LMFDB - Embedded newform 117.3.k.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.09261i q^{2} +(1.33417 + 2.68700i) q^{3} -5.56427 q^{4} +(6.70477 - 3.87100i) q^{5} +(8.30987 - 4.12608i) q^{6} +(6.32403 + 10.9535i) q^{7} +4.83767i q^{8} +(-5.43998 + 7.16984i) q^{9} +(-11.9715 - 20.7353i) q^{10} -5.58835i q^{11} +(-7.42368 - 14.9512i) q^{12} +(-4.52972 - 12.1853i) q^{13} +(33.8751 - 19.5578i) q^{14} +(19.3467 + 12.8512i) q^{15} -7.29600 q^{16} +(-13.1669 - 7.60194i) q^{17} +(22.1736 + 16.8238i) q^{18} +(-1.34728 + 2.33356i) q^{19} +(-37.3072 + 21.5393i) q^{20} +(-20.9949 + 31.6066i) q^{21} -17.2826 q^{22} +(8.74785 + 5.05057i) q^{23} +(-12.9988 + 6.45428i) q^{24} +(17.4693 - 30.2578i) q^{25} +(-37.6845 + 14.0087i) q^{26} +(-26.5233 - 5.05145i) q^{27} +(-35.1886 - 60.9484i) q^{28} +34.9691i q^{29} +(39.7437 - 59.8319i) q^{30} +(-1.95095 - 3.37914i) q^{31} +41.9144i q^{32} +(15.0159 - 7.45581i) q^{33} +(-23.5099 + 40.7203i) q^{34} +(84.8024 + 48.9607i) q^{35} +(30.2695 - 39.8949i) q^{36} +(10.0226 + 17.3596i) q^{37} +(7.21681 + 4.16663i) q^{38} +(26.6985 - 28.4286i) q^{39} +(18.7267 + 32.4355i) q^{40} +(-54.5456 - 31.4919i) q^{41} +(97.7470 + 64.9290i) q^{42} +(-12.5741 - 21.7790i) q^{43} +31.0951i q^{44} +(-8.71934 + 69.1303i) q^{45} +(15.6195 - 27.0537i) q^{46} +(40.0880 + 23.1448i) q^{47} +(-9.73411 - 19.6044i) q^{48} +(-55.4867 + 96.1057i) q^{49} +(-93.5756 - 54.0259i) q^{50} +(2.85949 - 45.5219i) q^{51} +(25.2045 + 67.8023i) q^{52} -37.9847i q^{53} +(-15.6222 + 82.0262i) q^{54} +(-21.6325 - 37.4686i) q^{55} +(-52.9896 + 30.5936i) q^{56} +(-8.06780 - 0.506784i) q^{57} +108.146 q^{58} -19.8505i q^{59} +(-107.650 - 71.5074i) q^{60} +(11.3598 + 19.6757i) q^{61} +(-10.4504 + 6.03353i) q^{62} +(-112.938 - 14.2447i) q^{63} +100.441 q^{64} +(-77.5401 - 64.1652i) q^{65} +(-23.0580 - 46.4385i) q^{66} +(-10.7619 + 18.6401i) q^{67} +(73.2644 + 42.2992i) q^{68} +(-1.89979 + 30.2438i) q^{69} +(151.416 - 262.261i) q^{70} +(-76.4358 - 44.1302i) q^{71} +(-34.6854 - 26.3168i) q^{72} -58.2411 q^{73} +(53.6866 - 30.9960i) q^{74} +(104.610 + 6.57113i) q^{75} +(7.49664 - 12.9846i) q^{76} +(61.2122 - 35.3409i) q^{77} +(-87.9188 - 82.5683i) q^{78} +(-62.2120 + 107.754i) q^{79} +(-48.9181 + 28.2429i) q^{80} +(-21.8133 - 78.0076i) q^{81} +(-97.3923 + 168.688i) q^{82} +(40.9017 + 23.6146i) q^{83} +(116.821 - 175.867i) q^{84} -117.708 q^{85} +(-67.3540 + 38.8869i) q^{86} +(-93.9621 + 46.6547i) q^{87} +27.0346 q^{88} +(93.6727 - 54.0819i) q^{89} +(213.794 + 26.9656i) q^{90} +(104.826 - 126.677i) q^{91} +(-48.6754 - 28.1027i) q^{92} +(6.47686 - 9.75055i) q^{93} +(71.5779 - 123.977i) q^{94} +20.8613i q^{95} +(-112.624 + 55.9210i) q^{96} +(10.5852 + 18.3341i) q^{97} +(297.218 + 171.599i) q^{98} +(40.0676 + 30.4005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	3.09261i		−	1.54631i	−0.634219	−	0.773154i	$-0.718678\pi$
$2$		−	3.09261i		−	1.54631i	0.634219	−	0.773154i	$-0.281322\pi$
$3$	1.33417	+	2.68700i	0.444724	+	0.895668i
$3$	1.33417	+	2.68700i	0.444724	+	0.895668i
$4$	−5.56427			−1.39107
$5$	6.70477	−	3.87100i	1.34095	−	0.774201i	0.354007	−	0.935243i	$-0.384819\pi$
$5$	6.70477	−	3.87100i	1.34095	−	0.774201i	0.986948	+	0.161042i	$0.0514855\pi$
$6$	8.30987	−	4.12608i	1.38498	−	0.687679i
$7$	6.32403	+	10.9535i	0.903433	+	1.56479i	0.823007	+	0.568031i	$0.192294\pi$
$7$	6.32403	+	10.9535i	0.903433	+	1.56479i	0.0804252	+	0.996761i	$0.474372\pi$
$8$			4.83767i			0.604709i
$9$	−5.43998	+	7.16984i	−0.604442	+	0.796649i
$10$	−11.9715	−	20.7353i	−1.19715	−	2.07353i
$11$		−	5.58835i		−	0.508032i	−0.967200	−	0.254016i	$-0.918248\pi$
$11$		−	5.58835i		−	0.508032i	0.967200	−	0.254016i	$-0.0817516\pi$
$12$	−7.42368	−	14.9512i	−0.618640	−	1.24593i
$13$	−4.52972	−	12.1853i	−0.348440	−	0.937331i
$13$	−4.52972	−	12.1853i	−0.348440	−	0.937331i
$14$	33.8751	−	19.5578i	2.41965	−	1.39698i
$15$	19.3467	+	12.8512i	1.28978	+	0.856745i
$16$	−7.29600			−0.456000
$17$	−13.1669	−	7.60194i	−0.774526	−	0.447173i	0.0599608	−	0.998201i	$-0.480902\pi$
$17$	−13.1669	−	7.60194i	−0.774526	−	0.447173i	−0.834487	+	0.551028i	$0.814236\pi$
$18$	22.1736	+	16.8238i	1.23186	+	0.934653i
$19$	−1.34728	+	2.33356i	−0.0709096	+	0.122819i	−0.899300	−	0.437332i	$-0.855924\pi$
$19$	−1.34728	+	2.33356i	−0.0709096	+	0.122819i	0.828391	+	0.560151i	$0.189257\pi$
$20$	−37.3072	+	21.5393i	−1.86536	+	1.07696i
$21$	−20.9949	+	31.6066i	−0.999756	+	1.50508i
$22$	−17.2826			−0.785574
$23$	8.74785	+	5.05057i	0.380341	+	0.219590i	0.677967	−	0.735093i	$-0.262861\pi$
$23$	8.74785	+	5.05057i	0.380341	+	0.219590i	−0.297626	+	0.954683i	$0.596195\pi$
$24$	−12.9988	+	6.45428i	−0.541619	+	0.268928i
$25$	17.4693	−	30.2578i	0.698773	−	1.21031i
$26$	−37.6845	+	14.0087i	−1.44940	+	0.538795i
$27$	−26.5233	−	5.05145i	−0.982343	−	0.187091i
$28$	−35.1886	−	60.9484i	−1.25674	−	2.17673i
$29$			34.9691i			1.20583i	0.797805	+	0.602916i	$0.205994\pi$
$29$			34.9691i			1.20583i	−0.797805	+	0.602916i	$0.794006\pi$
$30$	39.7437	−	59.8319i	1.32479	−	1.99440i
$31$	−1.95095	−	3.37914i	−0.0629338	−	0.109004i	0.832842	−	0.553511i	$-0.186712\pi$
$31$	−1.95095	−	3.37914i	−0.0629338	−	0.109004i	−0.895776	+	0.444507i	$0.853379\pi$
$32$			41.9144i			1.30983i
$33$	15.0159	−	7.45581i	0.455028	−	0.225934i
$34$	−23.5099	+	40.7203i	−0.691467	+	1.19766i
$35$	84.8024	+	48.9607i	2.42292	+	1.39888i
$36$	30.2695	−	39.8949i	0.840819	−	1.10819i
$37$	10.0226	+	17.3596i	0.270881	+	0.469179i	0.969088	−	0.246717i	$-0.0793518\pi$
$37$	10.0226	+	17.3596i	0.270881	+	0.469179i	−0.698207	+	0.715896i	$0.746018\pi$
$38$	7.21681	+	4.16663i	0.189916	+	0.109648i
$39$	26.6985	−	28.4286i	0.684578	−	0.728939i
$40$	18.7267	+	32.4355i	0.468166	+	0.810888i
$41$	−54.5456	−	31.4919i	−1.33038	−	0.768095i	−0.345022	−	0.938595i	$-0.612128\pi$
$41$	−54.5456	−	31.4919i	−1.33038	−	0.768095i	−0.985358	+	0.170500i	$0.945462\pi$
$42$	97.7470	+	64.9290i	2.32731	+	1.54593i
$43$	−12.5741	−	21.7790i	−0.292421	−	0.506488i	0.681961	−	0.731389i	$-0.261128\pi$
$43$	−12.5741	−	21.7790i	−0.292421	−	0.506488i	−0.974382	+	0.224901i	$0.927794\pi$
$44$			31.0951i			0.706706i
$45$	−8.71934	+	69.1303i	−0.193763	+	1.53623i
$46$	15.6195	−	27.0537i	0.339554	−	0.588124i
$47$	40.0880	+	23.1448i	0.852935	+	0.492442i	0.861640	−	0.507520i	$-0.169438\pi$
$47$	40.0880	+	23.1448i	0.852935	+	0.492442i	−0.00870479	+	0.999962i	$0.502771\pi$
$48$	−9.73411	−	19.6044i	−0.202794	−	0.408425i
$49$	−55.4867	+	96.1057i	−1.13238	+	1.96134i
$50$	−93.5756	−	54.0259i	−1.87151	−	1.08052i
$51$	2.85949	−	45.5219i	0.0560684	−	0.892586i
$52$	25.2045	+	67.8023i	0.484703	+	1.30389i
$53$		−	37.9847i		−	0.716693i	−0.933589	−	0.358347i	$-0.883341\pi$
$53$		−	37.9847i		−	0.716693i	0.933589	−	0.358347i	$-0.116659\pi$
$54$	−15.6222	+	82.0262i	−0.289300	+	1.51900i
$55$	−21.6325	−	37.4686i	−0.393319	−	0.681248i
$56$	−52.9896	+	30.5936i	−0.946244	+	0.546314i
$57$	−8.06780	−	0.506784i	−0.141540	−	0.00889095i
$58$	108.146			1.86459
$59$		−	19.8505i		−	0.336450i	−0.985749	−	0.168225i	$-0.946197\pi$
$59$		−	19.8505i		−	0.336450i	0.985749	−	0.168225i	$-0.0538035\pi$
$60$	−107.650	−	71.5074i	−1.79417	−	1.19179i
$61$	11.3598	+	19.6757i	0.186226	+	0.322553i	0.943989	−	0.329977i	$-0.107041\pi$
$61$	11.3598	+	19.6757i	0.186226	+	0.322553i	−0.757763	+	0.652530i	$0.773708\pi$
$62$	−10.4504	+	6.03353i	−0.168554	+	0.0973150i
$63$	−112.938	−	14.2447i	−1.79266	−	0.226107i
$64$	100.441			1.56939
$65$	−77.5401	−	64.1652i	−1.19292	−	0.987157i
$66$	−23.0580	−	46.4385i	−0.349363	−	0.703613i
$67$	−10.7619	+	18.6401i	−0.160625	+	0.278211i	−0.935093	−	0.354402i	$-0.884684\pi$
$67$	−10.7619	+	18.6401i	−0.160625	+	0.278211i	0.774468	+	0.632613i	$0.218018\pi$
$68$	73.2644	+	42.2992i	1.07742	+	0.622047i
$69$	−1.89979	+	30.2438i	−0.0275331	+	0.438316i
$70$	151.416	−	262.261i	2.16309	−	3.74659i
$71$	−76.4358	−	44.1302i	−1.07656	−	0.621552i	−0.146594	−	0.989197i	$-0.546831\pi$
$71$	−76.4358	−	44.1302i	−1.07656	−	0.621552i	−0.929966	+	0.367644i	$0.880164\pi$
$72$	−34.6854	−	26.3168i	−0.481741	−	0.365512i
$73$	−58.2411			−0.797823			−0.398912	−	0.916989i	$-0.630612\pi$
$73$	−58.2411			−0.797823			−0.398912	+	0.916989i	$0.630612\pi$
$74$	53.6866	−	30.9960i	0.725495	−	0.418865i
$75$	104.610	+	6.57113i	1.39480	+	0.0876151i
$76$	7.49664	−	12.9846i	0.0986400	−	0.170850i
$77$	61.2122	−	35.3409i	0.794964	−	0.458973i
$78$	−87.9188	−	82.5683i	−1.12716	−	1.05857i
$79$	−62.2120	+	107.754i	−0.787494	+	1.36398i	0.140004	+	0.990151i	$0.455288\pi$
$79$	−62.2120	+	107.754i	−0.787494	+	1.36398i	−0.927498	+	0.373829i	$0.878045\pi$
$80$	−48.9181	+	28.2429i	−0.611476	+	0.353036i
$81$	−21.8133	−	78.0076i	−0.269300	−	0.963056i
$82$	−97.3923	+	168.688i	−1.18771	+	2.05718i
$83$	40.9017	+	23.6146i	0.492791	+	0.284513i	0.725732	−	0.687978i	$-0.241501\pi$
$83$	40.9017	+	23.6146i	0.492791	+	0.284513i	−0.232941	+	0.972491i	$0.574835\pi$
$84$	116.821	−	175.867i	1.39073	−	2.09366i
$85$	−117.708			−1.38481
$86$	−67.3540	+	38.8869i	−0.783186	+	0.452173i
$87$	−93.9621	+	46.6547i	−1.08002	+	0.536261i
$88$	27.0346			0.307212
$89$	93.6727	−	54.0819i	1.05250	−	0.607662i	0.129153	−	0.991625i	$-0.458774\pi$
$89$	93.6727	−	54.0819i	1.05250	−	0.607662i	0.923349	+	0.383962i	$0.125441\pi$
$90$	213.794	+	26.9656i	2.37548	+	0.299617i
$91$	104.826	−	126.677i	1.15194	−	1.39205i
$92$	−48.6754	−	28.1027i	−0.529080	−	0.305464i
$93$	6.47686	−	9.75055i	0.0696437	−	0.104845i
$94$	71.5779	−	123.977i	0.761467	−	1.31890i
$95$			20.8613i			0.219593i
$96$	−112.624	+	55.9210i	−1.17317	+	0.582510i
$97$	10.5852	+	18.3341i	0.109126	+	0.189012i	0.915416	−	0.402508i	$-0.131862\pi$
$97$	10.5852	+	18.3341i	0.109126	+	0.189012i	−0.806291	+	0.591520i	$0.798528\pi$
$98$	297.218	+	171.599i	3.03284	+	1.75101i
$99$	40.0676	+	30.4005i	0.404723	+	0.307076i
$100$	−97.2040	+	168.362i	−0.972040	+	1.68362i
$101$			86.7652i			0.859062i	0.903052	+	0.429531i	$0.141321\pi$
$101$			86.7652i			0.859062i	−0.903052	+	0.429531i	$0.858679\pi$
$102$	−140.782	−	8.84329i	−1.38021	−	0.0866990i
$103$	5.38045	+	9.31921i	0.0522374	+	0.0904778i	0.890962	−	0.454078i	$-0.150031\pi$
$103$	5.38045	+	9.31921i	0.0522374	+	0.0904778i	−0.838724	+	0.544556i	$0.816698\pi$
$104$	58.9485	−	21.9133i	0.566813	−	0.210705i
$105$	−18.4167	+	293.186i	−0.175397	+	2.79225i
$106$	−117.472			−1.10823
$107$	34.0074	−	19.6342i	0.317826	−	0.183497i	−0.332597	−	0.943069i	$-0.607925\pi$
$107$	34.0074	−	19.6342i	0.317826	−	0.183497i	0.650423	+	0.759572i	$0.274592\pi$
$108$	147.582	+	28.1076i	1.36650	+	0.260256i
$109$	126.219			1.15798			0.578988	−	0.815336i	$-0.303448\pi$
$109$	126.219			1.15798			0.578988	+	0.815336i	$0.303448\pi$
$110$	−115.876	+	66.9011i	−1.05342	+	0.608192i
$111$	−33.2735	+	50.0914i	−0.299762	+	0.451274i
$112$	−46.1401	−	79.9171i	−0.411966	−	0.713545i
$113$		−	142.648i		−	1.26237i	−0.775632	−	0.631185i	$-0.782569\pi$
$113$		−	142.648i		−	1.26237i	0.775632	−	0.631185i	$-0.217431\pi$
$114$	−1.56729	+	24.9506i	−0.0137481	+	0.218865i
$115$	78.2031			0.680027
$116$		−	194.577i		−	1.67739i
$117$	112.008	+	33.8104i	0.957336	+	0.288978i
$118$	−61.3900			−0.520255
$119$		−	192.299i		−	1.61596i
$120$	−62.1698	+	93.5931i	−0.518082	+	0.779942i
$121$	89.7703			0.741904
$122$	60.8494	−	35.1314i	0.498766	−	0.287962i
$123$	11.8458	−	188.580i	0.0963070	−	1.53317i
$124$	10.8556	+	18.8024i	0.0875451	+	0.151633i
$125$		−	76.9452i		−	0.615562i
$126$	−44.0534	+	349.273i	−0.349630	+	2.77201i
$127$	−32.4044	−	56.1261i	−0.255153	−	0.441938i	0.709784	−	0.704419i	$-0.248793\pi$
$127$	−32.4044	−	56.1261i	−0.255153	−	0.441938i	−0.964937	+	0.262481i	$0.915459\pi$
$128$		−	142.968i		−	1.11694i
$129$	41.7442	−	62.8436i	0.323599	−	0.487159i
$130$	−198.438	+	239.802i	−1.52645	+	1.84463i
$131$	151.471	−	87.4520i	1.15627	−	0.667573i	0.205863	−	0.978581i	$-0.434000\pi$
$131$	151.471	−	87.4520i	1.15627	−	0.667573i	0.950407	+	0.311008i	$0.100667\pi$
$132$	−83.5526	+	41.4861i	−0.632974	+	0.314289i
$133$	−34.0810			−0.256248
$134$	57.6467	+	33.2823i	0.430199	+	0.248376i
$135$	−197.387	+	68.8028i	−1.46212	+	0.509650i
$136$	36.7757	−	63.6974i	0.270410	−	0.468363i
$137$	−7.82537	+	4.51798i	−0.0571195	+	0.0329779i	−0.528288	−	0.849065i	$-0.677166\pi$
$137$	−7.82537	+	4.51798i	−0.0571195	+	0.0329779i	0.471168	+	0.882043i	$0.343832\pi$
$138$	93.5325	+	5.87530i	0.677772	+	0.0425747i
$139$	21.0897			0.151724			0.0758622	−	0.997118i	$-0.475829\pi$
$139$	21.0897			0.151724			0.0758622	+	0.997118i	$0.475829\pi$
$140$	−471.863	−	272.430i	−3.37045	−	1.94593i
$141$	−8.70597	+	138.596i	−0.0617445	+	0.982948i
$142$	−136.478	+	236.386i	−0.961111	+	1.66469i
$143$	−68.0958	+	25.3136i	−0.476194	+	0.177018i
$144$	39.6901	−	52.3112i	0.275626	−	0.363272i
$145$	135.366	+	234.460i	0.933555	+	1.61696i
$146$			180.117i			1.23368i
$147$	−332.265	−	20.8715i	−2.26031	−	0.141983i
$148$	−55.7683	−	96.5936i	−0.376813	−	0.652659i
$149$		−	1.85128i		−	0.0124247i	−0.999981	−	0.00621236i	$-0.998023\pi$
$149$		−	1.85128i		−	0.0124247i	0.999981	−	0.00621236i	$-0.00197747\pi$
$150$	20.3220	−	323.518i	0.135480	−	2.15679i
$151$	49.3351	−	85.4508i	0.326722	−	0.565899i	−0.655137	−	0.755510i	$-0.727389\pi$
$151$	49.3351	−	85.4508i	0.326722	−	0.565899i	0.981859	+	0.189610i	$0.0607225\pi$
$152$	−11.2890	−	6.51772i	−0.0742698	−	0.0428797i
$153$	126.133	−	53.0505i	0.824396	−	0.346735i
$154$	−109.296	−	189.306i	−0.709713	−	1.22926i
$155$	−26.1613	−	15.1042i	−0.168783	−	0.0974467i
$156$	−148.558	+	158.185i	−0.952294	+	1.01400i
$157$	−138.473	−	239.842i	−0.881994	−	1.52766i	−0.849120	−	0.528200i	$-0.822867\pi$
$157$	−138.473	−	239.842i	−0.881994	−	1.52766i	−0.0328743	−	0.999459i	$-0.510466\pi$
$158$	333.243	+	192.398i	2.10913	+	1.21771i
$159$	102.065	−	50.6781i	0.641919	−	0.318730i
$160$	162.251	+	281.027i	1.01407	+	1.75642i
$161$			127.760i			0.793539i
$162$	−241.247	+	67.4601i	−1.48918	+	0.416420i
$163$	−151.394	+	262.223i	−0.928800	+	1.60873i	−0.143467	+	0.989655i	$0.545825\pi$
$163$	−151.394	+	262.223i	−0.928800	+	1.60873i	−0.785333	+	0.619073i	$0.787508\pi$
$164$	303.506	+	175.229i	1.85065	+	1.06847i
$165$	71.8169	−	108.116i	0.435254	−	0.655250i
$166$	73.0308	−	126.493i	0.439945	−	0.762006i
$167$	17.4098	+	10.0515i	0.104250	+	0.0601888i	0.551219	−	0.834361i	$-0.314163\pi$
$167$	17.4098	+	10.0515i	0.104250	+	0.0601888i	−0.446968	+	0.894550i	$0.647496\pi$
$168$	−152.902	−	101.566i	−0.910133	−	0.604561i
$169$	−127.963	+	110.392i	−0.757180	+	0.653207i
$170$			364.027i			2.14134i
$171$	−9.40209	−	22.3543i	−0.0549830	−	0.130727i
$172$	69.9657	+	121.184i	0.406777	+	0.704559i
$173$	−133.596	+	77.1319i	−0.772234	+	0.445849i	−0.833671	−	0.552262i	$-0.813765\pi$
$173$	−133.596	+	77.1319i	−0.772234	+	0.445849i	0.0614372	+	0.998111i	$0.480432\pi$
$174$	144.285	+	290.589i	0.829225	+	1.67005i
$175$	441.906			2.52518
$176$			40.7726i			0.231663i
$177$	53.3384	−	26.4840i	0.301347	−	0.149627i
$178$	−167.255	−	289.694i	−0.939633	−	1.62749i
$179$	161.401	−	93.1847i	0.901680	−	0.520585i	0.0239350	−	0.999714i	$-0.492381\pi$
$179$	161.401	−	93.1847i	0.901680	−	0.520585i	0.877745	+	0.479128i	$0.159047\pi$
$180$	48.5167	−	384.660i	0.269537	−	2.13700i
$181$	311.480			1.72089			0.860443	−	0.509546i	$-0.170187\pi$
$181$	311.480			1.72089			0.860443	+	0.509546i	$0.170187\pi$
$182$	−391.762	−	324.187i	−2.15254	−	1.78125i
$183$	−37.7128	+	56.7745i	−0.206081	+	0.310243i
$184$	−24.4330	+	42.3192i	−0.132788	+	0.229996i
$185$	134.398	+	77.5949i	0.726477	+	0.419432i
$186$	−30.1547	−	20.0304i	−0.162122	−	0.107691i
$187$	−42.4823	+	73.5815i	−0.227178	+	0.393484i
$188$	−223.060	−	128.784i	−1.18649	−	0.685020i
$189$	−112.403	−	322.469i	−0.594723	−	1.70618i
$190$	64.5161			0.339559
$191$	121.460	−	70.1248i	0.635915	−	0.367145i	−0.147124	−	0.989118i	$-0.547002\pi$
$191$	121.460	−	70.1248i	0.635915	−	0.367145i	0.783039	+	0.621973i	$0.213668\pi$
$192$	134.006	+	269.886i	0.697946	+	1.40566i
$193$	−40.2413	+	69.6999i	−0.208504	+	0.361140i	−0.951243	−	0.308441i	$-0.900193\pi$
$193$	−40.2413	+	69.6999i	−0.208504	+	0.361140i	0.742739	+	0.669581i	$0.233526\pi$
$194$	56.7004	−	32.7360i	0.292270	−	0.168742i
$195$	68.9604	−	293.958i	0.353643	−	1.50748i
$196$	308.743	−	534.758i	1.57522	−	2.72836i
$197$	−8.10582	+	4.67990i	−0.0411463	+	0.0237558i	−0.520432	−	0.853903i	$-0.674229\pi$
$197$	−8.10582	+	4.67990i	−0.0411463	+	0.0237558i	0.479286	+	0.877659i	$0.340896\pi$
$198$	94.0171	−	123.914i	0.474834	−	0.625826i
$199$	110.946	−	192.164i	0.557518	−	0.965649i	−0.440185	−	0.897907i	$-0.645087\pi$
$199$	110.946	−	192.164i	0.557518	−	0.965649i	0.997703	−	0.0677419i	$-0.0215794\pi$
$200$	146.377	+	84.5109i	0.731886	+	0.422555i
$201$	−64.4442	−	4.04811i	−0.320618	−	0.0201398i
$202$	268.331			1.32837
$203$	−383.035	+	221.146i	−1.88687	+	1.08939i
$204$	−15.9110	+	253.296i	−0.0779949	+	1.24165i
$205$	−487.621			−2.37864
$206$	28.8207	−	16.6397i	0.139906	−	0.0807750i
$207$	−83.7999	+	35.2457i	−0.404830	+	0.170269i
$208$	33.0488	+	88.9040i	0.158889	+	0.427423i
$209$	13.0408	+	7.52909i	0.0623960	+	0.0360244i
$210$	906.712	+	56.9557i	4.31768	+	0.271218i
$211$	97.8006	−	169.396i	0.463510	−	0.802823i	−0.535623	−	0.844457i	$-0.679923\pi$
$211$	97.8006	−	169.396i	0.463510	−	0.802823i	0.999133	+	0.0416343i	$0.0132564\pi$
$212$			211.357i			0.996968i
$213$	16.5997	−	264.260i	0.0779328	−	1.24066i
$214$	−60.7210	−	105.172i	−0.283743	−	0.491457i
$215$	−168.613	−	97.3488i	−0.784247	−	0.452785i
$216$	24.4373	−	128.311i	0.113135	−	0.594032i
$217$	24.6757	−	42.7395i	0.113713	−	0.196956i
$218$		−	390.348i		−	1.79059i
$219$	−77.7036	−	156.494i	−0.354811	−	0.714585i
$220$	120.369	+	208.485i	0.547132	+	0.947661i
$221$	−32.9894	+	194.878i	−0.149273	+	0.881800i
$222$	154.913	+	102.902i	0.697808	+	0.463524i
$223$	234.679			1.05237			0.526185	−	0.850370i	$-0.323622\pi$
$223$	234.679			1.05237			0.526185	+	0.850370i	$0.323622\pi$
$224$	−459.111	+	265.068i	−2.04960	+	1.18334i
$225$	121.911	+	289.854i	0.541825	+	1.28824i
$226$	−441.155			−1.95201
$227$	−153.247	+	88.4770i	−0.675096	+	0.389767i	−0.798005	−	0.602651i	$-0.794111\pi$
$227$	−153.247	+	88.4770i	−0.675096	+	0.389767i	0.122909	+	0.992418i	$0.460778\pi$
$228$	44.8914	+	2.81988i	0.196892	+	0.0123679i
$229$	64.5827	+	111.861i	0.282021	+	0.488474i	0.971882	−	0.235467i	$-0.0756620\pi$
$229$	64.5827	+	111.861i	0.282021	+	0.488474i	−0.689862	+	0.723941i	$0.742329\pi$
$230$		−	241.852i		−	1.05153i
$231$	176.629	+	117.327i	0.764626	+	0.507908i
$232$	−169.169			−0.729177
$233$			159.159i			0.683084i	0.939866	+	0.341542i	$0.110949\pi$
$233$			159.159i			0.683084i	−0.939866	+	0.341542i	$0.889051\pi$
$234$	104.563	−	346.398i	0.446849	−	1.48034i
$235$	358.374			1.52500
$236$			110.454i			0.468024i
$237$	−372.538	−	23.4012i	−1.57189	−	0.0987393i
$238$	−594.708			−2.49877
$239$	204.696	−	118.181i	0.856470	−	0.494483i	−0.00635882	−	0.999980i	$-0.502024\pi$
$239$	204.696	−	118.181i	0.856470	−	0.494483i	0.862828	+	0.505497i	$0.168691\pi$
$240$	−141.154	−	93.7622i	−0.588140	−	0.390676i
$241$	−58.1959	−	100.798i	−0.241477	−	0.418250i	0.719658	−	0.694328i	$-0.244298\pi$
$241$	−58.1959	−	100.798i	−0.241477	−	0.418250i	−0.961135	+	0.276078i	$0.910965\pi$
$242$		−	277.625i		−	1.14721i
$243$	180.504	−	162.688i	0.742815	−	0.669497i
$244$	−63.2088	−	109.481i	−0.259053	−	0.448692i
$245$			859.156i			3.50676i
$246$	−583.204	−	36.6344i	−2.37075	−	0.148920i
$247$	34.5380	+	5.84668i	0.139830	+	0.0236708i
$248$	16.3472	−	9.43805i	0.0659160	−	0.0380566i
$249$	−8.88268	+	141.409i	−0.0356734	+	0.567907i
$250$	−237.962			−0.951848
$251$	11.8161	+	6.82204i	0.0470762	+	0.0271795i	0.523353	−	0.852116i	$-0.324681\pi$
$251$	11.8161	+	6.82204i	0.0470762	+	0.0271795i	−0.476277	+	0.879295i	$0.658014\pi$
$252$	628.416	+	79.2614i	2.49371	+	0.314529i
$253$	28.2244	−	48.8860i	0.111559	−	0.193225i
$254$	−173.577	+	100.214i	−0.683372	+	0.394545i
$255$	−157.043	−	316.283i	−0.615856	−	1.24033i
$256$	−40.3807			−0.157737
$257$	−252.731	−	145.914i	−0.983389	−	0.567760i	−0.0800976	−	0.996787i	$-0.525523\pi$
$257$	−252.731	−	145.914i	−0.983389	−	0.567760i	−0.903292	+	0.429027i	$0.858857\pi$
$258$	−194.351	−	129.099i	−0.753298	−	0.500383i
$259$	−126.766	+	219.566i	−0.489445	+	0.847743i
$260$	431.454	+	357.032i	1.65944	+	1.37320i
$261$	−250.723	−	190.231i	−0.960624	−	0.728855i
$262$	−270.455	−	468.443i	−1.03227	−	1.78795i
$263$		−	200.566i		−	0.762608i	−0.924450	−	0.381304i	$-0.875475\pi$
$263$		−	200.566i		−	0.762608i	0.924450	−	0.381304i	$-0.124525\pi$
$264$	36.0688	+	72.6421i	0.136624	+	0.275160i
$265$	−147.039	−	254.679i	−0.554864	−	0.961053i
$266$			105.399i			0.396239i
$267$	270.294	+	179.544i	1.01234	+	0.672451i
$268$	59.8819	−	103.719i	0.223440	−	0.387010i
$269$	−49.4104	−	28.5271i	−0.183682	−	0.106049i	0.405340	−	0.914166i	$-0.367153\pi$
$269$	−49.4104	−	28.5271i	−0.183682	−	0.106049i	−0.589021	+	0.808117i	$0.700487\pi$
$270$	212.780	+	610.441i	0.788076	+	2.26089i
$271$	100.592	+	174.230i	0.371187	+	0.642915i	0.989748	−	0.142822i	$-0.0456175\pi$
$271$	100.592	+	174.230i	0.371187	+	0.642915i	−0.618561	+	0.785736i	$0.712284\pi$
$272$	96.0661	+	55.4638i	0.353184	+	0.203911i
$273$	480.237	+	112.660i	1.75911	+	0.412674i
$274$	13.9724	+	24.2008i	0.0509940	+	0.0883242i
$275$	−169.091	−	97.6248i	−0.614877	−	0.354999i
$276$	10.5709	−	168.285i	0.0383004	−	0.609727i
$277$	118.651	+	205.509i	0.428343	+	0.741911i	0.996726	−	0.0808527i	$-0.0257643\pi$
$277$	118.651	+	205.509i	0.428343	+	0.741911i	−0.568384	+	0.822764i	$0.692431\pi$
$278$		−	65.2223i		−	0.234612i
$279$	34.8410	+	4.39446i	0.124878	+	0.0157508i
$280$	−236.856	+	410.246i	−0.845913	+	1.46517i
$281$	−150.238	−	86.7398i	−0.534654	−	0.308682i	0.208256	−	0.978074i	$-0.433221\pi$
$281$	−150.238	−	86.7398i	−0.534654	−	0.308682i	−0.742909	+	0.669392i	$0.766555\pi$
$282$	428.623	+	26.9242i	1.51994	+	0.0954760i
$283$	−62.5556	+	108.350i	−0.221045	+	0.382861i	−0.955125	−	0.296202i	$-0.904280\pi$
$283$	−62.5556	+	108.350i	−0.221045	+	0.382861i	0.734081	+	0.679062i	$0.237613\pi$
$284$	425.309	+	245.552i	1.49757	+	0.864621i
$285$	−56.0545	+	27.8326i	−0.196683	+	0.0976582i
$286$	78.2853	+	210.594i	0.273725	+	0.736343i
$287$		−	796.623i		−	2.77569i
$288$	−300.520	−	228.014i	−1.04347	−	0.791714i
$289$	−28.9211	−	50.0928i	−0.100073	−	0.173332i
$290$	725.094	−	418.633i	2.50032	−	1.44356i
$291$	−35.1414	+	52.9033i	−0.120761	+	0.181798i
$292$	324.069			1.10983
$293$			65.2174i			0.222585i	0.993788	+	0.111292i	$0.0354990\pi$
$293$			65.2174i			0.222585i	−0.993788	+	0.111292i	$0.964501\pi$
$294$	−64.5474	+	1027.57i	−0.219549	+	3.49513i
$295$	−76.8415	−	133.093i	−0.260480	−	0.451164i
$296$	−83.9802	+	48.4860i	−0.283717	+	0.163804i
$297$	−28.2293	+	148.221i	−0.0950480	+	0.499061i
$298$	−5.72531			−0.0192124
$299$	21.9175	−	129.473i	0.0733027	−	0.433020i
$300$	−582.077	−	36.5635i	−1.94026	−	0.121878i
$301$	159.038	−	275.462i	0.528366	−	0.915156i
$302$	−264.266	−	152.574i	−0.875055	−	0.505213i
$303$	−233.138	+	115.760i	−0.769434	+	0.382045i
$304$	9.82978	−	17.0257i	0.0323348	−	0.0560055i
$305$	152.329	+	87.9475i	0.499441	+	0.288352i
$306$	−164.065	−	390.079i	−0.536160	−	1.27477i
$307$	−516.260			−1.68163			−0.840814	−	0.541324i	$-0.817923\pi$
$307$	−516.260			−1.68163			−0.840814	+	0.541324i	$0.817923\pi$
$308$	−340.601	+	196.646i	−1.10585	+	0.638461i
$309$	−17.8623	+	26.8907i	−0.0578068	+	0.0870249i
$310$	−46.7116	+	80.9069i	−0.150683	+	0.260990i
$311$	−127.871	+	73.8265i	−0.411162	+	0.237384i	−0.691289	−	0.722579i	$-0.742957\pi$
$311$	−127.871	+	73.8265i	−0.411162	+	0.237384i	0.280127	+	0.959963i	$0.409623\pi$
$312$	137.528	+	129.159i	0.440796	+	0.413971i
$313$	−192.767	+	333.882i	−0.615869	+	1.06672i	0.374363	+	0.927282i	$0.377861\pi$
$313$	−192.767	+	333.882i	−0.615869	+	1.06672i	−0.990231	+	0.139433i	$0.955472\pi$
$314$	−741.740	+	428.244i	−2.36223	+	1.36383i
$315$	−812.363	+	341.675i	−2.57893	+	1.08468i
$316$	346.164	−	599.574i	1.09546	−	1.89739i
$317$	361.661	+	208.805i	1.14089	+	0.658691i	0.946650	−	0.322264i	$-0.104444\pi$
$317$	361.661	+	208.805i	1.14089	+	0.658691i	0.194236	+	0.980955i	$0.437777\pi$
$318$	−156.728	−	315.648i	−0.492855	−	0.992604i
$319$	195.420			0.612601
$320$	673.435	−	388.808i	2.10449	−	1.21503i
$321$	98.1288	+	65.1827i	0.305697	+	0.203061i
$322$	395.112			1.22706
$323$	35.4792	−	20.4839i	0.109843	−	0.0634177i
$324$	121.375	+	434.055i	0.374614	+	1.33968i
$325$	−447.831	−	75.8101i	−1.37794	−	0.233262i
$326$	810.954	+	468.204i	2.48759	+	1.43621i
$327$	168.398	+	339.152i	0.514979	+	1.03716i
$328$	152.348	−	263.874i	0.464474	−	0.804493i
$329$			585.473i			1.77955i
$330$	−334.362	−	222.102i	−1.01322	−	0.673036i
$331$	119.991	+	207.831i	0.362512	+	0.627889i	0.988374	−	0.152045i	$-0.0485859\pi$
$331$	119.991	+	207.831i	0.362512	+	0.627889i	−0.625862	+	0.779934i	$0.715253\pi$
$332$	−227.588	−	131.398i	−0.685505	−	0.395777i
$333$	−178.988	−	22.5756i	−0.537503	−	0.0677947i
$334$	31.0855	−	53.8417i	0.0930704	−	0.161203i
$335$			166.637i			0.497424i
$336$	153.179	−	230.602i	0.455889	−	0.686315i
$337$	156.113	+	270.395i	0.463242	+	0.802359i	0.999120	−	0.0419364i	$-0.0133527\pi$
$337$	156.113	+	270.395i	0.463242	+	0.802359i	−0.535878	+	0.844295i	$0.680019\pi$
$338$	341.400	+	395.741i	1.01006	+	1.17083i
$339$	383.295	−	190.317i	1.13066	−	0.561406i
$340$	654.961			1.92636
$341$	−18.8838	+	10.9026i	−0.0553778	+	0.0319724i
$342$	−69.1334	+	29.0770i	−0.202144	+	0.0850206i
$343$	−783.842			−2.28525
$344$	105.360	−	60.8294i	0.306278	−	0.176830i
$345$	104.336	+	210.132i	0.302424	+	0.609079i
$346$	238.539	+	413.162i	0.689420	+	1.19411i
$347$		−	309.828i		−	0.892877i	−0.894814	−	0.446439i	$-0.852692\pi$
$347$		−	309.828i		−	0.892877i	0.894814	−	0.446439i	$-0.147308\pi$
$348$	522.830	−	259.599i	1.50239	−	0.745975i
$349$	142.661			0.408771			0.204385	−	0.978890i	$-0.434480\pi$
$349$	142.661			0.408771			0.204385	+	0.978890i	$0.434480\pi$
$350$		−	1366.65i		−	3.90470i
$351$	58.5893	+	346.076i	0.166921	+	0.985970i
$352$	234.233			0.665433
$353$		−	20.5564i		−	0.0582335i	−0.999576	−	0.0291168i	$-0.990731\pi$
$353$		−	20.5564i		−	0.0582335i	0.999576	−	0.0291168i	$-0.00926946\pi$
$354$	−81.9048	−	164.955i	−0.231369	−	0.465975i
$355$	−683.313			−1.92483
$356$	−521.220	+	300.926i	−1.46410	+	0.845299i
$357$	516.709	−	256.560i	1.44737	−	0.718656i
$358$	−288.184	−	499.150i	−0.804985	−	1.39427i
$359$		−	147.021i		−	0.409529i	−0.978811	−	0.204765i	$-0.934357\pi$
$359$		−	147.021i		−	0.409529i	0.978811	−	0.204765i	$-0.0656429\pi$
$360$	−334.430	−	42.1813i	−0.928972	−	0.117170i
$361$	176.870	+	306.347i	0.489944	+	0.848607i
$362$		−	963.289i		−	2.66102i
$363$	119.769	+	241.213i	0.329942	+	0.664499i
$364$	−583.281	+	704.863i	−1.60242	+	1.93644i
$365$	−390.493	+	225.451i	−1.06985	+	0.617675i
$366$	175.582	+	116.631i	0.479731	+	0.318665i
$367$	389.190			1.06046			0.530231	−	0.847853i	$-0.322105\pi$
$367$	389.190			1.06046			0.530231	+	0.847853i	$0.322105\pi$
$368$	−63.8243	−	36.8490i	−0.173436	−	0.100133i
$369$	522.519	−	219.768i	1.41604	−	0.595577i
$370$	239.971	−	415.642i	0.648571	−	1.12336i
$371$	416.067	−	240.217i	1.12148	−	0.647484i
$372$	−36.0390	+	54.2547i	−0.0968790	+	0.145846i
$373$	−403.663			−1.08221			−0.541103	−	0.840956i	$-0.681993\pi$
$373$	−403.663			−1.08221			−0.541103	+	0.840956i	$0.681993\pi$
$374$	227.559	+	131.381i	0.608447	+	0.351287i
$375$	206.752	−	102.658i	0.551339	−	0.273755i
$376$	−111.967	+	193.932i	−0.297785	+	0.515778i
$377$	426.109	−	158.400i	1.13026	−	0.420159i
$378$	−997.272	+	347.618i	−2.63829	+	0.919624i
$379$	78.4185	+	135.825i	0.206909	+	0.358377i	0.950739	−	0.309992i	$-0.100326\pi$
$379$	78.4185	+	135.825i	0.206909	+	0.358377i	−0.743830	+	0.668369i	$0.766993\pi$
$380$		−	116.078i		−	0.305469i
$381$	107.578	−	161.953i	0.282357	−	0.425073i
$382$	−216.869	−	375.628i	−0.567720	−	0.983319i
$383$		−	292.349i		−	0.763314i	−0.924304	−	0.381657i	$-0.875354\pi$
$383$		−	292.349i		−	0.763314i	0.924304	−	0.381657i	$-0.124646\pi$
$384$	384.156	−	190.744i	1.00041	−	0.496729i
$385$	273.609	−	473.905i	0.710674	−	1.23092i
$386$	215.555	+	124.451i	0.558433	+	0.322411i
$387$	224.555	+	28.3229i	0.580245	+	0.0731857i
$388$	−58.8989	−	102.016i	−0.151801	−	0.262928i
$389$	−657.425	−	379.564i	−1.69004	−	0.975744i	−0.954477	−	0.298286i	$-0.903585\pi$
$389$	−657.425	−	379.564i	−1.69004	−	0.975744i	−0.735561	−	0.677458i	$-0.763081\pi$
$390$	−909.098	−	213.268i	−2.33102	−	0.546841i
$391$	−76.7883	−	133.001i	−0.196389	−	0.340156i
$392$	−464.928	−	268.426i	−1.18604	−	0.684761i
$393$	437.073	+	290.328i	1.11214	+	0.738749i
$394$	14.4731	+	25.0682i	0.0367338	+	0.0636248i
$395$			963.292i			2.43871i
$396$	−222.947	−	169.157i	−0.562997	−	0.427163i
$397$	325.534	−	563.842i	0.819985	−	1.42026i	−0.0857071	−	0.996320i	$-0.527315\pi$
$397$	325.534	−	563.842i	0.819985	−	1.42026i	0.905692	−	0.423936i	$-0.139352\pi$
$398$	−594.290	−	343.113i	−1.49319	−	0.862094i
$399$	−45.4699	−	91.5758i	−0.113960	−	0.229513i
$400$	−127.456	+	220.761i	−0.318641	+	0.551902i
$401$	−357.827	−	206.591i	−0.892336	−	0.515191i	−0.0176303	−	0.999845i	$-0.505612\pi$
$401$	−357.827	−	206.591i	−0.892336	−	0.515191i	−0.874706	+	0.484654i	$0.838946\pi$
$402$	−12.5192	+	199.301i	−0.0311424	+	0.495774i
$403$	−32.3386	+	39.0794i	−0.0802447	+	0.0969713i
$404$		−	482.785i		−	1.19501i
$405$	−448.221	−	438.584i	−1.10672	−	1.08292i
$406$	683.918	+	1184.58i	1.68453	+	2.91769i
$407$	97.0117	−	56.0097i	0.238358	−	0.137616i
$408$	220.220	+	13.8333i	0.539755	+	0.0339051i
$409$	−606.340			−1.48249			−0.741247	−	0.671233i	$-0.765765\pi$
$409$	−606.340			−1.48249			−0.741247	+	0.671233i	$0.765765\pi$
$410$			1508.02i			3.67811i
$411$	−22.5802	−	14.9990i	−0.0549396	−	0.0364940i
$412$	−29.9382	−	51.8546i	−0.0726656	−	0.125861i
$413$	217.434	−	125.535i	0.526473	−	0.303960i
$414$	109.001	+	259.161i	0.263288	+	0.625992i
$415$	365.648			0.881081
$416$	510.740	−	189.860i	1.22774	−	0.456395i
$417$	28.1372	+	56.6680i	0.0674754	+	0.135895i
$418$	23.2846	−	40.3301i	0.0557047	−	0.0964834i
$419$	478.132	+	276.050i	1.14113	+	0.658830i	0.946709	−	0.322089i	$-0.104385\pi$
$419$	478.132	+	276.050i	1.14113	+	0.658830i	0.194417	+	0.980919i	$0.437718\pi$
$420$	102.475	−	1631.37i	0.243989	−	3.88420i
$421$	188.723	−	326.878i	0.448274	−	0.776433i	−0.550000	−	0.835165i	$-0.685372\pi$
$421$	188.723	−	326.878i	0.448274	−	0.776433i	0.998274	+	0.0587318i	$0.0187057\pi$
$422$	−523.876	−	302.460i	−1.24141	−	0.716729i
$423$	−384.022	+	161.517i	−0.907854	+	0.381837i
$424$	183.758			0.433391
$425$	−460.035	+	265.602i	−1.08244	+	0.624945i
$426$	−817.256	−	51.3365i	−1.91844	−	0.120508i
$427$	−143.679	+	248.860i	−0.336485	+	0.582809i
$428$	−189.226	+	109.250i	−0.442118	+	0.255257i
$429$	−158.869	−	149.201i	−0.370325	−	0.347788i
$430$	−301.062	+	521.455i	−0.700145	+	1.21269i
$431$	−317.790	+	183.476i	−0.737332	+	0.425699i	−0.821099	−	0.570786i	$-0.806638\pi$
$431$	−317.790	+	183.476i	−0.737332	+	0.425699i	0.0837662	+	0.996485i	$0.473305\pi$
$432$	193.514	+	36.8554i	0.447949	+	0.0853134i
$433$	389.105	−	673.950i	0.898626	−	1.55647i	0.0693753	−	0.997591i	$-0.477899\pi$
$433$	389.105	−	673.950i	0.898626	−	1.55647i	0.829251	−	0.558876i	$-0.188767\pi$
$434$	−132.177	−	76.3124i	−0.304555	−	0.175835i
$435$	−449.394	+	676.537i	−1.03309	+	1.55526i
$436$	−702.318			−1.61082
$437$	−23.5717	+	13.6091i	−0.0539397	+	0.0311421i
$438$	−483.976	+	240.307i	−1.10497	+	0.548647i
$439$	628.382			1.43139			0.715697	−	0.698411i	$-0.246109\pi$
$439$	628.382			1.43139			0.715697	+	0.698411i	$0.246109\pi$
$440$	181.261	−	104.651i	0.411957	−	0.237843i
$441$	−387.217	−	920.644i	−0.878042	−	2.08763i
$442$	602.682	+	102.024i	1.36353	+	0.230823i
$443$	552.260	+	318.848i	1.24664	+	0.719747i	0.970437	−	0.241353i	$-0.0775913\pi$
$443$	552.260	+	318.848i	1.24664	+	0.719747i	0.276200	+	0.961100i	$0.410925\pi$
$444$	185.143	−	278.722i	0.416988	−	0.627752i
$445$	418.703	−	725.214i	0.940905	−	1.62970i
$446$		−	725.770i		−	1.62729i
$447$	4.97441	−	2.46993i	0.0111284	−	0.00552557i
$448$	635.193	+	1100.19i	1.41784	+	2.45577i
$449$	632.272	+	365.043i	1.40818	+	0.813013i	0.995213	−	0.0977336i	$-0.0311593\pi$
$449$	632.272	+	365.043i	1.40818	+	0.813013i	0.412966	+	0.910746i	$0.364493\pi$
$450$	896.407	−	377.023i	1.99201	−	0.837828i
$451$	−175.988	+	304.820i	−0.390217	+	0.675875i
$452$			793.731i			1.75604i
$453$	295.428	+	18.5575i	0.652159	+	0.0409658i
$454$	273.625	+	473.933i	0.602699	+	1.04391i
$455$	212.470	−	1255.12i	0.466967	−	2.75851i
$456$	2.45166	−	39.0294i	0.00537644	−	0.0855907i
$457$	−470.363			−1.02924			−0.514621	−	0.857418i	$-0.672067\pi$
$457$	−470.363			−1.02924			−0.514621	+	0.857418i	$0.672067\pi$
$458$	345.941	−	199.729i	0.755331	−	0.436090i
$459$	310.829	+	268.140i	0.677188	+	0.584183i
$460$	−435.143			−0.945963
$461$	−9.99962	+	5.77328i	−0.0216911	+	0.0125234i	−0.510806	−	0.859696i	$-0.670653\pi$
$461$	−9.99962	+	5.77328i	−0.0216911	+	0.0125234i	0.489115	+	0.872219i	$0.337320\pi$
$462$	362.846	−	546.244i	0.785381	−	1.18235i
$463$	308.597	+	534.506i	0.666517	+	1.15444i	0.978872	+	0.204476i	$0.0655490\pi$
$463$	308.597	+	534.506i	0.666517	+	1.15444i	−0.312354	+	0.949966i	$0.601118\pi$
$464$		−	255.135i		−	0.549859i
$465$	5.68150	−	90.4472i	0.0122183	−	0.194510i
$466$	492.216			1.05626
$467$			786.834i			1.68487i	0.538799	+	0.842435i	$0.318878\pi$
$467$			786.834i			1.68487i	−0.538799	+	0.842435i	$0.681122\pi$
$468$	−623.244	−	188.130i	−1.33172	−	0.401988i
$469$	−272.234			−0.580455
$470$		−	1108.31i		−	2.35811i
$471$	459.711	−	692.069i	0.976032	−	1.46936i
$472$	96.0304			0.203454
$473$	−121.709	+	70.2685i	−0.257312	+	0.148559i
$474$	−72.3709	+	1152.12i	−0.152681	+	2.43062i
$475$	47.0723	+	81.5316i	0.0990995	+	0.171645i
$476$			1070.01i			2.24791i
$477$	272.345	+	206.636i	0.570953	+	0.433199i
$478$	−365.490	−	633.047i	−0.764623	−	1.32437i
$479$			575.137i			1.20070i	0.799736	+	0.600352i	$0.204973\pi$
$479$			575.137i			1.20070i	−0.799736	+	0.600352i	$0.795027\pi$
$480$	−538.650	+	810.906i	−1.12219	+	1.68939i
$481$	166.133	−	200.762i	0.345391	−	0.417385i
$482$	−311.730	+	179.977i	−0.646743	+	0.373397i
$483$	−343.291	+	170.453i	−0.710748	+	0.352906i
$484$	−499.506			−1.03204
$485$	141.943	+	81.9508i	0.292666	+	0.168971i
$486$	−503.131	−	558.229i	−1.03525	−	1.14862i
$487$	−225.808	+	391.111i	−0.463672	+	0.803103i	−0.999140	−	0.0414523i	$-0.986802\pi$
$487$	−225.808	+	391.111i	−0.463672	+	0.803103i	0.535469	+	0.844555i	$0.320135\pi$
$488$	−95.1847	+	54.9549i	−0.195051	+	0.112612i
$489$	−906.579	−	56.9474i	−1.85395	−	0.116457i
$490$	2657.04			5.42253
$491$	−549.987	−	317.535i	−1.12014	−	0.646711i	−0.178700	−	0.983904i	$-0.557189\pi$
$491$	−549.987	−	317.535i	−1.12014	−	0.646711i	−0.941436	+	0.337193i	$0.890522\pi$
$492$	−65.9129	+	1049.31i	−0.133969	+	2.13274i
$493$	265.833	−	460.436i	0.539215	−	0.933947i
$494$	18.0815	−	106.813i	0.0366023	−	0.216220i
$495$	386.325	+	48.7267i	0.780454	+	0.0984379i
$496$	14.2341	+	24.6542i	0.0286978	+	0.0497061i
$497$		−	1116.32i		−	2.24612i
$498$	437.323	+	27.4707i	0.878158	+	0.0551621i
$499$	413.055	+	715.432i	0.827766	+	1.43373i	0.899787	+	0.436329i	$0.143722\pi$
$499$	413.055	+	715.432i	0.827766	+	1.43373i	−0.0720217	+	0.997403i	$0.522945\pi$
$500$			428.144i			0.856287i
$501$	−3.78091	+	60.1906i	−0.00754673	+	0.120141i
$502$	21.0980	−	36.5427i	0.0420278	−	0.0727943i
$503$	−555.930	−	320.966i	−1.10523	−	0.638104i	−0.167639	−	0.985848i	$-0.553614\pi$
$503$	−555.930	−	320.966i	−1.10523	−	0.638104i	−0.937589	+	0.347745i	$0.886948\pi$
$504$	68.9113	−	546.356i	0.136729	−	1.08404i
$505$	335.868	+	581.741i	0.665086	+	1.15196i
$506$	−151.186	−	87.2871i	−0.298786	−	0.172504i
$507$	−467.348	−	196.556i	−0.921792	−	0.387685i
$508$	180.307	+	312.301i	0.354935	+	0.614765i
$509$	229.706	+	132.621i	0.451288	+	0.260551i	0.708374	−	0.705837i	$-0.249429\pi$
$509$	229.706	+	132.621i	0.451288	+	0.260551i	−0.257086	+	0.966389i	$0.582762\pi$
$510$	−978.142	+	485.674i	−1.91793	+	0.952302i
$511$	−368.318	−	637.946i	−0.720780	−	1.24843i
$512$		−	446.991i		−	0.873028i
$513$	47.5222	−	55.0879i	0.0926359	−	0.107384i
$514$	−451.257	+	781.600i	−0.877932	+	1.52062i
$515$	72.1494	+	41.6555i	0.140096	+	0.0808844i
$516$	−232.276	+	349.678i	−0.450147	+	0.677671i
$517$	129.341	−	224.026i	0.250176	−	0.433318i
$518$	679.032	+	392.039i	1.31087	+	0.756832i
$519$	−385.494	−	256.067i	−0.742763	−	0.493385i
$520$	310.410	−	375.114i	0.596943	−	0.721372i
$521$			157.335i			0.301987i	0.988535	+	0.150993i	$0.0482472\pi$
$521$			157.335i			0.301987i	−0.988535	+	0.150993i	$0.951753\pi$
$522$	−588.312	+	775.389i	−1.12703	+	1.48542i
$523$	−20.3177	−	35.1913i	−0.0388484	−	0.0672874i	0.845947	−	0.533266i	$-0.179036\pi$
$523$	−20.3177	−	35.1913i	−0.0388484	−	0.0672874i	−0.884796	+	0.465979i	$0.845702\pi$
$524$	−842.827	+	486.606i	−1.60845	+	0.928638i
$525$	589.578	+	1187.40i	1.12301	+	2.26172i
$526$	−620.273			−1.17923
$527$			59.3239i			0.112569i
$528$	−109.556	+	54.3976i	−0.207493	+	0.103026i
$529$	−213.483	−	369.764i	−0.403560	−	0.698987i
$530$	−787.624	+	454.735i	−1.48608	+	0.857991i
$531$	142.325	+	107.986i	0.268032	+	0.203364i
$532$	189.636			0.356458
$533$	−136.662	+	807.304i	−0.256402	+	1.51464i
$534$	555.261	−	835.914i	1.03982	−	1.56538i
$535$	152.008	−	263.286i	0.284127	−	0.492123i
$536$	−90.1748	−	52.0624i	−0.168237	−	0.0971314i
$537$	465.724	+	309.360i	0.867270	+	0.576089i
$538$	−88.2233	+	152.807i	−0.163984	+	0.284028i
$539$	537.073	+	310.079i	0.996424	+	0.575286i
$540$	1098.31	−	382.837i	2.03391	−	0.708957i
$541$	−491.446			−0.908404			−0.454202	−	0.890899i	$-0.650075\pi$
$541$	−491.446			−0.908404			−0.454202	+	0.890899i	$0.650075\pi$
$542$	538.826	−	311.091i	0.994144	−	0.573969i
$543$	415.568	+	836.949i	0.765319	+	1.54134i
$544$	318.631	−	551.885i	0.585718	−	1.01449i
$545$	846.272	−	488.595i	1.55279	−	0.896505i
$546$	348.414	−	1485.19i	0.638121	−	2.72012i
$547$	−469.686	+	813.519i	−0.858657	+	1.48724i	0.0145528	+	0.999894i	$0.495368\pi$
$547$	−469.686	+	813.519i	−0.858657	+	1.48724i	−0.873210	+	0.487344i	$0.837966\pi$
$548$	43.5424	−	25.1392i	0.0794570	−	0.0458745i
$549$	−202.869	−	25.5876i	−0.369524	−	0.0466077i
$550$	−301.916	+	522.934i	−0.548938	+	0.950788i
$551$	−81.6026	−	47.1133i	−0.148099	−	0.0855050i
$552$	−146.310	−	9.19054i	−0.265054	−	0.0166495i
$553$	−1573.72			−2.84579
$554$	635.561	−	366.941i	1.14722	−	0.662349i
$555$	−29.1875	+	464.654i	−0.0525901	+	0.837214i
$556$	−117.349			−0.211059
$557$	−657.510	+	379.614i	−1.18045	+	0.681533i	−0.956119	−	0.292980i	$-0.905353\pi$
$557$	−657.510	+	379.614i	−1.18045	+	0.681533i	−0.224331	+	0.974513i	$0.572020\pi$
$558$	13.5904	−	107.750i	0.0243555	−	0.193100i
$559$	−208.427	+	251.872i	−0.372856	+	0.450576i
$560$	−618.718	−	357.217i	−1.10485	−	0.637888i
$561$	−254.392	−	15.9798i	−0.453462	−	0.0284845i
$562$	−268.253	+	464.627i	−0.477318	+	0.826739i
$563$		−	113.917i		−	0.202340i	−0.994869	−	0.101170i	$-0.967741\pi$
$563$		−	113.917i		−	0.202340i	0.994869	−	0.101170i	$-0.0322586\pi$
$564$	48.4424	−	771.183i	0.0858907	−	1.36735i
$565$	−552.190	−	956.422i	−0.977328	−	1.69278i
$566$	335.083	+	193.460i	0.592020	+	0.341803i
$567$	716.511	−	732.255i	1.26369	−	1.29145i
$568$	213.488	−	369.771i	0.375858	−	0.651006i
$569$		−	510.755i		−	0.897636i	−0.893623	−	0.448818i	$-0.851845\pi$
$569$		−	510.755i		−	0.897636i	0.893623	−	0.448818i	$-0.148155\pi$
$570$	86.0755	+	173.355i	0.151010	+	0.304132i
$571$	−483.591	−	837.605i	−0.846920	−	1.46691i	−0.883943	−	0.467594i	$-0.845121\pi$
$571$	−483.591	−	837.605i	−0.846920	−	1.46691i	0.0370235	−	0.999314i	$-0.488212\pi$
$572$	378.903	−	140.852i	0.662418	−	0.246244i
$573$	350.473	+	232.804i	0.611647	+	0.406290i
$574$	−2463.65			−4.29207
$575$	305.638	−	176.460i	0.531545	−	0.306887i
$576$	−546.398	+	720.147i	−0.948607	+	1.25026i
$577$	122.569			0.212424			0.106212	−	0.994343i	$-0.466128\pi$
$577$	122.569			0.212424			0.106212	+	0.994343i	$0.466128\pi$
$578$	−154.918	+	89.4418i	−0.268024	+	0.154744i
$579$	−240.973	−	15.1369i	−0.416188	−	0.0261431i
$580$	−753.210	−	1304.60i	−1.29864	−	2.24931i
$581$			597.357i			1.02815i
$582$	163.610	+	108.679i	0.281116	+	0.186733i
$583$	−212.272			−0.364103
$584$		−	281.751i		−	0.482451i
$585$	881.871	−	206.893i	1.50747	−	0.353663i
$586$	201.692			0.344185
$587$			302.976i			0.516144i	0.966126	+	0.258072i	$0.0830871\pi$
$587$			302.976i			0.516144i	−0.966126	+	0.258072i	$0.916913\pi$
$588$	1848.81	+	116.134i	3.14424	+	0.197507i
$589$	10.5139			0.0178504
$590$	−411.606	+	237.641i	−0.697638	+	0.402781i
$591$	−23.3895	−	15.5366i	−0.0395761	−	0.0262886i
$592$	−73.1248	−	126.656i	−0.123522	−	0.213946i
$593$		−	163.570i		−	0.275835i	−0.990444	−	0.137918i	$-0.955959\pi$
$593$		−	163.570i		−	0.275835i	0.990444	−	0.137918i	$-0.0440409\pi$
$594$	458.391	+	87.3022i	0.771702	+	0.146973i
$595$	−744.392	−	1289.32i	−1.25108	−	2.16693i
$596$			10.3010i			0.0172836i
$597$	664.367	+	41.7326i	1.11284	+	0.0699039i
$598$	−400.410	−	67.7824i	−0.669581	−	0.113348i
$599$	−228.183	+	131.742i	−0.380940	+	0.219936i	−0.678227	−	0.734852i	$-0.737252\pi$
$599$	−228.183	+	131.742i	−0.380940	+	0.219936i	0.297287	+	0.954788i	$0.403918\pi$
$600$	−31.7890	+	506.068i	−0.0529817	+	0.843447i
$601$	−888.347			−1.47812			−0.739058	−	0.673642i	$-0.764729\pi$
$601$	−888.347			−1.47812			−0.739058	+	0.673642i	$0.764729\pi$
$602$	−851.898	−	491.843i	−1.41511	−	0.817015i
$603$	−75.1023	−	178.563i	−0.124548	−	0.296124i
$604$	−274.513	+	475.471i	−0.454492	+	0.787204i
$605$	601.890	−	347.501i	0.994859	−	0.574382i
$606$	358.000	+	721.008i	0.590759	+	1.18978i
$607$	194.775			0.320882			0.160441	−	0.987045i	$-0.448708\pi$
$607$	194.775			0.320882			0.160441	+	0.987045i	$0.448708\pi$
$608$	−97.8099	−	56.4706i	−0.160872	−	0.0928793i
$609$	−1105.25	−	734.172i	−1.81487	−	1.20554i
$610$	271.988	−	471.096i	0.445881	−	0.772289i
$611$	100.439	−	593.323i	0.164385	−	0.971069i
$612$	−701.835	+	295.187i	−1.14679	+	0.482332i
$613$	−153.947	−	266.645i	−0.251138	−	0.434984i	0.712702	−	0.701467i	$-0.247471\pi$
$613$	−153.947	−	266.645i	−0.251138	−	0.434984i	−0.963839	+	0.266484i	$0.914138\pi$
$614$			1596.59i			2.60031i
$615$	−650.569	−	1310.24i	−1.05784	−	2.13047i
$616$	170.968	+	296.125i	0.277545	+	0.480722i
$617$			173.904i			0.281854i	0.990020	+	0.140927i	$0.0450082\pi$
$617$			173.904i			0.281854i	−0.990020	+	0.140927i	$0.954992\pi$
$618$	83.1626	+	55.2413i	0.134567	+	0.0893871i
$619$	−227.450	+	393.956i	−0.367448	+	0.636439i	−0.989166	−	0.146803i	$-0.953102\pi$
$619$	−227.450	+	393.956i	−0.367448	+	0.636439i	0.621718	+	0.783241i	$0.286435\pi$
$620$	145.569	+	84.0440i	0.234788	+	0.135555i
$621$	−206.509	−	178.147i	−0.332542	−	0.286871i
$622$	228.317	+	395.457i	0.367069	+	0.635782i
$623$	1184.78	+	684.032i	1.90173	+	1.09796i
$624$	−194.793	+	207.415i	−0.312168	+	0.332397i
$625$	138.878	+	240.544i	0.222205	+	0.384870i
$626$	1032.57	+	596.154i	1.64947	+	0.952322i
$627$	−2.83209	+	45.0857i	−0.00451688	+	0.0719070i
$628$	770.501	+	1334.55i	1.22691	+	2.12508i
$629$		−	304.764i		−	0.484522i
$630$	1056.67	+	2512.33i	1.67725	+	3.98782i
$631$	2.06774	−	3.58143i	0.00327693	−	0.00567580i	−0.864382	−	0.502835i	$-0.832290\pi$
$631$	2.06774	−	3.58143i	0.00327693	−	0.00567580i	0.867659	+	0.497159i	$0.165624\pi$
$632$	−521.281	−	300.961i	−0.824811	−	0.476205i
$633$	585.650	+	36.7880i	0.925197	+	0.0581168i
$634$	645.753	−	1118.48i	1.01854	−	1.76416i
$635$	−434.529	−	250.875i	−0.684298	−	0.395079i
$636$	−567.918	+	281.987i	−0.892952	+	0.443375i
$637$	1422.42	+	240.790i	2.23299	+	0.378007i
$638$		−	604.358i		−	0.947269i
$639$	732.216	−	307.965i	1.14588	−	0.481949i
$640$	−553.430	−	958.569i	−0.864734	−	1.49776i
$641$	190.061	−	109.732i	0.296507	−	0.171188i	−0.344366	−	0.938836i	$-0.611906\pi$
$641$	190.061	−	109.732i	0.296507	−	0.171188i	0.640873	+	0.767647i	$0.278573\pi$
$642$	201.585	−	303.475i	0.313995	−	0.472702i
$643$	832.551			1.29479			0.647395	−	0.762154i	$-0.275858\pi$
$643$	832.551			1.29479			0.647395	+	0.762154i	$0.275858\pi$
$644$		−	710.890i		−	1.10387i
$645$	36.6180	−	582.944i	0.0567721	−	0.903789i
$646$	−63.3489	−	109.723i	−0.0980633	−	0.169851i
$647$	345.359	−	199.393i	0.533786	−	0.308181i	−0.208771	−	0.977965i	$-0.566946\pi$
$647$	345.359	−	199.393i	0.533786	−	0.308181i	0.742557	+	0.669783i	$0.233613\pi$
$648$	377.375	−	105.526i	0.582369	−	0.162848i
$649$	−110.932			−0.170927
$650$	−234.451	+	1384.97i	−0.360694	+	2.13072i
$651$	147.763	+	9.28182i	0.226978	+	0.0142578i
$652$	842.399	−	1459.08i	1.29202	−	2.23785i
$653$	−960.778	−	554.705i	−1.47133	−	0.849472i	−0.471848	−	0.881680i	$-0.656413\pi$
$653$	−960.778	−	554.705i	−1.47133	−	0.849472i	−0.999481	+	0.0322076i	$0.989746\pi$
$654$	1048.87	−	520.790i	1.60377	−	0.796316i
$655$	677.054	−	1172.69i	1.03367	−	1.79037i
$656$	397.965	+	229.765i	0.606653	+	0.350252i
$657$	316.830	−	417.580i	0.482238	−	0.635585i
$658$	1810.64			2.75174
$659$	−452.167	+	261.059i	−0.686142	+	0.396144i	−0.802165	−	0.597102i	$-0.796319\pi$
$659$	−452.167	+	261.059i	−0.686142	+	0.396144i	0.116023	+	0.993246i	$0.462985\pi$
$660$	−399.608	+	601.587i	−0.605467	+	0.911496i
$661$	141.464	−	245.023i	0.214015	−	0.370685i	−0.738952	−	0.673758i	$-0.764679\pi$
$661$	141.464	−	245.023i	0.214015	−	0.370685i	0.952967	+	0.303073i	$0.0980125\pi$
$662$	642.742	−	371.087i	0.970909	−	0.560555i
$663$	−567.651	+	171.358i	−0.856185	+	0.258458i
$664$	−114.240	+	197.869i	−0.172048	+	0.297995i
$665$	−228.506	+	131.928i	−0.343617	+	0.198388i
$666$	−69.8177	+	553.542i	−0.104831	+	0.831144i
$667$	−176.614	+	305.904i	−0.264789	+	0.458627i
$668$	−96.8726	−	55.9294i	−0.145019	−	0.0837267i
$669$	313.101	+	630.582i	0.468014	+	0.942574i
$670$	515.344			0.769170
$671$	109.955	−	63.4824i	0.163867	−	0.0946087i
$672$	−1324.77	−	879.988i	−1.97139	−	1.30951i
$673$	554.927			0.824557			0.412279	−	0.911058i	$-0.364733\pi$
$673$	554.927			0.824557			0.412279	+	0.911058i	$0.364733\pi$
$674$	836.228	−	482.796i	1.24069	−	0.716315i
$675$	−616.189	+	714.289i	−0.912873	+	1.05821i
$676$	712.022	−	614.250i	1.05329	−	0.908654i
$677$	−513.136	−	296.259i	−0.757956	−	0.437606i	0.0706053	−	0.997504i	$-0.477507\pi$
$677$	−513.136	−	296.259i	−0.757956	−	0.437606i	−0.828561	+	0.559898i	$0.810840\pi$
$678$	−588.576	−	1185.38i	−0.868106	−	1.74835i
$679$	−133.882	+	231.891i	−0.197176	+	0.341518i
$680$		−	569.435i		−	0.837405i
$681$	−442.195	−	293.731i	−0.649332	−	0.431323i
$682$	33.7175	+	58.4004i	0.0494391	+	0.0856310i
$683$	−1020.77	−	589.343i	−1.49454	−	0.862874i	−0.494561	−	0.869143i	$-0.664671\pi$
$683$	−1020.77	−	589.343i	−1.49454	−	0.862874i	−0.999980	+	0.00626870i	$0.998005\pi$
$684$	52.3157	+	124.385i	0.0764850	+	0.181850i
$685$	−34.9782	+	60.5840i	−0.0510631	+	0.0884439i
$686$			2424.12i			3.53371i
$687$	−214.405	+	322.775i	−0.312089	+	0.469833i
$688$	91.7407	+	158.900i	0.133344	+	0.230959i
$689$	−462.856	+	172.060i	−0.671779	+	0.249724i
$690$	649.858	−	322.672i	0.941823	−	0.467641i
$691$	407.940			0.590361			0.295181	−	0.955441i	$-0.404620\pi$
$691$	407.940			0.590361			0.295181	+	0.955441i	$0.404620\pi$
$692$	743.366	−	429.183i	1.07423	−	0.620206i
$693$	−79.6045	+	631.136i	−0.114869	+	0.910730i
$694$	−958.180			−1.38066
$695$	141.402	−	81.6382i	0.203455	−	0.117465i
$696$	−225.700	−	454.558i	−0.324282	−	0.653101i
$697$	478.799	+	829.304i	0.686942	+	1.18982i
$698$		−	441.196i		−	0.632086i
$699$	−427.660	+	212.345i	−0.611817	+	0.303784i
$700$	−2458.88			−3.51269
$701$		−	388.806i		−	0.554644i	−0.960777	−	0.277322i	$-0.910553\pi$
$701$		−	388.806i		−	0.554644i	0.960777	−	0.277322i	$-0.0894469\pi$
$702$	1070.28	−	181.194i	1.52461	−	0.258112i
$703$	−54.0130			−0.0768322
$704$		−	561.300i		−	0.797302i
$705$	478.132	+	962.953i	0.678202	+	1.36589i
$706$	−63.5731			−0.0900469
$707$	−950.386	+	548.706i	−1.34425	+	0.776104i
$708$	−296.789	+	147.364i	−0.419194	+	0.208141i
$709$	243.148	+	421.144i	0.342945	+	0.593998i	0.984978	−	0.172679i	$-0.0552423\pi$
$709$	243.148	+	421.144i	0.342945	+	0.593998i	−0.642033	+	0.766677i	$0.721909\pi$
$710$			2113.22i			2.97637i
$711$	−434.150	−	1032.23i	−0.610619	−	1.45180i
$712$	261.631	+	453.158i	0.367459	+	0.636458i
$713$		−	39.4136i		−	0.0552785i
$714$	−793.442	−	1597.98i	−1.11126	−	2.23807i
$715$	−358.578	+	433.321i	−0.501507	+	0.606044i
$716$	−898.076	+	518.505i	−1.25430	+	0.724169i
$717$	590.654	+	392.345i	0.823785	+	0.547204i
$718$	−454.679			−0.633258
$719$	548.518	+	316.687i	0.762890	+	0.440455i	0.830332	−	0.557269i	$-0.188151\pi$
$719$	548.518	+	316.687i	0.762890	+	0.440455i	−0.0674425	+	0.997723i	$0.521484\pi$
$720$	63.6163	−	504.375i	0.0883560	−	0.700521i
$721$	−68.0522	+	117.870i	−0.0943859	+	0.163481i
$722$	947.414	−	546.990i	1.31221	−	0.757603i
$723$	193.202	−	290.855i	0.267223	−	0.402288i
$724$	−1733.16			−2.39387
$725$	1058.09	+	610.887i	1.45943	+	0.842603i
$726$	745.980	−	370.399i	1.02752	−	0.510192i
$727$	−263.153	+	455.794i	−0.361971	+	0.626951i	−0.988285	−	0.152619i	$-0.951229\pi$
$727$	−263.153	+	455.794i	−0.361971	+	0.626951i	0.626315	+	0.779570i	$0.284563\pi$
$728$	612.820	+	507.115i	0.841786	+	0.696586i
$729$	677.966	+	267.962i	0.929994	+	0.367574i
$730$	697.235	+	1207.65i	0.955116	+	1.65431i
$731$			382.350i			0.523051i
$732$	209.844	−	315.909i	0.286672	−	0.431569i
$733$	623.923	+	1080.67i	0.851191	+	1.47431i	0.880134	+	0.474725i	$0.157452\pi$
$733$	623.923	+	1080.67i	0.851191	+	1.47431i	−0.0289432	+	0.999581i	$0.509214\pi$
$734$		−	1203.61i		−	1.63980i
$735$	−2308.56	+	1146.26i	−3.14089	+	1.55954i
$736$	−211.692	+	366.661i	−0.287625	+	0.498181i
$737$	104.167	+	60.1411i	0.141340	+	0.0816026i
$738$	−679.657	−	1615.95i	−0.920945	−	2.18963i
$739$	241.687	+	418.615i	0.327047	+	0.566461i	0.981924	−	0.189274i	$-0.0606133\pi$
$739$	241.687	+	418.615i	0.327047	+	0.566461i	−0.654878	+	0.755735i	$0.727280\pi$
$740$	−747.828	−	431.759i	−1.01058	−	0.583458i
$741$	30.3695	+	100.604i	0.0409845	+	0.135768i
$742$	−742.897	−	1286.74i	−1.00121	−	1.73415i
$743$	−606.999	−	350.451i	−0.816957	−	0.471671i	0.0324087	−	0.999475i	$-0.489682\pi$
$743$	−606.999	−	350.451i	−0.816957	−	0.471671i	−0.849366	+	0.527804i	$0.823016\pi$
$744$	47.1700	+	31.3330i	0.0634005	+	0.0421142i
$745$	−7.16632	−	12.4124i	−0.00961923	−	0.0166610i
$746$			1248.37i			1.67342i
$747$	−391.817	+	164.796i	−0.524521	+	0.220610i
$748$	236.383	−	409.427i	0.316020	−	0.547362i
$749$	430.128	+	248.334i	0.574269	+	0.331555i
$750$	−317.482	−	639.405i	−0.423309	−	0.852539i
$751$	−16.9091	+	29.2874i	−0.0225154	+	0.0389979i	−0.877064	−	0.480374i	$-0.840501\pi$
$751$	−16.9091	+	29.2874i	−0.0225154	+	0.0389979i	0.854548	+	0.519372i	$0.173834\pi$
$752$	−292.482	−	168.865i	−0.388939	−	0.224554i
$753$	−2.56613	+	40.8517i	−0.00340787	+	0.0542520i
$754$	−489.870	−	1317.79i	−0.649696	−	1.74773i
$755$		−	763.905i		−	1.01179i
$756$	625.438	+	1794.30i	0.827299	+	2.37342i
$757$	−579.869	−	1004.36i	−0.766009	−	1.32677i	−0.939711	−	0.341968i	$-0.888906\pi$
$757$	−579.869	−	1004.36i	−0.766009	−	1.32677i	0.173702	−	0.984798i	$-0.444427\pi$
$758$	420.054	−	242.518i	0.554161	−	0.319945i
$759$	169.013	+	10.6167i	0.222679	+	0.0139877i
$760$	−100.920			−0.132790
$761$		−	11.0168i		−	0.0144767i	−0.999974	−	0.00723836i	$-0.997696\pi$
$761$		−	11.0168i		−	0.0144767i	0.999974	−	0.00723836i	$-0.00230406\pi$
$762$	−500.857	−	332.698i	−0.657293	−	0.436611i
$763$	798.215	+	1382.55i	1.04615	+	1.81199i
$764$	−675.834	+	390.193i	−0.884600	+	0.510724i
$765$	640.332	−	843.951i	0.837035	−	1.10320i
$766$	−904.123			−1.18032
$767$	−241.885	+	89.9172i	−0.315365	+	0.117232i
$768$	−53.8747	−	108.503i	−0.0701494	−	0.141280i
$769$	323.693	−	560.652i	0.420927	−	0.729067i	−0.575104	−	0.818081i	$-0.695038\pi$
$769$	323.693	−	560.652i	0.420927	−	0.729067i	0.996030	+	0.0890140i	$0.0283716\pi$
$770$	−1465.61

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.09261i q^{2} +(1.33417 + 2.68700i) q^{3} -5.56427 q^{4} +(6.70477 - 3.87100i) q^{5} +(8.30987 - 4.12608i) q^{6} +(6.32403 + 10.9535i) q^{7} +4.83767i q^{8} +(-5.43998 + 7.16984i) q^{9} +(-11.9715 - 20.7353i) q^{10} -5.58835i q^{11} +(-7.42368 - 14.9512i) q^{12} +(-4.52972 - 12.1853i) q^{13} +(33.8751 - 19.5578i) q^{14} +(19.3467 + 12.8512i) q^{15} -7.29600 q^{16} +(-13.1669 - 7.60194i) q^{17} +(22.1736 + 16.8238i) q^{18} +(-1.34728 + 2.33356i) q^{19} +(-37.3072 + 21.5393i) q^{20} +(-20.9949 + 31.6066i) q^{21} -17.2826 q^{22} +(8.74785 + 5.05057i) q^{23} +(-12.9988 + 6.45428i) q^{24} +(17.4693 - 30.2578i) q^{25} +(-37.6845 + 14.0087i) q^{26} +(-26.5233 - 5.05145i) q^{27} +(-35.1886 - 60.9484i) q^{28} +34.9691i q^{29} +(39.7437 - 59.8319i) q^{30} +(-1.95095 - 3.37914i) q^{31} +41.9144i q^{32} +(15.0159 - 7.45581i) q^{33} +(-23.5099 + 40.7203i) q^{34} +(84.8024 + 48.9607i) q^{35} +(30.2695 - 39.8949i) q^{36} +(10.0226 + 17.3596i) q^{37} +(7.21681 + 4.16663i) q^{38} +(26.6985 - 28.4286i) q^{39} +(18.7267 + 32.4355i) q^{40} +(-54.5456 - 31.4919i) q^{41} +(97.7470 + 64.9290i) q^{42} +(-12.5741 - 21.7790i) q^{43} +31.0951i q^{44} +(-8.71934 + 69.1303i) q^{45} +(15.6195 - 27.0537i) q^{46} +(40.0880 + 23.1448i) q^{47} +(-9.73411 - 19.6044i) q^{48} +(-55.4867 + 96.1057i) q^{49} +(-93.5756 - 54.0259i) q^{50} +(2.85949 - 45.5219i) q^{51} +(25.2045 + 67.8023i) q^{52} -37.9847i q^{53} +(-15.6222 + 82.0262i) q^{54} +(-21.6325 - 37.4686i) q^{55} +(-52.9896 + 30.5936i) q^{56} +(-8.06780 - 0.506784i) q^{57} +108.146 q^{58} -19.8505i q^{59} +(-107.650 - 71.5074i) q^{60} +(11.3598 + 19.6757i) q^{61} +(-10.4504 + 6.03353i) q^{62} +(-112.938 - 14.2447i) q^{63} +100.441 q^{64} +(-77.5401 - 64.1652i) q^{65} +(-23.0580 - 46.4385i) q^{66} +(-10.7619 + 18.6401i) q^{67} +(73.2644 + 42.2992i) q^{68} +(-1.89979 + 30.2438i) q^{69} +(151.416 - 262.261i) q^{70} +(-76.4358 - 44.1302i) q^{71} +(-34.6854 - 26.3168i) q^{72} -58.2411 q^{73} +(53.6866 - 30.9960i) q^{74} +(104.610 + 6.57113i) q^{75} +(7.49664 - 12.9846i) q^{76} +(61.2122 - 35.3409i) q^{77} +(-87.9188 - 82.5683i) q^{78} +(-62.2120 + 107.754i) q^{79} +(-48.9181 + 28.2429i) q^{80} +(-21.8133 - 78.0076i) q^{81} +(-97.3923 + 168.688i) q^{82} +(40.9017 + 23.6146i) q^{83} +(116.821 - 175.867i) q^{84} -117.708 q^{85} +(-67.3540 + 38.8869i) q^{86} +(-93.9621 + 46.6547i) q^{87} +27.0346 q^{88} +(93.6727 - 54.0819i) q^{89} +(213.794 + 26.9656i) q^{90} +(104.826 - 126.677i) q^{91} +(-48.6754 - 28.1027i) q^{92} +(6.47686 - 9.75055i) q^{93} +(71.5779 - 123.977i) q^{94} +20.8613i q^{95} +(-112.624 + 55.9210i) q^{96} +(10.5852 + 18.3341i) q^{97} +(297.218 + 171.599i) q^{98} +(40.0676 + 30.4005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

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Database

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