LMFDB - Embedded newform 357.2.bl.a.10.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$357 = 3 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$ , degree $16$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.20
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.20

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11462 - 0.278396i) q^{2} +(0.442289 + 0.896873i) q^{3} +(2.46228 - 0.659766i) q^{4} +(0.750143 - 0.657858i) q^{5} +(1.18496 + 1.77342i) q^{6} +(0.498513 + 2.59836i) q^{7} +(1.08209 - 0.448216i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(1.40313 - 1.59996i) q^{10} +(0.174523 - 0.0114388i) q^{11} +(1.68076 + 1.91654i) q^{12} +(-2.14977 - 2.14977i) q^{13} +(1.77754 + 5.35578i) q^{14} +(0.921794 + 0.381820i) q^{15} +(-2.25181 + 1.30008i) q^{16} +(2.60102 - 3.19917i) q^{17} +(-1.06644 + 1.84712i) q^{18} +(-1.07664 - 8.17790i) q^{19} +(1.41303 - 2.11475i) q^{20} +(-2.10991 + 1.59633i) q^{21} +(0.365866 - 0.0727753i) q^{22} +(0.650984 + 0.321030i) q^{23} +(0.880588 + 0.772255i) q^{24} +(-0.522693 + 3.97025i) q^{25} +(-5.14444 - 3.94747i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(2.94179 + 6.06899i) q^{28} +(-0.261149 - 1.31288i) q^{29} +(2.05555 + 0.550782i) q^{30} +(-2.49122 + 1.22854i) q^{31} +(-6.25822 + 4.80210i) q^{32} +(0.0874487 + 0.151466i) q^{33} +(4.60955 - 7.48915i) q^{34} +(2.08331 + 1.62119i) q^{35} +(-0.975514 + 2.35510i) q^{36} +(0.389478 - 5.94229i) q^{37} +(-4.55338 - 16.9934i) q^{38} +(0.977251 - 2.87889i) q^{39} +(0.516859 - 1.04809i) q^{40} +(-0.0270503 + 0.135991i) q^{41} +(-4.01726 + 3.96303i) q^{42} +(3.28609 + 7.93332i) q^{43} +(0.422178 - 0.143310i) q^{44} +(0.0652555 + 0.995607i) q^{45} +(1.46596 + 0.497626i) q^{46} +(-3.14663 + 11.7434i) q^{47} +(-2.16196 - 1.44457i) q^{48} +(-6.50297 + 2.59063i) q^{49} +8.54110i q^{50} +(4.01965 + 0.917831i) q^{51} +(-6.71168 - 3.87499i) q^{52} +(-3.01180 - 3.92505i) q^{53} +(-2.12830 - 0.139496i) q^{54} +(0.123392 - 0.123392i) q^{55} +(1.70406 + 2.58822i) q^{56} +(6.85835 - 4.58260i) q^{57} +(-0.917732 - 2.70355i) q^{58} +(1.10425 + 0.145377i) q^{59} +(2.52163 + 0.331979i) q^{60} +(-3.10539 - 9.14818i) q^{61} +(-4.92599 + 3.29144i) q^{62} +(-2.36489 - 1.18629i) q^{63} +(-8.21970 + 8.21970i) q^{64} +(-3.02688 - 0.198392i) q^{65} +(0.227089 + 0.295948i) q^{66} +(-1.28026 - 0.739156i) q^{67} +(4.29374 - 9.59332i) q^{68} +0.725837i q^{69} +(4.85675 + 2.84823i) q^{70} +(11.0881 + 7.40881i) q^{71} +(-0.303140 + 1.13134i) q^{72} +(-4.35552 - 1.47850i) q^{73} +(-0.830707 - 12.6741i) q^{74} +(-3.79199 + 1.28721i) q^{75} +(-8.04649 - 19.4259i) q^{76} +(0.116724 + 0.447771i) q^{77} +(1.26505 - 6.35983i) q^{78} +(1.71827 - 3.48430i) q^{79} +(-0.833909 + 2.45662i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.0193419 + 0.295100i) q^{82} +(4.03690 - 9.74595i) q^{83} +(-4.14199 + 5.32266i) q^{84} +(-0.153459 - 4.11094i) q^{85} +(9.15745 + 15.8612i) q^{86} +(1.06199 - 0.814890i) q^{87} +(0.183722 - 0.0906018i) q^{88} +(0.409264 + 0.109662i) q^{89} +(0.415163 + 2.08717i) q^{90} +(4.51419 - 6.65757i) q^{91} +(1.81471 + 0.360968i) q^{92} +(-2.20368 - 1.69094i) q^{93} +(-3.38463 + 25.7088i) q^{94} +(-6.18752 - 5.42631i) q^{95} +(-7.07481 - 3.48891i) q^{96} +(9.57276 - 1.90414i) q^{97} +(-13.0301 + 7.28861i) q^{98} +(-0.0971678 + 0.145422i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100})$ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$ .

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

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

)

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

$2$	2.11462	−	0.278396i	1.49527	−	0.196855i	0.661906	−	0.749587i	$-0.269748\pi$
$2$	2.11462	−	0.278396i	1.49527	−	0.196855i	0.833359	+	0.552732i	$0.186415\pi$
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	2.46228	−	0.659766i	1.23114	−	0.329883i
$5$	0.750143	−	0.657858i	0.335474	−	0.294203i	−0.474990	−	0.879991i	$-0.657548\pi$
$5$	0.750143	−	0.657858i	0.335474	−	0.294203i	0.810464	+	0.585788i	$0.199215\pi$
$6$	1.18496	+	1.77342i	0.483758	+	0.723995i
$7$	0.498513	+	2.59836i	0.188420	+	0.982089i
$7$	0.498513	+	2.59836i	0.188420	+	0.982089i
$8$	1.08209	−	0.448216i	0.382576	−	0.158468i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	1.40313	−	1.59996i	0.443707	−	0.505951i
$11$	0.174523	−	0.0114388i	0.0526207	−	0.00344894i	−0.0390701	−	0.999236i	$-0.512440\pi$
$11$	0.174523	−	0.0114388i	0.0526207	−	0.00344894i	0.0916907	+	0.995788i	$0.470773\pi$
$12$	1.68076	+	1.91654i	0.485195	+	0.553259i
$13$	−2.14977	−	2.14977i	−0.596239	−	0.596239i	0.343071	−	0.939310i	$-0.388533\pi$
$13$	−2.14977	−	2.14977i	−0.596239	−	0.596239i	−0.939310	+	0.343071i	$0.888533\pi$
$14$	1.77754	+	5.35578i	0.475067	+	1.43139i
$15$	0.921794	+	0.381820i	0.238006	+	0.0985854i
$16$	−2.25181	+	1.30008i	−0.562952	+	0.325021i
$17$	2.60102	−	3.19917i	0.630841	−	0.775912i
$17$	2.60102	−	3.19917i	0.630841	−	0.775912i
$18$	−1.06644	+	1.84712i	−0.251361	+	0.435371i
$19$	−1.07664	−	8.17790i	−0.246998	−	1.87614i	−0.444419	−	0.895819i	$-0.646590\pi$
$19$	−1.07664	−	8.17790i	−0.246998	−	1.87614i	0.197421	−	0.980319i	$-0.436743\pi$
$20$	1.41303	−	2.11475i	0.315963	−	0.472872i
$21$	−2.10991	+	1.59633i	−0.460421	+	0.348347i
$22$	0.365866	−	0.0727753i	0.0780029	−	0.0155157i
$23$	0.650984	+	0.321030i	0.135740	+	0.0669393i	0.508890	−	0.860831i	$-0.330056\pi$
$23$	0.650984	+	0.321030i	0.135740	+	0.0669393i	−0.373151	+	0.927771i	$0.621723\pi$
$24$	0.880588	+	0.772255i	0.179749	+	0.157636i
$25$	−0.522693	+	3.97025i	−0.104539	+	0.794050i
$26$	−5.14444	−	3.94747i	−1.00891	−	0.774162i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	2.94179	+	6.06899i	0.555946	+	1.14693i
$29$	−0.261149	−	1.31288i	−0.0484941	−	0.243796i	0.948934	−	0.315476i	$-0.102164\pi$
$29$	−0.261149	−	1.31288i	−0.0484941	−	0.243796i	−0.997428	+	0.0716796i	$0.977164\pi$
$30$	2.05555	+	0.550782i	0.375290	+	0.100559i
$31$	−2.49122	+	1.22854i	−0.447437	+	0.220652i	−0.652026	−	0.758196i	$-0.726081\pi$
$31$	−2.49122	+	1.22854i	−0.447437	+	0.220652i	0.204589	+	0.978848i	$0.434414\pi$
$32$	−6.25822	+	4.80210i	−1.10631	+	0.848899i
$33$	0.0874487	+	0.151466i	0.0152229	+	0.0263668i
$34$	4.60955	−	7.48915i	0.790532	−	1.28438i
$35$	2.08331	+	1.62119i	0.352143	+	0.274032i
$36$	−0.975514	+	2.35510i	−0.162586	+	0.392516i
$37$	0.389478	−	5.94229i	0.0640298	−	0.976906i	−0.838121	−	0.545485i	$-0.816346\pi$
$37$	0.389478	−	5.94229i	0.0640298	−	0.976906i	0.902150	−	0.431421i	$-0.141988\pi$
$38$	−4.55338	−	16.9934i	−0.738656	−	2.75670i
$39$	0.977251	−	2.87889i	0.156485	−	0.460991i
$40$	0.516859	−	1.04809i	0.0817226	−	0.165717i
$41$	−0.0270503	+	0.135991i	−0.00422454	+	0.0212382i	−0.982840	−	0.184460i	$-0.940946\pi$
$41$	−0.0270503	+	0.135991i	−0.00422454	+	0.0212382i	0.978616	+	0.205698i	$0.0659465\pi$
$42$	−4.01726	+	3.96303i	−0.619877	+	0.611508i
$43$	3.28609	+	7.93332i	0.501124	+	1.20982i	0.948872	+	0.315660i	$0.102226\pi$
$43$	3.28609	+	7.93332i	0.501124	+	1.20982i	−0.447748	+	0.894160i	$0.647774\pi$
$44$	0.422178	−	0.143310i	0.0636457	−	0.0216048i
$45$	0.0652555	+	0.995607i	0.00972772	+	0.148416i
$46$	1.46596	+	0.497626i	0.216144	+	0.0733710i
$47$	−3.14663	+	11.7434i	−0.458983	+	1.71295i	0.217125	+	0.976144i	$0.430332\pi$
$47$	−3.14663	+	11.7434i	−0.458983	+	1.71295i	−0.676107	+	0.736803i	$0.736334\pi$
$48$	−2.16196	−	1.44457i	−0.312052	−	0.208506i
$49$	−6.50297	+	2.59063i	−0.928996	+	0.370090i
$50$			8.54110i			1.20789i
$51$	4.01965	+	0.917831i	0.562864	+	0.128522i
$52$	−6.71168	−	3.87499i	−0.930742	−	0.537364i
$53$	−3.01180	−	3.92505i	−0.413702	−	0.539147i	0.539299	−	0.842115i	$-0.318689\pi$
$53$	−3.01180	−	3.92505i	−0.413702	−	0.539147i	−0.953001	+	0.302967i	$0.902023\pi$
$54$	−2.12830	−	0.139496i	−0.289626	−	0.0189831i
$55$	0.123392	−	0.123392i	0.0166382	−	0.0166382i
$56$	1.70406	+	2.58822i	0.227715	+	0.345865i
$57$	6.85835	−	4.58260i	0.908410	−	0.606980i
$58$	−0.917732	−	2.70355i	−0.120504	−	0.354994i
$59$	1.10425	+	0.145377i	0.143761	+	0.0189265i	0.202063	−	0.979372i	$-0.435235\pi$
$59$	1.10425	+	0.145377i	0.143761	+	0.0189265i	−0.0583021	+	0.998299i	$0.518569\pi$
$60$	2.52163	+	0.331979i	0.325541	+	0.0428582i
$61$	−3.10539	−	9.14818i	−0.397604	−	1.17130i	−0.942904	−	0.333064i	$-0.891918\pi$
$61$	−3.10539	−	9.14818i	−0.397604	−	1.17130i	0.545300	−	0.838241i	$-0.316416\pi$
$62$	−4.92599	+	3.29144i	−0.625601	+	0.418013i
$63$	−2.36489	−	1.18629i	−0.297949	−	0.149458i
$64$	−8.21970	+	8.21970i	−1.02746	+	1.02746i
$65$	−3.02688	−	0.198392i	−0.375438	−	0.0246075i
$66$	0.227089	+	0.295948i	0.0279527	+	0.0364286i
$67$	−1.28026	−	0.739156i	−0.156408	−	0.0903022i	0.419753	−	0.907638i	$-0.362117\pi$
$67$	−1.28026	−	0.739156i	−0.156408	−	0.0903022i	−0.576161	+	0.817336i	$0.695450\pi$
$68$	4.29374	−	9.59332i	0.520693	−	1.16336i
$69$			0.725837i			0.0873806i
$70$	4.85675	+	2.84823i	0.580492	+	0.340428i
$71$	11.0881	+	7.40881i	1.31591	+	0.879264i	0.997635	−	0.0687337i	$-0.0218959\pi$
$71$	11.0881	+	7.40881i	1.31591	+	0.879264i	0.318277	+	0.947998i	$0.396896\pi$
$72$	−0.303140	+	1.13134i	−0.0357254	+	0.133329i
$73$	−4.35552	−	1.47850i	−0.509775	−	0.173045i	0.0546880	−	0.998503i	$-0.482584\pi$
$73$	−4.35552	−	1.47850i	−0.509775	−	0.173045i	−0.564463	+	0.825458i	$0.690917\pi$
$74$	−0.830707	−	12.6741i	−0.0965677	−	1.47334i
$75$	−3.79199	+	1.28721i	−0.437861	+	0.148634i
$76$	−8.04649	−	19.4259i	−0.922995	−	2.22831i
$77$	0.116724	+	0.447771i	0.0133020	+	0.0510283i
$78$	1.26505	−	6.35983i	0.143239	−	0.720109i
$79$	1.71827	−	3.48430i	0.193320	−	0.392014i	−0.778532	−	0.627604i	$-0.784036\pi$
$79$	1.71827	−	3.48430i	0.193320	−	0.392014i	0.971853	+	0.235590i	$0.0757023\pi$
$80$	−0.833909	+	2.45662i	−0.0932339	+	0.274658i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	−0.0193419	+	0.295100i	−0.00213595	+	0.0325884i
$83$	4.03690	−	9.74595i	0.443108	−	1.06976i	−0.531744	−	0.846905i	$-0.678463\pi$
$83$	4.03690	−	9.74595i	0.443108	−	1.06976i	0.974852	−	0.222852i	$-0.0715367\pi$
$84$	−4.14199	+	5.32266i	−0.451929	+	0.580750i
$85$	−0.153459	−	4.11094i	−0.0166449	−	0.445894i
$86$	9.15745	+	15.8612i	0.987473	+	1.71035i
$87$	1.06199	−	0.814890i	0.113857	−	0.0873654i
$88$	0.183722	−	0.0906018i	0.0195849	−	0.00965819i
$89$	0.409264	+	0.109662i	0.0433819	+	0.0116241i	0.280445	−	0.959870i	$-0.409518\pi$
$89$	0.409264	+	0.109662i	0.0433819	+	0.0116241i	−0.237063	+	0.971494i	$0.576185\pi$
$90$	0.415163	+	2.08717i	0.0437621	+	0.220007i
$91$	4.51419	−	6.65757i	0.473216	−	0.697903i
$92$	1.81471	+	0.360968i	0.189196	+	0.0376335i
$93$	−2.20368	−	1.69094i	−0.228511	−	0.175343i
$94$	−3.38463	+	25.7088i	−0.349098	+	2.65166i
$95$	−6.18752	−	5.42631i	−0.634827	−	0.556728i
$96$	−7.07481	−	3.48891i	−0.722070	−	0.356085i
$97$	9.57276	−	1.90414i	0.971967	−	0.193336i	0.316527	−	0.948584i	$-0.397483\pi$
$97$	9.57276	−	1.90414i	0.971967	−	0.193336i	0.655440	+	0.755247i	$0.272483\pi$
$98$	−13.0301	+	7.28861i	−1.31624	+	0.736261i
$99$	−0.0971678	+	0.145422i	−0.00976573	+	0.0146155i
$100$	1.33242	+	10.1207i	0.133242	+	1.01207i
$101$	−8.49376	+	14.7116i	−0.845160	+	1.46386i	0.0403215	+	0.999187i	$0.487162\pi$
$101$	−8.49376	+	14.7116i	−0.845160	+	1.46386i	−0.885482	+	0.464674i	$0.846172\pi$
$102$	8.75557	+	0.821814i	0.866931	+	0.0813717i
$103$	6.59390	−	3.80699i	0.649716	−	0.375114i	−0.138631	−	0.990344i	$-0.544270\pi$
$103$	6.59390	−	3.80699i	0.649716	−	0.375114i	0.788347	+	0.615230i	$0.210937\pi$
$104$	−3.28980	−	1.36268i	−0.322592	−	0.133622i
$105$	−0.532580	+	2.58550i	−0.0519744	+	0.252319i
$106$	−7.46154	−	7.46154i	−0.724729	−	0.724729i
$107$	7.19007	+	8.19870i	0.695090	+	0.792598i	0.986458	−	0.164013i	$-0.0524439\pi$
$107$	7.19007	+	8.19870i	0.695090	+	0.792598i	−0.291368	+	0.956611i	$0.594111\pi$
$108$	−2.54368	+	0.166722i	−0.244766	+	0.0160428i
$109$	1.16748	−	1.33126i	0.111824	−	0.127511i	−0.693219	−	0.720727i	$-0.743808\pi$
$109$	1.16748	−	1.33126i	0.111824	−	0.127511i	0.805044	+	0.593215i	$0.202142\pi$
$110$	0.226576	−	0.295280i	0.0216032	−	0.0281538i
$111$	5.50174	−	2.27890i	0.522202	−	0.216303i
$112$	−4.50064	−	5.20291i	−0.425271	−	0.491629i
$113$	10.1954	+	15.2585i	0.959100	+	1.43540i	0.899374	+	0.437180i	$0.144023\pi$
$113$	10.1954	+	15.2585i	0.959100	+	1.43540i	0.0597265	+	0.998215i	$0.480977\pi$
$114$	13.2270	−	11.5998i	1.23883	−	1.08642i
$115$	0.699523	−	0.187437i	0.0652308	−	0.0174785i
$116$	−1.50922	−	3.06039i	−0.140127	−	0.284150i
$117$	3.01422	−	0.396830i	0.278665	−	0.0366869i
$118$	2.37555			0.218687
$119$	9.60924	+	5.16357i	0.880878	+	0.473344i
$120$	1.16860			0.106678
$121$	−10.8756	+	1.43180i	−0.988688	+	0.130163i
$122$	−9.11354	−	18.4804i	−0.825101	−	1.67314i
$123$	−0.133931	+	0.0358866i	−0.0120761	+	0.00323578i
$124$	−5.32355	+	4.66863i	−0.478069	+	0.419255i
$125$	4.99135	+	7.47008i	0.446440	+	0.668144i
$126$	−5.33112	−	1.85017i	−0.474934	−	0.164826i
$127$	−9.61394	+	3.98222i	−0.853099	+	0.353365i	−0.766005	−	0.642835i	$-0.777758\pi$
$127$	−9.61394	+	3.98222i	−0.853099	+	0.353365i	−0.0870942	+	0.996200i	$0.527758\pi$
$128$	−5.48906	+	7.15348i	−0.485169	+	0.632284i
$129$	−5.66178	+	6.45602i	−0.498492	+	0.568421i
$130$	−6.45594	+	0.423144i	−0.566223	+	0.0371122i
$131$	11.0374	+	12.5857i	0.964342	+	1.09962i	0.994978	+	0.100090i	$0.0319131\pi$
$131$	11.0374	+	12.5857i	0.964342	+	1.09962i	−0.0306368	+	0.999531i	$0.509754\pi$
$132$	0.315255	+	0.315255i	0.0274394	+	0.0274394i
$133$	20.7124	−	6.87429i	1.79599	−	0.596076i
$134$	−2.91304	−	1.20662i	−0.251648	−	0.104236i
$135$	−0.864071	+	0.498871i	−0.0743674	+	0.0429360i
$136$	1.38062	−	4.62761i	0.118387	−	0.396814i
$137$	−6.08247	+	10.5352i	−0.519661	+	0.900079i	0.480078	+	0.877226i	$0.340608\pi$
$137$	−6.08247	+	10.5352i	−0.519661	+	0.900079i	−0.999739	+	0.0228532i	$0.992725\pi$
$138$	0.202070	+	1.53487i	0.0172013	+	0.130657i
$139$	11.0792	−	16.5812i	0.939728	−	1.40640i	0.0261856	−	0.999657i	$-0.491664\pi$
$139$	11.0792	−	16.5812i	0.939728	−	1.40640i	0.913542	−	0.406745i	$-0.133336\pi$
$140$	6.19930	+	2.61733i	0.523936	+	0.221205i
$141$	−11.9240	+	2.37184i	−1.00418	+	0.199745i
$142$	25.5097	+	12.5800i	2.14072	+	1.05569i
$143$	−0.399775	−	0.350593i	−0.0334309	−	0.0293181i
$144$	0.339390	−	2.57792i	0.0282825	−	0.214827i
$145$	−1.05959	−	0.813051i	−0.0879941	−	0.0675202i
$146$	−9.62190	−	1.91392i	−0.796314	−	0.158397i
$147$	−5.19966	−	4.68653i	−0.428861	−	0.386538i
$148$	−2.96152	−	14.8885i	−0.243435	−	1.22383i
$149$	2.88363	+	0.772665i	0.236236	+	0.0632992i	0.374995	−	0.927027i	$-0.377645\pi$
$149$	2.88363	+	0.772665i	0.236236	+	0.0632992i	−0.138759	+	0.990326i	$0.544311\pi$
$150$	−7.66028	+	3.77763i	−0.625459	+	0.308442i
$151$	−2.98150	+	2.28778i	−0.242631	+	0.186177i	−0.722917	−	0.690934i	$-0.757199\pi$
$151$	−2.98150	+	2.28778i	−0.242631	+	0.186177i	0.480287	+	0.877112i	$0.340533\pi$
$152$	−4.83048	−	8.36664i	−0.391804	−	0.678624i
$153$	0.954669	+	4.01106i	0.0771804	+	0.324275i
$154$	0.371485	+	0.914373i	0.0299351	+	0.0736823i
$155$	−1.06057	+	2.56045i	−0.0851872	+	0.205660i
$156$	0.506873	−	7.73339i	0.0405823	−	0.619166i
$157$	−1.08363	−	4.04417i	−0.0864834	−	0.322760i	0.909108	−	0.416561i	$-0.136765\pi$
$157$	−1.08363	−	4.04417i	−0.0864834	−	0.322760i	−0.995591	+	0.0938011i	$0.970098\pi$
$158$	2.66347	−	7.84634i	0.211895	−	0.624221i
$159$	2.18819	−	4.43721i	0.173535	−	0.351893i
$160$	−1.53546	+	7.71927i	−0.121389	+	0.610262i
$161$	−0.509628	+	1.85153i	−0.0401643	+	0.145921i
$162$	−0.816215	−	1.97052i	−0.0641279	−	0.154818i
$163$	12.5655	−	4.26541i	0.984205	−	0.334093i	0.217478	−	0.976065i	$-0.430217\pi$
$163$	12.5655	−	4.26541i	0.984205	−	0.334093i	0.766728	+	0.641973i	$0.221884\pi$
$164$	0.0231168	+	0.352694i	0.00180512	+	0.0275408i
$165$	0.165242	+	0.0560921i	0.0128641	+	0.00436676i
$166$	5.82331	−	21.7329i	0.451976	−	1.68680i
$167$	−2.67295	−	1.78601i	−0.206839	−	0.138205i	0.447837	−	0.894115i	$-0.352195\pi$
$167$	−2.67295	−	1.78601i	−0.206839	−	0.138205i	−0.654675	+	0.755910i	$0.727195\pi$
$168$	−1.56761	+	2.67307i	−0.120944	+	0.206232i
$169$		−	3.75698i		−	0.288999i
$170$	−1.46897	−	8.65036i	−0.112665	−	0.663453i
$171$	7.14338	+	4.12423i	0.546268	+	0.315388i
$172$	13.3254	+	17.3660i	1.01605	+	1.32415i
$173$	−1.69987	−	0.111415i	−0.129239	−	0.00847076i	0.000646421	−	1.00000i	$-0.499794\pi$
$173$	−1.69987	−	0.111415i	−0.129239	−	0.00847076i	−0.129885	+	0.991529i	$0.541461\pi$
$174$	2.01884	−	2.01884i	0.153048	−	0.153048i
$175$	−10.5767	+	0.621074i	−0.799525	+	0.0469488i
$176$	−0.378121	+	0.252652i	−0.0285019	+	0.0190444i
$177$	0.358012	+	1.05467i	0.0269099	+	0.0792739i
$178$	0.895969	+	0.117957i	0.0671557	+	0.00884121i
$179$	−8.55244	−	1.12595i	−0.639240	−	0.0841575i	−0.196062	−	0.980591i	$-0.562815\pi$
$179$	−8.55244	−	1.12595i	−0.639240	−	0.0841575i	−0.443177	+	0.896434i	$0.646149\pi$
$180$	0.817545	+	2.40841i	0.0609362	+	0.179512i
$181$	−7.32293	+	4.89302i	−0.544309	+	0.363696i	−0.797121	−	0.603820i	$-0.793645\pi$
$181$	−7.32293	+	4.89302i	−0.544309	+	0.363696i	0.252812	+	0.967515i	$0.418645\pi$
$182$	7.69238	−	15.3350i	0.570197	−	1.13670i
$183$	6.83128	−	6.83128i	0.504982	−	0.504982i
$184$	0.848313	+	0.0556014i	0.0625385	+	0.00409899i
$185$	−3.61702	−	4.71379i	−0.265928	−	0.346565i
$186$	−5.13071	−	2.96222i	−0.376202	−	0.217200i
$187$	0.417344	−	0.588081i	0.0305192	−	0.0430047i
$188$			30.9915i			2.26029i
$189$	0.0179813	−	2.64569i	0.00130795	−	0.192446i
$190$	−14.5950	−	9.75203i	−1.05883	−	0.707487i
$191$	5.72154	−	21.3531i	0.413996	−	1.54505i	−0.372842	−	0.927895i	$-0.621617\pi$
$191$	5.72154	−	21.3531i	0.413996	−	1.54505i	0.786838	−	0.617160i	$-0.211717\pi$
$192$	−11.0075	−	3.73655i	−0.794398	−	0.269662i
$193$	−0.492705	−	7.51723i	−0.0354657	−	0.541102i	−0.978214	−	0.207598i	$-0.933435\pi$
$193$	−0.492705	−	7.51723i	−0.0354657	−	0.541102i	0.942749	−	0.333504i	$-0.108231\pi$
$194$	19.7127	−	6.69156i	1.41529	−	0.480426i
$195$	−1.16082	−	2.80247i	−0.0831281	−	0.200689i
$196$	−14.3029	+	10.6693i	−1.02164	+	0.762093i
$197$	0.780793	−	3.92531i	0.0556292	−	0.279667i	−0.942951	−	0.332931i	$-0.891962\pi$
$197$	0.780793	−	3.92531i	0.0556292	−	0.279667i	0.998580	+	0.0532640i	$0.0169625\pi$
$198$	−0.164989	+	0.334564i	−0.0117252	+	0.0237764i
$199$	−5.44882	+	16.0517i	−0.386257	+	1.13788i	0.563830	+	0.825891i	$0.309327\pi$
$199$	−5.44882	+	16.0517i	−0.386257	+	1.13788i	−0.950087	+	0.311985i	$0.899006\pi$
$200$	1.21393	+	4.53044i	0.0858377	+	0.320351i
$201$	0.0966862	−	1.47515i	0.00681972	−	0.104049i
$202$	−13.8655	+	33.4742i	−0.975570	+	2.35523i
$203$	3.28116	−	1.33305i	0.230292	−	0.0935616i
$204$	10.5031	−	0.392072i	0.735361	−	0.0274505i
$205$	0.0691711	+	0.119808i	0.00483112	+	0.00836774i
$206$	12.8838	−	9.88606i	0.897655	−	0.688795i
$207$	−0.650984	+	0.321030i	−0.0452465	+	0.0223131i
$208$	7.63575	+	2.04599i	0.529444	+	0.141864i
$209$	−0.281444	−	1.41492i	−0.0194679	−	0.0978717i
$210$	−0.406415	+	5.61562i	−0.0280453	+	0.387515i
$211$	−22.5961	−	4.49464i	−1.55558	−	0.309424i	−0.658943	−	0.752193i	$-0.728996\pi$
$211$	−22.5961	−	4.49464i	−1.55558	−	0.309424i	−0.896636	+	0.442769i	$0.853996\pi$
$212$	−10.0055	−	7.67749i	−0.687181	−	0.527292i
$213$	−1.74063	+	13.2214i	−0.119266	+	0.905917i
$214$	17.4868	+	15.3355i	1.19537	+	1.04831i
$215$	7.68403	+	3.78935i	0.524047	+	0.258431i
$216$	−1.14874	+	0.228499i	−0.0781618	+	0.0155474i
$217$	−4.43409	−	5.86066i	−0.301006	−	0.397848i
$218$	2.09817	−	3.14013i	0.142106	−	0.212677i
$219$	−0.600372	−	4.56027i	−0.0405693	−	0.308155i
$220$	0.222416	−	0.385236i	0.0149953	−	0.0259726i
$221$	−12.4691	+	1.28587i	−0.838761	+	0.0864973i
$222$	10.9997	−	6.35067i	0.738250	−	0.426229i
$223$	21.8858	+	9.06541i	1.46558	+	0.607064i	0.965847	−	0.259113i	$-0.0834303\pi$
$223$	21.8858	+	9.06541i	1.46558	+	0.607064i	0.499736	+	0.866178i	$0.333430\pi$
$224$	−15.5974	−	13.8672i	−1.04214	−	0.926541i
$225$	−2.83162	−	2.83162i	−0.188774	−	0.188774i
$226$	25.8073	+	29.4276i	1.71667	+	1.95749i
$227$	−8.74512	+	0.573185i	−0.580434	+	0.0380437i	−0.352793	−	0.935701i	$-0.614768\pi$
$227$	−8.74512	+	0.573185i	−0.580434	+	0.0380437i	−0.227641	+	0.973745i	$0.573101\pi$
$228$	13.8637	−	15.8085i	0.918148	−	1.04695i
$229$	−5.87060	+	7.65071i	−0.387940	+	0.505573i	−0.945973	−	0.324246i	$-0.894890\pi$
$229$	−5.87060	+	7.65071i	−0.387940	+	0.505573i	0.558033	+	0.829819i	$0.311556\pi$
$230$	1.42705	−	0.591102i	0.0940966	−	0.0389761i
$231$	−0.349968	+	0.302731i	−0.0230262	+	0.0199182i
$232$	−0.871041	−	1.30361i	−0.0571867	−	0.0855859i
$233$	12.9060	−	11.3182i	0.845497	−	0.741481i	−0.122493	−	0.992469i	$-0.539089\pi$
$233$	12.9060	−	11.3182i	0.845497	−	0.741481i	0.967990	+	0.250988i	$0.0807555\pi$
$234$	6.26347	−	1.67829i	0.409456	−	0.109713i
$235$	5.36505	+	10.8792i	0.349977	+	0.709683i
$236$	2.81489	−	0.370587i	0.183234	−	0.0241232i
$237$	3.88494			0.252354
$238$	21.7575	+	8.24385i	1.41033	+	0.534369i
$239$	20.2579			1.31038			0.655188	−	0.755466i	$-0.272590\pi$
$239$	20.2579			1.31038			0.655188	+	0.755466i	$0.272590\pi$
$240$	−2.57210	+	0.338624i	−0.166028	+	0.0218581i
$241$	−1.87459	−	3.80129i	−0.120753	−	0.244863i	0.828100	−	0.560580i	$-0.189422\pi$
$241$	−1.87459	−	3.80129i	−0.120753	−	0.244863i	−0.948853	+	0.315717i	$0.897755\pi$
$242$	−22.5991	+	6.05542i	−1.45273	+	0.389257i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	−13.6820	−	20.4766i	−0.875900	−	1.31088i
$245$	−3.17389	+	6.22137i	−0.202772	+	0.397469i
$246$	−0.273222	+	0.113172i	−0.0174200	+	0.00721560i
$247$	−15.2661	+	19.8951i	−0.971356	+	1.26590i
$248$	−2.14508	+	2.44599i	−0.136213	+	0.155321i
$249$	10.5264	−	0.689934i	0.667081	−	0.0437228i
$250$	12.6345	+	14.4068i	0.799073	+	0.911168i
$251$	−6.78242	−	6.78242i	−0.428103	−	0.428103i	0.459879	−	0.887982i	$-0.347893\pi$
$251$	−6.78242	−	6.78242i	−0.428103	−	0.428103i	−0.887982	+	0.459879i	$0.847893\pi$
$252$	−6.60570	−	1.36069i	−0.416120	−	0.0857155i
$253$	0.117284	+	0.0485806i	0.00737357	+	0.00305423i
$254$	−19.2212	+	11.0974i	−1.20605	+	0.696312i
$255$	3.61911	−	1.95585i	0.226638	−	0.122480i
$256$	2.00862	−	3.47902i	0.125538	−	0.217439i
$257$	0.0442763	+	0.336312i	0.00276188	+	0.0209785i	0.992770	−	0.120030i	$-0.0382990\pi$
$257$	0.0442763	+	0.336312i	0.00276188	+	0.0209785i	−0.990008	+	0.141008i	$0.954966\pi$
$258$	−10.1752	+	15.2283i	−0.633481	+	0.948071i
$259$	15.6344	−	1.95030i	0.971473	−	0.121186i
$260$	−7.58391	+	1.50853i	−0.470334	+	0.0935553i
$261$	1.20056	+	0.592049i	0.0743126	+	0.0366469i
$262$	26.8438	+	23.5413i	1.65841	+	1.45439i
$263$	3.37428	−	25.6302i	0.208067	−	1.58043i	−0.494737	−	0.869042i	$-0.664736\pi$
$263$	3.37428	−	25.6302i	0.208067	−	1.58043i	0.702804	−	0.711383i	$-0.251931\pi$
$264$	0.162517	+	0.124703i	0.0100022	+	0.00767496i
$265$	−4.84140	−	0.963015i	−0.297405	−	0.0591575i
$266$	41.8852	−	20.3028i	2.56815	−	1.24484i
$267$	0.0826600	+	0.415560i	0.00505871	+	0.0254318i
$268$	−3.64002	−	0.975340i	−0.222349	−	0.0595783i
$269$	2.48194	−	1.22396i	0.151327	−	0.0746261i	−0.365049	−	0.930988i	$-0.618948\pi$
$269$	2.48194	−	1.22396i	0.151327	−	0.0746261i	0.516375	+	0.856362i	$0.327281\pi$
$270$	−1.68830	+	1.29548i	−0.102747	+	0.0788404i
$271$	7.00749	+	12.1373i	0.425675	+	0.737290i	0.996483	−	0.0837932i	$-0.0267035\pi$
$271$	7.00749	+	12.1373i	0.425675	+	0.737290i	−0.570809	+	0.821083i	$0.693370\pi$
$272$	−1.69782	+	10.5855i	−0.102946	+	0.641838i
$273$	7.96757	+	1.10409i	0.482219	+	0.0668225i
$274$	−9.92921	+	23.9712i	−0.599845	+	1.44815i
$275$	−0.0458069	+	0.698879i	−0.00276226	+	0.0421440i
$276$	0.478883	+	1.78721i	0.0288254	+	0.107578i
$277$	−3.20622	+	9.44522i	−0.192643	+	0.567509i	−0.999737	−	0.0229141i	$-0.992706\pi$
$277$	−3.20622	+	9.44522i	−0.192643	+	0.567509i	0.807094	+	0.590423i	$0.201039\pi$
$278$	18.8123	−	38.1475i	1.12828	−	2.28793i
$279$	0.541898	−	2.72431i	0.0324426	−	0.163100i
$280$	2.98097	+	0.820503i	0.178147	+	0.0490344i
$281$	−2.88176	−	6.95720i	−0.171912	−	0.415031i	0.814317	−	0.580421i	$-0.197112\pi$
$281$	−2.88176	−	6.95720i	−0.171912	−	0.415031i	−0.986228	+	0.165389i	$0.947112\pi$
$282$	−24.5545	+	8.33514i	−1.46220	+	0.496350i
$283$	−0.766969	−	11.7017i	−0.0455915	−	0.695593i	−0.958082	−	0.286494i	$-0.907510\pi$
$283$	−0.766969	−	11.7017i	−0.0455915	−	0.695593i	0.912490	−	0.409098i	$-0.134157\pi$
$284$	32.1900	+	10.9270i	1.91013	+	0.648400i
$285$	2.13004	−	7.94942i	0.126173	−	0.470883i
$286$	−0.942978	−	0.630077i	−0.0557594	−	0.0372573i
$287$	−0.366838	−	0.00249320i	−0.0216538	−	0.000147169i
$288$		−	7.88831i		−	0.464823i
$289$	−3.46936	−	16.6422i	−0.204080	−	0.978954i
$290$	−2.46698	−	1.42431i	−0.144866	−	0.0836385i
$291$	5.94170	+	7.74337i	0.348308	+	0.453924i
$292$	−11.7000	−	0.766857i	−0.684690	−	0.0448769i
$293$	−6.39307	+	6.39307i	−0.373487	+	0.373487i	−0.868746	−	0.495258i	$-0.835073\pi$
$293$	−6.39307	+	6.39307i	−0.373487	+	0.373487i	0.495258	+	0.868746i	$0.335073\pi$
$294$	−12.3000	−	8.46269i	−0.717352	−	0.493554i
$295$	0.923983	−	0.617386i	0.0537964	−	0.0359456i
$296$	−2.24198	−	6.60466i	−0.130312	−	0.383888i
$297$	−0.173401	−	0.0228287i	−0.0100618	−	0.00132466i
$298$	6.31289	+	0.831108i	0.365696	+	0.0481448i
$299$	−0.709325	−	2.08960i	−0.0410213	−	0.120845i
$300$	−8.48769	+	5.67129i	−0.490037	+	0.327432i
$301$	−18.9755	+	12.4933i	−1.09373	+	0.720102i
$302$	−5.66784	+	5.66784i	−0.326148	+	0.326148i
$303$	−16.9511	−	1.11104i	−0.973818	−	0.0638274i
$304$	13.0563	+	17.0153i	0.748832	+	0.975897i
$305$	−8.34769	−	4.81954i	−0.477987	−	0.275966i
$306$	3.13543	+	8.21611i	0.179240	+	0.469684i
$307$		−	19.6680i		−	1.12251i	−0.827643	−	0.561255i	$-0.810319\pi$
$307$		−	19.6680i		−	1.12251i	0.827643	−	0.561255i	$-0.189681\pi$
$308$	0.582832	+	1.02553i	0.0332099	+	0.0584349i
$309$	6.33079	+	4.23010i	0.360146	+	0.240642i
$310$	−1.52990	+	5.70965i	−0.0868922	+	0.324286i
$311$	−3.82094	−	1.29703i	−0.216666	−	0.0735481i	0.210996	−	0.977487i	$-0.432329\pi$
$311$	−3.82094	−	1.29703i	−0.216666	−	0.0735481i	−0.427662	+	0.903939i	$0.640663\pi$
$312$	−0.232891	−	3.55323i	−0.0131849	−	0.201162i
$313$	−25.8917	+	8.78904i	−1.46348	+	0.496786i	−0.935762	−	0.352632i	$-0.885287\pi$
$313$	−25.8917	+	8.78904i	−1.46348	+	0.496786i	−0.527721	+	0.849418i	$0.676953\pi$
$314$	−3.41736	−	8.25023i	−0.192853	−	0.465588i
$315$	−2.55442	+	0.665880i	−0.143925	+	0.0375181i
$316$	1.93203	−	9.71297i	0.108685	−	0.546397i
$317$	−7.23269	+	14.6664i	−0.406228	+	0.823749i	0.593592	+	0.804766i	$0.297709\pi$
$317$	−7.23269	+	14.6664i	−0.406228	+	0.823749i	−0.999820	+	0.0189827i	$0.993957\pi$
$318$	3.39190	−	9.99220i	0.190208	−	0.560335i
$319$	−0.0605943	−	0.226141i	−0.00339263	−	0.0126615i
$320$	−0.758557	+	11.5733i	−0.0424046	+	0.646970i
$321$	−4.17310	+	10.0748i	−0.232920	+	0.562319i
$322$	−0.562213	+	4.05717i	−0.0313309	+	0.226097i
$323$	−28.9628	−	17.8265i	−1.61154	−	0.991895i
$324$	−1.27457	−	2.20762i	−0.0708094	−	0.122646i
$325$	9.65879	−	7.41145i	0.535773	−	0.411113i
$326$	25.3838	−	12.5179i	1.40588	−	0.693303i
$327$	1.71033	+	0.458282i	0.0945816	+	0.0253431i
$328$	0.0316825	+	0.159279i	0.00174937	+	0.00879469i
$329$	−32.0822	−	2.32186i	−1.76875	−	0.128008i
$330$	0.365040	+	0.0726110i	0.0200948	+	0.00399710i
$331$	11.4945	+	8.82005i	0.631796	+	0.484794i	0.874319	−	0.485352i	$-0.161308\pi$
$331$	11.4945	+	8.82005i	0.631796	+	0.484794i	−0.242523	+	0.970146i	$0.577975\pi$
$332$	3.50994	−	26.6607i	0.192633	−	1.46319i
$333$	4.47724	+	3.92643i	0.245351	+	0.215167i
$334$	−6.14949	−	3.03259i	−0.336485	−	0.165936i
$335$	−1.44663	+	0.287753i	−0.0790380	+	0.0157216i
$336$	2.67576	−	6.33769i	0.145975	−	0.345749i
$337$	16.8443	−	25.2092i	0.917566	−	1.37323i	−0.0101505	−	0.999948i	$-0.503231\pi$
$337$	16.8443	−	25.2092i	0.917566	−	1.37323i	0.927716	−	0.373286i	$-0.121769\pi$
$338$	−1.04593	−	7.94461i	−0.0568910	−	0.432130i
$339$	−9.17560	+	15.8926i	−0.498350	+	0.863168i
$340$	−3.09011	−	10.0210i	−0.167585	−	0.543467i
$341$	−0.420723	+	0.242905i	−0.0227834	+	0.0131540i
$342$	16.2537	+	6.73251i	0.878901	+	0.364053i
$343$	−9.97322	−	15.6056i	−0.538503	−	0.842624i
$344$	7.11168	+	7.11168i	0.383436	+	0.383436i
$345$	0.477498	+	0.544482i	0.0257076	+	0.0293139i
$346$	−3.62561	+	0.237635i	−0.194914	+	0.0127753i
$347$	−11.8700	+	13.5351i	−0.637212	+	0.726602i	−0.976843	−	0.213957i	$-0.931365\pi$
$347$	−11.8700	+	13.5351i	−0.637212	+	0.726602i	0.339631	+	0.940559i	$0.389698\pi$
$348$	2.07727	−	2.70715i	0.111353	−	0.145118i
$349$	−20.5483	+	8.51140i	−1.09993	+	0.455605i	−0.857458	−	0.514554i	$-0.827957\pi$
$349$	−20.5483	+	8.51140i	−1.09993	+	0.455605i	−0.242469	+	0.970159i	$0.577957\pi$
$350$	−22.1929	+	4.25785i	−1.18626	+	0.227592i
$351$	1.68906	+	2.52786i	0.0901555	+	0.134927i
$352$	−1.03727	+	0.909663i	−0.0552868	+	0.0484852i
$353$	21.6265	−	5.79482i	1.15106	−	0.308427i	0.367673	−	0.929955i	$-0.380155\pi$
$353$	21.6265	−	5.79482i	1.15106	−	0.308427i	0.783392	+	0.621528i	$0.213488\pi$
$354$	1.05068	+	2.13056i	0.0558429	+	0.113238i
$355$	13.1916	−	1.73670i	0.700136	−	0.0921747i
$356$	1.08007			0.0572438
$357$	−0.381009	+	10.9021i	−0.0201652	+	0.576998i
$358$	−18.3987			−0.972399
$359$	−23.6819	+	3.11778i	−1.24988	+	0.164550i	−0.726271	−	0.687408i	$-0.758748\pi$
$359$	−23.6819	+	3.11778i	−1.24988	+	0.164550i	−0.523610	+	0.851958i	$0.675415\pi$
$360$	0.516859	+	1.04809i	0.0272409	+	0.0552390i
$361$	−47.3662	+	12.6917i	−2.49296	+	0.667986i
$362$	−14.1230	+	12.3856i	−0.742291	+	0.650971i
$363$	−6.09428	−	9.12073i	−0.319867	−	0.478714i
$364$	6.72277	−	19.3711i	0.352369	−	1.01532i
$365$	−4.23991	+	1.75623i	−0.221927	+	0.0919251i
$366$	12.5438	−	16.3474i	0.655674	−	0.854491i
$367$	−11.4155	+	13.0169i	−0.595885	+	0.679477i	−0.968644	−	0.248451i	$-0.920078\pi$
$367$	−11.4155	+	13.0169i	−0.595885	+	0.679477i	0.372759	+	0.927928i	$0.378412\pi$
$368$	−1.88326	+	0.123435i	−0.0981715	+	0.00643450i
$369$	−0.0914216	−	0.104246i	−0.00475922	−	0.00542685i
$370$	−8.96093	−	8.96093i	−0.465856	−	0.465856i
$371$	8.69729	−	9.78243i	0.451541	−	0.507878i
$372$	−6.54171	−	2.70966i	−0.339172	−	0.140490i
$373$	4.71553	−	2.72251i	0.244161	−	0.140966i	−0.372927	−	0.927861i	$-0.621646\pi$
$373$	4.71553	−	2.72251i	0.244161	−	0.140966i	0.617088	+	0.786894i	$0.288312\pi$
$374$	0.718806	−	1.35976i	0.0371686	−	0.0703114i
$375$	−4.49209	+	7.78053i	−0.231971	+	0.401785i
$376$	1.85864	+	14.1177i	0.0958518	+	0.728067i
$377$	−2.26099	+	3.38380i	−0.116447	+	0.174275i
$378$	−0.698525	−	5.59965i	−0.0359282	−	0.288015i
$379$	1.20901	−	0.240487i	0.0621028	−	0.0123530i	−0.163941	−	0.986470i	$-0.552421\pi$
$379$	1.20901	−	0.240487i	0.0621028	−	0.0123530i	0.226044	+	0.974117i	$0.427421\pi$
$380$	−18.8155	−	9.27879i	−0.965216	−	0.475992i
$381$	−7.82368	−	6.86119i	−0.400819	−	0.351509i
$382$	6.15431	−	46.7466i	0.314882	−	2.39176i
$383$	−25.0375	−	19.2119i	−1.27936	−	0.981684i	−0.999767	−	0.0215646i	$-0.993135\pi$
$383$	−25.0375	−	19.2119i	−1.27936	−	0.981684i	−0.279589	−	0.960120i	$-0.590198\pi$
$384$	−8.84351	−	1.75908i	−0.451293	−	0.0897678i
$385$	0.382130	+	0.259105i	0.0194751	+	0.0132052i
$386$	−3.13465	−	15.7590i	−0.159549	−	0.802109i
$387$	−8.29437	−	2.22247i	−0.421627	−	0.112975i
$388$	22.3145	−	11.0043i	1.13285	−	0.558659i
$389$	4.39266	−	3.37061i	0.222717	−	0.170897i	−0.491376	−	0.870947i	$-0.663506\pi$
$389$	4.39266	−	3.37061i	0.222717	−	0.170897i	0.714093	+	0.700051i	$0.246839\pi$
$390$	−3.23489	−	5.60300i	−0.163805	−	0.283719i
$391$	2.72025	−	1.24760i	0.137569	−	0.0630939i
$392$	−5.87563	+	5.71803i	−0.296764	+	0.288804i
$393$	−6.40609	+	15.4657i	−0.323144	+	0.780140i
$394$	0.558294	−	8.51792i	0.0281265	−	0.429127i
$395$	−1.00323	−	3.74410i	−0.0504779	−	0.188386i
$396$	−0.143310	+	0.422178i	−0.00720160	+	0.0212152i
$397$	−14.1685	+	28.7310i	−0.711099	+	1.44197i	0.177896	+	0.984049i	$0.443071\pi$
$397$	−14.1685	+	28.7310i	−0.711099	+	1.44197i	−0.888995	+	0.457917i	$0.848596\pi$
$398$	−7.05349	+	35.4603i	−0.353559	+	1.77746i
$399$	15.3262	+	15.5360i	0.767271	+	0.777772i
$400$	−3.98465	−	9.61979i	−0.199232	−	0.480990i
$401$	19.2357	−	6.52964i	0.960585	−	0.326075i	0.203269	−	0.979123i	$-0.434843\pi$
$401$	19.2357	−	6.52964i	0.960585	−	0.326075i	0.757316	+	0.653048i	$0.226510\pi$
$402$	−0.206219	−	3.14630i	−0.0102853	−	0.156923i
$403$	7.99663	+	2.71449i	0.398340	+	0.135218i
$404$	−11.2078	+	41.8280i	−0.557608	+	2.08102i
$405$	−0.829593	−	0.554316i	−0.0412228	−	0.0275442i
$406$	6.56730	−	3.73235i	0.325930	−	0.185234i
$407$		−	1.04152i		−	0.0516263i
$408$	4.76101	−	0.808497i	0.235705	−	0.0400266i
$409$	−20.4554	−	11.8099i	−1.01146	−	0.583964i	−0.0998380	−	0.995004i	$-0.531832\pi$
$409$	−20.4554	−	11.8099i	−1.01146	−	0.583964i	−0.911617	+	0.411040i	$0.865166\pi$
$410$	0.179625	+	0.234092i	0.00887103	+	0.0115610i
$411$	−12.1389	−	0.795626i	−0.598768	−	0.0392453i
$412$	13.7243	−	13.7243i	0.676148	−	0.676148i
$413$	0.172740	+	2.94171i	0.00849998	+	0.144752i
$414$	−1.28721	+	0.860088i	−0.0632631	+	0.0422710i
$415$	−3.38319	−	9.96656i	−0.166074	−	0.489239i
$416$	23.7771	+	3.13032i	1.16577	+	0.153476i
$417$	19.7715	+	2.60296i	0.968213	+	0.127468i
$418$	−0.989055	−	2.91366i	−0.0483762	−	0.142512i
$419$	11.9425	−	7.97969i	0.583427	−	0.389833i	−0.228542	−	0.973534i	$-0.573396\pi$
$419$	11.9425	−	7.97969i	0.583427	−	0.389833i	0.811969	+	0.583701i	$0.198396\pi$
$420$	0.394463	+	6.71760i	0.0192478	+	0.327785i
$421$	−4.05606	+	4.05606i	−0.197680	+	0.197680i	−0.799005	−	0.601325i	$-0.794640\pi$
$421$	−4.05606	+	4.05606i	−0.197680	+	0.197680i	0.601325	+	0.799005i	$0.294640\pi$
$422$	−49.0335	−	3.21383i	−2.38691	−	0.156447i
$423$	−7.40110	−	9.64530i	−0.359854	−	0.468971i
$424$	−5.01830	−	2.89732i	−0.243710	−	0.140706i
$425$	11.3420	+	11.9989i	0.550166	+	0.582032i
$426$			28.4429i			1.37806i
$427$	22.2222	−	12.6294i	1.07541	−	0.611180i
$428$	23.1132	+	15.4437i	1.11722	+	0.746501i
$429$	0.137622	−	0.513611i	0.00664443	−	0.0247974i
$430$	17.3038	+	5.87384i	0.834462	+	0.283262i
$431$	0.459021	+	7.00331i	0.0221103	+	0.337338i	0.994556	+	0.104207i	$0.0332304\pi$
$431$	0.459021	+	7.00331i	0.0221103	+	0.337338i	−0.972445	+	0.233131i	$0.925103\pi$
$432$	2.46218	−	0.835796i	0.118461	−	0.0402122i
$433$	−12.7612	−	30.8082i	−0.613262	−	1.48055i	−0.859397	−	0.511310i	$-0.829161\pi$
$433$	−12.7612	−	30.8082i	−0.613262	−	1.48055i	0.246135	−	0.969236i	$-0.420839\pi$
$434$	−11.0080	−	11.1587i	−0.528402	−	0.535633i
$435$	0.260559	−	1.30992i	0.0124929	−	0.0628058i
$436$	1.99635	−	4.04819i	0.0956078	−	0.193873i
$437$	1.92447	−	5.66931i	0.0920600	−	0.271200i
$438$	−2.53912	−	9.47613i	−0.121324	−	0.452787i
$439$	1.30021	−	19.8373i	0.0620555	−	0.946785i	−0.847392	−	0.530967i	$-0.821829\pi$
$439$	1.30021	−	19.8373i	0.0620555	−	0.946785i	0.909448	−	0.415818i	$-0.136505\pi$
$440$	0.0782149	−	0.188827i	0.00372875	−	0.00900200i
$441$	1.90347	−	6.73623i	0.0906414	−	0.320773i
$442$	−26.0094	+	6.19048i	−1.23714	+	0.294451i
$443$	3.31567	+	5.74291i	0.157532	+	0.272854i	0.933978	−	0.357330i	$-0.116313\pi$
$443$	3.31567	+	5.74291i	0.157532	+	0.272854i	−0.776446	+	0.630184i	$0.782980\pi$
$444$	12.0433	−	9.24114i	0.571549	−	0.438565i
$445$	0.379148	−	0.186975i	0.0179734	−	0.00886348i
$446$	48.8041	+	13.0770i	2.31094	+	0.619214i
$447$	0.582413	+	2.92799i	0.0275472	+	0.138489i
$448$	−25.4554	−	17.2601i	−1.20265	−	0.815465i
$449$	−10.1106	−	2.01112i	−0.477148	−	0.0949107i	−0.0493436	−	0.998782i	$-0.515713\pi$
$449$	−10.1106	−	2.01112i	−0.477148	−	0.0949107i	−0.427805	+	0.903871i	$0.640713\pi$
$450$	−6.77611	−	5.19949i	−0.319429	−	0.245106i
$451$	−0.00316531	+	0.0240430i	−0.000149049	+	0.00113214i
$452$	35.1709	+	30.8440i	1.65430	+	1.45078i
$453$	−3.37053	−	1.66216i	−0.158362	−	0.0780953i
$454$	−18.3331	+	3.64667i	−0.860414	+	0.171147i
$455$	−0.993442	−	7.96382i	−0.0465733	−	0.373350i
$456$	5.36735	−	8.03280i	0.251349	−	0.376170i
$457$	4.35497	+	33.0793i	0.203717	+	1.54738i	0.721829	+	0.692071i	$0.243302\pi$
$457$	4.35497	+	33.0793i	0.203717	+	1.54738i	−0.518112	+	0.855313i	$0.673365\pi$
$458$	−10.2842	+	17.8127i	−0.480548	+	0.832334i
$459$	−3.17517	+	2.63026i	−0.148204	+	0.122770i
$460$	1.59876	−	0.923042i	0.0745424	−	0.0430371i
$461$	−5.34910	−	2.21567i	−0.249132	−	0.103194i	0.254623	−	0.967040i	$-0.418049\pi$
$461$	−5.34910	−	2.21567i	−0.249132	−	0.103194i	−0.503755	+	0.863846i	$0.668049\pi$
$462$	−0.655772	+	0.737592i	−0.0305093	+	0.0343159i
$463$	20.6609	+	20.6609i	0.960194	+	0.960194i	0.999238	−	0.0390435i	$-0.0124311\pi$
$463$	20.6609	+	20.6609i	0.960194	+	0.960194i	−0.0390435	+	0.999238i	$0.512431\pi$
$464$	2.29491	+	2.61685i	0.106539	+	0.121484i
$465$	−2.76548	+	0.181259i	−0.128246	+	0.00840568i
$466$	24.1403	−	27.5267i	1.11828	−	1.27515i
$467$	−2.59057	+	3.37609i	−0.119877	+	0.156227i	−0.849437	−	0.527690i	$-0.823058\pi$
$467$	−2.59057	+	3.37609i	−0.119877	+	0.156227i	0.729560	+	0.683917i	$0.239725\pi$
$468$	7.16005	−	2.96579i	0.330973	−	0.137094i
$469$	1.28237	−	3.69505i	0.0592144	−	0.170621i
$470$	14.3738	+	21.5119i	0.663014	+	0.992270i
$471$	3.14783	−	2.76057i	0.145044	−	0.127201i
$472$	1.26006	−	0.337631i	0.0579988	−	0.0155407i
$473$	0.664246	+	1.34696i	0.0305421	+	0.0619332i
$474$	8.21519	−	1.08155i	0.377336	−	0.0496773i
$475$	33.0310			1.51557
$476$	27.0674	+	6.37431i	1.24063	+	0.292166i
$477$	4.94742			0.226527
$478$	42.8379	−	5.63971i	1.95936	−	0.257954i
$479$	16.2571	+	32.9661i	0.742805	+	1.50626i	0.858410	+	0.512964i	$0.171453\pi$
$479$	16.2571	+	32.9661i	0.742805	+	1.50626i	−0.115605	+	0.993295i	$0.536881\pi$
$480$	−7.60232	+	2.03704i	−0.346997	+	0.0929776i
$481$	−13.6118	+	11.9373i	−0.620646	+	0.544292i
$482$	−5.02232	−	7.51643i	−0.228760	−	0.342364i
$483$	−1.88599	+	0.361839i	−0.0858154	+	0.0164643i
$484$	−25.8340	+	10.7008i	−1.17427	+	0.486400i
$485$	5.92828	−	7.72589i	0.269190	−	0.350815i
$486$	1.40630	−	1.60358i	0.0637911	−	0.0727398i
$487$	−9.41395	+	0.617023i	−0.426587	+	0.0279600i	−0.277185	−	0.960817i	$-0.589401\pi$
$487$	−9.41395	+	0.617023i	−0.426587	+	0.0279600i	−0.149402	+	0.988777i	$0.547735\pi$
$488$	−7.46067	−	8.50726i	−0.337729	−	0.385106i
$489$	9.38311	+	9.38311i	0.424319	+	0.424319i
$490$	−4.97958	+	14.0395i	−0.224954	+	0.634238i
$491$	20.1039	+	8.32730i	0.907276	+	0.375806i	0.787013	−	0.616936i	$-0.211626\pi$
$491$	20.1039	+	8.32730i	0.907276	+	0.375806i	0.120263	+	0.992742i	$0.461626\pi$
$492$	−0.306098	+	0.176726i	−0.0138000	+	0.00796740i
$493$	−4.87939	−	2.57938i	−0.219757	−	0.116169i
$494$	−26.7433	+	46.3207i	−1.20324	+	2.08407i
$495$	0.0227772	+	0.173010i	0.00102376	+	0.00777621i
$496$	4.01256	−	6.00523i	0.180169	−	0.269643i
$497$	−13.7232	+	32.5042i	−0.615571	+	1.45801i
$498$	22.0672	−	4.38944i	0.988855	−	0.196696i
$499$	−19.1527	−	9.44506i	−0.857392	−	0.422819i	−0.0402051	−	0.999191i	$-0.512801\pi$
$499$	−19.1527	−	9.44506i	−0.857392	−	0.422819i	−0.817187	+	0.576372i	$0.804468\pi$
$500$	17.2186	+	15.1003i	0.770039	+	0.675306i
$501$	0.419606	−	3.18722i	0.0187466	−	0.142395i
$502$	−16.2305	−	12.4541i	−0.724401	−	0.555853i
$503$	4.47835	+	0.890800i	0.199680	+	0.0397188i	0.293917	−	0.955831i	$-0.405041\pi$
$503$	4.47835	+	0.890800i	0.199680	+	0.0397188i	−0.0942369	+	0.995550i	$0.530041\pi$
$504$	−3.09074	−	0.223683i	−0.137672	−	0.00996365i
$505$	3.30662	+	16.6235i	0.147143	+	0.739736i
$506$	0.261536	+	0.0700783i	0.0116267	+	0.00311536i
$507$	3.36954	−	1.66167i	0.149646	−	0.0737974i
$508$	−21.0449	+	16.1483i	−0.933715	+	0.716465i
$509$	−3.31656	−	5.74444i	−0.147004	−	0.254618i	0.783115	−	0.621877i	$-0.213630\pi$
$509$	−3.31656	−	5.74444i	−0.147004	−	0.254618i	−0.930119	+	0.367259i	$0.880296\pi$
$510$	7.10856	−	5.14344i	0.314773	−	0.227755i
$511$	1.67040	−	12.0543i	0.0738940	−	0.533250i
$512$	10.1801	−	24.5768i	0.449899	−	1.08615i
$513$	−0.539475	+	8.23080i	−0.0238184	+	0.363399i
$514$	0.187255	+	0.698847i	0.00825948	+	0.0308248i
$515$	2.44191	−	7.19363i	0.107603	−	0.316989i
$516$	−9.68142	+	19.6320i	−0.426201	+	0.864250i
$517$	−0.414828	+	2.08548i	−0.0182441	+	0.0917194i
$518$	32.5179	−	8.47670i	1.42875	−	0.372445i
$519$	−0.651909	−	1.57385i	−0.0286156	−	0.0690842i
$520$	−3.36427	+	1.14202i	−0.147533	+	0.0500807i
$521$	−1.10227	−	16.8174i	−0.0482914	−	0.736785i	−0.951513	−	0.307610i	$-0.900471\pi$
$521$	−1.10227	−	16.8174i	−0.0482914	−	0.736785i	0.903221	−	0.429175i	$-0.141196\pi$
$522$	2.70355	+	0.917732i	0.118331	+	0.0401680i
$523$	−3.38727	+	12.6415i	−0.148115	+	0.552773i	0.851482	+	0.524384i	$0.175704\pi$
$523$	−3.38727	+	12.6415i	−0.148115	+	0.552773i	−0.999597	+	0.0283892i	$0.990962\pi$
$524$	35.4808	+	23.7075i	1.54999	+	1.03567i
$525$	−5.23499	−	9.21127i	−0.228474	−	0.402013i
$526$		−	55.1376i		−	2.40411i
$527$	−2.54944	+	11.1653i	−0.111055	+	0.486368i
$528$	−0.393836	−	0.227381i	−0.0171395	−	0.00989549i
$529$	−13.6808	−	17.8292i	−0.594817	−	0.775181i
$530$	−10.5058	−	0.688590i	−0.456345	−	0.0299104i
$531$	−0.787561	+	0.787561i	−0.0341772	+	0.0341772i
$532$	46.4643	−	30.5918i	2.01448	−	1.32632i
$533$	0.350501	−	0.234197i	0.0151819	−	0.0101442i
$534$	0.290485	+	0.855741i	0.0125705	+	0.0370315i
$535$	10.7872	+	1.42016i	0.466369	+	0.0613987i
$536$	−1.71665	−	0.226001i	−0.0741481	−	0.00976178i
$537$	−2.77281	−	8.16845i	−0.119656	−	0.352495i
$538$	4.90763	−	3.27918i	0.211583	−	0.141375i
$539$	−1.10528	+	0.526511i	−0.0476079	+	0.0226785i
$540$	−1.79845	+	1.79845i	−0.0773928	+	0.0773928i
$541$	2.08021	+	0.136344i	0.0894351	+	0.00586188i	0.110055	−	0.993926i	$-0.464897\pi$
$541$	2.08021	+	0.136344i	0.0894351	+	0.00586188i	−0.0206199	+	0.999787i	$0.506564\pi$
$542$	18.1972	+	23.7150i	0.781636	+	1.01865i
$543$	−7.62727	−	4.40360i	−0.327317	−	0.188977i
$544$	−0.915043	+	32.5115i	−0.0392322	+	1.39392i
$545$		−	1.76667i		−	0.0756758i
$546$	17.1558	+	0.116599i	0.734200	+	0.00498996i
$547$	37.3955	+	24.9869i	1.59892	+	1.06836i	0.952131	+	0.305689i	$0.0988869\pi$
$547$	37.3955	+	24.9869i	1.59892	+	1.06836i	0.646785	+	0.762672i	$0.276113\pi$
$548$	−8.02602	+	29.9535i	−0.342855	+	1.27955i
$549$	9.14818	+	3.10539i	0.390435	+	0.132535i
$550$	0.0977003	+	1.49062i	0.00416596	+	0.0635602i
$551$	−10.4555	+	3.54915i	−0.445417	+	0.151199i
$552$	0.325332	+	0.785421i	0.0138470	+	0.0334297i
$553$	9.91005	+	2.72771i	0.421418	+	0.115994i
$554$	−4.15045	+	20.8657i	−0.176336	+	0.886499i
$555$	2.62790	−	5.32886i	0.111548	−	0.226197i
$556$	16.3404	−	48.1373i	0.692988	−	2.04148i
$557$	−10.7710	−	40.1980i	−0.456383	−	1.70324i	−0.683991	−	0.729491i	$-0.739757\pi$
$557$	−10.7710	−	40.1980i	−0.456383	−	1.70324i	0.227608	−	0.973753i	$-0.426910\pi$
$558$	0.387476	−	5.91175i	0.0164032	−	0.250264i
$559$	9.99048	−	24.1191i	0.422552	−	1.02013i
$560$	−6.79890	−	0.942143i	−0.287306	−	0.0398128i
$561$	0.712020	+	0.114202i	0.0300615	+	0.00482163i
$562$	−8.03070	−	13.9096i	−0.338755	−	0.586740i
$563$	−13.8580	+	10.6336i	−0.584043	+	0.448152i	−0.858043	−	0.513578i	$-0.828320\pi$
$563$	−13.8580	+	10.6336i	−0.584043	+	0.448152i	0.274000	+	0.961730i	$0.411653\pi$
$564$	−27.7954	+	13.7072i	−1.17040	+	0.577177i
$565$	17.6859	+	4.73892i	0.744051	+	0.199368i
$566$	−4.87955	−	24.5311i	−0.205103	−	1.03112i
$567$	2.38080	−	1.15403i	0.0999842	−	0.0484648i
$568$	15.3190	+	3.04714i	0.642772	+	0.127855i
$569$	12.5328	+	9.61679i	0.525404	+	0.403157i	0.837121	−	0.547019i	$-0.184237\pi$
$569$	12.5328	+	9.61679i	0.525404	+	0.403157i	−0.311717	+	0.950175i	$0.600904\pi$
$570$	2.29115	−	17.4030i	0.0959658	−	0.728933i
$571$	−0.922545	−	0.809051i	−0.0386073	−	0.0338577i	0.639825	−	0.768521i	$-0.279007\pi$
$571$	−0.922545	−	0.809051i	−0.0386073	−	0.0338577i	−0.678432	+	0.734663i	$0.737340\pi$
$572$	−1.21567	−	0.599501i	−0.0508296	−	0.0250664i
$573$	21.6816	−	4.31273i	0.905761	−	0.180167i
$574$	−0.776419	+	0.0968540i	−0.0324071	+	0.00404261i
$575$	−1.61483	+	2.41677i	−0.0673432	+	0.100786i
$576$	−1.51729	−	11.5250i	−0.0632204	−	0.480207i
$577$	18.8050	−	32.5712i	0.782862	−	1.35596i	−0.147407	−	0.989076i	$-0.547093\pi$
$577$	18.8050	−	32.5712i	0.782862	−	1.35596i	0.930268	−	0.366880i	$-0.119574\pi$
$578$	−11.9695	−	34.2262i	−0.497866	−	1.42362i
$579$	6.52408	−	3.76668i	0.271132	−	0.156538i
$580$	−3.14543	−	1.30288i	−0.130607	−	0.0540991i
$581$	27.3360	+	5.63086i	1.13409	+	0.233607i
$582$	14.7202	+	14.7202i	0.610171	+	0.610171i
$583$	−0.570526	−	0.650560i	−0.0236288	−	0.0269435i
$584$	−5.37575	+	0.352345i	−0.222450	+	0.0145802i
$585$	2.00004	−	2.28061i	0.0826915	−	0.0942916i
$586$	−11.7391	+	15.2988i	−0.484940	+	0.631986i
$587$	31.6625	−	13.1150i	1.30685	−	0.541316i	0.382887	−	0.923795i	$-0.374930\pi$
$587$	31.6625	−	13.1150i	1.30685	−	0.541316i	0.923964	+	0.382479i	$0.124930\pi$
$588$	−15.8950	−	8.10899i	−0.655500	−	0.334409i
$589$	12.7290	+	19.0503i	0.524489	+	0.784953i
$590$	1.78200	−	1.56277i	0.0733638	−	0.0643383i
$591$	3.86584	−	1.03585i	0.159019	−	0.0426091i
$592$	6.84844	+	13.8873i	0.281469	+	0.570763i
$593$	−31.1008	+	4.09450i	−1.27716	+	0.168141i	−0.738425	−	0.674336i	$-0.764430\pi$
$593$	−31.1008	+	4.09450i	−1.27716	+	0.168141i	−0.538732	+	0.842477i	$0.681097\pi$
$594$	−0.373034			−0.0153058
$595$	10.6052	−	2.44809i	0.434771	−	0.100362i
$596$	7.61007			0.311721
$597$	−16.8063	+	2.21259i	−0.687836	+	0.0905553i
$598$	−2.08169	−	4.22126i	−0.0851268	−	0.172620i
$599$	−42.0958	+	11.2795i	−1.71999	+	0.460869i	−0.977838	−	0.209365i	$-0.932860\pi$
$599$	−42.0958	+	11.2795i	−1.71999	+	0.460869i	−0.742150	+	0.670234i	$0.766194\pi$
$600$	−3.52632	+	3.09250i	−0.143962	+	0.126251i
$601$	3.28345	+	4.91404i	0.133935	+	0.200448i	0.892375	−	0.451296i	$-0.149038\pi$
$601$	3.28345	+	4.91404i	0.133935	+	0.200448i	−0.758440	+	0.651743i	$0.774038\pi$
$602$	−36.6479	+	31.7013i	−1.49366	+	1.29205i
$603$	1.36578	−	0.565725i	0.0556189	−	0.0230381i
$604$	−5.83188	+	7.60026i	−0.237296	+	0.309250i
$605$	−7.21631	+	8.22863i	−0.293385	+	0.334541i
$606$	−36.1546	+	2.36970i	−1.46868	+	0.0962624i
$607$	21.2809	+	24.2662i	0.863766	+	0.984936i	0.999984	−	0.00574249i	$-0.00182790\pi$
$607$	21.2809	+	24.2662i	0.863766	+	0.984936i	−0.136217	+	0.990679i	$0.543495\pi$
$608$	46.0089	+	46.0089i	1.86591	+	1.86591i
$609$	2.64679	+	2.35319i	0.107253	+	0.0953561i
$610$	−18.9940	−	7.86755i	−0.769043	−	0.318548i
$611$	32.0101	−	18.4810i	1.29499	−	0.747662i
$612$	4.99702	+	9.24650i	0.201993	+	0.373767i
$613$	4.03255	−	6.98459i	0.162873	−	0.282105i	−0.773025	−	0.634376i	$-0.781257\pi$
$613$	4.03255	−	6.98459i	0.162873	−	0.282105i	0.935898	+	0.352271i	$0.114590\pi$
$614$	−5.47547	−	41.5903i	−0.220972	−	1.67845i
$615$	−0.0768588	+	0.115027i	−0.00309924	+	0.00463835i
$616$	0.327004	+	0.432211i	0.0131754	+	0.0174143i
$617$	30.9254	−	6.15145i	1.24501	−	0.247648i	0.471747	−	0.881734i	$-0.343623\pi$
$617$	30.9254	−	6.15145i	1.24501	−	0.247648i	0.773263	+	0.634086i	$0.218623\pi$
$618$	14.5649	+	7.18261i	0.585886	+	0.288927i
$619$	14.8050	+	12.9837i	0.595064	+	0.521857i	0.903051	−	0.429533i	$-0.141322\pi$
$619$	14.8050	+	12.9837i	0.595064	+	0.521857i	−0.307987	+	0.951391i	$0.599655\pi$
$620$	−0.922130	+	7.00427i	−0.0370336	+	0.281298i
$621$	−0.575846	−	0.441862i	−0.0231079	−	0.0177313i
$622$	−8.44094	−	1.67901i	−0.338451	−	0.0673221i
$623$	−0.0809181	+	1.11808i	−0.00324192	+	0.0447951i
$624$	1.54221	+	7.75321i	0.0617378	+	0.310377i
$625$	−10.6818	−	2.86219i	−0.427273	−	0.114487i
$626$	−52.3043	+	25.7936i	−2.09050	+	1.03092i
$627$	1.14452	−	0.878221i	0.0457077	−	0.0350727i
$628$	−5.33642	−	9.24295i	−0.212946	−	0.368834i
$629$	−17.9973	−	16.7020i	−0.717601	−	0.665954i
$630$	−5.21625	+	2.11922i	−0.207820	+	0.0844319i
$631$	−12.9826	+	31.3429i	−0.516831	+	1.24774i	0.423010	+	0.906125i	$0.360974\pi$
$631$	−12.9826	+	31.3429i	−0.516831	+	1.24774i	−0.939840	+	0.341614i	$0.889026\pi$
$632$	0.297598	−	4.54048i	0.0118378	−	0.180610i
$633$	−5.96287	−	22.2537i	−0.237003	−	0.884507i
$634$	−11.2113	+	33.0275i	−0.445259	+	1.31169i
$635$	−4.59209	+	9.31184i	−0.182232	+	0.369529i
$636$	2.46041	−	12.3693i	0.0975617	−	0.490476i
$637$	19.5491	+	8.41062i	0.774565	+	0.333241i
$638$	−0.191091	−	0.461334i	−0.00756536	−	0.0182644i
$639$	−12.6278	+	4.28656i	−0.499548	+	0.169574i
$640$	0.588394	+	8.97715i	0.0232583	+	0.354853i
$641$	35.2771	+	11.9750i	1.39336	+	0.472983i	0.914386	−	0.404844i	$-0.132674\pi$
$641$	35.2771	+	11.9750i	1.39336	+	0.472983i	0.478977	+	0.877827i	$0.341008\pi$
$642$	−6.01978	+	22.4661i	−0.237582	+	0.886667i
$643$	24.9595	+	16.6774i	0.984307	+	0.657693i	0.939946	−	0.341323i	$-0.110875\pi$
$643$	24.9595	+	16.6774i	0.984307	+	0.657693i	0.0443608	+	0.999016i	$0.485875\pi$
$644$	−0.0332701	+	4.89522i	−0.00131103	+	0.192899i
$645$			8.56758i			0.337348i
$646$	−66.2083	−	29.6333i	−2.60493	−	1.16591i
$647$	−17.9646	−	10.3719i	−0.706261	−	0.407760i	0.103414	−	0.994638i	$-0.467023\pi$
$647$	−17.9646	−	10.3719i	−0.706261	−	0.407760i	−0.809675	+	0.586878i	$0.800357\pi$
$648$	−0.713009	−	0.929211i	−0.0280096	−	0.0365029i
$649$	0.194380	+	0.0127403i	0.00763008	+	0.000500102i
$650$	18.3614	−	18.3614i	0.720193	−	0.720193i
$651$	3.29512	−	6.56892i	0.129146	−	0.257456i
$652$	28.1256	−	18.7929i	1.10148	−	0.735988i
$653$	−12.9011	−	38.0053i	−0.504858	−	1.48726i	−0.838679	−	0.544627i	$-0.816671\pi$
$653$	−12.9011	−	38.0053i	−0.504858	−	1.48726i	0.333821	−	0.942637i	$-0.391662\pi$
$654$	3.74430	+	0.492946i	0.146414	+	0.0192757i
$655$	16.5592	+	2.18007i	0.647023	+	0.0851822i
$656$	−0.115887	−	0.341393i	−0.00452464	−	0.0133292i
$657$	3.82445	−	2.55541i	0.149206	−	0.0996962i
$658$	−68.4881	+	4.02168i	−2.66995	+	0.156781i
$659$	32.8413	−	32.8413i	1.27932	−	1.27932i	0.338267	−	0.941050i	$-0.390159\pi$
$659$	32.8413	−	32.8413i	1.27932	−	1.27932i	0.941050	−	0.338267i	$-0.109841\pi$
$660$	0.443879	+	0.0290934i	0.0172780	+	0.00113246i
$661$	−9.16755	−	11.9474i	−0.356576	−	0.464699i	0.580278	−	0.814418i	$-0.302944\pi$
$661$	−9.16755	−	11.9474i	−0.356576	−	0.464699i	−0.936855	+	0.349719i	$0.886277\pi$
$662$	26.7620	+	15.4511i	1.04014	+	0.600523i
$663$	−6.66820	−	10.6144i	−0.258971	−	0.412231i
$664$		−	12.3554i		−	0.479482i
$665$	11.0150	−	18.7825i	0.427142	−	0.728355i
$666$	10.5608	+	7.05648i	0.409222	+	0.273433i
$667$	0.251471	−	0.938502i	0.00973699	−	0.0363389i
$668$	−7.75989	−	2.63413i	−0.300239	−	0.101917i
$669$	1.54934	+	23.6383i	0.0599009	+	0.913910i
$670$	−2.97898	+	1.01123i	−0.115088	+	0.0390671i
$671$	−0.646606	−	1.56105i	−0.0249620	−	0.0602635i
$672$	5.53857	−	20.1222i	0.213655	−	0.776230i
$673$	8.73541	−	43.9159i	0.336725	−	1.69283i	−0.327136	−	0.944977i	$-0.606084\pi$
$673$	8.73541	−	43.9159i	0.336725	−	1.69283i	0.663862	−	0.747855i	$-0.268916\pi$
$674$	28.6012	−	57.9974i	1.10168	−	2.23398i
$675$	1.28721	−	3.79199i	0.0495446	−	0.145954i
$676$	−2.47873	−	9.25075i	−0.0953358	−	0.355798i
$677$	−0.629230	+	9.60019i	−0.0241833	+	0.368965i	0.968566	+	0.248758i	$0.0800225\pi$
$677$	−0.629230	+	9.60019i	−0.0241833	+	0.368965i	−0.992749	+	0.120207i	$0.961644\pi$
$678$	−14.9785	+	36.1613i	−0.575246	+	1.38877i
$679$	9.71979	+	23.9243i	0.373011	+	0.918129i
$680$	−2.00864	−	4.37962i	−0.0770279	−	0.167951i
$681$	−4.38194	−	7.58975i	−0.167916	−	0.290840i
$682$	−0.822047	+	0.630779i	−0.0314778	+	0.0241538i
$683$	31.0637	−	15.3189i	1.18862	−	0.586162i	0.263065	−	0.964778i	$-0.415267\pi$
$683$	31.0637	−	15.3189i	1.18862	−	0.586162i	0.925554	+	0.378616i	$0.123600\pi$
$684$	20.3100	+	5.44205i	0.776573	+	0.208082i
$685$	2.36791	+	11.9043i	0.0904731	+	0.454839i
$686$	−25.4341	−	30.2235i	−0.971080	−	1.15394i
$687$	−9.45821	−	1.88135i	−0.360853	−	0.0717782i
$688$	−17.7136	−	13.5921i	−0.675325	−	0.518195i
$689$	−1.96328	+	14.9126i	−0.0747952	+	0.568126i
$690$	1.16131	+	1.01844i	0.0442103	+	0.0387714i
$691$	−22.7566	−	11.2223i	−0.865701	−	0.426916i	−0.0454811	−	0.998965i	$-0.514482\pi$
$691$	−22.7566	−	11.2223i	−0.865701	−	0.426916i	−0.820220	+	0.572049i	$0.806149\pi$
$692$	−4.25907	+	0.847181i	−0.161905	+	0.0322050i
$693$	−0.426298	−	0.179982i	−0.0161937	−	0.00683697i
$694$	−21.3324	+	31.9262i	−0.809766	+	1.21190i
$695$	−2.59709	−	19.7268i	−0.0985132	−	0.748282i
$696$	0.783916	−	1.35778i	0.0297143	−	0.0514666i
$697$	0.364699	+	0.440254i	0.0138140	+	0.0166758i
$698$	−41.0825	+	23.7190i	−1.55499	+	0.897776i
$699$	15.8592	+	6.56908i	0.599849	+	0.248465i
$700$	−25.6331	+	8.50741i	−0.968839	+	0.321550i
$701$	24.6845	+	24.6845i	0.932321	+	0.932321i	0.997851	−	0.0655299i	$-0.0208738\pi$
$701$	24.6845	+	24.6845i	0.932321	+	0.932321i	−0.0655299	+	0.997851i	$0.520874\pi$
$702$	4.27548	+	4.87525i	0.161368	+	0.184004i
$703$	−49.0147	+	3.21260i	−1.84863	+	0.121165i
$704$	−1.34050	+	1.52855i	−0.0505221	+	0.0576094i
$705$	−7.38439	+	9.62353i	−0.278112	+	0.362443i
$706$	44.1188	−	18.2746i	1.66043	−	0.687773i
$707$	−42.4604	−	14.7359i	−1.59689	−	0.554202i
$708$	1.57736	+	2.36069i	0.0592809	+	0.0887202i
$709$	7.11253	−	6.23752i	0.267117	−	0.234255i	−0.515301	−	0.857009i	$-0.672320\pi$
$709$	7.11253	−	6.23752i	0.267117	−	0.234255i	0.782417	+	0.622754i	$0.213986\pi$
$710$	27.4117	−	7.34495i	1.02874	−	0.275651i
$711$	1.71827	+	3.48430i	0.0644400	+	0.130671i
$712$	0.492012	−	0.0647746i	0.0184389	−	0.00242753i
$713$	−2.01614			−0.0755052
$714$	2.22939	+	23.1598i	0.0834329	+	0.866735i
$715$	−0.530529			−0.0198407
$716$	−21.8014	+	2.87020i	−0.814755	+	0.107265i
$717$	8.95984	+	18.1688i	0.334611	+	0.678525i
$718$	−49.2103	+	13.1859i	−1.83651	+	0.492092i
$719$	−20.5188	+	17.9945i	−0.765222	+	0.671082i	−0.950193	−	0.311662i	$-0.899114\pi$
$719$	−20.5188	+	17.9945i	−0.765222	+	0.671082i	0.184971	+	0.982744i	$0.440781\pi$
$720$	−1.44131	−	2.15708i	−0.0537146	−	0.0803896i
$721$	13.1791	+	15.2355i	0.490814	+	0.567400i
$722$	−96.6284	+	40.0248i	−3.59614	+	1.48957i
$723$	2.58017	−	3.36254i	0.0959574	−	0.125054i
$724$	−14.8028	+	16.8794i	−0.550143	+	0.627318i
$725$	5.34897	−	0.350590i	0.198656	−	0.0130206i
$726$	−15.4263	−	17.5903i	−0.572523	−	0.652837i
$727$	−35.5281	−	35.5281i	−1.31766	−	1.31766i	−0.915620	−	0.402045i	$-0.868300\pi$
$727$	−35.5281	−	35.5281i	−1.31766	−	1.31766i	−0.402045	−	0.915620i	$-0.631700\pi$
$728$	1.90073	−	9.22741i	0.0704457	−	0.341991i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	−8.47689	+	4.89413i	−0.313744	+	0.181140i
$731$	33.9272	+	10.1220i	1.25484	+	0.374376i
$732$	12.3135	−	21.3276i	0.455119	−	0.788289i
$733$	−5.13530	−	39.0064i	−0.189676	−	1.44074i	−0.776038	−	0.630686i	$-0.782773\pi$
$733$	−5.13530	−	39.0064i	−0.189676	−	1.44074i	0.586361	−	0.810050i	$-0.300560\pi$
$734$	−20.5157	+	30.7039i	−0.757248	+	1.13330i
$735$	−6.98356	−	0.0949312i	−0.257592	−	0.00350159i
$736$	−5.61561	+	1.11701i	−0.206994	+	0.0411737i
$737$	−0.231889	−	0.114355i	−0.00854174	−	0.00421232i
$738$	−0.222344	−	0.194991i	−0.00818460	−	0.00717770i
$739$	−2.18106	+	16.5668i	−0.0802315	+	0.609419i	0.903343	+	0.428918i	$0.141105\pi$
$739$	−2.18106	+	16.5668i	−0.0802315	+	0.609419i	−0.983575	+	0.180501i	$0.942228\pi$
$740$	−12.0161	−	9.22028i	−0.441721	−	0.338944i
$741$	−24.5954	−	4.89233i	−0.903534	−	0.179724i
$742$	15.6681	−	23.1074i	0.575194	−	0.848301i
$743$	−8.77644	−	44.1221i	−0.321976	−	1.61868i	−0.714978	−	0.699147i	$-0.753563\pi$
$743$	−8.77644	−	44.1221i	−0.321976	−	1.61868i	0.393002	−	0.919538i	$-0.371437\pi$
$744$	−3.14249	−	0.842027i	−0.115209	−	0.0308702i
$745$	2.67144	−	1.31741i	0.0978738	−	0.0482660i
$746$	9.21364	−	7.06987i	0.337335	−	0.258846i
$747$	5.27447	+	9.13565i	0.192983	+	0.334256i
$748$	0.639621	−	1.72337i	0.0233869	−	0.0630126i
$749$	−17.7188	+	22.7695i	−0.647433	+	0.831981i
$750$	−7.33302	+	17.7035i	−0.267764	+	0.646440i
$751$	−1.80863	+	27.5943i	−0.0659977	+	1.00693i	0.828538	+	0.559933i	$0.189173\pi$
$751$	−1.80863	+	27.5943i	−0.0659977	+	1.00693i	−0.894535	+	0.446997i	$0.852493\pi$
$752$	−8.18175	−	30.5347i	−0.298358	−	1.11349i
$753$	3.08318	−	9.08276i	0.112357	−	0.330994i
$754$	−3.83910	+	7.78492i	−0.139812	+	0.283510i
$755$	−0.731514	+	3.67757i	−0.0266225	+	0.133840i
$756$	−1.70126	−	6.52629i	−0.0618743	−	0.237359i
$757$	0.919396	+	2.21962i	0.0334160	+	0.0806734i	0.939707	−	0.341982i	$-0.111098\pi$
$757$	0.919396	+	2.21962i	0.0334160	+	0.0806734i	−0.906291	+	0.422655i	$0.861098\pi$
$758$	2.48966	−	0.845124i	0.0904284	−	0.0306963i
$759$	0.00830274	+	0.126675i	0.000301370	+	0.00459802i
$760$	−9.12761	−	3.09841i	−0.331093	−	0.112391i
$761$	−6.54562	+	24.4286i	−0.237279	+	0.885536i	0.739830	+	0.672794i	$0.234906\pi$
$761$	−6.54562	+	24.4286i	−0.237279	+	0.885536i	−0.977108	+	0.212742i	$0.931761\pi$
$762$	−18.4543	−	12.3308i	−0.668528	−	0.446696i
$763$	4.04109	+	2.36989i	0.146297	+	0.0857958i
$764$		−	56.3521i		−	2.03875i
$765$	3.35484	+	2.38083i	0.121295	+	0.0860792i
$766$	−58.2934	−	33.6557i	−2.10623	−	1.21603i
$767$	−2.06136	−	2.68641i	−0.0744312	−	0.0970007i
$768$	4.00863	+	0.262740i	0.144649	+	0.00948080i
$769$	0.459052	−	0.459052i	0.0165538	−	0.0165538i	−0.698781	−	0.715335i	$-0.746274\pi$
$769$	0.459052	−	0.459052i	0.0165538	−	0.0165538i	0.715335	+	0.698781i	$0.246274\pi$
$770$	0.880194	+	0.441526i	0.0317200	+	0.0159115i
$771$	−0.282046	+	0.188457i	−0.0101576	+	0.00678711i
$772$	−6.17279	−	18.1845i	−0.222164	−	0.654473i
$773$	6.92150	+	0.911232i	0.248949	+	0.0327747i	0.253968	−	0.967213i	$-0.418264\pi$
$773$	6.92150	+	0.911232i	0.248949	+	0.0327747i	−0.00501895	+	0.999987i	$0.501598\pi$
$774$	−18.1582	−	2.39057i	−0.652683	−	0.0859274i
$775$	−3.57545	−	10.5329i	−0.128434	−	0.378354i
$776$	9.50511	−	6.35111i	0.341214	−	0.227992i
$777$	8.66408	+	13.1595i	0.310822	+	0.472093i
$778$	8.35047	−	8.35047i	0.299379	−	0.299379i
$779$	1.14124	+	0.0748010i	0.0408893	+	0.00268002i
$780$	−4.70724	−	6.13459i	−0.168546	−	0.219654i
$781$	2.01987	+	1.16617i	0.0722767	+	0.0417290i
$782$	5.40498	−	3.39551i	0.193282	−	0.121423i
$783$			1.33860i			0.0478378i
$784$	11.2754	−	14.2880i	0.402693	−	0.510286i
$785$	−3.47337	−	2.32083i	−0.123970	−	0.0828341i
$786$	−9.24090	+	34.4875i	−0.329612	+	1.23013i
$787$	24.2151	+	8.21992i	0.863175	+	0.293009i	0.717699	−	0.696353i	$-0.245195\pi$
$787$	24.2151	+	8.21992i	0.863175	+	0.293009i	0.145476	+	0.989362i	$0.453529\pi$
$788$	−0.667256	−	10.1804i	−0.0237700	−	0.362660i
$789$	24.4794	−	8.30965i	0.871491	−	0.295831i
$790$	−3.16379	−	7.63806i	−0.112563	−	0.271750i
$791$	−34.5645	+	34.0978i	−1.22897	+	1.21238i
$792$	−0.0399638	+	0.200912i	−0.00142005	+	0.00713908i
$793$	−12.9906	+	26.3423i	−0.461310	+	0.935444i
$794$	−21.9626	+	64.6997i	−0.779423	+	2.29611i
$795$	−1.27760	−	4.76805i	−0.0453117	−	0.169105i
$796$	−2.82615	+	43.1188i	−0.100170	+	1.52830i
$797$	6.66235	−	16.0843i	0.235993	−	0.569736i	−0.760869	−	0.648906i	$-0.775227\pi$
$797$	6.66235	−	16.0843i	0.235993	−	0.569736i	0.996861	+	0.0791695i	$0.0252268\pi$
$798$	36.7344	+	28.5860i	1.30038	+	1.01193i
$799$	29.3846	+	40.6114i	1.03955	+	1.43673i
$800$	−15.7944	−	27.3567i	−0.558416	−	0.967206i
$801$	−0.336145	+	0.257933i	−0.0118771	+	0.00911361i
$802$	38.8585	−	19.1629i	1.37214	−	0.676665i
$803$	−0.777051	−	0.208210i	−0.0274215	−	0.00734758i
$804$	−0.735183	−	3.69601i	−0.0259279	−	0.130348i
$805$	0.835749	+	1.72417i	0.0294563	+	0.0607691i
$806$	17.6656	+	3.51390i	0.622243	+	0.123772i
$807$	2.19547	+	1.68464i	0.0772843	+	0.0593023i
$808$	−2.59702	+	19.7263i	−0.0913628	+	0.693969i
$809$	25.5970	+	22.4480i	0.899942	+	0.789228i	0.978191	−	0.207705i	$-0.0665996\pi$
$809$	25.5970	+	22.4480i	0.899942	+	0.789228i	−0.0782489	+	0.996934i	$0.524933\pi$
$810$	−1.90860	−	0.941216i	−0.0670612	−	0.0330709i
$811$	−16.9448	+	3.37052i	−0.595011	+	0.118355i	−0.483404	−	0.875397i	$-0.660600\pi$
$811$	−16.9448	+	3.37052i	−0.595011	+	0.118355i	−0.111607	+	0.993752i	$0.535600\pi$
$812$	7.19963	−	5.44713i	0.252658	−	0.191157i
$813$	−7.78630	+	11.6530i	−0.273078	+	0.408689i
$814$	−0.289955	−	2.20243i	−0.0101629	−	0.0771950i
$815$	6.61988	−	11.4660i	0.231884	−	0.401635i
$816$	−10.2447	+	3.15910i	−0.358638	+	0.110591i
$817$	61.3399	−	35.4146i	2.14601	−	1.23900i
$818$	−46.5434	−	19.2789i	−1.62735	−	0.674071i
$819$	2.53374	+	7.63422i	0.0885359	+	0.266761i
$820$	0.249364	+	0.249364i	0.00870816	+	0.00870816i
$821$	4.00376	+	4.56541i	0.139732	+	0.159334i	0.817473	−	0.575967i	$-0.195374\pi$
$821$	4.00376	+	4.56541i	0.139732	+	0.159334i	−0.677741	+	0.735301i	$0.737041\pi$
$822$	−25.8907	+	1.69697i	−0.903042	+	0.0591885i
$823$	6.01034	−	6.85348i	0.209507	−	0.238897i	−0.637537	−	0.770420i	$-0.720047\pi$
$823$	6.01034	−	6.85348i	0.209507	−	0.238897i	0.847044	+	0.531523i	$0.178380\pi$
$824$	5.42883	−	7.07499i	0.189122	−	0.246469i
$825$	−0.647065	+	0.268023i	−0.0225279	+	0.00933137i
$826$	1.18424	+	6.17253i	0.0412050	+	0.214770i
$827$	−27.4311	−	41.0536i	−0.953875	−	1.42757i	−0.903376	−	0.428850i	$-0.858919\pi$
$827$	−27.4311	−	41.0536i	−0.953875	−	1.42757i	−0.0504988	−	0.998724i	$-0.516081\pi$
$828$	−1.39110	+	1.21996i	−0.0483441	+	0.0423966i
$829$	10.6814	−	2.86209i	0.370982	−	0.0994043i	−0.0685109	−	0.997650i	$-0.521825\pi$
$829$	10.6814	−	2.86209i	0.370982	−	0.0994043i	0.439493	+	0.898246i	$0.355158\pi$
$830$	−9.92883	−	20.1337i	−0.344635	−	0.698850i
$831$	−9.88924	+	1.30194i	−0.343054	+	0.0451639i
$832$	35.3409			1.22523
$833$	−8.62650	+	27.5424i	−0.298891	+	0.954287i
$834$	42.5339			1.47283
$835$	−3.18003	+	0.418659i	−0.110049	+	0.0144883i
$836$	−1.62651	−	3.29823i	−0.0562539	−	0.114072i
$837$	2.68303	−	0.718916i	0.0927392	−	0.0248494i
$838$	23.0323	−	20.1988i	0.795637	−	0.697755i
$839$	−7.29402	−	10.9163i	−0.251818	−	0.376872i	0.683927	−	0.729551i	$-0.260271\pi$
$839$	−7.29402	−	10.9163i	−0.251818	−	0.376872i	−0.935744	+	0.352679i	$0.885271\pi$
$840$	0.582563	+	3.03645i	0.0201003	+	0.104767i
$841$	25.1370	−	10.4121i	0.866795	−	0.359038i
$842$	−7.44785	+	9.70623i	−0.256670	+	0.334499i
$843$	4.96515	−	5.66166i	0.171009	−	0.194998i
$844$	−58.6033	+	3.84106i	−2.01721	+	0.132215i
$845$	−2.47156	−	2.81827i	−0.0850243	−	0.0969516i
$846$	−18.3358	−	18.3358i	−0.630396	−	0.630396i
$847$	−9.14193	−	27.5449i	−0.314120	−	0.946454i
$848$	11.8849	+	4.92288i	0.408129	+	0.169052i
$849$	10.1557	−	5.86339i	0.348543	−	0.201231i
$850$	27.3244	+	22.2156i	0.937220	+	0.761989i
$851$	2.16120	−	3.74330i	0.0740848	−	0.128319i
$852$	4.43712	+	33.7033i	0.152013	+	1.15465i
$853$	−19.9365	+	29.8371i	−0.682613	+	1.02160i	0.314761	+	0.949171i	$0.398076\pi$
$853$	−19.9365	+	29.8371i	−0.682613	+	1.02160i	−0.997373	+	0.0724309i	$0.976924\pi$
$854$	43.4757	−	32.8930i	1.48771	−	1.12558i
$855$	8.07171	−	1.60556i	0.276047	−	0.0549091i
$856$	11.4551	+	5.64902i	0.391527	+	0.193080i
$857$	−22.9600	−	20.1354i	−0.784300	−	0.687813i	0.170402	−	0.985375i	$-0.445493\pi$
$857$	−22.9600	−	20.1354i	−0.784300	−	0.687813i	−0.954703	+	0.297562i	$0.903827\pi$
$858$	0.148031	−	1.12441i	0.00505369	−	0.0383866i
$859$	−17.7850	−	13.6469i	−0.606816	−	0.465626i	0.259076	−	0.965857i	$-0.416582\pi$
$859$	−17.7850	−	13.6469i	−0.606816	−	0.465626i	−0.865892	+	0.500231i	$0.833249\pi$
$860$	21.4203	+	4.26077i	0.730427	+	0.145291i
$861$	−0.160012	−	0.330110i	−0.00545321	−	0.0112501i
$862$	2.92035	+	14.6816i	0.0994674	+	0.500057i
$863$	26.8069	+	7.18289i	0.912518	+	0.244509i	0.684385	−	0.729121i	$-0.260071\pi$
$863$	26.8069	+	7.18289i	0.912518	+	0.244509i	0.228134	+	0.973630i	$0.426738\pi$
$864$	7.07481	−	3.48891i	0.240690	−	0.118695i
$865$	−1.34844	+	1.03470i	−0.0458484	+	0.0351807i
$866$	−35.5619	−	61.5950i	−1.20844	−	2.09308i
$867$	13.3915	−	10.4722i	0.454799	−	0.355656i
$868$	−14.7846	−	11.5051i	−0.501823	−	0.390510i
$869$	0.260021	−	0.627745i	0.00882059	−	0.0212948i
$870$	0.186309	−	2.84253i	0.00631647	−	0.0963707i
$871$	1.16324	+	4.34127i	0.0394149	+	0.147098i
$872$	0.666628	−	1.96382i	0.0225749	−	0.0665035i
$873$	−4.31687	+	8.75375i	−0.146104	+	0.296269i
$874$	2.49122	−	12.5242i	0.0842669	−	0.423638i
$875$	−16.9217	+	16.6933i	−0.572058	+	0.564335i
$876$	−4.48700	−	10.8326i	−0.151602	−	0.365999i
$877$	9.00885	−	3.05809i	0.304207	−	0.103264i	−0.165162	−	0.986266i	$-0.552815\pi$
$877$	9.00885	−	3.05809i	0.304207	−	0.103264i	0.469369	+	0.883002i	$0.344481\pi$
$878$	−2.77318	−	42.3105i	−0.0935902	−	1.42791i
$879$	−8.56136	−	2.90619i	−0.288767	−	0.0980233i
$880$	−0.117435	+	0.438275i	−0.00395875	+	0.0147743i
$881$	19.4999	+	13.0294i	0.656967	+	0.438971i	0.838860	−	0.544347i	$-0.183223\pi$
$881$	19.4999	+	13.0294i	0.656967	+	0.438971i	−0.181893	+	0.983318i	$0.558223\pi$
$882$	2.14979	−	14.7745i	0.0723871	−	0.497484i
$883$			10.0886i			0.339509i	0.985486	+	0.169755i	$0.0542975\pi$
$883$			10.0886i			0.339509i	−0.985486	+	0.169755i	$0.945703\pi$
$884$	−29.8540	+	11.3929i	−1.00410	+	0.383183i
$885$	0.962384	+	0.555632i	0.0323502	+	0.0186774i
$886$	8.61019	+	11.2210i	0.289265	+	0.376978i
$887$	52.0348	+	3.41054i	1.74716	+	0.114515i	0.905188	−	0.425012i	$-0.139730\pi$
$887$	52.0348	+	3.41054i	1.74716	+	0.114515i	0.841968	+	0.539527i	$0.181397\pi$
$888$	4.93193	−	4.93193i	0.165505	−	0.165505i
$889$	−15.1399	−	22.9953i	−0.507777	−	0.771238i
$890$	0.749703	−	0.500936i	0.0251301	−	0.0167914i
$891$	−0.0562189	−	0.165616i	−0.00188341	−	0.00554833i
$892$	59.8701	+	7.88205i	2.00460	+	0.263910i
$893$	99.4239	+	13.0894i	3.32709	+	0.438020i
$894$	2.04672	+	6.02945i	0.0684526	+	0.201655i
$895$	−7.15627	+	4.78167i	−0.239208	+	0.159833i
$896$	−21.3237	−	10.6965i	−0.712375	−	0.357344i
$897$	1.56038	−	1.56038i	0.0520997	−	0.0520997i
$898$	−21.9400	−	1.43802i	−0.732147	−	0.0479874i
$899$	2.26350	+	2.94986i	0.0754921	+	0.0983832i
$900$	−8.84043	−	5.10403i	−0.294681	−	0.170134i
$901$	−20.3907	−	0.573900i	−0.679311	−	0.0191194i
$902$			0.0517230i			0.00172219i
$903$	−19.5976	−	11.4929i	−0.652166	−	0.382461i
$904$	17.8714	+	11.9413i	0.594394	+	0.397161i
$905$	−2.27433	+	8.48791i	−0.0756012	+	0.282148i
$906$	−7.59015	−	2.57651i	−0.252166	−	0.0855988i
$907$	2.71837	+	41.4743i	0.0902621	+	1.37713i	0.767349	+	0.641230i	$0.221575\pi$
$907$	2.71837	+	41.4743i	0.0902621	+	1.37713i	−0.677087	+	0.735903i	$0.736758\pi$
$908$	−21.1548	+	7.18108i	−0.702046	+	0.238312i
$909$	−6.50084	−	15.6944i	−0.215619	−	0.520551i
$910$	−4.31785	−	16.5639i	−0.143135	−	0.549089i
$911$	0.444051	−	2.23239i	0.0147121	−	0.0739625i	−0.972732	−	0.231933i	$-0.925495\pi$
$911$	0.444051	−	2.23239i	0.0147121	−	0.0739625i	0.987444	+	0.157970i	$0.0504950\pi$
$912$	−9.48593	+	19.2356i	−0.314110	+	0.636953i
$913$	0.593050	−	1.74707i	0.0196271	−	0.0578196i
$914$	18.4183	+	68.7379i	0.609222	+	2.27365i
$915$	0.630426	−	9.61844i	0.0208412	−	0.317976i
$916$	−9.40737	+	22.7114i	−0.310828	+	0.750406i
$917$	−27.2000	+	34.9533i	−0.898224	+	1.15426i
$918$	−5.98204	+	6.44597i	−0.197437	+	0.212749i
$919$	14.8478	+	25.7172i	0.489785	+	0.848332i	0.999931	−	0.0117556i	$-0.00374200\pi$
$919$	14.8478	+	25.7172i	0.489785	+	0.848332i	−0.510146	+	0.860088i	$0.670409\pi$
$920$	0.672934	−	0.516360i	0.0221860	−	0.0170239i
$921$	17.6397	−	8.69891i	0.581246	−	0.286639i
$922$	−11.9282	−	3.19614i	−0.392833	−	0.105259i
$923$	−7.90956	−	39.7640i	−0.260346	−	1.30885i
$924$	−0.661988	+	0.976306i	−0.0217778	+	0.0321181i
$925$	23.3888	+	4.65232i	0.769019	+	0.152967i
$926$	49.4420	+	37.9382i	1.62476	+	1.24673i
$927$	−0.993823	+	7.54884i	−0.0326414	+	0.247936i
$928$	7.93892	+	6.96224i	0.260608	+	0.228547i
$929$	−17.8141	−	8.78493i	−0.584461	−	0.288224i	0.125921	−	0.992040i	$-0.459811\pi$
$929$	−17.8141	−	8.78493i	−0.584461	−	0.288224i	−0.710382	+	0.703816i	$0.751478\pi$
$930$	−5.79748	+	1.15319i	−0.190107	+	0.0378146i
$931$	28.1873	+	50.3914i	0.923801	+	1.65151i
$932$	24.3107	−	36.3835i	0.796324	−	1.19178i
$933$	−0.526684	−	4.00056i	−0.0172429	−	0.130973i
$934$	−4.53819	+	7.86037i	−0.148494	+	0.257199i
$935$	−0.0738064	−	0.715697i	−0.00241373	−	0.0234058i
$936$	3.08379	−	1.78043i	0.100797	−	0.0581951i
$937$	−35.6120	−	14.7510i	−1.16339	−	0.481893i	−0.284389	−	0.958709i	$-0.591791\pi$
$937$	−35.6120	−	14.7510i	−1.16339	−	0.481893i	−0.879003	+	0.476816i	$0.841791\pi$
$938$	1.68305	−	8.17064i	0.0549535	−	0.266781i
$939$	−19.3342	−	19.3342i	−0.630949	−	0.630949i
$940$	20.3880	+	23.2481i	0.664983	+	0.758268i
$941$	16.2568	−	1.06553i	0.529957	−	0.0347352i	0.201923	−	0.979401i	$-0.435281\pi$
$941$	16.2568	−	1.06553i	0.529957	−	0.0347352i	0.328033	+	0.944666i	$0.393614\pi$
$942$	5.88795	−	6.71392i	0.191840	−	0.218751i
$943$	−0.0612664	+	0.0798439i	−0.00199511	+	0.00260008i
$944$	−2.67556	+	1.10825i	−0.0870822	+	0.0360706i
$945$	−1.72700	−	1.99647i	−0.0561793	−	0.0649453i
$946$	1.77962	+	2.66339i	0.0578604	+	0.0865942i
$947$	42.3568	−	37.1459i	1.37641	−	1.20708i	0.422732	−	0.906255i	$-0.361071\pi$
$947$	42.3568	−	37.1459i	1.37641	−	1.20708i	0.953679	−	0.300826i	$-0.0972623\pi$
$948$	9.56582	−	2.56315i	0.310683	−	0.0832473i
$949$	6.18493	+	12.5418i	0.200771	+	0.407124i
$950$	69.8482	−	9.19570i	2.26618	−	0.298348i
$951$	−16.3529			−0.530278
$952$	12.7125	+	1.28043i	0.412013	+	0.0414990i
$953$	22.2772			0.721629			0.360815	−	0.932638i	$-0.382499\pi$
$953$	22.2772			0.721629			0.360815	+	0.932638i	$0.382499\pi$
$954$	10.4619	−	1.37734i	0.338718	−	0.0445930i
$955$	−9.75532	−	19.7818i	−0.315675	−	0.640125i
$956$	49.8806	−	13.3655i	1.61326	−	0.432270i
$957$	0.176020	−	0.154365i	0.00568990	−	0.00498991i
$958$	43.5552	+	65.1850i	1.40721	+	2.10603i
$959$	−30.4063	−	10.5526i	−0.981872	−	0.340760i
$960$	−10.7153	+	4.43843i	−0.345835	+	0.143250i
$961$	−14.1747	+	18.4728i	−0.457249	+	0.595898i
$962$	−25.4606	+	29.0323i	−0.820884	+	0.936039i
$963$	−10.8815	+	0.713211i	−0.350651	+	0.0229829i
$964$	−7.12373	−	8.12306i	−0.229440	−	0.261626i
$965$	−5.31487	−	5.31487i	−0.171092	−	0.171092i
$966$	−3.88742	+	1.29020i	−0.125076	+	0.0415117i
$967$	−13.0277	−	5.39626i	−0.418943	−	0.173532i	0.163246	−	0.986585i	$-0.447804\pi$
$967$	−13.0277	−	5.39626i	−0.418943	−	0.173532i	−0.582189	+	0.813053i	$0.697804\pi$
$968$	−11.1266	+	6.42393i	−0.357622	+	0.206473i
$969$	3.17821	−	33.8605i	0.102099	−	1.08775i
$970$	10.3852	−	17.9878i	0.333450	−	0.577552i
$971$	2.77562	+	21.0830i	0.0890740	+	0.676584i	0.976482	+	0.215599i	$0.0691705\pi$
$971$	2.77562	+	21.0830i	0.0890740	+	0.676584i	−0.887408	+	0.460985i	$0.847496\pi$
$972$	1.41623	−	2.11953i	0.0454255	−	0.0679840i
$973$	48.6072	+	20.5219i	1.55827	+	0.657901i
$974$	−19.7352	+	3.92557i	−0.632356	+	0.125783i
$975$	10.9191	+	5.38471i	0.349691	+	0.172449i
$976$	18.8861	+	16.5627i	0.604530	+	0.530159i
$977$	6.02681	−	45.7782i	0.192815	−	1.46457i	−0.571963	−	0.820279i	$-0.693818\pi$
$977$	6.02681	−	45.7782i	0.192815	−	1.46457i	0.764778	−	0.644294i	$-0.222849\pi$
$978$	22.4540	+	17.2295i	0.717998	+	0.550940i
$979$	0.0726803	+	0.0144570i	0.00232287	+	0.000462048i
$980$	−3.71035	+	17.4128i	−0.118523	+	0.556231i
$981$	0.345440	+	1.73664i	0.0110290	+	0.0554468i
$982$	44.8304	+	12.0123i	1.43060	+	0.383327i
$983$	22.4641	−	11.0781i	0.716495	−	0.353336i	−0.0472247	−	0.998884i	$-0.515038\pi$
$983$	22.4641	−	11.0781i	0.716495	−	0.353336i	0.763720	+	0.645548i	$0.223371\pi$
$984$	−0.128840	+	0.0988623i	−0.00410726	+	0.00315161i
$985$	−1.99659	−	3.45819i	−0.0636166	−	0.110187i
$986$	−11.0362	−	4.09602i	−0.351463	−	0.130444i
$987$	−12.1072	−	29.8006i	−0.385375	−	0.948562i
$988$	−24.4632	+	59.0594i	−0.778278	+	1.87893i
$989$	−0.407641	+	6.21940i	−0.0129622	+	0.197765i
$990$	0.0963303	+	0.359510i	0.00306158	+	0.0114260i
$991$	−2.96557	+	8.73628i	−0.0942043	+	0.277517i	−0.983811	−	0.179211i	$-0.942645\pi$
$991$	−2.96557	+	8.73628i	−0.0942043	+	0.277517i	0.889606	+	0.456728i	$0.150979\pi$
$992$	9.69107	−	19.6515i	0.307692	−	0.623937i
$993$	−2.82657	+	14.2101i	−0.0896985	+	0.450945i
$994$	−19.9704	+	72.5547i	−0.633424	+	2.30129i
$995$	6.47235	+	15.6256i	0.205187	+	0.495366i
$996$	25.4636	−	8.64374i	0.806846	−	0.273887i
$997$	−3.98242	−	60.7600i	−0.126125	−	1.92429i	−0.327638	−	0.944803i	$-0.606253\pi$
$997$	−3.98242	−	60.7600i	−0.126125	−	1.92429i	0.201513	−	0.979486i	$-0.435414\pi$
$998$	−43.1302	−	14.6407i	−1.36526	−	0.463444i
$999$	−1.54128	+	5.75213i	−0.0487639	+	0.181989i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.20	✓	384
7.5	odd	6	inner	357.2.bl.a.61.5	yes	384
17.12	odd	16	inner	357.2.bl.a.199.5	yes	384
119.12	even	48	inner	357.2.bl.a.250.20	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.20	✓	384	1.1	even	1	trivial
357.2.bl.a.61.5	yes	384	7.5	odd	6	inner
357.2.bl.a.199.5	yes	384	17.12	odd	16	inner
357.2.bl.a.250.20	yes	384	119.12	even	48	inner

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	357.2.bl.a.10.20

Level	$357$
Weight	$2$
Character	357.10
Analytic conductor	$2.851$
Analytic rank	$0$
Dimension	$384$
Inner twists	$4$