LMFDB - Embedded newform 494.2.m.b.381.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [494,2,Mod(153,494)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(494, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("494.153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.m (of order $6$, degree $2$, 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:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			381.2
Character	$\chi$	$=$	494.381
Dual form			494.2.m.b.153.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.785510 + 1.36054i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.81950i q^{5} +(1.36054 - 0.785510i) q^{6} +(4.00004 - 2.30942i) q^{7} -1.00000i q^{8} +(0.265948 + 0.460635i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.785510 + 1.36054i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.81950i q^{5} +(1.36054 - 0.785510i) q^{6} +(4.00004 - 2.30942i) q^{7} -1.00000i q^{8} +(0.265948 + 0.460635i) q^{9} +(1.40975 - 2.44175i) q^{10} +(0.145049 + 0.0837438i) q^{11} -1.57102 q^{12} +(2.99710 - 2.00434i) q^{13} -4.61884 q^{14} +(-3.83605 - 2.21474i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.06309 + 1.84132i) q^{17} -0.531896i q^{18} +(0.866025 - 0.500000i) q^{19} +(-2.44175 + 1.40975i) q^{20} +7.25630i q^{21} +(-0.0837438 - 0.145049i) q^{22} +(1.88716 - 3.26866i) q^{23} +(1.36054 + 0.785510i) q^{24} -2.94955 q^{25} +(-3.59774 + 0.237262i) q^{26} -5.54868 q^{27} +(4.00004 + 2.30942i) q^{28} +(-4.68934 + 8.12217i) q^{29} +(2.21474 + 3.83605i) q^{30} +2.76469i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.227874 + 0.131563i) q^{33} -2.12617i q^{34} +(6.51141 + 11.2781i) q^{35} +(-0.265948 + 0.460635i) q^{36} +(1.33378 + 0.770056i) q^{37} -1.00000 q^{38} +(0.372744 + 5.65212i) q^{39} +2.81950 q^{40} +(-0.404305 - 0.233426i) q^{41} +(3.62815 - 6.28414i) q^{42} +(4.76110 + 8.24646i) q^{43} +0.167488i q^{44} +(-1.29876 + 0.749839i) q^{45} +(-3.26866 + 1.88716i) q^{46} -4.35742i q^{47} +(-0.785510 - 1.36054i) q^{48} +(7.16686 - 12.4134i) q^{49} +(2.55439 + 1.47478i) q^{50} -3.34026 q^{51} +(3.23436 + 1.59339i) q^{52} -6.10204 q^{53} +(4.80530 + 2.77434i) q^{54} +(-0.236115 + 0.408964i) q^{55} +(-2.30942 - 4.00004i) q^{56} +1.57102i q^{57} +(8.12217 - 4.68934i) q^{58} +(-3.37916 + 1.95096i) q^{59} -4.42948i q^{60} +(-7.14466 - 12.3749i) q^{61} +(1.38235 - 2.39429i) q^{62} +(2.12760 + 1.22837i) q^{63} -1.00000 q^{64} +(5.65124 + 8.45031i) q^{65} +0.263126 q^{66} +(-1.07818 - 0.622486i) q^{67} +(-1.06309 + 1.84132i) q^{68} +(2.96477 + 5.13514i) q^{69} -13.0228i q^{70} +(13.9464 - 8.05198i) q^{71} +(0.460635 - 0.265948i) q^{72} +12.6389i q^{73} +(-0.770056 - 1.33378i) q^{74} +(2.31690 - 4.01300i) q^{75} +(0.866025 + 0.500000i) q^{76} +0.773599 q^{77} +(2.50325 - 5.08125i) q^{78} -9.73309 q^{79} +(-2.44175 - 1.40975i) q^{80} +(3.56070 - 6.16731i) q^{81} +(0.233426 + 0.404305i) q^{82} +4.41971i q^{83} +(-6.28414 + 3.62815i) q^{84} +(-5.19159 + 2.99737i) q^{85} -9.52220i q^{86} +(-7.36704 - 12.7601i) q^{87} +(0.0837438 - 0.145049i) q^{88} +(-1.81103 - 1.04560i) q^{89} +1.49968 q^{90} +(7.35963 - 14.9390i) q^{91} +3.77433 q^{92} +(-3.76149 - 2.17169i) q^{93} +(-2.17871 + 3.77363i) q^{94} +(1.40975 + 2.44175i) q^{95} +1.57102i q^{96} +(-13.9567 + 8.05789i) q^{97} +(-12.4134 + 7.16686i) q^{98} +0.0890860i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} + 14 q^{4} - 18 q^{9}+O(q^{10}) $ 28 * q - 4 * q^3 + 14 * q^4 - 18 * q^9	$ 28 q - 4 q^{3} + 14 q^{4} - 18 q^{9} - 2 q^{10} - 6 q^{11} - 8 q^{12} + 8 q^{13} + 4 q^{14} + 42 q^{15} - 14 q^{16} + 2 q^{17} - 10 q^{22} + 12 q^{23} - 88 q^{25} + 2 q^{26} + 20 q^{27} - 4 q^{29} - 4 q^{30} - 54 q^{33} - 14 q^{35} + 18 q^{36} + 6 q^{37} - 28 q^{38} + 60 q^{39} - 4 q^{40} + 42 q^{41} + 18 q^{42} + 28 q^{43} - 30 q^{45} - 12 q^{46} - 4 q^{48} + 28 q^{49} + 12 q^{50} - 20 q^{51} + 4 q^{52} + 24 q^{53} + 54 q^{54} + 2 q^{55} + 2 q^{56} - 6 q^{58} - 96 q^{59} - 30 q^{61} + 4 q^{62} + 12 q^{63} - 28 q^{64} + 82 q^{65} + 24 q^{66} - 6 q^{67} - 2 q^{68} - 42 q^{69} - 6 q^{71} + 12 q^{72} - 18 q^{74} + 46 q^{75} - 136 q^{77} + 50 q^{78} + 68 q^{79} + 6 q^{81} + 6 q^{82} + 12 q^{84} - 72 q^{85} - 52 q^{87} + 10 q^{88} + 48 q^{89} - 16 q^{90} + 44 q^{91} + 24 q^{92} + 30 q^{93} + 20 q^{94} - 2 q^{95} + 12 q^{97} - 72 q^{98}+O(q^{100}) $ 28 * q - 4 * q^3 + 14 * q^4 - 18 * q^9 - 2 * q^10 - 6 * q^11 - 8 * q^12 + 8 * q^13 + 4 * q^14 + 42 * q^15 - 14 * q^16 + 2 * q^17 - 10 * q^22 + 12 * q^23 - 88 * q^25 + 2 * q^26 + 20 * q^27 - 4 * q^29 - 4 * q^30 - 54 * q^33 - 14 * q^35 + 18 * q^36 + 6 * q^37 - 28 * q^38 + 60 * q^39 - 4 * q^40 + 42 * q^41 + 18 * q^42 + 28 * q^43 - 30 * q^45 - 12 * q^46 - 4 * q^48 + 28 * q^49 + 12 * q^50 - 20 * q^51 + 4 * q^52 + 24 * q^53 + 54 * q^54 + 2 * q^55 + 2 * q^56 - 6 * q^58 - 96 * q^59 - 30 * q^61 + 4 * q^62 + 12 * q^63 - 28 * q^64 + 82 * q^65 + 24 * q^66 - 6 * q^67 - 2 * q^68 - 42 * q^69 - 6 * q^71 + 12 * q^72 - 18 * q^74 + 46 * q^75 - 136 * q^77 + 50 * q^78 + 68 * q^79 + 6 * q^81 + 6 * q^82 + 12 * q^84 - 72 * q^85 - 52 * q^87 + 10 * q^88 + 48 * q^89 - 16 * q^90 + 44 * q^91 + 24 * q^92 + 30 * q^93 + 20 * q^94 - 2 * q^95 + 12 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.785510	+	1.36054i	−0.453514	+	0.785510i	−0.998601	−	0.0528694i	$-0.983163\pi$
$3$	−0.785510	+	1.36054i	−0.453514	+	0.785510i	0.545087	+	0.838379i	$0.316497\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			2.81950i			1.26092i	0.776223	+	0.630458i	$0.217133\pi$
$5$			2.81950i			1.26092i	−0.776223	+	0.630458i	$0.782867\pi$
$6$	1.36054	−	0.785510i	0.555440	−	0.320683i
$7$	4.00004	−	2.30942i	1.51187	−	0.872879i	0.511968	−	0.859005i	$-0.328917\pi$
$7$	4.00004	−	2.30942i	1.51187	−	0.872879i	0.999904	−	0.0138749i	$-0.00441666\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.265948	+	0.460635i	0.0886493	+	0.153545i
$10$	1.40975	−	2.44175i	0.445801	−	0.772151i
$11$	0.145049	+	0.0837438i	0.0437338	+	0.0252497i	0.521707	−	0.853124i	$-0.325295\pi$
$11$	0.145049	+	0.0837438i	0.0437338	+	0.0252497i	−0.477974	+	0.878374i	$0.658629\pi$
$12$	−1.57102			−0.453514
$13$	2.99710	−	2.00434i	0.831246	−	0.555905i
$13$	2.99710	−	2.00434i	0.831246	−	0.555905i
$14$	−4.61884			−1.23444
$15$	−3.83605	−	2.21474i	−0.990463	−	0.571844i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.06309	+	1.84132i	0.257836	+	0.446585i	0.965662	−	0.259802i	$-0.0836572\pi$
$17$	1.06309	+	1.84132i	0.257836	+	0.446585i	−0.707826	+	0.706387i	$0.750324\pi$
$18$		−	0.531896i		−	0.125369i
$19$	0.866025	−	0.500000i	0.198680	−	0.114708i
$19$	0.866025	−	0.500000i	0.198680	−	0.114708i
$20$	−2.44175	+	1.40975i	−0.545993	+	0.315229i
$21$			7.25630i			1.58345i
$22$	−0.0837438	−	0.145049i	−0.0178542	−	0.0309245i
$23$	1.88716	−	3.26866i	0.393501	−	0.681563i	−0.599408	−	0.800444i	$-0.704597\pi$
$23$	1.88716	−	3.26866i	0.393501	−	0.681563i	0.992909	+	0.118881i	$0.0379305\pi$
$24$	1.36054	+	0.785510i	0.277720	+	0.160342i
$25$	−2.94955			−0.589911
$26$	−3.59774	+	0.237262i	−0.705574	+	0.0465309i
$27$	−5.54868			−1.06784
$28$	4.00004	+	2.30942i	0.755936	+	0.436440i
$29$	−4.68934	+	8.12217i	−0.870788	+	1.50825i	−0.00960459	+	0.999954i	$0.503057\pi$
$29$	−4.68934	+	8.12217i	−0.870788	+	1.50825i	−0.861183	+	0.508295i	$0.830276\pi$
$30$	2.21474	+	3.83605i	0.404355	+	0.700363i
$31$			2.76469i			0.496554i	0.968689	+	0.248277i	$0.0798643\pi$
$31$			2.76469i			0.496554i	−0.968689	+	0.248277i	$0.920136\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.227874	+	0.131563i	−0.0396678	+	0.0229022i
$34$		−	2.12617i		−	0.364636i
$35$	6.51141	+	11.2781i	1.10063	+	1.90634i
$36$	−0.265948	+	0.460635i	−0.0443246	+	0.0767725i
$37$	1.33378	+	0.770056i	0.219272	+	0.126596i	0.605613	−	0.795759i	$-0.292928\pi$
$37$	1.33378	+	0.770056i	0.219272	+	0.126596i	−0.386341	+	0.922356i	$0.626261\pi$
$38$	−1.00000			−0.162221
$39$	0.372744	+	5.65212i	0.0596868	+	0.905063i
$40$	2.81950			0.445801
$41$	−0.404305	−	0.233426i	−0.0631418	−	0.0364550i	0.468097	−	0.883677i	$-0.344940\pi$
$41$	−0.404305	−	0.233426i	−0.0631418	−	0.0364550i	−0.531239	+	0.847222i	$0.678273\pi$
$42$	3.62815	−	6.28414i	0.559835	−	0.969663i
$43$	4.76110	+	8.24646i	0.726061	+	1.25757i	0.958536	+	0.284972i	$0.0919842\pi$
$43$	4.76110	+	8.24646i	0.726061	+	1.25757i	−0.232475	+	0.972602i	$0.574682\pi$
$44$			0.167488i			0.0252497i
$45$	−1.29876	+	0.749839i	−0.193608	+	0.111779i
$46$	−3.26866	+	1.88716i	−0.481938	+	0.278247i
$47$		−	4.35742i		−	0.635595i	−0.948159	−	0.317797i	$-0.897057\pi$
$47$		−	4.35742i		−	0.635595i	0.948159	−	0.317797i	$-0.102943\pi$
$48$	−0.785510	−	1.36054i	−0.113379	−	0.196378i
$49$	7.16686	−	12.4134i	1.02384	−	1.77334i
$50$	2.55439	+	1.47478i	0.361245	+	0.208565i
$51$	−3.34026			−0.467730
$52$	3.23436	+	1.59339i	0.448525	+	0.220964i
$53$	−6.10204			−0.838179			−0.419090	−	0.907945i	$-0.637651\pi$
$53$	−6.10204			−0.838179			−0.419090	+	0.907945i	$0.637651\pi$
$54$	4.80530	+	2.77434i	0.653918	+	0.377540i
$55$	−0.236115	+	0.408964i	−0.0318378	+	0.0551447i
$56$	−2.30942	−	4.00004i	−0.308610	−	0.534527i
$57$			1.57102i			0.208087i
$58$	8.12217	−	4.68934i	1.06649	−	0.615740i
$59$	−3.37916	+	1.95096i	−0.439929	+	0.253993i	−0.703568	−	0.710628i	$-0.748411\pi$
$59$	−3.37916	+	1.95096i	−0.439929	+	0.253993i	0.263638	+	0.964622i	$0.415077\pi$
$60$		−	4.42948i		−	0.571844i
$61$	−7.14466	−	12.3749i	−0.914779	−	1.58444i	−0.807224	−	0.590245i	$-0.799031\pi$
$61$	−7.14466	−	12.3749i	−0.914779	−	1.58444i	−0.107556	−	0.994199i	$-0.534302\pi$
$62$	1.38235	−	2.39429i	0.175558	−	0.304076i
$63$	2.12760	+	1.22837i	0.268053	+	0.154760i
$64$	−1.00000			−0.125000
$65$	5.65124	+	8.45031i	0.700950	+	1.04813i
$66$	0.263126			0.0323886
$67$	−1.07818	−	0.622486i	−0.131720	−	0.0760488i	0.432692	−	0.901542i	$-0.357564\pi$
$67$	−1.07818	−	0.622486i	−0.131720	−	0.0760488i	−0.564412	+	0.825493i	$0.690897\pi$
$68$	−1.06309	+	1.84132i	−0.128918	+	0.223293i
$69$	2.96477	+	5.13514i	0.356917	+	0.618198i
$70$		−	13.0228i		−	1.55652i
$71$	13.9464	−	8.05198i	1.65514	−	0.955594i	0.680225	−	0.733004i	$-0.261882\pi$
$71$	13.9464	−	8.05198i	1.65514	−	0.955594i	0.974912	−	0.222590i	$-0.0714511\pi$
$72$	0.460635	−	0.265948i	0.0542864	−	0.0313423i
$73$			12.6389i			1.47927i	0.673006	+	0.739637i	$0.265003\pi$
$73$			12.6389i			1.47927i	−0.673006	+	0.739637i	$0.734997\pi$
$74$	−0.770056	−	1.33378i	−0.0895172	−	0.155048i
$75$	2.31690	−	4.01300i	0.267533	−	0.463381i
$76$	0.866025	+	0.500000i	0.0993399	+	0.0573539i
$77$	0.773599			0.0881598
$78$	2.50325	−	5.08125i	0.283438	−	0.575338i
$79$	−9.73309			−1.09506			−0.547529	−	0.836787i	$-0.684431\pi$
$79$	−9.73309			−1.09506			−0.547529	+	0.836787i	$0.684431\pi$
$80$	−2.44175	−	1.40975i	−0.272996	−	0.157615i
$81$	3.56070	−	6.16731i	0.395633	−	0.685257i
$82$	0.233426	+	0.404305i	0.0257775	+	0.0446480i
$83$			4.41971i			0.485126i	0.970136	+	0.242563i	$0.0779881\pi$
$83$			4.41971i			0.485126i	−0.970136	+	0.242563i	$0.922012\pi$
$84$	−6.28414	+	3.62815i	−0.685656	+	0.395863i
$85$	−5.19159	+	2.99737i	−0.563107	+	0.325110i
$86$		−	9.52220i		−	1.02680i
$87$	−7.36704	−	12.7601i	−0.789830	−	1.36803i
$88$	0.0837438	−	0.145049i	0.00892712	−	0.0154622i
$89$	−1.81103	−	1.04560i	−0.191969	−	0.110833i	0.400935	−	0.916106i	$-0.368685\pi$
$89$	−1.81103	−	1.04560i	−0.191969	−	0.110833i	−0.592904	+	0.805273i	$0.702019\pi$
$90$	1.49968			0.158080
$91$	7.35963	−	14.9390i	0.771499	−	1.56603i
$92$	3.77433			0.393501
$93$	−3.76149	−	2.17169i	−0.390048	−	0.225194i
$94$	−2.17871	+	3.77363i	−0.224717	+	0.389221i
$95$	1.40975	+	2.44175i	0.144637	+	0.250519i
$96$			1.57102i			0.160342i
$97$	−13.9567	+	8.05789i	−1.41709	+	0.818155i	−0.996042	−	0.0888852i	$-0.971670\pi$
$97$	−13.9567	+	8.05789i	−1.41709	+	0.818155i	−0.421044	+	0.907040i	$0.638336\pi$
$98$	−12.4134	+	7.16686i	−1.25394	+	0.723962i
$99$			0.0890860i			0.00895348i
$100$	−1.47478	−	2.55439i	−0.147478	−	0.255439i
$101$	0.107761	−	0.186648i	0.0107226	−	0.0185722i	−0.860614	−	0.509257i	$-0.829920\pi$
$101$	0.107761	−	0.186648i	0.0107226	−	0.0185722i	0.871337	+	0.490685i	$0.163253\pi$
$102$	2.89275	+	1.67013i	0.286425	+	0.165367i
$103$	−4.81809			−0.474741			−0.237370	−	0.971419i	$-0.576285\pi$
$103$	−4.81809			−0.474741			−0.237370	+	0.971419i	$0.576285\pi$
$104$	−2.00434	−	2.99710i	−0.196542	−	0.293890i
$105$	−20.4591			−1.99660
$106$	5.28452	+	3.05102i	0.513278	+	0.296341i
$107$	1.09184	−	1.89112i	0.105552	−	0.182822i	−0.808412	−	0.588618i	$-0.799672\pi$
$107$	1.09184	−	1.89112i	0.105552	−	0.182822i	0.913964	+	0.405796i	$0.133006\pi$
$108$	−2.77434	−	4.80530i	−0.266961	−	0.462390i
$109$		−	11.7354i		−	1.12405i	−0.827121	−	0.562024i	$-0.810023\pi$
$109$		−	11.7354i		−	1.12405i	0.827121	−	0.562024i	$-0.189977\pi$
$110$	0.408964	−	0.236115i	0.0389932	−	0.0225127i
$111$	−2.09539	+	1.20977i	−0.198886	+	0.114827i
$112$			4.61884i			0.436440i
$113$	−2.70439	−	4.68414i	−0.254407	−	0.440646i	0.710327	−	0.703872i	$-0.248547\pi$
$113$	−2.70439	−	4.68414i	−0.254407	−	0.440646i	−0.964734	+	0.263225i	$0.915214\pi$
$114$	0.785510	−	1.36054i	0.0735698	−	0.127427i
$115$	9.21598	+	5.32085i	0.859395	+	0.496172i
$116$	−9.37867			−0.870788
$117$	1.72034	+	0.847519i	0.159046	+	0.0783532i
$118$	3.90192			0.359201
$119$	8.50477	+	4.91023i	0.779631	+	0.450120i
$120$	−2.21474	+	3.83605i	−0.202177	+	0.350181i
$121$	−5.48597	−	9.50199i	−0.498725	−	0.863817i
$122$			14.2893i			1.29369i
$123$	0.635171	−	0.366716i	0.0572715	−	0.0330657i
$124$	−2.39429	+	1.38235i	−0.215014	+	0.124138i
$125$			5.78122i			0.517088i
$126$	−1.22837	−	2.12760i	−0.109432	−	0.189542i
$127$	8.58361	−	14.8672i	0.761672	−	1.31925i	−0.180316	−	0.983609i	$-0.557712\pi$
$127$	8.58361	−	14.8672i	0.761672	−	1.31925i	0.941988	−	0.335646i	$-0.108954\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−14.9596			−1.31712
$130$	−0.668960	−	10.1438i	−0.0586716	−	0.889670i
$131$	15.5641			1.35984			0.679920	−	0.733286i	$-0.262014\pi$
$131$	15.5641			1.35984			0.679920	+	0.733286i	$0.262014\pi$
$132$	−0.227874	−	0.131563i	−0.0198339	−	0.0114511i
$133$	2.30942	−	4.00004i	0.200252	−	0.346847i
$134$	0.622486	+	1.07818i	0.0537746	+	0.0931403i
$135$		−	15.6445i		−	1.34646i
$136$	1.84132	−	1.06309i	0.157892	−	0.0911589i
$137$	4.94835	−	2.85693i	0.422766	−	0.244084i	−0.273494	−	0.961874i	$-0.588179\pi$
$137$	4.94835	−	2.85693i	0.422766	−	0.244084i	0.696260	+	0.717789i	$0.254846\pi$
$138$		−	5.92954i		−	0.504756i
$139$	4.60740	+	7.98025i	0.390795	+	0.676876i	0.992555	−	0.121801i	$-0.0388670\pi$
$139$	4.60740	+	7.98025i	0.390795	+	0.676876i	−0.601760	+	0.798677i	$0.705534\pi$
$140$	−6.51141	+	11.2781i	−0.550314	+	0.953172i
$141$	5.92845	+	3.42279i	0.499266	+	0.288251i
$142$	−16.1040			−1.35141
$143$	0.602576	−	0.0397385i	0.0503900	−	0.00332310i
$144$	−0.531896			−0.0443246
$145$	−22.9004	−	13.2216i	−1.90178	−	1.09799i
$146$	6.31947	−	10.9456i	0.523003	−	0.905867i
$147$	11.2593	+	19.5016i	0.928650	+	1.60847i
$148$			1.54011i			0.126596i
$149$	−16.1799	+	9.34147i	−1.32551	+	0.765283i	−0.984602	−	0.174814i	$-0.944068\pi$
$149$	−16.1799	+	9.34147i	−1.32551	+	0.765283i	−0.340908	+	0.940097i	$0.610734\pi$
$150$	−4.01300	+	2.31690i	−0.327660	+	0.189174i
$151$		−	13.3473i		−	1.08619i	−0.839672	−	0.543094i	$-0.817253\pi$
$151$		−	13.3473i		−	1.08619i	0.839672	−	0.543094i	$-0.182747\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	−0.565451	+	0.979390i	−0.0457140	+	0.0791790i
$154$	−0.669957	−	0.386800i	−0.0539866	−	0.0311692i
$155$	−7.79504			−0.626113
$156$	−4.70850	+	3.14886i	−0.376982	+	0.252111i
$157$	16.2275			1.29510			0.647549	−	0.762024i	$-0.275794\pi$
$157$	16.2275			1.29510			0.647549	+	0.762024i	$0.275794\pi$
$158$	8.42910	+	4.86654i	0.670583	+	0.387161i
$159$	4.79321	−	8.30209i	0.380127	−	0.658398i
$160$	1.40975	+	2.44175i	0.111450	+	0.193038i
$161$		−	17.4330i		−	1.37391i
$162$	−6.16731	+	3.56070i	−0.484550	+	0.279755i
$163$	4.99088	−	2.88148i	0.390916	−	0.225695i	−0.291641	−	0.956528i	$-0.594201\pi$
$163$	4.99088	−	2.88148i	0.390916	−	0.225695i	0.682557	+	0.730833i	$0.260868\pi$
$164$		−	0.466851i		−	0.0364550i
$165$	−0.370942	−	0.642490i	−0.0288778	−	0.0500178i
$166$	2.20985	−	3.82758i	0.171518	−	0.297078i
$167$	12.3491	+	7.12973i	0.955599	+	0.551715i	0.894816	−	0.446436i	$-0.147307\pi$
$167$	12.3491	+	7.12973i	0.955599	+	0.551715i	0.0607833	+	0.998151i	$0.480640\pi$
$168$	7.25630			0.559835
$169$	4.96522	−	12.0144i	0.381940	−	0.924187i
$170$	5.99473			0.459775
$171$	0.460635	+	0.265948i	0.0352257	+	0.0203375i
$172$	−4.76110	+	8.24646i	−0.363030	+	0.628787i
$173$	−9.57662	−	16.5872i	−0.728097	−	1.26110i	−0.957687	−	0.287813i	$-0.907072\pi$
$173$	−9.57662	−	16.5872i	−0.728097	−	1.26110i	0.229590	−	0.973287i	$-0.426262\pi$
$174$			14.7341i			1.11699i
$175$	−11.7983	+	6.81177i	−0.891870	+	0.514921i
$176$	−0.145049	+	0.0837438i	−0.0109334	+	0.00631243i
$177$		−	6.13000i		−	0.460759i
$178$	1.04560	+	1.81103i	0.0783709	+	0.135742i
$179$	5.32093	−	9.21612i	0.397705	−	0.688845i	−0.595738	−	0.803179i	$-0.703140\pi$
$179$	5.32093	−	9.21612i	0.397705	−	0.688845i	0.993442	+	0.114334i	$0.0364735\pi$
$180$	−1.29876	−	0.749839i	−0.0968038	−	0.0558897i
$181$	−0.786741			−0.0584780			−0.0292390	−	0.999572i	$-0.509308\pi$
$181$	−0.786741			−0.0584780			−0.0292390	+	0.999572i	$0.509308\pi$
$182$	−13.8431	+	9.25775i	−1.02612	+	0.686230i
$183$	22.4488			1.65946
$184$	−3.26866	−	1.88716i	−0.240969	−	0.139124i
$185$	−2.17117	+	3.76058i	−0.159628	+	0.276483i
$186$	2.17169	+	3.76149i	0.159236	+	0.275805i
$187$			0.356108i			0.0260412i
$188$	3.77363	−	2.17871i	0.275220	−	0.158899i
$189$	−22.1949	+	12.8142i	−1.61444	+	0.932099i
$190$		−	2.81950i		−	0.204548i
$191$	−1.39340	−	2.41344i	−0.100823	−	0.174630i	0.811201	−	0.584767i	$-0.198814\pi$
$191$	−1.39340	−	2.41344i	−0.100823	−	0.174630i	−0.912024	+	0.410137i	$0.865481\pi$
$192$	0.785510	−	1.36054i	0.0566893	−	0.0981888i
$193$	18.3572	+	10.5985i	1.32138	+	0.762898i	0.983948	−	0.178453i	$-0.0571093\pi$
$193$	18.3572	+	10.5985i	1.32138	+	0.762898i	0.337429	+	0.941351i	$0.390443\pi$
$194$	16.1158			1.15705
$195$	−15.9361	+	1.05095i	−1.14121	+	0.0752600i
$196$	14.3337			1.02384
$197$	−5.01701	−	2.89657i	−0.357447	−	0.206372i	0.310513	−	0.950569i	$-0.399499\pi$
$197$	−5.01701	−	2.89657i	−0.357447	−	0.206372i	−0.667960	+	0.744197i	$0.732832\pi$
$198$	0.0445430	−	0.0771507i	0.00316553	−	0.00548286i
$199$	−5.02543	−	8.70430i	−0.356243	−	0.617031i	0.631087	−	0.775712i	$-0.282609\pi$
$199$	−5.02543	−	8.70430i	−0.356243	−	0.617031i	−0.987330	+	0.158681i	$0.949276\pi$
$200$			2.94955i			0.208565i
$201$	1.69384	−	0.977938i	0.119474	−	0.0689784i
$202$	−0.186648	+	0.107761i	−0.0131325	+	0.00758205i
$203$			43.3186i			3.04037i
$204$	−1.67013	−	2.89275i	−0.116932	−	0.202533i
$205$	0.658142	−	1.13994i	0.0459667	−	0.0796166i
$206$	4.17259	+	2.40905i	0.290718	+	0.167846i
$207$	2.00755			0.139534
$208$	0.237262	+	3.59774i	0.0164512	+	0.249458i
$209$	0.167488			0.0115854
$210$	17.7181	+	10.2295i	1.22266	+	0.705906i
$211$	3.07920	−	5.33333i	0.211981	−	0.367162i	−0.740353	−	0.672218i	$-0.765342\pi$
$211$	3.07920	−	5.33333i	0.211981	−	0.367162i	0.952334	+	0.305056i	$0.0986752\pi$
$212$	−3.05102	−	5.28452i	−0.209545	−	0.362942i
$213$			25.2996i			1.73350i
$214$	−1.89112	+	1.09184i	−0.129274	+	0.0746366i
$215$	−23.2509	+	13.4239i	−1.58570	+	0.915502i
$216$			5.54868i			0.377540i
$217$	6.38484	+	11.0589i	0.433431	+	0.750725i
$218$	−5.86770	+	10.1632i	−0.397411	+	0.688336i
$219$	−17.1958	−	9.92801i	−1.16199	−	0.670873i
$220$	−0.472231			−0.0318378
$221$	6.87681	+	3.38783i	0.462584	+	0.227890i
$222$	2.41955			0.162389
$223$	15.2242	+	8.78971i	1.01949	+	0.588602i	0.913956	−	0.405814i	$-0.133012\pi$
$223$	15.2242	+	8.78971i	1.01949	+	0.588602i	0.105533	+	0.994416i	$0.466345\pi$
$224$	2.30942	−	4.00004i	0.154305	−	0.267264i
$225$	−0.784428	−	1.35867i	−0.0522952	−	0.0905779i
$226$			5.40877i			0.359786i
$227$	11.7238	−	6.76873i	0.778135	−	0.449256i	−0.0576342	−	0.998338i	$-0.518356\pi$
$227$	11.7238	−	6.76873i	0.778135	−	0.449256i	0.835769	+	0.549082i	$0.185022\pi$
$228$	−1.36054	+	0.785510i	−0.0901042	+	0.0520217i
$229$			28.1954i			1.86320i	0.363480	+	0.931602i	$0.381589\pi$
$229$			28.1954i			1.86320i	−0.363480	+	0.931602i	$0.618411\pi$
$230$	−5.32085	−	9.21598i	−0.350846	−	0.607684i
$231$	−0.607670	+	1.05252i	−0.0399818	+	0.0692504i
$232$	8.12217	+	4.68934i	0.533246	+	0.307870i
$233$	−16.5004			−1.08097			−0.540487	−	0.841352i	$-0.681760\pi$
$233$	−16.5004			−1.08097			−0.540487	+	0.841352i	$0.681760\pi$
$234$	−1.06610	−	1.59414i	−0.0696932	−	0.104212i
$235$	12.2857			0.801432
$236$	−3.37916	−	1.95096i	−0.219965	−	0.126997i
$237$	7.64544	−	13.2423i	0.496625	−	0.860179i
$238$	−4.91023	−	8.50477i	−0.318283	−	0.551282i
$239$		−	3.54175i		−	0.229096i	−0.993418	−	0.114548i	$-0.963458\pi$
$239$		−	3.54175i		−	0.229096i	0.993418	−	0.114548i	$-0.0365420\pi$
$240$	3.83605	−	2.21474i	0.247616	−	0.142961i
$241$	14.8369	−	8.56607i	0.955727	−	0.551789i	0.0608714	−	0.998146i	$-0.480612\pi$
$241$	14.8369	−	8.56607i	0.955727	−	0.551789i	0.894855	+	0.446357i	$0.147279\pi$
$242$			10.9719i			0.705304i
$243$	−2.72909	−	4.72692i	−0.175071	−	0.303232i
$244$	7.14466	−	12.3749i	0.457390	−	0.792222i
$245$	34.9994	+	20.2069i	2.23603	+	1.29097i
$246$	−0.733433			−0.0467620
$247$	1.59339	−	3.23436i	0.101385	−	0.205798i
$248$	2.76469			0.175558
$249$	−6.01320	−	3.47172i	−0.381071	−	0.220012i
$250$	2.89061	−	5.00668i	0.182818	−	0.316651i
$251$	−5.91634	−	10.2474i	−0.373436	−	0.646811i	0.616655	−	0.787233i	$-0.288487\pi$
$251$	−5.91634	−	10.2474i	−0.373436	−	0.646811i	−0.990092	+	0.140423i	$0.955154\pi$
$252$			2.45674i			0.154760i
$253$	0.547461	−	0.316077i	0.0344186	−	0.0198716i
$254$	−14.8672	+	8.58361i	−0.932854	+	0.538583i
$255$		−	9.41785i		−	0.589768i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.67678	−	15.0286i	0.541243	−	0.937460i	−0.457590	−	0.889163i	$-0.651287\pi$
$257$	8.67678	−	15.0286i	0.541243	−	0.937460i	0.998833	−	0.0482970i	$-0.0153794\pi$
$258$	12.9554	+	7.47978i	0.806565	+	0.465671i
$259$	7.11354			0.442014
$260$	−4.49256	+	9.11927i	−0.278617	+	0.565553i
$261$	−4.98847			−0.308779
$262$	−13.4789	−	7.78204i	−0.832729	−	0.480776i
$263$	0.780888	−	1.35254i	0.0481516	−	0.0834010i	−0.840945	−	0.541121i	$-0.818000\pi$
$263$	0.780888	−	1.35254i	0.0481516	−	0.0834010i	0.889097	+	0.457720i	$0.151334\pi$
$264$	0.131563	+	0.227874i	0.00809716	+	0.0140247i
$265$		−	17.2047i		−	1.05687i
$266$	−4.00004	+	2.30942i	−0.245258	+	0.141600i
$267$	2.84516	−	1.64265i	0.174121	−	0.100529i
$268$		−	1.24497i		−	0.0760488i
$269$	1.37273	+	2.37765i	0.0836971	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$269$	1.37273	+	2.37765i	0.0836971	+	0.144968i	−0.821138	+	0.570729i	$0.806661\pi$
$270$	−7.82224	+	13.5485i	−0.476046	+	0.824536i
$271$	−14.6220	−	8.44202i	−0.888223	−	0.512816i	−0.0148625	−	0.999890i	$-0.504731\pi$
$271$	−14.6220	−	8.44202i	−0.888223	−	0.512816i	−0.873361	+	0.487073i	$0.838064\pi$
$272$	−2.12617			−0.128918
$273$	14.5441	+	21.7478i	0.880250	+	1.31624i
$274$	−5.71387			−0.345187
$275$	−0.427829	−	0.247007i	−0.0257990	−	0.0148951i
$276$	−2.96477	+	5.13514i	−0.178458	+	0.309099i
$277$	−2.79239	−	4.83656i	−0.167778	−	0.290600i	0.769860	−	0.638213i	$-0.220326\pi$
$277$	−2.79239	−	4.83656i	−0.167778	−	0.290600i	−0.937638	+	0.347612i	$0.886993\pi$
$278$		−	9.21480i		−	0.552667i
$279$	−1.27352	+	0.735264i	−0.0762434	+	0.0440191i
$280$	11.2781	−	6.51141i	0.673994	−	0.389131i
$281$			24.2016i			1.44375i	0.692024	+	0.721874i	$0.256719\pi$
$281$			24.2016i			1.44375i	−0.692024	+	0.721874i	$0.743281\pi$
$282$	−3.42279	−	5.92845i	−0.203824	−	0.353034i
$283$	−12.9737	+	22.4712i	−0.771209	+	1.33577i	0.165692	+	0.986178i	$0.447014\pi$
$283$	−12.9737	+	22.4712i	−0.771209	+	1.33577i	−0.936901	+	0.349596i	$0.886319\pi$
$284$	13.9464	+	8.05198i	0.827568	+	0.477797i
$285$	−4.42948			−0.262380
$286$	−0.541716	−	0.266874i	−0.0320323	−	0.0157806i
$287$	−2.15631			−0.127283
$288$	0.460635	+	0.265948i	0.0271432	+	0.0156711i
$289$	6.23970	−	10.8075i	0.367041	−	0.635734i
$290$	13.2216	+	22.9004i	0.776397	+	1.34476i
$291$		−	25.3182i		−	1.48418i
$292$	−10.9456	+	6.31947i	−0.640545	+	0.369819i
$293$	12.4966	−	7.21494i	0.730061	−	0.421501i	−0.0883834	−	0.996087i	$-0.528170\pi$
$293$	12.4966	−	7.21494i	0.730061	−	0.421501i	0.818445	+	0.574585i	$0.194837\pi$
$294$		−	22.5186i		−	1.31331i
$295$	−5.50072	−	9.52753i	−0.320265	−	0.554714i
$296$	0.770056	−	1.33378i	0.0447586	−	0.0775242i
$297$	−0.804828	−	0.464668i	−0.0467009	−	0.0269628i
$298$	18.6829			1.08227
$299$	−0.895505	−	13.5790i	−0.0517884	−	0.785296i
$300$	4.63381			0.267533
$301$	38.0891	+	21.9908i	2.19542	+	1.26753i
$302$	−6.67365	+	11.5591i	−0.384025	+	0.665151i
$303$	0.169295	+	0.293227i	0.00972574	+	0.0168455i
$304$			1.00000i			0.0573539i
$305$	34.8910	−	20.1443i	1.99785	−	1.15346i
$306$	0.979390	−	0.565451i	0.0559880	−	0.0323247i
$307$			1.27895i			0.0729934i	0.999334	+	0.0364967i	$0.0116198\pi$
$307$			1.27895i			0.0729934i	−0.999334	+	0.0364967i	$0.988380\pi$
$308$	0.386800	+	0.669957i	0.0220400	+	0.0381743i
$309$	3.78466	−	6.55522i	0.215302	−	0.372914i
$310$	6.75070	+	3.89752i	0.383414	+	0.221364i
$311$	−8.19033			−0.464431			−0.232215	−	0.972664i	$-0.574597\pi$
$311$	−8.19033			−0.464431			−0.232215	+	0.972664i	$0.574597\pi$
$312$	5.65212	−	0.372744i	0.319988	−	0.0211025i
$313$	−3.25848			−0.184180			−0.0920901	−	0.995751i	$-0.529355\pi$
$313$	−3.25848			−0.184180			−0.0920901	+	0.995751i	$0.529355\pi$
$314$	−14.0534	−	8.11376i	−0.793082	−	0.457886i
$315$	−3.46339	+	5.99876i	−0.195140	+	0.337992i
$316$	−4.86654	−	8.42910i	−0.273764	−	0.474174i
$317$			17.4705i			0.981242i	0.871373	+	0.490621i	$0.163230\pi$
$317$			17.4705i			0.981242i	−0.871373	+	0.490621i	$0.836770\pi$
$318$	−8.30209	+	4.79321i	−0.465558	+	0.268790i
$319$	−1.36036	+	0.785406i	−0.0761657	+	0.0439743i
$320$		−	2.81950i		−	0.157615i
$321$	1.71530	+	2.97099i	0.0957388	+	0.165824i
$322$	−8.71651	+	15.0974i	−0.485752	+	0.841348i
$323$	1.84132	+	1.06309i	0.102454	+	0.0591517i
$324$	7.12140			0.395633
$325$	−8.84011	+	5.91192i	−0.490361	+	0.327934i
$326$	−5.76297			−0.319181
$327$	15.9665	+	9.21828i	0.882951	+	0.509772i
$328$	−0.233426	+	0.404305i	−0.0128888	+	0.0223240i
$329$	−10.0631	−	17.4298i	−0.554797	−	0.960937i
$330$			0.741884i			0.0408394i
$331$	−23.2276	+	13.4104i	−1.27670	+	0.737105i	−0.976241	−	0.216689i	$-0.930474\pi$
$331$	−23.2276	+	13.4104i	−1.27670	+	0.737105i	−0.300462	+	0.953794i	$0.597141\pi$
$332$	−3.82758	+	2.20985i	−0.210066	+	0.121281i
$333$			0.819179i			0.0448907i
$334$	−7.12973	−	12.3491i	−0.390122	−	0.675711i
$335$	1.75510	−	3.03992i	0.0958912	−	0.166088i
$336$	−6.28414	−	3.62815i	−0.342828	−	0.197932i
$337$	−9.26426			−0.504656			−0.252328	−	0.967642i	$-0.581196\pi$
$337$	−9.26426			−0.504656			−0.252328	+	0.967642i	$0.581196\pi$
$338$	−10.3072	+	7.92220i	−0.560639	+	0.430911i
$339$	8.49729			0.461510
$340$	−5.19159	−	2.99737i	−0.281554	−	0.162555i
$341$	−0.231526	+	0.401015i	−0.0125378	+	0.0217162i
$342$	−0.265948	−	0.460635i	−0.0143808	−	0.0249083i
$343$		−	33.8733i		−	1.82899i
$344$	8.24646	−	4.76110i	0.444620	−	0.256701i
$345$	−14.4785	+	8.35916i	−0.779496	+	0.450042i
$346$			19.1532i			1.02968i
$347$	−15.0557	−	26.0773i	−0.808234	−	1.39990i	−0.914086	−	0.405520i	$-0.867090\pi$
$347$	−15.0557	−	26.0773i	−0.808234	−	1.39990i	0.105852	−	0.994382i	$-0.466243\pi$
$348$	7.36704	−	12.7601i	0.394915	−	0.684013i
$349$	−7.02994	−	4.05874i	−0.376304	−	0.217259i	0.299905	−	0.953969i	$-0.403045\pi$
$349$	−7.02994	−	4.05874i	−0.376304	−	0.217259i	−0.676209	+	0.736710i	$0.736378\pi$
$350$	13.6235			0.728208
$351$	−16.6299	+	11.1215i	−0.887641	+	0.593620i
$352$	0.167488			0.00892712
$353$	−15.8907	−	9.17448i	−0.845775	−	0.488308i	0.0134482	−	0.999910i	$-0.495719\pi$
$353$	−15.8907	−	9.17448i	−0.845775	−	0.488308i	−0.859223	+	0.511601i	$0.829053\pi$
$354$	−3.06500	+	5.30873i	−0.162903	+	0.282156i
$355$	22.7025	+	39.3219i	1.20492	+	2.08699i
$356$		−	2.09120i		−	0.110833i
$357$	−13.3612	+	7.71407i	−0.707148	+	0.408272i
$358$	−9.21612	+	5.32093i	−0.487087	+	0.281220i
$359$		−	18.1510i		−	0.957973i	−0.877822	−	0.478987i	$-0.841004\pi$
$359$		−	18.1510i		−	0.957973i	0.877822	−	0.478987i	$-0.158996\pi$
$360$	0.749839	+	1.29876i	0.0395200	+	0.0684506i
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	0.681338	+	0.393370i	0.0358103	+	0.0206751i
$363$	17.2372			0.904716
$364$	16.6174	−	1.09588i	0.870988	−	0.0574396i
$365$	−35.6354			−1.86524
$366$	−19.4412	−	11.2244i	−1.01621	−	0.586709i
$367$	−11.8897	+	20.5935i	−0.620637	+	1.07497i	0.368731	+	0.929536i	$0.379793\pi$
$367$	−11.8897	+	20.5935i	−0.620637	+	1.07497i	−0.989367	+	0.145438i	$0.953541\pi$
$368$	1.88716	+	3.26866i	0.0983752	+	0.170391i
$369$		−	0.248316i		−	0.0129268i
$370$	3.76058	−	2.17117i	0.195503	−	0.112874i
$371$	−24.4084	+	14.0922i	−1.26722	+	0.731630i
$372$		−	4.34339i		−	0.225194i
$373$	6.04193	+	10.4649i	0.312839	+	0.541853i	0.978976	−	0.203977i	$-0.0653866\pi$
$373$	6.04193	+	10.4649i	0.312839	+	0.541853i	−0.666137	+	0.745830i	$0.732053\pi$
$374$	0.178054	−	0.308398i	0.00920694	−	0.0159469i
$375$	−7.86560	−	4.54121i	−0.406178	−	0.234507i
$376$	−4.35742			−0.224717
$377$	2.22520	+	33.7420i	0.114604	+	1.73780i
$378$	25.6285			1.31819
$379$	1.10624	+	0.638685i	0.0568235	+	0.0328071i	0.528143	−	0.849156i	$-0.322889\pi$
$379$	1.10624	+	0.638685i	0.0568235	+	0.0328071i	−0.471319	+	0.881963i	$0.656222\pi$
$380$	−1.40975	+	2.44175i	−0.0723185	+	0.125259i
$381$	13.4850	+	23.3567i	0.690858	+	1.19660i
$382$			2.78680i			0.142585i
$383$	−15.2129	+	8.78315i	−0.777341	+	0.448798i	−0.835487	−	0.549510i	$-0.814814\pi$
$383$	−15.2129	+	8.78315i	−0.777341	+	0.448798i	0.0581464	+	0.998308i	$0.481481\pi$
$384$	−1.36054	+	0.785510i	−0.0694299	+	0.0400854i
$385$			2.18116i			0.111162i
$386$	−10.5985	−	18.3572i	−0.539450	−	0.934355i
$387$	−2.53241	+	4.38626i	−0.128730	+	0.222966i
$388$	−13.9567	−	8.05789i	−0.708543	−	0.409077i
$389$	−0.0492487			−0.00249701			−0.00124850	−	0.999999i	$-0.500397\pi$
$389$	−0.0492487			−0.00249701			−0.00124850	+	0.999999i	$0.500397\pi$
$390$	14.3266	+	7.05791i	0.725453	+	0.357391i
$391$	8.02487			0.405835
$392$	−12.4134	−	7.16686i	−0.626970	−	0.361981i
$393$	−12.2257	+	21.1756i	−0.616707	+	1.06817i
$394$	2.89657	+	5.01701i	0.145927	+	0.252753i
$395$		−	27.4424i		−	1.38078i
$396$	−0.0771507	+	0.0445430i	−0.00387697	+	0.00223837i
$397$	29.3110	−	16.9227i	1.47108	−	0.849326i	0.471603	−	0.881811i	$-0.343676\pi$
$397$	29.3110	−	16.9227i	1.47108	−	0.849326i	0.999472	+	0.0324855i	$0.0103423\pi$
$398$			10.0509i			0.503804i
$399$	3.62815	+	6.28414i	0.181635	+	0.314600i
$400$	1.47478	−	2.55439i	0.0737389	−	0.127719i
$401$	−21.9620	−	12.6797i	−1.09673	−	0.633196i	−0.161368	−	0.986894i	$-0.551591\pi$
$401$	−21.9620	−	12.6797i	−1.09673	−	0.633196i	−0.935360	+	0.353698i	$0.884924\pi$
$402$	−1.95588			−0.0975502
$403$	5.54139	+	8.28606i	0.276037	+	0.412758i
$404$	0.215522			0.0107226
$405$	17.3887	+	10.0394i	0.864052	+	0.498861i
$406$	21.6593	−	37.5150i	1.07493	−	1.86184i
$407$	0.128975	+	0.223391i	0.00639305	+	0.0110731i
$408$			3.34026i			0.165367i
$409$	−22.4706	+	12.9734i	−1.11110	+	0.641495i	−0.939114	−	0.343605i	$-0.888352\pi$
$409$	−22.4706	+	12.9734i	−1.11110	+	0.641495i	−0.171987	+	0.985099i	$0.555019\pi$
$410$	−1.13994	+	0.658142i	−0.0562974	+	0.0325033i
$411$			8.97660i			0.442783i
$412$	−2.40905	−	4.17259i	−0.118685	−	0.205569i
$413$	−9.01118	+	15.6078i	−0.443411	+	0.768011i
$414$	−1.73859	−	1.00377i	−0.0854469	−	0.0493328i
$415$	−12.4613			−0.611703
$416$	1.59339	−	3.23436i	0.0781225	−	0.158578i
$417$	−14.4766			−0.708924
$418$	−0.145049	−	0.0837438i	−0.00709456	−	0.00409604i
$419$	17.2041	−	29.7984i	0.840475	−	1.45575i	−0.0490177	−	0.998798i	$-0.515609\pi$
$419$	17.2041	−	29.7984i	0.840475	−	1.45575i	0.889493	−	0.456948i	$-0.151058\pi$
$420$	−10.2295	−	17.7181i	−0.499151	−	0.864555i
$421$		−	23.3518i		−	1.13809i	−0.822305	−	0.569047i	$-0.807312\pi$
$421$		−	23.3518i		−	1.13809i	0.822305	−	0.569047i	$-0.192688\pi$
$422$	−5.33333	+	3.07920i	−0.259623	+	0.149893i
$423$	2.00718	−	1.15885i	0.0975924	−	0.0563450i
$424$			6.10204i			0.296341i
$425$	−3.13563	−	5.43107i	−0.152100	−	0.263446i
$426$	12.6498	−	21.9101i	0.612886	−	1.06155i
$427$	−57.1578	−	33.0001i	−2.76606	−	1.59698i
$428$	2.18368			0.105552
$429$	−0.419264	+	0.851046i	−0.0202423	+	0.0410889i
$430$	26.8478			1.29472
$431$	−17.7933	−	10.2730i	−0.857074	−	0.494832i	0.00595706	−	0.999982i	$-0.498104\pi$
$431$	−17.7933	−	10.2730i	−0.857074	−	0.494832i	−0.863032	+	0.505150i	$0.831437\pi$
$432$	2.77434	−	4.80530i	0.133480	−	0.231195i
$433$	−10.2384	−	17.7334i	−0.492026	−	0.852214i	0.507932	−	0.861397i	$-0.330410\pi$
$433$	−10.2384	−	17.7334i	−0.492026	−	0.852214i	−0.999958	+	0.00918317i	$0.997077\pi$
$434$		−	12.7697i		−	0.612965i
$435$	35.9770	−	20.7713i	1.72497	−	0.995909i
$436$	10.1632	−	5.86770i	0.486727	−	0.281012i
$437$		−	3.77433i		−	0.180551i
$438$	9.92801	+	17.1958i	0.474379	+	0.821648i
$439$	−0.751168	+	1.30106i	−0.0358513	+	0.0620963i	−0.883394	−	0.468630i	$-0.844748\pi$
$439$	−0.751168	+	1.30106i	−0.0358513	+	0.0620963i	0.847543	+	0.530727i	$0.178081\pi$
$440$	0.408964	+	0.236115i	0.0194966	+	0.0112564i
$441$	7.62404			0.363050
$442$	−4.26158	−	6.37235i	−0.202703	−	0.303102i
$443$	19.6984			0.935899			0.467949	−	0.883755i	$-0.344993\pi$
$443$	19.6984			0.935899			0.467949	+	0.883755i	$0.344993\pi$
$444$	−2.09539	−	1.20977i	−0.0994428	−	0.0574133i
$445$	2.94806	−	5.10619i	0.139751	−	0.242056i
$446$	−8.78971	−	15.2242i	−0.416205	−	0.720888i
$447$		−	29.3513i		−	1.38827i
$448$	−4.00004	+	2.30942i	−0.188984	+	0.109110i
$449$	−16.7532	+	9.67248i	−0.790634	+	0.456473i	−0.840186	−	0.542299i	$-0.817554\pi$
$449$	−16.7532	+	9.67248i	−0.790634	+	0.456473i	0.0495519	+	0.998772i	$0.484221\pi$
$450$			1.56886i			0.0739566i
$451$	−0.0390959	−	0.0677161i	−0.00184095	−	0.00318863i
$452$	2.70439	−	4.68414i	0.127204	−	0.220323i
$453$	18.1596	+	10.4844i	0.853211	+	0.492602i
$454$	−13.5375			−0.635344
$455$	42.1205	+	20.7505i	1.97464	+	0.972796i
$456$	1.57102			0.0735698
$457$	−10.1208	−	5.84322i	−0.473429	−	0.273334i	0.244245	−	0.969714i	$-0.421460\pi$
$457$	−10.1208	−	5.84322i	−0.473429	−	0.273334i	−0.717674	+	0.696379i	$0.754793\pi$
$458$	14.0977	−	24.4179i	0.658742	−	1.14097i
$459$	−5.89872	−	10.2169i	−0.275329	−	0.476884i
$460$			10.6417i			0.496172i
$461$	17.7411	−	10.2428i	0.826287	−	0.477057i	−0.0262929	−	0.999654i	$-0.508370\pi$
$461$	17.7411	−	10.2428i	0.826287	−	0.477057i	0.852580	+	0.522597i	$0.175037\pi$
$462$	1.05252	−	0.607670i	0.0489674	−	0.0282714i
$463$		−	0.112903i		−	0.00524706i	−0.999997	−	0.00262353i	$-0.999165\pi$
$463$		−	0.112903i		−	0.00524706i	0.999997	−	0.00262353i	$-0.000835097\pi$
$464$	−4.68934	−	8.12217i	−0.217697	−	0.377062i
$465$	6.12308	−	10.6055i	0.283951	−	0.491818i
$466$	14.2897	+	8.25018i	0.661959	+	0.382182i
$467$	−41.2449			−1.90859			−0.954293	−	0.298871i	$-0.903390\pi$
$467$	−41.2449			−1.90859			−0.954293	+	0.298871i	$0.903390\pi$
$468$	0.126199	+	1.91362i	0.00583354	+	0.0884571i
$469$	−5.75033			−0.265526
$470$	−10.6397	−	6.14286i	−0.490775	−	0.283349i
$471$	−12.7469	+	22.0783i	−0.587345	+	1.01731i
$472$	1.95096	+	3.37916i	0.0898002	+	0.155539i
$473$			1.59485i			0.0733313i
$474$	−13.2423	+	7.64544i	−0.608238	+	0.351167i
$475$	−2.55439	+	1.47478i	−0.117203	+	0.0676674i
$476$			9.82046i			0.450120i
$477$	−1.62282	−	2.81081i	−0.0743040	−	0.128698i
$478$	−1.77087	+	3.06724i	−0.0809978	+	0.140292i
$479$	−13.8943	−	8.02190i	−0.634849	−	0.366530i	0.147779	−	0.989020i	$-0.452788\pi$
$479$	−13.8943	−	8.02190i	−0.634849	−	0.366530i	−0.782627	+	0.622490i	$0.786121\pi$
$480$	−4.42948			−0.202177
$481$	5.54092	−	0.365411i	0.252644	−	0.0166613i
$482$	−17.1321			−0.780347
$483$	23.7184	+	13.6938i	1.07922	+	0.623090i
$484$	5.48597	−	9.50199i	0.249362	−	0.431908i
$485$	−22.7192	−	39.3508i	−1.03163	−	1.78683i
$486$			5.45818i			0.247588i
$487$	35.2950	−	20.3776i	1.59937	−	0.923397i	0.607762	−	0.794119i	$-0.292068\pi$
$487$	35.2950	−	20.3776i	1.59937	−	0.923397i	0.991608	−	0.129277i	$-0.0412658\pi$
$488$	−12.3749	+	7.14466i	−0.560186	+	0.323423i
$489$			9.05374i			0.409424i
$490$	−20.2069	−	34.9994i	−0.912856	−	1.58111i
$491$	3.15626	−	5.46680i	0.142440	−	0.246713i	−0.785975	−	0.618258i	$-0.787839\pi$
$491$	3.15626	−	5.46680i	0.142440	−	0.246713i	0.928415	+	0.371545i	$0.121172\pi$
$492$	0.635171	+	0.366716i	0.0286357	+	0.0165328i
$493$	−19.9407			−0.898083
$494$	−2.99710	+	2.00434i	−0.134846	+	0.0901797i
$495$	−0.251177			−0.0112896
$496$	−2.39429	−	1.38235i	−0.107507	−	0.0620692i
$497$	37.1908	−	64.4164i	1.66824	−	2.88947i
$498$	3.47172	+	6.01320i	0.155572	+	0.269458i
$499$		−	21.5861i		−	0.966325i	−0.875531	−	0.483163i	$-0.839488\pi$
$499$		−	21.5861i		−	0.966325i	0.875531	−	0.483163i	$-0.160512\pi$
$500$	−5.00668	+	2.89061i	−0.223906	+	0.129272i
$501$	−19.4006	+	11.2010i	−0.866756	+	0.500422i
$502$			11.8327i			0.528119i
$503$	20.9464	+	36.2803i	0.933955	+	1.61766i	0.776488	+	0.630132i	$0.216999\pi$
$503$	20.9464	+	36.2803i	0.933955	+	1.61766i	0.157467	+	0.987524i	$0.449667\pi$
$504$	1.22837	−	2.12760i	0.0547160	−	0.0947709i
$505$	0.526253	+	0.303832i	0.0234179	+	0.0135204i
$506$	−0.632153			−0.0281026
$507$	12.4459	+	16.1929i	0.552743	+	0.719150i
$508$	17.1672			0.761672
$509$	29.8886	+	17.2562i	1.32479	+	0.764868i	0.984489	−	0.175448i	$-0.0561374\pi$
$509$	29.8886	+	17.2562i	1.32479	+	0.764868i	0.340302	+	0.940316i	$0.389471\pi$
$510$	−4.70892	+	8.15609i	−0.208515	+	0.361158i
$511$	29.1886	+	50.5562i	1.29123	+	2.23647i
$512$			1.00000i			0.0441942i
$513$	−4.80530	+	2.77434i	−0.212159	+	0.122490i
$514$	−15.0286	+	8.67678i	−0.662885	+	0.382717i
$515$		−	13.5846i		−	0.598608i
$516$	−7.47978	−	12.9554i	−0.329279	−	0.570328i
$517$	0.364907	−	0.632037i	0.0160486	−	0.0277970i
$518$	−6.16051	−	3.55677i	−0.270677	−	0.156276i
$519$	30.0901			1.32081
$520$	8.45031	−	5.65124i	0.370571	−	0.247823i
$521$	−19.8718			−0.870600			−0.435300	−	0.900285i	$-0.643358\pi$
$521$	−19.8718			−0.870600			−0.435300	+	0.900285i	$0.643358\pi$
$522$	4.32015	+	2.49424i	0.189088	+	0.109170i
$523$	−0.645607	+	1.11822i	−0.0282304	+	0.0488965i	−0.879795	−	0.475352i	$-0.842321\pi$
$523$	−0.645607	+	1.11822i	−0.0282304	+	0.0488965i	0.851565	+	0.524249i	$0.175654\pi$
$524$	7.78204	+	13.4789i	0.339960	+	0.588828i
$525$		−	21.4028i		−	0.934097i
$526$	−1.35254	+	0.780888i	−0.0589734	+	0.0340483i
$527$	−5.09068	+	2.93911i	−0.221754	+	0.128030i
$528$		−	0.263126i		−	0.0114511i
$529$	4.37723	+	7.58158i	0.190314	+	0.329634i
$530$	−8.60234	+	14.8997i	−0.373662	+	0.647201i
$531$	−1.79736	−	1.03771i	−0.0779989	−	0.0450327i
$532$	4.61884			0.200252
$533$	−1.67961	+	0.110766i	−0.0727519	+	0.00479781i
$534$	−3.28531			−0.142169
$535$	5.33201	+	3.07844i	0.230523	+	0.133092i
$536$	−0.622486	+	1.07818i	−0.0268873	+	0.0465702i
$537$	8.35928	+	14.4787i	0.360730	+	0.624802i
$538$		−	2.74547i		−	0.118366i
$539$	2.07909	−	1.20036i	0.0895526	−	0.0517032i
$540$	13.5485	−	7.82224i	0.583035	−	0.336616i
$541$		−	0.428319i		−	0.0184149i	−0.999958	−	0.00920744i	$-0.997069\pi$
$541$		−	0.428319i		−	0.0184149i	0.999958	−	0.00920744i	$-0.00293086\pi$
$542$	8.44202	+	14.6220i	0.362616	+	0.628069i
$543$	0.617993	−	1.07040i	0.0265206	−	0.0459351i
$544$	1.84132	+	1.06309i	0.0789459	+	0.0455794i
$545$	33.0879			1.41733
$546$	−1.72165	−	26.1062i	−0.0736796	−	1.11724i
$547$	−44.0511			−1.88349			−0.941745	−	0.336328i	$-0.890815\pi$
$547$	−44.0511			−1.88349			−0.941745	+	0.336328i	$0.890815\pi$
$548$	4.94835	+	2.85693i	0.211383	+	0.122042i
$549$	3.80021	−	6.58216i	0.162189	−	0.280920i
$550$	0.247007	+	0.427829i	0.0105324	+	0.0182427i
$551$			9.37867i			0.399545i
$552$	5.13514	−	2.96477i	0.218566	−	0.126189i
$553$	−38.9327	+	22.4778i	−1.65559	+	0.955854i
$554$			5.58477i			0.237274i
$555$	−3.41095	−	5.90794i	−0.144787	−	0.250778i
$556$	−4.60740	+	7.98025i	−0.195397	+	0.338438i
$557$	18.8004	+	10.8544i	0.796600	+	0.459917i	0.842281	−	0.539039i	$-0.181212\pi$
$557$	18.8004	+	10.8544i	0.796600	+	0.459917i	−0.0456811	+	0.998956i	$0.514546\pi$
$558$	1.47053			0.0622524
$559$	30.7982	+	15.1726i	1.30263	+	0.641733i
$560$	−13.0228			−0.550314
$561$	−0.484500	−	0.279726i	−0.0204556	−	0.0118100i
$562$	12.1008	−	20.9592i	0.510442	−	0.884112i
$563$	9.19210	+	15.9212i	0.387401	+	0.670998i	0.992099	−	0.125457i	$-0.0400396\pi$
$563$	9.19210	+	15.9212i	0.387401	+	0.670998i	−0.604698	+	0.796455i	$0.706706\pi$
$564$			6.84559i			0.288251i
$565$	13.2069	−	7.62501i	0.555618	−	0.320786i
$566$	22.4712	−	12.9737i	0.944534	−	0.545327i
$567$		−	32.8926i		−	1.38136i
$568$	−8.05198	−	13.9464i	−0.337853	−	0.585179i
$569$	16.0595	−	27.8158i	0.673248	−	1.16610i	−0.303730	−	0.952758i	$-0.598232\pi$
$569$	16.0595	−	27.8158i	0.673248	−	1.16610i	0.976978	−	0.213341i	$-0.0684346\pi$
$570$	3.83605	+	2.21474i	0.160674	+	0.0927653i
$571$	−15.2549			−0.638396			−0.319198	−	0.947688i	$-0.603414\pi$
$571$	−15.2549			−0.638396			−0.319198	+	0.947688i	$0.603414\pi$
$572$	0.335703	+	0.501977i	0.0140364	+	0.0209887i
$573$	4.37811			0.182898
$574$	1.86742	+	1.07816i	0.0779447	+	0.0450014i
$575$	−5.56629	+	9.64110i	−0.232130	+	0.402062i
$576$	−0.265948	−	0.460635i	−0.0110812	−	0.0191931i
$577$			26.9122i			1.12037i	0.828367	+	0.560185i	$0.189270\pi$
$577$			26.9122i			1.12037i	−0.828367	+	0.560185i	$0.810730\pi$
$578$	−10.8075	+	6.23970i	−0.449532	+	0.259537i
$579$	−28.8395	+	16.6505i	−1.19853	+	0.691970i
$580$		−	26.4431i		−	1.09799i
$581$	10.2070	+	17.6790i	0.423456	+	0.733448i
$582$	−12.6591	+	21.9262i	−0.524737	+	0.908871i
$583$	−0.885092	−	0.511008i	−0.0366568	−	0.0211638i
$584$	12.6389			0.523003
$585$	−2.38958	+	4.85050i	−0.0987968	+	0.200543i
$586$	−14.4299			−0.596092
$587$	−29.8739	−	17.2477i	−1.23303	−	0.711889i	−0.265367	−	0.964147i	$-0.585493\pi$
$587$	−29.8739	−	17.2477i	−1.23303	−	0.711889i	−0.967660	+	0.252259i	$0.918827\pi$
$588$	−11.2593	+	19.5016i	−0.464325	+	0.804234i
$589$	1.38235	+	2.39429i	0.0569586	+	0.0986552i
$590$			11.0014i			0.452922i
$591$	7.88182	−	4.55057i	0.324215	−	0.187186i
$592$	−1.33378	+	0.770056i	−0.0548179	+	0.0316491i
$593$		−	3.67243i		−	0.150808i	−0.997153	−	0.0754042i	$-0.975975\pi$
$593$		−	3.67243i		−	0.150808i	0.997153	−	0.0754042i	$-0.0240247\pi$
$594$	0.464668	+	0.804828i	0.0190655	+	0.0330225i
$595$	−13.8444	+	23.9791i	−0.567564	+	0.983049i
$596$	−16.1799	−	9.34147i	−0.662755	−	0.382642i
$597$	15.7901			0.646246
$598$	−6.01399	+	12.2075i	−0.245930	+	0.499203i
$599$	−3.02725			−0.123690			−0.0618451	−	0.998086i	$-0.519698\pi$
$599$	−3.02725			−0.123690			−0.0618451	+	0.998086i	$0.519698\pi$
$600$	−4.01300	−	2.31690i	−0.163830	−	0.0945872i
$601$	−17.8532	+	30.9226i	−0.728246	+	1.26136i	0.229378	+	0.973337i	$0.426331\pi$
$601$	−17.8532	+	30.9226i	−0.728246	+	1.26136i	−0.957624	+	0.288021i	$0.907003\pi$
$602$	−21.9908	−	38.0891i	−0.896277	−	1.55240i
$603$		−	0.662195i		−	0.0269667i
$604$	11.5591	−	6.67365i	0.470333	−	0.271547i
$605$	26.7908	−	15.4677i	1.08920	−	0.628851i
$606$		−	0.338590i		−	0.0137543i
$607$	18.3034	+	31.7024i	0.742912	+	1.28676i	0.951164	+	0.308686i	$0.0998893\pi$
$607$	18.3034	+	31.7024i	0.742912	+	1.28676i	−0.208252	+	0.978075i	$0.566777\pi$
$608$	0.500000	−	0.866025i	0.0202777	−	0.0351220i
$609$	−58.9369	−	34.0272i	−2.38824	−	1.37885i
$610$	−40.2886			−1.63124
$611$	−8.73376	−	13.0596i	−0.353330	−	0.528335i
$612$	−1.13090			−0.0457140
$613$	21.5826	+	12.4607i	0.871712	+	0.503283i	0.867917	−	0.496710i	$-0.165459\pi$
$613$	21.5826	+	12.4607i	0.871712	+	0.503283i	0.00379513	+	0.999993i	$0.498792\pi$
$614$	0.639473	−	1.10760i	0.0258070	−	0.0446991i
$615$	1.03396	+	1.79086i	0.0416931	+	0.0722146i
$616$		−	0.773599i		−	0.0311692i
$617$	13.7228	−	7.92288i	0.552460	−	0.318963i	−0.197654	−	0.980272i	$-0.563332\pi$
$617$	13.7228	−	7.92288i	0.552460	−	0.318963i	0.750114	+	0.661309i	$0.229999\pi$
$618$	−6.55522	+	3.78466i	−0.263690	+	0.152241i
$619$			22.1605i			0.890706i	0.895355	+	0.445353i	$0.146922\pi$
$619$			22.1605i			0.890706i	−0.895355	+	0.445353i	$0.853078\pi$
$620$	−3.89752	−	6.75070i	−0.156528	−	0.271115i
$621$	−10.4713	+	18.1368i	−0.420197	+	0.727803i
$622$	7.09303	+	4.09516i	0.284405	+	0.164201i
$623$	−9.65891			−0.386976
$624$	−5.08125	−	2.50325i	−0.203413	−	0.100210i
$625$	−31.0479			−1.24192
$626$	2.82193	+	1.62924i	0.112787	+	0.0651175i
$627$	−0.131563	+	0.227874i	−0.00525413	+	0.00910042i
$628$	8.11376	+	14.0534i	0.323774	+	0.560794i
$629$			3.27454i			0.130565i
$630$	5.99876	−	3.46339i	0.238996	−	0.137985i
$631$	41.5456	−	23.9864i	1.65391	−	0.954883i	0.678461	−	0.734636i	$-0.262647\pi$
$631$	41.5456	−	23.9864i	1.65391	−	0.954883i	0.975444	−	0.220247i	$-0.0706863\pi$
$632$			9.73309i			0.387161i
$633$	4.83749	+	8.37878i	0.192273	+	0.333026i
$634$	8.73526	−	15.1299i	0.346921	−	0.600886i
$635$	41.9181	+	24.2014i	1.66347	+	0.960405i
$636$	9.58643			0.380127
$637$	−3.40085	−	51.5689i	−0.134747	−	2.04324i
$638$	1.57081			0.0621890
$639$	7.41805	+	4.28281i	0.293453	+	0.169425i
$640$	−1.40975	+	2.44175i	−0.0557252	+	0.0965188i
$641$	10.0534	+	17.4129i	0.397084	+	0.687769i	0.993365	−	0.115006i	$-0.0366889\pi$
$641$	10.0534	+	17.4129i	0.397084	+	0.687769i	−0.596281	+	0.802776i	$0.703356\pi$
$642$		−	3.43060i		−	0.135395i
$643$	7.77968	−	4.49160i	0.306801	−	0.177131i	−0.338693	−	0.940897i	$-0.609985\pi$
$643$	7.77968	−	4.49160i	0.306801	−	0.177131i	0.645494	+	0.763765i	$0.276652\pi$
$644$	15.0974	−	8.71651i	0.594923	−	0.343479i
$645$		−	42.1784i		−	1.66077i
$646$	−1.06309	−	1.84132i	−0.0418266	−	0.0724457i
$647$	−2.49983	+	4.32984i	−0.0982786	+	0.170224i	−0.910972	−	0.412468i	$-0.864667\pi$
$647$	−2.49983	+	4.32984i	−0.0982786	+	0.170224i	0.812694	+	0.582691i	$0.198000\pi$
$648$	−6.16731	−	3.56070i	−0.242275	−	0.139878i
$649$	−0.653523			−0.0256530
$650$	10.6117	−	0.699818i	0.416226	−	0.0274491i
$651$	−20.0614			−0.786270
$652$	4.99088	+	2.88148i	0.195458	+	0.112848i
$653$	6.91017	−	11.9688i	0.270416	−	0.468374i	−0.698553	−	0.715559i	$-0.746172\pi$
$653$	6.91017	−	11.9688i	0.270416	−	0.468374i	0.968968	+	0.247185i	$0.0795055\pi$
$654$	−9.21828	−	15.9665i	−0.360463	−	0.624341i
$655$			43.8829i			1.71465i
$656$	0.404305	−	0.233426i	0.0157855	−	0.00911374i
$657$	−5.82194	+	3.36130i	−0.227135	+	0.131137i
$658$			20.1262i			0.784602i
$659$	−12.9551	−	22.4389i	−0.504660	−	0.874097i	−0.999985	−	0.00538921i	$-0.998285\pi$
$659$	−12.9551	−	22.4389i	−0.504660	−	0.874097i	0.495326	−	0.868707i	$-0.335049\pi$
$660$	0.370942	−	0.642490i	0.0144389	−	0.0250089i
$661$	11.9001	+	6.87055i	0.462862	+	0.267233i	0.713247	−	0.700913i	$-0.247224\pi$
$661$	11.9001	+	6.87055i	0.462862	+	0.267233i	−0.250385	+	0.968146i	$0.580557\pi$
$662$	26.8209			1.04242
$663$	−10.0111	+	6.69503i	−0.388799	+	0.260013i
$664$	4.41971			0.171518
$665$	11.2781	+	6.51141i	0.437345	+	0.252501i
$666$	0.409590	−	0.709430i	0.0158713	−	0.0274899i
$667$	17.6991	+	30.6557i	0.685311	+	1.18699i
$668$			14.2595i			0.551715i
$669$	−23.9176	+	13.8088i	−0.924706	+	0.533879i
$670$	−3.03992	+	1.75510i	−0.117442	+	0.0678053i
$671$		−	2.39328i		−	0.0923917i
$672$	3.62815	+	6.28414i	0.139959	+	0.242416i
$673$	−7.50345	+	12.9964i	−0.289237	+	0.500973i	−0.973628	−	0.228142i	$-0.926735\pi$
$673$	−7.50345	+	12.9964i	−0.289237	+	0.500973i	0.684391	+	0.729115i	$0.260068\pi$
$674$	8.02308	+	4.63213i	0.309038	+	0.178423i
$675$	16.3661			0.629933
$676$	12.8874	−	1.70721i	0.495670	−	0.0656621i
$677$	2.95246			0.113472			0.0567362	−	0.998389i	$-0.481931\pi$
$677$	2.95246			0.113472			0.0567362	+	0.998389i	$0.481931\pi$
$678$	−7.35887	−	4.24865i	−0.282616	−	0.163168i
$679$	−37.2181	+	64.4637i	−1.42830	+	2.47389i
$680$	2.99737	+	5.19159i	0.114944	+	0.199088i
$681$			21.2676i			0.814977i
$682$	0.401015	−	0.231526i	0.0153557	−	0.00886559i
$683$	19.1060	−	11.0308i	0.731069	−	0.422083i	−0.0877440	−	0.996143i	$-0.527966\pi$
$683$	19.1060	−	11.0308i	0.731069	−	0.422083i	0.818813	+	0.574060i	$0.194632\pi$
$684$			0.531896i			0.0203375i
$685$	8.05511	+	13.9519i	0.307770	+	0.533073i
$686$	−16.9367	+	29.3351i	−0.646645	+	1.12002i
$687$	−38.3611	−	22.1478i	−1.46357	−	0.844990i
$688$	−9.52220			−0.363030
$689$	−18.2884	+	12.2306i	−0.696733	+	0.465948i
$690$	16.7183			0.636456
$691$	−26.0609	−	15.0463i	−0.991402	−	0.572386i	−0.0857092	−	0.996320i	$-0.527316\pi$
$691$	−26.0609	−	15.0463i	−0.991402	−	0.572386i	−0.905693	+	0.423934i	$0.860649\pi$
$692$	9.57662	−	16.5872i	0.364048	−	0.630550i
$693$	0.205737	+	0.356347i	0.00781531	+	0.0135365i
$694$			30.1115i			1.14302i
$695$	−22.5003	+	12.9905i	−0.853484	+	0.492759i
$696$	−12.7601	+	7.36704i	−0.483670	+	0.279247i
$697$		−	0.992606i		−	0.0375976i
$698$	4.05874	+	7.02994i	0.153625	+	0.266087i
$699$	12.9612	−	22.4495i	0.490238	−	0.849116i
$700$	−11.7983	−	6.81177i	−0.445935	−	0.257461i
$701$	−31.1252			−1.17558			−0.587792	−	0.809012i	$-0.700003\pi$
$701$	−31.1252			−1.17558			−0.587792	+	0.809012i	$0.700003\pi$
$702$	19.9627	−	1.31649i	0.753443	−	0.0496878i
$703$	1.54011			0.0580864
$704$	−0.145049	−	0.0837438i	−0.00546672	−	0.00315621i
$705$	−9.65055	+	16.7152i	−0.363461	+	0.629533i
$706$	9.17448	+	15.8907i	0.345286	+	0.598053i
$707$		−	0.995464i		−	0.0374383i
$708$	5.30873	−	3.06500i	0.199514	−	0.115190i
$709$	2.29193	−	1.32325i	0.0860754	−	0.0496956i	−0.456345	−	0.889803i	$-0.650842\pi$
$709$	2.29193	−	1.32325i	0.0860754	−	0.0496956i	0.542420	+	0.840108i	$0.317508\pi$
$710$		−	45.4050i		−	1.70402i
$711$	−2.58849	−	4.48340i	−0.0970761	−	0.168141i
$712$	−1.04560	+	1.81103i	−0.0391854	+	0.0678712i
$713$	9.03685	+	5.21743i	0.338433	+	0.195394i
$714$	15.4281			0.577384
$715$	0.112042	+	1.69896i	0.00419015	+	0.0635376i
$716$	10.6419			0.397705
$717$	4.81870	+	2.78208i	0.179958	+	0.103899i
$718$	−9.07550	+	15.7192i	−0.338695	+	0.586636i
$719$	4.59225	+	7.95401i	0.171262	+	0.296634i	0.938861	−	0.344296i	$-0.111882\pi$
$719$	4.59225	+	7.95401i	0.171262	+	0.296634i	−0.767599	+	0.640930i	$0.778549\pi$
$720$		−	1.49968i		−	0.0558897i
$721$	−19.2725	+	11.1270i	−0.717747	+	0.414391i
$722$	−0.866025	+	0.500000i	−0.0322301	+	0.0186081i
$723$			26.9149i			1.00098i
$724$	−0.393370	−	0.681338i	−0.0146195	−	0.0253217i
$725$	13.8315	−	23.9568i	0.513687	−	0.889732i
$726$	−14.9278	−	8.61858i	−0.554023	−	0.319865i
$727$	−22.2003			−0.823365			−0.411683	−	0.911327i	$-0.635059\pi$
$727$	−22.2003			−0.823365			−0.411683	+	0.911327i	$0.635059\pi$
$728$	−14.9390	−	7.35963i	−0.553677	−	0.272766i
$729$	29.9391			1.10886
$730$	30.8612	+	17.8177i	1.14222	+	0.659463i
$731$	−10.1229	+	17.5334i	−0.374409	+	0.648496i
$732$	11.2244	+	19.4412i	0.414866	+	0.718568i
$733$		−	29.8331i		−	1.10191i	−0.834535	−	0.550955i	$-0.814264\pi$
$733$		−	29.8331i		−	1.10191i	0.834535	−	0.550955i	$-0.185736\pi$
$734$	20.5935	−	11.8897i	0.760122	−	0.438856i
$735$	−54.9848	+	31.7455i	−2.02815	+	1.17095i
$736$		−	3.77433i		−	0.139124i
$737$	−0.104259	−	0.180581i	−0.00384042	−	0.00665180i
$738$	−0.124158	+	0.215048i	−0.00457032	+	0.00791603i
$739$	−9.47912	−	5.47277i	−0.348695	−	0.201319i	0.315415	−	0.948954i	$-0.397856\pi$
$739$	−9.47912	−	5.47277i	−0.348695	−	0.201319i	−0.664110	+	0.747634i	$0.731190\pi$
$740$	−4.34234			−0.159628
$741$	3.14886	+	4.70850i	0.115676	+	0.172971i
$742$	28.1844			1.03468
$743$	39.6103	+	22.8690i	1.45316	+	0.838984i	0.998659	−	0.0517618i	$-0.0164837\pi$
$743$	39.6103	+	22.8690i	1.45316	+	0.838984i	0.454503	+	0.890745i	$0.349817\pi$
$744$	−2.17169	+	3.76149i	−0.0796182	+	0.137903i
$745$	−26.3382	−	45.6192i	−0.964958	−	1.67136i
$746$		−	12.0839i		−	0.442421i
$747$	−2.03587	+	1.17541i	−0.0744887	+	0.0430061i
$748$	−0.308398	+	0.178054i	−0.0112762	+	0.00651029i
$749$		−	10.0861i		−	0.368537i
$750$	4.54121	+	7.86560i	0.165821	+	0.287211i
$751$	7.73290	−	13.3938i	0.282178	−	0.488746i	−0.689743	−	0.724054i	$-0.742277\pi$
$751$	7.73290	−	13.3938i	0.282178	−	0.488746i	0.971921	+	0.235308i	$0.0756099\pi$
$752$	3.77363	+	2.17871i	0.137610	+	0.0794493i
$753$	18.5894			0.677435
$754$	14.9439	−	30.3340i	0.544225	−	1.10470i
$755$	37.6326			1.36959
$756$	−22.1949	−	12.8142i	−0.807221	−	0.466049i
$757$	12.5969	−	21.8184i	0.457841	−	0.793005i	−0.541005	−	0.841019i	$-0.681956\pi$
$757$	12.5969	−	21.8184i	0.457841	−	0.793005i	0.998847	+	0.0480147i	$0.0152894\pi$
$758$	−0.638685	−	1.10624i	−0.0231981	−	0.0401803i
$759$			0.993125i			0.0360482i
$760$	2.44175	−	1.40975i	0.0885718	−	0.0511369i
$761$	2.74112	−	1.58259i	0.0993655	−	0.0573687i	−0.449494	−	0.893283i	$-0.648396\pi$
$761$	2.74112	−	1.58259i	0.0993655	−	0.0573687i	0.548859	+	0.835915i	$0.315062\pi$
$762$		−	26.9700i		−	0.977021i
$763$	−27.1020	−	46.9421i	−0.981158	−	1.69942i
$764$	1.39340	−	2.41344i	0.0504114	−	0.0873150i
$765$	−2.76138	−	1.59429i	−0.0998381	−	0.0576415i
$766$	17.5663			0.634696
$767$	−6.21729	+	12.6202i	−0.224493	+	0.455690i
$768$	1.57102			0.0566893
$769$	−9.23075	−	5.32937i	−0.332869	−	0.192182i	0.324245	−	0.945973i	$-0.394890\pi$
$769$	−9.23075	−	5.32937i	−0.332869	−	0.192182i	−0.657114	+	0.753791i	$0.728223\pi$
$770$	1.09058	−	1.88894i	0.0393018	−	0.0680727i
$771$	13.6314	+	23.6103i	0.490923	+	0.850304i
$772$			21.1970i			0.762898i
$773$	45.4389	−	26.2342i	1.63432	−	0.943578i	0.651587	−	0.758574i	$-0.274104\pi$
$773$	45.4389	−	26.2342i	1.63432	−	0.943578i	0.982738	−	0.185004i	$-0.0592298\pi$
$774$	4.38626	−	2.53241i	0.157661	−	0.0910255i
$775$		−	8.15462i		−	0.292922i
$776$	8.05789	+	13.9567i	0.289261	+	0.501016i
$777$	−5.58776	+	9.67828i	−0.200460	+	0.347206i
$778$	0.0426507	+	0.0246244i	0.00152910	+	0.000882826i
$779$	−0.466851			−0.0167267
$780$	−8.87821	−	13.2756i	−0.317891	−	0.475343i
$781$	2.69721			0.0965139
$782$	−6.94974	−	4.01243i	−0.248522	−	0.143484i
$783$	26.0196	−	45.0673i	0.929865	−	1.61057i
$784$	7.16686	+	12.4134i	0.255959	+	0.443335i
$785$			45.7534i			1.63301i
$786$	21.1756	−	12.2257i	0.755309	−	0.436078i
$787$	−19.8311	+	11.4495i	−0.706902	+	0.408130i	−0.809913	−	0.586550i	$-0.800486\pi$
$787$	−19.8311	+	11.4495i	−0.706902	+	0.408130i	0.103011	+	0.994680i	$0.467152\pi$
$788$		−	5.79314i		−	0.206372i
$789$	1.22679	+	2.12486i	0.0436749	+	0.0756471i
$790$	−13.7212	+	23.7658i	−0.488178	+	0.845550i
$791$	−21.6353	−	12.4911i	−0.769262	−	0.444134i
$792$	0.0890860			0.00316553
$793$	−46.2168	−	22.7685i	−1.64121	−	0.808533i
$794$	−33.8454			−1.20113
$795$	23.4077	+	13.5144i	0.830186	+	0.479308i
$796$	5.02543	−	8.70430i	0.178122	−	0.308516i
$797$	9.62199	+	16.6658i	0.340828	+	0.590332i	0.984587	−	0.174897i	$-0.0559592\pi$
$797$	9.62199	+	16.6658i	0.340828	+	0.590332i	−0.643759	+	0.765229i	$0.722626\pi$
$798$		−	7.25630i		−	0.256870i
$799$	8.02339	−	4.63231i	0.283847	−	0.163879i
$800$	−2.55439	+	1.47478i	−0.0903113	+	0.0521413i
$801$		−	1.11230i		−	0.0393011i
$802$	12.6797	+	21.9620i	0.447737	+	0.775504i
$803$	−1.05843	+	1.83326i	−0.0373513	+	0.0646943i
$804$	1.69384	+	0.977938i	0.0597371	+	0.0344892i
$805$	49.1523			1.73239
$806$	−0.655957	−	9.94664i	−0.0231051	−	0.350355i
$807$	−4.31319			−0.151831
$808$	−0.186648	−	0.107761i	−0.00656625	−	0.00379102i
$809$	−8.42265	+	14.5885i	−0.296125	+	0.512903i	−0.975246	−	0.221123i	$-0.929028\pi$
$809$	−8.42265	+	14.5885i	−0.296125	+	0.512903i	0.679121	+	0.734026i	$0.262361\pi$
$810$	−10.0394	−	17.3887i	−0.352748	−	0.610977i
$811$			3.83311i			0.134599i	0.997733	+	0.0672994i	$0.0214383\pi$
$811$			3.83311i			0.134599i	−0.997733	+	0.0672994i	$0.978562\pi$
$812$	−37.5150	+	21.6593i	−1.31652	+	0.760093i
$813$	22.9715	−	13.2626i	0.805644	−	0.465139i
$814$		−	0.257950i		−	0.00904114i
$815$	8.12433	+	14.0718i	0.284583	+	0.492912i
$816$	1.67013	−	2.89275i	0.0584662	−	0.101266i
$817$	8.24646	+	4.76110i	0.288507	+	0.166570i
$818$	25.9468			0.907210
$819$	8.83871	−	0.582892i	0.308850	−	0.0203679i
$820$	1.31628			0.0459667
$821$	−29.9114	−	17.2694i	−1.04392	−	0.602705i	−0.122976	−	0.992410i	$-0.539244\pi$
$821$	−29.9114	−	17.2694i	−1.04392	−	0.602705i	−0.920940	+	0.389705i	$0.872577\pi$
$822$	4.48830	−	7.77396i	0.156547	−	0.271148i
$823$	−2.31510	−	4.00986i	−0.0806992	−	0.139775i	0.822851	−	0.568257i	$-0.192382\pi$
$823$	−2.31510	−	4.00986i	−0.0806992	−	0.139775i	−0.903550	+	0.428482i	$0.859049\pi$
$824$			4.81809i			0.167846i
$825$	0.672127	−	0.388053i	0.0234005	−	0.0135103i
$826$	15.6078	−	9.01118i	0.543066	−	0.313539i
$827$		−	22.7184i		−	0.789996i	−0.918682	−	0.394998i	$-0.870745\pi$
$827$		−	22.7184i		−	0.789996i	0.918682	−	0.394998i	$-0.129255\pi$
$828$	1.00377	+	1.73859i	0.0348836	+	0.0604201i
$829$	−22.6177	+	39.1750i	−0.785546	+	1.36061i	0.143127	+	0.989704i	$0.454284\pi$
$829$	−22.6177	+	39.1750i	−0.785546	+	1.36061i	−0.928673	+	0.370901i	$0.879049\pi$
$830$	10.7918	+	6.23067i	0.374590	+	0.216270i
$831$	8.77379			0.304359
$832$	−2.99710	+	2.00434i	−0.103906	+	0.0694881i
$833$	30.4760			1.05593
$834$	12.5371	+	7.23832i	0.434125	+	0.250642i
$835$	−20.1023	+	34.8181i	−0.695667	+	1.20493i
$836$	0.0837438	+	0.145049i	0.00289634	+	0.00501661i
$837$		−	15.3404i		−	0.530242i
$838$	−29.7984	+	17.2041i	−1.02937	+	0.594306i
$839$	2.55994	−	1.47798i	0.0883790	−	0.0510257i	−0.455159	−	0.890410i	$-0.650418\pi$
$839$	2.55994	−	1.47798i	0.0883790	−	0.0510257i	0.543538	+	0.839384i	$0.317084\pi$
$840$			20.4591i			0.705906i
$841$	−29.4797	−	51.0604i	−1.01654	−	1.76070i
$842$	−11.6759	+	20.2232i	−0.402377	+	0.696938i
$843$	−32.9274	−	19.0106i	−1.13408	−	0.654761i
$844$	6.15840			0.211981
$845$	33.8746	+	13.9994i	1.16532	+	0.481594i
$846$	−2.31769			−0.0796839
$847$	−43.8882	−	25.3389i	−1.50802	−	0.870653i
$848$	3.05102	−	5.28452i	0.104772	−	0.181471i
$849$	−20.3820	−	35.3027i	−0.699509	−	1.21158i
$850$			6.27126i			0.215102i
$851$	5.03411	−	2.90644i	0.172567	−	0.0996316i
$852$	−21.9101	+	12.6498i	−0.750628	+	0.433376i
$853$			11.7157i			0.401139i	0.979679	+	0.200570i	$0.0642792\pi$
$853$			11.7157i			0.401139i	−0.979679	+	0.200570i	$0.935721\pi$
$854$	33.0001	+	57.1578i	1.12924	+	1.95590i
$855$	−0.749839	+	1.29876i	−0.0256439	+	0.0444166i
$856$	−1.89112	−	1.09184i	−0.0646372	−	0.0373183i
$857$	−2.91516			−0.0995798			−0.0497899	−	0.998760i	$-0.515855\pi$
$857$	−2.91516			−0.0995798			−0.0497899	+	0.998760i	$0.515855\pi$
$858$	0.788616	−	0.527396i	0.0269229	−	0.0180050i
$859$	27.1979			0.927980			0.463990	−	0.885840i	$-0.346417\pi$
$859$	27.1979			0.927980			0.463990	+	0.885840i	$0.346417\pi$
$860$	−23.2509	−	13.4239i	−0.792848	−	0.457751i
$861$	1.69381	−	2.93376i	0.0577247	−	0.0999822i
$862$	10.2730	+	17.7933i	0.349899	+	0.606043i
$863$			11.2008i			0.381279i	0.981660	+	0.190640i	$0.0610562\pi$
$863$			11.2008i			0.381279i	−0.981660	+	0.190640i	$0.938944\pi$
$864$	−4.80530	+	2.77434i	−0.163480	+	0.0943850i
$865$	46.7675	−	27.0012i	1.59014	−	0.918069i
$866$			20.4768i			0.695830i
$867$	9.80269	+	16.9788i	0.332917	+	0.576629i
$868$	−6.38484	+	11.0589i	−0.216716	+	0.375363i
$869$	−1.41177	−	0.815086i	−0.0478910	−	0.0276499i
$870$	−41.5427			−1.40843
$871$	−4.47908	+	0.295385i	−0.151768	+	0.0100087i
$872$	−11.7354			−0.397411
$873$	−7.42350	−	4.28596i	−0.251247	−	0.145058i
$874$	−1.88716	+	3.26866i	−0.0638343	+	0.110564i
$875$	13.3513	+	23.1251i	0.451356	+	0.781771i
$876$		−	19.8560i		−	0.670873i
$877$	−30.2425	+	17.4605i	−1.02122	+	0.589600i	−0.914456	−	0.404684i	$-0.867381\pi$
$877$	−30.2425	+	17.4605i	−1.02122	+	0.589600i	−0.106761	+	0.994285i	$0.534048\pi$
$878$	1.30106	−	0.751168i	0.0439087	−	0.0253507i
$879$			22.6696i			0.764627i
$880$	−0.236115	−	0.408964i	−0.00795945	−	0.0137862i
$881$	−0.981745	+	1.70043i	−0.0330758	+	0.0572890i	−0.882089	−	0.471082i	$-0.843864\pi$
$881$	−0.981745	+	1.70043i	−0.0330758	+	0.0572890i	0.849014	+	0.528371i	$0.177197\pi$
$882$	−6.60262	−	3.81202i	−0.222322	−	0.128357i
$883$	41.6115			1.40034			0.700169	−	0.713977i	$-0.253108\pi$
$883$	41.6115			1.40034			0.700169	+	0.713977i	$0.253108\pi$
$884$	0.504460	+	7.64941i	0.0169668	+	0.257277i
$885$	17.2835			0.580978
$886$	−17.0593	−	9.84919i	−0.573118	−	0.330890i
$887$	22.8051	−	39.4996i	0.765721	−	1.32627i	−0.174143	−	0.984720i	$-0.555716\pi$
$887$	22.8051	−	39.4996i	0.765721	−	1.32627i	0.939864	−	0.341548i	$-0.110951\pi$
$888$	1.20977	+	2.09539i	0.0405974	+	0.0703167i
$889$		−	79.2927i		−	2.65939i
$890$	−5.10619	+	2.94806i	−0.171160	+	0.0988191i
$891$	1.03295	−	0.596373i	0.0346051	−	0.0199793i
$892$			17.5794i			0.588602i
$893$	−2.17871	−	3.77363i	−0.0729077	−	0.126280i
$894$	−14.6756	+	25.4190i	−0.490827	+	0.850137i
$895$	25.9848	+	15.0023i	0.868576	+	0.501473i
$896$	4.61884			0.154305
$897$	19.1783	+	9.44809i	0.640344	+	0.315463i
$898$	19.3450			0.645550
$899$	−22.4553	−	12.9646i	−0.748926	−	0.432393i
$900$	0.784428	−	1.35867i	0.0261476	−	0.0452890i
$901$	−6.48699	−	11.2358i	−0.216113	−	0.374319i
$902$			0.0781918i			0.00260350i
$903$	−59.8388	+	34.5479i	−1.99131	+	1.14968i
$904$	−4.68414	+	2.70439i	−0.155792	+	0.0899466i
$905$		−	2.21821i		−	0.0737359i
$906$	−10.4844	−	18.1596i	−0.348322	−	0.603312i
$907$	−2.71848	+	4.70855i	−0.0902657	+	0.156345i	−0.907623	−	0.419786i	$-0.862105\pi$
$907$	−2.71848	+	4.70855i	−0.0902657	+	0.156345i	0.817357	+	0.576131i	$0.195438\pi$
$908$	11.7238	+	6.76873i	0.389067	+	0.224628i
$909$	0.114635			0.00380222
$910$	−26.1022	−	39.0307i	−0.865279	−	1.29385i
$911$	−39.0965			−1.29532			−0.647662	−	0.761928i	$-0.724253\pi$
$911$	−39.0965			−1.29532			−0.647662	+	0.761928i	$0.724253\pi$
$912$	−1.36054	−	0.785510i	−0.0450521	−	0.0260108i
$913$	−0.370123	+	0.641072i	−0.0122493	+	0.0212164i
$914$	5.84322	+	10.1208i	0.193277	+	0.334765i
$915$			63.2943i			2.09244i
$916$	−24.4179	+	14.0977i	−0.806791	+	0.465801i
$917$	62.2569	−	35.9441i	2.05590	−	1.18698i
$918$			11.7974i			0.389374i
$919$	−2.19182	−	3.79634i	−0.0723014	−	0.125230i	0.827608	−	0.561306i	$-0.189701\pi$
$919$	−2.19182	−	3.79634i	−0.0723014	−	0.125230i	−0.899910	+	0.436077i	$0.856368\pi$
$920$	5.32085	−	9.21598i	0.175423	−	0.303842i
$921$	−1.74006	−	1.00463i	−0.0573370	−	0.0331035i
$922$	−20.4857			−0.674660
$923$	25.6599	−	52.0860i	0.844607	−	1.71443i
$924$	−1.21534			−0.0399818
$925$	−3.93405	−	2.27132i	−0.129351	−	0.0746806i
$926$	−0.0564517	+	0.0977771i	−0.00185512	+	0.00321316i
$927$	−1.28136	−	2.21938i	−0.0420854	−	0.0728941i
$928$			9.37867i			0.307870i
$929$	4.08576	−	2.35892i	0.134050	−	0.0773935i	−0.431476	−	0.902125i	$-0.642007\pi$
$929$	4.08576	−	2.35892i	0.134050	−	0.0773935i	0.565525	+	0.824731i	$0.308674\pi$
$930$	−10.6055	+	6.12308i	−0.347768	+	0.200784i
$931$		−	14.3337i		−	0.469769i
$932$	−8.25018	−	14.2897i	−0.270244	−	0.468076i
$933$	6.43358	−	11.1433i	0.210626	−	0.364815i
$934$	35.7191	+	20.6225i	1.16877	+	0.674787i
$935$	−1.00404			−0.0328357
$936$	0.847519	−	1.72034i	0.0277020	−	0.0562312i
$937$	43.0137			1.40520			0.702599	−	0.711586i	$-0.252023\pi$
$937$	43.0137			1.40520			0.702599	+	0.711586i	$0.252023\pi$
$938$	4.97993	+	2.87517i	0.162601	+	0.0938775i
$939$	2.55957	−	4.43330i	0.0835284	−	0.144675i
$940$	6.14286	+	10.6397i	0.200358	+	0.347030i
$941$			44.9256i			1.46453i	0.681018	+	0.732267i	$0.261538\pi$
$941$			44.9256i			1.46453i	−0.681018	+	0.732267i	$0.738462\pi$
$942$	22.0783	−	12.7469i	0.719348	−	0.415316i
$943$	−1.52598	+	0.881024i	−0.0496927	+	0.0286901i
$944$		−	3.90192i		−	0.126997i
$945$	−36.1297	−	62.5785i	−1.17530	−	2.03568i
$946$	0.797425	−	1.38118i	0.0259265	−	0.0449061i
$947$	−23.0481	−	13.3068i	−0.748962	−	0.432414i	0.0763565	−	0.997081i	$-0.475671\pi$
$947$	−23.0481	−	13.3068i	−0.748962	−	0.432414i	−0.825319	+	0.564667i	$0.809005\pi$
$948$	15.2909			0.496625
$949$	25.3328	+	37.8801i	0.822336	+	1.22964i
$950$	2.94955			0.0956962
$951$	−23.7694	−	13.7233i	−0.770775	−	0.445007i
$952$	4.91023	−	8.50477i	0.159141	−	0.275641i
$953$	9.64832	+	16.7114i	0.312540	+	0.541335i	0.978911	−	0.204285i	$-0.0654869\pi$
$953$	9.64832	+	16.7114i	0.312540	+	0.541335i	−0.666372	+	0.745620i	$0.732154\pi$
$954$			3.24565i			0.105082i
$955$	6.80467	−	3.92868i	0.220194	−	0.127129i
$956$	3.06724	−	1.77087i	0.0992017	−	0.0572741i
$957$		−	2.46778i		−	0.0797719i
$958$	8.02190	+	13.8943i	0.259176	+	0.448906i
$959$	13.1957	−	22.8557i	0.426112	−	0.738048i
$960$	3.83605	+	2.21474i	0.123808	+	0.0714805i
$961$	23.3565			0.753434
$962$	−4.98128	−	2.45400i	−0.160603	−	0.0791203i
$963$	1.16149			0.0374285
$964$	14.8369	+	8.56607i	0.477863	+	0.275894i
$965$	−29.8825	+	51.7579i	−0.961950	+	1.66615i
$966$	−13.6938	−	23.7184i	−0.440591	−	0.763127i
$967$			17.2205i			0.553773i	0.960903	+	0.276886i	$0.0893026\pi$
$967$			17.2205i			0.553773i	−0.960903	+	0.276886i	$0.910697\pi$
$968$	−9.50199	+	5.48597i	−0.305405	+	0.176326i
$969$	−2.89275	+	1.67013i	−0.0929285	+	0.0536523i
$970$			45.4384i			1.45894i
$971$	−30.2187	−	52.3403i	−0.969764	−	1.67968i	−0.696232	−	0.717817i	$-0.745142\pi$
$971$	−30.2187	−	52.3403i	−0.969764	−	1.67968i	−0.273532	−	0.961863i	$-0.588192\pi$
$972$	2.72909	−	4.72692i	0.0875355	−	0.151616i
$973$	36.8595	+	21.2809i	1.18166	+	0.682233i
$974$	−40.7552			−1.30588
$975$	−1.09943	−	16.6712i	−0.0352099	−	0.533907i
$976$	14.2893			0.457390
$977$	40.7625	+	23.5342i	1.30411	+	0.752927i	0.981106	−	0.193471i	$-0.0619746\pi$
$977$	40.7625	+	23.5342i	1.30411	+	0.752927i	0.323002	+	0.946398i	$0.395308\pi$
$978$	4.52687	−	7.84077i	0.144753	−	0.250720i
$979$	−0.175125	−	0.303325i	−0.00559701	−	0.00969430i
$980$			40.4139i			1.29097i
$981$	5.40574	−	3.12101i	0.172592	−	0.0996461i
$982$	−5.46680	+	3.15626i	−0.174453	+	0.100720i
$983$		−	43.8752i		−	1.39940i	−0.714436	−	0.699700i	$-0.753317\pi$
$983$		−	43.8752i		−	1.39940i	0.714436	−	0.699700i	$-0.246683\pi$
$984$	−0.366716	−	0.635171i	−0.0116905	−	0.0202485i
$985$	8.16687	−	14.1454i	0.260218	−	0.450711i
$986$	17.2691	+	9.97033i	0.549961	+	0.317520i
$987$	31.6187			1.00643
$988$	3.59774	−	0.237262i	0.114459	−	0.00754832i
$989$	35.9399			1.14282
$990$	0.217526	+	0.125589i	0.00691343	+	0.00399147i
$991$	−8.37903	+	14.5129i	−0.266169	+	0.461018i	−0.967869	−	0.251454i	$-0.919091\pi$
$991$	−8.37903	+	14.5129i	−0.266169	+	0.461018i	0.701700	+	0.712472i	$0.252425\pi$
$992$	1.38235	+	2.39429i	0.0438896	+	0.0760189i
$993$		−	42.1362i		−	1.33715i
$994$	−64.4164	+	37.1908i	−2.04316	+	1.17962i
$995$	24.5417	−	14.1692i	0.778025	−	0.449193i
$996$		−	6.94345i		−	0.220012i
$997$	1.21134	+	2.09811i	0.0383636	+	0.0664477i	0.884570	−	0.466408i	$-0.154452\pi$
$997$	1.21134	+	2.09811i	0.0383636	+	0.0664477i	−0.846206	+	0.532856i	$0.821119\pi$
$998$	−10.7930	+	18.6941i	−0.341647	+	0.591751i
$999$	−7.40070	−	4.27280i	−0.234148	−	0.135185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.m.b.381.2	yes	28
13.6	odd	12		6422.2.a.bn.1.10		14
13.7	odd	12		6422.2.a.bm.1.10		14
13.10	even	6	inner	494.2.m.b.153.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.2	✓	28	13.10	even	6	inner
494.2.m.b.381.2	yes	28	1.1	even	1	trivial
6422.2.a.bm.1.10		14	13.7	odd	12
6422.2.a.bn.1.10		14	13.6	odd	12

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:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.785510 + 1.36054i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.81950i q^{5} +(1.36054 - 0.785510i) q^{6} +(4.00004 - 2.30942i) q^{7} -1.00000i q^{8} +(0.265948 + 0.460635i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.785510 + 1.36054i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.81950i q^{5} +(1.36054 - 0.785510i) q^{6} +(4.00004 - 2.30942i) q^{7} -1.00000i q^{8} +(0.265948 + 0.460635i) q^{9} +(1.40975 - 2.44175i) q^{10} +(0.145049 + 0.0837438i) q^{11} -1.57102 q^{12} +(2.99710 - 2.00434i) q^{13} -4.61884 q^{14} +(-3.83605 - 2.21474i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.06309 + 1.84132i) q^{17} -0.531896i q^{18} +(0.866025 - 0.500000i) q^{19} +(-2.44175 + 1.40975i) q^{20} +7.25630i q^{21} +(-0.0837438 - 0.145049i) q^{22} +(1.88716 - 3.26866i) q^{23} +(1.36054 + 0.785510i) q^{24} -2.94955 q^{25} +(-3.59774 + 0.237262i) q^{26} -5.54868 q^{27} +(4.00004 + 2.30942i) q^{28} +(-4.68934 + 8.12217i) q^{29} +(2.21474 + 3.83605i) q^{30} +2.76469i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.227874 + 0.131563i) q^{33} -2.12617i q^{34} +(6.51141 + 11.2781i) q^{35} +(-0.265948 + 0.460635i) q^{36} +(1.33378 + 0.770056i) q^{37} -1.00000 q^{38} +(0.372744 + 5.65212i) q^{39} +2.81950 q^{40} +(-0.404305 - 0.233426i) q^{41} +(3.62815 - 6.28414i) q^{42} +(4.76110 + 8.24646i) q^{43} +0.167488i q^{44} +(-1.29876 + 0.749839i) q^{45} +(-3.26866 + 1.88716i) q^{46} -4.35742i q^{47} +(-0.785510 - 1.36054i) q^{48} +(7.16686 - 12.4134i) q^{49} +(2.55439 + 1.47478i) q^{50} -3.34026 q^{51} +(3.23436 + 1.59339i) q^{52} -6.10204 q^{53} +(4.80530 + 2.77434i) q^{54} +(-0.236115 + 0.408964i) q^{55} +(-2.30942 - 4.00004i) q^{56} +1.57102i q^{57} +(8.12217 - 4.68934i) q^{58} +(-3.37916 + 1.95096i) q^{59} -4.42948i q^{60} +(-7.14466 - 12.3749i) q^{61} +(1.38235 - 2.39429i) q^{62} +(2.12760 + 1.22837i) q^{63} -1.00000 q^{64} +(5.65124 + 8.45031i) q^{65} +0.263126 q^{66} +(-1.07818 - 0.622486i) q^{67} +(-1.06309 + 1.84132i) q^{68} +(2.96477 + 5.13514i) q^{69} -13.0228i q^{70} +(13.9464 - 8.05198i) q^{71} +(0.460635 - 0.265948i) q^{72} +12.6389i q^{73} +(-0.770056 - 1.33378i) q^{74} +(2.31690 - 4.01300i) q^{75} +(0.866025 + 0.500000i) q^{76} +0.773599 q^{77} +(2.50325 - 5.08125i) q^{78} -9.73309 q^{79} +(-2.44175 - 1.40975i) q^{80} +(3.56070 - 6.16731i) q^{81} +(0.233426 + 0.404305i) q^{82} +4.41971i q^{83} +(-6.28414 + 3.62815i) q^{84} +(-5.19159 + 2.99737i) q^{85} -9.52220i q^{86} +(-7.36704 - 12.7601i) q^{87} +(0.0837438 - 0.145049i) q^{88} +(-1.81103 - 1.04560i) q^{89} +1.49968 q^{90} +(7.35963 - 14.9390i) q^{91} +3.77433 q^{92} +(-3.76149 - 2.17169i) q^{93} +(-2.17871 + 3.77363i) q^{94} +(1.40975 + 2.44175i) q^{95} +1.57102i q^{96} +(-13.9567 + 8.05789i) q^{97} +(-12.4134 + 7.16686i) q^{98} +0.0890860i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 14 q^{4} - 18 q^{9}+O(q^{10}) \) 28 * q - 4 * q^3 + 14 * q^4 - 18 * q^9	\( 28 q - 4 q^{3} + 14 q^{4} - 18 q^{9} - 2 q^{10} - 6 q^{11} - 8 q^{12} + 8 q^{13} + 4 q^{14} + 42 q^{15} - 14 q^{16} + 2 q^{17} - 10 q^{22} + 12 q^{23} - 88 q^{25} + 2 q^{26} + 20 q^{27} - 4 q^{29} - 4 q^{30} - 54 q^{33} - 14 q^{35} + 18 q^{36} + 6 q^{37} - 28 q^{38} + 60 q^{39} - 4 q^{40} + 42 q^{41} + 18 q^{42} + 28 q^{43} - 30 q^{45} - 12 q^{46} - 4 q^{48} + 28 q^{49} + 12 q^{50} - 20 q^{51} + 4 q^{52} + 24 q^{53} + 54 q^{54} + 2 q^{55} + 2 q^{56} - 6 q^{58} - 96 q^{59} - 30 q^{61} + 4 q^{62} + 12 q^{63} - 28 q^{64} + 82 q^{65} + 24 q^{66} - 6 q^{67} - 2 q^{68} - 42 q^{69} - 6 q^{71} + 12 q^{72} - 18 q^{74} + 46 q^{75} - 136 q^{77} + 50 q^{78} + 68 q^{79} + 6 q^{81} + 6 q^{82} + 12 q^{84} - 72 q^{85} - 52 q^{87} + 10 q^{88} + 48 q^{89} - 16 q^{90} + 44 q^{91} + 24 q^{92} + 30 q^{93} + 20 q^{94} - 2 q^{95} + 12 q^{97} - 72 q^{98}+O(q^{100}) \) 28 * q - 4 * q^3 + 14 * q^4 - 18 * q^9 - 2 * q^10 - 6 * q^11 - 8 * q^12 + 8 * q^13 + 4 * q^14 + 42 * q^15 - 14 * q^16 + 2 * q^17 - 10 * q^22 + 12 * q^23 - 88 * q^25 + 2 * q^26 + 20 * q^27 - 4 * q^29 - 4 * q^30 - 54 * q^33 - 14 * q^35 + 18 * q^36 + 6 * q^37 - 28 * q^38 + 60 * q^39 - 4 * q^40 + 42 * q^41 + 18 * q^42 + 28 * q^43 - 30 * q^45 - 12 * q^46 - 4 * q^48 + 28 * q^49 + 12 * q^50 - 20 * q^51 + 4 * q^52 + 24 * q^53 + 54 * q^54 + 2 * q^55 + 2 * q^56 - 6 * q^58 - 96 * q^59 - 30 * q^61 + 4 * q^62 + 12 * q^63 - 28 * q^64 + 82 * q^65 + 24 * q^66 - 6 * q^67 - 2 * q^68 - 42 * q^69 - 6 * q^71 + 12 * q^72 - 18 * q^74 + 46 * q^75 - 136 * q^77 + 50 * q^78 + 68 * q^79 + 6 * q^81 + 6 * q^82 + 12 * q^84 - 72 * q^85 - 52 * q^87 + 10 * q^88 + 48 * q^89 - 16 * q^90 + 44 * q^91 + 24 * q^92 + 30 * q^93 + 20 * q^94 - 2 * q^95 + 12 * q^97 - 72 * q^98

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