LMFDB - Embedded newform 315.2.k.c.16.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.10
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.129832 + 0.224875i) q^{2} +(-0.458568 - 1.67024i) q^{3} +(0.966288 - 1.67366i) q^{4} +1.00000 q^{5} +(0.316059 - 0.319971i) q^{6} +(2.52961 - 0.775284i) q^{7} +1.02114 q^{8} +(-2.57943 + 1.53184i) q^{9} +O(q^{10})$	\(q+(0.129832 + 0.224875i) q^{2} +(-0.458568 - 1.67024i) q^{3} +(0.966288 - 1.67366i) q^{4} +1.00000 q^{5} +(0.316059 - 0.319971i) q^{6} +(2.52961 - 0.775284i) q^{7} +1.02114 q^{8} +(-2.57943 + 1.53184i) q^{9} +(0.129832 + 0.224875i) q^{10} -1.45333 q^{11} +(-3.23853 - 0.846450i) q^{12} +(-0.192262 - 0.333007i) q^{13} +(0.502765 + 0.468190i) q^{14} +(-0.458568 - 1.67024i) q^{15} +(-1.80000 - 3.11769i) q^{16} +(2.42509 + 4.20038i) q^{17} +(-0.679364 - 0.381168i) q^{18} +(0.194577 - 0.337018i) q^{19} +(0.966288 - 1.67366i) q^{20} +(-2.45491 - 3.86955i) q^{21} +(-0.188688 - 0.326817i) q^{22} -7.95180 q^{23} +(-0.468264 - 1.70556i) q^{24} +1.00000 q^{25} +(0.0499233 - 0.0864697i) q^{26} +(3.74139 + 3.60583i) q^{27} +(1.14677 - 4.98285i) q^{28} +(2.48443 - 4.30317i) q^{29} +(0.316059 - 0.319971i) q^{30} +(4.69746 - 8.13624i) q^{31} +(1.48854 - 2.57822i) q^{32} +(0.666450 + 2.42742i) q^{33} +(-0.629707 + 1.09068i) q^{34} +(2.52961 - 0.775284i) q^{35} +(0.0713050 + 5.79729i) q^{36} +(-5.98734 + 10.3704i) q^{37} +0.101049 q^{38} +(-0.468038 + 0.473830i) q^{39} +1.02114 q^{40} +(3.47579 + 6.02024i) q^{41} +(0.551439 - 1.05444i) q^{42} +(-1.06032 + 1.83652i) q^{43} +(-1.40433 + 2.43238i) q^{44} +(-2.57943 + 1.53184i) q^{45} +(-1.03239 - 1.78816i) q^{46} +(4.31165 + 7.46800i) q^{47} +(-4.38188 + 4.43611i) q^{48} +(5.79787 - 3.92233i) q^{49} +(0.129832 + 0.224875i) q^{50} +(5.90360 - 5.97665i) q^{51} -0.743121 q^{52} +(2.14561 + 3.71630i) q^{53} +(-0.325110 + 1.30949i) q^{54} -1.45333 q^{55} +(2.58310 - 0.791677i) q^{56} +(-0.652129 - 0.170446i) q^{57} +1.29023 q^{58} +(-4.41340 + 7.64423i) q^{59} +(-3.23853 - 0.846450i) q^{60} +(-3.87733 - 6.71574i) q^{61} +2.43952 q^{62} +(-5.33735 + 5.87475i) q^{63} -6.42696 q^{64} +(-0.192262 - 0.333007i) q^{65} +(-0.459338 + 0.465023i) q^{66} +(2.15001 - 3.72393i) q^{67} +9.37334 q^{68} +(3.64644 + 13.2814i) q^{69} +(0.502765 + 0.468190i) q^{70} -1.38250 q^{71} +(-2.63397 + 1.56423i) q^{72} +(5.49914 + 9.52479i) q^{73} -3.10938 q^{74} +(-0.458568 - 1.67024i) q^{75} +(-0.376035 - 0.651312i) q^{76} +(-3.67636 + 1.12674i) q^{77} +(-0.167319 - 0.0437319i) q^{78} +(0.839967 + 1.45487i) q^{79} +(-1.80000 - 3.11769i) q^{80} +(4.30693 - 7.90255i) q^{81} +(-0.902534 + 1.56323i) q^{82} +(6.11318 - 10.5883i) q^{83} +(-8.84846 + 0.369588i) q^{84} +(2.42509 + 4.20038i) q^{85} -0.550651 q^{86} +(-8.32662 - 2.17632i) q^{87} -1.48406 q^{88} +(-3.23965 + 5.61124i) q^{89} +(-0.679364 - 0.381168i) q^{90} +(-0.744523 - 0.693321i) q^{91} +(-7.68372 + 13.3086i) q^{92} +(-15.7436 - 4.11489i) q^{93} +(-1.11958 + 1.93916i) q^{94} +(0.194577 - 0.337018i) q^{95} +(-4.98886 - 1.30393i) q^{96} +(-0.759552 + 1.31558i) q^{97} +(1.63478 + 0.794552i) q^{98} +(3.74876 - 2.22627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.129832	+	0.224875i	0.0918048	+	0.159011i	0.908271	−	0.418383i	$-0.137403\pi$
$2$	0.129832	+	0.224875i	0.0918048	+	0.159011i	−0.816466	+	0.577394i	$0.804070\pi$
$3$	−0.458568	−	1.67024i	−0.264754	−	0.964316i
$3$	−0.458568	−	1.67024i	−0.264754	−	0.964316i
$4$	0.966288	−	1.67366i	0.483144	−	0.836830i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.316059	−	0.319971i	0.129031	−	0.130628i
$7$	2.52961	−	0.775284i	0.956103	−	0.293030i
$7$	2.52961	−	0.775284i	0.956103	−	0.293030i
$8$	1.02114			0.361029
$9$	−2.57943	+	1.53184i	−0.859811	+	0.510613i
$10$	0.129832	+	0.224875i	0.0410563	+	0.0711117i
$11$	−1.45333			−0.438195			−0.219098	−	0.975703i	$-0.570311\pi$
$11$	−1.45333			−0.438195			−0.219098	+	0.975703i	$0.570311\pi$
$12$	−3.23853	−	0.846450i	−0.934882	−	0.244349i
$13$	−0.192262	−	0.333007i	−0.0533238	−	0.0923596i	0.838131	−	0.545468i	$-0.183648\pi$
$13$	−0.192262	−	0.333007i	−0.0533238	−	0.0923596i	−0.891455	+	0.453109i	$0.850315\pi$
$14$	0.502765	+	0.468190i	0.134370	+	0.125129i
$15$	−0.458568	−	1.67024i	−0.118402	−	0.431255i
$16$	−1.80000	−	3.11769i	−0.450000	−	0.779422i
$17$	2.42509	+	4.20038i	0.588171	+	1.01874i	0.994472	+	0.105003i	$0.0334852\pi$
$17$	2.42509	+	4.20038i	0.588171	+	1.01874i	−0.406301	+	0.913739i	$0.633181\pi$
$18$	−0.679364	−	0.381168i	−0.160128	−	0.0898422i
$19$	0.194577	−	0.337018i	0.0446391	−	0.0773172i	−0.842843	−	0.538160i	$-0.819120\pi$
$19$	0.194577	−	0.337018i	0.0446391	−	0.0773172i	0.887482	+	0.460843i	$0.152453\pi$
$20$	0.966288	−	1.67366i	0.216068	−	0.374242i
$21$	−2.45491	−	3.86955i	−0.535706	−	0.844405i
$22$	−0.188688	−	0.326817i	−0.0402284	−	0.0696777i
$23$	−7.95180			−1.65806			−0.829032	−	0.559201i	$-0.811108\pi$
$23$	−7.95180			−1.65806			−0.829032	+	0.559201i	$0.811108\pi$
$24$	−0.468264	−	1.70556i	−0.0955840	−	0.348146i
$25$	1.00000			0.200000
$26$	0.0499233	−	0.0864697i	0.00979076	−	0.0169581i
$27$	3.74139	+	3.60583i	0.720031	+	0.693942i
$28$	1.14677	−	4.98285i	0.216719	−	0.941671i
$29$	2.48443	−	4.30317i	0.461348	−	0.799078i	−0.537681	−	0.843149i	$-0.680699\pi$
$29$	2.48443	−	4.30317i	0.461348	−	0.799078i	0.999028	+	0.0440708i	$0.0140327\pi$
$30$	0.316059	−	0.319971i	0.0577043	−	0.0584184i
$31$	4.69746	−	8.13624i	0.843689	−	1.46131i	−0.0430656	−	0.999072i	$-0.513712\pi$
$31$	4.69746	−	8.13624i	0.843689	−	1.46131i	0.886755	−	0.462240i	$-0.152954\pi$
$32$	1.48854	−	2.57822i	0.263139	−	0.455770i
$33$	0.666450	+	2.42742i	0.116014	+	0.422559i
$34$	−0.629707	+	1.09068i	−0.107994	+	0.187051i
$35$	2.52961	−	0.775284i	0.427582	−	0.131047i
$36$	0.0713050	+	5.79729i	0.0118842	+	0.966214i
$37$	−5.98734	+	10.3704i	−0.984313	+	1.70488i	−0.339361	+	0.940656i	$0.610211\pi$
$37$	−5.98734	+	10.3704i	−0.984313	+	1.70488i	−0.644952	+	0.764223i	$0.723123\pi$
$38$	0.101049			0.0163923
$39$	−0.468038	+	0.473830i	−0.0749461	+	0.0758736i
$40$	1.02114			0.161457
$41$	3.47579	+	6.02024i	0.542827	+	0.940203i	0.998740	+	0.0501794i	$0.0159793\pi$
$41$	3.47579	+	6.02024i	0.542827	+	0.940203i	−0.455914	+	0.890024i	$0.650687\pi$
$42$	0.551439	−	1.05444i	0.0850889	−	0.162703i
$43$	−1.06032	+	1.83652i	−0.161697	+	0.280067i	−0.935477	−	0.353387i	$-0.885030\pi$
$43$	−1.06032	+	1.83652i	−0.161697	+	0.280067i	0.773780	+	0.633454i	$0.218363\pi$
$44$	−1.40433	+	2.43238i	−0.211711	+	0.366695i
$45$	−2.57943	+	1.53184i	−0.384519	+	0.228353i
$46$	−1.03239	−	1.78816i	−0.152218	−	0.263650i
$47$	4.31165	+	7.46800i	0.628919	+	1.08932i	0.987769	+	0.155925i	$0.0498358\pi$
$47$	4.31165	+	7.46800i	0.628919	+	1.08932i	−0.358850	+	0.933395i	$0.616831\pi$
$48$	−4.38188	+	4.43611i	−0.632470	+	0.640297i
$49$	5.79787	−	3.92233i	0.828267	−	0.560334i
$50$	0.129832	+	0.224875i	0.0183610	+	0.0318021i
$51$	5.90360	−	5.97665i	0.826669	−	0.836899i
$52$	−0.743121			−0.103052
$53$	2.14561	+	3.71630i	0.294722	+	0.510473i	0.974920	−	0.222555i	$-0.0714397\pi$
$53$	2.14561	+	3.71630i	0.294722	+	0.510473i	−0.680198	+	0.733028i	$0.738106\pi$
$54$	−0.325110	+	1.30949i	−0.0442418	+	0.178200i
$55$	−1.45333			−0.195967
$56$	2.58310	−	0.791677i	0.345181	−	0.105792i
$57$	−0.652129	−	0.170446i	−0.0863766	−	0.0225762i
$58$	1.29023			0.169416
$59$	−4.41340	+	7.64423i	−0.574576	+	0.995194i	0.421512	+	0.906823i	$0.361500\pi$
$59$	−4.41340	+	7.64423i	−0.574576	+	0.995194i	−0.996088	+	0.0883715i	$0.971834\pi$
$60$	−3.23853	−	0.846450i	−0.418092	−	0.109276i
$61$	−3.87733	−	6.71574i	−0.496442	−	0.859862i	0.503550	−	0.863966i	$-0.332027\pi$
$61$	−3.87733	−	6.71574i	−0.496442	−	0.859862i	−0.999992	+	0.00410406i	$0.998694\pi$
$62$	2.43952			0.309819
$63$	−5.33735	+	5.87475i	−0.672443	+	0.740149i
$64$	−6.42696			−0.803370
$65$	−0.192262	−	0.333007i	−0.0238471	−	0.0413044i
$66$	−0.459338	+	0.465023i	−0.0565407	+	0.0572404i
$67$	2.15001	−	3.72393i	0.262666	−	0.454951i	−0.704283	−	0.709919i	$-0.748732\pi$
$67$	2.15001	−	3.72393i	0.262666	−	0.454951i	0.966950	+	0.254968i	$0.0820649\pi$
$68$	9.37334			1.13668
$69$	3.64644	+	13.2814i	0.438979	+	1.59890i
$70$	0.502765	+	0.468190i	0.0600919	+	0.0559594i
$71$	−1.38250			−0.164073			−0.0820363	−	0.996629i	$-0.526142\pi$
$71$	−1.38250			−0.164073			−0.0820363	+	0.996629i	$0.526142\pi$
$72$	−2.63397	+	1.56423i	−0.310417	+	0.184346i
$73$	5.49914	+	9.52479i	0.643626	+	1.11479i	0.984617	+	0.174726i	$0.0559040\pi$
$73$	5.49914	+	9.52479i	0.643626	+	1.11479i	−0.340991	+	0.940066i	$0.610763\pi$
$74$	−3.10938			−0.361458
$75$	−0.458568	−	1.67024i	−0.0529508	−	0.192863i
$76$	−0.376035	−	0.651312i	−0.0431342	−	0.0747106i
$77$	−3.67636	+	1.12674i	−0.418960	+	0.128404i
$78$	−0.167319	−	0.0437319i	−0.0189451	−	0.00495166i
$79$	0.839967	+	1.45487i	0.0945037	+	0.163685i	0.909401	−	0.415920i	$-0.136540\pi$
$79$	0.839967	+	1.45487i	0.0945037	+	0.163685i	−0.814898	+	0.579605i	$0.803207\pi$
$80$	−1.80000	−	3.11769i	−0.201246	−	0.348568i
$81$	4.30693	−	7.90255i	0.478548	−	0.878061i
$82$	−0.902534	+	1.56323i	−0.0996682	+	0.172630i
$83$	6.11318	−	10.5883i	0.671008	−	1.16222i	−0.306610	−	0.951835i	$-0.599195\pi$
$83$	6.11318	−	10.5883i	0.671008	−	1.16222i	0.977618	−	0.210386i	$-0.0674719\pi$
$84$	−8.84846	+	0.369588i	−0.965446	+	0.0403253i
$85$	2.42509	+	4.20038i	0.263038	+	0.455595i
$86$	−0.550651			−0.0593782
$87$	−8.32662	−	2.17632i	−0.892707	−	0.233326i
$88$	−1.48406			−0.158201
$89$	−3.23965	+	5.61124i	−0.343402	+	0.594790i	−0.985062	−	0.172199i	$-0.944913\pi$
$89$	−3.23965	+	5.61124i	−0.343402	+	0.594790i	0.641660	+	0.766989i	$0.278246\pi$
$90$	−0.679364	−	0.381168i	−0.0716112	−	0.0401787i
$91$	−0.744523	−	0.693321i	−0.0780472	−	0.0726798i
$92$	−7.68372	+	13.3086i	−0.801083	+	1.38752i
$93$	−15.7436	−	4.11489i	−1.63254	−	0.426694i
$94$	−1.11958	+	1.93916i	−0.115476	+	0.200010i
$95$	0.194577	−	0.337018i	0.0199632	−	0.0345773i
$96$	−4.98886	−	1.30393i	−0.509173	−	0.133082i
$97$	−0.759552	+	1.31558i	−0.0771208	+	0.133577i	−0.902007	−	0.431722i	$-0.857906\pi$
$97$	−0.759552	+	1.31558i	−0.0771208	+	0.133577i	0.824886	+	0.565299i	$0.191239\pi$
$98$	1.63478	+	0.794552i	0.165138	+	0.0802619i
$99$	3.74876	−	2.22627i	0.376765	−	0.223748i
$100$	0.966288	−	1.67366i	0.0966288	−	0.167366i
$101$	−8.61299			−0.857024			−0.428512	−	0.903536i	$-0.640962\pi$
$101$	−8.61299			−0.857024			−0.428512	+	0.903536i	$0.640962\pi$
$102$	2.11047	+	0.551612i	0.208968	+	0.0546177i
$103$	17.5414			1.72841			0.864205	−	0.503140i	$-0.167822\pi$
$103$	17.5414			1.72841			0.864205	+	0.503140i	$0.167822\pi$
$104$	−0.196327	−	0.340048i	−0.0192515	−	0.0333445i
$105$	−2.45491	−	3.86955i	−0.239575	−	0.377629i
$106$	−0.557135	+	0.964986i	−0.0541138	+	0.0937278i
$107$	1.00477	−	1.74032i	0.0971350	−	0.168243i	−0.813363	−	0.581757i	$-0.802365\pi$
$107$	1.00477	−	1.74032i	0.0971350	−	0.168243i	0.910498	+	0.413514i	$0.135699\pi$
$108$	9.65019	−	2.77754i	0.928590	−	0.267269i
$109$	3.55442	+	6.15643i	0.340452	+	0.589679i	0.984517	−	0.175291i	$-0.0560867\pi$
$109$	3.55442	+	6.15643i	0.340452	+	0.589679i	−0.644065	+	0.764971i	$0.722753\pi$
$110$	−0.188688	−	0.326817i	−0.0179907	−	0.0311608i
$111$	20.0667	+	5.24480i	1.90464	+	0.497814i
$112$	−6.97039	−	6.49103i	−0.658640	−	0.613345i
$113$	−2.71447	−	4.70160i	−0.255356	−	0.442290i	0.709636	−	0.704568i	$-0.248859\pi$
$113$	−2.71447	−	4.70160i	−0.255356	−	0.442290i	−0.964992	+	0.262279i	$0.915526\pi$
$114$	−0.0463379	−	0.168777i	−0.00433994	−	0.0158074i
$115$	−7.95180			−0.741509
$116$	−4.80136	−	8.31619i	−0.445795	−	0.772139i
$117$	1.00604	+	0.564455i	0.0930084	+	0.0521839i
$118$	−2.29199			−0.210995
$119$	9.39103	+	8.74520i	0.860874	+	0.801671i
$120$	−0.468264	−	1.70556i	−0.0427464	−	0.155696i
$121$	−8.88783			−0.807985
$122$	1.00680	−	1.74383i	0.0911514	−	0.157879i
$123$	8.46139	−	8.56610i	0.762938	−	0.772379i
$124$	−9.07820	−	15.7239i	−0.815246	−	1.41205i
$125$	1.00000			0.0894427
$126$	−2.01404	−	0.437507i	−0.179425	−	0.0389763i
$127$	0.0390679			0.00346672			0.00173336	−	0.999998i	$-0.499448\pi$
$127$	0.0390679			0.00346672			0.00173336	+	0.999998i	$0.499448\pi$
$128$	−3.81150	−	6.60171i	−0.336892	−	0.583514i
$129$	3.55367	+	0.928819i	0.312883	+	0.0817780i
$130$	0.0499233	−	0.0864697i	0.00437856	−	0.00758389i
$131$	11.8190			1.03263			0.516317	−	0.856397i	$-0.327302\pi$
$131$	11.8190			1.03263			0.516317	+	0.856397i	$0.327302\pi$
$132$	4.70665	+	1.23017i	0.409661	+	0.107073i
$133$	0.230921	−	1.00338i	0.0200234	−	0.0870038i
$134$	1.11656			0.0964560
$135$	3.74139	+	3.60583i	0.322008	+	0.310340i
$136$	2.47637	+	4.28920i	0.212347	+	0.367796i
$137$	−2.75619			−0.235477			−0.117738	−	0.993045i	$-0.537564\pi$
$137$	−2.75619			−0.235477			−0.117738	+	0.993045i	$0.537564\pi$
$138$	−2.51324	+	2.54434i	−0.213941	+	0.216589i
$139$	2.12249	+	3.67627i	0.180028	+	0.311817i	0.941890	−	0.335922i	$-0.109048\pi$
$139$	2.12249	+	3.67627i	0.180028	+	0.311817i	−0.761862	+	0.647739i	$0.775715\pi$
$140$	1.14677	−	4.98285i	0.0969198	−	0.421128i
$141$	10.4962	−	10.6261i	0.883940	−	0.894879i
$142$	−0.179492	−	0.310889i	−0.0150626	−	0.0260893i
$143$	0.279420	+	0.483969i	0.0233662	+	0.0404715i
$144$	9.41877	+	5.28455i	0.784898	+	0.440380i
$145$	2.48443	−	4.30317i	0.206321	−	0.357358i
$146$	−1.42792	+	2.47324i	−0.118176	+	0.204687i
$147$	−9.20997	−	7.88520i	−0.759626	−	0.650361i
$148$	11.5710	+	20.0415i	0.951129	+	1.64740i
$149$	−3.26656			−0.267607			−0.133804	−	0.991008i	$-0.542719\pi$
$149$	−3.26656			−0.267607			−0.133804	+	0.991008i	$0.542719\pi$
$150$	0.316059	−	0.319971i	0.0258061	−	0.0261255i
$151$	11.5731			0.941803			0.470902	−	0.882186i	$-0.343929\pi$
$151$	11.5731			0.941803			0.470902	+	0.882186i	$0.343929\pi$
$152$	0.198692	−	0.344144i	0.0161160	−	0.0279138i
$153$	−12.6897	−	7.11975i	−1.02590	−	0.575597i
$154$	−0.730684	−	0.680434i	−0.0588802	−	0.0548309i
$155$	4.69746	−	8.13624i	0.377309	−	0.653519i
$156$	0.340771	+	1.24119i	0.0272835	+	0.0993750i
$157$	−4.18869	+	7.25503i	−0.334294	+	0.579014i	−0.983349	−	0.181727i	$-0.941831\pi$
$157$	−4.18869	+	7.25503i	−0.334294	+	0.579014i	0.649055	+	0.760742i	$0.275165\pi$
$158$	−0.218109	+	0.377775i	−0.0173518	+	0.0300542i
$159$	5.22322	−	5.28786i	0.414229	−	0.419355i
$160$	1.48854	−	2.57822i	0.117679	−	0.203826i
$161$	−20.1150	+	6.16490i	−1.58528	+	0.485862i
$162$	2.33626	−	0.0574794i	0.183554	−	0.00451601i
$163$	−4.23150	+	7.32917i	−0.331436	+	0.574065i	−0.982794	−	0.184706i	$-0.940867\pi$
$163$	−4.23150	+	7.32917i	−0.331436	+	0.574065i	0.651357	+	0.758771i	$0.274200\pi$
$164$	13.4344			1.04905
$165$	0.666450	+	2.42742i	0.0518830	+	0.188974i
$166$	3.17473			0.246407
$167$	−7.04377	−	12.2002i	−0.545064	−	0.944078i	−0.998603	−	0.0528416i	$-0.983172\pi$
$167$	−7.04377	−	12.2002i	−0.545064	−	0.944078i	0.453539	−	0.891236i	$-0.350161\pi$
$168$	−2.50682	−	3.95137i	−0.193405	−	0.304855i
$169$	6.42607	−	11.1303i	0.494313	−	0.856175i
$170$	−0.629707	+	1.09068i	−0.0482963	+	0.0836517i
$171$	0.0143584	+	1.16738i	0.00109801	+	0.0892715i
$172$	2.04914	+	3.54922i	0.156246	+	0.270626i
$173$	−6.36427	−	11.0232i	−0.483867	−	0.838082i	0.515962	−	0.856612i	$-0.327435\pi$
$173$	−6.36427	−	11.0232i	−0.483867	−	0.838082i	−0.999828	+	0.0185299i	$0.994101\pi$
$174$	−0.591658	−	2.15500i	−0.0448535	−	0.163370i
$175$	2.52961	−	0.775284i	0.191221	−	0.0586060i
$176$	2.61599	+	4.53103i	0.197188	+	0.341539i
$177$	14.7916	+	3.86606i	1.11180	+	0.290591i
$178$	−1.68244			−0.126104
$179$	−11.6017	−	20.0947i	−0.867150	−	1.50195i	−0.864897	−	0.501950i	$-0.832616\pi$
$179$	−11.6017	−	20.0947i	−0.867150	−	1.50195i	−0.00225274	−	0.999997i	$-0.500717\pi$
$180$	0.0713050	+	5.79729i	0.00531476	+	0.432104i
$181$	−15.2704			−1.13504			−0.567521	−	0.823359i	$-0.692097\pi$
$181$	−15.2704			−1.13504			−0.567521	+	0.823359i	$0.692097\pi$
$182$	0.0592480	−	0.257439i	0.00439175	−	0.0190827i
$183$	−9.43890	+	9.55571i	−0.697744	+	0.706379i
$184$	−8.11993			−0.598609
$185$	−5.98734	+	10.3704i	−0.440198	+	0.762445i
$186$	−1.11868	−	4.07459i	−0.0820258	−	0.298763i
$187$	−3.52446	−	6.10454i	−0.257734	−	0.446408i
$188$	16.6652			1.21543
$189$	12.2598	+	6.22071i	0.891770	+	0.452490i
$190$	0.101049			0.00733087
$191$	−5.40360	−	9.35931i	−0.390991	−	0.677216i	0.601590	−	0.798805i	$-0.294534\pi$
$191$	−5.40360	−	9.35931i	−0.390991	−	0.677216i	−0.992580	+	0.121589i	$0.961201\pi$
$192$	2.94719	+	10.7346i	0.212695	+	0.774702i
$193$	−11.5274	+	19.9660i	−0.829759	+	1.43719i	0.0684677	+	0.997653i	$0.478189\pi$
$193$	−11.5274	+	19.9660i	−0.829759	+	1.43719i	−0.898227	+	0.439532i	$0.855144\pi$
$194$	−0.394455			−0.0283202
$195$	−0.468038	+	0.473830i	−0.0335169	+	0.0339317i
$196$	−0.962242	−	13.4938i	−0.0687316	−	0.963840i
$197$	−4.80076			−0.342040			−0.171020	−	0.985268i	$-0.554706\pi$
$197$	−4.80076			−0.342040			−0.171020	+	0.985268i	$0.554706\pi$
$198$	0.987340	+	0.553963i	0.0701672	+	0.0393684i
$199$	3.35959	+	5.81897i	0.238155	+	0.412496i	0.960185	−	0.279366i	$-0.0901241\pi$
$199$	3.35959	+	5.81897i	0.238155	+	0.412496i	−0.722030	+	0.691862i	$0.756791\pi$
$200$	1.02114			0.0722058
$201$	−7.20581	−	1.88337i	−0.508258	−	0.132843i
$202$	−1.11824	−	1.93684i	−0.0786789	−	0.136276i
$203$	2.94848	−	12.8115i	0.206943	−	0.899190i
$204$	−4.29831	−	15.6558i	−0.300942	−	1.09612i
$205$	3.47579	+	6.02024i	0.242759	+	0.420472i
$206$	2.27743	+	3.94463i	0.158676	+	0.274835i
$207$	20.5111	−	12.1809i	1.42562	−	0.846629i
$208$	−0.692142	+	1.19882i	−0.0479914	+	0.0831235i
$209$	−0.282785	+	0.489798i	−0.0195606	+	0.0338800i
$210$	0.551439	−	1.05444i	0.0380529	−	0.0727631i
$211$	−7.05805	−	12.2249i	−0.485896	−	0.841597i	0.513972	−	0.857807i	$-0.328173\pi$
$211$	−7.05805	−	12.2249i	−0.485896	−	0.841597i	−0.999869	+	0.0162097i	$0.994840\pi$
$212$	8.29310			0.569572
$213$	0.633970	+	2.30911i	0.0434389	+	0.158218i
$214$	0.521804			0.0356698
$215$	−1.06032	+	1.83652i	−0.0723131	+	0.125250i
$216$	3.82050	+	3.68207i	0.259952	+	0.250533i
$217$	5.57486	−	24.2234i	0.378446	−	1.64439i
$218$	−0.922952	+	1.59860i	−0.0625102	+	0.108271i
$219$	13.3870	−	13.5527i	0.904610	−	0.915805i
$220$	−1.40433	+	2.43238i	−0.0946802	+	0.163991i
$221$	0.932505	−	1.61515i	0.0627271	−	0.108646i
$222$	1.42586	+	5.19343i	0.0956976	+	0.348560i
$223$	−10.4277	+	18.0613i	−0.698290	+	1.20947i	0.270769	+	0.962644i	$0.412722\pi$
$223$	−10.4277	+	18.0613i	−0.698290	+	1.20947i	−0.969059	+	0.246829i	$0.920611\pi$
$224$	1.76657	−	7.67594i	0.118034	−	0.512871i
$225$	−2.57943	+	1.53184i	−0.171962	+	0.102123i
$226$	0.704848	−	1.22083i	0.0468858	−	0.0812086i
$227$	−26.1303			−1.73433			−0.867163	−	0.498024i	$-0.834059\pi$
$227$	−26.1303			−1.73433			−0.867163	+	0.498024i	$0.834059\pi$
$228$	−0.915413	+	0.926742i	−0.0606247	+	0.0613750i
$229$	5.51600			0.364508			0.182254	−	0.983251i	$-0.441661\pi$
$229$	5.51600			0.364508			0.182254	+	0.983251i	$0.441661\pi$
$230$	−1.03239	−	1.78816i	−0.0680740	−	0.117908i
$231$	3.56780	+	5.62373i	0.234744	+	0.370014i
$232$	2.53697	−	4.39416i	0.166560	−	0.288490i
$233$	8.15040	−	14.1169i	0.533951	−	0.924830i	−0.465263	−	0.885173i	$-0.654040\pi$
$233$	8.15040	−	14.1169i	0.533951	−	0.924830i	0.999213	−	0.0396570i	$-0.0126265\pi$
$234$	0.00368398	+	0.299517i	0.000240829	+	0.0195800i
$235$	4.31165	+	7.46800i	0.281261	+	0.487159i
$236$	8.52923	+	14.7731i	0.555205	+	0.961644i
$237$	2.04480	−	2.07010i	0.132824	−	0.134468i
$238$	−0.747324	+	3.24721i	−0.0484418	+	0.210485i
$239$	0.318826	+	0.552223i	0.0206232	+	0.0357203i	0.876153	−	0.482033i	$-0.160102\pi$
$239$	0.318826	+	0.552223i	0.0206232	+	0.0357203i	−0.855530	+	0.517754i	$0.826768\pi$
$240$	−4.38188	+	4.43611i	−0.282849	+	0.286350i
$241$	−10.9351			−0.704389			−0.352195	−	0.935927i	$-0.614564\pi$
$241$	−10.9351			−0.704389			−0.352195	+	0.935927i	$0.614564\pi$
$242$	−1.15392	−	1.99865i	−0.0741769	−	0.128478i
$243$	−15.1742	−	3.56978i	−0.973426	−	0.229001i
$244$	−14.9865			−0.959411
$245$	5.79787	−	3.92233i	0.370412	−	0.250589i
$246$	3.02486	+	0.790603i	0.192858	+	0.0504070i
$247$	−0.149639			−0.00952131
$248$	4.79679	−	8.30828i	0.304596	−	0.527576i
$249$	−20.4884	−	5.35503i	−1.29840	−	0.339361i
$250$	0.129832	+	0.224875i	0.00821127	+	0.0142223i
$251$	1.27707			0.0806077			0.0403038	−	0.999187i	$-0.487167\pi$
$251$	1.27707			0.0806077			0.0403038	+	0.999187i	$0.487167\pi$
$252$	4.67492	+	14.6096i	0.294492	+	0.920318i
$253$	11.5566			0.726556
$254$	0.00507225	+	0.00878539i	0.000318261	+	0.000551244i
$255$	5.90360	−	5.97665i	0.369698	−	0.374273i
$256$	−5.43725	+	9.41759i	−0.339828	+	0.588600i
$257$	−8.14428			−0.508026			−0.254013	−	0.967201i	$-0.581751\pi$
$257$	−8.14428			−0.508026			−0.254013	+	0.967201i	$0.581751\pi$
$258$	0.252511	+	0.919721i	0.0157206	+	0.0572593i
$259$	−7.10566	+	30.8749i	−0.441524	+	1.91847i
$260$	−0.743121			−0.0460864
$261$	0.183333	+	14.9055i	0.0113480	+	0.922626i
$262$	1.53449	+	2.65781i	0.0948008	+	0.164200i
$263$	−16.5488			−1.02045			−0.510223	−	0.860042i	$-0.670437\pi$
$263$	−16.5488			−1.02045			−0.510223	+	0.860042i	$0.670437\pi$
$264$	0.680542	+	2.47874i	0.0418844	+	0.152556i
$265$	2.14561	+	3.71630i	0.131804	+	0.228291i
$266$	0.255615	−	0.0783418i	0.0156728	−	0.00480344i
$267$	10.8577	+	2.83788i	0.664483	+	0.173675i
$268$	−4.15506	−	7.19678i	−0.253811	−	0.439613i
$269$	−5.85110	−	10.1344i	−0.356748	−	0.617905i	0.630668	−	0.776053i	$-0.282781\pi$
$269$	−5.85110	−	10.1344i	−0.356748	−	0.617905i	−0.987415	+	0.158148i	$0.949448\pi$
$270$	−0.325110	+	1.30949i	−0.0197855	+	0.0796933i
$271$	−11.0726	+	19.1784i	−0.672614	+	1.16500i	0.304546	+	0.952498i	$0.401495\pi$
$271$	−11.0726	+	19.1784i	−0.672614	+	1.16500i	−0.977160	+	0.212504i	$0.931838\pi$
$272$	8.73032	−	15.1214i	0.529354	−	0.916867i
$273$	−0.816602	+	1.56147i	−0.0494230	+	0.0945044i
$274$	−0.357840	−	0.619797i	−0.0216179	−	0.0374433i
$275$	−1.45333			−0.0876391
$276$	25.7521	+	6.73080i	1.55009	+	0.405147i
$277$	−1.29097			−0.0775666			−0.0387833	−	0.999248i	$-0.512348\pi$
$277$	−1.29097			−0.0775666			−0.0387833	+	0.999248i	$0.512348\pi$
$278$	−0.551133	+	0.954591i	−0.0330548	+	0.0572526i
$279$	0.346639	+	28.1826i	0.0207527	+	1.68725i
$280$	2.58310	−	0.791677i	0.154370	−	0.0473118i
$281$	−15.2100	+	26.3444i	−0.907351	+	1.57158i	−0.0896199	+	0.995976i	$0.528565\pi$
$281$	−15.2100	+	26.3444i	−0.907351	+	1.57158i	−0.817731	+	0.575601i	$0.804768\pi$
$282$	3.75228	+	0.980730i	0.223445	+	0.0584016i
$283$	9.01110	−	15.6077i	0.535654	−	0.927780i	−0.463477	−	0.886109i	$-0.653398\pi$
$283$	9.01110	−	15.6077i	0.535654	−	0.927780i	0.999131	−	0.0416713i	$-0.0132682\pi$
$284$	−1.33589	+	2.31383i	−0.0792706	+	0.137301i
$285$	−0.652129	−	0.170446i	−0.0386288	−	0.0100964i
$286$	−0.0725550	+	0.125669i	−0.00429027	+	0.00743096i
$287$	13.4598	+	12.5341i	0.794506	+	0.739867i
$288$	0.109843	+	8.93055i	0.00647258	+	0.526238i
$289$	−3.26214	+	5.65019i	−0.191891	+	0.332364i
$290$	1.29023			0.0757650
$291$	2.54565	+	0.665354i	0.149229	+	0.0390037i
$292$	21.2550			1.24386
$293$	−12.1760	−	21.0895i	−0.711332	−	1.23206i	−0.964357	−	0.264604i	$-0.914759\pi$
$293$	−12.1760	−	21.0895i	−0.711332	−	1.23206i	0.253025	−	0.967460i	$-0.418575\pi$
$294$	0.577439	−	3.09484i	0.0336769	−	0.180495i
$295$	−4.41340	+	7.64423i	−0.256958	+	0.445064i
$296$	−6.11394	+	10.5897i	−0.355366	+	0.615511i
$297$	−5.43747	−	5.24046i	−0.315514	−	0.304082i
$298$	−0.424103	−	0.734568i	−0.0245676	−	0.0425524i
$299$	1.52883	+	2.64800i	0.0884143	+	0.153138i
$300$	−3.23853	−	0.846450i	−0.186976	−	0.0488698i
$301$	−1.25836	+	5.46774i	−0.0725309	+	0.315155i
$302$	1.50255	+	2.60249i	0.0864620	+	0.149757i
$303$	3.94964	+	14.3858i	0.226901	+	0.826442i
$304$	−1.40096			−0.0803503
$305$	−3.87733	−	6.71574i	−0.222015	−	0.384542i
$306$	−0.0464678	−	3.77796i	−0.00265639	−	0.215971i
$307$	−1.28372			−0.0732660			−0.0366330	−	0.999329i	$-0.511663\pi$
$307$	−1.28372			−0.0732660			−0.0366330	+	0.999329i	$0.511663\pi$
$308$	−1.66664	+	7.24173i	−0.0949654	+	0.412636i
$309$	−8.04394	−	29.2985i	−0.457603	−	1.66673i
$310$	2.43952			0.138555
$311$	4.18316	−	7.24545i	0.237205	−	0.410852i	−0.722706	−	0.691156i	$-0.757102\pi$
$311$	4.18316	−	7.24545i	0.237205	−	0.410852i	0.959911	+	0.280304i	$0.0904352\pi$
$312$	−0.477935	+	0.483849i	−0.0270577	+	0.0273926i
$313$	4.24284	+	7.34882i	0.239820	+	0.415380i	0.960662	−	0.277719i	$-0.0895783\pi$
$313$	4.24284	+	7.34882i	0.239820	+	0.415380i	−0.720843	+	0.693099i	$0.756245\pi$
$314$	−2.17530			−0.122759
$315$	−5.33735	+	5.87475i	−0.300726	+	0.331005i
$316$	3.24660			0.182635
$317$	11.9629	+	20.7203i	0.671902	+	1.16377i	0.977364	+	0.211564i	$0.0678555\pi$
$317$	11.9629	+	20.7203i	0.671902	+	1.16377i	−0.305463	+	0.952204i	$0.598811\pi$
$318$	1.86725	+	0.488040i	0.104710	+	0.0273679i
$319$	−3.61070	+	6.25392i	−0.202160	+	0.350152i
$320$	−6.42696			−0.359278
$321$	−3.36751	−	0.880162i	−0.187956	−	0.0491258i
$322$	−3.99789	−	3.72295i	−0.222794	−	0.207472i
$323$	1.88747			0.105022
$324$	−9.06444	−	14.8445i	−0.503580	−	0.824693i
$325$	−0.192262	−	0.333007i	−0.0106648	−	0.0184719i
$326$	−2.19753			−0.121710
$327$	8.65281	−	8.75989i	0.478501	−	0.484423i
$328$	3.54928	+	6.14754i	0.195976	+	0.339441i
$329$	16.6966	+	15.5484i	0.920515	+	0.857211i
$330$	−0.459338	+	0.465023i	−0.0252857	+	0.0255987i
$331$	3.03000	+	5.24811i	0.166544	+	0.288462i	0.937202	−	0.348786i	$-0.113406\pi$
$331$	3.03000	+	5.24811i	0.166544	+	0.288462i	−0.770659	+	0.637248i	$0.780073\pi$
$332$	−11.8142	−	20.4628i	−0.648387	−	1.12304i
$333$	−0.441822	−	35.9213i	−0.0242117	−	1.96848i
$334$	1.82901	−	3.16794i	0.100079	−	0.173342i
$335$	2.15001	−	3.72393i	0.117468	−	0.203460i
$336$	−7.64521	+	14.6188i	−0.417081	+	0.797523i
$337$	−0.317148	−	0.549316i	−0.0172761	−	0.0299232i	0.857258	−	0.514887i	$-0.172166\pi$
$337$	−0.317148	−	0.549316i	−0.0172761	−	0.0299232i	−0.874534	+	0.484964i	$0.838833\pi$
$338$	3.33723			0.181521
$339$	−6.60806	+	6.68984i	−0.358900	+	0.363342i
$340$	9.37334			0.508341
$341$	−6.82696	+	11.8246i	−0.369701	+	0.640340i
$342$	−0.260649	+	0.154791i	−0.0140943	+	0.00837014i
$343$	11.6254	−	14.4170i	0.627714	−	0.778444i
$344$	−1.08274	+	1.87536i	−0.0583773	+	0.101112i
$345$	3.64644	+	13.2814i	0.196318	+	0.715049i
$346$	1.65257	−	2.86233i	0.0888426	−	0.153880i
$347$	−10.6546	+	18.4543i	−0.571969	+	0.990680i	0.424395	+	0.905477i	$0.360487\pi$
$347$	−10.6546	+	18.4543i	−0.571969	+	0.990680i	−0.996364	+	0.0852022i	$0.972846\pi$
$348$	−11.6883	+	11.8330i	−0.626560	+	0.634314i
$349$	2.14306	−	3.71189i	0.114715	−	0.198693i	−0.802951	−	0.596046i	$-0.796738\pi$
$349$	2.14306	−	3.71189i	0.114715	−	0.198693i	0.917666	+	0.397353i	$0.130071\pi$
$350$	0.502765	+	0.468190i	0.0268739	+	0.0250258i
$351$	0.481440	−	1.93917i	0.0256974	−	0.103505i
$352$	−2.16334	+	3.74701i	−0.115306	+	0.199716i
$353$	20.2546			1.07805			0.539023	−	0.842291i	$-0.318794\pi$
$353$	20.2546			1.07805			0.539023	+	0.842291i	$0.318794\pi$
$354$	1.05103	+	3.82819i	0.0558619	+	0.203466i
$355$	−1.38250			−0.0733755
$356$	6.26087	+	10.8441i	0.331825	+	0.574738i
$357$	10.3002	−	19.6956i	0.545144	−	1.04240i
$358$	3.01253	−	5.21785i	0.159217	−	0.275772i
$359$	14.0695	−	24.3691i	0.742561	−	1.28615i	−0.208764	−	0.977966i	$-0.566944\pi$
$359$	14.0695	−	24.3691i	0.742561	−	1.28615i	0.951326	−	0.308188i	$-0.0997225\pi$
$360$	−2.63397	+	1.56423i	−0.138823	+	0.0824422i
$361$	9.42428	+	16.3233i	0.496015	+	0.859123i
$362$	−1.98258	−	3.43393i	−0.104202	−	0.180484i
$363$	4.07567	+	14.8449i	0.213917	+	0.779153i
$364$	−1.87981	+	0.576129i	−0.0985286	+	0.0301974i
$365$	5.49914	+	9.52479i	0.287838	+	0.498550i
$366$	−3.37431	−	0.881939i	−0.176378	−	0.0460997i
$367$	−19.0728			−0.995590			−0.497795	−	0.867295i	$-0.665857\pi$
$367$	−19.0728			−0.995590			−0.497795	+	0.867295i	$0.665857\pi$
$368$	14.3132	+	24.7912i	0.746128	+	1.29233i
$369$	−18.1876	−	10.2044i	−0.946808	−	0.531222i
$370$	−3.10938			−0.161649
$371$	8.30874	+	7.73734i	0.431368	+	0.401703i
$372$	−22.0998	+	22.3733i	−1.14582	+	1.16000i
$373$	6.35989			0.329303			0.164651	−	0.986352i	$-0.447350\pi$
$373$	6.35989			0.329303			0.164651	+	0.986352i	$0.447350\pi$
$374$	0.915172	−	1.58512i	0.0473224	−	0.0819648i
$375$	−0.458568	−	1.67024i	−0.0236803	−	0.0862510i
$376$	4.40282	+	7.62591i	0.227058	+	0.393276i
$377$	−1.91065			−0.0984033
$378$	0.192829	+	3.56457i	0.00991807	+	0.183341i
$379$	19.7528			1.01463			0.507317	−	0.861760i	$-0.330638\pi$
$379$	19.7528			1.01463			0.507317	+	0.861760i	$0.330638\pi$
$380$	−0.376035	−	0.651312i	−0.0192902	−	0.0334116i
$381$	−0.0179153	−	0.0652529i	−0.000917827	−	0.00334301i
$382$	1.40312	−	2.43027i	0.0717896	−	0.124343i
$383$	2.97911			0.152226			0.0761128	−	0.997099i	$-0.475749\pi$
$383$	2.97911			0.152226			0.0761128	+	0.997099i	$0.475749\pi$
$384$	−9.27863	+	9.39346i	−0.473498	+	0.479358i
$385$	−3.67636	+	1.12674i	−0.187365	+	0.0574241i
$386$	−5.98647			−0.304703
$387$	−0.0782437	−	6.36143i	−0.00397735	−	0.323369i
$388$	1.46789	+	2.54246i	0.0745209	+	0.129074i
$389$	−23.4041			−1.18663			−0.593317	−	0.804969i	$-0.702182\pi$
$389$	−23.4041			−1.18663			−0.593317	+	0.804969i	$0.702182\pi$
$390$	−0.167319	−	0.0437319i	−0.00847251	−	0.00221445i
$391$	−19.2838	−	33.4006i	−0.975225	−	1.68914i
$392$	5.92046	−	4.00527i	0.299029	−	0.202297i
$393$	−5.41983	−	19.7407i	−0.273394	−	0.995786i
$394$	−0.623291	−	1.07957i	−0.0314009	−	0.0543880i
$395$	0.839967	+	1.45487i	0.0422633	+	0.0732022i
$396$	−0.103630	−	8.42537i	−0.00520759	−	0.423391i
$397$	7.02360	−	12.1652i	0.352504	−	0.610555i	−0.634183	−	0.773183i	$-0.718664\pi$
$397$	7.02360	−	12.1652i	0.352504	−	0.610555i	0.986688	+	0.162627i	$0.0519969\pi$
$398$	−0.872361	+	1.51097i	−0.0437275	+	0.0757382i
$399$	−1.78178	+	0.0744224i	−0.0892004	+	0.00372578i
$400$	−1.80000	−	3.11769i	−0.0899999	−	0.155884i
$401$	−18.7977			−0.938711			−0.469355	−	0.883009i	$-0.655514\pi$
$401$	−18.7977			−0.938711			−0.469355	+	0.883009i	$0.655514\pi$
$402$	−0.512018	−	1.86493i	−0.0255371	−	0.0930140i
$403$	−3.61257			−0.179955
$404$	−8.32262	+	14.4152i	−0.414066	+	0.717183i
$405$	4.30693	−	7.90255i	0.214013	−	0.392681i
$406$	3.26379	−	1.00030i	0.161979	−	0.0496439i
$407$	8.70158	−	15.0716i	0.431321	−	0.747070i
$408$	6.02843	−	6.10303i	0.298452	−	0.302145i
$409$	12.1992	−	21.1296i	0.603209	−	1.04479i	−0.389123	−	0.921186i	$-0.627222\pi$
$409$	12.1992	−	21.1296i	0.603209	−	1.04479i	0.992332	−	0.123603i	$-0.0394449\pi$
$410$	−0.902534	+	1.56323i	−0.0445730	+	0.0772026i
$411$	1.26390	+	4.60350i	0.0623435	+	0.227074i
$412$	16.9501	−	29.3584i	0.835070	−	1.44638i
$413$	−5.23774	+	22.7586i	−0.257732	+	1.11988i
$414$	5.40216	+	3.03097i	0.265502	+	0.148964i
$415$	6.11318	−	10.5883i	0.300084	−	0.519761i
$416$	−1.14476			−0.0561263
$417$	5.16696	−	5.23090i	0.253027	−	0.256158i
$418$	−0.146858			−0.00718304
$419$	2.00160	+	3.46687i	0.0977845	+	0.169368i	0.910767	−	0.412920i	$-0.135491\pi$
$419$	2.00160	+	3.46687i	0.0977845	+	0.169368i	−0.812983	+	0.582288i	$0.802158\pi$
$420$	−8.84846	+	0.369588i	−0.431760	+	0.0180340i
$421$	11.6479	−	20.1748i	0.567685	−	0.983259i	−0.429110	−	0.903252i	$-0.641173\pi$
$421$	11.6479	−	20.1748i	0.567685	−	0.983259i	0.996794	−	0.0800064i	$-0.0254941\pi$
$422$	1.83272	−	3.17436i	0.0892152	−	0.154525i
$423$	−22.5614	−	12.6584i	−1.09697	−	0.615474i
$424$	2.19098	+	3.79488i	0.106403	+	0.184296i
$425$	2.42509	+	4.20038i	0.117634	+	0.203748i
$426$	−0.436952	+	0.442359i	−0.0211704	+	0.0214324i
$427$	−15.0147	−	13.9822i	−0.726615	−	0.676645i
$428$	−1.94180	−	3.36329i	−0.0938603	−	0.162571i
$429$	0.680214	−	0.688632i	0.0328410	−	0.0332474i
$430$	−0.550651			−0.0265547
$431$	15.5346	+	26.9067i	0.748274	+	1.29605i	0.948649	+	0.316329i	$0.102450\pi$
$431$	15.5346	+	26.9067i	0.748274	+	1.29605i	−0.200376	+	0.979719i	$0.564216\pi$
$432$	4.50735	−	18.1550i	0.216860	−	0.873482i
$433$	−3.34476			−0.160739			−0.0803695	−	0.996765i	$-0.525610\pi$
$433$	−3.34476			−0.160739			−0.0803695	+	0.996765i	$0.525610\pi$
$434$	6.17103	−	1.89132i	0.296219	−	0.0907861i
$435$	−8.32662	−	2.17632i	−0.399231	−	0.104347i
$436$	13.7384			0.657948
$437$	−1.54724	+	2.67990i	−0.0740145	+	0.128197i
$438$	4.78571	+	1.25084i	0.228670	+	0.0597672i
$439$	−9.83991	−	17.0432i	−0.469633	−	0.813429i	0.529764	−	0.848145i	$-0.322280\pi$
$439$	−9.83991	−	17.0432i	−0.469633	−	0.813429i	−0.999397	+	0.0347166i	$0.988947\pi$
$440$	−1.48406			−0.0707498
$441$	−8.94682	+	18.9988i	−0.426039	+	0.904705i
$442$	0.484274			0.0230346
$443$	−8.44288	−	14.6235i	−0.401133	−	0.694783i	0.592730	−	0.805401i	$-0.298050\pi$
$443$	−8.44288	−	14.6235i	−0.401133	−	0.694783i	−0.993863	+	0.110618i	$0.964717\pi$
$444$	28.1682	−	28.5168i	1.33680	−	1.35335i
$445$	−3.23965	+	5.61124i	−0.153574	+	0.265998i
$446$	−5.41537			−0.256425
$447$	1.49794	+	5.45596i	0.0708501	+	0.258058i
$448$	−16.2577	+	4.98272i	−0.768104	+	0.235411i
$449$	20.2057			0.953568			0.476784	−	0.879021i	$-0.341802\pi$
$449$	20.2057			0.953568			0.476784	+	0.879021i	$0.341802\pi$
$450$	−0.679364	−	0.381168i	−0.0320255	−	0.0179684i
$451$	−5.05146	−	8.74939i	−0.237864	−	0.411993i
$452$	−10.4918			−0.493495
$453$	−5.30704	−	19.3299i	−0.249346	−	0.908196i
$454$	−3.39253	−	5.87604i	−0.159219	−	0.275776i
$455$	−0.744523	−	0.693321i	−0.0349038	−	0.0325034i
$456$	−0.665918	−	0.174050i	−0.0311845	−	0.00815065i
$457$	14.8480	+	25.7175i	0.694559	+	1.20301i	0.970329	+	0.241788i	$0.0777339\pi$
$457$	14.8480	+	25.7175i	0.694559	+	1.20301i	−0.275770	+	0.961224i	$0.588933\pi$
$458$	0.716151	+	1.24041i	0.0334636	+	0.0579606i
$459$	−6.07264	+	24.4597i	−0.283447	+	1.14168i
$460$	−7.68372	+	13.3086i	−0.358255	+	0.620516i
$461$	6.84501	−	11.8559i	0.318804	−	0.552184i	−0.661435	−	0.750003i	$-0.730052\pi$
$461$	6.84501	−	11.8559i	0.318804	−	0.552184i	0.980239	+	0.197818i	$0.0633856\pi$
$462$	−0.801423	+	1.53245i	−0.0372856	+	0.0712958i
$463$	−17.8333	−	30.8881i	−0.828783	−	1.43549i	−0.898994	−	0.437962i	$-0.855700\pi$
$463$	−17.8333	−	30.8881i	−0.828783	−	1.43549i	0.0702107	−	0.997532i	$-0.477633\pi$
$464$	−17.8879			−0.830425
$465$	−15.7436	−	4.11489i	−0.730093	−	0.190824i
$466$	4.23272			0.196077
$467$	3.02952	−	5.24728i	0.140189	−	0.242815i	−0.787379	−	0.616470i	$-0.788562\pi$
$467$	3.02952	−	5.24728i	0.140189	−	0.242815i	0.927568	+	0.373655i	$0.121896\pi$
$468$	1.91683	−	1.13834i	0.0886054	−	0.0526199i
$469$	2.55159	−	11.0870i	0.117822	−	0.511949i
$470$	−1.11958	+	1.93916i	−0.0516423	+	0.0894470i
$471$	14.0385	+	3.66922i	0.646858	+	0.169069i
$472$	−4.50672	+	7.80587i	−0.207439	+	0.359294i
$473$	1.54099	−	2.66907i	0.0708548	−	0.122724i
$474$	0.730994	+	0.191059i	0.0335757	+	0.00877564i
$475$	0.194577	−	0.337018i	0.00892782	−	0.0154634i
$476$	23.7109	−	7.26700i	1.08679	−	0.333083i
$477$	−11.2272	−	6.29922i	−0.514059	−	0.288421i
$478$	−0.0827874	+	0.143392i	−0.00378661	+	0.00655860i
$479$	35.1882			1.60779			0.803894	−	0.594772i	$-0.202758\pi$
$479$	35.1882			1.60779			0.803894	+	0.594772i	$0.202758\pi$
$480$	−4.98886	−	1.30393i	−0.227709	−	0.0595161i
$481$	4.60455			0.209949
$482$	−1.41972	−	2.45902i	−0.0646663	−	0.112005i
$483$	19.5210	+	30.7699i	0.888234	+	1.40008i
$484$	−8.58820	+	14.8752i	−0.390373	+	0.676146i
$485$	−0.759552	+	1.31558i	−0.0344895	+	0.0597375i
$486$	−1.16734	−	3.87577i	−0.0529515	−	0.175808i
$487$	−11.1314	−	19.2802i	−0.504412	−	0.873668i	−0.999987	−	0.00510246i	$-0.998376\pi$
$487$	−11.1314	−	19.2802i	−0.504412	−	0.873668i	0.495575	−	0.868565i	$-0.334958\pi$
$488$	−3.95932	−	6.85774i	−0.179230	−	0.310435i
$489$	14.1819	+	3.70671i	0.641329	+	0.167623i
$490$	1.63478	+	0.794552i	0.0738519	+	0.0358942i
$491$	−4.30406	−	7.45485i	−0.194239	−	0.336433i	0.752411	−	0.658693i	$-0.228891\pi$
$491$	−4.30406	−	7.45485i	−0.194239	−	0.336433i	−0.946651	+	0.322261i	$0.895557\pi$
$492$	−6.16060	−	22.4388i	−0.277741	−	1.01162i
$493$	24.0999			1.08541
$494$	−0.0194279	−	0.0336501i	−0.000874102	−	0.00151399i
$495$	3.74876	−	2.22627i	0.168494	−	0.100063i
$496$	−33.8217			−1.51864
$497$	−3.49719	+	1.07183i	−0.156870	+	0.0480781i
$498$	−1.45583	−	5.30258i	−0.0652373	−	0.237614i
$499$	−19.5619			−0.875710			−0.437855	−	0.899046i	$-0.644262\pi$
$499$	−19.5619			−0.875710			−0.437855	+	0.899046i	$0.644262\pi$
$500$	0.966288	−	1.67366i	0.0432137	−	0.0748483i
$501$	−17.1472	+	17.3594i	−0.766081	+	0.775562i
$502$	0.165803	+	0.287180i	0.00740017	+	0.0128175i
$503$	29.0221			1.29403			0.647015	−	0.762477i	$-0.276017\pi$
$503$	29.0221			1.29403			0.647015	+	0.762477i	$0.276017\pi$
$504$	−5.45021	+	5.99897i	−0.242771	+	0.267215i
$505$	−8.61299			−0.383273
$506$	1.50041	+	2.59878i	0.0667013	+	0.115530i
$507$	−21.5371	−	5.62912i	−0.956495	−	0.249998i
$508$	0.0377508	−	0.0653864i	0.00167492	−	0.00290105i
$509$	−19.0420			−0.844022			−0.422011	−	0.906591i	$-0.638676\pi$
$509$	−19.0420			−0.844022			−0.422011	+	0.906591i	$0.638676\pi$
$510$	2.11047	+	0.551612i	0.0934533	+	0.0244258i
$511$	21.2951	+	19.8306i	0.942040	+	0.877255i
$512$	−18.0697			−0.798575
$513$	1.94322	−	0.559303i	0.0857952	−	0.0246938i
$514$	−1.05739	−	1.83144i	−0.0466393	−	0.0807816i
$515$	17.5414			0.772968
$516$	4.98839	−	5.05013i	0.219602	−	0.222319i
$517$	−6.26625	−	10.8535i	−0.275590	−	0.477335i
$518$	−7.86553	+	2.41065i	−0.345592	+	0.105918i
$519$	−15.4931	+	15.6848i	−0.680070	+	0.688486i
$520$	−0.196327	−	0.340048i	−0.00860951	−	0.0149121i
$521$	−0.360177	−	0.623844i	−0.0157796	−	0.0273311i	0.858028	−	0.513603i	$-0.171690\pi$
$521$	−0.360177	−	0.623844i	−0.0157796	−	0.0273311i	−0.873807	+	0.486272i	$0.838356\pi$
$522$	−3.32806	+	1.97643i	−0.145665	+	0.0865059i
$523$	2.26550	−	3.92397i	0.0990636	−	0.171583i	−0.812234	−	0.583332i	$-0.801749\pi$
$523$	2.26550	−	3.92397i	0.0990636	−	0.171583i	0.911297	+	0.411749i	$0.135082\pi$
$524$	11.4206	−	19.7811i	0.498911	−	0.864139i
$525$	−2.45491	−	3.86955i	−0.107141	−	0.168881i
$526$	−2.14856	−	3.72142i	−0.0936817	−	0.162262i
$527$	45.5671			1.98493
$528$	6.36832	−	6.44713i	0.277145	−	0.280575i
$529$	40.2311			1.74918
$530$	−0.557135	+	0.964986i	−0.0242004	+	0.0419163i
$531$	−0.325677	−	26.4784i	−0.0141332	−	1.14906i
$532$	−1.45618	−	1.35603i	−0.0631332	−	0.0587915i
$533$	1.33652	−	2.31492i	0.0578912	−	0.100270i
$534$	0.771511	+	2.81008i	0.0333865	+	0.121604i
$535$	1.00477	−	1.74032i	0.0434401	−	0.0752404i
$536$	2.19548	−	3.80268i	0.0948301	−	0.164251i
$537$	−28.2429	+	28.5924i	−1.21877	+	1.23385i
$538$	1.51931	−	2.63153i	0.0655023	−	0.113453i
$539$	−8.42621	+	5.70044i	−0.362943	+	0.245536i
$540$	9.65019	−	2.77754i	0.415278	−	0.119526i
$541$	20.0492	−	34.7262i	0.861981	−	1.49300i	−0.00803202	−	0.999968i	$-0.502557\pi$
$541$	20.0492	−	34.7262i	0.861981	−	1.49300i	0.870013	−	0.493028i	$-0.164110\pi$
$542$	−5.75031			−0.246997
$543$	7.00252	+	25.5053i	0.300507	+	1.09454i
$544$	14.4394			0.619083
$545$	3.55442	+	6.15643i	0.152255	+	0.263713i
$546$	−0.457156	+	0.0190948i	−0.0195645	+	0.000817181i
$547$	−14.1400	+	24.4912i	−0.604584	+	1.04717i	0.387533	+	0.921856i	$0.373327\pi$
$547$	−14.1400	+	24.4912i	−0.604584	+	1.04717i	−0.992117	+	0.125314i	$0.960006\pi$
$548$	−2.66327	+	4.61292i	−0.113769	+	0.197054i
$549$	20.2887	+	11.3833i	0.865903	+	0.485829i
$550$	−0.188688	−	0.326817i	−0.00804569	−	0.0139355i
$551$	−0.966829	−	1.67460i	−0.0411883	−	0.0713402i
$552$	3.72354	+	13.5623i	0.158484	+	0.577249i
$553$	3.25273	+	3.02903i	0.138320	+	0.128808i
$554$	−0.167608	−	0.290306i	−0.00712098	−	0.0123339i
$555$	20.0667	+	5.24480i	0.851782	+	0.222629i
$556$	8.20376			0.347917
$557$	7.24549	+	12.5496i	0.307001	+	0.531742i	0.977705	−	0.209984i	$-0.0673411\pi$
$557$	7.24549	+	12.5496i	0.307001	+	0.531742i	−0.670704	+	0.741725i	$0.734008\pi$
$558$	−6.29256	+	3.73695i	−0.266385	+	0.158198i
$559$	0.815434			0.0344892
$560$	−6.97039	−	6.49103i	−0.294553	−	0.274296i
$561$	−8.57987	+	8.68605i	−0.362242	+	0.366725i
$562$	−7.89893			−0.333196
$563$	−3.20755	+	5.55564i	−0.135182	+	0.234142i	−0.925667	−	0.378339i	$-0.876495\pi$
$563$	−3.20755	+	5.55564i	−0.135182	+	0.234142i	0.790485	+	0.612482i	$0.209829\pi$
$564$	−7.64212	−	27.8349i	−0.321791	−	1.17206i
$565$	−2.71447	−	4.70160i	−0.114199	−	0.197798i
$566$	4.67970			0.196702
$567$	4.76815	−	23.3295i	0.200243	−	0.979746i
$568$	−1.41173			−0.0592350
$569$	4.60579	+	7.97747i	0.193085	+	0.334433i	0.946271	−	0.323375i	$-0.104817\pi$
$569$	4.60579	+	7.97747i	0.193085	+	0.334433i	−0.753186	+	0.657807i	$0.771484\pi$
$570$	−0.0463379	−	0.168777i	−0.00194088	−	0.00706928i
$571$	−22.8660	+	39.6051i	−0.956912	+	1.65742i	−0.226982	+	0.973899i	$0.572886\pi$
$571$	−22.8660	+	39.6051i	−0.956912	+	1.65742i	−0.729930	+	0.683522i	$0.760447\pi$
$572$	1.08000			0.0451570
$573$	−13.1544	+	13.3172i	−0.549534	+	0.556334i
$574$	−1.07111	+	4.65410i	−0.0447072	+	0.194258i
$575$	−7.95180			−0.331613
$576$	16.5779	−	9.84507i	0.690746	−	0.410211i
$577$	−3.86259	−	6.69021i	−0.160802	−	0.278517i	0.774355	−	0.632752i	$-0.218075\pi$
$577$	−3.86259	−	6.69021i	−0.160802	−	0.278517i	−0.935156	+	0.354235i	$0.884741\pi$
$578$	−1.69412			−0.0704659
$579$	38.6342	+	10.0978i	1.60558	+	0.419649i
$580$	−4.80136	−	8.31619i	−0.199365	−	0.345311i
$581$	7.25500	−	31.5238i	0.300988	−	1.30783i
$582$	0.180884	+	0.658836i	0.00749790	+	0.0273096i
$583$	−3.11827	−	5.40101i	−0.129146	−	0.223687i
$584$	5.61542	+	9.72619i	0.232368	+	0.402473i
$585$	1.00604	+	0.564455i	0.0415946	+	0.0233373i
$586$	3.16167	−	5.47617i	0.130607	−	0.226219i
$587$	23.4786	−	40.6661i	0.969064	−	1.67847i	0.270790	−	0.962638i	$-0.412715\pi$
$587$	23.4786	−	40.6661i	0.969064	−	1.67847i	0.698274	−	0.715830i	$-0.253952\pi$
$588$	−22.0966	+	7.79498i	−0.911249	+	0.321460i
$589$	−1.82804	−	3.16626i	−0.0753231	−	0.130463i
$590$	−2.29199			−0.0943599
$591$	2.20148	+	8.01845i	0.0905566	+	0.329835i
$592$	43.1088			1.77176
$593$	−1.24064	+	2.14885i	−0.0509469	+	0.0882426i	−0.890374	−	0.455229i	$-0.849557\pi$
$593$	−1.24064	+	2.14885i	−0.0509469	+	0.0882426i	0.839427	+	0.543472i	$0.182891\pi$
$594$	0.472491	−	1.90313i	0.0193866	−	0.0780863i
$595$	9.39103	+	8.74520i	0.384995	+	0.358518i
$596$	−3.15644	+	5.46711i	−0.129293	+	0.223942i
$597$	8.17851	−	8.27972i	0.334724	−	0.338866i
$598$	−0.396980	+	0.687589i	−0.0162337	+	0.0281176i
$599$	−15.9035	+	27.5458i	−0.649801	+	1.12549i	0.333369	+	0.942797i	$0.391815\pi$
$599$	−15.9035	+	27.5458i	−0.649801	+	1.12549i	−0.983170	+	0.182692i	$0.941519\pi$
$600$	−0.468264	−	1.70556i	−0.0191168	−	0.0696292i
$601$	−20.4365	+	35.3970i	−0.833621	+	1.44387i	0.0615277	+	0.998105i	$0.480403\pi$
$601$	−20.4365	+	35.3970i	−0.833621	+	1.44387i	−0.895148	+	0.445768i	$0.852931\pi$
$602$	−1.39293	+	0.426911i	−0.0567717	+	0.0173996i
$603$	0.158655	+	12.8991i	0.00646095	+	0.525292i
$604$	11.1829	−	19.3694i	0.455026	−	0.788129i
$605$	−8.88783			−0.361342
$606$	−2.72222	+	2.75590i	−0.110582	+	0.111951i
$607$	−10.5705			−0.429042			−0.214521	−	0.976719i	$-0.568819\pi$
$607$	−10.5705			−0.429042			−0.214521	+	0.976719i	$0.568819\pi$
$608$	−0.579272	−	1.00333i	−0.0234926	−	0.0406903i
$609$	−22.7504	+	0.950252i	−0.921892	+	0.0385062i
$610$	1.00680	−	1.74383i	0.0407642	−	0.0706056i
$611$	1.65793	−	2.87162i	0.0670728	−	0.116173i
$612$	−24.1779	+	14.3585i	−0.977334	+	0.580406i
$613$	−15.3891	−	26.6548i	−0.621562	−	1.07658i	−0.989195	−	0.146606i	$-0.953165\pi$
$613$	−15.3891	−	26.6548i	−0.621562	−	1.07658i	0.367633	−	0.929971i	$-0.380168\pi$
$614$	−0.166668	−	0.288677i	−0.00672617	−	0.0116501i
$615$	8.46139	−	8.56610i	0.341196	−	0.345418i
$616$	−3.75409	+	1.15057i	−0.151257	+	0.0463577i
$617$	17.8950	+	30.9951i	0.720426	+	1.24781i	0.960829	+	0.277141i	$0.0893869\pi$
$617$	17.8950	+	30.9951i	0.720426	+	1.24781i	−0.240404	+	0.970673i	$0.577280\pi$
$618$	5.54414	−	5.61275i	0.223018	−	0.225778i
$619$	25.3056			1.01712			0.508560	−	0.861027i	$-0.330178\pi$
$619$	25.3056			1.01712			0.508560	+	0.861027i	$0.330178\pi$
$620$	−9.07820	−	15.7239i	−0.364589	−	0.631487i
$621$	−29.7508	−	28.6728i	−1.19386	−	1.15060i
$622$	2.17243			0.0871064
$623$	−3.84475	+	16.7059i	−0.154037	+	0.669308i
$624$	2.31972	+	0.606304i	0.0928633	+	0.0242716i
$625$	1.00000			0.0400000
$626$	−1.10171	+	1.90822i	−0.0440332	+	0.0762677i
$627$	0.947758	+	0.247715i	0.0378498	+	0.00989277i
$628$	8.09496	+	14.0209i	0.323024	+	0.559494i
$629$	−58.0794			−2.31578
$630$	−2.01404	−	0.437507i	−0.0802413	−	0.0174307i
$631$	10.6214			0.422832			0.211416	−	0.977396i	$-0.432192\pi$
$631$	10.6214			0.422832			0.211416	+	0.977396i	$0.432192\pi$
$632$	0.857728	+	1.48563i	0.0341186	+	0.0590951i
$633$	−17.1820	+	17.3946i	−0.682922	+	0.691374i
$634$	−3.10632	+	5.38030i	−0.123368	+	0.213679i
$635$	0.0390679			0.00155036
$636$	−3.80294	−	13.8515i	−0.150797	−	0.549248i
$637$	−2.42087	−	1.17662i	−0.0959185	−	0.0466193i
$638$	−1.87513			−0.0742372
$639$	3.56606	−	2.11777i	0.141071	−	0.0837776i
$640$	−3.81150	−	6.60171i	−0.150663	−	0.260955i
$641$	−23.3399			−0.921872			−0.460936	−	0.887433i	$-0.652486\pi$
$641$	−23.3399			−0.921872			−0.460936	+	0.887433i	$0.652486\pi$
$642$	−0.239283	−	0.871541i	−0.00944373	−	0.0343970i
$643$	1.96963	+	3.41150i	0.0776747	+	0.134537i	0.902246	−	0.431221i	$-0.141917\pi$
$643$	1.96963	+	3.41150i	0.0776747	+	0.134537i	−0.824572	+	0.565758i	$0.808584\pi$
$644$	−9.11889	+	39.6226i	−0.359335	+	1.56135i
$645$	3.55367	+	0.928819i	0.139926	+	0.0365722i
$646$	0.245053	+	0.424445i	0.00964150	+	0.0166996i
$647$	12.3853	+	21.4520i	0.486918	+	0.843366i	0.999887	−	0.0150409i	$-0.00478785\pi$
$647$	12.3853	+	21.4520i	0.486918	+	0.843366i	−0.512969	+	0.858407i	$0.671455\pi$
$648$	4.39800	−	8.06965i	0.172770	−	0.317006i
$649$	6.41412	−	11.1096i	0.251776	−	0.436090i
$650$	0.0499233	−	0.0864697i	0.00195815	−	0.00339162i
$651$	−43.0154	+	1.79670i	−1.68591	+	0.0704181i
$652$	8.17769	+	14.1642i	0.320263	+	0.554712i
$653$	40.8710			1.59941			0.799704	−	0.600395i	$-0.204990\pi$
$653$	40.8710			1.59941			0.799704	+	0.600395i	$0.204990\pi$
$654$	3.09329	+	0.808489i	0.120957	+	0.0316144i
$655$	11.8190			0.461808
$656$	12.5128	−	21.6728i	0.488544	−	0.846182i
$657$	−28.7751	−	16.1447i	−1.12262	−	0.629867i
$658$	−1.32869	+	5.77332i	−0.0517978	+	0.225068i
$659$	5.73599	−	9.93502i	0.223442	−	0.387013i	−0.732409	−	0.680865i	$-0.761604\pi$
$659$	5.73599	−	9.93502i	0.223442	−	0.387013i	0.955851	+	0.293852i	$0.0949372\pi$
$660$	4.70665	+	1.23017i	0.183206	+	0.0478844i
$661$	−0.361963	+	0.626938i	−0.0140787	+	0.0243851i	−0.872979	−	0.487758i	$-0.837815\pi$
$661$	−0.361963	+	0.626938i	−0.0140787	+	0.0243851i	0.858900	+	0.512143i	$0.171148\pi$
$662$	−0.786779	+	1.36274i	−0.0305790	+	0.0529644i
$663$	−3.12530	−	0.816857i	−0.121377	−	0.0317241i
$664$	6.24244	−	10.8122i	0.242254	−	0.419596i
$665$	0.230921	−	1.00338i	0.00895472	−	0.0389093i
$666$	8.02044	−	4.76308i	0.310786	−	0.184565i
$667$	−19.7557	+	34.2179i	−0.764944	+	1.32492i
$668$	−27.2252			−1.05338
$669$	34.9486	+	9.13447i	1.35119	+	0.353159i
$670$	1.11656			0.0431364
$671$	5.63504	+	9.76018i	0.217538	+	0.376788i
$672$	−13.6308	+	0.569339i	−0.525819	+	0.0219627i
$673$	2.87908	−	4.98671i	0.110980	−	0.192223i	−0.805185	−	0.593023i	$-0.797934\pi$
$673$	2.87908	−	4.98671i	0.110980	−	0.192223i	0.916166	+	0.400800i	$0.131268\pi$
$674$	0.0823516	−	0.142637i	0.00317206	−	0.00549418i
$675$	3.74139	+	3.60583i	0.144006	+	0.138788i
$676$	−12.4189	−	21.5101i	−0.477649	−	0.827312i
$677$	21.3798	+	37.0309i	0.821692	+	1.42321i	0.904421	+	0.426641i	$0.140303\pi$
$677$	21.3798	+	37.0309i	0.821692	+	1.42321i	−0.0827286	+	0.996572i	$0.526363\pi$
$678$	−2.36231	−	0.617434i	−0.0907240	−	0.0237124i
$679$	−0.901421	+	3.91678i	−0.0345934	+	0.150312i
$680$	2.47637	+	4.28920i	0.0949644	+	0.164483i
$681$	11.9825	+	43.6439i	0.459170	+	1.67244i
$682$	−3.54542			−0.135761
$683$	−11.5228	−	19.9581i	−0.440908	−	0.763674i	0.556849	−	0.830613i	$-0.312010\pi$
$683$	−11.5228	−	19.9581i	−0.440908	−	0.763674i	−0.997757	+	0.0669390i	$0.978677\pi$
$684$	1.96766	+	1.10399i	0.0752355	+	0.0422121i
$685$	−2.75619			−0.105308
$686$	4.75136	+	0.742489i	0.181408	+	0.0283484i
$687$	−2.52946	−	9.21307i	−0.0965049	−	0.351501i
$688$	7.63428			0.291054
$689$	0.825037	−	1.42901i	0.0314314	−	0.0544408i
$690$	−2.51324	+	2.54434i	−0.0956774	+	0.0968614i
$691$	−12.8581	−	22.2709i	−0.489146	−	0.847226i	0.510776	−	0.859714i	$-0.329358\pi$
$691$	−12.8581	−	22.2709i	−0.489146	−	0.847226i	−0.999922	+	0.0124877i	$0.996025\pi$
$692$	−24.5989			−0.935109
$693$	7.75693	−	8.53795i	0.294661	−	0.324330i
$694$	−5.53322			−0.210038
$695$	2.12249	+	3.67627i	0.0805108	+	0.139449i
$696$	−8.50268	−	2.22234i	−0.322293	−	0.0842375i
$697$	−16.8582	+	29.1993i	−0.638550	+	1.10600i
$698$	1.11295			0.0421257
$699$	−27.3162	−	7.13961i	−1.03319	−	0.270045i
$700$	1.14677	−	4.98285i	0.0433439	−	0.188334i
$701$	38.7442			1.46335			0.731673	−	0.681655i	$-0.238740\pi$
$701$	38.7442			1.46335			0.731673	+	0.681655i	$0.238740\pi$
$702$	0.498577	−	0.143502i	0.0188176	−	0.00541613i
$703$	2.33000	+	4.03568i	0.0878777	+	0.152209i
$704$	9.34049			0.352033
$705$	10.4962	−	10.6261i	0.395310	−	0.400202i
$706$	2.62969	+	4.55476i	0.0989698	+	0.171421i
$707$	−21.7875	+	6.67751i	−0.819404	+	0.251134i
$708$	20.7634	−	21.0203i	0.780336	−	0.789993i
$709$	−14.2929	−	24.7560i	−0.536780	−	0.929731i	−0.999075	−	0.0430042i	$-0.986307\pi$
$709$	−14.2929	−	24.7560i	−0.536780	−	0.929731i	0.462295	−	0.886726i	$-0.347026\pi$
$710$	−0.179492	−	0.310889i	−0.00673622	−	0.0116675i
$711$	−4.39526	−	2.46603i	−0.164835	−	0.0924834i
$712$	−3.30815	+	5.72989i	−0.123978	+	0.214737i
$713$	−37.3533	+	64.6977i	−1.39889	+	2.42295i
$714$	5.76633	−	0.240852i	0.215800	−	0.00901365i
$715$	0.279420	+	0.483969i	0.0104497	+	0.0180994i
$716$	−44.8422			−1.67583
$717$	0.776144	−	0.785749i	0.0289856	−	0.0293443i
$718$	7.30667			0.272683
$719$	0.588137	−	1.01868i	0.0219338	−	0.0379905i	−0.854850	−	0.518875i	$-0.826351\pi$
$719$	0.588137	−	1.01868i	0.0219338	−	0.0379905i	0.876784	+	0.480884i	$0.159684\pi$
$720$	9.41877	+	5.28455i	0.351017	+	0.196944i
$721$	44.3730	−	13.5996i	1.65254	−	0.506475i
$722$	−2.44714	+	4.23857i	−0.0910730	+	0.157743i
$723$	5.01446	+	18.2642i	0.186490	+	0.679254i
$724$	−14.7556	+	25.5575i	−0.548388	+	0.949836i
$725$	2.48443	−	4.30317i	0.0922696	−	0.159816i
$726$	−2.80908	+	2.84385i	−0.104255	+	0.105545i
$727$	−2.88560	+	4.99801i	−0.107021	+	0.185366i	−0.914562	−	0.404445i	$-0.867465\pi$
$727$	−2.88560	+	4.99801i	−0.107021	+	0.185366i	0.807541	+	0.589811i	$0.200798\pi$
$728$	−0.760265	−	0.707981i	−0.0281773	−	0.0262395i
$729$	0.996001	+	26.9816i	0.0368889	+	0.999319i
$730$	−1.42792	+	2.47324i	−0.0528498	+	0.0915386i
$731$	−10.2855			−0.380422
$732$	6.87231	+	25.0311i	0.254008	+	0.925175i
$733$	−33.8696			−1.25100			−0.625501	−	0.780224i	$-0.715105\pi$
$733$	−33.8696			−1.25100			−0.625501	+	0.780224i	$0.715105\pi$
$734$	−2.47625	−	4.28898i	−0.0913999	−	0.158309i
$735$	−9.20997	−	7.88520i	−0.339715	−	0.290850i
$736$	−11.8365	+	20.5015i	−0.436301	+	0.755695i
$737$	−3.12468	+	5.41210i	−0.115099	+	0.199357i
$738$	−0.0666004	−	5.41479i	−0.00245160	−	0.199321i
$739$	−16.5555	−	28.6749i	−0.609003	−	1.05482i	−0.991405	−	0.130828i	$-0.958236\pi$
$739$	−16.5555	−	28.6749i	−0.609003	−	1.05482i	0.382402	−	0.923996i	$-0.375097\pi$
$740$	11.5710	+	20.0415i	0.425358	+	0.736741i
$741$	0.0686197	+	0.249934i	0.00252081	+	0.00918155i
$742$	−0.661197	+	2.87298i	−0.0242733	+	0.105470i
$743$	−23.4791	−	40.6669i	−0.861363	−	1.49192i	−0.870614	−	0.491967i	$-0.836278\pi$
$743$	−23.4791	−	40.6669i	−0.861363	−	1.49192i	0.00925070	−	0.999957i	$-0.497055\pi$
$744$	−16.0765	−	4.20190i	−0.589394	−	0.154049i
$745$	−3.26656			−0.119678
$746$	0.825715	+	1.43018i	0.0302316	+	0.0523626i
$747$	0.451108	+	36.6763i	0.0165052	+	1.34192i
$748$	−13.6226			−0.498090
$749$	1.19244	−	5.18131i	0.0435709	−	0.189321i
$750$	0.316059	−	0.319971i	0.0115409	−	0.0116837i
$751$	38.2015			1.39399			0.696997	−	0.717074i	$-0.254519\pi$
$751$	38.2015			1.39399			0.696997	+	0.717074i	$0.254519\pi$
$752$	15.5219	−	26.8848i	0.566027	−	0.980387i
$753$	−0.585621	−	2.13301i	−0.0213412	−	0.0777313i
$754$	−0.248062	−	0.429656i	−0.00903389	−	0.0156472i
$755$	11.5731			0.421187
$756$	22.2578	−	14.5077i	0.809510	−	0.527642i
$757$	46.1131			1.67601			0.838005	−	0.545663i	$-0.183722\pi$
$757$	46.1131			1.67601			0.838005	+	0.545663i	$0.183722\pi$
$758$	2.56454	+	4.44191i	0.0931482	+	0.161337i
$759$	−5.29947	−	19.3023i	−0.192359	−	0.700629i
$760$	0.198692	−	0.344144i	0.00720730	−	0.0124834i
$761$	23.5655			0.854250			0.427125	−	0.904193i	$-0.359526\pi$
$761$	23.5655			0.854250			0.427125	+	0.904193i	$0.359526\pi$
$762$	0.0123478	−	0.0125006i	0.000447313	−	0.000452848i
$763$	13.7643	+	12.8177i	0.498301	+	0.464032i
$764$	−20.8857			−0.755619
$765$	−12.6897	−	7.11975i	−0.458796	−	0.257415i
$766$	0.386783	+	0.669928i	0.0139750	+	0.0242055i
$767$	3.39411			0.122554
$768$	18.2230	+	4.76293i	0.657567	+	0.171868i
$769$	16.8384	+	29.1650i	0.607209	+	1.05172i	0.991698	+	0.128587i	$0.0410441\pi$
$769$	16.8384	+	29.1650i	0.607209	+	1.05172i	−0.384490	+	0.923129i	$0.625623\pi$
$770$	−0.730684	−	0.680434i	−0.0263320	−	0.0245211i
$771$	3.73470	+	13.6029i	0.134502	+	0.489898i
$772$	22.2775	+	38.5858i	0.801786	+	1.38873i
$773$	5.43410	+	9.41215i	0.195451	+	0.338531i	0.947048	−	0.321091i	$-0.104050\pi$
$773$	5.43410	+	9.41215i	0.195451	+	0.338531i	−0.751597	+	0.659622i	$0.770716\pi$
$774$	1.42037	−	0.843509i	0.0510540	−	0.0303193i
$775$	4.69746	−	8.13624i	0.168738	−	0.292262i
$776$	−0.775612	+	1.34340i	−0.0278429	+	0.0482252i
$777$	54.8271	−	2.29005i	1.96691	−	0.0821552i
$778$	−3.03859	−	5.26299i	−0.108939	−	0.188687i
$779$	2.70524			0.0969252
$780$	0.340771	+	1.24119i	0.0122016	+	0.0444418i
$781$	2.00923			0.0718958
$782$	5.00730	−	8.67290i	0.179061	−	0.310142i
$783$	24.8117	−	7.14138i	0.886698	−	0.255212i
$784$	−22.6648	−	11.0158i	−0.809456	−	0.393420i
$785$	−4.18869	+	7.25503i	−0.149501	+	0.258943i
$786$	3.73552	−	3.78175i	0.133242	−	0.134891i
$787$	−3.98307	+	6.89888i	−0.141981	+	0.245919i	−0.928243	−	0.371975i	$-0.878681\pi$
$787$	−3.98307	+	6.89888i	−0.141981	+	0.245919i	0.786261	+	0.617894i	$0.212014\pi$
$788$	−4.63892	+	8.03484i	−0.165255	+	0.286229i
$789$	7.58876	+	27.6406i	0.270167	+	0.984031i
$790$	−0.218109	+	0.377775i	−0.00775995	+	0.0134406i
$791$	−10.5116	−	9.78875i	−0.373751	−	0.348048i
$792$	3.82803	−	2.27334i	0.136023	−	0.0807797i
$793$	−1.49093	+	2.58236i	−0.0529443	+	0.0917022i
$794$	3.64754			0.129446
$795$	5.22322	−	5.28786i	0.185249	−	0.187541i
$796$	12.9853			0.460252
$797$	−11.0163	−	19.0808i	−0.390217	−	0.675875i	0.602261	−	0.798299i	$-0.294267\pi$
$797$	−11.0163	−	19.0808i	−0.390217	−	0.675875i	−0.992478	+	0.122424i	$0.960933\pi$
$798$	−0.248067	−	0.391015i	−0.00878146	−	0.0138418i
$799$	−20.9123	+	36.2212i	−0.739824	+	1.28141i
$800$	1.48854	−	2.57822i	0.0526278	−	0.0911540i
$801$	−0.239063	−	19.4364i	−0.00844686	−	0.686753i
$802$	−2.44053	−	4.22712i	−0.0861782	−	0.149265i
$803$	−7.99206	−	13.8427i	−0.282034	−	0.488497i
$804$	−10.1150	+	10.2402i	−0.356729	+	0.361143i
$805$	−20.1150	+	6.16490i	−0.708959	+	0.217284i
$806$	−0.469026	−	0.812376i	−0.0165207	−	0.0286147i
$807$	−14.2438	+	14.4201i	−0.501406	+	0.507611i
$808$	−8.79511			−0.309411
$809$	−18.7850	−	32.5366i	−0.660446	−	1.14393i	−0.980499	−	0.196526i	$-0.937034\pi$
$809$	−18.7850	−	32.5366i	−0.660446	−	1.14393i	0.320052	−	0.947400i	$-0.396299\pi$
$810$	2.33626	−	0.0574794i	0.0820878	−	0.00201962i
$811$	10.6226			0.373011			0.186505	−	0.982454i	$-0.440284\pi$
$811$	10.6226			0.373011			0.186505	+	0.982454i	$0.440284\pi$
$812$	−18.5930	−	17.3143i	−0.652485	−	0.607613i
$813$	37.1101	+	9.69942i	1.30151	+	0.340174i
$814$	4.51896			0.158389
$815$	−4.23150	+	7.32917i	−0.148223	+	0.256730i
$816$	−29.2598	−	7.64760i	−1.02430	−	0.267720i
$817$	0.412628	+	0.714692i	0.0144360	+	0.0250039i
$818$	6.33534			0.221510
$819$	2.98250	+	0.647885i	0.104217	+	0.0226389i
$820$	13.4344			0.469151
$821$	−27.0961	−	46.9319i	−0.945662	−	1.63793i	−0.754421	−	0.656391i	$-0.772082\pi$
$821$	−27.0961	−	46.9319i	−0.945662	−	1.63793i	−0.191241	−	0.981543i	$-0.561251\pi$
$822$	−0.871119	+	0.881899i	−0.0303838	+	0.0307598i
$823$	0.224300	−	0.388499i	0.00781861	−	0.0135422i	−0.862090	−	0.506756i	$-0.830845\pi$
$823$	0.224300	−	0.388499i	0.00781861	−	0.0135422i	0.869908	+	0.493214i	$0.164178\pi$
$824$	17.9123			0.624006
$825$	0.666450	+	2.42742i	0.0232028	+	0.0845118i
$826$	−5.79786	+	1.77695i	−0.201733	+	0.0618279i
$827$	−15.0339			−0.522779			−0.261390	−	0.965233i	$-0.584181\pi$
$827$	−15.0339			−0.522779			−0.261390	+	0.965233i	$0.584181\pi$
$828$	−0.567003	−	46.0988i	−0.0197047	−	1.60205i
$829$	18.8594	+	32.6655i	0.655015	+	1.13452i	0.981890	+	0.189451i	$0.0606709\pi$
$829$	18.8594	+	32.6655i	0.655015	+	1.13452i	−0.326875	+	0.945067i	$0.605996\pi$
$830$	3.17473			0.110197
$831$	0.591995	+	2.15623i	0.0205361	+	0.0747987i
$832$	1.23566	+	2.14022i	0.0428387	+	0.0741989i
$833$	30.5357	+	14.8412i	1.05800	+	0.514219i
$834$	1.84713	+	0.482783i	0.0639610	+	0.0167174i
$835$	−7.04377	−	12.2002i	−0.243760	−	0.422204i
$836$	0.546503	+	0.946571i	0.0189012	+	0.0327379i
$837$	46.9129	−	13.5026i	1.62155	−	0.466719i
$838$	−0.519742	+	0.900219i	−0.0179542	+	0.0310975i
$839$	−1.59156	+	2.75666i	−0.0549467	+	0.0951704i	−0.892190	−	0.451659i	$-0.850832\pi$
$839$	−1.59156	+	2.75666i	−0.0549467	+	0.0951704i	0.837244	+	0.546830i	$0.184166\pi$
$840$	−2.50682	−	3.95137i	−0.0864935	−	0.136335i
$841$	2.15518	+	3.73287i	0.0743164	+	0.128720i
$842$	6.04907			0.208465
$843$	50.9764	+	13.3237i	1.75572	+	0.458891i
$844$	−27.2804			−0.939031
$845$	6.42607	−	11.1303i	0.221064	−	0.382893i
$846$	−0.0826167	−	6.71696i	−0.00284042	−	0.230934i
$847$	−22.4828	+	6.89059i	−0.772517	+	0.236764i
$848$	7.72418	−	13.3787i	0.265249	−	0.459425i
$849$	−30.2008	−	7.89356i	−1.03649	−	0.270906i
$850$	−0.629707	+	1.09068i	−0.0215988	+	0.0374102i
$851$	47.6101	−	82.4631i	1.63205	−	2.82680i
$852$	4.47726	+	1.17022i	0.153389	+	0.0400910i
$853$	8.66370	−	15.0060i	0.296639	−	0.513794i	−0.678726	−	0.734392i	$-0.737467\pi$
$853$	8.66370	−	15.0060i	0.296639	−	0.513794i	0.975365	+	0.220598i	$0.0708008\pi$
$854$	1.19485	−	5.19177i	0.0408870	−	0.177659i
$855$	0.0143584	+	1.16738i	0.000491047	+	0.0399234i
$856$	1.02602	−	1.77711i	0.0350686	−	0.0607405i
$857$	15.3889			0.525675			0.262837	−	0.964840i	$-0.415342\pi$
$857$	15.3889			0.525675			0.262837	+	0.964840i	$0.415342\pi$
$858$	0.243169	+	0.0635569i	0.00830166	+	0.00216980i
$859$	−23.8995			−0.815442			−0.407721	−	0.913107i	$-0.633676\pi$
$859$	−23.8995			−0.815442			−0.407721	+	0.913107i	$0.633676\pi$
$860$	2.04914	+	3.54922i	0.0698752	+	0.121027i
$861$	14.7629	−	28.2289i	0.503117	−	0.962038i
$862$	−4.03375	+	6.98667i	−0.137390	+	0.237967i
$863$	−10.8364	+	18.7692i	−0.368875	+	0.638910i	−0.989390	−	0.145284i	$-0.953590\pi$
$863$	−10.8364	+	18.7692i	−0.368875	+	0.638910i	0.620515	+	0.784195i	$0.286924\pi$
$864$	14.8658	−	4.27873i	0.505746	−	0.145565i
$865$	−6.36427	−	11.0232i	−0.216392	−	0.374802i
$866$	−0.434256	−	0.752153i	−0.0147566	−	0.0255592i
$867$	10.9331	+	2.85758i	0.371308	+	0.0970484i
$868$	−35.1548	−	32.7372i	−1.19323	−	1.11117i
$869$	−1.22075	−	2.11440i	−0.0414111	−	0.0717261i
$870$	−0.591658	−	2.15500i	−0.0200591	−	0.0730614i
$871$	−1.65346			−0.0560254
$872$	3.62958	+	6.28661i	0.122913	+	0.212891i
$873$	−0.0560494	−	4.55697i	−0.00189698	−	0.154230i
$874$	−0.803522			−0.0271795
$875$	2.52961	−	0.775284i	0.0855165	−	0.0262094i
$876$	−9.74686	−	35.5011i	−0.329316	−	1.19947i
$877$	1.14170			0.0385526			0.0192763	−	0.999814i	$-0.493864\pi$
$877$	1.14170			0.0385526			0.0192763	+	0.999814i	$0.493864\pi$
$878$	2.55506	−	4.42550i	0.0862291	−	0.149353i
$879$	−29.6411	+	30.0079i	−0.999770	+	1.01214i
$880$	2.61599	+	4.53103i	0.0881850	+	0.152741i
$881$	9.29854			0.313276			0.156638	−	0.987656i	$-0.449934\pi$
$881$	9.29854			0.313276			0.156638	+	0.987656i	$0.449934\pi$
$882$	−5.43393	+	0.454729i	−0.182970	+	0.0153115i
$883$	5.51880			0.185722			0.0928612	−	0.995679i	$-0.470399\pi$
$883$	5.51880			0.185722			0.0928612	+	0.995679i	$0.470399\pi$
$884$	−1.80214	−	3.12139i	−0.0606124	−	0.104984i
$885$	14.7916	+	3.86606i	0.497214	+	0.129956i
$886$	2.19230	−	3.79718i	0.0736519	−	0.127569i
$887$	−31.1437			−1.04570			−0.522852	−	0.852423i	$-0.675132\pi$
$887$	−31.1437			−1.04570			−0.522852	+	0.852423i	$0.675132\pi$
$888$	20.4910	+	5.35570i	0.687632	+	0.179726i
$889$	0.0988266	−	0.0302887i	0.00331454	−	0.00101585i
$890$	−1.68244			−0.0563954
$891$	−6.25939	+	11.4850i	−0.209698	+	0.384762i
$892$	20.1523	+	34.9048i	0.674749	+	1.16870i
$893$	3.35580			0.112298
$894$	−1.03243	+	1.04520i	−0.0345295	+	0.0349569i
$895$	−11.6017	−	20.0947i	−0.387801	−	0.671691i
$896$	−14.7598	−	13.7448i	−0.493091	−	0.459180i
$897$	3.72174	−	3.76780i	0.124265	−	0.125803i
$898$	2.62334	+	4.54376i	0.0875421	+	0.151627i
$899$	−23.3411	−	40.4279i	−0.778468	−	1.34835i
$900$	0.0713050	+	5.79729i	0.00237683	+	0.193243i
$901$	−10.4066	+	18.0247i	−0.346694	+	0.600491i
$902$	1.31168	−	2.27189i	0.0436741	−	0.0756458i
$903$	9.70951	−	0.405553i	0.323112	−	0.0134960i
$904$	−2.77187	−	4.80102i	−0.0921910	−	0.159680i
$905$	−15.2704			−0.507606
$906$	3.65778	−	3.70304i	0.121522	−	0.123025i
$907$	−38.7026			−1.28510			−0.642549	−	0.766244i	$-0.722123\pi$
$907$	−38.7026			−1.28510			−0.642549	+	0.766244i	$0.722123\pi$
$908$	−25.2494	+	43.7332i	−0.837929	+	1.45134i
$909$	22.2166	−	13.1937i	0.736878	−	0.437608i
$910$	0.0592480	−	0.257439i	0.00196405	−	0.00853403i
$911$	21.1953	−	36.7113i	0.702231	−	1.21630i	−0.265451	−	0.964124i	$-0.585521\pi$
$911$	21.1953	−	36.7113i	0.702231	−	1.21630i	0.967682	−	0.252175i	$-0.0811458\pi$
$912$	0.642433	+	2.33994i	0.0212731	+	0.0774831i
$913$	−8.88446	+	15.3883i	−0.294033	+	0.509280i
$914$	−3.85547	+	6.67788i	−0.127528	+	0.220884i
$915$	−9.43890	+	9.55571i	−0.312040	+	0.315902i
$916$	5.33005	−	9.23191i	0.176110	−	0.305031i
$917$	29.8976	−	9.16312i	0.987306	−	0.302593i
$918$	−6.28880	+	1.81006i	−0.207561	+	0.0597409i
$919$	−21.6000	+	37.4122i	−0.712517	+	1.23412i	0.251393	+	0.967885i	$0.419111\pi$
$919$	−21.6000	+	37.4122i	−0.712517	+	1.23412i	−0.963910	+	0.266230i	$0.914222\pi$
$920$	−8.11993			−0.267706
$921$	0.588674	+	2.14413i	0.0193975	+	0.0706516i
$922$	3.55479			0.117071
$923$	0.265802	+	0.460382i	0.00874897	+	0.0151537i
$924$	12.8597	−	0.537133i	0.423054	−	0.0176704i
$925$	−5.98734	+	10.3704i	−0.196863	+	0.340976i
$926$	4.63065	−	8.02051i	0.152172	−	0.263570i
$927$	−45.2469	+	26.8707i	−1.48610	+	0.882549i
$928$	−7.39635	−	12.8109i	−0.242797	−	0.420537i
$929$	−2.64149	−	4.57519i	−0.0866644	−	0.150107i	0.819435	−	0.573172i	$-0.194287\pi$
$929$	−2.64149	−	4.57519i	−0.0866644	−	0.150107i	−0.906099	+	0.423065i	$0.860954\pi$
$930$	−1.11868	−	4.07459i	−0.0366831	−	0.133611i
$931$	−0.193763	−	2.71718i	−0.00635032	−	0.0890521i
$932$	−15.7513	−	27.2820i	−0.515950	−	0.893651i
$933$	−14.0199	−	3.66437i	−0.458992	−	0.119966i
$934$	1.57331			0.0514802
$935$	−3.52446	−	6.10454i	−0.115262	−	0.199640i
$936$	1.02731	+	0.576390i	0.0335787	+	0.0188399i
$937$	34.9221			1.14086			0.570428	−	0.821348i	$-0.306777\pi$
$937$	34.9221			1.14086			0.570428	+	0.821348i	$0.306777\pi$
$938$	2.82446	−	0.865650i	0.0922219	−	0.0282645i
$939$	10.3287	−	10.4565i	0.337064	−	0.341236i
$940$	16.6652			0.543559
$941$	−14.4585	+	25.0429i	−0.471334	+	0.816375i	−0.999462	−	0.0327899i	$-0.989561\pi$
$941$	−14.4585	+	25.0429i	−0.471334	+	0.816375i	0.528128	+	0.849165i	$0.322894\pi$
$942$	0.997521	+	3.63328i	0.0325010	+	0.118379i
$943$	−27.6387	−	47.8717i	−0.900041	−	1.55892i
$944$	31.7765			1.03424
$945$	12.2598	+	6.22071i	0.398811	+	0.202360i
$946$	0.800277			0.0260193
$947$	2.41152	+	4.17687i	0.0783638	+	0.135730i	0.902544	−	0.430597i	$-0.141697\pi$
$947$	2.41152	+	4.17687i	0.0783638	+	0.135730i	−0.824180	+	0.566327i	$0.808364\pi$
$948$	−1.48879	−	5.42261i	−0.0483535	−	0.176118i
$949$	2.11455	−	3.66251i	0.0686412	−	0.118890i
$950$	0.101049			0.00327847
$951$	29.1222	−	29.4826i	0.944351	−	0.956038i
$952$	9.58960	+	8.93012i	0.310801	+	0.289427i
$953$	−34.1659			−1.10674			−0.553372	−	0.832934i	$-0.686659\pi$
$953$	−34.1659			−1.10674			−0.553372	+	0.832934i	$0.686659\pi$
$954$	−0.0411125	−	3.34256i	−0.00133107	−	0.108219i
$955$	−5.40360	−	9.35931i	−0.174856	−	0.302860i
$956$	1.23231			0.0398558
$957$	12.1013	+	3.16291i	0.391180	+	0.102242i
$958$	4.56854	+	7.91293i	0.147603	+	0.255655i
$959$	−6.97208	+	2.13683i	−0.225140	+	0.0690017i
$960$	2.94719	+	10.7346i	0.0951203	+	0.346457i
$961$	−28.6323	−	49.5926i	−0.923623	−	1.59976i
$962$	0.597815	+	1.03545i	0.0192743	+	0.0333841i
$963$	0.0741449	+	6.02818i	0.00238928	+	0.194255i
$964$	−10.5664	+	18.3016i	−0.340321	+	0.589454i
$965$	−11.5274	+	19.9660i	−0.371080	+	0.642729i
$966$	−4.38493	+	8.38467i	−0.141083	+	0.269772i
$967$	−16.8619	−	29.2056i	−0.542241	−	0.939189i	−0.998775	−	0.0494833i	$-0.984243\pi$
$967$	−16.8619	−	29.2056i	−0.542241	−	0.939189i	0.456534	−	0.889706i	$-0.349091\pi$
$968$	−9.07576			−0.291706
$969$	−0.865533	−	3.15254i	−0.0278049	−	0.101274i
$970$	−0.394455			−0.0126652
$971$	25.2620	−	43.7550i	0.810695	−	1.40417i	−0.101683	−	0.994817i	$-0.532423\pi$
$971$	25.2620	−	43.7550i	0.810695	−	1.40417i	0.912378	−	0.409349i	$-0.134244\pi$
$972$	−20.6372	+	21.9470i	−0.661940	+	0.703951i
$973$	8.21924	+	7.65399i	0.263497	+	0.245376i
$974$	2.89042	−	5.00635i	0.0926149	−	0.160414i
$975$	−0.468038	+	0.473830i	−0.0149892	+	0.0151747i
$976$	−13.9584	+	24.1766i	−0.446797	+	0.773875i
$977$	−3.54639	+	6.14253i	−0.113459	+	0.196517i	−0.917163	−	0.398513i	$-0.869526\pi$
$977$	−3.54639	+	6.14253i	−0.113459	+	0.196517i	0.803704	+	0.595030i	$0.202860\pi$
$978$	1.00771	+	3.67041i	0.0322232	+	0.117367i
$979$	4.70828	−	8.15498i	0.150477	−	0.260634i
$980$	−0.962242	−	13.4938i	−0.0307377	−	0.431042i
$981$	−18.5991	−	10.4353i	−0.593822	−	0.333174i
$982$	1.11761	−	1.93575i	0.0356642	−	0.0617722i
$983$	−30.0298			−0.957803			−0.478901	−	0.877869i	$-0.658965\pi$
$983$	−30.0298			−0.957803			−0.478901	+	0.877869i	$0.658965\pi$
$984$	8.64030	−	8.74723i	0.275443	−	0.278851i
$985$	−4.80076			−0.152965
$986$	3.12893	+	5.41947i	0.0996454	+	0.172591i
$987$	18.3131	−	35.0174i	0.582912	−	1.11462i
$988$	−0.144594	+	0.250445i	−0.00460016	+	0.00796771i
$989$	8.43143	−	14.6037i	0.268104	−	0.464370i
$990$	0.987340	+	0.553963i	0.0313797	+	0.0176061i
$991$	10.7975	+	18.7018i	0.342994	+	0.594083i	0.984987	−	0.172627i	$-0.0552257\pi$
$991$	10.7975	+	18.7018i	0.342994	+	0.594083i	−0.641993	+	0.766710i	$0.721892\pi$
$992$	−13.9847	−	24.2222i	−0.444015	−	0.769056i
$993$	7.37617	−	7.46745i	0.234076	−	0.236972i
$994$	−0.695073	−	0.647272i	−0.0220464	−	0.0205302i
$995$	3.35959	+	5.81897i	0.106506	+	0.184474i
$996$	−28.7602	+	29.1161i	−0.911302	+	0.922579i
$997$	−18.6694			−0.591266			−0.295633	−	0.955302i	$-0.595530\pi$
$997$	−18.6694			−0.591266			−0.295633	+	0.955302i	$0.595530\pi$
$998$	−2.53975	−	4.39897i	−0.0803943	−	0.139247i
$999$	−59.7948	+	17.2103i	−1.89182	+	0.544510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.10	✓	36
3.2	odd	2		945.2.k.c.856.9		36
7.4	even	3		315.2.l.c.151.9	yes	36
9.4	even	3		315.2.l.c.121.9	yes	36
9.5	odd	6		945.2.l.c.226.10		36
21.11	odd	6		945.2.l.c.46.10		36
63.4	even	3	inner	315.2.k.c.256.10	yes	36
63.32	odd	6		945.2.k.c.361.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.10	✓	36	1.1	even	1	trivial
315.2.k.c.256.10	yes	36	63.4	even	3	inner
315.2.l.c.121.9	yes	36	9.4	even	3
315.2.l.c.151.9	yes	36	7.4	even	3
945.2.k.c.361.9		36	63.32	odd	6
945.2.k.c.856.9		36	3.2	odd	2
945.2.l.c.46.10		36	21.11	odd	6
945.2.l.c.226.10		36	9.5	odd	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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.129832 + 0.224875i) q^{2} +(-0.458568 - 1.67024i) q^{3} +(0.966288 - 1.67366i) q^{4} +1.00000 q^{5} +(0.316059 - 0.319971i) q^{6} +(2.52961 - 0.775284i) q^{7} +1.02114 q^{8} +(-2.57943 + 1.53184i) q^{9} +O(q^{10})\)	\(q+(0.129832 + 0.224875i) q^{2} +(-0.458568 - 1.67024i) q^{3} +(0.966288 - 1.67366i) q^{4} +1.00000 q^{5} +(0.316059 - 0.319971i) q^{6} +(2.52961 - 0.775284i) q^{7} +1.02114 q^{8} +(-2.57943 + 1.53184i) q^{9} +(0.129832 + 0.224875i) q^{10} -1.45333 q^{11} +(-3.23853 - 0.846450i) q^{12} +(-0.192262 - 0.333007i) q^{13} +(0.502765 + 0.468190i) q^{14} +(-0.458568 - 1.67024i) q^{15} +(-1.80000 - 3.11769i) q^{16} +(2.42509 + 4.20038i) q^{17} +(-0.679364 - 0.381168i) q^{18} +(0.194577 - 0.337018i) q^{19} +(0.966288 - 1.67366i) q^{20} +(-2.45491 - 3.86955i) q^{21} +(-0.188688 - 0.326817i) q^{22} -7.95180 q^{23} +(-0.468264 - 1.70556i) q^{24} +1.00000 q^{25} +(0.0499233 - 0.0864697i) q^{26} +(3.74139 + 3.60583i) q^{27} +(1.14677 - 4.98285i) q^{28} +(2.48443 - 4.30317i) q^{29} +(0.316059 - 0.319971i) q^{30} +(4.69746 - 8.13624i) q^{31} +(1.48854 - 2.57822i) q^{32} +(0.666450 + 2.42742i) q^{33} +(-0.629707 + 1.09068i) q^{34} +(2.52961 - 0.775284i) q^{35} +(0.0713050 + 5.79729i) q^{36} +(-5.98734 + 10.3704i) q^{37} +0.101049 q^{38} +(-0.468038 + 0.473830i) q^{39} +1.02114 q^{40} +(3.47579 + 6.02024i) q^{41} +(0.551439 - 1.05444i) q^{42} +(-1.06032 + 1.83652i) q^{43} +(-1.40433 + 2.43238i) q^{44} +(-2.57943 + 1.53184i) q^{45} +(-1.03239 - 1.78816i) q^{46} +(4.31165 + 7.46800i) q^{47} +(-4.38188 + 4.43611i) q^{48} +(5.79787 - 3.92233i) q^{49} +(0.129832 + 0.224875i) q^{50} +(5.90360 - 5.97665i) q^{51} -0.743121 q^{52} +(2.14561 + 3.71630i) q^{53} +(-0.325110 + 1.30949i) q^{54} -1.45333 q^{55} +(2.58310 - 0.791677i) q^{56} +(-0.652129 - 0.170446i) q^{57} +1.29023 q^{58} +(-4.41340 + 7.64423i) q^{59} +(-3.23853 - 0.846450i) q^{60} +(-3.87733 - 6.71574i) q^{61} +2.43952 q^{62} +(-5.33735 + 5.87475i) q^{63} -6.42696 q^{64} +(-0.192262 - 0.333007i) q^{65} +(-0.459338 + 0.465023i) q^{66} +(2.15001 - 3.72393i) q^{67} +9.37334 q^{68} +(3.64644 + 13.2814i) q^{69} +(0.502765 + 0.468190i) q^{70} -1.38250 q^{71} +(-2.63397 + 1.56423i) q^{72} +(5.49914 + 9.52479i) q^{73} -3.10938 q^{74} +(-0.458568 - 1.67024i) q^{75} +(-0.376035 - 0.651312i) q^{76} +(-3.67636 + 1.12674i) q^{77} +(-0.167319 - 0.0437319i) q^{78} +(0.839967 + 1.45487i) q^{79} +(-1.80000 - 3.11769i) q^{80} +(4.30693 - 7.90255i) q^{81} +(-0.902534 + 1.56323i) q^{82} +(6.11318 - 10.5883i) q^{83} +(-8.84846 + 0.369588i) q^{84} +(2.42509 + 4.20038i) q^{85} -0.550651 q^{86} +(-8.32662 - 2.17632i) q^{87} -1.48406 q^{88} +(-3.23965 + 5.61124i) q^{89} +(-0.679364 - 0.381168i) q^{90} +(-0.744523 - 0.693321i) q^{91} +(-7.68372 + 13.3086i) q^{92} +(-15.7436 - 4.11489i) q^{93} +(-1.11958 + 1.93916i) q^{94} +(0.194577 - 0.337018i) q^{95} +(-4.98886 - 1.30393i) q^{96} +(-0.759552 + 1.31558i) q^{97} +(1.63478 + 0.794552i) q^{98} +(3.74876 - 2.22627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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