LMFDB - Embedded newform 97.3.l.a.5.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,3,Mod(5,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(96)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	97.l (of order $96$, degree $32$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.64305856429$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$15$ over $\Q(\zeta_{96})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{96}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	97.5
Dual form			97.3.l.a.39.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.846508 + 1.71655i) q^{2} +(-2.95510 + 3.36964i) q^{3} +(0.205082 - 0.267268i) q^{4} +(-8.04921 - 0.263504i) q^{5} +(-8.28567 - 2.22014i) q^{6} +(-0.649793 - 1.04495i) q^{7} +(8.14099 + 1.61934i) q^{8} +(-1.44715 - 10.9922i) q^{9} +(-6.36141 - 14.0399i) q^{10} +(-13.9564 + 4.73757i) q^{11} +(0.294561 + 1.48086i) q^{12} +(13.7267 + 14.6559i) q^{13} +(1.24366 - 1.99996i) q^{14} +(24.6741 - 26.3443i) q^{15} +(3.76296 + 14.0436i) q^{16} +(-16.6956 + 3.89286i) q^{17} +(17.6437 - 11.7891i) q^{18} +(-11.7287 + 6.26914i) q^{19} +(-1.72118 + 2.09726i) q^{20} +(5.44132 + 0.898365i) q^{21} +(-19.9465 - 19.9465i) q^{22} +(-3.95512 + 2.83420i) q^{23} +(-29.5140 + 22.6469i) q^{24} +(39.7739 + 2.60692i) q^{25} +(-13.5377 + 35.9689i) q^{26} +(7.77754 + 5.19679i) q^{27} +(-0.412544 - 0.0406320i) q^{28} +(20.3601 + 9.22503i) q^{29} +(66.1081 + 20.0537i) q^{30} +(2.44968 + 37.3749i) q^{31} +(4.04143 - 3.54424i) q^{32} +(25.2787 - 61.0282i) q^{33} +(-20.8152 - 25.3634i) q^{34} +(4.95497 + 8.58227i) q^{35} +(-3.23466 - 1.86753i) q^{36} +(59.7048 - 9.85731i) q^{37} +(-20.6898 - 14.8261i) q^{38} +(-89.9489 + 2.94462i) q^{39} +(-65.1018 - 15.1796i) q^{40} +(1.98623 - 0.747565i) q^{41} +(3.06403 + 10.1008i) q^{42} +(-4.85859 - 0.639646i) q^{43} +(-1.59601 + 4.70171i) q^{44} +(8.75195 + 88.8601i) q^{45} +(-8.21309 - 4.38999i) q^{46} +(46.4042 - 19.2213i) q^{47} +(-58.4417 - 28.8203i) q^{48} +(21.0025 - 42.5888i) q^{49} +(29.1940 + 70.4806i) q^{50} +(36.2195 - 67.7619i) q^{51} +(6.73216 - 0.663060i) q^{52} +(-48.1900 - 16.3583i) q^{53} +(-2.33679 + 17.7497i) q^{54} +(113.587 - 34.4562i) q^{55} +(-3.59782 - 9.55918i) q^{56} +(13.5348 - 58.0476i) q^{57} +(1.39976 + 42.7581i) q^{58} +(-14.1769 + 19.7839i) q^{59} +(-1.98077 - 11.9974i) q^{60} +(-45.8162 + 79.3559i) q^{61} +(-62.0822 + 35.8432i) q^{62} +(-10.5460 + 8.65488i) q^{63} +(63.2340 + 26.1924i) q^{64} +(-106.628 - 121.585i) q^{65} +(126.156 - 8.26873i) q^{66} +(-31.7951 + 104.814i) q^{67} +(-2.38353 + 5.26056i) q^{68} +(2.13753 - 21.7027i) q^{69} +(-10.5375 + 15.7704i) q^{70} +(-66.2195 - 24.9233i) q^{71} +(6.01892 - 91.8310i) q^{72} +(-75.6079 - 98.5341i) q^{73} +(67.4612 + 94.1420i) q^{74} +(-126.320 + 126.320i) q^{75} +(-0.729813 + 4.42041i) q^{76} +(14.0193 + 11.5054i) q^{77} +(-81.1971 - 151.909i) q^{78} +(-28.1312 - 42.1013i) q^{79} +(-26.5883 - 114.031i) q^{80} +(55.8889 - 14.9754i) q^{81} +(2.96459 + 2.77664i) q^{82} +(78.6328 + 48.8970i) q^{83} +(1.35602 - 1.27005i) q^{84} +(135.412 - 26.9351i) q^{85} +(-3.01485 - 8.88147i) q^{86} +(-91.2510 + 41.3453i) q^{87} +(-121.291 + 15.9683i) q^{88} +(-14.5480 + 73.1378i) q^{89} +(-145.124 + 90.2439i) q^{90} +(6.39516 - 23.8671i) q^{91} +(-0.0536332 + 1.63832i) q^{92} +(-133.179 - 102.192i) q^{93} +(72.2758 + 63.3842i) q^{94} +(96.0591 - 47.3711i) q^{95} +24.0917i q^{96} +(91.7078 - 31.6018i) q^{97} +90.8844 q^{98} +(72.2736 + 146.556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) $ 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{96}\right)$

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 $

$2$	0.846508	+	1.71655i	0.423254	+	0.858274i	0.999169	+	0.0407646i	$0.0129794\pi$
$2$	0.846508	+	1.71655i	0.423254	+	0.858274i	−0.575915	+	0.817510i	$0.695354\pi$
$3$	−2.95510	+	3.36964i	−0.985032	+	1.12321i	0.00734483	+	0.999973i	$0.497662\pi$
$3$	−2.95510	+	3.36964i	−0.985032	+	1.12321i	−0.992377	+	0.123241i	$0.960671\pi$
$4$	0.205082	−	0.267268i	0.0512706	−	0.0668171i
$5$	−8.04921	−	0.263504i	−1.60984	−	0.0527008i	−0.785525	−	0.618829i	$-0.787607\pi$
$5$	−8.04921	−	0.263504i	−1.60984	−	0.0527008i	−0.824317	+	0.566129i	$0.808441\pi$
$6$	−8.28567	−	2.22014i	−1.38094	−	0.370023i
$7$	−0.649793	−	1.04495i	−0.0928276	−	0.149279i	0.799502	−	0.600664i	$-0.205097\pi$
$7$	−0.649793	−	1.04495i	−0.0928276	−	0.149279i	−0.892329	+	0.451385i	$0.850930\pi$
$8$	8.14099	+	1.61934i	1.01762	+	0.202418i
$9$	−1.44715	−	10.9922i	−0.160795	−	1.22136i
$10$	−6.36141	−	14.0399i	−0.636141	−	1.40399i
$11$	−13.9564	+	4.73757i	−1.26877	+	0.430688i	−0.873026	−	0.487674i	$-0.837846\pi$
$11$	−13.9564	+	4.73757i	−1.26877	+	0.430688i	−0.395741	+	0.918362i	$0.629512\pi$
$12$	0.294561	+	1.48086i	0.0245467	+	0.123405i
$13$	13.7267	+	14.6559i	1.05590	+	1.12738i	0.991586	+	0.129446i	$0.0413200\pi$
$13$	13.7267	+	14.6559i	1.05590	+	1.12738i	0.0643163	+	0.997930i	$0.479513\pi$
$14$	1.24366	−	1.99996i	0.0888326	−	0.142854i
$15$	24.6741	−	26.3443i	1.64494	−	1.75629i
$16$	3.76296	+	14.0436i	0.235185	+	0.877723i
$17$	−16.6956	+	3.89286i	−0.982093	+	0.228992i	−0.687144	−	0.726521i	$-0.741136\pi$
$17$	−16.6956	+	3.89286i	−0.982093	+	0.228992i	−0.294949	+	0.955513i	$0.595303\pi$
$18$	17.6437	−	11.7891i	0.980203	−	0.654951i
$19$	−11.7287	+	6.26914i	−0.617302	+	0.329955i	−0.750236	−	0.661170i	$-0.770060\pi$
$19$	−11.7287	+	6.26914i	−0.617302	+	0.329955i	0.132934	+	0.991125i	$0.457560\pi$
$20$	−1.72118	+	2.09726i	−0.0860588	+	0.104863i
$21$	5.44132	+	0.898365i	0.259110	+	0.0427793i
$22$	−19.9465	−	19.9465i	−0.906660	−	0.906660i
$23$	−3.95512	+	2.83420i	−0.171962	+	0.123226i	−0.665191	−	0.746673i	$-0.731650\pi$
$23$	−3.95512	+	2.83420i	−0.171962	+	0.123226i	0.493229	+	0.869900i	$0.335816\pi$
$24$	−29.5140	+	22.6469i	−1.22975	+	0.943621i
$25$	39.7739	+	2.60692i	1.59096	+	0.104277i
$26$	−13.5377	+	35.9689i	−0.520683	+	1.38342i
$27$	7.77754	+	5.19679i	0.288057	+	0.192474i
$28$	−0.412544	−	0.0406320i	−0.0147337	−	0.00145114i
$29$	20.3601	+	9.22503i	0.702072	+	0.318105i	0.731863	−	0.681452i	$-0.238651\pi$
$29$	20.3601	+	9.22503i	0.702072	+	0.318105i	−0.0297915	+	0.999556i	$0.509484\pi$
$30$	66.1081	+	20.0537i	2.20360	+	0.668455i
$31$	2.44968	+	37.3749i	0.0790220	+	1.20564i	0.834702	+	0.550701i	$0.185640\pi$
$31$	2.44968	+	37.3749i	0.0790220	+	1.20564i	−0.755680	+	0.654941i	$0.772694\pi$
$32$	4.04143	−	3.54424i	0.126295	−	0.110758i
$33$	25.2787	−	61.0282i	0.766021	−	1.84934i
$34$	−20.8152	−	25.3634i	−0.612213	−	0.745983i
$35$	4.95497	+	8.58227i	0.141571	+	0.245208i
$36$	−3.23466	−	1.86753i	−0.0898516	−	0.0518759i
$37$	59.7048	−	9.85731i	1.61364	−	0.266414i	0.713063	−	0.701100i	$-0.247308\pi$
$37$	59.7048	−	9.85731i	1.61364	−	0.266414i	0.900582	+	0.434687i	$0.143141\pi$
$38$	−20.6898	−	14.8261i	−0.544468	−	0.390160i
$39$	−89.9489	+	2.94462i	−2.30638	+	0.0755031i
$40$	−65.1018	−	15.1796i	−1.62755	−	0.379490i
$41$	1.98623	−	0.747565i	0.0484447	−	0.0182333i	−0.327910	−	0.944709i	$-0.606344\pi$
$41$	1.98623	−	0.747565i	0.0484447	−	0.0182333i	0.376354	+	0.926476i	$0.377178\pi$
$42$	3.06403	+	10.1008i	0.0729531	+	0.240494i
$43$	−4.85859	−	0.639646i	−0.112991	−	0.0148755i	0.0738189	−	0.997272i	$-0.476481\pi$
$43$	−4.85859	−	0.639646i	−0.112991	−	0.0148755i	−0.186809	+	0.982396i	$0.559815\pi$
$44$	−1.59601	+	4.70171i	−0.0362731	+	0.106857i
$45$	8.75195	+	88.8601i	0.194488	+	1.97467i
$46$	−8.21309	−	4.38999i	−0.178545	−	0.0954345i
$47$	46.4042	−	19.2213i	0.987324	−	0.408963i	0.170190	−	0.985411i	$-0.445562\pi$
$47$	46.4042	−	19.2213i	0.987324	−	0.408963i	0.817134	+	0.576448i	$0.195562\pi$
$48$	−58.4417	−	28.8203i	−1.21754	−	0.600422i
$49$	21.0025	−	42.5888i	0.428621	−	0.869158i
$50$	29.1940	+	70.4806i	0.583881	+	1.40961i
$51$	36.2195	−	67.7619i	0.710186	−	1.32866i
$52$	6.73216	−	0.663060i	0.129465	−	0.0127512i
$53$	−48.1900	−	16.3583i	−0.909246	−	0.308647i	−0.172652	−	0.984983i	$-0.555234\pi$
$53$	−48.1900	−	16.3583i	−0.909246	−	0.308647i	−0.736594	+	0.676336i	$0.763567\pi$
$54$	−2.33679	+	17.7497i	−0.0432738	+	0.328697i
$55$	113.587	−	34.4562i	2.06521	−	0.626475i
$56$	−3.59782	−	9.55918i	−0.0642468	−	0.170700i
$57$	13.5348	−	58.0476i	0.237453	−	1.01838i
$58$	1.39976	+	42.7581i	0.0241337	+	0.737209i
$59$	−14.1769	+	19.7839i	−0.240287	+	0.335320i	−0.915511	−	0.402293i	$-0.868213\pi$
$59$	−14.1769	+	19.7839i	−0.240287	+	0.335320i	0.675225	+	0.737612i	$0.264047\pi$
$60$	−1.98077	−	11.9974i	−0.0330128	−	0.199956i
$61$	−45.8162	+	79.3559i	−0.751085	+	1.30092i	0.196212	+	0.980561i	$0.437136\pi$
$61$	−45.8162	+	79.3559i	−0.751085	+	1.30092i	−0.947297	+	0.320356i	$0.896198\pi$
$62$	−62.0822	+	35.8432i	−1.00133	+	0.578115i
$63$	−10.5460	+	8.65488i	−0.167397	+	0.137379i
$64$	63.2340	+	26.1924i	0.988031	+	0.409256i
$65$	−106.628	−	121.585i	−1.64042	−	1.87054i
$66$	126.156	−	8.26873i	1.91146	−	0.125284i
$67$	−31.7951	+	104.814i	−0.474554	+	1.56439i	0.313997	+	0.949424i	$0.398332\pi$
$67$	−31.7951	+	104.814i	−0.474554	+	1.56439i	−0.788551	+	0.614970i	$0.789168\pi$
$68$	−2.38353	+	5.26056i	−0.0350519	+	0.0773611i
$69$	2.13753	−	21.7027i	0.0309787	−	0.314532i
$70$	−10.5375	+	15.7704i	−0.150535	+	0.225292i
$71$	−66.2195	−	24.9233i	−0.932669	−	0.351032i	−0.160926	−	0.986966i	$-0.551448\pi$
$71$	−66.2195	−	24.9233i	−0.932669	−	0.351032i	−0.771743	+	0.635934i	$0.780615\pi$
$72$	6.01892	−	91.8310i	0.0835961	−	1.27543i
$73$	−75.6079	−	98.5341i	−1.03572	−	1.34978i	−0.934913	−	0.354876i	$-0.884523\pi$
$73$	−75.6079	−	98.5341i	−1.03572	−	1.34978i	−0.100811	−	0.994906i	$-0.532144\pi$
$74$	67.4612	+	94.1420i	0.911638	+	1.27219i
$75$	−126.320	+	126.320i	−1.68427	+	1.68427i
$76$	−0.729813	+	4.42041i	−0.00960280	+	0.0581633i
$77$	14.0193	+	11.5054i	0.182069	+	0.149420i
$78$	−81.1971	−	151.909i	−1.04099	−	1.94755i
$79$	−28.1312	−	42.1013i	−0.356091	−	0.532928i	0.609570	−	0.792732i	$-0.291342\pi$
$79$	−28.1312	−	42.1013i	−0.356091	−	0.532928i	−0.965661	+	0.259804i	$0.916342\pi$
$80$	−26.5883	−	114.031i	−0.332354	−	1.42539i
$81$	55.8889	−	14.9754i	0.689987	−	0.184881i
$82$	2.96459	+	2.77664i	0.0361536	+	0.0338615i
$83$	78.6328	+	48.8970i	0.947383	+	0.589121i	0.911972	−	0.410252i	$-0.134559\pi$
$83$	78.6328	+	48.8970i	0.947383	+	0.589121i	0.0354108	+	0.999373i	$0.488726\pi$
$84$	1.35602	−	1.27005i	0.0161431	−	0.0151197i
$85$	135.412	−	26.9351i	1.59308	−	0.316884i
$86$	−3.01485	−	8.88147i	−0.0350564	−	0.103273i
$87$	−91.2510	+	41.3453i	−1.04886	+	0.475233i
$88$	−121.291	+	15.9683i	−1.37831	+	0.181457i
$89$	−14.5480	+	73.1378i	−0.163461	+	0.821773i	0.808838	+	0.588032i	$0.200097\pi$
$89$	−14.5480	+	73.1378i	−0.163461	+	0.821773i	−0.972299	+	0.233741i	$0.924903\pi$
$90$	−145.124	+	90.2439i	−1.61249	+	1.00271i
$91$	6.39516	−	23.8671i	0.0702765	−	0.262276i
$92$	−0.0536332	+	1.63832i	−0.000582969	+	0.0178079i
$93$	−133.179	−	102.192i	−1.43203	−	1.09884i
$94$	72.2758	+	63.3842i	0.768891	+	0.674300i
$95$	96.0591	−	47.3711i	1.01115	−	0.498643i
$96$			24.0917i			0.250956i
$97$	91.7078	−	31.6018i	0.945442	−	0.325792i
$97$	91.7078	−	31.6018i	0.945442	−	0.325792i
$98$	90.8844			0.927392
$99$	72.2736	+	146.556i	0.730036	+	1.48037i
$100$	8.85367	−	10.0957i	0.0885367	−	0.100957i
$101$	−3.42798	+	4.46744i	−0.0339404	+	0.0442320i	−0.810015	−	0.586409i	$-0.800541\pi$
$101$	−3.42798	+	4.46744i	−0.0339404	+	0.0442320i	0.776075	+	0.630641i	$0.217208\pi$
$102$	146.977	+	4.81152i	1.44095	+	0.0471718i
$103$	−92.7606	−	24.8551i	−0.900589	−	0.241312i	−0.221320	−	0.975201i	$-0.571036\pi$
$103$	−92.7606	−	24.8551i	−0.900589	−	0.241312i	−0.679269	+	0.733889i	$0.737703\pi$
$104$	88.0163	+	141.542i	0.846310	+	1.36098i
$105$	−43.5616	−	8.66494i	−0.414872	−	0.0825232i
$106$	−12.7134	−	96.5680i	−0.119938	−	0.911019i
$107$	40.3556	+	89.0666i	0.377155	+	0.832398i	0.998794	+	0.0490948i	$0.0156337\pi$
$107$	40.3556	+	89.0666i	0.377155	+	0.832398i	−0.621639	+	0.783304i	$0.713533\pi$
$108$	2.98397	−	1.01292i	0.0276294	−	0.00937891i
$109$	−26.6415	−	133.936i	−0.244417	−	1.22877i	−0.886716	−	0.462314i	$-0.847019\pi$
$109$	−26.6415	−	133.936i	−0.244417	−	1.22877i	0.642299	−	0.766454i	$-0.277981\pi$
$110$	155.298	+	165.810i	1.41180	+	1.50736i
$111$	−143.218	+	230.313i	−1.29025	+	2.07489i
$112$	12.2297	−	13.0575i	0.109194	−	0.116585i
$113$	28.6955	+	107.093i	0.253942	+	0.947725i	0.968676	+	0.248328i	$0.0798812\pi$
$113$	28.6955	+	107.093i	0.253942	+	0.947725i	−0.714734	+	0.699397i	$0.753452\pi$
$114$	111.099	−	25.9046i	0.974551	−	0.227233i
$115$	32.5824	−	21.7709i	0.283326	−	0.189312i
$116$	6.64105	−	3.54971i	0.0572504	−	0.0306010i
$117$	141.236	−	172.097i	1.20715	−	1.47091i
$118$	−45.9608	−	7.58816i	−0.389498	−	0.0643065i
$119$	14.9165	+	14.9165i	0.125349	+	0.125349i
$120$	243.532	−	174.513i	2.02943	−	1.45427i
$121$	76.3418	−	58.5792i	0.630924	−	0.484125i
$122$	−175.002	−	11.4702i	−1.43444	−	0.0940184i
$123$	−3.35048	+	8.90201i	−0.0272397	+	0.0723741i
$124$	10.4915	+	7.01021i	0.0846090	+	0.0565339i
$125$	−119.093	−	11.7296i	−0.952745	−	0.0938371i
$126$	−23.7838	−	10.7763i	−0.188760	−	0.0855262i
$127$	4.74017	+	1.43792i	0.0373242	+	0.0113222i	0.308892	−	0.951097i	$-0.400042\pi$
$127$	4.74017	+	1.43792i	0.0373242	+	0.0113222i	−0.271567	+	0.962419i	$0.587542\pi$
$128$	7.16133	+	109.261i	0.0559479	+	0.853600i
$129$	16.5130	−	14.4815i	0.128008	−	0.112260i
$130$	118.446	−	285.954i	0.911124	−	2.19965i
$131$	102.505	+	124.902i	0.782479	+	0.953453i	0.999743	−	0.0226594i	$-0.00721334\pi$
$131$	102.505	+	124.902i	0.782479	+	0.953453i	−0.217264	+	0.976113i	$0.569713\pi$
$132$	−11.1267	−	19.2720i	−0.0842931	−	0.146000i
$133$	14.1722	+	8.18233i	0.106558	+	0.0615213i
$134$	−206.834	+	34.1484i	−1.54354	+	0.254839i
$135$	−61.2337	−	43.8795i	−0.453583	−	0.325033i
$136$	−142.222	+	4.65588i	−1.04575	+	0.0342344i
$137$	160.184	+	37.3497i	1.16923	+	0.272626i	0.766225	−	0.642573i	$-0.222133\pi$
$137$	160.184	+	37.3497i	1.16923	+	0.272626i	0.403003	+	0.915198i	$0.367966\pi$
$138$	39.0631	−	14.7023i	0.283066	−	0.106539i
$139$	30.1539	+	99.4041i	0.216935	+	0.715138i	0.996093	+	0.0883105i	$0.0281468\pi$
$139$	30.1539	+	99.4041i	0.216935	+	0.715138i	−0.779158	+	0.626827i	$0.784353\pi$
$140$	3.30995	+	0.435763i	0.0236425	+	0.00311259i
$141$	−72.3602	+	213.166i	−0.513193	+	1.51182i
$142$	−13.2734	−	134.767i	−0.0934744	−	0.949062i
$143$	−261.010	−	139.513i	−1.82524	−	0.975612i
$144$	148.924	−	61.6865i	1.03420	−	0.428379i
$145$	−161.452	−	79.6192i	−1.11346	−	0.549098i
$146$	105.136	−	213.194i	0.720109	−	1.46024i
$147$	81.4446	+	196.625i	0.554045	+	1.33758i
$148$	9.60985	−	17.9788i	0.0649314	−	0.121478i
$149$	34.6524	−	3.41297i	0.232567	−	0.0229058i	0.0189376	−	0.999821i	$-0.493972\pi$
$149$	34.6524	−	3.41297i	0.232567	−	0.0229058i	0.213629	+	0.976915i	$0.431472\pi$
$150$	−323.766	−	109.904i	−2.15844	−	0.732691i
$151$	−10.3239	+	78.4175i	−0.0683699	+	0.519321i	0.922653	+	0.385631i	$0.126016\pi$
$151$	−10.3239	+	78.4175i	−0.0683699	+	0.519321i	−0.991023	+	0.133691i	$0.957317\pi$
$152$	−105.635	+	32.0442i	−0.694970	+	0.210817i
$153$	66.9523	+	177.888i	0.437597	+	1.16267i
$154$	−7.88205	+	33.8043i	−0.0511821	+	0.219508i
$155$	−9.86957	−	301.484i	−0.0636746	−	1.94506i
$156$	−17.6599	+	24.6444i	−0.113205	+	0.157977i
$157$	−38.5630	−	233.573i	−0.245624	−	1.48772i	−0.770990	−	0.636848i	$-0.780238\pi$
$157$	−38.5630	−	233.573i	−0.245624	−	1.48772i	0.525365	−	0.850877i	$-0.323929\pi$
$158$	48.4556	−	83.9276i	0.306681	−	0.531188i
$159$	197.528	−	114.043i	1.24231	−	0.717250i
$160$	−33.4643	+	27.4634i	−0.209152	+	0.171646i
$161$	5.53162	+	2.29127i	0.0343579	+	0.0142315i
$162$	73.0164	+	83.2593i	0.450719	+	0.513946i
$163$	−30.6542	+	2.00918i	−0.188062	+	0.0123263i	−0.159143	−	0.987256i	$-0.550873\pi$
$163$	−30.6542	+	2.00918i	−0.188062	+	0.0123263i	−0.0289191	+	0.999582i	$0.509207\pi$
$164$	0.207540	−	0.684169i	0.00126549	−	0.00417176i
$165$	−219.555	+	484.568i	−1.33063	+	2.93677i
$166$	−17.3708	+	176.369i	−0.104643	+	1.06246i
$167$	−61.1413	+	91.5044i	−0.366116	+	0.547931i	−0.968096	−	0.250580i	$-0.919379\pi$
$167$	−61.1413	+	91.5044i	−0.366116	+	0.547931i	0.601980	+	0.798511i	$0.294379\pi$
$168$	42.8429	+	16.1249i	0.255017	+	0.0959818i
$169$	−15.3186	+	233.717i	−0.0906427	+	1.38294i
$170$	160.863	+	209.641i	0.946252	+	1.23318i
$171$	85.8851	+	119.853i	0.502252	+	0.700892i
$172$	−1.16737	+	1.16737i	−0.00678702	+	0.00678702i
$173$	−8.00289	+	48.4728i	−0.0462595	+	0.280190i	−0.999776	−	0.0211502i	$-0.993267\pi$
$173$	−8.00289	+	48.4728i	−0.0462595	+	0.280190i	0.953517	+	0.301340i	$0.0974338\pi$
$174$	−148.216	−	121.638i	−0.851816	−	0.699067i
$175$	−23.1207	−	43.2558i	−0.132118	−	0.247176i
$176$	−119.050	−	178.171i	−0.676420	−	1.01233i
$177$	−24.7704	−	106.234i	−0.139946	−	0.600194i
$178$	−137.860	+	36.9394i	−0.774492	+	0.207525i
$179$	−53.1045	−	49.7378i	−0.296673	−	0.277865i	0.520988	−	0.853564i	$-0.325563\pi$
$179$	−53.1045	−	49.7378i	−0.296673	−	0.277865i	−0.817662	+	0.575699i	$0.804730\pi$
$180$	25.5443	+	15.8845i	0.141913	+	0.0882472i
$181$	−149.286	+	139.821i	−0.824783	+	0.772493i	−0.976406	−	0.215945i	$-0.930717\pi$
$181$	−149.286	+	139.821i	−0.824783	+	0.772493i	0.151623	+	0.988438i	$0.451550\pi$
$182$	46.3826	−	9.22607i	0.254849	−	0.0506927i
$183$	−132.010	−	388.889i	−0.721365	−	2.12507i
$184$	−36.7882	+	16.6685i	−0.199936	+	0.0905896i
$185$	−483.174	+	63.6111i	−2.61175	+	0.343844i
$186$	62.6802	−	315.115i	0.336990	−	1.69416i
$187$	214.568	−	133.427i	1.14742	−	0.713514i
$188$	4.37945	−	16.3443i	0.0232949	−	0.0869379i
$189$	0.376602	−	11.5040i	0.00199260	−	0.0608677i
$190$	162.630	+	124.790i	0.855945	+	0.656790i
$191$	−10.3676	−	9.09211i	−0.0542805	−	0.0476027i	0.631776	−	0.775151i	$-0.282326\pi$
$191$	−10.3676	−	9.09211i	−0.0542805	−	0.0476027i	−0.686056	+	0.727548i	$0.740660\pi$
$192$	−275.121	+	135.675i	−1.43292	+	0.706640i
$193$			53.1779i			0.275533i	0.990465	+	0.137767i	$0.0439924\pi$
$193$			53.1779i			0.275533i	−0.990465	+	0.137767i	$0.956008\pi$
$194$	131.877	+	130.670i	0.679781	+	0.673556i
$195$	724.794			3.71689
$196$	−7.07540	−	14.3475i	−0.0360990	−	0.0732015i
$197$	87.9005	−	100.231i	0.446196	−	0.508789i	−0.484395	−	0.874849i	$-0.660960\pi$
$197$	87.9005	−	100.231i	0.446196	−	0.508789i	0.930591	+	0.366061i	$0.119294\pi$
$198$	−190.391	+	248.122i	−0.961570	+	1.25314i
$199$	−118.656	−	3.88439i	−0.596260	−	0.0195195i	−0.266900	−	0.963724i	$-0.585999\pi$
$199$	−118.656	−	3.88439i	−0.596260	−	0.0195195i	−0.329360	+	0.944205i	$0.606833\pi$
$200$	319.577	+	85.6305i	1.59789	+	0.428153i
$201$	−259.229	−	416.875i	−1.28970	−	2.07400i
$202$	−10.5704	−	2.10258i	−0.0523287	−	0.0104088i
$203$	−3.59012	−	27.2697i	−0.0176853	−	0.134333i
$204$	−10.6826	−	23.5771i	−0.0523659	−	0.115574i
$205$	−16.1846	+	5.49393i	−0.0789492	+	0.0267996i
$206$	−35.8576	−	180.268i	−0.174066	−	0.875088i
$207$	36.8778	+	39.3741i	0.178154	+	0.190213i
$208$	−154.168	+	247.922i	−0.741191	+	1.19193i
$209$	133.991	−	143.061i	0.641105	−	0.684501i
$210$	−22.0014	−	82.1105i	−0.104769	−	0.391002i
$211$	−143.800	+	33.5295i	−0.681517	+	0.158908i	−0.553481	−	0.832862i	$-0.686701\pi$
$211$	−143.800	+	33.5295i	−0.681517	+	0.158908i	−0.128036	+	0.991769i	$0.540867\pi$
$212$	−14.2550	+	9.52487i	−0.0672404	+	0.0449286i
$213$	279.668	−	149.485i	1.31299	−	0.701809i
$214$	−118.726	+	144.668i	−0.554794	+	0.676018i
$215$	38.9393	+	6.42890i	0.181113	+	0.0299019i
$216$	54.9015	+	54.9015i	0.254174	+	0.254174i
$217$	37.4632	−	26.8458i	0.172642	−	0.123713i
$218$	207.355	−	159.109i	0.951170	−	0.729858i
$219$	555.453	+	36.4063i	2.53631	+	0.166239i
$220$	14.0856	−	37.4245i	0.0640253	−	0.170111i
$221$	−286.229	−	191.252i	−1.29515	−	0.865395i
$222$	−516.579	−	50.8786i	−2.32693	−	0.229183i
$223$	135.139	+	61.2306i	0.606003	+	0.274576i	0.692205	−	0.721701i	$-0.256640\pi$
$223$	135.139	+	61.2306i	0.606003	+	0.274576i	−0.0862015	+	0.996278i	$0.527473\pi$
$224$	−6.32966	−	1.92008i	−0.0282574	−	0.00857179i
$225$	−28.9031	−	440.976i	−0.128458	−	1.95989i
$226$	−159.539	+	139.912i	−0.705926	+	0.619081i
$227$	120.895	−	291.866i	0.532576	−	1.28575i	−0.397235	−	0.917717i	$-0.630030\pi$
$227$	120.895	−	291.866i	0.532576	−	1.28575i	0.929811	−	0.368036i	$-0.119970\pi$
$228$	−12.7385	−	15.5219i	−0.0558708	−	0.0680787i
$229$	125.836	+	217.955i	0.549503	+	0.951766i	0.998309	+	0.0581372i	$0.0185161\pi$
$229$	125.836	+	217.955i	0.549503	+	0.951766i	−0.448806	+	0.893629i	$0.648151\pi$
$230$	64.9521	+	37.5001i	0.282400	+	0.163044i
$231$	−80.1975	+	13.2407i	−0.347175	+	0.0573188i
$232$	150.813	+	108.071i	0.650055	+	0.465823i
$233$	126.771	−	4.15006i	0.544082	−	0.0178114i	0.240557	−	0.970635i	$-0.422670\pi$
$233$	126.771	−	4.15006i	0.544082	−	0.0178114i	0.303525	+	0.952824i	$0.401836\pi$
$234$	414.970	+	96.7574i	1.77338	+	0.413493i
$235$	−378.582	+	142.488i	−1.61099	+	0.606333i
$236$	2.38017	+	7.84636i	0.0100854	+	0.0332473i
$237$	224.997	+	29.6214i	0.949353	+	0.124985i
$238$	−12.9780	+	38.2319i	−0.0545294	+	0.160638i
$239$	−27.0945	−	275.095i	−0.113366	−	1.15102i	−0.868581	−	0.495547i	$-0.834968\pi$
$239$	−27.0945	−	275.095i	−0.113366	−	1.15102i	0.755215	−	0.655477i	$-0.227532\pi$
$240$	462.815	+	247.380i	1.92840	+	1.03075i
$241$	418.050	−	173.162i	1.73465	−	0.718514i	0.735485	−	0.677541i	$-0.236954\pi$
$241$	418.050	−	173.162i	1.73465	−	0.718514i	0.999160	−	0.0409729i	$-0.0130457\pi$
$242$	165.178	+	81.4568i	0.682554	+	0.336598i
$243$	−151.930	+	308.083i	−0.625226	+	1.26783i
$244$	11.8132	+	28.5197i	0.0484150	+	0.116884i
$245$	−180.275	+	337.272i	−0.735818	+	1.37662i
$246$	−18.1169	+	1.78436i	−0.0736461	+	0.00725351i
$247$	−252.877	−	85.8402i	−1.02379	−	0.347531i
$248$	−40.5800	+	308.236i	−0.163629	+	1.24289i
$249$	−397.133	+	120.469i	−1.59491	+	0.483811i
$250$	−80.6787	−	214.358i	−0.322715	−	0.857433i
$251$	37.6071	−	161.288i	0.149829	−	0.642582i	−0.844438	−	0.535654i	$-0.820065\pi$
$251$	37.6071	−	161.288i	0.149829	−	0.642582i	0.994267	−	0.106928i	$-0.0341014\pi$
$252$	0.150378	+	4.59357i	0.000596738	+	0.0182285i
$253$	41.7722	−	58.2930i	0.165108	−	0.230407i
$254$	1.54434	+	9.35395i	0.00608009	+	0.0368266i
$255$	−309.394	+	535.886i	−1.21331	+	2.10151i
$256$	55.6076	−	32.1051i	0.217217	−	0.125410i
$257$	180.710	−	148.305i	0.703153	−	0.577063i	−0.213405	−	0.976964i	$-0.568456\pi$
$257$	180.710	−	148.305i	0.703153	−	0.577063i	0.916558	+	0.399901i	$0.130956\pi$
$258$	38.8366	+	16.0866i	0.150529	+	0.0623513i
$259$	−49.0962	−	55.9835i	−0.189561	−	0.216153i
$260$	−54.3633	+	3.56316i	−0.209090	+	0.0137045i
$261$	71.9394	−	237.153i	0.275630	−	0.908630i
$262$	−127.630	+	281.685i	−0.487137	+	1.07513i
$263$	−37.6812	+	382.583i	−0.143274	+	1.45469i	0.607599	+	0.794244i	$0.292133\pi$
$263$	−37.6812	+	382.583i	−0.143274	+	1.45469i	−0.750873	+	0.660446i	$0.770367\pi$
$264$	304.619	−	455.895i	1.15386	−	1.72687i
$265$	383.581	+	144.370i	1.44748	+	0.544792i
$266$	−2.04848	+	31.2537i	−0.00770104	+	0.117495i
$267$	−203.457	−	265.151i	−0.762013	−	0.993074i
$268$	21.4930	+	29.9934i	0.0801976	+	0.111916i
$269$	−246.210	+	246.210i	−0.915280	+	0.915280i	−0.996681	−	0.0814011i	$-0.974061\pi$
$269$	−246.210	+	246.210i	−0.915280	+	0.915280i	0.0814011	+	0.996681i	$0.474061\pi$
$270$	23.4864	−	142.255i	0.0869866	−	0.526870i
$271$	202.503	+	166.190i	0.747244	+	0.613247i	0.928993	−	0.370098i	$-0.120676\pi$
$271$	202.503	+	166.190i	0.747244	+	0.613247i	−0.181749	+	0.983345i	$0.558176\pi$
$272$	−117.495	−	219.817i	−0.431965	−	0.808150i
$273$	61.5252	+	92.0789i	0.225367	+	0.337285i
$274$	71.4846	+	306.581i	0.260893	+	1.11891i
$275$	−567.453	+	152.048i	−2.06346	+	0.552903i
$276$	−5.36207	−	5.02213i	−0.0194278	−	0.0181961i
$277$	367.640	+	228.613i	1.32722	+	0.825318i	0.993107	−	0.117215i	$-0.0373967\pi$
$277$	367.640	+	228.613i	1.32722	+	0.825318i	0.334113	+	0.942533i	$0.391563\pi$
$278$	−145.107	+	135.907i	−0.521966	+	0.488874i
$279$	407.288	−	81.0147i	1.45981	−	0.290375i
$280$	26.4407	+	77.8919i	0.0944312	+	0.278185i
$281$	132.177	−	59.8886i	0.470381	−	0.213127i	−0.163522	−	0.986540i	$-0.552285\pi$
$281$	132.177	−	59.8886i	0.470381	−	0.213127i	0.633902	+	0.773413i	$0.281452\pi$
$282$	−427.164	+	56.2372i	−1.51476	+	0.199423i
$283$	68.1559	−	342.643i	0.240834	−	1.21075i	−0.651243	−	0.758869i	$-0.725752\pi$
$283$	68.1559	−	342.643i	0.240834	−	1.21075i	0.892077	−	0.451884i	$-0.149248\pi$
$284$	−20.2416	+	12.5871i	−0.0712734	+	0.0443207i
$285$	−124.240	+	463.671i	−0.435931	+	1.62692i
$286$	18.5333	−	566.134i	0.0648018	−	1.97949i
$287$	−2.07181	−	1.58975i	−0.00721885	−	0.00553922i
$288$	−44.8077	−	39.2953i	−0.155582	−	0.136442i
$289$	4.39179	−	2.16579i	0.0151965	−	0.00749409i
$290$		−	344.538i		−	1.18806i
$291$	−164.519	+	402.409i	−0.565357	+	1.38285i
$292$	−41.8409			−0.143291
$293$	−82.5453	−	167.385i	−0.281725	−	0.571281i	0.709308	−	0.704898i	$-0.249007\pi$
$293$	−82.5453	−	167.385i	−0.281725	−	0.571281i	−0.991033	+	0.133617i	$0.957341\pi$
$294$	−268.572	+	306.248i	−0.913511	+	1.04166i
$295$	119.326	−	155.509i	0.404495	−	0.527148i
$296$	502.019	+	16.4344i	1.69601	+	0.0555216i
$297$	−133.167	−	35.6820i	−0.448374	−	0.120141i
$298$	35.1921	+	56.5935i	0.118094	+	0.189911i
$299$	−95.8287	−	19.0615i	−0.320497	−	0.0637509i
$300$	7.85536	+	59.6674i	0.0261845	+	0.198891i
$301$	2.48868	+	5.49263i	0.00826804	+	0.0182480i
$302$	−143.347	+	48.6597i	−0.474658	+	0.161125i
$303$	−4.92363	−	24.7528i	−0.0162496	−	0.0816924i
$304$	−132.176	−	141.123i	−0.434789	−	0.464220i
$305$	389.695	−	626.680i	1.27769	−	2.05469i
$306$	−248.678	+	265.510i	−0.812672	+	0.867681i
$307$	−78.3651	−	292.462i	−0.255261	−	0.952646i	−0.967945	−	0.251161i	$-0.919188\pi$
$307$	−78.3651	−	292.462i	−0.255261	−	0.952646i	0.712684	−	0.701485i	$-0.247479\pi$
$308$	5.95014	−	1.38738i	0.0193186	−	0.00450447i
$309$	357.869	−	239.121i	1.15815	−	0.773853i
$310$	509.157	−	272.150i	1.64244	−	0.877904i
$311$	19.1416	−	23.3241i	0.0615485	−	0.0749970i	−0.741326	−	0.671145i	$-0.765803\pi$
$311$	19.1416	−	23.3241i	0.0615485	−	0.0749970i	0.802875	+	0.596148i	$0.203303\pi$
$312$	−737.041	−	121.686i	−2.36231	−	0.390019i
$313$	−80.9238	−	80.9238i	−0.258542	−	0.258542i	0.565919	−	0.824461i	$-0.308522\pi$
$313$	−80.9238	−	80.9238i	−0.258542	−	0.258542i	−0.824461	+	0.565919i	$0.808522\pi$
$314$	368.295	−	263.916i	1.17291	−	0.840498i
$315$	87.1676	−	66.8860i	0.276722	−	0.212337i
$316$	−17.0216	−	1.11565i	−0.0538657	−	0.00353054i
$317$	−46.8224	+	124.404i	−0.147705	+	0.392442i	−0.988957	−	0.148200i	$-0.952652\pi$
$317$	−46.8224	+	124.404i	−0.147705	+	0.392442i	0.841253	+	0.540642i	$0.181819\pi$
$318$	362.969	+	242.528i	1.14141	+	0.762667i
$319$	−327.858	−	32.2912i	−1.02777	−	0.101226i
$320$	−502.082	−	227.490i	−1.56901	−	0.710908i
$321$	−419.377	−	127.217i	−1.30647	−	0.396314i
$322$	0.749481	+	11.4349i	0.00232758	+	0.0355120i
$323$	171.413	−	150.325i	0.530691	−	0.465404i
$324$	7.45938	−	18.0085i	0.0230228	−	0.0555819i
$325$	507.759	+	618.706i	1.56234	+	1.90371i
$326$	−29.3978	−	50.9186i	−0.0901775	−	0.156192i
$327$	530.043	+	306.021i	1.62093	+	0.935843i
$328$	17.3804	−	2.86952i	0.0529892	−	0.00874855i
$329$	−50.2384	−	36.0004i	−0.152700	−	0.109424i
$330$	−1017.64	+	33.3140i	−3.08375	+	0.100952i
$331$	−413.343	−	96.3782i	−1.24877	−	0.291173i	−0.450121	−	0.892968i	$-0.648619\pi$
$331$	−413.343	−	96.3782i	−1.24877	−	0.291173i	−0.798651	+	0.601795i	$0.794452\pi$
$332$	29.1948	−	10.9881i	0.0879362	−	0.0330968i
$333$	−194.756	−	642.024i	−0.584852	−	1.92800i
$334$	−208.828	−	27.4928i	−0.625235	−	0.0823137i
$335$	283.544	−	835.295i	0.846401	−	2.49342i
$336$	7.85922	+	79.7960i	0.0233905	+	0.237488i
$337$	259.688	+	138.806i	0.770589	+	0.411888i	0.809325	−	0.587361i	$-0.199833\pi$
$337$	259.688	+	138.806i	0.770589	+	0.411888i	−0.0387361	+	0.999249i	$0.512333\pi$
$338$	−414.154	+	171.548i	−1.22531	+	0.507539i
$339$	−445.663	−	219.777i	−1.31464	−	0.648308i
$340$	20.5717	−	41.7153i	0.0605050	−	0.122692i
$341$	−211.255	−	510.015i	−0.619517	−	1.49565i
$342$	−133.030	+	248.882i	−0.388977	+	0.727726i
$343$	−118.155	+	11.6373i	−0.344476	+	0.0339279i
$344$	−38.5179	−	13.0751i	−0.111971	−	0.0380089i
$345$	−22.9242	+	174.126i	−0.0664468	+	0.504714i
$346$	−89.9804	+	27.2953i	−0.260059	+	0.0788880i
$347$	206.225	+	547.926i	0.594307	+	1.57904i	0.799728	+	0.600363i	$0.204977\pi$
$347$	206.225	+	547.926i	0.594307	+	1.57904i	−0.205421	+	0.978674i	$0.565856\pi$
$348$	−7.66367	+	32.8677i	−0.0220220	+	0.0944474i
$349$	11.0543	+	337.674i	0.0316742	+	0.967548i	0.890418	+	0.455143i	$0.150412\pi$
$349$	11.0543	+	337.674i	0.0316742	+	0.967548i	−0.858744	+	0.512405i	$0.828755\pi$
$350$	54.6788	−	76.3042i	0.156225	−	0.218012i
$351$	30.5967	+	185.322i	0.0871702	+	0.527982i
$352$	−39.6129	+	68.6116i	−0.112537	+	0.194919i
$353$	387.641	−	223.805i	1.09813	−	0.634007i	0.162403	−	0.986725i	$-0.448076\pi$
$353$	387.641	−	223.805i	1.09813	−	0.634007i	0.935730	+	0.352717i	$0.114742\pi$
$354$	161.388	−	132.448i	0.455898	−	0.374146i
$355$	526.448	+	218.062i	1.48295	+	0.614259i
$356$	16.5639	+	18.8875i	0.0465278	+	0.0530547i
$357$	−94.3431	+	6.18358i	−0.264266	+	0.0173209i
$358$	40.4240	−	133.260i	0.112916	−	0.372235i
$359$	−52.6239	+	116.143i	−0.146585	+	0.323519i	−0.969678	−	0.244387i	$-0.921413\pi$
$359$	−52.6239	+	116.143i	−0.146585	+	0.323519i	0.823093	+	0.567907i	$0.192247\pi$
$360$	−72.6454	+	737.581i	−0.201793	+	2.04884i
$361$	−102.300	+	153.102i	−0.283378	+	0.424106i
$362$	−366.382	−	137.896i	−1.01210	−	0.380929i
$363$	−28.2067	+	430.352i	−0.0777045	+	1.18554i
$364$	−5.06738	−	6.60394i	−0.0139214	−	0.0181427i
$365$	582.620	+	813.045i	1.59622	+	2.22752i
$366$	555.799	−	555.799i	1.51858	−	1.51858i
$367$	−96.1803	+	582.555i	−0.262072	+	1.58734i	0.455095	+	0.890443i	$0.349605\pi$
$367$	−96.1803	+	582.555i	−0.262072	+	1.58734i	−0.717167	+	0.696902i	$0.754561\pi$
$368$	−54.6853	−	44.8790i	−0.148601	−	0.121954i
$369$	−11.0918	−	20.7513i	−0.0300590	−	0.0562365i
$370$	−518.203	−	775.545i	−1.40055	−	2.09607i
$371$	14.2199	+	60.9858i	0.0383286	+	0.164382i
$372$	−54.6253	+	14.6368i	−0.146842	+	0.0393463i
$373$	−46.7676	−	43.8027i	−0.125382	−	0.117433i	0.618375	−	0.785883i	$-0.287791\pi$
$373$	−46.7676	−	43.8027i	−0.125382	−	0.117433i	−0.743757	+	0.668450i	$0.766958\pi$
$374$	410.668	+	255.370i	1.09804	+	0.682806i
$375$	391.456	−	366.639i	1.04388	−	0.977703i
$376$	408.902	−	81.3357i	1.08751	−	0.216318i
$377$	144.276	+	425.025i	0.382696	+	1.12739i
$378$	20.0660	−	9.09177i	0.0530846	−	0.0240523i
$379$	219.684	−	28.9219i	0.579641	−	0.0763112i	0.164996	−	0.986294i	$-0.447239\pi$
$379$	219.684	−	28.9219i	0.579641	−	0.0763112i	0.414645	+	0.909983i	$0.363906\pi$
$380$	7.03921	−	35.3885i	0.0185242	−	0.0931277i
$381$	−18.8529	+	11.7235i	−0.0494828	+	0.0307704i
$382$	6.83083	−	25.4930i	0.0178817	−	0.0667356i
$383$	16.6426	−	508.380i	0.0434534	−	1.32736i	−0.725572	−	0.688146i	$-0.758425\pi$
$383$	16.6426	−	508.380i	0.0434534	−	1.32736i	0.769026	−	0.639218i	$-0.220742\pi$
$384$	−389.332	−	298.745i	−1.01389	−	0.777982i
$385$	−109.813	−	96.3033i	−0.285228	−	0.250139i
$386$	−91.2824	+	45.0155i	−0.236483	+	0.116620i
$387$			54.3324i			0.140394i
$388$	10.3615	−	30.9916i	0.0267049	−	0.0798752i
$389$	−55.7217			−0.143243			−0.0716217	−	0.997432i	$-0.522817\pi$
$389$	−55.7217			−0.143243			−0.0716217	+	0.997432i	$0.522817\pi$
$390$	613.544	+	1244.14i	1.57319	+	3.19011i
$391$	54.9999	−	62.7154i	0.140665	−	0.160397i
$392$	239.947	−	312.704i	0.612108	−	0.797715i
$393$	−723.788	−	23.6944i	−1.84170	−	0.0602910i
$394$	246.461	+	66.0389i	0.625534	+	0.167611i
$395$	215.340	+	346.295i	0.545165	+	0.876696i
$396$	53.9919	+	10.7397i	0.136343	+	0.0271203i
$397$	−70.9108	−	538.621i	−0.178617	−	1.35673i	−0.812347	−	0.583174i	$-0.801811\pi$
$397$	−70.9108	−	538.621i	−0.178617	−	1.35673i	0.633731	−	0.773554i	$-0.281523\pi$
$398$	−93.7753	−	206.967i	−0.235616	−	0.520016i
$399$	−69.4518	+	23.5757i	−0.174065	+	0.0590870i
$400$	113.057	+	568.377i	0.282643	+	1.42094i
$401$	−91.6336	−	97.8362i	−0.228513	−	0.243981i	0.605341	−	0.795967i	$-0.293037\pi$
$401$	−91.6336	−	97.8362i	−0.228513	−	0.243981i	−0.833853	+	0.551986i	$0.813870\pi$
$402$	496.146	−	797.867i	1.23419	−	1.98474i
$403$	−514.136	+	548.938i	−1.27577	+	1.36213i
$404$	0.490986	+	1.83238i	0.00121531	+	0.00453560i
$405$	−453.808	+	105.813i	−1.12051	+	0.261267i
$406$	43.7707	−	29.2466i	0.107810	−	0.0720360i
$407$	−786.567	+	420.429i	−1.93260	+	1.03299i
$408$	404.592	−	492.997i	0.991647	−	1.20833i
$409$	38.7471	+	6.39718i	0.0947363	+	0.0156410i	0.210076	−	0.977685i	$-0.432629\pi$
$409$	38.7471	+	6.39718i	0.0947363	+	0.0156410i	−0.115339	+	0.993326i	$0.536796\pi$
$410$	−23.1310	−	23.1310i	−0.0564170	−	0.0564170i
$411$	−599.215	+	429.391i	−1.45794	+	1.04475i
$412$	−25.6665	+	19.6946i	−0.0622974	+	0.0478025i
$413$	29.8852	+	1.95878i	0.0723614	+	0.00474281i
$414$	−36.3701	+	96.6331i	−0.0878505	+	0.233413i
$415$	−620.047	−	414.302i	−1.49409	−	0.998319i
$416$	107.420	+	10.5799i	0.258220	+	0.0254325i
$417$	−424.064	−	192.141i	−1.01694	−	0.460770i
$418$	358.995	+	108.900i	0.858840	+	0.260526i
$419$	−25.3080	−	386.126i	−0.0604010	−	0.921541i	−0.915307	−	0.402758i	$-0.868052\pi$
$419$	−25.3080	−	386.126i	−0.0604010	−	0.921541i	0.854906	−	0.518783i	$-0.173615\pi$
$420$	−11.2496	+	9.86561i	−0.0267847	+	0.0234895i
$421$	−124.578	+	300.757i	−0.295909	+	0.714387i	0.704082	+	0.710118i	$0.251359\pi$
$421$	−124.578	+	300.757i	−0.295909	+	0.714387i	−0.999991	+	0.00426820i	$0.998641\pi$
$422$	−179.283	−	218.457i	−0.424841	−	0.517670i
$423$	−278.438	−	482.269i	−0.658247	−	1.14012i
$424$	−365.825	−	211.209i	−0.862794	−	0.498134i
$425$	−674.197	+	111.310i	−1.58635	+	0.261907i
$426$	493.340	+	353.522i	1.15807	+	0.829865i
$427$	112.694	−	3.68923i	0.263921	−	0.00863988i
$428$	32.0809	+	7.48022i	0.0749554	+	0.0174771i
$429$	1241.42	−	467.236i	2.89374	−	1.08913i
$430$	21.9269	+	72.2833i	0.0509928	+	0.168101i
$431$	263.421	+	34.6800i	0.611186	+	0.0804641i	0.429764	−	0.902941i	$-0.358597\pi$
$431$	263.421	+	34.6800i	0.611186	+	0.0804641i	0.181422	+	0.983405i	$0.441930\pi$
$432$	−43.7148	+	128.780i	−0.101192	+	0.298101i
$433$	25.6834	+	260.768i	0.0593150	+	0.602236i	0.978194	+	0.207695i	$0.0665962\pi$
$433$	25.6834	+	260.768i	0.0593150	+	0.602236i	−0.918879	+	0.394541i	$0.870904\pi$
$434$	77.7950	+	41.5823i	0.179251	+	0.0958117i
$435$	745.394	−	308.752i	1.71355	−	0.709775i
$436$	−41.2605	−	20.3474i	−0.0946341	−	0.0466684i
$437$	28.6206	−	58.0369i	0.0654934	−	0.132807i
$438$	407.702	+	984.280i	0.930827	+	2.24722i
$439$	−209.479	+	391.908i	−0.477173	+	0.892728i	0.522034	+	0.852924i	$0.325173\pi$
$439$	−209.479	+	391.908i	−0.477173	+	0.892728i	−0.999208	+	0.0398036i	$0.987327\pi$
$440$	980.504	−	96.5712i	2.22842	−	0.219480i
$441$	−498.539	−	169.231i	−1.13047	−	0.383744i
$442$	85.9984	−	653.223i	0.194567	−	1.47788i
$443$	211.646	−	64.2021i	0.477756	−	0.144926i	−0.0422169	−	0.999108i	$-0.513442\pi$
$443$	211.646	−	64.2021i	0.477756	−	0.144926i	0.519973	+	0.854183i	$0.325942\pi$
$444$	32.1840	+	85.5108i	0.0724864	+	0.192592i
$445$	136.372	−	584.868i	0.306454	−	1.31431i
$446$	9.29079	+	283.804i	0.0208314	+	0.636333i
$447$	−90.9008	+	126.852i	−0.203358	+	0.283785i
$448$	−13.7192	−	83.0961i	−0.0306233	−	0.185482i
$449$	108.957	−	188.718i	0.242665	−	0.420308i	−0.718807	−	0.695209i	$-0.755312\pi$
$449$	108.957	−	188.718i	0.242665	−	0.420308i	0.961473	+	0.274901i	$0.0886450\pi$
$450$	732.490	−	422.904i	1.62776	−	0.939786i
$451$	−24.1791	+	19.8433i	−0.0536121	+	0.0439983i
$452$	34.5075	+	14.2935i	0.0763440	+	0.0316227i
$453$	−233.731	−	266.519i	−0.515962	−	0.588342i
$454$	603.341	−	39.5450i	1.32894	−	0.0871036i
$455$	−57.7651	+	190.426i	−0.126956	+	0.418519i
$456$	204.186	−	450.647i	0.447775	−	0.988261i
$457$	−19.9573	+	202.630i	−0.0436702	+	0.443391i	0.948342	+	0.317250i	$0.102759\pi$
$457$	−19.9573	+	202.630i	−0.0436702	+	0.443391i	−0.992012	+	0.126141i	$0.959741\pi$
$458$	−267.608	+	400.504i	−0.584297	+	0.874463i
$459$	−150.081	−	56.4865i	−0.326974	−	0.123064i
$460$	0.863409	−	13.1731i	0.00187698	−	0.0286371i
$461$	−330.447	−	430.647i	−0.716805	−	0.934159i	0.282882	−	0.959155i	$-0.408709\pi$
$461$	−330.447	−	430.647i	−0.716805	−	0.934159i	−0.999688	+	0.0249959i	$0.992043\pi$
$462$	−90.6160	−	126.455i	−0.196139	−	0.273711i
$463$	159.536	−	159.536i	0.344571	−	0.344571i	−0.513511	−	0.858083i	$-0.671656\pi$
$463$	159.536	−	159.536i	0.344571	−	0.344571i	0.858083	+	0.513511i	$0.171656\pi$
$464$	−52.9381	+	320.642i	−0.114091	+	0.691038i
$465$	1045.06	+	857.657i	2.24744	+	1.84442i
$466$	114.437	+	214.096i	0.245572	+	0.459433i
$467$	172.022	+	257.449i	0.368355	+	0.551282i	0.968629	−	0.248512i	$-0.0799416\pi$
$467$	172.022	+	257.449i	0.368355	+	0.551282i	−0.600274	+	0.799795i	$0.704942\pi$
$468$	−17.0310	−	73.0419i	−0.0363910	−	0.156072i
$469$	130.186	−	34.8833i	0.277583	−	0.0743780i
$470$	−565.061	−	529.237i	−1.20226	−	1.12604i
$471$	901.014	+	560.286i	1.91298	+	1.18957i
$472$	−147.451	+	138.103i	−0.312396	+	0.292591i
$473$	70.8390	−	14.0908i	0.149765	−	0.0297902i
$474$	139.615	+	411.292i	0.294546	+	0.867705i
$475$	−482.841	+	218.772i	−1.01651	+	0.460574i
$476$	7.04583	−	0.927601i	0.0148022	−	0.00194874i
$477$	−110.076	+	553.388i	−0.230767	+	1.16014i
$478$	449.278	−	279.379i	0.939912	−	0.584475i
$479$	133.535	−	498.359i	0.278779	−	1.04042i	−0.674488	−	0.738286i	$-0.735636\pi$
$479$	133.535	−	498.359i	0.278779	−	1.04042i	0.953267	−	0.302130i	$-0.0976977\pi$
$480$	6.34827	−	193.920i	0.0132256	−	0.403999i
$481$	964.020	+	739.719i	2.00420	+	1.53788i
$482$	651.123	+	571.020i	1.35088	+	1.18469i
$483$	−24.0672	+	11.8686i	−0.0498286	+	0.0245728i
$484$		−	32.4173i		−	0.0669779i
$485$	−746.503	+	230.204i	−1.53918	+	0.474648i
$486$	−657.450			−1.35278
$487$	46.4426	+	94.1762i	0.0953646	+	0.193380i	0.939328	−	0.343021i	$-0.111450\pi$
$487$	46.4426	+	94.1762i	0.0953646	+	0.193380i	−0.843963	+	0.536401i	$0.819783\pi$
$488$	−501.493	+	571.844i	−1.02765	+	1.17181i
$489$	83.8158	−	109.231i	0.171402	−	0.223376i
$490$	−731.548	−	23.9484i	−1.49296	−	0.0488743i
$491$	−53.6331	−	14.3709i	−0.109232	−	0.0292687i	0.203789	−	0.979015i	$-0.434674\pi$
$491$	−53.6331	−	14.3709i	−0.109232	−	0.0292687i	−0.313021	+	0.949746i	$0.601341\pi$
$492$	1.69210	+	2.72112i	0.00343923	+	0.00553073i
$493$	−375.835	−	74.7583i	−0.762343	−	0.151639i
$494$	−66.7137	−	506.741i	−0.135048	−	1.02579i
$495$	−543.127	−	1198.71i	−1.09723	−	2.42163i
$496$	−515.659	+	175.043i	−1.03964	+	0.352909i
$497$	16.9854	+	85.3912i	0.0341758	+	0.171813i
$498$	−542.967	−	579.720i	−1.09029	−	1.16410i
$499$	118.256	−	190.171i	0.236986	−	0.381105i	−0.709054	−	0.705154i	$-0.750878\pi$
$499$	118.256	−	190.171i	0.236986	−	0.381105i	0.946040	+	0.324049i	$0.105044\pi$
$500$	−27.5588	+	29.4243i	−0.0551177	+	0.0588485i
$501$	−127.659	−	476.429i	−0.254808	−	0.950956i
$502$	308.693	−	71.9772i	0.614927	−	0.143381i
$503$	98.1314	−	65.5693i	0.195092	−	0.130357i	−0.454188	−	0.890906i	$-0.650070\pi$
$503$	98.1314	−	65.5693i	0.195092	−	0.130357i	0.649280	+	0.760550i	$0.275070\pi$
$504$	−99.8701	+	53.3817i	−0.198155	+	0.105916i
$505$	28.7698	−	35.0561i	0.0569698	−	0.0694179i
$506$	135.423	+	22.3585i	0.267635	+	0.0441867i
$507$	−742.274	−	742.274i	−1.46405	−	1.46405i
$508$	1.35644	−	0.972008i	0.00267015	−	0.00191340i
$509$	−478.371	+	367.067i	−0.939825	+	0.721153i	−0.960397	−	0.278635i	$-0.910118\pi$
$509$	−478.371	+	367.067i	−0.939825	+	0.721153i	0.0205718	+	0.999788i	$0.493451\pi$
$510$	−1181.78	−	77.4579i	−2.31721	−	0.151878i
$511$	−53.8340	+	143.033i	−0.105350	+	0.279909i
$512$	466.350	+	311.605i	0.910840	+	0.608604i
$513$	−123.800	−	12.1933i	−0.241326	−	0.0237685i
$514$	407.546	+	184.657i	0.792890	+	0.359254i
$515$	740.101	+	224.507i	1.43709	+	0.435936i
$516$	−0.483927	−	7.38329i	−0.000937842	−	0.0143087i
$517$	−556.576	+	488.104i	−1.07655	+	0.944108i
$518$	54.5381	−	131.667i	0.105286	−	0.254182i
$519$	−139.687	−	170.209i	−0.269146	−	0.327955i
$520$	−671.165	−	1162.49i	−1.29070	−	2.23556i
$521$	−482.958	−	278.836i	−0.926983	−	0.535194i	−0.0411269	−	0.999154i	$-0.513095\pi$
$521$	−482.958	−	278.836i	−0.926983	−	0.535194i	−0.885856	+	0.463960i	$0.846428\pi$
$522$	467.981	−	77.2640i	0.896516	−	0.148015i
$523$	−425.010	−	304.558i	−0.812638	−	0.582328i	0.0981643	−	0.995170i	$-0.468703\pi$
$523$	−425.010	−	304.558i	−0.812638	−	0.582328i	−0.910803	+	0.412842i	$0.864536\pi$
$524$	54.4044	−	1.78101i	0.103825	−	0.00339888i
$525$	214.080	+	49.9166i	0.407772	+	0.0950791i
$526$	−688.621	+	259.178i	−1.30916	+	0.492735i
$527$	−186.394	−	614.459i	−0.353689	−	1.16596i
$528$	952.176	+	125.356i	1.80336	+	0.237417i
$529$	−162.431	+	478.507i	−0.307053	+	0.904550i
$530$	76.8869	+	780.646i	0.145070	+	1.47292i
$531$	237.985	+	127.205i	0.448182	+	0.239558i
$532$	5.09335	−	2.10973i	0.00957396	−	0.00396566i
$533$	38.2207	+	18.8484i	0.0717086	+	0.0353628i
$534$	282.916	−	573.697i	0.529805	−	1.07434i
$535$	−301.361	−	727.550i	−0.563292	−	1.35991i
$536$	−428.574	+	801.805i	−0.799578	+	1.49591i
$537$	324.528	−	31.9632i	0.604335	−	0.0595218i
$538$	−631.051	−	214.213i	−1.17296	−	0.398166i
$539$	−91.3521	+	693.888i	−0.169484	+	1.28736i
$540$	−24.2855	+	7.36694i	−0.0449732	+	0.0136425i
$541$	114.077	+	303.095i	0.210863	+	0.560250i	0.998432	−	0.0559767i	$-0.0178273\pi$
$541$	114.077	+	303.095i	0.210863	+	0.560250i	−0.787569	+	0.616226i	$0.788661\pi$
$542$	−113.853	+	488.288i	−0.210060	+	0.900900i
$543$	−29.9941	−	916.225i	−0.0552377	−	1.68734i
$544$	−53.6768	+	74.9059i	−0.0986706	+	0.137695i
$545$	179.150	+	1085.10i	0.328716	+	1.99100i
$546$	−105.976	+	183.557i	−0.194096	+	0.336184i
$547$	318.063	−	183.634i	0.581468	−	0.335711i	−0.180249	−	0.983621i	$-0.557690\pi$
$547$	318.063	−	183.634i	0.581468	−	0.335711i	0.761717	+	0.647910i	$0.224357\pi$
$548$	42.8333	−	35.1524i	0.0781630	−	0.0641467i
$549$	938.601	+	388.781i	1.70966	+	0.708163i
$550$	−741.352	−	845.350i	−1.34791	−	1.53700i
$551$	−296.631	+	19.4422i	−0.538351	+	0.0352854i
$552$	52.5457	−	173.220i	0.0951914	−	0.313804i
$553$	−25.7144	+	56.7529i	−0.0464998	+	0.102627i
$554$	−81.2155	+	824.594i	−0.146598	+	1.48844i
$555$	1213.48	−	1816.10i	2.18645	−	3.27225i
$556$	32.7516	+	12.3268i	0.0589058	+	0.0221706i
$557$	7.08236	−	108.056i	0.0127152	−	0.193996i	−0.986776	−	0.162092i	$-0.948176\pi$
$557$	7.08236	−	108.056i	0.0127152	−	0.193996i	0.999491	−	0.0319047i	$-0.0101573\pi$
$558$	483.838	+	630.550i	0.867094	+	1.13002i
$559$	−57.3180	−	79.9872i	−0.102537	−	0.143090i
$560$	−101.880	+	101.880i	−0.181929	+	0.181929i
$561$	−184.468	+	1117.31i	−0.328820	+	1.99164i
$562$	214.691	+	176.192i	0.382012	+	0.313509i
$563$	−293.289	−	548.704i	−0.520939	−	0.974608i	−0.995534	−	0.0944037i	$-0.969906\pi$
$563$	−293.289	−	548.704i	−0.520939	−	0.974608i	0.474595	−	0.880204i	$-0.342594\pi$
$564$	42.1328	+	63.0562i	0.0747035	+	0.111802i
$565$	−202.757	−	869.575i	−0.358861	−	1.53907i
$566$	645.858	−	173.057i	1.14109	−	0.305755i
$567$	−51.9648	−	48.6704i	−0.0916487	−	0.0858384i
$568$	−498.733	−	310.132i	−0.878051	−	0.546007i
$569$	−176.629	+	165.431i	−0.310421	+	0.290741i	−0.823167	−	0.567800i	$-0.807795\pi$
$569$	−176.629	+	165.431i	−0.310421	+	0.290741i	0.512746	+	0.858540i	$0.328628\pi$
$570$	−901.084	+	179.237i	−1.58085	+	0.314450i
$571$	−99.0151	−	291.689i	−0.173407	−	0.510839i	0.825129	−	0.564945i	$-0.191103\pi$
$571$	−99.0151	−	291.689i	−0.173407	−	0.510839i	−0.998535	+	0.0541057i	$0.982769\pi$
$572$	−90.8157	+	41.1481i	−0.158769	+	0.0719372i
$573$	61.2743	−	8.06692i	0.106936	−	0.0140784i
$574$	0.975089	−	4.90210i	0.00169876	−	0.00854025i
$575$	−164.699	+	102.417i	−0.286433	+	0.178116i
$576$	196.403	−	732.987i	0.340978	−	1.27255i
$577$	−10.9319	+	333.936i	−0.0189462	+	0.578746i	0.947184	+	0.320691i	$0.103915\pi$
$577$	−10.9319	+	333.936i	−0.0189462	+	0.578746i	−0.966130	+	0.258055i	$0.916918\pi$
$578$	7.43538	+	5.70536i	0.0128640	+	0.00987087i
$579$	−179.190	−	157.146i	−0.309483	−	0.271409i
$580$	−54.3906	+	26.8225i	−0.0937769	+	0.0462456i
$581$		−	113.940i		−	0.196111i
$582$	−830.021	+	58.2379i	−1.42615	+	0.100065i
$583$	750.060			1.28655
$584$	−455.962	−	924.600i	−0.780757	−	1.58322i
$585$	−1182.19	+	1348.03i	−2.02083	+	2.30432i
$586$	217.450	−	283.386i	0.371075	−	0.483594i
$587$	−62.0820	−	2.03235i	−0.105761	−	0.00346227i	−0.0202075	−	0.999796i	$-0.506433\pi$
$587$	−62.0820	−	2.03235i	−0.105761	−	0.00346227i	−0.0855540	+	0.996334i	$0.527266\pi$
$588$	69.2544	+	18.5567i	0.117780	+	0.0315589i
$589$	−263.040	−	423.003i	−0.446588	−	0.718172i
$590$	367.949	+	73.1896i	0.623642	+	0.124050i
$591$	77.9892	+	592.386i	0.131961	+	1.00235i
$592$	363.099	+	801.376i	0.613343	+	1.35368i
$593$	−70.3382	+	23.8766i	−0.118614	+	0.0402641i	−0.380115	−	0.924939i	$-0.624116\pi$
$593$	−70.3382	+	23.8766i	−0.118614	+	0.0402641i	0.261501	+	0.965203i	$0.415782\pi$
$594$	−51.4771	−	258.793i	−0.0866617	−	0.435678i
$595$	−116.136	−	123.997i	−0.195186	−	0.208398i
$596$	6.19442	−	9.96144i	0.0103933	−	0.0167138i
$597$	363.728	−	388.349i	0.609260	−	0.650500i
$598$	−48.3997	−	180.630i	−0.0809360	−	0.302057i
$599$	724.789	−	168.997i	1.21000	−	0.282132i	0.427056	−	0.904225i	$-0.359551\pi$
$599$	724.789	−	168.997i	1.21000	−	0.282132i	0.782943	+	0.622093i	$0.213717\pi$
$600$	−1232.93	+	823.815i	−2.05488	+	1.37302i
$601$	754.216	−	403.137i	1.25494	−	0.670777i	0.296214	−	0.955122i	$-0.404276\pi$
$601$	754.216	−	403.137i	1.25494	−	0.670777i	0.958722	+	0.284345i	$0.0917759\pi$
$602$	−7.32169	+	8.92150i	−0.0121623	+	0.0148198i
$603$	1198.16	+	197.816i	1.98699	+	0.328053i
$604$	18.8413	+	18.8413i	0.0311942	+	0.0311942i
$605$	−629.928	+	451.400i	−1.04120	+	0.746115i
$606$	38.3215	−	29.4051i	0.0632367	−	0.0485233i
$607$	−719.499	−	47.1585i	−1.18534	−	0.0776910i	−0.540051	−	0.841633i	$-0.681595\pi$
$607$	−719.499	−	47.1585i	−1.18534	−	0.0776910i	−0.645286	+	0.763941i	$0.723262\pi$
$608$	−25.1816	+	66.9058i	−0.0414170	+	0.110042i
$609$	102.498	+	68.4871i	0.168306	+	0.112458i
$610$	1405.61	+	138.440i	2.30427	+	0.226951i
$611$	918.683	+	416.250i	1.50357	+	0.681260i
$612$	61.2745	+	18.5874i	0.100122	+	0.0303716i
$613$	24.1721	+	368.795i	0.0394325	+	0.601623i	0.971155	+	0.238451i	$0.0766397\pi$
$613$	24.1721	+	368.795i	0.0394325	+	0.601623i	−0.931722	+	0.363172i	$0.881694\pi$
$614$	435.689	−	382.089i	0.709592	−	0.622295i
$615$	29.3144	−	70.7713i	0.0476658	−	0.115075i
$616$	95.5001	+	116.367i	0.155033	+	0.188908i
$617$	382.770	+	662.977i	0.620373	+	1.07452i	0.989416	+	0.145105i	$0.0463520\pi$
$617$	382.770	+	662.977i	0.620373	+	1.07452i	−0.369044	+	0.929412i	$0.620315\pi$
$618$	713.402	+	411.883i	1.15437	+	0.666477i
$619$	85.4825	−	14.1132i	0.138098	−	0.0228000i	−0.0934472	−	0.995624i	$-0.529789\pi$
$619$	85.4825	−	14.1132i	0.138098	−	0.0228000i	0.231545	+	0.972824i	$0.425622\pi$
$620$	−82.6012	−	59.1912i	−0.133228	−	0.0954697i
$621$	−45.4899	+	1.48918i	−0.0732526	+	0.00239804i
$622$	56.2404	+	13.1134i	0.0904187	+	0.0210827i
$623$	85.8787	−	32.3225i	0.137847	−	0.0518820i
$624$	−379.827	−	1252.12i	−0.608698	−	2.00661i
$625$	−32.4416	−	4.27102i	−0.0519066	−	0.00683363i
$626$	70.4070	−	207.412i	0.112471	−	0.331329i
$627$	86.1070	+	874.260i	0.137332	+	1.39435i
$628$	−70.3352	−	37.5949i	−0.111999	−	0.0598645i
$629$	−958.434	+	396.996i	−1.52374	+	0.631155i
$630$	188.601	+	93.0078i	0.299367	+	0.147631i
$631$	−249.165	+	505.256i	−0.394873	+	0.800723i	0.605117	+	0.796137i	$0.293126\pi$
$631$	−249.165	+	505.256i	−0.394873	+	0.800723i	−0.999989	+	0.00458601i	$0.998540\pi$
$632$	−160.839	−	388.300i	−0.254492	−	0.614399i
$633$	311.961	−	583.638i	0.492829	−	0.922018i
$634$	−253.181	+	24.9362i	−0.399340	+	0.0393315i
$635$	−37.7758	−	12.8231i	−0.0594894	−	0.0201939i
$636$	10.0294	−	76.1811i	0.0157695	−	0.119782i
$637$	912.471	−	276.795i	1.43245	−	0.434529i
$638$	−222.105	−	590.120i	−0.348128	−	0.924953i
$639$	−178.132	+	763.968i	−0.278767	+	1.19557i
$640$	−28.8524	−	881.350i	−0.0450819	−	1.37711i
$641$	−129.923	+	181.308i	−0.202688	+	0.282851i	−0.901793	−	0.432168i	$-0.857749\pi$
$641$	−129.923	+	181.308i	−0.202688	+	0.282851i	0.699105	+	0.715019i	$0.253582\pi$
$642$	−136.633	−	827.571i	−0.212823	−	1.28905i
$643$	445.473	−	771.582i	0.692804	−	1.19997i	−0.278112	−	0.960549i	$-0.589709\pi$
$643$	445.473	−	771.582i	0.692804	−	1.19997i	0.970915	−	0.239423i	$-0.0769581\pi$
$644$	1.74682	−	1.00853i	0.00271245	−	0.00156604i
$645$	−136.732	+	112.213i	−0.211988	+	0.173974i
$646$	403.144	+	166.988i	0.624061	+	0.258495i
$647$	714.965	+	815.262i	1.10505	+	1.26006i	0.962795	+	0.270234i	$0.0871011\pi$
$647$	714.965	+	815.262i	1.10505	+	1.26006i	0.142252	+	0.989830i	$0.454566\pi$
$648$	479.241	−	31.4111i	0.739570	−	0.0484740i
$649$	104.132	−	343.276i	0.160449	−	0.528931i
$650$	−632.217	+	1395.33i	−0.972642	+	2.14667i
$651$	−20.2468	+	205.569i	−0.0311011	+	0.315775i
$652$	−5.74963	+	8.60493i	−0.00881845	+	0.0131978i
$653$	890.135	+	335.023i	1.36315	+	0.513052i	0.922974	−	0.384862i	$-0.125751\pi$
$653$	890.135	+	335.023i	1.36315	+	0.513052i	0.440172	+	0.897913i	$0.354917\pi$
$654$	−76.6134	+	1168.89i	−0.117146	+	1.78730i
$655$	−792.170	−	1032.38i	−1.20942	−	1.57615i
$656$	17.9726	+	25.0807i	0.0273972	+	0.0382328i
$657$	−973.692	+	973.692i	−1.48203	+	1.48203i
$658$	19.2691	−	116.711i	0.0292844	−	0.177373i
$659$	−19.2791	−	15.8219i	−0.0292550	−	0.0240090i	0.619652	−	0.784877i	$-0.287274\pi$
$659$	−19.2791	−	15.8219i	−0.0292550	−	0.0240090i	−0.648907	+	0.760868i	$0.724774\pi$
$660$	84.4828	+	158.056i	0.128004	+	0.239479i
$661$	207.512	+	310.564i	0.313936	+	0.469839i	0.954561	−	0.298015i	$-0.0963245\pi$
$661$	207.512	+	310.564i	0.313936	+	0.469839i	−0.640625	+	0.767854i	$0.721325\pi$
$662$	−184.461	−	791.109i	−0.278642	−	1.19503i
$663$	1490.29	−	399.321i	2.24779	−	0.602294i
$664$	560.967	+	525.403i	0.844831	+	0.791270i
$665$	−111.919	−	69.5958i	−0.168299	−	0.104655i
$666$	937.203	−	877.786i	1.40721	−	1.31800i
$667$	−106.672	+	21.2184i	−0.159928	+	0.0318117i
$668$	11.9172	+	35.1071i	0.0178402	+	0.0525555i
$669$	−605.673	+	274.427i	−0.905341	+	0.410204i
$670$	1673.85	−	220.366i	2.49828	−	0.328905i
$671$	263.476	−	1324.58i	0.392662	−	1.97404i
$672$	25.1747	−	15.6547i	0.0374624	−	0.0232956i
$673$	32.9221	−	122.867i	0.0489184	−	0.182566i	−0.937144	−	0.348944i	$-0.886540\pi$
$673$	32.9221	−	122.867i	0.0489184	−	0.182566i	0.986062	+	0.166378i	$0.0532071\pi$
$674$	−18.4395	+	563.269i	−0.0273583	+	0.835710i
$675$	295.796	+	226.972i	0.438216	+	0.336255i
$676$	59.3235	+	52.0253i	0.0877567	+	0.0769606i
$677$	1130.80	−	557.647i	1.67030	−	0.823702i	0.673913	−	0.738810i	$-0.264612\pi$
$677$	1130.80	−	557.647i	1.67030	−	0.823702i	0.996390	−	0.0848920i	$-0.0270545\pi$
$678$		−	951.044i		−	1.40272i
$679$	−92.6135	−	75.2957i	−0.136397	−	0.110892i
$680$	1146.01			1.68530
$681$	626.228	+	1269.86i	0.919571	+	1.86471i
$682$	696.636	−	794.362i	1.02146	−	1.16475i
$683$	−594.561	+	774.848i	−0.870515	+	1.13448i	0.119405	+	0.992846i	$0.461901\pi$
$683$	−594.561	+	774.848i	−0.870515	+	1.13448i	−0.989920	+	0.141631i	$0.954765\pi$
$684$	49.6463	+	1.62525i	0.0725823	+	0.00237610i
$685$	−1279.52	−	342.845i	−1.86791	−	0.500504i
$686$	−119.995	−	192.968i	−0.174920	−	0.281295i
$687$	−1106.29	−	220.054i	−1.61031	−	0.320311i
$688$	−9.29979	−	70.6389i	−0.0135171	−	0.102673i
$689$	−421.746	−	930.814i	−0.612114	−	1.35096i
$690$	−318.302	+	108.049i	−0.461307	+	0.156593i
$691$	−118.531	−	595.897i	−0.171536	−	0.862368i	−0.966688	−	0.255958i	$-0.917609\pi$
$691$	−118.531	−	595.897i	−0.171536	−	0.862368i	0.795152	−	0.606410i	$-0.207391\pi$
$692$	11.3140	+	12.0798i	0.0163497	+	0.0174564i
$693$	106.181	−	170.754i	0.153220	−	0.246398i
$694$	−765.970	+	817.818i	−1.10370	+	1.17841i
$695$	−216.522	−	808.071i	−0.311542	−	1.16269i
$696$	−809.826	+	188.825i	−1.16354	+	0.271300i
$697$	−30.2511	+	20.2132i	−0.0434019	+	0.0290002i
$698$	−570.277	+	304.819i	−0.817015	+	0.436704i
$699$	−360.637	+	439.437i	−0.515932	+	0.628665i
$700$	−16.3026	−	2.69156i	−0.0232894	−	0.00384509i
$701$	−757.031	−	757.031i	−1.07993	−	1.07993i	−0.996515	−	0.0834159i	$-0.973417\pi$
$701$	−757.031	−	757.031i	−1.07993	−	1.07993i	−0.0834159	−	0.996515i	$-0.526583\pi$
$702$	−292.213	+	209.397i	−0.416258	+	0.298287i
$703$	−638.466	+	489.912i	−0.908202	+	0.696888i
$704$	−1006.61	−	65.9767i	−1.42984	−	0.0937169i
$705$	638.613	−	1696.75i	0.905834	−	2.40674i
$706$	712.313	+	475.952i	1.00894	+	0.674153i
$707$	6.89574	+	0.679171i	0.00975352	+	0.000960638i
$708$	−33.4730	−	15.1664i	−0.0472783	−	0.0214215i
$709$	−901.345	−	273.420i	−1.27129	−	0.385642i	−0.418654	−	0.908146i	$-0.637498\pi$
$709$	−901.345	−	273.420i	−1.27129	−	0.385642i	−0.852637	+	0.522504i	$0.824998\pi$
$710$	71.3286	+	1088.26i	0.100463	+	1.53277i
$711$	−422.077	+	370.151i	−0.593638	+	0.520607i
$712$	−236.870	+	571.856i	−0.332683	+	0.803168i
$713$	−115.617	−	140.879i	−0.162155	−	0.197587i
$714$	−90.4766	−	156.710i	−0.126718	−	0.219482i
$715$	2064.16	+	1191.74i	2.88694	+	1.66677i
$716$	−24.1841	+	3.99282i	−0.0337767	+	0.00557656i
$717$	1007.04	+	721.633i	1.40452	+	1.00646i
$718$	−243.912	+	7.98487i	−0.339711	+	0.0111210i
$719$	−944.484	−	220.223i	−1.31361	−	0.306290i	−0.489143	−	0.872204i	$-0.662690\pi$
$719$	−944.484	−	220.223i	−1.31361	−	0.306290i	−0.824465	+	0.565913i	$0.808524\pi$
$720$	−1214.98	+	457.286i	−1.68747	+	0.635119i
$721$	34.3028	+	113.081i	0.0475767	+	0.156839i
$722$	−349.405	−	46.0000i	−0.483940	−	0.0637119i
$723$	−651.883	+	1920.39i	−0.901637	+	2.65614i
$724$	6.75397	+	68.5742i	0.00932869	+	0.0947157i
$725$	785.751	+	419.993i	1.08379	+	0.579300i
$726$	−762.597	+	315.878i	−1.05041	+	0.435094i
$727$	1114.92	+	549.819i	1.53359	+	0.756285i	0.996204	−	0.0870480i	$-0.0277433\pi$
$727$	1114.92	+	549.819i	1.53359	+	0.756285i	0.537391	+	0.843333i	$0.319410\pi$
$728$	90.7120	−	183.946i	0.124604	−	0.252673i
$729$	−389.882	−	941.260i	−0.534818	−	1.29117i
$730$	−902.439	+	1688.34i	−1.23622	+	2.31280i
$731$	83.6071	−	8.23458i	0.114374	−	0.0112648i
$732$	−131.010	−	44.4721i	−0.178976	−	0.0607542i
$733$	−7.49351	+	56.9189i	−0.0102231	+	0.0776519i	−0.995796	−	0.0916001i	$-0.970802\pi$
$733$	−7.49351	+	56.9189i	−0.0102231	+	0.0776519i	0.985573	+	0.169252i	$0.0541352\pi$
$734$	−1081.40	+	328.040i	−1.47330	+	0.446921i
$735$	−603.753	−	1604.13i	−0.821433	−	2.18250i
$736$	−5.93927	+	25.4721i	−0.00806966	+	0.0346089i
$737$	−52.8194	−	1613.47i	−0.0716682	−	2.18924i
$738$	26.2313	−	36.6057i	0.0355437	−	0.0496012i
$739$	−150.811	−	913.450i	−0.204075	−	1.23606i	−0.871130	−	0.491053i	$-0.836612\pi$
$739$	−150.811	−	913.450i	−0.204075	−	1.23606i	0.667055	−	0.745009i	$-0.267555\pi$
$740$	−82.0892	+	142.183i	−0.110931	+	0.192139i
$741$	1036.53	−	598.439i	1.39882	−	0.807610i
$742$	−92.6478	+	76.0341i	−0.124862	+	0.102472i
$743$	578.061	+	239.441i	0.778010	+	0.322262i	0.736112	−	0.676860i	$-0.236660\pi$
$743$	578.061	+	239.441i	0.778010	+	0.322262i	0.0418978	+	0.999122i	$0.486660\pi$
$744$	−918.725	−	1047.61i	−1.23485	−	1.40807i
$745$	−279.824	+	18.3406i	−0.375603	+	0.0246183i
$746$	35.6002	−	117.358i	0.0477215	−	0.157317i
$747$	423.693	−	935.110i	0.567193	−	1.25182i
$748$	8.34328	−	84.7108i	0.0111541	−	0.113250i
$749$	66.8476	−	100.045i	0.0892492	−	0.133571i
$750$	960.724	+	361.591i	1.28097	+	0.482121i
$751$	−19.9982	+	305.113i	−0.0266288	+	0.406276i	0.963649	+	0.267172i	$0.0860891\pi$
$751$	−19.9982	+	305.113i	−0.0266288	+	0.406276i	−0.990278	+	0.139105i	$0.955578\pi$
$752$	444.552	+	579.352i	0.591160	+	0.770415i
$753$	432.350	+	603.344i	0.574170	+	0.801253i
$754$	−607.444	+	607.444i	−0.805629	+	0.805629i
$755$	103.762	−	628.479i	0.137433	−	0.832422i
$756$	−2.99742	−	2.45992i	−0.00396484	−	0.00325386i
$757$	−236.453	−	442.372i	−0.312355	−	0.584375i	0.675935	−	0.736961i	$-0.263740\pi$
$757$	−236.453	−	442.372i	−0.312355	−	0.584375i	−0.988290	+	0.152586i	$0.951240\pi$
$758$	235.610	+	352.616i	0.310831	+	0.465192i
$759$	72.9858	+	313.019i	0.0961604	+	0.412410i
$760$	858.726	−	230.095i	1.12990	−	0.302756i
$761$	−140.327	−	131.431i	−0.184398	−	0.172708i	0.585917	−	0.810371i	$-0.300735\pi$
$761$	−140.327	−	131.431i	−0.184398	−	0.172708i	−0.770315	+	0.637663i	$0.779901\pi$
$762$	−36.0831	−	22.4379i	−0.0473532	−	0.0294461i
$763$	−122.645	+	114.870i	−0.160741	+	0.150550i
$764$	−4.55624	+	0.906292i	−0.00596366	+	0.00118625i
$765$	−492.039	−	1449.50i	−0.643188	−	1.89477i
$766$	886.748	−	401.780i	1.15763	−	0.524517i
$767$	−484.553	+	63.7926i	−0.631750	+	0.0831715i
$768$	−56.1432	+	282.251i	−0.0731032	+	0.367515i
$769$	130.069	−	80.8820i	0.169140	−	0.105178i	−0.440873	−	0.897570i	$-0.645331\pi$
$769$	130.069	−	80.8820i	0.169140	−	0.105178i	0.610013	+	0.792392i	$0.291164\pi$
$770$	72.3518	−	270.021i	0.0939634	−	0.350676i
$771$	−34.2813	+	1047.18i	−0.0444634	+	1.35822i
$772$	14.2128	+	10.9058i	0.0184103	+	0.0141267i
$773$	788.384	+	691.394i	1.01990	+	0.894429i	0.994446	−	0.105247i	$-0.0335632\pi$
$773$	788.384	+	691.394i	1.01990	+	0.894429i	0.0254550	+	0.999676i	$0.491897\pi$
$774$	−93.2642	+	45.9928i	−0.120496	+	0.0594222i
$775$			1492.93i			1.92636i
$776$	797.766	−	108.763i	1.02805	−	0.140159i
$777$	333.728			0.429509
$778$	−47.1689	−	95.6490i	−0.0606284	−	0.122942i
$779$	−18.6094	+	21.2200i	−0.0238888	+	0.0272400i
$780$	148.642	−	193.714i	0.190567	−	0.248352i
$781$	1042.26	+	34.1202i	1.33453	+	0.0436879i
$782$	154.212	+	41.3210i	0.197202	+	0.0528401i
$783$	110.411	+	177.555i	0.141010	+	0.226763i
$784$	677.130	+	134.689i	0.863686	+	0.171798i
$785$	248.855	+	1890.24i	0.317012	+	2.40795i
$786$	−572.020	−	1262.47i	−0.727760	−	1.60620i
$787$	1346.08	−	456.933i	1.71040	−	0.580601i	0.717180	−	0.696888i	$-0.245433\pi$
$787$	1346.08	−	456.933i	1.71040	−	0.580601i	0.993216	+	0.116287i	$0.0370994\pi$
$788$	−8.76183	−	44.0487i	−0.0111191	−	0.0558994i
$789$	−1177.82	−	1257.54i	−1.49280	−	1.59384i
$790$	−412.145	+	662.783i	−0.521703	+	0.838966i
$791$	93.2609	−	99.5737i	0.117903	−	0.125883i
$792$	351.053	+	1310.15i	0.443249	+	1.65423i
$793$	−1791.94	+	417.821i	−2.25970	+	0.526887i
$794$	864.542	−	577.669i	1.08884	−	0.727543i
$795$	−1619.99	+	865.905i	−2.03773	+	1.08919i
$796$	−25.3724	+	30.9163i	−0.0318748	+	0.0388396i
$797$	−966.148	−	159.512i	−1.21223	−	0.200140i	−0.477582	−	0.878587i	$-0.658487\pi$
$797$	−966.148	−	159.512i	−1.21223	−	0.200140i	−0.734649	+	0.678447i	$0.762653\pi$
$798$	−99.2603	−	99.2603i	−0.124386	−	0.124386i
$799$	−699.920	+	501.555i	−0.875995	+	0.627729i
$800$	169.983	−	130.433i	0.212479	−	0.163041i
$801$	825.000	+	54.0734i	1.02996	+	0.0675073i
$802$	90.3721	−	240.113i	0.112683	−	0.299392i
$803$	1522.03	+	1016.99i	1.89543	+	1.26648i
$804$	−164.581	−	16.2098i	−0.204702	−	0.0201614i
$805$	−43.9214	−	19.9005i	−0.0545607	−	0.0247212i
$806$	−1377.50	−	417.860i	−1.70906	−	0.518436i
$807$	−102.065	−	1557.22i	−0.126475	−	1.92964i
$808$	−35.1415	+	30.8183i	−0.0434920	+	0.0381414i
$809$	−399.655	+	964.854i	−0.494012	+	1.19265i	0.458650	+	0.888617i	$0.348333\pi$
$809$	−399.655	+	964.854i	−0.494012	+	1.19265i	−0.952662	+	0.304033i	$0.901667\pi$
$810$	−565.785	−	689.412i	−0.698501	−	0.851125i
$811$	−592.071	−	1025.50i	−0.730050	−	1.26448i	−0.956861	−	0.290545i	$-0.906163\pi$
$811$	−592.071	−	1025.50i	−0.730050	−	1.26448i	0.226811	−	0.973939i	$-0.427170\pi$
$812$	−8.02459	−	4.63300i	−0.00988250	−	0.00570567i
$813$	−1158.42	+	191.255i	−1.42487	+	0.235247i
$814$	−1387.52	−	994.284i	−1.70457	−	1.22148i
$815$	247.271	−	8.09482i	0.303400	−	0.00993230i
$816$	1087.91	+	253.665i	1.33322	+	0.310864i
$817$	60.9952	−	22.9570i	0.0746575	−	0.0280991i
$818$	21.8187	+	71.9266i	0.0266732	+	0.0879299i
$819$	−271.607	−	35.7577i	−0.331633	−	0.0436602i
$820$	−1.85082	+	5.45233i	−0.00225709	+	0.00664919i
$821$	−8.13296	−	82.5753i	−0.00990616	−	0.100579i	0.988960	−	0.148181i	$-0.0473419\pi$
$821$	−8.13296	−	82.5753i	−0.00990616	−	0.100579i	−0.998866	+	0.0476024i	$0.984842\pi$
$822$	−1244.31	−	665.098i	−1.51376	−	0.809122i
$823$	902.529	−	373.840i	1.09663	−	0.454240i	0.240318	−	0.970694i	$-0.422748\pi$
$823$	902.529	−	373.840i	1.09663	−	0.454240i	0.856315	+	0.516454i	$0.172748\pi$
$824$	−714.914	−	352.557i	−0.867614	−	0.427860i
$825$	1164.53	−	2361.43i	1.41155	−	2.86234i
$826$	21.9358	+	52.9576i	0.0265566	+	0.0641133i
$827$	356.767	−	667.464i	0.431399	−	0.807090i	−0.568480	−	0.822697i	$-0.692468\pi$
$827$	356.767	−	667.464i	0.431399	−	0.807090i	0.999878	+	0.0156073i	$0.00496815\pi$
$828$	18.0864	−	1.78136i	0.0218435	−	0.00215140i
$829$	32.5683	+	11.0555i	0.0392863	+	0.0133359i	0.341013	−	0.940058i	$-0.389230\pi$
$829$	32.5683	+	11.0555i	0.0392863	+	0.0133359i	−0.301727	+	0.953394i	$0.597563\pi$
$830$	186.295	−	1415.05i	0.224452	−	1.70488i
$831$	−1856.75	+	563.240i	−2.23436	+	0.677786i
$832$	484.124	+	1286.29i	0.581880	+	1.54602i
$833$	−184.856	+	792.804i	−0.221916	+	0.951745i
$834$	−29.1544	−	890.575i	−0.0349573	−	1.06784i
$835$	516.251	−	720.428i	0.618265	−	0.862788i
$836$	−10.7564	−	65.1507i	−0.0128665	−	0.0779315i
$837$	−175.177	+	303.415i	−0.209291	+	0.362503i
$838$	641.380	−	370.301i	0.765370	−	0.441887i
$839$	217.526	−	178.519i	0.259268	−	0.212776i	−0.495775	−	0.868451i	$-0.665116\pi$
$839$	217.526	−	178.519i	0.259268	−	0.212776i	0.755043	+	0.655675i	$0.227616\pi$
$840$	−340.603	−	141.082i	−0.405480	−	0.167955i
$841$	−225.078	−	256.652i	−0.267632	−	0.305175i
$842$	−621.720	+	40.7497i	−0.738384	+	0.0483963i
$843$	−188.793	+	622.366i	−0.223953	+	0.738275i
$844$	−20.5295	+	45.3095i	−0.0243240	+	0.0536843i
$845$	184.888	−	1877.20i	0.218802	−	2.22154i
$846$	592.139	−	886.198i	0.699927	−	1.04752i
$847$	−110.819	−	41.7093i	−0.130837	−	0.0492435i
$848$	48.3918	−	738.316i	0.0570658	−	0.870655i
$849$	953.177	+	1242.20i	1.12270	+	1.46314i
$850$	−761.783	−	1063.07i	−0.896215	−	1.25067i
$851$	−208.202	+	208.202i	−0.244656	+	0.244656i
$852$	17.4021	−	105.403i	0.0204250	−	0.123713i
$853$	−675.909	−	554.704i	−0.792390	−	0.650298i	0.148537	−	0.988907i	$-0.452544\pi$
$853$	−675.909	−	554.704i	−0.792390	−	0.650298i	−0.940927	+	0.338609i	$0.890044\pi$
$854$	101.729	+	190.322i	0.119121	+	0.222860i
$855$	−659.726	−	987.350i	−0.771609	−	1.15479i
$856$	184.305	+	790.440i	0.215309	+	0.923411i
$857$	471.853	−	126.433i	0.550587	−	0.147529i	0.0272087	−	0.999630i	$-0.491338\pi$
$857$	471.853	−	126.433i	0.550587	−	0.147529i	0.523378	+	0.852100i	$0.324671\pi$
$858$	1852.90	+	1735.43i	2.15956	+	2.02265i
$859$	1145.00	+	712.005i	1.33294	+	0.828877i	0.993727	−	0.111832i	$-0.0356719\pi$
$859$	1145.00	+	712.005i	1.33294	+	0.828877i	0.339215	+	0.940709i	$0.389839\pi$
$860$	9.70400	−	9.08878i	0.0112837	−	0.0105684i
$861$	11.4793	−	2.28337i	0.0133325	−	0.00265200i
$862$	163.458	+	481.532i	0.189627	+	0.558622i
$863$	−373.562	+	169.259i	−0.432865	+	0.196128i	−0.617319	−	0.786713i	$-0.711781\pi$
$863$	−373.562	+	169.259i	−0.432865	+	0.196128i	0.184455	+	0.982841i	$0.440948\pi$
$864$	49.8511	−	6.56302i	0.0576980	−	0.00759609i
$865$	77.1897	−	388.059i	0.0892367	−	0.448623i
$866$	−425.880	+	264.829i	−0.491778	+	0.305807i
$867$	−5.68022	+	21.1989i	−0.00655158	+	0.0244508i
$868$	0.508017	−	15.5183i	0.000585273	−	0.0178782i
$869$	592.069	+	454.311i	0.681322	+	0.522797i
$870$	1160.97	+	1018.14i	1.33445	+	1.17028i
$871$	−1972.59	+	972.774i	−2.26474	+	1.11685i
$872$		−	1133.51i		−	1.29990i
$873$	−480.089	−	962.340i	−0.549930	−	1.10234i
$874$	123.851			0.141706
$875$	65.1289	+	132.068i	0.0744331	+	0.150935i
$876$	123.644	−	140.989i	0.141146	−	0.160946i
$877$	−382.914	+	499.023i	−0.436618	+	0.569011i	−0.958894	−	0.283765i	$-0.908416\pi$
$877$	−382.914	+	499.023i	−0.436618	+	0.569011i	0.522276	+	0.852776i	$0.325083\pi$
$878$	−850.054	−	27.8279i	−0.968171	−	0.0316946i
$879$	807.958	+	216.492i	0.919178	+	0.246293i
$880$	911.310	+	1465.51i	1.03558	+	1.66535i
$881$	610.480	+	121.432i	0.692940	+	0.137834i	0.528982	−	0.848633i	$-0.322574\pi$
$881$	610.480	+	121.432i	0.692940	+	0.137834i	0.163958	+	0.986467i	$0.447574\pi$
$882$	−131.524	−	999.022i	−0.149120	−	1.13268i
$883$	565.816	+	1248.78i	0.640788	+	1.41425i	0.894544	+	0.446980i	$0.147501\pi$
$883$	565.816	+	1248.78i	0.640788	+	1.41425i	−0.253756	+	0.967268i	$0.581666\pi$
$884$	−109.816	+	37.2776i	−0.124226	+	0.0421692i
$885$	171.389	+	861.629i	0.193660	+	0.973592i
$886$	289.366	+	308.953i	0.326598	+	0.348705i
$887$	451.800	−	726.554i	0.509358	−	0.819114i	−0.489235	−	0.872152i	$-0.662724\pi$
$887$	451.800	−	726.554i	0.509358	−	0.819114i	0.998592	+	0.0530382i	$0.0168905\pi$
$888$	−1538.89	+	1643.06i	−1.73299	+	1.85029i
$889$	−1.57758	−	5.88761i	−0.00177455	−	0.00662273i
$890$	1119.39	−	261.006i	1.25775	−	0.293266i
$891$	−709.063	+	473.781i	−0.795806	+	0.531741i
$892$	44.0795	−	23.5610i	0.0494165	−	0.0264137i
$893$	−423.762	+	516.356i	−0.474538	+	0.578226i
$894$	−294.696	−	48.6545i	−0.329637	−	0.0544234i
$895$	414.344	+	414.344i	0.462954	+	0.462954i
$896$	109.519	−	78.4802i	0.122231	−	0.0875895i
$897$	347.413	−	266.580i	0.387306	−	0.297190i
$898$	416.177	+	27.2777i	0.463449	+	0.0303761i
$899$	−294.909	+	783.554i	−0.328041	+	0.871585i
$900$	−123.786	−	82.7115i	−0.137541	−	0.0919017i
$901$	868.241	+	85.5143i	0.963642	+	0.0949104i
$902$	−54.5297	−	24.7071i	−0.0604542	−	0.0273914i
$903$	−25.8625	−	7.84530i	−0.0286406	−	0.00868804i
$904$	60.1892	+	918.310i	0.0665810	+	1.01583i
$905$	1238.48	−	1086.11i	1.36848	−	1.20013i
$906$	259.638	−	626.821i	0.286576	−	0.691855i
$907$	−942.149	−	1148.01i	−1.03875	−	1.26572i	−0.963258	−	0.268578i	$-0.913446\pi$
$907$	−942.149	−	1148.01i	−1.03875	−	1.26572i	−0.0754952	−	0.997146i	$-0.524054\pi$
$908$	−53.2132	−	92.1679i	−0.0586048	−	0.101506i
$909$	54.0679	+	31.2161i	0.0594806	+	0.0343411i
$910$	−375.774	+	62.0406i	−0.412939	+	0.0681765i
$911$	−426.210	−	305.418i	−0.467848	−	0.335255i	0.323912	−	0.946087i	$-0.395002\pi$
$911$	−426.210	−	305.418i	−0.467848	−	0.335255i	−0.791760	+	0.610832i	$0.790835\pi$
$912$	866.126	−	28.3540i	0.949700	−	0.0310899i
$913$	−1329.09	−	309.900i	−1.45574	−	0.339430i
$914$	−364.718	+	137.270i	−0.399035	+	0.150186i
$915$	960.102	+	3165.03i	1.04929	+	3.45905i
$916$	84.0591	+	11.0666i	0.0917676	+	0.0120814i
$917$	63.9102	−	188.273i	0.0696948	−	0.205314i
$918$	−30.0830	−	305.438i	−0.0327701	−	0.332721i
$919$	−344.532	−	184.156i	−0.374899	−	0.200388i	0.273176	−	0.961964i	$-0.411926\pi$
$919$	−344.532	−	184.156i	−0.374899	−	0.200388i	−0.648075	+	0.761576i	$0.724426\pi$
$920$	300.508	−	124.474i	0.326639	−	0.135298i
$921$	1217.07	+	600.192i	1.32147	+	0.651675i
$922$	459.501	−	931.775i	0.498374	−	1.01060i
$923$	−543.705	−	1312.62i	−0.589063	−	1.42212i
$924$	−12.9083	+	24.1497i	−0.0139700	+	0.0261360i
$925$	2400.39	−	236.418i	2.59502	−	0.255587i
$926$	408.901	+	138.803i	0.441578	+	0.149895i
$927$	−138.974	+	1055.61i	−0.149918	+	1.13874i
$928$	114.980	−	34.8787i	0.123900	−	0.0375848i
$929$	−29.3153	−	77.8888i	−0.0315557	−	0.0838416i	0.919189	−	0.393817i	$-0.128846\pi$
$929$	−29.3153	−	77.8888i	−0.0315557	−	0.0838416i	−0.950744	+	0.309976i	$0.899679\pi$
$930$	−587.560	+	2519.91i	−0.631785	+	2.70958i
$931$	20.6627	+	631.180i	0.0221941	+	0.677959i
$932$	24.8893	−	34.7330i	0.0267053	−	0.0372672i
$933$	22.0286	+	133.425i	0.0236105	+	0.143007i
$934$	−296.306	+	513.217i	−0.317244	+	0.549482i
$935$	−1762.26	+	1017.44i	−1.88477	+	1.08817i
$936$	1428.48	−	1172.33i	1.52616	−	1.25249i
$937$	−424.183	−	175.703i	−0.452704	−	0.187516i	0.144668	−	0.989480i	$-0.453788\pi$
$937$	−424.183	−	175.703i	−0.452704	−	0.187516i	−0.597372	+	0.801964i	$0.703788\pi$
$938$	170.083	+	193.942i	0.181325	+	0.206761i
$939$	511.822	−	33.5466i	0.545071	−	0.0357258i
$940$	−39.5579	+	130.405i	−0.0420829	+	0.138729i
$941$	−387.523	+	855.281i	−0.411820	+	0.908907i	0.583485	+	0.812124i	$0.301689\pi$
$941$	−387.523	+	855.281i	−0.411820	+	0.908907i	−0.995306	+	0.0967830i	$0.969145\pi$
$942$	−199.043	+	2020.92i	−0.211299	+	2.14535i
$943$	−5.73704	+	8.58609i	−0.00608382	+	0.00910508i
$944$	−331.183	−	124.648i	−0.350830	−	0.132043i
$945$	−6.06270	+	92.4989i	−0.00641555	+	0.0978824i
$946$	84.1533	+	109.671i	0.0889569	+	0.115931i
$947$	862.436	+	1203.53i	0.910704	+	1.27089i	0.962237	+	0.272214i	$0.0877560\pi$
$947$	862.436	+	1203.53i	0.910704	+	1.27089i	−0.0515329	+	0.998671i	$0.516411\pi$
$948$	54.0597	−	54.0597i	0.0570250	−	0.0570250i
$949$	406.255	−	2460.65i	0.428088	−	2.59289i
$950$	−784.262	−	643.628i	−0.825539	−	0.677503i
$951$	−280.833	−	525.401i	−0.295302	−	0.552472i
$952$	97.2803	+	145.590i	0.102185	+	0.152931i
$953$	40.9051	+	175.432i	0.0429224	+	0.184084i	0.990979	−	0.134018i	$-0.0427879\pi$
$953$	40.9051	+	175.432i	0.0429224	+	0.184084i	−0.948057	+	0.318102i	$0.896955\pi$
$954$	−1043.10	+	279.497i	−1.09339	+	0.292974i
$955$	81.0550	+	75.9163i	0.0848743	+	0.0794935i
$956$	−79.0807	−	49.1756i	−0.0827204	−	0.0514389i
$957$	1077.66	−	1009.34i	1.12608	−	1.05469i
$958$	968.496	−	192.646i	1.01096	−	0.201092i
$959$	−65.0579	−	191.655i	−0.0678394	−	0.199848i
$960$	2250.26	−	1019.58i	2.34402	−	1.06206i
$961$	−438.104	+	57.6775i	−0.455884	+	0.0600182i
$962$	−453.712	+	2280.97i	−0.471634	+	2.37107i
$963$	920.640	−	572.490i	0.956012	−	0.594486i
$964$	39.4539	−	147.244i	0.0409272	−	0.152743i
$965$	14.0126	−	428.040i	0.0145208	−	0.443565i
$966$	−40.7462	−	31.2657i	−0.0421803	−	0.0323661i
$967$	−168.839	−	148.068i	−0.174601	−	0.153121i	0.567585	−	0.823315i	$-0.307878\pi$
$967$	−168.839	−	148.068i	−0.174601	−	0.153121i	−0.742186	+	0.670194i	$0.766211\pi$
$968$	716.358	−	353.269i	0.740039	−	0.364947i
$969$			1021.83i			1.05452i
$970$	−1027.08	−	1086.54i	−1.05884	−	1.12014i
$971$	−1451.79			−1.49515			−0.747573	−	0.664180i	$-0.768781\pi$
$971$	−1451.79			−1.49515			−0.747573	+	0.664180i	$0.768781\pi$
$972$	51.1828	+	103.788i	0.0526572	+	0.106778i
$973$	84.2788	−	96.1015i	0.0866175	−	0.0987683i
$974$	−122.344	+	159.442i	−0.125610	+	0.163698i
$975$	−3585.30	−	117.370i	−3.67723	−	0.120380i
$976$	−1286.85	−	344.809i	−1.31849	−	0.353288i
$977$	−971.888	−	1562.92i	−0.994768	−	1.59972i	−0.782640	−	0.622475i	$-0.786127\pi$
$977$	−971.888	−	1562.92i	−0.994768	−	1.59972i	−0.212128	−	0.977242i	$-0.568039\pi$
$978$	258.451	+	51.4091i	0.264265	+	0.0525655i
$979$	−143.457	−	1089.67i	−0.146534	−	1.11304i
$980$	53.1708	+	117.350i	0.0542559	+	0.119745i
$981$	−1433.70	+	486.674i	−1.46146	+	0.496100i
$982$	−20.7324	−	104.229i	−0.0211124	−	0.106139i
$983$	520.525	+	555.759i	0.529527	+	0.565370i	0.937661	−	0.347552i	$-0.112987\pi$
$983$	520.525	+	555.759i	0.529527	+	0.565370i	−0.408134	+	0.912922i	$0.633820\pi$
$984$	−41.6916	+	67.0456i	−0.0423695	+	0.0681358i
$985$	−733.941	+	783.621i	−0.745118	+	0.795555i
$986$	−189.821	−	708.423i	−0.192517	−	0.718482i
$987$	269.768	−	62.9010i	0.273321	−	0.0637295i
$988$	−74.8030	+	49.9818i	−0.0757115	+	0.0505888i
$989$	21.0292	−	11.2403i	0.0212631	−	0.0113654i
$990$	1597.88	−	1947.02i	1.61402	−	1.96669i
$991$	740.794	+	122.306i	0.747522	+	0.123416i	0.524516	−	0.851401i	$-0.324246\pi$
$991$	740.794	+	122.306i	0.747522	+	0.123416i	0.223006	+	0.974817i	$0.428413\pi$
$992$	142.366	+	142.366i	0.143514	+	0.143514i
$993$	1546.23	−	1108.01i	1.55713	−	1.11582i
$994$	−132.200	+	101.441i	−0.132998	+	0.102053i
$995$	954.062	+	62.5325i	0.958856	+	0.0628467i
$996$	−49.2473	+	130.847i	−0.0494451	+	0.131373i
$997$	−438.304	−	292.865i	−0.439623	−	0.293747i	0.315993	−	0.948761i	$-0.397662\pi$
$997$	−438.304	−	292.865i	−0.439623	−	0.293747i	−0.755616	+	0.655015i	$0.772662\pi$
$998$	426.543	+	42.0108i	0.427398	+	0.0420950i
$999$	515.583	+	233.608i	0.516099	+	0.233842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.3.l.a.5.11	✓	480
97.39	odd	96	inner	97.3.l.a.39.11	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.3.l.a.5.11	✓	480	1.1	even	1	trivial
97.3.l.a.39.11	yes	480	97.39	odd	96	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	97.l (of order \(96\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.846508 + 1.71655i) q^{2} +(-2.95510 + 3.36964i) q^{3} +(0.205082 - 0.267268i) q^{4} +(-8.04921 - 0.263504i) q^{5} +(-8.28567 - 2.22014i) q^{6} +(-0.649793 - 1.04495i) q^{7} +(8.14099 + 1.61934i) q^{8} +(-1.44715 - 10.9922i) q^{9} +(-6.36141 - 14.0399i) q^{10} +(-13.9564 + 4.73757i) q^{11} +(0.294561 + 1.48086i) q^{12} +(13.7267 + 14.6559i) q^{13} +(1.24366 - 1.99996i) q^{14} +(24.6741 - 26.3443i) q^{15} +(3.76296 + 14.0436i) q^{16} +(-16.6956 + 3.89286i) q^{17} +(17.6437 - 11.7891i) q^{18} +(-11.7287 + 6.26914i) q^{19} +(-1.72118 + 2.09726i) q^{20} +(5.44132 + 0.898365i) q^{21} +(-19.9465 - 19.9465i) q^{22} +(-3.95512 + 2.83420i) q^{23} +(-29.5140 + 22.6469i) q^{24} +(39.7739 + 2.60692i) q^{25} +(-13.5377 + 35.9689i) q^{26} +(7.77754 + 5.19679i) q^{27} +(-0.412544 - 0.0406320i) q^{28} +(20.3601 + 9.22503i) q^{29} +(66.1081 + 20.0537i) q^{30} +(2.44968 + 37.3749i) q^{31} +(4.04143 - 3.54424i) q^{32} +(25.2787 - 61.0282i) q^{33} +(-20.8152 - 25.3634i) q^{34} +(4.95497 + 8.58227i) q^{35} +(-3.23466 - 1.86753i) q^{36} +(59.7048 - 9.85731i) q^{37} +(-20.6898 - 14.8261i) q^{38} +(-89.9489 + 2.94462i) q^{39} +(-65.1018 - 15.1796i) q^{40} +(1.98623 - 0.747565i) q^{41} +(3.06403 + 10.1008i) q^{42} +(-4.85859 - 0.639646i) q^{43} +(-1.59601 + 4.70171i) q^{44} +(8.75195 + 88.8601i) q^{45} +(-8.21309 - 4.38999i) q^{46} +(46.4042 - 19.2213i) q^{47} +(-58.4417 - 28.8203i) q^{48} +(21.0025 - 42.5888i) q^{49} +(29.1940 + 70.4806i) q^{50} +(36.2195 - 67.7619i) q^{51} +(6.73216 - 0.663060i) q^{52} +(-48.1900 - 16.3583i) q^{53} +(-2.33679 + 17.7497i) q^{54} +(113.587 - 34.4562i) q^{55} +(-3.59782 - 9.55918i) q^{56} +(13.5348 - 58.0476i) q^{57} +(1.39976 + 42.7581i) q^{58} +(-14.1769 + 19.7839i) q^{59} +(-1.98077 - 11.9974i) q^{60} +(-45.8162 + 79.3559i) q^{61} +(-62.0822 + 35.8432i) q^{62} +(-10.5460 + 8.65488i) q^{63} +(63.2340 + 26.1924i) q^{64} +(-106.628 - 121.585i) q^{65} +(126.156 - 8.26873i) q^{66} +(-31.7951 + 104.814i) q^{67} +(-2.38353 + 5.26056i) q^{68} +(2.13753 - 21.7027i) q^{69} +(-10.5375 + 15.7704i) q^{70} +(-66.2195 - 24.9233i) q^{71} +(6.01892 - 91.8310i) q^{72} +(-75.6079 - 98.5341i) q^{73} +(67.4612 + 94.1420i) q^{74} +(-126.320 + 126.320i) q^{75} +(-0.729813 + 4.42041i) q^{76} +(14.0193 + 11.5054i) q^{77} +(-81.1971 - 151.909i) q^{78} +(-28.1312 - 42.1013i) q^{79} +(-26.5883 - 114.031i) q^{80} +(55.8889 - 14.9754i) q^{81} +(2.96459 + 2.77664i) q^{82} +(78.6328 + 48.8970i) q^{83} +(1.35602 - 1.27005i) q^{84} +(135.412 - 26.9351i) q^{85} +(-3.01485 - 8.88147i) q^{86} +(-91.2510 + 41.3453i) q^{87} +(-121.291 + 15.9683i) q^{88} +(-14.5480 + 73.1378i) q^{89} +(-145.124 + 90.2439i) q^{90} +(6.39516 - 23.8671i) q^{91} +(-0.0536332 + 1.63832i) q^{92} +(-133.179 - 102.192i) q^{93} +(72.2758 + 63.3842i) q^{94} +(96.0591 - 47.3711i) q^{95} +24.0917i q^{96} +(91.7078 - 31.6018i) q^{97} +90.8844 q^{98} +(72.2736 + 146.556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) \) 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Introduction

L-functions

Modular forms

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Database

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