LMFDB - Embedded newform 315.2.l.c.121.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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([2, 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("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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			121.7
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17766 q^{2} +(1.55400 + 0.764908i) q^{3} -0.613115 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.83009 - 0.900802i) q^{6} +(-1.48383 - 2.19049i) q^{7} +3.07736 q^{8} +(1.82983 + 2.37733i) q^{9} +O(q^{10})$	\(q-1.17766 q^{2} +(1.55400 + 0.764908i) q^{3} -0.613115 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.83009 - 0.900802i) q^{6} +(-1.48383 - 2.19049i) q^{7} +3.07736 q^{8} +(1.82983 + 2.37733i) q^{9} +(0.588830 + 1.01988i) q^{10} +(0.803681 - 1.39202i) q^{11} +(-0.952781 - 0.468976i) q^{12} +(2.48616 - 4.30615i) q^{13} +(1.74745 + 2.57965i) q^{14} +(-0.114571 - 1.72826i) q^{15} -2.39786 q^{16} +(0.876227 + 1.51767i) q^{17} +(-2.15492 - 2.79969i) q^{18} +(3.57754 - 6.19648i) q^{19} +(0.306558 + 0.530973i) q^{20} +(-0.630356 - 4.53901i) q^{21} +(-0.946464 + 1.63932i) q^{22} +(3.73875 + 6.47570i) q^{23} +(4.78222 + 2.35390i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.92785 + 5.07118i) q^{26} +(1.02512 + 5.09403i) q^{27} +(0.909761 + 1.34302i) q^{28} +(-1.18010 - 2.04400i) q^{29} +(0.134925 + 2.03530i) q^{30} -4.03840 q^{31} -3.33086 q^{32} +(2.31369 - 1.54845i) q^{33} +(-1.03190 - 1.78730i) q^{34} +(-1.15510 + 2.38028i) q^{35} +(-1.12190 - 1.45758i) q^{36} +(4.22323 - 7.31485i) q^{37} +(-4.21313 + 7.29735i) q^{38} +(7.15730 - 4.79008i) q^{39} +(-1.53868 - 2.66507i) q^{40} +(2.20143 - 3.81300i) q^{41} +(0.742346 + 5.34542i) q^{42} +(-0.404008 - 0.699762i) q^{43} +(-0.492749 + 0.853467i) q^{44} +(1.14391 - 2.77335i) q^{45} +(-4.40298 - 7.62618i) q^{46} +8.46599 q^{47} +(-3.72627 - 1.83414i) q^{48} +(-2.59648 + 6.50064i) q^{49} +(0.588830 - 1.01988i) q^{50} +(0.200780 + 3.02869i) q^{51} +(-1.52430 + 2.64017i) q^{52} +(1.44386 + 2.50083i) q^{53} +(-1.20724 - 5.99904i) q^{54} -1.60736 q^{55} +(-4.56629 - 6.74093i) q^{56} +(10.2992 - 6.89284i) q^{57} +(1.38976 + 2.40714i) q^{58} -13.3986 q^{59} +(0.0702450 + 1.05962i) q^{60} -10.8893 q^{61} +4.75587 q^{62} +(2.49235 - 7.53579i) q^{63} +8.71834 q^{64} -4.97231 q^{65} +(-2.72474 + 1.82355i) q^{66} -8.11941 q^{67} +(-0.537228 - 0.930506i) q^{68} +(0.856702 + 12.9230i) q^{69} +(1.36032 - 2.80316i) q^{70} -2.85904 q^{71} +(5.63106 + 7.31592i) q^{72} +(5.87110 + 10.1690i) q^{73} +(-4.97353 + 8.61441i) q^{74} +(-1.43943 + 0.963350i) q^{75} +(-2.19344 + 3.79916i) q^{76} +(-4.24173 + 0.305067i) q^{77} +(-8.42887 + 5.64109i) q^{78} +1.91775 q^{79} +(1.19893 + 2.07661i) q^{80} +(-2.30342 + 8.70024i) q^{81} +(-2.59254 + 4.49042i) q^{82} +(0.628986 + 1.08944i) q^{83} +(0.386481 + 2.78294i) q^{84} +(0.876227 - 1.51767i) q^{85} +(0.475784 + 0.824082i) q^{86} +(-0.270410 - 4.07904i) q^{87} +(2.47322 - 4.28374i) q^{88} +(-3.79432 + 6.57195i) q^{89} +(-1.34714 + 3.26606i) q^{90} +(-13.1216 + 0.943711i) q^{91} +(-2.29228 - 3.97035i) q^{92} +(-6.27568 - 3.08900i) q^{93} -9.97007 q^{94} -7.15508 q^{95} +(-5.17616 - 2.54780i) q^{96} +(5.89502 + 10.2105i) q^{97} +(3.05777 - 7.65555i) q^{98} +(4.77989 - 0.636540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.17766			−0.832732			−0.416366	−	0.909197i	$-0.636696\pi$
$2$	−1.17766			−0.832732			−0.416366	+	0.909197i	$0.636696\pi$
$3$	1.55400	+	0.764908i	0.897202	+	0.441620i
$3$	1.55400	+	0.764908i	0.897202	+	0.441620i
$4$	−0.613115			−0.306558
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.83009	−	0.900802i	−0.747129	−	0.367751i
$7$	−1.48383	−	2.19049i	−0.560836	−	0.827927i
$7$	−1.48383	−	2.19049i	−0.560836	−	0.827927i
$8$	3.07736			1.08801
$9$	1.82983	+	2.37733i	0.609944	+	0.792444i
$10$	0.588830	+	1.01988i	0.186205	+	0.322516i
$11$	0.803681	−	1.39202i	0.242319	−	0.419709i	−0.719055	−	0.694953i	$-0.755425\pi$
$11$	0.803681	−	1.39202i	0.242319	−	0.419709i	0.961374	+	0.275244i	$0.0887586\pi$
$12$	−0.952781	−	0.468976i	−0.275044	−	0.135382i
$13$	2.48616	−	4.30615i	0.689536	−	1.19431i	−0.282452	−	0.959281i	$-0.591148\pi$
$13$	2.48616	−	4.30615i	0.689536	−	1.19431i	0.971988	−	0.235030i	$-0.0755188\pi$
$14$	1.74745	+	2.57965i	0.467026	+	0.689441i
$15$	−0.114571	−	1.72826i	−0.0295820	−	0.446234i
$16$	−2.39786			−0.599465
$17$	0.876227	+	1.51767i	0.212516	+	0.368089i	0.952501	−	0.304534i	$-0.0985008\pi$
$17$	0.876227	+	1.51767i	0.212516	+	0.368089i	−0.739985	+	0.672623i	$0.765168\pi$
$18$	−2.15492	−	2.79969i	−0.507920	−	0.659894i
$19$	3.57754	−	6.19648i	0.820744	−	1.42157i	−0.0843851	−	0.996433i	$-0.526893\pi$
$19$	3.57754	−	6.19648i	0.820744	−	1.42157i	0.905129	−	0.425137i	$-0.139774\pi$
$20$	0.306558	+	0.530973i	0.0685483	+	0.118729i
$21$	−0.630356	−	4.53901i	−0.137555	−	0.990494i
$22$	−0.946464	+	1.63932i	−0.201787	+	0.349505i
$23$	3.73875	+	6.47570i	0.779583	+	1.35028i	0.932182	+	0.361990i	$0.117902\pi$
$23$	3.73875	+	6.47570i	0.779583	+	1.35028i	−0.152599	+	0.988288i	$0.548764\pi$
$24$	4.78222	+	2.35390i	0.976167	+	0.480487i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.92785	+	5.07118i	−0.574199	+	0.994541i
$27$	1.02512	+	5.09403i	0.197285	+	0.980346i
$28$	0.909761	+	1.34302i	0.171929	+	0.253807i
$29$	−1.18010	−	2.04400i	−0.219140	−	0.379561i	0.735406	−	0.677627i	$-0.236992\pi$
$29$	−1.18010	−	2.04400i	−0.219140	−	0.379561i	−0.954545	+	0.298066i	$0.903658\pi$
$30$	0.134925	+	2.03530i	0.0246339	+	0.371593i
$31$	−4.03840			−0.725318			−0.362659	−	0.931922i	$-0.618131\pi$
$31$	−4.03840			−0.725318			−0.362659	+	0.931922i	$0.618131\pi$
$32$	−3.33086			−0.588819
$33$	2.31369	−	1.54845i	0.402761	−	0.269551i
$34$	−1.03190	−	1.78730i	−0.176969	−	0.306519i
$35$	−1.15510	+	2.38028i	−0.195248	+	0.402341i
$36$	−1.12190	−	1.45758i	−0.186983	−	0.242930i
$37$	4.22323	−	7.31485i	0.694295	−	1.20255i	−0.276123	−	0.961122i	$-0.589050\pi$
$37$	4.22323	−	7.31485i	0.694295	−	1.20255i	0.970418	−	0.241431i	$-0.0776169\pi$
$38$	−4.21313	+	7.29735i	−0.683460	+	1.18379i
$39$	7.15730	−	4.79008i	1.14608	−	0.767026i
$40$	−1.53868	−	2.66507i	−0.243287	−	0.421385i
$41$	2.20143	−	3.81300i	0.343806	−	0.595490i	−0.641330	−	0.767265i	$-0.721617\pi$
$41$	2.20143	−	3.81300i	0.343806	−	0.595490i	0.985136	+	0.171775i	$0.0549503\pi$
$42$	0.742346	+	5.34542i	0.114546	+	0.824816i
$43$	−0.404008	−	0.699762i	−0.0616106	−	0.106713i	0.833575	−	0.552406i	$-0.186290\pi$
$43$	−0.404008	−	0.699762i	−0.0616106	−	0.106713i	−0.895185	+	0.445694i	$0.852957\pi$
$44$	−0.492749	+	0.853467i	−0.0742847	+	0.128665i
$45$	1.14391	−	2.77335i	0.170525	−	0.413426i
$46$	−4.40298	−	7.62618i	−0.649184	−	1.12442i
$47$	8.46599			1.23489			0.617446	−	0.786613i	$-0.288167\pi$
$47$	8.46599			1.23489			0.617446	+	0.786613i	$0.288167\pi$
$48$	−3.72627	−	1.83414i	−0.537841	−	0.264735i
$49$	−2.59648	+	6.50064i	−0.370925	+	0.928663i
$50$	0.588830	−	1.01988i	0.0832732	−	0.144233i
$51$	0.200780	+	3.02869i	0.0281148	+	0.424101i
$52$	−1.52430	+	2.64017i	−0.211382	+	0.366125i
$53$	1.44386	+	2.50083i	0.198329	+	0.343516i	0.947987	−	0.318310i	$-0.103115\pi$
$53$	1.44386	+	2.50083i	0.198329	+	0.343516i	−0.749658	+	0.661826i	$0.769782\pi$
$54$	−1.20724	−	5.99904i	−0.164285	−	0.816366i
$55$	−1.60736			−0.216737
$56$	−4.56629	−	6.74093i	−0.610197	−	0.900794i
$57$	10.2992	−	6.89284i	1.36417	−	0.912980i
$58$	1.38976	+	2.40714i	0.182484	+	0.316072i
$59$	−13.3986			−1.74435			−0.872173	−	0.489198i	$-0.837290\pi$
$59$	−13.3986			−1.74435			−0.872173	+	0.489198i	$0.837290\pi$
$60$	0.0702450	+	1.05962i	0.00906859	+	0.136796i
$61$	−10.8893			−1.39424			−0.697119	−	0.716956i	$-0.745535\pi$
$61$	−10.8893			−1.39424			−0.697119	+	0.716956i	$0.745535\pi$
$62$	4.75587			0.603996
$63$	2.49235	−	7.53579i	0.314007	−	0.949421i
$64$	8.71834			1.08979
$65$	−4.97231			−0.616740
$66$	−2.72474	+	1.82355i	−0.335392	+	0.224464i
$67$	−8.11941			−0.991944			−0.495972	−	0.868339i	$-0.665188\pi$
$67$	−8.11941			−0.991944			−0.495972	+	0.868339i	$0.665188\pi$
$68$	−0.537228	−	0.930506i	−0.0651484	−	0.112840i
$69$	0.856702	+	12.9230i	0.103135	+	1.55575i
$70$	1.36032	−	2.80316i	0.162589	−	0.335042i
$71$	−2.85904			−0.339306			−0.169653	−	0.985504i	$-0.554265\pi$
$71$	−2.85904			−0.339306			−0.169653	+	0.985504i	$0.554265\pi$
$72$	5.63106	+	7.31592i	0.663627	+	0.862189i
$73$	5.87110	+	10.1690i	0.687160	+	1.19020i	0.972753	+	0.231845i	$0.0744762\pi$
$73$	5.87110	+	10.1690i	0.687160	+	1.19020i	−0.285593	+	0.958351i	$0.592191\pi$
$74$	−4.97353	+	8.61441i	−0.578161	+	1.00140i
$75$	−1.43943	+	0.963350i	−0.166211	+	0.111238i
$76$	−2.19344	+	3.79916i	−0.251605	+	0.435793i
$77$	−4.24173	+	0.305067i	−0.483390	+	0.0347656i
$78$	−8.42887	+	5.64109i	−0.954381	+	0.638727i
$79$	1.91775			0.215764			0.107882	−	0.994164i	$-0.465593\pi$
$79$	1.91775			0.215764			0.107882	+	0.994164i	$0.465593\pi$
$80$	1.19893	+	2.07661i	0.134044	+	0.232172i
$81$	−2.30342	+	8.70024i	−0.255936	+	0.966694i
$82$	−2.59254	+	4.49042i	−0.286298	+	0.495883i
$83$	0.628986	+	1.08944i	0.0690402	+	0.119581i	0.898479	−	0.439016i	$-0.144673\pi$
$83$	0.628986	+	1.08944i	0.0690402	+	0.119581i	−0.829439	+	0.558598i	$0.811340\pi$
$84$	0.386481	+	2.78294i	0.0421685	+	0.303643i
$85$	0.876227	−	1.51767i	0.0950401	−	0.164614i
$86$	0.475784	+	0.824082i	0.0513051	+	0.0888630i
$87$	−0.270410	−	4.07904i	−0.0289910	−	0.437319i
$88$	2.47322	−	4.28374i	0.263646	−	0.456648i
$89$	−3.79432	+	6.57195i	−0.402197	+	0.696625i	−0.993991	−	0.109464i	$-0.965087\pi$
$89$	−3.79432	+	6.57195i	−0.402197	+	0.696625i	0.591794	+	0.806089i	$0.298420\pi$
$90$	−1.34714	+	3.26606i	−0.142001	+	0.344273i
$91$	−13.1216	+	0.943711i	−1.37552	+	0.0989278i
$92$	−2.29228	−	3.97035i	−0.238987	−	0.413938i
$93$	−6.27568	−	3.08900i	−0.650757	−	0.320315i
$94$	−9.97007			−1.02833
$95$	−7.15508			−0.734096
$96$	−5.17616	−	2.54780i	−0.528289	−	0.260034i
$97$	5.89502	+	10.2105i	0.598549	+	1.03672i	0.993036	+	0.117815i	$0.0375890\pi$
$97$	5.89502	+	10.2105i	0.598549	+	1.03672i	−0.394487	+	0.918902i	$0.629078\pi$
$98$	3.05777	−	7.65555i	0.308881	−	0.773327i
$99$	4.77989	−	0.636540i	0.480397	−	0.0639747i
$100$	0.306558	−	0.530973i	0.0306558	−	0.0530973i
$101$	6.24003	−	10.8081i	0.620907	−	1.07544i	−0.368411	−	0.929663i	$-0.620098\pi$
$101$	6.24003	−	10.8081i	0.620907	−	1.07544i	0.989317	−	0.145779i	$-0.0465687\pi$
$102$	−0.236451	−	3.56677i	−0.0234121	−	0.353163i
$103$	2.30925	+	3.99973i	0.227537	+	0.394106i	0.957078	−	0.289832i	$-0.0935994\pi$
$103$	2.30925	+	3.99973i	0.227537	+	0.394106i	−0.729541	+	0.683937i	$0.760266\pi$
$104$	7.65081	−	13.2516i	0.750224	−	1.29943i
$105$	−3.61572	+	2.81541i	−0.352858	+	0.274756i
$106$	−1.70037	−	2.94513i	−0.165155	−	0.286057i
$107$	−7.72051	+	13.3723i	−0.746370	+	1.29275i	0.203183	+	0.979141i	$0.434871\pi$
$107$	−7.72051	+	13.3723i	−0.746370	+	1.29275i	−0.949552	+	0.313609i	$0.898462\pi$
$108$	−0.628517	−	3.12323i	−0.0604791	−	0.300533i
$109$	−5.86738	−	10.1626i	−0.561993	−	0.973401i	−0.997322	−	0.0731296i	$-0.976701\pi$
$109$	−5.86738	−	10.1626i	−0.561993	−	0.973401i	0.435329	−	0.900271i	$-0.356632\pi$
$110$	1.89293			0.180484
$111$	12.1581	−	8.13689i	1.15399	−	0.772320i
$112$	3.55802	+	5.25248i	0.336202	+	0.496313i
$113$	−4.92553	+	8.53126i	−0.463355	+	0.802554i	−0.999126	−	0.0418097i	$-0.986688\pi$
$113$	−4.92553	+	8.53126i	−0.463355	+	0.802554i	0.535771	+	0.844363i	$0.320021\pi$
$114$	−12.1290	+	8.11743i	−1.13599	+	0.760267i
$115$	3.73875	−	6.47570i	0.348640	−	0.603863i
$116$	0.723539	+	1.25321i	0.0671789	+	0.116357i
$117$	14.7864	−	1.96911i	1.36700	−	0.182045i
$118$	15.7790			1.45257
$119$	2.02426	−	4.17133i	0.185564	−	0.382385i
$120$	−0.352576	−	5.31848i	−0.0321856	−	0.485508i
$121$	4.20819	+	7.28880i	0.382563	+	0.662618i
$122$	12.8240			1.16103
$123$	6.33762	−	4.24150i	0.571444	−	0.382443i
$124$	2.47601			0.222352
$125$	1.00000			0.0894427
$126$	−2.93515	+	8.87461i	−0.261484	+	0.790613i
$127$	−8.26362			−0.733278			−0.366639	−	0.930363i	$-0.619492\pi$
$127$	−8.26362			−0.733278			−0.366639	+	0.930363i	$0.619492\pi$
$128$	−3.60553			−0.318687
$129$	−0.0925749	−	1.39646i	−0.00815076	−	0.122951i
$130$	5.85570			0.513579
$131$	3.29787	+	5.71207i	0.288136	+	0.499066i	0.973365	−	0.229262i	$-0.0736311\pi$
$131$	3.29787	+	5.71207i	0.288136	+	0.499066i	−0.685229	+	0.728328i	$0.740298\pi$
$132$	−1.41856	+	0.949380i	−0.123469	+	0.0826329i
$133$	−18.8818	+	1.35799i	−1.63726	+	0.117752i
$134$	9.56191			0.826023
$135$	3.89900	−	3.43479i	0.335572	−	0.295620i
$136$	2.69647	+	4.67042i	0.231220	+	0.400485i
$137$	3.58366	−	6.20708i	0.306173	−	0.530307i	−0.671349	−	0.741141i	$-0.734285\pi$
$137$	3.58366	−	6.20708i	0.306173	−	0.530307i	0.977522	+	0.210835i	$0.0676182\pi$
$138$	−1.00890	−	15.2190i	−0.0858837	−	1.29552i
$139$	4.12443	−	7.14371i	0.349829	−	0.605922i	−0.636390	−	0.771368i	$-0.719573\pi$
$139$	4.12443	−	7.14371i	0.349829	−	0.605922i	0.986219	+	0.165446i	$0.0529063\pi$
$140$	0.708210	−	1.45939i	0.0598547	−	0.123341i
$141$	13.1562	+	6.47570i	1.10795	+	0.545352i
$142$	3.36698			0.282551
$143$	−3.99616	−	6.92155i	−0.334175	−	0.578809i
$144$	−4.38768	−	5.70051i	−0.365640	−	0.475043i
$145$	−1.18010	+	2.04400i	−0.0980022	+	0.169745i
$146$	−6.91416	−	11.9757i	−0.572220	−	0.991114i
$147$	−9.00731	+	8.11593i	−0.742911	+	0.669390i
$148$	−2.58933	+	4.48484i	−0.212841	+	0.368652i
$149$	2.99448	+	5.18659i	0.245317	+	0.424902i	0.962221	−	0.272270i	$-0.0877745\pi$
$149$	2.99448	+	5.18659i	0.245317	+	0.424902i	−0.716903	+	0.697172i	$0.754441\pi$
$150$	1.69516	−	1.13450i	0.138409	−	0.0926315i
$151$	−0.732378	+	1.26852i	−0.0596001	+	0.103230i	−0.894286	−	0.447496i	$-0.852316\pi$
$151$	−0.732378	+	1.26852i	−0.0596001	+	0.103230i	0.834686	+	0.550726i	$0.185649\pi$
$152$	11.0094	−	19.0688i	0.892979	−	1.54669i
$153$	−2.00466	+	4.86016i	−0.162067	+	0.392921i
$154$	4.99531	−	0.359265i	0.402534	−	0.0289504i
$155$	2.01920	+	3.49736i	0.162186	+	0.280915i
$156$	−4.38825	+	2.93687i	−0.351341	+	0.235138i
$157$	15.1420			1.20846			0.604231	−	0.796809i	$-0.293480\pi$
$157$	15.1420			1.20846			0.604231	+	0.796809i	$0.293480\pi$
$158$	−2.25846			−0.179673
$159$	0.330847	+	4.99071i	0.0262379	+	0.395789i
$160$	1.66543	+	2.88461i	0.131664	+	0.228048i
$161$	8.63727	−	17.7986i	0.680712	−	1.40272i
$162$	2.71265	−	10.2459i	0.213126	−	0.804997i
$163$	−1.99957	+	3.46336i	−0.156619	+	0.271271i	−0.933647	−	0.358194i	$-0.883393\pi$
$163$	−1.99957	+	3.46336i	−0.156619	+	0.271271i	0.777029	+	0.629465i	$0.216726\pi$
$164$	−1.34973	+	2.33780i	−0.105396	+	0.182552i
$165$	−2.49784	−	1.22948i	−0.194457	−	0.0957152i
$166$	−0.740732	−	1.28299i	−0.0574920	−	0.0995790i
$167$	8.07580	−	13.9877i	0.624924	−	1.08240i	−0.363631	−	0.931543i	$-0.618463\pi$
$167$	8.07580	−	13.9877i	0.624924	−	1.08240i	0.988556	−	0.150857i	$-0.0482034\pi$
$168$	−1.93983	−	13.9682i	−0.149662	−	1.07767i
$169$	−5.86196	−	10.1532i	−0.450920	−	0.781016i
$170$	−1.03190	+	1.78730i	−0.0791429	+	0.137080i
$171$	21.2774	−	2.83352i	1.62712	−	0.216685i
$172$	0.247703	+	0.429034i	0.0188872	+	0.0327136i
$173$	10.8334			0.823652			0.411826	−	0.911263i	$-0.364891\pi$
$173$	10.8334			0.823652			0.411826	+	0.911263i	$0.364891\pi$
$174$	0.318452	+	4.80373i	0.0241418	+	0.364170i
$175$	2.63894	−	0.189793i	0.199485	−	0.0143470i
$176$	−1.92712	+	3.33786i	−0.145262	+	0.251601i
$177$	−20.8214	−	10.2487i	−1.56503	−	0.770337i
$178$	4.46842	−	7.73953i	0.334922	−	0.580102i
$179$	1.14877	+	1.98973i	0.0858634	+	0.148720i	0.905759	−	0.423794i	$-0.139302\pi$
$179$	1.14877	+	1.98973i	0.0858634	+	0.148720i	−0.819895	+	0.572513i	$0.805968\pi$
$180$	−0.701351	+	1.70038i	−0.0522756	+	0.126739i
$181$	21.2841			1.58204			0.791019	−	0.611792i	$-0.209551\pi$
$181$	21.2841			1.58204			0.791019	+	0.611792i	$0.209551\pi$
$182$	15.4528	−	1.11137i	1.14544	−	0.0823804i
$183$	−16.9220	−	8.32934i	−1.25091	−	0.615723i
$184$	11.5055	+	19.9281i	0.848196	+	1.46912i
$185$	−8.44646			−0.620996
$186$	7.39062	+	3.63780i	0.541907	+	0.266736i
$187$	2.81683			0.205987
$188$	−5.19063			−0.378565
$189$	9.63730	−	9.80420i	0.701011	−	0.713151i
$190$	8.42626			0.611305
$191$	−7.27065			−0.526086			−0.263043	−	0.964784i	$-0.584726\pi$
$191$	−7.27065			−0.526086			−0.263043	+	0.964784i	$0.584726\pi$
$192$	13.5483	+	6.66873i	0.977765	+	0.481274i
$193$	15.9102			1.14524			0.572620	−	0.819821i	$-0.305927\pi$
$193$	15.9102			1.14524			0.572620	+	0.819821i	$0.305927\pi$
$194$	−6.94233	−	12.0245i	−0.498430	−	0.863307i
$195$	−7.72698	−	3.80336i	−0.553340	−	0.272364i
$196$	1.59194	−	3.98564i	0.113710	−	0.284689i
$197$	−10.9249			−0.778364			−0.389182	−	0.921161i	$-0.627242\pi$
$197$	−10.9249			−0.778364			−0.389182	+	0.921161i	$0.627242\pi$
$198$	−5.62909	+	0.749629i	−0.400042	+	0.0532738i
$199$	1.63900	+	2.83882i	0.116185	+	0.201239i	0.918253	−	0.395994i	$-0.129600\pi$
$199$	1.63900	+	2.83882i	0.116185	+	0.201239i	−0.802068	+	0.597233i	$0.796267\pi$
$200$	−1.53868	+	2.66507i	−0.108801	+	0.188449i
$201$	−12.6176	−	6.21060i	−0.889974	−	0.438062i
$202$	−7.34864	+	12.7282i	−0.517049	+	0.895555i
$203$	−2.72628	+	5.61795i	−0.191347	+	0.394303i
$204$	−0.123101	−	1.85694i	−0.00861880	−	0.130011i
$205$	−4.40287			−0.307510
$206$	−2.71951	−	4.71033i	−0.189477	−	0.328184i
$207$	−8.55362	+	20.7377i	−0.594518	+	1.44137i
$208$	−5.96146	+	10.3255i	−0.413353	+	0.715948i
$209$	−5.75040	−	9.95999i	−0.397764	−	0.688947i
$210$	4.25810	−	3.31560i	0.293837	−	0.228798i
$211$	−9.44405	+	16.3576i	−0.650155	+	1.12610i	0.332930	+	0.942952i	$0.391963\pi$
$211$	−9.44405	+	16.3576i	−0.650155	+	1.12610i	−0.983085	+	0.183150i	$0.941371\pi$
$212$	−0.885250	−	1.53330i	−0.0607992	−	0.105307i
$213$	−4.44295	−	2.18690i	−0.304426	−	0.149844i
$214$	9.09214	−	15.7480i	0.621526	−	1.07651i
$215$	−0.404008	+	0.699762i	−0.0275531	+	0.0477234i
$216$	3.15467	+	15.6762i	0.214648	+	1.06663i
$217$	5.99232	+	8.84607i	0.406785	+	0.600511i
$218$	6.90979	+	11.9681i	0.467990	+	0.810582i
$219$	1.34531	+	20.2935i	0.0909077	+	1.37131i
$220$	0.985498			0.0664423
$221$	8.71375			0.586150
$222$	−14.3181	+	9.58250i	−0.960968	+	0.643135i
$223$	−6.01501	−	10.4183i	−0.402795	−	0.697662i	0.591267	−	0.806476i	$-0.298628\pi$
$223$	−6.01501	−	10.4183i	−0.402795	−	0.697662i	−0.994062	+	0.108814i	$0.965295\pi$
$224$	4.94244	+	7.29621i	0.330231	+	0.487499i
$225$	−2.97375	+	0.396015i	−0.198250	+	0.0264010i
$226$	5.80060	−	10.0469i	0.385850	−	0.668312i
$227$	−6.99397	+	12.1139i	−0.464206	+	0.804029i	−0.999165	−	0.0408493i	$-0.986994\pi$
$227$	−6.99397	+	12.1139i	−0.464206	+	0.804029i	0.534959	+	0.844878i	$0.320327\pi$
$228$	−6.31461	+	4.22611i	−0.418196	+	0.279881i
$229$	2.04643	+	3.54452i	0.135232	+	0.234228i	0.925686	−	0.378293i	$-0.123489\pi$
$229$	2.04643	+	3.54452i	0.135232	+	0.234228i	−0.790454	+	0.612521i	$0.790155\pi$
$230$	−4.40298	+	7.62618i	−0.290324	+	0.502856i
$231$	−6.82499	−	2.77045i	−0.449051	−	0.182283i
$232$	−3.63160	−	6.29012i	−0.238426	−	0.412967i
$233$	6.24685	−	10.8199i	0.409244	−	0.708832i	−0.585561	−	0.810628i	$-0.699126\pi$
$233$	6.24685	−	10.8199i	0.409244	−	0.708832i	0.994805	+	0.101796i	$0.0324590\pi$
$234$	−17.4134	+	2.31895i	−1.13835	+	0.151594i
$235$	−4.23300	−	7.33177i	−0.276130	−	0.478272i
$236$	8.21487			0.534742
$237$	2.98018	+	1.46690i	0.193584	+	0.0952855i
$238$	−2.38389	+	4.91241i	−0.154525	+	0.318425i
$239$	−6.07011	+	10.5137i	−0.392643	+	0.680077i	−0.992797	−	0.119807i	$-0.961772\pi$
$239$	−6.07011	+	10.5137i	−0.392643	+	0.680077i	0.600155	+	0.799884i	$0.295106\pi$
$240$	0.274725	+	4.14412i	0.0177334	+	0.267502i
$241$	−3.78363	+	6.55344i	−0.243725	+	0.422144i	−0.961772	−	0.273850i	$-0.911703\pi$
$241$	−3.78363	+	6.55344i	−0.243725	+	0.422144i	0.718047	+	0.695994i	$0.245036\pi$
$242$	−4.95582	−	8.58374i	−0.318572	−	0.551784i
$243$	−10.2344	+	11.7583i	−0.656537	+	0.754294i
$244$	6.67642			0.427414
$245$	6.92796	−	1.00170i	0.442611	−	0.0639965i
$246$	−7.46356	+	4.99505i	−0.475859	+	0.318473i
$247$	−17.7887	−	30.8109i	−1.13186	−	1.96045i
$248$	−12.4276			−0.789155
$249$	0.144127	+	2.17410i	0.00913366	+	0.137778i
$250$	−1.17766			−0.0744818
$251$	−2.11183			−0.133298			−0.0666488	−	0.997776i	$-0.521231\pi$
$251$	−2.11183			−0.133298			−0.0666488	+	0.997776i	$0.521231\pi$
$252$	−1.52810	+	4.62031i	−0.0962612	+	0.291052i
$253$	12.0191			0.755631
$254$	9.73174			0.610624
$255$	2.52253	−	1.68823i	0.157967	−	0.105721i
$256$	−13.1906			−0.824412
$257$	7.01607	+	12.1522i	0.437651	+	0.758033i	0.997508	−	0.0705560i	$-0.0224774\pi$
$257$	7.01607	+	12.1522i	0.437651	+	0.758033i	−0.559857	+	0.828589i	$0.689144\pi$
$258$	0.109022	+	1.64455i	0.00678740	+	0.102385i
$259$	−22.2897	+	1.60308i	−1.38501	+	0.0996106i
$260$	3.04860			0.189066
$261$	2.69987	−	6.54567i	0.167118	−	0.405167i
$262$	−3.88377	−	6.72689i	−0.239940	−	0.415588i
$263$	−15.0083	+	25.9951i	−0.925451	+	1.60293i	−0.134618	+	0.990898i	$0.542981\pi$
$263$	−15.0083	+	25.9951i	−0.925451	+	1.60293i	−0.790834	+	0.612031i	$0.790353\pi$
$264$	7.12005	−	4.76515i	0.438209	−	0.293275i
$265$	1.44386	−	2.50083i	0.0886954	−	0.153625i
$266$	22.2363	−	1.59925i	1.36340	−	0.0980561i
$267$	−10.9233	+	7.31051i	−0.668495	+	0.447396i
$268$	4.97813			0.304088
$269$	−7.46179	−	12.9242i	−0.454953	−	0.788002i	0.543732	−	0.839259i	$-0.317011\pi$
$269$	−7.46179	−	12.9242i	−0.454953	−	0.788002i	−0.998686	+	0.0512568i	$0.983677\pi$
$270$	−4.59170	+	4.04502i	−0.279442	+	0.246172i
$271$	−8.77299	+	15.1953i	−0.532921	+	0.923046i	0.466340	+	0.884606i	$0.345572\pi$
$271$	−8.77299	+	15.1953i	−0.532921	+	0.923046i	−0.999261	+	0.0384405i	$0.987761\pi$
$272$	−2.10107	−	3.63916i	−0.127396	−	0.220656i
$273$	−21.1128	−	8.57029i	−1.27781	−	0.518698i
$274$	−4.22034	+	7.30984i	−0.254960	+	0.441603i
$275$	0.803681	+	1.39202i	0.0484638	+	0.0839418i
$276$	−0.525257	−	7.92331i	−0.0316168	−	0.476927i
$277$	1.98042	−	3.43019i	0.118992	−	0.206100i	−0.800377	−	0.599498i	$-0.795367\pi$
$277$	1.98042	−	3.43019i	0.118992	−	0.206100i	0.919368	+	0.393398i	$0.128700\pi$
$278$	−4.85717	+	8.41287i	−0.291314	+	0.504571i
$279$	−7.38960	−	9.60063i	−0.442404	−	0.574774i
$280$	−3.55467	+	7.32499i	−0.212432	+	0.437752i
$281$	11.1885	+	19.3791i	0.667451	+	1.15606i	0.978614	+	0.205703i	$0.0659481\pi$
$281$	11.1885	+	19.3791i	0.667451	+	1.15606i	−0.311163	+	0.950357i	$0.600719\pi$
$282$	−15.4935	−	7.62618i	−0.922624	−	0.454132i
$283$	29.6009			1.75959			0.879794	−	0.475354i	$-0.157680\pi$
$283$	29.6009			1.75959			0.879794	+	0.475354i	$0.157680\pi$
$284$	1.75292			0.104017
$285$	−11.1190	−	5.47297i	−0.658632	−	0.324191i
$286$	4.70612	+	8.15123i	0.278279	+	0.481993i
$287$	−11.6189	+	0.835634i	−0.685841	+	0.0493259i
$288$	−6.09492	−	7.91856i	−0.359147	−	0.466606i
$289$	6.96445	−	12.0628i	0.409674	−	0.709576i
$290$	1.38976	−	2.40714i	0.0816095	−	0.141352i
$291$	1.35079	+	20.3762i	0.0791849	+	1.19448i
$292$	−3.59966	−	6.23479i	−0.210654	−	0.364863i
$293$	7.62430	−	13.2057i	0.445416	−	0.771483i	−0.552665	−	0.833404i	$-0.686389\pi$
$293$	7.62430	−	13.2057i	0.445416	−	0.771483i	0.998081	+	0.0619201i	$0.0197224\pi$
$294$	10.6076	−	9.55781i	0.618646	−	0.557423i
$295$	6.69929	+	11.6035i	0.390048	+	0.675582i
$296$	12.9964	−	22.5104i	0.755401	−	1.30839i
$297$	7.91485	+	2.66699i	0.459266	+	0.154754i
$298$	−3.52648	−	6.10805i	−0.204284	−	0.353830i
$299$	37.1805			2.15020
$300$	0.882536	−	0.590644i	0.0509532	−	0.0341009i
$301$	−0.933340	+	1.92330i	−0.0537968	+	0.110857i
$302$	0.862493	−	1.49388i	0.0496309	−	0.0859632i
$303$	17.9642	−	12.0227i	1.03202	−	0.690684i
$304$	−8.57844	+	14.8583i	−0.492007	+	0.852182i
$305$	5.44467	+	9.43045i	0.311761	+	0.539986i
$306$	2.36080	−	5.72362i	0.134958	−	0.327198i
$307$	−26.9708			−1.53931			−0.769653	−	0.638463i	$-0.779571\pi$
$307$	−26.9708			−1.53931			−0.769653	+	0.638463i	$0.779571\pi$
$308$	2.60067	−	0.187041i	0.148187	−	0.0106576i
$309$	0.529144	+	7.98195i	0.0301020	+	0.454077i
$310$	−2.37793	−	4.11870i	−0.135058	−	0.233927i
$311$	13.8220			0.783776			0.391888	−	0.920013i	$-0.371822\pi$
$311$	13.8220			0.783776			0.391888	+	0.920013i	$0.371822\pi$
$312$	22.0256	−	14.7408i	1.24695	−	0.834534i
$313$	14.4477			0.816632			0.408316	−	0.912841i	$-0.366116\pi$
$313$	14.4477			0.816632			0.408316	+	0.912841i	$0.366116\pi$
$314$	−17.8321			−1.00632
$315$	−7.77236	+	1.60946i	−0.437923	+	0.0906826i
$316$	−1.17580			−0.0661440
$317$	−25.3366			−1.42305			−0.711523	−	0.702663i	$-0.751994\pi$
$317$	−25.3366			−1.42305			−0.711523	+	0.702663i	$0.751994\pi$
$318$	−0.389626	−	5.87737i	−0.0218491	−	0.329586i
$319$	−3.79371			−0.212407
$320$	−4.35917	−	7.55031i	−0.243685	−	0.422075i
$321$	−22.2262	+	14.8751i	−1.24055	+	0.830247i
$322$	−10.1718	+	20.9607i	−0.566851	+	1.16809i
$323$	12.5389			0.697685
$324$	1.41226	−	5.33425i	0.0784591	−	0.296347i
$325$	2.48616	+	4.30615i	0.137907	+	0.238862i
$326$	2.35482	−	4.07866i	0.130421	−	0.225896i
$327$	−1.34446	−	20.2807i	−0.0743488	−	1.12152i
$328$	6.77461	−	11.7340i	0.374065	−	0.647900i
$329$	−12.5621	−	18.5447i	−0.692572	−	1.02240i
$330$	2.94161	+	1.44792i	0.161930	+	0.0797051i
$331$	7.65339			0.420668			0.210334	−	0.977630i	$-0.432545\pi$
$331$	7.65339			0.420668			0.210334	+	0.977630i	$0.432545\pi$
$332$	−0.385641	−	0.667950i	−0.0211648	−	0.0366585i
$333$	25.1176	−	3.34493i	1.37644	−	0.183301i
$334$	−9.51055	+	16.4728i	−0.520394	+	0.901349i
$335$	4.05970	+	7.03161i	0.221805	+	0.384178i
$336$	1.51151	+	10.8839i	0.0824594	+	0.593767i
$337$	9.51431	−	16.4793i	0.518278	−	0.897683i	−0.481497	−	0.876448i	$-0.659907\pi$
$337$	9.51431	−	16.4793i	0.518278	−	0.897683i	0.999775	−	0.0212354i	$-0.00675996\pi$
$338$	6.90340	+	11.9570i	0.375495	+	0.650377i
$339$	−14.1799	+	9.49001i	−0.770146	+	0.515427i
$340$	−0.537228	+	0.930506i	−0.0291353	+	0.0504638i
$341$	−3.24559	+	5.62152i	−0.175758	+	0.304423i
$342$	−25.0576	+	3.33693i	−1.35496	+	0.180440i
$343$	18.0923	−	3.95831i	0.976893	−	0.213729i
$344$	−1.24328	−	2.15342i	−0.0670331	−	0.116105i
$345$	10.7633	−	7.20345i	0.579478	−	0.387821i
$346$	−12.7581			−0.685881
$347$	−26.2905			−1.41135			−0.705675	−	0.708535i	$-0.749356\pi$
$347$	−26.2905			−1.41135			−0.705675	+	0.708535i	$0.749356\pi$
$348$	0.165793	+	2.50092i	0.00888742	+	0.134063i
$349$	1.95792	+	3.39122i	0.104805	+	0.181528i	0.913659	−	0.406482i	$-0.133245\pi$
$349$	1.95792	+	3.39122i	0.104805	+	0.181528i	−0.808853	+	0.588010i	$0.799911\pi$
$350$	−3.10777	+	0.223512i	−0.166117	+	0.0119472i
$351$	24.4843	+	8.25023i	1.30687	+	0.440365i
$352$	−2.67695	+	4.63662i	−0.142682	+	0.247132i
$353$	−10.8995	+	18.8785i	−0.580121	+	1.00480i	0.415343	+	0.909665i	$0.363661\pi$
$353$	−10.8995	+	18.8785i	−0.580121	+	1.00480i	−0.995464	+	0.0951346i	$0.969672\pi$
$354$	24.5205	+	12.0695i	1.30325	+	0.641484i
$355$	1.42952	+	2.47600i	0.0758711	+	0.131413i
$356$	2.32635	−	4.02936i	0.123296	−	0.213556i
$357$	6.33639	−	4.93388i	0.335357	−	0.261128i
$358$	−1.35287	−	2.34323i	−0.0715012	−	0.123844i
$359$	−7.67176	+	13.2879i	−0.404900	+	0.701308i	−0.994310	−	0.106527i	$-0.966027\pi$
$359$	−7.67176	+	13.2879i	−0.404900	+	0.701308i	0.589410	+	0.807834i	$0.299360\pi$
$360$	3.52024	−	8.53460i	0.185533	−	0.449813i
$361$	−16.0976	−	27.8818i	−0.847241	−	1.46746i
$362$	−25.0655			−1.31741
$363$	0.964271	+	14.5457i	0.0506111	+	0.763450i
$364$	8.04506	−	0.578604i	0.421676	−	0.0303271i
$365$	5.87110	−	10.1690i	0.307307	−	0.532272i
$366$	19.9284	+	9.80914i	1.04168	+	0.512732i
$367$	5.80726	−	10.0585i	0.303136	−	0.525048i	−0.673708	−	0.738997i	$-0.735300\pi$
$367$	5.80726	−	10.0585i	0.303136	−	0.525048i	0.976845	+	0.213950i	$0.0686329\pi$
$368$	−8.96500	−	15.5278i	−0.467333	−	0.809444i
$369$	13.0930	−	1.74360i	0.681595	−	0.0907684i
$370$	9.94706			0.517123
$371$	3.33560	−	6.87357i	0.173176	−	0.356858i
$372$	3.84771	+	1.89391i	0.199495	+	0.0981949i
$373$	−10.9355	−	18.9409i	−0.566221	−	0.980723i	−0.996935	−	0.0782348i	$-0.975072\pi$
$373$	−10.9355	−	18.9409i	−0.566221	−	0.980723i	0.430714	−	0.902488i	$-0.358262\pi$
$374$	−3.31727			−0.171532
$375$	1.55400	+	0.764908i	0.0802482	+	0.0394997i
$376$	26.0529			1.34358
$377$	−11.7357			−0.604418
$378$	−11.3495	+	11.5460i	−0.583754	+	0.593864i
$379$	−18.8100			−0.966207			−0.483103	−	0.875563i	$-0.660490\pi$
$379$	−18.8100			−0.966207			−0.483103	+	0.875563i	$0.660490\pi$
$380$	4.38689			0.225043
$381$	−12.8417	−	6.32091i	−0.657899	−	0.323830i
$382$	8.56236			0.438089
$383$	4.33093	+	7.50140i	0.221300	+	0.383303i	0.955203	−	0.295951i	$-0.0956366\pi$
$383$	4.33093	+	7.50140i	0.221300	+	0.383303i	−0.733903	+	0.679255i	$0.762303\pi$
$384$	−5.60299	−	2.75790i	−0.285927	−	0.140738i
$385$	2.38506	+	3.52091i	0.121554	+	0.179442i
$386$	−18.7368			−0.953679
$387$	0.924300	−	2.24091i	0.0469848	−	0.113912i
$388$	−3.61433	−	6.26019i	−0.183490	−	0.317813i
$389$	10.1904	−	17.6504i	0.516676	−	0.894909i	−0.483137	−	0.875545i	$-0.660503\pi$
$389$	10.1904	−	17.6504i	0.516676	−	0.894909i	0.999813	−	0.0193639i	$-0.00616410\pi$
$390$	9.09976	+	4.47907i	0.460784	+	0.226806i
$391$	−6.55198	+	11.3484i	−0.331348	+	0.573912i
$392$	−7.99030	+	20.0048i	−0.403571	+	1.01040i
$393$	0.755678	+	11.3991i	0.0381189	+	0.575010i
$394$	12.8658			0.648169
$395$	−0.958875	−	1.66082i	−0.0482462	−	0.0835649i
$396$	−2.93062	+	0.390273i	−0.147269	+	0.0196119i
$397$	−5.35451	+	9.27428i	−0.268735	+	0.465463i	−0.968535	−	0.248876i	$-0.919939\pi$
$397$	−5.35451	+	9.27428i	−0.268735	+	0.465463i	0.699800	+	0.714339i	$0.253272\pi$
$398$	−1.93018	−	3.34317i	−0.0967512	−	0.167578i
$399$	−30.3810	−	12.3325i	−1.52095	−	0.617398i
$400$	1.19893	−	2.07661i	0.0599465	−	0.103830i
$401$	−12.4699	−	21.5985i	−0.622718	−	1.07858i	−0.988977	−	0.148066i	$-0.952695\pi$
$401$	−12.4699	−	21.5985i	−0.622718	−	1.07858i	0.366259	−	0.930513i	$-0.380638\pi$
$402$	14.8592	+	7.31398i	0.741110	+	0.364788i
$403$	−10.0401	+	17.3900i	−0.500133	+	0.866256i
$404$	−3.82586	+	6.62658i	−0.190344	+	0.329685i
$405$	8.68634	−	2.35530i	0.431628	−	0.117036i
$406$	3.21063	−	6.61604i	0.159341	−	0.328349i
$407$	−6.78826	−	11.7576i	−0.336482	−	0.582803i
$408$	0.617872	+	9.32038i	0.0305892	+	0.461428i
$409$	−22.3479			−1.10503			−0.552516	−	0.833503i	$-0.686332\pi$
$409$	−22.3479			−1.10503			−0.552516	+	0.833503i	$0.686332\pi$
$410$	5.18508			0.256073
$411$	10.3168	−	6.90464i	0.508893	−	0.340581i
$412$	−1.41583	−	2.45230i	−0.0697532	−	0.120816i
$413$	19.8812	+	29.3494i	0.978292	+	1.44419i
$414$	10.0733	−	24.4220i	0.495074	−	1.20028i
$415$	0.628986	−	1.08944i	0.0308757	−	0.0534783i
$416$	−8.28104	+	14.3432i	−0.406012	+	0.703233i
$417$	11.8736	−	7.94653i	0.581455	−	0.389143i
$418$	6.77203	+	11.7295i	0.331231	+	0.573708i
$419$	9.93735	−	17.2120i	0.485471	−	0.840861i	−0.514389	−	0.857557i	$-0.671981\pi$
$419$	9.93735	−	17.2120i	0.485471	−	0.840861i	0.999861	+	0.0166960i	$0.00531475\pi$
$420$	2.21685	−	1.72617i	0.108171	−	0.0842285i
$421$	1.00473	+	1.74024i	0.0489674	+	0.0848141i	0.889470	−	0.456993i	$-0.151074\pi$
$421$	1.00473	+	1.74024i	0.0489674	+	0.0848141i	−0.840503	+	0.541807i	$0.817740\pi$
$422$	11.1219	−	19.2637i	0.541405	−	0.937741i
$423$	15.4914	+	20.1265i	0.753215	+	0.978583i
$424$	4.44327	+	7.69597i	0.215784	+	0.373749i
$425$	−1.75245			−0.0850065
$426$	5.23229	+	2.57543i	0.253505	+	0.124780i
$427$	16.1580	+	23.8530i	0.781939	+	1.15433i
$428$	4.73356	−	8.19876i	0.228805	−	0.396302i
$429$	−0.915685	−	13.8128i	−0.0442097	−	0.666887i
$430$	0.475784	−	0.824082i	0.0229443	−	0.0397408i
$431$	14.1006	+	24.4229i	0.679201	+	1.17641i	0.975222	+	0.221229i	$0.0710069\pi$
$431$	14.1006	+	24.4229i	0.679201	+	1.17641i	−0.296021	+	0.955181i	$0.595660\pi$
$432$	−2.45810	−	12.2148i	−0.118265	−	0.587683i
$433$	−9.44136			−0.453723			−0.226861	−	0.973927i	$-0.572846\pi$
$433$	−9.44136			−0.453723			−0.226861	+	0.973927i	$0.572846\pi$
$434$	−7.05691	−	10.4177i	−0.338743	−	0.500064i
$435$	−3.39735	+	2.27370i	−0.162890	+	0.109016i
$436$	3.59738	+	6.23085i	0.172283	+	0.298403i
$437$	53.5021			2.55935
$438$	−1.58432	−	23.8989i	−0.0757018	−	1.14193i
$439$	−27.8122			−1.32740			−0.663702	−	0.747997i	$-0.731016\pi$
$439$	−27.8122			−1.32740			−0.663702	+	0.747997i	$0.731016\pi$
$440$	−4.94644			−0.235812
$441$	−20.2053	+	5.72239i	−0.962157	+	0.272495i
$442$	−10.2618			−0.488106
$443$	−34.2329			−1.62645			−0.813227	−	0.581947i	$-0.802291\pi$
$443$	−34.2329			−1.62645			−0.813227	+	0.581947i	$0.802291\pi$
$444$	−7.45430	+	4.98885i	−0.353766	+	0.236760i
$445$	7.58864			0.359736
$446$	7.08365	+	12.2692i	0.335420	+	0.580965i
$447$	0.686159	+	10.3505i	0.0324542	+	0.489560i
$448$	−12.9366	−	19.0974i	−0.611195	−	0.902269i
$449$	−23.5806			−1.11284			−0.556418	−	0.830903i	$-0.687824\pi$
$449$	−23.5806			−1.11284			−0.556418	+	0.830903i	$0.687824\pi$
$450$	3.50207	−	0.466372i	0.165089	−	0.0219850i
$451$	−3.53850	−	6.12887i	−0.166622	−	0.288597i
$452$	3.01991	−	5.23064i	0.142045	−	0.246029i
$453$	−2.10841	+	1.41107i	−0.0990619	+	0.0662980i
$454$	8.23652	−	14.2661i	0.386559	−	0.669540i
$455$	7.37809	+	10.8918i	0.345890	+	0.510615i
$456$	31.6945	−	21.2118i	1.48423	−	0.993333i
$457$	31.9154			1.49294			0.746471	−	0.665418i	$-0.231747\pi$
$457$	31.9154			1.49294			0.746471	+	0.665418i	$0.231747\pi$
$458$	−2.41000	−	4.17424i	−0.112612	−	0.195049i
$459$	−6.83281	+	6.01932i	−0.318928	+	0.280958i
$460$	−2.29228	+	3.97035i	−0.106878	+	0.185119i
$461$	2.51227	+	4.35138i	0.117008	+	0.202664i	0.918581	−	0.395234i	$-0.129336\pi$
$461$	2.51227	+	4.35138i	0.117008	+	0.202664i	−0.801573	+	0.597897i	$0.796003\pi$
$462$	8.03752	+	3.26266i	0.373939	+	0.151793i
$463$	−2.74525	+	4.75491i	−0.127582	+	0.220979i	−0.922739	−	0.385424i	$-0.874055\pi$
$463$	−2.74525	+	4.75491i	−0.127582	+	0.220979i	0.795157	+	0.606404i	$0.207388\pi$
$464$	2.82972	+	4.90122i	0.131366	+	0.227533i
$465$	0.462683	+	6.97940i	0.0214564	+	0.323662i
$466$	−7.35667	+	12.7421i	−0.340791	+	0.590267i
$467$	−5.54814	+	9.60965i	−0.256737	+	0.444682i	−0.965366	−	0.260900i	$-0.915981\pi$
$467$	−5.54814	+	9.60965i	−0.256737	+	0.444682i	0.708629	+	0.705582i	$0.249314\pi$
$468$	−9.06577	+	1.20729i	−0.419065	+	0.0558071i
$469$	12.0478	+	17.7855i	0.556318	+	0.821257i
$470$	4.98503	+	8.63433i	0.229942	+	0.398272i
$471$	23.5306	+	11.5822i	1.08423	+	0.533680i
$472$	−41.2323			−1.89787
$473$	−1.29877			−0.0597177
$474$	−3.50965	−	1.72751i	−0.161203	−	0.0793473i
$475$	3.57754	+	6.19648i	0.164149	+	0.284314i
$476$	−1.24111	+	2.55751i	−0.0568860	+	0.117223i
$477$	−3.30330	+	8.00864i	−0.151248	+	0.366690i
$478$	7.14853	−	12.3816i	0.326966	−	0.566322i
$479$	−2.72254	+	4.71558i	−0.124396	+	0.215460i	−0.921497	−	0.388386i	$-0.873033\pi$
$479$	−2.72254	+	4.71558i	−0.124396	+	0.215460i	0.797101	+	0.603846i	$0.206366\pi$
$480$	0.381619	+	5.75658i	0.0174184	+	0.262751i
$481$	−20.9992	−	36.3717i	−0.957482	−	1.65841i
$482$	4.45583	−	7.71773i	0.202958	−	0.351533i
$483$	27.0366	−	21.0522i	1.23021	−	0.957910i
$484$	−2.58011	−	4.46887i	−0.117278	−	0.203131i
$485$	5.89502	−	10.2105i	0.267679	−	0.463634i
$486$	12.0527	−	13.8473i	0.546719	−	0.628124i
$487$	−7.59443	−	13.1539i	−0.344136	−	0.596062i	0.641060	−	0.767491i	$-0.278495\pi$
$487$	−7.59443	−	13.1539i	−0.344136	−	0.596062i	−0.985196	+	0.171429i	$0.945162\pi$
$488$	−33.5105			−1.51695
$489$	−5.75649	+	3.85258i	−0.260317	+	0.174220i
$490$	−8.15878	+	1.17967i	−0.368576	+	0.0532919i
$491$	−9.81633	+	17.0024i	−0.443005	+	0.767307i	−0.997911	−	0.0646062i	$-0.979421\pi$
$491$	−9.81633	+	17.0024i	−0.443005	+	0.767307i	0.554906	+	0.831913i	$0.312754\pi$
$492$	−3.88569	+	2.60053i	−0.175180	+	0.117241i
$493$	2.06807	−	3.58201i	0.0931414	−	0.161326i
$494$	20.9490	+	36.2847i	0.942540	+	1.63253i
$495$	−2.94121	−	3.82124i	−0.132197	−	0.171752i
$496$	9.68352			0.434803
$497$	4.24234	+	6.26270i	0.190295	+	0.280920i
$498$	−0.169732	−	2.56035i	−0.00760589	−	0.114732i
$499$	−4.53221	−	7.85002i	−0.202890	−	0.351415i	0.746569	−	0.665308i	$-0.231700\pi$
$499$	−4.53221	−	7.85002i	−0.202890	−	0.351415i	−0.949458	+	0.313893i	$0.898367\pi$
$500$	−0.613115			−0.0274193
$501$	23.2491	−	15.5596i	1.03869	−	0.695153i
$502$	2.48702			0.111001
$503$	−7.65457			−0.341300			−0.170650	−	0.985332i	$-0.554587\pi$
$503$	−7.65457			−0.341300			−0.170650	+	0.985332i	$0.554587\pi$
$504$	7.66987	−	23.1904i	0.341643	−	1.03298i
$505$	−12.4801			−0.555356
$506$	−14.1544			−0.629238
$507$	−1.34322	−	20.2619i	−0.0596544	−	0.899864i
$508$	5.06655			0.224792
$509$	−3.77597	−	6.54017i	−0.167367	−	0.289888i	0.770126	−	0.637891i	$-0.220193\pi$
$509$	−3.77597	−	6.54017i	−0.167367	−	0.289888i	−0.937493	+	0.348003i	$0.886860\pi$
$510$	−2.97069	+	1.98816i	−0.131544	+	0.0880371i
$511$	13.5634	−	27.9497i	0.600011	−	1.23642i
$512$	22.7451			1.00520
$513$	35.2325	+	11.8719i	1.55555	+	0.524159i
$514$	−8.26255	−	14.3112i	−0.364446	−	0.631238i
$515$	2.30925	−	3.99973i	0.101758	−	0.176249i
$516$	0.0567591	+	0.856190i	0.00249868	+	0.0376916i
$517$	6.80396	−	11.7848i	0.299238	−	0.518295i
$518$	26.2497	−	1.88788i	1.15334	−	0.0829489i
$519$	16.8352	+	8.28659i	0.738982	+	0.363741i
$520$	−15.3016			−0.671020
$521$	1.88176	+	3.25930i	0.0824412	+	0.142792i	0.904298	−	0.426902i	$-0.140395\pi$
$521$	1.88176	+	3.25930i	0.0824412	+	0.142792i	−0.821857	+	0.569694i	$0.807062\pi$
$522$	−3.17953	+	7.70858i	−0.139164	+	0.337395i
$523$	11.0026	−	19.0571i	0.481111	−	0.833309i	−0.518654	−	0.854984i	$-0.673567\pi$
$523$	11.0026	−	19.0571i	0.481111	−	0.833309i	0.999765	+	0.0216752i	$0.00689997\pi$
$524$	−2.02197	−	3.50216i	−0.0883303	−	0.152992i
$525$	4.24608	+	1.72360i	0.185314	+	0.0752242i
$526$	17.6747	−	30.6135i	0.770653	−	1.33481i
$527$	−3.53856	−	6.12896i	−0.154142	−	0.266982i
$528$	−5.54789	+	3.71297i	−0.241441	+	0.161586i
$529$	−16.4565	+	28.5035i	−0.715500	+	1.23928i
$530$	−1.70037	+	2.94513i	−0.0738595	+	0.127928i
$531$	−24.5172	−	31.8529i	−1.06395	−	1.38230i
$532$	11.5767	−	0.832601i	0.501914	−	0.0360978i
$533$	−10.9462	−	18.9594i	−0.474134	−	0.821223i
$534$	12.8639	−	8.60930i	0.556677	−	0.372561i
$535$	15.4410			0.667573
$536$	−24.9864			−1.07925
$537$	0.263232	+	3.97075i	0.0113593	+	0.171351i
$538$	8.78745	+	15.2203i	0.378854	+	0.656194i
$539$	6.96226	+	8.83878i	0.299886	+	0.380713i
$540$	−2.39053	+	2.10592i	−0.102872	+	0.0906246i
$541$	−11.5596	+	20.0217i	−0.496984	+	0.860802i	−0.999994	−	0.00347895i	$-0.998893\pi$
$541$	−11.5596	+	20.0217i	−0.496984	+	0.860802i	0.503010	+	0.864281i	$0.332226\pi$
$542$	10.3316	−	17.8949i	0.443780	−	0.768650i
$543$	33.0755	+	16.2804i	1.41941	+	0.698659i
$544$	−2.91859	−	5.05514i	−0.125133	−	0.216738i
$545$	−5.86738	+	10.1626i	−0.251331	+	0.435318i
$546$	24.8638	+	10.0929i	1.06407	+	0.431936i
$547$	−14.6676	−	25.4049i	−0.627139	−	1.08624i	−0.988123	−	0.153665i	$-0.950892\pi$
$547$	−14.6676	−	25.4049i	−0.627139	−	1.08624i	0.360984	−	0.932572i	$-0.382441\pi$
$548$	−2.19720	+	3.80565i	−0.0938595	+	0.162569i
$549$	−19.9257	−	25.8876i	−0.850407	−	1.10486i
$550$	−0.946464	−	1.63932i	−0.0403574	−	0.0699010i
$551$	−16.8875			−0.719430
$552$	2.63638	+	39.7689i	0.112212	+	1.69268i
$553$	−2.84562	−	4.20081i	−0.121008	−	0.178637i
$554$	−2.33226	+	4.03959i	−0.0990883	+	0.171626i
$555$	−13.1258	−	6.46076i	−0.557159	−	0.274244i
$556$	−2.52875	+	4.37992i	−0.107243	+	0.185750i
$557$	15.0497	+	26.0668i	0.637674	+	1.10448i	0.985942	+	0.167089i	$0.0534367\pi$
$557$	15.0497	+	26.0668i	0.637674	+	1.10448i	−0.348268	+	0.937395i	$0.613230\pi$
$558$	8.70244	+	11.3063i	0.368404	+	0.478633i
$559$	−4.01771			−0.169931
$560$	2.76977	−	5.70758i	0.117044	−	0.241189i
$561$	4.37735	+	2.15461i	0.184812	+	0.0909678i
$562$	−13.1763	−	22.8220i	−0.555808	−	0.962688i
$563$	−21.7920			−0.918423			−0.459212	−	0.888327i	$-0.651868\pi$
$563$	−21.7920			−0.918423			−0.459212	+	0.888327i	$0.651868\pi$
$564$	−8.06624	−	3.97035i	−0.339650	−	0.167182i
$565$	9.85105			0.414437
$566$	−34.8598			−1.46527
$567$	22.4757	−	7.86409i	0.943890	−	0.330261i
$568$	−8.79831			−0.369169
$569$	31.1695			1.30670			0.653348	−	0.757058i	$-0.273364\pi$
$569$	31.1695			1.30670			0.653348	+	0.757058i	$0.273364\pi$
$570$	13.0944	+	6.44531i	0.548464	+	0.269964i
$571$	23.8556			0.998327			0.499164	−	0.866508i	$-0.333641\pi$
$571$	23.8556			0.998327			0.499164	+	0.866508i	$0.333641\pi$
$572$	2.45010	+	4.24370i	0.102444	+	0.177438i
$573$	−11.2986	−	5.56138i	−0.472006	−	0.232330i
$574$	13.6831	−	0.984094i	0.571122	−	0.0410753i
$575$	−7.47750			−0.311833
$576$	15.9531	+	20.7264i	0.664713	+	0.863600i
$577$	5.84044	+	10.1159i	0.243141	+	0.421132i	0.961607	−	0.274429i	$-0.0884889\pi$
$577$	5.84044	+	10.1159i	0.243141	+	0.421132i	−0.718466	+	0.695562i	$0.755156\pi$
$578$	−8.20176	+	14.2059i	−0.341148	+	0.590886i
$579$	24.7244	+	12.1698i	1.02751	+	0.505761i
$580$	0.723539	−	1.25321i	0.0300433	−	0.0520365i
$581$	1.45309	−	2.99433i	0.0602842	−	0.124226i
$582$	−1.59078	−	23.9963i	−0.0659398	−	0.994678i
$583$	4.64160			0.192236
$584$	18.0675	+	31.2938i	0.747638	+	1.29495i
$585$	−9.09850	−	11.8208i	−0.376177	−	0.488732i
$586$	−8.97883	+	15.5518i	−0.370912	+	0.642439i
$587$	2.39441	+	4.14725i	0.0988280	+	0.171175i	0.911200	−	0.411965i	$-0.135157\pi$
$587$	2.39441	+	4.14725i	0.0988280	+	0.171175i	−0.812372	+	0.583140i	$0.801824\pi$
$588$	5.52252	−	4.97600i	0.227745	−	0.205207i
$589$	−14.4475	+	25.0239i	−0.595301	+	1.03109i
$590$	−7.88949	−	13.6650i	−0.324805	−	0.562579i
$591$	−16.9772	−	8.35651i	−0.698350	−	0.343741i
$592$	−10.1267	+	17.5400i	−0.416205	+	0.720889i
$593$	21.0432	−	36.4480i	0.864142	−	1.49674i	−0.00375417	−	0.999993i	$-0.501195\pi$
$593$	21.0432	−	36.4480i	0.864142	−	1.49674i	0.867896	−	0.496745i	$-0.165472\pi$
$594$	−9.32100	−	3.14081i	−0.382445	−	0.128869i
$595$	−4.62461	+	0.332604i	−0.189591	+	0.0136354i
$596$	−1.83596	−	3.17998i	−0.0752039	−	0.130257i
$597$	0.375562	+	5.66521i	0.0153707	+	0.231862i
$598$	−43.7860			−1.79054
$599$	−33.0067			−1.34862			−0.674308	−	0.738450i	$-0.735558\pi$
$599$	−33.0067			−1.34862			−0.674308	+	0.738450i	$0.735558\pi$
$600$	−4.42965	+	2.96458i	−0.180840	+	0.121028i
$601$	14.2290	+	24.6453i	0.580412	+	1.00530i	0.995430	+	0.0954900i	$0.0304418\pi$
$601$	14.2290	+	24.6453i	0.580412	+	1.00530i	−0.415018	+	0.909813i	$0.636225\pi$
$602$	1.09916	−	2.26500i	0.0447983	−	0.0923145i
$603$	−14.8572	−	19.3025i	−0.605030	−	0.786060i
$604$	0.449032	−	0.777746i	0.0182708	−	0.0316460i
$605$	4.20819	−	7.28880i	0.171087	−	0.296332i
$606$	−21.1557	+	14.1586i	−0.859392	+	0.575155i
$607$	−3.52819	−	6.11100i	−0.143205	−	0.248038i	0.785497	−	0.618866i	$-0.212407\pi$
$607$	−3.52819	−	6.11100i	−0.143205	−	0.248038i	−0.928702	+	0.370828i	$0.879074\pi$
$608$	−11.9163	+	20.6396i	−0.483269	+	0.837047i
$609$	−8.53385	+	6.64495i	−0.345809	+	0.269267i
$610$	−6.41198	−	11.1059i	−0.259613	−	0.449664i
$611$	21.0478	−	36.4558i	0.851502	−	1.47485i
$612$	1.22908	−	2.97984i	0.0496828	−	0.120453i
$613$	−9.36330	−	16.2177i	−0.378180	−	0.655027i	0.612618	−	0.790379i	$-0.290117\pi$
$613$	−9.36330	−	16.2177i	−0.378180	−	0.655027i	−0.990797	+	0.135353i	$0.956783\pi$
$614$	31.7625			1.28183
$615$	−6.84206	−	3.36779i	−0.275898	−	0.135802i
$616$	−13.0533	+	0.938801i	−0.525934	+	0.0378254i
$617$	5.18057	−	8.97300i	0.208562	−	0.361240i	−0.742700	−	0.669624i	$-0.766455\pi$
$617$	5.18057	−	8.97300i	0.208562	−	0.361240i	0.951262	+	0.308385i	$0.0997884\pi$
$618$	−0.623153	−	9.40003i	−0.0250669	−	0.378125i
$619$	18.9692	−	32.8557i	0.762438	−	1.32058i	−0.179153	−	0.983821i	$-0.557336\pi$
$619$	18.9692	−	32.8557i	0.762438	−	1.32058i	0.941591	−	0.336760i	$-0.109331\pi$
$620$	−1.23800	−	2.14428i	−0.0497194	−	0.0861165i
$621$	−29.1548	+	25.6837i	−1.16994	+	1.03065i
$622$	−16.2777			−0.652676
$623$	20.0259	−	1.44027i	0.802321	−	0.0577033i
$624$	−17.1622	+	11.4859i	−0.687038	+	0.459805i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−17.0145			−0.680036
$627$	−1.31766	−	19.8764i	−0.0526221	−	0.793785i
$628$	−9.28378			−0.370463
$629$	14.8020			0.590195
$630$	9.15321	−	1.89539i	0.364673	−	0.0755143i
$631$	−6.06904			−0.241605			−0.120802	−	0.992677i	$-0.538547\pi$
$631$	−6.06904			−0.241605			−0.120802	+	0.992677i	$0.538547\pi$
$632$	5.90161			0.234754
$633$	−27.1881	+	18.1958i	−1.08063	+	0.723220i
$634$	29.8379			1.18502
$635$	4.13181	+	7.15651i	0.163966	+	0.283997i
$636$	−0.202848	−	3.05988i	−0.00804343	−	0.121332i
$637$	21.5375	+	27.3424i	0.853346	+	1.08335i
$638$	4.46770			0.176878
$639$	−5.23157	−	6.79689i	−0.206958	−	0.268881i
$640$	1.80277	+	3.12248i	0.0712605	+	0.123427i
$641$	4.63667	−	8.03094i	0.183137	−	0.317203i	−0.759810	−	0.650145i	$-0.774708\pi$
$641$	4.63667	−	8.03094i	0.183137	−	0.317203i	0.942947	+	0.332942i	$0.108041\pi$
$642$	26.1750	−	17.5178i	1.03304	−	0.691373i
$643$	−3.82825	+	6.63073i	−0.150972	+	0.261490i	−0.931585	−	0.363524i	$-0.881574\pi$
$643$	−3.82825	+	6.63073i	−0.150972	+	0.261490i	0.780613	+	0.625014i	$0.214907\pi$
$644$	−5.29564	+	10.9126i	−0.208678	+	0.430015i
$645$	−1.16308	+	0.778401i	−0.0457963	+	0.0306495i
$646$	−14.7666			−0.580985
$647$	−0.663635	−	1.14945i	−0.0260902	−	0.0451895i	0.852686	−	0.522425i	$-0.174972\pi$
$647$	−0.663635	−	1.14945i	−0.0260902	−	0.0451895i	−0.878776	+	0.477235i	$0.841639\pi$
$648$	−7.08847	+	26.7738i	−0.278461	+	1.05177i
$649$	−10.7682	+	18.6510i	−0.422688	+	0.732117i
$650$	−2.92785	−	5.07118i	−0.114840	−	0.198908i
$651$	2.54563	+	18.3304i	0.0997712	+	0.718424i
$652$	1.22597	−	2.12344i	0.0480126	−	0.0831603i
$653$	22.0525	+	38.1961i	0.862981	+	1.49473i	0.869038	+	0.494745i	$0.164739\pi$
$653$	22.0525	+	38.1961i	0.862981	+	1.49473i	−0.00605690	+	0.999982i	$0.501928\pi$
$654$	1.58332	+	23.8838i	0.0619126	+	0.933930i
$655$	3.29787	−	5.71207i	0.128858	−	0.223189i
$656$	−5.27873	+	9.14303i	−0.206100	+	0.356975i
$657$	−13.4321	+	32.5652i	−0.524035	+	1.27049i
$658$	14.7939	+	21.8393i	0.576727	+	0.851385i
$659$	0.473550	+	0.820212i	0.0184469	+	0.0319509i	0.875101	−	0.483939i	$-0.160795\pi$
$659$	0.473550	+	0.820212i	0.0184469	+	0.0319509i	−0.856655	+	0.515890i	$0.827461\pi$
$660$	1.53146	+	0.753815i	0.0596122	+	0.0293422i
$661$	6.65498			0.258849			0.129424	−	0.991589i	$-0.458687\pi$
$661$	6.65498			0.258849			0.129424	+	0.991589i	$0.458687\pi$
$662$	−9.01310			−0.350304
$663$	13.5412	+	6.66521i	0.525895	+	0.258855i
$664$	1.93562	+	3.35259i	0.0751166	+	0.130106i
$665$	10.6169	+	15.6731i	0.411707	+	0.607777i
$666$	−29.5801	+	3.93919i	−1.14620	+	0.152641i
$667$	8.82422	−	15.2840i	0.341675	−	0.591798i
$668$	−4.95139	+	8.57607i	−0.191575	+	0.331818i
$669$	−1.37829	−	20.7910i	−0.0532877	−	0.803826i
$670$	−4.78095	−	8.28086i	−0.184704	−	0.319917i
$671$	−8.75156	+	15.1582i	−0.337850	+	0.585174i
$672$	2.09963	+	15.1188i	0.0809949	+	0.583221i
$673$	21.6445	+	37.4894i	0.834336	+	1.44511i	0.894570	+	0.446928i	$0.147482\pi$
$673$	21.6445	+	37.4894i	0.834336	+	1.44511i	−0.0602342	+	0.998184i	$0.519185\pi$
$674$	−11.2046	+	19.4070i	−0.431586	+	0.747530i
$675$	−4.92412	−	1.65923i	−0.189529	−	0.0638639i
$676$	3.59405	+	6.22508i	0.138233	+	0.239426i
$677$	−1.48064			−0.0569056			−0.0284528	−	0.999595i	$-0.509058\pi$
$677$	−1.48064			−0.0569056			−0.0284528	+	0.999595i	$0.509058\pi$
$678$	16.6991	−	11.1760i	0.641325	−	0.429212i
$679$	13.6187	−	28.0636i	0.522638	−	1.07698i
$680$	2.69647	−	4.67042i	0.103405	−	0.179102i
$681$	−20.1347	+	13.4753i	−0.771562	+	0.516374i
$682$	3.82220	−	6.62025i	0.146360	−	0.253502i
$683$	−14.0585	−	24.3500i	−0.537932	−	0.931726i	−0.999015	−	0.0443687i	$-0.985872\pi$
$683$	−14.0585	−	24.3500i	−0.537932	−	0.931726i	0.461083	−	0.887357i	$-0.347461\pi$
$684$	−13.0455	+	1.73727i	−0.498807	+	0.0664264i
$685$	−7.16732			−0.273849
$686$	−21.3066	+	4.66155i	−0.813490	+	0.177979i
$687$	0.468921	+	7.07351i	0.0178905	+	0.269871i
$688$	0.968754	+	1.67793i	0.0369334	+	0.0639705i
$689$	14.3586			0.547020
$690$	−12.6756	+	8.48322i	−0.482550	+	0.322951i
$691$	16.2756			0.619153			0.309576	−	0.950875i	$-0.399813\pi$
$691$	16.2756			0.619153			0.309576	+	0.950875i	$0.399813\pi$
$692$	−6.64215			−0.252497
$693$	−8.48690	−	9.52577i	−0.322390	−	0.361854i
$694$	30.9613			1.17528
$695$	−8.24885			−0.312897
$696$	−0.832151	−	12.5527i	−0.0315426	−	0.475809i
$697$	7.71582			0.292258
$698$	−2.30577	−	3.99371i	−0.0872747	−	0.151164i
$699$	17.9838	−	12.0358i	0.680209	−	0.455236i
$700$	−1.61797	+	0.116365i	−0.0611535	+	0.00439819i
$701$	0.626032			0.0236449			0.0118225	−	0.999930i	$-0.496237\pi$
$701$	0.626032			0.0236449			0.0118225	+	0.999930i	$0.496237\pi$
$702$	−28.8342	−	9.71597i	−1.08828	−	0.366706i
$703$	−30.2175	−	52.3383i	−1.13968	−	1.97398i
$704$	7.00677	−	12.1361i	0.264078	−	0.457396i
$705$	−0.969955	−	14.6314i	−0.0365306	−	0.551051i
$706$	12.8359	−	22.2324i	0.483085	−	0.836729i
$707$	−32.9341	+	2.36863i	−1.23861	+	0.0890816i
$708$	12.7659	+	6.28361i	0.479772	+	0.236153i
$709$	−9.30412			−0.349424			−0.174712	−	0.984620i	$-0.555899\pi$
$709$	−9.30412			−0.349424			−0.174712	+	0.984620i	$0.555899\pi$
$710$	−1.68349	−	2.91589i	−0.0631803	−	0.109431i
$711$	3.50916	+	4.55913i	0.131604	+	0.170981i
$712$	−11.6765	+	20.2243i	−0.437595	+	0.757937i
$713$	−15.0986	−	26.1515i	−0.565446	−	0.979381i
$714$	−7.46211	+	5.81043i	−0.279263	+	0.217450i
$715$	−3.99616	+	6.92155i	−0.149448	+	0.258851i
$716$	−0.704331	−	1.21994i	−0.0263221	−	0.0455912i
$717$	−17.4750	+	11.6953i	−0.652615	+	0.436768i
$718$	9.03473	−	15.6486i	0.337173	−	0.584001i
$719$	5.22955	−	9.05785i	0.195029	−	0.337801i	−0.751881	−	0.659299i	$-0.770853\pi$
$719$	5.22955	−	9.05785i	0.195029	−	0.337801i	0.946910	+	0.321498i	$0.104186\pi$
$720$	−2.74295	+	6.65010i	−0.102224	+	0.247835i
$721$	5.33483	−	10.9933i	0.198680	−	0.409413i
$722$	18.9575	+	32.8353i	0.705525	+	1.22200i
$723$	−10.8925	+	7.28992i	−0.405098	+	0.271115i
$724$	−13.0496			−0.484985
$725$	2.36021			0.0876558
$726$	−1.13558	−	17.1299i	−0.0421455	−	0.635749i
$727$	24.3299	+	42.1406i	0.902346	+	1.56291i	0.824440	+	0.565949i	$0.191490\pi$
$727$	24.3299	+	42.1406i	0.902346	+	1.56291i	0.0779060	+	0.996961i	$0.475177\pi$
$728$	−40.3800	+	2.90414i	−1.49658	+	0.107635i
$729$	−24.8983	+	10.4440i	−0.922158	+	0.386814i
$730$	−6.91416	+	11.9757i	−0.255905	+	0.443240i
$731$	0.708005	−	1.22630i	0.0261865	−	0.0453563i
$732$	10.3752	+	5.10684i	0.383477	+	0.188754i
$733$	−13.1315	−	22.7444i	−0.485022	−	0.840082i	0.514830	−	0.857292i	$-0.327855\pi$
$733$	−13.1315	−	22.7444i	−0.485022	−	0.840082i	−0.999852	+	0.0172098i	$0.994522\pi$
$734$	−6.83898	+	11.8455i	−0.252431	+	0.437224i
$735$	11.5323	+	3.74260i	0.425374	+	0.138048i
$736$	−12.4533	−	21.5697i	−0.459033	−	0.795069i
$737$	−6.52542	+	11.3024i	−0.240367	+	0.416328i
$738$	−15.4191	+	2.05337i	−0.567586	+	0.0755857i
$739$	0.240735	+	0.416966i	0.00885560	+	0.0153383i	0.870419	−	0.492311i	$-0.163848\pi$
$739$	0.240735	+	0.416966i	0.00885560	+	0.0153383i	−0.861564	+	0.507650i	$0.830514\pi$
$740$	5.17865			0.190371
$741$	−4.07612	−	61.4867i	−0.149740	−	2.25877i
$742$	−3.92821	+	8.09474i	−0.144209	+	0.297167i
$743$	22.4502	−	38.8849i	0.823618	−	1.42655i	−0.0793529	−	0.996847i	$-0.525285\pi$
$743$	22.4502	−	38.8849i	0.823618	−	1.42655i	0.902971	−	0.429702i	$-0.141381\pi$
$744$	−19.3125	−	9.50599i	−0.708032	−	0.348506i
$745$	2.99448	−	5.18659i	0.109709	−	0.190022i
$746$	12.8784	+	22.3060i	0.471510	+	0.816679i
$747$	−1.43901	+	3.48880i	−0.0526507	+	0.127648i
$748$	−1.72704			−0.0631468
$749$	40.7478	−	2.93060i	1.48889	−	0.107082i
$750$	−1.83009	−	0.900802i	−0.0668253	−	0.0328926i
$751$	6.27692	+	10.8719i	0.229048	+	0.396723i	0.957526	−	0.288346i	$-0.0931054\pi$
$751$	6.27692	+	10.8719i	0.229048	+	0.396723i	−0.728478	+	0.685069i	$0.759772\pi$
$752$	−20.3003			−0.740274
$753$	−3.28178	−	1.61536i	−0.119595	−	0.0588668i
$754$	13.8207			0.503318
$755$	1.46476			0.0533079
$756$	−5.90877	+	6.01111i	−0.214900	+	0.218622i
$757$	19.1344			0.695453			0.347727	−	0.937596i	$-0.386954\pi$
$757$	19.1344			0.695453			0.347727	+	0.937596i	$0.386954\pi$
$758$	22.1518			0.804591
$759$	18.6776	+	9.19347i	0.677954	+	0.333702i
$760$	−22.0188			−0.798705
$761$	5.98425	+	10.3650i	0.216929	+	0.375732i	0.953868	−	0.300228i	$-0.0970627\pi$
$761$	5.98425	+	10.3650i	0.216929	+	0.375732i	−0.736939	+	0.675960i	$0.763729\pi$
$762$	15.1231	+	7.44388i	0.547853	+	0.269663i
$763$	−13.5548	+	27.9320i	−0.490718	+	1.01121i
$764$	4.45775			0.161276
$765$	5.21135	−	0.693998i	0.188417	−	0.0250916i
$766$	−5.10037	−	8.83410i	−0.184284	−	0.319189i
$767$	−33.3110	+	57.6963i	−1.20279	+	2.08329i
$768$	−20.4982	−	10.0896i	−0.739665	−	0.364077i
$769$	3.00699	−	5.20826i	0.108435	−	0.187815i	−0.806702	−	0.590959i	$-0.798749\pi$
$769$	3.00699	−	5.20826i	0.108435	−	0.187815i	0.915136	+	0.403144i	$0.132083\pi$
$770$	−2.80879	−	4.14644i	−0.101222	−	0.149427i
$771$	1.60767	+	24.2512i	0.0578989	+	0.873384i
$772$	−9.75478			−0.351082
$773$	−19.6799	−	34.0866i	−0.707837	−	1.22601i	−0.965658	−	0.259817i	$-0.916338\pi$
$773$	−19.6799	−	34.0866i	−0.707837	−	1.22601i	0.257821	−	0.966193i	$-0.416996\pi$
$774$	−1.08851	+	2.63903i	−0.0391258	+	0.0948579i
$775$	2.01920	−	3.49736i	0.0725318	−	0.125629i
$776$	18.1411	+	31.4213i	0.651228	+	1.12796i
$777$	−35.8643	−	14.5583i	−1.28663	−	0.522277i
$778$	−12.0009	+	20.7861i	−0.430252	+	0.745219i
$779$	−15.7514	−	27.2823i	−0.564354	−	0.977489i
$780$	4.73753	+	2.33190i	0.169631	+	0.0834953i
$781$	−2.29776	+	3.97983i	−0.0822203	+	0.142410i
$782$	7.71601	−	13.3645i	0.275924	−	0.477915i
$783$	9.20243	−	8.10682i	0.328868	−	0.289714i
$784$	6.22599	−	15.5876i	0.222357	−	0.556701i
$785$	−7.57099	−	13.1133i	−0.270220	−	0.468035i
$786$	−0.889932	−	13.4243i	−0.0317428	−	0.478829i
$787$	49.2539			1.75571			0.877856	−	0.478924i	$-0.158973\pi$
$787$	49.2539			1.75571			0.877856	+	0.478924i	$0.158973\pi$
$788$	6.69820			0.238613
$789$	−43.2068	+	28.9165i	−1.53820	+	1.02945i
$790$	1.12923	+	1.95588i	0.0401762	+	0.0695872i
$791$	25.9963	−	1.86966i	0.924322	−	0.0664776i
$792$	14.7095	−	1.95887i	0.522678	−	0.0696053i
$793$	−27.0726	+	46.8912i	−0.961377	+	1.66515i
$794$	6.30580	−	10.9220i	0.223784	−	0.387606i
$795$	4.15666	−	2.78188i	0.147422	−	0.0986631i
$796$	−1.00489	−	1.74053i	−0.0356175	−	0.0616913i
$797$	−6.82813	+	11.8267i	−0.241865	+	0.418922i	−0.961245	−	0.275694i	$-0.911092\pi$
$797$	−6.82813	+	11.8267i	−0.241865	+	0.418922i	0.719381	+	0.694616i	$0.244426\pi$
$798$	35.7786	+	14.5235i	1.26655	+	0.514127i
$799$	7.41813	+	12.8486i	0.262435	+	0.454550i
$800$	1.66543	−	2.88461i	0.0588819	−	0.101986i
$801$	−22.5667	+	3.00522i	−0.797355	+	0.106184i
$802$	14.6853	+	25.4357i	0.518557	+	0.898167i
$803$	18.8740			0.666048
$804$	7.73602	+	3.80781i	0.272828	+	0.134291i
$805$	−19.7326	+	1.41918i	−0.695484	+	0.0500195i
$806$	11.8238	−	20.4795i	0.416477	−	0.721359i
$807$	−1.70980	−	25.7918i	−0.0601880	−	0.907913i
$808$	19.2029	−	33.2603i	0.675554	−	1.17009i
$809$	−12.7564	−	22.0948i	−0.448492	−	0.776811i	0.549796	−	0.835299i	$-0.314705\pi$
$809$	−12.7564	−	22.0948i	−0.448492	−	0.776811i	−0.998288	+	0.0584877i	$0.981372\pi$
$810$	−10.2296	+	2.77374i	−0.359430	+	0.0974594i
$811$	37.9267			1.33179			0.665893	−	0.746047i	$-0.268051\pi$
$811$	37.9267			1.33179			0.665893	+	0.746047i	$0.268051\pi$
$812$	1.67152	−	3.44445i	0.0586589	−	0.120877i
$813$	−25.2562	+	16.9029i	−0.885773	+	0.592811i
$814$	7.99427	+	13.8465i	0.280199	+	0.485319i
$815$	3.99915			0.140084
$816$	−0.481442	−	7.26238i	−0.0168538	−	0.254234i
$817$	−5.78141			−0.202266
$818$	26.3182			0.920195
$819$	−26.2539	−	29.4676i	−0.917385	−	1.02968i
$820$	2.69946			0.0942694
$821$	−45.3579			−1.58300			−0.791501	−	0.611168i	$-0.790700\pi$
$821$	−45.3579			−1.58300			−0.791501	+	0.611168i	$0.790700\pi$
$822$	−12.1497	+	8.13132i	−0.423771	+	0.283612i
$823$	−7.25389			−0.252855			−0.126427	−	0.991976i	$-0.540351\pi$
$823$	−7.25389			−0.252855			−0.126427	+	0.991976i	$0.540351\pi$
$824$	7.10639	+	12.3086i	0.247563	+	0.428792i
$825$	0.184157	+	2.77794i	0.00641151	+	0.0967153i
$826$	−23.4134	−	34.5637i	−0.814655	−	1.20262i
$827$	15.2005			0.528572			0.264286	−	0.964444i	$-0.414864\pi$
$827$	15.2005			0.528572			0.264286	+	0.964444i	$0.414864\pi$
$828$	5.24435	−	12.7146i	0.182254	−	0.441863i
$829$	26.6868	+	46.2229i	0.926872	+	1.60539i	0.788523	+	0.615005i	$0.210846\pi$
$829$	26.6868	+	46.2229i	0.926872	+	1.60539i	0.138349	+	0.990384i	$0.455821\pi$
$830$	−0.740732	+	1.28299i	−0.0257112	+	0.0445331i
$831$	5.70135	−	3.81567i	0.197777	−	0.132364i
$832$	21.6752	−	37.5425i	0.751451	−	1.30155i
$833$	−12.1409	+	1.75544i	−0.420658	+	0.0608224i
$834$	−13.9831	+	9.35831i	−0.484196	+	0.324052i
$835$	−16.1516			−0.558949
$836$	3.52566	+	6.10662i	0.121937	+	0.211202i
$837$	−4.13985	−	20.5717i	−0.143094	−	0.711063i
$838$	−11.7028	+	20.2699i	−0.404267	+	0.700212i
$839$	12.9952	+	22.5083i	0.448644	+	0.777073i	0.998298	−	0.0583187i	$-0.0185739\pi$
$839$	12.9952	+	22.5083i	0.448644	+	0.777073i	−0.549654	+	0.835392i	$0.685241\pi$
$840$	−11.1269	+	8.66404i	−0.383914	+	0.298938i
$841$	11.7147	−	20.2905i	0.403956	−	0.699672i
$842$	−1.18323	−	2.04941i	−0.0407767	−	0.0706274i
$843$	2.56375	+	38.6733i	0.0883004	+	1.33198i
$844$	5.79029	−	10.0291i	0.199310	−	0.345215i
$845$	−5.86196	+	10.1532i	−0.201657	+	0.349281i
$846$	−18.2436	−	23.7022i	−0.627226	−	0.814897i
$847$	9.72178	−	20.0334i	0.334044	−	0.688355i
$848$	−3.46217	−	5.99665i	−0.118891	−	0.205926i
$849$	45.9997	+	22.6419i	1.57871	+	0.777069i
$850$	2.06380			0.0707876
$851$	63.1584			2.16504
$852$	2.72404	+	1.34082i	0.0933241	+	0.0459358i
$853$	−5.33160	−	9.23460i	−0.182550	−	0.316187i	0.760198	−	0.649692i	$-0.225102\pi$
$853$	−5.33160	−	9.23460i	−0.182550	−	0.316187i	−0.942748	+	0.333505i	$0.891769\pi$
$854$	−19.0286	−	28.0907i	−0.651146	−	0.961245i
$855$	−13.0926	−	17.0100i	−0.447757	−	0.581730i
$856$	−23.7588	+	41.1515i	−0.812059	+	1.40653i
$857$	25.7932	−	44.6751i	0.881079	−	1.52607i	0.0309356	−	0.999521i	$-0.490151\pi$
$857$	25.7932	−	44.6751i	0.881079	−	1.52607i	0.850143	−	0.526552i	$-0.176515\pi$
$858$	1.07837	+	16.2668i	0.0368148	+	0.555338i
$859$	−0.216902	−	0.375685i	−0.00740060	−	0.0128182i	0.862301	−	0.506395i	$-0.169022\pi$
$859$	−0.216902	−	0.375685i	−0.00740060	−	0.0128182i	−0.869702	+	0.493577i	$0.835689\pi$
$860$	0.247703	−	0.429034i	0.00844661	−	0.0146300i
$861$	−18.6949	−	7.58880i	−0.637121	−	0.258625i
$862$	−16.6057	−	28.7619i	−0.565592	−	0.979635i
$863$	−3.30629	+	5.72666i	−0.112547	+	0.194938i	−0.916797	−	0.399354i	$-0.869234\pi$
$863$	−3.30629	+	5.72666i	−0.112547	+	0.194938i	0.804249	+	0.594292i	$0.202568\pi$
$864$	−3.41453	−	16.9675i	−0.116165	−	0.577246i
$865$	−5.41672	−	9.38204i	−0.184174	−	0.318999i
$866$	11.1187			0.377830
$867$	20.0497	−	13.4184i	0.680923	−	0.455713i
$868$	−3.67398	−	5.42366i	−0.124703	−	0.184091i
$869$	1.54126	−	2.66954i	0.0522837	−	0.0905580i
$870$	4.00092	−	2.67765i	0.135644	−	0.0907809i
$871$	−20.1861	+	34.9634i	−0.683981	+	1.18469i
$872$	−18.0561	−	31.2740i	−0.611456	−	1.05907i
$873$	−13.4868	+	32.6979i	−0.456459	+	1.10666i
$874$	−63.0073			−2.13125
$875$	−1.48383	−	2.19049i	−0.0501627	−	0.0740520i
$876$	−0.824831	−	12.4423i	−0.0278684	−	0.420385i
$877$	23.9635	+	41.5060i	0.809190	+	1.40156i	0.913426	+	0.407006i	$0.133427\pi$
$877$	23.9635	+	41.5060i	0.809190	+	1.40156i	−0.104236	+	0.994553i	$0.533240\pi$
$878$	32.7533			1.10537
$879$	21.9493	−	14.6897i	0.740331	−	0.495472i
$880$	3.85423			0.129926
$881$	−15.2584			−0.514068			−0.257034	−	0.966402i	$-0.582745\pi$
$881$	−15.2584			−0.514068			−0.257034	+	0.966402i	$0.582745\pi$
$882$	23.7950	−	6.73904i	0.801219	−	0.226915i
$883$	−20.3889			−0.686141			−0.343071	−	0.939310i	$-0.611467\pi$
$883$	−20.3889			−0.686141			−0.343071	+	0.939310i	$0.611467\pi$
$884$	−5.34253			−0.179689
$885$	1.53508	+	23.1562i	0.0516013	+	0.778387i
$886$	40.3147			1.35440
$887$	−6.10586	−	10.5757i	−0.205015	−	0.355096i	0.745123	−	0.666927i	$-0.232391\pi$
$887$	−6.10586	−	10.5757i	−0.205015	−	0.355096i	−0.950137	+	0.311831i	$0.899058\pi$
$888$	37.4148	−	25.0402i	1.25556	−	0.840293i
$889$	12.2618	+	18.1014i	0.411249	+	0.607100i
$890$	−8.93684			−0.299563
$891$	10.2597	+	10.1986i	0.343712	+	0.341667i
$892$	3.68790	+	6.38762i	0.123480	+	0.213873i
$893$	30.2874	−	52.4594i	1.01353	−	1.75549i
$894$	−0.808063	−	12.1893i	−0.0270257	−	0.407672i
$895$	1.14877	−	1.98973i	0.0383993	−	0.0665095i
$896$	5.35001	+	7.89787i	0.178731	+	0.263849i
$897$	57.7785	+	28.4396i	1.92917	+	0.949572i
$898$	27.7699			0.926693
$899$	4.76573	+	8.25448i	0.158946	+	0.275302i
$900$	1.82325	−	0.242803i	0.0607750	−	0.00809343i
$901$	−2.53029	+	4.38259i	−0.0842962	+	0.146005i
$902$	4.16716	+	7.21773i	0.138751	+	0.240324i
$903$	−2.92156	+	2.27490i	−0.0972234	+	0.0757038i
$904$	−15.1576	+	26.2538i	−0.504135	+	0.873188i
$905$	−10.6421	−	18.4326i	−0.353754	−	0.612720i
$906$	2.48299	−	1.66176i	0.0824920	−	0.0552084i
$907$	−12.7218	+	22.0348i	−0.422420	+	0.731653i	−0.996176	−	0.0873736i	$-0.972153\pi$
$907$	−12.7218	+	22.0348i	−0.422420	+	0.731653i	0.573756	+	0.819027i	$0.305486\pi$
$908$	4.28811	−	7.42722i	0.142306	−	0.246481i
$909$	37.1126	−	4.94230i	1.23095	−	0.163926i
$910$	−8.68888	−	12.8268i	−0.288034	−	0.425206i
$911$	−3.03816	−	5.26226i	−0.100659	−	0.174346i	0.811297	−	0.584634i	$-0.198762\pi$
$911$	−3.03816	−	5.26226i	−0.100659	−	0.174346i	−0.911956	+	0.410287i	$0.865428\pi$
$912$	−24.6961	+	16.5281i	−0.817770	+	0.547299i
$913$	2.02202			0.0669190
$914$	−37.5856			−1.24322
$915$	1.24760	+	18.8196i	0.0412444	+	0.622156i
$916$	−1.25470	−	2.17320i	−0.0414563	−	0.0718044i
$917$	7.61875	−	15.6997i	0.251593	−	0.518450i
$918$	8.04673	−	7.08871i	0.265582	−	0.233962i
$919$	13.9957	−	24.2412i	0.461674	−	0.799643i	−0.537371	−	0.843346i	$-0.680582\pi$
$919$	13.9957	−	24.2412i	0.461674	−	0.799643i	0.999045	+	0.0437034i	$0.0139157\pi$
$920$	11.5055	−	19.9281i	0.379325	−	0.657010i
$921$	−41.9126	−	20.6302i	−1.38107	−	0.679787i
$922$	−2.95860	−	5.12445i	−0.0974363	−	0.168765i
$923$	−7.10803	+	12.3115i	−0.233964	+	0.405237i
$924$	4.18450	+	1.69861i	0.137660	+	0.0558801i
$925$	4.22323	+	7.31485i	0.138859	+	0.240511i
$926$	3.23297	−	5.59967i	0.106242	−	0.184017i
$927$	−5.28316	+	12.8087i	−0.173522	+	0.420693i
$928$	3.93076	+	6.80827i	0.129033	+	0.223492i
$929$	−59.2465			−1.94381			−0.971907	−	0.235365i	$-0.924371\pi$
$929$	−59.2465			−1.94381			−0.971907	+	0.235365i	$0.924371\pi$
$930$	−0.544883	−	8.21936i	−0.0178674	−	0.269524i
$931$	30.9921	+	39.3453i	1.01572	+	1.28949i
$932$	−3.83003	+	6.63382i	−0.125457	+	0.217298i
$933$	21.4795	+	10.5726i	0.703206	+	0.346131i
$934$	6.53382	−	11.3169i	0.213793	−	0.370301i
$935$	−1.40841	−	2.43944i	−0.0460601	−	0.0797784i
$936$	45.5031	−	6.05968i	1.48732	−	0.198067i
$937$	−19.9446			−0.651560			−0.325780	−	0.945446i	$-0.605627\pi$
$937$	−19.9446			−0.651560			−0.325780	+	0.945446i	$0.605627\pi$
$938$	−14.1883	−	20.9452i	−0.463264	−	0.683887i
$939$	22.4517	+	11.0512i	0.732684	+	0.360641i
$940$	2.59531	+	4.49522i	0.0846498	+	0.146618i
$941$	−21.4227			−0.698359			−0.349179	−	0.937056i	$-0.613540\pi$
$941$	−21.4227			−0.698359			−0.349179	+	0.937056i	$0.613540\pi$
$942$	−27.7111	−	13.6399i	−0.902877	−	0.444413i
$943$	32.9224			1.07210
$944$	32.1279			1.04567
$945$	−13.3093	−	3.44405i	−0.432953	−	0.112035i
$946$	1.52951			0.0497288
$947$	43.5489			1.41515			0.707575	−	0.706638i	$-0.249789\pi$
$947$	43.5489			1.41515			0.707575	+	0.706638i	$0.249789\pi$
$948$	−1.82720	−	0.899379i	−0.0593445	−	0.0292105i
$949$	58.3859			1.89529
$950$	−4.21313	−	7.29735i	−0.136692	−	0.236757i
$951$	−39.3731	−	19.3802i	−1.27676	−	0.628445i
$952$	6.22939	−	12.8367i	0.201896	−	0.416040i
$953$	14.1810			0.459368			0.229684	−	0.973265i	$-0.426231\pi$
$953$	14.1810			0.459368			0.229684	+	0.973265i	$0.426231\pi$
$954$	3.89016	−	9.43146i	0.125949	−	0.305355i
$955$	3.63533	+	6.29657i	0.117636	+	0.203752i
$956$	3.72167	−	6.44613i	0.120368	−	0.208483i
$957$	−5.89542	−	2.90183i	−0.190572	−	0.0938030i
$958$	3.20623	−	5.55335i	0.103589	−	0.179421i
$959$	−18.9141	+	1.36031i	−0.610768	+	0.0439266i
$960$	−0.998867	−	15.0675i	−0.0322383	−	0.486303i
$961$	−14.6913			−0.473913
$962$	24.7300	+	42.8336i	0.797326	+	1.38101i
$963$	−45.9177	+	6.11488i	−1.47968	+	0.197049i
$964$	2.31980	−	4.01801i	0.0747157	−	0.129411i
$965$	−7.95510	−	13.7786i	−0.256084	−	0.443550i
$966$	−31.8399	+	24.7924i	−1.02443	+	0.797682i
$967$	−13.7181	+	23.7605i	−0.441145	+	0.764086i	−0.997775	−	0.0666752i	$-0.978761\pi$
$967$	−13.7181	+	23.7605i	−0.441145	+	0.764086i	0.556630	+	0.830761i	$0.312094\pi$
$968$	12.9501	+	22.4303i	0.416233	+	0.720937i
$969$	19.4855	+	9.59113i	0.625965	+	0.308112i
$970$	−6.94233	+	12.0245i	−0.222905	+	0.386083i
$971$	17.4646	−	30.2495i	0.560465	−	0.970753i	−0.436991	−	0.899466i	$-0.643956\pi$
$971$	17.4646	−	30.2495i	0.560465	−	0.970753i	0.997456	−	0.0712874i	$-0.0227108\pi$
$972$	6.27487	−	7.20918i	0.201266	−	0.231234i
$973$	−21.7682	+	1.56558i	−0.697856	+	0.0501900i
$974$	8.94366	+	15.4909i	0.286573	+	0.496360i
$975$	0.569682	+	8.59344i	0.0182444	+	0.275210i
$976$	26.1111			0.835797
$977$	−9.49723			−0.303843			−0.151922	−	0.988393i	$-0.548546\pi$
$977$	−9.49723			−0.303843			−0.151922	+	0.988393i	$0.548546\pi$
$978$	6.77919	−	4.53703i	0.216775	−	0.145078i
$979$	6.09885	+	10.5635i	0.194920	+	0.337611i
$980$	−4.24763	+	0.614160i	−0.135686	+	0.0196186i
$981$	13.4236	−	32.5446i	0.428581	−	1.03907i
$982$	11.5603	−	20.0230i	0.368904	−	0.638961i
$983$	1.29375	−	2.24084i	0.0412642	−	0.0714717i	−0.844656	−	0.535310i	$-0.820195\pi$
$983$	1.29375	−	2.24084i	0.0412642	−	0.0714717i	0.885920	+	0.463838i	$0.153528\pi$
$984$	19.5032	−	13.0526i	0.621738	−	0.416103i
$985$	5.46243	+	9.46121i	0.174048	+	0.301459i
$986$	−2.43549	+	4.21839i	−0.0775618	+	0.134341i
$987$	−5.33659	−	38.4273i	−0.169866	−	1.22315i
$988$	10.9065	+	18.8906i	0.346982	+	0.600990i
$989$	3.02097	−	5.23247i	0.0960612	−	0.166383i
$990$	3.46374	+	4.50012i	0.110085	+	0.143023i
$991$	−18.2359	−	31.5855i	−0.579282	−	1.00335i	−0.995562	−	0.0941096i	$-0.970000\pi$
$991$	−18.2359	−	31.5855i	−0.579282	−	1.00335i	0.416280	−	0.909237i	$-0.363334\pi$
$992$	13.4514			0.427081
$993$	11.8934	+	5.85414i	0.377425	+	0.185775i
$994$	−4.99604	−	7.37533i	−0.158465	−	0.233931i
$995$	1.63900	−	2.83882i	0.0519597	−	0.0899968i
$996$	−0.0883663	−	1.33297i	−0.00279999	−	0.0422369i
$997$	27.0724	−	46.8909i	0.857393	−	1.48505i	−0.0170139	−	0.999855i	$-0.505416\pi$
$997$	27.0724	−	46.8909i	0.857393	−	1.48505i	0.874407	−	0.485193i	$-0.161251\pi$
$998$	5.33741	+	9.24466i	0.168953	+	0.292635i
$999$	41.5914	+	14.0146i	1.31589	+	0.443404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.7	yes	36
3.2	odd	2		945.2.l.c.226.12		36
7.4	even	3		315.2.k.c.256.12	yes	36
9.2	odd	6		945.2.k.c.856.7		36
9.7	even	3		315.2.k.c.16.12	✓	36
21.11	odd	6		945.2.k.c.361.7		36
63.11	odd	6		945.2.l.c.46.12		36
63.25	even	3	inner	315.2.l.c.151.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.12	✓	36	9.7	even	3
315.2.k.c.256.12	yes	36	7.4	even	3
315.2.l.c.121.7	yes	36	1.1	even	1	trivial
315.2.l.c.151.7	yes	36	63.25	even	3	inner
945.2.k.c.361.7		36	21.11	odd	6
945.2.k.c.856.7		36	9.2	odd	6
945.2.l.c.46.12		36	63.11	odd	6
945.2.l.c.226.12		36	3.2	odd	2

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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.17766 q^{2} +(1.55400 + 0.764908i) q^{3} -0.613115 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.83009 - 0.900802i) q^{6} +(-1.48383 - 2.19049i) q^{7} +3.07736 q^{8} +(1.82983 + 2.37733i) q^{9} +O(q^{10})\)	\(q-1.17766 q^{2} +(1.55400 + 0.764908i) q^{3} -0.613115 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.83009 - 0.900802i) q^{6} +(-1.48383 - 2.19049i) q^{7} +3.07736 q^{8} +(1.82983 + 2.37733i) q^{9} +(0.588830 + 1.01988i) q^{10} +(0.803681 - 1.39202i) q^{11} +(-0.952781 - 0.468976i) q^{12} +(2.48616 - 4.30615i) q^{13} +(1.74745 + 2.57965i) q^{14} +(-0.114571 - 1.72826i) q^{15} -2.39786 q^{16} +(0.876227 + 1.51767i) q^{17} +(-2.15492 - 2.79969i) q^{18} +(3.57754 - 6.19648i) q^{19} +(0.306558 + 0.530973i) q^{20} +(-0.630356 - 4.53901i) q^{21} +(-0.946464 + 1.63932i) q^{22} +(3.73875 + 6.47570i) q^{23} +(4.78222 + 2.35390i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.92785 + 5.07118i) q^{26} +(1.02512 + 5.09403i) q^{27} +(0.909761 + 1.34302i) q^{28} +(-1.18010 - 2.04400i) q^{29} +(0.134925 + 2.03530i) q^{30} -4.03840 q^{31} -3.33086 q^{32} +(2.31369 - 1.54845i) q^{33} +(-1.03190 - 1.78730i) q^{34} +(-1.15510 + 2.38028i) q^{35} +(-1.12190 - 1.45758i) q^{36} +(4.22323 - 7.31485i) q^{37} +(-4.21313 + 7.29735i) q^{38} +(7.15730 - 4.79008i) q^{39} +(-1.53868 - 2.66507i) q^{40} +(2.20143 - 3.81300i) q^{41} +(0.742346 + 5.34542i) q^{42} +(-0.404008 - 0.699762i) q^{43} +(-0.492749 + 0.853467i) q^{44} +(1.14391 - 2.77335i) q^{45} +(-4.40298 - 7.62618i) q^{46} +8.46599 q^{47} +(-3.72627 - 1.83414i) q^{48} +(-2.59648 + 6.50064i) q^{49} +(0.588830 - 1.01988i) q^{50} +(0.200780 + 3.02869i) q^{51} +(-1.52430 + 2.64017i) q^{52} +(1.44386 + 2.50083i) q^{53} +(-1.20724 - 5.99904i) q^{54} -1.60736 q^{55} +(-4.56629 - 6.74093i) q^{56} +(10.2992 - 6.89284i) q^{57} +(1.38976 + 2.40714i) q^{58} -13.3986 q^{59} +(0.0702450 + 1.05962i) q^{60} -10.8893 q^{61} +4.75587 q^{62} +(2.49235 - 7.53579i) q^{63} +8.71834 q^{64} -4.97231 q^{65} +(-2.72474 + 1.82355i) q^{66} -8.11941 q^{67} +(-0.537228 - 0.930506i) q^{68} +(0.856702 + 12.9230i) q^{69} +(1.36032 - 2.80316i) q^{70} -2.85904 q^{71} +(5.63106 + 7.31592i) q^{72} +(5.87110 + 10.1690i) q^{73} +(-4.97353 + 8.61441i) q^{74} +(-1.43943 + 0.963350i) q^{75} +(-2.19344 + 3.79916i) q^{76} +(-4.24173 + 0.305067i) q^{77} +(-8.42887 + 5.64109i) q^{78} +1.91775 q^{79} +(1.19893 + 2.07661i) q^{80} +(-2.30342 + 8.70024i) q^{81} +(-2.59254 + 4.49042i) q^{82} +(0.628986 + 1.08944i) q^{83} +(0.386481 + 2.78294i) q^{84} +(0.876227 - 1.51767i) q^{85} +(0.475784 + 0.824082i) q^{86} +(-0.270410 - 4.07904i) q^{87} +(2.47322 - 4.28374i) q^{88} +(-3.79432 + 6.57195i) q^{89} +(-1.34714 + 3.26606i) q^{90} +(-13.1216 + 0.943711i) q^{91} +(-2.29228 - 3.97035i) q^{92} +(-6.27568 - 3.08900i) q^{93} -9.97007 q^{94} -7.15508 q^{95} +(-5.17616 - 2.54780i) q^{96} +(5.89502 + 10.2105i) q^{97} +(3.05777 - 7.65555i) q^{98} +(4.77989 - 0.636540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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