LMFDB - Embedded newform 92.5.g.a.31.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,5,Mod(3,92)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("92.3"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 16])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.g (of order $22$, degree $10$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			31.12
Character	$\chi$	$=$	92.31
Dual form			92.5.g.a.3.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.93523 + 2.71744i) q^{2} +(-14.4864 + 6.61573i) q^{3} +(1.23109 - 15.9526i) q^{4} +(17.8216 + 20.5672i) q^{5} +(24.5431 - 58.7846i) q^{6} +(31.8403 - 49.5444i) q^{7} +(39.7365 + 50.1698i) q^{8} +(113.045 - 130.461i) q^{9} +(-108.200 - 11.9404i) q^{10} +(39.3070 - 5.65149i) q^{11} +(87.7038 + 239.240i) q^{12} +(-28.0412 + 18.0210i) q^{13} +(41.1754 + 231.948i) q^{14} +(-394.239 - 180.043i) q^{15} +(-252.969 - 39.2782i) q^{16} +(410.671 - 120.584i) q^{17} +(22.7065 + 690.126i) q^{18} +(-200.532 + 682.948i) q^{19} +(350.040 - 258.980i) q^{20} +(-133.479 + 928.369i) q^{21} +(-100.017 + 123.403i) q^{22} +(-28.1234 - 528.252i) q^{23} +(-907.551 - 463.895i) q^{24} +(-16.4544 + 114.443i) q^{25} +(33.3364 - 129.096i) q^{26} +(-411.099 + 1400.07i) q^{27} +(-751.163 - 568.928i) q^{28} +(-415.421 + 121.978i) q^{29} +(1646.43 - 542.852i) q^{30} +(971.656 + 443.740i) q^{31} +(849.256 - 572.136i) q^{32} +(-532.029 + 341.915i) q^{33} +(-877.732 + 1469.91i) q^{34} +(1586.44 - 228.095i) q^{35} +(-1942.02 - 1963.97i) q^{36} +(288.476 - 332.919i) q^{37} +(-1267.26 - 2549.54i) q^{38} +(286.996 - 446.574i) q^{39} +(-323.685 + 1711.38i) q^{40} +(1102.30 + 1272.13i) q^{41} +(-2130.99 - 3087.69i) q^{42} +(972.694 - 444.214i) q^{43} +(-41.7652 - 634.005i) q^{44} +4697.87 q^{45} +(1518.04 + 1474.11i) q^{46} +3742.96i q^{47} +(3924.47 - 1104.57i) q^{48} +(-443.436 - 970.990i) q^{49} +(-262.694 - 380.629i) q^{50} +(-5151.40 + 4463.72i) q^{51} +(252.960 + 469.515i) q^{52} +(601.662 + 386.665i) q^{53} +(-2597.94 - 5226.67i) q^{54} +(816.749 + 707.717i) q^{55} +(3750.86 - 371.304i) q^{56} +(-1613.21 - 11220.1i) q^{57} +(887.884 - 1486.91i) q^{58} +(-520.278 - 809.569i) q^{59} +(-3357.49 + 6067.47i) q^{60} +(-719.901 + 1576.36i) q^{61} +(-4057.86 + 1337.93i) q^{62} +(-2864.23 - 9754.68i) q^{63} +(-938.017 + 3987.15i) q^{64} +(-870.382 - 255.567i) q^{65} +(632.496 - 2449.35i) q^{66} +(-533.696 - 76.7340i) q^{67} +(-1418.05 - 6699.70i) q^{68} +(3902.18 + 7466.43i) q^{69} +(-4036.71 + 4980.55i) q^{70} +(5617.44 + 807.666i) q^{71} +(11037.2 + 487.383i) q^{72} +(-6046.65 - 1775.46i) q^{73} +(57.9439 + 1761.11i) q^{74} +(-518.758 - 1766.73i) q^{75} +(10647.9 + 4039.77i) q^{76} +(971.545 - 2127.39i) q^{77} +(371.139 + 2090.69i) q^{78} +(3053.09 + 4750.70i) q^{79} +(-3700.46 - 5902.87i) q^{80} +(-1317.23 - 9161.52i) q^{81} +(-6692.43 - 738.538i) q^{82} +(-4177.41 - 3619.75i) q^{83} +(14645.5 + 3272.25i) q^{84} +(9798.88 + 6297.36i) q^{85} +(-1647.95 + 3947.10i) q^{86} +(5210.99 - 4515.35i) q^{87} +(1845.46 + 1747.45i) q^{88} +(2054.20 + 4498.08i) q^{89} +(-13789.3 + 12766.2i) q^{90} +1963.08i q^{91} +(-8461.60 - 201.687i) q^{92} -17011.5 q^{93} +(-10171.2 - 10986.4i) q^{94} +(-17620.1 + 8046.84i) q^{95} +(-8517.60 + 13906.7i) q^{96} +(8231.99 + 9500.22i) q^{97} +(3940.19 + 1645.07i) q^{98} +(3706.17 - 5766.91i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) $ 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$-1$

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 $

$2$	−2.93523	+	2.71744i	−0.733806	+	0.679359i
$2$	−2.93523	+	2.71744i	−0.733806	+	0.679359i
$3$	−14.4864	+	6.61573i	−1.60960	+	0.735082i	−0.998408	−	0.0563977i	$-0.982039\pi$
$3$	−14.4864	+	6.61573i	−1.60960	+	0.735082i	−0.611196	+	0.791479i	$0.709311\pi$
$4$	1.23109	−	15.9526i	0.0769434	−	0.997035i
$5$	17.8216	+	20.5672i	0.712864	+	0.822689i	0.990430	−	0.138018i	$-0.0440731\pi$
$5$	17.8216	+	20.5672i	0.712864	+	0.822689i	−0.277566	+	0.960707i	$0.589528\pi$
$6$	24.5431	−	58.7846i	0.681754	−	1.63291i
$7$	31.8403	−	49.5444i	0.649801	−	1.01111i	−0.347499	−	0.937680i	$-0.612969\pi$
$7$	31.8403	−	49.5444i	0.649801	−	1.01111i	0.997300	−	0.0734304i	$-0.0233947\pi$
$8$	39.7365	+	50.1698i	0.620883	+	0.783903i
$9$	113.045	−	130.461i	1.39562	−	1.61063i
$10$	−108.200	−	11.9404i	−1.08200	−	0.119404i
$11$	39.3070	−	5.65149i	0.324851	−	0.0467065i	0.0220399	−	0.999757i	$-0.492984\pi$
$11$	39.3070	−	5.65149i	0.324851	−	0.0467065i	0.302811	+	0.953051i	$0.402075\pi$
$12$	87.7038	+	239.240i	0.609054	+	1.66139i
$13$	−28.0412	+	18.0210i	−0.165925	+	0.106633i	−0.620968	−	0.783836i	$-0.713260\pi$
$13$	−28.0412	+	18.0210i	−0.165925	+	0.106633i	0.455043	+	0.890469i	$0.349624\pi$
$14$	41.1754	+	231.948i	0.210079	+	1.18341i
$15$	−394.239	−	180.043i	−1.75217	−	0.800190i
$16$	−252.969	−	39.2782i	−0.988159	−	0.153431i
$17$	410.671	−	120.584i	1.42101	−	0.417245i	0.521162	−	0.853458i	$-0.325499\pi$
$17$	410.671	−	120.584i	1.42101	−	0.417245i	0.899843	+	0.436213i	$0.143681\pi$
$18$	22.7065	+	690.126i	0.0700818	+	2.13002i
$19$	−200.532	+	682.948i	−0.555489	+	1.89182i	−0.116874	+	0.993147i	$0.537287\pi$
$19$	−200.532	+	682.948i	−0.555489	+	1.89182i	−0.438615	+	0.898675i	$0.644531\pi$
$20$	350.040	−	258.980i	0.875100	−	0.647450i
$21$	−133.479	+	928.369i	−0.302674	+	2.10515i
$22$	−100.017	+	123.403i	−0.206647	+	0.254964i
$23$	−28.1234	−	528.252i	−0.0531633	−	0.998586i
$23$	−28.1234	−	528.252i	−0.0531633	−	0.998586i
$24$	−907.551	−	463.895i	−1.57561	−	0.805374i
$25$	−16.4544	+	114.443i	−0.0263270	+	0.183109i
$26$	33.3364	−	129.096i	0.0493143	−	0.190970i
$27$	−411.099	+	1400.07i	−0.563922	+	1.92054i
$28$	−751.163	−	568.928i	−0.958115	−	0.725673i
$29$	−415.421	+	121.978i	−0.493960	+	0.145040i	−0.519219	−	0.854641i	$-0.673777\pi$
$29$	−415.421	+	121.978i	−0.493960	+	0.145040i	0.0252589	+	0.999681i	$0.491959\pi$
$30$	1646.43	−	542.852i	1.82937	−	0.603169i
$31$	971.656	+	443.740i	1.01109	+	0.461749i	0.850894	−	0.525337i	$-0.176061\pi$
$31$	971.656	+	443.740i	1.01109	+	0.461749i	0.160194	+	0.987086i	$0.448788\pi$
$32$	849.256	−	572.136i	0.829352	−	0.558726i
$33$	−532.029	+	341.915i	−0.488549	+	0.313971i
$34$	−877.732	+	1469.91i	−0.759284	+	1.27155i
$35$	1586.44	−	228.095i	1.29505	−	0.186200i
$36$	−1942.02	−	1963.97i	−1.49847	−	1.51541i
$37$	288.476	−	332.919i	0.210720	−	0.243184i	−0.640544	−	0.767922i	$-0.721291\pi$
$37$	288.476	−	332.919i	0.210720	−	0.243184i	0.851264	+	0.524737i	$0.175836\pi$
$38$	−1267.26	−	2549.54i	−0.877604	−	1.76561i
$39$	286.996	−	446.574i	0.188689	−	0.293605i
$40$	−323.685	+	1711.38i	−0.202303	+	1.06961i
$41$	1102.30	+	1272.13i	0.655743	+	0.756768i	0.982076	−	0.188487i	$-0.0603585\pi$
$41$	1102.30	+	1272.13i	0.655743	+	0.756768i	−0.326333	+	0.945255i	$0.605813\pi$
$42$	−2130.99	−	3087.69i	−1.20804	−	1.75039i
$43$	972.694	−	444.214i	0.526065	−	0.240246i	−0.134636	−	0.990895i	$-0.542987\pi$
$43$	972.694	−	444.214i	0.526065	−	0.240246i	0.660701	+	0.750649i	$0.270259\pi$
$44$	−41.7652	−	634.005i	−0.0215729	−	0.327482i
$45$	4697.87			2.31994
$46$	1518.04	+	1474.11i	0.717410	+	0.696652i
$47$			3742.96i			1.69441i	0.531264	+	0.847206i	$0.321717\pi$
$47$			3742.96i			1.69441i	−0.531264	+	0.847206i	$0.678283\pi$
$48$	3924.47	−	1104.57i	1.70333	−	0.479415i
$49$	−443.436	−	970.990i	−0.184688	−	0.404411i
$50$	−262.694	−	380.629i	−0.105077	−	0.152252i
$51$	−5151.40	+	4463.72i	−1.98055	+	1.71615i
$52$	252.960	+	469.515i	0.0935503	+	0.173637i
$53$	601.662	+	386.665i	0.214191	+	0.137652i	0.643337	−	0.765583i	$-0.277549\pi$
$53$	601.662	+	386.665i	0.214191	+	0.137652i	−0.429147	+	0.903235i	$0.641186\pi$
$54$	−2597.94	−	5226.67i	−0.890927	−	1.79241i
$55$	816.749	+	707.717i	0.270000	+	0.233956i
$56$	3750.86	−	371.304i	1.19606	−	0.118400i
$57$	−1613.21	−	11220.1i	−0.496526	−	3.45341i
$58$	887.884	−	1486.91i	0.263937	−	0.442007i
$59$	−520.278	−	809.569i	−0.149462	−	0.232568i	0.758447	−	0.651735i	$-0.225959\pi$
$59$	−520.278	−	809.569i	−0.149462	−	0.232568i	−0.907909	+	0.419167i	$0.862322\pi$
$60$	−3357.49	+	6067.47i	−0.932636	+	1.68541i
$61$	−719.901	+	1576.36i	−0.193470	+	0.423640i	−0.981361	−	0.192175i	$-0.938446\pi$
$61$	−719.901	+	1576.36i	−0.193470	+	0.423640i	0.787891	+	0.615815i	$0.211173\pi$
$62$	−4057.86	+	1337.93i	−1.05564	+	0.348058i
$63$	−2864.23	−	9754.68i	−0.721651	−	2.45772i
$64$	−938.017	+	3987.15i	−0.229008	+	0.973425i
$65$	−870.382	−	255.567i	−0.206008	−	0.0604893i
$66$	632.496	−	2449.35i	0.145201	−	0.562294i
$67$	−533.696	−	76.7340i	−0.118890	−	0.0170938i	0.0826130	−	0.996582i	$-0.473673\pi$
$67$	−533.696	−	76.7340i	−0.118890	−	0.0170938i	−0.201503	+	0.979488i	$0.564583\pi$
$68$	−1418.05	−	6699.70i	−0.306671	−	1.44890i
$69$	3902.18	+	7466.43i	0.819614	+	1.56825i
$70$	−4036.71	+	4980.55i	−0.823819	+	1.01644i
$71$	5617.44	+	807.666i	1.11435	+	0.160219i	0.674802	−	0.737999i	$-0.264229\pi$
$71$	5617.44	+	807.666i	1.11435	+	0.160219i	0.439549	+	0.898219i	$0.355138\pi$
$72$	11037.2	+	487.383i	2.12910	+	0.0940168i
$73$	−6046.65	−	1775.46i	−1.13467	−	0.333169i	−0.340128	−	0.940379i	$-0.610470\pi$
$73$	−6046.65	−	1775.46i	−1.13467	−	0.333169i	−0.794541	+	0.607210i	$0.792288\pi$
$74$	57.9439	+	1761.11i	0.0105814	+	0.321605i
$75$	−518.758	−	1766.73i	−0.0922236	−	0.314085i
$76$	10647.9	+	4039.77i	1.84347	+	0.699405i
$77$	971.545	−	2127.39i	0.163863	−	0.358810i
$78$	371.139	+	2090.69i	0.0610024	+	0.343637i
$79$	3053.09	+	4750.70i	0.489198	+	0.761208i	0.994831	−	0.101541i	$-0.0323774\pi$
$79$	3053.09	+	4750.70i	0.489198	+	0.761208i	−0.505633	+	0.862749i	$0.668741\pi$
$80$	−3700.46	−	5902.87i	−0.578198	−	0.922323i
$81$	−1317.23	−	9161.52i	−0.200766	−	1.39636i
$82$	−6692.43	−	738.538i	−0.995305	−	0.109836i
$83$	−4177.41	−	3619.75i	−0.606388	−	0.525438i	0.296657	−	0.954984i	$-0.404128\pi$
$83$	−4177.41	−	3619.75i	−0.606388	−	0.525438i	−0.903045	+	0.429546i	$0.858674\pi$
$84$	14645.5	+	3272.25i	2.07562	+	0.463754i
$85$	9798.88	+	6297.36i	1.35625	+	0.871606i
$86$	−1647.95	+	3947.10i	−0.222817	+	0.533681i
$87$	5210.99	−	4515.35i	0.688465	−	0.596558i
$88$	1845.46	+	1747.45i	0.238308	+	0.225652i
$89$	2054.20	+	4498.08i	0.259336	+	0.567867i	0.993851	−	0.110725i	$-0.0353174\pi$
$89$	2054.20	+	4498.08i	0.259336	+	0.567867i	−0.734515	+	0.678593i	$0.762590\pi$
$90$	−13789.3	+	12766.2i	−1.70238	+	1.57607i
$91$			1963.08i			0.237059i
$92$	−8461.60	−	201.687i	−0.999716	−	0.0238288i
$93$	−17011.5			−1.96687
$94$	−10171.2	−	10986.4i	−1.15111	−	1.24337i
$95$	−17620.1	+	8046.84i	−1.95237	+	0.891617i
$96$	−8517.60	+	13906.7i	−0.924219	+	1.50897i
$97$	8231.99	+	9500.22i	0.874906	+	1.00970i	0.999846	+	0.0175312i	$0.00558065\pi$
$97$	8231.99	+	9500.22i	0.874906	+	1.00970i	−0.124940	+	0.992164i	$0.539874\pi$
$98$	3940.19	+	1645.07i	0.410265	+	0.171290i
$99$	3706.17	−	5766.91i	0.378142	−	0.588400i
$100$	1805.40	+	403.380i	0.180540	+	0.0403380i
$101$	−9616.33	+	11097.8i	−0.942685	+	1.08792i	0.0533158	+	0.998578i	$0.483021\pi$
$101$	−9616.33	+	11097.8i	−0.942685	+	1.08792i	−0.996001	+	0.0893393i	$0.971524\pi$
$102$	2990.67	−	27100.6i	0.287454	−	2.60483i
$103$	6784.31	−	975.437i	0.639487	−	0.0919443i	0.185058	−	0.982728i	$-0.440753\pi$
$103$	6784.31	−	975.437i	0.639487	−	0.0919443i	0.454428	+	0.890783i	$0.349844\pi$
$104$	−2018.37	−	690.731i	−0.186610	−	0.0638620i
$105$	−21472.8	+	13799.7i	−1.94764	+	1.25168i
$106$	−2816.75	+	500.030i	−0.250690	+	0.0445025i
$107$	13233.7	+	6043.65i	1.15589	+	0.527875i	0.898733	−	0.438495i	$-0.144488\pi$
$107$	13233.7	+	6043.65i	1.15589	+	0.527875i	0.257152	+	0.966371i	$0.417216\pi$
$108$	21828.7	+	8281.71i	1.87146	+	0.710023i
$109$	5207.74	−	1529.13i	0.438325	−	0.128704i	−0.0551220	−	0.998480i	$-0.517555\pi$
$109$	5207.74	−	1529.13i	0.438325	−	0.128704i	0.493447	+	0.869776i	$0.335737\pi$
$110$	−4320.52	+	142.153i	−0.357067	+	0.0117482i
$111$	−1976.49	+	6731.30i	−0.160416	+	0.546327i
$112$	−10000.6	+	11282.6i	−0.797243	+	0.899439i
$113$	3114.88	−	21664.5i	0.243941	−	1.69665i	−0.388025	−	0.921649i	$-0.626842\pi$
$113$	3114.88	−	21664.5i	0.243941	−	1.69665i	0.631965	−	0.774997i	$-0.282248\pi$
$114$	35225.2	+	28549.8i	2.71046	+	2.19682i
$115$	10363.5	−	9992.71i	0.783627	−	0.755593i
$116$	1434.45	+	6777.19i	0.106603	+	0.503656i
$117$	−818.887	+	5695.48i	−0.0598208	+	0.416063i
$118$	3727.09	+	962.445i	0.267674	+	0.0691213i
$119$	7101.61	−	24185.9i	0.501491	−	1.70792i
$120$	−6632.97	−	26933.2i	−0.460623	−	1.87036i
$121$	−12534.8	+	3680.56i	−0.856146	+	0.251387i
$122$	−2170.59	−	6583.27i	−0.145834	−	0.442305i
$123$	−24384.5	−	11136.0i	−1.61177	−	0.736072i
$124$	8275.00	−	14954.1i	0.538176	−	0.972562i
$125$	11661.8	−	7494.60i	0.746357	−	0.479655i
$126$	34914.9	+	20848.8i	2.19922	+	1.31323i
$127$	10004.1	−	1438.37i	0.620253	−	0.0891789i	0.174977	−	0.984573i	$-0.444015\pi$
$127$	10004.1	−	1438.37i	0.620253	−	0.0891789i	0.445275	+	0.895394i	$0.353106\pi$
$128$	−8081.52	−	14252.2i	−0.493257	−	0.869884i
$129$	−11152.1	+	12870.2i	−0.670156	+	0.773401i
$130$	3249.25	−	1615.06i	0.192264	−	0.0955656i
$131$	13140.4	−	20446.9i	0.765714	−	1.19147i	−0.211117	−	0.977461i	$-0.567710\pi$
$131$	13140.4	−	20446.9i	0.765714	−	1.19147i	0.976831	−	0.214013i	$-0.0686536\pi$
$132$	4799.44	+	8908.16i	0.275450	+	0.511258i
$133$	27451.3	+	31680.5i	1.55188	+	1.79097i
$134$	1775.04	−	1225.05i	0.0988549	−	0.0682253i
$135$	−36122.1	+	16496.4i	−1.98201	+	0.905152i
$136$	22368.3	+	15811.7i	1.20936	+	0.854870i
$137$	9343.49			0.497815			0.248908	−	0.968527i	$-0.419928\pi$
$137$	9343.49			0.497815			0.248908	+	0.968527i	$0.419928\pi$
$138$	−31743.3	−	11311.7i	−1.66684	−	0.593979i
$139$		−	9064.53i		−	0.469154i	−0.972098	−	0.234577i	$-0.924629\pi$
$139$		−	9064.53i		−	0.469154i	0.972098	−	0.234577i	$-0.0753705\pi$
$140$	−1685.65	−	25588.5i	−0.0860025	−	1.30554i
$141$	−24762.4	−	54222.1i	−1.24553	−	2.72733i
$142$	−18683.2	+	12894.4i	−0.926564	+	0.639474i
$143$	−1000.37	+	866.827i	−0.0489203	+	0.0423897i
$144$	−33721.2	+	28562.4i	−1.62622	+	1.37743i
$145$	−9912.22	−	6370.19i	−0.471449	−	0.302982i
$146$	22573.0	−	11220.0i	1.05897	−	0.526366i
$147$	12847.6	+	11132.5i	0.594550	+	0.515180i
$148$	−4955.78	−	5011.79i	−0.226250	−	0.228807i
$149$	−1243.89	−	8651.44i	−0.0560285	−	0.389687i	−0.998469	−	0.0553131i	$-0.982384\pi$
$149$	−1243.89	−	8651.44i	−0.0560285	−	0.389687i	0.942441	−	0.334374i	$-0.108525\pi$
$150$	6323.64	+	3776.05i	0.281051	+	0.167825i
$151$	−10598.1	−	16491.0i	−0.464810	−	0.723259i	0.527155	−	0.849769i	$-0.323259\pi$
$151$	−10598.1	−	16491.0i	−0.464810	−	0.723259i	−0.991965	+	0.126510i	$0.959622\pi$
$152$	−42231.8	+	17077.3i	−1.82790	+	0.739151i
$153$	30692.9	−	67208.0i	1.31116	−	2.87103i
$154$	2929.33	+	8884.47i	0.123517	+	0.374619i
$155$	8189.95	+	27892.4i	0.340893	+	1.16097i
$156$	−6770.68	−	5128.09i	−0.278217	−	0.210720i
$157$	23078.2	+	6776.36i	0.936272	+	0.274914i	0.714060	−	0.700084i	$-0.246854\pi$
$157$	23078.2	+	6776.36i	0.936272	+	0.274914i	0.222212	+	0.974998i	$0.428672\pi$
$158$	−21871.2	−	5647.80i	−0.876110	−	0.226238i
$159$	−11274.0	−	1620.96i	−0.445948	−	0.0641177i
$160$	26902.3	+	7270.47i	1.05087	+	0.284003i
$161$	−27067.4	−	15426.3i	−1.04423	−	0.595129i
$162$	28762.2	+	23311.6i	1.09595	+	0.888266i
$163$	−35453.2	−	5097.40i	−1.33438	−	0.191855i	−0.562065	−	0.827093i	$-0.689993\pi$
$163$	−35453.2	−	5097.40i	−1.33438	−	0.191855i	−0.772316	+	0.635238i	$0.780902\pi$
$164$	21650.7	−	16018.5i	0.804979	−	0.595571i
$165$	−16513.8	−	4848.90i	−0.606569	−	0.178105i
$166$	22098.1	−	727.069i	0.801933	−	0.0263852i
$167$	−2970.07	−	10115.1i	−0.106496	−	0.362692i	0.888952	−	0.458001i	$-0.151434\pi$
$167$	−2970.07	−	10115.1i	−0.106496	−	0.362692i	−0.995448	+	0.0953086i	$0.969616\pi$
$168$	−51880.1	+	30193.5i	−1.83816	+	1.06978i
$169$	−11403.1	+	24969.3i	−0.399255	+	0.874246i
$170$	−45874.6	+	8143.65i	−1.58736	+	0.281787i
$171$	66429.0	+	103366.i	2.27178	+	3.53495i
$172$	−5888.88	−	16063.8i	−0.199056	−	0.542991i
$173$	−323.978	−	2253.31i	−0.0108249	−	0.0752886i	0.983693	−	0.179856i	$-0.0575632\pi$
$173$	−323.978	−	2253.31i	−0.0108249	−	0.0752886i	−0.994518	+	0.104568i	$0.966654\pi$
$174$	−3025.26	+	27414.1i	−0.0999228	+	0.905472i
$175$	5146.09	+	4459.12i	0.168036	+	0.145604i
$176$	−10165.4	−	114.257i	−0.328171	−	0.00368857i
$177$	12892.9	+	8285.75i	0.411532	+	0.264475i
$178$	−18252.8	−	7620.71i	−0.576088	−	0.240522i
$179$	2375.39	−	2058.28i	0.0741359	−	0.0642391i	−0.617005	−	0.786960i	$-0.711654\pi$
$179$	2375.39	−	2058.28i	0.0741359	−	0.0642391i	0.691140	+	0.722720i	$0.257109\pi$
$180$	5783.52	−	74943.1i	0.178504	−	2.31306i
$181$	4457.02	+	9759.50i	0.136046	+	0.297900i	0.965377	−	0.260858i	$-0.0840054\pi$
$181$	4457.02	+	9759.50i	0.136046	+	0.297900i	−0.829331	+	0.558758i	$0.811278\pi$
$182$	−5334.55	−	5762.09i	−0.161048	−	0.173955i
$183$		−	27598.6i		−	0.824109i
$184$	25384.8	−	22401.8i	0.749786	−	0.661680i
$185$	11988.3			0.350280
$186$	49932.6	−	46227.6i	1.44331	−	1.33621i
$187$	15460.7	−	7060.68i	0.442127	−	0.201913i
$188$	59709.8	+	4607.93i	1.68939	+	0.130374i
$189$	56276.4	+	64946.4i	1.57544	+	1.81816i
$190$	29852.3	−	71500.8i	0.826933	−	1.98063i
$191$	−12444.6	+	19364.2i	−0.341126	+	0.530802i	−0.968855	−	0.247630i	$-0.920348\pi$
$191$	−12444.6	+	19364.2i	−0.341126	+	0.530802i	0.627729	+	0.778432i	$0.283985\pi$
$192$	−12789.4	−	63965.2i	−0.346934	−	1.73517i
$193$	−21703.9	+	25047.6i	−0.582670	+	0.672437i	−0.968177	−	0.250268i	$-0.919481\pi$
$193$	−21703.9	+	25047.6i	−0.582670	+	0.672437i	0.385507	+	0.922705i	$0.374027\pi$
$194$	−49979.0	−	5515.40i	−1.32796	−	0.146546i
$195$	14299.5	−	2055.96i	0.376055	−	0.0540686i
$196$	−16035.7	+	5878.57i	−0.417422	+	0.153024i
$197$	47347.9	−	30428.7i	1.22002	−	0.784062i	0.237716	−	0.971335i	$-0.423601\pi$
$197$	47347.9	−	30428.7i	1.22002	−	0.784062i	0.982308	+	0.187273i	$0.0599648\pi$
$198$	4792.76	+	26998.4i	0.122252	+	0.688666i
$199$	−30907.9	−	14115.2i	−0.780483	−	0.356435i	−0.0149973	−	0.999888i	$-0.504774\pi$
$199$	−30907.9	−	14115.2i	−0.780483	−	0.356435i	−0.765486	+	0.643453i	$0.777501\pi$
$200$	−6395.42	+	3722.05i	−0.159885	+	0.0930512i
$201$	8239.01	−	2419.19i	0.203931	−	0.0598795i
$202$	−1931.56	−	58706.4i	−0.0473374	−	1.43874i
$203$	−7183.75	+	24465.6i	−0.174325	+	0.593696i
$204$	64865.9	+	87673.4i	1.55868	+	2.10672i
$205$	−6519.29	+	45342.6i	−0.155129	+	1.07894i
$206$	−17262.8	+	21299.1i	−0.406796	+	0.501910i
$207$	−72095.6	−	56047.4i	−1.68255	−	1.30802i
$208$	7801.39	−	3457.34i	0.180321	−	0.0799127i
$209$	−4022.62	+	27977.9i	−0.0920908	+	0.640505i
$210$	25527.6	−	98856.2i	0.578857	−	2.24164i
$211$	−299.861	+	1021.23i	−0.00673528	+	0.0229383i	−0.962792	−	0.270243i	$-0.912896\pi$
$211$	−299.861	+	1021.23i	−0.00673528	+	0.0229383i	0.956057	+	0.293182i	$0.0947140\pi$
$212$	6909.00	−	9122.03i	0.153725	−	0.202964i
$213$	−86720.0	+	25463.3i	−1.91144	+	0.561249i
$214$	−55267.2	+	18222.4i	−1.20681	+	0.397903i
$215$	26471.2	+	12089.0i	0.572660	+	0.261525i
$216$	−86577.1	+	35009.3i	−1.85565	+	0.750372i
$217$	52922.7	−	34011.3i	1.12389	−	0.722277i
$218$	−11130.6	+	18640.0i	−0.234210	+	0.392224i
$219$	99340.4	−	14283.0i	2.07127	−	0.297804i
$220$	12295.4	−	12158.0i	0.254037	−	0.251198i
$221$	−9342.67	+	10782.0i	−0.191287	+	0.220758i
$222$	−12490.4	−	25128.8i	−0.253438	−	0.509878i
$223$	−30939.3	+	48142.5i	−0.622158	+	0.968097i	0.376965	+	0.926228i	$0.376968\pi$
$223$	−30939.3	+	48142.5i	−0.622158	+	0.968097i	−0.999123	+	0.0418695i	$0.986669\pi$
$224$	−1305.59	−	60292.9i	−0.0260202	−	1.20163i
$225$	13070.3	+	15083.9i	0.258178	+	0.297953i
$226$	49728.9	+	72054.6i	0.973626	+	1.41073i
$227$	40419.9	−	18459.1i	0.784411	−	0.358228i	0.0173883	−	0.999849i	$-0.494465\pi$
$227$	40419.9	−	18459.1i	0.784411	−	0.358228i	0.767022	+	0.641621i	$0.221738\pi$
$228$	−180976.	+	11921.8i	−3.48138	+	0.229337i
$229$	49668.9			0.947139			0.473570	−	0.880756i	$-0.342965\pi$
$229$	49668.9			0.947139			0.473570	+	0.880756i	$0.342965\pi$
$230$	−3264.57	+	57492.9i	−0.0617121	+	1.08682i
$231$			37245.8i			0.697996i
$232$	−22627.0	−	15994.6i	−0.420389	−	0.297164i
$233$	20715.0	+	45359.5i	0.381569	+	0.835520i	0.998811	+	0.0487463i	$0.0155226\pi$
$233$	20715.0	+	45359.5i	0.381569	+	0.835520i	−0.617242	+	0.786773i	$0.711750\pi$
$234$	−13073.5	−	18942.8i	−0.238759	−	0.345949i
$235$	−76982.2	+	66705.5i	−1.39397	+	1.20789i
$236$	−13555.2	+	7303.12i	−0.243379	+	0.131125i
$237$	−75657.7	−	48622.3i	−1.34697	−	0.865642i
$238$	44878.7	+	90289.1i	0.792294	+	1.59397i
$239$	63362.6	+	54904.0i	1.10927	+	0.961188i	0.999463	−	0.0327644i	$-0.0104311\pi$
$239$	63362.6	+	54904.0i	1.10927	+	0.961188i	0.109807	+	0.993953i	$0.464977\pi$
$240$	92658.3	+	61030.2i	1.60865	+	1.05955i
$241$	−3060.41	−	21285.6i	−0.0526922	−	0.366482i	−0.999058	−	0.0433861i	$-0.986185\pi$
$241$	−3060.41	−	21285.6i	−0.0526922	−	0.366482i	0.946366	−	0.323096i	$-0.104724\pi$
$242$	26790.9	−	44865.9i	0.457463	−	0.766100i
$243$	15791.8	+	24572.5i	0.267435	+	0.416138i
$244$	24260.8	+	13424.9i	0.407498	+	0.225493i
$245$	12067.8	−	26424.8i	0.201047	−	0.440231i
$246$	101835.	−	33576.6i	1.68279	−	0.554838i
$247$	−6684.26	−	22764.5i	−0.109562	−	0.373133i
$248$	16347.9	+	66380.5i	0.265802	+	1.07929i
$249$	84463.1	+	24800.6i	1.36229	+	0.400003i
$250$	−13864.0	+	53688.6i	−0.221824	+	0.859018i
$251$	50182.3	+	7215.12i	0.796531	+	0.114524i	0.528552	−	0.848901i	$-0.322735\pi$
$251$	50182.3	+	7215.12i	0.796531	+	0.114524i	0.267979	+	0.963425i	$0.413644\pi$
$252$	−159138.	+	33682.9i	−2.50596	+	0.530407i
$253$	−4090.86	−	20605.1i	−0.0639107	−	0.321909i
$254$	−25455.5	+	31407.3i	−0.394561	+	0.486814i
$255$	−183612.	−	26399.5i	−2.82372	−	0.405990i
$256$	62450.4	+	19872.3i	0.952918	+	0.303228i
$257$	−42189.8	−	12388.1i	−0.638766	−	0.187559i	−0.0537165	−	0.998556i	$-0.517107\pi$
$257$	−42189.8	−	12388.1i	−0.638766	−	0.187559i	−0.585049	+	0.810998i	$0.698925\pi$
$258$	−2240.03	−	68081.9i	−0.0336522	−	1.02280i
$259$	−7309.13	−	24892.6i	−0.108960	−	0.371083i
$260$	−5148.47	+	13570.2i	−0.0761609	+	0.200743i
$261$	−31047.9	+	67985.3i	−0.455775	+	0.998009i
$262$	16993.0	+	95724.4i	0.247553	+	1.39451i
$263$	−6012.11	−	9355.03i	−0.0869192	−	0.135249i	0.795072	−	0.606516i	$-0.207433\pi$
$263$	−6012.11	−	9355.03i	−0.0869192	−	0.135249i	−0.881991	+	0.471267i	$0.843797\pi$
$264$	−38294.8	−	13105.3i	−0.549455	−	0.188035i
$265$	2769.96	+	19265.5i	0.0394441	+	0.274340i
$266$	−166665.	−	18392.2i	−2.35549	−	0.259939i
$267$	−59516.2	−	51571.1i	−0.834858	−	0.723409i
$268$	−1881.13	+	8419.36i	−0.0261909	+	0.117222i
$269$	−119003.	−	76478.3i	−1.64457	−	1.05690i	−0.936447	−	0.350809i	$-0.885907\pi$
$269$	−119003.	−	76478.3i	−1.64457	−	1.05690i	−0.708121	−	0.706091i	$-0.750457\pi$
$270$	61198.5	−	146580.i	0.839486	−	2.01070i
$271$	−85252.4	+	73871.7i	−1.16083	+	1.00586i	−0.161008	+	0.986953i	$0.551474\pi$
$271$	−85252.4	+	73871.7i	−1.16083	+	1.00586i	−0.999821	+	0.0189108i	$0.993980\pi$
$272$	−108623.	+	14373.5i	−1.46820	+	0.194279i
$273$	−12987.2	−	28438.1i	−0.174257	−	0.381570i
$274$	−27425.3	+	25390.3i	−0.365300	+	0.338195i
$275$			4591.40i			0.0607127i
$276$	123913.	−	53058.0i	1.62666	−	0.696518i
$277$	−76329.8			−0.994798			−0.497399	−	0.867522i	$-0.665711\pi$
$277$	−76329.8			−0.994798			−0.497399	+	0.867522i	$0.665711\pi$
$278$	24632.3	+	26606.4i	0.318724	+	0.344268i
$279$	167732.	−	76600.6i	2.15480	−	0.984065i
$280$	74482.9	+	70527.4i	0.950037	+	0.899585i
$281$	40815.2	+	47103.2i	0.516903	+	0.596538i	0.952853	−	0.303433i	$-0.0981329\pi$
$281$	40815.2	+	47103.2i	0.516903	+	0.596538i	−0.435950	+	0.899971i	$0.643587\pi$
$282$	220028.	+	91863.9i	2.76682	+	1.15517i
$283$	71100.9	−	110635.i	0.887773	−	1.38140i	−0.0363628	−	0.999339i	$-0.511577\pi$
$283$	71100.9	−	110635.i	0.887773	−	1.38140i	0.924136	−	0.382064i	$-0.124786\pi$
$284$	19800.0	−	88618.3i	0.245486	−	1.09872i
$285$	202017.	−	233140.i	2.48713	−	2.87030i
$286$	580.770	−	5262.78i	0.00710022	−	0.0643403i
$287$	98124.4	−	14108.2i	1.19128	−	0.171280i
$288$	21362.9	−	175472.i	0.257558	−	2.11555i
$289$	83847.5	−	53885.5i	1.00391	−	0.645173i
$290$	46405.2	−	8237.85i	0.551786	−	0.0979530i
$291$	−182103.	−	83163.8i	−2.15046	−	0.982083i
$292$	−35767.1	+	94273.8i	−0.419486	+	1.10567i
$293$	−28936.7	+	8496.59i	−0.337066	+	0.0989714i	−0.445885	−	0.895090i	$-0.647111\pi$
$293$	−28936.7	+	8496.59i	−0.337066	+	0.0989714i	0.108820	+	0.994062i	$0.465293\pi$
$294$	−67962.6	+	2236.10i	−0.786277	+	0.0258700i
$295$	7378.39	−	25128.5i	0.0847847	−	0.288750i
$296$	28165.5	+	1243.74i	0.321466	+	0.0141953i
$297$	−8246.55	+	57356.0i	−0.0934888	+	0.650229i
$298$	27160.8	+	22013.7i	0.305851	+	0.247891i
$299$	10308.3	+	14306.0i	0.115304	+	0.160021i
$300$	−28822.5	+	6100.51i	−0.320250	+	0.0677835i
$301$	8962.49	−	62335.5i	0.0989226	−	0.688022i
$302$	75921.2	+	19605.1i	0.832433	+	0.214959i
$303$	65886.1	−	224387.i	0.717643	−	2.44407i
$304$	77553.2	−	164888.i	0.839175	−	1.78419i
$305$	−45251.2	+	13287.0i	−0.486441	+	0.142832i
$306$	92542.9	+	280676.i	0.988326	+	2.99753i
$307$	6951.73	+	3174.75i	0.0737592	+	0.0336847i	0.451953	−	0.892042i	$-0.350727\pi$
$307$	6951.73	+	3174.75i	0.0737592	+	0.0336847i	−0.378194	+	0.925726i	$0.623455\pi$
$308$	−32741.2	−	18117.7i	−0.345139	−	0.190986i
$309$	−91827.3	+	59013.8i	−0.961734	+	0.618069i
$310$	−99835.2	−	59614.9i	−1.03887	−	0.620342i
$311$	−66821.7	+	9607.52i	−0.690871	+	0.0993323i	−0.478803	−	0.877923i	$-0.658929\pi$
$311$	−66821.7	+	9607.52i	−0.690871	+	0.0993323i	−0.212068	+	0.977255i	$0.568020\pi$
$312$	33808.7	−	3346.78i	0.347312	−	0.0343810i
$313$	−48984.8	+	56531.5i	−0.500004	+	0.577035i	−0.948511	−	0.316744i	$-0.897410\pi$
$313$	−48984.8	+	56531.5i	−0.500004	+	0.577035i	0.448507	+	0.893779i	$0.351956\pi$
$314$	−86154.0	+	42823.3i	−0.873808	+	0.434331i
$315$	149581.	−	232753.i	1.50750	−	2.34571i
$316$	79544.4	−	42856.0i	0.796591	−	0.429178i
$317$	−65080.2	−	75106.5i	−0.647635	−	0.747410i	0.333071	−	0.942902i	$-0.391915\pi$
$317$	−65080.2	−	75106.5i	−0.647635	−	0.747410i	−0.980705	+	0.195492i	$0.937370\pi$
$318$	37496.6	−	25878.5i	0.370798	−	0.255909i
$319$	−15639.6	+	7142.35i	−0.153689	+	0.0701875i
$320$	−98721.5	+	51764.9i	−0.964077	+	0.505517i
$321$	−231693.			−2.24855
$322$	121369.	−	28274.1i	1.17057	−	0.272695i
$323$			304647.i			2.92006i
$324$	−147771.	+	9734.47i	−1.40767	+	0.0927305i
$325$	−1600.97	−	3505.65i	−0.0151572	−	0.0331895i
$326$	117915.	−	81379.7i	1.10952	−	0.765739i
$327$	−65325.3	+	56604.7i	−0.610922	+	0.529367i
$328$	−20020.6	+	105852.i	−0.186093	+	0.983903i
$329$	185443.	+	119177.i	1.71324	+	1.10103i
$330$	61648.4	−	30642.7i	0.566101	−	0.281384i
$331$	−14380.4	−	12460.7i	−0.131255	−	0.113733i	0.586760	−	0.809761i	$-0.300403\pi$
$331$	−14380.4	−	12460.7i	−0.131255	−	0.113733i	−0.718014	+	0.696028i	$0.754949\pi$
$332$	−62887.0	+	62184.2i	−0.570538	+	0.564162i
$333$	−10822.2	−	75269.9i	−0.0975947	−	0.678786i
$334$	36205.0	+	21619.2i	0.324546	+	0.193797i
$335$	−7933.12	−	12344.2i	−0.0706894	−	0.109995i
$336$	70230.8	−	229606.i	0.622084	−	2.03378i
$337$	−25240.3	+	55268.6i	−0.222246	+	0.486652i	−0.987606	−	0.156951i	$-0.949834\pi$
$337$	−25240.3	+	55268.6i	−0.222246	+	0.486652i	0.765360	+	0.643602i	$0.222561\pi$
$338$	−34381.8	−	104278.i	−0.300951	−	0.912764i
$339$	98202.9	+	334448.i	0.854525	+	2.91024i
$340$	112522.	−	148565.i	0.973376	−	1.28516i
$341$	40700.7	+	11950.8i	0.350020	+	0.102775i
$342$	−475873.	−	122885.i	−4.06855	−	1.05062i
$343$	77737.9	+	11177.0i	0.660761	+	0.0950031i
$344$	60937.6	+	31148.3i	0.514954	+	0.263219i
$345$	−84020.6	+	213321.i	−0.705907	+	1.79223i
$346$	7074.18	+	5733.59i	0.0590913	+	0.0478933i
$347$	−56611.4	−	8139.49i	−0.470159	−	0.0675987i	−0.0968366	−	0.995300i	$-0.530872\pi$
$347$	−56611.4	−	8139.49i	−0.470159	−	0.0675987i	−0.373323	+	0.927702i	$0.621782\pi$
$348$	−65616.2	−	88687.5i	−0.541817	−	0.732325i
$349$	−62516.4	−	18356.5i	−0.513267	−	0.150709i	0.0148347	−	0.999890i	$-0.495278\pi$
$349$	−62516.4	−	18356.5i	−0.513267	−	0.150709i	−0.528102	+	0.849181i	$0.677096\pi$
$350$	−27222.3	+	895.667i	−0.222223	+	0.00731157i
$351$	−13703.0	−	46668.2i	−0.111225	−	0.378798i
$352$	30148.3	−	27288.5i	0.243320	−	0.220239i
$353$	83664.5	−	183200.i	0.671416	−	1.47020i	−0.200073	−	0.979781i	$-0.564118\pi$
$353$	83664.5	−	183200.i	0.671416	−	1.47020i	0.871489	−	0.490415i	$-0.163155\pi$
$354$	−60359.5	+	10715.0i	−0.481658	+	0.0855040i
$355$	83500.3	+	129929.i	0.662570	+	1.03098i
$356$	74284.8	−	27232.3i	0.586138	−	0.214874i
$357$	57130.2	+	397349.i	0.448259	+	3.11771i
$358$	−1379.04	+	12496.5i	−0.0107600	+	0.0975039i
$359$	−49402.8	−	42807.8i	−0.383321	−	0.332150i	0.441792	−	0.897118i	$-0.354343\pi$
$359$	−49402.8	−	42807.8i	−0.383321	−	0.332150i	−0.825113	+	0.564968i	$0.808889\pi$
$360$	186677.	+	235691.i	1.44041	+	1.81860i
$361$	−316572.	−	203448.i	−2.42917	−	1.56113i
$362$	−39603.2	−	16534.7i	−0.302213	−	0.126177i
$363$	157236.	−	136245.i	1.19327	−	1.03397i
$364$	31316.2	+	2416.74i	0.236356	+	0.0182401i
$365$	−71244.7	−	156004.i	−0.534770	−	1.17098i
$366$	74997.4	+	81008.1i	0.559866	+	0.604736i
$367$		−	141495.i		−	1.05053i	−0.850937	−	0.525267i	$-0.823965\pi$
$367$		−	141495.i		−	1.05053i	0.850937	−	0.525267i	$-0.176035\pi$
$368$	−13634.5	+	134736.i	−0.100680	+	0.994919i
$369$	290573.			2.13404
$370$	−35188.4	+	32577.5i	−0.257038	+	0.237966i
$371$	38314.2	−	17497.5i	0.278363	−	0.127124i
$372$	−20942.8	+	271377.i	−0.151338	+	1.96104i
$373$	−19743.3	−	22784.9i	−0.141906	−	0.163768i	0.680347	−	0.732890i	$-0.261829\pi$
$373$	−19743.3	−	22784.9i	−0.141906	−	0.163768i	−0.822254	+	0.569121i	$0.807283\pi$
$374$	−26193.8	+	62738.3i	−0.187264	+	0.448528i
$375$	−119356.	+	185722.i	−0.848754	+	1.32069i
$376$	−187783.	+	148732.i	−1.32826	+	1.05203i
$377$	9450.74	−	10906.7i	0.0664941	−	0.0767382i
$378$	−341671.	−	37704.9i	−2.39125	−	0.263885i
$379$	52814.4	−	7593.56i	0.367683	−	0.0528648i	0.0440029	−	0.999031i	$-0.485989\pi$
$379$	52814.4	−	7593.56i	0.367683	−	0.0528648i	0.323680	+	0.946167i	$0.395080\pi$
$380$	106676.	+	290993.i	0.738752	+	2.01518i
$381$	−135407.	+	87021.0i	−0.932807	+	0.599479i
$382$	−16093.2	−	90655.7i	−0.110285	−	0.621253i
$383$	13116.3	+	5990.02i	0.0894158	+	0.0408348i	0.459621	−	0.888115i	$-0.347985\pi$
$383$	13116.3	+	5990.02i	0.0894158	+	0.0408348i	−0.370205	+	0.928950i	$0.620713\pi$
$384$	211361.	+	152998.i	1.43338	+	1.03758i
$385$	61068.9	−	17931.5i	0.412001	−	0.120975i
$386$	−4359.48	−	132499.i	−0.0292591	−	0.889280i
$387$	52005.7	−	177115.i	0.347239	−	1.18259i
$388$	161687.	−	119626.i	1.07402	−	0.794623i
$389$	28317.7	−	196954.i	0.187136	−	1.30156i	−0.652240	−	0.758012i	$-0.726171\pi$
$389$	28317.7	−	196954.i	0.187136	−	1.30156i	0.839377	−	0.543550i	$-0.182920\pi$
$390$	−36385.3	+	44892.7i	−0.239220	+	0.295152i
$391$	−75248.0	−	213546.i	−0.492200	−	1.39681i
$392$	31093.8	−	60830.9i	0.202349	−	0.395869i
$393$	−55086.7	+	383136.i	−0.356666	+	2.48066i
$394$	−56288.9	+	217980.i	−0.362602	+	1.40418i
$395$	−43297.7	+	147458.i	−0.277505	+	0.945095i
$396$	−87434.4	−	66222.5i	−0.557560	−	0.422294i
$397$	35509.6	−	10426.5i	0.225302	−	0.0661545i	−0.167133	−	0.985934i	$-0.553451\pi$
$397$	35509.6	−	10426.5i	0.225302	−	0.0661545i	0.392435	+	0.919780i	$0.371633\pi$
$398$	129079.	−	42559.0i	0.814870	−	0.268674i
$399$	−607261.	−	277327.i	−3.81443	−	1.74199i
$400$	8657.56	−	28304.2i	0.0541098	−	0.176901i
$401$	249105.	−	160090.i	1.54915	−	0.995577i	0.563626	−	0.826030i	$-0.309406\pi$
$401$	249105.	−	160090.i	1.54915	−	0.995577i	0.985522	−	0.169547i	$-0.0542305\pi$
$402$	−17609.4	+	29489.9i	−0.108966	+	0.182482i
$403$	−35243.1	+	5067.19i	−0.217002	+	0.0312002i
$404$	165200.	+	167068.i	1.01216	+	1.02360i
$405$	164952.	−	190365.i	1.00565	−	1.16058i
$406$	−45397.8	−	91333.4i	−0.275412	−	0.554087i
$407$	9457.64	−	14716.4i	0.0570944	−	0.0888407i
$408$	−428643.	−	81072.3i	−2.57499	−	0.487026i
$409$	183386.	+	211639.i	1.09628	+	1.26517i	0.961652	+	0.274274i	$0.0884375\pi$
$409$	183386.	+	211639.i	1.09628	+	1.26517i	0.134625	+	0.990897i	$0.457017\pi$
$410$	−104080.	−	150807.i	−0.619156	−	0.897124i
$411$	−135354.	+	61814.1i	−0.801285	+	0.365935i
$412$	−7208.60	−	109428.i	−0.0424675	−	0.644665i
$413$	−56675.5			−0.332273
$414$	363922.	−	31403.4i	2.12328	−	0.183222i
$415$		−	150427.i		−	0.873435i
$416$	−13503.7	+	31347.9i	−0.0780310	+	0.181143i
$417$	59968.5	+	131313.i	0.344867	+	0.755152i
$418$	−64220.9	−	93052.7i	−0.367556	−	0.532570i
$419$	−153334.	+	132865.i	−0.873395	+	0.756801i	−0.971165	−	0.238408i	$-0.923374\pi$
$419$	−153334.	+	132865.i	−0.873395	+	0.756801i	0.0977701	+	0.995209i	$0.468829\pi$
$420$	193706.	+	359535.i	1.09811	+	2.03818i
$421$	−123393.	−	79299.9i	−0.696188	−	0.447413i	0.144093	−	0.989564i	$-0.453974\pi$
$421$	−123393.	−	79299.9i	−0.696188	−	0.447413i	−0.840281	+	0.542151i	$0.817610\pi$
$422$	−1894.98	−	3812.41i	−0.0106409	−	0.0214079i
$423$	488311.	+	423124.i	2.72907	+	2.36476i
$424$	4509.07	+	45550.0i	0.0250816	+	0.253371i
$425$	7042.61	+	48982.4i	0.0389902	+	0.271183i
$426$	185348.	−	310397.i	1.02134	−	1.71040i
$427$	55178.2	+	85859.0i	0.302630	+	0.470901i
$428$	112704.	−	203672.i	0.615248	−	1.11184i
$429$	8757.12	−	19175.4i	0.0475825	−	0.104191i
$430$	−110550.	+	36449.9i	−0.597891	+	0.197133i
$431$	−10579.0	−	36028.8i	−0.0569496	−	0.193953i	0.926105	−	0.377266i	$-0.123136\pi$
$431$	−10579.0	−	36028.8i	−0.0569496	−	0.193953i	−0.983054	+	0.183314i	$0.941318\pi$
$432$	158988.	−	338028.i	0.851914	−	1.81128i
$433$	−156.900	−	46.0699i	−0.000836847	−	0.000245720i	0.281314	−	0.959616i	$-0.409230\pi$
$433$	−156.900	−	46.0699i	−0.000836847	−	0.000245720i	−0.282151	+	0.959370i	$0.591048\pi$
$434$	−62916.3	+	243645.i	−0.334029	+	1.29353i
$435$	185736.	+	26704.8i	0.981563	+	0.141127i
$436$	−17982.3	−	84959.4i	−0.0945961	−	0.446929i
$437$	366408.	+	86724.4i	1.91868	+	0.454128i
$438$	−252773.	+	311875.i	−1.31760	+	1.62567i
$439$	−139492.	−	20056.0i	−0.723805	−	0.104067i	−0.229441	−	0.973323i	$-0.573690\pi$
$439$	−139492.	−	20056.0i	−0.723805	−	0.104067i	−0.494364	+	0.869255i	$0.664599\pi$
$440$	−3051.25	+	69098.3i	−0.0157606	+	0.356913i
$441$	−176805.	−	51914.6i	−0.909111	−	0.266939i
$442$	−1876.59	−	57035.8i	−0.00960560	−	0.291946i
$443$	−32822.9	−	111785.i	−0.167251	−	0.569606i	−0.999876	−	0.0157677i	$-0.994981\pi$
$443$	−32822.9	−	111785.i	−0.167251	−	0.569606i	0.832624	−	0.553838i	$-0.186837\pi$
$444$	104948.	+	39816.9i	0.532364	+	0.201977i
$445$	−55903.8	+	122412.i	−0.282307	+	0.618165i
$446$	−40010.3	−	225385.i	−0.201142	−	1.13306i
$447$	75255.1	+	117099.i	0.376635	+	0.586056i
$448$	167674.	+	173425.i	0.835430	+	0.864085i
$449$	−29027.2	−	201889.i	−0.143983	−	1.00143i	−0.925826	−	0.377951i	$-0.876629\pi$
$449$	−29027.2	−	201889.i	−0.143983	−	1.00143i	0.781842	−	0.623476i	$-0.214280\pi$
$450$	−79353.6	−	8757.01i	−0.391870	−	0.0432445i
$451$	50517.6	+	43773.8i	0.248365	+	0.215209i
$452$	−341769.	−	76361.3i	−1.67285	−	0.373763i
$453$	262630.	+	168782.i	1.27982	+	0.822487i
$454$	−68480.0	+	164020.i	−0.332240	+	0.795766i
$455$	−40375.1	+	34985.2i	−0.195025	+	0.168990i
$456$	498809.	−	526784.i	2.39886	−	2.53340i
$457$	−63483.8	−	139010.i	−0.303970	−	0.665601i	0.694581	−	0.719414i	$-0.255590\pi$
$457$	−63483.8	−	139010.i	−0.303970	−	0.665601i	−0.998551	+	0.0538133i	$0.982862\pi$
$458$	−145789.	+	134972.i	−0.695017	+	0.643447i
$459$			624541.i			2.96439i
$460$	−146651.	−	177626.i	−0.693058	−	0.839442i
$461$	18754.2			0.0882464			0.0441232	−	0.999026i	$-0.485951\pi$
$461$	18754.2			0.0882464			0.0441232	+	0.999026i	$0.485951\pi$
$462$	−101213.	−	109325.i	−0.474190	−	0.512194i
$463$	−4875.58	+	2226.60i	−0.0227439	+	0.0103868i	−0.426754	−	0.904368i	$-0.640343\pi$
$463$	−4875.58	+	2226.60i	−0.0227439	+	0.0103868i	0.404011	+	0.914754i	$0.367616\pi$
$464$	109880.	−	14539.8i	0.510365	−	0.0675339i
$465$	−303172.	−	349879.i	−1.40211	−	1.61813i
$466$	−184065.	−	76848.7i	−0.847615	−	0.353887i
$467$	−4099.80	+	6379.41i	−0.0187987	+	0.0292514i	−0.850526	−	0.525933i	$-0.823716\pi$
$467$	−4099.80	+	6379.41i	−0.0187987	+	0.0292514i	0.831727	+	0.555185i	$0.187352\pi$
$468$	89849.5	+	20075.0i	0.410227	+	0.0916567i
$469$	−20794.8	+	23998.5i	−0.0945385	+	0.109103i
$470$	44692.4	−	404990.i	0.202319	−	1.83336i
$471$	−379151.	+	54513.7i	−1.70911	+	0.245733i
$472$	19941.9	−	58271.7i	0.0895121	−	0.261562i
$473$	35723.2	−	22957.9i	0.159672	−	0.102615i
$474$	354200.	−	62877.6i	1.57649	−	0.279859i
$475$	−74858.9	−	34186.9i	−0.331784	−	0.151521i
$476$	−377084.	−	143064.i	−1.66427	−	0.631417i
$477$	118460.	−	34782.9i	0.520636	−	0.152873i
$478$	−335182.	+	11028.1i	−1.46698	+	0.0482666i
$479$	73088.0	−	248915.i	0.318548	−	1.08487i	−0.632173	−	0.774827i	$-0.717837\pi$
$479$	73088.0	−	248915.i	0.318548	−	1.08487i	0.950721	−	0.310048i	$-0.100345\pi$
$480$	−437819.	+	72655.6i	−1.90025	+	0.315346i
$481$	−2089.69	+	14534.1i	−0.00903216	+	0.0628200i
$482$	66825.3	+	54161.7i	0.287639	+	0.233130i
$483$	494167.	+	44401.8i	2.11826	+	0.190330i
$484$	43282.8	+	204494.i	0.184767	+	0.872951i
$485$	−48686.0	+	338618.i	−0.206976	+	1.43955i
$486$	−113127.	−	29212.7i	−0.478952	−	0.123680i
$487$	−95523.8	+	325324.i	−0.402767	+	1.37170i	0.469615	+	0.882872i	$0.344393\pi$
$487$	−95523.8	+	325324.i	−0.402767	+	1.37170i	−0.872381	+	0.488826i	$0.837425\pi$
$488$	−107692.	+	26521.9i	−0.452215	+	0.111369i
$489$	547313.	−	160706.i	2.28885	−	0.672068i
$490$	36386.0	+	110356.i	0.151545	+	0.459627i
$491$	225285.	+	102884.i	0.934477	+	0.426761i	0.823663	−	0.567080i	$-0.191927\pi$
$491$	225285.	+	102884.i	0.934477	+	0.426761i	0.110814	+	0.993841i	$0.464654\pi$
$492$	−207668.	+	375286.i	−0.857905	+	1.55036i
$493$	−155892.	+	100186.i	−0.641403	+	0.412205i
$494$	81480.8	+	48654.9i	0.333889	+	0.199376i
$495$	184659.	−	26550.0i	0.753634	−	0.108356i
$496$	−228369.	−	150417.i	−0.928270	−	0.611413i
$497$	218876.	−	252597.i	0.886106	−	1.02262i
$498$	−315312.	+	156728.i	−1.27140	+	0.631956i
$499$	176619.	−	274825.i	0.709311	−	1.10371i	−0.280297	−	0.959913i	$-0.590433\pi$
$499$	176619.	−	274825.i	0.709311	−	1.10371i	0.989607	−	0.143796i	$-0.0459308\pi$
$500$	−105201.	−	195263.i	−0.420805	−	0.781051i
$501$	109945.	+	126883.i	0.438025	+	0.505508i
$502$	−166903.	+	115189.i	−0.662303	+	0.457092i
$503$	38568.0	−	17613.4i	0.152437	−	0.0696157i	−0.337736	−	0.941241i	$-0.609661\pi$
$503$	38568.0	−	17613.4i	0.152437	−	0.0696157i	0.490173	+	0.871625i	$0.336934\pi$
$504$	375576.	−	531315.i	1.47855	−	2.09166i
$505$	−399630.			−1.56702
$506$	68000.5	+	49363.8i	0.265589	+	0.192800i
$507$		−	437157.i		−	1.70067i
$508$	−10629.7	−	161361.i	−0.0411902	−	0.625275i
$509$	205208.	+	449342.i	0.792060	+	1.73437i	0.670660	+	0.741765i	$0.266011\pi$
$509$	205208.	+	449342.i	0.792060	+	1.73437i	0.121400	+	0.992604i	$0.461262\pi$
$510$	610683.	−	421466.i	2.34788	−	1.62040i
$511$	−280491.	+	243047.i	−1.07418	+	0.930782i
$512$	−237308.	+	111375.i	−0.905258	+	0.424863i
$513$	−873739.	−	561518.i	−3.32007	−	2.13368i
$514$	157500.	−	78286.4i	0.596150	−	0.296320i
$515$	140969.	+	122151.i	0.531508	+	0.460555i
$516$	191583.	+	193748.i	0.719544	+	0.727677i
$517$	21153.3	+	147124.i	0.0791402	+	0.550432i
$518$	89098.0	+	53203.4i	0.332054	+	0.198280i
$519$	19600.6	+	30499.1i	0.0727671	+	0.113228i
$520$	−21764.2	−	53822.2i	−0.0804889	−	0.199047i
$521$	25589.2	−	56032.6i	0.0942718	−	0.206426i	−0.856621	−	0.515945i	$-0.827441\pi$
$521$	25589.2	−	56032.6i	0.0942718	−	0.206426i	0.950893	+	0.309519i	$0.100168\pi$
$522$	−93613.3	−	283923.i	−0.343555	−	1.04198i
$523$	−148636.	−	506206.i	−0.543400	−	1.85065i	−0.525473	−	0.850811i	$-0.676111\pi$
$523$	−148636.	−	506206.i	−0.543400	−	1.85065i	−0.0179272	−	0.999839i	$-0.505707\pi$
$524$	−310003.	−	234795.i	−1.12903	−	0.855120i
$525$	−104049.	−	30551.5i	−0.377502	−	0.110845i
$526$	43068.6	+	11121.6i	0.155664	+	0.0401972i
$527$	452538.	+	65065.2i	1.62942	+	0.234276i
$528$	148017.	−	65596.6i	0.530937	−	0.235295i
$529$	−278259.	+	29712.5i	−0.994347	+	0.106176i
$530$	−60483.2	−	49021.4i	−0.215319	−	0.174515i
$531$	−164432.	−	23641.8i	−0.583174	−	0.0838478i
$532$	539180.	−	398917.i	1.90507	−	1.40948i
$533$	−53835.0	−	15807.4i	−0.189500	−	0.0556423i
$534$	314834.	−	10358.7i	1.10408	−	0.0363263i
$535$	111545.	+	379889.i	0.389712	+	1.32724i
$536$	−17357.5	−	29824.6i	−0.0604168	−	0.103811i
$537$	−20793.8	+	45532.1i	−0.0721084	+	0.157895i
$538$	557124.	−	98900.7i	1.92481	−	0.341692i
$539$	−22917.7	−	35660.6i	−0.0788848	−	0.122747i
$540$	218690.	+	596548.i	0.749966	+	2.04578i
$541$	−6158.19	−	42831.2i	−0.0210406	−	0.146341i	0.976593	−	0.215096i	$-0.0690064\pi$
$541$	−6158.19	−	42831.2i	−0.0210406	−	0.146341i	−0.997634	+	0.0687550i	$0.978097\pi$
$542$	49493.7	−	448498.i	0.168481	−	1.52673i
$543$	−129133.	−	111894.i	−0.437962	−	0.379496i
$544$	279774.	−	337366.i	0.945388	−	1.14000i
$545$	124260.	+	79857.2i	0.418349	+	0.268857i
$546$	115399.	+	48180.2i	0.387094	+	0.161616i
$547$	−262709.	+	227638.i	−0.878010	+	0.760800i	−0.972051	−	0.234768i	$-0.924567\pi$
$547$	−262709.	+	227638.i	−0.878010	+	0.760800i	0.0940413	+	0.995568i	$0.470021\pi$
$548$	11502.7	−	149053.i	0.0383036	−	0.496339i
$549$	124273.	+	272120.i	0.412317	+	0.902849i
$550$	−12476.8	−	13476.8i	−0.0412457	−	0.0445513i
$551$		−	308171.i		−	1.01505i
$552$	−219530.	+	492462.i	−0.720470	+	1.61620i
$553$	332582.			1.08755
$554$	224045.	−	207421.i	0.729989	−	0.675825i
$555$	−173668.	+	79311.6i	−0.563812	+	0.257484i
$556$	−144602.	−	11159.3i	−0.467763	−	0.0360983i
$557$	−60184.7	−	69456.8i	−0.193988	−	0.223874i	0.650420	−	0.759575i	$-0.274593\pi$
$557$	−60184.7	−	69456.8i	−0.193988	−	0.223874i	−0.844408	+	0.535701i	$0.820048\pi$
$558$	−284174.	+	680641.i	−0.912674	+	2.18600i
$559$	−19270.4	+	29985.3i	−0.0616689	+	0.0959586i
$560$	−410278.	−	4611.44i	−1.30828	−	0.0147048i
$561$	−177259.	+	204568.i	−0.563227	+	0.649999i
$562$	−247802.	−	27346.0i	−0.784570	−	0.0865807i
$563$	−264241.	+	37992.1i	−0.833649	+	0.119861i	−0.545905	−	0.837847i	$-0.683814\pi$
$563$	−264241.	+	37992.1i	−0.833649	+	0.119861i	−0.287743	+	0.957708i	$0.592905\pi$
$564$	−895467.	+	328272.i	−2.81508	+	1.03199i
$565$	501090.	−	322031.i	1.56971	−	1.00879i
$566$	91946.7	+	517951.i	0.287014	+	1.61680i
$567$	−495843.	−	226444.i	−1.54233	−	0.704360i
$568$	182697.	+	313920.i	0.566285	+	0.973021i
$569$	−6282.50	+	1844.71i	−0.0194048	+	0.00569775i	−0.291421	−	0.956595i	$-0.594128\pi$
$569$	−6282.50	+	1844.71i	−0.0194048	+	0.00569775i	0.272016	+	0.962293i	$0.412310\pi$
$570$	40577.6	+	1.23329e6i	0.124892	+	3.79590i
$571$	125871.	−	428676.i	0.386058	−	1.31479i	−0.505868	−	0.862611i	$-0.668828\pi$
$571$	125871.	−	428676.i	0.386058	−	1.31479i	0.891926	−	0.452181i	$-0.149354\pi$
$572$	12596.6	+	17025.6i	0.0384999	+	0.0520369i
$573$	52169.7	−	362849.i	0.158895	−	1.10514i
$574$	−249679.	+	308057.i	−0.757807	+	0.934992i
$575$	60917.4	+	5473.55i	0.184249	+	0.0165551i
$576$	414130.	+	573103.i	1.24822	+	1.72738i
$577$	34421.7	−	239408.i	0.103390	−	0.719096i	−0.870515	−	0.492142i	$-0.836214\pi$
$577$	34421.7	−	239408.i	0.103390	−	0.719096i	0.973905	−	0.226954i	$-0.0728767\pi$
$578$	−99680.9	+	386016.i	−0.298371	+	1.15545i
$579$	148703.	−	506438.i	0.443572	−	1.51067i
$580$	−113824.	+	150283.i	−0.338359	+	0.446739i
$581$	−312348.	+	91713.7i	−0.925309	+	0.271695i
$582$	760506.	−	250749.i	2.24521	−	0.740276i
$583$	25834.8	+	11798.3i	0.0760094	+	0.0347123i
$584$	−151199.	−	373910.i	−0.443325	−	1.09633i
$585$	−131734.	+	84660.4i	−0.384934	+	0.247382i
$586$	61846.9	−	103573.i	0.180104	−	0.301614i
$587$	90170.0	−	12964.5i	0.261689	−	0.0376252i	−0.0102214	−	0.999948i	$-0.503254\pi$
$587$	90170.0	−	12964.5i	0.261689	−	0.0376252i	0.271911	+	0.962323i	$0.412345\pi$
$588$	193409.	−	191247.i	0.559400	−	0.553147i
$589$	−497899.	+	574606.i	−1.43519	+	1.65630i
$590$	46627.8	+	93808.1i	0.133949	+	0.269486i
$591$	−484595.	+	754044.i	−1.38741	+	2.15885i
$592$	−86051.9	+	72887.4i	−0.245537	+	0.207974i
$593$	−181310.	−	209243.i	−0.515600	−	0.595034i	0.436924	−	0.899499i	$-0.356068\pi$
$593$	−181310.	−	209243.i	−0.515600	−	0.595034i	−0.952524	+	0.304464i	$0.901523\pi$
$594$	−131656.	−	190762.i	−0.373136	−	0.540654i
$595$	623998.	−	284970.i	1.76258	−	0.804944i
$596$	−139544.	+	9192.49i	−0.392843	+	0.0258786i
$597$	541128.			1.51828
$598$	−69132.7	−	13979.4i	−0.193322	−	0.0390919i
$599$			298331.i			0.831466i	0.909487	+	0.415733i	$0.136475\pi$
$599$			298331.i			0.831466i	−0.909487	+	0.415733i	$0.863525\pi$
$600$	68022.7	−	96229.6i	0.188952	−	0.267304i
$601$	−109280.	−	239291.i	−0.302547	−	0.662487i	0.695903	−	0.718136i	$-0.255004\pi$
$601$	−109280.	−	239291.i	−0.302547	−	0.662487i	−0.998450	+	0.0556493i	$0.982277\pi$
$602$	143086.	+	207324.i	0.394824	+	0.572079i
$603$	−70342.6	+	60952.2i	−0.193457	+	0.167631i
$604$	−276122.	+	148766.i	−0.756879	+	0.407782i
$605$	−299090.	−	192213.i	−0.817129	−	0.525137i
$606$	416368.	+	837668.i	1.13379	+	2.28101i
$607$	−216404.	−	187515.i	−0.587338	−	0.508931i	0.309730	−	0.950825i	$-0.399761\pi$
$607$	−216404.	−	187515.i	−0.587338	−	0.508931i	−0.897068	+	0.441893i	$0.854307\pi$
$608$	220436.	+	694729.i	0.596315	+	1.87935i
$609$	−57791.0	−	401945.i	−0.155821	−	1.08376i
$610$	96716.1	−	161967.i	0.259920	−	0.435279i
$611$	−67451.9	−	104957.i	−0.180681	−	0.281145i
$612$	−1.03435e6	−	572369.i	−2.76164	−	1.52818i
$613$	21299.9	−	46640.3i	0.0566836	−	0.124120i	−0.879171	−	0.476507i	$-0.841903\pi$
$613$	21299.9	−	46640.3i	0.0566836	−	0.124120i	0.935854	+	0.352387i	$0.114630\pi$
$614$	−29032.1	+	9572.27i	−0.0770089	+	0.0253909i
$615$	−205534.	−	699983.i	−0.543416	−	1.85071i
$616$	145336.	−	35792.8i	0.383013	−	0.0943265i
$617$	192433.	+	56503.3i	0.505485	+	0.148424i	0.524525	−	0.851395i	$-0.324243\pi$
$617$	192433.	+	56503.3i	0.505485	+	0.148424i	−0.0190403	+	0.999819i	$0.506061\pi$
$618$	109168.	−	422754.i	0.285836	−	1.10691i
$619$	−333223.	−	47910.2i	−0.869668	−	0.125039i	−0.306987	−	0.951714i	$-0.599321\pi$
$619$	−333223.	−	47910.2i	−0.869668	−	0.125039i	−0.562681	+	0.826674i	$0.690230\pi$
$620$	455038.	−	96312.6i	1.18376	−	0.250553i
$621$	751153.	+	177789.i	1.94780	+	0.461022i
$622$	170029.	−	209784.i	0.439483	−	0.542240i
$623$	288261.	+	41445.7i	0.742694	+	0.106783i
$624$	−90141.5	+	101697.i	−0.231503	+	0.261178i
$625$	431311.	+	126644.i	1.10416	+	0.324209i
$626$	−9839.19	−	299046.i	−0.0251079	−	0.763114i
$627$	−126821.	−	431913.i	−0.322594	−	1.09865i
$628$	136512.	−	359814.i	0.346139	−	0.912344i
$629$	78324.0	−	171506.i	0.197967	−	0.433488i
$630$	193437.	+	1.08966e6i	0.487369	+	2.74543i
$631$	−187255.	−	291374.i	−0.470299	−	0.731800i	0.522363	−	0.852724i	$-0.325051\pi$
$631$	−187255.	−	291374.i	−0.470299	−	0.731800i	−0.992662	+	0.120924i	$0.961414\pi$
$632$	−117022.	+	341949.i	−0.292978	+	0.856105i
$633$	−2412.29	−	16777.9i	−0.00602036	−	0.0418725i
$634$	395122.	+	43603.4i	0.982998	+	0.108478i
$635$	207871.	+	180122.i	0.515522	+	0.446702i
$636$	−39737.8	+	177854.i	−0.0982403	+	0.439693i
$637$	29932.7	+	19236.6i	0.0737679	+	0.0474078i
$638$	26496.8	−	63463.9i	0.0650956	−	0.155914i
$639$	740394.	−	641555.i	1.81327	−	1.57120i
$640$	149102.	−	420211.i	0.364018	−	1.02591i
$641$	284044.	+	621971.i	0.691306	+	1.51375i	0.850204	+	0.526454i	$0.176479\pi$
$641$	284044.	+	621971.i	0.691306	+	1.51375i	−0.158898	+	0.987295i	$0.550794\pi$
$642$	680071.	−	629610.i	1.65000	−	1.52757i
$643$			624447.i			1.51034i	0.655531	+	0.755168i	$0.272445\pi$
$643$			624447.i			1.51034i	−0.655531	+	0.755168i	$0.727555\pi$
$644$	−279412.	+	412803.i	−0.673711	+	0.995340i
$645$	−463451.			−1.11400
$646$	−827859.	−	894209.i	−1.98377	−	2.14276i
$647$	495790.	−	226420.i	1.18438	−	0.540886i	0.276862	−	0.960910i	$-0.410705\pi$
$647$	495790.	−	226420.i	1.18438	−	0.540886i	0.907513	+	0.420024i	$0.137978\pi$
$648$	407290.	−	430132.i	0.969959	−	1.02436i
$649$	−25025.9	−	28881.4i	−0.0594155	−	0.0685691i
$650$	14225.6	+	5939.31i	0.0336700	+	0.0140575i
$651$	−541651.	+	842825.i	−1.27808	+	1.98873i
$652$	−124963.	+	559294.i	−0.293958	+	1.31566i
$653$	−86373.8	+	99680.7i	−0.202561	+	0.233768i	−0.847937	−	0.530097i	$-0.822155\pi$
$653$	−86373.8	+	99680.7i	−0.202561	+	0.233768i	0.645376	+	0.763865i	$0.276701\pi$
$654$	37924.9	−	343665.i	0.0886684	−	0.803488i
$655$	654719.	−	94134.3i	1.52606	−	0.219415i
$656$	−228882.	−	365105.i	−0.531867	−	0.848418i
$657$	−915173.	+	588146.i	−2.12018	+	1.36256i
$658$	−868171.	+	154118.i	−2.00518	+	0.355960i
$659$	−259376.	−	118453.i	−0.597253	−	0.272756i	0.0937643	−	0.995594i	$-0.470110\pi$
$659$	−259376.	−	118453.i	−0.597253	−	0.272756i	−0.691018	+	0.722838i	$0.742837\pi$
$660$	−97682.5	+	257469.i	−0.224248	+	0.591067i
$661$	−798906.	+	234580.i	−1.82849	+	0.536894i	−0.999742	−	0.0227257i	$-0.992766\pi$
$661$	−798906.	+	234580.i	−1.82849	+	0.536894i	−0.828750	+	0.559619i	$0.810947\pi$
$662$	76070.9	−	2502.88i	0.173581	−	0.00571116i
$663$	64011.1	−	218002.i	0.145622	−	0.495944i
$664$	15606.2	−	353416.i	0.0353965	−	0.801586i
$665$	−162353.	+	1.12919e6i	−0.367129	+	2.55344i
$666$	236306.	+	191525.i	0.532755	+	0.431795i
$667$	76118.4	+	216016.i	0.171095	+	0.485551i
$668$	−165019.	+	34927.6i	−0.369811	+	0.0782736i
$669$	129702.	−	902100.i	0.289798	−	2.01559i
$670$	56830.0	+	14675.2i	0.126598	+	0.0326915i
$671$	−19388.3	+	66030.6i	−0.0430622	+	0.146656i
$672$	417795.	+	864792.i	0.925177	+	1.91502i
$673$	−55490.1	+	16293.4i	−0.122514	+	0.0359733i	−0.342415	−	0.939549i	$-0.611245\pi$
$673$	−55490.1	+	16293.4i	−0.122514	+	0.0359733i	0.219901	+	0.975522i	$0.429427\pi$
$674$	−76102.7	−	230815.i	−0.167525	−	0.508093i
$675$	−153464.	−	70084.7i	−0.336821	−	0.153821i
$676$	384287.	+	212649.i	0.840934	+	0.465339i
$677$	−597351.	+	383894.i	−1.30332	+	0.837595i	−0.993570	−	0.113222i	$-0.963883\pi$
$677$	−597351.	+	383894.i	−1.30332	+	0.837595i	−0.309754	+	0.950817i	$0.600247\pi$
$678$	−1.19709e6	−	714821.i	−2.60416	−	1.55503i
$679$	732792.	−	105360.i	1.58943	−	0.228525i
$680$	73436.3	+	741843.i	0.158815	+	1.60433i
$681$	−463419.	+	534815.i	−0.999264	+	1.15321i
$682$	−151941.	+	75523.1i	−0.326668	+	0.162372i
$683$	−185650.	+	288876.i	−0.397972	+	0.619256i	−0.981187	−	0.193062i	$-0.938158\pi$
$683$	−185650.	+	288876.i	−0.397972	+	0.619256i	0.583215	+	0.812318i	$0.301795\pi$
$684$	1.73073e6	−	932461.i	3.69927	−	1.99305i
$685$	166516.	+	192170.i	0.354874	+	0.409547i
$686$	−258551.	+	178441.i	−0.549412	+	0.379180i
$687$	−719526.	+	328596.i	−1.52452	+	0.696225i
$688$	−263509.	+	74166.7i	−0.556697	+	0.156687i
$689$	−23839.4			−0.0502178
$690$	−333066.	−	854465.i	−0.699571	−	1.79472i
$691$		−	258157.i		−	0.540665i	−0.962767	−	0.270333i	$-0.912866\pi$
$691$		−	258157.i		−	0.540665i	0.962767	−	0.270333i	$-0.0871336\pi$
$692$	−36345.0	+	2394.23i	−0.0758983	+	0.00499982i
$693$	−167713.	−	367240.i	−0.349221	−	0.764686i
$694$	188286.	−	129947.i	0.390930	−	0.269802i
$695$	186432.	−	161544.i	0.385968	−	0.334443i
$696$	433601.	+	82010.0i	0.895100	+	0.169297i
$697$	606081.	+	389505.i	1.24757	+	0.801765i
$698$	233382.	−	116004.i	0.479024	−	0.238101i
$699$	−600173.	−	520053.i	−1.22835	−	1.06437i
$700$	77469.7	−	76603.8i	0.158101	−	0.156334i
$701$	−10723.5	−	74583.7i	−0.0218223	−	0.151778i	0.975997	−	0.217785i	$-0.0698831\pi$
$701$	−10723.5	−	74583.7i	−0.0218223	−	0.151778i	−0.997819	+	0.0660072i	$0.978974\pi$
$702$	167039.	+	99744.7i	0.338957	+	0.202402i
$703$	169518.	+	263775.i	0.343008	+	0.533732i
$704$	−14337.3	+	162024.i	−0.0289282	+	0.326914i
$705$	673893.	−	1.47562e6i	1.35585	−	2.96890i
$706$	252259.	+	765085.i	0.506101	+	1.53497i
$707$	243650.	+	829794.i	0.487446	+	1.66009i
$708$	148051.	−	195474.i	0.295356	−	0.389962i
$709$	57487.6	+	16879.9i	0.114362	+	0.0335797i	0.338413	−	0.940998i	$-0.390110\pi$
$709$	57487.6	+	16879.9i	0.114362	+	0.0335797i	−0.224051	+	0.974577i	$0.571928\pi$
$710$	−598166.	−	154464.i	−1.18660	−	0.306416i
$711$	964918.	+	138734.i	1.90876	+	0.274438i
$712$	−144041.	+	281797.i	−0.284135	+	0.555874i
$713$	207080.	−	525759.i	0.407343	−	1.03421i
$714$	−1.24746e6	−	1.01106e6i	−2.44698	−	1.98327i
$715$	−35656.4	−	5126.62i	−0.0697470	−	0.0100281i
$716$	−29910.6	−	40427.5i	−0.0583444	−	0.0788589i
$717$	−1.28113e6	−	376174.i	−2.49204	−	0.731729i
$718$	261336.	−	8598.46i	0.506932	−	0.0166791i
$719$	106383.	+	362308.i	0.205786	+	0.700841i	0.996107	+	0.0881492i	$0.0280952\pi$
$719$	106383.	+	362308.i	0.205786	+	0.700841i	−0.790322	+	0.612692i	$0.790087\pi$
$720$	−1.18841e6	−	184524.i	−2.29247	−	0.355949i
$721$	167687.	−	367183.i	0.322573	−	0.706337i
$722$	1.48207e6	−	263097.i	2.84311	−	0.504709i
$723$	185155.	+	288106.i	0.354208	+	0.551158i
$724$	161176.	−	59086.0i	0.307485	−	0.112722i
$725$	−7124.07	−	49549.0i	−0.0135535	−	0.0942668i
$726$	−91283.8	+	827188.i	−0.173189	+	1.56939i
$727$	−120245.	−	104193.i	−0.227510	−	0.197138i	0.533645	−	0.845709i	$-0.320822\pi$
$727$	−120245.	−	104193.i	−0.227510	−	0.197138i	−0.761155	+	0.648570i	$0.775367\pi$
$728$	−98487.4	+	78006.0i	−0.185831	+	0.147186i
$729$	239368.	+	153832.i	0.450412	+	0.289462i
$730$	633051.	+	264305.i	1.18794	+	0.495974i
$731$	345892.	−	299717.i	0.647300	−	0.560888i
$732$	−440268.	−	33976.4i	−0.821666	−	0.0634097i
$733$	153461.	+	336032.i	0.285621	+	0.625422i	0.997001	−	0.0773851i	$-0.0246571\pi$
$733$	153461.	+	336032.i	0.285621	+	0.625422i	−0.711381	+	0.702807i	$0.751930\pi$
$734$	384505.	+	415321.i	0.713690	+	0.770889i
$735$			462639.i			0.856383i
$736$	−326116.	−	432531.i	−0.602027	−	0.798475i
$737$	−21411.7			−0.0394199
$738$	−852898.	+	789614.i	−1.56597	+	1.44978i
$739$	−540132.	+	246670.i	−0.989034	+	0.451677i	−0.843181	−	0.537630i	$-0.819320\pi$
$739$	−540132.	+	246670.i	−0.989034	+	0.451677i	−0.145853	+	0.989306i	$0.546593\pi$
$740$	14758.8	−	191245.i	0.0269517	−	0.349241i
$741$	247435.	+	285555.i	0.450635	+	0.520060i
$742$	−64912.4	+	155475.i	−0.117902	+	0.282393i
$743$	−285862.	+	444810.i	−0.517820	+	0.805744i	−0.997423	−	0.0717414i	$-0.977144\pi$
$743$	−285862.	+	444810.i	−0.517820	+	0.805744i	0.479603	+	0.877486i	$0.340781\pi$
$744$	−675978.	−	853464.i	−1.22120	−	1.54184i
$745$	155768.	−	179766.i	0.280650	−	0.323888i
$746$	119867.	+	13227.9i	0.215389	+	0.0237691i
$747$	−944472.	+	135795.i	−1.69258	+	0.243356i
$748$	−93602.4	−	255331.i	−0.167295	−	0.456352i
$749$	720795.	−	463227.i	1.28484	−	0.825714i
$750$	−154350.	−	869477.i	−0.274399	−	1.54574i
$751$	−694042.	−	316958.i	−1.23057	−	0.561982i	−0.309320	−	0.950958i	$-0.600101\pi$
$751$	−694042.	−	316958.i	−1.23057	−	0.561982i	−0.921248	+	0.388976i	$0.872829\pi$
$752$	147017.	−	946852.i	0.259975	−	1.67435i
$753$	−774696.	+	227471.i	−1.36628	+	0.401177i
$754$	1898.29	+	57695.5i	0.00333903	+	0.101484i
$755$	150299.	−	511871.i	0.263671	−	0.897979i
$756$	1.10534e6	−	817798.i	1.93399	−	1.43088i
$757$	28671.7	−	199416.i	0.0500337	−	0.347992i	−0.949392	−	0.314095i	$-0.898299\pi$
$757$	28671.7	−	199416.i	0.0500337	−	0.347992i	0.999425	−	0.0338971i	$-0.0107918\pi$
$758$	−134387.	+	165808.i	−0.233894	+	0.288581i
$759$	195579.	+	271430.i	0.339500	+	0.471166i
$760$	−1.10387e6	−	564245.i	−1.91113	−	0.976878i
$761$	19419.7	−	135067.i	0.0335330	−	0.233227i	−0.966162	−	0.257937i	$-0.916957\pi$
$761$	19419.7	−	135067.i	0.0335330	−	0.233227i	0.999695	+	0.0247101i	$0.00786628\pi$
$762$	160977.	−	623387.i	0.277239	−	1.07361i
$763$	90056.0	−	306703.i	0.154690	−	0.526827i
$764$	293588.	+	222363.i	0.502981	+	0.380956i
$765$	1.92928e6	−	566487.i	3.29664	−	0.967981i
$766$	−54776.8	+	18060.7i	−0.0933553	+	0.0307805i
$767$	29178.5	+	13325.4i	0.0495989	+	0.0226511i
$768$	−1.03615e6	+	125276.i	−1.75672	+	0.212396i
$769$	750175.	−	482108.i	1.26856	−	0.815252i	0.279126	−	0.960255i	$-0.409955\pi$
$769$	750175.	−	482108.i	1.26856	−	0.815252i	0.989431	+	0.145002i	$0.0463190\pi$
$770$	−130523.	+	218584.i	−0.220144	+	0.368669i
$771$	693137.	−	99658.0i	1.16603	−	0.167650i
$772$	372854.	+	377068.i	0.625611	+	0.632682i
$773$	−43098.9	+	49738.8i	−0.0721285	+	0.0832408i	−0.790667	−	0.612247i	$-0.790266\pi$
$773$	−43098.9	+	49738.8i	−0.0721285	+	0.0832408i	0.718538	+	0.695487i	$0.244811\pi$
$774$	328650.	+	661195.i	0.548595	+	1.10369i
$775$	−66770.9	+	103898.i	−0.111169	+	0.172982i
$776$	−149514.	+	790503.i	−0.248289	+	1.31274i
$777$	270566.	+	312250.i	0.448159	+	0.517203i
$778$	452090.	+	655055.i	0.746906	+	1.08223i
$779$	−1.08984e6	+	497714.i	−1.79593	+	0.820173i
$780$	−15193.8	−	230645.i	−0.0249733	−	0.379101i
$781$	225369.			0.369481
$782$	801168.	+	422325.i	1.31012	+	0.690610i
$783$		−	631765.i		−	1.03046i
$784$	74036.8	+	263048.i	0.120452	+	0.427959i
$785$	271919.	+	595420.i	0.441266	+	0.966237i
$786$	−879456.	−	1.27429e6i	−1.42354	−	2.06263i
$787$	280987.	−	243477.i	0.453667	−	0.393105i	−0.397834	−	0.917457i	$-0.630238\pi$
$787$	280987.	−	243477.i	0.453667	−	0.393105i	0.851501	+	0.524353i	$0.175693\pi$
$788$	−427125.	−	792781.i	−0.687865	−	1.27674i
$789$	148985.	+	95746.5i	0.239324	+	0.153805i
$790$	−273620.	−	550483.i	−0.438424	−	0.882042i
$791$	−974175.	−	844128.i	−1.55698	−	1.34913i
$792$	436595.	−	43219.3i	0.696031	−	0.0689013i
$793$	−8220.75	−	57176.6i	−0.0130727	−	0.0909226i
$794$	−75895.1	+	127099.i	−0.120385	+	0.201605i
$795$	−167582.	−	260763.i	−0.265151	−	0.412584i
$796$	−263224.	+	475683.i	−0.415431	+	0.750744i
$797$	176098.	−	385601.i	0.277228	−	0.607045i	−0.718885	−	0.695129i	$-0.755347\pi$
$797$	176098.	−	385601.i	0.277228	−	0.607045i	0.996113	+	0.0880839i	$0.0280744\pi$
$798$	2.53606e6	−	836175.i	3.98249	−	1.31308i
$799$	451340.	+	1.53712e6i	0.706985	+	2.40777i
$800$	51502.9	+	106605.i	0.0804732	+	0.166571i
$801$	819042.	+	240493.i	1.27656	+	0.374832i
$802$	−296144.	+	1.14683e6i	−0.460421	+	1.78299i
$803$	−247710.	−	35615.3i	−0.384160	−	0.0552338i
$804$	−28449.3	−	134412.i	−0.0440109	−	0.207934i
$805$	−165108.	−	831623.i	−0.254786	−	1.28332i
$806$	89676.6	−	110644.i	0.138041	−	0.170317i
$807$	2.22988e6	+	320609.i	3.42401	+	0.492299i
$808$	−938896.	−	41459.8i	−1.43812	−	0.0635046i
$809$	−721859.	−	211957.i	−1.10295	−	0.323855i	−0.320925	−	0.947105i	$-0.603994\pi$
$809$	−721859.	−	211957.i	−1.10295	−	0.323855i	−0.782023	+	0.623250i	$0.785812\pi$
$810$	33132.6	+	1.00701e6i	0.0504993	+	1.53484i
$811$	169008.	+	575590.i	0.256961	+	0.875127i	0.982392	+	0.186833i	$0.0598222\pi$
$811$	169008.	+	575590.i	0.256961	+	0.875127i	−0.725431	+	0.688295i	$0.758360\pi$
$812$	381445.	+	144719.i	0.578523	+	0.219489i
$813$	746289.	−	1.63414e6i	1.12908	−	2.47235i
$814$	12230.5	+	68896.4i	0.0184584	+	0.103979i
$815$	−526993.	−	820017.i	−0.793395	−	1.23455i
$816$	1.47847e6	−	926843.i	2.22041	−	1.39196i
$817$	108319.	+	753378.i	0.162279	+	1.12867i
$818$	−1.11340e6	−	122868.i	−1.66396	−	0.183625i
$819$	256106.	+	221917.i	0.381814	+	0.330844i
$820$	715306.	+	159820.i	1.06381	+	0.237687i
$821$	216399.	+	139071.i	0.321047	+	0.206324i	0.691230	−	0.722634i	$-0.257069\pi$
$821$	216399.	+	139071.i	0.321047	+	0.206324i	−0.370184	+	0.928959i	$0.620705\pi$
$822$	229319.	−	549254.i	0.339387	−	0.812885i
$823$	139050.	−	120488.i	0.205292	−	0.177886i	−0.546147	−	0.837690i	$-0.683906\pi$
$823$	139050.	−	120488.i	0.205292	−	0.177886i	0.751438	+	0.659803i	$0.229360\pi$
$824$	318523.	+	301607.i	0.469122	+	0.444209i
$825$	−30375.5	−	66513.0i	−0.0446288	−	0.0977234i
$826$	166355.	−	154012.i	0.243824	−	0.225732i
$827$		−	682927.i		−	0.998535i	−0.866448	−	0.499267i	$-0.833603\pi$
$827$		−	682927.i		−	0.998535i	0.866448	−	0.499267i	$-0.166397\pi$
$828$	−982856.	+	1.08111e6i	−1.43360	+	1.57692i
$829$	−583849.			−0.849554			−0.424777	−	0.905298i	$-0.639648\pi$
$829$	−583849.			−0.849554			−0.424777	+	0.905298i	$0.639648\pi$
$830$	408776.	+	441538.i	0.593376	+	0.640932i
$831$	1.10575e6	−	504978.i	1.60123	−	0.731258i
$832$	−45549.3	−	128709.i	−0.0658014	−	0.185935i
$833$	−299192.	−	345286.i	−0.431181	−	0.497610i
$834$	−532855.	−	222472.i	−0.766085	−	0.319848i
$835$	155109.	−	241354.i	0.222466	−	0.346163i
$836$	441367.	+	98614.5i	0.631521	+	0.141100i
$837$	−1.02072e6	+	1.17797e6i	−1.45698	+	1.68145i
$838$	89018.8	−	806663.i	0.126763	−	1.14869i
$839$	−584540.	+	84044.2i	−0.830406	+	0.119394i	−0.544392	−	0.838831i	$-0.683240\pi$
$839$	−584540.	+	84044.2i	−0.830406	+	0.119394i	−0.286014	+	0.958225i	$0.592330\pi$
$840$	−1.54558e6	−	528932.i	−2.19045	−	0.749621i
$841$	−437307.	+	281040.i	−0.618293	+	0.397353i
$842$	577679.	−	102550.i	0.814821	−	0.144647i
$843$	−902889.	−	412336.i	−1.27051	−	0.580224i
$844$	15922.2	+	6040.80i	0.0223520	+	0.00848026i
$845$	−716771.	+	210463.i	−1.00385	+	0.294756i
$846$	−2.58311e6	+	84989.4i	−3.60913	+	0.118747i
$847$	−216761.	+	738221.i	−0.302145	+	1.02901i
$848$	−137014.	−	121446.i	−0.190535	−	0.168886i
$849$	−298066.	+	2.07309e6i	−0.413520	+	2.87610i
$850$	−153778.	−	124637.i	−0.212842	−	0.172507i
$851$	−183978.	−	143025.i	−0.254043	−	0.197494i
$852$	299445.	+	1.41476e6i	0.412513	+	1.94896i
$853$	126596.	−	880493.i	0.173989	−	1.21012i	−0.696364	−	0.717689i	$-0.745200\pi$
$853$	126596.	−	880493.i	0.173989	−	1.21012i	0.870353	−	0.492429i	$-0.163891\pi$
$854$	−395277.	−	102072.i	−0.541983	−	0.139956i
$855$	−942071.	+	3.20840e6i	−1.28870	+	4.38891i
$856$	222654.	+	904087.i	0.303867	+	1.23385i
$857$	−674077.	+	197927.i	−0.917800	+	0.269490i	−0.706321	−	0.707892i	$-0.749646\pi$
$857$	−674077.	+	197927.i	−0.917800	+	0.269490i	−0.211479	+	0.977382i	$0.567828\pi$
$858$	26403.8	+	80081.1i	0.0358668	+	0.108782i
$859$	−17112.0	−	7814.79i	−0.0231907	−	0.0105909i	0.403786	−	0.914854i	$-0.367694\pi$
$859$	−17112.0	−	7814.79i	−0.0231907	−	0.0105909i	−0.426977	+	0.904263i	$0.640421\pi$
$860$	225439.	−	407401.i	0.304812	−	0.550840i
$861$	−1.32814e6	+	853542.i	−1.79158	+	1.15138i
$862$	128958.	+	77004.9i	0.173553	+	0.103634i
$863$	64469.0	−	9269.24i	0.0865624	−	0.0124458i	−0.0988975	−	0.995098i	$-0.531532\pi$
$863$	64469.0	−	9269.24i	0.0865624	−	0.0124458i	0.185460	+	0.982652i	$0.440623\pi$
$864$	451904.	+	1.42423e6i	0.605367	+	1.90788i
$865$	40570.6	−	46821.0i	0.0542224	−	0.0625760i
$866$	585.727	−	291.139i	0.000781015	−	0.000388208i
$867$	−858159.	+	1.33532e6i	−1.14164	+	1.77643i
$868$	−477415.	−	886123.i	−0.633661	−	1.17613i
$869$	146856.	+	169481.i	0.194470	+	0.224430i
$870$	−617746.	+	426341.i	−0.816153	+	0.563273i
$871$	16348.3	−	7466.04i	0.0215495	−	0.00984133i
$872$	283654.	+	200509.i	0.373040	+	0.263694i
$873$	2.17000e6			2.84728
$874$	−1.31116e6	+	741135.i	−1.71645	+	0.970229i
$875$		−	816409.i		−	1.06633i
$876$	−105553.	−	1.60232e6i	−0.137551	−	2.08805i
$877$	350749.	+	768034.i	0.456034	+	0.998576i	0.988374	+	0.152045i	$0.0485858\pi$
$877$	350749.	+	768034.i	0.456034	+	0.998576i	−0.532339	+	0.846531i	$0.678687\pi$
$878$	463943.	−	320193.i	0.601832	−	0.415358i
$879$	362979.	−	314523.i	0.469790	−	0.407075i
$880$	−178814.	−	211111.i	−0.230907	−	0.272612i
$881$	993241.	+	638317.i	1.27968	+	0.822403i	0.990849	−	0.134976i	$-0.0430957\pi$
$881$	993241.	+	638317.i	1.27968	+	0.822403i	0.288835	+	0.957379i	$0.406732\pi$
$882$	660037.	−	328075.i	0.848459	−	0.421731i
$883$	−4.00218	−	3.46791i	−5.13305e−6	−	4.44781e-6i	0.654858	−	0.755752i	$-0.272728\pi$
$883$	−4.00218	−	3.46791i	−5.13305e−6	−	4.44781e-6i	−0.654863	+	0.755747i	$0.727274\pi$
$884$	160499.	+	162313.i	0.205385	+	0.207706i
$885$	59356.8	+	412836.i	0.0757852	+	0.527097i
$886$	400110.	+	238919.i	0.509697	+	0.304357i
$887$	−205500.	−	319765.i	−0.261195	−	0.406428i	0.685743	−	0.727844i	$-0.259478\pi$
$887$	−205500.	−	319765.i	−0.261195	−	0.406428i	−0.946938	+	0.321416i	$0.895841\pi$
$888$	−416246.	+	168318.i	−0.527867	+	0.213455i
$889$	247269.	−	541443.i	0.312871	−	0.685093i
$890$	−168557.	−	511222.i	−0.212798	−	0.645401i
$891$	−103552.	−	352667.i	−0.130438	−	0.444232i
$892$	729907.	+	552829.i	0.917356	+	0.694802i
$893$	−2.55624e6	−	750581.i	−3.20553	−	0.941228i
$894$	−539101.	−	139212.i	−0.674520	−	0.174181i
$895$	84666.4	+	12173.2i	0.105698	+	0.0151970i
$896$	−963434.	−	53398.7i	−1.20007	−	0.0665142i
$897$	−243975.	−	139047.i	−0.303222	−	0.172813i
$898$	633821.	+	513709.i	0.785984	+	0.637037i
$899$	−457773.	−	65817.8i	−0.566409	−	0.0814374i
$900$	256717.	−	189934.i	0.316935	−	0.234487i
$901$	293710.	+	86241.1i	0.361801	+	0.106234i
$902$	−267233.	+	8792.49i	−0.328456	+	0.0108068i
$903$	282560.	+	962312.i	0.346526	+	1.18016i
$904$	1.21068e6	−	704598.i	1.48146	−	0.862193i
$905$	−121295.	+	265598.i	−0.148096	+	0.324286i
$906$	−1.22953e6	+	218266.i	−1.49790	+	0.265907i
$907$	−151708.	−	236062.i	−0.184414	−	0.286954i	0.736721	−	0.676197i	$-0.236373\pi$
$907$	−151708.	−	236062.i	−0.184414	−	0.286954i	−0.921135	+	0.389243i	$0.872737\pi$
$908$	−244710.	−	667526.i	−0.296811	−	0.809648i
$909$	360756.	+	2.50912e6i	0.436603	+	3.03664i
$910$	23440.0	−	212406.i	0.0283057	−	0.256498i
$911$	−19707.1	−	17076.3i	−0.0237458	−	0.0205758i	0.642907	−	0.765944i	$-0.277728\pi$
$911$	−19707.1	−	17076.3i	−0.0237458	−	0.0205758i	−0.666653	+	0.745368i	$0.732274\pi$
$912$	−32614.6	+	2.90171e6i	−0.0392123	+	3.48871i
$913$	−184658.	−	118673.i	−0.221527	−	0.142367i
$914$	564090.	+	235513.i	0.675237	+	0.281918i
$915$	567626.	−	491851.i	0.677985	−	0.587477i
$916$	61147.1	−	792347.i	0.0728761	−	0.944331i
$917$	−594635.	−	1.30207e6i	−0.707150	−	1.54844i
$918$	−1.69715e6	−	1.83317e6i	−2.01389	−	2.17529i
$919$		−	18410.5i		−	0.0217989i	−0.999941	−	0.0108994i	$-0.996531\pi$
$919$		−	18410.5i		−	0.0217989i	0.999941	−	0.0108994i	$-0.00346947\pi$
$920$	913141.	+	122857.i	1.07885	+	0.145153i
$921$	−121709.			−0.143484
$922$	−55047.9	+	50963.4i	−0.0647558	+	0.0599510i
$923$	−172075.	+	78584.1i	−0.201983	+	0.0922425i
$924$	594165.	+	45853.0i	0.695927	+	0.0537061i
$925$	33353.5	+	38492.0i	0.0389815	+	0.0449870i
$926$	8260.28	−	19784.7i	0.00963325	−	0.0230731i
$927$	639678.	−	995358.i	0.744392	−	1.15830i
$928$	−283010.	+	341268.i	−0.328629	+	0.396278i
$929$	492937.	−	568879.i	0.571163	−	0.659157i	−0.394518	−	0.918888i	$-0.629089\pi$
$929$	492937.	−	568879.i	0.571163	−	0.659157i	0.965681	+	0.259731i	$0.0836340\pi$
$930$	1.84065e6	+	203124.i	2.12817	+	0.234852i
$931$	752058.	−	108130.i	0.867665	−	0.124751i
$932$	749103.	−	274616.i	0.862402	−	0.316150i
$933$	904448.	−	581254.i	1.03901	−	0.667732i
$934$	−5301.80	−	29866.0i	−0.00607757	−	0.0342360i
$935$	420754.	+	192152.i	0.481288	+	0.219797i
$936$	−318281.	+	185235.i	−0.363295	+	0.211433i
$937$	314109.	−	92230.8i	0.357768	−	0.105050i	−0.0979090	−	0.995195i	$-0.531215\pi$
$937$	314109.	−	92230.8i	0.357768	−	0.105050i	0.455677	+	0.890145i	$0.349397\pi$
$938$	−4176.88	−	126949.i	−0.00474730	−	0.144286i
$939$	335618.	−	1.14301e6i	0.380640	−	1.29634i
$940$	969351.	+	1.31018e6i	1.09705	+	1.48278i
$941$	−101226.	+	704039.i	−0.114317	+	0.795092i	0.849320	+	0.527878i	$0.177012\pi$
$941$	−101226.	+	704039.i	−0.114317	+	0.795092i	−0.963637	+	0.267214i	$0.913897\pi$
$942$	964757.	−	1.19033e6i	1.08722	−	1.34142i
$943$	641003.	−	618071.i	0.720836	−	0.695048i
$944$	99815.8	+	225231.i	0.112010	+	0.252746i
$945$	−332832.	+	2.31490e6i	−0.372702	+	2.59220i
$946$	−42469.0	+	164462.i	−0.0474559	+	0.183774i
$947$	−107018.	+	364468.i	−0.119331	+	0.406406i	−0.997395	−	0.0721392i	$-0.977017\pi$
$947$	−107018.	+	364468.i	−0.119331	+	0.406406i	0.878063	+	0.478545i	$0.158836\pi$
$948$	−868792.	+	1.14708e6i	−0.966716	+	1.27637i
$949$	201551.	−	59180.7i	0.223796	−	0.0657125i
$950$	312628.	−	103078.i	0.346403	−	0.114214i
$951$	1.43966e6	+	657473.i	1.59184	+	0.726970i
$952$	1.49559e6	−	604776.i	1.65021	−	0.667299i
$953$	−90989.8	+	58475.6i	−0.100186	+	0.0643856i	−0.589774	−	0.807568i	$-0.700783\pi$
$953$	−90989.8	+	58475.6i	−0.100186	+	0.0643856i	0.489589	+	0.871954i	$0.337147\pi$
$954$	−253186.	+	424002.i	−0.278191	+	0.465877i
$955$	−620051.	+	89149.8i	−0.679861	+	0.0977493i
$956$	953866.	−	943205.i	1.04369	−	1.03203i
$957$	179310.	−	206935.i	0.195785	−	0.225948i
$958$	461880.	+	929233.i	0.503267	+	1.01250i
$959$	297499.	−	462918.i	0.323481	−	0.503346i
$960$	1.08766e6	−	1.40300e6i	1.18019	−	1.52236i
$961$	142432.	+	164375.i	0.154227	+	0.177987i
$962$	−33361.8	−	48339.5i	−0.0360495	−	0.0522338i
$963$	2.28447e6	−	1.04328e6i	2.46339	−	1.12499i
$964$	−343328.	+	22616.8i	−0.369450	+	0.0243376i
$965$	−901957.			−0.968570
$966$	−1.57115e6	+	1.21254e6i	−1.68369	+	1.29939i
$967$			279792.i			0.299214i	0.988746	+	0.149607i	$0.0478009\pi$
$967$			279792.i			0.299214i	−0.988746	+	0.149607i	$0.952199\pi$
$968$	−682744.	−	482618.i	−0.728630	−	0.515054i
$969$	−2.01547e6	−	4.41326e6i	−2.14649	−	4.70015i
$970$	−777269.	−	1.12622e6i	−0.826091	−	1.19696i
$971$	1.01978e6	−	883647.i	1.08161	−	0.937217i	0.0833662	−	0.996519i	$-0.473433\pi$
$971$	1.01978e6	−	883647.i	1.08161	−	0.937217i	0.998240	+	0.0593018i	$0.0188874\pi$
$972$	411436.	−	221669.i	0.435481	−	0.234624i
$973$	−449097.	−	288617.i	−0.474367	−	0.304857i
$974$	−603663.	−	1.21448e6i	−0.636322	−	1.28018i
$975$	46384.8	+	40192.7i	0.0487941	+	0.0422803i
$976$	244029.	−	370495.i	0.256178	−	0.388940i
$977$	−21532.1	−	149759.i	−0.0225578	−	0.156893i	0.975429	−	0.220314i	$-0.0707081\pi$
$977$	−21532.1	−	149759.i	−0.0225578	−	0.156893i	−0.997987	+	0.0634207i	$0.979799\pi$
$978$	−1.16978e6	+	1.95900e6i	−1.22300	+	2.04812i
$979$	106165.	+	165197.i	0.110769	+	0.172360i
$980$	−406687.	−	225044.i	−0.423456	−	0.234323i
$981$	389218.	−	852269.i	0.404441	−	0.885602i
$982$	−940841.	+	310208.i	−0.975649	+	0.321685i
$983$	−196006.	−	667534.i	−0.202844	−	0.690823i	−0.996585	−	0.0825676i	$-0.973688\pi$
$983$	−196006.	−	667534.i	−0.202844	−	0.690823i	0.793742	−	0.608255i	$-0.208130\pi$
$984$	−410263.	−	1.66587e6i	−0.423714	−	1.72049i
$985$	1.46965e6	+	431528.i	1.51475	+	0.444771i
$986$	185330.	−	717696.i	0.190631	−	0.738221i
$987$	−3.47485e6	−	499608.i	−3.56699	−	0.512855i
$988$	−371381.	+	78605.8i	−0.380457	+	0.0805269i
$989$	−262013.	−	501335.i	−0.267873	−	0.512549i
$990$	−469868.	+	579729.i	−0.479408	+	0.591500i
$991$	−1.73282e6	−	249141.i	−1.76443	−	0.253687i	−0.817686	−	0.575665i	$-0.804743\pi$
$991$	−1.73282e6	−	249141.i	−1.76443	−	0.253687i	−0.946747	+	0.321978i	$0.895652\pi$
$992$	1.07906e6	−	179070.i	1.09654	−	0.181970i
$993$	290758.	+	85374.2i	0.294872	+	0.0865821i
$994$	43963.9	+	1.33621e6i	0.0444963	+	1.35239i
$995$	−260519.	−	887245.i	−0.263143	−	0.896184i
$996$	499615.	−	1.31687e6i	0.503636	−	1.32747i
$997$	415523.	−	909868.i	0.418027	−	0.915352i	−0.577093	−	0.816679i	$-0.695813\pi$
$997$	415523.	−	909868.i	0.418027	−	0.915352i	0.995120	−	0.0986730i	$-0.0314598\pi$
$998$	228401.	+	1.28662e6i	0.229318	+	1.29179i
$999$	347519.	+	540751.i	0.348215	+	0.541834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.g.a.31.12	yes	460
4.3	odd	2	inner	92.5.g.a.31.31	yes	460
23.3	even	11	inner	92.5.g.a.3.31	yes	460
92.3	odd	22	inner	92.5.g.a.3.12	✓	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.12	✓	460	92.3	odd	22	inner
92.5.g.a.3.31	yes	460	23.3	even	11	inner
92.5.g.a.31.12	yes	460	1.1	even	1	trivial
92.5.g.a.31.31	yes	460	4.3	odd	2	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.93523 + 2.71744i) q^{2} +(-14.4864 + 6.61573i) q^{3} +(1.23109 - 15.9526i) q^{4} +(17.8216 + 20.5672i) q^{5} +(24.5431 - 58.7846i) q^{6} +(31.8403 - 49.5444i) q^{7} +(39.7365 + 50.1698i) q^{8} +(113.045 - 130.461i) q^{9} +(-108.200 - 11.9404i) q^{10} +(39.3070 - 5.65149i) q^{11} +(87.7038 + 239.240i) q^{12} +(-28.0412 + 18.0210i) q^{13} +(41.1754 + 231.948i) q^{14} +(-394.239 - 180.043i) q^{15} +(-252.969 - 39.2782i) q^{16} +(410.671 - 120.584i) q^{17} +(22.7065 + 690.126i) q^{18} +(-200.532 + 682.948i) q^{19} +(350.040 - 258.980i) q^{20} +(-133.479 + 928.369i) q^{21} +(-100.017 + 123.403i) q^{22} +(-28.1234 - 528.252i) q^{23} +(-907.551 - 463.895i) q^{24} +(-16.4544 + 114.443i) q^{25} +(33.3364 - 129.096i) q^{26} +(-411.099 + 1400.07i) q^{27} +(-751.163 - 568.928i) q^{28} +(-415.421 + 121.978i) q^{29} +(1646.43 - 542.852i) q^{30} +(971.656 + 443.740i) q^{31} +(849.256 - 572.136i) q^{32} +(-532.029 + 341.915i) q^{33} +(-877.732 + 1469.91i) q^{34} +(1586.44 - 228.095i) q^{35} +(-1942.02 - 1963.97i) q^{36} +(288.476 - 332.919i) q^{37} +(-1267.26 - 2549.54i) q^{38} +(286.996 - 446.574i) q^{39} +(-323.685 + 1711.38i) q^{40} +(1102.30 + 1272.13i) q^{41} +(-2130.99 - 3087.69i) q^{42} +(972.694 - 444.214i) q^{43} +(-41.7652 - 634.005i) q^{44} +4697.87 q^{45} +(1518.04 + 1474.11i) q^{46} +3742.96i q^{47} +(3924.47 - 1104.57i) q^{48} +(-443.436 - 970.990i) q^{49} +(-262.694 - 380.629i) q^{50} +(-5151.40 + 4463.72i) q^{51} +(252.960 + 469.515i) q^{52} +(601.662 + 386.665i) q^{53} +(-2597.94 - 5226.67i) q^{54} +(816.749 + 707.717i) q^{55} +(3750.86 - 371.304i) q^{56} +(-1613.21 - 11220.1i) q^{57} +(887.884 - 1486.91i) q^{58} +(-520.278 - 809.569i) q^{59} +(-3357.49 + 6067.47i) q^{60} +(-719.901 + 1576.36i) q^{61} +(-4057.86 + 1337.93i) q^{62} +(-2864.23 - 9754.68i) q^{63} +(-938.017 + 3987.15i) q^{64} +(-870.382 - 255.567i) q^{65} +(632.496 - 2449.35i) q^{66} +(-533.696 - 76.7340i) q^{67} +(-1418.05 - 6699.70i) q^{68} +(3902.18 + 7466.43i) q^{69} +(-4036.71 + 4980.55i) q^{70} +(5617.44 + 807.666i) q^{71} +(11037.2 + 487.383i) q^{72} +(-6046.65 - 1775.46i) q^{73} +(57.9439 + 1761.11i) q^{74} +(-518.758 - 1766.73i) q^{75} +(10647.9 + 4039.77i) q^{76} +(971.545 - 2127.39i) q^{77} +(371.139 + 2090.69i) q^{78} +(3053.09 + 4750.70i) q^{79} +(-3700.46 - 5902.87i) q^{80} +(-1317.23 - 9161.52i) q^{81} +(-6692.43 - 738.538i) q^{82} +(-4177.41 - 3619.75i) q^{83} +(14645.5 + 3272.25i) q^{84} +(9798.88 + 6297.36i) q^{85} +(-1647.95 + 3947.10i) q^{86} +(5210.99 - 4515.35i) q^{87} +(1845.46 + 1747.45i) q^{88} +(2054.20 + 4498.08i) q^{89} +(-13789.3 + 12766.2i) q^{90} +1963.08i q^{91} +(-8461.60 - 201.687i) q^{92} -17011.5 q^{93} +(-10171.2 - 10986.4i) q^{94} +(-17620.1 + 8046.84i) q^{95} +(-8517.60 + 13906.7i) q^{96} +(8231.99 + 9500.22i) q^{97} +(3940.19 + 1645.07i) q^{98} +(3706.17 - 5766.91i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) \) 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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