LMFDB - Embedded newform 92.5.g.a.3.9

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)

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")

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);

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			3.9
Character	$\chi$	$=$	92.3
Dual form			92.5.g.a.31.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.28360 + 2.28429i) q^{2} +(2.55088 + 1.16495i) q^{3} +(5.56402 - 15.0014i) q^{4} +(24.3881 - 28.1454i) q^{5} +(-11.0372 + 2.00174i) q^{6} +(6.42136 + 9.99183i) q^{7} +(15.9975 + 61.9684i) q^{8} +(-47.8938 - 55.2724i) q^{9} +(-15.7885 + 148.128i) q^{10} +(-198.623 - 28.5577i) q^{11} +(31.6690 - 31.7850i) q^{12} +(-188.239 - 120.974i) q^{13} +(-43.9094 - 18.1409i) q^{14} +(94.9991 - 43.3846i) q^{15} +(-194.083 - 166.936i) q^{16} +(457.444 + 134.318i) q^{17} +(283.522 + 72.0889i) q^{18} +(8.28991 + 28.2328i) q^{19} +(-286.524 - 522.457i) q^{20} +(4.74016 + 32.9685i) q^{21} +(717.433 - 359.941i) q^{22} +(-277.098 - 450.619i) q^{23} +(-31.3822 + 176.710i) q^{24} +(-108.435 - 754.185i) q^{25} +(894.440 - 32.7633i) q^{26} +(-121.777 - 414.735i) q^{27} +(185.620 - 40.7345i) q^{28} +(-843.875 - 247.784i) q^{29} +(-212.836 + 359.463i) q^{30} +(782.527 - 357.368i) q^{31} +(1018.62 + 104.808i) q^{32} +(-473.396 - 304.233i) q^{33} +(-1808.88 + 603.890i) q^{34} +(437.828 + 62.9502i) q^{35} +(-1095.65 + 410.937i) q^{36} +(-543.697 - 627.459i) q^{37} +(-91.7127 - 73.7687i) q^{38} +(-339.247 - 527.879i) q^{39} +(2134.27 + 1061.03i) q^{40} +(-857.023 + 989.057i) q^{41} +(-90.8745 - 97.4275i) q^{42} +(2553.98 + 1166.36i) q^{43} +(-1533.55 + 2820.73i) q^{44} -2723.70 q^{45} +(1939.22 + 846.680i) q^{46} -2699.33i q^{47} +(-300.612 - 651.932i) q^{48} +(938.809 - 2055.70i) q^{49} +(2078.84 + 2228.74i) q^{50} +(1010.41 + 875.527i) q^{51} +(-2862.14 + 2150.74i) q^{52} +(328.661 - 211.218i) q^{53} +(1347.24 + 1083.65i) q^{54} +(-5647.81 + 4893.85i) q^{55} +(-516.452 + 557.766i) q^{56} +(-11.7432 + 81.6760i) q^{57} +(3336.96 - 1114.03i) q^{58} +(306.670 - 477.187i) q^{59} +(-122.252 - 1666.51i) q^{60} +(2488.69 + 5449.47i) q^{61} +(-1753.17 + 2960.97i) q^{62} +(244.729 - 833.471i) q^{63} +(-3584.16 + 1982.68i) q^{64} +(-7995.64 + 2347.73i) q^{65} +(2249.40 - 82.3954i) q^{66} +(4852.60 - 697.699i) q^{67} +(4560.18 - 6114.95i) q^{68} +(-181.896 - 1472.28i) q^{69} +(-1581.45 + 793.425i) q^{70} +(-1062.71 + 152.794i) q^{71} +(2658.96 - 3852.12i) q^{72} +(-55.5902 + 16.3228i) q^{73} +(3218.58 + 818.362i) q^{74} +(601.981 - 2050.16i) q^{75} +(469.657 + 32.7280i) q^{76} +(-990.087 - 2167.99i) q^{77} +(2319.78 + 958.402i) q^{78} +(6394.04 - 9949.32i) q^{79} +(-9431.80 + 1391.29i) q^{80} +(-670.568 + 4663.91i) q^{81} +(554.823 - 5205.36i) q^{82} +(-9507.60 + 8238.39i) q^{83} +(520.948 + 112.329i) q^{84} +(14936.6 - 9599.17i) q^{85} +(-11050.6 + 2004.17i) q^{86} +(-1863.97 - 1615.14i) q^{87} +(-1407.81 - 12765.2i) q^{88} +(2237.97 - 4900.46i) q^{89} +(8943.54 - 6221.73i) q^{90} -2657.67i q^{91} +(-8301.69 + 1649.60i) q^{92} +2412.45 q^{93} +(6166.06 + 8863.52i) q^{94} +(996.798 + 455.223i) q^{95} +(2476.29 + 1454.00i) q^{96} +(3234.37 - 3732.66i) q^{97} +(1613.16 + 8894.62i) q^{98} +(7934.37 + 12346.1i) 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 $

$2$	−3.28360	+	2.28429i	−0.820899	+	0.571073i
$2$	−3.28360	+	2.28429i	−0.820899	+	0.571073i
$3$	2.55088	+	1.16495i	0.283431	+	0.129439i	0.552058	−	0.833806i	$-0.313843\pi$
$3$	2.55088	+	1.16495i	0.283431	+	0.129439i	−0.268627	+	0.963244i	$0.586570\pi$
$4$	5.56402	−	15.0014i	0.347752	−	0.937587i
$5$	24.3881	−	28.1454i	0.975524	−	1.12581i	−0.0165126	−	0.999864i	$-0.505256\pi$
$5$	24.3881	−	28.1454i	0.975524	−	1.12581i	0.992036	−	0.125951i	$-0.0401982\pi$
$6$	−11.0372	+	2.00174i	−0.306588	+	0.0556038i
$7$	6.42136	+	9.99183i	0.131048	+	0.203915i	0.900576	−	0.434698i	$-0.143145\pi$
$7$	6.42136	+	9.99183i	0.131048	+	0.203915i	−0.769528	+	0.638613i	$0.779509\pi$
$8$	15.9975	+	61.9684i	0.249961	+	0.968256i
$9$	−47.8938	−	55.2724i	−0.591282	−	0.682376i
$10$	−15.7885	+	148.128i	−0.157885	+	1.48128i
$11$	−198.623	−	28.5577i	−1.64151	−	0.236014i	−0.741209	−	0.671274i	$-0.765747\pi$
$11$	−198.623	−	28.5577i	−1.64151	−	0.236014i	−0.900305	+	0.435260i	$0.856656\pi$
$12$	31.6690	−	31.7850i	0.219924	−	0.220729i
$13$	−188.239	−	120.974i	−1.11384	−	0.715821i	−0.151713	−	0.988425i	$-0.548479\pi$
$13$	−188.239	−	120.974i	−1.11384	−	0.715821i	−0.962127	+	0.272603i	$0.912115\pi$
$14$	−43.9094	−	18.1409i	−0.224028	−	0.0925556i
$15$	94.9991	−	43.3846i	0.422218	−	0.192821i
$16$	−194.083	−	166.936i	−0.758138	−	0.652094i
$17$	457.444	+	134.318i	1.58285	+	0.464767i	0.950709	−	0.310086i	$-0.100358\pi$
$17$	457.444	+	134.318i	1.58285	+	0.464767i	0.632142	+	0.774853i	$0.282176\pi$
$18$	283.522	+	72.0889i	0.875069	+	0.222497i
$19$	8.28991	+	28.2328i	0.0229637	+	0.0782073i	0.970178	−	0.242395i	$-0.0779329\pi$
$19$	8.28991	+	28.2328i	0.0229637	+	0.0782073i	−0.947214	+	0.320602i	$0.896115\pi$
$20$	−286.524	−	522.457i	−0.716309	−	1.30614i
$21$	4.74016	+	32.9685i	0.0107487	+	0.0747586i
$22$	717.433	−	359.941i	1.48230	−	0.743680i
$23$	−277.098	−	450.619i	−0.523815	−	0.851832i
$23$	−277.098	−	450.619i	−0.523815	−	0.851832i
$24$	−31.3822	+	176.710i	−0.0544829	+	0.306789i
$25$	−108.435	−	754.185i	−0.173497	−	1.20670i
$26$	894.440	−	32.7633i	1.32314	−	0.0484664i
$27$	−121.777	−	414.735i	−0.167047	−	0.568909i
$28$	185.620	−	40.7345i	0.236760	−	0.0519573i
$29$	−843.875	−	247.784i	−1.00342	−	0.294630i	−0.261560	−	0.965187i	$-0.584237\pi$
$29$	−843.875	−	247.784i	−1.00342	−	0.294630i	−0.741858	+	0.670557i	$0.766055\pi$
$30$	−212.836	+	359.463i	−0.236484	+	0.399404i
$31$	782.527	−	357.368i	0.814284	−	0.371871i	0.0356616	−	0.999364i	$-0.488646\pi$
$31$	782.527	−	357.368i	0.814284	−	0.371871i	0.778622	+	0.627493i	$0.215919\pi$
$32$	1018.62	+	104.808i	0.994748	+	0.102352i
$33$	−473.396	−	304.233i	−0.434707	−	0.279369i
$34$	−1808.88	+	603.890i	−1.56478	+	0.522396i
$35$	437.828	+	62.9502i	0.357411	+	0.0513879i
$36$	−1095.65	+	410.937i	−0.845405	+	0.317081i
$37$	−543.697	−	627.459i	−0.397149	−	0.458334i	0.521592	−	0.853195i	$-0.325338\pi$
$37$	−543.697	−	627.459i	−0.397149	−	0.458334i	−0.918741	+	0.394861i	$0.870793\pi$
$38$	−91.7127	−	73.7687i	−0.0635130	−	0.0510864i
$39$	−339.247	−	527.879i	−0.223042	−	0.347060i
$40$	2134.27	+	1061.03i	1.33392	+	0.663147i
$41$	−857.023	+	989.057i	−0.509829	+	0.588374i	−0.951055	−	0.309022i	$-0.899998\pi$
$41$	−857.023	+	989.057i	−0.509829	+	0.588374i	0.441226	+	0.897396i	$0.354544\pi$
$42$	−90.8745	−	97.4275i	−0.0515162	−	0.0552310i
$43$	2553.98	+	1166.36i	1.38128	+	0.630808i	0.960990	−	0.276583i	$-0.0892021\pi$
$43$	2553.98	+	1166.36i	1.38128	+	0.630808i	0.420287	+	0.907391i	$0.361929\pi$
$44$	−1533.55	+	2820.73i	−0.792122	+	1.45699i
$45$	−2723.70			−1.34504
$46$	1939.22	+	846.680i	0.916457	+	0.400132i
$47$		−	2699.33i		−	1.22197i	−0.791642	−	0.610985i	$-0.790774\pi$
$47$		−	2699.33i		−	1.22197i	0.791642	−	0.610985i	$-0.209226\pi$
$48$	−300.612	−	651.932i	−0.130474	−	0.282956i
$49$	938.809	−	2055.70i	0.391007	−	0.856187i
$50$	2078.84	+	2228.74i	0.831535	+	0.891497i
$51$	1010.41	+	875.527i	0.388471	+	0.336612i
$52$	−2862.14	+	2150.74i	−1.05848	+	0.795393i
$53$	328.661	−	211.218i	0.117003	−	0.0751931i	−0.480831	−	0.876814i	$-0.659665\pi$
$53$	328.661	−	211.218i	0.117003	−	0.0751931i	0.597833	+	0.801620i	$0.296028\pi$
$54$	1347.24	+	1083.65i	0.462017	+	0.371621i
$55$	−5647.81	+	4893.85i	−1.86704	+	1.61780i
$56$	−516.452	+	557.766i	−0.164685	+	0.177859i
$57$	−11.7432	+	81.6760i	−0.00361441	+	0.0251388i
$58$	3336.96	−	1114.03i	0.991961	−	0.331163i
$59$	306.670	−	477.187i	0.0880981	−	0.137083i	−0.794408	−	0.607385i	$-0.792219\pi$
$59$	306.670	−	477.187i	0.0880981	−	0.137083i	0.882506	+	0.470302i	$0.155855\pi$
$60$	−122.252	−	1666.51i	−0.0339590	−	0.462920i
$61$	2488.69	+	5449.47i	0.668823	+	1.46452i	0.874066	+	0.485807i	$0.161474\pi$
$61$	2488.69	+	5449.47i	0.668823	+	1.46452i	−0.205244	+	0.978711i	$0.565799\pi$
$62$	−1753.17	+	2960.97i	−0.456080	+	0.770284i
$63$	244.729	−	833.471i	0.0616602	−	0.209995i
$64$	−3584.16	+	1982.68i	−0.875039	+	0.484053i
$65$	−7995.64	+	2347.73i	−1.89246	+	0.555676i
$66$	2249.40	−	82.3954i	0.516391	−	0.0189154i
$67$	4852.60	−	697.699i	1.08100	−	0.155424i	0.421275	−	0.906933i	$-0.361583\pi$
$67$	4852.60	−	697.699i	1.08100	−	0.155424i	0.659723	+	0.751509i	$0.270674\pi$
$68$	4560.18	−	6114.95i	0.986198	−	1.32244i
$69$	−181.896	−	1472.28i	−0.0382054	−	0.309238i
$70$	−1581.45	+	793.425i	−0.322745	+	0.161923i
$71$	−1062.71	+	152.794i	−0.210813	+	0.0303104i	−0.246912	−	0.969038i	$-0.579416\pi$
$71$	−1062.71	+	152.794i	−0.210813	+	0.0303104i	0.0360990	+	0.999348i	$0.488507\pi$
$72$	2658.96	−	3852.12i	0.512916	−	0.743080i
$73$	−55.5902	+	16.3228i	−0.0104316	+	0.00306301i	−0.286944	−	0.957947i	$-0.592639\pi$
$73$	−55.5902	+	16.3228i	−0.0104316	+	0.00306301i	0.276513	+	0.961010i	$0.410821\pi$
$74$	3218.58	+	818.362i	0.587761	+	0.149445i
$75$	601.981	−	2050.16i	0.107019	−	0.364473i
$76$	469.657	+	32.7280i	0.0813118	+	0.00566621i
$77$	−990.087	−	2167.99i	−0.166991	−	0.365658i
$78$	2319.78	+	958.402i	0.381292	+	0.157528i
$79$	6394.04	−	9949.32i	1.02452	−	1.59419i	0.243282	−	0.969956i	$-0.421776\pi$
$79$	6394.04	−	9949.32i	1.02452	−	1.59419i	0.781240	−	0.624231i	$-0.214588\pi$
$80$	−9431.80	+	1391.29i	−1.47372	+	0.217389i
$81$	−670.568	+	4663.91i	−0.102205	+	0.710853i
$82$	554.823	−	5205.36i	0.0825139	−	0.774146i
$83$	−9507.60	+	8238.39i	−1.38011	+	1.19588i	−0.423012	+	0.906124i	$0.639027\pi$
$83$	−9507.60	+	8238.39i	−1.38011	+	1.19588i	−0.957102	+	0.289751i	$0.906427\pi$
$84$	520.948	+	112.329i	0.0738305	+	0.0159196i
$85$	14936.6	−	9599.17i	2.06735	−	1.32860i
$86$	−11050.6	+	2004.17i	−1.49413	+	0.270980i
$87$	−1863.97	−	1615.14i	−0.246264	−	0.213389i
$88$	−1407.81	−	12765.2i	−0.181793	−	1.64840i
$89$	2237.97	−	4900.46i	0.282536	−	0.618667i	−0.714152	−	0.699991i	$-0.753187\pi$
$89$	2237.97	−	4900.46i	0.282536	−	0.618667i	0.996688	+	0.0813236i	$0.0259147\pi$
$90$	8943.54	−	6221.73i	1.10414	−	0.768115i
$91$		−	2657.67i		−	0.320936i
$92$	−8301.69	+	1649.60i	−0.980824	+	0.194896i
$93$	2412.45			0.278928
$94$	6166.06	+	8863.52i	0.697834	+	1.00311i
$95$	996.798	+	455.223i	0.110449	+	0.0504402i
$96$	2476.29	+	1454.00i	0.268695	+	0.157769i
$97$	3234.37	−	3732.66i	0.343753	−	0.396712i	−0.557378	−	0.830259i	$-0.688193\pi$
$97$	3234.37	−	3732.66i	0.343753	−	0.396712i	0.901131	+	0.433547i	$0.142738\pi$
$98$	1613.16	+	8894.62i	0.167967	+	0.926137i
$99$	7934.37	+	12346.1i	0.809547	+	1.25968i
$100$	−11917.2	−	2569.62i	−1.19172	−	0.256962i
$101$	5761.68	+	6649.34i	0.564815	+	0.651832i	0.964270	−	0.264921i	$-0.0853460\pi$
$101$	5761.68	+	6649.34i	0.564815	+	0.651832i	−0.399455	+	0.916753i	$0.630800\pi$
$102$	−5317.75	−	566.803i	−0.511125	−	0.0544793i
$103$	1244.08	+	178.871i	0.117266	+	0.0168603i	0.200698	−	0.979653i	$-0.435679\pi$
$103$	1244.08	+	178.871i	0.117266	+	0.0168603i	−0.0834319	+	0.996513i	$0.526588\pi$
$104$	4485.19	−	13600.1i	0.414681	−	1.25741i
$105$	1043.52	+	670.627i	0.0946499	+	0.0608278i
$106$	−596.708	+	1444.31i	−0.0531068	+	0.128543i
$107$	−15617.2	+	7132.11i	−1.36406	+	0.622946i	−0.956902	−	0.290410i	$-0.906208\pi$
$107$	−15617.2	+	7132.11i	−1.36406	+	0.622946i	−0.407160	+	0.913357i	$0.633481\pi$
$108$	−6899.17	−	480.768i	−0.591492	−	0.0412181i
$109$	−4618.99	−	1356.26i	−0.388771	−	0.114153i	0.0815048	−	0.996673i	$-0.474027\pi$
$109$	−4618.99	−	1356.26i	−0.388771	−	0.114153i	−0.470276	+	0.882519i	$0.655846\pi$
$110$	7366.14	−	28970.7i	0.608772	−	2.39427i
$111$	−655.948	−	2233.95i	−0.0532382	−	0.181313i
$112$	421.719	−	3011.20i	0.0336192	−	0.240051i
$113$	756.883	+	5264.24i	0.0592750	+	0.412267i	0.997757	+	0.0669389i	$0.0213232\pi$
$113$	756.883	+	5264.24i	0.0592750	+	0.412267i	−0.938482	+	0.345328i	$0.887768\pi$
$114$	−148.012	−	295.016i	−0.0113890	−	0.0227005i
$115$	−19440.7	−	3190.73i	−1.47000	−	0.241265i
$116$	−8412.44	+	11280.6i	−0.625182	+	0.838334i
$117$	2328.97	+	16198.3i	0.170134	+	1.18331i
$118$	83.0552	+	2267.41i	0.00596490	+	0.162842i
$119$	1595.33	+	5433.20i	0.112657	+	0.383674i
$120$	4208.23	+	5192.89i	0.292238	+	0.360618i
$121$	24587.7	+	7219.59i	1.67937	+	0.493108i
$122$	−20620.0	−	12209.0i	−1.38538	−	0.820275i
$123$	−3338.37	+	1524.58i	−0.220660	+	0.100772i
$124$	−1007.02	−	13727.4i	−0.0654929	−	0.892780i
$125$	−4290.31	−	2757.22i	−0.274580	−	0.176462i
$126$	1100.30	+	3295.82i	0.0693058	+	0.207597i
$127$	17662.2	+	2539.44i	1.09506	+	0.157446i	0.666088	−	0.745873i	$-0.267967\pi$
$127$	17662.2	+	2539.44i	1.09506	+	0.157446i	0.428970	+	0.903319i	$0.358876\pi$
$128$	7239.91	−	14697.6i	0.441889	−	0.897070i
$129$	5156.15	+	5950.52i	0.309846	+	0.357582i
$130$	20891.6	−	25973.4i	1.23619	−	1.53689i
$131$	−8691.92	−	13524.9i	−0.506492	−	0.788118i	0.490007	−	0.871719i	$-0.336994\pi$
$131$	−8691.92	−	13524.9i	−0.506492	−	0.788118i	−0.996499	+	0.0836010i	$0.973358\pi$
$132$	−7197.91	+	5408.84i	−0.413103	+	0.310425i
$133$	−228.865	+	264.125i	−0.0129383	+	0.0149316i
$134$	−14340.2	+	13375.7i	−0.798632	+	0.744916i
$135$	−14642.8	−	6687.13i	−0.803444	−	0.366921i
$136$	−1005.47	+	30495.8i	−0.0543617	+	1.64878i
$137$	3420.95			0.182266			0.0911331	−	0.995839i	$-0.470951\pi$
$137$	3420.95			0.182266			0.0911331	+	0.995839i	$0.470951\pi$
$138$	3960.39	+	4418.88i	0.207960	+	0.232035i
$139$			6209.84i			0.321404i	0.987003	+	0.160702i	$0.0513758\pi$
$139$			6209.84i			0.321404i	−0.987003	+	0.160702i	$0.948624\pi$
$140$	3380.43	−	6217.78i	0.172471	−	0.317234i
$141$	3144.58	−	6885.68i	0.158170	−	0.346345i
$142$	3140.48	−	2929.25i	0.155747	−	0.145271i
$143$	33933.9	+	29403.9i	1.65944	+	1.43791i
$144$	68.4244	+	18722.7i	0.00329979	+	0.902906i
$145$	−27554.5	+	17708.2i	−1.31056	+	0.842244i
$146$	145.250	−	180.582i	0.00681413	−	0.00847165i
$147$	4789.58	−	4150.20i	0.221648	−	0.192059i
$148$	−12437.9	+	4665.00i	−0.567837	+	0.212975i
$149$	1458.00	−	10140.6i	0.0656727	−	0.456764i	−0.930277	−	0.366857i	$-0.880434\pi$
$149$	1458.00	−	10140.6i	0.0656727	−	0.456764i	0.995950	−	0.0899070i	$-0.0286570\pi$
$150$	2706.50	+	8107.00i	0.120289	+	0.360311i
$151$	−6263.32	+	9745.92i	−0.274695	+	0.427434i	−0.951001	−	0.309187i	$-0.899943\pi$
$151$	−6263.32	+	9745.92i	−0.274695	+	0.427434i	0.676306	+	0.736621i	$0.263580\pi$
$152$	−1616.92	+	965.368i	−0.0699846	+	0.0417836i
$153$	−14484.7	−	31717.0i	−0.618765	−	1.35491i
$154$	8203.36	+	4857.15i	0.345900	+	0.204805i
$155$	9026.09	−	30740.0i	0.375696	−	1.27950i
$156$	−9806.49	+	2152.05i	−0.402962	+	0.0884306i
$157$	−12075.4	+	3545.65i	−0.489892	+	0.143845i	−0.517344	−	0.855778i	$-0.673079\pi$
$157$	−12075.4	+	3545.65i	−0.489892	+	0.143845i	0.0274512	+	0.999623i	$0.491261\pi$
$158$	1731.70	+	47275.4i	0.0693677	+	1.89374i
$159$	1084.43	−	155.918i	0.0428952	−	0.00616740i
$160$	27792.1	−	26113.4i	1.08563	−	1.02006i
$161$	2723.17	−	5662.30i	0.105056	−	0.218445i
$162$	−8451.84	−	16846.2i	−0.322049	−	0.641905i
$163$	35254.3	−	5068.80i	1.32690	−	0.190779i	0.557834	−	0.829953i	$-0.311633\pi$
$163$	35254.3	−	5068.80i	1.32690	−	0.190779i	0.769062	+	0.639174i	$0.220724\pi$
$164$	10068.7	+	18359.7i	0.374358	+	0.682617i
$165$	−20108.0	+	5904.24i	−0.738585	+	0.216868i
$166$	12400.3	−	48769.7i	0.450003	−	1.76984i
$167$	212.089	−	722.309i	0.00760475	−	0.0258994i	−0.955603	−	0.294657i	$-0.904795\pi$
$167$	212.089	−	722.309i	0.00760475	−	0.0258994i	0.963208	+	0.268757i	$0.0866129\pi$
$168$	−1967.18	+	821.155i	−0.0696987	+	0.0290942i
$169$	8934.56	+	19564.0i	0.312824	+	0.684988i
$170$	−27118.5	+	65639.4i	−0.938356	+	2.27126i
$171$	1163.46	−	1810.38i	0.0397887	−	0.0619124i
$172$	31707.5	−	31823.6i	1.07178	−	1.07570i
$173$	220.541	−	1533.90i	0.00736882	−	0.0512512i	−0.985805	−	0.167893i	$-0.946304\pi$
$173$	220.541	−	1533.90i	0.00736882	−	0.0512512i	0.993174	+	0.116642i	$0.0372129\pi$
$174$	9809.97	+	1045.62i	0.324018	+	0.0345361i
$175$	6839.39	−	5926.36i	0.223327	−	0.193514i
$176$	33782.1	+	38700.0i	1.09059	+	1.24935i
$177$	1338.18	−	859.994i	0.0427137	−	0.0274504i
$178$	3845.51	+	21203.3i	0.121371	+	0.669212i
$179$	5157.51	+	4469.01i	0.160966	+	0.139478i	0.731620	−	0.681713i	$-0.238765\pi$
$179$	5157.51	+	4469.01i	0.160966	+	0.139478i	−0.570654	+	0.821191i	$0.693310\pi$
$180$	−15154.7	+	40859.3i	−0.467739	+	1.26109i
$181$	1984.49	−	4345.43i	0.0605749	−	0.132640i	−0.876924	−	0.480630i	$-0.840408\pi$
$181$	1984.49	−	4345.43i	0.0605749	−	0.132640i	0.937499	+	0.347989i	$0.113135\pi$
$182$	6070.89	+	8726.71i	0.183278	+	0.263456i
$183$			16800.2i			0.501662i
$184$	23491.3	−	24380.1i	0.693858	−	0.720112i
$185$	−30919.8			−0.903427
$186$	−7921.51	+	5510.74i	−0.228972	+	0.159288i
$187$	−87023.1	−	39742.1i	−2.48858	−	1.13650i
$188$	−40493.7	−	15019.1i	−1.14570	−	0.424942i
$189$	3361.98	−	3879.94i	0.0941179	−	0.108618i
$190$	−4312.95	+	782.211i	−0.119472	+	0.0216679i
$191$	19150.0	+	29798.0i	0.524931	+	0.816809i	0.997934	−	0.0642519i	$-0.0204661\pi$
$191$	19150.0	+	29798.0i	0.524931	+	0.816809i	−0.473002	+	0.881061i	$0.656830\pi$
$192$	−11452.5	+	882.226i	−0.310669	+	0.0239319i
$193$	−20198.9	−	23310.8i	−0.542267	−	0.625809i	0.416797	−	0.909000i	$-0.363153\pi$
$193$	−20198.9	−	23310.8i	−0.542267	−	0.625809i	−0.959064	+	0.283191i	$0.908607\pi$
$194$	−2093.88	+	19644.8i	−0.0556351	+	0.521968i
$195$	−23130.9	−	3325.73i	−0.608308	−	0.0874616i
$196$	−25614.9	−	25521.4i	−0.666776	−	0.664343i
$197$	−12322.0	−	7918.86i	−0.317503	−	0.204047i	0.372175	−	0.928162i	$-0.378612\pi$
$197$	−12322.0	−	7918.86i	−0.317503	−	0.204047i	−0.689679	+	0.724115i	$0.742248\pi$
$198$	−54255.4	−	22415.3i	−1.38393	−	0.571760i
$199$	10877.6	−	4967.64i	0.274680	−	0.125442i	−0.273313	−	0.961925i	$-0.588119\pi$
$199$	10877.6	−	4967.64i	0.274680	−	0.125442i	0.547993	+	0.836483i	$0.315392\pi$
$200$	45000.9	−	18784.7i	1.12502	−	0.469617i
$201$	13191.2	+	3873.29i	0.326507	+	0.0958710i
$202$	−34108.1	−	8672.38i	−0.835900	−	0.212537i
$203$	−2943.01	−	10023.0i	−0.0714166	−	0.243223i
$204$	18756.1	−	10286.1i	0.450694	−	0.247168i
$205$	6936.22	+	48242.4i	0.165050	+	1.14795i
$206$	−4493.64	+	2254.49i	−0.105892	+	0.0531269i
$207$	−11635.5	+	36897.8i	−0.271548	+	0.861111i
$208$	16339.1	+	54902.9i	0.377661	+	1.26902i
$209$	−840.303	−	5844.43i	−0.0192373	−	0.133798i
$210$	−4958.39	+	181.626i	−0.112435	+	0.00411849i
$211$	−121.087	−	412.383i	−0.00271976	−	0.00926267i	0.958122	−	0.286361i	$-0.0924455\pi$
$211$	−121.087	−	412.383i	−0.00271976	−	0.00926267i	−0.960842	+	0.277098i	$0.910627\pi$
$212$	−1339.88	−	6105.59i	−0.0298122	−	0.135849i
$213$	−2888.84	−	848.241i	−0.0636744	−	0.0186965i
$214$	34988.6	−	59093.1i	0.764010	−	1.29036i
$215$	95114.5	−	43437.3i	2.05764	−	0.939693i
$216$	23752.3	−	14181.1i	0.509094	−	0.303949i
$217$	8595.65	+	5524.09i	0.182540	+	0.117312i
$218$	18265.0	−	6097.71i	0.384332	−	0.128308i
$219$	−160.819	−	23.1223i	−0.00335313	−	0.000482107i
$220$	41990.0	+	111954.i	0.867563	+	2.31311i
$221$	−69859.8	−	80622.5i	−1.43035	−	1.65071i
$222$	7256.87	+	5837.03i	0.147246	+	0.118437i
$223$	−12473.2	−	19408.7i	−0.250824	−	0.390290i	0.692895	−	0.721039i	$-0.256335\pi$
$223$	−12473.2	−	19408.7i	−0.250824	−	0.390290i	−0.943719	+	0.330749i	$0.892699\pi$
$224$	5493.71	+	10850.9i	0.109489	+	0.216257i
$225$	−36492.3	+	42114.3i	−0.720835	+	0.831888i
$226$	−14510.3	−	15556.7i	−0.284093	−	0.304579i
$227$	1039.19	+	474.580i	0.0201670	+	0.00920996i	0.425473	−	0.904971i	$-0.360108\pi$
$227$	1039.19	+	474.580i	0.0201670	+	0.00920996i	−0.405306	+	0.914181i	$0.632835\pi$
$228$	1159.91	+	630.612i	0.0223129	+	0.0121309i
$229$	67172.8			1.28092			0.640461	−	0.767991i	$-0.278743\pi$
$229$	67172.8			1.28092			0.640461	+	0.767991i	$0.278743\pi$
$230$	71124.1	−	33931.2i	1.34450	−	0.641422i
$231$		−	6683.68i		−	0.125254i
$232$	1854.86	−	56257.5i	0.0344616	−	1.04521i
$233$	41409.4	−	90673.9i	0.762758	−	1.67021i	0.0207800	−	0.999784i	$-0.493385\pi$
$233$	41409.4	−	90673.9i	0.762758	−	1.67021i	0.741978	−	0.670424i	$-0.233888\pi$
$234$	−44649.1	−	47868.7i	−0.815419	−	0.874219i
$235$	−75973.7	−	65831.5i	−1.37571	−	1.19206i
$236$	−5452.15	−	7255.55i	−0.0978913	−	0.130271i
$237$	27900.9	−	17930.8i	0.496731	−	0.319230i
$238$	−17649.4	−	14196.2i	−0.311585	−	0.250622i
$239$	30361.7	−	26308.6i	0.531534	−	0.460576i	−0.347267	−	0.937766i	$-0.612890\pi$
$239$	30361.7	−	26308.6i	0.531534	−	0.460576i	0.878800	+	0.477190i	$0.158345\pi$
$240$	−25680.2	−	7438.55i	−0.445837	−	0.129142i
$241$	8887.28	−	61812.4i	0.153015	−	1.06425i	−0.758113	−	0.652123i	$-0.773879\pi$
$241$	8887.28	−	61812.4i	0.153015	−	1.06425i	0.911129	−	0.412122i	$-0.135212\pi$
$242$	−97227.7	+	32459.2i	−1.66020	+	0.554251i
$243$	−26072.5	+	40569.6i	−0.441540	+	0.687050i
$244$	95596.7	−	7012.81i	1.60570	−	0.117791i
$245$	−34962.8	−	76557.8i	−0.582470	−	1.27543i
$246$	7479.26	−	12631.9i	0.123592	−	0.208737i
$247$	1854.95	−	6317.38i	0.0304045	−	0.103548i
$248$	34664.0	+	42774.9i	0.563606	+	0.695482i
$249$	−33850.1	+	9939.28i	−0.545960	+	0.160308i
$250$	20385.9	−	746.736i	0.326175	−	0.0119478i
$251$	−22182.2	+	3189.31i	−0.352092	+	0.0506232i	−0.316092	−	0.948729i	$-0.602371\pi$
$251$	−22182.2	+	3189.31i	−0.352092	+	0.0506232i	−0.0360003	+	0.999352i	$0.511462\pi$
$252$	−11141.5	−	8308.73i	−0.175446	−	0.130838i
$253$	42169.4	+	97416.7i	0.658804	+	1.52192i
$254$	−63796.4	+	32007.1i	−0.988846	+	0.496111i
$255$	49284.1	−	7085.98i	0.757925	−	0.108973i
$256$	9800.63	+	64799.0i	0.149546	+	0.988755i
$257$	−25655.7	+	7533.20i	−0.388435	+	0.114055i	−0.470118	−	0.882604i	$-0.655789\pi$
$257$	−25655.7	+	7533.20i	−0.388435	+	0.114055i	0.0816832	+	0.996658i	$0.473970\pi$
$258$	−30523.4	−	7760.95i	−0.458558	−	0.116594i
$259$	2778.20	−	9461.67i	0.0414155	−	0.141048i
$260$	−9268.70	+	133009.i	−0.137111	+	1.96758i
$261$	26720.8	+	58510.3i	0.392254	+	0.858917i
$262$	59435.5	+	24555.4i	0.865852	+	0.357721i
$263$	14157.5	−	22029.5i	0.204680	−	0.318488i	−0.723704	−	0.690110i	$-0.757562\pi$
$263$	14157.5	−	22029.5i	0.204680	−	0.318488i	0.928384	+	0.371622i	$0.121198\pi$
$264$	11279.7	−	34202.6i	0.161841	−	0.490739i
$265$	2070.62	−	14401.5i	0.0294855	−	0.205076i
$266$	148.164	−	1390.07i	0.00209401	−	0.0196460i
$267$	11417.6	−	9893.39i	0.160159	−	0.138779i
$268$	16533.5	−	76677.8i	0.230195	−	1.06758i
$269$	1248.43	−	802.320i	0.0172529	−	0.0110877i	−0.531986	−	0.846753i	$-0.678554\pi$
$269$	1248.43	−	802.320i	0.0172529	−	0.0110877i	0.549239	+	0.835665i	$0.314918\pi$
$270$	63356.3	−	11490.5i	0.869085	−	0.157620i
$271$	57969.5	+	50230.9i	0.789335	+	0.683962i	0.953140	−	0.302530i	$-0.0978314\pi$
$271$	57969.5	+	50230.9i	0.789335	+	0.683962i	−0.163805	+	0.986493i	$0.552377\pi$
$272$	−66359.7	−	102433.i	−0.896947	−	1.38453i
$273$	3096.05	−	6779.40i	0.0415415	−	0.0909632i
$274$	−11233.0	+	7814.45i	−0.149622	+	0.104087i
$275$			152895.i			2.02176i
$276$	−23098.3	−	5463.12i	−0.303223	−	0.0717171i
$277$	−51406.2			−0.669970			−0.334985	−	0.942223i	$-0.608731\pi$
$277$	−51406.2			−0.669970			−0.334985	+	0.942223i	$0.608731\pi$
$278$	−14185.1	−	20390.6i	−0.183545	−	0.263840i
$279$	−57230.8	−	26136.4i	−0.735227	−	0.335767i
$280$	3103.25	+	28138.6i	0.0395823	+	0.358910i
$281$	−62412.7	+	72028.0i	−0.790424	+	0.912198i	−0.997816	−	0.0660602i	$-0.978957\pi$
$281$	−62412.7	+	72028.0i	−0.790424	+	0.912198i	0.207392	+	0.978258i	$0.433503\pi$
$282$	5403.35	+	29792.9i	0.0679461	+	0.374641i
$283$	−21043.5	−	32744.4i	−0.262752	−	0.408850i	0.684662	−	0.728861i	$-0.259950\pi$
$283$	−21043.5	−	32744.4i	−0.262752	−	0.408850i	−0.947414	+	0.320011i	$0.896313\pi$
$284$	−3620.81	+	16792.3i	−0.0448920	+	0.208196i
$285$	2012.40	+	2322.44i	0.0247757	+	0.0285927i
$286$	−178592.	−	19035.6i	−2.18339	−	0.232720i
$287$	−15385.7	−	2212.14i	−0.186790	−	0.0268564i
$288$	−42992.7	−	61321.4i	−0.518334	−	0.739311i
$289$	120951.	+	77730.6i	1.44815	+	0.930672i
$290$	50027.1	−	121089.i	0.594853	−	1.43982i
$291$	12598.9	−	5753.71i	0.148780	−	0.0679457i
$292$	−64.4412	+	924.750i	−0.000755785	+	0.0108457i
$293$	−13849.3	−	4066.53i	−0.161322	−	0.0473684i	0.200074	−	0.979781i	$-0.435882\pi$
$293$	−13849.3	−	4066.53i	−0.161322	−	0.0473684i	−0.361396	+	0.932412i	$0.617700\pi$
$294$	−6246.80	+	24568.4i	−0.0722708	+	0.284238i
$295$	−5951.52	−	20269.0i	−0.0683886	−	0.232910i
$296$	30184.8	−	43729.8i	0.344513	−	0.499107i
$297$	12343.9	+	85853.6i	0.139939	+	0.973297i
$298$	18376.6	+	36628.2i	0.206935	+	0.412461i
$299$	−2352.52	+	118346.i	−0.0263143	+	1.32376i
$300$	−27405.8	−	20437.7i	−0.304509	−	0.227086i
$301$	4745.92	+	33008.6i	0.0523826	+	0.364329i
$302$	−1696.29	−	46308.9i	−0.0185989	−	0.507751i
$303$	6951.24	+	23673.7i	0.0757141	+	0.257859i
$304$	3104.15	−	6863.41i	0.0335889	−	0.0742664i
$305$	214072.	+	62857.1i	2.30123	+	0.675701i
$306$	120013.	+	71058.7i	1.28169	+	0.758882i
$307$	−104630.	+	47782.8i	−1.11014	+	0.506984i	−0.884177	−	0.467152i	$-0.845280\pi$
$307$	−104630.	+	47782.8i	−1.11014	+	0.506984i	−0.225963	+	0.974136i	$0.572553\pi$
$308$	−38031.7	+	2789.94i	−0.400908	+	0.0294099i
$309$	2965.12	+	1905.56i	0.0310545	+	0.0199575i
$310$	40581.2	+	121556.i	0.422280	+	1.26489i
$311$	−84145.3	−	12098.3i	−0.869980	−	0.125084i	−0.307154	−	0.951660i	$-0.599377\pi$
$311$	−84145.3	−	12098.3i	−0.869980	−	0.125084i	−0.562826	+	0.826576i	$0.690286\pi$
$312$	27284.7	−	29467.3i	0.280291	−	0.302713i
$313$	8053.46	+	9294.19i	0.0822042	+	0.0948686i	0.795362	−	0.606135i	$-0.207281\pi$
$313$	8053.46	+	9294.19i	0.0822042	+	0.0948686i	−0.713157	+	0.701004i	$0.752736\pi$
$314$	31551.3	−	39226.1i	0.320006	−	0.397847i
$315$	−17489.9	−	27214.8i	−0.176265	−	0.274273i
$316$	−113677.	−	151278.i	−1.13841	−	1.51496i
$317$	69738.7	−	80482.7i	0.693993	−	0.800911i	−0.293935	−	0.955826i	$-0.594965\pi$
$317$	69738.7	−	80482.7i	0.693993	−	0.800911i	0.987928	+	0.154915i	$0.0495103\pi$
$318$	−3204.68	+	2989.13i	−0.0316906	+	0.0295591i
$319$	160537.	+	73314.7i	1.57759	+	0.720460i
$320$	−31607.5	+	149231.i	−0.308667	+	1.45734i
$321$	−48146.1			−0.467252
$322$	3992.57	+	24813.2i	0.0385071	+	0.239316i
$323$			14028.4i			0.134463i
$324$	66234.0	+	36009.5i	0.630944	+	0.343026i
$325$	−70824.9	+	155085.i	−0.670532	+	1.46826i
$326$	−104182.	+	97175.0i	−0.980299	+	0.914364i
$327$	−10202.5	−	8840.54i	−0.0954140	−	0.0826767i
$328$	−75000.5	−	37285.8i	−0.697135	−	0.346574i
$329$	26971.3	−	17333.4i	0.249178	−	0.160137i
$330$	52539.5	−	65319.6i	0.482457	−	0.599813i
$331$	−91107.9	+	78945.4i	−0.831572	+	0.720561i	−0.962632	−	0.270813i	$-0.912707\pi$
$331$	−91107.9	+	78945.4i	−0.831572	+	0.720561i	0.131060	+	0.991374i	$0.458162\pi$
$332$	70686.7	+	188466.i	0.641300	+	1.70984i
$333$	−8641.49	+	60102.9i	−0.0779292	+	0.542009i
$334$	953.549	+	2856.24i	0.00854772	+	0.0256037i
$335$	98708.7	−	153594.i	0.879561	−	1.36862i
$336$	4583.66	−	7189.95i	0.0406007	−	0.0636865i
$337$	−43796.0	−	95899.8i	−0.385633	−	0.844419i	−0.998527	−	0.0542538i	$-0.982722\pi$
$337$	−43796.0	−	95899.8i	−0.385633	−	0.844419i	0.612894	−	0.790165i	$-0.290005\pi$
$338$	−74027.3	−	43831.0i	−0.647975	−	0.383661i
$339$	−4201.85	+	14310.2i	−0.0365629	+	0.124522i
$340$	−60893.3	−	277480.i	−0.526758	−	2.40034i
$341$	−165634.	+	48634.4i	−1.42442	+	0.418249i
$342$	315.100	+	8602.25i	0.00269399	+	0.0735461i
$343$	54795.8	−	7878.45i	0.465757	−	0.0669657i
$344$	−31420.3	+	176925.i	−0.265518	+	1.49511i
$345$	−45874.0	−	30786.6i	−0.385415	−	0.258657i
$346$	2779.70	+	5540.48i	0.0232191	+	0.0462802i
$347$	77100.0	−	11085.3i	0.640317	−	0.0920637i	0.185494	−	0.982645i	$-0.440612\pi$
$347$	77100.0	−	11085.3i	0.640317	−	0.0920637i	0.454823	+	0.890582i	$0.349702\pi$
$348$	−34600.5	+	18975.5i	−0.285709	+	0.156687i
$349$	122698.	−	36027.3i	1.00736	−	0.295788i	0.263888	−	0.964553i	$-0.414995\pi$
$349$	122698.	−	36027.3i	1.00736	−	0.295788i	0.743474	+	0.668765i	$0.233177\pi$
$350$	−8920.26	+	35083.0i	−0.0728184	+	0.286391i
$351$	−27248.8	+	92801.0i	−0.221174	+	0.753249i
$352$	−199329.	−	49906.9i	−1.60874	−	0.402787i
$353$	−52171.9	−	114240.i	−0.418685	−	0.916791i	−0.995029	−	0.0995845i	$-0.968249\pi$
$353$	−52171.9	−	114240.i	−0.418685	−	0.916791i	0.576345	−	0.817207i	$-0.304479\pi$
$354$	−2429.56	+	5880.66i	−0.0193874	+	0.0469267i
$355$	−21617.0	+	33636.7i	−0.171529	+	0.266905i
$356$	−61061.6	−	60838.9i	−0.481802	−	0.480044i
$357$	−2259.90	+	15717.9i	−0.0177318	+	0.123327i
$358$	−27143.7	−	2893.17i	−0.211789	−	0.0225739i
$359$	54022.0	−	46810.3i	0.419162	−	0.363206i	−0.419595	−	0.907711i	$-0.637828\pi$
$359$	54022.0	−	46810.3i	0.419162	−	0.363206i	0.838757	+	0.544505i	$0.183283\pi$
$360$	−43572.5	−	168783.i	−0.336208	−	1.30234i
$361$	108905.	−	69988.8i	0.835664	−	0.537049i
$362$	3409.96	+	18801.8i	0.0260215	+	0.143477i
$363$	54309.8	+	47059.7i	0.412159	+	0.357138i
$364$	−39868.7	−	14787.3i	−0.300905	−	0.111606i
$365$	−896.329	+	1962.69i	−0.00672794	+	0.0147321i
$366$	−38376.5	−	55164.9i	−0.286485	−	0.411814i
$367$			15077.3i			0.111942i	0.998432	+	0.0559708i	$0.0178254\pi$
$367$			15077.3i			0.111942i	−0.998432	+	0.0559708i	$0.982175\pi$
$368$	−21444.6	+	133715.i	−0.158351	+	0.987383i
$369$	95713.7			0.702945
$370$	101528.	−	70629.8i	0.741623	−	0.515923i
$371$	4220.90	+	1927.62i	0.0306660	+	0.0140047i
$372$	13422.9	−	36190.1i	0.0969977	−	0.261519i
$373$	126884.	−	146432.i	0.911989	−	1.05249i	−0.0864282	−	0.996258i	$-0.527545\pi$
$373$	126884.	−	146432.i	0.911989	−	1.05249i	0.998418	−	0.0562338i	$-0.0179092\pi$
$374$	376531.	−	68289.0i	2.69189	−	0.488211i
$375$	−7732.07	−	12031.3i	−0.0549836	−	0.0855561i
$376$	167273.	−	43182.6i	1.18318	−	0.305445i
$377$	128875.	+	148729.i	0.906745	+	1.04644i
$378$	−2176.50	+	20419.9i	−0.0152326	+	0.142912i
$379$	45423.8	+	6530.96i	0.316232	+	0.0454672i	0.298603	−	0.954377i	$-0.403479\pi$
$379$	45423.8	+	6530.96i	0.316232	+	0.0454672i	0.0176284	+	0.999845i	$0.494388\pi$
$380$	12375.2	−	12420.5i	0.0857007	−	0.0860145i
$381$	42095.9	+	27053.4i	0.289994	+	0.186368i
$382$	−130948.	−	54100.5i	−0.897374	−	0.370744i
$383$	−51364.3	+	23457.3i	−0.350158	+	0.159912i	−0.582727	−	0.812668i	$-0.698014\pi$
$383$	−51364.3	+	23457.3i	−0.350158	+	0.159912i	0.232569	+	0.972580i	$0.425287\pi$
$384$	35590.1	−	29057.7i	0.241361	−	0.197060i
$385$	−85165.2	−	25006.7i	−0.574567	−	0.168708i
$386$	119574.	+	30403.0i	0.802529	+	0.204052i
$387$	−57852.2	−	197026.i	−0.386276	−	1.31553i
$388$	−37999.0	−	69288.7i	−0.252411	−	0.460255i
$389$	−27895.9	−	194020.i	−0.184349	−	1.28217i	−0.846332	−	0.532656i	$-0.821194\pi$
$389$	−27895.9	−	194020.i	−0.184349	−	1.28217i	0.661983	−	0.749519i	$-0.269715\pi$
$390$	83549.6	−	41917.4i	0.549307	−	0.275591i
$391$	−66230.6	−	243352.i	−0.433217	−	1.59177i
$392$	142407.	+	25290.3i	0.926744	+	0.164582i
$393$	−6416.25	−	44626.0i	−0.0415429	−	0.288937i
$394$	58549.5	−	2144.66i	0.377164	−	0.0138155i
$395$	−124089.	−	422608.i	−0.795313	−	2.70859i
$396$	229356.	−	50332.4i	1.46258	−	0.320965i
$397$	−258826.	−	75998.3i	−1.64221	−	0.482195i	−0.675345	−	0.737502i	$-0.736005\pi$
$397$	−258826.	−	75998.3i	−1.64221	−	0.482195i	−0.966860	+	0.255307i	$0.917824\pi$
$398$	−24370.2	+	41159.4i	−0.153848	+	0.259838i
$399$	−891.500	+	407.134i	−0.00559984	+	0.00255736i
$400$	−104855.	+	164477.i	−0.655346	+	1.02798i
$401$	−17447.0	−	11212.5i	−0.108501	−	0.0697291i	0.485265	−	0.874367i	$-0.338723\pi$
$401$	−17447.0	−	11212.5i	−0.108501	−	0.0697291i	−0.593766	+	0.804638i	$0.702359\pi$
$402$	−52162.3	+	17414.2i	−0.322779	+	0.107759i
$403$	−190534.	−	27394.7i	−1.17317	−	0.168677i
$404$	131807.	−	49436.2i	0.807564	−	0.302888i
$405$	114913.	+	132617.i	0.700585	+	0.808518i
$406$	32559.0	+	26188.7i	0.197524	+	0.158877i
$407$	90071.9	+	140155.i	0.543752	+	0.846094i
$408$	−38090.9	+	76619.9i	−0.228824	+	0.460279i
$409$	−212246.	+	244945.i	−1.26880	+	1.46427i	−0.446965	+	0.894551i	$0.647495\pi$
$409$	−212246.	+	244945.i	−1.26880	+	1.46427i	−0.821837	+	0.569723i	$0.807050\pi$
$410$	−132976.	−	142564.i	−0.791050	−	0.848093i
$411$	8726.45	+	3985.24i	0.0516599	+	0.0235923i
$412$	9605.39	−	17667.6i	0.0565875	−	0.104084i
$413$	6737.21			0.0394984
$414$	−46078.8	−	147736.i	−0.268844	−	0.861959i
$415$			468514.i			2.72036i
$416$	−179065.	−	142956.i	−1.03472	−	0.826066i
$417$	−7234.15	+	15840.6i	−0.0416021	+	0.0910959i
$418$	16109.6	+	17271.3i	0.0922003	+	0.0988489i
$419$	44435.3	+	38503.4i	0.253105	+	0.219317i	0.772167	−	0.635420i	$-0.219173\pi$
$419$	44435.3	+	38503.4i	0.253105	+	0.219317i	−0.519062	+	0.854737i	$0.673719\pi$
$420$	15866.5	−	11922.8i	0.0899460	−	0.0675895i
$421$	130047.	−	83575.9i	0.733728	−	0.471538i	−0.119660	−	0.992815i	$-0.538180\pi$
$421$	130047.	−	83575.9i	0.733728	−	0.471538i	0.853388	+	0.521277i	$0.174544\pi$
$422$	1339.60	+	1077.50i	0.00752231	+	0.00605053i
$423$	−149199.	+	129281.i	−0.833842	+	0.722528i
$424$	18346.6	+	16987.6i	0.102052	+	0.0944933i
$425$	51697.2	−	359562.i	0.286213	−	1.99066i
$426$	11423.4	−	3813.68i	0.0629473	−	0.0210148i
$427$	−38469.4	+	59859.6i	−0.210989	+	0.328305i
$428$	20097.4	+	273962.i	0.109712	+	1.49556i
$429$	52307.3	+	114537.i	0.284216	+	0.622345i
$430$	−213094.	+	359900.i	−1.15248	+	1.94646i
$431$	92692.4	−	315681.i	0.498988	−	1.69940i	−0.196197	−	0.980565i	$-0.562859\pi$
$431$	92692.4	−	315681.i	0.498988	−	1.69940i	0.695184	−	0.718831i	$-0.255323\pi$
$432$	−45599.3	+	100822.i	−0.244338	+	0.540242i
$433$	−217425.	+	63841.7i	−1.15967	+	0.340509i	−0.804303	−	0.594219i	$-0.797461\pi$
$433$	−217425.	+	63841.7i	−1.15967	+	0.340509i	−0.355364	+	0.934728i	$0.615643\pi$
$434$	−40843.3	+	1496.09i	−0.216841	+	0.00794287i
$435$	−90917.3	+	13071.9i	−0.480472	+	0.0690815i
$436$	−46045.9	+	61745.0i	−0.242225	+	0.324810i
$437$	10425.1	−	11558.9i	0.0545908	−	0.0605274i
$438$	580.884	−	291.434i	0.00302790	−	0.00151912i
$439$	161285.	−	23189.3i	0.836885	−	0.120326i	0.289470	−	0.957187i	$-0.406521\pi$
$439$	161285.	−	23189.3i	0.836885	−	0.120326i	0.547415	+	0.836861i	$0.315612\pi$
$440$	−393615.	−	271696.i	−2.03314	−	1.40339i
$441$	−158587.	+	46565.3i	−0.815436	+	0.239434i
$442$	413557.	+	105152.i	2.11685	+	0.538235i
$443$	−109916.	+	374340.i	−0.560085	+	1.90747i	−0.175102	+	0.984550i	$0.556026\pi$
$443$	−109916.	+	374340.i	−0.560085	+	1.90747i	−0.384983	+	0.922924i	$0.625793\pi$
$444$	−37162.1	−	2589.64i	−0.188510	−	0.0131363i
$445$	−83345.6	−	182501.i	−0.420884	−	0.921608i
$446$	85292.3	+	35237.9i	0.428785	+	0.177150i
$447$	15532.5	−	24169.0i	0.0777367	−	0.120961i
$448$	−42825.8	−	23080.8i	−0.213378	−	0.114999i
$449$	−18100.6	+	125892.i	−0.0897841	+	0.624462i	0.894394	+	0.447280i	$0.147607\pi$
$449$	−18100.6	+	125892.i	−0.0897841	+	0.624462i	−0.984178	+	0.177182i	$0.943302\pi$
$450$	23624.5	−	221645.i	0.116664	−	1.09455i
$451$	198470.	−	171975.i	0.975756	−	0.845498i
$452$	83182.2	+	17936.0i	0.407149	+	0.0877909i
$453$	−27330.5	+	17564.2i	−0.133184	+	0.0855920i
$454$	−4496.35	+	815.472i	−0.0218146	+	0.00395638i
$455$	−74801.0	−	64815.5i	−0.361314	−	0.313080i
$456$	−5249.19	+	578.905i	−0.0252443	+	0.00278405i
$457$	6719.10	−	14712.8i	0.0321720	−	0.0704470i	−0.892864	−	0.450327i	$-0.851307\pi$
$457$	6719.10	−	14712.8i	0.0321720	−	0.0704470i	0.925036	+	0.379880i	$0.124035\pi$
$458$	−220568.	+	153442.i	−1.05151	+	0.731499i
$459$		−	206075.i		−	0.978136i
$460$	−156034.	+	273885.i	−0.737401	+	1.29435i
$461$	83684.9			0.393772			0.196886	−	0.980426i	$-0.436917\pi$
$461$	83684.9			0.393772			0.196886	+	0.980426i	$0.436917\pi$
$462$	15267.5	+	21946.5i	0.0715292	+	0.102821i
$463$	268188.	+	122477.i	1.25106	+	0.571339i	0.927129	−	0.374743i	$-0.122269\pi$
$463$	268188.	+	122477.i	1.25106	+	0.571339i	0.323928	+	0.946082i	$0.394996\pi$
$464$	122418.	+	188964.i	0.568603	+	0.877694i
$465$	58835.1	−	67899.3i	0.272101	−	0.314021i
$466$	71153.9	+	392328.i	0.327663	+	1.80666i
$467$	−10667.1	−	16598.4i	−0.0489119	−	0.0761084i	0.815936	−	0.578142i	$-0.196222\pi$
$467$	−10667.1	−	16598.4i	−0.0489119	−	0.0761084i	−0.864848	+	0.502033i	$0.832586\pi$
$468$	255956.	+	55190.1i	1.16862	+	0.251982i
$469$	38131.6	+	44006.2i	0.173356	+	0.200064i
$470$	399845.	+	42618.3i	1.81007	+	0.192930i
$471$	−34933.3	−	5022.65i	−0.157470	−	0.0226408i
$472$	34476.5	+	11370.0i	0.154753	+	0.0510360i
$473$	−473971.	−	304603.i	−2.11851	−	1.36148i
$474$	−50656.1	+	122611.i	−0.225463	+	0.545725i
$475$	20393.9	−	9313.57i	0.0903883	−	0.0412790i
$476$	90382.0	+	6298.27i	0.398904	+	0.0277976i
$477$	−27415.3	−	8049.87i	−0.120492	−	0.0353795i
$478$	−39599.2	+	155742.i	−0.173313	+	0.681631i
$479$	−100203.	−	341261.i	−0.436728	−	1.48736i	−0.824637	−	0.565663i	$-0.808620\pi$
$479$	−100203.	−	341261.i	−0.436728	−	1.48736i	0.387908	−	0.921698i	$-0.373198\pi$
$480$	101315.	−	34235.8i	0.439736	−	0.148593i
$481$	26438.7	+	183885.i	0.114275	+	0.794798i
$482$	112015.	+	223268.i	0.482151	+	0.961021i
$483$	13542.8	−	11271.5i	0.0580515	−	0.0483157i
$484$	245110.	−	328679.i	1.04634	−	1.40308i
$485$	−26177.0	−	182065.i	−0.111285	−	0.774004i
$486$	−7061.21	−	192772.i	−0.0298956	−	0.816151i
$487$	11945.7	+	40683.4i	0.0503680	+	0.171538i	0.980836	−	0.194836i	$-0.0624174\pi$
$487$	11945.7	+	40683.4i	0.0503680	+	0.171538i	−0.930468	+	0.366374i	$0.880599\pi$
$488$	−297882.	+	241398.i	−1.25085	+	1.01366i
$489$	95834.5	+	28139.5i	0.400778	+	0.117679i
$490$	289684.	+	171520.i	1.20651	+	0.714368i
$491$	−156839.	+	71625.9i	−0.650565	+	0.297103i	−0.713228	−	0.700932i	$-0.752768\pi$
$491$	−156839.	+	71625.9i	−0.650565	+	0.297103i	0.0626634	+	0.998035i	$0.480041\pi$
$492$	4296.08	+	58562.9i	0.0177477	+	0.241932i
$493$	−352743.	−	226694.i	−1.45133	−	0.932711i
$494$	8339.83	+	24981.0i	0.0341746	+	0.102366i
$495$	540990.	+	77782.6i	2.20790	+	0.317448i
$496$	−211533.	−	61272.9i	−0.859834	−	0.249061i
$497$	−8350.73	−	9637.26i	−0.0338074	−	0.0390158i
$498$	88445.8	−	109960.i	0.356631	−	0.443380i
$499$	−109332.	−	170124.i	−0.439083	−	0.683227i	0.549229	−	0.835672i	$-0.314922\pi$
$499$	−109332.	−	170124.i	−0.439083	−	0.683227i	−0.988312	+	0.152445i	$0.951285\pi$
$500$	−65233.5	+	49019.4i	−0.260934	+	0.196078i
$501$	1382.47	−	1595.45i	0.00550782	−	0.00635636i
$502$	65552.0	−	61142.9i	0.260123	−	0.242627i
$503$	369392.	+	168696.i	1.46000	+	0.666758i	0.977845	−	0.209330i	$-0.0671283\pi$
$503$	369392.	+	168696.i	1.46000	+	0.666758i	0.482151	+	0.876088i	$0.339856\pi$
$504$	55563.9	+	1831.99i	0.218742	+	0.00721211i
$505$	327664.			1.28483
$506$	−360995.	−	223550.i	−1.40994	−	0.873119i
$507$			60313.7i			0.234639i
$508$	136368.	−	250828.i	0.528427	−	0.971961i
$509$	−158569.	+	347217.i	−0.612043	+	1.34019i	0.309125	+	0.951021i	$0.399964\pi$
$509$	−158569.	+	347217.i	−0.612043	+	1.34019i	−0.921168	+	0.389166i	$0.872763\pi$
$510$	−145643.	+	135847.i	−0.559948	+	0.522286i
$511$	−520.059	−	450.634i	−0.00199164	−	0.00172577i
$512$	−180201.	−	190386.i	−0.687413	−	0.726267i
$513$	10699.6	−	6876.22i	0.0406568	−	0.0261285i
$514$	67035.0	−	83341.2i	0.253732	−	0.315452i
$515$	35375.0	−	30652.7i	0.133377	−	0.115572i
$516$	117955.	−	44240.6i	0.443013	−	0.166158i
$517$	−77086.7	+	536150.i	−0.288402	+	2.00588i
$518$	12490.7	+	37414.5i	0.0465509	+	0.139438i
$519$	2349.49	−	3655.88i	0.00872245	−	0.0135724i
$520$	−273396.	−	457919.i	−1.01108	−	1.69349i
$521$	−41706.6	−	91324.7i	−0.153649	−	0.336444i	0.817117	−	0.576472i	$-0.195571\pi$
$521$	−41706.6	−	91324.7i	−0.153649	−	0.336444i	−0.970766	+	0.240027i	$0.922844\pi$
$522$	−221395.	−	131086.i	−0.812506	−	0.481079i
$523$	57320.7	−	195216.i	0.209560	−	0.713696i	−0.785886	−	0.618371i	$-0.787793\pi$
$523$	57320.7	−	195216.i	0.209560	−	0.713696i	0.995446	−	0.0953246i	$-0.0303889\pi$
$524$	−251254.	+	55138.0i	−0.915062	+	0.200811i
$525$	24350.4	−	7149.92i	0.0883461	−	0.0259408i
$526$	3834.27	+	104676.i	0.0138584	+	0.378334i
$527$	405963.	−	58368.6i	1.46172	−	0.210164i
$528$	41090.7	+	138073.i	0.147393	+	0.495271i
$529$	−126275.	+	249731.i	−0.451237	+	0.892404i
$530$	26098.1	+	52018.5i	0.0929088	+	0.185185i
$531$	−41062.9	+	5903.95i	−0.145633	+	0.0209389i
$532$	2688.82	+	4902.89i	0.00950034	+	0.0173232i
$533$	280975.	−	82501.7i	0.989039	−	0.290408i
$534$	−14891.3	+	58567.0i	−0.0522218	+	0.205386i
$535$	−180137.	+	613489.i	−0.629353	+	2.14338i
$536$	120865.	+	289546.i	0.420698	+	1.00783i
$537$	7950.03	+	17408.1i	0.0275690	+	0.0603676i
$538$	−2266.62	+	5486.28i	−0.00783095	+	0.0189546i
$539$	−245175.	+	381500.i	−0.843916	+	1.31316i
$540$	−181789.	+	182455.i	−0.623419	+	0.625701i
$541$	−52344.6	+	364065.i	−0.178845	+	1.24390i	0.680595	+	0.732660i	$0.261721\pi$
$541$	−52344.6	+	364065.i	−0.178845	+	1.24390i	−0.859440	+	0.511236i	$0.829188\pi$
$542$	−305091.	−	32518.7i	−1.03856	−	0.110697i
$543$	10124.4	−	8772.86i	0.0343376	−	0.0297537i
$544$	451885.	+	184763.i	1.52697	+	0.624334i
$545$	−150821.	+	96926.6i	−0.507771	+	0.326325i
$546$	5319.95	+	29333.1i	0.0178452	+	0.0983949i
$547$	−383890.	−	332642.i	−1.28302	−	1.11174i	−0.987704	−	0.156338i	$-0.950031\pi$
$547$	−383890.	−	332642.i	−1.28302	−	1.11174i	−0.295312	−	0.955401i	$-0.595424\pi$
$548$	19034.3	−	51319.0i	0.0633833	−	0.170890i
$549$	182013.	−	398552.i	0.603888	−	1.32233i
$550$	−349258.	−	502047.i	−1.15457	−	1.65966i
$551$		−	25879.1i		−	0.0852404i
$552$	88325.0	−	34824.7i	0.289872	−	0.114290i
$553$	140470.			0.459340
$554$	168797.	−	117427.i	0.549978	−	0.382602i
$555$	−78872.8	−	36020.0i	−0.256060	−	0.116939i
$556$	93156.2	+	34551.7i	0.301344	+	0.111769i
$557$	4022.08	−	4641.73i	0.0129640	−	0.0149613i	−0.749231	−	0.662309i	$-0.769576\pi$
$557$	4022.08	−	4641.73i	0.0129640	−	0.0149613i	0.762195	+	0.647348i	$0.224122\pi$
$558$	247626.	−	44910.3i	0.795295	−	0.144237i
$559$	−339659.	−	528520.i	−1.08698	−	1.69137i
$560$	−74466.5	−	85307.0i	−0.237457	−	0.272025i
$561$	−175688.	−	202755.i	−0.558235	−	0.644237i
$562$	40405.0	−	379080.i	0.127927	−	1.20021i
$563$	−38365.7	−	5516.16i	−0.121039	−	0.0174028i	0.0815289	−	0.996671i	$-0.474020\pi$
$563$	−38365.7	−	5516.16i	−0.121039	−	0.0174028i	−0.202568	+	0.979268i	$0.564929\pi$
$564$	−85798.2	−	85485.2i	−0.269724	−	0.268740i
$565$	166623.	+	107082.i	0.521960	+	0.335444i
$566$	143896.	+	59449.8i	0.449176	+	0.185574i
$567$	−50906.9	+	23248.4i	−0.158347	+	0.0723148i
$568$	−26469.1	−	63410.0i	−0.0820433	−	0.196545i
$569$	399649.	+	117347.i	1.23439	+	0.362451i	0.832907	−	0.553414i	$-0.186675\pi$
$569$	399649.	+	117347.i	1.23439	+	0.362451i	0.401488	+	0.915864i	$0.368493\pi$
$570$	−11913.1	−	3029.04i	−0.0366668	−	0.00932298i
$571$	92378.7	+	314613.i	0.283335	+	0.964949i	0.971032	+	0.238951i	$0.0768035\pi$
$571$	92378.7	+	314613.i	0.283335	+	0.964949i	−0.687697	+	0.725998i	$0.741378\pi$
$572$	629908.	−	345451.i	1.92524	−	1.05583i
$573$	14136.3	+	98320.1i	0.0430553	+	0.299456i
$574$	55573.8	−	27881.8i	0.168673	−	0.0846246i
$575$	−309803.	+	257846.i	−0.937023	+	0.779875i
$576$	281247.	+	103147.i	0.847700	+	0.310893i
$577$	−32278.3	−	224500.i	−0.0969524	−	0.674319i	−0.979105	−	0.203355i	$-0.934815\pi$
$577$	−32278.3	−	224500.i	−0.0969524	−	0.674319i	0.882153	−	0.470964i	$-0.156094\pi$
$578$	−574715.	+	21051.8i	−1.72027	+	0.0630134i
$579$	−24369.1	−	82993.7i	−0.0726914	−	0.247564i
$580$	112334.	+	511884.i	0.333929	+	1.52165i
$581$	−143368.	−	42096.7i	−0.424718	−	0.124709i
$582$	−28226.4	+	47672.3i	−0.0833317	+	0.140741i
$583$	−71311.5	+	32566.9i	−0.209808	+	0.0958163i
$584$	−1900.80	−	3183.71i	−0.00557328	−	0.00933486i
$585$	512707.	+	329497.i	1.49816	+	0.962807i
$586$	54764.8	−	18283.1i	0.159480	−	0.0532420i
$587$	79078.2	+	11369.7i	0.229499	+	0.0329970i	0.256105	−	0.966649i	$-0.417561\pi$
$587$	79078.2	+	11369.7i	0.229499	+	0.0329970i	−0.0266058	+	0.999646i	$0.508470\pi$
$588$	−35609.4	−	94942.2i	−0.102993	−	0.274602i
$589$	16576.6	+	19130.4i	0.0477820	+	0.0551434i
$590$	65842.7	+	52960.3i	0.189149	+	0.152141i
$591$	−22206.9	−	34554.6i	−0.0635789	−	0.0989306i
$592$	776.762	+	212542.i	0.00221638	+	0.606459i
$593$	181529.	−	209496.i	0.516223	−	0.595753i	−0.436458	−	0.899725i	$-0.643767\pi$
$593$	181529.	−	209496.i	0.516223	−	0.595753i	0.952681	+	0.303971i	$0.0983127\pi$
$594$	−236647.	−	253712.i	−0.670700	−	0.719064i
$595$	191827.	+	87604.3i	0.541845	+	0.247452i
$596$	−144011.	−	78294.6i	−0.405418	−	0.220414i
$597$	33534.6			0.0940901
$598$	−262611.	−	393973.i	−0.734363	−	1.10170i
$599$		−	164519.i		−	0.458525i	−0.973365	−	0.229263i	$-0.926369\pi$
$599$		−	164519.i		−	0.458525i	0.973365	−	0.229263i	$-0.0736314\pi$
$600$	136675.	+	4506.31i	0.379654	+	0.0125175i
$601$	−44541.0	+	97531.2i	−0.123314	+	0.270019i	−0.961214	−	0.275804i	$-0.911056\pi$
$601$	−44541.0	+	97531.2i	−0.123314	+	0.270019i	0.837900	+	0.545823i	$0.183783\pi$
$602$	−90984.9	−	97545.9i	−0.251059	−	0.269163i
$603$	−270973.	−	234800.i	−0.745232	−	0.645747i
$604$	111353.	+	148185.i	0.305231	+	0.406191i
$605$	802845.	−	515957.i	2.19341	−	1.40962i
$606$	−76902.8	−	61856.4i	−0.209410	−	0.168438i
$607$	−394879.	+	342165.i	−1.07173	+	0.928663i	−0.997645	−	0.0685890i	$-0.978150\pi$
$607$	−394879.	+	342165.i	−1.07173	+	0.928663i	−0.0740888	+	0.997252i	$0.523605\pi$
$608$	5485.25	+	29627.4i	0.0148385	+	0.0801470i
$609$	4168.97	−	28995.9i	0.0112407	−	0.0781810i
$610$	−846509.	+	282605.i	−2.27495	+	0.759486i
$611$	−326548.	+	508119.i	−0.874712	+	1.36108i
$612$	−556392.	+	40816.0i	−1.48552	+	0.108975i
$613$	−165038.	−	361382.i	−0.439200	−	0.961714i	−0.991744	−	0.128230i	$-0.959070\pi$
$613$	−165038.	−	361382.i	−0.439200	−	0.961714i	0.552544	−	0.833483i	$-0.313657\pi$
$614$	234412.	−	395904.i	0.621789	−	1.05015i
$615$	−38506.5	+	131141.i	−0.101809	+	0.346728i
$616$	118508.	−	96036.5i	0.312310	−	0.253090i
$617$	249996.	−	73405.4i	0.656693	−	0.192823i	0.0636239	−	0.997974i	$-0.479734\pi$
$617$	249996.	−	73405.4i	0.656693	−	0.192823i	0.593069	+	0.805151i	$0.297916\pi$
$618$	−14089.1	+	516.083i	−0.0368898	+	0.00135127i
$619$	667447.	−	95964.4i	1.74195	−	0.250454i	0.803360	−	0.595493i	$-0.203043\pi$
$619$	667447.	−	95964.4i	1.74195	−	0.250454i	0.938588	+	0.345039i	$0.112134\pi$
$620$	−410922.	−	306442.i	−1.06900	−	0.797196i
$621$	−153143.	+	169797.i	−0.397114	+	0.440299i
$622$	303935.	−	152487.i	0.785598	−	0.394140i
$623$	63335.4	−	9106.25i	0.163181	−	0.0234619i
$624$	−22279.9	+	159085.i	−0.0572194	+	0.408564i
$625$	274688.	−	80655.6i	0.703200	−	0.206478i
$626$	−47674.9	−	12121.9i	−0.121658	−	0.0309330i
$627$	4664.95	−	15887.4i	0.0118662	−	0.0404126i
$628$	−13998.0	+	200875.i	−0.0354933	+	0.509339i
$629$	−164432.	−	360055.i	−0.415609	−	0.910056i
$630$	119596.	+	49410.4i	0.301326	+	0.124491i
$631$	−45454.8	+	70729.1i	−0.114162	+	0.177639i	−0.893633	−	0.448799i	$-0.851852\pi$
$631$	−45454.8	+	70729.1i	−0.114162	+	0.177639i	0.779471	+	0.626439i	$0.215488\pi$
$632$	718832.	+	237064.i	1.79967	+	0.593514i
$633$	171.528	−	1193.00i	0.000428082	−	0.00297737i
$634$	−45147.7	+	423576.i	−0.112320	+	1.05379i
$635$	502221.	−	435177.i	1.24551	−	1.07924i
$636$	3694.83	−	17135.5i	0.00913439	−	0.0423627i
$637$	−425407.	+	273392.i	−1.04840	+	0.673763i
$638$	−694611.	+	125977.i	−1.70648	+	0.309492i
$639$	59342.5	+	51420.6i	0.145333	+	0.125932i
$640$	−237101.	−	562216.i	−0.578861	−	1.37260i
$641$	−172869.	+	378531.i	−0.420729	+	0.921267i	0.574013	+	0.818847i	$0.305386\pi$
$641$	−172869.	+	378531.i	−0.420729	+	0.921267i	−0.994741	+	0.102421i	$0.967341\pi$
$642$	158092.	−	109980.i	0.383566	−	0.266835i
$643$			229004.i			0.553888i	0.960886	+	0.276944i	$0.0893217\pi$
$643$			229004.i			0.553888i	−0.960886	+	0.276944i	$0.910678\pi$
$644$	−69790.7	−	72356.5i	−0.168277	−	0.174464i
$645$	293228.			0.704833
$646$	−32045.0	−	46063.7i	−0.0767883	−	0.110381i
$647$	137847.	+	62952.7i	0.329298	+	0.150385i	0.573202	−	0.819414i	$-0.305701\pi$
$647$	137847.	+	62952.7i	0.329298	+	0.150385i	−0.243904	+	0.969799i	$0.578428\pi$
$648$	−299742.	+	33056.9i	−0.713835	+	0.0787250i
$649$	−74539.0	+	86022.6i	−0.176968	+	0.204232i
$650$	−121699.	−	671021.i	−0.288044	−	1.58822i
$651$	15491.2	+	24104.8i	0.0365530	+	0.0568776i
$652$	120117.	−	557066.i	0.282558	−	1.31042i
$653$	130013.	+	150043.i	0.304902	+	0.351876i	0.887436	−	0.460931i	$-0.152484\pi$
$653$	130013.	+	150043.i	0.304902	+	0.351876i	−0.582534	+	0.812806i	$0.697939\pi$
$654$	53695.4	+	5723.23i	0.125540	+	0.0133809i
$655$	−592642.	−	85209.1i	−1.38137	−	0.198611i
$656$	331443.	−	48891.3i	0.770196	−	0.113612i
$657$	3564.63	+	2290.85i	0.00825816	+	0.00530720i
$658$	−48968.3	+	118526.i	−0.113100	+	0.273755i
$659$	222362.	−	101549.i	0.512023	−	0.233833i	−0.142611	−	0.989779i	$-0.545550\pi$
$659$	222362.	−	101549.i	0.512023	−	0.233833i	0.654634	+	0.755946i	$0.272823\pi$
$660$	−23309.6	+	334499.i	−0.0535114	+	0.767904i
$661$	−335079.	−	98388.0i	−0.766909	−	0.225185i	−0.125199	−	0.992132i	$-0.539957\pi$
$661$	−335079.	−	98388.0i	−0.766909	−	0.225185i	−0.641711	+	0.766947i	$0.721775\pi$
$662$	118827.	−	467342.i	0.271144	−	1.06640i
$663$	−84283.0	−	287042.i	−0.191740	−	0.653007i
$664$	−662618.	−	457377.i	−1.50289	−	1.03738i
$665$	1852.29	+	12883.0i	0.00418858	+	0.0291322i
$666$	−108917.	−	217093.i	−0.245555	−	0.489438i
$667$	122180.	+	448927.i	0.274630	+	1.00908i
$668$	−9655.57	−	7200.57i	−0.0216384	−	0.0161367i
$669$	−9207.57	−	64040.1i	−0.0205728	−	0.143087i
$670$	26733.3	+	729820.i	0.0595528	+	1.62580i
$671$	−338687.	−	1.15346e6i	−0.752235	−	2.56188i
$672$	1373.05	+	34079.3i	0.00304053	+	0.0754661i
$673$	137678.	+	40425.9i	0.303972	+	0.0892543i	0.430162	−	0.902752i	$-0.358457\pi$
$673$	137678.	+	40425.9i	0.303972	+	0.0892543i	−0.126189	+	0.992006i	$0.540275\pi$
$674$	362872.	+	214854.i	0.798791	+	0.472958i
$675$	−299582.	+	136814.i	−0.657518	+	0.300279i
$676$	343199.	−	25176.5i	0.751021	−	0.0550936i
$677$	649369.	+	417324.i	1.41682	+	0.910533i	0.999999	+	0.00154384i	$0.000491420\pi$
$677$	649369.	+	417324.i	1.41682	+	0.910533i	0.416819	+	0.908990i	$0.363145\pi$
$678$	−18891.4	−	56587.1i	−0.0410966	−	0.123100i
$679$	58065.2	+	8348.51i	0.125944	+	0.0181080i
$680$	833794.	+	772034.i	1.80319	+	1.66962i
$681$	2097.98	+	2421.20i	0.00452383	+	0.00522078i
$682$	432779.	−	538051.i	0.930459	−	1.15679i
$683$	−136134.	−	211828.i	−0.291826	−	0.454091i	0.664123	−	0.747624i	$-0.268805\pi$
$683$	−136134.	−	211828.i	−0.291826	−	0.454091i	−0.955949	+	0.293533i	$0.905169\pi$
$684$	−20684.7	−	27526.5i	−0.0442117	−	0.0588355i
$685$	83430.5	−	96284.0i	0.177805	−	0.205198i
$686$	−161931.	+	151039.i	−0.344097	+	0.320953i
$687$	171350.	+	78252.9i	0.363053	+	0.165801i
$688$	−300977.	−	652724.i	−0.635852	−	1.37896i
$689$	−87418.6			−0.184147
$690$	220957.	−	3698.68i	0.464099	−	0.00776871i
$691$			357936.i			0.749633i	0.927099	+	0.374817i	$0.122294\pi$
$691$			357936.i			0.749633i	−0.927099	+	0.374817i	$0.877706\pi$
$692$	−21783.5	−	11843.1i	−0.0454900	−	0.0247316i
$693$	−72410.9	+	158558.i	−0.150778	+	0.330157i
$694$	−227843.	+	212518.i	−0.473061	+	0.441243i
$695$	174778.	+	151446.i	0.361841	+	0.313537i
$696$	70268.6	−	141345.i	0.145058	−	0.291785i
$697$	−524888.	+	337325.i	−1.08044	+	0.694357i
$698$	−320593.	+	398576.i	−0.658026	+	0.818089i
$699$	211261.	−	183059.i	0.432379	−	0.374659i
$700$	−50849.2	−	135575.i	−0.103774	−	0.276683i
$701$	−88187.5	+	613357.i	−0.179461	+	1.24818i	0.678552	+	0.734553i	$0.262608\pi$
$701$	−88187.5	+	613357.i	−0.179461	+	1.24818i	−0.858013	+	0.513628i	$0.828301\pi$
$702$	−122510.	−	366966.i	−0.248599	−	0.744648i
$703$	13207.8	−	20551.7i	0.0267250	−	0.0415850i
$704$	768518.	−	291451.i	1.55063	−	0.588058i
$705$	−117109.	−	256434.i	−0.235621	−	0.515938i
$706$	432270.	+	255944.i	0.867253	+	0.513494i
$707$	−29441.2	+	100268.i	−0.0589002	+	0.200596i
$708$	−5455.46	−	24859.5i	−0.0108834	−	0.0495937i
$709$	353164.	−	103698.i	0.702561	−	0.206291i	0.0891082	−	0.996022i	$-0.471598\pi$
$709$	353164.	−	103698.i	0.702561	−	0.206291i	0.613453	+	0.789731i	$0.289780\pi$
$710$	−5854.52	−	159829.i	−0.0116138	−	0.317058i
$711$	−856158.	+	123097.i	−1.69362	+	0.243505i
$712$	339476.	+	60287.8i	0.669651	+	0.118924i
$713$	−377873.	−	253596.i	−0.743305	−	0.498842i
$714$	−28483.8	−	56773.7i	−0.0558729	−	0.111365i
$715$	1.65517e6	−	237977.i	3.23765	−	0.465503i
$716$	95737.8	−	52504.1i	0.186749	−	0.102416i
$717$	108097.	−	31740.3i	0.210270	−	0.0617408i
$718$	−70458.1	+	277108.i	−0.136673	+	0.537527i
$719$	−148502.	+	505751.i	−0.287259	+	0.978315i	0.681811	+	0.731529i	$0.261193\pi$
$719$	−148502.	+	505751.i	−0.287259	+	0.978315i	−0.969070	+	0.246787i	$0.920625\pi$
$720$	528625.	+	454684.i	1.01972	+	0.877092i
$721$	6201.41	+	13579.2i	0.0119294	+	0.0261218i
$722$	−197724.	+	478585.i	−0.379302	+	0.918088i
$723$	94678.7	−	147323.i	0.181124	−	0.281834i
$724$	−54145.8	−	53948.2i	−0.103297	−	0.102920i
$725$	−95369.1	+	663307.i	−0.181439	+	1.26194i
$726$	−285830.	−	30465.7i	−0.542293	−	0.0578014i
$727$	5528.23	−	4790.24i	0.0104597	−	0.00906334i	−0.649615	−	0.760263i	$-0.725070\pi$
$727$	5528.23	−	4790.24i	0.0104597	−	0.00906334i	0.660075	+	0.751200i	$0.270525\pi$
$728$	164691.	−	42516.1i	0.310748	−	0.0802215i
$729$	207304.	−	133226.i	0.390080	−	0.250689i
$730$	−1540.17	−	8492.15i	−0.00289016	−	0.0159357i
$731$	1.01164e6	+	876591.i	1.89318	+	1.64045i
$732$	252026.	+	93476.5i	0.470352	+	0.174454i
$733$	108484.	−	237547.i	0.201910	−	0.442122i	−0.781407	−	0.624022i	$-0.785497\pi$
$733$	108484.	−	237547.i	0.201910	−	0.442122i	0.983317	+	0.181900i	$0.0582247\pi$
$734$	−34440.9	−	49507.8i	−0.0639268	−	0.0918927i
$735$		−	236020.i		−	0.436892i
$736$	−235029.	−	488053.i	−0.433877	−	0.900972i
$737$	−983764.			−1.81116
$738$	−314285.	+	218638.i	−0.577047	+	0.401433i
$739$	−826435.	−	377420.i	−1.51328	−	0.691092i	−0.526060	−	0.850448i	$-0.676331\pi$
$739$	−826435.	−	377420.i	−1.51328	−	0.691092i	−0.987221	+	0.159355i	$0.949058\pi$
$740$	−172038.	+	463840.i	−0.314168	+	0.847041i
$741$	12091.2	−	13954.0i	0.0220208	−	0.0254133i
$742$	−18263.0	+	3312.24i	−0.0331714	+	0.00601608i
$743$	−169023.	−	263004.i	−0.306173	−	0.476415i	0.653737	−	0.756722i	$-0.273200\pi$
$743$	−169023.	−	263004.i	−0.306173	−	0.476415i	−0.959911	+	0.280307i	$0.909564\pi$
$744$	38593.2	+	149496.i	0.0697213	+	0.270074i
$745$	−249853.	−	288346.i	−0.450166	−	0.519519i
$746$	−82142.8	+	770665.i	−0.147602	+	1.38480i
$747$	910711.	+	130940.i	1.63207	+	0.234657i
$748$	−1.08039e6	+	1.08434e6i	−1.93097	+	1.93804i
$749$	−171546.	−	110246.i	−0.305786	−	0.196517i
$750$	52872.1	+	21843.8i	0.0939948	+	0.0388333i
$751$	−563217.	+	257213.i	−0.998610	+	0.456050i	−0.846543	−	0.532320i	$-0.821320\pi$
$751$	−563217.	+	257213.i	−0.998610	+	0.456050i	−0.152067	+	0.988370i	$0.548593\pi$
$752$	−450616.	+	523895.i	−0.796840	+	0.926421i
$753$	−60299.5	−	17705.5i	−0.106347	−	0.0312262i
$754$	−762914.	−	193980.i	−1.34194	−	0.341204i
$755$	121552.	+	413968.i	0.213240	+	0.726228i
$756$	−39498.3	−	72022.5i	−0.0691090	−	0.126016i
$757$	−70987.4	−	493728.i	−0.123877	−	0.861581i	−0.953098	−	0.302661i	$-0.902125\pi$
$757$	−70987.4	−	493728.i	−0.123877	−	0.861581i	0.829222	−	0.558920i	$-0.188784\pi$
$758$	−164072.	+	82316.2i	−0.285559	+	0.143267i
$759$	−5916.28	+	297624.i	−0.0102699	+	0.516635i
$760$	−12263.1	+	69052.4i	−0.0212311	+	0.119551i
$761$	51137.1	+	355666.i	0.0883012	+	0.614149i	0.985135	+	0.171781i	$0.0549522\pi$
$761$	51137.1	+	355666.i	0.0883012	+	0.614149i	−0.896834	+	0.442367i	$0.854139\pi$
$762$	−200024.	+	7326.86i	−0.344486	+	0.0126185i
$763$	−16108.7	−	54861.2i	−0.0276701	−	0.0942358i
$764$	553563.	−	121480.i	0.948375	−	0.208122i
$765$	−1.24594e6	−	365841.i	−2.12899	−	0.625129i
$766$	115076.	−	194356.i	0.196123	−	0.331237i
$767$	−115454.	+	52726.2i	−0.196254	+	0.0896264i
$768$	−50487.3	+	176712.i	−0.0855972	+	0.299601i
$769$	527883.	+	339250.i	0.892659	+	0.573677i	0.904605	−	0.426252i	$-0.140166\pi$
$769$	527883.	+	339250.i	0.892659	+	0.573677i	−0.0119460	+	0.999929i	$0.503803\pi$
$770$	336771.	−	112430.i	0.568006	−	0.189627i
$771$	−74220.5	−	10671.3i	−0.124858	−	0.0179518i
$772$	−462081.	+	173310.i	−0.775324	+	0.290796i
$773$	−191200.	−	220656.i	−0.319984	−	0.369281i	0.572855	−	0.819657i	$-0.305836\pi$
$773$	−191200.	−	220656.i	−0.319984	−	0.369281i	−0.892839	+	0.450375i	$0.851290\pi$
$774$	640029.	+	514804.i	1.06836	+	0.859330i
$775$	−354375.	−	551419.i	−0.590011	−	0.918075i
$776$	283049.	+	140715.i	0.470044	+	0.233678i
$777$	18109.2	−	20899.1i	0.0299956	−	0.0346168i
$778$	534797.	+	573361.i	0.883547	+	0.947260i
$779$	−35028.5	−	15997.0i	−0.0577227	−	0.0263611i
$780$	−178592.	+	328492.i	−0.293543	+	0.539927i
$781$	215442.			0.353206
$782$	773362.	+	647780.i	1.26465	+	1.05929i
$783$			380159.i			0.620071i
$784$	−525378.	+	242257.i	−0.854752	+	0.394134i
$785$	−194702.	+	426337.i	−0.315959	+	0.691853i
$786$	123007.	+	131877.i	0.199107	+	0.213464i
$787$	−683491.	−	592248.i	−1.10353	−	0.956212i	−0.104263	−	0.994550i	$-0.533248\pi$
$787$	−683491.	−	592248.i	−1.10353	−	0.956212i	−0.999265	+	0.0383373i	$0.987794\pi$
$788$	−187354.	+	140786.i	−0.301724	+	0.226729i
$789$	61777.4	−	39701.9i	0.0992375	−	0.0637760i
$790$	1.37282e6	+	1.10422e6i	2.19967	+	1.76930i
$791$	−47739.1	+	41366.2i	−0.0762995	+	0.0661139i
$792$	−638139.	+	689187.i	−1.01734	+	1.09872i
$793$	190775.	−	1.32687e6i	0.303372	−	2.11000i
$794$	1.02348e6	−	341687.i	1.62345	−	0.541985i
$795$	22058.9	−	34324.3i	0.0349019	−	0.0543085i
$796$	−13998.2	−	190819.i	−0.0220925	−	0.301159i
$797$	−310783.	−	680520.i	−0.489261	−	1.07133i	−0.979812	−	0.199920i	$-0.935932\pi$
$797$	−310783.	−	680520.i	−0.489261	−	1.07133i	0.490551	−	0.871412i	$-0.336795\pi$
$798$	1997.31	−	3373.31i	0.00313646	−	0.00529725i
$799$	362568.	−	1.23479e6i	0.567931	−	1.93420i
$800$	−31409.8	−	779595.i	−0.0490779	−	1.21812i
$801$	−378045.	+	111004.i	−0.589222	+	0.173011i
$802$	82901.6	−	3036.68i	0.128889	−	0.00472118i
$803$	11507.6	−	1654.55i	0.0178466	−	0.00256595i
$804$	131501.	−	176335.i	0.203431	−	0.272789i
$805$	−92954.8	−	214737.i	−0.143443	−	0.331372i
$806$	688215.	−	345282.i	1.05939	−	0.531501i
$807$	4119.27	−	592.262i	0.00632519	−	0.000909425i
$808$	−319876.	+	463415.i	−0.489958	+	0.709819i
$809$	−326841.	+	95969.3i	−0.499390	+	0.146634i	−0.521721	−	0.853116i	$-0.674710\pi$
$809$	−326841.	+	95969.3i	−0.499390	+	0.146634i	0.0223303	+	0.999751i	$0.492891\pi$
$810$	−680266.	−	172966.i	−1.03683	−	0.263627i
$811$	64646.2	−	220165.i	0.0982881	−	0.334739i	−0.895639	−	0.444783i	$-0.853281\pi$
$811$	64646.2	−	220165.i	0.0982881	−	0.334739i	0.993927	+	0.110044i	$0.0350992\pi$
$812$	−166733.	−	11618.8i	−0.252878	−	0.0176218i
$813$	89357.0	+	195665.i	0.135191	+	0.296027i
$814$	−615914.	−	254461.i	−0.929547	−	0.384036i
$815$	717122.	−	1.11586e6i	1.07964	−	1.67995i
$816$	−49947.0	−	338600.i	−0.0750117	−	0.508518i
$817$	−11757.5	+	81775.2i	−0.0176145	+	0.122512i
$818$	137405.	−	1.28913e6i	0.205351	−	1.92660i
$819$	−146896.	+	127286.i	−0.218999	+	0.189763i
$820$	762297.	+	164369.i	1.13370	+	0.244452i
$821$	−580752.	+	373227.i	−0.861598	+	0.553715i	−0.895172	−	0.445721i	$-0.852947\pi$
$821$	−580752.	+	373227.i	−0.861598	+	0.553715i	0.0335742	+	0.999436i	$0.489311\pi$
$822$	−37757.6	+	6847.84i	−0.0558805	+	0.0101347i
$823$	879866.	+	762408.i	1.29902	+	1.12561i	0.984315	+	0.176421i	$0.0564521\pi$
$823$	879866.	+	762408.i	1.29902	+	1.12561i	0.314708	+	0.949188i	$0.398093\pi$
$824$	8817.79	+	79954.9i	0.0129869	+	0.117758i
$825$	−178115.	+	390018.i	−0.261694	+	0.573029i
$826$	−22122.3	+	15389.8i	−0.0324242	+	0.0225565i
$827$			516289.i			0.754887i	0.926033	+	0.377444i	$0.123197\pi$
$827$			516289.i			0.754887i	−0.926033	+	0.377444i	$0.876803\pi$
$828$	488777.	+	379849.i	0.712935	+	0.554052i
$829$	575009.			0.836692			0.418346	−	0.908288i	$-0.362610\pi$
$829$	575009.			0.836692			0.418346	+	0.908288i	$0.362610\pi$
$830$	−1.07022e6	−	1.53841e6i	−1.55352	−	2.23314i
$831$	−131131.	−	59885.6i	−0.189891	−	0.0867202i
$832$	914531.	+	60371.4i	1.32115	+	0.0872137i
$833$	705569.	−	814271.i	1.01683	−	1.17349i
$834$	−12430.5	−	68539.0i	−0.0178713	−	0.0985384i
$835$	−15157.2	−	23585.1i	−0.0217393	−	0.0338270i
$836$	−92350.1	−	19912.9i	−0.132137	−	0.0284919i
$837$	−243507.	−	281022.i	−0.347584	−	0.401134i
$838$	−233861.	−	24926.5i	−0.333019	−	0.0354955i
$839$	−1.20308e6	−	172977.i	−1.70911	−	0.245733i	−0.782742	−	0.622346i	$-0.786180\pi$
$839$	−1.20308e6	−	172977.i	−1.70911	−	0.245733i	−0.926371	+	0.376613i	$0.877089\pi$
$840$	−24864.0	+	75393.3i	−0.0352381	+	0.106850i
$841$	55725.0	+	35812.3i	0.0787877	+	0.0506337i
$842$	−236109.	+	571494.i	−0.333034	+	0.806097i
$843$	−243116.	+	111028.i	−0.342105	+	0.156234i
$844$	−6860.05	−	478.043i	−0.00963036	−	0.000671091i
$845$	768532.	+	225661.i	1.07634	+	0.316041i
$846$	194592.	−	765321.i	0.271884	−	1.06931i
$847$	85749.4	+	292035.i	0.119526	+	0.407070i
$848$	−99047.4	−	13871.6i	−0.137737	−	0.0192901i
$849$	−15534.1	−	108042.i	−0.0215511	−	0.149891i
$850$	651592.	+	1.29875e6i	0.901857	+	1.79758i
$851$	−132088.	+	418868.i	−0.182391	+	0.578386i
$852$	−28798.4	+	38617.0i	−0.0396725	+	0.0531985i
$853$	−5742.49	−	39939.9i	−0.00789227	−	0.0548920i	0.985495	−	0.169706i	$-0.0542818\pi$
$853$	−5742.49	−	39939.9i	−0.00789227	−	0.0548920i	−0.993387	+	0.114814i	$0.963373\pi$
$854$	−10418.7	−	284430.i	−0.0142855	−	0.389996i
$855$	−22579.2	−	76897.8i	−0.0308871	−	0.105192i
$856$	−691801.	−	853673.i	−0.944134	−	1.16505i
$857$	478461.	+	140489.i	0.651455	+	0.191285i	0.590729	−	0.806870i	$-0.298840\pi$
$857$	478461.	+	140489.i	0.651455	+	0.191285i	0.0607262	+	0.998154i	$0.480658\pi$
$858$	−433392.	−	256608.i	−0.588717	−	0.348575i
$859$	244677.	−	111740.i	0.331594	−	0.151434i	−0.242659	−	0.970112i	$-0.578020\pi$
$859$	244677.	−	111740.i	0.331594	−	0.151434i	0.574253	+	0.818678i	$0.305292\pi$
$860$	−122401.	−	1.66854e6i	−0.165496	−	2.25600i
$861$	−36670.2	−	23566.5i	−0.0494660	−	0.0317899i
$862$	416744.	+	1.24831e6i	0.560860	+	1.67999i
$863$	483054.	+	69452.6i	0.648595	+	0.0932539i	0.458757	−	0.888562i	$-0.348295\pi$
$863$	483054.	+	69452.6i	0.648595	+	0.0932539i	0.189838	+	0.981815i	$0.439204\pi$
$864$	−80577.2	−	435221.i	−0.107941	−	0.583019i
$865$	−37793.5	−	43616.1i	−0.0505109	−	0.0582927i
$866$	568102.	−	706292.i	0.757514	−	0.941778i
$867$	217980.	+	339184.i	0.289987	+	0.451229i
$868$	130695.	−	98210.5i	0.173469	−	0.130352i
$869$	−1.55413e6	+	1.79357e6i	−2.05802	+	2.37508i
$870$	268676.	−	250605.i	0.354969	−	0.331094i
$871$	−997852.	−	455704.i	−1.31531	−	0.600684i
$872$	10152.7	−	307928.i	0.0133520	−	0.404964i
$873$	−361220.			−0.473961
$874$	−7828.19	+	61768.7i	−0.0102480	+	0.0808622i
$875$		−	60573.1i		−	0.0791160i
$876$	−1241.67	+	2283.86i	−0.00161807	+	0.00297619i
$877$	494546.	−	1.08290e6i	0.642995	−	1.40796i	−0.254559	−	0.967057i	$-0.581930\pi$
$877$	494546.	−	1.08290e6i	0.642995	−	1.40796i	0.897554	−	0.440905i	$-0.145342\pi$
$878$	−476625.	+	444567.i	−0.618283	+	0.576698i
$879$	−30590.7	−	26507.0i	−0.0395924	−	0.0343070i
$880$	1.91311e6	−	6991.69i	2.47044	−	0.00902853i
$881$	450986.	−	289831.i	0.581047	−	0.373416i	−0.216855	−	0.976204i	$-0.569580\pi$
$881$	450986.	−	289831.i	0.581047	−	0.373416i	0.797902	+	0.602788i	$0.205943\pi$
$882$	414367.	−	515160.i	0.532657	−	0.662225i
$883$	367785.	−	318688.i	0.471708	−	0.408737i	−0.386300	−	0.922373i	$-0.626247\pi$
$883$	367785.	−	318688.i	0.471708	−	0.408737i	0.858008	+	0.513636i	$0.171702\pi$
$884$	−1.59815e6	+	599408.i	−2.04509	+	0.767041i
$885$	8430.74	−	58637.1i	0.0107641	−	0.0748662i
$886$	−494181.	−	1.48026e6i	−0.629533	−	1.88569i
$887$	357833.	−	556799.i	0.454813	−	0.707703i	−0.535808	−	0.844340i	$-0.679993\pi$
$887$	357833.	−	556799.i	0.454813	−	0.707703i	0.990621	+	0.136637i	$0.0436293\pi$
$888$	127941.	−	76385.8i	0.162250	−	0.0968694i
$889$	88041.7	+	192784.i	0.111400	+	0.243932i
$890$	690560.	+	408875.i	0.871809	+	0.516192i
$891$	266381.	−	907210.i	0.335542	−	1.14275i
$892$	−360559.	+	79125.2i	−0.453155	+	0.0994454i
$893$	76209.8	−	22377.2i	0.0955669	−	0.0280610i
$894$	4206.66	+	114842.i	0.00526335	+	0.143690i
$895$	251564.	−	36169.4i	0.314052	−	0.0451539i
$896$	193346.	−	22038.6i	0.240835	−	0.0274516i
$897$	−143868.	+	299145.i	−0.178804	+	0.371790i
$898$	−228139.	−	454726.i	−0.282910	−	0.563894i
$899$	−748905.	+	107676.i	−0.926632	+	0.133230i
$900$	428729.	+	781760.i	0.529295	+	0.965135i
$901$	178714.	−	52475.2i	0.220145	−	0.0646405i
$902$	−258854.	+	1.01806e6i	−0.318157	+	1.25130i
$903$	−26347.0	+	89729.8i	−0.0323114	+	0.110043i
$904$	−314108.	+	131118.i	−0.384363	+	0.160444i
$905$	−73905.8	−	161831.i	−0.0902363	−	0.197590i
$906$	49620.5	−	120105.i	0.0604512	−	0.146320i
$907$	626316.	−	974567.i	0.761340	−	1.18467i	−0.216697	−	0.976239i	$-0.569528\pi$
$907$	626316.	−	974567.i	0.761340	−	1.18467i	0.978037	−	0.208430i	$-0.0668353\pi$
$908$	12901.4	−	12948.6i	0.0156482	−	0.0157055i
$909$	91575.9	−	636924.i	0.110829	−	0.770832i
$910$	393674.	+	41960.5i	0.475394	+	0.0506708i
$911$	−626637.	+	542984.i	−0.755057	+	0.654260i	−0.944828	−	0.327568i	$-0.893771\pi$
$911$	−626637.	+	542984.i	−0.755057	+	0.654260i	0.189771	+	0.981828i	$0.439225\pi$
$912$	15913.8	−	13891.6i	0.0191331	−	0.0167017i
$913$	2.12370e6	−	1.36482e6i	2.54772	−	1.63732i
$914$	11545.5	+	63659.2i	0.0138203	+	0.0762025i
$915$	472846.	+	409724.i	0.564778	+	0.489383i
$916$	373751.	−	1.00769e6i	0.445442	−	1.20097i
$917$	79324.4	−	173696.i	0.0943340	−	0.206563i
$918$	470734.	+	676666.i	0.558587	+	0.802951i
$919$			549567.i			0.650713i	0.945591	+	0.325356i	$0.105484\pi$
$919$			549567.i			0.650713i	−0.945591	+	0.325356i	$0.894516\pi$
$920$	−113280.	−	1.25575e6i	−0.133837	−	1.48364i
$921$	−322562.			−0.380272
$922$	−274787.	+	191161.i	−0.323247	+	0.224873i
$923$	218527.	+	99798.1i	0.256509	+	0.117144i
$924$	−100265.	−	37188.2i	−0.117437	−	0.0435573i
$925$	−414265.	+	478087.i	−0.484166	+	0.558758i
$926$	−1.16039e6	+	210453.i	−1.35327	+	0.245433i
$927$	−49696.9	−	77329.9i	−0.0578322	−	0.0899887i
$928$	−833620.	−	340843.i	−0.967993	−	0.395785i
$929$	1.03833e6	+	1.19830e6i	1.20311	+	1.38846i	0.900222	+	0.435431i	$0.143404\pi$
$929$	1.03833e6	+	1.19830e6i	1.20311	+	1.38846i	0.302884	+	0.953027i	$0.402051\pi$
$930$	−38088.9	+	357350.i	−0.0440385	+	0.413170i
$931$	65821.0	+	9463.63i	0.0759390	+	0.0109184i
$932$	−1.12983e6	−	1.12571e6i	−1.30071	−	1.29597i
$933$	−200551.	−	128886.i	−0.230389	−	0.148062i
$934$	72942.2	+	30135.6i	0.0836152	+	0.0345451i
$935$	−3.24088e6	+	1.48006e6i	−3.70715	+	1.69300i
$936$	−966526.	+	403455.i	−1.10322	+	0.460515i
$937$	949581.	+	278822.i	1.08157	+	0.317576i	0.773505	−	0.633790i	$-0.218502\pi$
$937$	949581.	+	278822.i	1.08157	+	0.317576i	0.308061	+	0.951367i	$0.400320\pi$
$938$	−225732.	−	57395.0i	−0.256559	−	0.0652331i
$939$	9716.17	+	33090.2i	0.0110196	+	0.0375292i
$940$	−1.41028e6	+	773422.i	−1.59607	+	0.875308i
$941$	148431.	+	1.03236e6i	0.167627	+	1.16587i	0.883771	+	0.467920i	$0.154997\pi$
$941$	148431.	+	1.03236e6i	0.167627	+	1.16587i	−0.716143	+	0.697953i	$0.754094\pi$
$942$	126180.	−	63305.5i	0.142197	−	0.0713411i
$943$	683168.	+	112125.i	0.768252	+	0.126090i
$944$	−139179.	+	41419.8i	−0.156182	+	0.0464798i
$945$	−27209.8	−	189249.i	−0.0304693	−	0.211919i
$946$	2.25213e6	−	82495.4i	2.51658	−	0.0921823i
$947$	−450458.	−	1.53412e6i	−0.502290	−	1.71064i	−0.685946	−	0.727652i	$-0.740612\pi$
$947$	−450458.	−	1.53412e6i	−0.502290	−	1.71064i	0.183657	−	0.982990i	$-0.441207\pi$
$948$	−113746.	−	518320.i	−0.126567	−	0.576741i
$949$	12438.9	+	3652.38i	0.0138117	+	0.00405549i
$950$	−45690.4	+	77167.6i	−0.0506264	+	0.0855042i
$951$	271653.	−	124060.i	0.300368	−	0.137174i
$952$	−311165.	+	185778.i	−0.343334	+	0.204984i
$953$	−1.03540e6	−	665414.i	−1.14005	−	0.732666i	−0.172417	−	0.985024i	$-0.555158\pi$
$953$	−1.03540e6	−	665414.i	−1.14005	−	0.732666i	−0.967634	+	0.252358i	$0.918794\pi$
$954$	108409.	−	36192.1i	0.119116	−	0.0397665i
$955$	1.30571e6	+	187733.i	1.43166	+	0.205841i
$956$	−225732.	−	601850.i	−0.246989	−	0.658525i
$957$	324103.	+	374035.i	0.353882	+	0.408402i
$958$	1.10857e6	+	891671.i	1.20790	+	0.971569i
$959$	21967.2	+	34181.6i	0.0238856	+	0.0371668i
$960$	−254474.	+	343850.i	−0.276122	+	0.373101i
$961$	−120141.	+	138650.i	−0.130091	+	0.150132i
$962$	−506862.	−	543412.i	−0.547696	−	0.587190i
$963$	1.14217e6	+	521613.i	1.23163	+	0.562466i
$964$	−877823.	−	477247.i	−0.944611	−	0.513558i
$965$	−1.14870e6			−1.23354
$966$	−18721.6	+	67946.8i	−0.0200626	+	0.0728140i
$967$			432707.i			0.462745i	0.972865	+	0.231372i	$0.0743215\pi$
$967$			432707.i			0.462745i	−0.972865	+	0.231372i	$0.925678\pi$
$968$	−54044.4	+	1.63915e6i	−0.0576766	+	1.74932i
$969$	−16342.4	+	35784.8i	−0.0174048	+	0.0381111i
$970$	501844.	+	538032.i	0.533366	+	0.571827i
$971$	365692.	+	316874.i	0.387862	+	0.336084i	0.826864	−	0.562402i	$-0.190123\pi$
$971$	365692.	+	316874.i	0.387862	+	0.336084i	−0.439002	+	0.898486i	$0.644668\pi$
$972$	463533.	+	616854.i	0.490623	+	0.652905i
$973$	−62047.7	+	39875.6i	−0.0655390	+	0.0421194i
$974$	−132158.	−	106301.i	−0.139308	−	0.112051i
$975$	−361332.	+	313096.i	−0.380099	+	0.329358i
$976$	426701.	−	1.47310e6i	0.447944	−	1.54644i
$977$	−2367.86	+	16468.8i	−0.00248065	+	0.0172533i	−0.991024	−	0.133683i	$-0.957320\pi$
$977$	−2367.86	+	16468.8i	−0.00248065	+	0.0172533i	0.988544	+	0.150936i	$0.0482288\pi$
$978$	−378961.	+	126515.i	−0.396202	+	0.132271i
$979$	−584458.	+	909434.i	−0.609801	+	0.948868i
$980$	−1.34301e6	+	98520.7i	−1.39838	+	0.102583i
$981$	146257.	+	320259.i	0.151978	+	0.332785i
$982$	351381.	−	593456.i	0.364381	−	0.615412i
$983$	−340975.	+	1.16126e6i	−0.352871	+	1.20177i	0.571605	+	0.820529i	$0.306321\pi$
$983$	−340975.	+	1.16126e6i	−0.352871	+	1.20177i	−0.924476	+	0.381239i	$0.875497\pi$
$984$	−147881.	−	182484.i	−0.152730	−	0.188466i
$985$	−523389.	+	153681.i	−0.539451	+	0.158397i
$986$	1.67610e6	−	61395.6i	1.72404	−	0.0631514i
$987$	88993.0	−	12795.3i	0.0913527	−	0.0131345i
$988$	−84448.5	−	62976.9i	−0.0865123	−	0.0645160i
$989$	−182117.	−	1.47407e6i	−0.186190	−	1.50704i
$990$	−1.95407e6	+	980372.i	−1.99375	+	1.00028i
$991$	814162.	−	117059.i	0.829017	−	0.119195i	0.285274	−	0.958446i	$-0.407916\pi$
$991$	814162.	−	117059.i	0.829017	−	0.119195i	0.543744	+	0.839251i	$0.317006\pi$
$992$	834554.	−	282008.i	0.848069	−	0.286574i
$993$	−324373.	+	95244.5i	−0.328962	+	0.0965920i
$994$	49434.8	+	12569.4i	0.0500334	+	0.0127216i
$995$	125468.	−	427306.i	0.126732	−	0.431611i
$996$	−39239.7	+	563101.i	−0.0395555	+	0.567633i
$997$	307788.	+	673963.i	0.309644	+	0.678025i	0.998919	−	0.0464742i	$-0.0147985\pi$
$997$	307788.	+	673963.i	0.309644	+	0.678025i	−0.689276	+	0.724499i	$0.742071\pi$
$998$	747616.	+	308873.i	0.750616	+	0.310112i
$999$	−194019.	+	301900.i	−0.194408	+	0.302505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.g.a.3.9	✓	460
4.3	odd	2	inner	92.5.g.a.3.42	yes	460
23.8	even	11	inner	92.5.g.a.31.42	yes	460
92.31	odd	22	inner	92.5.g.a.31.9	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.9	✓	460	1.1	even	1	trivial
92.5.g.a.3.42	yes	460	4.3	odd	2	inner
92.5.g.a.31.9	yes	460	92.31	odd	22	inner
92.5.g.a.31.42	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+(-3.28360 + 2.28429i) q^{2} +(2.55088 + 1.16495i) q^{3} +(5.56402 - 15.0014i) q^{4} +(24.3881 - 28.1454i) q^{5} +(-11.0372 + 2.00174i) q^{6} +(6.42136 + 9.99183i) q^{7} +(15.9975 + 61.9684i) q^{8} +(-47.8938 - 55.2724i) q^{9} +(-15.7885 + 148.128i) q^{10} +(-198.623 - 28.5577i) q^{11} +(31.6690 - 31.7850i) q^{12} +(-188.239 - 120.974i) q^{13} +(-43.9094 - 18.1409i) q^{14} +(94.9991 - 43.3846i) q^{15} +(-194.083 - 166.936i) q^{16} +(457.444 + 134.318i) q^{17} +(283.522 + 72.0889i) q^{18} +(8.28991 + 28.2328i) q^{19} +(-286.524 - 522.457i) q^{20} +(4.74016 + 32.9685i) q^{21} +(717.433 - 359.941i) q^{22} +(-277.098 - 450.619i) q^{23} +(-31.3822 + 176.710i) q^{24} +(-108.435 - 754.185i) q^{25} +(894.440 - 32.7633i) q^{26} +(-121.777 - 414.735i) q^{27} +(185.620 - 40.7345i) q^{28} +(-843.875 - 247.784i) q^{29} +(-212.836 + 359.463i) q^{30} +(782.527 - 357.368i) q^{31} +(1018.62 + 104.808i) q^{32} +(-473.396 - 304.233i) q^{33} +(-1808.88 + 603.890i) q^{34} +(437.828 + 62.9502i) q^{35} +(-1095.65 + 410.937i) q^{36} +(-543.697 - 627.459i) q^{37} +(-91.7127 - 73.7687i) q^{38} +(-339.247 - 527.879i) q^{39} +(2134.27 + 1061.03i) q^{40} +(-857.023 + 989.057i) q^{41} +(-90.8745 - 97.4275i) q^{42} +(2553.98 + 1166.36i) q^{43} +(-1533.55 + 2820.73i) q^{44} -2723.70 q^{45} +(1939.22 + 846.680i) q^{46} -2699.33i q^{47} +(-300.612 - 651.932i) q^{48} +(938.809 - 2055.70i) q^{49} +(2078.84 + 2228.74i) q^{50} +(1010.41 + 875.527i) q^{51} +(-2862.14 + 2150.74i) q^{52} +(328.661 - 211.218i) q^{53} +(1347.24 + 1083.65i) q^{54} +(-5647.81 + 4893.85i) q^{55} +(-516.452 + 557.766i) q^{56} +(-11.7432 + 81.6760i) q^{57} +(3336.96 - 1114.03i) q^{58} +(306.670 - 477.187i) q^{59} +(-122.252 - 1666.51i) q^{60} +(2488.69 + 5449.47i) q^{61} +(-1753.17 + 2960.97i) q^{62} +(244.729 - 833.471i) q^{63} +(-3584.16 + 1982.68i) q^{64} +(-7995.64 + 2347.73i) q^{65} +(2249.40 - 82.3954i) q^{66} +(4852.60 - 697.699i) q^{67} +(4560.18 - 6114.95i) q^{68} +(-181.896 - 1472.28i) q^{69} +(-1581.45 + 793.425i) q^{70} +(-1062.71 + 152.794i) q^{71} +(2658.96 - 3852.12i) q^{72} +(-55.5902 + 16.3228i) q^{73} +(3218.58 + 818.362i) q^{74} +(601.981 - 2050.16i) q^{75} +(469.657 + 32.7280i) q^{76} +(-990.087 - 2167.99i) q^{77} +(2319.78 + 958.402i) q^{78} +(6394.04 - 9949.32i) q^{79} +(-9431.80 + 1391.29i) q^{80} +(-670.568 + 4663.91i) q^{81} +(554.823 - 5205.36i) q^{82} +(-9507.60 + 8238.39i) q^{83} +(520.948 + 112.329i) q^{84} +(14936.6 - 9599.17i) q^{85} +(-11050.6 + 2004.17i) q^{86} +(-1863.97 - 1615.14i) q^{87} +(-1407.81 - 12765.2i) q^{88} +(2237.97 - 4900.46i) q^{89} +(8943.54 - 6221.73i) q^{90} -2657.67i q^{91} +(-8301.69 + 1649.60i) q^{92} +2412.45 q^{93} +(6166.06 + 8863.52i) q^{94} +(996.798 + 455.223i) q^{95} +(2476.29 + 1454.00i) q^{96} +(3234.37 - 3732.66i) q^{97} +(1613.16 + 8894.62i) q^{98} +(7934.37 + 12346.1i) 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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