LMFDB - Embedded newform 184.4.j.a.11.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,4,Mod(11,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.11"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 9])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	184.j (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			11.34
Character	$\chi$	$=$	184.11
Dual form			184.4.j.a.67.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.186841 + 2.82225i) q^{2} +(0.730695 - 5.08210i) q^{3} +(-7.93018 - 1.05462i) q^{4} +(-14.1524 + 4.15552i) q^{5} +(14.2064 + 3.01175i) q^{6} +(11.2898 + 13.0291i) q^{7} +(4.45809 - 22.1839i) q^{8} +(0.612524 + 0.179853i) q^{9} +(-9.08368 - 40.7181i) q^{10} +(15.9098 - 24.7561i) q^{11} +(-11.1542 + 39.5313i) q^{12} +(-27.8279 - 24.1130i) q^{13} +(-38.8807 + 29.4282i) q^{14} +(10.7777 + 74.9604i) q^{15} +(61.7755 + 16.7267i) q^{16} +(61.2777 - 27.9846i) q^{17} +(-0.622036 + 1.69509i) q^{18} +(73.3374 + 33.4921i) q^{19} +(116.614 - 18.0286i) q^{20} +(74.4645 - 47.8554i) q^{21} +(66.8954 + 49.5269i) q^{22} +(74.9087 + 80.9672i) q^{23} +(-109.483 - 38.8661i) q^{24} +(77.8658 - 50.0413i) q^{25} +(73.2524 - 74.0321i) q^{26} +(58.9496 - 129.082i) q^{27} +(-75.7892 - 115.229i) q^{28} +(123.688 - 56.4864i) q^{29} +(-213.571 + 16.4116i) q^{30} +(179.925 - 25.8694i) q^{31} +(-58.7491 + 171.221i) q^{32} +(-114.188 - 98.9444i) q^{33} +(67.5304 + 178.170i) q^{34} +(-213.920 - 137.478i) q^{35} +(-4.66775 - 2.07225i) q^{36} +(126.554 + 37.1597i) q^{37} +(-108.225 + 200.719i) q^{38} +(-142.879 + 123.805i) q^{39} +(29.0930 + 332.482i) q^{40} +(113.198 - 33.2381i) q^{41} +(121.147 + 219.099i) q^{42} +(-194.601 - 27.9794i) q^{43} +(-152.276 + 179.542i) q^{44} -9.41609 q^{45} +(-242.506 + 196.283i) q^{46} -111.728i q^{47} +(130.146 - 301.727i) q^{48} +(6.51572 - 45.3179i) q^{49} +(126.681 + 229.107i) q^{50} +(-97.4451 - 331.868i) q^{51} +(195.250 + 220.569i) q^{52} +(-165.182 - 190.630i) q^{53} +(353.286 + 190.488i) q^{54} +(-122.287 + 416.473i) q^{55} +(339.367 - 192.366i) q^{56} +(223.797 - 348.235i) q^{57} +(136.309 + 359.632i) q^{58} +(-317.617 + 366.549i) q^{59} +(-6.41404 - 605.816i) q^{60} +(76.8738 + 534.669i) q^{61} +(39.3924 + 512.628i) q^{62} +(4.57193 + 10.0111i) q^{63} +(-472.251 - 197.796i) q^{64} +(494.035 + 225.618i) q^{65} +(300.581 - 303.780i) q^{66} +(-201.714 - 313.874i) q^{67} +(-515.457 + 157.298i) q^{68} +(466.219 - 321.531i) q^{69} +(427.967 - 578.050i) q^{70} +(-495.207 - 770.557i) q^{71} +(6.72054 - 12.7864i) q^{72} +(-90.8848 + 199.010i) q^{73} +(-128.520 + 350.225i) q^{74} +(-197.419 - 432.287i) q^{75} +(-546.257 - 342.941i) q^{76} +(502.168 - 72.2009i) q^{77} +(-322.713 - 426.371i) q^{78} +(-138.703 + 160.072i) q^{79} +(-943.781 + 19.9867i) q^{80} +(-598.431 - 384.588i) q^{81} +(72.6560 + 325.684i) q^{82} +(249.387 - 849.333i) q^{83} +(-640.986 + 300.970i) q^{84} +(-750.937 + 650.691i) q^{85} +(115.324 - 543.986i) q^{86} +(-196.691 - 669.869i) q^{87} +(-478.261 - 463.307i) q^{88} +(394.947 + 56.7848i) q^{89} +(1.75931 - 26.5745i) q^{90} -634.803i q^{91} +(-508.650 - 721.085i) q^{92} -933.300i q^{93} +(315.324 + 20.8753i) q^{94} +(-1177.08 - 169.238i) q^{95} +(827.233 + 423.679i) q^{96} +(463.485 + 1578.49i) q^{97} +(126.681 + 26.8562i) q^{98} +(14.1976 - 12.3023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 700 q - 7 q^{2} - 18 q^{3} - 11 q^{4} + 10 q^{6} - 40 q^{8} - 612 q^{9} - 11 q^{10} - 22 q^{11} + 6 q^{12} - 11 q^{14} - 27 q^{16} - 22 q^{17} + 244 q^{18} - 22 q^{19} - 11 q^{20} - 194 q^{24} - 1568 q^{25}+ \cdots - 22 q^{99}+O(q^{100}) $ 700 * q - 7 * q^2 - 18 * q^3 - 11 * q^4 + 10 * q^6 - 40 * q^8 - 612 * q^9 - 11 * q^10 - 22 * q^11 + 6 * q^12 - 11 * q^14 - 27 * q^16 - 22 * q^17 + 244 * q^18 - 22 * q^19 - 11 * q^20 - 194 * q^24 - 1568 * q^25 + 380 * q^26 + 222 * q^27 - 11 * q^28 - 11 * q^30 - 427 * q^32 - 22 * q^33 + 1903 * q^34 + 482 * q^35 - 1329 * q^36 + 594 * q^38 + 1309 * q^40 - 18 * q^41 - 3641 * q^42 - 22 * q^43 + 3300 * q^44 - 2727 * q^46 + 3204 * q^48 - 2860 * q^49 - 80 * q^50 - 22 * q^51 + 934 * q^52 + 2088 * q^54 - 3586 * q^56 - 22 * q^57 + 6159 * q^58 + 1002 * q^59 - 3641 * q^60 - 618 * q^62 + 1666 * q^64 - 22 * q^65 + 286 * q^66 - 22 * q^67 - 1474 * q^70 + 89 * q^72 - 18 * q^73 + 2354 * q^74 + 590 * q^75 + 8184 * q^76 + 10268 * q^78 + 4048 * q^80 - 5516 * q^81 - 4052 * q^82 - 22 * q^83 - 5401 * q^84 - 6721 * q^86 - 6963 * q^88 - 22 * q^89 - 18700 * q^90 - 4776 * q^92 - 8575 * q^94 - 5643 * q^96 - 22 * q^97 - 3995 * q^98 - 22 * q^99

Character values

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

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	−0.186841	+	2.82225i	−0.0660582	+	0.997816i
$2$	−0.186841	+	2.82225i	−0.0660582	+	0.997816i
$3$	0.730695	−	5.08210i	0.140622	−	0.978050i	−0.790271	−	0.612758i	$-0.790060\pi$
$3$	0.730695	−	5.08210i	0.140622	−	0.978050i	0.930893	−	0.365292i	$-0.119031\pi$
$4$	−7.93018	−	1.05462i	−0.991273	−	0.131828i
$5$	−14.1524	+	4.15552i	−1.26583	+	0.371681i	−0.844662	−	0.535301i	$-0.820198\pi$
$5$	−14.1524	+	4.15552i	−1.26583	+	0.371681i	−0.421169	+	0.906982i	$0.638380\pi$
$6$	14.2064	+	3.01175i	0.966624	+	0.204923i
$7$	11.2898	+	13.0291i	0.609590	+	0.703505i	0.973696	−	0.227853i	$-0.0731706\pi$
$7$	11.2898	+	13.0291i	0.609590	+	0.703505i	−0.364105	+	0.931358i	$0.618625\pi$
$8$	4.45809	−	22.1839i	0.197021	−	0.980399i
$9$	0.612524	+	0.179853i	0.0226861	+	0.00666124i
$10$	−9.08368	−	40.7181i	−0.287251	−	1.28762i
$11$	15.9098	−	24.7561i	0.436090	−	0.678569i	−0.551756	−	0.834006i	$-0.686042\pi$
$11$	15.9098	−	24.7561i	0.436090	−	0.678569i	0.987846	+	0.155437i	$0.0496784\pi$
$12$	−11.1542	+	39.5313i	−0.268329	+	0.950976i
$13$	−27.8279	−	24.1130i	−0.593698	−	0.514443i	0.305380	−	0.952231i	$-0.401217\pi$
$13$	−27.8279	−	24.1130i	−0.593698	−	0.514443i	−0.899078	+	0.437788i	$0.855762\pi$
$14$	−38.8807	+	29.4282i	−0.742237	+	0.561787i
$15$	10.7777	+	74.9604i	0.185519	+	1.29031i
$16$	61.7755	+	16.7267i	0.965243	+	0.261355i
$17$	61.2777	−	27.9846i	0.874237	−	0.399251i	0.0728121	−	0.997346i	$-0.476803\pi$
$17$	61.2777	−	27.9846i	0.874237	−	0.399251i	0.801425	+	0.598095i	$0.204075\pi$
$18$	−0.622036	+	1.69509i	−0.00814529	+	0.0221965i
$19$	73.3374	+	33.4921i	0.885513	+	0.404400i	0.805640	−	0.592405i	$-0.201821\pi$
$19$	73.3374	+	33.4921i	0.885513	+	0.404400i	0.0798725	+	0.996805i	$0.474549\pi$
$20$	116.614	−	18.0286i	1.30378	−	0.201566i
$21$	74.4645	−	47.8554i	0.773785	−	0.497281i
$22$	66.8954	+	49.5269i	0.648280	+	0.479962i
$23$	74.9087	+	80.9672i	0.679110	+	0.734036i
$23$	74.9087	+	80.9672i	0.679110	+	0.734036i
$24$	−109.483	−	38.8661i	−0.931174	−	0.330563i
$25$	77.8658	−	50.0413i	0.622927	−	0.400331i
$26$	73.2524	−	74.0321i	0.552538	−	0.558418i
$27$	58.9496	−	129.082i	0.420180	−	0.920065i
$28$	−75.7892	−	115.229i	−0.511529	−	0.777726i
$29$	123.688	−	56.4864i	0.792010	−	0.361699i	0.0220221	−	0.999757i	$-0.492990\pi$
$29$	123.688	−	56.4864i	0.792010	−	0.361699i	0.769988	+	0.638059i	$0.220262\pi$
$30$	−213.571	+	16.4116i	−1.29975	+	0.0998780i
$31$	179.925	−	25.8694i	1.04244	−	0.149880i	0.400233	−	0.916414i	$-0.368929\pi$
$31$	179.925	−	25.8694i	1.04244	−	0.149880i	0.642204	+	0.766534i	$0.278020\pi$
$32$	−58.7491	+	171.221i	−0.324546	+	0.945870i
$33$	−114.188	−	98.9444i	−0.602350	−	0.521940i
$34$	67.5304	+	178.170i	0.340628	+	0.898702i
$35$	−213.920	−	137.478i	−1.03312	−	0.663944i
$36$	−4.66775	−	2.07225i	−0.0216100	−	0.00959376i
$37$	126.554	+	37.1597i	0.562309	+	0.165109i	0.550520	−	0.834822i	$-0.314429\pi$
$37$	126.554	+	37.1597i	0.562309	+	0.165109i	0.0117883	+	0.999931i	$0.496248\pi$
$38$	−108.225	+	200.719i	−0.462012	+	0.856865i
$39$	−142.879	+	123.805i	−0.586638	+	0.508324i
$40$	29.0930	+	332.482i	0.115000	+	1.31425i
$41$	113.198	−	33.2381i	0.431186	−	0.126608i	−0.0589355	−	0.998262i	$-0.518771\pi$
$41$	113.198	−	33.2381i	0.431186	−	0.126608i	0.490121	+	0.871654i	$0.336952\pi$
$42$	121.147	+	219.099i	0.445080	+	0.804944i
$43$	−194.601	−	27.9794i	−0.690149	−	0.0992285i	−0.211688	−	0.977337i	$-0.567896\pi$
$43$	−194.601	−	27.9794i	−0.690149	−	0.0992285i	−0.478461	+	0.878109i	$0.658805\pi$
$44$	−152.276	+	179.542i	−0.521738	+	0.615158i
$45$	−9.41609			−0.0311926
$46$	−242.506	+	196.283i	−0.777294	+	0.629138i
$47$		−	111.728i		−	0.346748i	−0.984856	−	0.173374i	$-0.944533\pi$
$47$		−	111.728i		−	0.346748i	0.984856	−	0.173374i	$-0.0554670\pi$
$48$	130.146	−	301.727i	0.391352	−	0.907303i
$49$	6.51572	−	45.3179i	0.0189963	−	0.132122i
$50$	126.681	+	229.107i	0.358307	+	0.648011i
$51$	−97.4451	−	331.868i	−0.267550	−	0.911191i
$52$	195.250	+	220.569i	0.520699	+	0.588219i
$53$	−165.182	−	190.630i	−0.428103	−	0.494057i	0.500186	−	0.865918i	$-0.333265\pi$
$53$	−165.182	−	190.630i	−0.428103	−	0.494057i	−0.928288	+	0.371861i	$0.878720\pi$
$54$	353.286	+	190.488i	0.890300	+	0.480040i
$55$	−122.287	+	416.473i	−0.299804	+	1.02104i
$56$	339.367	−	192.366i	0.809818	−	0.459036i
$57$	223.797	−	348.235i	0.520046	−	0.809208i
$58$	136.309	+	359.632i	0.308590	+	0.814173i
$59$	−317.617	+	366.549i	−0.700850	+	0.808824i	−0.988867	−	0.148801i	$-0.952459\pi$
$59$	−317.617	+	366.549i	−0.700850	+	0.808824i	0.288017	+	0.957625i	$0.407004\pi$
$60$	−6.41404	−	605.816i	−0.0138008	−	1.30351i
$61$	76.8738	+	534.669i	0.161356	+	1.12225i	0.896082	+	0.443889i	$0.146401\pi$
$61$	76.8738	+	534.669i	0.161356	+	1.12225i	−0.734726	+	0.678364i	$0.762689\pi$
$62$	39.3924	+	512.628i	0.0806910	+	1.05006i
$63$	4.57193	+	10.0111i	0.00914301	+	0.0200204i
$64$	−472.251	−	197.796i	−0.922365	−	0.386319i
$65$	494.035	+	225.618i	0.942730	+	0.430531i
$66$	300.581	−	303.780i	0.560590	−	0.566556i
$67$	−201.714	−	313.874i	−0.367811	−	0.572325i	0.607181	−	0.794563i	$-0.292300\pi$
$67$	−201.714	−	313.874i	−0.367811	−	0.572325i	−0.974992	+	0.222238i	$0.928664\pi$
$68$	−515.457	+	157.298i	−0.919240	+	0.280518i
$69$	466.219	−	321.531i	0.813422	−	0.560982i
$70$	427.967	−	578.050i	0.730740	−	0.987002i
$71$	−495.207	−	770.557i	−0.827750	−	1.28800i	−0.955141	−	0.296151i	$-0.904297\pi$
$71$	−495.207	−	770.557i	−0.827750	−	1.28800i	0.127392	−	0.991853i	$-0.459340\pi$
$72$	6.72054	−	12.7864i	0.0110003	−	0.0209290i
$73$	−90.8848	+	199.010i	−0.145716	+	0.319074i	−0.968390	−	0.249439i	$-0.919754\pi$
$73$	−90.8848	+	199.010i	−0.145716	+	0.319074i	0.822674	+	0.568513i	$0.192481\pi$
$74$	−128.520	+	350.225i	−0.201893	+	0.550174i
$75$	−197.419	−	432.287i	−0.303946	−	0.665549i
$76$	−546.257	−	342.941i	−0.824474	−	0.517606i
$77$	502.168	−	72.2009i	0.743213	−	0.106858i
$78$	−322.713	−	426.371i	−0.468462	−	0.618935i
$79$	−138.703	+	160.072i	−0.197536	+	0.227968i	−0.845872	−	0.533386i	$-0.820920\pi$
$79$	−138.703	+	160.072i	−0.197536	+	0.227968i	0.648337	+	0.761354i	$0.275465\pi$
$80$	−943.781	+	19.9867i	−1.31897	+	0.0279323i
$81$	−598.431	−	384.588i	−0.820893	−	0.527556i
$82$	72.6560	+	325.684i	0.0978477	+	0.438608i
$83$	249.387	−	849.333i	0.329804	−	1.12321i	−0.613061	−	0.790035i	$-0.710062\pi$
$83$	249.387	−	849.333i	0.329804	−	1.12321i	0.942865	−	0.333174i	$-0.108120\pi$
$84$	−640.986	+	300.970i	−0.832587	+	0.390935i
$85$	−750.937	+	650.691i	−0.958242	+	0.830322i
$86$	115.324	−	543.986i	0.144602	−	0.682087i
$87$	−196.691	−	669.869i	−0.242385	−	0.825488i
$88$	−478.261	−	463.307i	−0.579349	−	0.561235i
$89$	394.947	+	56.7848i	0.470386	+	0.0676313i	0.373432	−	0.927658i	$-0.378181\pi$
$89$	394.947	+	56.7848i	0.470386	+	0.0676313i	0.0969539	+	0.995289i	$0.469090\pi$
$90$	1.75931	−	26.5745i	0.00206053	−	0.0311245i
$91$		−	634.803i		−	0.731269i
$92$	−508.650	−	721.085i	−0.576417	−	0.817156i
$93$		−	933.300i		−	1.04063i
$94$	315.324	+	20.8753i	0.345991	+	0.0229056i
$95$	−1177.08	−	169.238i	−1.27122	−	0.182773i
$96$	827.233	+	423.679i	0.879470	+	0.450432i
$97$	463.485	+	1578.49i	0.485152	+	1.65228i	0.730554	+	0.682855i	$0.239262\pi$
$97$	463.485	+	1578.49i	0.485152	+	1.65228i	−0.245401	+	0.969422i	$0.578920\pi$
$98$	126.681	+	26.8562i	0.130579	+	0.0276825i
$99$	14.1976	−	12.3023i	0.0144133	−	0.0124892i
$100$	−670.265	+	314.718i	−0.670265	+	0.314718i
$101$	507.560	−	1728.59i	0.500041	−	1.70298i	−0.192233	−	0.981349i	$-0.561573\pi$
$101$	507.560	−	1728.59i	0.500041	−	1.70298i	0.692274	−	0.721634i	$-0.256609\pi$
$102$	954.820	−	213.008i	0.926875	−	0.206774i
$103$	285.432	+	183.436i	0.273053	+	0.175481i	0.670000	−	0.742361i	$-0.266294\pi$
$103$	285.432	+	183.436i	0.273053	+	0.175481i	−0.396947	+	0.917841i	$0.629930\pi$
$104$	−658.981	+	509.834i	−0.621330	+	0.480705i
$105$	−854.988	+	986.709i	−0.794650	+	0.917075i
$106$	568.867	−	430.566i	0.521257	−	0.394531i
$107$	2050.66	−	294.841i	1.85276	−	0.266387i	0.876249	−	0.481858i	$-0.160038\pi$
$107$	2050.66	−	294.841i	1.85276	−	0.266387i	0.976510	+	0.215472i	$0.0691289\pi$
$108$	−603.613	+	961.471i	−0.537803	+	0.856644i
$109$	374.820	+	820.742i	0.329369	+	0.721218i	0.999784	−	0.0207681i	$-0.00661117\pi$
$109$	374.820	+	820.742i	0.329369	+	0.721218i	−0.670415	+	0.741986i	$0.733884\pi$
$110$	−1152.54	−	422.940i	−0.999005	−	0.366598i
$111$	281.322	−	616.009i	0.240558	−	0.526748i
$112$	479.498	+	993.720i	0.404539	+	0.838372i
$113$	833.114	+	1296.35i	0.693564	+	1.07921i	0.992178	+	0.124833i	$0.0398394\pi$
$113$	833.114	+	1296.35i	0.693564	+	1.07921i	−0.298614	+	0.954374i	$0.596524\pi$
$114$	940.992	+	696.676i	0.773087	+	0.572365i
$115$	−1396.60	−	834.597i	−1.13247	−	0.676753i
$116$	−1040.44	+	317.503i	−0.832780	+	0.254133i
$117$	−12.7085	−	19.7748i	−0.0100419	−	0.0156255i
$118$	−975.149	−	964.879i	−0.760760	−	0.752749i
$119$	1056.43	+	482.453i	0.813802	+	0.371651i
$120$	1710.96	+	95.0890i	1.30157	+	0.0723367i
$121$	193.173	+	422.989i	0.145133	+	0.317798i
$122$	−1523.33	+	117.059i	−1.13046	+	0.0868692i
$123$	−86.2055	−	599.572i	−0.0631942	−	0.439525i
$124$	−1454.12	+	15.3954i	−1.05310	+	0.0111496i
$125$	313.349	−	361.624i	0.224214	−	0.258757i
$126$	−29.1082	+	11.0326i	−0.0205806	+	0.00780053i
$127$	−1269.88	+	1975.97i	−0.887270	+	1.38062i	0.0371773	+	0.999309i	$0.488163\pi$
$127$	−1269.88	+	1975.97i	−0.887270	+	1.38062i	−0.924447	+	0.381310i	$0.875473\pi$
$128$	646.464	−	1295.85i	0.446405	−	0.894831i
$129$	−284.389	+	968.538i	−0.194101	+	0.661047i
$130$	−729.056	+	1352.13i	−0.491865	+	0.912231i
$131$	1271.09	+	1466.92i	0.847754	+	0.978360i	0.999950	−	0.00999011i	$-0.00318000\pi$
$131$	1271.09	+	1466.92i	0.847754	+	0.978360i	−0.152196	+	0.988350i	$0.548635\pi$
$132$	801.182	+	905.072i	0.528287	+	0.596791i
$133$	391.591	+	1333.64i	0.255303	+	0.869481i
$134$	923.519	−	510.644i	0.595372	−	0.329201i
$135$	−297.877	+	2071.78i	−0.189905	+	1.32082i
$136$	−347.626	−	1484.14i	−0.219182	−	0.935763i
$137$		−	2667.82i		−	1.66370i	−0.554998	−	0.831852i	$-0.687281\pi$
$137$		−	2667.82i		−	1.66370i	0.554998	−	0.831852i	$-0.312719\pi$
$138$	820.331	+	1375.86i	0.506023	+	0.848703i
$139$	1042.06			0.635873			0.317937	−	0.948112i	$-0.397010\pi$
$139$	1042.06			0.635873			0.317937	+	0.948112i	$0.397010\pi$
$140$	1551.44	+	1315.83i	0.936575	+	0.794344i
$141$	−567.811	−	81.6389i	−0.339137	−	0.0487606i
$142$	2267.23	−	1253.63i	1.33987	−	0.740858i
$143$	−1039.68	+	305.278i	−0.607991	+	0.178522i
$144$	34.8307	+	21.3560i	0.0201566	+	0.0123588i
$145$	−1515.75	+	1313.41i	−0.868114	+	0.752225i
$146$	−544.675	−	293.683i	−0.308751	−	0.166475i
$147$	−225.549	−	66.2271i	−0.126551	−	0.0371586i
$148$	−964.410	−	428.150i	−0.535635	−	0.237796i
$149$	1293.18	+	831.077i	0.711017	+	0.456943i	0.845502	−	0.533973i	$-0.179301\pi$
$149$	1293.18	+	831.077i	0.711017	+	0.456943i	−0.134485	+	0.990916i	$0.542938\pi$
$150$	1256.91	−	476.396i	0.684173	−	0.259317i
$151$	−833.230	−	721.998i	−0.449055	−	0.389108i	0.400765	−	0.916181i	$-0.368744\pi$
$151$	−833.230	−	721.998i	−0.449055	−	0.389108i	−0.849820	+	0.527072i	$0.823290\pi$
$152$	1069.93	−	1477.60i	0.570939	−	0.788481i
$153$	42.5672	−	6.12025i	0.0224925	−	0.00323394i
$154$	109.943	+	1430.73i	0.0575292	+	0.748648i
$155$	−2438.88	+	1113.80i	−1.26384	+	0.577177i
$156$	1263.62	−	831.113i	0.648529	−	0.426553i
$157$	67.0498	−	146.819i	0.0340838	−	0.0746331i	−0.891824	−	0.452382i	$-0.850574\pi$
$157$	67.0498	−	146.819i	0.0340838	−	0.0746331i	0.925908	+	0.377749i	$0.123302\pi$
$158$	−425.847	−	421.363i	−0.214422	−	0.212163i
$159$	−1089.50	+	700.177i	−0.543413	+	0.349230i
$160$	119.929	−	2667.32i	0.0592578	−	1.31794i
$161$	−209.227	+	1890.09i	−0.102419	+	0.925219i
$162$	1197.21	−	1617.06i	0.580630	−	0.784250i
$163$	−1677.49	+	1078.06i	−0.806082	+	0.518037i	−0.877595	−	0.479402i	$-0.840853\pi$
$163$	−1677.49	+	1078.06i	−0.806082	+	0.518037i	0.0715135	+	0.997440i	$0.477217\pi$
$164$	−932.737	+	144.202i	−0.444113	+	0.0686604i
$165$	2027.20	+	925.792i	0.956469	+	0.436805i
$166$	2350.43	+	862.521i	1.09897	+	0.403281i
$167$	175.819	−	80.2940i	0.0814689	−	0.0372056i	−0.374264	−	0.927322i	$-0.622105\pi$
$167$	175.819	−	80.2940i	0.0814689	−	0.0372056i	0.455733	+	0.890117i	$0.349377\pi$
$168$	−729.651	−	1865.26i	−0.335082	−	0.856593i
$169$	−119.711	−	832.606i	−0.0544882	−	0.378974i
$170$	−1696.11	−	2240.91i	−0.765208	−	1.01100i
$171$	38.8973	+	33.7047i	0.0173950	+	0.0150729i
$172$	1513.72	+	427.113i	0.671045	+	0.189343i
$173$	244.370	−	380.248i	0.107394	−	0.167108i	−0.783397	−	0.621522i	$-0.786515\pi$
$173$	244.370	−	380.248i	0.107394	−	0.167108i	0.890791	+	0.454414i	$0.150151\pi$
$174$	1927.29	−	429.953i	0.839696	−	0.187325i
$175$	1531.08	+	449.566i	0.661365	+	0.194194i
$176$	1396.93	−	1263.21i	0.598280	−	0.541010i
$177$	1630.76	+	1881.99i	0.692515	+	0.799205i
$178$	−234.053	+	1104.03i	−0.0985563	+	0.464891i
$179$	−3207.76	+	941.883i	−1.33944	+	0.393294i	−0.871468	−	0.490452i	$-0.836832\pi$
$179$	−3207.76	+	941.883i	−1.33944	+	0.393294i	−0.467968	+	0.883746i	$0.655014\pi$
$180$	74.6713	+	9.93041i	0.0309204	+	0.00411205i
$181$	200.672	−	1395.70i	0.0824079	−	0.573160i	−0.906223	−	0.422799i	$-0.861048\pi$
$181$	200.672	−	1395.70i	0.0824079	−	0.573160i	0.988631	−	0.150360i	$-0.0480434\pi$
$182$	1791.57	+	118.607i	0.729672	+	0.0483063i
$183$	2773.41			1.12031
$184$	2130.12	−	1300.81i	0.853448	−	0.521178i
$185$	−1945.47			−0.773155
$186$	2634.01	+	174.379i	1.03836	+	0.0687422i
$187$	282.126	−	1962.23i	0.110327	−	0.767340i
$188$	−117.831	+	886.021i	−0.0457110	+	0.343722i
$189$	2347.34	−	689.242i	0.903408	−	0.265265i
$190$	697.559	−	3290.39i	0.266349	−	1.25637i
$191$	−2230.95	−	2574.66i	−0.845163	−	0.975370i	0.154758	−	0.987952i	$-0.450540\pi$
$191$	−2230.95	−	2574.66i	−0.845163	−	0.975370i	−0.999921	+	0.0125821i	$0.995995\pi$
$192$	−1350.29	+	2255.50i	−0.507545	+	0.847794i
$193$	3890.53	+	1142.36i	1.45102	+	0.426057i	0.909878	−	0.414875i	$-0.136175\pi$
$193$	3890.53	+	1142.36i	1.45102	+	0.426057i	0.541140	+	0.840932i	$0.317993\pi$
$194$	−4541.48	+	1013.14i	−1.68072	+	0.374946i
$195$	1507.60	−	2345.87i	0.553649	−	0.861495i
$196$	−99.4641	+	352.507i	−0.0362478	+	0.128465i
$197$	−3600.21	−	3119.60i	−1.30205	−	1.12824i	−0.983613	−	0.180293i	$-0.942295\pi$
$197$	−3600.21	−	3119.60i	−1.30205	−	1.12824i	−0.318441	−	0.947943i	$-0.603159\pi$
$198$	32.0675	+	42.3678i	0.0115098	+	0.0152068i
$199$	−445.341	−	3097.41i	−0.158640	−	1.10337i	−0.901143	−	0.433522i	$-0.857271\pi$
$199$	−445.341	−	3097.41i	−0.158640	−	1.10337i	0.742503	−	0.669843i	$-0.233639\pi$
$200$	−762.979	−	1950.46i	−0.269754	−	0.689590i
$201$	−1742.53	+	795.786i	−0.611485	+	0.279256i
$202$	4783.69	+	1755.43i	1.66623	+	0.611445i
$203$	2132.38	+	973.823i	0.737258	+	0.336695i
$204$	422.763	+	2734.54i	0.145095	+	0.938510i
$205$	−1463.91	+	940.798i	−0.498751	+	0.320528i
$206$	−571.033	+	771.287i	−0.193135	+	0.260865i
$207$	31.3212	+	63.0670i	0.0105168	+	0.0211761i
$208$	−1315.75	−	1955.07i	−0.438611	−	0.651728i
$209$	1995.92	−	1282.70i	0.660577	−	0.424527i
$210$	−2624.99	−	2597.35i	−0.862579	−	0.853495i
$211$	−1805.00	+	3952.40i	−0.588917	+	1.28955i	0.347177	+	0.937799i	$0.387140\pi$
$211$	−1805.00	+	3952.40i	−0.588917	+	1.28955i	−0.936094	+	0.351749i	$0.885587\pi$
$212$	1108.88	+	1685.93i	0.359236	+	0.546181i
$213$	−4277.89	+	1953.65i	−1.37613	+	0.628458i
$214$	448.967	+	5842.57i	0.143415	+	1.86631i
$215$	2870.35	−	412.694i	0.910494	−	0.130909i
$216$	−2600.73	−	1883.19i	−0.819247	−	0.593217i
$217$	2368.37	+	2052.20i	0.740901	+	0.641994i
$218$	−2386.37	+	904.488i	−0.741400	+	0.281008i
$219$	944.979	+	607.301i	0.291579	+	0.187386i
$220$	1408.98	−	3173.74i	0.431789	−	0.972606i
$221$	−2380.03	−	698.839i	−0.724425	−	0.212710i
$222$	1685.97	+	909.056i	0.509706	+	0.274828i
$223$	−279.839	+	242.482i	−0.0840332	+	0.0728152i	−0.695864	−	0.718173i	$-0.744979\pi$
$223$	−279.839	+	242.482i	−0.0840332	+	0.0728152i	0.611831	+	0.790988i	$0.290433\pi$
$224$	−2894.11	+	1167.60i	−0.863264	+	0.348274i
$225$	56.6948	−	16.6471i	0.0167985	−	0.00493248i
$226$	−3814.28	+	2109.04i	−1.12267	+	0.620759i
$227$	−3527.06	−	507.115i	−1.03127	−	0.148275i	−0.394158	−	0.919043i	$-0.628964\pi$
$227$	−3527.06	−	507.115i	−1.03127	−	0.148275i	−0.637116	+	0.770768i	$0.719873\pi$
$228$	−2142.01	+	2525.55i	−0.622184	+	0.733589i
$229$	218.488			0.0630485			0.0315242	−	0.999503i	$-0.489964\pi$
$229$	218.488			0.0630485			0.0315242	+	0.999503i	$0.489964\pi$
$230$	2616.38	−	3785.62i	0.750083	−	1.08529i
$231$		−	2604.82i		−	0.741926i
$232$	−701.677	−	2995.70i	−0.198566	−	0.847748i
$233$	878.388	−	6109.32i	0.246975	−	1.71775i	−0.368532	−	0.929615i	$-0.620139\pi$
$233$	878.388	−	6109.32i	0.246975	−	1.71775i	0.615506	−	0.788132i	$-0.288952\pi$
$234$	58.1838	−	32.1717i	0.0162547	−	0.00898775i
$235$	464.287	+	1581.22i	0.128880	+	0.438925i
$236$	2905.33	−	2571.83i	0.801359	−	0.709374i
$237$	712.151	+	821.866i	0.195186	+	0.225257i
$238$	−1558.99	+	2891.35i	−0.424597	+	0.787473i
$239$	−1291.82	+	4399.54i	−0.349627	+	1.19072i	0.577630	+	0.816298i	$0.303978\pi$
$239$	−1291.82	+	4399.54i	−0.349627	+	1.19072i	−0.927258	+	0.374423i	$0.877841\pi$
$240$	−588.042	+	4810.99i	−0.158158	+	1.29395i
$241$	3325.76	−	5174.99i	0.888926	−	1.38320i	−0.0344942	−	0.999405i	$-0.510982\pi$
$241$	3325.76	−	5174.99i	0.888926	−	1.38320i	0.923420	−	0.383791i	$-0.125382\pi$
$242$	−1229.87	+	466.150i	−0.326691	+	0.123823i
$243$	117.277	−	135.345i	0.0309603	−	0.0357301i
$244$	−45.7494	−	4321.10i	−0.0120033	−	1.13373i
$245$	96.1062	+	668.434i	0.0250612	+	0.174305i
$246$	1708.25	−	131.269i	0.442740	−	0.0340219i
$247$	−1233.23	−	2700.40i	−0.317687	−	0.695637i
$248$	228.240	−	4106.77i	0.0584404	−	1.05153i
$249$	−4134.17	−	1888.01i	−1.05218	−	0.480513i
$250$	962.046	+	951.915i	0.243381	+	0.240817i
$251$	2256.21	+	3510.74i	0.567375	+	0.882852i	0.999823	−	0.0188065i	$-0.00598665\pi$
$251$	2256.21	+	3510.74i	0.567375	+	0.882852i	−0.432449	+	0.901659i	$0.642350\pi$
$252$	−25.6983	−	84.2118i	−0.00642397	−	0.0210510i
$253$	3196.22	−	566.277i	0.794247	−	0.140718i
$254$	−5339.40	−	3953.10i	−1.31899	−	0.976533i
$255$	2758.17	+	4291.79i	0.677346	+	1.05397i
$256$	3536.44	+	2066.60i	0.863388	+	0.504541i
$257$	−2947.06	+	6453.15i	−0.715301	+	1.56629i	0.105074	+	0.994464i	$0.466492\pi$
$257$	−2947.06	+	6453.15i	−0.715301	+	1.56629i	−0.820375	+	0.571826i	$0.806235\pi$
$258$	−2680.32	−	983.578i	−0.646781	−	0.237344i
$259$	944.613	+	2068.41i	0.226623	+	0.496235i
$260$	−3679.84	−	2310.21i	−0.877747	−	0.551051i
$261$	85.9212	−	12.3536i	0.0203770	−	0.00292977i
$262$	−4377.50	+	3313.26i	−1.03222	+	0.781274i
$263$	−350.045	+	403.974i	−0.0820712	+	0.0947152i	−0.795300	−	0.606216i	$-0.792687\pi$
$263$	−350.045	+	403.974i	−0.0820712	+	0.0947152i	0.713229	+	0.700931i	$0.247232\pi$
$264$	−2704.03	+	2092.03i	−0.630385	+	0.487711i
$265$	3129.89	+	2011.46i	0.725537	+	0.466275i
$266$	−3837.02	+	855.990i	−0.884447	+	0.197309i
$267$	577.172	−	1965.67i	0.132293	−	0.450550i
$268$	1268.61	+	2701.81i	0.289153	+	0.615818i
$269$	−2037.07	+	1765.13i	−0.461718	+	0.400081i	−0.854418	−	0.519586i	$-0.826086\pi$
$269$	−2037.07	+	1765.13i	−0.461718	+	0.400081i	0.392701	+	0.919666i	$0.371541\pi$
$270$	−5791.43	−	1227.78i	−1.30539	−	0.276741i
$271$	1575.09	+	5364.28i	0.353063	+	1.20242i	0.924309	+	0.381644i	$0.124642\pi$
$271$	1575.09	+	5364.28i	0.353063	+	1.20242i	−0.571246	+	0.820779i	$0.693540\pi$
$272$	4253.56	−	703.791i	0.948197	−	0.156888i
$273$	−3226.13	−	463.848i	−0.715217	−	0.102833i
$274$	7529.26	+	498.458i	1.66007	+	0.109901i
$275$		−	2723.81i		−	0.597279i
$276$	−4036.29	+	2058.11i	−0.880276	+	0.448854i
$277$			723.925i			0.157027i	0.996913	+	0.0785135i	$0.0250174\pi$
$277$			723.925i			0.157027i	−0.996913	+	0.0785135i	$0.974983\pi$
$278$	−194.699	+	2940.95i	−0.0420046	+	0.634484i
$279$	114.861	+	16.5146i	0.0246472	+	0.00354373i
$280$	−4003.48	+	4132.70i	−0.854477	+	0.882056i
$281$	−1007.40	−	3430.88i	−0.213866	−	0.728359i	−0.994626	−	0.103529i	$-0.966986\pi$
$281$	−1007.40	−	3430.88i	−0.213866	−	0.728359i	0.780761	−	0.624830i	$-0.214832\pi$
$282$	336.496	−	1587.25i	0.0710568	−	0.335175i
$283$	−5195.40	+	4501.84i	−1.09129	+	0.945606i	−0.998744	−	0.0501030i	$-0.984045\pi$
$283$	−5195.40	+	4501.84i	−1.09129	+	0.945606i	−0.0925430	+	0.995709i	$0.529500\pi$
$284$	3114.43	+	6632.91i	0.650731	+	1.38588i
$285$	−1720.17	+	5858.36i	−0.357523	+	1.21761i
$286$	−667.317	−	2991.28i	−0.137969	−	0.618455i
$287$	1711.05	+	1099.62i	0.351916	+	0.226163i
$288$	−66.7799	+	94.3107i	−0.0136633	+	0.0192962i
$289$	−245.507	+	283.330i	−0.0499709	+	0.0576695i
$290$	−3423.56	−	4523.23i	−0.693236	−	0.915908i
$291$	8360.68	−	1202.08i	1.68423	−	0.242156i
$292$	930.614	−	1482.34i	0.186507	−	0.297079i
$293$	−3482.31	−	7625.20i	−0.694331	−	1.52037i	−0.846713	−	0.532050i	$-0.821422\pi$
$293$	−3482.31	−	7625.20i	−0.694331	−	1.52037i	0.152382	−	0.988322i	$-0.451306\pi$
$294$	229.051	−	624.181i	0.0454372	−	0.123820i
$295$	2971.84	−	6507.42i	0.586533	−	1.28433i
$296$	1388.54	−	2641.81i	0.272659	−	0.518757i
$297$	−2257.69	−	3513.03i	−0.441092	−	0.686352i
$298$	−2587.13	+	3494.40i	−0.502913	+	0.679279i
$299$	−132.188	−	4059.43i	−0.0255673	−	0.785159i
$300$	1109.67	+	3636.31i	0.213555	+	0.699809i
$301$	−1832.46	−	2851.36i	−0.350901	−	0.546012i
$302$	2193.34	−	2216.68i	0.417922	−	0.422370i
$303$	−8414.00	−	3842.55i	−1.59529	−	0.728543i
$304$	3970.24	+	3295.68i	0.749043	+	0.621777i
$305$	−3309.78	−	7247.41i	−0.621369	−	1.36061i
$306$	9.31956	+	121.279i	0.00174106	+	0.0226570i
$307$	−211.652	−	1472.07i	−0.0393474	−	0.273667i	0.960644	−	0.277782i	$-0.0895992\pi$
$307$	−211.652	−	1472.07i	−0.0393474	−	0.273667i	−0.999992	+	0.00411498i	$0.998690\pi$
$308$	−4058.43	+	42.9684i	−0.750813	+	0.00794920i
$309$	1140.80	−	1316.56i	0.210026	−	0.242383i
$310$	−2687.73	−	7091.22i	−0.492429	−	1.29921i
$311$	−300.918	+	468.238i	−0.0548666	+	0.0853740i	−0.867603	−	0.497257i	$-0.834340\pi$
$311$	−300.918	+	468.238i	−0.0548666	+	0.0853740i	0.812737	+	0.582631i	$0.197977\pi$
$312$	2109.51	+	3721.54i	0.382781	+	0.675290i
$313$	−77.2003	+	262.920i	−0.0139413	+	0.0474796i	−0.966170	−	0.257907i	$-0.916967\pi$
$313$	−77.2003	+	262.920i	−0.0139413	+	0.0474796i	0.952229	+	0.305386i	$0.0987855\pi$
$314$	401.831	+	216.663i	0.0722185	+	0.0389395i
$315$	−106.305	−	122.683i	−0.0190147	−	0.0219441i
$316$	1268.76	−	1123.12i	0.225864	−	0.199938i
$317$	2371.24	+	8075.71i	0.420133	+	1.43084i	0.849441	+	0.527684i	$0.176940\pi$
$317$	2371.24	+	8075.71i	0.420133	+	1.43084i	−0.429307	+	0.903158i	$0.641242\pi$
$318$	−1772.51	−	3205.65i	−0.312571	−	0.565296i
$319$	569.467	−	3960.73i	0.0999499	−	0.695166i
$320$	7505.44	+	836.835i	1.31115	+	0.146189i
$321$		−	10637.1i		−	1.84955i
$322$	−5295.22	−	943.638i	−0.916432	−	0.163313i
$323$	5431.21			0.935606
$324$	4340.07	+	3680.97i	0.744182	+	0.631168i
$325$	−3373.49	−	485.035i	−0.575778	−	0.0827843i
$326$	−2729.13	−	4935.73i	−0.463657	−	0.838542i
$327$	4444.97	−	1305.16i	0.751704	−	0.220720i
$328$	−232.701	−	2659.36i	−0.0391731	−	0.447679i
$329$	1455.71	−	1261.38i	0.243939	−	0.211374i
$330$	−2991.58	+	5548.29i	−0.499033	+	0.925525i
$331$	−4973.12	−	1460.24i	−0.825823	−	0.242484i	−0.158602	−	0.987343i	$-0.550699\pi$
$331$	−4973.12	−	1460.24i	−0.825823	−	0.242484i	−0.667222	+	0.744859i	$0.732517\pi$
$332$	−2873.41	+	6472.35i	−0.474996	+	1.06993i
$333$	70.8344	+	45.5225i	0.0116568	+	0.00749134i
$334$	193.759	+	511.208i	0.0317427	+	0.0837487i
$335$	4159.06	+	3603.84i	0.678309	+	0.587758i
$336$	5400.55	−	1710.75i	0.876857	−	0.277765i
$337$	−5562.32	+	799.740i	−0.899106	+	0.129272i	−0.576343	−	0.817208i	$-0.695521\pi$
$337$	−5562.32	+	799.740i	−0.899106	+	0.129272i	−0.322763	+	0.946480i	$0.604612\pi$
$338$	2372.19	−	182.289i	0.381746	−	0.0293349i
$339$	7196.93	−	3286.73i	1.15305	−	0.526580i
$340$	6641.30	−	4368.14i	1.05934	−	0.696752i
$341$	2222.15	−	4865.83i	0.352892	−	0.772726i
$342$	−102.391	+	103.480i	−0.0161890	+	0.0163613i
$343$	5638.60	−	3623.71i	0.887626	−	0.570443i
$344$	−1488.24	+	4192.28i	−0.233258	+	0.657072i
$345$	−5261.99	+	6487.82i	−0.821148	+	1.01244i
$346$	1027.50	+	760.720i	0.159649	+	0.118198i
$347$	307.321	−	197.503i	0.0475443	−	0.0305549i	−0.516653	−	0.856195i	$-0.672822\pi$
$347$	307.321	−	197.503i	0.0475443	−	0.0305549i	0.564197	+	0.825640i	$0.309186\pi$
$348$	853.338	+	5519.61i	0.131448	+	0.850237i
$349$	5118.38	+	2337.49i	0.785045	+	0.358518i	0.767270	−	0.641324i	$-0.221615\pi$
$349$	5118.38	+	2337.49i	0.785045	+	0.358518i	0.0177747	+	0.999842i	$0.494342\pi$
$350$	−1554.85	+	4237.09i	−0.237459	+	0.647092i
$351$	−4753.00	+	2170.62i	−0.722781	+	0.330083i
$352$	3304.08	+	4178.49i	0.500307	+	0.632711i
$353$	−392.586	−	2730.49i	−0.0591933	−	0.411698i	−0.997777	−	0.0666458i	$-0.978770\pi$
$353$	−392.586	−	2730.49i	−0.0591933	−	0.411698i	0.938583	−	0.345052i	$-0.112139\pi$
$354$	−5616.15	+	4250.77i	−0.843206	+	0.638208i
$355$	10210.4	+	8847.40i	1.52652	+	1.32274i
$356$	−3072.12	−	866.834i	−0.457365	−	0.129051i
$357$	3223.80	−	5016.33i	0.477932	−	0.743676i
$358$	−2058.89	−	9229.07i	−0.303954	−	1.36249i
$359$	3320.40	+	974.958i	0.488145	+	0.143332i	0.516538	−	0.856265i	$-0.327221\pi$
$359$	3320.40	+	974.958i	0.488145	+	0.143332i	−0.0283925	+	0.999597i	$0.509039\pi$
$360$	−41.9777	+	208.886i	−0.00614561	+	0.0305812i
$361$	−235.038	−	271.248i	−0.0342671	−	0.0395463i
$362$	3901.53	+	827.121i	0.566464	+	0.120090i
$363$	2290.82	−	672.646i	0.331231	−	0.0972582i
$364$	−669.478	+	5034.10i	−0.0964015	+	0.724887i
$365$	459.249	−	3194.15i	0.0658581	−	0.458053i
$366$	−518.186	+	7827.26i	−0.0740056	+	1.11786i
$367$	−993.018			−0.141240			−0.0706200	−	0.997503i	$-0.522498\pi$
$367$	−993.018			−0.141240			−0.0706200	+	0.997503i	$0.522498\pi$
$368$	3273.21	+	6254.77i	0.463663	+	0.886012i
$369$	75.3148			0.0106253
$370$	363.493	−	5490.60i	0.0510732	−	0.771466i
$371$	618.870	−	4304.33i	0.0866041	−	0.602345i
$372$	−984.279	+	7401.24i	−0.137184	+	1.03155i
$373$	−6033.36	+	1771.55i	−0.837521	+	0.245918i	−0.672245	−	0.740329i	$-0.734670\pi$
$373$	−6033.36	+	1771.55i	−0.837521	+	0.245918i	−0.165276	+	0.986247i	$0.552852\pi$
$374$	5485.19	+	1162.85i	0.758376	+	0.160775i
$375$	−1608.84	−	1856.71i	−0.221548	−	0.255680i
$376$	−2478.56	−	498.092i	−0.339952	−	0.0683169i
$377$	−4804.04	−	1410.59i	−0.656288	−	0.192704i
$378$	1506.63	+	6753.57i	0.205008	+	0.918958i
$379$	−655.064	+	1019.30i	−0.0887820	+	0.138148i	−0.882804	−	0.469742i	$-0.844347\pi$
$379$	−655.064	+	1019.30i	−0.0887820	+	0.138148i	0.794022	+	0.607889i	$0.207983\pi$
$380$	9155.96	+	2583.46i	1.23603	+	0.348760i
$381$	9114.15	+	7897.46i	1.22554	+	1.06194i
$382$	7683.16	−	5815.26i	1.02907	−	0.778886i
$383$	−1320.88	−	9186.95i	−0.176225	−	1.22567i	−0.865403	−	0.501077i	$-0.832937\pi$
$383$	−1320.88	−	9186.95i	−0.176225	−	1.22567i	0.689178	−	0.724592i	$-0.257972\pi$
$384$	−6113.28	−	4232.27i	−0.812415	−	0.562440i
$385$	−6806.86	+	3108.59i	−0.901064	+	0.411502i
$386$	−3950.94	+	10766.6i	−0.520978	+	1.41970i
$387$	−114.166	−	52.1378i	−0.0149958	−	0.00684836i
$388$	−2010.81	−	13006.5i	−0.263102	−	1.70181i
$389$	−10786.1	+	6931.83i	−1.40586	+	0.903490i	−0.999946	−	0.0104215i	$-0.996683\pi$
$389$	−10786.1	+	6931.83i	−1.40586	+	0.903490i	−0.405913	+	0.913912i	$0.633046\pi$
$390$	6338.96	+	4693.13i	0.823040	+	0.609349i
$391$	6856.07	+	2865.20i	0.886768	+	0.370586i
$392$	−976.279	−	346.575i	−0.125790	−	0.0446548i
$393$	8383.80	−	5387.94i	1.07610	−	0.691566i
$394$	9476.96	−	9577.83i	1.21178	−	1.22468i
$395$	1297.80	−	2841.79i	0.165315	−	0.361990i
$396$	−125.564	+	82.5864i	−0.0159339	+	0.0104801i
$397$	−1108.54	+	506.254i	−0.140141	+	0.0640004i	−0.484251	−	0.874929i	$-0.660908\pi$
$397$	−1108.54	+	506.254i	−0.140141	+	0.0640004i	0.344110	+	0.938929i	$0.388181\pi$
$398$	8824.88	−	678.139i	1.11143	−	0.0854072i
$399$	7063.80	−	1015.62i	0.886297	−	0.127430i
$400$	5647.23	−	1788.89i	0.705904	−	0.223612i
$401$	5355.80	+	4640.83i	0.666973	+	0.577935i	0.921143	−	0.389224i	$-0.127257\pi$
$401$	5355.80	+	4640.83i	0.666973	+	0.577935i	−0.254170	+	0.967159i	$0.581802\pi$
$402$	−1920.33	−	5066.54i	−0.238252	−	0.628597i
$403$	−5630.74	−	3618.66i	−0.695998	−	0.447291i
$404$	−5848.06	+	13172.8i	−0.720178	+	1.62220i
$405$	10067.4	+	2956.06i	1.23519	+	0.362686i
$406$	−3146.79	+	5836.15i	−0.384661	+	0.713407i
$407$	2933.39	−	2541.80i	0.357255	−	0.309563i
$408$	−7796.54	+	682.218i	−0.946044	+	0.0827815i
$409$	6855.64	−	2013.00i	0.828826	−	0.243365i	0.160313	−	0.987066i	$-0.448750\pi$
$409$	6855.64	−	2013.00i	0.828826	−	0.243365i	0.668512	+	0.743701i	$0.266931\pi$
$410$	−2381.65	−	4307.30i	−0.286881	−	0.518835i
$411$	−13558.1	−	1949.36i	−1.62719	−	0.233954i
$412$	−2070.07	−	1755.70i	−0.247537	−	0.209945i
$413$	−8361.62			−0.996243
$414$	−183.843	+	76.6127i	−0.0218246	+	0.00909494i
$415$			13056.4i			1.54438i
$416$	5763.52	−	3348.10i	0.679278	−	0.394601i
$417$	761.428	−	5295.85i	0.0894180	−	0.621916i
$418$	3247.18	+	5872.64i	0.379963	+	0.687177i
$419$	109.047	+	371.379i	0.0127143	+	0.0433008i	0.965606	−	0.260010i	$-0.0837260\pi$
$419$	109.047	+	371.379i	0.0127143	+	0.0433008i	−0.952892	+	0.303311i	$0.901908\pi$
$420$	7820.81	−	6923.09i	0.908611	−	0.804315i
$421$	660.484	+	762.239i	0.0764608	+	0.0882405i	0.792691	−	0.609624i	$-0.208679\pi$
$421$	660.484	+	762.239i	0.0764608	+	0.0882405i	−0.716230	+	0.697864i	$0.754134\pi$
$422$	−10817.4	−	5832.64i	−1.24783	−	0.672816i
$423$	20.0946	−	68.4360i	0.00230977	−	0.00786636i
$424$	−4965.31	+	2814.53i	−0.568718	+	0.322372i
$425$	3371.06	−	5245.46i	0.384753	−	0.598688i
$426$	−4714.39	−	12438.3i	−0.536181	−	1.41464i
$427$	−6098.37	+	7037.89i	−0.691149	+	0.797629i
$428$	−16573.1	+	175.467i	−1.87171	+	0.0198166i
$429$	791.763	+	5506.83i	0.0891065	+	0.619749i
$430$	628.427	+	8177.95i	0.0704778	+	0.917153i
$431$	−3049.78	−	6678.09i	−0.340842	−	0.746340i	0.659142	−	0.752019i	$-0.270920\pi$
$431$	−3049.78	−	6678.09i	−0.340842	−	0.746340i	−0.999984	+	0.00567879i	$0.998192\pi$
$432$	5800.75	−	6988.06i	0.646039	−	0.778271i
$433$	−5080.11	−	2320.01i	−0.563821	−	0.257488i	0.113051	−	0.993589i	$-0.463938\pi$
$433$	−5080.11	−	2320.01i	−0.563821	−	0.257488i	−0.676872	+	0.736101i	$0.736665\pi$
$434$	−6234.34	+	6300.69i	−0.689534	+	0.696873i
$435$	5567.31	+	8662.91i	0.613637	+	0.954838i
$436$	−2106.82	−	6903.92i	−0.231418	−	0.758344i
$437$	2781.85	+	8446.77i	0.304517	+	0.924631i
$438$	−1890.52	+	2553.50i	−0.206238	+	0.278564i
$439$	2050.88	+	3191.24i	0.222969	+	0.346946i	0.934658	−	0.355548i	$-0.115706\pi$
$439$	2050.88	+	3191.24i	0.222969	+	0.346946i	−0.711689	+	0.702495i	$0.752070\pi$
$440$	8693.83	+	4569.49i	0.941959	+	0.495095i
$441$	12.1416	−	26.5864i	0.00131105	−	0.00287079i
$442$	2416.98	−	6586.46i	0.260100	−	0.708791i
$443$	2044.16	+	4476.09i	0.219235	+	0.480058i	0.987009	−	0.160662i	$-0.0513631\pi$
$443$	2044.16	+	4476.09i	0.219235	+	0.480058i	−0.767774	+	0.640720i	$0.778636\pi$
$444$	−2880.59	+	4588.38i	−0.307898	+	0.490439i
$445$	−5825.43	+	837.570i	−0.620566	+	0.0892239i
$446$	−632.059	−	835.081i	−0.0671051	−	0.0886597i
$447$	5168.54	−	5964.81i	0.546898	−	0.631154i
$448$	−2754.51	−	8386.07i	−0.290487	−	0.884385i
$449$	1445.21	+	928.782i	0.151902	+	0.0976212i	0.614384	−	0.789007i	$-0.289405\pi$
$449$	1445.21	+	928.782i	0.151902	+	0.0976212i	−0.462482	+	0.886629i	$0.653041\pi$
$450$	36.3894	+	163.117i	0.00381203	+	0.0170876i
$451$	978.119	−	3331.17i	0.102124	−	0.347802i
$452$	−5239.58	−	11158.9i	−0.545242	−	1.16122i
$453$	−4278.10	+	3707.00i	−0.443715	+	0.384481i
$454$	2090.20	−	9859.49i	0.216075	−	1.01923i
$455$	2637.94	+	8984.00i	0.271799	+	0.925663i
$456$	−6727.51	−	6517.15i	−0.690887	−	0.669285i
$457$	−4653.87	−	669.126i	−0.476365	−	0.0684910i	−0.100050	−	0.994982i	$-0.531900\pi$
$457$	−4653.87	−	669.126i	−0.476365	−	0.0684910i	−0.376316	+	0.926491i	$0.622809\pi$
$458$	−40.8225	+	616.628i	−0.00416487	+	0.0629108i
$459$		−	9559.51i		−	0.972113i
$460$	10195.1	+	8091.39i	1.03337	+	0.820137i
$461$			9102.56i			0.919628i	0.888015	+	0.459814i	$0.152084\pi$
$461$			9102.56i			0.919628i	−0.888015	+	0.459814i	$0.847916\pi$
$462$	7351.46	+	486.687i	0.740305	+	0.0490103i
$463$	−11585.9	−	1665.79i	−1.16294	−	0.167205i	−0.466299	−	0.884627i	$-0.654413\pi$
$463$	−11585.9	−	1665.79i	−1.16294	−	0.167205i	−0.696639	+	0.717422i	$0.745322\pi$
$464$	8585.72	−	1420.59i	0.859013	−	0.142132i
$465$	3878.35	+	13208.5i	0.386783	+	1.31726i
$466$	17077.9	+	3620.50i	1.69768	+	0.359907i
$467$	−12248.9	+	10613.7i	−1.21373	+	1.05170i	−0.216576	+	0.976266i	$0.569489\pi$
$467$	−12248.9	+	10613.7i	−1.21373	+	1.05170i	−0.997151	+	0.0754344i	$0.975966\pi$
$468$	79.9256	+	170.220i	0.00789436	+	0.0168129i
$469$	1812.18	−	6171.72i	0.178419	−	0.607641i
$470$	−4549.34	+	1014.90i	−0.446479	+	0.0996038i
$471$	−697.153	−	448.033i	−0.0682019	−	0.0438307i
$472$	6715.52	+	8680.08i	0.654888	+	0.846468i
$473$	−3788.73	+	4372.43i	−0.368301	+	0.425042i
$474$	−2452.57	+	1856.31i	−0.237659	+	0.179880i
$475$	7386.46	−	1062.01i	0.713503	−	0.102586i
$476$	−7868.84	−	4940.07i	−0.757705	−	0.475689i
$477$	−66.8924	−	146.474i	−0.00642095	−	0.0140599i
$478$	−12175.2	−	4467.85i	−1.16503	−	0.427521i
$479$	340.858	−	746.375i	0.0325140	−	0.0711957i	−0.892678	−	0.450695i	$-0.851176\pi$
$479$	340.858	−	746.375i	0.0325140	−	0.0711957i	0.925192	+	0.379499i	$0.123904\pi$
$480$	−13467.9	−	2558.49i	−1.28068	−	0.243289i
$481$	−2625.71	−	4085.69i	−0.248903	−	0.387300i
$482$	13983.7	+	10353.0i	1.32145	+	0.978356i
$483$	9452.75	+	2444.40i	0.890508	+	0.230277i
$484$	−1085.80	−	3558.10i	−0.101972	−	0.334157i
$485$	−13118.9	−	20413.4i	−1.22824	−	1.91118i
$486$	360.066	+	356.274i	0.0336069	+	0.0332529i
$487$	−11944.0	−	5454.64i	−1.11136	−	0.507543i	−0.226790	−	0.973944i	$-0.572823\pi$
$487$	−11944.0	−	5454.64i	−1.11136	−	0.507543i	−0.884574	+	0.466401i	$0.845550\pi$
$488$	12203.8	+	678.241i	1.13205	+	0.0629150i
$489$	4253.06	+	9312.91i	0.393313	+	0.861236i
$490$	−1904.44	+	146.345i	−0.175579	+	0.0134922i
$491$	2785.57	+	19374.0i	0.256030	+	1.78073i	0.560447	+	0.828190i	$0.310629\pi$
$491$	2785.57	+	19374.0i	0.256030	+	1.78073i	−0.304417	+	0.952539i	$0.598461\pi$
$492$	51.3028	+	4845.63i	0.00470104	+	0.444020i
$493$	5998.57	−	6922.72i	0.547996	−	0.632421i
$494$	7851.62	−	2975.94i	0.715104	−	0.271040i
$495$	−149.808	+	233.106i	−0.0136028	+	0.0211663i
$496$	11547.7	+	1411.46i	1.04538	+	0.127775i
$497$	4448.88	−	15151.5i	0.401528	−	1.36748i
$498$	6100.87	−	11314.9i	0.548969	−	1.01814i
$499$	−2462.16	−	2841.49i	−0.220885	−	0.254915i	0.634482	−	0.772938i	$-0.281214\pi$
$499$	−2462.16	−	2841.49i	−0.220885	−	0.254915i	−0.855367	+	0.518023i	$0.826668\pi$
$500$	−2866.29	+	2537.28i	−0.256369	+	0.226941i
$501$	−279.592	−	952.201i	−0.0249326	−	0.0849126i
$502$	−10329.7	+	5711.65i	−0.918403	+	0.507816i
$503$	−1462.47	+	10171.7i	−0.129638	+	0.901655i	0.816374	+	0.577524i	$0.195981\pi$
$503$	−1462.47	+	10171.7i	−0.129638	+	0.901655i	−0.946012	+	0.324131i	$0.894928\pi$
$504$	242.468	−	56.7928i	0.0214294	−	0.00501935i
$505$			26572.9i			2.34154i
$506$	1000.99	+	9126.33i	0.0879437	+	0.801808i
$507$	−4318.86			−0.378318
$508$	12154.2	−	14330.5i	1.06153	−	1.25160i
$509$	11319.2	+	1627.46i	0.985690	+	0.141721i	0.616264	−	0.787539i	$-0.288645\pi$
$509$	11319.2	+	1627.46i	0.985690	+	0.141721i	0.369426	+	0.929260i	$0.379554\pi$
$510$	−12627.8	+	6982.36i	−1.09641	+	0.606243i
$511$	−3618.99	+	1062.63i	−0.313297	+	0.0919922i
$512$	−6493.21	+	9594.58i	−0.560473	+	0.828173i
$513$	8646.42	−	7492.16i	0.744149	−	0.644809i
$514$	−17661.8	−	9523.04i	−1.51562	−	0.817205i
$515$	−4801.83	−	1409.94i	−0.410862	−	0.120640i
$516$	3276.69	−	7380.76i	0.279551	−	0.629690i
$517$	−2765.95	−	1777.57i	−0.235293	−	0.151213i
$518$	−6014.07	+	2279.47i	−0.510122	+	0.193348i
$519$	−1753.90	−	1519.76i	−0.148338	−	0.128536i
$520$	7207.54	−	9953.79i	0.607830	−	0.839428i
$521$	20294.5	−	2917.91i	1.70656	−	0.245367i	0.781154	−	0.624338i	$-0.214631\pi$
$521$	20294.5	−	2917.91i	1.70656	−	0.245367i	0.925408	+	0.378972i	$0.123722\pi$
$522$	18.8114	+	244.799i	0.00157730	+	0.0205260i
$523$	12358.2	−	5643.79i	1.03324	−	0.471866i	0.174707	−	0.984620i	$-0.444102\pi$
$523$	12358.2	−	5643.79i	1.03324	−	0.471866i	0.858535	+	0.512754i	$0.171375\pi$
$524$	−8532.94	−	12973.4i	−0.711380	−	1.08158i
$525$	3403.49	−	7452.60i	0.282934	−	0.619539i
$526$	−1074.71	−	1063.39i	−0.0890869	−	0.0881487i
$527$	10301.5	−	6620.36i	0.851498	−	0.547224i
$528$	−5399.01	−	8022.33i	−0.445003	−	0.661225i
$529$	−944.380	+	12130.3i	−0.0776181	+	0.996983i
$530$	−6261.62	+	8457.50i	−0.513184	+	0.693151i
$531$	−260.473	+	167.396i	−0.0212873	+	0.0136805i
$532$	−1698.91	−	10989.0i	−0.138453	−	0.895549i
$533$	−3951.55	−	1804.61i	−0.321127	−	0.146654i
$534$	5439.76	+	1996.19i	0.440827	+	0.161767i
$535$	−27796.6	+	12694.3i	−2.24627	+	1.02584i
$536$	−7862.21	+	3075.54i	−0.633574	+	0.247841i
$537$	2442.85	+	16990.4i	0.196306	+	1.36534i
$538$	−4601.02	−	6078.90i	−0.368707	−	0.487138i
$539$	−1018.23	−	882.303i	−0.0813698	−	0.0705074i
$540$	4547.17	−	16115.5i	0.362369	−	1.28426i
$541$	11201.3	−	17429.6i	0.890170	−	1.38513i	−0.0324719	−	0.999473i	$-0.510338\pi$
$541$	11201.3	−	17429.6i	0.890170	−	1.38513i	0.922642	−	0.385658i	$-0.126026\pi$
$542$	−15433.6	+	3443.04i	−1.22312	+	0.272862i
$543$	−6946.47	−	2039.67i	−0.548990	−	0.161198i
$544$	1191.54	+	12136.1i	0.0939093	+	0.956490i
$545$	−8715.22	−	10057.9i	−0.684989	−	0.790520i
$546$	1911.87	−	9018.28i	0.149854	−	0.706862i
$547$	−22731.3	+	6674.51i	−1.77682	+	0.521721i	−0.994829	−	0.101568i	$-0.967614\pi$
$547$	−22731.3	+	6674.51i	−1.77682	+	0.521721i	−0.781991	+	0.623289i	$0.785796\pi$
$548$	−2813.54	+	21156.3i	−0.219322	+	1.64918i
$549$	−49.0750	+	341.324i	−0.00381506	+	0.0265343i
$550$	7687.26	+	508.918i	0.595974	+	0.0394551i
$551$	10962.8			0.847606
$552$	−5054.36	−	11776.0i	−0.389725	−	0.908004i
$553$	−3651.52			−0.280793
$554$	−2043.10	−	135.259i	−0.156684	−	0.0103729i
$555$	−1421.54	+	9887.06i	−0.108723	+	0.756184i
$556$	−8263.72	−	1098.98i	−0.630324	−	0.0838257i
$557$	−8016.30	+	2353.80i	−0.609805	+	0.179055i	−0.572032	−	0.820231i	$-0.693845\pi$
$557$	−8016.30	+	2353.80i	−0.609805	+	0.179055i	−0.0377734	+	0.999286i	$0.512026\pi$
$558$	−68.0690	+	321.082i	−0.00516414	+	0.0243593i
$559$	4740.68	+	5471.04i	0.358693	+	0.413954i
$560$	−10915.5	−	12071.0i	−0.823685	−	0.910878i
$561$	−9766.10	−	2867.58i	−0.734982	−	0.215810i
$562$	9871.01	−	2202.10i	0.740896	−	0.165284i
$563$	−6762.97	+	10523.4i	−0.506262	+	0.787759i	−0.996479	−	0.0838415i	$-0.973281\pi$
$563$	−6762.97	+	10523.4i	−0.506262	+	0.787759i	0.490217	+	0.871600i	$0.336917\pi$
$564$	4416.75	+	1246.24i	0.329749	+	0.0930427i
$565$	−17177.6	−	14884.5i	−1.27906	−	1.10831i
$566$	−11734.6	−	15503.8i	−0.871452	−	1.15137i
$567$	−1745.31	−	12138.9i	−0.129270	−	0.899095i
$568$	−19301.6	+	7550.41i	−1.42584	+	0.557761i
$569$	−4359.57	+	1990.95i	−0.321200	+	0.146687i	−0.569489	−	0.821999i	$-0.692859\pi$
$569$	−4359.57	+	1990.95i	−0.321200	+	0.146687i	0.248289	+	0.968686i	$0.420132\pi$
$570$	−16212.4	−	5949.33i	−1.19134	−	0.437175i
$571$	3572.16	+	1631.35i	0.261804	+	0.119562i	0.541993	−	0.840383i	$-0.317670\pi$
$571$	3572.16	+	1631.35i	0.261804	+	0.119562i	−0.280189	+	0.959945i	$0.590397\pi$
$572$	8566.83	−	1324.44i	0.626219	−	0.0968141i
$573$	−14714.8	+	9456.63i	−1.07281	+	0.689453i
$574$	−3423.10	+	4623.54i	−0.248915	+	0.336207i
$575$	9884.53	+	2556.05i	0.716893	+	0.185382i
$576$	−253.691	−	206.091i	−0.0183515	−	0.0149082i
$577$	−979.533	+	629.508i	−0.0706733	+	0.0454190i	−0.575500	−	0.817802i	$-0.695193\pi$
$577$	−979.533	+	629.508i	−0.0706733	+	0.0454190i	0.504827	+	0.863221i	$0.331556\pi$
$578$	−753.758	−	745.820i	−0.0542426	−	0.0536713i
$579$	8648.39	−	18937.3i	0.620751	−	1.35926i
$580$	13405.3	−	8817.01i	0.959701	−	0.631218i
$581$	13881.6	−	6339.49i	0.991229	−	0.452679i
$582$	1830.47	+	23820.5i	0.130370	+	1.69655i
$583$	−7347.27	+	1056.38i	−0.521943	+	0.0750441i
$584$	4009.65	+	2903.38i	0.284110	+	0.205724i
$585$	262.030	+	227.050i	0.0185190	+	0.0160468i
$586$	22170.9	−	8403.26i	1.56292	−	0.592381i
$587$	−2602.52	−	1672.54i	−0.182994	−	0.117603i	0.445937	−	0.895064i	$-0.352871\pi$
$587$	−2602.52	−	1672.54i	−0.182994	−	0.117603i	−0.628931	+	0.777462i	$0.716507\pi$
$588$	1718.80	+	763.061i	0.120548	+	0.0535172i
$589$	14061.7	+	4128.88i	0.983703	+	0.288841i
$590$	17810.3	+	9603.12i	1.24278	+	0.670092i
$591$	−18484.8	+	16017.2i	−1.28657	+	1.11482i
$592$	7196.41	+	4412.40i	0.499612	+	0.306332i
$593$	−3094.32	+	908.575i	−0.214281	+	0.0629186i	−0.387111	−	0.922033i	$-0.626527\pi$
$593$	−3094.32	+	908.575i	−0.214281	+	0.0629186i	0.172830	+	0.984952i	$0.444709\pi$
$594$	10336.5	−	5715.38i	0.713991	−	0.394789i
$595$	−16955.8	−	2437.88i	−1.16827	−	0.167972i
$596$	−9378.69	−	7954.41i	−0.644574	−	0.546687i
$597$	−16066.8			−1.10145
$598$	11481.4	+	385.399i	0.785133	+	0.0263547i
$599$		−	12746.4i		−	0.869455i	−0.900562	−	0.434728i	$-0.856845\pi$
$599$		−	12746.4i		−	0.869455i	0.900562	−	0.434728i	$-0.143155\pi$
$600$	−10469.9	+	2452.34i	−0.712387	+	0.166861i
$601$	−3520.19	+	24483.4i	−0.238921	+	1.66173i	0.418506	+	0.908214i	$0.362554\pi$
$601$	−3520.19	+	24483.4i	−0.238921	+	1.66173i	−0.657427	+	0.753518i	$0.728355\pi$
$602$	8389.63	−	4638.90i	0.567999	−	0.314066i
$603$	−67.1038	−	228.534i	−0.00453180	−	0.0154339i
$604$	5846.23	+	6604.32i	0.393841	+	0.444910i
$605$	−4491.60	−	5183.58i	−0.301834	−	0.348335i
$606$	12416.7	−	23028.5i	0.832333	−	1.54368i
$607$	−108.928	+	370.975i	−0.00728378	+	0.0248063i	−0.963055	−	0.269306i	$-0.913206\pi$
$607$	−108.928	+	370.975i	−0.00728378	+	0.0248063i	0.955771	+	0.294112i	$0.0950239\pi$
$608$	−10043.0	+	10589.3i	−0.669900	+	0.706334i
$609$	6507.18	−	10125.4i	0.432979	−	0.673729i
$610$	21072.4	−	7986.92i	1.39868	−	0.530133i
$611$	−2694.10	+	3109.15i	−0.178382	+	0.205864i
$612$	−344.020	+	3.64230i	−0.0227226	+	0.000240574i
$613$	−2346.21	−	16318.2i	−0.154588	−	1.07518i	−0.908403	−	0.418096i	$-0.862698\pi$
$613$	−2346.21	−	16318.2i	−0.154588	−	1.07518i	0.753815	−	0.657087i	$-0.228211\pi$
$614$	4194.11	−	322.292i	0.275668	−	0.0211835i
$615$	3711.55	+	8127.17i	0.243356	+	0.532876i
$616$	637.012	−	11461.9i	0.0416655	−	0.749698i
$617$	−22230.9	−	10152.5i	−1.45054	−	0.662439i	−0.474544	−	0.880232i	$-0.657387\pi$
$617$	−22230.9	−	10152.5i	−1.45054	−	0.662439i	−0.975995	+	0.217793i	$0.930114\pi$
$618$	3502.51	+	3465.62i	0.227980	+	0.225579i
$619$	219.508	+	341.561i	0.0142533	+	0.0221785i	0.848307	−	0.529505i	$-0.177622\pi$
$619$	219.508	+	341.561i	0.0142533	+	0.0221785i	−0.834054	+	0.551683i	$0.813986\pi$
$620$	20515.4	−	6260.53i	1.32890	−	0.405530i
$621$	14867.2	−	4896.35i	0.960710	−	0.316399i
$622$	−1265.26	−	936.752i	−0.0815632	−	0.0603864i
$623$	3719.01	+	5786.89i	0.239164	+	0.372146i
$624$	−10897.2	+	5258.23i	−0.699101	+	0.337336i
$625$	−7738.22	+	16944.3i	−0.495246	+	1.08444i
$626$	−727.602	−	267.003i	−0.0464550	−	0.0170472i
$627$	−5060.39	−	11080.7i	−0.322317	−	0.705775i
$628$	−686.555	+	1093.59i	−0.0436250	+	0.0694885i
$629$	8794.87	−	1264.51i	0.557511	−	0.0801580i
$630$	366.104	−	277.098i	0.0231523	−	0.0175236i
$631$	11497.4	−	13268.7i	0.725362	−	0.837112i	−0.266579	−	0.963813i	$-0.585893\pi$
$631$	11497.4	−	13268.7i	0.725362	−	0.837112i	0.991941	+	0.126701i	$0.0404389\pi$
$632$	2932.67	+	3790.59i	0.184581	+	0.238578i
$633$	18767.6	+	12061.2i	1.17843	+	0.757330i
$634$	−23234.7	+	5183.37i	−1.45547	+	0.324697i
$635$	9760.64	−	33241.7i	0.609983	−	2.07741i
$636$	9378.33	−	4403.52i	0.584709	−	0.274546i
$637$	−1274.07	+	1103.99i	−0.0792473	+	0.0686681i
$638$	11071.8	+	2347.20i	0.687046	+	0.145653i
$639$	−164.739	−	561.049i	−0.0101987	−	0.0347336i
$640$	−3764.08	+	21025.9i	−0.232482	+	1.29862i
$641$	24006.5	+	3451.61i	1.47925	+	0.212684i	0.834202	−	0.551460i	$-0.185929\pi$
$641$	24006.5	+	3451.61i	1.47925	+	0.212684i	0.645046	+	0.764143i	$0.276838\pi$
$642$	30020.6	+	1987.45i	1.84551	+	0.122178i
$643$			15132.6i			0.928107i	0.885807	+	0.464053i	$0.153605\pi$
$643$			15132.6i			0.928107i	−0.885807	+	0.464053i	$0.846395\pi$
$644$	3652.54	−	14768.1i	0.223494	−	0.903642i
$645$		−	14888.9i		−	0.908917i
$646$	−1014.77	+	15328.2i	−0.0618044	+	0.933562i
$647$	16428.3	+	2362.04i	0.998244	+	0.143526i	0.622019	−	0.783002i	$-0.286313\pi$
$647$	16428.3	+	2362.04i	0.998244	+	0.143526i	0.376225	+	0.926528i	$0.377222\pi$
$648$	−11199.5	+	11561.0i	−0.678949	+	0.700863i
$649$	4021.12	+	13694.7i	0.243209	+	0.828295i
$650$	1999.20	−	9430.21i	0.120638	−	0.569051i
$651$	12160.1	−	10536.7i	0.732089	−	0.634359i
$652$	14439.8	−	6780.08i	0.867338	−	0.407252i
$653$	−6431.41	+	21903.4i	−0.385422	+	1.31263i	0.507203	+	0.861826i	$0.330679\pi$
$653$	−6431.41	+	21903.4i	−0.385422	+	1.31263i	−0.892625	+	0.450800i	$0.851139\pi$
$654$	2852.99	+	12788.7i	0.170582	+	0.764643i
$655$	−24084.8	−	15478.4i	−1.43675	−	0.923344i
$656$	7548.86	−	159.864i	0.449289	−	0.00951470i
$657$	−91.4618	+	105.553i	−0.00543115	+	0.00626788i
$658$	3287.94	+	4344.06i	0.194799	+	0.257369i
$659$	−2095.72	+	301.318i	−0.123881	+	0.0178114i	−0.203976	−	0.978976i	$-0.565387\pi$
$659$	−2095.72	+	301.318i	−0.123881	+	0.0178114i	0.0800955	+	0.996787i	$0.474477\pi$
$660$	−15099.7	−	9479.63i	−0.890538	−	0.559082i
$661$	12270.0	+	26867.6i	0.722009	+	1.58098i	0.811067	+	0.584953i	$0.198887\pi$
$661$	12270.0	+	26867.6i	0.722009	+	1.58098i	−0.0890578	+	0.996026i	$0.528386\pi$
$662$	5050.34	−	13762.6i	0.296506	−	0.808002i
$663$	−5290.64	+	11584.9i	−0.309912	+	0.678612i
$664$	−17729.7	−	9318.77i	−1.03622	−	0.544636i
$665$	−11083.9	−	17246.9i	−0.646340	−	1.00572i
$666$	−141.711	+	191.407i	−0.00824500	+	0.0111364i
$667$	13838.9	+	5783.35i	0.803362	+	0.335730i
$668$	−1478.96	+	451.323i	−0.0856626	+	0.0261410i
$669$	1027.84	+	1599.35i	0.0593999	+	0.0924281i
$670$	−10948.0	+	11064.6i	−0.631282	+	0.638002i
$671$	14459.4	+	6603.39i	0.831891	+	0.379912i
$672$	3819.12	+	15561.3i	0.219235	+	0.893290i
$673$	−5846.38	−	12801.8i	−0.334861	−	0.733243i	0.665047	−	0.746801i	$-0.268411\pi$
$673$	−5846.38	−	12801.8i	−0.334861	−	0.733243i	−0.999908	+	0.0135586i	$0.995684\pi$
$674$	−1217.80	−	15847.7i	−0.0695963	−	0.905681i
$675$	−1869.26	−	13001.0i	−0.106589	−	0.741344i
$676$	71.2426	+	6728.97i	0.00405340	+	0.382850i
$677$	6877.89	−	7937.51i	0.390456	−	0.450610i	−0.526156	−	0.850388i	$-0.676367\pi$
$677$	6877.89	−	7937.51i	0.390456	−	0.450610i	0.916612	+	0.399778i	$0.130913\pi$
$678$	7931.28	+	20925.6i	0.449261	+	1.18532i
$679$	−15333.6	+	23859.5i	−0.866641	+	1.34852i
$680$	11087.1	+	19559.6i	0.625252	+	1.10305i
$681$	−5154.41	+	17554.3i	−0.290040	+	0.987786i
$682$	13317.4	+	7180.60i	0.747727	+	0.403166i
$683$	−10058.5	−	11608.2i	−0.563512	−	0.650328i	0.400465	−	0.916312i	$-0.368849\pi$
$683$	−10058.5	−	11608.2i	−0.563512	−	0.650328i	−0.963977	+	0.265984i	$0.914303\pi$
$684$	−272.917	−	308.306i	−0.0152562	−	0.0172345i
$685$	11086.2	+	37756.1i	0.618368	+	2.10597i
$686$	9173.49	+	16590.6i	0.510562	+	0.923370i
$687$	159.648	−	1110.38i	0.00886602	−	0.0616645i
$688$	−11553.6	−	4983.48i	−0.640228	−	0.276153i
$689$			9287.86i			0.513555i
$690$	−17327.1	−	16062.8i	−0.955987	−	0.886234i
$691$	−3256.24			−0.179267			−0.0896333	−	0.995975i	$-0.528570\pi$
$691$	−3256.24			−0.179267			−0.0896333	+	0.995975i	$0.528570\pi$
$692$	−2338.92	+	2757.72i	−0.128486	+	0.151492i
$693$	320.576	+	46.0919i	0.0175724	+	0.00252653i
$694$	499.983	+	904.239i	0.0273474	+	0.0494588i
$695$	−14747.7	+	4330.31i	−0.804908	+	0.236342i
$696$	−15737.2	+	1377.04i	−0.857063	+	0.0749953i
$697$	6006.39	−	5204.57i	0.326411	−	0.282836i
$698$	−7553.29	+	14008.6i	−0.409594	+	0.759647i
$699$	−30406.3	−	8928.11i	−1.64531	−	0.483107i
$700$	−11667.6	−	5179.85i	−0.629992	−	0.279686i
$701$	28077.9	+	18044.6i	1.51282	+	0.972232i	0.993020	+	0.117946i	$0.0376309\pi$
$701$	28077.9	+	18044.6i	1.51282	+	0.972232i	0.519803	+	0.854286i	$0.326006\pi$
$702$	−5237.98	−	13819.7i	−0.281616	−	0.743007i
$703$	8036.61	+	6963.76i	0.431162	+	0.373604i
$704$	−12410.1	+	8544.22i	−0.664378	+	0.457418i
$705$	8375.15	−	1204.17i	0.447414	−	0.0643284i
$706$	7779.48	−	597.807i	0.414709	−	0.0318679i
$707$	28252.2	−	12902.4i	1.50288	−	0.686341i
$708$	−10947.4	−	16644.4i	−0.581114	−	0.883523i
$709$	3335.79	−	7304.37i	0.176697	−	0.386913i	−0.800474	−	0.599368i	$-0.795419\pi$
$709$	3335.79	−	7304.37i	0.176697	−	0.386913i	0.977171	+	0.212455i	$0.0681459\pi$
$710$	−26877.3	+	27163.3i	−1.42068	+	1.43581i
$711$	−113.749	+	73.1017i	−0.00599986	+	0.00385588i
$712$	3020.42	−	8508.32i	0.158982	−	0.447841i
$713$	15572.5	+	12630.2i	0.817947	+	0.663401i
$714$	13555.0	+	10035.6i	0.710480	+	0.526014i
$715$	13445.4	−	8640.86i	0.703260	−	0.451958i
$716$	26431.4	−	4086.33i	1.37959	−	0.213287i
$717$	21415.0	+	9779.88i	1.11542	+	0.509395i
$718$	−3371.96	+	9188.84i	−0.175265	+	0.477611i
$719$	603.940	−	275.810i	0.0313257	−	0.0143060i	−0.399691	−	0.916650i	$-0.630882\pi$
$719$	603.940	−	275.810i	0.0313257	−	0.0143060i	0.431016	+	0.902344i	$0.358155\pi$
$720$	−581.684	−	157.500i	−0.0301084	−	0.00815233i
$721$	832.458	+	5789.87i	0.0429991	+	0.299065i
$722$	809.445	−	612.656i	0.0417236	−	0.0315799i
$723$	−23869.7	−	20683.2i	−1.22783	−	1.06392i
$724$	−3063.31	+	10856.6i	−0.157247	+	0.557294i
$725$	6804.41	−	10587.9i	0.348565	−	0.542378i
$726$	1470.36	+	6590.94i	0.0751653	+	0.336932i
$727$	4467.06	+	1311.65i	0.227887	+	0.0669137i	0.393682	−	0.919246i	$-0.371201\pi$
$727$	4467.06	+	1311.65i	0.227887	+	0.0669137i	−0.165795	+	0.986160i	$0.553019\pi$
$728$	−14082.4	−	2830.01i	−0.716935	−	0.144076i
$729$	−13179.8	−	15210.3i	−0.669603	−	0.772763i
$730$	8928.87	+	1892.91i	0.452702	+	0.0959724i
$731$	−12707.7	+	3731.32i	−0.642972	+	0.188793i
$732$	−21993.7	−	2924.90i	−1.11053	−	0.147688i
$733$	−1468.43	+	10213.2i	−0.0739943	+	0.514642i	0.918792	+	0.394743i	$0.129166\pi$
$733$	−1468.43	+	10213.2i	−0.0739943	+	0.514642i	−0.992786	+	0.119899i	$0.961743\pi$
$734$	185.536	−	2802.54i	0.00933006	−	0.140932i
$735$	3467.27			0.174003
$736$	−18264.1	+	8069.17i	−0.914705	+	0.404122i
$737$	−10979.5			−0.548761
$738$	−14.0719	+	212.557i	−0.000701887	+	0.0106021i
$739$	3490.98	−	24280.3i	0.173772	−	1.20861i	−0.697052	−	0.717020i	$-0.745505\pi$
$739$	3490.98	−	24280.3i	0.173772	−	1.20861i	0.870825	−	0.491594i	$-0.163586\pi$
$740$	15427.9	+	2051.73i	0.766408	+	0.101923i
$741$	−14624.8	+	4294.23i	−0.725042	+	0.212891i
$742$	12032.3	+	2550.83i	0.595308	+	0.126205i
$743$	−26398.1	−	30465.0i	−1.30344	−	1.50424i	−0.725673	−	0.688040i	$-0.758471\pi$
$743$	−26398.1	−	30465.0i	−1.30344	−	1.50424i	−0.577763	−	0.816205i	$-0.696074\pi$
$744$	−20704.2	−	4160.73i	−1.02023	−	0.205027i
$745$	−21755.2	−	6387.91i	−1.06986	−	0.314141i
$746$	−3872.49	−	17358.6i	−0.190056	−	0.851937i
$747$	305.511	−	475.384i	0.0149639	−	0.0232843i
$748$	−4306.72	+	15263.3i	−0.210521	+	0.746099i
$749$	26993.0	+	23389.6i	1.31683	+	1.14104i
$750$	5540.68	−	4193.65i	0.269756	−	0.204174i
$751$	−343.604	−	2389.82i	−0.0166955	−	0.116119i	0.979769	−	0.200130i	$-0.0641363\pi$
$751$	−343.604	−	2389.82i	−0.0166955	−	0.116119i	−0.996465	+	0.0840101i	$0.973227\pi$
$752$	1868.84	−	6902.04i	0.0906242	−	0.334696i
$753$	19490.5	−	8901.02i	0.943259	−	0.430772i
$754$	4878.64	−	13294.6i	0.235636	−	0.642125i
$755$	14792.5	+	6755.51i	0.713052	+	0.325640i
$756$	−19341.7	+	2990.26i	−0.930493	+	0.143855i
$757$	26205.2	−	16841.1i	1.25818	−	0.808586i	0.270150	−	0.962818i	$-0.412927\pi$
$757$	26205.2	−	16841.1i	1.25818	−	0.808586i	0.988035	+	0.154232i	$0.0492904\pi$
$758$	−2754.33	−	2039.20i	−0.131981	−	0.0977139i
$759$	−542.414	−	16657.3i	−0.0259399	−	0.796602i
$760$	−9001.88	+	25357.7i	−0.429648	+	1.21029i
$761$	32950.3	−	21175.9i	1.56958	−	1.00871i	0.590058	−	0.807361i	$-0.299105\pi$
$761$	32950.3	−	21175.9i	1.56958	−	1.00871i	0.979520	−	0.201346i	$-0.0645316\pi$
$762$	−23991.5	+	24246.8i	−1.14058	+	1.15272i
$763$	−6461.88	+	14149.5i	−0.306600	+	0.671361i
$764$	14976.6	+	22770.3i	0.709206	+	1.07827i
$765$	−576.997	+	263.505i	−0.0272697	+	0.0124537i
$766$	26174.6	−	2011.37i	1.23463	−	0.0948742i
$767$	17677.2	−	2541.60i	0.832187	−	0.119650i
$768$	13086.7	−	16462.5i	0.614878	−	0.773486i
$769$	12250.2	+	10614.9i	0.574454	+	0.497767i	0.892949	−	0.450157i	$-0.148632\pi$
$769$	12250.2	+	10614.9i	0.574454	+	0.497767i	−0.318495	+	0.947924i	$0.603177\pi$
$770$	−7501.42	−	19791.5i	−0.351081	−	0.926279i
$771$	30642.1	+	19692.5i	1.43132	+	0.919855i
$772$	−29647.9	−	13162.2i	−1.38219	−	0.613624i
$773$	−30445.6	−	8939.64i	−1.41663	−	0.415959i	−0.518267	−	0.855219i	$-0.673422\pi$
$773$	−30445.6	−	8939.64i	−1.41663	−	0.415959i	−0.898360	+	0.439260i	$0.855241\pi$
$774$	168.477	−	312.463i	0.00782399	−	0.0145107i
$775$	12715.5	−	11018.0i	0.589360	−	0.510684i
$776$	37083.2	−	3244.88i	1.71548	−	0.150109i
$777$	11202.1	−	3289.23i	0.517211	−	0.151867i
$778$	−17548.1	−	31736.3i	−0.808648	−	1.46247i
$779$	9414.88	+	1353.66i	0.433021	+	0.0622590i
$780$	−14429.6	+	17013.3i	−0.662386	+	0.780990i
$781$	−26954.7			−1.23497
$782$	−9367.30	+	18814.2i	−0.428355	+	0.860351i
$783$		−	19295.7i		−	0.880679i
$784$	1160.53	−	2690.55i	0.0528667	−	0.122565i
$785$	−338.808	+	2356.46i	−0.0154046	+	0.107141i
$786$	13639.7	+	24667.8i	0.618971	+	1.11943i
$787$	−7442.05	−	25345.3i	−0.337078	−	1.14798i	−0.937409	−	0.348231i	$-0.886783\pi$
$787$	−7442.05	−	25345.3i	−0.337078	−	1.14798i	0.600331	−	0.799752i	$-0.295036\pi$
$788$	25260.3	+	28535.9i	1.14196	+	1.29004i
$789$	1797.26	+	2074.15i	0.0810952	+	0.0935888i
$790$	7777.75	+	4193.68i	0.350278	+	0.188866i
$791$	−7484.60	+	25490.2i	−0.336437	+	1.14580i
$792$	−209.619	−	369.803i	−0.00940466	−	0.0165914i
$793$	10753.3	−	16732.4i	0.481538	−	0.749288i
$794$	−1221.65	−	3223.17i	−0.0546031	−	0.144063i
$795$	12509.4	−	14436.6i	0.558067	−	0.644043i
$796$	265.032	+	25032.7i	0.0118013	+	1.11465i
$797$	−141.643	−	985.148i	−0.00629517	−	0.0437839i	0.986432	−	0.164172i	$-0.0524952\pi$
$797$	−141.643	−	985.148i	−0.00629517	−	0.0437839i	−0.992727	+	0.120388i	$0.961586\pi$
$798$	1546.53	+	20125.6i	0.0686048	+	0.892779i
$799$	−3126.66	−	6846.42i	−0.138440	−	0.303140i
$800$	3993.57	+	16272.1i	0.176492	+	0.719133i
$801$	231.702	+	105.815i	0.0102207	+	0.00466764i
$802$	−14098.3	+	14248.3i	−0.620732	+	0.627339i
$803$	3480.76	+	5416.17i	0.152968	+	0.238023i
$804$	14657.8	−	4473.02i	0.642962	−	0.196208i
$805$	−4893.26	−	27618.8i	−0.214242	−	1.20924i
$806$	11264.8	−	15215.2i	0.492290	−	0.664930i
$807$	7482.07	+	11642.3i	0.326371	+	0.507843i
$808$	−36084.2	−	18965.9i	−1.57108	−	0.825764i
$809$	10059.8	−	22027.9i	0.437187	−	0.957307i	−0.554918	−	0.831905i	$-0.687251\pi$
$809$	10059.8	−	22027.9i	0.437187	−	0.957307i	0.992106	−	0.125402i	$-0.0400222\pi$
$810$	−10223.7	+	27860.4i	−0.443488	+	1.20854i
$811$	9688.02	+	21213.8i	0.419473	+	0.918517i	0.994919	+	0.100678i	$0.0321011\pi$
$811$	9688.02	+	21213.8i	0.419473	+	0.918517i	−0.575446	+	0.817840i	$0.695172\pi$
$812$	−15883.1	−	9971.45i	−0.686438	−	0.430947i
$813$	28412.7	−	4085.13i	1.22568	−	0.176226i
$814$	6625.50	+	8753.66i	0.285287	+	0.376924i
$815$	19260.7	−	22228.0i	0.827818	−	0.955353i
$816$	−468.679	−	22131.2i	−0.0201067	−	0.949446i
$817$	−13334.5	−	8569.54i	−0.571008	−	0.366965i
$818$	4400.27	+	19724.4i	0.188083	+	0.843092i
$819$	114.172	−	388.833i	0.00487116	−	0.0165896i
$820$	12601.3	−	5916.82i	0.536652	−	0.251981i
$821$	−19111.2	+	16559.9i	−0.812406	+	0.703954i	−0.958430	−	0.285327i	$-0.907898\pi$
$821$	−19111.2	+	16559.9i	−0.812406	+	0.703954i	0.146024	+	0.989281i	$0.453352\pi$
$822$	8034.80	−	37900.2i	0.340932	−	1.60818i
$823$	6480.37	+	22070.1i	0.274473	+	0.934770i	0.975197	+	0.221338i	$0.0710423\pi$
$823$	6480.37	+	22070.1i	0.274473	+	0.934770i	−0.700724	+	0.713432i	$0.747140\pi$
$824$	5341.81	−	5514.23i	0.225838	−	0.233128i
$825$	−13842.6	−	1990.27i	−0.584169	−	0.0839908i
$826$	1562.29	−	23598.6i	0.0658100	−	0.994067i
$827$			4467.47i			0.187847i	0.995579	+	0.0939233i	$0.0299409\pi$
$827$			4467.47i			0.187847i	−0.995579	+	0.0939233i	$0.970059\pi$
$828$	−181.871	−	533.165i	−0.00763339	−	0.0223777i
$829$		−	20542.6i		−	0.860645i	−0.902675	−	0.430323i	$-0.858400\pi$
$829$		−	20542.6i		−	0.860645i	0.902675	−	0.430323i	$-0.141600\pi$
$830$	−36848.5	−	2439.48i	−1.54100	−	0.102019i
$831$	3679.06	+	528.969i	0.153580	+	0.0220815i
$832$	8372.31	+	16891.6i	0.348867	+	0.703861i
$833$	−868.934	−	2959.32i	−0.0361426	−	0.123090i
$834$	14803.9	+	3138.42i	0.614650	+	0.130305i
$835$	−2154.61	+	1866.98i	−0.0892972	+	0.0773765i
$836$	−17180.8	+	8067.09i	−0.710776	+	0.333740i
$837$	7267.27	−	24750.0i	0.300112	−	1.02209i
$838$	−1068.50	+	238.368i	−0.0440461	+	0.00982613i
$839$	−30789.4	−	19787.1i	−1.26695	−	0.814217i	−0.277727	−	0.960660i	$-0.589581\pi$
$839$	−30789.4	−	19787.1i	−1.26695	−	0.814217i	−0.989219	+	0.146443i	$0.953218\pi$
$840$	18077.4	+	23365.8i	0.742537	+	0.959758i
$841$	−3863.39	+	4458.59i	−0.158407	+	0.182812i
$842$	−2274.63	+	1721.63i	−0.0930986	+	0.0704648i
$843$	−18172.1	+	2612.76i	−0.742446	+	0.106748i
$844$	18482.3	−	29439.7i	0.753776	−	1.20066i
$845$	5154.11	+	11285.9i	0.209830	+	0.459465i
$846$	189.389	+	69.4986i	0.00769660	+	0.00282436i
$847$	−3330.29	+	7292.31i	−0.135100	+	0.295829i
$848$	−7015.58	−	14539.2i	−0.284099	−	0.588772i
$849$	19082.5	+	29693.0i	0.771390	+	1.20031i
$850$	14174.2	+	10494.0i	0.571964	+	0.423461i
$851$	6471.30	+	13030.3i	0.260674	+	0.524882i
$852$	35984.8	−	10981.2i	1.44697	−	0.441561i
$853$	−12694.0	−	19752.3i	−0.509537	−	0.792855i	0.487224	−	0.873277i	$-0.338009\pi$
$853$	−12694.0	−	19752.3i	−0.509537	−	0.792855i	−0.996761	+	0.0804222i	$0.974373\pi$
$854$	−18723.3	−	18526.1i	−0.750230	−	0.742329i
$855$	−690.551	−	315.364i	−0.0276215	−	0.0126143i
$856$	2601.32	−	46806.2i	0.103868	−	1.86893i
$857$	−16407.9	−	35928.4i	−0.654008	−	1.43208i	−0.888002	−	0.459840i	$-0.847907\pi$
$857$	−16407.9	−	35928.4i	−0.654008	−	1.43208i	0.233994	−	0.972238i	$-0.424820\pi$
$858$	−15689.6	+	1205.65i	−0.624282	+	0.0479724i
$859$	−5670.35	−	39438.2i	−0.225227	−	1.56649i	−0.717820	−	0.696228i	$-0.754860\pi$
$859$	−5670.35	−	39438.2i	−0.225227	−	1.56649i	0.492594	−	0.870260i	$-0.336049\pi$
$860$	−23197.6	+	245.604i	−0.919805	+	0.00973839i
$861$	6838.64	−	7892.21i	0.270685	−	0.312388i
$862$	19417.1	−	7359.51i	0.767225	−	0.290796i
$863$	−13255.7	+	20626.3i	−0.522863	+	0.813590i	−0.997791	−	0.0664344i	$-0.978838\pi$
$863$	−13255.7	+	20626.3i	−0.522863	+	0.813590i	0.474928	+	0.880025i	$0.342474\pi$
$864$	18638.2	+	17676.8i	0.733895	+	0.696039i
$865$	−1878.30	+	6396.91i	−0.0738315	+	0.251447i
$866$	7496.81	−	13903.9i	0.294171	−	0.545580i
$867$	1260.52	+	1454.72i	0.0493767	+	0.0569837i
$868$	−16617.3	−	18772.1i	−0.649802	−	0.734062i
$869$	1756.02	+	5980.47i	0.0685489	+	0.233456i
$870$	−25489.1	+	14093.8i	−0.993288	+	0.549222i
$871$	−1955.16	+	13598.4i	−0.0760596	+	0.529006i
$872$	19878.2	−	4656.03i	0.771975	−	0.180818i
$873$			1050.22i			0.0407154i
$874$	−24358.6	+	6272.86i	−0.942727	+	0.242772i
$875$	8249.27			0.318716
$876$	−6853.38	−	5812.60i	−0.264331	−	0.224189i
$877$	−22935.6	−	3297.63i	−0.883100	−	0.126971i	−0.314180	−	0.949363i	$-0.601730\pi$
$877$	−22935.6	−	3297.63i	−0.883100	−	0.126971i	−0.568920	+	0.822393i	$0.692639\pi$
$878$	−9389.65	+	5191.85i	−0.360917	+	0.199563i
$879$	−41296.5	+	12125.7i	−1.58464	+	0.465292i
$880$	−14520.6	+	23682.4i	−0.556237	+	0.907196i
$881$	−6869.37	+	5952.34i	−0.262696	+	0.227627i	−0.776242	−	0.630435i	$-0.782877\pi$
$881$	−6869.37	+	5952.34i	−0.262696	+	0.227627i	0.513547	+	0.858062i	$0.328331\pi$
$882$	72.7650	+	39.2341i	0.00277792	+	0.00149782i
$883$	−41485.6	−	12181.3i	−1.58109	−	0.464250i	−0.630886	−	0.775876i	$-0.717308\pi$
$883$	−41485.6	−	12181.3i	−1.58109	−	0.464250i	−0.950205	+	0.311626i	$0.899126\pi$
$884$	18137.0	+	8051.95i	0.690061	+	0.306353i
$885$	−30899.8	−	19858.1i	−1.17366	−	0.754263i
$886$	−13014.6	+	4932.82i	−0.493492	+	0.187045i
$887$	5199.60	+	4505.48i	0.196827	+	0.170551i	0.747698	−	0.664039i	$-0.231159\pi$
$887$	5199.60	+	4505.48i	0.196827	+	0.170551i	−0.550871	+	0.834590i	$0.685704\pi$
$888$	−12411.3	−	8987.04i	−0.469028	−	0.339623i
$889$	−40081.6	+	5762.87i	−1.51214	+	0.217413i
$890$	−1275.40	−	16597.3i	−0.0480356	−	0.625104i
$891$	−19041.8	+	8696.12i	−0.715966	+	0.326971i
$892$	2474.90	−	1627.80i	0.0928989	−	0.0611018i
$893$	3741.99	−	8193.82i	0.140225	−	0.307050i
$894$	15868.5	+	15701.4i	0.593648	+	0.587396i
$895$	41483.5	−	26659.8i	1.54932	−	0.995687i
$896$	24182.2	−	6207.05i	0.901642	−	0.231432i
$897$	−20727.0	−	2294.41i	−0.771520	−	0.0854049i
$898$	−2891.28	+	3905.22i	−0.107442	+	0.145121i
$899$	20793.3	−	13363.1i	0.771409	−	0.495754i
$900$	−467.157	+	72.2229i	−0.0173021	+	0.00267492i
$901$	−15456.7	−	7058.82i	−0.571516	−	0.261003i
$902$	9218.63	+	3382.89i	0.340296	+	0.124876i
$903$	−15829.9	+	7229.25i	−0.583372	+	0.266417i
$904$	32472.2	−	12702.5i	1.19470	−	0.467343i
$905$	2959.89	+	20586.5i	0.108718	+	0.756153i
$906$	−9662.74	−	12766.5i	−0.354330	−	0.468143i
$907$	4092.93	+	3546.54i	0.149838	+	0.129836i	0.726554	−	0.687109i	$-0.241121\pi$
$907$	4092.93	+	3546.54i	0.149838	+	0.129836i	−0.576716	+	0.816945i	$0.695666\pi$
$908$	27435.4	+	7741.22i	1.00273	+	0.282931i
$909$	621.786	−	967.519i	0.0226880	−	0.0353032i
$910$	−25848.0	+	5766.35i	−0.941595	+	0.210058i
$911$	34986.6	+	10273.0i	1.27240	+	0.373611i	0.847097	−	0.531439i	$-0.178349\pi$
$911$	34986.6	+	10273.0i	1.27240	+	0.373611i	0.425305	+	0.905050i	$0.360167\pi$
$912$	19650.0	−	17769.0i	0.713461	−	0.645166i
$913$	−17058.5	−	19686.6i	−0.618351	−	0.713615i
$914$	2757.97	−	13009.4i	0.0998092	−	0.470800i
$915$	−39250.5	+	11525.0i	−1.41812	+	0.416398i
$916$	−1732.65	−	230.422i	−0.0624982	−	0.00831154i
$917$	−4762.27	+	33122.3i	−0.171498	+	1.19280i
$918$	26979.3	+	1786.11i	0.969989	+	0.0642160i
$919$	−17068.8			−0.612673			−0.306336	−	0.951923i	$-0.599103\pi$
$919$	−17068.8			−0.612673			−0.306336	+	0.951923i	$0.599103\pi$
$920$	−24740.8	+	27261.3i	−0.886608	+	0.976934i
$921$	−7635.88			−0.273193
$922$	−25689.7	−	1700.73i	−0.917619	−	0.0607489i
$923$	−4799.88	+	33383.9i	−0.171170	+	1.19052i
$924$	−2747.11	+	20656.7i	−0.0978064	+	0.735451i
$925$	11713.8	−	3439.48i	0.416375	−	0.122259i
$926$	6866.00	−	32386.9i	0.243662	−	1.14935i
$927$	141.843	+	163.695i	0.00502559	+	0.00579984i
$928$	2405.09	+	24496.5i	0.0850765	+	0.866526i
$929$	−1225.37	−	359.801i	−0.0432756	−	0.0127069i	0.260023	−	0.965602i	$-0.416270\pi$
$929$	−1225.37	−	359.801i	−0.0432756	−	0.0127069i	−0.303299	+	0.952896i	$0.598088\pi$
$930$	−38002.2	+	8477.80i	−1.33994	+	0.298923i
$931$	1995.63	−	3105.27i	0.0702516	−	0.109314i
$932$	−13408.8	+	47521.7i	−0.471266	+	1.67020i
$933$	2159.75	+	1871.43i	0.0757846	+	0.0656677i
$934$	−27665.9	−	36552.5i	−0.969226	−	1.28055i
$935$	4161.33	+	28942.7i	0.145551	+	1.01233i
$936$	−495.337	+	193.766i	−0.0172976	+	0.00676649i
$937$	4231.15	−	1932.30i	0.147519	−	0.0673699i	−0.340287	−	0.940322i	$-0.610524\pi$
$937$	4231.15	−	1932.30i	0.147519	−	0.0673699i	0.487807	+	0.872952i	$0.337797\pi$
$938$	17079.5	+	6267.55i	0.594528	+	0.218169i
$939$	1279.78	+	584.454i	0.0444770	+	0.0203120i
$940$	−2014.30	−	13029.0i	−0.0698927	−	0.452084i
$941$	−36261.3	+	23303.7i	−1.25620	+	0.807312i	−0.987760	−	0.155984i	$-0.950145\pi$
$941$	−36261.3	+	23303.7i	−1.25620	+	0.807312i	−0.268442	+	0.963296i	$0.586509\pi$
$942$	1394.72	−	1883.83i	0.0482403	−	0.0651576i
$943$	11170.7	+	6675.54i	0.385757	+	0.230525i
$944$	−25752.1	+	17331.1i	−0.887880	+	0.597541i
$945$	−30356.4	+	19508.9i	−1.04497	+	0.671560i
$946$	−11632.2	−	11509.7i	−0.399784	−	0.395574i
$947$	−9584.40	+	20986.9i	−0.328882	+	0.720151i	−0.999771	−	0.0214070i	$-0.993185\pi$
$947$	−9584.40	+	20986.9i	−0.328882	+	0.720151i	0.670889	+	0.741558i	$0.265913\pi$
$948$	−4780.73	−	7268.60i	−0.163788	−	0.249022i
$949$	7327.87	−	3346.53i	0.250656	−	0.114471i
$950$	1617.17	+	21044.9i	0.0552295	+	0.718722i
$951$	42774.2	−	6150.00i	1.45852	−	0.209703i
$952$	15412.3	−	21284.8i	0.524702	−	0.724627i
$953$	−24955.1	−	21623.7i	−0.848242	−	0.735006i	0.117897	−	0.993026i	$-0.462385\pi$
$953$	−24955.1	−	21623.7i	−0.848242	−	0.735006i	−0.966140	+	0.258020i	$0.916930\pi$
$954$	425.884	−	161.420i	0.0144534	−	0.00547815i
$955$	42272.5	+	27166.9i	1.43236	+	0.920522i
$956$	14884.2	−	33526.8i	0.503546	−	1.13424i
$957$	−19712.7	−	5788.17i	−0.665852	−	0.195512i
$958$	2042.77	+	1101.44i	0.0688924	+	0.0371460i
$959$	34759.3	−	30119.1i	1.17042	−	1.01418i
$960$	9737.06	−	37531.9i	0.327356	−	1.26181i
$961$	3119.64	−	916.010i	0.104718	−	0.0307479i
$962$	12021.4	−	6647.04i	0.402896	−	0.222775i
$963$	1309.11	+	188.222i	0.0438063	+	0.00629840i
$964$	−31831.5	+	37531.2i	−1.06351	+	1.25394i
$965$	−59807.5			−1.99510
$966$	−8664.85	+	26221.3i	−0.288599	+	0.873351i
$967$		−	4259.48i		−	0.141650i	−0.997489	−	0.0708251i	$-0.977437\pi$
$967$		−	4259.48i		−	0.141650i	0.997489	−	0.0708251i	$-0.0225632\pi$
$968$	10244.7	−	2399.60i	0.340163	−	0.0796757i
$969$	3968.56	−	27601.9i	0.131567	−	0.915069i
$970$	60062.7	−	33210.7i	1.98814	−	1.09931i
$971$	5417.54	+	18450.4i	0.179049	+	0.609787i	0.999287	+	0.0377631i	$0.0120232\pi$
$971$	5417.54	+	18450.4i	0.179049	+	0.609787i	−0.820237	+	0.572023i	$0.806159\pi$
$972$	−1072.77	+	949.630i	−0.0354003	+	0.0313368i
$973$	11764.6	+	13577.1i	0.387622	+	0.447340i
$974$	17626.0	−	32689.8i	0.579849	−	1.07541i
$975$	−4929.99	+	16790.0i	−0.161934	+	0.551498i
$976$	−4194.32	+	34315.3i	−0.137558	+	1.12542i
$977$	15025.5	−	23380.1i	0.492024	−	0.765605i	−0.503101	−	0.864228i	$-0.667807\pi$
$977$	15025.5	−	23380.1i	0.492024	−	0.765605i	0.995125	+	0.0986231i	$0.0314438\pi$
$978$	−27078.0	+	10263.2i	−0.885336	+	0.335562i
$979$	7689.31	−	8873.94i	0.251023	−	0.289696i
$980$	−57.1950	−	5402.15i	−0.00186431	−	0.176087i
$981$	81.9733	+	570.137i	0.00266790	+	0.0185556i
$982$	−55198.8	+	4241.70i	−1.79375	+	0.137839i
$983$	24421.6	+	53475.9i	0.792400	+	1.73511i	0.669650	+	0.742677i	$0.266444\pi$
$983$	24421.6	+	53475.9i	0.792400	+	1.73511i	0.122751	+	0.992438i	$0.460828\pi$
$984$	−13685.2	−	760.571i	−0.443361	−	0.0246404i
$985$	63915.3	+	29189.1i	2.06752	+	0.944206i
$986$	18416.9	+	18222.9i	0.594840	+	0.588576i
$987$	−5346.78	−	8319.75i	−0.172431	−	0.268309i
$988$	6931.85	+	22715.3i	0.223210	+	0.731446i
$989$	−12311.9	−	17852.2i	−0.395850	−	0.573982i
$990$	−629.893	−	466.350i	−0.0202215	−	0.0149713i
$991$	−975.286	−	1517.57i	−0.0312623	−	0.0486451i	0.825271	−	0.564737i	$-0.191023\pi$
$991$	−975.286	−	1517.57i	−0.0312623	−	0.0486451i	−0.856533	+	0.516092i	$0.827386\pi$
$992$	−6141.08	+	32326.8i	−0.196552	+	1.03465i
$993$	−11054.9	+	24206.9i	−0.353290	+	0.773598i
$994$	41930.1	+	15386.8i	1.33797	+	0.490985i
$995$	19174.0	+	41985.2i	0.610912	+	1.33771i
$996$	30793.5	+	19332.2i	0.979649	+	0.615026i
$997$	488.071	−	70.1740i	0.0155039	−	0.00222912i	−0.134559	−	0.990906i	$-0.542962\pi$
$997$	488.071	−	70.1740i	0.0155039	−	0.00222912i	0.150062	+	0.988677i	$0.452053\pi$
$998$	8479.42	−	6417.93i	0.268949	−	0.203563i
$999$	12257.0	−	14145.3i	0.388182	−	0.447985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.j.a.11.34	yes	700
8.3	odd	2	inner	184.4.j.a.11.8	✓	700
23.21	odd	22	inner	184.4.j.a.67.8	yes	700
184.67	even	22	inner	184.4.j.a.67.34	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.j.a.11.8	✓	700	8.3	odd	2	inner
184.4.j.a.11.34	yes	700	1.1	even	1	trivial
184.4.j.a.67.8	yes	700	23.21	odd	22	inner
184.4.j.a.67.34	yes	700	184.67	even	22	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.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.186841 + 2.82225i) q^{2} +(0.730695 - 5.08210i) q^{3} +(-7.93018 - 1.05462i) q^{4} +(-14.1524 + 4.15552i) q^{5} +(14.2064 + 3.01175i) q^{6} +(11.2898 + 13.0291i) q^{7} +(4.45809 - 22.1839i) q^{8} +(0.612524 + 0.179853i) q^{9} +(-9.08368 - 40.7181i) q^{10} +(15.9098 - 24.7561i) q^{11} +(-11.1542 + 39.5313i) q^{12} +(-27.8279 - 24.1130i) q^{13} +(-38.8807 + 29.4282i) q^{14} +(10.7777 + 74.9604i) q^{15} +(61.7755 + 16.7267i) q^{16} +(61.2777 - 27.9846i) q^{17} +(-0.622036 + 1.69509i) q^{18} +(73.3374 + 33.4921i) q^{19} +(116.614 - 18.0286i) q^{20} +(74.4645 - 47.8554i) q^{21} +(66.8954 + 49.5269i) q^{22} +(74.9087 + 80.9672i) q^{23} +(-109.483 - 38.8661i) q^{24} +(77.8658 - 50.0413i) q^{25} +(73.2524 - 74.0321i) q^{26} +(58.9496 - 129.082i) q^{27} +(-75.7892 - 115.229i) q^{28} +(123.688 - 56.4864i) q^{29} +(-213.571 + 16.4116i) q^{30} +(179.925 - 25.8694i) q^{31} +(-58.7491 + 171.221i) q^{32} +(-114.188 - 98.9444i) q^{33} +(67.5304 + 178.170i) q^{34} +(-213.920 - 137.478i) q^{35} +(-4.66775 - 2.07225i) q^{36} +(126.554 + 37.1597i) q^{37} +(-108.225 + 200.719i) q^{38} +(-142.879 + 123.805i) q^{39} +(29.0930 + 332.482i) q^{40} +(113.198 - 33.2381i) q^{41} +(121.147 + 219.099i) q^{42} +(-194.601 - 27.9794i) q^{43} +(-152.276 + 179.542i) q^{44} -9.41609 q^{45} +(-242.506 + 196.283i) q^{46} -111.728i q^{47} +(130.146 - 301.727i) q^{48} +(6.51572 - 45.3179i) q^{49} +(126.681 + 229.107i) q^{50} +(-97.4451 - 331.868i) q^{51} +(195.250 + 220.569i) q^{52} +(-165.182 - 190.630i) q^{53} +(353.286 + 190.488i) q^{54} +(-122.287 + 416.473i) q^{55} +(339.367 - 192.366i) q^{56} +(223.797 - 348.235i) q^{57} +(136.309 + 359.632i) q^{58} +(-317.617 + 366.549i) q^{59} +(-6.41404 - 605.816i) q^{60} +(76.8738 + 534.669i) q^{61} +(39.3924 + 512.628i) q^{62} +(4.57193 + 10.0111i) q^{63} +(-472.251 - 197.796i) q^{64} +(494.035 + 225.618i) q^{65} +(300.581 - 303.780i) q^{66} +(-201.714 - 313.874i) q^{67} +(-515.457 + 157.298i) q^{68} +(466.219 - 321.531i) q^{69} +(427.967 - 578.050i) q^{70} +(-495.207 - 770.557i) q^{71} +(6.72054 - 12.7864i) q^{72} +(-90.8848 + 199.010i) q^{73} +(-128.520 + 350.225i) q^{74} +(-197.419 - 432.287i) q^{75} +(-546.257 - 342.941i) q^{76} +(502.168 - 72.2009i) q^{77} +(-322.713 - 426.371i) q^{78} +(-138.703 + 160.072i) q^{79} +(-943.781 + 19.9867i) q^{80} +(-598.431 - 384.588i) q^{81} +(72.6560 + 325.684i) q^{82} +(249.387 - 849.333i) q^{83} +(-640.986 + 300.970i) q^{84} +(-750.937 + 650.691i) q^{85} +(115.324 - 543.986i) q^{86} +(-196.691 - 669.869i) q^{87} +(-478.261 - 463.307i) q^{88} +(394.947 + 56.7848i) q^{89} +(1.75931 - 26.5745i) q^{90} -634.803i q^{91} +(-508.650 - 721.085i) q^{92} -933.300i q^{93} +(315.324 + 20.8753i) q^{94} +(-1177.08 - 169.238i) q^{95} +(827.233 + 423.679i) q^{96} +(463.485 + 1578.49i) q^{97} +(126.681 + 26.8562i) q^{98} +(14.1976 - 12.3023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 700 q - 7 q^{2} - 18 q^{3} - 11 q^{4} + 10 q^{6} - 40 q^{8} - 612 q^{9} - 11 q^{10} - 22 q^{11} + 6 q^{12} - 11 q^{14} - 27 q^{16} - 22 q^{17} + 244 q^{18} - 22 q^{19} - 11 q^{20} - 194 q^{24} - 1568 q^{25}+ \cdots - 22 q^{99}+O(q^{100}) \) 700 * q - 7 * q^2 - 18 * q^3 - 11 * q^4 + 10 * q^6 - 40 * q^8 - 612 * q^9 - 11 * q^10 - 22 * q^11 + 6 * q^12 - 11 * q^14 - 27 * q^16 - 22 * q^17 + 244 * q^18 - 22 * q^19 - 11 * q^20 - 194 * q^24 - 1568 * q^25 + 380 * q^26 + 222 * q^27 - 11 * q^28 - 11 * q^30 - 427 * q^32 - 22 * q^33 + 1903 * q^34 + 482 * q^35 - 1329 * q^36 + 594 * q^38 + 1309 * q^40 - 18 * q^41 - 3641 * q^42 - 22 * q^43 + 3300 * q^44 - 2727 * q^46 + 3204 * q^48 - 2860 * q^49 - 80 * q^50 - 22 * q^51 + 934 * q^52 + 2088 * q^54 - 3586 * q^56 - 22 * q^57 + 6159 * q^58 + 1002 * q^59 - 3641 * q^60 - 618 * q^62 + 1666 * q^64 - 22 * q^65 + 286 * q^66 - 22 * q^67 - 1474 * q^70 + 89 * q^72 - 18 * q^73 + 2354 * q^74 + 590 * q^75 + 8184 * q^76 + 10268 * q^78 + 4048 * q^80 - 5516 * q^81 - 4052 * q^82 - 22 * q^83 - 5401 * q^84 - 6721 * q^86 - 6963 * q^88 - 22 * q^89 - 18700 * q^90 - 4776 * q^92 - 8575 * q^94 - 5643 * q^96 - 22 * q^97 - 3995 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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