LMFDB - Embedded newform 153.2.s.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63540 - 2.13130i) q^{2} +(1.11938 + 1.32173i) q^{3} +(-1.35025 + 5.03920i) q^{4} +(-2.13674 - 0.140050i) q^{5} +(0.986361 - 4.54731i) q^{6} +(0.0884715 + 1.34981i) q^{7} +(7.98434 - 3.30722i) q^{8} +(-0.493955 + 2.95906i) q^{9} +O(q^{10})$	\(q+(-1.63540 - 2.13130i) q^{2} +(1.11938 + 1.32173i) q^{3} +(-1.35025 + 5.03920i) q^{4} +(-2.13674 - 0.140050i) q^{5} +(0.986361 - 4.54731i) q^{6} +(0.0884715 + 1.34981i) q^{7} +(7.98434 - 3.30722i) q^{8} +(-0.493955 + 2.95906i) q^{9} +(3.19595 + 4.78307i) q^{10} +(4.13110 + 3.62288i) q^{11} +(-8.17193 + 3.85614i) q^{12} +(2.78970 + 0.747498i) q^{13} +(2.73217 - 2.39605i) q^{14} +(-2.20673 - 2.98097i) q^{15} +(-11.0702 - 6.39140i) q^{16} +(-4.09908 + 0.444433i) q^{17} +(7.11444 - 3.78648i) q^{18} +(1.52287 + 0.630791i) q^{19} +(3.59088 - 10.5784i) q^{20} +(-1.68506 + 1.62790i) q^{21} +(0.965420 - 14.7295i) q^{22} +(-0.0345185 - 0.101688i) q^{23} +(13.3088 + 6.85111i) q^{24} +(-0.411165 - 0.0541309i) q^{25} +(-2.96914 - 7.16814i) q^{26} +(-4.46401 + 2.65945i) q^{27} +(-6.92145 - 1.37676i) q^{28} +(-0.787167 + 0.388188i) q^{29} +(-2.74445 + 9.57829i) q^{30} +(0.607062 + 0.692221i) q^{31} +(2.22624 + 16.9100i) q^{32} +(-0.164185 + 9.51560i) q^{33} +(7.65087 + 8.00954i) q^{34} -2.89660i q^{35} +(-14.2443 - 6.48460i) q^{36} +(-1.25589 - 6.31378i) q^{37} +(-1.14609 - 4.27728i) q^{38} +(2.13476 + 4.52398i) q^{39} +(-17.5237 + 5.94848i) q^{40} +(-3.74023 + 7.58443i) q^{41} +(6.22528 + 0.929097i) q^{42} +(0.342294 - 2.59998i) q^{43} +(-23.8344 + 15.9257i) q^{44} +(1.46987 - 6.25356i) q^{45} +(-0.160276 + 0.239870i) q^{46} +(12.1391 - 3.25265i) q^{47} +(-3.94413 - 21.7863i) q^{48} +(5.12594 - 0.674843i) q^{49} +(0.557051 + 0.964840i) q^{50} +(-5.17587 - 4.92040i) q^{51} +(-7.53359 + 13.0486i) q^{52} +(2.54885 - 6.15346i) q^{53} +(12.9685 + 5.16486i) q^{54} +(-8.31972 - 8.31972i) q^{55} +(5.17052 + 10.4848i) q^{56} +(0.870934 + 2.71892i) q^{57} +(2.11468 + 1.04284i) q^{58} +(-7.11310 - 5.45808i) q^{59} +(18.0014 - 7.09510i) q^{60} +(6.73835 - 0.441655i) q^{61} +(0.482539 - 2.42589i) q^{62} +(-4.03788 - 0.404955i) q^{63} +(14.3217 - 14.3217i) q^{64} +(-5.85619 - 1.98791i) q^{65} +(20.5491 - 15.2119i) q^{66} +(-1.16824 + 0.674481i) q^{67} +(3.29520 - 21.2562i) q^{68} +(0.0957652 - 0.159453i) q^{69} +(-6.17351 + 4.73710i) q^{70} +(-2.51930 + 0.501121i) q^{71} +(5.84235 + 25.2597i) q^{72} +(5.63586 + 3.76576i) q^{73} +(-11.4027 + 13.0022i) q^{74} +(-0.388705 - 0.604043i) q^{75} +(-5.23493 + 6.82230i) q^{76} +(-4.52473 + 5.89674i) q^{77} +(6.15076 - 11.9483i) q^{78} +(4.94717 - 5.64117i) q^{79} +(22.7591 + 15.2072i) q^{80} +(-8.51202 - 2.92328i) q^{81} +(22.2815 - 4.43206i) q^{82} +(-0.745951 + 0.572388i) q^{83} +(-5.92805 - 10.6894i) q^{84} +(8.82093 - 0.375565i) q^{85} +(-6.10113 + 3.52249i) q^{86} +(-1.39422 - 0.605893i) q^{87} +(44.9658 + 15.2638i) q^{88} +(0.774108 - 0.774108i) q^{89} +(-15.7320 + 7.09436i) q^{90} +(-0.762175 + 3.83171i) q^{91} +(0.559036 - 0.0366412i) q^{92} +(-0.235396 + 1.57723i) q^{93} +(-26.7846 - 20.5526i) q^{94} +(-3.16563 - 1.56112i) q^{95} +(-19.8584 + 21.8712i) q^{96} +(-1.47586 - 2.99274i) q^{97} +(-9.82127 - 9.82127i) q^{98} +(-12.7609 + 10.4346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.63540	−	2.13130i	−1.15640	−	1.50705i	−0.826408	−	0.563072i	$-0.809619\pi$
$2$	−1.63540	−	2.13130i	−1.15640	−	1.50705i	−0.329996	−	0.943982i	$-0.607047\pi$
$3$	1.11938	+	1.32173i	0.646277	+	0.763103i
$3$	1.11938	+	1.32173i	0.646277	+	0.763103i
$4$	−1.35025	+	5.03920i	−0.675125	+	2.51960i
$5$	−2.13674	−	0.140050i	−0.955581	−	0.0626321i	−0.420372	−	0.907352i	$-0.638100\pi$
$5$	−2.13674	−	0.140050i	−0.955581	−	0.0626321i	−0.535209	+	0.844720i	$0.679767\pi$
$6$	0.986361	−	4.54731i	0.402680	−	1.85643i
$7$	0.0884715	+	1.34981i	0.0334391	+	0.510182i	0.981422	+	0.191861i	$0.0614523\pi$
$7$	0.0884715	+	1.34981i	0.0334391	+	0.510182i	−0.947983	+	0.318321i	$0.896881\pi$
$8$	7.98434	−	3.30722i	2.82289	−	1.16928i
$9$	−0.493955	+	2.95906i	−0.164652	+	0.986352i
$10$	3.19595	+	4.78307i	1.01065	+	1.51254i
$11$	4.13110	+	3.62288i	1.24557	+	1.09234i	0.992159	+	0.124981i	$0.0398869\pi$
$11$	4.13110	+	3.62288i	1.24557	+	1.09234i	0.253414	+	0.967358i	$0.418446\pi$
$12$	−8.17193	+	3.85614i	−2.35903	+	1.11317i
$13$	2.78970	+	0.747498i	0.773724	+	0.207319i	0.624016	−	0.781412i	$-0.285500\pi$
$13$	2.78970	+	0.747498i	0.773724	+	0.207319i	0.149708	+	0.988730i	$0.452167\pi$
$14$	2.73217	−	2.39605i	0.730203	−	0.640371i
$15$	−2.20673	−	2.98097i	−0.569775	−	0.769684i
$16$	−11.0702	−	6.39140i	−2.76756	−	1.59785i
$17$	−4.09908	+	0.444433i	−0.994174	+	0.107791i
$17$	−4.09908	+	0.444433i	−0.994174	+	0.107791i
$18$	7.11444	−	3.78648i	1.67689	−	0.892482i
$19$	1.52287	+	0.630791i	0.349369	+	0.144713i	0.550465	−	0.834858i	$-0.314450\pi$
$19$	1.52287	+	0.630791i	0.349369	+	0.144713i	−0.201096	+	0.979572i	$0.564450\pi$
$20$	3.59088	−	10.5784i	0.802944	−	2.36540i
$21$	−1.68506	+	1.62790i	−0.367710	+	0.355236i
$22$	0.965420	−	14.7295i	0.205828	−	3.14033i
$23$	−0.0345185	−	0.101688i	−0.00719761	−	0.0212035i	0.943272	−	0.332021i	$-0.107731\pi$
$23$	−0.0345185	−	0.101688i	−0.00719761	−	0.0212035i	−0.950470	+	0.310818i	$0.899397\pi$
$24$	13.3088	+	6.85111i	2.71665	+	1.39848i
$25$	−0.411165	−	0.0541309i	−0.0822329	−	0.0108262i
$26$	−2.96914	−	7.16814i	−0.582297	−	1.40579i
$27$	−4.46401	+	2.65945i	−0.859098	+	0.511810i
$28$	−6.92145	−	1.37676i	−1.30803	−	0.260183i
$29$	−0.787167	+	0.388188i	−0.146173	+	0.0720847i	−0.513904	−	0.857848i	$-0.671801\pi$
$29$	−0.787167	+	0.388188i	−0.146173	+	0.0720847i	0.367731	+	0.929932i	$0.380135\pi$
$30$	−2.74445	+	9.57829i	−0.501066	+	1.74875i
$31$	0.607062	+	0.692221i	0.109031	+	0.124327i	0.803781	−	0.594925i	$-0.202818\pi$
$31$	0.607062	+	0.692221i	0.109031	+	0.124327i	−0.694750	+	0.719252i	$0.744485\pi$
$32$	2.22624	+	16.9100i	0.393547	+	2.98929i
$33$	−0.164185	+	9.51560i	−0.0285809	+	1.65645i
$34$	7.65087	+	8.00954i	1.31211	+	1.37362i
$35$		−	2.89660i		−	0.489614i
$36$	−14.2443	−	6.48460i	−2.37405	−	1.08077i
$37$	−1.25589	−	6.31378i	−0.206467	−	1.03798i	−0.935453	−	0.353451i	$-0.885008\pi$
$37$	−1.25589	−	6.31378i	−0.206467	−	1.03798i	0.728986	−	0.684529i	$-0.239992\pi$
$38$	−1.14609	−	4.27728i	−0.185921	−	0.693866i
$39$	2.13476	+	4.52398i	0.341835	+	0.724416i
$40$	−17.5237	+	5.94848i	−2.77074	+	0.940538i
$41$	−3.74023	+	7.58443i	−0.584125	+	1.18449i	0.381456	+	0.924387i	$0.375423\pi$
$41$	−3.74023	+	7.58443i	−0.584125	+	1.18449i	−0.965581	+	0.260102i	$0.916244\pi$
$42$	6.22528	+	0.929097i	0.960582	+	0.143363i
$43$	0.342294	−	2.59998i	0.0521994	−	0.396494i	−0.945322	−	0.326137i	$-0.894253\pi$
$43$	0.342294	−	2.59998i	0.0521994	−	0.396494i	0.997522	−	0.0703568i	$-0.0224138\pi$
$44$	−23.8344	+	15.9257i	−3.59318	+	2.40088i
$45$	1.46987	−	6.25356i	0.219115	−	0.932226i
$46$	−0.160276	+	0.239870i	−0.0236314	+	0.0353670i
$47$	12.1391	−	3.25265i	1.77067	−	0.474448i	0.781834	−	0.623487i	$-0.214285\pi$
$47$	12.1391	−	3.25265i	1.77067	−	0.474448i	0.988831	+	0.149039i	$0.0476179\pi$
$48$	−3.94413	−	21.7863i	−0.569286	−	3.14459i
$49$	5.12594	−	0.674843i	0.732278	−	0.0964062i
$50$	0.557051	+	0.964840i	0.0787788	+	0.136449i
$51$	−5.17587	−	4.92040i	−0.724767	−	0.688994i
$52$	−7.53359	+	13.0486i	−1.04472	+	1.80951i
$53$	2.54885	−	6.15346i	0.350111	−	0.845243i	−0.646494	−	0.762919i	$-0.723766\pi$
$53$	2.54885	−	6.15346i	0.350111	−	0.845243i	0.996606	−	0.0823245i	$-0.0262344\pi$
$54$	12.9685	+	5.16486i	1.76479	+	0.702849i
$55$	−8.31972	−	8.31972i	−1.12183	−	1.12183i
$56$	5.17052	+	10.4848i	0.690940	+	1.40109i
$57$	0.870934	+	2.71892i	0.115358	+	0.360130i
$58$	2.11468	+	1.04284i	0.277671	+	0.136932i
$59$	−7.11310	−	5.45808i	−0.926047	−	0.710581i	0.0313035	−	0.999510i	$-0.490034\pi$
$59$	−7.11310	−	5.45808i	−0.926047	−	0.710581i	−0.957351	+	0.288929i	$0.906701\pi$
$60$	18.0014	−	7.09510i	2.32397	−	0.915974i
$61$	6.73835	−	0.441655i	0.862758	−	0.0565481i	0.372403	−	0.928071i	$-0.378534\pi$
$61$	6.73835	−	0.441655i	0.862758	−	0.0565481i	0.490355	+	0.871523i	$0.336867\pi$
$62$	0.482539	−	2.42589i	0.0612825	−	0.308088i
$63$	−4.03788	−	0.404955i	−0.508725	−	0.0510196i
$64$	14.3217	−	14.3217i	1.79022	−	1.79022i
$65$	−5.85619	−	1.98791i	−0.726371	−	0.246570i
$66$	20.5491	−	15.2119i	2.52942	−	1.87246i
$67$	−1.16824	+	0.674481i	−0.142723	+	0.0824010i	−0.569661	−	0.821880i	$-0.692926\pi$
$67$	−1.16824	+	0.674481i	−0.142723	+	0.0824010i	0.426938	+	0.904281i	$0.359592\pi$
$68$	3.29520	−	21.2562i	0.399602	−	2.57769i
$69$	0.0957652	−	0.159453i	0.0115288	−	0.0191958i
$70$	−6.17351	+	4.73710i	−0.737876	+	0.566192i
$71$	−2.51930	+	0.501121i	−0.298986	+	0.0594721i	−0.342304	−	0.939589i	$-0.611207\pi$
$71$	−2.51930	+	0.501121i	−0.298986	+	0.0594721i	0.0433176	+	0.999061i	$0.486207\pi$
$72$	5.84235	+	25.2597i	0.688528	+	2.97689i
$73$	5.63586	+	3.76576i	0.659628	+	0.440749i	0.839807	−	0.542885i	$-0.182668\pi$
$73$	5.63586	+	3.76576i	0.659628	+	0.440749i	−0.180180	+	0.983634i	$0.557668\pi$
$74$	−11.4027	+	13.0022i	−1.32553	+	1.51148i
$75$	−0.388705	−	0.604043i	−0.0448838	−	0.0697489i
$76$	−5.23493	+	6.82230i	−0.600488	+	0.782571i
$77$	−4.52473	+	5.89674i	−0.515641	+	0.671996i
$78$	6.15076	−	11.9483i	0.696436	−	1.35288i
$79$	4.94717	−	5.64117i	0.556600	−	0.634681i	−0.403285	−	0.915074i	$-0.632132\pi$
$79$	4.94717	−	5.64117i	0.556600	−	0.634681i	0.959885	+	0.280394i	$0.0904650\pi$
$80$	22.7591	+	15.2072i	2.54455	+	1.70021i
$81$	−8.51202	−	2.92328i	−0.945780	−	0.324809i
$82$	22.2815	−	4.43206i	2.46057	−	0.489439i
$83$	−0.745951	+	0.572388i	−0.0818787	+	0.0628278i	−0.648890	−	0.760882i	$-0.724766\pi$
$83$	−0.745951	+	0.572388i	−0.0818787	+	0.0628278i	0.567011	+	0.823710i	$0.308100\pi$
$84$	−5.92805	−	10.6894i	−0.646803	−	1.16631i
$85$	8.82093	−	0.375565i	0.956764	−	0.0407357i
$86$	−6.10113	+	3.52249i	−0.657902	+	0.379840i
$87$	−1.39422	−	0.605893i	−0.149476	−	0.0649585i
$88$	44.9658	+	15.2638i	4.79337	+	1.62713i
$89$	0.774108	−	0.774108i	0.0820553	−	0.0820553i	−0.664888	−	0.746943i	$-0.731521\pi$
$89$	0.774108	−	0.774108i	0.0820553	−	0.0820553i	0.746943	+	0.664888i	$0.231521\pi$
$90$	−15.7320	+	7.09436i	−1.65830	+	0.747811i
$91$	−0.762175	+	3.83171i	−0.0798976	+	0.401672i
$92$	0.559036	−	0.0366412i	0.0582836	−	0.00382011i
$93$	−0.235396	+	1.57723i	−0.0244094	+	0.163552i
$94$	−26.7846	−	20.5526i	−2.76262	−	2.11984i
$95$	−3.16563	−	1.56112i	−0.324787	−	0.160167i
$96$	−19.8584	+	21.8712i	−2.02679	+	2.23222i
$97$	−1.47586	−	2.99274i	−0.149851	−	0.303867i	0.808985	−	0.587830i	$-0.200017\pi$
$97$	−1.47586	−	2.99274i	−0.149851	−	0.303867i	−0.958835	+	0.283963i	$0.908351\pi$
$98$	−9.82127	−	9.82127i	−0.992098	−	0.992098i
$99$	−12.7609	+	10.4346i	−1.28252	+	1.04872i
$100$	0.827952	−	1.99885i	0.0827952	−	0.199885i
$101$	3.24652	−	5.62314i	0.323041	−	0.559524i	−0.658073	−	0.752954i	$-0.728628\pi$
$101$	3.24652	−	5.62314i	0.323041	−	0.559524i	0.981114	+	0.193431i	$0.0619615\pi$
$102$	−2.02220	+	19.0782i	−0.200228	+	1.88902i
$103$	−5.09455	−	8.82403i	−0.501981	−	0.869457i	−0.999997	−	0.00228936i	$-0.999271\pi$
$103$	−5.09455	−	8.82403i	−0.501981	−	0.869457i	0.498016	−	0.867168i	$-0.334062\pi$
$104$	24.7461	−	3.25788i	2.42655	−	0.319462i
$105$	3.82853	−	3.24241i	0.373626	−	0.316427i
$106$	−17.2833	+	4.63103i	−1.67870	+	0.449806i
$107$	3.03362	−	4.54013i	0.293271	−	0.438911i	−0.655350	−	0.755325i	$-0.727479\pi$
$107$	3.03362	−	4.54013i	0.293271	−	0.438911i	0.948621	+	0.316414i	$0.102479\pi$
$108$	−7.37396	−	26.0859i	−0.709559	−	2.51012i
$109$	−4.35869	+	2.91238i	−0.417486	+	0.278955i	−0.746520	−	0.665363i	$-0.768277\pi$
$109$	−4.35869	+	2.91238i	−0.417486	+	0.278955i	0.329034	+	0.944318i	$0.393277\pi$
$110$	−4.12571	+	31.3379i	−0.393371	+	2.98795i
$111$	6.93931	−	8.72750i	0.658650	−	0.828378i
$112$	7.64781	−	15.5082i	0.722650	−	1.46539i
$113$	17.9151	−	6.08137i	1.68531	−	0.572087i	0.696020	−	0.718023i	$-0.254953\pi$
$113$	17.9151	−	6.08137i	1.68531	−	0.572087i	0.989294	+	0.145936i	$0.0466193\pi$
$114$	4.37050	−	6.30275i	0.409334	−	0.590306i
$115$	0.0595158	+	0.222116i	0.00554988	+	0.0207124i
$116$	−0.893285	−	4.49085i	−0.0829394	−	0.416964i
$117$	−3.58988	+	7.88565i	−0.331884	+	0.729029i
$118$			24.0863i			2.21732i
$119$	−0.962554	−	5.49368i	−0.0882372	−	0.503605i
$120$	−27.4780	−	16.5030i	−2.50839	−	1.50651i
$121$	2.50496	+	19.0270i	0.227723	+	1.72973i
$122$	−11.9612	−	13.6392i	−1.08292	−	1.23483i
$123$	−14.2113	+	3.54632i	−1.28139	+	0.319761i
$124$	−4.30793	+	2.12443i	−0.386863	+	0.190780i
$125$	11.3719	+	2.26201i	1.01713	+	0.202320i
$126$	5.74047	+	9.26818i	0.511402	+	0.825675i
$127$	−5.31191	−	12.8241i	−0.471356	−	1.13795i	−0.963564	−	0.267477i	$-0.913810\pi$
$127$	−5.31191	−	12.8241i	−0.471356	−	1.13795i	0.492208	−	0.870478i	$-0.336190\pi$
$128$	−20.1257	−	2.64960i	−1.77888	−	0.234194i
$129$	3.81964	−	2.45796i	0.336301	−	0.216411i
$130$	5.34040	+	15.7323i	0.468384	+	1.37981i
$131$	−0.807115	+	12.3142i	−0.0705180	+	1.07590i	0.805178	+	0.593033i	$0.202070\pi$
$131$	−0.807115	+	12.3142i	−0.0705180	+	1.07590i	−0.875696	+	0.482863i	$0.839597\pi$
$132$	−47.7294	−	13.6758i	−4.15431	−	1.19033i
$133$	−0.716721	+	2.11139i	−0.0621476	+	0.183081i
$134$	3.34806	+	1.38681i	0.289228	+	0.119802i
$135$	9.91089	−	5.05737i	0.852994	−	0.435269i
$136$	−31.2586	+	17.1051i	−2.68041	+	1.46675i
$137$	9.11866	+	5.26466i	0.779059	+	0.449790i	0.836097	−	0.548582i	$-0.184832\pi$
$137$	9.11866	+	5.26466i	0.779059	+	0.449790i	−0.0570374	+	0.998372i	$0.518165\pi$
$138$	−0.496455	+	0.0566649i	−0.0422611	+	0.00482363i
$139$	−6.98979	+	6.12988i	−0.592866	+	0.519930i	−0.902366	−	0.430970i	$-0.858172\pi$
$139$	−6.98979	+	6.12988i	−0.592866	+	0.519930i	0.309500	+	0.950899i	$0.399838\pi$
$140$	14.5965	+	3.91113i	1.23363	+	0.330551i
$141$	17.8874	+	12.4036i	1.50639	+	1.04457i
$142$	5.18811	+	4.54985i	0.435377	+	0.381815i
$143$	8.81644	+	13.1947i	0.737268	+	1.10340i
$144$	24.3807	−	29.6004i	2.03173	−	2.46670i
$145$	1.73634	−	0.719216i	0.144195	−	0.0597276i
$146$	−1.19094	−	18.1702i	−0.0985629	−	1.50378i
$147$	6.62986	+	6.01972i	0.546822	+	0.496498i
$148$	33.5122	+	2.19651i	2.75469	+	0.180552i
$149$	−4.12354	+	15.3893i	−0.337814	+	1.26074i	0.562973	+	0.826475i	$0.309658\pi$
$149$	−4.12354	+	15.3893i	−0.337814	+	1.26074i	−0.900787	+	0.434262i	$0.857009\pi$
$150$	−0.651706	+	1.81630i	−0.0532116	+	0.148300i
$151$	−7.31129	−	9.52826i	−0.594984	−	0.775399i	0.394677	−	0.918820i	$-0.370856\pi$
$151$	−7.31129	−	9.52826i	−0.594984	−	0.775399i	−0.989662	+	0.143421i	$0.954190\pi$
$152$	14.2452			1.15544
$153$	0.709660	−	12.3489i	0.0573726	−	0.998353i
$154$	19.9675			1.60902
$155$	−1.20019	−	1.56412i	−0.0964016	−	0.125633i
$156$	−25.6797	+	4.64897i	−2.05602	+	0.372215i
$157$	0.746012	−	2.78415i	0.0595382	−	0.222200i	−0.929746	−	0.368201i	$-0.879974\pi$
$157$	0.746012	−	2.78415i	0.0595382	−	0.222200i	0.989284	+	0.146002i	$0.0466404\pi$
$158$	−20.1136	−	1.31832i	−1.60015	−	0.104880i
$159$	10.9864	−	3.51920i	0.871276	−	0.279091i
$160$	−2.38867	−	36.4440i	−0.188841	−	2.88115i
$161$	0.134206	−	0.0555901i	0.0105769	−	0.00438111i
$162$	7.69019	+	22.9224i	0.604198	+	1.80095i
$163$	8.96357	+	13.4149i	0.702081	+	1.05074i	0.995501	+	0.0947544i	$0.0302066\pi$
$163$	8.96357	+	13.4149i	0.702081	+	1.05074i	−0.293420	+	0.955984i	$0.594793\pi$
$164$	−33.1692	−	29.0886i	−2.59008	−	2.27144i
$165$	1.68348	−	20.3094i	0.131059	−	1.58109i
$166$	2.43986	+	0.653758i	0.189370	+	0.0507415i
$167$	5.29475	−	4.64337i	0.409720	−	0.359315i	−0.429537	−	0.903049i	$-0.641323\pi$
$167$	5.29475	−	4.64337i	0.409720	−	0.359315i	0.839258	+	0.543734i	$0.182990\pi$
$168$	−8.07028	+	18.5706i	−0.622635	+	1.43275i
$169$	−4.03465	−	2.32941i	−0.310358	−	0.179185i
$170$	−15.2262	−	18.1858i	−1.16780	−	1.39479i
$171$	−2.61877	+	4.19466i	−0.200263	+	0.320774i
$172$	12.6397	+	5.23552i	0.963765	+	0.399205i
$173$	−4.18371	+	12.3248i	−0.318082	+	0.937039i	0.663860	+	0.747857i	$0.268917\pi$
$173$	−4.18371	+	12.3248i	−0.318082	+	0.937039i	−0.981942	+	0.189182i	$0.939416\pi$
$174$	0.988778	+	3.96238i	0.0749591	+	0.300387i
$175$	0.0366902	−	0.559785i	0.00277352	−	0.0423158i
$176$	−22.5770	−	66.5096i	−1.70180	−	5.01335i
$177$	−0.748182	−	15.5113i	−0.0562368	−	1.16590i
$178$	−2.91583	−	0.383876i	−0.218551	−	0.0287728i
$179$	−8.51837	−	20.5652i	−0.636693	−	1.53711i	−0.831059	−	0.556184i	$-0.812265\pi$
$179$	−8.51837	−	20.5652i	−0.636693	−	1.53711i	0.194366	−	0.980929i	$-0.437735\pi$
$180$	29.5283	+	15.8508i	2.20091	+	1.18145i
$181$	−5.64730	−	1.12332i	−0.419760	−	0.0834955i	−0.0193091	−	0.999814i	$-0.506147\pi$
$181$	−5.64730	−	1.12332i	−0.419760	−	0.0834955i	−0.400451	+	0.916318i	$0.631147\pi$
$182$	9.41298	−	4.64197i	0.697736	−	0.344085i
$183$	8.12656	+	8.41192i	0.600733	+	0.621827i
$184$	−0.611913	−	0.697754i	−0.0451109	−	0.0514391i
$185$	1.79927	+	13.6668i	0.132285	+	1.00480i
$186$	3.74652	−	2.07771i	0.274708	−	0.152345i
$187$	−18.5438	−	13.0145i	−1.35606	−	0.951713i
$188$			65.5631i			4.78168i
$189$	−3.98469	−	5.79029i	−0.289844	−	0.421182i
$190$	1.84988	+	9.29995i	0.134204	+	0.674689i
$191$	3.00617	+	11.2192i	0.217519	+	0.811793i	0.985265	+	0.171038i	$0.0547119\pi$
$191$	3.00617	+	11.2192i	0.217519	+	0.811793i	−0.767745	+	0.640755i	$0.778621\pi$
$192$	34.9610	+	2.89797i	2.52310	+	0.209143i
$193$	4.08616	−	1.38706i	0.294128	−	0.0998431i	−0.170475	−	0.985362i	$-0.554530\pi$
$193$	4.08616	−	1.38706i	0.294128	−	0.0998431i	0.464603	+	0.885519i	$0.346197\pi$
$194$	−3.96480	+	8.03982i	−0.284656	+	0.577226i
$195$	−3.92785	−	9.96555i	−0.281279	−	0.713648i
$196$	−3.52063	+	26.7419i	−0.251474	+	1.91013i
$197$	11.8959	−	7.94858i	0.847547	−	0.566313i	−0.0542232	−	0.998529i	$-0.517268\pi$
$197$	11.8959	−	7.94858i	0.847547	−	0.566313i	0.901770	+	0.432216i	$0.142268\pi$
$198$	43.1084	+	10.1324i	3.06358	+	0.720080i
$199$	4.98036	−	7.45364i	0.353049	−	0.528375i	−0.611858	−	0.790968i	$-0.709578\pi$
$199$	4.98036	−	7.45364i	0.353049	−	0.528375i	0.964907	+	0.262593i	$0.0845776\pi$
$200$	−3.46190	+	0.927614i	−0.244793	+	0.0655922i
$201$	−2.19919	−	0.789092i	−0.155119	−	0.0556582i
$202$	−17.2940	+	2.27679i	−1.21680	+	0.160195i
$203$	−0.593623	−	1.02819i	−0.0416642	−	0.0721645i
$204$	31.7836	−	19.4385i	2.22530	−	1.36097i
$205$	9.05411	−	15.6822i	0.632366	−	1.09529i
$206$	−10.4750	+	25.2888i	−0.729826	+	1.76196i
$207$	0.317952	−	0.0519128i	0.0220992	−	0.00360819i
$208$	−26.1051	−	26.1051i	−1.81006	−	1.81006i
$209$	4.00583	+	8.12302i	0.277089	+	0.561881i
$210$	−13.1717	−	2.85709i	−0.908935	−	0.197158i
$211$	−7.98844	−	3.93946i	−0.549947	−	0.271204i	0.146015	−	0.989282i	$-0.453355\pi$
$211$	−7.98844	−	3.93946i	−0.549947	−	0.271204i	−0.695962	+	0.718079i	$0.745022\pi$
$212$	27.5670	+	21.1529i	1.89331	+	1.45279i
$213$	−3.48242	−	2.76890i	−0.238611	−	0.189722i
$214$	−14.6376	+	0.959396i	−1.00060	+	0.0655830i
$215$	−1.09552	+	5.50756i	−0.0747140	+	0.375613i
$216$	−26.8468	+	35.9974i	−1.82669	+	2.44931i
$217$	−0.880662	+	0.880662i	−0.0597832	+	0.0597832i
$218$	13.3353	+	4.52674i	0.903184	+	0.306590i
$219$	1.33137	+	11.6644i	0.0899654	+	0.788210i
$220$	53.1585	−	30.6910i	3.58394	−	2.06919i
$221$	−11.7674	−	1.82422i	−0.791563	−	0.122710i
$222$	−29.9495	−	0.516757i	−2.01008	−	0.0346825i
$223$	−13.7870	+	10.5792i	−0.923249	+	0.708434i	−0.956721	−	0.291006i	$-0.906010\pi$
$223$	−13.7870	+	10.5792i	−0.923249	+	0.708434i	0.0334725	+	0.999440i	$0.489343\pi$
$224$	−22.6283	+	4.50106i	−1.51192	+	0.300740i
$225$	0.363273	−	1.18992i	0.0242182	−	0.0793281i
$226$	−42.2596	−	28.2370i	−2.81107	−	1.87830i
$227$	−10.4614	+	11.9289i	−0.694346	+	0.791750i	−0.986349	−	0.164667i	$-0.947345\pi$
$227$	−10.4614	+	11.9289i	−0.694346	+	0.791750i	0.292003	+	0.956417i	$0.405678\pi$
$228$	−14.8772	+	0.717594i	−0.985264	+	0.0475238i
$229$	−7.96014	+	10.3739i	−0.526021	+	0.685523i	−0.978499	−	0.206252i	$-0.933873\pi$
$229$	−7.96014	+	10.3739i	−0.526021	+	0.685523i	0.452478	+	0.891775i	$0.350540\pi$
$230$	0.376063	−	0.490095i	0.0247969	−	0.0323159i
$231$	−12.8588	+	0.620241i	−0.846049	+	0.0408088i
$232$	−5.00119	+	5.70276i	−0.328344	+	0.374405i
$233$	−6.58183	−	4.39784i	−0.431190	−	0.288112i	0.320974	−	0.947088i	$-0.395990\pi$
$233$	−6.58183	−	4.39784i	−0.431190	−	0.288112i	−0.752164	+	0.658976i	$0.770990\pi$
$234$	22.6776	−	5.24511i	1.48248	−	0.342884i
$235$	−26.3936	+	5.25002i	−1.72173	+	0.342473i
$236$	37.1088	−	28.4746i	2.41558	−	1.85354i
$237$	12.9939	+	0.224201i	0.844045	+	0.0145634i
$238$	−10.1345	+	11.0359i	−0.656922	+	0.715349i
$239$	17.2098	−	9.93607i	1.11321	−	0.642711i	0.173550	−	0.984825i	$-0.444476\pi$
$239$	17.2098	−	9.93607i	1.11321	−	0.642711i	0.939658	+	0.342114i	$0.111143\pi$
$240$	5.37642	+	47.1042i	0.347046	+	3.04056i
$241$	21.7174	+	7.37205i	1.39894	+	0.474875i	0.916141	−	0.400857i	$-0.131288\pi$
$241$	21.7174	+	7.37205i	1.39894	+	0.474875i	0.482797	+	0.875732i	$0.339621\pi$
$242$	36.4557	−	36.4557i	2.34346	−	2.34346i
$243$	−5.66443	−	14.5229i	−0.363373	−	0.931644i
$244$	−6.87288	+	34.5523i	−0.439991	+	2.21198i
$245$	−11.0473	+	0.724081i	−0.705788	+	0.0462598i
$246$	30.7995	+	24.4890i	1.96371	+	1.56136i
$247$	3.77682	+	2.89806i	0.240313	+	0.184399i
$248$	7.13632	+	3.51924i	0.453157	+	0.223472i
$249$	−1.59155	−	0.345225i	−0.100860	−	0.0218777i
$250$	−13.7766	−	27.9362i	−0.871308	−	1.76684i
$251$	6.33520	+	6.33520i	0.399874	+	0.399874i	0.878189	−	0.478314i	$-0.158752\pi$
$251$	6.33520	+	6.33520i	0.399874	+	0.399874i	−0.478314	+	0.878189i	$0.658752\pi$
$252$	7.49280	−	19.8009i	0.472002	−	1.24734i
$253$	0.225805	−	0.545141i	0.0141962	−	0.0342727i
$254$	−18.6448	+	32.2938i	−1.16988	+	2.02629i
$255$	10.3704	+	11.2385i	0.649421	+	0.703783i
$256$	7.01259	+	12.1462i	0.438287	+	0.759135i
$257$	−23.8299	+	3.13727i	−1.48647	+	0.195697i	−0.829622	−	0.558326i	$-0.811444\pi$
$257$	−23.8299	+	3.13727i	−1.48647	+	0.195697i	−0.656847	+	0.754023i	$0.728110\pi$
$258$	−11.4853	−	4.12104i	−0.715043	−	0.256565i
$259$	8.41133	−	2.25381i	0.522654	−	0.140045i
$260$	17.9248	−	26.8264i	1.11165	−	1.66370i
$261$	−0.759844	−	2.52102i	−0.0470332	−	0.156047i
$262$	27.5652	−	18.4185i	1.70298	−	1.13790i
$263$	1.98287	−	15.0614i	0.122269	−	0.928728i	−0.814839	−	0.579688i	$-0.803174\pi$
$263$	1.98287	−	15.0614i	0.122269	−	0.928728i	0.937108	−	0.349040i	$-0.113492\pi$
$264$	30.1593	+	76.5188i	1.85618	+	4.70941i
$265$	−6.30803	+	12.7914i	−0.387499	+	0.785770i
$266$	5.67213	−	1.92543i	0.347781	−	0.118056i
$267$	1.88969	+	0.156639i	0.115647	+	0.00958616i
$268$	−1.82144	−	6.79770i	−0.111262	−	0.415235i
$269$	1.56768	+	7.88124i	0.0955830	+	0.480528i	0.998693	+	0.0511180i	$0.0162785\pi$
$269$	1.56768	+	7.88124i	0.0955830	+	0.480528i	−0.903110	+	0.429410i	$0.858722\pi$
$270$	−26.9870	−	12.8522i	−1.64238	−	0.782161i
$271$			6.41953i			0.389959i	0.980807	+	0.194979i	$0.0624640\pi$
$271$			6.41953i			0.389959i	−0.980807	+	0.194979i	$0.937536\pi$
$272$	48.2184	+	21.2789i	2.92367	+	1.29022i
$273$	−5.91766	+	3.28177i	−0.358153	+	0.198622i
$274$	−3.69212	−	28.0444i	−0.223049	−	1.69422i
$275$	−1.50245	−	1.71322i	−0.0906013	−	0.103311i
$276$	0.674207	+	0.697881i	0.0405825	+	0.0420075i
$277$	−7.96059	+	3.92573i	−0.478305	+	0.235874i	−0.665427	−	0.746463i	$-0.731751\pi$
$277$	−7.96059	+	3.92573i	−0.478305	+	0.235874i	0.187122	+	0.982337i	$0.440084\pi$
$278$	24.4957	+	4.87250i	1.46915	+	0.292233i
$279$	−2.34818	+	1.45440i	−0.140582	+	0.0870728i
$280$	−9.57969	−	23.1274i	−0.572496	−	1.38213i
$281$	24.3868	+	3.21058i	1.45479	+	0.191527i	0.816089	−	0.577926i	$-0.196138\pi$
$281$	24.3868	+	3.21058i	1.45479	+	0.191527i	0.638704	+	0.769453i	$0.279471\pi$
$282$	−2.81730	−	58.4083i	−0.167768	−	3.47817i
$283$	−4.01907	−	11.8398i	−0.238909	−	0.703803i	−0.998569	−	0.0534825i	$-0.982968\pi$
$283$	−4.01907	−	11.8398i	−0.238909	−	0.703803i	0.759660	−	0.650321i	$-0.225365\pi$
$284$	0.876442	−	13.3719i	0.0520073	−	0.793478i
$285$	−1.48018	−	5.93161i	−0.0876783	−	0.351358i
$286$	13.7035	−	40.3691i	0.810304	−	2.38708i
$287$	−10.5685	−	4.37761i	−0.623838	−	0.258402i
$288$	−51.1372	−	1.76520i	−3.01329	−	0.104015i
$289$	16.6050	−	3.64354i	0.976762	−	0.214326i
$290$	−4.37248	−	2.52445i	−0.256761	−	0.148241i
$291$	2.30355	−	5.30072i	0.135037	−	0.310734i
$292$	−26.5863	+	23.3155i	−1.55584	+	1.36444i
$293$	−8.29762	−	2.22334i	−0.484752	−	0.129889i	0.00816244	−	0.999967i	$-0.497402\pi$
$293$	−8.29762	−	2.22334i	−0.484752	−	0.129889i	−0.492914	+	0.870078i	$0.664068\pi$
$294$	1.98731	−	23.9749i	0.115902	−	1.39824i
$295$	14.4345	+	12.6587i	0.840408	+	0.737018i
$296$	−30.9085	−	46.2579i	−1.79652	−	2.68869i
$297$	−28.0761	−	5.18611i	−1.62914	−	0.300929i
$298$	39.5427	−	16.3791i	2.29065	−	0.948818i
$299$	−0.0202845	−	0.309482i	−0.00117309	−	0.0178978i
$300$	3.56874	−	1.14315i	0.206042	−	0.0660000i
$301$	3.53978	+	0.232009i	0.204029	+	0.0133728i
$302$	−8.35066	+	31.1651i	−0.480526	+	1.79335i
$303$	11.0664	−	2.00342i	0.635748	−	0.115094i
$304$	−12.8268	−	16.7163i	−0.735669	−	0.958743i
$305$	−14.4600			−0.827977
$306$	−27.4798	+	18.6830i	−1.57092	+	1.06804i
$307$	−4.86313			−0.277553			−0.138777	−	0.990324i	$-0.544317\pi$
$307$	−4.86313			−0.277553			−0.138777	+	0.990324i	$0.544317\pi$
$308$	−23.6053	−	30.7631i	−1.34504	−	1.75289i
$309$	5.96024	−	16.6111i	0.339066	−	0.944974i
$310$	−1.37081	+	5.11592i	−0.0778566	+	0.290565i
$311$	15.1912	+	0.995686i	0.861416	+	0.0564602i	0.489705	−	0.871888i	$-0.337105\pi$
$311$	15.1912	+	0.995686i	0.861416	+	0.0564602i	0.371711	+	0.928349i	$0.378771\pi$
$312$	32.0064	+	29.0609i	1.81201	+	1.64525i
$313$	0.926814	+	14.1405i	0.0523867	+	0.799266i	0.940532	+	0.339704i	$0.110327\pi$
$313$	0.926814	+	14.1405i	0.0523867	+	0.799266i	−0.888146	+	0.459562i	$0.848006\pi$
$314$	−7.15389	+	2.96324i	−0.403717	+	0.167225i
$315$	8.57119	+	1.43079i	0.482932	+	0.0806158i
$316$	21.7471	+	32.5468i	1.22337	+	1.83090i
$317$	−25.6641	−	22.5068i	−1.44144	−	1.26411i	−0.908454	−	0.417985i	$-0.862736\pi$
$317$	−25.6641	−	22.5068i	−1.44144	−	1.26411i	−0.532986	−	0.846124i	$-0.678930\pi$
$318$	−25.4676	−	17.6599i	−1.42815	−	0.990320i
$319$	−4.65822	−	1.24817i	−0.260810	−	0.0698839i
$320$	−32.6076	+	28.5961i	−1.82282	+	1.59857i
$321$	9.39663	−	1.07252i	0.524469	−	0.0598623i
$322$	−0.337960	−	0.195121i	−0.0188338	−	0.0108737i
$323$	−6.52269	−	1.90885i	−0.362932	−	0.106211i
$324$	26.2244	−	38.9466i	1.45691	−	2.16370i
$325$	−1.10656	−	0.458354i	−0.0613811	−	0.0254249i
$326$	13.9322	−	41.0428i	0.771631	−	2.27315i
$327$	−8.72843	−	2.50094i	−0.482684	−	0.138302i
$328$	−4.77985	+	72.9265i	−0.263923	+	4.02669i
$329$	5.46444	+	16.0977i	0.301264	+	0.887496i
$330$	−46.0386	+	29.6261i	−2.53434	+	1.63086i
$331$	19.8109	+	2.60816i	1.08891	+	0.143357i	0.653537	−	0.756895i	$-0.273284\pi$
$331$	19.8109	+	2.60816i	1.08891	+	0.143357i	0.435370	+	0.900252i	$0.356618\pi$
$332$	−1.87716	−	4.53186i	−0.103023	−	0.248718i
$333$	19.3032	−	0.597522i	1.05781	−	0.0327440i
$334$	−18.5555	−	3.69091i	−1.01531	−	0.201958i
$335$	2.59068	−	1.27758i	0.141544	−	0.0698018i
$336$	29.0586	−	7.25131i	1.58527	−	0.395591i
$337$	−1.57300	−	1.79367i	−0.0856870	−	0.0977073i	0.707407	−	0.706806i	$-0.249865\pi$
$337$	−1.57300	−	1.79367i	−0.0856870	−	0.0977073i	−0.793094	+	0.609099i	$0.791531\pi$
$338$	1.63362	+	12.4086i	0.0888571	+	0.674936i
$339$	28.0919	+	16.8716i	1.52574	+	0.916341i
$340$	−10.0179	+	44.9576i	−0.543298	+	2.43817i
$341$			5.05894i			0.273957i
$342$	13.2228	−	1.27857i	0.715008	−	0.0691371i
$343$	3.21172	+	16.1464i	0.173416	+	0.871823i
$344$	−5.86573	−	21.8912i	−0.316259	−	1.18029i
$345$	−0.226957	+	0.327297i	−0.0122190	+	0.0176211i
$346$	33.1099	−	11.2393i	1.78000	−	0.604228i
$347$	8.14283	−	16.5120i	0.437130	−	0.886412i	−0.561146	−	0.827717i	$-0.689639\pi$
$347$	8.14283	−	16.5120i	0.437130	−	0.886412i	0.998276	−	0.0586950i	$-0.0186939\pi$
$348$	4.93577	−	6.20767i	0.264585	−	0.332766i
$349$	−2.43018	+	18.4590i	−0.130084	+	0.988089i	0.794541	+	0.607211i	$0.207712\pi$
$349$	−2.43018	+	18.4590i	−0.130084	+	0.988089i	−0.924625	+	0.380878i	$0.875622\pi$
$350$	−1.25307	+	0.837276i	−0.0669795	+	0.0447543i
$351$	−14.4412	+	4.08222i	−0.770813	+	0.217893i
$352$	−52.0659	+	77.9221i	−2.77512	+	4.15326i
$353$	−2.89651	+	0.776118i	−0.154166	+	0.0413086i	−0.335076	−	0.942191i	$-0.608762\pi$
$353$	−2.89651	+	0.776118i	−0.154166	+	0.0413086i	0.180911	+	0.983500i	$0.442095\pi$
$354$	−31.8356	+	26.9618i	−1.69204	+	1.43300i
$355$	5.45329	−	0.717939i	0.289431	−	0.0381043i
$356$	2.85565	+	4.94612i	0.151349	+	0.262144i
$357$	6.18371	−	7.42178i	0.327277	−	0.392802i
$358$	−29.8995	+	51.7875i	−1.58024	+	2.73705i
$359$	0.582339	−	1.40589i	0.0307347	−	0.0742001i	−0.907767	−	0.419475i	$-0.862214\pi$
$359$	0.582339	−	1.40589i	0.0307347	−	0.0742001i	0.938502	+	0.345275i	$0.112214\pi$
$360$	−8.94599	−	54.7918i	−0.471495	−	2.88778i
$361$	−11.5138	−	11.5138i	−0.605990	−	0.605990i
$362$	6.84148	+	13.8731i	0.359580	+	0.729156i
$363$	−22.3447	+	24.6095i	−1.17279	+	1.29166i
$364$	−18.2796	−	9.01452i	−0.958113	−	0.472489i
$365$	−11.5150	−	8.83577i	−0.602723	−	0.462485i
$366$	4.63811	−	31.0770i	0.242438	−	1.62442i
$367$	−12.7162	+	0.833467i	−0.663783	+	0.0435066i	−0.393571	−	0.919294i	$-0.628760\pi$
$367$	−12.7162	+	0.833467i	−0.663783	+	0.0435066i	−0.270212	+	0.962801i	$0.587094\pi$
$368$	−0.267803	+	1.34633i	−0.0139602	+	0.0701825i
$369$	−20.5953	−	14.8139i	−1.07215	−	0.771181i
$370$	26.1855	−	26.1855i	1.36132	−	1.36132i
$371$	8.53153	+	2.89607i	0.442935	+	0.150356i
$372$	−7.63016	−	3.31587i	−0.395606	−	0.171920i
$373$	−32.9021	+	18.9960i	−1.70361	+	0.983577i	−0.761558	+	0.648096i	$0.775565\pi$
$373$	−32.9021	+	18.9960i	−1.70361	+	0.983577i	−0.942047	+	0.335481i	$0.891101\pi$
$374$	2.58893	+	60.8063i	0.133870	+	3.14422i
$375$	9.73975	+	17.5627i	0.502958	+	0.906932i
$376$	86.1652	−	66.1169i	4.44363	−	3.40972i
$377$	−2.48613	+	0.494522i	−0.128042	+	0.0254692i
$378$	−5.82426	+	17.9620i	−0.299568	+	0.923867i
$379$	9.22745	+	6.16558i	0.473982	+	0.316705i	0.769516	−	0.638627i	$-0.220497\pi$
$379$	9.22745	+	6.16558i	0.473982	+	0.316705i	−0.295534	+	0.955332i	$0.595497\pi$
$380$	12.1412	−	13.8444i	0.622829	−	0.710200i
$381$	11.0040	−	21.3760i	0.563750	−	1.09513i
$382$	18.9951	−	24.7549i	0.971876	−	1.26657i
$383$	10.4902	−	13.6710i	0.536022	−	0.698558i	−0.444319	−	0.895869i	$-0.646554\pi$
$383$	10.4902	−	13.6710i	0.536022	−	0.698558i	0.980341	+	0.197311i	$0.0632209\pi$
$384$	−19.0264	−	29.5668i	−0.970936	−	1.50882i
$385$	10.4940	−	11.9661i	0.534825	−	0.609851i
$386$	−9.63876	−	6.44041i	−0.490600	−	0.327808i
$387$	7.52442	+	2.29714i	0.382488	+	0.116770i
$388$	17.0738	−	3.39619i	0.866791	−	0.172415i
$389$	−12.4857	+	9.58058i	−0.633048	+	0.485755i	−0.874736	−	0.484599i	$-0.838965\pi$
$389$	−12.4857	+	9.58058i	−0.633048	+	0.485755i	0.241689	+	0.970354i	$0.422299\pi$
$390$	−14.8159	+	24.6691i	−0.750235	+	1.24917i
$391$	0.186688	+	0.401487i	0.00944121	+	0.0203041i
$392$	38.6954	−	22.3408i	1.95441	−	1.12838i
$393$	−17.1795	+	12.7175i	−0.866593	+	0.641515i
$394$	−36.3953	−	12.3546i	−1.83357	−	0.622413i
$395$	−11.3609	+	11.3609i	−0.571628	+	0.571628i
$396$	−35.3518	−	78.3940i	−1.77649	−	3.93944i
$397$	3.25651	−	16.3716i	0.163440	−	0.821667i	−0.808873	−	0.587983i	$-0.799922\pi$
$397$	3.25651	−	16.3716i	0.163440	−	0.821667i	0.972313	−	0.233684i	$-0.0750780\pi$
$398$	−24.0308	+	1.57506i	−1.20456	+	0.0789508i
$399$	−3.59298	+	1.41615i	−0.179874	+	0.0708960i
$400$	4.20572	+	3.22716i	0.210286	+	0.161358i
$401$	−17.6509	−	8.70445i	−0.881442	−	0.434679i	−0.0555163	−	0.998458i	$-0.517680\pi$
$401$	−17.6509	−	8.70445i	−0.881442	−	0.434679i	−0.825926	+	0.563779i	$0.809347\pi$
$402$	1.91477	+	5.97761i	0.0955001	+	0.298136i
$403$	1.17609	+	2.38487i	0.0585850	+	0.118799i
$404$	23.9525	+	23.9525i	1.19168	+	1.19168i
$405$	17.7786	+	7.43841i	0.883425	+	0.369617i
$406$	−1.22056	+	2.94668i	−0.0605752	+	0.146242i
$407$	17.6859	−	30.6328i	0.876656	−	1.51841i
$408$	−57.5988	−	22.1684i	−2.85157	−	1.09750i
$409$	8.54524	+	14.8008i	0.422535	+	0.731852i	0.996187	−	0.0872476i	$-0.0278071\pi$
$409$	8.54524	+	14.8008i	0.422535	+	0.731852i	−0.573652	+	0.819099i	$0.694474\pi$
$410$	−48.2305	+	6.34966i	−2.38193	+	0.313587i
$411$	3.24881	+	17.9456i	0.160252	+	0.885192i
$412$	51.3450	−	13.7578i	2.52959	−	0.677800i
$413$	6.73808	−	10.0843i	0.331559	−	0.496214i
$414$	−0.630620	−	0.592751i	−0.0309933	−	0.0291321i
$415$	1.67407	−	1.11858i	0.0821768	−	0.0549088i
$416$	−6.42962	+	48.8378i	−0.315238	+	2.39447i
$417$	−15.9263	−	2.37694i	−0.779915	−	0.116399i
$418$	10.7614	−	21.8220i	0.526358	−	1.06735i
$419$	24.1055	−	8.18271i	1.17763	−	0.399752i	0.337075	−	0.941478i	$-0.390562\pi$
$419$	24.1055	−	8.18271i	1.17763	−	0.399752i	0.840555	+	0.541726i	$0.182229\pi$
$420$	11.1697	+	23.6708i	0.545024	+	1.15502i
$421$	−4.57867	−	17.0878i	−0.223151	−	0.832810i	−0.983137	−	0.182871i	$-0.941461\pi$
$421$	−4.57867	−	17.0878i	−0.223151	−	0.832810i	0.759986	−	0.649939i	$-0.225206\pi$
$422$	4.66814	+	23.4683i	0.227242	+	1.14242i
$423$	3.62863	+	37.5268i	0.176430	+	1.82462i
$424$		−	57.5610i		−	2.79541i
$425$	1.70946	+	0.0391516i	0.0829208	+	0.00189913i
$426$	−0.206195	+	11.9503i	−0.00999016	+	0.578996i
$427$	1.19230	+	9.05645i	0.0576997	+	0.438273i
$428$	18.7825	+	21.4173i	0.907887	+	1.03525i
$429$	−7.57092	+	26.4230i	−0.365528	+	1.27571i
$430$	13.5299	−	6.67219i	0.652468	−	0.321762i
$431$	−15.8411	−	3.15099i	−0.763039	−	0.151778i	−0.201794	−	0.979428i	$-0.564677\pi$
$431$	−15.8411	−	3.15099i	−0.763039	−	0.151778i	−0.561244	+	0.827650i	$0.689677\pi$
$432$	66.4152	−	0.909420i	3.19540	−	0.0437545i
$433$	−6.22809	−	15.0359i	−0.299303	−	0.722581i	−0.999959	−	0.00908181i	$-0.997109\pi$
$433$	−6.22809	−	15.0359i	−0.299303	−	0.722581i	0.700656	−	0.713499i	$-0.252891\pi$
$434$	3.31719	+	0.436716i	0.159230	+	0.0209631i
$435$	2.89424	+	1.48990i	0.138768	+	0.0714352i
$436$	−8.79076	−	25.8967i	−0.421001	−	1.24023i
$437$	0.0115770	−	0.176631i	0.000553805	−	0.00844943i
$438$	22.6831	−	21.9136i	1.08384	−	1.04707i
$439$	4.05998	−	11.9603i	0.193772	−	0.570835i	−0.806006	−	0.591908i	$-0.798375\pi$
$439$	4.05998	−	11.9603i	0.193772	−	0.570835i	0.999778	+	0.0210729i	$0.00670821\pi$
$440$	−93.9427	−	38.9123i	−4.47854	−	1.85507i
$441$	−0.535087	+	15.5013i	−0.0254803	+	0.738157i
$442$	15.3565	+	28.0632i	0.730435	+	1.33483i
$443$	−5.31356	−	3.06778i	−0.252455	−	0.145755i	0.368433	−	0.929654i	$-0.379894\pi$
$443$	−5.31356	−	3.06778i	−0.252455	−	0.145755i	−0.620888	+	0.783900i	$0.713228\pi$
$444$	34.6099	+	46.7529i	1.64251	+	2.21879i
$445$	−1.76248	+	1.54566i	−0.0835497	+	0.0732711i
$446$	45.0947	+	12.0831i	2.13530	+	0.572151i
$447$	−24.9563	+	11.7763i	−1.18039	+	0.556999i
$448$	20.5987	+	18.0646i	0.973199	+	0.853473i
$449$	1.16530	+	1.74400i	0.0549941	+	0.0823045i	0.857948	−	0.513737i	$-0.171739\pi$
$449$	1.16530	+	1.74400i	0.0549941	+	0.0823045i	−0.802954	+	0.596042i	$0.796739\pi$
$450$	−3.13017	+	1.17176i	−0.147558	+	0.0552371i
$451$	−42.9287	+	17.7817i	−2.02143	+	0.837306i
$452$	6.45533	+	98.4893i	0.303633	+	4.63255i
$453$	4.40967	−	20.3294i	0.207184	−	0.955157i
$454$	42.5326	+	2.78773i	1.99615	+	0.130835i
$455$	2.16520	−	8.08064i	0.101506	−	0.378826i
$456$	15.9459	+	18.8284i	0.746736	+	0.881721i
$457$	21.1900	+	27.6153i	0.991225	+	1.29179i	0.956296	+	0.292400i	$0.0944538\pi$
$457$	21.1900	+	27.6153i	0.991225	+	1.29179i	0.0349289	+	0.999390i	$0.488880\pi$
$458$	35.1278			1.64141
$459$	17.1164	−	12.8852i	0.798924	−	0.601431i
$460$	−1.19965			−0.0559339
$461$	−3.43307	−	4.47406i	−0.159894	−	0.208378i	0.706535	−	0.707678i	$-0.250257\pi$
$461$	−3.43307	−	4.47406i	−0.159894	−	0.208378i	−0.866429	+	0.499300i	$0.833591\pi$
$462$	22.3513	+	26.3916i	1.03987	+	1.22785i
$463$	9.42436	−	35.1722i	0.437987	−	1.63459i	−0.295829	−	0.955241i	$-0.595596\pi$
$463$	9.42436	−	35.1722i	0.437987	−	1.63459i	0.733816	−	0.679349i	$-0.237738\pi$
$464$	11.1952	+	0.733771i	0.519724	+	0.0340645i
$465$	0.723871	−	3.33718i	0.0335687	−	0.154758i
$466$	1.39084	+	21.2201i	0.0644293	+	0.983001i
$467$	−14.8717	+	6.16006i	−0.688180	+	0.285054i	−0.699242	−	0.714885i	$-0.746479\pi$
$467$	−14.8717	+	6.16006i	−0.688180	+	0.285054i	0.0110614	+	0.999939i	$0.496479\pi$
$468$	−34.8902	−	28.7377i	−1.61280	−	1.32840i
$469$	−1.01378	−	1.51723i	−0.0468120	−	0.0700592i
$470$	54.3535	+	47.6667i	2.50714	+	2.19870i
$471$	4.51498	−	2.13051i	0.208039	−	0.0981688i
$472$	−74.8445	−	20.0545i	−3.44500	−	0.923085i
$473$	10.8335	−	9.50070i	0.498124	−	0.436843i
$474$	−20.7724	−	28.0605i	−0.954109	−	1.28886i
$475$	−0.592003	−	0.341793i	−0.0271630	−	0.0156825i
$476$	28.9835	+	2.56734i	1.32845	+	0.117674i
$477$	16.9494	+	10.5817i	0.776061	+	0.484504i
$478$	−49.3216	−	20.4297i	−2.25592	−	0.934432i
$479$	−4.65452	+	13.7118i	−0.212670	+	0.626507i	0.787281	+	0.616595i	$0.211488\pi$
$479$	−4.65452	+	13.7118i	−0.212670	+	0.626507i	−0.999951	+	0.00991166i	$0.996845\pi$
$480$	45.4954	−	43.9521i	2.07657	−	2.00613i
$481$	1.21599	−	18.5523i	0.0554441	−	0.845914i
$482$	−19.8046	−	58.3424i	−0.902074	−	2.65742i
$483$	0.223704	+	0.115158i	0.0101789	+	0.00523988i
$484$	−99.2635	−	13.0683i	−4.51198	−	0.594013i
$485$	2.73439	+	6.60141i	0.124162	+	0.299755i
$486$	−21.6890	+	35.8233i	−0.983832	+	1.62498i
$487$	39.9633	+	7.94920i	1.81091	+	0.360213i	0.980435	−	0.196841i	$-0.0630682\pi$
$487$	39.9633	+	7.94920i	1.81091	+	0.360213i	0.830477	+	0.557054i	$0.188068\pi$
$488$	52.3407	−	25.8116i	2.36935	−	1.16843i
$489$	−7.69727	+	26.8639i	−0.348082	+	1.21483i
$490$	19.6101	+	22.3610i	0.885892	+	1.01017i
$491$	−2.19843	−	16.6987i	−0.0992136	−	0.753602i	−0.966658	−	0.256069i	$-0.917573\pi$
$491$	−2.19843	−	16.6987i	−0.0992136	−	0.753602i	0.867445	−	0.497533i	$-0.165761\pi$
$492$	1.31827	−	76.4023i	0.0594321	−	3.44448i
$493$	3.05414	−	1.94106i	0.137552	−	0.0874208i
$494$		−	12.7890i		−	0.575405i
$495$	28.7281	−	20.5089i	1.29123	−	0.921808i
$496$	−2.29605	−	11.5430i	−0.103096	−	0.518297i
$497$	−0.899307	−	3.35626i	−0.0403394	−	0.150549i
$498$	1.86705	+	3.95665i	0.0836644	+	0.177302i
$499$	41.0228	−	13.9254i	1.83643	−	0.623385i	0.839661	−	0.543110i	$-0.182753\pi$
$499$	41.0228	−	13.9254i	1.83643	−	0.623385i	0.996773	−	0.0802750i	$-0.0255798\pi$
$500$	−26.7536	+	54.2510i	−1.19646	+	2.42618i
$501$	12.0642	+	1.80053i	0.538987	+	0.0804416i
$502$	3.14160	−	23.8628i	0.140216	−	1.06505i
$503$	−12.8121	+	8.56079i	−0.571265	+	0.381707i	−0.807392	−	0.590015i	$-0.799122\pi$
$503$	−12.8121	+	8.56079i	−0.571265	+	0.381707i	0.236127	+	0.971722i	$0.424122\pi$
$504$	−33.5791	+	10.1209i	−1.49573	+	0.450819i
$505$	−7.72450	+	11.5605i	−0.343736	+	0.514437i
$506$	−1.53114	+	0.410267i	−0.0680674	+	0.0182386i
$507$	−1.43747	−	7.94023i	−0.0638405	−	0.352638i
$508$	71.7956	−	9.45207i	3.18542	−	0.419368i
$509$	−19.4150	−	33.6277i	−0.860553	−	1.49052i	−0.871396	−	0.490580i	$-0.836785\pi$
$509$	−19.4150	−	33.6277i	−0.860553	−	1.49052i	0.0108439	−	0.999941i	$-0.496548\pi$
$510$	6.99282	−	40.4819i	0.309647	−	1.79257i
$511$	−4.58447	+	7.94053i	−0.202805	+	0.351268i
$512$	−1.11782	+	2.69865i	−0.0494010	+	0.119264i
$513$	−8.47563	+	1.23412i	−0.374208	+	0.0544877i
$514$	45.6579	+	45.6579i	2.01388	+	2.01388i
$515$	9.64996	+	19.5682i	0.425228	+	0.862277i
$516$	7.22869	+	22.5668i	0.318225	+	0.993449i
$517$	61.9317	+	30.5413i	2.72375	+	1.34321i
$518$	−18.5594	−	14.2412i	−0.815455	−	0.625720i
$519$	−20.9733	+	8.26647i	−0.920626	+	0.362858i
$520$	−53.3323	+	3.49558i	−2.33878	+	0.153291i
$521$	−3.69545	+	18.5783i	−0.161901	+	0.813930i	0.811417	+	0.584468i	$0.198697\pi$
$521$	−3.69545	+	18.5783i	−0.161901	+	0.813930i	−0.973318	+	0.229462i	$0.926303\pi$
$522$	−4.13039	+	5.74233i	−0.180782	+	0.251335i
$523$	−14.3445	+	14.3445i	−0.627239	+	0.627239i	−0.947373	−	0.320133i	$-0.896272\pi$
$523$	−14.3445	+	14.3445i	−0.627239	+	0.627239i	0.320133	+	0.947373i	$0.396272\pi$
$524$	−60.9639	−	20.6945i	−2.66322	−	0.904042i
$525$	0.780957	−	0.578120i	0.0340837	−	0.0252312i
$526$	−35.3432	+	20.4054i	−1.54104	+	0.889717i
$527$	−2.79604	−	2.56767i	−0.121797	−	0.111850i
$528$	62.6356	−	104.291i	2.72587	−	4.53867i
$529$	18.2380	−	13.9945i	0.792956	−	0.608456i
$530$	37.5784	−	7.47482i	1.63230	−	0.324685i
$531$	19.6643	−	18.3520i	0.853358	−	0.796410i
$532$	−9.67198	−	6.46261i	−0.419333	−	0.280190i
$533$	−16.1035	+	18.3625i	−0.697519	+	0.795368i
$534$	−2.75655	−	4.28365i	−0.119288	−	0.185372i
$535$	−7.11791	+	9.27624i	−0.307734	+	0.401047i
$536$	−7.09694	+	9.24891i	−0.306541	+	0.399492i
$537$	17.6463	−	34.2793i	0.761495	−	1.47926i
$538$	14.2335	−	16.2302i	0.613649	−	0.699733i
$539$	23.6207	+	15.7828i	1.01741	+	0.679814i
$540$	12.1029	+	56.7717i	0.520827	+	2.44307i
$541$	−24.8810	+	4.94913i	−1.06972	+	0.212780i	−0.698386	−	0.715721i	$-0.746098\pi$
$541$	−24.8810	+	4.94913i	−1.06972	+	0.212780i	−0.371330	+	0.928501i	$0.621098\pi$
$542$	13.6819	−	10.4985i	0.587689	−	0.450950i
$543$	−4.83677	−	8.72164i	−0.207566	−	0.374282i
$544$	−16.6409	−	68.3259i	−0.713472	−	2.92945i
$545$	9.72127	−	5.61258i	0.416413	−	0.240416i
$546$	16.6722	+	7.24529i	0.713504	+	0.310070i
$547$	−7.80764	−	2.65034i	−0.333830	−	0.113320i	0.149491	−	0.988763i	$-0.452236\pi$
$547$	−7.80764	−	2.65034i	−0.333830	−	0.113320i	−0.483322	+	0.875443i	$0.660570\pi$
$548$	−38.8422	+	38.8422i	−1.65925	+	1.65925i
$549$	−2.02156	+	20.1573i	−0.0862782	+	0.860294i
$550$	−1.19426	+	6.00398i	−0.0509236	+	0.256010i
$551$	−1.44361	+	0.0946195i	−0.0615001	+	0.00403093i
$552$	0.237277	−	1.58984i	0.0100992	−	0.0676681i
$553$	8.05221	+	6.17868i	0.342415	+	0.262744i
$554$	21.3856	+	10.5462i	0.908589	+	0.448067i
$555$	−16.0498	+	17.6766i	−0.681277	+	0.750330i
$556$	−21.4517	−	43.4998i	−0.909756	−	1.84480i
$557$	−27.8062	−	27.8062i	−1.17819	−	1.17819i	−0.980206	−	0.197983i	$-0.936561\pi$
$557$	−27.8062	−	27.8062i	−1.17819	−	1.17819i	−0.197983	−	0.980206i	$-0.563439\pi$
$558$	6.93998	+	2.62614i	0.293793	+	0.111173i
$559$	2.89838	−	6.99731i	0.122589	−	0.295955i
$560$	−18.5133	+	32.0660i	−0.782331	+	1.35504i
$561$	−3.55604	−	39.0782i	−0.150136	−	1.64988i
$562$	−33.0395	−	57.2260i	−1.39369	−	2.41394i
$563$	−29.7214	+	3.91290i	−1.25261	+	0.164909i	−0.727489	−	0.686119i	$-0.759313\pi$
$563$	−29.7214	+	3.91290i	−1.25261	+	0.164909i	−0.525120	+	0.851028i	$0.675979\pi$
$564$	−86.6569	+	73.3904i	−3.64891	+	3.09029i
$565$	−39.1317	+	10.4853i	−1.64628	+	0.441121i
$566$	−18.6613	+	27.9287i	−0.784395	+	1.17393i
$567$	3.19281	−	11.7483i	0.134086	−	0.493381i
$568$	−18.4577	+	12.3330i	−0.774467	+	0.517482i
$569$	1.83464	−	13.9355i	0.0769121	−	0.584205i	−0.908982	−	0.416835i	$-0.863139\pi$
$569$	1.83464	−	13.9355i	0.0769121	−	0.584205i	0.985894	−	0.167370i	$-0.0535275\pi$
$570$	−10.2213	+	12.8553i	−0.428124	+	0.538448i
$571$	2.90629	−	5.89338i	0.121624	−	0.246630i	−0.827542	−	0.561403i	$-0.810262\pi$
$571$	2.90629	−	5.89338i	0.121624	−	0.246630i	0.949167	+	0.314773i	$0.101928\pi$
$572$	−78.3953	+	26.6116i	−3.27787	+	1.11269i
$573$	−11.4637	+	16.5320i	−0.478904	+	0.690632i
$574$	7.95373	+	29.6837i	0.331982	+	1.23897i
$575$	0.00868832	+	0.0436791i	0.000362328	+	0.00182155i
$576$	35.3045	+	49.4531i	1.47102	+	2.06055i
$577$			16.7198i			0.696054i	0.937485	+	0.348027i	$0.113148\pi$
$577$			16.7198i			0.696054i	−0.937485	+	0.348027i	$0.886852\pi$
$578$	−34.9212	−	29.4315i	−1.45253	−	1.22419i
$579$	6.40731	+	3.84815i	0.266279	+	0.159924i
$580$	1.27978	+	9.72089i	0.0531399	+	0.403638i
$581$	−0.838613	−	0.956255i	−0.0347915	−	0.0396721i
$582$	−15.0646	+	3.75925i	−0.624449	+	0.155826i
$583$	32.8228	−	16.1864i	1.35938	−	0.670373i
$584$	57.4529	+	11.4281i	2.37742	+	0.472898i
$585$	8.77503	−	16.3469i	0.362803	−	0.675859i
$586$	8.83134	+	21.3207i	0.364819	+	0.880752i
$587$	−47.1130	−	6.20254i	−1.94456	−	0.256006i	−0.946740	−	0.322000i	$-0.895645\pi$
$587$	−47.1130	−	6.20254i	−1.94456	−	0.256006i	−0.997820	+	0.0659940i	$0.978978\pi$
$588$	−39.2866	+	25.2811i	−1.62015	+	1.04258i
$589$	0.487826	+	1.43709i	0.0201005	+	0.0592142i
$590$	3.37327	−	51.4662i	0.138875	−	2.11883i
$591$	23.8220	+	6.82567i	0.979905	+	0.280770i
$592$	−26.4509	+	77.9220i	−1.08713	+	3.20257i
$593$	−1.98655	−	0.822857i	−0.0815780	−	0.0337907i	0.341521	−	0.939874i	$-0.389058\pi$
$593$	−1.98655	−	0.822857i	−0.0815780	−	0.0337907i	−0.423099	+	0.906083i	$0.639058\pi$
$594$	34.8626	+	68.3199i	1.43043	+	2.80320i
$595$	1.28734	+	11.8734i	0.0527760	+	0.486762i
$596$	−71.9818	−	41.5587i	−2.94849	−	1.70231i
$597$	15.4267	−	1.76078i	0.631371	−	0.0720640i
$598$	−0.626425	+	0.549360i	−0.0256164	+	0.0224650i
$599$	6.33654	+	1.69787i	0.258904	+	0.0693731i	0.385936	−	0.922525i	$-0.373878\pi$
$599$	6.33654	+	1.69787i	0.258904	+	0.0693731i	−0.127032	+	0.991899i	$0.540545\pi$
$600$	−5.10126	−	3.53735i	−0.208258	−	0.144412i
$601$	−2.71156	−	2.37798i	−0.110607	−	0.0969997i	0.602256	−	0.798303i	$-0.294269\pi$
$601$	−2.71156	−	2.37798i	−0.110607	−	0.0969997i	−0.712863	+	0.701303i	$0.752602\pi$
$602$	−5.29448	−	7.92375i	−0.215787	−	0.322948i
$603$	−1.41877	−	3.79004i	−0.0577769	−	0.154342i
$604$	57.8869	−	23.9775i	2.35539	−	0.975632i
$605$	−2.68772	−	41.0067i	−0.109271	−	1.66716i
$606$	−22.3679	−	20.3094i	−0.908634	−	0.825012i
$607$	−3.36588	−	0.220611i	−0.136617	−	0.00895434i	−0.00305874	−	0.999995i	$-0.500974\pi$
$607$	−3.36588	−	0.220611i	−0.136617	−	0.00895434i	−0.133558	+	0.991041i	$0.542640\pi$
$608$	−7.27639	+	27.1559i	−0.295097	+	1.10132i
$609$	0.694494	−	1.93555i	0.0281423	−	0.0784323i
$610$	23.6479	+	30.8185i	0.957475	+	1.24781i
$611$	36.2957			1.46837
$612$	61.2706	+	20.2503i	2.47672	+	0.818569i
$613$	7.06861			0.285499			0.142749	−	0.989759i	$-0.454406\pi$
$613$	7.06861			0.285499			0.142749	+	0.989759i	$0.454406\pi$
$614$	7.95317	+	10.3648i	0.320964	+	0.418288i
$615$	30.8627	−	5.58728i	1.24450	−	0.225301i
$616$	−16.6251	+	62.0459i	−0.669846	+	2.49990i
$617$	18.8780	+	1.23733i	0.760001	+	0.0498131i	0.440475	−	0.897765i	$-0.354810\pi$
$617$	18.8780	+	1.23733i	0.760001	+	0.0498131i	0.319525	+	0.947578i	$0.396477\pi$
$618$	−45.1506	+	14.4628i	−1.81622	+	0.581780i
$619$	−1.87414	−	28.5938i	−0.0753280	−	1.14928i	−0.853452	−	0.521172i	$-0.825495\pi$
$619$	−1.87414	−	28.5938i	−0.0753280	−	1.14928i	0.778124	−	0.628111i	$-0.216172\pi$
$620$	9.50246	−	3.93605i	0.381628	−	0.158076i
$621$	0.424525	+	0.362137i	0.0170356	+	0.0145321i
$622$	−22.7217	−	34.0054i	−0.911056	−	1.36349i
$623$	1.11339	+	0.976415i	0.0446070	+	0.0391192i
$624$	5.28231	−	63.7256i	0.211462	−	2.55106i
$625$	−21.9791	−	5.88929i	−0.879164	−	0.235571i
$626$	28.6218	−	25.1006i	1.14396	−	1.00322i
$627$	−6.25239	+	14.3874i	−0.249697	+	0.574578i
$628$	13.0226	+	7.51861i	0.519659	+	0.300025i
$629$	7.95405	+	25.3226i	0.317149	+	1.00968i
$630$	−10.9679	−	20.6077i	−0.436972	−	0.821029i
$631$	14.5996	+	6.04736i	0.581202	+	0.240742i	0.653860	−	0.756615i	$-0.273148\pi$
$631$	14.5996	+	6.04736i	0.581202	+	0.240742i	−0.0726586	+	0.997357i	$0.523148\pi$
$632$	20.8433	−	61.4024i	0.829102	−	2.44246i
$633$	−3.73522	−	14.9684i	−0.148462	−	0.594939i
$634$	−5.99759	+	91.5055i	−0.238195	+	3.63415i
$635$	9.55419	+	28.1457i	0.379146	+	1.11693i
$636$	2.89959	+	60.1144i	0.114976	+	2.38369i
$637$	14.8043	+	1.94902i	0.586567	+	0.0772231i
$638$	4.95785	+	11.9693i	0.196283	+	0.473870i
$639$	−0.238421	−	7.70229i	−0.00943179	−	0.304698i
$640$	42.6325	+	8.48013i	1.68520	+	0.335206i
$641$	−24.8775	+	12.2682i	−0.982600	+	0.484565i	−0.861325	−	0.508054i	$-0.830365\pi$
$641$	−24.8775	+	12.2682i	−0.982600	+	0.484565i	−0.121275	+	0.992619i	$0.538698\pi$
$642$	−17.6531	−	18.2730i	−0.696714	−	0.721178i
$643$	−22.5954	−	25.7651i	−0.891074	−	1.01608i	−0.999758	−	0.0219988i	$-0.992997\pi$
$643$	−22.5954	−	25.7651i	−0.891074	−	1.01608i	0.108684	−	0.994076i	$-0.465336\pi$
$644$	0.0989176	+	0.751354i	0.00389790	+	0.0296075i
$645$	−8.50584	+	4.71709i	−0.334917	+	0.185735i
$646$	6.59889	+	17.0235i	0.259630	+	0.669782i
$647$		−	42.2825i		−	1.66230i	−0.556051	−	0.831148i	$-0.687684\pi$
$647$		−	42.2825i		−	1.66230i	0.556051	−	0.831148i	$-0.312316\pi$
$648$	−77.6308	+	4.81066i	−3.04963	+	0.188981i
$649$	−9.61100	−	48.3178i	−0.377265	−	1.89664i
$650$	0.832788	+	3.10801i	0.0326647	+	0.121906i
$651$	−2.14980	−	0.178200i	−0.0842573	−	0.00698421i
$652$	−79.7036	+	27.0557i	−3.12143	+	1.05958i
$653$	−2.26793	+	4.59890i	−0.0887509	+	0.179969i	−0.936723	−	0.350072i	$-0.886157\pi$
$653$	−2.26793	+	4.59890i	−0.0887509	+	0.179969i	0.847972	+	0.530041i	$0.177824\pi$
$654$	8.94425	+	22.6929i	0.349748	+	0.887364i
$655$	3.44920	−	26.1992i	0.134771	−	1.02369i
$656$	89.8804	−	60.0561i	3.50924	−	2.34480i
$657$	−13.9270	+	14.8167i	−0.543343	+	0.578055i
$658$	25.3725	−	37.9726i	0.989122	−	1.48033i
$659$	18.6131	−	4.98736i	0.725063	−	0.194280i	0.122633	−	0.992452i	$-0.460866\pi$
$659$	18.6131	−	4.98736i	0.725063	−	0.194280i	0.602430	+	0.798172i	$0.294199\pi$
$660$	100.070	+	35.9062i	3.89522	+	1.39765i
$661$	−32.0756	+	4.22283i	−1.24760	+	0.164249i	−0.725250	−	0.688485i	$-0.758276\pi$
$661$	−32.0756	+	4.22283i	−1.24760	+	0.164249i	−0.522345	+	0.852734i	$0.674943\pi$
$662$	−26.8401	−	46.4883i	−1.04317	−	1.80682i
$663$	−10.7611	−	17.5954i	−0.417928	−	0.683349i
$664$	−4.06291	+	7.03717i	−0.157672	+	0.273095i
$665$	1.82715	−	4.41113i	0.0708538	−	0.171056i
$666$	−32.8420	−	40.1636i	−1.27260	−	1.55631i
$667$	0.0666460	+	0.0666460i	0.00258054	+	0.00258054i
$668$	16.2497	+	32.9511i	0.628718	+	1.27491i
$669$	−29.4158	−	6.38062i	−1.13728	−	0.246689i
$670$	−6.95972	−	3.43215i	−0.268877	−	0.132596i
$671$	29.4369	+	22.5877i	1.13640	+	0.871989i
$672$	−31.2790	−	24.8702i	−1.20661	−	0.959389i
$673$	−11.4451	+	0.750152i	−0.441176	+	0.0289162i	−0.284373	−	0.958714i	$-0.591785\pi$
$673$	−11.4451	+	0.750152i	−0.441176	+	0.0289162i	−0.156803	+	0.987630i	$0.550119\pi$
$674$	−1.25034	+	6.28591i	−0.0481615	+	0.242124i
$675$	1.97940	−	0.851829i	0.0761871	−	0.0327869i
$676$	17.1861	−	17.1861i	0.661005	−	0.661005i
$677$	7.93740	+	2.69438i	0.305059	+	0.103554i	0.469772	−	0.882788i	$-0.344336\pi$
$677$	7.93740	+	2.69438i	0.305059	+	0.103554i	−0.164712	+	0.986342i	$0.552670\pi$
$678$	−9.98305	−	87.4640i	−0.383397	−	3.35903i
$679$	3.90907	−	2.25690i	0.150016	−	0.0866120i
$680$	69.1873	−	32.1714i	2.65321	−	1.23372i
$681$	−27.4771	−	0.474099i	−1.05293	−	0.0181675i
$682$	10.7821	−	8.27341i	0.412868	−	0.316805i
$683$	3.33345	−	0.663064i	0.127551	−	0.0253714i	−0.130902	−	0.991395i	$-0.541787\pi$
$683$	3.33345	−	0.663064i	0.127551	−	0.0253714i	0.258453	+	0.966024i	$0.416787\pi$
$684$	−17.6017	−	18.8604i	−0.673019	−	0.721144i
$685$	−18.7469	−	12.5263i	−0.716283	−	0.478605i
$686$	29.1603	−	33.2510i	1.11335	−	1.26953i
$687$	−22.6219	+	1.09116i	−0.863080	+	0.0416303i
$688$	−20.4068	+	26.5947i	−0.778003	+	1.01391i
$689$	11.7102	−	15.2611i	0.446124	−	0.581400i
$690$	1.06873	−	0.0515500i	0.0406860	−	0.00196247i
$691$	−26.0416	+	29.6947i	−0.990668	+	1.12964i	0.000893049		1.00000i	$0.499716\pi$
$691$	−26.0416	+	29.6947i	−0.990668	+	1.12964i	−0.991561	+	0.129641i	$0.958618\pi$
$692$	−56.4582	−	37.7242i	−2.14622	−	1.43406i
$693$	−15.2138	−	16.3016i	−0.577923	−	0.619248i
$694$	−48.5088	+	9.64900i	−1.84137	+	0.366271i
$695$	15.7939	−	12.1191i	0.599096	−	0.459702i
$696$	−13.1358	−	0.226649i	−0.497911	−	0.00859110i
$697$	11.9607	−	32.7515i	0.453045	−	1.24055i
$698$	43.3160	−	25.0085i	1.63953	−	0.946585i
$699$	−1.55483	−	13.6223i	−0.0588092	−	0.515243i
$700$	2.77133	+	0.940739i	0.104746	+	0.0355566i
$701$	−12.5259	+	12.5259i	−0.473097	+	0.473097i	−0.902915	−	0.429819i	$-0.858577\pi$
$701$	−12.5259	+	12.5259i	−0.473097	+	0.473097i	0.429819	+	0.902915i	$0.358577\pi$
$702$	32.3175	+	24.1024i	1.21975	+	0.909685i
$703$	2.07013	−	10.4072i	0.0780764	−	0.392517i
$704$	111.050	−	7.27863i	4.18537	−	0.274324i
$705$	−36.4837	−	29.0085i	−1.37406	−	1.09252i
$706$	6.39109	+	4.90406i	0.240532	+	0.184567i
$707$	7.87742	+	3.88471i	0.296261	+	0.146100i
$708$	79.1749	+	17.1739i	2.97557	+	0.645435i
$709$	13.5590	+	27.4950i	0.509220	+	1.03260i	0.987970	+	0.154645i	$0.0494233\pi$
$709$	13.5590	+	27.4950i	0.509220	+	1.03260i	−0.478750	+	0.877951i	$0.658910\pi$
$710$	−10.4485	−	10.4485i	−0.392124	−	0.392124i
$711$	14.2488	+	17.4254i	0.534374	+	0.653505i
$712$	3.62059	−	8.74089i	0.135688	−	0.327579i
$713$	0.0494359	−	0.0856255i	0.00185139	−	0.00320670i
$714$	−25.9309	−	1.04173i	−0.970439	−	0.0389856i
$715$	−16.9906	−	29.4285i	−0.635411	−	1.10056i
$716$	115.134	−	15.1577i	4.30276	−	0.566469i
$717$	32.3972	+	11.6244i	1.20990	+	0.434123i
$718$	−3.94873	+	1.05806i	−0.147365	+	0.0394864i
$719$	5.05283	−	7.56210i	0.188439	−	0.282019i	−0.725206	−	0.688532i	$-0.758255\pi$
$719$	5.05283	−	7.56210i	0.188439	−	0.282019i	0.913645	+	0.406513i	$0.133255\pi$
$720$	−56.2408	+	59.8339i	−2.09597	+	2.22988i
$721$	11.4601	−	7.65738i	0.426795	−	0.285176i
$722$	−5.70964	+	43.3691i	−0.212491	+	1.61403i
$723$	14.5662	+	36.9567i	0.541723	+	1.37443i
$724$	13.2859	−	26.9411i	0.493766	−	1.00126i
$725$	0.344668	−	0.116999i	0.0128007	−	0.00434524i
$726$	88.9926	+	7.37673i	3.30282	+	0.273776i
$727$	11.8752	+	44.3189i	0.440427	+	1.64370i	0.727735	+	0.685858i	$0.240573\pi$
$727$	11.8752	+	44.3189i	0.440427	+	1.64370i	−0.287308	+	0.957838i	$0.592760\pi$
$728$	6.58686	+	33.1144i	0.244125	+	1.22730i
$729$	12.8547	−	23.7436i	0.476100	−	0.879391i
$730$			38.9919i			1.44316i
$731$	−0.247574	+	10.8097i	−0.00915685	+	0.399810i
$732$	−53.3623	+	29.5932i	−1.97233	+	1.09380i
$733$	4.84705	+	36.8170i	0.179030	+	1.35987i	0.811078	+	0.584938i	$0.198881\pi$
$733$	4.84705	+	36.8170i	0.179030	+	1.35987i	−0.632048	+	0.774929i	$0.717786\pi$
$734$	22.5725	+	25.7390i	0.833168	+	0.950046i
$735$	−13.3233	−	13.7911i	−0.491436	−	0.508692i
$736$	1.64270	−	0.810089i	0.0605506	−	0.0298603i
$737$	−7.26966	−	1.44603i	−0.267782	−	0.0532651i
$738$	2.10866	+	68.1213i	0.0776210	+	2.50758i
$739$	14.1419	+	34.1416i	0.520218	+	1.25592i	0.937768	+	0.347264i	$0.112889\pi$
$739$	14.1419	+	34.1416i	0.520218	+	1.25592i	−0.417549	+	0.908654i	$0.637111\pi$
$740$	−71.2994	−	9.38674i	−2.62102	−	0.345063i
$741$	0.397260	+	8.23599i	0.0145937	+	0.302557i
$742$	−7.78011	−	22.9195i	−0.285617	−	0.841400i
$743$	−2.61450	+	39.8895i	−0.0959166	+	1.46341i	0.630521	+	0.776172i	$0.282841\pi$
$743$	−2.61450	+	39.8895i	−0.0959166	+	1.46341i	−0.726437	+	0.687233i	$0.758825\pi$
$744$	3.33679	+	13.3717i	0.122333	+	0.490230i
$745$	10.9662	−	32.3054i	0.401771	−	1.18358i
$746$	94.2943	+	39.0580i	3.45236	+	1.43001i
$747$	−1.32526	−	2.49004i	−0.0484888	−	0.0911059i
$748$	90.6214	−	75.8734i	3.31345	−	2.77421i
$749$	6.39673	+	3.69315i	0.233731	+	0.134945i
$750$	21.5028	−	49.4803i	0.785173	−	1.80677i
$751$	−13.9754	+	12.2561i	−0.509968	+	0.447230i	−0.875253	−	0.483666i	$-0.839305\pi$
$751$	−13.9754	+	12.2561i	−0.509968	+	0.447230i	0.365285	+	0.930896i	$0.380972\pi$
$752$	−155.171	−	41.5780i	−5.65852	−	1.51619i
$753$	−1.28191	+	15.4650i	−0.0467156	+	0.563575i
$754$	5.11980	+	4.48994i	0.186452	+	0.163514i
$755$	14.2879	+	21.3834i	0.519991	+	0.778221i
$756$	34.5588	−	12.2613i	1.25689	−	0.445940i
$757$	34.1052	−	14.1268i	1.23958	−	0.513449i	0.335994	−	0.941864i	$-0.390928\pi$
$757$	34.1052	−	14.1268i	1.23958	−	0.513449i	0.903582	+	0.428415i	$0.140928\pi$
$758$	−1.94989	−	29.7496i	−0.0708234	−	1.08056i
$759$	0.973293	−	0.311769i	0.0353283	−	0.0113165i
$760$	−30.4384	−	1.99504i	−1.10412	−	0.0723677i
$761$	−0.747308	+	2.78899i	−0.0270899	+	0.101101i	−0.978147	−	0.207914i	$-0.933333\pi$
$761$	−0.747308	+	2.78899i	−0.0270899	+	0.101101i	0.951057	+	0.309015i	$0.0999993\pi$
$762$	−63.5546	+	11.5057i	−2.30234	+	0.416808i
$763$	−4.31679	−	5.62575i	−0.156278	−	0.203666i
$764$	−60.5949			−2.19225
$765$	−3.24583	+	26.2871i	−0.117353	+	0.950413i
$766$	−46.2927			−1.67262
$767$	−15.7635	−	20.5434i	−0.569188	−	0.741780i
$768$	−8.20419	+	22.8650i	−0.296043	+	0.825069i
$769$	9.23276	−	34.4571i	0.332942	−	1.24256i	−0.573141	−	0.819457i	$-0.694275\pi$
$769$	9.23276	−	34.4571i	0.332942	−	1.24256i	0.906083	−	0.423100i	$-0.139058\pi$
$770$	−42.6653	−	2.79643i	−1.53755	−	0.100776i
$771$	−30.8215	−	27.9850i	−1.11001	−	1.00785i
$772$	1.47236	+	22.4639i	0.0529914	+	0.808492i
$773$	45.2182	−	18.7300i	1.62639	−	0.673671i	0.631567	−	0.775322i	$-0.282412\pi$
$773$	45.2182	−	18.7300i	1.62639	−	0.673671i	0.994820	+	0.101650i	$0.0324123\pi$
$774$	−7.40955	−	19.7935i	−0.266331	−	0.711464i
$775$	−0.212132	−	0.317478i	−0.00762000	−	0.0114041i
$776$	−21.6814	−	19.0141i	−0.778317	−	0.682566i
$777$	12.3944	+	8.59465i	0.444648	+	0.308331i
$778$	40.8381	+	10.9425i	1.46412	+	0.392309i
$779$	−10.4801	+	9.19076i	−0.375487	+	0.329293i
$780$	55.5220	−	6.33722i	1.98801	−	0.226909i
$781$	−12.2230	−	7.05695i	−0.437373	−	0.252518i
$782$	0.550379	−	1.05448i	0.0196815	−	0.0377081i
$783$	2.48155	−	3.82630i	0.0886835	−	0.136741i
$784$	−61.0586	−	25.2913i	−2.18066	−	0.903260i
$785$	−1.98395	+	5.84454i	−0.0708104	+	0.208601i
$786$	55.2003	+	15.8164i	1.96893	+	0.564154i
$787$	−0.353545	+	5.39406i	−0.0126025	+	0.192277i	0.986916	+	0.161238i	$0.0515485\pi$
$787$	−0.353545	+	5.39406i	−0.0126025	+	0.192277i	−0.999518	+	0.0310398i	$0.990118\pi$
$788$	23.9921	+	70.6783i	0.854682	+	2.51781i
$789$	22.1268	−	14.2387i	0.787734	−	0.506911i
$790$	42.7930	+	5.63381i	1.52251	+	0.200442i
$791$	9.79370	+	23.6441i	0.348224	+	0.840686i
$792$	−67.3776	+	125.517i	−2.39416	+	4.46004i
$793$	19.1281	+	3.80482i	0.679260	+	0.135113i
$794$	−40.2184	+	19.8335i	−1.42730	+	0.703866i
$795$	−23.9679	+	5.98099i	−0.850055	+	0.212124i
$796$	30.8357	+	35.1613i	1.09294	+	1.24626i
$797$	−1.22950	−	9.33896i	−0.0435510	−	0.330803i	−0.999326	−	0.0367045i	$-0.988314\pi$
$797$	−1.22950	−	9.33896i	−0.0435510	−	0.330803i	0.955775	−	0.294098i	$-0.0950194\pi$
$798$	8.89420	+	5.34174i	0.314851	+	0.189096i
$799$	−48.3135	+	18.7279i	−1.70921	+	0.662545i
$800$		−	7.07329i		−	0.250078i
$801$	1.90825	+	2.67300i	0.0674248	+	0.0944459i
$802$	10.3145	+	51.8545i	0.364218	+	1.83105i
$803$	9.63941	+	35.9748i	0.340167	+	1.26952i
$804$	6.94585	−	10.0167i	0.244961	−	0.353262i
$805$	−0.294550	+	0.0999862i	−0.0103815	+	0.00352405i
$806$	3.15949	−	6.40681i	0.111288	−	0.225670i
$807$	−8.66207	+	10.8942i	−0.304919	+	0.383494i
$808$	7.32436	−	55.6341i	0.257670	−	1.95720i
$809$	−18.1807	+	12.1480i	−0.639201	+	0.427100i	−0.832489	−	0.554042i	$-0.813085\pi$
$809$	−18.1807	+	12.1480i	−0.639201	+	0.427100i	0.193288	+	0.981142i	$0.438085\pi$
$810$	−13.2217	−	50.0562i	−0.464563	−	1.75880i
$811$	−0.595178	+	0.890746i	−0.0208995	+	0.0312783i	−0.841772	−	0.539833i	$-0.818487\pi$
$811$	−0.595178	+	0.890746i	−0.0208995	+	0.0312783i	0.820873	+	0.571111i	$0.193487\pi$
$812$	5.98278	−	1.60308i	0.209954	−	0.0562571i
$813$	−8.48491	+	7.18593i	−0.297579	+	0.252022i
$814$	−94.2111	+	12.4031i	−3.30210	+	0.434729i
$815$	−17.2741	−	29.9196i	−0.605085	−	1.04804i
$816$	25.8499	+	87.5511i	0.904926	+	3.06490i
$817$	2.16132	−	3.74351i	0.0756149	−	0.130969i
$818$	17.5700	−	42.4177i	0.614320	−	1.48310i
$819$	−10.9618	−	4.14801i	−0.383035	−	0.144943i
$820$	66.8003	+	66.8003i	2.33277	+	2.33277i
$821$	−5.24118	−	10.6281i	−0.182919	−	0.370922i	0.786029	−	0.618190i	$-0.212134\pi$
$821$	−5.24118	−	10.6281i	−0.182919	−	0.370922i	−0.968947	+	0.247268i	$0.920467\pi$
$822$	32.9343	−	36.2725i	1.14872	−	1.26515i
$823$	−8.13427	−	4.01138i	−0.283543	−	0.139828i	0.294957	−	0.955511i	$-0.404695\pi$
$823$	−8.13427	−	4.01138i	−0.283543	−	0.139828i	−0.578499	+	0.815683i	$0.696361\pi$
$824$	−69.8597	−	53.6052i	−2.43368	−	1.86743i
$825$	0.582595	−	3.90359i	0.0202834	−	0.135906i
$826$	−32.5120	+	2.13095i	−1.13124	+	0.0741452i
$827$	2.09798	−	10.5473i	0.0729540	−	0.366765i	−0.927012	−	0.375032i	$-0.877632\pi$
$827$	2.09798	−	10.5473i	0.0729540	−	0.366765i	0.999966	+	0.00826751i	$0.00263166\pi$
$828$	−0.167716	+	1.67232i	−0.00582852	+	0.0581171i
$829$	7.07223	−	7.07223i	0.245629	−	0.245629i	−0.573545	−	0.819174i	$-0.694432\pi$
$829$	7.07223	−	7.07223i	0.245629	−	0.245629i	0.819174	+	0.573545i	$0.194432\pi$
$830$	−5.12179	−	1.73861i	−0.177780	−	0.0603482i
$831$	−14.0997	−	6.12737i	−0.489114	−	0.212556i
$832$	50.6588	−	29.2479i	1.75628	−	1.01399i
$833$	−20.7117	+	5.04438i	−0.717619	+	0.174777i
$834$	20.9800	+	37.8310i	0.726477	+	1.30998i
$835$	−11.9638	+	9.18017i	−0.414026	+	0.317693i
$836$	−46.3424	+	9.21807i	−1.60279	+	0.318814i
$837$	−4.55085	−	1.47563i	−0.157300	−	0.0510053i
$838$	−56.8619	−	37.9939i	−1.96426	−	1.31248i
$839$	3.58778	−	4.09108i	0.123864	−	0.141240i	−0.686584	−	0.727051i	$-0.740891\pi$
$839$	3.58778	−	4.09108i	0.123864	−	0.141240i	0.810448	+	0.585811i	$0.199224\pi$
$840$	19.8449	−	38.5503i	0.684715	−	1.33011i
$841$	−17.1851	+	22.3961i	−0.592591	+	0.772280i
$842$	−28.9313	+	37.7040i	−0.997037	+	1.29936i
$843$	23.0547	+	35.8267i	0.794045	+	1.23394i
$844$	30.6381	−	34.9361i	1.05461	−	1.20255i
$845$	8.29478	+	5.54240i	0.285349	+	0.190664i
$846$	74.0466	−	69.1051i	2.54577	−	2.37588i
$847$	−25.4614	+	5.06458i	−0.874863	+	0.174021i
$848$	−67.5456	+	51.8296i	−2.31953	+	1.77983i
$849$	11.1502	−	18.5654i	0.382673	−	0.637164i
$850$	−2.71220	−	3.70739i	−0.0930278	−	0.127162i
$851$	−0.598686	+	0.345652i	−0.0205227	+	0.0118488i
$852$	18.6552	−	13.8099i	0.639116	−	0.473120i
$853$	−5.20773	−	1.76779i	−0.178309	−	0.0605279i	0.230857	−	0.972988i	$-0.425847\pi$
$853$	−5.20773	−	1.76779i	−0.178309	−	0.0605279i	−0.409166	+	0.912460i	$0.634180\pi$
$854$	17.3521	−	17.3521i	0.593777	−	0.593777i
$855$	6.18311	−	8.59615i	0.211458	−	0.293982i
$856$	9.20623	−	46.2828i	0.314662	−	1.58192i
$857$	−0.764461	+	0.0501054i	−0.0261135	+	0.00171157i	−0.0784543	−	0.996918i	$-0.524998\pi$
$857$	−0.764461	+	0.0501054i	−0.0261135	+	0.00171157i	0.0523408	+	0.998629i	$0.483332\pi$
$858$	68.6967	−	27.0763i	2.34527	−	0.924369i
$859$	−19.5778	−	15.0226i	−0.667985	−	0.512563i	0.218194	−	0.975905i	$-0.429983\pi$
$859$	−19.5778	−	15.0226i	−0.667985	−	0.512563i	−0.886179	+	0.463342i	$0.846650\pi$
$860$	−26.2745	−	12.9571i	−0.895953	−	0.441835i
$861$	−6.04417	−	18.8689i	−0.205985	−	0.643051i
$862$	19.1909	+	38.9152i	0.653643	+	1.32546i
$863$	−4.87961	−	4.87961i	−0.166104	−	0.166104i	0.619161	−	0.785264i	$-0.287473\pi$
$863$	−4.87961	−	4.87961i	−0.166104	−	0.166104i	−0.785264	+	0.619161i	$0.787473\pi$
$864$	−54.9090	−	69.5656i	−1.86804	−	2.36667i
$865$	10.6656	−	25.7491i	0.362641	−	0.875494i
$866$	−21.8606	+	37.8637i	−0.742854	+	1.28666i
$867$	23.4031	+	17.8688i	0.794812	+	0.606856i
$868$	−3.24872	−	5.62695i	−0.110269	−	0.190991i
$869$	40.8745	−	5.38123i	1.38657	−	0.182546i
$870$	−1.55783	−	8.60507i	−0.0528155	−	0.291739i
$871$	−3.76320	+	1.00835i	−0.127511	+	0.0341665i
$872$	−25.1693	+	37.6686i	−0.852342	+	1.27562i
$873$	9.58469	−	2.88886i	0.324393	−	0.0977732i
$874$	−0.395387	+	0.264189i	−0.0133742	+	0.00893634i
$875$	−2.04720	+	15.5501i	−0.0692081	+	0.525688i
$876$	−60.5772	−	9.04089i	−2.04671	−	0.305463i
$877$	−20.5947	+	41.7620i	−0.695434	+	1.41020i	0.206551	+	0.978436i	$0.433776\pi$
$877$	−20.5947	+	41.7620i	−0.695434	+	1.41020i	−0.901986	+	0.431766i	$0.857891\pi$
$878$	−32.1307	+	10.9069i	−1.08436	+	0.368090i
$879$	−6.34957	−	13.4560i	−0.214166	−	0.453860i
$880$	38.9266	+	145.276i	1.31221	+	4.89725i
$881$	6.38399	+	32.0945i	0.215082	+	1.08129i	0.925858	+	0.377872i	$0.123344\pi$
$881$	6.38399	+	32.0945i	0.215082	+	1.08129i	−0.710776	+	0.703419i	$0.751656\pi$
$882$	33.9129	−	24.2104i	1.14191	−	0.815207i
$883$			12.7389i			0.428698i	0.976757	+	0.214349i	$0.0687630\pi$
$883$			12.7389i			0.428698i	−0.976757	+	0.214349i	$0.931237\pi$
$884$	25.0816	−	56.8353i	0.843585	−	1.91158i
$885$	−0.573679	+	33.2485i	−0.0192840	+	1.11764i
$886$	2.15144	+	16.3418i	0.0722791	+	0.549014i
$887$	−18.9467	−	21.6046i	−0.636169	−	0.725411i	0.340481	−	0.940252i	$-0.389410\pi$
$887$	−18.9467	−	21.6046i	−0.636169	−	0.725411i	−0.976649	+	0.214840i	$0.931077\pi$
$888$	26.5420	−	92.6332i	0.890692	−	3.10857i
$889$	16.8402	−	8.30467i	0.564802	−	0.278530i
$890$	6.17662	+	1.22861i	0.207041	+	0.0411830i
$891$	−24.5733	−	42.9144i	−0.823237	−	1.43769i
$892$	−34.6946	−	83.7602i	−1.16166	−	2.80450i
$893$	20.5379	+	2.70387i	0.687275	+	0.0904815i
$894$	65.9124	+	33.9304i	2.20444	+	1.13480i
$895$	15.3214	+	45.1355i	0.512139	+	1.50871i
$896$	1.79592	−	27.4004i	0.0599974	−	0.915384i
$897$	0.386347	−	0.373241i	0.0128997	−	0.0124621i
$898$	1.81124	−	5.33576i	0.0604420	−	0.178056i
$899$	−0.746571	−	0.309240i	−0.0248995	−	0.0103137i
$900$	5.50574	+	3.43730i	0.183525	+	0.114577i
$901$	−7.71314	+	26.3563i	−0.256962	+	0.878057i
$902$	108.104	+	62.4137i	3.59946	+	2.07815i
$903$	3.65572	+	4.93835i	0.121655	+	0.164338i
$904$	122.928	−	107.805i	4.08853	−	3.58554i
$905$	11.9095	+	3.19114i	0.395885	+	0.106077i
$906$	−50.5395	+	23.8484i	−1.67906	+	0.792309i
$907$	−41.7512	−	36.6148i	−1.38632	−	1.21577i	−0.948525	−	0.316702i	$-0.897425\pi$
$907$	−41.7512	−	36.6148i	−1.38632	−	1.21577i	−0.437799	−	0.899073i	$-0.644242\pi$
$908$	−45.9867	−	68.8240i	−1.52612	−	2.28401i
$909$	15.0356	+	12.3842i	0.498698	+	0.410759i
$910$	−20.7632	+	8.60041i	−0.688294	+	0.285101i
$911$	0.271167	+	4.13721i	0.00898417	+	0.137072i	0.999995	+	0.00328730i	$0.00104638\pi$
$911$	0.271167	+	4.13721i	0.00898417	+	0.137072i	−0.991010	+	0.133785i	$0.957287\pi$
$912$	7.73626	−	35.6656i	0.256173	−	1.18100i
$913$	−5.15529	−	0.337895i	−0.170615	−	0.0111827i
$914$	24.2023	−	90.3243i	0.800541	−	2.98766i
$915$	−16.1863	−	19.1122i	−0.535102	−	0.631831i
$916$	−41.5278	−	54.1200i	−1.37212	−	1.78818i
$917$	−16.6933			−0.551261
$918$	−55.4544	−	15.4076i	−1.83027	−	0.508525i
$919$	26.4411			0.872211			0.436105	−	0.899896i	$-0.356357\pi$
$919$	26.4411			0.872211			0.436105	+	0.899896i	$0.356357\pi$
$920$	1.20978	+	1.57662i	0.0398853	+	0.0519796i
$921$	−5.44371	−	6.42775i	−0.179376	−	0.211802i
$922$	−3.92111	+	14.6338i	−0.129135	+	0.481938i
$923$	−7.40269	−	0.485198i	−0.243663	−	0.0159705i
$924$	14.2371	−	65.6357i	0.468367	−	2.15926i
$925$	0.174607	+	2.66399i	0.00574104	+	0.0875914i
$926$	−90.3750	+	37.4345i	−2.96991	+	1.23018i
$927$	28.6273	−	10.7164i	0.940243	−	0.351973i
$928$	−8.31666	−	12.4468i	−0.273008	−	0.408585i
$929$	−4.24340	−	3.72137i	−0.139222	−	0.122094i	0.586903	−	0.809657i	$-0.300347\pi$
$929$	−4.24340	−	3.72137i	−0.139222	−	0.122094i	−0.726124	+	0.687563i	$0.758680\pi$
$930$	−8.29634	+	3.91484i	−0.272048	+	0.128373i
$931$	8.23180	+	2.20571i	0.269786	+	0.0722891i
$932$	31.0487	−	27.2290i	1.01703	−	0.891916i
$933$	15.6888	+	21.1933i	0.513628	+	0.693837i
$934$	37.4501	+	21.6218i	1.22541	+	0.707488i
$935$	37.8008	+	30.4057i	1.23622	+	0.994371i
$936$	−2.58319	+	74.8343i	−0.0844343	+	2.44603i
$937$	39.2584	+	16.2614i	1.28252	+	0.531236i	0.916746	−	0.399470i	$-0.130806\pi$
$937$	39.2584	+	16.2614i	1.28252	+	0.531236i	0.365770	+	0.930705i	$0.380806\pi$
$938$	−1.57573	+	4.64195i	−0.0514494	+	0.151565i
$939$	−17.6524	+	17.0536i	−0.576066	+	0.556524i
$940$	9.18209	−	140.092i	0.299487	−	4.56928i
$941$	16.1133	+	47.4682i	0.525278	+	1.54742i	0.808579	+	0.588388i	$0.200237\pi$
$941$	16.1133	+	47.4682i	0.525278	+	1.54742i	−0.283301	+	0.959031i	$0.591429\pi$
$942$	−11.9246	−	6.13852i	−0.388523	−	0.200004i
$943$	0.900355	+	0.118534i	0.0293196	+	0.00386000i
$944$	43.8590	+	105.885i	1.42749	+	3.44626i
$945$	7.70334	+	12.9304i	0.250590	+	0.420627i
$946$	−37.9659	−	7.55189i	−1.23438	−	0.245533i
$947$	−21.3323	+	10.5199i	−0.693205	+	0.341851i	−0.754529	−	0.656267i	$-0.772134\pi$
$947$	−21.3323	+	10.5199i	−0.693205	+	0.341851i	0.0613237	+	0.998118i	$0.480468\pi$
$948$	−18.6748	+	65.1762i	−0.606530	+	2.11682i
$949$	12.9075	+	14.7181i	0.418994	+	0.477771i
$950$	0.239700	+	1.82070i	0.00777690	+	0.0590714i
$951$	1.01999	−	59.1149i	0.0330753	−	1.91693i
$952$	−25.8542	−	40.6801i	−0.837939	−	1.31845i
$953$			40.8027i			1.32173i	0.750505	+	0.660865i	$0.229810\pi$
$953$			40.8027i			1.32173i	−0.750505	+	0.660865i	$0.770190\pi$
$954$	−5.16633	−	53.4296i	−0.167266	−	1.72985i
$955$	−4.85218	−	24.3936i	−0.157013	−	0.789357i
$956$	26.8324	+	100.140i	0.867821	+	3.23875i
$957$	−3.56460	−	7.55411i	−0.115227	−	0.244190i
$958$	36.8359	−	12.5041i	1.19011	−	0.403989i
$959$	−6.29957	+	12.7743i	−0.203424	+	0.412503i
$960$	−74.2969	−	11.0885i	−2.39792	−	0.357880i
$961$	3.93567	−	29.8943i	0.126957	−	0.964334i
$962$	−41.5292	+	27.7489i	−1.33895	+	0.894661i
$963$	11.9360	+	11.2193i	0.384633	+	0.361536i
$964$	−66.4731	+	99.4840i	−2.14095	+	3.20417i
$965$	−8.92533	+	2.39154i	−0.287317	+	0.0769863i
$966$	−0.120409	−	0.665109i	−0.00387410	−	0.0213995i
$967$	19.0724	−	2.51093i	0.613326	−	0.0807460i	0.182538	−	0.983199i	$-0.441569\pi$
$967$	19.0724	−	2.51093i	0.613326	−	0.0807460i	0.430789	+	0.902453i	$0.358235\pi$
$968$	82.9271	+	143.634i	2.66538	+	4.61657i
$969$	−4.77841	−	10.7580i	−0.153505	−	0.345597i
$970$	9.59774	−	16.6238i	0.308165	−	0.533757i
$971$	3.32478	−	8.02673i	0.106697	−	0.257590i	−0.861509	−	0.507742i	$-0.830480\pi$
$971$	3.32478	−	8.02673i	0.106697	−	0.257590i	0.968207	+	0.250152i	$0.0804804\pi$
$972$	80.8322	−	8.93466i	2.59269	−	0.286579i
$973$	−8.89260	−	8.89260i	−0.285084	−	0.285084i
$974$	−48.4140	−	98.1739i	−1.55129	−	3.14569i
$975$	−0.632850	−	1.97566i	−0.0202674	−	0.0632716i
$976$	−77.4180	−	38.1783i	−2.47809	−	1.22206i
$977$	39.8114	+	30.5483i	1.27368	+	0.977328i	0.999879	+	0.0155413i	$0.00494716\pi$
$977$	39.8114	+	30.5483i	1.27368	+	0.977328i	0.273800	+	0.961787i	$0.411720\pi$
$978$	69.8431	−	27.5281i	2.23334	−	0.880252i
$979$	6.00241	−	0.393419i	0.191838	−	0.0125737i
$980$	11.2679	−	56.6475i	0.359939	−	1.80954i
$981$	−6.46490	−	14.3362i	−0.206408	−	0.457719i
$982$	−31.9946	+	31.9946i	−1.02099	+	1.02099i
$983$	30.7361	+	10.4335i	0.980330	+	0.332777i	0.765189	−	0.643806i	$-0.222646\pi$
$983$	30.7361	+	10.4335i	0.980330	+	0.332777i	0.215141	+	0.976583i	$0.430979\pi$
$984$	−101.740	+	75.3151i	−3.24335	+	2.40096i
$985$	−26.5317	+	15.3181i	−0.845369	+	0.488074i
$986$	−9.13171	−	3.33487i	−0.290813	−	0.106204i
$987$	−15.1601	+	25.2421i	−0.482550	+	0.803464i
$988$	−19.7036	+	15.1191i	−0.626854	+	0.481002i
$989$	−0.276203	+	0.0549403i	−0.00878276	+	0.00174700i
$990$	−90.6926	−	27.6877i	−2.88240	−	0.879973i
$991$	0.415084	+	0.277350i	0.0131856	+	0.00881033i	0.562146	−	0.827038i	$-0.309976\pi$
$991$	0.415084	+	0.277350i	0.0131856	+	0.00881033i	−0.548960	+	0.835849i	$0.684976\pi$
$992$	−10.3540	+	11.8064i	−0.328739	+	0.374855i
$993$	18.7288	+	29.1043i	0.594339	+	0.923596i
$994$	−5.68246	+	7.40552i	−0.180237	+	0.234889i
$995$	−11.6856	+	15.2290i	−0.370460	+	0.482792i
$996$	3.88865	−	7.55400i	0.123217	−	0.239358i
$997$	−28.1939	+	32.1489i	−0.892908	+	1.01817i	0.106806	+	0.994280i	$0.465937\pi$
$997$	−28.1939	+	32.1489i	−0.892908	+	1.01817i	−0.999715	+	0.0238869i	$0.992396\pi$
$998$	−96.7679	−	64.6583i	−3.06313	−	2.04672i
$999$	22.3975	+	24.8448i	0.708624	+	0.786055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.1	✓	256
3.2	odd	2		459.2.y.a.62.16		256
9.4	even	3		459.2.y.a.368.16		256
9.5	odd	6	inner	153.2.s.a.113.1	yes	256
17.14	odd	16	inner	153.2.s.a.65.1	yes	256
51.14	even	16		459.2.y.a.116.16		256
153.14	even	48	inner	153.2.s.a.14.1	yes	256
153.31	odd	48		459.2.y.a.422.16		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.1	✓	256	1.1	even	1	trivial
153.2.s.a.14.1	yes	256	153.14	even	48	inner
153.2.s.a.65.1	yes	256	17.14	odd	16	inner
153.2.s.a.113.1	yes	256	9.5	odd	6	inner
459.2.y.a.62.16		256	3.2	odd	2
459.2.y.a.116.16		256	51.14	even	16
459.2.y.a.368.16		256	9.4	even	3
459.2.y.a.422.16		256	153.31	odd	48

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63540 - 2.13130i) q^{2} +(1.11938 + 1.32173i) q^{3} +(-1.35025 + 5.03920i) q^{4} +(-2.13674 - 0.140050i) q^{5} +(0.986361 - 4.54731i) q^{6} +(0.0884715 + 1.34981i) q^{7} +(7.98434 - 3.30722i) q^{8} +(-0.493955 + 2.95906i) q^{9} +O(q^{10})\)	\(q+(-1.63540 - 2.13130i) q^{2} +(1.11938 + 1.32173i) q^{3} +(-1.35025 + 5.03920i) q^{4} +(-2.13674 - 0.140050i) q^{5} +(0.986361 - 4.54731i) q^{6} +(0.0884715 + 1.34981i) q^{7} +(7.98434 - 3.30722i) q^{8} +(-0.493955 + 2.95906i) q^{9} +(3.19595 + 4.78307i) q^{10} +(4.13110 + 3.62288i) q^{11} +(-8.17193 + 3.85614i) q^{12} +(2.78970 + 0.747498i) q^{13} +(2.73217 - 2.39605i) q^{14} +(-2.20673 - 2.98097i) q^{15} +(-11.0702 - 6.39140i) q^{16} +(-4.09908 + 0.444433i) q^{17} +(7.11444 - 3.78648i) q^{18} +(1.52287 + 0.630791i) q^{19} +(3.59088 - 10.5784i) q^{20} +(-1.68506 + 1.62790i) q^{21} +(0.965420 - 14.7295i) q^{22} +(-0.0345185 - 0.101688i) q^{23} +(13.3088 + 6.85111i) q^{24} +(-0.411165 - 0.0541309i) q^{25} +(-2.96914 - 7.16814i) q^{26} +(-4.46401 + 2.65945i) q^{27} +(-6.92145 - 1.37676i) q^{28} +(-0.787167 + 0.388188i) q^{29} +(-2.74445 + 9.57829i) q^{30} +(0.607062 + 0.692221i) q^{31} +(2.22624 + 16.9100i) q^{32} +(-0.164185 + 9.51560i) q^{33} +(7.65087 + 8.00954i) q^{34} -2.89660i q^{35} +(-14.2443 - 6.48460i) q^{36} +(-1.25589 - 6.31378i) q^{37} +(-1.14609 - 4.27728i) q^{38} +(2.13476 + 4.52398i) q^{39} +(-17.5237 + 5.94848i) q^{40} +(-3.74023 + 7.58443i) q^{41} +(6.22528 + 0.929097i) q^{42} +(0.342294 - 2.59998i) q^{43} +(-23.8344 + 15.9257i) q^{44} +(1.46987 - 6.25356i) q^{45} +(-0.160276 + 0.239870i) q^{46} +(12.1391 - 3.25265i) q^{47} +(-3.94413 - 21.7863i) q^{48} +(5.12594 - 0.674843i) q^{49} +(0.557051 + 0.964840i) q^{50} +(-5.17587 - 4.92040i) q^{51} +(-7.53359 + 13.0486i) q^{52} +(2.54885 - 6.15346i) q^{53} +(12.9685 + 5.16486i) q^{54} +(-8.31972 - 8.31972i) q^{55} +(5.17052 + 10.4848i) q^{56} +(0.870934 + 2.71892i) q^{57} +(2.11468 + 1.04284i) q^{58} +(-7.11310 - 5.45808i) q^{59} +(18.0014 - 7.09510i) q^{60} +(6.73835 - 0.441655i) q^{61} +(0.482539 - 2.42589i) q^{62} +(-4.03788 - 0.404955i) q^{63} +(14.3217 - 14.3217i) q^{64} +(-5.85619 - 1.98791i) q^{65} +(20.5491 - 15.2119i) q^{66} +(-1.16824 + 0.674481i) q^{67} +(3.29520 - 21.2562i) q^{68} +(0.0957652 - 0.159453i) q^{69} +(-6.17351 + 4.73710i) q^{70} +(-2.51930 + 0.501121i) q^{71} +(5.84235 + 25.2597i) q^{72} +(5.63586 + 3.76576i) q^{73} +(-11.4027 + 13.0022i) q^{74} +(-0.388705 - 0.604043i) q^{75} +(-5.23493 + 6.82230i) q^{76} +(-4.52473 + 5.89674i) q^{77} +(6.15076 - 11.9483i) q^{78} +(4.94717 - 5.64117i) q^{79} +(22.7591 + 15.2072i) q^{80} +(-8.51202 - 2.92328i) q^{81} +(22.2815 - 4.43206i) q^{82} +(-0.745951 + 0.572388i) q^{83} +(-5.92805 - 10.6894i) q^{84} +(8.82093 - 0.375565i) q^{85} +(-6.10113 + 3.52249i) q^{86} +(-1.39422 - 0.605893i) q^{87} +(44.9658 + 15.2638i) q^{88} +(0.774108 - 0.774108i) q^{89} +(-15.7320 + 7.09436i) q^{90} +(-0.762175 + 3.83171i) q^{91} +(0.559036 - 0.0366412i) q^{92} +(-0.235396 + 1.57723i) q^{93} +(-26.7846 - 20.5526i) q^{94} +(-3.16563 - 1.56112i) q^{95} +(-19.8584 + 21.8712i) q^{96} +(-1.47586 - 2.99274i) q^{97} +(-9.82127 - 9.82127i) q^{98} +(-12.7609 + 10.4346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

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