LMFDB - Embedded newform 322.2.e.c.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$-1.54162 + 1.88572i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.c.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.937623 + 1.62401i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.603998 + 1.04616i) q^{5} -1.87525 q^{6} +(2.64562 + 0.0264594i) q^{7} -1.00000 q^{8} +(-0.258274 - 0.447344i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.937623 + 1.62401i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.603998 + 1.04616i) q^{5} -1.87525 q^{6} +(2.64562 + 0.0264594i) q^{7} -1.00000 q^{8} +(-0.258274 - 0.447344i) q^{9} +(-0.603998 + 1.04616i) q^{10} +(-1.40389 + 2.43161i) q^{11} +(-0.937623 - 1.62401i) q^{12} -1.15070 q^{13} +(1.29990 + 2.30440i) q^{14} -2.26529 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.896002 + 1.55192i) q^{17} +(0.258274 - 0.447344i) q^{18} +(-3.20379 - 5.54912i) q^{19} -1.20800 q^{20} +(-2.52356 + 4.27170i) q^{21} -2.80779 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.937623 - 1.62401i) q^{24} +(1.77037 - 3.06638i) q^{25} +(-0.575351 - 0.996537i) q^{26} -4.65708 q^{27} +(-1.34572 + 2.27794i) q^{28} +6.14054 q^{29} +(-1.13264 - 1.96180i) q^{30} +(-1.52865 + 2.64769i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.63264 - 4.55987i) q^{33} -1.79200 q^{34} +(1.57027 + 2.78371i) q^{35} +0.516548 q^{36} +(4.19870 + 7.27237i) q^{37} +(3.20379 - 5.54912i) q^{38} +(1.07892 - 1.86875i) q^{39} +(-0.603998 - 1.04616i) q^{40} +5.26529 q^{41} +(-4.96119 - 0.0496178i) q^{42} +7.14229 q^{43} +(-1.40389 - 2.43161i) q^{44} +(0.311994 - 0.540389i) q^{45} +(0.500000 - 0.866025i) q^{46} +(2.73243 + 4.73272i) q^{47} +1.87525 q^{48} +(6.99860 + 0.140003i) q^{49} +3.54075 q^{50} +(-1.68022 - 2.91023i) q^{51} +(0.575351 - 0.996537i) q^{52} +(2.75382 - 4.76976i) q^{53} +(-2.32854 - 4.03315i) q^{54} -3.39179 q^{55} +(-2.64562 - 0.0264594i) q^{56} +12.0158 q^{57} +(3.07027 + 5.31786i) q^{58} +(-5.61189 + 9.72008i) q^{59} +(1.13264 - 1.96180i) q^{60} +(-2.53016 - 4.38236i) q^{61} -3.05729 q^{62} +(-0.671458 - 1.19033i) q^{63} +1.00000 q^{64} +(-0.695022 - 1.20381i) q^{65} +(2.63264 - 4.55987i) q^{66} +(-2.31287 + 4.00601i) q^{67} +(-0.896002 - 1.55192i) q^{68} +1.87525 q^{69} +(-1.62563 + 2.75175i) q^{70} +7.31719 q^{71} +(0.258274 + 0.447344i) q^{72} +(5.33643 - 9.24297i) q^{73} +(-4.19870 + 7.27237i) q^{74} +(3.31988 + 5.75021i) q^{75} +6.40758 q^{76} +(-3.77850 + 6.39598i) q^{77} +2.15785 q^{78} +(-7.69362 - 13.3257i) q^{79} +(0.603998 - 1.04616i) q^{80} +(5.14141 - 8.90519i) q^{81} +(2.63264 + 4.55987i) q^{82} +2.94096 q^{83} +(-2.43762 - 4.32132i) q^{84} -2.16473 q^{85} +(3.57114 + 6.18540i) q^{86} +(-5.75751 + 9.97230i) q^{87} +(1.40389 - 2.43161i) q^{88} +(-3.45330 - 5.98128i) q^{89} +0.623988 q^{90} +(-3.04432 - 0.0304469i) q^{91} +1.00000 q^{92} +(-2.86659 - 4.96508i) q^{93} +(-2.73243 + 4.73272i) q^{94} +(3.87016 - 6.70332i) q^{95} +(0.937623 + 1.62401i) q^{96} +5.25862 q^{97} +(3.37805 + 6.13097i) q^{98} +1.45036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.937623	+	1.62401i	−0.541337	+	0.937623i	0.457491	+	0.889214i	$0.348748\pi$
$3$	−0.937623	+	1.62401i	−0.541337	+	0.937623i	−0.998828	+	0.0484086i	$0.984585\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.603998	+	1.04616i	0.270116	+	0.467855i	0.968891	−	0.247486i	$-0.0796046\pi$
$5$	0.603998	+	1.04616i	0.270116	+	0.467855i	−0.698775	+	0.715341i	$0.746271\pi$
$6$	−1.87525			−0.765566
$7$	2.64562	+	0.0264594i	0.999950	+	0.0100007i
$7$	2.64562	+	0.0264594i	0.999950	+	0.0100007i
$8$	−1.00000			−0.353553
$9$	−0.258274	−	0.447344i	−0.0860913	−	0.149115i
$10$	−0.603998	+	1.04616i	−0.191001	+	0.330823i
$11$	−1.40389	+	2.43161i	−0.423290	+	0.733159i	−0.996259	−	0.0864176i	$-0.972458\pi$
$11$	−1.40389	+	2.43161i	−0.423290	+	0.733159i	0.572969	+	0.819577i	$0.305791\pi$
$12$	−0.937623	−	1.62401i	−0.270668	−	0.468812i
$13$	−1.15070			−0.319147			−0.159574	−	0.987186i	$-0.551012\pi$
$13$	−1.15070			−0.319147			−0.159574	+	0.987186i	$0.551012\pi$
$14$	1.29990	+	2.30440i	0.347412	+	0.615878i
$15$	−2.26529			−0.584895
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.896002	+	1.55192i	−0.217312	+	0.376396i	−0.953985	−	0.299853i	$-0.903062\pi$
$17$	−0.896002	+	1.55192i	−0.217312	+	0.376396i	0.736673	+	0.676249i	$0.236396\pi$
$18$	0.258274	−	0.447344i	0.0608758	−	0.105440i
$19$	−3.20379	−	5.54912i	−0.734999	−	1.27306i	−0.954724	−	0.297494i	$-0.903849\pi$
$19$	−3.20379	−	5.54912i	−0.734999	−	1.27306i	0.219724	−	0.975562i	$-0.429484\pi$
$20$	−1.20800			−0.270116
$21$	−2.52356	+	4.27170i	−0.550687	+	0.932162i
$22$	−2.80779			−0.598622
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	0.937623	−	1.62401i	0.191392	−	0.331500i
$25$	1.77037	−	3.06638i	0.354075	−	0.613275i
$26$	−0.575351	−	0.996537i	−0.112836	−	0.195437i
$27$	−4.65708			−0.896256
$28$	−1.34572	+	2.27794i	−0.254318	+	0.430491i
$29$	6.14054			1.14027			0.570134	−	0.821551i	$-0.306891\pi$
$29$	6.14054			1.14027			0.570134	+	0.821551i	$0.306891\pi$
$30$	−1.13264	−	1.96180i	−0.206792	−	0.358174i
$31$	−1.52865	+	2.64769i	−0.274553	+	0.475540i	−0.970022	−	0.243016i	$-0.921863\pi$
$31$	−1.52865	+	2.64769i	−0.274553	+	0.475540i	0.695469	+	0.718556i	$0.255197\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.63264	−	4.55987i	−0.458285	−	0.793772i
$34$	−1.79200			−0.307326
$35$	1.57027	+	2.78371i	0.265424	+	0.470533i
$36$	0.516548			0.0860913
$37$	4.19870	+	7.27237i	0.690263	+	1.19557i	0.971752	+	0.236006i	$0.0758384\pi$
$37$	4.19870	+	7.27237i	0.690263	+	1.19557i	−0.281489	+	0.959565i	$0.590828\pi$
$38$	3.20379	−	5.54912i	0.519723	−	0.900187i
$39$	1.07892	−	1.86875i	0.172766	−	0.299240i
$40$	−0.603998	−	1.04616i	−0.0955005	−	0.165412i
$41$	5.26529			0.822300			0.411150	−	0.911568i	$-0.365127\pi$
$41$	5.26529			0.822300			0.411150	+	0.911568i	$0.365127\pi$
$42$	−4.96119	−	0.0496178i	−0.765528	−	0.00765620i
$43$	7.14229			1.08919			0.544594	−	0.838700i	$-0.316684\pi$
$43$	7.14229			1.08919			0.544594	+	0.838700i	$0.316684\pi$
$44$	−1.40389	−	2.43161i	−0.211645	−	0.366580i
$45$	0.311994	−	0.540389i	0.0465093	−	0.0805565i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	2.73243	+	4.73272i	0.398567	+	0.690338i	0.993549	−	0.113401i	$-0.0361744\pi$
$47$	2.73243	+	4.73272i	0.398567	+	0.690338i	−0.594983	+	0.803738i	$0.702841\pi$
$48$	1.87525			0.270668
$49$	6.99860	+	0.140003i	0.999800	+	0.0200004i
$50$	3.54075			0.500737
$51$	−1.68022	−	2.91023i	−0.235278	−	0.407514i
$52$	0.575351	−	0.996537i	0.0797868	−	0.138195i
$53$	2.75382	−	4.76976i	0.378267	−	0.655178i	−0.612543	−	0.790437i	$-0.709853\pi$
$53$	2.75382	−	4.76976i	0.378267	−	0.655178i	0.990810	+	0.135259i	$0.0431868\pi$
$54$	−2.32854	−	4.03315i	−0.316874	−	0.548843i
$55$	−3.39179			−0.457349
$56$	−2.64562	−	0.0264594i	−0.353536	−	0.00353578i
$57$	12.0158			1.59153
$58$	3.07027	+	5.31786i	0.403146	+	0.698269i
$59$	−5.61189	+	9.72008i	−0.730606	+	1.26545i	0.226019	+	0.974123i	$0.427429\pi$
$59$	−5.61189	+	9.72008i	−0.730606	+	1.26545i	−0.956625	+	0.291323i	$0.905904\pi$
$60$	1.13264	−	1.96180i	0.146224	−	0.253267i
$61$	−2.53016	−	4.38236i	−0.323953	−	0.561104i	0.657347	−	0.753588i	$-0.271679\pi$
$61$	−2.53016	−	4.38236i	−0.323953	−	0.561104i	−0.981300	+	0.192485i	$0.938345\pi$
$62$	−3.05729			−0.388277
$63$	−0.671458	−	1.19033i	−0.0845958	−	0.149968i
$64$	1.00000			0.125000
$65$	−0.695022	−	1.20381i	−0.0862068	−	0.149315i
$66$	2.63264	−	4.55987i	0.324056	−	0.561282i
$67$	−2.31287	+	4.00601i	−0.282562	+	0.489412i	−0.972015	−	0.234919i	$-0.924518\pi$
$67$	−2.31287	+	4.00601i	−0.282562	+	0.489412i	0.689453	+	0.724330i	$0.257851\pi$
$68$	−0.896002	−	1.55192i	−0.108656	−	0.188198i
$69$	1.87525			0.225753
$70$	−1.62563	+	2.75175i	−0.194300	+	0.328897i
$71$	7.31719			0.868390			0.434195	−	0.900819i	$-0.357033\pi$
$71$	7.31719			0.868390			0.434195	+	0.900819i	$0.357033\pi$
$72$	0.258274	+	0.447344i	0.0304379	+	0.0527200i
$73$	5.33643	−	9.24297i	0.624582	−	1.08181i	−0.364039	−	0.931384i	$-0.618603\pi$
$73$	5.33643	−	9.24297i	0.624582	−	1.08181i	0.988621	−	0.150425i	$-0.0480641\pi$
$74$	−4.19870	+	7.27237i	−0.488090	+	0.845396i
$75$	3.31988	+	5.75021i	0.383347	+	0.663977i
$76$	6.40758			0.734999
$77$	−3.77850	+	6.39598i	−0.430601	+	0.728889i
$78$	2.15785			0.244328
$79$	−7.69362	−	13.3257i	−0.865600	−	1.49926i	−0.866450	−	0.499264i	$-0.833604\pi$
$79$	−7.69362	−	13.3257i	−0.865600	−	1.49926i	0.000850067	−	1.00000i	$-0.499729\pi$
$80$	0.603998	−	1.04616i	0.0675290	−	0.116964i
$81$	5.14141	−	8.90519i	0.571268	−	0.989465i
$82$	2.63264	+	4.55987i	0.290727	+	0.503554i
$83$	2.94096			0.322812			0.161406	−	0.986888i	$-0.448397\pi$
$83$	2.94096			0.322812			0.161406	+	0.986888i	$0.448397\pi$
$84$	−2.43762	−	4.32132i	−0.265966	−	0.471495i
$85$	−2.16473			−0.234798
$86$	3.57114	+	6.18540i	0.385086	+	0.666989i
$87$	−5.75751	+	9.97230i	−0.617270	+	1.06914i
$88$	1.40389	−	2.43161i	0.149655	−	0.259211i
$89$	−3.45330	−	5.98128i	−0.366049	−	0.634015i	0.622895	−	0.782305i	$-0.285956\pi$
$89$	−3.45330	−	5.98128i	−0.366049	−	0.634015i	−0.988944	+	0.148290i	$0.952623\pi$
$90$	0.623988			0.0657741
$91$	−3.04432	−	0.0304469i	−0.319131	−	0.00319170i
$92$	1.00000			0.104257
$93$	−2.86659	−	4.96508i	−0.297251	−	0.514855i
$94$	−2.73243	+	4.73272i	−0.281829	+	0.488142i
$95$	3.87016	−	6.70332i	0.397070	−	0.687746i
$96$	0.937623	+	1.62401i	0.0956958	+	0.165750i
$97$	5.25862			0.533932			0.266966	−	0.963706i	$-0.413979\pi$
$97$	5.25862			0.533932			0.266966	+	0.963706i	$0.413979\pi$
$98$	3.37805	+	6.13097i	0.341235	+	0.619321i
$99$	1.45036			0.145766
$100$	1.77037	+	3.06638i	0.177037	+	0.306638i
$101$	−7.20291	+	12.4758i	−0.716717	+	1.24139i	0.245577	+	0.969377i	$0.421023\pi$
$101$	−7.20291	+	12.4758i	−0.716717	+	1.24139i	−0.962294	+	0.272013i	$0.912311\pi$
$102$	1.68022	−	2.91023i	0.166367	−	0.288156i
$103$	−2.59534	−	4.49526i	−0.255727	−	0.442931i	0.709366	−	0.704840i	$-0.248981\pi$
$103$	−2.59534	−	4.49526i	−0.255727	−	0.442931i	−0.965093	+	0.261909i	$0.915648\pi$
$104$	1.15070			0.112836
$105$	−5.99309	−	0.0599382i	−0.584866	−	0.00584936i
$106$	5.50765			0.534950
$107$	−2.73752	−	4.74152i	−0.264646	−	0.458380i	0.702825	−	0.711363i	$-0.251922\pi$
$107$	−2.73752	−	4.74152i	−0.264646	−	0.458380i	−0.967471	+	0.252983i	$0.918588\pi$
$108$	2.32854	−	4.03315i	0.224064	−	0.388090i
$109$	1.71816	−	2.97594i	0.164570	−	0.285044i	−0.771932	−	0.635705i	$-0.780710\pi$
$109$	1.71816	−	2.97594i	0.164570	−	0.285044i	0.936503	+	0.350661i	$0.114043\pi$
$110$	−1.69590	−	2.93738i	−0.161697	−	0.280068i
$111$	−15.7472			−1.49466
$112$	−1.29990	−	2.30440i	−0.122829	−	0.217746i
$113$	8.46614			0.796427			0.398214	−	0.917293i	$-0.369630\pi$
$113$	8.46614			0.796427			0.398214	+	0.917293i	$0.369630\pi$
$114$	6.00789	+	10.4060i	0.562691	+	0.974609i
$115$	0.603998	−	1.04616i	0.0563231	−	0.0975545i
$116$	−3.07027	+	5.31786i	−0.285067	+	0.493751i
$117$	0.297196	+	0.514759i	0.0274758	+	0.0475895i
$118$	−11.2238			−1.03323
$119$	−2.41154	+	4.08208i	−0.221066	+	0.374204i
$120$	2.26529			0.206792
$121$	1.55817	+	2.69883i	0.141652	+	0.245348i
$122$	2.53016	−	4.38236i	0.229070	−	0.396760i
$123$	−4.93686	+	8.55089i	−0.445141	+	0.771008i
$124$	−1.52865	−	2.64769i	−0.137277	−	0.237770i
$125$	10.3172			0.922797
$126$	0.695131	−	1.17667i	0.0619272	−	0.104826i
$127$	−6.11094			−0.542258			−0.271129	−	0.962543i	$-0.587397\pi$
$127$	−6.11094			−0.542258			−0.271129	+	0.962543i	$0.587397\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.69677	+	11.5991i	−0.589618	+	1.02125i
$130$	0.695022	−	1.20381i	0.0609574	−	0.105581i
$131$	−9.91904	−	17.1803i	−0.866631	−	1.50105i	−0.865419	−	0.501049i	$-0.832948\pi$
$131$	−9.91904	−	17.1803i	−0.866631	−	1.50105i	−0.00121169	−	0.999999i	$-0.500386\pi$
$132$	5.26529			0.458285
$133$	−8.32918	−	14.7656i	−0.722231	−	1.28034i
$134$	−4.62574			−0.399603
$135$	−2.81287	−	4.87203i	−0.242093	−	0.419318i
$136$	0.896002	−	1.55192i	0.0768315	−	0.133076i
$137$	5.42476	−	9.39596i	0.463468	−	0.802751i	−0.535663	−	0.844432i	$-0.679938\pi$
$137$	5.42476	−	9.39596i	0.463468	−	0.802751i	0.999131	+	0.0416814i	$0.0132714\pi$
$138$	0.937623	+	1.62401i	0.0798158	+	0.138245i
$139$	1.17363			0.0995461			0.0497731	−	0.998761i	$-0.484150\pi$
$139$	1.17363			0.0995461			0.0497731	+	0.998761i	$0.484150\pi$
$140$	−3.19590	−	0.0319628i	−0.270103	−	0.00270135i
$141$	−10.2480			−0.863035
$142$	3.65859	+	6.33687i	0.307022	+	0.531778i
$143$	1.61546	−	2.79806i	0.135092	−	0.233986i
$144$	−0.258274	+	0.447344i	−0.0215228	+	0.0372786i
$145$	3.70887	+	6.42395i	0.308005	+	0.533480i
$146$	10.6729			0.883293
$147$	−6.78941	+	11.2345i	−0.559981	+	0.926609i
$148$	−8.39741			−0.690263
$149$	9.43177	+	16.3363i	0.772681	+	1.33832i	0.936089	+	0.351764i	$0.114418\pi$
$149$	9.43177	+	16.3363i	0.772681	+	1.33832i	−0.163408	+	0.986559i	$0.552249\pi$
$150$	−3.31988	+	5.75021i	−0.271067	+	0.469503i
$151$	−0.0249639	+	0.0432387i	−0.00203153	+	0.00351872i	−0.867039	−	0.498240i	$-0.833980\pi$
$151$	−0.0249639	+	0.0432387i	−0.00203153	+	0.00351872i	0.865008	+	0.501758i	$0.167313\pi$
$152$	3.20379	+	5.54912i	0.259862	+	0.450093i
$153$	0.925656			0.0748349
$154$	−7.42833	−	0.0742923i	−0.598592	−	0.00598664i
$155$	−3.69320			−0.296645
$156$	1.07892	+	1.86875i	0.0863831	+	0.149620i
$157$	2.67871	−	4.63967i	0.213785	−	0.370286i	−0.739111	−	0.673583i	$-0.764754\pi$
$157$	2.67871	−	4.63967i	0.213785	−	0.370286i	0.952896	+	0.303297i	$0.0980876\pi$
$158$	7.69362	−	13.3257i	0.612072	−	1.06014i
$159$	5.16410	+	8.94448i	0.409540	+	0.709344i
$160$	1.20800			0.0955005
$161$	−1.29990	−	2.30440i	−0.102446	−	0.181612i
$162$	10.2828			0.807895
$163$	−0.858064	−	1.48621i	−0.0672088	−	0.116409i	0.830463	−	0.557074i	$-0.188076\pi$
$163$	−0.858064	−	1.48621i	−0.0672088	−	0.116409i	−0.897672	+	0.440665i	$0.854743\pi$
$164$	−2.63264	+	4.55987i	−0.205575	+	0.356066i
$165$	3.18022	−	5.50831i	0.247580	−	0.428821i
$166$	1.47048	+	2.54694i	0.114131	+	0.197681i
$167$	17.7989			1.37732			0.688660	−	0.725085i	$-0.258199\pi$
$167$	17.7989			1.37732			0.688660	+	0.725085i	$0.258199\pi$
$168$	2.52356	−	4.27170i	0.194697	−	0.329569i
$169$	−11.6759			−0.898145
$170$	−1.08237	−	1.87471i	−0.0830137	−	0.143784i
$171$	−1.65491	+	2.86639i	−0.126554	+	0.219198i
$172$	−3.57114	+	6.18540i	−0.272297	+	0.471632i
$173$	−0.766690	−	1.32795i	−0.0582904	−	0.100962i	0.835408	−	0.549631i	$-0.185232\pi$
$173$	−0.766690	−	1.32795i	−0.0582904	−	0.100962i	−0.893698	+	0.448669i	$0.851898\pi$
$174$	−11.5150			−0.872951
$175$	4.76487	−	8.06562i	0.360190	−	0.609703i
$176$	2.80779			0.211645
$177$	−10.5237	−	18.2275i	−0.791008	−	1.37007i
$178$	3.45330	−	5.98128i	0.258835	−	0.448316i
$179$	−7.74096	+	13.4077i	−0.578587	+	1.00214i	0.417055	+	0.908881i	$0.363062\pi$
$179$	−7.74096	+	13.4077i	−0.578587	+	1.00214i	−0.995642	+	0.0932601i	$0.970271\pi$
$180$	0.311994	+	0.540389i	0.0232547	+	0.0402782i
$181$	−23.3633			−1.73658			−0.868289	−	0.496059i	$-0.834780\pi$
$181$	−23.3633			−1.73658			−0.868289	+	0.496059i	$0.834780\pi$
$182$	−1.49579	−	2.65168i	−0.110875	−	0.196556i
$183$	9.48933			0.701472
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−5.07202	+	8.78499i	−0.372902	+	0.645886i
$186$	2.86659	−	4.96508i	0.210189	−	0.364057i
$187$	−2.51578	−	4.35746i	−0.183972	−	0.318649i
$188$	−5.46487			−0.398567
$189$	−12.3209	−	0.123224i	−0.896211	−	0.00896319i
$190$	7.74033			0.561542
$191$	9.35397	+	16.2015i	0.676829	+	1.17230i	0.975931	+	0.218081i	$0.0699798\pi$
$191$	9.35397	+	16.2015i	0.676829	+	1.17230i	−0.299101	+	0.954221i	$0.596687\pi$
$192$	−0.937623	+	1.62401i	−0.0676671	+	0.117203i
$193$	0.000875238	−	0.00151596i	6.30010e−5	−	0.000109121i	−0.865994	−	0.500055i	$-0.833313\pi$
$193$	0.000875238	−	0.00151596i	6.30010e−5	−	0.000109121i	0.866057	+	0.499945i	$0.166647\pi$
$194$	2.62931	+	4.55410i	0.188774	+	0.326965i
$195$	2.60667			0.186668
$196$	−3.62055	+	5.99096i	−0.258610	+	0.427926i
$197$	−16.1840			−1.15306			−0.576532	−	0.817075i	$-0.695594\pi$
$197$	−16.1840			−1.15306			−0.576532	+	0.817075i	$0.695594\pi$
$198$	0.725178	+	1.25605i	0.0515362	+	0.0892632i
$199$	−1.03198	+	1.78744i	−0.0731551	+	0.126708i	−0.900283	−	0.435306i	$-0.856640\pi$
$199$	−1.03198	+	1.78744i	−0.0731551	+	0.126708i	0.827127	+	0.562014i	$0.189973\pi$
$200$	−1.77037	+	3.06638i	−0.125184	+	0.216826i
$201$	−4.33720	−	7.51225i	−0.305922	−	0.529873i
$202$	−14.4058			−1.01359
$203$	16.2455	+	0.162475i	1.14021	+	0.0114035i
$204$	3.36045			0.235278
$205$	3.18022	+	5.50831i	0.222117	+	0.384717i
$206$	2.59534	−	4.49526i	0.180826	−	0.313200i
$207$	−0.258274	+	0.447344i	−0.0179513	+	0.0310925i
$208$	0.575351	+	0.996537i	0.0398934	+	0.0690974i
$209$	17.9911			1.24447
$210$	−2.94464	−	5.22014i	−0.203199	−	0.360224i
$211$	−16.1507			−1.11186			−0.555930	−	0.831229i	$-0.687638\pi$
$211$	−16.1507			−1.11186			−0.555930	+	0.831229i	$0.687638\pi$
$212$	2.75382	+	4.76976i	0.189133	+	0.327589i
$213$	−6.86076	+	11.8832i	−0.470092	+	0.814223i
$214$	2.73752	−	4.74152i	0.187133	−	0.324124i
$215$	4.31393	+	7.47194i	0.294207	+	0.509582i
$216$	4.65708			0.316874
$217$	−4.11427	+	6.96434i	−0.279295	+	0.472770i
$218$	3.43632			0.232737
$219$	10.0071	+	17.3328i	0.676219	+	1.17125i
$220$	1.69590	−	2.93738i	0.114337	−	0.198038i
$221$	1.03103	−	1.78580i	0.0693547	−	0.120126i
$222$	−7.87360	−	13.6375i	−0.528442	−	0.915288i
$223$	−5.83325			−0.390623			−0.195312	−	0.980741i	$-0.562572\pi$
$223$	−5.83325			−0.390623			−0.195312	+	0.980741i	$0.562572\pi$
$224$	1.34572	−	2.27794i	0.0899150	−	0.152202i
$225$	−1.82897			−0.121931
$226$	4.23307	+	7.33189i	0.281580	+	0.487710i
$227$	−5.41091	+	9.37197i	−0.359135	+	0.622039i	−0.987816	−	0.155623i	$-0.950261\pi$
$227$	−5.41091	+	9.37197i	−0.359135	+	0.622039i	0.628682	+	0.777663i	$0.283595\pi$
$228$	−6.00789	+	10.4060i	−0.397882	+	0.689152i
$229$	−8.41266	−	14.5712i	−0.555924	−	0.962889i	−0.997831	−	0.0658279i	$-0.979031\pi$
$229$	−8.41266	−	14.5712i	−0.555924	−	0.962889i	0.441907	−	0.897061i	$-0.354302\pi$
$230$	1.20800			0.0796529
$231$	−6.84432	−	12.1333i	−0.450323	−	0.798316i
$232$	−6.14054			−0.403146
$233$	−7.78692	−	13.4873i	−0.510138	−	0.883585i	−0.999931	−	0.0117464i	$-0.996261\pi$
$233$	−7.78692	−	13.4873i	−0.510138	−	0.883585i	0.489793	−	0.871839i	$-0.337072\pi$
$234$	−0.297196	+	0.514759i	−0.0194283	+	0.0336509i
$235$	−3.30077	+	5.71710i	−0.215319	+	0.372943i
$236$	−5.61189	−	9.72008i	−0.365303	−	0.632723i
$237$	28.8549			1.87433
$238$	−4.74096	−	0.0474153i	−0.307311	−	0.00307348i
$239$	−19.5970			−1.26762			−0.633812	−	0.773487i	$-0.718511\pi$
$239$	−19.5970			−1.26762			−0.633812	+	0.773487i	$0.718511\pi$
$240$	1.13264	+	1.96180i	0.0731119	+	0.126634i
$241$	−1.14498	+	1.98317i	−0.0737550	+	0.127747i	−0.900544	−	0.434765i	$-0.856832\pi$
$241$	−1.14498	+	1.98317i	−0.0737550	+	0.127747i	0.826789	+	0.562512i	$0.190165\pi$
$242$	−1.55817	+	2.69883i	−0.100163	+	0.173487i
$243$	2.65579	+	4.59996i	0.170369	+	0.295087i
$244$	5.06031			0.323953
$245$	4.08068	+	7.40618i	0.260705	+	0.473164i
$246$	−9.87371			−0.629525
$247$	3.68661	+	6.38539i	0.234573	+	0.406293i
$248$	1.52865	−	2.64769i	0.0970692	−	0.168129i
$249$	−2.75751	+	4.77614i	−0.174750	+	0.302676i
$250$	5.15859	+	8.93495i	0.326258	+	0.565096i
$251$	9.51480			0.600569			0.300284	−	0.953850i	$-0.402918\pi$
$251$	9.51480			0.600569			0.300284	+	0.953850i	$0.402918\pi$
$252$	1.36659	+	0.0136675i	0.0860870	+	0.000860974i
$253$	2.80779			0.176524
$254$	−3.05547	−	5.29223i	−0.191717	−	0.332064i
$255$	2.02970	−	3.51555i	0.127105	−	0.220152i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.986392	+	1.70848i	0.0615294	+	0.106572i	0.895149	−	0.445767i	$-0.147069\pi$
$257$	0.986392	+	1.70848i	0.0615294	+	0.106572i	−0.833620	+	0.552339i	$0.813736\pi$
$258$	−13.3935			−0.833846
$259$	10.9158	+	19.3510i	0.678272	+	1.20241i
$260$	1.39004			0.0862068
$261$	−1.58594	−	2.74693i	−0.0981673	−	0.170031i
$262$	9.91904	−	17.1803i	0.612800	−	1.06140i
$263$	12.2862	−	21.2802i	0.757597	−	1.31220i	−0.186476	−	0.982459i	$-0.559707\pi$
$263$	12.2862	−	21.2802i	0.757597	−	1.31220i	0.944073	−	0.329737i	$-0.106960\pi$
$264$	2.63264	+	4.55987i	0.162028	+	0.280641i
$265$	6.65322			0.408704
$266$	8.62283	−	14.5961i	0.528700	−	0.894944i
$267$	12.9516			0.792623
$268$	−2.31287	−	4.00601i	−0.141281	−	0.244706i
$269$	−4.40466	+	7.62909i	−0.268557	+	0.465154i	−0.968489	−	0.249055i	$-0.919880\pi$
$269$	−4.40466	+	7.62909i	−0.268557	+	0.465154i	0.699933	+	0.714209i	$0.253213\pi$
$270$	2.81287	−	4.87203i	0.171186	−	0.296502i
$271$	−13.3106	−	23.0546i	−0.808561	−	1.40047i	−0.913861	−	0.406028i	$-0.866913\pi$
$271$	−13.3106	−	23.0546i	−0.808561	−	1.40047i	0.105300	−	0.994441i	$-0.466420\pi$
$272$	1.79200			0.108656
$273$	2.90387	−	4.91546i	0.175750	−	0.297497i
$274$	10.8495			0.655443
$275$	4.97083	+	8.60973i	0.299752	+	0.519186i
$276$	−0.937623	+	1.62401i	−0.0564383	+	0.0977540i
$277$	15.3854	−	26.6483i	0.924420	−	1.60114i	0.131929	−	0.991259i	$-0.457883\pi$
$277$	15.3854	−	26.6483i	0.924420	−	1.60114i	0.792491	−	0.609884i	$-0.208784\pi$
$278$	0.586816	+	1.01639i	0.0351949	+	0.0609593i
$279$	1.57924			0.0945466
$280$	−1.57027	−	2.78371i	−0.0938415	−	0.166358i
$281$	2.57559			0.153647			0.0768235	−	0.997045i	$-0.475522\pi$
$281$	2.57559			0.153647			0.0768235	+	0.997045i	$0.475522\pi$
$282$	−5.12399	−	8.87501i	−0.305129	−	0.528499i
$283$	11.2210	−	19.4353i	0.667017	−	1.15531i	−0.311717	−	0.950175i	$-0.600904\pi$
$283$	11.2210	−	19.4353i	0.667017	−	1.15531i	0.978734	−	0.205133i	$-0.0657627\pi$
$284$	−3.65859	+	6.33687i	−0.217098	+	0.376024i
$285$	7.25751	+	12.5704i	0.429898	+	0.744605i
$286$	3.23093			0.191049
$287$	13.9300	+	0.139316i	0.822259	+	0.00822358i
$288$	−0.516548			−0.0304379
$289$	6.89436	+	11.9414i	0.405551	+	0.702434i
$290$	−3.70887	+	6.42395i	−0.217792	+	0.377228i
$291$	−4.93061	+	8.54006i	−0.289037	+	0.500627i
$292$	5.33643	+	9.24297i	0.312291	+	0.540904i
$293$	7.81690			0.456668			0.228334	−	0.973583i	$-0.426672\pi$
$293$	7.81690			0.456668			0.228334	+	0.973583i	$0.426672\pi$
$294$	−13.1241	−	0.262540i	−0.765413	−	0.0153116i
$295$	−13.5583			−0.789393
$296$	−4.19870	−	7.27237i	−0.244045	−	0.422698i
$297$	6.53805	−	11.3242i	0.379376	−	0.657098i
$298$	−9.43177	+	16.3363i	−0.546368	+	0.946337i
$299$	0.575351	+	0.996537i	0.0332734	+	0.0576312i
$300$	−6.63977			−0.383347
$301$	18.8958	+	0.188980i	1.08913	+	0.0108927i
$302$	−0.0499278			−0.00287302
$303$	−13.5072	−	23.3952i	−0.775970	−	1.34402i
$304$	−3.20379	+	5.54912i	−0.183750	+	0.318264i
$305$	3.05642	−	5.29387i	0.175010	−	0.303126i
$306$	0.462828	+	0.801642i	0.0264581	+	0.0458268i
$307$	18.9412			1.08103			0.540515	−	0.841334i	$-0.318229\pi$
$307$	18.9412			1.08103			0.540515	+	0.841334i	$0.318229\pi$
$308$	−3.64983	−	6.47027i	−0.207968	−	0.368678i
$309$	9.73381			0.553737
$310$	−1.84660	−	3.19840i	−0.104880	−	0.181657i
$311$	8.15783	−	14.1298i	0.462588	−	0.801226i	−0.536501	−	0.843900i	$-0.680254\pi$
$311$	8.15783	−	14.1298i	0.462588	−	0.801226i	0.999089	+	0.0426738i	$0.0135876\pi$
$312$	−1.07892	+	1.86875i	−0.0610821	+	0.105797i
$313$	2.70315	+	4.68200i	0.152791	+	0.264642i	0.932253	−	0.361808i	$-0.117840\pi$
$313$	2.70315	+	4.68200i	0.152791	+	0.264642i	−0.779461	+	0.626450i	$0.784507\pi$
$314$	5.35743			0.302337
$315$	0.839715	−	1.42141i	0.0473126	−	0.0800873i
$316$	15.3872			0.865600
$317$	−6.44054	−	11.1553i	−0.361737	−	0.626546i	0.626510	−	0.779413i	$-0.284483\pi$
$317$	−6.44054	−	11.1553i	−0.361737	−	0.626546i	−0.988247	+	0.152867i	$0.951149\pi$
$318$	−5.16410	+	8.94448i	−0.289588	+	0.501582i
$319$	−8.62066	+	14.9314i	−0.482664	+	0.835999i
$320$	0.603998	+	1.04616i	0.0337645	+	0.0584819i
$321$	10.2670			0.573050
$322$	1.34572	−	2.27794i	0.0749943	−	0.126945i
$323$	11.4824			0.638898
$324$	5.14141	+	8.90519i	0.285634	+	0.494733i
$325$	−2.03717	+	3.52849i	−0.113002	+	0.195725i
$326$	0.858064	−	1.48621i	0.0475238	−	0.0823136i
$327$	3.22198	+	5.58063i	0.178176	+	0.308609i
$328$	−5.26529			−0.290727
$329$	7.10376	+	12.5933i	0.391643	+	0.694289i
$330$	6.36045			0.350131
$331$	−3.44120	−	5.96033i	−0.189145	−	0.327609i	0.755820	−	0.654779i	$-0.227238\pi$
$331$	−3.44120	−	5.96033i	−0.189145	−	0.327609i	−0.944966	+	0.327170i	$0.893905\pi$
$332$	−1.47048	+	2.54694i	−0.0807030	+	0.139782i
$333$	2.16883	−	3.75653i	0.118851	−	0.205856i
$334$	8.89944	+	15.4143i	0.486956	+	0.843432i
$335$	−5.58787			−0.305298
$336$	4.96119	+	0.0496178i	0.270655	+	0.00270688i
$337$	−20.3762			−1.10996			−0.554982	−	0.831862i	$-0.687275\pi$
$337$	−20.3762			−1.10996			−0.554982	+	0.831862i	$0.687275\pi$
$338$	−5.83794	−	10.1116i	−0.317542	−	0.549999i
$339$	−7.93805	+	13.7491i	−0.431135	+	0.746749i
$340$	1.08237	−	1.87471i	0.0586996	−	0.101671i
$341$	−4.29211	−	7.43416i	−0.232431	−	0.402582i
$342$	−3.30982			−0.178975
$343$	18.5119	+	0.555573i	0.999550	+	0.0299981i
$344$	−7.14229			−0.385086
$345$	1.13264	+	1.96180i	0.0609795	+	0.105620i
$346$	0.766690	−	1.32795i	0.0412175	−	0.0713908i
$347$	−17.0900	+	29.6007i	−0.917438	+	1.58905i	−0.114146	+	0.993464i	$0.536413\pi$
$347$	−17.0900	+	29.6007i	−0.917438	+	1.58905i	−0.803292	+	0.595585i	$0.796920\pi$
$348$	−5.75751	−	9.97230i	−0.308635	−	0.534571i
$349$	5.00863			0.268106			0.134053	−	0.990974i	$-0.457201\pi$
$349$	5.00863			0.268106			0.134053	+	0.990974i	$0.457201\pi$
$350$	9.36746	+	0.0936859i	0.500712	+	0.00500772i
$351$	5.35892			0.286038
$352$	1.40389	+	2.43161i	0.0748277	+	0.129605i
$353$	−1.21385	+	2.10244i	−0.0646065	+	0.111902i	−0.896519	−	0.443005i	$-0.853913\pi$
$353$	−1.21385	+	2.10244i	−0.0646065	+	0.111902i	0.831913	+	0.554906i	$0.187246\pi$
$354$	10.5237	−	18.2275i	0.559327	−	0.968783i
$355$	4.41957	+	7.65491i	0.234566	+	0.406281i
$356$	6.90659			0.366049
$357$	−4.36823	−	7.74383i	−0.231191	−	0.409847i
$358$	−15.4819			−0.818245
$359$	−14.6119	−	25.3085i	−0.771186	−	1.33573i	−0.936913	−	0.349562i	$-0.886330\pi$
$359$	−14.6119	−	25.3085i	−0.771186	−	1.33573i	0.165727	−	0.986172i	$-0.447003\pi$
$360$	−0.311994	+	0.540389i	−0.0164435	+	0.0284810i
$361$	−11.0285	+	19.1019i	−0.580448	+	1.00537i
$362$	−11.6816	−	20.2332i	−0.613973	−	1.06343i
$363$	−5.84390			−0.306725
$364$	1.54853	−	2.62123i	0.0811649	−	0.137390i
$365$	12.8928			0.674839
$366$	4.74467	+	8.21800i	0.248008	+	0.429562i
$367$	17.7220	−	30.6953i	0.925078	−	1.60228i	0.133644	−	0.991029i	$-0.457332\pi$
$367$	17.7220	−	30.6953i	0.925078	−	1.60228i	0.791435	−	0.611254i	$-0.209334\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	−1.35989	−	2.35539i	−0.0707929	−	0.122617i
$370$	−10.1440			−0.527363
$371$	7.41178	−	12.5461i	0.384800	−	0.651362i
$372$	5.73318			0.297251
$373$	−17.5738	−	30.4387i	−0.909938	−	1.57606i	−0.814148	−	0.580657i	$-0.802796\pi$
$373$	−17.5738	−	30.4387i	−0.909938	−	1.57606i	−0.0957896	−	0.995402i	$-0.530538\pi$
$374$	2.51578	−	4.35746i	0.130088	−	0.225319i
$375$	−9.67363	+	16.7552i	−0.499544	+	0.865236i
$376$	−2.73243	−	4.73272i	−0.140915	−	0.244071i
$377$	−7.06593			−0.363914
$378$	−6.05372	−	10.7318i	−0.311370	−	0.551984i
$379$	15.6687			0.804849			0.402424	−	0.915453i	$-0.368168\pi$
$379$	15.6687			0.804849			0.402424	+	0.915453i	$0.368168\pi$
$380$	3.87016	+	6.70332i	0.198535	+	0.343873i
$381$	5.72976	−	9.92423i	0.293544	−	0.508434i
$382$	−9.35397	+	16.2015i	−0.478590	+	0.828943i
$383$	−17.0699	−	29.5659i	−0.872229	−	1.51074i	−0.859686	−	0.510823i	$-0.829341\pi$
$383$	−17.0699	−	29.5659i	−0.872229	−	1.51074i	−0.0125428	−	0.999921i	$-0.503993\pi$
$384$	−1.87525			−0.0956958
$385$	−8.97339	−	0.0897448i	−0.457327	−	0.00457382i
$386$	0.00175048			8.90969e−5
$387$	−1.84467	−	3.19506i	−0.0937697	−	0.162414i
$388$	−2.62931	+	4.55410i	−0.133483	+	0.231200i
$389$	−1.74681	+	3.02556i	−0.0885667	+	0.153402i	−0.906906	−	0.421334i	$-0.861562\pi$
$389$	−1.74681	+	3.02556i	−0.0885667	+	0.153402i	0.818339	+	0.574736i	$0.194895\pi$
$390$	1.30334	+	2.25745i	0.0659970	+	0.114310i
$391$	1.79200			0.0906255
$392$	−6.99860	−	0.140003i	−0.353483	−	0.00707121i
$393$	37.2013			1.87656
$394$	−8.09201	−	14.0158i	−0.407669	−	0.706104i
$395$	9.29386	−	16.0974i	0.467625	−	0.809950i
$396$	−0.725178	+	1.25605i	−0.0364416	+	0.0631186i
$397$	5.36214	+	9.28750i	0.269118	+	0.466126i	0.968634	−	0.248490i	$-0.0799345\pi$
$397$	5.36214	+	9.28750i	0.269118	+	0.466126i	−0.699516	+	0.714617i	$0.746601\pi$
$398$	−2.06396			−0.103457
$399$	31.7892	+	0.317930i	1.59145	+	0.0159164i
$400$	−3.54075			−0.177037
$401$	16.1895	+	28.0411i	0.808466	+	1.40030i	0.913926	+	0.405881i	$0.133035\pi$
$401$	16.1895	+	28.0411i	0.808466	+	1.40030i	−0.105460	+	0.994424i	$0.533631\pi$
$402$	4.33720	−	7.51225i	0.216320	−	0.374677i
$403$	1.75902	−	3.04671i	0.0876229	−	0.151767i
$404$	−7.20291	−	12.4758i	−0.358358	−	0.620695i
$405$	12.4216			0.617235
$406$	7.98205	+	14.1503i	0.396143	+	0.702266i
$407$	−23.5781			−1.16872
$408$	1.68022	+	2.91023i	0.0831835	+	0.144078i
$409$	2.66855	−	4.62206i	0.131951	−	0.228546i	−0.792477	−	0.609901i	$-0.791209\pi$
$409$	2.66855	−	4.62206i	0.131951	−	0.228546i	0.924429	+	0.381355i	$0.124542\pi$
$410$	−3.18022	+	5.50831i	−0.157060	+	0.272036i
$411$	10.1728	+	17.6197i	0.501785	+	0.869117i
$412$	5.19068			0.255727
$413$	−15.1041	+	25.5671i	−0.743225	+	1.25808i
$414$	−0.516548			−0.0253869
$415$	1.77633	+	3.07670i	0.0871967	+	0.151029i
$416$	−0.575351	+	0.996537i	−0.0282089	+	0.0488593i
$417$	−1.10042	+	1.90599i	−0.0538880	+	0.0933368i
$418$	8.99555	+	15.5808i	0.439987	+	0.762079i
$419$	−15.6627			−0.765173			−0.382586	−	0.923920i	$-0.624967\pi$
$419$	−15.6627			−0.765173			−0.382586	+	0.923920i	$0.624967\pi$
$420$	3.04845	−	5.16020i	0.148749	−	0.251792i
$421$	−24.5101			−1.19455			−0.597275	−	0.802037i	$-0.703750\pi$
$421$	−24.5101			−1.19455			−0.597275	+	0.802037i	$0.703750\pi$
$422$	−8.07535	−	13.9869i	−0.393102	−	0.680873i
$423$	1.41143	−	2.44467i	0.0686263	−	0.118864i
$424$	−2.75382	+	4.76976i	−0.133738	+	0.231640i
$425$	3.17252	+	5.49496i	0.153890	+	0.266545i
$426$	−13.7215			−0.664810
$427$	−6.57787	−	11.6610i	−0.318326	−	0.564315i
$428$	5.47504			0.264646
$429$	3.02939	+	5.24706i	0.146260	+	0.253330i
$430$	−4.31393	+	7.47194i	−0.208036	+	0.360329i
$431$	5.38584	−	9.32854i	0.259427	−	0.449340i	−0.706662	−	0.707551i	$-0.749800\pi$
$431$	5.38584	−	9.32854i	0.259427	−	0.449340i	0.966088	+	0.258211i	$0.0831331\pi$
$432$	2.32854	+	4.03315i	0.112032	+	0.194045i
$433$	−6.81795			−0.327650			−0.163825	−	0.986489i	$-0.552383\pi$
$433$	−6.81795			−0.327650			−0.163825	+	0.986489i	$0.552383\pi$
$434$	−8.08843	−	0.0808941i	−0.388257	−	0.00388304i
$435$	−13.9101			−0.666938
$436$	1.71816	+	2.97594i	0.0822851	+	0.142522i
$437$	−3.20379	+	5.54912i	−0.153258	+	0.265451i
$438$	−10.0071	+	17.3328i	−0.478159	+	0.828196i
$439$	20.2345	+	35.0471i	0.965739	+	1.67271i	0.707617	+	0.706597i	$0.249770\pi$
$439$	20.2345	+	35.0471i	0.965739	+	1.67271i	0.258122	+	0.966112i	$0.416896\pi$
$440$	3.39179			0.161697
$441$	−1.74493	−	3.16694i	−0.0830918	−	0.150807i
$442$	2.06206			0.0980823
$443$	−8.00281	−	13.8613i	−0.380225	−	0.658569i	0.610869	−	0.791731i	$-0.290820\pi$
$443$	−8.00281	−	13.8613i	−0.380225	−	0.658569i	−0.991094	+	0.133163i	$0.957487\pi$
$444$	7.87360	−	13.6375i	0.373665	−	0.647206i
$445$	4.17157	−	7.22537i	0.197751	−	0.342515i
$446$	−2.91663	−	5.05174i	−0.138106	−	0.239207i
$447$	−35.3738			−1.67312
$448$	2.64562	+	0.0264594i	0.124994	+	0.00125009i
$449$	−25.9058			−1.22257			−0.611284	−	0.791411i	$-0.709347\pi$
$449$	−25.9058			−1.22257			−0.611284	+	0.791411i	$0.709347\pi$
$450$	−0.914483	−	1.58393i	−0.0431091	−	0.0746672i
$451$	−7.39190	+	12.8032i	−0.348071	+	0.602877i
$452$	−4.23307	+	7.33189i	−0.199107	+	0.344863i
$453$	−0.0468134	−	0.0810832i	−0.00219949	−	0.00380962i
$454$	−10.8218			−0.507893
$455$	−1.80691	−	3.20322i	−0.0847093	−	0.150169i
$456$	−12.0158			−0.562691
$457$	17.6546	+	30.5786i	0.825846	+	1.43041i	0.901271	+	0.433255i	$0.142635\pi$
$457$	17.6546	+	30.5786i	0.825846	+	1.43041i	−0.0754253	+	0.997151i	$0.524031\pi$
$458$	8.41266	−	14.5712i	0.393098	−	0.680865i
$459$	4.17276	−	7.22743i	0.194768	−	0.337347i
$460$	0.603998	+	1.04616i	0.0281616	+	0.0487772i
$461$	−32.0076			−1.49074			−0.745371	−	0.666650i	$-0.767728\pi$
$461$	−32.0076			−1.49074			−0.745371	+	0.666650i	$0.767728\pi$
$462$	7.08563	−	11.9940i	0.329653	−	0.558013i
$463$	−12.1887			−0.566458			−0.283229	−	0.959052i	$-0.591406\pi$
$463$	−12.1887			−0.566458			−0.283229	+	0.959052i	$0.591406\pi$
$464$	−3.07027	−	5.31786i	−0.142534	−	0.246875i
$465$	3.46283	−	5.99779i	0.160585	−	0.278141i
$466$	7.78692	−	13.4873i	0.360722	−	0.624789i
$467$	18.7055	+	32.3988i	0.865586	+	1.49924i	0.866464	+	0.499240i	$0.166387\pi$
$467$	18.7055	+	32.3988i	0.865586	+	1.49924i	−0.000877424		1.00000i	$0.500279\pi$
$468$	−0.594393			−0.0274758
$469$	−6.22497	+	10.5372i	−0.287442	+	0.486561i
$470$	−6.60154			−0.304506
$471$	5.02325	+	8.70052i	0.231459	+	0.400899i
$472$	5.61189	−	9.72008i	0.258308	−	0.447403i
$473$	−10.0270	+	17.3673i	−0.461042	+	0.798549i
$474$	14.4274	+	24.9890i	0.662674	+	1.14779i
$475$	−22.6876			−1.04098
$476$	−2.32942	−	4.12950i	−0.106769	−	0.189275i
$477$	−2.84497			−0.130262
$478$	−9.79849	−	16.9715i	−0.448173	−	0.776258i
$479$	1.00456	−	1.73995i	0.0458994	−	0.0795002i	−0.842163	−	0.539223i	$-0.818718\pi$
$479$	1.00456	−	1.73995i	0.0458994	−	0.0795002i	0.888062	+	0.459723i	$0.152051\pi$
$480$	−1.13264	+	1.96180i	−0.0516979	+	0.0895434i
$481$	−4.83146	−	8.36833i	−0.220296	−	0.381563i
$482$	−2.28997			−0.104305
$483$	4.96119	+	0.0496178i	0.225742	+	0.00225769i
$484$	−3.11634			−0.141652
$485$	3.17620	+	5.50134i	0.144224	+	0.249803i
$486$	−2.65579	+	4.59996i	−0.120469	+	0.208658i
$487$	−18.8166	+	32.5912i	−0.852659	+	1.47685i	0.0261402	+	0.999658i	$0.491678\pi$
$487$	−18.8166	+	32.5912i	−0.852659	+	1.47685i	−0.878800	+	0.477191i	$0.841655\pi$
$488$	2.53016	+	4.38236i	0.114535	+	0.198380i
$489$	3.21816			0.145530
$490$	−4.37360	+	7.23706i	−0.197579	+	0.326937i
$491$	−25.3836			−1.14555			−0.572773	−	0.819714i	$-0.694132\pi$
$491$	−25.3836			−1.14555			−0.572773	+	0.819714i	$0.694132\pi$
$492$	−4.93686	−	8.55089i	−0.222571	−	0.385504i
$493$	−5.50193	+	9.52963i	−0.247795	+	0.429193i
$494$	−3.68661	+	6.38539i	−0.165868	+	0.287292i
$495$	0.876012	+	1.51730i	0.0393738	+	0.0681975i
$496$	3.05729			0.137277
$497$	19.3585	+	0.193608i	0.868347	+	0.00868451i
$498$	−5.51502			−0.247134
$499$	−0.863781	−	1.49611i	−0.0386682	−	0.0669752i	0.846044	−	0.533114i	$-0.178978\pi$
$499$	−0.863781	−	1.49611i	−0.0386682	−	0.0669752i	−0.884712	+	0.466138i	$0.845645\pi$
$500$	−5.15859	+	8.93495i	−0.230699	+	0.399583i
$501$	−16.6886	+	28.9056i	−0.745594	+	1.29141i
$502$	4.75740	+	8.24006i	0.212333	+	0.367772i
$503$	−12.1723			−0.542736			−0.271368	−	0.962476i	$-0.587476\pi$
$503$	−12.1723			−0.542736			−0.271368	+	0.962476i	$0.587476\pi$
$504$	0.671458	+	1.19033i	0.0299091	+	0.0530217i
$505$	−17.4022			−0.774387
$506$	1.40389	+	2.43161i	0.0624107	+	0.108098i
$507$	10.9476	−	18.9618i	0.486199	−	0.842121i
$508$	3.05547	−	5.29223i	0.135565	−	0.234805i
$509$	10.4585	+	18.1146i	0.463564	+	0.802917i	0.999135	−	0.0415731i	$-0.0132370\pi$
$509$	10.4585	+	18.1146i	0.463564	+	0.802917i	−0.535571	+	0.844490i	$0.679904\pi$
$510$	4.05941			0.179754
$511$	14.3627	−	24.3122i	0.635370	−	1.07551i
$512$	−1.00000			−0.0441942
$513$	14.9203	+	25.8427i	0.658748	+	1.14098i
$514$	−0.986392	+	1.70848i	−0.0435079	+	0.0753578i
$515$	3.13516	−	5.43026i	0.138152	−	0.239286i
$516$	−6.69677	−	11.5991i	−0.294809	−	0.510624i
$517$	−15.3442			−0.674836
$518$	−11.3006	+	19.1288i	−0.496520	+	0.840472i
$519$	2.87546			0.126219
$520$	0.695022	+	1.20381i	0.0304787	+	0.0527907i
$521$	−15.5988	+	27.0179i	−0.683395	+	1.18368i	0.290543	+	0.956862i	$0.406164\pi$
$521$	−15.5988	+	27.0179i	−0.683395	+	1.18368i	−0.973938	+	0.226813i	$0.927169\pi$
$522$	1.58594	−	2.74693i	0.0694147	−	0.120230i
$523$	20.6973	+	35.8488i	0.905030	+	1.56756i	0.820877	+	0.571105i	$0.193485\pi$
$523$	20.6973	+	35.8488i	0.905030	+	1.56756i	0.0841529	+	0.996453i	$0.473182\pi$
$524$	19.8381			0.866631
$525$	8.63100	+	15.3007i	0.376688	+	0.667778i
$526$	24.5723			1.07140
$527$	−2.73934	−	4.74468i	−0.119328	−	0.206681i
$528$	−2.63264	+	4.55987i	−0.114571	+	0.198443i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	3.32661	+	5.76186i	0.144499	+	0.250279i
$531$	5.79762			0.251595
$532$	16.9520	+	0.169540i	0.734963	+	0.00735051i
$533$	−6.05878			−0.262435
$534$	6.47578	+	11.2164i	0.280234	+	0.485380i
$535$	3.30691	−	5.72774i	0.142970	−	0.247632i
$536$	2.31287	−	4.00601i	0.0999007	−	0.173033i
$537$	−14.5162	−	25.1428i	−0.626420	−	1.08499i
$538$	−8.80932			−0.379797
$539$	−10.1657	+	16.8213i	−0.437868	+	0.724547i
$540$	5.62574			0.242093
$541$	1.15817	+	2.00601i	0.0497936	+	0.0862451i	0.889848	−	0.456257i	$-0.150810\pi$
$541$	1.15817	+	2.00601i	0.0497936	+	0.0862451i	−0.840054	+	0.542502i	$0.817477\pi$
$542$	13.3106	−	23.0546i	0.571739	−	0.990281i
$543$	21.9059	−	37.9422i	0.940074	−	1.62826i
$544$	0.896002	+	1.55192i	0.0384158	+	0.0665381i
$545$	4.15107			0.177812
$546$	5.70885	+	0.0570954i	0.244316	+	0.00244346i
$547$	37.5598			1.60594			0.802971	−	0.596018i	$-0.203251\pi$
$547$	37.5598			1.60594			0.802971	+	0.596018i	$0.203251\pi$
$548$	5.42476	+	9.39596i	0.231734	+	0.401375i
$549$	−1.30695	+	2.26370i	−0.0557791	+	0.0966123i
$550$	−4.97083	+	8.60973i	−0.211957	+	0.367120i
$551$	−19.6730	−	34.0746i	−0.838097	−	1.45163i
$552$	−1.87525			−0.0798158
$553$	−20.0018	−	35.4584i	−0.850563	−	1.50784i
$554$	30.7708			1.30733
$555$	−9.51128	−	16.4740i	−0.403731	−	0.699283i
$556$	−0.586816	+	1.01639i	−0.0248865	+	0.0431047i
$557$	14.4642	−	25.0528i	0.612869	−	1.06152i	−0.377885	−	0.925853i	$-0.623349\pi$
$557$	14.4642	−	25.0528i	0.612869	−	1.06152i	0.990754	−	0.135668i	$-0.0433181\pi$
$558$	0.789619	+	1.36766i	0.0334273	+	0.0578977i
$559$	−8.21864			−0.347612
$560$	1.62563	−	2.75175i	0.0686954	−	0.116283i
$561$	9.43542			0.398364
$562$	1.28780	+	2.23053i	0.0543224	+	0.0940892i
$563$	3.93815	−	6.82107i	0.165973	−	0.287474i	−0.771027	−	0.636802i	$-0.780257\pi$
$563$	3.93815	−	6.82107i	0.165973	−	0.287474i	0.937000	+	0.349328i	$0.113590\pi$
$564$	5.12399	−	8.87501i	0.215759	−	0.373705i
$565$	5.11353	+	8.85689i	0.215128	+	0.372612i
$566$	22.4419			0.943305
$567$	13.8378	−	23.4237i	0.581135	−	0.983702i
$568$	−7.31719			−0.307022
$569$	−21.5026	−	37.2437i	−0.901437	−	1.56134i	−0.825629	−	0.564213i	$-0.809180\pi$
$569$	−21.5026	−	37.2437i	−0.901437	−	1.56134i	−0.0758078	−	0.997122i	$-0.524154\pi$
$570$	−7.25751	+	12.5704i	−0.303984	+	0.526515i
$571$	11.5102	−	19.9362i	0.481686	−	0.834304i	−0.518093	−	0.855324i	$-0.673358\pi$
$571$	11.5102	−	19.9362i	0.481686	−	0.834304i	0.999779	+	0.0210199i	$0.00669133\pi$
$572$	1.61546	+	2.79806i	0.0675459	+	0.116993i
$573$	−35.0820			−1.46557
$574$	6.84432	+	12.1333i	0.285677	+	0.506436i
$575$	−3.54075			−0.147659
$576$	−0.258274	−	0.447344i	−0.0107614	−	0.0186393i
$577$	−19.6049	+	33.9566i	−0.816162	+	1.41363i	0.0923288	+	0.995729i	$0.470569\pi$
$577$	−19.6049	+	33.9566i	−0.816162	+	1.41363i	−0.908491	+	0.417905i	$0.862764\pi$
$578$	−6.89436	+	11.9414i	−0.286768	+	0.496696i
$579$	0.00164129	+	0.00284279i	6.82096e−5	+	0.000118142i
$580$	−7.41774			−0.308005
$581$	7.78065	+	0.0778159i	0.322796	+	0.00322835i
$582$	−9.86121			−0.408760
$583$	7.73215	+	13.3925i	0.320233	+	0.554660i
$584$	−5.33643	+	9.24297i	−0.220823	+	0.382477i
$585$	−0.359012	+	0.621827i	−0.0148433	+	0.0257094i
$586$	3.90845	+	6.76964i	0.161457	+	0.279651i
$587$	26.3668			1.08827			0.544136	−	0.838997i	$-0.316857\pi$
$587$	26.3668			1.08827			0.544136	+	0.838997i	$0.316857\pi$
$588$	−6.33468	−	11.4971i	−0.261238	−	0.474131i
$589$	19.5898			0.807185
$590$	−6.77914	−	11.7418i	−0.279093	−	0.483403i
$591$	15.1745	−	26.2830i	0.624196	−	1.08114i
$592$	4.19870	−	7.27237i	0.172566	−	0.298893i
$593$	8.86975	+	15.3629i	0.364237	+	0.630877i	0.988653	−	0.150215i	$-0.0479965\pi$
$593$	8.86975	+	15.3629i	0.364237	+	0.630877i	−0.624417	+	0.781092i	$0.714663\pi$
$594$	13.0761			0.536519
$595$	−5.72706	−	0.0572775i	−0.234787	−	0.00234815i
$596$	−18.8635			−0.772681
$597$	−1.93522	−	3.35189i	−0.0792031	−	0.137184i
$598$	−0.575351	+	0.996537i	−0.0235279	+	0.0407514i
$599$	9.12995	−	15.8135i	0.373039	−	0.646123i	−0.616992	−	0.786969i	$-0.711649\pi$
$599$	9.12995	−	15.8135i	0.373039	−	0.646123i	0.990032	+	0.140846i	$0.0449823\pi$
$600$	−3.31988	−	5.75021i	−0.135534	−	0.234751i
$601$	−25.6197			−1.04505			−0.522524	−	0.852625i	$-0.675009\pi$
$601$	−25.6197			−1.04505			−0.522524	+	0.852625i	$0.675009\pi$
$602$	9.28422	+	16.4587i	0.378397	+	0.670807i
$603$	2.38942			0.0973045
$604$	−0.0249639	−	0.0432387i	−0.00101577	−	0.00175936i
$605$	−1.88226	+	3.26017i	−0.0765248	+	0.132545i
$606$	13.5072	−	23.3952i	0.548694	−	0.950366i
$607$	5.32724	+	9.22706i	0.216226	+	0.374515i	0.953651	−	0.300914i	$-0.0972918\pi$
$607$	5.32724	+	9.22706i	0.216226	+	0.374515i	−0.737425	+	0.675429i	$0.763958\pi$
$608$	−6.40758			−0.259862
$609$	−15.4960	+	26.2306i	−0.627931	+	1.06292i
$610$	6.11284			0.247502
$611$	−3.14422	−	5.44595i	−0.127201	−	0.220319i
$612$	−0.462828	+	0.801642i	−0.0187087	+	0.0324044i
$613$	5.72378	−	9.91387i	0.231181	−	0.400418i	−0.726975	−	0.686664i	$-0.759074\pi$
$613$	5.72378	−	9.91387i	0.231181	−	0.400418i	0.958156	+	0.286247i	$0.0924076\pi$
$614$	9.47059	+	16.4035i	0.382202	+	0.661993i
$615$	−11.9274			−0.480959
$616$	3.77850	−	6.39598i	0.152240	−	0.257701i
$617$	−11.4763			−0.462019			−0.231009	−	0.972952i	$-0.574203\pi$
$617$	−11.4763			−0.462019			−0.231009	+	0.972952i	$0.574203\pi$
$618$	4.86690	+	8.42972i	0.195776	+	0.339093i
$619$	15.6116	−	27.0402i	0.627485	−	1.08684i	−0.360570	−	0.932732i	$-0.617418\pi$
$619$	15.6116	−	27.0402i	0.627485	−	1.08684i	0.988055	−	0.154104i	$-0.0492490\pi$
$620$	1.84660	−	3.19840i	0.0741612	−	0.128451i
$621$	2.32854	+	4.03315i	0.0934412	+	0.161845i
$622$	16.3157			0.654198
$623$	−8.97784	−	15.9156i	−0.359690	−	0.637644i
$624$	−2.15785			−0.0863831
$625$	−2.62030	−	4.53850i	−0.104812	−	0.181540i
$626$	−2.70315	+	4.68200i	−0.108040	+	0.187130i
$627$	−16.8689	+	29.2177i	−0.673678	+	1.16684i
$628$	2.67871	+	4.63967i	0.106892	+	0.185143i
$629$	−15.0482			−0.600011
$630$	1.65083	+	0.0165103i	0.0657708	+	0.000657787i
$631$	−19.9315			−0.793460			−0.396730	−	0.917935i	$-0.629855\pi$
$631$	−19.9315			−0.793460			−0.396730	+	0.917935i	$0.629855\pi$
$632$	7.69362	+	13.3257i	0.306036	+	0.530070i
$633$	15.1433	−	26.2289i	0.601891	−	1.04251i
$634$	6.44054	−	11.1553i	0.255787	−	0.443035i
$635$	−3.69100	−	6.39299i	−0.146473	−	0.253698i
$636$	−10.3282			−0.409540
$637$	−8.05330	−	0.161102i	−0.319084	−	0.00638308i
$638$	−17.2413			−0.682590
$639$	−1.88984	−	3.27330i	−0.0747609	−	0.129490i
$640$	−0.603998	+	1.04616i	−0.0238751	+	0.0413529i
$641$	5.73739	−	9.93744i	0.226613	−	0.392505i	−0.730189	−	0.683245i	$-0.760568\pi$
$641$	5.73739	−	9.93744i	0.226613	−	0.392505i	0.956802	+	0.290740i	$0.0939014\pi$
$642$	5.13352	+	8.89152i	0.202604	+	0.350920i
$643$	8.52588			0.336228			0.168114	−	0.985768i	$-0.446232\pi$
$643$	8.52588			0.336228			0.168114	+	0.985768i	$0.446232\pi$
$644$	2.64562	+	0.0264594i	0.104252	+	0.00104265i
$645$	−16.1793			−0.637061
$646$	5.74120	+	9.94405i	0.225885	+	0.391243i
$647$	−13.1308	+	22.7433i	−0.516226	+	0.894129i	0.483597	+	0.875291i	$0.339330\pi$
$647$	−13.1308	+	22.7433i	−0.516226	+	0.894129i	−0.999823	+	0.0188385i	$0.994003\pi$
$648$	−5.14141	+	8.90519i	−0.201974	+	0.349829i
$649$	−15.7570	−	27.2919i	−0.618516	−	1.07130i
$650$	−4.07434			−0.159809
$651$	−7.45253	−	13.2116i	−0.292088	−	0.517802i
$652$	1.71613			0.0672088
$653$	2.84345	+	4.92500i	0.111273	+	0.192730i	0.916284	−	0.400530i	$-0.131174\pi$
$653$	2.84345	+	4.92500i	0.111273	+	0.192730i	−0.805011	+	0.593260i	$0.797841\pi$
$654$	−3.22198	+	5.58063i	−0.125989	+	0.218220i
$655$	11.9822	−	20.7537i	0.468182	−	0.810915i
$656$	−2.63264	−	4.55987i	−0.102788	−	0.178033i
$657$	−5.51305			−0.215084
$658$	−7.35421	+	12.4487i	−0.286697	+	0.485299i
$659$	−30.9850			−1.20700			−0.603502	−	0.797361i	$-0.706229\pi$
$659$	−30.9850			−1.20700			−0.603502	+	0.797361i	$0.706229\pi$
$660$	3.18022	+	5.50831i	0.123790	+	0.214411i
$661$	21.6785	−	37.5482i	0.843195	−	1.46046i	−0.0439842	−	0.999032i	$-0.514005\pi$
$661$	21.6785	−	37.5482i	0.843195	−	1.46046i	0.887179	−	0.461425i	$-0.152662\pi$
$662$	3.44120	−	5.96033i	0.133746	−	0.231655i
$663$	1.93344	+	3.34881i	0.0750885	+	0.130057i
$664$	−2.94096			−0.114131
$665$	10.4163	−	17.6320i	0.403928	−	0.683741i
$666$	4.33766			0.168081
$667$	−3.07027	−	5.31786i	−0.118881	−	0.205908i
$668$	−8.89944	+	15.4143i	−0.344330	+	0.596397i
$669$	5.46939	−	9.47326i	0.211459	−	0.366258i
$670$	−2.79394	−	4.83924i	−0.107939	−	0.186956i
$671$	14.2083			0.548504
$672$	2.43762	+	4.32132i	0.0940334	+	0.166699i
$673$	−13.5886			−0.523801			−0.261901	−	0.965095i	$-0.584349\pi$
$673$	−13.5886			−0.523801			−0.261901	+	0.965095i	$0.584349\pi$
$674$	−10.1881	−	17.6463i	−0.392432	−	0.679711i
$675$	−8.24477	+	14.2804i	−0.317342	+	0.549652i
$676$	5.83794	−	10.1116i	0.224536	−	0.388908i
$677$	−3.34228	−	5.78900i	−0.128454	−	0.222489i	0.794624	−	0.607102i	$-0.207668\pi$
$677$	−3.34228	−	5.78900i	−0.128454	−	0.222489i	−0.923078	+	0.384613i	$0.874335\pi$
$678$	−15.8761			−0.609718
$679$	13.9123	+	0.139140i	0.533906	+	0.00533970i
$680$	2.16473			0.0830137
$681$	−10.1468	−	17.5747i	−0.388826	−	0.673466i
$682$	4.29211	−	7.43416i	0.164354	−	0.284669i
$683$	−0.0720912	+	0.124866i	−0.00275849	+	0.00477785i	−0.867401	−	0.497609i	$-0.834211\pi$
$683$	−0.0720912	+	0.124866i	−0.00275849	+	0.00477785i	0.864643	+	0.502387i	$0.167545\pi$
$684$	−1.65491	−	2.86639i	−0.0632771	−	0.109599i
$685$	13.1062			0.500761
$686$	8.77482	+	16.3096i	0.335024	+	0.622703i
$687$	31.5516			1.20377
$688$	−3.57114	−	6.18540i	−0.136149	−	0.235816i
$689$	−3.16883	+	5.48858i	−0.120723	+	0.209098i
$690$	−1.13264	+	1.96180i	−0.0431191	+	0.0746844i
$691$	23.8516	+	41.3121i	0.907356	+	1.57159i	0.817723	+	0.575612i	$0.195236\pi$
$691$	23.8516	+	41.3121i	0.907356	+	1.57159i	0.0896330	+	0.995975i	$0.471431\pi$
$692$	1.53338			0.0582904
$693$	3.83709	+	0.0383755i	0.145759	+	0.00145777i
$694$	−34.1799			−1.29745
$695$	0.708871	+	1.22780i	0.0268890	+	0.0465731i
$696$	5.75751	−	9.97230i	0.218238	−	0.377999i
$697$	−4.71771	+	8.17131i	−0.178696	+	0.309511i
$698$	2.50432	+	4.33760i	0.0947898	+	0.164181i
$699$	29.2048			1.10463
$700$	4.60260	+	8.15931i	0.173962	+	0.308393i
$701$	18.6212			0.703313			0.351656	−	0.936129i	$-0.385619\pi$
$701$	18.6212			0.703313			0.351656	+	0.936129i	$0.385619\pi$
$702$	2.67946	+	4.64096i	0.101130	+	0.175162i
$703$	26.9035	−	46.5983i	1.01469	−	1.75749i
$704$	−1.40389	+	2.43161i	−0.0529112	+	0.0916449i
$705$	−6.18976	−	10.7210i	−0.233120	−	0.403775i
$706$	−2.42769			−0.0913673
$707$	−19.3863	+	32.8157i	−0.729096	+	1.23416i
$708$	21.0473			0.791008
$709$	−1.28570	−	2.22689i	−0.0482853	−	0.0836326i	0.840873	−	0.541233i	$-0.182042\pi$
$709$	−1.28570	−	2.22689i	−0.0482853	−	0.0836326i	−0.889158	+	0.457600i	$0.848709\pi$
$710$	−4.41957	+	7.65491i	−0.165863	+	0.287284i
$711$	−3.97412	+	6.88339i	−0.149041	+	0.258147i
$712$	3.45330	+	5.98128i	0.129418	+	0.224158i
$713$	3.05729			0.114497
$714$	4.52224	−	7.65491i	0.169240	−	0.286478i
$715$	3.90294			0.145962
$716$	−7.74096	−	13.4077i	−0.289293	−	0.501071i
$717$	18.3746	−	31.8257i	0.686212	−	1.18855i
$718$	14.6119	−	25.3085i	0.545311	−	0.944506i
$719$	−10.2783	−	17.8025i	−0.383315	−	0.663920i	0.608219	−	0.793769i	$-0.291884\pi$
$719$	−10.2783	−	17.8025i	−0.383315	−	0.663920i	−0.991534	+	0.129849i	$0.958551\pi$
$720$	−0.623988			−0.0232547
$721$	−6.74734	−	11.9614i	−0.251284	−	0.445467i
$722$	−22.0570			−0.820878
$723$	−2.14713	−	3.71894i	−0.0798526	−	0.138309i
$724$	11.6816	−	20.2332i	0.434144	−	0.751960i
$725$	10.8710	−	18.8292i	0.403740	−	0.699299i
$726$	−2.92195	−	5.06097i	−0.108444	−	0.187830i
$727$	36.4761			1.35282			0.676412	−	0.736524i	$-0.263534\pi$
$727$	36.4761			1.35282			0.676412	+	0.736524i	$0.263534\pi$
$728$	3.04432	+	0.0304469i	0.112830	+	0.00112844i
$729$	20.8880			0.773628
$730$	6.44639	+	11.1655i	0.238592	+	0.413253i
$731$	−6.39950	+	11.0843i	−0.236694	+	0.409966i
$732$	−4.74467	+	8.21800i	−0.175368	+	0.303746i
$733$	10.7512	+	18.6217i	0.397106	+	0.687808i	0.993368	−	0.114983i	$-0.0366812\pi$
$733$	10.7512	+	18.6217i	0.397106	+	0.687808i	−0.596262	+	0.802790i	$0.703348\pi$
$734$	35.4439			1.30826
$735$	−15.8539	−	0.317147i	−0.584778	−	0.0116981i
$736$	−1.00000			−0.0368605
$737$	−6.49404	−	11.2480i	−0.239211	−	0.414326i
$738$	1.35989	−	2.35539i	0.0500581	−	0.0867032i
$739$	−13.8368	+	23.9660i	−0.508994	+	0.881604i	0.490951	+	0.871187i	$0.336649\pi$
$739$	−13.8368	+	23.9660i	−0.508994	+	0.881604i	−0.999946	+	0.0104170i	$0.996684\pi$
$740$	−5.07202	−	8.78499i	−0.186451	−	0.322943i
$741$	−13.8266			−0.507932
$742$	14.5711	+	0.145729i	0.534923	+	0.00534988i
$743$	−14.7728			−0.541961			−0.270981	−	0.962585i	$-0.587348\pi$
$743$	−14.7728			−0.541961			−0.270981	+	0.962585i	$0.587348\pi$
$744$	2.86659	+	4.96508i	0.105094	+	0.182029i
$745$	−11.3935	+	19.7342i	−0.417427	+	0.723005i
$746$	17.5738	−	30.4387i	0.643423	−	1.11444i
$747$	−0.759572	−	1.31562i	−0.0277913	−	0.0481359i
$748$	5.03156			0.183972
$749$	−7.11697	−	12.6167i	−0.260049	−	0.461004i
$750$	−19.3473			−0.706462
$751$	19.9319	+	34.5230i	0.727325	+	1.25976i	0.958010	+	0.286735i	$0.0925699\pi$
$751$	19.9319	+	34.5230i	0.727325	+	1.25976i	−0.230685	+	0.973028i	$0.574097\pi$
$752$	2.73243	−	4.73272i	0.0996416	−	0.172584i
$753$	−8.92129	+	15.4521i	−0.325110	+	0.563107i
$754$	−3.53296	−	6.11927i	−0.128663	−	0.222851i
$755$	−0.0603125			−0.00219500
$756$	6.26715	−	10.6086i	0.227934	−	0.385830i
$757$	11.6553			0.423620			0.211810	−	0.977311i	$-0.432064\pi$
$757$	11.6553			0.423620			0.211810	+	0.977311i	$0.432064\pi$
$758$	7.83437	+	13.5695i	0.284557	+	0.492867i
$759$	−2.63264	+	4.55987i	−0.0955590	+	0.165513i
$760$	−3.87016	+	6.70332i	−0.140386	+	0.243155i
$761$	3.78727	+	6.55975i	0.137288	+	0.237791i	0.926469	−	0.376370i	$-0.122828\pi$
$761$	3.78727	+	6.55975i	0.137288	+	0.237791i	−0.789181	+	0.614161i	$0.789495\pi$
$762$	11.4595			0.415135
$763$	4.62434	−	7.82775i	0.167413	−	0.283384i
$764$	−18.7079			−0.676829
$765$	0.559094	+	0.968380i	0.0202141	+	0.0350118i
$766$	17.0699	−	29.5659i	0.616759	−	1.06826i
$767$	6.45761	−	11.1849i	0.233171	−	0.403864i
$768$	−0.937623	−	1.62401i	−0.0338336	−	0.0586014i
$769$	52.1816			1.88172			0.940858	−	0.338801i	$-0.110021\pi$
$769$	52.1816			1.88172			0.940858	+	0.338801i	$0.110021\pi$
$770$	−4.40898	−	7.81606i	−0.158888	−	0.281671i

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.937623 + 1.62401i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.603998 + 1.04616i) q^{5} -1.87525 q^{6} +(2.64562 + 0.0264594i) q^{7} -1.00000 q^{8} +(-0.258274 - 0.447344i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.937623 + 1.62401i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.603998 + 1.04616i) q^{5} -1.87525 q^{6} +(2.64562 + 0.0264594i) q^{7} -1.00000 q^{8} +(-0.258274 - 0.447344i) q^{9} +(-0.603998 + 1.04616i) q^{10} +(-1.40389 + 2.43161i) q^{11} +(-0.937623 - 1.62401i) q^{12} -1.15070 q^{13} +(1.29990 + 2.30440i) q^{14} -2.26529 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.896002 + 1.55192i) q^{17} +(0.258274 - 0.447344i) q^{18} +(-3.20379 - 5.54912i) q^{19} -1.20800 q^{20} +(-2.52356 + 4.27170i) q^{21} -2.80779 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.937623 - 1.62401i) q^{24} +(1.77037 - 3.06638i) q^{25} +(-0.575351 - 0.996537i) q^{26} -4.65708 q^{27} +(-1.34572 + 2.27794i) q^{28} +6.14054 q^{29} +(-1.13264 - 1.96180i) q^{30} +(-1.52865 + 2.64769i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.63264 - 4.55987i) q^{33} -1.79200 q^{34} +(1.57027 + 2.78371i) q^{35} +0.516548 q^{36} +(4.19870 + 7.27237i) q^{37} +(3.20379 - 5.54912i) q^{38} +(1.07892 - 1.86875i) q^{39} +(-0.603998 - 1.04616i) q^{40} +5.26529 q^{41} +(-4.96119 - 0.0496178i) q^{42} +7.14229 q^{43} +(-1.40389 - 2.43161i) q^{44} +(0.311994 - 0.540389i) q^{45} +(0.500000 - 0.866025i) q^{46} +(2.73243 + 4.73272i) q^{47} +1.87525 q^{48} +(6.99860 + 0.140003i) q^{49} +3.54075 q^{50} +(-1.68022 - 2.91023i) q^{51} +(0.575351 - 0.996537i) q^{52} +(2.75382 - 4.76976i) q^{53} +(-2.32854 - 4.03315i) q^{54} -3.39179 q^{55} +(-2.64562 - 0.0264594i) q^{56} +12.0158 q^{57} +(3.07027 + 5.31786i) q^{58} +(-5.61189 + 9.72008i) q^{59} +(1.13264 - 1.96180i) q^{60} +(-2.53016 - 4.38236i) q^{61} -3.05729 q^{62} +(-0.671458 - 1.19033i) q^{63} +1.00000 q^{64} +(-0.695022 - 1.20381i) q^{65} +(2.63264 - 4.55987i) q^{66} +(-2.31287 + 4.00601i) q^{67} +(-0.896002 - 1.55192i) q^{68} +1.87525 q^{69} +(-1.62563 + 2.75175i) q^{70} +7.31719 q^{71} +(0.258274 + 0.447344i) q^{72} +(5.33643 - 9.24297i) q^{73} +(-4.19870 + 7.27237i) q^{74} +(3.31988 + 5.75021i) q^{75} +6.40758 q^{76} +(-3.77850 + 6.39598i) q^{77} +2.15785 q^{78} +(-7.69362 - 13.3257i) q^{79} +(0.603998 - 1.04616i) q^{80} +(5.14141 - 8.90519i) q^{81} +(2.63264 + 4.55987i) q^{82} +2.94096 q^{83} +(-2.43762 - 4.32132i) q^{84} -2.16473 q^{85} +(3.57114 + 6.18540i) q^{86} +(-5.75751 + 9.97230i) q^{87} +(1.40389 - 2.43161i) q^{88} +(-3.45330 - 5.98128i) q^{89} +0.623988 q^{90} +(-3.04432 - 0.0304469i) q^{91} +1.00000 q^{92} +(-2.86659 - 4.96508i) q^{93} +(-2.73243 + 4.73272i) q^{94} +(3.87016 - 6.70332i) q^{95} +(0.937623 + 1.62401i) q^{96} +5.25862 q^{97} +(3.37805 + 6.13097i) q^{98} +1.45036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

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