LMFDB - Embedded newform 256.2.m.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14085 - 0.835738i) q^{2} +(0.284707 - 1.91934i) q^{3} +(0.603086 + 1.90691i) q^{4} +(2.56674 + 0.126096i) q^{5} +(-1.92887 + 1.95174i) q^{6} +(2.08571 + 1.11483i) q^{7} +(0.905641 - 2.67952i) q^{8} +(-0.731981 - 0.222044i) q^{9} +O(q^{10})$	\(q+(-1.14085 - 0.835738i) q^{2} +(0.284707 - 1.91934i) q^{3} +(0.603086 + 1.90691i) q^{4} +(2.56674 + 0.126096i) q^{5} +(-1.92887 + 1.95174i) q^{6} +(2.08571 + 1.11483i) q^{7} +(0.905641 - 2.67952i) q^{8} +(-0.731981 - 0.222044i) q^{9} +(-2.82289 - 2.28898i) q^{10} +(2.61069 + 4.35568i) q^{11} +(3.83170 - 0.614616i) q^{12} +(-0.191530 + 0.211320i) q^{13} +(-1.44778 - 3.01497i) q^{14} +(0.972789 - 4.89054i) q^{15} +(-3.27258 + 2.30005i) q^{16} +(1.38955 + 6.98573i) q^{17} +(0.649512 + 0.865064i) q^{18} +(-3.45446 - 7.30385i) q^{19} +(1.30751 + 4.97057i) q^{20} +(2.73356 - 3.68578i) q^{21} +(0.661790 - 7.15104i) q^{22} +(-6.37159 - 5.22902i) q^{23} +(-4.88506 - 2.50111i) q^{24} +(1.59632 + 0.157224i) q^{25} +(0.395115 - 0.0810167i) q^{26} +(1.85423 - 3.92044i) q^{27} +(-0.868023 + 4.64959i) q^{28} +(-4.54921 + 1.13952i) q^{29} +(-5.19702 + 4.76638i) q^{30} +(-6.55223 - 2.71402i) q^{31} +(5.65577 + 0.110994i) q^{32} +(9.10331 - 3.77071i) q^{33} +(4.25297 - 9.13098i) q^{34} +(5.21289 + 3.12449i) q^{35} +(-0.0180303 - 1.52973i) q^{36} +(0.655951 + 1.83326i) q^{37} +(-2.16307 + 11.2196i) q^{38} +(0.351065 + 0.427774i) q^{39} +(2.66242 - 6.76342i) q^{40} +(-6.23544 + 0.614137i) q^{41} +(-6.19893 + 1.92039i) q^{42} +(4.45308 - 0.660553i) q^{43} +(-6.73140 + 7.60519i) q^{44} +(-1.85081 - 0.662229i) q^{45} +(2.89894 + 11.2905i) q^{46} +(-2.80157 + 4.19285i) q^{47} +(3.48286 + 6.93602i) q^{48} +(-0.781665 - 1.16984i) q^{49} +(-1.68977 - 1.51348i) q^{50} +(13.8036 - 0.678127i) q^{51} +(-0.518477 - 0.237785i) q^{52} +(7.52193 + 1.88414i) q^{53} +(-5.39186 + 2.92299i) q^{54} +(6.15174 + 11.5091i) q^{55} +(4.87612 - 4.57905i) q^{56} +(-15.0021 + 4.55083i) q^{57} +(6.14231 + 2.50192i) q^{58} +(-0.479613 - 0.529171i) q^{59} +(9.91247 - 1.09440i) q^{60} +(-2.60027 - 3.50606i) q^{61} +(5.20692 + 8.57225i) q^{62} +(-1.27916 - 1.27916i) q^{63} +(-6.35963 - 4.85336i) q^{64} +(-0.518253 + 0.518253i) q^{65} +(-13.5369 - 3.30615i) q^{66} +(-2.39442 + 1.77582i) q^{67} +(-12.4831 + 6.86273i) q^{68} +(-11.8503 + 10.7405i) q^{69} +(-3.33589 - 7.92119i) q^{70} +(-2.18628 - 7.20720i) q^{71} +(-1.25788 + 1.76026i) q^{72} +(8.28249 - 4.42708i) q^{73} +(0.783781 - 2.63968i) q^{74} +(0.756251 - 3.01912i) q^{75} +(11.8444 - 10.9922i) q^{76} +(0.589285 + 11.9952i) q^{77} +(-0.0430064 - 0.781426i) q^{78} +(-5.72737 + 3.82691i) q^{79} +(-8.68987 + 5.49098i) q^{80} +(-8.90475 - 5.94997i) q^{81} +(7.62697 + 4.51055i) q^{82} +(-1.10215 + 3.08031i) q^{83} +(8.67701 + 2.98980i) q^{84} +(2.68574 + 18.1058i) q^{85} +(-5.63236 - 2.96802i) q^{86} +(0.891929 + 9.05590i) q^{87} +(14.0355 - 3.05072i) q^{88} +(2.88894 - 2.37089i) q^{89} +(1.55805 + 2.30229i) q^{90} +(-0.635062 + 0.227229i) q^{91} +(6.12864 - 15.3036i) q^{92} +(-7.07460 + 11.8033i) q^{93} +(6.70030 - 2.44204i) q^{94} +(-7.94572 - 19.1827i) q^{95} +(1.82327 - 10.8237i) q^{96} +(4.45346 - 10.7516i) q^{97} +(-0.0859190 + 1.98789i) q^{98} +(-0.943826 - 3.76797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{64}\right)$	$1$

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 $

$2$	−1.14085	−	0.835738i	−0.806704	−	0.590956i
$2$	−1.14085	−	0.835738i	−0.806704	−	0.590956i
$3$	0.284707	−	1.91934i	0.164376	−	1.10813i	−0.737252	−	0.675618i	$-0.763877\pi$
$3$	0.284707	−	1.91934i	0.164376	−	1.10813i	0.901628	−	0.432513i	$-0.142373\pi$
$4$	0.603086	+	1.90691i	0.301543	+	0.953453i
$5$	2.56674	+	0.126096i	1.14788	+	0.0563917i	0.614098	−	0.789230i	$-0.289520\pi$
$5$	2.56674	+	0.126096i	1.14788	+	0.0563917i	0.533783	+	0.845622i	$0.320770\pi$
$6$	−1.92887	+	1.95174i	−0.787459	+	0.796795i
$7$	2.08571	+	1.11483i	0.788324	+	0.421368i	0.815858	−	0.578253i	$-0.196265\pi$
$7$	2.08571	+	1.11483i	0.788324	+	0.421368i	−0.0275336	+	0.999621i	$0.508765\pi$
$8$	0.905641	−	2.67952i	0.320192	−	0.947353i
$9$	−0.731981	−	0.222044i	−0.243994	−	0.0740147i
$10$	−2.82289	−	2.28898i	−0.892675	−	0.723838i
$11$	2.61069	+	4.35568i	0.787154	+	1.31329i	0.945408	+	0.325888i	$0.105663\pi$
$11$	2.61069	+	4.35568i	0.787154	+	1.31329i	−0.158254	+	0.987398i	$0.550587\pi$
$12$	3.83170	−	0.614616i	1.10612	−	0.177424i
$13$	−0.191530	+	0.211320i	−0.0531207	+	0.0586097i	−0.766932	−	0.641729i	$-0.778218\pi$
$13$	−0.191530	+	0.211320i	−0.0531207	+	0.0586097i	0.713811	+	0.700338i	$0.246968\pi$
$14$	−1.44778	−	3.01497i	−0.386934	−	0.805784i
$15$	0.972789	−	4.89054i	0.251173	−	1.26273i
$16$	−3.27258	+	2.30005i	−0.818144	+	0.575014i
$17$	1.38955	+	6.98573i	0.337015	+	1.69429i	0.662760	+	0.748832i	$0.269385\pi$
$17$	1.38955	+	6.98573i	0.337015	+	1.69429i	−0.325745	+	0.945458i	$0.605615\pi$
$18$	0.649512	+	0.865064i	0.153091	+	0.203897i
$19$	−3.45446	−	7.30385i	−0.792508	−	1.67562i	−0.735773	−	0.677229i	$-0.763181\pi$
$19$	−3.45446	−	7.30385i	−0.792508	−	1.67562i	−0.0567357	−	0.998389i	$-0.518069\pi$
$20$	1.30751	+	4.97057i	0.292368	+	1.11145i
$21$	2.73356	−	3.68578i	0.596512	−	0.804303i
$22$	0.661790	−	7.15104i	0.141094	−	1.52461i
$23$	−6.37159	−	5.22902i	−1.32857	−	1.09033i	−0.988709	−	0.149851i	$-0.952121\pi$
$23$	−6.37159	−	5.22902i	−1.32857	−	1.09033i	−0.339859	−	0.940477i	$-0.610379\pi$
$24$	−4.88506	−	2.50111i	−0.997158	−	0.510537i
$25$	1.59632	+	0.157224i	0.319265	+	0.0314448i
$26$	0.395115	−	0.0810167i	0.0774885	−	0.0158887i
$27$	1.85423	−	3.92044i	0.356846	−	0.754488i
$28$	−0.868023	+	4.64959i	−0.164041	+	0.878690i
$29$	−4.54921	+	1.13952i	−0.844767	+	0.211603i	−0.641119	−	0.767441i	$-0.721530\pi$
$29$	−4.54921	+	1.13952i	−0.844767	+	0.211603i	−0.203648	+	0.979044i	$0.565280\pi$
$30$	−5.19702	+	4.76638i	−0.948841	+	0.870219i
$31$	−6.55223	−	2.71402i	−1.17682	−	0.487453i	−0.293376	−	0.955997i	$-0.594779\pi$
$31$	−6.55223	−	2.71402i	−1.17682	−	0.487453i	−0.883440	+	0.468544i	$0.844779\pi$
$32$	5.65577	+	0.110994i	0.999807	+	0.0196211i
$33$	9.10331	−	3.77071i	1.58468	−	0.656397i
$34$	4.25297	−	9.13098i	0.729378	−	1.56595i
$35$	5.21289	+	3.12449i	0.881140	+	0.528135i
$36$	−0.0180303	−	1.52973i	−0.00300504	−	0.254955i
$37$	0.655951	+	1.83326i	0.107838	+	0.301386i	0.983326	−	0.181854i	$-0.0582099\pi$
$37$	0.655951	+	1.83326i	0.107838	+	0.301386i	−0.875488	+	0.483240i	$0.839460\pi$
$38$	−2.16307	+	11.2196i	−0.350896	+	1.82006i
$39$	0.351065	+	0.427774i	0.0562155	+	0.0684987i
$40$	2.66242	−	6.76342i	0.420966	−	1.06939i
$41$	−6.23544	+	0.614137i	−0.973811	+	0.0959121i	−0.572390	−	0.819981i	$-0.693984\pi$
$41$	−6.23544	+	0.614137i	−0.973811	+	0.0959121i	−0.401421	+	0.915893i	$0.631484\pi$
$42$	−6.19893	+	1.92039i	−0.956516	+	0.296323i
$43$	4.45308	−	0.660553i	0.679089	−	0.100733i	0.201729	−	0.979441i	$-0.435344\pi$
$43$	4.45308	−	0.660553i	0.679089	−	0.100733i	0.477360	+	0.878708i	$0.341594\pi$
$44$	−6.73140	+	7.60519i	−1.01480	+	1.14653i
$45$	−1.85081	−	0.662229i	−0.275902	−	0.0987193i
$46$	2.89894	+	11.2905i	0.427426	+	1.66470i
$47$	−2.80157	+	4.19285i	−0.408651	+	0.611590i	−0.977521	−	0.210838i	$-0.932381\pi$
$47$	−2.80157	+	4.19285i	−0.408651	+	0.611590i	0.568870	+	0.822428i	$0.307381\pi$
$48$	3.48286	+	6.93602i	0.502707	+	1.00113i
$49$	−0.781665	−	1.16984i	−0.111666	−	0.167121i
$50$	−1.68977	−	1.51348i	−0.238970	−	0.214038i
$51$	13.8036	−	0.678127i	1.93289	−	0.0949568i
$52$	−0.518477	−	0.237785i	−0.0718998	−	0.0329748i
$53$	7.52193	+	1.88414i	1.03322	+	0.258807i	0.722263	−	0.691618i	$-0.243102\pi$
$53$	7.52193	+	1.88414i	1.03322	+	0.258807i	0.310953	+	0.950425i	$0.399352\pi$
$54$	−5.39186	+	2.92299i	−0.733739	+	0.397768i
$55$	6.15174	+	11.5091i	0.829500	+	1.55189i
$56$	4.87612	−	4.57905i	0.651599	−	0.611902i
$57$	−15.0021	+	4.55083i	−1.98707	+	0.602772i
$58$	6.14231	+	2.50192i	0.806525	+	0.328519i
$59$	−0.479613	−	0.529171i	−0.0624402	−	0.0688922i	0.708930	−	0.705279i	$-0.249178\pi$
$59$	−0.479613	−	0.529171i	−0.0624402	−	0.0688922i	−0.771370	+	0.636387i	$0.780428\pi$
$60$	9.91247	−	1.09440i	1.27969	−	0.141286i
$61$	−2.60027	−	3.50606i	−0.332931	−	0.448905i	0.604744	−	0.796420i	$-0.293276\pi$
$61$	−2.60027	−	3.50606i	−0.332931	−	0.448905i	−0.937674	+	0.347515i	$0.887026\pi$
$62$	5.20692	+	8.57225i	0.661279	+	1.08868i
$63$	−1.27916	−	1.27916i	−0.161159	−	0.161159i
$64$	−6.35963	−	4.85336i	−0.794954	−	0.606670i
$65$	−0.518253	+	0.518253i	−0.0642814	+	0.0642814i
$66$	−13.5369	−	3.30615i	−1.66627	−	0.406959i
$67$	−2.39442	+	1.77582i	−0.292524	+	0.216951i	−0.732002	−	0.681303i	$-0.761414\pi$
$67$	−2.39442	+	1.77582i	−0.292524	+	0.216951i	0.439477	+	0.898254i	$0.355164\pi$
$68$	−12.4831	+	6.86273i	−1.51380	+	0.832229i
$69$	−11.8503	+	10.7405i	−1.42661	+	1.29300i
$70$	−3.33589	−	7.92119i	−0.398715	−	0.946763i
$71$	−2.18628	−	7.20720i	−0.259464	−	0.855337i	−0.985789	−	0.167987i	$-0.946273\pi$
$71$	−2.18628	−	7.20720i	−0.259464	−	0.855337i	0.726326	−	0.687351i	$-0.241227\pi$
$72$	−1.25788	+	1.76026i	−0.148243	+	0.207449i
$73$	8.28249	−	4.42708i	0.969392	−	0.518151i	0.0908750	−	0.995862i	$-0.471034\pi$
$73$	8.28249	−	4.42708i	0.969392	−	0.518151i	0.878517	+	0.477712i	$0.158534\pi$
$74$	0.783781	−	2.63968i	0.0911127	−	0.306856i
$75$	0.756251	−	3.01912i	0.0873243	−	0.348618i
$76$	11.8444	−	10.9922i	1.35865	−	1.26089i
$77$	0.589285	+	11.9952i	0.0671553	+	1.36698i
$78$	−0.0430064	−	0.781426i	−0.00486952	−	0.0884791i
$79$	−5.72737	+	3.82691i	−0.644379	+	0.430561i	−0.834354	−	0.551228i	$-0.814159\pi$
$79$	−5.72737	+	3.82691i	−0.644379	+	0.430561i	0.189975	+	0.981789i	$0.439159\pi$
$80$	−8.68987	+	5.49098i	−0.971557	+	0.613910i
$81$	−8.90475	−	5.94997i	−0.989417	−	0.661107i
$82$	7.62697	+	4.51055i	0.842257	+	0.498107i
$83$	−1.10215	+	3.08031i	−0.120977	+	0.338108i	−0.986731	−	0.162361i	$-0.948089\pi$
$83$	−1.10215	+	3.08031i	−0.120977	+	0.338108i	0.865754	+	0.500469i	$0.166839\pi$
$84$	8.67701	+	2.98980i	0.946739	+	0.326214i
$85$	2.68574	+	18.1058i	0.291309	+	1.96385i
$86$	−5.63236	−	2.96802i	−0.607353	−	0.320049i
$87$	0.891929	+	9.05590i	0.0956248	+	0.970895i
$88$	14.0355	−	3.05072i	1.49619	−	0.325208i
$89$	2.88894	−	2.37089i	0.306227	−	0.251314i	−0.468711	−	0.883352i	$-0.655281\pi$
$89$	2.88894	−	2.37089i	0.306227	−	0.251314i	0.774938	+	0.632038i	$0.217781\pi$
$90$	1.55805	+	2.30229i	0.164232	+	0.242683i
$91$	−0.635062	+	0.227229i	−0.0665726	+	0.0238201i
$92$	6.12864	−	15.3036i	0.638955	−	1.59551i
$93$	−7.07460	+	11.8033i	−0.733602	+	1.22394i
$94$	6.70030	−	2.44204i	0.691083	−	0.251877i
$95$	−7.94572	−	19.1827i	−0.815214	−	1.96810i
$96$	1.82327	−	10.8237i	0.186087	−	1.10469i
$97$	4.45346	−	10.7516i	0.452180	−	1.09166i	−0.519311	−	0.854585i	$-0.673811\pi$
$97$	4.45346	−	10.7516i	0.452180	−	1.09166i	0.971491	−	0.237075i	$-0.0761886\pi$
$98$	−0.0859190	+	1.98789i	−0.00867913	+	0.200807i
$99$	−0.943826	−	3.76797i	−0.0948581	−	0.378695i
$100$	0.662908	+	3.13886i	0.0662908	+	0.313886i
$101$	−0.511240	−	0.241799i	−0.0508703	−	0.0240599i	0.401951	−	0.915661i	$-0.368332\pi$
$101$	−0.511240	−	0.241799i	−0.0508703	−	0.0240599i	−0.452821	+	0.891601i	$0.649582\pi$
$102$	−16.3146	−	10.7625i	−1.61539	−	1.06565i
$103$	−0.0812582	+	0.825028i	−0.00800661	+	0.0812925i	−0.998358	−	0.0572891i	$-0.981754\pi$
$103$	−0.0812582	+	0.825028i	−0.00800661	+	0.0812925i	0.990351	+	0.138582i	$0.0442543\pi$
$104$	0.392779	+	0.704587i	0.0385152	+	0.0690905i
$105$	7.48110	−	9.11575i	0.730080	−	0.889606i
$106$	−7.00675	−	8.43589i	−0.680556	−	0.819366i
$107$	6.06919	+	4.50122i	0.586730	+	0.435149i	0.847909	−	0.530141i	$-0.177861\pi$
$107$	6.06919	+	4.50122i	0.586730	+	0.435149i	−0.261179	+	0.965290i	$0.584111\pi$
$108$	8.59416	+	1.17148i	0.826973	+	0.112726i
$109$	−3.64416	+	1.72356i	−0.349047	+	0.165087i	−0.594035	−	0.804439i	$-0.702466\pi$
$109$	−3.64416	+	1.72356i	−0.349047	+	0.165087i	0.244988	+	0.969526i	$0.421216\pi$
$110$	2.60036	−	18.2714i	0.247934	−	1.74211i
$111$	3.70540	−	0.737050i	0.351701	−	0.0699577i
$112$	−9.38982	+	1.14886i	−0.887255	+	0.108557i
$113$	2.17761	+	0.433154i	0.204853	+	0.0407477i	0.296450	−	0.955048i	$-0.404197\pi$
$113$	2.17761	+	0.433154i	0.204853	+	0.0407477i	−0.0915973	+	0.995796i	$0.529197\pi$
$114$	20.9184	+	7.34597i	1.95919	+	0.688013i
$115$	−15.6948	−	14.2250i	−1.46355	−	1.32649i
$116$	−4.91652	−	7.98769i	−0.456487	−	0.741638i
$117$	0.187119	−	0.112155i	0.0172991	−	0.0103687i
$118$	0.104919	+	1.00454i	0.00965856	+	0.0924750i
$119$	−4.88974	+	16.1193i	−0.448242	+	1.47766i
$120$	−12.2233	−	7.03568i	−1.11583	−	0.642267i
$121$	−6.97086	+	13.0416i	−0.633714	+	1.18560i
$122$	0.0363782	+	6.17304i	0.00329353	+	0.558881i
$123$	−0.596536	+	12.1428i	−0.0537878	+	1.09488i
$124$	1.22383	−	14.1313i	0.109903	−	1.26903i
$125$	−8.63258	−	1.28052i	−0.772121	−	0.114533i
$126$	0.390289	+	2.52837i	0.0347697	+	0.225245i
$127$		−	7.70356i		−	0.683581i	−0.939776	−	0.341790i	$-0.888967\pi$
$127$		−	7.70356i		−	0.683581i	0.939776	−	0.341790i	$-0.111033\pi$
$128$	3.19926	+	10.8519i	0.282777	+	0.959186i
$129$		−	8.73504i		−	0.769077i
$130$	1.02437	−	0.158126i	0.0898435	−	0.0138686i
$131$	18.6806	+	2.77100i	1.63213	+	0.242104i	0.898988	−	0.437973i	$-0.144303\pi$
$131$	18.6806	+	2.77100i	1.63213	+	0.242104i	0.733141	+	0.680076i	$0.238053\pi$
$132$	12.6805	+	15.0851i	1.10369	+	1.31299i
$133$	0.937579	−	19.0849i	0.0812984	−	1.65487i
$134$	4.21579	−	0.0248440i	0.364189	−	0.00214619i
$135$	5.25367	−	9.82893i	0.452164	−	0.845939i
$136$	19.9768	+	2.60325i	1.71300	+	0.223227i
$137$	1.48630	−	4.89967i	0.126983	−	0.418607i	−0.870279	−	0.492560i	$-0.836061\pi$
$137$	1.48630	−	4.89967i	0.126983	−	0.418607i	0.997262	+	0.0739527i	$0.0235614\pi$
$138$	22.4957	−	2.34956i	1.91496	−	0.200008i
$139$	7.12616	−	4.27126i	0.604433	−	0.362283i	−0.178917	−	0.983864i	$-0.557259\pi$
$139$	7.12616	−	4.27126i	0.604433	−	0.362283i	0.783350	+	0.621581i	$0.213509\pi$
$140$	−2.81428	+	11.8248i	−0.237850	+	0.999381i
$141$	7.24987	+	6.57090i	0.610549	+	0.553370i
$142$	−3.52911	+	10.0495i	−0.296156	+	0.843336i
$143$	−1.42047	−	0.282549i	−0.118786	−	0.0236279i
$144$	2.90618	−	0.956941i	0.242182	−	0.0797450i
$145$	−11.8203	+	2.35121i	−0.981624	+	0.195257i
$146$	−13.1490	−	1.87134i	−1.08822	−	0.154873i
$147$	−2.46787	+	1.16722i	−0.203547	+	0.0962705i
$148$	−3.10026	+	2.35645i	−0.254840	+	0.193699i
$149$	8.71125	+	6.46070i	0.713653	+	0.529281i	0.890515	−	0.454955i	$-0.150345\pi$
$149$	8.71125	+	6.46070i	0.713653	+	0.529281i	−0.176862	+	0.984236i	$0.556595\pi$
$150$	−3.38596	+	2.81234i	−0.276463	+	0.229627i
$151$	2.49923	−	3.04533i	0.203385	−	0.247825i	−0.661322	−	0.750102i	$-0.730004\pi$
$151$	2.49923	−	3.04533i	0.203385	−	0.247825i	0.864707	+	0.502277i	$0.167504\pi$
$152$	−22.6993	+	2.64163i	−1.84116	+	0.214264i
$153$	0.534017	−	5.42197i	0.0431727	−	0.438340i
$154$	9.35253	−	14.1772i	0.753648	−	1.14243i
$155$	−16.4756	−	7.79240i	−1.32336	−	0.625901i
$156$	−0.604003	+	0.927433i	−0.0483589	+	0.0742541i
$157$	−1.36691	−	5.45702i	−0.109092	−	0.435518i	0.890728	−	0.454538i	$-0.150195\pi$
$157$	−1.36691	−	5.45702i	−0.109092	−	0.435518i	−0.999819	+	0.0190197i	$0.993945\pi$
$158$	9.73237	+	0.420645i	0.774266	+	0.0334647i
$159$	5.75786	−	13.9007i	0.456628	−	1.10240i
$160$	14.5029	+	0.998060i	1.14655	+	0.0789036i
$161$	−7.45978	−	18.0095i	−0.587913	−	1.41935i
$162$	5.18639	+	14.2301i	0.407482	+	1.11802i
$163$	1.51159	−	2.52194i	0.118397	−	0.197534i	−0.792825	−	0.609450i	$-0.791390\pi$
$163$	1.51159	−	2.52194i	0.118397	−	0.197534i	0.911222	+	0.411916i	$0.135140\pi$
$164$	−4.93160	−	11.5200i	−0.385093	−	0.899562i
$165$	23.8413	−	8.53055i	1.85604	−	0.664102i
$166$	3.83173	−	2.59307i	0.297400	−	0.201261i
$167$	−16.7984	+	13.7861i	−1.29990	+	1.06680i	−0.306529	+	0.951861i	$0.599168\pi$
$167$	−16.7984	+	13.7861i	−1.29990	+	1.06680i	−0.993372	+	0.114940i	$0.963332\pi$
$168$	−7.40049	−	10.6626i	−0.570960	−	0.822639i
$169$	1.26625	+	12.8565i	0.0974039	+	0.988958i
$170$	12.0676	−	22.9006i	0.925546	−	1.75639i
$171$	0.906826	+	6.11333i	0.0693467	+	0.467498i
$172$	3.94520	+	8.09324i	0.300819	+	0.617104i
$173$	1.97014	−	5.50619i	0.149787	−	0.418628i	−0.843089	−	0.537773i	$-0.819266\pi$
$173$	1.97014	−	5.50619i	0.149787	−	0.418628i	0.992877	+	0.119146i	$0.0380156\pi$
$174$	6.55080	−	11.0769i	0.496615	−	0.839735i
$175$	3.15419	+	2.10756i	0.238434	+	0.159317i
$176$	−18.5620	−	8.24955i	−1.39916	−	0.621834i
$177$	−1.15221	+	0.769880i	−0.0866052	+	0.0578677i
$178$	−5.27729	+	0.290440i	−0.395550	+	0.0217694i
$179$	0.860391	+	17.5137i	0.0643087	+	1.30903i	0.786608	+	0.617452i	$0.211835\pi$
$179$	0.860391	+	17.5137i	0.0643087	+	1.30903i	−0.722300	+	0.691580i	$0.756915\pi$
$180$	0.146614	−	3.92869i	0.0109279	−	0.292827i
$181$	3.56860	−	14.2466i	0.265252	−	1.05895i	−0.680159	−	0.733065i	$-0.738089\pi$
$181$	3.56860	−	14.2466i	0.265252	−	1.05895i	0.945411	−	0.325880i	$-0.105661\pi$
$182$	0.914416	+	0.271511i	0.0677810	+	0.0201257i
$183$	−7.46964	+	3.99260i	−0.552172	+	0.295142i
$184$	−19.7816	+	12.3372i	−1.45832	+	0.909507i
$185$	1.45249	+	4.78821i	0.106789	+	0.352036i
$186$	17.9355	−	7.55326i	1.31509	−	0.553832i
$187$	−26.7999	+	24.2900i	−1.95980	+	1.77626i
$188$	−9.68496	−	2.81369i	−0.706348	−	0.205209i
$189$	8.23802	−	6.10973i	0.599228	−	0.444418i
$190$	−6.96678	+	28.5251i	−0.505424	+	2.06943i
$191$	−13.8377	+	13.8377i	−1.00126	+	1.00126i	−0.00126493	+	0.999999i	$0.500403\pi$
$191$	−13.8377	+	13.8377i	−1.00126	+	1.00126i	−0.999999	+	0.00126493i	$0.999597\pi$
$192$	−11.1259	+	10.8245i	−0.802941	+	0.781191i
$193$	2.23783	+	2.23783i	0.161083	+	0.161083i	0.783046	−	0.621964i	$-0.213665\pi$
$193$	2.23783	+	2.23783i	0.161083	+	0.161083i	−0.621964	+	0.783046i	$0.713665\pi$
$194$	−14.0663	+	8.54406i	−1.00990	+	0.613428i
$195$	0.847153	+	1.14225i	0.0606659	+	0.0817984i
$196$	1.75937	−	2.19608i	0.125669	−	0.156863i
$197$	10.3388	+	11.4071i	0.736610	+	0.812724i	0.987884	−	0.155192i	$-0.0495997\pi$
$197$	10.3388	+	11.4071i	0.736610	+	0.812724i	−0.251275	+	0.967916i	$0.580850\pi$
$198$	−2.07226	+	5.08748i	−0.147269	+	0.361552i
$199$	−11.6833	+	3.54410i	−0.828209	+	0.251234i	−0.675802	−	0.737083i	$-0.736203\pi$
$199$	−11.6833	+	3.54410i	−0.828209	+	0.251234i	−0.152407	+	0.988318i	$0.548703\pi$
$200$	1.86698	−	4.13499i	0.132015	−	0.292388i
$201$	2.72669	+	5.10128i	0.192326	+	0.359817i
$202$	0.381169	+	0.703119i	0.0268190	+	0.0494713i
$203$	−10.7587	−	2.69491i	−0.755113	−	0.189146i
$204$	9.61788	+	25.9132i	0.673386	+	1.81429i
$205$	−16.0822	+	0.790067i	−1.12323	+	0.0551806i
$206$	0.782211	−	0.873325i	0.0544992	−	0.0608474i
$207$	3.50281	+	5.24232i	0.243462	+	0.364367i
$208$	0.140747	−	1.13209i	0.00975904	−	0.0784963i
$209$	22.7947	−	34.1147i	1.57674	−	2.35976i
$210$	−16.1532	+	4.14748i	−1.11468	+	0.286203i
$211$	16.7114	+	5.97945i	1.15046	+	0.411642i	0.841938	−	0.539574i	$-0.181415\pi$
$211$	16.7114	+	5.97945i	1.15046	+	0.411642i	0.308525	+	0.951216i	$0.400165\pi$
$212$	0.943480	+	15.4799i	0.0647985	+	1.06316i
$213$	−14.4555	+	2.14427i	−0.990475	+	0.146923i
$214$	−3.16221	−	10.2075i	−0.216164	−	0.697768i
$215$	11.5132	−	1.13395i	0.785193	−	0.0773348i
$216$	−8.82561	−	8.51895i	−0.600507	−	0.579641i
$217$	−10.6404	−	12.9653i	−0.722315	−	0.880143i
$218$	5.59789	+	1.07924i	0.379137	+	0.0730951i
$219$	−6.13899	−	17.1573i	−0.414834	−	1.15938i
$220$	−18.2367	+	18.6717i	−1.22952	+	1.25885i
$221$	−1.74237	−	1.04433i	−0.117204	−	0.0702495i
$222$	−4.84329	−	2.25588i	−0.325060	−	0.151405i
$223$	2.39426	−	0.991736i	0.160332	−	0.0664116i	−0.301074	−	0.953601i	$-0.597345\pi$
$223$	2.39426	−	0.991736i	0.160332	−	0.0664116i	0.461406	+	0.887189i	$0.347345\pi$
$224$	11.6725	+	6.53674i	0.779905	+	0.436755i
$225$	−1.13357	−	0.469539i	−0.0755712	−	0.0313026i
$226$	−2.12233	−	2.31408i	−0.141175	−	0.153930i
$227$	7.68234	−	1.92433i	0.509895	−	0.127722i	0.0205094	−	0.999790i	$-0.493471\pi$
$227$	7.68234	−	1.92433i	0.509895	−	0.127722i	0.489385	+	0.872068i	$0.337221\pi$
$228$	−17.7255	−	25.8630i	−1.17390	−	1.71282i
$229$	−4.01924	+	8.49798i	−0.265599	+	0.561562i	−0.992078	−	0.125627i	$-0.959906\pi$
$229$	−4.01924	+	8.49798i	−0.265599	+	0.561562i	0.726478	+	0.687189i	$0.241156\pi$
$230$	6.01714	+	29.3453i	0.396758	+	1.93497i
$231$	23.1906	+	2.28407i	1.52583	+	0.150281i
$232$	−1.06659	+	13.2217i	−0.0700253	+	0.868046i
$233$	1.64904	+	1.35333i	0.108032	+	0.0886596i	0.686859	−	0.726791i	$-0.258989\pi$
$233$	1.64904	+	1.35333i	0.108032	+	0.0886596i	−0.578827	+	0.815451i	$0.696489\pi$
$234$	−0.307206	−	0.0284303i	−0.0200827	−	0.00185855i
$235$	−7.71961	+	10.4087i	−0.503572	+	0.678988i
$236$	0.719831	−	1.23371i	0.0468570	−	0.0803077i
$237$	5.71451	+	12.0823i	0.371197	+	0.784830i
$238$	19.0500	−	14.3032i	1.23483	−	0.927140i
$239$	0.504171	+	2.53464i	0.0326121	+	0.163952i	0.993659	−	0.112432i	$-0.0358639\pi$
$239$	0.504171	+	2.53464i	0.0326121	+	0.163952i	−0.961047	+	0.276384i	$0.910864\pi$
$240$	8.06498	+	18.2421i	0.520592	+	1.17752i
$241$	−4.27492	+	21.4915i	−0.275372	+	1.38439i	0.557157	+	0.830407i	$0.311892\pi$
$241$	−4.27492	+	21.4915i	−0.275372	+	1.38439i	−0.832529	+	0.553982i	$0.813108\pi$
$242$	18.8520	−	9.05268i	1.21185	−	0.581928i
$243$	−5.21796	+	5.75713i	−0.334732	+	0.369320i
$244$	5.11754	−	7.07293i	0.327617	−	0.452798i
$245$	−1.85882	−	3.10125i	−0.118756	−	0.198132i
$246$	10.8287	−	13.3545i	0.690414	−	0.851455i
$247$	2.20508	+	0.668905i	0.140306	+	0.0425614i
$248$	−13.2062	+	15.0989i	−0.838598	+	0.958781i
$249$	5.59837	+	2.99239i	0.354783	+	0.189635i
$250$	8.77831	+	8.67546i	0.555189	+	0.548684i
$251$	9.37157	+	0.460396i	0.591529	+	0.0290599i	0.342631	−	0.939470i	$-0.388682\pi$
$251$	9.37157	+	0.460396i	0.591529	+	0.0290599i	0.248897	+	0.968530i	$0.419932\pi$
$252$	1.66779	−	3.21067i	0.105061	−	0.202253i
$253$	6.14170	−	41.4040i	0.386125	−	2.60305i
$254$	−6.43816	+	8.78862i	−0.403966	+	0.551447i
$255$	35.5157			2.22408
$256$	5.41950	−	15.0542i	0.338719	−	0.940888i
$257$	7.27874			0.454035			0.227018	−	0.973891i	$-0.427103\pi$
$257$	7.27874			0.454035			0.227018	+	0.973891i	$0.427103\pi$
$258$	−7.30020	+	9.96538i	−0.454491	+	0.620418i
$259$	−0.675659	+	4.55492i	−0.0419834	+	0.283029i
$260$	−1.30081	−	0.675708i	−0.0806728	−	0.0419057i
$261$	3.58296	+	0.176020i	0.221780	+	0.0108953i
$262$	−18.9959	−	18.7734i	−1.17357	−	1.15982i
$263$	22.6851	+	12.1254i	1.39882	+	0.747687i	0.986563	−	0.163379i	$-0.0522392\pi$
$263$	22.6851	+	12.1254i	1.39882	+	0.747687i	0.412261	+	0.911066i	$0.364739\pi$
$264$	−1.85936	−	27.8074i	−0.114436	−	1.71143i
$265$	19.0692	+	5.78459i	1.17141	+	0.355345i
$266$	−17.0196	+	20.9894i	−1.04354	+	1.28694i
$267$	−3.72804	−	6.21986i	−0.228152	−	0.380649i
$268$	−4.83036	−	3.49495i	−0.295061	−	0.213488i
$269$	10.9692	−	12.1026i	0.668802	−	0.737909i	−0.308158	−	0.951335i	$-0.599712\pi$
$269$	10.9692	−	12.1026i	0.668802	−	0.737909i	0.976959	+	0.213427i	$0.0684624\pi$
$270$	−14.2081	+	6.82266i	−0.864675	+	0.415214i
$271$	−3.62752	+	18.2368i	−0.220356	+	1.10780i	0.699225	+	0.714902i	$0.253529\pi$
$271$	−3.62752	+	18.2368i	−0.220356	+	1.10780i	−0.919580	+	0.392902i	$0.871471\pi$
$272$	−20.6150	−	19.6653i	−1.24997	−	1.19238i
$273$	0.255323	+	1.28359i	0.0154528	+	0.0776866i
$274$	−5.79048	+	4.34764i	−0.349816	+	0.262650i
$275$	3.48269	+	7.36354i	0.210014	+	0.444038i
$276$	−27.6278	−	16.1200i	−1.66300	−	0.970308i
$277$	−7.66063	+	10.3292i	−0.460283	+	0.620620i	−0.970986	−	0.239138i	$-0.923135\pi$
$277$	−7.66063	+	10.3292i	−0.460283	+	0.620620i	0.510703	+	0.859757i	$0.329385\pi$
$278$	−11.6995	−	1.08273i	−0.701692	−	0.0649378i
$279$	4.19348	+	3.44150i	0.251057	+	0.206037i
$280$	13.0931	−	11.1384i	0.782464	−	0.665645i
$281$	22.8109	+	2.24668i	1.36078	+	0.134026i	0.751923	−	0.659251i	$-0.229126\pi$
$281$	22.8109	+	2.24668i	1.36078	+	0.134026i	0.608862	+	0.793277i	$0.291626\pi$
$282$	−2.77948	−	13.5554i	−0.165516	−	0.807213i
$283$	2.30375	−	4.87086i	0.136943	−	0.289543i	−0.823850	−	0.566808i	$-0.808178\pi$
$283$	2.30375	−	4.87086i	0.136943	−	0.289543i	0.960793	+	0.277265i	$0.0894281\pi$
$284$	12.4249	−	8.51559i	0.737284	−	0.505307i
$285$	−39.0802	+	9.78909i	−2.31491	+	0.579856i
$286$	1.38441	+	1.50949i	0.0818617	+	0.0892577i
$287$	−13.6900	−	5.67057i	−0.808093	−	0.334723i
$288$	−4.11527	−	1.33707i	−0.242495	−	0.0787879i
$289$	−31.1637	+	12.9084i	−1.83316	+	0.759319i
$290$	15.4502	+	7.19631i	0.907269	+	0.422582i
$291$	−19.3680	−	11.6088i	−1.13537	−	0.680517i
$292$	13.4371	+	13.1240i	0.786345	+	0.768025i
$293$	−3.20642	−	8.96134i	−0.187321	−	0.523527i	0.810765	−	0.585372i	$-0.199052\pi$
$293$	−3.20642	−	8.96134i	−0.187321	−	0.523527i	−0.998086	+	0.0618451i	$0.980302\pi$
$294$	3.79097	+	0.730873i	0.221094	+	0.0426254i
$295$	−1.16431	−	1.41872i	−0.0677890	−	0.0826011i
$296$	5.50631	−	0.0973562i	0.320048	−	0.00565872i
$297$	21.9170	−	2.15864i	1.27175	−	0.125257i
$298$	−4.53879	−	14.6510i	−0.262925	−	0.848711i
$299$	2.32535	−	0.344933i	0.134478	−	0.0199480i
$300$	6.21326	−	0.378690i	0.358723	−	0.0218637i
$301$	10.0242	+	3.58673i	0.577788	+	0.206736i
$302$	−5.39635	+	1.38556i	−0.310525	+	0.0797301i
$303$	−0.609647	+	0.912402i	−0.0350233	+	0.0524161i
$304$	28.1042	+	15.9569i	1.61189	+	0.915194i
$305$	−6.23212	−	9.32703i	−0.356850	−	0.534064i
$306$	−5.14058	+	5.73936i	−0.293867	+	0.328098i
$307$	11.5926	−	0.569507i	0.661623	−	0.0325035i	0.284513	−	0.958672i	$-0.408168\pi$
$307$	11.5926	−	0.569507i	0.661623	−	0.0325035i	0.377110	+	0.926169i	$0.376918\pi$
$308$	−22.5183	+	8.35783i	−1.28310	+	0.476231i
$309$	1.56037	+	0.390853i	0.0887666	+	0.0222349i
$310$	12.2839	+	22.6593i	0.697677	+	1.28696i
$311$	−9.62090	−	17.9994i	−0.545551	−	1.02065i	−0.992047	−	0.125869i	$-0.959828\pi$
$311$	−9.62090	−	17.9994i	−0.545551	−	1.02065i	0.446496	−	0.894786i	$-0.352672\pi$
$312$	1.46417	−	0.553276i	0.0828922	−	0.0313231i
$313$	−19.9297	+	6.04559i	−1.12649	+	0.341717i	−0.797921	−	0.602762i	$-0.794067\pi$
$313$	−19.9297	+	6.04559i	−1.12649	+	0.341717i	−0.328570	+	0.944480i	$0.606567\pi$
$314$	−3.00119	+	7.36804i	−0.169367	+	0.415802i
$315$	−3.12197	−	3.44456i	−0.175903	−	0.194079i
$316$	−10.7516	−	8.61360i	−0.604827	−	0.484553i
$317$	−4.46302	−	6.01769i	−0.250668	−	0.337987i	0.659894	−	0.751359i	$-0.270601\pi$
$317$	−4.46302	−	6.01769i	−0.250668	−	0.337987i	−0.910562	+	0.413372i	$0.864351\pi$
$318$	−18.1862	+	11.0466i	−1.01983	+	0.619461i
$319$	−16.8400	−	16.8400i	−0.942857	−	0.942857i
$320$	−15.7115	−	13.2592i	−0.878300	−	0.741214i
$321$	10.3673	−	10.3673i	0.578646	−	0.578646i
$322$	−6.54071	+	26.7806i	−0.364499	+	1.49242i
$323$	46.2226	−	34.2810i	2.57189	−	1.90745i
$324$	5.97569	−	20.5689i	0.331983	−	1.14271i
$325$	−0.338968	+	0.307222i	−0.0188025	+	0.0170416i
$326$	−3.83219	+	1.61387i	−0.212245	+	0.0893838i
$327$	2.27058	+	7.48509i	0.125563	+	0.413926i
$328$	−4.00148	+	17.2641i	−0.220945	+	0.953253i
$329$	−10.5176	+	5.62178i	−0.579854	+	0.309939i
$330$	−34.3287	−	10.1930i	−1.88973	−	0.561104i
$331$	1.03022	−	4.11287i	0.0566261	−	0.226064i	−0.935110	−	0.354357i	$-0.884700\pi$
$331$	1.03022	−	4.11287i	0.0566261	−	0.226064i	0.991736	+	0.128293i	$0.0409498\pi$
$332$	−6.53856	−	0.244010i	−0.358850	−	0.0133918i
$333$	−0.0730792	−	1.48756i	−0.00400472	−	0.0815179i
$334$	30.6861	−	1.68884i	1.67907	−	0.0924090i
$335$	−6.36976	+	4.25614i	−0.348017	+	0.232538i
$336$	−0.468291	+	18.3493i	−0.0255474	+	1.00104i
$337$	20.1969	+	13.4951i	1.10019	+	0.735126i	0.966697	−	0.255923i	$-0.0823793\pi$
$337$	20.1969	+	13.4951i	1.10019	+	0.735126i	0.133497	+	0.991049i	$0.457379\pi$
$338$	9.30002	−	15.7256i	0.505854	−	0.855358i
$339$	1.45135	−	4.05625i	0.0788266	−	0.220305i
$340$	−32.9063	+	16.0408i	−1.78459	+	0.869933i
$341$	−5.28446	−	35.6249i	−0.286169	−	1.92920i
$342$	4.07458	−	7.73227i	0.220328	−	0.418113i
$343$	−1.94879	−	19.7864i	−0.105225	−	1.06836i
$344$	2.26293	−	12.5303i	0.122009	−	0.675591i
$345$	−31.7710	+	26.0738i	−1.71049	+	1.40376i
$346$	−6.84937	+	4.63522i	−0.368224	+	0.249191i
$347$	−19.4627	+	6.96385i	−1.04481	+	0.373839i	−0.802683	−	0.596405i	$-0.796595\pi$
$347$	−19.4627	+	6.96385i	−1.04481	+	0.373839i	−0.242127	+	0.970245i	$0.577845\pi$
$348$	−16.7308	+	7.16231i	−0.896867	+	0.383940i
$349$	3.01804	−	5.03529i	0.161552	−	0.269533i	−0.766299	−	0.642484i	$-0.777904\pi$
$349$	3.01804	−	5.03529i	0.161552	−	0.269533i	0.927851	+	0.372951i	$0.121654\pi$
$350$	−1.83709	−	5.04049i	−0.0981967	−	0.269425i
$351$	0.473328	+	1.14272i	0.0252644	+	0.0609937i
$352$	14.2820	+	24.9245i	0.761234	+	1.32848i
$353$	12.4852	−	30.1420i	0.664521	−	1.60430i	−0.126119	−	0.992015i	$-0.540252\pi$
$353$	12.4852	−	30.1420i	0.664521	−	1.60430i	0.790640	−	0.612281i	$-0.209748\pi$
$354$	1.95792	+	0.0846236i	0.104062	+	0.00449769i
$355$	−4.70281	−	18.7747i	−0.249599	−	0.996457i
$356$	6.26334	+	4.07908i	0.331956	+	0.216191i
$357$	29.5463	+	13.9744i	1.56376	+	0.739601i
$358$	13.6552	−	20.6996i	0.721702	−	1.09401i
$359$	1.05905	−	10.7527i	0.0558944	−	0.567505i	−0.925928	−	0.377701i	$-0.876715\pi$
$359$	1.05905	−	10.7527i	0.0558944	−	0.567505i	0.981822	−	0.189804i	$-0.0607853\pi$
$360$	−3.45062	+	4.35953i	−0.181864	+	0.229767i
$361$	−29.3594	+	35.7746i	−1.54523	+	1.88287i
$362$	−15.9777	+	13.2709i	−0.839769	+	0.697503i
$363$	23.0465	+	17.0925i	1.20963	+	0.897122i
$364$	−0.816301	−	1.07397i	−0.0427858	−	0.0562911i
$365$	21.8172	−	10.3188i	1.14197	−	0.540109i
$366$	11.8585	+	1.68769i	0.619855	+	0.0882168i
$367$	7.36065	−	1.46412i	0.384223	−	0.0764267i	0.000800237	−	1.00000i	$-0.499745\pi$
$367$	7.36065	−	1.46412i	0.384223	−	0.0764267i	0.383423	+	0.923573i	$0.374745\pi$
$368$	32.8785	+	2.45739i	1.71391	+	0.128100i
$369$	4.70059	+	0.935005i	0.244703	+	0.0486744i
$370$	2.34461	−	6.67654i	0.121891	−	0.347097i
$371$	13.5880	+	12.3155i	0.705456	+	0.639388i
$372$	−26.7743	−	6.37222i	−1.38818	−	0.330384i
$373$	−3.93841	+	2.36059i	−0.203923	+	0.122227i	−0.612419	−	0.790533i	$-0.709803\pi$
$373$	−3.93841	+	2.36059i	−0.203923	+	0.122227i	0.408496	+	0.912760i	$0.366053\pi$
$374$	50.8748	−	5.31363i	2.63068	−	0.274761i
$375$	−4.91551	+	16.2043i	−0.253836	+	0.836785i
$376$	8.69760	+	11.3041i	0.448544	+	0.582963i
$377$	0.630505	−	1.17959i	0.0324727	−	0.0607521i
$378$	−14.5045	+	0.0854761i	−0.746031	+	0.00439641i
$379$	0.0213741	−	0.435080i	0.00109791	−	0.0223485i	−0.998184	−	0.0602389i	$-0.980814\pi$
$379$	0.0213741	−	0.435080i	0.00109791	−	0.0223485i	0.999282	+	0.0378903i	$0.0120638\pi$
$380$	31.7876	−	26.7205i	1.63067	−	1.37073i
$381$	−14.7857	−	2.19326i	−0.757497	−	0.112364i
$382$	27.3515	−	4.22209i	1.39943	−	0.216021i
$383$			33.8923i			1.73181i	0.500204	+	0.865907i	$0.333258\pi$
$383$			33.8923i			1.73181i	−0.500204	+	0.865907i	$0.666742\pi$
$384$	21.7394	−	3.05083i	1.10938	−	0.155687i
$385$			30.8628i			1.57291i
$386$	−0.682795	−	4.42328i	−0.0347533	−	0.225139i
$387$	−3.40625	−	0.505269i	−0.173149	−	0.0256843i
$388$	23.1881	+	2.00819i	1.17720	+	0.101950i
$389$	1.62669	−	33.1121i	0.0824767	−	1.67885i	−0.500017	−	0.866016i	$-0.666673\pi$
$389$	1.62669	−	33.1121i	0.0824767	−	1.67885i	0.582493	−	0.812835i	$-0.302077\pi$
$390$	−0.0118518	−	2.01114i	−0.000600139	−	0.101838i
$391$	27.6749	−	51.7762i	1.39958	−	2.61843i
$392$	−3.84253	+	1.03503i	−0.194077	+	0.0522767i
$393$	10.6370	−	35.0654i	0.536565	−	1.76882i
$394$	−2.26169	−	21.6544i	−0.113942	−	1.09093i
$395$	−15.1832	+	9.10047i	−0.763951	+	0.457894i
$396$	6.61595	−	4.07219i	0.332464	−	0.204635i
$397$	14.3896	+	13.0420i	0.722194	+	0.654559i	0.947510	−	0.319727i	$-0.103591\pi$
$397$	14.3896	+	13.0420i	0.722194	+	0.654559i	−0.225315	+	0.974286i	$0.572341\pi$
$398$	16.2909	+	5.72090i	0.816588	+	0.286763i
$399$	−36.3634	−	7.23313i	−1.82045	−	0.362109i
$400$	−5.58571	+	3.15710i	−0.279286	+	0.157855i
$401$	−26.8271	+	5.33624i	−1.33968	+	0.266479i	−0.812345	−	0.583177i	$-0.801809\pi$
$401$	−26.8271	+	5.33624i	−1.33968	+	0.266479i	−0.527336	+	0.849657i	$0.676809\pi$
$402$	1.15258	−	8.09861i	0.0574855	−	0.403922i
$403$	1.82847	−	0.864804i	0.0910828	−	0.0430790i
$404$	0.152766	−	1.12071i	0.00760037	−	0.0557575i
$405$	−22.1059	−	16.3949i	−1.09845	−	0.814667i
$406$	10.0218	+	12.0660i	0.497376	+	0.598823i
$407$	−6.27260	+	7.64319i	−0.310921	+	0.378859i
$408$	10.6841	−	37.6011i	0.528940	−	1.86153i
$409$	−0.790068	+	8.02169i	−0.0390663	+	0.396647i	0.955690	+	0.294375i	$0.0951114\pi$
$409$	−0.790068	+	8.02169i	−0.0390663	+	0.396647i	−0.994756	+	0.102272i	$0.967389\pi$
$410$	19.0077	+	12.5391i	0.938722	+	0.619263i
$411$	−8.98096	−	4.24768i	−0.442998	−	0.209523i
$412$	−1.62226	+	0.342611i	−0.0799229	+	0.0168792i
$413$	−0.410394	−	1.63839i	−0.0201942	−	0.0806197i
$414$	0.385021	−	8.90814i	0.0189228	−	0.437811i
$415$	−3.21736	+	7.76738i	−0.157934	+	0.381286i
$416$	−1.10670	+	1.17392i	−0.0542605	+	0.0575561i
$417$	−6.16912	−	14.8936i	−0.302103	−	0.729342i
$418$	−54.5162	+	19.8694i	−2.66648	+	0.971844i
$419$	−7.67642	+	12.8073i	−0.375018	+	0.625679i	−0.986151	−	0.165848i	$-0.946964\pi$
$419$	−7.67642	+	12.8073i	−0.375018	+	0.625679i	0.611134	+	0.791527i	$0.290714\pi$
$420$	21.8946	+	8.76817i	1.06835	+	0.427843i
$421$	−11.8713	+	4.24762i	−0.578572	+	0.207016i	−0.609881	−	0.792493i	$-0.708783\pi$
$421$	−11.8713	+	4.24762i	−0.578572	+	0.207016i	0.0313083	+	0.999510i	$0.490033\pi$
$422$	−14.0680	−	20.7880i	−0.684821	−	1.01195i
$423$	2.98170	−	2.44702i	0.144975	−	0.118978i
$424$	11.8608	−	18.4488i	0.576010	−	0.895952i
$425$	1.11984	+	11.3700i	0.0543204	+	0.551524i
$426$	18.2836	+	9.63471i	0.885845	+	0.466803i
$427$	−1.51473	−	10.2115i	−0.0733031	−	0.494169i
$428$	−4.92315	+	14.2880i	−0.237970	+	0.690636i
$429$	−0.946724	+	2.64592i	−0.0457083	+	0.127746i
$430$	−14.0825	−	8.32834i	−0.679120	−	0.401628i
$431$	17.0163	+	11.3699i	0.819648	+	0.547671i	0.893221	−	0.449619i	$-0.148440\pi$
$431$	17.0163	+	11.3699i	0.819648	+	0.547671i	−0.0735729	+	0.997290i	$0.523440\pi$
$432$	2.94911	+	17.0948i	0.141889	+	0.822472i
$433$	23.4440	−	15.6648i	1.12665	−	0.752800i	0.154689	−	0.987963i	$-0.450562\pi$
$433$	23.4440	−	15.6648i	1.12665	−	0.752800i	0.971956	+	0.235163i	$0.0755624\pi$
$434$	1.30347	+	23.6841i	0.0625687	+	1.13687i
$435$	1.14744	+	23.3566i	0.0550154	+	1.11986i
$436$	−5.48441	−	5.90962i	−0.262655	−	0.283019i
$437$	−16.1816	+	64.6006i	−0.774071	+	3.09026i
$438$	−7.33534	+	24.7045i	−0.350496	+	1.18043i
$439$	−7.89027	+	4.21744i	−0.376582	+	0.201287i	−0.648819	−	0.760943i	$-0.724737\pi$
$439$	−7.89027	+	4.21744i	−0.376582	+	0.201287i	0.272237	+	0.962230i	$0.412237\pi$
$440$	36.4101	−	6.06058i	1.73578	−	0.288927i
$441$	0.312407	+	1.02987i	0.0148765	+	0.0490414i
$442$	1.11499	+	2.64759i	0.0530348	+	0.125933i
$443$	−14.9286	+	13.5305i	−0.709278	+	0.642852i	−0.944280	−	0.329143i	$-0.893240\pi$
$443$	−14.9286	+	13.5305i	−0.709278	+	0.642852i	0.235002	+	0.971995i	$0.424490\pi$
$444$	3.64016	+	6.62134i	0.172754	+	0.314235i
$445$	7.71411	−	5.72117i	0.365684	−	0.271210i
$446$	−3.56033	−	0.869551i	−0.168586	−	0.0411744i
$447$	14.8804	−	14.8804i	0.703820	−	0.703820i
$448$	−7.85364	−	17.2126i	−0.371050	−	0.813221i
$449$	14.1269	+	14.1269i	0.666688	+	0.666688i	0.956948	−	0.290260i	$-0.0937418\pi$
$449$	14.1269	+	14.1269i	0.666688	+	0.666688i	−0.290260	+	0.956948i	$0.593742\pi$
$450$	0.900822	+	1.48304i	0.0424651	+	0.0699112i
$451$	−18.9538	−	25.5562i	−0.892500	−	1.20340i
$452$	0.487303	+	4.41373i	0.0229208	+	0.207604i
$453$	−5.13346	−	5.66390i	−0.241191	−	0.266113i
$454$	−10.3726	−	4.22505i	−0.486812	−	0.198291i
$455$	−1.65869	+	0.503159i	−0.0777606	+	0.0235884i
$456$	−1.39247	+	44.3197i	−0.0652083	+	2.07546i
$457$	−2.95086	−	5.52066i	−0.138035	−	0.258246i	0.803400	−	0.595440i	$-0.203022\pi$
$457$	−2.95086	−	5.52066i	−0.138035	−	0.258246i	−0.941435	+	0.337194i	$0.890522\pi$
$458$	11.6874	−	6.33590i	0.546118	−	0.296057i
$459$	29.9637	+	7.50551i	1.39858	+	0.350327i
$460$	17.6603	−	38.5074i	0.823418	−	1.79542i
$461$	12.0008	−	0.589563i	0.558934	−	0.0274587i	0.232359	−	0.972630i	$-0.425355\pi$
$461$	12.0008	−	0.589563i	0.558934	−	0.0274587i	0.326575	+	0.945171i	$0.394105\pi$
$462$	−24.5481	−	21.9870i	−1.14208	−	1.02293i
$463$	11.5630	+	17.3052i	0.537378	+	0.804243i	0.996453	−	0.0841546i	$-0.0268190\pi$
$463$	11.5630	+	17.3052i	0.537378	+	0.804243i	−0.459075	+	0.888398i	$0.651819\pi$
$464$	12.2667	−	14.1926i	0.569466	−	0.658874i
$465$	−19.6470	+	29.4038i	−0.911107	+	1.36357i
$466$	−0.750279	−	2.92211i	−0.0347560	−	0.135364i
$467$	−6.51508	−	2.33113i	−0.301482	−	0.107872i	0.181803	−	0.983335i	$-0.441807\pi$
$467$	−6.51508	−	2.33113i	−0.301482	−	0.107872i	−0.483285	+	0.875463i	$0.660557\pi$
$468$	0.326717	+	0.289179i	0.0151025	+	0.0133673i
$469$	−6.97380	+	1.03447i	−0.322020	+	0.0477672i
$470$	17.5059	−	5.42320i	0.807485	−	0.250154i
$471$	−10.8630	+	1.06992i	−0.500543	+	0.0492992i
$472$	−1.85228	+	0.805891i	−0.0852581	+	0.0370942i
$473$	14.5028	+	17.6717i	0.666839	+	0.812546i
$474$	3.57823	−	18.5599i	0.164354	−	0.852487i
$475$	−4.36610	−	12.2024i	−0.200330	−	0.559886i
$476$	−33.6870	+	0.397053i	−1.54404	+	0.0181989i
$477$	−5.08755	−	3.04936i	−0.232943	−	0.139621i
$478$	1.54311	−	3.31300i	0.0705801	−	0.151533i
$479$	−10.5546	+	4.37185i	−0.482251	+	0.199755i	−0.610545	−	0.791981i	$-0.709050\pi$
$479$	−10.5546	+	4.37185i	−0.482251	+	0.199755i	0.128295	+	0.991736i	$0.459050\pi$
$480$	6.04468	−	27.5518i	0.275901	−	1.25756i
$481$	−0.513039	−	0.212508i	−0.0233926	−	0.00968951i
$482$	22.8383	−	20.9459i	1.04026	−	0.954060i
$483$	−36.6902	+	9.19041i	−1.66946	+	0.418178i
$484$	−29.0730	−	5.42759i	−1.32150	−	0.246709i
$485$	12.7866	−	27.0350i	0.580610	−	1.22760i
$486$	10.7644	−	2.20719i	0.488282	−	0.100120i
$487$	2.77825	+	0.273634i	0.125894	+	0.0123995i	0.160768	−	0.986992i	$-0.448603\pi$
$487$	2.77825	+	0.273634i	0.125894	+	0.0123995i	−0.0348736	+	0.999392i	$0.511103\pi$
$488$	−11.7495	+	3.79224i	−0.531874	+	0.171667i
$489$	−4.41010	−	3.61928i	−0.199432	−	0.163669i
$490$	−0.471196	+	5.09155i	−0.0212864	+	0.230013i
$491$	−8.87653	+	11.9686i	−0.400592	+	0.540136i	−0.956739	−	0.290948i	$-0.906029\pi$
$491$	−8.87653	+	11.9686i	−0.400592	+	0.540136i	0.556147	+	0.831084i	$0.312279\pi$
$492$	−23.5149	+	6.18559i	−1.06013	+	0.278868i
$493$	−14.2817	−	30.1962i	−0.643216	−	1.35997i
$494$	−1.95664	−	2.60599i	−0.0880336	−	0.117249i
$495$	−1.94743	−	9.79040i	−0.0875305	−	0.440046i
$496$	27.6851	−	6.18864i	1.24310	−	0.277878i
$497$	3.47489	−	17.4695i	0.155870	−	0.783613i
$498$	−3.88606	−	8.09265i	−0.174138	−	0.362640i
$499$	−4.18110	+	4.61314i	−0.187172	+	0.206512i	−0.827307	−	0.561750i	$-0.810128\pi$
$499$	−4.18110	+	4.61314i	−0.187172	+	0.206512i	0.640135	+	0.768262i	$0.278878\pi$
$500$	−2.76435	−	17.2338i	−0.123625	−	0.770718i
$501$	21.6776	+	36.1669i	0.968483	+	1.61582i
$502$	−10.3068	−	8.35742i	−0.460015	−	0.373010i
$503$	−11.9836	−	3.63520i	−0.534324	−	0.162085i	0.0115804	−	0.999933i	$-0.496314\pi$
$503$	−11.9836	−	3.63520i	−0.534324	−	0.162085i	−0.545904	+	0.837848i	$0.683814\pi$
$504$	−4.58598	+	2.26907i	−0.204276	+	0.101072i
$505$	−1.28173	−	0.685099i	−0.0570363	−	0.0304865i
$506$	−41.6096	+	42.1029i	−1.84977	+	1.87170i
$507$	25.0364	+	1.22996i	1.11191	+	0.0546244i
$508$	14.6900	−	4.64591i	0.651762	−	0.206129i
$509$	2.50606	−	16.8945i	0.111079	−	0.748834i	−0.860038	−	0.510230i	$-0.829560\pi$
$509$	2.50606	−	16.8945i	0.111079	−	0.748834i	0.971117	−	0.238604i	$-0.0766897\pi$
$510$	−40.5182	−	29.6818i	−1.79418	−	1.31433i
$511$	22.2103			0.982527
$512$	−18.7642	+	12.6453i	−0.829269	+	0.558850i
$513$	−35.0396			−1.54704
$514$	−8.30396	−	6.08311i	−0.366272	−	0.268315i
$515$	−0.312601	+	2.10739i	−0.0137749	+	0.0928625i
$516$	16.6569	−	5.26798i	0.733279	−	0.231910i
$517$	−25.5768	−	1.25651i	−1.12486	−	0.0552611i
$518$	4.57755	−	4.63182i	0.201126	−	0.203510i
$519$	−10.0073	−	5.34902i	−0.439273	−	0.234796i
$520$	0.919317	+	1.85802i	0.0403147	+	0.0814795i
$521$	−0.846391	−	0.256750i	−0.0370811	−	0.0112484i	0.271690	−	0.962385i	$-0.412418\pi$
$521$	−0.846391	−	0.256750i	−0.0370811	−	0.0112484i	−0.308771	+	0.951136i	$0.599918\pi$
$522$	−3.94052	−	3.19523i	−0.172472	−	0.139851i
$523$	−11.5444	−	19.2607i	−0.504802	−	0.842210i	0.494840	−	0.868984i	$-0.335227\pi$
$523$	−11.5444	−	19.2607i	−0.504802	−	0.842210i	−0.999642	+	0.0267737i	$0.991477\pi$
$524$	5.98195	+	37.2932i	0.261323	+	1.62916i
$525$	4.94314	−	5.45392i	0.215736	−	0.238028i
$526$	−15.7467	−	32.7921i	−0.686587	−	1.42981i
$527$	9.85480	−	49.5434i	0.429282	−	2.15815i
$528$	−21.1184	+	33.2780i	−0.919061	+	1.44824i
$529$	8.76732	+	44.0763i	0.381188	+	1.91636i
$530$	−16.9208	−	22.5362i	−0.734991	−	0.978912i
$531$	0.233568	+	0.493838i	0.0101360	+	0.0214308i
$532$	36.9585	−	9.72193i	1.60235	−	0.421499i
$533$	1.06449	−	1.43530i	0.0461082	−	0.0621697i
$534$	−0.945029	+	10.2116i	−0.0408954	+	0.441899i
$535$	15.0104	+	12.3187i	0.648958	+	0.532586i
$536$	2.58986	+	8.02413i	0.111865	+	0.346590i
$537$	33.8596	+	3.33488i	1.46115	+	0.143911i
$538$	−22.6288	+	4.63994i	−0.975596	+	0.200042i
$539$	3.05478	−	6.45879i	0.131579	−	0.278200i
$540$	21.9112	+	4.09057i	0.942910	+	0.176030i
$541$	41.2439	−	10.3311i	1.77321	−	0.444167i	0.788026	−	0.615642i	$-0.211103\pi$
$541$	41.2439	−	10.3311i	1.77321	−	0.444167i	0.985188	+	0.171475i	$0.0548534\pi$
$542$	19.3796	−	17.7738i	0.832425	−	0.763449i
$543$	−26.3281	−	10.9055i	−1.12985	−	0.467999i
$544$	7.08359	+	39.6639i	0.303706	+	1.70058i
$545$	−9.57094	+	3.96441i	−0.409974	+	0.169817i
$546$	0.781462	−	1.67777i	0.0334435	−	0.0718020i
$547$	−28.7227	−	17.2157i	−1.22809	−	0.736090i	−0.255097	−	0.966915i	$-0.582108\pi$
$547$	−28.7227	−	17.2157i	−1.22809	−	0.736090i	−0.972995	+	0.230825i	$0.925858\pi$
$548$	10.2396	−	0.120689i	0.437413	−	0.00515559i
$549$	1.12485	+	3.14375i	0.0480075	+	0.134172i
$550$	2.18075	−	11.3113i	0.0929874	−	0.482316i
$551$	24.0379	+	29.2903i	1.02405	+	1.24781i
$552$	18.0472	+	41.4801i	0.768140	+	1.76551i
$553$	−16.2120	+	1.59674i	−0.689404	+	0.0679004i
$554$	17.3721	−	5.38177i	0.738071	−	0.228650i
$555$	9.60373	−	1.42458i	0.407656	−	0.0604700i
$556$	12.4426	+	11.0130i	0.527682	+	0.467055i
$557$	−37.7513	−	13.5076i	−1.59957	−	0.572337i	−0.622016	−	0.783004i	$-0.713686\pi$
$557$	−37.7513	−	13.5076i	−1.59957	−	0.572337i	−0.977558	+	0.210667i	$0.932436\pi$
$558$	−1.90795	−	7.43089i	−0.0807699	−	0.314575i
$559$	−0.713309	+	1.06754i	−0.0301698	+	0.0451522i
$560$	−24.2461	+	1.76481i	−1.02458	+	0.0745770i
$561$	38.9907	+	58.3537i	1.64619	+	2.46369i
$562$	−24.1462	−	21.6271i	−1.01855	−	0.912282i
$563$	−32.7875	+	1.61075i	−1.38183	+	0.0678849i	−0.726348	−	0.687327i	$-0.758784\pi$
$563$	−32.7875	+	1.61075i	−1.38183	+	0.0678849i	−0.655481	+	0.755212i	$0.727534\pi$
$564$	−8.15779	+	17.7876i	−0.343505	+	0.748995i
$565$	5.53474	+	1.38638i	0.232848	+	0.0583255i
$566$	−6.69899	+	3.63160i	−0.281580	+	0.152648i
$567$	−11.9395	−	22.3372i	−0.501412	−	0.938075i
$568$	−21.2918	−	0.668961i	−0.893384	−	0.0280690i
$569$	−30.3145	+	9.19580i	−1.27085	+	0.385508i	−0.852476	−	0.522767i	$-0.824900\pi$
$569$	−30.3145	+	9.19580i	−1.27085	+	0.385508i	−0.418374	+	0.908275i	$0.637400\pi$
$570$	52.7659	+	21.4929i	2.21012	+	0.900239i
$571$	−16.9756	−	18.7297i	−0.710408	−	0.783814i	0.273618	−	0.961838i	$-0.411780\pi$
$571$	−16.9756	−	18.7297i	−0.710408	−	0.783814i	−0.984026	+	0.178024i	$0.943030\pi$
$572$	−0.317870	−	2.87910i	−0.0132908	−	0.120381i
$573$	22.6196	+	30.4990i	0.944948	+	1.27411i
$574$	10.8791	+	17.9105i	0.454085	+	0.747570i
$575$	−9.34898	−	9.34898i	−0.389879	−	0.389879i
$576$	3.57747	+	4.96469i	0.149061	+	0.206862i
$577$	4.10888	−	4.10888i	0.171055	−	0.171055i	−0.616388	−	0.787443i	$-0.711405\pi$
$577$	4.10888	−	4.10888i	0.171055	−	0.171055i	0.787443	+	0.616388i	$0.211405\pi$
$578$	46.3412	+	11.3181i	1.92754	+	0.470769i
$579$	4.93228	−	3.65803i	0.204979	−	0.152023i
$580$	−11.6122	−	21.1223i	−0.482170	−	0.877054i
$581$	−5.73281	+	5.19592i	−0.237837	+	0.215563i
$582$	12.3942	+	29.4305i	0.513756	+	1.21993i
$583$	11.4307	+	37.6820i	0.473412	+	1.56063i
$584$	−4.36148	−	26.2024i	−0.180479	−	1.08426i
$585$	0.494427	−	0.264276i	0.0204420	−	0.0109265i
$586$	−3.83128	+	12.9033i	−0.158269	+	0.533030i
$587$	4.52561	−	18.0673i	0.186792	−	0.745716i	−0.802114	−	0.597171i	$-0.796291\pi$
$587$	4.52561	−	18.0673i	0.186792	−	0.745716i	0.988906	−	0.148544i	$-0.0474588\pi$
$588$	−3.71411	−	4.00207i	−0.153167	−	0.165043i
$589$	2.81163	+	57.2320i	0.115851	+	2.35820i
$590$	0.142632	+	2.59161i	0.00587205	+	0.106695i
$591$	24.8377	−	16.5960i	1.02168	−	0.682668i
$592$	−6.36324	−	4.49076i	−0.261528	−	0.184569i
$593$	19.6472	+	13.1278i	0.806812	+	0.539095i	0.889207	−	0.457505i	$-0.151257\pi$
$593$	19.6472	+	13.1278i	0.806812	+	0.539095i	−0.0823948	+	0.996600i	$0.526257\pi$
$594$	−26.8081	−	15.8542i	−1.09995	−	0.650504i
$595$	−14.5833	+	40.7575i	−0.597856	+	1.67090i
$596$	−7.06632	+	20.5079i	−0.289448	+	0.840035i
$597$	3.47600	+	23.4333i	0.142263	+	0.959061i
$598$	−2.94115	−	1.54986i	−0.120273	−	0.0633786i
$599$	0.306909	+	3.11610i	0.0125400	+	0.127320i	0.999417	−	0.0341562i	$-0.0108744\pi$
$599$	0.306909	+	3.11610i	0.0125400	+	0.127320i	−0.986877	+	0.161477i	$0.948374\pi$
$600$	−7.40490	−	4.76063i	−0.302304	−	0.194352i
$601$	−3.88657	+	3.18963i	−0.158537	+	0.130108i	−0.710317	−	0.703882i	$-0.751449\pi$
$601$	−3.88657	+	3.18963i	−0.158537	+	0.130108i	0.551781	+	0.833989i	$0.313949\pi$
$602$	−8.43861	−	12.4696i	−0.343932	−	0.508222i
$603$	2.14698	−	0.768201i	0.0874317	−	0.0312836i
$604$	7.31440	+	2.92921i	0.297619	+	0.119188i
$605$	−19.5369	+	32.5953i	−0.794286	+	1.32519i
$606$	1.45805	−	0.531410i	0.0592291	−	0.0215871i
$607$	3.85123	+	9.29769i	0.156317	+	0.377381i	0.982564	−	0.185926i	$-0.0595286\pi$
$607$	3.85123	+	9.29769i	0.156317	+	0.377381i	−0.826247	+	0.563308i	$0.809529\pi$
$608$	−18.7270	−	41.6923i	−0.759478	−	1.69085i
$609$	−8.23553	+	19.8823i	−0.333721	+	0.805673i
$610$	−0.685021	+	15.8492i	−0.0277357	+	0.641714i
$611$	−0.349450	−	1.39508i	−0.0141372	−	0.0564391i
$612$	10.6612	−	2.25159i	0.430955	−	0.0910151i
$613$	33.6841	+	15.9314i	1.36049	+	0.643463i	0.961833	−	0.273638i	$-0.0882269\pi$
$613$	33.6841	+	15.9314i	1.36049	+	0.643463i	0.398656	+	0.917101i	$0.369477\pi$
$614$	−13.7014	−	9.03863i	−0.552942	−	0.364769i
$615$	−3.06230	+	31.0921i	−0.123484	+	1.25375i
$616$	32.6750	+	9.28432i	1.31651	+	0.374076i
$617$	7.64785	−	9.31894i	0.307891	−	0.375166i	−0.595960	−	0.803014i	$-0.703228\pi$
$617$	7.64785	−	9.31894i	0.307891	−	0.375166i	0.903851	+	0.427848i	$0.140728\pi$
$618$	−1.45350	−	1.74997i	−0.0584685	−	0.0703941i
$619$	4.64897	+	3.44791i	0.186858	+	0.138583i	0.685085	−	0.728464i	$-0.259765\pi$
$619$	4.64897	+	3.44791i	0.186858	+	0.138583i	−0.498227	+	0.867047i	$0.666015\pi$
$620$	4.92314	−	36.1170i	0.197718	−	1.45049i
$621$	−32.3144	+	15.2836i	−1.29673	+	0.613309i
$622$	−4.06679	+	28.5752i	−0.163063	+	1.14576i
$623$	8.66864	−	1.72430i	0.347302	−	0.0690826i
$624$	−2.13279	−	0.592455i	−0.0853800	−	0.0237172i
$625$	−29.8622	−	5.93997i	−1.19449	−	0.237599i
$626$	27.7893	+	9.75883i	1.11068	+	0.390041i
$627$	−58.9878	−	53.4634i	−2.35574	−	2.13512i
$628$	9.58166	−	5.89763i	0.382350	−	0.235341i
$629$	−11.8952	+	7.12970i	−0.474292	+	0.284280i
$630$	0.682954	+	6.53888i	0.0272095	+	0.260515i
$631$	5.79043	−	19.0885i	0.230513	−	0.759901i	−0.763022	−	0.646373i	$-0.776285\pi$
$631$	5.79043	−	19.0885i	0.230513	−	0.759901i	0.993535	−	0.113528i	$-0.0362150\pi$
$632$	5.06732	+	18.8124i	0.201567	+	0.748317i
$633$	16.2345	−	30.3725i	0.645262	−	1.20720i
$634$	0.0624383	+	10.5952i	0.00247974	+	0.420789i
$635$	0.971387	−	19.7730i	0.0385483	−	0.784669i
$636$	29.9798	+	2.59638i	1.18878	+	0.102953i
$637$	0.396924	+	0.0588781i	0.0157267	+	0.00233284i
$638$	5.13811	+	33.2857i	0.203420	+	1.31779i
$639$			5.76099i			0.227901i
$640$	6.84327	+	28.2575i	0.270504	+	1.11698i
$641$		−	3.69753i		−	0.146044i	−0.997330	−	0.0730218i	$-0.976736\pi$
$641$		−	3.69753i		−	0.146044i	0.997330	−	0.0730218i	$-0.0232643\pi$
$642$	−20.4919	+	3.16321i	−0.808750	+	0.124842i
$643$	16.2348	+	2.40821i	0.640239	+	0.0949704i	0.458954	−	0.888460i	$-0.348224\pi$
$643$	16.2348	+	2.40821i	0.640239	+	0.0949704i	0.181285	+	0.983431i	$0.441974\pi$
$644$	29.8435	−	25.0863i	1.17600	−	0.988541i
$645$	1.10145	−	22.4206i	0.0433696	−	0.882809i
$646$	−81.3831	+	0.479597i	−3.20197	+	0.0188695i
$647$	7.87323	−	14.7298i	0.309529	−	0.579088i	−0.678272	−	0.734811i	$-0.737271\pi$
$647$	7.87323	−	14.7298i	0.309529	−	0.579088i	0.987801	+	0.155723i	$0.0497709\pi$
$648$	−24.0075	+	18.4719i	−0.943106	+	0.725645i
$649$	1.05278	−	3.47054i	0.0413251	−	0.136231i
$650$	0.643469	−	0.0672072i	0.0252389	−	0.00263608i
$651$	−27.9142	+	16.7311i	−1.09404	+	0.655745i
$652$	5.72073	+	1.36152i	0.224041	+	0.0533212i
$653$	−23.4232	−	21.2296i	−0.916621	−	0.830777i	0.0693671	−	0.997591i	$-0.477902\pi$
$653$	−23.4232	−	21.2296i	−0.916621	−	0.830777i	−0.985988	+	0.166814i	$0.946652\pi$
$654$	3.66518	−	10.4370i	0.143320	−	0.408118i
$655$	47.5987	+	9.46798i	1.85984	+	0.369945i
$656$	18.9934	−	16.3516i	0.741567	−	0.638425i
$657$	−7.04563	+	1.40146i	−0.274876	+	0.0546763i
$658$	16.6974	+	2.37634i	0.650931	+	0.0926395i
$659$	−25.7886	+	12.1971i	−1.00458	+	0.475132i	−0.857771	−	0.514032i	$-0.828151\pi$
$659$	−25.7886	+	12.1971i	−1.00458	+	0.475132i	−0.146812	+	0.989164i	$0.546901\pi$
$660$	30.6453	+	40.3184i	1.19287	+	1.56939i
$661$	−28.5523	−	21.1758i	−1.11055	−	0.823643i	−0.124858	−	0.992175i	$-0.539848\pi$
$661$	−28.5523	−	21.1758i	−1.11055	−	0.823643i	−0.985696	+	0.168532i	$0.946098\pi$
$662$	−4.61261	+	3.83119i	−0.179274	+	0.148903i
$663$	−2.50050	+	3.04686i	−0.0971112	+	0.118330i
$664$	7.25560	+	5.74290i	0.281572	+	0.222868i
$665$	4.81304	−	48.8676i	0.186642	−	1.89501i
$666$	−1.15984	+	1.75816i	−0.0449428	+	0.0681274i
$667$	34.9442	+	16.5274i	1.35305	+	0.639943i
$668$	−36.4197	−	23.7188i	−1.40912	−	0.917708i
$669$	−1.22181	−	4.87775i	−0.0472381	−	0.188585i
$670$	10.8240	+	0.467826i	0.418166	+	0.0180737i
$671$	8.48277	−	20.4792i	0.327474	−	0.790591i
$672$	15.8695	−	20.5425i	0.612178	−	0.792444i
$673$	−11.2508	−	27.1619i	−0.433687	−	1.04701i	−0.978089	−	0.208188i	$-0.933243\pi$
$673$	−11.2508	−	27.1619i	−0.433687	−	1.04701i	0.544402	−	0.838825i	$-0.316757\pi$
$674$	−11.7633	−	32.2752i	−0.453104	−	1.24320i
$675$	3.57633	−	5.96675i	0.137653	−	0.229660i
$676$	−23.7524	+	10.1682i	−0.913553	+	0.391083i
$677$	43.0018	−	15.3863i	1.65269	−	0.591343i	0.664875	−	0.746955i	$-0.268485\pi$
$677$	43.0018	−	15.3863i	1.65269	−	0.591343i	0.987818	+	0.155612i	$0.0497349\pi$
$678$	−5.04574	+	3.41464i	−0.193780	+	0.131138i
$679$	21.2749	−	17.4598i	0.816455	−	0.670047i
$680$	50.9470	+	9.20085i	1.95373	+	0.352836i
$681$	−1.50622	−	15.2929i	−0.0577184	−	0.586024i
$682$	−23.7443	+	45.0592i	−0.909216	+	1.72540i
$683$	−3.61703	−	24.3840i	−0.138402	−	0.933029i	−0.941459	−	0.337127i	$-0.890545\pi$
$683$	−3.61703	−	24.3840i	−0.138402	−	0.933029i	0.803057	−	0.595902i	$-0.203205\pi$
$684$	−11.1106	+	5.41609i	−0.424826	+	0.207089i
$685$	4.43277	−	12.3887i	0.169367	−	0.473350i
$686$	−14.3130	+	24.2020i	−0.546471	+	0.924037i
$687$	15.1662	+	10.1337i	0.578626	+	0.386626i
$688$	−13.0537	+	12.4040i	−0.497669	+	0.472900i
$689$	−1.83883	+	1.22867i	−0.0700538	+	0.0468085i
$690$	58.0368	−	3.19410i	2.20942	−	0.121597i
$691$	−0.515694	−	10.4972i	−0.0196179	−	0.399332i	−0.988444	−	0.151589i	$-0.951561\pi$
$691$	−0.515694	−	10.4972i	−0.0196179	−	0.399332i	0.968826	−	0.247743i	$-0.0796890\pi$
$692$	11.6879	+	0.436179i	0.444309	+	0.0165810i
$693$	2.23211	−	8.91109i	0.0847909	−	0.338504i
$694$	28.0240	+	8.32095i	1.06378	+	0.315859i
$695$	18.8296	−	10.0646i	0.714247	−	0.381773i
$696$	25.0732	+	5.81146i	0.950398	+	0.220283i
$697$	−12.9546	−	42.7057i	−0.490692	−	1.61759i
$698$	−7.65132	+	3.22224i	−0.289607	+	0.121963i
$699$	3.06699	−	2.77976i	0.116004	−	0.105140i
$700$	−2.11667	+	7.28577i	−0.0800027	+	0.275376i
$701$	−38.0568	+	28.2249i	−1.43739	+	1.06604i	−0.452709	+	0.891658i	$0.649542\pi$
$701$	−38.0568	+	28.2249i	−1.43739	+	1.06604i	−0.984678	+	0.174380i	$0.944208\pi$
$702$	0.415013	−	1.69925i	0.0156637	−	0.0641340i
$703$	11.1239	−	11.1239i	0.419545	−	0.419545i
$704$	4.53665	−	40.3711i	0.170981	−	1.52154i
$705$	17.7800	+	17.7800i	0.669632	+	0.669632i
$706$	−39.4346	+	23.9532i	−1.48414	+	0.901490i
$707$	−0.796733	−	1.07427i	−0.0299642	−	0.0404021i
$708$	−2.16297	−	1.73285i	−0.0812893	−	0.0651244i
$709$	−19.7306	−	21.7693i	−0.740998	−	0.817565i	0.247486	−	0.968891i	$-0.420395\pi$
$709$	−19.7306	−	21.7693i	−0.740998	−	0.817565i	−0.988484	+	0.151327i	$0.951645\pi$
$710$	−10.3255	+	25.3494i	−0.387509	+	0.951348i
$711$	5.04207	−	1.52950i	0.189092	−	0.0573605i
$712$	−3.73650	−	9.88814i	−0.140031	−	0.370574i
$713$	27.5564	+	51.5544i	1.03200	+	1.93073i
$714$	−22.0291	−	40.6356i	−0.824417	−	1.52075i
$715$	−3.61034	−	0.904344i	−0.135019	−	0.0338205i
$716$	−32.8780	+	12.2029i	−1.22871	+	0.456045i
$717$	5.00837	−	0.246045i	0.187041	−	0.00918873i
$718$	−10.1946	+	11.3821i	−0.380461	+	0.424777i
$719$	26.3988	+	39.5086i	0.984510	+	1.47342i	0.877738	+	0.479140i	$0.159052\pi$
$719$	26.3988	+	39.5086i	0.984510	+	1.47342i	0.106772	+	0.994284i	$0.465948\pi$
$720$	7.58007	−	2.08976i	0.282492	−	0.0778807i
$721$	−1.08925	+	1.63018i	−0.0405658	+	0.0607111i
$722$	63.3929	−	16.2767i	2.35924	−	0.605756i
$723$	40.0324	+	14.3238i	1.48882	+	0.532708i
$724$	29.3192	−	1.78697i	1.08964	−	0.0664121i
$725$	−7.44117	+	1.10379i	−0.276358	+	0.0409938i
$726$	−12.0078	−	38.7608i	−0.445653	−	1.43855i
$727$	21.8602	−	2.15305i	0.810751	−	0.0798520i	0.315859	−	0.948806i	$-0.397707\pi$
$727$	21.8602	−	2.15305i	0.810751	−	0.0798520i	0.494892	+	0.868954i	$0.335207\pi$
$728$	0.0337253	+	1.90745i	0.00124994	+	0.0706947i
$729$	−10.8181	−	13.1819i	−0.400671	−	0.488219i
$730$	−33.5140	−	6.46127i	−1.24041	−	0.239142i
$731$	10.8022	+	30.1902i	0.399535	+	1.11662i
$732$	−12.1183	−	11.8360i	−0.447907	−	0.437472i
$733$	33.5907	+	20.1335i	1.24070	+	0.743648i	0.975384	−	0.220513i	$-0.0707733\pi$
$733$	33.5907	+	20.1335i	1.24070	+	0.743648i	0.265317	+	0.964161i	$0.414523\pi$
$734$	−9.62104	−	4.48122i	−0.355119	−	0.165405i
$735$	−6.48157	+	2.68475i	−0.239076	+	0.0990286i
$736$	−35.4558	−	30.2813i	−1.30692	−	1.11619i
$737$	−13.9860	−	5.79319i	−0.515181	−	0.213395i
$738$	−4.58126	−	4.99516i	−0.168638	−	0.183874i
$739$	10.6235	−	2.66105i	0.390792	−	0.0978883i	−0.0426036	−	0.999092i	$-0.513565\pi$
$739$	10.6235	−	2.66105i	0.390792	−	0.0978883i	0.433396	+	0.901204i	$0.357315\pi$
$740$	−8.25469	+	5.65746i	−0.303448	+	0.207972i
$741$	1.91166	−	4.04186i	0.0702265	−	0.148481i
$742$	−5.20943	−	25.4062i	−0.191244	−	0.932690i
$743$	−7.26021	−	0.715068i	−0.266351	−	0.0262333i	−0.0360401	−	0.999350i	$-0.511474\pi$
$743$	−7.26021	−	0.715068i	−0.266351	−	0.0262333i	−0.230311	+	0.973117i	$0.573974\pi$
$744$	25.2200	+	29.6460i	0.924609	+	1.08688i
$745$	21.5448	+	17.6814i	0.789341	+	0.647796i
$746$	6.46598	+	0.598391i	0.236736	+	0.0219087i
$747$	1.49072	−	2.01001i	0.0545427	−	0.0735423i
$748$	−62.4815	−	36.4560i	−2.28455	−	1.33296i
$749$	7.64045	+	16.1544i	0.279176	+	0.590268i
$750$	19.1504	−	14.3786i	0.699273	−	0.525032i
$751$	−6.17873	−	31.0626i	−0.225465	−	1.13349i	−0.913195	−	0.407523i	$-0.866393\pi$
$751$	−6.17873	−	31.0626i	−0.225465	−	1.13349i	0.687730	−	0.725966i	$-0.258607\pi$
$752$	−0.475422	−	20.1652i	−0.0173369	−	0.735349i
$753$	3.55181	−	17.8561i	0.129435	−	0.650714i
$754$	−1.70514	+	0.818803i	−0.0620976	+	0.0298190i
$755$	6.79888	−	7.50141i	0.247437	−	0.273004i
$756$	16.6189	+	12.0244i	0.604424	+	0.437324i
$757$	−22.5849	−	37.6806i	−0.820861	−	1.36952i	−0.926957	−	0.375169i	$-0.877585\pi$
$757$	−22.5849	−	37.6806i	−0.820861	−	1.36952i	0.106095	−	0.994356i	$-0.466165\pi$
$758$	−0.387997	+	0.478498i	−0.0140927	+	0.0173798i
$759$	−77.7196	−	23.5760i	−2.82104	−	0.855754i
$760$	−58.5963	+	3.91809i	−2.12551	+	0.142124i
$761$	−38.4412	−	20.5473i	−1.39349	−	0.744837i	−0.407749	−	0.913094i	$-0.633686\pi$
$761$	−38.4412	−	20.5473i	−1.39349	−	0.744837i	−0.985743	+	0.168257i	$0.946186\pi$
$762$	15.0354	+	14.8592i	0.544673	+	0.538291i
$763$	−9.52215	−	0.467793i	−0.344725	−	0.0169352i
$764$	−34.7326	−	18.0419i	−1.25658	−	0.652734i
$765$	2.05437	−	13.8494i	0.0742759	−	0.500727i
$766$	28.3251	−	38.6661i	1.02343	−	1.39706i
$767$	0.203685			0.00735462
$768$	−27.3511	−	14.6879i	−0.986949	−	0.530004i
$769$	9.49388			0.342358			0.171179	−	0.985240i	$-0.445242\pi$
$769$	9.49388			0.342358			0.171179	+	0.985240i	$0.445242\pi$
$770$	25.7932	−	35.2099i	0.929522	−	1.26888i
$771$	2.07231	−	13.9704i	0.0746323	−	0.503130i
$772$	−2.91773	+	5.61694i	−0.105011	+	0.202158i
$773$	22.8988	+	1.12494i	0.823612	+	0.0404614i	0.456509	−	0.889719i	$-0.349100\pi$
$773$	22.8988	+	1.12494i	0.823612	+	0.0404614i	0.367103	+	0.930180i	$0.380350\pi$
$774$	3.46375	+	3.42316i	0.124502	+	0.123043i
$775$	−10.0328	−	5.36263i	−0.360388	−	0.192631i
$776$	−24.7759	−	21.6702i	−0.889402	−	0.777916i
$777$	8.55007	+	2.59364i	0.306732	+	0.0930462i
$778$	−29.5289	+	36.4165i	−1.05866	+	1.30560i
$779$	26.0256	+	43.4212i	0.932466	+	1.55572i
$780$	−1.66726	+	2.30432i	−0.0596976	+	0.0825078i
$781$	25.6845	−	28.3385i	0.919065	−	1.01403i
$782$	−74.8443	+	35.9400i	−2.67643	+	1.28521i
$783$	−3.96787	+	19.9478i	−0.141800	+	0.712877i
$784$	5.24877	+	2.03053i	0.187456	+	0.0725190i
$785$	−2.82040	−	14.1791i	−0.100664	−	0.506074i
$786$	−41.4407	+	31.1147i	−1.47814	+	1.10983i
$787$	20.0872	+	42.4708i	0.716032	+	1.51392i	0.852189	+	0.523235i	$0.175275\pi$
$787$	20.0872	+	42.4708i	0.716032	+	1.51392i	−0.136157	+	0.990687i	$0.543475\pi$
$788$	−15.5171	+	26.5946i	−0.552774	+	0.947393i
$789$	29.7315	−	40.0882i	1.05847	−	1.42718i
$790$	24.9274	+	2.30690i	0.886877	+	0.0820757i
$791$	4.05897	+	3.33111i	0.144320	+	0.118441i
$792$	−10.9511	−	0.883426i	−0.389130	−	0.0313912i
$793$	1.23893	+	0.122024i	0.0439958	+	0.00433320i
$794$	−5.51674	−	26.9049i	−0.195782	−	0.954820i
$795$	16.5317	−	34.9534i	0.586320	−	1.23967i
$796$	−13.8043	−	20.1416i	−0.489281	−	0.713900i
$797$	38.5410	−	9.65401i	1.36519	−	0.341963i	0.509955	−	0.860201i	$-0.329662\pi$
$797$	38.5410	−	9.65401i	1.36519	−	0.341963i	0.855236	+	0.518238i	$0.173412\pi$
$798$	35.4402	+	38.6422i	1.25457	+	1.36792i
$799$	−33.1831	−	13.7449i	−1.17393	−	0.486259i
$800$	9.01098	+	1.06640i	0.318586	+	0.0377031i
$801$	−2.64109	+	1.09398i	−0.0933184	+	0.0386538i
$802$	35.0654	+	16.3326i	1.23820	+	0.576722i
$803$	40.9060	+	24.5181i	1.44354	+	0.865225i
$804$	−8.08323	+	8.27605i	−0.285074	+	0.291874i
$805$	−16.8764	−	47.1663i	−0.594814	−	1.66239i
$806$	−2.80877	−	0.541512i	−0.0989346	−	0.0190739i
$807$	−20.1060	−	24.4992i	−0.707765	−	0.862414i
$808$	−1.11090	+	1.15089i	−0.0390815	+	0.0404883i
$809$	26.1228	−	2.57287i	0.918427	−	0.0904572i	0.372255	−	0.928130i	$-0.378585\pi$
$809$	26.1228	−	2.57287i	0.918427	−	0.0904572i	0.546172	+	0.837673i	$0.316085\pi$
$810$	11.5178	+	37.1788i	0.404693	+	1.30633i
$811$	45.2706	−	6.71526i	1.58967	−	0.235805i	0.707490	−	0.706724i	$-0.249828\pi$
$811$	45.2706	−	6.71526i	1.58967	−	0.235805i	0.882176	+	0.470919i	$0.156078\pi$
$812$	−1.34947	−	22.1411i	−0.0473571	−	0.777000i
$813$	33.9697	+	12.1546i	1.19137	+	0.426279i
$814$	13.5438	−	3.47750i	0.474710	−	0.121886i
$815$	4.19787	−	6.28256i	0.147045	−	0.220069i
$816$	−43.6136	+	33.9683i	−1.52678	+	1.18913i
$817$	−20.2076	−	30.2428i	−0.706974	−	1.05806i
$818$	7.60538	−	8.49127i	0.265916	−	0.296890i
$819$	0.515309	−	0.0253155i	0.0180063	−	0.000884595i
$820$	−11.2055	−	30.1907i	−0.391313	−	1.05431i
$821$	−21.9671	−	5.50248i	−0.766658	−	0.192038i	−0.160126	−	0.987097i	$-0.551190\pi$
$821$	−21.9671	−	5.50248i	−0.766658	−	0.192038i	−0.606533	+	0.795059i	$0.707440\pi$
$822$	6.69600	+	12.3517i	0.233550	+	0.430815i
$823$	−1.03743	−	1.94089i	−0.0361625	−	0.0676553i	0.863191	−	0.504877i	$-0.168462\pi$
$823$	−1.03743	−	1.94089i	−0.0361625	−	0.0676553i	−0.899354	+	0.437222i	$0.855962\pi$
$824$	2.13709	+	0.964913i	0.0744490	+	0.0336143i
$825$	15.1247	−	4.58802i	0.526573	−	0.159734i
$826$	−0.901061	+	2.21214i	−0.0313519	+	0.0769701i
$827$	4.61417	+	5.09095i	0.160450	+	0.177030i	0.815870	−	0.578235i	$-0.196258\pi$
$827$	4.61417	+	5.09095i	0.160450	+	0.177030i	−0.655420	+	0.755265i	$0.727508\pi$
$828$	−7.88412	+	9.84109i	−0.273992	+	0.342002i
$829$	6.30685	+	8.50381i	0.219046	+	0.295349i	0.899038	−	0.437870i	$-0.144267\pi$
$829$	6.30685	+	8.50381i	0.219046	+	0.295349i	−0.679992	+	0.733219i	$0.738017\pi$
$830$	10.1620	−	6.17257i	0.352729	−	0.214253i
$831$	17.6441	+	17.6441i	0.612068	+	0.612068i
$832$	2.24367	−	0.414356i	0.0777853	−	0.0143652i
$833$	7.08606	−	7.08606i	0.245517	−	0.245517i
$834$	−5.40907	+	22.1471i	−0.187301	+	0.766892i
$835$	−44.8555	+	33.2671i	−1.55229	+	1.15126i
$836$	78.8006	+	22.8932i	2.72537	+	0.791779i
$837$	−22.7895	+	20.6552i	−0.787720	+	0.713948i
$838$	19.4612	−	8.19580i	0.672277	−	0.283119i
$839$	−10.2430	−	33.7666i	−0.353628	−	1.16575i	−0.935753	−	0.352655i	$-0.885279\pi$
$839$	−10.2430	−	33.7666i	−0.353628	−	1.16575i	0.582126	−	0.813099i	$-0.302221\pi$
$840$	−17.6506	−	28.3013i	−0.609004	−	0.976489i
$841$	−6.17890	+	3.30269i	−0.213066	+	0.113886i
$842$	17.0933	+	5.07539i	0.589074	+	0.174910i
$843$	10.8066	−	43.1422i	0.372198	−	1.48590i
$844$	−1.32382	+	35.4733i	−0.0455676	+	1.22104i
$845$	1.62899	+	33.1588i	0.0560389	+	1.14070i
$846$	−5.44674	+	0.299766i	−0.187263	+	0.0103062i
$847$	−29.0784	+	19.4295i	−0.999145	+	0.667607i
$848$	−28.9497	+	11.1348i	−0.994137	+	0.382372i
$849$	−8.69294	−	5.80843i	−0.298341	−	0.199345i
$850$	8.22473	−	13.9073i	0.282106	−	0.477018i
$851$	5.40671	−	15.1107i	0.185340	−	0.517990i
$852$	−12.8068	−	26.2721i	−0.438755	−	0.900068i
$853$	3.71715	+	25.0590i	0.127273	+	0.858003i	0.954943	+	0.296788i	$0.0959156\pi$
$853$	3.71715	+	25.0590i	0.127273	+	0.858003i	−0.827671	+	0.561214i	$0.810334\pi$
$854$	−6.80605	+	12.9157i	−0.232898	+	0.441967i
$855$	1.55672	+	15.8057i	0.0532387	+	0.540542i
$856$	17.5576	−	12.1860i	0.600106	−	0.416509i
$857$	−19.8964	+	16.3286i	−0.679648	+	0.557773i	−0.909629	−	0.415422i	$-0.863634\pi$
$857$	−19.8964	+	16.3286i	−0.679648	+	0.557773i	0.229980	+	0.973195i	$0.426134\pi$
$858$	3.29136	−	2.22739i	0.112365	−	0.0760417i
$859$	52.2641	−	18.7004i	1.78323	−	0.638049i	0.783365	−	0.621563i	$-0.213502\pi$
$859$	52.2641	−	18.7004i	1.78323	−	0.638049i	0.999864	−	0.0164869i	$-0.00524817\pi$
$860$	9.10578	+	21.2707i	0.310504	+	0.725325i
$861$	−14.7814	+	24.6612i	−0.503748	+	0.840453i
$862$	−9.91082	−	27.1926i	−0.337564	−	0.926184i
$863$	4.58715	+	11.0744i	0.156148	+	0.376975i	0.982522	−	0.186147i	$-0.0596000\pi$
$863$	4.58715	+	11.0744i	0.156148	+	0.376975i	−0.826374	+	0.563122i	$0.809600\pi$
$864$	10.9222	−	21.9673i	0.371582	−	0.747341i
$865$	5.75115	−	13.8845i	0.195545	−	0.472088i
$866$	−39.8377	−	1.72184i	−1.35374	−	0.0585104i
$867$	15.9031	+	63.4888i	0.540098	+	2.15619i
$868$	18.3066	−	28.1094i	0.621366	−	0.954094i
$869$	−31.6212	−	14.9557i	−1.07268	−	0.507338i
$870$	18.2109	−	27.6054i	0.617409	−	0.935910i
$871$	0.0833346	−	0.846111i	0.00282369	−	0.0286694i
$872$	1.31801	+	11.3255i	0.0446333	+	0.383531i
$873$	−5.64718	+	6.88111i	−0.191128	+	0.232890i
$874$	72.4499	−	60.1761i	2.45066	−	2.03549i
$875$	−16.5775	−	12.2947i	−0.560421	−	0.415637i
$876$	29.0150	−	22.0538i	0.980328	−	0.745129i
$877$	1.81899	−	0.860321i	0.0614231	−	0.0290510i	−0.396597	−	0.917993i	$-0.629809\pi$
$877$	1.81899	−	0.860321i	0.0614231	−	0.0290510i	0.458020	+	0.888942i	$0.348559\pi$
$878$	12.5263	+	1.78272i	0.422742	+	0.0601640i
$879$	−18.1127	+	3.60285i	−0.610927	+	0.121521i
$880$	−46.6035	−	23.5150i	−1.57101	−	0.792692i
$881$	29.3352	+	5.83513i	0.988328	+	0.196591i	0.662682	−	0.748901i	$-0.269418\pi$
$881$	29.3352	+	5.83513i	0.988328	+	0.196591i	0.325646	+	0.945492i	$0.394418\pi$
$882$	0.504290	−	1.43602i	0.0169803	−	0.0483532i
$883$	5.54500	+	5.02569i	0.186604	+	0.169128i	0.759515	−	0.650489i	$-0.225436\pi$
$883$	5.54500	+	5.02569i	0.186604	+	0.169128i	−0.572911	+	0.819617i	$0.694186\pi$
$884$	0.940651	−	3.95235i	0.0316375	−	0.132932i
$885$	−3.05449	+	1.83079i	−0.102676	+	0.0615414i
$886$	28.3392	−	2.95989i	0.952074	−	0.0994395i
$887$	−16.6994	+	55.0505i	−0.560710	+	1.84841i	−0.0322107	+	0.999481i	$0.510255\pi$
$887$	−16.6994	+	55.0505i	−0.560710	+	1.84841i	−0.528500	+	0.848933i	$0.677245\pi$
$888$	1.38082	−	10.5962i	0.0463374	−	0.355585i
$889$	8.58820	−	16.0674i	0.288039	−	0.538883i
$890$	−13.5821	+	0.0800401i	−0.455272	+	0.00268295i
$891$	2.66856	−	54.3198i	0.0894001	−	1.81978i
$892$	3.33509	+	3.96753i	0.111667	+	0.132843i
$893$	40.3019	+	5.97822i	1.34865	+	0.200053i
$894$	−29.4125	+	4.54023i	−0.983701	+	0.151848i
$895$			45.0615i			1.50624i
$896$	−5.42541	+	26.2006i	−0.181250	+	0.875302i
$897$		−	4.56133i		−	0.152298i
$898$	−4.31031	−	27.9230i	−0.143837	−	0.931803i
$899$	32.9002	+	4.88028i	1.09728	+	0.162766i
$900$	0.211728	−	2.44478i	0.00705761	−	0.0814926i
$901$	−2.71005	+	55.1643i	−0.0902848	+	1.83779i
$902$	0.265166	+	44.9963i	0.00882908	+	1.49821i
$903$	9.73812	−	18.2188i	0.324065	−	0.606282i
$904$	3.13278	−	5.44267i	0.104195	−	0.181020i
$905$	10.9561	−	36.1174i	0.364193	−	1.20058i
$906$	1.12298	+	10.7519i	0.0373086	+	0.357208i
$907$	−21.5427	+	12.9122i	−0.715313	+	0.428742i	−0.824932	−	0.565231i	$-0.808787\pi$
$907$	−21.5427	+	12.9122i	−0.715313	+	0.428742i	0.109619	+	0.993974i	$0.465037\pi$
$908$	8.30261	+	13.4890i	0.275532	+	0.447647i
$909$	0.320529	+	0.290510i	0.0106313	+	0.00963561i
$910$	2.31283	+	0.812201i	0.0766695	+	0.0269242i
$911$	−30.3665	−	6.04028i	−1.00609	−	0.200123i	−0.335569	−	0.942016i	$-0.608929\pi$
$911$	−30.3665	−	6.04028i	−1.00609	−	0.200123i	−0.670519	+	0.741892i	$0.733929\pi$
$912$	38.6283	−	49.3985i	1.27911	−	1.63575i
$913$	−16.2942	+	3.24113i	−0.539261	+	0.107266i
$914$	−1.24734	+	8.76440i	−0.0412582	+	0.289901i
$915$	−19.6761	+	9.30608i	−0.650470	+	0.307650i
$916$	−18.6288	−	2.53931i	−0.615512	−	0.0839012i
$917$	35.8730	+	26.6053i	1.18463	+	0.878583i
$918$	−27.9115	−	33.6044i	−0.921216	−	1.10911i
$919$	−2.09318	+	2.55055i	−0.0690478	+	0.0841350i	−0.806389	−	0.591386i	$-0.798581\pi$
$919$	−2.09318	+	2.55055i	−0.0690478	+	0.0841350i	0.737341	+	0.675521i	$0.236081\pi$
$920$	−52.3299	+	29.1719i	−1.72527	+	0.961768i
$921$	2.20741	−	22.4122i	0.0727366	−	0.738508i
$922$	−14.1839	−	9.35694i	−0.467122	−	0.308154i
$923$	1.94177	+	0.918387i	0.0639140	+	0.0302291i
$924$	9.63039	+	45.5997i	0.316817	+	1.50012i
$925$	0.758877	+	3.02960i	0.0249517	+	0.0996128i
$926$	1.27098	−	29.4064i	0.0417670	−	0.966353i
$927$	0.242672	−	0.585863i	0.00797040	−	0.0192423i
$928$	−25.8557	+	5.93991i	−0.848756	+	0.194987i
$929$	13.6999	+	33.0745i	0.449479	+	1.08514i	0.972518	+	0.232829i	$0.0747982\pi$
$929$	13.6999	+	33.0745i	0.449479	+	1.08514i	−0.523039	+	0.852309i	$0.675202\pi$
$930$	46.9881	−	17.1256i	1.54080	−	0.561572i
$931$	−5.84414	+	9.75035i	−0.191534	+	0.319555i
$932$	−1.58616	+	3.96073i	−0.0519565	+	0.129738i
$933$	−37.2862	+	13.3412i	−1.22069	+	0.436771i
$934$	5.48453	+	8.10438i	0.179459	+	0.265183i
$935$	−71.8513	+	58.9668i	−2.34979	+	1.92842i
$936$	−0.131058	−	0.602959i	−0.00428376	−	0.0197083i
$937$	−1.19353	−	12.1181i	−0.0389909	−	0.395881i	−0.994797	−	0.101882i	$-0.967514\pi$
$937$	−1.19353	−	12.1181i	−0.0389909	−	0.395881i	0.955806	−	0.293999i	$-0.0949863\pi$
$938$	8.82061	+	4.64810i	0.288003	+	0.151766i
$939$	5.92943	+	39.9730i	0.193500	+	1.30447i
$940$	−24.5040	−	8.44323i	−0.799231	−	0.275388i
$941$	5.60898	−	15.6760i	0.182848	−	0.511025i	−0.814787	−	0.579760i	$-0.803146\pi$
$941$	5.60898	−	15.6760i	0.182848	−	0.511025i	0.997635	+	0.0687353i	$0.0218964\pi$
$942$	13.2873	+	7.85804i	0.432923	+	0.256029i
$943$	42.9409	+	28.6922i	1.39835	+	0.934347i
$944$	2.78669	+	0.628617i	0.0906990	+	0.0204597i
$945$	21.9153	−	14.6433i	0.712903	−	0.476347i
$946$	−1.77663	−	32.2813i	−0.0577632	−	1.04956i
$947$	−2.32908	−	47.4094i	−0.0756848	−	1.54060i	−0.673634	−	0.739065i	$-0.735268\pi$
$947$	−2.32908	−	47.4094i	−0.0756848	−	1.54060i	0.597949	−	0.801534i	$-0.295982\pi$
$948$	−19.5935	+	18.1837i	−0.636367	+	0.590579i
$949$	−0.650809	+	2.59817i	−0.0211262	+	0.0843403i
$950$	−5.21696	+	17.5701i	−0.169260	+	0.570048i
$951$	−12.8206	+	6.85277i	−0.415738	+	0.222216i
$952$	38.7637	+	27.7005i	1.25634	+	0.897778i
$953$	−3.74279	−	12.3383i	−0.121241	−	0.399678i	0.875221	−	0.483723i	$-0.160716\pi$
$953$	−3.74279	−	12.3383i	−0.121241	−	0.399678i	−0.996462	+	0.0840456i	$0.973216\pi$
$954$	3.25567	+	7.73072i	0.105406	+	0.250291i
$955$	−37.2628	+	33.7730i	−1.20579	+	1.09287i
$956$	−4.52925	+	2.49001i	−0.146487	+	0.0805326i
$957$	−37.1161	+	27.5271i	−1.19979	+	0.889826i
$958$	15.6949	+	3.83322i	0.507080	+	0.123846i
$959$	8.56230	−	8.56230i	0.276491	−	0.276491i
$960$	−29.9221	+	26.3807i	−0.965733	+	0.851434i
$961$	13.6455	+	13.6455i	0.440178	+	0.440178i
$962$	0.407701	+	0.671206i	0.0131448	+	0.0216405i
$963$	−3.44306	−	4.64243i	−0.110951	−	0.149600i
$964$	−43.5604	+	4.80933i	−1.40299	+	0.154898i
$965$	5.46175	+	6.02611i	0.175820	+	0.193987i
$966$	49.5388	+	20.1785i	1.59388	+	0.649231i
$967$	16.7042	−	5.06716i	0.537170	−	0.162949i	−0.0100313	−	0.999950i	$-0.503193\pi$
$967$	16.7042	−	5.06716i	0.537170	−	0.162949i	0.547202	+	0.837001i	$0.315693\pi$
$968$	28.6320	+	30.4895i	0.920267	+	0.979970i
$969$	−52.6370	−	98.4769i	−1.69094	−	3.16353i
$970$	−37.1818	+	20.1567i	−1.19383	+	0.647192i
$971$	−36.7506	−	9.20556i	−1.17938	−	0.295420i	−0.396764	−	0.917920i	$-0.629867\pi$
$971$	−36.7506	−	9.20556i	−1.17938	−	0.295420i	−0.782620	+	0.622500i	$0.786117\pi$
$972$	−14.1252	−	6.47811i	−0.453065	−	0.207785i
$973$	19.6249	−	0.964107i	0.629144	−	0.0309079i
$974$	−2.94088	−	2.63406i	−0.0942320	−	0.0844008i
$975$	0.493157	+	0.738062i	0.0157937	+	0.0236369i
$976$	16.5737	+	5.49309i	0.530512	+	0.175829i
$977$	−10.5750	+	15.8266i	−0.338325	+	0.506339i	−0.961152	−	0.276021i	$-0.910984\pi$
$977$	−10.5750	+	15.8266i	−0.338325	+	0.506339i	0.622827	+	0.782360i	$0.285984\pi$
$978$	2.00651	+	7.81475i	0.0641610	+	0.249888i
$979$	17.8690	+	6.39362i	0.571095	+	0.204341i
$980$	4.79276	−	5.41491i	0.153099	−	0.172973i
$981$	3.05016	−	0.452449i	0.0973843	−	0.0144456i
$982$	20.1294	−	6.23596i	0.642356	−	0.198998i
$983$	15.3770	−	1.51451i	0.490451	−	0.0483053i	0.150231	−	0.988651i	$-0.451998\pi$
$983$	15.3770	−	1.51451i	0.490451	−	0.0483053i	0.340221	+	0.940346i	$0.389498\pi$
$984$	31.9965	+	12.5954i	1.02001	+	0.401527i
$985$	25.0986	+	30.5828i	0.799709	+	0.974448i
$986$	−8.94274	+	46.3851i	−0.284795	+	1.47720i
$987$	7.79566	+	21.7874i	0.248138	+	0.693500i
$988$	0.0543159	+	4.60829i	0.00172802	+	0.146609i
$989$	−31.8272	−	19.0765i	−1.01205	−	0.606598i
$990$	−5.96047	+	12.7969i	−0.189436	+	0.406713i
$991$	−17.0905	+	7.07911i	−0.542897	+	0.224875i	−0.637241	−	0.770664i	$-0.719925\pi$
$991$	−17.0905	+	7.07911i	−0.542897	+	0.224875i	0.0943441	+	0.995540i	$0.469925\pi$
$992$	−36.7567	−	16.0771i	−1.16702	−	0.510450i
$993$	−7.60069	−	3.14831i	−0.241201	−	0.0999085i
$994$	−18.5642	+	17.0260i	−0.588822	+	0.540031i
$995$	−30.4349	+	7.62356i	−0.964852	+	0.241683i
$996$	−2.32991	+	12.4802i	−0.0738261	+	0.395451i
$997$	−3.88444	+	8.21296i	−0.123022	+	0.260107i	−0.956096	−	0.293054i	$-0.905329\pi$
$997$	−3.88444	+	8.21296i	−0.123022	+	0.260107i	0.833074	+	0.553161i	$0.186579\pi$
$998$	8.62539	−	1.76860i	0.273032	−	0.0559840i
$999$	8.40346	+	0.827668i	0.265874	+	0.0261863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.7	✓	992
256.205	even	64	inner	256.2.m.a.205.7	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.7	✓	992	1.1	even	1	trivial
256.2.m.a.205.7	yes	992	256.205	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14085 - 0.835738i) q^{2} +(0.284707 - 1.91934i) q^{3} +(0.603086 + 1.90691i) q^{4} +(2.56674 + 0.126096i) q^{5} +(-1.92887 + 1.95174i) q^{6} +(2.08571 + 1.11483i) q^{7} +(0.905641 - 2.67952i) q^{8} +(-0.731981 - 0.222044i) q^{9} +O(q^{10})\)	\(q+(-1.14085 - 0.835738i) q^{2} +(0.284707 - 1.91934i) q^{3} +(0.603086 + 1.90691i) q^{4} +(2.56674 + 0.126096i) q^{5} +(-1.92887 + 1.95174i) q^{6} +(2.08571 + 1.11483i) q^{7} +(0.905641 - 2.67952i) q^{8} +(-0.731981 - 0.222044i) q^{9} +(-2.82289 - 2.28898i) q^{10} +(2.61069 + 4.35568i) q^{11} +(3.83170 - 0.614616i) q^{12} +(-0.191530 + 0.211320i) q^{13} +(-1.44778 - 3.01497i) q^{14} +(0.972789 - 4.89054i) q^{15} +(-3.27258 + 2.30005i) q^{16} +(1.38955 + 6.98573i) q^{17} +(0.649512 + 0.865064i) q^{18} +(-3.45446 - 7.30385i) q^{19} +(1.30751 + 4.97057i) q^{20} +(2.73356 - 3.68578i) q^{21} +(0.661790 - 7.15104i) q^{22} +(-6.37159 - 5.22902i) q^{23} +(-4.88506 - 2.50111i) q^{24} +(1.59632 + 0.157224i) q^{25} +(0.395115 - 0.0810167i) q^{26} +(1.85423 - 3.92044i) q^{27} +(-0.868023 + 4.64959i) q^{28} +(-4.54921 + 1.13952i) q^{29} +(-5.19702 + 4.76638i) q^{30} +(-6.55223 - 2.71402i) q^{31} +(5.65577 + 0.110994i) q^{32} +(9.10331 - 3.77071i) q^{33} +(4.25297 - 9.13098i) q^{34} +(5.21289 + 3.12449i) q^{35} +(-0.0180303 - 1.52973i) q^{36} +(0.655951 + 1.83326i) q^{37} +(-2.16307 + 11.2196i) q^{38} +(0.351065 + 0.427774i) q^{39} +(2.66242 - 6.76342i) q^{40} +(-6.23544 + 0.614137i) q^{41} +(-6.19893 + 1.92039i) q^{42} +(4.45308 - 0.660553i) q^{43} +(-6.73140 + 7.60519i) q^{44} +(-1.85081 - 0.662229i) q^{45} +(2.89894 + 11.2905i) q^{46} +(-2.80157 + 4.19285i) q^{47} +(3.48286 + 6.93602i) q^{48} +(-0.781665 - 1.16984i) q^{49} +(-1.68977 - 1.51348i) q^{50} +(13.8036 - 0.678127i) q^{51} +(-0.518477 - 0.237785i) q^{52} +(7.52193 + 1.88414i) q^{53} +(-5.39186 + 2.92299i) q^{54} +(6.15174 + 11.5091i) q^{55} +(4.87612 - 4.57905i) q^{56} +(-15.0021 + 4.55083i) q^{57} +(6.14231 + 2.50192i) q^{58} +(-0.479613 - 0.529171i) q^{59} +(9.91247 - 1.09440i) q^{60} +(-2.60027 - 3.50606i) q^{61} +(5.20692 + 8.57225i) q^{62} +(-1.27916 - 1.27916i) q^{63} +(-6.35963 - 4.85336i) q^{64} +(-0.518253 + 0.518253i) q^{65} +(-13.5369 - 3.30615i) q^{66} +(-2.39442 + 1.77582i) q^{67} +(-12.4831 + 6.86273i) q^{68} +(-11.8503 + 10.7405i) q^{69} +(-3.33589 - 7.92119i) q^{70} +(-2.18628 - 7.20720i) q^{71} +(-1.25788 + 1.76026i) q^{72} +(8.28249 - 4.42708i) q^{73} +(0.783781 - 2.63968i) q^{74} +(0.756251 - 3.01912i) q^{75} +(11.8444 - 10.9922i) q^{76} +(0.589285 + 11.9952i) q^{77} +(-0.0430064 - 0.781426i) q^{78} +(-5.72737 + 3.82691i) q^{79} +(-8.68987 + 5.49098i) q^{80} +(-8.90475 - 5.94997i) q^{81} +(7.62697 + 4.51055i) q^{82} +(-1.10215 + 3.08031i) q^{83} +(8.67701 + 2.98980i) q^{84} +(2.68574 + 18.1058i) q^{85} +(-5.63236 - 2.96802i) q^{86} +(0.891929 + 9.05590i) q^{87} +(14.0355 - 3.05072i) q^{88} +(2.88894 - 2.37089i) q^{89} +(1.55805 + 2.30229i) q^{90} +(-0.635062 + 0.227229i) q^{91} +(6.12864 - 15.3036i) q^{92} +(-7.07460 + 11.8033i) q^{93} +(6.70030 - 2.44204i) q^{94} +(-7.94572 - 19.1827i) q^{95} +(1.82327 - 10.8237i) q^{96} +(4.45346 - 10.7516i) q^{97} +(-0.0859190 + 1.98789i) q^{98} +(-0.943826 - 3.76797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more