LMFDB - Embedded newform 72.4.l.b.59.26

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			59.26
Character	$\chi$	$=$	72.59
Dual form			72.4.l.b.11.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.31471 + 1.62546i) q^{2} +(-3.80768 - 3.53576i) q^{3} +(2.71576 + 7.52494i) q^{4} +(-10.8653 + 18.8192i) q^{5} +(-3.06642 - 14.3735i) 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} +(16.2657 - 38.2548i) q^{12} +(24.0118 + 13.8632i) q^{13} +(34.3478 + 3.05199i) q^{14} +(107.912 - 33.2404i) q^{15} +(-49.2493 + 40.8718i) q^{16} -56.3777i q^{17} +(-39.1453 + 65.5717i) q^{18} +80.9703 q^{19} +(-171.121 - 30.6521i) q^{20} +(-61.7558 - 14.1206i) q^{21} +(-74.1948 - 6.59262i) q^{22} +(4.32694 - 7.49448i) q^{23} +(99.8319 - 62.1095i) 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} +(303.815 + 98.4643i) q^{30} +(174.690 + 100.857i) q^{31} +(-180.433 + 14.5536i) q^{32} +(133.399 + 30.5020i) q^{33} +(91.6397 - 130.498i) q^{34} +264.931i q^{35} +(-197.194 + 88.1503i) q^{36} +53.3684i q^{37} +(187.423 + 131.614i) q^{38} +(-42.4122 - 137.687i) q^{39} +(-346.271 - 349.101i) q^{40} +(398.128 + 229.859i) q^{41} +(-119.994 - 133.067i) 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} +(332.038 + 18.5073i) q^{48} +(-97.1821 + 168.324i) q^{49} +(86.9206 - 978.224i) q^{50} +(-199.338 + 214.668i) q^{51} +(-39.1097 + 218.337i) q^{52} -84.2497 q^{53} +(380.898 - 111.267i) q^{54} -572.278i q^{55} +(70.3143 + 266.753i) q^{56} +(-308.309 - 286.292i) q^{57} +(-21.9388 + 246.904i) q^{58} +(-86.9772 - 50.2163i) q^{59} +(543.194 + 721.756i) 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} +(259.200 + 287.438i) q^{66} +(68.5689 - 118.765i) q^{67} +(424.239 - 153.108i) q^{68} +(-42.9743 + 13.2375i) q^{69} +(-430.635 + 613.238i) q^{70} -766.570 q^{71} +(-599.732 - 116.489i) q^{72} +464.449 q^{73} +(-86.7482 + 123.532i) q^{74} +(-402.154 + 1758.80i) q^{75} +(219.896 + 609.297i) q^{76} +(-160.534 + 278.054i) q^{77} +(125.633 - 387.644i) 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} +(-61.4571 - 503.056i) q^{84} +(1060.98 + 612.560i) q^{85} +(52.6072 - 592.052i) q^{86} +(101.504 - 443.921i) q^{87} +(-151.886 - 576.215i) q^{88} -403.445i q^{89} +(-808.683 - 1449.14i) q^{90} +338.031 q^{91} +(68.1464 + 12.2068i) q^{92} +(-308.555 - 1001.69i) q^{93} +(-84.5898 + 951.992i) q^{94} +(-879.765 + 1523.80i) q^{95} +(738.489 + 582.554i) 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 $

$2$	2.31471	+	1.62546i	0.818373	+	0.574687i
$2$	2.31471	+	1.62546i	0.818373	+	0.574687i
$3$	−3.80768	−	3.53576i	−0.732787	−	0.680458i
$3$	−3.80768	−	3.53576i	−0.732787	−	0.680458i
$4$	2.71576	+	7.52494i	0.339470	+	0.940617i
$5$	−10.8653	+	18.8192i	−0.971820	+	1.68324i	−0.281767	+	0.959483i	$0.590920\pi$
$5$	−10.8653	+	18.8192i	−0.971820	+	1.68324i	−0.690053	+	0.723758i	$0.742413\pi$
$6$	−3.06642	−	14.3735i	−0.208644	−	0.977992i
$7$	10.5583	−	6.09581i	0.570092	−	0.329143i	−0.187094	−	0.982342i	$-0.559907\pi$
$7$	10.5583	−	6.09581i	0.570092	−	0.329143i	0.757186	+	0.653199i	$0.226574\pi$
$8$	−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	$0.450872\pi$
$12$	16.2657	−	38.2548i	0.391291	−	0.920267i
$13$	24.0118	+	13.8632i	0.512284	+	0.295767i	0.733772	−	0.679396i	$-0.237758\pi$
$13$	24.0118	+	13.8632i	0.512284	+	0.295767i	−0.221488	+	0.975163i	$0.571091\pi$
$14$	34.3478	+	3.05199i	0.655703	+	0.0582628i
$15$	107.912	−	33.2404i	1.85751	−	0.572176i
$16$	−49.2493	+	40.8718i	−0.769521	+	0.638622i
$17$		−	56.3777i		−	0.804330i	−0.915567	−	0.402165i	$-0.868258\pi$
$17$		−	56.3777i		−	0.804330i	0.915567	−	0.402165i	$-0.131742\pi$
$18$	−39.1453	+	65.5717i	−0.512591	+	0.858633i
$19$	80.9703			0.977677			0.488839	−	0.872374i	$-0.337421\pi$
$19$	80.9703			0.977677			0.488839	+	0.872374i	$0.337421\pi$
$20$	−171.121	−	30.6521i	−1.91319	−	0.342701i
$21$	−61.7558	−	14.1206i	−0.641724	−	0.146732i
$22$	−74.1948	−	6.59262i	−0.719017	−	0.0638887i
$23$	4.32694	−	7.49448i	0.0392274	−	0.0679438i	−0.845745	−	0.533587i	$-0.820844\pi$
$23$	4.32694	−	7.49448i	0.0392274	−	0.0679438i	0.884973	+	0.465643i	$0.154177\pi$
$24$	99.8319	−	62.1095i	0.849087	−	0.528252i
$25$	−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	0.971529	−	0.236922i	$-0.0761385\pi$
$29$	43.8188	+	75.8963i	0.280584	+	0.485986i	−0.690945	+	0.722908i	$0.742805\pi$
$30$	303.815	+	98.4643i	1.84896	+	0.599234i
$31$	174.690	+	100.857i	1.01210	+	0.584338i	0.911807	−	0.410620i	$-0.134688\pi$
$31$	174.690	+	100.857i	1.01210	+	0.584338i	0.100296	+	0.994958i	$0.468021\pi$
$32$	−180.433	+	14.5536i	−0.996763	+	0.0803978i
$33$	133.399	+	30.5020i	0.703689	+	0.160900i
$34$	91.6397	−	130.498i	0.462238	−	0.658242i
$35$			264.931i			1.27947i
$36$	−197.194	+	88.1503i	−0.912936	+	0.408103i
$37$			53.3684i			0.237127i	0.992946	+	0.118564i	$0.0378290\pi$
$37$			53.3684i			0.237127i	−0.992946	+	0.118564i	$0.962171\pi$
$38$	187.423	+	131.614i	0.800105	+	0.561858i
$39$	−42.4122	−	137.687i	−0.174138	−	0.565322i
$40$	−346.271	−	349.101i	−1.36876	−	1.37994i
$41$	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	$0.327158\pi$
$42$	−119.994	−	133.067i	−0.440845	−	0.488872i
$43$	−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	$0.00902405\pi$
$47$	168.953	+	292.635i	0.524348	+	0.908197i	−0.475251	+	0.879850i	$0.657643\pi$
$48$	332.038	+	18.5073i	0.998450	+	0.0556519i
$49$	−97.1821	+	168.324i	−0.283330	+	0.490742i
$50$	86.9206	−	978.224i	0.245849	−	2.76683i
$51$	−199.338	+	214.668i	−0.547312	+	0.589403i
$52$	−39.1097	+	218.337i	−0.104299	+	0.582267i
$53$	−84.2497			−0.218351			−0.109175	−	0.994023i	$-0.534821\pi$
$53$	−84.2497			−0.218351			−0.109175	+	0.994023i	$0.534821\pi$
$54$	380.898	−	111.267i	0.959883	−	0.280399i
$55$		−	572.278i		−	1.40302i
$56$	70.3143	+	266.753i	0.167788	+	0.636543i
$57$	−308.309	−	286.292i	−0.716430	−	0.665268i
$58$	−21.9388	+	246.904i	−0.0496672	+	0.558966i
$59$	−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	$0.702010\pi$
$60$	543.194	+	721.756i	1.16877	+	1.55297i
$61$	−342.447	+	197.712i	−0.718783	+	0.414990i	−0.814305	−	0.580438i	$-0.802882\pi$
$61$	−342.447	+	197.712i	−0.718783	+	0.414990i	0.0955213	+	0.995427i	$0.469548\pi$
$62$	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
$66$	259.200	+	287.438i	0.483413	+	0.536078i
$67$	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	$0.126764\pi$
$68$	424.239	−	153.108i	0.756566	−	0.273046i
$69$	−42.9743	+	13.2375i	−0.0749782	+	0.0230958i
$70$	−430.635	+	613.238i	−0.735295	+	1.04708i
$71$	−766.570			−1.28134			−0.640670	−	0.767816i	$-0.721343\pi$
$71$	−766.570			−1.28134			−0.640670	+	0.767816i	$0.721343\pi$
$72$	−599.732	−	116.489i	−0.981654	−	0.190671i
$73$	464.449			0.744652			0.372326	−	0.928102i	$-0.378560\pi$
$73$	464.449			0.744652			0.372326	+	0.928102i	$0.378560\pi$
$74$	−86.7482	+	123.532i	−0.136274	+	0.194059i
$75$	−402.154	+	1758.80i	−0.619157	+	2.70785i
$76$	219.896	+	609.297i	0.331892	+	0.919620i
$77$	−160.534	+	278.054i	−0.237592	+	0.411521i
$78$	125.633	−	387.644i	0.182373	−	0.562719i
$79$	906.822	−	523.554i	1.29146	−	0.745626i	0.312548	−	0.949902i	$-0.398817\pi$
$79$	906.822	−	523.554i	1.29146	−	0.745626i	0.978913	+	0.204276i	$0.0654840\pi$
$80$	−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	$-1.87193e-5\pi$
$84$	−61.4571	−	503.056i	−0.0798275	−	0.653428i
$85$	1060.98	+	612.560i	1.35388	+	0.781664i
$86$	52.6072	−	592.052i	0.0659625	−	0.742356i
$87$	101.504	−	443.921i	0.125084	−	0.547050i
$88$	−151.886	−	576.215i	−0.183990	−	0.698008i
$89$		−	403.445i		−	0.480506i	−0.970710	−	0.240253i	$-0.922770\pi$
$89$		−	403.445i		−	0.480506i	0.970710	−	0.240253i	$-0.0772304\pi$
$90$	−808.683	−	1449.14i	−0.947141	−	1.69725i
$91$	338.031			0.389399
$92$	68.1464	+	12.2068i	0.0772256	+	0.0138331i
$93$	−308.555	−	1001.69i	−0.344039	−	1.11689i
$94$	−84.5898	+	951.992i	−0.0928167	+	1.04458i
$95$	−879.765	+	1523.80i	−0.950126	+	1.64567i
$96$	738.489	+	582.554i	0.785123	+	0.619340i
$97$	−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	$-0.932608\pi$
$101$	−680.909	−	1179.37i	−0.670822	−	1.16190i	0.306850	−	0.951758i	$-0.400725\pi$
$102$	−810.344	+	172.878i	−0.786628	+	0.167818i
$103$	−878.637	−	507.281i	−0.840531	−	0.485281i	0.0169138	−	0.999857i	$-0.494616\pi$
$103$	−878.637	−	507.281i	−0.840531	−	0.485281i	−0.857445	+	0.514576i	$0.827949\pi$
$104$	−445.425	+	441.815i	−0.419976	+	0.416572i
$105$	936.732	−	1008.77i	0.870626	−	0.937580i
$106$	−195.014	−	136.945i	−0.178692	−	0.125483i
$107$		−	1008.18i		−	0.910879i	−0.890267	−	0.455440i	$-0.849482\pi$
$107$		−	1008.18i		−	0.910879i	0.890267	−	0.455440i	$-0.150518\pi$
$108$	1062.53	+	361.584i	0.946685	+	0.322161i
$109$			1319.53i			1.15952i	0.814786	+	0.579762i	$0.196854\pi$
$109$			1319.53i			1.15952i	−0.814786	+	0.579762i	$0.803146\pi$
$110$	930.215	−	1324.66i	0.806295	−	1.14819i
$111$	188.698	−	203.209i	0.161355	−	0.173764i
$112$	−270.840	+	731.750i	−0.228500	+	0.617356i
$113$	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	$0.390644\pi$
$114$	−248.289	−	1163.83i	−0.203986	−	0.956160i
$115$	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
$120$	84.1513	+	2553.59i	0.0640160	+	1.94259i
$121$	−318.729	+	552.056i	−0.239466	+	0.414768i
$122$	−1114.04	−	98.9884i	−0.826722	−	0.0734589i
$123$	−703.215	−	2282.92i	−0.515502	−	1.67353i
$124$	−284.528	+	1588.43i	−0.206060	+	1.15037i
$125$	4828.90			3.45528
$126$	−13.5932	+	930.945i	−0.00961091	+	0.658216i
$127$		−	14.1680i		−	0.00989929i	−0.999988	−	0.00494964i	$-0.998424\pi$
$127$		−	14.1680i		−	0.00989929i	0.999988	−	0.00494964i	$-0.00157553\pi$
$128$	−599.528	−	1318.23i	−0.413994	−	0.910279i
$129$	−243.397	+	1064.48i	−0.166123	+	0.726531i
$130$	−1697.47	−	150.830i	−1.14522	−	0.101759i
$131$	−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	$0.772016\pi$
$132$	132.754	+	1086.65i	0.0875357	+	0.716523i
$133$	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	$0.311091\pi$
$138$	−120.990	−	39.2120i	−0.0746330	−	0.0241880i
$139$	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	$0.135782\pi$
$140$	−1993.59	+	719.488i	−1.20349	+	0.434342i
$141$	391.370	−	1711.64i	0.233754	−	1.02231i
$142$	−1774.39	−	1246.03i	−1.04861	−	0.736370i
$143$	−730.182			−0.426999
$144$	−1198.86	−	1244.48i	−0.693783	−	0.720184i
$145$	−1904.41			−1.09071
$146$	1075.06	+	754.943i	0.609403	+	0.427942i
$147$	965.193	−	297.312i	0.541549	−	0.166815i
$148$	−401.594	+	144.936i	−0.223046	+	0.0804975i
$149$	811.049	−	1404.78i	0.445931	−	0.772375i	−0.552186	−	0.833721i	$-0.686206\pi$
$149$	811.049	−	1404.78i	0.445931	−	0.772375i	0.998117	+	0.0613461i	$0.0195393\pi$
$150$	−3789.73	+	3417.43i	−2.06287	+	1.86021i
$151$	−710.557	+	410.240i	−0.382942	+	0.221092i	−0.679098	−	0.734048i	$-0.737629\pi$
$151$	−710.557	+	410.240i	−0.382942	+	0.221092i	0.296155	+	0.955140i	$0.404295\pi$
$152$	−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
$156$	920.904	−	693.073i	0.472637	−	0.355707i
$157$	436.444	+	251.981i	0.221860	+	0.128091i	0.606811	−	0.794846i	$-0.292448\pi$
$157$	436.444	+	251.981i	0.221860	+	0.128091i	−0.384951	+	0.922937i	$0.625782\pi$
$158$	2950.05	+	262.128i	1.48540	+	0.131986i
$159$	320.796	+	297.887i	0.160005	+	0.148578i
$160$	1686.57	−	3553.74i	0.833345	−	1.75592i
$161$		−	105.505i		−	0.0516456i
$162$	−1843.75	−	923.096i	−0.894190	−	0.447687i
$163$	2496.71			1.19974			0.599870	−	0.800097i	$-0.295219\pi$
$163$	2496.71			1.19974			0.599870	+	0.800097i	$0.295219\pi$
$164$	−648.458	+	3620.13i	−0.308756	+	1.72369i
$165$	−2023.44	+	2179.05i	−0.954693	+	1.02811i
$166$	3690.03	+	327.880i	1.72531	+	0.153304i
$167$	−709.405	+	1228.73i	−0.328715	+	0.569351i	−0.982257	−	0.187539i	$-0.939949\pi$
$167$	−709.405	+	1228.73i	−0.328715	+	0.569351i	0.653542	+	0.756890i	$0.273282\pi$
$168$	675.443	−	1264.33i	0.310188	−	0.580624i
$169$	−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	0.927719	−	0.373280i	$-0.121767\pi$
$173$	319.906	+	554.094i	0.140590	+	0.243508i	−0.787129	+	0.616788i	$0.788434\pi$
$174$	956.528	−	862.558i	0.416748	−	0.375807i
$175$	−3666.01	−	2116.57i	−1.58357	−	0.914272i
$176$	585.042	−	1580.65i	0.250564	−	0.676968i
$177$	153.628	+	498.738i	0.0652395	+	0.211793i
$178$	655.783	−	933.857i	0.276141	−	0.393233i
$179$		−	1730.89i		−	0.722754i	−0.932420	−	0.361377i	$-0.882307\pi$
$179$		−	1730.89i		−	0.722754i	0.932420	−	0.361377i	$-0.117693\pi$
$180$	483.649	−	4668.82i	0.200273	−	1.93329i
$181$		−	1880.76i		−	0.772354i	−0.922425	−	0.386177i	$-0.873795\pi$
$181$		−	1880.76i		−	0.772354i	0.922425	−	0.386177i	$-0.126205\pi$
$182$	782.444	+	549.456i	0.318673	+	0.223782i
$183$	2002.99	+	457.988i	0.809098	+	0.185002i
$184$	137.898	+	139.024i	0.0552497	+	0.0557011i
$185$	−1004.35	−	579.862i	−0.399142	−	0.230445i
$186$	913.996	−	2820.17i	0.360309	−	1.11175i
$187$	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	$-0.899647\pi$
$191$	−1963.62	−	3401.09i	−0.743887	−	1.28845i	0.206826	−	0.978378i	$-0.433687\pi$
$192$	762.470	+	2548.83i	0.286597	+	0.958051i
$193$	−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	$0.318544\pi$
$194$	15.0052	−	168.872i	0.00555315	−	0.0624964i
$195$	3051.98	+	697.842i	1.12080	+	0.256275i
$196$	−1530.55	−	274.161i	−0.557782	−	0.0999129i
$197$	−2671.57			−0.966201			−0.483101	−	0.875565i	$-0.660489\pi$
$197$	−2671.57			−0.966201			−0.483101	+	0.875565i	$0.660489\pi$
$198$	29.3626	−	2010.94i	0.0105389	−	0.721773i
$199$		−	537.481i		−	0.191462i	−0.995407	−	0.0957312i	$-0.969481\pi$
$199$		−	537.481i		−	0.191462i	0.995407	−	0.0957312i	$-0.0305189\pi$
$200$	7597.13	−	2002.55i	2.68599	−	0.708007i
$201$	−681.012	+	209.774i	−0.238979	+	0.0736137i
$202$	340.911	−	3836.69i	0.118745	−	1.33638i
$203$	925.300	+	534.222i	0.319918	+	0.184705i
$204$	−2156.72	−	917.020i	−0.740198	−	0.314727i
$205$	−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
$210$	3807.98	−	812.389i	1.25131	−	0.266953i
$211$	−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	$0.172901\pi$
$212$	−228.802	−	633.974i	−0.0741235	−	0.205384i
$213$	2918.85	+	2710.41i	0.938950	+	0.871898i
$214$	1638.75	−	2333.63i	0.523470	−	0.745439i
$215$	4566.61			1.44856
$216$	1871.71	+	2564.06i	0.589600	+	0.807696i
$217$	2459.22			0.769322
$218$	−2144.84	+	3054.33i	−0.666363	+	0.948924i
$219$	−1768.47	−	1642.18i	−0.545672	−	0.506704i
$220$	4306.35	−	1554.17i	1.31970	−	0.476282i
$221$	781.578	−	1353.73i	0.237894	−	0.412045i
$222$	767.090	−	163.650i	0.231909	−	0.0494751i
$223$	2835.47	−	1637.06i	0.851468	−	0.491595i	−0.00967800	−	0.999953i	$-0.503081\pi$
$223$	2835.47	−	1637.06i	0.851468	−	0.491595i	0.861146	+	0.508358i	$0.169747\pi$
$224$	−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	$0.366614\pi$
$228$	1317.04	−	3097.50i	0.382556	−	0.899724i
$229$	2011.19	+	1161.16i	0.580364	+	0.335073i	0.761278	−	0.648426i	$-0.224572\pi$
$229$	2011.19	+	1161.16i	0.580364	+	0.335073i	−0.180914	+	0.983499i	$0.557906\pi$
$230$	−47.0764	+	529.809i	−0.0134962	+	0.151889i
$231$	1594.39	−	491.127i	0.454127	−	0.139886i
$232$	−1917.51	+	505.443i	−0.542633	+	0.143034i
$233$			3568.38i			1.00332i	0.865066	+	0.501658i	$0.167276\pi$
$233$			3568.38i			1.00332i	−0.865066	+	0.501658i	$0.832724\pi$
$234$	−1848.99	+	1031.82i	−0.516547	+	0.288256i
$235$	−7342.89			−2.03829
$236$	141.665	−	790.873i	0.0390747	−	0.218142i
$237$	−5304.05	−	1212.78i	−1.45373	−	0.332400i
$238$	172.064	−	1936.45i	0.0468625	−	0.527401i
$239$	−672.246	+	1164.37i	−0.181941	+	0.315132i	−0.942542	−	0.334089i	$-0.891571\pi$
$239$	−672.246	+	1164.37i	−0.181941	+	0.315132i	0.760600	+	0.649221i	$0.224905\pi$
$240$	−3955.98	+	6047.61i	−1.06399	+	1.62655i
$241$	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
$246$	2083.05	−	6427.34i	0.539880	−	1.66582i
$247$	1944.25	+	1122.51i	0.500848	+	0.289165i
$248$	−3240.53	+	3214.27i	−0.829734	+	0.823009i
$249$	−6634.50	−	1517.00i	−1.68853	−	0.386087i
$250$	11177.5	+	7849.18i	2.82771	+	1.98570i
$251$		−	2908.91i		−	0.731510i	−0.930711	−	0.365755i	$-0.880811\pi$
$251$		−	2908.91i		−	0.731510i	0.930711	−	0.365755i	$-0.119189\pi$
$252$	−1544.68	+	2132.77i	−0.386133	+	0.533143i
$253$			227.901i			0.0566326i
$254$	23.0296	−	32.7949i	0.00568899	−	0.00810131i
$255$	−1874.02	−	6083.82i	−0.460218	−	1.49405i
$256$	754.990	−	4025.82i	0.184324	−	0.982866i
$257$	−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	$0.866033\pi$
$258$	−2293.67	+	2068.34i	−0.553479	+	0.499105i
$259$	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	0.923752	−	0.382992i	$-0.125106\pi$
$263$	555.302	+	961.811i	0.130195	+	0.225505i	−0.793556	+	0.608497i	$0.791773\pi$
$264$	−1459.03	+	2731.07i	−0.340140	+	0.636689i
$265$	915.396	−	1585.51i	0.212198	−	0.367537i
$266$	2781.15	+	247.121i	0.641066	+	0.0569622i
$267$	−1426.48	+	1536.19i	−0.326964	+	0.352109i
$268$	1079.91	+	193.440i	0.246143	+	0.0440904i
$269$	−426.485			−0.0966664			−0.0483332	−	0.998831i	$-0.515391\pi$
$269$	−426.485			−0.0966664			−0.0483332	+	0.998831i	$0.515391\pi$
$270$	−2044.60	+	8377.16i	−0.460854	+	1.88821i
$271$			4297.17i			0.963226i	0.876384	+	0.481613i	$0.159949\pi$
$271$			4297.17i			0.963226i	−0.876384	+	0.481613i	$0.840051\pi$
$272$	2304.26	+	2776.56i	0.513663	+	0.618948i
$273$	−1287.11	−	1195.20i	−0.285346	−	0.264969i
$274$	630.856	+	56.0551i	0.139093	+	0.0123592i
$275$	7918.95	+	4572.01i	1.73648	+	1.00255i
$276$	−216.319	−	287.429i	−0.0471771	−	0.0626854i
$277$	3296.42	−	1903.19i	0.715028	−	0.412822i	−0.0978918	−	0.995197i	$-0.531210\pi$
$277$	3296.42	−	1903.19i	0.715028	−	0.412822i	0.812920	+	0.582375i	$0.197877\pi$
$278$	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	$0.310234\pi$
$282$	3688.11	−	3325.79i	0.778807	−	0.702297i
$283$	−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	$0.209203\pi$
$284$	−2081.82	−	5768.39i	−0.434976	−	1.20525i
$285$	8737.65	−	2691.49i	1.81605	−	0.559403i
$286$	−1690.16	−	1186.88i	−0.349445	−	0.245391i
$287$	5604.72			1.15274
$288$	−752.156	−	4829.30i	−0.153893	−	0.988088i
$289$	1734.55			0.353054
$290$	−4408.16	−	3095.55i	−0.892607	−	0.626816i
$291$	−69.4244	+	303.624i	−0.0139853	+	0.0611641i
$292$	1261.33	+	3494.95i	0.252787	+	0.700432i
$293$	−2512.00	+	4350.91i	−0.500862	+	0.867518i	0.499138	+	0.866523i	$0.333650\pi$
$293$	−2512.00	+	4350.91i	−0.500862	+	0.867518i	−1.00000		0.000995098i	$0.999683\pi$
$294$	2717.41	+	880.692i	0.539056	+	0.174704i
$295$	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
$300$	−14327.0	+	1750.29i	−2.75724	+	0.336844i
$301$	−2218.78	−	1281.02i	−0.424879	−	0.245304i
$302$	−2311.56	−	205.395i	−0.440448	−	0.0391363i
$303$	−1577.29	+	6898.19i	−0.299052	+	1.30789i
$304$	−3987.73	+	3309.40i	−0.752343	+	0.624366i
$305$		−	8592.77i		−	1.61318i
$306$	3696.78	+	2206.92i	0.690624	+	0.412292i
$307$	3396.30			0.631392			0.315696	−	0.948860i	$-0.397762\pi$
$307$	3396.30			0.631392			0.315696	+	0.948860i	$0.397762\pi$
$308$	−2528.31	−	452.884i	−0.467739	−	0.0837840i
$309$	1551.94	+	5038.21i	0.285717	+	0.927553i
$310$	−12349.4	−	1097.31i	−2.26257	−	0.201042i
$311$	2587.42	−	4481.55i	0.471767	−	0.817124i	−0.527712	−	0.849424i	$-0.676950\pi$
$311$	2587.42	−	4481.55i	0.471767	−	0.817124i	0.999478	+	0.0322999i	$0.0102832\pi$
$312$	3258.19	−	107.370i	0.591213	−	0.0194829i
$313$	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	0.998169	−	0.0604940i	$-0.0192676\pi$
$317$	2521.16	+	4366.77i	0.446695	+	0.773698i	−0.551474	+	0.834192i	$0.685934\pi$
$318$	258.345	+	1210.96i	0.0455575	+	0.213545i
$319$	−1998.74	−	1153.97i	−0.350809	−	0.202540i
$320$	9680.39	−	5484.42i	1.69109	−	0.958089i
$321$	−3564.67	+	3838.81i	−0.619815	+	0.667481i
$322$	171.494	−	244.213i	0.0296801	−	0.0422654i
$323$		−	4564.92i		−	0.786375i
$324$	−2767.29	−	5133.64i	−0.474502	−	0.880255i
$325$		−	9627.11i		−	1.64313i
$326$	5779.17	+	4058.31i	0.981836	+	0.689475i
$327$	4665.55	−	5024.34i	0.789007	−	0.849685i
$328$	−7385.37	+	7325.51i	−1.24326	+	1.23318i
$329$	3567.70	+	2059.81i	0.597853	+	0.345171i
$330$	−8225.63	+	1754.84i	−1.37214	+	0.292730i
$331$	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
$336$	3618.56	−	1828.64i	0.587526	−	0.296906i
$337$	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	$0.0537807\pi$
$338$	357.539	−	4023.82i	0.0575372	−	0.647536i
$339$	−2802.06	−	9096.60i	−0.448929	−	1.45740i
$340$	−1728.09	+	9647.40i	−0.275644	+	1.53883i
$341$	−5312.18			−0.843608
$342$	−3169.61	+	5309.36i	−0.501148	+	0.839466i
$343$			6551.34i			1.03131i
$344$	4598.02	−	1212.01i	0.720665	−	0.189962i
$345$	217.808	−	952.571i	0.0339895	−	0.148651i
$346$	−160.168	+	1802.56i	−0.0248863	+	0.280076i
$347$	−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	$0.858083\pi$
$348$	3616.14	−	441.774i	0.557027	−	0.0680505i
$349$	6046.48	−	3490.94i	0.927394	−	0.535431i	0.0414078	−	0.999142i	$-0.486816\pi$
$349$	6046.48	−	3490.94i	0.927394	−	0.535431i	0.885987	+	0.463711i	$0.153482\pi$
$350$	−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	$-0.0667939\pi$
$354$	−455.075	+	1404.15i	−0.0683247	+	0.210818i
$355$	8329.00	−	14426.2i	1.24523	−	2.15681i
$356$	3035.89	−	1095.66i	0.451972	−	0.163117i
$357$	−796.088	+	3481.65i	−0.118021	+	0.516158i
$358$	2813.50	−	4006.51i	0.415357	−	0.591483i
$359$	−10010.3			−1.47166			−0.735830	−	0.677167i	$-0.763208\pi$
$359$	−10010.3			−1.47166			−0.735830	+	0.677167i	$0.763208\pi$
$360$	8708.48	−	10020.8i	1.27494	−	1.46706i
$361$	−302.804			−0.0441469
$362$	3057.11	−	4353.42i	0.443862	−	0.632074i
$363$	3165.56	−	975.097i	0.457710	−	0.140990i
$364$	918.011	+	2543.66i	0.132189	+	0.366275i
$365$	−5046.36	+	8740.56i	−0.723668	+	1.25343i
$366$	3891.89	+	4315.88i	0.555826	+	0.616379i
$367$	7534.90	−	4350.28i	1.07171	−	0.618754i	0.143064	−	0.989713i	$-0.454305\pi$
$367$	7534.90	−	4350.28i	1.07171	−	0.618754i	0.928649	+	0.370960i	$0.120971\pi$
$368$	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
$372$	6699.71	−	5042.21i	0.933773	−	0.702759i
$373$	5355.18	+	3091.81i	0.743380	+	0.429191i	0.823297	−	0.567611i	$-0.192132\pi$
$373$	5355.18	+	3091.81i	0.743380	+	0.429191i	−0.0799170	+	0.996802i	$0.525466\pi$
$374$	−371.677	+	4182.93i	−0.0513876	+	0.578327i
$375$	−18386.9	−	17073.8i	−2.53198	−	2.35117i
$376$	−7393.40	+	1948.85i	−1.01406	+	0.267298i
$377$			2429.88i			0.331950i
$378$	3343.36	−	3496.68i	0.454931	−	0.475792i
$379$	−11734.4			−1.59039			−0.795193	−	0.606356i	$-0.792630\pi$
$379$	−11734.4			−1.59039			−0.795193	+	0.606356i	$0.792630\pi$
$380$	−13855.7	−	2481.91i	−1.87048	−	0.335051i
$381$	−50.0948	+	53.9473i	−0.00673605	+	0.00725407i
$382$	983.126	−	11064.3i	0.131678	−	1.48194i
$383$	2243.57	−	3885.98i	0.299324	−	0.518445i	−0.676657	−	0.736298i	$-0.736572\pi$
$383$	2243.57	−	3885.98i	0.299324	−	0.518445i	0.975981	+	0.217853i	$0.0699055\pi$
$384$	−2378.12	+	7139.16i	−0.316037	+	0.948747i
$385$	−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	0.984634	−	0.174632i	$-0.0558734\pi$
$389$	2616.87	+	4532.56i	0.341082	+	0.590771i	−0.643552	+	0.765402i	$0.722540\pi$
$390$	5930.13	+	6576.17i	0.769958	+	0.853840i
$391$	−422.522	−	243.943i	−0.0546492	−	0.0315517i
$392$	−3097.15	−	3122.46i	−0.399055	−	0.402316i
$393$	1490.58	+	4839.02i	0.191323	+	0.621111i
$394$	−6183.91	−	4342.53i	−0.790713	−	0.555263i
$395$			22754.2i			2.89846i
$396$	3336.66	−	4607.01i	0.423418	−	0.584623i
$397$		−	10075.8i		−	1.27377i	−0.770958	−	0.636886i	$-0.780222\pi$
$397$		−	10075.8i		−	1.27377i	0.770958	−	0.636886i	$-0.219778\pi$
$398$	873.654	−	1244.11i	0.110031	−	0.156688i
$399$	−5000.39	−	1143.35i	−0.627399	−	0.143456i
$400$	20840.2	+	7713.51i	2.60503	+	0.964189i
$401$	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	$0.553538\pi$
$402$	−1917.32	−	621.391i	−0.237879	−	0.0770949i
$403$	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
$408$	−3501.59	−	5628.29i	−0.424889	−	0.682946i
$409$	−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	$0.259751\pi$
$410$	−28145.0	−	2500.84i	−3.39020	−	0.301238i
$411$	−1134.25	−	259.349i	−0.136128	−	0.0311259i
$412$	1431.09	−	7989.34i	0.171128	−	0.955356i
$413$	−1224.44			−0.145885
$414$	322.046	+	577.098i	0.0382312	+	0.0685093i
$415$			28461.9i			3.36660i
$416$	−4534.30	−	2151.93i	−0.534404	−	0.253623i
$417$	−1576.77	+	485.696i	−0.185167	+	0.0570376i
$418$	−6007.58	−	533.807i	−0.702967	−	0.0624625i
$419$	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	$0.542315\pi$
$420$	10134.9	+	4309.27i	1.17745	+	0.500645i
$421$	−3908.99	+	2256.86i	−0.452524	+	0.261265i	−0.708896	−	0.705313i	$-0.750806\pi$
$421$	−3908.99	+	2256.86i	−0.452524	+	0.261265i	0.256371	+	0.966578i	$0.417473\pi$
$422$	−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
$426$	2350.63	+	11018.3i	0.267343	+	1.25314i
$427$	−2410.43	+	4174.98i	−0.273182	+	0.473165i
$428$	7586.46	−	2737.96i	0.856788	−	0.309216i
$429$	2780.29	+	2581.75i	0.312900	+	0.290555i
$430$	10570.4	+	7422.84i	1.18546	+	0.832468i
$431$	616.879			0.0689420			0.0344710	−	0.999406i	$-0.489025\pi$
$431$	616.879			0.0689420			0.0344710	+	0.999406i	$0.489025\pi$
$432$	164.680	+	8977.44i	0.0183407	+	0.999832i
$433$	−2095.37			−0.232557			−0.116278	−	0.993217i	$-0.537096\pi$
$433$	−2095.37			−0.232557			−0.116278	+	0.993217i	$0.537096\pi$
$434$	5692.39	+	3997.37i	0.629593	+	0.442120i
$435$	7251.38	+	6733.55i	0.799258	+	0.742181i
$436$	−9929.38	+	3583.53i	−1.09067	+	0.393623i
$437$	350.354	−	606.831i	0.0383517	−	0.0664271i
$438$	−1424.19	−	6675.74i	−0.155367	−	0.728263i
$439$	−8410.24	+	4855.65i	−0.914348	+	0.527899i	−0.881827	−	0.471572i	$-0.843687\pi$
$439$	−8410.24	+	4855.65i	−0.914348	+	0.527899i	−0.0325203	+	0.999471i	$0.510353\pi$
$440$	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	$0.176357\pi$
$444$	2041.60	+	868.072i	0.218220	+	0.0927857i
$445$	7592.51	+	4383.54i	0.808808	+	0.466965i
$446$	9224.27	+	819.628i	0.979332	+	0.0870191i
$447$	−8055.17	+	2481.26i	−0.852341	+	0.262550i
$448$	−6241.91	−	50.7988i	−0.658264	−	0.00535718i
$449$			80.1769i			0.00842713i	0.999991	+	0.00421357i	$0.00134122\pi$
$449$			80.1769i			0.00842713i	−0.999991	+	0.00421357i	$0.998659\pi$
$450$	26513.3	+	387.132i	2.77744	+	0.0405546i
$451$	−12106.8			−1.26405
$452$	−2583.87	+	14424.9i	−0.268883	+	1.50109i
$453$	4156.08	+	950.298i	0.431059	+	0.0985627i
$454$	−2011.22	−	178.708i	−0.207910	−	0.0184740i
$455$	−3672.80	+	6361.48i	−0.378425	+	0.655452i
$456$	8083.42	−	5029.03i	0.830134	−	0.516460i
$457$	−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	$-0.943046\pi$
$461$	−6395.61	−	11077.5i	−0.646146	−	1.11916i	0.337889	−	0.941186i	$-0.390287\pi$
$462$	4488.86	+	1454.81i	0.452036	+	0.146502i
$463$	−10395.3	−	6001.71i	−1.04343	−	0.602426i	−0.122629	−	0.992453i	$-0.539133\pi$
$463$	−10395.3	−	6001.71i	−1.04343	−	0.602426i	−0.920804	+	0.390026i	$0.872466\pi$
$464$	−5260.06	−	1946.89i	−0.526277	−	0.194789i
$465$	22203.6	+	5076.90i	2.21434	+	0.506313i
$466$	−5800.26	+	8259.77i	−0.576592	+	0.821087i
$467$			1913.91i			0.189647i	0.995494	+	0.0948234i	$0.0302287\pi$
$467$			1913.91i			0.189647i	−0.995494	+	0.0948234i	$0.969771\pi$
$468$	−5957.04	−	617.099i	−0.588386	−	0.0609517i
$469$		−	1671.93i		−	0.164611i
$470$	−16996.6	−	11935.6i	−1.66808	−	1.17138i
$471$	−770.893	−	2502.63i	−0.0754159	−	0.244830i
$472$	1613.45	−	1600.37i	0.157341	−	0.156066i
$473$	4792.80	+	2767.13i	0.465906	+	0.268991i
$474$	−10306.0	−	11428.8i	−0.998671	−	1.10747i
$475$	−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	0.959215	−	0.282676i	$-0.0912221\pi$
$479$	2461.54	+	4263.51i	0.234803	+	0.406691i	−0.724412	+	0.689367i	$0.757889\pi$
$480$	−18987.1	+	7568.18i	−1.80550	+	0.719664i
$481$	−739.859	+	1281.47i	−0.0701344	+	0.121476i
$482$	−424.108	+	4773.01i	−0.0400780	+	0.451047i
$483$	−373.040	+	401.728i	−0.0351427	+	0.0378453i
$484$	−5019.78	−	899.169i	−0.471429	−	0.0844449i
$485$	1302.54			0.121949
$486$	3756.56	+	10033.9i	0.350620	+	0.936518i
$487$		−	20038.3i		−	1.86452i	−0.361783	−	0.932262i	$-0.617832\pi$
$487$		−	20038.3i		−	1.86452i	0.361783	−	0.932262i	$-0.382168\pi$
$488$	−2280.57	−	8651.88i	−0.211551	−	0.802566i
$489$	−9506.67	−	8827.78i	−0.879155	−	0.816373i
$490$	1057.33	−	11899.4i	0.0974799	−	1.09706i
$491$	−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	$0.891350\pi$
$492$	15269.0	−	11491.5i	1.39915	−	1.05300i
$493$	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
$498$	−12891.1	−	14295.5i	−1.15997	−	1.28634i
$499$	−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	$0.276733\pi$
$500$	13114.1	+	36337.1i	1.17296	+	3.25009i
$501$	7045.66	−	2170.30i	0.628297	−	0.193537i
$502$	4728.32	−	6733.29i	0.420389	−	0.598648i
$503$	12944.3			1.14743			0.573716	−	0.819055i	$-0.305501\pi$
$503$	12944.3			1.14743			0.573716	+	0.819055i	$0.305501\pi$
$504$	−7042.22	+	2425.93i	−0.622392	+	0.214404i
$505$	29593.1			2.60767
$506$	−370.445	+	527.525i	−0.0325460	+	0.0463466i
$507$	−1654.22	+	7234.65i	−0.144904	+	0.633732i
$508$	106.614	−	38.4769i	0.00931144	−	0.00336051i
$509$	−1935.70	+	3352.73i	−0.168563	+	0.291959i	−0.937915	−	0.346866i	$-0.887246\pi$
$509$	−1935.70	+	3352.73i	−0.168563	+	0.291959i	0.769352	+	0.638825i	$0.220579\pi$
$510$	5551.19	−	17128.4i	0.481982	−	1.48717i
$511$	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
$516$	−8671.17	+	1059.33i	−0.739781	+	0.0903771i
$517$	−7706.60	−	4449.41i	−0.655582	−	0.378500i
$518$	−162.880	+	1833.09i	−0.0138157	+	0.155485i
$519$	741.044	−	3240.92i	0.0626748	−	0.274105i
$520$	−3474.94	−	13183.0i	−0.293050	−	1.11176i
$521$			1410.78i			0.118632i	0.998239	+	0.0593162i	$0.0188920\pi$
$521$			1410.78i			0.118632i	−0.998239	+	0.0593162i	$0.981108\pi$
$522$	−6691.95	−	97.7121i	−0.561108	−	0.00819300i
$523$	18732.3			1.56617			0.783085	−	0.621915i	$-0.213645\pi$
$523$	18732.3			1.56617			0.783085	+	0.621915i	$0.213645\pi$
$524$	1374.51	−	7673.48i	0.114591	−	0.639728i
$525$	6475.28	+	21021.3i	0.538294	+	1.74752i
$526$	−278.023	+	3128.93i	−0.0230464	+	0.259369i
$527$	5686.09	−	9848.60i	0.470000	−	0.814064i
$528$	−7816.47	+	3950.05i	−0.644258	+	0.325575i
$529$	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
$534$	−5798.90	+	1237.13i	−0.469931	+	0.100254i
$535$	18973.1	+	10954.1i	1.53323	+	0.885210i
$536$	2185.26	+	2203.11i	0.176098	+	0.177537i
$537$	−6120.02	+	6590.68i	−0.491803	+	0.529625i
$538$	−987.190	−	693.235i	−0.0791092	−	0.0555529i
$539$		−	5118.61i		−	0.409043i
$540$	−18349.4	+	16067.3i	−1.46228	+	1.28042i
$541$		−	16968.0i		−	1.34845i	−0.738525	−	0.674226i	$-0.764477\pi$
$541$		−	16968.0i		−	1.34845i	0.738525	−	0.674226i	$-0.235523\pi$
$542$	−6984.88	+	9946.70i	−0.553554	+	0.788279i
$543$	−6649.93	+	7161.34i	−0.525554	+	0.565971i
$544$	820.496	+	10172.4i	0.0646663	+	0.801726i
$545$	−24832.5	−	14337.1i	−1.95176	−	1.12685i
$546$	−1036.55	−	4858.68i	−0.0812455	−	0.380829i
$547$	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
$552$	−33.5120	−	1016.93i	−0.00258400	−	0.0784122i
$553$	6382.98	−	11055.6i	0.490835	−	0.850151i
$554$	10723.8	+	952.871i	0.822403	+	0.0730751i
$555$	1773.99	+	5759.07i	0.135679	+	0.440467i
$556$	2500.35	+	447.877i	0.190717	+	0.0341622i
$557$	−5552.85			−0.422409			−0.211204	−	0.977442i	$-0.567739\pi$
$557$	−5552.85			−0.422409			−0.211204	+	0.977442i	$0.567739\pi$
$558$	−13451.6	+	7506.61i	−1.02053	+	0.569499i
$559$		−	5826.63i		−	0.440859i
$560$	−10828.2	−	13047.7i	−0.817098	−	0.984579i
$561$	1719.63	−	7520.72i	0.129417	−	0.565998i
$562$	1924.39	+	170.993i	0.144441	+	0.0128344i
$563$	−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	$0.749104\pi$
$564$	13942.8	−	1703.36i	1.04096	−	0.127171i
$565$	−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	$0.116412\pi$
$570$	24600.0	+	7972.68i	1.80769	+	0.585858i
$571$	−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	$0.259171\pi$
$572$	−1983.00	−	5494.57i	−0.144953	−	0.401643i
$573$	−4548.61	+	19893.1i	−0.331625	+	1.45034i
$574$	12973.3	+	9110.25i	0.943371	+	0.662464i
$575$	−3004.77			−0.217927
$576$	6108.81	−	12401.0i	0.441899	−	0.897065i
$577$	−15947.8			−1.15063			−0.575317	−	0.817931i	$-0.695121\pi$
$577$	−15947.8			−1.15063			−0.575317	+	0.817931i	$0.695121\pi$
$578$	4014.99	+	2819.45i	0.288930	+	0.202895i
$579$	12229.3	−	3767.02i	0.877774	−	0.270384i
$580$	−5171.92	−	14330.6i	−0.370263	−	1.02594i
$581$	7984.07	−	13828.8i	0.570112	−	0.987463i
$582$	−654.226	+	589.955i	−0.0465954	+	0.0420179i
$583$	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	$0.511661\pi$
$588$	4858.48	+	6455.59i	0.340749	+	0.452762i
$589$	14144.7	+	8166.43i	0.989510	+	0.571294i
$590$	6148.69	+	546.346i	0.429047	+	0.0381232i
$591$	10172.5	+	9446.04i	0.708020	+	0.657459i
$592$	−2181.26	−	2628.36i	−0.151435	−	0.182474i
$593$		−	12320.9i		−	0.853216i	−0.904437	−	0.426608i	$-0.859708\pi$
$593$		−	12320.9i		−	0.853216i	0.904437	−	0.426608i	$-0.140292\pi$
$594$	−7222.00	+	7553.18i	−0.498859	+	0.521735i
$595$	14936.2			1.02912
$596$	12773.5	+	2288.05i	0.877889	+	0.157252i
$597$	−1900.40	+	2046.55i	−0.130282	+	0.140301i
$598$	675.994	+	60.0659i	0.0462265	+	0.00410748i
$599$	10407.9	−	18027.0i	0.709942	−	1.22965i	−0.254937	−	0.966958i	$-0.582055\pi$
$599$	10407.9	−	18027.0i	0.709942	−	1.22965i	0.964878	−	0.262697i	$-0.0846120\pi$
$600$	−36007.9	−	19236.6i	−2.45003	−	1.30888i
$601$	−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
$606$	−14863.7	+	13403.5i	−0.996364	+	0.898481i
$607$	−22006.3	−	12705.3i	−1.47151	−	0.849578i	−0.472025	−	0.881585i	$-0.656477\pi$
$607$	−22006.3	−	12705.3i	−1.47151	−	0.849578i	−0.999488	+	0.0320069i	$0.989810\pi$
$608$	−14609.8	+	1178.41i	−0.974513	+	0.0786031i
$609$	−1634.36	−	5305.78i	−0.108748	−	0.353040i
$610$	13967.2	−	19889.8i	0.927074	−	1.32018i
$611$			9368.95i			0.620339i
$612$	4969.71	+	11117.4i	0.328250	+	0.734301i
$613$			15189.6i			1.00082i	0.865788	+	0.500411i	$0.166818\pi$
$613$			15189.6i			1.00082i	−0.865788	+	0.500411i	$0.833182\pi$
$614$	7861.46	+	5520.56i	0.516714	+	0.362853i
$615$	50603.3	+	11570.6i	3.31792	+	0.758651i
$616$	−5116.15	−	5157.96i	−0.334636	−	0.337370i
$617$	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	$0.589264\pi$
$618$	−4597.13	+	14184.6i	−0.299229	+	0.923283i
$619$	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
$624$	7716.28	+	5047.52i	0.495030	+	0.323818i
$625$	−30766.3	+	53288.7i	−1.96904	+	3.41048i
$626$	−378.475	+	4259.45i	−0.0241644	+	0.271952i
$627$	10801.3	+	2469.75i	0.687981	+	0.157309i
$628$	−710.866	+	3968.54i	−0.0451698	+	0.252169i
$629$	3008.79			0.190729
$630$	−17372.0	−	10370.8i	−1.09860	−	0.655845i
$631$			15335.4i			0.967498i	0.875207	+	0.483749i	$0.160725\pi$
$631$			15335.4i			0.967498i	−0.875207	+	0.483749i	$0.839275\pi$
$632$	6039.12	+	22910.8i	0.380100	+	1.44200i
$633$	596.173	−	183.641i	0.0374340	−	0.0115309i
$634$	−1262.27	+	14205.9i	−0.0790711	+	0.889884i
$635$	266.631	+	153.940i	0.0166629	+	0.00962032i
$636$	−1370.38	+	3222.95i	−0.0854386	+	0.200941i
$637$	−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	$0.0442803\pi$
$642$	−14491.0	+	3091.49i	−0.890832	+	0.190049i
$643$	−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	$0.968612\pi$
$644$	793.917	−	286.526i	0.0485788	−	0.0175321i
$645$	−17388.2	−	16146.4i	−1.06149	−	0.985683i
$646$	7420.10	−	10566.5i	0.451919	−	0.643548i
$647$	−19485.5			−1.18401			−0.592003	−	0.805935i	$-0.701663\pi$
$647$	−19485.5			−1.18401			−0.592003	+	0.805935i	$0.701663\pi$
$648$	1939.05	−	16381.0i	0.117551	−	0.993067i
$649$	2644.91			0.159972
$650$	15648.5	−	22284.0i	0.944283	−	1.34469i
$651$	−9363.92	−	8695.23i	−0.563750	−	0.523491i
$652$	6780.47	+	18787.6i	0.407276	+	1.12850i
$653$	7917.43	−	13713.4i	0.474476	−	0.821817i	−0.525097	−	0.851043i	$-0.675971\pi$
$653$	7917.43	−	13713.4i	0.474476	−	0.821817i	0.999573	+	0.0292257i	$0.00930416\pi$
$654$	18966.3	−	4046.24i	1.13400	−	0.241927i
$655$	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	$0.460650\pi$
$660$	−21892.4	−	9308.47i	−1.29115	−	0.548988i
$661$	−3627.99	−	2094.62i	−0.213483	−	0.123255i	0.389446	−	0.921049i	$-0.372667\pi$
$661$	−3627.99	−	2094.62i	−0.213483	−	0.123255i	−0.602929	+	0.797795i	$0.706000\pi$
$662$	−1613.68	+	18160.7i	−0.0947393	+	1.06622i
$663$	−7762.47	+	2391.10i	−0.454705	+	0.140064i
$664$	7553.95	+	28657.7i	0.441491	+	1.67490i
$665$			21451.5i			1.25091i
$666$	−3499.46	−	2089.12i	−0.203605	−	0.121549i
$667$	758.405			0.0440263
$668$	−11172.7	−	2001.31i	−0.647130	−	0.115917i
$669$	−16584.8	−	3792.16i	−0.958455	−	0.219153i
$670$	−746.019	+	8395.86i	−0.0430167	+	0.484120i
$671$	5206.77	−	9018.39i	0.299560	−	0.518854i
$672$	11348.3	+	1649.06i	0.651444	+	0.0946637i
$673$	−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	$0.269897\pi$
$677$	17266.4	+	29906.2i	0.980207	+	1.69777i	0.318652	+	0.947872i	$0.396770\pi$
$678$	8300.21	−	25610.6i	0.470159	−	1.45069i
$679$	−632.867	−	365.386i	−0.0357691	−	0.0206513i
$680$	−19681.5	+	19522.0i	−1.10993	+	1.10093i
$681$	3616.08	+	826.826i	0.203478	+	0.0465258i
$682$	−12296.1	−	8634.73i	−0.690387	−	0.484811i
$683$		−	19300.4i		−	1.08127i	−0.841256	−	0.540637i	$-0.818183\pi$
$683$		−	19300.4i		−	1.08127i	0.841256	−	0.540637i	$-0.181817\pi$
$684$	−15966.9	+	7137.56i	−0.892557	+	0.398993i
$685$			4865.90i			0.271411i
$686$	−10648.9	+	15164.5i	−0.592680	+	0.843997i
$687$	−3552.37	−	11532.4i	−0.197280	−	0.640450i
$688$	12613.2	+	4668.47i	0.698942	+	0.258697i
$689$	−2022.99	−	1167.97i	−0.111857	−	0.0645810i
$690$	2052.53	−	1850.89i	0.113244	−	0.102119i
$691$	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
$696$	9088.39	+	4855.31i	0.494964	+	0.264425i
$697$	12959.0	−	22445.6i	0.704240	−	1.21978i
$698$	19670.2	+	1747.81i	1.06666	+	0.0947787i
$699$	12616.9	−	13587.2i	0.682714	−	0.735217i
$700$	5971.07	−	33334.6i	0.322407	−	1.79990i
$701$	−29692.1			−1.59979			−0.799897	−	0.600138i	$-0.795112\pi$
$701$	−29692.1			−1.59979			−0.799897	+	0.600138i	$0.795112\pi$
$702$	10688.6	+	2608.75i	0.574666	+	0.140258i
$703$			4321.26i			0.231834i
$704$	13483.2	+	109.731i	0.721826	+	0.00587447i
$705$	27959.3	+	25962.7i	1.49363	+	1.38697i
$706$	35546.1	+	3158.47i	1.89489	+	0.168372i
$707$	−14378.4	−	8301.39i	−0.764861	−	0.441593i
$708$	−3335.75	+	2510.49i	−0.177070	+	0.133263i
$709$	12389.7	−	7153.20i	0.656284	−	0.378906i	−0.134576	−	0.990903i	$-0.542967\pi$
$709$	12389.7	−	7153.20i	0.656284	−	0.378906i	0.790860	+	0.611998i	$0.209634\pi$
$710$	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
$714$	−7501.99	+	6765.00i	−0.393214	+	0.354585i
$715$	7933.63	−	13741.4i	0.414966	−	0.718743i
$716$	13024.9	−	4700.69i	0.679835	−	0.245353i
$717$	6676.61	−	2056.62i	0.347758	−	0.107121i
$718$	−23171.0	−	16271.4i	−1.20437	−	0.845744i
$719$	−34830.8			−1.80663			−0.903316	−	0.428977i	$-0.858874\pi$
$719$	−34830.8			−1.80663			−0.903316	+	0.428977i	$0.858874\pi$
$720$	36446.0	−	9039.94i	1.88648	−	0.467915i
$721$	−12369.2			−0.638907
$722$	−700.902	−	492.195i	−0.0361287	−	0.0253707i
$723$	1962.21	−	8581.65i	0.100934	−	0.441431i
$724$	14152.6	−	5107.70i	0.726490	−	0.262191i
$725$	15214.6	−	26352.5i	0.779389	−	1.34994i
$726$	8912.32	+	2888.42i	0.455602	+	0.147657i
$727$	−28755.6	+	16602.0i	−1.46697	+	0.846954i	−0.999317	−	0.0369588i	$-0.988233\pi$
$727$	−28755.6	+	16602.0i	−1.46697	+	0.846954i	−0.467651	+	0.883913i	$0.654900\pi$
$728$	−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
$732$	1993.30	+	16316.1i	0.100648	+	0.823854i
$733$	−14167.9	−	8179.82i	−0.713918	−	0.412181i	0.0985919	−	0.995128i	$-0.468566\pi$
$733$	−14167.9	−	8179.82i	−0.713918	−	0.412181i	−0.812510	+	0.582947i	$0.801900\pi$
$734$	24512.3	+	2178.05i	1.23265	+	0.109528i
$735$	−4891.91	+	21394.5i	−0.245498	+	1.07367i
$736$	−671.653	+	1415.23i	−0.0336378	+	0.0708776i
$737$			3611.55i			0.180506i
$738$	−30657.1	+	17108.0i	−1.52914	+	0.853327i
$739$	8406.84			0.418472			0.209236	−	0.977865i	$-0.432902\pi$
$739$	8406.84			0.418472			0.209236	+	0.977865i	$0.432902\pi$
$740$	1635.85	−	9132.44i	0.0812637	−	0.453669i
$741$	−3434.13	−	11148.6i	−0.170251	−	0.552702i
$742$	−2893.79	−	257.130i	−0.143173	−	0.0127217i
$743$	−17253.8	+	29884.4i	−0.851924	+	1.47558i	0.0275453	+	0.999621i	$0.491231\pi$
$743$	−17253.8	+	29884.4i	−0.851924	+	1.47558i	−0.879469	+	0.475955i	$0.842102\pi$
$744$	23703.8	−	781.135i	1.16804	−	0.0384917i
$745$	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
$750$	−14807.4	−	69408.1i	−0.720921	−	3.37923i
$751$	−25214.0	−	14557.3i	−1.22513	−	0.707329i	−0.259123	−	0.965844i	$-0.583433\pi$
$751$	−25214.0	−	14557.3i	−1.22513	−	0.707329i	−0.966007	+	0.258515i	$0.916767\pi$
$752$	−20281.4	−	7506.67i	−0.983491	−	0.364016i
$753$	−10285.2	+	11076.2i	−0.497761	+	0.536041i
$754$	−3949.67	+	5624.47i	−0.190767	+	0.271659i
$755$		−	17829.5i		−	0.859446i
$756$	13422.6	−	2659.29i	0.645735	−	0.127933i
$757$			22457.3i			1.07824i	0.842230	+	0.539119i	$0.181243\pi$
$757$			22457.3i			1.07824i	−0.842230	+	0.539119i	$0.818757\pi$
$758$	−27161.8	−	19073.8i	−1.30153	−	0.913974i
$759$	805.805	−	867.774i	0.0385361	−	0.0414996i
$760$	−28037.7	−	28266.8i	−1.33820	−	1.34914i
$761$	−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	$0.810923\pi$
$762$	−203.644	+	43.4452i	−0.00968142	+	0.00206542i
$763$	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
$768$	−17109.1	+	12659.5i	−0.803869	+	0.594807i
$769$	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	$-0.00330874\pi$
$770$	1746.59	−	19656.5i	0.0817437	−	0.919962i
$771$	7388.42	+	23985.8i	0.345120	+	1.12040i
$772$	−19392.5	−	3473.70i	−0.904084	−	0.161944i
$773$	38982.8			1.81386			0.906930	−	0.421281i	$-0.138419\pi$
$773$	38982.8			1.81386			0.906930	+	0.421281i	$0.138419\pi$
$774$	16046.7	+	234.305i	0.745202	+	0.0108810i
$775$		−	70038.6i		−	3.24627i
$776$	1311.50	−	345.702i	0.0606703	−	0.0159923i
$777$	753.594	−	3295.81i	0.0347941	−	0.152170i
$778$	−1310.19	+	14745.2i	−0.0603761	+	0.679486i
$779$	32236.6	+	18611.8i	1.48266	+	0.856017i
$780$	3037.22	+	24861.1i	0.139423	+	1.14124i
$781$	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
$786$	−4415.38	+	13623.8i	−0.200371	+	0.618251i
$787$	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	$-0.174926\pi$
$788$	−7255.34	−	20103.4i	−0.327996	−	0.908825i
$789$	1286.33	−	5625.68i	0.0580411	−	0.253840i
$790$	−36986.1	+	52669.4i	−1.66570	+	2.37202i
$791$	22332.8			1.00387
$792$	15211.9	−	5240.27i	0.682490	−	0.235107i
$793$	−10963.7			−0.490961
$794$	16377.7	−	23322.5i	0.732021	−	1.04242i
$795$	−9091.53	+	2800.50i	−0.405589	+	0.124935i
$796$	4044.51	−	1459.67i	0.180093	−	0.0649957i
$797$	7370.19	−	12765.5i	0.327560	−	0.567351i	−0.654467	−	0.756091i	$-0.727107\pi$
$797$	7370.19	−	12765.5i	0.327560	−	0.567351i	0.982027	+	0.188740i	$0.0604402\pi$
$798$	−9715.97	−	10774.5i	−0.431004	−	0.477959i
$799$	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
$804$	−3428.00	−	4554.87i	−0.150369	−	0.199799i
$805$	1985.52	+	1146.34i	0.0869321	+	0.0501903i
$806$	−1400.08	+	15756.8i	−0.0611858	+	0.688598i
$807$	1623.92	+	1507.95i	0.0708359	+	0.0657774i
$808$	29796.7	−	7854.18i	1.29733	−	0.341967i
$809$			41957.2i			1.82341i	0.410850	+	0.911703i	$0.365232\pi$
$809$			41957.2i			1.82341i	−0.410850	+	0.911703i	$0.634768\pi$
$810$	37404.8	−	24668.3i	1.62256	−	1.07007i
$811$	−33724.2			−1.46020			−0.730098	−	0.683343i	$-0.760525\pi$
$811$	−33724.2			−1.46020			−0.730098	+	0.683343i	$0.760525\pi$
$812$	−1507.10	+	8413.64i	−0.0651339	+	0.363622i
$813$	15193.8	−	16362.2i	0.655435	−	0.705840i
$814$	351.837	−	3959.66i	0.0151498	−	0.170499i
$815$	−27127.5	+	46986.2i	−1.16593	+	2.01945i
$816$	1043.40	−	18719.6i	0.0447625	−	0.803083i
$817$	−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	0.858509	−	0.512798i	$-0.171391\pi$
$821$	−349.128	−	604.707i	−0.0148412	−	0.0257058i	−0.873351	+	0.487092i	$0.838058\pi$
$822$	−2203.90	−	2444.00i	−0.0935155	−	0.103703i
$823$	17635.1	+	10181.6i	0.746928	+	0.431239i	0.824583	−	0.565741i	$-0.191410\pi$
$823$	17635.1	+	10181.6i	0.746928	+	0.431239i	−0.0776551	+	0.996980i	$0.524743\pi$
$824$	16298.9	−	16166.8i	0.689077	−	0.683492i
$825$	−13987.3	−	45408.2i	−0.590271	−	1.91626i
$826$	−2834.22	−	1990.27i	−0.119389	−	0.0838383i
$827$		−	10885.2i		−	0.457697i	−0.973462	−	0.228849i	$-0.926504\pi$
$827$		−	10885.2i		−	0.457697i	0.973462	−	0.228849i	$-0.0734961\pi$
$828$	−192.606	+	1859.29i	−0.00808398	+	0.0780371i
$829$			35477.5i			1.48635i	0.669096	+	0.743176i	$0.266681\pi$
$829$			35477.5i			1.48635i	−0.669096	+	0.743176i	$0.733319\pi$
$830$	−46263.6	+	65880.9i	−1.93474	+	2.75513i
$831$	−19280.9	−	4408.63i	−0.804871	−	0.184036i
$832$	−6997.70	−	12351.4i	−0.291588	−	0.514674i
$833$	9489.74	+	5478.91i	0.394718	+	0.227891i
$834$	−4439.23	−	1438.72i	−0.184314	−	0.0597349i
$835$	−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	0.677179	−	0.735819i	$-0.263202\pi$
$839$	−7257.77	−	12570.8i	−0.298648	−	0.517274i	−0.975827	+	0.218544i	$0.929869\pi$
$840$	16454.7	+	26448.5i	0.675883	+	1.08638i
$841$	8354.33	−	14470.1i	0.342545	−	0.593306i
$842$	−12716.6	−	1129.94i	−0.520479	−	0.0462475i
$843$	−3459.97	−	791.131i	−0.141362	−	0.0323227i
$844$	−945.381	−	169.342i	−0.0385561	−	0.00690637i
$845$	31036.5			1.26354
$846$	−25802.3	−	376.751i	−1.04858	−	0.0153108i
$847$			7771.66i			0.315274i
$848$	4149.24	−	3443.44i	0.168025	−	0.139444i
$849$	6299.81	−	1940.55i	0.254663	−	0.0784447i
$850$	−55150.0	−	4900.39i	−2.22545	−	0.197743i
$851$	399.968	+	230.922i	0.0161113	+	0.00930188i
$852$	−12468.8	+	29325.0i	−0.501377	+	1.17918i
$853$	−4907.37	+	2833.27i	−0.196981	+	0.113727i	−0.595247	−	0.803543i	$-0.702946\pi$
$853$	−4907.37	+	2833.27i	−0.196981	+	0.113727i	0.398265	+	0.917270i	$0.369612\pi$
$854$	−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	$0.449229\pi$
$858$	2239.04	+	10495.3i	0.0890906	+	0.417602i
$859$	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	$0.0404165\pi$
$860$	12401.8	+	34363.4i	0.491742	+	1.36254i
$861$	−21341.0	−	19817.0i	−0.844713	−	0.784391i
$862$	1427.90	+	1002.71i	0.0564203	+	0.0396201i
$863$	15645.4			0.617120			0.308560	−	0.951205i	$-0.400153\pi$
$863$	15645.4			0.617120			0.308560	+	0.951205i	$0.400153\pi$
$864$	−14211.3	+	21047.8i	−0.559581	+	0.828776i
$865$	−13903.5			−0.546511
$866$	−4850.17	−	3405.94i	−0.190318	−	0.133647i
$867$	−6604.61	−	6132.96i	−0.258713	−	0.240238i
$868$	6678.66	+	18505.5i	0.261162	+	0.723638i
$869$	−13787.9	+	23881.3i	−0.538230	+	0.932242i
$870$	5839.73	+	27373.0i	0.227569	+	1.06670i
$871$	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
$876$	7554.56	−	17767.4i	0.291375	−	0.685279i
$877$	33993.4	+	19626.1i	1.30886	+	0.755673i	0.981907	−	0.189366i	$-0.0606432\pi$
$877$	33993.4	+	19626.1i	1.30886	+	0.755673i	0.326958	+	0.945039i	$0.393977\pi$
$878$	−27359.9	−	2431.08i	−1.05165	−	0.0934454i
$879$	24948.6	−	7685.02i	0.957334	−	0.294891i
$880$	23390.0	+	28184.3i	0.895997	+	1.07965i
$881$			4220.62i			0.161403i	0.996738	+	0.0807017i	$0.0257161\pi$
$881$			4220.62i			0.161403i	−0.996738	+	0.0807017i	$0.974284\pi$
$882$	−7233.09	−	12961.5i	−0.276135	−	0.494826i
$883$	−48035.9			−1.83073			−0.915365	−	0.402624i	$-0.868098\pi$
$883$	−48035.9			−1.83073			−0.915365	+	0.402624i	$0.868098\pi$
$884$	12309.3	+	2204.91i	0.468334	+	0.0838906i
$885$	−11055.1	−	2527.77i	−0.419901	−	0.0960113i
$886$	24871.9	+	2210.00i	0.943101	+	0.0837997i
$887$	2102.75	−	3642.06i	0.0795978	−	0.137867i	−0.823479	−	0.567347i	$-0.807970\pi$
$887$	2102.75	−	3642.06i	0.0795978	−	0.137867i	0.903076	+	0.429480i	$0.141303\pi$
$888$	3314.69	+	5327.87i	0.125263	+	0.201342i
$889$	−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
$894$	−22678.6	−	7349.96i	−0.848417	−	0.274966i
$895$	32574.0	+	18806.6i	1.21657	+	0.702387i
$896$	−14365.6	−	10263.6i	−0.535627	−	0.382680i
$897$	−1215.41	−	277.906i	−0.0452411	−	0.0103445i
$898$	−130.324	+	185.586i	−0.00484296	+	0.00689654i
$899$			17677.7i			0.655823i
$900$	60741.3	+	43992.4i	2.24968	+	1.62935i
$901$			4749.81i			0.175626i
$902$	−28023.7	−	19679.1i	−1.03446	−	0.726432i
$903$	3919.04	+	12722.8i	0.144427	+	0.468868i
$904$	−29428.0	+	29189.5i	−1.08270	+	1.07393i
$905$	35394.5	+	20435.0i	1.30006	+	0.750589i
$906$	8075.45	+	8955.21i	0.296125	+	0.328385i
$907$	−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	$0.0482623\pi$
$911$	17187.2	+	29769.1i	0.625069	+	1.08265i	−0.363459	+	0.931610i	$0.618404\pi$
$912$	26885.3	+	1498.54i	0.976162	+	0.0544096i
$913$	−17246.4	+	29871.7i	−0.625162	+	1.08281i
$914$	934.116	−	10512.7i	0.0338051	−	0.380449i
$915$	−30382.0	+	32718.5i	−1.09770	+	1.18212i
$916$	−3275.76	+	18287.5i	−0.118160	+	0.659647i
$917$	−11880.1			−0.427827
$918$	−6273.00	−	21474.2i	−0.225534	−	0.772063i
$919$			18530.2i			0.665132i	0.943080	+	0.332566i	$0.107914\pi$
$919$			18530.2i			0.665132i	−0.943080	+	0.332566i	$0.892086\pi$
$920$	−4114.62	+	1084.58i	−0.147451	+	0.0388671i
$921$	−12932.0	−	12008.5i	−0.462676	−	0.429635i
$922$	3202.09	−	36037.1i	0.114377	−	1.28722i
$923$	−18406.8	−	10627.2i	−0.656410	−	0.378978i
$924$	8025.68	+	10663.9i	0.285742	+	0.379673i
$925$	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	$0.176747\pi$
$930$	43142.5	+	47842.6i	1.52118	+	1.68690i
$931$	−7868.87	+	13629.3i	−0.277005	+	0.479787i
$932$	−26851.8	+	9690.86i	−0.943736	+	0.340595i
$933$	−25697.8	+	7915.77i	−0.901723	+	0.277761i
$934$	−3110.98	+	4430.14i	−0.108988	+	0.155202i
$935$	−32263.7			−1.12849
$936$	−12785.8	−	11111.3i	−0.446491	−	0.388019i
$937$	12325.5			0.429731			0.214866	−	0.976644i	$-0.431069\pi$
$937$	12325.5			0.429731			0.214866	+	0.976644i	$0.431069\pi$
$938$	2717.66	−	3870.04i	0.0945999	−	0.134713i
$939$	1751.09	−	7658.29i	0.0608568	−	0.266154i
$940$	−19941.5	−	55254.7i	−0.691936	−	1.91725i
$941$	2589.25	−	4484.71i	0.0896993	−	0.155364i	−0.817685	−	0.575666i	$-0.804743\pi$
$941$	2589.25	−	4484.71i	0.0896993	−	0.155364i	0.907384	+	0.420303i	$0.138076\pi$
$942$	2283.53	−	7045.91i	0.0789823	−	0.243703i
$943$	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	$0.528187\pi$
$948$	−5278.39	−	43206.2i	−0.180838	−	1.48025i
$949$	11152.3	+	6438.76i	0.381473	+	0.220244i
$950$	7037.99	−	79207.1i	0.240361	−	2.70507i
$951$	5840.12	−	25541.5i	0.199137	−	0.870913i
$952$	15039.0	−	3964.16i	0.511991	−	0.134957i
$953$			31313.4i			1.06437i	0.846629	+	0.532184i	$0.178628\pi$
$953$			31313.4i			1.06437i	−0.846629	+	0.532184i	$0.821372\pi$
$954$	3297.98	−	5524.40i	0.111925	−	0.187483i
$955$	85341.0			2.89170
$956$	−10587.4	−	1896.48i	−0.358182	−	0.0641595i
$957$	3530.38	+	11461.0i	0.119249	+	0.387129i
$958$	−1232.42	+	13869.9i	−0.0415634	+	0.467763i
$959$	1364.97	−	2364.20i	0.0459618	−	0.0796081i
$960$	−56251.4	−	13344.6i	−1.89115	−	0.448642i
$961$	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
$966$	−1516.47	+	323.522i	−0.0505090	+	0.0107755i
$967$	−26936.3	−	15551.7i	−0.895774	−	0.517175i	−0.0199473	−	0.999801i	$-0.506350\pi$
$967$	−26936.3	−	15551.7i	−0.895774	−	0.517175i	−0.875827	+	0.482626i	$0.839683\pi$
$968$	−10157.8	−	10240.8i	−0.337275	−	0.340032i
$969$	−16140.5	+	17381.7i	−0.535095	+	0.576246i
$970$	3015.00	+	2117.23i	0.0997999	+	0.0700826i
$971$			13249.7i			0.437902i	0.975736	+	0.218951i	$0.0702635\pi$
$971$			13249.7i			0.437902i	−0.975736	+	0.218951i	$0.929737\pi$
$972$	−7614.38	+	29331.7i	−0.251267	+	0.967918i
$973$		−	3871.07i		−	0.127544i
$974$	32571.5	−	46382.9i	1.07152	−	1.52588i
$975$	−34039.2	+	36656.9i	−1.11808	+	1.20406i
$976$	8784.43	−	23733.6i	0.288097	−	0.778374i
$977$	−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	$0.759797\pi$
$978$	−7655.98	−	35886.5i	−0.250318	−	1.17334i
$979$	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	$-0.938536\pi$
$983$	−20245.4	−	35066.1i	−0.656895	−	1.13778i	0.324520	−	0.945879i	$-0.394797\pi$
$984$	54022.4	−	1780.26i	1.75017	−	0.0576753i
$985$	29027.4	−	50276.9i	0.938973	−	1.62635i
$986$	13919.9	+	1236.86i	0.449593	+	0.0399488i
$987$	−6301.64	−	20457.6i	−0.203225	−	0.659750i
$988$	−3166.72	+	17678.8i	−0.101971	+	0.569269i
$989$	−1818.59			−0.0584708
$990$	37525.2	+	22402.0i	1.20468	+	0.719173i
$991$		−	3021.88i		−	0.0968650i	−0.998826	−	0.0484325i	$-0.984577\pi$
$991$		−	3021.88i		−	0.0968650i	0.998826	−	0.0484325i	$-0.0154226\pi$
$992$	−32987.7	−	15655.6i	−1.05581	−	0.501075i
$993$	7465.99	−	32652.1i	0.238596	−	1.04349i
$994$	−26330.0	−	2339.57i	−0.840178	−	0.0746545i
$995$	10115.0	+	5839.88i	0.322277	+	0.186067i
$996$	−6602.41	−	54044.0i	−0.210046	−	1.71933i
$997$	33345.3	−	19251.9i	1.05923	−	0.611549i	0.134014	−	0.990979i	$-0.457213\pi$
$997$	33345.3	−	19251.9i	1.05923	−	0.611549i	0.925220	+	0.379431i	$0.123880\pi$
$998$	−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.59.26	yes	64
3.2	odd	2		216.4.l.b.179.7		64
4.3	odd	2		288.4.p.b.239.23		64
8.3	odd	2	inner	72.4.l.b.59.15	yes	64
8.5	even	2		288.4.p.b.239.24		64
9.2	odd	6	inner	72.4.l.b.11.15	✓	64
9.7	even	3		216.4.l.b.35.18		64
12.11	even	2		864.4.p.b.719.32		64
24.5	odd	2		864.4.p.b.719.1		64
24.11	even	2		216.4.l.b.179.18		64
36.7	odd	6		864.4.p.b.143.1		64
36.11	even	6		288.4.p.b.47.24		64
72.11	even	6	inner	72.4.l.b.11.26	yes	64
72.29	odd	6		288.4.p.b.47.23		64
72.43	odd	6		216.4.l.b.35.7		64
72.61	even	6		864.4.p.b.143.32		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.15	✓	64	9.2	odd	6	inner
72.4.l.b.11.26	yes	64	72.11	even	6	inner
72.4.l.b.59.15	yes	64	8.3	odd	2	inner
72.4.l.b.59.26	yes	64	1.1	even	1	trivial
216.4.l.b.35.7		64	72.43	odd	6
216.4.l.b.35.18		64	9.7	even	3
216.4.l.b.179.7		64	3.2	odd	2
216.4.l.b.179.18		64	24.11	even	2
288.4.p.b.47.23		64	72.29	odd	6
288.4.p.b.47.24		64	36.11	even	6
288.4.p.b.239.23		64	4.3	odd	2
288.4.p.b.239.24		64	8.5	even	2
864.4.p.b.143.1		64	36.7	odd	6
864.4.p.b.143.32		64	72.61	even	6
864.4.p.b.719.1		64	24.5	odd	2
864.4.p.b.719.32		64	12.11	even	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+(2.31471 + 1.62546i) q^{2} +(-3.80768 - 3.53576i) q^{3} +(2.71576 + 7.52494i) q^{4} +(-10.8653 + 18.8192i) q^{5} +(-3.06642 - 14.3735i) 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} +(16.2657 - 38.2548i) q^{12} +(24.0118 + 13.8632i) q^{13} +(34.3478 + 3.05199i) q^{14} +(107.912 - 33.2404i) q^{15} +(-49.2493 + 40.8718i) q^{16} -56.3777i q^{17} +(-39.1453 + 65.5717i) q^{18} +80.9703 q^{19} +(-171.121 - 30.6521i) q^{20} +(-61.7558 - 14.1206i) q^{21} +(-74.1948 - 6.59262i) q^{22} +(4.32694 - 7.49448i) q^{23} +(99.8319 - 62.1095i) 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} +(303.815 + 98.4643i) q^{30} +(174.690 + 100.857i) q^{31} +(-180.433 + 14.5536i) q^{32} +(133.399 + 30.5020i) q^{33} +(91.6397 - 130.498i) q^{34} +264.931i q^{35} +(-197.194 + 88.1503i) q^{36} +53.3684i q^{37} +(187.423 + 131.614i) q^{38} +(-42.4122 - 137.687i) q^{39} +(-346.271 - 349.101i) q^{40} +(398.128 + 229.859i) q^{41} +(-119.994 - 133.067i) 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} +(332.038 + 18.5073i) q^{48} +(-97.1821 + 168.324i) q^{49} +(86.9206 - 978.224i) q^{50} +(-199.338 + 214.668i) q^{51} +(-39.1097 + 218.337i) q^{52} -84.2497 q^{53} +(380.898 - 111.267i) q^{54} -572.278i q^{55} +(70.3143 + 266.753i) q^{56} +(-308.309 - 286.292i) q^{57} +(-21.9388 + 246.904i) q^{58} +(-86.9772 - 50.2163i) q^{59} +(543.194 + 721.756i) 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} +(259.200 + 287.438i) q^{66} +(68.5689 - 118.765i) q^{67} +(424.239 - 153.108i) q^{68} +(-42.9743 + 13.2375i) q^{69} +(-430.635 + 613.238i) q^{70} -766.570 q^{71} +(-599.732 - 116.489i) q^{72} +464.449 q^{73} +(-86.7482 + 123.532i) q^{74} +(-402.154 + 1758.80i) q^{75} +(219.896 + 609.297i) q^{76} +(-160.534 + 278.054i) q^{77} +(125.633 - 387.644i) 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} +(-61.4571 - 503.056i) q^{84} +(1060.98 + 612.560i) q^{85} +(52.6072 - 592.052i) q^{86} +(101.504 - 443.921i) q^{87} +(-151.886 - 576.215i) q^{88} -403.445i q^{89} +(-808.683 - 1449.14i) q^{90} +338.031 q^{91} +(68.1464 + 12.2068i) q^{92} +(-308.555 - 1001.69i) q^{93} +(-84.5898 + 951.992i) q^{94} +(-879.765 + 1523.80i) q^{95} +(738.489 + 582.554i) 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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