LMFDB - Embedded newform 322.2.e.c.93.2

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			93.2
Root			$-1.54162 - 1.88572i$ of defining polynomial
Character	$\chi$	$=$	322.93
Dual form			322.2.e.c.277.2

$q$-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} +(-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} + 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}+ \cdots - 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

Character values

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

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

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	−0.998828	−	0.0484086i	$-0.984585\pi$
$3$	−0.937623	−	1.62401i	−0.541337	−	0.937623i	0.457491	−	0.889214i	$-0.348748\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.603998	−	1.04616i	0.270116	−	0.467855i	−0.698775	−	0.715341i	$-0.746271\pi$
$5$	0.603998	−	1.04616i	0.270116	−	0.467855i	0.968891	+	0.247486i	$0.0796046\pi$
$6$	−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	0.572969	−	0.819577i	$-0.305791\pi$
$11$	−1.40389	−	2.43161i	−0.423290	−	0.733159i	−0.996259	+	0.0864176i	$0.972458\pi$
$12$	−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	0.736673	−	0.676249i	$-0.236396\pi$
$17$	−0.896002	−	1.55192i	−0.217312	−	0.376396i	−0.953985	+	0.299853i	$0.903062\pi$
$18$	0.258274	+	0.447344i	0.0608758	+	0.105440i
$19$	−3.20379	+	5.54912i	−0.734999	+	1.27306i	0.219724	+	0.975562i	$0.429484\pi$
$19$	−3.20379	+	5.54912i	−0.734999	+	1.27306i	−0.954724	+	0.297494i	$0.903849\pi$
$20$	−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	0.695469	−	0.718556i	$-0.255197\pi$
$31$	−1.52865	−	2.64769i	−0.274553	−	0.475540i	−0.970022	+	0.243016i	$0.921863\pi$
$32$	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	−0.281489	−	0.959565i	$-0.590828\pi$
$37$	4.19870	−	7.27237i	0.690263	−	1.19557i	0.971752	−	0.236006i	$-0.0758384\pi$
$38$	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	−0.594983	−	0.803738i	$-0.702841\pi$
$47$	2.73243	−	4.73272i	0.398567	−	0.690338i	0.993549	+	0.113401i	$0.0361744\pi$
$48$	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	0.990810	−	0.135259i	$-0.0431868\pi$
$53$	2.75382	+	4.76976i	0.378267	+	0.655178i	−0.612543	+	0.790437i	$0.709853\pi$
$54$	−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	−0.956625	−	0.291323i	$-0.905904\pi$
$59$	−5.61189	−	9.72008i	−0.730606	−	1.26545i	0.226019	−	0.974123i	$-0.427429\pi$
$60$	1.13264	+	1.96180i	0.146224	+	0.253267i
$61$	−2.53016	+	4.38236i	−0.323953	+	0.561104i	−0.981300	−	0.192485i	$-0.938345\pi$
$61$	−2.53016	+	4.38236i	−0.323953	+	0.561104i	0.657347	+	0.753588i	$0.271679\pi$
$62$	−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	0.689453	−	0.724330i	$-0.257851\pi$
$67$	−2.31287	−	4.00601i	−0.282562	−	0.489412i	−0.972015	+	0.234919i	$0.924518\pi$
$68$	−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	0.988621	+	0.150425i	$0.0480641\pi$
$73$	5.33643	+	9.24297i	0.624582	+	1.08181i	−0.364039	+	0.931384i	$0.618603\pi$
$74$	−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	0.000850067		1.00000i	$0.499729\pi$
$79$	−7.69362	+	13.3257i	−0.865600	+	1.49926i	−0.866450	+	0.499264i	$0.833604\pi$
$80$	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	−0.988944	−	0.148290i	$-0.952623\pi$
$89$	−3.45330	+	5.98128i	−0.366049	+	0.634015i	0.622895	+	0.782305i	$0.285956\pi$
$90$	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	−0.962294	−	0.272013i	$-0.912311\pi$
$101$	−7.20291	−	12.4758i	−0.716717	−	1.24139i	0.245577	−	0.969377i	$-0.421023\pi$
$102$	1.68022	+	2.91023i	0.166367	+	0.288156i
$103$	−2.59534	+	4.49526i	−0.255727	+	0.442931i	−0.965093	−	0.261909i	$-0.915648\pi$
$103$	−2.59534	+	4.49526i	−0.255727	+	0.442931i	0.709366	+	0.704840i	$0.248981\pi$
$104$	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	−0.967471	−	0.252983i	$-0.918588\pi$
$107$	−2.73752	+	4.74152i	−0.264646	+	0.458380i	0.702825	+	0.711363i	$0.251922\pi$
$108$	2.32854	+	4.03315i	0.224064	+	0.388090i
$109$	1.71816	+	2.97594i	0.164570	+	0.285044i	0.936503	−	0.350661i	$-0.114043\pi$
$109$	1.71816	+	2.97594i	0.164570	+	0.285044i	−0.771932	+	0.635705i	$0.780710\pi$
$110$	−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	−0.00121169	+	0.999999i	$0.500386\pi$
$131$	−9.91904	+	17.1803i	−0.866631	+	1.50105i	−0.865419	+	0.501049i	$0.832948\pi$
$132$	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	0.999131	−	0.0416814i	$-0.0132714\pi$
$137$	5.42476	+	9.39596i	0.463468	+	0.802751i	−0.535663	+	0.844432i	$0.679938\pi$
$138$	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	−0.163408	−	0.986559i	$-0.552249\pi$
$149$	9.43177	−	16.3363i	0.772681	−	1.33832i	0.936089	−	0.351764i	$-0.114418\pi$
$150$	−3.31988	−	5.75021i	−0.271067	−	0.469503i
$151$	−0.0249639	−	0.0432387i	−0.00203153	−	0.00351872i	0.865008	−	0.501758i	$-0.167313\pi$
$151$	−0.0249639	−	0.0432387i	−0.00203153	−	0.00351872i	−0.867039	+	0.498240i	$0.833980\pi$
$152$	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	0.952896	−	0.303297i	$-0.0980876\pi$
$157$	2.67871	+	4.63967i	0.213785	+	0.370286i	−0.739111	+	0.673583i	$0.764754\pi$
$158$	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	−0.897672	−	0.440665i	$-0.854743\pi$
$163$	−0.858064	+	1.48621i	−0.0672088	+	0.116409i	0.830463	+	0.557074i	$0.188076\pi$
$164$	−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	−0.893698	−	0.448669i	$-0.851898\pi$
$173$	−0.766690	+	1.32795i	−0.0582904	+	0.100962i	0.835408	+	0.549631i	$0.185232\pi$
$174$	−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	−0.995642	−	0.0932601i	$-0.970271\pi$
$179$	−7.74096	−	13.4077i	−0.578587	−	1.00214i	0.417055	−	0.908881i	$-0.363062\pi$
$180$	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	−0.299101	−	0.954221i	$-0.596687\pi$
$191$	9.35397	−	16.2015i	0.676829	−	1.17230i	0.975931	−	0.218081i	$-0.0699798\pi$
$192$	−0.937623	−	1.62401i	−0.0676671	−	0.117203i
$193$	0.000875238		0.00151596i	6.30010e−5		0.000109121i	0.866057	−	0.499945i	$-0.166647\pi$
$193$	0.000875238		0.00151596i	6.30010e−5		0.000109121i	−0.865994	+	0.500055i	$0.833313\pi$
$194$	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	0.827127	−	0.562014i	$-0.189973\pi$
$199$	−1.03198	−	1.78744i	−0.0731551	−	0.126708i	−0.900283	+	0.435306i	$0.856640\pi$
$200$	−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	0.628682	−	0.777663i	$-0.283595\pi$
$227$	−5.41091	−	9.37197i	−0.359135	−	0.622039i	−0.987816	+	0.155623i	$0.950261\pi$
$228$	−6.00789	−	10.4060i	−0.397882	−	0.689152i
$229$	−8.41266	+	14.5712i	−0.555924	+	0.962889i	0.441907	+	0.897061i	$0.354302\pi$
$229$	−8.41266	+	14.5712i	−0.555924	+	0.962889i	−0.997831	+	0.0658279i	$0.979031\pi$
$230$	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	0.489793	+	0.871839i	$0.337072\pi$
$233$	−7.78692	+	13.4873i	−0.510138	+	0.883585i	−0.999931	+	0.0117464i	$0.996261\pi$
$234$	−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	0.826789	−	0.562512i	$-0.190165\pi$
$241$	−1.14498	−	1.98317i	−0.0737550	−	0.127747i	−0.900544	+	0.434765i	$0.856832\pi$
$242$	−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	−0.833620	−	0.552339i	$-0.813736\pi$
$257$	0.986392	−	1.70848i	0.0615294	−	0.106572i	0.895149	+	0.445767i	$0.147069\pi$
$258$	−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	0.944073	+	0.329737i	$0.106960\pi$
$263$	12.2862	+	21.2802i	0.757597	+	1.31220i	−0.186476	+	0.982459i	$0.559707\pi$
$264$	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	0.699933	−	0.714209i	$-0.253213\pi$
$269$	−4.40466	−	7.62909i	−0.268557	−	0.465154i	−0.968489	+	0.249055i	$0.919880\pi$
$270$	2.81287	+	4.87203i	0.171186	+	0.296502i
$271$	−13.3106	+	23.0546i	−0.808561	+	1.40047i	0.105300	+	0.994441i	$0.466420\pi$
$271$	−13.3106	+	23.0546i	−0.808561	+	1.40047i	−0.913861	+	0.406028i	$0.866913\pi$
$272$	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	0.792491	+	0.609884i	$0.208784\pi$
$277$	15.3854	+	26.6483i	0.924420	+	1.60114i	0.131929	+	0.991259i	$0.457883\pi$
$278$	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	0.978734	+	0.205133i	$0.0657627\pi$
$283$	11.2210	+	19.4353i	0.667017	+	1.15531i	−0.311717	+	0.950175i	$0.600904\pi$
$284$	−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	0.999089	−	0.0426738i	$-0.0135876\pi$
$311$	8.15783	+	14.1298i	0.462588	+	0.801226i	−0.536501	+	0.843900i	$0.680254\pi$
$312$	−1.07892	−	1.86875i	−0.0610821	−	0.105797i
$313$	2.70315	−	4.68200i	0.152791	−	0.264642i	−0.779461	−	0.626450i	$-0.784507\pi$
$313$	2.70315	−	4.68200i	0.152791	−	0.264642i	0.932253	+	0.361808i	$0.117840\pi$
$314$	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	−0.988247	−	0.152867i	$-0.951149\pi$
$317$	−6.44054	+	11.1553i	−0.361737	+	0.626546i	0.626510	+	0.779413i	$0.284483\pi$
$318$	−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	−0.944966	−	0.327170i	$-0.893905\pi$
$331$	−3.44120	+	5.96033i	−0.189145	+	0.327609i	0.755820	+	0.654779i	$0.227238\pi$
$332$	−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	−0.803292	−	0.595585i	$-0.796920\pi$
$347$	−17.0900	−	29.6007i	−0.917438	−	1.58905i	−0.114146	−	0.993464i	$-0.536413\pi$
$348$	−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	0.831913	−	0.554906i	$-0.187246\pi$
$353$	−1.21385	−	2.10244i	−0.0646065	−	0.111902i	−0.896519	+	0.443005i	$0.853913\pi$
$354$	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	0.165727	+	0.986172i	$0.447003\pi$
$359$	−14.6119	+	25.3085i	−0.771186	+	1.33573i	−0.936913	+	0.349562i	$0.886330\pi$
$360$	−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	0.791435	+	0.611254i	$0.209334\pi$
$367$	17.7220	+	30.6953i	0.925078	+	1.60228i	0.133644	+	0.991029i	$0.457332\pi$
$368$	−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	−0.0957896	+	0.995402i	$0.530538\pi$
$373$	−17.5738	+	30.4387i	−0.909938	+	1.57606i	−0.814148	+	0.580657i	$0.802796\pi$
$374$	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	−0.0125428	+	0.999921i	$0.503993\pi$
$383$	−17.0699	+	29.5659i	−0.872229	+	1.51074i	−0.859686	+	0.510823i	$0.829341\pi$
$384$	−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	0.818339	−	0.574736i	$-0.194895\pi$
$389$	−1.74681	−	3.02556i	−0.0885667	−	0.153402i	−0.906906	+	0.421334i	$0.861562\pi$
$390$	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	−0.699516	−	0.714617i	$-0.746601\pi$
$397$	5.36214	−	9.28750i	0.269118	−	0.466126i	0.968634	+	0.248490i	$0.0799345\pi$
$398$	−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	−0.105460	−	0.994424i	$-0.533631\pi$
$401$	16.1895	−	28.0411i	0.808466	−	1.40030i	0.913926	−	0.405881i	$-0.133035\pi$
$402$	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	0.924429	−	0.381355i	$-0.124542\pi$
$409$	2.66855	+	4.62206i	0.131951	+	0.228546i	−0.792477	+	0.609901i	$0.791209\pi$
$410$	−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	0.966088	−	0.258211i	$-0.0831331\pi$
$431$	5.38584	+	9.32854i	0.259427	+	0.449340i	−0.706662	+	0.707551i	$0.749800\pi$
$432$	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	0.258122	−	0.966112i	$-0.416896\pi$
$439$	20.2345	−	35.0471i	0.965739	−	1.67271i	0.707617	−	0.706597i	$-0.249770\pi$
$440$	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	−0.991094	−	0.133163i	$-0.957487\pi$
$443$	−8.00281	+	13.8613i	−0.380225	+	0.658569i	0.610869	+	0.791731i	$0.290820\pi$
$444$	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	−0.0754253	−	0.997151i	$-0.524031\pi$
$457$	17.6546	−	30.5786i	0.825846	−	1.43041i	0.901271	−	0.433255i	$-0.142635\pi$
$458$	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	−0.000877424	−	1.00000i	$-0.500279\pi$
$467$	18.7055	−	32.3988i	0.865586	−	1.49924i	0.866464	−	0.499240i	$-0.166387\pi$
$468$	−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	0.888062	−	0.459723i	$-0.152051\pi$
$479$	1.00456	+	1.73995i	0.0458994	+	0.0795002i	−0.842163	+	0.539223i	$0.818718\pi$
$480$	−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	−0.878800	−	0.477191i	$-0.841655\pi$
$487$	−18.8166	−	32.5912i	−0.852659	−	1.47685i	0.0261402	−	0.999658i	$-0.491678\pi$
$488$	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	−0.884712	−	0.466138i	$-0.845645\pi$
$499$	−0.863781	+	1.49611i	−0.0386682	+	0.0669752i	0.846044	+	0.533114i	$0.178978\pi$
$500$	−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	−0.535571	−	0.844490i	$-0.679904\pi$
$509$	10.4585	−	18.1146i	0.463564	−	0.802917i	0.999135	+	0.0415731i	$0.0132370\pi$
$510$	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	−0.973938	−	0.226813i	$-0.927169\pi$
$521$	−15.5988	−	27.0179i	−0.683395	−	1.18368i	0.290543	−	0.956862i	$-0.406164\pi$
$522$	1.58594	+	2.74693i	0.0694147	+	0.120230i
$523$	20.6973	−	35.8488i	0.905030	−	1.56756i	0.0841529	−	0.996453i	$-0.473182\pi$
$523$	20.6973	−	35.8488i	0.905030	−	1.56756i	0.820877	−	0.571105i	$-0.193485\pi$
$524$	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	−0.840054	−	0.542502i	$-0.817477\pi$
$541$	1.15817	−	2.00601i	0.0497936	−	0.0862451i	0.889848	+	0.456257i	$0.150810\pi$
$542$	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	0.990754	+	0.135668i	$0.0433181\pi$
$557$	14.4642	+	25.0528i	0.612869	+	1.06152i	−0.377885	+	0.925853i	$0.623349\pi$
$558$	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	0.937000	−	0.349328i	$-0.113590\pi$
$563$	3.93815	+	6.82107i	0.165973	+	0.287474i	−0.771027	+	0.636802i	$0.780257\pi$
$564$	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	−0.0758078	+	0.997122i	$0.524154\pi$
$569$	−21.5026	+	37.2437i	−0.901437	+	1.56134i	−0.825629	+	0.564213i	$0.809180\pi$
$570$	−7.25751	−	12.5704i	−0.303984	−	0.526515i
$571$	11.5102	+	19.9362i	0.481686	+	0.834304i	0.999779	−	0.0210199i	$-0.00669133\pi$
$571$	11.5102	+	19.9362i	0.481686	+	0.834304i	−0.518093	+	0.855324i	$0.673358\pi$
$572$	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	−0.908491	−	0.417905i	$-0.862764\pi$
$577$	−19.6049	−	33.9566i	−0.816162	−	1.41363i	0.0923288	−	0.995729i	$-0.470569\pi$
$578$	−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	−0.624417	−	0.781092i	$-0.714663\pi$
$593$	8.86975	−	15.3629i	0.364237	−	0.630877i	0.988653	+	0.150215i	$0.0479965\pi$
$594$	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	0.990032	−	0.140846i	$-0.0449823\pi$
$599$	9.12995	+	15.8135i	0.373039	+	0.646123i	−0.616992	+	0.786969i	$0.711649\pi$
$600$	−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	−0.737425	−	0.675429i	$-0.763958\pi$
$607$	5.32724	−	9.22706i	0.216226	−	0.374515i	0.953651	+	0.300914i	$0.0972918\pi$
$608$	−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	0.958156	−	0.286247i	$-0.0924076\pi$
$613$	5.72378	+	9.91387i	0.231181	+	0.400418i	−0.726975	+	0.686664i	$0.759074\pi$
$614$	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	0.988055	+	0.154104i	$0.0492490\pi$
$619$	15.6116	+	27.0402i	0.627485	+	1.08684i	−0.360570	+	0.932732i	$0.617418\pi$
$620$	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	0.956802	−	0.290740i	$-0.0939014\pi$
$641$	5.73739	+	9.93744i	0.226613	+	0.392505i	−0.730189	+	0.683245i	$0.760568\pi$
$642$	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	−0.999823	−	0.0188385i	$-0.994003\pi$
$647$	−13.1308	−	22.7433i	−0.516226	−	0.894129i	0.483597	−	0.875291i	$-0.339330\pi$
$648$	−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	−0.805011	−	0.593260i	$-0.797841\pi$
$653$	2.84345	−	4.92500i	0.111273	−	0.192730i	0.916284	+	0.400530i	$0.131174\pi$
$654$	−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	0.887179	+	0.461425i	$0.152662\pi$
$661$	21.6785	+	37.5482i	0.843195	+	1.46046i	−0.0439842	+	0.999032i	$0.514005\pi$
$662$	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	−0.923078	−	0.384613i	$-0.874335\pi$
$677$	−3.34228	+	5.78900i	−0.128454	+	0.222489i	0.794624	+	0.607102i	$0.207668\pi$
$678$	−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	0.864643	−	0.502387i	$-0.167545\pi$
$683$	−0.0720912	−	0.124866i	−0.00275849	−	0.00477785i	−0.867401	+	0.497609i	$0.834211\pi$
$684$	−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	0.0896330	−	0.995975i	$-0.471431\pi$
$691$	23.8516	−	41.3121i	0.907356	−	1.57159i	0.817723	−	0.575612i	$-0.195236\pi$
$692$	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	−0.889158	−	0.457600i	$-0.848709\pi$
$709$	−1.28570	+	2.22689i	−0.0482853	+	0.0836326i	0.840873	+	0.541233i	$0.182042\pi$
$710$	−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	−0.991534	−	0.129849i	$-0.958551\pi$
$719$	−10.2783	+	17.8025i	−0.383315	+	0.663920i	0.608219	+	0.793769i	$0.291884\pi$
$720$	−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	−0.596262	−	0.802790i	$-0.703348\pi$
$733$	10.7512	−	18.6217i	0.397106	−	0.687808i	0.993368	+	0.114983i	$0.0366812\pi$
$734$	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	−0.999946	−	0.0104170i	$-0.996684\pi$
$739$	−13.8368	−	23.9660i	−0.508994	−	0.881604i	0.490951	−	0.871187i	$-0.336649\pi$
$740$	−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	−0.230685	−	0.973028i	$-0.574097\pi$
$751$	19.9319	−	34.5230i	0.727325	−	1.25976i	0.958010	−	0.286735i	$-0.0925699\pi$
$752$	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	−0.789181	−	0.614161i	$-0.789495\pi$
$761$	3.78727	−	6.55975i	0.137288	−	0.237791i	0.926469	+	0.376370i	$0.122828\pi$
$762$	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
$771$	−3.69945			−0.133233
$772$	0.000875238	−	0.00151596i	3.15005e−5	−	5.45605e-5i
$773$	−16.3542	−	28.3264i	−0.588221	−	1.01883i	−0.994465	−	0.105065i	$-0.966495\pi$
$773$	−16.3542	−	28.3264i	−0.588221	−	1.01883i	0.406244	−	0.913765i	$-0.366838\pi$
$774$	1.84467	+	3.19506i	0.0663052	+	0.114844i
$775$	5.41255	−	9.37481i	0.194425	−	0.336753i
$776$	−5.25862			−0.188774
$777$	−41.6611	+	0.416661i	−1.49458	+	0.0149476i
$778$	−3.49362			−0.125252
$779$	−16.8689	+	29.2177i	−0.604390	+	1.04683i
$780$	−1.30334	−	2.25745i	−0.0466669	−	0.0808295i
$781$	−10.2725	−	17.7926i	−0.367581	−	0.636668i
$782$	0.896002	−	1.55192i	0.0320410	−	0.0554966i
$783$	−28.5970			−1.02197
$784$	−3.37805	+	6.13097i	−0.120645	+	0.218963i
$785$	6.47175			0.230987
$786$	18.6006	−	32.2173i	0.663463	−	1.14915i
$787$	14.5071	+	25.1271i	0.517123	+	0.895684i	0.999802	+	0.0198863i	$0.00633042\pi$
$787$	14.5071	+	25.1271i	0.517123	+	0.895684i	−0.482679	+	0.875797i	$0.660336\pi$
$788$	8.09201	+	14.0158i	0.288266	+	0.499291i
$789$	23.0396	−	39.9057i	0.820230	−	1.42068i
$790$	18.5877			0.661322
$791$	22.3982	−	0.224009i	0.796387	−	0.00796483i
$792$	−1.45036			−0.0515362
$793$	2.91146	−	5.04279i	0.103389	−	0.179075i
$794$	−5.36214	−	9.28750i	−0.190295	−	0.329601i
$795$	−6.23821	−	10.8049i	−0.221247	−	0.383210i
$796$	−1.03198	+	1.78744i	−0.0365775	+	0.0633542i
$797$	7.06899			0.250397			0.125198	−	0.992132i	$-0.460043\pi$
$797$	7.06899			0.250397			0.125198	+	0.992132i	$0.460043\pi$
$798$	15.6193	−	27.6892i	0.552916	−	0.980187i
$799$	−9.79307			−0.346454
$800$	−1.77037	+	3.06638i	−0.0625921	+	0.108413i
$801$	−1.78379	−	3.08962i	−0.0630272	−	0.109166i
$802$	−16.1895	−	28.0411i	−0.571672	−	0.990165i
$803$	14.9836	−	25.9523i	0.528758	−	0.915836i
$804$	8.67440			0.305922
$805$	1.62563	+	2.75175i	0.0572959	+	0.0969863i
$806$	3.51803			0.123917
$807$	−8.25982	+	14.3064i	−0.290759	+	0.503610i
$808$	7.20291	+	12.4758i	0.253398	+	0.438897i
$809$	1.39449	+	2.41533i	0.0490278	+	0.0849186i	0.889498	−	0.456939i	$-0.151054\pi$
$809$	1.39449	+	2.41533i	0.0490278	+	0.0849186i	−0.840470	+	0.541858i	$0.817721\pi$
$810$	6.21080	−	10.7574i	0.218225	−	0.377977i
$811$	55.0611			1.93346			0.966729	−	0.255804i	$-0.0823403\pi$
$811$	55.0611			1.93346			0.966729	+	0.255804i	$0.0823403\pi$
$812$	−8.26347	−	13.9878i	−0.289991	−	0.490875i
$813$	49.9213			1.75082
$814$	−11.7891	+	20.4193i	−0.413206	+	0.715695i
$815$	1.03654	+	1.79534i	0.0363083	+	0.0628879i
$816$	−1.68022	−	2.91023i	−0.0588196	−	0.101879i
$817$	−22.8824	+	39.6334i	−0.800553	+	1.38660i
$818$	5.33710			0.186607
$819$	0.772648	−	1.36972i	0.0269985	−	0.0478619i
$820$	−6.36045			−0.222117
$821$	9.92476	−	17.1902i	0.346376	−	0.599942i	−0.639226	−	0.769019i	$-0.720745\pi$
$821$	9.92476	−	17.1902i	0.346376	−	0.599942i	0.985603	+	0.169077i	$0.0540787\pi$
$822$	−10.1728	−	17.6197i	−0.354816	−	0.614559i
$823$	11.1825	+	19.3687i	0.389798	+	0.675149i	0.992422	−	0.122876i	$-0.0392116\pi$
$823$	11.1825	+	19.3687i	0.389798	+	0.675149i	−0.602624	+	0.798025i	$0.705878\pi$
$824$	2.59534	−	4.49526i	0.0904130	−	0.156600i
$825$	−18.6431			−0.649068
$826$	−29.6938	+	0.296974i	−1.03318	+	0.0103331i
$827$	−46.7107			−1.62429			−0.812146	−	0.583454i	$-0.801701\pi$
$827$	−46.7107			−1.62429			−0.812146	+	0.583454i	$0.801701\pi$
$828$	−0.258274	+	0.447344i	−0.00897564	+	0.0155463i
$829$	−26.9529	−	46.6837i	−0.936111	−	1.62139i	−0.772640	−	0.634844i	$-0.781064\pi$
$829$	−26.9529	−	46.6837i	−0.936111	−	1.62139i	−0.163471	−	0.986548i	$-0.552269\pi$
$830$	−1.77633	−	3.07670i	−0.0616574	−	0.106794i
$831$	28.8514	−	49.9722i	1.00085	−	1.73352i
$832$	−1.15070			−0.0398934
$833$	−6.48803	−	10.7358i	−0.224797	−	0.371975i
$834$	−2.20085			−0.0762091
$835$	10.7505	−	18.6204i	0.372036	−	0.644385i
$836$	−8.99555	−	15.5808i	−0.311118	−	0.538872i
$837$	7.11904	+	12.3305i	0.246070	+	0.426206i
$838$	−7.83135	+	13.5643i	−0.270529	+	0.468571i
$839$	−31.1784			−1.07640			−0.538199	−	0.842818i	$-0.680895\pi$
$839$	−31.1784			−1.07640			−0.538199	+	0.842818i	$0.680895\pi$
$840$	5.99309	−	0.0599382i	0.206781	−	0.00206806i
$841$	8.70618			0.300213
$842$	−12.2551	+	21.2264i	−0.422337	+	0.731509i
$843$	−2.41493	−	4.18279i	−0.0831748	−	0.144063i
$844$	8.07535	+	13.9869i	0.277965	+	0.481450i
$845$	−7.05221	+	12.2148i	−0.242603	+	0.420201i
$846$	2.82287			0.0970522
$847$	4.05091	−	7.18130i	0.139191	−	0.246752i
$848$	−5.50765			−0.189133
$849$	21.0421	−	36.4460i	0.722162	−	1.25082i
$850$	−3.17252	−	5.49496i	−0.108816	−	0.188475i
$851$	4.19870	+	7.27237i	0.143930	+	0.249294i
$852$	−6.86076	+	11.8832i	−0.235046	+	0.407111i
$853$	−36.5851			−1.25265			−0.626325	−	0.779562i	$-0.715441\pi$
$853$	−36.5851			−1.25265			−0.626325	+	0.779562i	$0.715441\pi$
$854$	6.80978	+	11.5271i	0.233026	+	0.394449i
$855$	−3.99825			−0.136737
$856$	2.73752	−	4.74152i	0.0935664	−	0.162062i
$857$	−18.0294	−	31.2278i	−0.615872	−	1.06672i	−0.990231	−	0.139438i	$-0.955470\pi$
$857$	−18.0294	−	31.2278i	−0.615872	−	1.06672i	0.374359	−	0.927284i	$-0.377863\pi$
$858$	−3.02939	−	5.24706i	−0.103422	−	0.179132i
$859$	−3.52722	+	6.10932i	−0.120347	+	0.208447i	−0.919905	−	0.392142i	$-0.871734\pi$
$859$	−3.52722	+	6.10932i	−0.120347	+	0.208447i	0.799557	+	0.600590i	$0.205067\pi$
$860$	−8.62785			−0.294207
$861$	−13.2873	−	22.4918i	−0.452830	−	0.766517i
$862$	10.7717			0.366885
$863$	10.5274	−	18.2339i	0.358355	−	0.620690i	−0.629331	−	0.777137i	$-0.716671\pi$
$863$	10.5274	−	18.2339i	0.358355	−	0.620690i	0.987686	+	0.156448i	$0.0500043\pi$
$864$	−2.32854	−	4.03315i	−0.0792186	−	0.137211i
$865$	0.926158	+	1.60415i	0.0314903	+	0.0545428i
$866$	−3.40898	+	5.90452i	−0.115842	+	0.200644i
$867$	−25.8572			−0.878158
$868$	−3.97416	+	7.04524i	−0.134892	+	0.239131i
$869$	43.2041			1.46560
$870$	−6.95505	+	12.0465i	−0.235798	+	0.408414i
$871$	2.66142	+	4.60972i	0.0901789	+	0.156194i
$872$	−1.71816	−	2.97594i	−0.0581843	−	0.100778i
$873$	−1.35817	+	2.35241i	−0.0459669	+	0.0796171i
$874$	−6.40758			−0.216739
$875$	27.2953	−	0.272986i	0.922751	−	0.00922862i
$876$	−20.0142			−0.676219
$877$	−27.0233	+	46.8057i	−0.912511	+	1.58051i	−0.102005	+	0.994784i	$0.532526\pi$
$877$	−27.0233	+	46.8057i	−0.912511	+	1.58051i	−0.810506	+	0.585731i	$0.800808\pi$
$878$	−20.2345	−	35.0471i	−0.682881	−	1.18278i
$879$	−7.32931	−	12.6947i	−0.247211	−	0.428183i
$880$	1.69590	−	2.93738i	0.0571687	−	0.0990191i
$881$	−12.9926			−0.437733			−0.218867	−	0.975755i	$-0.570236\pi$
$881$	−12.9926			−0.437733			−0.218867	+	0.975755i	$0.570236\pi$
$882$	1.87019	+	3.09462i	0.0629724	+	0.104201i
$883$	46.3699			1.56047			0.780235	−	0.625486i	$-0.215099\pi$
$883$	46.3699			1.56047			0.780235	+	0.625486i	$0.215099\pi$
$884$	1.03103	−	1.78580i	0.0346773	−	0.0600629i
$885$	12.7126	+	22.0188i	0.427328	+	0.740154i
$886$	8.00281	+	13.8613i	0.268860	+	0.465678i
$887$	10.8924	−	18.8662i	0.365732	−	0.633466i	−0.623161	−	0.782093i	$-0.714152\pi$
$887$	10.8924	−	18.8662i	0.365732	−	0.633466i	0.988893	+	0.148627i	$0.0474854\pi$
$888$	15.7472			0.528442
$889$	−16.1672	+	0.161692i	−0.542231	+	0.00542297i
$890$	8.34313			0.279663
$891$	14.4360	−	25.0039i	0.483624	−	0.837661i
$892$	2.91663	+	5.05174i	0.0976559	+	0.169145i
$893$	17.5083	+	30.3252i	0.585892	+	1.01480i
$894$	−17.6869	+	30.6346i	−0.591538	+	1.02457i
$895$	−18.7021			−0.625142
$896$	1.29990	−	2.30440i	0.0434264	−	0.0769847i
$897$	−2.15785			−0.0720485
$898$	−12.9529	+	22.4350i	−0.432243	+	0.748667i
$899$	−9.38671	−	16.2583i	−0.313064	−	0.542243i
$900$	0.914483	+	1.58393i	0.0304828	+	0.0527977i
$901$	4.93487	−	8.54744i	0.164404	−	0.284756i
$902$	−14.7838			−0.492247
$903$	−18.0240	−	30.5097i	−0.599802	−	1.01530i
$904$	−8.46614			−0.281580
$905$	−14.1114	+	24.4416i	−0.469078	+	0.812466i
$906$	0.0468134	+	0.0810832i	0.00155527	+	0.00269381i
$907$	−10.6585	−	18.4610i	−0.353908	−	0.612987i	0.633022	−	0.774134i	$-0.281814\pi$
$907$	−10.6585	−	18.4610i	−0.353908	−	0.612987i	−0.986931	+	0.161146i	$0.948481\pi$
$908$	−5.41091	+	9.37197i	−0.179567	+	0.311020i
$909$	7.44130			0.246812
$910$	1.87062	+	3.16644i	0.0620103	+	0.104966i
$911$	−11.7549			−0.389458			−0.194729	−	0.980857i	$-0.562383\pi$
$911$	−11.7549			−0.389458			−0.194729	+	0.980857i	$0.562383\pi$
$912$	−6.00789	+	10.4060i	−0.198941	+	0.344576i
$913$	−4.12879	−	7.15127i	−0.136643	−	0.236672i
$914$	−17.6546	−	30.5786i	−0.583961	−	1.01145i
$915$	5.73154	−	9.92731i	0.189479	−	0.328187i
$916$	16.8253			0.555924
$917$	−25.7874	+	45.7149i	−0.851576	+	1.50964i
$918$	8.34551			0.275443
$919$	23.4758	−	40.6612i	0.774395	−	1.34129i	−0.160740	−	0.986997i	$-0.551388\pi$
$919$	23.4758	−	40.6612i	0.774395	−	1.34129i	0.935134	−	0.354294i	$-0.115279\pi$
$920$	−0.603998	−	1.04616i	−0.0199132	−	0.0344907i
$921$	−17.7597	−	30.7607i	−0.585201	−	1.01360i
$922$	−16.0038	+	27.7194i	−0.527057	+	0.912889i
$923$	−8.41990			−0.277144
$924$	13.9300	−	0.139316i	0.458262	−	0.00458317i
$925$	29.7331			0.977618
$926$	−6.09436	+	10.5557i	−0.200273	+	0.346883i
$927$	−1.34062	−	2.32202i	−0.0440317	−	0.0762651i
$928$	3.07027	+	5.31786i	0.100786	+	0.174567i
$929$	−17.7670	+	30.7734i	−0.582918	+	1.00964i	0.412214	+	0.911087i	$0.364756\pi$
$929$	−17.7670	+	30.7734i	−0.582918	+	1.00964i	−0.995132	+	0.0985559i	$0.968578\pi$
$930$	6.92566			0.227101
$931$	−21.6451	+	39.2846i	−0.709391	+	1.28750i
$932$	15.5738			0.510138
$933$	15.2979	−	26.4968i	0.500832	−	0.867466i
$934$	−18.7055	−	32.3988i	−0.612062	−	1.06012i
$935$	3.03905	+	5.26380i	0.0993877	+	0.172145i
$936$	−0.297196	+	0.514759i	−0.00971417	+	0.0168254i
$937$	−3.12814			−0.102192			−0.0510959	−	0.998694i	$-0.516271\pi$
$937$	−3.12814			−0.102192			−0.0510959	+	0.998694i	$0.516271\pi$
$938$	−12.2379	+	0.122394i	−0.399583	+	0.00399631i
$939$	−10.1382			−0.330846
$940$	−3.30077	+	5.71710i	−0.107659	+	0.186471i
$941$	5.19748	+	9.00230i	0.169433	+	0.293467i	0.938221	−	0.346038i	$-0.112473\pi$
$941$	5.19748	+	9.00230i	0.169433	+	0.293467i	−0.768788	+	0.639504i	$0.779140\pi$
$942$	−5.02325	−	8.70052i	−0.163666	−	0.283478i
$943$	−2.63264	+	4.55987i	−0.0857307	+	0.148490i
$944$	11.2238			0.365303
$945$	−7.31287	+	12.9640i	−0.237888	+	0.421718i
$946$	−20.0540			−0.652012
$947$	−19.7388	+	34.1886i	−0.641425	+	1.11098i	0.343690	+	0.939083i	$0.388323\pi$
$947$	−19.7388	+	34.1886i	−0.641425	+	1.11098i	−0.985115	+	0.171897i	$0.945010\pi$
$948$	−14.4274	−	24.9890i	−0.468581	−	0.811607i
$949$	−6.14064	−	10.6359i	−0.199334	−	0.345256i
$950$	−11.3438	+	19.6480i	−0.368041	+	0.637466i
$951$	24.1552			0.783286
$952$	2.41154	+	4.08208i	0.0781586	+	0.132301i
$953$	15.4638			0.500922			0.250461	−	0.968127i	$-0.419418\pi$
$953$	15.4638			0.500922			0.250461	+	0.968127i	$0.419418\pi$
$954$	−1.42248	+	2.46381i	−0.0460546	+	0.0797689i
$955$	−11.2996	−	19.5714i	−0.365645	−	0.633316i
$956$	9.79849	+	16.9715i	0.316906	+	0.548897i
$957$	−16.1658	+	28.0001i	−0.522568	+	0.905114i
$958$	2.00912			0.0649116
$959$	14.6005	+	24.7146i	0.471473	+	0.798076i
$960$	−2.26529			−0.0731119
$961$	10.8265	−	18.7520i	0.349241	−	0.604904i
$962$	4.83146	+	8.36833i	0.155772	+	0.269806i
$963$	−1.41406	−	2.44922i	−0.0455674	−	0.0789251i
$964$	−1.14498	+	1.98317i	−0.0368775	+	0.0638737i
$965$	0.00211457			6.80704e−5
$966$	2.43762	−	4.32132i	0.0784292	−	0.139036i
$967$	14.9405			0.480453			0.240227	−	0.970717i	$-0.422778\pi$
$967$	14.9405			0.480453			0.240227	+	0.970717i	$0.422778\pi$
$968$	−1.55817	+	2.69883i	−0.0500814	+	0.0867436i
$969$	−10.7662	−	18.6475i	−0.345859	−	0.599045i
$970$	−3.17620	−	5.50134i	−0.101982	−	0.176637i
$971$	4.21104	−	7.29374i	0.135139	−	0.234067i	−0.790512	−	0.612447i	$-0.790185\pi$
$971$	4.21104	−	7.29374i	0.135139	−	0.234067i	0.925650	+	0.378380i	$0.123519\pi$
$972$	−5.31157			−0.170369
$973$	3.10498	−	0.0310536i	0.0995412	−	0.000995532i
$974$	−37.6331			−1.20584
$975$	−3.82020	+	6.61678i	−0.122344	+	0.211907i
$976$	−2.53016	−	4.38236i	−0.0809883	−	0.140276i
$977$	−19.6805	−	34.0877i	−0.629635	−	1.09056i	−0.987625	−	0.156835i	$-0.949871\pi$
$977$	−19.6805	−	34.0877i	−0.629635	−	1.09056i	0.357989	−	0.933726i	$-0.383462\pi$
$978$	1.60908	−	2.78701i	0.0514527	−	0.0891188i
$979$	19.3922			0.619778
$980$	−8.45428	+	0.169123i	−0.270062	+	0.00540243i
$981$	−1.77503			−0.0566722
$982$	−12.6918	+	21.9828i	−0.405012	+	0.701501i
$983$	7.55396	+	13.0838i	0.240934	+	0.417310i	0.960981	−	0.276616i	$-0.0892130\pi$
$983$	7.55396	+	13.0838i	0.240934	+	0.417310i	−0.720047	+	0.693926i	$0.755880\pi$
$984$	4.93686	+	8.55089i	0.157381	+	0.272592i
$985$	−9.77511	+	16.9310i	−0.311461	+	0.539466i
$986$	−11.0039			−0.350434
$987$	−27.1122	+	0.271155i	−0.862992	+	0.00863096i
$988$	−7.37321			−0.234573
$989$	−3.57114	+	6.18540i	−0.113556	+	0.196684i
$990$	−0.876012	−	1.51730i	−0.0278415	−	0.0482229i
$991$	−16.6740	−	28.8802i	−0.529667	−	0.917410i	−0.999401	−	0.0346024i	$-0.988984\pi$
$991$	−16.6740	−	28.8802i	−0.529667	−	0.917410i	0.469734	−	0.882808i	$-0.344350\pi$
$992$	1.52865	−	2.64769i	0.0485346	−	0.0840644i
$993$	12.9062			0.409565
$994$	9.51157	−	16.8617i	0.301689	−	0.534822i
$995$	−2.49325			−0.0790415
$996$	−2.75751	+	4.77614i	−0.0873750	+	0.151338i
$997$	5.80154	+	10.0486i	0.183737	+	0.318241i	0.943150	−	0.332367i	$-0.107847\pi$
$997$	5.80154	+	10.0486i	0.183737	+	0.318241i	−0.759413	+	0.650608i	$0.774514\pi$
$998$	0.863781	+	1.49611i	0.0273425	+	0.0473586i
$999$	−19.5537	+	33.8680i	−0.618652	+	1.07154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.c.93.2	✓	8
7.2	even	3		2254.2.a.v.1.3		4
7.4	even	3	inner	322.2.e.c.277.2	yes	8
7.5	odd	6		2254.2.a.q.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.c.93.2	✓	8	1.1	even	1	trivial
322.2.e.c.277.2	yes	8	7.4	even	3	inner
2254.2.a.q.1.2		4	7.5	odd	6
2254.2.a.v.1.3		4	7.2	even	3

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21}+ \cdots - 18 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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