LMFDB - Embedded newform 184.4.p.a.85.53

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,4,Mod(13,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 14])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.13"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	184.p (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8563514411$
Analytic rank:	$0$
Dimension:	$700$
Relative dimension:	$70$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.53
Character	$\chi$	$=$	184.85
Dual form			184.4.p.a.13.53

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.93800 + 2.06013i) q^{2} +(4.76362 + 7.41234i) q^{3} +(-0.488295 + 7.98508i) q^{4} +(-11.6365 + 5.31419i) q^{5} +(-6.03849 + 24.1788i) q^{6} +(6.99300 - 2.05333i) q^{7} +(-17.3967 + 14.4692i) q^{8} +(-21.0345 + 46.0590i) q^{9} +(-33.4994 - 13.6737i) q^{10} +(47.8965 - 41.5026i) q^{11} +(-61.5142 + 34.4185i) q^{12} +(11.7738 - 40.0978i) q^{13} +(17.7826 + 10.4271i) q^{14} +(-94.8222 - 60.9385i) q^{15} +(-63.5231 - 7.79815i) q^{16} +(-12.7541 + 88.7065i) q^{17} +(-135.653 + 45.9287i) q^{18} +(29.7073 - 4.27127i) q^{19} +(-36.7522 - 95.5130i) q^{20} +(48.5319 + 42.0532i) q^{21} +(178.324 + 18.2411i) q^{22} +(105.562 + 31.9943i) q^{23} +(-190.121 - 60.0243i) q^{24} +(25.3089 - 29.2080i) q^{25} +(105.424 - 53.4541i) q^{26} +(-206.128 + 29.6367i) q^{27} +(12.9814 + 56.8423i) q^{28} +(49.3299 + 7.09257i) q^{29} +(-58.2242 - 313.445i) q^{30} +(-122.333 - 78.6185i) q^{31} +(-107.043 - 145.979i) q^{32} +(535.792 + 157.323i) q^{33} +(-207.465 + 145.638i) q^{34} +(-70.4619 + 61.0556i) q^{35} +(-357.514 - 190.452i) q^{36} +(-103.985 - 47.4883i) q^{37} +(66.3722 + 52.9233i) q^{38} +(353.304 - 103.739i) q^{39} +(125.543 - 260.819i) q^{40} +(108.830 + 238.305i) q^{41} +(7.41990 + 181.481i) q^{42} +(217.161 + 337.908i) q^{43} +(308.014 + 402.723i) q^{44} -647.745i q^{45} +(138.667 + 279.477i) q^{46} -380.955 q^{47} +(-244.798 - 508.002i) q^{48} +(-243.864 + 156.722i) q^{49} +(109.221 - 4.46552i) q^{50} +(-718.278 + 328.027i) q^{51} +(314.435 + 113.594i) q^{52} +(-110.902 - 377.698i) q^{53} +(-460.532 - 367.215i) q^{54} +(-336.793 + 737.474i) q^{55} +(-91.9448 + 136.904i) q^{56} +(173.174 + 199.854i) q^{57} +(80.9899 + 115.372i) q^{58} +(153.082 - 521.348i) q^{59} +(532.901 - 727.407i) q^{60} +(-152.023 + 236.552i) q^{61} +(-75.1166 - 404.385i) q^{62} +(-52.5195 + 365.281i) q^{63} +(93.2869 - 503.430i) q^{64} +(76.0823 + 529.164i) q^{65} +(714.260 + 1408.69i) q^{66} +(194.548 + 168.577i) q^{67} +(-702.101 - 145.157i) q^{68} +(265.706 + 934.871i) q^{69} +(-262.338 - 26.8350i) q^{70} +(497.669 - 574.340i) q^{71} +(-300.506 - 1105.62i) q^{72} +(-82.9602 - 577.001i) q^{73} +(-103.691 - 306.255i) q^{74} +(337.062 + 48.4621i) q^{75} +(19.6005 + 239.301i) q^{76} +(249.722 - 388.575i) q^{77} +(898.421 + 526.806i) q^{78} +(790.457 + 232.099i) q^{79} +(780.625 - 246.831i) q^{80} +(-306.307 - 353.497i) q^{81} +(-280.027 + 686.040i) q^{82} +(820.726 + 374.813i) q^{83} +(-359.496 + 366.997i) q^{84} +(-322.991 - 1100.01i) q^{85} +(-275.279 + 1102.25i) q^{86} +(182.416 + 399.436i) q^{87} +(-232.732 + 1415.03i) q^{88} +(772.899 - 496.712i) q^{89} +(1334.44 - 1255.33i) q^{90} -304.579i q^{91} +(-307.022 + 827.300i) q^{92} -1281.28i q^{93} +(-738.292 - 784.818i) q^{94} +(-322.989 + 207.573i) q^{95} +(572.134 - 1488.82i) q^{96} +(-487.556 - 1067.60i) q^{97} +(-795.477 - 198.665i) q^{98} +(904.091 + 3079.05i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 700 q - 7 q^{2} + 13 q^{4} - 52 q^{6} + 10 q^{7} - 46 q^{8} + 576 q^{9} + 35 q^{10} - 24 q^{12} + 77 q^{14} - 246 q^{15} - 27 q^{16} - 18 q^{17} - 230 q^{18} + 53 q^{20} + 182 q^{22} + 144 q^{23} + 154 q^{24}+ \cdots - 7727 q^{98}+O(q^{100}) $ 700 * q - 7 * q^2 + 13 * q^4 - 52 * q^6 + 10 * q^7 - 46 * q^8 + 576 * q^9 + 35 * q^10 - 24 * q^12 + 77 * q^14 - 246 * q^15 - 27 * q^16 - 18 * q^17 - 230 * q^18 + 53 * q^20 + 182 * q^22 + 144 * q^23 + 154 * q^24 + 1532 * q^25 + 50 * q^26 + 151 * q^28 + 39 * q^30 - 546 * q^31 + 53 * q^32 - 126 * q^33 - 1175 * q^34 + 2613 * q^36 + 60 * q^38 + 174 * q^39 - 1565 * q^40 - 18 * q^41 + 2983 * q^42 - 2596 * q^44 + 3645 * q^46 - 40 * q^47 - 3908 * q^48 - 2860 * q^49 + 1858 * q^50 - 1154 * q^52 - 432 * q^54 - 518 * q^55 + 4562 * q^56 - 126 * q^57 - 4499 * q^58 + 2651 * q^60 - 1540 * q^62 - 14 * q^63 - 158 * q^64 - 518 * q^65 + 2368 * q^66 - 1270 * q^68 - 2006 * q^70 - 1498 * q^71 + 2103 * q^72 - 18 * q^73 + 2216 * q^74 + 6852 * q^76 + 7956 * q^78 + 1834 * q^79 + 2362 * q^80 - 3268 * q^81 + 1098 * q^82 - 7971 * q^84 - 8759 * q^86 - 2154 * q^87 - 4495 * q^88 - 866 * q^89 - 13676 * q^90 - 10844 * q^92 - 12229 * q^94 + 722 * q^95 - 12211 * q^96 - 18 * q^97 - 7727 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	1.93800	+	2.06013i	0.685187	+	0.728367i
$2$	1.93800	+	2.06013i	0.685187	+	0.728367i
$3$	4.76362	+	7.41234i	0.916759	+	1.42650i	0.904450	+	0.426581i	$0.140282\pi$
$3$	4.76362	+	7.41234i	0.916759	+	1.42650i	0.0123095	+	0.999924i	$0.496082\pi$
$4$	−0.488295	+	7.98508i	−0.0610369	+	0.998136i
$5$	−11.6365	+	5.31419i	−1.04080	+	0.475316i	−0.861116	−	0.508409i	$-0.830234\pi$
$5$	−11.6365	+	5.31419i	−1.04080	+	0.475316i	−0.179681	+	0.983725i	$0.557506\pi$
$6$	−6.03849	+	24.1788i	−0.410867	+	1.64516i
$7$	6.99300	−	2.05333i	0.377586	−	0.110869i	−0.0874318	−	0.996171i	$-0.527866\pi$
$7$	6.99300	−	2.05333i	0.377586	−	0.110869i	0.465018	+	0.885301i	$0.346048\pi$
$8$	−17.3967	+	14.4692i	−0.768831	+	0.639452i
$9$	−21.0345	+	46.0590i	−0.779054	+	1.70589i
$10$	−33.4994	−	13.6737i	−1.05934	−	0.432401i
$11$	47.8965	−	41.5026i	1.31285	−	1.13759i	0.331903	−	0.943313i	$-0.392309\pi$
$11$	47.8965	−	41.5026i	1.31285	−	1.13759i	0.980947	−	0.194277i	$-0.0622362\pi$
$12$	−61.5142	+	34.4185i	−1.47980	+	0.827980i
$13$	11.7738	−	40.0978i	0.251189	−	0.855471i	−0.733282	−	0.679924i	$-0.762013\pi$
$13$	11.7738	−	40.0978i	0.251189	−	0.855471i	0.984471	−	0.175547i	$-0.0561693\pi$
$14$	17.7826	+	10.4271i	0.339471	+	0.199055i
$15$	−94.8222	−	60.9385i	−1.63220	−	1.04895i
$16$	−63.5231	−	7.79815i	−0.992549	−	0.121846i
$17$	−12.7541	+	88.7065i	−0.181960	+	1.26556i	0.670162	+	0.742215i	$0.266225\pi$
$17$	−12.7541	+	88.7065i	−0.181960	+	1.26556i	−0.852122	+	0.523343i	$0.824685\pi$
$18$	−135.653	+	45.9287i	−1.77631	+	0.601417i
$19$	29.7073	−	4.27127i	0.358701	−	0.0515734i	0.0393915	−	0.999224i	$-0.487458\pi$
$19$	29.7073	−	4.27127i	0.358701	−	0.0515734i	0.319310	+	0.947650i	$0.396549\pi$
$20$	−36.7522	−	95.5130i	−0.410903	−	1.06787i
$21$	48.5319	+	42.0532i	0.504311	+	0.436988i
$22$	178.324	+	18.2411i	1.72813	+	0.176774i
$23$	105.562	+	31.9943i	0.957010	+	0.290055i
$23$	105.562	+	31.9943i	0.957010	+	0.290055i
$24$	−190.121	−	60.0243i	−1.61701	−	0.510517i
$25$	25.3089	−	29.2080i	0.202471	−	0.233664i
$26$	105.424	−	53.4541i	0.795208	−	0.403200i
$27$	−206.128	+	29.6367i	−1.46924	+	0.211244i
$28$	12.9814	+	56.8423i	0.0876159	+	0.383649i
$29$	49.3299	+	7.09257i	0.315874	+	0.0454158i	0.298428	−	0.954432i	$-0.403538\pi$
$29$	49.3299	+	7.09257i	0.315874	+	0.0454158i	0.0174453	+	0.999848i	$0.494447\pi$
$30$	−58.2242	−	313.445i	−0.354341	−	1.90757i
$31$	−122.333	−	78.6185i	−0.708762	−	0.455493i	0.135950	−	0.990716i	$-0.456591\pi$
$31$	−122.333	−	78.6185i	−0.708762	−	0.455493i	−0.844711	+	0.535222i	$0.820228\pi$
$32$	−107.043	−	145.979i	−0.591333	−	0.806427i
$33$	535.792	+	157.323i	2.82635	+	0.829890i
$34$	−207.465	+	145.638i	−1.04647	+	0.734611i
$35$	−70.4619	+	61.0556i	−0.340292	+	0.294865i
$36$	−357.514	−	190.452i	−1.65516	−	0.881724i
$37$	−103.985	−	47.4883i	−0.462027	−	0.211001i	0.170782	−	0.985309i	$-0.445371\pi$
$37$	−103.985	−	47.4883i	−0.462027	−	0.211001i	−0.632809	+	0.774308i	$0.718098\pi$
$38$	66.3722	+	52.9233i	0.283342	+	0.225929i
$39$	353.304	−	103.739i	1.45061	−	0.425939i
$40$	125.543	−	260.819i	0.496254	−	1.03098i
$41$	108.830	+	238.305i	0.414547	+	0.907731i	0.995586	+	0.0938552i	$0.0299191\pi$
$41$	108.830	+	238.305i	0.414547	+	0.907731i	−0.581039	+	0.813876i	$0.697354\pi$
$42$	7.41990	+	181.481i	0.0272599	+	0.666742i
$43$	217.161	+	337.908i	0.770155	+	1.19839i	0.975565	+	0.219709i	$0.0705108\pi$
$43$	217.161	+	337.908i	0.770155	+	1.19839i	−0.205410	+	0.978676i	$0.565853\pi$
$44$	308.014	+	402.723i	1.05534	+	1.37984i
$45$		−	647.745i		−	2.14578i
$46$	138.667	+	279.477i	0.444464	+	0.895796i
$47$	−380.955			−1.18230			−0.591149	−	0.806562i	$-0.701325\pi$
$47$	−380.955			−1.18230			−0.591149	+	0.806562i	$0.701325\pi$
$48$	−244.798	−	508.002i	−0.736114	−	1.52758i
$49$	−243.864	+	156.722i	−0.710974	+	0.456915i
$50$	109.221	−	4.46552i	0.308924	−	0.0126304i
$51$	−718.278	+	328.027i	−1.97214	+	0.900645i
$52$	314.435	+	113.594i	0.838544	+	0.302936i
$53$	−110.902	−	377.698i	−0.287426	−	0.978882i	−0.968985	−	0.247119i	$-0.920516\pi$
$53$	−110.902	−	377.698i	−0.287426	−	0.978882i	0.681559	−	0.731763i	$-0.261302\pi$
$54$	−460.532	−	367.215i	−1.16056	−	0.925401i
$55$	−336.793	+	737.474i	−0.825694	+	1.80802i
$56$	−91.9448	+	136.904i	−0.219404	+	0.326688i
$57$	173.174	+	199.854i	0.402412	+	0.464409i
$58$	80.9899	+	115.372i	0.183353	+	0.261190i
$59$	153.082	−	521.348i	0.337788	−	1.15040i	−0.599071	−	0.800696i	$-0.704463\pi$
$59$	153.082	−	521.348i	0.337788	−	1.15040i	0.936860	−	0.349706i	$-0.113718\pi$
$60$	532.901	−	727.407i	1.14662	−	1.56513i
$61$	−152.023	+	236.552i	−0.319090	+	0.496514i	−0.963334	−	0.268307i	$-0.913536\pi$
$61$	−152.023	+	236.552i	−0.319090	+	0.496514i	0.644244	+	0.764820i	$0.277172\pi$
$62$	−75.1166	−	404.385i	−0.153868	−	0.828337i
$63$	−52.5195	+	365.281i	−0.105029	+	0.730494i
$64$	93.2869	−	503.430i	0.182201	−	0.983261i
$65$	76.0823	+	529.164i	0.145182	+	1.00977i
$66$	714.260	+	1408.69i	1.33211	+	2.62725i
$67$	194.548	+	168.577i	0.354744	+	0.307387i	0.813941	−	0.580947i	$-0.197318\pi$
$67$	194.548	+	168.577i	0.354744	+	0.307387i	−0.459198	+	0.888334i	$0.651863\pi$
$68$	−702.101	−	145.157i	−1.25209	−	0.258866i
$69$	265.706	+	934.871i	0.463582	+	1.63109i
$70$	−262.338	−	26.8350i	−0.447934	−	0.0458200i
$71$	497.669	−	574.340i	0.831865	−	0.960023i	−0.167802	−	0.985821i	$-0.553667\pi$
$71$	497.669	−	574.340i	0.831865	−	0.960023i	0.999667	+	0.0257975i	$0.00821250\pi$
$72$	−300.506	−	1105.62i	−0.491875	−	1.80971i
$73$	−82.9602	−	577.001i	−0.133010	−	0.925108i	−0.941600	−	0.336734i	$-0.890678\pi$
$73$	−82.9602	−	577.001i	−0.133010	−	0.925108i	0.808589	−	0.588373i	$-0.200232\pi$
$74$	−103.691	−	306.255i	−0.162889	−	0.481100i
$75$	337.062	+	48.4621i	0.518940	+	0.0746123i
$76$	19.6005	+	239.301i	0.0295833	+	0.361180i
$77$	249.722	−	388.575i	0.369590	−	0.575093i
$78$	898.421	+	526.806i	1.30418	+	0.764731i
$79$	790.457	+	232.099i	1.12574	+	0.330547i	0.791031	−	0.611776i	$-0.209544\pi$
$79$	790.457	+	232.099i	1.12574	+	0.330547i	0.334707	+	0.942322i	$0.391363\pi$
$80$	780.625	−	246.831i	1.09096	−	0.344957i
$81$	−306.307	−	353.497i	−0.420174	−	0.484907i
$82$	−280.027	+	686.040i	−0.377119	+	0.923908i
$83$	820.726	+	374.813i	1.08538	+	0.495676i	0.876075	−	0.482175i	$-0.160153\pi$
$83$	820.726	+	374.813i	1.08538	+	0.495676i	0.209303	+	0.977851i	$0.432880\pi$
$84$	−359.496	+	366.997i	−0.466955	+	0.476699i
$85$	−322.991	−	1100.01i	−0.412157	−	1.40368i
$86$	−275.279	+	1102.25i	−0.345163	+	1.38207i
$87$	182.416	+	399.436i	0.224794	+	0.492231i
$88$	−232.732	+	1415.03i	−0.281924	+	1.71412i
$89$	772.899	−	496.712i	0.920529	−	0.591588i	0.00771795	−	0.999970i	$-0.497543\pi$
$89$	772.899	−	496.712i	0.920529	−	0.591588i	0.912811	+	0.408382i	$0.133907\pi$
$90$	1334.44	−	1255.33i	1.56292	−	1.47026i
$91$		−	304.579i		−	0.350863i
$92$	−307.022	+	827.300i	−0.347927	+	0.937522i
$93$		−	1281.28i		−	1.42863i
$94$	−738.292	−	784.818i	−0.810095	−	0.861147i
$95$	−322.989	+	207.573i	−0.348821	+	0.224174i
$96$	572.134	−	1488.82i	0.608262	−	1.58284i
$97$	−487.556	−	1067.60i	−0.510348	−	1.11751i	−0.972966	−	0.230949i	$-0.925817\pi$
$97$	−487.556	−	1067.60i	−0.510348	−	1.11751i	0.462618	−	0.886558i	$-0.346910\pi$
$98$	−795.477	−	198.665i	−0.819952	−	0.204778i
$99$	904.091	+	3079.05i	0.917824	+	3.12582i
$100$	220.870	+	216.356i	0.220870	+	0.216356i
$101$	564.254	+	257.686i	0.555895	+	0.253869i	0.673494	−	0.739192i	$-0.264793\pi$
$101$	564.254	+	257.686i	0.555895	+	0.253869i	−0.117599	+	0.993061i	$0.537520\pi$
$102$	−2067.80	−	844.032i	−2.00728	−	0.819330i
$103$	347.608	+	401.161i	0.332533	+	0.383763i	0.897251	−	0.441521i	$-0.145561\pi$
$103$	347.608	+	401.161i	0.332533	+	0.383763i	−0.564719	+	0.825284i	$0.691015\pi$
$104$	375.357	+	867.924i	0.353911	+	0.818336i
$105$	−788.218	−	231.442i	−0.732593	−	0.215109i
$106$	563.179	−	960.451i	0.516045	−	0.880069i
$107$	660.606	−	1027.92i	0.596852	−	0.928721i	−0.403056	−	0.915175i	$-0.632052\pi$
$107$	660.606	−	1027.92i	0.596852	−	0.928721i	0.999908	−	0.0135451i	$-0.00431168\pi$
$108$	−136.001	−	1660.42i	−0.121173	−	1.47939i
$109$	1014.54	+	145.870i	0.891521	+	0.128181i	0.572827	−	0.819676i	$-0.305847\pi$
$109$	1014.54	+	145.870i	0.891521	+	0.128181i	0.318694	+	0.947858i	$0.396756\pi$
$110$	−2172.00	+	735.388i	−1.88266	+	0.637423i
$111$	−143.345	−	996.986i	−0.122574	−	0.852520i
$112$	−460.229	+	75.9014i	−0.388282	+	0.0640358i
$113$	−906.027	+	1045.61i	−0.754264	+	0.870467i	−0.994974	−	0.100130i	$-0.968074\pi$
$113$	−906.027	+	1045.61i	−0.754264	+	0.870467i	0.240710	+	0.970597i	$0.422620\pi$
$114$	−76.1132	+	744.079i	−0.0625321	+	0.611311i
$115$	−1398.39	+	188.677i	−1.13392	+	0.152994i
$116$	−80.7223	+	390.440i	−0.0646110	+	0.312513i
$117$	1599.21	+	1385.72i	1.26365	+	1.09496i
$118$	1370.72	−	695.005i	1.06936	−	0.542207i
$119$	92.9545	+	646.513i	0.0716061	+	0.498031i
$120$	2531.32	−	311.871i	1.92564	−	0.237248i
$121$	382.193	−	2658.21i	0.287147	−	1.99715i
$122$	−781.948	+	145.251i	−0.580281	+	0.107790i
$123$	−1247.97	+	1941.88i	−0.914843	+	1.42352i
$124$	687.510	−	938.448i	0.497905	−	0.679638i
$125$	311.219	−	1059.91i	0.222690	−	0.758413i
$126$	−854.311	+	599.719i	−0.604032	+	0.424025i
$127$	1718.08	+	1982.77i	1.20043	+	1.38537i	0.902447	+	0.430800i	$0.141769\pi$
$127$	1718.08	+	1982.77i	1.20043	+	1.38537i	0.297983	+	0.954571i	$0.403686\pi$
$128$	1217.92	−	783.465i	0.841017	−	0.541009i
$129$	−1470.22	+	3219.33i	−1.00346	+	2.19726i
$130$	−942.701	+	1182.26i	−0.636003	+	0.797624i
$131$	318.444	+	1084.52i	0.212386	+	0.723321i	0.994916	+	0.100708i	$0.0321107\pi$
$131$	318.444	+	1084.52i	0.212386	+	0.723321i	−0.782530	+	0.622613i	$0.786071\pi$
$132$	−1517.86	+	4201.52i	−1.00085	+	2.77042i
$133$	198.973	−	90.8678i	0.129723	−	0.0592424i
$134$	29.7438	+	727.497i	0.0191752	+	0.469001i
$135$	2241.10	−	1440.27i	1.42877	−	0.918213i
$136$	−1061.63	−	1727.74i	−0.669368	−	1.08935i
$137$	−328.664			−0.204961			−0.102480	−	0.994735i	$-0.532678\pi$
$137$	−328.664			−0.204961			−0.102480	+	0.994735i	$0.532678\pi$
$138$	−1411.02	+	2359.17i	−0.870391	+	1.45526i
$139$		−	1901.22i		−	1.16014i	−0.814566	−	0.580071i	$-0.803025\pi$
$139$		−	1901.22i		−	1.16014i	0.814566	−	0.580071i	$-0.196975\pi$
$140$	−453.128	−	592.457i	−0.273545	−	0.357656i
$141$	−1814.72	−	2823.77i	−1.08388	−	1.68655i
$142$	2147.70	−	87.8091i	1.26923	−	0.0518928i
$143$	−1100.24	−	2409.19i	−0.643403	−	1.40886i
$144$	1695.35	−	2761.78i	0.981105	−	1.59826i
$145$	−611.717	+	179.616i	−0.350347	+	0.102871i
$146$	1027.92	−	1289.14i	0.582681	−	0.730752i
$147$	−2323.35	−	1061.04i	−1.30358	−	0.595327i
$148$	429.973	−	807.139i	0.238808	−	0.448287i
$149$	2537.85	−	2199.06i	1.39536	−	1.20909i	0.445948	−	0.895059i	$-0.352867\pi$
$149$	2537.85	−	2199.06i	1.39536	−	1.20909i	0.949414	−	0.314028i	$-0.101679\pi$
$150$	553.388	+	788.311i	0.301226	+	0.429102i
$151$	−3230.58	−	948.584i	−1.74107	−	0.511223i	−0.752059	−	0.659095i	$-0.770939\pi$
$151$	−3230.58	−	948.584i	−1.74107	−	0.511223i	−0.989006	+	0.147872i	$0.952758\pi$
$152$	−455.006	+	504.145i	−0.242802	+	0.269024i
$153$	−3817.46	−	2453.33i	−2.01715	−	1.29634i
$154$	1284.48	−	238.599i	0.672118	−	0.124849i
$155$	1841.31	+	264.741i	0.954180	+	0.137190i
$156$	655.851	+	2871.82i	0.336603	+	1.47391i
$157$	−3199.32	+	459.993i	−1.62633	+	0.233831i	−0.894308	−	0.447451i	$-0.852332\pi$
$157$	−3199.32	+	459.993i	−1.62633	+	0.233831i	−0.732021	+	0.681282i	$0.761423\pi$
$158$	1053.75	+	2078.25i	0.530582	+	1.04644i
$159$	2271.33	−	2621.25i	1.13288	−	1.30741i
$160$	2021.36	+	1129.83i	0.998765	+	0.558257i
$161$	803.890	+	6.98204i	0.393512	+	0.00341777i
$162$	134.627	−	1316.11i	0.0652922	−	0.638293i
$163$	−2933.38	−	2541.79i	−1.40957	−	1.22140i	−0.941191	−	0.337876i	$-0.890291\pi$
$163$	−2933.38	−	2541.79i	−1.40957	−	1.22140i	−0.468383	−	0.883526i	$-0.655163\pi$
$164$	−1956.03	+	752.655i	−0.931341	+	0.358369i
$165$	−7070.76	+	1016.62i	−3.33611	+	0.479660i
$166$	818.404	+	2417.19i	0.382654	+	1.13018i
$167$	−334.888	+	2329.19i	−0.155176	+	1.07927i	0.752195	+	0.658941i	$0.228995\pi$
$167$	−334.888	+	2329.19i	−0.155176	+	1.07927i	−0.907371	+	0.420331i	$0.861914\pi$
$168$	−1452.77	−	29.3679i	−0.667163	−	0.0134868i
$169$	379.024	+	243.584i	0.172519	+	0.110871i
$170$	1640.20	−	2797.22i	0.739987	−	1.26198i
$171$	−428.147	+	1458.13i	−0.191469	+	0.652083i
$172$	−2804.27	+	1569.05i	−1.24316	+	0.695574i
$173$	−225.819	+	195.674i	−0.0992412	+	0.0859930i	−0.703068	−	0.711122i	$-0.748187\pi$
$173$	−225.819	+	195.674i	−0.0992412	+	0.0859930i	0.603827	+	0.797115i	$0.293642\pi$
$174$	−469.368	+	1149.91i	−0.204498	+	0.501003i
$175$	117.011	−	256.219i	0.0505441	−	0.110676i
$176$	−3366.18	+	2262.87i	−1.44168	+	0.969149i
$177$	4593.63	−	1348.81i	1.95072	−	0.572784i
$178$	2521.17	+	629.645i	1.06163	+	0.265134i
$179$	−353.877	+	161.610i	−0.147766	+	0.0674823i	−0.487925	−	0.872885i	$-0.662246\pi$
$179$	−353.877	+	161.610i	−0.147766	+	0.0674823i	0.340160	+	0.940368i	$0.389519\pi$
$180$	5172.30	+	316.291i	2.14178	+	0.130972i
$181$	454.784	+	707.657i	0.186761	+	0.290606i	0.921991	−	0.387212i	$-0.126562\pi$
$181$	454.784	+	707.657i	0.186761	+	0.290606i	−0.735229	+	0.677818i	$0.762926\pi$
$182$	627.473	−	590.275i	0.255557	−	0.240407i
$183$	−2477.58			−1.00081
$184$	−2299.36	+	970.802i	−0.921255	+	0.388959i
$185$	1462.38			0.581168
$186$	2639.61	−	2483.12i	1.04057	−	0.978879i
$187$	3070.67	+	4778.06i	1.20080	+	1.86848i
$188$	186.018	−	3041.96i	0.0721638	−	1.18009i
$189$	−1380.60	+	630.498i	−0.531343	+	0.242656i
$190$	−1053.58	−	263.125i	−0.402289	−	0.100469i
$191$	−635.518	+	186.605i	−0.240756	+	0.0706925i	−0.399885	−	0.916565i	$-0.630950\pi$
$191$	−635.518	+	186.605i	−0.240756	+	0.0706925i	0.159128	+	0.987258i	$0.449132\pi$
$192$	4175.97	−	1706.67i	1.56966	−	0.641503i
$193$	−341.417	+	747.600i	−0.127336	+	0.278826i	−0.962553	−	0.271094i	$-0.912615\pi$
$193$	−341.417	+	747.600i	−0.127336	+	0.278826i	0.835217	+	0.549920i	$0.185342\pi$
$194$	1254.51	−	3073.44i	0.464271	−	1.13742i
$195$	−3559.92	+	3084.68i	−1.30734	+	1.13281i
$196$	−1132.36	−	2023.80i	−0.412668	−	0.737537i
$197$	149.419	−	508.875i	0.0540390	−	0.184040i	−0.928051	−	0.372454i	$-0.878516\pi$
$197$	149.419	−	508.875i	0.0540390	−	0.184040i	0.982090	+	0.188414i	$0.0603347\pi$
$198$	−4591.13	+	7829.76i	−1.64786	+	2.81029i
$199$	−2306.83	−	1482.51i	−0.821742	−	0.528102i	0.0609017	−	0.998144i	$-0.480602\pi$
$199$	−2306.83	−	1482.51i	−0.821742	−	0.528102i	−0.882644	+	0.470042i	$0.844239\pi$
$200$	−17.6745	+	874.320i	−0.00624889	+	0.309119i
$201$	−322.795	+	2245.09i	−0.113275	+	0.787843i
$202$	562.658	+	1661.83i	0.195982	+	0.578843i
$203$	359.527	−	51.6922i	0.124305	−	0.0178723i
$204$	−2268.59	−	5895.68i	−0.778593	−	2.02343i
$205$	−2532.80	−	2194.68i	−0.862917	−	0.747722i
$206$	−152.780	+	1493.57i	−0.0516732	+	0.505155i
$207$	−3694.07	+	4189.11i	−1.24036	+	1.40659i
$208$	−1060.60	+	2455.32i	−0.353553	+	0.818491i
$209$	1245.61	−	1437.51i	0.412251	−	0.475763i
$210$	−1050.77	−	2072.37i	−0.345285	−	0.680986i
$211$	−1309.67	+	188.302i	−0.427305	+	0.0614372i	−0.352613	−	0.935769i	$-0.614707\pi$
$211$	−1309.67	+	188.302i	−0.427305	+	0.0614372i	−0.0746925	+	0.997207i	$0.523798\pi$
$212$	3070.10	−	701.134i	0.994600	−	0.227142i
$213$	6627.91	+	952.949i	2.13210	+	0.306549i
$214$	3397.91	−	631.181i	1.08541	−	0.201620i
$215$	−4322.69	−	2778.02i	−1.37119	−	0.881208i
$216$	3157.12	−	3498.08i	0.994513	−	1.10192i
$217$	−1016.90	−	298.589i	−0.318119	−	0.0934081i
$218$	1665.68	+	2372.79i	0.517496	+	0.737182i
$219$	3881.74	−	3363.54i	1.19773	−	1.03784i
$220$	−5724.34	−	3049.43i	−1.75425	−	0.934511i
$221$	3406.77	+	1555.82i	1.03694	+	0.473556i
$222$	1776.12	−	2227.47i	0.536962	−	0.673415i
$223$	−3753.92	+	1102.25i	−1.12727	+	0.330996i	−0.791633	−	0.610997i	$-0.790769\pi$
$223$	−3753.92	+	1102.25i	−1.12727	+	0.330996i	−0.335635	+	0.941992i	$0.608951\pi$
$224$	−1048.29	−	801.036i	−0.312687	−	0.238935i
$225$	812.934	+	1780.08i	0.240869	+	0.527430i
$226$	−3909.98	+	159.860i	−1.15083	+	0.0470520i
$227$	−2614.64	−	4068.46i	−0.764493	−	1.18957i	−0.977172	−	0.212452i	$-0.931855\pi$
$227$	−2614.64	−	4068.46i	−0.764493	−	1.18957i	0.212679	−	0.977122i	$-0.431781\pi$
$228$	−1680.41	+	1285.22i	−0.488105	+	0.373316i
$229$			1378.19i			0.397702i	0.980030	+	0.198851i	$0.0637209\pi$
$229$			1378.19i			0.397702i	−0.980030	+	0.198851i	$0.936279\pi$
$230$	−3098.79	−	2515.22i	−0.888383	−	0.721081i
$231$	4069.83			1.15920
$232$	−960.799	+	590.375i	−0.271895	+	0.167069i
$233$	4347.89	−	2794.22i	1.22249	−	0.785645i	0.239783	−	0.970827i	$-0.422924\pi$
$233$	4347.89	−	2794.22i	1.22249	−	0.785645i	0.982704	+	0.185182i	$0.0592874\pi$
$234$	244.498	+	5980.12i	0.0683049	+	1.67065i
$235$	4432.97	−	2024.47i	1.23053	−	0.561965i
$236$	4088.26	+	1476.94i	1.12764	+	0.407376i
$237$	2045.04	+	6964.76i	0.560505	+	1.90890i
$238$	−1151.76	+	1444.44i	−0.313686	+	0.393400i
$239$	−514.230	+	1126.01i	−0.139175	+	0.304750i	−0.966366	−	0.257170i	$-0.917210\pi$
$239$	−514.230	+	1126.01i	−0.139175	+	0.304750i	0.827191	+	0.561920i	$0.189937\pi$
$240$	5548.20	+	4610.45i	1.49223	+	1.24001i
$241$	−2242.85	−	2588.39i	−0.599480	−	0.691837i	0.372196	−	0.928154i	$-0.378605\pi$
$241$	−2242.85	−	2588.39i	−0.599480	−	0.691837i	−0.971676	+	0.236317i	$0.924059\pi$
$242$	6216.95	−	4364.24i	1.65141	−	1.15927i
$243$	−422.985	+	1440.55i	−0.111665	+	0.380294i
$244$	−1814.65	−	1329.42i	−0.476112	−	0.348801i
$245$	2004.86	−	3119.63i	0.522800	−	0.813493i
$246$	−6419.10	+	1192.38i	−1.66369	+	0.309039i
$247$	178.499	−	1241.49i	0.0459822	−	0.319813i
$248$	3265.72	−	402.354i	0.836184	−	0.103022i
$249$	1131.39	+	7868.96i	0.287947	+	2.00271i
$250$	2786.71	−	1412.96i	0.704987	−	0.357455i
$251$	−2585.88	−	2240.68i	−0.650276	−	0.563468i	0.266020	−	0.963967i	$-0.414291\pi$
$251$	−2585.88	−	2240.68i	−0.650276	−	0.563468i	−0.916297	+	0.400500i	$0.868837\pi$
$252$	−2891.16	−	597.738i	−0.722721	−	0.149420i
$253$	6383.91	−	2848.69i	1.58637	−	0.707887i
$254$	−755.126	+	7382.07i	−0.186539	+	1.82359i
$255$	6615.01	−	7634.13i	1.62450	−	1.87478i
$256$	3974.38	+	990.726i	0.970307	+	0.241877i
$257$	−460.299	−	3201.45i	−0.111722	−	0.777047i	−0.966244	−	0.257630i	$-0.917058\pi$
$257$	−460.299	−	3201.45i	−0.111722	−	0.777047i	0.854521	−	0.519417i	$-0.173851\pi$
$258$	−9481.55	+	3210.23i	−2.28797	+	0.774651i
$259$	−824.674	−	118.570i	−0.197848	−	0.0284463i
$260$	−4262.57	+	349.136i	−1.01674	+	0.0832787i
$261$	−1364.31	+	2122.90i	−0.323557	+	0.503464i
$262$	−1617.11	+	2757.84i	−0.381319	+	0.650305i
$263$	−248.982	−	73.1077i	−0.0583760	−	0.0171407i	0.252414	−	0.967619i	$-0.418775\pi$
$263$	−248.982	−	73.1077i	−0.0583760	−	0.0171407i	−0.310790	+	0.950479i	$0.600594\pi$
$264$	−11597.3	+	5015.57i	−2.70366	+	1.16927i
$265$	3297.66	+	3805.71i	0.764430	+	0.882199i
$266$	572.809	+	233.808i	0.132035	+	0.0538936i
$267$	7363.59	+	3362.84i	1.68781	+	0.770795i
$268$	−1441.10	+	1471.17i	−0.328466	+	0.335320i
$269$	−1175.91	−	4004.78i	−0.266530	−	0.907717i	−0.978628	−	0.205638i	$-0.934073\pi$
$269$	−1175.91	−	4004.78i	−0.266530	−	0.907717i	0.712098	−	0.702080i	$-0.247745\pi$
$270$	7310.42	+	1825.73i	1.64777	+	0.411519i
$271$	−1186.88	−	2598.90i	−0.266044	−	0.582554i	0.728714	−	0.684818i	$-0.240119\pi$
$271$	−1186.88	−	2598.90i	−0.266044	−	0.582554i	−0.994757	+	0.102264i	$0.967391\pi$
$272$	1501.93	−	5535.46i	0.334807	−	1.23396i
$273$	2257.64	−	1450.90i	0.500508	−	0.321657i
$274$	−636.951	−	677.091i	−0.140437	−	0.149287i
$275$		−	2449.35i		−	0.537095i
$276$	−7594.76	+	1665.19i	−1.65634	+	0.363161i
$277$			6702.31i			1.45380i	0.686743	+	0.726900i	$0.259040\pi$
$277$			6702.31i			1.45380i	−0.686743	+	0.726900i	$0.740960\pi$
$278$	3916.77	−	3684.58i	0.845009	−	0.794914i
$279$	6194.29	−	3980.83i	1.32919	−	0.854216i
$280$	342.378	−	2081.69i	0.0730750	−	0.444302i
$281$	−941.960	−	2062.61i	−0.199974	−	0.437882i	0.782903	−	0.622143i	$-0.213738\pi$
$281$	−941.960	−	2062.61i	−0.199974	−	0.437882i	−0.982877	+	0.184262i	$0.941011\pi$
$282$	2300.39	−	9211.04i	0.485768	−	1.94507i
$283$	1287.26	+	4384.01i	0.270388	+	0.920857i	0.976997	+	0.213253i	$0.0684057\pi$
$283$	1287.26	+	4384.01i	0.270388	+	0.920857i	−0.706609	+	0.707604i	$0.749776\pi$
$284$	4343.15	+	4254.37i	0.907459	+	0.888911i
$285$	−3077.20	−	1405.31i	−0.639570	−	0.292082i
$286$	2830.98	−	6935.65i	0.585312	−	1.43396i
$287$	1250.37	+	1443.00i	0.257167	+	0.296786i
$288$	8975.24	−	1859.70i	1.83636	−	0.380499i
$289$	−2992.19	−	878.586i	−0.609035	−	0.178829i
$290$	−1555.54	−	912.121i	−0.314981	−	0.184695i
$291$	5590.87	−	8699.56i	1.12626	−	1.75250i
$292$	4647.91	−	380.698i	0.931501	−	0.0762967i
$293$	−49.5387	−	7.12259i	−0.00987741	−	0.00142016i	0.137374	−	0.990519i	$-0.456134\pi$
$293$	−49.5387	−	7.12259i	−0.00987741	−	0.00142016i	−0.147252	+	0.989099i	$0.547043\pi$
$294$	−2316.78	−	6842.71i	−0.459583	−	1.35740i
$295$	989.215	+	6880.14i	0.195235	+	1.35789i
$296$	2496.10	−	678.436i	0.490145	−	0.133221i
$297$	−8642.82	+	9974.34i	−1.68858	+	1.94872i
$298$	9448.72	+	966.526i	1.83674	+	0.187884i
$299$	2525.76	−	3856.11i	0.488524	−	0.745836i
$300$	−551.560	+	2667.80i	−0.106148	+	0.513419i
$301$	2212.44	+	1917.09i	0.423664	+	0.367107i
$302$	−4306.66	−	8493.78i	−0.820598	−	1.61842i
$303$	777.835	+	5409.96i	0.147477	+	1.02572i
$304$	−1920.41	+	39.6621i	−0.362313	+	0.00748282i
$305$	511.923	−	3560.50i	0.0961069	−	0.668438i
$306$	−2344.06	−	12619.0i	−0.437911	−	2.35746i
$307$	977.333	−	1520.76i	0.181692	−	0.282718i	−0.738446	−	0.674312i	$-0.764440\pi$
$307$	977.333	−	1520.76i	0.181692	−	0.282718i	0.920138	+	0.391595i	$0.128076\pi$
$308$	2980.86	+	2183.79i	0.551463	+	0.404003i
$309$	−1317.67	+	4487.57i	−0.242588	+	0.826177i
$310$	3023.07	+	4306.42i	0.553867	+	0.788994i
$311$	1868.98	+	2156.92i	0.340773	+	0.393273i	0.900107	−	0.435670i	$-0.143488\pi$
$311$	1868.98	+	2156.92i	0.340773	+	0.393273i	−0.559334	+	0.828942i	$0.688943\pi$
$312$	−4645.28	+	6916.73i	−0.842909	+	1.25507i
$313$	394.607	−	864.069i	0.0712604	−	0.156039i	−0.870650	−	0.491903i	$-0.836301\pi$
$313$	394.607	−	864.069i	0.0712604	−	0.156039i	0.941910	+	0.335865i	$0.109029\pi$
$314$	−7147.94	−	5699.56i	−1.28465	−	1.02435i
$315$	−1330.03	−	4529.68i	−0.237901	−	0.810217i
$316$	−2239.31	+	6198.53i	−0.398642	+	1.10346i
$317$	−5388.45	+	2460.82i	−0.954717	+	0.436005i	−0.830975	−	0.556310i	$-0.812217\pi$
$317$	−5388.45	+	2460.82i	−0.954717	+	0.436005i	−0.123742	+	0.992314i	$0.539490\pi$
$318$	9801.96	−	400.755i	1.72851	−	0.0706705i
$319$	2657.09	−	1707.61i	0.466359	−	0.299711i
$320$	1589.79	+	6353.88i	0.277725	+	1.10998i
$321$	10766.2			1.87199
$322$	1543.56	+	1669.65i	0.267140	+	0.288963i
$323$			2689.71i			0.463342i
$324$	2972.27	−	2273.28i	0.509649	−	0.389794i
$325$	−873.196	−	1358.72i	−0.149034	−	0.231902i
$326$	−448.476	−	10969.2i	−0.0761926	−	1.86358i
$327$	3751.67	+	8215.01i	0.634458	+	1.38927i
$328$	−5341.35	−	2571.03i	−0.899167	−	0.432808i
$329$	−2664.02	+	782.226i	−0.446419	+	0.131081i
$330$	−15797.5	−	12596.5i	−2.63523	−	2.10126i
$331$	313.806	+	143.310i	0.0521098	+	0.0237977i	0.441299	−	0.897360i	$-0.354518\pi$
$331$	313.806	+	143.310i	0.0521098	+	0.0237977i	−0.389190	+	0.921158i	$0.627245\pi$
$332$	−3393.67	+	6370.55i	−0.560999	+	1.05310i
$333$	4374.53	−	3790.55i	0.719888	−	0.623786i
$334$	−5447.46	+	3824.07i	−0.892431	+	0.626479i
$335$	−3159.70	−	927.771i	−0.515322	−	0.151312i
$336$	−2754.96	−	3049.81i	−0.447308	−	0.495181i
$337$	6623.35	+	4256.57i	1.07061	+	0.688042i	0.952371	−	0.304943i	$-0.0986373\pi$
$337$	6623.35	+	4256.57i	1.07061	+	0.688042i	0.118243	+	0.992985i	$0.462274\pi$
$338$	232.734	+	1252.90i	0.0374528	+	0.201624i
$339$	−12066.4	−	1734.88i	−1.93320	−	0.277953i
$340$	8941.36	−	2041.98i	1.42622	−	0.325712i
$341$	−9122.18	+	1311.57i	−1.44866	+	0.208286i
$342$	−3833.70	+	1943.83i	−0.606148	+	0.307340i
$343$	−3020.60	+	3485.96i	−0.475501	+	0.548758i
$344$	−8667.12	−	2736.34i	−1.35843	−	0.428877i
$345$	−8059.95	−	9466.57i	−1.25778	−	1.47728i
$346$	−840.752	−	86.0020i	−0.130633	−	0.0133627i
$347$	−8191.25	−	7097.76i	−1.26723	−	1.09806i	−0.990557	−	0.137099i	$-0.956222\pi$
$347$	−8191.25	−	7097.76i	−1.26723	−	1.09806i	−0.276674	−	0.960964i	$-0.589232\pi$
$348$	−3278.61	+	1261.57i	−0.505034	+	0.194331i
$349$	−2519.09	+	362.190i	−0.386372	+	0.0555519i	−0.332764	−	0.943010i	$-0.607981\pi$
$349$	−2519.09	+	362.190i	−0.386372	+	0.0555519i	−0.0536080	+	0.998562i	$0.517072\pi$
$350$	754.613	−	255.494i	0.115245	−	0.0390192i
$351$	−1238.54	+	8614.21i	−0.188342	+	1.30995i
$352$	−11185.5	−	2549.33i	−1.69372	−	0.386023i
$353$	5884.33	+	3781.63i	0.887228	+	0.570187i	0.902977	−	0.429689i	$-0.141377\pi$
$353$	5884.33	+	3781.63i	0.887228	+	0.570187i	−0.0157491	+	0.999876i	$0.505013\pi$
$354$	11681.2	+	6849.48i	1.75381	+	1.02838i
$355$	−2738.95	+	9327.99i	−0.409488	+	1.39459i
$356$	3588.88	+	6414.20i	0.534299	+	0.954921i
$357$	−4349.37	+	3768.75i	−0.644798	+	0.558721i
$358$	−1018.75	−	415.833i	−0.150399	−	0.0613896i
$359$	2252.96	−	4933.28i	0.331216	−	0.725261i	−0.668616	−	0.743608i	$-0.733113\pi$
$359$	2252.96	−	4933.28i	0.331216	−	0.725261i	0.999832	+	0.0183467i	$0.00584027\pi$
$360$	9372.33	+	11268.6i	1.37212	+	1.64974i
$361$	−5716.88	+	1678.63i	−0.833486	+	0.244734i
$362$	−576.496	+	2308.36i	−0.0837016	+	0.335151i
$363$	21524.1	−	9829.75i	3.11219	−	1.42129i
$364$	2432.09	+	148.724i	0.350209	+	0.0214156i
$365$	4031.66	+	6273.38i	0.578155	+	0.899627i
$366$	−4801.55	−	5104.14i	−0.685741	−	0.728955i
$367$	−5411.30			−0.769667			−0.384834	−	0.922986i	$-0.625741\pi$
$367$	−5411.30			−0.769667			−0.384834	+	0.922986i	$0.625741\pi$
$368$	−6456.14	−	2855.57i	−0.914537	−	0.404502i
$369$	−13265.3			−1.87144
$370$	2834.09	+	3012.69i	0.398209	+	0.423303i
$371$	−1551.07	−	2413.52i	−0.217056	−	0.337746i
$372$	10231.1	+	625.643i	1.42597	+	0.0871991i
$373$	5568.58	−	2543.08i	0.773003	−	0.353018i	0.0104506	−	0.999945i	$-0.496673\pi$
$373$	5568.58	−	2543.08i	0.773003	−	0.353018i	0.762552	+	0.646927i	$0.223946\pi$
$374$	−3892.47	+	15585.9i	−0.538168	+	2.15489i
$375$	9338.96	−	2742.17i	1.28603	−	0.377613i
$376$	6627.34	−	5512.10i	0.908987	−	0.756023i
$377$	865.196	−	1894.51i	0.118196	−	0.258813i
$378$	−3974.51	−	1622.31i	−0.540812	−	0.220748i
$379$	3926.03	−	3401.92i	0.532102	−	0.461069i	−0.346890	−	0.937906i	$-0.612762\pi$
$379$	3926.03	−	3401.92i	0.532102	−	0.461069i	0.878992	+	0.476837i	$0.158217\pi$
$380$	−1499.77	−	2680.45i	−0.202465	−	0.361854i
$381$	−6512.67	+	22180.1i	−0.875733	+	2.98247i
$382$	−1616.07	−	947.611i	−0.216453	−	0.126921i
$383$	9114.49	+	5857.53i	1.21600	+	0.781477i	0.981653	−	0.190675i	$-0.0610678\pi$
$383$	9114.49	+	5857.53i	1.21600	+	0.781477i	0.234349	+	0.972153i	$0.424704\pi$
$384$	11609.0	+	5295.52i	1.54276	+	0.703740i
$385$	−840.916	+	5848.70i	−0.111317	+	0.774227i
$386$	−2201.82	+	745.485i	−0.290336	+	0.0983010i
$387$	−20131.6	+	2894.49i	−2.64431	+	0.380194i
$388$	8762.93	−	3371.87i	1.14657	−	0.441188i
$389$	3293.52	+	2853.85i	0.429276	+	0.371969i	0.842533	−	0.538645i	$-0.181064\pi$
$389$	3293.52	+	2853.85i	0.429276	+	0.371969i	−0.413257	+	0.910614i	$0.635609\pi$
$390$	−13254.0	−	1355.77i	−1.72088	−	0.176031i
$391$	−4184.45	+	8955.99i	−0.541219	+	1.15837i
$392$	1974.78	−	6254.95i	0.254443	−	0.805925i
$393$	−6521.89	+	7526.66i	−0.837114	+	0.966081i
$394$	1337.93	−	678.378i	0.171075	−	0.0867416i
$395$	−10431.5	+	1499.83i	−1.32878	+	0.191049i
$396$	−25028.0	+	5715.76i	−3.17602	+	0.725323i
$397$	−14412.2	−	2072.17i	−1.82199	−	0.261963i	−0.855341	−	0.518066i	$-0.826652\pi$
$397$	−14412.2	−	2072.17i	−1.82199	−	0.261963i	−0.966649	+	0.256103i	$0.917561\pi$
$398$	−1416.47	−	7625.48i	−0.178396	−	0.960378i
$399$	1621.37	+	1041.99i	0.203434	+	0.130739i
$400$	−1835.47	+	1658.02i	−0.229434	+	0.207253i
$401$	420.397	+	123.440i	0.0523532	+	0.0153723i	0.307804	−	0.951450i	$-0.400406\pi$
$401$	420.397	+	123.440i	0.0523532	+	0.0153723i	−0.255451	+	0.966822i	$0.582224\pi$
$402$	−5250.76	+	3685.99i	−0.651453	+	0.457315i
$403$	−4592.74	+	3979.64i	−0.567695	+	0.491910i
$404$	−2333.17	+	4379.79i	−0.287325	+	0.539363i
$405$	5442.88	+	2485.68i	0.667800	+	0.304974i
$406$	803.258	+	640.494i	0.0981897	+	0.0782936i
$407$	−6951.40	+	2041.11i	−0.846604	+	0.248585i
$408$	7749.36	−	16099.4i	0.940320	−	1.95353i
$409$	−4338.14	−	9499.20i	−0.524468	−	1.14842i	−0.967720	−	0.252027i	$-0.918903\pi$
$409$	−4338.14	−	9499.20i	−0.524468	−	1.14842i	0.443253	−	0.896397i	$-0.353824\pi$
$410$	−387.231	−	9471.19i	−0.0466439	−	1.14085i
$411$	−1565.63	−	2436.17i	−0.187900	−	0.292378i
$412$	−3373.04	+	2579.80i	−0.403344	+	0.308489i
$413$		−	3960.11i		−	0.471826i
$414$	−15789.2	+	508.231i	−1.87439	+	0.0603338i
$415$	−11542.2			−1.36526
$416$	−7113.73	+	2573.45i	−0.838412	+	0.303303i
$417$	14092.5	−	9056.71i	1.65495	−	1.06357i
$418$	5375.45	−	219.776i	0.629000	−	0.0257168i
$419$	10157.2	−	4638.64i	1.18428	−	0.540842i	0.276794	−	0.960929i	$-0.410728\pi$
$419$	10157.2	−	4638.64i	1.18428	−	0.540842i	0.907484	+	0.420088i	$0.138001\pi$
$420$	2232.96	−	6180.98i	0.259423	−	0.718097i
$421$	−720.166	−	2452.66i	−0.0833699	−	0.283932i	0.907247	−	0.420598i	$-0.138180\pi$
$421$	−720.166	−	2452.66i	−0.0833699	−	0.283932i	−0.990617	+	0.136666i	$0.956361\pi$
$422$	−2926.07	−	2333.16i	−0.337533	−	0.269139i
$423$	8013.18	−	17546.4i	0.921074	−	2.01687i
$424$	7394.29	+	4966.01i	0.846930	+	0.568799i
$425$	2268.15	+	2617.58i	0.258874	+	0.298756i
$426$	10881.7	+	15501.2i	1.23761	+	1.76299i
$427$	−577.375	+	1966.36i	−0.0654359	+	0.222854i
$428$	7885.48	+	5776.93i	0.890559	+	0.652426i
$429$	12616.6	−	19631.8i	1.41989	−	2.20940i
$430$	−2654.28	−	14289.1i	−0.297677	−	1.60252i
$431$	−1046.59	+	7279.16i	−0.116966	+	0.813515i	0.843900	+	0.536501i	$0.180254\pi$
$431$	−1046.59	+	7279.16i	−0.116966	+	0.813515i	−0.960866	+	0.277014i	$0.910655\pi$
$432$	13325.0	−	275.201i	1.48403	−	0.0306495i
$433$	210.440	+	1463.64i	0.0233558	+	0.162443i	0.998161	−	0.0606132i	$-0.0193056\pi$
$433$	210.440	+	1463.64i	0.0233558	+	0.162443i	−0.974805	+	0.223057i	$0.928397\pi$
$434$	−1355.62	−	2673.62i	−0.149936	−	0.295709i
$435$	−4245.36	−	3678.63i	−0.467930	−	0.405464i
$436$	−1660.18	+	8030.00i	−0.182358	+	0.882035i
$437$	3272.62	+	499.580i	0.358240	+	0.0546868i
$438$	14452.2	+	1478.34i	1.57660	+	0.161273i
$439$	1552.45	−	1791.62i	0.168780	−	0.194782i	−0.665058	−	0.746792i	$-0.731593\pi$
$439$	1552.45	−	1791.62i	0.168780	−	0.194782i	0.833838	+	0.552009i	$0.186139\pi$
$440$	−4811.56	−	17702.7i	−0.521323	−	1.91805i
$441$	−2088.91	−	14528.7i	−0.225560	−	1.56881i
$442$	3397.13	+	10033.6i	0.365577	+	1.07975i
$443$	7298.92	+	1049.43i	0.782804	+	0.112550i	0.522118	−	0.852873i	$-0.325142\pi$
$443$	7298.92	+	1049.43i	0.782804	+	0.112550i	0.260686	+	0.965424i	$0.416051\pi$
$444$	8031.01	−	657.798i	0.858412	−	0.0703102i
$445$	−6354.18	+	9887.30i	−0.676892	+	1.05326i
$446$	−9545.88	−	5597.40i	−1.01348	−	0.594271i
$447$	28389.5	+	8335.92i	3.00398	+	0.882048i
$448$	−381.352	−	3712.03i	−0.0402169	−	0.391466i
$449$	−688.143	−	794.160i	−0.0723285	−	0.0834715i	0.718432	−	0.695597i	$-0.244860\pi$
$449$	−688.143	−	794.160i	−0.0723285	−	0.0834715i	−0.790761	+	0.612126i	$0.790315\pi$
$450$	−2091.73	+	5124.55i	−0.219122	+	0.536830i
$451$	15102.9	+	6897.24i	1.57686	+	0.720130i
$452$	−7906.88	−	7745.27i	−0.822806	−	0.805988i
$453$	−8358.03	−	28464.8i	−0.866876	−	2.95231i
$454$	3314.39	−	13271.2i	0.342626	−	1.37191i
$455$	1618.59	+	3544.22i	0.166771	+	0.365177i
$456$	−5904.37	−	971.101i	−0.606354	−	0.0997280i
$457$	−10.4699	+	6.72862i	−0.00107169	+	0.000688734i	−0.541177	−	0.840909i	$-0.682021\pi$
$457$	−10.4699	+	6.72862i	−0.00107169	+	0.000688734i	0.540105	+	0.841598i	$0.318385\pi$
$458$	−2839.26	+	2670.94i	−0.289673	+	0.272500i
$459$		−	18662.9i		−	1.89784i
$460$	−823.777	−	11258.4i	−0.0834974	−	1.14114i
$461$		−	5112.59i		−	0.516523i	−0.966075	−	0.258261i	$-0.916850\pi$
$461$		−	5112.59i		−	0.516523i	0.966075	−	0.258261i	$-0.0831496\pi$
$462$	7887.33	+	8384.38i	0.794268	+	0.844322i
$463$	−13287.5	+	8539.33i	−1.33374	+	0.857141i	−0.996444	−	0.0842583i	$-0.973148\pi$
$463$	−13287.5	+	8539.33i	−1.33374	+	0.857141i	−0.337294	+	0.941399i	$0.609512\pi$
$464$	−3078.28	−	835.225i	−0.307986	−	0.0835654i
$465$	6808.97	+	14909.6i	0.679050	+	1.48691i
$466$	14182.7	+	3542.02i	1.40987	+	0.352105i
$467$	1474.51	+	5021.71i	0.146107	+	0.497595i	0.999729	−	0.0232987i	$-0.00741689\pi$
$467$	1474.51	+	5021.71i	0.146107	+	0.497595i	−0.853621	+	0.520894i	$0.825599\pi$
$468$	−11846.0	+	12093.2i	−1.17005	+	1.19446i
$469$	1706.62	+	779.386i	0.168026	+	0.0767349i
$470$	12761.8	+	5209.08i	1.25246	+	0.511227i
$471$	−18650.0	−	21523.2i	−1.82451	−	2.10560i
$472$	4880.36	+	11284.7i	0.475925	+	1.10046i
$473$	24425.3	+	7171.92i	2.37437	+	0.697178i
$474$	−10385.0	+	17710.8i	−1.00633	+	1.71621i
$475$	627.104	−	975.792i	0.0605758	−	0.0942577i
$476$	−5207.85	+	426.560i	−0.501473	+	0.0410743i
$477$	19729.1	+	2836.62i	1.89379	+	0.272285i
$478$	−3316.30	+	1122.82i	−0.317331	+	0.107441i
$479$	−2737.58	−	19040.3i	−0.261134	−	1.81622i	−0.524367	−	0.851492i	$-0.675698\pi$
$479$	−2737.58	−	19040.3i	−0.261134	−	1.81622i	0.263233	−	0.964732i	$-0.415211\pi$
$480$	1254.29	+	20365.1i	0.119271	+	1.93653i
$481$	−3128.47	+	3610.44i	−0.296561	+	0.342250i
$482$	985.773	−	9636.87i	0.0931550	−	0.910679i
$483$	3777.67	+	5991.97i	0.355880	+	0.564480i
$484$	21039.4	+	4349.83i	1.97590	+	0.408511i
$485$	11346.8	+	9832.10i	1.06234	+	0.920521i
$486$	−3787.48	+	1920.39i	−0.353505	+	0.179240i
$487$	17.4459	+	121.339i	0.00162331	+	0.0112904i	0.990617	−	0.136667i	$-0.0436391\pi$
$487$	17.4459	+	121.339i	0.00162331	+	0.0112904i	−0.988994	+	0.147958i	$0.952730\pi$
$488$	−778.021	−	6314.85i	−0.0721708	−	0.585778i
$489$	4867.09	−	33851.4i	0.450097	−	3.13049i
$490$	10312.3	−	1915.56i	0.950737	−	0.176605i
$491$	1467.21	−	2283.03i	0.134856	−	0.209840i	−0.767257	−	0.641340i	$-0.778379\pi$
$491$	1467.21	−	2283.03i	0.134856	−	0.209840i	0.902113	+	0.431499i	$0.142015\pi$
$492$	−14896.7	−	10913.4i	−1.36503	−	1.00002i
$493$	−1258.31	+	4285.43i	−0.114953	+	0.391493i
$494$	2903.56	−	2038.27i	0.264448	−	0.185640i
$495$	−26883.1	−	31024.7i	−2.44102	−	2.81709i
$496$	7157.88	+	5948.06i	0.647981	+	0.538459i
$497$	2300.89	−	5038.24i	0.207664	−	0.454720i
$498$	−14018.5	+	17580.9i	−1.26141	+	1.58196i
$499$	−1495.19	−	5092.15i	−0.134136	−	0.456826i	0.864841	−	0.502046i	$-0.167419\pi$
$499$	−1495.19	−	5092.15i	−0.134136	−	0.456826i	−0.998977	+	0.0452203i	$0.985601\pi$
$500$	8311.53	+	3002.66i	0.743406	+	0.268566i
$501$	−18860.1	+	8613.10i	−1.68185	+	0.768073i
$502$	−395.347	−	9669.70i	−0.0351498	−	0.859721i
$503$	−14293.5	+	9185.87i	−1.26703	+	0.814270i	−0.989230	−	0.146370i	$-0.953241\pi$
$503$	−14293.5	+	9185.87i	−1.26703	+	0.814270i	−0.277799	+	0.960639i	$0.589605\pi$
$504$	−4371.65	−	7114.58i	−0.386367	−	0.628787i
$505$	−7935.31			−0.699241
$506$	18240.7	+	7630.93i	1.60256	+	0.670428i
$507$			3969.79i			0.347741i
$508$	−16671.5	+	12750.8i	−1.45606	+	1.11363i
$509$	6848.12	+	10655.9i	0.596341	+	0.927925i	0.999916	+	0.0129783i	$0.00413122\pi$
$509$	6848.12	+	10655.9i	0.596341	+	0.927925i	−0.403575	+	0.914947i	$0.632232\pi$
$510$	28547.2	−	1167.16i	2.47861	−	0.101339i
$511$	−1764.91	−	3864.62i	−0.152789	−	0.334561i
$512$	5661.33	+	10107.8i	0.488667	+	0.872470i
$513$	−5996.92	+	1760.86i	−0.516122	+	0.151547i
$514$	5703.35	−	7152.70i	0.489424	−	0.613798i
$515$	−6176.77	−	2820.84i	−0.528507	−	0.241361i
$516$	−24988.8	−	13311.8i	−2.13192	−	1.13570i
$517$	−18246.4	+	15810.6i	−1.55218	+	1.34497i
$518$	−1353.95	−	1928.73i	−0.114844	−	0.163597i
$519$	−2526.12	−	741.734i	−0.213650	−	0.0627332i
$520$	−8980.14	−	8104.84i	−0.757317	−	0.683501i
$521$	678.680	+	436.161i	0.0570700	+	0.0366767i	0.568865	−	0.822431i	$-0.307383\pi$
$521$	678.680	+	436.161i	0.0570700	+	0.0366767i	−0.511795	+	0.859108i	$0.671019\pi$
$522$	−7017.48	+	1303.54i	−0.588404	+	0.109299i
$523$	18378.6	+	2642.45i	1.53660	+	0.220929i	0.858027	−	0.513605i	$-0.171690\pi$
$523$	18378.6	+	2642.45i	1.53660	+	0.220929i	0.678571	+	0.734535i	$0.262600\pi$
$524$	−8815.48	+	2013.24i	−0.734936	+	0.167841i
$525$	2456.58	−	353.203i	0.204217	−	0.0293620i
$526$	−331.916	−	654.619i	−0.0275137	−	0.0542638i
$527$	8534.21	−	9849.01i	0.705420	−	0.814098i
$528$	−32808.4	−	14171.8i	−2.70417	−	1.16809i
$529$	10119.7	+	6754.77i	0.831736	+	0.555171i
$530$	−1449.38	+	14169.1i	−0.118787	+	1.16126i
$531$	20792.8	+	18017.1i	1.69930	+	1.47245i
$532$	628.430	+	1633.18i	0.0512141	+	0.133097i
$533$	10836.8	−	1558.10i	0.880667	−	0.126621i
$534$	7342.76	+	21687.2i	0.595042	+	1.75748i
$535$	−2224.53	+	15472.0i	−0.179766	+	1.25030i
$536$	−5823.65	−	117.726i	−0.469297	−	0.00948692i
$537$	−2883.65	−	1853.21i	−0.231729	−	0.148923i
$538$	5971.47	−	10183.8i	0.478529	−	0.816088i
$539$	−5175.88	+	17627.4i	−0.413620	+	1.40866i
$540$	10406.4	+	18598.7i	0.829294	+	1.48215i
$541$	15338.5	−	13290.9i	1.21896	−	1.05623i	0.222261	−	0.974987i	$-0.428656\pi$
$541$	15338.5	−	13290.9i	1.21896	−	1.05623i	0.996694	−	0.0812439i	$-0.0258893\pi$
$542$	3053.91	−	7481.81i	0.242023	−	0.592936i
$543$	−3078.98	+	6742.02i	−0.243336	+	0.532832i
$544$	14314.5	−	7633.56i	1.12818	−	0.601629i
$545$	−12580.9	+	3694.08i	−0.988818	+	0.290343i
$546$	7364.36	+	1839.20i	0.577226	+	0.144158i
$547$	−12834.0	+	5861.11i	−1.00319	+	0.458141i	−0.848143	−	0.529767i	$-0.822279\pi$
$547$	−12834.0	+	5861.11i	−1.00319	+	0.458141i	−0.155045	+	0.987907i	$0.549552\pi$
$548$	160.485	−	2624.41i	0.0125102	−	0.204579i
$549$	−7697.63	−	11977.7i	−0.598410	−	0.931144i
$550$	5045.98	−	4746.84i	0.391202	−	0.368011i
$551$	1495.75			0.115647
$552$	−18149.2	−	12419.1i	−1.39942	−	0.957593i
$553$	6004.24			0.461711
$554$	−13807.6	+	12989.1i	−1.05890	+	0.996126i
$555$	6966.20	+	10839.6i	0.532791	+	0.829039i
$556$	15181.4	+	928.358i	1.15798	+	0.0708114i
$557$	−805.057	+	367.657i	−0.0612412	+	0.0279679i	−0.445800	−	0.895132i	$-0.647081\pi$
$557$	−805.057	+	367.657i	−0.0612412	+	0.0279679i	0.384559	+	0.923100i	$0.374354\pi$
$558$	20205.6	+	5046.21i	1.53292	+	0.382837i
$559$	16106.2	−	4729.20i	1.21864	−	0.357824i
$560$	4952.08	−	3328.97i	0.373685	−	0.251205i
$561$	−20789.1	+	45521.7i	−1.56456	+	3.42590i
$562$	2423.72	−	5937.90i	0.181919	−	0.445685i
$563$	−2858.26	+	2476.70i	−0.213963	+	0.185400i	−0.755248	−	0.655439i	$-0.772484\pi$
$563$	−2858.26	+	2476.70i	−0.213963	+	0.185400i	0.541285	+	0.840839i	$0.317938\pi$
$564$	23434.1	−	13111.9i	1.74957	−	0.978919i
$565$	4986.37	−	16982.0i	0.371289	−	1.26449i
$566$	−6536.93	+	11148.2i	−0.485455	+	0.827901i
$567$	−2867.85	−	1843.06i	−0.212413	−	0.136510i
$568$	−347.548	+	17192.4i	−0.0256739	+	1.27003i
$569$	−830.418	+	5775.68i	−0.0611826	+	0.425535i	0.936092	+	0.351755i	$0.114415\pi$
$569$	−830.418	+	5775.68i	−0.0611826	+	0.425535i	−0.997275	+	0.0737793i	$0.976494\pi$
$570$	−3068.49	−	9062.93i	−0.225482	−	0.665972i
$571$	−17969.8	+	2583.66i	−1.31701	+	0.189357i	−0.764755	−	0.644321i	$-0.777140\pi$
$571$	−17969.8	+	2583.66i	−1.31701	+	0.189357i	−0.552251	+	0.833678i	$0.686231\pi$
$572$	19774.8	−	7609.10i	1.44550	−	0.556211i
$573$	−4410.55	−	3821.76i	−0.321559	−	0.278632i
$574$	−549.559	+	5372.46i	−0.0399619	+	0.390666i
$575$	3606.15	−	2273.52i	0.261542	−	0.164891i
$576$	21225.3	+	14886.1i	1.53539	+	1.07683i
$577$	2846.04	−	3284.50i	0.205341	−	0.236977i	−0.643733	−	0.765250i	$-0.722615\pi$
$577$	2846.04	−	3284.50i	0.205341	−	0.236977i	0.849074	+	0.528274i	$0.177161\pi$
$578$	−3988.87	−	7867.01i	−0.287050	−	0.566132i
$579$	−7167.84	+	1030.58i	−0.514482	+	0.0739714i
$580$	−1135.55	−	4972.32i	−0.0812953	−	0.355973i
$581$	6508.95	+	935.845i	0.464779	+	0.0668251i
$582$	28757.4	−	5341.84i	2.04816	−	0.380457i
$583$	−20987.2	−	13487.7i	−1.49091	−	0.958152i
$584$	9791.95	+	8837.52i	0.693825	+	0.626197i
$585$	−25973.1	−	7626.40i	−1.83565	−	0.538996i
$586$	−81.3326	−	115.860i	−0.00573348	−	0.00816745i
$587$	−13132.1	+	11379.0i	−0.923370	+	0.800105i	−0.980145	−	0.198282i	$-0.936464\pi$
$587$	−13132.1	+	11379.0i	−0.923370	+	0.800105i	0.0567746	+	0.998387i	$0.481918\pi$
$588$	9606.97	−	18034.1i	0.673784	−	1.26482i
$589$	−3969.98	−	1813.03i	−0.277725	−	0.126833i
$590$	−12256.9	+	15371.7i	−0.855270	+	1.07261i
$591$	4483.73	−	1316.54i	0.312075	−	0.0916334i
$592$	6235.12	+	3827.49i	0.432875	+	0.265725i
$593$	−964.139	−	2111.17i	−0.0667664	−	0.146198i	0.873307	−	0.487170i	$-0.161971\pi$
$593$	−964.139	−	2111.17i	−0.0667664	−	0.146198i	−0.940073	+	0.340973i	$0.889244\pi$
$594$	−37298.3	+	1524.95i	−2.57638	+	0.105336i
$595$	−4517.35	−	7029.14i	−0.311249	−	0.484313i
$596$	16320.5	+	21338.7i	1.12166	+	1.46656i
$597$		−	24161.1i		−	1.65636i
$598$	12839.0	−	2269.75i	0.877973	−	0.155212i
$599$	9273.68			0.632575			0.316288	−	0.948663i	$-0.397564\pi$
$599$	9273.68			0.632575			0.316288	+	0.948663i	$0.397564\pi$
$600$	−6564.95	+	4033.92i	−0.446688	+	0.274473i
$601$	531.207	−	341.386i	0.0360539	−	0.0231704i	−0.522490	−	0.852646i	$-0.674997\pi$
$601$	531.207	−	341.386i	0.0360539	−	0.0231704i	0.558544	+	0.829475i	$0.311360\pi$
$602$	338.253	+	8273.25i	0.0229006	+	0.560120i
$603$	−11856.7	+	5414.77i	−0.800733	+	0.365682i
$604$	9152.00	−	25333.3i	0.616539	−	1.70662i
$605$	9678.86	+	32963.2i	0.650416	+	2.21511i
$606$	−9637.79	+	12087.0i	−0.646054	+	0.810229i
$607$	1338.60	−	2931.14i	0.0895096	−	0.195999i	−0.859583	−	0.510996i	$-0.829277\pi$
$607$	1338.60	−	2931.14i	0.0895096	−	0.195999i	0.949092	+	0.314998i	$0.102004\pi$
$608$	−3803.47	−	3879.43i	−0.253702	−	0.258769i
$609$	2095.81	+	2418.70i	0.139452	+	0.160937i
$610$	8327.21	−	5845.63i	0.552720	−	0.388004i
$611$	−4485.28	+	15275.4i	−0.296980	+	1.01142i
$612$	21454.1	−	29284.8i	1.41704	−	1.93426i
$613$	5850.15	−	9103.01i	0.385457	−	0.599784i	−0.593256	−	0.805014i	$-0.702158\pi$
$613$	5850.15	−	9103.01i	0.385457	−	0.599784i	0.978714	+	0.205230i	$0.0657943\pi$
$614$	5027.04	−	933.800i	0.330415	−	0.0613764i
$615$	4202.43	−	29228.5i	0.275542	−	1.91644i
$616$	1278.03	+	10373.2i	0.0835927	+	0.678485i
$617$	−1490.48	−	10366.5i	−0.0972522	−	0.676404i	−0.978877	−	0.204452i	$-0.934459\pi$
$617$	−1490.48	−	10366.5i	−0.0972522	−	0.676404i	0.881624	−	0.471952i	$-0.156450\pi$
$618$	−11798.6	+	5982.34i	−0.767978	+	0.389393i
$619$	−1706.27	−	1478.49i	−0.110793	−	0.0960027i	0.597703	−	0.801718i	$-0.296080\pi$
$619$	−1706.27	−	1478.49i	−0.110793	−	0.0960027i	−0.708496	+	0.705715i	$0.750626\pi$
$620$	−3013.08	+	14573.8i	−0.195175	+	0.944027i
$621$	−22707.5	−	3466.40i	−1.46735	−	0.223997i
$622$	−821.451	+	8030.47i	−0.0529537	+	0.517673i
$623$	4384.96	−	5060.52i	0.281990	−	0.325434i
$624$	−23252.0	+	3834.73i	−1.49170	+	0.246013i
$625$	2698.62	+	18769.3i	0.172712	+	1.20124i
$626$	2544.85	−	861.625i	0.162480	−	0.0550119i
$627$	16588.9	+	2385.12i	1.05661	+	0.151918i
$628$	−2110.87	−	25771.5i	−0.134129	−	1.63757i
$629$	5538.75	−	8618.46i	0.351104	−	0.546328i
$630$	6754.13	−	11518.6i	0.427129	−	0.728430i
$631$	7665.25	+	2250.72i	0.483596	+	0.141996i	0.514438	−	0.857528i	$-0.328001\pi$
$631$	7665.25	+	2250.72i	0.483596	+	0.141996i	−0.0308420	+	0.999524i	$0.509819\pi$
$632$	−17109.6	+	7399.50i	−1.07687	+	0.465722i
$633$	−7634.53	−	8810.71i	−0.479376	−	0.553230i
$634$	−15512.4	−	6331.84i	−0.971731	−	0.396639i
$635$	−30529.1	−	13942.2i	−1.90789	−	0.871305i
$636$	19821.8	+	19416.7i	1.23583	+	1.21057i
$637$	3413.00	+	11623.6i	0.212289	+	0.722990i
$638$	8667.35	+	2164.61i	0.537843	+	0.134323i
$639$	15985.4	+	35003.1i	0.989627	+	2.16698i
$640$	−10008.8	+	15589.0i	−0.618177	+	0.962829i
$641$	23371.7	−	15020.1i	1.44013	−	0.925518i	0.440519	−	0.897743i	$-0.354794\pi$
$641$	23371.7	−	15020.1i	1.44013	−	0.925518i	0.999614	−	0.0277745i	$-0.00884203\pi$
$642$	20864.9	+	22179.8i	1.28267	+	1.36350i
$643$		−	12696.3i		−	0.778684i	−0.921093	−	0.389342i	$-0.872702\pi$
$643$		−	12696.3i		−	0.778684i	0.921093	−	0.389342i	$-0.127298\pi$
$644$	−448.288	+	6415.72i	−0.0274301	+	0.392570i
$645$		−	45274.7i		−	2.76386i
$646$	−5541.15	+	5212.66i	−0.337483	+	0.317476i
$647$	16498.4	−	10602.9i	1.00250	−	0.644271i	0.0670618	−	0.997749i	$-0.478638\pi$
$647$	16498.4	−	10602.9i	1.00250	−	0.644271i	0.935443	+	0.353478i	$0.115001\pi$
$648$	10443.5	+	1717.66i	0.633118	+	0.104130i
$649$	−14305.2	−	31324.0i	−0.865221	−	1.89457i
$650$	1106.89	−	4432.10i	0.0667933	−	0.267448i
$651$	−2630.89	−	8959.99i	−0.158391	−	0.539431i
$652$	21728.8	−	22182.2i	1.30516	−	1.33239i
$653$	−4216.15	−	1925.45i	−0.252666	−	0.115389i	0.285056	−	0.958511i	$-0.407988\pi$
$653$	−4216.15	−	1925.45i	−0.252666	−	0.115389i	−0.537722	+	0.843122i	$0.680715\pi$
$654$	−9653.27	+	23649.7i	−0.577176	+	1.41403i
$655$	−9468.91	−	10927.7i	−0.564856	−	0.651879i
$656$	−5054.90	−	15986.5i	−0.300854	−	0.951478i
$657$	28321.1	+	8315.84i	1.68175	+	0.493808i
$658$	−6774.36	−	3972.27i	−0.401356	−	0.235342i
$659$	5032.27	−	7830.36i	0.297465	−	0.462864i	−0.660061	−	0.751212i	$-0.729470\pi$
$659$	5032.27	−	7830.36i	0.297465	−	0.462864i	0.957526	+	0.288348i	$0.0931059\pi$
$660$	−4665.20	−	56957.0i	−0.275140	−	3.35917i
$661$	−9320.74	−	1340.12i	−0.548464	−	0.0788572i	−0.137488	−	0.990503i	$-0.543903\pi$
$661$	−9320.74	−	1340.12i	−0.548464	−	0.0788572i	−0.410976	+	0.911646i	$0.634812\pi$
$662$	312.918	+	924.218i	0.0183715	+	0.0542610i
$663$	4696.30	+	32663.5i	0.275097	+	1.91334i
$664$	−19701.1	+	5354.72i	−1.15143	+	0.312957i
$665$	−1832.45	+	2114.76i	−0.106856	+	0.123319i
$666$	16286.9	+	1666.01i	0.947603	+	0.0969320i
$667$	4980.45	+	2326.98i	0.289121	+	0.135084i
$668$	−18435.3	−	3811.44i	−1.06779	−	0.220762i
$669$	−26052.5	−	22574.6i	−1.50560	−	1.30461i
$670$	−4212.17	−	8307.42i	−0.242881	−	0.479020i
$671$	2536.15	+	17639.3i	0.145912	+	1.01484i
$672$	943.884	−	11586.1i	0.0541832	−	0.665096i
$673$	1520.82	−	10577.5i	0.0871073	−	0.605844i	−0.898776	−	0.438409i	$-0.855542\pi$
$673$	1520.82	−	10577.5i	0.0871073	−	0.605844i	0.985883	−	0.167436i	$-0.0535486\pi$
$674$	4066.97	+	21894.2i	0.232424	+	1.25124i
$675$	−4351.24	+	6770.66i	−0.248118	+	0.386079i
$676$	−2130.11	+	2907.59i	−0.121194	+	0.165430i
$677$	−3674.36	+	12513.7i	−0.208593	+	0.710401i	0.787028	+	0.616917i	$0.211619\pi$
$677$	−3674.36	+	12513.7i	−0.208593	+	0.710401i	−0.995621	+	0.0934841i	$0.970200\pi$
$678$	−19810.6	−	28220.6i	−1.12216	−	1.59853i
$679$	−5601.61	−	6464.60i	−0.316598	−	0.365373i
$680$	21535.1	+	14463.0i	1.21446	+	0.815635i
$681$	17701.6	−	38761.2i	0.996077	−	2.18111i
$682$	−20380.8	−	16251.1i	−1.14431	−	0.912443i
$683$	−7010.08	−	23874.1i	−0.392728	−	1.33751i	−0.884401	−	0.466729i	$-0.845432\pi$
$683$	−7010.08	−	23874.1i	−0.392728	−	1.33751i	0.491673	−	0.870780i	$-0.336386\pi$
$684$	−11434.3	−	4130.79i	−0.639181	−	0.230913i
$685$	3824.48	−	1746.58i	0.213323	−	0.0974212i
$686$	−13035.5	+	532.957i	−0.725505	+	0.0296624i
$687$	−10215.6	+	6565.19i	−0.567323	+	0.364596i
$688$	−11159.7	−	23158.5i	−0.618398	−	1.28330i
$689$	−16450.6			−0.909603
$690$	3882.19	−	34950.8i	0.214192	−	1.92834i
$691$			16558.5i			0.911598i	0.890083	+	0.455799i	$0.150646\pi$
$691$			16558.5i			0.911598i	−0.890083	+	0.455799i	$0.849354\pi$
$692$	−1452.20	−	1898.73i	−0.0797753	−	0.104305i
$693$	12644.6	+	19675.4i	0.693116	+	1.07851i
$694$	−1252.33	−	30630.5i	−0.0684985	−	1.67539i
$695$	10103.5	+	22123.5i	0.551434	+	1.20747i
$696$	−8952.94	−	4309.44i	−0.487587	−	0.234697i
$697$	−22527.2	+	6614.59i	−1.22422	+	0.359463i
$698$	−5628.16	−	4487.73i	−0.305199	−	0.243357i
$699$	41423.3	+	18917.4i	2.24145	+	1.02364i
$700$	1988.79	+	1059.46i	0.107385	+	0.0572052i
$701$	5256.14	−	4554.47i	0.283198	−	0.245392i	−0.501665	−	0.865062i	$-0.667279\pi$
$701$	5256.14	−	4554.47i	0.283198	−	0.245392i	0.784863	+	0.619670i	$0.212733\pi$
$702$	−20146.7	+	14142.8i	−1.08317	+	0.760379i
$703$	−3291.94	−	966.602i	−0.176612	−	0.0518579i
$704$	−16425.5	−	27984.2i	−0.879346	−	1.49814i
$705$	36123.0	+	23214.8i	1.92975	+	1.24017i
$706$	3613.19	+	19451.3i	0.192612	+	1.03691i
$707$	4474.94	+	643.399i	0.238044	+	0.0342256i
$708$	8527.32	+	37339.1i	0.452650	+	1.98205i
$709$	−21471.6	+	3087.15i	−1.13735	+	0.163527i	−0.685159	−	0.728393i	$-0.740268\pi$
$709$	−21471.6	+	3087.15i	−1.13735	+	0.163527i	−0.452194	+	0.891920i	$0.649358\pi$
$710$	−24525.0	+	12435.1i	−1.29635	+	0.657296i
$711$	−27317.1	+	31525.6i	−1.44089	+	1.66287i
$712$	−6258.85	+	19824.3i	−0.329438	+	1.04347i
$713$	−10398.4	−	12213.1i	−0.546174	−	0.641492i
$714$	−16193.2	−	1656.43i	−0.848761	−	0.0868213i
$715$	25605.8	+	22187.5i	1.33930	+	1.16051i
$716$	−1117.68	−	2904.65i	−0.0583373	−	0.151609i
$717$	−10795.9	+	1552.22i	−0.562317	+	0.0808490i
$718$	14529.5	−	4919.33i	0.755201	−	0.255693i
$719$	−4589.18	+	31918.5i	−0.238036	+	1.65557i	0.423674	+	0.905815i	$0.360740\pi$
$719$	−4589.18	+	31918.5i	−0.238036	+	1.65557i	−0.661710	+	0.749760i	$0.730169\pi$
$720$	−5051.22	+	41146.8i	−0.261455	+	2.12979i
$721$	3254.54	+	2091.56i	0.168107	+	0.108036i
$722$	−14537.5	−	8524.35i	−0.749350	−	0.439395i
$723$	8501.91	−	28954.8i	0.437330	−	1.48941i
$724$	−5872.77	+	3285.94i	−0.301464	+	0.168675i
$725$	1455.65	−	1261.32i	0.0745673	−	0.0646130i
$726$	61964.4	+	25292.5i	3.16765	+	1.29297i
$727$	1456.72	−	3189.77i	0.0743147	−	0.162727i	−0.868829	−	0.495113i	$-0.835127\pi$
$727$	1456.72	−	3189.77i	0.0743147	−	0.162727i	0.943143	+	0.332387i	$0.107854\pi$
$728$	4407.00	+	5298.66i	0.224360	+	0.269754i
$729$	−24810.3	+	7284.97i	−1.26049	+	0.370115i
$730$	−5110.64	+	20463.6i	−0.259114	+	1.03752i
$731$	−32744.4	+	14953.8i	−1.65676	+	0.756618i
$732$	1209.79	−	19783.7i	0.0610862	−	0.998942i
$733$	2750.26	+	4279.48i	0.138585	+	0.215643i	0.903608	−	0.428360i	$-0.140909\pi$
$733$	2750.26	+	4279.48i	0.138585	+	0.215643i	−0.765023	+	0.644003i	$0.777272\pi$
$734$	−10487.1	−	11148.0i	−0.527366	−	0.560600i
$735$	32674.1			1.63973
$736$	−6629.17	−	18834.6i	−0.332003	−	0.943278i
$737$	16314.5			0.815406
$738$	−25708.1	−	27328.2i	−1.28229	−	1.36310i
$739$	7392.14	+	11502.4i	0.367963	+	0.572561i	0.975026	−	0.222093i	$-0.0712888\pi$
$739$	7392.14	+	11502.4i	0.367963	+	0.572561i	−0.607063	+	0.794654i	$0.707652\pi$
$740$	−714.071	+	11677.2i	−0.0354727	+	0.580084i
$741$	10052.6	−	4590.87i	0.498370	−	0.227598i
$742$	1966.18	−	7872.82i	0.0972788	−	0.389515i
$743$	9665.11	−	2837.93i	0.477225	−	0.140126i	−0.0342690	−	0.999413i	$-0.510910\pi$
$743$	9665.11	−	2837.93i	0.477225	−	0.140126i	0.511494	+	0.859287i	$0.329092\pi$
$744$	18539.0	+	22290.0i	0.913541	+	1.09837i
$745$	−17845.4	+	39075.9i	−0.877589	+	1.92165i
$746$	16031.0	+	6543.51i	0.786779	+	0.321146i
$747$	−34527.1	+	29917.9i	−1.69114	+	1.46538i
$748$	−39652.6	+	22186.5i	−1.93829	+	1.08452i
$749$	2508.95	−	8544.70i	0.122397	−	0.416845i
$750$	23748.2	+	13925.2i	1.15621	+	0.677968i
$751$	−2879.24	−	1850.37i	−0.139900	−	0.0899082i	0.468819	−	0.883294i	$-0.344680\pi$
$751$	−2879.24	−	1850.37i	−0.139900	−	0.0899082i	−0.608719	+	0.793386i	$0.708316\pi$
$752$	24199.5	+	2970.75i	1.17349	+	0.144058i
$753$	4290.51	−	29841.2i	0.207643	−	1.44419i
$754$	5579.70	−	1889.15i	0.269497	−	0.0912453i
$755$	42633.5	−	6129.77i	2.05509	−	0.295477i
$756$	−4360.44	−	11332.1i	−0.209772	−	0.545163i
$757$	10658.1	+	9235.26i	0.511722	+	0.443410i	0.872051	−	0.489416i	$-0.162790\pi$
$757$	10658.1	+	9235.26i	0.511722	+	0.443410i	−0.360328	+	0.932826i	$0.617335\pi$
$758$	14617.1	+	1495.21i	0.700417	+	0.0716469i
$759$	51525.9	+	33749.6i	2.46413	+	1.61401i
$760$	2615.53	−	8284.45i	0.124836	−	0.395406i
$761$	−23814.8	+	27483.7i	−1.13441	+	1.30918i	−0.189486	+	0.981884i	$0.560682\pi$
$761$	−23814.8	+	27483.7i	−1.13441	+	1.30918i	−0.944923	+	0.327293i	$0.893863\pi$
$762$	−58315.6	+	29568.1i	−2.77237	+	1.40570i
$763$	7394.23	−	1063.13i	0.350837	−	0.0504428i
$764$	−1179.74	−	5165.79i	−0.0558657	−	0.244622i
$765$	57459.2	+	8261.39i	2.71561	+	0.390446i
$766$	5596.62	+	30129.0i	0.263987	+	1.42115i
$767$	−19102.5	−	12276.5i	−0.899287	−	0.577936i
$768$	11588.8	+	34178.9i	0.544500	+	1.60589i
$769$	−35333.5	−	10374.9i	−1.65691	−	0.486511i	−0.686326	−	0.727294i	$-0.740778\pi$
$769$	−35333.5	−	10374.9i	−1.65691	−	0.486511i	−0.970579	+	0.240782i	$0.922596\pi$
$770$	−13678.8	+	9602.40i	−0.640195	+	0.449411i
$771$	21537.5	−	18662.4i	1.00604	−	0.871737i
$772$	−5802.93	−	3091.29i	−0.270534	−	0.144117i
$773$	−19839.3	−	9060.33i	−0.923120	−	0.421575i	−0.103596	−	0.994619i	$-0.533035\pi$
$773$	−19839.3	−	9060.33i	−0.923120	−	0.421575i	−0.819524	+	0.573045i	$0.805762\pi$
$774$	−44978.1	−	35864.2i	−2.08877	−	1.66552i
$775$	−5392.40	+	1583.35i	−0.249936	+	0.0733879i
$776$	23929.1	+	11518.1i	1.10696	+	0.532830i
$777$	−3049.55	−	6677.59i	−0.140801	−	0.308310i
$778$	503.537	+	12315.9i	0.0232039	+	0.567539i
$779$	4250.91	+	6614.55i	0.195513	+	0.304225i
$780$	−22893.2	−	29932.5i	−1.05091	−	1.37404i
$781$		−	48163.4i		−	2.20669i
$782$	−26560.0	+	8736.21i	−1.21456	+	0.399497i
$783$	−10378.5			−0.473687
$784$	16713.2	−	8053.78i	0.761350	−	0.366881i
$785$	34784.3	−	22354.5i	1.58153	−	1.01639i
$786$	−28145.3	+	1150.73i	−1.27724	+	0.0522202i
$787$	8473.43	−	3869.68i	0.383793	−	0.175272i	−0.214169	−	0.976797i	$-0.568704\pi$
$787$	8473.43	−	3869.68i	0.383793	−	0.175272i	0.597962	+	0.801524i	$0.295977\pi$
$788$	3990.45	+	1441.61i	0.180398	+	0.0651715i
$789$	−644.157	−	2193.80i	−0.0290654	−	0.0989876i
$790$	−23306.2	−	18583.7i	−1.04962	−	0.836934i
$791$	−4188.86	+	9172.32i	−0.188292	+	0.412301i
$792$	−60279.5	−	40483.8i	−2.70447	−	1.81632i
$793$	7695.32	+	8880.87i	0.344601	+	0.397691i
$794$	−23662.0	−	33707.0i	−1.05760	−	1.50657i
$795$	−12500.4	+	42572.3i	−0.557663	+	1.89923i
$796$	12964.4	−	17696.3i	0.577274	−	0.787976i
$797$	−13588.1	+	21143.6i	−0.603910	+	0.939703i	0.395861	+	0.918311i	$0.370446\pi$
$797$	−13588.1	+	21143.6i	−0.603910	+	0.939703i	−0.999771	+	0.0213923i	$0.993190\pi$
$798$	995.580	+	5359.63i	0.0441644	+	0.237755i
$799$	4858.73	−	33793.2i	0.215131	−	1.49627i
$800$	−6972.89	−	568.059i	−0.308161	−	0.0251049i
$801$	6620.56	+	46047.0i	0.292043	+	2.03120i
$802$	560.428	+	1105.30i	0.0246751	+	0.0486652i
$803$	−27920.5	−	24193.3i	−1.22702	−	1.06322i
$804$	−17769.6	−	3673.81i	−0.779460	−	0.161151i
$805$	−9391.54	+	4190.78i	−0.411190	+	0.183485i
$806$	−17099.3	−	1749.12i	−0.747268	−	0.0764394i
$807$	24083.2	−	27793.5i	1.05052	−	1.21236i
$808$	−13544.6	+	3681.40i	−0.589726	+	0.160286i
$809$	−1735.96	−	12073.9i	−0.0754427	−	0.524716i	−0.992140	−	0.125133i	$-0.960064\pi$
$809$	−1735.96	−	12073.9i	−0.0754427	−	0.524716i	0.916697	−	0.399583i	$-0.130845\pi$
$810$	5427.48	+	16030.3i	0.235435	+	0.695367i
$811$	−21423.2	−	3080.20i	−0.927585	−	0.133367i	−0.338067	−	0.941122i	$-0.609773\pi$
$811$	−21423.2	−	3080.20i	−0.927585	−	0.133367i	−0.589518	+	0.807755i	$0.700682\pi$
$812$	237.211	+	2896.10i	0.0102518	+	0.125164i
$813$	13610.1	−	21177.7i	0.587118	−	0.913574i
$814$	−17676.8	−	10365.1i	−0.761144	−	0.446311i
$815$	47641.8	+	13988.9i	2.04763	+	0.601238i
$816$	48185.3	−	15236.0i	2.06718	−	0.653637i
$817$	7894.55	+	9110.80i	0.338060	+	0.390143i
$818$	11162.3	−	27346.6i	0.477115	−	1.16889i
$819$	14028.6	+	6406.66i	0.598534	+	0.273341i
$820$	18761.5	−	19152.9i	0.798998	−	0.815670i
$821$	3275.14	+	11154.1i	0.139224	+	0.474154i	0.999355	−	0.0359198i	$-0.0114361\pi$
$821$	3275.14	+	11154.1i	0.139224	+	0.474154i	−0.860130	+	0.510074i	$0.829618\pi$
$822$	1984.63	−	7946.70i	0.0842118	−	0.337194i
$823$	−10090.6	−	22095.4i	−0.427384	−	0.935840i	−0.993744	−	0.111682i	$-0.964376\pi$
$823$	−10090.6	−	22095.4i	−0.427384	−	0.935840i	0.566360	−	0.824158i	$-0.308351\pi$
$824$	−11851.7	−	1949.26i	−0.501059	−	0.0824100i
$825$	18155.4	−	11667.8i	0.766169	−	0.492387i
$826$	8158.35	−	7674.70i	0.343663	−	0.323289i
$827$			20542.6i			0.863768i	0.901929	+	0.431884i	$0.142151\pi$
$827$			20542.6i			0.863768i	−0.901929	+	0.431884i	$0.857849\pi$
$828$	−31646.6	−	31543.0i	−1.32825	−	1.32391i
$829$			15720.4i			0.658616i	0.944223	+	0.329308i	$0.106815\pi$
$829$			15720.4i			0.658616i	−0.944223	+	0.329308i	$0.893185\pi$
$830$	−22368.8	−	23778.4i	−0.935459	−	0.994410i
$831$	−49679.8	+	31927.3i	−2.07385	+	1.33278i
$832$	−19088.1	−	9667.87i	−0.795385	−	0.402852i
$833$	−10792.0	−	23631.2i	−0.448884	−	0.982919i
$834$	45969.3	+	11480.5i	1.90862	+	0.476664i
$835$	−8480.88	−	28883.2i	−0.351489	−	1.19706i
$836$	10870.4	+	10648.2i	0.449714	+	0.440522i
$837$	27546.2	+	12579.9i	1.13756	+	0.519505i
$838$	29240.9	+	11935.5i	1.20538	+	0.492011i
$839$	25919.6	+	29912.8i	1.06656	+	1.23088i	0.971907	+	0.235365i	$0.0756285\pi$
$839$	25919.6	+	29912.8i	1.06656	+	1.23088i	0.0946525	+	0.995510i	$0.469826\pi$
$840$	17061.1	−	7378.54i	0.700791	−	0.303076i
$841$	−21017.9	−	6171.42i	−0.861779	−	0.253041i
$842$	3657.12	−	6236.90i	0.149683	−	0.255270i
$843$	10801.6	−	16807.6i	0.441312	−	0.686696i
$844$	−864.103	−	10549.8i	−0.0352413	−	0.430258i
$845$	−5704.94	−	820.247i	−0.232256	−	0.0333933i
$846$	51677.5	−	17496.8i	2.10013	−	0.711054i
$847$	−2785.50	−	19373.6i	−0.113000	−	0.785932i
$848$	4099.50	+	24857.4i	0.166011	+	1.00661i
$849$	−26363.7	+	30425.4i	−1.06573	+	1.22991i
$850$	−996.892	+	9745.57i	−0.0402272	+	0.393259i
$851$	−9457.50	−	8339.88i	−0.380963	−	0.335943i
$852$	−10845.8	+	52459.1i	−0.436114	+	2.10941i
$853$	9027.88	+	7822.70i	0.362378	+	0.314002i	0.816951	−	0.576707i	$-0.195663\pi$
$853$	9027.88	+	7822.70i	0.362378	+	0.314002i	−0.454573	+	0.890710i	$0.650208\pi$
$854$	−5169.91	+	2621.34i	−0.207155	+	0.105035i
$855$	−2766.69	−	19242.8i	−0.110665	−	0.769694i
$856$	3380.85	+	27440.8i	0.134994	+	1.09569i
$857$	−4731.35	+	32907.3i	−0.188588	+	1.31166i	0.647079	+	0.762423i	$0.275990\pi$
$857$	−4731.35	+	32907.3i	−0.188588	+	1.31166i	−0.835667	+	0.549236i	$0.814919\pi$
$858$	64895.1	−	12054.6i	2.58215	−	0.479648i
$859$	−16609.6	+	25845.0i	−0.659733	+	1.02657i	0.336653	+	0.941629i	$0.390705\pi$
$859$	−16609.6	+	25845.0i	−0.659733	+	1.02657i	−0.996386	+	0.0849363i	$0.972931\pi$
$860$	24293.5	−	33160.5i	0.963258	−	1.31484i
$861$	−4739.73	+	16142.0i	−0.187607	+	0.638931i
$862$	−17024.3	+	11950.9i	−0.672681	+	0.472216i
$863$	−30366.4	−	35044.7i	−1.19778	−	1.38231i	−0.904604	−	0.426253i	$-0.859833\pi$
$863$	−30366.4	−	35044.7i	−1.19778	−	1.38231i	−0.293176	−	0.956059i	$-0.594712\pi$
$864$	26390.9	+	26918.0i	1.03916	+	1.05992i
$865$	1587.89	−	3476.99i	0.0624160	−	0.136672i
$866$	−2607.46	+	3270.07i	−0.102315	+	0.128316i
$867$	−7741.28	−	26364.4i	−0.303238	−	1.03273i
$868$	2880.81	−	7974.25i	0.112651	−	0.311824i
$869$	47492.9	−	21689.3i	1.85395	−	0.846672i
$870$	−649.060	−	15875.2i	−0.0252933	−	0.618643i
$871$	9050.12	−	5816.16i	0.352068	−	0.226261i
$872$	−19760.3	+	12142.0i	−0.767394	+	0.471535i
$873$	59428.0			2.30393
$874$	5313.15	+	7710.22i	0.205629	+	0.298401i
$875$		−	8051.01i		−	0.311056i
$876$	24962.7	+	32638.4i	0.962800	+	1.25885i
$877$	−25985.7	−	40434.5i	−1.00054	−	1.55687i	−0.819245	−	0.573443i	$-0.805607\pi$
$877$	−25985.7	−	40434.5i	−1.00054	−	1.55687i	−0.181296	−	0.983429i	$-0.558029\pi$
$878$	6699.63	−	273.916i	0.257519	−	0.0105287i
$879$	−183.188	−	401.127i	−0.00702934	−	0.0153921i
$880$	27145.1	−	44220.3i	1.03984	−	1.69394i
$881$	−23659.4	+	6947.03i	−0.904774	+	0.265666i	−0.700840	−	0.713319i	$-0.747191\pi$
$881$	−23659.4	+	6947.03i	−0.904774	+	0.265666i	−0.203935	+	0.978985i	$0.565373\pi$
$882$	25882.8	−	32460.1i	0.988115	−	1.23922i
$883$	13878.1	+	6337.91i	0.528918	+	0.241549i	0.661930	−	0.749566i	$-0.269738\pi$
$883$	13878.1	+	6337.91i	0.528918	+	0.241549i	−0.133012	+	0.991114i	$0.542465\pi$
$884$	−14086.9	+	26443.7i	−0.535964	+	1.00610i
$885$	−46285.7	+	40106.8i	−1.75805	+	1.52336i
$886$	11983.4	+	17070.5i	0.454389	+	0.647286i
$887$	−5614.27	−	1648.50i	−0.212524	−	0.0624027i	0.173737	−	0.984792i	$-0.444416\pi$
$887$	−5614.27	−	1648.50i	−0.212524	−	0.0624027i	−0.386262	+	0.922389i	$0.626234\pi$
$888$	16919.3	+	15270.1i	0.639385	+	0.577063i
$889$	16085.8	+	10337.7i	0.606861	+	0.390006i
$890$	−32683.6	+	6071.15i	−1.23096	+	0.228658i
$891$	−29342.1	−	4218.76i	−1.10325	−	0.158624i
$892$	−6968.53	−	30513.6i	−0.261574	−	1.14537i
$893$	−11317.1	+	1627.16i	−0.424092	+	0.0609752i
$894$	37845.9	+	74641.2i	1.41583	+	2.79237i
$895$	3259.05	−	3761.15i	0.121719	−	0.140471i
$896$	6908.22	−	7979.56i	0.257575	−	0.297521i
$897$	40614.6	+	352.750i	1.51180	+	0.0131304i
$898$	302.451	−	2956.75i	0.0112393	−	0.109875i
$899$	−5477.06	−	4745.90i	−0.203193	−	0.176067i
$900$	−14611.0	+	5622.15i	−0.541149	+	0.208228i
$901$	34918.7	−	5020.55i	1.29113	−	0.185637i
$902$	15060.1	+	44480.8i	0.555928	+	1.64196i
$903$	−3670.90	+	25531.6i	−0.135282	+	0.940908i
$904$	632.726	−	31299.6i	0.0232789	−	1.15156i
$905$	−9052.70	−	5817.81i	−0.332510	−	0.213691i
$906$	42443.5	−	72383.6i	1.55639	−	2.65429i
$907$	8222.43	−	28003.0i	0.301016	−	1.02517i	−0.660594	−	0.750744i	$-0.729695\pi$
$907$	8222.43	−	28003.0i	0.301016	−	1.02517i	0.961609	−	0.274422i	$-0.0884865\pi$
$908$	33763.7	−	18891.5i	1.23402	−	0.690459i
$909$	−23737.6	+	20568.7i	−0.866144	+	0.750518i
$910$	−4164.73	+	10203.2i	−0.151714	+	0.371685i
$911$	4384.35	−	9600.39i	0.159451	−	0.349149i	−0.812997	−	0.582268i	$-0.802166\pi$
$911$	4384.35	−	9600.39i	0.159451	−	0.349149i	0.972448	+	0.233118i	$0.0748929\pi$
$912$	−9442.09	−	14045.8i	−0.342828	−	0.509981i
$913$	54865.6	−	16110.0i	1.98881	−	0.583969i
$914$	−34.1526	−	8.52938i	−0.00123596	−	0.000308673i
$915$	28830.2	−	13166.3i	1.04164	−	0.475700i
$916$	−11005.0	−	672.965i	−0.396960	−	0.0242745i
$917$	4453.76	+	6930.18i	0.160388	+	0.249569i
$918$	38448.0	−	36168.7i	1.38232	−	1.30038i
$919$	4039.61			0.144999			0.0724997	−	0.997368i	$-0.476902\pi$
$919$	4039.61			0.144999			0.0724997	+	0.997368i	$0.476902\pi$
$920$	21597.4	−	23515.9i	0.773960	−	0.842714i
$921$	15928.0			0.569866
$922$	10532.6	−	9908.21i	0.376218	−	0.353915i
$923$	−17170.3	−	26717.6i	−0.612317	−	0.952784i
$924$	−1987.28	+	32497.9i	−0.0707539	+	1.15704i
$925$	−4018.78	+	1835.31i	−0.142850	+	0.0652376i
$926$	−43343.3	−	10824.7i	−1.53817	−	0.384148i
$927$	−25788.8	+	7572.29i	−0.913718	+	0.268292i
$928$	−4245.04	−	7960.34i	−0.150162	−	0.281585i
$929$	−17895.9	+	39186.6i	−0.632019	+	1.38393i	0.274427	+	0.961608i	$0.411512\pi$
$929$	−17895.9	+	39186.6i	−0.632019	+	1.38393i	−0.906446	+	0.422321i	$0.861216\pi$
$930$	−17519.9	+	42922.1i	−0.617741	+	1.51341i
$931$	−6575.14	+	5697.40i	−0.231463	+	0.200563i
$932$	20189.0	+	36082.6i	0.709563	+	1.26816i
$933$	−7084.70	+	24128.3i	−0.248599	+	0.846650i
$934$	−7487.79	+	12769.8i	−0.262321	+	0.447365i
$935$	−61123.3	−	39281.6i	−2.13791	−	1.37395i
$936$	−47871.2	−	967.723i	−1.67171	−	0.0337938i
$937$	−3002.13	+	20880.2i	−0.104669	+	0.727991i	0.868129	+	0.496338i	$0.165322\pi$
$937$	−3002.13	+	20880.2i	−0.104669	+	0.727991i	−0.972799	+	0.231653i	$0.925587\pi$
$938$	1701.79	+	5026.31i	0.0592381	+	0.174962i
$939$	8284.53	−	1191.14i	0.287918	−	0.0413964i
$940$	14001.0	+	36386.1i	0.485809	+	1.26254i
$941$	−10738.3	−	9304.78i	−0.372007	−	0.322346i	0.448714	−	0.893675i	$-0.351882\pi$
$941$	−10738.3	−	9304.78i	−0.372007	−	0.322346i	−0.820721	+	0.571330i	$0.806428\pi$
$942$	8197.00	−	80133.5i	0.283517	−	2.77165i
$943$	3863.96	+	28637.9i	0.133433	+	0.988949i
$944$	−13789.8	+	31923.9i	−0.475444	+	1.10067i
$945$	12714.7	−	14673.5i	0.437681	−	0.505111i
$946$	32561.2	+	64218.6i	1.11909	+	2.20711i
$947$	6378.37	−	917.070i	0.218869	−	0.0314686i	−0.0320078	−	0.999488i	$-0.510190\pi$
$947$	6378.37	−	917.070i	0.218869	−	0.0314686i	0.250877	+	0.968019i	$0.419281\pi$
$948$	−56612.8	+	12929.0i	−1.93956	+	0.442946i
$949$	−24113.2	−	3466.96i	−0.824814	−	0.118590i
$950$	3225.59	−	599.171i	0.110160	−	0.0204628i
$951$	−43908.9	−	28218.6i	−1.49721	−	0.962197i
$952$	−10971.6	−	9902.18i	−0.373520	−	0.337113i
$953$	−17720.8	−	5203.29i	−0.602342	−	0.176864i	−0.0336772	−	0.999433i	$-0.510722\pi$
$953$	−17720.8	−	5203.29i	−0.602342	−	0.176864i	−0.568665	+	0.822569i	$0.692540\pi$
$954$	32391.3	+	46142.0i	1.09927	+	1.56594i
$955$	6403.53	−	5548.69i	0.216977	−	0.188012i
$956$	−8740.15	−	4655.99i	−0.295687	−	0.157516i
$957$	25314.8	+	11560.9i	0.855078	+	0.390501i
$958$	33920.0	−	42539.8i	1.14395	−	1.43466i
$959$	−2298.35	+	674.855i	−0.0773904	+	0.0227239i
$960$	−39524.0	+	42051.6i	−1.32878	+	1.41376i
$961$	−3591.19	−	7863.62i	−0.120546	−	0.263959i
$962$	−13501.0	+	551.990i	−0.452483	+	0.0184999i
$963$	33449.7	+	52048.7i	1.11932	+	1.74169i
$964$	21763.7	−	16645.4i	0.727137	−	0.556135i
$965$		−	10513.8i		−	0.350726i
$966$	−5023.10	+	19395.0i	−0.167304	+	0.645986i
$967$	31666.9			1.05309			0.526546	−	0.850147i	$-0.323487\pi$
$967$	31666.9			1.05309			0.526546	+	0.850147i	$0.323487\pi$
$968$	31813.2	+	51773.9i	1.05632	+	1.71909i
$969$	−19937.0	+	12812.7i	−0.660959	+	0.424773i
$970$	1734.78	+	42430.6i	0.0574232	+	1.40450i
$971$	−50800.6	+	23199.9i	−1.67896	+	0.766755i	−0.679507	+	0.733669i	$0.737806\pi$
$971$	−50800.6	+	23199.9i	−1.67896	+	0.766755i	−0.999453	+	0.0330857i	$0.989467\pi$
$972$	−11296.4	−	4080.98i	−0.372770	−	0.134668i
$973$	−3903.84	−	13295.2i	−0.128624	−	0.438054i
$974$	−216.165	+	271.096i	−0.00711125	+	0.00891837i
$975$	5911.71	−	12944.8i	0.194181	−	0.425197i
$976$	11501.6	−	13841.0i	0.377211	−	0.453934i
$977$	31356.0	+	36186.8i	1.02678	+	1.18497i	0.982559	+	0.185951i	$0.0595365\pi$
$977$	31356.0	+	36186.8i	1.02678	+	1.18497i	0.0442254	+	0.999022i	$0.485918\pi$
$978$	79170.7	−	55577.2i	2.58855	−	1.81714i
$979$	16404.3	−	55868.1i	0.535531	−	1.82385i
$980$	23931.5	+	17532.3i	0.780066	+	0.571479i
$981$	−28059.0	+	43660.7i	−0.913206	+	1.42098i
$982$	7546.80	−	1401.86i	0.245242	−	0.0455551i
$983$	2769.85	−	19264.7i	0.0898723	−	0.625076i	−0.894248	−	0.447572i	$-0.852289\pi$
$983$	2769.85	−	19264.7i	0.0898723	−	0.625076i	0.984120	−	0.177504i	$-0.0568021\pi$
$984$	−6386.86	−	51839.3i	−0.206916	−	1.67945i
$985$	965.550	+	6715.55i	0.0312335	+	0.217234i
$986$	−11267.2	+	5712.87i	−0.363914	+	0.184518i
$987$	−18488.5	−	16020.4i	−0.596246	−	0.516650i
$988$	9826.21	+	2031.54i	0.316410	+	0.0654169i
$989$	12112.8	+	42618.2i	0.389449	+	1.37025i
$990$	11815.6	−	115509.i	0.379318	−	3.70819i
$991$	9255.98	−	10682.0i	0.296696	−	0.342406i	−0.587755	−	0.809039i	$-0.699988\pi$
$991$	9255.98	−	10682.0i	0.296696	−	0.342406i	0.884451	+	0.466634i	$0.154533\pi$
$992$	1618.19	+	26273.5i	0.0517919	+	0.840913i
$993$	432.588	+	3008.71i	0.0138245	+	0.0961517i
$994$	14838.6	−	5023.98i	0.473491	−	0.160313i
$995$	34721.6	+	4992.22i	1.10628	+	0.159059i
$996$	−63386.8	+	5191.84i	−2.01655	+	0.165170i
$997$	8238.74	−	12819.7i	0.261709	−	0.407226i	−0.685387	−	0.728179i	$-0.740367\pi$
$997$	8238.74	−	12819.7i	0.261709	−	0.407226i	0.947095	+	0.320953i	$0.104003\pi$
$998$	7592.83	−	12948.9i	0.240828	−	0.410711i
$999$	22841.6	+	6706.89i	0.723399	+	0.212409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.p.a.85.53	yes	700
8.5	even	2	inner	184.4.p.a.85.14	yes	700
23.13	even	11	inner	184.4.p.a.13.14	✓	700
184.13	even	22	inner	184.4.p.a.13.53	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.p.a.13.14	✓	700	23.13	even	11	inner
184.4.p.a.13.53	yes	700	184.13	even	22	inner
184.4.p.a.85.14	yes	700	8.5	even	2	inner
184.4.p.a.85.53	yes	700	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	184.p (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93800 + 2.06013i) q^{2} +(4.76362 + 7.41234i) q^{3} +(-0.488295 + 7.98508i) q^{4} +(-11.6365 + 5.31419i) q^{5} +(-6.03849 + 24.1788i) q^{6} +(6.99300 - 2.05333i) q^{7} +(-17.3967 + 14.4692i) q^{8} +(-21.0345 + 46.0590i) q^{9} +(-33.4994 - 13.6737i) q^{10} +(47.8965 - 41.5026i) q^{11} +(-61.5142 + 34.4185i) q^{12} +(11.7738 - 40.0978i) q^{13} +(17.7826 + 10.4271i) q^{14} +(-94.8222 - 60.9385i) q^{15} +(-63.5231 - 7.79815i) q^{16} +(-12.7541 + 88.7065i) q^{17} +(-135.653 + 45.9287i) q^{18} +(29.7073 - 4.27127i) q^{19} +(-36.7522 - 95.5130i) q^{20} +(48.5319 + 42.0532i) q^{21} +(178.324 + 18.2411i) q^{22} +(105.562 + 31.9943i) q^{23} +(-190.121 - 60.0243i) q^{24} +(25.3089 - 29.2080i) q^{25} +(105.424 - 53.4541i) q^{26} +(-206.128 + 29.6367i) q^{27} +(12.9814 + 56.8423i) q^{28} +(49.3299 + 7.09257i) q^{29} +(-58.2242 - 313.445i) q^{30} +(-122.333 - 78.6185i) q^{31} +(-107.043 - 145.979i) q^{32} +(535.792 + 157.323i) q^{33} +(-207.465 + 145.638i) q^{34} +(-70.4619 + 61.0556i) q^{35} +(-357.514 - 190.452i) q^{36} +(-103.985 - 47.4883i) q^{37} +(66.3722 + 52.9233i) q^{38} +(353.304 - 103.739i) q^{39} +(125.543 - 260.819i) q^{40} +(108.830 + 238.305i) q^{41} +(7.41990 + 181.481i) q^{42} +(217.161 + 337.908i) q^{43} +(308.014 + 402.723i) q^{44} -647.745i q^{45} +(138.667 + 279.477i) q^{46} -380.955 q^{47} +(-244.798 - 508.002i) q^{48} +(-243.864 + 156.722i) q^{49} +(109.221 - 4.46552i) q^{50} +(-718.278 + 328.027i) q^{51} +(314.435 + 113.594i) q^{52} +(-110.902 - 377.698i) q^{53} +(-460.532 - 367.215i) q^{54} +(-336.793 + 737.474i) q^{55} +(-91.9448 + 136.904i) q^{56} +(173.174 + 199.854i) q^{57} +(80.9899 + 115.372i) q^{58} +(153.082 - 521.348i) q^{59} +(532.901 - 727.407i) q^{60} +(-152.023 + 236.552i) q^{61} +(-75.1166 - 404.385i) q^{62} +(-52.5195 + 365.281i) q^{63} +(93.2869 - 503.430i) q^{64} +(76.0823 + 529.164i) q^{65} +(714.260 + 1408.69i) q^{66} +(194.548 + 168.577i) q^{67} +(-702.101 - 145.157i) q^{68} +(265.706 + 934.871i) q^{69} +(-262.338 - 26.8350i) q^{70} +(497.669 - 574.340i) q^{71} +(-300.506 - 1105.62i) q^{72} +(-82.9602 - 577.001i) q^{73} +(-103.691 - 306.255i) q^{74} +(337.062 + 48.4621i) q^{75} +(19.6005 + 239.301i) q^{76} +(249.722 - 388.575i) q^{77} +(898.421 + 526.806i) q^{78} +(790.457 + 232.099i) q^{79} +(780.625 - 246.831i) q^{80} +(-306.307 - 353.497i) q^{81} +(-280.027 + 686.040i) q^{82} +(820.726 + 374.813i) q^{83} +(-359.496 + 366.997i) q^{84} +(-322.991 - 1100.01i) q^{85} +(-275.279 + 1102.25i) q^{86} +(182.416 + 399.436i) q^{87} +(-232.732 + 1415.03i) q^{88} +(772.899 - 496.712i) q^{89} +(1334.44 - 1255.33i) q^{90} -304.579i q^{91} +(-307.022 + 827.300i) q^{92} -1281.28i q^{93} +(-738.292 - 784.818i) q^{94} +(-322.989 + 207.573i) q^{95} +(572.134 - 1488.82i) q^{96} +(-487.556 - 1067.60i) q^{97} +(-795.477 - 198.665i) q^{98} +(904.091 + 3079.05i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 700 q - 7 q^{2} + 13 q^{4} - 52 q^{6} + 10 q^{7} - 46 q^{8} + 576 q^{9} + 35 q^{10} - 24 q^{12} + 77 q^{14} - 246 q^{15} - 27 q^{16} - 18 q^{17} - 230 q^{18} + 53 q^{20} + 182 q^{22} + 144 q^{23} + 154 q^{24}+ \cdots - 7727 q^{98}+O(q^{100}) \) 700 * q - 7 * q^2 + 13 * q^4 - 52 * q^6 + 10 * q^7 - 46 * q^8 + 576 * q^9 + 35 * q^10 - 24 * q^12 + 77 * q^14 - 246 * q^15 - 27 * q^16 - 18 * q^17 - 230 * q^18 + 53 * q^20 + 182 * q^22 + 144 * q^23 + 154 * q^24 + 1532 * q^25 + 50 * q^26 + 151 * q^28 + 39 * q^30 - 546 * q^31 + 53 * q^32 - 126 * q^33 - 1175 * q^34 + 2613 * q^36 + 60 * q^38 + 174 * q^39 - 1565 * q^40 - 18 * q^41 + 2983 * q^42 - 2596 * q^44 + 3645 * q^46 - 40 * q^47 - 3908 * q^48 - 2860 * q^49 + 1858 * q^50 - 1154 * q^52 - 432 * q^54 - 518 * q^55 + 4562 * q^56 - 126 * q^57 - 4499 * q^58 + 2651 * q^60 - 1540 * q^62 - 14 * q^63 - 158 * q^64 - 518 * q^65 + 2368 * q^66 - 1270 * q^68 - 2006 * q^70 - 1498 * q^71 + 2103 * q^72 - 18 * q^73 + 2216 * q^74 + 6852 * q^76 + 7956 * q^78 + 1834 * q^79 + 2362 * q^80 - 3268 * q^81 + 1098 * q^82 - 7971 * q^84 - 8759 * q^86 - 2154 * q^87 - 4495 * q^88 - 866 * q^89 - 13676 * q^90 - 10844 * q^92 - 12229 * q^94 + 722 * q^95 - 12211 * q^96 - 18 * q^97 - 7727 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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