LMFDB - Embedded newform 315.2.t.b.101.11

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			101.11
Character	$\chi$	$=$	315.101
Dual form			315.2.t.b.131.5

$q$-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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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	$0.143918\pi$
$2$			1.23569i			0.873766i	−0.899518	+	0.436883i	$0.856082\pi$
$3$	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	−0.656656	−	0.754190i	$-0.728030\pi$
$11$	−1.10058	+	0.635419i	−0.331837	+	0.191586i	0.324820	+	0.945776i	$0.394696\pi$
$12$	0.217754	+	0.789910i	0.0628600	+	0.228027i
$13$	1.67710	−	0.968277i	0.465145	−	0.268552i	−0.249060	−	0.968488i	$-0.580122\pi$
$13$	1.67710	−	0.968277i	0.465145	−	0.268552i	0.714205	+	0.699936i	$0.246788\pi$
$14$	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	−0.772192	−	0.635390i	$-0.780839\pi$
$17$	0.676881	−	1.17239i	0.164168	−	0.284347i	0.936359	+	0.351043i	$0.114173\pi$
$18$	−1.89950	−	3.18344i	−0.447717	−	0.750344i
$19$	−0.724595	+	0.418345i	−0.166233	+	0.0959749i	−0.580809	−	0.814040i	$-0.697264\pi$
$19$	−0.724595	+	0.418345i	−0.166233	+	0.0959749i	0.414575	+	0.910015i	$0.363930\pi$
$20$	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	0.401615	−	0.915808i	$-0.368449\pi$
$23$	−0.914519	−	0.527998i	−0.190690	−	0.110095i	−0.592306	+	0.805713i	$0.701782\pi$
$24$	−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	−0.995235	−	0.0975049i	$-0.968914\pi$
$29$	−8.49399	−	4.90401i	−1.57729	−	0.910651i	−0.582059	−	0.813146i	$-0.697753\pi$
$30$	−0.539070	+	2.07128i	−0.0984202	+	0.378162i
$31$			2.24847i			0.403838i	0.979402	+	0.201919i	$0.0647177\pi$
$31$			2.24847i			0.403838i	−0.979402	+	0.201919i	$0.935282\pi$
$32$			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	−0.960953	−	0.276712i	$-0.910755\pi$
$37$	−4.38029	−	7.58689i	−0.720116	−	1.24728i	0.240837	−	0.970566i	$-0.422578\pi$
$38$	−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	0.998750	+	0.0499771i	$0.0159148\pi$
$41$	3.47470	+	6.01835i	0.542657	+	0.939909i	−0.456094	+	0.889932i	$0.650752\pi$
$42$	−4.58035	+	3.32956i	−0.706764	+	0.513762i
$43$	3.63907	−	6.30306i	0.554953	−	0.961208i	−0.442954	−	0.896544i	$-0.646069\pi$
$43$	3.63907	−	6.30306i	0.554953	−	0.961208i	0.997907	−	0.0646631i	$-0.0205973\pi$
$44$	−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	0.489794	−	0.871838i	$-0.337072\pi$
$53$	−0.148100	−	0.0855054i	−0.0203431	−	0.0117451i	−0.510137	+	0.860093i	$0.670405\pi$
$54$	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	$0.0583793\pi$
$61$			2.84883i			0.364755i	−0.983229	+	0.182378i	$0.941621\pi$
$62$	−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	$0.125824\pi$
$71$			6.48936i			0.770145i	−0.922886	+	0.385072i	$0.874176\pi$
$72$	−4.69759	−	7.87286i	−0.553617	−	0.927826i
$73$	9.10680	+	5.25781i	1.06587	+	0.615380i	0.927050	−	0.374937i	$-0.122336\pi$
$73$	9.10680	+	5.25781i	1.06587	+	0.615380i	0.138820	+	0.990318i	$0.455669\pi$
$74$	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	−0.498974	−	0.866617i	$-0.666290\pi$
$83$	4.56456	−	7.90605i	0.501026	−	0.867802i	0.999999	−	0.00118486i	$-0.000377154\pi$
$84$	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	−0.551898	−	0.833912i	$-0.686096\pi$
$89$	−9.41641	−	16.3097i	−0.998138	−	1.72883i	−0.446240	−	0.894913i	$-0.647237\pi$
$90$	−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	0.0260423	−	0.999661i	$-0.491710\pi$
$97$	−8.14174	−	4.70063i	−0.826668	−	0.477277i	−0.852711	+	0.522384i	$0.825043\pi$
$98$	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	0.990510	+	0.137438i	$0.0438869\pi$
$101$	6.17344	+	10.6927i	0.614280	+	1.06396i	−0.376230	+	0.926526i	$0.622780\pi$
$102$	−0.729772	+	2.80402i	−0.0722582	+	0.277640i
$103$	8.07033	+	4.65941i	0.795194	+	0.459105i	0.841788	−	0.539809i	$-0.181503\pi$
$103$	8.07033	+	4.65941i	0.795194	+	0.459105i	−0.0465942	+	0.998914i	$0.514837\pi$
$104$	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	−0.0461137	−	0.998936i	$-0.514684\pi$
$107$	8.23320	−	4.75344i	0.795934	−	0.459532i	0.842047	+	0.539404i	$0.181350\pi$
$108$	−1.77523	−	1.70027i	−0.170822	−	0.163608i
$109$	−3.22701	+	5.58935i	−0.309092	+	0.535363i	−0.978164	−	0.207835i	$-0.933358\pi$
$109$	−3.22701	+	5.58935i	−0.309092	+	0.535363i	0.669072	+	0.743197i	$0.266692\pi$
$110$	−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	−0.935455	−	0.353446i	$-0.885010\pi$
$113$	−11.6622	+	6.73319i	−1.09709	+	0.633405i	−0.161635	+	0.986851i	$0.551677\pi$
$114$	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	−0.452667	−	0.891680i	$-0.649527\pi$
$131$	6.24793	−	10.8217i	0.545884	−	0.945499i	0.998551	−	0.0538192i	$-0.0171395\pi$
$132$	−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	−0.504845	−	0.863210i	$-0.668450\pi$
$137$	−0.113595	+	0.0655839i	−0.00970505	+	0.00560321i	0.495140	+	0.868813i	$0.335117\pi$
$138$	2.18726	+	0.569256i	0.186192	+	0.0484583i
$139$	−3.27427	+	1.89040i	−0.277720	+	0.160342i	−0.632391	−	0.774650i	$-0.717926\pi$
$139$	−3.27427	+	1.89040i	−0.277720	+	0.160342i	0.354671	+	0.934991i	$0.384593\pi$
$140$	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	0.582761	−	0.812644i	$-0.301973\pi$
$149$	2.07964	+	1.20068i	0.170371	+	0.0983635i	−0.412390	+	0.911007i	$0.635306\pi$
$150$	1.52425	+	1.50249i	0.124454	+	0.122678i
$151$	−10.8621	−	18.8137i	−0.883946	−	1.53104i	−0.846917	−	0.531725i	$-0.821544\pi$
$151$	−10.8621	−	18.8137i	−0.883946	−	1.53104i	−0.0370284	−	0.999314i	$-0.511789\pi$
$152$	−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	$0.162096\pi$
$157$			12.2170i			0.975024i	−0.873116	+	0.487512i	$0.837904\pi$
$158$		−	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	0.973731	+	0.227703i	$0.0731216\pi$
$163$	8.73352	+	15.1269i	0.684062	+	1.18483i	−0.289668	+	0.957127i	$0.593545\pi$
$164$	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	0.678719	−	0.734398i	$-0.262535\pi$
$167$	−3.83353	−	6.63987i	−0.296648	−	0.513809i	−0.975367	+	0.220589i	$0.929202\pi$
$168$	−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	−0.103470	−	0.994633i	$-0.532995\pi$
$179$	−13.6009	−	7.85251i	−1.01658	−	0.586924i	−0.913112	+	0.407708i	$0.866328\pi$
$180$	0.0204034	+	1.41905i	0.00152078	+	0.105770i
$181$			6.50920i			0.483825i	0.970298	+	0.241912i	$0.0777747\pi$
$181$			6.50920i			0.483825i	−0.970298	+	0.241912i	$0.922225\pi$
$182$	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	$-0.890342\pi$
$191$		−	9.33494i		−	0.675452i	0.941244	−	0.337726i	$-0.109658\pi$
$192$	−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	$0.0818400\pi$
$197$			7.13811i			0.508569i	−0.967129	+	0.254284i	$0.918160\pi$
$198$	4.11337	+	2.29665i	0.292324	+	0.163216i
$199$	9.64089	+	5.56617i	0.683425	+	0.394575i	0.801144	−	0.598471i	$-0.204225\pi$
$199$	9.64089	+	5.56617i	0.683425	+	0.394575i	−0.117719	+	0.993047i	$0.537558\pi$
$200$	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	0.977043	−	0.213042i	$-0.0683370\pi$
$211$	4.41618	+	7.64904i	0.304022	+	0.526582i	−0.673021	+	0.739623i	$0.735004\pi$
$212$	−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	0.718301	−	0.695732i	$-0.244920\pi$
$223$	7.09222	+	4.09470i	0.474930	+	0.274201i	−0.243371	+	0.969933i	$0.578253\pi$
$224$	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	0.997370	−	0.0724804i	$-0.0230915\pi$
$227$	6.56772	+	11.3756i	0.435915	+	0.755027i	−0.561455	+	0.827507i	$0.689758\pi$
$228$	−0.488238	−	0.481268i	−0.0323343	−	0.0318728i
$229$	−9.67845	−	5.58785i	−0.639570	−	0.369256i	0.144879	−	0.989449i	$-0.453721\pi$
$229$	−9.67845	−	5.58785i	−0.639570	−	0.369256i	−0.784449	+	0.620194i	$0.787054\pi$
$230$	−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	0.0522289	−	0.998635i	$-0.483367\pi$
$233$	14.3971	−	8.31218i	0.943187	−	0.544549i	0.890958	+	0.454086i	$0.150034\pi$
$234$	−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	−0.887803	−	0.460223i	$-0.847769\pi$
$239$	−14.4260	+	8.32885i	−0.933140	+	0.538748i	−0.0453365	+	0.998972i	$0.514436\pi$
$240$	−4.74381	−	1.23462i	−0.306212	−	0.0796944i
$241$	−13.8667	+	8.00595i	−0.893233	+	0.515709i	−0.874999	−	0.484125i	$-0.839138\pi$
$241$	−13.8667	+	8.00595i	−0.893233	+	0.515709i	−0.0182347	+	0.999834i	$0.505805\pi$
$242$	−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	−0.720910	−	0.693029i	$-0.756276\pi$
$257$	3.84310	−	6.65644i	0.239726	−	0.415217i	0.960636	+	0.277812i	$0.0896091\pi$
$258$	−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	0.105109	−	0.994461i	$-0.466481\pi$
$263$	16.5237	−	9.53994i	1.01889	−	0.588258i	0.913783	+	0.406203i	$0.133147\pi$
$264$	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	−0.490595	−	0.871388i	$-0.663220\pi$
$269$	8.35391	−	14.4694i	0.509347	−	0.882215i	0.999941	−	0.0108266i	$-0.00344629\pi$
$270$	−1.79519	−	6.16478i	−0.109252	−	0.375177i
$271$	−16.5843	+	9.57497i	−1.00743	+	0.581638i	−0.910437	−	0.413648i	$-0.864255\pi$
$271$	−16.5843	+	9.57497i	−1.00743	+	0.581638i	−0.0969893	+	0.995285i	$0.530921\pi$
$272$	−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	0.999995	+	0.00302404i	$0.000962584\pi$
$277$	8.36521	+	14.4890i	0.502617	+	0.870558i	−0.497379	+	0.867533i	$0.665704\pi$
$278$	−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	0.210872	−	0.977514i	$-0.432370\pi$
$281$	−8.88850	−	5.13178i	−0.530244	−	0.306136i	−0.741116	+	0.671377i	$0.765703\pi$
$282$	3.49655	−	0.963891i	0.208217	−	0.0573989i
$283$		−	10.5602i		−	0.627737i	−0.949466	−	0.313869i	$-0.898375\pi$
$283$		−	10.5602i		−	0.627737i	0.949466	−	0.313869i	$-0.101625\pi$
$284$			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	0.635504	−	0.772098i	$-0.280792\pi$
$293$	−6.00652	−	10.4036i	−0.350904	−	0.607784i	−0.986408	+	0.164314i	$0.947459\pi$
$294$	−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	$-0.781424\pi$
$307$		−	22.2161i		−	1.26794i	0.773358	−	0.633970i	$-0.218576\pi$
$308$	−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	$0.318971\pi$
$313$			29.8139i			1.68518i	−0.538553	+	0.842591i	$0.681029\pi$
$314$	−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	$0.0526206\pi$
$317$			5.85984i			0.329121i	−0.986367	+	0.164561i	$0.947379\pi$
$318$	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	0.896520	−	0.443003i	$-0.146087\pi$
$337$	1.18605	+	2.05430i	0.0646084	+	0.111905i	−0.831912	+	0.554908i	$0.812754\pi$
$338$	−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	$0.303949\pi$
$347$			30.4100i			1.63249i	−0.577704	+	0.816246i	$0.696051\pi$
$348$	2.02413	−	7.77735i	0.108505	−	0.416910i
$349$	20.4722	+	11.8196i	1.09585	+	0.632690i	0.935128	−	0.354309i	$-0.115284\pi$
$349$	20.4722	+	11.8196i	1.09585	+	0.632690i	0.160723	+	0.987000i	$0.448617\pi$
$350$	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	0.972206	−	0.234129i	$-0.0752238\pi$
$353$	5.32349	+	9.22056i	0.283341	+	0.490761i	−0.688865	+	0.724890i	$0.741891\pi$
$354$	−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	−0.628532	−	0.777784i	$-0.716344\pi$
$359$	−5.10095	+	2.94504i	−0.269218	+	0.155433i	0.359314	+	0.933217i	$0.383011\pi$
$360$	−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	−0.517290	−	0.855810i	$-0.673059\pi$
$367$	−0.666312	+	0.384696i	−0.0347812	+	0.0200810i	0.482509	+	0.875891i	$0.339726\pi$
$368$	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	−0.0927956	−	0.995685i	$-0.529580\pi$
$373$	15.7575	−	27.2927i	0.815891	−	1.41316i	0.908686	−	0.417479i	$-0.137086\pi$
$374$	−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	−0.455109	−	0.890436i	$-0.650400\pi$
$383$	10.6382	−	18.4259i	0.543585	−	0.941517i	0.998694	−	0.0510816i	$-0.0162669\pi$
$384$	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	−0.358820	−	0.933407i	$-0.616821\pi$
$389$	5.32769	−	3.07594i	0.270124	−	0.155956i	0.628944	+	0.777450i	$0.283487\pi$
$390$	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	−0.954173	−	0.299255i	$-0.903262\pi$
$397$	−23.3539	+	13.4834i	−1.17210	+	0.676711i	−0.217924	+	0.975966i	$0.569929\pi$
$398$	−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	0.846278	−	0.532741i	$-0.178838\pi$
$401$	16.1812	+	9.34221i	0.808050	+	0.466528i	−0.0382283	+	0.999269i	$0.512171\pi$
$402$	−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	$-0.998076\pi$
$409$		−	0.244490i		−	0.0120893i	0.999982	−	0.00604463i	$-0.00192408\pi$
$410$			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	0.967805	+	0.251701i	$0.0809898\pi$
$419$	14.3672	+	24.8847i	0.701882	+	1.21569i	−0.265923	+	0.963994i	$0.585677\pi$
$420$	2.15593	−	0.227139i	0.105199	−	0.0110832i
$421$	−12.7923	+	22.1570i	−0.623460	+	1.07986i	0.365377	+	0.930860i	$0.380940\pi$
$421$	−12.7923	+	22.1570i	−0.623460	+	1.07986i	−0.988837	+	0.149004i	$0.952393\pi$
$422$	−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	0.362635	−	0.931931i	$-0.381877\pi$
$431$	−5.46258	−	3.15382i	−0.263123	−	0.151914i	−0.625758	+	0.780017i	$0.715210\pi$
$432$	10.6202	+	10.1717i	0.510964	+	0.489387i
$433$		−	0.0928113i		−	0.00446023i	−0.999998	−	0.00223011i	$-0.999290\pi$
$433$		−	0.0928113i		−	0.00446023i	0.999998	−	0.00223011i	$-0.000709868\pi$
$434$	−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	$-0.905609\pi$
$439$		−	12.2450i		−	0.584424i	0.956354	−	0.292212i	$-0.0943912\pi$
$440$	−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	$0.323884\pi$
$443$			35.8146i			1.70160i	−0.525486	+	0.850802i	$0.676116\pi$
$444$	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	$0.0944805\pi$
$449$			12.3951i			0.584960i	−0.956272	+	0.292480i	$0.905520\pi$
$450$	−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	0.499353	+	0.866399i	$0.333571\pi$
$461$	−10.7493	+	18.6184i	−0.500647	+	0.867146i	−1.00000		0.000747358i	$0.999762\pi$
$462$	2.92537	−	6.57488i	0.136100	−	0.305891i
$463$	8.69322	+	15.0571i	0.404008	+	0.699763i	0.994205	−	0.107496i	$-0.0342834\pi$
$463$	8.69322	+	15.0571i	0.404008	+	0.699763i	−0.590197	+	0.807259i	$0.700950\pi$
$464$	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	0.980981	+	0.194103i	$0.0621794\pi$
$467$	14.2322	+	24.6509i	0.658588	+	1.14071i	−0.322393	+	0.946606i	$0.604487\pi$
$468$	−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	0.997982	−	0.0634898i	$-0.0202230\pi$
$479$	9.71758	+	16.8313i	0.444007	+	0.769044i	−0.553975	+	0.832533i	$0.686890\pi$
$480$	−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	−0.925920	−	0.377720i	$-0.876708\pi$
$487$	−2.99784	+	5.19242i	−0.135845	+	0.235291i	0.790075	+	0.613010i	$0.210042\pi$
$488$	−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	0.198478	−	0.980105i	$-0.436400\pi$
$491$	25.4050	−	14.6676i	1.14651	−	0.661939i	0.948035	+	0.318166i	$0.103067\pi$
$492$	−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	−0.500434	−	0.865775i	$-0.666826\pi$
$499$	11.1595	−	19.3288i	0.499566	−	0.865274i	1.00000		0.000500987i	$0.000159469\pi$
$500$	−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	−0.791057	−	0.611742i	$-0.790469\pi$
$509$	3.02895	−	5.24629i	0.134256	−	0.232538i	0.925313	+	0.379205i	$0.123802\pi$
$510$	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	−0.898046	−	0.439902i	$-0.855013\pi$
$521$	−1.55342	+	2.69061i	−0.0680568	+	0.117878i	0.829989	+	0.557780i	$0.188347\pi$
$522$	0.522723	+	36.3553i	0.0228790	+	1.59123i
$523$	18.9223	−	10.9248i	0.827417	−	0.477709i	−0.0255507	−	0.999674i	$-0.508134\pi$
$523$	18.9223	−	10.9248i	0.827417	−	0.477709i	0.852967	+	0.521964i	$0.174801\pi$
$524$	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	0.906055	−	0.423159i	$-0.139079\pi$
$541$	2.01335	+	3.48723i	0.0865608	+	0.149928i	−0.819494	+	0.573087i	$0.805746\pi$
$542$	−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	−0.340942	−	0.940084i	$-0.610746\pi$
$547$	15.0541	−	26.0744i	0.643666	−	1.11486i	0.984608	−	0.174777i	$-0.0559206\pi$
$548$	−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	0.337070	−	0.941480i	$-0.390564\pi$
$557$	−7.31014	−	4.22051i	−0.309740	−	0.178829i	−0.646810	+	0.762651i	$0.723897\pi$
$558$	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	$-0.797049\pi$
$569$		−	28.3984i		−	1.19052i	0.803533	−	0.595261i	$-0.202951\pi$
$570$	−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	−0.363261	−	0.931687i	$-0.618337\pi$
$577$	−32.4703	−	18.7467i	−1.35176	−	0.780437i	−0.988495	+	0.151250i	$0.951670\pi$
$578$	−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	−0.910040	−	0.414521i	$-0.863949\pi$
$587$	−2.32671	+	4.02998i	−0.0960337	+	0.166335i	0.814006	+	0.580857i	$0.197282\pi$
$588$	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	−0.880406	−	0.474221i	$-0.842730\pi$
$593$	−20.7205	−	35.8890i	−0.850890	−	1.47379i	0.0295154	−	0.999564i	$-0.490604\pi$
$594$	−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	$0.183522\pi$
$599$			26.6839i			1.09027i	−0.838347	+	0.545137i	$0.816478\pi$
$600$	3.76956	+	3.71575i	0.153892	+	0.151695i
$601$	34.4248	+	19.8752i	1.40422	+	0.810726i	0.994822	−	0.101631i	$-0.0324062\pi$
$601$	34.4248	+	19.8752i	1.40422	+	0.810726i	0.409396	+	0.912357i	$0.365740\pi$
$602$	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	−0.994005	−	0.109331i	$-0.965129\pi$
$607$	−39.0673	−	22.5555i	−1.58569	−	0.915500i	−0.591686	−	0.806168i	$-0.701538\pi$
$608$	−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	−0.868012	−	0.496544i	$-0.834602\pi$
$613$	−0.0987025	+	0.170958i	−0.00398656	+	0.00690492i	0.864025	+	0.503448i	$0.167936\pi$
$614$	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	−0.896326	−	0.443396i	$-0.853773\pi$
$617$	−23.8582	+	13.7746i	−0.960496	+	0.554543i	−0.0641702	+	0.997939i	$0.520440\pi$
$618$	−19.3019	−	5.02349i	−0.776436	−	0.202075i
$619$	17.5302	−	10.1211i	0.704599	−	0.406800i	−0.104459	−	0.994529i	$-0.533311\pi$
$619$	17.5302	−	10.1211i	0.704599	−	0.406800i	0.809058	+	0.587729i	$0.199978\pi$
$620$	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	−0.500860	−	0.865528i	$-0.666983\pi$
$641$	−0.0435721	+	0.0251564i	−0.00172100	+	0.000993617i	0.499139	+	0.866522i	$0.333650\pi$
$642$	−14.2840	+	14.4908i	−0.563744	+	0.571908i
$643$	33.9516	−	19.6020i	1.33892	−	0.773026i	0.352273	−	0.935897i	$-0.385409\pi$
$643$	33.9516	−	19.6020i	1.33892	−	0.773026i	0.986647	+	0.162871i	$0.0520755\pi$
$644$	−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	−0.615759	−	0.787935i	$-0.711150\pi$
$647$	9.52565	−	16.4989i	0.374492	−	0.648639i	0.990251	+	0.139296i	$0.0444838\pi$
$648$	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	0.784282	−	0.620405i	$-0.213032\pi$
$653$	16.3324	+	9.42952i	0.639136	+	0.369006i	−0.145145	+	0.989410i	$0.546365\pi$
$654$	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	0.0451672	−	0.998979i	$-0.485618\pi$
$659$	−20.4698	−	11.8183i	−0.797391	−	0.460374i	−0.842558	+	0.538606i	$0.818951\pi$
$660$	−1.00385	+	0.276729i	−0.0390747	+	0.0107717i
$661$		−	49.0412i		−	1.90748i	−0.300627	−	0.953742i	$-0.597196\pi$
$661$		−	49.0412i		−	1.90748i	0.300627	−	0.953742i	$-0.402804\pi$
$662$		−	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	−0.937865	−	0.347000i	$-0.887200\pi$
$673$	−4.36922	+	7.56772i	−0.168421	+	0.291714i	0.769444	+	0.638715i	$0.220534\pi$
$674$	−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	0.555544	−	0.831487i	$-0.312510\pi$
$683$	2.95909	+	1.70843i	0.113227	+	0.0653714i	−0.442317	+	0.896859i	$0.645843\pi$
$684$	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	$-0.661096\pi$
$691$		−	45.9833i		−	1.74929i	0.484767	−	0.874643i	$-0.338904\pi$
$692$	−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	$-0.805130\pi$
$701$		−	30.4305i		−	1.14934i	0.818384	−	0.574672i	$-0.194870\pi$
$702$	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	0.976676	−	0.214719i	$-0.0688834\pi$
$719$	8.10824	+	14.0439i	0.302386	+	0.523748i	−0.674290	+	0.738467i	$0.735550\pi$
$720$	−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	0.994287	−	0.106736i	$-0.0340401\pi$
$727$	37.7210	+	21.7782i	1.39899	+	0.807710i	0.404707	+	0.914446i	$0.367373\pi$
$728$	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	−0.0777969	−	0.996969i	$-0.524789\pi$
$733$	−26.5351	−	15.3200i	−0.980096	−	0.565859i	−0.902299	+	0.431111i	$0.858122\pi$
$734$	−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	−0.503115	−	0.864220i	$-0.667813\pi$
$739$	13.5074	−	23.3956i	0.496879	−	0.860619i	0.999994	+	0.00360021i	$0.00114598\pi$
$740$	−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	−0.0408419	−	0.999166i	$-0.513004\pi$
$743$	21.9165	−	12.6535i	0.804040	−	0.464213i	0.844882	+	0.534953i	$0.179671\pi$
$744$	−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	0.316853	+	0.948475i	$0.397374\pi$
$751$	−18.1685	+	31.4687i	−0.662977	+	1.14831i	−0.979830	+	0.199835i	$0.935960\pi$
$752$	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	0.253925	−	0.967224i	$-0.418278\pi$
$761$	26.6098	−	46.0894i	0.964603	−	1.67074i	0.710678	−	0.703517i	$-0.248388\pi$
$762$	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	−0.426968	−	0.904267i	$-0.640418\pi$
$769$	3.95625	−	2.28414i	0.142666	−	0.0823682i	0.569634	+	0.821899i	$0.307085\pi$
$770$	−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	−0.893412	−	0.449238i	$-0.851696\pi$
$773$	−1.60297	+	2.77642i	−0.0576548	+	0.0998610i	0.835757	+	0.549099i	$0.185029\pi$
$774$	−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	$-0.988945\pi$
$787$		−	1.94824i		−	0.0694472i	0.999397	−	0.0347236i	$-0.0110551\pi$
$788$			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	−0.989749	−	0.142819i	$-0.954383\pi$
$797$	−17.4627	−	30.2462i	−0.618559	−	1.07138i	0.371190	−	0.928557i	$-0.378950\pi$
$798$	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	−0.354460	−	0.935071i	$-0.615335\pi$
$809$	−38.1558	−	22.0292i	−1.34148	−	0.774507i	−0.987025	+	0.160565i	$0.948668\pi$
$810$	9.46741	−	5.83522i	0.332651	−	0.205029i
$811$			5.63536i			0.197884i	0.995093	+	0.0989420i	$0.0315458\pi$
$811$			5.63536i			0.197884i	−0.995093	+	0.0989420i	$0.968454\pi$
$812$	−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	$-0.707332\pi$
$821$		−	45.5736i		−	1.59053i	0.606262	−	0.795265i	$-0.292668\pi$
$822$	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	$0.211538\pi$
$827$			35.4707i			1.23344i	−0.787184	+	0.616718i	$0.788462\pi$
$828$	1.49851	−	0.0215459i	0.0520769	−	0.000748772i
$829$	7.87390	+	4.54600i	0.273472	+	0.157889i	0.630464	−	0.776218i	$-0.282864\pi$
$829$	7.87390	+	4.54600i	0.273472	+	0.157889i	−0.356992	+	0.934107i	$0.616198\pi$
$830$	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	−0.791564	−	0.611086i	$-0.790733\pi$
$839$	3.86499	−	6.69435i	0.133434	−	0.231115i	0.924998	+	0.379971i	$0.124066\pi$
$840$	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	−0.133110	−	0.991101i	$-0.542496\pi$
$853$	−30.8996	−	17.8399i	−1.05798	−	0.610827i	−0.924874	+	0.380274i	$0.875830\pi$
$854$	−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	0.999853	−	0.0171176i	$-0.00544897\pi$
$857$	14.2012	+	24.5971i	0.485102	+	0.840222i	−0.514751	+	0.857340i	$0.672116\pi$
$858$	1.32668	−	5.09752i	0.0452920	−	0.174026i
$859$	16.2603	+	9.38788i	0.554794	+	0.320310i	0.751053	−	0.660242i	$-0.229546\pi$
$859$	16.2603	+	9.38788i	0.554794	+	0.320310i	−0.196259	+	0.980552i	$0.562879\pi$
$860$	−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	−0.801223	−	0.598366i	$-0.795817\pi$
$863$	−20.0830	+	11.5949i	−0.683634	+	0.394696i	0.117589	+	0.993062i	$0.462483\pi$
$864$	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	−0.121163	−	0.992633i	$-0.538662\pi$
$877$	23.6636	−	40.9866i	0.799064	−	1.38402i	0.920227	−	0.391386i	$-0.128004\pi$
$878$	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	−0.999335	−	0.0364598i	$-0.988392\pi$
$887$	−13.9410	+	24.1465i	−0.468092	+	0.810760i	0.531243	+	0.847220i	$0.321725\pi$
$888$	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	0.769941	−	0.638115i	$-0.220286\pi$
$907$	−5.04914	−	8.74536i	−0.167654	−	0.290385i	−0.937595	+	0.347730i	$0.886952\pi$
$908$	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	0.415913	−	0.909404i	$-0.363462\pi$
$911$	−4.94086	−	2.85261i	−0.163698	−	0.0945111i	−0.579611	+	0.814893i	$0.696795\pi$
$912$	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	0.986111	−	0.166086i	$-0.0531128\pi$
$919$	10.5866	+	18.3366i	0.349221	+	0.604869i	−0.636890	+	0.770955i	$0.719780\pi$
$920$	−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	$-0.998641\pi$
$937$		−	0.261382i		−	0.00853898i	0.999991	−	0.00426949i	$-0.00135902\pi$
$938$	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	$-0.984691\pi$
$947$		−	2.95899i		−	0.0961542i	0.998844	−	0.0480771i	$-0.0153093\pi$
$948$	−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	$0.0917711\pi$
$953$			17.5549i			0.568660i	−0.958726	+	0.284330i	$0.908229\pi$
$954$	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	0.903973	−	0.427589i	$-0.140637\pi$
$967$	2.54007	+	4.39953i	0.0816832	+	0.141479i	−0.822290	+	0.569069i	$0.807304\pi$
$968$	−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	0.902998	+	0.429644i	$0.141361\pi$
$971$	25.6635	+	44.4505i	0.823582	+	1.42649i	−0.0794166	+	0.996842i	$0.525306\pi$
$972$	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	$-0.642694\pi$
$977$		−	56.3370i		−	1.80238i	0.433423	−	0.901191i	$-0.357306\pi$
$978$	−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	0.952737	+	0.303798i	$0.0982547\pi$
$983$	23.1843	+	40.1564i	0.739465	+	1.28079i	−0.213272	+	0.976993i	$0.568412\pi$
$984$	−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	−0.961694	−	0.274125i	$-0.911612\pi$
$991$	−7.66378	+	13.2741i	−0.243448	+	0.421665i	0.718246	+	0.695789i	$0.244945\pi$
$992$	−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	−0.941570	−	0.336818i	$-0.890649\pi$
$997$	−35.3852	+	20.4297i	−1.12066	+	0.647014i	−0.179092	+	0.983832i	$0.557316\pi$
$998$	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.101.11	✓	30
3.2	odd	2		945.2.t.b.521.5		30
7.5	odd	6		315.2.be.b.236.11	yes	30
9.4	even	3		945.2.be.b.206.5		30
9.5	odd	6		315.2.be.b.311.11	yes	30
21.5	even	6		945.2.be.b.656.5		30
63.5	even	6	inner	315.2.t.b.131.5	yes	30
63.40	odd	6		945.2.t.b.341.11		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.11	✓	30	1.1	even	1	trivial
315.2.t.b.131.5	yes	30	63.5	even	6	inner
315.2.be.b.236.11	yes	30	7.5	odd	6
315.2.be.b.311.11	yes	30	9.5	odd	6
945.2.t.b.341.11		30	63.40	odd	6
945.2.t.b.521.5		30	3.2	odd	2
945.2.be.b.206.5		30	9.4	even	3
945.2.be.b.656.5		30	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
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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