LMFDB - Embedded newform 64.2.i.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

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("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	64.61
Dual form			64.2.i.a.21.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0941531 + 1.41108i) q^{2} +(0.553854 - 2.78441i) q^{3} +(-1.98227 + 0.265714i) q^{4} +(2.59756 + 1.73564i) q^{5} +(3.98116 + 0.519369i) q^{6} +(-1.96508 + 0.813965i) q^{7} +(-0.561580 - 2.77212i) q^{8} +(-4.67456 - 1.93627i) q^{9} +O(q^{10})$	\(q+(0.0941531 + 1.41108i) q^{2} +(0.553854 - 2.78441i) q^{3} +(-1.98227 + 0.265714i) q^{4} +(2.59756 + 1.73564i) q^{5} +(3.98116 + 0.519369i) q^{6} +(-1.96508 + 0.813965i) q^{7} +(-0.561580 - 2.77212i) q^{8} +(-4.67456 - 1.93627i) q^{9} +(-2.20455 + 3.82878i) q^{10} +(-2.02382 + 0.402563i) q^{11} +(-0.358030 + 5.66663i) q^{12} +(-1.99644 + 1.33398i) q^{13} +(-1.33358 - 2.69625i) q^{14} +(6.27140 - 6.27140i) q^{15} +(3.85879 - 1.05344i) q^{16} +(-2.31120 - 2.31120i) q^{17} +(2.29209 - 6.77846i) q^{18} +(2.37703 + 3.55748i) q^{19} +(-5.61026 - 2.75029i) q^{20} +(1.17804 + 5.92242i) q^{21} +(-0.758596 - 2.81786i) q^{22} +(0.993213 - 2.39783i) q^{23} +(-8.02975 + 0.0283233i) q^{24} +(1.82149 + 4.39746i) q^{25} +(-2.07032 - 2.69153i) q^{26} +(-3.24866 + 4.86196i) q^{27} +(3.67905 - 2.13565i) q^{28} +(2.34079 + 0.465613i) q^{29} +(9.43989 + 8.25895i) q^{30} +1.81094i q^{31} +(1.84980 + 5.34586i) q^{32} +5.85811i q^{33} +(3.04367 - 3.47888i) q^{34} +(-6.51718 - 1.29635i) q^{35} +(9.78074 + 2.59610i) q^{36} +(1.40742 - 2.10635i) q^{37} +(-4.79607 + 3.68912i) q^{38} +(2.60861 + 6.29775i) q^{39} +(3.35265 - 8.17545i) q^{40} +(4.66056 - 11.2516i) q^{41} +(-8.24607 + 2.21992i) q^{42} +(0.452227 + 2.27350i) q^{43} +(3.90479 - 1.33575i) q^{44} +(-8.78181 - 13.1429i) q^{45} +(3.47703 + 1.17574i) q^{46} +(-2.27298 - 2.27298i) q^{47} +(-0.795992 - 11.3279i) q^{48} +(-1.75073 + 1.75073i) q^{49} +(-6.03365 + 2.98429i) q^{50} +(-7.71539 + 5.15526i) q^{51} +(3.60303 - 3.17479i) q^{52} +(7.98970 - 1.58925i) q^{53} +(-7.16647 - 4.12634i) q^{54} +(-5.95570 - 2.46693i) q^{55} +(3.35996 + 4.99034i) q^{56} +(11.2220 - 4.64831i) q^{57} +(-0.436622 + 3.34687i) q^{58} +(7.08029 + 4.73090i) q^{59} +(-10.7652 + 14.0980i) q^{60} +(-1.95998 + 9.85346i) q^{61} +(-2.55537 + 0.170505i) q^{62} +10.7620 q^{63} +(-7.36926 + 3.11353i) q^{64} -7.50119 q^{65} +(-8.26624 + 0.551559i) q^{66} +(2.88943 - 14.5262i) q^{67} +(5.19553 + 3.96730i) q^{68} +(-6.12645 - 4.09356i) q^{69} +(1.21563 - 9.31829i) q^{70} +(-6.41451 + 2.65698i) q^{71} +(-2.74241 + 14.0458i) q^{72} +(-3.36337 - 1.39315i) q^{73} +(3.10474 + 1.78766i) q^{74} +(13.2532 - 2.63622i) q^{75} +(-5.65719 - 6.42027i) q^{76} +(3.64930 - 2.43839i) q^{77} +(-8.64099 + 4.27390i) q^{78} +(-10.9490 + 10.9490i) q^{79} +(11.8518 + 3.96109i) q^{80} +(1.00516 + 1.00516i) q^{81} +(16.3157 + 5.51703i) q^{82} +(-3.72793 - 5.57925i) q^{83} +(-3.90887 - 11.4268i) q^{84} +(-1.99208 - 10.0149i) q^{85} +(-3.16550 + 0.852183i) q^{86} +(2.59292 - 6.25985i) q^{87} +(2.25249 + 5.38419i) q^{88} +(-3.10595 - 7.49842i) q^{89} +(17.7188 - 13.6293i) q^{90} +(2.83736 - 4.24642i) q^{91} +(-1.33168 + 5.01705i) q^{92} +(5.04240 + 1.00299i) q^{93} +(2.99334 - 3.42136i) q^{94} +13.3664i q^{95} +(15.9096 - 2.18976i) q^{96} +8.49286i q^{97} +(-2.63525 - 2.30558i) q^{98} +(10.2399 + 2.03685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

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 $

$2$	0.0941531	+	1.41108i	0.0665763	+	0.997781i
$2$	0.0941531	+	1.41108i	0.0665763	+	0.997781i
$3$	0.553854	−	2.78441i	0.319768	−	1.60758i	−0.402131	−	0.915582i	$-0.631730\pi$
$3$	0.553854	−	2.78441i	0.319768	−	1.60758i	0.721898	−	0.691999i	$-0.243270\pi$
$4$	−1.98227	+	0.265714i	−0.991135	+	0.132857i
$5$	2.59756	+	1.73564i	1.16167	+	0.776200i	0.978371	−	0.206858i	$-0.0663237\pi$
$5$	2.59756	+	1.73564i	1.16167	+	0.776200i	0.183295	+	0.983058i	$0.441324\pi$
$6$	3.98116	+	0.519369i	1.62530	+	0.212031i
$7$	−1.96508	+	0.813965i	−0.742732	+	0.307650i	−0.721772	−	0.692131i	$-0.756672\pi$
$7$	−1.96508	+	0.813965i	−0.742732	+	0.307650i	−0.0209598	+	0.999780i	$0.506672\pi$
$8$	−0.561580	−	2.77212i	−0.198549	−	0.980091i
$9$	−4.67456	−	1.93627i	−1.55819	−	0.645422i
$10$	−2.20455	+	3.82878i	−0.697139	+	1.21077i
$11$	−2.02382	+	0.402563i	−0.610205	+	0.121377i	−0.490513	−	0.871434i	$-0.663191\pi$
$11$	−2.02382	+	0.402563i	−0.610205	+	0.121377i	−0.119692	+	0.992811i	$0.538191\pi$
$12$	−0.358030	+	5.66663i	−0.103354	+	1.63581i
$13$	−1.99644	+	1.33398i	−0.553713	+	0.369979i	−0.800724	−	0.599033i	$-0.795552\pi$
$13$	−1.99644	+	1.33398i	−0.553713	+	0.369979i	0.247011	+	0.969013i	$0.420552\pi$
$14$	−1.33358	−	2.69625i	−0.356415	−	0.720602i
$15$	6.27140	−	6.27140i	1.61927	−	1.61927i
$16$	3.85879	−	1.05344i	0.964698	−	0.263359i
$17$	−2.31120	−	2.31120i	−0.560547	−	0.560547i	0.368916	−	0.929463i	$-0.379729\pi$
$17$	−2.31120	−	2.31120i	−0.560547	−	0.560547i	−0.929463	+	0.368916i	$0.879729\pi$
$18$	2.29209	−	6.77846i	0.540252	−	1.59770i
$19$	2.37703	+	3.55748i	0.545328	+	0.816142i	0.997109	−	0.0759875i	$-0.0242109\pi$
$19$	2.37703	+	3.55748i	0.545328	+	0.816142i	−0.451780	+	0.892129i	$0.649211\pi$
$20$	−5.61026	−	2.75029i	−1.25449	−	0.614984i
$21$	1.17804	+	5.92242i	0.257070	+	1.29238i
$22$	−0.758596	−	2.81786i	−0.161733	−	0.600770i
$23$	0.993213	−	2.39783i	0.207099	−	0.499982i	−0.785865	−	0.618398i	$-0.787782\pi$
$23$	0.993213	−	2.39783i	0.207099	−	0.499982i	0.992964	+	0.118417i	$0.0377819\pi$
$24$	−8.02975	+	0.0283233i	−1.63907	+	0.00578146i
$25$	1.82149	+	4.39746i	0.364297	+	0.879491i
$26$	−2.07032	−	2.69153i	−0.406023	−	0.527853i
$27$	−3.24866	+	4.86196i	−0.625205	+	0.935685i
$28$	3.67905	−	2.13565i	0.695274	−	0.403600i
$29$	2.34079	+	0.465613i	0.434674	+	0.0864621i	0.407577	−	0.913171i	$-0.366374\pi$
$29$	2.34079	+	0.465613i	0.434674	+	0.0864621i	0.0270970	+	0.999633i	$0.491374\pi$
$30$	9.43989	+	8.25895i	1.72348	+	1.50787i
$31$			1.81094i			0.325254i	0.986688	+	0.162627i	$0.0519967\pi$
$31$			1.81094i			0.325254i	−0.986688	+	0.162627i	$0.948003\pi$
$32$	1.84980	+	5.34586i	0.327001	+	0.945024i
$33$			5.85811i			1.01977i
$34$	3.04367	−	3.47888i	0.521985	−	0.596623i
$35$	−6.51718	−	1.29635i	−1.10160	−	0.219123i
$36$	9.78074	+	2.59610i	1.63012	+	0.432684i
$37$	1.40742	−	2.10635i	0.231378	−	0.346282i	−0.697554	−	0.716533i	$-0.745728\pi$
$37$	1.40742	−	2.10635i	0.231378	−	0.346282i	0.928932	+	0.370250i	$0.120728\pi$
$38$	−4.79607	+	3.68912i	−0.778025	+	0.598454i
$39$	2.60861	+	6.29775i	0.417712	+	1.00845i
$40$	3.35265	−	8.17545i	0.530100	−	1.29265i
$41$	4.66056	−	11.2516i	0.727858	−	1.75720i	0.0782501	−	0.996934i	$-0.475067\pi$
$41$	4.66056	−	11.2516i	0.727858	−	1.75720i	0.649607	−	0.760270i	$-0.274933\pi$
$42$	−8.24607	+	2.21992i	−1.27240	+	0.342542i
$43$	0.452227	+	2.27350i	0.0689639	+	0.346705i	0.999826	−	0.0186663i	$-0.00594202\pi$
$43$	0.452227	+	2.27350i	0.0689639	+	0.346705i	−0.930862	+	0.365371i	$0.880942\pi$
$44$	3.90479	−	1.33575i	0.588669	−	0.201371i
$45$	−8.78181	−	13.1429i	−1.30912	−	1.95923i
$46$	3.47703	+	1.17574i	0.512660	+	0.173353i
$47$	−2.27298	−	2.27298i	−0.331549	−	0.331549i	0.521626	−	0.853174i	$-0.325326\pi$
$47$	−2.27298	−	2.27298i	−0.331549	−	0.331549i	−0.853174	+	0.521626i	$0.825326\pi$
$48$	−0.795992	−	11.3279i	−0.114892	−	1.63504i
$49$	−1.75073	+	1.75073i	−0.250104	+	0.250104i
$50$	−6.03365	+	2.98429i	−0.853287	+	0.422042i
$51$	−7.71539	+	5.15526i	−1.08037	+	0.721881i
$52$	3.60303	−	3.17479i	0.499650	−	0.440264i
$53$	7.98970	−	1.58925i	1.09747	−	0.218300i	0.387036	−	0.922065i	$-0.373499\pi$
$53$	7.98970	−	1.58925i	1.09747	−	0.218300i	0.710433	+	0.703764i	$0.248499\pi$
$54$	−7.16647	−	4.12634i	−0.975233	−	0.561523i
$55$	−5.95570	−	2.46693i	−0.803067	−	0.332641i
$56$	3.35996	+	4.99034i	0.448993	+	0.666862i
$57$	11.2220	−	4.64831i	1.48639	−	0.615684i
$58$	−0.436622	+	3.34687i	−0.0573312	+	0.439466i
$59$	7.08029	+	4.73090i	0.921775	+	0.615911i	0.923296	−	0.384088i	$-0.125484\pi$
$59$	7.08029	+	4.73090i	0.921775	+	0.615911i	−0.00152111	+	0.999999i	$0.500484\pi$
$60$	−10.7652	+	14.0980i	−1.38978	+	1.82005i
$61$	−1.95998	+	9.85346i	−0.250949	+	1.26161i	0.625543	+	0.780190i	$0.284878\pi$
$61$	−1.95998	+	9.85346i	−0.250949	+	1.26161i	−0.876492	+	0.481417i	$0.840122\pi$
$62$	−2.55537	+	0.170505i	−0.324532	+	0.0216542i
$63$	10.7620			1.35588
$64$	−7.36926	+	3.11353i	−0.921157	+	0.389191i
$65$	−7.50119			−0.930408
$66$	−8.26624	+	0.551559i	−1.01750	+	0.0678923i
$67$	2.88943	−	14.5262i	0.353000	−	1.77465i	−0.241342	−	0.970440i	$-0.577587\pi$
$67$	2.88943	−	14.5262i	0.353000	−	1.77465i	0.594342	−	0.804212i	$-0.297413\pi$
$68$	5.19553	+	3.96730i	0.630051	+	0.481106i
$69$	−6.12645	−	4.09356i	−0.737537	−	0.492807i
$70$	1.21563	−	9.31829i	0.145296	−	1.11375i
$71$	−6.41451	+	2.65698i	−0.761263	+	0.315325i	−0.729328	−	0.684165i	$-0.760167\pi$
$71$	−6.41451	+	2.65698i	−0.761263	+	0.315325i	−0.0319351	+	0.999490i	$0.510167\pi$
$72$	−2.74241	+	14.0458i	−0.323197	+	1.65531i
$73$	−3.36337	−	1.39315i	−0.393653	−	0.163056i	0.177072	−	0.984198i	$-0.443338\pi$
$73$	−3.36337	−	1.39315i	−0.393653	−	0.163056i	−0.570724	+	0.821142i	$0.693338\pi$
$74$	3.10474	+	1.78766i	0.360918	+	0.207811i
$75$	13.2532	−	2.63622i	1.53034	−	0.304404i
$76$	−5.65719	−	6.42027i	−0.648925	−	0.736456i
$77$	3.64930	−	2.43839i	0.415877	−	0.277880i
$78$	−8.64099	+	4.27390i	−0.978400	+	0.483924i
$79$	−10.9490	+	10.9490i	−1.23186	+	1.23186i	−0.268617	+	0.963247i	$0.586567\pi$
$79$	−10.9490	+	10.9490i	−1.23186	+	1.23186i	−0.963247	+	0.268617i	$0.913433\pi$
$80$	11.8518	+	3.96109i	1.32508	+	0.442864i
$81$	1.00516	+	1.00516i	0.111685	+	0.111685i
$82$	16.3157	+	5.51703i	1.80176	+	0.609255i
$83$	−3.72793	−	5.57925i	−0.409194	−	0.612402i	0.568438	−	0.822726i	$-0.307548\pi$
$83$	−3.72793	−	5.57925i	−0.409194	−	0.612402i	−0.977632	+	0.210324i	$0.932548\pi$
$84$	−3.90887	−	11.4268i	−0.426493	−	1.24677i
$85$	−1.99208	−	10.0149i	−0.216072	−	1.08627i
$86$	−3.16550	+	0.852183i	−0.341344	+	0.0918932i
$87$	2.59292	−	6.25985i	0.277990	−	0.671126i
$88$	2.25249	+	5.38419i	0.240116	+	0.573957i
$89$	−3.10595	−	7.49842i	−0.329230	−	0.794831i	−0.998650	−	0.0519471i	$-0.983457\pi$
$89$	−3.10595	−	7.49842i	−0.329230	−	0.794831i	0.669420	−	0.742884i	$-0.266543\pi$
$90$	17.7188	−	13.6293i	1.86773	−	1.43665i
$91$	2.83736	−	4.24642i	0.297437	−	0.445145i
$92$	−1.33168	+	5.01705i	−0.138837	+	0.523064i
$93$	5.04240	+	1.00299i	0.522872	+	0.104006i
$94$	2.99334	−	3.42136i	0.308740	−	0.352887i
$95$			13.3664i			1.37137i
$96$	15.9096	−	2.18976i	1.62377	−	0.223492i
$97$			8.49286i			0.862319i	0.902276	+	0.431160i	$0.141895\pi$
$97$			8.49286i			0.862319i	−0.902276	+	0.431160i	$0.858105\pi$
$98$	−2.63525	−	2.30558i	−0.266200	−	0.232898i
$99$	10.2399	+	2.03685i	1.02915	+	0.204711i
$100$	−4.77915	−	8.23295i	−0.477915	−	0.823295i
$101$	−8.24152	+	12.3343i	−0.820062	+	1.22731i	0.151013	+	0.988532i	$0.451747\pi$
$101$	−8.24152	+	12.3343i	−0.820062	+	1.22731i	−0.971074	+	0.238777i	$0.923253\pi$
$102$	−8.00089	−	10.4016i	−0.792206	−	1.02991i
$103$	−2.14828	−	5.18641i	−0.211676	−	0.511032i	0.782005	−	0.623273i	$-0.214197\pi$
$103$	−2.14828	−	5.18641i	−0.211676	−	0.511032i	−0.993681	+	0.112241i	$0.964197\pi$
$104$	4.81911	+	4.78523i	0.472553	+	0.469231i
$105$	−7.21913	+	17.4285i	−0.704515	+	1.70085i
$106$	2.99481	+	11.1244i	0.290881	+	1.08050i
$107$	2.52870	+	12.7126i	0.244458	+	1.22897i	0.886654	+	0.462434i	$0.153024\pi$
$107$	2.52870	+	12.7126i	0.244458	+	1.22897i	−0.642195	+	0.766541i	$0.721976\pi$
$108$	5.14783	−	10.5009i	0.495350	−	1.01045i
$109$	5.38971	+	8.06626i	0.516240	+	0.772608i	0.994402	−	0.105664i	$-0.0336967\pi$
$109$	5.38971	+	8.06626i	0.516240	+	0.772608i	−0.478162	+	0.878272i	$0.658697\pi$
$110$	2.92028	−	8.63622i	0.278438	−	0.823431i
$111$	−5.08545	−	5.08545i	−0.482689	−	0.482689i
$112$	−6.72539	+	5.21101i	−0.635490	+	0.492394i
$113$	4.75634	−	4.75634i	0.447439	−	0.447439i	−0.447063	−	0.894502i	$-0.647530\pi$
$113$	4.75634	−	4.75634i	0.447439	−	0.447439i	0.894502	+	0.447063i	$0.147530\pi$
$114$	7.61571	+	15.3975i	0.713277	+	1.44210i
$115$	6.74169	−	4.50465i	0.628666	−	0.420061i
$116$	−4.76380	−	0.300988i	−0.442308	−	0.0279460i
$117$	11.9154	−	2.37013i	1.10158	−	0.219118i
$118$	−6.00903	+	10.4363i	−0.553176	+	0.960735i
$119$	6.42293	+	2.66046i	0.588789	+	0.243884i
$120$	−20.9069	−	13.8632i	−1.90853	−	1.26553i
$121$	−6.22889	+	2.58009i	−0.566262	+	0.234554i
$122$	−14.0885	−	1.83794i	−1.27551	−	0.166399i
$123$	−28.7478	−	19.2087i	−2.59210	−	1.73199i
$124$	−0.481192	−	3.58977i	−0.0432123	−	0.322371i
$125$	0.146412	−	0.736062i	0.0130955	−	0.0658354i
$126$	1.01327	+	15.1859i	0.0902694	+	1.35287i
$127$	0.302397			0.0268334			0.0134167	−	0.999910i	$-0.495729\pi$
$127$	0.302397			0.0268334			0.0134167	+	0.999910i	$0.495729\pi$
$128$	−5.08727	−	10.1054i	−0.449655	−	0.893202i
$129$	6.58082			0.579409
$130$	−0.706261	−	10.5847i	−0.0619432	−	0.928344i
$131$	−1.05063	+	5.28186i	−0.0917938	+	0.461478i	0.907360	+	0.420354i	$0.138094\pi$
$131$	−1.05063	+	5.28186i	−0.0917938	+	0.461478i	−0.999154	+	0.0411246i	$0.986906\pi$
$132$	−1.55658	−	11.6124i	−0.135483	−	1.01073i
$133$	−7.56673	−	5.05593i	−0.656119	−	0.438404i
$134$	20.7696	+	2.70953i	1.79422	+	0.234067i
$135$	−16.8772	+	6.99077i	−1.45256	+	0.601669i
$136$	−5.10898	+	7.70483i	−0.438092	+	0.660683i
$137$	15.9084	+	6.58948i	1.35915	+	0.562978i	0.938824	−	0.344397i	$-0.111917\pi$
$137$	15.9084	+	6.58948i	1.35915	+	0.562978i	0.420324	+	0.907374i	$0.361917\pi$
$138$	5.19950	−	9.03030i	0.442611	−	0.768710i
$139$	11.7049	−	2.32824i	0.992793	−	0.197479i	0.328138	−	0.944630i	$-0.393579\pi$
$139$	11.7049	−	2.32824i	0.992793	−	0.197479i	0.664654	+	0.747151i	$0.268579\pi$
$140$	13.2633	+	0.838003i	1.12095	+	0.0708241i
$141$	−7.58783	+	5.07002i	−0.639010	+	0.426973i
$142$	−4.35314	−	8.80120i	−0.365308	−	0.738581i
$143$	3.50343	−	3.50343i	0.292971	−	0.292971i
$144$	−20.0779	−	2.54730i	−1.67316	−	0.212275i
$145$	5.27222	+	5.27222i	0.437834	+	0.437834i
$146$	1.64917	−	4.87714i	0.136487	−	0.403635i
$147$	3.90511	+	5.84440i	0.322088	+	0.482038i
$148$	−2.23020	+	4.54933i	−0.183321	+	0.373953i
$149$	−2.62919	−	13.2179i	−0.215392	−	1.08285i	−0.925498	−	0.378753i	$-0.876353\pi$
$149$	−2.62919	−	13.2179i	−0.215392	−	1.08285i	0.710106	−	0.704095i	$-0.248647\pi$
$150$	4.96773	+	18.4530i	0.405614	+	1.50668i
$151$	−0.726711	+	1.75444i	−0.0591389	+	0.142774i	−0.950687	−	0.310152i	$-0.899620\pi$
$151$	−0.726711	+	1.75444i	−0.0591389	+	0.142774i	0.891548	+	0.452926i	$0.149620\pi$
$152$	8.52685	−	8.58722i	0.691619	−	0.696515i
$153$	6.32873	+	15.2789i	0.511648	+	1.23523i
$154$	3.78434	+	4.91986i	0.304951	+	0.396454i
$155$	−3.14313	+	4.70402i	−0.252462	+	0.377836i
$156$	−6.84438	−	11.7907i	−0.547989	−	0.944011i
$157$	−18.2962	−	3.63933i	−1.46019	−	0.290450i	−0.599828	−	0.800129i	$-0.704764\pi$
$157$	−18.2962	−	3.63933i	−1.46019	−	0.290450i	−0.860365	+	0.509679i	$0.829764\pi$
$158$	−16.4808	−	14.4191i	−1.31114	−	1.14712i
$159$		−	23.1268i		−	1.83408i
$160$	−4.47352	+	17.0968i	−0.353662	+	1.35162i
$161$			5.52037i			0.435066i
$162$	−1.32372	+	1.51300i	−0.104002	+	0.118873i
$163$	−3.25039	−	0.646543i	−0.254590	−	0.0506412i	0.0661449	−	0.997810i	$-0.478930\pi$
$163$	−3.25039	−	0.646543i	−0.254590	−	0.0506412i	−0.320735	+	0.947169i	$0.603930\pi$
$164$	−6.24878	+	23.5421i	−0.487948	+	1.83833i
$165$	−10.1676	+	15.2168i	−0.791543	+	1.18463i
$166$	7.52174	−	5.78570i	0.583800	−	0.449057i
$167$	0.0933446	+	0.225354i	0.00722322	+	0.0174384i	0.927450	−	0.373947i	$-0.121996\pi$
$167$	0.0933446	+	0.225354i	0.00722322	+	0.0174384i	−0.920227	+	0.391386i	$0.871996\pi$
$168$	15.7561	−	6.59159i	1.21561	−	0.508552i
$169$	−2.76861	+	6.68401i	−0.212970	+	0.514154i
$170$	13.9442	−	3.75391i	1.06947	−	0.287912i
$171$	−4.22335	−	21.2322i	−0.322968	−	1.62367i
$172$	−1.50054	−	4.38652i	−0.114415	−	0.334469i
$173$	−8.24361	−	12.3374i	−0.626750	−	0.937998i	−0.999948	−	0.0102459i	$-0.996739\pi$
$173$	−8.24361	−	12.3374i	−0.626750	−	0.937998i	0.373197	−	0.927752i	$-0.378261\pi$
$174$	9.07726	+	3.06942i	0.688145	+	0.232692i
$175$	−7.15875	−	7.15875i	−0.541151	−	0.541151i
$176$	−7.38542	+	3.68537i	−0.556697	+	0.277795i
$177$	17.0942	−	17.0942i	1.28488	−	1.28488i
$178$	10.2884	−	5.08873i	0.771149	−	0.381416i
$179$	9.58585	−	6.40506i	0.716480	−	0.478736i	−0.143119	−	0.989705i	$-0.545713\pi$
$179$	9.58585	−	6.40506i	0.716480	−	0.478736i	0.859599	+	0.510969i	$0.170713\pi$
$180$	20.9002	+	23.7194i	1.55781	+	1.76794i
$181$	−8.33755	+	1.65844i	−0.619726	+	0.123271i	−0.494961	−	0.868915i	$-0.664818\pi$
$181$	−8.33755	+	1.65844i	−0.619726	+	0.123271i	−0.124765	+	0.992186i	$0.539818\pi$
$182$	6.25916	+	3.60392i	0.463960	+	0.267141i
$183$	26.3506	+	10.9148i	1.94789	+	0.806842i
$184$	−7.20482	−	1.40673i	−0.531147	−	0.103705i
$185$	7.31172	−	3.02862i	0.537569	−	0.222668i
$186$	−0.940544	+	7.20964i	−0.0689641	+	0.528636i
$187$	5.60785	+	3.74704i	0.410086	+	0.274011i
$188$	5.10963	+	3.90170i	0.372658	+	0.284561i
$189$	2.42642	−	12.1985i	0.176496	−	0.887307i
$190$	−18.8611	+	1.25849i	−1.36833	+	0.0913007i
$191$	6.31207			0.456725			0.228363	−	0.973576i	$-0.426663\pi$
$191$	6.31207			0.456725			0.228363	+	0.973576i	$0.426663\pi$
$192$	4.58786	+	22.2435i	0.331101	+	1.60529i
$193$	−10.5158			−0.756940			−0.378470	−	0.925614i	$-0.623550\pi$
$193$	−10.5158			−0.756940			−0.378470	+	0.925614i	$0.623550\pi$
$194$	−11.9841	+	0.799629i	−0.860406	+	0.0574100i
$195$	−4.15456	+	20.8864i	−0.297515	+	1.49571i
$196$	3.00523	−	3.93561i	0.214659	−	0.281115i
$197$	13.0604	+	8.72666i	0.930513	+	0.621749i	0.925708	−	0.378240i	$-0.123470\pi$
$197$	13.0604	+	8.72666i	0.930513	+	0.621749i	0.00480529	+	0.999988i	$0.498470\pi$
$198$	−1.91003	+	14.6411i	−0.135740	+	1.04050i
$199$	25.4075	−	10.5241i	1.80109	−	0.746037i	0.815085	−	0.579342i	$-0.196690\pi$
$199$	25.4075	−	10.5241i	1.80109	−	0.746037i	0.986008	−	0.166695i	$-0.0533095\pi$
$200$	11.1674	−	7.51890i	0.789651	−	0.531666i
$201$	−38.8465	−	16.0907i	−2.74002	−	1.13495i
$202$	−18.1806	−	10.4681i	−1.27918	−	0.736532i
$203$	−4.97885	+	0.990354i	−0.349447	+	0.0695092i
$204$	13.9242	−	12.2692i	0.974886	−	0.859016i
$205$	31.6348	−	21.1377i	2.20947	−	1.47632i
$206$	7.11615	−	3.51970i	0.495805	−	0.245229i
$207$	−9.28566	+	9.28566i	−0.645398	+	0.645398i
$208$	−6.29859	+	7.25067i	−0.436729	+	0.502744i
$209$	−6.24279	−	6.24279i	−0.431823	−	0.431823i
$210$	−25.2727	−	8.54579i	−1.74398	−	0.589716i
$211$	12.5416	+	18.7698i	0.863399	+	1.29217i	0.955071	+	0.296378i	$0.0957789\pi$
$211$	12.5416	+	18.7698i	0.863399	+	1.29217i	−0.0916719	+	0.995789i	$0.529221\pi$
$212$	−15.4155	+	5.27330i	−1.05874	+	0.362172i
$213$	3.84542	+	19.3322i	0.263484	+	1.32462i
$214$	−17.7004	+	4.76512i	−1.20997	+	0.325737i
$215$	−2.77128	+	6.69045i	−0.189000	+	0.456285i
$216$	15.3023	+	6.27528i	1.04119	+	0.426979i
$217$	−1.47404	−	3.55864i	−0.100064	−	0.241576i
$218$	−10.8747	+	8.36475i	−0.736524	+	0.566532i
$219$	−5.74193	+	8.59341i	−0.388004	+	0.580689i
$220$	12.4613	+	3.30761i	0.840142	+	0.222999i
$221$	7.69726	+	1.53108i	0.517774	+	0.102992i
$222$	6.69714	−	7.65476i	0.449483	−	0.513754i
$223$			8.11318i			0.543298i	0.962396	+	0.271649i	$0.0875690\pi$
$223$			8.11318i			0.543298i	−0.962396	+	0.271649i	$0.912431\pi$
$224$	−7.98635	−	8.99940i	−0.533610	−	0.601298i
$225$		−	24.0831i		−	1.60554i
$226$	7.15938	+	6.26373i	0.476235	+	0.416657i
$227$	−11.3933	−	2.26626i	−0.756197	−	0.150417i	−0.198087	−	0.980184i	$-0.563473\pi$
$227$	−11.3933	−	2.26626i	−0.756197	−	0.150417i	−0.558109	+	0.829767i	$0.688473\pi$
$228$	−21.0100	+	12.1961i	−1.39142	+	0.807704i
$229$	12.2867	−	18.3883i	0.811926	−	1.21513i	−0.161668	−	0.986845i	$-0.551687\pi$
$229$	12.2867	−	18.3883i	0.811926	−	1.21513i	0.973594	−	0.228288i	$-0.0733127\pi$
$230$	6.99116	+	9.08891i	0.460983	+	0.599305i
$231$	−4.76829	−	11.5117i	−0.313731	−	0.757413i
$232$	−0.0238107	−	6.75043i	−0.00156325	−	0.443187i
$233$	0.609526	−	1.47153i	0.0399314	−	0.0964028i	−0.902656	−	0.430364i	$-0.858385\pi$
$233$	0.609526	−	1.47153i	0.0399314	−	0.0964028i	0.942587	+	0.333961i	$0.108385\pi$
$234$	4.46630	+	16.5904i	0.291971	+	1.08455i
$235$	−1.95915	−	9.84930i	−0.127801	−	0.642497i
$236$	−15.2921	−	7.49658i	−0.995432	−	0.487986i
$237$	24.4225	+	36.5508i	1.58641	+	2.37423i
$238$	−3.14938	+	9.31373i	−0.204144	+	0.603719i
$239$	−1.07033	−	1.07033i	−0.0692337	−	0.0692337i	0.671642	−	0.740876i	$-0.265589\pi$
$239$	−1.07033	−	1.07033i	−0.0692337	−	0.0692337i	−0.740876	+	0.671642i	$0.765589\pi$
$240$	17.5935	−	30.8065i	1.13566	−	1.98855i
$241$	11.5889	−	11.5889i	0.746509	−	0.746509i	−0.227313	−	0.973822i	$-0.572994\pi$
$241$	11.5889	−	11.5889i	0.746509	−	0.746509i	0.973822	+	0.227313i	$0.0729940\pi$
$242$	−4.22717	−	8.54651i	−0.271733	−	0.549390i
$243$	−11.2304	+	7.50390i	−0.720429	+	0.481375i
$244$	1.26699	−	20.0530i	0.0811110	−	1.28376i
$245$	−7.58626	+	1.50900i	−0.484669	+	0.0964066i
$246$	24.3982	−	42.3739i	1.55557	−	2.70166i
$247$	−9.49121	−	3.93139i	−0.603911	−	0.250148i
$248$	5.02013	−	1.01699i	0.318778	−	0.0645787i
$249$	−17.5997	+	7.29002i	−1.11533	+	0.461986i
$250$	1.05242	+	0.137296i	0.0665612	+	0.00868334i
$251$	−3.20465	−	2.14128i	−0.202276	−	0.135156i	0.450307	−	0.892874i	$-0.351315\pi$
$251$	−3.20465	−	2.14128i	−0.202276	−	0.135156i	−0.652583	+	0.757717i	$0.726315\pi$
$252$	−21.3331	+	2.85961i	−1.34386	+	0.180138i
$253$	−1.04481	+	5.25260i	−0.0656865	+	0.330228i
$254$	0.0284717	+	0.426706i	0.00178647	+	0.0267739i
$255$	−28.9889			−1.81535
$256$	13.7805	−	8.12998i	0.861284	−	0.508124i
$257$	−12.4093			−0.774071			−0.387035	−	0.922065i	$-0.626501\pi$
$257$	−12.4093			−0.774071			−0.387035	+	0.922065i	$0.626501\pi$
$258$	0.619605	+	9.28604i	0.0385749	+	0.578123i
$259$	−1.05120	+	5.28475i	−0.0653185	+	0.328378i
$260$	14.8694	−	1.99317i	0.922160	−	0.123611i
$261$	−10.0406	−	6.70893i	−0.621499	−	0.415272i
$262$	−7.55203	−	0.985212i	−0.466566	−	0.0608666i
$263$	1.63628	−	0.677769i	0.100897	−	0.0417930i	−0.331664	−	0.943398i	$-0.607610\pi$
$263$	1.63628	−	0.677769i	0.100897	−	0.0417930i	0.432561	+	0.901605i	$0.357610\pi$
$264$	16.2394	−	3.28980i	0.999464	−	0.202473i
$265$	23.5121	+	9.73904i	1.44434	+	0.598264i
$266$	6.42187	−	11.1533i	0.393750	−	0.683850i
$267$	−22.5989	+	4.49521i	−1.38303	+	0.275102i
$268$	−1.86783	+	29.5625i	−0.114096	+	1.80582i
$269$	−26.2384	+	17.5320i	−1.59978	+	1.06894i	−0.648238	+	0.761438i	$0.724494\pi$
$269$	−26.2384	+	17.5320i	−1.59978	+	1.06894i	−0.951547	+	0.307505i	$0.900506\pi$
$270$	−11.4535	−	23.1568i	−0.697040	−	1.40928i
$271$	−1.58765	+	1.58765i	−0.0964427	+	0.0964427i	−0.753682	−	0.657239i	$-0.771724\pi$
$271$	−1.58765	+	1.58765i	−0.0964427	+	0.0964427i	0.657239	+	0.753682i	$0.271724\pi$
$272$	−11.3531	−	6.48373i	−0.688384	−	0.393134i
$273$	−10.2523	−	10.2523i	−0.620497	−	0.620497i
$274$	−7.80043	+	23.0684i	−0.471241	+	1.39361i
$275$	−5.45661	−	8.16640i	−0.329046	−	0.492452i
$276$	13.2320	+	6.48666i	0.796472	+	0.390451i
$277$	−0.970436	−	4.87871i	−0.0583079	−	0.293133i	0.940618	−	0.339466i	$-0.110246\pi$
$277$	−0.970436	−	4.87871i	−0.0583079	−	0.293133i	−0.998926	+	0.0463330i	$0.985246\pi$
$278$	4.38737	+	16.2972i	0.263137	+	0.977443i
$279$	3.50646	−	8.46533i	0.209926	−	0.506806i
$280$	0.0662932	+	18.7944i	0.00396178	+	1.12318i
$281$	−0.758051	−	1.83010i	−0.0452216	−	0.109175i	0.899655	−	0.436602i	$-0.143818\pi$
$281$	−0.758051	−	1.83010i	−0.0452216	−	0.109175i	−0.944876	+	0.327428i	$0.893818\pi$
$282$	−7.86861	−	10.2296i	−0.468569	−	0.609166i
$283$	5.42628	−	8.12100i	0.322559	−	0.482744i	−0.634385	−	0.773018i	$-0.718746\pi$
$283$	5.42628	−	8.12100i	0.322559	−	0.482744i	0.956944	+	0.290274i	$0.0937464\pi$
$284$	12.0093	−	6.97128i	0.712621	−	0.413669i
$285$	37.2177	+	7.40306i	2.20459	+	0.438519i
$286$	5.27346	+	4.61374i	0.311826	+	0.272816i
$287$			25.9039i			1.52906i
$288$	1.70404	−	28.5713i	0.100411	−	1.68358i
$289$		−	6.31674i		−	0.371573i
$290$	−6.94311	+	7.93590i	−0.407714	+	0.466012i
$291$	23.6476	+	4.70380i	1.38625	+	0.275742i
$292$	7.03729	+	1.86791i	0.411826	+	0.109311i
$293$	6.65651	−	9.96217i	0.388877	−	0.581996i	−0.584446	−	0.811432i	$-0.698688\pi$
$293$	6.65651	−	9.96217i	0.388877	−	0.581996i	0.973324	+	0.229436i	$0.0736883\pi$
$294$	−7.87922	+	6.06067i	−0.459525	+	0.353465i
$295$	10.1804	+	24.5776i	0.592725	+	1.43096i
$296$	−6.62943	−	2.71864i	−0.385328	−	0.158018i
$297$	4.61746	−	11.1475i	0.267932	−	0.646845i
$298$	18.4038	−	4.95449i	1.06611	−	0.287006i
$299$	1.21576	+	6.11205i	0.0703093	+	0.353469i
$300$	−25.5709	+	8.74726i	−1.47634	+	0.505023i
$301$	−2.73921	−	4.09952i	−0.157885	−	0.236292i
$302$	−2.54406	−	0.860259i	−0.146394	−	0.0495023i
$303$	29.7792	+	29.7792i	1.71077	+	1.71077i
$304$	12.9200	+	11.2235i	0.741015	+	0.643713i
$305$	−22.1932	+	22.1932i	−1.27078	+	1.27078i
$306$	−20.9638	+	10.3689i	−1.19842	+	0.592750i
$307$	−9.59801	+	6.41318i	−0.547787	+	0.366020i	−0.798456	−	0.602053i	$-0.794350\pi$
$307$	−9.59801	+	6.41318i	−0.547787	+	0.366020i	0.250669	+	0.968073i	$0.419350\pi$
$308$	−6.58599	+	5.80322i	−0.375272	+	0.330669i
$309$	−15.6309	+	3.10919i	−0.889213	+	0.176875i
$310$	−6.93367	−	3.99229i	−0.393806	−	0.226747i
$311$	−21.5704	−	8.93477i	−1.22315	−	0.506644i	−0.324738	−	0.945804i	$-0.605276\pi$
$311$	−21.5704	−	8.93477i	−1.22315	−	0.506644i	−0.898409	+	0.439160i	$0.855276\pi$
$312$	15.9931	−	10.7681i	0.905433	−	0.609622i
$313$	−1.66011	+	0.687642i	−0.0938352	+	0.0388678i	−0.429107	−	0.903254i	$-0.641172\pi$
$313$	−1.66011	+	0.687642i	−0.0938352	+	0.0388678i	0.335272	+	0.942121i	$0.391172\pi$
$314$	3.41273	−	26.1599i	0.192592	−	1.47629i
$315$	27.9549	+	18.6788i	1.57508	+	1.05243i
$316$	18.7947	−	24.6133i	1.05728	−	1.38461i
$317$	−2.90261	+	14.5924i	−0.163027	+	0.819590i	0.809558	+	0.587040i	$0.199707\pi$
$317$	−2.90261	+	14.5924i	−0.163027	+	0.819590i	−0.972584	+	0.232550i	$0.925293\pi$
$318$	32.6337	−	2.17746i	1.83001	−	0.122106i
$319$	−4.92478			−0.275735
$320$	−24.5461	−	4.70275i	−1.37217	−	0.262892i
$321$	36.7977			2.05385
$322$	−7.78966	+	0.519760i	−0.434101	+	0.0289651i
$323$	2.72825	−	13.7158i	0.151804	−	0.763169i
$324$	−2.25960	−	1.72542i	−0.125533	−	0.0958568i
$325$	−9.50261	−	6.34944i	−0.527110	−	0.352204i
$326$	0.606287	−	4.64743i	0.0335791	−	0.257397i
$327$	25.4449	−	10.5396i	1.40711	−	0.582843i
$328$	−33.8080	−	6.60095i	−1.86673	−	0.364476i
$329$	6.31673	+	2.61648i	0.348253	+	0.144251i
$330$	−22.4294	−	12.9145i	−1.23470	−	0.710918i
$331$	5.51285	−	1.09657i	0.303014	−	0.0602732i	−0.0412418	−	0.999149i	$-0.513131\pi$
$331$	5.51285	−	1.09657i	0.303014	−	0.0602732i	0.344255	+	0.938876i	$0.388131\pi$
$332$	8.87226	+	10.0690i	0.486928	+	0.552609i
$333$	−10.6575	+	7.12113i	−0.584029	+	0.390236i
$334$	−0.309203	+	0.152934i	−0.0169188	+	0.00836818i
$335$	32.7176	−	32.7176i	1.78755	−	1.78755i
$336$	10.7847	+	21.6124i	0.588354	+	1.17905i
$337$	2.17791	+	2.17791i	0.118638	+	0.118638i	0.763933	−	0.645295i	$-0.223266\pi$
$337$	2.17791	+	2.17791i	0.118638	+	0.118638i	−0.645295	+	0.763933i	$0.723266\pi$
$338$	−9.69232	−	3.27739i	−0.527192	−	0.178267i
$339$	−10.6093	−	15.8779i	−0.576218	−	0.862371i
$340$	6.60994	+	19.3229i	0.358475	+	1.04793i
$341$	−0.729016	−	3.66501i	−0.0394784	−	0.198471i
$342$	29.5626	−	7.95855i	1.59856	−	0.430349i
$343$	7.71305	−	18.6210i	0.416466	−	1.00544i
$344$	6.04844	−	2.53038i	0.326110	−	0.136429i
$345$	−8.80890	−	21.2666i	−0.474255	−	1.14495i
$346$	16.6329	−	12.7940i	0.894190	−	0.687808i
$347$	5.32825	−	7.97430i	0.286036	−	0.428083i	−0.660430	−	0.750888i	$-0.729626\pi$
$347$	5.32825	−	7.97430i	0.286036	−	0.428083i	0.946465	+	0.322805i	$0.104626\pi$
$348$	−3.47653	+	13.0977i	−0.186361	+	0.702110i
$349$	−1.63592	−	0.325405i	−0.0875689	−	0.0174185i	0.151111	−	0.988517i	$-0.451715\pi$
$349$	−1.63592	−	0.325405i	−0.0875689	−	0.0174185i	−0.238680	+	0.971098i	$0.576715\pi$
$350$	9.42752	−	10.7756i	0.503922	−	0.575978i
$351$		−	14.0403i		−	0.749414i
$352$	−5.89570	−	10.0744i	−0.314242	−	0.536968i
$353$			5.92592i			0.315405i	0.987487	+	0.157702i	$0.0504087\pi$
$353$			5.92592i			0.315405i	−0.987487	+	0.157702i	$0.949591\pi$
$354$	25.7307	+	22.5118i	1.36757	+	1.19649i
$355$	−21.2737	−	4.23159i	−1.12909	−	0.224590i
$356$	8.14927	+	14.0386i	0.431910	+	0.744045i
$357$	10.9652	−	16.4106i	0.580340	−	0.868539i
$358$	9.94056	+	12.9233i	0.525375	+	0.683018i
$359$	−12.0537	−	29.1002i	−0.636170	−	1.53585i	−0.831743	−	0.555161i	$-0.812657\pi$
$359$	−12.0537	−	29.1002i	−0.636170	−	1.53585i	0.195573	−	0.980689i	$-0.437343\pi$
$360$	−31.5020	+	31.7250i	−1.66030	+	1.67205i
$361$	0.265606	−	0.641230i	0.0139793	−	0.0337489i
$362$	−3.12520	−	11.6088i	−0.164257	−	0.610144i
$363$	3.73414	+	18.7728i	0.195991	+	0.985315i
$364$	−4.49609	+	9.17147i	−0.235659	+	0.480716i
$365$	−6.31856	−	9.45639i	−0.330729	−	0.494970i
$366$	−12.9206	+	38.2103i	−0.675369	+	1.99728i
$367$	−18.9541	−	18.9541i	−0.989396	−	0.989396i	0.0105483	−	0.999944i	$-0.496642\pi$
$367$	−18.9541	−	18.9541i	−0.989396	−	0.989396i	−0.999944	+	0.0105483i	$0.996642\pi$
$368$	1.30664	−	10.2990i	0.0681135	−	0.536873i
$369$	−43.5722	+	43.5722i	−2.26828	+	2.26828i
$370$	4.96203	+	10.0322i	0.257964	+	0.521552i
$371$	−14.4068	+	9.62634i	−0.747966	+	0.499775i
$372$	−10.2619	−	0.648370i	−0.532055	−	0.0336164i
$373$	−21.0597	+	4.18903i	−1.09043	+	0.216899i	−0.707383	−	0.706830i	$-0.750124\pi$
$373$	−21.0597	+	4.18903i	−1.09043	+	0.216899i	−0.383044	+	0.923730i	$0.625124\pi$
$374$	−4.75937	+	8.26589i	−0.246101	+	0.427419i
$375$	−1.96841	−	0.815342i	−0.101648	−	0.0421041i
$376$	−5.02451	+	7.57744i	−0.259119	+	0.390777i
$377$	−5.29437	+	2.19300i	−0.272674	+	0.112945i
$378$	17.4414	+	2.27535i	0.897089	+	0.117031i
$379$	3.08942	+	2.06428i	0.158693	+	0.106035i	0.632381	−	0.774657i	$-0.282078\pi$
$379$	3.08942	+	2.06428i	0.158693	+	0.106035i	−0.473688	+	0.880693i	$0.657078\pi$
$380$	−3.55166	−	26.4959i	−0.182196	−	1.35921i
$381$	0.167484	−	0.841999i	0.00858046	−	0.0431369i
$382$	0.594301	+	8.90680i	0.0304071	+	0.455712i
$383$	16.3597			0.835942			0.417971	−	0.908460i	$-0.362741\pi$
$383$	16.3597			0.835942			0.417971	+	0.908460i	$0.362741\pi$
$384$	−30.9553	+	8.56812i	−1.57968	+	0.437240i
$385$	13.7115			0.698800
$386$	−0.990091	−	14.8385i	−0.0503943	−	0.755261i
$387$	2.28813	−	11.5032i	0.116312	−	0.584742i
$388$	−2.25668	−	16.8351i	−0.114565	−	0.854675i
$389$	21.6591	+	14.4722i	1.09816	+	0.733768i	0.966279	−	0.257498i	$-0.0828980\pi$
$389$	21.6591	+	14.4722i	1.09816	+	0.733768i	0.131882	+	0.991265i	$0.457898\pi$
$390$	−29.8635	−	3.89589i	−1.51220	−	0.197276i
$391$	−7.83736	+	3.24634i	−0.396352	+	0.164174i
$392$	5.83640	+	3.87005i	0.294783	+	0.195467i
$393$	14.1250	+	5.85076i	0.712511	+	0.295132i
$394$	−11.0843	+	19.2508i	−0.558419	+	0.969842i
$395$	−47.4444	+	9.43728i	−2.38719	+	0.474841i
$396$	−20.8395	−	1.31669i	−1.04723	−	0.0661661i
$397$	3.68511	−	2.46232i	0.184951	−	0.123580i	−0.459648	−	0.888101i	$-0.652024\pi$
$397$	3.68511	−	2.46232i	0.184951	−	0.123580i	0.644599	+	0.764521i	$0.277024\pi$
$398$	17.2426	+	34.8611i	0.864292	+	1.74743i
$399$	−18.2686	+	18.2686i	−0.914576	+	0.914576i
$400$	11.6612	+	15.0501i	0.583059	+	0.752503i
$401$	8.30297	+	8.30297i	0.414630	+	0.414630i	0.883348	−	0.468718i	$-0.155284\pi$
$401$	8.30297	+	8.30297i	0.414630	+	0.414630i	−0.468718	+	0.883348i	$0.655284\pi$
$402$	19.0477	−	56.3303i	0.950015	−	2.80950i
$403$	−2.41575	−	3.61543i	−0.120337	−	0.180097i
$404$	13.0595	−	26.6398i	0.649735	−	1.32538i
$405$	0.866379	+	4.35558i	0.0430507	+	0.216431i
$406$	−1.86624	−	6.93229i	−0.0926199	−	0.344044i
$407$	−2.00042	+	4.82945i	−0.0991573	+	0.239387i
$408$	18.6238	+	18.4929i	0.922015	+	0.915533i
$409$	12.9503	+	31.2648i	0.640350	+	1.54594i	0.826207	+	0.563366i	$0.190494\pi$
$409$	12.9503	+	31.2648i	0.640350	+	1.54594i	−0.185857	+	0.982577i	$0.559506\pi$
$410$	32.8054	+	42.6489i	1.62014	+	2.10628i
$411$	27.1588	−	40.6460i	1.33964	−	2.00492i
$412$	5.63658	+	9.71003i	0.277694	+	0.478379i
$413$	−17.7641	−	3.53351i	−0.874117	−	0.173873i
$414$	−13.9771	−	12.2285i	−0.686935	−	0.600998i
$415$		−	20.9628i		−	1.02902i
$416$	−10.8243	−	8.20512i	−0.530704	−	0.402289i
$417$		−	33.8806i		−	1.65914i
$418$	8.22127	−	9.39683i	0.402116	−	0.459614i
$419$	15.5325	+	3.08960i	0.758811	+	0.150937i	0.559307	−	0.828960i	$-0.311067\pi$
$419$	15.5325	+	3.08960i	0.758811	+	0.150937i	0.199503	+	0.979897i	$0.436067\pi$
$420$	9.67926	−	36.4663i	0.472300	−	1.77937i
$421$	1.42193	−	2.12807i	0.0693006	−	0.103716i	−0.795201	−	0.606346i	$-0.792634\pi$
$421$	1.42193	−	2.12807i	0.0693006	−	0.103716i	0.864501	+	0.502631i	$0.167634\pi$
$422$	−25.3048	+	19.4644i	−1.23182	+	0.947511i
$423$	6.22410	+	15.0263i	0.302626	+	0.730604i
$424$	−8.89244	−	21.2559i	−0.431855	−	1.03228i
$425$	5.95357	−	14.3732i	0.288791	−	0.697203i
$426$	−26.9172	+	7.24637i	−1.30414	+	0.351088i
$427$	−4.16885	−	20.9582i	−0.201745	−	1.01424i
$428$	−8.39049	−	24.5279i	−0.405569	−	1.18560i
$429$	−7.81460	−	11.6954i	−0.377292	−	0.564658i
$430$	−9.70166	−	3.28055i	−0.467856	−	0.158202i
$431$	13.2163	+	13.2163i	0.636606	+	0.636606i	0.949717	−	0.313111i	$-0.101371\pi$
$431$	13.2163	+	13.2163i	0.636606	+	0.636606i	−0.313111	+	0.949717i	$0.601371\pi$
$432$	−7.41413	+	22.1836i	−0.356713	+	1.06731i
$433$	−5.42276	+	5.42276i	−0.260601	+	0.260601i	−0.825298	−	0.564697i	$-0.808993\pi$
$433$	−5.42276	+	5.42276i	−0.260601	+	0.260601i	0.564697	+	0.825298i	$0.308993\pi$
$434$	4.88273	−	2.41504i	0.234379	−	0.115926i
$435$	17.6001	−	11.7600i	0.843860	−	0.563849i
$436$	−12.8272	−	14.5574i	−0.614310	−	0.697173i
$437$	10.8911	−	2.16638i	0.520993	−	0.103632i
$438$	−12.6666	−	7.29320i	−0.605232	−	0.348483i
$439$	−15.4472	−	6.39844i	−0.737255	−	0.305381i	−0.0177256	−	0.999843i	$-0.505643\pi$
$439$	−15.4472	−	6.39844i	−0.737255	−	0.305381i	−0.719530	+	0.694462i	$0.755643\pi$
$440$	−3.49402	+	17.8953i	−0.166571	+	0.853124i
$441$	11.5738	−	4.79401i	0.551132	−	0.228286i
$442$	−1.43575	+	11.0056i	−0.0682916	+	0.523482i
$443$	8.77140	+	5.86086i	0.416742	+	0.278458i	0.746213	−	0.665708i	$-0.231870\pi$
$443$	8.77140	+	5.86086i	0.416742	+	0.278458i	−0.329471	+	0.944166i	$0.606870\pi$
$444$	11.4320	+	8.72946i	0.542539	+	0.414282i
$445$	4.94664	−	24.8684i	0.234493	−	1.17888i
$446$	−11.4483	+	0.763881i	−0.542093	+	0.0361708i
$447$	−38.2601			−1.80964
$448$	11.9469	−	12.1167i	0.564438	−	0.572459i
$449$	11.0927			0.523498			0.261749	−	0.965136i	$-0.415701\pi$
$449$	11.0927			0.523498			0.261749	+	0.965136i	$0.415701\pi$
$450$	33.9830	−	2.26750i	1.60198	−	0.106891i
$451$	−4.90267	+	24.6474i	−0.230857	+	1.16060i
$452$	−8.16452	+	10.6922i	−0.384027	+	0.502918i
$453$	4.48258	+	2.99516i	0.210610	+	0.140725i
$454$	2.12515	−	16.2901i	0.0997384	−	0.764533i
$455$	14.7405	−	6.10570i	0.691044	−	0.286240i
$456$	−19.1877	−	28.4983i	−0.898548	−	1.33456i
$457$	20.2978	+	8.40761i	0.949490	+	0.393292i	0.803039	−	0.595926i	$-0.203215\pi$
$457$	20.2978	+	8.40761i	0.949490	+	0.393292i	0.146451	+	0.989218i	$0.453215\pi$
$458$	27.1041	+	15.6061i	1.26649	+	0.729226i
$459$	18.7452	−	3.72866i	0.874953	−	0.174039i
$460$	−12.1669	+	10.7208i	−0.567285	+	0.499860i
$461$	19.1714	−	12.8099i	0.892903	−	0.596619i	−0.0222379	−	0.999753i	$-0.507079\pi$
$461$	19.1714	−	12.8099i	0.892903	−	0.596619i	0.915141	+	0.403134i	$0.132079\pi$
$462$	15.7949	−	7.81228i	0.734845	−	0.363460i
$463$	−9.19024	+	9.19024i	−0.427107	+	0.427107i	−0.887642	−	0.460535i	$-0.847658\pi$
$463$	−9.19024	+	9.19024i	−0.427107	+	0.427107i	0.460535	+	0.887642i	$0.347658\pi$
$464$	9.52312	−	0.669173i	0.442100	−	0.0310656i
$465$	11.3571	+	11.3571i	0.526673	+	0.526673i
$466$	2.13382	+	0.721538i	0.0988474	+	0.0334246i
$467$	0.319653	+	0.478395i	0.0147918	+	0.0221375i	0.838792	−	0.544452i	$-0.183262\pi$
$467$	0.319653	+	0.478395i	0.0147918	+	0.0221375i	−0.824000	+	0.566590i	$0.808262\pi$
$468$	−22.9898	+	7.86433i	−1.06270	+	0.363529i
$469$	6.14580	+	30.8970i	0.283787	+	1.42669i
$470$	13.7136	−	3.69185i	0.632563	−	0.170292i
$471$	−20.2668	+	48.9284i	−0.933845	+	2.25450i
$472$	9.13845	−	22.2842i	0.420631	−	1.02571i
$473$	−1.83045	−	4.41910i	−0.0841642	−	0.203190i
$474$	−49.2766	+	37.9034i	−2.26335	+	1.74096i
$475$	−11.3141	+	16.9328i	−0.519128	+	0.776930i
$476$	−13.4389	−	3.56709i	−0.615971	−	0.163497i
$477$	−40.4255	−	8.04114i	−1.85096	−	0.368178i
$478$	1.40954	−	1.61109i	0.0644707	−	0.0736894i
$479$		−	33.0010i		−	1.50786i	−0.656957	−	0.753928i	$-0.728157\pi$
$479$		−	33.0010i		−	1.50786i	0.656957	−	0.753928i	$-0.271843\pi$
$480$	45.1269	+	21.9252i	2.05975	+	1.00075i
$481$			6.08268i			0.277346i
$482$	17.4440	+	15.2617i	0.794552	+	0.695153i
$483$	15.3710	+	3.05748i	0.699404	+	0.139120i
$484$	11.6618	−	6.76954i	0.530080	−	0.307706i
$485$	−14.7405	+	22.0607i	−0.669332	+	1.00173i
$486$	−11.6459	−	15.1404i	−0.528271	−	0.686783i
$487$	14.4792	+	34.9559i	0.656116	+	1.58400i	0.803753	+	0.594963i	$0.202833\pi$
$487$	14.4792	+	34.9559i	0.656116	+	1.58400i	−0.147637	+	0.989042i	$0.547167\pi$
$488$	28.4156	−	0.100230i	1.28631	−	0.00453721i
$489$	−3.60049	+	8.69235i	−0.162820	+	0.393081i
$490$	−2.84359	−	10.5627i	−0.128460	−	0.477175i
$491$	4.13764	+	20.8013i	0.186729	+	0.938750i	0.954542	+	0.298076i	$0.0963450\pi$
$491$	4.13764	+	20.8013i	0.186729	+	0.938750i	−0.767813	+	0.640674i	$0.778655\pi$
$492$	62.0899	+	30.4381i	2.79923	+	1.37225i
$493$	−4.33391	−	6.48615i	−0.195189	−	0.292122i
$494$	4.65386	−	13.7630i	0.209387	−	0.619225i
$495$	23.0637	+	23.0637i	1.03663	+	1.03663i
$496$	1.90771	+	6.98803i	0.0856585	+	0.313772i
$497$	10.4424	−	10.4424i	0.468404	−	0.468404i
$498$	−11.9438	−	24.1481i	−0.535216	−	1.08210i
$499$	34.2079	−	22.8570i	1.53135	−	1.02322i	0.549079	−	0.835770i	$-0.314979\pi$
$499$	34.2079	−	22.8570i	1.53135	−	1.02322i	0.982275	−	0.187448i	$-0.0600215\pi$
$500$	−0.0946455	+	1.49798i	−0.00423268	+	0.0669916i
$501$	0.679177	−	0.135097i	0.0303434	−	0.00603568i
$502$	2.71978	−	4.72361i	0.121390	−	0.210825i
$503$	−16.6755	−	6.90723i	−0.743525	−	0.307978i	−0.0214284	−	0.999770i	$-0.506821\pi$
$503$	−16.6755	−	6.90723i	−0.743525	−	0.307978i	−0.722097	+	0.691792i	$0.756821\pi$
$504$	−6.04370	−	29.8334i	−0.269208	−	1.32888i
$505$	−42.8157	+	17.7349i	−1.90528	+	0.789191i
$506$	−7.51019	−	0.979753i	−0.333869	−	0.0435554i
$507$	17.0776	+	11.4109i	0.758444	+	0.506776i
$508$	−0.599433	+	0.0803513i	−0.0265955	+	0.00356501i
$509$	4.55107	−	22.8798i	0.201722	−	1.01413i	−0.738678	−	0.674058i	$-0.764550\pi$
$509$	4.55107	−	22.8798i	0.201722	−	1.01413i	0.940401	−	0.340069i	$-0.110450\pi$
$510$	−2.72939	−	40.9055i	−0.120860	−	1.81133i
$511$	7.74328			0.342543
$512$	12.7695	+	18.6799i	0.564337	+	0.825544i
$513$	−25.0185			−1.10459
$514$	−1.16837	−	17.5105i	−0.0515348	−	0.772353i
$515$	3.42142	−	17.2007i	0.150766	−	0.757952i
$516$	−13.0450	+	1.74862i	−0.574273	+	0.0769787i
$517$	5.51513	+	3.68509i	0.242555	+	0.162070i
$518$	−7.55615	−	0.985750i	−0.331998	−	0.0433114i
$519$	−38.9183	+	16.1205i	−1.70832	+	0.707610i
$520$	4.21252	+	20.7942i	0.184731	+	0.911885i
$521$	−25.8128	−	10.6920i	−1.13088	−	0.468426i	−0.262801	−	0.964850i	$-0.584646\pi$
$521$	−25.8128	−	10.6920i	−1.13088	−	0.468426i	−0.868080	+	0.496424i	$0.834646\pi$
$522$	8.52146	−	14.7998i	0.372974	−	0.647768i
$523$	−3.91430	+	0.778602i	−0.171160	+	0.0340459i	−0.279926	−	0.960021i	$-0.590310\pi$
$523$	−3.91430	+	0.778602i	−0.171160	+	0.0340459i	0.108766	+	0.994067i	$0.465310\pi$
$524$	0.679161	−	10.7492i	0.0296693	−	0.469583i
$525$	−23.8978	+	15.9680i	−1.04299	+	0.696901i
$526$	1.11044	+	2.24510i	0.0484176	+	0.0978909i
$527$	4.18543	−	4.18543i	0.182320	−	0.182320i
$528$	6.17114	+	22.6052i	0.268565	+	0.983766i
$529$	11.5004	+	11.5004i	0.500015	+	0.500015i
$530$	−11.5288	+	34.0943i	−0.500778	+	1.48096i
$531$	−23.9370	−	35.8242i	−1.03878	−	1.55464i
$532$	16.3427	+	8.01162i	0.708547	+	0.347348i
$533$	5.70486	+	28.6802i	0.247105	+	1.24228i
$534$	−8.47084	−	31.4656i	−0.366569	−	1.36165i
$535$	−15.4960	+	37.4107i	−0.669952	+	1.61741i
$536$	−41.8908	+	0.147761i	−1.80941	+	0.00638231i
$537$	−12.5252	−	30.2384i	−0.540501	−	1.30488i
$538$	−27.2093	−	35.3737i	−1.17308	−	1.52507i
$539$	2.83838	−	4.24794i	0.122258	−	0.182972i
$540$	31.5976	−	18.3421i	1.35975	−	0.789318i
$541$	−23.5841	−	4.69116i	−1.01396	−	0.201689i	−0.339974	−	0.940435i	$-0.610418\pi$
$541$	−23.5841	−	4.69116i	−1.01396	−	0.201689i	−0.673984	+	0.738746i	$0.735418\pi$
$542$	−2.38977	−	2.09081i	−0.102650	−	0.0898080i
$543$			24.1337i			1.03568i
$544$	8.08010	−	16.6306i	0.346431	−	0.713030i
$545$			30.3072i			1.29822i
$546$	13.5015	−	15.4320i	0.577810	−	0.660430i
$547$	−18.9505	−	3.76948i	−0.810263	−	0.161171i	−0.227463	−	0.973787i	$-0.573043\pi$
$547$	−18.9505	−	3.76948i	−0.810263	−	0.161171i	−0.582800	+	0.812615i	$0.698043\pi$
$548$	−33.2857	−	8.83504i	−1.42190	−	0.377414i
$549$	28.2409	−	42.2656i	1.20529	−	1.80385i
$550$	11.0097	−	8.46859i	0.469453	−	0.361102i
$551$	3.90773	+	9.43410i	0.166475	+	0.401906i
$552$	−7.90733	+	19.2821i	−0.336558	+	0.820700i
$553$	12.6037	−	30.4279i	0.535962	−	1.29393i
$554$	6.79286	−	1.82871i	0.288601	−	0.0776942i
$555$	−4.38329	−	22.0363i	−0.186060	−	0.935387i
$556$	−22.5835	+	7.72535i	−0.957755	+	0.327628i
$557$	9.35372	+	13.9988i	0.396330	+	0.593149i	0.974944	−	0.222452i	$-0.0714062\pi$
$557$	9.35372	+	13.9988i	0.396330	+	0.593149i	−0.578614	+	0.815602i	$0.696406\pi$
$558$	12.2754	+	4.15084i	0.519658	+	0.175719i
$559$	−3.93564	−	3.93564i	−0.166460	−	0.166460i
$560$	−26.5141	+	1.86309i	−1.12042	+	0.0787301i
$561$	13.5392	−	13.5392i	0.571627	−	0.571627i
$562$	2.51103	−	1.24198i	0.105922	−	0.0523897i
$563$	33.2172	−	22.1950i	1.39994	−	0.935409i	0.400119	−	0.916463i	$-0.368969\pi$
$563$	33.2172	−	22.1950i	1.39994	−	0.935409i	0.999821	−	0.0189460i	$-0.00603105\pi$
$564$	13.6939	−	12.0664i	0.576619	−	0.508085i
$565$	20.6102	−	4.09962i	0.867077	−	0.172472i
$566$	11.9703	+	6.89228i	0.503147	+	0.289704i
$567$	−2.79340	−	1.15706i	−0.117312	−	0.0485922i
$568$	10.9677	+	16.2897i	0.460195	+	0.683499i
$569$	14.9275	−	6.18318i	0.625794	−	0.259212i	−0.0471707	−	0.998887i	$-0.515020\pi$
$569$	14.9275	−	6.18318i	0.625794	−	0.259212i	0.672965	+	0.739674i	$0.265020\pi$
$570$	−6.94212	+	53.2140i	−0.290773	+	2.22889i
$571$	−10.6636	−	7.12517i	−0.446257	−	0.298179i	0.312064	−	0.950061i	$-0.398980\pi$
$571$	−10.6636	−	7.12517i	−0.446257	−	0.298179i	−0.758320	+	0.651882i	$0.773980\pi$
$572$	−6.01383	+	7.87565i	−0.251451	+	0.329298i
$573$	3.49596	−	17.5754i	0.146046	−	0.734223i
$574$	−36.5523	+	2.43893i	−1.52566	+	0.101799i
$575$	12.3535			0.515175
$576$	40.4767	−	0.285549i	1.68653	−	0.0118979i
$577$	−18.6883			−0.778002			−0.389001	−	0.921237i	$-0.627180\pi$
$577$	−18.6883			−0.778002			−0.389001	+	0.921237i	$0.627180\pi$
$578$	8.91340	−	0.594741i	0.370749	−	0.0247380i
$579$	−5.82419	+	29.2802i	−0.242045	+	1.21684i
$580$	−11.8519	−	9.05007i	−0.492123	−	0.375784i
$581$	11.8670	+	7.92928i	0.492327	+	0.328962i
$582$	−4.41093	+	33.8115i	−0.182839	+	1.40153i
$583$	−15.5299	+	6.43271i	−0.643184	+	0.266416i
$584$	−1.97318	+	10.1060i	−0.0816508	+	0.418190i
$585$	35.0648	+	14.5243i	1.44975	+	0.600506i
$586$	14.6841	+	8.45487i	0.606595	+	0.349267i
$587$	16.9938	−	3.38028i	0.701409	−	0.139519i	0.168513	−	0.985699i	$-0.446104\pi$
$587$	16.9938	−	3.38028i	0.701409	−	0.139519i	0.532896	+	0.846180i	$0.321104\pi$
$588$	−9.29392	−	10.5475i	−0.383275	−	0.434973i
$589$	−6.44237	+	4.30465i	−0.265453	+	0.177370i
$590$	−33.7224	+	16.6794i	−1.38833	+	0.686678i
$591$	31.5322	−	31.5322i	1.29706	−	1.29706i
$592$	3.21203	−	9.61060i	0.132014	−	0.394993i
$593$	−5.79685	−	5.79685i	−0.238048	−	0.238048i	0.577993	−	0.816042i	$-0.303836\pi$
$593$	−5.79685	−	5.79685i	−0.238048	−	0.238048i	−0.816042	+	0.577993i	$0.803836\pi$
$594$	16.1648	+	5.46601i	0.663248	+	0.224273i
$595$	12.0664	+	18.0586i	0.494673	+	0.740330i
$596$	8.72395	+	25.5027i	0.357347	+	1.04463i
$597$	−15.2315	−	76.5739i	−0.623384	−	3.13396i
$598$	−8.51010	+	2.29100i	−0.348004	+	0.0936860i
$599$	−6.07554	+	14.6677i	−0.248240	+	0.599304i	−0.998055	−	0.0623435i	$-0.980143\pi$
$599$	−6.07554	+	14.6677i	−0.248240	+	0.599304i	0.749815	+	0.661648i	$0.230143\pi$
$600$	−14.7506	−	35.2589i	−0.602192	−	1.43944i
$601$	−9.70092	−	23.4201i	−0.395709	−	0.955325i	−0.988672	−	0.150095i	$-0.952042\pi$
$601$	−9.70092	−	23.4201i	−0.395709	−	0.955325i	0.592963	−	0.805230i	$-0.297958\pi$
$602$	5.52682	−	4.25121i	0.225256	−	0.173267i
$603$	−41.6333	+	62.3087i	−1.69544	+	2.53741i
$604$	0.974359	−	3.67086i	0.0396461	−	0.149365i
$605$	−20.6580	−	4.10914i	−0.839868	−	0.167060i
$606$	−39.2169	+	44.8245i	−1.59308	+	1.82087i
$607$		−	0.795354i		−	0.0322824i	−0.999870	−	0.0161412i	$-0.994862\pi$
$607$		−	0.795354i		−	0.0322824i	0.999870	−	0.0161412i	$-0.00513813\pi$
$608$	−14.6208	+	19.2879i	−0.592951	+	0.782227i
$609$			14.4117i			0.583991i
$610$	−33.4058	−	29.2267i	−1.35256	−	1.18336i
$611$	7.57000	+	1.50577i	0.306249	+	0.0609168i
$612$	−16.6051	−	28.6053i	−0.671221	−	1.15630i
$613$	−2.28756	+	3.42358i	−0.0923939	+	0.138277i	−0.874787	−	0.484508i	$-0.838999\pi$
$613$	−2.28756	+	3.42358i	−0.0923939	+	0.138277i	0.782393	+	0.622785i	$0.213999\pi$
$614$	−9.95317	−	12.9397i	−0.401677	−	0.522204i
$615$	−41.3350	−	99.7915i	−1.66679	−	4.02398i
$616$	−8.80887	−	8.74694i	−0.354919	−	0.352424i
$617$	−16.1612	+	39.0166i	−0.650626	+	1.57075i	0.161246	+	0.986914i	$0.448449\pi$
$617$	−16.1612	+	39.0166i	−0.650626	+	1.57075i	−0.811872	+	0.583836i	$0.801551\pi$
$618$	−5.85900	−	21.7637i	−0.235683	−	0.875464i
$619$	2.87121	+	14.4345i	0.115404	+	0.580173i	0.994606	+	0.103725i	$0.0330761\pi$
$619$	2.87121	+	14.4345i	0.115404	+	0.580173i	−0.879202	+	0.476448i	$0.841924\pi$
$620$	4.98060	−	10.1598i	0.200026	−	0.408028i
$621$	8.43154	+	12.6187i	0.338346	+	0.506370i
$622$	10.5767	−	31.2788i	0.424087	−	1.25416i
$623$	12.2069	+	12.2069i	0.489059	+	0.489059i
$624$	16.7004	+	21.5537i	0.668550	+	0.862838i
$625$	18.4862	−	18.4862i	0.739448	−	0.739448i
$626$	−1.12662	−	2.27780i	−0.0450288	−	0.0910393i
$627$	−20.8401	+	13.9249i	−0.832274	+	0.556107i
$628$	37.2350	+	2.35259i	1.48584	+	0.0938784i
$629$	−8.12102	+	1.61537i	−0.323806	+	0.0644090i
$630$	−23.7252	+	41.2051i	−0.945236	+	1.64165i
$631$	35.2699	+	14.6093i	1.40407	+	0.581586i	0.950806	−	0.309788i	$-0.100258\pi$
$631$	35.2699	+	14.6093i	1.40407	+	0.581586i	0.453268	+	0.891374i	$0.350258\pi$
$632$	36.5008	+	24.2033i	1.45192	+	0.962754i
$633$	59.2091	−	24.5252i	2.35335	−	0.974790i
$634$	−20.8643	−	2.72188i	−0.828625	−	0.108100i
$635$	0.785496	+	0.524852i	0.0311715	+	0.0208281i
$636$	6.14513	+	45.8436i	0.243670	+	1.81782i
$637$	1.15979	−	5.83067i	0.0459526	−	0.231020i
$638$	−0.463684	−	6.94924i	−0.0183574	−	0.275123i
$639$	35.1296			1.38971
$640$	4.32485	−	35.0791i	0.170955	−	1.38663i
$641$	11.8042			0.466237			0.233119	−	0.972448i	$-0.425107\pi$
$641$	11.8042			0.466237			0.233119	+	0.972448i	$0.425107\pi$
$642$	3.46462	+	51.9243i	0.136738	+	2.04929i
$643$	−2.84656	+	14.3106i	−0.112257	+	0.564355i	0.883188	+	0.469019i	$0.155393\pi$
$643$	−2.84656	+	14.3106i	−0.112257	+	0.564355i	−0.995445	+	0.0953360i	$0.969607\pi$
$644$	−1.46684	−	10.9429i	−0.0578017	−	0.431210i
$645$	17.0941	+	11.4219i	0.673080	+	0.449737i
$646$	19.6109	+	2.55837i	0.771582	+	0.100658i
$647$	−6.76078	+	2.80041i	−0.265794	+	0.110095i	−0.511600	−	0.859224i	$-0.670947\pi$
$647$	−6.76078	+	2.80041i	−0.265794	+	0.110095i	0.245807	+	0.969319i	$0.420947\pi$
$648$	2.22195	−	3.35091i	0.0872866	−	0.131636i
$649$	−16.2337	−	6.72422i	−0.637229	−	0.263949i
$650$	8.06484	−	14.0067i	0.316329	−	0.549389i
$651$	−10.7251	+	2.13336i	−0.420351	+	0.0836130i
$652$	6.61495	+	0.417947i	0.259062	+	0.0163681i
$653$	9.41350	−	6.28990i	0.368379	−	0.246143i	−0.357578	−	0.933883i	$-0.616397\pi$
$653$	9.41350	−	6.28990i	0.368379	−	0.246143i	0.725957	+	0.687741i	$0.241397\pi$
$654$	17.2679	+	34.9124i	0.675230	+	1.36518i
$655$	−11.8965	+	11.8965i	−0.464833	+	0.464833i
$656$	6.13131	−	48.3272i	0.239387	−	1.88686i
$657$	13.0248	+	13.0248i	0.508144	+	0.508144i
$658$	−3.09731	+	9.15974i	−0.120746	+	0.357084i
$659$	−6.27371	−	9.38927i	−0.244389	−	0.365754i	0.688914	−	0.724843i	$-0.258088\pi$
$659$	−6.27371	−	9.38927i	−0.244389	−	0.365754i	−0.933303	+	0.359089i	$0.883088\pi$
$660$	16.1115	−	32.8655i	0.627140	−	1.27929i
$661$	−0.0233980	−	0.117629i	−0.000910075	−	0.00457526i	0.980328	−	0.197377i	$-0.0632424\pi$
$661$	−0.0233980	−	0.117629i	−0.000910075	−	0.00457526i	−0.981238	+	0.192802i	$0.938242\pi$
$662$	2.06640	+	7.67580i	0.0803130	+	0.298329i
$663$	8.52632	−	20.5843i	0.331135	−	0.799430i
$664$	−13.3728	+	13.4675i	−0.518965	+	0.522639i
$665$	−10.8798	−	26.2662i	−0.421901	−	1.01856i
$666$	−11.0519	−	14.3681i	−0.428252	−	0.556753i
$667$	3.44136	−	5.15036i	0.133250	−	0.199423i
$668$	−0.244914	−	0.421909i	−0.00947601	−	0.0163242i
$669$	22.5904	+	4.49352i	0.873396	+	0.173729i
$670$	49.2475	+	43.0866i	1.90260	+	1.66458i
$671$		−	20.7306i		−	0.800298i
$672$	−29.4813	+	17.2529i	−1.13727	+	0.665546i
$673$		−	41.1783i		−	1.58731i	−0.608371	−	0.793653i	$-0.708177\pi$
$673$		−	41.1783i		−	1.58731i	0.608371	−	0.793653i	$-0.291823\pi$
$674$	−2.86814	+	3.27826i	−0.110477	+	0.126274i
$675$	−27.2977	−	5.42984i	−1.05069	−	0.208995i
$676$	3.71209	−	13.9852i	0.142773	−	0.537891i
$677$	−13.0241	+	19.4920i	−0.500557	+	0.749137i	−0.992599	−	0.121435i	$-0.961251\pi$
$677$	−13.0241	+	19.4920i	−0.500557	+	0.749137i	0.492042	+	0.870571i	$0.336251\pi$
$678$	21.4061	−	16.4655i	0.822095	−	0.632353i
$679$	−6.91289	−	16.6892i	−0.265292	−	0.640472i
$680$	−26.6437	+	11.1464i	−1.02174	+	0.427447i
$681$	−12.6204	+	30.4683i	−0.483615	+	1.16755i
$682$	5.10297	−	1.37377i	0.195403	−	0.0526043i
$683$	2.94439	+	14.8024i	0.112664	+	0.566399i	0.995341	+	0.0964191i	$0.0307389\pi$
$683$	2.94439	+	14.8024i	0.112664	+	0.566399i	−0.882677	+	0.469980i	$0.844261\pi$
$684$	14.0135	+	40.9658i	0.535821	+	1.56637i
$685$	29.8862	+	44.7278i	1.14189	+	1.70896i
$686$	27.0018	+	9.13048i	1.03093	+	0.348603i
$687$	−44.3956	−	44.3956i	−1.69380	−	1.69380i
$688$	4.14003	+	8.29656i	0.157837	+	0.316303i
$689$	−13.8309	+	13.8309i	−0.526917	+	0.526917i
$690$	29.1794	−	14.4323i	1.11084	−	0.549430i
$691$	−23.4953	+	15.6991i	−0.893805	+	0.597221i	−0.915400	−	0.402546i	$-0.868125\pi$
$691$	−23.4953	+	15.6991i	−0.893805	+	0.597221i	0.0215953	+	0.999767i	$0.493125\pi$
$692$	19.6193	+	22.2657i	0.745814	+	0.846414i
$693$	−21.7803	+	4.33236i	−0.827364	+	0.164573i
$694$	11.7540	+	6.76777i	0.446176	+	0.256901i
$695$	34.4451	+	14.2676i	1.30658	+	0.541202i
$696$	−18.8092	−	3.67245i	−0.712959	−	0.139204i
$697$	−36.7761	+	15.2332i	−1.39299	+	0.576997i
$698$	0.305144	−	2.33905i	0.0115499	−	0.0885343i
$699$	−3.75975	−	2.51218i	−0.142207	−	0.0950194i
$700$	16.0928	+	12.2884i	0.608249	+	0.464458i
$701$	1.68037	−	8.44781i	0.0634668	−	0.319069i	−0.935990	−	0.352027i	$-0.885493\pi$
$701$	1.68037	−	8.44781i	0.0634668	−	0.319069i	0.999457	+	0.0329575i	$0.0104926\pi$
$702$	19.8119	−	1.32194i	0.747752	−	0.0498932i
$703$	10.8388			0.408792
$704$	13.6607	−	9.26781i	0.514855	−	0.349294i
$705$	−28.5096			−1.07373
$706$	−8.36192	+	0.557944i	−0.314705	+	0.0209985i
$707$	6.15559	−	30.9462i	0.231505	−	1.16385i
$708$	−29.3432	+	38.4275i	−1.10278	+	1.44420i
$709$	−9.70687	−	6.48592i	−0.364549	−	0.243584i	0.359782	−	0.933036i	$-0.382851\pi$
$709$	−9.70687	−	6.48592i	−0.364549	−	0.243584i	−0.724331	+	0.689453i	$0.757851\pi$
$710$	3.96812	−	30.4172i	0.148921	−	1.14154i
$711$	72.3823	−	29.9817i	2.71455	−	1.12440i
$712$	−19.0423	+	12.8210i	−0.713639	+	0.480488i
$713$	4.34231	+	1.79865i	0.162621	+	0.0673598i
$714$	24.1890	+	13.9276i	0.905249	+	0.521228i
$715$	15.1811	−	3.01970i	0.567739	−	0.112930i
$716$	−17.2998	+	15.2437i	−0.646525	+	0.569682i
$717$	−3.57303	+	2.38743i	−0.133437	+	0.0891600i
$718$	39.9277	−	19.7486i	1.49009	−	0.737010i
$719$	−22.6553	+	22.6553i	−0.844899	+	0.844899i	−0.989491	−	0.144592i	$-0.953813\pi$
$719$	−22.6553	+	22.6553i	−0.844899	+	0.844899i	0.144592	+	0.989491i	$0.453813\pi$
$720$	−47.7324	−	41.4647i	−1.77888	−	1.54530i
$721$	8.44310	+	8.44310i	0.314438	+	0.314438i
$722$	0.929831	+	0.314416i	0.0346047	+	0.0117014i
$723$	−25.8498	−	38.6869i	−0.961364	−	1.43878i
$724$	16.0866	−	5.50289i	0.597854	−	0.204513i
$725$	2.21621	+	11.1416i	0.0823080	+	0.413790i
$726$	−26.1382	+	7.03667i	−0.970081	+	0.261155i
$727$	14.7776	−	35.6764i	0.548072	−	1.32316i	−0.370839	−	0.928697i	$-0.620930\pi$
$727$	14.7776	−	35.6764i	0.548072	−	1.32316i	0.918911	−	0.394466i	$-0.129070\pi$
$728$	−13.3650	−	5.48080i	−0.495339	−	0.203132i
$729$	16.3059	+	39.3660i	0.603923	+	1.45800i
$730$	12.7488	−	9.80632i	0.471853	−	0.362948i
$731$	4.20931	−	6.29968i	0.155687	−	0.233002i
$732$	−55.1341	−	14.6343i	−2.03782	−	0.540899i
$733$	12.4550	+	2.47746i	0.460037	+	0.0915071i	0.419668	−	0.907678i	$-0.362147\pi$
$733$	12.4550	+	2.47746i	0.460037	+	0.0915071i	0.0403693	+	0.999185i	$0.487147\pi$
$734$	24.9611	−	28.5303i	0.921331	−	1.05307i
$735$			21.9591i			0.809972i
$736$	14.6557	+	0.874090i	0.540216	+	0.0322194i
$737$			30.5615i			1.12575i
$738$	−65.5861	−	57.3812i	−2.41426	−	2.11223i
$739$	0.370926	+	0.0737817i	0.0136447	+	0.00271410i	0.201908	−	0.979405i	$-0.435286\pi$
$739$	0.370926	+	0.0737817i	0.0136447	+	0.00271410i	−0.188263	+	0.982119i	$0.560286\pi$
$740$	−13.6891	+	7.94636i	−0.503220	+	0.292114i
$741$	−16.2034	+	24.2500i	−0.595245	+	0.890847i
$742$	−14.9399	−	19.4228i	−0.548463	−	0.713033i
$743$	−10.5484	−	25.4660i	−0.386983	−	0.934259i	−0.990576	−	0.136966i	$-0.956265\pi$
$743$	−10.5484	−	25.4660i	−0.386983	−	0.934259i	0.603593	−	0.797292i	$-0.293735\pi$
$744$	−0.0512916	−	14.5414i	−0.00188044	−	0.533112i
$745$	16.1119	−	38.8975i	0.590294	−	1.42510i
$746$	−7.89386	−	29.3224i	−0.289015	−	1.07357i
$747$	6.62354	+	33.2988i	0.242343	+	1.21834i
$748$	−12.1119	−	5.93757i	−0.442855	−	0.217099i
$749$	−15.3167	−	22.9231i	−0.559661	−	0.837591i
$750$	0.965177	−	2.85434i	0.0352433	−	0.104226i
$751$	33.7123	+	33.7123i	1.23018	+	1.23018i	0.963894	+	0.266286i	$0.0857967\pi$
$751$	33.7123	+	33.7123i	1.23018	+	1.23018i	0.266286	+	0.963894i	$0.414203\pi$
$752$	−11.1654	−	6.37653i	−0.407161	−	0.232528i
$753$	−7.73712	+	7.73712i	−0.281956	+	0.281956i
$754$	−3.59297	−	7.26429i	−0.130848	−	0.264550i
$755$	−4.93274	+	3.29595i	−0.179521	+	0.119952i
$756$	−1.56852	+	24.8254i	−0.0570466	+	0.902890i
$757$	0.880215	−	0.175086i	0.0319920	−	0.00636360i	−0.179068	−	0.983837i	$-0.557308\pi$
$757$	0.880215	−	0.175086i	0.0319920	−	0.00636360i	0.211060	+	0.977473i	$0.432308\pi$
$758$	−2.62198	+	4.55376i	−0.0952347	+	0.165400i
$759$	14.0467	+	5.81835i	0.509864	+	0.211193i
$760$	37.0533	−	7.50633i	1.34407	−	0.272283i
$761$	25.8419	−	10.7040i	0.936766	−	0.388021i	0.138525	−	0.990359i	$-0.455764\pi$
$761$	25.8419	−	10.7040i	0.936766	−	0.388021i	0.798241	+	0.602338i	$0.205764\pi$
$762$	1.20389	+	0.157056i	0.0436125	+	0.00568953i
$763$	−17.1569	−	11.4639i	−0.621121	−	0.415020i
$764$	−12.5122	+	1.67721i	−0.452676	+	0.0606792i
$765$	−10.0794	+	50.6724i	−0.364420	+	1.83206i
$766$	1.54032	+	23.0848i	0.0556539	+	0.834087i
$767$	−20.4463			−0.738273
$768$	−15.0048	−	42.8735i	−0.541439	−	1.54707i
$769$	−30.4304			−1.09735			−0.548674	−	0.836036i	$-0.684867\pi$
$769$	−30.4304			−1.09735			−0.548674	+	0.836036i	$0.684867\pi$
$770$	1.29098	+	19.3479i	0.0465236	+	0.697250i
$771$	−6.87294	+	34.5526i	−0.247523	+	1.24438i
$772$	20.8451	−	2.79419i	0.750230	−	0.100565i
$773$	−7.79837	−	5.21070i	−0.280488	−	0.187416i	0.407366	−	0.913265i	$-0.366447\pi$
$773$	−7.79837	−	5.21070i	−0.280488	−	0.187416i	−0.687854	+	0.725849i	$0.741447\pi$
$774$	16.4474	+	2.14567i	0.591188	+	0.0771244i
$775$	−7.96352	+	3.29860i	−0.286058	+	0.118489i
$776$	23.5432	−	4.76942i	0.845151	−	0.171212i
$777$	14.1327	+	5.85396i	0.507008	+	0.210010i
$778$	−18.3820	+	31.9253i	−0.659028	+	1.14458i
$779$	51.1056	−	10.1655i	1.83105	−	0.364218i
$780$	2.68565	−	42.5064i	0.0961617	−	1.52197i
$781$	11.9122	−	7.95949i	0.426253	−	0.284813i
$782$	−5.31874	−	10.7535i	−0.190198	−	0.384543i
$783$	−9.86823	+	9.86823i	−0.352662	+	0.352662i
$784$	−4.91142	+	8.59998i	−0.175408	+	0.307142i
$785$	−41.2089	−	41.2089i	−1.47081	−	1.47081i
$786$	−6.92596	+	20.4823i	−0.247041	+	0.730579i
$787$	19.4919	+	29.1717i	0.694813	+	1.03986i	0.996262	+	0.0863785i	$0.0275294\pi$
$787$	19.4919	+	29.1717i	0.694813	+	1.03986i	−0.301450	+	0.953482i	$0.597471\pi$
$788$	−28.2080	−	13.8283i	−1.00487	−	0.492612i
$789$	−0.980928	−	4.93146i	−0.0349220	−	0.175565i
$790$	−17.7838	−	66.0591i	−0.632718	−	2.35028i
$791$	−5.47512	+	13.2181i	−0.194673	+	0.469982i
$792$	−0.104161	−	29.5301i	−0.00370121	−	1.04931i
$793$	−9.23134	−	22.2864i	−0.327815	−	0.791414i
$794$	3.82148	+	4.96814i	0.135619	+	0.176313i
$795$	40.1398	−	60.0734i	1.42361	−	2.13058i
$796$	−47.5682	+	27.6129i	−1.68601	+	0.978712i
$797$	−11.1662	−	2.22109i	−0.395526	−	0.0786751i	−0.00667994	−	0.999978i	$-0.502126\pi$
$797$	−11.1662	−	2.22109i	−0.395526	−	0.0786751i	−0.388846	+	0.921303i	$0.627126\pi$
$798$	−27.4985	−	24.0584i	−0.973436	−	0.851658i
$799$			10.5066i			0.371698i
$800$	−20.1388	+	17.8718i	−0.712015	+	0.631864i
$801$			41.0658i			1.45099i
$802$	−10.9344	+	12.4979i	−0.386106	+	0.441315i
$803$	7.36769	+	1.46552i	0.260000	+	0.0517172i
$804$	81.2798	+	21.5741i	2.86652	+	0.760861i
$805$	−9.58136	+	14.3395i	−0.337699	+	0.505402i
$806$	4.87420	−	3.74922i	0.171686	−	0.132060i
$807$	34.2839	+	82.7687i	1.20685	+	2.91360i
$808$	38.8204	+	15.9197i	1.36570	+	0.560055i
$809$	−3.82483	+	9.23396i	−0.134474	+	0.324649i	−0.976745	−	0.214406i	$-0.931218\pi$
$809$	−3.82483	+	9.23396i	−0.134474	+	0.324649i	0.842271	+	0.539055i	$0.181218\pi$
$810$	−6.06448	+	1.63262i	−0.213084	+	0.0573644i
$811$	−9.50273	−	47.7735i	−0.333686	−	1.67755i	−0.675168	−	0.737664i	$-0.735929\pi$
$811$	−9.50273	−	47.7735i	−0.333686	−	1.67755i	0.341482	−	0.939888i	$-0.389071\pi$
$812$	9.60627	−	3.28610i	0.337114	−	0.115320i
$813$	3.54134	+	5.29999i	0.124200	+	0.185879i
$814$	−7.00307	−	2.36804i	−0.245457	−	0.0829998i
$815$	−7.32094	−	7.32094i	−0.256441	−	0.256441i
$816$	−24.3413	+	28.0207i	−0.852118	+	0.980922i
$817$	−7.01296	+	7.01296i	−0.245352	+	0.245352i
$818$	−42.8976	+	21.2175i	−1.49988	+	0.741853i
$819$	−21.4856	+	14.3562i	−0.750768	+	0.501647i
$820$	−57.0921	+	50.3064i	−1.99374	+	1.75678i
$821$	13.9146	−	2.76779i	0.485623	−	0.0965965i	0.0537945	−	0.998552i	$-0.482868\pi$
$821$	13.9146	−	2.76779i	0.485623	−	0.0965965i	0.431829	+	0.901956i	$0.357868\pi$
$822$	59.9117	+	34.4962i	2.08966	+	1.20319i
$823$	−42.1742	−	17.4691i	−1.47010	−	0.608935i	−0.503217	−	0.864160i	$-0.667850\pi$
$823$	−42.1742	−	17.4691i	−1.47010	−	0.608935i	−0.966882	+	0.255225i	$0.917850\pi$
$824$	−13.1709	+	8.86787i	−0.458830	+	0.308927i
$825$	−25.7608	+	10.6705i	−0.896876	+	0.371498i
$826$	3.31350	−	25.3993i	0.115291	−	0.883753i
$827$	−18.5286	−	12.3804i	−0.644302	−	0.430509i	0.190025	−	0.981779i	$-0.439143\pi$
$827$	−18.5286	−	12.3804i	−0.644302	−	0.430509i	−0.834326	+	0.551271i	$0.814143\pi$
$828$	15.9394	−	20.8740i	0.553931	−	0.725423i
$829$	−8.53766	+	42.9217i	−0.296525	+	1.49073i	0.489208	+	0.872167i	$0.337286\pi$
$829$	−8.53766	+	42.9217i	−0.296525	+	1.49073i	−0.785733	+	0.618565i	$0.787714\pi$
$830$	29.5801	−	1.97371i	1.02674	−	0.0685086i
$831$	−14.1218			−0.489881
$832$	10.5589	−	16.0464i	0.366064	−	0.556310i
$833$	8.09256			0.280391
$834$	47.8082	−	3.18997i	1.65546	−	0.110460i
$835$	−0.148664	+	0.747383i	−0.00514472	+	0.0258643i
$836$	14.0337	+	10.7161i	0.485366	+	0.370624i
$837$	−8.80471	−	5.88312i	−0.304335	−	0.203350i
$838$	−2.89723	+	22.2084i	−0.100083	+	0.767176i
$839$	−31.4108	+	13.0108i	−1.08442	+	0.449182i	−0.852059	−	0.523446i	$-0.824646\pi$
$839$	−31.4108	+	13.0108i	−1.08442	+	0.449182i	−0.232364	+	0.972629i	$0.574646\pi$
$840$	52.3680	+	10.2248i	1.80687	+	0.352788i
$841$	−21.5300	−	8.91801i	−0.742414	−	0.307518i
$842$	3.13674	+	1.80609i	0.108099	+	0.0622418i
$843$	−5.51560	+	1.09712i	−0.189967	+	0.0377868i
$844$	−29.8482	−	33.8744i	−1.02742	−	1.16600i
$845$	−18.7926	+	12.5568i	−0.646487	+	0.431969i
$846$	−20.6172	+	10.1975i	−0.708835	+	0.350596i
$847$	10.1402	−	10.1402i	0.348421	−	0.348421i
$848$	29.1564	−	14.5492i	1.00124	−	0.499622i
$849$	−19.6069	−	19.6069i	−0.672906	−	0.672906i
$850$	20.8422	+	7.04766i	0.714882	+	0.241733i
$851$	−3.65280	−	5.46680i	−0.125216	−	0.187400i
$852$	−12.7595	−	37.2999i	−0.437134	−	1.27787i
$853$	10.2217	+	51.3880i	0.349984	+	1.75949i	0.608568	+	0.793502i	$0.291744\pi$
$853$	10.2217	+	51.3880i	0.349984	+	1.75949i	−0.258583	+	0.965989i	$0.583256\pi$
$854$	29.1811	−	7.85585i	0.998558	−	0.268822i
$855$	25.8810	−	62.4822i	0.885111	−	2.13685i
$856$	33.8208	−	14.1490i	1.15597	−	0.483603i
$857$	5.90193	+	14.2485i	0.201606	+	0.486720i	0.992055	−	0.125808i	$-0.0401524\pi$
$857$	5.90193	+	14.2485i	0.201606	+	0.486720i	−0.790448	+	0.612529i	$0.790152\pi$
$858$	15.7673	−	12.1282i	0.538287	−	0.414048i
$859$	−32.4534	+	48.5700i	−1.10730	+	1.65719i	−0.484550	+	0.874764i	$0.661017\pi$
$859$	−32.4534	+	48.5700i	−1.10730	+	1.65719i	−0.622747	+	0.782423i	$0.713983\pi$
$860$	3.71567	−	13.9987i	0.126703	−	0.477350i
$861$	72.1270	+	14.3470i	2.45808	+	0.488943i
$862$	−17.4048	+	19.8935i	−0.592811	+	0.677576i
$863$		−	32.8866i		−	1.11947i	−0.828671	−	0.559736i	$-0.810902\pi$
$863$		−	32.8866i		−	1.11947i	0.828671	−	0.559736i	$-0.189098\pi$
$864$	−32.0007	−	8.37325i	−1.08869	−	0.284864i
$865$		−	46.3552i		−	1.57612i
$866$	−8.16250	−	7.14136i	−0.277373	−	0.242673i
$867$	−17.5884	−	3.49855i	−0.597334	−	0.118817i
$868$	3.86753	+	6.66252i	0.131272	+	0.226141i
$869$	17.7512	−	26.5666i	0.602169	−	0.901209i
$870$	18.2514	+	23.7278i	0.618779	+	0.804448i
$871$	13.6090	+	32.8551i	0.461124	+	1.11325i
$872$	19.3339	−	19.4707i	0.654727	−	0.659363i
$873$	16.4444	−	39.7004i	0.556560	−	1.34365i
$874$	4.08236	+	15.1642i	0.138088	+	0.512938i
$875$	0.311417	+	1.56560i	0.0105278	+	0.0529269i
$876$	9.09867	−	18.5602i	0.307415	−	0.627090i
$877$	6.14533	+	9.19714i	0.207513	+	0.310565i	0.920597	−	0.390513i	$-0.127702\pi$
$877$	6.14533	+	9.19714i	0.207513	+	0.310565i	−0.713084	+	0.701078i	$0.752702\pi$
$878$	7.57429	−	22.3996i	0.255620	−	0.755951i
$879$	−24.0520	−	24.0520i	−0.811255	−	0.811255i
$880$	−25.5806	−	3.24543i	−0.862321	−	0.109403i
$881$	11.2198	−	11.2198i	0.378006	−	0.378006i	−0.492376	−	0.870382i	$-0.663872\pi$
$881$	11.2198	−	11.2198i	0.378006	−	0.378006i	0.870382	+	0.492376i	$0.163872\pi$
$882$	7.85442	+	15.8801i	0.264472	+	0.534711i
$883$	29.8483	−	19.9440i	1.00447	−	0.671168i	0.0594714	−	0.998230i	$-0.481059\pi$
$883$	29.8483	−	19.9440i	1.00447	−	0.671168i	0.945003	+	0.327062i	$0.106059\pi$
$884$	−15.6649	−	0.989741i	−0.526867	−	0.0332886i
$885$	74.0727	−	14.7340i	2.48993	−	0.495277i
$886$	−7.44427	+	12.9289i	−0.250095	+	0.434356i
$887$	−32.5314	−	13.4749i	−1.09230	−	0.452444i	−0.237489	−	0.971390i	$-0.576324\pi$
$887$	−32.5314	−	13.4749i	−1.09230	−	0.452444i	−0.854807	+	0.518946i	$0.826324\pi$
$888$	−11.2416	+	16.9533i	−0.377242	+	0.568917i
$889$	−0.594236	+	0.246141i	−0.0199300	+	0.00825529i
$890$	35.5570	+	4.63864i	1.19187	+	0.155488i
$891$	−2.43891	−	1.62963i	−0.0817067	−	0.0545947i
$892$	−2.15579	−	16.0825i	−0.0721811	−	0.538482i
$893$	2.68314	−	13.4891i	0.0897878	−	0.451394i
$894$	−3.60231	−	53.9880i	−0.120479	−	1.80563i
$895$	36.0167			1.20391
$896$	18.2224	+	15.7172i	0.608767	+	0.525074i
$897$	17.6918			0.590713
$898$	1.04442	+	15.6527i	0.0348526	+	0.522337i
$899$	−0.843195	+	4.23903i	−0.0281221	+	0.141379i
$900$	6.39922	+	47.7391i	0.213307	+	1.59130i
$901$	−22.1388	−	14.7927i	−0.737551	−	0.492816i
$902$	−35.2409	−	4.59741i	−1.17339	−	0.153077i
$903$	−12.9319	+	5.35655i	−0.430346	+	0.178255i
$904$	−15.8562	−	10.5141i	−0.527369	−	0.349692i
$905$	−24.5358	−	10.1631i	−0.815597	−	0.337831i
$906$	−3.80435	+	6.60726i	−0.126391	+	0.219512i
$907$	−49.0725	+	9.76113i	−1.62943	+	0.324113i	−0.923331	−	0.384004i	$-0.874545\pi$
$907$	−49.0725	+	9.76113i	−1.62943	+	0.324113i	−0.706095	+	0.708117i	$0.749545\pi$
$908$	23.1867	+	1.46499i	0.769477	+	0.0486173i
$909$	62.4080	−	41.6997i	2.06994	−	1.38309i
$910$	10.0035	+	20.2251i	0.331612	+	0.670454i
$911$	−0.673519	+	0.673519i	−0.0223147	+	0.0223147i	−0.718176	−	0.695861i	$-0.755023\pi$
$911$	−0.673519	+	0.673519i	−0.0223147	+	0.0223147i	0.695861	+	0.718176i	$0.255023\pi$
$912$	38.4067	−	29.7585i	1.27177	−	0.985404i
$913$	9.79066	+	9.79066i	0.324024	+	0.324024i
$914$	−9.95268	+	29.4333i	−0.329205	+	0.973567i
$915$	49.5032	+	74.0868i	1.63653	+	2.44923i
$916$	−19.4695	+	39.7153i	−0.643289	+	1.31223i
$917$	−2.23468	−	11.2345i	−0.0737955	−	0.370995i
$918$	7.02634	+	26.0999i	0.231904	+	0.861425i
$919$	18.8450	−	45.4958i	0.621639	−	1.50077i	−0.228139	−	0.973628i	$-0.573264\pi$
$919$	18.8450	−	45.4958i	0.621639	−	1.50077i	0.849778	−	0.527140i	$-0.176736\pi$
$920$	−16.2734	−	16.1590i	−0.536519	−	0.532747i
$921$	12.5411	+	30.2768i	0.413242	+	0.997654i
$922$	19.8809	+	25.8463i	0.654741	+	0.851201i
$923$	9.26185	−	13.8613i	0.304857	−	0.456251i
$924$	12.5109	+	21.5523i	0.411577	+	0.709017i
$925$	11.8262	+	2.35238i	0.388843	+	0.0773456i
$926$	−13.8334	−	12.1028i	−0.454594	−	0.397724i
$927$			28.4038i			0.932904i
$928$	1.84089	+	13.3748i	0.0604300	+	0.439051i
$929$		−	37.0292i		−	1.21489i	−0.794362	−	0.607445i	$-0.792195\pi$
$929$		−	37.0292i		−	1.21489i	0.794362	−	0.607445i	$-0.207805\pi$
$930$	−14.9564	+	17.0951i	−0.490441	+	0.560569i
$931$	−10.3897	−	2.06664i	−0.340510	−	0.0677316i
$932$	−0.817239	+	3.07892i	−0.0267696	+	0.100853i
$933$	−36.8250	+	55.1124i	−1.20559	+	1.80430i
$934$	−0.644955	+	0.496097i	−0.0211036	+	0.0162328i
$935$	8.06323	+	19.4664i	0.263696	+	0.636618i
$936$	−13.2617	−	31.6999i	−0.433473	−	1.03614i
$937$	−13.0321	+	31.4623i	−0.425740	+	1.02783i	0.554884	+	0.831928i	$0.312763\pi$
$937$	−13.0321	+	31.4623i	−0.425740	+	1.02783i	−0.980624	+	0.195900i	$0.937237\pi$
$938$	−43.0194	+	11.5812i	−1.40463	+	0.378141i
$939$	0.995217	+	5.00329i	0.0324777	+	0.163276i
$940$	6.50066	+	19.0034i	0.212028	+	0.619822i
$941$	−14.1954	−	21.2450i	−0.462758	−	0.692566i	0.524551	−	0.851379i	$-0.324233\pi$
$941$	−14.1954	−	21.2450i	−0.462758	−	0.692566i	−0.987309	+	0.158813i	$0.949233\pi$
$942$	−70.9499	−	23.9912i	−2.31167	−	0.781677i
$943$	−22.3504	−	22.3504i	−0.727831	−	0.727831i
$944$	32.3051	+	10.7969i	1.05144	+	0.351410i
$945$	27.4749	−	27.4749i	0.893758	−	0.893758i
$946$	6.06334	−	2.99898i	0.197136	−	0.0975051i
$947$	−43.8404	+	29.2932i	−1.42462	+	0.951902i	−0.425730	+	0.904850i	$0.639983\pi$
$947$	−43.8404	+	29.2932i	−1.42462	+	0.951902i	−0.998892	+	0.0470518i	$0.985017\pi$
$948$	−58.1241	−	65.9642i	−1.88778	−	2.14242i
$949$	8.57321	−	1.70532i	0.278298	−	0.0553570i
$950$	−24.9587	−	14.3708i	−0.809768	−	0.466251i
$951$	39.0236	+	16.1641i	1.26543	+	0.524157i
$952$	3.76812	−	19.2992i	0.122126	−	0.625489i
$953$	2.18380	−	0.904560i	0.0707403	−	0.0293016i	−0.347033	−	0.937853i	$-0.612811\pi$
$953$	2.18380	−	0.904560i	0.0707403	−	0.0293016i	0.417773	+	0.908551i	$0.362811\pi$
$954$	7.54047	−	57.8006i	0.244132	−	1.87136i
$955$	16.3960	+	10.9555i	0.530562	+	0.354510i
$956$	2.40608	+	1.83728i	0.0778181	+	0.0594217i
$957$	−2.72761	+	13.7126i	−0.0881711	+	0.443266i
$958$	46.5670	−	3.10715i	1.50451	−	0.100388i
$959$	−36.6250			−1.18268
$960$	−26.6893	+	65.7417i	−0.861395	+	2.12181i
$961$	27.7205			0.894210
$962$	−8.58312	+	0.572703i	−0.276731	+	0.0184647i
$963$	12.7945	−	64.3221i	0.412296	−	2.07275i
$964$	−19.8931	+	26.0517i	−0.640712	+	0.839070i
$965$	−27.3153	−	18.2515i	−0.879312	−	0.587537i
$966$	−2.86711	+	21.9775i	−0.0922478	+	0.707115i
$967$	44.4518	−	18.4125i	1.42947	−	0.592107i	0.472251	−	0.881464i	$-0.343441\pi$
$967$	44.4518	−	18.4125i	1.42947	−	0.592107i	0.957221	+	0.289357i	$0.0934415\pi$
$968$	10.6503	+	15.8183i	0.342314	+	0.508418i
$969$	−36.6794	−	15.1931i	−1.17831	−	0.488074i
$970$	−32.5172	−	18.7229i	−1.04407	−	0.601156i
$971$	−8.20968	+	1.63301i	−0.263461	+	0.0524057i	−0.325053	−	0.945696i	$-0.605382\pi$
$971$	−8.20968	+	1.63301i	−0.263461	+	0.0524057i	0.0615920	+	0.998101i	$0.480382\pi$
$972$	20.2678	−	17.8588i	0.650088	−	0.572822i
$973$	−21.1059	+	14.1025i	−0.676625	+	0.452106i
$974$	−47.9622	+	23.7225i	−1.53681	+	0.760118i
$975$	−22.9425	+	22.9425i	−0.734749	+	0.734749i
$976$	2.81685	+	40.0872i	0.0901653	+	1.28316i
$977$	13.9697	+	13.9697i	0.446930	+	0.446930i	0.894333	−	0.447403i	$-0.147651\pi$
$977$	13.9697	+	13.9697i	0.446930	+	0.446930i	−0.447403	+	0.894333i	$0.647651\pi$
$978$	−12.6046	−	4.26215i	−0.403049	−	0.136289i
$979$	9.30447	+	13.9251i	0.297372	+	0.445049i
$980$	14.6371	−	5.00703i	0.467564	−	0.159944i
$981$	−9.57607	−	48.1421i	−0.305740	−	1.53706i
$982$	−28.9627	+	7.79703i	−0.924236	+	0.248813i
$983$	−18.1142	+	43.7315i	−0.577753	+	1.39482i	0.317072	+	0.948401i	$0.397300\pi$
$983$	−18.1142	+	43.7315i	−0.577753	+	1.39482i	−0.894825	+	0.446417i	$0.852700\pi$
$984$	−37.1045	+	90.4795i	−1.18285	+	2.88438i
$985$	18.7788	+	45.3361i	0.598344	+	1.44453i
$986$	8.74440	−	6.72617i	0.278479	−	0.214205i
$987$	10.7839	−	16.1392i	0.343255	−	0.513718i
$988$	19.8588	+	5.27112i	0.631792	+	0.167697i
$989$	5.90061	+	1.17370i	0.187628	+	0.0373216i
$990$	−30.3731	+	34.7161i	−0.965319	+	1.10335i
$991$		−	14.8761i		−	0.472553i	−0.971686	−	0.236277i	$-0.924073\pi$
$991$		−	14.8761i		−	0.472553i	0.971686	−	0.236277i	$-0.0759272\pi$
$992$	−9.68102	+	3.34986i	−0.307373	+	0.106358i
$993$		−	15.9574i		−	0.506392i
$994$	15.7182	+	13.7518i	0.498550	+	0.436181i
$995$	84.2638	+	16.7611i	2.67134	+	0.531363i
$996$	32.9502	−	19.1273i	1.04407	−	0.606071i
$997$	17.6104	−	26.3559i	0.557728	−	0.834698i	−0.440276	−	0.897863i	$-0.645119\pi$
$997$	17.6104	−	26.3559i	0.557728	−	0.834698i	0.998003	+	0.0631644i	$0.0201193\pi$
$998$	35.4737	+	46.1178i	1.12290	+	1.45983i
$999$	5.66878	+	13.6856i	0.179352	+	0.432994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.61.4	yes	56
3.2	odd	2		576.2.bd.a.253.4		56
4.3	odd	2		256.2.i.a.81.1		56
8.3	odd	2		512.2.i.a.417.7		56
8.5	even	2		512.2.i.b.417.1		56
64.11	odd	16		512.2.i.a.97.7		56
64.21	even	16	inner	64.2.i.a.21.4	✓	56
64.43	odd	16		256.2.i.a.177.1		56
64.53	even	16		512.2.i.b.97.1		56
192.149	odd	16		576.2.bd.a.469.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.4	✓	56	64.21	even	16	inner
64.2.i.a.61.4	yes	56	1.1	even	1	trivial
256.2.i.a.81.1		56	4.3	odd	2
256.2.i.a.177.1		56	64.43	odd	16
512.2.i.a.97.7		56	64.11	odd	16
512.2.i.a.417.7		56	8.3	odd	2
512.2.i.b.97.1		56	64.53	even	16
512.2.i.b.417.1		56	8.5	even	2
576.2.bd.a.253.4		56	3.2	odd	2
576.2.bd.a.469.4		56	192.149	odd	16

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0941531 + 1.41108i) q^{2} +(0.553854 - 2.78441i) q^{3} +(-1.98227 + 0.265714i) q^{4} +(2.59756 + 1.73564i) q^{5} +(3.98116 + 0.519369i) q^{6} +(-1.96508 + 0.813965i) q^{7} +(-0.561580 - 2.77212i) q^{8} +(-4.67456 - 1.93627i) q^{9} +O(q^{10})\)	\(q+(0.0941531 + 1.41108i) q^{2} +(0.553854 - 2.78441i) q^{3} +(-1.98227 + 0.265714i) q^{4} +(2.59756 + 1.73564i) q^{5} +(3.98116 + 0.519369i) q^{6} +(-1.96508 + 0.813965i) q^{7} +(-0.561580 - 2.77212i) q^{8} +(-4.67456 - 1.93627i) q^{9} +(-2.20455 + 3.82878i) q^{10} +(-2.02382 + 0.402563i) q^{11} +(-0.358030 + 5.66663i) q^{12} +(-1.99644 + 1.33398i) q^{13} +(-1.33358 - 2.69625i) q^{14} +(6.27140 - 6.27140i) q^{15} +(3.85879 - 1.05344i) q^{16} +(-2.31120 - 2.31120i) q^{17} +(2.29209 - 6.77846i) q^{18} +(2.37703 + 3.55748i) q^{19} +(-5.61026 - 2.75029i) q^{20} +(1.17804 + 5.92242i) q^{21} +(-0.758596 - 2.81786i) q^{22} +(0.993213 - 2.39783i) q^{23} +(-8.02975 + 0.0283233i) q^{24} +(1.82149 + 4.39746i) q^{25} +(-2.07032 - 2.69153i) q^{26} +(-3.24866 + 4.86196i) q^{27} +(3.67905 - 2.13565i) q^{28} +(2.34079 + 0.465613i) q^{29} +(9.43989 + 8.25895i) q^{30} +1.81094i q^{31} +(1.84980 + 5.34586i) q^{32} +5.85811i q^{33} +(3.04367 - 3.47888i) q^{34} +(-6.51718 - 1.29635i) q^{35} +(9.78074 + 2.59610i) q^{36} +(1.40742 - 2.10635i) q^{37} +(-4.79607 + 3.68912i) q^{38} +(2.60861 + 6.29775i) q^{39} +(3.35265 - 8.17545i) q^{40} +(4.66056 - 11.2516i) q^{41} +(-8.24607 + 2.21992i) q^{42} +(0.452227 + 2.27350i) q^{43} +(3.90479 - 1.33575i) q^{44} +(-8.78181 - 13.1429i) q^{45} +(3.47703 + 1.17574i) q^{46} +(-2.27298 - 2.27298i) q^{47} +(-0.795992 - 11.3279i) q^{48} +(-1.75073 + 1.75073i) q^{49} +(-6.03365 + 2.98429i) q^{50} +(-7.71539 + 5.15526i) q^{51} +(3.60303 - 3.17479i) q^{52} +(7.98970 - 1.58925i) q^{53} +(-7.16647 - 4.12634i) q^{54} +(-5.95570 - 2.46693i) q^{55} +(3.35996 + 4.99034i) q^{56} +(11.2220 - 4.64831i) q^{57} +(-0.436622 + 3.34687i) q^{58} +(7.08029 + 4.73090i) q^{59} +(-10.7652 + 14.0980i) q^{60} +(-1.95998 + 9.85346i) q^{61} +(-2.55537 + 0.170505i) q^{62} +10.7620 q^{63} +(-7.36926 + 3.11353i) q^{64} -7.50119 q^{65} +(-8.26624 + 0.551559i) q^{66} +(2.88943 - 14.5262i) q^{67} +(5.19553 + 3.96730i) q^{68} +(-6.12645 - 4.09356i) q^{69} +(1.21563 - 9.31829i) q^{70} +(-6.41451 + 2.65698i) q^{71} +(-2.74241 + 14.0458i) q^{72} +(-3.36337 - 1.39315i) q^{73} +(3.10474 + 1.78766i) q^{74} +(13.2532 - 2.63622i) q^{75} +(-5.65719 - 6.42027i) q^{76} +(3.64930 - 2.43839i) q^{77} +(-8.64099 + 4.27390i) q^{78} +(-10.9490 + 10.9490i) q^{79} +(11.8518 + 3.96109i) q^{80} +(1.00516 + 1.00516i) q^{81} +(16.3157 + 5.51703i) q^{82} +(-3.72793 - 5.57925i) q^{83} +(-3.90887 - 11.4268i) q^{84} +(-1.99208 - 10.0149i) q^{85} +(-3.16550 + 0.852183i) q^{86} +(2.59292 - 6.25985i) q^{87} +(2.25249 + 5.38419i) q^{88} +(-3.10595 - 7.49842i) q^{89} +(17.7188 - 13.6293i) q^{90} +(2.83736 - 4.24642i) q^{91} +(-1.33168 + 5.01705i) q^{92} +(5.04240 + 1.00299i) q^{93} +(2.99334 - 3.42136i) q^{94} +13.3664i q^{95} +(15.9096 - 2.18976i) q^{96} +8.49286i q^{97} +(-2.63525 - 2.30558i) q^{98} +(10.2399 + 2.03685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more