LMFDB - Embedded newform 72.4.l.b.59.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [72,4,Mod(11,72)] 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("72.11"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(72, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	72.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.24813752041$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.15
Character	$\chi$	$=$	72.59
Dual form			72.4.l.b.11.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.250335 - 2.81733i) q^{2} +(-3.80768 - 3.53576i) q^{3} +(-7.87466 + 1.41055i) q^{4} +(10.8653 - 18.8192i) q^{5} +(-9.00820 + 11.6126i) q^{6} +(-10.5583 + 6.09581i) q^{7} +(5.94529 + 21.8324i) q^{8} +(1.99678 + 26.9261i) q^{9} +(-55.7398 - 25.8999i) q^{10} +(-22.8069 + 13.1676i) q^{11} +(34.9715 + 22.4720i) q^{12} +(-24.0118 - 13.8632i) q^{13} +(19.8170 + 28.2201i) q^{14} +(-107.912 + 33.2404i) q^{15} +(60.0207 - 22.2153i) q^{16} -56.3777i q^{17} +(75.3597 - 12.3661i) q^{18} +80.9703 q^{19} +(-59.0149 + 163.521i) q^{20} +(61.7558 + 14.1206i) q^{21} +(42.8068 + 60.9583i) q^{22} +(-4.32694 + 7.49448i) q^{23} +(54.5564 - 104.152i) q^{24} +(-173.608 - 300.699i) q^{25} +(-33.0463 + 71.1197i) q^{26} +(87.6010 - 109.586i) q^{27} +(74.5443 - 62.8955i) q^{28} +(-43.8188 - 75.8963i) q^{29} +(120.663 + 295.701i) q^{30} +(-174.690 - 100.857i) q^{31} +(-77.6129 - 163.537i) q^{32} +(133.399 + 30.5020i) q^{33} +(-158.834 + 14.1133i) q^{34} +264.931i q^{35} +(-53.7046 - 209.217i) q^{36} -53.3684i q^{37} +(-20.2697 - 228.120i) q^{38} +(42.4122 + 137.687i) q^{39} +(475.466 + 125.329i) q^{40} +(398.128 + 229.859i) q^{41} +(24.3227 - 177.521i) q^{42} +(-105.073 - 181.993i) q^{43} +(161.023 - 135.861i) q^{44} +(528.423 + 254.981i) q^{45} +(22.1976 + 10.3143i) q^{46} +(-168.953 - 292.635i) q^{47} +(-307.087 - 127.630i) q^{48} +(-97.1821 + 168.324i) q^{49} +(-803.706 + 564.387i) q^{50} +(-199.338 + 214.668i) q^{51} +(208.640 + 75.2984i) q^{52} +84.2497 q^{53} +(-330.669 - 219.368i) q^{54} +572.278i q^{55} +(-195.858 - 194.271i) q^{56} +(-308.309 - 286.292i) q^{57} +(-202.855 + 142.451i) q^{58} +(-86.9772 - 50.2163i) q^{59} +(802.881 - 413.972i) q^{60} +(342.447 - 197.712i) q^{61} +(-240.416 + 517.406i) q^{62} +(-185.219 - 272.120i) q^{63} +(-441.307 + 259.600i) q^{64} +(-521.791 + 301.256i) q^{65} +(52.5396 - 383.464i) q^{66} +(68.5689 - 118.765i) q^{67} +(79.5237 + 443.956i) q^{68} +(42.9743 - 13.2375i) q^{69} +(746.397 - 66.3215i) q^{70} +766.570 q^{71} +(-575.989 + 203.678i) q^{72} +464.449 q^{73} +(-150.356 + 13.3600i) q^{74} +(-402.154 + 1758.80i) q^{75} +(-637.614 + 114.213i) q^{76} +(160.534 - 278.054i) q^{77} +(377.292 - 153.957i) q^{78} +(-906.822 + 523.554i) q^{79} +(234.068 - 1370.92i) q^{80} +(-721.026 + 107.531i) q^{81} +(547.924 - 1179.20i) q^{82} +(1134.29 - 654.881i) q^{83} +(-506.224 - 24.0853i) q^{84} +(-1060.98 - 612.560i) q^{85} +(-486.429 + 341.585i) q^{86} +(-101.504 + 443.921i) q^{87} +(-423.074 - 419.645i) q^{88} -403.445i q^{89} +(586.083 - 1552.57i) q^{90} +338.031 q^{91} +(23.5018 - 65.1199i) q^{92} +(308.555 + 1001.69i) q^{93} +(-782.154 + 549.253i) q^{94} +(879.765 - 1523.80i) q^{95} +(-282.702 + 897.115i) q^{96} +(-29.9703 - 51.9100i) q^{97} +(498.553 + 231.656i) q^{98} +(-400.092 - 587.808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9} + 12 q^{10} + 48 q^{11} + 318 q^{12} + 72 q^{14} + 127 q^{16} + 330 q^{18} - 220 q^{19} - 234 q^{20} - 217 q^{22} + 189 q^{24} - 902 q^{25} - 252 q^{27}+ \cdots - 2118 q^{99}+O(q^{100}) $ 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9 + 12 * q^10 + 48 * q^11 + 318 * q^12 + 72 * q^14 + 127 * q^16 + 330 * q^18 - 220 * q^19 - 234 * q^20 - 217 * q^22 + 189 * q^24 - 902 * q^25 - 252 * q^27 - 132 * q^28 + 420 * q^30 - 693 * q^32 - 660 * q^33 + 509 * q^34 - 537 * q^36 - 1977 * q^38 - 36 * q^40 + 1620 * q^41 + 72 * q^42 - 292 * q^43 + 48 * q^46 + 765 * q^48 + 1762 * q^49 - 1227 * q^50 - 1794 * q^51 + 330 * q^52 - 645 * q^54 + 942 * q^56 - 294 * q^57 - 282 * q^58 + 5592 * q^59 + 1236 * q^60 + 1090 * q^64 - 6 * q^65 + 3522 * q^66 + 68 * q^67 - 2025 * q^68 + 600 * q^70 + 1875 * q^72 - 868 * q^73 - 420 * q^74 - 4254 * q^75 - 1471 * q^76 + 3228 * q^78 + 498 * q^81 + 362 * q^82 + 3654 * q^83 - 2028 * q^84 - 4119 * q^86 + 3155 * q^88 + 2958 * q^90 - 1380 * q^91 - 744 * q^92 - 138 * q^94 - 4782 * q^96 - 1912 * q^97 - 2118 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.250335	−	2.81733i	−0.0885069	−	0.996076i
$2$	−0.250335	−	2.81733i	−0.0885069	−	0.996076i
$3$	−3.80768	−	3.53576i	−0.732787	−	0.680458i
$3$	−3.80768	−	3.53576i	−0.732787	−	0.680458i
$4$	−7.87466	+	1.41055i	−0.984333	+	0.176319i
$5$	10.8653	−	18.8192i	0.971820	−	1.68324i	0.281767	−	0.959483i	$-0.409080\pi$
$5$	10.8653	−	18.8192i	0.971820	−	1.68324i	0.690053	−	0.723758i	$-0.257587\pi$
$6$	−9.00820	+	11.6126i	−0.612931	+	0.790137i
$7$	−10.5583	+	6.09581i	−0.570092	+	0.329143i	−0.757186	−	0.653199i	$-0.773426\pi$
$7$	−10.5583	+	6.09581i	−0.570092	+	0.329143i	0.187094	+	0.982342i	$0.440093\pi$
$8$	5.94529	+	21.8324i	0.262747	+	0.964865i
$9$	1.99678	+	26.9261i	0.0739548	+	0.997262i
$10$	−55.7398	−	25.8999i	−1.76265	−	0.819028i
$11$	−22.8069	+	13.1676i	−0.625141	+	0.360925i	−0.778868	−	0.627188i	$-0.784206\pi$
$11$	−22.8069	+	13.1676i	−0.625141	+	0.360925i	0.153727	+	0.988113i	$0.450872\pi$
$12$	34.9715	+	22.4720i	0.841285	+	0.540593i
$13$	−24.0118	−	13.8632i	−0.512284	−	0.295767i	0.221488	−	0.975163i	$-0.428909\pi$
$13$	−24.0118	−	13.8632i	−0.512284	−	0.295767i	−0.733772	+	0.679396i	$0.762242\pi$
$14$	19.8170	+	28.2201i	0.378308	+	0.538724i
$15$	−107.912	+	33.2404i	−1.85751	+	0.572176i
$16$	60.0207	−	22.2153i	0.937823	−	0.347113i
$17$		−	56.3777i		−	0.804330i	−0.915567	−	0.402165i	$-0.868258\pi$
$17$		−	56.3777i		−	0.804330i	0.915567	−	0.402165i	$-0.131742\pi$
$18$	75.3597	−	12.3661i	0.986802	−	0.161929i
$19$	80.9703			0.977677			0.488839	−	0.872374i	$-0.337421\pi$
$19$	80.9703			0.977677			0.488839	+	0.872374i	$0.337421\pi$
$20$	−59.0149	+	163.521i	−0.659807	+	1.82822i
$21$	61.7558	+	14.1206i	0.641724	+	0.146732i
$22$	42.8068	+	60.9583i	0.414838	+	0.590743i
$23$	−4.32694	+	7.49448i	−0.0392274	+	0.0679438i	−0.884973	−	0.465643i	$-0.845823\pi$
$23$	−4.32694	+	7.49448i	−0.0392274	+	0.0679438i	0.845745	+	0.533587i	$0.179156\pi$
$24$	54.5564	−	104.152i	0.464012	−	0.885829i
$25$	−173.608	−	300.699i	−1.38887	−	2.40559i
$26$	−33.0463	+	71.1197i	−0.249266	+	0.536451i
$27$	87.6010	−	109.586i	0.624401	−	0.781104i
$28$	74.5443	−	62.8955i	0.503127	−	0.424504i
$29$	−43.8188	−	75.8963i	−0.280584	−	0.485986i	0.690945	−	0.722908i	$-0.257195\pi$
$29$	−43.8188	−	75.8963i	−0.280584	−	0.485986i	−0.971529	+	0.236922i	$0.923861\pi$
$30$	120.663	+	295.701i	0.734333	+	1.79958i
$31$	−174.690	−	100.857i	−1.01210	−	0.584338i	−0.100296	−	0.994958i	$-0.531979\pi$
$31$	−174.690	−	100.857i	−1.01210	−	0.584338i	−0.911807	+	0.410620i	$0.865312\pi$
$32$	−77.6129	−	163.537i	−0.428755	−	0.903421i
$33$	133.399	+	30.5020i	0.703689	+	0.160900i
$34$	−158.834	+	14.1133i	−0.801173	+	0.0711887i
$35$			264.931i			1.27947i
$36$	−53.7046	−	209.217i	−0.248632	−	0.968598i
$37$		−	53.3684i		−	0.237127i	−0.992946	−	0.118564i	$-0.962171\pi$
$37$		−	53.3684i		−	0.237127i	0.992946	−	0.118564i	$-0.0378290\pi$
$38$	−20.2697	−	228.120i	−0.0865312	−	0.973841i
$39$	42.4122	+	137.687i	0.174138	+	0.565322i
$40$	475.466	+	125.329i	1.87944	+	0.495408i
$41$	398.128	+	229.859i	1.51652	+	0.875561i	0.999812	+	0.0193980i	$0.00617496\pi$
$41$	398.128	+	229.859i	1.51652	+	0.875561i	0.516705	+	0.856163i	$0.327158\pi$
$42$	24.3227	−	177.521i	0.0893590	−	0.652193i
$43$	−105.073	−	181.993i	−0.372641	−	0.645433i	0.617330	−	0.786704i	$-0.288214\pi$
$43$	−105.073	−	181.993i	−0.372641	−	0.645433i	−0.989971	+	0.141272i	$0.954881\pi$
$44$	161.023	−	135.861i	0.551709	−	0.465495i
$45$	528.423	+	254.981i	1.75050	+	0.844675i
$46$	22.1976	+	10.3143i	0.0711490	+	0.0330599i
$47$	−168.953	−	292.635i	−0.524348	−	0.908197i	−0.999598	−	0.0283461i	$-0.990976\pi$
$47$	−168.953	−	292.635i	−0.524348	−	0.908197i	0.475251	−	0.879850i	$-0.342357\pi$
$48$	−307.087	−	127.630i	−0.923421	−	0.383789i
$49$	−97.1821	+	168.324i	−0.283330	+	0.490742i
$50$	−803.706	+	564.387i	−2.27322	+	1.59633i
$51$	−199.338	+	214.668i	−0.547312	+	0.589403i
$52$	208.640	+	75.2984i	0.556407	+	0.200808i
$53$	84.2497			0.218351			0.109175	−	0.994023i	$-0.465179\pi$
$53$	84.2497			0.218351			0.109175	+	0.994023i	$0.465179\pi$
$54$	−330.669	−	219.368i	−0.833302	−	0.552818i
$55$			572.278i			1.40302i
$56$	−195.858	−	194.271i	−0.467369	−	0.463581i
$57$	−308.309	−	286.292i	−0.716430	−	0.665268i
$58$	−202.855	+	142.451i	−0.459245	+	0.322496i
$59$	−86.9772	−	50.2163i	−0.191923	−	0.110807i	0.400959	−	0.916096i	$-0.368677\pi$
$59$	−86.9772	−	50.2163i	−0.191923	−	0.110807i	−0.592883	+	0.805289i	$0.702010\pi$
$60$	802.881	−	413.972i	1.72752	−	0.890726i
$61$	342.447	−	197.712i	0.718783	−	0.414990i	−0.0955213	−	0.995427i	$-0.530452\pi$
$61$	342.447	−	197.712i	0.718783	−	0.414990i	0.814305	+	0.580438i	$0.197118\pi$
$62$	−240.416	+	517.406i	−0.492466	+	1.05985i
$63$	−185.219	−	272.120i	−0.370403	−	0.544190i
$64$	−441.307	+	259.600i	−0.861928	+	0.507031i
$65$	−521.791	+	301.256i	−0.995695	+	0.574865i
$66$	52.5396	−	383.464i	0.0979875	−	0.715169i
$67$	68.5689	−	118.765i	0.125030	−	0.216559i	−0.796715	−	0.604356i	$-0.793431\pi$
$67$	68.5689	−	118.765i	0.125030	−	0.216559i	0.921745	+	0.387797i	$0.126764\pi$
$68$	79.5237	+	443.956i	0.141819	+	0.791728i
$69$	42.9743	−	13.2375i	0.0749782	−	0.0230958i
$70$	746.397	−	66.3215i	1.27445	−	0.113242i
$71$	766.570			1.28134			0.640670	−	0.767816i	$-0.278657\pi$
$71$	766.570			1.28134			0.640670	+	0.767816i	$0.278657\pi$
$72$	−575.989	+	203.678i	−0.942791	+	0.333384i
$73$	464.449			0.744652			0.372326	−	0.928102i	$-0.378560\pi$
$73$	464.449			0.744652			0.372326	+	0.928102i	$0.378560\pi$
$74$	−150.356	+	13.3600i	−0.236197	+	0.0209874i
$75$	−402.154	+	1758.80i	−0.619157	+	2.70785i
$76$	−637.614	+	114.213i	−0.962360	+	0.172383i
$77$	160.534	−	278.054i	0.237592	−	0.411521i
$78$	377.292	−	153.957i	0.547691	−	0.223489i
$79$	−906.822	+	523.554i	−1.29146	+	0.745626i	−0.978913	−	0.204276i	$-0.934516\pi$
$79$	−906.822	+	523.554i	−1.29146	+	0.745626i	−0.312548	+	0.949902i	$0.601183\pi$
$80$	234.068	−	1370.92i	0.327120	−	1.91591i
$81$	−721.026	+	107.531i	−0.989061	+	0.147505i
$82$	547.924	−	1179.20i	0.737903	−	1.58806i
$83$	1134.29	−	654.881i	1.50005	−	0.866055i	0.500051	−	0.865996i	$-0.333315\pi$
$83$	1134.29	−	654.881i	1.50005	−	0.866055i	1.00000		5.88083e-5i	$-1.87193e-5\pi$
$84$	−506.224	−	24.0853i	−0.657542	−	0.0312848i
$85$	−1060.98	−	612.560i	−1.35388	−	0.781664i
$86$	−486.429	+	341.585i	−0.609918	+	0.428303i
$87$	−101.504	+	443.921i	−0.125084	+	0.547050i
$88$	−423.074	−	419.645i	−0.512498	−	0.508344i
$89$		−	403.445i		−	0.480506i	−0.970710	−	0.240253i	$-0.922770\pi$
$89$		−	403.445i		−	0.480506i	0.970710	−	0.240253i	$-0.0772304\pi$
$90$	586.083	−	1552.57i	0.686428	−	1.81839i
$91$	338.031			0.389399
$92$	23.5018	−	65.1199i	0.0266330	−	0.0737958i
$93$	308.555	+	1001.69i	0.344039	+	1.11689i
$94$	−782.154	+	549.253i	−0.858224	+	0.602671i
$95$	879.765	−	1523.80i	0.950126	−	1.64567i
$96$	−282.702	+	897.115i	−0.300553	+	0.953765i
$97$	−29.9703	−	51.9100i	−0.0313713	−	0.0543367i	0.849913	−	0.526922i	$-0.176654\pi$
$97$	−29.9703	−	51.9100i	−0.0313713	−	0.0543367i	−0.881285	+	0.472586i	$0.843321\pi$
$98$	498.553	+	231.656i	0.513892	+	0.238784i
$99$	−400.092	−	587.808i	−0.406169	−	0.596737i
$100$	1791.26	+	2123.02i	1.79126	+	2.12302i
$101$	680.909	+	1179.37i	0.670822	+	1.16190i	0.977671	+	0.210140i	$0.0673918\pi$
$101$	680.909	+	1179.37i	0.670822	+	1.16190i	−0.306850	+	0.951758i	$0.599275\pi$
$102$	654.691	+	507.862i	0.635531	+	0.492998i
$103$	878.637	+	507.281i	0.840531	+	0.485281i	0.857445	−	0.514576i	$-0.172051\pi$
$103$	878.637	+	507.281i	0.840531	+	0.485281i	−0.0169138	+	0.999857i	$0.505384\pi$
$104$	159.910	−	606.657i	0.150774	−	0.571996i
$105$	936.732	−	1008.77i	0.870626	−	0.937580i
$106$	−21.0907	−	237.359i	−0.0193255	−	0.217494i
$107$		−	1008.18i		−	0.910879i	−0.890267	−	0.455440i	$-0.849482\pi$
$107$		−	1008.18i		−	0.910879i	0.890267	−	0.455440i	$-0.150518\pi$
$108$	−535.252	+	986.518i	−0.476895	+	0.878960i
$109$		−	1319.53i		−	1.15952i	−0.814786	−	0.579762i	$-0.803146\pi$
$109$		−	1319.53i		−	1.15952i	0.814786	−	0.579762i	$-0.196854\pi$
$110$	1612.29	−	143.261i	1.39751	−	0.124177i
$111$	−188.698	+	203.209i	−0.161355	+	0.173764i
$112$	−498.294	+	600.429i	−0.420396	+	0.506565i
$113$	1586.40	+	915.907i	1.32067	+	0.762489i	0.983835	−	0.179075i	$-0.0573104\pi$
$113$	1586.40	+	915.907i	1.32067	+	0.762489i	0.336834	+	0.941564i	$0.390644\pi$
$114$	−729.397	+	940.276i	−0.599248	+	0.772499i
$115$	94.0268	+	162.859i	0.0762439	+	0.132058i
$116$	452.114	+	535.849i	0.361877	+	0.428900i
$117$	325.336	−	674.226i	0.257071	−	0.532754i
$118$	−119.702	+	257.614i	−0.0933855	+	0.200977i
$119$	343.668	+	595.251i	0.264740	+	0.458542i
$120$	−1367.28	−	2158.35i	−1.04013	−	1.64191i
$121$	−318.729	+	552.056i	−0.239466	+	0.414768i
$122$	−642.745	−	915.290i	−0.476979	−	0.679233i
$123$	−703.215	−	2282.92i	−0.515502	−	1.67353i
$124$	1517.89	+	547.807i	1.09928	+	0.396730i
$125$	−4828.90			−3.45528
$126$	−720.285	+	589.943i	−0.509271	+	0.417114i
$127$			14.1680i			0.00989929i	0.999988	+	0.00494964i	$0.00157553\pi$
$127$			14.1680i			0.00989929i	−0.999988	+	0.00494964i	$0.998424\pi$
$128$	841.853	+	1178.32i	0.581328	+	0.813669i
$129$	−243.397	+	1064.48i	−0.166123	+	0.726531i
$130$	979.359	+	1394.64i	0.660735	+	0.940908i
$131$	−843.900	−	487.226i	−0.562839	−	0.324955i	0.191445	−	0.981503i	$-0.438682\pi$
$131$	−843.900	−	487.226i	−0.562839	−	0.324955i	−0.754284	+	0.656548i	$0.772016\pi$
$132$	−1093.50	−	52.0267i	−0.721035	−	0.0343057i
$133$	−854.906	+	493.580i	−0.557366	+	0.321796i
$134$	−351.764	−	163.450i	−0.226775	−	0.105373i
$135$	−1110.51	−	2839.26i	−0.707981	−	1.81011i
$136$	1230.86	−	335.182i	0.776069	−	0.211335i
$137$	193.920	−	111.960i	0.120932	−	0.0698203i	−0.438314	−	0.898822i	$-0.644424\pi$
$137$	193.920	−	111.960i	0.120932	−	0.0698203i	0.559246	+	0.829002i	$0.311091\pi$
$138$	−48.0524	−	117.759i	−0.0296412	−	0.0726398i
$139$	158.759	−	274.979i	0.0968762	−	0.167795i	−0.813514	−	0.581545i	$-0.802448\pi$
$139$	158.759	−	274.979i	0.0968762	−	0.167795i	0.910390	+	0.413751i	$0.135782\pi$
$140$	−373.699	−	2086.24i	−0.225595	−	1.25943i
$141$	−391.370	+	1711.64i	−0.233754	+	1.02231i
$142$	−191.900	−	2159.68i	−0.113407	−	1.27631i
$143$	730.182			0.426999
$144$	718.017	+	1571.76i	0.415519	+	0.909584i
$145$	−1904.41			−1.09071
$146$	−116.268	−	1308.50i	−0.0659068	−	0.741730i
$147$	965.193	−	297.312i	0.541549	−	0.166815i
$148$	75.2789	+	420.258i	0.0418101	+	0.233412i
$149$	−811.049	+	1404.78i	−0.445931	+	0.772375i	−0.998117	−	0.0613461i	$-0.980461\pi$
$149$	−811.049	+	1404.78i	−0.445931	+	0.772375i	0.552186	+	0.833721i	$0.313794\pi$
$150$	5055.79	+	692.710i	2.75202	+	0.377064i
$151$	710.557	−	410.240i	0.382942	−	0.221092i	−0.296155	−	0.955140i	$-0.595705\pi$
$151$	710.557	−	410.240i	0.382942	−	0.221092i	0.679098	+	0.734048i	$0.262371\pi$
$152$	481.392	+	1767.78i	0.256882	+	0.943326i
$153$	1518.03	−	112.574i	0.802127	−	0.0594841i
$154$	−823.555	−	382.671i	−0.430935	−	0.200237i
$155$	−3796.10	+	2191.68i	−1.96716	+	1.13574i
$156$	−528.196	−	1024.41i	−0.271087	−	0.525761i
$157$	−436.444	−	251.981i	−0.221860	−	0.128091i	0.384951	−	0.922937i	$-0.374218\pi$
$157$	−436.444	−	251.981i	−0.221860	−	0.128091i	−0.606811	+	0.794846i	$0.707552\pi$
$158$	1702.03	+	2423.75i	0.857003	+	1.22040i
$159$	−320.796	−	297.887i	−0.160005	−	0.148578i
$160$	−3920.92	−	316.257i	−1.93735	−	0.156264i
$161$		−	105.505i		−	0.0516456i
$162$	483.448	+	2004.45i	0.234464	+	0.972125i
$163$	2496.71			1.19974			0.599870	−	0.800097i	$-0.295219\pi$
$163$	2496.71			1.19974			0.599870	+	0.800097i	$0.295219\pi$
$164$	−3459.36	−	1248.49i	−1.64714	−	0.594453i
$165$	2023.44	−	2179.05i	0.954693	−	1.02811i
$166$	−2128.97	−	3031.72i	−0.995421	−	1.41751i
$167$	709.405	−	1228.73i	0.328715	−	0.569351i	−0.653542	−	0.756890i	$-0.726718\pi$
$167$	709.405	−	1228.73i	0.328715	−	0.569351i	0.982257	+	0.187539i	$0.0600511\pi$
$168$	58.8694	+	1432.23i	0.0270350	+	0.657731i
$169$	−714.121	−	1236.89i	−0.325044	−	0.562992i
$170$	−1460.18	+	3142.48i	−0.658768	+	1.41775i
$171$	161.680	+	2180.21i	0.0723040	+	0.975000i
$172$	1084.13	+	1284.92i	0.480605	+	0.569617i
$173$	−319.906	−	554.094i	−0.140590	−	0.243508i	0.787129	−	0.616788i	$-0.211566\pi$
$173$	−319.906	−	554.094i	−0.140590	−	0.243508i	−0.927719	+	0.373280i	$0.878233\pi$
$174$	1276.08	+	174.840i	0.555974	+	0.0761758i
$175$	3666.01	+	2116.57i	1.58357	+	0.914272i
$176$	−1076.37	+	1296.99i	−0.460989	+	0.555479i
$177$	153.628	+	498.738i	0.0652395	+	0.211793i
$178$	−1136.64	+	100.996i	−0.478620	+	0.0425281i
$179$		−	1730.89i		−	0.722754i	−0.932420	−	0.361377i	$-0.882307\pi$
$179$		−	1730.89i		−	0.722754i	0.932420	−	0.361377i	$-0.117693\pi$
$180$	−4520.82	−	1262.52i	−1.87201	−	0.522794i
$181$			1880.76i			0.772354i	0.922425	+	0.386177i	$0.126205\pi$
$181$			1880.76i			0.772354i	−0.922425	+	0.386177i	$0.873795\pi$
$182$	−84.6211	−	952.344i	−0.0344645	−	0.387871i
$183$	−2002.99	−	457.988i	−0.809098	−	0.185002i
$184$	−189.347	−	49.9106i	−0.0758634	−	0.0199970i
$185$	−1004.35	−	579.862i	−0.399142	−	0.230445i
$186$	2744.85	−	1120.06i	1.08205	−	0.441541i
$187$	742.358	+	1285.80i	0.290303	+	0.502819i
$188$	1743.23	+	2066.09i	0.676265	+	0.801515i
$189$	−256.900	+	1691.04i	−0.0988714	+	0.650819i
$190$	−4513.27	−	2097.13i	−1.72330	−	0.800745i
$191$	1963.62	+	3401.09i	0.743887	+	1.28845i	0.950713	+	0.310072i	$0.100353\pi$
$191$	1963.62	+	3401.09i	0.743887	+	1.28845i	−0.206826	+	0.978378i	$0.566313\pi$
$192$	2598.24	+	571.884i	0.976623	+	0.214959i
$193$	−1231.33	+	2132.72i	−0.459237	+	0.795422i	−0.998921	−	0.0464461i	$-0.985210\pi$
$193$	−1231.33	+	2132.72i	−0.459237	+	0.795422i	0.539684	+	0.841868i	$0.318544\pi$
$194$	−138.745	+	97.4309i	−0.0513469	+	0.0360574i
$195$	3051.98	+	697.842i	1.12080	+	0.256275i
$196$	527.846	−	1462.58i	0.192364	−	0.533010i
$197$	2671.57			0.966201			0.483101	−	0.875565i	$-0.339511\pi$
$197$	2671.57			0.966201			0.483101	+	0.875565i	$0.339511\pi$
$198$	−1555.89	+	1274.34i	−0.558446	+	0.457390i
$199$			537.481i			0.191462i	0.995407	+	0.0957312i	$0.0305189\pi$
$199$			537.481i			0.191462i	−0.995407	+	0.0957312i	$0.969481\pi$
$200$	5532.82	−	5578.03i	1.95615	−	1.97213i
$201$	−681.012	+	209.774i	−0.238979	+	0.0736137i
$202$	3152.21	−	2213.58i	1.09797	−	0.771025i
$203$	925.300	+	534.222i	0.319918	+	0.184705i
$204$	1266.92	−	1971.62i	0.434815	−	0.676670i
$205$	8651.55	−	4994.97i	2.94756	−	1.70178i
$206$	1209.22	−	2602.40i	0.408983	−	0.880183i
$207$	−210.437	−	101.543i	−0.0706588	−	0.0340952i
$208$	−1749.18	−	298.652i	−0.583096	−	0.0995568i
$209$	−1846.68	+	1066.18i	−0.611186	+	0.352868i
$210$	−3076.53	−	2386.55i	−1.01096	−	0.784227i
$211$	−60.0267	+	103.969i	−0.0195849	+	0.0339220i	−0.875652	−	0.482943i	$-0.839568\pi$
$211$	−60.0267	+	103.969i	−0.0195849	+	0.0339220i	0.856067	+	0.516865i	$0.172901\pi$
$212$	−663.438	+	118.839i	−0.214930	+	0.0384994i
$213$	−2918.85	−	2710.41i	−0.938950	−	0.871898i
$214$	−2840.36	+	252.382i	−0.907304	+	0.0806191i
$215$	−4566.61			−1.44856
$216$	2913.34	+	1261.02i	0.917719	+	0.397230i
$217$	2459.22			0.769322
$218$	−3717.55	+	330.325i	−1.15497	+	0.102626i
$219$	−1768.47	−	1642.18i	−0.545672	−	0.506704i
$220$	−807.228	−	4506.50i	−0.247379	−	1.38104i
$221$	−781.578	+	1353.73i	−0.237894	+	0.412045i
$222$	619.745	+	480.753i	0.187363	+	0.145343i
$223$	−2835.47	+	1637.06i	−0.851468	+	0.491595i	−0.861146	−	0.508358i	$-0.830253\pi$
$223$	−2835.47	+	1637.06i	−0.851468	+	0.491595i	0.00967800	+	0.999953i	$0.496919\pi$
$224$	1816.35	+	1253.55i	0.541785	+	0.373912i
$225$	7749.97	−	5275.02i	2.29629	−	1.56297i
$226$	2183.28	−	4698.68i	0.642608	−	1.38297i
$227$	−618.234	+	356.938i	−0.180765	+	0.104365i	−0.587652	−	0.809114i	$-0.699948\pi$
$227$	−618.234	+	356.938i	−0.180765	+	0.104365i	0.406887	+	0.913478i	$0.366614\pi$
$228$	2831.66	+	1819.57i	0.822505	+	0.528525i
$229$	−2011.19	−	1161.16i	−0.580364	−	0.335073i	0.180914	−	0.983499i	$-0.442094\pi$
$229$	−2011.19	−	1161.16i	−0.580364	−	0.335073i	−0.761278	+	0.648426i	$0.775428\pi$
$230$	435.289	−	305.674i	0.124792	−	0.0876327i
$231$	−1594.39	+	491.127i	−0.454127	+	0.139886i
$232$	1396.48	−	1407.89i	0.395188	−	0.398417i
$233$			3568.38i			1.00332i	0.865066	+	0.501658i	$0.167276\pi$
$233$			3568.38i			1.00332i	−0.865066	+	0.501658i	$0.832724\pi$
$234$	−1980.96	−	747.796i	−0.553416	−	0.208910i
$235$	−7342.89			−2.03829
$236$	755.749	+	272.751i	0.208454	+	0.0752312i
$237$	5304.05	+	1212.78i	1.45373	+	0.332400i
$238$	1590.98	−	1117.24i	0.433311	−	0.304285i
$239$	672.246	−	1164.37i	0.181941	−	0.315132i	−0.760600	−	0.649221i	$-0.775095\pi$
$239$	672.246	−	1164.37i	0.181941	−	0.315132i	0.942542	+	0.334089i	$0.108429\pi$
$240$	−5738.49	+	4392.40i	−1.54341	+	1.18137i
$241$	847.081	+	1467.19i	0.226412	+	0.392157i	0.956742	−	0.290937i	$-0.0939671\pi$
$241$	847.081	+	1467.19i	0.226412	+	0.392157i	−0.730330	+	0.683094i	$0.760634\pi$
$242$	1635.11	+	759.766i	0.434334	+	0.201817i
$243$	3125.64	+	2139.93i	0.825142	+	0.564925i
$244$	−2417.77	+	2039.95i	−0.634352	+	0.535223i
$245$	2111.82	+	3657.78i	0.550691	+	0.953825i
$246$	−6255.68	+	2552.68i	−1.62133	+	0.661598i
$247$	−1944.25	−	1122.51i	−0.500848	−	0.289165i
$248$	1163.37	−	4413.52i	0.297879	−	1.13007i
$249$	−6634.50	−	1517.00i	−1.68853	−	0.386087i
$250$	1208.84	+	13604.6i	0.305816	+	3.44172i
$251$		−	2908.91i		−	0.731510i	−0.930711	−	0.365755i	$-0.880811\pi$
$251$		−	2908.91i		−	0.731510i	0.930711	−	0.365755i	$-0.119189\pi$
$252$	1842.38	+	1881.60i	0.460551	+	0.470355i
$253$		−	227.901i		−	0.0566326i
$254$	39.9160	−	3.54676i	0.00986044	−	0.000876155i
$255$	1874.02	+	6083.82i	0.460218	+	1.49405i
$256$	3108.97	−	2666.75i	0.759025	−	0.651062i
$257$	−4182.99	−	2415.05i	−1.01528	−	0.586173i	−0.102548	−	0.994728i	$-0.532700\pi$
$257$	−4182.99	−	2415.05i	−1.01528	−	0.586173i	−0.912734	+	0.408555i	$0.866033\pi$
$258$	3059.93	+	419.250i	0.738383	+	0.101168i
$259$	325.324	+	563.477i	0.0780488	+	0.135184i
$260$	3683.99	−	3108.30i	0.878736	−	0.741418i
$261$	1956.09	−	1331.41i	0.463905	−	0.315757i
$262$	−1161.42	+	2499.51i	−0.273865	+	0.589390i
$263$	−555.302	−	961.811i	−0.130195	−	0.225505i	0.793556	−	0.608497i	$-0.208227\pi$
$263$	−555.302	−	961.811i	−0.130195	−	0.225505i	−0.923752	+	0.382992i	$0.874894\pi$
$264$	127.164	+	3093.76i	0.0296455	+	0.721241i
$265$	915.396	−	1585.51i	0.212198	−	0.367537i
$266$	1604.59	+	2284.99i	0.369864	+	0.526698i
$267$	−1426.48	+	1536.19i	−0.326964	+	0.352109i
$268$	−372.433	+	1031.95i	−0.0848879	+	0.235211i
$269$	426.485			0.0966664			0.0483332	−	0.998831i	$-0.484609\pi$
$269$	426.485			0.0966664			0.0483332	+	0.998831i	$0.484609\pi$
$270$	−7721.13	+	3839.44i	−1.74035	+	0.865410i
$271$		−	4297.17i		−	0.963226i	−0.876384	−	0.481613i	$-0.840051\pi$
$271$		−	4297.17i		−	0.963226i	0.876384	−	0.481613i	$-0.159949\pi$
$272$	−1252.45	−	3383.83i	−0.279194	−	0.754319i
$273$	−1287.11	−	1195.20i	−0.285346	−	0.264969i
$274$	−363.973	−	518.310i	−0.0802497	−	0.114278i
$275$	7918.95	+	4572.01i	1.73648	+	1.00255i
$276$	−319.736	+	164.858i	−0.0697313	+	0.0359540i
$277$	−3296.42	+	1903.19i	−0.715028	+	0.412822i	−0.812920	−	0.582375i	$-0.802123\pi$
$277$	−3296.42	+	1903.19i	−0.715028	+	0.412822i	0.0978918	+	0.995197i	$0.468790\pi$
$278$	−814.450	−	378.440i	−0.175710	−	0.0816451i
$279$	2366.87	−	4905.09i	0.507888	−	1.05255i
$280$	−5784.07	+	1575.09i	−1.23452	+	0.336178i
$281$	591.545	−	341.528i	0.125582	−	0.0725049i	−0.435893	−	0.899999i	$-0.643567\pi$
$281$	591.545	−	341.528i	0.125582	−	0.0725049i	0.561475	+	0.827494i	$0.310234\pi$
$282$	4920.22	+	674.135i	1.03899	+	0.142355i
$283$	−634.307	+	1098.65i	−0.133236	+	0.230771i	−0.924922	−	0.380157i	$-0.875870\pi$
$283$	−634.307	+	1098.65i	−0.133236	+	0.230771i	0.791687	+	0.610928i	$0.209203\pi$
$284$	−6036.48	+	1081.29i	−1.26127	+	0.225925i
$285$	−8737.65	+	2691.49i	−1.81605	+	0.559403i
$286$	−182.790	−	2057.16i	−0.0377923	−	0.425323i
$287$	−5604.72			−1.15274
$288$	4248.42	−	2416.36i	0.869238	−	0.494393i
$289$	1734.55			0.353054
$290$	476.741	+	5365.35i	0.0965352	+	1.08643i
$291$	−69.4244	+	303.624i	−0.0139853	+	0.0611641i
$292$	−3657.38	+	655.129i	−0.732986	+	0.131296i
$293$	2512.00	−	4350.91i	0.500862	−	0.867518i	−0.499138	−	0.866523i	$-0.666350\pi$
$293$	2512.00	−	4350.91i	0.500862	−	0.867518i	1.00000		0.000995098i	$-0.000316750\pi$
$294$	−1079.25	−	2644.84i	−0.214092	−	0.524660i
$295$	−1890.06	+	1091.23i	−0.373029	+	0.215369i
$296$	1165.16	−	317.291i	0.228796	−	0.0623046i
$297$	−554.930	+	3652.81i	−0.108418	+	0.713662i
$298$	4160.75	+	1933.32i	0.808812	+	0.375820i
$299$	207.796	−	119.971i	0.0401911	−	0.0232043i
$300$	685.949	−	14417.2i	0.132011	−	2.77460i
$301$	2218.78	+	1281.02i	0.424879	+	0.245304i
$302$	−1333.66	−	1899.17i	−0.254117	−	0.361871i
$303$	1577.29	−	6898.19i	0.299052	−	1.30789i
$304$	4859.90	−	1798.78i	0.916889	−	0.339365i
$305$		−	8592.77i		−	1.61318i
$306$	−697.174	−	4248.61i	−0.130244	−	0.793715i
$307$	3396.30			0.631392			0.315696	−	0.948860i	$-0.397762\pi$
$307$	3396.30			0.631392			0.315696	+	0.948860i	$0.397762\pi$
$308$	−871.945	+	2416.02i	−0.161311	+	0.446966i
$309$	−1551.94	−	5038.21i	−0.285717	−	0.927553i
$310$	7124.98	+	10146.2i	1.30539	+	1.85892i
$311$	−2587.42	+	4481.55i	−0.471767	+	0.817124i	−0.999478	−	0.0322999i	$-0.989717\pi$
$311$	−2587.42	+	4481.55i	−0.471767	+	0.817124i	0.527712	+	0.849424i	$0.323050\pi$
$312$	−2753.88	+	1744.55i	−0.499705	+	0.316556i
$313$	755.937	+	1309.32i	0.136512	+	0.236445i	0.926174	−	0.377097i	$-0.123078\pi$
$313$	755.937	+	1309.32i	0.136512	+	0.236445i	−0.789662	+	0.613542i	$0.789744\pi$
$314$	−600.656	+	1292.69i	−0.107952	+	0.232327i
$315$	−7133.54	+	529.009i	−1.27597	+	0.0946231i
$316$	6402.42	−	5401.93i	1.13976	−	0.961653i
$317$	−2521.16	−	4366.77i	−0.446695	−	0.773698i	0.551474	−	0.834192i	$-0.314066\pi$
$317$	−2521.16	−	4366.77i	−0.446695	−	0.773698i	−0.998169	+	0.0604940i	$0.980732\pi$
$318$	−758.938	+	978.357i	−0.133834	+	0.172527i
$319$	1998.74	+	1153.97i	0.350809	+	0.202540i
$320$	90.5446	+	11125.7i	0.0158175	+	1.94358i
$321$	−3564.67	+	3838.81i	−0.619815	+	0.667481i
$322$	−297.242	+	26.4116i	−0.0514430	+	0.00457099i
$323$		−	4564.92i		−	0.786375i
$324$	5526.16	−	1863.81i	0.947558	−	0.319584i
$325$			9627.11i			1.64313i
$326$	−625.015	−	7034.06i	−0.106185	−	1.19503i
$327$	−4665.55	+	5024.34i	−0.789007	+	0.849685i
$328$	−2651.39	+	10058.7i	−0.446338	+	1.69329i
$329$	3567.70	+	2059.81i	0.597853	+	0.345171i
$330$	−6645.63	−	5155.19i	−1.10858	−	0.859952i
$331$	3223.04	+	5582.47i	0.535209	+	0.927009i	0.999153	+	0.0411448i	$0.0131005\pi$
$331$	3223.04	+	5582.47i	0.535209	+	0.927009i	−0.463944	+	0.885864i	$0.653566\pi$
$332$	−8008.39	+	6756.94i	−1.32385	+	1.11697i
$333$	1437.00	−	106.565i	0.236478	−	0.0175367i
$334$	−3639.31	−	1691.03i	−0.596210	−	0.277033i
$335$	−1490.04	−	2580.82i	−0.243014	−	0.420912i
$336$	4020.32	−	524.391i	0.652757	−	0.0851425i
$337$	2148.29	−	3720.94i	0.347254	−	0.601462i	−0.638506	−	0.769617i	$-0.720447\pi$
$337$	2148.29	−	3720.94i	0.347254	−	0.601462i	0.985761	+	0.168154i	$0.0537807\pi$
$338$	−3305.96	+	2321.55i	−0.532014	+	0.373597i
$339$	−2802.06	−	9096.60i	−0.448929	−	1.45740i
$340$	9218.94	+	3327.13i	1.47049	+	0.530702i
$341$	5312.18			0.843608
$342$	6101.90	−	1001.29i	0.964774	−	0.158314i
$343$		−	6551.34i		−	1.03131i
$344$	3348.64	−	3376.00i	0.524845	−	0.529133i
$345$	217.808	−	952.571i	0.0339895	−	0.148651i
$346$	−1480.98	+	1039.99i	−0.230110	+	0.161590i
$347$	−6334.11	−	3657.00i	−0.979922	−	0.565758i	−0.0776756	−	0.996979i	$-0.524750\pi$
$347$	−6334.11	−	3657.00i	−0.979922	−	0.565758i	−0.902247	+	0.431220i	$0.858083\pi$
$348$	173.133	−	3638.91i	0.0266693	−	0.560534i
$349$	−6046.48	+	3490.94i	−0.927394	+	0.535431i	−0.885987	−	0.463711i	$-0.846518\pi$
$349$	−6046.48	+	3490.94i	−0.927394	+	0.535431i	−0.0414078	+	0.999142i	$0.513184\pi$
$350$	5045.34	−	10858.2i	0.770528	−	1.65827i
$351$	−3622.68	+	1416.92i	−0.550895	+	0.215469i
$352$	3923.49	+	2707.79i	0.594099	+	0.410017i
$353$	10926.6	−	6308.48i	1.64749	−	0.951180i	0.669428	−	0.742877i	$-0.266539\pi$
$353$	10926.6	−	6308.48i	1.64749	−	0.951180i	0.978064	−	0.208303i	$-0.0667939\pi$
$354$	1366.65	−	557.672i	0.205188	−	0.0837286i
$355$	8329.00	−	14426.2i	1.24523	−	2.15681i
$356$	569.080	+	3176.99i	0.0847224	+	0.472978i
$357$	796.088	−	3481.65i	0.118021	−	0.516158i
$358$	−4876.49	+	433.303i	−0.719918	+	0.0639687i
$359$	10010.3			1.47166			0.735830	−	0.677167i	$-0.236792\pi$
$359$	10010.3			1.47166			0.735830	+	0.677167i	$0.236792\pi$
$360$	−2425.22	+	13052.7i	−0.355057	+	1.91093i
$361$	−302.804			−0.0441469
$362$	5298.73	−	470.822i	0.769323	−	0.0683587i
$363$	3165.56	−	975.097i	0.457710	−	0.140990i
$364$	−2661.88	+	476.810i	−0.383298	+	0.0686584i
$365$	5046.36	−	8740.56i	0.723668	−	1.25343i
$366$	−788.883	+	5757.72i	−0.112666	+	0.822297i
$367$	−7534.90	+	4350.28i	−1.07171	+	0.618754i	−0.928649	−	0.370960i	$-0.879029\pi$
$367$	−7534.90	+	4350.28i	−1.07171	+	0.618754i	−0.143064	+	0.989713i	$0.545695\pi$
$368$	−93.2141	+	545.948i	−0.0132041	+	0.0773356i
$369$	−5394.24	+	11179.0i	−0.761010	+	1.57712i
$370$	−1382.24	+	2974.75i	−0.194214	+	0.417972i
$371$	−889.530	+	513.570i	−0.124480	+	0.0718686i
$372$	−3842.70	−	7452.75i	−0.535577	−	1.03873i
$373$	−5355.18	−	3091.81i	−0.743380	−	0.429191i	0.0799170	−	0.996802i	$-0.474534\pi$
$373$	−5355.18	−	3091.81i	−0.743380	−	0.429191i	−0.823297	+	0.567611i	$0.807868\pi$
$374$	3436.69	−	2413.35i	0.475152	−	0.333666i
$375$	18386.9	+	17073.8i	2.53198	+	2.35117i
$376$	5384.45	−	5428.45i	0.738516	−	0.744551i
$377$			2429.88i			0.331950i
$378$	4828.51	+	300.445i	0.657015	+	0.0408815i
$379$	−11734.4			−1.59039			−0.795193	−	0.606356i	$-0.792630\pi$
$379$	−11734.4			−1.59039			−0.795193	+	0.606356i	$0.792630\pi$
$380$	−4778.46	+	13240.4i	−0.645078	+	1.78741i
$381$	50.0948	−	53.9473i	0.00673605	−	0.00725407i
$382$	9090.41	−	6383.57i	1.21755	−	0.855004i
$383$	−2243.57	+	3885.98i	−0.299324	+	0.518445i	−0.975981	−	0.217853i	$-0.930095\pi$
$383$	−2243.57	+	3885.98i	−0.299324	+	0.518445i	0.676657	+	0.736298i	$0.263428\pi$
$384$	960.754	−	7463.25i	0.127678	−	0.991816i
$385$	−3488.50	−	6042.26i	−0.461793	−	0.799849i
$386$	6316.81	+	2935.15i	0.832946	+	0.387034i
$387$	4690.53	−	3192.61i	0.616106	−	0.419353i
$388$	309.227	+	366.499i	0.0404604	+	0.0479541i
$389$	−2616.87	−	4532.56i	−0.341082	−	0.590771i	0.643552	−	0.765402i	$-0.277460\pi$
$389$	−2616.87	−	4532.56i	−0.341082	−	0.590771i	−0.984634	+	0.174632i	$0.944127\pi$
$390$	1202.03	−	8773.12i	0.156070	−	1.13909i
$391$	422.522	+	243.943i	0.0546492	+	0.0315517i
$392$	−4252.70	−	1120.98i	−0.547943	−	0.144434i
$393$	1490.58	+	4839.02i	0.191323	+	0.621111i
$394$	−668.788	−	7526.69i	−0.0855154	−	0.962409i
$395$			22754.2i			2.89846i
$396$	3979.72	+	4064.44i	0.505021	+	0.515772i
$397$			10075.8i			1.27377i	0.770958	+	0.636886i	$0.219778\pi$
$397$			10075.8i			1.27377i	−0.770958	+	0.636886i	$0.780222\pi$
$398$	1514.26	−	134.550i	0.190711	−	0.0169457i
$399$	5000.39	+	1143.35i	0.627399	+	0.143456i
$400$	−17100.2	−	14191.4i	−2.13752	−	1.77392i
$401$	4839.70	+	2794.20i	0.602701	+	0.347970i	0.770103	−	0.637919i	$-0.220205\pi$
$401$	4839.70	+	2794.20i	0.602701	+	0.347970i	−0.167402	+	0.985889i	$0.553538\pi$
$402$	761.485	+	1866.12i	0.0944761	+	0.231526i
$403$	2796.41	+	4843.53i	0.345656	+	0.598693i
$404$	−7025.49	−	8326.68i	−0.865177	−	1.02542i
$405$	−5810.50	+	14737.5i	−0.712904	+	1.80818i
$406$	1273.44	−	2740.61i	0.155665	−	0.335010i
$407$	702.733	+	1217.17i	0.0855852	+	0.148238i
$408$	−5871.84	−	3075.77i	−0.712499	−	0.373218i
$409$	−2384.52	+	4130.12i	−0.288282	+	0.499318i	−0.973400	−	0.229114i	$-0.926417\pi$
$409$	−2384.52	+	4130.12i	−0.288282	+	0.499318i	0.685118	+	0.728432i	$0.259751\pi$
$410$	−16238.3	−	23123.8i	−1.95598	−	2.78538i
$411$	−1134.25	−	259.349i	−0.136128	−	0.0311259i
$412$	−7634.52	−	2755.31i	−0.912926	−	0.329476i
$413$	1224.44			0.145885
$414$	−233.399	+	618.289i	−0.0277076	+	0.0733991i
$415$		−	28461.9i		−	3.36660i
$416$	−403.519	+	5002.78i	−0.0475580	+	0.589619i
$417$	−1576.77	+	485.696i	−0.185167	+	0.0570376i
$418$	3466.08	+	4935.81i	0.405578	+	0.577556i
$419$	5656.93	+	3266.03i	0.659568	+	0.380802i	0.792112	−	0.610375i	$-0.208981\pi$
$419$	5656.93	+	3266.03i	0.659568	+	0.380802i	−0.132544	+	0.991177i	$0.542315\pi$
$420$	−5953.53	+	9265.04i	−0.691672	+	1.07640i
$421$	3908.99	−	2256.86i	0.452524	−	0.261265i	−0.256371	−	0.966578i	$-0.582527\pi$
$421$	3908.99	−	2256.86i	0.452524	−	0.261265i	0.708896	+	0.705313i	$0.249194\pi$
$422$	307.942	+	143.088i	0.0355223	+	0.0165057i
$423$	7542.15	−	5133.57i	0.866932	−	0.590077i
$424$	500.889	+	1839.37i	0.0573711	+	0.210679i
$425$	−16952.7	+	9787.65i	−1.93489	+	1.11711i
$426$	−6905.42	+	8901.87i	−0.785373	+	1.01243i
$427$	−2410.43	+	4174.98i	−0.273182	+	0.473165i
$428$	1422.09	+	7939.05i	0.160605	+	0.896608i
$429$	−2780.29	−	2581.75i	−0.312900	−	0.290555i
$430$	1143.18	+	12865.6i	0.128207	+	1.44287i
$431$	−616.879			−0.0689420			−0.0344710	−	0.999406i	$-0.510975\pi$
$431$	−616.879			−0.0689420			−0.0344710	+	0.999406i	$0.510975\pi$
$432$	2823.40	−	8523.50i	0.314446	−	0.949275i
$433$	−2095.37			−0.232557			−0.116278	−	0.993217i	$-0.537096\pi$
$433$	−2095.37			−0.232557			−0.116278	+	0.993217i	$0.537096\pi$
$434$	−615.630	−	6928.44i	−0.0680903	−	0.766303i
$435$	7251.38	+	6733.55i	0.799258	+	0.742181i
$436$	1861.27	+	10390.9i	0.204446	+	1.14136i
$437$	−350.354	+	606.831i	−0.0383517	+	0.0664271i
$438$	−4183.85	+	5393.45i	−0.456420	+	0.588377i
$439$	8410.24	−	4855.65i	0.914348	−	0.527899i	0.0325203	−	0.999471i	$-0.489647\pi$
$439$	8410.24	−	4855.65i	0.914348	−	0.527899i	0.881827	+	0.471572i	$0.156313\pi$
$440$	−12494.2	+	3402.36i	−1.35372	+	0.368639i
$441$	−4726.36	−	2280.62i	−0.510351	−	0.246261i
$442$	4009.57	+	1863.07i	0.431483	+	0.200492i
$443$	7645.43	−	4414.09i	0.819967	−	0.473408i	−0.0304381	−	0.999537i	$-0.509690\pi$
$443$	7645.43	−	4414.09i	0.819967	−	0.473408i	0.850405	+	0.526129i	$0.176357\pi$
$444$	1199.30	−	1866.37i	0.128189	−	0.199492i
$445$	−7592.51	−	4383.54i	−0.808808	−	0.466965i
$446$	5321.96	+	7578.64i	0.565027	+	0.804617i
$447$	8055.17	−	2481.26i	0.852341	−	0.262550i
$448$	3076.96	−	5431.05i	0.324493	−	0.572752i
$449$			80.1769i			0.00842713i	0.999991	+	0.00421357i	$0.00134122\pi$
$449$			80.1769i			0.00842713i	−0.999991	+	0.00421357i	$0.998659\pi$
$450$	−16801.6	−	20513.7i	−1.76007	−	2.14894i
$451$	−12106.8			−1.26405
$452$	−13784.3	−	4974.76i	−1.43442	−	0.517684i
$453$	−4156.08	−	950.298i	−0.431059	−	0.0985627i
$454$	1160.38	+	1652.41i	0.119954	+	0.170819i
$455$	3672.80	−	6361.48i	0.378425	−	0.655452i
$456$	4417.45	−	8433.21i	0.453654	−	0.866055i
$457$	−1865.73	−	3231.54i	−0.190974	−	0.330777i	0.754599	−	0.656186i	$-0.227831\pi$
$457$	−1865.73	−	3231.54i	−0.190974	−	0.330777i	−0.945573	+	0.325409i	$0.894498\pi$
$458$	−2767.90	+	5956.86i	−0.282392	+	0.607742i
$459$	−6178.20	−	4938.75i	−0.628265	−	0.502224i
$460$	−970.151	−	1149.83i	−0.0983337	−	0.116546i
$461$	6395.61	+	11077.5i	0.646146	+	1.11916i	0.984036	+	0.177972i	$0.0569537\pi$
$461$	6395.61	+	11077.5i	0.646146	+	1.11916i	−0.337889	+	0.941186i	$0.609713\pi$
$462$	1782.80	+	4368.98i	0.179531	+	0.439964i
$463$	10395.3	+	6001.71i	1.04343	+	0.602426i	0.920804	−	0.390026i	$-0.127534\pi$
$463$	10395.3	+	6001.71i	1.04343	+	0.602426i	0.122629	+	0.992453i	$0.460867\pi$
$464$	−4316.09	−	3581.90i	−0.431830	−	0.358374i
$465$	22203.6	+	5076.90i	2.21434	+	0.506313i
$466$	10053.3	−	893.292i	0.999378	−	0.0888003i
$467$			1913.91i			0.189647i	0.995494	+	0.0948234i	$0.0302287\pi$
$467$			1913.91i			0.189647i	−0.995494	+	0.0948234i	$0.969771\pi$
$468$	−1610.88	+	5768.21i	−0.159109	+	0.569734i
$469$			1671.93i			0.164611i
$470$	1838.18	+	20687.3i	0.180402	+	2.03029i
$471$	770.893	+	2502.63i	0.0754159	+	0.244830i
$472$	579.237	−	2197.47i	0.0564863	−	0.214294i
$473$	4792.80	+	2767.13i	0.465906	+	0.268991i
$474$	2089.02	−	15246.8i	0.202430	−	1.47745i
$475$	−14057.1	−	24347.7i	−1.35786	−	2.35189i
$476$	−3545.90	−	4202.64i	−0.341442	−	0.404680i
$477$	168.228	+	2268.51i	0.0161481	+	0.217753i
$478$	−3448.68	−	1602.46i	−0.329998	−	0.153336i
$479$	−2461.54	−	4263.51i	−0.234803	−	0.406691i	0.724412	−	0.689367i	$-0.242111\pi$
$479$	−2461.54	−	4263.51i	−0.234803	−	0.406691i	−0.959215	+	0.282676i	$0.908778\pi$
$480$	13811.4	+	15067.6i	1.31333	+	1.43279i
$481$	−739.859	+	1281.47i	−0.0701344	+	0.121476i
$482$	3921.49	−	2753.79i	0.370579	−	0.260232i
$483$	−373.040	+	401.728i	−0.0351427	+	0.0378453i
$484$	1731.18	−	4796.84i	0.162583	−	0.450492i
$485$	−1302.54			−0.121949
$486$	5246.43	−	9341.64i	0.489677	−	0.871904i
$487$			20038.3i			1.86452i	0.361783	+	0.932262i	$0.382168\pi$
$487$			20038.3i			1.86452i	−0.361783	+	0.932262i	$0.617832\pi$
$488$	6352.46	+	6300.98i	0.589267	+	0.584491i
$489$	−9506.67	−	8827.78i	−0.879155	−	0.816373i
$490$	9776.50	−	6865.36i	0.901342	−	0.632950i
$491$	−12224.2	−	7057.66i	−1.12357	−	0.648692i	−0.181258	−	0.983436i	$-0.558017\pi$
$491$	−12224.2	−	7057.66i	−1.12357	−	0.648692i	−0.942309	+	0.334743i	$0.891350\pi$
$492$	8757.76	+	16985.3i	0.802500	+	1.55641i
$493$	−4278.86	+	2470.40i	−0.390893	+	0.225682i
$494$	−2675.77	+	5758.58i	−0.243702	+	0.524476i
$495$	−15409.2	+	1142.71i	−1.39917	+	0.103760i
$496$	−12725.6	−	2172.74i	−1.15200	−	0.196691i
$497$	−8093.65	+	4672.87i	−0.730482	+	0.421744i
$498$	−2613.02	+	19071.3i	−0.235125	+	1.71608i
$499$	−3778.03	+	6543.74i	−0.338934	+	0.587050i	−0.984232	−	0.176880i	$-0.943400\pi$
$499$	−3778.03	+	6543.74i	−0.338934	+	0.587050i	0.645299	+	0.763930i	$0.276733\pi$
$500$	38026.0	−	6811.41i	3.40114	−	0.609231i
$501$	−7045.66	+	2170.30i	−0.628297	+	0.193537i
$502$	−8195.36	+	728.203i	−0.728639	+	0.0647436i
$503$	−12944.3			−1.14743			−0.573716	−	0.819055i	$-0.694499\pi$
$503$	−12944.3			−1.14743			−0.573716	+	0.819055i	$0.694499\pi$
$504$	4839.86	−	5661.61i	0.427747	−	0.500373i
$505$	29593.1			2.60767
$506$	−642.073	+	57.0517i	−0.0564103	+	0.00501237i
$507$	−1654.22	+	7234.65i	−0.144904	+	0.633732i
$508$	−19.9847	−	111.568i	−0.00174543	−	0.00974420i
$509$	1935.70	−	3352.73i	0.168563	−	0.291959i	−0.769352	−	0.638825i	$-0.779421\pi$
$509$	1935.70	−	3352.73i	0.168563	−	0.291959i	0.937915	+	0.346866i	$0.112754\pi$
$510$	16671.0	−	6802.72i	1.44746	−	0.590646i
$511$	−4903.77	+	2831.19i	−0.424520	+	0.245097i
$512$	−8291.39	−	8091.39i	−0.715686	−	0.698422i
$513$	7093.09	−	8873.20i	0.610463	−	0.763668i
$514$	−5756.83	+	12389.4i	−0.494014	+	1.06318i
$515$	19093.3	−	11023.5i	1.63369	−	0.943211i
$516$	415.158	−	8725.77i	0.0354192	−	0.744439i
$517$	7706.60	+	4449.41i	0.655582	+	0.378500i
$518$	1506.06	−	1057.60i	0.127746	−	0.0897072i
$519$	−741.044	+	3240.92i	−0.0626748	+	0.274105i
$520$	−9679.34	−	9600.89i	−0.816283	−	0.809667i
$521$			1410.78i			0.118632i	0.998239	+	0.0593162i	$0.0188920\pi$
$521$			1410.78i			0.118632i	−0.998239	+	0.0593162i	$0.981108\pi$
$522$	−4240.71	−	5177.65i	−0.355576	−	0.434137i
$523$	18732.3			1.56617			0.783085	−	0.621915i	$-0.213645\pi$
$523$	18732.3			1.56617			0.783085	+	0.621915i	$0.213645\pi$
$524$	7332.68	+	2646.37i	0.611316	+	0.220625i
$525$	−6475.28	−	21021.3i	−0.538294	−	1.74752i
$526$	−2570.73	+	1805.24i	−0.213097	+	0.149643i
$527$	−5686.09	+	9848.60i	−0.470000	+	0.814064i
$528$	8684.30	−	1132.74i	0.715787	−	0.0933639i
$529$	6046.06	+	10472.1i	0.496922	+	0.860695i
$530$	−4696.06	−	2182.06i	−0.384876	−	0.178835i
$531$	1178.45	−	2442.22i	0.0963098	−	0.199592i
$532$	6035.88	−	5092.67i	0.491896	−	0.415028i
$533$	−6373.20	−	11038.7i	−0.517925	−	0.897072i
$534$	4685.04	+	3634.31i	0.379666	+	0.294517i
$535$	−18973.1	−	10954.1i	−1.53323	−	0.885210i
$536$	3000.58	+	790.931i	0.241801	+	0.0637370i
$537$	−6120.02	+	6590.68i	−0.491803	+	0.529625i
$538$	−106.764	−	1201.55i	−0.00855564	−	0.0962871i
$539$		−	5118.61i		−	0.409043i
$540$	12749.8	+	20791.8i	1.01605	+	1.65692i
$541$			16968.0i			1.34845i	0.738525	+	0.674226i	$0.235523\pi$
$541$			16968.0i			1.34845i	−0.738525	+	0.674226i	$0.764477\pi$
$542$	−12106.5	+	1075.73i	−0.959446	+	0.0852522i
$543$	6649.93	−	7161.34i	0.525554	−	0.565971i
$544$	−9219.82	+	4375.64i	−0.726648	+	0.344860i
$545$	−24832.5	−	14337.1i	−1.95176	−	1.12685i
$546$	−3045.05	+	3925.42i	−0.238674	+	0.307678i
$547$	1376.35	+	2383.90i	0.107584	+	0.186341i	0.914791	−	0.403928i	$-0.132355\pi$
$547$	1376.35	+	2383.90i	0.107584	+	0.186341i	−0.807207	+	0.590268i	$0.799022\pi$
$548$	−1369.13	+	1155.18i	−0.106727	+	0.0900492i
$549$	6007.39	+	8825.95i	0.467011	+	0.686125i
$550$	10898.5	−	23454.8i	0.844930	−	1.81839i
$551$	−3548.02	−	6145.35i	−0.274321	−	0.475137i
$552$	544.501	+	859.530i	0.0419846	+	0.0662754i
$553$	6382.98	−	11055.6i	0.490835	−	0.850151i
$554$	6187.12	+	8810.67i	0.474487	+	0.675685i
$555$	1773.99	+	5759.07i	0.135679	+	0.440467i
$556$	−862.304	+	2389.31i	−0.0657731	+	0.182247i
$557$	5552.85			0.422409			0.211204	−	0.977442i	$-0.432261\pi$
$557$	5552.85			0.422409			0.211204	+	0.977442i	$0.432261\pi$
$558$	−14411.8	−	5440.32i	−1.09337	−	0.412737i
$559$			5826.63i			0.440859i
$560$	5885.51	+	15901.3i	0.444121	+	1.19992i
$561$	1719.63	−	7520.72i	0.129417	−	0.565998i
$562$	−1110.28	−	1581.08i	−0.0833353	−	0.118672i
$563$	−5925.60	−	3421.15i	−0.443578	−	0.256100i	0.261536	−	0.965194i	$-0.415771\pi$
$563$	−5925.60	−	3421.15i	−0.443578	−	0.256100i	−0.705114	+	0.709094i	$0.749104\pi$
$564$	667.554	−	14030.6i	0.0498388	−	1.04751i
$565$	34473.3	−	19903.2i	2.56691	−	1.48200i
$566$	3254.05	+	1512.02i	0.241657	+	0.112288i
$567$	6957.29	−	5530.58i	0.515306	−	0.409634i
$568$	4557.49	+	16736.1i	0.336669	+	1.23632i
$569$	14809.1	−	8550.07i	1.09109	−	0.629943i	0.157226	−	0.987563i	$-0.449745\pi$
$569$	14809.1	−	8550.07i	1.09109	−	0.629943i	0.933867	+	0.357620i	$0.116412\pi$
$570$	9770.14	+	23943.0i	0.717941	+	1.75941i
$571$	−3909.64	+	6771.70i	−0.286539	+	0.496299i	−0.972981	−	0.230885i	$-0.925838\pi$
$571$	−3909.64	+	6771.70i	−0.286539	+	0.496299i	0.686443	+	0.727184i	$0.259171\pi$
$572$	−5749.94	+	1029.96i	−0.420309	+	0.0752881i
$573$	4548.61	−	19893.1i	0.331625	−	1.45034i
$574$	1403.06	+	15790.3i	0.102025	+	1.14822i
$575$	3004.77			0.217927
$576$	−7871.20	−	11364.3i	−0.569386	−	0.822070i
$577$	−15947.8			−1.15063			−0.575317	−	0.817931i	$-0.695121\pi$
$577$	−15947.8			−1.15063			−0.575317	+	0.817931i	$0.695121\pi$
$578$	−434.220	−	4886.80i	−0.0312477	−	0.351668i
$579$	12229.3	−	3767.02i	0.877774	−	0.270384i
$580$	14996.6	−	2686.27i	1.07362	−	0.192313i
$581$	−7984.07	+	13828.8i	−0.570112	+	0.987463i
$582$	872.788	+	119.583i	0.0621619	+	0.00851700i
$583$	−1921.48	+	1109.37i	−0.136500	+	0.0788082i
$584$	2761.28	+	10140.0i	0.195655	+	0.718488i
$585$	−9153.54	−	13448.2i	−0.646927	−	0.950454i
$586$	−12886.8	−	5987.93i	−0.908443	−	0.422115i
$587$	−13089.6	+	7557.29i	−0.920385	+	0.531384i	−0.883758	−	0.467945i	$-0.844995\pi$
$587$	−13089.6	+	7557.29i	−0.920385	+	0.531384i	−0.0366271	+	0.999329i	$0.511661\pi$
$588$	−7181.20	+	3702.68i	−0.503652	+	0.259687i
$589$	−14144.7	−	8166.43i	−0.989510	−	0.571294i
$590$	3547.50	+	5051.75i	0.247539	+	0.352504i
$591$	−10172.5	−	9446.04i	−0.708020	−	0.657459i
$592$	−1185.59	−	3203.21i	−0.0823100	−	0.222383i
$593$		−	12320.9i		−	0.853216i	−0.904437	−	0.426608i	$-0.859708\pi$
$593$		−	12320.9i		−	0.853216i	0.904437	−	0.426608i	$-0.140292\pi$
$594$	10430.1	+	648.992i	0.720457	+	0.0448290i
$595$	14936.2			1.02912
$596$	4405.23	−	12206.2i	0.302760	−	0.838900i
$597$	1900.40	−	2046.55i	0.130282	−	0.140301i
$598$	−390.016	−	555.395i	−0.0266704	−	0.0379796i
$599$	−10407.9	+	18027.0i	−0.709942	+	1.22965i	0.254937	+	0.966958i	$0.417945\pi$
$599$	−10407.9	+	18027.0i	−0.709942	+	1.22965i	−0.964878	+	0.262697i	$0.915388\pi$
$600$	−40789.8	+	1676.60i	−2.77539	+	0.114078i
$601$	−10608.7	−	18374.8i	−0.720031	−	1.24713i	−0.960987	−	0.276595i	$-0.910794\pi$
$601$	−10608.7	−	18374.8i	−0.720031	−	1.24713i	0.240955	−	0.970536i	$-0.422539\pi$
$602$	3053.60	−	6571.73i	0.206737	−	0.444923i
$603$	3334.78	+	1609.14i	0.225212	+	0.108672i
$604$	−5016.73	+	4232.78i	−0.337960	+	0.285148i
$605$	6926.17	+	11996.5i	0.465436	+	0.806159i
$606$	−19829.3	−	2716.88i	−1.32923	−	0.182121i
$607$	22006.3	+	12705.3i	1.47151	+	0.849578i	0.999488	−	0.0320069i	$-0.0101899\pi$
$607$	22006.3	+	12705.3i	1.47151	+	0.849578i	0.472025	+	0.881585i	$0.343523\pi$
$608$	−6284.35	−	13241.6i	−0.419184	−	0.883254i
$609$	−1634.36	−	5305.78i	−0.108748	−	0.353040i
$610$	−24208.6	+	2151.07i	−1.60685	+	0.142778i
$611$			9368.95i			0.620339i
$612$	−11795.2	+	3027.74i	−0.779072	+	0.199982i
$613$		−	15189.6i		−	1.00082i	−0.865788	−	0.500411i	$-0.833182\pi$
$613$		−	15189.6i		−	1.00082i	0.865788	−	0.500411i	$-0.166818\pi$
$614$	−850.214	−	9568.50i	−0.0558825	−	0.628914i
$615$	−50603.3	−	11570.6i	−3.31792	−	0.758651i
$616$	7025.00	+	1851.74i	0.459489	+	0.121118i
$617$	6391.51	+	3690.14i	0.417038	+	0.240777i	0.693809	−	0.720159i	$-0.255931\pi$
$617$	6391.51	+	3690.14i	0.417038	+	0.240777i	−0.276771	+	0.960936i	$0.589264\pi$
$618$	−13805.8	+	5633.56i	−0.898625	+	0.366691i
$619$	13126.9	+	22736.5i	0.852368	+	1.47634i	0.879066	+	0.476701i	$0.158168\pi$
$619$	13126.9	+	22736.5i	0.852368	+	1.47634i	−0.0266977	+	0.999644i	$0.508499\pi$
$620$	26801.5	−	22613.3i	1.73609	−	1.46480i
$621$	442.244	+	1130.70i	0.0285775	+	0.0730648i
$622$	13273.7	+	6167.73i	0.855671	+	0.397594i
$623$	2459.32	+	4259.67i	0.158155	+	0.273933i
$624$	5604.36	+	7321.86i	0.359541	+	0.469726i
$625$	−30766.3	+	53288.7i	−1.96904	+	3.41048i
$626$	3499.55	−	2457.49i	0.223435	−	0.156903i
$627$	10801.3	+	2469.75i	0.687981	+	0.157309i
$628$	3792.29	+	1368.64i	0.240969	+	0.0869661i
$629$	−3008.79			−0.190729
$630$	3276.17	+	19965.1i	0.207184	+	1.26258i
$631$		−	15335.4i		−	0.967498i	−0.875207	−	0.483749i	$-0.839275\pi$
$631$		−	15335.4i		−	0.967498i	0.875207	−	0.483749i	$-0.160725\pi$
$632$	−16821.8	−	16685.4i	−1.05876	−	1.05017i
$633$	596.173	−	183.641i	0.0374340	−	0.0115309i
$634$	−11671.5	+	8196.08i	−0.731126	+	0.513420i
$635$	266.631	+	153.940i	0.0166629	+	0.00962032i
$636$	2946.34	+	1893.26i	0.183695	+	0.118039i
$637$	4667.04	−	2694.52i	0.290290	−	0.167599i
$638$	2750.77	−	5919.99i	0.170696	−	0.367358i
$639$	1530.67	+	20640.7i	0.0947613	+	1.27783i
$640$	31322.0	−	3040.24i	1.93455	−	0.187775i
$641$	22159.2	−	12793.6i	1.36542	−	0.788328i	0.375085	−	0.926991i	$-0.377614\pi$
$641$	22159.2	−	12793.6i	1.36542	−	0.788328i	0.990340	+	0.138663i	$0.0442803\pi$
$642$	11707.5	+	9081.85i	0.719719	+	0.558306i
$643$	−9502.96	+	16459.6i	−0.582831	+	1.00949i	0.412311	+	0.911043i	$0.364722\pi$
$643$	−9502.96	+	16459.6i	−0.582831	+	1.00949i	−0.995142	+	0.0984496i	$0.968612\pi$
$644$	148.820	+	830.816i	0.00910611	+	0.0508365i
$645$	17388.2	+	16146.4i	1.06149	+	0.985683i
$646$	−12860.9	+	1142.76i	−0.783289	+	0.0695996i
$647$	19485.5			1.18401			0.592003	−	0.805935i	$-0.298337\pi$
$647$	19485.5			1.18401			0.592003	+	0.805935i	$0.298337\pi$
$648$	−6634.37	−	15102.4i	−0.402195	−	0.915554i
$649$	2644.91			0.159972
$650$	27122.7	−	2410.00i	1.63668	−	0.145428i
$651$	−9363.92	−	8695.23i	−0.563750	−	0.523491i
$652$	−19660.8	+	3521.74i	−1.18094	+	0.211537i
$653$	−7917.43	+	13713.4i	−0.474476	+	0.821817i	−0.999573	−	0.0292257i	$-0.990696\pi$
$653$	−7917.43	+	13713.4i	−0.474476	+	0.821817i	0.525097	+	0.851043i	$0.324029\pi$
$654$	15323.2	+	11886.6i	0.916183	+	0.710708i
$655$	−18338.4	+	10587.7i	−1.09396	+	0.631595i
$656$	29002.3	+	4951.80i	1.72614	+	0.294719i
$657$	927.402	+	12505.8i	0.0550706	+	0.742613i
$658$	4910.04	−	10567.0i	0.290902	−	0.626057i
$659$	−11409.9	+	6587.49i	−0.674455	+	0.389397i	−0.797762	−	0.602972i	$-0.793983\pi$
$659$	−11409.9	+	6587.49i	−0.674455	+	0.389397i	0.123308	+	0.992368i	$0.460650\pi$
$660$	−12860.2	+	20013.4i	−0.758460	+	1.18034i
$661$	3627.99	+	2094.62i	0.213483	+	0.123255i	0.602929	−	0.797795i	$-0.294000\pi$
$661$	3627.99	+	2094.62i	0.213483	+	0.123255i	−0.389446	+	0.921049i	$0.627333\pi$
$662$	14920.8	−	10477.8i	0.876002	−	0.615155i
$663$	7762.47	−	2391.10i	0.454705	−	0.140064i
$664$	21041.3	+	20870.8i	1.22976	+	1.21979i
$665$			21451.5i			1.25091i
$666$	−659.960	−	4021.82i	−0.0383978	−	0.233998i
$667$	758.405			0.0440263
$668$	−3853.14	+	10676.5i	−0.223178	+	0.618390i
$669$	16584.8	+	3792.16i	0.958455	+	0.219153i
$670$	−6898.02	+	4844.00i	−0.397752	+	0.279314i
$671$	−5206.77	+	9018.39i	−0.299560	+	0.518854i
$672$	−2483.81	−	11195.3i	−0.142582	−	0.642659i
$673$	−4599.36	−	7966.32i	−0.263436	−	0.456284i	0.703717	−	0.710481i	$-0.251522\pi$
$673$	−4599.36	−	7966.32i	−0.263436	−	0.456284i	−0.967153	+	0.254196i	$0.918189\pi$
$674$	−11020.9	−	5120.95i	−0.629836	−	0.292658i
$675$	−48160.6	−	7316.49i	−2.74623	−	0.417203i
$676$	7368.17	+	8732.82i	0.419217	+	0.496860i
$677$	−17266.4	−	29906.2i	−0.980207	−	1.69777i	−0.661555	−	0.749897i	$-0.730103\pi$
$677$	−17266.4	−	29906.2i	−0.980207	−	1.69777i	−0.318652	−	0.947872i	$-0.603230\pi$
$678$	−24926.6	+	10171.5i	−1.41195	+	0.576157i
$679$	632.867	+	365.386i	0.0357691	+	0.0206513i
$680$	7065.78	−	26805.7i	0.398471	−	1.51169i
$681$	3616.08	+	826.826i	0.203478	+	0.0465258i
$682$	−1329.82	−	14966.1i	−0.0746651	−	0.840298i
$683$		−	19300.4i		−	1.08127i	−0.841256	−	0.540637i	$-0.818183\pi$
$683$		−	19300.4i		−	1.08127i	0.841256	−	0.540637i	$-0.181817\pi$
$684$	−4348.48	−	16940.4i	−0.243082	−	0.946976i
$685$		−	4865.90i		−	0.271411i
$686$	−18457.3	+	1640.03i	−1.02726	+	0.0912780i
$687$	3552.37	+	11532.4i	0.197280	+	0.640450i
$688$	−10349.6	−	8589.08i	−0.573509	−	0.475953i
$689$	−2022.99	−	1167.97i	−0.111857	−	0.0645810i
$690$	−2738.23	−	375.174i	−0.151076	−	0.0206994i
$691$	3581.32	+	6203.02i	0.197163	+	0.341496i	0.947607	−	0.319437i	$-0.103494\pi$
$691$	3581.32	+	6203.02i	0.197163	+	0.341496i	−0.750444	+	0.660934i	$0.770161\pi$
$692$	3300.73	+	3912.06i	0.181322	+	0.214905i
$693$	7807.44	+	3767.34i	0.427965	+	0.206507i
$694$	−8717.32	+	18760.7i	−0.476808	+	1.02615i
$695$	−3449.93	−	5975.45i	−0.188292	−	0.326132i
$696$	−10295.3	+	423.173i	−0.560695	+	0.0230465i
$697$	12959.0	−	22445.6i	0.704240	−	1.21978i
$698$	11348.8	+	16161.0i	0.615411	+	0.876365i
$699$	12616.9	−	13587.2i	0.682714	−	0.735217i
$700$	−31854.1	−	11496.2i	−1.71996	−	0.620736i
$701$	29692.1			1.59979			0.799897	−	0.600138i	$-0.204888\pi$
$701$	29692.1			1.59979			0.799897	+	0.600138i	$0.204888\pi$
$702$	4898.82	+	9851.56i	0.263382	+	0.529663i
$703$		−	4321.26i		−	0.231834i
$704$	6646.55	−	11731.6i	0.355826	−	0.628057i
$705$	27959.3	+	25962.7i	1.49363	+	1.38697i
$706$	−20508.4	−	29204.6i	−1.09326	−	1.55684i
$707$	−14378.4	−	8301.39i	−0.764861	−	0.441593i
$708$	−1913.26	−	3710.69i	−0.101561	−	0.196972i
$709$	−12389.7	+	7153.20i	−0.656284	+	0.378906i	−0.790860	−	0.611998i	$-0.790366\pi$
$709$	−12389.7	+	7153.20i	−0.656284	+	0.378906i	0.134576	+	0.990903i	$0.457033\pi$
$710$	−42728.5	−	19854.1i	−2.25855	−	1.04945i
$711$	−15908.0	−	23371.7i	−0.839094	−	1.23278i
$712$	8808.16	−	2398.60i	0.463623	−	0.126252i
$713$	1511.74	−	872.805i	0.0794042	−	0.0458440i
$714$	−10008.2	−	1371.26i	−0.524578	−	0.0718741i
$715$	7933.63	−	13741.4i	0.414966	−	0.718743i
$716$	2441.51	+	13630.2i	0.127435	+	0.711431i
$717$	−6676.61	+	2056.62i	−0.347758	+	0.107121i
$718$	−2505.94	−	28202.4i	−0.130252	−	1.46588i
$719$	34830.8			1.80663			0.903316	−	0.428977i	$-0.141126\pi$
$719$	34830.8			1.80663			0.903316	+	0.428977i	$0.141126\pi$
$720$	37380.8	+	3565.10i	1.93486	+	0.184533i
$721$	−12369.2			−0.638907
$722$	75.8024	+	853.097i	0.00390730	+	0.0439737i
$723$	1962.21	−	8581.65i	0.100934	−	0.441431i
$724$	−2652.92	−	14810.4i	−0.136181	−	0.760254i
$725$	−15214.6	+	26352.5i	−0.779389	+	1.34994i
$726$	−3539.62	−	8674.30i	−0.180947	−	0.443435i
$727$	28755.6	−	16602.0i	1.46697	−	0.846954i	0.467651	−	0.883913i	$-0.345100\pi$
$727$	28755.6	−	16602.0i	1.46697	−	0.846954i	0.999317	+	0.0369588i	$0.0117670\pi$
$728$	2009.69	+	7380.03i	0.102313	+	0.375717i
$729$	−4335.11	−	19199.7i	−0.220247	−	0.975444i
$730$	−25888.3	−	12029.2i	−1.31256	−	0.609891i
$731$	−10260.3	+	5923.80i	−0.519141	+	0.299726i
$732$	16418.9	+	781.183i	0.829042	+	0.0394445i
$733$	14167.9	+	8179.82i	0.713918	+	0.412181i	0.812510	−	0.582947i	$-0.198100\pi$
$733$	14167.9	+	8179.82i	0.713918	+	0.412181i	−0.0985919	+	0.995128i	$0.531434\pi$
$734$	14142.4	+	20139.3i	0.711179	+	1.01274i
$735$	4891.91	−	21394.5i	0.245498	−	1.07367i
$736$	1561.45	+	125.945i	0.0782008	+	0.00630759i
$737$			3611.55i			0.180506i
$738$	32845.3	+	12398.8i	1.63828	+	0.618438i
$739$	8406.84			0.418472			0.209236	−	0.977865i	$-0.432902\pi$
$739$	8406.84			0.418472			0.209236	+	0.977865i	$0.432902\pi$
$740$	8726.85	+	3149.53i	0.433521	+	0.156458i
$741$	3434.13	+	11148.6i	0.170251	+	0.552702i
$742$	1669.58	+	2377.53i	0.0826039	+	0.117631i
$743$	17253.8	−	29884.4i	0.851924	−	1.47558i	−0.0275453	−	0.999621i	$-0.508769\pi$
$743$	17253.8	−	29884.4i	0.851924	−	1.47558i	0.879469	−	0.475955i	$-0.157898\pi$
$744$	−20034.9	+	12691.8i	−0.987250	+	0.625410i
$745$	17624.5	+	30526.6i	0.866729	+	1.50122i
$746$	−7370.06	+	15861.3i	−0.361712	+	0.778449i
$747$	19898.3	+	29234.2i	0.974619	+	1.43189i
$748$	−7659.51	−	9078.13i	−0.374411	−	0.443756i
$749$	6145.65	+	10644.6i	0.299809	+	0.519285i
$750$	43499.7	−	56076.0i	2.11785	−	2.73014i
$751$	25214.0	+	14557.3i	1.22513	+	0.707329i	0.966007	−	0.258515i	$-0.0832332\pi$
$751$	25214.0	+	14557.3i	1.22513	+	0.707329i	0.259123	+	0.965844i	$0.416567\pi$
$752$	−16641.6	−	13810.8i	−0.806992	−	0.669720i
$753$	−10285.2	+	11076.2i	−0.497761	+	0.536041i
$754$	6845.77	−	608.285i	0.330647	−	0.0293799i
$755$		−	17829.5i		−	0.859446i
$756$	−362.295	−	13678.7i	−0.0174293	−	0.658055i
$757$		−	22457.3i		−	1.07824i	−0.842230	−	0.539119i	$-0.818757\pi$
$757$		−	22457.3i		−	1.07824i	0.842230	−	0.539119i	$-0.181243\pi$
$758$	2937.54	+	33059.7i	0.140760	+	1.58414i
$759$	−805.805	+	867.774i	−0.0385361	+	0.0414996i
$760$	38498.6	+	10148.0i	1.83749	+	0.484349i
$761$	−15920.4	−	9191.63i	−0.758361	−	0.437840i	0.0703459	−	0.997523i	$-0.477590\pi$
$761$	−15920.4	−	9191.63i	−0.758361	−	0.437840i	−0.828707	+	0.559683i	$0.810923\pi$
$762$	−164.528	−	127.628i	−0.00782179	−	0.00606758i
$763$	8043.61	+	13931.9i	0.381649	+	0.661036i
$764$	−20260.2	−	24012.6i	−0.959411	−	1.13710i
$765$	14375.3	−	29791.3i	0.679397	−	1.40798i
$766$	11509.7	+	5348.08i	0.542902	+	0.252264i
$767$	1392.32	+	2411.57i	0.0655461	+	0.113529i
$768$	−21266.9	−	838.444i	−0.999224	−	0.0393942i
$769$	10853.9	−	18799.5i	0.508975	−	0.881570i	−0.490971	−	0.871176i	$-0.663358\pi$
$769$	10853.9	−	18799.5i	0.508975	−	0.881570i	0.999946	−	0.0103945i	$-0.00330874\pi$
$770$	−16149.7	+	11340.8i	−0.755838	+	0.530773i
$771$	7388.42	+	23985.8i	0.345120	+	1.12040i
$772$	6687.96	−	18531.3i	0.311794	−	0.863932i
$773$	−38982.8			−1.81386			−0.906930	−	0.421281i	$-0.861581\pi$
$773$	−38982.8			−1.81386			−0.906930	+	0.421281i	$0.861581\pi$
$774$	−10168.8	−	12415.5i	−0.472237	−	0.576573i
$775$			70038.6i			3.24627i
$776$	955.138	−	962.943i	0.0441849	−	0.0445459i
$777$	753.594	−	3295.81i	0.0347941	−	0.152170i
$778$	−12114.6	+	8507.25i	−0.558264	+	0.392030i
$779$	32236.6	+	18611.8i	1.48266	+	0.856017i
$780$	−25017.7	−	1190.30i	−1.14843	−	0.0546405i
$781$	−17483.1	+	10093.9i	−0.801018	+	0.462468i
$782$	581.495	−	1251.45i	0.0265911	−	0.0572273i
$783$	−12155.7	−	1846.68i	−0.554803	−	0.0842848i
$784$	−2093.57	+	12261.9i	−0.0953703	+	0.558576i
$785$	−9484.18	+	5475.69i	−0.431216	+	0.248963i
$786$	13260.0	−	5410.83i	0.601740	−	0.245545i
$787$	19400.2	−	33602.1i	0.878706	−	1.52196i	0.0259442	−	0.999663i	$-0.491741\pi$
$787$	19400.2	−	33602.1i	0.878706	−	1.52196i	0.852762	−	0.522300i	$-0.174926\pi$
$788$	−21037.7	+	3768.39i	−0.951064	+	0.170360i
$789$	−1286.33	+	5625.68i	−0.0580411	+	0.253840i
$790$	64106.1	−	5696.19i	2.88708	−	0.256533i
$791$	−22332.8			−1.00387
$792$	10454.6	−	12229.6i	0.469050	−	0.548689i
$793$	−10963.7			−0.490961
$794$	28386.7	−	2522.32i	1.26877	−	0.112738i
$795$	−9091.53	+	2800.50i	−0.405589	+	0.124935i
$796$	−758.145	−	4232.48i	−0.0337585	−	0.188463i
$797$	−7370.19	+	12765.5i	−0.327560	+	0.567351i	−0.982027	−	0.188740i	$-0.939560\pi$
$797$	−7370.19	+	12765.5i	−0.327560	+	0.567351i	0.654467	+	0.756091i	$0.272893\pi$
$798$	1969.42	−	14373.9i	0.0873643	−	0.637634i
$799$	−16498.1	+	9525.19i	−0.730489	+	0.421748i
$800$	−35701.0	+	51729.5i	−1.57778	+	2.28614i
$801$	10863.2	−	805.590i	0.479190	−	0.0355357i
$802$	6660.63	−	14334.5i	0.293261	−	0.631133i
$803$	−10592.6	+	6115.67i	−0.465512	+	0.268764i
$804$	5066.84	−	2612.51i	0.222256	−	0.114597i
$805$	−1985.52	−	1146.34i	−0.0869321	−	0.0501903i
$806$	12945.8	−	9090.91i	0.565751	−	0.397288i
$807$	−1623.92	−	1507.95i	−0.0708359	−	0.0657774i
$808$	−21700.3	+	21877.6i	−0.944817	+	0.952538i
$809$			41957.2i			1.82341i	0.410850	+	0.911703i	$0.365232\pi$
$809$			41957.2i			1.82341i	−0.410850	+	0.911703i	$0.634768\pi$
$810$	42974.9	+	12680.8i	1.86418	+	0.550070i
$811$	−33724.2			−1.46020			−0.730098	−	0.683343i	$-0.760525\pi$
$811$	−33724.2			−1.46020			−0.730098	+	0.683343i	$0.760525\pi$
$812$	−8039.97	−	2901.64i	−0.347473	−	0.125403i
$813$	−15193.8	+	16362.2i	−0.655435	+	0.705840i
$814$	3253.24	−	2284.53i	0.140081	−	0.0983694i
$815$	27127.5	−	46986.2i	1.16593	−	2.01945i
$816$	−7195.51	+	17312.9i	−0.308693	+	0.742735i
$817$	−8507.83	−	14736.0i	−0.364322	−	0.631025i
$818$	12232.8	+	5684.07i	0.522874	+	0.242957i
$819$	674.974	+	9101.84i	0.0287979	+	0.388332i
$820$	−61082.4	+	51537.2i	−2.60133	+	2.19483i
$821$	349.128	+	604.707i	0.0148412	+	0.0257058i	0.873351	−	0.487092i	$-0.161942\pi$
$821$	349.128	+	604.707i	0.0148412	+	0.0257058i	−0.858509	+	0.512798i	$0.828609\pi$
$822$	−446.728	+	3260.48i	−0.0189555	+	0.138348i
$823$	−17635.1	−	10181.6i	−0.746928	−	0.431239i	0.0776551	−	0.996980i	$-0.475257\pi$
$823$	−17635.1	−	10181.6i	−0.746928	−	0.431239i	−0.824583	+	0.565741i	$0.808590\pi$
$824$	−5851.41	+	22198.7i	−0.247383	+	0.938505i
$825$	−13987.3	−	45408.2i	−0.590271	−	1.91626i
$826$	−306.520	−	3449.64i	−0.0129118	−	0.145313i
$827$		−	10885.2i		−	0.457697i	−0.973462	−	0.228849i	$-0.926504\pi$
$827$		−	10885.2i		−	0.457697i	0.973462	−	0.228849i	$-0.0734961\pi$
$828$	1800.35	+	502.782i	0.0755634	+	0.0211025i
$829$		−	35477.5i		−	1.48635i	−0.669096	−	0.743176i	$-0.733319\pi$
$829$		−	35477.5i		−	1.48635i	0.669096	−	0.743176i	$-0.266681\pi$
$830$	−80186.4	+	7125.01i	−3.35339	+	0.297967i
$831$	19280.9	+	4408.63i	0.804871	+	0.184036i
$832$	14195.5	−	115.528i	0.591515	−	0.00481395i
$833$	9489.74	+	5478.91i	0.394718	+	0.227891i
$834$	1763.09	+	4320.68i	0.0732022	+	0.179392i
$835$	−15415.8	−	26700.9i	−0.638904	−	1.10661i
$836$	13038.1	−	11000.7i	0.539393	−	0.455104i
$837$	−26355.5	+	10308.3i	−1.08839	+	0.425696i
$838$	7785.35	−	16755.0i	0.320931	−	0.690683i
$839$	7257.77	+	12570.8i	0.298648	+	0.517274i	0.975827	−	0.218544i	$-0.0701309\pi$
$839$	7257.77	+	12570.8i	0.298648	+	0.517274i	−0.677179	+	0.735819i	$0.736798\pi$
$840$	27593.0	+	14453.7i	1.13339	+	0.593689i
$841$	8354.33	−	14470.1i	0.342545	−	0.593306i
$842$	−7336.87	−	10447.9i	−0.300291	−	0.427625i
$843$	−3459.97	−	791.131i	−0.141362	−	0.0323227i
$844$	326.036	−	903.394i	0.0132969	−	0.0368437i
$845$	−31036.5			−1.26354
$846$	−16351.0	−	19963.6i	−0.664491	−	0.811303i
$847$		−	7771.66i		−	0.315274i
$848$	5056.72	−	1871.63i	0.204774	−	0.0757924i
$849$	6299.81	−	1940.55i	0.254663	−	0.0784447i
$850$	31818.9	+	45311.1i	1.28397	+	1.82842i
$851$	399.968	+	230.922i	0.0161113	+	0.00930188i
$852$	26808.1	+	17226.4i	1.07797	+	0.692683i
$853$	4907.37	−	2833.27i	0.196981	−	0.113727i	−0.398265	−	0.917270i	$-0.630388\pi$
$853$	4907.37	−	2833.27i	0.196981	−	0.113727i	0.595247	+	0.803543i	$0.297054\pi$
$854$	12365.7	+	5745.82i	0.495487	+	0.230232i
$855$	42786.6	+	20645.9i	1.71143	+	0.825820i
$856$	22010.9	−	5993.90i	0.878875	−	0.239331i
$857$	−15474.3	+	8934.09i	−0.616793	+	0.356106i	−0.775619	−	0.631201i	$-0.782562\pi$
$857$	−15474.3	+	8934.09i	−0.616793	+	0.356106i	0.158826	+	0.987307i	$0.449229\pi$
$858$	−6577.62	+	8479.30i	−0.261721	+	0.337388i
$859$	9725.78	−	16845.5i	0.386309	−	0.669107i	−0.605641	−	0.795738i	$-0.707083\pi$
$859$	9725.78	−	16845.5i	0.386309	−	0.669107i	0.991950	+	0.126631i	$0.0404165\pi$
$860$	35960.5	−	6441.44i	1.42586	−	0.255408i
$861$	21341.0	+	19817.0i	0.844713	+	0.784391i
$862$	154.427	+	1737.95i	0.00610184	+	0.0686715i
$863$	−15645.4			−0.617120			−0.308560	−	0.951205i	$-0.599847\pi$
$863$	−15645.4			−0.617120			−0.308560	+	0.951205i	$0.599847\pi$
$864$	−24720.3	−	5820.70i	−0.973381	−	0.229195i
$865$	−13903.5			−0.546511
$866$	524.545	+	5903.34i	0.0205829	+	0.231644i
$867$	−6604.61	−	6132.96i	−0.258713	−	0.240238i
$868$	−19365.6	+	3468.86i	−0.757270	+	0.135646i
$869$	13787.9	−	23881.3i	0.538230	−	0.932242i
$870$	17155.3	−	22115.2i	0.668529	−	0.861809i
$871$	−3292.93	+	1901.17i	−0.128102	+	0.0739596i
$872$	28808.5	−	7845.00i	1.11878	−	0.304662i
$873$	1337.89	−	910.634i	0.0518679	−	0.0353039i
$874$	1797.35	+	835.150i	0.0695608	+	0.0323219i
$875$	50984.8	−	29436.1i	1.96983	−	1.13728i
$876$	16242.5	+	10437.1i	0.626464	+	0.402553i
$877$	−33993.4	−	19626.1i	−1.30886	−	0.755673i	−0.326958	−	0.945039i	$-0.606023\pi$
$877$	−33993.4	−	19626.1i	−1.30886	−	0.755673i	−0.981907	+	0.189366i	$0.939357\pi$
$878$	−15785.3	−	22478.8i	−0.606753	−	0.864037i
$879$	−24948.6	+	7685.02i	−0.957334	+	0.294891i
$880$	12713.3	+	34348.5i	0.487006	+	1.31578i
$881$			4220.62i			0.161403i	0.996738	+	0.0807017i	$0.0257161\pi$
$881$			4220.62i			0.161403i	−0.996738	+	0.0807017i	$0.974284\pi$
$882$	−5242.09	+	13886.6i	−0.200125	+	0.530144i
$883$	−48035.9			−1.83073			−0.915365	−	0.402624i	$-0.868098\pi$
$883$	−48035.9			−1.83073			−0.915365	+	0.402624i	$0.868098\pi$
$884$	4245.15	−	11762.7i	0.161516	−	0.447535i
$885$	11055.1	+	2527.77i	0.419901	+	0.0960113i
$886$	−14349.9	−	20434.7i	−0.544123	−	0.774849i
$887$	−2102.75	+	3642.06i	−0.0795978	+	0.137867i	−0.903076	−	0.429480i	$-0.858697\pi$
$887$	−2102.75	+	3642.06i	−0.0795978	+	0.137867i	0.823479	+	0.567347i	$0.192030\pi$
$888$	−5558.41	−	2911.59i	−0.210054	−	0.110030i
$889$	−86.3657	−	149.590i	−0.00325828	−	0.00564351i
$890$	−10449.2	+	22487.9i	−0.393548	+	0.846963i
$891$	15028.5	−	11946.6i	0.565064	−	0.449188i
$892$	20019.2	−	16890.9i	0.751450	−	0.634023i
$893$	−13680.2	−	23694.8i	−0.512643	−	0.887923i
$894$	−9007.02	−	22072.9i	−0.336957	−	0.825759i
$895$	−32574.0	−	18806.6i	−1.21657	−	0.702387i
$896$	−16071.3	−	7309.22i	−0.599224	−	0.272527i
$897$	−1215.41	−	277.906i	−0.0452411	−	0.0103445i
$898$	225.885	−	20.0711i	0.00839406	−	0.000745859i
$899$			17677.7i			0.655823i
$900$	−53587.8	+	52470.8i	−1.98473	+	1.94336i
$901$		−	4749.81i		−	0.175626i
$902$	3030.75	+	34108.7i	0.111877	+	1.25909i
$903$	−3919.04	−	12722.8i	−0.144427	−	0.468868i
$904$	−10564.8	+	40080.2i	−0.388696	+	1.47461i
$905$	35394.5	+	20435.0i	1.30006	+	0.750589i
$906$	−1636.89	+	11946.9i	−0.0600242	+	0.438091i
$907$	−21359.3	−	36995.5i	−0.781946	−	1.35437i	−0.930806	−	0.365513i	$-0.880894\pi$
$907$	−21359.3	−	36995.5i	−0.781946	−	1.35437i	0.148860	−	0.988858i	$-0.452440\pi$
$908$	4364.91	−	3682.82i	0.159531	−	0.134602i
$909$	−30396.2	+	20689.1i	−1.10911	+	0.754913i
$910$	−18841.8	−	8754.98i	−0.686373	−	0.318928i
$911$	−17187.2	−	29769.1i	−0.625069	−	1.08265i	−0.988528	−	0.151040i	$-0.951738\pi$
$911$	−17187.2	−	29769.1i	−0.625069	−	1.08265i	0.363459	−	0.931610i	$-0.381596\pi$
$912$	−24864.9	−	10334.3i	−0.902808	−	0.375221i
$913$	−17246.4	+	29871.7i	−0.625162	+	1.08281i
$914$	−8637.25	+	6065.34i	−0.312576	+	0.219501i
$915$	−30382.0	+	32718.5i	−1.09770	+	1.18212i
$916$	17475.3	+	6306.87i	0.630351	+	0.227494i
$917$	11880.1			0.427827
$918$	−12367.4	+	18642.4i	−0.444648	+	0.670250i
$919$		−	18530.2i		−	0.665132i	−0.943080	−	0.332566i	$-0.892086\pi$
$919$		−	18530.2i		−	0.665132i	0.943080	−	0.332566i	$-0.107914\pi$
$920$	−2996.59	+	3021.08i	−0.107385	+	0.108263i
$921$	−12932.0	−	12008.5i	−0.462676	−	0.429635i
$922$	29608.0	−	20791.6i	1.05758	−	0.742664i
$923$	−18406.8	−	10627.2i	−0.656410	−	0.378978i
$924$	11862.6	−	6116.43i	0.422348	−	0.217766i
$925$	−16047.8	+	9265.21i	−0.570431	+	0.329338i
$926$	14306.5	−	30789.3i	0.507711	−	1.09266i
$927$	−11904.6	+	24671.2i	−0.421790	+	0.874118i
$928$	−9010.93	+	13056.5i	−0.318748	+	0.461854i
$929$	23164.8	−	13374.2i	0.818097	−	0.472328i	−0.0316631	−	0.999499i	$-0.510080\pi$
$929$	23164.8	−	13374.2i	0.818097	−	0.472328i	0.849760	+	0.527170i	$0.176747\pi$
$930$	8744.96	−	63825.7i	0.308342	−	2.25046i
$931$	−7868.87	+	13629.3i	−0.277005	+	0.479787i
$932$	−5033.39	−	28099.8i	−0.176904	−	0.987597i
$933$	25697.8	−	7915.77i	0.901723	−	0.277761i
$934$	5392.10	−	479.118i	0.188903	−	0.0167850i
$935$	32263.7			1.12849
$936$	16654.2	+	3094.40i	0.581581	+	0.108059i
$937$	12325.5			0.429731			0.214866	−	0.976644i	$-0.431069\pi$
$937$	12325.5			0.429731			0.214866	+	0.976644i	$0.431069\pi$
$938$	4710.38	−	418.544i	0.163965	−	0.0145692i
$939$	1751.09	−	7658.29i	0.0608568	−	0.266154i
$940$	57822.8	−	10357.5i	2.00635	−	0.359389i
$941$	−2589.25	+	4484.71i	−0.0896993	+	0.155364i	−0.907384	−	0.420303i	$-0.861924\pi$
$941$	−2589.25	+	4484.71i	−0.0896993	+	0.155364i	0.817685	+	0.575666i	$0.195257\pi$
$942$	6857.74	−	2798.35i	0.237194	−	0.0967890i
$943$	−3445.35	+	1989.18i	−0.118978	+	0.0686919i
$944$	−6336.00	−	1081.80i	−0.218452	−	0.0372982i
$945$	29032.7	+	23208.2i	0.999400	+	0.798903i
$946$	6596.09	−	14195.6i	0.226699	−	0.487885i
$947$	−29005.0	+	16746.1i	−0.995287	+	0.574629i	−0.906850	−	0.421453i	$-0.861520\pi$
$947$	−29005.0	+	16746.1i	−0.995287	+	0.574629i	−0.0884365	+	0.996082i	$0.528187\pi$
$948$	−43478.3	−	2068.63i	−1.48957	−	0.0708712i
$949$	−11152.3	−	6438.76i	−0.381473	−	0.220244i
$950$	−65076.4	+	45698.6i	−2.22248	+	1.56069i
$951$	−5840.12	+	25541.5i	−0.199137	+	0.870913i
$952$	−10952.5	+	11042.0i	−0.372872	+	0.375919i
$953$			31313.4i			1.06437i	0.846629	+	0.532184i	$0.178628\pi$
$953$			31313.4i			1.06437i	−0.846629	+	0.532184i	$0.821372\pi$
$954$	6349.03	−	1041.84i	0.215469	−	0.0353573i
$955$	85341.0			2.89170
$956$	−3651.32	+	10117.2i	−0.123527	+	0.342274i
$957$	−3530.38	−	11461.0i	−0.119249	−	0.387129i
$958$	−11395.5	+	8002.27i	−0.384313	+	0.269877i
$959$	−1364.97	+	2364.20i	−0.0459618	+	0.0796081i
$960$	38993.0	−	42683.1i	1.31093	−	1.43499i
$961$	5448.80	+	9437.59i	0.182901	+	0.316793i
$962$	3795.54	+	1763.63i	0.127207	+	0.0591077i
$963$	27146.2	−	2013.11i	0.908385	−	0.0673639i
$964$	−8740.02	−	10358.8i	−0.292009	−	0.346092i
$965$	26757.4	+	46345.1i	0.892591	+	1.54601i
$966$	1225.19	+	950.409i	0.0408071	+	0.0316552i
$967$	26936.3	+	15551.7i	0.895774	+	0.517175i	0.875827	−	0.482626i	$-0.160317\pi$
$967$	26936.3	+	15551.7i	0.895774	+	0.517175i	0.0199473	+	0.999801i	$0.493650\pi$
$968$	−13947.6	−	3676.50i	−0.463114	−	0.122073i
$969$	−16140.5	+	17381.7i	−0.535095	+	0.576246i
$970$	326.072	+	3669.68i	0.0107933	+	0.121471i
$971$			13249.7i			0.437902i	0.975736	+	0.218951i	$0.0702635\pi$
$971$			13249.7i			0.437902i	−0.975736	+	0.218951i	$0.929737\pi$
$972$	−27631.8	−	12442.4i	−0.911822	−	0.410586i
$973$			3871.07i			0.127544i
$974$	56454.5	−	5016.30i	1.85721	−	0.165023i
$975$	34039.2	−	36656.9i	1.11808	−	1.20406i
$976$	16161.7	−	19474.3i	0.530043	−	0.638686i
$977$	−15255.7	−	8807.87i	−0.499562	−	0.288422i	0.228970	−	0.973433i	$-0.426464\pi$
$977$	−15255.7	−	8807.87i	−0.499562	−	0.288422i	−0.728533	+	0.685011i	$0.759797\pi$
$978$	−22490.9	+	28993.3i	−0.735357	+	0.947959i
$979$	5312.39	+	9201.33i	0.173427	+	0.300384i
$980$	−21789.4	−	25825.0i	−0.710241	−	0.841784i
$981$	35529.8	−	2634.81i	1.15635	−	0.0857524i
$982$	−16823.6	+	36206.4i	−0.546703	+	1.17657i
$983$	20245.4	+	35066.1i	0.656895	+	1.13778i	0.981415	+	0.191897i	$0.0614640\pi$
$983$	20245.4	+	35066.1i	0.656895	+	1.13778i	−0.324520	+	0.945879i	$0.605203\pi$
$984$	45660.7	−	28925.5i	1.47928	−	0.937104i
$985$	29027.4	−	50276.9i	0.938973	−	1.62635i
$986$	8031.08	+	11436.5i	0.259393	+	0.369384i
$987$	−6301.64	−	20457.6i	−0.203225	−	0.659750i
$988$	16893.7	+	6096.94i	0.543987	+	0.196325i
$989$	1818.59			0.0584708
$990$	7076.86	+	43126.7i	0.227189	+	1.38450i
$991$			3021.88i			0.0968650i	0.998826	+	0.0484325i	$0.0154226\pi$
$991$			3021.88i			0.0968650i	−0.998826	+	0.0484325i	$0.984577\pi$
$992$	−2935.66	+	36396.0i	−0.0939589	+	1.16489i
$993$	7465.99	−	32652.1i	0.238596	−	1.04349i
$994$	15191.1	+	21632.7i	0.484742	+	0.690288i
$995$	10115.0	+	5839.88i	0.322277	+	0.186067i
$996$	54384.3	+	2587.52i	1.73015	+	0.0823179i
$997$	−33345.3	+	19251.9i	−1.05923	+	0.611549i	−0.925220	−	0.379431i	$-0.876120\pi$
$997$	−33345.3	+	19251.9i	−1.05923	+	0.611549i	−0.134014	+	0.990979i	$0.542787\pi$
$998$	19381.6	+	9005.82i	0.614744	+	0.285645i
$999$	−5848.42	−	4675.13i	−0.185221	−	0.148063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.4.l.b.59.15	yes	64
3.2	odd	2		216.4.l.b.179.18		64
4.3	odd	2		288.4.p.b.239.24		64
8.3	odd	2	inner	72.4.l.b.59.26	yes	64
8.5	even	2		288.4.p.b.239.23		64
9.2	odd	6	inner	72.4.l.b.11.26	yes	64
9.7	even	3		216.4.l.b.35.7		64
12.11	even	2		864.4.p.b.719.1		64
24.5	odd	2		864.4.p.b.719.32		64
24.11	even	2		216.4.l.b.179.7		64
36.7	odd	6		864.4.p.b.143.32		64
36.11	even	6		288.4.p.b.47.23		64
72.11	even	6	inner	72.4.l.b.11.15	✓	64
72.29	odd	6		288.4.p.b.47.24		64
72.43	odd	6		216.4.l.b.35.18		64
72.61	even	6		864.4.p.b.143.1		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.15	✓	64	72.11	even	6	inner
72.4.l.b.11.26	yes	64	9.2	odd	6	inner
72.4.l.b.59.15	yes	64	1.1	even	1	trivial
72.4.l.b.59.26	yes	64	8.3	odd	2	inner
216.4.l.b.35.7		64	9.7	even	3
216.4.l.b.35.18		64	72.43	odd	6
216.4.l.b.179.7		64	24.11	even	2
216.4.l.b.179.18		64	3.2	odd	2
288.4.p.b.47.23		64	36.11	even	6
288.4.p.b.47.24		64	72.29	odd	6
288.4.p.b.239.23		64	8.5	even	2
288.4.p.b.239.24		64	4.3	odd	2
864.4.p.b.143.1		64	72.61	even	6
864.4.p.b.143.32		64	36.7	odd	6
864.4.p.b.719.1		64	12.11	even	2
864.4.p.b.719.32		64	24.5	odd	2

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.250335 - 2.81733i) q^{2} +(-3.80768 - 3.53576i) q^{3} +(-7.87466 + 1.41055i) q^{4} +(10.8653 - 18.8192i) q^{5} +(-9.00820 + 11.6126i) q^{6} +(-10.5583 + 6.09581i) q^{7} +(5.94529 + 21.8324i) q^{8} +(1.99678 + 26.9261i) q^{9} +(-55.7398 - 25.8999i) q^{10} +(-22.8069 + 13.1676i) q^{11} +(34.9715 + 22.4720i) q^{12} +(-24.0118 - 13.8632i) q^{13} +(19.8170 + 28.2201i) q^{14} +(-107.912 + 33.2404i) q^{15} +(60.0207 - 22.2153i) q^{16} -56.3777i q^{17} +(75.3597 - 12.3661i) q^{18} +80.9703 q^{19} +(-59.0149 + 163.521i) q^{20} +(61.7558 + 14.1206i) q^{21} +(42.8068 + 60.9583i) q^{22} +(-4.32694 + 7.49448i) q^{23} +(54.5564 - 104.152i) q^{24} +(-173.608 - 300.699i) q^{25} +(-33.0463 + 71.1197i) q^{26} +(87.6010 - 109.586i) q^{27} +(74.5443 - 62.8955i) q^{28} +(-43.8188 - 75.8963i) q^{29} +(120.663 + 295.701i) q^{30} +(-174.690 - 100.857i) q^{31} +(-77.6129 - 163.537i) q^{32} +(133.399 + 30.5020i) q^{33} +(-158.834 + 14.1133i) q^{34} +264.931i q^{35} +(-53.7046 - 209.217i) q^{36} -53.3684i q^{37} +(-20.2697 - 228.120i) q^{38} +(42.4122 + 137.687i) q^{39} +(475.466 + 125.329i) q^{40} +(398.128 + 229.859i) q^{41} +(24.3227 - 177.521i) q^{42} +(-105.073 - 181.993i) q^{43} +(161.023 - 135.861i) q^{44} +(528.423 + 254.981i) q^{45} +(22.1976 + 10.3143i) q^{46} +(-168.953 - 292.635i) q^{47} +(-307.087 - 127.630i) q^{48} +(-97.1821 + 168.324i) q^{49} +(-803.706 + 564.387i) q^{50} +(-199.338 + 214.668i) q^{51} +(208.640 + 75.2984i) q^{52} +84.2497 q^{53} +(-330.669 - 219.368i) q^{54} +572.278i q^{55} +(-195.858 - 194.271i) q^{56} +(-308.309 - 286.292i) q^{57} +(-202.855 + 142.451i) q^{58} +(-86.9772 - 50.2163i) q^{59} +(802.881 - 413.972i) q^{60} +(342.447 - 197.712i) q^{61} +(-240.416 + 517.406i) q^{62} +(-185.219 - 272.120i) q^{63} +(-441.307 + 259.600i) q^{64} +(-521.791 + 301.256i) q^{65} +(52.5396 - 383.464i) q^{66} +(68.5689 - 118.765i) q^{67} +(79.5237 + 443.956i) q^{68} +(42.9743 - 13.2375i) q^{69} +(746.397 - 66.3215i) q^{70} +766.570 q^{71} +(-575.989 + 203.678i) q^{72} +464.449 q^{73} +(-150.356 + 13.3600i) q^{74} +(-402.154 + 1758.80i) q^{75} +(-637.614 + 114.213i) q^{76} +(160.534 - 278.054i) q^{77} +(377.292 - 153.957i) q^{78} +(-906.822 + 523.554i) q^{79} +(234.068 - 1370.92i) q^{80} +(-721.026 + 107.531i) q^{81} +(547.924 - 1179.20i) q^{82} +(1134.29 - 654.881i) q^{83} +(-506.224 - 24.0853i) q^{84} +(-1060.98 - 612.560i) q^{85} +(-486.429 + 341.585i) q^{86} +(-101.504 + 443.921i) q^{87} +(-423.074 - 419.645i) q^{88} -403.445i q^{89} +(586.083 - 1552.57i) q^{90} +338.031 q^{91} +(23.5018 - 65.1199i) q^{92} +(308.555 + 1001.69i) q^{93} +(-782.154 + 549.253i) q^{94} +(879.765 - 1523.80i) q^{95} +(-282.702 + 897.115i) q^{96} +(-29.9703 - 51.9100i) q^{97} +(498.553 + 231.656i) q^{98} +(-400.092 - 587.808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9} + 12 q^{10} + 48 q^{11} + 318 q^{12} + 72 q^{14} + 127 q^{16} + 330 q^{18} - 220 q^{19} - 234 q^{20} - 217 q^{22} + 189 q^{24} - 902 q^{25} - 252 q^{27}+ \cdots - 2118 q^{99}+O(q^{100}) \) 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9 + 12 * q^10 + 48 * q^11 + 318 * q^12 + 72 * q^14 + 127 * q^16 + 330 * q^18 - 220 * q^19 - 234 * q^20 - 217 * q^22 + 189 * q^24 - 902 * q^25 - 252 * q^27 - 132 * q^28 + 420 * q^30 - 693 * q^32 - 660 * q^33 + 509 * q^34 - 537 * q^36 - 1977 * q^38 - 36 * q^40 + 1620 * q^41 + 72 * q^42 - 292 * q^43 + 48 * q^46 + 765 * q^48 + 1762 * q^49 - 1227 * q^50 - 1794 * q^51 + 330 * q^52 - 645 * q^54 + 942 * q^56 - 294 * q^57 - 282 * q^58 + 5592 * q^59 + 1236 * q^60 + 1090 * q^64 - 6 * q^65 + 3522 * q^66 + 68 * q^67 - 2025 * q^68 + 600 * q^70 + 1875 * q^72 - 868 * q^73 - 420 * q^74 - 4254 * q^75 - 1471 * q^76 + 3228 * q^78 + 498 * q^81 + 362 * q^82 + 3654 * q^83 - 2028 * q^84 - 4119 * q^86 + 3155 * q^88 + 2958 * q^90 - 1380 * q^91 - 744 * q^92 - 138 * q^94 - 4782 * q^96 - 1912 * q^97 - 2118 * q^99

Introduction

L-functions

Modular forms

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