LMFDB - Embedded newform 64.2.i.a.61.3

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			61.3
Character	$\chi$	$=$	64.61
Dual form			64.2.i.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.887839 + 1.10079i) q^{2} +(-0.435353 + 2.18867i) q^{3} +(-0.423482 - 1.95465i) q^{4} +(0.649649 + 0.434082i) q^{5} +(-2.02274 - 2.42242i) q^{6} +(-3.64486 + 1.50975i) q^{7} +(2.52765 + 1.26925i) q^{8} +(-1.82909 - 0.757635i) q^{9} +O(q^{10})$	\(q+(-0.887839 + 1.10079i) q^{2} +(-0.435353 + 2.18867i) q^{3} +(-0.423482 - 1.95465i) q^{4} +(0.649649 + 0.434082i) q^{5} +(-2.02274 - 2.42242i) q^{6} +(-3.64486 + 1.50975i) q^{7} +(2.52765 + 1.26925i) q^{8} +(-1.82909 - 0.757635i) q^{9} +(-1.05462 + 0.329733i) q^{10} +(5.80194 - 1.15408i) q^{11} +(4.46245 - 0.0758981i) q^{12} +(2.03484 - 1.35963i) q^{13} +(1.57413 - 5.35264i) q^{14} +(-1.23289 + 1.23289i) q^{15} +(-3.64133 + 1.65552i) q^{16} +(0.960477 + 0.960477i) q^{17} +(2.45794 - 1.34079i) q^{18} +(0.435978 + 0.652487i) q^{19} +(0.573364 - 1.45366i) q^{20} +(-1.71754 - 8.63465i) q^{21} +(-3.88079 + 7.41136i) q^{22} +(0.421603 - 1.01784i) q^{23} +(-3.87839 + 4.97961i) q^{24} +(-1.67980 - 4.05540i) q^{25} +(-0.309935 + 3.44707i) q^{26} +(-1.26483 + 1.89295i) q^{27} +(4.49456 + 6.48507i) q^{28} +(-1.43977 - 0.286388i) q^{29} +(-0.262545 - 2.45176i) q^{30} -6.88004i q^{31} +(1.41053 - 5.47818i) q^{32} +13.2009i q^{33} +(-1.91003 + 0.204535i) q^{34} +(-3.02323 - 0.601358i) q^{35} +(-0.706324 + 3.89608i) q^{36} +(-1.07856 + 1.61417i) q^{37} +(-1.10533 - 0.0993831i) q^{38} +(2.08991 + 5.04550i) q^{39} +(1.09113 + 1.92177i) q^{40} +(-2.79324 + 6.74347i) q^{41} +(11.0298 + 5.77553i) q^{42} +(-1.20307 - 6.04824i) q^{43} +(-4.71284 - 10.8520i) q^{44} +(-0.859393 - 1.28617i) q^{45} +(0.746114 + 1.36778i) q^{46} +(-6.30014 - 6.30014i) q^{47} +(-2.03812 - 8.69038i) q^{48} +(6.05588 - 6.05588i) q^{49} +(5.95554 + 1.75143i) q^{50} +(-2.52031 + 1.68402i) q^{51} +(-3.51933 - 3.40161i) q^{52} +(10.2655 - 2.04194i) q^{53} +(-0.960779 - 3.07295i) q^{54} +(4.27019 + 1.76877i) q^{55} +(-11.1292 - 0.810126i) q^{56} +(-1.61788 + 0.670148i) q^{57} +(1.59354 - 1.33062i) q^{58} +(4.21278 + 2.81489i) q^{59} +(2.93197 + 1.88776i) q^{60} +(-2.08276 + 10.4707i) q^{61} +(7.57348 + 6.10837i) q^{62} +7.81061 q^{63} +(4.77800 + 6.41644i) q^{64} +1.91212 q^{65} +(-14.5315 - 11.7203i) q^{66} +(1.42195 - 7.14864i) q^{67} +(1.47065 - 2.28414i) q^{68} +(2.04417 + 1.36587i) q^{69} +(3.34611 - 2.79404i) q^{70} +(2.49385 - 1.03299i) q^{71} +(-3.66167 - 4.23661i) q^{72} +(-1.90488 - 0.789026i) q^{73} +(-0.819282 - 2.62039i) q^{74} +(9.60722 - 1.91099i) q^{75} +(1.09076 - 1.12850i) q^{76} +(-19.4049 + 12.9659i) q^{77} +(-7.40955 - 2.17903i) q^{78} +(-6.20432 + 6.20432i) q^{79} +(-3.08422 - 0.505126i) q^{80} +(-7.79217 - 7.79217i) q^{81} +(-4.94320 - 9.06188i) q^{82} +(1.13685 + 1.70141i) q^{83} +(-16.1504 + 7.01381i) q^{84} +(0.207047 + 1.04090i) q^{85} +(7.72599 + 4.04554i) q^{86} +(1.25361 - 3.02649i) q^{87} +(16.1301 + 4.44702i) q^{88} +(1.15743 + 2.79429i) q^{89} +(2.17881 + 0.195902i) q^{90} +(-5.36398 + 8.02776i) q^{91} +(-2.16806 - 0.393050i) q^{92} +(15.0581 + 2.99524i) q^{93} +(12.5287 - 1.34163i) q^{94} +0.613137i q^{95} +(11.3758 + 5.47212i) q^{96} -13.1193i q^{97} +(1.28961 + 12.0429i) q^{98} +(-11.4867 - 2.28484i) 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 $

$2$	−0.887839	+	1.10079i	−0.627797	+	0.778377i
$2$	−0.887839	+	1.10079i	−0.627797	+	0.778377i
$3$	−0.435353	+	2.18867i	−0.251351	+	1.26363i	0.624492	+	0.781031i	$0.285306\pi$
$3$	−0.435353	+	2.18867i	−0.251351	+	1.26363i	−0.875843	+	0.482596i	$0.839694\pi$
$4$	−0.423482	−	1.95465i	−0.211741	−	0.977326i
$5$	0.649649	+	0.434082i	0.290532	+	0.194127i	0.692292	−	0.721618i	$-0.256601\pi$
$5$	0.649649	+	0.434082i	0.290532	+	0.194127i	−0.401760	+	0.915745i	$0.631601\pi$
$6$	−2.02274	−	2.42242i	−0.825781	−	0.988948i
$7$	−3.64486	+	1.50975i	−1.37763	+	0.570631i	−0.943845	−	0.330387i	$-0.892821\pi$
$7$	−3.64486	+	1.50975i	−1.37763	+	0.570631i	−0.433780	+	0.901019i	$0.642821\pi$
$8$	2.52765	+	1.26925i	0.893658	+	0.448748i
$9$	−1.82909	−	0.757635i	−0.609697	−	0.252545i
$10$	−1.05462	+	0.329733i	−0.333499	+	0.104271i
$11$	5.80194	−	1.15408i	1.74935	−	0.347968i	0.786415	−	0.617698i	$-0.211935\pi$
$11$	5.80194	−	1.15408i	1.74935	−	0.347968i	0.962936	+	0.269730i	$0.0869346\pi$
$12$	4.46245	−	0.0758981i	1.28820	−	0.0219099i
$13$	2.03484	−	1.35963i	0.564362	−	0.377095i	−0.240417	−	0.970670i	$-0.577284\pi$
$13$	2.03484	−	1.35963i	0.564362	−	0.377095i	0.804779	+	0.593575i	$0.202284\pi$
$14$	1.57413	−	5.35264i	0.420704	−	1.43055i
$15$	−1.23289	+	1.23289i	−0.318330	+	0.318330i
$16$	−3.64133	+	1.65552i	−0.910331	+	0.413880i
$17$	0.960477	+	0.960477i	0.232950	+	0.232950i	0.813923	−	0.580973i	$-0.197328\pi$
$17$	0.960477	+	0.960477i	0.232950	+	0.232950i	−0.580973	+	0.813923i	$0.697328\pi$
$18$	2.45794	−	1.34079i	0.579341	−	0.316027i
$19$	0.435978	+	0.652487i	0.100020	+	0.149691i	0.878104	−	0.478469i	$-0.158808\pi$
$19$	0.435978	+	0.652487i	0.100020	+	0.149691i	−0.778084	+	0.628160i	$0.783808\pi$
$20$	0.573364	−	1.45366i	0.128208	−	0.325049i
$21$	−1.71754	−	8.63465i	−0.374798	−	1.88423i
$22$	−3.88079	+	7.41136i	−0.827388	+	1.58011i
$23$	0.421603	−	1.01784i	0.0879104	−	0.212234i	−0.873810	−	0.486268i	$-0.838358\pi$
$23$	0.421603	−	1.01784i	0.0879104	−	0.212234i	0.961720	+	0.274033i	$0.0883579\pi$
$24$	−3.87839	+	4.97961i	−0.791672	+	1.01646i
$25$	−1.67980	−	4.05540i	−0.335960	−	0.811079i
$26$	−0.309935	+	3.44707i	−0.0607832	+	0.676025i
$27$	−1.26483	+	1.89295i	−0.243417	+	0.364299i
$28$	4.49456	+	6.48507i	0.849393	+	1.22556i
$29$	−1.43977	−	0.286388i	−0.267358	−	0.0531809i	0.0595906	−	0.998223i	$-0.481020\pi$
$29$	−1.43977	−	0.286388i	−0.267358	−	0.0531809i	−0.326949	+	0.945042i	$0.606020\pi$
$30$	−0.262545	−	2.45176i	−0.0479340	−	0.447627i
$31$		−	6.88004i		−	1.23569i	−0.786300	−	0.617845i	$-0.788006\pi$
$31$		−	6.88004i		−	1.23569i	0.786300	−	0.617845i	$-0.211994\pi$
$32$	1.41053	−	5.47818i	0.249349	−	0.968414i
$33$			13.2009i			2.29799i
$34$	−1.91003	+	0.204535i	−0.327568	+	0.0350775i
$35$	−3.02323	−	0.601358i	−0.511019	−	0.101648i
$36$	−0.706324	+	3.89608i	−0.117721	+	0.649347i
$37$	−1.07856	+	1.61417i	−0.177313	+	0.265368i	−0.909471	−	0.415767i	$-0.863513\pi$
$37$	−1.07856	+	1.61417i	−0.177313	+	0.265368i	0.732158	+	0.681135i	$0.238513\pi$
$38$	−1.10533	−	0.0993831i	−0.179308	−	0.0161221i
$39$	2.08991	+	5.04550i	0.334654	+	0.807926i
$40$	1.09113	+	1.92177i	0.172522	+	0.303859i
$41$	−2.79324	+	6.74347i	−0.436230	+	1.05315i	0.541010	+	0.841016i	$0.318042\pi$
$41$	−2.79324	+	6.74347i	−0.436230	+	1.05315i	−0.977240	+	0.212136i	$0.931958\pi$
$42$	11.0298	+	5.77553i	1.70194	+	0.891184i
$43$	−1.20307	−	6.04824i	−0.183467	−	0.922349i	−0.957330	−	0.288996i	$-0.906678\pi$
$43$	−1.20307	−	6.04824i	−0.183467	−	0.922349i	0.773864	−	0.633352i	$-0.218322\pi$
$44$	−4.71284	−	10.8520i	−0.710487	−	1.63601i
$45$	−0.859393	−	1.28617i	−0.128111	−	0.191731i
$46$	0.746114	+	1.36778i	0.110008	+	0.201668i
$47$	−6.30014	−	6.30014i	−0.918970	−	0.918970i	0.0779845	−	0.996955i	$-0.475152\pi$
$47$	−6.30014	−	6.30014i	−0.918970	−	0.918970i	−0.996955	+	0.0779845i	$0.975152\pi$
$48$	−2.03812	−	8.69038i	−0.294177	−	1.25435i
$49$	6.05588	−	6.05588i	0.865126	−	0.865126i
$50$	5.95554	+	1.75143i	0.842240	+	0.247690i
$51$	−2.52031	+	1.68402i	−0.352914	+	0.235810i
$52$	−3.51933	−	3.40161i	−0.488043	−	0.471719i
$53$	10.2655	−	2.04194i	1.41008	−	0.280482i	0.569421	−	0.822046i	$-0.307168\pi$
$53$	10.2655	−	2.04194i	1.41008	−	0.280482i	0.840660	+	0.541564i	$0.182168\pi$
$54$	−0.960779	−	3.07295i	−0.130745	−	0.418176i
$55$	4.27019	+	1.76877i	0.575792	+	0.238501i
$56$	−11.1292	−	0.810126i	−1.48720	−	0.108258i
$57$	−1.61788	+	0.670148i	−0.214293	+	0.0887632i
$58$	1.59354	−	1.33062i	0.209242	−	0.174719i
$59$	4.21278	+	2.81489i	0.548458	+	0.366468i	0.798713	−	0.601712i	$-0.205515\pi$
$59$	4.21278	+	2.81489i	0.548458	+	0.366468i	−0.250255	+	0.968180i	$0.580515\pi$
$60$	2.93197	+	1.88776i	0.378516	+	0.243709i
$61$	−2.08276	+	10.4707i	−0.266670	+	1.34064i	0.582633	+	0.812736i	$0.302023\pi$
$61$	−2.08276	+	10.4707i	−0.266670	+	1.34064i	−0.849303	+	0.527906i	$0.822977\pi$
$62$	7.57348	+	6.10837i	0.961833	+	0.775763i
$63$	7.81061			0.984045
$64$	4.77800	+	6.41644i	0.597250	+	0.802055i
$65$	1.91212			0.237169
$66$	−14.5315	−	11.7203i	−1.78870	−	1.44267i
$67$	1.42195	−	7.14864i	0.173719	−	0.873345i	−0.791353	−	0.611360i	$-0.790623\pi$
$67$	1.42195	−	7.14864i	0.173719	−	0.873345i	0.965072	−	0.261985i	$-0.0843771\pi$
$68$	1.47065	−	2.28414i	0.178343	−	0.276993i
$69$	2.04417	+	1.36587i	0.246089	+	0.164431i
$70$	3.34611	−	2.79404i	0.399937	−	0.333951i
$71$	2.49385	−	1.03299i	0.295965	−	0.122593i	−0.229760	−	0.973247i	$-0.573794\pi$
$71$	2.49385	−	1.03299i	0.295965	−	0.122593i	0.525725	+	0.850655i	$0.323794\pi$
$72$	−3.66167	−	4.23661i	−0.431532	−	0.499289i
$73$	−1.90488	−	0.789026i	−0.222949	−	0.0923485i	0.268413	−	0.963304i	$-0.413501\pi$
$73$	−1.90488	−	0.789026i	−0.222949	−	0.0923485i	−0.491362	+	0.870955i	$0.663501\pi$
$74$	−0.819282	−	2.62039i	−0.0952396	−	0.304614i
$75$	9.60722	−	1.91099i	1.10935	−	0.220663i
$76$	1.09076	−	1.12850i	0.125118	−	0.129448i
$77$	−19.4049	+	12.9659i	−2.21139	+	1.47760i
$78$	−7.40955	−	2.17903i	−0.838966	−	0.246727i
$79$	−6.20432	+	6.20432i	−0.698040	+	0.698040i	−0.963988	−	0.265947i	$-0.914315\pi$
$79$	−6.20432	+	6.20432i	−0.698040	+	0.698040i	0.265947	+	0.963988i	$0.414315\pi$
$80$	−3.08422	−	0.505126i	−0.344826	−	0.0564748i
$81$	−7.79217	−	7.79217i	−0.865797	−	0.865797i
$82$	−4.94320	−	9.06188i	−0.545885	−	1.00072i
$83$	1.13685	+	1.70141i	0.124785	+	0.186755i	0.888602	−	0.458678i	$-0.151677\pi$
$83$	1.13685	+	1.70141i	0.124785	+	0.186755i	−0.763817	+	0.645433i	$0.776677\pi$
$84$	−16.1504	+	7.01381i	−1.76215	+	0.765269i
$85$	0.207047	+	1.04090i	0.0224575	+	0.112901i
$86$	7.72599	+	4.04554i	0.833115	+	0.436242i
$87$	1.25361	−	3.02649i	0.134402	−	0.324474i
$88$	16.1301	+	4.44702i	1.71947	+	0.474054i
$89$	1.15743	+	2.79429i	0.122688	+	0.296194i	0.973276	−	0.229638i	$-0.0737541\pi$
$89$	1.15743	+	2.79429i	0.122688	+	0.296194i	−0.850589	+	0.525832i	$0.823754\pi$
$90$	2.17881	+	0.195902i	0.229667	+	0.0206499i
$91$	−5.36398	+	8.02776i	−0.562298	+	0.841538i
$92$	−2.16806	−	0.393050i	−0.226036	−	0.0409783i
$93$	15.0581	+	2.99524i	1.56145	+	0.310592i
$94$	12.5287	−	1.34163i	1.29223	−	0.138378i
$95$			0.613137i			0.0629066i
$96$	11.3758	+	5.47212i	1.16104	+	0.558496i
$97$		−	13.1193i		−	1.33207i	−0.745922	−	0.666034i	$-0.767991\pi$
$97$		−	13.1193i		−	1.33207i	0.745922	−	0.666034i	$-0.232009\pi$
$98$	1.28961	+	12.0429i	0.130270	+	1.21652i
$99$	−11.4867	−	2.28484i	−1.15445	−	0.229635i
$100$	−7.21552	+	5.00081i	−0.721552	+	0.500081i
$101$	−2.49376	+	3.73217i	−0.248138	+	0.371365i	−0.934540	−	0.355857i	$-0.884189\pi$
$101$	−2.49376	+	3.73217i	−0.248138	+	0.371365i	0.686402	+	0.727222i	$0.259189\pi$
$102$	0.383879	−	4.26947i	0.0380097	−	0.422741i
$103$	4.09230	+	9.87970i	0.403227	+	0.973476i	0.986878	+	0.161471i	$0.0516237\pi$
$103$	4.09230	+	9.87970i	0.403227	+	0.973476i	−0.583651	+	0.812005i	$0.698376\pi$
$104$	6.86906	−	0.853956i	0.673567	−	0.0837373i
$105$	2.63235	−	6.35504i	0.256891	−	0.620189i
$106$	−6.86640	+	13.1131i	−0.666924	+	1.27366i
$107$	0.745466	+	3.74771i	0.0720669	+	0.362305i	0.999944	−	0.0105812i	$-0.00336817\pi$
$107$	0.745466	+	3.74771i	0.0720669	+	0.362305i	−0.927877	+	0.372886i	$0.878368\pi$
$108$	4.23570	+	1.67067i	0.407580	+	0.160760i
$109$	−5.47688	−	8.19674i	−0.524590	−	0.785105i	0.470674	−	0.882307i	$-0.344011\pi$
$109$	−5.47688	−	8.19674i	−0.524590	−	0.785105i	−0.995265	+	0.0972021i	$0.969011\pi$
$110$	−5.73829	+	3.13020i	−0.547125	+	0.298453i
$111$	−3.06333	−	3.06333i	−0.290759	−	0.290759i
$112$	10.7727	−	11.5316i	1.01792	−	1.08964i
$113$	−3.26239	+	3.26239i	−0.306900	+	0.306900i	−0.843706	−	0.536806i	$-0.819631\pi$
$113$	−3.26239	+	3.26239i	−0.306900	+	0.306900i	0.536806	+	0.843706i	$0.319631\pi$
$114$	0.698725	−	2.37593i	0.0654416	−	0.222526i
$115$	0.715720	−	0.478229i	0.0667412	−	0.0445951i
$116$	0.0499280	+	2.93552i	0.00463569	+	0.272557i
$117$	−4.75201	+	0.945233i	−0.439323	+	0.0873868i
$118$	−6.83888	+	2.13822i	−0.629570	+	0.196839i
$119$	−4.95088	−	2.05072i	−0.453846	−	0.187989i
$120$	−4.68115	+	1.55146i	−0.427328	+	0.141628i
$121$	22.1680	−	9.18227i	2.01527	−	0.834752i
$122$	−9.67695	−	11.5890i	−0.876109	−	1.04922i
$123$	−13.5432	−	9.04925i	−1.22115	−	0.815943i
$124$	−13.4481	+	2.91357i	−1.20767	+	0.261646i
$125$	1.43124	−	7.19532i	0.128014	−	0.643569i
$126$	−6.93457	+	8.59785i	−0.617781	+	0.765958i
$127$	6.57619			0.583543			0.291771	−	0.956488i	$-0.405755\pi$
$127$	6.57619			0.583543			0.291771	+	0.956488i	$0.405755\pi$
$128$	−11.3053	−	0.437187i	−0.999253	−	0.0386422i
$129$	13.7614			1.21162
$130$	−1.69766	+	2.10485i	−0.148894	+	0.184607i
$131$	0.948444	−	4.76815i	0.0828659	−	0.416595i	−0.916978	−	0.398937i	$-0.869379\pi$
$131$	0.948444	−	4.76815i	0.0828659	−	0.416595i	0.999844	−	0.0176578i	$-0.00562093\pi$
$132$	25.8033	−	5.59037i	2.24589	−	0.486579i
$133$	−2.57417	−	1.72000i	−0.223209	−	0.149143i
$134$	6.60669	+	7.91211i	0.570731	+	0.683502i
$135$	−1.64339	+	0.680715i	−0.141441	+	0.0585866i
$136$	1.20866	+	3.64683i	0.103642	+	0.312713i
$137$	−19.4588	−	8.06010i	−1.66248	−	0.688621i	−0.664214	−	0.747542i	$-0.731234\pi$
$137$	−19.4588	−	8.06010i	−1.66248	−	0.688621i	−0.998263	+	0.0589215i	$0.981234\pi$
$138$	−3.31843	+	1.03753i	−0.282483	+	0.0883203i
$139$	−18.8196	+	3.74344i	−1.59625	+	0.317515i	−0.911513	−	0.411272i	$-0.865085\pi$
$139$	−18.8196	+	3.74344i	−1.59625	+	0.317515i	−0.684741	+	0.728786i	$0.740085\pi$
$140$	0.104839	+	6.16403i	0.00886051	+	0.520956i
$141$	16.5317	−	11.0461i	1.39222	−	0.930252i
$142$	−1.07704	+	3.66233i	−0.0903828	+	0.307336i
$143$	10.2369	−	10.2369i	0.856050	−	0.856050i
$144$	7.91460	−	0.269304i	0.659550	−	0.0224420i
$145$	−0.811028	−	0.811028i	−0.0673522	−	0.0673522i
$146$	2.55978	−	1.39634i	0.211849	−	0.115562i
$147$	10.6179	+	15.8908i	0.875747	+	1.31065i
$148$	3.61189	+	1.42463i	0.296896	+	0.117104i
$149$	0.183778	+	0.923914i	0.0150557	+	0.0756900i	0.987583	−	0.157100i	$-0.0502145\pi$
$149$	0.183778	+	0.923914i	0.0150557	+	0.0756900i	−0.972527	+	0.232790i	$0.925215\pi$
$150$	−6.42606	+	12.2722i	−0.524686	+	1.00202i
$151$	4.16374	−	10.0522i	0.338841	−	0.818034i	−0.658987	−	0.752154i	$-0.729015\pi$
$151$	4.16374	−	10.0522i	0.338841	−	0.818034i	0.997828	−	0.0658792i	$-0.0209852\pi$
$152$	0.273828	+	2.20262i	0.0222104	+	0.178656i
$153$	−1.02911	−	2.48449i	−0.0831986	−	0.200859i
$154$	2.95564	−	32.8724i	0.238172	−	2.64893i
$155$	2.98650	−	4.46961i	0.239881	−	0.359008i
$156$	8.97715	−	6.22173i	0.718747	−	0.498137i
$157$	2.16776	+	0.431195i	0.173006	+	0.0344131i	0.280833	−	0.959757i	$-0.409389\pi$
$157$	2.16776	+	0.431195i	0.173006	+	0.0344131i	−0.107827	+	0.994170i	$0.534389\pi$
$158$	−1.32122	−	12.3381i	−0.105111	−	0.981567i
$159$			23.3568i			1.85232i
$160$	3.29433	−	2.94661i	0.260439	−	0.232950i
$161$			4.34640i			0.342544i
$162$	15.4958	−	1.65936i	1.21746	−	0.130371i
$163$	−10.1978	−	2.02847i	−0.798753	−	0.158882i	−0.221193	−	0.975230i	$-0.570995\pi$
$163$	−10.1978	−	2.02847i	−0.798753	−	0.158882i	−0.577560	+	0.816348i	$0.695995\pi$
$164$	14.3640	+	2.60406i	1.12164	+	0.203343i
$165$	−5.73029	+	8.57598i	−0.446102	+	0.667640i
$166$	−2.88224	−	0.259150i	−0.223705	−	0.0201139i
$167$	5.67541	+	13.7016i	0.439176	+	1.06027i	0.976234	+	0.216720i	$0.0695358\pi$
$167$	5.67541	+	13.7016i	0.439176	+	1.06027i	−0.537058	+	0.843546i	$0.680464\pi$
$168$	6.61821	−	24.0053i	0.510606	−	1.85205i
$169$	−2.68293	+	6.47717i	−0.206379	+	0.498244i
$170$	−1.32964	−	0.696234i	−0.101978	−	0.0533987i
$171$	−0.303097	−	1.52377i	−0.0231784	−	0.116526i
$172$	−11.3127	+	4.91291i	−0.862588	+	0.374606i
$173$	2.81628	+	4.21486i	0.214118	+	0.320450i	0.922945	−	0.384933i	$-0.125775\pi$
$173$	2.81628	+	4.21486i	0.214118	+	0.320450i	−0.708827	+	0.705382i	$0.750775\pi$
$174$	2.21853	+	4.06701i	0.168186	+	0.308319i
$175$	12.2453	+	12.2453i	0.925654	+	0.925654i
$176$	−19.2162	+	13.8076i	−1.44847	+	1.04079i
$177$	−7.99491	+	7.99491i	−0.600934	+	0.600934i
$178$	−4.10354	−	1.20679i	−0.307574	−	0.0904526i
$179$	2.53753	−	1.69552i	0.189664	−	0.126729i	−0.457113	−	0.889409i	$-0.651117\pi$
$179$	2.53753	−	1.69552i	0.189664	−	0.126729i	0.646777	+	0.762679i	$0.276117\pi$
$180$	−2.15008	+	2.22448i	−0.160258	+	0.165803i
$181$	−6.51424	+	1.29576i	−0.484200	+	0.0963133i	−0.431153	−	0.902279i	$-0.641893\pi$
$181$	−6.51424	+	1.29576i	−0.484200	+	0.0963133i	−0.0530464	+	0.998592i	$0.516893\pi$
$182$	−4.07454	−	13.0320i	−0.302025	−	0.965995i
$183$	−22.0102	−	9.11694i	−1.62704	−	0.673943i
$184$	2.35756	−	2.03762i	0.173802	−	0.150215i
$185$	−1.40136	+	0.580464i	−0.103030	+	0.0426766i
$186$	−16.6663	+	13.9165i	−1.22203	+	1.02041i
$187$	6.68109	+	4.46416i	0.488570	+	0.326452i
$188$	−9.64658	+	14.9826i	−0.703549	+	1.09272i
$189$	1.75224	−	8.80912i	0.127457	−	0.640769i
$190$	−0.674936	−	0.544367i	−0.0489650	−	0.0394926i
$191$	−1.58154			−0.114436			−0.0572181	−	0.998362i	$-0.518223\pi$
$191$	−1.58154			−0.114436			−0.0572181	+	0.998362i	$0.518223\pi$
$192$	−16.1236	+	7.66404i	−1.16362	+	0.553104i
$193$	−16.3932			−1.18001			−0.590004	−	0.807401i	$-0.700874\pi$
$193$	−16.3932			−1.18001			−0.590004	+	0.807401i	$0.700874\pi$
$194$	14.4417	+	11.6479i	1.03685	+	0.836269i
$195$	−0.832448	+	4.18500i	−0.0596128	+	0.299694i
$196$	−14.4017	−	9.27258i	−1.02869	−	0.662327i
$197$	−2.24425	−	1.49956i	−0.159896	−	0.106839i	0.473048	−	0.881037i	$-0.343154\pi$
$197$	−2.24425	−	1.49956i	−0.159896	−	0.106839i	−0.632944	+	0.774197i	$0.718154\pi$
$198$	12.7134	−	10.6158i	0.903504	−	0.754435i
$199$	12.1675	−	5.03992i	0.862528	−	0.357271i	0.0928322	−	0.995682i	$-0.470408\pi$
$199$	12.1675	−	5.03992i	0.862528	−	0.357271i	0.769696	+	0.638411i	$0.220408\pi$
$200$	0.901375	−	12.3827i	0.0637369	−	0.875589i
$201$	15.0269	+	6.22436i	1.05992	+	0.439032i
$202$	−1.89428	−	6.05867i	−0.133281	−	0.426287i
$203$	5.68012	−	1.12985i	0.398666	−	0.0792996i
$204$	4.35897	+	4.21318i	0.305189	+	0.294981i
$205$	−4.74184	+	3.16839i	−0.331184	+	0.221290i
$206$	−14.5088	−	4.26681i	−1.01088	−	0.297283i
$207$	−1.54230	+	1.54230i	−0.107197	+	0.107197i
$208$	−5.15860	+	8.31958i	−0.357684	+	0.576859i
$209$	3.28254	+	3.28254i	0.227058	+	0.227058i
$210$	4.65848	+	8.53992i	0.321465	+	0.589311i
$211$	3.81684	+	5.71230i	0.262762	+	0.393251i	0.939267	−	0.343187i	$-0.111506\pi$
$211$	3.81684	+	5.71230i	0.262762	+	0.393251i	−0.676505	+	0.736438i	$0.736506\pi$
$212$	−8.33856	−	19.2008i	−0.572695	−	1.31872i
$213$	1.17516	+	5.90791i	0.0805205	+	0.404804i
$214$	−4.78730	−	2.50676i	−0.327253	−	0.171359i
$215$	1.84386	−	4.45147i	0.125750	−	0.303588i
$216$	−5.59968	+	3.17933i	−0.381010	+	0.216326i
$217$	10.3871	+	25.0767i	0.705124	+	1.70232i
$218$	13.8855	+	1.24848i	0.940444	+	0.0845578i
$219$	2.55621	−	3.82564i	0.172733	−	0.258512i
$220$	1.64898	−	9.09578i	0.111174	−	0.613237i
$221$	3.26031	+	0.648516i	0.219312	+	0.0436239i
$222$	6.09184	−	0.652342i	0.408857	−	0.0437823i
$223$			3.88311i			0.260032i	0.991512	+	0.130016i	$0.0415029\pi$
$223$			3.88311i			0.260032i	−0.991512	+	0.130016i	$0.958497\pi$
$224$	3.12949	+	22.0967i	0.209098	+	1.47640i
$225$			8.69037i			0.579358i
$226$	−0.694732	−	6.48769i	−0.0462129	−	0.431555i
$227$	22.5337	+	4.48224i	1.49562	+	0.297497i	0.874039	−	0.485856i	$-0.161492\pi$
$227$	22.5337	+	4.48224i	1.49562	+	0.297497i	0.621577	+	0.783353i	$0.286492\pi$
$228$	1.99505	+	2.87860i	0.132125	+	0.190640i
$229$	−3.41606	+	5.11250i	−0.225740	+	0.337844i	−0.927000	−	0.375062i	$-0.877621\pi$
$229$	−3.41606	+	5.11250i	−0.225740	+	0.337844i	0.701260	+	0.712906i	$0.252621\pi$
$230$	−0.109014	+	1.21245i	−0.00718820	+	0.0799465i
$231$	−19.9301	−	48.1156i	−1.31131	−	3.16577i
$232$	−3.27573	−	2.55131i	−0.215062	−	0.167502i
$233$	0.733834	−	1.77163i	0.0480751	−	0.116064i	−0.898018	−	0.439960i	$-0.854993\pi$
$233$	0.733834	−	1.77163i	0.0480751	−	0.116064i	0.946093	+	0.323896i	$0.104993\pi$
$234$	3.17852	−	6.07018i	0.207786	−	0.396820i
$235$	−1.35811	−	6.82766i	−0.0885930	−	0.445387i
$236$	3.71809	−	9.42658i	0.242027	−	0.613618i
$237$	−10.8781	−	16.2803i	−0.706610	−	1.05752i
$238$	6.65300	−	3.62917i	0.431250	−	0.235244i
$239$	−6.09870	−	6.09870i	−0.394492	−	0.394492i	0.481793	−	0.876285i	$-0.339986\pi$
$239$	−6.09870	−	6.09870i	−0.394492	−	0.394492i	−0.876285	+	0.481793i	$0.839986\pi$
$240$	2.44827	−	6.53041i	0.158035	−	0.421536i
$241$	5.21549	−	5.21549i	0.335959	−	0.335959i	−0.518885	−	0.854844i	$-0.673653\pi$
$241$	5.21549	−	5.21549i	0.335959	−	0.335959i	0.854844	+	0.518885i	$0.173653\pi$
$242$	−9.57383	+	32.5547i	−0.615429	+	2.09269i
$243$	14.7680	−	9.86763i	0.947365	−	0.633009i
$244$	21.3487	−	0.363102i	1.36671	−	0.0232452i
$245$	6.56295	−	1.30545i	0.419291	−	0.0834022i
$246$	21.9855	−	6.87391i	1.40174	−	0.438264i
$247$	1.77429	+	0.734933i	0.112895	+	0.0467627i
$248$	8.73249	−	17.3903i	0.554514	−	1.10429i
$249$	−4.21876	+	1.74747i	−0.267353	+	0.110741i
$250$	6.64984	+	7.96379i	0.420573	+	0.503674i
$251$	3.73150	+	2.49331i	0.235530	+	0.157376i	0.667735	−	0.744399i	$-0.267264\pi$
$251$	3.73150	+	2.49331i	0.235530	+	0.157376i	−0.432204	+	0.901776i	$0.642264\pi$
$252$	−3.30766	−	15.2670i	−0.208363	−	0.961732i
$253$	1.27145	−	6.39201i	0.0799354	−	0.401862i
$254$	−5.83860	+	7.23901i	−0.366347	+	0.454216i
$255$	−2.36832			−0.148310
$256$	10.5185	−	12.0566i	0.657407	−	0.753536i
$257$	−5.86891			−0.366092			−0.183046	−	0.983104i	$-0.558596\pi$
$257$	−5.86891			−0.366092			−0.183046	+	0.983104i	$0.558596\pi$
$258$	−12.2179	+	15.1484i	−0.760651	+	0.943096i
$259$	1.49418	−	7.51177i	0.0928441	−	0.466759i
$260$	−0.809749	−	3.73753i	−0.0502185	−	0.231792i
$261$	2.41649	+	1.61465i	0.149577	+	0.0999442i
$262$	4.40667	+	5.27739i	0.272245	+	0.326038i
$263$	−27.1667	+	11.2528i	−1.67517	+	0.693877i	−0.999078	−	0.0429417i	$-0.986327\pi$
$263$	−27.1667	+	11.2528i	−1.67517	+	0.693877i	−0.676090	+	0.736819i	$0.736327\pi$
$264$	−16.7553	+	33.3673i	−1.03122	+	2.05362i
$265$	7.55537	+	3.12954i	0.464123	+	0.192246i
$266$	4.17881	−	1.30653i	0.256219	−	0.0801087i
$267$	−6.61966	+	1.31673i	−0.405117	+	0.0805827i
$268$	−14.5753	+	0.247899i	−0.890326	+	0.0151428i
$269$	9.18707	−	6.13860i	0.560145	−	0.374277i	−0.243031	−	0.970019i	$-0.578142\pi$
$269$	9.18707	−	6.13860i	0.560145	−	0.374277i	0.803176	+	0.595741i	$0.203142\pi$
$270$	0.709743	−	2.41340i	0.0431936	−	0.146875i
$271$	−17.2217	+	17.2217i	−1.04614	+	1.04614i	−0.0472600	+	0.998883i	$0.515049\pi$
$271$	−17.2217	+	17.2217i	−1.04614	+	1.04614i	−0.998883	+	0.0472600i	$0.984951\pi$
$272$	−5.08750	−	1.90732i	−0.308475	−	0.115648i
$273$	−15.2349	−	15.2349i	−0.922056	−	0.922056i
$274$	26.1488	−	14.2640i	1.57970	−	0.861720i
$275$	−14.4263	−	21.5906i	−0.869941	−	1.30196i
$276$	1.80413	−	4.57406i	0.108596	−	0.275326i
$277$	5.36979	+	26.9957i	0.322639	+	1.62202i	0.712868	+	0.701299i	$0.247396\pi$
$277$	5.36979	+	26.9957i	0.322639	+	1.62202i	−0.390228	+	0.920718i	$0.627604\pi$
$278$	12.5880	−	24.0400i	0.754978	−	1.44182i
$279$	−5.21255	+	12.5842i	−0.312067	+	0.753397i
$280$	−6.87839	−	5.35726i	−0.411062	−	0.320158i
$281$	−6.20216	−	14.9733i	−0.369990	−	0.893234i	−0.993751	−	0.111619i	$-0.964396\pi$
$281$	−6.20216	−	14.9733i	−0.369990	−	0.893234i	0.623762	−	0.781615i	$-0.285604\pi$
$282$	−2.51801	+	28.0051i	−0.149946	+	1.66768i
$283$	−4.95606	+	7.41727i	−0.294607	+	0.440911i	−0.949015	−	0.315231i	$-0.897918\pi$
$283$	−4.95606	+	7.41727i	−0.294607	+	0.440911i	0.654408	+	0.756142i	$0.272918\pi$
$284$	−3.07523	−	4.43715i	−0.182481	−	0.263297i
$285$	−1.34195	−	0.266931i	−0.0794904	−	0.0158116i
$286$	2.17996	+	20.3574i	0.128904	+	1.20376i
$287$		−	28.7960i		−	1.69978i
$288$	−6.73044	+	8.95142i	−0.396595	+	0.527467i
$289$		−	15.1550i		−	0.891469i
$290$	1.61284	−	0.172710i	0.0947090	−	0.0101419i
$291$	28.7139	+	5.71155i	1.68324	+	0.334817i
$292$	−0.735589	+	4.05751i	−0.0430471	+	0.237448i
$293$	13.5525	−	20.2828i	0.791747	−	1.18493i	−0.187500	−	0.982265i	$-0.560039\pi$
$293$	13.5525	−	20.2828i	0.791747	−	1.18493i	0.979247	−	0.202669i	$-0.0649615\pi$
$294$	−26.9194	−	2.42039i	−1.56997	−	0.141160i
$295$	1.51494	+	3.65738i	0.0882031	+	0.212941i
$296$	−4.77500	+	2.71110i	−0.277541	+	0.157579i
$297$	−5.15386	+	12.4425i	−0.299057	+	0.721988i
$298$	−1.18020	−	0.617986i	−0.0683673	−	0.0357990i
$299$	−0.525997	−	2.64436i	−0.0304192	−	0.152928i
$300$	−7.80381	−	17.9695i	−0.450553	−	1.03747i
$301$	13.5163	+	20.2286i	0.779069	+	1.16596i
$302$	7.36860	+	13.5081i	0.424015	+	0.777305i
$303$	−7.08281	−	7.08281i	−0.406897	−	0.406897i
$304$	−2.66774	−	1.65415i	−0.153005	−	0.0948718i
$305$	−5.89822	+	5.89822i	−0.337731	+	0.337731i
$306$	3.64859	+	1.07299i	0.208576	+	0.0613390i
$307$	8.15880	−	5.45154i	0.465647	−	0.311136i	−0.300521	−	0.953775i	$-0.597161\pi$
$307$	8.15880	−	5.45154i	0.465647	−	0.311136i	0.766169	+	0.642639i	$0.222161\pi$
$308$	33.5615	+	32.4389i	1.91234	+	1.84838i
$309$	−23.4050	+	4.65554i	−1.33146	+	0.264844i
$310$	2.26858	+	7.25580i	0.128846	+	0.412102i
$311$	28.3647	+	11.7490i	1.60842	+	0.666227i	0.992574	−	0.121643i	$-0.0388163\pi$
$311$	28.3647	+	11.7490i	1.60842	+	0.666227i	0.615841	+	0.787870i	$0.288816\pi$
$312$	−1.12144	+	15.4059i	−0.0634891	+	0.872185i
$313$	−22.4586	+	9.30264i	−1.26943	+	0.525816i	−0.912792	−	0.408425i	$-0.866078\pi$
$313$	−22.4586	+	9.30264i	−1.26943	+	0.525816i	−0.356641	+	0.934242i	$0.616078\pi$
$314$	−2.39928	+	2.00342i	−0.135399	+	0.113060i
$315$	5.07416	+	3.39044i	0.285896	+	0.191030i
$316$	14.7547	+	9.49986i	0.830017	+	0.534409i
$317$	1.29802	−	6.52557i	0.0729039	−	0.366513i	−0.927061	−	0.374911i	$-0.877673\pi$
$317$	1.29802	−	6.52557i	0.0729039	−	0.366513i	0.999965	+	0.00839833i	$0.00267330\pi$
$318$	−25.7110	−	20.7371i	−1.44180	−	1.16288i
$319$	−8.68396			−0.486209
$320$	0.318766	+	6.24248i	0.0178195	+	0.348965i
$321$	−8.52703			−0.475933
$322$	−4.78447	−	3.85890i	−0.266628	−	0.215048i
$323$	−0.207952	+	1.04544i	−0.0115707	+	0.0581701i
$324$	−11.9311	+	18.5308i	−0.662841	+	1.02949i
$325$	−8.93197	−	5.96815i	−0.495457	−	0.331054i
$326$	11.2869	−	9.42469i	0.625125	−	0.521985i
$327$	20.3243	−	8.41860i	1.12394	−	0.465550i
$328$	−15.6195	+	13.4998i	−0.862441	+	0.745401i
$329$	32.4747	+	13.4515i	1.79039	+	0.741604i
$330$	−4.35279	−	13.9220i	−0.239613	−	0.766378i
$331$	3.84304	−	0.764428i	0.211233	−	0.0420168i	−0.0883396	−	0.996090i	$-0.528156\pi$
$331$	3.84304	−	0.764428i	0.211233	−	0.0420168i	0.299572	+	0.954074i	$0.403156\pi$
$332$	2.84424	−	2.94266i	0.156098	−	0.161500i
$333$	3.19573	−	2.13532i	0.175125	−	0.117015i
$334$	−20.1215	−	5.91742i	−1.10100	−	0.323787i
$335$	4.02686	−	4.02686i	0.220011	−	0.220011i
$336$	20.5489	+	28.5981i	1.12104	+	1.56016i
$337$	13.8621	+	13.8621i	0.755119	+	0.755119i	0.975430	−	0.220311i	$-0.0707072\pi$
$337$	13.8621	+	13.8621i	0.755119	+	0.755119i	−0.220311	+	0.975430i	$0.570707\pi$
$338$	−4.74800	−	8.70404i	−0.258257	−	0.473437i
$339$	−5.72000	−	8.56058i	−0.310668	−	0.464947i
$340$	1.94691	−	0.845507i	0.105586	−	0.0458541i
$341$	−7.94010	−	39.9176i	−0.429980	−	2.16166i
$342$	1.94645	+	1.01922i	0.105252	+	0.0551129i
$343$	−2.36172	+	5.70170i	−0.127521	+	0.307863i
$344$	4.63580	−	16.8148i	0.249946	−	0.906595i
$345$	0.735093	+	1.77467i	0.0395761	+	0.0955451i
$346$	−7.14008	−	0.641984i	−0.383853	−	0.0345132i
$347$	−13.7444	+	20.5699i	−0.737836	+	1.10425i	0.252773	+	0.967526i	$0.418657\pi$
$347$	−13.7444	+	20.5699i	−0.737836	+	1.10425i	−0.990609	+	0.136724i	$0.956343\pi$
$348$	−6.44662	−	1.16871i	−0.345575	−	0.0626496i
$349$	−34.6278	−	6.88789i	−1.85358	−	0.368700i	−0.862953	−	0.505284i	$-0.831388\pi$
$349$	−34.6278	−	6.88789i	−1.85358	−	0.368700i	−0.990628	+	0.136584i	$0.956388\pi$
$350$	−24.3513	+	2.60765i	−1.30163	+	0.139385i
$351$			5.57155i			0.297388i
$352$	1.86158	−	33.4119i	0.0992224	−	1.78086i
$353$			16.3511i			0.870283i	0.900362	+	0.435141i	$0.143302\pi$
$353$			16.3511i			0.870283i	−0.900362	+	0.435141i	$0.856698\pi$
$354$	−1.70253	−	15.8989i	−0.0904884	−	0.845018i
$355$	2.06853	+	0.411455i	0.109786	+	0.0218378i
$356$	4.97171	−	3.44571i	0.263500	−	0.182622i
$357$	6.64372	−	9.94303i	0.351623	−	0.526241i
$358$	−0.386502	+	4.29864i	−0.0204272	+	0.227190i
$359$	−0.837827	−	2.02269i	−0.0442188	−	0.106754i	0.900227	−	0.435421i	$-0.143401\pi$
$359$	−0.837827	−	2.02269i	−0.0442188	−	0.106754i	−0.944446	+	0.328667i	$0.893401\pi$
$360$	−0.539766	−	4.34177i	−0.0284482	−	0.228832i
$361$	7.03532	−	16.9848i	0.370280	−	0.893935i
$362$	4.35723	−	8.32125i	0.229011	−	0.437355i
$363$	10.4460	+	52.5158i	0.548275	+	2.75636i
$364$	17.9630	+	7.08509i	0.941518	+	0.371360i
$365$	−0.895000	−	1.33946i	−0.0468464	−	0.0701106i
$366$	29.5774	−	16.1343i	1.54604	−	0.843353i
$367$	20.9060	+	20.9060i	1.09129	+	1.09129i	0.995392	+	0.0958935i	$0.0305708\pi$
$367$	20.9060	+	20.9060i	1.09129	+	1.09129i	0.0958935	+	0.995392i	$0.469429\pi$
$368$	0.149860	+	4.40426i	0.00781201	+	0.229588i
$369$	10.2182	−	10.2182i	0.531936	−	0.531936i
$370$	0.605217	−	2.05797i	0.0314637	−	0.106989i
$371$	−34.3336	+	22.9410i	−1.78251	+	1.19104i
$372$	−0.522182	−	30.7018i	−0.0270739	−	1.59181i
$373$	23.8329	−	4.74066i	1.23402	−	0.245462i	0.465362	−	0.885121i	$-0.345924\pi$
$373$	23.8329	−	4.74066i	1.23402	−	0.245462i	0.768659	+	0.639659i	$0.220924\pi$
$374$	−10.8459	+	3.39103i	−0.560826	+	0.175346i
$375$	15.1251	+	6.26501i	0.781055	+	0.323524i
$376$	−7.92807	−	23.9210i	−0.408859	−	1.23363i
$377$	−3.31907	+	1.37481i	−0.170941	+	0.0708061i
$378$	8.14129	+	9.74993i	0.418743	+	0.501482i
$379$	−20.7596	−	13.8712i	−1.06635	−	0.712513i	−0.106867	−	0.994273i	$-0.534082\pi$
$379$	−20.7596	−	13.8712i	−1.06635	−	0.712513i	−0.959485	+	0.281760i	$0.909082\pi$
$380$	1.19847	−	0.259653i	0.0614802	−	0.0133199i
$381$	−2.86296	+	14.3931i	−0.146674	+	0.737381i
$382$	1.40415	−	1.74094i	0.0718427	−	0.0890744i
$383$	−24.5463			−1.25426			−0.627128	−	0.778916i	$-0.715770\pi$
$383$	−24.5463			−1.25426			−0.627128	+	0.778916i	$0.715770\pi$
$384$	5.87863	−	24.5531i	0.299993	−	1.25297i
$385$	−18.2346			−0.929323
$386$	14.5545	−	18.0455i	0.740806	−	0.918491i
$387$	−2.38183	+	11.9743i	−0.121075	+	0.608687i
$388$	−25.6437	+	5.55581i	−1.30186	+	0.282053i
$389$	19.0280	+	12.7141i	0.964758	+	0.644630i	0.934895	−	0.354924i	$-0.115493\pi$
$389$	19.0280	+	12.7141i	0.964758	+	0.644630i	0.0298624	+	0.999554i	$0.490493\pi$
$390$	−3.86773	−	4.63196i	−0.195850	−	0.234548i
$391$	1.38255	−	0.572672i	0.0699187	−	0.0289613i
$392$	22.9936	−	7.62070i	1.16135	−	0.384903i
$393$	10.0230	+	4.15166i	0.505593	+	0.209423i
$394$	3.64324	−	1.13908i	0.183544	−	0.0573862i
$395$	−6.72381	+	1.33745i	−0.338312	+	0.0672944i
$396$	0.398332	+	23.4200i	0.0200169	+	1.17690i
$397$	20.2490	−	13.5300i	1.01627	−	0.679050i	0.0683838	−	0.997659i	$-0.478216\pi$
$397$	20.2490	−	13.5300i	1.01627	−	0.679050i	0.947886	+	0.318609i	$0.103216\pi$
$398$	−5.25484	+	17.8685i	−0.263401	+	0.895665i
$399$	4.88518	−	4.88518i	0.244565	−	0.244565i
$400$	12.8305	+	11.9861i	0.641524	+	0.599304i
$401$	13.4688	+	13.4688i	0.672599	+	0.672599i	0.958314	−	0.285716i	$-0.0922312\pi$
$401$	13.4688	+	13.4688i	0.672599	+	0.672599i	−0.285716	+	0.958314i	$0.592231\pi$
$402$	−20.1932	+	11.0153i	−1.00715	+	0.549392i
$403$	−9.35433	−	13.9997i	−0.465972	−	0.697377i
$404$	8.35115	+	3.29392i	0.415485	+	0.163878i
$405$	−1.67974	−	8.44462i	−0.0834669	−	0.419616i
$406$	−3.79931	+	7.25575i	−0.188557	+	0.360097i
$407$	−4.39483	+	10.6101i	−0.217844	+	0.525922i
$408$	−8.50789	+	1.05769i	−0.421204	+	0.0523637i
$409$	−3.05166	−	7.36736i	−0.150895	−	0.364293i	0.830299	−	0.557319i	$-0.188170\pi$
$409$	−3.05166	−	7.36736i	−0.150895	−	0.364293i	−0.981194	+	0.193026i	$0.938170\pi$
$410$	0.722250	−	8.03280i	0.0356694	−	0.396712i
$411$	26.1123	−	39.0798i	1.28803	−	1.92767i
$412$	17.5783	−	12.1829i	0.866023	−	0.600209i
$413$	−19.6048	−	3.89963i	−0.964688	−	0.191888i
$414$	−0.328436	−	3.06707i	−0.0161417	−	0.150738i
$415$			1.59881i			0.0784824i
$416$	−4.57811	−	13.0650i	−0.224460	−	0.640564i
$417$		−	42.8195i		−	2.09688i
$418$	−6.52775	+	0.699022i	−0.319283	+	0.0341903i
$419$	−12.5395	−	2.49426i	−0.612593	−	0.121852i	−0.120964	−	0.992657i	$-0.538598\pi$
$419$	−12.5395	−	2.49426i	−0.612593	−	0.121852i	−0.491629	+	0.870805i	$0.663598\pi$
$420$	−13.5366	−	2.45407i	−0.660521	−	0.119746i
$421$	−10.8903	+	16.2984i	−0.530759	+	0.794337i	−0.995858	−	0.0909215i	$-0.971019\pi$
$421$	−10.8903	+	16.2984i	−0.530759	+	0.794337i	0.465099	+	0.885259i	$0.346019\pi$
$422$	−9.67679	−	0.870065i	−0.471059	−	0.0423541i
$423$	6.75033	+	16.2967i	0.328212	+	0.792375i
$424$	28.5394	+	7.86824i	1.38600	+	0.382115i
$425$	2.28170	−	5.50852i	0.110679	−	0.267203i
$426$	−7.54673	−	3.95168i	−0.365640	−	0.191459i
$427$	−8.21683	−	41.3088i	−0.397640	−	1.99907i
$428$	7.00978	−	3.04422i	0.338830	−	0.147148i
$429$	17.9485	+	26.8618i	0.866560	+	1.29690i
$430$	3.26309	+	5.98189i	0.157360	+	0.288472i
$431$	18.4810	+	18.4810i	0.890199	+	0.890199i	0.994541	−	0.104343i	$-0.0332739\pi$
$431$	18.4810	+	18.4810i	0.890199	+	0.890199i	−0.104343	+	0.994541i	$0.533274\pi$
$432$	1.47184	−	8.98681i	0.0708139	−	0.432378i
$433$	6.00332	−	6.00332i	0.288501	−	0.288501i	−0.547986	−	0.836487i	$-0.684605\pi$
$433$	6.00332	−	6.00332i	0.288501	−	0.288501i	0.836487	+	0.547986i	$0.184605\pi$
$434$	−36.8263	−	10.8301i	−1.76772	−	0.519860i
$435$	2.12815	−	1.42199i	0.102037	−	0.0681791i
$436$	−13.7024	+	14.1766i	−0.656226	+	0.678935i
$437$	0.847937	−	0.168665i	0.0405623	−	0.00806835i
$438$	1.94172	+	6.21040i	0.0927791	+	0.296744i
$439$	−19.8680	−	8.22958i	−0.948246	−	0.392777i	−0.145675	−	0.989333i	$-0.546535\pi$
$439$	−19.8680	−	8.22958i	−0.948246	−	0.392777i	−0.802571	+	0.596556i	$0.796535\pi$
$440$	8.54852	+	9.89077i	0.407535	+	0.471524i
$441$	−15.6649	+	6.48862i	−0.745948	+	0.308982i
$442$	−3.60851	+	3.01314i	−0.171639	+	0.143320i
$443$	15.5336	+	10.3792i	0.738023	+	0.493131i	0.866871	−	0.498533i	$-0.166128\pi$
$443$	15.5336	+	10.3792i	0.738023	+	0.493131i	−0.128848	+	0.991664i	$0.541128\pi$
$444$	−4.69048	+	7.28501i	−0.222600	+	0.345731i
$445$	−0.461025	+	2.31773i	−0.0218547	+	0.109871i
$446$	−4.27449	−	3.44757i	−0.202403	−	0.163247i
$447$	−2.10215			−0.0994282
$448$	−27.1023	−	16.1734i	−1.28047	−	0.764122i
$449$	32.6778			1.54216			0.771081	−	0.636737i	$-0.219716\pi$
$449$	32.6778			1.54216			0.771081	+	0.636737i	$0.219716\pi$
$450$	−9.56628	−	7.71565i	−0.450959	−	0.363719i
$451$	−8.42370	+	42.3488i	−0.396657	+	1.99413i
$452$	7.75840	+	4.99527i	0.364925	+	0.234958i
$453$	20.1881	+	13.4893i	0.948522	+	0.633782i
$454$	−24.9403	+	20.8254i	−1.17051	+	0.977386i
$455$	−6.96941	+	2.88682i	−0.326731	+	0.135336i
$456$	−4.94002	−	0.359599i	−0.231337	−	0.0168398i
$457$	−23.3834	−	9.68573i	−1.09383	−	0.453079i	−0.238489	−	0.971145i	$-0.576652\pi$
$457$	−23.3834	−	9.68573i	−1.09383	−	0.453079i	−0.855341	+	0.518066i	$0.826652\pi$
$458$	−2.59488	−	8.29945i	−0.121251	−	0.387808i
$459$	−3.03298	+	0.603297i	−0.141567	+	0.0281595i
$460$	−1.23787	−	1.19646i	−0.0577158	−	0.0557853i
$461$	2.39596	−	1.60093i	0.111591	−	0.0745627i	−0.498522	−	0.866877i	$-0.666124\pi$
$461$	2.39596	−	1.60093i	0.111591	−	0.0745627i	0.610113	+	0.792314i	$0.291124\pi$
$462$	70.6599	+	20.7800i	3.28740	+	0.966773i
$463$	24.5897	−	24.5897i	1.14278	−	1.14278i	0.154840	−	0.987940i	$-0.450514\pi$
$463$	24.5897	−	24.5897i	1.14278	−	1.14278i	0.987940	−	0.154840i	$-0.0494863\pi$
$464$	5.71678	−	1.34073i	0.265395	−	0.0622420i
$465$	8.48230	+	8.48230i	0.393357	+	0.393357i
$466$	1.29867	+	2.38072i	0.0601598	+	0.110285i
$467$	−7.08500	−	10.6035i	−0.327855	−	0.490670i	0.630524	−	0.776170i	$-0.282840\pi$
$467$	−7.08500	−	10.6035i	−0.327855	−	0.490670i	−0.958379	+	0.285500i	$0.907840\pi$
$468$	3.85999	+	8.88823i	0.178428	+	0.410858i
$469$	5.60983	+	28.2025i	0.259038	+	1.30227i
$470$	8.72160	+	4.56687i	0.402298	+	0.210654i
$471$	−1.88748	+	4.55679i	−0.0869707	+	0.209966i
$472$	7.07563	+	12.4621i	0.325682	+	0.573616i
$473$	−13.9603	−	33.7031i	−0.641895	−	1.54967i
$474$	27.5792	+	2.47972i	1.26675	+	0.113897i
$475$	1.91374	−	2.86411i	0.0878082	−	0.131414i
$476$	−1.91184	+	10.5457i	−0.0876288	+	0.483361i
$477$	−20.3237	−	4.04263i	−0.930556	−	0.185099i
$478$	12.1281	−	1.29873i	0.554724	−	0.0594024i
$479$		−	8.39981i		−	0.383797i	−0.981415	−	0.191899i	$-0.938536\pi$
$479$		−	8.39981i		−	0.383797i	0.981415	−	0.191899i	$-0.0614644\pi$
$480$	5.01495	+	8.49299i	0.228900	+	0.387650i
$481$			4.75101i			0.216628i
$482$	1.11065	+	10.3717i	0.0505886	+	0.472417i
$483$	−9.51281	−	1.89222i	−0.432848	−	0.0860988i
$484$	−27.3359	−	39.4421i	−1.24254	−	1.79282i
$485$	5.69487	−	8.52297i	0.258591	−	0.387008i
$486$	−2.24937	+	25.0173i	−0.102034	+	1.13481i
$487$	−6.40268	−	15.4574i	−0.290133	−	0.700443i	0.709859	−	0.704343i	$-0.248758\pi$
$487$	−6.40268	−	15.4574i	−0.290133	−	0.700443i	−0.999992	+	0.00390038i	$0.998758\pi$
$488$	−18.5545	+	23.8228i	−0.839922	+	1.07841i
$489$	8.87928	−	21.4365i	0.401535	−	0.969391i
$490$	−4.38982	+	8.38347i	−0.198312	+	0.378726i
$491$	1.85105	+	9.30587i	0.0835368	+	0.419968i	0.999811	+	0.0194174i	$0.00618114\pi$
$491$	1.85105	+	9.30587i	0.0835368	+	0.419968i	−0.916275	+	0.400551i	$0.868819\pi$
$492$	−11.9528	+	30.3043i	−0.538876	+	1.36623i
$493$	−1.10779	−	1.65793i	−0.0498926	−	0.0746695i
$494$	−2.38429	+	1.30062i	−0.107274	+	0.0585174i
$495$	−6.47049	−	6.47049i	−0.290827	−	0.290827i
$496$	11.3900	+	25.0524i	0.511428	+	1.12489i
$497$	−7.53017	+	7.53017i	−0.337774	+	0.337774i
$498$	1.82199	−	6.19545i	0.0816451	−	0.277625i
$499$	12.4453	−	8.31569i	0.557129	−	0.372261i	−0.244899	−	0.969549i	$-0.578755\pi$
$499$	12.4453	−	8.31569i	0.557129	−	0.372261i	0.802027	+	0.597287i	$0.203755\pi$
$500$	−14.6705	+	0.249518i	−0.656083	+	0.0111588i
$501$	−32.4591	+	6.45653i	−1.45017	+	0.288456i
$502$	−6.05759	+	1.89395i	−0.270363	+	0.0845309i
$503$	7.01440	+	2.90546i	0.312757	+	0.129548i	0.533540	−	0.845775i	$-0.320861\pi$
$503$	7.01440	+	2.90546i	0.312757	+	0.129548i	−0.220783	+	0.975323i	$0.570861\pi$
$504$	19.7425	+	9.91363i	0.879400	+	0.441588i
$505$	−3.24013	+	1.34211i	−0.144184	+	0.0597230i
$506$	5.90743	+	7.07468i	0.262617	+	0.314508i
$507$	−13.0083	−	8.69190i	−0.577721	−	0.386021i
$508$	−2.78490	−	12.8542i	−0.123560	−	0.570311i
$509$	−6.73996	+	33.8841i	−0.298743	+	1.50188i	0.481521	+	0.876435i	$0.340085\pi$
$509$	−6.73996	+	33.8841i	−0.298743	+	1.50188i	−0.780264	+	0.625450i	$0.784915\pi$
$510$	2.10269	−	2.60702i	0.0931085	−	0.115441i
$511$	8.13423			0.359837
$512$	3.93303	+	22.2830i	0.173817	+	0.984778i
$513$	−1.78656			−0.0788787
$514$	5.21065	−	6.46044i	0.229832	−	0.284958i
$515$	−1.63003	+	8.19473i	−0.0718279	+	0.361103i
$516$	−5.82769	−	26.8986i	−0.256550	−	1.18415i
$517$	−43.8239	−	29.2822i	−1.92737	−	1.28783i
$518$	6.94230	+	8.31403i	0.305027	+	0.365298i
$519$	−10.4510	+	4.32894i	−0.458748	+	0.190020i
$520$	4.83317	+	2.42696i	0.211948	+	0.106429i
$521$	−35.4201	−	14.6715i	−1.55178	−	0.642770i	−0.568146	−	0.822928i	$-0.692339\pi$
$521$	−35.4201	−	14.6715i	−1.55178	−	0.642770i	−0.983638	+	0.180158i	$0.942339\pi$
$522$	−3.92284	+	1.22650i	−0.171698	+	0.0536826i
$523$	−3.91974	+	0.779685i	−0.171398	+	0.0340933i	−0.280043	−	0.959987i	$-0.590349\pi$
$523$	−3.91974	+	0.779685i	−0.171398	+	0.0340933i	0.108645	+	0.994081i	$0.465349\pi$
$524$	−9.72172	+	0.165349i	−0.424695	+	0.00722330i
$525$	−32.1318	+	21.4698i	−1.40235	+	0.937018i
$526$	11.7326	−	39.8955i	0.511568	−	1.73953i
$527$	6.60811	−	6.60811i	0.287854	−	0.287854i
$528$	−21.8544	−	48.0690i	−0.951092	−	2.09193i
$529$	15.4052	+	15.4052i	0.669792	+	0.669792i
$530$	−10.1529	+	5.53836i	−0.441015	+	0.240571i
$531$	−5.57291	−	8.34045i	−0.241844	−	0.361945i
$532$	−2.27189	+	5.75999i	−0.0984990	+	0.249727i
$533$	3.48487	+	17.5196i	0.150946	+	0.758859i
$534$	4.42775	−	8.45591i	0.191607	−	0.365923i
$535$	−1.14252	+	2.75829i	−0.0493955	+	0.119251i
$536$	12.6676	−	16.2644i	0.547157	−	0.702516i
$537$	2.60621	+	6.29195i	0.112466	+	0.271518i
$538$	−1.39932	+	15.5631i	−0.0603291	+	0.670974i
$539$	28.1469	−	42.1248i	1.21237	−	1.81445i
$540$	2.02651	+	2.92399i	0.0872070	+	0.125828i
$541$	37.1103	+	7.38169i	1.59550	+	0.317364i	0.911239	−	0.411878i	$-0.135127\pi$
$541$	37.1103	+	7.38169i	1.59550	+	0.317364i	0.684256	+	0.729242i	$0.260127\pi$
$542$	−3.66739	−	34.2476i	−0.157528	−	1.47106i
$543$		−	14.8216i		−	0.636056i
$544$	6.61644	−	3.90688i	0.283678	−	0.167506i
$545$		−	7.70242i		−	0.329935i
$546$	30.2965	−	3.24429i	1.29657	−	0.138843i
$547$	6.05489	+	1.20439i	0.258888	+	0.0514961i	0.322828	−	0.946458i	$-0.395366\pi$
$547$	6.05489	+	1.20439i	0.258888	+	0.0514961i	−0.0639395	+	0.997954i	$0.520366\pi$
$548$	−7.51423	+	41.4485i	−0.320992	+	1.77059i
$549$	11.7426	−	17.5740i	0.501160	−	0.750039i
$550$	36.5750	+	3.28855i	1.55956	+	0.140224i
$551$	−0.440842	−	1.06429i	−0.0187805	−	0.0453402i
$552$	3.43330	+	6.04700i	0.146131	+	0.257377i
$553$	13.2469	−	31.9808i	0.563315	−	1.35996i
$554$	−34.4842	−	18.0569i	−1.46509	−	0.767163i
$555$	−0.660355	−	3.31983i	−0.0280305	−	0.140919i
$556$	15.2869	+	35.2004i	0.648308	+	1.49283i
$557$	10.4706	+	15.6704i	0.443653	+	0.663974i	0.984143	−	0.177377i	$-0.0567610\pi$
$557$	10.4706	+	15.6704i	0.443653	+	0.663974i	−0.540490	+	0.841351i	$0.681761\pi$
$558$	−9.22468	−	16.9107i	−0.390512	−	0.715887i
$559$	−10.6714	−	10.6714i	−0.451354	−	0.451354i
$560$	12.0041	−	2.81528i	0.507267	−	0.118967i
$561$	−12.6792	+	12.6792i	−0.535316	+	0.535316i
$562$	21.9890	+	6.46663i	0.927551	+	0.272778i
$563$	−31.7318	+	21.2025i	−1.33733	+	0.893578i	−0.998876	−	0.0474033i	$-0.984905\pi$
$563$	−31.7318	+	21.2025i	−1.33733	+	0.893578i	−0.338458	+	0.940981i	$0.609905\pi$
$564$	−28.5922	−	27.6359i	−1.20395	−	1.16368i
$565$	−3.53555	+	0.703266i	−0.148742	+	0.0295866i
$566$	−3.76468	−	12.0409i	−0.158241	−	0.506118i
$567$	40.1656	+	16.6371i	1.68680	+	0.698694i
$568$	7.61469	+	0.554297i	0.319505	+	0.0232578i
$569$	5.70005	−	2.36104i	0.238958	−	0.0989798i	−0.259991	−	0.965611i	$-0.583719\pi$
$569$	5.70005	−	2.36104i	0.238958	−	0.0989798i	0.498949	+	0.866631i	$0.333719\pi$
$570$	1.48527	−	1.24022i	0.0622113	−	0.0519470i
$571$	25.4415	+	16.9994i	1.06469	+	0.711405i	0.959118	−	0.283007i	$-0.0913319\pi$
$571$	25.4415	+	16.9994i	1.06469	+	0.711405i	0.105574	+	0.994411i	$0.466332\pi$
$572$	−24.3447	−	15.6744i	−1.01790	−	0.655379i
$573$	0.688527	−	3.46146i	0.0287636	−	0.144605i
$574$	31.6984	+	25.5663i	1.32307	+	1.06712i
$575$	−4.83596			−0.201673
$576$	−3.87809	−	15.3562i	−0.161587	−	0.639843i
$577$	13.1957			0.549345			0.274673	−	0.961538i	$-0.411431\pi$
$577$	13.1957			0.549345			0.274673	+	0.961538i	$0.411431\pi$
$578$	16.6825	+	13.4552i	0.693899	+	0.559662i
$579$	7.13682	−	35.8792i	0.296596	−	1.49109i
$580$	−1.24182	+	1.92873i	−0.0515638	+	0.0800863i
$581$	−6.71236	−	4.48506i	−0.278476	−	0.186071i
$582$	−31.7805	+	26.5370i	−1.31735	+	1.10000i
$583$	57.2035	−	23.6945i	2.36913	−	0.981324i
$584$	−3.81338	−	4.41215i	−0.157799	−	0.182576i
$585$	−3.49745	−	1.44869i	−0.144602	−	0.0598959i
$586$	10.2946	+	32.9264i	0.425268	+	1.36018i
$587$	28.1626	−	5.60188i	1.16239	−	0.231215i	0.424050	−	0.905639i	$-0.360608\pi$
$587$	28.1626	−	5.60188i	1.16239	−	0.231215i	0.738344	+	0.674424i	$0.235608\pi$
$588$	26.5644	−	27.4837i	1.09550	−	1.13341i
$589$	4.48913	−	2.99954i	0.184971	−	0.123594i
$590$	−5.37104	−	1.57954i	−0.221122	−	0.0650286i
$591$	4.25908	−	4.25908i	0.175195	−	0.175195i
$592$	1.25508	−	7.66330i	0.0515833	−	0.314960i
$593$	8.50593	+	8.50593i	0.349297	+	0.349297i	0.859848	−	0.510551i	$-0.170559\pi$
$593$	8.50593	+	8.50593i	0.349297	+	0.349297i	−0.510551	+	0.859848i	$0.670559\pi$
$594$	−9.12081	−	16.7203i	−0.374231	−	0.686041i
$595$	−2.32615	−	3.48133i	−0.0953630	−	0.142721i
$596$	1.72810	−	0.750483i	0.0707859	−	0.0307410i
$597$	5.73358	+	28.8246i	0.234660	+	1.17971i
$598$	3.37789	+	1.76876i	0.138132	+	0.0723299i
$599$	−17.7398	+	42.8278i	−0.724831	+	1.74990i	−0.0657345	+	0.997837i	$0.520939\pi$
$599$	−17.7398	+	42.8278i	−0.724831	+	1.74990i	−0.659096	+	0.752059i	$0.729061\pi$
$600$	26.7092	+	7.36365i	1.09040	+	0.300620i
$601$	9.36011	+	22.5973i	0.381807	+	0.921763i	0.991617	+	0.129215i	$0.0412459\pi$
$601$	9.36011	+	22.5973i	0.381807	+	0.921763i	−0.609810	+	0.792548i	$0.708754\pi$
$602$	−34.2679	−	3.08111i	−1.39665	−	0.125577i
$603$	−8.01693	+	11.9982i	−0.326475	+	0.488604i
$604$	−21.4117	−	3.88175i	−0.871232	−	0.157946i
$605$	18.3872	+	3.65745i	0.747548	+	0.148697i
$606$	14.0851	−	1.50830i	0.572168	−	0.0612703i
$607$		−	19.9552i		−	0.809956i	−0.914326	−	0.404978i	$-0.867279\pi$
$607$		−	19.9552i		−	0.809956i	0.914326	−	0.404978i	$-0.132721\pi$
$608$	4.18940	−	1.46801i	0.169902	−	0.0595356i
$609$			12.9238i			0.523698i
$610$	−1.25604	−	11.7294i	−0.0508554	−	0.474909i
$611$	−21.3856	−	4.25387i	−0.865170	−	0.172093i
$612$	−4.42050	+	3.06369i	−0.178688	+	0.123842i
$613$	15.7066	−	23.5066i	0.634384	−	0.949423i	−0.365443	−	0.930834i	$-0.619083\pi$
$613$	15.7066	−	23.5066i	0.634384	−	0.949423i	0.999827	−	0.0185890i	$-0.00591740\pi$
$614$	−1.24270	+	13.8212i	−0.0501514	+	0.557779i
$615$	−4.87019	−	11.7577i	−0.196385	−	0.474115i
$616$	−65.5057	+	8.14361i	−2.63930	+	0.328116i
$617$	−7.93425	+	19.1550i	−0.319421	+	0.771150i	0.679864	+	0.733338i	$0.262039\pi$
$617$	−7.93425	+	19.1550i	−0.319421	+	0.771150i	−0.999285	+	0.0378118i	$0.987961\pi$
$618$	15.6551	−	29.8973i	0.629740	−	1.20265i
$619$	−1.06040	−	5.33101i	−0.0426212	−	0.214271i	0.953606	−	0.301059i	$-0.0973400\pi$
$619$	−1.06040	−	5.33101i	−0.0426212	−	0.214271i	−0.996227	+	0.0867872i	$0.972340\pi$
$620$	−10.0013	−	3.94476i	−0.401660	−	0.158425i
$621$	1.39347	+	2.08547i	0.0559179	+	0.0836871i
$622$	−38.1166	+	20.7924i	−1.52833	+	0.833697i
$623$	−8.43735	−	8.43735i	−0.338035	−	0.338035i
$624$	−15.9630	−	14.9124i	−0.639031	−	0.596974i
$625$	−11.4662	+	11.4662i	−0.458647	+	0.458647i
$626$	9.69933	−	32.9814i	0.387663	−	1.31820i
$627$	−8.61344	+	5.75532i	−0.343988	+	0.229845i
$628$	−0.0751732	−	4.41982i	−0.00299974	−	0.176370i
$629$	−2.58630	+	0.514447i	−0.103123	+	0.0205124i
$630$	−8.23721	+	2.57542i	−0.328178	+	0.102607i
$631$	−35.9213	−	14.8791i	−1.43000	−	0.592327i	−0.472652	−	0.881249i	$-0.656703\pi$
$631$	−35.9213	−	14.8791i	−1.43000	−	0.592327i	−0.957353	+	0.288922i	$0.906703\pi$
$632$	−23.5572	+	7.80749i	−0.937054	+	0.310565i
$633$	−14.1640	+	5.86692i	−0.562968	+	0.233189i
$634$	6.03086	+	7.22250i	0.239516	+	0.286842i
$635$	4.27222	+	2.85460i	0.169538	+	0.113282i
$636$	45.6544	−	9.89119i	1.81032	−	0.392211i
$637$	4.08894	−	20.5565i	0.162010	−	0.814479i
$638$	7.70997	−	9.55923i	0.305240	−	0.378454i
$639$	−5.34410			−0.211409
$640$	−7.15468	−	5.19142i	−0.282813	−	0.205209i
$641$	2.72233			0.107526			0.0537629	−	0.998554i	$-0.482878\pi$
$641$	2.72233			0.107526			0.0537629	+	0.998554i	$0.482878\pi$
$642$	7.57064	−	9.38648i	0.298789	−	0.370455i
$643$	0.135549	−	0.681448i	0.00534551	−	0.0268737i	−0.978020	−	0.208509i	$-0.933139\pi$
$643$	0.135549	−	0.681448i	0.00534551	−	0.0268737i	0.983366	+	0.181635i	$0.0581390\pi$
$644$	8.49569	−	1.84062i	0.334777	−	0.0725306i
$645$	8.94005	+	5.97355i	0.352014	+	0.235208i
$646$	−0.966188	−	1.15710i	−0.0380142	−	0.0455254i
$647$	−29.4862	+	12.2136i	−1.15922	+	0.480165i	−0.877616	−	0.479365i	$-0.840867\pi$
$647$	−29.4862	+	12.2136i	−1.15922	+	0.480165i	−0.281606	+	0.959530i	$0.590867\pi$
$648$	−9.80564	−	29.5861i	−0.385202	−	1.16225i
$649$	27.6909	+	11.4700i	1.08696	+	0.450235i
$650$	14.4998	−	4.53347i	0.568731	−	0.177817i
$651$	−59.4067	+	11.8167i	−2.32833	+	0.463134i
$652$	0.353637	+	20.7922i	0.0138495	+	0.814284i
$653$	−35.6443	+	23.8167i	−1.39487	+	0.932021i	−0.394956	+	0.918700i	$0.629240\pi$
$653$	−35.6443	+	23.8167i	−1.39487	+	0.932021i	−0.999911	+	0.0133207i	$0.995760\pi$
$654$	−8.77760	+	29.8472i	−0.343231	+	1.16712i
$655$	2.68592	−	2.68592i	0.104948	−	0.104948i
$656$	−0.992865	−	29.1794i	−0.0387649	−	1.13926i
$657$	2.88640	+	2.88640i	0.112609	+	0.112609i
$658$	−43.6396	+	23.8051i	−1.70125	+	0.928021i
$659$	19.0570	+	28.5207i	0.742354	+	1.11101i	0.989849	+	0.142122i	$0.0453924\pi$
$659$	19.0570	+	28.5207i	0.742354	+	1.11101i	−0.247496	+	0.968889i	$0.579608\pi$
$660$	19.1897	+	7.56894i	0.746960	+	0.294621i
$661$	−2.62496	−	13.1966i	−0.102099	−	0.513287i	−0.997661	−	0.0683508i	$-0.978226\pi$
$661$	−2.62496	−	13.1966i	−0.102099	−	0.513287i	0.895562	−	0.444936i	$-0.146774\pi$
$662$	−2.57053	+	4.90907i	−0.0999064	+	0.190797i
$663$	−2.83877	+	6.85340i	−0.110249	+	0.266164i
$664$	0.714030	+	5.74352i	0.0277097	+	0.222892i
$665$	−0.925683	−	2.23480i	−0.0358965	−	0.0866617i
$666$	−0.486755	+	5.41365i	−0.0188614	+	0.209775i
$667$	−0.898508	+	1.34471i	−0.0347904	+	0.0520675i
$668$	24.3785	−	16.8958i	0.943233	−	0.653720i
$669$	−8.49882	−	1.69052i	−0.328584	−	0.0653593i
$670$	0.857527	+	8.00794i	0.0331292	+	0.309374i
$671$			63.1543i			2.43805i
$672$	−49.7248	−	2.77046i	−1.91817	−	0.106873i
$673$			23.6665i			0.912275i	0.889909	+	0.456137i	$0.150767\pi$
$673$			23.6665i			0.912275i	−0.889909	+	0.456137i	$0.849233\pi$
$674$	−27.5667	+	2.95197i	−1.06183	+	0.113705i
$675$	9.80133	+	1.94961i	0.377254	+	0.0750404i
$676$	13.7968	+	2.50123i	0.530646	+	0.0962012i
$677$	14.9427	−	22.3633i	0.574294	−	0.859491i	−0.424654	−	0.905356i	$-0.639604\pi$
$677$	14.9427	−	22.3633i	0.574294	−	0.859491i	0.998948	+	0.0458647i	$0.0146043\pi$
$678$	14.5019	+	1.30390i	0.556940	+	0.0500760i
$679$	19.8069	+	47.8181i	0.760120	+	1.83509i
$680$	−0.797818	+	2.89382i	−0.0305949	+	0.110973i
$681$	−19.6203	+	47.3675i	−0.751850	+	1.81513i
$682$	50.9904	+	26.7000i	1.95252	+	1.02240i
$683$	4.84474	+	24.3562i	0.185379	+	0.931963i	0.955708	+	0.294316i	$0.0950920\pi$
$683$	4.84474	+	24.3562i	0.185379	+	0.931963i	−0.770329	+	0.637647i	$0.779908\pi$
$684$	−2.85008	+	1.23774i	−0.108976	+	0.0473261i
$685$	−9.14265	−	13.6829i	−0.349323	−	0.522798i
$686$	−4.17955	−	7.66195i	−0.159576	−	0.292535i
$687$	−9.70237	−	9.70237i	−0.370168	−	0.370168i
$688$	14.3938	+	20.0319i	0.548757	+	0.763710i
$689$	18.1124	−	18.1124i	0.690027	−	0.690027i
$690$	−2.60619	−	0.766439i	−0.0992158	−	0.0291779i
$691$	11.5361	−	7.70819i	0.438855	−	0.293233i	−0.316448	−	0.948610i	$-0.602490\pi$
$691$	11.5361	−	7.70819i	0.438855	−	0.293233i	0.755302	+	0.655377i	$0.227490\pi$
$692$	7.04594	−	7.28976i	0.267846	−	0.277115i
$693$	45.3167	−	9.01406i	1.72144	−	0.342416i
$694$	−10.4404	−	33.3924i	−0.396311	−	1.26756i
$695$	−13.8511	−	5.73730i	−0.525401	−	0.217628i
$696$	7.01008	−	6.05875i	0.265716	−	0.229656i
$697$	−9.15978	+	3.79410i	−0.346951	+	0.143712i
$698$	38.3260	−	32.0026i	1.45066	−	1.21132i
$699$	3.55804	+	2.37740i	0.134577	+	0.0899217i
$700$	18.7496	−	29.1209i	0.708667	−	1.10067i
$701$	7.20549	−	36.2244i	0.272148	−	1.36818i	−0.566750	−	0.823890i	$-0.691800\pi$
$701$	7.20549	−	36.2244i	0.272148	−	1.36818i	0.838898	−	0.544289i	$-0.183200\pi$
$702$	−6.13312	−	4.94665i	−0.231480	−	0.186699i
$703$	−1.52345			−0.0574581
$704$	35.1268	+	31.7136i	1.32389	+	1.19525i
$705$	15.5347			0.585072
$706$	−17.9992	−	14.5172i	−0.677408	−	0.546361i
$707$	3.45474	−	17.3682i	0.129929	−	0.653197i
$708$	19.0130	+	12.2416i	0.714551	+	0.460066i
$709$	−20.0441	−	13.3930i	−0.752770	−	0.502985i	0.119003	−	0.992894i	$-0.462030\pi$
$709$	−20.0441	−	13.3930i	−0.752770	−	0.502985i	−0.871774	+	0.489909i	$0.837030\pi$
$710$	−2.28945	+	1.91171i	−0.0859214	+	0.0717452i
$711$	16.0489	−	6.64766i	0.601880	−	0.249307i
$712$	−0.621074	+	8.53205i	−0.0232757	+	0.319752i
$713$	−7.00278	−	2.90065i	−0.262256	−	0.108630i
$714$	5.04664	+	16.1412i	0.188866	+	0.604068i
$715$	11.0940	−	2.20674i	0.414893	−	0.0825273i
$716$	−4.38875	−	4.24196i	−0.164015	−	0.158529i
$717$	16.0031	−	10.6929i	0.597647	−	0.399335i
$718$	2.97042	+	0.873555i	0.110855	+	0.0326008i
$719$	5.08606	−	5.08606i	0.189678	−	0.189678i	−0.605879	−	0.795557i	$-0.707178\pi$
$719$	5.08606	−	5.08606i	0.189678	−	0.189678i	0.795557	+	0.605879i	$0.207178\pi$
$720$	5.25861	+	3.26063i	0.195977	+	0.121516i
$721$	−29.8317	−	29.8317i	−1.11099	−	1.11099i
$722$	12.4504	+	22.8242i	0.463358	+	0.849428i
$723$	9.14439	+	13.6855i	0.340084	+	0.508971i
$724$	5.29143	+	12.1843i	0.196654	+	0.452827i
$725$	1.25711	+	6.31990i	0.0466878	+	0.234715i
$726$	−67.0833	−	35.1267i	−2.48970	−	1.30367i
$727$	16.1339	−	38.9506i	0.598372	−	1.44460i	−0.276867	−	0.960908i	$-0.589296\pi$
$727$	16.1339	−	38.9506i	0.598372	−	1.44460i	0.875240	−	0.483690i	$-0.160704\pi$
$728$	−23.7475	+	13.4831i	−0.880140	+	0.499717i
$729$	2.51641	+	6.07515i	0.0932003	+	0.225006i
$730$	2.26908	+	0.204019i	0.0839826	+	0.00755109i
$731$	4.65368	−	6.96472i	0.172122	−	0.257599i
$732$	−8.49949	+	46.8832i	−0.314150	+	1.73285i
$733$	−32.2035	−	6.40567i	−1.18946	−	0.236599i	−0.439601	−	0.898193i	$-0.644880\pi$
$733$	−32.2035	−	6.40567i	−1.18946	−	0.236599i	−0.749862	+	0.661595i	$0.769880\pi$
$734$	−41.5743	+	4.45197i	−1.53454	+	0.164325i
$735$			14.9324i			0.550791i
$736$	−4.98122	−	3.74531i	−0.183610	−	0.138054i
$737$		−	43.1170i		−	1.58824i
$738$	2.17598	+	20.3202i	0.0800988	+	0.747995i
$739$	−1.11174	−	0.221139i	−0.0408961	−	0.00813474i	0.174600	−	0.984639i	$-0.444137\pi$
$739$	−1.11174	−	0.221139i	−0.0408961	−	0.00813474i	−0.215496	+	0.976505i	$0.569137\pi$
$740$	1.72806	+	2.49336i	0.0635247	+	0.0916579i
$741$	−2.38096	+	3.56336i	−0.0874669	+	0.130903i
$742$	5.22950	−	58.1620i	0.191981	−	2.13519i
$743$	−11.1248	−	26.8577i	−0.408130	−	0.985313i	−0.985629	−	0.168922i	$-0.945972\pi$
$743$	−11.1248	−	26.8577i	−0.408130	−	0.985313i	0.577500	−	0.816391i	$-0.304028\pi$
$744$	34.2599	+	26.6834i	1.25603	+	0.978262i
$745$	−0.281663	+	0.679995i	−0.0103193	+	0.0249131i
$746$	−15.9413	+	30.4440i	−0.583653	+	1.11463i
$747$	−0.790350	−	3.97336i	−0.0289174	−	0.145378i
$748$	5.89656	−	14.9497i	0.215600	−	0.546615i
$749$	−8.37522	−	12.5344i	−0.306024	−	0.457997i
$750$	−20.3251	+	11.0872i	−0.742168	+	0.404848i
$751$	−19.2670	−	19.2670i	−0.703061	−	0.703061i	0.262005	−	0.965066i	$-0.415616\pi$
$751$	−19.2670	−	19.2670i	−0.703061	−	0.703061i	−0.965066	+	0.262005i	$0.915616\pi$
$752$	33.3709	+	12.5109i	1.21691	+	0.456224i
$753$	−7.08155	+	7.08155i	−0.258066	+	0.258066i
$754$	1.43343	−	4.87421i	0.0522025	−	0.177508i
$755$	7.06843	−	4.72298i	0.257247	−	0.171887i
$756$	−17.9608	+	0.305481i	−0.653228	+	0.0111102i
$757$	3.81457	−	0.758766i	0.138643	−	0.0275778i	−0.125281	−	0.992121i	$-0.539983\pi$
$757$	3.81457	−	0.758766i	0.138643	−	0.0275778i	0.263924	+	0.964544i	$0.414983\pi$
$758$	33.7005	−	10.5367i	1.22406	−	0.382709i
$759$	13.4365	+	5.56556i	0.487713	+	0.202017i
$760$	−0.778225	+	1.54979i	−0.0282292	+	0.0562170i
$761$	14.1327	−	5.85394i	0.512309	−	0.212205i	−0.111526	−	0.993762i	$-0.535574\pi$
$761$	14.1327	−	5.85394i	0.512309	−	0.212205i	0.623835	+	0.781556i	$0.285574\pi$
$762$	−13.3019	−	15.9303i	−0.481878	−	0.577093i
$763$	32.3375	+	21.6072i	1.17069	+	0.782233i
$764$	0.669753	+	3.09136i	0.0242308	+	0.111841i
$765$	0.409911	−	2.06076i	0.0148204	−	0.0745071i
$766$	21.7932	−	27.0203i	0.787419	−	0.976285i
$767$	12.3995			0.447722
$768$	21.8086	+	28.2704i	0.786949	+	1.02012i
$769$	−47.4209			−1.71004			−0.855020	−	0.518595i	$-0.826455\pi$
$769$	−47.4209			−1.71004			−0.855020	+	0.518595i	$0.826455\pi$
$770$	16.1894	−	20.0725i	0.583426	−	0.723363i
$771$	2.55505	−	12.8451i	0.0920178	−	0.462604i
$772$	6.94222	+	32.0430i	0.249856	+	1.15325i
$773$	18.9615	+	12.6697i	0.681998	+	0.455697i	0.847698	−	0.530480i	$-0.177988\pi$
$773$	18.9615	+	12.6697i	0.681998	+	0.455697i	−0.165699	+	0.986176i	$0.552988\pi$
$774$	−11.0665	−	13.2531i	−0.397777	−	0.476374i
$775$	−27.9013	+	11.5571i	−1.00224	+	0.415143i
$776$	16.6517	−	33.1611i	0.597763	−	1.19041i
$777$	15.7903	+	6.54054i	0.566473	+	0.234641i
$778$	−30.8894	+	9.65777i	−1.10744	+	0.346248i
$779$	−5.61781	+	1.11745i	−0.201279	+	0.0400369i
$780$	8.53274	−	0.145126i	0.305521	−	0.00519636i
$781$	13.2770	−	8.87142i	0.475089	−	0.317444i
$782$	−0.597092	+	2.03034i	−0.0213520	+	0.0726049i
$783$	2.36318	−	2.36318i	0.0844532	−	0.0844532i
$784$	−12.0258	+	32.0771i	−0.429493	+	1.14561i
$785$	1.22111	+	1.22111i	0.0435833	+	0.0435833i
$786$	−13.4689	+	7.34721i	−0.480420	+	0.262066i
$787$	8.45960	+	12.6607i	0.301552	+	0.451305i	0.951040	−	0.309067i	$-0.100017\pi$
$787$	8.45960	+	12.6607i	0.301552	+	0.451305i	−0.649488	+	0.760372i	$0.725017\pi$
$788$	−1.98072	+	5.02177i	−0.0705603	+	0.178893i
$789$	−12.8015	−	64.3577i	−0.455747	−	2.29119i
$790$	4.49741	−	8.58895i	0.160011	−	0.305581i
$791$	6.96556	−	16.8163i	0.247667	−	0.597920i
$792$	−26.1342	−	20.3547i	−0.928637	−	0.723273i
$793$	9.99830	+	24.1380i	0.355050	+	0.857167i
$794$	−3.08422	+	34.3024i	−0.109455	+	1.21735i
$795$	−10.1388	+	15.1737i	−0.359585	+	0.538157i
$796$	−15.0040	−	21.6488i	−0.531802	−	0.767322i
$797$	1.21865	+	0.242404i	0.0431668	+	0.00858640i	0.216626	−	0.976255i	$-0.430495\pi$
$797$	1.21865	+	0.242404i	0.0431668	+	0.00858640i	−0.173460	+	0.984841i	$0.555495\pi$
$798$	1.04031	+	9.71483i	0.0368265	+	0.343901i
$799$		−	12.1023i		−	0.428148i
$800$	−24.5856	+	3.48198i	−0.869232	+	0.123107i
$801$		−	5.98792i		−	0.211573i
$802$	−26.7844	+	2.86820i	−0.945791	+	0.101280i
$803$	−11.9626	−	2.37950i	−0.422150	−	0.0839709i
$804$	5.80282	−	32.0083i	0.204650	−	1.12885i
$805$	−1.88669	+	2.82363i	−0.0664971	+	0.0995200i
$806$	23.7159	+	2.13236i	0.835358	+	0.0751092i
$807$	9.43574	+	22.7799i	0.332154	+	0.801890i
$808$	−11.0404	+	6.26840i	−0.388400	+	0.220522i
$809$	11.5600	−	27.9083i	0.406428	−	0.981203i	−0.579642	−	0.814871i	$-0.696808\pi$
$809$	11.5600	−	27.9083i	0.406428	−	0.981203i	0.986070	−	0.166332i	$-0.0531923\pi$
$810$	10.7871	+	5.64842i	0.379020	+	0.198465i
$811$	1.27743	+	6.42210i	0.0448568	+	0.225510i	0.996711	−	0.0810417i	$-0.0258247\pi$
$811$	1.27743	+	6.42210i	0.0448568	+	0.225510i	−0.951854	+	0.306552i	$0.900825\pi$
$812$	−4.61388	−	10.6242i	−0.161916	−	0.372836i
$813$	−30.1950	−	45.1900i	−1.05899	−	1.58488i
$814$	−7.77756	−	14.2578i	−0.272603	−	0.499737i
$815$	−5.74447	−	5.74447i	−0.201220	−	0.201220i
$816$	6.38934	−	10.3045i	0.223672	−	0.360729i
$817$	3.42189	−	3.42189i	0.119717	−	0.119717i
$818$	10.8193	+	3.18179i	0.378288	+	0.111249i
$819$	15.8933	−	10.6196i	0.555357	−	0.371078i
$820$	8.20119	+	7.92688i	0.286398	+	0.276819i
$821$	0.732994	−	0.145802i	0.0255817	−	0.00508851i	−0.182283	−	0.983246i	$-0.558349\pi$
$821$	0.732994	−	0.145802i	0.0255817	−	0.00508851i	0.207865	+	0.978158i	$0.433349\pi$
$822$	19.8352	+	63.4408i	0.691832	+	2.21275i
$823$	−40.6921	−	16.8552i	−1.41844	−	0.587535i	−0.463969	−	0.885852i	$-0.653575\pi$
$823$	−40.6921	−	16.8552i	−1.41844	−	0.587535i	−0.954467	+	0.298316i	$0.903575\pi$
$824$	−2.19592	+	30.1666i	−0.0764984	+	1.05090i
$825$	53.5351	−	22.1750i	1.86385	−	0.772033i
$826$	21.6986	−	18.1185i	0.754990	−	0.630423i
$827$	−17.5797	−	11.7464i	−0.611308	−	0.408463i	0.211016	−	0.977483i	$-0.432323\pi$
$827$	−17.5797	−	11.7464i	−0.611308	−	0.408463i	−0.822324	+	0.569020i	$0.807323\pi$
$828$	3.66780	+	2.36153i	0.127465	+	0.0820687i
$829$	−8.12158	+	40.8299i	−0.282074	+	1.41808i	0.536607	+	0.843833i	$0.319706\pi$
$829$	−8.12158	+	40.8299i	−0.282074	+	1.41808i	−0.818681	+	0.574249i	$0.805294\pi$
$830$	−1.75995	−	1.41948i	−0.0610889	−	0.0492710i
$831$	−61.4224			−2.13072
$832$	18.4465	+	6.56007i	0.639516	+	0.227429i
$833$	11.6331			0.403062
$834$	47.1353	+	38.0168i	1.63216	+	1.31641i
$835$	−2.26061	+	11.3649i	−0.0782316	+	0.393297i
$836$	5.02612	−	7.80631i	0.173832	−	0.269987i
$837$	13.0236	+	8.70208i	0.450161	+	0.300788i
$838$	13.8787	−	11.5888i	0.479431	−	0.400330i
$839$	33.4505	−	13.8556i	1.15484	−	0.478350i	0.278686	−	0.960382i	$-0.410101\pi$
$839$	33.4505	−	13.8556i	1.15484	−	0.478350i	0.876154	+	0.482032i	$0.160101\pi$
$840$	14.7198	−	12.7222i	0.507881	−	0.438958i
$841$	−24.8016	−	10.2732i	−0.855227	−	0.354247i
$842$	−8.27236	−	26.4583i	−0.285085	−	0.911813i
$843$	35.4718	−	7.05577i	1.22171	−	0.243014i
$844$	9.54919	−	9.87964i	0.328697	−	0.340071i
$845$	−4.55459	+	3.04328i	−0.156683	+	0.104692i
$846$	−23.9325	−	7.03819i	−0.822817	−	0.241978i
$847$	−66.9361	+	66.9361i	−2.29995	+	2.29995i
$848$	−33.9997	+	24.4302i	−1.16755	+	0.838936i
$849$	−14.0763	−	14.0763i	−0.483097	−	0.483097i
$850$	4.03794	+	7.40236i	0.138500	+	0.253899i
$851$	1.18825	+	1.77834i	0.0407326	+	0.0609606i
$852$	11.0503	−	4.79892i	0.378576	−	0.164408i
$853$	−2.29019	−	11.5136i	−0.0784145	−	0.394217i	−0.999982	−	0.00599829i	$-0.998091\pi$
$853$	−2.29019	−	11.5136i	−0.0784145	−	0.394217i	0.921567	−	0.388218i	$-0.126909\pi$
$854$	52.7676	+	27.6306i	1.80567	+	0.945498i
$855$	0.464534	−	1.12148i	0.0158867	−	0.0383540i
$856$	−2.87251	+	10.4191i	−0.0981805	+	0.356117i
$857$	−3.96261	−	9.56660i	−0.135360	−	0.326789i	0.841636	−	0.540045i	$-0.181593\pi$
$857$	−3.96261	−	9.56660i	−0.135360	−	0.326789i	−0.976996	+	0.213257i	$0.931593\pi$
$858$	−45.5045	−	4.09143i	−1.55350	−	0.139679i
$859$	−22.7757	+	34.0863i	−0.777098	+	1.16301i	0.205753	+	0.978604i	$0.434036\pi$
$859$	−22.7757	+	34.0863i	−0.777098	+	1.16301i	−0.982850	+	0.184405i	$0.940964\pi$
$860$	−9.48191	−	1.71898i	−0.323330	−	0.0586168i
$861$	63.0249	+	12.5364i	2.14788	+	0.427241i
$862$	−36.7519	+	3.93556i	−1.25177	+	0.134046i
$863$		−	22.4117i		−	0.762902i	−0.924389	−	0.381451i	$-0.875424\pi$
$863$		−	22.4117i		−	0.762902i	0.924389	−	0.381451i	$-0.124576\pi$
$864$	8.58584	+	9.59903i	0.292096	+	0.326566i
$865$			3.96067i			0.134667i
$866$	1.27842	+	11.9384i	0.0434424	+	0.405683i
$867$	33.1692	+	6.59776i	1.12648	+	0.224072i
$868$	44.6175	−	30.9228i	1.51442	−	1.04959i
$869$	−28.8368	+	43.1574i	−0.978223	+	1.46401i
$870$	−0.324148	+	3.60515i	−0.0109897	+	0.122226i
$871$	−6.82609	−	16.4796i	−0.231293	−	0.558391i
$872$	−3.43991	−	27.6700i	−0.116490	−	0.937024i
$873$	−9.93967	+	23.9965i	−0.336407	+	0.812158i
$874$	−0.567167	+	1.08315i	−0.0191847	+	0.0366381i
$875$	5.64647	+	28.3867i	0.190886	+	0.959646i
$876$	−8.56029	−	3.37641i	−0.289225	−	0.114078i
$877$	22.8368	+	34.1777i	0.771145	+	1.15410i	0.984200	+	0.177060i	$0.0566587\pi$
$877$	22.8368	+	34.1777i	0.771145	+	1.15410i	−0.213055	+	0.977040i	$0.568341\pi$
$878$	26.6986	−	14.5639i	0.901035	−	0.491509i
$879$	38.4921	+	38.4921i	1.29831	+	1.29831i
$880$	−18.4774	+	0.628716i	−0.622873	+	0.0211940i
$881$	−19.2835	+	19.2835i	−0.649677	+	0.649677i	−0.952915	−	0.303238i	$-0.901932\pi$
$881$	−19.2835	+	19.2835i	−0.649677	+	0.649677i	0.303238	+	0.952915i	$0.401932\pi$
$882$	6.76531	−	23.0047i	0.227800	−	0.774607i
$883$	43.0348	−	28.7549i	1.44824	−	0.967681i	0.451068	−	0.892490i	$-0.351043\pi$
$883$	43.0348	−	28.7549i	1.44824	−	0.967681i	0.997169	−	0.0751915i	$-0.0239568\pi$
$884$	−0.113060	−	6.64740i	−0.00380263	−	0.223576i
$885$	−8.66433	+	1.72344i	−0.291248	+	0.0579329i
$886$	−25.2167	+	7.88416i	−0.847171	+	0.264874i
$887$	−2.36214	−	0.978431i	−0.0793129	−	0.0328525i	0.342674	−	0.939454i	$-0.388667\pi$
$887$	−2.36214	−	0.978431i	−0.0793129	−	0.0328525i	−0.421987	+	0.906602i	$0.638667\pi$
$888$	−3.85488	−	11.6312i	−0.129361	−	0.390316i
$889$	−23.9693	+	9.92840i	−0.803904	+	0.332988i
$890$	−2.14202	−	2.56526i	−0.0718006	−	0.0859878i
$891$	−54.2025	−	36.2170i	−1.81585	−	1.21331i
$892$	7.59012	−	1.64443i	0.254136	−	0.0550595i
$893$	1.36404	−	6.85748i	0.0456458	−	0.229477i
$894$	1.86637	−	2.31403i	0.0624208	−	0.0773926i
$895$	2.38450			0.0797049
$896$	41.8661	−	15.4746i	1.39865	−	0.516971i
$897$	6.01663			0.200889
$898$	−29.0127	+	35.9715i	−0.968165	+	1.20038i
$899$	−1.97036	+	9.90565i	−0.0657151	+	0.330372i
$900$	16.9866	−	3.68021i	0.566221	−	0.122674i
$901$	11.8210	+	7.89857i	0.393816	+	0.263140i
$902$	−39.1383	−	46.8717i	−1.30316	−	1.56066i
$903$	−50.1581	+	20.7762i	−1.66916	+	0.691388i
$904$	−12.3870	+	4.10538i	−0.411985	+	0.136543i
$905$	−4.79444	−	1.98592i	−0.159372	−	0.0660142i
$906$	−32.7727	+	10.2466i	−1.08880	+	0.340421i
$907$	21.3347	−	4.24373i	0.708405	−	0.140911i	0.172279	−	0.985048i	$-0.444887\pi$
$907$	21.3347	−	4.24373i	0.708405	−	0.140911i	0.536127	+	0.844138i	$0.319887\pi$
$908$	−0.781420	−	45.9437i	−0.0259323	−	1.52470i
$909$	7.38893	−	4.93712i	0.245075	−	0.163754i
$910$	3.00993	−	10.2349i	0.0997781	−	0.339284i
$911$	1.38797	−	1.38797i	0.0459856	−	0.0459856i	−0.683740	−	0.729726i	$-0.739648\pi$
$911$	1.38797	−	1.38797i	0.0459856	−	0.0459856i	0.729726	+	0.683740i	$0.239648\pi$
$912$	4.78178	−	5.11866i	0.158341	−	0.169496i
$913$	8.55950	+	8.55950i	0.283278	+	0.283278i
$914$	31.4227	−	17.1409i	1.03937	−	0.566970i
$915$	−10.3414	−	15.4771i	−0.341877	−	0.511655i
$916$	11.4398	+	4.51216i	0.377982	+	0.149086i
$917$	3.74177	+	18.8111i	0.123564	+	0.621198i
$918$	2.02869	−	3.87430i	0.0669568	−	0.127871i
$919$	1.63873	−	3.95625i	0.0540568	−	0.130505i	−0.894544	−	0.446980i	$-0.852499\pi$
$919$	1.63873	−	3.95625i	0.0540568	−	0.130505i	0.948601	+	0.316475i	$0.102499\pi$
$920$	2.41608	−	0.300365i	0.0796558	−	0.00990275i
$921$	8.37964	+	20.2302i	0.276119	+	0.666609i
$922$	−0.364939	+	4.05882i	−0.0120186	+	0.133670i
$923$	3.67009	−	5.49268i	0.120802	−	0.180794i
$924$	−85.6091	+	59.3325i	−2.81633	+	1.95190i
$925$	8.35786	+	1.66248i	0.274805	+	0.0546621i
$926$	5.23641	+	48.8998i	0.172079	+	1.60695i
$927$		−	21.1713i		−	0.695358i
$928$	−3.59972	+	7.48334i	−0.118167	+	0.245653i
$929$			53.4969i			1.75518i	0.479415	+	0.877589i	$0.340849\pi$
$929$			53.4969i			1.75518i	−0.479415	+	0.877589i	$0.659151\pi$
$930$	−16.8682	+	1.80632i	−0.553129	+	0.0592316i
$931$	6.59161	+	1.31115i	0.216031	+	0.0429713i
$932$	−3.77369	−	0.684136i	−0.123611	−	0.0224096i
$933$	−38.0634	+	56.9659i	−1.24614	+	1.86498i
$934$	17.9625	+	1.61506i	0.587752	+	0.0528463i
$935$	2.40255	+	5.80028i	0.0785719	+	0.189689i
$936$	−13.2111	−	3.64228i	−0.431819	−	0.119052i
$937$	9.69070	−	23.3954i	0.316582	−	0.764295i	−0.682849	−	0.730559i	$-0.739259\pi$
$937$	9.69070	−	23.3954i	0.316582	−	0.764295i	0.999431	−	0.0337361i	$-0.0107406\pi$
$938$	−36.0257	−	18.8641i	−1.17628	−	0.615934i
$939$	−10.5830	−	53.2042i	−0.345362	−	1.73625i
$940$	−12.7706	+	5.54601i	−0.416530	+	0.180891i
$941$	−14.9326	−	22.3482i	−0.486788	−	0.728529i	0.504037	−	0.863682i	$-0.331847\pi$
$941$	−14.9326	−	22.3482i	−0.486788	−	0.728529i	−0.990825	+	0.135153i	$0.956847\pi$
$942$	−3.34029	−	6.12342i	−0.108833	−	0.199512i
$943$	5.68614	+	5.68614i	0.185166	+	0.185166i
$944$	−20.0002	−	3.27559i	−0.650952	−	0.106611i
$945$	4.96222	−	4.96222i	0.161421	−	0.161421i
$946$	49.4946	+	14.5556i	1.60921	+	0.473243i
$947$	15.6970	−	10.4884i	0.510083	−	0.340827i	−0.273747	−	0.961802i	$-0.588263\pi$
$947$	15.6970	−	10.4884i	0.510083	−	0.340827i	0.783830	+	0.620975i	$0.213263\pi$
$948$	−27.2155	+	28.1573i	−0.883920	+	0.914508i
$949$	−4.94890	+	0.984397i	−0.160648	+	0.0319549i
$950$	1.45369	+	4.64949i	0.0471641	+	0.150849i
$951$	13.7172	+	5.68185i	0.444811	+	0.184247i
$952$	−9.91119	−	11.4674i	−0.321224	−	0.371661i
$953$	31.0836	−	12.8753i	1.00690	−	0.417070i	0.182575	−	0.983192i	$-0.441557\pi$
$953$	31.0836	−	12.8753i	1.00690	−	0.417070i	0.824322	+	0.566122i	$0.191557\pi$
$954$	22.4942	−	18.7829i	0.728278	−	0.608119i
$955$	−1.02745	−	0.686517i	−0.0332473	−	0.0222152i
$956$	−9.33814	+	14.5035i	−0.302017	+	0.469077i
$957$	3.78059	−	19.0063i	0.122209	−	0.614387i
$958$	9.24643	+	7.45768i	0.298739	+	0.240947i
$959$	83.0932			2.68322
$960$	−13.8015	−	2.02001i	−0.445441	−	0.0651955i
$961$	−16.3349			−0.526932
$962$	−5.22988	−	4.21814i	−0.168618	−	0.135998i
$963$	1.47587	−	7.41970i	0.0475592	−	0.239096i
$964$	−12.4031	−	7.98580i	−0.399478	−	0.257205i
$965$	−10.6498	−	7.11598i	−0.342830	−	0.229072i
$966$	10.5288	−	8.79164i	0.338758	−	0.282866i
$967$	−39.0826	+	16.1886i	−1.25681	+	0.520589i	−0.908930	−	0.416949i	$-0.863099\pi$
$967$	−39.0826	+	16.1886i	−1.25681	+	0.520589i	−0.347883	+	0.937538i	$0.613099\pi$
$968$	67.6874	+	4.92718i	2.17555	+	0.158365i
$969$	−2.19760	−	0.910274i	−0.0705970	−	0.0292422i
$970$	4.32588	+	13.8359i	0.138896	+	0.444244i
$971$	15.9123	−	3.16514i	0.510649	−	0.101574i	0.0669606	−	0.997756i	$-0.478670\pi$
$971$	15.9123	−	3.16514i	0.510649	−	0.101574i	0.443688	+	0.896181i	$0.353670\pi$
$972$	−25.5418	−	24.6874i	−0.819252	−	0.791850i
$973$	62.9429	−	42.0571i	2.01786	−	1.34829i
$974$	22.7000	+	6.67571i	0.727353	+	0.213903i
$975$	16.9509	−	16.9509i	0.542862	−	0.542862i
$976$	−9.75052	−	41.5754i	−0.312106	−	1.33080i
$977$	−14.4085	−	14.4085i	−0.460970	−	0.460970i	0.438004	−	0.898973i	$-0.355686\pi$
$977$	−14.4085	−	14.4085i	−0.460970	−	0.460970i	−0.898973	+	0.438004i	$0.855686\pi$
$978$	15.7137	+	28.8064i	0.502469	+	0.921126i
$979$	9.94018	+	14.8765i	0.317690	+	0.475456i
$980$	−5.33099	−	12.2754i	−0.170292	−	0.392125i
$981$	3.80759	+	19.1421i	0.121567	+	0.611159i
$982$	−11.8873	−	6.22450i	−0.379338	−	0.198632i
$983$	14.2810	−	34.4773i	0.455492	−	1.09966i	−0.514711	−	0.857364i	$-0.672101\pi$
$983$	14.2810	−	34.4773i	0.455492	−	1.09966i	0.970203	−	0.242292i	$-0.0778991\pi$
$984$	−22.7466	−	40.0630i	−0.725134	−	1.27716i
$985$	−0.807045	−	1.94838i	−0.0257146	−	0.0620805i
$986$	2.80858	+	0.252527i	0.0894434	+	0.00804209i
$987$	−43.5788	+	65.2202i	−1.38713	+	2.07598i
$988$	0.685160	−	3.77934i	0.0217978	−	0.120237i
$989$	−6.66337	−	1.32543i	−0.211883	−	0.0421461i
$990$	12.8674	−	1.37790i	0.408953	−	0.0437926i
$991$			5.17247i			0.164309i	0.996620	+	0.0821544i	$0.0261801\pi$
$991$			5.17247i			0.164309i	−0.996620	+	0.0821544i	$0.973820\pi$
$992$	−37.6900	−	9.70450i	−1.19666	−	0.308118i
$993$			8.74393i			0.277480i
$994$	−1.60356	−	14.9747i	−0.0508619	−	0.474969i
$995$	10.0923	+	2.00749i	0.319948	+	0.0636416i
$996$	5.20226	+	7.50619i	0.164840	+	0.237843i
$997$	−11.3818	+	17.0341i	−0.360466	+	0.539476i	−0.966734	−	0.255785i	$-0.917666\pi$
$997$	−11.3818	+	17.0341i	−0.360466	+	0.539476i	0.606267	+	0.795261i	$0.292666\pi$
$998$	−1.89560	+	21.0827i	−0.0600041	+	0.667361i
$999$	−1.69136	−	4.08331i	−0.0535123	−	0.129190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.61.3	yes	56
3.2	odd	2		576.2.bd.a.253.5		56
4.3	odd	2		256.2.i.a.81.6		56
8.3	odd	2		512.2.i.a.417.2		56
8.5	even	2		512.2.i.b.417.6		56
64.11	odd	16		512.2.i.a.97.2		56
64.21	even	16	inner	64.2.i.a.21.3	✓	56
64.43	odd	16		256.2.i.a.177.6		56
64.53	even	16		512.2.i.b.97.6		56
192.149	odd	16		576.2.bd.a.469.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.3	✓	56	64.21	even	16	inner
64.2.i.a.61.3	yes	56	1.1	even	1	trivial
256.2.i.a.81.6		56	4.3	odd	2
256.2.i.a.177.6		56	64.43	odd	16
512.2.i.a.97.2		56	64.11	odd	16
512.2.i.a.417.2		56	8.3	odd	2
512.2.i.b.97.6		56	64.53	even	16
512.2.i.b.417.6		56	8.5	even	2
576.2.bd.a.253.5		56	3.2	odd	2
576.2.bd.a.469.5		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)

\(f(q)\)	\(=\)	\(q+(-0.887839 + 1.10079i) q^{2} +(-0.435353 + 2.18867i) q^{3} +(-0.423482 - 1.95465i) q^{4} +(0.649649 + 0.434082i) q^{5} +(-2.02274 - 2.42242i) q^{6} +(-3.64486 + 1.50975i) q^{7} +(2.52765 + 1.26925i) q^{8} +(-1.82909 - 0.757635i) q^{9} +O(q^{10})\)	\(q+(-0.887839 + 1.10079i) q^{2} +(-0.435353 + 2.18867i) q^{3} +(-0.423482 - 1.95465i) q^{4} +(0.649649 + 0.434082i) q^{5} +(-2.02274 - 2.42242i) q^{6} +(-3.64486 + 1.50975i) q^{7} +(2.52765 + 1.26925i) q^{8} +(-1.82909 - 0.757635i) q^{9} +(-1.05462 + 0.329733i) q^{10} +(5.80194 - 1.15408i) q^{11} +(4.46245 - 0.0758981i) q^{12} +(2.03484 - 1.35963i) q^{13} +(1.57413 - 5.35264i) q^{14} +(-1.23289 + 1.23289i) q^{15} +(-3.64133 + 1.65552i) q^{16} +(0.960477 + 0.960477i) q^{17} +(2.45794 - 1.34079i) q^{18} +(0.435978 + 0.652487i) q^{19} +(0.573364 - 1.45366i) q^{20} +(-1.71754 - 8.63465i) q^{21} +(-3.88079 + 7.41136i) q^{22} +(0.421603 - 1.01784i) q^{23} +(-3.87839 + 4.97961i) q^{24} +(-1.67980 - 4.05540i) q^{25} +(-0.309935 + 3.44707i) q^{26} +(-1.26483 + 1.89295i) q^{27} +(4.49456 + 6.48507i) q^{28} +(-1.43977 - 0.286388i) q^{29} +(-0.262545 - 2.45176i) q^{30} -6.88004i q^{31} +(1.41053 - 5.47818i) q^{32} +13.2009i q^{33} +(-1.91003 + 0.204535i) q^{34} +(-3.02323 - 0.601358i) q^{35} +(-0.706324 + 3.89608i) q^{36} +(-1.07856 + 1.61417i) q^{37} +(-1.10533 - 0.0993831i) q^{38} +(2.08991 + 5.04550i) q^{39} +(1.09113 + 1.92177i) q^{40} +(-2.79324 + 6.74347i) q^{41} +(11.0298 + 5.77553i) q^{42} +(-1.20307 - 6.04824i) q^{43} +(-4.71284 - 10.8520i) q^{44} +(-0.859393 - 1.28617i) q^{45} +(0.746114 + 1.36778i) q^{46} +(-6.30014 - 6.30014i) q^{47} +(-2.03812 - 8.69038i) q^{48} +(6.05588 - 6.05588i) q^{49} +(5.95554 + 1.75143i) q^{50} +(-2.52031 + 1.68402i) q^{51} +(-3.51933 - 3.40161i) q^{52} +(10.2655 - 2.04194i) q^{53} +(-0.960779 - 3.07295i) q^{54} +(4.27019 + 1.76877i) q^{55} +(-11.1292 - 0.810126i) q^{56} +(-1.61788 + 0.670148i) q^{57} +(1.59354 - 1.33062i) q^{58} +(4.21278 + 2.81489i) q^{59} +(2.93197 + 1.88776i) q^{60} +(-2.08276 + 10.4707i) q^{61} +(7.57348 + 6.10837i) q^{62} +7.81061 q^{63} +(4.77800 + 6.41644i) q^{64} +1.91212 q^{65} +(-14.5315 - 11.7203i) q^{66} +(1.42195 - 7.14864i) q^{67} +(1.47065 - 2.28414i) q^{68} +(2.04417 + 1.36587i) q^{69} +(3.34611 - 2.79404i) q^{70} +(2.49385 - 1.03299i) q^{71} +(-3.66167 - 4.23661i) q^{72} +(-1.90488 - 0.789026i) q^{73} +(-0.819282 - 2.62039i) q^{74} +(9.60722 - 1.91099i) q^{75} +(1.09076 - 1.12850i) q^{76} +(-19.4049 + 12.9659i) q^{77} +(-7.40955 - 2.17903i) q^{78} +(-6.20432 + 6.20432i) q^{79} +(-3.08422 - 0.505126i) q^{80} +(-7.79217 - 7.79217i) q^{81} +(-4.94320 - 9.06188i) q^{82} +(1.13685 + 1.70141i) q^{83} +(-16.1504 + 7.01381i) q^{84} +(0.207047 + 1.04090i) q^{85} +(7.72599 + 4.04554i) q^{86} +(1.25361 - 3.02649i) q^{87} +(16.1301 + 4.44702i) q^{88} +(1.15743 + 2.79429i) q^{89} +(2.17881 + 0.195902i) q^{90} +(-5.36398 + 8.02776i) q^{91} +(-2.16806 - 0.393050i) q^{92} +(15.0581 + 2.99524i) q^{93} +(12.5287 - 1.34163i) q^{94} +0.613137i q^{95} +(11.3758 + 5.47212i) q^{96} -13.1193i q^{97} +(1.28961 + 12.0429i) q^{98} +(-11.4867 - 2.28484i) 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

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