LMFDB - Embedded newform 231.2.i.f.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15x^{8} + 72x^{6} + 120x^{4} + 72x^{2} + 12 $ x^10 + 15x^8 + 72x^6 + 120x^4 + 72x^2 + 12
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			67.5
Root			$0.886226i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.f.100.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24646 + 2.15892i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.10730 + 3.64995i) q^{4} +(0.440463 + 0.762904i) q^{5} +2.49291 q^{6} +(-2.14580 + 1.54775i) q^{7} -5.52081 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.24646 + 2.15892i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.10730 + 3.64995i) q^{4} +(0.440463 + 0.762904i) q^{5} +2.49291 q^{6} +(-2.14580 + 1.54775i) q^{7} -5.52081 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.09804 + 1.90185i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(2.10730 + 3.64995i) q^{12} +7.12343 q^{13} +(-6.01613 - 2.70341i) q^{14} +0.880926 q^{15} +(-2.66684 - 4.61910i) q^{16} +(1.24646 - 2.15892i) q^{17} +(1.24646 - 2.15892i) q^{18} +(-1.31526 - 2.27810i) q^{19} -3.71275 q^{20} +(0.267494 + 2.63219i) q^{21} -2.49291 q^{22} +(-2.66684 - 4.61910i) q^{23} +(-2.76040 + 4.78116i) q^{24} +(2.11198 - 3.65806i) q^{25} +(8.87904 + 15.3789i) q^{26} -1.00000 q^{27} +(-1.12738 - 11.0937i) q^{28} +0.773136 q^{29} +(1.09804 + 1.90185i) q^{30} +(0.607302 - 1.05188i) q^{31} +(1.12738 - 1.95268i) q^{32} +(0.500000 + 0.866025i) q^{33} +6.21460 q^{34} +(-2.12593 - 0.955312i) q^{35} +4.21460 q^{36} +(-4.43337 - 7.67883i) q^{37} +(3.27882 - 5.67909i) q^{38} +(3.56171 - 6.16907i) q^{39} +(-2.43171 - 4.21185i) q^{40} -6.19607 q^{41} +(-5.34929 + 3.85841i) q^{42} +3.22921 q^{43} +(-2.10730 - 3.64995i) q^{44} +(0.440463 - 0.762904i) q^{45} +(6.64819 - 11.5150i) q^{46} +(4.87852 + 8.44984i) q^{47} -5.33368 q^{48} +(2.20892 - 6.64234i) q^{49} +10.5300 q^{50} +(-1.24646 - 2.15892i) q^{51} +(-15.0112 + 26.0002i) q^{52} +(-4.46836 + 7.73943i) q^{53} +(-1.24646 - 2.15892i) q^{54} -0.880926 q^{55} +(11.8466 - 8.54485i) q^{56} -2.63052 q^{57} +(0.963679 + 1.66914i) q^{58} +(-2.66684 + 4.61910i) q^{59} +(-1.85638 + 3.21534i) q^{60} +(4.54185 + 7.86671i) q^{61} +3.02790 q^{62} +(2.41329 + 1.08444i) q^{63} -5.04643 q^{64} +(3.13761 + 5.43450i) q^{65} +(-1.24646 + 2.15892i) q^{66} +(-5.63520 + 9.76045i) q^{67} +(5.25332 + 9.09901i) q^{68} -5.33368 q^{69} +(-0.587436 - 5.78048i) q^{70} -7.62963 q^{71} +(2.76040 + 4.78116i) q^{72} +(6.38830 - 11.0649i) q^{73} +(11.0520 - 19.1426i) q^{74} +(-2.11198 - 3.65806i) q^{75} +11.0866 q^{76} +(-0.267494 - 2.63219i) q^{77} +17.7581 q^{78} +(3.47948 + 6.02663i) q^{79} +(2.34929 - 4.06909i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.72312 - 13.3768i) q^{82} -1.20524 q^{83} +(-10.1711 - 4.57049i) q^{84} +2.19607 q^{85} +(4.02507 + 6.97162i) q^{86} +(0.386568 - 0.669555i) q^{87} +(2.76040 - 4.78116i) q^{88} +(-3.14697 - 5.45072i) q^{89} +2.19607 q^{90} +(-15.2855 + 11.0253i) q^{91} +22.4793 q^{92} +(-0.607302 - 1.05188i) q^{93} +(-12.1617 + 21.0647i) q^{94} +(1.15865 - 2.00683i) q^{95} +(-1.12738 - 1.95268i) q^{96} +1.29862 q^{97} +(17.0936 - 3.51050i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.24646	+	2.15892i	0.881377	+	1.52659i	0.849811	+	0.527088i	$0.176716\pi$
$2$	1.24646	+	2.15892i	0.881377	+	1.52659i	0.0315664	+	0.999502i	$0.489950\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.10730	+	3.64995i	−1.05365	+	1.82498i
$5$	0.440463	+	0.762904i	0.196981	+	0.341181i	0.947548	−	0.319613i	$-0.103553\pi$
$5$	0.440463	+	0.762904i	0.196981	+	0.341181i	−0.750567	+	0.660794i	$0.770220\pi$
$6$	2.49291			1.01773
$7$	−2.14580	+	1.54775i	−0.811036	+	0.584996i
$7$	−2.14580	+	1.54775i	−0.811036	+	0.584996i
$8$	−5.52081			−1.95190
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.09804	+	1.90185i	−0.347229	+	0.601419i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	2.10730	+	3.64995i	0.608326	+	1.05365i
$13$	7.12343			1.97568			0.987842	−	0.155462i	$-0.0496867\pi$
$13$	7.12343			1.97568			0.987842	+	0.155462i	$0.0496867\pi$
$14$	−6.01613	−	2.70341i	−1.60788	−	0.722518i
$15$	0.880926			0.227454
$16$	−2.66684	−	4.61910i	−0.666710	−	1.15478i
$17$	1.24646	−	2.15892i	0.302310	−	0.523616i	−0.674349	−	0.738413i	$-0.735576\pi$
$17$	1.24646	−	2.15892i	0.302310	−	0.523616i	0.976659	+	0.214797i	$0.0689089\pi$
$18$	1.24646	−	2.15892i	0.293792	−	0.508863i
$19$	−1.31526	−	2.27810i	−0.301741	−	0.522631i	0.674789	−	0.738010i	$-0.264234\pi$
$19$	−1.31526	−	2.27810i	−0.301741	−	0.522631i	−0.976530	+	0.215379i	$0.930901\pi$
$20$	−3.71275			−0.830197
$21$	0.267494	+	2.63219i	0.0583720	+	0.574392i
$22$	−2.49291			−0.531490
$23$	−2.66684	−	4.61910i	−0.556074	−	0.963149i	−0.997819	−	0.0660082i	$-0.978974\pi$
$23$	−2.66684	−	4.61910i	−0.556074	−	0.963149i	0.441745	−	0.897141i	$-0.354360\pi$
$24$	−2.76040	+	4.78116i	−0.563465	+	0.975950i
$25$	2.11198	−	3.65806i	0.422397	−	0.731613i
$26$	8.87904	+	15.3789i	1.74132	+	3.01606i
$27$	−1.00000			−0.192450
$28$	−1.12738	−	11.0937i	−0.213055	−	2.09650i
$29$	0.773136			0.143568			0.0717839	−	0.997420i	$-0.477131\pi$
$29$	0.773136			0.143568			0.0717839	+	0.997420i	$0.477131\pi$
$30$	1.09804	+	1.90185i	0.200473	+	0.347229i
$31$	0.607302	−	1.05188i	0.109075	−	0.188923i	−0.806321	−	0.591478i	$-0.798545\pi$
$31$	0.607302	−	1.05188i	0.109075	−	0.188923i	0.915396	+	0.402555i	$0.131878\pi$
$32$	1.12738	−	1.95268i	0.199295	−	0.345189i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	6.21460			1.06580
$35$	−2.12593	−	0.955312i	−0.359348	−	0.161477i
$36$	4.21460			0.702434
$37$	−4.43337	−	7.67883i	−0.728842	−	1.26239i	−0.957373	−	0.288855i	$-0.906725\pi$
$37$	−4.43337	−	7.67883i	−0.728842	−	1.26239i	0.228531	−	0.973537i	$-0.426608\pi$
$38$	3.27882	−	5.67909i	0.531895	−	0.921270i
$39$	3.56171	−	6.16907i	0.570331	−	0.987842i
$40$	−2.43171	−	4.21185i	−0.384488	−	0.665952i
$41$	−6.19607			−0.967664			−0.483832	−	0.875161i	$-0.660755\pi$
$41$	−6.19607			−0.967664			−0.483832	+	0.875161i	$0.660755\pi$
$42$	−5.34929	+	3.85841i	−0.825413	+	0.595366i
$43$	3.22921			0.492450			0.246225	−	0.969213i	$-0.420810\pi$
$43$	3.22921			0.492450			0.246225	+	0.969213i	$0.420810\pi$
$44$	−2.10730	−	3.64995i	−0.317688	−	0.550251i
$45$	0.440463	−	0.762904i	0.0656604	−	0.113727i
$46$	6.64819	−	11.5150i	0.980222	−	1.69779i
$47$	4.87852	+	8.44984i	0.711605	+	1.23254i	0.964254	+	0.264978i	$0.0853648\pi$
$47$	4.87852	+	8.44984i	0.711605	+	1.23254i	−0.252649	+	0.967558i	$0.581302\pi$
$48$	−5.33368			−0.769850
$49$	2.20892	−	6.64234i	0.315559	−	0.948906i
$50$	10.5300			1.48916
$51$	−1.24646	−	2.15892i	−0.174539	−	0.302310i
$52$	−15.0112	+	26.0002i	−2.08168	+	3.60558i
$53$	−4.46836	+	7.73943i	−0.613777	+	1.06309i	0.376821	+	0.926286i	$0.377017\pi$
$53$	−4.46836	+	7.73943i	−0.613777	+	1.06309i	−0.990598	+	0.136806i	$0.956316\pi$
$54$	−1.24646	−	2.15892i	−0.169621	−	0.293792i
$55$	−0.880926			−0.118784
$56$	11.8466	−	8.54485i	1.58306	−	1.14185i
$57$	−2.63052			−0.348421
$58$	0.963679	+	1.66914i	0.126537	+	0.219169i
$59$	−2.66684	+	4.61910i	−0.347193	+	0.601356i	−0.985750	−	0.168219i	$-0.946198\pi$
$59$	−2.66684	+	4.61910i	−0.347193	+	0.601356i	0.638557	+	0.769575i	$0.279532\pi$
$60$	−1.85638	+	3.21534i	−0.239657	+	0.415099i
$61$	4.54185	+	7.86671i	0.581524	+	1.00723i	0.995299	+	0.0968500i	$0.0308767\pi$
$61$	4.54185	+	7.86671i	0.581524	+	1.00723i	−0.413775	+	0.910379i	$0.635790\pi$
$62$	3.02790			0.384544
$63$	2.41329	+	1.08444i	0.304046	+	0.136627i
$64$	−5.04643			−0.630804
$65$	3.13761	+	5.43450i	0.389172	+	0.674066i
$66$	−1.24646	+	2.15892i	−0.153428	+	0.265745i
$67$	−5.63520	+	9.76045i	−0.688449	+	1.19243i	0.283890	+	0.958857i	$0.408375\pi$
$67$	−5.63520	+	9.76045i	−0.688449	+	1.19243i	−0.972339	+	0.233572i	$0.924958\pi$
$68$	5.25332	+	9.09901i	0.637058	+	1.10342i
$69$	−5.33368			−0.642099
$70$	−0.587436	−	5.78048i	−0.0702120	−	0.690900i
$71$	−7.62963			−0.905471			−0.452735	−	0.891645i	$-0.649552\pi$
$71$	−7.62963			−0.905471			−0.452735	+	0.891645i	$0.649552\pi$
$72$	2.76040	+	4.78116i	0.325317	+	0.563465i
$73$	6.38830	−	11.0649i	0.747694	−	1.29504i	−0.201231	−	0.979544i	$-0.564494\pi$
$73$	6.38830	−	11.0649i	0.747694	−	1.29504i	0.948925	−	0.315501i	$-0.102172\pi$
$74$	11.0520	−	19.1426i	1.28477	−	2.22529i
$75$	−2.11198	−	3.65806i	−0.243871	−	0.422397i
$76$	11.0866			1.27172
$77$	−0.267494	−	2.63219i	−0.0304838	−	0.299966i
$78$	17.7581			2.01071
$79$	3.47948	+	6.02663i	0.391472	+	0.678049i	0.992644	−	0.121070i	$-0.0386327\pi$
$79$	3.47948	+	6.02663i	0.391472	+	0.678049i	−0.601172	+	0.799120i	$0.705299\pi$
$80$	2.34929	−	4.06909i	0.262658	−	0.454938i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.72312	−	13.3768i	−0.852876	−	1.47723i
$83$	−1.20524			−0.132292			−0.0661461	−	0.997810i	$-0.521070\pi$
$83$	−1.20524			−0.132292			−0.0661461	+	0.997810i	$0.521070\pi$
$84$	−10.1711	−	4.57049i	−1.10976	−	0.498681i
$85$	2.19607			0.238197
$86$	4.02507	+	6.97162i	0.434034	+	0.751769i
$87$	0.386568	−	0.669555i	0.0414444	−	0.0717839i
$88$	2.76040	−	4.78116i	0.294260	−	0.509674i
$89$	−3.14697	−	5.45072i	−0.333578	−	0.577775i	0.649632	−	0.760249i	$-0.274923\pi$
$89$	−3.14697	−	5.45072i	−0.333578	−	0.577775i	−0.983211	+	0.182474i	$0.941590\pi$
$90$	2.19607			0.231486
$91$	−15.2855	+	11.0253i	−1.60235	+	1.15577i
$92$	22.4793			2.34363
$93$	−0.607302	−	1.05188i	−0.0629743	−	0.109075i
$94$	−12.1617	+	21.0647i	−1.25438	+	2.17266i
$95$	1.15865	−	2.00683i	0.118875	−	0.205897i
$96$	−1.12738	−	1.95268i	−0.115063	−	0.199295i
$97$	1.29862			0.131855			0.0659275	−	0.997824i	$-0.478999\pi$
$97$	1.29862			0.131855			0.0659275	+	0.997824i	$0.478999\pi$
$98$	17.0936	−	3.51050i	1.72672	−	0.354614i
$99$	1.00000			0.100504
$100$	8.90118	+	15.4173i	0.890118	+	1.54173i
$101$	4.94711	−	8.56865i	0.492256	−	0.852612i	−0.507704	−	0.861531i	$-0.669506\pi$
$101$	4.94711	−	8.56865i	0.492256	−	0.852612i	0.999960	+	0.00891925i	$0.00283912\pi$
$102$	3.10730	−	5.38200i	0.307669	−	0.532898i
$103$	−5.59212	−	9.68583i	−0.551008	−	0.954374i	−0.998202	−	0.0599367i	$-0.980910\pi$
$103$	−5.59212	−	9.68583i	−0.551008	−	0.954374i	0.447194	−	0.894437i	$-0.352423\pi$
$104$	−39.3271			−3.85634
$105$	−1.89029	+	1.36346i	−0.184474	+	0.133060i
$106$	−22.2785			−2.16387
$107$	−3.63302	−	6.29258i	−0.351218	−	0.608327i	0.635245	−	0.772310i	$-0.280899\pi$
$107$	−3.63302	−	6.29258i	−0.351218	−	0.608327i	−0.986463	+	0.163984i	$0.947566\pi$
$108$	2.10730	−	3.64995i	0.202775	−	0.351217i
$109$	−0.228037	+	0.394971i	−0.0218420	+	0.0378314i	−0.876740	−	0.480965i	$-0.840286\pi$
$109$	−0.228037	+	0.394971i	−0.0218420	+	0.0378314i	0.854898	+	0.518796i	$0.173620\pi$
$110$	−1.09804	−	1.90185i	−0.104694	−	0.181335i
$111$	−8.86675			−0.841594
$112$	12.8717	+	5.78406i	1.21626	+	0.546542i
$113$	−14.3518			−1.35010			−0.675050	−	0.737772i	$-0.735878\pi$
$113$	−14.3518			−1.35010			−0.675050	+	0.737772i	$0.735878\pi$
$114$	−3.27882	−	5.67909i	−0.307090	−	0.531895i
$115$	2.34929	−	4.06909i	0.219072	−	0.379444i
$116$	−1.62923	+	2.82191i	−0.151270	+	0.262008i
$117$	−3.56171	−	6.16907i	−0.329281	−	0.570331i
$118$	−13.2964			−1.22403
$119$	0.666839	+	6.56183i	0.0611290	+	0.601522i
$120$	−4.86343			−0.443968
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−11.3224	+	19.6110i	−1.02508	+	1.77550i
$123$	−3.09804	+	5.36595i	−0.279340	+	0.483832i
$124$	2.55954	+	4.43325i	0.229853	+	0.398117i
$125$	8.12564			0.726779
$126$	0.666839	+	6.56183i	0.0594067	+	0.584574i
$127$	8.91977			0.791502			0.395751	−	0.918358i	$-0.370484\pi$
$127$	8.91977			0.791502			0.395751	+	0.918358i	$0.370484\pi$
$128$	−8.54492	−	14.8002i	−0.755271	−	1.30817i
$129$	1.61460	−	2.79658i	0.142158	−	0.246225i
$130$	−7.82178	+	13.5477i	−0.686015	+	1.18821i
$131$	−6.19357	−	10.7276i	−0.541134	−	0.937272i	−0.998839	−	0.0481680i	$-0.984662\pi$
$131$	−6.19357	−	10.7276i	−0.541134	−	0.937272i	0.457705	−	0.889104i	$-0.348672\pi$
$132$	−4.21460			−0.366834
$133$	6.34821	+	2.85264i	0.550460	+	0.247355i
$134$	−28.0961			−2.42713
$135$	−0.440463	−	0.762904i	−0.0379090	−	0.0656604i
$136$	−6.88144	+	11.9190i	−0.590079	+	1.02205i
$137$	−11.0628	+	19.1614i	−0.945160	+	1.63707i	−0.189730	+	0.981836i	$0.560761\pi$
$137$	−11.0628	+	19.1614i	−0.945160	+	1.63707i	−0.755430	+	0.655229i	$0.772572\pi$
$138$	−6.64819	−	11.5150i	−0.565932	−	0.980222i
$139$	2.63553			0.223543			0.111771	−	0.993734i	$-0.464348\pi$
$139$	2.63553			0.223543			0.111771	+	0.993734i	$0.464348\pi$
$140$	7.96683	−	5.74643i	0.673320	−	0.485662i
$141$	9.75704			0.821691
$142$	−9.51000	−	16.4718i	−0.798061	−	1.38228i
$143$	−3.56171	+	6.16907i	−0.297846	+	0.515884i
$144$	−2.66684	+	4.61910i	−0.222237	+	0.384925i
$145$	0.340538	+	0.589829i	0.0282801	+	0.0489826i
$146$	31.8509			2.63600
$147$	−4.64798	−	5.23415i	−0.383359	−	0.431705i
$148$	37.3698			3.07178
$149$	−0.384063	−	0.665216i	−0.0314636	−	0.0544966i	0.849865	−	0.527001i	$-0.176684\pi$
$149$	−0.384063	−	0.665216i	−0.0314636	−	0.0544966i	−0.881328	+	0.472504i	$0.843350\pi$
$150$	5.26499	−	9.11923i	0.429885	−	0.744582i
$151$	7.01767	−	12.1550i	0.571090	−	0.989157i	−0.425364	−	0.905022i	$-0.639854\pi$
$151$	7.01767	−	12.1550i	0.571090	−	0.989157i	0.996454	−	0.0841349i	$-0.0268127\pi$
$152$	7.26129	+	12.5769i	0.588969	+	1.02012i
$153$	−2.49291			−0.201540
$154$	5.34929	−	3.85841i	0.431058	−	0.310920i
$155$	1.06998			0.0859426
$156$	15.0112	+	26.0002i	1.20186	+	2.08168i
$157$	−2.81905	+	4.88274i	−0.224985	+	0.389685i	−0.956315	−	0.292339i	$-0.905567\pi$
$157$	−2.81905	+	4.88274i	−0.224985	+	0.389685i	0.731330	+	0.682024i	$0.238900\pi$
$158$	−8.67403	+	15.0239i	−0.690069	+	1.19523i
$159$	4.46836	+	7.73943i	0.354364	+	0.613777i
$160$	1.98628			0.157029
$161$	12.8717	+	5.78406i	1.01443	+	0.455847i
$162$	−2.49291			−0.195862
$163$	−5.44983	−	9.43938i	−0.426864	−	0.739349i	0.569729	−	0.821833i	$-0.307048\pi$
$163$	−5.44983	−	9.43938i	−0.426864	−	0.739349i	−0.996592	+	0.0824834i	$0.973715\pi$
$164$	13.0570	−	22.6154i	1.01958	−	1.76596i
$165$	−0.440463	+	0.762904i	−0.0342900	+	0.0593920i
$166$	−1.50228	−	2.60202i	−0.116599	−	0.201956i
$167$	9.17688			0.710128			0.355064	−	0.934842i	$-0.384459\pi$
$167$	9.17688			0.710128			0.355064	+	0.934842i	$0.384459\pi$
$168$	−1.47678	−	14.5318i	−0.113936	−	1.12116i
$169$	37.7432			2.90333
$170$	2.73730	+	4.74115i	0.209942	+	0.363630i
$171$	−1.31526	+	2.27810i	−0.100580	+	0.174210i
$172$	−6.80492	+	11.7865i	−0.518870	+	0.898710i
$173$	1.25919	+	2.18097i	0.0957342	+	0.165816i	0.909915	−	0.414795i	$-0.136147\pi$
$173$	1.25919	+	2.18097i	0.0957342	+	0.165816i	−0.814181	+	0.580612i	$0.802813\pi$
$174$	1.92736			0.146113
$175$	1.12989	+	11.1183i	0.0854114	+	0.840465i
$176$	5.33368			0.402041
$177$	2.66684	+	4.61910i	0.200452	+	0.347193i
$178$	7.84512	−	13.5881i	0.588017	−	1.01847i
$179$	−12.2656	+	21.2447i	−0.916778	+	1.58791i	−0.112500	+	0.993652i	$0.535886\pi$
$179$	−12.2656	+	21.2447i	−0.916778	+	1.58791i	−0.804278	+	0.594254i	$0.797447\pi$
$180$	1.85638	+	3.21534i	0.138366	+	0.239657i
$181$	12.8187			0.952805			0.476403	−	0.879227i	$-0.341940\pi$
$181$	12.8187			0.952805			0.476403	+	0.879227i	$0.341940\pi$
$182$	−42.8555	−	19.2576i	−3.17666	−	1.42747i
$183$	9.08370			0.671486
$184$	14.7231	+	25.5012i	1.08540	+	1.87997i
$185$	3.90547	−	6.76448i	0.287136	−	0.497335i
$186$	1.51395	−	2.62224i	0.111008	−	0.192272i
$187$	1.24646	+	2.15892i	0.0911498	+	0.157876i
$188$	−41.1221			−2.99913
$189$	2.14580	−	1.54775i	0.156084	−	0.112583i
$190$	5.77680			0.419093
$191$	−11.0393	−	19.1206i	−0.798774	−	1.38352i	−0.920415	−	0.390943i	$-0.872149\pi$
$191$	−11.0393	−	19.1206i	−0.798774	−	1.38352i	0.121641	−	0.992574i	$-0.461184\pi$
$192$	−2.52322	+	4.37034i	−0.182097	+	0.315402i
$193$	−9.22264	+	15.9741i	−0.663860	+	1.14984i	0.315733	+	0.948848i	$0.397750\pi$
$193$	−9.22264	+	15.9741i	−0.663860	+	1.14984i	−0.979593	+	0.200991i	$0.935584\pi$
$194$	1.61867	+	2.80362i	0.116214	+	0.201288i
$195$	6.27521			0.449377
$196$	19.5894	+	22.0599i	1.39924	+	1.57570i
$197$	−4.57707			−0.326102			−0.163051	−	0.986618i	$-0.552134\pi$
$197$	−4.57707			−0.326102			−0.163051	+	0.986618i	$0.552134\pi$
$198$	1.24646	+	2.15892i	0.0885817	+	0.153428i
$199$	1.09553	−	1.89751i	0.0776601	−	0.134511i	−0.824580	−	0.565746i	$-0.808588\pi$
$199$	1.09553	−	1.89751i	0.0776601	−	0.134511i	0.902240	+	0.431234i	$0.141922\pi$
$200$	−11.6599	+	20.1955i	−0.824477	+	1.42804i
$201$	5.63520	+	9.76045i	0.397476	+	0.688449i
$202$	24.6654			1.73545
$203$	−1.65899	+	1.19662i	−0.116439	+	0.0839865i
$204$	10.5066			0.735611
$205$	−2.72914	−	4.72701i	−0.190611	−	0.330149i
$206$	13.9407	−	24.1459i	0.971291	−	1.68233i
$207$	−2.66684	+	4.61910i	−0.185358	+	0.321050i
$208$	−18.9970	−	32.9038i	−1.31721	−	2.28147i
$209$	2.63052			0.181957
$210$	−5.29976	−	2.38151i	−0.365718	−	0.164340i
$211$	−9.97047			−0.686395			−0.343198	−	0.939263i	$-0.611510\pi$
$211$	−9.97047			−0.686395			−0.343198	+	0.939263i	$0.611510\pi$
$212$	−18.8324	−	32.6186i	−1.29341	−	2.24026i
$213$	−3.81482	+	6.60746i	−0.261387	+	0.452735i
$214$	9.05680	−	15.6868i	0.619110	−	1.07233i
$215$	1.42235	+	2.46358i	0.0970033	+	0.168015i
$216$	5.52081			0.375644
$217$	0.324899	+	3.19707i	0.0220556	+	0.217031i
$218$	−1.13695			−0.0770040
$219$	−6.38830	−	11.0649i	−0.431681	−	0.747694i
$220$	1.85638	−	3.21534i	0.125157	−	0.216778i
$221$	8.87904	−	15.3789i	0.597269	−	1.03450i
$222$	−11.0520	−	19.1426i	−0.741762	−	1.28477i
$223$	−15.2015			−1.01796			−0.508982	−	0.860777i	$-0.669978\pi$
$223$	−15.2015			−1.01796			−0.508982	+	0.860777i	$0.669978\pi$
$224$	0.603136	+	5.93497i	0.0402987	+	0.396547i
$225$	−4.22397			−0.281598
$226$	−17.8888	−	30.9843i	−1.18995	−	2.06105i
$227$	5.53307	−	9.58356i	0.367243	−	0.636083i	−0.621891	−	0.783104i	$-0.713635\pi$
$227$	5.53307	−	9.58356i	0.367243	−	0.636083i	0.989133	+	0.147021i	$0.0469685\pi$
$228$	5.54330	−	9.60127i	0.367114	−	0.635860i
$229$	1.43289	+	2.48183i	0.0946877	+	0.164004i	0.909478	−	0.415752i	$-0.136481\pi$
$229$	1.43289	+	2.48183i	0.0946877	+	0.164004i	−0.814791	+	0.579755i	$0.803148\pi$
$230$	11.7131			0.772341
$231$	−2.41329	−	1.08444i	−0.158783	−	0.0713509i
$232$	−4.26834			−0.280230
$233$	7.30241	+	12.6482i	0.478397	+	0.828608i	0.999693	−	0.0247679i	$-0.00788467\pi$
$233$	7.30241	+	12.6482i	0.478397	+	0.828608i	−0.521296	+	0.853376i	$0.674551\pi$
$234$	8.87904	−	15.3789i	0.580441	−	1.00535i
$235$	−4.29762	+	7.44369i	−0.280346	+	0.485573i
$236$	−11.2397	−	19.4677i	−0.731640	−	1.26724i
$237$	6.95896			0.452033
$238$	−13.3353	+	9.61868i	−0.864399	+	0.623486i
$239$	18.4800			1.19537			0.597686	−	0.801730i	$-0.296087\pi$
$239$	18.4800			1.19537			0.597686	+	0.801730i	$0.296087\pi$
$240$	−2.34929	−	4.06909i	−0.151646	−	0.262658i
$241$	−12.9716	+	22.4675i	−0.835577	+	1.44726i	0.0579828	+	0.998318i	$0.481533\pi$
$241$	−12.9716	+	22.4675i	−0.835577	+	1.44726i	−0.893560	+	0.448944i	$0.851800\pi$
$242$	1.24646	−	2.15892i	0.0801252	−	0.138781i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−38.2842			−2.45089
$245$	6.04042	−	1.24051i	0.385908	−	0.0792535i
$246$	−15.4462			−0.984817
$247$	−9.36915	−	16.2279i	−0.596145	−	1.03255i
$248$	−3.35280	+	5.80722i	−0.212903	+	0.368759i
$249$	−0.602619	+	1.04377i	−0.0381894	+	0.0661461i
$250$	10.1282	+	17.5426i	0.640566	+	1.10949i
$251$	26.4331			1.66844			0.834221	−	0.551430i	$-0.185918\pi$
$251$	26.4331			1.66844			0.834221	+	0.551430i	$0.185918\pi$
$252$	−9.04370	+	6.52317i	−0.569699	+	0.410921i
$253$	5.33368			0.335325
$254$	11.1181	+	19.2571i	0.697612	+	1.20830i
$255$	1.09804	−	1.90185i	0.0687616	−	0.119099i
$256$	16.2553	−	28.1550i	1.01595	−	1.75969i
$257$	2.31950	+	4.01749i	0.144686	+	0.250604i	0.929256	−	0.369437i	$-0.120449\pi$
$257$	2.31950	+	4.01749i	0.144686	+	0.250604i	−0.784570	+	0.620041i	$0.787116\pi$
$258$	8.05013			0.501179
$259$	21.3981	+	9.61546i	1.32961	+	0.597476i
$260$	−26.4475			−1.64021
$261$	−0.386568	−	0.669555i	−0.0239280	−	0.0414444i
$262$	15.4400	−	26.7429i	0.953887	−	1.65218i
$263$	−9.81330	+	16.9971i	−0.605114	+	1.04809i	0.386920	+	0.922113i	$0.373539\pi$
$263$	−9.81330	+	16.9971i	−0.605114	+	1.04809i	−0.992034	+	0.125974i	$0.959794\pi$
$264$	−2.76040	−	4.78116i	−0.169891	−	0.294260i
$265$	−7.87259			−0.483610
$266$	1.75413	+	17.2610i	0.107553	+	1.05834i
$267$	−6.29395			−0.385183
$268$	−23.7501	−	41.1364i	−1.45077	−	2.51281i
$269$	11.2817	−	19.5404i	0.687855	−	1.19140i	−0.284676	−	0.958624i	$-0.591886\pi$
$269$	11.2817	−	19.5404i	0.687855	−	1.19140i	0.972530	−	0.232776i	$-0.0747807\pi$
$270$	1.09804	−	1.90185i	0.0668243	−	0.115743i
$271$	8.57677	+	14.8554i	0.521002	+	0.902401i	0.999702	+	0.0244227i	$0.00777475\pi$
$271$	8.57677	+	14.8554i	0.521002	+	0.902401i	−0.478700	+	0.877978i	$0.658892\pi$
$272$	−13.2964			−0.806212
$273$	1.90547	+	18.7502i	0.115325	+	1.13482i
$274$	−55.1572			−3.33217
$275$	2.11198	+	3.65806i	0.127357	+	0.220590i
$276$	11.2397	−	19.4677i	0.676549	−	1.17182i
$277$	13.0748	−	22.6462i	0.785587	−	1.36068i	−0.143060	−	0.989714i	$-0.545694\pi$
$277$	13.0748	−	22.6462i	0.785587	−	1.36068i	0.928648	−	0.370963i	$-0.120972\pi$
$278$	3.28507	+	5.68991i	0.197025	+	0.341258i
$279$	−1.21460			−0.0727164
$280$	11.7369	+	5.27410i	0.701413	+	0.315188i
$281$	8.79972			0.524947			0.262474	−	0.964939i	$-0.415462\pi$
$281$	8.79972			0.524947			0.262474	+	0.964939i	$0.415462\pi$
$282$	12.1617	+	21.0647i	0.724220	+	1.25438i
$283$	−6.87494	+	11.9077i	−0.408673	+	0.707842i	−0.994741	−	0.102419i	$-0.967342\pi$
$283$	−6.87494	+	11.9077i	−0.408673	+	0.707842i	0.586069	+	0.810261i	$0.300675\pi$
$284$	16.0779	−	27.8478i	0.954050	−	1.65246i
$285$	−1.15865	−	2.00683i	−0.0686323	−	0.118875i
$286$	−17.7581			−1.05006
$287$	13.2955	−	9.58999i	0.784810	−	0.566079i
$288$	−2.25476			−0.132863
$289$	5.39270	+	9.34043i	0.317218	+	0.549437i
$290$	−0.848930	+	1.47039i	−0.0498509	+	0.0863443i
$291$	0.649310	−	1.12464i	0.0380632	−	0.0659275i
$292$	26.9242	+	46.6340i	1.57562	+	2.72905i
$293$	17.4266			1.01807			0.509037	−	0.860744i	$-0.330001\pi$
$293$	17.4266			1.01807			0.509037	+	0.860744i	$0.330001\pi$
$294$	5.50663	−	16.5588i	0.321153	−	0.965727i
$295$	−4.69858			−0.273562
$296$	24.4758	+	42.3934i	1.42263	+	2.46406i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	0.957434	−	1.65832i	0.0554627	−	0.0960642i
$299$	−18.9970	−	32.9038i	−1.09863	−	1.90288i
$300$	17.8024			1.02782
$301$	−6.92924	+	4.99802i	−0.399395	+	0.288081i
$302$	34.9889			2.01338
$303$	−4.94711	−	8.56865i	−0.284204	−	0.492256i
$304$	−7.01517	+	12.1506i	−0.402347	+	0.696886i
$305$	−4.00103	+	6.92999i	−0.229098	+	0.396810i
$306$	−3.10730	−	5.38200i	−0.177633	−	0.307669i
$307$	−0.804963			−0.0459416			−0.0229708	−	0.999736i	$-0.507312\pi$
$307$	−0.804963			−0.0459416			−0.0229708	+	0.999736i	$0.507312\pi$
$308$	10.1711	+	4.57049i	0.579551	+	0.260428i
$309$	−11.1842			−0.636249
$310$	1.33368	+	2.31000i	0.0757478	+	0.131199i
$311$	5.41250	−	9.37473i	0.306915	−	0.531592i	−0.670771	−	0.741665i	$-0.734037\pi$
$311$	5.41250	−	9.37473i	0.306915	−	0.531592i	0.977686	+	0.210072i	$0.0673700\pi$
$312$	−19.6635	+	34.0583i	−1.11323	+	1.92817i
$313$	−12.3657	−	21.4181i	−0.698953	−	1.21062i	−0.968830	−	0.247727i	$-0.920316\pi$
$313$	−12.3657	−	21.4181i	−0.698953	−	1.21062i	0.269877	−	0.962895i	$-0.413017\pi$
$314$	−14.0553			−0.793186
$315$	0.235643	+	2.31877i	0.0132770	+	0.130648i
$316$	−29.3292			−1.64990
$317$	6.14096	+	10.6365i	0.344911	+	0.597403i	0.985338	−	0.170616i	$-0.0545759\pi$
$317$	6.14096	+	10.6365i	0.344911	+	0.597403i	−0.640427	+	0.768019i	$0.721243\pi$
$318$	−11.1392	+	19.2937i	−0.624657	+	1.08194i
$319$	−0.386568	+	0.669555i	−0.0216436	+	0.0374879i
$320$	−2.22277	−	3.84995i	−0.124256	−	0.215219i
$321$	−7.26605			−0.405551
$322$	3.55670	+	34.9987i	0.198207	+	1.95040i
$323$	−6.55765			−0.364877
$324$	−2.10730	−	3.64995i	−0.117072	−	0.202775i
$325$	15.0446	−	26.0580i	0.834523	−	1.44544i
$326$	13.5859	−	23.5315i	0.752455	−	1.30329i
$327$	0.228037	+	0.394971i	0.0126105	+	0.0218420i
$328$	34.2073			1.88878
$329$	−23.5466	−	10.5809i	−1.29817	−	0.583345i
$330$	−2.19607			−0.120890
$331$	6.59937	+	11.4304i	0.362734	+	0.628274i	0.988410	−	0.151809i	$-0.0485100\pi$
$331$	6.59937	+	11.4304i	0.362734	+	0.628274i	−0.625676	+	0.780083i	$0.715177\pi$
$332$	2.53980	−	4.39907i	0.139390	−	0.241430i
$333$	−4.43337	+	7.67883i	−0.242947	+	0.420797i
$334$	11.4386	+	19.8122i	0.625891	+	1.08407i
$335$	−9.92839			−0.542446
$336$	11.4450	−	8.25522i	0.624376	−	0.450359i
$337$	0.468940			0.0255448			0.0127724	−	0.999918i	$-0.495934\pi$
$337$	0.468940			0.0255448			0.0127724	+	0.999918i	$0.495934\pi$
$338$	47.0453	+	81.4848i	2.55892	+	4.43219i
$339$	−7.17588	+	12.4290i	−0.389740	+	0.675050i
$340$	−4.62778	+	8.01556i	−0.250977	+	0.434705i
$341$	0.607302	+	1.05188i	0.0328872	+	0.0569624i
$342$	−6.55765			−0.354597
$343$	5.54082	+	17.6720i	0.299176	+	0.954198i
$344$	−17.8278			−0.961213
$345$	−2.34929	−	4.06909i	−0.126481	−	0.219072i
$346$	−3.13904	+	5.43698i	−0.168756	+	0.292294i
$347$	−1.74709	+	3.02604i	−0.0937885	+	0.162447i	−0.909102	−	0.416573i	$-0.863231\pi$
$347$	−1.74709	+	3.02604i	−0.0937885	+	0.162447i	0.815314	+	0.579019i	$0.196564\pi$
$348$	1.62923	+	2.82191i	0.0873359	+	0.151270i
$349$	−15.7180			−0.841365			−0.420683	−	0.907208i	$-0.638209\pi$
$349$	−15.7180			−0.841365			−0.420683	+	0.907208i	$0.638209\pi$
$350$	−22.5952	+	16.2978i	−1.20777	+	0.871155i
$351$	−7.12343			−0.380221
$352$	1.12738	+	1.95268i	0.0600896	+	0.104078i
$353$	−17.6121	+	30.5051i	−0.937398	+	1.62362i	−0.167096	+	0.985941i	$0.553439\pi$
$353$	−17.6121	+	30.5051i	−0.937398	+	1.62362i	−0.770301	+	0.637680i	$0.779894\pi$
$354$	−6.64819	+	11.5150i	−0.353347	+	0.612016i
$355$	−3.36057	−	5.82068i	−0.178361	−	0.308930i
$356$	26.5265			1.40590
$357$	6.01613	+	2.70341i	0.318407	+	0.143080i
$358$	−61.1543			−3.23211
$359$	−11.6095	−	20.1082i	−0.612725	−	1.06127i	−0.990779	−	0.135487i	$-0.956740\pi$
$359$	−11.6095	−	20.1082i	−0.612725	−	1.06127i	0.378054	−	0.925783i	$-0.376593\pi$
$360$	−2.43171	+	4.21185i	−0.128163	+	0.221984i
$361$	6.04019	−	10.4619i	0.317905	−	0.550627i
$362$	15.9779	+	27.6746i	0.839781	+	1.45454i
$363$	−1.00000			−0.0524864
$364$	−8.03082	−	79.0249i	−0.420929	−	4.14203i
$365$	11.2552			0.589127
$366$	11.3224	+	19.6110i	0.591832	+	1.02508i
$367$	−9.87536	+	17.1046i	−0.515490	+	0.892854i	0.484349	+	0.874875i	$0.339057\pi$
$367$	−9.87536	+	17.1046i	−0.515490	+	0.892854i	−0.999838	+	0.0179791i	$0.994277\pi$
$368$	−14.2241	+	24.6368i	−0.741480	+	1.28428i
$369$	3.09804	+	5.36595i	0.161277	+	0.279340i
$370$	19.4720			1.01230
$371$	−2.39052	−	23.5232i	−0.124110	−	1.22126i
$372$	5.11907			0.265412
$373$	12.4828	+	21.6208i	0.646335	+	1.11948i	0.983991	+	0.178215i	$0.0570324\pi$
$373$	12.4828	+	21.6208i	0.646335	+	1.11948i	−0.337657	+	0.941269i	$0.609634\pi$
$374$	−3.10730	+	5.38200i	−0.160675	+	0.278297i
$375$	4.06282	−	7.03701i	0.209803	−	0.363389i
$376$	−26.9334	−	46.6500i	−1.38898	−	2.40579i
$377$	5.50738			0.283644
$378$	6.01613	+	2.70341i	0.309436	+	0.139049i
$379$	−16.3261			−0.838613			−0.419307	−	0.907845i	$-0.637727\pi$
$379$	−16.3261			−0.838613			−0.419307	+	0.907845i	$0.637727\pi$
$380$	4.88323	+	8.45801i	0.250505	+	0.433887i
$381$	4.45989	−	7.72475i	0.228487	−	0.395751i
$382$	27.5199	−	47.6659i	1.40804	−	2.43880i
$383$	−6.05397	−	10.4858i	−0.309343	−	0.535798i	0.668876	−	0.743374i	$-0.266776\pi$
$383$	−6.05397	−	10.4858i	−0.309343	−	0.535798i	−0.978219	+	0.207576i	$0.933443\pi$
$384$	−17.0898			−0.872112
$385$	1.89029	−	1.36346i	0.0963382	−	0.0694882i
$386$	−45.9824			−2.34044
$387$	−1.61460	−	2.79658i	−0.0820750	−	0.142158i
$388$	−2.73659	+	4.73990i	−0.138929	+	0.240632i
$389$	9.09988	−	15.7615i	0.461382	−	0.799138i	−0.537648	−	0.843170i	$-0.680687\pi$
$389$	9.09988	−	15.7615i	0.461382	−	0.799138i	0.999030	+	0.0440317i	$0.0140203\pi$
$390$	7.82178	+	13.5477i	0.396071	+	0.686015i
$391$	−13.2964			−0.672427
$392$	−12.1950	+	36.6711i	−0.615941	+	1.85217i
$393$	−12.3871			−0.624848
$394$	−5.70511	−	9.88154i	−0.287419	−	0.497825i
$395$	−3.06516	+	5.30902i	−0.154225	+	0.267126i
$396$	−2.10730	+	3.64995i	−0.105896	+	0.183417i
$397$	0.0289729	+	0.0501825i	0.00145411	+	0.00251859i	0.866752	−	0.498740i	$-0.166204\pi$
$397$	0.0289729	+	0.0501825i	0.00145411	+	0.00251859i	−0.865297	+	0.501259i	$0.832870\pi$
$398$	5.46212			0.273791
$399$	5.64457	−	4.07139i	0.282582	−	0.203825i
$400$	−22.5293			−1.12646
$401$	8.44247	+	14.6228i	0.421597	+	0.730227i	0.996096	−	0.0882780i	$-0.0281364\pi$
$401$	8.44247	+	14.6228i	0.421597	+	0.730227i	−0.574499	+	0.818505i	$0.694803\pi$
$402$	−14.0481	+	24.3319i	−0.700653	+	1.21357i
$403$	4.32607	−	7.49298i	0.215497	−	0.373252i
$404$	20.8501	+	36.1134i	1.03733	+	1.79671i
$405$	−0.880926			−0.0437736
$406$	−4.65128	−	2.09011i	−0.230839	−	0.103730i
$407$	8.86675			0.439508
$408$	6.88144	+	11.9190i	0.340682	+	0.590079i
$409$	0.543181	−	0.940817i	0.0268586	−	0.0465204i	−0.852284	−	0.523080i	$-0.824783\pi$
$409$	0.543181	−	0.940817i	0.0268586	−	0.0465204i	0.879142	+	0.476559i	$0.158116\pi$
$410$	6.80350	−	11.7840i	0.336001	−	0.581971i
$411$	11.0628	+	19.1614i	0.545689	+	0.945160i
$412$	47.1371			2.32228
$413$	−1.42673	−	14.0393i	−0.0702047	−	0.690828i
$414$	−13.2964			−0.653482
$415$	−0.530863	−	0.919482i	−0.0260590	−	0.0451356i
$416$	8.03082	−	13.9098i	0.393743	−	0.681984i
$417$	1.31776	−	2.28243i	0.0645312	−	0.111771i
$418$	3.27882	+	5.67909i	0.160372	+	0.277773i
$419$	18.7222			0.914638			0.457319	−	0.889303i	$-0.348810\pi$
$419$	18.7222			0.914638			0.457319	+	0.889303i	$0.348810\pi$
$420$	−0.993140	−	9.77269i	−0.0484603	−	0.476859i
$421$	10.6579			0.519433			0.259716	−	0.965685i	$-0.416371\pi$
$421$	10.6579			0.519433			0.259716	+	0.965685i	$0.416371\pi$
$422$	−12.4277	−	21.5255i	−0.604973	−	1.04784i
$423$	4.87852	−	8.44984i	0.237202	−	0.410845i
$424$	24.6690	−	42.7279i	1.19803	−	2.07505i
$425$	−5.26499	−	9.11923i	−0.255389	−	0.442348i
$426$	−19.0200			−0.921522
$427$	−21.9216	−	9.85073i	−1.06086	−	0.476710i
$428$	30.6235			1.48024
$429$	3.56171	+	6.16907i	0.171961	+	0.297846i
$430$	−3.54579	+	6.14148i	−0.170993	+	0.296168i
$431$	−9.87449	+	17.1031i	−0.475638	+	0.823828i	−0.999611	−	0.0279064i	$-0.991116\pi$
$431$	−9.87449	+	17.1031i	−0.475638	+	0.823828i	0.523973	+	0.851735i	$0.324449\pi$
$432$	2.66684	+	4.61910i	0.128308	+	0.222237i
$433$	−34.6826			−1.66674			−0.833370	−	0.552715i	$-0.813592\pi$
$433$	−34.6826			−1.66674			−0.833370	+	0.552715i	$0.813592\pi$
$434$	−6.49727	+	4.68644i	−0.311879	+	0.224956i
$435$	0.681076			0.0326551
$436$	−0.961085	−	1.66465i	−0.0460276	−	0.0797221i
$437$	−7.01517	+	12.1506i	−0.335581	+	0.581243i
$438$	15.9255	−	27.5837i	0.760948	−	1.31800i
$439$	2.79516	+	4.84137i	0.133406	+	0.231066i	0.924987	−	0.379998i	$-0.124075\pi$
$439$	2.79516	+	4.84137i	0.133406	+	0.231066i	−0.791581	+	0.611064i	$0.790742\pi$
$440$	4.86343			0.231855
$441$	−6.85689	+	1.40819i	−0.326519	+	0.0670568i
$442$	44.2693			2.10568
$443$	−5.45327	−	9.44534i	−0.259093	−	0.448762i	0.706907	−	0.707307i	$-0.250090\pi$
$443$	−5.45327	−	9.44534i	−0.259093	−	0.448762i	−0.965999	+	0.258545i	$0.916757\pi$
$444$	18.6849	−	32.3632i	0.886747	−	1.53589i
$445$	2.77225	−	4.80168i	0.131417	−	0.227621i
$446$	−18.9479	−	32.8188i	−0.897211	−	1.55401i
$447$	−0.768125			−0.0363311
$448$	10.8286	−	7.81063i	0.511605	−	0.369018i
$449$	9.97164			0.470591			0.235295	−	0.971924i	$-0.424394\pi$
$449$	9.97164			0.470591			0.235295	+	0.971924i	$0.424394\pi$
$450$	−5.26499	−	9.11923i	−0.248194	−	0.429885i
$451$	3.09804	−	5.36595i	0.145881	−	0.252673i
$452$	30.2435	−	52.3832i	1.42253	−	2.46390i
$453$	−7.01767	−	12.1550i	−0.329719	−	0.571090i
$454$	27.5869			1.29472
$455$	−15.1439	−	6.80510i	−0.709959	−	0.319028i
$456$	14.5226			0.680083
$457$	2.88402	+	4.99526i	0.134909	+	0.233669i	0.925563	−	0.378595i	$-0.123593\pi$
$457$	2.88402	+	4.99526i	0.134909	+	0.233669i	−0.790654	+	0.612263i	$0.790259\pi$
$458$	−3.57206	+	6.18698i	−0.166911	+	0.289099i
$459$	−1.24646	+	2.15892i	−0.0581796	+	0.100770i
$460$	9.90132	+	17.1496i	0.461651	+	0.799604i
$461$	−25.9921			−1.21057			−0.605286	−	0.796008i	$-0.706941\pi$
$461$	−25.9921			−1.21057			−0.605286	+	0.796008i	$0.706941\pi$
$462$	−0.666839	−	6.56183i	−0.0310241	−	0.305284i
$463$	6.09937			0.283462			0.141731	−	0.989905i	$-0.454733\pi$
$463$	6.09937			0.283462			0.141731	+	0.989905i	$0.454733\pi$
$464$	−2.06183	−	3.57119i	−0.0957180	−	0.165788i
$465$	0.534988	−	0.926627i	0.0248095	−	0.0429713i
$466$	−18.2043	+	31.5307i	−0.843296	+	1.46063i
$467$	11.9270	+	20.6582i	0.551915	+	0.955945i	0.998136	+	0.0610225i	$0.0194362\pi$
$467$	11.9270	+	20.6582i	0.551915	+	0.955945i	−0.446221	+	0.894923i	$0.647231\pi$
$468$	30.0224			1.38779
$469$	−3.01477	−	29.6659i	−0.139209	−	1.36984i
$470$	−21.4271			−0.988360
$471$	2.81905	+	4.88274i	0.129895	+	0.224985i
$472$	14.7231	−	25.5012i	0.677686	−	1.17379i
$473$	−1.61460	+	2.79658i	−0.0742396	+	0.128587i
$474$	8.67403	+	15.0239i	0.398411	+	0.690069i
$475$	−11.1112			−0.509818
$476$	−25.3556	−	11.3938i	−1.16217	−	0.522235i
$477$	8.93672			0.409184
$478$	23.0345	+	39.8969i	1.05357	+	1.82484i
$479$	4.63445	−	8.02710i	0.211753	−	0.366767i	−0.740510	−	0.672045i	$-0.765416\pi$
$479$	4.63445	−	8.02710i	0.211753	−	0.366767i	0.952263	+	0.305278i	$0.0987494\pi$
$480$	0.993140	−	1.72017i	0.0453304	−	0.0785146i
$481$	−31.5808	−	54.6996i	−1.43996	−	2.49409i
$482$	−64.6743			−2.94583
$483$	11.4450	−	8.25522i	0.520766	−	0.375626i
$484$	4.21460			0.191573
$485$	0.571994	+	0.990723i	0.0259729	+	0.0449864i
$486$	−1.24646	+	2.15892i	−0.0565404	+	0.0979308i
$487$	−19.2061	+	33.2660i	−0.870313	+	1.50743i	−0.00864048	+	0.999963i	$0.502750\pi$
$487$	−19.2061	+	33.2660i	−0.870313	+	1.50743i	−0.861673	+	0.507464i	$0.830583\pi$
$488$	−25.0747	−	43.4306i	−1.13508	−	1.96601i
$489$	−10.8997			−0.492900
$490$	10.2073	+	11.4946i	0.461118	+	0.519271i
$491$	−12.1820			−0.549767			−0.274884	−	0.961477i	$-0.588639\pi$
$491$	−12.1820			−0.549767			−0.274884	+	0.961477i	$0.588639\pi$
$492$	−13.0570	−	22.6154i	−0.588655	−	1.01958i
$493$	0.963679	−	1.66914i	0.0434019	−	0.0751744i
$494$	23.3565	−	40.4546i	1.05086	−	1.82014i
$495$	0.440463	+	0.762904i	0.0197973	+	0.0342900i
$496$	−6.47831			−0.290884
$497$	16.3717	−	11.8088i	0.734370	−	0.529697i
$498$	−3.00455			−0.134637
$499$	−3.60730	−	6.24803i	−0.161485	−	0.279700i	0.773916	−	0.633288i	$-0.218295\pi$
$499$	−3.60730	−	6.24803i	−0.161485	−	0.279700i	−0.935401	+	0.353587i	$0.884962\pi$
$500$	−17.1232	+	29.6582i	−0.765771	+	1.32635i
$501$	4.58844	−	7.94741i	0.204996	−	0.355064i
$502$	32.9477	+	57.0671i	1.47053	+	2.54703i
$503$	3.49548			0.155856			0.0779280	−	0.996959i	$-0.475170\pi$
$503$	3.49548			0.155856			0.0779280	+	0.996959i	$0.475170\pi$
$504$	−13.3233	−	5.98699i	−0.593469	−	0.266682i
$505$	8.71608			0.387860
$506$	6.64819	+	11.5150i	0.295548	+	0.511904i
$507$	18.8716	−	32.6866i	0.838118	−	1.45166i
$508$	−18.7967	+	32.5568i	−0.833967	+	1.44447i
$509$	−17.1363	−	29.6809i	−0.759552	−	1.31558i	−0.943080	−	0.332567i	$-0.892085\pi$
$509$	−17.1363	−	29.6809i	−0.759552	−	1.31558i	0.183528	−	0.983014i	$-0.441248\pi$
$510$	5.47461			0.242420
$511$	3.41767	+	33.6305i	0.151189	+	1.48773i
$512$	46.8663			2.07122
$513$	1.31526	+	2.27810i	0.0580701	+	0.100580i
$514$	−5.78230	+	10.0152i	−0.255046	+	0.441753i
$515$	4.92624	−	8.53250i	0.217076	−	0.375987i
$516$	6.80492	+	11.7865i	0.299570	+	0.518870i
$517$	−9.75704			−0.429114
$518$	5.91269	+	58.1820i	0.259789	+	2.55637i
$519$	2.51837			0.110544
$520$	−17.3221	−	30.0028i	−0.759626	−	1.31571i
$521$	3.00393	−	5.20296i	0.131604	−	0.227946i	−0.792691	−	0.609624i	$-0.791320\pi$
$521$	3.00393	−	5.20296i	0.131604	−	0.227946i	0.924295	+	0.381678i	$0.124654\pi$
$522$	0.963679	−	1.66914i	0.0421791	−	0.0730563i
$523$	−1.49366	−	2.58709i	−0.0653130	−	0.113125i	0.831520	−	0.555495i	$-0.187471\pi$
$523$	−1.49366	−	2.58709i	−0.0653130	−	0.113125i	−0.896833	+	0.442370i	$0.854138\pi$
$524$	52.2068			2.28067
$525$	10.1937	+	4.58064i	0.444889	+	0.199916i
$526$	−48.9273			−2.13333
$527$	−1.51395	−	2.62224i	−0.0659487	−	0.114226i
$528$	2.66684	−	4.61910i	0.116059	−	0.201021i
$529$	−2.72406	+	4.71821i	−0.118437	+	0.205139i
$530$	−9.81284	−	16.9963i	−0.426242	−	0.738273i
$531$	5.33368			0.231462
$532$	−23.7896	+	17.1593i	−1.03141	+	0.743951i
$533$	−44.1373			−1.91180
$534$	−7.84512	−	13.5881i	−0.339492	−	0.588017i
$535$	3.20043	−	5.54330i	0.138366	−	0.239658i
$536$	31.1109	−	53.8856i	1.34378	−	2.32750i
$537$	12.2656	+	21.2447i	0.529302	+	0.916778i
$538$	56.2483			2.42504
$539$	4.64798	+	5.23415i	0.200203	+	0.225451i
$540$	3.71275			0.159772
$541$	0.0186732	+	0.0323429i	0.000802822	+	0.00139053i	0.866427	−	0.499305i	$-0.166411\pi$
$541$	0.0186732	+	0.0323429i	0.000802822	+	0.00139053i	−0.865624	+	0.500695i	$0.833078\pi$
$542$	−21.3811	+	37.0332i	−0.918398	+	1.59071i
$543$	6.40934	−	11.1013i	0.275051	−	0.476403i
$544$	−2.81046	−	4.86786i	−0.120498	−	0.208708i
$545$	−0.401767			−0.0172098
$546$	−38.1053	+	27.4851i	−1.63076	+	1.17625i
$547$	−16.1882			−0.692156			−0.346078	−	0.938206i	$-0.612487\pi$
$547$	−16.1882			−0.692156			−0.346078	+	0.938206i	$0.612487\pi$
$548$	−46.6254	−	80.7576i	−1.99174	−	3.44979i
$549$	4.54185	−	7.86671i	0.193841	−	0.335743i
$550$	−5.26499	+	9.11923i	−0.224500	+	0.388845i
$551$	−1.01687	−	1.76128i	−0.0433203	−	0.0750329i
$552$	29.4462			1.25331
$553$	−16.7940	−	7.54657i	−0.714154	−	0.320913i
$554$	65.1885			2.76959
$555$	−3.90547	−	6.76448i	−0.165778	−	0.287136i
$556$	−5.55385	+	9.61956i	−0.235536	+	0.407960i
$557$	−16.7079	+	28.9390i	−0.707937	+	1.22618i	0.257684	+	0.966229i	$0.417041\pi$
$557$	−16.7079	+	28.9390i	−0.707937	+	1.22618i	−0.965621	+	0.259954i	$0.916293\pi$
$558$	−1.51395	−	2.62224i	−0.0640906	−	0.111008i
$559$	23.0030			0.972925
$560$	1.25684	+	12.3676i	0.0531112	+	0.522625i
$561$	2.49291			0.105251
$562$	10.9685	+	18.9979i	0.462677	+	0.801379i
$563$	−0.142122	+	0.246163i	−0.00598974	+	0.0103745i	−0.869005	−	0.494804i	$-0.835240\pi$
$563$	−0.142122	+	0.246163i	−0.00598974	+	0.0103745i	0.863015	+	0.505178i	$0.168573\pi$
$564$	−20.5610	+	35.6127i	−0.865775	+	1.49957i
$565$	−6.32142	−	10.9490i	−0.265944	−	0.460629i
$566$	−34.2772			−1.44078
$567$	−0.267494	−	2.63219i	−0.0112337	−	0.110542i
$568$	42.1217			1.76739
$569$	7.73745	+	13.4017i	0.324371	+	0.561827i	0.981385	−	0.192052i	$-0.0615142\pi$
$569$	7.73745	+	13.4017i	0.324371	+	0.561827i	−0.657014	+	0.753878i	$0.728181\pi$
$570$	2.88840	−	5.00286i	0.120982	−	0.209547i
$571$	5.36670	−	9.29540i	0.224589	−	0.389000i	−0.731607	−	0.681727i	$-0.761229\pi$
$571$	5.36670	−	9.29540i	0.224589	−	0.389000i	0.956196	+	0.292727i	$0.0945626\pi$
$572$	−15.0112	−	26.0002i	−0.627650	−	1.08712i
$573$	−22.0785			−0.922345
$574$	37.2763	+	16.7505i	1.55588	+	0.699154i
$575$	−22.5293			−0.939536
$576$	2.52322	+	4.37034i	0.105134	+	0.182097i
$577$	−5.99535	+	10.3842i	−0.249589	+	0.432302i	−0.963412	−	0.268025i	$-0.913629\pi$
$577$	−5.99535	+	10.3842i	−0.249589	+	0.432302i	0.713822	+	0.700327i	$0.246962\pi$
$578$	−13.4435	+	23.2849i	−0.559177	+	0.968522i
$579$	9.22264	+	15.9741i	0.383280	+	0.663860i
$580$	−2.87046			−0.119190
$581$	2.58620	−	1.86541i	0.107294	−	0.0773904i
$582$	3.23734			0.134192
$583$	−4.46836	−	7.73943i	−0.185061	−	0.320534i
$584$	−35.2686	+	61.0870i	−1.45943	+	2.52780i
$585$	3.13761	−	5.43450i	0.129724	−	0.224689i
$586$	21.7215	+	37.6228i	0.897308	+	1.55418i
$587$	34.2223			1.41251			0.706254	−	0.707959i	$-0.250384\pi$
$587$	34.2223			1.41251			0.706254	+	0.707959i	$0.250384\pi$
$588$	28.8991	−	5.93497i	1.19178	−	0.244754i
$589$	−3.19504			−0.131649
$590$	−5.85657	−	10.1439i	−0.241111	−	0.417616i
$591$	−2.28853	+	3.96386i	−0.0941377	+	0.163051i
$592$	−23.6462	+	40.9564i	−0.971852	+	1.68330i
$593$	14.7502	+	25.5480i	0.605716	+	1.04913i	0.991938	+	0.126725i	$0.0404467\pi$
$593$	14.7502	+	25.5480i	0.605716	+	1.04913i	−0.386222	+	0.922406i	$0.626220\pi$
$594$	2.49291			0.102285
$595$	−4.71233	+	3.39898i	−0.193187	+	0.139344i
$596$	3.23734			0.132607
$597$	−1.09553	−	1.89751i	−0.0448371	−	0.0776601i
$598$	47.3579	−	82.0263i	1.93661	−	3.35431i
$599$	10.5531	−	18.2784i	0.431186	−	0.746837i	−0.565789	−	0.824550i	$-0.691428\pi$
$599$	10.5531	−	18.2784i	0.431186	−	0.746837i	0.996976	+	0.0777130i	$0.0247618\pi$
$600$	11.6599	+	20.1955i	0.476012	+	0.824477i
$601$	20.4406			0.833789			0.416894	−	0.908955i	$-0.363118\pi$
$601$	20.4406			0.833789			0.416894	+	0.908955i	$0.363118\pi$
$602$	−19.4273	−	8.72989i	−0.791799	−	0.355804i
$603$	11.2704			0.458966
$604$	29.5767	+	51.2284i	1.20346	+	2.08445i
$605$	0.440463	−	0.762904i	0.0179074	−	0.0310165i
$606$	12.3327	−	21.3609i	0.500982	−	0.867726i
$607$	21.2816	+	36.8609i	0.863795	+	1.49614i	0.868239	+	0.496147i	$0.165252\pi$
$607$	21.2816	+	36.8609i	0.863795	+	1.49614i	−0.00444371	+	0.999990i	$0.501414\pi$
$608$	−5.93119			−0.240542
$609$	0.206809	+	2.03504i	0.00838033	+	0.0824641i
$610$	−19.9484			−0.807689
$611$	34.7518	+	60.1919i	1.40591	+	2.43510i
$612$	5.25332	−	9.09901i	0.212353	−	0.367806i
$613$	0.348283	−	0.603244i	0.0140670	−	0.0243648i	−0.858906	−	0.512133i	$-0.828856\pi$
$613$	0.348283	−	0.603244i	0.0140670	−	0.0243648i	0.872973	+	0.487768i	$0.162189\pi$
$614$	−1.00335	−	1.73785i	−0.0404919	−	0.0701341i
$615$	−5.45828			−0.220099
$616$	1.47678	+	14.5318i	0.0595013	+	0.585505i
$617$	−13.6494			−0.549504			−0.274752	−	0.961515i	$-0.588596\pi$
$617$	−13.6494			−0.549504			−0.274752	+	0.961515i	$0.588596\pi$
$618$	−13.9407	−	24.1459i	−0.560775	−	0.971291i
$619$	17.6396	−	30.5526i	0.708994	−	1.22801i	−0.256237	−	0.966614i	$-0.582483\pi$
$619$	17.6396	−	30.5526i	0.708994	−	1.22801i	0.965231	−	0.261399i	$-0.0841838\pi$
$620$	−2.25476	+	3.90536i	−0.0905535	+	0.156843i
$621$	2.66684	+	4.61910i	0.107017	+	0.185358i
$622$	26.9858			1.08203
$623$	15.1891	+	6.82541i	0.608540	+	0.273454i
$624$	−37.9941			−1.52098
$625$	−6.98088	−	12.0912i	−0.279235	−	0.483650i
$626$	30.8267	−	53.3934i	1.23208	−	2.13403i
$627$	1.31526	−	2.27810i	0.0525264	−	0.0909784i
$628$	−11.8812	−	20.5788i	−0.474111	−	0.821184i
$629$	−22.1040			−0.881345
$630$	−4.71233	+	3.39898i	−0.187744	+	0.135418i
$631$	16.4853			0.656271			0.328136	−	0.944631i	$-0.393580\pi$
$631$	16.4853			0.656271			0.328136	+	0.944631i	$0.393580\pi$
$632$	−19.2095	−	33.2719i	−0.764114	−	1.32348i
$633$	−4.98523	+	8.63468i	−0.198145	+	0.343198i
$634$	−15.3089	+	26.5157i	−0.607992	+	1.05307i
$635$	3.92883	+	6.80493i	0.155911	+	0.270046i
$636$	−37.6648			−1.49350
$637$	15.7351	−	47.3162i	0.623446	−	1.87474i
$638$	−1.92736			−0.0763049
$639$	3.81482	+	6.60746i	0.150912	+	0.261387i
$640$	7.52744	−	13.0379i	0.297548	−	0.515369i
$641$	−3.23434	+	5.60204i	−0.127749	+	0.221267i	−0.922804	−	0.385270i	$-0.874108\pi$
$641$	−3.23434	+	5.60204i	−0.127749	+	0.221267i	0.795055	+	0.606537i	$0.207442\pi$
$642$	−9.05680	−	15.6868i	−0.357443	−	0.619110i
$643$	−18.2913			−0.721338			−0.360669	−	0.932694i	$-0.617452\pi$
$643$	−18.2913			−0.721338			−0.360669	+	0.932694i	$0.617452\pi$
$644$	−48.2362	+	34.7925i	−1.90077	+	1.37102i
$645$	2.84469			0.112010
$646$	−8.17381	−	14.1575i	−0.321594	−	0.557018i
$647$	9.00103	−	15.5902i	0.353867	−	0.612916i	−0.633056	−	0.774106i	$-0.718200\pi$
$647$	9.00103	−	15.5902i	0.353867	−	0.612916i	0.986923	+	0.161190i	$0.0515332\pi$
$648$	2.76040	−	4.78116i	0.108439	−	0.187822i
$649$	−2.66684	−	4.61910i	−0.104683	−	0.181316i
$650$	75.0095			2.94212
$651$	2.93120	+	1.31717i	0.114883	+	0.0516238i
$652$	45.9377			1.79906
$653$	2.50442	+	4.33779i	0.0980057	+	0.169751i	0.910859	−	0.412718i	$-0.135420\pi$
$653$	2.50442	+	4.33779i	0.0980057	+	0.169751i	−0.812853	+	0.582468i	$0.802087\pi$
$654$	−0.568475	+	0.984628i	−0.0222291	+	0.0385020i
$655$	5.45607	−	9.45020i	0.213186	−	0.369250i
$656$	16.5239	+	28.6203i	0.645151	+	1.11743i
$657$	−12.7766			−0.498463
$658$	−6.50637	−	64.0240i	−0.253645	−	2.49591i
$659$	43.2762			1.68580			0.842901	−	0.538068i	$-0.180846\pi$
$659$	43.2762			1.68580			0.842901	+	0.538068i	$0.180846\pi$
$660$	−1.85638	−	3.21534i	−0.0722594	−	0.125157i
$661$	−9.52074	+	16.4904i	−0.370314	+	0.641402i	−0.989614	−	0.143752i	$-0.954083\pi$
$661$	−9.52074	+	16.4904i	−0.370314	+	0.641402i	0.619300	+	0.785155i	$0.287417\pi$
$662$	−16.4516	+	28.4951i	−0.639411	+	1.10749i
$663$	−8.87904	−	15.3789i	−0.344833	−	0.597269i
$664$	6.65389			0.258221
$665$	0.619862	+	6.09956i	0.0240372	+	0.236531i
$666$	−22.1040			−0.856513
$667$	−2.06183	−	3.57119i	−0.0798343	−	0.138277i
$668$	−19.3385	+	33.4952i	−0.748227	+	1.29597i
$669$	−7.60073	+	13.1648i	−0.293861	+	0.508982i
$670$	−12.3753	−	21.4346i	−0.478099	−	0.828092i
$671$	−9.08370			−0.350672
$672$	5.44141	+	2.44516i	0.209907	+	0.0943240i
$673$	9.68181			0.373206			0.186603	−	0.982435i	$-0.440252\pi$
$673$	9.68181			0.373206			0.186603	+	0.982435i	$0.440252\pi$
$674$	0.584513	+	1.01241i	0.0225146	+	0.0389964i
$675$	−2.11198	+	3.65806i	−0.0812903	+	0.140799i
$676$	−79.5364	+	137.761i	−3.05909	+	5.29850i
$677$	−11.7498	−	20.3512i	−0.451580	−	0.782160i	0.546904	−	0.837195i	$-0.315806\pi$
$677$	−11.7498	−	20.3512i	−0.451580	−	0.782160i	−0.998484	+	0.0550354i	$0.982473\pi$
$678$	−35.7776			−1.37403
$679$	−2.78658	+	2.00994i	−0.106939	+	0.0771346i
$680$	−12.1241			−0.464937
$681$	−5.53307	−	9.58356i	−0.212028	−	0.367243i
$682$	−1.51395	+	2.62224i	−0.0579721	+	0.100411i
$683$	13.2113	−	22.8827i	0.505517	−	0.875581i	−0.494463	−	0.869199i	$-0.664635\pi$
$683$	13.2113	−	22.8827i	0.505517	−	0.875581i	0.999980	−	0.00638201i	$-0.00203147\pi$
$684$	−5.54330	−	9.60127i	−0.211953	−	0.367114i
$685$	−19.4911			−0.744715
$686$	−31.2461	+	33.9896i	−1.19298	+	1.29773i
$687$	2.86577			0.109336
$688$	−8.61178	−	14.9160i	−0.328321	−	0.568669i
$689$	−31.8301	+	55.1313i	−1.21263	+	2.10033i
$690$	5.85657	−	10.1439i	0.222956	−	0.386170i
$691$	−14.5176	−	25.1451i	−0.552274	−	0.956567i	−0.998110	−	0.0614519i	$-0.980427\pi$
$691$	−14.5176	−	25.1451i	−0.552274	−	0.956567i	0.445836	−	0.895115i	$-0.352906\pi$
$692$	−10.6139			−0.403482
$693$	−2.14580	+	1.54775i	−0.0815122	+	0.0587943i
$694$	−8.71066			−0.330652
$695$	1.16085	+	2.01066i	0.0440337	+	0.0762685i
$696$	−2.13417	+	3.69649i	−0.0808954	+	0.140115i
$697$	−7.72312	+	13.3768i	−0.292534	+	0.506684i
$698$	−19.5918	−	33.9340i	−0.741560	−	1.28442i
$699$	14.6048			0.552405
$700$	−42.9623	−	19.3056i	−1.62382	−	0.729683i
$701$	14.9866			0.566037			0.283019	−	0.959114i	$-0.408664\pi$
$701$	14.9866			0.566037			0.283019	+	0.959114i	$0.408664\pi$
$702$	−8.87904	−	15.3789i	−0.335118	−	0.580441i
$703$	−11.6621	+	20.1993i	−0.439843	+	0.761831i
$704$	2.52322	−	4.37034i	0.0950973	−	0.164713i
$705$	4.29762	+	7.44369i	0.161858	+	0.280346i
$706$	−87.8108			−3.30480
$707$	2.64665	+	26.0435i	0.0995373	+	0.979467i
$708$	−22.4793			−0.844825
$709$	2.14746	+	3.71951i	0.0806496	+	0.139689i	0.903529	−	0.428527i	$-0.140967\pi$
$709$	2.14746	+	3.71951i	0.0806496	+	0.139689i	−0.822880	+	0.568216i	$0.807634\pi$
$710$	8.37760	−	14.5104i	0.314406	−	0.544567i
$711$	3.47948	−	6.02663i	0.130491	−	0.226016i
$712$	17.3738	+	30.0924i	0.651112	+	1.12776i
$713$	−6.47831			−0.242614
$714$	1.66237	+	16.3580i	0.0622126	+	0.612184i
$715$	−6.27521			−0.234680
$716$	−51.6949	−	89.5381i	−1.93193	−	3.34620i
$717$	9.24000	−	16.0041i	0.345074	−	0.597686i
$718$	28.9414	−	50.1280i	1.08008	−	1.87076i
$719$	−13.0236	−	22.5575i	−0.485697	−	0.841252i	0.514168	−	0.857690i	$-0.328101\pi$
$719$	−13.0236	−	22.5575i	−0.485697	−	0.841252i	−0.999865	+	0.0164373i	$0.994768\pi$
$720$	−4.69858			−0.175106
$721$	26.9909	+	12.1286i	1.00519	+	0.451694i
$722$	30.1153			1.12078
$723$	12.9716	+	22.4675i	0.482421	+	0.835577i
$724$	−27.0128	+	46.7876i	−1.00392	+	1.73885i
$725$	1.63285	−	2.82818i	0.0606426	−	0.105036i
$726$	−1.24646	−	2.15892i	−0.0462603	−	0.0801252i
$727$	39.2855			1.45702			0.728510	−	0.685035i	$-0.240213\pi$
$727$	39.2855			1.45702			0.728510	+	0.685035i	$0.240213\pi$
$728$	84.3881	−	60.8687i	3.12763	−	2.25594i
$729$	1.00000			0.0370370
$730$	14.0292	+	24.2992i	0.519243	+	0.899355i
$731$	4.02507	−	6.97162i	0.148872	−	0.257855i
$732$	−19.1421	+	33.1551i	−0.707512	+	1.22545i
$733$	−4.27905	−	7.41154i	−0.158050	−	0.273751i	0.776115	−	0.630591i	$-0.217188\pi$
$733$	−4.27905	−	7.41154i	−0.158050	−	0.273751i	−0.934166	+	0.356840i	$0.883854\pi$
$734$	−49.2368			−1.81736
$735$	1.94589	−	5.85141i	0.0717753	−	0.215833i
$736$	−12.0262			−0.443291
$737$	−5.63520	−	9.76045i	−0.207575	−	0.359531i
$738$	−7.72312	+	13.3768i	−0.284292	+	0.492408i
$739$	6.11309	−	10.5882i	0.224874	−	0.389492i	−0.731408	−	0.681940i	$-0.761136\pi$
$739$	6.11309	−	10.5882i	0.224874	−	0.389492i	0.956282	+	0.292448i	$0.0944698\pi$
$740$	16.4600	+	28.5096i	0.605083	+	1.04803i
$741$	−18.7383			−0.688369
$742$	47.8051	−	34.4816i	1.75498	−	1.26586i
$743$	−24.0257			−0.881416			−0.440708	−	0.897650i	$-0.645273\pi$
$743$	−24.0257			−0.881416			−0.440708	+	0.897650i	$0.645273\pi$
$744$	3.35280	+	5.80722i	0.122920	+	0.212903i
$745$	0.338331	−	0.586006i	0.0123955	−	0.0214696i
$746$	−31.1185	+	53.8988i	−1.13933	+	1.97338i
$747$	0.602619	+	1.04377i	0.0220487	+	0.0381894i
$748$	−10.5066			−0.384160
$749$	17.5351	+	7.87960i	0.640719	+	0.287914i
$750$	20.2565			0.739662
$751$	−3.75659	−	6.50661i	−0.137080	−	0.237429i	0.789310	−	0.613995i	$-0.210438\pi$
$751$	−3.75659	−	6.50661i	−0.137080	−	0.237429i	−0.926390	+	0.376565i	$0.877105\pi$
$752$	26.0205	−	45.0687i	0.948868	−	1.64349i
$753$	13.2166	−	22.8917i	0.481638	−	0.834221i
$754$	6.86470	+	11.8900i	0.249998	+	0.433009i
$755$	12.3641			0.449976
$756$	1.12738	+	11.0937i	0.0410025	+	0.403472i
$757$	8.97814			0.326316			0.163158	−	0.986600i	$-0.447832\pi$
$757$	8.97814			0.326316			0.163158	+	0.986600i	$0.447832\pi$
$758$	−20.3497	−	35.2467i	−0.739135	−	1.28022i
$759$	2.66684	−	4.61910i	0.0968001	−	0.167663i
$760$	−6.39666	+	11.0793i	−0.232031	+	0.401890i
$761$	−1.39666	−	2.41908i	−0.0506287	−	0.0876915i	0.839600	−	0.543205i	$-0.182789\pi$
$761$	−1.39666	−	2.41908i	−0.0506287	−	0.0876915i	−0.890229	+	0.455513i	$0.849456\pi$
$762$	22.2362			0.805532
$763$	−0.121997	−	1.20047i	−0.00441659	−	0.0434601i
$764$	93.0523			3.36652
$765$	−1.09804	−	1.90185i	−0.0396995	−	0.0687616i
$766$	15.0920	−	26.1401i	0.545296	−	0.944481i
$767$	−18.9970	+	32.9038i	−0.685943	+	1.18809i
$768$	−16.2553	−	28.1550i	−0.586562	−	1.01595i
$769$	−5.83905			−0.210561			−0.105281	−	0.994443i	$-0.533574\pi$
$769$	−5.83905			−0.210561			−0.105281	+	0.994443i	$0.533574\pi$
$770$	5.29976	+	2.38151i	0.190990	+	0.0858236i
$771$	4.63900			0.167069
$772$	−38.8698	−	67.3244i	−1.39895	−	2.42306i
$773$	−2.56578	+	4.44406i	−0.0922848	+	0.159842i	−0.908472	−	0.417945i	$-0.862750\pi$
$773$	−2.56578	+	4.44406i	−0.0922848	+	0.159842i	0.816187	+	0.577787i	$0.196084\pi$
$774$	4.02507	−	6.97162i	0.144678	−	0.250590i
$775$	−2.56522	−	4.44310i	−0.0921456	−	0.159601i
$776$	−7.16944			−0.257368
$777$	19.0263	−	13.7235i	0.682564	−	0.492329i
$778$	45.3704			1.62661
$779$	8.14944	+	14.1152i	0.291984	+	0.505731i
$780$	−13.2238	+	22.9042i	−0.473487	+	0.820104i
$781$	3.81482	−	6.60746i	0.136505	−	0.236433i
$782$	−16.5733	−	28.7059i	−0.592662	−	1.02652i
$783$	−0.773136			−0.0276296
$784$	−36.5725	+	7.51085i	−1.30616	+	0.268245i
$785$	−4.96675			−0.177271
$786$	−15.4400	−	26.7429i	−0.550727	−	0.953887i
$787$	−5.43218	+	9.40882i	−0.193636	+	0.335388i	−0.946453	−	0.322843i	$-0.895362\pi$
$787$	−5.43218	+	9.40882i	−0.193636	+	0.335388i	0.752816	+	0.658231i	$0.228695\pi$
$788$	9.64526	−	16.7061i	0.343598	−	0.595129i
$789$	9.81330	+	16.9971i	0.349363	+	0.605114i
$790$	−15.2824			−0.543722
$791$	30.7960	−	22.2130i	1.09498	−	0.789803i
$792$	−5.52081			−0.196173
$793$	32.3535	+	56.0380i	1.14891	+	1.98997i
$794$	−0.0722269	+	0.125101i	−0.00256324	+	0.00443965i
$795$	−3.93630	+	6.81787i	−0.139606	+	0.241805i
$796$	4.61722	+	7.99727i	0.163653	+	0.283456i
$797$	15.9000			0.563208			0.281604	−	0.959531i	$-0.409134\pi$
$797$	15.9000			0.563208			0.281604	+	0.959531i	$0.409134\pi$
$798$	15.8255	+	7.11138i	0.560218	+	0.251740i
$799$	24.3234			0.860501
$800$	−4.76202	−	8.24807i	−0.168363	−	0.291613i
$801$	−3.14697	+	5.45072i	−0.111193	+	0.192592i
$802$	−21.0463	+	36.4533i	−0.743172	+	1.28721i
$803$	6.38830	+	11.0649i	0.225438	+	0.390471i
$804$	−47.5003			−1.67521
$805$	1.25684	+	12.3676i	0.0442978	+	0.435899i
$806$	21.5690			0.759736
$807$	−11.2817	−	19.5404i	−0.397133	−	0.687855i
$808$	−27.3121	+	47.3059i	−0.960835	+	1.66421i
$809$	19.7011	−	34.1233i	0.692653	−	1.19971i	−0.278312	−	0.960491i	$-0.589775\pi$
$809$	19.7011	−	34.1233i	0.692653	−	1.19971i	0.970965	−	0.239220i	$-0.0768916\pi$
$810$	−1.09804	−	1.90185i	−0.0385810	−	0.0668243i
$811$	14.2370			0.499928			0.249964	−	0.968255i	$-0.419581\pi$
$811$	14.2370			0.499928			0.249964	+	0.968255i	$0.419581\pi$
$812$	−0.871619	−	8.57690i	−0.0305878	−	0.300990i
$813$	17.1535			0.601601
$814$	11.0520	+	19.1426i	0.387373	+	0.670949i
$815$	4.80090	−	8.31540i	0.168168	−	0.291276i
$816$	−6.64819	+	11.5150i	−0.232733	+	0.403106i
$817$	−4.24725	−	7.35645i	−0.148592	−	0.257370i
$818$	2.70820			0.0946901
$819$	17.1909	+	7.72493i	0.600700	+	0.269931i
$820$	23.0045			0.803352
$821$	15.6321	+	27.0757i	0.545565	+	0.944947i	0.998571	+	0.0534393i	$0.0170184\pi$
$821$	15.6321	+	27.0757i	0.545565	+	0.944947i	−0.453006	+	0.891508i	$0.649648\pi$
$822$	−27.5786	+	47.7676i	−0.961915	+	1.66609i
$823$	−17.3842	+	30.1103i	−0.605975	+	1.04958i	0.385921	+	0.922532i	$0.373884\pi$
$823$	−17.3842	+	30.1103i	−0.605975	+	1.04958i	−0.991897	+	0.127048i	$0.959450\pi$
$824$	30.8730	+	53.4736i	1.07551	+	1.86284i
$825$	4.22397			0.147060
$826$	28.5314	−	20.5795i	0.992734	−	0.716053i
$827$	8.62027			0.299756			0.149878	−	0.988704i	$-0.452112\pi$
$827$	8.62027			0.299756			0.149878	+	0.988704i	$0.452112\pi$
$828$	−11.2397	−	19.4677i	−0.390606	−	0.676549i
$829$	−2.27915	+	3.94761i	−0.0791582	+	0.137106i	−0.902887	−	0.429878i	$-0.858557\pi$
$829$	−2.27915	+	3.94761i	−0.0791582	+	0.137106i	0.823729	+	0.566984i	$0.191890\pi$
$830$	1.32339	−	2.29219i	0.0459357	−	0.0795629i
$831$	−13.0748	−	22.6462i	−0.453559	−	0.785587i
$832$	−35.9479			−1.24627
$833$	−11.5870	−	13.0483i	−0.401466	−	0.452096i
$834$	6.57014			0.227505
$835$	4.04208	+	7.00108i	0.139882	+	0.242282i
$836$	−5.54330	+	9.60127i	−0.191719	+	0.332067i
$837$	−0.607302	+	1.05188i	−0.0209914	+	0.0363582i
$838$	23.3364	+	40.4198i	0.806141	+	1.39628i
$839$	5.51585			0.190428			0.0952141	−	0.995457i	$-0.469646\pi$
$839$	5.51585			0.190428			0.0952141	+	0.995457i	$0.469646\pi$
$840$	10.4359	−	7.52739i	0.360074	−	0.259719i
$841$	−28.4023			−0.979388
$842$	13.2846	+	23.0095i	0.457816	+	0.792961i
$843$	4.39986	−	7.62078i	0.151539	−	0.262474i
$844$	21.0108	−	36.3918i	0.723221	−	1.25266i
$845$	16.6245	+	28.7945i	0.571900	+	0.990560i
$846$	24.3234			0.836257
$847$	2.41329	+	1.08444i	0.0829218	+	0.0372618i
$848$	47.6656			1.63684
$849$	6.87494	+	11.9077i	0.235947	+	0.408673i
$850$	13.1251	−	22.7334i	0.450189	−	0.779750i
$851$	−23.6462	+	40.9564i	−0.810581	+	1.40397i
$852$	−16.0779	−	27.8478i	−0.550821	−	0.954050i
$853$	41.9614			1.43673			0.718366	−	0.695666i	$-0.244890\pi$
$853$	41.9614			1.43673			0.718366	+	0.695666i	$0.244890\pi$
$854$	−6.05736	−	59.6056i	−0.207279	−	2.03966i
$855$	−2.31729			−0.0792497
$856$	20.0572	+	34.7401i	0.685542	+	1.18739i
$857$	−4.55675	+	7.89252i	−0.155656	+	0.269603i	−0.933298	−	0.359104i	$-0.883082\pi$
$857$	−4.55675	+	7.89252i	−0.155656	+	0.269603i	0.777642	+	0.628707i	$0.216416\pi$
$858$	−8.87904	+	15.3789i	−0.303125	+	0.525028i
$859$	−21.1496	−	36.6321i	−0.721614	−	1.24987i	−0.960353	−	0.278788i	$-0.910067\pi$
$859$	−21.1496	−	36.6321i	−0.721614	−	1.24987i	0.238739	−	0.971084i	$-0.423266\pi$
$860$	−11.9893			−0.408830
$861$	−1.65741	−	16.3093i	−0.0564845	−	0.555818i
$862$	−49.2325			−1.67686
$863$	6.88674	+	11.9282i	0.234427	+	0.406040i	0.959106	−	0.283047i	$-0.0913452\pi$
$863$	6.88674	+	11.9282i	0.234427	+	0.406040i	−0.724679	+	0.689087i	$0.758012\pi$
$864$	−1.12738	+	1.95268i	−0.0383543	+	0.0664316i
$865$	−1.10925	+	1.92128i	−0.0377156	+	0.0653254i
$866$	−43.2303	−	74.8772i	−1.46903	−	2.54443i
$867$	10.7854			0.366291
$868$	−12.3538	−	5.55133i	−0.419316	−	0.188424i
$869$	−6.95896			−0.236066
$870$	0.848930	+	1.47039i	0.0287814	+	0.0498509i
$871$	−40.1420	+	69.5279i	−1.36016	+	2.35586i
$872$	1.25895	−	2.18056i	0.0426333	−	0.0738431i
$873$	−0.649310	−	1.12464i	−0.0219758	−	0.0380632i
$874$	−34.9764			−1.18309
$875$	−17.4360	+	12.5765i	−0.589444	+	0.425163i
$876$	53.8483			1.81937
$877$	−22.0599	−	38.2088i	−0.744908	−	1.29022i	−0.950238	−	0.311526i	$-0.899160\pi$
$877$	−22.0599	−	38.2088i	−0.744908	−	1.29022i	0.205329	−	0.978693i	$-0.434173\pi$
$878$	−6.96809	+	12.0691i	−0.235162	+	0.407312i
$879$	8.71332	−	15.0919i	0.293893	−	0.509037i
$880$	2.34929	+	4.06909i	0.0791945	+	0.137169i
$881$	−57.8355			−1.94853			−0.974263	−	0.225414i	$-0.927627\pi$
$881$	−57.8355			−1.94853			−0.974263	+	0.225414i	$0.927627\pi$
$882$	−11.5870	−	13.0483i	−0.390154	−	0.439358i
$883$	−11.2117			−0.377303			−0.188651	−	0.982044i	$-0.560412\pi$
$883$	−11.2117			−0.377303			−0.188651	+	0.982044i	$0.560412\pi$
$884$	37.4216	+	64.8161i	1.25863	+	2.18000i
$885$	−2.34929	+	4.06909i	−0.0789705	+	0.136781i
$886$	13.5945	−	23.5464i	0.456716	−	0.791056i
$887$	11.0662	+	19.1672i	0.371567	+	0.643573i	0.989807	−	0.142417i	$-0.0454873\pi$
$887$	11.0662	+	19.1672i	0.371567	+	0.643573i	−0.618240	+	0.785989i	$0.712154\pi$
$888$	48.9516			1.64271
$889$	−19.1401	+	13.8056i	−0.641937	+	0.463025i
$890$	13.8219			0.463313
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	32.0341	−	55.4846i	1.07258	−	1.85776i
$893$	12.8330	−	22.2275i	0.429441	−	0.743814i
$894$	−0.957434	−	1.65832i	−0.0320214	−	0.0554627i
$895$	−21.6103			−0.722351
$896$	41.2428	+	18.5329i	1.37782	+	0.619141i
$897$	−37.9941			−1.26859
$898$	12.4292	+	21.5280i	0.414768	+	0.718399i
$899$	0.469527	−	0.813244i	0.0156596	−	0.0271232i
$900$	8.90118	−	15.4173i	0.296706	−	0.513910i
$901$	11.1392	+	19.2937i	0.371101	+	0.642767i
$902$	15.4462			0.514304
$903$	0.863794	+	8.49991i	0.0287453	+	0.282859i
$904$	79.2333			2.63526
$905$	5.64616	+	9.77943i	0.187685	+	0.325079i
$906$	17.4944	−	30.3012i	0.581214	−	1.00669i
$907$	13.0046	−	22.5247i	0.431812	−	0.747920i	−0.565218	−	0.824942i	$-0.691208\pi$
$907$	13.0046	−	22.5247i	0.431812	−	0.747920i	0.997029	+	0.0770219i	$0.0245411\pi$
$908$	23.3197	+	40.3909i	0.773891	+	1.34042i
$909$	−9.89422			−0.328171
$910$	−4.18456	−	41.1769i	−0.138717	−	1.36500i
$911$	32.6978			1.08333			0.541664	−	0.840595i	$-0.317795\pi$
$911$	32.6978			1.08333			0.541664	+	0.840595i	$0.317795\pi$
$912$	7.01517	+	12.1506i	0.232295	+	0.402347i
$913$	0.602619	−	1.04377i	0.0199438	−	0.0345437i
$914$	−7.18960	+	12.4527i	−0.237811	+	0.411900i
$915$	4.00103	+	6.92999i	0.132270	+	0.229098i
$916$	−12.0781			−0.399071
$917$	29.8938	+	13.4331i	0.987180	+	0.443600i
$918$	−6.21460			−0.205112
$919$	0.0618998	+	0.107214i	0.00204189	+	0.00353665i	0.867045	−	0.498231i	$-0.166017\pi$
$919$	0.0618998	+	0.107214i	0.00204189	+	0.00353665i	−0.865003	+	0.501767i	$0.832683\pi$
$920$	−12.9700	+	22.4647i	−0.427607	+	0.740638i
$921$	−0.402481	+	0.697118i	−0.0132622	+	0.0229708i
$922$	−32.3980	−	56.1150i	−1.06697	−	1.84805i
$923$	−54.3491			−1.78892
$924$	9.04370	−	6.52317i	0.297516	−	0.214597i
$925$	−37.4529			−1.23144
$926$	7.60259	+	13.1681i	0.249837	+	0.432730i
$927$	−5.59212	+	9.68583i	−0.183669	+	0.318125i
$928$	0.871619	−	1.50969i	0.0286123	−	0.0495580i
$929$	3.46780	+	6.00640i	0.113775	+	0.197064i	0.917289	−	0.398221i	$-0.130372\pi$
$929$	3.46780	+	6.00640i	0.113775	+	0.197064i	−0.803515	+	0.595285i	$0.797039\pi$
$930$	2.66736			0.0874660
$931$	−18.0372	+	3.70428i	−0.591145	+	0.121403i
$932$	−61.5536			−2.01625
$933$	−5.41250	−	9.37473i	−0.177197	−	0.306915i
$934$	−29.7329	+	51.4989i	−0.972891	+	1.68510i
$935$	−1.09804	+	1.90185i	−0.0359096	+	0.0621972i
$936$	19.6635	+	34.0583i	0.642723	+	1.11323i
$937$	−29.6703			−0.969288			−0.484644	−	0.874712i	$-0.661051\pi$
$937$	−29.6703			−0.969288			−0.484644	+	0.874712i	$0.661051\pi$
$938$	60.2886	−	43.4859i	1.96849	−	1.41986i
$939$	−24.7315			−0.807082
$940$	−18.1127	−	31.3722i	−0.590773	−	1.02325i
$941$	18.1157	−	31.3772i	0.590554	−	1.02287i	−0.403604	−	0.914934i	$-0.632243\pi$
$941$	18.1157	−	31.3772i	0.590554	−	1.02287i	0.994158	−	0.107935i	$-0.0344239\pi$
$942$	−7.02764	+	12.1722i	−0.228973	+	0.396593i
$943$	16.5239	+	28.6203i	0.538093	+	0.932004i
$944$	28.4481			0.925907
$945$	2.12593	+	0.955312i	0.0691566	+	0.0310763i
$946$	−8.05013			−0.261732
$947$	−9.05998	−	15.6924i	−0.294410	−	0.509933i	0.680438	−	0.732806i	$-0.261790\pi$
$947$	−9.05998	−	15.6924i	−0.294410	−	0.509933i	−0.974847	+	0.222873i	$0.928456\pi$
$948$	−14.6646	+	25.3999i	−0.476285	+	0.824949i
$949$	45.5066	−	78.8198i	1.47721	−	2.55860i
$950$	−13.8496	−	23.9883i	−0.449342	−	0.778283i
$951$	12.2819			0.398268
$952$	−3.68149	−	36.2266i	−0.119318	−	1.17411i
$953$	−58.5262			−1.89585			−0.947924	−	0.318496i	$-0.896822\pi$
$953$	−58.5262			−1.89585			−0.947924	+	0.318496i	$0.896822\pi$
$954$	11.1392	+	19.2937i	0.360646	+	0.624657i
$955$	9.72479	−	16.8438i	0.314687	−	0.545053i
$956$	−38.9429	+	67.4511i	−1.25950	+	2.18153i
$957$	0.386568	+	0.669555i	0.0124960	+	0.0216436i
$958$	23.1065			0.746538
$959$	−5.91848	−	58.2390i	−0.191118	−	1.88063i
$960$	−4.44553			−0.143479
$961$	14.7624	+	25.5692i	0.476205	+	0.824812i
$962$	78.7282	−	136.361i	2.53830	−	4.39646i
$963$	−3.63302	+	6.29258i	−0.117073	+	0.202776i
$964$	−54.6703	−	94.6918i	−1.76081	−	3.04982i
$965$	−16.2489			−0.523071
$966$	32.0881	+	14.4191i	1.03242	+	0.463928i
$967$	50.1143			1.61157			0.805783	−	0.592210i	$-0.201745\pi$
$967$	50.1143			1.61157			0.805783	+	0.592210i	$0.201745\pi$
$968$	2.76040	+	4.78116i	0.0887228	+	0.153672i
$969$	−3.27882	+	5.67909i	−0.105331	+	0.182439i
$970$	−1.42593	+	2.46978i	−0.0457839	+	0.0793000i
$971$	−3.31973	−	5.74994i	−0.106535	−	0.184524i	0.807829	−	0.589417i	$-0.200642\pi$
$971$	−3.31973	−	5.74994i	−0.106535	−	0.184524i	−0.914364	+	0.404892i	$0.867309\pi$
$972$	−4.21460			−0.135183
$973$	−5.65532	+	4.07915i	−0.181301	+	0.130772i
$974$	−95.7584			−3.06830
$975$	−15.0446	−	26.0580i	−0.481812	−	0.834523i
$976$	24.2248	−	41.9585i	0.775415	−	1.34306i
$977$	14.3178	−	24.7992i	0.458068	−	0.793397i	−0.540791	−	0.841157i	$-0.681875\pi$
$977$	14.3178	−	24.7992i	0.458068	−	0.793397i	0.998859	+	0.0477598i	$0.0152082\pi$
$978$	−13.5859	−	23.5315i	−0.434430	−	0.752455i
$979$	6.29395			0.201155
$980$	−8.20116	+	24.6614i	−0.261977	+	0.787779i
$981$	0.456074			0.0145613
$982$	−15.1844	−	26.3001i	−0.484552	−	0.839269i
$983$	−1.83440	+	3.17728i	−0.0585084	+	0.101340i	−0.893796	−	0.448474i	$-0.851968\pi$
$983$	−1.83440	+	3.17728i	−0.0585084	+	0.101340i	0.835288	+	0.549813i	$0.185301\pi$
$984$	17.1037	−	29.6244i	0.545245	−	0.944392i
$985$	−2.01603	−	3.49186i	−0.0642360	−	0.111260i
$986$	4.80473			0.153014
$987$	−20.9367	+	15.1015i	−0.666421	+	0.480686i
$988$	78.9745			2.51252
$989$	−8.61178	−	14.9160i	−0.273839	−	0.474303i
$990$	−1.09804	+	1.90185i	−0.0348978	+	0.0604448i
$991$	16.5167	−	28.6078i	0.524670	−	0.908756i	−0.474917	−	0.880031i	$-0.657522\pi$
$991$	16.5167	−	28.6078i	0.524670	−	0.908756i	0.999587	−	0.0287252i	$-0.00914477\pi$
$992$	−1.36932	−	2.37174i	−0.0434760	−	0.0753027i
$993$	13.1987			0.418849
$994$	45.9008	+	20.6261i	1.45589	+	0.654219i
$995$	1.93016			0.0611902
$996$	−2.53980	−	4.39907i	−0.0804767	−	0.139390i
$997$	−6.18869	+	10.7191i	−0.195998	+	0.339478i	−0.947227	−	0.320563i	$-0.896128\pi$
$997$	−6.18869	+	10.7191i	−0.195998	+	0.339478i	0.751229	+	0.660041i	$0.229461\pi$
$998$	8.99268	−	15.5758i	0.284658	−	0.493043i
$999$	4.43337	+	7.67883i	0.140266	+	0.242947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.f.67.5	✓	10
3.2	odd	2		693.2.i.j.298.1		10
7.2	even	3	inner	231.2.i.f.100.5	yes	10
7.3	odd	6		1617.2.a.bb.1.1		5
7.4	even	3		1617.2.a.ba.1.1		5
21.2	odd	6		693.2.i.j.100.1		10
21.11	odd	6		4851.2.a.ca.1.5		5
21.17	even	6		4851.2.a.bz.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.5	✓	10	1.1	even	1	trivial
231.2.i.f.100.5	yes	10	7.2	even	3	inner
693.2.i.j.100.1		10	21.2	odd	6
693.2.i.j.298.1		10	3.2	odd	2
1617.2.a.ba.1.1		5	7.4	even	3
1617.2.a.bb.1.1		5	7.3	odd	6
4851.2.a.bz.1.5		5	21.17	even	6
4851.2.a.ca.1.5		5	21.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24646 + 2.15892i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.10730 + 3.64995i) q^{4} +(0.440463 + 0.762904i) q^{5} +2.49291 q^{6} +(-2.14580 + 1.54775i) q^{7} -5.52081 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.24646 + 2.15892i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.10730 + 3.64995i) q^{4} +(0.440463 + 0.762904i) q^{5} +2.49291 q^{6} +(-2.14580 + 1.54775i) q^{7} -5.52081 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.09804 + 1.90185i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(2.10730 + 3.64995i) q^{12} +7.12343 q^{13} +(-6.01613 - 2.70341i) q^{14} +0.880926 q^{15} +(-2.66684 - 4.61910i) q^{16} +(1.24646 - 2.15892i) q^{17} +(1.24646 - 2.15892i) q^{18} +(-1.31526 - 2.27810i) q^{19} -3.71275 q^{20} +(0.267494 + 2.63219i) q^{21} -2.49291 q^{22} +(-2.66684 - 4.61910i) q^{23} +(-2.76040 + 4.78116i) q^{24} +(2.11198 - 3.65806i) q^{25} +(8.87904 + 15.3789i) q^{26} -1.00000 q^{27} +(-1.12738 - 11.0937i) q^{28} +0.773136 q^{29} +(1.09804 + 1.90185i) q^{30} +(0.607302 - 1.05188i) q^{31} +(1.12738 - 1.95268i) q^{32} +(0.500000 + 0.866025i) q^{33} +6.21460 q^{34} +(-2.12593 - 0.955312i) q^{35} +4.21460 q^{36} +(-4.43337 - 7.67883i) q^{37} +(3.27882 - 5.67909i) q^{38} +(3.56171 - 6.16907i) q^{39} +(-2.43171 - 4.21185i) q^{40} -6.19607 q^{41} +(-5.34929 + 3.85841i) q^{42} +3.22921 q^{43} +(-2.10730 - 3.64995i) q^{44} +(0.440463 - 0.762904i) q^{45} +(6.64819 - 11.5150i) q^{46} +(4.87852 + 8.44984i) q^{47} -5.33368 q^{48} +(2.20892 - 6.64234i) q^{49} +10.5300 q^{50} +(-1.24646 - 2.15892i) q^{51} +(-15.0112 + 26.0002i) q^{52} +(-4.46836 + 7.73943i) q^{53} +(-1.24646 - 2.15892i) q^{54} -0.880926 q^{55} +(11.8466 - 8.54485i) q^{56} -2.63052 q^{57} +(0.963679 + 1.66914i) q^{58} +(-2.66684 + 4.61910i) q^{59} +(-1.85638 + 3.21534i) q^{60} +(4.54185 + 7.86671i) q^{61} +3.02790 q^{62} +(2.41329 + 1.08444i) q^{63} -5.04643 q^{64} +(3.13761 + 5.43450i) q^{65} +(-1.24646 + 2.15892i) q^{66} +(-5.63520 + 9.76045i) q^{67} +(5.25332 + 9.09901i) q^{68} -5.33368 q^{69} +(-0.587436 - 5.78048i) q^{70} -7.62963 q^{71} +(2.76040 + 4.78116i) q^{72} +(6.38830 - 11.0649i) q^{73} +(11.0520 - 19.1426i) q^{74} +(-2.11198 - 3.65806i) q^{75} +11.0866 q^{76} +(-0.267494 - 2.63219i) q^{77} +17.7581 q^{78} +(3.47948 + 6.02663i) q^{79} +(2.34929 - 4.06909i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.72312 - 13.3768i) q^{82} -1.20524 q^{83} +(-10.1711 - 4.57049i) q^{84} +2.19607 q^{85} +(4.02507 + 6.97162i) q^{86} +(0.386568 - 0.669555i) q^{87} +(2.76040 - 4.78116i) q^{88} +(-3.14697 - 5.45072i) q^{89} +2.19607 q^{90} +(-15.2855 + 11.0253i) q^{91} +22.4793 q^{92} +(-0.607302 - 1.05188i) q^{93} +(-12.1617 + 21.0647i) q^{94} +(1.15865 - 2.00683i) q^{95} +(-1.12738 - 1.95268i) q^{96} +1.29862 q^{97} +(17.0936 - 3.51050i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Introduction

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