LMFDB - Embedded newform 87.2.g.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			7.2
Root			$0.824998 - 0.397298i$ of defining polynomial
Character	$\chi$	$=$	87.7
Dual form			87.2.g.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.203758 + 0.892721i) q^{2} +(0.900969 + 0.433884i) q^{3} +(1.04650 - 0.503970i) q^{4} +(-0.0634200 - 0.277861i) q^{5} +(-0.203758 + 0.892721i) q^{6} +(-4.54015 - 2.18642i) q^{7} +(1.80497 + 2.26336i) q^{8} +(0.623490 + 0.781831i) q^{9} +(0.235130 - 0.113233i) q^{10} +(-2.60766 + 3.26990i) q^{11} +1.16153 q^{12} +(1.41861 - 1.77888i) q^{13} +(1.02677 - 4.49858i) q^{14} +(0.0634200 - 0.277861i) q^{15} +(-0.204365 + 0.256265i) q^{16} -3.40834 q^{17} +(-0.570916 + 0.715906i) q^{18} +(-0.768127 + 0.369911i) q^{19} +(-0.206403 - 0.258821i) q^{20} +(-3.14188 - 3.93979i) q^{21} +(-3.45044 - 1.66164i) q^{22} +(1.61144 - 7.06017i) q^{23} +(0.644186 + 2.82237i) q^{24} +(4.43166 - 2.13417i) q^{25} +(1.87710 + 0.903962i) q^{26} +(0.222521 + 0.974928i) q^{27} -5.85318 q^{28} +(2.41553 + 4.81302i) q^{29} +0.260975 q^{30} +(0.728037 + 3.18974i) q^{31} +(4.94610 + 2.38192i) q^{32} +(-3.76817 + 1.81466i) q^{33} +(-0.694475 - 3.04269i) q^{34} +(-0.319585 + 1.40019i) q^{35} +(1.04650 + 0.503970i) q^{36} +(0.237365 + 0.297647i) q^{37} +(-0.486739 - 0.610351i) q^{38} +(2.04995 - 0.987204i) q^{39} +(0.514429 - 0.645074i) q^{40} -5.56008 q^{41} +(2.87695 - 3.60758i) q^{42} +(-1.75856 + 7.70474i) q^{43} +(-1.08099 + 4.73615i) q^{44} +(0.177699 - 0.222827i) q^{45} +6.63110 q^{46} +(4.07504 - 5.10993i) q^{47} +(-0.295316 + 0.142216i) q^{48} +(11.4681 + 14.3805i) q^{49} +(2.80821 + 3.52138i) q^{50} +(-3.07081 - 1.47882i) q^{51} +(0.588079 - 2.57654i) q^{52} +(-0.643658 - 2.82005i) q^{53} +(-0.824998 + 0.397298i) q^{54} +(1.07396 + 0.517190i) q^{55} +(-3.24617 - 14.2224i) q^{56} -0.852557 q^{57} +(-3.80450 + 3.13709i) q^{58} -4.68212 q^{59} +(-0.0736644 - 0.322745i) q^{60} +(6.25207 + 3.01084i) q^{61} +(-2.69920 + 1.29987i) q^{62} +(-1.12132 - 4.91284i) q^{63} +(-1.26445 + 5.53994i) q^{64} +(-0.584250 - 0.281360i) q^{65} +(-2.38778 - 2.99418i) q^{66} +(-1.77109 - 2.22087i) q^{67} +(-3.56684 + 1.71770i) q^{68} +(4.51515 - 5.66182i) q^{69} -1.31510 q^{70} +(-7.16657 + 8.98660i) q^{71} +(-0.644186 + 2.82237i) q^{72} +(2.51970 - 11.0395i) q^{73} +(-0.217350 + 0.272549i) q^{74} +4.91877 q^{75} +(-0.617425 + 0.774227i) q^{76} +(18.9885 - 9.14439i) q^{77} +(1.29899 + 1.62888i) q^{78} +(-4.22068 - 5.29256i) q^{79} +(0.0841670 + 0.0405327i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-1.13291 - 4.96360i) q^{82} +(-5.65795 + 2.72473i) q^{83} +(-5.27353 - 2.53960i) q^{84} +(0.216157 + 0.947045i) q^{85} -7.23650 q^{86} +(0.0880280 + 5.38445i) q^{87} -12.1077 q^{88} +(-1.26972 - 5.56302i) q^{89} +(0.235130 + 0.113233i) q^{90} +(-10.3301 + 4.97470i) q^{91} +(-1.87174 - 8.20062i) q^{92} +(-0.728037 + 3.18974i) q^{93} +(5.39206 + 2.59668i) q^{94} +(0.151498 + 0.189973i) q^{95} +(3.42281 + 4.29207i) q^{96} +(-0.453007 + 0.218157i) q^{97} +(-10.5011 + 13.1679i) q^{98} -4.18236 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

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 $

$2$	0.203758	+	0.892721i	0.144078	+	0.631249i	0.994463	+	0.105087i	$0.0335122\pi$
$2$	0.203758	+	0.892721i	0.144078	+	0.631249i	−0.850385	+	0.526162i	$0.823631\pi$
$3$	0.900969	+	0.433884i	0.520175	+	0.250503i
$3$	0.900969	+	0.433884i	0.520175	+	0.250503i
$4$	1.04650	−	0.503970i	0.523252	−	0.251985i
$5$	−0.0634200	−	0.277861i	−0.0283623	−	0.124263i	0.958765	−	0.284200i	$-0.0917281\pi$
$5$	−0.0634200	−	0.277861i	−0.0283623	−	0.124263i	−0.987127	+	0.159937i	$0.948871\pi$
$6$	−0.203758	+	0.892721i	−0.0831837	+	0.364452i
$7$	−4.54015	−	2.18642i	−1.71601	−	0.826389i	−0.990391	−	0.138298i	$-0.955837\pi$
$7$	−4.54015	−	2.18642i	−1.71601	−	0.826389i	−0.725624	−	0.688092i	$-0.758449\pi$
$8$	1.80497	+	2.26336i	0.638153	+	0.800219i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	0.235130	−	0.113233i	0.0743547	−	0.0358073i
$11$	−2.60766	+	3.26990i	−0.786238	+	0.985912i	0.213721	+	0.976895i	$0.431442\pi$
$11$	−2.60766	+	3.26990i	−0.786238	+	0.985912i	−0.999959	+	0.00901707i	$0.997130\pi$
$12$	1.16153			0.335306
$13$	1.41861	−	1.77888i	0.393452	−	0.493373i	−0.545168	−	0.838327i	$-0.683534\pi$
$13$	1.41861	−	1.77888i	0.393452	−	0.493373i	0.938620	+	0.344954i	$0.112106\pi$
$14$	1.02677	−	4.49858i	0.274416	−	1.20230i
$15$	0.0634200	−	0.277861i	0.0163750	−	0.0717435i
$16$	−0.204365	+	0.256265i	−0.0510912	+	0.0640663i
$17$	−3.40834			−0.826644			−0.413322	−	0.910585i	$-0.635632\pi$
$17$	−3.40834			−0.826644			−0.413322	+	0.910585i	$0.635632\pi$
$18$	−0.570916	+	0.715906i	−0.134566	+	0.168741i
$19$	−0.768127	+	0.369911i	−0.176221	+	0.0848633i	−0.519914	−	0.854218i	$-0.674036\pi$
$19$	−0.768127	+	0.369911i	−0.176221	+	0.0848633i	0.343694	+	0.939082i	$0.388322\pi$
$20$	−0.206403	−	0.258821i	−0.0461531	−	0.0578742i
$21$	−3.14188	−	3.93979i	−0.685614	−	0.859733i
$22$	−3.45044	−	1.66164i	−0.735636	−	0.354263i
$23$	1.61144	−	7.06017i	0.336008	−	1.47215i	−0.471277	−	0.881985i	$-0.656207\pi$
$23$	1.61144	−	7.06017i	0.336008	−	1.47215i	0.807285	−	0.590162i	$-0.200936\pi$
$24$	0.644186	+	2.82237i	0.131494	+	0.576113i
$25$	4.43166	−	2.13417i	0.886332	−	0.426835i
$26$	1.87710	+	0.903962i	0.368129	+	0.177281i
$27$	0.222521	+	0.974928i	0.0428242	+	0.187625i
$28$	−5.85318			−1.10615
$29$	2.41553	+	4.81302i	0.448553	+	0.893756i
$29$	2.41553	+	4.81302i	0.448553	+	0.893756i
$30$	0.260975			0.0476473
$31$	0.728037	+	3.18974i	0.130759	+	0.572894i	0.997277	+	0.0737475i	$0.0234959\pi$
$31$	0.728037	+	3.18974i	0.130759	+	0.572894i	−0.866518	+	0.499146i	$0.833647\pi$
$32$	4.94610	+	2.38192i	0.874355	+	0.421067i
$33$	−3.76817	+	1.81466i	−0.655955	+	0.315891i
$34$	−0.694475	−	3.04269i	−0.119101	−	0.521818i
$35$	−0.319585	+	1.40019i	−0.0540197	+	0.236676i
$36$	1.04650	+	0.503970i	0.174417	+	0.0839950i
$37$	0.237365	+	0.297647i	0.0390226	+	0.0489328i	0.800960	−	0.598718i	$-0.204323\pi$
$37$	0.237365	+	0.297647i	0.0390226	+	0.0489328i	−0.761937	+	0.647651i	$0.775752\pi$
$38$	−0.486739	−	0.610351i	−0.0789594	−	0.0990120i
$39$	2.04995	−	0.987204i	0.328255	−	0.158079i
$40$	0.514429	−	0.645074i	0.0813384	−	0.101995i
$41$	−5.56008			−0.868339			−0.434169	−	0.900831i	$-0.642958\pi$
$41$	−5.56008			−0.868339			−0.434169	+	0.900831i	$0.642958\pi$
$42$	2.87695	−	3.60758i	0.443923	−	0.556662i
$43$	−1.75856	+	7.70474i	−0.268177	+	1.17496i	0.643954	+	0.765064i	$0.277293\pi$
$43$	−1.75856	+	7.70474i	−0.268177	+	1.17496i	−0.912131	+	0.409898i	$0.865564\pi$
$44$	−1.08099	+	4.73615i	−0.162966	+	0.714001i
$45$	0.177699	−	0.222827i	0.0264898	−	0.0332172i
$46$	6.63110			0.977702
$47$	4.07504	−	5.10993i	0.594405	−	0.745360i	−0.390089	−	0.920777i	$-0.627556\pi$
$47$	4.07504	−	5.10993i	0.594405	−	0.745360i	0.984494	+	0.175417i	$0.0561273\pi$
$48$	−0.295316	+	0.142216i	−0.0426251	+	0.0205272i
$49$	11.4681	+	14.3805i	1.63830	+	2.05436i
$50$	2.80821	+	3.52138i	0.397140	+	0.497998i
$51$	−3.07081	−	1.47882i	−0.429999	−	0.207077i
$52$	0.588079	−	2.57654i	0.0815520	−	0.357302i
$53$	−0.643658	−	2.82005i	−0.0884132	−	0.387363i	0.911289	−	0.411767i	$-0.135088\pi$
$53$	−0.643658	−	2.82005i	−0.0884132	−	0.387363i	−0.999702	+	0.0244039i	$0.992231\pi$
$54$	−0.824998	+	0.397298i	−0.112268	+	0.0540654i
$55$	1.07396	+	0.517190i	0.144812	+	0.0697379i
$56$	−3.24617	−	14.2224i	−0.433788	−	1.90055i
$57$	−0.852557			−0.112924
$58$	−3.80450	+	3.13709i	−0.499556	+	0.411920i
$59$	−4.68212			−0.609560			−0.304780	−	0.952423i	$-0.598583\pi$
$59$	−4.68212			−0.609560			−0.304780	+	0.952423i	$0.598583\pi$
$60$	−0.0736644	−	0.322745i	−0.00951004	−	0.0416662i
$61$	6.25207	+	3.01084i	0.800495	+	0.385498i	0.788967	−	0.614435i	$-0.210616\pi$
$61$	6.25207	+	3.01084i	0.800495	+	0.385498i	0.0115280	+	0.999934i	$0.496330\pi$
$62$	−2.69920	+	1.29987i	−0.342799	+	0.165083i
$63$	−1.12132	−	4.91284i	−0.141274	−	0.618960i
$64$	−1.26445	+	5.53994i	−0.158057	+	0.692492i
$65$	−0.584250	−	0.281360i	−0.0724673	−	0.0348984i
$66$	−2.38778	−	2.99418i	−0.293915	−	0.368558i
$67$	−1.77109	−	2.22087i	−0.216373	−	0.271323i	0.661785	−	0.749693i	$-0.269799\pi$
$67$	−1.77109	−	2.22087i	−0.216373	−	0.271323i	−0.878158	+	0.478370i	$0.841228\pi$
$68$	−3.56684	+	1.71770i	−0.432543	+	0.208302i
$69$	4.51515	−	5.66182i	0.543560	−	0.681602i
$70$	−1.31510			−0.157184
$71$	−7.16657	+	8.98660i	−0.850516	+	1.06651i	0.146492	+	0.989212i	$0.453202\pi$
$71$	−7.16657	+	8.98660i	−0.850516	+	1.06651i	−0.997008	+	0.0773013i	$0.975370\pi$
$72$	−0.644186	+	2.82237i	−0.0759181	+	0.332619i
$73$	2.51970	−	11.0395i	0.294908	−	1.29208i	−0.582695	−	0.812691i	$-0.698002\pi$
$73$	2.51970	−	11.0395i	0.294908	−	1.29208i	0.877603	−	0.479387i	$-0.159141\pi$
$74$	−0.217350	+	0.272549i	−0.0252665	+	0.0316832i
$75$	4.91877			0.567971
$76$	−0.617425	+	0.774227i	−0.0708235	+	0.0888099i
$77$	18.9885	−	9.14439i	2.16394	−	1.04210i
$78$	1.29899	+	1.62888i	0.147082	+	0.184435i
$79$	−4.22068	−	5.29256i	−0.474863	−	0.595460i	0.485491	−	0.874241i	$-0.338641\pi$
$79$	−4.22068	−	5.29256i	−0.474863	−	0.595460i	−0.960354	+	0.278782i	$0.910069\pi$
$80$	0.0841670	+	0.0405327i	0.00941016	+	0.00453169i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	−1.13291	−	4.96360i	−0.125109	−	0.548138i
$83$	−5.65795	+	2.72473i	−0.621041	+	0.299078i	−0.717821	−	0.696228i	$-0.754860\pi$
$83$	−5.65795	+	2.72473i	−0.621041	+	0.299078i	0.0967793	+	0.995306i	$0.469146\pi$
$84$	−5.27353	−	2.53960i	−0.575389	−	0.277093i
$85$	0.216157	+	0.947045i	0.0234455	+	0.102721i
$86$	−7.23650			−0.780332
$87$	0.0880280	+	5.38445i	0.00943759	+	0.577273i
$88$	−12.1077			−1.29069
$89$	−1.26972	−	5.56302i	−0.134590	−	0.589679i	−0.996571	−	0.0827384i	$-0.973633\pi$
$89$	−1.26972	−	5.56302i	−0.134590	−	0.589679i	0.861981	−	0.506941i	$-0.169224\pi$
$90$	0.235130	+	0.113233i	0.0247849	+	0.0119358i
$91$	−10.3301	+	4.97470i	−1.08289	+	0.521491i
$92$	−1.87174	−	8.20062i	−0.195142	−	0.854974i
$93$	−0.728037	+	3.18974i	−0.0754939	+	0.330760i
$94$	5.39206	+	2.59668i	0.556149	+	0.267827i
$95$	0.151498	+	0.189973i	0.0155434	+	0.0194908i
$96$	3.42281	+	4.29207i	0.349339	+	0.438057i
$97$	−0.453007	+	0.218157i	−0.0459959	+	0.0221505i	−0.456740	−	0.889600i	$-0.650983\pi$
$97$	−0.453007	+	0.218157i	−0.0459959	+	0.0221505i	0.410744	+	0.911751i	$0.365269\pi$
$98$	−10.5011	+	13.1679i	−1.06077	+	1.33016i
$99$	−4.18236			−0.420343
$100$	3.56219	−	4.46685i	0.356219	−	0.446685i
$101$	1.00310	−	4.39485i	0.0998117	−	0.437304i	−0.900187	−	0.435504i	$-0.856570\pi$
$101$	1.00310	−	4.39485i	0.0998117	−	0.437304i	0.999998	−	0.00179942i	$-0.000572775\pi$
$102$	0.694475	−	3.04269i	0.0687633	−	0.301272i
$103$	5.06515	−	6.35150i	0.499085	−	0.625832i	−0.466938	−	0.884290i	$-0.654643\pi$
$103$	5.06515	−	6.35150i	0.499085	−	0.625832i	0.966023	+	0.258458i	$0.0832143\pi$
$104$	6.58680			0.645889
$105$	−0.895458	+	1.12287i	−0.0873877	+	0.109581i
$106$	2.38636	−	1.14921i	0.231784	−	0.111621i
$107$	5.93513	+	7.44241i	0.573770	+	0.719485i	0.981036	−	0.193824i	$-0.0620892\pi$
$107$	5.93513	+	7.44241i	0.573770	+	0.719485i	−0.407266	+	0.913310i	$0.633518\pi$
$108$	0.724204	+	0.908123i	0.0696866	+	0.0873842i
$109$	6.69547	+	3.22437i	0.641309	+	0.308838i	0.726129	−	0.687558i	$-0.241317\pi$
$109$	6.69547	+	3.22437i	0.641309	+	0.308838i	−0.0848202	+	0.996396i	$0.527032\pi$
$110$	−0.242879	+	1.06412i	−0.0231576	+	0.101460i
$111$	0.0847148	+	0.371160i	0.00804077	+	0.0352289i
$112$	1.48815	−	0.716655i	0.140617	−	0.0677175i
$113$	−3.81835	−	1.83882i	−0.359200	−	0.172981i	0.245576	−	0.969377i	$-0.421023\pi$
$113$	−3.81835	−	1.83882i	−0.359200	−	0.172981i	−0.604776	+	0.796396i	$0.706737\pi$
$114$	−0.173715	−	0.761095i	−0.0162699	−	0.0712831i
$115$	−2.06394			−0.192464
$116$	4.95349	+	3.81950i	0.459920	+	0.354631i
$117$	2.27527			0.210349
$118$	−0.954018	−	4.17983i	−0.0878245	−	0.384784i
$119$	15.4744	+	7.45206i	1.41853	+	0.683129i
$120$	0.743372	−	0.357989i	0.0678602	−	0.0326798i
$121$	−1.44463	−	6.32935i	−0.131330	−	0.575396i
$122$	−1.41393	+	6.19483i	−0.128011	+	0.560854i
$123$	−5.00946	−	2.41243i	−0.451688	−	0.217521i
$124$	2.36943	+	2.97117i	0.212781	+	0.266819i
$125$	−1.76256	−	2.21017i	−0.157648	−	0.197684i
$126$	4.15732	−	2.00206i	0.370363	−	0.178357i
$127$	−10.5989	+	13.2906i	−0.940501	+	1.17935i	0.0431137	+	0.999070i	$0.486272\pi$
$127$	−10.5989	+	13.2906i	−0.940501	+	1.17935i	−0.983615	+	0.180281i	$0.942299\pi$
$128$	5.77626			0.510554
$129$	−4.92737	+	6.17872i	−0.433831	+	0.544006i
$130$	0.132130	−	0.578901i	0.0115886	−	0.0507730i
$131$	2.82494	−	12.3769i	0.246816	−	1.08137i	−0.687852	−	0.725851i	$-0.741446\pi$
$131$	2.82494	−	12.3769i	0.246816	−	1.08137i	0.934668	−	0.355521i	$-0.115697\pi$
$132$	−3.02888	+	3.79810i	−0.263630	+	0.330582i
$133$	4.29619			0.372527
$134$	1.62175	−	2.03361i	0.140098	−	0.175677i
$135$	0.256782	−	0.123660i	0.0221003	−	0.0106429i
$136$	−6.15195	−	7.71430i	−0.527525	−	0.661496i
$137$	6.07484	+	7.61760i	0.519008	+	0.650816i	0.970398	−	0.241511i	$-0.0776430\pi$
$137$	6.07484	+	7.61760i	0.519008	+	0.650816i	−0.451390	+	0.892327i	$0.649072\pi$
$138$	5.97441	+	2.87713i	0.508576	+	0.244917i
$139$	2.77783	−	12.1705i	0.235612	−	1.03228i	−0.709286	−	0.704921i	$-0.750983\pi$
$139$	2.77783	−	12.1705i	0.235612	−	1.03228i	0.944898	−	0.327364i	$-0.106160\pi$
$140$	0.371209	+	1.62637i	0.0313729	+	0.137453i
$141$	5.88860	−	2.83580i	0.495909	−	0.238817i
$142$	−9.48277	−	4.56666i	−0.795776	−	0.383226i
$143$	2.11751	+	9.27742i	0.177075	+	0.775817i
$144$	−0.327776			−0.0273146
$145$	1.18416	−	0.976425i	0.0983391	−	0.0810877i
$146$	10.3686			0.858113
$147$	4.09291	+	17.9322i	0.337578	+	1.47902i
$148$	0.398409	+	0.191864i	0.0327490	+	0.0157711i
$149$	20.3625	−	9.80607i	1.66816	−	0.803345i	0.670025	−	0.742338i	$-0.266283\pi$
$149$	20.3625	−	9.80607i	1.66816	−	0.803345i	0.998137	−	0.0610063i	$-0.0194310\pi$
$150$	1.00224	+	4.39109i	0.0818323	+	0.358531i
$151$	1.47657	−	6.46927i	0.120161	−	0.526462i	−0.878639	−	0.477487i	$-0.841548\pi$
$151$	1.47657	−	6.46927i	0.120161	−	0.526462i	0.998800	−	0.0489743i	$-0.0155952\pi$
$152$	−2.22369	−	1.07087i	−0.180365	−	0.0868592i
$153$	−2.12506	−	2.66475i	−0.171801	−	0.215432i
$154$	12.0324	+	15.0882i	0.969602	+	1.21584i
$155$	0.840133	−	0.404587i	0.0674811	−	0.0324972i
$156$	1.64776	−	2.06623i	0.131927	−	0.165431i
$157$	−13.3793			−1.06778			−0.533890	−	0.845554i	$-0.679270\pi$
$157$	−13.3793			−1.06778			−0.533890	+	0.845554i	$0.679270\pi$
$158$	3.86478	−	4.84628i	0.307466	−	0.385550i
$159$	0.643658	−	2.82005i	0.0510454	−	0.223644i
$160$	0.348161	−	1.52539i	0.0275245	−	0.120593i
$161$	−22.7527	+	28.5309i	−1.79316	+	2.24855i
$162$	−0.915678			−0.0719425
$163$	6.33230	−	7.94046i	0.495984	−	0.621944i	−0.469334	−	0.883021i	$-0.655506\pi$
$163$	6.33230	−	7.94046i	0.495984	−	0.621944i	0.965318	+	0.261076i	$0.0840774\pi$
$164$	−5.81865	+	2.80212i	−0.454360	+	0.218808i
$165$	0.743201	+	0.931944i	0.0578581	+	0.0725518i
$166$	−3.58527	−	4.49579i	−0.278271	−	0.348941i
$167$	−22.1004	−	10.6430i	−1.71018	−	0.823579i	−0.991781	−	0.127947i	$-0.959161\pi$
$167$	−22.1004	−	10.6430i	−1.71018	−	0.823579i	−0.718398	−	0.695632i	$-0.755124\pi$
$168$	3.24617	−	14.2224i	0.250448	−	1.09728i
$169$	1.74081	+	7.62699i	0.133908	+	0.586691i
$170$	−0.801403	+	0.385935i	−0.0614648	+	0.0295999i
$171$	−0.768127	−	0.369911i	−0.0587402	−	0.0282878i
$172$	2.04262	+	8.94931i	0.155748	+	0.682379i
$173$	−22.0884			−1.67935			−0.839674	−	0.543091i	$-0.817254\pi$
$173$	−22.0884			−1.67935			−0.839674	+	0.543091i	$0.817254\pi$
$174$	−4.78887	+	1.17571i	−0.363043	+	0.0891301i
$175$	−24.7866			−1.87369
$176$	−0.305048	−	1.33650i	−0.0229939	−	0.100743i
$177$	−4.21845	−	2.03150i	−0.317078	−	0.152697i
$178$	4.70751	−	2.26702i	0.352843	−	0.169920i
$179$	−0.163565	−	0.716626i	−0.0122254	−	0.0535631i	0.968447	−	0.249219i	$-0.0801737\pi$
$179$	−0.163565	−	0.716626i	−0.0122254	−	0.0535631i	−0.980673	+	0.195655i	$0.937317\pi$
$180$	0.0736644	−	0.322745i	0.00549062	−	0.0240560i
$181$	−12.3221	−	5.93399i	−0.915892	−	0.441070i	−0.0842890	−	0.996441i	$-0.526862\pi$
$181$	−12.3221	−	5.93399i	−0.915892	−	0.441070i	−0.831603	+	0.555371i	$0.812576\pi$
$182$	−6.54585	−	8.20824i	−0.485211	−	0.608435i
$183$	4.32656	+	5.42534i	0.319829	+	0.401053i
$184$	18.8883	−	9.09613i	1.39246	−	0.670576i
$185$	0.0676508	−	0.0848314i	0.00497379	−	0.00623693i
$186$	−2.99589			−0.219669
$187$	8.88778	−	11.1449i	0.649939	−	0.814998i
$188$	1.68929	−	7.40127i	0.123204	−	0.539793i
$189$	1.12132	−	4.91284i	0.0815643	−	0.357357i
$190$	−0.138724	+	0.173954i	−0.0100641	+	0.0126200i
$191$	1.16101			0.0840075			0.0420038	−	0.999117i	$-0.486626\pi$
$191$	1.16101			0.0840075			0.0420038	+	0.999117i	$0.486626\pi$
$192$	−3.54292	+	4.44268i	−0.255688	+	0.320623i
$193$	−18.5608	+	8.93843i	−1.33604	+	0.643402i	−0.959161	−	0.282861i	$-0.908717\pi$
$193$	−18.5608	+	8.93843i	−1.33604	+	0.643402i	−0.376878	+	0.926263i	$0.623002\pi$
$194$	−0.287057	−	0.359958i	−0.0206095	−	0.0258434i
$195$	−0.404314	−	0.506993i	−0.0289535	−	0.0363065i
$196$	19.2488	+	9.26971i	1.37491	+	0.662122i
$197$	−1.14781	+	5.02887i	−0.0817778	+	0.358292i	−0.999216	−	0.0395860i	$-0.987396\pi$
$197$	−1.14781	+	5.02887i	−0.0817778	+	0.358292i	0.917438	+	0.397878i	$0.130253\pi$
$198$	−0.852187	−	3.73368i	−0.0605623	−	0.265341i
$199$	2.52796	−	1.21740i	0.179203	−	0.0862995i	−0.342131	−	0.939652i	$-0.611149\pi$
$199$	2.52796	−	1.21740i	0.179203	−	0.0862995i	0.521334	+	0.853353i	$0.325435\pi$
$200$	12.8294	+	6.17832i	0.907177	+	0.436874i
$201$	−0.632094	−	2.76938i	−0.0445845	−	0.195337i
$202$	4.12776			0.290428
$203$	−0.443589	−	27.1332i	−0.0311339	−	1.90438i
$204$	−3.95890			−0.277178
$205$	0.352620	+	1.54493i	0.0246281	+	0.107903i
$206$	6.70218	+	3.22760i	0.466963	+	0.224878i
$207$	6.52458	−	3.14207i	0.453489	−	0.218389i
$208$	0.165951	+	0.727081i	0.0115067	+	0.0504140i
$209$	0.793443	−	3.47630i	0.0548836	−	0.240461i
$210$	−1.18486	−	0.570600i	−0.0817634	−	0.0393752i
$211$	−3.02315	−	3.79091i	−0.208122	−	0.260977i	0.666804	−	0.745233i	$-0.267662\pi$
$211$	−3.02315	−	3.79091i	−0.208122	−	0.260977i	−0.874926	+	0.484256i	$0.839090\pi$
$212$	−2.09481	−	2.62681i	−0.143872	−	0.180410i
$213$	−10.3560	+	4.98719i	−0.709581	+	0.341716i
$214$	−5.43467	+	6.81486i	−0.371506	+	0.465854i
$215$	2.25238			0.153611
$216$	−1.80497	+	2.26336i	−0.122813	+	0.154002i
$217$	3.66871	−	16.0737i	0.249048	−	1.09115i
$218$	−1.51421	+	6.63417i	−0.102555	+	0.449323i
$219$	7.06004	−	8.85301i	0.477073	−	0.598231i
$220$	1.38455			0.0933463
$221$	−4.83510	+	6.06303i	−0.325244	+	0.407843i
$222$	−0.314081	+	0.151253i	−0.0210797	+	0.0101515i
$223$	6.48155	+	8.12761i	0.434037	+	0.544265i	0.949961	−	0.312370i	$-0.101123\pi$
$223$	6.48155	+	8.12761i	0.434037	+	0.544265i	−0.515924	+	0.856634i	$0.672551\pi$
$224$	−17.2482	−	21.6285i	−1.15244	−	1.44512i
$225$	4.43166	+	2.13417i	0.295444	+	0.142278i
$226$	0.863534	−	3.78339i	0.0574414	−	0.251667i
$227$	6.22713	+	27.2828i	0.413309	+	1.81083i	0.568195	+	0.822894i	$0.307642\pi$
$227$	6.22713	+	27.2828i	0.413309	+	1.81083i	−0.154886	+	0.987932i	$0.549501\pi$
$228$	−0.892205	+	0.429663i	−0.0590877	+	0.0284552i
$229$	3.14998	+	1.51695i	0.208156	+	0.100243i	0.535057	−	0.844816i	$-0.320290\pi$
$229$	3.14998	+	1.51695i	0.208156	+	0.100243i	−0.326901	+	0.945059i	$0.606004\pi$
$230$	−0.420544	−	1.84253i	−0.0277299	−	0.121493i
$231$	21.0757			1.38668
$232$	−6.53364	+	14.1546i	−0.428955	+	0.929294i
$233$	−3.35269			−0.219642			−0.109821	−	0.993951i	$-0.535028\pi$
$233$	−3.35269			−0.219642			−0.109821	+	0.993951i	$0.535028\pi$
$234$	0.463604	+	2.03118i	0.0303068	+	0.132783i
$235$	−1.67829	−	0.808222i	−0.109480	−	0.0527226i
$236$	−4.89986	+	2.35965i	−0.318954	+	0.153600i
$237$	−1.50634	−	6.59971i	−0.0978474	−	0.428698i
$238$	−3.49959	+	15.3327i	−0.226845	+	0.993871i
$239$	16.5718	+	7.98057i	1.07194	+	0.516220i	0.884732	−	0.466100i	$-0.154341\pi$
$239$	16.5718	+	7.98057i	1.07194	+	0.516220i	0.187210	+	0.982320i	$0.440056\pi$
$240$	0.0582454	+	0.0730374i	0.00375972	+	0.00471454i
$241$	3.50723	+	4.39793i	0.225921	+	0.283295i	0.881853	−	0.471524i	$-0.156296\pi$
$241$	3.50723	+	4.39793i	0.225921	+	0.283295i	−0.655933	+	0.754819i	$0.727724\pi$
$242$	5.35599	−	2.57931i	0.344296	−	0.165804i
$243$	−0.623490	+	0.781831i	−0.0399969	+	0.0501545i
$244$	8.06019			0.516001
$245$	3.26848	−	4.09855i	0.208816	−	0.261847i
$246$	1.13291	−	4.96360i	0.0722316	−	0.316468i
$247$	−0.431646	+	1.89117i	−0.0274650	+	0.120332i
$248$	−5.90545	+	7.40519i	−0.374996	+	0.470230i
$249$	−6.27986			−0.397970
$250$	1.61393	−	2.02381i	0.102074	−	0.127997i
$251$	24.1560	−	11.6329i	1.52472	−	0.734264i	0.531124	−	0.847294i	$-0.321770\pi$
$251$	24.1560	−	11.6329i	1.52472	−	0.734264i	0.993592	+	0.113030i	$0.0360555\pi$
$252$	−3.64940	−	4.57620i	−0.229890	−	0.288273i
$253$	18.8840	+	23.6797i	1.18722	+	1.48873i
$254$	−14.0244	−	6.75380i	−0.879970	−	0.423771i
$255$	−0.216157	+	0.947045i	−0.0135363	+	0.0593063i
$256$	3.70587	+	16.2365i	0.231617	+	1.01478i
$257$	3.33896	−	1.60796i	0.208279	−	0.100302i	−0.326836	−	0.945081i	$-0.605983\pi$
$257$	3.33896	−	1.60796i	0.208279	−	0.100302i	0.535115	+	0.844779i	$0.320268\pi$
$258$	−6.51986	−	3.13980i	−0.405909	−	0.195475i
$259$	−0.426893	−	1.87034i	−0.0265259	−	0.116217i
$260$	−0.753218			−0.0467126
$261$	−2.25691	+	4.88941i	−0.139699	+	0.302647i
$262$	11.6247			0.718176
$263$	−3.92794	−	17.2094i	−0.242207	−	1.06118i	−0.939003	−	0.343910i	$-0.888249\pi$
$263$	−3.92794	−	17.2094i	−0.242207	−	1.06118i	0.696796	−	0.717270i	$-0.254608\pi$
$264$	−10.9087	−	5.25334i	−0.671382	−	0.323321i
$265$	−0.742761	+	0.357695i	−0.0456275	+	0.0219730i
$266$	0.875382	+	3.83530i	0.0536731	+	0.235157i
$267$	1.26972	−	5.56302i	0.0777058	−	0.340451i
$268$	−2.97271	−	1.43158i	−0.181587	−	0.0874477i
$269$	−8.93835	−	11.2083i	−0.544981	−	0.683385i	0.430721	−	0.902485i	$-0.358259\pi$
$269$	−8.93835	−	11.2083i	−0.544981	−	0.683385i	−0.975702	+	0.219100i	$0.929688\pi$
$270$	0.162715	+	0.204038i	0.00990253	+	0.0124174i
$271$	−27.2004	+	13.0990i	−1.65231	+	0.795709i	−0.653044	+	0.757320i	$0.726508\pi$
$271$	−27.2004	+	13.0990i	−1.65231	+	0.795709i	−0.999263	+	0.0383890i	$0.987777\pi$
$272$	0.696544	−	0.873439i	0.0422342	−	0.0529600i
$273$	−11.4655			−0.693925
$274$	−5.56260	+	6.97528i	−0.336049	+	0.421392i
$275$	−4.57771	+	20.0563i	−0.276047	+	1.20944i
$276$	1.87174	−	8.20062i	0.112665	−	0.493619i
$277$	5.26579	−	6.60309i	0.316391	−	0.396741i	−0.598052	−	0.801457i	$-0.704058\pi$
$277$	5.26579	−	6.60309i	0.316391	−	0.396741i	0.914442	+	0.404716i	$0.132630\pi$
$278$	11.4308			0.685575
$279$	−2.03991	+	2.55797i	−0.122126	+	0.153142i
$280$	−3.74599	+	1.80397i	−0.223866	+	0.107808i
$281$	−7.90311	−	9.91018i	−0.471460	−	0.591192i	0.488068	−	0.872806i	$-0.337702\pi$
$281$	−7.90311	−	9.91018i	−0.471460	−	0.591192i	−0.959528	+	0.281614i	$0.909130\pi$
$282$	3.73142	+	4.67906i	0.222203	+	0.278634i
$283$	22.2025	+	10.6921i	1.31980	+	0.635582i	0.955305	−	0.295623i	$-0.0955273\pi$
$283$	22.2025	+	10.6921i	1.31980	+	0.635582i	0.364495	+	0.931205i	$0.381242\pi$
$284$	−2.97088	+	13.0163i	−0.176289	+	0.772373i
$285$	0.0540692	+	0.236893i	0.00320278	+	0.0140323i
$286$	−7.85069	+	3.78069i	−0.464221	+	0.223557i
$287$	25.2436	+	12.1567i	1.49008	+	0.717586i
$288$	1.22159	+	5.35212i	0.0719827	+	0.315377i
$289$	−5.38323			−0.316661
$290$	1.11296	+	0.858169i	0.0653551	+	0.0503934i
$291$	−0.502800			−0.0294746
$292$	−2.92671	−	12.8228i	−0.171273	−	0.750396i
$293$	4.15097	+	1.99900i	0.242502	+	0.116783i	0.551188	−	0.834381i	$-0.314175\pi$
$293$	4.15097	+	1.99900i	0.242502	+	0.116783i	−0.308686	+	0.951164i	$0.599889\pi$
$294$	−15.1745	+	7.30765i	−0.884995	+	0.426191i
$295$	0.296940	+	1.30098i	0.0172885	+	0.0757460i
$296$	−0.245245	+	1.07449i	−0.0142546	+	0.0624533i
$297$	−3.76817	−	1.81466i	−0.218652	−	0.105297i
$298$	12.9031	+	16.1800i	0.747457	+	0.937281i
$299$	−10.2732	−	12.8822i	−0.594114	−	0.744996i
$300$	5.14752	−	2.47891i	0.297192	−	0.143120i
$301$	24.8299	−	31.1357i	1.43117	−	1.79463i
$302$	6.07611			0.349641
$303$	2.81061	−	3.52439i	0.161465	−	0.202471i
$304$	0.0621829	−	0.272441i	0.00356643	−	0.0156256i
$305$	0.440089	−	1.92815i	0.0251994	−	0.110406i
$306$	1.94588	−	2.44005i	0.111238	−	0.139488i
$307$	2.80588			0.160140			0.0800700	−	0.996789i	$-0.474486\pi$
$307$	2.80588			0.160140			0.0800700	+	0.996789i	$0.474486\pi$
$308$	15.2631	−	19.1393i	0.869695	−	1.09056i
$309$	7.31936	−	3.52482i	0.416384	−	0.200520i
$310$	0.532366	+	0.667566i	0.0302364	+	0.0379152i
$311$	9.80146	+	12.2906i	0.555790	+	0.696939i	0.977773	−	0.209665i	$-0.0672373\pi$
$311$	9.80146	+	12.2906i	0.555790	+	0.696939i	−0.421983	+	0.906604i	$0.638666\pi$
$312$	5.93450	+	2.85790i	0.335975	+	0.161797i
$313$	−4.05540	+	17.7679i	−0.229225	+	1.00430i	0.721049	+	0.692884i	$0.243660\pi$
$313$	−4.05540	+	17.7679i	−0.229225	+	1.00430i	−0.950274	+	0.311415i	$0.899197\pi$
$314$	−2.72612	−	11.9439i	−0.153844	−	0.674035i
$315$	−1.29397	+	0.623145i	−0.0729072	+	0.0351102i
$316$	−7.08425	−	3.41160i	−0.398520	−	0.191917i
$317$	−0.418332	−	1.83283i	−0.0234959	−	0.102942i	0.961820	−	0.273682i	$-0.0882415\pi$
$317$	−0.418332	−	1.83283i	−0.0234959	−	0.102942i	−0.985316	+	0.170740i	$0.945384\pi$
$318$	2.64866			0.148530
$319$	−22.0370	−	4.65217i	−1.23383	−	0.260471i
$320$	1.61952			0.0905342
$321$	2.11822	+	9.28054i	0.118228	+	0.517989i
$322$	−30.1062	−	14.4984i	−1.67775	−	0.807963i
$323$	2.61804	−	1.26078i	0.145672	−	0.0701517i
$324$	0.258465	+	1.13241i	0.0143592	+	0.0629117i
$325$	2.49035	−	10.9110i	0.138140	−	0.605231i
$326$	8.37886	+	4.03505i	0.464062	+	0.223481i
$327$	4.63341	+	5.81011i	0.256228	+	0.321300i
$328$	−10.0358	−	12.5845i	−0.554133	−	0.694861i
$329$	−29.6737	+	14.2901i	−1.63597	+	0.787839i
$330$	−0.680533	+	0.853361i	−0.0374621	+	0.0469760i
$331$	6.14086			0.337532			0.168766	−	0.985656i	$-0.446022\pi$
$331$	6.14086			0.337532			0.168766	+	0.985656i	$0.446022\pi$
$332$	−4.54790	+	5.70288i	−0.249598	+	0.312986i
$333$	−0.0847148	+	0.371160i	−0.00464234	+	0.0203394i
$334$	4.99809	−	21.8981i	0.273483	−	1.19821i
$335$	−0.504772	+	0.632965i	−0.0275787	+	0.0345825i
$336$	1.65172			0.0901088
$337$	−4.52153	+	5.66982i	−0.246304	+	0.308855i	−0.889580	−	0.456779i	$-0.849003\pi$
$337$	−4.52153	+	5.66982i	−0.246304	+	0.308855i	0.643277	+	0.765634i	$0.277575\pi$
$338$	−6.45407	+	3.10811i	−0.351055	+	0.169059i
$339$	−2.64238	−	3.31344i	−0.143514	−	0.179961i
$340$	0.703492	+	0.882151i	0.0381522	+	0.0478413i
$341$	−12.3286	−	5.93714i	−0.667631	−	0.321514i
$342$	0.173715	−	0.761095i	0.00939343	−	0.0411553i
$343$	−12.7757	−	55.9738i	−0.689821	−	3.02230i
$344$	−20.6128	+	9.92658i	−1.11137	+	0.535205i
$345$	−1.85955	−	0.895512i	−0.100115	−	0.0482127i
$346$	−4.50068	−	19.7187i	−0.241958	−	1.06009i
$347$	−1.50956			−0.0810374			−0.0405187	−	0.999179i	$-0.512901\pi$
$347$	−1.50956			−0.0810374			−0.0405187	+	0.999179i	$0.512901\pi$
$348$	2.80572	+	5.59049i	0.150402	+	0.299681i
$349$	14.5718			0.780011			0.390006	−	0.920813i	$-0.372473\pi$
$349$	14.5718			0.780011			0.390006	+	0.920813i	$0.372473\pi$
$350$	−5.05046	−	22.1275i	−0.269958	−	1.18276i
$351$	2.04995	+	0.987204i	0.109418	+	0.0526931i
$352$	−20.6864	+	9.96203i	−1.10259	+	0.530978i
$353$	4.85202	+	21.2581i	0.258247	+	1.13145i	0.923124	+	0.384501i	$0.125627\pi$
$353$	4.85202	+	21.2581i	0.258247	+	1.13145i	−0.664877	+	0.746953i	$0.731516\pi$
$354$	0.954018	−	4.17983i	0.0507055	−	0.222155i
$355$	2.95153	+	1.42138i	0.156651	+	0.0754392i
$356$	−4.13237	−	5.18183i	−0.219015	−	0.274636i
$357$	10.7086	+	13.4281i	0.566759	+	0.710693i
$358$	0.606419	−	0.292036i	0.0320502	−	0.0154346i
$359$	5.27111	−	6.60976i	0.278198	−	0.348850i	−0.623027	−	0.782200i	$-0.714097\pi$
$359$	5.27111	−	6.60976i	0.278198	−	0.348850i	0.901225	+	0.433351i	$0.142669\pi$
$360$	0.825080			0.0434855
$361$	−11.3931	+	14.2865i	−0.599638	+	0.751922i
$362$	2.78668	−	12.2093i	0.146465	−	0.641704i
$363$	1.44463	−	6.32935i	0.0758236	−	0.332205i
$364$	−8.30338	+	10.4121i	−0.435215	+	0.545743i
$365$	−3.22725			−0.168922
$366$	−3.96174	+	4.96787i	−0.207084	+	0.259675i
$367$	6.20750	−	2.98937i	0.324029	−	0.156044i	−0.264797	−	0.964304i	$-0.585305\pi$
$367$	6.20750	−	2.98937i	0.324029	−	0.156044i	0.588825	+	0.808260i	$0.299591\pi$
$368$	1.47995	+	1.85580i	0.0771480	+	0.0967405i
$369$	−3.46665	−	4.34705i	−0.180467	−	0.226298i
$370$	0.0895151	+	0.0431082i	0.00465367	+	0.00224109i
$371$	−3.24351	+	14.2107i	−0.168395	+	0.737785i
$372$	0.845639	+	3.70499i	0.0438443	+	0.192095i
$373$	17.3533	−	8.35690i	0.898519	−	0.432704i	0.0731653	−	0.997320i	$-0.476690\pi$
$373$	17.3533	−	8.35690i	0.898519	−	0.432704i	0.825354	+	0.564616i	$0.190976\pi$
$374$	11.7603	+	5.66344i	0.608108	+	0.292850i
$375$	−0.629049	−	2.75604i	−0.0324839	−	0.142321i
$376$	18.9209			0.975773
$377$	11.9885	+	2.53086i	0.617439	+	0.130346i
$378$	4.61427			0.237333
$379$	7.78248	+	34.0973i	0.399759	+	1.75146i	0.628344	+	0.777936i	$0.283733\pi$
$379$	7.78248	+	34.0973i	0.399759	+	1.75146i	−0.228585	+	0.973524i	$0.573410\pi$
$380$	0.254285	+	0.122457i	0.0130445	+	0.00628192i
$381$	−15.3159	+	7.37574i	−0.784656	+	0.377870i
$382$	0.236564	+	1.03645i	0.0121037	+	0.0530296i
$383$	4.55743	−	19.9674i	0.232874	−	1.02029i	−0.714369	−	0.699769i	$-0.753286\pi$
$383$	4.55743	−	19.9674i	0.232874	−	1.02029i	0.947243	−	0.320517i	$-0.103857\pi$
$384$	5.20423	+	2.50623i	0.265577	+	0.127895i
$385$	−3.74512	−	4.69624i	−0.190869	−	0.239342i
$386$	−11.7614	−	14.7484i	−0.598641	−	0.750672i
$387$	−7.12025	+	3.42893i	−0.361943	+	0.174302i
$388$	−0.364130	+	0.456604i	−0.0184859	+	0.0231806i
$389$	−7.13745			−0.361883			−0.180942	−	0.983494i	$-0.557914\pi$
$389$	−7.13745			−0.361883			−0.180942	+	0.983494i	$0.557914\pi$
$390$	0.370221	−	0.464243i	0.0187469	−	0.0235079i
$391$	−5.49232	+	24.0634i	−0.277759	+	1.21694i
$392$	−11.8488	+	51.9128i	−0.598453	+	2.62199i
$393$	7.91531	−	9.92548i	0.399274	−	0.500674i
$394$	−4.72325			−0.237954
$395$	−1.20292	+	1.50842i	−0.0605256	+	0.0758967i
$396$	−4.37686	+	2.10778i	−0.219945	+	0.105920i
$397$	−16.4091	−	20.5763i	−0.823548	−	1.03270i	−0.998839	−	0.0481802i	$-0.984658\pi$
$397$	−16.4091	−	20.5763i	−0.823548	−	1.03270i	0.175290	−	0.984517i	$-0.443914\pi$
$398$	1.60189	+	2.00871i	0.0802957	+	0.100688i
$399$	3.87074	+	1.86405i	0.193779	+	0.0933191i
$400$	−0.358760	+	1.57183i	−0.0179380	+	0.0785915i
$401$	1.12506	+	4.92921i	0.0561828	+	0.246153i	0.995219	−	0.0976641i	$-0.0311371\pi$
$401$	1.12506	+	4.92921i	0.0561828	+	0.246153i	−0.939037	+	0.343817i	$0.888280\pi$
$402$	2.34349	−	1.12857i	0.116883	−	0.0562878i
$403$	6.70696	+	3.22990i	0.334098	+	0.160893i
$404$	−1.16513	−	5.10476i	−0.0579673	−	0.253971i
$405$	0.285007			0.0141621
$406$	24.1320	−	5.92460i	1.19765	−	0.294033i
$407$	−1.59224			−0.0789246
$408$	−2.19561	−	9.61958i	−0.108699	−	0.476240i
$409$	−5.81490	−	2.80031i	−0.287529	−	0.138466i	0.284560	−	0.958658i	$-0.408152\pi$
$409$	−5.81490	−	2.80031i	−0.287529	−	0.138466i	−0.572089	+	0.820192i	$0.693867\pi$
$410$	−1.30734	+	0.629583i	−0.0645651	+	0.0310929i
$411$	2.16808	+	9.49900i	0.106944	+	0.468551i
$412$	2.09974	−	9.19957i	0.103447	−	0.453230i
$413$	21.2575	+	10.2371i	1.04601	+	0.503734i
$414$	4.13442	+	5.18440i	0.203196	+	0.254799i
$415$	1.11592	+	1.39932i	0.0547785	+	0.0686901i
$416$	11.2537	−	5.41951i	0.551760	−	0.265713i
$417$	7.78330	−	9.75995i	0.381150	−	0.477947i
$418$	3.26503			0.159698
$419$	0.767911	−	0.962930i	0.0375149	−	0.0470422i	−0.762720	−	0.646729i	$-0.776137\pi$
$419$	0.767911	−	0.962930i	0.0375149	−	0.0470422i	0.800235	+	0.599686i	$0.204708\pi$
$420$	−0.371209	+	1.62637i	−0.0181131	+	0.0793588i
$421$	−1.96888	+	8.62624i	−0.0959574	+	0.420417i	−0.999975	−	0.00707841i	$-0.997747\pi$
$421$	−1.96888	+	8.62624i	−0.0959574	+	0.420417i	0.904018	+	0.427495i	$0.140604\pi$
$422$	2.76823	−	3.47125i	0.134755	−	0.168978i
$423$	6.53585			0.317784
$424$	5.22100	−	6.54693i	0.253554	−	0.317947i
$425$	−15.1046	+	7.27399i	−0.732681	+	0.352840i
$426$	−6.56228	−	8.22884i	−0.317943	−	0.398688i
$427$	−21.8024	−	27.3393i	−1.05509	−	1.32304i
$428$	9.96189	+	4.79739i	0.481526	+	0.231891i
$429$	−2.11751	+	9.27742i	−0.102234	+	0.447918i
$430$	0.458939	+	2.01074i	0.0221320	+	0.0969667i
$431$	8.89025	−	4.28132i	0.428228	−	0.206224i	−0.207339	−	0.978269i	$-0.566480\pi$
$431$	8.89025	−	4.28132i	0.428228	−	0.206224i	0.635568	+	0.772045i	$0.280766\pi$
$432$	−0.295316	−	0.142216i	−0.0142084	−	0.00684239i
$433$	7.36319	+	32.2602i	0.353852	+	1.55033i	0.768200	+	0.640210i	$0.221153\pi$
$433$	7.36319	+	32.2602i	0.353852	+	1.55033i	−0.414348	+	0.910119i	$0.635990\pi$
$434$	15.0968			0.724671
$435$	1.49055	−	0.365941i	0.0714662	−	0.0175455i
$436$	8.63182			0.413389
$437$	1.37384	+	6.01920i	0.0657198	+	0.287937i
$438$	9.34180	+	4.49877i	0.446368	+	0.214960i
$439$	9.70775	−	4.67500i	0.463326	−	0.223126i	−0.187633	−	0.982239i	$-0.560082\pi$
$439$	9.70775	−	4.67500i	0.463326	−	0.223126i	0.650958	+	0.759113i	$0.274367\pi$
$440$	0.767871	+	3.36426i	0.0366068	+	0.160385i
$441$	−4.09291	+	17.9322i	−0.194901	+	0.853915i
$442$	−6.39778	−	3.08101i	−0.304311	−	0.146549i
$443$	21.2232	+	26.6130i	1.00834	+	1.26442i	0.964138	+	0.265401i	$0.0855042\pi$
$443$	21.2232	+	26.6130i	1.00834	+	1.26442i	0.0442056	+	0.999022i	$0.485924\pi$
$444$	0.275708	+	0.345727i	0.0130845	+	0.0164075i
$445$	−1.46522	+	0.705614i	−0.0694582	+	0.0334493i
$446$	−5.93502	+	7.44227i	−0.281031	+	0.352402i
$447$	22.6007			1.06898
$448$	17.8534	−	22.3875i	0.843495	−	1.05771i
$449$	4.86933	−	21.3339i	0.229798	−	1.00681i	−0.720007	−	0.693967i	$-0.755861\pi$
$449$	4.86933	−	21.3339i	0.229798	−	1.00681i	0.949805	−	0.312843i	$-0.101282\pi$
$450$	−1.00224	+	4.39109i	−0.0472459	+	0.206998i
$451$	14.4988	−	18.1809i	0.682721	−	0.856106i
$452$	−4.92263			−0.231541
$453$	4.13725	−	5.18795i	0.194385	−	0.243751i
$454$	−23.0871	+	11.1182i	−1.08353	+	0.521802i
$455$	2.03741	+	2.55483i	0.0955153	+	0.119772i
$456$	−1.53884	−	1.92964i	−0.0720628	−	0.0903639i
$457$	−26.2149	−	12.6244i	−1.22628	−	0.590546i	−0.295227	−	0.955427i	$-0.595395\pi$
$457$	−26.2149	−	12.6244i	−1.22628	−	0.590546i	−0.931054	+	0.364881i	$0.881110\pi$
$458$	−0.712379	+	3.12114i	−0.0332873	+	0.145841i
$459$	−0.758427	−	3.32288i	−0.0354003	−	0.155099i
$460$	−2.15993	+	1.04017i	−0.100707	+	0.0484980i
$461$	−16.8951	−	8.13623i	−0.786882	−	0.378942i	−0.00311295	−	0.999995i	$-0.500991\pi$
$461$	−16.8951	−	8.13623i	−0.786882	−	0.378942i	−0.783769	+	0.621053i	$0.786705\pi$
$462$	4.29433	+	18.8147i	0.199790	+	0.875338i
$463$	22.8658			1.06266			0.531332	−	0.847164i	$-0.321692\pi$
$463$	22.8658			1.06266			0.531332	+	0.847164i	$0.321692\pi$
$464$	−1.72706	−	0.364595i	−0.0801768	−	0.0169259i
$465$	0.932477			0.0432426
$466$	−0.683136	−	2.99301i	−0.0316456	−	0.138649i
$467$	−17.6886	−	8.51838i	−0.818530	−	0.394183i	−0.0227293	−	0.999742i	$-0.507236\pi$
$467$	−17.6886	−	8.51838i	−0.818530	−	0.394183i	−0.795801	+	0.605558i	$0.792950\pi$
$468$	2.38109	−	1.14667i	0.110066	−	0.0530048i
$469$	3.18524	+	13.9554i	0.147081	+	0.644402i
$470$	0.379552	−	1.66293i	0.0175074	−	0.0767051i
$471$	−12.0543	−	5.80504i	−0.555432	−	0.267482i
$472$	−8.45109	−	10.5973i	−0.388993	−	0.487782i
$473$	−20.6080	−	25.8416i	−0.947558	−	1.18820i
$474$	5.58477	−	2.68948i	0.256517	−	0.123532i
$475$	−2.61463	+	3.27864i	−0.119967	+	0.150434i
$476$	19.9496			0.914389
$477$	1.80349	−	2.26150i	0.0825761	−	0.103547i
$478$	−3.74778	+	16.4201i	−0.171420	+	0.751038i
$479$	−5.01171	+	21.9577i	−0.228991	+	1.00327i	0.721474	+	0.692442i	$0.243465\pi$
$479$	−5.01171	+	21.9577i	−0.228991	+	1.00327i	−0.950465	+	0.310833i	$0.899392\pi$
$480$	0.975524	−	1.22327i	0.0445264	−	0.0558343i
$481$	0.866207			0.0394957
$482$	−3.21150	+	4.02709i	−0.146280	+	0.183429i
$483$	−32.8785	+	15.8335i	−1.49603	+	0.720448i
$484$	−4.70162	−	5.89565i	−0.213710	−	0.267984i
$485$	0.0893470	+	0.112038i	0.00405704	+	0.00508737i
$486$	−0.824998	−	0.397298i	−0.0374227	−	0.0180218i
$487$	−0.382806	+	1.67718i	−0.0173466	+	0.0760003i	−0.982860	−	0.184352i	$-0.940981\pi$
$487$	−0.382806	+	1.67718i	−0.0173466	+	0.0760003i	0.965514	+	0.260352i	$0.0838386\pi$
$488$	4.47018	+	19.5852i	0.202356	+	0.886578i
$489$	9.15044	−	4.40662i	0.413797	−	0.199274i
$490$	4.32484	+	2.08273i	0.195376	+	0.0940882i
$491$	−6.55025	−	28.6985i	−0.295609	−	1.29515i	−0.876593	−	0.481232i	$-0.840190\pi$
$491$	−6.55025	−	28.6985i	−0.295609	−	1.29515i	0.580985	−	0.813914i	$-0.302668\pi$
$492$	−6.45822			−0.291159
$493$	−8.23296	−	16.4044i	−0.370794	−	0.738818i
$494$	−1.77623			−0.0799165
$495$	0.265245	+	1.16212i	0.0119219	+	0.0522332i
$496$	−0.966204	−	0.465299i	−0.0433838	−	0.0208926i
$497$	52.1858	−	25.1313i	2.34085	−	1.12730i
$498$	−1.27957	−	5.60616i	−0.0573388	−	0.251218i
$499$	3.09035	−	13.5397i	0.138343	−	0.606121i	−0.857456	−	0.514557i	$-0.827956\pi$
$499$	3.09035	−	13.5397i	0.138343	−	0.606121i	0.995799	−	0.0915640i	$-0.0291866\pi$
$500$	−2.95838	−	1.42468i	−0.132303	−	0.0637138i
$501$	−15.2939	−	19.1780i	−0.683283	−	0.856810i
$502$	15.3069	+	19.1943i	0.683182	+	0.856683i
$503$	23.8857	−	11.5027i	1.06501	−	0.512881i	0.182514	−	0.983203i	$-0.441576\pi$
$503$	23.8857	−	11.5027i	1.06501	−	0.512881i	0.882495	+	0.470322i	$0.155862\pi$
$504$	9.09558	−	11.4055i	0.405149	−	0.508041i
$505$	−1.28477			−0.0571717
$506$	−17.2916	+	21.6830i	−0.768707	+	0.963928i
$507$	−1.74081	+	7.62699i	−0.0773121	+	0.338726i
$508$	−4.39374	+	19.2502i	−0.194941	+	0.854091i
$509$	−3.59869	+	4.51261i	−0.159509	+	0.200018i	−0.855163	−	0.518359i	$-0.826543\pi$
$509$	−3.59869	+	4.51261i	−0.159509	+	0.200018i	0.695654	+	0.718377i	$0.255115\pi$
$510$	−0.889490			−0.0393873
$511$	−35.5768	+	44.6119i	−1.57383	+	1.97352i
$512$	−3.33106	+	1.60415i	−0.147213	+	0.0708942i
$513$	−0.531561	−	0.666556i	−0.0234690	−	0.0294292i
$514$	2.11580	+	2.65313i	0.0933239	+	0.117024i
$515$	−2.08607	−	1.00460i	−0.0919232	−	0.0442679i
$516$	−2.04262	+	8.94931i	−0.0899214	+	0.393972i
$517$	6.08267	+	26.6499i	0.267515	+	1.17206i
$518$	1.58271	−	0.762193i	0.0695403	−	0.0334888i
$519$	−19.9009	−	9.58379i	−0.873554	−	0.420682i
$520$	−0.417735	−	1.83022i	−0.0183189	−	0.0802603i
$521$	23.7796			1.04180			0.520901	−	0.853617i	$-0.325596\pi$
$521$	23.7796			1.04180			0.520901	+	0.853617i	$0.325596\pi$
$522$	−4.82474	−	1.01854i	−0.211173	−	0.0445802i
$523$	24.9044			1.08899			0.544497	−	0.838763i	$-0.316720\pi$
$523$	24.9044			1.08899			0.544497	+	0.838763i	$0.316720\pi$
$524$	−3.28126	−	14.3761i	−0.143343	−	0.628025i
$525$	−22.3319	−	10.7545i	−0.974646	−	0.469365i
$526$	14.5629	−	7.01311i	0.634971	−	0.305786i
$527$	−2.48140	−	10.8717i	−0.108091	−	0.473579i
$528$	0.305048	−	1.33650i	0.0132755	−	0.0581639i
$529$	−26.5270	−	12.7747i	−1.15335	−	0.555422i
$530$	−0.470665	−	0.590195i	−0.0204444	−	0.0256364i
$531$	−2.91925	−	3.66063i	−0.126685	−	0.158858i
$532$	4.49599	−	2.16515i	0.194926	−	0.0938713i
$533$	−7.88759	+	9.89072i	−0.341649	+	0.428415i
$534$	5.22494			0.226105
$535$	1.69155	−	2.12114i	0.0731322	−	0.0917048i
$536$	1.82988	−	8.01722i	0.0790387	−	0.346291i
$537$	0.163565	−	0.716626i	0.00705836	−	0.0309247i
$538$	8.18466	−	10.2632i	0.352866	−	0.442480i
$539$	−76.9277			−3.31351
$540$	0.206403	−	0.258821i	0.00888218	−	0.0111379i
$541$	18.8102	−	9.05851i	0.808713	−	0.389456i	0.0166244	−	0.999862i	$-0.494708\pi$
$541$	18.8102	−	9.05851i	0.808713	−	0.389456i	0.792089	+	0.610406i	$0.208994\pi$
$542$	−17.2361	−	21.6133i	−0.740352	−	0.928372i
$543$	−8.52713	−	10.6927i	−0.365934	−	0.458867i
$544$	−16.8580	−	8.11838i	−0.722780	−	0.348073i
$545$	0.471300	−	2.06490i	0.0201883	−	0.0884506i
$546$	−2.33619	−	10.2355i	−0.0999796	−	0.438039i
$547$	−0.170736	+	0.0822219i	−0.00730012	+	0.00351555i	−0.437530	−	0.899204i	$-0.644147\pi$
$547$	−0.170736	+	0.0822219i	−0.00730012	+	0.00351555i	0.430230	+	0.902719i	$0.358432\pi$
$548$	10.1964	+	4.91032i	0.435568	+	0.209759i
$549$	1.54413	+	6.76529i	0.0659020	+	0.288735i
$550$	−18.8374			−0.803229
$551$	−3.63583	−	2.80348i	−0.154891	−	0.119432i
$552$	20.9644			0.892306
$553$	7.59073	+	33.2572i	0.322791	+	1.41424i
$554$	6.96766	+	3.35545i	0.296027	+	0.142559i
$555$	0.0977583	−	0.0470779i	0.00414961	−	0.00199835i
$556$	−3.22654	−	14.1364i	−0.136836	−	0.599516i
$557$	5.48081	−	24.0130i	0.232229	−	1.01746i	−0.715556	−	0.698555i	$-0.753827\pi$
$557$	5.48081	−	24.0130i	0.232229	−	1.01746i	0.947786	−	0.318908i	$-0.103316\pi$
$558$	−2.69920	−	1.29987i	−0.114266	−	0.0550278i
$559$	11.2111	+	14.0583i	0.474179	+	0.594602i
$560$	−0.293509	−	0.368049i	−0.0124030	−	0.0155529i
$561$	12.8432	−	6.18497i	0.542241	−	0.261129i
$562$	7.23671	−	9.07454i	0.305262	−	0.382786i
$563$	−24.8717			−1.04822			−0.524109	−	0.851651i	$-0.675602\pi$
$563$	−24.8717			−1.04822			−0.524109	+	0.851651i	$0.675602\pi$
$564$	4.73329	−	5.93535i	0.199307	−	0.249924i
$565$	−0.268777	+	1.17759i	−0.0113075	+	0.0495415i
$566$	−5.02117	+	21.9992i	−0.211056	+	0.924695i
$567$	3.14188	−	3.93979i	0.131947	−	0.165456i
$568$	−33.2754			−1.39620
$569$	−8.90531	+	11.1669i	−0.373330	+	0.468141i	−0.932635	−	0.360821i	$-0.882497\pi$
$569$	−8.90531	+	11.1669i	−0.373330	+	0.468141i	0.559305	+	0.828962i	$0.311068\pi$
$570$	−0.200462	+	0.0965373i	−0.00839642	+	0.00404350i
$571$	6.56913	+	8.23743i	0.274909	+	0.344726i	0.900050	−	0.435787i	$-0.143530\pi$
$571$	6.56913	+	8.23743i	0.274909	+	0.344726i	−0.625141	+	0.780512i	$0.714958\pi$
$572$	6.89153	+	8.64171i	0.288149	+	0.361328i
$573$	1.04603	+	0.503742i	0.0436986	+	0.0210441i
$574$	−5.70894	+	25.0125i	−0.238286	+	1.04400i
$575$	−7.92629	−	34.7274i	−0.330549	−	1.44823i
$576$	−5.11967	+	2.46550i	−0.213320	+	0.102729i
$577$	−7.60750	−	3.66358i	−0.316704	−	0.152517i	0.268778	−	0.963202i	$-0.413380\pi$
$577$	−7.60750	−	3.66358i	−0.316704	−	0.152517i	−0.585482	+	0.810686i	$0.699095\pi$
$578$	−1.09687	−	4.80572i	−0.0456239	−	0.199892i
$579$	−20.6010			−0.856148
$580$	0.747140	−	1.61862i	0.0310233	−	0.0672093i
$581$	31.6454			1.31287
$582$	−0.102449	−	0.448860i	−0.00424666	−	0.0186058i
$583$	10.8997	+	5.24903i	0.451420	+	0.217392i
$584$	29.5344	−	14.2230i	1.22214	−	0.588553i
$585$	−0.144298	−	0.632210i	−0.00596598	−	0.0261387i
$586$	−0.938757	+	4.11296i	−0.0387797	+	0.169905i
$587$	−8.42975	−	4.05955i	−0.347933	−	0.167556i	0.251752	−	0.967792i	$-0.418993\pi$
$587$	−8.42975	−	4.05955i	−0.347933	−	0.167556i	−0.599685	+	0.800236i	$0.704708\pi$
$588$	13.3206	+	16.7034i	0.549330	+	0.688839i
$589$	−1.73914	−	2.18082i	−0.0716602	−	0.0898590i
$590$	−1.10091	+	0.530169i	−0.0453237	+	0.0218267i
$591$	−3.21608	+	4.03284i	−0.132292	+	0.165889i
$592$	−0.124786			−0.00512866
$593$	−3.16050	+	3.96314i	−0.129786	+	0.162747i	−0.842478	−	0.538730i	$-0.818904\pi$
$593$	−3.16050	+	3.96314i	−0.129786	+	0.162747i	0.712692	+	0.701477i	$0.247476\pi$
$594$	0.852187	−	3.73368i	0.0349657	−	0.153195i
$595$	1.08925	−	4.77234i	0.0446551	−	0.195647i
$596$	16.3675	−	20.5242i	0.670439	−	0.840704i
$597$	2.80583			0.114835
$598$	9.40694	−	11.7959i	0.384679	−	0.482372i
$599$	−20.9430	+	10.0856i	−0.855707	+	0.412087i	−0.809693	−	0.586854i	$-0.800366\pi$
$599$	−20.9430	+	10.0856i	−0.855707	+	0.412087i	−0.0460140	+	0.998941i	$0.514652\pi$
$600$	8.87824	+	11.1330i	0.362452	+	0.454501i
$601$	−3.78317	−	4.74395i	−0.154319	−	0.193510i	0.698662	−	0.715452i	$-0.253779\pi$
$601$	−3.78317	−	4.74395i	−0.154319	−	0.193510i	−0.852981	+	0.521942i	$0.825208\pi$
$602$	32.8548	+	15.8220i	1.33906	+	0.644858i
$603$	0.632094	−	2.76938i	0.0257409	−	0.112778i
$604$	−1.71508	−	7.51427i	−0.0697857	−	0.305751i
$605$	−1.66706	+	0.802815i	−0.0677758	+	0.0326391i
$606$	3.71898	+	1.79097i	0.151073	+	0.0727531i
$607$	8.74796	+	38.3273i	0.355069	+	1.55566i	0.765299	+	0.643675i	$0.222591\pi$
$607$	8.74796	+	38.3273i	0.355069	+	1.55566i	−0.410230	+	0.911982i	$0.634552\pi$
$608$	−4.68033			−0.189813
$609$	11.3730	−	24.6386i	0.460857	−	0.998408i
$610$	1.81097			0.0733242
$611$	−3.30907	−	14.4980i	−0.133871	−	0.586526i
$612$	−3.56684	−	1.71770i	−0.144181	−	0.0694340i
$613$	−22.2460	+	10.7131i	−0.898506	+	0.432698i	−0.825349	−	0.564623i	$-0.809022\pi$
$613$	−22.2460	+	10.7131i	−0.898506	+	0.432698i	−0.0731567	+	0.997320i	$0.523307\pi$
$614$	0.571719	+	2.50487i	0.0230727	+	0.101088i
$615$	−0.352620	+	1.54493i	−0.0142190	+	0.0622976i
$616$	54.9708	+	26.4725i	2.21484	+	1.06661i
$617$	11.8195	+	14.8212i	0.475837	+	0.596680i	0.960590	−	0.277971i	$-0.0896618\pi$
$617$	11.8195	+	14.8212i	0.475837	+	0.596680i	−0.484753	+	0.874651i	$0.661090\pi$
$618$	4.63805	+	5.81594i	0.186570	+	0.233951i
$619$	25.7787	−	12.4143i	1.03613	−	0.498975i	0.163085	−	0.986612i	$-0.447855\pi$
$619$	25.7787	−	12.4143i	1.03613	−	0.498975i	0.873046	+	0.487637i	$0.162141\pi$
$620$	0.675303	−	0.846804i	0.0271208	−	0.0340085i
$621$	7.24173			0.290601
$622$	−8.97499	+	11.2543i	−0.359864	+	0.451256i
$623$	−6.39837	+	28.0331i	−0.256345	+	1.12312i
$624$	−0.165951	+	0.727081i	−0.00664338	+	0.0291065i
$625$	14.8317	−	18.5983i	0.593267	−	0.743933i
$626$	−16.6881			−0.666989
$627$	2.22318	−	2.78778i	0.0887852	−	0.111333i
$628$	−14.0015	+	6.74275i	−0.558719	+	0.269065i
$629$	−0.809022	−	1.01448i	−0.0322578	−	0.0404500i
$630$	−0.819951	−	1.02819i	−0.0326676	−	0.0409639i
$631$	−18.9321	−	9.11724i	−0.753676	−	0.362951i	0.0172705	−	0.999851i	$-0.494502\pi$
$631$	−18.9321	−	9.11724i	−0.753676	−	0.362951i	−0.770947	+	0.636899i	$0.780217\pi$
$632$	4.36078	−	19.1058i	0.173463	−	0.759989i
$633$	−1.07895	−	4.72718i	−0.0428844	−	0.187889i
$634$	1.55097	−	0.746907i	0.0615968	−	0.0296635i
$635$	4.36513	+	2.10214i	0.173225	+	0.0834207i
$636$	−0.747629	−	3.27558i	−0.0296454	−	0.129885i
$637$	41.8500			1.65816
$638$	−0.337120	−	20.6208i	−0.0133467	−	0.816385i
$639$	−11.4943			−0.454707
$640$	−0.366331	−	1.60500i	−0.0144805	−	0.0634432i
$641$	−5.46803	−	2.63327i	−0.215974	−	0.104008i	0.322769	−	0.946478i	$-0.395386\pi$
$641$	−5.46803	−	2.63327i	−0.215974	−	0.104008i	−0.538743	+	0.842470i	$0.681101\pi$
$642$	−7.85332	+	3.78196i	−0.309946	+	0.149262i
$643$	10.0678	+	44.1097i	0.397033	+	1.73952i	0.638976	+	0.769226i	$0.279358\pi$
$643$	10.0678	+	44.1097i	0.397033	+	1.73952i	−0.241943	+	0.970291i	$0.577785\pi$
$644$	−9.43203	+	41.3244i	−0.371674	+	1.62841i
$645$	2.02932	+	0.977270i	0.0799045	+	0.0384800i
$646$	1.65897	+	2.08028i	0.0652713	+	0.0818476i
$647$	−7.22803	−	9.06366i	−0.284163	−	0.356329i	0.619179	−	0.785250i	$-0.287465\pi$
$647$	−7.22803	−	9.06366i	−0.284163	−	0.356329i	−0.903342	+	0.428921i	$0.858894\pi$
$648$	−2.60826	+	1.25607i	−0.102462	+	0.0493431i
$649$	12.2094	−	15.3101i	0.479260	−	0.600973i
$650$	10.2479			0.401954
$651$	10.2795	−	12.8901i	0.402886	−	0.505202i
$652$	2.62503	−	11.5010i	0.102804	−	0.450415i
$653$	−2.81311	+	12.3250i	−0.110086	+	0.482316i	0.889588	+	0.456764i	$0.150992\pi$
$653$	−2.81311	+	12.3250i	−0.110086	+	0.482316i	−0.999673	+	0.0255523i	$0.991866\pi$
$654$	−4.24271	+	5.32019i	−0.165903	+	0.208036i
$655$	−3.61821			−0.141375
$656$	1.13628	−	1.42486i	0.0443645	−	0.0556313i
$657$	10.2021	−	4.91305i	0.398020	−	0.191676i
$658$	−18.8033	−	23.5786i	−0.733030	−	0.919190i
$659$	28.8673	+	36.1984i	1.12451	+	1.41009i	0.900148	+	0.435583i	$0.143458\pi$
$659$	28.8673	+	36.1984i	1.12451	+	1.41009i	0.224360	+	0.974506i	$0.427971\pi$
$660$	1.24744	+	0.600733i	0.0485564	+	0.0233835i
$661$	0.706721	−	3.09635i	0.0274882	−	0.120434i	−0.959322	−	0.282313i	$-0.908898\pi$
$661$	0.706721	−	3.09635i	0.0274882	−	0.120434i	0.986811	+	0.161879i	$0.0517555\pi$
$662$	1.25125	+	5.48207i	0.0486311	+	0.213067i
$663$	−6.98693	+	3.36473i	−0.271350	+	0.130675i
$664$	−16.3795	−	7.88794i	−0.635647	−	0.306112i
$665$	−0.272465	−	1.19375i	−0.0105657	−	0.0462915i
$666$	−0.348603			−0.0135081
$667$	37.8732	−	9.29819i	1.46646	−	0.360027i
$668$	−28.4919			−1.10239
$669$	2.31324	+	10.1350i	0.0894350	+	0.391840i
$670$	−0.667912	−	0.321649i	−0.0258037	−	0.0124264i
$671$	−26.1484	+	12.5924i	−1.00945	+	0.486124i
$672$	−6.15580	−	26.9703i	−0.237465	−	1.04040i
$673$	−2.51910	+	11.0369i	−0.0971043	+	0.425442i	−0.999990	−	0.00443874i	$-0.998587\pi$
$673$	−2.51910	+	11.0369i	−0.0971043	+	0.425442i	0.902886	+	0.429880i	$0.141444\pi$
$674$	−5.98287	−	2.88120i	−0.230451	−	0.110980i
$675$	3.06680	+	3.84565i	0.118041	+	0.148019i
$676$	5.66554	+	7.10436i	0.217905	+	0.273245i
$677$	−4.00868	+	1.93048i	−0.154066	+	0.0741943i	−0.509328	−	0.860573i	$-0.670106\pi$
$677$	−4.00868	+	1.93048i	−0.154066	+	0.0741943i	0.355262	+	0.934767i	$0.384392\pi$
$678$	2.41957	−	3.03404i	0.0929229	−	0.116522i
$679$	2.53370			0.0972345
$680$	−1.75335	+	2.19863i	−0.0672379	+	0.0843136i
$681$	−6.22713	+	27.2828i	−0.238624	+	1.04548i
$682$	2.78816	−	12.2157i	0.106764	−	0.467764i
$683$	15.5911	−	19.5506i	0.596577	−	0.748084i	−0.388263	−	0.921549i	$-0.626925\pi$
$683$	15.5911	−	19.5506i	0.596577	−	0.748084i	0.984840	+	0.173465i	$0.0554962\pi$
$684$	−0.990273			−0.0378640
$685$	1.73137	−	2.17107i	0.0661523	−	0.0829523i
$686$	47.3659	−	22.8102i	1.80844	−	0.870897i
$687$	2.17985	+	2.73345i	0.0831665	+	0.104287i
$688$	−1.61507	−	2.02523i	−0.0615740	−	0.0772114i
$689$	−5.92963	−	2.85556i	−0.225901	−	0.108788i
$690$	0.420544	−	1.84253i	0.0160099	−	0.0701438i
$691$	2.00976	+	8.80534i	0.0764549	+	0.334971i	0.998661	−	0.0517274i	$-0.0164727\pi$
$691$	2.00976	+	8.80534i	0.0764549	+	0.334971i	−0.922206	+	0.386698i	$0.873616\pi$
$692$	−23.1156	+	11.1319i	−0.878723	+	0.423171i
$693$	18.9885	+	9.14439i	0.721314	+	0.347367i
$694$	−0.307584	−	1.34761i	−0.0116757	−	0.0511548i
$695$	−3.55787			−0.134958
$696$	−12.0281	+	9.91800i	−0.455922	+	0.375941i
$697$	18.9506			0.717807
$698$	2.96912	+	13.0086i	0.112383	+	0.492381i
$699$	−3.02067	−	1.45468i	−0.114252	−	0.0550209i
$700$	−25.9393	+	12.4917i	−0.980413	+	0.472142i
$701$	5.98486	+	26.2214i	0.226045	+	0.990368i	0.952830	+	0.303504i	$0.0981564\pi$
$701$	5.98486	+	26.2214i	0.226045	+	0.990368i	−0.726785	+	0.686865i	$0.758986\pi$
$702$	−0.463604	+	2.03118i	−0.0174976	+	0.0766621i
$703$	−0.292430	−	0.140827i	−0.0110292	−	0.00531138i
$704$	−14.8178	−	18.5809i	−0.558466	−	0.700294i
$705$	−1.16141	−	1.45637i	−0.0437414	−	0.0548499i
$706$	−17.9889	+	8.66300i	−0.677021	+	0.326036i
$707$	−14.1632	+	17.7601i	−0.532661	+	0.667936i
$708$	−5.43844			−0.204389
$709$	−22.0688	+	27.6734i	−0.828811	+	1.03930i	0.169740	+	0.985489i	$0.445707\pi$
$709$	−22.0688	+	27.6734i	−0.828811	+	1.03930i	−0.998551	+	0.0538071i	$0.982864\pi$
$710$	−0.667500	+	2.92451i	−0.0250508	+	0.109755i
$711$	1.50634	−	6.59971i	0.0564922	−	0.247509i
$712$	10.2993	−	12.9149i	0.385983	−	0.484008i
$713$	23.6933			0.887320
$714$	−9.80563	+	12.2959i	−0.366966	+	0.460161i
$715$	2.44354	−	1.17675i	0.0913834	−	0.0440079i
$716$	−0.532330	−	0.667521i	−0.0198941	−	0.0249464i
$717$	11.4681	+	14.3805i	0.428282	+	0.537049i
$718$	6.97470	+	3.35884i	0.260293	+	0.125351i
$719$	−2.35378	+	10.3126i	−0.0877813	+	0.384595i	−0.999666	−	0.0258519i	$-0.991770\pi$
$719$	−2.35378	+	10.3126i	−0.0877813	+	0.384595i	0.911884	+	0.410447i	$0.134627\pi$
$720$	0.0207875	+	0.0910761i	0.000774706	+	0.00339421i
$721$	−36.8836	+	17.7622i	−1.37362	+	0.661499i
$722$	−15.0753	−	7.25988i	−0.561045	−	0.270185i
$723$	1.25172	+	5.48413i	0.0465518	+	0.203957i
$724$	−15.8857			−0.590386
$725$	20.9767	+	16.1745i	0.779053	+	0.600706i
$726$	5.94470			0.220628
$727$	−10.2003	−	44.6903i	−0.378307	−	1.65747i	−0.702653	−	0.711532i	$-0.748001\pi$
$727$	−10.2003	−	44.6903i	−0.378307	−	1.65747i	0.324346	−	0.945938i	$-0.394856\pi$
$728$	−29.9050	−	14.4015i	−1.10835	−	0.533755i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	−0.657578	−	2.88104i	−0.0243380	−	0.106632i
$731$	5.99376	−	26.2604i	0.221687	−	0.971275i
$732$	7.26198	+	3.49719i	0.268411	+	0.129260i
$733$	−32.3666	−	40.5865i	−1.19549	−	1.49910i	−0.820093	−	0.572231i	$-0.806078\pi$
$733$	−32.3666	−	40.5865i	−1.19549	−	1.49910i	−0.375396	−	0.926864i	$-0.622493\pi$
$734$	3.93350	+	4.93245i	0.145188	+	0.182060i
$735$	4.72310	−	2.27452i	0.174214	−	0.0838970i
$736$	24.7871	−	31.0820i	0.913663	−	1.14570i
$737$	11.8804			0.437621
$738$	3.17434	−	3.98050i	0.116849	−	0.146524i
$739$	3.60556	−	15.7970i	0.132633	−	0.581102i	−0.864309	−	0.502960i	$-0.832244\pi$
$739$	3.60556	−	15.7970i	0.132633	−	0.581102i	0.996942	−	0.0781419i	$-0.0248987\pi$
$740$	0.0280444	−	0.122871i	0.00103093	−	0.00451681i
$741$	−1.20945	+	1.51660i	−0.0444301	+	0.0557136i
$742$	−13.3471			−0.489988
$743$	22.5216	−	28.2412i	0.826238	−	1.03607i	−0.172458	−	0.985017i	$-0.555171\pi$
$743$	22.5216	−	28.2412i	0.826238	−	1.03607i	0.998696	−	0.0510523i	$-0.0162575\pi$
$744$	−8.53362	+	4.10957i	−0.312858	+	0.150664i
$745$	−4.01612	−	5.03605i	−0.147139	−	0.184507i
$746$	10.9962	+	13.7889i	0.402601	+	0.504846i
$747$	−5.65795	−	2.72473i	−0.207014	−	0.0996926i
$748$	3.68440	−	16.1424i	0.134715	−	0.590224i
$749$	−10.6741	−	46.7663i	−0.390023	−	1.70880i
$750$	2.33220	−	1.12313i	0.0851600	−	0.0410109i
$751$	−37.5435	−	18.0800i	−1.36998	−	0.659748i	−0.403143	−	0.915137i	$-0.632082\pi$
$751$	−37.5435	−	18.0800i	−1.36998	−	0.659748i	−0.966838	+	0.255389i	$0.917797\pi$
$752$	0.476705	+	2.08858i	0.0173836	+	0.0761627i
$753$	26.8112			0.977054
$754$	0.183399	+	11.2181i	0.00667900	+	0.408538i
$755$	−1.89120			−0.0688279
$756$	−1.30245	−	5.70643i	−0.0473698	−	0.207541i
$757$	−7.04277	−	3.39162i	−0.255974	−	0.123271i	0.301497	−	0.953467i	$-0.402514\pi$
$757$	−7.04277	−	3.39162i	−0.255974	−	0.123271i	−0.557471	+	0.830197i	$0.688228\pi$
$758$	−28.8536	+	13.8952i	−1.04801	+	0.504695i
$759$	6.73961	+	29.5282i	0.244632	+	1.07180i
$760$	−0.156527	+	0.685792i	−0.00567785	+	0.0248763i
$761$	19.4919	+	9.38680i	0.706580	+	0.340271i	0.752426	−	0.658677i	$-0.228884\pi$
$761$	19.4919	+	9.38680i	0.706580	+	0.340271i	−0.0458451	+	0.998949i	$0.514598\pi$
$762$	−9.70520	−	12.1699i	−0.351582	−	0.440870i
$763$	−23.3486	−	29.2782i	−0.845275	−	1.05994i
$764$	1.21500	−	0.585113i	0.0439571	−	0.0211686i
$765$	−0.605658	+	0.759471i	−0.0218976	+	0.0274587i
$766$	18.7539			0.677606
$767$	−6.64210	+	8.32893i	−0.239832	+	0.300740i
$768$	−3.70587	+	16.2365i	−0.133724	+	0.585883i
$769$	−0.982842	+	4.30611i	−0.0354422	+	0.155282i	−0.989552	−	0.144173i	$-0.953948\pi$
$769$	−0.982842	+	4.30611i	−0.0354422	+	0.155282i	0.954110	+	0.299455i	$0.0968050\pi$
$770$	3.42933	−	4.30024i	0.123584	−	0.154970i
$771$	3.70597			0.133467
$772$	−14.9193	+	18.7082i	−0.536958	+	0.673324i
$773$	−2.71734	+	1.30860i	−0.0977360	+	0.0470672i	−0.482113	−	0.876109i	$-0.660131\pi$
$773$	−2.71734	+	1.30860i	−0.0977360	+	0.0470672i	0.384377	+	0.923176i	$0.374416\pi$
$774$	−4.51189	−	5.65773i	−0.162176	−	0.203363i
$775$	10.0339	+	12.5821i	0.360427	+	0.451962i
$776$	−1.31143	−	0.631552i	−0.0470777	−	0.0226714i
$777$	0.426893	−	1.87034i	0.0153147	−	0.0670981i
$778$	−1.45431	−	6.37175i	−0.0521395	−	0.228438i
$779$	4.27085	−	2.05673i	0.153019	−	0.0736901i
$780$	−0.678626	−	0.326809i	−0.0242987	−	0.0117016i
$781$	−10.6973	−	46.8680i	−0.382780	−	1.67707i
$782$	−22.6010			−0.808211
$783$	−4.15484	+	3.42597i	−0.148482	+	0.122434i
$784$	−6.02890			−0.215318
$785$	0.848512	+	3.71758i	0.0302847	+	0.132686i
$786$	10.4735	+	5.04376i	0.373577	+	0.179905i
$787$	25.0389	−	12.0581i	0.892541	−	0.429825i	0.0693519	−	0.997592i	$-0.477907\pi$
$787$	25.0389	−	12.0581i	0.892541	−	0.429825i	0.823189	+	0.567767i	$0.192193\pi$
$788$	1.33321	+	5.84120i	0.0474938	+	0.208084i
$789$	3.92794	−	17.2094i	0.139838	−	0.612672i
$790$	−1.59170	−	0.766522i	−0.0566301	−	0.0272716i
$791$	13.3154	+	16.6970i	0.473442	+	0.593678i
$792$	−7.54903	−	9.46619i	−0.268243	−	0.336366i
$793$	14.2252	−	6.85048i	0.505150	−	0.243268i
$794$	15.0254	−	18.8413i	0.533233	−	0.668653i
$795$	−0.824403			−0.0292386
$796$	2.03199	−	2.54804i	0.0720221	−	0.0903128i
$797$	−6.26644	+	27.4551i	−0.221969	+	0.972509i	0.734025	+	0.679122i	$0.237639\pi$
$797$	−6.26644	+	27.4551i	−0.221969	+	0.972509i	−0.955994	+	0.293386i	$0.905218\pi$
$798$	−0.875382	+	3.83530i	−0.0309882	+	0.135768i
$799$	−13.8891	+	17.4164i	−0.491361	+	0.616147i
$800$	27.0029			0.954695
$801$	3.55769	−	4.46120i	0.125705	−	0.157629i
$802$	−4.17117	+	2.00873i	−0.147289	+	0.0709307i
$803$	29.5276	+	37.0265i	1.04201	+	1.30664i
$804$	−2.05718	−	2.57962i	−0.0725510	−	0.0909761i
$805$	9.37061	+	4.51265i	0.330271	+	0.159050i
$806$	−1.51681	+	6.64556i	−0.0534272	+	0.234080i
$807$	−3.19006	−	13.9766i	−0.112295	−	0.491999i
$808$	11.7577	−	5.66220i	0.413634	−	0.199196i
$809$	22.4014	+	10.7879i	0.787590	+	0.379283i	0.784040	−	0.620710i	$-0.213156\pi$
$809$	22.4014	+	10.7879i	0.787590	+	0.379283i	0.00355013	+	0.999994i	$0.498870\pi$
$810$	0.0580723	+	0.254432i	0.00204045	+	0.00893981i
$811$	−17.5911			−0.617705			−0.308853	−	0.951110i	$-0.599945\pi$
$811$	−17.5911			−0.617705			−0.308853	+	0.951110i	$0.599945\pi$
$812$	−14.1385	−	28.1715i	−0.496166	−	0.988625i
$813$	−30.1902			−1.05882
$814$	−0.324432	−	1.42143i	−0.0113713	−	0.0498210i
$815$	−2.60794	−	1.25592i	−0.0913521	−	0.0439929i
$816$	1.00654	−	0.484722i	0.0352358	−	0.0169687i
$817$	−1.49927	−	6.56873i	−0.0524528	−	0.229811i
$818$	1.31506	−	5.76167i	0.0459801	−	0.201452i
$819$	−10.3301	−	4.97470i	−0.360962	−	0.173830i
$820$	1.14762	+	1.43907i	0.0400766	+	0.0502544i
$821$	−8.92358	−	11.1898i	−0.311435	−	0.390527i	0.601338	−	0.798995i	$-0.294635\pi$
$821$	−8.92358	−	11.1898i	−0.311435	−	0.390527i	−0.912773	+	0.408468i	$0.866063\pi$
$822$	−8.03819	+	3.87099i	−0.280364	+	0.135016i
$823$	9.47190	−	11.8774i	0.330170	−	0.414020i	−0.588843	−	0.808247i	$-0.700416\pi$
$823$	9.47190	−	11.8774i	0.330170	−	0.414020i	0.919013	+	0.394228i	$0.128988\pi$
$824$	23.5182			0.819295
$825$	−12.8265	+	16.0839i	−0.446560	+	0.559969i
$826$	−4.80747	+	21.0629i	−0.167273	+	0.732872i
$827$	7.86953	−	34.4787i	0.273650	−	1.19894i	−0.632018	−	0.774954i	$-0.717773\pi$
$827$	7.86953	−	34.4787i	0.273650	−	1.19894i	0.905668	−	0.423987i	$-0.139370\pi$
$828$	5.24449	−	6.57638i	0.182259	−	0.228545i
$829$	19.3932			0.673555			0.336777	−	0.941584i	$-0.390663\pi$
$829$	19.3932			0.673555			0.336777	+	0.941584i	$0.390663\pi$
$830$	−1.02183	+	1.28133i	−0.0354681	+	0.0444756i
$831$	7.60928	−	3.66444i	0.263963	−	0.127118i
$832$	8.06112	+	10.1083i	0.279469	+	0.350443i
$833$	−39.0871	−	49.0137i	−1.35429	−	1.69822i
$834$	10.2988	+	4.95965i	0.356619	+	0.171739i
$835$	−1.55567	+	6.81582i	−0.0538361	+	0.235871i
$836$	−0.921610	−	4.03784i	−0.0318745	−	0.139652i
$837$	−2.94776	+	1.41957i	−0.101890	+	0.0490674i
$838$	1.01610	+	0.489326i	0.0351004	+	0.0169035i
$839$	7.94453	+	34.8073i	0.274276	+	1.20168i	0.904911	+	0.425601i	$0.139937\pi$
$839$	7.94453	+	34.8073i	0.274276	+	1.20168i	−0.630635	+	0.776079i	$0.717206\pi$
$840$	−4.15773			−0.143455
$841$	−17.3304	+	23.2520i	−0.597600	+	0.801795i
$842$	−8.10199			−0.279213
$843$	−2.82059	−	12.3578i	−0.0971462	−	0.425625i
$844$	−5.07424	−	2.44363i	−0.174663	−	0.0841131i
$845$	2.00884	−	0.967407i	0.0691063	−	0.0332798i
$846$	1.33173	+	5.83469i	0.0457858	+	0.200601i
$847$	−7.27977	+	31.8948i	−0.250136	+	1.09592i
$848$	0.854221	+	0.411371i	0.0293341	+	0.0141265i
$849$	15.3646	+	19.2666i	0.527311	+	0.661227i
$850$	−9.57132	−	12.0021i	−0.328293	−	0.411667i
$851$	2.48394	−	1.19620i	0.0851483	−	0.0410052i
$852$	−8.32421	+	10.4382i	−0.285183	+	0.357608i
$853$	−2.67243			−0.0915024			−0.0457512	−	0.998953i	$-0.514568\pi$
$853$	−2.67243			−0.0915024			−0.0457512	+	0.998953i	$0.514568\pi$
$854$	19.9639	−	25.0340i	0.683152	−	0.856646i
$855$	−0.0540692	+	0.236893i	−0.00184913	+	0.00810156i
$856$	−6.13214	+	26.8667i	−0.209592	+	0.918284i
$857$	−20.0381	+	25.1270i	−0.684489	+	0.858322i	−0.995759	−	0.0919992i	$-0.970674\pi$
$857$	−20.0381	+	25.1270i	−0.684489	+	0.858322i	0.311270	+	0.950322i	$0.399246\pi$
$858$	−8.71361			−0.297478
$859$	−7.33901	+	9.20283i	−0.250404	+	0.313997i	−0.891108	−	0.453791i	$-0.850071\pi$
$859$	−7.33901	+	9.20283i	−0.250404	+	0.313997i	0.640704	+	0.767788i	$0.278643\pi$
$860$	2.35712	−	1.13513i	0.0803773	−	0.0387077i
$861$	17.4691	+	21.9056i	0.595346	+	0.746540i
$862$	5.63347	+	7.06415i	0.191877	+	0.240606i
$863$	−28.7516	−	13.8460i	−0.978715	−	0.471324i	−0.125052	−	0.992150i	$-0.539910\pi$
$863$	−28.7516	−	13.8460i	−0.978715	−	0.471324i	−0.853663	+	0.520826i	$0.825624\pi$
$864$	−1.22159	+	5.35212i	−0.0415592	+	0.182083i
$865$	1.40085	+	6.13750i	0.0476302	+	0.208681i
$866$	−27.2991	+	13.1465i	−0.927660	+	0.446738i
$867$	−4.85012	−	2.33570i	−0.164719	−	0.0793244i
$868$	−4.26133	−	18.6701i	−0.144639	−	0.633705i
$869$	28.3122			0.960426
$870$	0.630393	+	1.25608i	0.0213723	+	0.0425850i
$871$	−6.46315			−0.218996
$872$	4.78721	+	20.9741i	0.162115	+	0.710274i
$873$	−0.453007	−	0.218157i	−0.0153320	−	0.00738348i
$874$	−5.09353	+	2.45291i	−0.172291	+	0.0829711i
$875$	3.16989	+	13.8882i	0.107162	+	0.469507i
$876$	2.92671	−	12.8228i	0.0988845	−	0.433241i
$877$	−7.98753	−	3.84659i	−0.269720	−	0.129890i	0.294136	−	0.955764i	$-0.404968\pi$
$877$	−7.98753	−	3.84659i	−0.269720	−	0.129890i	−0.563855	+	0.825874i	$0.690682\pi$
$878$	6.15150	+	7.71374i	0.207603	+	0.260326i
$879$	2.87256	+	3.60207i	0.0968890	+	0.121495i
$880$	−0.352017	+	0.169522i	−0.0118665	+	0.00571459i
$881$	2.59928	−	3.25939i	0.0875718	−	0.109812i	−0.736115	−	0.676856i	$-0.763342\pi$
$881$	2.59928	−	3.25939i	0.0875718	−	0.109812i	0.823687	+	0.567045i	$0.191913\pi$
$882$	−16.8424			−0.567114
$883$	14.6554	−	18.3772i	0.493192	−	0.618443i	−0.471487	−	0.881873i	$-0.656282\pi$
$883$	14.6554	−	18.3772i	0.493192	−	0.618443i	0.964678	+	0.263430i	$0.0848539\pi$
$884$	−2.00437	+	8.78174i	−0.0674144	+	0.295362i
$885$	−0.296940	+	1.30098i	−0.00998154	+	0.0437320i
$886$	−19.4336	+	24.3690i	−0.652885	+	0.818692i
$887$	20.2426			0.679680			0.339840	−	0.940483i	$-0.389627\pi$
$887$	20.2426			0.679680			0.339840	+	0.940483i	$0.389627\pi$
$888$	−0.687161	+	0.861672i	−0.0230596	+	0.0289158i
$889$	77.1795	−	37.1677i	2.58852	−	1.24656i
$890$	−0.928466	−	1.16426i	−0.0311223	−	0.0390261i
$891$	−2.60766	−	3.26990i	−0.0873598	−	0.109546i
$892$	10.8790	+	5.23907i	0.364257	+	0.175417i
$893$	−1.23993	+	5.43248i	−0.0414926	+	0.181791i
$894$	4.60506	+	20.1761i	0.154016	+	0.674790i
$895$	−0.188749	+	0.0908968i	−0.00630919	+	0.00303835i
$896$	−26.2251	−	12.6293i	−0.876118	−	0.421916i
$897$	−3.66646	−	16.0638i	−0.122420	−	0.536355i
$898$	20.0374			0.668657
$899$	−13.5937	+	11.2090i	−0.453375	+	0.373840i
$900$	5.71331			0.190444
$901$	2.19380	+	9.61168i	0.0730862	+	0.320211i
$902$	19.1847	+	9.23887i	0.638781	+	0.307621i
$903$	35.8803	−	17.2790i	1.19402	−	0.575010i
$904$	−2.73009	−	11.9613i	−0.0908015	−	0.397827i
$905$	−0.867361	+	3.80016i	−0.0288321	+	0.126321i
$906$	5.47439	+	2.63633i	0.181874	+	0.0875861i
$907$	−1.42139	−	1.78237i	−0.0471965	−	0.0591826i	0.757673	−	0.652634i	$-0.226336\pi$
$907$	−1.42139	−	1.78237i	−0.0471965	−	0.0591826i	−0.804870	+	0.593452i	$0.797765\pi$
$908$	20.2665	+	25.4133i	0.672566	+	0.843371i
$909$	4.06145	−	1.95589i	0.134710	−	0.0648728i
$910$	−1.86561	+	2.33941i	−0.0618445	+	0.0775505i
$911$	−18.8815			−0.625572			−0.312786	−	0.949824i	$-0.601262\pi$
$911$	−18.8815			−0.625572			−0.312786	+	0.949824i	$0.601262\pi$
$912$	0.174233	−	0.218481i	0.00576942	−	0.00723462i
$913$	5.84443	−	25.6061i	0.193422	−	0.847438i
$914$	5.92860	−	25.9749i	0.196101	−	0.859173i
$915$	1.23310	−	1.54626i	0.0407651	−	0.0511178i
$916$	4.06096			0.134178
$917$	−39.8867	+	50.0163i	−1.31717	+	1.65168i
$918$	2.81187	−	1.35413i	0.0928056	−	0.0446928i
$919$	−10.2122	−	12.8057i	−0.336869	−	0.422420i	0.584328	−	0.811518i	$-0.301358\pi$
$919$	−10.2122	−	12.8057i	−0.336869	−	0.422420i	−0.921197	+	0.389098i	$0.872787\pi$
$920$	−3.72536	−	4.67145i	−0.122821	−	0.154013i
$921$	2.52801	+	1.21743i	0.0833007	+	0.0401155i
$922$	3.82088	−	16.7404i	0.125834	−	0.551315i
$923$	5.81951	+	25.4970i	0.191552	+	0.839243i
$924$	22.0558	−	10.6215i	0.725582	−	0.349422i
$925$	1.68715	+	0.812490i	0.0554733	+	0.0267145i
$926$	4.65908	+	20.4128i	0.153107	+	0.670805i
$927$	8.12388			0.266823
$928$	0.483252	+	29.5593i	0.0158635	+	0.970332i
$929$	31.0737			1.01950			0.509748	−	0.860324i	$-0.329739\pi$
$929$	31.0737			1.01950			0.509748	+	0.860324i	$0.329739\pi$
$930$	0.189999	+	0.832441i	0.00623032	+	0.0272968i
$931$	−14.1285	−	6.80391i	−0.463041	−	0.222989i
$932$	−3.50860	+	1.68965i	−0.114928	+	0.0553465i
$933$	3.49810	+	15.3262i	0.114523	+	0.501757i
$934$	4.00034	−	17.5267i	0.130895	−	0.573490i
$935$	−3.66041	−	1.76276i	−0.119708	−	0.0576484i
$936$	4.10680	+	5.14977i	0.134235	+	0.168325i
$937$	16.3021	+	20.4422i	0.532567	+	0.667818i	0.973224	−	0.229858i	$-0.0738261\pi$
$937$	16.3021	+	20.4422i	0.532567	+	0.667818i	−0.440657	+	0.897675i	$0.645255\pi$
$938$	−11.8093	+	5.68705i	−0.385587	+	0.185689i
$939$	−11.3630	+	14.2487i	−0.370817	+	0.464989i
$940$	−2.16366			−0.0705708
$941$	24.9721	−	31.3140i	0.814068	−	1.02081i	−0.185206	−	0.982700i	$-0.559295\pi$
$941$	24.9721	−	31.3140i	0.814068	−	1.02081i	0.999274	−	0.0381090i	$-0.0121334\pi$
$942$	2.72612	−	11.9439i	0.0888219	−	0.389154i
$943$	−8.95972	+	39.2551i	−0.291769	+	1.27832i
$944$	0.956860	−	1.19986i	0.0311432	−	0.0390523i
$945$	−1.43620			−0.0467197
$946$	18.8703	−	23.6626i	0.613527	−	0.769339i
$947$	−37.7132	+	18.1617i	−1.22551	+	0.590177i	−0.930842	−	0.365421i	$-0.880925\pi$
$947$	−37.7132	+	18.1617i	−1.22551	+	0.590177i	−0.294673	+	0.955598i	$0.595211\pi$
$948$	−4.90245	−	6.14748i	−0.159224	−	0.199661i
$949$	−16.0635	−	20.1430i	−0.521444	−	0.653870i
$950$	−3.45966	−	1.66608i	−0.112246	−	0.0540549i
$951$	0.418332	−	1.83283i	0.0135653	−	0.0594336i
$952$	11.0641	+	48.4748i	0.358588	+	1.57108i
$953$	27.6890	−	13.3343i	0.896934	−	0.431941i	0.0721537	−	0.997394i	$-0.477013\pi$
$953$	27.6890	−	13.3343i	0.896934	−	0.431941i	0.824781	+	0.565453i	$0.191299\pi$
$954$	2.38636	+	1.14921i	0.0772614	+	0.0372071i
$955$	−0.0736311	−	0.322599i	−0.00238265	−	0.0104391i
$956$	21.3645			0.690976
$957$	−17.8361	−	13.7529i	−0.576561	−	0.444570i
$958$	−20.6233			−0.666309
$959$	−10.9254	−	47.8672i	−0.352799	−	1.54571i
$960$	1.45914	+	0.702686i	0.0470936	+	0.0226791i
$961$	18.2856	−	8.80590i	0.589859	−	0.284061i
$962$	0.176496	+	0.773281i	0.00569047	+	0.0249316i
$963$	−2.11822	+	9.28054i	−0.0682587	+	0.299061i
$964$	5.88676	+	2.83491i	0.189600	+	0.0913064i
$965$	3.66077	+	4.59046i	0.117844	+	0.147772i
$966$	−20.8341	−	26.1252i	−0.670327	−	0.840563i
$967$	10.3394	−	4.97917i	0.332491	−	0.160119i	−0.260188	−	0.965558i	$-0.583785\pi$
$967$	10.3394	−	4.97917i	0.332491	−	0.160119i	0.592679	+	0.805439i	$0.298070\pi$
$968$	11.7181	−	14.6940i	0.376634	−	0.472284i
$969$	2.90580			0.0933479
$970$	−0.0818131	+	0.102590i	−0.00262686	+	0.00329398i
$971$	2.87015	−	12.5749i	0.0921074	−	0.403549i	−0.907766	−	0.419477i	$-0.862213\pi$
$971$	2.87015	−	12.5749i	0.0921074	−	0.403549i	0.999873	+	0.0159286i	$0.00507046\pi$
$972$	−0.258465	+	1.13241i	−0.00829028	+	0.0363221i
$973$	−39.2215	+	49.1822i	−1.25738	+	1.57671i
$974$	−1.57525			−0.0504744
$975$	6.97782	−	8.74991i	0.223469	−	0.280221i
$976$	−2.04927	+	0.986879i	−0.0655957	+	0.0315892i
$977$	−38.6812	−	48.5047i	−1.23752	−	1.55180i	−0.714871	−	0.699257i	$-0.753514\pi$
$977$	−38.6812	−	48.5047i	−1.23752	−	1.55180i	−0.522651	−	0.852547i	$-0.675057\pi$
$978$	5.79835	+	7.27090i	0.185411	+	0.232498i
$979$	21.5015	+	10.3546i	0.687192	+	0.330934i
$980$	1.35494	−	5.93637i	0.0432819	−	0.189630i
$981$	1.65364	+	7.24508i	0.0527968	+	0.231318i
$982$	24.2851	−	11.6951i	0.774969	−	0.373205i
$983$	−8.01683	−	3.86070i	−0.255697	−	0.123137i	0.301645	−	0.953420i	$-0.402464\pi$
$983$	−8.01683	−	3.86070i	−0.255697	−	0.123137i	−0.557342	+	0.830283i	$0.688179\pi$
$984$	−3.58173	−	15.6926i	−0.114181	−	0.500261i
$985$	1.47012			0.0468420
$986$	12.9670	−	10.6923i	0.412954	−	0.340511i
$987$	−32.9353			−1.04834
$988$	0.501371	+	2.19665i	0.0159507	+	0.0698848i
$989$	51.5630	+	24.8314i	1.63961	+	0.789593i
$990$	−0.983399	+	0.473580i	−0.0312545	+	0.0150514i
$991$	−0.631754	−	2.76790i	−0.0200683	−	0.0879251i	0.963902	−	0.266257i	$-0.0857870\pi$
$991$	−0.631754	−	2.76790i	−0.0200683	−	0.0879251i	−0.983970	+	0.178332i	$0.942930\pi$
$992$	−3.99675	+	17.5109i	−0.126897	+	0.555971i
$993$	5.53273	+	2.66442i	0.175576	+	0.0845528i
$994$	33.0685	+	41.4666i	1.04887	+	1.31524i
$995$	−0.498593	−	0.625216i	−0.0158065	−	0.0198207i
$996$	−6.57190	+	3.16486i	−0.208239	+	0.100282i
$997$	−35.5570	+	44.5871i	−1.12610	+	1.41209i	−0.227248	+	0.973837i	$0.572973\pi$
$997$	−35.5570	+	44.5871i	−1.12610	+	1.41209i	−0.898853	+	0.438249i	$0.855599\pi$
$998$	12.7169			0.402546
$999$	−0.237365	+	0.297647i	−0.00750991	+	0.00941713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.g.b.7.2	✓	18
3.2	odd	2		261.2.k.b.181.2		18
29.5	even	14		2523.2.a.q.1.6		9
29.24	even	7		2523.2.a.p.1.4		9
29.25	even	7	inner	87.2.g.b.25.2	yes	18
87.5	odd	14		7569.2.a.bk.1.4		9
87.53	odd	14		7569.2.a.bl.1.6		9
87.83	odd	14		261.2.k.b.199.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.7.2	✓	18	1.1	even	1	trivial
87.2.g.b.25.2	yes	18	29.25	even	7	inner
261.2.k.b.181.2		18	3.2	odd	2
261.2.k.b.199.2		18	87.83	odd	14
2523.2.a.p.1.4		9	29.24	even	7
2523.2.a.q.1.6		9	29.5	even	14
7569.2.a.bk.1.4		9	87.5	odd	14
7569.2.a.bl.1.6		9	87.53	odd	14

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203758 + 0.892721i) q^{2} +(0.900969 + 0.433884i) q^{3} +(1.04650 - 0.503970i) q^{4} +(-0.0634200 - 0.277861i) q^{5} +(-0.203758 + 0.892721i) q^{6} +(-4.54015 - 2.18642i) q^{7} +(1.80497 + 2.26336i) q^{8} +(0.623490 + 0.781831i) q^{9} +(0.235130 - 0.113233i) q^{10} +(-2.60766 + 3.26990i) q^{11} +1.16153 q^{12} +(1.41861 - 1.77888i) q^{13} +(1.02677 - 4.49858i) q^{14} +(0.0634200 - 0.277861i) q^{15} +(-0.204365 + 0.256265i) q^{16} -3.40834 q^{17} +(-0.570916 + 0.715906i) q^{18} +(-0.768127 + 0.369911i) q^{19} +(-0.206403 - 0.258821i) q^{20} +(-3.14188 - 3.93979i) q^{21} +(-3.45044 - 1.66164i) q^{22} +(1.61144 - 7.06017i) q^{23} +(0.644186 + 2.82237i) q^{24} +(4.43166 - 2.13417i) q^{25} +(1.87710 + 0.903962i) q^{26} +(0.222521 + 0.974928i) q^{27} -5.85318 q^{28} +(2.41553 + 4.81302i) q^{29} +0.260975 q^{30} +(0.728037 + 3.18974i) q^{31} +(4.94610 + 2.38192i) q^{32} +(-3.76817 + 1.81466i) q^{33} +(-0.694475 - 3.04269i) q^{34} +(-0.319585 + 1.40019i) q^{35} +(1.04650 + 0.503970i) q^{36} +(0.237365 + 0.297647i) q^{37} +(-0.486739 - 0.610351i) q^{38} +(2.04995 - 0.987204i) q^{39} +(0.514429 - 0.645074i) q^{40} -5.56008 q^{41} +(2.87695 - 3.60758i) q^{42} +(-1.75856 + 7.70474i) q^{43} +(-1.08099 + 4.73615i) q^{44} +(0.177699 - 0.222827i) q^{45} +6.63110 q^{46} +(4.07504 - 5.10993i) q^{47} +(-0.295316 + 0.142216i) q^{48} +(11.4681 + 14.3805i) q^{49} +(2.80821 + 3.52138i) q^{50} +(-3.07081 - 1.47882i) q^{51} +(0.588079 - 2.57654i) q^{52} +(-0.643658 - 2.82005i) q^{53} +(-0.824998 + 0.397298i) q^{54} +(1.07396 + 0.517190i) q^{55} +(-3.24617 - 14.2224i) q^{56} -0.852557 q^{57} +(-3.80450 + 3.13709i) q^{58} -4.68212 q^{59} +(-0.0736644 - 0.322745i) q^{60} +(6.25207 + 3.01084i) q^{61} +(-2.69920 + 1.29987i) q^{62} +(-1.12132 - 4.91284i) q^{63} +(-1.26445 + 5.53994i) q^{64} +(-0.584250 - 0.281360i) q^{65} +(-2.38778 - 2.99418i) q^{66} +(-1.77109 - 2.22087i) q^{67} +(-3.56684 + 1.71770i) q^{68} +(4.51515 - 5.66182i) q^{69} -1.31510 q^{70} +(-7.16657 + 8.98660i) q^{71} +(-0.644186 + 2.82237i) q^{72} +(2.51970 - 11.0395i) q^{73} +(-0.217350 + 0.272549i) q^{74} +4.91877 q^{75} +(-0.617425 + 0.774227i) q^{76} +(18.9885 - 9.14439i) q^{77} +(1.29899 + 1.62888i) q^{78} +(-4.22068 - 5.29256i) q^{79} +(0.0841670 + 0.0405327i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-1.13291 - 4.96360i) q^{82} +(-5.65795 + 2.72473i) q^{83} +(-5.27353 - 2.53960i) q^{84} +(0.216157 + 0.947045i) q^{85} -7.23650 q^{86} +(0.0880280 + 5.38445i) q^{87} -12.1077 q^{88} +(-1.26972 - 5.56302i) q^{89} +(0.235130 + 0.113233i) q^{90} +(-10.3301 + 4.97470i) q^{91} +(-1.87174 - 8.20062i) q^{92} +(-0.728037 + 3.18974i) q^{93} +(5.39206 + 2.59668i) q^{94} +(0.151498 + 0.189973i) q^{95} +(3.42281 + 4.29207i) q^{96} +(-0.453007 + 0.218157i) q^{97} +(-10.5011 + 13.1679i) q^{98} -4.18236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

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