LMFDB - Embedded newform 455.2.j.g.261.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [455,2,Mod(261,455)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("455.261"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(455, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 455 = 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	455.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,1,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.63319329197$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 17 x^{18} - 12 x^{17} + 181 x^{16} - 114 x^{15} + 1154 x^{14} - 605 x^{13} + \cdots + 625 $ x^20 - x^19 + 17x^18 - 12x^17 + 181x^16 - 114x^15 + 1154x^14 - 605x^13 + 5287x^12 - 2528x^11 + 15737x^10 - 5902x^9 + 32767x^8 - 10275x^7 + 37264x^6 - 2882x^5 + 24959x^4 - 2550x^3 + 7231x^2 + 1475x + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			261.7
Root			$0.633675 + 1.09756i$ of defining polynomial
Character	$\chi$	$=$	455.261
Dual form			455.2.j.g.326.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.633675 - 1.09756i) q^{2} +(-0.868620 - 1.50449i) q^{3} +(0.196912 + 0.341062i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.20169 q^{6} +(2.54129 + 0.736100i) q^{7} +3.03381 q^{8} +(-0.00900122 + 0.0155906i) q^{9} +(-0.633675 - 1.09756i) q^{10} +(-0.296227 - 0.513081i) q^{11} +(0.342083 - 0.592506i) q^{12} -1.00000 q^{13} +(2.41826 - 2.32276i) q^{14} -1.73724 q^{15} +(1.52863 - 2.64766i) q^{16} +(0.579124 + 1.00307i) q^{17} +(0.0114077 + 0.0197587i) q^{18} +(2.13104 - 3.69107i) q^{19} +0.393824 q^{20} +(-1.09996 - 4.46275i) q^{21} -0.750848 q^{22} +(-3.36124 + 5.82184i) q^{23} +(-2.63523 - 4.56435i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.633675 + 1.09756i) q^{26} -5.18045 q^{27} +(0.249355 + 1.01168i) q^{28} +0.792739 q^{29} +(-1.10085 + 1.90672i) q^{30} +(-4.37750 - 7.58206i) q^{31} +(1.09651 + 1.89921i) q^{32} +(-0.514618 + 0.891345i) q^{33} +1.46791 q^{34} +(1.90813 - 1.83277i) q^{35} -0.00708979 q^{36} +(0.531172 - 0.920018i) q^{37} +(-2.70077 - 4.67787i) q^{38} +(0.868620 + 1.50449i) q^{39} +(1.51691 - 2.62736i) q^{40} -8.58753 q^{41} +(-5.59514 - 1.62066i) q^{42} +1.48656 q^{43} +(0.116661 - 0.202064i) q^{44} +(0.00900122 + 0.0155906i) q^{45} +(4.25987 + 7.37831i) q^{46} +(-2.41813 + 4.18832i) q^{47} -5.31118 q^{48} +(5.91631 + 3.74129i) q^{49} -1.26735 q^{50} +(1.00608 - 1.74258i) q^{51} +(-0.196912 - 0.341062i) q^{52} +(4.62745 + 8.01498i) q^{53} +(-3.28272 + 5.68584i) q^{54} -0.592455 q^{55} +(7.70980 + 2.23319i) q^{56} -7.40425 q^{57} +(0.502339 - 0.870076i) q^{58} +(7.08234 + 12.2670i) q^{59} +(-0.342083 - 0.592506i) q^{60} +(2.87009 - 4.97115i) q^{61} -11.0957 q^{62} +(-0.0343509 + 0.0329944i) q^{63} +8.89383 q^{64} +(-0.500000 + 0.866025i) q^{65} +(0.652201 + 1.12965i) q^{66} +(0.568626 + 0.984890i) q^{67} +(-0.228073 + 0.395034i) q^{68} +11.6786 q^{69} +(-0.802441 - 3.25566i) q^{70} -6.87452 q^{71} +(-0.0273080 + 0.0472988i) q^{72} +(-1.76014 - 3.04865i) q^{73} +(-0.673181 - 1.16598i) q^{74} +(-0.868620 + 1.50449i) q^{75} +1.67851 q^{76} +(-0.375121 - 1.52194i) q^{77} +2.20169 q^{78} +(-1.55532 + 2.69389i) q^{79} +(-1.52863 - 2.64766i) q^{80} +(4.52684 + 7.84072i) q^{81} +(-5.44170 + 9.42530i) q^{82} +9.21811 q^{83} +(1.30548 - 1.25392i) q^{84} +1.15825 q^{85} +(0.941994 - 1.63158i) q^{86} +(-0.688589 - 1.19267i) q^{87} +(-0.898698 - 1.55659i) q^{88} +(5.50461 - 9.53427i) q^{89} +0.0228154 q^{90} +(-2.54129 - 0.736100i) q^{91} -2.64747 q^{92} +(-7.60477 + 13.1718i) q^{93} +(3.06461 + 5.30807i) q^{94} +(-2.13104 - 3.69107i) q^{95} +(1.90490 - 3.29938i) q^{96} +3.80297 q^{97} +(7.85530 - 4.12273i) q^{98} +0.0106656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 4 q^{3} - 13 q^{4} + 10 q^{5} - 18 q^{6} + q^{7} - 6 q^{8} - 14 q^{9} - q^{10} - 7 q^{11} + 7 q^{12} - 20 q^{13} + 3 q^{14} + 8 q^{15} - 7 q^{16} + 6 q^{17} + 5 q^{18} + 10 q^{19} - 26 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) $ 20 * q + q^2 + 4 * q^3 - 13 * q^4 + 10 * q^5 - 18 * q^6 + q^7 - 6 * q^8 - 14 * q^9 - q^10 - 7 * q^11 + 7 * q^12 - 20 * q^13 + 3 * q^14 + 8 * q^15 - 7 * q^16 + 6 * q^17 + 5 * q^18 + 10 * q^19 - 26 * q^20 + 16 * q^21 - 22 * q^22 - 7 * q^23 + 20 * q^24 - 10 * q^25 - q^26 - 32 * q^27 + 36 * q^28 + 6 * q^29 - 9 * q^30 + 26 * q^31 + 22 * q^32 + 18 * q^33 - 6 * q^34 + 2 * q^35 + 56 * q^36 + 2 * q^37 - 25 * q^38 - 4 * q^39 - 3 * q^40 - 38 * q^41 + 21 * q^42 - 2 * q^43 - 33 * q^44 + 14 * q^45 + 20 * q^46 + 31 * q^47 - 46 * q^48 - 25 * q^49 - 2 * q^50 - 34 * q^51 + 13 * q^52 + 22 * q^53 + 42 * q^54 - 14 * q^55 + 30 * q^56 - 46 * q^57 + 7 * q^58 - q^59 - 7 * q^60 + 14 * q^61 + 30 * q^62 - 17 * q^63 - 10 * q^64 - 10 * q^65 - 45 * q^66 + 26 * q^67 + 12 * q^68 - 2 * q^69 + 3 * q^70 + 14 * q^71 - 40 * q^72 + 30 * q^73 + 13 * q^74 + 4 * q^75 - 86 * q^76 - 25 * q^77 + 18 * q^78 - 10 * q^79 + 7 * q^80 - 22 * q^81 + 9 * q^82 - 40 * q^83 + 46 * q^84 + 12 * q^85 - 17 * q^86 + 52 * q^88 + q^89 + 10 * q^90 - q^91 + 30 * q^92 + 32 * q^93 + 22 * q^94 - 10 * q^95 - 22 * q^96 - 38 * q^97 - 26 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/455\mathbb{Z}\right)^\times$.

$n$	$66$	$92$	$106$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.633675	−	1.09756i	0.448076	−	0.776090i	−0.550185	−	0.835043i	$-0.685443\pi$
$2$	0.633675	−	1.09756i	0.448076	−	0.776090i	0.998261	+	0.0589527i	$0.0187761\pi$
$3$	−0.868620	−	1.50449i	−0.501498	−	0.868620i	−0.999999	−	0.00173056i	$-0.999449\pi$
$3$	−0.868620	−	1.50449i	−0.501498	−	0.868620i	0.498501	−	0.866889i	$-0.333884\pi$
$4$	0.196912	+	0.341062i	0.0984560	+	0.170531i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−2.20169			−0.898837
$7$	2.54129	+	0.736100i	0.960518	+	0.278220i
$7$	2.54129	+	0.736100i	0.960518	+	0.278220i
$8$	3.03381			1.07261
$9$	−0.00900122	+	0.0155906i	−0.00300041	+	0.00519685i
$10$	−0.633675	−	1.09756i	−0.200386	−	0.347078i
$11$	−0.296227	−	0.513081i	−0.0893159	−	0.154700i	0.817906	−	0.575352i	$-0.195135\pi$
$11$	−0.296227	−	0.513081i	−0.0893159	−	0.154700i	−0.907222	+	0.420652i	$0.861801\pi$
$12$	0.342083	−	0.592506i	0.0987510	−	0.171042i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.41826	−	2.32276i	0.646308	−	0.620785i
$15$	−1.73724			−0.448553
$16$	1.52863	−	2.64766i	0.382157	−	0.661915i
$17$	0.579124	+	1.00307i	0.140458	+	0.243281i	0.927669	−	0.373403i	$-0.121809\pi$
$17$	0.579124	+	1.00307i	0.140458	+	0.243281i	−0.787211	+	0.616684i	$0.788476\pi$
$18$	0.0114077	+	0.0197587i	0.00268882	+	0.00465717i
$19$	2.13104	−	3.69107i	0.488894	−	0.846788i	−0.511025	−	0.859566i	$-0.670734\pi$
$19$	2.13104	−	3.69107i	0.488894	−	0.846788i	0.999918	+	0.0127775i	$0.00406732\pi$
$20$	0.393824			0.0880618
$21$	−1.09996	−	4.46275i	−0.240031	−	0.973851i
$22$	−0.750848			−0.160081
$23$	−3.36124	+	5.82184i	−0.700867	+	1.21394i	0.267296	+	0.963615i	$0.413870\pi$
$23$	−3.36124	+	5.82184i	−0.700867	+	1.21394i	−0.968162	+	0.250323i	$0.919463\pi$
$24$	−2.63523	−	4.56435i	−0.537914	−	0.931695i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.633675	+	1.09756i	−0.124274	+	0.215249i
$27$	−5.18045			−0.996977
$28$	0.249355	+	1.01168i	0.0471237	+	0.191190i
$29$	0.792739			0.147208			0.0736039	−	0.997288i	$-0.476550\pi$
$29$	0.792739			0.147208			0.0736039	+	0.997288i	$0.476550\pi$
$30$	−1.10085	+	1.90672i	−0.200986	+	0.348118i
$31$	−4.37750	−	7.58206i	−0.786223	−	1.36178i	−0.928266	−	0.371917i	$-0.878701\pi$
$31$	−4.37750	−	7.58206i	−0.786223	−	1.36178i	0.142043	−	0.989860i	$-0.454633\pi$
$32$	1.09651	+	1.89921i	0.193837	+	0.335735i
$33$	−0.514618	+	0.891345i	−0.0895835	+	0.155163i
$34$	1.46791			0.251744
$35$	1.90813	−	1.83277i	0.322532	−	0.309795i
$36$	−0.00708979			−0.00118163
$37$	0.531172	−	0.920018i	0.0873242	−	0.151250i	−0.819055	−	0.573715i	$-0.805502\pi$
$37$	0.531172	−	0.920018i	0.0873242	−	0.151250i	0.906379	+	0.422465i	$0.138835\pi$
$38$	−2.70077	−	4.67787i	−0.438123	−	0.758851i
$39$	0.868620	+	1.50449i	0.139091	+	0.240912i
$40$	1.51691	−	2.62736i	0.239844	−	0.415422i
$41$	−8.58753			−1.34115			−0.670573	−	0.741843i	$-0.733952\pi$
$41$	−8.58753			−1.34115			−0.670573	+	0.741843i	$0.733952\pi$
$42$	−5.59514	−	1.62066i	−0.863348	−	0.250074i
$43$	1.48656			0.226698			0.113349	−	0.993555i	$-0.463842\pi$
$43$	1.48656			0.226698			0.113349	+	0.993555i	$0.463842\pi$
$44$	0.116661	−	0.202064i	0.0175874	−	0.0304622i
$45$	0.00900122	+	0.0155906i	0.00134182	+	0.00232410i
$46$	4.25987	+	7.37831i	0.628083	+	1.08787i
$47$	−2.41813	+	4.18832i	−0.352720	+	0.610929i	−0.986725	−	0.162400i	$-0.948077\pi$
$47$	−2.41813	+	4.18832i	−0.352720	+	0.610929i	0.634005	+	0.773329i	$0.281410\pi$
$48$	−5.31118			−0.766603
$49$	5.91631	+	3.74129i	0.845188	+	0.534469i
$50$	−1.26735			−0.179230
$51$	1.00608	−	1.74258i	0.140879	−	0.244010i
$52$	−0.196912	−	0.341062i	−0.0273068	−	0.0472967i
$53$	4.62745	+	8.01498i	0.635629	+	1.10094i	0.986381	+	0.164474i	$0.0525927\pi$
$53$	4.62745	+	8.01498i	0.635629	+	1.10094i	−0.350752	+	0.936468i	$0.614074\pi$
$54$	−3.28272	+	5.68584i	−0.446721	+	0.773744i
$55$	−0.592455			−0.0798866
$56$	7.70980	+	2.23319i	1.03027	+	0.298422i
$57$	−7.40425			−0.980716
$58$	0.502339	−	0.870076i	0.0659603	−	0.114247i
$59$	7.08234	+	12.2670i	0.922042	+	1.59702i	0.796251	+	0.604966i	$0.206813\pi$
$59$	7.08234	+	12.2670i	0.922042	+	1.59702i	0.125791	+	0.992057i	$0.459853\pi$
$60$	−0.342083	−	0.592506i	−0.0441628	−	0.0764922i
$61$	2.87009	−	4.97115i	0.367478	−	0.636490i	−0.621693	−	0.783261i	$-0.713555\pi$
$61$	2.87009	−	4.97115i	0.367478	−	0.636490i	0.989170	+	0.146771i	$0.0468881\pi$
$62$	−11.0957			−1.40915
$63$	−0.0343509	+	0.0329944i	−0.00432781	+	0.00415690i
$64$	8.89383			1.11173
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	0.652201	+	1.12965i	0.0802804	+	0.139050i
$67$	0.568626	+	0.984890i	0.0694688	+	0.120323i	0.898668	−	0.438630i	$-0.144536\pi$
$67$	0.568626	+	0.984890i	0.0694688	+	0.120323i	−0.829199	+	0.558954i	$0.811203\pi$
$68$	−0.228073	+	0.395034i	−0.0276579	+	0.0479049i
$69$	11.6786			1.40593
$70$	−0.802441	−	3.25566i	−0.0959100	−	0.389126i
$71$	−6.87452			−0.815855			−0.407927	−	0.913014i	$-0.633748\pi$
$71$	−6.87452			−0.815855			−0.407927	+	0.913014i	$0.633748\pi$
$72$	−0.0273080	+	0.0472988i	−0.00321828	+	0.00557422i
$73$	−1.76014	−	3.04865i	−0.206009	−	0.356818i	0.744445	−	0.667684i	$-0.232714\pi$
$73$	−1.76014	−	3.04865i	−0.206009	−	0.356818i	−0.950454	+	0.310866i	$0.899381\pi$
$74$	−0.673181	−	1.16598i	−0.0782557	−	0.135543i
$75$	−0.868620	+	1.50449i	−0.100300	+	0.173724i
$76$	1.67851			0.192538
$77$	−0.375121	−	1.52194i	−0.0427490	−	0.173441i
$78$	2.20169			0.249292
$79$	−1.55532	+	2.69389i	−0.174987	+	0.303087i	−0.940157	−	0.340742i	$-0.889322\pi$
$79$	−1.55532	+	2.69389i	−0.174987	+	0.303087i	0.765170	+	0.643829i	$0.222655\pi$
$80$	−1.52863	−	2.64766i	−0.170906	−	0.296017i
$81$	4.52684	+	7.84072i	0.502982	+	0.871191i
$82$	−5.44170	+	9.42530i	−0.600935	+	1.04085i
$83$	9.21811			1.01182			0.505909	−	0.862587i	$-0.331157\pi$
$83$	9.21811			1.01182			0.505909	+	0.862587i	$0.331157\pi$
$84$	1.30548	−	1.25392i	0.142439	−	0.136814i
$85$	1.15825			0.125630
$86$	0.941994	−	1.63158i	0.101578	−	0.175938i
$87$	−0.688589	−	1.19267i	−0.0738245	−	0.127868i
$88$	−0.898698	−	1.55659i	−0.0958016	−	0.165933i
$89$	5.50461	−	9.53427i	0.583488	−	1.01063i	−0.411574	−	0.911376i	$-0.635021\pi$
$89$	5.50461	−	9.53427i	0.583488	−	1.01063i	0.995062	−	0.0992545i	$-0.0316458\pi$
$90$	0.0228154			0.00240495
$91$	−2.54129	−	0.736100i	−0.266400	−	0.0771642i
$92$	−2.64747			−0.276018
$93$	−7.60477	+	13.1718i	−0.788578	+	1.36586i
$94$	3.06461	+	5.30807i	0.316091	+	0.547485i
$95$	−2.13104	−	3.69107i	−0.218640	−	0.378695i
$96$	1.90490	−	3.29938i	0.194418	−	0.336741i
$97$	3.80297			0.386133			0.193066	−	0.981186i	$-0.438157\pi$
$97$	3.80297			0.386133			0.193066	+	0.981186i	$0.438157\pi$
$98$	7.85530	−	4.12273i	0.793505	−	0.416459i
$99$	0.0106656			0.00107194
$100$	0.196912	−	0.341062i	0.0196912	−	0.0341062i
$101$	0.742641	+	1.28629i	0.0738955	+	0.127991i	0.900605	−	0.434638i	$-0.143124\pi$
$101$	0.742641	+	1.28629i	0.0738955	+	0.127991i	−0.826710	+	0.562628i	$0.809790\pi$
$102$	−1.27505	−	2.20846i	−0.126249	−	0.218670i
$103$	−3.41108	+	5.90817i	−0.336104	+	0.582149i	−0.983696	−	0.179838i	$-0.942443\pi$
$103$	−3.41108	+	5.90817i	−0.336104	+	0.582149i	0.647592	+	0.761987i	$0.275776\pi$
$104$	−3.03381			−0.297490
$105$	−4.41483	−	1.27878i	−0.430843	−	0.124796i
$106$	11.7292			1.13924
$107$	−1.57687	+	2.73122i	−0.152442	+	0.264037i	−0.932125	−	0.362138i	$-0.882047\pi$
$107$	−1.57687	+	2.73122i	−0.152442	+	0.264037i	0.779683	+	0.626175i	$0.215380\pi$
$108$	−1.02009	−	1.76685i	−0.0981584	−	0.170015i
$109$	7.47123	+	12.9406i	0.715614	+	1.23948i	0.962722	+	0.270492i	$0.0871865\pi$
$109$	7.47123	+	12.9406i	0.715614	+	1.23948i	−0.247108	+	0.968988i	$0.579480\pi$
$110$	−0.375424	+	0.650253i	−0.0357953	+	0.0619992i
$111$	−1.84555			−0.175172
$112$	5.83363	−	5.60325i	0.551226	−	0.529457i
$113$	−1.21550			−0.114345			−0.0571724	−	0.998364i	$-0.518208\pi$
$113$	−1.21550			−0.114345			−0.0571724	+	0.998364i	$0.518208\pi$
$114$	−4.69189	+	8.12658i	−0.439435	+	0.761124i
$115$	3.36124	+	5.82184i	0.313437	+	0.542889i
$116$	0.156100	+	0.270373i	0.0144935	+	0.0251035i
$117$	0.00900122	−	0.0155906i	0.000832163	−	0.00144135i
$118$	17.9516			1.65258
$119$	0.733361	+	2.97539i	0.0672271	+	0.272754i
$120$	−5.27046			−0.481125
$121$	5.32450	−	9.22230i	0.484045	−	0.838391i
$122$	−3.63741	−	6.30018i	−0.329316	−	0.570392i
$123$	7.45930	+	12.9199i	0.672582	+	1.16495i
$124$	1.72397	−	2.98600i	0.154817	−	0.268150i
$125$	−1.00000			−0.0894427
$126$	0.0144459	+	0.0586098i	0.00128694	+	0.00522137i
$127$	−19.6600			−1.74454			−0.872272	−	0.489022i	$-0.837354\pi$
$127$	−19.6600			−1.74454			−0.872272	+	0.489022i	$0.837354\pi$
$128$	3.44278	−	5.96307i	0.304302	−	0.527066i
$129$	−1.29125	−	2.23652i	−0.113689	−	0.196914i
$130$	0.633675	+	1.09756i	0.0555770	+	0.0962621i
$131$	−7.69543	+	13.3289i	−0.672353	+	1.16455i	0.304882	+	0.952390i	$0.401383\pi$
$131$	−7.69543	+	13.3289i	−0.672353	+	1.16455i	−0.977235	+	0.212160i	$0.931950\pi$
$132$	−0.405338			−0.0352801
$133$	8.13258	−	7.81141i	0.705184	−	0.677335i
$134$	1.44130			0.124509
$135$	−2.59022	+	4.48640i	−0.222931	+	0.386128i
$136$	1.75695	+	3.04313i	0.150658	+	0.260947i
$137$	6.15179	+	10.6552i	0.525583	+	0.910336i	0.999556	+	0.0297970i	$0.00948608\pi$
$137$	6.15179	+	10.6552i	0.525583	+	0.910336i	−0.473973	+	0.880539i	$0.657181\pi$
$138$	7.40041	−	12.8179i	0.629965	−	1.09113i
$139$	−15.8383			−1.34339			−0.671693	−	0.740830i	$-0.734433\pi$
$139$	−15.8383			−1.34339			−0.671693	+	0.740830i	$0.734433\pi$
$140$	1.00082	+	0.289894i	0.0845849	+	0.0245005i
$141$	8.40173			0.707554
$142$	−4.35621	+	7.54517i	−0.365565	+	0.633177i
$143$	0.296227	+	0.513081i	0.0247718	+	0.0429060i
$144$	0.0275190	+	0.0476643i	0.00229325	+	0.00397203i
$145$	0.396369	−	0.686532i	0.0329167	−	0.0570134i
$146$	−4.46143			−0.369230
$147$	0.489713	−	12.1508i	0.0403909	−	1.00218i
$148$	0.418377			0.0343904
$149$	−5.80544	+	10.0553i	−0.475600	+	0.823763i	−0.999609	−	0.0279493i	$-0.991102\pi$
$149$	−5.80544	+	10.0553i	−0.475600	+	0.823763i	0.524009	+	0.851712i	$0.324436\pi$
$150$	1.10085	+	1.90672i	0.0898837	+	0.155683i
$151$	−8.68058	−	15.0352i	−0.706416	−	1.22355i	−0.966178	−	0.257875i	$-0.916978\pi$
$151$	−8.68058	−	15.0352i	−0.706416	−	1.22355i	0.259763	−	0.965672i	$-0.416356\pi$
$152$	6.46517	−	11.1980i	0.524394	−	0.908278i
$153$	−0.0208513			−0.00168573
$154$	−1.90812	−	0.552699i	−0.153761	−	0.0445377i
$155$	−8.75500			−0.703219
$156$	−0.342083	+	0.592506i	−0.0273886	+	0.0474384i
$157$	5.40499	+	9.36173i	0.431366	+	0.747147i	0.996991	−	0.0775151i	$-0.0246986\pi$
$157$	5.40499	+	9.36173i	0.431366	+	0.747147i	−0.565626	+	0.824662i	$0.691365\pi$
$158$	1.97114	+	3.41411i	0.156815	+	0.271612i
$159$	8.03899	−	13.9239i	0.637534	−	1.10424i
$160$	2.19301			0.173373
$161$	−12.8273	+	12.3208i	−1.01094	+	0.971013i
$162$	11.4742			0.901497
$163$	1.36714	−	2.36795i	0.107082	−	0.185472i	−0.807505	−	0.589861i	$-0.799182\pi$
$163$	1.36714	−	2.36795i	0.107082	−	0.185472i	0.914587	+	0.404389i	$0.132516\pi$
$164$	−1.69099	−	2.92888i	−0.132044	−	0.228707i
$165$	0.514618	+	0.891345i	0.0400630	+	0.0693911i
$166$	5.84129	−	10.1174i	0.453372	−	0.785263i
$167$	−21.5563			−1.66807			−0.834037	−	0.551709i	$-0.813976\pi$
$167$	−21.5563			−1.66807			−0.834037	+	0.551709i	$0.813976\pi$
$168$	−3.33707	−	13.5391i	−0.257460	−	1.04457i
$169$	1.00000			0.0769231
$170$	0.733953	−	1.27124i	0.0562916	−	0.0974999i
$171$	0.0383639	+	0.0664481i	0.00293376	+	0.00508142i
$172$	0.292721	+	0.507008i	0.0223198	+	0.0386590i
$173$	−0.340464	+	0.589701i	−0.0258850	+	0.0448342i	−0.878678	−	0.477415i	$-0.841574\pi$
$173$	−0.340464	+	0.589701i	−0.0258850	+	0.0448342i	0.852793	+	0.522250i	$0.174907\pi$
$174$	−1.74537			−0.132316
$175$	−0.633164	−	2.56887i	−0.0478627	−	0.194188i
$176$	−1.81128			−0.136531
$177$	12.3037	−	21.3107i	0.924804	−	1.60181i
$178$	−6.97627	−	12.0833i	−0.522894	−	0.905679i
$179$	−10.4899	−	18.1690i	−0.784050	−	1.35802i	−0.929565	−	0.368659i	$-0.879817\pi$
$179$	−10.4899	−	18.1690i	−0.784050	−	1.35802i	0.145514	−	0.989356i	$-0.453516\pi$
$180$	−0.00354490	+	0.00613994i	−0.000264221	+	0.000457644i
$181$	−10.4730			−0.778449			−0.389224	−	0.921143i	$-0.627257\pi$
$181$	−10.4730			−0.778449			−0.389224	+	0.921143i	$0.627257\pi$
$182$	−2.41826	+	2.32276i	−0.179254	+	0.172175i
$183$	−9.97208			−0.737157
$184$	−10.1974	+	17.6624i	−0.751760	+	1.30209i
$185$	−0.531172	−	0.920018i	−0.0390526	−	0.0676410i
$186$	9.63791	+	16.6933i	0.706686	+	1.22402i
$187$	0.343105	−	0.594275i	0.0250903	−	0.0434577i
$188$	−1.90463			−0.138910
$189$	−13.1650	−	3.81332i	−0.957614	−	0.277378i
$190$	−5.40154			−0.391869
$191$	3.56022	−	6.16648i	0.257608	−	0.446191i	−0.707992	−	0.706220i	$-0.750399\pi$
$191$	3.56022	−	6.16648i	0.257608	−	0.446191i	0.965601	+	0.260029i	$0.0837322\pi$
$192$	−7.72535	−	13.3807i	−0.557529	−	0.965669i
$193$	7.77034	+	13.4586i	0.559321	+	0.968772i	0.997553	+	0.0699106i	$0.0222714\pi$
$193$	7.77034	+	13.4586i	0.559321	+	0.968772i	−0.438232	+	0.898862i	$0.644395\pi$
$194$	2.40984	−	4.17397i	0.173017	−	0.299674i
$195$	1.73724			0.124406
$196$	−0.111016	+	2.75453i	−0.00792969	+	0.196752i
$197$	11.9733			0.853064			0.426532	−	0.904472i	$-0.359735\pi$
$197$	11.9733			0.853064			0.426532	+	0.904472i	$0.359735\pi$
$198$	0.00675854	−	0.0117061i	0.000480309	−	0.000831919i
$199$	7.97032	+	13.8050i	0.565001	+	0.978611i	0.997050	+	0.0767603i	$0.0244576\pi$
$199$	7.97032	+	13.8050i	0.565001	+	0.978611i	−0.432048	+	0.901850i	$0.642209\pi$
$200$	−1.51691	−	2.62736i	−0.107261	−	0.185782i
$201$	0.987841	−	1.71099i	0.0696769	−	0.120684i
$202$	1.88237			0.132443
$203$	2.01458	+	0.583535i	0.141396	+	0.0409561i
$204$	0.792435			0.0554816
$205$	−4.29376	+	7.43702i	−0.299889	+	0.519424i
$206$	4.32304	+	7.48772i	0.301200	+	0.521694i
$207$	−0.0605105	−	0.104807i	−0.00420577	−	0.00728461i
$208$	−1.52863	+	2.64766i	−0.105991	+	0.183582i
$209$	−2.52509			−0.174664
$210$	−4.20110	+	4.03520i	−0.289904	+	0.278455i
$211$	0.594297			0.0409131			0.0204565	−	0.999791i	$-0.493488\pi$
$211$	0.594297			0.0409131			0.0204565	+	0.999791i	$0.493488\pi$
$212$	−1.82240	+	3.15649i	−0.125163	+	0.216789i
$213$	5.97134	+	10.3427i	0.409150	+	0.708668i
$214$	1.99845	+	3.46141i	0.136611	+	0.236617i
$215$	0.743279	−	1.28740i	0.0506912	−	0.0877997i
$216$	−15.7165			−1.06937
$217$	−5.54336	−	22.4905i	−0.376307	−	1.52675i
$218$	18.9373			1.28260
$219$	−3.05779	+	5.29624i	−0.206626	+	0.357887i
$220$	−0.116661	−	0.202064i	−0.00786532	−	0.0136231i
$221$	−0.579124	−	1.00307i	−0.0389561	−	0.0674740i
$222$	−1.16948	+	2.02559i	−0.0784902	+	0.135949i
$223$	−26.3653			−1.76555			−0.882776	−	0.469794i	$-0.844328\pi$
$223$	−26.3653			−1.76555			−0.882776	+	0.469794i	$0.844328\pi$
$224$	1.38854	+	5.63357i	0.0927756	+	0.376409i
$225$	0.0180024			0.00120016
$226$	−0.770234	+	1.33408i	−0.0512352	+	0.0887419i
$227$	11.7950	+	20.4295i	0.782862	+	1.35596i	0.930268	+	0.366880i	$0.119574\pi$
$227$	11.7950	+	20.4295i	0.782862	+	1.35596i	−0.147407	+	0.989076i	$0.547093\pi$
$228$	−1.45799	−	2.52531i	−0.0965575	−	0.167242i
$229$	14.3829	−	24.9119i	0.950447	−	1.64622i	0.205988	−	0.978554i	$-0.433959\pi$
$229$	14.3829	−	24.9119i	0.950447	−	1.64622i	0.744459	−	0.667668i	$-0.232708\pi$
$230$	8.51973			0.561775
$231$	−1.96391	+	1.88636i	−0.129216	+	0.124113i
$232$	2.40502			0.157897
$233$	1.57069	−	2.72052i	0.102899	−	0.178227i	−0.809979	−	0.586459i	$-0.800521\pi$
$233$	1.57069	−	2.72052i	0.102899	−	0.178227i	0.912878	+	0.408232i	$0.133855\pi$
$234$	−0.0114077	−	0.0197587i	−0.000745744	−	0.00129167i
$235$	2.41813	+	4.18832i	0.157741	+	0.273216i
$236$	−2.78920	+	4.83103i	−0.181561	+	0.314473i
$237$	5.40393			0.351023
$238$	3.73038	+	1.08053i	0.241804	+	0.0700400i
$239$	12.6810			0.820264			0.410132	−	0.912026i	$-0.365483\pi$
$239$	12.6810			0.820264			0.410132	+	0.912026i	$0.365483\pi$
$240$	−2.65559	+	4.59962i	−0.171418	+	0.296904i
$241$	10.9699	+	19.0004i	0.706631	+	1.22392i	0.966100	+	0.258169i	$0.0831191\pi$
$241$	10.9699	+	19.0004i	0.706631	+	1.22392i	−0.259469	+	0.965751i	$0.583548\pi$
$242$	−6.74800	−	11.6879i	−0.433778	−	0.751326i
$243$	0.0935421	−	0.162020i	0.00600073	−	0.0103936i
$244$	2.26062			0.144722
$245$	6.19821	−	3.25304i	0.395989	−	0.207829i
$246$	18.9071			1.20547
$247$	−2.13104	+	3.69107i	−0.135595	+	0.234857i
$248$	−13.2805	−	23.0025i	−0.843314	−	1.46066i
$249$	−8.00703	−	13.8686i	−0.507425	−	0.878886i
$250$	−0.633675	+	1.09756i	−0.0400771	+	0.0694156i
$251$	6.62840			0.418381			0.209190	−	0.977875i	$-0.432917\pi$
$251$	6.62840			0.418381			0.209190	+	0.977875i	$0.432917\pi$
$252$	−0.0180172	−	0.00521879i	−0.00113498	−	0.000328753i
$253$	3.98277			0.250394
$254$	−12.4581	+	21.5780i	−0.781688	+	1.35392i
$255$	−1.00608	−	1.74258i	−0.0630030	−	0.109124i
$256$	4.53062	+	7.84726i	0.283164	+	0.490454i
$257$	2.19610	−	3.80375i	0.136989	−	0.237272i	−0.789367	−	0.613922i	$-0.789591\pi$
$257$	2.19610	−	3.80375i	0.136989	−	0.237272i	0.926355	+	0.376650i	$0.122924\pi$
$258$	−3.27294			−0.203764
$259$	2.02709	−	1.94704i	0.125957	−	0.120983i
$260$	−0.393824			−0.0244239
$261$	−0.00713561	+	0.0123592i	−0.000441683	+	0.000765018i
$262$	9.75281	+	16.8924i	0.602531	+	1.04361i
$263$	−15.2072	−	26.3396i	−0.937714	−	1.62417i	−0.769721	−	0.638381i	$-0.779605\pi$
$263$	−15.2072	−	26.3396i	−0.937714	−	1.62417i	−0.167993	−	0.985788i	$-0.553729\pi$
$264$	−1.56125	+	2.70417i	−0.0960886	+	0.166430i
$265$	9.25490			0.568524
$266$	−3.42006	−	13.8759i	−0.209697	−	0.850784i
$267$	−19.1257			−1.17047
$268$	−0.223939	+	0.387873i	−0.0136792	+	0.0236931i
$269$	−9.46940	−	16.4015i	−0.577360	−	1.00002i	−0.995781	−	0.0917630i	$-0.970750\pi$
$269$	−9.46940	−	16.4015i	−0.577360	−	1.00002i	0.418421	−	0.908253i	$-0.362584\pi$
$270$	3.28272	+	5.68584i	0.199780	+	0.346029i
$271$	9.94216	−	17.2203i	0.603943	−	1.04606i	−0.388274	−	0.921544i	$-0.626929\pi$
$271$	9.94216	−	17.2203i	0.603943	−	1.04606i	0.992218	−	0.124516i	$-0.0397379\pi$
$272$	3.54106			0.214708
$273$	1.09996	+	4.46275i	0.0665725	+	0.270098i
$274$	15.5929			0.942004
$275$	−0.296227	+	0.513081i	−0.0178632	+	0.0309399i
$276$	2.29965	+	3.98311i	0.138423	+	0.239755i
$277$	−10.9688	−	18.9986i	−0.659054	−	1.14151i	−0.980861	−	0.194710i	$-0.937624\pi$
$277$	−10.9688	−	18.9986i	−0.659054	−	1.14151i	0.321807	−	0.946805i	$-0.395710\pi$
$278$	−10.0363	+	17.3834i	−0.601939	+	1.04259i
$279$	0.157611			0.00943594
$280$	5.78890	−	5.56029i	0.345953	−	0.332291i
$281$	−15.8032			−0.942738			−0.471369	−	0.881936i	$-0.656240\pi$
$281$	−15.8032			−0.942738			−0.471369	+	0.881936i	$0.656240\pi$
$282$	5.32397	−	9.22138i	0.317038	−	0.549125i
$283$	−4.45262	−	7.71216i	−0.264681	−	0.458440i	0.702799	−	0.711388i	$-0.251933\pi$
$283$	−4.45262	−	7.71216i	−0.264681	−	0.458440i	−0.967480	+	0.252948i	$0.918600\pi$
$284$	−1.35367	−	2.34463i	−0.0803258	−	0.139128i
$285$	−3.70212	+	6.41227i	−0.219295	+	0.379830i
$286$	0.750848			0.0443985
$287$	−21.8234	−	6.32128i	−1.28819	−	0.373133i
$288$	−0.0394796			−0.00232636
$289$	7.82923	−	13.5606i	0.460543	−	0.797684i
$290$	−0.502339	−	0.870076i	−0.0294983	−	0.0510926i
$291$	−3.30333	−	5.72154i	−0.193645	−	0.335403i
$292$	0.693186	−	1.20063i	0.0405656	−	0.0702617i
$293$	3.39480			0.198326			0.0991632	−	0.995071i	$-0.468383\pi$
$293$	3.39480			0.198326			0.0991632	+	0.995071i	$0.468383\pi$
$294$	−13.0259	−	8.23716i	−0.759686	−	0.480401i
$295$	14.1647			0.824699
$296$	1.61148	−	2.79116i	0.0936652	−	0.162233i
$297$	1.53459	+	2.65799i	0.0890459	+	0.154232i
$298$	7.35752	+	12.7436i	0.426210	+	0.738217i
$299$	3.36124	−	5.82184i	0.194386	−	0.336686i
$300$	−0.684167			−0.0395004
$301$	3.77778	+	1.09425i	0.217747	+	0.0630718i
$302$	−22.0027			−1.26611
$303$	1.29014	−	2.23460i	0.0741169	−	0.128374i
$304$	−6.51512	−	11.2845i	−0.373668	−	0.647212i
$305$	−2.87009	−	4.97115i	−0.164341	−	0.284647i
$306$	−0.0132129	+	0.0228855i	−0.000755333	+	0.00130828i
$307$	1.67003			0.0953135			0.0476567	−	0.998864i	$-0.484825\pi$
$307$	1.67003			0.0953135			0.0476567	+	0.998864i	$0.484825\pi$
$308$	0.445210	−	0.427628i	0.0253682	−	0.0243664i
$309$	11.8517			0.674222
$310$	−5.54783	+	9.60912i	−0.315095	+	0.545761i
$311$	−5.69952	−	9.87186i	−0.323190	−	0.559782i	0.657954	−	0.753058i	$-0.271422\pi$
$311$	−5.69952	−	9.87186i	−0.323190	−	0.559782i	−0.981144	+	0.193276i	$0.938089\pi$
$312$	2.63523	+	4.56435i	0.149191	+	0.258406i
$313$	3.54764	−	6.14470i	0.200525	−	0.347319i	−0.748173	−	0.663504i	$-0.769069\pi$
$313$	3.54764	−	6.14470i	0.200525	−	0.347319i	0.948698	+	0.316185i	$0.102402\pi$
$314$	13.7000			0.773138
$315$	0.0113985	+	0.0462459i	0.000642232	+	0.00260566i
$316$	−1.22505			−0.0689142
$317$	12.2516	−	21.2204i	0.688119	−	1.19186i	−0.284327	−	0.958727i	$-0.591770\pi$
$317$	12.2516	−	21.2204i	0.688119	−	1.19186i	0.972446	−	0.233129i	$-0.0748966\pi$
$318$	−10.1882	−	17.6465i	−0.571327	−	0.989567i
$319$	−0.234831	−	0.406739i	−0.0131480	−	0.0227730i
$320$	4.44691	−	7.70228i	0.248590	−	0.430570i
$321$	5.47880			0.305797
$322$	5.39439	+	21.8861i	0.300618	+	1.21967i
$323$	4.93654			0.274676
$324$	−1.78278	+	3.08786i	−0.0990433	+	0.171548i
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$	−1.73264	−	3.00102i	−0.0959621	−	0.166211i
$327$	12.9793	−	22.4808i	0.717758	−	1.24319i
$328$	−26.0530			−1.43853
$329$	−9.22818	+	8.86375i	−0.508766	+	0.488675i
$330$	1.30440			0.0718050
$331$	−3.62560	+	6.27973i	−0.199281	+	0.345165i	−0.948296	−	0.317389i	$-0.897194\pi$
$331$	−3.62560	+	6.27973i	−0.199281	+	0.345165i	0.749014	+	0.662554i	$0.230527\pi$
$332$	1.81516	+	3.14394i	0.0996197	+	0.172546i
$333$	0.00956239	+	0.0165626i	0.000524016	+	0.000907622i
$334$	−13.6597	+	23.6592i	−0.747423	+	1.29458i
$335$	1.13725			0.0621348
$336$	−13.4973	−	3.90956i	−0.736336	−	0.213284i
$337$	14.4260			0.785835			0.392918	−	0.919574i	$-0.371466\pi$
$337$	14.4260			0.785835			0.392918	+	0.919574i	$0.371466\pi$
$338$	0.633675	−	1.09756i	0.0344674	−	0.0596992i
$339$	1.05581	+	1.82872i	0.0573437	+	0.0993222i
$340$	0.228073	+	0.395034i	0.0123690	+	0.0214237i
$341$	−2.59347	+	4.49202i	−0.140444	+	0.243257i
$342$	0.0972409			0.00525818
$343$	12.2811	+	13.8627i	0.663118	+	0.748515i
$344$	4.50994			0.243160
$345$	5.83928	−	10.1139i	0.314376	−	0.544516i
$346$	0.431487	+	0.747358i	0.0231969	+	0.0401782i
$347$	0.169742	+	0.294001i	0.00911222	+	0.0157828i	0.870546	−	0.492088i	$-0.163766\pi$
$347$	0.169742	+	0.294001i	0.00911222	+	0.0157828i	−0.861433	+	0.507871i	$0.830433\pi$
$348$	0.271183	−	0.469702i	0.0145369	−	0.0251787i
$349$	18.3725			0.983459			0.491729	−	0.870748i	$-0.336365\pi$
$349$	18.3725			0.983459			0.491729	+	0.870748i	$0.336365\pi$
$350$	−3.22070	−	0.932896i	−0.172154	−	0.0498654i
$351$	5.18045			0.276512
$352$	0.649631	−	1.12519i	0.0346254	−	0.0599730i
$353$	8.74824	+	15.1524i	0.465622	+	0.806480i	0.999229	−	0.0392518i	$-0.0124974\pi$
$353$	8.74824	+	15.1524i	0.465622	+	0.806480i	−0.533608	+	0.845732i	$0.679164\pi$
$354$	−15.5931	−	27.0081i	−0.828765	−	1.43546i
$355$	−3.43726	+	5.95350i	−0.182431	+	0.315979i
$356$	4.33570			0.229792
$357$	3.83945	−	3.68782i	0.203205	−	0.195180i
$358$	−26.5887			−1.40526
$359$	−5.07337	+	8.78734i	−0.267762	+	0.463778i	−0.968284	−	0.249853i	$-0.919618\pi$
$359$	−5.07337	+	8.78734i	−0.267762	+	0.463778i	0.700521	+	0.713632i	$0.252951\pi$
$360$	0.0273080	+	0.0472988i	0.00143926	+	0.00249287i
$361$	0.417358	+	0.722886i	0.0219662	+	0.0380466i
$362$	−6.63645	+	11.4947i	−0.348804	+	0.604146i
$363$	−18.4999			−0.970991
$364$	−0.249355	−	1.01168i	−0.0130698	−	0.0530266i
$365$	−3.52028			−0.184260
$366$	−6.31906	+	10.9449i	−0.330302	+	0.572101i
$367$	7.79248	+	13.4970i	0.406764	+	0.704536i	0.994525	−	0.104498i	$-0.0333237\pi$
$367$	7.79248	+	13.4970i	0.406764	+	0.704536i	−0.587761	+	0.809035i	$0.699990\pi$
$368$	10.2762	+	17.7988i	0.535682	+	0.927829i
$369$	0.0772982	−	0.133884i	0.00402398	−	0.00696974i
$370$	−1.34636			−0.0699941
$371$	5.85987	+	23.7747i	0.304230	+	1.23432i
$372$	−5.98988			−0.310561
$373$	−3.87479	+	6.71134i	−0.200629	+	0.347500i	−0.948731	−	0.316084i	$-0.897632\pi$
$373$	−3.87479	+	6.71134i	−0.200629	+	0.347500i	0.748102	+	0.663584i	$0.230965\pi$
$374$	−0.434834	−	0.753154i	−0.0224847	−	0.0389447i
$375$	0.868620	+	1.50449i	0.0448553	+	0.0776917i
$376$	−7.33615	+	12.7066i	−0.378333	+	0.655292i
$377$	−0.792739			−0.0408281
$378$	−12.5277	+	12.0330i	−0.644354	+	0.618908i
$379$	22.6740			1.16469			0.582343	−	0.812943i	$-0.302136\pi$
$379$	22.6740			1.16469			0.582343	+	0.812943i	$0.302136\pi$
$380$	0.839254	−	1.45363i	0.0430528	−	0.0745697i
$381$	17.0771	+	29.5784i	0.874885	+	1.51535i
$382$	−4.51204	−	7.81509i	−0.230856	−	0.399855i
$383$	−0.935006	+	1.61948i	−0.0477766	+	0.0827514i	−0.888925	−	0.458053i	$-0.848547\pi$
$383$	−0.935006	+	1.61948i	−0.0477766	+	0.0827514i	0.841148	+	0.540805i	$0.181880\pi$
$384$	−11.9619			−0.610427
$385$	−1.50560	−	0.436106i	−0.0767325	−	0.0222260i
$386$	19.6955			1.00247
$387$	−0.0133808	+	0.0231763i	−0.000680186	+	0.00117812i
$388$	0.748850	+	1.29705i	0.0380171	+	0.0658476i
$389$	−13.5749	−	23.5124i	−0.688274	−	1.19212i	−0.972396	−	0.233337i	$-0.925036\pi$
$389$	−13.5749	−	23.5124i	−0.688274	−	1.19212i	0.284122	−	0.958788i	$-0.408298\pi$
$390$	1.10085	−	1.90672i	0.0557435	−	0.0965505i
$391$	−7.78630			−0.393770
$392$	17.9490	+	11.3504i	0.906561	+	0.573280i
$393$	26.7376			1.34874
$394$	7.58720	−	13.1414i	0.382238	−	0.662055i
$395$	1.55532	+	2.69389i	0.0782567	+	0.135545i
$396$	0.00210019	+	0.00363764i	0.000105539	+	0.000182798i
$397$	−3.16012	+	5.47349i	−0.158602	+	0.274706i	−0.934365	−	0.356318i	$-0.884032\pi$
$397$	−3.16012	+	5.47349i	−0.158602	+	0.274706i	0.775763	+	0.631024i	$0.217365\pi$
$398$	20.2024			1.01265
$399$	−18.8163	−	5.45026i	−0.941995	−	0.272854i
$400$	−3.05725			−0.152863
$401$	8.16164	−	14.1364i	0.407573	−	0.705937i	−0.587044	−	0.809555i	$-0.699709\pi$
$401$	8.16164	−	14.1364i	0.407573	−	0.705937i	0.994617	+	0.103618i	$0.0330418\pi$
$402$	−1.25194	−	2.16842i	−0.0624411	−	0.108151i
$403$	4.37750	+	7.58206i	0.218059	+	0.377689i
$404$	−0.292470	+	0.506573i	−0.0145509	+	0.0252029i
$405$	9.05368			0.449881
$406$	1.91705	−	1.84134i	0.0951417	−	0.0913844i
$407$	−0.629391			−0.0311978
$408$	3.05225	−	5.28665i	0.151109	−	0.261728i
$409$	4.92271	+	8.52639i	0.243412	+	0.421603i	0.961684	−	0.274160i	$-0.0883998\pi$
$409$	4.92271	+	8.52639i	0.243412	+	0.421603i	−0.718272	+	0.695763i	$0.755066\pi$
$410$	5.44170	+	9.42530i	0.268746	+	0.465483i
$411$	10.6871	−	18.5107i	0.527158	−	0.913064i
$412$	−2.68673			−0.132366
$413$	8.96856	+	36.3872i	0.441314	+	1.79050i
$414$	−0.153376			−0.00753802
$415$	4.60905	−	7.98312i	0.226250	−	0.391876i
$416$	−1.09651	−	1.89921i	−0.0537607	−	0.0931163i
$417$	13.7575	+	23.8286i	0.673705	+	1.16689i
$418$	−1.60008	+	2.77143i	−0.0782627	+	0.135555i
$419$	−3.53691			−0.172789			−0.0863946	−	0.996261i	$-0.527535\pi$
$419$	−3.53691			−0.172789			−0.0863946	+	0.996261i	$0.527535\pi$
$420$	−0.433190	−	1.75754i	−0.0211375	−	0.0857590i
$421$	−12.6472			−0.616388			−0.308194	−	0.951323i	$-0.599725\pi$
$421$	−12.6472			−0.616388			−0.308194	+	0.951323i	$0.599725\pi$
$422$	0.376591	−	0.652275i	0.0183322	−	0.0317522i
$423$	−0.0435322	−	0.0753999i	−0.00211661	−	0.00366607i
$424$	14.0388	+	24.3160i	0.681786	+	1.18089i
$425$	0.579124	−	1.00307i	0.0280916	−	0.0486562i
$426$	15.1356			0.733320
$427$	10.9530	−	10.5205i	0.530053	−	0.509121i
$428$	−1.24202			−0.0600352
$429$	0.514618	−	0.891345i	0.0248460	−	0.0430345i
$430$	−0.941994	−	1.63158i	−0.0454270	−	0.0786819i
$431$	−13.2060	−	22.8735i	−0.636112	−	1.10178i	−0.986278	−	0.165091i	$-0.947208\pi$
$431$	−13.2060	−	22.8735i	−0.636112	−	1.10178i	0.350167	−	0.936687i	$-0.386125\pi$
$432$	−7.91897	+	13.7161i	−0.381002	+	0.659914i
$433$	−18.1877			−0.874045			−0.437023	−	0.899450i	$-0.643967\pi$
$433$	−18.1877			−0.874045			−0.437023	+	0.899450i	$0.643967\pi$
$434$	−28.1973	−	8.16751i	−1.35351	−	0.392053i
$435$	−1.37718			−0.0660306
$436$	−2.94235	+	5.09630i	−0.140913	+	0.244069i
$437$	14.3259	+	24.8131i	0.685299	+	1.18697i
$438$	3.87528	+	6.71219i	0.185168	+	0.320721i
$439$	4.96032	−	8.59153i	0.236743	−	0.410051i	−0.723035	−	0.690812i	$-0.757253\pi$
$439$	4.96032	−	8.59153i	0.236743	−	0.410051i	0.959778	+	0.280760i	$0.0905866\pi$
$440$	−1.79740			−0.0856875
$441$	−0.111583	+	0.0585626i	−0.00531347	+	0.00278869i
$442$	−1.46791			−0.0698212
$443$	17.6506	−	30.5718i	0.838606	−	1.45251i	−0.0524536	−	0.998623i	$-0.516704\pi$
$443$	17.6506	−	30.5718i	0.838606	−	1.45251i	0.891060	−	0.453886i	$-0.149963\pi$
$444$	−0.363411	−	0.629446i	−0.0172467	−	0.0298722i
$445$	−5.50461	−	9.53427i	−0.260944	−	0.451968i
$446$	−16.7070	+	28.9374i	−0.791101	+	1.37023i
$447$	20.1709			0.954050
$448$	22.6018	+	6.54674i	1.06783	+	0.309304i
$449$	−15.1260			−0.713840			−0.356920	−	0.934135i	$-0.616173\pi$
$449$	−15.1260			−0.713840			−0.356920	+	0.934135i	$0.616173\pi$
$450$	0.0114077	−	0.0197587i	0.000537764	−	0.000931434i
$451$	2.54386	+	4.40610i	0.119786	+	0.207475i
$452$	−0.239347	−	0.414561i	−0.0112579	−	0.0194993i
$453$	−15.0802	+	26.1198i	−0.708532	+	1.22721i
$454$	29.8968			1.40313
$455$	−1.90813	+	1.83277i	−0.0894543	+	0.0859217i
$456$	−22.4631			−1.05193
$457$	16.7714	−	29.0489i	0.784534	−	1.35885i	−0.144743	−	0.989469i	$-0.546236\pi$
$457$	16.7714	−	29.0489i	0.784534	−	1.35885i	0.929277	−	0.369383i	$-0.120431\pi$
$458$	−18.2281	−	31.5721i	−0.851745	−	1.47527i
$459$	−3.00012	−	5.19636i	−0.140034	−	0.242545i
$460$	−1.32374	+	2.29278i	−0.0617196	+	0.106901i
$461$	−22.1077			−1.02966			−0.514830	−	0.857292i	$-0.672145\pi$
$461$	−22.1077			−1.02966			−0.514830	+	0.857292i	$0.672145\pi$
$462$	0.825901	+	3.35084i	0.0384244	+	0.155895i
$463$	−34.9430			−1.62394			−0.811970	−	0.583699i	$-0.801605\pi$
$463$	−34.9430			−1.62394			−0.811970	+	0.583699i	$0.801605\pi$
$464$	1.21180	−	2.09890i	0.0562565	−	0.0974391i
$465$	7.60477	+	13.1718i	0.352663	+	0.610830i
$466$	−1.99061	−	3.44785i	−0.0922134	−	0.159718i
$467$	−18.1741	+	31.4785i	−0.840998	+	1.45665i	0.0480538	+	0.998845i	$0.484698\pi$
$467$	−18.1741	+	31.4785i	−0.840998	+	1.45665i	−0.889052	+	0.457807i	$0.848635\pi$
$468$	0.00708979			0.000327726
$469$	0.720068	+	2.92146i	0.0332496	+	0.134900i
$470$	6.12923			0.282720
$471$	9.38977	−	16.2636i	0.432658	−	0.749385i
$472$	21.4865	+	37.2157i	0.988996	+	1.71299i
$473$	−0.440359	−	0.762724i	−0.0202477	−	0.0350701i
$474$	3.42434	−	5.93112i	0.157285	−	0.272426i
$475$	−4.26207			−0.195557
$476$	−0.870384	+	0.836012i	−0.0398940	+	0.0383185i
$477$	−0.166611			−0.00762858
$478$	8.03562	−	13.9181i	0.367541	−	0.636599i
$479$	8.38811	+	14.5286i	0.383262	+	0.663830i	0.991526	−	0.129905i	$-0.0414672\pi$
$479$	8.38811	+	14.5286i	0.383262	+	0.663830i	−0.608264	+	0.793735i	$0.708134\pi$
$480$	−1.90490	−	3.29938i	−0.0869462	−	0.150595i
$481$	−0.531172	+	0.920018i	−0.0242194	+	0.0419492i
$482$	27.8053			1.26650
$483$	29.6786	+	8.59658i	1.35042	+	0.391158i
$484$	4.19383			0.190629
$485$	1.90148	−	3.29347i	0.0863419	−	0.149549i
$486$	−0.118551	−	0.205336i	−0.00537756	−	0.00931421i
$487$	7.60142	+	13.1660i	0.344453	+	0.596610i	0.985254	−	0.171097i	$-0.0547310\pi$
$487$	7.60142	+	13.1660i	0.344453	+	0.596610i	−0.640801	+	0.767707i	$0.721398\pi$
$488$	8.70733	−	15.0815i	0.394162	−	0.682709i
$489$	−4.75009			−0.214806
$490$	0.357255	−	8.86425i	0.0161391	−	0.400446i
$491$	13.5771			0.612726			0.306363	−	0.951915i	$-0.400888\pi$
$491$	13.5771			0.612726			0.306363	+	0.951915i	$0.400888\pi$
$492$	−2.93765	+	5.08816i	−0.132440	+	0.229392i
$493$	0.459094	+	0.795174i	0.0206766	+	0.0358129i
$494$	2.70077	+	4.67787i	0.121513	+	0.210467i
$495$	0.00533281	−	0.00923670i	0.000239692	−	0.000415159i
$496$	−26.7663			−1.20184
$497$	−17.4701	−	5.06033i	−0.783643	−	0.226987i
$498$	−20.2954			−0.909460
$499$	−8.22686	+	14.2493i	−0.368285	+	0.637888i	−0.989298	−	0.145912i	$-0.953388\pi$
$499$	−8.22686	+	14.2493i	−0.368285	+	0.637888i	0.621013	+	0.783801i	$0.286722\pi$
$500$	−0.196912	−	0.341062i	−0.00880618	−	0.0152527i
$501$	18.7242	+	32.4313i	0.836535	+	1.44892i
$502$	4.20025	−	7.27505i	0.187466	−	0.324701i
$503$	−18.2607			−0.814205			−0.407102	−	0.913383i	$-0.633461\pi$
$503$	−18.2607			−0.814205			−0.407102	+	0.913383i	$0.633461\pi$
$504$	−0.104214	+	0.100099i	−0.00464207	+	0.00445875i
$505$	1.48528			0.0660941
$506$	2.52378	−	4.37131i	0.112196	−	0.194329i
$507$	−0.868620	−	1.50449i	−0.0385768	−	0.0668169i
$508$	−3.87129	−	6.70528i	−0.171761	−	0.297498i
$509$	−17.2903	+	29.9476i	−0.766378	+	1.32741i	0.173137	+	0.984898i	$0.444610\pi$
$509$	−17.2903	+	29.9476i	−0.766378	+	1.32741i	−0.939515	+	0.342508i	$0.888724\pi$
$510$	−2.55010			−0.112921
$511$	−2.22892	−	9.04315i	−0.0986014	−	0.400045i
$512$	25.2549			1.11612
$513$	−11.0397	+	19.1214i	−0.487416	+	0.844229i
$514$	−2.78323	−	4.82069i	−0.122763	−	0.212631i
$515$	3.41108	+	5.90817i	0.150310	+	0.260345i
$516$	0.508527	−	0.880794i	0.0223866	−	0.0387748i
$517$	2.86526			0.126014
$518$	−0.852469	−	3.45863i	−0.0374553	−	0.151964i
$519$	1.18294			0.0519251
$520$	−1.51691	+	2.62736i	−0.0665207	+	0.115217i
$521$	−15.8775	−	27.5006i	−0.695604	−	1.20482i	−0.969977	−	0.243198i	$-0.921803\pi$
$521$	−15.8775	−	27.5006i	−0.695604	−	1.20482i	0.274372	−	0.961624i	$-0.411530\pi$
$522$	0.00904332	+	0.0156635i	0.000395815	+	0.000685572i
$523$	0.142515	−	0.246843i	0.00623174	−	0.0107937i	−0.862893	−	0.505387i	$-0.831350\pi$
$523$	0.142515	−	0.246843i	0.00623174	−	0.0107937i	0.869124	+	0.494593i	$0.164683\pi$
$524$	−6.06130			−0.264789
$525$	−3.31487	+	3.18397i	−0.144673	+	0.138960i
$526$	−38.5456			−1.68067
$527$	5.07023	−	8.78190i	0.220863	−	0.382546i
$528$	1.57332	+	2.72507i	0.0684699	+	0.118593i
$529$	−11.0959	−	19.2186i	−0.482429	−	0.835592i
$530$	5.86460	−	10.1578i	0.254742	−	0.441226i
$531$	−0.254999			−0.0110660
$532$	4.26558	+	1.23555i	0.184936	+	0.0535678i
$533$	8.58753			0.371967
$534$	−12.1195	+	20.9915i	−0.524460	+	0.908392i
$535$	1.57687	+	2.73122i	0.0681740	+	0.118081i
$536$	1.72511	+	2.98797i	0.0745132	+	0.129061i
$537$	−18.2234	+	31.5639i	−0.786399	+	1.36208i
$538$	−24.0021			−1.03480
$539$	0.167008	−	4.14382i	0.00719354	−	0.178487i
$540$	−2.04018			−0.0877956
$541$	−0.127643	+	0.221085i	−0.00548781	+	0.00950517i	−0.868756	−	0.495240i	$-0.835080\pi$
$541$	−0.127643	+	0.221085i	−0.00548781	+	0.00950517i	0.863268	+	0.504745i	$0.168413\pi$
$542$	−12.6002	−	21.8242i	−0.541225	−	0.937429i
$543$	9.09702	+	15.7565i	0.390390	+	0.676176i
$544$	−1.27003	+	2.19975i	−0.0544520	+	0.0943136i
$545$	14.9425			0.640065
$546$	5.59514	+	1.62066i	0.239450	+	0.0693580i
$547$	34.6935			1.48339			0.741694	−	0.670738i	$-0.234023\pi$
$547$	34.6935			1.48339			0.741694	+	0.670738i	$0.234023\pi$
$548$	−2.42272	+	4.19628i	−0.103494	+	0.179256i
$549$	0.0516687	+	0.0894927i	0.00220516	+	0.00381946i
$550$	0.375424	+	0.650253i	0.0160081	+	0.0277269i
$551$	1.68936	−	2.92605i	0.0719690	−	0.124654i
$552$	35.4306			1.50803
$553$	−5.93550	+	5.70110i	−0.252403	+	0.242435i
$554$	−27.8027			−1.18122
$555$	−0.922774	+	1.59829i	−0.0391696	+	0.0678437i
$556$	−3.11875	−	5.40183i	−0.132264	−	0.229089i
$557$	16.0806	+	27.8524i	0.681357	+	1.18014i	0.974567	+	0.224097i	$0.0719431\pi$
$557$	16.0806	+	27.8524i	0.681357	+	1.18014i	−0.293210	+	0.956048i	$0.594724\pi$
$558$	0.0998744	−	0.172987i	0.00422802	−	0.00732314i
$559$	−1.48656			−0.0628747
$560$	−1.93574	−	7.85369i	−0.0818001	−	0.331879i
$561$	−1.19211			−0.0503310
$562$	−10.0141	+	17.3449i	−0.422418	+	0.731650i
$563$	−9.10209	−	15.7653i	−0.383608	−	0.664428i	0.607967	−	0.793962i	$-0.291985\pi$
$563$	−9.10209	−	15.7653i	−0.383608	−	0.664428i	−0.991575	+	0.129534i	$0.958652\pi$
$564$	1.65440	+	2.86551i	0.0696629	+	0.120660i
$565$	−0.607751	+	1.05266i	−0.0255683	+	0.0442856i
$566$	−11.2860			−0.474388
$567$	5.73247	+	23.2578i	0.240741	+	0.976734i
$568$	−20.8560			−0.875098
$569$	−6.65539	+	11.5275i	−0.279008	+	0.483257i	−0.971139	−	0.238516i	$-0.923339\pi$
$569$	−6.65539	+	11.5275i	−0.279008	+	0.483257i	0.692130	+	0.721773i	$0.256672\pi$
$570$	4.69189	+	8.12658i	0.196521	+	0.340385i
$571$	−18.3271	−	31.7435i	−0.766967	−	1.32843i	−0.939200	−	0.343370i	$-0.888432\pi$
$571$	−18.3271	−	31.7435i	−0.766967	−	1.32843i	0.172233	−	0.985056i	$-0.444902\pi$
$572$	−0.116661	+	0.202064i	−0.00487786	+	0.00844871i
$573$	−12.3699			−0.516760
$574$	−20.7669	+	19.9468i	−0.866794	+	0.832563i
$575$	6.72248			0.280347
$576$	−0.0800552	+	0.138660i	−0.00333564	+	0.00577749i
$577$	−1.82112	−	3.15427i	−0.0758142	−	0.131314i	0.825626	−	0.564218i	$-0.190822\pi$
$577$	−1.82112	−	3.15427i	−0.0758142	−	0.131314i	−0.901440	+	0.432904i	$0.857489\pi$
$578$	−9.92237	−	17.1861i	−0.412716	−	0.714846i
$579$	13.4989	−	23.3808i	0.560997	−	0.971675i
$580$	0.312200			0.0129634
$581$	23.4259	+	6.78545i	0.971870	+	0.281508i
$582$	−8.37296			−0.347070
$583$	2.74156	−	4.74851i	0.113544	−	0.196663i
$584$	−5.33994	−	9.24904i	−0.220968	−	0.382728i
$585$	−0.00900122	−	0.0155906i	−0.000372154	−	0.000644590i
$586$	2.15120	−	3.72599i	0.0888653	−	0.153919i
$587$	28.7909			1.18833			0.594163	−	0.804345i	$-0.297483\pi$
$587$	28.7909			1.18833			0.594163	+	0.804345i	$0.297483\pi$
$588$	4.24061	−	2.22562i	0.174880	−	0.0917830i
$589$	−37.3145			−1.53752
$590$	8.97580	−	15.5465i	0.369528	−	0.640041i
$591$	−10.4003	−	18.0138i	−0.427810	−	0.740989i
$592$	−1.62393	−	2.81273i	−0.0667431	−	0.115602i
$593$	−2.51211	+	4.35111i	−0.103160	+	0.178679i	−0.912985	−	0.407993i	$-0.866229\pi$
$593$	−2.51211	+	4.35111i	−0.103160	+	0.178679i	0.809825	+	0.586672i	$0.199562\pi$
$594$	3.88972			0.159597
$595$	2.94345	+	0.852586i	0.120669	+	0.0349526i
$596$	−4.57264			−0.187303
$597$	13.8464	−	23.9826i	0.566694	−	0.981543i
$598$	−4.25987	−	7.37831i	−0.174199	−	0.301721i
$599$	−7.03799	−	12.1901i	−0.287564	−	0.498076i	0.685664	−	0.727919i	$-0.259512\pi$
$599$	−7.03799	−	12.1901i	−0.287564	−	0.498076i	−0.973228	+	0.229843i	$0.926179\pi$
$600$	−2.63523	+	4.56435i	−0.107583	+	0.186339i
$601$	6.52858			0.266306			0.133153	−	0.991095i	$-0.457490\pi$
$601$	6.52858			0.266306			0.133153	+	0.991095i	$0.457490\pi$
$602$	3.59489	−	3.45292i	0.146517	−	0.140731i
$603$	−0.0204733			−0.000833738
$604$	3.41862	−	5.92123i	0.139102	−	0.240931i
$605$	−5.32450	−	9.22230i	−0.216472	−	0.374940i
$606$	−1.63507	−	2.83202i	−0.0664200	−	0.115043i
$607$	3.28677	−	5.69285i	0.133406	−	0.231066i	−0.791582	−	0.611064i	$-0.790742\pi$
$607$	3.28677	−	5.69285i	0.133406	−	0.231066i	0.924987	+	0.379998i	$0.124075\pi$
$608$	9.34679			0.379063
$609$	−0.871979	−	3.53779i	−0.0353344	−	0.143359i
$610$	−7.27483			−0.294549
$611$	2.41813	−	4.18832i	0.0978270	−	0.169441i
$612$	−0.00410587	−	0.00711157i	−0.000165970	−	0.000287468i
$613$	−3.93667	−	6.81851i	−0.159001	−	0.275397i	0.775508	−	0.631338i	$-0.217494\pi$
$613$	−3.93667	−	6.81851i	−0.159001	−	0.275397i	−0.934509	+	0.355941i	$0.884161\pi$
$614$	1.05825	−	1.83295i	0.0427077	−	0.0739718i
$615$	14.9186			0.601576
$616$	−1.13805	−	4.61728i	−0.0458532	−	0.186036i
$617$	−28.0147			−1.12783			−0.563915	−	0.825833i	$-0.690705\pi$
$617$	−28.0147			−1.12783			−0.563915	+	0.825833i	$0.690705\pi$
$618$	7.51015	−	13.0080i	0.302103	−	0.523257i
$619$	2.53268	+	4.38673i	0.101797	+	0.176317i	0.912425	−	0.409244i	$-0.134207\pi$
$619$	2.53268	+	4.38673i	0.101797	+	0.176317i	−0.810628	+	0.585561i	$0.800874\pi$
$620$	−1.72397	−	2.98600i	−0.0692361	−	0.119921i
$621$	17.4127	−	30.1597i	0.698748	−	1.21027i
$622$	−14.4466			−0.579255
$623$	21.0070	−	20.1774i	0.841628	−	0.808391i
$624$	5.31118			0.212618
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.49610	−	7.78748i	−0.179700	−	0.311250i
$627$	2.19334	+	3.79898i	0.0875936	+	0.151717i
$628$	−2.12862	+	3.68687i	−0.0849411	+	0.147122i
$629$	1.23046			0.0490616
$630$	0.0579805	+	0.0167944i	0.00231000	+	0.000669105i
$631$	37.1478			1.47883			0.739415	−	0.673250i	$-0.235102\pi$
$631$	37.1478			1.47883			0.739415	+	0.673250i	$0.235102\pi$
$632$	−4.71855	+	8.17277i	−0.187694	+	0.325095i
$633$	−0.516218	−	0.894116i	−0.0205178	−	0.0355379i
$634$	−15.5271	−	26.8937i	−0.616659	−	1.06808i
$635$	−9.83000	+	17.0261i	−0.390092	+	0.675659i
$636$	6.33190			0.251076
$637$	−5.91631	−	3.74129i	−0.234413	−	0.148235i
$638$	−0.595226			−0.0235652
$639$	0.0618790	−	0.107178i	0.00244790	−	0.00423988i
$640$	−3.44278	−	5.96307i	−0.136088	−	0.235711i
$641$	−11.2851	−	19.5464i	−0.445734	−	0.772035i	0.552369	−	0.833600i	$-0.313724\pi$
$641$	−11.2851	−	19.5464i	−0.445734	−	0.772035i	−0.998103	+	0.0615652i	$0.980391\pi$
$642$	3.47178	−	6.01330i	0.137020	−	0.237326i
$643$	−13.7935			−0.543963			−0.271982	−	0.962302i	$-0.587679\pi$
$643$	−13.7935			−0.543963			−0.271982	+	0.962302i	$0.587679\pi$
$644$	−6.72800	−	1.94881i	−0.265120	−	0.0767937i
$645$	−2.58251			−0.101686
$646$	3.12816	−	5.41814i	0.123076	−	0.213174i
$647$	1.29095	+	2.23599i	0.0507524	+	0.0879057i	0.890286	−	0.455403i	$-0.150505\pi$
$647$	1.29095	+	2.23599i	0.0507524	+	0.0879057i	−0.839533	+	0.543308i	$0.817171\pi$
$648$	13.7336	+	23.7873i	0.539506	+	0.934452i
$649$	4.19596	−	7.26762i	0.164706	−	0.285279i
$650$	1.26735			0.0497096
$651$	−29.0217	+	27.8756i	−1.13745	+	1.09253i
$652$	1.07682			0.0421716
$653$	22.0215	−	38.1424i	0.861769	−	1.49263i	−0.00845059	−	0.999964i	$-0.502690\pi$
$653$	22.0215	−	38.1424i	0.861769	−	1.49263i	0.870220	−	0.492664i	$-0.163977\pi$
$654$	−16.4493	−	28.4911i	−0.643220	−	1.11409i
$655$	7.69543	+	13.3289i	0.300686	+	0.520803i
$656$	−13.1271	+	22.7369i	−0.512528	+	0.887725i
$657$	0.0633736			0.00247244
$658$	3.88081	+	15.7452i	0.151290	+	0.613812i
$659$	16.2970			0.634841			0.317420	−	0.948285i	$-0.397183\pi$
$659$	16.2970			0.634841			0.317420	+	0.948285i	$0.397183\pi$
$660$	−0.202669	+	0.351033i	−0.00788888	+	0.0136639i
$661$	−19.5031	−	33.7804i	−0.758583	−	1.31390i	−0.943573	−	0.331164i	$-0.892559\pi$
$661$	−19.5031	−	33.7804i	−0.758583	−	1.31390i	0.184990	−	0.982740i	$-0.440775\pi$
$662$	4.59491	+	7.95862i	0.178586	+	0.309320i
$663$	−1.00608	+	1.74258i	−0.0390728	+	0.0676761i
$664$	27.9660			1.08529
$665$	−2.69859	−	10.9487i	−0.104647	−	0.424573i
$666$	0.0242378			0.000939196
$667$	−2.66458	+	4.61520i	−0.103173	+	0.178701i
$668$	−4.24469	−	7.35201i	−0.164232	−	0.284458i
$669$	22.9014	+	39.6664i	0.885421	+	1.53359i
$670$	0.720649	−	1.24820i	0.0278411	−	0.0482222i
$671$	−3.40080			−0.131286
$672$	7.26957	−	6.98248i	0.280430	−	0.269355i
$673$	−34.2222			−1.31917			−0.659585	−	0.751630i	$-0.729268\pi$
$673$	−34.2222			−1.31917			−0.659585	+	0.751630i	$0.729268\pi$
$674$	9.14141	−	15.8334i	0.352114	−	0.609879i
$675$	2.59022	+	4.48640i	0.0996977	+	0.172682i
$676$	0.196912	+	0.341062i	0.00757354	+	0.0131178i
$677$	10.8156	−	18.7331i	0.415676	−	0.719971i	−0.579823	−	0.814742i	$-0.696878\pi$
$677$	10.8156	−	18.7331i	0.415676	−	0.719971i	0.995499	+	0.0947708i	$0.0302118\pi$
$678$	2.67616			0.102777
$679$	9.66444	+	2.79936i	0.370887	+	0.107430i
$680$	3.51391			0.134752
$681$	20.4907	−	35.4910i	0.785207	−	1.36002i
$682$	3.28684	+	5.69297i	0.125859	+	0.217995i
$683$	−16.7440	−	29.0015i	−0.640691	−	1.10971i	−0.985279	−	0.170956i	$-0.945315\pi$
$683$	−16.7440	−	29.0015i	−0.640691	−	1.10971i	0.344587	−	0.938754i	$-0.388019\pi$
$684$	−0.0151086	+	0.0261689i	−0.000577692	+	0.00100059i
$685$	12.3036			0.470096
$686$	22.9973	−	4.69479i	0.878042	−	0.179248i
$687$	−49.9730			−1.90659
$688$	2.27239	−	3.93590i	0.0866342	−	0.150055i
$689$	−4.62745	−	8.01498i	−0.176292	−	0.305347i
$690$	−7.40041	−	12.8179i	−0.281729	−	0.487969i
$691$	23.5904	−	40.8598i	0.897422	−	1.55438i	0.0666443	−	0.997777i	$-0.478771\pi$
$691$	23.5904	−	40.8598i	0.897422	−	1.55438i	0.830778	−	0.556604i	$-0.187896\pi$
$692$	−0.268166			−0.0101941
$693$	0.0271045	+	0.00785096i	0.00102961	+	0.000298233i
$694$	0.430245			0.0163319
$695$	−7.91914	+	13.7164i	−0.300390	+	0.520291i
$696$	−2.08905	−	3.61834i	−0.0791852	−	0.137153i
$697$	−4.97325	−	8.61391i	−0.188375	−	0.326275i
$698$	11.6422	−	20.1649i	0.440664	−	0.763253i
$699$	−5.45733			−0.206415
$700$	0.751466	−	0.721790i	0.0284028	−	0.0272811i
$701$	20.0423			0.756985			0.378493	−	0.925604i	$-0.376443\pi$
$701$	20.0423			0.756985			0.378493	+	0.925604i	$0.376443\pi$
$702$	3.28272	−	5.68584i	0.123898	−	0.214598i
$703$	−2.26390	−	3.92118i	−0.0853845	−	0.147890i
$704$	−2.63459	−	4.56325i	−0.0992950	−	0.171984i
$705$	4.20087	−	7.27611i	0.158214	−	0.274034i
$706$	22.1742			0.834535
$707$	0.940427	+	3.81550i	0.0353684	+	0.143497i
$708$	9.69100			0.364210
$709$	−16.6567	+	28.8503i	−0.625556	+	1.08349i	0.362878	+	0.931837i	$0.381794\pi$
$709$	−16.6567	+	28.8503i	−0.625556	+	1.08349i	−0.988433	+	0.151657i	$0.951539\pi$
$710$	4.35621	+	7.54517i	0.163486	+	0.283165i
$711$	−0.0279996	−	0.0484967i	−0.00105007	−	0.00181877i
$712$	16.7000	−	28.9252i	0.625858	−	1.08402i
$713$	58.8553			2.20415
$714$	−1.61464	−	6.55089i	−0.0604262	−	0.245161i
$715$	0.592455			0.0221566
$716$	4.13117	−	7.15539i	0.154389	−	0.267410i
$717$	−11.0149	−	19.0785i	−0.411361	−	0.712498i
$718$	6.42974	+	11.1366i	0.239956	+	0.415616i
$719$	−25.0484	+	43.3850i	−0.934146	+	1.61799i	−0.157998	+	0.987440i	$0.550504\pi$
$719$	−25.0484	+	43.3850i	−0.934146	+	1.61799i	−0.776149	+	0.630550i	$0.782830\pi$
$720$	0.0550380			0.00205115
$721$	−13.0176	+	12.5035i	−0.484799	+	0.465654i
$722$	1.05788			0.0393702
$723$	19.0573	−	33.0082i	0.708748	−	1.22759i
$724$	−2.06225	−	3.57192i	−0.0766430	−	0.132750i
$725$	−0.396369	−	0.686532i	−0.0147208	−	0.0254972i
$726$	−11.7229	+	20.3047i	−0.435078	+	0.753577i
$727$	−53.5421			−1.98577			−0.992883	−	0.119090i	$-0.962002\pi$
$727$	−53.5421			−1.98577			−0.992883	+	0.119090i	$0.962002\pi$
$728$	−7.70980	−	2.23319i	−0.285744	−	0.0827675i
$729$	26.8360			0.993927
$730$	−2.23071	+	3.86371i	−0.0825624	+	0.143002i
$731$	0.860902	+	1.49113i	0.0318416	+	0.0551513i
$732$	−1.96362	−	3.40110i	−0.0725776	−	0.125708i
$733$	−6.38991	+	11.0676i	−0.236017	+	0.408793i	−0.959568	−	0.281478i	$-0.909175\pi$
$733$	−6.38991	+	11.0676i	−0.236017	+	0.408793i	0.723551	+	0.690271i	$0.242509\pi$
$734$	19.7516			0.729045
$735$	−10.2781	−	6.49951i	−0.379112	−	0.239738i
$736$	−14.7425			−0.543416
$737$	0.336885	−	0.583503i	0.0124093	−	0.0214936i
$738$	−0.0979639	−	0.169678i	−0.00360610	−	0.00624595i
$739$	−26.7056	−	46.2555i	−0.982383	−	1.70154i	−0.653033	−	0.757329i	$-0.726504\pi$
$739$	−26.7056	−	46.2555i	−0.982383	−	1.70154i	−0.329350	−	0.944208i	$-0.606830\pi$
$740$	0.209188	−	0.362325i	0.00768992	−	0.0133193i
$741$	7.40425			0.272002
$742$	29.8073	+	8.63386i	1.09426	+	0.316959i
$743$	39.1593			1.43662			0.718308	−	0.695725i	$-0.244917\pi$
$743$	39.1593			1.43662			0.718308	+	0.695725i	$0.244917\pi$
$744$	−23.0715	+	39.9609i	−0.845840	+	1.46504i
$745$	5.80544	+	10.0553i	0.212695	+	0.368398i
$746$	4.91072	+	8.50562i	0.179794	+	0.311413i
$747$	−0.0829742	+	0.143716i	−0.00303587	+	0.00525828i
$748$	0.270246			0.00988117
$749$	−6.01773	+	5.78009i	−0.219883	+	0.211200i
$750$	2.20169			0.0803944
$751$	−6.27462	+	10.8680i	−0.228964	+	0.396577i	−0.957501	−	0.288429i	$-0.906867\pi$
$751$	−6.27462	+	10.8680i	−0.228964	+	0.396577i	0.728537	+	0.685006i	$0.240200\pi$
$752$	7.39283	+	12.8048i	0.269589	+	0.466941i
$753$	−5.75756	−	9.97238i	−0.209817	−	0.363414i
$754$	−0.502339	+	0.870076i	−0.0182941	+	0.0316863i
$755$	−17.3612			−0.631837
$756$	−1.29177	−	5.24097i	−0.0469813	−	0.190612i
$757$	46.5833			1.69310			0.846550	−	0.532309i	$-0.178676\pi$
$757$	46.5833			1.69310			0.846550	+	0.532309i	$0.178676\pi$
$758$	14.3680	−	24.8860i	0.521868	−	0.903901i
$759$	−3.45951	−	5.99205i	−0.125572	−	0.217497i
$760$	−6.46517	−	11.1980i	−0.234516	−	0.406194i
$761$	5.04536	−	8.73881i	0.182894	−	0.316782i	−0.759971	−	0.649957i	$-0.774787\pi$
$761$	5.04536	−	8.73881i	0.182894	−	0.316782i	0.942865	+	0.333175i	$0.108120\pi$
$762$	43.2853			1.56806
$763$	9.46103	+	38.3853i	0.342512	+	1.38964i
$764$	2.80420			0.101452
$765$	−0.0104256	+	0.0180577i	−0.000376940	+	0.000652879i
$766$	1.18498	+	2.05244i	0.0428150	+	0.0741578i
$767$	−7.08234	−	12.2670i	−0.255728	−	0.442935i
$768$	7.87077	−	13.6326i	0.284012	−	0.491923i
$769$	−5.38474			−0.194179			−0.0970893	−	0.995276i	$-0.530953\pi$
$769$	−5.38474			−0.194179			−0.0970893	+	0.995276i	$0.530953\pi$
$770$	−1.43271	+	1.37613i	−0.0516314	+	0.0495924i
$771$	−7.63030			−0.274799
$772$	−3.06015	+	5.30033i	−0.110137	+	0.190763i
$773$	17.4734	+	30.2648i	0.628473	+	1.08855i	0.987858	+	0.155358i	$0.0496532\pi$
$773$	17.4734	+	30.2648i	0.628473	+	1.08855i	−0.359385	+	0.933189i	$0.617013\pi$
$774$	0.0169582	+	0.0293724i	0.000609550	+	0.00105577i
$775$	−4.37750	+	7.58206i	−0.157245	+	0.272355i
$776$	11.5375			0.414172
$777$	−4.69007	−	1.35851i	−0.168255	−	0.0487362i
$778$	−34.4082			−1.23360
$779$	−18.3003	+	31.6971i	−0.655678	+	1.13567i
$780$	0.342083	+	0.592506i	0.0122486	+	0.0212151i
$781$	2.03642	+	3.52718i	0.0728688	+	0.126213i
$782$	−4.93398	+	8.54591i	−0.176439	+	0.305601i
$783$	−4.10674			−0.146763
$784$	18.9495	−	9.94536i	0.676768	−	0.355191i
$785$	10.8100			0.385825
$786$	16.9430	−	29.3461i	0.604336	−	1.04674i
$787$	−14.7376	−	25.5262i	−0.525338	−	0.909912i	−0.999565	−	0.0295090i	$-0.990606\pi$
$787$	−14.7376	−	25.5262i	−0.525338	−	0.909912i	0.474227	−	0.880403i	$-0.342728\pi$
$788$	2.35769	+	4.08364i	0.0839893	+	0.145474i
$789$	−26.4185	+	45.7582i	−0.940524	+	1.62903i
$790$	3.94227			0.140260
$791$	−3.08895	−	0.894731i	−0.109830	−	0.0318130i
$792$	0.0323575			0.00114977
$793$	−2.87009	+	4.97115i	−0.101920	+	0.176531i
$794$	4.00498	+	6.93682i	0.142131	+	0.246179i
$795$	−8.03899	−	13.9239i	−0.285114	−	0.493832i
$796$	−3.13891	+	5.43674i	−0.111256	+	0.192700i
$797$	−1.74984			−0.0619824			−0.0309912	−	0.999520i	$-0.509866\pi$
$797$	−1.74984			−0.0619824			−0.0309912	+	0.999520i	$0.509866\pi$
$798$	−17.9054	+	17.1983i	−0.633845	+	0.608814i
$799$	−5.60158			−0.198170
$800$	1.09651	−	1.89921i	0.0387674	−	0.0671471i
$801$	0.0990964	+	0.171640i	0.00350140	+	0.00606460i
$802$	−10.3437	−	17.9157i	−0.365247	−	0.632627i
$803$	−1.04280	+	1.80619i	−0.0367997	+	0.0637390i
$804$	0.778071			0.0274404
$805$	4.25643	+	17.2692i	0.150020	+	0.608659i
$806$	11.0957			0.390828
$807$	−16.4506	+	28.4933i	−0.579089	+	1.00301i
$808$	2.25303	+	3.90237i	0.0792614	+	0.137285i
$809$	1.11561	+	1.93229i	0.0392226	+	0.0679355i	0.884970	−	0.465647i	$-0.154179\pi$
$809$	1.11561	+	1.93229i	0.0392226	+	0.0679355i	−0.845748	+	0.533583i	$0.820845\pi$
$810$	5.73709	−	9.93694i	0.201581	−	0.349148i
$811$	50.8443			1.78539			0.892693	−	0.450666i	$-0.148813\pi$
$811$	50.8443			1.78539			0.892693	+	0.450666i	$0.148813\pi$
$812$	0.197674	+	0.802001i	0.00693699	+	0.0281447i
$813$	−34.5438			−1.21151
$814$	−0.398829	+	0.690793i	−0.0139790	+	0.0242123i
$815$	−1.36714	−	2.36795i	−0.0478887	−	0.0829457i
$816$	−3.07583	−	5.32750i	−0.107676	−	0.186500i
$817$	3.16791	−	5.48698i	0.110831	−	0.191965i
$818$	12.4776			0.436269
$819$	0.0343509	−	0.0329944i	0.00120032	−	0.00115292i
$820$	−3.38198			−0.118104
$821$	−10.9845	+	19.0258i	−0.383363	+	0.664004i	−0.991541	−	0.129797i	$-0.958567\pi$
$821$	−10.9845	+	19.0258i	−0.383363	+	0.664004i	0.608178	+	0.793801i	$0.291901\pi$
$822$	−13.5443	−	23.4595i	−0.472413	−	0.818244i
$823$	−14.4639	−	25.0522i	−0.504180	−	0.873265i	−0.999988	−	0.00483312i	$-0.998462\pi$
$823$	−14.4639	−	25.0522i	−0.504180	−	0.873265i	0.495809	−	0.868432i	$-0.334872\pi$
$824$	−10.3486	+	17.9243i	−0.360510	+	0.624422i
$825$	1.02924			0.0358334
$826$	45.6202	+	13.2142i	1.58733	+	0.459780i
$827$	−30.6557			−1.06600			−0.533002	−	0.846114i	$-0.678936\pi$
$827$	−30.6557			−1.06600			−0.533002	+	0.846114i	$0.678936\pi$
$828$	0.0238305	−	0.0412756i	0.000828167	−	0.00143443i
$829$	−10.5965	−	18.3536i	−0.368030	−	0.637447i	0.621227	−	0.783631i	$-0.286634\pi$
$829$	−10.5965	−	18.3536i	−0.368030	−	0.637447i	−0.989258	+	0.146183i	$0.953301\pi$
$830$	−5.84129	−	10.1174i	−0.202754	−	0.351180i
$831$	−19.0555	+	33.0051i	−0.661028	+	1.14493i
$832$	−8.89383			−0.308338
$833$	−0.326500	+	8.10116i	−0.0113126	+	0.280689i
$834$	34.8710			1.20748
$835$	−10.7781	+	18.6683i	−0.372993	+	0.646042i
$836$	−0.497220	−	0.861210i	−0.0171967	−	0.0297856i
$837$	22.6774	+	39.2784i	0.783846	+	1.35766i
$838$	−2.24125	+	3.88196i	−0.0774226	+	0.134100i
$839$	42.7695			1.47657			0.738284	−	0.674490i	$-0.235637\pi$
$839$	42.7695			1.47657			0.738284	+	0.674490i	$0.235637\pi$
$840$	−13.3938	−	3.87958i	−0.462129	−	0.133858i
$841$	−28.3716			−0.978330
$842$	−8.01423	+	13.8811i	−0.276189	+	0.478373i
$843$	13.7270	+	23.7758i	0.472781	+	0.818881i
$844$	0.117024	+	0.202692i	0.00402814	+	0.00697694i
$845$	0.500000	−	0.866025i	0.0172005	−	0.0297922i
$846$	−0.110341			−0.00379360
$847$	20.3196	−	19.5172i	0.698191	−	0.670618i
$848$	28.2946			0.971640
$849$	−7.73526	+	13.3979i	−0.265474	+	0.459814i
$850$	−0.733953	−	1.27124i	−0.0251744	−	0.0436033i
$851$	3.57080	+	6.18480i	0.122405	+	0.212012i
$852$	−2.35166	+	4.07319i	−0.0805665	+	0.139545i
$853$	−49.3099			−1.68834			−0.844169	−	0.536078i	$-0.819905\pi$
$853$	−49.3099			−1.68834			−0.844169	+	0.536078i	$0.819905\pi$
$854$	−4.60616	−	18.6881i	−0.157620	−	0.639493i
$855$	0.0767277			0.00262403
$856$	−4.78393	+	8.28601i	−0.163511	+	0.283210i
$857$	−17.2016	−	29.7940i	−0.587594	−	1.01774i	−0.994547	−	0.104293i	$-0.966742\pi$
$857$	−17.2016	−	29.7940i	−0.587594	−	1.01774i	0.406953	−	0.913449i	$-0.366591\pi$
$858$	−0.652201	−	1.12965i	−0.0222658	−	0.0385655i
$859$	15.7745	−	27.3222i	0.538218	−	0.932221i	−0.460782	−	0.887513i	$-0.652431\pi$
$859$	15.7745	−	27.3222i	0.538218	−	0.932221i	0.999000	−	0.0447079i	$-0.0142357\pi$
$860$	0.585442			0.0199634
$861$	9.44592	+	38.3240i	0.321916	+	1.30608i
$862$	−33.4733			−1.14011
$863$	−7.00975	+	12.1412i	−0.238615	+	0.413293i	−0.960317	−	0.278911i	$-0.910027\pi$
$863$	−7.00975	+	12.1412i	−0.238615	+	0.413293i	0.721702	+	0.692203i	$0.243360\pi$
$864$	−5.68040	−	9.83873i	−0.193251	−	0.334721i
$865$	0.340464	+	0.589701i	0.0115761	+	0.0200505i
$866$	−11.5251	+	19.9620i	−0.391639	+	0.678338i
$867$	−27.2025			−0.923845
$868$	6.57909	−	6.31927i	0.223309	−	0.214490i
$869$	1.84291			0.0625166
$870$	−0.872683	+	1.51153i	−0.0295867	+	0.0512457i
$871$	−0.568626	−	0.984890i	−0.0192672	−	0.0333717i
$872$	22.6663	+	39.2592i	0.767579	+	1.32949i
$873$	−0.0342313	+	0.0592904i	−0.00115855	+	0.00200668i
$874$	36.3117			1.22826
$875$	−2.54129	−	0.736100i	−0.0859113	−	0.0248847i
$876$	−2.40846			−0.0813743
$877$	−5.14983	+	8.91977i	−0.173897	+	0.301199i	−0.939779	−	0.341782i	$-0.888969\pi$
$877$	−5.14983	+	8.91977i	−0.173897	+	0.301199i	0.765882	+	0.642981i	$0.222303\pi$
$878$	−6.28647	−	10.8885i	−0.212158	−	0.367468i
$879$	−2.94879	−	5.10746i	−0.0994603	−	0.172270i
$880$	−0.905642	+	1.56862i	−0.0305292	+	0.0528781i
$881$	−10.5642			−0.355916			−0.177958	−	0.984038i	$-0.556949\pi$
$881$	−10.5642			−0.355916			−0.177958	+	0.984038i	$0.556949\pi$
$882$	−0.00643146	+	0.159578i	−0.000216559	+	0.00537327i
$883$	47.5619			1.60059			0.800293	−	0.599608i	$-0.204677\pi$
$883$	47.5619			1.60059			0.800293	+	0.599608i	$0.204677\pi$
$884$	0.228073	−	0.395034i	0.00767093	−	0.0132864i
$885$	−12.3037	−	21.3107i	−0.413585	−	0.716350i
$886$	−22.3695	−	38.7451i	−0.751519	−	1.30167i
$887$	−13.3571	+	23.1353i	−0.448489	+	0.776806i	−0.998288	−	0.0584913i	$-0.981371\pi$
$887$	−13.3571	+	23.1353i	−0.448489	+	0.776806i	0.549799	+	0.835297i	$0.314704\pi$
$888$	−5.59905			−0.187892
$889$	−49.9618	−	14.4717i	−1.67566	−	0.485366i
$890$	−13.9525			−0.467690
$891$	2.68195	−	4.64527i	0.0898487	−	0.155622i
$892$	−5.19165	−	8.99220i	−0.173829	−	0.301081i
$893$	10.3062	+	17.8509i	0.344885	+	0.597359i
$894$	12.7818	−	22.1387i	0.427487	−	0.740428i
$895$	−20.9798			−0.701276
$896$	13.1385	−	12.6197i	0.438927	−	0.421593i
$897$	−11.6786			−0.389936
$898$	−9.58497	+	16.6017i	−0.319855	+	0.554004i
$899$	−3.47022	−	6.01059i	−0.115738	−	0.200464i
$900$	0.00354490	+	0.00613994i	0.000118163	+	0.000204665i
$901$	−5.35974	+	9.28334i	−0.178559	+	0.309273i
$902$	6.44792			0.214692
$903$	−1.63515	−	6.63413i	−0.0544144	−	0.220770i
$904$	−3.68761			−0.122648
$905$	−5.23648	+	9.06985i	−0.174066	+	0.301492i
$906$	19.1120	+	33.1029i	0.634952	+	1.09977i
$907$	−27.6457	−	47.8838i	−0.917961	−	1.58995i	−0.802508	−	0.596642i	$-0.796501\pi$
$907$	−27.6457	−	47.8838i	−0.917961	−	1.58995i	−0.115453	−	0.993313i	$-0.536832\pi$
$908$	−4.64516	+	8.04564i	−0.154155	+	0.267004i
$909$	−0.0267387			−0.000886866
$910$	0.802441	+	3.25566i	0.0266006	+	0.107924i
$911$	−16.5736			−0.549109			−0.274555	−	0.961571i	$-0.588530\pi$
$911$	−16.5736			−0.549109			−0.274555	+	0.961571i	$0.588530\pi$
$912$	−11.3183	+	19.6039i	−0.374787	+	0.649151i
$913$	−2.73066	−	4.72964i	−0.0903715	−	0.156528i
$914$	−21.2553	−	36.8152i	−0.703061	−	1.21774i
$915$	−4.98604	+	8.63608i	−0.164833	+	0.285500i
$916$	11.3286			0.374309
$917$	−29.3677	+	28.2080i	−0.969808	+	0.931509i
$918$	−7.60441			−0.250983
$919$	−4.26930	+	7.39464i	−0.140831	+	0.243927i	−0.927810	−	0.373053i	$-0.878311\pi$
$919$	−4.26930	+	7.39464i	−0.140831	+	0.243927i	0.786979	+	0.616980i	$0.211644\pi$
$920$	10.1974	+	17.6624i	0.336197	+	0.582311i
$921$	−1.45062	−	2.51254i	−0.0477995	−	0.0827912i
$922$	−14.0091	+	24.2645i	−0.461366	+	0.799109i
$923$	6.87452			0.226277
$924$	−1.03008	−	0.298369i	−0.0338872	−	0.00981562i
$925$	−1.06234			−0.0349297
$926$	−22.1425	+	38.3520i	−0.727648	+	1.26032i
$927$	−0.0614078	−	0.106361i	−0.00201690	−	0.00349337i
$928$	0.869244	+	1.50557i	0.0285343	+	0.0494229i
$929$	13.6500	−	23.6425i	0.447842	−	0.775685i	−0.550403	−	0.834899i	$-0.685526\pi$
$929$	13.6500	−	23.6425i	0.447842	−	0.775685i	0.998245	+	0.0592138i	$0.0188594\pi$
$930$	19.2758			0.632079
$931$	26.4172	−	13.8647i	0.865789	−	0.454397i
$932$	1.23715			0.0405243
$933$	−9.90144	+	17.1498i	−0.324158	+	0.561459i
$934$	23.0330	+	39.8943i	0.753662	+	1.30538i
$935$	−0.343105	−	0.594275i	−0.0112207	−	0.0194349i
$936$	0.0273080	−	0.0472988i	0.000892590	−	0.00154601i
$937$	26.1032			0.852754			0.426377	−	0.904546i	$-0.359790\pi$
$937$	26.1032			0.852754			0.426377	+	0.904546i	$0.359790\pi$
$938$	3.66276	+	1.06094i	0.119593	+	0.0346409i
$939$	−12.3262			−0.402251
$940$	−0.952317	+	1.64946i	−0.0310612	+	0.0537995i
$941$	−18.6483	−	32.2999i	−0.607919	−	1.05295i	−0.991583	−	0.129474i	$-0.958671\pi$
$941$	−18.6483	−	32.2999i	−0.607919	−	1.05295i	0.383664	−	0.923473i	$-0.374662\pi$
$942$	−11.9001	−	20.6116i	−0.387727	−	0.671563i
$943$	28.8647	−	49.9952i	0.939965	−	1.62807i
$944$	43.3050			1.40946
$945$	−9.88494	+	9.49458i	−0.321557	+	0.308859i
$946$	−1.11618			−0.0362901
$947$	20.5613	−	35.6132i	0.668153	−	1.15728i	−0.310267	−	0.950649i	$-0.600418\pi$
$947$	20.5613	−	35.6132i	0.668153	−	1.15728i	0.978420	−	0.206626i	$-0.0662482\pi$
$948$	1.06410	+	1.84307i	0.0345603	+	0.0598603i
$949$	1.76014	+	3.04865i	0.0571366	+	0.0989634i
$950$	−2.70077	+	4.67787i	−0.0876246	+	0.151770i
$951$	−42.5680			−1.38036
$952$	2.22488	+	9.02678i	0.0721088	+	0.292560i
$953$	16.3831			0.530701			0.265350	−	0.964152i	$-0.414512\pi$
$953$	16.3831			0.530701			0.265350	+	0.964152i	$0.414512\pi$
$954$	−0.105577	+	0.182865i	−0.00341818	+	0.00592047i
$955$	−3.56022	−	6.16648i	−0.115206	−	0.199543i
$956$	2.49704	+	4.32500i	0.0807600	+	0.139880i
$957$	−0.407958	+	0.706603i	−0.0131874	+	0.0228412i
$958$	21.2613			0.686923
$959$	7.79019	+	31.6063i	0.251558	+	1.02062i
$960$	−15.4507			−0.498669
$961$	−22.8250	+	39.5341i	−0.736292	+	1.27529i
$962$	0.673181	+	1.16598i	0.0217042	+	0.0375928i
$963$	−0.0283875	−	0.0491686i	−0.000914774	−	0.00158444i
$964$	−4.32020	+	7.48280i	−0.139144	+	0.241005i
$965$	15.5407			0.500272
$966$	28.2418	−	27.1265i	0.908666	−	0.872782i
$967$	−47.8673			−1.53931			−0.769654	−	0.638461i	$-0.779571\pi$
$967$	−47.8673			−1.53931			−0.769654	+	0.638461i	$0.779571\pi$
$968$	16.1535	−	27.9787i	0.519194	−	0.899271i
$969$	−4.28798	−	7.42700i	−0.137750	−	0.238589i
$970$	−2.40984	−	4.17397i	−0.0773755	−	0.134018i
$971$	−28.0299	+	48.5492i	−0.899522	+	1.55802i	−0.0714159	+	0.997447i	$0.522752\pi$
$971$	−28.0299	+	48.5492i	−0.899522	+	1.55802i	−0.828106	+	0.560571i	$0.810582\pi$
$972$	0.0736783			0.00236323
$973$	−40.2497	−	11.6586i	−1.29035	−	0.373756i
$974$	19.2673			0.617365
$975$	0.868620	−	1.50449i	0.0278181	−	0.0481824i
$976$	−8.77461	−	15.1981i	−0.280868	−	0.486478i
$977$	−10.4422	−	18.0865i	−0.334076	−	0.578637i	0.649231	−	0.760591i	$-0.275091\pi$
$977$	−10.4422	−	18.0865i	−0.334076	−	0.578637i	−0.983307	+	0.181955i	$0.941758\pi$
$978$	−3.01001	+	5.21349i	−0.0962496	+	0.166709i
$979$	−6.52247			−0.208459
$980$	2.32999	+	1.47341i	0.0744287	+	0.0470663i
$981$	−0.269001			−0.00858853
$982$	8.60347	−	14.9016i	0.274548	−	0.475530i
$983$	16.0909	+	27.8703i	0.513220	+	0.888924i	0.999882	+	0.0153336i	$0.00488102\pi$
$983$	16.0909	+	27.8703i	0.513220	+	0.888924i	−0.486662	+	0.873590i	$0.661786\pi$
$984$	22.6301	+	39.1965i	0.721422	+	1.24954i
$985$	5.98666	−	10.3692i	0.190751	−	0.330390i
$986$	1.16367			0.0370587
$987$	21.3512	+	6.18451i	0.679618	+	0.196855i
$988$	−1.67851			−0.0534005
$989$	−4.99668	+	8.65450i	−0.158885	+	0.275197i
$990$	−0.00675854	−	0.0117061i	−0.000214801	−	0.000372045i
$991$	19.8249	+	34.3378i	0.629760	+	1.09078i	0.987600	+	0.156993i	$0.0501802\pi$
$991$	19.8249	+	34.3378i	0.629760	+	1.09078i	−0.357839	+	0.933783i	$0.616487\pi$
$992$	9.59993	−	16.6276i	0.304798	−	0.527926i
$993$	12.5971			0.399756
$994$	−16.6244	+	15.9679i	−0.527294	+	0.506470i
$995$	15.9406			0.505352
$996$	3.15336	−	5.46179i	0.0999181	−	0.173063i
$997$	13.7808	+	23.8690i	0.436442	+	0.755940i	0.997412	−	0.0718960i	$-0.0229050\pi$
$997$	13.7808	+	23.8690i	0.436442	+	0.755940i	−0.560970	+	0.827836i	$0.689572\pi$
$998$	10.4263	+	18.0589i	0.330039	+	0.571645i
$999$	−2.75171	+	4.76610i	−0.0870602	+	0.150793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	455.2.j.g.261.7	✓	20
7.2	even	3		3185.2.a.bb.1.4		10
7.4	even	3	inner	455.2.j.g.326.7	yes	20
7.5	odd	6		3185.2.a.bc.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
455.2.j.g.261.7	✓	20	1.1	even	1	trivial
455.2.j.g.326.7	yes	20	7.4	even	3	inner
3185.2.a.bb.1.4		10	7.2	even	3
3185.2.a.bc.1.4		10	7.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.633675 - 1.09756i) q^{2} +(-0.868620 - 1.50449i) q^{3} +(0.196912 + 0.341062i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.20169 q^{6} +(2.54129 + 0.736100i) q^{7} +3.03381 q^{8} +(-0.00900122 + 0.0155906i) q^{9} +(-0.633675 - 1.09756i) q^{10} +(-0.296227 - 0.513081i) q^{11} +(0.342083 - 0.592506i) q^{12} -1.00000 q^{13} +(2.41826 - 2.32276i) q^{14} -1.73724 q^{15} +(1.52863 - 2.64766i) q^{16} +(0.579124 + 1.00307i) q^{17} +(0.0114077 + 0.0197587i) q^{18} +(2.13104 - 3.69107i) q^{19} +0.393824 q^{20} +(-1.09996 - 4.46275i) q^{21} -0.750848 q^{22} +(-3.36124 + 5.82184i) q^{23} +(-2.63523 - 4.56435i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.633675 + 1.09756i) q^{26} -5.18045 q^{27} +(0.249355 + 1.01168i) q^{28} +0.792739 q^{29} +(-1.10085 + 1.90672i) q^{30} +(-4.37750 - 7.58206i) q^{31} +(1.09651 + 1.89921i) q^{32} +(-0.514618 + 0.891345i) q^{33} +1.46791 q^{34} +(1.90813 - 1.83277i) q^{35} -0.00708979 q^{36} +(0.531172 - 0.920018i) q^{37} +(-2.70077 - 4.67787i) q^{38} +(0.868620 + 1.50449i) q^{39} +(1.51691 - 2.62736i) q^{40} -8.58753 q^{41} +(-5.59514 - 1.62066i) q^{42} +1.48656 q^{43} +(0.116661 - 0.202064i) q^{44} +(0.00900122 + 0.0155906i) q^{45} +(4.25987 + 7.37831i) q^{46} +(-2.41813 + 4.18832i) q^{47} -5.31118 q^{48} +(5.91631 + 3.74129i) q^{49} -1.26735 q^{50} +(1.00608 - 1.74258i) q^{51} +(-0.196912 - 0.341062i) q^{52} +(4.62745 + 8.01498i) q^{53} +(-3.28272 + 5.68584i) q^{54} -0.592455 q^{55} +(7.70980 + 2.23319i) q^{56} -7.40425 q^{57} +(0.502339 - 0.870076i) q^{58} +(7.08234 + 12.2670i) q^{59} +(-0.342083 - 0.592506i) q^{60} +(2.87009 - 4.97115i) q^{61} -11.0957 q^{62} +(-0.0343509 + 0.0329944i) q^{63} +8.89383 q^{64} +(-0.500000 + 0.866025i) q^{65} +(0.652201 + 1.12965i) q^{66} +(0.568626 + 0.984890i) q^{67} +(-0.228073 + 0.395034i) q^{68} +11.6786 q^{69} +(-0.802441 - 3.25566i) q^{70} -6.87452 q^{71} +(-0.0273080 + 0.0472988i) q^{72} +(-1.76014 - 3.04865i) q^{73} +(-0.673181 - 1.16598i) q^{74} +(-0.868620 + 1.50449i) q^{75} +1.67851 q^{76} +(-0.375121 - 1.52194i) q^{77} +2.20169 q^{78} +(-1.55532 + 2.69389i) q^{79} +(-1.52863 - 2.64766i) q^{80} +(4.52684 + 7.84072i) q^{81} +(-5.44170 + 9.42530i) q^{82} +9.21811 q^{83} +(1.30548 - 1.25392i) q^{84} +1.15825 q^{85} +(0.941994 - 1.63158i) q^{86} +(-0.688589 - 1.19267i) q^{87} +(-0.898698 - 1.55659i) q^{88} +(5.50461 - 9.53427i) q^{89} +0.0228154 q^{90} +(-2.54129 - 0.736100i) q^{91} -2.64747 q^{92} +(-7.60477 + 13.1718i) q^{93} +(3.06461 + 5.30807i) q^{94} +(-2.13104 - 3.69107i) q^{95} +(1.90490 - 3.29938i) q^{96} +3.80297 q^{97} +(7.85530 - 4.12273i) q^{98} +0.0106656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 4 q^{3} - 13 q^{4} + 10 q^{5} - 18 q^{6} + q^{7} - 6 q^{8} - 14 q^{9} - q^{10} - 7 q^{11} + 7 q^{12} - 20 q^{13} + 3 q^{14} + 8 q^{15} - 7 q^{16} + 6 q^{17} + 5 q^{18} + 10 q^{19} - 26 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) \) 20 * q + q^2 + 4 * q^3 - 13 * q^4 + 10 * q^5 - 18 * q^6 + q^7 - 6 * q^8 - 14 * q^9 - q^10 - 7 * q^11 + 7 * q^12 - 20 * q^13 + 3 * q^14 + 8 * q^15 - 7 * q^16 + 6 * q^17 + 5 * q^18 + 10 * q^19 - 26 * q^20 + 16 * q^21 - 22 * q^22 - 7 * q^23 + 20 * q^24 - 10 * q^25 - q^26 - 32 * q^27 + 36 * q^28 + 6 * q^29 - 9 * q^30 + 26 * q^31 + 22 * q^32 + 18 * q^33 - 6 * q^34 + 2 * q^35 + 56 * q^36 + 2 * q^37 - 25 * q^38 - 4 * q^39 - 3 * q^40 - 38 * q^41 + 21 * q^42 - 2 * q^43 - 33 * q^44 + 14 * q^45 + 20 * q^46 + 31 * q^47 - 46 * q^48 - 25 * q^49 - 2 * q^50 - 34 * q^51 + 13 * q^52 + 22 * q^53 + 42 * q^54 - 14 * q^55 + 30 * q^56 - 46 * q^57 + 7 * q^58 - q^59 - 7 * q^60 + 14 * q^61 + 30 * q^62 - 17 * q^63 - 10 * q^64 - 10 * q^65 - 45 * q^66 + 26 * q^67 + 12 * q^68 - 2 * q^69 + 3 * q^70 + 14 * q^71 - 40 * q^72 + 30 * q^73 + 13 * q^74 + 4 * q^75 - 86 * q^76 - 25 * q^77 + 18 * q^78 - 10 * q^79 + 7 * q^80 - 22 * q^81 + 9 * q^82 - 40 * q^83 + 46 * q^84 + 12 * q^85 - 17 * q^86 + 52 * q^88 + q^89 + 10 * q^90 - q^91 + 30 * q^92 + 32 * q^93 + 22 * q^94 - 10 * q^95 - 22 * q^96 - 38 * q^97 - 26 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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