	−	0.410332i
$612$	−3.86607			−0.156277
$613$	−1.42481	−	2.46785i	−0.0575477	−	0.0996755i	0.835816	−	0.549009i	$-0.184995\pi$
$613$	−1.42481	−	2.46785i	−0.0575477	−	0.0996755i	−0.893364	+	0.449334i	$0.851661\pi$
$614$	−1.46296	−	2.53392i	−0.0590402	−	0.102261i
$615$	−10.6186	+	18.3920i	−0.428184	+	0.741637i
$616$	0.336407			0.0135542
$617$	−10.6162	+	18.3878i	−0.427392	+	0.740264i	−0.996640	−	0.0819014i	$-0.973901\pi$
$617$	−10.6162	+	18.3878i	−0.427392	+	0.740264i	0.569249	+	0.822165i	$0.307234\pi$
$618$	1.02778	−	1.78017i	0.0413436	−	0.0716091i
$619$	−11.0933			−0.445878			−0.222939	−	0.974832i	$-0.571565\pi$
$619$	−11.0933			−0.445878			−0.222939	+	0.974832i	$0.571565\pi$
$620$	−1.32240	+	2.29047i	−0.0531089	+	0.0919873i
$621$	5.61215	+	9.72053i	0.225208	+	0.390072i
$622$	1.41073	+	2.44346i	0.0565653	+	0.0979740i
$623$	2.30210			0.0922317
$624$	13.9733	−	12.4860i	0.559379	−	0.499841i
$625$	0.222787			0.00891147
$626$	0.191822	+	0.332245i	0.00766675	+	0.0132792i
$627$	0.668180	+	1.15732i	0.0266846	+	0.0462190i
$628$	−2.99214	+	5.18254i	−0.119399	+	0.206806i
$629$	−16.6650			−0.664475
$630$	−0.0778010	+	0.134755i	−0.00309967	+	0.00536878i
$631$	20.0237	−	34.6820i	0.797130	−	1.38067i	−0.124347	−	0.992239i	$-0.539684\pi$
$631$	20.0237	−	34.6820i	0.797130	−	1.38067i	0.921478	−	0.388431i	$-0.126983\pi$
$632$	−2.96463			−0.117927
$633$	16.5883	−	28.7319i	0.659328	−	1.14199i
$634$	−1.63996	−	2.84050i	−0.0651312	−	0.112811i
$635$	13.8534	+	23.9948i	0.549755	+	0.952203i
$636$	−31.4205			−1.24590
$637$	−4.98451	−	23.8953i	−0.197493	−	0.946767i
$638$	0.0383157			0.00151693
$639$	−2.12261	−	3.67646i	−0.0839690	−	0.145439i
$640$	5.50545	+	9.53572i	0.217622	+	0.376932i
$641$	6.82195	−	11.8160i	0.269451	−	0.466703i	−0.699269	−	0.714858i	$-0.746491\pi$
$641$	6.82195	−	11.8160i	0.269451	−	0.466703i	0.968720	+	0.248156i	$0.0798244\pi$
$642$	−0.776372			−0.0306410
$643$	0.680491	−	1.17864i	0.0268359	−	0.0464812i	−0.852296	−	0.523061i	$-0.824790\pi$
$643$	0.680491	−	1.17864i	0.0268359	−	0.0464812i	0.879131	+	0.476579i	$0.158123\pi$
$644$	−0.917066	+	1.58841i	−0.0361375	+	0.0625920i
$645$	18.3407			0.722164
$646$	−0.456693	+	0.791015i	−0.0179683	+	0.0311221i
$647$	−17.2802	−	29.9301i	−0.679354	−	1.17668i	−0.975176	−	0.221432i	$-0.928927\pi$
$647$	−17.2802	−	29.9301i	−0.679354	−	1.17668i	0.295822	−	0.955243i	$-0.404407\pi$
$648$	3.08767	+	5.34801i	0.121295	+	0.210090i
$649$	1.08674			0.0426582
$650$	0.631917	+	3.02936i	0.0247858	+	0.118821i
$651$	−0.702315			−0.0275259
$652$	−9.30860	−	16.1230i	−0.364553	−	0.631424i
$653$	−7.72595	−	13.3817i	−0.302340	−	0.523668i	0.674326	−	0.738434i	$-0.264434\pi$
$653$	−7.72595	−	13.3817i	−0.302340	−	0.523668i	−0.976665	+	0.214766i	$0.931101\pi$
$654$	1.97553	−	3.42172i	0.0772494	−	0.133800i
$655$	0.612974			0.0239509
$656$	18.7173	−	32.4193i	0.730787	−	1.26576i
$657$	2.71623	−	4.70465i	0.105970	−	0.183546i
$658$	1.19088			0.0464255
$659$	−13.3438	+	23.1121i	−0.519799	+	0.900319i	0.479936	+	0.877304i	$0.340660\pi$
$659$	−13.3438	+	23.1121i	−0.519799	+	0.900319i	−0.999735	+	0.0230154i	$0.992673\pi$
$660$	1.25459	+	2.17302i	0.0488350	+	0.0845847i
$661$	20.2142	+	35.0121i	0.786243	+	1.36181i	0.928254	+	0.371948i	$0.121310\pi$
$661$	20.2142	+	35.0121i	0.786243	+	1.36181i	−0.142011	+	0.989865i	$0.545357\pi$
$662$	−6.65643			−0.258709
$663$	11.7853	+	3.87872i	0.457702	+	0.150637i
$664$	6.93366			0.269078
$665$	−0.464323	−	0.804231i	−0.0180057	−	0.0311868i
$666$	−0.836973	−	1.44968i	−0.0324321	−	0.0561740i
$667$	−0.213037	+	0.368991i	−0.00824883	+	0.0142874i
$668$	−18.5943			−0.719436
$669$	−6.13637	+	10.6285i	−0.237246	+	0.410922i
$670$	−0.835103	+	1.44644i	−0.0322629	+	0.0558809i
$671$	0.588637			0.0227241
$672$	−1.10442	+	1.91291i	−0.0426039	+	0.0737921i
$673$	6.18814	+	10.7182i	0.238535	+	0.413155i	0.960294	−	0.278989i	$-0.0899994\pi$
$673$	6.18814	+	10.7182i	0.238535	+	0.413155i	−0.721759	+	0.692144i	$0.756666\pi$
$674$	−1.80917	−	3.13357i	−0.0696865	−	0.120701i
$675$	17.5594			0.675862
$676$	22.9242	−	9.99894i	0.881699	−	0.384575i
$677$	21.4334			0.823753			0.411876	−	0.911240i	$-0.364874\pi$
$677$	21.4334			0.823753			0.411876	+	0.911240i	$0.364874\pi$
$678$	1.48181	+	2.56657i	0.0569086	+	0.0985685i
$679$	2.59346	+	4.49200i	0.0995278	+	0.172387i
$680$	−1.74894	+	3.02926i	−0.0670689	+	0.116167i
$681$	21.4899			0.823495
$682$	−0.0893882	+	0.154825i	−0.00342285	+	0.00592855i
$683$	−24.5624	+	42.5433i	−0.939853	+	1.62787i	−0.174110	+	0.984726i	$0.555705\pi$
$683$	−24.5624	+	42.5433i	−0.939853	+	1.62787i	−0.765743	+	0.643147i	$0.777628\pi$
$684$	2.31762			0.0886164
$685$	13.7554	−	23.8251i	0.525568	−	0.910311i
$686$	0.911185	+	1.57822i	0.0347892	+	0.0602567i
$687$	0.0136772	+	0.0236896i	0.000521818	+	0.000903815i
$688$	−32.3288			−1.23253
$689$	−38.1939	−	12.5702i	−1.45507	−	0.478888i
$690$	1.10456			0.0420500
$691$	0.429641	+	0.744159i	0.0163443	+	0.0283092i	0.874082	−	0.485779i	$-0.161464\pi$
$691$	0.429641	+	0.744159i	0.0163443	+	0.0283092i	−0.857738	+	0.514088i	$0.828131\pi$
$692$	−9.42616	−	16.3266i	−0.358329	−	0.620644i
$693$	0.132847	−	0.230099i	0.00504646	−	0.00874072i
$694$	−2.63708			−0.100102
$695$	6.94596	−	12.0308i	0.263475	−	0.456353i
$696$	−0.169940	+	0.294345i	−0.00644157	+	0.0111571i
$697$	24.7854			0.938815
$698$	−1.06496	+	1.84456i	−0.0403092	+	0.0698175i
$699$	−19.8988	−	34.4658i	−0.752642	−	1.30361i
$700$	1.43467	+	2.48492i	0.0542253	+	0.0939210i
$701$	34.0301			1.28530			0.642649	−	0.766161i	$-0.277835\pi$
$701$	34.0301			1.28530			0.642649	+	0.766161i	$0.277835\pi$
$702$	1.14718	+	5.49949i	0.0432976	+	0.207565i
$703$	9.99025			0.376790
$704$	−2.01786	−	3.49504i	−0.0760511	−	0.131724i
$705$	9.05837	+	15.6896i	0.341158	+	0.590903i
$706$	−3.67157	+	6.35934i	−0.138181	+	0.239337i
$707$	3.40776			0.128162
$708$	−2.36321	+	4.09319i	−0.0888148	+	0.153832i
$709$	23.5041	−	40.7103i	0.882716	−	1.52891i	0.0344058	−	0.999408i	$-0.489046\pi$
$709$	23.5041	−	40.7103i	0.882716	−	1.52891i	0.848310	−	0.529500i	$-0.177621\pi$
$710$	−1.88319			−0.0706747
$711$	−1.17074	+	2.02777i	−0.0439060	+	0.0760474i
$712$	2.59909	+	4.50176i	0.0974051	+	0.168711i
$713$	−0.994005	−	1.72167i	−0.0372258	−	0.0644770i
$714$	−0.455410			−0.0170433
$715$	0.655703	+	3.14339i	0.0245219	+	0.117556i
$716$	−41.9933			−1.56936
$717$	−12.7571	−	22.0959i	−0.476422	−	0.825186i
$718$	1.51041	+	2.61612i	0.0563682	+	0.0976326i
$719$	1.56068	−	2.70317i	0.0582034	−	0.100811i	−0.835456	−	0.549558i	$-0.814796\pi$
$719$	1.56068	−	2.70317i	0.0582034	−	0.100811i	0.893659	+	0.448747i	$0.148129\pi$
$720$	4.17254			0.155501
$721$	1.21954	−	2.11231i	0.0454181	−	0.0786665i
$722$	−2.34792	+	4.06672i	−0.0873806	+	0.151348i
$723$	6.64992			0.247313
$724$	−15.8360	+	27.4288i	−0.588541	+	1.01938i
$725$	0.333277	+	0.577253i	0.0123776	+	0.0214387i
$726$	−2.13805	−	3.70321i	−0.0793505	−	0.137439i
$727$	16.8580			0.625230			0.312615	−	0.949880i	$-0.398795\pi$
$727$	16.8580			0.625230			0.312615	+	0.949880i	$0.398795\pi$
$728$	−1.39616	+	1.24756i	−0.0517452	+	0.0462376i
$729$	29.6830			1.09937
$730$	−1.20493	−	2.08699i	−0.0445963	−	0.0772431i
$731$	−10.7025	−	18.5372i	−0.395845	−	0.685624i
$732$	−1.28004	+	2.21710i	−0.0473118	+	0.0819464i
$733$	18.1596			0.670741			0.335370	−	0.942086i	$-0.391139\pi$
$733$	18.1596			0.670741			0.335370	+	0.942086i	$0.391139\pi$
$734$	−1.33115	+	2.30561i	−0.0491335	+	0.0851018i
$735$	−6.81511	+	11.8041i	−0.251379	+	0.435402i
$736$	−6.25246			−0.230469
$737$	1.42596	−	2.46984i	0.0525260	−	0.0909777i
$738$	1.24481	+	2.15608i	0.0458222	+	0.0793663i
$739$	−12.1064	−	20.9689i	−0.445341	−	0.771353i	0.552735	−	0.833357i	$-0.313584\pi$
$739$	−12.1064	−	20.9689i	−0.445341	−	0.771353i	−0.998076	+	0.0620039i	$0.980251\pi$
$740$	18.7580			0.689557
$741$	−7.06500	−	2.32520i	−0.259539	−	0.0854185i
$742$	1.47590			0.0541820
$743$	8.80158	+	15.2448i	0.322899	+	0.559277i	0.981085	−	0.193578i	$-0.0620093\pi$
$743$	8.80158	+	15.2448i	0.322899	+	0.559277i	−0.658186	+	0.752855i	$0.728676\pi$
$744$	−0.792921	−	1.37338i	−0.0290699	−	0.0503505i
$745$	2.05962	−	3.56737i	0.0754587	−	0.130698i
$746$	−6.07433			−0.222397
$747$	2.73811	−	4.74255i	0.100182	−	0.173521i
$748$	1.46420	−	2.53608i	0.0535366	−	0.0927281i
$749$	−0.921222			−0.0336607
$750$	2.25303	−	3.90236i	0.0822689	−	0.142494i
$751$	13.6592	+	23.6585i	0.498432	+	0.863310i	0.999998	−	0.00180922i	$-0.000575893\pi$
$751$	13.6592	+	23.6585i	0.498432	+	0.863310i	−0.501566	+	0.865119i	$0.667243\pi$
$752$	−15.9671	−	27.6557i	−0.582258	−	1.00850i
$753$	0.0984178			0.00358654
$754$	−0.159019	+	0.142093i	−0.00579112	+	0.00517473i
$755$	−24.1551			−0.879094
$756$	2.60449	+	4.51111i	0.0947244	+	0.164068i
$757$	8.61671	+	14.9246i	0.313179	+	0.542443i	0.979049	−	0.203626i	$-0.0652725\pi$
$757$	8.61671	+	14.9246i	0.313179	+	0.542443i	−0.665869	+	0.746068i	$0.731939\pi$
$758$	3.01541	−	5.22284i	0.109525	−	0.189702i
$759$	−1.88607			−0.0684602
$760$	1.04845	−	1.81597i	0.0380313	−	0.0658722i
$761$	10.2588	−	17.7687i	0.371880	−	0.644115i	−0.617975	−	0.786198i	$-0.712047\pi$
$761$	10.2588	−	17.7687i	0.371880	−	0.644115i	0.989855	+	0.142083i	$0.0453800\pi$
$762$	−8.14536			−0.295075
$763$	2.34411	−	4.06012i	0.0848626	−	0.146986i
$764$	−2.30029	−	3.98421i	−0.0832215	−	0.144144i
$765$	1.38132	+	2.39252i	0.0499417	+	0.0865016i
$766$	−3.10375			−0.112143
$767$	−4.51019	+	4.03014i	−0.162854	+	0.145520i
$768$	15.0099			0.541623
$769$	24.5046	+	42.4432i	0.883659	+	1.53054i	0.847244	+	0.531205i	$0.178260\pi$
$769$	24.5046	+	42.4432i	0.883659	+	1.53054i	0.0364150	+	0.999337i	$0.488406\pi$
$770$	−0.0589314	−	0.102072i	−0.00212374	−	0.00367843i
$771$	−10.3773	+	17.9740i	−0.373728	+	0.647316i
$772$	18.8351			0.677890
$773$	−1.37115	+	2.37490i	−0.0493168	+	0.0854192i	−0.889630	−	0.456682i	$-0.849038\pi$
$773$	−1.37115	+	2.37490i	−0.0493168	+	0.0854192i	0.840313	+	0.542101i	$0.182371\pi$
$774$	1.07503	−	1.86201i	0.0386412	−	0.0669285i
$775$	−3.11006			−0.111717
$776$	−5.85608	+	10.1430i	−0.210221	+	0.364114i
$777$	2.49055	+	4.31376i	0.0893479	+	0.154755i
$778$	−0.481032	−	0.833171i	−0.0172458	−	0.0298706i
$779$	−14.8583			−0.532353
$780$	−13.2654	−	4.36587i	−0.474979	−	0.156323i
$781$	3.21559			0.115063
$782$	−0.644554	−	1.11640i	−0.0230492	−	0.0399224i
$783$	0.605031	+	1.04794i	0.0216220	+	0.0374505i
$784$	12.0129	−	20.8069i	0.429032	−	0.743105i
$785$	4.27628			0.152627
$786$	−0.0901025	+	0.156062i	−0.00321385	+	0.00556655i
$787$	−4.90054	+	8.48798i	−0.174685	+	0.302564i	−0.940052	−	0.341030i	$-0.889224\pi$
$787$	−4.90054	+	8.48798i	−0.174685	+	0.302564i	0.765367	+	0.643594i	$0.222558\pi$
$788$	−37.6362			−1.34073
$789$	19.7084	−	34.1359i	0.701637	−	1.21527i
$790$	0.519341	+	0.899525i	0.0184773	+	0.0320037i
$791$	1.75828	+	3.04542i	0.0625171	+	0.108283i
$792$	0.599945			0.0213181
$793$	−2.44297	+	2.18295i	−0.0867525	+	0.0775188i
$794$	−0.332518			−0.0118006
$795$	11.2263	+	19.4446i	0.398157	+	0.689628i
$796$	−6.57165	−	11.3824i	−0.232926	−	0.403440i
$797$	−14.1100	+	24.4393i	−0.499803	+	0.865685i	−1.00000		0.000226985i	$-0.999928\pi$
$797$	−14.1100	+	24.4393i	−0.499803	+	0.865685i	0.500197	+	0.865912i	$0.333261\pi$
$798$	0.273008			0.00966437
$799$	10.5718	−	18.3109i	0.374003	−	0.647792i
$800$	−4.89070	+	8.47094i	−0.172912	+	0.299493i
$801$	4.10554			0.145062
$802$	−4.46582	+	7.73502i	−0.157693	+	0.273133i
$803$	2.05745	+	3.56360i	0.0726057	+	0.125757i
$804$	6.20177	+	10.7418i	0.218720	+	0.378833i
$805$	1.31065			0.0461942
$806$	−0.203185	−	0.974052i	−0.00715688	−	0.0343095i
$807$	28.9089			1.01764
$808$	3.84740	+	6.66389i	0.135351	+	0.234435i
$809$	−17.9697	−	31.1245i	−0.631783	−	1.09428i	−0.987187	−	0.159567i	$-0.948990\pi$
$809$	−17.9697	−	31.1245i	−0.631783	−	1.09428i	0.355404	−	0.934713i	$-0.384343\pi$
$810$	1.08179	−	1.87372i	0.0380103	−	0.0658358i
$811$	10.2445			0.359731			0.179866	−	0.983691i	$-0.442434\pi$
$811$	10.2445			0.359731			0.179866	+	0.983691i	$0.442434\pi$
$812$	−0.0988665	+	0.171242i	−0.00346953	+	0.00600941i
$813$	−11.3865	+	19.7221i	−0.399343	+	0.691683i
$814$	1.26795			0.0444417
$815$	−6.65179	+	11.5212i	−0.233002	+	0.403572i
$816$	6.10602	+	10.5759i	0.213753	+	0.370232i
$817$	6.41588	+	11.1126i	0.224463	+	0.388782i
$818$	2.52118			0.0881508
$819$	0.301970	+	1.44762i	0.0105517	+	0.0505840i
$820$	−27.8983			−0.974252
$821$	−3.92234	−	6.79369i	−0.136891	−	0.237101i	0.789428	−	0.613844i	$-0.210378\pi$
$821$	−3.92234	−	6.79369i	−0.136891	−	0.237101i	−0.926318	+	0.376742i	$0.877044\pi$
$822$	4.04389	+	7.00422i	0.141047	+	0.244300i
$823$	−13.2367	+	22.9266i	−0.461402	+	0.799171i	−0.999031	−	0.0440101i	$-0.985987\pi$
$823$	−13.2367	+	22.9266i	−0.461402	+	0.799171i	0.537629	+	0.843181i	$0.319320\pi$
$824$	5.50750			0.191863
$825$	−1.47530	+	2.55529i	−0.0513632	+	0.0889637i
$826$	0.111006	−	0.192268i	0.00386238	−	0.00668985i
$827$	44.7520			1.55618			0.778089	−	0.628154i	$-0.216189\pi$
$827$	44.7520			1.55618			0.778089	+	0.628154i	$0.216189\pi$
$828$	−1.63549	+	2.83275i	−0.0568371	+	0.0984448i
$829$	−0.324838	−	0.562637i	−0.0112821	−	0.0195412i	0.860329	−	0.509739i	$-0.170258\pi$
$829$	−0.324838	−	0.562637i	−0.0112821	−	0.0195412i	−0.871611	+	0.490198i	$0.836925\pi$
$830$	−1.21463	−	2.10381i	−0.0421605	−	0.0730242i
$831$	19.4337			0.674147
$832$	21.3359	+	7.02198i	0.739689	+	0.243443i
$833$	15.9075			0.551161
$834$	2.04201	+	3.53686i	0.0707089	+	0.122471i
$835$	6.64362	+	11.5071i	0.229912	+	0.398219i
$836$	−0.877756	+	1.52032i	−0.0303578	+	0.0525813i
$837$	−5.64600			−0.195154
$838$	−2.09821	+	3.63420i	−0.0724813	+	0.125541i
$839$	−17.9106	+	31.0221i	−0.618343	+	1.07100i	0.371445	+	0.928455i	$0.378862\pi$
$839$	−17.9106	+	31.0221i	−0.618343	+	1.07100i	−0.989788	+	0.142546i	$0.954471\pi$
$840$	1.04551			0.0360734
$841$	14.4770	−	25.0750i	0.499208	−	0.864654i
$842$	3.63091	+	6.28891i	0.125129	+	0.216730i
$843$	18.3220	+	31.7346i	0.631043	+	1.09300i
$844$	43.5826			1.50018
$845$	−14.3785	−	10.6141i	−0.494635	−	0.365135i
$846$	2.12381			0.0730181
$847$	−2.53695	−	4.39413i	−0.0871707	−	0.150984i
$848$	−19.7885	−	34.2746i	−0.679539	−	1.17700i
$849$	−18.5867	+	32.1931i	−0.637893	+	1.10486i
$850$	−2.01669			−0.0691719
$851$	−7.04988	+	12.2107i	−0.241667	+	0.418579i
$852$	−6.99259	+	12.1115i	−0.239562	+	0.414934i
$853$	−50.3787			−1.72494			−0.862468	−	0.506112i	$-0.831082\pi$
$853$	−50.3787			−1.72494			−0.862468	+	0.506112i	$0.831082\pi$
$854$	0.0601269	−	0.104143i	0.00205750	−	0.00356369i
$855$	−0.828069	−	1.43426i	−0.0283194	−	0.0490506i
$856$	−1.04007	−	1.80145i	−0.0355488	−	0.0615724i
$857$	32.3249			1.10420			0.552098	−	0.833779i	$-0.313827\pi$
$857$	32.3249			1.10420			0.552098	+	0.833779i	$0.313827\pi$
$858$	−0.896683	−	0.295113i	−0.0306123	−	0.0100750i
$859$	−41.7146			−1.42329			−0.711643	−	0.702542i	$-0.752048\pi$
$859$	−41.7146			−1.42329			−0.711643	+	0.702542i	$0.752048\pi$
$860$	12.0466	+	20.8654i	0.410787	+	0.711504i
$861$	−3.70414	−	6.41575i	−0.126237	−	0.218648i
$862$	−2.73800	+	4.74235i	−0.0932565	+	0.161525i
$863$	−6.05943			−0.206265			−0.103133	−	0.994668i	$-0.532887\pi$
$863$	−6.05943			−0.206265			−0.103133	+	0.994668i	$0.532887\pi$
$864$	−8.87856	+	15.3781i	−0.302055	+	0.523174i
$865$	−6.73580	+	11.6668i	−0.229024	+	0.396682i
$866$	−0.555341			−0.0188713
$867$	8.40545	−	14.5587i	0.285464	−	0.494438i
$868$	−0.461299	−	0.798993i	−0.0156575	−	0.0271196i
$869$	−0.886790	−	1.53596i	−0.0300823	−	0.0521040i
$870$	0.119080			0.00403719
$871$	3.24130	+	15.5385i	0.109827	+	0.526503i
$872$	10.5861			0.358491
$873$	4.62515	+	8.01100i	0.156538	+	0.271131i
$874$	0.386395	+	0.669256i	0.0130700	+	0.0226379i
$875$	2.67338	−	4.63043i	0.0903768	−	0.156537i
$876$	−17.8964			−0.604664
$877$	−10.0658	+	17.4345i	−0.339899	+	0.588723i	−0.984413	−	0.175870i	$-0.943726\pi$
$877$	−10.0658	+	17.4345i	−0.339899	+	0.588723i	0.644514	+	0.764592i	$0.277060\pi$
$878$	1.19645	−	2.07231i	0.0403782	−	0.0699370i
$879$	5.49587			0.185371
$880$	−1.58027	+	2.73712i	−0.0532710	+	0.0922681i
$881$	28.9819	+	50.1981i	0.976425	+	1.69122i	0.675148	+	0.737682i	$0.264080\pi$
$881$	28.9819	+	50.1981i	0.976425	+	1.69122i	0.301277	+	0.953537i	$0.402587\pi$
$882$	0.798930	+	1.38379i	0.0269014	+	0.0465945i
$883$	22.5446			0.758687			0.379343	−	0.925256i	$-0.376150\pi$
$883$	22.5446			0.758687			0.379343	+	0.925256i	$0.376150\pi$
$884$	3.32823	+	15.9552i	0.111940	+	0.536633i
$885$	3.37743			0.113531
$886$	−0.342855	−	0.593843i	−0.0115184	−	0.0199505i
$887$	−24.8882	−	43.1076i	−0.835664	−	1.44741i	−0.893489	−	0.449085i	$-0.851750\pi$
$887$	−24.8882	−	43.1076i	−0.835664	−	1.44741i	0.0578253	−	0.998327i	$-0.481583\pi$
$888$	−5.62371	+	9.74055i	−0.188719	+	0.326871i
$889$	−9.66506			−0.324156
$890$	0.910614	−	1.57723i	0.0305238	−	0.0528689i
$891$	−1.84719	+	3.19943i	−0.0618832	+	0.107185i
$892$	−16.1221			−0.539808
$893$	−6.33754	+	10.9769i	−0.212078	+	0.367329i
$894$	0.605497	+	1.04875i	0.0202508	+	0.0350755i
$895$	15.0039	+	25.9875i	0.501526	+	0.868668i
$896$	−3.84098			−0.128318
$897$	7.82762	−	6.99447i	0.261357	−	0.233539i
$898$	−2.93067			−0.0977979
$899$	−0.107161	−	0.185608i	−0.00357402	−	0.00619038i
$900$	2.55857	+	4.43158i	0.0852857	+	0.147719i
$901$	13.1020	−	22.6933i	0.436489	−	0.756022i
$902$	−1.88580			−0.0627902
$903$	−3.19893	+	5.54071i	−0.106454	+	0.184383i
$904$	−3.97022	+	6.87663i	−0.132048	+	0.228713i
$905$	22.6324			0.752327
$906$	3.55061	−	6.14984i	0.117961	−	0.204315i
$907$	−2.66060	−	4.60829i	−0.0883437	−	0.153016i	0.818467	−	0.574553i	$-0.194824\pi$
$907$	−2.66060	−	4.60829i	−0.0883437	−	0.153016i	−0.906811	+	0.421537i	$0.861491\pi$
$908$	14.1151	+	24.4481i	0.468427	+	0.811339i
$909$	6.07737			0.201574
$910$	0.623111	+	0.205076i	0.0206559	+	0.00679820i
$911$	−50.5978			−1.67638			−0.838189	−	0.545380i	$-0.816386\pi$
$911$	−50.5978			−1.67638			−0.838189	+	0.545380i	$0.816386\pi$
$912$	−3.66041	−	6.34002i	−0.121208	−	0.209939i
$913$	2.07402	+	3.59231i	0.0686401	+	0.118888i
$914$	4.64972	−	8.05354i	0.153799	−	0.266388i
$915$	1.82940			0.0604782
$916$	−0.0179671	+	0.0311199i	−0.000593649	+	0.00102823i
$917$	−0.106913	+	0.185179i	−0.00353058	+	0.00611515i
$918$	−3.66110			−0.120834
$919$	18.1208	−	31.3861i	0.597750	−	1.03533i	−0.395403	−	0.918508i	$-0.629395\pi$
$919$	18.1208	−	31.3861i	0.597750	−	1.03533i	0.993153	−	0.116825i	$-0.0372717\pi$
$920$	1.47973	+	2.56297i	0.0487853	+	0.0844987i
$921$	7.76358	+	13.4469i	0.255819	+	0.443091i
$922$	1.93919			0.0638638
$923$	−13.3454	+	11.9250i	−0.439269	+	0.392515i
$924$	−0.875291			−0.0287950
$925$	11.0289	+	19.1026i	0.362628	+	0.628090i
$926$	−0.196237	−	0.339893i	−0.00644875	−	0.0111696i
$927$	2.17492	−	3.76707i	0.0714337	−	0.123727i
$928$	−0.674060			−0.0221271
$929$	−26.9723	+	46.7175i	−0.884934	+	1.53275i	−0.0391448	+	0.999234i	$0.512463\pi$
$929$	−26.9723	+	46.7175i	−0.884934	+	1.53275i	−0.845789	+	0.533517i	$0.820870\pi$
$930$	−0.277806	+	0.481175i	−0.00910963	+	0.0157783i
$931$	−9.53616			−0.312535
$932$	26.1401	−	45.2760i	0.856248	−	1.48306i
$933$	−7.48644	−	12.9669i	−0.245095	−	0.424517i
$934$	−2.19663	−	3.80467i	−0.0718759	−	0.124493i
$935$	−2.09260			−0.0684353
$936$	−2.48990	+	2.22488i	−0.0813849	+	0.0727226i
$937$	47.9951			1.56793			0.783966	−	0.620804i	$-0.213194\pi$
$937$	47.9951			1.56793			0.783966	+	0.620804i	$0.213194\pi$
$938$	−0.291313	−	0.504568i	−0.00951169	−	0.0164747i
$939$	−1.01795	−	1.76315i	−0.0332197	−	0.0575382i
$940$	−11.8995	+	20.6106i	−0.388120	+	0.672244i
$941$	−39.2007			−1.27791			−0.638953	−	0.769246i	$-0.720632\pi$
$941$	−39.2007			−1.27791			−0.638953	+	0.769246i	$0.720632\pi$
$942$	−0.628581	+	1.08873i	−0.0204803	+	0.0354729i
$943$	10.4851	−	18.1608i	0.341443	−	0.591396i
$944$	−5.95334			−0.193765
$945$	1.86113	−	3.22358i	0.0605427	−	0.104863i
$946$	0.814297	+	1.41040i	0.0264751	+	0.0458562i
$947$	20.6736	+	35.8077i	0.671802	+	1.16359i	0.977393	+	0.211432i	$0.0678126\pi$
$947$	20.6736	+	35.8077i	0.671802	+	1.16359i	−0.305591	+	0.952163i	$0.598854\pi$
$948$	7.71361			0.250526
$949$	−21.7544	−	7.15972i	−0.706178	−	0.232414i
$950$	1.20896			0.0392238
$951$	8.70289	+	15.0739i	0.282211	+	0.488803i
$952$	−0.610091	−	1.05671i	−0.0197732	−	0.0342481i
$953$	8.47178	−	14.6736i	0.274428	−	0.475323i	−0.695563	−	0.718465i	$-0.744845\pi$
$953$	8.47178	−	14.6736i	0.274428	−	0.475323i	0.969991	+	0.243142i	$0.0781782\pi$
$954$	2.63211			0.0852176
$955$	−1.64375	+	2.84706i	−0.0531906	+	0.0921288i
$956$	16.7583	−	29.0263i	0.542004	−	0.938778i
$957$	−0.203333			−0.00657281
$958$	1.40830	−	2.43925i	0.0455002	−	0.0788086i
$959$	4.79837	+	8.31102i	0.154947	+	0.268377i
$960$	−6.27125	−	10.8621i	−0.202404	−	0.350573i
$961$	1.00000			0.0322581
$962$	−5.26228	+	4.70218i	−0.169663	+	0.151604i
$963$	−1.64290			−0.0529417
$964$	4.36784	+	7.56532i	0.140679	+	0.243663i
$965$	−6.72965	−	11.6561i	−0.216635	−	0.375223i
$966$	−0.192655	+	0.333688i	−0.00619857	+	0.0107362i
$967$	21.2770			0.684224			0.342112	−	0.939659i	$-0.388858\pi$
$967$	21.2770			0.684224			0.342112	+	0.939659i	$0.388858\pi$
$968$	5.72849	−	9.92204i	0.184121	−	0.318906i
$969$	2.42356	−	4.19773i	0.0778560	−	0.134851i
$970$	4.10346			0.131754
$971$	−1.89724	+	3.28612i	−0.0608854	+	0.105457i	−0.894861	−	0.446344i	$-0.852726\pi$
$971$	−1.89724	+	3.28612i	−0.0608854	+	0.105457i	0.833976	+	0.551801i	$0.186059\pi$
$972$	8.25925	+	14.3054i	0.264916	+	0.458847i
$973$	2.42299	+	4.19674i	0.0776775	+	0.134541i
$974$	5.12239			0.164132
$975$	−3.35344	−	16.0761i	−0.107396	−	0.514847i
$976$	−3.22466			−0.103219
$977$	−8.73096	−	15.1225i	−0.279328	−	0.483810i	0.691890	−	0.722003i	$-0.256778\pi$
$977$	−8.73096	−	15.1225i	−0.279328	−	0.483810i	−0.971218	+	0.238193i	$0.923445\pi$
$978$	−1.95552	−	3.38707i	−0.0625308	−	0.108306i
$979$	−1.55490	+	2.69316i	−0.0496948	+	0.0860739i
$980$	−17.9054			−0.571966
$981$	4.18047	−	7.24078i	0.133472	−	0.231180i
$982$	1.81448	−	3.14277i	0.0579023	−	0.100290i
$983$	34.1328			1.08867			0.544334	−	0.838868i	$-0.316782\pi$
$983$	34.1328			1.08867			0.544334	+	0.838868i	$0.316782\pi$
$984$	8.36402	−	14.4869i	0.266635	−	0.461826i
$985$	13.4471	+	23.2911i	0.428462	+	0.742117i
$986$	−0.0694876	−	0.120356i	−0.00221294	−	0.00383292i
$987$	−6.31974			−0.201160
$988$	−1.99519	−	9.56479i	−0.0634756	−	0.304297i
$989$	−18.1101			−0.575868
$990$	−0.105098	−	0.182035i	−0.00334023	−	0.00578544i
$991$	−24.1200	−	41.7770i	−0.766196	−	1.32709i	−0.939612	−	0.342242i	$-0.888814\pi$
$991$	−24.1200	−	41.7770i	−0.766196	−	1.32709i	0.173416	−	0.984849i	$-0.444520\pi$
$992$	1.57254	−	2.72372i	0.0499282	−	0.0864782i
$993$	35.3241			1.12098
$994$	0.328460	−	0.568909i	0.0104181	−	0.0180447i
$995$	−4.69601	+	8.13373i	−0.148874	+	0.257857i
$996$	−18.0406			−0.571637
$997$	11.7543	−	20.3591i	0.372263	−	0.644778i	−0.617651	−	0.786453i	$-0.711915\pi$
$997$	11.7543	−	20.3591i	0.372263	−	0.644778i	0.989913	+	0.141675i	$0.0452487\pi$
$998$	−0.300890	−	0.521156i	−0.00952450	−	0.0164969i
$999$	20.0218	+	34.6788i	0.633463	+	1.09719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.12	✓	36
13.3	even	3		5239.2.a.p.1.7		18
13.9	even	3	inner	403.2.f.c.373.12	yes	36
13.10	even	6		5239.2.a.o.1.12		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.12	✓	36	1.1	even	1	trivial
403.2.f.c.373.12	yes	36	13.9	even	3	inner
5239.2.a.o.1.12		18	13.10	even	6
5239.2.a.p.1.7		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.137984 + 0.238996i) q^{2} +(-0.732250 - 1.26829i) q^{3} +(0.961921 - 1.66610i) q^{4} -1.37475 q^{5} +(0.202078 - 0.350009i) q^{6} +(0.239780 - 0.415311i) q^{7} +1.08286 q^{8} +(0.427621 - 0.740662i) q^{9} +O(q^{10})\)	\(q+(0.137984 + 0.238996i) q^{2} +(-0.732250 - 1.26829i) q^{3} +(0.961921 - 1.66610i) q^{4} -1.37475 q^{5} +(0.202078 - 0.350009i) q^{6} +(0.239780 - 0.415311i) q^{7} +1.08286 q^{8} +(0.427621 - 0.740662i) q^{9} +(-0.189694 - 0.328559i) q^{10} +(0.323908 + 0.561024i) q^{11} -2.81746 q^{12} +(-3.42483 - 1.12717i) q^{13} +0.132343 q^{14} +(1.00666 + 1.74359i) q^{15} +(-1.77442 - 3.07339i) q^{16} +(1.17485 - 2.03489i) q^{17} +0.236020 q^{18} +(-0.704293 + 1.21987i) q^{19} +(-1.32240 + 2.29047i) q^{20} -0.702315 q^{21} +(-0.0893882 + 0.154825i) q^{22} +(-0.994005 - 1.72167i) q^{23} +(-0.792921 - 1.37338i) q^{24} -3.11006 q^{25} +(-0.203185 - 0.974052i) q^{26} -5.64600 q^{27} +(-0.461299 - 0.798993i) q^{28} +(-0.107161 - 0.185608i) q^{29} +(-0.277806 + 0.481175i) q^{30} +1.00000 q^{31} +(1.57254 - 2.72372i) q^{32} +(0.474362 - 0.821620i) q^{33} +0.648441 q^{34} +(-0.329638 + 0.570949i) q^{35} +(-0.822676 - 1.42492i) q^{36} +(-3.54620 - 6.14220i) q^{37} -0.388725 q^{38} +(1.07825 + 5.16906i) q^{39} -1.48866 q^{40} +(5.27418 + 9.13515i) q^{41} +(-0.0969084 - 0.167850i) q^{42} +(4.55483 - 7.88920i) q^{43} +1.24629 q^{44} +(-0.587873 + 1.01823i) q^{45} +(0.274314 - 0.475126i) q^{46} +8.99844 q^{47} +(-2.59864 + 4.50098i) q^{48} +(3.38501 + 5.86301i) q^{49} +(-0.429139 - 0.743291i) q^{50} -3.44112 q^{51} +(-5.17239 + 4.62186i) q^{52} +11.1521 q^{53} +(-0.779058 - 1.34937i) q^{54} +(-0.445292 - 0.771268i) q^{55} +(0.259647 - 0.449722i) q^{56} +2.06287 q^{57} +(0.0295730 - 0.0512220i) q^{58} +(0.838771 - 1.45279i) q^{59} +3.87331 q^{60} +(0.454325 - 0.786914i) q^{61} +(0.137984 + 0.238996i) q^{62} +(-0.205070 - 0.355192i) q^{63} -6.22976 q^{64} +(4.70829 + 1.54957i) q^{65} +0.261818 q^{66} +(-2.20119 - 3.81257i) q^{67} +(-2.26022 - 3.91481i) q^{68} +(-1.45572 + 2.52138i) q^{69} -0.181939 q^{70} +(2.48188 - 4.29873i) q^{71} +(0.463052 - 0.802030i) q^{72} +6.35196 q^{73} +(0.978638 - 1.69505i) q^{74} +(2.27734 + 3.94447i) q^{75} +(1.35495 + 2.34684i) q^{76} +0.310666 q^{77} +(-1.08660 + 0.970947i) q^{78} -2.73779 q^{79} +(2.43939 + 4.22515i) q^{80} +(2.85142 + 4.93880i) q^{81} +(-1.45551 + 2.52101i) q^{82} +6.40312 q^{83} +(-0.675571 + 1.17012i) q^{84} +(-1.61512 + 2.79747i) q^{85} +2.51398 q^{86} +(-0.156937 + 0.271823i) q^{87} +(0.350745 + 0.607509i) q^{88} +(2.40022 + 4.15730i) q^{89} -0.324468 q^{90} +(-1.28933 + 1.15210i) q^{91} -3.82462 q^{92} +(-0.732250 - 1.26829i) q^{93} +(1.24164 + 2.15059i) q^{94} +(0.968228 - 1.67702i) q^{95} -4.60597 q^{96} +(-5.40800 + 9.36693i) q^{97} +(-0.934156 + 1.61801i) q^{98} +0.554039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more