LMFDB - Embedded newform 184.4.p.a.13.14

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			13.14
Character	$\chi$	$=$	184.13
Dual form			184.4.p.a.85.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.31497 + 1.62509i) q^{2} +(-4.76362 + 7.41234i) q^{3} +(2.71817 - 7.52406i) q^{4} +(11.6365 + 5.31419i) q^{5} +(-1.01807 - 24.9006i) q^{6} +(6.99300 + 2.05333i) q^{7} +(5.93478 + 21.8353i) q^{8} +(-21.0345 - 46.0590i) q^{9} +(-35.5741 + 6.60808i) q^{10} +(-47.8965 - 41.5026i) q^{11} +(42.8225 + 55.9898i) q^{12} +(-11.7738 - 40.0978i) q^{13} +(-19.5254 + 6.61084i) q^{14} +(-94.8222 + 60.9385i) q^{15} +(-49.2231 - 40.9034i) q^{16} +(-12.7541 - 88.7065i) q^{17} +(123.544 + 72.4424i) q^{18} +(-29.7073 - 4.27127i) q^{19} +(71.6142 - 73.1085i) 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} +(92.4184 + 73.6917i) q^{26} +(206.128 + 29.6367i) q^{27} +(34.4576 - 47.0344i) q^{28} +(-49.3299 + 7.09257i) q^{29} +(120.480 - 295.165i) q^{30} +(-122.333 + 78.6185i) q^{31} +(180.422 + 14.6984i) q^{32} +(535.792 - 157.323i) q^{33} +(173.681 + 184.626i) q^{34} +(70.4619 + 61.0556i) q^{35} +(-403.726 + 33.0681i) q^{36} +(103.985 - 47.4883i) q^{37} +(75.7127 - 38.3892i) q^{38} +(353.304 + 103.739i) q^{39} +(-46.9769 + 285.624i) q^{40} +(108.830 - 238.305i) q^{41} +(44.0099 - 176.221i) q^{42} +(-217.161 + 337.908i) q^{43} +(-442.459 + 247.565i) q^{44} -647.745i q^{45} +(-192.380 + 245.614i) q^{46} -380.955 q^{47} +(537.670 - 170.010i) q^{48} +(-243.864 - 156.722i) q^{49} +(-106.055 - 26.4865i) q^{50} +(718.278 + 328.027i) q^{51} +(-333.701 - 20.4061i) q^{52} +(110.902 - 377.698i) q^{53} +(-525.343 + 266.368i) q^{54} +(-336.793 - 737.474i) q^{55} +(-3.33307 + 164.880i) q^{56} +(173.174 - 199.854i) q^{57} +(102.671 - 96.5846i) q^{58} +(-153.082 - 521.348i) q^{59} +(200.762 + 879.090i) q^{60} +(152.023 + 236.552i) q^{61} +(155.435 - 380.801i) q^{62} +(-52.5195 - 365.281i) q^{63} +(-441.557 + 259.175i) q^{64} +(76.0823 - 529.164i) q^{65} +(-984.679 + 1234.91i) 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} +(880.876 - 732.643i) q^{72} +(-82.9602 + 577.001i) q^{73} +(-163.549 + 278.918i) q^{74} +(-337.062 + 48.4621i) q^{75} +(-112.887 + 211.910i) q^{76} +(-249.722 - 388.575i) q^{77} +(-986.474 + 333.997i) q^{78} +(790.457 - 232.099i) q^{79} +(-355.413 - 737.552i) q^{80} +(-306.307 + 353.497i) q^{81} +(135.328 + 728.527i) q^{82} +(-820.726 + 374.813i) q^{83} +(184.492 + 479.465i) q^{84} +(322.991 - 1100.01i) q^{85} +(-46.4109 - 1135.15i) q^{86} +(182.416 - 399.436i) q^{87} +(621.964 - 1292.14i) q^{88} +(772.899 + 496.712i) q^{89} +(1052.64 + 1499.51i) q^{90} -304.579i q^{91} +(46.2093 - 881.222i) q^{92} -1281.28i q^{93} +(881.899 - 619.086i) q^{94} +(-322.989 - 207.573i) q^{95} +(-968.409 + 1267.33i) q^{96} +(-487.556 + 1067.60i) q^{97} +(819.225 - 33.4942i) 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 $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−2.31497	+	1.62509i	−0.818466	+	0.574556i
$2$	−2.31497	+	1.62509i	−0.818466	+	0.574556i
$3$	−4.76362	+	7.41234i	−0.916759	+	1.42650i	−0.0123095	+	0.999924i	$0.503918\pi$
$3$	−4.76362	+	7.41234i	−0.916759	+	1.42650i	−0.904450	+	0.426581i	$0.859718\pi$
$4$	2.71817	−	7.52406i	0.339772	−	0.940508i
$5$	11.6365	+	5.31419i	1.04080	+	0.475316i	0.861116	−	0.508409i	$-0.169766\pi$
$5$	11.6365	+	5.31419i	1.04080	+	0.475316i	0.179681	+	0.983725i	$0.442494\pi$
$6$	−1.01807	−	24.9006i	−0.0692707	−	1.69427i
$7$	6.99300	+	2.05333i	0.377586	+	0.110869i	0.465018	−	0.885301i	$-0.346048\pi$
$7$	6.99300	+	2.05333i	0.377586	+	0.110869i	−0.0874318	+	0.996171i	$0.527866\pi$
$8$	5.93478	+	21.8353i	0.262283	+	0.964991i
$9$	−21.0345	−	46.0590i	−0.779054	−	1.70589i
$10$	−35.5741	+	6.60808i	−1.12495	+	0.208966i
$11$	−47.8965	−	41.5026i	−1.31285	−	1.13759i	−0.980947	−	0.194277i	$-0.937764\pi$
$11$	−47.8965	−	41.5026i	−1.31285	−	1.13759i	−0.331903	−	0.943313i	$-0.607691\pi$
$12$	42.8225	+	55.9898i	1.03015	+	1.34691i
$13$	−11.7738	−	40.0978i	−0.251189	−	0.855471i	−0.984471	−	0.175547i	$-0.943831\pi$
$13$	−11.7738	−	40.0978i	−0.251189	−	0.855471i	0.733282	−	0.679924i	$-0.237987\pi$
$14$	−19.5254	+	6.61084i	−0.372742	+	0.126202i
$15$	−94.8222	+	60.9385i	−1.63220	+	1.04895i
$16$	−49.2231	−	40.9034i	−0.769110	−	0.639116i
$17$	−12.7541	−	88.7065i	−0.181960	−	1.26556i	−0.852122	−	0.523343i	$-0.824685\pi$
$17$	−12.7541	−	88.7065i	−0.181960	−	1.26556i	0.670162	−	0.742215i	$-0.266225\pi$
$18$	123.544	+	72.4424i	1.61776	+	0.948603i
$19$	−29.7073	−	4.27127i	−0.358701	−	0.0515734i	−0.0393915	−	0.999224i	$-0.512542\pi$
$19$	−29.7073	−	4.27127i	−0.358701	−	0.0515734i	−0.319310	+	0.947650i	$0.603451\pi$
$20$	71.6142	−	73.1085i	0.800671	−	0.817378i
$21$	−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
$26$	92.4184	+	73.6917i	0.697105	+	0.555852i
$27$	206.128	+	29.6367i	1.46924	+	0.211244i
$28$	34.4576	−	47.0344i	0.232567	−	0.317453i
$29$	−49.3299	+	7.09257i	−0.315874	+	0.0454158i	−0.298428	−	0.954432i	$-0.596462\pi$
$29$	−49.3299	+	7.09257i	−0.315874	+	0.0454158i	−0.0174453	+	0.999848i	$0.505553\pi$
$30$	120.480	−	295.165i	0.733218	−	1.79632i
$31$	−122.333	+	78.6185i	−0.708762	+	0.455493i	−0.844711	−	0.535222i	$-0.820228\pi$
$31$	−122.333	+	78.6185i	−0.708762	+	0.455493i	0.135950	+	0.990716i	$0.456591\pi$
$32$	180.422	+	14.6984i	0.996698	+	0.0811978i
$33$	535.792	−	157.323i	2.82635	−	0.829890i
$34$	173.681	+	184.626i	0.876061	+	0.931270i
$35$	70.4619	+	61.0556i	0.340292	+	0.294865i
$36$	−403.726	+	33.0681i	−1.86910	+	0.153093i
$37$	103.985	−	47.4883i	0.462027	−	0.211001i	−0.170782	−	0.985309i	$-0.554629\pi$
$37$	103.985	−	47.4883i	0.462027	−	0.211001i	0.632809	+	0.774308i	$0.281902\pi$
$38$	75.7127	−	38.3892i	0.323216	−	0.163883i
$39$	353.304	+	103.739i	1.45061	+	0.425939i
$40$	−46.9769	+	285.624i	−0.185693	+	1.12903i
$41$	108.830	−	238.305i	0.414547	−	0.907731i	−0.581039	−	0.813876i	$-0.697354\pi$
$41$	108.830	−	238.305i	0.414547	−	0.907731i	0.995586	−	0.0938552i	$-0.0299191\pi$
$42$	44.0099	−	176.221i	0.161687	−	0.647415i
$43$	−217.161	+	337.908i	−0.770155	+	1.19839i	0.205410	+	0.978676i	$0.434147\pi$
$43$	−217.161	+	337.908i	−0.770155	+	1.19839i	−0.975565	+	0.219709i	$0.929489\pi$
$44$	−442.459	+	247.565i	−1.51598	+	0.848225i
$45$		−	647.745i		−	2.14578i
$46$	−192.380	+	245.614i	−0.616627	+	0.787256i
$47$	−380.955			−1.18230			−0.591149	−	0.806562i	$-0.701325\pi$
$47$	−380.955			−1.18230			−0.591149	+	0.806562i	$0.701325\pi$
$48$	537.670	−	170.010i	1.61679	−	0.511224i
$49$	−243.864	−	156.722i	−0.710974	−	0.456915i
$50$	−106.055	−	26.4865i	−0.299969	−	0.0749151i
$51$	718.278	+	328.027i	1.97214	+	0.900645i
$52$	−333.701	−	20.4061i	−0.889924	−	0.0544197i
$53$	110.902	−	377.698i	0.287426	−	0.978882i	−0.681559	−	0.731763i	$-0.738698\pi$
$53$	110.902	−	377.698i	0.287426	−	0.978882i	0.968985	−	0.247119i	$-0.0794839\pi$
$54$	−525.343	+	266.368i	−1.32389	+	0.671262i
$55$	−336.793	−	737.474i	−0.825694	−	1.80802i
$56$	−3.33307	+	164.880i	−0.00795359	+	0.393446i
$57$	173.174	−	199.854i	0.402412	−	0.464409i
$58$	102.671	−	96.5846i	0.232438	−	0.218658i
$59$	−153.082	−	521.348i	−0.337788	−	1.15040i	−0.936860	−	0.349706i	$-0.886282\pi$
$59$	−153.082	−	521.348i	−0.337788	−	1.15040i	0.599071	−	0.800696i	$-0.295537\pi$
$60$	200.762	+	879.090i	0.431971	+	1.89150i
$61$	152.023	+	236.552i	0.319090	+	0.496514i	0.963334	−	0.268307i	$-0.0864640\pi$
$61$	152.023	+	236.552i	0.319090	+	0.496514i	−0.644244	+	0.764820i	$0.722828\pi$
$62$	155.435	−	380.801i	0.318391	−	0.780029i
$63$	−52.5195	−	365.281i	−0.105029	−	0.730494i
$64$	−441.557	+	259.175i	−0.862416	+	0.506201i
$65$	76.0823	−	529.164i	0.145182	−	1.00977i
$66$	−984.679	+	1234.91i	−1.83645	+	2.30313i
$67$	−194.548	+	168.577i	−0.354744	+	0.307387i	−0.813941	−	0.580947i	$-0.802682\pi$
$67$	−194.548	+	168.577i	−0.354744	+	0.307387i	0.459198	+	0.888334i	$0.348137\pi$
$68$	−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	0.999667	−	0.0257975i	$-0.00821250\pi$
$71$	497.669	+	574.340i	0.831865	+	0.960023i	−0.167802	+	0.985821i	$0.553667\pi$
$72$	880.876	−	732.643i	1.44184	−	1.19921i
$73$	−82.9602	+	577.001i	−0.133010	+	0.925108i	0.808589	+	0.588373i	$0.200232\pi$
$73$	−82.9602	+	577.001i	−0.133010	+	0.925108i	−0.941600	+	0.336734i	$0.890678\pi$
$74$	−163.549	+	278.918i	−0.256921	+	0.438157i
$75$	−337.062	+	48.4621i	−0.518940	+	0.0746123i
$76$	−112.887	+	211.910i	−0.170382	+	0.319838i
$77$	−249.722	−	388.575i	−0.369590	−	0.575093i
$78$	−986.474	+	333.997i	−1.43200	+	0.484842i
$79$	790.457	−	232.099i	1.12574	−	0.330547i	0.334707	−	0.942322i	$-0.391363\pi$
$79$	790.457	−	232.099i	1.12574	−	0.330547i	0.791031	+	0.611776i	$0.209544\pi$
$80$	−355.413	−	737.552i	−0.496705	−	1.03076i
$81$	−306.307	+	353.497i	−0.420174	+	0.484907i
$82$	135.328	+	728.527i	0.182250	+	0.981127i
$83$	−820.726	+	374.813i	−1.08538	+	0.495676i	−0.876075	−	0.482175i	$-0.839847\pi$
$83$	−820.726	+	374.813i	−1.08538	+	0.495676i	−0.209303	+	0.977851i	$0.567120\pi$
$84$	184.492	+	479.465i	0.239640	+	0.622785i
$85$	322.991	−	1100.01i	0.412157	−	1.40368i
$86$	−46.4109	−	1135.15i	−0.0581933	−	1.42333i
$87$	182.416	−	399.436i	0.224794	−	0.492231i
$88$	621.964	−	1292.14i	0.753427	−	1.56526i
$89$	772.899	+	496.712i	0.920529	+	0.591588i	0.912811	−	0.408382i	$-0.133907\pi$
$89$	772.899	+	496.712i	0.920529	+	0.591588i	0.00771795	+	0.999970i	$0.497543\pi$
$90$	1052.64	+	1499.51i	1.23287	+	1.75625i
$91$		−	304.579i		−	0.350863i
$92$	46.2093	−	881.222i	0.0523658	−	0.998628i
$93$		−	1281.28i		−	1.42863i
$94$	881.899	−	619.086i	0.967670	−	0.679296i
$95$	−322.989	−	207.573i	−0.348821	−	0.224174i
$96$	−968.409	+	1267.33i	−1.02956	+	1.34736i
$97$	−487.556	+	1067.60i	−0.510348	+	1.11751i	0.462618	+	0.886558i	$0.346910\pi$
$97$	−487.556	+	1067.60i	−0.510348	+	1.11751i	−0.972966	+	0.230949i	$0.925817\pi$
$98$	819.225	−	33.4942i	0.844431	−	0.0345247i
$99$	−904.091	+	3079.05i	−0.917824	+	3.12582i
$100$	288.557	−	111.033i	0.288557	−	0.111033i
$101$	−564.254	+	257.686i	−0.555895	+	0.253869i	−0.673494	−	0.739192i	$-0.735207\pi$
$101$	−564.254	+	257.686i	−0.555895	+	0.253869i	0.117599	+	0.993061i	$0.462480\pi$
$102$	−2195.86	+	407.894i	−2.13160	+	0.395956i
$103$	347.608	−	401.161i	0.332533	−	0.383763i	−0.564719	−	0.825284i	$-0.691015\pi$
$103$	347.608	−	401.161i	0.332533	−	0.383763i	0.897251	+	0.441521i	$0.145561\pi$
$104$	805.671	−	495.055i	0.759639	−	0.466770i
$105$	−788.218	+	231.442i	−0.732593	+	0.215109i
$106$	357.057	+	1054.58i	0.327174	+	0.966323i
$107$	−660.606	−	1027.92i	−0.596852	−	0.928721i	−0.999908	−	0.0135451i	$-0.995688\pi$
$107$	−660.606	−	1027.92i	−0.596852	−	0.928721i	0.403056	−	0.915175i	$-0.367948\pi$
$108$	783.281	−	1470.36i	0.697882	−	1.31005i
$109$	−1014.54	+	145.870i	−0.891521	+	0.128181i	−0.572827	−	0.819676i	$-0.694153\pi$
$109$	−1014.54	+	145.870i	−0.891521	+	0.128181i	−0.318694	+	0.947858i	$0.603244\pi$
$110$	1978.13	+	1159.91i	1.71461	+	1.00539i
$111$	−143.345	+	996.986i	−0.122574	+	0.852520i
$112$	−260.228	−	387.109i	−0.219547	−	0.326592i
$113$	−906.027	−	1045.61i	−0.754264	−	0.870467i	0.240710	−	0.970597i	$-0.422620\pi$
$113$	−906.027	−	1045.61i	−0.754264	−	0.870467i	−0.994974	+	0.100130i	$0.968074\pi$
$114$	−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
$118$	1201.62	+	958.133i	0.937438	+	0.747486i
$119$	92.9545	−	646.513i	0.0716061	−	0.498031i
$120$	−1893.36	−	1708.81i	−1.44033	−	1.29994i
$121$	382.193	+	2658.21i	0.287147	+	1.99715i
$122$	−736.345	−	300.560i	−0.546439	−	0.223044i
$123$	1247.97	+	1941.88i	0.914843	+	1.42352i
$124$	259.009	+	1134.14i	0.187578	+	0.821360i
$125$	−311.219	−	1059.91i	−0.222690	−	0.758413i
$126$	715.196	+	760.266i	0.505672	+	0.537539i
$127$	1718.08	−	1982.77i	1.20043	−	1.38537i	0.297983	−	0.954571i	$-0.403686\pi$
$127$	1718.08	−	1982.77i	1.20043	−	1.38537i	0.902447	−	0.430800i	$-0.141769\pi$
$128$	601.009	−	1317.55i	0.415017	−	0.909814i
$129$	−1470.22	−	3219.33i	−1.00346	−	2.19726i
$130$	683.810	+	1348.64i	0.461340	+	0.909873i
$131$	−318.444	+	1084.52i	−0.212386	+	0.723321i	0.782530	+	0.622613i	$0.213929\pi$
$131$	−318.444	+	1084.52i	−0.212386	+	0.723321i	−0.994916	+	0.100708i	$0.967889\pi$
$132$	272.670	−	4458.96i	0.179794	−	2.94017i
$133$	−198.973	−	90.8678i	−0.129723	−	0.0592424i
$134$	176.421	−	706.408i	0.113734	−	0.455406i
$135$	2241.10	+	1440.27i	1.42877	+	0.918213i
$136$	1861.24	−	804.942i	1.17353	−	0.507524i
$137$	−328.664			−0.204961			−0.102480	−	0.994735i	$-0.532678\pi$
$137$	−328.664			−0.204961			−0.102480	+	0.994735i	$0.532678\pi$
$138$	−904.147	−	2595.99i	−0.557726	−	1.60134i
$139$		−	1901.22i		−	1.16014i	−0.814566	−	0.580071i	$-0.803025\pi$
$139$		−	1901.22i		−	1.16014i	0.814566	−	0.580071i	$-0.196975\pi$
$140$	650.914	−	364.200i	0.392945	−	0.219861i
$141$	1814.72	−	2823.77i	1.08388	−	1.68655i
$142$	−2085.44	−	520.825i	−1.23244	−	0.307793i
$143$	−1100.24	+	2409.19i	−0.643403	+	1.40886i
$144$	−848.592	+	3127.55i	−0.491083	+	1.80992i
$145$	−611.717	−	179.616i	−0.350347	−	0.102871i
$146$	−745.627	−	1470.56i	−0.422661	−	0.833591i
$147$	2323.35	−	1061.04i	1.30358	−	0.595327i
$148$	−74.6560	−	911.470i	−0.0414641	−	0.506232i
$149$	−2537.85	−	2199.06i	−1.39536	−	1.20909i	−0.949414	−	0.314028i	$-0.898321\pi$
$149$	−2537.85	−	2199.06i	−1.39536	−	1.20909i	−0.445948	−	0.895059i	$-0.647133\pi$
$150$	701.532	−	659.943i	0.381866	−	0.359228i
$151$	−3230.58	+	948.584i	−1.74107	+	0.511223i	−0.989006	−	0.147872i	$-0.952758\pi$
$151$	−3230.58	+	948.584i	−1.74107	+	0.511223i	−0.752059	+	0.659095i	$0.770939\pi$
$152$	−83.0421	−	674.016i	−0.0443132	−	0.359670i
$153$	−3817.46	+	2453.33i	−2.01715	+	1.29634i
$154$	1209.57	+	493.719i	0.632920	+	0.258344i
$155$	−1841.31	+	264.741i	−0.954180	+	0.137190i
$156$	1740.88	−	2376.30i	0.893476	−	1.21959i
$157$	3199.32	+	459.993i	1.62633	+	0.233831i	0.894308	−	0.447451i	$-0.147668\pi$
$157$	3199.32	+	459.993i	1.62633	+	0.233831i	0.732021	+	0.681282i	$0.238577\pi$
$158$	−1452.70	+	1821.86i	−0.731461	+	0.917340i
$159$	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	0.468383	−	0.883526i	$-0.344837\pi$
$163$	2933.38	−	2541.79i	1.40957	−	1.22140i	0.941191	−	0.337876i	$-0.109709\pi$
$164$	−1497.20	−	1466.60i	−0.712877	−	0.698306i
$165$	7070.76	+	1016.62i	3.33611	+	0.479660i
$166$	1290.85	−	2201.43i	0.603551	−	1.02930i
$167$	−334.888	−	2329.19i	−0.155176	−	1.07927i	−0.907371	−	0.420331i	$-0.861914\pi$
$167$	−334.888	−	2329.19i	−0.155176	−	1.07927i	0.752195	−	0.658941i	$-0.228995\pi$
$168$	−1206.27	−	810.131i	−0.553962	−	0.372041i
$169$	379.024	−	243.584i	0.172519	−	0.110871i
$170$	1039.89	+	3071.37i	0.469154	+	1.38567i
$171$	428.147	+	1458.13i	0.191469	+	0.652083i
$172$	1952.16	+	2552.42i	0.865414	+	1.13151i
$173$	225.819	+	195.674i	0.0992412	+	0.0859930i	0.703068	−	0.711122i	$-0.251813\pi$
$173$	225.819	+	195.674i	0.0992412	+	0.0859930i	−0.603827	+	0.797115i	$0.706358\pi$
$174$	226.831	+	1221.13i	0.0988276	+	0.532031i
$175$	117.011	+	256.219i	0.0505441	+	0.110676i
$176$	660.016	+	4002.02i	0.282674	+	1.71400i
$177$	4593.63	+	1348.81i	1.95072	+	0.572784i
$178$	−2596.44	+	106.156i	−1.09332	+	0.0447006i
$179$	353.877	+	161.610i	0.147766	+	0.0674823i	0.487925	−	0.872885i	$-0.337754\pi$
$179$	353.877	+	161.610i	0.147766	+	0.0674823i	−0.340160	+	0.940368i	$0.610481\pi$
$180$	−4873.68	−	1760.68i	−2.01812	−	0.729076i
$181$	−454.784	+	707.657i	−0.186761	+	0.290606i	−0.921991	−	0.387212i	$-0.873438\pi$
$181$	−454.784	+	707.657i	−0.186761	+	0.290606i	0.735229	+	0.677818i	$0.237074\pi$
$182$	494.968	+	705.091i	0.201590	+	0.287170i
$183$	−2477.58			−1.00081
$184$	1325.09	+	2115.10i	0.530908	+	0.847430i
$185$	1462.38			0.581168
$186$	2082.19	+	2966.13i	0.820827	+	1.16928i
$187$	−3070.67	+	4778.06i	−1.20080	+	1.86848i
$188$	−1035.50	+	2866.33i	−0.401711	+	1.11196i
$189$	1380.60	+	630.498i	0.531343	+	0.242656i
$190$	1085.03	−	44.3618i	0.414298	−	0.0169387i
$191$	−635.518	−	186.605i	−0.240756	−	0.0706925i	0.159128	−	0.987258i	$-0.449132\pi$
$191$	−635.518	−	186.605i	−0.240756	−	0.0706925i	−0.399885	+	0.916565i	$0.630950\pi$
$192$	182.317	−	4507.58i	0.0685293	−	1.69430i
$193$	−341.417	−	747.600i	−0.127336	−	0.278826i	0.835217	−	0.549920i	$-0.185342\pi$
$193$	−341.417	−	747.600i	−0.127336	−	0.278826i	−0.962553	+	0.271094i	$0.912615\pi$
$194$	−606.265	−	3263.78i	−0.224367	−	1.20786i
$195$	3559.92	+	3084.68i	1.30734	+	1.13281i
$196$	−1842.05	+	1408.85i	−0.671301	+	0.513430i
$197$	−149.419	−	508.875i	−0.0540390	−	0.184040i	0.928051	−	0.372454i	$-0.121484\pi$
$197$	−149.419	−	508.875i	−0.0540390	−	0.184040i	−0.982090	+	0.188414i	$0.939665\pi$
$198$	−2910.79	−	8597.14i	−1.04475	−	3.08572i
$199$	−2306.83	+	1482.51i	−0.821742	+	0.528102i	−0.882644	−	0.470042i	$-0.844239\pi$
$199$	−2306.83	+	1482.51i	−0.821742	+	0.528102i	0.0609017	+	0.998144i	$0.480602\pi$
$200$	−487.562	+	725.969i	−0.172379	+	0.256669i
$201$	−322.795	−	2245.09i	−0.113275	−	0.787843i
$202$	887.468	−	1513.50i	0.309119	−	0.527175i
$203$	−359.527	−	51.6922i	−0.124305	−	0.0178723i
$204$	4420.50	−	4512.74i	1.51714	−	1.54880i
$205$	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
$210$	1448.59	−	1816.71i	0.476010	−	0.596974i
$211$	1309.67	+	188.302i	0.427305	+	0.0614372i	0.352613	−	0.935769i	$-0.385293\pi$
$211$	1309.67	+	188.302i	0.427305	+	0.0614372i	0.0746925	+	0.997207i	$0.476202\pi$
$212$	−2540.37	−	1861.08i	−0.822987	−	0.602923i
$213$	−6627.91	+	952.949i	−2.13210	+	0.306549i
$214$	3199.75	+	1306.07i	1.02210	+	0.417201i
$215$	−4322.69	+	2778.02i	−1.37119	+	0.881208i
$216$	576.199	+	4676.75i	0.181506	+	1.47321i
$217$	−1016.90	+	298.589i	−0.318119	+	0.0934081i
$218$	2111.59	−	1986.41i	0.656032	−	0.617140i
$219$	−3881.74	−	3363.54i	−1.19773	−	1.03784i
$220$	−6464.27	+	529.470i	−1.98100	+	0.162259i
$221$	−3406.77	+	1555.82i	−1.03694	+	0.473556i
$222$	−1288.35	−	2540.94i	−0.389498	−	0.768184i
$223$	−3753.92	−	1102.25i	−1.12727	−	0.330996i	−0.335635	−	0.941992i	$-0.608951\pi$
$223$	−3753.92	−	1102.25i	−1.12727	−	0.330996i	−0.791633	+	0.610997i	$0.790769\pi$
$224$	1231.51	+	473.250i	0.367337	+	0.141162i
$225$	812.934	−	1780.08i	0.240869	−	0.527430i
$226$	3796.64	+	948.184i	1.11747	+	0.279081i
$227$	2614.64	−	4068.46i	0.764493	−	1.18957i	−0.212679	−	0.977122i	$-0.568219\pi$
$227$	2614.64	−	4068.46i	0.764493	−	1.18957i	0.977172	−	0.212452i	$-0.0681448\pi$
$228$	−1033.00	−	1846.21i	−0.300052	−	0.536265i
$229$			1378.19i			0.397702i	0.980030	+	0.198851i	$0.0637209\pi$
$229$			1378.19i			0.397702i	−0.980030	+	0.198851i	$0.936279\pi$
$230$	−3543.86	+	1835.73i	−1.01598	+	0.526280i
$231$	4069.83			1.15920
$232$	−447.630	−	1035.04i	−0.126674	−	0.292904i
$233$	4347.89	+	2794.22i	1.22249	+	0.785645i	0.982704	−	0.185182i	$-0.0592874\pi$
$233$	4347.89	+	2794.22i	1.22249	+	0.785645i	0.239783	+	0.970827i	$0.422924\pi$
$234$	1450.20	−	5806.77i	0.405139	−	1.62222i
$235$	−4432.97	−	2024.47i	−1.23053	−	0.561965i
$236$	−4338.76	−	265.319i	−1.19673	−	0.0731813i
$237$	−2045.04	+	6964.76i	−0.560505	+	1.90890i
$238$	835.453	+	1647.72i	0.227539	+	0.448763i
$239$	−514.230	−	1126.01i	−0.139175	−	0.304750i	0.827191	−	0.561920i	$-0.189937\pi$
$239$	−514.230	−	1126.01i	−0.139175	−	0.304750i	−0.966366	+	0.257170i	$0.917210\pi$
$240$	7160.04	+	878.972i	1.92574	+	0.236406i
$241$	−2242.85	+	2588.39i	−0.599480	+	0.691837i	−0.971676	−	0.236317i	$-0.924059\pi$
$241$	−2242.85	+	2588.39i	−0.599480	+	0.691837i	0.372196	+	0.928154i	$0.378605\pi$
$242$	−5204.59	−	5532.57i	−1.38249	−	1.46962i
$243$	422.985	+	1440.55i	0.111665	+	0.380294i
$244$	2193.05	−	500.839i	0.575393	−	0.131405i
$245$	−2004.86	−	3119.63i	−0.522800	−	0.813493i
$246$	−6044.74	−	2467.33i	−1.56666	−	0.639477i
$247$	178.499	+	1241.49i	0.0459822	+	0.319813i
$248$	−2442.67	−	2204.58i	−0.625443	−	0.564481i
$249$	1131.39	−	7868.96i	0.287947	−	2.00271i
$250$	2442.92	+	1947.91i	0.618014	+	0.492787i
$251$	2585.88	−	2240.68i	0.650276	−	0.563468i	−0.266020	−	0.963967i	$-0.585709\pi$
$251$	2585.88	−	2240.68i	0.650276	−	0.563468i	0.916297	+	0.400500i	$0.131163\pi$
$252$	−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
$256$	749.820	+	4026.78i	0.183061	+	0.983101i
$257$	−460.299	+	3201.45i	−0.111722	+	0.777047i	0.854521	+	0.519417i	$0.173851\pi$
$257$	−460.299	+	3201.45i	−0.111722	+	0.777047i	−0.966244	+	0.257630i	$0.917058\pi$
$258$	8635.22	+	5063.42i	2.08374	+	1.22184i
$259$	824.674	−	118.570i	0.197848	−	0.0284463i
$260$	−3774.66	−	2010.81i	−0.900363	−	0.479635i
$261$	1364.31	+	2122.90i	0.323557	+	0.503464i
$262$	−1025.25	−	3028.13i	−0.241757	−	0.714041i
$263$	−248.982	+	73.1077i	−0.0583760	+	0.0171407i	−0.310790	−	0.950479i	$-0.600594\pi$
$263$	−248.982	+	73.1077i	−0.0583760	+	0.0171407i	0.252414	+	0.967619i	$0.418775\pi$
$264$	6614.99	+	10765.5i	1.54214	+	2.50973i
$265$	3297.66	−	3805.71i	0.764430	−	0.882199i
$266$	608.284	−	112.992i	0.140212	−	0.0260451i
$267$	−7363.59	+	3362.84i	−1.68781	+	0.770795i
$268$	739.567	+	1922.01i	0.168568	+	0.438081i
$269$	1175.91	−	4004.78i	0.266530	−	0.907717i	−0.712098	−	0.702080i	$-0.752255\pi$
$269$	1175.91	−	4004.78i	0.266530	−	0.907717i	0.978628	−	0.205638i	$-0.0659268\pi$
$270$	−7528.66	+	307.811i	−1.69696	+	0.0693806i
$271$	−1186.88	+	2598.90i	−0.266044	+	0.582554i	−0.994757	−	0.102264i	$-0.967391\pi$
$271$	−1186.88	+	2598.90i	−0.266044	+	0.582554i	0.728714	+	0.684818i	$0.240119\pi$
$272$	−3000.61	+	4888.09i	−0.668891	+	1.08965i
$273$	2257.64	+	1450.90i	0.500508	+	0.321657i
$274$	760.847	−	534.108i	0.167753	−	0.117761i
$275$		−	2449.35i		−	0.537095i
$276$	6311.79	+	4540.33i	1.37654	+	0.990201i
$277$			6702.31i			1.45380i	0.686743	+	0.726900i	$0.259040\pi$
$277$			6702.31i			1.45380i	−0.686743	+	0.726900i	$0.740960\pi$
$278$	3089.66	+	4401.28i	0.666566	+	0.949536i
$279$	6194.29	+	3980.83i	1.32919	+	0.854216i
$280$	−914.989	+	1900.91i	−0.195289	+	0.405717i
$281$	−941.960	+	2062.61i	−0.199974	+	0.437882i	−0.982877	−	0.184262i	$-0.941011\pi$
$281$	−941.960	+	2062.61i	−0.199974	+	0.437882i	0.782903	+	0.622143i	$0.213738\pi$
$282$	387.838	+	9486.02i	0.0818986	+	2.00314i
$283$	−1287.26	+	4384.01i	−0.270388	+	0.920857i	0.706609	+	0.707604i	$0.250224\pi$
$283$	−1287.26	+	4384.01i	−0.270388	+	0.920857i	−0.976997	+	0.213253i	$0.931594\pi$
$284$	5674.12	−	2183.33i	1.18555	−	0.456187i
$285$	3077.20	−	1405.31i	0.639570	−	0.292082i
$286$	−1368.12	−	7365.18i	−0.282863	−	1.52277i
$287$	1250.37	−	1443.00i	0.257167	−	0.296786i
$288$	−3118.08	−	8619.22i	−0.637967	−	1.76351i
$289$	−2992.19	+	878.586i	−0.609035	+	0.178829i
$290$	1708.00	−	578.288i	0.345852	−	0.117097i
$291$	−5590.87	−	8699.56i	−1.12626	−	1.75250i
$292$	4115.89	+	2192.59i	0.824878	+	0.439423i
$293$	49.5387	−	7.12259i	0.00987741	−	0.00142016i	−0.137374	−	0.990519i	$-0.543866\pi$
$293$	49.5387	−	7.12259i	0.00987741	−	0.00142016i	0.147252	+	0.989099i	$0.452957\pi$
$294$	−3654.21	+	6231.93i	−0.724890	+	1.23624i
$295$	989.215	−	6880.14i	0.195235	−	1.35789i
$296$	1654.05	+	1988.70i	0.324795	+	0.390510i
$297$	−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
$302$	5937.16	−	7445.92i	1.13128	−	1.41876i
$303$	777.835	−	5409.96i	0.147477	−	1.02572i
$304$	1287.58	+	1425.38i	0.242919	+	0.268917i
$305$	511.923	+	3560.50i	0.0961069	+	0.668438i
$306$	4850.43	−	11883.1i	0.906145	−	2.21997i
$307$	−977.333	−	1520.76i	−0.181692	−	0.282718i	0.738446	−	0.674312i	$-0.235560\pi$
$307$	−977.333	−	1520.76i	−0.181692	−	0.282718i	−0.920138	+	0.391595i	$0.871924\pi$
$308$	−3602.45	+	822.709i	−0.666456	+	0.152202i
$309$	1317.67	+	4487.57i	0.242588	+	0.826177i
$310$	3832.36	−	3605.16i	0.702140	−	0.660515i
$311$	1868.98	−	2156.92i	0.340773	−	0.393273i	−0.559334	−	0.828942i	$-0.688943\pi$
$311$	1868.98	−	2156.92i	0.340773	−	0.393273i	0.900107	+	0.435670i	$0.143488\pi$
$312$	−168.395	+	8330.15i	−0.0305561	+	1.51155i
$313$	394.607	+	864.069i	0.0712604	+	0.156039i	0.941910	−	0.335865i	$-0.109029\pi$
$313$	394.607	+	864.069i	0.0712604	+	0.156039i	−0.870650	+	0.491903i	$0.836301\pi$
$314$	−8153.87	+	4134.31i	−1.46544	+	0.743034i
$315$	1330.03	−	4529.68i	0.237901	−	0.810217i
$316$	402.271	−	6578.33i	0.0716124	−	1.17108i
$317$	5388.45	+	2460.82i	0.954717	+	0.436005i	0.830975	−	0.556310i	$-0.187783\pi$
$317$	5388.45	+	2460.82i	0.954717	+	0.436005i	0.123742	+	0.992314i	$0.460510\pi$
$318$	−9517.82	−	2377.01i	−1.67840	−	0.419170i
$319$	2657.09	+	1707.61i	0.466359	+	0.299711i
$320$	−6515.46	+	669.359i	−1.13820	+	0.116932i
$321$	10766.2			1.87199
$322$	−1849.64	+	1322.56i	−0.320112	+	0.228892i
$323$			2689.71i			0.463342i
$324$	1827.14	+	3265.54i	0.313296	+	0.559935i
$325$	873.196	−	1358.72i	0.149034	−	0.231902i
$326$	−2660.06	+	10651.2i	−0.451924	+	1.80955i
$327$	3751.67	−	8215.01i	0.634458	−	1.38927i
$328$	5849.33	+	962.048i	0.984681	+	0.161952i
$329$	−2664.02	−	782.226i	−0.446419	−	0.131081i
$330$	−18020.7	+	9137.17i	−3.00608	+	1.52420i
$331$	−313.806	+	143.310i	−0.0521098	+	0.0237977i	−0.441299	−	0.897360i	$-0.645482\pi$
$331$	−313.806	+	143.310i	−0.0521098	+	0.0237977i	0.389190	+	0.921158i	$0.372755\pi$
$332$	589.241	+	7194.00i	0.0974060	+	1.18922i
$333$	−4374.53	−	3790.55i	−0.719888	−	0.623786i
$334$	4560.40	+	4847.79i	0.747108	+	0.794190i
$335$	−3159.70	+	927.771i	−0.515322	+	0.151312i
$336$	4109.01	−	84.8631i	0.667157	−	0.0137788i
$337$	6623.35	−	4256.57i	1.07061	−	0.688042i	0.118243	−	0.992985i	$-0.462274\pi$
$337$	6623.35	−	4256.57i	1.07061	−	0.688042i	0.952371	+	0.304943i	$0.0986373\pi$
$338$	−481.583	+	1179.84i	−0.0774990	+	0.189866i
$339$	12066.4	−	1734.88i	1.93320	−	0.277953i
$340$	−7398.58	−	5420.22i	−1.18013	−	0.864566i
$341$	9122.18	+	1311.57i	1.44866	+	0.208286i
$342$	−3360.74	−	2679.76i	−0.531369	−	0.423698i
$343$	−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	0.276674	−	0.960964i	$-0.410768\pi$
$347$	8191.25	−	7097.76i	1.26723	−	1.09806i	0.990557	−	0.137099i	$-0.0437777\pi$
$348$	−2509.54	−	2458.25i	−0.386568	−	0.378667i
$349$	2519.09	+	362.190i	0.386372	+	0.0555519i	0.332764	−	0.943010i	$-0.392019\pi$
$349$	2519.09	+	362.190i	0.386372	+	0.0555519i	0.0536080	+	0.998562i	$0.482928\pi$
$350$	−687.256	−	402.986i	−0.104958	−	0.0615442i
$351$	−1238.54	−	8614.21i	−0.188342	−	1.30995i
$352$	−8031.55	−	8191.96i	−1.21615	−	1.24044i
$353$	5884.33	−	3781.63i	0.887228	−	0.570187i	−0.0157491	−	0.999876i	$-0.505013\pi$
$353$	5884.33	−	3781.63i	0.887228	−	0.570187i	0.902977	+	0.429689i	$0.141377\pi$
$354$	−12826.0	+	4342.60i	−1.92570	+	0.651995i
$355$	2738.95	+	9327.99i	0.409488	+	1.39459i
$356$	5838.16	−	4465.19i	0.869163	−	0.664760i
$357$	4349.37	+	3768.75i	0.644798	+	0.558721i
$358$	−1081.85	+	200.959i	−0.159713	+	0.0296676i
$359$	2252.96	+	4933.28i	0.331216	+	0.725261i	0.999832	−	0.0183467i	$-0.00584027\pi$
$359$	2252.96	+	4933.28i	0.331216	+	0.725261i	−0.668616	+	0.743608i	$0.733113\pi$
$360$	14143.7	−	3844.22i	2.07066	−	0.562801i
$361$	−5716.88	−	1678.63i	−0.833486	−	0.244734i
$362$	−97.1951	−	2377.27i	−0.0141118	−	0.345156i
$363$	−21524.1	−	9829.75i	−3.11219	−	1.42129i
$364$	−2291.67	−	827.899i	−0.329990	−	0.119213i
$365$	−4031.66	+	6273.38i	−0.578155	+	0.899627i
$366$	5735.52	−	4026.28i	0.819127	−	0.575020i
$367$	−5411.30			−0.769667			−0.384834	−	0.922986i	$-0.625741\pi$
$367$	−5411.30			−0.769667			−0.384834	+	0.922986i	$0.625741\pi$
$368$	−6504.77	−	2743.00i	−0.921425	−	0.388556i
$369$	−13265.3			−1.87144
$370$	−3385.36	+	2376.49i	−0.475666	+	0.333913i
$371$	1551.07	−	2413.52i	0.217056	−	0.337746i
$372$	−9640.43	−	3482.74i	−1.34364	−	0.485408i
$373$	−5568.58	−	2543.08i	−0.773003	−	0.353018i	−0.0104506	−	0.999945i	$-0.503327\pi$
$373$	−5568.58	−	2543.08i	−0.773003	−	0.353018i	−0.762552	+	0.646927i	$0.776054\pi$
$374$	−656.256	−	16051.2i	−0.0907331	−	2.21922i
$375$	9338.96	+	2742.17i	1.28603	+	0.377613i
$376$	−2260.88	−	8318.25i	−0.310096	−	1.14091i
$377$	865.196	+	1894.51i	0.118196	+	0.258813i
$378$	−4220.66	+	784.011i	−0.574305	+	0.106680i
$379$	−3926.03	−	3401.92i	−0.532102	−	0.461069i	0.346890	−	0.937906i	$-0.387238\pi$
$379$	−3926.03	−	3401.92i	−0.532102	−	0.461069i	−0.878992	+	0.476837i	$0.841783\pi$
$380$	−2439.73	+	1865.97i	−0.329357	+	0.251901i
$381$	6512.67	+	22180.1i	0.875733	+	2.98247i
$382$	1774.46	−	600.789i	0.237668	−	0.0804686i
$383$	9114.49	−	5857.53i	1.21600	−	0.781477i	0.234349	−	0.972153i	$-0.424704\pi$
$383$	9114.49	−	5857.53i	1.21600	−	0.781477i	0.981653	+	0.190675i	$0.0610678\pi$
$384$	6903.15	+	10731.2i	0.917383	+	1.42610i
$385$	−840.916	−	5848.70i	−0.111317	−	0.774227i
$386$	2005.29	+	1175.84i	0.264421	+	0.155048i
$387$	20131.6	+	2894.49i	2.64431	+	0.380194i
$388$	6707.42	+	6570.32i	0.877622	+	0.859684i
$389$	−3293.52	+	2853.85i	−0.429276	+	0.371969i	−0.842533	−	0.538645i	$-0.818936\pi$
$389$	−3293.52	+	2853.85i	−0.429276	+	0.371969i	0.413257	+	0.910614i	$0.364391\pi$
$390$	−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
$394$	1172.87	+	935.212i	0.149970	+	0.119582i
$395$	10431.5	+	1499.83i	1.32878	+	0.191049i
$396$	20709.5	+	15171.8i	2.62801	+	1.92529i
$397$	14412.2	−	2072.17i	1.82199	−	0.261963i	0.855341	−	0.518066i	$-0.173348\pi$
$397$	14412.2	−	2072.17i	1.82199	−	0.261963i	0.966649	+	0.256103i	$0.0824387\pi$
$398$	2931.03	−	7180.76i	0.369144	−	0.904370i
$399$	1621.37	−	1041.99i	0.203434	−	0.130739i
$400$	−51.0732	−	2472.93i	−0.00638415	−	0.309116i
$401$	420.397	−	123.440i	0.0523532	−	0.0153723i	−0.255451	−	0.966822i	$-0.582224\pi$
$401$	420.397	−	123.440i	0.0523532	−	0.0153723i	0.307804	+	0.951450i	$0.400406\pi$
$402$	4395.73	+	4672.75i	0.545371	+	0.579740i
$403$	4592.74	+	3979.64i	0.567695	+	0.491910i
$404$	405.107	+	4945.92i	0.0498881	+	0.609081i
$405$	−5442.88	+	2485.68i	−0.667800	+	0.304974i
$406$	916.299	−	464.598i	0.112008	−	0.0567921i
$407$	−6951.40	−	2041.11i	−0.846604	−	0.248585i
$408$	−2899.72	+	17630.6i	−0.351857	+	2.13932i
$409$	−4338.14	+	9499.20i	−0.524468	+	1.14842i	0.443253	+	0.896397i	$0.353824\pi$
$409$	−4338.14	+	9499.20i	−0.524468	+	1.14842i	−0.967720	+	0.252027i	$0.918903\pi$
$410$	−2296.80	+	9196.63i	−0.276660	+	1.10778i
$411$	1565.63	−	2436.17i	0.187900	−	0.292378i
$412$	−2073.50	−	3705.85i	−0.247947	−	0.443141i
$413$		−	3960.11i		−	0.471826i
$414$	15359.3	+	3694.47i	1.82336	+	0.438583i
$415$	−11542.2			−1.36526
$416$	−1534.87	−	7407.56i	−0.180897	−	0.873042i
$417$	14092.5	+	9056.71i	1.65495	+	1.06357i
$418$	−5219.63	−	1303.57i	−0.610766	−	0.152535i
$419$	−10157.2	−	4638.64i	−1.18428	−	0.540842i	−0.276794	−	0.960929i	$-0.589272\pi$
$419$	−10157.2	−	4638.64i	−1.18428	−	0.540842i	−0.907484	+	0.420088i	$0.861999\pi$
$420$	−401.132	+	6559.70i	−0.0466029	+	0.762097i
$421$	720.166	−	2452.66i	0.0833699	−	0.283932i	−0.907247	−	0.420598i	$-0.861820\pi$
$421$	720.166	−	2452.66i	0.0833699	−	0.283932i	0.990617	+	0.136666i	$0.0436386\pi$
$422$	−3337.85	+	1692.42i	−0.385034	+	0.195226i
$423$	8013.18	+	17546.4i	0.921074	+	2.01687i
$424$	8905.30	+	180.022i	1.02000	+	0.0206195i
$425$	2268.15	−	2617.58i	0.258874	−	0.298756i
$426$	13794.8	−	12977.0i	1.56892	−	1.47591i
$427$	577.375	+	1966.36i	0.0654359	+	0.222854i
$428$	−9529.80	+	2176.37i	−1.07626	+	0.245791i
$429$	−12616.6	−	19631.8i	−1.41989	−	2.20940i
$430$	5492.36	−	13455.8i	0.615966	−	1.50906i
$431$	−1046.59	−	7279.16i	−0.116966	−	0.813515i	−0.960866	−	0.277014i	$-0.910655\pi$
$431$	−1046.59	−	7279.16i	−0.116966	−	0.813515i	0.843900	−	0.536501i	$-0.180254\pi$
$432$	−8934.01	−	9890.15i	−0.994995	−	1.10148i
$433$	210.440	−	1463.64i	0.0233558	−	0.162443i	−0.974805	−	0.223057i	$-0.928397\pi$
$433$	210.440	−	1463.64i	0.0233558	−	0.162443i	0.998161	+	0.0606132i	$0.0193056\pi$
$434$	1868.86	−	2343.78i	0.206701	−	0.259228i
$435$	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	0.833838	−	0.552009i	$-0.186139\pi$
$439$	1552.45	+	1791.62i	0.168780	+	0.194782i	−0.665058	+	0.746792i	$0.731593\pi$
$440$	14104.1	−	11730.7i	1.52816	−	1.27100i
$441$	−2088.91	+	14528.7i	−0.225560	+	1.56881i
$442$	5358.23	−	9137.98i	0.576617	−	0.983370i
$443$	−7298.92	+	1049.43i	−0.782804	+	0.112550i	−0.522118	−	0.852873i	$-0.674858\pi$
$443$	−7298.92	+	1049.43i	−0.782804	+	0.112550i	−0.260686	+	0.965424i	$0.583949\pi$
$444$	7111.75	+	3788.52i	0.760155	+	0.404944i
$445$	6354.18	+	9887.30i	0.676892	+	1.05326i
$446$	10481.5	−	3548.77i	1.11281	−	0.376770i
$447$	28389.5	−	8335.92i	3.00398	−	0.882048i
$448$	−3619.98	+	905.747i	−0.381758	+	0.0955191i
$449$	−688.143	+	794.160i	−0.0723285	+	0.0834715i	−0.790761	−	0.612126i	$-0.790315\pi$
$449$	−688.143	+	794.160i	−0.0723285	+	0.0834715i	0.718432	+	0.695597i	$0.244860\pi$
$450$	1010.87	+	5441.92i	0.105895	+	0.570077i
$451$	−15102.9	+	6897.24i	−1.57686	+	0.720130i
$452$	−10330.0	+	3974.85i	−1.07496	+	0.413631i
$453$	8358.03	−	28464.8i	0.866876	−	2.95231i
$454$	558.794	+	13667.4i	0.0577654	+	1.41287i
$455$	1618.59	−	3544.22i	0.166771	−	0.365177i
$456$	5391.61	+	2595.22i	0.553696	+	0.266518i
$457$	−10.4699	−	6.72862i	−0.00107169	−	0.000688734i	0.540105	−	0.841598i	$-0.318385\pi$
$457$	−10.4699	−	6.72862i	−0.00107169	−	0.000688734i	−0.541177	+	0.840909i	$0.682021\pi$
$458$	−2239.69	−	3190.48i	−0.228502	−	0.325505i
$459$		−	18662.9i		−	1.89784i
$460$	5220.70	−	10008.7i	0.529166	−	1.01448i
$461$		−	5112.59i		−	0.516523i	−0.966075	−	0.258261i	$-0.916850\pi$
$461$		−	5112.59i		−	0.516523i	0.966075	−	0.258261i	$-0.0831496\pi$
$462$	−9421.53	+	6613.83i	−0.948764	+	0.666024i
$463$	−13287.5	−	8539.33i	−1.33374	−	0.857141i	−0.337294	−	0.941399i	$-0.609512\pi$
$463$	−13287.5	−	8539.33i	−1.33374	−	0.857141i	−0.996444	+	0.0842583i	$0.973148\pi$
$464$	2718.28	+	1668.64i	0.271968	+	0.166950i
$465$	6808.97	−	14909.6i	0.679050	−	1.48691i
$466$	−14606.1	+	597.172i	−1.45196	+	0.0593636i
$467$	−1474.51	+	5021.71i	−0.146107	+	0.497595i	−0.999729	−	0.0232987i	$-0.992583\pi$
$467$	−1474.51	+	5021.71i	−0.146107	+	0.497595i	0.853621	+	0.520894i	$0.174401\pi$
$468$	6079.34	+	15799.2i	0.600465	+	1.56051i
$469$	−1706.62	+	779.386i	−0.168026	+	0.0767349i
$470$	13552.1	−	2517.38i	1.33003	−	0.247060i
$471$	−18650.0	+	21523.2i	−1.82451	+	2.10560i
$472$	10475.3	−	6436.66i	1.02153	−	0.627693i
$473$	24425.3	−	7171.92i	2.37437	−	0.697178i
$474$	−6584.15	−	19446.6i	−0.638017	−	1.88441i
$475$	−627.104	−	975.792i	−0.0605758	−	0.0942577i
$476$	−4611.73	−	2456.73i	−0.444073	−	0.236563i
$477$	−19729.1	+	2836.62i	−1.89379	+	0.272285i
$478$	3020.28	+	1771.00i	0.289005	+	0.169464i
$479$	−2737.58	+	19040.3i	−0.261134	+	1.81622i	0.263233	+	0.964732i	$0.415211\pi$
$479$	−2737.58	+	19040.3i	−0.261134	+	1.81622i	−0.524367	+	0.851492i	$0.675698\pi$
$480$	−18003.7	+	9600.90i	−1.71198	+	0.912956i
$481$	−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
$486$	−3320.22	−	2647.45i	−0.309894	−	0.247100i
$487$	17.4459	−	121.339i	0.00162331	−	0.0112904i	−0.988994	−	0.147958i	$-0.952730\pi$
$487$	17.4459	−	121.339i	0.00162331	−	0.0112904i	0.990617	+	0.136667i	$0.0436391\pi$
$488$	−4262.95	+	4723.33i	−0.395440	+	0.438146i
$489$	4867.09	+	33851.4i	0.450097	+	3.13049i
$490$	9710.87	+	3963.77i	0.895291	+	0.365438i
$491$	−1467.21	−	2283.03i	−0.134856	−	0.209840i	0.767257	−	0.641340i	$-0.221621\pi$
$491$	−1467.21	−	2283.03i	−0.134856	−	0.209840i	−0.902113	+	0.431499i	$0.857985\pi$
$492$	18003.0	−	4111.44i	1.64967	−	0.376744i
$493$	1258.31	+	4285.43i	0.114953	+	0.391493i
$494$	−2430.74	−	2583.93i	−0.221385	−	0.235337i
$495$	−26883.1	+	31024.7i	−2.44102	+	2.81709i
$496$	9237.36	+	1133.99i	0.836229	+	0.102656i
$497$	2300.89	+	5038.24i	0.207664	+	0.454720i
$498$	10168.6	+	20055.0i	0.914995	+	1.80459i
$499$	1495.19	−	5092.15i	0.134136	−	0.456826i	−0.864841	−	0.502046i	$-0.832581\pi$
$499$	1495.19	−	5092.15i	0.134136	−	0.456826i	0.998977	+	0.0452203i	$0.0143990\pi$
$500$	−8820.80	−	539.400i	−0.788957	−	0.0482454i
$501$	18860.1	+	8613.10i	1.68185	+	0.768073i
$502$	−2344.94	+	9389.39i	−0.208485	+	0.834799i
$503$	−14293.5	−	9185.87i	−1.26703	−	0.814270i	−0.277799	−	0.960639i	$-0.589605\pi$
$503$	−14293.5	−	9185.87i	−1.26703	−	0.814270i	−0.989230	+	0.146370i	$0.953241\pi$
$504$	7664.32	−	3314.64i	0.677373	−	0.292948i
$505$	−7935.31			−0.699241
$506$	19407.9	−	3779.79i	1.70511	−	0.332079i
$507$			3969.79i			0.347741i
$508$	−10248.4	−	18316.4i	−0.895080	−	1.59972i
$509$	−6848.12	+	10655.9i	−0.596341	+	0.927925i	0.403575	+	0.914947i	$0.367768\pi$
$509$	−6848.12	+	10655.9i	−0.596341	+	0.927925i	−0.999916	+	0.0129783i	$0.995869\pi$
$510$	−27719.7	−	6922.81i	−2.40676	−	0.601073i
$511$	−1764.91	+	3864.62i	−0.152789	+	0.334561i
$512$	−8279.69	−	8103.36i	−0.714676	−	0.699456i
$513$	−5996.92	−	1760.86i	−0.516122	−	0.151547i
$514$	−4137.06	−	8159.29i	−0.355016	−	0.700177i
$515$	6176.77	−	2820.84i	0.528507	−	0.241361i
$516$	−28218.8	+	2311.32i	−2.40749	+	0.197191i
$517$	18246.4	+	15810.6i	1.55218	+	1.34497i
$518$	−1716.41	+	1614.66i	−0.145588	+	0.136957i
$519$	−2526.12	+	741.734i	−0.213650	+	0.0627332i
$520$	12006.0	−	1479.20i	1.01249	−	0.124744i
$521$	678.680	−	436.161i	0.0570700	−	0.0366767i	−0.511795	−	0.859108i	$-0.671019\pi$
$521$	678.680	−	436.161i	0.0570700	−	0.0366767i	0.568865	+	0.822431i	$0.307383\pi$
$522$	−6608.23	−	2697.33i	−0.554089	−	0.226167i
$523$	−18378.6	+	2642.45i	−1.53660	+	0.220929i	−0.858027	−	0.513605i	$-0.828310\pi$
$523$	−18378.6	+	2642.45i	−1.53660	+	0.220929i	−0.678571	+	0.734535i	$0.737400\pi$
$524$	7294.42	+	5343.91i	0.608126	+	0.445515i
$525$	−2456.58	−	353.203i	−0.204217	−	0.0293620i
$526$	457.579	−	573.860i	0.0379304	−	0.0475694i
$527$	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
$532$	−1224.54	+	1250.09i	−0.0997941	+	0.101876i
$533$	−10836.8	−	1558.10i	−0.880667	−	0.126621i
$534$	11581.6	−	19751.4i	0.938547	−	1.60061i
$535$	−2224.53	−	15472.0i	−0.179766	−	1.25030i
$536$	−4835.52	−	3247.54i	−0.389669	−	0.261702i
$537$	−2883.65	+	1853.21i	−0.231729	+	0.148923i
$538$	3785.93	+	11181.9i	0.303389	+	0.896072i
$539$	5175.88	+	17627.4i	0.413620	+	1.40866i
$540$	16928.4	−	12947.3i	1.34904	−	1.03178i
$541$	−15338.5	−	13290.9i	−1.21896	−	1.05623i	−0.996694	−	0.0812439i	$-0.974111\pi$
$541$	−15338.5	−	13290.9i	−1.21896	−	1.05623i	−0.222261	−	0.974987i	$-0.571344\pi$
$542$	−1475.86	−	7945.17i	−0.116962	−	0.629657i
$543$	−3078.98	−	6742.02i	−0.243336	−	0.532832i
$544$	−997.269	−	16192.0i	−0.0785985	−	1.27615i
$545$	−12580.9	−	3694.08i	−0.988818	−	0.290343i
$546$	−7584.21	+	310.082i	−0.594459	+	0.0243045i
$547$	12834.0	+	5861.11i	1.00319	+	0.458141i	0.848143	−	0.529767i	$-0.177721\pi$
$547$	12834.0	+	5861.11i	1.00319	+	0.458141i	0.155045	+	0.987907i	$0.450448\pi$
$548$	−893.366	+	2472.89i	−0.0696399	+	0.192767i
$549$	7697.63	−	11977.7i	0.598410	−	0.931144i
$550$	3980.41	+	5670.16i	0.308591	+	0.439594i
$551$	1495.75			0.115647
$552$	−21990.0	−	253.498i	−1.69558	−	0.0195463i
$553$	6004.24			0.461711
$554$	−10891.8	−	15515.6i	−0.835289	−	1.18989i
$555$	−6966.20	+	10839.6i	−0.532791	+	0.829039i
$556$	−14304.9	−	5167.86i	−1.09112	−	0.394183i
$557$	805.057	+	367.657i	0.0612412	+	0.0279679i	0.445800	−	0.895132i	$-0.352919\pi$
$557$	805.057	+	367.657i	0.0612412	+	0.0279679i	−0.384559	+	0.923100i	$0.625646\pi$
$558$	−20808.8	+	850.772i	−1.57869	+	0.0645449i
$559$	16106.2	+	4729.20i	1.21864	+	0.357824i
$560$	−970.968	−	5887.48i	−0.0732695	−	0.444270i
$561$	−20789.1	−	45521.7i	−1.56456	−	3.42590i
$562$	−1171.31	−	6305.64i	−0.0879156	−	0.473287i
$563$	2858.26	+	2476.70i	0.213963	+	0.185400i	0.755248	−	0.655439i	$-0.227516\pi$
$563$	2858.26	+	2476.70i	0.213963	+	0.185400i	−0.541285	+	0.840839i	$0.682062\pi$
$564$	−16313.5	−	21329.6i	−1.21794	−	1.59244i
$565$	−4986.37	−	16982.0i	−0.371289	−	1.26449i
$566$	−4144.43	−	12240.8i	−0.307780	−	0.909042i
$567$	−2867.85	+	1843.06i	−0.212413	+	0.136510i
$568$	−9587.31	+	14275.3i	−0.708230	+	1.05454i
$569$	−830.418	−	5775.68i	−0.0611826	−	0.425535i	−0.997275	−	0.0737793i	$-0.976494\pi$
$569$	−830.418	−	5775.68i	−0.0611826	−	0.425535i	0.936092	−	0.351755i	$-0.114415\pi$
$570$	−4839.87	+	8253.97i	−0.355649	+	0.606527i
$571$	17969.8	+	2583.66i	1.31701	+	0.189357i	0.764755	−	0.644321i	$-0.222860\pi$
$571$	17969.8	+	2583.66i	1.31701	+	0.189357i	0.552251	+	0.833678i	$0.313769\pi$
$572$	15136.2	+	14826.9i	1.10643	+	1.08381i
$573$	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	0.849074	−	0.528274i	$-0.177161\pi$
$577$	2846.04	+	3284.50i	0.205341	+	0.236977i	−0.643733	+	0.765250i	$0.722615\pi$
$578$	5499.05	−	6896.47i	0.395727	−	0.496290i
$579$	7167.84	+	1030.58i	0.514482	+	0.0739714i
$580$	−3014.20	+	4114.37i	−0.215789	+	0.294551i
$581$	−6508.95	+	935.845i	−0.464779	+	0.0668251i
$582$	27080.2	+	11053.6i	1.92872	+	0.787259i
$583$	−20987.2	+	13487.7i	−1.49091	+	0.958152i
$584$	−13091.3	+	1612.92i	−0.927607	+	0.114286i
$585$	−25973.1	+	7626.40i	−1.83565	+	0.538996i
$586$	−103.106	+	96.9933i	−0.00726836	+	0.00683747i
$587$	13132.1	+	11379.0i	0.923370	+	0.800105i	0.980145	−	0.198282i	$-0.0635362\pi$
$587$	13132.1	+	11379.0i	0.923370	+	0.800105i	−0.0567746	+	0.998387i	$0.518082\pi$
$588$	−1668.05	−	20365.1i	−0.116989	−	1.42831i
$589$	3969.98	−	1813.03i	0.277725	−	0.126833i
$590$	8890.84	+	17534.9i	0.620390	+	1.22356i
$591$	4483.73	+	1316.54i	0.312075	+	0.0916334i
$592$	−7060.88	−	1915.82i	−0.490204	−	0.133006i
$593$	−964.139	+	2111.17i	−0.0667664	+	0.146198i	−0.940073	−	0.340973i	$-0.889244\pi$
$593$	−964.139	+	2111.17i	−0.0667664	+	0.146198i	0.873307	+	0.487170i	$0.161971\pi$
$594$	36217.1	+	9044.96i	2.50169	+	0.624780i
$595$	4517.35	−	7029.14i	0.311249	−	0.484313i
$596$	−23444.2	+	13117.5i	−1.61126	+	0.901535i
$597$		−	24161.1i		−	1.65636i
$598$	12113.6	+	4822.20i	0.828364	+	0.329757i
$599$	9273.68			0.632575			0.316288	−	0.948663i	$-0.397564\pi$
$599$	9273.68			0.632575			0.316288	+	0.948663i	$0.397564\pi$
$600$	−3058.57	−	7072.21i	−0.208109	−	0.481203i
$601$	531.207	+	341.386i	0.0360539	+	0.0231704i	0.558544	−	0.829475i	$-0.311360\pi$
$601$	531.207	+	341.386i	0.0360539	+	0.0231704i	−0.522490	+	0.852646i	$0.674997\pi$
$602$	2006.29	−	8033.42i	0.135831	−	0.543883i
$603$	11856.7	+	5414.77i	0.800733	+	0.365682i
$604$	−1644.07	+	26885.5i	−0.110756	+	1.81119i
$605$	−9678.86	+	32963.2i	−0.650416	+	2.21511i
$606$	6991.00	+	13787.9i	0.468630	+	0.924252i
$607$	1338.60	+	2931.14i	0.0895096	+	0.195999i	0.949092	−	0.314998i	$-0.102004\pi$
$607$	1338.60	+	2931.14i	0.0895096	+	0.195999i	−0.859583	+	0.510996i	$0.829277\pi$
$608$	−5297.06	−	1207.28i	−0.353329	−	0.0805289i
$609$	2095.81	−	2418.70i	0.139452	−	0.160937i
$610$	−6971.21	−	7410.53i	−0.462715	−	0.491875i
$611$	4485.28	+	15275.4i	0.296980	+	1.01142i
$612$	8082.51	+	35391.4i	0.533850	+	2.33760i
$613$	−5850.15	−	9103.01i	−0.385457	−	0.599784i	0.593256	−	0.805014i	$-0.297842\pi$
$613$	−5850.15	−	9103.01i	−0.385457	−	0.599784i	−0.978714	+	0.205230i	$0.934206\pi$
$614$	4733.87	+	1932.26i	0.311145	+	0.127003i
$615$	4202.43	+	29228.5i	0.275542	+	1.91644i
$616$	7002.58	−	7758.84i	0.458023	−	0.507488i
$617$	−1490.48	+	10366.5i	−0.0972522	+	0.676404i	0.881624	+	0.471952i	$0.156450\pi$
$617$	−1490.48	+	10366.5i	−0.0972522	+	0.676404i	−0.978877	+	0.204452i	$0.934459\pi$
$618$	−10343.1	−	8247.26i	−0.673234	−	0.536818i
$619$	1706.27	−	1478.49i	0.110793	−	0.0960027i	−0.597703	−	0.801718i	$-0.703920\pi$
$619$	1706.27	−	1478.49i	0.110793	−	0.0960027i	0.708496	+	0.705715i	$0.249374\pi$
$620$	−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
$624$	−13147.4	−	19557.7i	−0.843458	−	1.25470i
$625$	2698.62	−	18769.3i	0.172712	−	1.20124i
$626$	−2317.69	−	1359.02i	−0.147977	−	0.0867691i
$627$	−16588.9	+	2385.12i	−1.05661	+	0.151918i
$628$	12157.3	−	22821.6i	0.772501	−	1.45013i
$629$	−5538.75	−	8618.46i	−0.351104	−	0.546328i
$630$	4282.14	+	12647.5i	0.270801	+	0.799823i
$631$	7665.25	−	2250.72i	0.483596	−	0.141996i	−0.0308420	−	0.999524i	$-0.509819\pi$
$631$	7665.25	−	2250.72i	0.483596	−	0.141996i	0.514438	+	0.857528i	$0.328001\pi$
$632$	9759.13	+	15882.4i	0.614236	+	0.999631i
$633$	−7634.53	+	8810.71i	−0.479376	+	0.553230i
$634$	−16473.1	+	3059.98i	−1.03191	+	0.191683i
$635$	30529.1	−	13942.2i	1.90789	−	0.871305i
$636$	25896.3	−	9964.59i	1.61455	−	0.621260i
$637$	−3413.00	+	11623.6i	−0.212289	+	0.722990i
$638$	−8926.11	+	364.945i	−0.553900	+	0.0226463i
$639$	15985.4	−	35003.1i	0.989627	−	2.16698i
$640$	13995.3	−	12137.7i	0.864397	−	0.749667i
$641$	23371.7	+	15020.1i	1.44013	+	0.925518i	0.999614	+	0.0277745i	$0.00884203\pi$
$641$	23371.7	+	15020.1i	1.44013	+	0.925518i	0.440519	+	0.897743i	$0.354794\pi$
$642$	−24923.4	+	17496.0i	−1.53216	+	1.07556i
$643$		−	12696.3i		−	0.778684i	−0.921093	−	0.389342i	$-0.872702\pi$
$643$		−	12696.3i		−	0.778684i	0.921093	−	0.389342i	$-0.127298\pi$
$644$	2132.58	−	6067.50i	0.130490	−	0.371262i
$645$		−	45274.7i		−	2.76386i
$646$	−4371.01	−	6226.59i	−0.266215	−	0.379229i
$647$	16498.4	+	10602.9i	1.00250	+	0.644271i	0.935443	−	0.353478i	$-0.115001\pi$
$647$	16498.4	+	10602.9i	1.00250	+	0.644271i	0.0670618	+	0.997749i	$0.478638\pi$
$648$	−9536.57	−	4590.37i	−0.578135	−	0.278282i
$649$	−14305.2	+	31324.0i	−0.865221	+	1.89457i
$650$	186.617	+	4564.41i	0.0112611	+	0.275432i
$651$	2630.89	−	8959.99i	0.158391	−	0.539431i
$652$	−11151.2	−	28980.0i	−0.669805	−	1.74071i
$653$	4216.15	−	1925.45i	0.252666	−	0.115389i	−0.285056	−	0.958511i	$-0.592012\pi$
$653$	4216.15	−	1925.45i	0.252666	−	0.115389i	0.537722	+	0.843122i	$0.319285\pi$
$654$	4665.12	+	25114.3i	0.278931	+	1.50160i
$655$	−9468.91	+	10927.7i	−0.564856	+	0.651879i
$656$	−15104.4	+	7278.57i	−0.898977	+	0.433202i
$657$	28321.1	−	8315.84i	1.68175	−	0.493808i
$658$	7438.31	−	2518.43i	0.440692	−	0.149208i
$659$	−5032.27	−	7830.36i	−0.297465	−	0.462864i	0.660061	−	0.751212i	$-0.270530\pi$
$659$	−5032.27	−	7830.36i	−0.297465	−	0.462864i	−0.957526	+	0.288348i	$0.906894\pi$
$660$	26868.7	−	50437.5i	1.58464	−	2.97466i
$661$	9320.74	−	1340.12i	0.548464	−	0.0788572i	0.137488	−	0.990503i	$-0.456097\pi$
$661$	9320.74	−	1340.12i	0.548464	−	0.0788572i	0.410976	+	0.911646i	$0.365188\pi$
$662$	493.560	−	841.722i	0.0289769	−	0.0494176i
$663$	4696.30	−	32663.5i	0.275097	−	1.91334i
$664$	−13055.0	−	15696.3i	−0.762998	−	0.917373i
$665$	−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
$670$	5806.90	−	7282.55i	0.334836	−	0.419925i
$671$	2536.15	−	17639.3i	0.145912	−	1.01484i
$672$	−9374.32	+	6873.96i	−0.538128	+	0.394596i
$673$	1520.82	+	10577.5i	0.0871073	+	0.605844i	0.985883	+	0.167436i	$0.0535486\pi$
$673$	1520.82	+	10577.5i	0.0871073	+	0.605844i	−0.898776	+	0.438409i	$0.855542\pi$
$674$	−8415.56	+	20617.4i	−0.480942	+	1.17827i
$675$	4351.24	+	6770.66i	0.248118	+	0.386079i
$676$	−802.487	−	3513.90i	−0.0456581	−	0.199926i
$677$	3674.36	+	12513.7i	0.208593	+	0.710401i	0.995621	+	0.0934841i	$0.0298004\pi$
$677$	3674.36	+	12513.7i	0.208593	+	0.710401i	−0.787028	+	0.616917i	$0.788381\pi$
$678$	−25114.0	+	23625.2i	−1.42256	+	1.33823i
$679$	−5601.61	+	6464.60i	−0.316598	+	0.365373i
$680$	25935.8	+	524.297i	1.46264	+	0.0295674i
$681$	17701.6	+	38761.2i	0.996077	+	2.18111i
$682$	−23249.0	+	11788.1i	−1.30535	+	0.661862i
$683$	7010.08	−	23874.1i	0.392728	−	1.33751i	−0.491673	−	0.870780i	$-0.663614\pi$
$683$	7010.08	−	23874.1i	0.392728	−	1.33751i	0.884401	−	0.466729i	$-0.154568\pi$
$684$	12134.9	+	742.058i	0.678345	+	0.0414814i
$685$	−3824.48	−	1746.58i	−0.213323	−	0.0974212i
$686$	12657.6	+	3161.15i	0.704474	+	0.175937i
$687$	−10215.6	−	6565.19i	−0.567323	−	0.364596i
$688$	24510.9	−	7750.28i	1.35824	−	0.429472i
$689$	−16450.6			−0.909603
$690$	3274.53	−	35013.0i	0.180666	−	1.93177i
$691$			16558.5i			0.911598i	0.890083	+	0.455799i	$0.150646\pi$
$691$			16558.5i			0.911598i	−0.890083	+	0.455799i	$0.849354\pi$
$692$	2086.08	−	1167.20i	0.114596	−	0.0641191i
$693$	−12644.6	+	19675.4i	−0.693116	+	1.07851i
$694$	−7428.01	+	29742.6i	−0.406287	+	1.62682i
$695$	10103.5	−	22123.5i	0.551434	−	1.20747i
$696$	9804.39	+	1612.54i	0.533958	+	0.0878208i
$697$	−22527.2	−	6614.59i	−1.22422	−	0.359463i
$698$	−6420.21	+	3255.28i	−0.348150	+	0.176525i
$699$	−41423.3	+	18917.4i	−2.24145	+	1.02364i
$700$	2245.86	−	183.953i	0.121265	−	0.00993251i
$701$	−5256.14	−	4554.47i	−0.283198	−	0.245392i	0.501665	−	0.865062i	$-0.332721\pi$
$701$	−5256.14	−	4554.47i	−0.283198	−	0.245392i	−0.784863	+	0.619670i	$0.787267\pi$
$702$	16866.0	+	17928.9i	0.906791	+	0.963936i
$703$	−3291.94	+	966.602i	−0.176612	+	0.0518579i
$704$	31905.5	+	5912.17i	1.70807	+	0.316510i
$705$	36123.0	−	23214.8i	1.92975	−	1.24017i
$706$	−7476.57	+	18316.9i	−0.398561	+	0.976440i
$707$	−4474.94	+	643.399i	−0.238044	+	0.0342256i
$708$	22634.8	−	30896.4i	1.20151	−	1.64006i
$709$	21471.6	+	3087.15i	1.13735	+	0.163527i	0.685159	−	0.728393i	$-0.259732\pi$
$709$	21471.6	+	3087.15i	1.13735	+	0.163527i	0.452194	+	0.891920i	$0.350642\pi$
$710$	−21499.4	−	17143.0i	−1.13642	−	0.906148i
$711$	−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
$716$	2177.87	−	2223.31i	0.113674	−	0.116046i
$717$	10795.9	+	1552.22i	0.562317	+	0.0808490i
$718$	−13232.5	−	7759.15i	−0.687791	−	0.403299i
$719$	−4589.18	−	31918.5i	−0.238036	−	1.65557i	−0.661710	−	0.749760i	$-0.730169\pi$
$719$	−4589.18	−	31918.5i	−0.238036	−	1.65557i	0.423674	−	0.905815i	$-0.360740\pi$
$720$	−26495.0	+	31884.0i	−1.37140	+	1.65034i
$721$	3254.54	−	2091.56i	0.168107	−	0.108036i
$722$	15962.3	−	5404.47i	0.822793	−	0.278578i
$723$	−8501.91	−	28954.8i	−0.437330	−	1.48941i
$724$	4088.28	+	5345.36i	0.209861	+	0.274390i
$725$	−1455.65	−	1261.32i	−0.0745673	−	0.0646130i
$726$	65802.0	−	12223.1i	3.36383	−	0.624850i
$727$	1456.72	+	3189.77i	0.0743147	+	0.162727i	0.943143	−	0.332387i	$-0.107854\pi$
$727$	1456.72	+	3189.77i	0.0743147	+	0.162727i	−0.868829	+	0.495113i	$0.835127\pi$
$728$	6650.56	−	1807.61i	0.338580	−	0.0920254i
$729$	−24810.3	−	7284.97i	−1.26049	−	0.370115i
$730$	−861.634	−	21074.5i	−0.0436856	−	1.06850i
$731$	32744.4	+	14953.8i	1.65676	+	0.756618i
$732$	−6734.49	+	18641.5i	−0.340046	+	0.941268i
$733$	−2750.26	+	4279.48i	−0.138585	+	0.215643i	−0.903608	−	0.428360i	$-0.859091\pi$
$733$	−2750.26	+	4279.48i	−0.138585	+	0.215643i	0.765023	+	0.644003i	$0.222728\pi$
$734$	12527.0	−	8793.85i	0.629946	−	0.442217i
$735$	32674.1			1.63973
$736$	19516.0	−	4220.87i	0.977402	−	0.211390i
$737$	16314.5			0.815406
$738$	30708.7	−	21557.2i	1.53171	−	1.07525i
$739$	−7392.14	+	11502.4i	−0.367963	+	0.572561i	−0.975026	−	0.222093i	$-0.928711\pi$
$739$	−7392.14	+	11502.4i	−0.367963	+	0.572561i	0.607063	+	0.794654i	$0.292348\pi$
$740$	3974.99	−	11003.0i	0.197464	−	0.546593i
$741$	−10052.6	−	4590.87i	−0.498370	−	0.227598i
$742$	331.491	+	8107.86i	0.0164008	+	0.401144i
$743$	9665.11	+	2837.93i	0.477225	+	0.140126i	0.511494	−	0.859287i	$-0.329092\pi$
$743$	9665.11	+	2837.93i	0.477225	+	0.140126i	−0.0342690	+	0.999413i	$0.510910\pi$
$744$	27977.1	−	7604.11i	1.37861	−	0.374705i
$745$	−17845.4	−	39075.9i	−0.877589	−	1.92165i
$746$	17023.8	−	3162.27i	0.835505	−	0.155200i
$747$	34527.1	+	29917.9i	1.69114	+	1.46538i
$748$	27603.8	+	36091.5i	1.34933	+	1.76422i
$749$	−2508.95	−	8544.70i	−0.122397	−	0.416845i
$750$	−26075.7	+	8828.61i	−1.26953	+	0.429834i
$751$	−2879.24	+	1850.37i	−0.139900	+	0.0899082i	−0.608719	−	0.793386i	$-0.708316\pi$
$751$	−2879.24	+	1850.37i	−0.139900	+	0.0899082i	0.468819	+	0.883294i	$0.344680\pi$
$752$	18751.8	+	15582.4i	0.909317	+	0.755625i
$753$	4290.51	+	29841.2i	0.207643	+	1.44419i
$754$	−5081.66	−	2979.72i	−0.245442	−	0.143919i
$755$	−42633.5	−	6129.77i	−2.05509	−	0.295477i
$756$	8496.62	−	8673.91i	0.408755	−	0.417284i
$757$	−10658.1	+	9235.26i	−0.511722	+	0.443410i	−0.872051	−	0.489416i	$-0.837210\pi$
$757$	−10658.1	+	9235.26i	−0.511722	+	0.443410i	0.360328	+	0.932826i	$0.382665\pi$
$758$	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	−0.944923	−	0.327293i	$-0.893863\pi$
$761$	−23814.8	−	27483.7i	−1.13441	−	1.30918i	−0.189486	−	0.981884i	$-0.560682\pi$
$762$	−51121.3	−	40762.6i	−2.43035	−	1.93789i
$763$	−7394.23	−	1063.13i	−0.350837	−	0.0504428i
$764$	−3131.48	+	4274.45i	−0.148289	+	0.202414i
$765$	−57459.2	+	8261.39i	−2.71561	+	0.390446i
$766$	−11580.8	+	28371.9i	−0.546254	+	1.33827i
$767$	−19102.5	+	12276.5i	−0.899287	+	0.577936i
$768$	−33419.7	−	13624.1i	−1.57022	−	0.640129i
$769$	−35333.5	+	10374.9i	−1.65691	+	0.486511i	−0.970579	−	0.240782i	$-0.922596\pi$
$769$	−35333.5	+	10374.9i	−1.65691	+	0.486511i	−0.686326	+	0.727294i	$0.740778\pi$
$770$	11451.4	+	12173.0i	0.535946	+	0.569720i
$771$	−21537.5	−	18662.4i	−1.00604	−	0.871737i
$772$	−6553.02	+	536.740i	−0.305503	+	0.0250229i
$773$	19839.3	−	9060.33i	0.923120	−	0.421575i	0.103596	−	0.994619i	$-0.466965\pi$
$773$	19839.3	−	9060.33i	0.923120	−	0.421575i	0.819524	+	0.573045i	$0.194238\pi$
$774$	−51307.8	+	26015.0i	−2.38272	+	1.20813i
$775$	−5392.40	−	1583.35i	−0.249936	−	0.0733879i
$776$	−26204.8	−	4309.95i	−1.21224	−	0.199379i
$777$	−3049.55	+	6677.59i	−0.140801	+	0.308310i
$778$	2986.64	−	11958.9i	0.137630	−	0.551087i
$779$	−4250.91	+	6614.55i	−0.195513	+	0.304225i
$780$	32885.8	−	18400.3i	1.50962	−	0.844663i
$781$		−	48163.4i		−	2.20669i
$782$	24241.2	+	13932.8i	1.10852	+	0.637128i
$783$	−10378.5			−0.473687
$784$	5593.27	+	17689.2i	0.254796	+	0.805813i
$785$	34784.3	+	22354.5i	1.58153	+	1.01639i
$786$	27329.5	+	6825.35i	1.24022	+	0.309735i
$787$	−8473.43	−	3869.68i	−0.383793	−	0.175272i	0.214169	−	0.976797i	$-0.431296\pi$
$787$	−8473.43	−	3869.68i	−0.383793	−	0.175272i	−0.597962	+	0.801524i	$0.704023\pi$
$788$	−4234.96	−	258.971i	−0.191452	−	0.0117075i
$789$	644.157	−	2193.80i	0.0290654	−	0.0989876i
$790$	−26586.0	+	13480.1i	−1.19733	+	0.607090i
$791$	−4188.86	−	9172.32i	−0.188292	−	0.412301i
$792$	−72597.5	−	1467.57i	−3.25712	−	0.0658432i
$793$	7695.32	−	8880.87i	0.344601	−	0.397691i
$794$	−29996.5	+	28218.2i	−1.34072	+	1.26124i
$795$	12500.4	+	42572.3i	0.557663	+	1.89923i
$796$	4884.13	+	21386.4i	0.217479	+	0.952289i
$797$	13588.1	+	21143.6i	0.603910	+	0.939703i	0.999771	+	0.0213923i	$0.00680989\pi$
$797$	13588.1	+	21143.6i	0.603910	+	0.939703i	−0.395861	+	0.918311i	$0.629554\pi$
$798$	−2060.10	+	5047.06i	−0.0913869	+	0.223890i
$799$	4858.73	+	33793.2i	0.215131	+	1.49627i
$800$	4136.96	+	5641.76i	0.182830	+	0.249333i
$801$	6620.56	−	46047.0i	0.292043	−	2.03120i
$802$	−772.606	+	968.942i	−0.0340170	+	0.0426615i
$803$	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
$808$	−8975.37	−	10791.3i	−0.390783	−	0.469848i
$809$	−1735.96	+	12073.9i	−0.0754427	+	0.524716i	0.916697	+	0.399583i	$0.130845\pi$
$809$	−1735.96	+	12073.9i	−0.0754427	+	0.524716i	−0.992140	+	0.125133i	$0.960064\pi$
$810$	8560.65	−	14599.4i	0.371347	−	0.633299i
$811$	21423.2	−	3080.20i	0.927585	−	0.133367i	0.338067	−	0.941122i	$-0.390227\pi$
$811$	21423.2	−	3080.20i	0.927585	−	0.133367i	0.589518	+	0.807755i	$0.299318\pi$
$812$	−1366.19	+	2564.60i	−0.0590443	+	0.110837i
$813$	−13610.1	−	21177.7i	−0.587118	−	0.913574i
$814$	19409.3	−	6571.52i	0.835743	−	0.282963i
$815$	47641.8	−	13988.9i	2.04763	−	0.601238i
$816$	−21938.4	−	45526.5i	−0.941175	−	1.95312i
$817$	7894.55	−	9110.80i	0.338060	−	0.390143i
$818$	−5394.38	−	29040.2i	−0.230575	−	1.24128i
$819$	−14028.6	+	6406.66i	−0.598534	+	0.273341i
$820$	−9628.33	−	25022.4i	−0.410044	−	1.06564i
$821$	−3275.14	+	11154.1i	−0.139224	+	0.474154i	−0.999355	−	0.0359198i	$-0.988564\pi$
$821$	−3275.14	+	11154.1i	−0.139224	+	0.474154i	0.860130	+	0.510074i	$0.170382\pi$
$822$	334.602	+	8183.94i	0.0141978	+	0.347260i
$823$	−10090.6	+	22095.4i	−0.427384	+	0.935840i	0.566360	+	0.824158i	$0.308351\pi$
$823$	−10090.6	+	22095.4i	−0.427384	+	0.935840i	−0.993744	+	0.111682i	$0.964376\pi$
$824$	10822.4	+	5209.31i	0.457545	+	0.220237i
$825$	18155.4	+	11667.8i	0.766169	+	0.492387i
$826$	6435.53	+	9167.53i	0.271090	+	0.386174i
$827$			20542.6i			0.863768i	0.901929	+	0.431884i	$0.142151\pi$
$827$			20542.6i			0.863768i	−0.901929	+	0.431884i	$0.857849\pi$
$828$	−41560.2	+	16407.7i	−1.74435	+	0.688655i
$829$			15720.4i			0.658616i	0.944223	+	0.329308i	$0.106815\pi$
$829$			15720.4i			0.658616i	−0.944223	+	0.329308i	$0.893185\pi$
$830$	26719.8	−	18757.0i	1.11742	−	0.784418i
$831$	−49679.8	−	31927.3i	−2.07385	−	1.33278i
$832$	15591.1	+	14654.0i	0.649669	+	0.610620i
$833$	−10792.0	+	23631.2i	−0.448884	+	0.982919i
$834$	−47341.7	+	1935.57i	−1.96560	+	0.0803638i
$835$	8480.88	−	28883.2i	0.351489	−	1.19706i
$836$	14201.7	−	5464.64i	0.587531	−	0.226075i
$837$	−27546.2	+	12579.9i	−1.13756	+	0.519505i
$838$	31051.9	−	5768.05i	1.28003	−	0.237773i
$839$	25919.6	−	29912.8i	1.06656	−	1.23088i	0.0946525	−	0.995510i	$-0.469826\pi$
$839$	25919.6	−	29912.8i	1.06656	−	1.23088i	0.971907	−	0.235365i	$-0.0756285\pi$
$840$	−9731.49	−	15837.4i	−0.399724	−	0.650526i
$841$	−21017.9	+	6171.42i	−0.861779	+	0.253041i
$842$	2318.63	+	6848.17i	0.0948992	+	0.280289i
$843$	−10801.6	−	16807.6i	−0.441312	−	0.686696i
$844$	4976.71	−	9342.20i	0.202968	−	0.381009i
$845$	5704.94	−	820.247i	0.232256	−	0.0333933i
$846$	−47064.8	−	27597.3i	−1.91267	−	1.12153i
$847$	−2785.50	+	19373.6i	−0.113000	+	0.785932i
$848$	−20908.1	+	14055.2i	−0.846681	+	0.569170i
$849$	−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	$-0.804337\pi$
$853$	−9027.88	+	7822.70i	−0.362378	+	0.314002i	0.454573	+	0.890710i	$0.349792\pi$
$854$	−4532.11	−	3613.77i	−0.181599	−	0.144802i
$855$	−2766.69	+	19242.8i	−0.110665	+	0.769694i
$856$	18524.4	−	20525.0i	0.739663	−	0.819545i
$857$	−4731.35	−	32907.3i	−0.188588	−	1.31166i	−0.835667	−	0.549236i	$-0.814919\pi$
$857$	−4731.35	−	32907.3i	−0.188588	−	1.31166i	0.647079	−	0.762423i	$-0.275990\pi$
$858$	61110.4	+	24943.9i	2.43156	+	0.992508i
$859$	16609.6	+	25845.0i	0.659733	+	1.02657i	0.996386	+	0.0849363i	$0.0270687\pi$
$859$	16609.6	+	25845.0i	0.659733	+	1.02657i	−0.336653	+	0.941629i	$0.609295\pi$
$860$	9152.21	+	40075.3i	0.362893	+	1.58902i
$861$	4739.73	+	16142.0i	0.187607	+	0.638931i
$862$	14252.1	+	15150.2i	0.563142	+	0.598631i
$863$	−30366.4	+	35044.7i	−1.19778	+	1.38231i	−0.293176	+	0.956059i	$0.594712\pi$
$863$	−30366.4	+	35044.7i	−1.19778	+	1.38231i	−0.904604	+	0.426253i	$0.859833\pi$
$864$	36754.3	+	8376.85i	1.44723	+	0.329845i
$865$	1587.89	+	3476.99i	0.0624160	+	0.136672i
$866$	1891.38	+	3730.26i	0.0742168	+	0.146374i
$867$	7741.28	−	26364.4i	0.303238	−	1.03273i
$868$	−517.511	+	8462.85i	−0.0202367	+	0.330931i
$869$	−47492.9	−	21689.3i	−1.85395	−	0.846672i
$870$	−3849.79	+	15415.0i	−0.150023	+	0.600710i
$871$	9050.12	+	5816.16i	0.352068	+	0.226261i
$872$	−9206.20	−	21287.1i	−0.357524	−	0.826690i
$873$	59428.0			2.30393
$874$	6764.16	−	6474.81i	0.261786	−	0.250588i
$875$		−	8051.01i		−	0.311056i
$876$	−35858.7	+	20063.7i	−1.38305	+	0.773848i
$877$	25985.7	−	40434.5i	1.00054	−	1.55687i	0.181296	−	0.983429i	$-0.441971\pi$
$877$	25985.7	−	40434.5i	1.00054	−	1.55687i	0.819245	−	0.573443i	$-0.194393\pi$
$878$	−6505.42	−	1624.68i	−0.250054	−	0.0624493i
$879$	−183.188	+	401.127i	−0.00702934	+	0.0153921i
$880$	−13587.2	+	50076.7i	−0.520483	+	1.91828i
$881$	−23659.4	−	6947.03i	−0.904774	−	0.265666i	−0.203935	−	0.978985i	$-0.565373\pi$
$881$	−23659.4	−	6947.03i	−0.904774	−	0.265666i	−0.700840	+	0.713319i	$0.747191\pi$
$882$	−18774.7	−	37028.2i	−0.716753	−	1.41361i
$883$	−13878.1	+	6337.91i	−0.528918	+	0.241549i	−0.661930	−	0.749566i	$-0.730262\pi$
$883$	−13878.1	+	6337.91i	−0.528918	+	0.241549i	0.133012	+	0.991114i	$0.457535\pi$
$884$	2445.89	+	29861.7i	0.0930592	+	1.13615i
$885$	46285.7	+	40106.8i	1.75805	+	1.52336i
$886$	15191.4	−	14290.8i	0.576032	−	0.541883i
$887$	−5614.27	+	1648.50i	−0.212524	+	0.0624027i	−0.386262	−	0.922389i	$-0.626234\pi$
$887$	−5614.27	+	1648.50i	−0.212524	+	0.0624027i	0.173737	+	0.984792i	$0.444416\pi$
$888$	−22620.2	+	2786.92i	−0.854823	+	0.105319i
$889$	16085.8	−	10337.7i	0.606861	−	0.390006i
$890$	−30777.5	−	12562.7i	−1.15917	−	0.473149i
$891$	29342.1	−	4218.76i	1.10325	−	0.158624i
$892$	−18497.2	+	25248.6i	−0.694318	+	0.947741i
$893$	11317.1	+	1627.16i	0.424092	+	0.0609752i
$894$	−52174.3	+	65432.9i	−1.95187	+	2.44788i
$895$	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
$900$	−11183.7	−	10955.1i	−0.414212	−	0.405746i
$901$	−34918.7	−	5020.55i	−1.29113	−	0.185637i
$902$	23754.0	−	40510.4i	0.876854	−	1.49540i
$903$	−3670.90	−	25531.6i	−0.135282	−	0.940908i
$904$	17454.1	−	25988.8i	0.642163	−	0.956167i
$905$	−9052.70	+	5817.81i	−0.332510	+	0.213691i
$906$	26909.3	+	79477.8i	0.986757	+	2.91443i
$907$	−8222.43	−	28003.0i	−0.301016	−	1.02517i	−0.961609	−	0.274422i	$-0.911514\pi$
$907$	−8222.43	−	28003.0i	−0.301016	−	1.02517i	0.660594	−	0.750744i	$-0.270305\pi$
$908$	−23504.3	−	30731.5i	−0.859051	−	1.12320i
$909$	23737.6	+	20568.7i	0.866144	+	0.750518i
$910$	2012.68	+	10835.1i	0.0733184	+	0.394704i
$911$	4384.35	+	9600.39i	0.159451	+	0.349149i	0.972448	−	0.233118i	$-0.0748929\pi$
$911$	4384.35	+	9600.39i	0.159451	+	0.349149i	−0.812997	+	0.582268i	$0.802166\pi$
$912$	−16698.9	+	2754.00i	−0.606310	+	0.0999933i
$913$	54865.6	+	16110.0i	1.98881	+	0.583969i
$914$	35.1722	−	1.43802i	0.00127286	−	5.20410e-5i
$915$	−28830.2	−	13166.3i	−1.04164	−	0.475700i
$916$	10369.6	+	3746.17i	0.374041	+	0.135128i
$917$	−4453.76	+	6930.18i	−0.160388	+	0.249569i
$918$	30328.9	+	43204.0i	1.09042	+	1.55332i
$919$	4039.61			0.144999			0.0724997	−	0.997368i	$-0.476902\pi$
$919$	4039.61			0.144999			0.0724997	+	0.997368i	$0.476902\pi$
$920$	4179.33	+	31654.0i	0.149770	+	1.13435i
$921$	15928.0			0.569866
$922$	8308.41	+	11835.5i	0.296771	+	0.422756i
$923$	17170.3	−	26717.6i	0.612317	−	0.952784i
$924$	11062.5	−	30621.6i	0.393863	−	1.09024i
$925$	4018.78	+	1835.31i	0.142850	+	0.0652376i
$926$	44637.2	−	1825.00i	1.58409	−	0.0647659i
$927$	−25788.8	−	7572.29i	−0.913718	−	0.268292i
$928$	−9004.43	+	554.584i	−0.318518	+	0.0196176i
$929$	−17895.9	−	39186.6i	−0.632019	−	1.38393i	−0.906446	−	0.422321i	$-0.861216\pi$
$929$	−17895.9	−	39186.6i	−0.632019	−	1.38393i	0.274427	−	0.961608i	$-0.411512\pi$
$930$	8466.80	+	45580.4i	0.298535	+	1.60714i
$931$	6575.14	+	5697.40i	0.231463	+	0.200563i
$932$	32842.2	−	25118.6i	1.15427	−	0.882819i
$933$	7084.70	+	24128.3i	0.248599	+	0.846650i
$934$	−4747.28	−	14021.3i	−0.166312	−	0.491211i
$935$	−61123.3	+	39281.6i	−2.13791	+	1.37395i
$936$	−39748.6	−	26695.2i	−1.38806	−	0.932222i
$937$	−3002.13	−	20880.2i	−0.104669	−	0.727991i	−0.972799	−	0.231653i	$-0.925587\pi$
$937$	−3002.13	−	20880.2i	−0.104669	−	0.727991i	0.868129	−	0.496338i	$-0.165322\pi$
$938$	2684.20	−	4577.66i	0.0934351	−	0.159345i
$939$	−8284.53	−	1191.14i	−0.287918	−	0.0413964i
$940$	−27281.8	+	27851.1i	−0.946632	+	0.966385i
$941$	10738.3	−	9304.78i	0.372007	−	0.322346i	−0.448714	−	0.893675i	$-0.648118\pi$
$941$	10738.3	−	9304.78i	0.372007	−	0.322346i	0.820721	+	0.571330i	$0.193572\pi$
$942$	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
$946$	−44888.9	+	56296.1i	−1.54277	+	1.93482i
$947$	−6378.37	−	917.070i	−0.218869	−	0.0314686i	0.0320078	−	0.999488i	$-0.489810\pi$
$947$	−6378.37	−	917.070i	−0.218869	−	0.0314686i	−0.250877	+	0.968019i	$0.580719\pi$
$948$	46844.6	+	34318.4i	1.60489	+	1.17575i
$949$	24113.2	−	3466.96i	0.824814	−	0.118590i
$950$	3037.48	+	1239.83i	0.103735	+	0.0423426i
$951$	−43908.9	+	28218.6i	−1.49721	+	0.962197i
$952$	14668.4	−	1807.22i	0.499377	−	0.0615257i
$953$	−17720.8	+	5203.29i	−0.602342	+	0.176864i	−0.568665	−	0.822569i	$-0.692540\pi$
$953$	−17720.8	+	5203.29i	−0.602342	+	0.176864i	−0.0336772	+	0.999433i	$0.510722\pi$
$954$	41062.6	−	38628.3i	1.39356	−	1.31094i
$955$	−6403.53	−	5548.69i	−0.216977	−	0.188012i
$956$	−9869.90	+	808.417i	−0.333907	+	0.0273494i
$957$	−25314.8	+	11560.9i	−0.855078	+	0.390501i
$958$	−24604.7	−	48526.4i	−0.829793	−	1.63655i
$959$	−2298.35	−	674.855i	−0.0773904	−	0.0227239i
$960$	26075.7	−	51483.4i	0.876654	−	1.73085i
$961$	−3591.19	+	7863.62i	−0.120546	+	0.263959i
$962$	13109.6	+	3274.03i	0.439366	+	0.109729i
$963$	−33449.7	+	52048.7i	−1.11932	+	1.74169i
$964$	13378.7	+	23911.0i	0.446992	+	0.798882i
$965$		−	10513.8i		−	0.350726i
$966$	−992.272	−	20010.3i	−0.0330495	−	0.666480i
$967$	31666.9			1.05309			0.526546	−	0.850147i	$-0.323487\pi$
$967$	31666.9			1.05309			0.526546	+	0.850147i	$0.323487\pi$
$968$	−55774.4	+	24121.1i	−1.85192	+	0.800912i
$969$	−19937.0	−	12812.7i	−0.660959	−	0.424773i
$970$	10289.6	−	41200.6i	0.340596	−	1.36379i
$971$	50800.6	+	23199.9i	1.67896	+	0.766755i	0.999453	+	0.0330857i	$0.0105334\pi$
$971$	50800.6	+	23199.9i	1.67896	+	0.766755i	0.679507	+	0.733669i	$0.262194\pi$
$972$	11988.6	+	733.111i	0.395610	+	0.0241919i
$973$	3903.84	−	13295.2i	0.128624	−	0.438054i
$974$	156.800	+	309.248i	0.00515831	+	0.0101734i
$975$	5911.71	+	12944.8i	0.194181	+	0.425197i
$976$	2192.76	−	17862.0i	0.0719144	−	0.585809i
$977$	31356.0	−	36186.8i	1.02678	−	1.18497i	0.0442254	−	0.999022i	$-0.485918\pi$
$977$	31356.0	−	36186.8i	1.02678	−	1.18497i	0.982559	−	0.185951i	$-0.0595365\pi$
$978$	−66278.6	−	70455.4i	−2.16703	−	2.30360i
$979$	−16404.3	−	55868.1i	−0.535531	−	1.82385i
$980$	−28921.9	+	6605.03i	−0.942729	+	0.215296i
$981$	28059.0	+	43660.7i	0.913206	+	1.42098i
$982$	7106.68	+	2900.79i	0.230940	+	0.0942647i
$983$	2769.85	+	19264.7i	0.0898723	+	0.625076i	0.984120	+	0.177504i	$0.0568021\pi$
$983$	2769.85	+	19264.7i	0.0898723	+	0.625076i	−0.894248	+	0.447572i	$0.852289\pi$
$984$	−34995.0	+	38774.4i	−1.13374	+	1.25618i
$985$	965.550	−	6715.55i	0.0312335	−	0.217234i
$986$	−9877.16	−	7875.76i	−0.319019	−	0.254377i
$987$	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	0.884451	−	0.466634i	$-0.154533\pi$
$991$	9255.98	+	10682.0i	0.296696	+	0.342406i	−0.587755	+	0.809039i	$0.699988\pi$
$992$	−23227.0	+	12386.4i	−0.743406	+	0.396440i
$993$	432.588	−	3008.71i	0.0138245	−	0.0961517i
$994$	−13514.1	−	7924.22i	−0.431227	−	0.252858i
$995$	−34721.6	+	4992.22i	−1.10628	+	0.159059i
$996$	−56131.3	−	29901.8i	−1.78573	−	0.951281i
$997$	−8238.74	−	12819.7i	−0.261709	−	0.407226i	0.685387	−	0.728179i	$-0.259633\pi$
$997$	−8238.74	−	12819.7i	−0.261709	−	0.407226i	−0.947095	+	0.320953i	$0.895997\pi$
$998$	4813.88	+	14218.0i	0.152686	+	0.450965i
$999$	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.13.14	✓	700
8.5	even	2	inner	184.4.p.a.13.53	yes	700
23.16	even	11	inner	184.4.p.a.85.53	yes	700
184.85	even	22	inner	184.4.p.a.85.14	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.p.a.13.14	✓	700	1.1	even	1	trivial
184.4.p.a.13.53	yes	700	8.5	even	2	inner
184.4.p.a.85.14	yes	700	184.85	even	22	inner
184.4.p.a.85.53	yes	700	23.16	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.31497 + 1.62509i) q^{2} +(-4.76362 + 7.41234i) q^{3} +(2.71817 - 7.52406i) q^{4} +(11.6365 + 5.31419i) q^{5} +(-1.01807 - 24.9006i) q^{6} +(6.99300 + 2.05333i) q^{7} +(5.93478 + 21.8353i) q^{8} +(-21.0345 - 46.0590i) q^{9} +(-35.5741 + 6.60808i) q^{10} +(-47.8965 - 41.5026i) q^{11} +(42.8225 + 55.9898i) q^{12} +(-11.7738 - 40.0978i) q^{13} +(-19.5254 + 6.61084i) q^{14} +(-94.8222 + 60.9385i) q^{15} +(-49.2231 - 40.9034i) q^{16} +(-12.7541 - 88.7065i) q^{17} +(123.544 + 72.4424i) q^{18} +(-29.7073 - 4.27127i) q^{19} +(71.6142 - 73.1085i) 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} +(92.4184 + 73.6917i) q^{26} +(206.128 + 29.6367i) q^{27} +(34.4576 - 47.0344i) q^{28} +(-49.3299 + 7.09257i) q^{29} +(120.480 - 295.165i) q^{30} +(-122.333 + 78.6185i) q^{31} +(180.422 + 14.6984i) q^{32} +(535.792 - 157.323i) q^{33} +(173.681 + 184.626i) q^{34} +(70.4619 + 61.0556i) q^{35} +(-403.726 + 33.0681i) q^{36} +(103.985 - 47.4883i) q^{37} +(75.7127 - 38.3892i) q^{38} +(353.304 + 103.739i) q^{39} +(-46.9769 + 285.624i) q^{40} +(108.830 - 238.305i) q^{41} +(44.0099 - 176.221i) q^{42} +(-217.161 + 337.908i) q^{43} +(-442.459 + 247.565i) q^{44} -647.745i q^{45} +(-192.380 + 245.614i) q^{46} -380.955 q^{47} +(537.670 - 170.010i) q^{48} +(-243.864 - 156.722i) q^{49} +(-106.055 - 26.4865i) q^{50} +(718.278 + 328.027i) q^{51} +(-333.701 - 20.4061i) q^{52} +(110.902 - 377.698i) q^{53} +(-525.343 + 266.368i) q^{54} +(-336.793 - 737.474i) q^{55} +(-3.33307 + 164.880i) q^{56} +(173.174 - 199.854i) q^{57} +(102.671 - 96.5846i) q^{58} +(-153.082 - 521.348i) q^{59} +(200.762 + 879.090i) q^{60} +(152.023 + 236.552i) q^{61} +(155.435 - 380.801i) q^{62} +(-52.5195 - 365.281i) q^{63} +(-441.557 + 259.175i) q^{64} +(76.0823 - 529.164i) q^{65} +(-984.679 + 1234.91i) 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} +(880.876 - 732.643i) q^{72} +(-82.9602 + 577.001i) q^{73} +(-163.549 + 278.918i) q^{74} +(-337.062 + 48.4621i) q^{75} +(-112.887 + 211.910i) q^{76} +(-249.722 - 388.575i) q^{77} +(-986.474 + 333.997i) q^{78} +(790.457 - 232.099i) q^{79} +(-355.413 - 737.552i) q^{80} +(-306.307 + 353.497i) q^{81} +(135.328 + 728.527i) q^{82} +(-820.726 + 374.813i) q^{83} +(184.492 + 479.465i) q^{84} +(322.991 - 1100.01i) q^{85} +(-46.4109 - 1135.15i) q^{86} +(182.416 - 399.436i) q^{87} +(621.964 - 1292.14i) q^{88} +(772.899 + 496.712i) q^{89} +(1052.64 + 1499.51i) q^{90} -304.579i q^{91} +(46.2093 - 881.222i) q^{92} -1281.28i q^{93} +(881.899 - 619.086i) q^{94} +(-322.989 - 207.573i) q^{95} +(-968.409 + 1267.33i) q^{96} +(-487.556 + 1067.60i) q^{97} +(819.225 - 33.4942i) 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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