LMFDB - Embedded newform 92.5.g.a.3.12

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			3.12
Character	$\chi$	$=$	92.3
Dual form			92.5.g.a.31.12

$q$-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 $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$

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	−0.611196	−	0.791479i	$-0.709311\pi$
$3$	−14.4864	−	6.61573i	−1.60960	−	0.735082i	−0.998408	+	0.0563977i	$0.982039\pi$
$4$	1.23109	+	15.9526i	0.0769434	+	0.997035i
$5$	17.8216	−	20.5672i	0.712864	−	0.822689i	−0.277566	−	0.960707i	$-0.589528\pi$
$5$	17.8216	−	20.5672i	0.712864	−	0.822689i	0.990430	+	0.138018i	$0.0440731\pi$
$6$	24.5431	+	58.7846i	0.681754	+	1.63291i
$7$	31.8403	+	49.5444i	0.649801	+	1.01111i	0.997300	+	0.0734304i	$0.0233947\pi$
$7$	31.8403	+	49.5444i	0.649801	+	1.01111i	−0.347499	+	0.937680i	$0.612969\pi$
$8$	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	0.302811	−	0.953051i	$-0.402075\pi$
$11$	39.3070	+	5.65149i	0.324851	+	0.0467065i	0.0220399	+	0.999757i	$0.492984\pi$
$12$	87.7038	−	239.240i	0.609054	−	1.66139i
$13$	−28.0412	−	18.0210i	−0.165925	−	0.106633i	0.455043	−	0.890469i	$-0.349624\pi$
$13$	−28.0412	−	18.0210i	−0.165925	−	0.106633i	−0.620968	+	0.783836i	$0.713260\pi$
$14$	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	0.899843	−	0.436213i	$-0.143681\pi$
$17$	410.671	+	120.584i	1.42101	+	0.417245i	0.521162	+	0.853458i	$0.325499\pi$
$18$	22.7065	−	690.126i	0.0700818	−	2.13002i
$19$	−200.532	−	682.948i	−0.555489	−	1.89182i	−0.438615	−	0.898675i	$-0.644531\pi$
$19$	−200.532	−	682.948i	−0.555489	−	1.89182i	−0.116874	−	0.993147i	$-0.537287\pi$
$20$	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	0.0252589	−	0.999681i	$-0.491959\pi$
$29$	−415.421	−	121.978i	−0.493960	−	0.145040i	−0.519219	+	0.854641i	$0.673777\pi$
$30$	1646.43	+	542.852i	1.82937	+	0.603169i
$31$	971.656	−	443.740i	1.01109	−	0.461749i	0.160194	−	0.987086i	$-0.448788\pi$
$31$	971.656	−	443.740i	1.01109	−	0.461749i	0.850894	+	0.525337i	$0.176061\pi$
$32$	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	0.851264	−	0.524737i	$-0.175836\pi$
$37$	288.476	+	332.919i	0.210720	+	0.243184i	−0.640544	+	0.767922i	$0.721291\pi$
$38$	−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	−0.326333	−	0.945255i	$-0.605813\pi$
$41$	1102.30	−	1272.13i	0.655743	−	0.756768i	0.982076	+	0.188487i	$0.0603585\pi$
$42$	−2130.99	+	3087.69i	−1.20804	+	1.75039i
$43$	972.694	+	444.214i	0.526065	+	0.240246i	0.660701	−	0.750649i	$-0.270259\pi$
$43$	972.694	+	444.214i	0.526065	+	0.240246i	−0.134636	+	0.990895i	$0.542987\pi$
$44$	−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	$-0.678283\pi$
$47$		−	3742.96i		−	1.69441i	0.531264	−	0.847206i	$-0.321717\pi$
$48$	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	−0.429147	−	0.903235i	$-0.641186\pi$
$53$	601.662	−	386.665i	0.214191	−	0.137652i	0.643337	+	0.765583i	$0.277549\pi$
$54$	−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	−0.907909	−	0.419167i	$-0.862322\pi$
$59$	−520.278	+	809.569i	−0.149462	+	0.232568i	0.758447	+	0.651735i	$0.225959\pi$
$60$	−3357.49	−	6067.47i	−0.932636	−	1.68541i
$61$	−719.901	−	1576.36i	−0.193470	−	0.423640i	0.787891	−	0.615815i	$-0.211173\pi$
$61$	−719.901	−	1576.36i	−0.193470	−	0.423640i	−0.981361	+	0.192175i	$0.938446\pi$
$62$	−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	−0.201503	−	0.979488i	$-0.564583\pi$
$67$	−533.696	+	76.7340i	−0.118890	+	0.0170938i	0.0826130	+	0.996582i	$0.473673\pi$
$68$	−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	0.439549	−	0.898219i	$-0.355138\pi$
$71$	5617.44	−	807.666i	1.11435	−	0.160219i	0.674802	+	0.737999i	$0.264229\pi$
$72$	11037.2	−	487.383i	2.12910	−	0.0940168i
$73$	−6046.65	+	1775.46i	−1.13467	+	0.333169i	−0.794541	−	0.607210i	$-0.792288\pi$
$73$	−6046.65	+	1775.46i	−1.13467	+	0.333169i	−0.340128	+	0.940379i	$0.610470\pi$
$74$	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	−0.505633	−	0.862749i	$-0.668741\pi$
$79$	3053.09	−	4750.70i	0.489198	−	0.761208i	0.994831	+	0.101541i	$0.0323774\pi$
$80$	−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	−0.903045	−	0.429546i	$-0.858674\pi$
$83$	−4177.41	+	3619.75i	−0.606388	+	0.525438i	0.296657	+	0.954984i	$0.404128\pi$
$84$	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	−0.734515	−	0.678593i	$-0.762590\pi$
$89$	2054.20	−	4498.08i	0.259336	−	0.567867i	0.993851	+	0.110725i	$0.0353174\pi$
$90$	−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	−0.124940	−	0.992164i	$-0.539874\pi$
$97$	8231.99	−	9500.22i	0.874906	−	1.00970i	0.999846	−	0.0175312i	$-0.00558065\pi$
$98$	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	−0.996001	−	0.0893393i	$-0.971524\pi$
$101$	−9616.33	−	11097.8i	−0.942685	−	1.08792i	0.0533158	−	0.998578i	$-0.483021\pi$
$102$	2990.67	+	27100.6i	0.287454	+	2.60483i
$103$	6784.31	+	975.437i	0.639487	+	0.0919443i	0.454428	−	0.890783i	$-0.349844\pi$
$103$	6784.31	+	975.437i	0.639487	+	0.0919443i	0.185058	+	0.982728i	$0.440753\pi$
$104$	−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	0.257152	−	0.966371i	$-0.417216\pi$
$107$	13233.7	−	6043.65i	1.15589	−	0.527875i	0.898733	+	0.438495i	$0.144488\pi$
$108$	21828.7	−	8281.71i	1.87146	−	0.710023i
$109$	5207.74	+	1529.13i	0.438325	+	0.128704i	0.493447	−	0.869776i	$-0.335737\pi$
$109$	5207.74	+	1529.13i	0.438325	+	0.128704i	−0.0551220	+	0.998480i	$0.517555\pi$
$110$	−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	0.631965	+	0.774997i	$0.282248\pi$
$113$	3114.88	+	21664.5i	0.243941	+	1.69665i	−0.388025	+	0.921649i	$0.626842\pi$
$114$	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	0.445275	−	0.895394i	$-0.353106\pi$
$127$	10004.1	+	1438.37i	0.620253	+	0.0891789i	0.174977	+	0.984573i	$0.444015\pi$
$128$	−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	0.976831	+	0.214013i	$0.0686536\pi$
$131$	13140.4	+	20446.9i	0.765714	+	1.19147i	−0.211117	+	0.977461i	$0.567710\pi$
$132$	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	$0.0753705\pi$
$139$			9064.53i			0.469154i	−0.972098	+	0.234577i	$0.924629\pi$
$140$	−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	0.942441	+	0.334374i	$0.108525\pi$
$149$	−1243.89	+	8651.44i	−0.0560285	+	0.389687i	−0.998469	+	0.0553131i	$0.982384\pi$
$150$	6323.64	−	3776.05i	0.281051	−	0.167825i
$151$	−10598.1	+	16491.0i	−0.464810	+	0.723259i	−0.991965	−	0.126510i	$-0.959622\pi$
$151$	−10598.1	+	16491.0i	−0.464810	+	0.723259i	0.527155	+	0.849769i	$0.323259\pi$
$152$	−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	0.222212	−	0.974998i	$-0.428672\pi$
$157$	23078.2	−	6776.36i	0.936272	−	0.274914i	0.714060	+	0.700084i	$0.246854\pi$
$158$	−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	−0.772316	−	0.635238i	$-0.780902\pi$
$163$	−35453.2	+	5097.40i	−1.33438	+	0.191855i	−0.562065	+	0.827093i	$0.689993\pi$
$164$	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	−0.995448	−	0.0953086i	$-0.969616\pi$
$167$	−2970.07	+	10115.1i	−0.106496	+	0.362692i	0.888952	+	0.458001i	$0.151434\pi$
$168$	−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	−0.994518	−	0.104568i	$-0.966654\pi$
$173$	−323.978	+	2253.31i	−0.0108249	+	0.0752886i	0.983693	+	0.179856i	$0.0575632\pi$
$174$	−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	0.691140	−	0.722720i	$-0.257109\pi$
$179$	2375.39	+	2058.28i	0.0741359	+	0.0642391i	−0.617005	+	0.786960i	$0.711654\pi$
$180$	5783.52	+	74943.1i	0.178504	+	2.31306i
$181$	4457.02	−	9759.50i	0.136046	−	0.297900i	−0.829331	−	0.558758i	$-0.811278\pi$
$181$	4457.02	−	9759.50i	0.136046	−	0.297900i	0.965377	+	0.260858i	$0.0840054\pi$
$182$	−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	0.627729	−	0.778432i	$-0.283985\pi$
$191$	−12444.6	−	19364.2i	−0.341126	−	0.530802i	−0.968855	+	0.247630i	$0.920348\pi$
$192$	−12789.4	+	63965.2i	−0.346934	+	1.73517i
$193$	−21703.9	−	25047.6i	−0.582670	−	0.672437i	0.385507	−	0.922705i	$-0.374027\pi$
$193$	−21703.9	−	25047.6i	−0.582670	−	0.672437i	−0.968177	+	0.250268i	$0.919481\pi$
$194$	−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	0.982308	−	0.187273i	$-0.0599648\pi$
$197$	47347.9	+	30428.7i	1.22002	+	0.784062i	0.237716	+	0.971335i	$0.423601\pi$
$198$	4792.76	−	26998.4i	0.122252	−	0.688666i
$199$	−30907.9	+	14115.2i	−0.780483	+	0.356435i	−0.765486	−	0.643453i	$-0.777501\pi$
$199$	−30907.9	+	14115.2i	−0.780483	+	0.356435i	−0.0149973	+	0.999888i	$0.504774\pi$
$200$	−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	0.956057	−	0.293182i	$-0.0947140\pi$
$211$	−299.861	−	1021.23i	−0.00673528	−	0.0229383i	−0.962792	+	0.270243i	$0.912896\pi$
$212$	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	−0.999123	−	0.0418695i	$-0.986669\pi$
$223$	−30939.3	−	48142.5i	−0.622158	−	0.968097i	0.376965	−	0.926228i	$-0.376968\pi$
$224$	−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	0.767022	−	0.641621i	$-0.221738\pi$
$227$	40419.9	+	18459.1i	0.784411	+	0.358228i	0.0173883	+	0.999849i	$0.494465\pi$
$228$	−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	−0.617242	−	0.786773i	$-0.711750\pi$
$233$	20715.0	−	45359.5i	0.381569	−	0.835520i	0.998811	−	0.0487463i	$-0.0155226\pi$
$234$	−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	0.109807	−	0.993953i	$-0.464977\pi$
$239$	63362.6	−	54904.0i	1.10927	−	0.961188i	0.999463	+	0.0327644i	$0.0104311\pi$
$240$	92658.3	−	61030.2i	1.60865	−	1.05955i
$241$	−3060.41	+	21285.6i	−0.0526922	+	0.366482i	0.946366	+	0.323096i	$0.104724\pi$
$241$	−3060.41	+	21285.6i	−0.0526922	+	0.366482i	−0.999058	+	0.0433861i	$0.986185\pi$
$242$	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	0.267979	−	0.963425i	$-0.413644\pi$
$251$	50182.3	−	7215.12i	0.796531	−	0.114524i	0.528552	+	0.848901i	$0.322735\pi$
$252$	−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	−0.585049	−	0.810998i	$-0.698925\pi$
$257$	−42189.8	+	12388.1i	−0.638766	+	0.187559i	−0.0537165	+	0.998556i	$0.517107\pi$
$258$	−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	−0.881991	−	0.471267i	$-0.843797\pi$
$263$	−6012.11	+	9355.03i	−0.0869192	+	0.135249i	0.795072	+	0.606516i	$0.207433\pi$
$264$	−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	−0.708121	+	0.706091i	$0.750457\pi$
$269$	−119003.	+	76478.3i	−1.64457	+	1.05690i	−0.936447	+	0.350809i	$0.885907\pi$
$270$	61198.5	+	146580.i	0.839486	+	2.01070i
$271$	−85252.4	−	73871.7i	−1.16083	−	1.00586i	−0.999821	−	0.0189108i	$-0.993980\pi$
$271$	−85252.4	−	73871.7i	−1.16083	−	1.00586i	−0.161008	−	0.986953i	$-0.551474\pi$
$272$	−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	−0.435950	−	0.899971i	$-0.643587\pi$
$281$	40815.2	−	47103.2i	0.516903	−	0.596538i	0.952853	+	0.303433i	$0.0981329\pi$
$282$	220028.	−	91863.9i	2.76682	−	1.15517i
$283$	71100.9	+	110635.i	0.887773	+	1.38140i	0.924136	+	0.382064i	$0.124786\pi$
$283$	71100.9	+	110635.i	0.887773	+	1.38140i	−0.0363628	+	0.999339i	$0.511577\pi$
$284$	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	0.108820	−	0.994062i	$-0.465293\pi$
$293$	−28936.7	−	8496.59i	−0.337066	−	0.0989714i	−0.445885	+	0.895090i	$0.647111\pi$
$294$	−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	−0.378194	−	0.925726i	$-0.623455\pi$
$307$	6951.73	−	3174.75i	0.0737592	−	0.0336847i	0.451953	+	0.892042i	$0.350727\pi$
$308$	−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	−0.212068	−	0.977255i	$-0.568020\pi$
$311$	−66821.7	−	9607.52i	−0.690871	−	0.0993323i	−0.478803	+	0.877923i	$0.658929\pi$
$312$	33808.7	+	3346.78i	0.347312	+	0.0343810i
$313$	−48984.8	−	56531.5i	−0.500004	−	0.577035i	0.448507	−	0.893779i	$-0.351956\pi$
$313$	−48984.8	−	56531.5i	−0.500004	−	0.577035i	−0.948511	+	0.316744i	$0.897410\pi$
$314$	−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	−0.980705	−	0.195492i	$-0.937370\pi$
$317$	−65080.2	+	75106.5i	−0.647635	+	0.747410i	0.333071	+	0.942902i	$0.391915\pi$
$318$	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	−0.718014	−	0.696028i	$-0.754949\pi$
$331$	−14380.4	+	12460.7i	−0.131255	+	0.113733i	0.586760	+	0.809761i	$0.300403\pi$
$332$	−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	0.765360	−	0.643602i	$-0.222561\pi$
$337$	−25240.3	−	55268.6i	−0.222246	−	0.486652i	−0.987606	+	0.156951i	$0.949834\pi$
$338$	−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	−0.373323	−	0.927702i	$-0.621782\pi$
$347$	−56611.4	+	8139.49i	−0.470159	+	0.0675987i	−0.0968366	+	0.995300i	$0.530872\pi$
$348$	−65616.2	+	88687.5i	−0.541817	+	0.732325i
$349$	−62516.4	+	18356.5i	−0.513267	+	0.150709i	−0.528102	−	0.849181i	$-0.677096\pi$
$349$	−62516.4	+	18356.5i	−0.513267	+	0.150709i	0.0148347	+	0.999890i	$0.495278\pi$
$350$	−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	0.871489	+	0.490415i	$0.163155\pi$
$353$	83664.5	+	183200.i	0.671416	+	1.47020i	−0.200073	+	0.979781i	$0.564118\pi$
$354$	−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	−0.825113	−	0.564968i	$-0.808889\pi$
$359$	−49402.8	+	42807.8i	−0.383321	+	0.332150i	0.441792	+	0.897118i	$0.354343\pi$
$360$	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	$0.176035\pi$
$367$			141495.i			1.05053i	−0.850937	+	0.525267i	$0.823965\pi$
$368$	−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	−0.822254	−	0.569121i	$-0.807283\pi$
$373$	−19743.3	+	22784.9i	−0.141906	+	0.163768i	0.680347	+	0.732890i	$0.261829\pi$
$374$	−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	0.323680	−	0.946167i	$-0.395080\pi$
$379$	52814.4	+	7593.56i	0.367683	+	0.0528648i	0.0440029	+	0.999031i	$0.485989\pi$
$380$	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	−0.370205	−	0.928950i	$-0.620713\pi$
$383$	13116.3	−	5990.02i	0.0894158	−	0.0408348i	0.459621	+	0.888115i	$0.347985\pi$
$384$	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	0.839377	+	0.543550i	$0.182920\pi$
$389$	28317.7	+	196954.i	0.187136	+	1.30156i	−0.652240	+	0.758012i	$0.726171\pi$
$390$	−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	0.392435	−	0.919780i	$-0.371633\pi$
$397$	35509.6	+	10426.5i	0.225302	+	0.0661545i	−0.167133	+	0.985934i	$0.553451\pi$
$398$	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	0.985522	+	0.169547i	$0.0542305\pi$
$401$	249105.	+	160090.i	1.54915	+	0.995577i	0.563626	+	0.826030i	$0.309406\pi$
$402$	−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	0.134625	−	0.990897i	$-0.457017\pi$
$409$	183386.	−	211639.i	1.09628	−	1.26517i	0.961652	−	0.274274i	$-0.0884375\pi$
$410$	−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	0.0977701	−	0.995209i	$-0.468829\pi$
$419$	−153334.	−	132865.i	−0.873395	−	0.756801i	−0.971165	+	0.238408i	$0.923374\pi$
$420$	193706.	−	359535.i	1.09811	−	2.03818i
$421$	−123393.	+	79299.9i	−0.696188	+	0.447413i	−0.840281	−	0.542151i	$-0.817610\pi$
$421$	−123393.	+	79299.9i	−0.696188	+	0.447413i	0.144093	+	0.989564i	$0.453974\pi$
$422$	−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	−0.983054	−	0.183314i	$-0.941318\pi$
$431$	−10579.0	+	36028.8i	−0.0569496	+	0.193953i	0.926105	+	0.377266i	$0.123136\pi$
$432$	158988.	+	338028.i	0.851914	+	1.81128i
$433$	−156.900	+	46.0699i	−0.000836847	+	0.000245720i	−0.282151	−	0.959370i	$-0.591048\pi$
$433$	−156.900	+	46.0699i	−0.000836847	+	0.000245720i	0.281314	+	0.959616i	$0.409230\pi$
$434$	−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	−0.494364	−	0.869255i	$-0.664599\pi$
$439$	−139492.	+	20056.0i	−0.723805	+	0.104067i	−0.229441	+	0.973323i	$0.573690\pi$
$440$	−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	0.832624	+	0.553838i	$0.186837\pi$
$443$	−32822.9	+	111785.i	−0.167251	+	0.569606i	−0.999876	+	0.0157677i	$0.994981\pi$
$444$	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	0.781842	+	0.623476i	$0.214280\pi$
$449$	−29027.2	+	201889.i	−0.143983	+	1.00143i	−0.925826	+	0.377951i	$0.876629\pi$
$450$	−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	−0.998551	−	0.0538133i	$-0.982862\pi$
$457$	−63483.8	+	139010.i	−0.303970	+	0.665601i	0.694581	+	0.719414i	$0.255590\pi$
$458$	−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	0.404011	−	0.914754i	$-0.367616\pi$
$463$	−4875.58	−	2226.60i	−0.0227439	−	0.0103868i	−0.426754	+	0.904368i	$0.640343\pi$
$464$	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	0.831727	−	0.555185i	$-0.187352\pi$
$467$	−4099.80	−	6379.41i	−0.0187987	−	0.0292514i	−0.850526	+	0.525933i	$0.823716\pi$
$468$	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	0.950721	+	0.310048i	$0.100345\pi$
$479$	73088.0	+	248915.i	0.318548	+	1.08487i	−0.632173	+	0.774827i	$0.717837\pi$
$480$	−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	−0.872381	−	0.488826i	$-0.837425\pi$
$487$	−95523.8	−	325324.i	−0.402767	−	1.37170i	0.469615	−	0.882872i	$-0.344393\pi$
$488$	−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	0.110814	−	0.993841i	$-0.464654\pi$
$491$	225285.	−	102884.i	0.934477	−	0.426761i	0.823663	+	0.567080i	$0.191927\pi$
$492$	−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	0.989607	+	0.143796i	$0.0459308\pi$
$499$	176619.	+	274825.i	0.709311	+	1.10371i	−0.280297	+	0.959913i	$0.590433\pi$
$500$	−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	0.490173	−	0.871625i	$-0.336934\pi$
$503$	38568.0	+	17613.4i	0.152437	+	0.0696157i	−0.337736	+	0.941241i	$0.609661\pi$
$504$	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	0.121400	−	0.992604i	$-0.461262\pi$
$509$	205208.	−	449342.i	0.792060	−	1.73437i	0.670660	−	0.741765i	$-0.266011\pi$
$510$	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	0.950893	−	0.309519i	$-0.100168\pi$
$521$	25589.2	+	56032.6i	0.0942718	+	0.206426i	−0.856621	+	0.515945i	$0.827441\pi$
$522$	−93613.3	+	283923.i	−0.343555	+	1.04198i
$523$	−148636.	+	506206.i	−0.543400	+	1.85065i	−0.0179272	+	0.999839i	$0.505707\pi$
$523$	−148636.	+	506206.i	−0.543400	+	1.85065i	−0.525473	+	0.850811i	$0.676111\pi$
$524$	−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	−0.997634	−	0.0687550i	$-0.978097\pi$
$541$	−6158.19	+	42831.2i	−0.0210406	+	0.146341i	0.976593	+	0.215096i	$0.0690064\pi$
$542$	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	0.0940413	−	0.995568i	$-0.470021\pi$
$547$	−262709.	−	227638.i	−0.878010	−	0.760800i	−0.972051	+	0.234768i	$0.924567\pi$
$548$	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	−0.844408	−	0.535701i	$-0.820048\pi$
$557$	−60184.7	+	69456.8i	−0.193988	+	0.223874i	0.650420	+	0.759575i	$0.274593\pi$
$558$	−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	−0.287743	−	0.957708i	$-0.592905\pi$
$563$	−264241.	−	37992.1i	−0.833649	−	0.119861i	−0.545905	+	0.837847i	$0.683814\pi$
$564$	−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	0.272016	−	0.962293i	$-0.412310\pi$
$569$	−6282.50	−	1844.71i	−0.0194048	−	0.00569775i	−0.291421	+	0.956595i	$0.594128\pi$
$570$	40577.6	−	1.23329e6i	0.124892	−	3.79590i
$571$	125871.	+	428676.i	0.386058	+	1.31479i	0.891926	+	0.452181i	$0.149354\pi$
$571$	125871.	+	428676.i	0.386058	+	1.31479i	−0.505868	+	0.862611i	$0.668828\pi$
$572$	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	0.973905	+	0.226954i	$0.0728767\pi$
$577$	34421.7	+	239408.i	0.103390	+	0.719096i	−0.870515	+	0.492142i	$0.836214\pi$
$578$	−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	0.271911	−	0.962323i	$-0.412345\pi$
$587$	90170.0	+	12964.5i	0.261689	+	0.0376252i	−0.0102214	+	0.999948i	$0.503254\pi$
$588$	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	−0.952524	−	0.304464i	$-0.901523\pi$
$593$	−181310.	+	209243.i	−0.515600	+	0.595034i	0.436924	+	0.899499i	$0.356068\pi$
$594$	−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	$-0.863525\pi$
$599$		−	298331.i		−	0.831466i	0.909487	−	0.415733i	$-0.136475\pi$
$600$	68022.7	+	96229.6i	0.188952	+	0.267304i
$601$	−109280.	+	239291.i	−0.302547	+	0.662487i	−0.998450	−	0.0556493i	$-0.982277\pi$
$601$	−109280.	+	239291.i	−0.302547	+	0.662487i	0.695903	+	0.718136i	$0.255004\pi$
$602$	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	−0.897068	−	0.441893i	$-0.854307\pi$
$607$	−216404.	+	187515.i	−0.587338	+	0.508931i	0.309730	+	0.950825i	$0.399761\pi$
$608$	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	0.935854	−	0.352387i	$-0.114630\pi$
$613$	21299.9	+	46640.3i	0.0566836	+	0.124120i	−0.879171	+	0.476507i	$0.841903\pi$
$614$	−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	−0.0190403	−	0.999819i	$-0.506061\pi$
$617$	192433.	−	56503.3i	0.505485	−	0.148424i	0.524525	+	0.851395i	$0.324243\pi$
$618$	109168.	+	422754.i	0.285836	+	1.10691i
$619$	−333223.	+	47910.2i	−0.869668	+	0.125039i	−0.562681	−	0.826674i	$-0.690230\pi$
$619$	−333223.	+	47910.2i	−0.869668	+	0.125039i	−0.306987	+	0.951714i	$0.599321\pi$
$620$	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	−0.992662	−	0.120924i	$-0.961414\pi$
$631$	−187255.	+	291374.i	−0.470299	+	0.731800i	0.522363	+	0.852724i	$0.325051\pi$
$632$	−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	−0.158898	−	0.987295i	$-0.550794\pi$
$641$	284044.	−	621971.i	0.691306	−	1.51375i	0.850204	−	0.526454i	$-0.176479\pi$
$642$	680071.	+	629610.i	1.65000	+	1.52757i
$643$		−	624447.i		−	1.51034i	−0.655531	−	0.755168i	$-0.727555\pi$
$643$		−	624447.i		−	1.51034i	0.655531	−	0.755168i	$-0.272445\pi$
$644$	−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	0.907513	−	0.420024i	$-0.137978\pi$
$647$	495790.	+	226420.i	1.18438	+	0.540886i	0.276862	+	0.960910i	$0.410705\pi$
$648$	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	0.645376	−	0.763865i	$-0.276701\pi$
$653$	−86373.8	−	99680.7i	−0.202561	−	0.233768i	−0.847937	+	0.530097i	$0.822155\pi$
$654$	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	−0.691018	−	0.722838i	$-0.742837\pi$
$659$	−259376.	+	118453.i	−0.597253	+	0.272756i	0.0937643	+	0.995594i	$0.470110\pi$
$660$	−97682.5	−	257469.i	−0.224248	−	0.591067i
$661$	−798906.	−	234580.i	−1.82849	−	0.536894i	−0.828750	−	0.559619i	$-0.810947\pi$
$661$	−798906.	−	234580.i	−1.82849	−	0.536894i	−0.999742	+	0.0227257i	$0.992766\pi$
$662$	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	0.219901	−	0.975522i	$-0.429427\pi$
$673$	−55490.1	−	16293.4i	−0.122514	−	0.0359733i	−0.342415	+	0.939549i	$0.611245\pi$
$674$	−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	−0.309754	−	0.950817i	$-0.600247\pi$
$677$	−597351.	−	383894.i	−1.30332	−	0.837595i	−0.993570	+	0.113222i	$0.963883\pi$
$678$	−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	0.583215	−	0.812318i	$-0.301795\pi$
$683$	−185650.	−	288876.i	−0.397972	−	0.619256i	−0.981187	+	0.193062i	$0.938158\pi$
$684$	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	$0.0871336\pi$
$691$			258157.i			0.540665i	−0.962767	+	0.270333i	$0.912866\pi$
$692$	−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	−0.997819	−	0.0660072i	$-0.978974\pi$
$701$	−10723.5	+	74583.7i	−0.0218223	+	0.151778i	0.975997	+	0.217785i	$0.0698831\pi$
$702$	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	−0.224051	−	0.974577i	$-0.571928\pi$
$709$	57487.6	−	16879.9i	0.114362	−	0.0335797i	0.338413	+	0.940998i	$0.390110\pi$
$710$	−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	−0.790322	−	0.612692i	$-0.790087\pi$
$719$	106383.	−	362308.i	0.205786	−	0.700841i	0.996107	−	0.0881492i	$-0.0280952\pi$
$720$	−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	−0.761155	−	0.648570i	$-0.775367\pi$
$727$	−120245.	+	104193.i	−0.227510	+	0.197138i	0.533645	+	0.845709i	$0.320822\pi$
$728$	−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	−0.711381	−	0.702807i	$-0.751930\pi$
$733$	153461.	−	336032.i	0.285621	−	0.625422i	0.997001	+	0.0773851i	$0.0246571\pi$
$734$	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	−0.145853	−	0.989306i	$-0.546593\pi$
$739$	−540132.	−	246670.i	−0.989034	−	0.451677i	−0.843181	+	0.537630i	$0.819320\pi$
$740$	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	0.479603	−	0.877486i	$-0.340781\pi$
$743$	−285862.	−	444810.i	−0.517820	−	0.805744i	−0.997423	+	0.0717414i	$0.977144\pi$
$744$	−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	−0.921248	−	0.388976i	$-0.872829\pi$
$751$	−694042.	+	316958.i	−1.23057	+	0.561982i	−0.309320	+	0.950958i	$0.600101\pi$
$752$	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	0.999425	+	0.0338971i	$0.0107918\pi$
$757$	28671.7	+	199416.i	0.0500337	+	0.347992i	−0.949392	+	0.314095i	$0.898299\pi$
$758$	−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	0.999695	−	0.0247101i	$-0.00786628\pi$
$761$	19419.7	+	135067.i	0.0335330	+	0.233227i	−0.966162	+	0.257937i	$0.916957\pi$
$762$	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	0.989431	−	0.145002i	$-0.0463190\pi$
$769$	750175.	+	482108.i	1.26856	+	0.815252i	0.279126	+	0.960255i	$0.409955\pi$
$770$	−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	0.718538	−	0.695487i	$-0.244811\pi$
$773$	−43098.9	−	49738.8i	−0.0721285	−	0.0832408i	−0.790667	+	0.612247i	$0.790266\pi$
$774$	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	0.851501	−	0.524353i	$-0.175693\pi$
$787$	280987.	+	243477.i	0.453667	+	0.393105i	−0.397834	+	0.917457i	$0.630238\pi$
$788$	−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	0.996113	−	0.0880839i	$-0.0280744\pi$
$797$	176098.	+	385601.i	0.277228	+	0.607045i	−0.718885	+	0.695129i	$0.755347\pi$
$798$	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	−0.782023	−	0.623250i	$-0.785812\pi$
$809$	−721859.	+	211957.i	−1.10295	+	0.323855i	−0.320925	+	0.947105i	$0.603994\pi$
$810$	33132.6	−	1.00701e6i	0.0504993	−	1.53484i
$811$	169008.	−	575590.i	0.256961	−	0.875127i	−0.725431	−	0.688295i	$-0.758360\pi$
$811$	169008.	−	575590.i	0.256961	−	0.875127i	0.982392	−	0.186833i	$-0.0598222\pi$
$812$	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	−0.370184	−	0.928959i	$-0.620705\pi$
$821$	216399.	−	139071.i	0.321047	−	0.206324i	0.691230	+	0.722634i	$0.257069\pi$
$822$	229319.	+	549254.i	0.339387	+	0.812885i
$823$	139050.	+	120488.i	0.205292	+	0.177886i	0.751438	−	0.659803i	$-0.229360\pi$
$823$	139050.	+	120488.i	0.205292	+	0.177886i	−0.546147	+	0.837690i	$0.683906\pi$
$824$	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	$0.166397\pi$
$827$			682927.i			0.998535i	−0.866448	+	0.499267i	$0.833603\pi$
$828$	−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	−0.286014	−	0.958225i	$-0.592330\pi$
$839$	−584540.	−	84044.2i	−0.830406	−	0.119394i	−0.544392	+	0.838831i	$0.683240\pi$
$840$	−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	0.870353	+	0.492429i	$0.163891\pi$
$853$	126596.	+	880493.i	0.173989	+	1.21012i	−0.696364	+	0.717689i	$0.745200\pi$
$854$	−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	−0.211479	−	0.977382i	$-0.567828\pi$
$857$	−674077.	−	197927.i	−0.917800	−	0.269490i	−0.706321	+	0.707892i	$0.749646\pi$
$858$	26403.8	−	80081.1i	0.0358668	−	0.108782i
$859$	−17112.0	+	7814.79i	−0.0231907	+	0.0105909i	−0.426977	−	0.904263i	$-0.640421\pi$
$859$	−17112.0	+	7814.79i	−0.0231907	+	0.0105909i	0.403786	+	0.914854i	$0.367694\pi$
$860$	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	0.185460	−	0.982652i	$-0.440623\pi$
$863$	64469.0	+	9269.24i	0.0865624	+	0.0124458i	−0.0988975	+	0.995098i	$0.531532\pi$
$864$	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	−0.532339	−	0.846531i	$-0.678687\pi$
$877$	350749.	−	768034.i	0.456034	−	0.998576i	0.988374	−	0.152045i	$-0.0485858\pi$
$878$	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	0.288835	−	0.957379i	$-0.406732\pi$
$881$	993241.	−	638317.i	1.27968	−	0.822403i	0.990849	+	0.134976i	$0.0430957\pi$
$882$	660037.	+	328075.i	0.848459	+	0.421731i
$883$	−4.00218	+	3.46791i	−5.13305e−6	+	4.44781e-6i	−0.654863	−	0.755747i	$-0.727274\pi$
$883$	−4.00218	+	3.46791i	−5.13305e−6	+	4.44781e-6i	0.654858	+	0.755752i	$0.272728\pi$
$884$	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	−0.946938	−	0.321416i	$-0.895841\pi$
$887$	−205500.	+	319765.i	−0.261195	+	0.406428i	0.685743	+	0.727844i	$0.259478\pi$
$888$	−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	−0.921135	−	0.389243i	$-0.872737\pi$
$907$	−151708.	+	236062.i	−0.184414	+	0.286954i	0.736721	+	0.676197i	$0.236373\pi$
$908$	−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	−0.666653	−	0.745368i	$-0.732274\pi$
$911$	−19707.1	+	17076.3i	−0.0237458	+	0.0205758i	0.642907	+	0.765944i	$0.277728\pi$
$912$	−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	$0.00346947\pi$
$919$			18410.5i			0.0217989i	−0.999941	+	0.0108994i	$0.996531\pi$
$920$	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	0.965681	−	0.259731i	$-0.0836340\pi$
$929$	492937.	+	568879.i	0.571163	+	0.659157i	−0.394518	+	0.918888i	$0.629089\pi$
$930$	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	0.455677	−	0.890145i	$-0.349397\pi$
$937$	314109.	+	92230.8i	0.357768	+	0.105050i	−0.0979090	+	0.995195i	$0.531215\pi$
$938$	−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	−0.963637	−	0.267214i	$-0.913897\pi$
$941$	−101226.	−	704039.i	−0.114317	−	0.795092i	0.849320	−	0.527878i	$-0.177012\pi$
$942$	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	0.878063	−	0.478545i	$-0.158836\pi$
$947$	−107018.	−	364468.i	−0.119331	−	0.406406i	−0.997395	+	0.0721392i	$0.977017\pi$
$948$	−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	0.489589	−	0.871954i	$-0.337147\pi$
$953$	−90989.8	−	58475.6i	−0.100186	−	0.0643856i	−0.589774	+	0.807568i	$0.700783\pi$
$954$	−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	$-0.952199\pi$
$967$		−	279792.i		−	0.299214i	0.988746	−	0.149607i	$-0.0478009\pi$
$968$	−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	0.998240	−	0.0593018i	$-0.0188874\pi$
$971$	1.01978e6	+	883647.i	1.08161	+	0.937217i	0.0833662	+	0.996519i	$0.473433\pi$
$972$	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	−0.997987	−	0.0634207i	$-0.979799\pi$
$977$	−21532.1	+	149759.i	−0.0225578	+	0.156893i	0.975429	+	0.220314i	$0.0707081\pi$
$978$	−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	0.793742	+	0.608255i	$0.208130\pi$
$983$	−196006.	+	667534.i	−0.202844	+	0.690823i	−0.996585	+	0.0825676i	$0.973688\pi$
$984$	−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	−0.946747	−	0.321978i	$-0.895652\pi$
$991$	−1.73282e6	+	249141.i	−1.76443	+	0.253687i	−0.817686	+	0.575665i	$0.804743\pi$
$992$	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	0.995120	+	0.0986730i	$0.0314598\pi$
$997$	415523.	+	909868.i	0.418027	+	0.915352i	−0.577093	+	0.816679i	$0.695813\pi$
$998$	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.3.12	✓	460
4.3	odd	2	inner	92.5.g.a.3.31	yes	460
23.8	even	11	inner	92.5.g.a.31.31	yes	460
92.31	odd	22	inner	92.5.g.a.31.12	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.12	✓	460	1.1	even	1	trivial
92.5.g.a.3.31	yes	460	4.3	odd	2	inner
92.5.g.a.31.12	yes	460	92.31	odd	22	inner
92.5.g.a.31.31	yes	460	23.8	even	11	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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