LMFDB - Embedded newform 315.2.t.b.131.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.5
Character	$\chi$	$=$	315.131
Dual form			315.2.t.b.101.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23569i q^{2} +(0.460303 - 1.66977i) q^{3} +0.473066 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.06332 - 0.568792i) q^{6} +(2.47654 + 0.930987i) q^{7} -3.05595i q^{8} +(-2.57624 - 1.53720i) q^{9} +O(q^{10})$	\(q-1.23569i q^{2} +(0.460303 - 1.66977i) q^{3} +0.473066 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.06332 - 0.568792i) q^{6} +(2.47654 + 0.930987i) q^{7} -3.05595i q^{8} +(-2.57624 - 1.53720i) q^{9} +(1.07014 - 0.617846i) q^{10} +(-1.10058 - 0.635419i) q^{11} +(0.217754 - 0.789910i) q^{12} +(1.67710 + 0.968277i) q^{13} +(1.15041 - 3.06024i) q^{14} +(1.67621 - 0.436249i) q^{15} -2.83008 q^{16} +(0.676881 + 1.17239i) q^{17} +(-1.89950 + 3.18344i) q^{18} +(-0.724595 - 0.418345i) q^{19} +(0.236533 + 0.409687i) q^{20} +(2.69449 - 3.70671i) q^{21} +(-0.785182 + 1.35997i) q^{22} +(-0.914519 + 0.527998i) q^{23} +(-5.10272 - 1.40666i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.19649 - 2.07238i) q^{26} +(-3.75261 + 3.59415i) q^{27} +(1.17157 + 0.440418i) q^{28} +(-8.49399 + 4.90401i) q^{29} +(-0.539070 - 2.07128i) q^{30} -2.24847i q^{31} -2.61479i q^{32} +(-1.56760 + 1.54522i) q^{33} +(1.44872 - 0.836416i) q^{34} +(0.432012 + 2.61024i) q^{35} +(-1.21873 - 0.727195i) q^{36} +(-4.38029 + 7.58689i) q^{37} +(-0.516945 + 0.895376i) q^{38} +(2.38877 - 2.35467i) q^{39} +(2.64653 - 1.52797i) q^{40} +(3.47470 - 6.01835i) q^{41} +(-4.58035 - 3.32956i) q^{42} +(3.63907 + 6.30306i) q^{43} +(-0.520646 - 0.300595i) q^{44} +(0.0431301 - 2.99969i) q^{45} +(0.652443 + 1.13006i) q^{46} -1.69463 q^{47} +(-1.30269 + 4.72557i) q^{48} +(5.26652 + 4.61126i) q^{49} +(1.07014 + 0.617846i) q^{50} +(2.26919 - 0.590578i) q^{51} +(0.793381 + 0.458059i) q^{52} +(-0.148100 + 0.0855054i) q^{53} +(4.44126 + 4.63707i) q^{54} -1.27084i q^{55} +(2.84505 - 7.56818i) q^{56} +(-1.03207 + 1.01734i) q^{57} +(6.05984 + 10.4960i) q^{58} +9.77894 q^{59} +(0.792959 - 0.206375i) q^{60} -2.84883i q^{61} -2.77842 q^{62} +(-4.94906 - 6.20538i) q^{63} -8.89123 q^{64} +1.93655i q^{65} +(1.90942 + 1.93707i) q^{66} +13.0901 q^{67} +(0.320209 + 0.554619i) q^{68} +(0.460678 + 1.77007i) q^{69} +(3.22546 - 0.533834i) q^{70} -6.48936i q^{71} +(-4.69759 + 7.87286i) q^{72} +(9.10680 - 5.25781i) q^{73} +(9.37506 + 5.41269i) q^{74} +(1.21591 + 1.23352i) q^{75} +(-0.342781 - 0.197905i) q^{76} +(-2.13406 - 2.59827i) q^{77} +(-2.90965 - 2.95179i) q^{78} -16.0108 q^{79} +(-1.41504 - 2.45092i) q^{80} +(4.27405 + 7.92038i) q^{81} +(-7.43683 - 4.29366i) q^{82} +(4.56456 + 7.90605i) q^{83} +(1.27467 - 1.75352i) q^{84} +(-0.676881 + 1.17239i) q^{85} +(7.78864 - 4.49677i) q^{86} +(4.27874 + 16.4403i) q^{87} +(-1.94181 + 3.36331i) q^{88} +(-9.41641 + 16.3097i) q^{89} +(-3.70669 - 0.0532955i) q^{90} +(3.25197 + 3.95934i) q^{91} +(-0.432628 + 0.249778i) q^{92} +(-3.75443 - 1.03498i) q^{93} +2.09404i q^{94} -0.836690i q^{95} +(-4.36609 - 1.20360i) q^{96} +(-8.14174 + 4.70063i) q^{97} +(5.69810 - 6.50780i) q^{98} +(1.85859 + 3.32880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.23569i		−	0.873766i	−0.899518	−	0.436883i	$-0.856082\pi$
$2$		−	1.23569i		−	0.873766i	0.899518	−	0.436883i	$-0.143918\pi$
$3$	0.460303	−	1.66977i	0.265756	−	0.964040i
$3$	0.460303	−	1.66977i	0.265756	−	0.964040i
$4$	0.473066			0.236533
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.06332	−	0.568792i	−0.842346	−	0.232209i
$7$	2.47654	+	0.930987i	0.936045	+	0.351880i
$7$	2.47654	+	0.930987i	0.936045	+	0.351880i
$8$		−	3.05595i		−	1.08044i
$9$	−2.57624	−	1.53720i	−0.858748	−	0.512399i
$10$	1.07014	−	0.617846i	0.338408	−	0.195380i
$11$	−1.10058	−	0.635419i	−0.331837	−	0.191586i	0.324820	−	0.945776i	$-0.394696\pi$
$11$	−1.10058	−	0.635419i	−0.331837	−	0.191586i	−0.656656	+	0.754190i	$0.728030\pi$
$12$	0.217754	−	0.789910i	0.0628600	−	0.228027i
$13$	1.67710	+	0.968277i	0.465145	+	0.268552i	0.714205	−	0.699936i	$-0.246788\pi$
$13$	1.67710	+	0.968277i	0.465145	+	0.268552i	−0.249060	+	0.968488i	$0.580122\pi$
$14$	1.15041	−	3.06024i	0.307461	−	0.817884i
$15$	1.67621	−	0.436249i	0.432796	−	0.112639i
$16$	−2.83008			−0.707519
$17$	0.676881	+	1.17239i	0.164168	+	0.284347i	0.936359	−	0.351043i	$-0.114173\pi$
$17$	0.676881	+	1.17239i	0.164168	+	0.284347i	−0.772192	+	0.635390i	$0.780839\pi$
$18$	−1.89950	+	3.18344i	−0.447717	+	0.750344i
$19$	−0.724595	−	0.418345i	−0.166233	−	0.0959749i	0.414575	−	0.910015i	$-0.363930\pi$
$19$	−0.724595	−	0.418345i	−0.166233	−	0.0959749i	−0.580809	+	0.814040i	$0.697264\pi$
$20$	0.236533	+	0.409687i	0.0528904	+	0.0916088i
$21$	2.69449	−	3.70671i	0.587986	−	0.808871i
$22$	−0.785182	+	1.35997i	−0.167401	+	0.289948i
$23$	−0.914519	+	0.527998i	−0.190690	+	0.110095i	−0.592306	−	0.805713i	$-0.701782\pi$
$23$	−0.914519	+	0.527998i	−0.190690	+	0.110095i	0.401615	+	0.915808i	$0.368449\pi$
$24$	−5.10272	−	1.40666i	−1.04159	−	0.287133i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.19649	−	2.07238i	0.234651	−	0.406428i
$27$	−3.75261	+	3.59415i	−0.722190	+	0.691694i
$28$	1.17157	+	0.440418i	0.221405	+	0.0832313i
$29$	−8.49399	+	4.90401i	−1.57729	+	0.910651i	−0.582059	+	0.813146i	$0.697753\pi$
$29$	−8.49399	+	4.90401i	−1.57729	+	0.910651i	−0.995235	+	0.0975049i	$0.968914\pi$
$30$	−0.539070	−	2.07128i	−0.0984202	−	0.378162i
$31$		−	2.24847i		−	0.403838i	−0.979402	−	0.201919i	$-0.935282\pi$
$31$		−	2.24847i		−	0.403838i	0.979402	−	0.201919i	$-0.0647177\pi$
$32$		−	2.61479i		−	0.462234i
$33$	−1.56760	+	1.54522i	−0.272884	+	0.268989i
$34$	1.44872	−	0.836416i	0.248453	−	0.143444i
$35$	0.432012	+	2.61024i	0.0730234	+	0.441211i
$36$	−1.21873	−	0.727195i	−0.203122	−	0.121199i
$37$	−4.38029	+	7.58689i	−0.720116	+	1.24728i	0.240837	+	0.970566i	$0.422578\pi$
$37$	−4.38029	+	7.58689i	−0.720116	+	1.24728i	−0.960953	+	0.276712i	$0.910755\pi$
$38$	−0.516945	+	0.895376i	−0.0838596	+	0.145249i
$39$	2.38877	−	2.35467i	0.382510	−	0.377050i
$40$	2.64653	−	1.52797i	0.418453	−	0.241594i
$41$	3.47470	−	6.01835i	0.542657	−	0.939909i	−0.456094	−	0.889932i	$-0.650752\pi$
$41$	3.47470	−	6.01835i	0.542657	−	0.939909i	0.998750	−	0.0499771i	$-0.0159148\pi$
$42$	−4.58035	−	3.32956i	−0.706764	−	0.513762i
$43$	3.63907	+	6.30306i	0.554953	+	0.961208i	0.997907	+	0.0646631i	$0.0205973\pi$
$43$	3.63907	+	6.30306i	0.554953	+	0.961208i	−0.442954	+	0.896544i	$0.646069\pi$
$44$	−0.520646	−	0.300595i	−0.0784903	−	0.0453164i
$45$	0.0431301	−	2.99969i	0.00642946	−	0.447167i
$46$	0.652443	+	1.13006i	0.0961974	+	0.166619i
$47$	−1.69463			−0.247187			−0.123593	−	0.992333i	$-0.539442\pi$
$47$	−1.69463			−0.247187			−0.123593	+	0.992333i	$0.539442\pi$
$48$	−1.30269	+	4.72557i	−0.188027	+	0.682077i
$49$	5.26652	+	4.61126i	0.752361	+	0.658751i
$50$	1.07014	+	0.617846i	0.151341	+	0.0873766i
$51$	2.26919	−	0.590578i	0.317750	−	0.0826975i
$52$	0.793381	+	0.458059i	0.110022	+	0.0635213i
$53$	−0.148100	+	0.0855054i	−0.0203431	+	0.0117451i	−0.510137	−	0.860093i	$-0.670405\pi$
$53$	−0.148100	+	0.0855054i	−0.0203431	+	0.0117451i	0.489794	+	0.871838i	$0.337072\pi$
$54$	4.44126	+	4.63707i	0.604379	+	0.631026i
$55$		−	1.27084i		−	0.171360i
$56$	2.84505	−	7.56818i	0.380186	−	1.01134i
$57$	−1.03207	+	1.01734i	−0.136701	+	0.134750i
$58$	6.05984	+	10.4960i	0.795696	+	1.37819i
$59$	9.77894			1.27311			0.636555	−	0.771232i	$-0.280359\pi$
$59$	9.77894			1.27311			0.636555	+	0.771232i	$0.280359\pi$
$60$	0.792959	−	0.206375i	0.102371	−	0.0266429i
$61$		−	2.84883i		−	0.364755i	−0.983229	−	0.182378i	$-0.941621\pi$
$61$		−	2.84883i		−	0.364755i	0.983229	−	0.182378i	$-0.0583793\pi$
$62$	−2.77842			−0.352860
$63$	−4.94906	−	6.20538i	−0.623523	−	0.781805i
$64$	−8.89123			−1.11140
$65$			1.93655i			0.240200i
$66$	1.90942	+	1.93707i	0.235033	+	0.238437i
$67$	13.0901			1.59921			0.799606	−	0.600525i	$-0.205042\pi$
$67$	13.0901			1.59921			0.799606	+	0.600525i	$0.205042\pi$
$68$	0.320209	+	0.554619i	0.0388311	+	0.0672574i
$69$	0.460678	+	1.77007i	0.0554591	+	0.213092i
$70$	3.22546	−	0.533834i	0.385516	−	0.0638054i
$71$		−	6.48936i		−	0.770145i	−0.922886	−	0.385072i	$-0.874176\pi$
$71$		−	6.48936i		−	0.770145i	0.922886	−	0.385072i	$-0.125824\pi$
$72$	−4.69759	+	7.87286i	−0.553617	+	0.927826i
$73$	9.10680	−	5.25781i	1.06587	−	0.615380i	0.138820	−	0.990318i	$-0.455669\pi$
$73$	9.10680	−	5.25781i	1.06587	−	0.615380i	0.927050	+	0.374937i	$0.122336\pi$
$74$	9.37506	+	5.41269i	1.08983	+	0.629213i
$75$	1.21591	+	1.23352i	0.140401	+	0.142434i
$76$	−0.342781	−	0.197905i	−0.0393197	−	0.0227012i
$77$	−2.13406	−	2.59827i	−0.243199	−	0.296100i
$78$	−2.90965	−	2.95179i	−0.329453	−	0.334224i
$79$	−16.0108			−1.80136			−0.900679	−	0.434486i	$-0.856930\pi$
$79$	−16.0108			−1.80136			−0.900679	+	0.434486i	$0.856930\pi$
$80$	−1.41504	−	2.45092i	−0.158206	−	0.274021i
$81$	4.27405	+	7.92038i	0.474895	+	0.880043i
$82$	−7.43683	−	4.29366i	−0.821260	−	0.474155i
$83$	4.56456	+	7.90605i	0.501026	+	0.867802i	0.999999	+	0.00118486i	$0.000377154\pi$
$83$	4.56456	+	7.90605i	0.501026	+	0.867802i	−0.498974	+	0.866617i	$0.666290\pi$
$84$	1.27467	−	1.75352i	0.139078	−	0.191325i
$85$	−0.676881	+	1.17239i	−0.0734181	+	0.127164i
$86$	7.78864	−	4.49677i	0.839871	−	0.484899i
$87$	4.27874	+	16.4403i	0.458729	+	1.76259i
$88$	−1.94181	+	3.36331i	−0.206997	+	0.358530i
$89$	−9.41641	+	16.3097i	−0.998138	+	1.72883i	−0.446240	+	0.894913i	$0.647237\pi$
$89$	−9.41641	+	16.3097i	−0.998138	+	1.72883i	−0.551898	+	0.833912i	$0.686096\pi$
$90$	−3.70669	−	0.0532955i	−0.390720	−	0.00561784i
$91$	3.25197	+	3.95934i	0.340899	+	0.415052i
$92$	−0.432628	+	0.249778i	−0.0451046	+	0.0260411i
$93$	−3.75443	−	1.03498i	−0.389316	−	0.107322i
$94$			2.09404i			0.215983i
$95$		−	0.836690i		−	0.0858426i
$96$	−4.36609	−	1.20360i	−0.445612	−	0.122841i
$97$	−8.14174	+	4.70063i	−0.826668	+	0.477277i	−0.852711	−	0.522384i	$-0.825043\pi$
$97$	−8.14174	+	4.70063i	−0.826668	+	0.477277i	0.0260423	+	0.999661i	$0.491710\pi$
$98$	5.69810	−	6.50780i	0.575595	−	0.657387i
$99$	1.85859	+	3.32880i	0.186795	+	0.334557i
$100$	−0.236533	+	0.409687i	−0.0236533	+	0.0409687i
$101$	6.17344	−	10.6927i	0.614280	−	1.06396i	−0.376230	−	0.926526i	$-0.622780\pi$
$101$	6.17344	−	10.6927i	0.614280	−	1.06396i	0.990510	−	0.137438i	$-0.0438869\pi$
$102$	−0.729772	−	2.80402i	−0.0722582	−	0.277640i
$103$	8.07033	−	4.65941i	0.795194	−	0.459105i	−0.0465942	−	0.998914i	$-0.514837\pi$
$103$	8.07033	−	4.65941i	0.795194	−	0.459105i	0.841788	+	0.539809i	$0.181503\pi$
$104$	2.95900	−	5.12514i	0.290154	−	0.502562i
$105$	4.55735	+	0.480142i	0.444752	+	0.0468571i
$106$	0.105658	+	0.183006i	0.0102624	+	0.0177751i
$107$	8.23320	+	4.75344i	0.795934	+	0.459532i	0.842047	−	0.539404i	$-0.181350\pi$
$107$	8.23320	+	4.75344i	0.795934	+	0.459532i	−0.0461137	+	0.998936i	$0.514684\pi$
$108$	−1.77523	+	1.70027i	−0.170822	+	0.163608i
$109$	−3.22701	−	5.58935i	−0.309092	−	0.535363i	0.669072	−	0.743197i	$-0.266692\pi$
$109$	−3.22701	−	5.58935i	−0.309092	−	0.535363i	−0.978164	+	0.207835i	$0.933358\pi$
$110$	−1.57036			−0.149728
$111$	10.6521	+	10.8063i	1.01105	+	1.02569i
$112$	−7.00881	−	2.63477i	−0.662270	−	0.248962i
$113$	−11.6622	−	6.73319i	−1.09709	−	0.633405i	−0.161635	−	0.986851i	$-0.551677\pi$
$113$	−11.6622	−	6.73319i	−1.09709	−	0.633405i	−0.935455	+	0.353446i	$0.885010\pi$
$114$	1.25712	+	1.27532i	0.117740	+	0.119445i
$115$	−0.914519	−	0.527998i	−0.0852794	−	0.0492361i
$116$	−4.01822	+	2.31992i	−0.373082	+	0.215399i
$117$	−2.83220	−	5.07256i	−0.261837	−	0.468958i
$118$		−	12.0838i		−	1.11240i
$119$	0.584842	+	3.53365i	0.0536124	+	0.323929i
$120$	−1.33316	−	5.12241i	−0.121700	−	0.467610i
$121$	−4.69249	−	8.12762i	−0.426590	−	0.738875i
$122$	−3.52027			−0.318711
$123$	−8.44983	−	8.57220i	−0.761896	−	0.772929i
$124$		−	1.06368i		−	0.0955209i
$125$	−1.00000			−0.0894427
$126$	−7.66794	+	6.11552i	−0.683114	+	0.544814i
$127$	−9.24610			−0.820459			−0.410229	−	0.911982i	$-0.634551\pi$
$127$	−9.24610			−0.820459			−0.410229	+	0.911982i	$0.634551\pi$
$128$			5.75724i			0.508873i
$129$	12.1997	−	3.17509i	1.07413	−	0.279551i
$130$	2.39298			0.209879
$131$	6.24793	+	10.8217i	0.545884	+	0.945499i	0.998551	+	0.0538192i	$0.0171395\pi$
$131$	6.24793	+	10.8217i	0.545884	+	0.945499i	−0.452667	+	0.891680i	$0.649527\pi$
$132$	−0.741578	+	0.730992i	−0.0645461	+	0.0636247i
$133$	−1.40502	−	1.71064i	−0.121830	−	0.148331i
$134$		−	16.1753i		−	1.39734i
$135$	−4.98893	−	1.45278i	−0.429379	−	0.125036i
$136$	3.58277	−	2.06851i	0.307220	−	0.177373i
$137$	−0.113595	−	0.0655839i	−0.00970505	−	0.00560321i	0.495140	−	0.868813i	$-0.335117\pi$
$137$	−0.113595	−	0.0655839i	−0.00970505	−	0.00560321i	−0.504845	+	0.863210i	$0.668450\pi$
$138$	2.18726	−	0.569256i	0.186192	−	0.0484583i
$139$	−3.27427	−	1.89040i	−0.277720	−	0.160342i	0.354671	−	0.934991i	$-0.384593\pi$
$139$	−3.27427	−	1.89040i	−0.277720	−	0.160342i	−0.632391	+	0.774650i	$0.717926\pi$
$140$	0.204370	+	1.23482i	0.0172724	+	0.104361i
$141$	−0.780041	+	2.82963i	−0.0656913	+	0.238298i
$142$	−8.01884			−0.672927
$143$	−1.23052	−	2.13133i	−0.102901	−	0.178231i
$144$	7.29096	+	4.35039i	0.607580	+	0.362532i
$145$	−8.49399	−	4.90401i	−0.705387	−	0.407256i
$146$	−6.49703	−	11.2532i	−0.537698	−	0.931321i
$147$	10.1239	−	6.67129i	0.835007	−	0.550239i
$148$	−2.07217	+	3.58910i	−0.170331	+	0.295022i
$149$	2.07964	−	1.20068i	0.170371	−	0.0983635i	−0.412390	−	0.911007i	$-0.635306\pi$
$149$	2.07964	−	1.20068i	0.170371	−	0.0983635i	0.582761	+	0.812644i	$0.301973\pi$
$150$	1.52425	−	1.50249i	0.124454	−	0.122678i
$151$	−10.8621	+	18.8137i	−0.883946	+	1.53104i	−0.0370284	+	0.999314i	$0.511789\pi$
$151$	−10.8621	+	18.8137i	−0.883946	+	1.53104i	−0.846917	+	0.531725i	$0.821544\pi$
$152$	−1.27844	+	2.21432i	−0.103695	+	0.179605i
$153$	0.0583879	−	4.06087i	0.00472038	−	0.328302i
$154$	−3.21065	+	2.63704i	−0.258722	+	0.212499i
$155$	1.94723	−	1.12424i	0.156406	−	0.0903008i
$156$	1.13005	−	1.11392i	0.0904762	−	0.0891846i
$157$		−	12.2170i		−	0.975024i	−0.873116	−	0.487512i	$-0.837904\pi$
$157$		−	12.2170i		−	0.975024i	0.873116	−	0.487512i	$-0.162096\pi$
$158$			19.7844i			1.57397i
$159$	0.0746034	+	0.286650i	0.00591643	+	0.0227328i
$160$	2.26448	−	1.30740i	0.179023	−	0.103359i
$161$	−2.75641	+	0.456203i	−0.217235	+	0.0359539i
$162$	9.78715	−	5.28141i	0.768951	−	0.414947i
$163$	8.73352	−	15.1269i	0.684062	−	1.18483i	−0.289668	−	0.957127i	$-0.593545\pi$
$163$	8.73352	−	15.1269i	0.684062	−	1.18483i	0.973731	−	0.227703i	$-0.0731216\pi$
$164$	1.64376	−	2.84708i	0.128356	−	0.222319i
$165$	−2.12200	−	0.584970i	−0.165198	−	0.0455399i
$166$	9.76944	−	5.64039i	0.758256	−	0.437779i
$167$	−3.83353	+	6.63987i	−0.296648	+	0.513809i	−0.975367	−	0.220589i	$-0.929202\pi$
$167$	−3.83353	+	6.63987i	−0.296648	+	0.513809i	0.678719	+	0.734398i	$0.262535\pi$
$168$	−11.3275	−	8.23422i	−0.873937	−	0.635284i
$169$	−4.62488	−	8.01053i	−0.355760	−	0.616194i
$170$	1.44872	+	0.836416i	0.111111	+	0.0641502i
$171$	1.22365	+	2.19160i	0.0935751	+	0.167596i
$172$	1.72152	+	2.98176i	0.131265	+	0.227357i
$173$	−16.0101			−1.21722			−0.608611	−	0.793469i	$-0.708273\pi$
$173$	−16.0101			−1.21722			−0.608611	+	0.793469i	$0.708273\pi$
$174$	20.3152	−	5.28721i	1.54009	−	0.400822i
$175$	−2.04453	+	1.67925i	−0.154552	+	0.126940i
$176$	3.11472	+	1.79828i	0.234781	+	0.135551i
$177$	4.50127	−	16.3285i	0.338336	−	1.22733i
$178$	20.1538	+	11.6358i	1.51059	+	0.872139i
$179$	−13.6009	+	7.85251i	−1.01658	+	0.586924i	−0.913112	−	0.407708i	$-0.866328\pi$
$179$	−13.6009	+	7.85251i	−1.01658	+	0.586924i	−0.103470	+	0.994633i	$0.532995\pi$
$180$	0.0204034	−	1.41905i	0.00152078	−	0.105770i
$181$		−	6.50920i		−	0.483825i	−0.970298	−	0.241912i	$-0.922225\pi$
$181$		−	6.50920i		−	0.483825i	0.970298	−	0.241912i	$-0.0777747\pi$
$182$	4.89253	−	4.01843i	0.362658	−	0.297866i
$183$	−4.75688	−	1.31132i	−0.351639	−	0.0969359i
$184$	1.61353	+	2.79472i	0.118951	+	0.206030i
$185$	−8.76059			−0.644091
$186$	−1.27891	+	4.63931i	−0.0937745	+	0.340171i
$187$		−	1.72041i		−	0.125809i
$188$	−0.801670			−0.0584678
$189$	−12.6396	+	5.40743i	−0.919396	+	0.393332i
$190$	−1.03389			−0.0750063
$191$			9.33494i			0.675452i	0.941244	+	0.337726i	$0.109658\pi$
$191$			9.33494i			0.675452i	−0.941244	+	0.337726i	$0.890342\pi$
$192$	−4.09266	+	14.8463i	−0.295362	+	1.07144i
$193$	−5.60000			−0.403097			−0.201548	−	0.979479i	$-0.564597\pi$
$193$	−5.60000			−0.403097			−0.201548	+	0.979479i	$0.564597\pi$
$194$	5.80854	+	10.0607i	0.417029	+	0.722315i
$195$	3.23359	+	0.891401i	0.231562	+	0.0638346i
$196$	2.49141	+	2.18143i	0.177958	+	0.155816i
$197$		−	7.13811i		−	0.508569i	−0.967129	−	0.254284i	$-0.918160\pi$
$197$		−	7.13811i		−	0.508569i	0.967129	−	0.254284i	$-0.0818400\pi$
$198$	4.11337	−	2.29665i	0.292324	−	0.163216i
$199$	9.64089	−	5.56617i	0.683425	−	0.394575i	−0.117719	−	0.993047i	$-0.537558\pi$
$199$	9.64089	−	5.56617i	0.683425	−	0.394575i	0.801144	+	0.598471i	$0.204225\pi$
$200$	2.64653	+	1.52797i	0.187138	+	0.108044i
$201$	6.02541	−	21.8574i	0.425000	−	1.54170i
$202$	−13.2129	−	7.62847i	−0.929656	−	0.536737i
$203$	−25.6013	+	4.23718i	−1.79686	+	0.297392i
$204$	1.07348	−	0.279382i	0.0751584	−	0.0195607i
$205$	6.94940			0.485367
$206$	−5.75759	−	9.97244i	−0.401151	−	0.694813i
$207$	3.16766	+	0.0455452i	0.220168	+	0.00316561i
$208$	−4.74634	−	2.74030i	−0.329099	−	0.190006i
$209$	0.531648	+	0.920842i	0.0367749	+	0.0636960i
$210$	0.593307	−	5.63148i	0.0409421	−	0.388609i
$211$	4.41618	−	7.64904i	0.304022	−	0.526582i	−0.673021	−	0.739623i	$-0.735004\pi$
$211$	4.41618	−	7.64904i	0.304022	−	0.526582i	0.977043	+	0.213042i	$0.0683370\pi$
$212$	−0.0700609	+	0.0404497i	−0.00481180	+	0.00277810i
$213$	−10.8357	−	2.98707i	−0.742451	−	0.204671i
$214$	5.87379	−	10.1737i	0.401524	−	0.695460i
$215$	−3.63907	+	6.30306i	−0.248183	+	0.429865i
$216$	10.9835	+	11.4678i	0.747334	+	0.780284i
$217$	2.09330	−	5.56844i	0.142102	−	0.378010i
$218$	−6.90671	+	3.98759i	−0.467782	+	0.270074i
$219$	−4.58743	−	17.6264i	−0.309990	−	1.19108i
$220$		−	0.601190i		−	0.0405322i
$221$			2.62163i			0.176350i
$222$	13.3533	−	13.1627i	0.896215	−	0.883422i
$223$	7.09222	−	4.09470i	0.474930	−	0.274201i	−0.243371	−	0.969933i	$-0.578253\pi$
$223$	7.09222	−	4.09470i	0.474930	−	0.274201i	0.718301	+	0.695732i	$0.244920\pi$
$224$	2.43434	−	6.47564i	0.162651	−	0.432672i
$225$	2.61937	−	1.46249i	0.174625	−	0.0974995i
$226$	−8.32014	+	14.4109i	−0.553448	+	0.958600i
$227$	6.56772	−	11.3756i	0.435915	−	0.755027i	−0.561455	−	0.827507i	$-0.689758\pi$
$227$	6.56772	−	11.3756i	0.435915	−	0.755027i	0.997370	+	0.0724804i	$0.0230915\pi$
$228$	−0.488238	+	0.481268i	−0.0323343	+	0.0318728i
$229$	−9.67845	+	5.58785i	−0.639570	+	0.369256i	−0.784449	−	0.620194i	$-0.787054\pi$
$229$	−9.67845	+	5.58785i	−0.639570	+	0.369256i	0.144879	+	0.989449i	$0.453721\pi$
$230$	−0.652443	+	1.13006i	−0.0430208	+	0.0745142i
$231$	−5.32081	+	2.36739i	−0.350084	+	0.155763i
$232$	14.9864	+	25.9572i	0.983905	+	1.70417i
$233$	14.3971	+	8.31218i	0.943187	+	0.544549i	0.890958	−	0.454086i	$-0.150034\pi$
$233$	14.3971	+	8.31218i	0.943187	+	0.544549i	0.0522289	+	0.998635i	$0.483367\pi$
$234$	−6.26812	+	3.49972i	−0.409760	+	0.228784i
$235$	−0.847313	−	1.46759i	−0.0552726	−	0.0957350i
$236$	4.62608			0.301132
$237$	−7.36982	+	26.7343i	−0.478721	+	1.73658i
$238$	4.36650	−	0.722684i	0.283038	−	0.0468447i
$239$	−14.4260	−	8.32885i	−0.933140	−	0.538748i	−0.0453365	−	0.998972i	$-0.514436\pi$
$239$	−14.4260	−	8.32885i	−0.933140	−	0.538748i	−0.887803	+	0.460223i	$0.847769\pi$
$240$	−4.74381	+	1.23462i	−0.306212	+	0.0796944i
$241$	−13.8667	−	8.00595i	−0.893233	−	0.515709i	−0.0182347	−	0.999834i	$-0.505805\pi$
$241$	−13.8667	−	8.00595i	−0.893233	−	0.515709i	−0.874999	+	0.484125i	$0.839138\pi$
$242$	−10.0432	+	5.79847i	−0.645604	+	0.372740i
$243$	15.1926	−	3.49090i	0.974603	−	0.223941i
$244$		−	1.34768i		−	0.0862766i
$245$	−1.36021	+	6.86657i	−0.0869004	+	0.438689i
$246$	−10.5926	+	10.4414i	−0.675359	+	0.665719i
$247$	−0.810148	−	1.40322i	−0.0515485	−	0.0892846i
$248$	−6.87121			−0.436322
$249$	15.3023	−	3.98258i	0.969747	−	0.252385i
$250$			1.23569i			0.0781520i
$251$	14.7836			0.933135			0.466567	−	0.884486i	$-0.345491\pi$
$251$	14.7836			0.933135			0.466567	+	0.884486i	$0.345491\pi$
$252$	−2.34123	−	2.93555i	−0.147484	−	0.184923i
$253$	1.34200			0.0843708
$254$			11.4253i			0.716889i
$255$	1.64605	+	1.66989i	0.103080	+	0.104573i
$256$	−10.6683			−0.666768
$257$	3.84310	+	6.65644i	0.239726	+	0.415217i	0.960636	−	0.277812i	$-0.0896091\pi$
$257$	3.84310	+	6.65644i	0.239726	+	0.415217i	−0.720910	+	0.693029i	$0.756276\pi$
$258$	−3.92343	−	15.0751i	−0.244262	−	0.938534i
$259$	−17.9113	+	14.7113i	−1.11295	+	0.914113i
$260$			0.916118i			0.0568152i
$261$	29.4210	+	0.423021i	1.82111	+	0.0261843i
$262$	13.3723	−	7.72051i	0.826145	−	0.476975i
$263$	16.5237	+	9.53994i	1.01889	+	0.588258i	0.913783	−	0.406203i	$-0.133147\pi$
$263$	16.5237	+	9.53994i	1.01889	+	0.588258i	0.105109	+	0.994461i	$0.466481\pi$
$264$	4.72212	+	4.79050i	0.290626	+	0.294835i
$265$	−0.148100	−	0.0855054i	−0.00909769	−	0.00525255i
$266$	−2.11382	+	1.73617i	−0.129607	+	0.106451i
$267$	22.8990	+	23.2306i	1.40140	+	1.42169i
$268$	6.19248			0.378266
$269$	8.35391	+	14.4694i	0.509347	+	0.882215i	0.999941	+	0.0108266i	$0.00344629\pi$
$269$	8.35391	+	14.4694i	0.509347	+	0.882215i	−0.490595	+	0.871388i	$0.663220\pi$
$270$	−1.79519	+	6.16478i	−0.109252	+	0.375177i
$271$	−16.5843	−	9.57497i	−1.00743	−	0.581638i	−0.0969893	−	0.995285i	$-0.530921\pi$
$271$	−16.5843	−	9.57497i	−1.00743	−	0.581638i	−0.910437	+	0.413648i	$0.864255\pi$
$272$	−1.91563	−	3.31796i	−0.116152	−	0.201181i
$273$	8.10807	−	3.60753i	0.490723	−	0.218338i
$274$	−0.0810415	+	0.140368i	−0.00489590	+	0.00847994i
$275$	1.10058	−	0.635419i	0.0663673	−	0.0383172i
$276$	0.217931	+	0.837361i	0.0131179	+	0.0504032i
$277$	8.36521	−	14.4890i	0.502617	−	0.870558i	−0.497379	−	0.867533i	$-0.665704\pi$
$277$	8.36521	−	14.4890i	0.502617	−	0.870558i	0.999995	−	0.00302404i	$-0.000962584\pi$
$278$	−2.33595	+	4.04599i	−0.140101	+	0.242662i
$279$	−3.45634	+	5.79261i	−0.206926	+	0.346795i
$280$	7.97676	−	1.32021i	0.476703	−	0.0788975i
$281$	−8.88850	+	5.13178i	−0.530244	+	0.306136i	−0.741116	−	0.671377i	$-0.765703\pi$
$281$	−8.88850	+	5.13178i	−0.530244	+	0.306136i	0.210872	+	0.977514i	$0.432370\pi$
$282$	3.49655	+	0.963891i	0.208217	+	0.0573989i
$283$			10.5602i			0.627737i	0.949466	+	0.313869i	$0.101625\pi$
$283$			10.5602i			0.627737i	−0.949466	+	0.313869i	$0.898375\pi$
$284$		−	3.06989i		−	0.182165i
$285$	−1.39708	−	0.385131i	−0.0827557	−	0.0228132i
$286$	−2.63366	+	1.52055i	−0.155732	+	0.0899118i
$287$	14.2082	−	11.6698i	0.838686	−	0.688847i
$288$	−4.01945	+	6.73634i	−0.236848	+	0.396942i
$289$	7.58366	−	13.1353i	0.446098	−	0.772664i
$290$	−6.05984	+	10.4960i	−0.355846	+	0.616344i
$291$	4.10130	+	15.7585i	0.240422	+	0.923781i
$292$	4.30811	−	2.48729i	0.252113	−	0.145558i
$293$	−6.00652	+	10.4036i	−0.350904	+	0.607784i	−0.986408	−	0.164314i	$-0.947459\pi$
$293$	−6.00652	+	10.4036i	−0.350904	+	0.607784i	0.635504	+	0.772098i	$0.280792\pi$
$294$	−8.24366	−	12.5101i	−0.480780	−	0.729601i
$295$	4.88947	+	8.46881i	0.284676	+	0.493073i
$296$	23.1851	+	13.3859i	1.34761	+	0.778042i
$297$	6.41383	−	1.57116i	0.372168	−	0.0911679i
$298$	−1.48367	−	2.56979i	−0.0859467	−	0.148864i
$299$	−2.04499			−0.118265
$300$	0.575205	+	0.583535i	0.0332095	+	0.0336904i
$301$	3.14425	+	18.9977i	0.181232	+	1.09501i
$302$	23.2480	+	13.4222i	1.33777	+	0.772362i
$303$	−15.0127	−	15.2301i	−0.862456	−	0.874946i
$304$	2.05066	+	1.18395i	0.117613	+	0.0679041i
$305$	2.46716	−	1.42441i	0.141269	−	0.0815617i
$306$	−5.01798	−	0.0721495i	−0.286859	−	0.00412451i
$307$			22.2161i			1.26794i	0.773358	+	0.633970i	$0.218576\pi$
$307$			22.2161i			1.26794i	−0.773358	+	0.633970i	$0.781424\pi$
$308$	−1.00955	−	1.22915i	−0.0575245	−	0.0700374i
$309$	−4.06533	−	15.6203i	−0.231269	−	0.888609i
$310$	−1.38921	−	2.40618i	−0.0789018	−	0.136662i
$311$	−29.3734			−1.66562			−0.832808	−	0.553562i	$-0.813268\pi$
$311$	−29.3734			−1.66562			−0.832808	+	0.553562i	$0.813268\pi$
$312$	−7.19576	−	7.29996i	−0.407380	−	0.413279i
$313$		−	29.8139i		−	1.68518i	−0.538553	−	0.842591i	$-0.681029\pi$
$313$		−	29.8139i		−	1.68518i	0.538553	−	0.842591i	$-0.318971\pi$
$314$	−15.0965			−0.851943
$315$	2.89949	−	7.38871i	0.163368	−	0.416306i
$316$	−7.57417			−0.426080
$317$		−	5.85984i		−	0.329121i	−0.986367	−	0.164561i	$-0.947379\pi$
$317$		−	5.85984i		−	0.329121i	0.986367	−	0.164561i	$-0.0526206\pi$
$318$	0.354211	−	0.0921868i	0.0198632	−	0.00516958i
$319$	12.4644			0.697872
$320$	−4.44562	−	7.70003i	−0.248517	−	0.430445i
$321$	11.7269	−	11.5595i	0.654532	−	0.645189i
$322$	0.563727	+	3.40607i	0.0314153	+	0.189813i
$323$		−	1.13268i		−	0.0630240i
$324$	2.02191	+	3.74686i	0.112328	+	0.208159i
$325$	−1.67710	+	0.968277i	−0.0930290	+	0.0537103i
$326$	−18.6922	−	10.7919i	−1.03526	−	0.597710i
$327$	−10.8183	+	2.81557i	−0.598254	+	0.155701i
$328$	−18.3918	−	10.6185i	−1.01552	−	0.586308i
$329$	−4.19682	−	1.57768i	−0.231378	−	0.0869801i
$330$	−0.722843	+	2.62214i	−0.0397912	+	0.144344i
$331$	−32.4278			−1.78239			−0.891195	−	0.453620i	$-0.850132\pi$
$331$	−32.4278			−1.78239			−0.891195	+	0.453620i	$0.850132\pi$
$332$	2.15934	+	3.74008i	0.118509	+	0.205264i
$333$	22.9472	−	12.8123i	1.25750	−	0.702110i
$334$	8.20484	+	4.73706i	0.448949	+	0.259201i
$335$	6.54506	+	11.3364i	0.357595	+	0.619372i
$336$	−7.62562	+	10.4903i	−0.416012	+	0.572292i
$337$	1.18605	−	2.05430i	0.0646084	−	0.111905i	−0.831912	−	0.554908i	$-0.812754\pi$
$337$	1.18605	−	2.05430i	0.0646084	−	0.111905i	0.896520	+	0.443003i	$0.146087\pi$
$338$	−9.89854	+	5.71493i	−0.538410	+	0.310851i
$339$	−16.6110	+	16.3739i	−0.902186	+	0.889308i
$340$	−0.320209	+	0.554619i	−0.0173658	+	0.0300784i
$341$	−1.42872	+	2.47462i	−0.0773696	+	0.134008i
$342$	2.70815	−	1.51206i	0.146440	−	0.0817628i
$343$	8.74975	+	16.3230i	0.472442	+	0.881362i
$344$	19.2618	−	11.1208i	1.03853	−	0.599594i
$345$	−1.30259	+	1.28399i	−0.0701290	+	0.0691280i
$346$			19.7835i			1.06357i
$347$		−	30.4100i		−	1.63249i	−0.577704	−	0.816246i	$-0.696051\pi$
$347$		−	30.4100i		−	1.63249i	0.577704	−	0.816246i	$-0.303949\pi$
$348$	2.02413	+	7.77735i	0.108505	+	0.416910i
$349$	20.4722	−	11.8196i	1.09585	−	0.632690i	0.160723	−	0.987000i	$-0.448617\pi$
$349$	20.4722	−	11.8196i	1.09585	−	0.632690i	0.935128	+	0.354309i	$0.115284\pi$
$350$	2.07504	+	2.52641i	0.110916	+	0.135042i
$351$	−9.77366	+	2.39420i	−0.521679	+	0.127793i
$352$	−1.66149	+	2.87778i	−0.0885576	+	0.153386i
$353$	5.32349	−	9.22056i	0.283341	−	0.490761i	−0.688865	−	0.724890i	$-0.741891\pi$
$353$	5.32349	−	9.22056i	0.283341	−	0.490761i	0.972206	+	0.234129i	$0.0752238\pi$
$354$	−20.1770	−	5.56219i	−1.07240	−	0.295627i
$355$	5.61995	−	3.24468i	0.298276	−	0.172210i
$356$	−4.45458	+	7.71556i	−0.236092	+	0.408924i
$357$	6.16957	+	0.649998i	0.326528	+	0.0344015i
$358$	9.70328	+	16.8066i	0.512834	+	0.888255i
$359$	−5.10095	−	2.94504i	−0.269218	−	0.155433i	0.359314	−	0.933217i	$-0.383011\pi$
$359$	−5.10095	−	2.94504i	−0.269218	−	0.155433i	−0.628532	+	0.777784i	$0.716344\pi$
$360$	−9.16689	−	0.131803i	−0.483138	−	0.00694665i
$361$	−9.14997	−	15.8482i	−0.481578	−	0.834117i
$362$	−8.04336			−0.422750
$363$	−15.7312	+	4.09419i	−0.825674	+	0.214889i
$364$	1.53839	+	1.87303i	0.0806338	+	0.0981734i
$365$	9.10680	+	5.25781i	0.476671	+	0.275206i
$366$	−1.62039	+	5.87804i	−0.0846993	+	0.307250i
$367$	−0.666312	−	0.384696i	−0.0347812	−	0.0200810i	0.482509	−	0.875891i	$-0.339726\pi$
$367$	−0.666312	−	0.384696i	−0.0347812	−	0.0200810i	−0.517290	+	0.855810i	$0.673059\pi$
$368$	2.58816	−	1.49427i	0.134917	−	0.0778945i
$369$	−18.2031	+	10.1634i	−0.947613	+	0.529088i
$370$			10.8254i			0.562785i
$371$	−0.446380	+	0.0738788i	−0.0231749	+	0.00383560i
$372$	−1.77609	−	0.489613i	−0.0920860	−	0.0253852i
$373$	15.7575	+	27.2927i	0.815891	+	1.41316i	0.908686	+	0.417479i	$0.137086\pi$
$373$	15.7575	+	27.2927i	0.815891	+	1.41316i	−0.0927956	+	0.995685i	$0.529580\pi$
$374$	−2.12590			−0.109928
$375$	−0.460303	+	1.66977i	−0.0237699	+	0.0862264i
$376$			5.17869i			0.267071i
$377$	−18.9937			−0.978228
$378$	6.68191	+	15.6187i	0.343680	+	0.803337i
$379$	20.1303			1.03403			0.517013	−	0.855978i	$-0.327044\pi$
$379$	20.1303			1.03403			0.517013	+	0.855978i	$0.327044\pi$
$380$		−	0.395809i		−	0.0203046i
$381$	−4.25601	+	15.4388i	−0.218042	+	0.790955i
$382$	11.5351			0.590187
$383$	10.6382	+	18.4259i	0.543585	+	0.941517i	0.998694	+	0.0510816i	$0.0162669\pi$
$383$	10.6382	+	18.4259i	0.543585	+	0.941517i	−0.455109	+	0.890436i	$0.650400\pi$
$384$	9.61324	+	2.65007i	0.490574	+	0.135236i
$385$	1.18313	−	3.14728i	0.0602981	−	0.160400i
$386$			6.91987i			0.352212i
$387$	0.313907	−	21.8322i	0.0159568	−	1.10979i
$388$	−3.85158	+	2.22371i	−0.195534	+	0.112892i
$389$	5.32769	+	3.07594i	0.270124	+	0.155956i	0.628944	−	0.777450i	$-0.283487\pi$
$389$	5.32769	+	3.07594i	0.270124	+	0.155956i	−0.358820	+	0.933407i	$0.616821\pi$
$390$	1.10150	−	3.99572i	0.0557765	−	0.202331i
$391$	−1.23804	−	0.714784i	−0.0626104	−	0.0361482i
$392$	14.0918	−	16.0942i	0.711742	−	0.812881i
$393$	20.9457	−	5.45131i	1.05657	−	0.274982i
$394$	−8.82050			−0.444370
$395$	−8.00541	−	13.8658i	−0.402796	−	0.697663i
$396$	0.879236	+	1.57474i	0.0441833	+	0.0791337i
$397$	−23.3539	−	13.4834i	−1.17210	−	0.676711i	−0.217924	−	0.975966i	$-0.569929\pi$
$397$	−23.3539	−	13.4834i	−1.17210	−	0.676711i	−0.954173	+	0.299255i	$0.903262\pi$
$398$	−6.87807	−	11.9132i	−0.344767	−	0.597153i
$399$	−3.50310	+	1.55864i	−0.175374	+	0.0780295i
$400$	1.41504	−	2.45092i	0.0707519	−	0.122546i
$401$	16.1812	−	9.34221i	0.808050	−	0.466528i	−0.0382283	−	0.999269i	$-0.512171\pi$
$401$	16.1812	−	9.34221i	0.808050	−	0.466528i	0.846278	+	0.532741i	$0.178838\pi$
$402$	−27.0091	−	7.44556i	−1.34709	−	0.371351i
$403$	2.17714	−	3.77092i	0.108451	−	0.187843i
$404$	2.92044	−	5.05836i	0.145298	−	0.251663i
$405$	−4.72223	+	7.66163i	−0.234649	+	0.380709i
$406$	5.23585	+	31.6353i	0.259851	+	1.57003i
$407$	9.64171	−	5.56664i	0.477922	−	0.275928i
$408$	−1.80478	−	6.93453i	−0.0893497	−	0.343310i
$409$			0.244490i			0.0120893i	0.999982	+	0.00604463i	$0.00192408\pi$
$409$			0.244490i			0.0120893i	−0.999982	+	0.00604463i	$0.998076\pi$
$410$		−	8.58731i		−	0.424097i
$411$	−0.161798	+	0.159488i	−0.00798090	+	0.00786697i
$412$	3.81780	−	2.20421i	0.188089	−	0.108594i
$413$	24.2180	+	9.10407i	1.19169	+	0.447982i
$414$	0.0562799	−	3.91425i	0.00276600	−	0.192375i
$415$	−4.56456	+	7.90605i	−0.224066	+	0.388093i
$416$	2.53184	−	4.38528i	0.124134	−	0.215006i
$417$	−4.66368	+	4.59711i	−0.228382	+	0.225121i
$418$	1.13788	−	0.656954i	0.0556554	−	0.0321327i
$419$	14.3672	−	24.8847i	0.701882	−	1.21569i	−0.265923	−	0.963994i	$-0.585677\pi$
$419$	14.3672	−	24.8847i	0.701882	−	1.21569i	0.967805	−	0.251701i	$-0.0809898\pi$
$420$	2.15593	+	0.227139i	0.105199	+	0.0110832i
$421$	−12.7923	−	22.1570i	−0.623460	−	1.07986i	−0.988837	−	0.149004i	$-0.952393\pi$
$421$	−12.7923	−	22.1570i	−0.623460	−	1.07986i	0.365377	−	0.930860i	$-0.380940\pi$
$422$	−9.45186	−	5.45703i	−0.460109	−	0.265644i
$423$	4.36577	+	2.60497i	0.212271	+	0.126658i
$424$	0.261300	+	0.452585i	0.0126898	+	0.0219795i
$425$	−1.35376			−0.0656671
$426$	−3.69110	+	13.3896i	−0.178834	+	0.648728i
$427$	2.65222	−	7.05525i	0.128350	−	0.341427i
$428$	3.89485	+	2.24869i	0.188264	+	0.108695i
$429$	−4.12523	+	1.07363i	−0.199168	+	0.0518353i
$430$	7.78864	+	4.49677i	0.375602	+	0.216854i
$431$	−5.46258	+	3.15382i	−0.263123	+	0.151914i	−0.625758	−	0.780017i	$-0.715210\pi$
$431$	−5.46258	+	3.15382i	−0.263123	+	0.151914i	0.362635	+	0.931931i	$0.381877\pi$
$432$	10.6202	−	10.1717i	0.510964	−	0.489387i
$433$			0.0928113i			0.00446023i	0.999998	+	0.00223011i	$0.000709868\pi$
$433$			0.0928113i			0.00446023i	−0.999998	+	0.00223011i	$0.999290\pi$
$434$	−6.88087	−	2.58667i	−0.330292	−	0.124164i
$435$	−12.0984	+	11.9257i	−0.580072	+	0.571791i
$436$	−1.52659	−	2.64413i	−0.0731104	−	0.126631i
$437$	0.883541			0.0422655
$438$	−21.7808	+	5.66866i	−1.04073	+	0.270859i
$439$			12.2450i			0.584424i	0.956354	+	0.292212i	$0.0943912\pi$
$439$			12.2450i			0.584424i	−0.956354	+	0.292212i	$0.905609\pi$
$440$	−3.88361			−0.185144
$441$	−6.47943	−	19.9754i	−0.308544	−	0.951210i
$442$	3.23953			0.154089
$443$		−	35.8146i		−	1.70160i	−0.525486	−	0.850802i	$-0.676116\pi$
$443$		−	35.8146i		−	1.70160i	0.525486	−	0.850802i	$-0.323884\pi$
$444$	5.03913	+	5.11211i	0.239147	+	0.242610i
$445$	−18.8328			−0.892761
$446$	−5.05978	−	8.76380i	−0.239588	−	0.414978i
$447$	−1.04759	−	4.02519i	−0.0495494	−	0.190385i
$448$	−22.0195	−	8.27762i	−1.04032	−	0.391081i
$449$		−	12.3951i		−	0.584960i	−0.956272	−	0.292480i	$-0.905520\pi$
$449$		−	12.3951i		−	0.584960i	0.956272	−	0.292480i	$-0.0944805\pi$
$450$	−1.80719	−	3.23674i	−0.0851918	−	0.152581i
$451$	−7.64835	+	4.41578i	−0.360147	+	0.207931i
$452$	−5.51700	−	3.18524i	−0.259498	−	0.149821i
$453$	26.4147	+	26.7972i	1.24107	+	1.25904i
$454$	−14.0568	−	8.11568i	−0.659717	−	0.380888i
$455$	−1.80291	+	4.79596i	−0.0845216	+	0.224838i
$456$	3.10893	+	3.15396i	0.145589	+	0.147698i
$457$	−26.7109			−1.24948			−0.624742	−	0.780831i	$-0.714796\pi$
$457$	−26.7109			−1.24948			−0.624742	+	0.780831i	$0.714796\pi$
$458$	6.90487	+	11.9596i	0.322643	+	0.558834i
$459$	−6.75382	−	1.96672i	−0.315242	−	0.0917987i
$460$	−0.432628	−	0.249778i	−0.0201714	−	0.0116459i
$461$	−10.7493	−	18.6184i	−0.500647	−	0.867146i	−1.00000		0.000747358i	$-0.999762\pi$
$461$	−10.7493	−	18.6184i	−0.500647	−	0.867146i	0.499353	−	0.866399i	$-0.333571\pi$
$462$	2.92537	+	6.57488i	0.136100	+	0.305891i
$463$	8.69322	−	15.0571i	0.404008	−	0.699763i	−0.590197	−	0.807259i	$-0.700950\pi$
$463$	8.69322	−	15.0571i	0.404008	−	0.699763i	0.994205	+	0.107496i	$0.0342834\pi$
$464$	24.0386	−	13.8787i	1.11597	−	0.644303i
$465$	−0.980895	−	3.76892i	−0.0454879	−	0.174779i
$466$	10.2713	−	17.7904i	0.475809	−	0.824125i
$467$	14.2322	−	24.6509i	0.658588	−	1.14071i	−0.322393	−	0.946606i	$-0.604487\pi$
$467$	14.2322	−	24.6509i	0.658588	−	1.14071i	0.980981	−	0.194103i	$-0.0621794\pi$
$468$	−1.33982	−	2.39965i	−0.0619330	−	0.110924i
$469$	32.4182	+	12.1867i	1.49693	+	0.562731i
$470$	−1.81349	+	1.04702i	−0.0836500	+	0.0482953i
$471$	−20.3996	−	5.62353i	−0.939963	−	0.259118i
$472$		−	29.8839i		−	1.37552i
$473$		−	9.24934i		−	0.425285i
$474$	33.0354	+	9.10683i	1.51737	+	0.418291i
$475$	0.724595	−	0.418345i	0.0332467	−	0.0191950i
$476$	0.276669	+	1.67165i	0.0126811	+	0.0766199i
$477$	0.512979	+	0.00737572i	0.0234877	+	0.000337711i
$478$	−10.2919	+	17.8261i	−0.470740	+	0.815346i
$479$	9.71758	−	16.8313i	0.444007	−	0.769044i	−0.553975	−	0.832533i	$-0.686890\pi$
$479$	9.71758	−	16.8313i	0.444007	−	0.769044i	0.997982	+	0.0634898i	$0.0202230\pi$
$480$	−1.14070	−	4.38294i	−0.0520657	−	0.200053i
$481$	−14.6924	+	8.48268i	−0.669917	+	0.386777i
$482$	−9.89289	+	17.1350i	−0.450609	+	0.780477i
$483$	−0.507028	+	4.81255i	−0.0230706	+	0.218978i
$484$	−2.21986	−	3.84490i	−0.100903	−	0.174768i
$485$	−8.14174	−	4.70063i	−0.369697	−	0.213445i
$486$	−4.31367	−	18.7733i	−0.195672	−	0.851575i
$487$	−2.99784	−	5.19242i	−0.135845	−	0.235291i	0.790075	−	0.613010i	$-0.210042\pi$
$487$	−2.99784	−	5.19242i	−0.135845	−	0.235291i	−0.925920	+	0.377720i	$0.876708\pi$
$488$	−8.70587			−0.394096
$489$	−21.2383	−	21.5459i	−0.960431	−	0.974339i
$490$	8.48497	+	1.68080i	0.383312	+	0.0759306i
$491$	25.4050	+	14.6676i	1.14651	+	0.661939i	0.948035	−	0.318166i	$-0.103067\pi$
$491$	25.4050	+	14.6676i	1.14651	+	0.661939i	0.198478	+	0.980105i	$0.436400\pi$
$492$	−3.99733	−	4.05522i	−0.180213	−	0.182823i
$493$	−11.4988	−	6.63886i	−0.517882	−	0.298999i
$494$	−1.73394	+	1.00109i	−0.0780138	+	0.0450413i
$495$	−1.95353	+	3.27399i	−0.0878045	+	0.147155i
$496$			6.36335i			0.285723i
$497$	6.04151	−	16.0712i	0.270999	−	0.720890i
$498$	−4.92124	−	18.9090i	−0.220526	−	0.847332i
$499$	11.1595	+	19.3288i	0.499566	+	0.865274i	1.00000		0.000500987i	$-0.000159469\pi$
$499$	11.1595	+	19.3288i	0.499566	+	0.865274i	−0.500434	+	0.865775i	$0.666826\pi$
$500$	−0.473066			−0.0211561
$501$	9.32245	+	9.45746i	0.416496	+	0.422528i
$502$		−	18.2680i		−	0.815341i
$503$	26.2714			1.17139			0.585693	−	0.810533i	$-0.300823\pi$
$503$	26.2714			1.17139			0.585693	+	0.810533i	$0.300823\pi$
$504$	−18.9633	+	15.1241i	−0.844693	+	0.673680i
$505$	12.3469			0.549429
$506$		−	1.65830i		−	0.0737203i
$507$	−15.5046	+	4.03520i	−0.688581	+	0.179210i
$508$	−4.37401			−0.194066
$509$	3.02895	+	5.24629i	0.134256	+	0.232538i	0.925313	−	0.379205i	$-0.123802\pi$
$509$	3.02895	+	5.24629i	0.134256	+	0.232538i	−0.791057	+	0.611742i	$0.790469\pi$
$510$	2.06347	−	2.03401i	0.0913719	−	0.0900676i
$511$	27.4483	−	4.54288i	1.21424	−	0.200965i
$512$			24.6972i			1.09147i
$513$	4.22272	−	1.03441i	0.186438	−	0.0456705i
$514$	8.22531	−	4.74888i	0.362803	−	0.209464i
$515$	8.07033	+	4.65941i	0.355621	+	0.205318i
$516$	5.77127	−	1.50203i	0.254066	−	0.0661230i
$517$	1.86507	+	1.07680i	0.0820256	+	0.0473575i
$518$	18.1786	+	22.1328i	0.798721	+	0.972461i
$519$	−7.36947	+	26.7331i	−0.323484	+	1.17345i
$520$	5.91801			0.259522
$521$	−1.55342	−	2.69061i	−0.0680568	−	0.117878i	0.829989	−	0.557780i	$-0.188347\pi$
$521$	−1.55342	−	2.69061i	−0.0680568	−	0.117878i	−0.898046	+	0.439902i	$0.855013\pi$
$522$	0.522723	−	36.3553i	0.0228790	−	1.59123i
$523$	18.9223	+	10.9248i	0.827417	+	0.477709i	0.852967	−	0.521964i	$-0.174801\pi$
$523$	18.9223	+	10.9248i	0.827417	+	0.477709i	−0.0255507	+	0.999674i	$0.508134\pi$
$524$	2.95568	+	5.11939i	0.129120	+	0.223642i
$525$	1.86286	+	4.18685i	0.0813019	+	0.182729i
$526$	11.7884	−	20.4181i	0.514000	−	0.890273i
$527$	2.63609	−	1.52195i	0.114830	−	0.0662971i
$528$	4.43643	−	4.37310i	0.193071	−	0.190315i
$529$	−10.9424	+	18.9529i	−0.475758	+	0.824037i
$530$	−0.105658	+	0.183006i	−0.00458950	+	0.00794925i
$531$	−25.1929	−	15.0322i	−1.09328	−	0.652340i
$532$	−0.664665	−	0.809244i	−0.0288169	−	0.0350852i
$533$	11.6549	−	6.72894i	0.504828	−	0.291463i
$534$	28.7059	−	28.2961i	1.24222	−	1.22449i
$535$			9.50688i			0.411018i
$536$		−	40.0027i		−	1.72785i
$537$	6.85131	+	26.3249i	0.295656	+	1.13601i
$538$	17.8797	−	10.3229i	0.770849	−	0.445050i
$539$	−2.86614	−	8.42150i	−0.123453	−	0.362740i
$540$	−2.36009	−	0.687262i	−0.101562	−	0.0295750i
$541$	2.01335	−	3.48723i	0.0865608	−	0.149928i	−0.819494	−	0.573087i	$-0.805746\pi$
$541$	2.01335	−	3.48723i	0.0865608	−	0.149928i	0.906055	+	0.423159i	$0.139079\pi$
$542$	−11.8317	+	20.4931i	−0.508215	+	0.880255i
$543$	−10.8688	−	2.99620i	−0.466427	−	0.128579i
$544$	3.06556	−	1.76990i	0.131435	−	0.0758840i
$545$	3.22701	−	5.58935i	0.138230	−	0.239421i
$546$	−4.45780	−	10.0191i	−0.190776	−	0.428777i
$547$	15.0541	+	26.0744i	0.643666	+	1.11486i	0.984608	+	0.174777i	$0.0559206\pi$
$547$	15.0541	+	26.0744i	0.643666	+	1.11486i	−0.340942	+	0.940084i	$0.610746\pi$
$548$	−0.0537378	−	0.0310255i	−0.00229556	−	0.00132534i
$549$	−4.37921	+	7.33927i	−0.186900	+	0.313233i
$550$	−0.785182	−	1.35997i	−0.0334803	−	0.0579895i
$551$	8.20627			0.349599
$552$	5.40925	−	1.40781i	0.230233	−	0.0599202i
$553$	−39.6515	−	14.9059i	−1.68615	−	0.633862i
$554$	−17.9039	−	10.3368i	−0.760664	−	0.439169i
$555$	−4.03252	+	14.6281i	−0.171171	+	0.620930i
$556$	−1.54895	−	0.894284i	−0.0656899	−	0.0379261i
$557$	−7.31014	+	4.22051i	−0.309740	+	0.178829i	−0.646810	−	0.762651i	$-0.723897\pi$
$557$	−7.31014	+	4.22051i	−0.309740	+	0.178829i	0.337070	+	0.941480i	$0.390564\pi$
$558$	7.15788	+	4.27098i	0.303017	+	0.180805i
$559$			14.0945i			0.596135i
$560$	−1.22263	−	7.38719i	−0.0516655	−	0.312166i
$561$	−2.87269	−	0.791910i	−0.121285	−	0.0334345i
$562$	6.34130	+	10.9834i	0.267491	+	0.463309i
$563$	−9.89938			−0.417209			−0.208605	−	0.978000i	$-0.566892\pi$
$563$	−9.89938			−0.417209			−0.208605	+	0.978000i	$0.566892\pi$
$564$	−0.369011	+	1.33860i	−0.0155382	+	0.0563653i
$565$		−	13.4664i		−	0.566535i
$566$	13.0491			0.548496
$567$	3.21109	+	23.5943i	0.134853	+	0.990866i
$568$	−19.8311			−0.832096
$569$			28.3984i			1.19052i	0.803533	+	0.595261i	$0.202951\pi$
$569$			28.3984i			1.19052i	−0.803533	+	0.595261i	$0.797049\pi$
$570$	−0.475903	+	1.72636i	−0.0199334	+	0.0723091i
$571$	13.2675			0.555229			0.277615	−	0.960693i	$-0.410456\pi$
$571$	13.2675			0.555229			0.277615	+	0.960693i	$0.410456\pi$
$572$	−0.582118	−	1.00826i	−0.0243396	−	0.0421574i
$573$	15.5872	+	4.29690i	0.651163	+	0.179506i
$574$	−14.4203	−	17.5570i	−0.601891	−	0.732816i
$575$		−	1.05600i		−	0.0440381i
$576$	22.9060	+	13.6676i	0.954415	+	0.569482i
$577$	−32.4703	+	18.7467i	−1.35176	+	0.780437i	−0.988495	−	0.151250i	$-0.951670\pi$
$577$	−32.4703	+	18.7467i	−1.35176	+	0.780437i	−0.363261	+	0.931687i	$0.618337\pi$
$578$	−16.2312	−	9.37107i	−0.675128	−	0.389785i
$579$	−2.57769	+	9.35069i	−0.107125	+	0.388601i
$580$	−4.01822	−	2.31992i	−0.166847	−	0.0963294i
$581$	3.94389	+	23.8292i	0.163620	+	0.988603i
$582$	19.4727	−	5.06794i	0.807168	−	0.210073i
$583$	0.217327			0.00900076
$584$	−16.0676	−	27.8299i	−0.664882	−	1.15161i
$585$	2.97686	−	4.98903i	0.123078	−	0.206271i
$586$	12.8556	+	7.42220i	0.531061	+	0.306608i
$587$	−2.32671	−	4.02998i	−0.0960337	−	0.166335i	0.814006	−	0.580857i	$-0.197282\pi$
$587$	−2.32671	−	4.02998i	−0.0960337	−	0.166335i	−0.910040	+	0.414521i	$0.863949\pi$
$588$	4.78928	−	3.15596i	0.197507	−	0.130150i
$589$	−0.940637	+	1.62923i	−0.0387583	+	0.0671313i
$590$	10.4648	−	6.04188i	0.430830	−	0.248740i
$591$	−11.9190	−	3.28569i	−0.490281	−	0.135155i
$592$	12.3966	−	21.4715i	0.509496	−	0.882473i
$593$	−20.7205	+	35.8890i	−0.850890	+	1.47379i	0.0295154	+	0.999564i	$0.490604\pi$
$593$	−20.7205	+	35.8890i	−0.850890	+	1.47379i	−0.880406	+	0.474221i	$0.842730\pi$
$594$	−1.94147	−	7.92552i	−0.0796594	−	0.325188i
$595$	−2.76781	+	2.27331i	−0.113469	+	0.0931967i
$596$	0.983805	−	0.568000i	0.0402982	−	0.0232662i
$597$	−4.85648	−	18.6602i	−0.198762	−	0.763710i
$598$			2.52698i			0.103336i
$599$		−	26.6839i		−	1.09027i	−0.838347	−	0.545137i	$-0.816478\pi$
$599$		−	26.6839i		−	1.09027i	0.838347	−	0.545137i	$-0.183522\pi$
$600$	3.76956	−	3.71575i	0.153892	−	0.151695i
$601$	34.4248	−	19.8752i	1.40422	−	0.810726i	0.409396	−	0.912357i	$-0.365740\pi$
$601$	34.4248	−	19.8752i	1.40422	−	0.810726i	0.994822	+	0.101631i	$0.0324062\pi$
$602$	23.4753	−	3.88532i	0.956783	−	0.158354i
$603$	−33.7233	−	20.1221i	−1.37332	−	0.819434i
$604$	−5.13849	+	8.90013i	−0.209082	+	0.362141i
$605$	4.69249	−	8.12762i	0.190777	−	0.330435i
$606$	−18.8197	+	18.5510i	−0.764498	+	0.753585i
$607$	−39.0673	+	22.5555i	−1.58569	+	0.915500i	−0.591686	+	0.806168i	$0.701538\pi$
$607$	−39.0673	+	22.5555i	−1.58569	+	0.915500i	−0.994005	+	0.109331i	$0.965129\pi$
$608$	−1.09388	+	1.89466i	−0.0443629	+	0.0768388i
$609$	−4.70924	+	44.6986i	−0.190828	+	1.81128i
$610$	−1.76014	−	3.04865i	−0.0712659	−	0.123436i
$611$	−2.84207	−	1.64087i	−0.114978	−	0.0663824i
$612$	0.0276213	−	1.92106i	0.00111653	−	0.0776541i
$613$	−0.0987025	−	0.170958i	−0.00398656	−	0.00690492i	0.864025	−	0.503448i	$-0.167936\pi$
$613$	−0.0987025	−	0.170958i	−0.00398656	−	0.00690492i	−0.868012	+	0.496544i	$0.834602\pi$
$614$	27.4523			1.10788
$615$	3.19883	−	11.6039i	0.128989	−	0.467913i
$616$	−7.94016	+	6.52157i	−0.319918	+	0.262762i
$617$	−23.8582	−	13.7746i	−0.960496	−	0.554543i	−0.0641702	−	0.997939i	$-0.520440\pi$
$617$	−23.8582	−	13.7746i	−0.960496	−	0.554543i	−0.896326	+	0.443396i	$0.853773\pi$
$618$	−19.3019	+	5.02349i	−0.776436	+	0.202075i
$619$	17.5302	+	10.1211i	0.704599	+	0.406800i	0.809058	−	0.587729i	$-0.199978\pi$
$619$	17.5302	+	10.1211i	0.704599	+	0.406800i	−0.104459	+	0.994529i	$0.533311\pi$
$620$	0.921170	−	0.531838i	0.0369951	−	0.0213591i
$621$	1.53413	−	5.26829i	0.0615626	−	0.211409i
$622$			36.2965i			1.45536i
$623$	−38.5043	+	31.6251i	−1.54264	+	1.26703i
$624$	−6.76041	+	6.66391i	−0.270633	+	0.266770i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−36.8408			−1.47246
$627$	1.78231	−	0.463863i	0.0711786	−	0.0185249i
$628$		−	5.77945i		−	0.230625i
$629$	−11.8598			−0.472879
$630$	−9.13016	−	3.58287i	−0.363754	−	0.142745i
$631$	18.5928			0.740166			0.370083	−	0.928999i	$-0.379329\pi$
$631$	18.5928			0.740166			0.370083	+	0.928999i	$0.379329\pi$
$632$			48.9282i			1.94626i
$633$	−10.7393	−	10.8949i	−0.426850	−	0.433032i
$634$	−7.24095			−0.287575
$635$	−4.62305	−	8.00736i	−0.183460	−	0.317762i
$636$	0.0352923	+	0.135604i	0.00139943	+	0.00537707i
$637$	4.36754	+	12.8330i	0.173048	+	0.508463i
$638$		−	15.4021i		−	0.609777i
$639$	−9.97542	+	16.7182i	−0.394621	+	0.661360i
$640$	−4.98591	+	2.87862i	−0.197086	+	0.113787i
$641$	−0.0435721	−	0.0251564i	−0.00172100	−	0.000993617i	0.499139	−	0.866522i	$-0.333650\pi$
$641$	−0.0435721	−	0.0251564i	−0.00172100	−	0.000993617i	−0.500860	+	0.865528i	$0.666983\pi$
$642$	−14.2840	−	14.4908i	−0.563744	−	0.571908i
$643$	33.9516	+	19.6020i	1.33892	+	0.773026i	0.986647	−	0.162871i	$-0.0520755\pi$
$643$	33.9516	+	19.6020i	1.33892	+	0.773026i	0.352273	+	0.935897i	$0.385409\pi$
$644$	−1.30396	+	0.215814i	−0.0513833	+	0.00850427i
$645$	8.84956	+	8.97772i	0.348451	+	0.353497i
$646$	−1.39964			−0.0550682
$647$	9.52565	+	16.4989i	0.374492	+	0.648639i	0.990251	−	0.139296i	$-0.0444838\pi$
$647$	9.52565	+	16.4989i	0.374492	+	0.648639i	−0.615759	+	0.787935i	$0.711150\pi$
$648$	24.2043	−	13.0613i	0.950834	−	0.513095i
$649$	−10.7625	−	6.21372i	−0.422464	−	0.243910i
$650$	1.19649	+	2.07238i	0.0469303	+	0.0812856i
$651$	−8.33444	−	6.05849i	−0.326653	−	0.237451i
$652$	4.13153	−	7.15602i	0.161803	−	0.280251i
$653$	16.3324	−	9.42952i	0.639136	−	0.369006i	−0.145145	−	0.989410i	$-0.546365\pi$
$653$	16.3324	−	9.42952i	0.639136	−	0.369006i	0.784282	+	0.620405i	$0.213032\pi$
$654$	3.47917	+	13.3681i	0.136046	+	0.522734i
$655$	−6.24793	+	10.8217i	−0.244127	+	0.422840i
$656$	−9.83366	+	17.0324i	−0.383940	+	0.665004i
$657$	−31.5436	−	0.453540i	−1.23063	−	0.0176943i
$658$	−1.94952	+	5.18597i	−0.0760003	+	0.202170i
$659$	−20.4698	+	11.8183i	−0.797391	+	0.460374i	−0.842558	−	0.538606i	$-0.818951\pi$
$659$	−20.4698	+	11.8183i	−0.797391	+	0.460374i	0.0451672	+	0.998979i	$0.485618\pi$
$660$	−1.00385	−	0.276729i	−0.0390747	−	0.0107717i
$661$			49.0412i			1.90748i	0.300627	+	0.953742i	$0.402804\pi$
$661$			49.0412i			1.90748i	−0.300627	+	0.953742i	$0.597196\pi$
$662$			40.0707i			1.55739i
$663$	4.37752	+	1.20675i	0.170009	+	0.0468661i
$664$	24.1605	−	13.9491i	0.937608	−	0.541329i
$665$	0.778948	−	2.07210i	0.0302063	−	0.0803525i
$666$	−15.8321	−	28.3557i	−0.613480	−	1.09876i
$667$	5.17861	−	8.96962i	0.200517	−	0.347305i
$668$	−1.81351	+	3.14110i	−0.0701669	+	0.121533i
$669$	−3.57262	−	13.7272i	−0.138125	−	0.530722i
$670$	14.0083	−	8.08767i	0.541186	−	0.312454i
$671$	−1.81020	+	3.13536i	−0.0698820	+	0.121039i
$672$	−9.69228	−	7.04553i	−0.373888	−	0.271787i
$673$	−4.36922	−	7.56772i	−0.168421	−	0.291714i	0.769444	−	0.638715i	$-0.220534\pi$
$673$	−4.36922	−	7.56772i	−0.168421	−	0.291714i	−0.937865	+	0.347000i	$0.887200\pi$
$674$	−2.53848	−	1.46559i	−0.0977787	−	0.0564526i
$675$	−1.23632	−	5.04693i	−0.0475859	−	0.194256i
$676$	−2.18787	−	3.78951i	−0.0841489	−	0.145750i
$677$	−7.92787			−0.304693			−0.152346	−	0.988327i	$-0.548683\pi$
$677$	−7.92787			−0.304693			−0.152346	+	0.988327i	$0.548683\pi$
$678$	20.2331	+	20.5261i	0.777047	+	0.788300i
$679$	−24.5396	+	4.06146i	−0.941743	+	0.155865i
$680$	3.58277	+	2.06851i	0.137393	+	0.0793238i
$681$	−15.9715	−	16.2028i	−0.612030	−	0.620893i
$682$	3.05787	+	1.76546i	0.117092	+	0.0676029i
$683$	2.95909	−	1.70843i	0.113227	−	0.0653714i	−0.442317	−	0.896859i	$-0.645843\pi$
$683$	2.95909	−	1.70843i	0.113227	−	0.0653714i	0.555544	+	0.831487i	$0.312510\pi$
$684$	0.578869	+	1.03677i	0.0221336	+	0.0396420i
$685$		−	0.131168i		−	0.00501167i
$686$	20.1703	−	10.8120i	0.770104	−	0.412804i
$687$	4.87540	+	18.7329i	0.186008	+	0.714703i
$688$	−10.2989	−	17.8381i	−0.392640	−	0.680073i
$689$	−0.331172			−0.0126166
$690$	1.58662	+	1.60960i	0.0604017	+	0.0612764i
$691$			45.9833i			1.74929i	0.484767	+	0.874643i	$0.338904\pi$
$691$			45.9833i			1.74929i	−0.484767	+	0.874643i	$0.661096\pi$
$692$	−7.57381			−0.287913
$693$	1.50381	+	9.97423i	0.0571251	+	0.378890i
$694$	−37.5773			−1.42642
$695$		−	3.78080i		−	0.143414i
$696$	50.2407	−	13.0756i	1.90437	−	0.495630i
$697$	9.40783			0.356347
$698$	−14.6054	−	25.2973i	−0.552823	−	0.957518i
$699$	20.5064	−	20.2137i	0.775625	−	0.764553i
$700$	−0.967197	+	0.794398i	−0.0365566	+	0.0300254i
$701$			30.4305i			1.14934i	0.818384	+	0.574672i	$0.194870\pi$
$701$			30.4305i			1.14934i	−0.818384	+	0.574672i	$0.805130\pi$
$702$	2.95849	+	12.0772i	0.111661	+	0.455825i
$703$	6.34788	−	3.66495i	0.239415	−	0.138226i
$704$	9.78549	+	5.64965i	0.368804	+	0.212929i
$705$	−2.84055	+	0.739280i	−0.106981	+	0.0278429i
$706$	−11.3938	−	6.57820i	−0.428810	−	0.247574i
$707$	25.2436	−	20.7336i	0.949382	−	0.779766i
$708$	2.12940	−	7.72448i	0.0800277	−	0.290304i
$709$	25.1986			0.946353			0.473177	−	0.880968i	$-0.343107\pi$
$709$	25.1986			0.946353			0.473177	+	0.880968i	$0.343107\pi$
$710$	−4.00942	−	6.94452i	−0.150471	−	0.260623i
$711$	41.2477	+	24.6118i	1.54691	+	0.923014i
$712$	49.8416	+	28.7761i	1.86789	+	1.07843i
$713$	1.18719	+	2.05627i	0.0444606	+	0.0770080i
$714$	0.803197	−	7.62369i	0.0300589	−	0.285309i
$715$	1.23052	−	2.13133i	0.0460189	−	0.0797071i
$716$	−6.43414	+	3.71476i	−0.240455	+	0.138827i
$717$	−20.5476	+	20.2542i	−0.767363	+	0.756409i
$718$	−3.63916	+	6.30320i	−0.135812	+	0.235233i
$719$	8.10824	−	14.0439i	0.302386	−	0.523748i	−0.674290	−	0.738467i	$-0.735550\pi$
$719$	8.10824	−	14.0439i	0.302386	−	0.523748i	0.976676	+	0.214719i	$0.0688834\pi$
$720$	−0.122062	+	8.48935i	−0.00454897	+	0.316380i
$721$	24.3244	−	4.02585i	0.905887	−	0.149930i
$722$	−19.5835	+	11.3065i	−0.728823	+	0.420786i
$723$	−19.7510	+	19.4690i	−0.734546	+	0.724060i
$724$		−	3.07928i		−	0.114441i
$725$		−	9.80801i		−	0.364261i
$726$	5.05916	+	19.4389i	0.187763	+	0.721446i
$727$	37.7210	−	21.7782i	1.39899	−	0.807710i	0.404707	−	0.914446i	$-0.367373\pi$
$727$	37.7210	−	21.7782i	1.39899	−	0.807710i	0.994287	+	0.106736i	$0.0340401\pi$
$728$	12.0995	−	9.93784i	0.448439	−	0.368321i
$729$	1.16419	−	26.9749i	0.0431182	−	0.999070i
$730$	6.49703	−	11.2532i	0.240466	−	0.416499i
$731$	−4.92644	+	8.53284i	−0.182211	+	0.315599i
$732$	−2.25032	−	0.620343i	−0.0831741	−	0.0229285i
$733$	−26.5351	+	15.3200i	−0.980096	+	0.565859i	−0.902299	−	0.431111i	$-0.858122\pi$
$733$	−26.5351	+	15.3200i	−0.980096	+	0.565859i	−0.0777969	+	0.996969i	$0.524789\pi$
$734$	−0.475365	+	0.823357i	−0.0175461	+	0.0303907i
$735$	10.8395	+	5.43193i	0.399820	+	0.200360i
$736$	1.38060	+	2.39128i	0.0508898	+	0.0881436i
$737$	−14.4067	−	8.31770i	−0.530677	−	0.306386i
$738$	12.5589	+	22.4934i	0.462299	+	0.827992i
$739$	13.5074	+	23.3956i	0.496879	+	0.860619i	0.999994	−	0.00360021i	$-0.00114598\pi$
$739$	13.5074	+	23.3956i	0.496879	+	0.860619i	−0.503115	+	0.864220i	$0.667813\pi$
$740$	−4.14434			−0.152349
$741$	−2.71596	+	0.706853i	−0.0997732	+	0.0259669i
$742$	0.0912914	+	0.551588i	0.00335141	+	0.0202494i
$743$	21.9165	+	12.6535i	0.804040	+	0.464213i	0.844882	−	0.534953i	$-0.179671\pi$
$743$	21.9165	+	12.6535i	0.804040	+	0.464213i	−0.0408419	+	0.999166i	$0.513004\pi$
$744$	−3.16284	+	11.4733i	−0.115955	+	0.420632i
$745$	2.07964	+	1.20068i	0.0761920	+	0.0439895i
$746$	33.7254	−	19.4714i	1.23478	−	0.712898i
$747$	0.393740	−	27.3845i	0.0144062	−	1.00195i
$748$		−	0.813868i		−	0.0297580i
$749$	15.9645	+	19.4371i	0.583329	+	0.710216i
$750$	2.06332	+	0.568792i	0.0753417	+	0.0207694i
$751$	−18.1685	−	31.4687i	−0.662977	−	1.14831i	−0.979830	−	0.199835i	$-0.935960\pi$
$751$	−18.1685	−	31.4687i	−0.662977	−	1.14831i	0.316853	−	0.948475i	$-0.397374\pi$
$752$	4.79592			0.174889
$753$	6.80495	−	24.6852i	0.247986	−	0.899580i
$754$			23.4704i			0.854742i
$755$	−21.7242			−0.790625
$756$	−5.97937	+	2.55807i	−0.217468	+	0.0930361i
$757$	11.5221			0.418778			0.209389	−	0.977832i	$-0.432853\pi$
$757$	11.5221			0.418778			0.209389	+	0.977832i	$0.432853\pi$
$758$		−	24.8749i		−	0.903496i
$759$	0.617726	−	2.24083i	0.0224220	−	0.0813368i
$760$	−2.55688			−0.0927478
$761$	26.6098	+	46.0894i	0.964603	+	1.67074i	0.710678	+	0.703517i	$0.248388\pi$
$761$	26.6098	+	46.0894i	0.964603	+	1.67074i	0.253925	+	0.967224i	$0.418278\pi$
$762$	19.0776	+	5.25911i	0.691110	+	0.190518i
$763$	−2.78822	−	16.8466i	−0.100940	−	0.609887i
$764$			4.41604i			0.159767i
$765$	3.54601	−	1.97987i	0.128206	−	0.0715823i
$766$	22.7687	−	13.1455i	0.822666	−	0.474966i
$767$	16.4003	+	9.46872i	0.592181	+	0.341896i
$768$	−4.91064	+	17.8136i	−0.177198	+	0.642791i
$769$	3.95625	+	2.28414i	0.142666	+	0.0823682i	0.569634	−	0.821899i	$-0.307085\pi$
$769$	3.95625	+	2.28414i	0.142666	+	0.0823682i	−0.426968	+	0.904267i	$0.640418\pi$
$770$	−3.88907	−	1.46199i	−0.140152	−	0.0526864i
$771$	12.8837	−	3.35310i	0.463995	−	0.120759i
$772$	−2.64917			−0.0953456
$773$	−1.60297	−	2.77642i	−0.0576548	−	0.0998610i	0.835757	−	0.549099i	$-0.185029\pi$
$773$	−1.60297	−	2.77642i	−0.0576548	−	0.0998610i	−0.893412	+	0.449238i	$0.851696\pi$
$774$	−26.9778	−	0.387893i	−0.969699	−	0.0139425i
$775$	1.94723	+	1.12424i	0.0699467	+	0.0403838i
$776$	14.3649	+	24.8807i	0.515669	+	0.893166i
$777$	16.3198	+	36.6793i	0.585468	+	1.31586i
$778$	3.80092	−	6.58338i	0.136269	−	0.236026i
$779$	−5.03550	+	2.90725i	−0.180415	+	0.104163i
$780$	1.52970	+	0.421692i	0.0547721	+	0.0150990i
$781$	−4.12346	+	7.14204i	−0.147549	+	0.255562i
$782$	−0.883252	+	1.52984i	−0.0315850	+	0.0547069i
$783$	14.2489	−	48.9315i	0.509215	−	1.74867i
$784$	−14.9047	−	13.0502i	−0.532310	−	0.466079i
$785$	10.5802	−	6.10851i	0.377625	−	0.218022i
$786$	−6.73614	−	25.8824i	−0.240270	−	0.923196i
$787$			1.94824i			0.0694472i	0.999397	+	0.0347236i	$0.0110551\pi$
$787$			1.94824i			0.0694472i	−0.999397	+	0.0347236i	$0.988945\pi$
$788$		−	3.37679i		−	0.120293i
$789$	23.5354	−	23.1994i	0.837881	−	0.825920i
$790$	−17.1338	+	9.89222i	−0.609594	+	0.351949i
$791$	−22.6135	−	27.5324i	−0.804043	−	0.978940i
$792$	10.1726	−	5.67976i	0.361469	−	0.201821i
$793$	2.75846	−	4.77778i	0.0979556	−	0.169664i
$794$	−16.6613	+	28.8582i	−0.591287	+	1.02414i
$795$	−0.210945	+	0.207934i	−0.00748144	+	0.00737464i
$796$	4.56078	−	2.63317i	0.161652	−	0.0933301i
$797$	−17.4627	+	30.2462i	−0.618559	+	1.07138i	0.371190	+	0.928557i	$0.378950\pi$
$797$	−17.4627	+	30.2462i	−0.618559	+	1.07138i	−0.989749	+	0.142819i	$0.954383\pi$
$798$	1.92600	+	4.32875i	0.0681795	+	0.153236i
$799$	−1.14706	−	1.98677i	−0.0405801	−	0.0702868i
$800$	2.26448	+	1.30740i	0.0800613	+	0.0462234i
$801$	49.3302	−	27.5429i	1.74300	−	0.973180i
$802$	−11.5441	−	19.9950i	−0.407636	−	0.706047i
$803$	−13.3636			−0.471593
$804$	2.85042	−	10.3400i	0.100526	−	0.364664i
$805$	−1.77329	−	2.15902i	−0.0625001	−	0.0760953i
$806$	−4.65970	−	2.69028i	−0.164131	−	0.0947610i
$807$	28.0058	−	7.28878i	0.985852	−	0.256577i
$808$	−32.6764	−	18.8657i	−1.14955	−	0.663693i
$809$	−38.1558	+	22.0292i	−1.34148	+	0.774507i	−0.987025	−	0.160565i	$-0.948668\pi$
$809$	−38.1558	+	22.0292i	−1.34148	+	0.774507i	−0.354460	+	0.935071i	$0.615335\pi$
$810$	9.46741	+	5.83522i	0.332651	+	0.205029i
$811$		−	5.63536i		−	0.197884i	−0.995093	−	0.0989420i	$-0.968454\pi$
$811$		−	5.63536i		−	0.197884i	0.995093	−	0.0989420i	$-0.0315458\pi$
$812$	−12.1111	+	2.00447i	−0.425016	+	0.0703430i
$813$	−23.6218	+	23.2846i	−0.828452	+	0.816626i
$814$	−6.87865	−	11.9142i	−0.241097	−	0.417592i
$815$	17.4670			0.611844
$816$	−6.42199	+	1.67138i	−0.224815	+	0.0585100i
$817$		−	6.08955i		−	0.213046i
$818$	0.302115			0.0105632
$819$	−2.29157	−	15.1991i	−0.0800739	−	0.531101i
$820$	3.28752			0.114805
$821$			45.5736i			1.59053i	0.606262	+	0.795265i	$0.292668\pi$
$821$			45.5736i			1.59053i	−0.606262	+	0.795265i	$0.707332\pi$
$822$	0.197078	+	0.199932i	0.00687389	+	0.00697344i
$823$	−18.4733			−0.643938			−0.321969	−	0.946750i	$-0.604345\pi$
$823$	−18.4733			−0.643938			−0.321969	+	0.946750i	$0.604345\pi$
$824$	−14.2389	−	24.6625i	−0.496036	−	0.859159i
$825$	−0.554402	−	2.13019i	−0.0193018	−	0.0741638i
$826$	11.2498	−	29.9259i	0.391431	−	1.04126i
$827$		−	35.4707i		−	1.23344i	−0.787184	−	0.616718i	$-0.788462\pi$
$827$		−	35.4707i		−	1.23344i	0.787184	−	0.616718i	$-0.211538\pi$
$828$	1.49851	+	0.0215459i	0.0520769	+	0.000748772i
$829$	7.87390	−	4.54600i	0.273472	−	0.157889i	−0.356992	−	0.934107i	$-0.616198\pi$
$829$	7.87390	−	4.54600i	0.273472	−	0.157889i	0.630464	+	0.776218i	$0.282864\pi$
$830$	9.76944	+	5.64039i	0.339102	+	0.195781i
$831$	−20.3427	−	20.6373i	−0.705679	−	0.715899i
$832$	−14.9115	−	8.60917i	−0.516964	−	0.298469i
$833$	−1.84140	+	9.29571i	−0.0638006	+	0.322077i
$834$	5.68061	+	5.76288i	0.196703	+	0.199552i
$835$	−7.66706			−0.265330
$836$	0.251505	+	0.435619i	0.00869847	+	0.0150662i
$837$	8.08134	+	8.43765i	0.279332	+	0.291648i
$838$	−30.7498	−	17.7534i	−1.06223	−	0.613280i
$839$	3.86499	+	6.69435i	0.133434	+	0.231115i	0.924998	−	0.379971i	$-0.124066\pi$
$839$	3.86499	+	6.69435i	0.133434	+	0.231115i	−0.791564	+	0.611086i	$0.790733\pi$
$840$	1.46729	−	13.9270i	0.0506263	−	0.480528i
$841$	33.5986	−	58.1944i	1.15857	−	2.00670i
$842$	−27.3792	+	15.8074i	−0.943548	+	0.544758i
$843$	4.47747	+	17.2039i	0.154212	+	0.592534i
$844$	2.08914	−	3.61850i	0.0719113	−	0.124554i
$845$	4.62488	−	8.01053i	0.159101	−	0.275570i
$846$	3.21895	−	5.39475i	0.110670	−	0.185475i
$847$	−4.05442	−	24.4971i	−0.139312	−	0.841729i
$848$	0.419134	−	0.241987i	0.0143931	−	0.00830986i
$849$	17.6330	+	4.86088i	0.605164	+	0.166825i
$850$			1.67283i			0.0573777i
$851$		−	9.25114i		−	0.317125i
$852$	−5.12601	−	1.41308i	−0.175614	−	0.0484113i
$853$	−30.8996	+	17.8399i	−1.05798	+	0.610827i	−0.924874	−	0.380274i	$-0.875830\pi$
$853$	−30.8996	+	17.8399i	−1.05798	+	0.610827i	−0.133110	+	0.991101i	$0.542496\pi$
$854$	−8.71811	−	3.27733i	−0.298328	−	0.112148i
$855$	−1.28616	+	2.15552i	−0.0439856	+	0.0737171i
$856$	14.5263	−	25.1602i	0.496497	−	0.859959i
$857$	14.2012	−	24.5971i	0.485102	−	0.840222i	−0.514751	−	0.857340i	$-0.672116\pi$
$857$	14.2012	−	24.5971i	0.485102	−	0.840222i	0.999853	+	0.0171176i	$0.00544897\pi$
$858$	1.32668	+	5.09752i	0.0452920	+	0.174026i
$859$	16.2603	−	9.38788i	0.554794	−	0.320310i	−0.196259	−	0.980552i	$-0.562879\pi$
$859$	16.2603	−	9.38788i	0.554794	−	0.320310i	0.751053	+	0.660242i	$0.229546\pi$
$860$	−1.72152	+	2.98176i	−0.0587034	+	0.101677i
$861$	−12.9458	−	29.0961i	−0.441190	−	0.991593i
$862$	3.89715	+	6.75006i	0.132737	+	0.229908i
$863$	−20.0830	−	11.5949i	−0.683634	−	0.394696i	0.117589	−	0.993062i	$-0.462483\pi$
$863$	−20.0830	−	11.5949i	−0.683634	−	0.394696i	−0.801223	+	0.598366i	$0.795817\pi$
$864$	9.39795	+	9.81230i	0.319725	+	0.333821i
$865$	−8.00503	−	13.8651i	−0.272179	−	0.471428i
$866$	0.114686			0.00389719
$867$	−18.4421	−	18.7092i	−0.626326	−	0.635396i
$868$	0.990269	−	2.63424i	0.0336119	−	0.0894119i
$869$	17.6211	+	10.1736i	0.597756	+	0.345115i
$870$	14.7364	+	14.9498i	0.499612	+	0.506847i
$871$	21.9535	+	12.6749i	0.743866	+	0.429471i
$872$	−17.0808	+	9.86158i	−0.578427	+	0.333955i
$873$	28.2009	+	0.405478i	0.954456	+	0.0137233i
$874$		−	1.09178i		−	0.0369302i
$875$	−2.47654	−	0.930987i	−0.0837224	−	0.0314731i
$876$	−2.17016	−	8.33845i	−0.0733229	−	0.281730i
$877$	23.6636	+	40.9866i	0.799064	+	1.38402i	0.920227	+	0.391386i	$0.128004\pi$
$877$	23.6636	+	40.9866i	0.799064	+	1.38402i	−0.121163	+	0.992633i	$0.538662\pi$
$878$	15.1311			0.510650
$879$	14.6068	+	14.8183i	0.492674	+	0.499808i
$880$			3.59657i			0.121240i
$881$	−28.9064			−0.973883			−0.486941	−	0.873435i	$-0.661887\pi$
$881$	−28.9064			−0.973883			−0.486941	+	0.873435i	$0.661887\pi$
$882$	−24.6834	+	8.00658i	−0.831135	+	0.269596i
$883$	−24.5641			−0.826648			−0.413324	−	0.910584i	$-0.635632\pi$
$883$	−24.5641			−0.826648			−0.413324	+	0.910584i	$0.635632\pi$
$884$			1.24021i			0.0417126i
$885$	16.3916	−	4.26606i	0.550997	−	0.143402i
$886$	−44.2559			−1.48680
$887$	−13.9410	−	24.1465i	−0.468092	−	0.810760i	0.531243	−	0.847220i	$-0.321725\pi$
$887$	−13.9410	−	24.1465i	−0.468092	−	0.810760i	−0.999335	+	0.0364598i	$0.988392\pi$
$888$	33.0236	−	32.5522i	1.10820	−	1.09238i
$889$	−22.8984	−	8.60800i	−0.767986	−	0.288703i
$890$			23.2716i			0.780065i
$891$	0.328834	−	11.4328i	0.0110164	−	0.383014i
$892$	3.35509	−	1.93706i	0.112337	−	0.0648576i
$893$	1.22792	+	0.708939i	0.0410907	+	0.0237237i
$894$	−4.97389	+	1.29450i	−0.166352	+	0.0432946i
$895$	−13.6009	−	7.85251i	−0.454630	−	0.262481i
$896$	−5.35992	+	14.2580i	−0.179062	+	0.476328i
$897$	−0.941316	+	3.41466i	−0.0314296	+	0.114012i
$898$	−15.3165			−0.511118
$899$	11.0265	+	19.0985i	0.367755	+	0.636971i
$900$	1.23914	−	0.691856i	0.0413045	−	0.0230619i
$901$	−0.200492	−	0.115754i	−0.00667935	−	0.00385632i
$902$	5.45654	+	9.45100i	0.181683	+	0.314684i
$903$	33.1691	+	3.49454i	1.10380	+	0.116291i
$904$	−20.5763	+	35.6391i	−0.684356	+	1.18534i
$905$	5.63713	−	3.25460i	0.187385	−	0.108187i
$906$	33.1131	−	32.6404i	1.10011	−	1.08440i
$907$	−5.04914	+	8.74536i	−0.167654	+	0.290385i	−0.937595	−	0.347730i	$-0.886952\pi$
$907$	−5.04914	+	8.74536i	−0.167654	+	0.290385i	0.769941	+	0.638115i	$0.220286\pi$
$908$	3.10697	−	5.38142i	0.103108	−	0.178589i
$909$	−32.3411	+	18.0572i	−1.07269	+	0.598920i
$910$	5.92633	+	2.22784i	0.196456	+	0.0738521i
$911$	−4.94086	+	2.85261i	−0.163698	+	0.0945111i	−0.579611	−	0.814893i	$-0.696795\pi$
$911$	−4.94086	+	2.85261i	−0.163698	+	0.0945111i	0.415913	+	0.909404i	$0.363462\pi$
$912$	2.92084	−	2.87915i	0.0967188	−	0.0953381i
$913$		−	11.6016i		−	0.383958i
$914$			33.0065i			1.09176i
$915$	−1.24280	−	4.77524i	−0.0410857	−	0.157865i
$916$	−4.57854	+	2.64342i	−0.151279	+	0.0873412i
$917$	5.39837	+	32.6172i	0.178270	+	1.07712i
$918$	−2.43026	+	8.34564i	−0.0802106	+	0.275447i
$919$	10.5866	−	18.3366i	0.349221	−	0.604869i	−0.636890	−	0.770955i	$-0.719780\pi$
$919$	10.5866	−	18.3366i	0.349221	−	0.604869i	0.986111	+	0.166086i	$0.0531128\pi$
$920$	−1.61353	+	2.79472i	−0.0531966	+	0.0921393i
$921$	37.0957	+	10.2261i	1.22235	+	0.336963i
$922$	−23.0066	+	13.2829i	−0.757683	+	0.437448i
$923$	6.28349	−	10.8833i	0.206824	−	0.358229i
$924$	−2.51709	+	1.11993i	−0.0828063	+	0.0368431i
$925$	−4.38029	−	7.58689i	−0.144023	−	0.249455i
$926$	−18.6059	−	10.7421i	−0.611429	−	0.353009i
$927$	−27.9536	−	0.401922i	−0.918116	−	0.0132008i
$928$	12.8230	+	22.2100i	0.420934	+	0.729079i
$929$	−2.90861			−0.0954284			−0.0477142	−	0.998861i	$-0.515194\pi$
$929$	−2.90861			−0.0954284			−0.0477142	+	0.998861i	$0.515194\pi$
$930$	−4.65722	+	1.21208i	−0.152716	+	0.0397458i
$931$	−1.88700	−	5.54452i	−0.0618439	−	0.181714i
$932$	6.81079	+	3.93221i	0.223095	+	0.128804i
$933$	−13.5207	+	49.0468i	−0.442647	+	1.60572i
$934$	−30.4609	−	17.5866i	−0.996712	−	0.575452i
$935$	1.48992	−	0.860206i	0.0487256	−	0.0281317i
$936$	−15.5015	+	8.65504i	−0.506681	+	0.282899i
$937$			0.261382i			0.00853898i	0.999991	+	0.00426949i	$0.00135902\pi$
$937$			0.261382i			0.00853898i	−0.999991	+	0.00426949i	$0.998641\pi$
$938$	15.0590	−	40.0589i	0.491695	−	1.30797i
$939$	−49.7823	−	13.7234i	−1.62458	−	0.447847i
$940$	−0.400835	−	0.694267i	−0.0130738	−	0.0226445i
$941$	−12.2499			−0.399336			−0.199668	−	0.979864i	$-0.563986\pi$
$941$	−12.2499			−0.399336			−0.199668	+	0.979864i	$0.563986\pi$
$942$	−6.94895	+	25.2076i	−0.226409	+	0.821307i
$943$			7.33853i			0.238976i
$944$	−27.6751			−0.900749
$945$	−11.0028	−	8.24251i	−0.357920	−	0.268129i
$946$	−11.4293			−0.371600
$947$			2.95899i			0.0961542i	0.998844	+	0.0480771i	$0.0153093\pi$
$947$			2.95899i			0.0961542i	−0.998844	+	0.0480771i	$0.984691\pi$
$948$	−3.48641	+	12.6471i	−0.113233	+	0.410759i
$949$	20.3641			0.661046
$950$	−0.516945	−	0.895376i	−0.0167719	−	0.0290498i
$951$	−9.78456	−	2.69730i	−0.317286	−	0.0874659i
$952$	10.7986	−	1.78725i	0.349986	−	0.0579250i
$953$		−	17.5549i		−	0.568660i	−0.958726	−	0.284330i	$-0.908229\pi$
$953$		−	17.5549i		−	0.568660i	0.958726	−	0.284330i	$-0.0917711\pi$
$954$	0.00911411	−	0.633884i	0.000295080	−	0.0205228i
$955$	−8.08429	+	4.66747i	−0.261602	+	0.151036i
$956$	−6.82444	−	3.94009i	−0.220718	−	0.127432i
$957$	5.73739	−	20.8126i	0.185464	−	0.672777i
$958$	−20.7983	−	12.0079i	−0.671964	−	0.387959i
$959$	−0.220264	−	0.268177i	−0.00711271	−	0.00865988i
$960$	−14.9036	+	3.87879i	−0.481011	+	0.125188i
$961$	25.9444			0.836915
$962$	10.4820	+	18.1553i	0.337952	+	0.585351i
$963$	−13.9037	−	24.9021i	−0.448042	−	0.802458i
$964$	−6.55987	−	3.78734i	−0.211279	−	0.121982i
$965$	−2.80000	−	4.84974i	−0.0901351	−	0.156119i
$966$	5.94682	+	0.626530i	0.191336	+	0.0201583i
$967$	2.54007	−	4.39953i	0.0816832	−	0.141479i	−0.822290	−	0.569069i	$-0.807304\pi$
$967$	2.54007	−	4.39953i	0.0816832	−	0.141479i	0.903973	+	0.427589i	$0.140637\pi$
$968$	−24.8376	+	14.3400i	−0.798310	+	0.460905i
$969$	−1.89131	−	0.521375i	−0.0607576	−	0.0167490i
$970$	−5.80854	+	10.0607i	−0.186501	+	0.323029i
$971$	25.6635	−	44.4505i	0.823582	−	1.42649i	−0.0794166	−	0.996842i	$-0.525306\pi$
$971$	25.6635	−	44.4505i	0.823582	−	1.42649i	0.902998	−	0.429644i	$-0.141361\pi$
$972$	7.18708	−	1.65142i	0.230526	−	0.0529694i
$973$	−6.34893	−	7.72996i	−0.203537	−	0.247811i
$974$	−6.41623	+	3.70441i	−0.205589	+	0.118697i
$975$	0.844821	+	3.24607i	0.0270559	+	0.103958i
$976$			8.06240i			0.258071i
$977$			56.3370i			1.80238i	0.433423	+	0.901191i	$0.357306\pi$
$977$			56.3370i			1.80238i	−0.433423	+	0.901191i	$0.642694\pi$
$978$	−26.6241	+	26.2440i	−0.851345	+	0.839192i
$979$	20.7270	−	11.9667i	0.662437	−	0.382458i
$980$	−0.643467	+	3.24834i	−0.0205548	+	0.103764i
$981$	−0.278363	+	19.3601i	−0.00888744	+	0.618120i
$982$	18.1246	−	31.3928i	0.578380	−	1.00178i
$983$	23.1843	−	40.1564i	0.739465	−	1.28079i	−0.213272	−	0.976993i	$-0.568412\pi$
$983$	23.1843	−	40.1564i	0.739465	−	1.28079i	0.952737	−	0.303798i	$-0.0982547\pi$
$984$	−26.1962	+	25.8222i	−0.835104	+	0.823183i
$985$	6.18178	−	3.56905i	0.196968	−	0.113719i
$986$	−8.20358	+	14.2090i	−0.261255	+	0.452507i
$987$	−4.56616	+	6.28149i	−0.145342	+	0.199942i
$988$	−0.383253	−	0.663814i	−0.0121929	−	0.0211187i
$989$	−6.65600	−	3.84285i	−0.211649	−	0.122195i
$990$	4.04564	+	2.41396i	0.128579	+	0.0767206i
$991$	−7.66378	−	13.2741i	−0.243448	−	0.421665i	0.718246	−	0.695789i	$-0.244945\pi$
$991$	−7.66378	−	13.2741i	−0.243448	−	0.421665i	−0.961694	+	0.274125i	$0.911612\pi$
$992$	−5.87929			−0.186668
$993$	−14.9266	+	54.1468i	−0.473681	+	1.71830i
$994$	−19.8590	−	7.46544i	−0.629890	−	0.236790i
$995$	9.64089	+	5.56617i	0.305637	+	0.176460i
$996$	7.23902	−	1.88402i	0.229377	−	0.0596975i
$997$	−35.3852	−	20.4297i	−1.12066	−	0.647014i	−0.179092	−	0.983832i	$-0.557316\pi$
$997$	−35.3852	−	20.4297i	−1.12066	−	0.647014i	−0.941570	+	0.336818i	$0.890649\pi$
$998$	23.8844	−	13.7897i	0.756047	−	0.436504i
$999$	−10.8309	−	44.2141i	−0.342674	−	1.39887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.b.131.5	yes	30
3.2	odd	2		945.2.t.b.341.11		30
7.3	odd	6		315.2.be.b.311.11	yes	30
9.2	odd	6		315.2.be.b.236.11	yes	30
9.7	even	3		945.2.be.b.656.5		30
21.17	even	6		945.2.be.b.206.5		30
63.38	even	6	inner	315.2.t.b.101.11	✓	30
63.52	odd	6		945.2.t.b.521.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.11	✓	30	63.38	even	6	inner
315.2.t.b.131.5	yes	30	1.1	even	1	trivial
315.2.be.b.236.11	yes	30	9.2	odd	6
315.2.be.b.311.11	yes	30	7.3	odd	6
945.2.t.b.341.11		30	3.2	odd	2
945.2.t.b.521.5		30	63.52	odd	6
945.2.be.b.206.5		30	21.17	even	6
945.2.be.b.656.5		30	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.23569i q^{2} +(0.460303 - 1.66977i) q^{3} +0.473066 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.06332 - 0.568792i) q^{6} +(2.47654 + 0.930987i) q^{7} -3.05595i q^{8} +(-2.57624 - 1.53720i) q^{9} +O(q^{10})\)	\(q-1.23569i q^{2} +(0.460303 - 1.66977i) q^{3} +0.473066 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.06332 - 0.568792i) q^{6} +(2.47654 + 0.930987i) q^{7} -3.05595i q^{8} +(-2.57624 - 1.53720i) q^{9} +(1.07014 - 0.617846i) q^{10} +(-1.10058 - 0.635419i) q^{11} +(0.217754 - 0.789910i) q^{12} +(1.67710 + 0.968277i) q^{13} +(1.15041 - 3.06024i) q^{14} +(1.67621 - 0.436249i) q^{15} -2.83008 q^{16} +(0.676881 + 1.17239i) q^{17} +(-1.89950 + 3.18344i) q^{18} +(-0.724595 - 0.418345i) q^{19} +(0.236533 + 0.409687i) q^{20} +(2.69449 - 3.70671i) q^{21} +(-0.785182 + 1.35997i) q^{22} +(-0.914519 + 0.527998i) q^{23} +(-5.10272 - 1.40666i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.19649 - 2.07238i) q^{26} +(-3.75261 + 3.59415i) q^{27} +(1.17157 + 0.440418i) q^{28} +(-8.49399 + 4.90401i) q^{29} +(-0.539070 - 2.07128i) q^{30} -2.24847i q^{31} -2.61479i q^{32} +(-1.56760 + 1.54522i) q^{33} +(1.44872 - 0.836416i) q^{34} +(0.432012 + 2.61024i) q^{35} +(-1.21873 - 0.727195i) q^{36} +(-4.38029 + 7.58689i) q^{37} +(-0.516945 + 0.895376i) q^{38} +(2.38877 - 2.35467i) q^{39} +(2.64653 - 1.52797i) q^{40} +(3.47470 - 6.01835i) q^{41} +(-4.58035 - 3.32956i) q^{42} +(3.63907 + 6.30306i) q^{43} +(-0.520646 - 0.300595i) q^{44} +(0.0431301 - 2.99969i) q^{45} +(0.652443 + 1.13006i) q^{46} -1.69463 q^{47} +(-1.30269 + 4.72557i) q^{48} +(5.26652 + 4.61126i) q^{49} +(1.07014 + 0.617846i) q^{50} +(2.26919 - 0.590578i) q^{51} +(0.793381 + 0.458059i) q^{52} +(-0.148100 + 0.0855054i) q^{53} +(4.44126 + 4.63707i) q^{54} -1.27084i q^{55} +(2.84505 - 7.56818i) q^{56} +(-1.03207 + 1.01734i) q^{57} +(6.05984 + 10.4960i) q^{58} +9.77894 q^{59} +(0.792959 - 0.206375i) q^{60} -2.84883i q^{61} -2.77842 q^{62} +(-4.94906 - 6.20538i) q^{63} -8.89123 q^{64} +1.93655i q^{65} +(1.90942 + 1.93707i) q^{66} +13.0901 q^{67} +(0.320209 + 0.554619i) q^{68} +(0.460678 + 1.77007i) q^{69} +(3.22546 - 0.533834i) q^{70} -6.48936i q^{71} +(-4.69759 + 7.87286i) q^{72} +(9.10680 - 5.25781i) q^{73} +(9.37506 + 5.41269i) q^{74} +(1.21591 + 1.23352i) q^{75} +(-0.342781 - 0.197905i) q^{76} +(-2.13406 - 2.59827i) q^{77} +(-2.90965 - 2.95179i) q^{78} -16.0108 q^{79} +(-1.41504 - 2.45092i) q^{80} +(4.27405 + 7.92038i) q^{81} +(-7.43683 - 4.29366i) q^{82} +(4.56456 + 7.90605i) q^{83} +(1.27467 - 1.75352i) q^{84} +(-0.676881 + 1.17239i) q^{85} +(7.78864 - 4.49677i) q^{86} +(4.27874 + 16.4403i) q^{87} +(-1.94181 + 3.36331i) q^{88} +(-9.41641 + 16.3097i) q^{89} +(-3.70669 - 0.0532955i) q^{90} +(3.25197 + 3.95934i) q^{91} +(-0.432628 + 0.249778i) q^{92} +(-3.75443 - 1.03498i) q^{93} +2.09404i q^{94} -0.836690i q^{95} +(-4.36609 - 1.20360i) q^{96} +(-8.14174 + 4.70063i) q^{97} +(5.69810 - 6.50780i) q^{98} +(1.85859 + 3.32880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

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