LMFDB - Embedded newform 64.2.i.a.21.3

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			21.3
Character	$\chi$	$=$	64.21
Dual form			64.2.i.a.61.3

$q$-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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$

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	−0.875843	−	0.482596i	$-0.839694\pi$
$3$	−0.435353	−	2.18867i	−0.251351	−	1.26363i	0.624492	−	0.781031i	$-0.285306\pi$
$4$	−0.423482	+	1.95465i	−0.211741	+	0.977326i
$5$	0.649649	−	0.434082i	0.290532	−	0.194127i	−0.401760	−	0.915745i	$-0.631601\pi$
$5$	0.649649	−	0.434082i	0.290532	−	0.194127i	0.692292	+	0.721618i	$0.256601\pi$
$6$	−2.02274	+	2.42242i	−0.825781	+	0.988948i
$7$	−3.64486	−	1.50975i	−1.37763	−	0.570631i	−0.433780	−	0.901019i	$-0.642821\pi$
$7$	−3.64486	−	1.50975i	−1.37763	−	0.570631i	−0.943845	+	0.330387i	$0.892821\pi$
$8$	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	0.962936	−	0.269730i	$-0.0869346\pi$
$11$	5.80194	+	1.15408i	1.74935	+	0.347968i	0.786415	+	0.617698i	$0.211935\pi$
$12$	4.46245	+	0.0758981i	1.28820	+	0.0219099i
$13$	2.03484	+	1.35963i	0.564362	+	0.377095i	0.804779	−	0.593575i	$-0.202284\pi$
$13$	2.03484	+	1.35963i	0.564362	+	0.377095i	−0.240417	+	0.970670i	$0.577284\pi$
$14$	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	−0.580973	−	0.813923i	$-0.697328\pi$
$17$	0.960477	−	0.960477i	0.232950	−	0.232950i	0.813923	+	0.580973i	$0.197328\pi$
$18$	2.45794	+	1.34079i	0.579341	+	0.316027i
$19$	0.435978	−	0.652487i	0.100020	−	0.149691i	−0.778084	−	0.628160i	$-0.783808\pi$
$19$	0.435978	−	0.652487i	0.100020	−	0.149691i	0.878104	+	0.478469i	$0.158808\pi$
$20$	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	0.961720	−	0.274033i	$-0.0883579\pi$
$23$	0.421603	+	1.01784i	0.0879104	+	0.212234i	−0.873810	+	0.486268i	$0.838358\pi$
$24$	−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	−0.326949	−	0.945042i	$-0.606020\pi$
$29$	−1.43977	+	0.286388i	−0.267358	+	0.0531809i	0.0595906	+	0.998223i	$0.481020\pi$
$30$	−0.262545	+	2.45176i	−0.0479340	+	0.447627i
$31$			6.88004i			1.23569i	0.786300	+	0.617845i	$0.211994\pi$
$31$			6.88004i			1.23569i	−0.786300	+	0.617845i	$0.788006\pi$
$32$	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	0.732158	−	0.681135i	$-0.238513\pi$
$37$	−1.07856	−	1.61417i	−0.177313	−	0.265368i	−0.909471	+	0.415767i	$0.863513\pi$
$38$	−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	−0.977240	−	0.212136i	$-0.931958\pi$
$41$	−2.79324	−	6.74347i	−0.436230	−	1.05315i	0.541010	−	0.841016i	$-0.318042\pi$
$42$	11.0298	−	5.77553i	1.70194	−	0.891184i
$43$	−1.20307	+	6.04824i	−0.183467	+	0.922349i	0.773864	+	0.633352i	$0.218322\pi$
$43$	−1.20307	+	6.04824i	−0.183467	+	0.922349i	−0.957330	+	0.288996i	$0.906678\pi$
$44$	−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	−0.996955	−	0.0779845i	$-0.975152\pi$
$47$	−6.30014	+	6.30014i	−0.918970	+	0.918970i	0.0779845	+	0.996955i	$0.475152\pi$
$48$	−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	0.840660	−	0.541564i	$-0.182168\pi$
$53$	10.2655	+	2.04194i	1.41008	+	0.280482i	0.569421	+	0.822046i	$0.307168\pi$
$54$	−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	−0.250255	−	0.968180i	$-0.580515\pi$
$59$	4.21278	−	2.81489i	0.548458	−	0.366468i	0.798713	+	0.601712i	$0.205515\pi$
$60$	2.93197	−	1.88776i	0.378516	−	0.243709i
$61$	−2.08276	−	10.4707i	−0.266670	−	1.34064i	−0.849303	−	0.527906i	$-0.822977\pi$
$61$	−2.08276	−	10.4707i	−0.266670	−	1.34064i	0.582633	−	0.812736i	$-0.302023\pi$
$62$	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	0.965072	+	0.261985i	$0.0843771\pi$
$67$	1.42195	+	7.14864i	0.173719	+	0.873345i	−0.791353	+	0.611360i	$0.790623\pi$
$68$	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	0.525725	−	0.850655i	$-0.323794\pi$
$71$	2.49385	+	1.03299i	0.295965	+	0.122593i	−0.229760	+	0.973247i	$0.573794\pi$
$72$	−3.66167	+	4.23661i	−0.431532	+	0.499289i
$73$	−1.90488	+	0.789026i	−0.222949	+	0.0923485i	−0.491362	−	0.870955i	$-0.663501\pi$
$73$	−1.90488	+	0.789026i	−0.222949	+	0.0923485i	0.268413	+	0.963304i	$0.413501\pi$
$74$	−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	0.265947	−	0.963988i	$-0.414315\pi$
$79$	−6.20432	−	6.20432i	−0.698040	−	0.698040i	−0.963988	+	0.265947i	$0.914315\pi$
$80$	−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	−0.763817	−	0.645433i	$-0.776677\pi$
$83$	1.13685	−	1.70141i	0.124785	−	0.186755i	0.888602	+	0.458678i	$0.151677\pi$
$84$	−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	−0.850589	−	0.525832i	$-0.823754\pi$
$89$	1.15743	−	2.79429i	0.122688	−	0.296194i	0.973276	+	0.229638i	$0.0737541\pi$
$90$	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	$0.232009\pi$
$97$			13.1193i			1.33207i	−0.745922	+	0.666034i	$0.767991\pi$
$98$	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	0.686402	−	0.727222i	$-0.259189\pi$
$101$	−2.49376	−	3.73217i	−0.248138	−	0.371365i	−0.934540	+	0.355857i	$0.884189\pi$
$102$	0.383879	+	4.26947i	0.0380097	+	0.422741i
$103$	4.09230	−	9.87970i	0.403227	−	0.973476i	−0.583651	−	0.812005i	$-0.698376\pi$
$103$	4.09230	−	9.87970i	0.403227	−	0.973476i	0.986878	−	0.161471i	$-0.0516237\pi$
$104$	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	−0.927877	−	0.372886i	$-0.878368\pi$
$107$	0.745466	−	3.74771i	0.0720669	−	0.362305i	0.999944	+	0.0105812i	$0.00336817\pi$
$108$	4.23570	−	1.67067i	0.407580	−	0.160760i
$109$	−5.47688	+	8.19674i	−0.524590	+	0.785105i	−0.995265	−	0.0972021i	$-0.969011\pi$
$109$	−5.47688	+	8.19674i	−0.524590	+	0.785105i	0.470674	+	0.882307i	$0.344011\pi$
$110$	−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	0.536806	−	0.843706i	$-0.319631\pi$
$113$	−3.26239	−	3.26239i	−0.306900	−	0.306900i	−0.843706	+	0.536806i	$0.819631\pi$
$114$	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	0.999844	+	0.0176578i	$0.00562093\pi$
$131$	0.948444	+	4.76815i	0.0828659	+	0.416595i	−0.916978	+	0.398937i	$0.869379\pi$
$132$	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	−0.998263	−	0.0589215i	$-0.981234\pi$
$137$	−19.4588	+	8.06010i	−1.66248	+	0.688621i	−0.664214	+	0.747542i	$0.731234\pi$
$138$	−3.31843	−	1.03753i	−0.282483	−	0.0883203i
$139$	−18.8196	−	3.74344i	−1.59625	−	0.317515i	−0.684741	−	0.728786i	$-0.740085\pi$
$139$	−18.8196	−	3.74344i	−1.59625	−	0.317515i	−0.911513	+	0.411272i	$0.865085\pi$
$140$	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	−0.972527	−	0.232790i	$-0.925215\pi$
$149$	0.183778	−	0.923914i	0.0150557	−	0.0756900i	0.987583	+	0.157100i	$0.0502145\pi$
$150$	−6.42606	−	12.2722i	−0.524686	−	1.00202i
$151$	4.16374	+	10.0522i	0.338841	+	0.818034i	0.997828	+	0.0658792i	$0.0209852\pi$
$151$	4.16374	+	10.0522i	0.338841	+	0.818034i	−0.658987	+	0.752154i	$0.729015\pi$
$152$	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	−0.107827	−	0.994170i	$-0.534389\pi$
$157$	2.16776	−	0.431195i	0.173006	−	0.0344131i	0.280833	+	0.959757i	$0.409389\pi$
$158$	−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	−0.577560	−	0.816348i	$-0.695995\pi$
$163$	−10.1978	+	2.02847i	−0.798753	+	0.158882i	−0.221193	+	0.975230i	$0.570995\pi$
$164$	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	−0.537058	−	0.843546i	$-0.680464\pi$
$167$	5.67541	−	13.7016i	0.439176	−	1.06027i	0.976234	−	0.216720i	$-0.0695358\pi$
$168$	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	−0.708827	−	0.705382i	$-0.750775\pi$
$173$	2.81628	−	4.21486i	0.214118	−	0.320450i	0.922945	+	0.384933i	$0.125775\pi$
$174$	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	0.646777	−	0.762679i	$-0.276117\pi$
$179$	2.53753	+	1.69552i	0.189664	+	0.126729i	−0.457113	+	0.889409i	$0.651117\pi$
$180$	−2.15008	−	2.22448i	−0.160258	−	0.165803i
$181$	−6.51424	−	1.29576i	−0.484200	−	0.0963133i	−0.0530464	−	0.998592i	$-0.516893\pi$
$181$	−6.51424	−	1.29576i	−0.484200	−	0.0963133i	−0.431153	+	0.902279i	$0.641893\pi$
$182$	−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	−0.632944	−	0.774197i	$-0.718154\pi$
$197$	−2.24425	+	1.49956i	−0.159896	+	0.106839i	0.473048	+	0.881037i	$0.343154\pi$
$198$	12.7134	+	10.6158i	0.903504	+	0.754435i
$199$	12.1675	+	5.03992i	0.862528	+	0.357271i	0.769696	−	0.638411i	$-0.220408\pi$
$199$	12.1675	+	5.03992i	0.862528	+	0.357271i	0.0928322	+	0.995682i	$0.470408\pi$
$200$	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	−0.676505	−	0.736438i	$-0.736506\pi$
$211$	3.81684	−	5.71230i	0.262762	−	0.393251i	0.939267	+	0.343187i	$0.111506\pi$
$212$	−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	$-0.958497\pi$
$223$		−	3.88311i		−	0.260032i	0.991512	−	0.130016i	$-0.0415029\pi$
$224$	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	0.621577	−	0.783353i	$-0.286492\pi$
$227$	22.5337	−	4.48224i	1.49562	−	0.297497i	0.874039	+	0.485856i	$0.161492\pi$
$228$	1.99505	−	2.87860i	0.132125	−	0.190640i
$229$	−3.41606	−	5.11250i	−0.225740	−	0.337844i	0.701260	−	0.712906i	$-0.252621\pi$
$229$	−3.41606	−	5.11250i	−0.225740	−	0.337844i	−0.927000	+	0.375062i	$0.877621\pi$
$230$	−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	0.946093	−	0.323896i	$-0.104993\pi$
$233$	0.733834	+	1.77163i	0.0480751	+	0.116064i	−0.898018	+	0.439960i	$0.854993\pi$
$234$	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	−0.876285	−	0.481793i	$-0.839986\pi$
$239$	−6.09870	+	6.09870i	−0.394492	+	0.394492i	0.481793	+	0.876285i	$0.339986\pi$
$240$	2.44827	+	6.53041i	0.158035	+	0.421536i
$241$	5.21549	+	5.21549i	0.335959	+	0.335959i	0.854844	−	0.518885i	$-0.173653\pi$
$241$	5.21549	+	5.21549i	0.335959	+	0.335959i	−0.518885	+	0.854844i	$0.673653\pi$
$242$	−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	−0.432204	−	0.901776i	$-0.642264\pi$
$251$	3.73150	−	2.49331i	0.235530	−	0.157376i	0.667735	+	0.744399i	$0.267264\pi$
$252$	−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	−0.676090	−	0.736819i	$-0.736327\pi$
$263$	−27.1667	−	11.2528i	−1.67517	−	0.693877i	−0.999078	+	0.0429417i	$0.986327\pi$
$264$	−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	0.803176	−	0.595741i	$-0.203142\pi$
$269$	9.18707	+	6.13860i	0.560145	+	0.374277i	−0.243031	+	0.970019i	$0.578142\pi$
$270$	0.709743	+	2.41340i	0.0431936	+	0.146875i
$271$	−17.2217	−	17.2217i	−1.04614	−	1.04614i	−0.998883	−	0.0472600i	$-0.984951\pi$
$271$	−17.2217	−	17.2217i	−1.04614	−	1.04614i	−0.0472600	−	0.998883i	$-0.515049\pi$
$272$	−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	−0.390228	−	0.920718i	$-0.627604\pi$
$277$	5.36979	−	26.9957i	0.322639	−	1.62202i	0.712868	−	0.701299i	$-0.247396\pi$
$278$	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	0.623762	+	0.781615i	$0.285604\pi$
$281$	−6.20216	+	14.9733i	−0.369990	+	0.893234i	−0.993751	+	0.111619i	$0.964396\pi$
$282$	−2.51801	−	28.0051i	−0.149946	−	1.66768i
$283$	−4.95606	−	7.41727i	−0.294607	−	0.440911i	0.654408	−	0.756142i	$-0.272918\pi$
$283$	−4.95606	−	7.41727i	−0.294607	−	0.440911i	−0.949015	+	0.315231i	$0.897918\pi$
$284$	−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	0.979247	+	0.202669i	$0.0649615\pi$
$293$	13.5525	+	20.2828i	0.791747	+	1.18493i	−0.187500	+	0.982265i	$0.560039\pi$
$294$	−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	0.766169	−	0.642639i	$-0.222161\pi$
$307$	8.15880	+	5.45154i	0.465647	+	0.311136i	−0.300521	+	0.953775i	$0.597161\pi$
$308$	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	0.615841	−	0.787870i	$-0.288816\pi$
$311$	28.3647	−	11.7490i	1.60842	−	0.666227i	0.992574	+	0.121643i	$0.0388163\pi$
$312$	−1.12144	−	15.4059i	−0.0634891	−	0.872185i
$313$	−22.4586	−	9.30264i	−1.26943	−	0.525816i	−0.356641	−	0.934242i	$-0.616078\pi$
$313$	−22.4586	−	9.30264i	−1.26943	−	0.525816i	−0.912792	+	0.408425i	$0.866078\pi$
$314$	−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	0.999965	−	0.00839833i	$-0.00267330\pi$
$317$	1.29802	+	6.52557i	0.0729039	+	0.366513i	−0.927061	+	0.374911i	$0.877673\pi$
$318$	−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	0.299572	−	0.954074i	$-0.403156\pi$
$331$	3.84304	+	0.764428i	0.211233	+	0.0420168i	−0.0883396	+	0.996090i	$0.528156\pi$
$332$	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	−0.220311	−	0.975430i	$-0.570707\pi$
$337$	13.8621	−	13.8621i	0.755119	−	0.755119i	0.975430	+	0.220311i	$0.0707072\pi$
$338$	−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	−0.990609	−	0.136724i	$-0.956343\pi$
$347$	−13.7444	−	20.5699i	−0.737836	−	1.10425i	0.252773	−	0.967526i	$-0.418657\pi$
$348$	−6.44662	+	1.16871i	−0.345575	+	0.0626496i
$349$	−34.6278	+	6.88789i	−1.85358	+	0.368700i	−0.990628	−	0.136584i	$-0.956388\pi$
$349$	−34.6278	+	6.88789i	−1.85358	+	0.368700i	−0.862953	+	0.505284i	$0.831388\pi$
$350$	−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	$-0.856698\pi$
$353$		−	16.3511i		−	0.870283i	0.900362	−	0.435141i	$-0.143302\pi$
$354$	−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	−0.944446	−	0.328667i	$-0.893401\pi$
$359$	−0.837827	+	2.02269i	−0.0442188	+	0.106754i	0.900227	+	0.435421i	$0.143401\pi$
$360$	−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	0.0958935	−	0.995392i	$-0.469429\pi$
$367$	20.9060	−	20.9060i	1.09129	−	1.09129i	0.995392	−	0.0958935i	$-0.0305708\pi$
$368$	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	0.768659	−	0.639659i	$-0.220924\pi$
$373$	23.8329	+	4.74066i	1.23402	+	0.245462i	0.465362	+	0.885121i	$0.345924\pi$
$374$	−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	−0.959485	−	0.281760i	$-0.909082\pi$
$379$	−20.7596	+	13.8712i	−1.06635	+	0.712513i	−0.106867	+	0.994273i	$0.534082\pi$
$380$	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	0.0298624	−	0.999554i	$-0.490493\pi$
$389$	19.0280	−	12.7141i	0.964758	−	0.644630i	0.934895	+	0.354924i	$0.115493\pi$
$390$	−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	0.947886	−	0.318609i	$-0.103216\pi$
$397$	20.2490	+	13.5300i	1.01627	+	0.679050i	0.0683838	+	0.997659i	$0.478216\pi$
$398$	−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	−0.285716	−	0.958314i	$-0.592231\pi$
$401$	13.4688	−	13.4688i	0.672599	−	0.672599i	0.958314	+	0.285716i	$0.0922312\pi$
$402$	−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	−0.981194	−	0.193026i	$-0.938170\pi$
$409$	−3.05166	+	7.36736i	−0.150895	+	0.364293i	0.830299	+	0.557319i	$0.188170\pi$
$410$	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	−0.491629	−	0.870805i	$-0.663598\pi$
$419$	−12.5395	+	2.49426i	−0.612593	+	0.121852i	−0.120964	+	0.992657i	$0.538598\pi$
$420$	−13.5366	+	2.45407i	−0.660521	+	0.119746i
$421$	−10.8903	−	16.2984i	−0.530759	−	0.794337i	0.465099	−	0.885259i	$-0.346019\pi$
$421$	−10.8903	−	16.2984i	−0.530759	−	0.794337i	−0.995858	+	0.0909215i	$0.971019\pi$
$422$	−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	−0.104343	−	0.994541i	$-0.533274\pi$
$431$	18.4810	−	18.4810i	0.890199	−	0.890199i	0.994541	+	0.104343i	$0.0332739\pi$
$432$	1.47184	+	8.98681i	0.0708139	+	0.432378i
$433$	6.00332	+	6.00332i	0.288501	+	0.288501i	0.836487	−	0.547986i	$-0.184605\pi$
$433$	6.00332	+	6.00332i	0.288501	+	0.288501i	−0.547986	+	0.836487i	$0.684605\pi$
$434$	−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	−0.802571	−	0.596556i	$-0.796535\pi$
$439$	−19.8680	+	8.22958i	−0.948246	+	0.392777i	−0.145675	+	0.989333i	$0.546535\pi$
$440$	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	−0.128848	−	0.991664i	$-0.541128\pi$
$443$	15.5336	−	10.3792i	0.738023	−	0.493131i	0.866871	+	0.498533i	$0.166128\pi$
$444$	−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	−0.855341	−	0.518066i	$-0.826652\pi$
$457$	−23.3834	+	9.68573i	−1.09383	+	0.453079i	−0.238489	+	0.971145i	$0.576652\pi$
$458$	−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	0.610113	−	0.792314i	$-0.291124\pi$
$461$	2.39596	+	1.60093i	0.111591	+	0.0745627i	−0.498522	+	0.866877i	$0.666124\pi$
$462$	70.6599	−	20.7800i	3.28740	−	0.966773i
$463$	24.5897	+	24.5897i	1.14278	+	1.14278i	0.987940	+	0.154840i	$0.0494863\pi$
$463$	24.5897	+	24.5897i	1.14278	+	1.14278i	0.154840	+	0.987940i	$0.450514\pi$
$464$	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	−0.958379	−	0.285500i	$-0.907840\pi$
$467$	−7.08500	+	10.6035i	−0.327855	+	0.490670i	0.630524	+	0.776170i	$0.282840\pi$
$468$	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	$0.0614644\pi$
$479$			8.39981i			0.383797i	−0.981415	+	0.191899i	$0.938536\pi$
$480$	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	−0.999992	−	0.00390038i	$-0.998758\pi$
$487$	−6.40268	+	15.4574i	−0.290133	+	0.700443i	0.709859	+	0.704343i	$0.248758\pi$
$488$	−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	−0.916275	−	0.400551i	$-0.868819\pi$
$491$	1.85105	−	9.30587i	0.0835368	−	0.419968i	0.999811	−	0.0194174i	$-0.00618114\pi$
$492$	−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	0.802027	−	0.597287i	$-0.203755\pi$
$499$	12.4453	+	8.31569i	0.557129	+	0.372261i	−0.244899	+	0.969549i	$0.578755\pi$
$500$	−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	−0.220783	−	0.975323i	$-0.570861\pi$
$503$	7.01440	−	2.90546i	0.312757	−	0.129548i	0.533540	+	0.845775i	$0.320861\pi$
$504$	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	−0.780264	−	0.625450i	$-0.784915\pi$
$509$	−6.73996	−	33.8841i	−0.298743	−	1.50188i	0.481521	−	0.876435i	$-0.340085\pi$
$510$	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	−0.983638	−	0.180158i	$-0.942339\pi$
$521$	−35.4201	+	14.6715i	−1.55178	+	0.642770i	−0.568146	+	0.822928i	$0.692339\pi$
$522$	−3.92284	−	1.22650i	−0.171698	−	0.0536826i
$523$	−3.91974	−	0.779685i	−0.171398	−	0.0340933i	0.108645	−	0.994081i	$-0.465349\pi$
$523$	−3.91974	−	0.779685i	−0.171398	−	0.0340933i	−0.280043	+	0.959987i	$0.590349\pi$
$524$	−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	0.684256	−	0.729242i	$-0.260127\pi$
$541$	37.1103	−	7.38169i	1.59550	−	0.317364i	0.911239	+	0.411878i	$0.135127\pi$
$542$	−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	−0.0639395	−	0.997954i	$-0.520366\pi$
$547$	6.05489	−	1.20439i	0.258888	−	0.0514961i	0.322828	+	0.946458i	$0.395366\pi$
$548$	−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	−0.540490	−	0.841351i	$-0.681761\pi$
$557$	10.4706	−	15.6704i	0.443653	−	0.663974i	0.984143	+	0.177377i	$0.0567610\pi$
$558$	−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	−0.338458	−	0.940981i	$-0.609905\pi$
$563$	−31.7318	−	21.2025i	−1.33733	−	0.893578i	−0.998876	+	0.0474033i	$0.984905\pi$
$564$	−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	0.498949	−	0.866631i	$-0.333719\pi$
$569$	5.70005	+	2.36104i	0.238958	+	0.0989798i	−0.259991	+	0.965611i	$0.583719\pi$
$570$	1.48527	+	1.24022i	0.0622113	+	0.0519470i
$571$	25.4415	−	16.9994i	1.06469	−	0.711405i	0.105574	−	0.994411i	$-0.466332\pi$
$571$	25.4415	−	16.9994i	1.06469	−	0.711405i	0.959118	+	0.283007i	$0.0913319\pi$
$572$	−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	0.738344	−	0.674424i	$-0.235608\pi$
$587$	28.1626	+	5.60188i	1.16239	+	0.231215i	0.424050	+	0.905639i	$0.360608\pi$
$588$	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	−0.510551	−	0.859848i	$-0.670559\pi$
$593$	8.50593	−	8.50593i	0.349297	−	0.349297i	0.859848	+	0.510551i	$0.170559\pi$
$594$	−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	−0.659096	−	0.752059i	$-0.729061\pi$
$599$	−17.7398	−	42.8278i	−0.724831	−	1.74990i	−0.0657345	−	0.997837i	$-0.520939\pi$
$600$	26.7092	−	7.36365i	1.09040	−	0.300620i
$601$	9.36011	−	22.5973i	0.381807	−	0.921763i	−0.609810	−	0.792548i	$-0.708754\pi$
$601$	9.36011	−	22.5973i	0.381807	−	0.921763i	0.991617	−	0.129215i	$-0.0412459\pi$
$602$	−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	$0.132721\pi$
$607$			19.9552i			0.809956i	−0.914326	+	0.404978i	$0.867279\pi$
$608$	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	0.999827	+	0.0185890i	$0.00591740\pi$
$613$	15.7066	+	23.5066i	0.634384	+	0.949423i	−0.365443	+	0.930834i	$0.619083\pi$
$614$	−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	−0.999285	−	0.0378118i	$-0.987961\pi$
$617$	−7.93425	−	19.1550i	−0.319421	−	0.771150i	0.679864	−	0.733338i	$-0.262039\pi$
$618$	15.6551	+	29.8973i	0.629740	+	1.20265i
$619$	−1.06040	+	5.33101i	−0.0426212	+	0.214271i	−0.996227	−	0.0867872i	$-0.972340\pi$
$619$	−1.06040	+	5.33101i	−0.0426212	+	0.214271i	0.953606	+	0.301059i	$0.0973400\pi$
$620$	−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	−0.957353	−	0.288922i	$-0.906703\pi$
$631$	−35.9213	+	14.8791i	−1.43000	+	0.592327i	−0.472652	+	0.881249i	$0.656703\pi$
$632$	−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	0.983366	−	0.181635i	$-0.0581390\pi$
$643$	0.135549	+	0.681448i	0.00534551	+	0.0268737i	−0.978020	+	0.208509i	$0.933139\pi$
$644$	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	−0.281606	−	0.959530i	$-0.590867\pi$
$647$	−29.4862	−	12.2136i	−1.15922	−	0.480165i	−0.877616	+	0.479365i	$0.840867\pi$
$648$	−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	−0.999911	−	0.0133207i	$-0.995760\pi$
$653$	−35.6443	−	23.8167i	−1.39487	−	0.932021i	−0.394956	−	0.918700i	$-0.629240\pi$
$654$	−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	−0.247496	−	0.968889i	$-0.579608\pi$
$659$	19.0570	−	28.5207i	0.742354	−	1.11101i	0.989849	−	0.142122i	$-0.0453924\pi$
$660$	19.1897	−	7.56894i	0.746960	−	0.294621i
$661$	−2.62496	+	13.1966i	−0.102099	+	0.513287i	0.895562	+	0.444936i	$0.146774\pi$
$661$	−2.62496	+	13.1966i	−0.102099	+	0.513287i	−0.997661	+	0.0683508i	$0.978226\pi$
$662$	−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	$-0.849233\pi$
$673$		−	23.6665i		−	0.912275i	0.889909	−	0.456137i	$-0.150767\pi$
$674$	−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	0.998948	−	0.0458647i	$-0.0146043\pi$
$677$	14.9427	+	22.3633i	0.574294	+	0.859491i	−0.424654	+	0.905356i	$0.639604\pi$
$678$	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	−0.770329	−	0.637647i	$-0.779908\pi$
$683$	4.84474	−	24.3562i	0.185379	−	0.931963i	0.955708	−	0.294316i	$-0.0950920\pi$
$684$	−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	0.755302	−	0.655377i	$-0.227490\pi$
$691$	11.5361	+	7.70819i	0.438855	+	0.293233i	−0.316448	+	0.948610i	$0.602490\pi$
$692$	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	0.838898	+	0.544289i	$0.183200\pi$
$701$	7.20549	+	36.2244i	0.272148	+	1.36818i	−0.566750	+	0.823890i	$0.691800\pi$
$702$	−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	−0.871774	−	0.489909i	$-0.837030\pi$
$709$	−20.0441	+	13.3930i	−0.752770	+	0.502985i	0.119003	+	0.992894i	$0.462030\pi$
$710$	−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	0.795557	−	0.605879i	$-0.207178\pi$
$719$	5.08606	+	5.08606i	0.189678	+	0.189678i	−0.605879	+	0.795557i	$0.707178\pi$
$720$	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	0.875240	+	0.483690i	$0.160704\pi$
$727$	16.1339	+	38.9506i	0.598372	+	1.44460i	−0.276867	+	0.960908i	$0.589296\pi$
$728$	−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	−0.749862	−	0.661595i	$-0.769880\pi$
$733$	−32.2035	+	6.40567i	−1.18946	+	0.236599i	−0.439601	+	0.898193i	$0.644880\pi$
$734$	−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	−0.215496	−	0.976505i	$-0.569137\pi$
$739$	−1.11174	+	0.221139i	−0.0408961	+	0.00813474i	0.174600	+	0.984639i	$0.444137\pi$
$740$	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	0.577500	+	0.816391i	$0.304028\pi$
$743$	−11.1248	+	26.8577i	−0.408130	+	0.985313i	−0.985629	+	0.168922i	$0.945972\pi$
$744$	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	−0.965066	−	0.262005i	$-0.915616\pi$
$751$	−19.2670	+	19.2670i	−0.703061	+	0.703061i	0.262005	+	0.965066i	$0.415616\pi$
$752$	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	0.263924	−	0.964544i	$-0.414983\pi$
$757$	3.81457	+	0.758766i	0.138643	+	0.0275778i	−0.125281	+	0.992121i	$0.539983\pi$
$758$	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	0.623835	−	0.781556i	$-0.285574\pi$
$761$	14.1327	+	5.85394i	0.512309	+	0.212205i	−0.111526	+	0.993762i	$0.535574\pi$
$762$	−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	−0.165699	−	0.986176i	$-0.552988\pi$
$773$	18.9615	−	12.6697i	0.681998	−	0.455697i	0.847698	+	0.530480i	$0.177988\pi$
$774$	−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	−0.649488	−	0.760372i	$-0.725017\pi$
$787$	8.45960	−	12.6607i	0.301552	−	0.451305i	0.951040	+	0.309067i	$0.100017\pi$
$788$	−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	−0.173460	−	0.984841i	$-0.555495\pi$
$797$	1.21865	−	0.242404i	0.0431668	−	0.00858640i	0.216626	+	0.976255i	$0.430495\pi$
$798$	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	0.986070	+	0.166332i	$0.0531923\pi$
$809$	11.5600	+	27.9083i	0.406428	+	0.981203i	−0.579642	+	0.814871i	$0.696808\pi$
$810$	10.7871	−	5.64842i	0.379020	−	0.198465i
$811$	1.27743	−	6.42210i	0.0448568	−	0.225510i	−0.951854	−	0.306552i	$-0.900825\pi$
$811$	1.27743	−	6.42210i	0.0448568	−	0.225510i	0.996711	+	0.0810417i	$0.0258247\pi$
$812$	−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	0.207865	−	0.978158i	$-0.433349\pi$
$821$	0.732994	+	0.145802i	0.0255817	+	0.00508851i	−0.182283	+	0.983246i	$0.558349\pi$
$822$	19.8352	−	63.4408i	0.691832	−	2.21275i
$823$	−40.6921	+	16.8552i	−1.41844	+	0.587535i	−0.954467	−	0.298316i	$-0.903575\pi$
$823$	−40.6921	+	16.8552i	−1.41844	+	0.587535i	−0.463969	+	0.885852i	$0.653575\pi$
$824$	−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	−0.822324	−	0.569020i	$-0.807323\pi$
$827$	−17.5797	+	11.7464i	−0.611308	+	0.408463i	0.211016	+	0.977483i	$0.432323\pi$
$828$	3.66780	−	2.36153i	0.127465	−	0.0820687i
$829$	−8.12158	−	40.8299i	−0.282074	−	1.41808i	−0.818681	−	0.574249i	$-0.805294\pi$
$829$	−8.12158	−	40.8299i	−0.282074	−	1.41808i	0.536607	−	0.843833i	$-0.319706\pi$
$830$	−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	0.876154	−	0.482032i	$-0.160101\pi$
$839$	33.4505	+	13.8556i	1.15484	+	0.478350i	0.278686	+	0.960382i	$0.410101\pi$
$840$	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	0.921567	+	0.388218i	$0.126909\pi$
$853$	−2.29019	+	11.5136i	−0.0784145	+	0.394217i	−0.999982	+	0.00599829i	$0.998091\pi$
$854$	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	−0.976996	−	0.213257i	$-0.931593\pi$
$857$	−3.96261	+	9.56660i	−0.135360	+	0.326789i	0.841636	+	0.540045i	$0.181593\pi$
$858$	−45.5045	+	4.09143i	−1.55350	+	0.139679i
$859$	−22.7757	−	34.0863i	−0.777098	−	1.16301i	−0.982850	−	0.184405i	$-0.940964\pi$
$859$	−22.7757	−	34.0863i	−0.777098	−	1.16301i	0.205753	−	0.978604i	$-0.434036\pi$
$860$	−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	$0.124576\pi$
$863$			22.4117i			0.762902i	−0.924389	+	0.381451i	$0.875424\pi$
$864$	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	−0.213055	−	0.977040i	$-0.568341\pi$
$877$	22.8368	−	34.1777i	0.771145	−	1.15410i	0.984200	−	0.177060i	$-0.0566587\pi$
$878$	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	0.303238	−	0.952915i	$-0.401932\pi$
$881$	−19.2835	−	19.2835i	−0.649677	−	0.649677i	−0.952915	+	0.303238i	$0.901932\pi$
$882$	6.76531	+	23.0047i	0.227800	+	0.774607i
$883$	43.0348	+	28.7549i	1.44824	+	0.967681i	0.997169	+	0.0751915i	$0.0239568\pi$
$883$	43.0348	+	28.7549i	1.44824	+	0.967681i	0.451068	+	0.892490i	$0.351043\pi$
$884$	−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	−0.421987	−	0.906602i	$-0.638667\pi$
$887$	−2.36214	+	0.978431i	−0.0793129	+	0.0328525i	0.342674	+	0.939454i	$0.388667\pi$
$888$	−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	0.536127	−	0.844138i	$-0.319887\pi$
$907$	21.3347	+	4.24373i	0.708405	+	0.140911i	0.172279	+	0.985048i	$0.444887\pi$
$908$	−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	0.729726	−	0.683740i	$-0.239648\pi$
$911$	1.38797	+	1.38797i	0.0459856	+	0.0459856i	−0.683740	+	0.729726i	$0.739648\pi$
$912$	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	0.948601	−	0.316475i	$-0.102499\pi$
$919$	1.63873	+	3.95625i	0.0540568	+	0.130505i	−0.894544	+	0.446980i	$0.852499\pi$
$920$	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	$-0.659151\pi$
$929$		−	53.4969i		−	1.75518i	0.479415	−	0.877589i	$-0.340849\pi$
$930$	−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	0.999431	+	0.0337361i	$0.0107406\pi$
$937$	9.69070	+	23.3954i	0.316582	+	0.764295i	−0.682849	+	0.730559i	$0.739259\pi$
$938$	−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	−0.990825	−	0.135153i	$-0.956847\pi$
$941$	−14.9326	+	22.3482i	−0.486788	+	0.728529i	0.504037	+	0.863682i	$0.331847\pi$
$942$	−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	0.783830	−	0.620975i	$-0.213263\pi$
$947$	15.6970	+	10.4884i	0.510083	+	0.340827i	−0.273747	+	0.961802i	$0.588263\pi$
$948$	−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	0.824322	−	0.566122i	$-0.191557\pi$
$953$	31.0836	+	12.8753i	1.00690	+	0.417070i	0.182575	+	0.983192i	$0.441557\pi$
$954$	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	−0.347883	−	0.937538i	$-0.613099\pi$
$967$	−39.0826	−	16.1886i	−1.25681	−	0.520589i	−0.908930	+	0.416949i	$0.863099\pi$
$968$	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	0.443688	−	0.896181i	$-0.353670\pi$
$971$	15.9123	+	3.16514i	0.510649	+	0.101574i	0.0669606	+	0.997756i	$0.478670\pi$
$972$	−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	−0.898973	−	0.438004i	$-0.855686\pi$
$977$	−14.4085	+	14.4085i	−0.460970	+	0.460970i	0.438004	+	0.898973i	$0.355686\pi$
$978$	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	0.970203	+	0.242292i	$0.0778991\pi$
$983$	14.2810	+	34.4773i	0.455492	+	1.09966i	−0.514711	+	0.857364i	$0.672101\pi$
$984$	−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	$-0.973820\pi$
$991$		−	5.17247i		−	0.164309i	0.996620	−	0.0821544i	$-0.0261801\pi$
$992$	−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	0.606267	−	0.795261i	$-0.292666\pi$
$997$	−11.3818	−	17.0341i	−0.360466	−	0.539476i	−0.966734	+	0.255785i	$0.917666\pi$
$998$	−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.21.3	✓	56
3.2	odd	2		576.2.bd.a.469.5		56
4.3	odd	2		256.2.i.a.177.6		56
8.3	odd	2		512.2.i.a.97.2		56
8.5	even	2		512.2.i.b.97.6		56
64.3	odd	16		256.2.i.a.81.6		56
64.29	even	16		512.2.i.b.417.6		56
64.35	odd	16		512.2.i.a.417.2		56
64.61	even	16	inner	64.2.i.a.61.3	yes	56
192.125	odd	16		576.2.bd.a.253.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.3	✓	56	1.1	even	1	trivial
64.2.i.a.61.3	yes	56	64.61	even	16	inner
256.2.i.a.81.6		56	64.3	odd	16
256.2.i.a.177.6		56	4.3	odd	2
512.2.i.a.97.2		56	8.3	odd	2
512.2.i.a.417.2		56	64.35	odd	16
512.2.i.b.97.6		56	8.5	even	2
512.2.i.b.417.6		56	64.29	even	16
576.2.bd.a.253.5		56	192.125	odd	16
576.2.bd.a.469.5		56	3.2	odd	2

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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Database

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