LMFDB - Embedded newform 525.2.bm.a.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(131,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 12, 25]))

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

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

chi := DirichletCharacter("525.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bm (of order $30$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			131.2
Character	$\chi$	$=$	525.131
Dual form			525.2.bm.a.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.572271 + 2.69232i) q^{2} +(-1.59928 + 0.665065i) q^{3} +(-5.09402 - 2.26800i) q^{4} +(-1.14863 + 1.91850i) q^{5} +(-0.875350 - 4.68637i) q^{6} +(-2.63822 - 0.199474i) q^{7} +(5.78563 - 7.96324i) q^{8} +(2.11538 - 2.12725i) q^{9} +O(q^{10})$	\(q+(-0.572271 + 2.69232i) q^{2} +(-1.59928 + 0.665065i) q^{3} +(-5.09402 - 2.26800i) q^{4} +(-1.14863 + 1.91850i) q^{5} +(-0.875350 - 4.68637i) q^{6} +(-2.63822 - 0.199474i) q^{7} +(5.78563 - 7.96324i) q^{8} +(2.11538 - 2.12725i) q^{9} +(-4.50790 - 4.19039i) q^{10} +(1.80137 + 1.62196i) q^{11} +(9.65512 + 0.239312i) q^{12} +(-3.57571 - 1.16182i) q^{13} +(2.04682 - 6.98879i) q^{14} +(0.561050 - 3.83213i) q^{15} +(10.6664 + 11.8462i) q^{16} +(-0.0334659 + 0.318407i) q^{17} +(4.51667 + 6.91264i) q^{18} +(-1.50899 - 3.38925i) q^{19} +(10.2023 - 7.16778i) q^{20} +(4.35191 - 1.43558i) q^{21} +(-5.39772 + 3.92167i) q^{22} +(-1.53018 + 7.19893i) q^{23} +(-3.95676 + 16.5832i) q^{24} +(-2.36130 - 4.40730i) q^{25} +(5.17426 - 8.96209i) q^{26} +(-1.96832 + 4.80892i) q^{27} +(12.9867 + 6.99961i) q^{28} +(-1.77836 - 2.44771i) q^{29} +(9.99626 + 3.70355i) q^{30} +(1.66904 + 0.175423i) q^{31} +(-20.9491 + 12.0950i) q^{32} +(-3.95960 - 1.39594i) q^{33} +(-0.838102 - 0.272316i) q^{34} +(3.41303 - 4.83231i) q^{35} +(-15.6004 + 6.03856i) q^{36} +(3.29878 + 3.66367i) q^{37} +(9.98850 - 2.12312i) q^{38} +(6.49123 - 0.520010i) q^{39} +(8.63193 + 20.2466i) q^{40} +(0.116529 - 0.358640i) q^{41} +(1.37456 + 12.5383i) q^{42} +4.64302 q^{43} +(-5.49760 - 12.3478i) q^{44} +(1.65134 + 6.50177i) q^{45} +(-18.5062 - 8.23948i) q^{46} +(-0.345253 - 3.28487i) q^{47} +(-24.9370 - 11.8515i) q^{48} +(6.92042 + 1.05251i) q^{49} +(13.2172 - 3.83520i) q^{50} +(-0.158240 - 0.531477i) q^{51} +(15.5797 + 14.0280i) q^{52} +(3.32854 - 7.47603i) q^{53} +(-11.8208 - 8.05135i) q^{54} +(-5.18084 + 1.59290i) q^{55} +(-16.8522 + 19.8547i) q^{56} +(4.66736 + 4.41677i) q^{57} +(7.60772 - 3.38717i) q^{58} +(-5.07894 + 1.07956i) q^{59} +(-11.5493 + 18.2485i) q^{60} +(2.02265 - 9.51584i) q^{61} +(-1.42744 + 4.39319i) q^{62} +(-6.00516 + 5.19019i) q^{63} +(-10.7232 - 33.0026i) q^{64} +(6.33612 - 5.52550i) q^{65} +(6.02428 - 9.86167i) q^{66} +(0.940886 - 8.95194i) q^{67} +(0.892623 - 1.54607i) q^{68} +(-2.34058 - 12.5308i) q^{69} +(11.0570 + 11.9544i) q^{70} +(3.01192 + 4.14555i) q^{71} +(-4.70099 - 29.1527i) q^{72} +(-7.64180 - 6.88071i) q^{73} +(-11.7516 + 6.78477i) q^{74} +(6.70751 + 5.47808i) q^{75} +20.6873i q^{76} +(-4.42888 - 4.63842i) q^{77} +(-2.31471 + 17.7741i) q^{78} +(-0.285223 - 2.71372i) q^{79} +(-34.9787 + 6.85654i) q^{80} +(-0.0503637 - 8.99986i) q^{81} +(0.898887 + 0.518973i) q^{82} +(6.42420 + 4.66746i) q^{83} +(-25.4246 - 2.55730i) q^{84} +(-0.572424 - 0.429936i) q^{85} +(-2.65706 + 12.5005i) q^{86} +(4.47198 + 2.73183i) q^{87} +(23.3381 - 4.96067i) q^{88} +(-0.282427 - 0.0600317i) q^{89} +(-18.4499 + 0.725167i) q^{90} +(9.20176 + 3.77839i) q^{91} +(24.1220 - 33.2010i) q^{92} +(-2.78592 + 0.829468i) q^{93} +(9.04150 + 0.950300i) q^{94} +(8.23555 + 0.997993i) q^{95} +(25.4595 - 33.2758i) q^{96} +(0.984636 + 1.35523i) q^{97} +(-6.79406 + 18.0297i) q^{98} +(7.26089 - 0.400902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	$ 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.572271	+	2.69232i	−0.404657	+	1.90376i	0.0228326	+	0.999739i	$0.492732\pi$
$2$	−0.572271	+	2.69232i	−0.404657	+	1.90376i	−0.427489	+	0.904020i	$0.640602\pi$
$3$	−1.59928	+	0.665065i	−0.923343	+	0.383976i
$3$	−1.59928	+	0.665065i	−0.923343	+	0.383976i
$4$	−5.09402	−	2.26800i	−2.54701	−	1.13400i
$5$	−1.14863	+	1.91850i	−0.513683	+	0.857980i
$5$	−1.14863	+	1.91850i	−0.513683	+	0.857980i
$6$	−0.875350	−	4.68637i	−0.357360	−	1.91320i
$7$	−2.63822	−	0.199474i	−0.997154	−	0.0753940i
$7$	−2.63822	−	0.199474i	−0.997154	−	0.0753940i
$8$	5.78563	−	7.96324i	2.04553	−	2.81543i
$9$	2.11538	−	2.12725i	0.705126	−	0.709082i
$10$	−4.50790	−	4.19039i	−1.42552	−	1.32512i
$11$	1.80137	+	1.62196i	0.543134	+	0.489040i	0.894420	−	0.447228i	$-0.147589\pi$
$11$	1.80137	+	1.62196i	0.543134	+	0.489040i	−0.351286	+	0.936268i	$0.614256\pi$
$12$	9.65512	+	0.239312i	2.78719	+	0.0690834i
$13$	−3.57571	−	1.16182i	−0.991723	−	0.322230i	−0.232170	−	0.972675i	$-0.574582\pi$
$13$	−3.57571	−	1.16182i	−0.991723	−	0.322230i	−0.759553	+	0.650445i	$0.774582\pi$
$14$	2.04682	−	6.98879i	0.547037	−	1.86783i
$15$	0.561050	−	3.83213i	0.144863	−	0.989452i
$16$	10.6664	+	11.8462i	2.66660	+	2.96155i
$17$	−0.0334659	+	0.318407i	−0.00811667	+	0.0772249i	−0.997830	−	0.0658372i	$-0.979028\pi$
$17$	−0.0334659	+	0.318407i	−0.00811667	+	0.0772249i	0.989714	+	0.143062i	$0.0456949\pi$
$18$	4.51667	+	6.91264i	1.06459	+	1.62932i
$19$	−1.50899	−	3.38925i	−0.346186	−	0.777546i	−0.999786	−	0.0207059i	$-0.993409\pi$
$19$	−1.50899	−	3.38925i	−0.346186	−	0.777546i	0.653600	−	0.756840i	$-0.273258\pi$
$20$	10.2023	−	7.16778i	2.28131	−	1.60276i
$21$	4.35191	−	1.43558i	0.949665	−	0.313268i
$22$	−5.39772	+	3.92167i	−1.15080	+	0.836103i
$23$	−1.53018	+	7.19893i	−0.319065	+	1.50108i	0.467733	+	0.883870i	$0.345071\pi$
$23$	−1.53018	+	7.19893i	−0.319065	+	1.50108i	−0.786798	+	0.617211i	$0.788263\pi$
$24$	−3.95676	+	16.5832i	−0.807669	+	3.38504i
$25$	−2.36130	−	4.40730i	−0.472259	−	0.881460i
$26$	5.17426	−	8.96209i	1.01476	−	1.75761i
$27$	−1.96832	+	4.80892i	−0.378803	+	0.925478i
$28$	12.9867	+	6.99961i	2.45426	+	1.32280i
$29$	−1.77836	−	2.44771i	−0.330234	−	0.454527i	0.611324	−	0.791381i	$-0.290637\pi$
$29$	−1.77836	−	2.44771i	−0.330234	−	0.454527i	−0.941557	+	0.336853i	$0.890637\pi$
$30$	9.99626	+	3.70355i	1.82506	+	0.676172i
$31$	1.66904	+	0.175423i	0.299768	+	0.0315069i	0.253218	−	0.967409i	$-0.418511\pi$
$31$	1.66904	+	0.175423i	0.299768	+	0.0315069i	0.0465493	+	0.998916i	$0.485178\pi$
$32$	−20.9491	+	12.0950i	−3.70332	+	2.13811i
$33$	−3.95960	−	1.39594i	−0.689278	−	0.243001i
$34$	−0.838102	−	0.272316i	−0.143733	−	0.0467018i
$35$	3.41303	−	4.83231i	0.576908	−	0.816809i
$36$	−15.6004	+	6.03856i	−2.60006	+	1.00643i
$37$	3.29878	+	3.66367i	0.542316	+	0.602303i	0.950549	−	0.310575i	$-0.100521\pi$
$37$	3.29878	+	3.66367i	0.542316	+	0.602303i	−0.408233	+	0.912878i	$0.633855\pi$
$38$	9.98850	−	2.12312i	1.62035	−	0.344416i
$39$	6.49123	−	0.520010i	1.03943	−	0.0832682i
$40$	8.63193	+	20.2466i	1.36483	+	3.20126i
$41$	0.116529	−	0.358640i	0.0181988	−	0.0560101i	−0.941545	−	0.336888i	$-0.890626\pi$
$41$	0.116529	−	0.358640i	0.0181988	−	0.0560101i	0.959743	+	0.280878i	$0.0906256\pi$
$42$	1.37456	+	12.5383i	0.212099	+	1.93470i
$43$	4.64302			0.708053			0.354027	−	0.935235i	$-0.384812\pi$
$43$	4.64302			0.708053			0.354027	+	0.935235i	$0.384812\pi$
$44$	−5.49760	−	12.3478i	−0.828794	−	1.86150i
$45$	1.65134	+	6.50177i	0.246167	+	0.969227i
$46$	−18.5062	−	8.23948i	−2.72859	−	1.21484i
$47$	−0.345253	−	3.28487i	−0.0503604	−	0.479147i	−0.990415	−	0.138123i	$-0.955893\pi$
$47$	−0.345253	−	3.28487i	−0.0503604	−	0.479147i	0.940055	−	0.341024i	$-0.110774\pi$
$48$	−24.9370	−	11.8515i	−3.59935	−	1.71062i
$49$	6.92042	+	1.05251i	0.988632	+	0.150359i
$50$	13.2172	−	3.83520i	1.86919	−	0.542379i
$51$	−0.158240	−	0.531477i	−0.0221580	−	0.0744217i
$52$	15.5797	+	14.0280i	2.16052	+	1.94534i
$53$	3.32854	−	7.47603i	0.457211	−	1.02691i	−0.526993	−	0.849870i	$-0.676681\pi$
$53$	3.32854	−	7.47603i	0.457211	−	1.02691i	0.984203	−	0.177042i	$-0.0566528\pi$
$54$	−11.8208	−	8.05135i	−1.60860	−	1.09565i
$55$	−5.18084	+	1.59290i	−0.698585	+	0.214786i
$56$	−16.8522	+	19.8547i	−2.25197	+	2.65320i
$57$	4.66736	+	4.41677i	0.618207	+	0.585015i
$58$	7.60772	−	3.38717i	0.998942	−	0.444758i
$59$	−5.07894	+	1.07956i	−0.661222	+	0.140547i	−0.526286	−	0.850307i	$-0.676416\pi$
$59$	−5.07894	+	1.07956i	−0.661222	+	0.140547i	−0.134935	+	0.990854i	$0.543083\pi$
$60$	−11.5493	+	18.2485i	−1.49101	+	2.35587i
$61$	2.02265	−	9.51584i	0.258974	−	1.21838i	−0.635798	−	0.771856i	$-0.719329\pi$
$61$	2.02265	−	9.51584i	0.258974	−	1.21838i	0.894772	−	0.446523i	$-0.147338\pi$
$62$	−1.42744	+	4.39319i	−0.181284	+	0.557936i
$63$	−6.00516	+	5.19019i	−0.756579	+	0.653902i
$64$	−10.7232	−	33.0026i	−1.34040	−	4.12532i
$65$	6.33612	−	5.52550i	0.785899	−	0.685354i
$66$	6.02428	−	9.86167i	0.741537	−	1.21389i
$67$	0.940886	−	8.95194i	0.114948	−	1.09365i	−0.773221	−	0.634136i	$-0.781356\pi$
$67$	0.940886	−	8.95194i	0.114948	−	1.09365i	0.888169	−	0.459517i	$-0.151977\pi$
$68$	0.892623	−	1.54607i	0.108246	−	0.187488i
$69$	−2.34058	−	12.5308i	−0.281772	−	1.50853i
$70$	11.0570	+	11.9544i	1.32156	+	1.42882i
$71$	3.01192	+	4.14555i	0.357449	+	0.491987i	0.949436	−	0.313961i	$-0.101656\pi$
$71$	3.01192	+	4.14555i	0.357449	+	0.491987i	−0.591987	+	0.805948i	$0.701656\pi$
$72$	−4.70099	−	29.1527i	−0.554017	−	3.43568i
$73$	−7.64180	−	6.88071i	−0.894405	−	0.805326i	0.0872113	−	0.996190i	$-0.472204\pi$
$73$	−7.64180	−	6.88071i	−0.894405	−	0.805326i	−0.981617	+	0.190864i	$0.938871\pi$
$74$	−11.7516	+	6.78477i	−1.36609	+	0.788714i
$75$	6.70751	+	5.47808i	0.774516	+	0.632554i
$76$			20.6873i			2.37299i
$77$	−4.42888	−	4.63842i	−0.504717	−	0.528597i
$78$	−2.31471	+	17.7741i	−0.262089	+	2.01252i
$79$	−0.285223	−	2.71372i	−0.0320901	−	0.305317i	−0.998781	−	0.0493690i	$-0.984279\pi$
$79$	−0.285223	−	2.71372i	−0.0320901	−	0.305317i	0.966690	−	0.255948i	$-0.0823877\pi$
$80$	−34.9787	+	6.85654i	−3.91074	+	0.766585i
$81$	−0.0503637	−	8.99986i	−0.00559596	−	0.999984i
$82$	0.898887	+	0.518973i	0.0992655	+	0.0573110i
$83$	6.42420	+	4.66746i	0.705148	+	0.512320i	0.881605	−	0.471988i	$-0.156464\pi$
$83$	6.42420	+	4.66746i	0.705148	+	0.512320i	−0.176457	+	0.984308i	$0.556464\pi$
$84$	−25.4246	−	2.55730i	−2.77405	−	0.279024i
$85$	−0.572424	−	0.429936i	−0.0620881	−	0.0466331i
$86$	−2.65706	+	12.5005i	−0.286518	+	1.34796i
$87$	4.47198	+	2.73183i	0.479446	+	0.292883i
$88$	23.3381	−	4.96067i	2.48785	−	0.528809i
$89$	−0.282427	−	0.0600317i	−0.0299372	−	0.00636334i	0.192919	−	0.981215i	$-0.438205\pi$
$89$	−0.282427	−	0.0600317i	−0.0299372	−	0.00636334i	−0.222856	+	0.974851i	$0.571538\pi$
$90$	−18.4499	+	0.725167i	−1.94479	+	0.0764393i
$91$	9.20176	+	3.77839i	0.964606	+	0.396083i
$92$	24.1220	−	33.2010i	2.51489	−	3.46145i
$93$	−2.78592	+	0.829468i	−0.288886	+	0.0860118i
$94$	9.04150	+	0.950300i	0.932560	+	0.0980160i
$95$	8.23555	+	0.997993i	0.844949	+	0.102392i
$96$	25.4595	−	33.2758i	2.59845	−	3.39620i
$97$	0.984636	+	1.35523i	0.0999746	+	0.137603i	0.856073	−	0.516854i	$-0.172897\pi$
$97$	0.984636	+	1.35523i	0.0999746	+	0.137603i	−0.756099	+	0.654457i	$0.772897\pi$
$98$	−6.79406	+	18.0297i	−0.686303	+	1.82127i
$99$	7.26089	−	0.400902i	0.729747	−	0.0402922i
$100$	2.03272	+	27.8063i	0.203272	+	2.78063i
$101$	−4.65695	−	8.06607i	−0.463384	−	0.802604i	0.535743	−	0.844381i	$-0.320032\pi$
$101$	−4.65695	−	8.06607i	−0.463384	−	0.802604i	−0.999127	+	0.0417767i	$0.986698\pi$
$102$	1.52147	−	0.121884i	0.150647	−	0.0120683i
$103$	−15.9043	+	1.67161i	−1.56709	+	0.164708i	−0.847921	−	0.530123i	$-0.822146\pi$
$103$	−15.9043	+	1.67161i	−1.56709	+	0.164708i	−0.719173	+	0.694831i	$0.755479\pi$
$104$	−29.9396	+	21.7524i	−2.93581	+	2.13299i
$105$	−2.24458	+	9.99809i	−0.219049	+	0.975714i
$106$	18.2231	+	13.2398i	1.76998	+	1.28597i
$107$	17.0026	+	9.81647i	1.64371	+	0.948994i	0.979500	+	0.201443i	$0.0645631\pi$
$107$	17.0026	+	9.81647i	1.64371	+	0.948994i	0.664205	+	0.747551i	$0.268770\pi$
$108$	20.9333	−	20.0326i	2.01431	−	1.92764i
$109$	9.97583	−	2.12043i	0.955512	−	0.203100i	0.296331	−	0.955085i	$-0.404237\pi$
$109$	9.97583	−	2.12043i	0.955512	−	0.203100i	0.659180	+	0.751985i	$0.270903\pi$
$110$	−1.32375	−	14.8601i	−0.126214	−	1.41685i
$111$	−7.71225	−	3.66532i	−0.732014	−	0.347897i
$112$	−25.7773	−	33.3806i	−2.43572	−	3.15417i
$113$	−16.5358	−	5.37282i	−1.55556	−	0.505432i	−0.599943	−	0.800043i	$-0.704810\pi$
$113$	−16.5358	−	5.37282i	−1.55556	−	0.505432i	−0.955617	+	0.294611i	$0.904810\pi$
$114$	−14.5624	+	10.0385i	−1.36389	+	0.940188i
$115$	−12.0535	−	11.2046i	−1.12400	−	1.04483i
$116$	3.50760	+	16.5020i	0.325673	+	1.53217i
$117$	−10.0354	+	5.14873i	−0.927777	+	0.476001i
$118$		−	14.2919i		−	1.31568i
$119$	0.151804	−	0.833351i	0.0139159	−	0.0763932i
$120$	−27.2701	−	26.6391i	−2.48941	−	2.43180i
$121$	−0.535636	−	5.09623i	−0.0486942	−	0.463294i
$122$	24.4622	+	10.8913i	2.21470	+	0.986050i
$123$	0.0521564	+	0.651064i	0.00470278	+	0.0587044i
$124$	−8.10424	−	4.67898i	−0.727782	−	0.420185i
$125$	11.1677	+	0.532209i	0.998866	+	0.0476022i
$126$	−10.5371	−	19.1380i	−0.938718	−	1.70495i
$127$	−1.37819	−	4.24163i	−0.122294	−	0.376383i	0.871104	−	0.491099i	$-0.163405\pi$
$127$	−1.37819	−	4.24163i	−0.122294	−	0.376383i	−0.993398	+	0.114715i	$0.963405\pi$
$128$	46.8751	−	4.92678i	4.14322	−	0.435470i
$129$	−7.42547	+	3.08791i	−0.653776	+	0.271875i
$130$	11.2505	+	20.2210i	0.986731	+	1.77350i
$131$	−1.52548	+	0.679188i	−0.133282	+	0.0593410i	−0.472294	−	0.881441i	$-0.656574\pi$
$131$	−1.52548	+	0.679188i	−0.133282	+	0.0593410i	0.339012	+	0.940782i	$0.389907\pi$
$132$	17.0043	+	16.0913i	1.48003	+	1.40057i
$133$	3.30498	+	9.24258i	0.286578	+	0.801434i
$134$	23.5631	+	7.65610i	2.03554	+	0.661386i
$135$	−6.96506	−	9.29989i	−0.599457	−	0.800407i
$136$	2.34193	+	2.10868i	0.200818	+	0.180818i
$137$	−3.23406	−	15.2151i	−0.276304	−	1.29991i	−0.869132	−	0.494580i	$-0.835322\pi$
$137$	−3.23406	−	15.2151i	−0.276304	−	1.29991i	0.592828	−	0.805329i	$-0.298012\pi$
$138$	35.0763	+	0.869401i	2.98589	+	0.0740083i
$139$	13.1100	−	4.25968i	1.11197	−	0.361301i	0.305273	−	0.952265i	$-0.401252\pi$
$139$	13.1100	−	4.25968i	1.11197	−	0.361301i	0.806698	+	0.590963i	$0.201252\pi$
$140$	−28.3457	+	16.8751i	−2.39565	+	1.42621i
$141$	2.73681	+	5.02380i	0.230481	+	0.423080i
$142$	−12.8848	+	5.73668i	−1.08127	+	0.481412i
$143$	−4.55675	−	7.89253i	−0.381055	−	0.660006i
$144$	47.7632	+	2.36918i	3.98027	+	0.197431i
$145$	6.73861	−	0.600281i	0.559611	−	0.0498506i
$146$	22.8983	−	16.6366i	1.89507	−	1.37685i
$147$	−11.7677	+	2.91927i	−0.970580	+	0.240778i
$148$	−8.49484	−	26.1444i	−0.698272	−	2.14906i
$149$	−3.39031	−	1.95740i	−0.277745	−	0.160356i	0.354657	−	0.934996i	$-0.384598\pi$
$149$	−3.39031	−	1.95740i	−0.277745	−	0.160356i	−0.632402	+	0.774640i	$0.717931\pi$
$150$	−18.5873	+	14.9238i	−1.51764	+	1.21853i
$151$	1.66666	+	2.88675i	0.135631	+	0.234920i	0.925838	−	0.377920i	$-0.123360\pi$
$151$	1.66666	+	2.88675i	0.135631	+	0.234920i	−0.790207	+	0.612840i	$0.790027\pi$
$152$	−35.7198	−	7.59248i	−2.89726	−	0.615832i
$153$	0.606537	+	0.744740i	0.0490356	+	0.0602087i
$154$	15.0226	−	9.26953i	1.21056	−	0.746960i
$155$	−2.25365	+	3.00055i	−0.181018	+	0.241010i
$156$	−34.2458	−	12.0732i	−2.74186	−	0.966629i
$157$	5.91188	−	3.41322i	0.471819	−	0.272405i	−0.245182	−	0.969477i	$-0.578848\pi$
$157$	5.91188	−	3.41322i	0.471819	−	0.272405i	0.717001	+	0.697072i	$0.245514\pi$
$158$	7.46944	+	0.785069i	0.594236	+	0.0624568i
$159$	−0.351216	+	14.1699i	−0.0278533	+	1.12375i
$160$	0.858564	−	54.0837i	0.0678754	−	4.27569i
$161$	5.47295	−	18.6871i	0.431329	−	1.47275i
$162$	24.2593	+	5.01476i	1.90599	+	0.393997i
$163$	−12.6735	−	14.0754i	−0.992666	−	1.10247i	−0.994736	−	0.102469i	$-0.967326\pi$
$163$	−12.6735	−	14.0754i	−0.992666	−	1.10247i	0.00207064	−	0.999998i	$-0.499341\pi$
$164$	−1.40700	+	1.56263i	−0.109868	+	0.122021i
$165$	7.22623	−	5.99308i	0.562561	−	0.466561i
$166$	−16.2427	+	14.6250i	−1.26068	+	1.13512i
$167$	−7.02180	−	5.10164i	−0.543364	−	0.394777i	0.281969	−	0.959423i	$-0.409012\pi$
$167$	−7.02180	−	5.10164i	−0.543364	−	0.394777i	−0.825333	+	0.564647i	$0.809012\pi$
$168$	13.7467	−	42.9610i	1.06058	−	3.31451i
$169$	0.918647	+	0.667436i	0.0706652	+	0.0513413i
$170$	1.48511	−	1.29511i	0.113903	−	0.0993303i
$171$	−10.4018	−	3.95954i	−0.795449	−	0.302793i
$172$	−23.6516	−	10.5304i	−1.80342	−	0.802933i
$173$	9.67702	+	2.05691i	0.735730	+	0.156384i	0.560513	−	0.828146i	$-0.310604\pi$
$173$	9.67702	+	2.05691i	0.735730	+	0.156384i	0.175217	+	0.984530i	$0.443937\pi$
$174$	−9.91416	+	10.4767i	−0.751590	+	0.794233i
$175$	5.35048	+	12.0984i	0.404458	+	0.914556i
$176$			38.6399i			2.91259i
$177$	7.40465	−	5.10434i	0.556568	−	0.383666i
$178$	0.323249	−	0.726030i	0.0242286	−	0.0544182i
$179$	2.32564	−	5.22347i	0.173827	−	0.390421i	−0.805532	−	0.592553i	$-0.798120\pi$
$179$	2.32564	−	5.22347i	0.173827	−	0.390421i	0.979358	+	0.202132i	$0.0647869\pi$
$180$	6.33408	−	36.8654i	0.472115	−	2.74778i
$181$	−13.1624	+	18.1165i	−0.978357	+	1.34659i	−0.0406466	+	0.999174i	$0.512942\pi$
$181$	−13.1624	+	18.1165i	−0.978357	+	1.34659i	−0.937710	+	0.347419i	$0.887058\pi$
$182$	−15.4385	+	22.6118i	−1.14438	+	1.67610i
$183$	3.09387	+	16.5637i	0.228705	+	1.22442i
$184$	48.4737	+	53.8355i	3.57353	+	3.96881i
$185$	−10.8178	+	2.12052i	−0.795343	+	0.155903i
$186$	−0.638895	−	7.97527i	−0.0468461	−	0.584776i
$187$	−0.576728	+	0.519288i	−0.0421745	+	0.0379741i
$188$	−5.69136	+	17.5162i	−0.415085	+	1.27750i
$189$	6.15211	−	12.2944i	0.447500	−	0.894284i
$190$	−7.39988	+	21.6016i	−0.536844	+	1.56715i
$191$	−14.1825	+	12.7699i	−1.02621	+	0.924001i	−0.997140	−	0.0755769i	$-0.975920\pi$
$191$	−14.1825	+	12.7699i	−1.02621	+	0.924001i	−0.0290666	+	0.999577i	$0.509253\pi$
$192$	39.0982	+	45.6486i	2.82167	+	3.29441i
$193$	−2.41529	−	4.18340i	−0.173856	−	0.301128i	0.765909	−	0.642949i	$-0.222289\pi$
$193$	−2.41529	−	4.18340i	−0.173856	−	0.301128i	−0.939765	+	0.341822i	$0.888956\pi$
$194$	−4.21221	+	1.87540i	−0.302419	+	0.134646i
$195$	−6.45839	+	13.0507i	−0.462495	+	0.934583i
$196$	−32.8656	−	21.0570i	−2.34755	−	1.50407i
$197$	2.68619	+	3.69722i	0.191383	+	0.263416i	0.893915	−	0.448236i	$-0.147947\pi$
$197$	2.68619	+	3.69722i	0.191383	+	0.263416i	−0.702533	+	0.711652i	$0.747947\pi$
$198$	−3.07584	+	19.7781i	−0.218590	+	1.40557i
$199$	−20.7738	+	11.9938i	−1.47262	+	0.850216i	−0.999526	−	0.0307967i	$-0.990196\pi$
$199$	−20.7738	+	11.9938i	−1.47262	+	0.850216i	−0.473092	+	0.881013i	$0.656862\pi$
$200$	−48.7579	−	6.69544i	−3.44771	−	0.473439i
$201$	4.44888	+	14.9424i	0.313800	+	1.05395i
$202$	24.3815	−	7.92203i	1.71548	−	0.557392i
$203$	4.20346	+	6.81232i	0.295025	+	0.478131i
$204$	−0.399315	+	3.06624i	−0.0279577	+	0.214680i
$205$	0.554202	+	0.635506i	0.0387071	+	0.0443856i
$206$	4.60104	−	43.7760i	0.320570	−	3.05002i
$207$	12.0770	+	18.4835i	0.839409	+	1.28469i
$208$	−24.3767	−	54.7510i	−1.69022	−	3.79630i
$209$	2.77898	−	8.55281i	0.192226	−	0.591610i
$210$	−25.6336	−	11.7648i	−1.76889	−	0.811846i
$211$	0.639885	+	1.96936i	0.0440515	+	0.135577i	0.970663	−	0.240443i	$-0.0772926\pi$
$211$	0.639885	+	1.96936i	0.0440515	+	0.135577i	−0.926612	+	0.376019i	$0.877293\pi$
$212$	−33.9113	+	30.5339i	−2.32904	+	2.09708i
$213$	−7.57396	−	4.62677i	−0.518959	−	0.317021i
$214$	−36.1592	+	40.1589i	−2.47179	+	2.74520i
$215$	−5.33311	+	8.90763i	−0.363715	+	0.607495i
$216$	26.9066	+	43.4968i	1.83076	+	2.95958i
$217$	−4.36829	−	0.795733i	−0.296539	−	0.0540179i
$218$			28.0716i			1.90125i
$219$	16.7975	+	5.92187i	1.13507	+	0.400163i
$220$	30.0040	+	3.63592i	2.02287	+	0.245134i
$221$	0.489595	−	1.09965i	0.0329337	−	0.0739703i
$222$	14.2817	−	18.6663i	0.958526	−	1.25280i
$223$	−22.9932	+	7.47093i	−1.53974	+	0.500291i	−0.951304	−	0.308256i	$-0.900255\pi$
$223$	−22.9932	+	7.47093i	−1.53974	+	0.500291i	−0.588433	+	0.808546i	$0.700255\pi$
$224$	57.6811	−	27.7305i	3.85398	−	1.85282i
$225$	−14.3704	−	4.30004i	−0.958030	−	0.286669i
$226$	23.9283	−	41.4451i	1.59169	−	2.75689i
$227$	8.68821	−	9.64923i	0.576657	−	0.640442i	−0.382285	−	0.924044i	$-0.624863\pi$
$227$	8.68821	−	9.64923i	0.576657	−	0.640442i	0.958942	+	0.283602i	$0.0915295\pi$
$228$	−13.7584	−	33.0847i	−0.911171	−	2.19109i
$229$	−3.36808	+	0.353999i	−0.222569	+	0.0233929i	−0.215156	−	0.976580i	$-0.569026\pi$
$229$	−3.36808	+	0.353999i	−0.222569	+	0.0233929i	−0.00741237	+	0.999973i	$0.502359\pi$
$230$	37.0642	−	26.0400i	2.44394	−	1.71703i
$231$	10.1679	+	4.47263i	0.668995	+	0.294277i
$232$	−29.7806			−1.95519
$233$	−5.46491	−	12.2744i	−0.358018	−	0.804122i	−0.999321	−	0.0368344i	$-0.988273\pi$
$233$	−5.46491	−	12.2744i	−0.358018	−	0.804122i	0.641303	−	0.767288i	$-0.278394\pi$
$234$	−8.11906	−	29.9651i	−0.530760	−	1.95888i
$235$	6.69859	+	3.11073i	0.436968	+	0.202922i
$236$	28.3207	+	6.01974i	1.84352	+	0.391852i
$237$	2.26095	+	4.15030i	0.146865	+	0.269591i
$238$	2.15678	+	0.885608i	0.139803	+	0.0574055i
$239$	−19.2675	+	6.26040i	−1.24631	+	0.404952i	−0.856598	−	0.515984i	$-0.827426\pi$
$239$	−19.2675	+	6.26040i	−1.24631	+	0.404952i	−0.389715	+	0.920936i	$0.627426\pi$
$240$	51.3806	−	34.2286i	3.31661	−	2.20945i
$241$	−2.27791	−	10.7167i	−0.146733	−	0.690326i	−0.988591	−	0.150626i	$-0.951871\pi$
$241$	−2.27791	−	10.7167i	−0.146733	−	0.690326i	0.841857	−	0.539700i	$-0.181462\pi$
$242$	14.0272	+	1.47432i	0.901705	+	0.0947730i
$243$	6.06604	+	14.3598i	0.389137	+	0.921180i
$244$	−31.8854	+	43.8865i	−2.04125	+	2.80954i
$245$	−9.96825	+	12.0679i	−0.636848	+	0.770989i
$246$	−1.78272	−	0.232163i	−0.113662	−	0.0148022i
$247$	1.45802	+	13.8721i	0.0927715	+	0.882662i
$248$	11.0534	−	12.2760i	0.701889	−	0.779527i
$249$	−13.3782	−	3.19204i	−0.847812	−	0.202288i
$250$	−7.82381	+	29.7624i	−0.494821	+	1.88234i
$251$	−25.4347			−1.60542			−0.802712	−	0.596367i	$-0.796610\pi$
$251$	−25.4347			−1.60542			−0.802712	+	0.596367i	$0.796610\pi$
$252$	42.3618	−	12.8192i	2.66854	−	0.807533i
$253$	−14.4328	+	10.4860i	−0.907383	+	0.659252i
$254$	12.2085	−	1.28317i	0.766031	−	0.0805131i
$255$	1.20140	+	0.306888i	0.0752346	+	0.0192181i
$256$	−6.30634	+	60.0008i	−0.394146	+	3.75005i
$257$	10.7255	−	18.5772i	0.669041	−	1.15881i	−0.309132	−	0.951019i	$-0.600038\pi$
$257$	10.7255	−	18.5772i	0.669041	−	1.15881i	0.978173	−	0.207794i	$-0.0666283\pi$
$258$	−4.06426	−	21.7589i	−0.253030	−	1.35465i
$259$	−7.97211	−	10.3236i	−0.495363	−	0.641476i
$260$	−44.8081	+	13.7767i	−2.77888	+	0.854393i
$261$	−8.96878	−	1.39480i	−0.555154	−	0.0863361i
$262$	−0.955605	−	4.49577i	−0.0590375	−	0.277750i
$263$	0.616923	+	2.90239i	0.0380411	+	0.178969i	0.993066	−	0.117555i	$-0.0375057\pi$
$263$	0.616923	+	2.90239i	0.0380411	+	0.178969i	−0.955025	+	0.296524i	$0.904172\pi$
$264$	−34.0250	+	23.4549i	−2.09409	+	1.44355i
$265$	10.5195	+	14.9730i	0.646208	+	0.919785i
$266$	−26.7754	+	3.60882i	−1.64170	+	0.221271i
$267$	0.491604	−	0.0918249i	0.0300857	−	0.00561959i
$268$	−25.0959	+	43.4674i	−1.53298	+	2.65519i
$269$	1.67201	−	15.9081i	0.101944	−	0.969936i	−0.817291	−	0.576226i	$-0.804525\pi$
$269$	1.67201	−	15.9081i	0.101944	−	0.969936i	0.919235	−	0.393710i	$-0.128808\pi$
$270$	29.0242	−	13.4301i	1.76636	−	0.817331i
$271$	13.9532	−	1.46654i	0.847597	−	0.0890860i	0.329235	−	0.944248i	$-0.393209\pi$
$271$	13.9532	−	1.46654i	0.847597	−	0.0890860i	0.518361	+	0.855162i	$0.326542\pi$
$272$	−4.12887	+	2.99980i	−0.250350	+	0.181890i
$273$	−17.2290	+	0.0770702i	−1.04275	+	0.00466450i
$274$	42.8146			2.58652
$275$	2.89490	−	11.7691i	0.174569	−	0.709704i
$276$	−16.4969	+	69.1403i	−0.992994	+	4.16176i
$277$	2.93508	−	3.25973i	0.176352	−	0.195858i	−0.648488	−	0.761225i	$-0.724598\pi$
$277$	2.93508	−	3.25973i	0.176352	−	0.195858i	0.824840	+	0.565366i	$0.191265\pi$
$278$	3.96599	+	37.7339i	0.237864	+	2.26313i
$279$	3.90381	−	3.17937i	0.233715	−	0.190344i
$280$	−18.7343	−	55.1367i	−1.11959	−	3.29505i
$281$	−17.7630	+	24.4487i	−1.05965	+	1.45849i	−0.179527	+	0.983753i	$0.557457\pi$
$281$	−17.7630	+	24.4487i	−1.05965	+	1.45849i	−0.880128	+	0.474736i	$0.842543\pi$
$282$	−15.0919	+	4.49339i	−0.898708	+	0.267578i
$283$	8.25090	+	0.867205i	0.490465	+	0.0515500i	0.346533	−	0.938038i	$-0.387359\pi$
$283$	8.25090	+	0.867205i	0.490465	+	0.0515500i	0.143932	+	0.989588i	$0.454025\pi$
$284$	−5.94065	−	27.9486i	−0.352513	−	1.65844i
$285$	−13.8347	+	3.88111i	−0.819494	+	0.229897i
$286$	23.8569	−	7.75158i	1.41069	−	0.458361i
$287$	−0.378969	+	0.922926i	−0.0223698	+	0.0544786i
$288$	−18.5863	+	70.1495i	−1.09521	+	4.13360i
$289$	16.5282	+	3.51319i	0.972250	+	0.206658i
$290$	−2.24016	+	18.4860i	−0.131547	+	1.08554i
$291$	−2.47603	−	1.51255i	−0.145147	−	0.0886672i
$292$	23.3220	+	52.3821i	1.36482	+	3.06543i
$293$	−2.18913			−0.127890			−0.0639452	−	0.997953i	$-0.520368\pi$
$293$	−2.18913			−0.127890			−0.0639452	+	0.997953i	$0.520368\pi$
$294$	−1.12534	−	33.3530i	−0.0656309	−	1.94518i
$295$	3.76268	−	10.9840i	0.219072	−	0.639511i
$296$	48.2602	−	5.07235i	2.80507	−	0.294824i
$297$	−11.3456	+	5.47012i	−0.658336	+	0.317408i
$298$	7.21012	−	8.00765i	0.417671	−	0.463870i
$299$	13.8353	−	23.9635i	0.800117	−	1.38584i
$300$	−21.7439	−	43.1181i	−1.25538	−	2.48942i
$301$	−12.2493	−	0.926159i	−0.706038	−	0.0533829i
$302$	−8.72584	+	2.83520i	−0.502115	+	0.163147i
$303$	12.8122	+	9.80271i	0.736043	+	0.563151i
$304$	24.0543	−	54.0268i	1.37961	−	3.09865i
$305$	15.9329	+	14.8107i	0.912314	+	0.848056i
$306$	−2.35218	+	1.20680i	−0.134465	+	0.0689881i
$307$		−	19.0400i		−	1.08667i	−0.839516	−	0.543334i	$-0.817162\pi$
$307$		−	19.0400i		−	1.08667i	0.839516	−	0.543334i	$-0.182838\pi$
$308$	12.0408	+	33.6729i	0.686089	+	1.91869i
$309$	24.3236	−	13.2507i	1.38372	−	0.753808i
$310$	−6.78875	−	7.78469i	−0.385575	−	0.442141i
$311$	−10.6608	+	11.8400i	−0.604518	+	0.671386i	−0.965263	−	0.261279i	$-0.915856\pi$
$311$	−10.6608	+	11.8400i	−0.604518	+	0.671386i	0.360745	+	0.932664i	$0.382522\pi$
$312$	33.4149	−	54.6998i	1.89175	−	3.09677i
$313$	2.25169	−	2.02743i	0.127273	−	0.114597i	−0.603036	−	0.797714i	$-0.706043\pi$
$313$	2.25169	−	2.02743i	0.127273	−	0.114597i	0.730309	+	0.683117i	$0.239376\pi$
$314$	5.80631	+	17.8700i	0.327669	+	1.00846i
$315$	−3.05967	−	17.4825i	−0.172393	−	0.985028i
$316$	−4.70179	+	14.4706i	−0.264496	+	0.814036i
$317$	−3.81876	−	8.57709i	−0.214483	−	0.481737i	0.773978	−	0.633213i	$-0.218264\pi$
$317$	−3.81876	−	8.57709i	−0.214483	−	0.481737i	−0.988461	+	0.151476i	$0.951598\pi$
$318$	−37.9491	−	9.05463i	−2.12808	−	0.507759i
$319$	0.766594	−	7.29366i	0.0429210	−	0.408366i
$320$	75.6324	+	17.3353i	4.22798	+	0.969073i
$321$	−33.7205	−	4.39140i	−1.88209	−	0.245104i
$322$	47.1798	+	25.4291i	2.62923	+	1.41711i
$323$	1.12966	−	0.367048i	0.0628559	−	0.0204231i
$324$	−20.1552	+	45.9597i	−1.11973	+	2.55331i
$325$	3.32283	+	18.5026i	0.184317	+	1.02634i
$326$	45.1481	−	26.0663i	2.50052	−	1.44368i
$327$	−14.5439	+	10.0257i	−0.804280	+	0.554424i
$328$	−2.18174	−	3.00290i	−0.120466	−	0.165808i
$329$	0.255610	+	8.73507i	0.0140923	+	0.481580i
$330$	12.0000	+	22.8850i	0.660576	+	1.25978i
$331$	29.6265	−	13.1906i	1.62842	−	0.725019i	0.629760	−	0.776789i	$-0.283153\pi$
$331$	29.6265	−	13.1906i	1.62842	−	0.725019i	0.998659	+	0.0517703i	$0.0164864\pi$
$332$	−22.1392	−	38.3462i	−1.21505	−	2.10452i
$333$	14.7717	+	0.732713i	0.809484	+	0.0401524i
$334$	17.7536	−	15.9854i	0.971436	−	0.874685i
$335$	16.0936	+	12.0876i	0.879286	+	0.660414i
$336$	63.4253	+	36.2413i	3.46013	+	1.97712i
$337$	−3.21746	+	9.90233i	−0.175266	+	0.539414i	−0.999646	−	0.0266237i	$-0.991524\pi$
$337$	−3.21746	+	9.90233i	−0.175266	+	0.539414i	0.824379	+	0.566038i	$0.191524\pi$
$338$	−2.32267	+	2.09134i	−0.126337	+	0.113754i
$339$	30.0187	−	2.40478i	1.63039	−	0.130610i
$340$	1.94084	+	3.48836i	0.105257	+	0.189183i
$341$	2.72202	+	3.02311i	0.147406	+	0.163711i
$342$	16.6130	−	25.7392i	0.898330	−	1.39182i
$343$	−18.0477	−	4.15720i	−0.974482	−	0.224468i
$344$	26.8628	−	36.9734i	1.44834	−	1.99347i
$345$	26.7287	+	9.90281i	1.43903	+	0.533149i
$346$	−11.0757	+	24.8765i	−0.595436	+	1.33737i
$347$	−5.47548	+	12.2981i	−0.293939	+	0.660198i	−0.998791	−	0.0491565i	$-0.984347\pi$
$347$	−5.47548	+	12.2981i	−0.293939	+	0.660198i	0.704852	+	0.709354i	$0.251013\pi$
$348$	−16.5845	−	24.0585i	−0.889024	−	1.28967i
$349$		−	9.88518i		−	0.529142i	−0.964366	−	0.264571i	$-0.914770\pi$
$349$		−	9.88518i		−	0.529142i	0.964366	−	0.264571i	$-0.0852303\pi$
$350$	−35.6348	+	7.48163i	−1.90476	+	0.399910i
$351$	12.6252	−	14.9085i	0.673884	−	0.795756i
$352$	−57.3548	−	12.1911i	−3.05702	−	0.649790i
$353$	2.91100	+	1.29606i	0.154937	+	0.0689824i	0.482740	−	0.875764i	$-0.339642\pi$
$353$	2.91100	+	1.29606i	0.154937	+	0.0689824i	−0.327803	+	0.944746i	$0.606308\pi$
$354$	9.50508	+	22.8568i	0.505189	+	1.21482i
$355$	−11.4128	+	1.01667i	−0.605730	+	0.0539590i
$356$	1.30253	+	0.946347i	0.0690342	+	0.0501563i
$357$	0.311456	+	1.43372i	0.0164840	+	0.0758805i
$358$	12.7324	+	9.25062i	0.672927	+	0.488910i
$359$	20.4084	−	18.3758i	1.07711	−	0.969836i	0.0774806	−	0.996994i	$-0.475312\pi$
$359$	20.4084	−	18.3758i	1.07711	−	0.969836i	0.999631	+	0.0271581i	$0.00864576\pi$
$360$	61.3292	+	24.4668i	3.23233	+	1.28952i
$361$	3.50354	−	3.89108i	0.184397	−	0.204794i
$362$	−41.2431	−	45.8051i	−2.16769	−	2.40746i
$363$	4.24596	+	7.79406i	0.222855	+	0.409082i
$364$	−38.3045	−	40.1168i	−2.00770	−	2.10269i
$365$	21.9783	−	6.75741i	1.15039	−	0.353699i
$366$	−46.3653	−	1.14921i	−2.42355	−	0.0600702i
$367$	−22.4720	−	2.36191i	−1.17303	−	0.123290i	−0.502099	−	0.864810i	$-0.667439\pi$
$367$	−22.4720	−	2.36191i	−1.17303	−	0.123290i	−0.670931	+	0.741520i	$0.734105\pi$
$368$	−101.602	+	58.6597i	−5.29635	+	3.05785i
$369$	−0.516412	−	1.00654i	−0.0268834	−	0.0523986i
$370$	0.481617	−	30.3386i	0.0250381	−	1.57723i
$371$	−10.2727	+	19.0595i	−0.533332	+	0.989518i
$372$	16.0728	+	2.09315i	0.833334	+	0.108525i
$373$	−5.30946	−	1.12856i	−0.274914	−	0.0584347i	0.0683917	−	0.997659i	$-0.478213\pi$
$373$	−5.30946	−	1.12856i	−0.274914	−	0.0584347i	−0.343305	+	0.939224i	$0.611547\pi$
$374$	−1.06805	−	1.84991i	−0.0552274	−	0.0956566i
$375$	−18.2141	+	6.57608i	−0.940575	+	0.339587i
$376$	−28.1557	−	16.2557i	−1.45202	−	0.838323i
$377$	3.51512	+	10.8184i	0.181038	+	0.557177i
$378$	29.5797	+	23.5992i	1.52142	+	1.21381i
$379$	1.12309	−	0.815976i	0.0576895	−	0.0419139i	−0.558567	−	0.829460i	$-0.688649\pi$
$379$	1.12309	−	0.815976i	0.0576895	−	0.0419139i	0.616256	+	0.787546i	$0.288649\pi$
$380$	−39.6886	−	23.7620i	−2.03598	−	1.21897i
$381$	5.02506	+	5.86695i	0.257442	+	0.300573i
$382$	−26.2646	−	45.4916i	−1.34381	−	2.32755i
$383$	1.37859	−	0.613789i	0.0704428	−	0.0313631i	−0.371213	−	0.928548i	$-0.621058\pi$
$383$	1.37859	−	0.613789i	0.0704428	−	0.0313631i	0.441656	+	0.897185i	$0.354391\pi$
$384$	−71.6897	+	39.0543i	−3.65840	+	1.99298i
$385$	13.9860	−	3.16897i	0.712790	−	0.161506i
$386$	12.6453	−	4.10869i	0.643627	−	0.209127i
$387$	9.82173	−	9.87684i	0.499266	−	0.502068i
$388$	−1.94208	−	9.13675i	−0.0985939	−	0.463848i
$389$	−5.87847	−	5.29300i	−0.298050	−	0.268366i	0.506513	−	0.862232i	$-0.330934\pi$
$389$	−5.87847	−	5.29300i	−0.298050	−	0.268366i	−0.804564	+	0.593867i	$0.797601\pi$
$390$	−31.4409	−	24.8566i	−1.59207	−	1.25866i
$391$	−2.24098	−	0.728138i	−0.113331	−	0.0368235i
$392$	48.4204	−	49.0195i	2.44560	−	2.47586i
$393$	1.98796	−	2.10076i	0.100280	−	0.105969i
$394$	−11.4913	+	5.11627i	−0.578925	+	0.257754i
$395$	5.53389	+	2.56986i	0.278440	+	0.129304i
$396$	−37.8963	−	14.4255i	−1.90436	−	0.724910i
$397$	16.9055	−	1.77684i	0.848465	−	0.0891772i	0.329691	−	0.944089i	$-0.393055\pi$
$397$	16.9055	−	1.77684i	0.848465	−	0.0891772i	0.518774	+	0.854912i	$0.326389\pi$
$398$	−20.4029	−	62.7935i	−1.02270	−	3.14756i
$399$	−11.4325	−	12.5834i	−0.572341	−	0.629959i
$400$	27.0233	−	74.9824i	1.35117	−	3.74912i
$401$	−14.3499	−	8.28493i	−0.716601	−	0.413730i	0.0968994	−	0.995294i	$-0.469108\pi$
$401$	−14.3499	−	8.28493i	−0.716601	−	0.413730i	−0.813500	+	0.581564i	$0.802441\pi$
$402$	−42.7757	+	3.42674i	−2.13346	+	0.170910i
$403$	−5.76418	−	2.56638i	−0.287134	−	0.127840i
$404$	5.42871	+	51.6507i	0.270088	+	2.56972i
$405$	17.3241	+	10.2409i	0.860841	+	0.508874i
$406$	−20.7465	+	7.41857i	−1.02963	+	0.368178i
$407$			11.9501i			0.592345i
$408$	−5.14780	−	1.81483i	−0.254854	−	0.0898475i
$409$	−2.17196	−	10.2183i	−0.107396	−	0.505260i	−0.998659	−	0.0517726i	$-0.983513\pi$
$409$	−2.17196	−	10.2183i	−0.107396	−	0.505260i	0.891262	−	0.453488i	$-0.149820\pi$
$410$	−2.02814	+	1.12841i	−0.100163	+	0.0557281i
$411$	15.2912	+	22.1822i	0.754257	+	1.09417i
$412$	84.8078	+	27.5557i	4.17818	+	1.35757i
$413$	13.6147	−	1.83501i	0.669936	−	0.0902949i
$414$	−56.6749	+	21.9376i	−2.78542	+	1.07817i
$415$	−16.3336	+	6.96366i	−0.801783	+	0.341833i
$416$	88.9602	−	18.9091i	4.36163	−	0.927094i
$417$	−18.1335	+	15.5314i	−0.888000	+	0.760575i
$418$	21.4366	+	12.3764i	1.04850	+	0.605351i
$419$	8.05076	+	5.84922i	0.393305	+	0.285753i	0.766809	−	0.641876i	$-0.221844\pi$
$419$	8.05076	+	5.84922i	0.393305	+	0.285753i	−0.373503	+	0.927629i	$0.621844\pi$
$420$	34.1096	−	45.8397i	1.66438	−	2.23675i
$421$	3.96831	−	2.88314i	0.193403	−	0.140516i	−0.486870	−	0.873475i	$-0.661861\pi$
$421$	3.96831	−	2.88314i	0.193403	−	0.140516i	0.680273	+	0.732959i	$0.261861\pi$
$422$	−5.66835	+	0.595767i	−0.275931	+	0.0290015i
$423$	−7.71807	−	6.21429i	−0.375265	−	0.302149i
$424$	−40.2757	−	69.7595i	−1.95596	−	3.38782i
$425$	1.48234	−	0.604358i	0.0719038	−	0.0293157i
$426$	16.7911	−	17.7438i	0.813532	−	0.859689i
$427$	−7.23437	+	24.7014i	−0.350096	+	1.19539i
$428$	−64.3479	−	88.5672i	−3.11037	−	4.28106i
$429$	12.5366	+	9.59180i	0.605271	+	0.463096i
$430$	−20.9302	−	19.4560i	−1.00935	−	0.938253i
$431$	0.360721	+	0.0379133i	0.0173753	+	0.00182622i	0.113212	−	0.993571i	$-0.463886\pi$
$431$	0.360721	+	0.0379133i	0.0173753	+	0.00182622i	−0.0958368	+	0.995397i	$0.530553\pi$
$432$	−77.9623	+	27.9767i	−3.75097	+	1.34603i
$433$	8.14108	−	11.2052i	0.391235	−	0.538489i	−0.567282	−	0.823524i	$-0.692005\pi$
$433$	8.14108	−	11.2052i	0.391235	−	0.538489i	0.958517	+	0.285034i	$0.0920051\pi$
$434$	4.64222	−	11.3055i	0.222834	−	0.542681i
$435$	−10.3777	+	5.44163i	−0.497571	+	0.260906i
$436$	−55.6262	−	11.8237i	−2.66401	−	0.566253i
$437$	26.7080	−	5.67695i	1.27762	−	0.271566i
$438$	−25.5563	+	41.8353i	−1.22113	+	1.99897i
$439$	−5.12436	+	24.1082i	−0.244572	+	1.15062i	0.668783	+	0.743458i	$0.266816\pi$
$439$	−5.12436	+	24.1082i	−0.244572	+	1.15062i	−0.913355	+	0.407164i	$0.866518\pi$
$440$	−17.2898	+	50.4722i	−0.824260	+	2.40617i
$441$	16.8782	−	12.4950i	0.803726	−	0.594999i
$442$	2.68043	+	1.94744i	0.127495	+	0.0926304i
$443$	−13.5758	−	7.83799i	−0.645006	−	0.372394i	0.141534	−	0.989933i	$-0.454796\pi$
$443$	−13.5758	−	7.83799i	−0.645006	−	0.372394i	−0.786540	+	0.617539i	$0.788130\pi$
$444$	30.9734	+	36.1626i	1.46993	+	1.71620i
$445$	0.439575	−	0.472882i	0.0208378	−	0.0224168i
$446$	−6.95584	−	66.1804i	−0.329369	−	3.13373i
$447$	6.72384	+	0.875642i	0.318027	+	0.0414165i
$448$	21.7070	+	89.2070i	1.02556	+	4.21464i
$449$		−	3.54973i		−	0.167522i	−0.996486	−	0.0837611i	$-0.973307\pi$
$449$		−	3.54973i		−	0.167522i	0.996486	−	0.0837611i	$-0.0266932\pi$
$450$	19.8009	−	36.2291i	0.933422	−	1.70786i
$451$	0.791612	−	0.457037i	0.0372755	−	0.0215210i
$452$	72.0482	+	64.8725i	3.38886	+	3.05135i
$453$	−4.58533	−	3.50827i	−0.215438	−	0.164833i
$454$	21.0068	+	28.9134i	0.985900	+	1.35698i
$455$	−17.8183	+	13.3136i	−0.835333	+	0.624151i
$456$	62.1754	−	11.6135i	2.91163	−	0.543853i
$457$	6.01713	−	10.4220i	0.281469	−	0.487519i	−0.690277	−	0.723545i	$-0.742512\pi$
$457$	6.01713	−	10.4220i	0.281469	−	0.487519i	0.971747	+	0.236025i	$0.0758449\pi$
$458$	0.974372	−	9.27053i	0.0455294	−	0.433184i
$459$	−1.46532	−	0.787660i	−0.0683953	−	0.0367648i
$460$	35.9890	+	84.4137i	1.67800	+	3.93581i
$461$	7.62552	+	23.4689i	0.355156	+	1.09306i	0.955919	+	0.293631i	$0.0948635\pi$
$461$	7.62552	+	23.4689i	0.355156	+	1.09306i	−0.600763	+	0.799427i	$0.705136\pi$
$462$	−17.8605	+	24.8156i	−0.830947	+	1.15453i
$463$	9.36826	−	28.8325i	0.435380	−	1.33996i	−0.457317	−	0.889304i	$-0.651189\pi$
$463$	9.36826	−	28.8325i	0.435380	−	1.33996i	0.892697	−	0.450658i	$-0.148811\pi$
$464$	10.0274	−	47.1750i	0.465508	−	2.19005i
$465$	1.60866	−	6.29754i	0.0745996	−	0.292042i
$466$	36.1740	−	7.68903i	1.67573	−	0.356187i
$467$	7.17007	−	3.19232i	0.331791	−	0.147723i	−0.234078	−	0.972218i	$-0.575207\pi$
$467$	7.17007	−	3.19232i	0.331791	−	0.147723i	0.565870	+	0.824495i	$0.308541\pi$
$468$	62.7981	−	3.46732i	2.90284	−	0.160277i
$469$	−4.26794	+	23.4295i	−0.197075	+	1.08187i
$470$	−12.2085	+	16.2546i	−0.563136	+	0.749768i
$471$	−7.18472	+	9.39048i	−0.331054	+	0.432690i
$472$	−20.7881	+	46.6907i	−0.956848	+	2.14912i
$473$	8.36379	+	7.53079i	0.384568	+	0.346266i
$474$	−12.4678	+	3.71212i	−0.572666	+	0.170503i
$475$	−11.3742	+	14.6536i	−0.521886	+	0.672352i
$476$	−2.66334	+	3.90081i	−0.122074	+	0.178794i
$477$	−8.86224	−	22.8953i	−0.405774	−	1.04830i
$478$	−5.82877	−	55.4571i	−0.266602	−	2.53655i
$479$	19.4741	+	8.67044i	0.889795	+	0.396162i	0.800142	−	0.599811i	$-0.204757\pi$
$479$	19.4741	+	8.67044i	0.889795	+	0.396162i	0.0896532	+	0.995973i	$0.471424\pi$
$480$	34.5961	+	87.0658i	1.57909	+	3.97399i
$481$	−7.53897	−	16.9328i	−0.343747	−	0.772069i
$482$	30.1565			1.37359
$483$	3.67540	+	33.5258i	0.167236	+	1.52548i
$484$	−8.82974	+	27.1751i	−0.401352	+	1.23523i
$485$	−3.73100	+	0.332361i	−0.169416	+	0.0150917i
$486$	−42.1326	+	8.11405i	−1.91117	+	0.368061i
$487$	0.660277	−	0.140346i	0.0299200	−	0.00635969i	−0.192927	−	0.981213i	$-0.561798\pi$
$487$	0.660277	−	0.140346i	0.0299200	−	0.00635969i	0.222847	+	0.974853i	$0.428465\pi$
$488$	−64.0746	−	71.1620i	−2.90052	−	3.22135i
$489$	29.6295	+	14.0817i	1.33989	+	0.636796i
$490$	−26.7861	−	33.7439i	−1.21007	−	1.52439i
$491$	−2.20735	−	0.717212i	−0.0996163	−	0.0323673i	0.258785	−	0.965935i	$-0.416678\pi$
$491$	−2.20735	−	0.717212i	−0.0996163	−	0.0323673i	−0.358401	+	0.933568i	$0.616678\pi$
$492$	1.21093	−	3.43482i	0.0545929	−	0.154854i
$493$	0.838880	−	0.484328i	0.0377812	−	0.0218130i
$494$	−38.1826	−	4.01316i	−1.71792	−	0.180560i
$495$	−7.57095	+	14.3905i	−0.340289	+	0.646806i
$496$	15.7245	+	21.6429i	0.706050	+	0.971794i
$497$	−7.11918	−	11.5377i	−0.319339	−	0.517536i
$498$	16.2500	−	34.1918i	0.728180	−	1.53217i
$499$	2.87709	−	4.98327i	0.128796	−	0.223082i	−0.794414	−	0.607376i	$-0.792222\pi$
$499$	2.87709	−	4.98327i	0.128796	−	0.223082i	0.923210	+	0.384295i	$0.125555\pi$
$500$	−55.6812	−	28.0394i	−2.49014	−	1.25396i
$501$	14.6227	+	3.48898i	0.653296	+	0.155876i
$502$	14.5555	−	68.4784i	0.649646	−	3.05634i
$503$	14.8399	−	10.7818i	0.661677	−	0.480736i	−0.205552	−	0.978646i	$-0.565899\pi$
$503$	14.8399	−	10.7818i	0.661677	−	0.480736i	0.867229	+	0.497910i	$0.165899\pi$
$504$	6.58705	+	77.8490i	0.293410	+	3.46767i
$505$	20.8239	+	0.330574i	0.926651	+	0.0147103i
$506$	−19.9724	−	44.8586i	−0.887879	−	1.99421i
$507$	−1.91306	−	0.456455i	−0.0849620	−	0.0202719i
$508$	−2.59951	+	24.7327i	−0.115334	+	1.09733i
$509$	0.182090	+	0.202232i	0.00807102	+	0.00896377i	0.747167	−	0.664637i	$-0.231414\pi$
$509$	0.182090	+	0.202232i	0.00807102	+	0.00896377i	−0.739096	+	0.673600i	$0.764747\pi$
$510$	−1.51377	+	3.05893i	−0.0670307	+	0.135452i
$511$	18.7882	+	19.6772i	0.831143	+	0.870467i
$512$	−68.2796	−	22.1854i	−3.01756	−	0.980465i
$513$	19.2688	−	0.585507i	0.850738	−	0.0258508i
$514$	43.8779	+	39.5078i	1.93537	+	1.74261i
$515$	15.0611	−	32.4324i	0.663673	−	1.42914i
$516$	44.8289	+	1.11113i	1.97348	+	0.0489147i
$517$	4.70600	−	6.47725i	0.206970	−	0.284869i
$518$	32.3566	−	15.5556i	1.42167	−	0.683474i
$519$	−16.8442	+	3.14627i	−0.739379	+	0.138106i
$520$	−7.34245	−	82.4245i	−0.321988	−	3.61455i
$521$	18.1188	+	8.06703i	0.793801	+	0.353423i	0.763244	−	0.646110i	$-0.223605\pi$
$521$	18.1188	+	8.06703i	0.793801	+	0.353423i	0.0305565	+	0.999533i	$0.490272\pi$
$522$	8.88783	−	23.3486i	0.389010	−	1.02194i
$523$	−5.08877	+	23.9408i	−0.222517	+	1.04686i	0.715056	+	0.699068i	$0.246401\pi$
$523$	−5.08877	+	23.9408i	−0.222517	+	1.04686i	−0.937572	+	0.347791i	$0.886932\pi$
$524$	9.31123			0.406763
$525$	−16.6032	−	15.7904i	−0.724621	−	0.689147i
$526$	−8.16723			−0.356108
$527$	−0.111712	+	0.525561i	−0.00486623	+	0.0228938i
$528$	−25.6980	−	61.7959i	−1.11836	−	2.68932i
$529$	−28.4716	−	12.6764i	−1.23790	−	0.551147i
$530$	−46.3322	+	19.7533i	−2.01254	+	0.858028i
$531$	−8.44737	+	13.0878i	−0.366585	+	0.567964i
$532$	4.12657	−	54.5776i	0.178909	−	2.36624i
$533$	−0.833348	+	1.14700i	−0.0360963	+	0.0496823i
$534$	−0.0341081	+	1.37610i	−0.00147600	+	0.0595499i
$535$	−38.3626	+	21.3441i	−1.65856	+	0.922784i
$536$	−65.8428	−	59.2851i	−2.84397	−	2.56073i
$537$	−0.245394	+	9.90049i	−0.0105895	+	0.427238i
$538$	41.8730	+	13.6054i	1.80527	+	0.586568i
$539$	10.7591	+	13.1206i	0.463428	+	0.565145i
$540$	14.3879	+	63.1706i	0.619158	+	2.71843i
$541$	10.5533	+	11.7206i	0.453721	+	0.503908i	0.925991	−	0.377546i	$-0.123232\pi$
$541$	10.5533	+	11.7206i	0.453721	+	0.503908i	−0.472270	+	0.881454i	$0.656565\pi$
$542$	−4.03661	+	38.4058i	−0.173387	+	1.64967i
$543$	9.00171	−	37.7273i	0.386300	−	1.61903i
$544$	−3.15005	−	7.07512i	−0.135057	−	0.303343i
$545$	−7.39050	+	21.5742i	−0.316574	+	0.924139i
$546$	9.65218	−	46.4302i	0.413075	−	1.98703i
$547$	−27.0356	+	19.6425i	−1.15596	+	0.839852i	−0.989262	−	0.146156i	$-0.953310\pi$
$547$	−27.0356	+	19.6425i	−1.15596	+	0.839852i	−0.166696	+	0.986008i	$0.553310\pi$
$548$	−18.0334	+	84.8406i	−0.770350	+	3.62421i
$549$	−15.9639	−	24.4323i	−0.681322	−	1.04274i
$550$	30.0296	+	14.5291i	1.28047	+	0.619524i
$551$	−5.61235	+	9.72087i	−0.239094	+	0.414123i
$552$	−113.327	−	53.8598i	−4.82352	−	2.29242i
$553$	0.211167	+	7.21629i	0.00897973	+	0.306868i
$554$	7.09659	+	9.76762i	0.301505	+	0.414987i
$555$	15.8904	−	10.5859i	0.674511	−	0.449345i
$556$	−76.4433	−	8.03451i	−3.24192	−	0.340739i
$557$	−0.243792	+	0.140754i	−0.0103298	+	0.00596392i	−0.505156	−	0.863028i	$-0.668565\pi$
$557$	−0.243792	+	0.140754i	−0.0103298	+	0.00596392i	0.494826	+	0.868992i	$0.335232\pi$
$558$	6.32585	+	12.3298i	0.267795	+	0.521961i
$559$	−16.6021	−	5.39434i	−0.702193	−	0.228156i
$560$	93.6493	−	11.1117i	3.95740	−	0.469557i
$561$	0.576987	−	1.21405i	0.0243604	−	0.0512571i
$562$	−55.6586	−	61.8152i	−2.34782	−	2.60752i
$563$	18.8431	−	4.00522i	0.794141	−	0.168800i	0.207060	−	0.978328i	$-0.433610\pi$
$563$	18.8431	−	4.00522i	0.794141	−	0.168800i	0.587081	+	0.809528i	$0.300277\pi$
$564$	−2.54735	−	31.7984i	−0.107263	−	1.33895i
$565$	29.3013	−	25.5526i	1.23272	−	1.07501i
$566$	−7.05655	+	21.7178i	−0.296609	+	0.912868i
$567$	−1.66236	+	23.7537i	−0.0698127	+	0.997560i
$568$	50.4379			2.11633
$569$	17.7463	+	39.8589i	0.743964	+	1.67097i	0.741481	+	0.670973i	$0.234124\pi$
$569$	17.7463	+	39.8589i	0.743964	+	1.67097i	0.00248244	+	0.999997i	$0.499210\pi$
$570$	−2.53202	−	39.4684i	−0.106055	−	1.65315i
$571$	7.99338	+	3.55888i	0.334512	+	0.148935i	0.567118	−	0.823637i	$-0.308058\pi$
$571$	7.99338	+	3.55888i	0.334512	+	0.148935i	−0.232605	+	0.972571i	$0.574725\pi$
$572$	5.31190	+	50.5394i	0.222102	+	2.11316i
$573$	14.1888	−	29.8549i	0.592747	−	1.24721i
$574$	−2.26794	−	1.54847i	−0.0946621	−	0.0646319i
$575$	35.3410	−	10.2548i	1.47382	−	0.427656i
$576$	−92.8882	−	47.0020i	−3.87034	−	1.95842i
$577$	23.0426	+	20.7477i	0.959276	+	0.863736i	0.990741	−	0.135769i	$-0.0433504\pi$
$577$	23.0426	+	20.7477i	0.959276	+	0.863736i	−0.0314642	+	0.999505i	$0.510017\pi$
$578$	−18.9173	+	42.4889i	−0.786855	+	1.76730i
$579$	6.64495	+	5.08409i	0.276155	+	0.211288i
$580$	−35.6880	−	12.2253i	−1.48186	−	0.507629i
$581$	−16.0174	−	13.5952i	−0.664515	−	0.564026i
$582$	5.48923	−	5.80067i	0.227536	−	0.240446i
$583$	18.1218	−	8.06833i	0.750527	−	0.334156i
$584$	−99.0053	+	21.0442i	−4.09687	+	0.870817i
$585$	1.64916	−	25.1670i	0.0681846	−	1.04053i
$586$	1.25278	−	5.89385i	0.0517517	−	0.243473i
$587$	−0.107640	+	0.331283i	−0.00444279	+	0.0136735i	−0.953253	−	0.302172i	$-0.902288\pi$
$587$	−0.107640	+	0.331283i	−0.00444279	+	0.0136735i	0.948811	+	0.315846i	$0.102288\pi$
$588$	66.5656	+	11.8183i	2.74512	+	0.487377i
$589$	−1.92401	−	5.92149i	−0.0792773	−	0.243991i
$590$	27.4191	+	16.4162i	1.12883	+	0.675843i
$591$	−6.75485	−	4.12639i	−0.277857	−	0.169737i
$592$	−8.21454	+	78.1562i	−0.337616	+	3.21220i
$593$	−11.1724	+	19.3512i	−0.458797	+	0.794660i	−0.998898	−	0.0469404i	$-0.985053\pi$
$593$	−11.1724	+	19.3512i	−0.458797	+	0.794660i	0.540100	+	0.841601i	$0.318386\pi$
$594$	−8.23460	−	33.6763i	−0.337870	−	1.38175i
$595$	1.42442	+	1.24845i	0.0583955	+	0.0511814i
$596$	12.8309	+	17.6602i	0.525575	+	0.723392i
$597$	25.2465	−	32.9973i	1.03327	−	1.35049i
$598$	56.5999	+	50.9628i	2.31454	+	2.08402i
$599$	−12.6550	+	7.30638i	−0.517070	+	0.298531i	−0.735735	−	0.677269i	$-0.763163\pi$
$599$	−12.6550	+	7.30638i	−0.517070	+	0.298531i	0.218665	+	0.975800i	$0.429830\pi$
$600$	82.4304	−	21.7193i	3.36521	−	0.886688i
$601$		−	34.1225i		−	1.39189i	−0.718096	−	0.695944i	$-0.754986\pi$
$601$		−	34.1225i		−	1.39189i	0.718096	−	0.695944i	$-0.245014\pi$
$602$	9.50344	−	32.4491i	0.387331	−	1.32252i
$603$	−17.0527	−	20.9382i	−0.694438	−	0.852670i
$604$	−1.94287	−	18.4851i	−0.0790541	−	0.752149i
$605$	10.3924	+	4.82607i	0.422510	+	0.196208i
$606$	−33.7241	+	28.8848i	−1.36995	+	1.17337i
$607$	19.7588	+	11.4077i	0.801984	+	0.463026i	0.844165	−	0.536084i	$-0.180097\pi$
$607$	19.7588	+	11.4077i	0.801984	+	0.463026i	−0.0421803	+	0.999110i	$0.513430\pi$
$608$	72.6050	+	52.7506i	2.94452	+	2.13932i
$609$	−11.2531	−	8.09922i	−0.456000	−	0.328197i
$610$	−48.9930	+	34.4207i	−1.98367	+	1.39365i
$611$	−2.58189	+	12.1468i	−0.104452	+	0.491409i
$612$	−1.40064	−	5.16935i	−0.0566174	−	0.208958i
$613$	−29.8465	+	6.34408i	−1.20549	+	0.256235i	−0.766492	−	0.642253i	$-0.778000\pi$
$613$	−29.8465	+	6.34408i	−1.20549	+	0.256235i	−0.438998	+	0.898488i	$0.644666\pi$
$614$	51.2618	+	10.8960i	2.06876	+	0.439728i
$615$	−1.30897	−	0.647769i	−0.0527830	−	0.0261206i
$616$	−62.5607	+	8.43201i	−2.52064	+	0.339735i
$617$	−18.9684	+	26.1078i	−0.763640	+	1.05106i	0.233262	+	0.972414i	$0.425060\pi$
$617$	−18.9684	+	26.1078i	−0.763640	+	1.05106i	−0.996903	+	0.0786470i	$0.974940\pi$
$618$	21.7556	+	73.0700i	0.875137	+	2.93931i
$619$	−21.9141	−	2.30326i	−0.880801	−	0.0925759i	−0.346679	−	0.937984i	$-0.612691\pi$
$619$	−21.9141	−	2.30326i	−0.880801	−	0.0925759i	−0.534121	+	0.845408i	$0.679357\pi$
$620$	18.2854	−	10.1736i	0.734360	−	0.408580i
$621$	−31.6072	−	21.5283i	−1.26835	−	0.863900i
$622$	−25.7763	−	35.4780i	−1.03353	−	1.42254i
$623$	0.733129	+	0.214713i	0.0293722	+	0.00860231i
$624$	75.3981	+	71.3499i	3.01834	+	2.85628i
$625$	−13.8486	+	20.8139i	−0.553943	+	0.832555i
$626$	4.16992	+	7.22251i	0.166664	+	0.288670i
$627$	1.24382	+	15.5265i	0.0496735	+	0.620069i
$628$	−37.8564	+	3.97887i	−1.51064	+	0.158774i
$629$	−1.27693	+	0.927746i	−0.0509146	+	0.0369917i
$630$	48.8195	+	1.76712i	1.94502	+	0.0704036i
$631$	−7.86572	−	5.71478i	−0.313129	−	0.227502i	0.420109	−	0.907474i	$-0.361992\pi$
$631$	−7.86572	−	5.71478i	−0.313129	−	0.227502i	−0.733238	+	0.679972i	$0.761992\pi$
$632$	−23.2602	−	13.4293i	−0.925241	−	0.534188i
$633$	−2.33311	−	2.72399i	−0.0927327	−	0.108269i
$634$	25.2777	−	5.37293i	1.00390	−	0.213386i
$635$	9.72060	+	2.22801i	0.385750	+	0.0884157i
$636$	33.9266	−	71.3854i	1.34528	−	2.83061i
$637$	−23.5226	−	11.8037i	−0.931998	−	0.467681i
$638$	19.1982	+	6.23787i	0.760063	+	0.246960i
$639$	15.1900	+	2.36231i	0.600906	+	0.0934514i
$640$	−44.3902	+	95.5891i	−1.75468	+	3.77849i
$641$	−8.82021	−	41.4958i	−0.348377	−	1.63899i	−0.708234	−	0.705978i	$-0.750508\pi$
$641$	−8.82021	−	41.4958i	−0.348377	−	1.63899i	0.359857	−	0.933008i	$-0.382826\pi$
$642$	31.1203	−	88.2734i	1.22822	−	3.48387i
$643$		−	48.1814i		−	1.90009i	−0.312116	−	0.950044i	$-0.601038\pi$
$643$		−	48.1814i		−	1.90009i	0.312116	−	0.950044i	$-0.398962\pi$
$644$	−70.2618	+	82.7799i	−2.76870	+	3.26199i
$645$	2.60497	−	17.7926i	0.102570	−	0.700585i
$646$	0.341742	+	3.25145i	0.0134456	+	0.127927i
$647$	−30.0257	−	13.3683i	−1.18043	−	0.525563i	−0.279764	−	0.960069i	$-0.590256\pi$
$647$	−30.0257	−	13.3683i	−1.18043	−	0.525563i	−0.900669	+	0.434506i	$0.856923\pi$
$648$	−71.9594	−	51.6688i	−2.82683	−	2.02974i
$649$	−10.9001	−	6.29315i	−0.427865	−	0.247028i
$650$	−51.7166	−	1.64239i	−2.02849	−	0.0644197i
$651$	7.51533	−	1.63260i	0.294549	−	0.0639867i
$652$	32.6361	+	100.444i	1.27813	+	3.93368i
$653$	−33.2920	+	3.49913i	−1.30282	+	0.136932i	−0.730393	−	0.683027i	$-0.760663\pi$
$653$	−33.2920	+	3.49913i	−1.30282	+	0.136932i	−0.572423	+	0.819958i	$0.693997\pi$
$654$	−18.6695	−	44.8943i	−0.730034	−	1.75551i
$655$	0.449191	−	3.70678i	0.0175514	−	0.144836i
$656$	5.49147	−	2.44496i	0.214406	−	0.0954596i
$657$	−30.8023	+	1.70071i	−1.20171	+	0.0663511i
$658$	−23.6639	−	4.31064i	−0.922516	−	0.168046i
$659$	−17.4863	−	5.68163i	−0.681168	−	0.221325i	−0.0520614	−	0.998644i	$-0.516579\pi$
$659$	−17.4863	−	5.68163i	−0.681168	−	0.221325i	−0.629107	+	0.777319i	$0.716579\pi$
$660$	−50.4029	+	14.1398i	−1.96193	+	0.550390i
$661$	16.5360	+	14.8891i	0.643175	+	0.579117i	0.924822	−	0.380401i	$-0.124214\pi$
$661$	16.5360	+	14.8891i	0.643175	+	0.579117i	−0.281647	+	0.959518i	$0.590881\pi$
$662$	18.5589	+	87.3127i	0.721311	+	3.39350i
$663$	−0.0516604	+	2.08425i	−0.00200632	+	0.0809457i
$664$	74.3361	−	24.1533i	2.88480	−	0.937329i
$665$	−21.5281	−	4.27570i	−0.834825	−	0.165805i
$666$	−10.4261	+	39.3509i	−0.404004	+	1.52481i
$667$	20.3421	−	9.05687i	0.787648	−	0.350684i
$668$	24.1987	+	41.9133i	0.936274	+	1.62167i
$669$	31.8038	−	27.2400i	1.22961	−	1.05316i
$670$	−41.7535	+	36.4117i	−1.61308	+	1.40671i
$671$	19.0779	−	13.8609i	0.736493	−	0.535094i
$672$	−73.8055	+	82.7104i	−2.84711	+	3.19062i
$673$	−5.57053	−	17.1443i	−0.214728	−	0.660865i	−0.999173	−	0.0406665i	$-0.987052\pi$
$673$	−5.57053	−	17.1443i	−0.214728	−	0.660865i	0.784445	−	0.620199i	$-0.212948\pi$
$674$	−24.8190	−	14.3293i	−0.955992	−	0.551942i
$675$	25.8421	−	2.68033i	0.994664	−	0.103166i
$676$	−3.16586	−	5.48343i	−0.121764	−	0.210901i
$677$	−30.2538	−	6.43064i	−1.16275	−	0.247150i	−0.414172	−	0.910199i	$-0.635929\pi$
$677$	−30.2538	−	6.43064i	−1.16275	−	0.247150i	−0.748576	+	0.663049i	$0.769262\pi$
$678$	−10.7044	+	82.1961i	−0.411098	+	3.15672i
$679$	−2.32735	−	3.77182i	−0.0893156	−	0.144749i
$680$	−6.73551	+	2.07089i	−0.258295	+	0.0794152i
$681$	−7.47749	+	21.2100i	−0.286538	+	0.812770i
$682$	−9.69693	+	5.59853i	−0.371315	+	0.214379i
$683$	0.00536304		0.000563678i	0.000205211		2.15685e-5i	0.104631	−	0.994511i	$-0.466634\pi$
$683$	0.00536304		0.000563678i	0.000205211		2.15685e-5i	−0.104426	+	0.994533i	$0.533300\pi$
$684$	44.0069	+	43.7614i	1.68265	+	1.67326i
$685$	32.9048	+	11.2719i	1.25723	+	0.430678i
$686$	21.5207	−	46.2111i	0.821663	−	1.76435i
$687$	5.15106	−	2.80613i	0.196525	−	0.107061i
$688$	49.5242	+	55.0022i	1.88809	+	2.09694i
$689$	−20.5877	+	22.8649i	−0.784328	+	0.871085i
$690$	−41.9576	+	66.2953i	−1.59730	+	2.52382i
$691$	24.1243	−	21.7216i	0.917730	−	0.826328i	−0.0674724	−	0.997721i	$-0.521493\pi$
$691$	24.1243	−	21.7216i	0.917730	−	0.826328i	0.985203	+	0.171393i	$0.0548268\pi$
$692$	−44.6298	−	32.4255i	−1.69657	−	1.23263i
$693$	−19.2358	−	0.390689i	−0.730708	−	0.0148410i
$694$	−29.9771	−	21.7796i	−1.13791	−	0.826743i
$695$	−6.88629	+	30.0443i	−0.261212	+	1.13964i
$696$	47.6274	−	19.8060i	1.80531	−	0.750746i
$697$	0.110293	+	0.0491058i	0.00417766	+	0.00186002i
$698$	26.6141	+	5.65700i	1.00736	+	0.214121i
$699$	16.9032	+	15.9956i	0.639337	+	0.605010i
$700$	0.183867	−	73.7646i	0.00694952	−	2.78804i
$701$			1.42508i			0.0538244i	0.999638	+	0.0269122i	$0.00856745\pi$
$701$			1.42508i			0.0538244i	−0.999638	+	0.0269122i	$0.991433\pi$
$702$	32.9134	+	42.5228i	1.24224	+	1.60492i
$703$	7.43925	−	16.7088i	0.280576	−	0.630185i
$704$	34.2124	−	76.8424i	1.28943	−	2.89611i
$705$	−12.7817	−	0.519920i	−0.481388	−	0.0195813i
$706$	−5.15530	+	7.09566i	−0.194022	+	0.267049i
$707$	10.6771	+	22.2090i	0.401553	+	0.835256i
$708$	−49.2961	+	9.20785i	−1.85266	+	0.346052i
$709$	−14.4297	−	16.0258i	−0.541917	−	0.601860i	0.408530	−	0.912745i	$-0.366041\pi$
$709$	−14.4297	−	16.0258i	−0.541917	−	0.601860i	−0.950448	+	0.310884i	$0.899375\pi$
$710$	3.79404	−	31.3088i	0.142388	−	1.17500i
$711$	−6.37611	−	5.13380i	−0.239123	−	0.192532i
$712$	−2.11206	+	1.90171i	−0.0791529	+	0.0712696i
$713$	−3.81678	+	11.7468i	−0.142940	+	0.439923i
$714$	−4.03827	+	0.0180643i	−0.151129	+	0.000676040i
$715$	20.3758	+	0.323461i	0.762013	+	0.0120968i
$716$	−23.6937	+	21.3339i	−0.885475	+	0.797286i
$717$	26.6506	−	22.8263i	0.995283	−	0.852463i
$718$	37.7944	+	65.4618i	1.41047	+	2.44301i
$719$	9.93627	−	4.42391i	0.370560	−	0.164984i	−0.213003	−	0.977051i	$-0.568325\pi$
$719$	9.93627	−	4.42391i	0.370560	−	0.164984i	0.583564	+	0.812067i	$0.301658\pi$
$720$	−59.4076	+	88.9126i	−2.21399	+	3.31358i
$721$	42.2924	−	1.23758i	1.57505	−	0.0460900i
$722$	8.47106	+	11.6594i	0.315260	+	0.433919i
$723$	10.7703	+	15.6241i	0.400554	+	0.581066i
$724$	108.138	−	62.4336i	4.01892	−	2.32032i
$725$	−6.58853	+	13.6175i	−0.244692	+	0.505742i
$726$	−23.4140	+	6.97118i	−0.868974	+	0.258725i
$727$	10.3750	−	3.37104i	0.384788	−	0.125025i	−0.110234	−	0.993906i	$-0.535160\pi$
$727$	10.3750	−	3.37104i	0.384788	−	0.125025i	0.495022	+	0.868881i	$0.335160\pi$
$728$	83.3262	−	51.4154i	3.08827	−	1.90558i
$729$	−19.2515	−	18.9310i	−0.713017	−	0.701146i
$730$	5.61563	+	63.0396i	0.207844	+	2.33320i
$731$	−0.155383	+	1.47837i	−0.00574703	+	0.0546794i
$732$	21.8062	−	91.3925i	0.805981	−	3.37797i
$733$	−2.97365	−	6.67893i	−0.109834	−	0.246692i	0.850263	−	0.526358i	$-0.176443\pi$
$733$	−2.97365	−	6.67893i	−0.109834	−	0.246692i	−0.960097	+	0.279666i	$0.909776\pi$
$734$	19.2191	−	59.1503i	0.709390	−	2.18328i
$735$	7.91606	−	25.9294i	0.291988	−	0.956422i
$736$	−55.0151	−	169.319i	−2.02788	−	6.24118i
$737$	16.2146	−	14.5997i	0.597272	−	0.537786i
$738$	3.00547	−	0.814333i	0.110633	−	0.0299760i
$739$	−0.211016	+	0.234357i	−0.00776235	+	0.00862096i	−0.747013	−	0.664809i	$-0.768513\pi$
$739$	−0.211016	+	0.234357i	−0.00776235	+	0.00862096i	0.739251	+	0.673430i	$0.235180\pi$
$740$	59.9156	+	13.7329i	2.20254	+	0.504833i
$741$	−11.5576	−	21.2157i	−0.424581	−	0.779378i
$742$	−45.4355	−	38.5646i	−1.66799	−	1.41575i
$743$			16.9192i			0.620705i	0.950622	+	0.310352i	$0.100447\pi$
$743$			16.9192i			0.620705i	−0.950622	+	0.310352i	$0.899553\pi$
$744$	−9.51305	+	26.9839i	−0.348765	+	0.989279i
$745$	7.64948	−	4.25599i	0.280255	−	0.155927i
$746$	6.07690	−	13.6489i	0.222491	−	0.499723i
$747$	23.5184	−	3.79244i	0.860495	−	0.138758i
$748$	4.11561	−	1.33724i	0.150481	−	0.0488944i
$749$	−42.8985	−	29.2896i	−1.56748	−	1.07022i
$750$	−7.28149	−	52.8017i	−0.265883	−	1.92804i
$751$	−16.5901	+	28.7349i	−0.605382	+	1.04855i	0.386609	+	0.922244i	$0.373646\pi$
$751$	−16.5901	+	28.7349i	−0.605382	+	1.04855i	−0.991991	+	0.126309i	$0.959687\pi$
$752$	35.2306	−	39.1276i	1.28473	−	1.42684i
$753$	40.6772	−	16.9157i	1.48236	−	0.616444i
$754$	−31.1383	+	3.27276i	−1.13399	+	0.119187i
$755$	−7.45261	−	0.118308i	−0.271228	−	0.00430568i
$756$	−59.2226	+	48.6748i	−2.15391	+	1.77028i
$757$	13.9387			0.506609			0.253305	−	0.967387i	$-0.418483\pi$
$757$	13.9387			0.506609			0.253305	+	0.967387i	$0.418483\pi$
$758$	1.55416	+	3.49069i	0.0564495	+	0.126788i
$759$	16.1082	−	26.3689i	0.584689	−	0.957129i
$760$	55.5951	−	59.8076i	2.01665	−	2.16945i
$761$	−4.35712	−	0.926134i	−0.157945	−	0.0335723i	0.128260	−	0.991741i	$-0.459061\pi$
$761$	−4.35712	−	0.926134i	−0.157945	−	0.0335723i	−0.286206	+	0.958168i	$0.592394\pi$
$762$	−18.6714	+	10.1716i	−0.676394	+	0.368478i
$763$	−26.7414	+	3.60424i	−0.968104	+	0.130482i
$764$	101.208	−	32.8845i	3.66157	−	1.18972i
$765$	−2.12547	+	0.308210i	−0.0768466	+	0.0111434i
$766$	0.863589	+	4.06287i	0.0312027	+	0.146797i
$767$	19.4151	+	2.04060i	0.701037	+	0.0736820i
$768$	−29.8188	−	100.152i	−1.07599	−	3.61392i
$769$	−23.9021	+	32.8985i	−0.861933	+	1.18635i	0.119172	+	0.992874i	$0.461976\pi$
$769$	−23.9021	+	32.8985i	−0.861933	+	1.18635i	−0.981105	+	0.193476i	$0.938024\pi$
$770$	0.528147	+	39.4682i	0.0190331	+	1.42234i
$771$	−4.79808	+	36.8433i	−0.172799	+	1.32688i
$772$	2.81555	+	26.7882i	0.101334	+	0.964128i
$773$	−6.53134	+	7.25379i	−0.234916	+	0.260901i	−0.849064	−	0.528290i	$-0.822833\pi$
$773$	−6.53134	+	7.25379i	−0.234916	+	0.260901i	0.614148	+	0.789191i	$0.289500\pi$
$774$	20.9710	+	32.0955i	0.753786	+	1.15365i
$775$	−3.16795	−	7.77017i	−0.113796	−	0.279113i
$776$	16.4888			0.591913
$777$	19.6155	+	11.2083i	0.703701	+	0.402096i
$778$	17.6145	−	12.7977i	0.631511	−	0.458820i
$779$	−1.39136	+	0.146238i	−0.0498506	+	0.00523951i
$780$	62.4983	−	51.8331i	2.23780	−	1.85592i
$781$	−1.29834	+	12.3529i	−0.0464583	+	0.442021i
$782$	3.24283	−	5.61674i	0.115963	−	0.200854i
$783$	15.2712	−	3.73415i	0.545748	−	0.133448i
$784$	61.3476	+	93.2073i	2.19098	+	3.32883i
$785$	−0.242288	+	15.2625i	−0.00864762	+	0.544741i
$786$	4.51826	+	6.55444i	0.161161	+	0.233789i
$787$	−8.76322	−	41.2277i	−0.312375	−	1.46961i	−0.801815	−	0.597572i	$-0.796132\pi$
$787$	−8.76322	−	41.2277i	−0.312375	−	1.46961i	0.489440	−	0.872037i	$-0.337201\pi$
$788$	−5.29818	−	24.9260i	−0.188740	−	0.887951i
$789$	−2.91691	−	4.23144i	−0.103845	−	0.150643i
$790$	−10.0858	+	13.4284i	−0.358836	+	0.477760i
$791$	42.5534	+	17.4731i	1.51303	+	0.621273i
$792$	38.8163	−	60.1397i	1.37928	−	2.13697i
$793$	−18.2881	+	31.6759i	−0.649430	+	1.12484i
$794$	−4.89071	+	46.5320i	−0.173565	+	1.65136i
$795$	−26.7816	−	16.9498i	−0.949847	−	0.601149i
$796$	133.024	−	13.9814i	4.71492	−	0.495558i
$797$	−15.3690	+	11.1663i	−0.544399	+	0.395529i	−0.825716	−	0.564086i	$-0.809229\pi$
$797$	−15.3690	+	11.1663i	−0.544399	+	0.395529i	0.281317	+	0.959615i	$0.409229\pi$
$798$	40.4211	−	23.5789i	1.43089	−	0.834683i
$799$	1.05748			0.0374109
$800$	102.773	+	63.7693i	3.63359	+	2.25459i
$801$	−0.725141	+	0.473802i	−0.0256216	+	0.0167410i
$802$	30.5178	−	33.8934i	1.07762	−	1.19682i
$803$	−2.60547	−	24.7894i	−0.0919451	−	0.874799i
$804$	11.2267	−	86.2068i	0.395934	−	3.04028i
$805$	29.5649	+	31.9645i	1.04203	+	1.12660i
$806$	10.2082	−	14.0504i	0.359568	−	0.494903i
$807$	7.90593	+	26.5535i	0.278302	+	0.934728i
$808$	−91.1754	−	9.58292i	−3.20754	−	0.337126i
$809$	3.59467	+	16.9116i	0.126382	+	0.594581i	0.995066	+	0.0992141i	$0.0316329\pi$
$809$	3.59467	+	16.9116i	0.126382	+	0.594581i	−0.868684	+	0.495366i	$0.835034\pi$
$810$	−37.4859	+	40.7815i	−1.31712	+	1.43292i
$811$	8.98934	−	2.92081i	0.315658	−	0.102564i	−0.146903	−	0.989151i	$-0.546931\pi$
$811$	8.98934	−	2.92081i	0.315658	−	0.102564i	0.462561	+	0.886587i	$0.346931\pi$
$812$	−5.96213	−	44.2356i	−0.209230	−	1.55236i
$813$	−21.3397	+	11.6252i	−0.748416	+	0.407713i
$814$	−32.1736	−	6.83871i	−1.12768	−	0.239697i
$815$	41.5608	−	8.14676i	1.45581	−	0.285368i
$816$	4.60815	−	7.54349i	0.161318	−	0.264075i
$817$	−7.00626	−	15.7363i	−0.245118	−	0.550544i
$818$	28.7538			1.00535
$819$	27.5028	−	11.5817i	0.961024	−	0.404697i
$820$	−1.38178	−	4.49421i	−0.0482540	−	0.156945i
$821$	−9.60491	+	1.00952i	−0.335214	+	0.0352324i	−0.270640	−	0.962681i	$-0.587235\pi$
$821$	−9.60491	+	1.00952i	−0.335214	+	0.0352324i	−0.0645735	+	0.997913i	$0.520569\pi$
$822$	−68.4724	+	28.4745i	−2.38825	+	0.993162i
$823$	25.6056	−	28.4380i	0.892557	−	0.991285i	−0.107439	−	0.994212i	$-0.534265\pi$
$823$	25.6056	−	28.4380i	0.892557	−	0.991285i	0.999996	+	0.00292704i	$0.000931708\pi$
$824$	−78.7048	+	136.321i	−2.74181	+	4.74896i
$825$	3.19748	+	20.7474i	0.111322	+	0.722331i
$826$	−2.85087	+	37.7053i	−0.0991943	+	1.31194i
$827$	−27.4348	+	8.91410i	−0.954001	+	0.309974i	−0.744340	−	0.667800i	$-0.767236\pi$
$827$	−27.4348	+	8.91410i	−0.954001	+	0.309974i	−0.209661	+	0.977774i	$0.567236\pi$
$828$	−19.5998	−	121.546i	−0.681139	−	4.22402i
$829$	−12.2324	+	27.4745i	−0.424851	+	0.954230i	0.566630	+	0.823973i	$0.308247\pi$
$829$	−12.2324	+	27.4745i	−0.424851	+	0.954230i	−0.991480	+	0.130257i	$0.958420\pi$
$830$	−9.40120	−	47.9603i	−0.326320	−	1.66473i
$831$	−2.52607	+	7.16523i	−0.0876283	+	0.248559i
$832$			130.466i			4.52309i
$833$	−0.566724	+	2.16828i	−0.0196358	+	0.0751266i
$834$	−31.4382	−	57.7093i	−1.08862	−	1.99831i
$835$	17.8530	−	7.61144i	0.617827	−	0.263405i
$836$	−33.5540	+	37.2654i	−1.16049	+	1.28885i
$837$	−4.12878	+	7.68098i	−0.142712	+	0.265493i
$838$	−20.3552	+	18.3279i	−0.703159	+	0.633127i
$839$	−8.81832	−	27.1400i	−0.304442	−	0.936976i	−0.979885	−	0.199564i	$-0.936047\pi$
$839$	−8.81832	−	27.1400i	−0.304442	−	0.936976i	0.675443	−	0.737412i	$-0.263953\pi$
$840$	66.6308	+	75.7194i	2.29898	+	2.61257i
$841$	6.13280	−	18.8748i	0.211476	−	0.650856i
$842$	5.49140	+	12.3339i	0.189246	+	0.425054i
$843$	12.1480	−	50.9139i	0.418401	−	1.75357i
$844$	1.20694	−	11.4832i	0.0415445	−	0.395269i
$845$	−2.33566	+	0.995788i	−0.0803493	+	0.0342562i
$846$	21.1477	−	17.2233i	0.727073	−	0.592148i
$847$	0.396561	+	13.5518i	0.0136260	+	0.465647i
$848$	124.066	−	40.3115i	4.26045	−	1.38430i
$849$	−13.7722	+	4.10049i	−0.472662	+	0.140728i
$850$	0.778829	+	4.33678i	0.0267136	+	0.148750i
$851$	−31.4222	+	18.1416i	−1.07714	+	0.621887i
$852$	28.0884	+	40.7466i	0.962291	+	1.39595i
$853$	−3.19537	−	4.39805i	−0.109407	−	0.150586i	0.750802	−	0.660527i	$-0.229667\pi$
$853$	−3.19537	−	4.39805i	−0.109407	−	0.150586i	−0.860209	+	0.509941i	$0.829667\pi$
$854$	−62.3642	−	33.6132i	−2.13406	−	1.15022i
$855$	19.5443	−	15.4079i	0.668400	−	0.526939i
$856$	176.542	−	78.6014i	6.03407	−	2.68654i
$857$	−3.99808	−	6.92488i	−0.136572	−	0.236550i	0.789625	−	0.613590i	$-0.210275\pi$
$857$	−3.99808	−	6.92488i	−0.136572	−	0.236550i	−0.926197	+	0.377040i	$0.876942\pi$
$858$	−32.9985	+	28.2633i	−1.12655	+	0.964895i
$859$	−14.4135	+	12.9780i	−0.491781	+	0.442802i	−0.877331	−	0.479885i	$-0.840678\pi$
$859$	−14.4135	+	12.9780i	−0.491781	+	0.442802i	0.385550	+	0.922687i	$0.374012\pi$
$860$	47.3695	−	33.2801i	1.61529	−	1.13484i
$861$	−0.00773006	−	1.72805i	−0.000263440	−	0.0588919i
$862$	−0.308505	+	0.949481i	−0.0105077	+	0.0323395i
$863$	17.9750	−	16.1847i	0.611875	−	0.550935i	−0.303860	−	0.952717i	$-0.598276\pi$
$863$	17.9750	−	16.1847i	0.611875	−	0.550935i	0.915736	+	0.401782i	$0.131609\pi$
$864$	−16.9294	−	124.550i	−0.575948	−	4.23726i
$865$	−15.0615	+	16.2027i	−0.512107	+	0.550910i
$866$	25.5092	+	28.3308i	0.866838	+	0.962721i
$867$	−28.7697	+	5.37380i	−0.977072	+	0.182504i
$868$	20.4474	+	13.9608i	0.694031	+	0.473860i
$869$	3.88776	−	5.35104i	0.131883	−	0.181521i
$870$	−8.71178	−	31.0541i	−0.295357	−	1.05283i
$871$	−13.7649	+	30.9164i	−0.466404	+	1.04756i
$872$	40.8310	−	91.7079i	1.38271	−	3.10562i
$873$	4.96580	+	0.772268i	0.168067	+	0.0261373i
$874$			75.1552i			2.54216i
$875$	−29.3566	−	3.63174i	−0.992435	−	0.122775i
$876$	−72.1359	−	68.2628i	−2.43724	−	2.30639i
$877$	−2.73868	−	0.582125i	−0.0924788	−	0.0196570i	0.161440	−	0.986883i	$-0.448386\pi$
$877$	−2.73868	−	0.582125i	−0.0924788	−	0.0196570i	−0.253919	+	0.967226i	$0.581720\pi$
$878$	−61.9745	−	27.5928i	−2.09154	−	0.931213i
$879$	3.50103	−	1.45592i	0.118087	−	0.0491068i
$880$	−74.1307	−	44.3830i	−2.49894	−	1.49615i
$881$	43.5710	+	31.6562i	1.46794	+	1.06652i	0.981203	+	0.192977i	$0.0618144\pi$
$881$	43.5710	+	31.6562i	1.46794	+	1.06652i	0.486741	+	0.873546i	$0.338186\pi$
$882$	23.9816	+	52.5922i	0.807503	+	1.77087i
$883$	16.8066	+	12.2107i	0.565588	+	0.410924i	0.833500	−	0.552519i	$-0.186334\pi$
$883$	16.8066	+	12.2107i	0.565588	+	0.410924i	−0.267912	+	0.963444i	$0.586334\pi$
$884$	−4.98801	+	4.49122i	−0.167765	+	0.151056i
$885$	1.28748	+	20.0688i	0.0432782	+	0.674607i
$886$	28.8714	−	32.0650i	0.969955	−	1.07724i
$887$	5.24631	+	5.82662i	0.176154	+	0.195639i	0.824756	−	0.565489i	$-0.191313\pi$
$887$	5.24631	+	5.82662i	0.176154	+	0.195639i	−0.648602	+	0.761128i	$0.724646\pi$
$888$	−73.8080	+	40.2083i	−2.47683	+	1.34930i
$889$	2.78987	+	11.4653i	0.0935693	+	0.384532i
$890$	1.02159	+	1.45409i	0.0342439	+	0.0487413i
$891$	14.5067	−	16.2938i	0.485993	−	0.545862i
$892$	134.072	+	14.0915i	4.48905	+	0.471818i
$893$	−10.6122	+	6.12698i	−0.355125	+	0.205032i
$894$	−6.20537	+	17.6016i	−0.207539	+	0.588687i
$895$	7.34994	+	10.4616i	0.245681	+	0.349692i
$896$	−124.650	+	3.64757i	−4.16426	+	0.121857i
$897$	−6.18924	+	47.5256i	−0.206653	+	1.58684i
$898$	9.55702	+	2.03141i	0.318922	+	0.0677889i
$899$	−2.53877	−	4.39727i	−0.0846726	−	0.146657i
$900$	63.4508	+	54.4967i	2.11503	+	1.81656i
$901$	2.26902	+	1.31002i	0.0755922	+	0.0436432i
$902$	0.777475	+	2.39282i	0.0258871	+	0.0796723i
$903$	20.2060	−	6.66540i	0.672413	−	0.221811i
$904$	−138.455	+	100.594i	−4.60495	+	3.34569i
$905$	−19.6378	−	46.0614i	−0.652784	−	1.53113i
$906$	12.0694	−	10.3375i	0.400980	−	0.343441i
$907$	10.0536	+	17.4134i	0.333825	+	0.578203i	0.983259	−	0.182216i	$-0.0583270\pi$
$907$	10.0536	+	17.4134i	0.333825	+	0.578203i	−0.649433	+	0.760419i	$0.724994\pi$
$908$	−66.1424	+	29.4485i	−2.19501	+	0.977282i
$909$	−27.0097	−	7.15630i	−0.895856	−	0.237359i
$910$	−25.6476	−	55.5915i	−0.850211	−	1.84284i
$911$	7.88845	−	2.56311i	0.261356	−	0.0849197i	−0.175408	−	0.984496i	$-0.556124\pi$
$911$	7.88845	−	2.56311i	0.261356	−	0.0849197i	0.436764	+	0.899576i	$0.356124\pi$
$912$	−2.53813	+	102.402i	−0.0840457	+	3.39085i
$913$	4.00194	+	18.8276i	0.132445	+	0.623104i
$914$	24.6159	+	22.1642i	0.814221	+	0.733128i
$915$	−35.3311	−	13.0899i	−1.16801	−	0.432740i
$916$	17.9599	+	5.83553i	0.593412	+	0.192811i
$917$	4.16004	−	1.48756i	0.137377	−	0.0491234i
$918$	2.95919	−	3.49436i	0.0976680	−	0.115331i
$919$	5.15996	−	2.29736i	0.170211	−	0.0757830i	−0.319862	−	0.947464i	$-0.603637\pi$
$919$	5.15996	−	2.29736i	0.170211	−	0.0757830i	0.490074	+	0.871681i	$0.336970\pi$
$920$	−158.962	+	31.1598i	−5.24082	+	1.02731i
$921$	12.6628	+	30.4502i	0.417254	+	1.00337i
$922$	−67.5498	+	7.09977i	−2.22464	+	0.233819i
$923$	−5.95337	−	18.3226i	−0.195958	−	0.603095i
$924$	−41.6513	−	45.8444i	−1.37023	−	1.50817i
$925$	8.35748	−	23.1897i	0.274792	−	0.762473i
$926$	72.2653	+	41.7224i	2.37479	+	1.37108i
$927$	−30.0876	+	37.3684i	−0.988206	+	1.22734i
$928$	66.8602	+	29.7681i	2.19479	+	0.977184i
$929$	−0.374999	−	3.56788i	−0.0123033	−	0.117058i	0.986646	−	0.162876i	$-0.0520772\pi$
$929$	−0.374999	−	3.56788i	−0.0123033	−	0.117058i	−0.998950	+	0.0458181i	$0.985411\pi$
$930$	16.0344	+	7.93492i	0.525790	+	0.260196i
$931$	−6.87562	−	25.0432i	−0.225339	−	0.820759i
$932$			74.9204i			2.45410i
$933$	9.17519	−	26.0256i	0.300382	−	0.852040i
$934$	4.49154	+	21.1310i	0.146968	+	0.691428i
$935$	−0.333808	−	1.70292i	−0.0109167	−	0.0556915i
$936$	−17.0608	+	109.703i	−0.557649	+	3.58576i
$937$	−39.6233	−	12.8744i	−1.29444	−	0.420588i	−0.420795	−	0.907156i	$-0.638249\pi$
$937$	−39.6233	−	12.8744i	−1.29444	−	0.420588i	−0.873643	+	0.486567i	$0.838249\pi$
$938$	−60.6374	−	24.8987i	−1.97988	−	0.812971i
$939$	−2.25270	+	4.73994i	−0.0735142	+	0.154682i
$940$	−27.0676	−	31.0385i	−0.882848	−	1.01237i
$941$	10.1052	−	2.14793i	0.329421	−	0.0700206i	−0.0402323	−	0.999190i	$-0.512810\pi$
$941$	10.1052	−	2.14793i	0.329421	−	0.0700206i	0.369653	+	0.929170i	$0.379476\pi$
$942$	−21.1706	−	24.7175i	−0.689775	−	0.805339i
$943$	2.40351	+	1.38767i	0.0782691	+	0.0451887i
$944$	−66.9626	−	48.6512i	−2.17945	−	1.58346i
$945$	16.5203	+	25.9245i	0.537405	+	0.843325i
$946$	−25.0617	+	18.2084i	−0.814825	+	0.592005i
$947$	−55.5617	+	5.83977i	−1.80551	+	0.189767i	−0.946612	−	0.322376i	$-0.895518\pi$
$947$	−55.5617	+	5.83977i	−1.80551	+	0.189767i	−0.858900	+	0.512143i	$0.828852\pi$
$948$	−2.10444	−	26.2695i	−0.0683490	−	0.853195i
$949$	19.3307	+	33.4818i	0.627502	+	1.08686i
$950$	−32.9430	−	39.0090i	−1.06881	−	1.26562i
$951$	11.8116	+	11.1774i	0.383017	+	0.362452i
$952$	−5.75789	−	6.03031i	−0.186614	−	0.195444i
$953$	22.9421	+	31.5770i	0.743166	+	1.02288i	0.998430	+	0.0560093i	$0.0178377\pi$
$953$	22.9421	+	31.5770i	0.743166	+	1.02288i	−0.255264	+	0.966871i	$0.582162\pi$
$954$	66.7130	−	10.7577i	2.15991	−	0.348295i
$955$	−8.20875	−	41.8770i	−0.265629	−	1.35511i
$956$	112.348	+	11.8082i	3.63359	+	0.381905i
$957$	3.62476	+	12.1744i	0.117172	+	0.393543i
$958$	−34.4881	+	47.4688i	−1.11426	+	1.53365i
$959$	5.49716	+	40.7858i	0.177513	+	1.31704i
$960$	−132.486	+	22.5765i	−4.27598	+	0.728654i
$961$	−27.5677	−	5.85969i	−0.889280	−	0.189022i
$962$	49.9029	−	10.6072i	1.60893	−	0.341989i
$963$	56.8490	−	15.4033i	1.83193	−	0.496363i
$964$	−12.7019	+	59.7576i	−0.409100	+	1.92466i
$965$	10.8001	+	0.171449i	0.347668	+	0.00551914i
$966$	−92.3656	−	9.29047i	−2.97181	−	0.298916i
$967$	−48.7741	−	35.4365i	−1.56847	−	1.13956i	−0.928604	−	0.371073i	$-0.878990\pi$
$967$	−48.7741	−	35.4365i	−1.56847	−	1.13956i	−0.639866	−	0.768486i	$-0.721010\pi$
$968$	−43.6815	−	25.2195i	−1.40398	−	0.810586i
$969$	−1.56253	+	1.33831i	−0.0501956	+	0.0429926i
$970$	1.24032	−	10.2353i	0.0398243	−	0.328635i
$971$	−1.30680	−	12.4334i	−0.0419371	−	0.399005i	−0.995275	−	0.0970989i	$-0.969044\pi$
$971$	−1.30680	−	12.4334i	−0.0419371	−	0.399005i	0.953338	−	0.301906i	$-0.0976230\pi$
$972$	1.66751	−	86.9067i	0.0534853	−	2.78754i
$973$	−35.4366	+	8.62289i	−1.13605	+	0.276437i
$974$			1.85799i			0.0595340i
$975$	−17.6196	−	27.3809i	−0.564278	−	0.876891i
$976$	134.301	−	77.5388i	4.29888	−	2.48196i
$977$	−21.6408	−	19.4854i	−0.692350	−	0.623395i	0.245924	−	0.969289i	$-0.420909\pi$
$977$	−21.6408	−	19.4854i	−0.692350	−	0.623395i	−0.938273	+	0.345895i	$0.887575\pi$
$978$	−54.8685	+	71.7136i	−1.75450	+	2.29315i
$979$	−0.411386	−	0.566225i	−0.0131480	−	0.0180966i
$980$	78.1485	−	38.8660i	2.49636	−	1.24153i
$981$	16.5920	−	25.7066i	0.529741	−	0.820748i
$982$	3.19417	−	5.53246i	0.101930	−	0.176548i
$983$	−3.28549	+	31.2593i	−0.104791	+	0.997017i	0.808164	+	0.588957i	$0.200461\pi$
$983$	−3.28549	+	31.2593i	−0.104791	+	0.997017i	−0.912955	+	0.408060i	$0.866205\pi$
$984$	5.48633	+	3.35148i	0.174898	+	0.106841i
$985$	−10.1786	+	0.906714i	−0.324316	+	0.0288903i
$986$	0.823900	+	2.53570i	0.0262383	+	0.0807532i
$987$	−6.21819	−	13.7998i	−0.197927	−	0.439253i
$988$	24.0348	−	73.9716i	0.764650	−	2.35335i
$989$	−7.10465	+	33.4247i	−0.225915	+	1.06284i
$990$	−34.4113	−	28.6187i	−1.09366	−	0.909562i
$991$	−17.5666	+	3.73389i	−0.558020	+	0.118611i	−0.478284	−	0.878205i	$-0.658741\pi$
$991$	−17.5666	+	3.73389i	−0.558020	+	0.118611i	−0.0797360	+	0.996816i	$0.525408\pi$
$992$	−37.0866	+	16.5120i	−1.17750	+	0.524257i
$993$	−38.6084	+	40.7989i	−1.22520	+	1.29471i
$994$	35.1373	−	12.5645i	1.11449	−	0.398520i
$995$	0.851378	−	53.6310i	0.0269905	−	1.70022i
$996$	60.9095	+	46.6022i	1.92999	+	1.47665i
$997$	17.6723	−	39.6927i	0.559688	−	1.25708i	−0.383105	−	0.923705i	$-0.625145\pi$
$997$	17.6723	−	39.6927i	0.559688	−	1.25708i	0.942794	−	0.333376i	$-0.108188\pi$
$998$	11.7701	+	10.5978i	0.372576	+	0.335469i
$999$	−24.1113	+	8.65233i	−0.762849	+	0.273748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bm.a.131.2	✓	608
3.2	odd	2	inner	525.2.bm.a.131.75	yes	608
7.3	odd	6	inner	525.2.bm.a.206.2	yes	608
21.17	even	6	inner	525.2.bm.a.206.75	yes	608
25.21	even	5	inner	525.2.bm.a.446.75	yes	608
75.71	odd	10	inner	525.2.bm.a.446.2	yes	608
175.171	odd	30	inner	525.2.bm.a.521.75	yes	608
525.521	even	30	inner	525.2.bm.a.521.2	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bm.a.131.2	✓	608	1.1	even	1	trivial
525.2.bm.a.131.75	yes	608	3.2	odd	2	inner
525.2.bm.a.206.2	yes	608	7.3	odd	6	inner
525.2.bm.a.206.75	yes	608	21.17	even	6	inner
525.2.bm.a.446.2	yes	608	75.71	odd	10	inner
525.2.bm.a.446.75	yes	608	25.21	even	5	inner
525.2.bm.a.521.2	yes	608	525.521	even	30	inner
525.2.bm.a.521.75	yes	608	175.171	odd	30	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.572271 + 2.69232i) q^{2} +(-1.59928 + 0.665065i) q^{3} +(-5.09402 - 2.26800i) q^{4} +(-1.14863 + 1.91850i) q^{5} +(-0.875350 - 4.68637i) q^{6} +(-2.63822 - 0.199474i) q^{7} +(5.78563 - 7.96324i) q^{8} +(2.11538 - 2.12725i) q^{9} +O(q^{10})\)	\(q+(-0.572271 + 2.69232i) q^{2} +(-1.59928 + 0.665065i) q^{3} +(-5.09402 - 2.26800i) q^{4} +(-1.14863 + 1.91850i) q^{5} +(-0.875350 - 4.68637i) q^{6} +(-2.63822 - 0.199474i) q^{7} +(5.78563 - 7.96324i) q^{8} +(2.11538 - 2.12725i) q^{9} +(-4.50790 - 4.19039i) q^{10} +(1.80137 + 1.62196i) q^{11} +(9.65512 + 0.239312i) q^{12} +(-3.57571 - 1.16182i) q^{13} +(2.04682 - 6.98879i) q^{14} +(0.561050 - 3.83213i) q^{15} +(10.6664 + 11.8462i) q^{16} +(-0.0334659 + 0.318407i) q^{17} +(4.51667 + 6.91264i) q^{18} +(-1.50899 - 3.38925i) q^{19} +(10.2023 - 7.16778i) q^{20} +(4.35191 - 1.43558i) q^{21} +(-5.39772 + 3.92167i) q^{22} +(-1.53018 + 7.19893i) q^{23} +(-3.95676 + 16.5832i) q^{24} +(-2.36130 - 4.40730i) q^{25} +(5.17426 - 8.96209i) q^{26} +(-1.96832 + 4.80892i) q^{27} +(12.9867 + 6.99961i) q^{28} +(-1.77836 - 2.44771i) q^{29} +(9.99626 + 3.70355i) q^{30} +(1.66904 + 0.175423i) q^{31} +(-20.9491 + 12.0950i) q^{32} +(-3.95960 - 1.39594i) q^{33} +(-0.838102 - 0.272316i) q^{34} +(3.41303 - 4.83231i) q^{35} +(-15.6004 + 6.03856i) q^{36} +(3.29878 + 3.66367i) q^{37} +(9.98850 - 2.12312i) q^{38} +(6.49123 - 0.520010i) q^{39} +(8.63193 + 20.2466i) q^{40} +(0.116529 - 0.358640i) q^{41} +(1.37456 + 12.5383i) q^{42} +4.64302 q^{43} +(-5.49760 - 12.3478i) q^{44} +(1.65134 + 6.50177i) q^{45} +(-18.5062 - 8.23948i) q^{46} +(-0.345253 - 3.28487i) q^{47} +(-24.9370 - 11.8515i) q^{48} +(6.92042 + 1.05251i) q^{49} +(13.2172 - 3.83520i) q^{50} +(-0.158240 - 0.531477i) q^{51} +(15.5797 + 14.0280i) q^{52} +(3.32854 - 7.47603i) q^{53} +(-11.8208 - 8.05135i) q^{54} +(-5.18084 + 1.59290i) q^{55} +(-16.8522 + 19.8547i) q^{56} +(4.66736 + 4.41677i) q^{57} +(7.60772 - 3.38717i) q^{58} +(-5.07894 + 1.07956i) q^{59} +(-11.5493 + 18.2485i) q^{60} +(2.02265 - 9.51584i) q^{61} +(-1.42744 + 4.39319i) q^{62} +(-6.00516 + 5.19019i) q^{63} +(-10.7232 - 33.0026i) q^{64} +(6.33612 - 5.52550i) q^{65} +(6.02428 - 9.86167i) q^{66} +(0.940886 - 8.95194i) q^{67} +(0.892623 - 1.54607i) q^{68} +(-2.34058 - 12.5308i) q^{69} +(11.0570 + 11.9544i) q^{70} +(3.01192 + 4.14555i) q^{71} +(-4.70099 - 29.1527i) q^{72} +(-7.64180 - 6.88071i) q^{73} +(-11.7516 + 6.78477i) q^{74} +(6.70751 + 5.47808i) q^{75} +20.6873i q^{76} +(-4.42888 - 4.63842i) q^{77} +(-2.31471 + 17.7741i) q^{78} +(-0.285223 - 2.71372i) q^{79} +(-34.9787 + 6.85654i) q^{80} +(-0.0503637 - 8.99986i) q^{81} +(0.898887 + 0.518973i) q^{82} +(6.42420 + 4.66746i) q^{83} +(-25.4246 - 2.55730i) q^{84} +(-0.572424 - 0.429936i) q^{85} +(-2.65706 + 12.5005i) q^{86} +(4.47198 + 2.73183i) q^{87} +(23.3381 - 4.96067i) q^{88} +(-0.282427 - 0.0600317i) q^{89} +(-18.4499 + 0.725167i) q^{90} +(9.20176 + 3.77839i) q^{91} +(24.1220 - 33.2010i) q^{92} +(-2.78592 + 0.829468i) q^{93} +(9.04150 + 0.950300i) q^{94} +(8.23555 + 0.997993i) q^{95} +(25.4595 - 33.2758i) q^{96} +(0.984636 + 1.35523i) q^{97} +(-6.79406 + 18.0297i) q^{98} +(7.26089 - 0.400902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9}+O(q^{10}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9	\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 9 * q^3 - 78 * q^4 - 36 * q^7 - 3 * q^9 - 30 * q^10 + 3 * q^12 + 16 * q^15 + 50 * q^16 - 8 * q^18 - 18 * q^19 - 21 * q^21 - 24 * q^22 - 66 * q^24 - 10 * q^25 - 30 * q^28 - 7 * q^30 - 36 * q^31 + 36 * q^33 - 100 * q^36 - 14 * q^37 - 31 * q^39 - 30 * q^40 + 20 * q^42 - 96 * q^43 - 117 * q^45 + 42 * q^46 - 28 * q^49 - 8 * q^51 - 66 * q^52 + 3 * q^54 + 48 * q^57 - 38 * q^58 - 49 * q^60 - 18 * q^61 + 4 * q^63 - 32 * q^64 - 3 * q^66 - 22 * q^67 - 270 * q^70 + 45 * q^72 + 102 * q^73 + 135 * q^75 + 58 * q^78 - 34 * q^79 - 55 * q^81 + 108 * q^82 - 75 * q^84 - 96 * q^85 - 9 * q^87 + 36 * q^88 + 38 * q^91 - 22 * q^93 + 30 * q^94 - 81 * q^96 + 36 * q^99

Introduction

L-functions

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