LMFDB - Embedded newform 184.4.p.a.85.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			85.2
Character	$\chi$	$=$	184.85
Dual form			184.4.p.a.13.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.79214 - 0.451587i) q^{2} +(-0.319292 - 0.496829i) q^{3} +(7.59214 + 2.52179i) q^{4} +(-11.7845 + 5.38181i) q^{5} +(0.667149 + 1.53141i) q^{6} +(16.5509 - 4.85977i) q^{7} +(-20.0595 - 10.4697i) q^{8} +(11.0713 - 24.2428i) q^{9} +(35.3344 - 9.70505i) q^{10} +(-24.5856 + 21.3035i) q^{11} +(-1.17121 - 4.57718i) q^{12} +(-1.84672 + 6.28935i) q^{13} +(-48.4070 + 6.09502i) q^{14} +(6.43655 + 4.13652i) q^{15} +(51.2811 + 38.2916i) q^{16} +(-1.32178 + 9.19320i) q^{17} +(-41.8604 + 62.6897i) q^{18} +(10.2692 - 1.47649i) q^{19} +(-103.042 + 11.1413i) q^{20} +(-7.69904 - 6.67125i) q^{21} +(78.2669 - 48.3800i) q^{22} +(25.4736 + 107.322i) q^{23} +(1.20320 + 13.3091i) q^{24} +(28.0535 - 32.3754i) q^{25} +(7.99650 - 16.7268i) q^{26} +(-31.3629 + 4.50930i) q^{27} +(137.912 + 4.84179i) q^{28} +(80.8901 + 11.6302i) q^{29} +(-16.1038 - 14.4564i) q^{30} +(189.593 + 121.844i) q^{31} +(-125.892 - 130.074i) q^{32} +(18.4342 + 5.41277i) q^{33} +(7.84214 - 25.0718i) q^{34} +(-168.890 + 146.344i) q^{35} +(145.190 - 156.135i) q^{36} +(263.995 + 120.562i) q^{37} +(-29.3398 - 0.514871i) q^{38} +(3.71437 - 1.09064i) q^{39} +(292.738 + 15.4240i) q^{40} +(188.289 + 412.295i) q^{41} +(18.4842 + 22.1039i) q^{42} +(135.387 + 210.666i) q^{43} +(-240.380 + 99.7396i) q^{44} +345.273i q^{45} +(-22.6607 - 311.163i) q^{46} -44.2984 q^{47} +(2.65069 - 37.7042i) q^{48} +(-38.2365 + 24.5731i) q^{49} +(-92.9497 + 77.7283i) q^{50} +(4.98948 - 2.27862i) q^{51} +(-29.8810 + 43.0926i) q^{52} +(120.769 + 411.301i) q^{53} +(89.6061 + 1.57246i) q^{54} +(175.078 - 383.367i) q^{55} +(-382.883 - 75.7981i) q^{56} +(-4.01244 - 4.63060i) q^{57} +(-220.605 - 69.0022i) q^{58} +(81.6366 - 278.029i) q^{59} +(38.4357 + 47.6367i) q^{60} +(-97.9082 + 152.348i) q^{61} +(-474.347 - 425.824i) q^{62} +(65.4253 - 455.043i) q^{63} +(292.770 + 420.035i) q^{64} +(-12.0854 - 84.0557i) q^{65} +(-49.0266 - 23.4379i) q^{66} +(-530.923 - 460.047i) q^{67} +(-33.2185 + 66.4628i) q^{68} +(45.1873 - 46.9233i) q^{69} +(537.651 - 332.344i) q^{70} +(556.232 - 641.926i) q^{71} +(-475.901 + 370.386i) q^{72} +(39.4464 + 274.356i) q^{73} +(-682.668 - 455.845i) q^{74} +(-25.0423 - 3.60054i) q^{75} +(81.6885 + 14.6871i) q^{76} +(-303.382 + 472.072i) q^{77} +(-10.8636 + 1.36786i) q^{78} +(-812.834 - 238.670i) q^{79} +(-810.402 - 175.263i) q^{80} +(-458.972 - 529.682i) q^{81} +(-339.542 - 1236.22i) q^{82} +(-396.619 - 181.130i) q^{83} +(-41.6286 - 70.0645i) q^{84} +(-33.8995 - 115.451i) q^{85} +(-282.885 - 649.347i) q^{86} +(-20.0494 - 43.9020i) q^{87} +(716.218 - 169.935i) q^{88} +(-257.975 + 165.790i) q^{89} +(155.921 - 964.053i) q^{90} +113.069i q^{91} +(-77.2454 + 879.046i) q^{92} -133.099i q^{93} +(123.687 + 20.0046i) q^{94} +(-113.071 + 72.6665i) q^{95} +(-24.4278 + 104.078i) q^{96} +(-54.5825 - 119.519i) q^{97} +(117.859 - 51.3445i) q^{98} +(244.263 + 831.882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 700 q - 7 q^{2} + 13 q^{4} - 52 q^{6} + 10 q^{7} - 46 q^{8} + 576 q^{9} + 35 q^{10} - 24 q^{12} + 77 q^{14} - 246 q^{15} - 27 q^{16} - 18 q^{17} - 230 q^{18} + 53 q^{20} + 182 q^{22} + 144 q^{23} + 154 q^{24}+ \cdots - 7727 q^{98}+O(q^{100}) $ 700 * q - 7 * q^2 + 13 * q^4 - 52 * q^6 + 10 * q^7 - 46 * q^8 + 576 * q^9 + 35 * q^10 - 24 * q^12 + 77 * q^14 - 246 * q^15 - 27 * q^16 - 18 * q^17 - 230 * q^18 + 53 * q^20 + 182 * q^22 + 144 * q^23 + 154 * q^24 + 1532 * q^25 + 50 * q^26 + 151 * q^28 + 39 * q^30 - 546 * q^31 + 53 * q^32 - 126 * q^33 - 1175 * q^34 + 2613 * q^36 + 60 * q^38 + 174 * q^39 - 1565 * q^40 - 18 * q^41 + 2983 * q^42 - 2596 * q^44 + 3645 * q^46 - 40 * q^47 - 3908 * q^48 - 2860 * q^49 + 1858 * q^50 - 1154 * q^52 - 432 * q^54 - 518 * q^55 + 4562 * q^56 - 126 * q^57 - 4499 * q^58 + 2651 * q^60 - 1540 * q^62 - 14 * q^63 - 158 * q^64 - 518 * q^65 + 2368 * q^66 - 1270 * q^68 - 2006 * q^70 - 1498 * q^71 + 2103 * q^72 - 18 * q^73 + 2216 * q^74 + 6852 * q^76 + 7956 * q^78 + 1834 * q^79 + 2362 * q^80 - 3268 * q^81 + 1098 * q^82 - 7971 * q^84 - 8759 * q^86 - 2154 * q^87 - 4495 * q^88 - 866 * q^89 - 13676 * q^90 - 10844 * q^92 - 12229 * q^94 + 722 * q^95 - 12211 * q^96 - 18 * q^97 - 7727 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−2.79214	−	0.451587i	−0.987172	−	0.159660i
$2$	−2.79214	−	0.451587i	−0.987172	−	0.159660i
$3$	−0.319292	−	0.496829i	−0.0614479	−	0.0956147i	0.809170	−	0.587574i	$-0.199917\pi$
$3$	−0.319292	−	0.496829i	−0.0614479	−	0.0956147i	−0.870618	+	0.491960i	$0.836281\pi$
$4$	7.59214	+	2.52179i	0.949017	+	0.315224i
$5$	−11.7845	+	5.38181i	−1.05404	+	0.481364i	−0.865608	−	0.500722i	$-0.833068\pi$
$5$	−11.7845	+	5.38181i	−1.05404	+	0.481364i	−0.188432	+	0.982086i	$0.560340\pi$
$6$	0.667149	+	1.53141i	0.0453937	+	0.104199i
$7$	16.5509	−	4.85977i	0.893662	−	0.262403i	0.197513	−	0.980300i	$-0.436713\pi$
$7$	16.5509	−	4.85977i	0.893662	−	0.262403i	0.696149	+	0.717897i	$0.254895\pi$
$8$	−20.0595	−	10.4697i	−0.886515	−	0.462701i
$9$	11.0713	−	24.2428i	0.410049	−	0.897881i
$10$	35.3344	−	9.70505i	1.11737	−	0.306901i
$11$	−24.5856	+	21.3035i	−0.673894	+	0.583933i	−0.923120	−	0.384513i	$-0.874369\pi$
$11$	−24.5856	+	21.3035i	−0.673894	+	0.583933i	0.249225	+	0.968445i	$0.419824\pi$
$12$	−1.17121	−	4.57718i	−0.0281750	−	0.110110i
$13$	−1.84672	+	6.28935i	−0.0393991	+	0.134181i	−0.976844	−	0.213953i	$-0.931366\pi$
$13$	−1.84672	+	6.28935i	−0.0393991	+	0.134181i	0.937445	+	0.348133i	$0.113184\pi$
$14$	−48.4070	+	6.09502i	−0.924094	+	0.116355i
$15$	6.43655	+	4.13652i	0.110794	+	0.0712030i
$16$	51.2811	+	38.2916i	0.801268	+	0.598306i
$17$	−1.32178	+	9.19320i	−0.0188576	+	0.131158i	−0.997075	−	0.0764234i	$-0.975650\pi$
$17$	−1.32178	+	9.19320i	−0.0188576	+	0.131158i	0.978218	+	0.207581i	$0.0665590\pi$
$18$	−41.8604	+	62.6897i	−0.548144	+	0.820895i
$19$	10.2692	−	1.47649i	0.123995	−	0.0178279i	−0.0800377	−	0.996792i	$-0.525504\pi$
$19$	10.2692	−	1.47649i	0.123995	−	0.0178279i	0.204033	+	0.978964i	$0.434595\pi$
$20$	−103.042	+	11.1413i	−1.15204	+	0.124564i
$21$	−7.69904	−	6.67125i	−0.0800032	−	0.0693232i
$22$	78.2669	−	48.3800i	0.758480	−	0.468848i
$23$	25.4736	+	107.322i	0.230940	+	0.972968i
$23$	25.4736	+	107.322i	0.230940	+	0.972968i
$24$	1.20320	+	13.3091i	0.0102334	+	0.113196i
$25$	28.0535	−	32.3754i	0.224428	−	0.259003i
$26$	7.99650	−	16.7268i	0.0603170	−	0.126169i
$27$	−31.3629	+	4.50930i	−0.223548	+	0.0321413i
$28$	137.912	+	4.84179i	0.930817	+	0.0326790i
$29$	80.8901	+	11.6302i	0.517962	+	0.0744718i	0.396338	−	0.918104i	$-0.370281\pi$
$29$	80.8901	+	11.6302i	0.517962	+	0.0744718i	0.121624	+	0.992576i	$0.461190\pi$
$30$	−16.1038	−	14.4564i	−0.0980044	−	0.0879790i
$31$	189.593	+	121.844i	1.09845	+	0.705930i	0.958746	−	0.284264i	$-0.0917492\pi$
$31$	189.593	+	121.844i	1.09845	+	0.705930i	0.139702	+	0.990194i	$0.455386\pi$
$32$	−125.892	−	130.074i	−0.695463	−	0.718562i
$33$	18.4342	+	5.41277i	0.0972419	+	0.0285528i
$34$	7.84214	−	25.0718i	0.0395563	−	0.126464i
$35$	−168.890	+	146.344i	−0.815644	+	0.706760i
$36$	145.190	−	156.135i	0.672177	−	0.722848i
$37$	263.995	+	120.562i	1.17299	+	0.535685i	0.904031	−	0.427467i	$-0.140594\pi$
$37$	263.995	+	120.562i	1.17299	+	0.535685i	0.268956	+	0.963152i	$0.413321\pi$
$38$	−29.3398	−	0.514871i	−0.125251	−	0.00219798i
$39$	3.71437	−	1.09064i	0.0152507	−	0.00447800i
$40$	292.738	+	15.4240i	1.15715	+	0.0609689i
$41$	188.289	+	412.295i	0.717214	+	1.57048i	0.817768	+	0.575547i	$0.195211\pi$
$41$	188.289	+	412.295i	0.717214	+	1.57048i	−0.100555	+	0.994932i	$0.532062\pi$
$42$	18.4842	+	22.1039i	0.0679088	+	0.0812072i
$43$	135.387	+	210.666i	0.480145	+	0.747121i	0.993837	−	0.110854i	$-0.0353587\pi$
$43$	135.387	+	210.666i	0.480145	+	0.747121i	−0.513691	+	0.857975i	$0.671722\pi$
$44$	−240.380	+	99.7396i	−0.823607	+	0.341734i
$45$			345.273i			1.14379i
$46$	−22.6607	−	311.163i	−0.0726334	−	0.997359i
$47$	−44.2984			−0.137481			−0.0687403	−	0.997635i	$-0.521898\pi$
$47$	−44.2984			−0.137481			−0.0687403	+	0.997635i	$0.521898\pi$
$48$	2.65069	−	37.7042i	0.00797072	−	0.113378i
$49$	−38.2365	+	24.5731i	−0.111477	+	0.0716417i
$50$	−92.9497	+	77.7283i	−0.262901	+	0.219849i
$51$	4.98948	−	2.27862i	0.0136994	−	0.00625628i
$52$	−29.8810	+	43.0926i	−0.0796874	+	0.114920i
$53$	120.769	+	411.301i	0.312998	+	1.06597i	0.954341	+	0.298718i	$0.0965590\pi$
$53$	120.769	+	411.301i	0.312998	+	1.06597i	−0.641344	+	0.767254i	$0.721623\pi$
$54$	89.6061	+	1.57246i	0.225812	+	0.00396267i
$55$	175.078	−	383.367i	0.429227	−	0.939876i
$56$	−382.883	−	75.7981i	−0.913659	−	0.180874i
$57$	−4.01244	−	4.63060i	−0.00932386	−	0.0107603i
$58$	−220.605	−	69.0022i	−0.499428	−	0.156214i
$59$	81.6366	−	278.029i	0.180139	−	0.613496i	−0.819069	−	0.573695i	$-0.805510\pi$
$59$	81.6366	−	278.029i	0.180139	−	0.613496i	0.999208	−	0.0398007i	$-0.0126723\pi$
$60$	38.4357	+	47.6367i	0.0827005	+	0.102498i
$61$	−97.9082	+	152.348i	−0.205506	+	0.319774i	−0.928673	−	0.370900i	$-0.879049\pi$
$61$	−97.9082	+	152.348i	−0.205506	+	0.319774i	0.723167	+	0.690673i	$0.242686\pi$
$62$	−474.347	−	425.824i	−0.971648	−	0.872252i
$63$	65.4253	−	455.043i	0.130838	−	0.910001i
$64$	292.770	+	420.035i	0.571816	+	0.820382i
$65$	−12.0854	−	84.0557i	−0.0230616	−	0.160397i
$66$	−49.0266	−	23.4379i	−0.0914358	−	0.0437122i
$67$	−530.923	−	460.047i	−0.968098	−	0.838862i	0.0188630	−	0.999822i	$-0.493995\pi$
$67$	−530.923	−	460.047i	−0.968098	−	0.838862i	−0.986961	+	0.160961i	$0.948541\pi$
$68$	−33.2185	+	66.4628i	−0.0592402	+	0.118526i
$69$	45.1873	−	46.9233i	0.0788393	−	0.0818681i
$70$	537.651	−	332.344i	0.918022	−	0.567468i
$71$	556.232	−	641.926i	0.929755	−	1.07300i	−0.0674077	−	0.997726i	$-0.521473\pi$
$71$	556.232	−	641.926i	0.929755	−	1.07300i	0.997163	−	0.0752695i	$-0.0239817\pi$
$72$	−475.901	+	370.386i	−0.778964	+	0.606255i
$73$	39.4464	+	274.356i	0.0632445	+	0.439875i	0.996699	+	0.0811805i	$0.0258690\pi$
$73$	39.4464	+	274.356i	0.0632445	+	0.439875i	−0.933455	+	0.358695i	$0.883222\pi$
$74$	−682.668	−	455.845i	−1.07241	−	0.716093i
$75$	−25.0423	−	3.60054i	−0.0385552	−	0.00554340i
$76$	81.6885	+	14.6871i	0.123294	+	0.0221674i
$77$	−303.382	+	472.072i	−0.449008	+	0.698670i
$78$	−10.8636	+	1.36786i	−0.0157700	+	0.00198563i
$79$	−812.834	−	238.670i	−1.15761	−	0.339904i	−0.354105	−	0.935206i	$-0.615214\pi$
$79$	−812.834	−	238.670i	−1.15761	−	0.339904i	−0.803502	+	0.595302i	$0.797033\pi$
$80$	−810.402	−	175.263i	−1.13257	−	0.244937i
$81$	−458.972	−	529.682i	−0.629592	−	0.726587i
$82$	−339.542	−	1236.22i	−0.457270	−	1.66484i
$83$	−396.619	−	181.130i	−0.524513	−	0.239537i	0.135519	−	0.990775i	$-0.456730\pi$
$83$	−396.619	−	181.130i	−0.524513	−	0.239537i	−0.660032	+	0.751238i	$0.729457\pi$
$84$	−41.6286	−	70.0645i	−0.0540721	−	0.0910078i
$85$	−33.8995	−	115.451i	−0.0432578	−	0.147323i
$86$	−282.885	−	649.347i	−0.354701	−	0.814197i
$87$	−20.0494	−	43.9020i	−0.0247071	−	0.0541010i
$88$	716.218	−	169.935i	0.867603	−	0.205853i
$89$	−257.975	+	165.790i	−0.307250	+	0.197458i	−0.685175	−	0.728379i	$-0.740274\pi$
$89$	−257.975	+	165.790i	−0.307250	+	0.197458i	0.377925	+	0.925836i	$0.376638\pi$
$90$	155.921	−	964.053i	0.182617	−	1.12911i
$91$			113.069i			0.130251i
$92$	−77.2454	+	879.046i	−0.0875368	+	0.996161i
$93$		−	133.099i		−	0.148406i
$94$	123.687	+	20.0046i	0.135717	+	0.0219502i
$95$	−113.071	+	72.6665i	−0.122114	+	0.0784782i
$96$	−24.4278	+	104.078i	−0.0259704	+	0.110651i
$97$	−54.5825	−	119.519i	−0.0571342	−	0.125106i	0.878912	−	0.476985i	$-0.158270\pi$
$97$	−54.5825	−	119.519i	−0.0571342	−	0.125106i	−0.936046	+	0.351878i	$0.885543\pi$
$98$	117.859	−	51.3445i	0.121485	−	0.0529243i
$99$	244.263	+	831.882i	0.247973	+	0.844518i
$100$	294.630	−	175.054i	0.294630	−	0.175054i
$101$	1723.16	+	786.943i	1.69764	+	0.775284i	0.998160	+	0.0606279i	$0.0193103\pi$
$101$	1723.16	+	786.943i	1.69764	+	0.775284i	0.699476	+	0.714656i	$0.253417\pi$
$102$	−14.9603	+	4.10905i	−0.0145225	+	0.00398879i
$103$	555.638	+	641.241i	0.531540	+	0.613430i	0.956482	−	0.291790i	$-0.0942510\pi$
$103$	555.638	+	641.241i	0.531540	+	0.613430i	−0.424942	+	0.905221i	$0.639706\pi$
$104$	102.892	−	106.827i	0.0970134	−	0.100723i
$105$	126.633	+	37.1828i	0.117696	+	0.0345587i
$106$	−151.466	−	1202.95i	−0.138789	−	1.10227i
$107$	−525.544	+	817.762i	−0.474824	+	0.738841i	−0.993214	−	0.116303i	$-0.962895\pi$
$107$	−525.544	+	817.762i	−0.474824	+	0.738841i	0.518389	+	0.855145i	$0.326532\pi$
$108$	−249.483	−	44.8555i	−0.222283	−	0.0399650i
$109$	588.426	+	84.6029i	0.517073	+	0.0743439i	0.395911	−	0.918289i	$-0.370429\pi$
$109$	588.426	+	84.6029i	0.517073	+	0.0743439i	0.121162	+	0.992633i	$0.461338\pi$
$110$	−661.966	+	991.353i	−0.573782	+	0.859289i
$111$	−24.3927	−	169.655i	−0.0208581	−	0.145072i
$112$	1034.83	+	384.544i	0.873060	+	0.324429i
$113$	−639.190	+	737.664i	−0.532123	+	0.614103i	−0.956624	−	0.291325i	$-0.905904\pi$
$113$	−639.190	+	737.664i	−0.532123	+	0.614103i	0.424501	+	0.905427i	$0.360450\pi$
$114$	9.11218	+	14.7413i	0.00748626	+	0.0121109i
$115$	−877.784	−	1127.65i	−0.711772	−	0.914381i
$116$	584.800	+	292.286i	0.468080	+	0.233949i
$117$	132.026	+	114.401i	0.104323	+	0.0903964i
$118$	−353.495	+	739.430i	−0.275779	+	0.576865i
$119$	22.8002	+	158.579i	0.0175638	+	0.122159i
$120$	−85.8060	−	150.365i	−0.0652748	−	0.114387i
$121$	−38.8103	+	269.932i	−0.0291588	+	0.202804i
$122$	342.172	−	381.164i	0.253925	−	0.282860i
$123$	144.721	−	225.190i	0.106090	−	0.165079i
$124$	1132.15	+	1403.17i	0.819920	+	1.01620i
$125$	299.882	−	1021.30i	0.214578	−	0.730785i
$126$	−388.169	+	1241.00i	−0.274451	+	0.877437i
$127$	12.1480	+	14.0195i	0.00848788	+	0.00979553i	0.759978	−	0.649949i	$-0.225210\pi$
$127$	12.1480	+	14.0195i	0.00848788	+	0.00979553i	−0.751490	+	0.659745i	$0.770664\pi$
$128$	−627.773	−	1305.01i	−0.433499	−	0.901154i
$129$	61.4368	−	134.528i	0.0419319	−	0.0918179i
$130$	−4.21434	+	240.153i	−0.00284324	+	0.162022i
$131$	−280.393	−	954.929i	−0.187008	−	0.636890i	−0.998611	−	0.0526814i	$-0.983223\pi$
$131$	−280.393	−	954.929i	−0.187008	−	0.636890i	0.811604	−	0.584208i	$-0.198595\pi$
$132$	126.305	+	87.5818i	0.0832837	+	0.0577501i
$133$	162.788	−	74.3430i	0.106132	−	0.0484688i
$134$	1274.66	+	1524.28i	0.821746	+	0.982667i
$135$	345.329	−	221.929i	0.220157	−	0.141486i
$136$	122.765	−	170.573i	0.0774042	−	0.107548i
$137$	−1374.43			−0.857121			−0.428560	−	0.903513i	$-0.640979\pi$
$137$	−1374.43			−0.857121			−0.428560	+	0.903513i	$0.640979\pi$
$138$	−147.359	+	110.611i	−0.0908990	+	0.0682304i
$139$		−	2413.00i		−	1.47243i	−0.676745	−	0.736217i	$-0.736610\pi$
$139$		−	2413.00i		−	1.47243i	0.676745	−	0.736217i	$-0.263390\pi$
$140$	−1651.28	+	685.157i	−0.996848	+	0.413616i
$141$	14.1441	+	22.0087i	0.00844788	+	0.0131452i
$142$	−1842.97	+	1541.16i	−1.08914	+	0.910786i
$143$	−88.5827	−	193.969i	−0.0518018	−	0.113430i
$144$	1496.04	−	819.259i	0.865767	−	0.474108i
$145$	−1015.84	+	298.278i	−0.581801	+	0.170832i
$146$	13.7555	−	783.854i	0.00779735	−	0.444330i
$147$	24.4173	+	11.1510i	0.0137000	+	0.00625658i
$148$	1700.25	+	1581.07i	0.944324	+	0.878128i
$149$	1730.21	−	1499.23i	0.951303	−	0.824309i	−0.0332406	−	0.999447i	$-0.510583\pi$
$149$	1730.21	−	1499.23i	0.951303	−	0.824309i	0.984544	+	0.175138i	$0.0560373\pi$
$150$	68.2958	+	21.3620i	0.0371755	+	0.0116280i
$151$	1784.79	+	524.063i	0.961884	+	0.282435i	0.724726	−	0.689037i	$-0.241966\pi$
$151$	1784.79	+	524.063i	0.961884	+	0.282435i	0.237157	+	0.971471i	$0.423784\pi$
$152$	−221.454	−	77.8979i	−0.118173	−	0.0415681i
$153$	208.235	+	133.824i	0.110031	+	0.0707129i
$154$	1060.27	−	1181.09i	0.554798	−	0.618019i
$155$	−2890.00	−	415.520i	−1.49762	−	0.215325i
$156$	30.9504	+	1.08660i	0.0158847	+	0.000557679i
$157$	−575.173	+	82.6973i	−0.292381	+	0.0420380i	−0.286944	−	0.957947i	$-0.592640\pi$
$157$	−575.173	+	82.6973i	−0.292381	+	0.0420380i	−0.00543628	+	0.999985i	$0.501730\pi$
$158$	2161.77	+	1033.47i	1.08849	+	0.520368i
$159$	165.785	−	191.327i	0.0826896	−	0.0954289i
$160$	2183.61	+	855.326i	1.07894	+	0.422622i
$161$	943.173	+	1652.48i	0.461692	+	0.808905i
$162$	1042.32	+	1686.21i	0.505508	+	0.817787i
$163$	−1182.56	−	1024.69i	−0.568252	−	0.492393i	0.322694	−	0.946503i	$-0.395412\pi$
$163$	−1182.56	−	1024.69i	−0.568252	−	0.492393i	−0.890945	+	0.454111i	$0.849957\pi$
$164$	389.792	+	3605.02i	0.185595	+	1.71649i
$165$	−246.369	+	35.4225i	−0.116241	+	0.0167130i
$166$	1025.62	+	684.848i	0.479540	+	0.320208i
$167$	−7.77091	+	54.0479i	−0.00360079	+	0.0250440i	−0.991543	−	0.129781i	$-0.958572\pi$
$167$	−7.77091	+	54.0479i	−0.00360079	+	0.0250440i	0.987942	+	0.154825i	$0.0494815\pi$
$168$	84.5929	+	214.429i	0.0388481	+	0.0984736i
$169$	1812.09	+	1164.56i	0.824801	+	0.530068i
$170$	42.5160	+	337.664i	0.0191814	+	0.152339i
$171$	77.8993	−	265.301i	0.0348369	−	0.118643i
$172$	496.618	+	1940.82i	0.220156	+	0.860384i
$173$	−1388.82	+	1203.42i	−0.610347	+	0.528868i	−0.904270	−	0.426960i	$-0.859584\pi$
$173$	−1388.82	+	1203.42i	−0.610347	+	0.528868i	0.293924	+	0.955829i	$0.405039\pi$
$174$	36.1551	+	131.635i	0.0157524	+	0.0573517i
$175$	306.972	−	672.175i	0.132599	−	0.290352i
$176$	−2076.52	+	151.048i	−0.889340	+	0.0646911i
$177$	−164.199	+	48.2130i	−0.0697284	+	0.0204741i
$178$	795.172	−	346.413i	0.334835	−	0.145869i
$179$	2918.10	−	1332.65i	1.21849	−	0.556464i	0.300768	−	0.953697i	$-0.402757\pi$
$179$	2918.10	−	1332.65i	1.21849	−	0.556464i	0.917717	+	0.397234i	$0.130030\pi$
$180$	−870.708	+	2621.36i	−0.360549	+	1.08547i
$181$	2129.82	+	3314.07i	0.874633	+	1.36096i	0.931945	+	0.362599i	$0.118111\pi$
$181$	2129.82	+	3314.07i	0.874633	+	1.36096i	−0.0573121	+	0.998356i	$0.518253\pi$
$182$	51.0604	−	315.704i	0.0207959	−	0.128580i
$183$	106.952			0.0432030
$184$	612.646	−	2419.54i	0.245461	−	0.969406i
$185$	−3759.90			−1.49423
$186$	−60.1058	+	371.632i	−0.0236945	+	0.146502i
$187$	−163.351	−	254.179i	−0.0638791	−	0.0993979i
$188$	−336.320	−	111.711i	−0.130471	−	0.0433372i
$189$	−497.169	+	227.049i	−0.191342	+	0.0873831i
$190$	348.527	−	151.834i	0.133078	−	0.0579747i
$191$	−1363.16	+	400.261i	−0.516413	+	0.151633i	−0.529546	−	0.848281i	$-0.677638\pi$
$191$	−1363.16	+	400.261i	−0.516413	+	0.151633i	0.0131328	+	0.999914i	$0.495820\pi$
$192$	115.207	−	279.571i	0.0433037	−	0.105085i
$193$	1537.51	−	3366.67i	0.573431	−	1.25564i	−0.371519	−	0.928425i	$-0.621163\pi$
$193$	1537.51	−	3366.67i	0.573431	−	1.25564i	0.944950	−	0.327214i	$-0.106110\pi$
$194$	98.4290	+	358.363i	0.0364268	+	0.132624i
$195$	−37.9025	+	32.8427i	−0.0139193	+	0.0120611i
$196$	−352.265	+	90.1379i	−0.128376	+	0.0328491i
$197$	808.503	−	2753.51i	0.292403	−	0.995835i	−0.673984	−	0.738746i	$-0.735418\pi$
$197$	808.503	−	2753.51i	0.292403	−	0.995835i	0.966388	−	0.257089i	$-0.0827634\pi$
$198$	−306.349	−	2433.04i	−0.109956	−	0.873276i
$199$	−649.489	−	417.401i	−0.231362	−	0.148687i	0.419824	−	0.907606i	$-0.362092\pi$
$199$	−649.489	−	417.401i	−0.231362	−	0.148687i	−0.651186	+	0.758918i	$0.725728\pi$
$200$	−901.701	+	355.724i	−0.318800	+	0.125767i
$201$	−59.0451	+	410.667i	−0.0207200	+	0.144111i
$202$	−4455.95	−	2975.42i	−1.55208	−	1.03638i
$203$	1395.32	−	200.617i	0.482425	−	0.0693623i
$204$	43.6270	−	4.71716i	0.0149731	−	0.00161896i
$205$	−4437.79	−	3845.36i	−1.51194	−	1.31011i
$206$	−1261.85	−	2041.36i	−0.426781	−	0.690427i
$207$	2883.82	+	570.647i	0.968306	+	0.191607i
$208$	−335.531	+	251.811i	−0.111850	+	0.0839421i
$209$	−221.020	+	255.070i	−0.0731496	+	0.0844191i
$210$	−336.786	−	161.005i	−0.110669	−	0.0529068i
$211$	−1926.04	+	276.922i	−0.628407	+	0.0903513i	−0.449158	−	0.893452i	$-0.648276\pi$
$211$	−1926.04	+	276.922i	−0.628407	+	0.0903513i	−0.179249	+	0.983804i	$0.557367\pi$
$212$	−120.322	+	3427.21i	−0.0389799	+	1.11029i
$213$	−496.528	−	71.3900i	−0.159726	−	0.0229651i
$214$	1836.68	−	2045.98i	0.586697	−	0.653553i
$215$	−2729.23	−	1753.97i	−0.865729	−	0.556370i
$216$	676.336	+	237.906i	0.213050	+	0.0749420i
$217$	3730.06	+	1095.24i	1.16688	+	0.342627i
$218$	−1604.76	−	501.949i	−0.498570	−	0.155946i
$219$	123.713	−	107.198i	0.0381723	−	0.0330765i
$220$	2295.99	−	2469.07i	0.703616	−	0.756656i
$221$	−55.3783	−	25.2904i	−0.0168559	−	0.00769781i
$222$	−8.50607	+	484.717i	−0.00257158	+	0.146541i
$223$	−5824.20	+	1710.14i	−1.74895	+	0.513539i	−0.990419	−	0.138092i	$-0.955903\pi$
$223$	−5824.20	+	1710.14i	−1.74895	+	0.513539i	−0.758536	+	0.651632i	$0.774085\pi$
$224$	−2715.75	−	1541.02i	−0.810062	−	0.459660i
$225$	−474.282	−	1038.53i	−0.140528	−	0.307714i
$226$	2117.83	−	1771.02i	0.623345	−	0.521266i
$227$	1579.02	+	2457.00i	0.461687	+	0.718400i	0.991556	−	0.129680i	$-0.0413951\pi$
$227$	1579.02	+	2457.00i	0.461687	+	0.718400i	−0.529868	+	0.848080i	$0.677759\pi$
$228$	−18.7856	−	45.2747i	−0.00545660	−	0.0131508i
$229$		−	694.960i		−	0.200543i	−0.994960	−	0.100271i	$-0.968029\pi$
$229$		−	694.960i		−	0.200543i	0.994960	−	0.100271i	$-0.0319711\pi$
$230$	1941.67	+	3544.95i	0.556651	+	1.01629i
$231$	331.407			0.0943938
$232$	−1500.85	−	1080.19i	−0.424723	−	0.305682i
$233$	−2489.82	+	1600.11i	−0.700059	+	0.449901i	−0.841649	−	0.540025i	$-0.818415\pi$
$233$	−2489.82	+	1600.11i	−0.700059	+	0.449901i	0.141590	+	0.989925i	$0.454779\pi$
$234$	−316.973	−	379.045i	−0.0885520	−	0.105893i
$235$	522.035	−	238.406i	0.144910	−	0.0661781i
$236$	1320.93	−	1904.96i	0.364343	−	0.525434i
$237$	140.954	+	480.045i	0.0386326	+	0.131571i
$238$	7.95074	−	453.071i	0.00216542	−	0.123396i
$239$	−88.2723	+	193.289i	−0.0238906	+	0.0523132i	−0.921201	−	0.389087i	$-0.872791\pi$
$239$	−88.2723	+	193.289i	−0.0238906	+	0.0523132i	0.897311	+	0.441400i	$0.145518\pi$
$240$	171.679	+	458.591i	0.0461744	+	0.123341i
$241$	4293.54	+	4955.00i	1.14760	+	1.32440i	0.938010	+	0.346608i	$0.112667\pi$
$241$	4293.54	+	4955.00i	1.14760	+	1.32440i	0.209587	+	0.977790i	$0.432788\pi$
$242$	230.262	−	736.162i	0.0611644	−	0.195547i
$243$	−357.639	+	1218.01i	−0.0944138	+	0.321544i
$244$	−1127.52	+	909.744i	−0.295829	+	0.238690i
$245$	318.351	−	495.364i	0.0830151	−	0.129174i
$246$	−505.774	+	563.409i	−0.131085	+	0.146023i
$247$	−9.67817	+	67.3132i	−0.00249315	+	0.0173402i
$248$	−2527.47	−	4429.12i	−0.647156	−	1.13407i
$249$	36.6469	+	254.885i	0.00932693	+	0.0648702i
$250$	−1298.52	+	2716.20i	−0.328502	+	0.687151i
$251$	662.322	+	573.905i	0.166555	+	0.144321i	0.734150	−	0.678987i	$-0.237581\pi$
$251$	662.322	+	573.905i	0.166555	+	0.144321i	−0.567595	+	0.823308i	$0.692126\pi$
$252$	1644.24	−	3289.76i	0.411022	−	0.822363i
$253$	−2912.63	−	2095.91i	−0.723777	−	0.520824i
$254$	−27.5879	−	44.6305i	−0.00681504	−	0.0110251i
$255$	−46.5355	+	53.7049i	−0.0114281	+	0.0131887i
$256$	1163.51	+	3927.27i	0.284059	+	0.958807i
$257$	−612.990	−	4263.44i	−0.148783	−	1.03481i	−0.918215	−	0.396081i	$-0.870370\pi$
$257$	−612.990	−	4263.44i	−0.148783	−	1.03481i	0.769432	−	0.638728i	$-0.220539\pi$
$258$	−232.291	+	347.877i	−0.0560536	+	0.0839453i
$259$	4955.25	+	712.457i	1.18882	+	0.170926i
$260$	120.217	−	668.639i	0.0286752	−	0.159489i
$261$	1177.51	−	1832.24i	0.279257	−	0.434532i
$262$	351.663	+	2792.92i	0.0829229	+	0.658578i
$263$	−4878.09	−	1432.34i	−1.14371	−	0.335824i	−0.345628	−	0.938372i	$-0.612334\pi$
$263$	−4878.09	−	1432.34i	−1.14371	−	0.335824i	−0.798083	+	0.602548i	$0.794152\pi$
$264$	−313.111	−	301.579i	−0.0729950	−	0.0703064i
$265$	−3636.74	−	4197.03i	−0.843032	−	0.972911i
$266$	−488.101	+	134.063i	−0.112509	+	0.0309020i
$267$	164.739	+	75.2337i	0.0377598	+	0.0172443i
$268$	−2870.70	−	4831.62i	−0.654312	−	1.10126i
$269$	982.881	+	3347.39i	0.222778	+	0.758713i	0.992704	+	0.120579i	$0.0384752\pi$
$269$	982.881	+	3347.39i	0.222778	+	0.758713i	−0.769926	+	0.638134i	$0.779707\pi$
$270$	−1064.43	+	463.712i	−0.239922	+	0.104521i
$271$	−1767.88	−	3871.11i	−0.396277	−	0.867725i	−0.997634	−	0.0687449i	$-0.978101\pi$
$271$	−1767.88	−	3871.11i	−0.396277	−	0.867725i	0.601358	−	0.798980i	$-0.294627\pi$
$272$	−419.805	+	420.824i	−0.0935823	+	0.0938096i
$273$	56.1758	−	36.1020i	0.0124539	−	0.00800363i
$274$	3837.61	+	620.675i	0.846126	+	0.136848i
$275$			1393.61i			0.305592i
$276$	461.399	−	242.295i	0.100627	−	0.0528422i
$277$			3051.89i			0.661987i	0.943633	+	0.330993i	$0.107384\pi$
$277$			3051.89i			0.661987i	−0.943633	+	0.330993i	$0.892616\pi$
$278$	−1089.68	+	6737.46i	−0.235089	+	1.45355i
$279$	5052.88	−	3247.29i	1.08426	−	0.696810i
$280$	4920.02	−	1167.36i	1.05010	−	0.249154i
$281$	−3341.16	−	7316.12i	−0.709313	−	1.55318i	−0.828301	−	0.560283i	$-0.810692\pi$
$281$	−3341.16	−	7316.12i	−0.709313	−	1.55318i	0.118988	−	0.992896i	$-0.462035\pi$
$282$	−29.5536	−	67.8388i	−0.00624076	−	0.0143253i
$283$	1969.56	+	6707.70i	0.413704	+	1.40894i	0.858270	+	0.513199i	$0.171540\pi$
$283$	1969.56	+	6707.70i	0.413704	+	1.40894i	−0.444566	+	0.895746i	$0.646642\pi$
$284$	5841.80	−	3470.89i	1.22059	−	0.725209i
$285$	72.2056	+	32.9752i	0.0150073	+	0.00685362i
$286$	159.742	+	581.592i	0.0330270	+	0.120246i
$287$	5120.00	+	5908.79i	1.05304	+	1.21528i
$288$	−4547.14	+	1611.90i	−0.930357	+	0.329798i
$289$	4631.22	+	1359.85i	0.942646	+	0.276786i
$290$	2971.08	−	374.095i	0.601613	−	0.0757503i
$291$	−41.9527	+	65.2797i	−0.00845125	+	0.0131504i
$292$	−392.386	+	2182.42i	−0.0786392	+	0.437385i
$293$	−1937.23	−	278.531i	−0.386260	−	0.0555357i	−0.0535502	−	0.998565i	$-0.517054\pi$
$293$	−1937.23	−	278.531i	−0.386260	−	0.0555357i	−0.332709	+	0.943029i	$0.607963\pi$
$294$	−63.1408	−	42.1617i	−0.0125253	−	0.00836367i
$295$	534.249	+	3715.79i	0.105441	+	0.733361i
$296$	−4033.36	−	5182.38i	−0.792008	−	1.01763i
$297$	675.012	−	779.005i	0.131879	−	0.152197i
$298$	−5508.03	+	3404.74i	−1.07071	+	0.661849i
$299$	−722.030	−	37.9817i	−0.139653	−	0.00734627i
$300$	−181.045	−	90.4873i	−0.0348421	−	0.0174143i
$301$	3264.55	+	2828.75i	0.625134	+	0.541682i
$302$	−4746.74	−	2269.25i	−0.904451	−	0.432386i
$303$	−159.218	−	1107.38i	−0.0301875	−	0.209959i
$304$	583.153	+	317.508i	0.110020	+	0.0599024i
$305$	333.893	−	2322.27i	0.0626840	−	0.435977i
$306$	−520.989	−	467.693i	−0.0973298	−	0.0873734i
$307$	2179.32	−	3391.08i	0.405147	−	0.630421i	−0.577394	−	0.816465i	$-0.695930\pi$
$307$	2179.32	−	3391.08i	0.405147	−	0.630421i	0.982541	+	0.186044i	$0.0595668\pi$
$308$	−3493.79	+	2818.97i	−0.646354	+	0.521512i
$309$	141.176	−	480.800i	0.0259910	−	0.0885171i
$310$	7881.66	+	2465.28i	1.44403	+	0.451672i
$311$	1956.42	+	2257.83i	0.356716	+	0.411672i	0.905537	−	0.424268i	$-0.139469\pi$
$311$	1956.42	+	2257.83i	0.356716	+	0.411672i	−0.548821	+	0.835940i	$0.684923\pi$
$312$	−85.9273	−	17.0108i	−0.0155919	−	0.00308668i
$313$	1353.11	−	2962.90i	0.244353	−	0.535058i	−0.747225	−	0.664571i	$-0.768614\pi$
$313$	1353.11	−	2962.90i	0.244353	−	0.535058i	0.991578	+	0.129513i	$0.0413415\pi$
$314$	1643.31	+	28.8377i	0.295342	+	0.00518282i
$315$	1677.95	+	5714.57i	0.300133	+	1.02216i
$316$	−5569.27	−	3861.81i	−0.991443	−	0.687481i
$317$	−6803.63	+	3107.11i	−1.20546	+	0.550514i	−0.913861	−	0.406028i	$-0.866914\pi$
$317$	−6803.63	+	3107.11i	−1.20546	+	0.550514i	−0.291596	+	0.956541i	$0.594186\pi$
$318$	−549.298	+	459.345i	−0.0968650	+	0.0810025i
$319$	−2236.50	+	1437.31i	−0.392538	+	0.252269i
$320$	−5710.70	−	3374.29i	−0.997619	−	0.589463i
$321$	574.090			0.0998211
$322$	−1887.23	−	5039.89i	−0.326620	−	0.872243i
$323$			96.3583i			0.0165991i
$324$	−2148.83	−	5178.85i	−0.368455	−	0.888006i
$325$	151.813	+	236.226i	0.0259111	+	0.0403184i
$326$	2839.13	+	3395.11i	0.482347	+	0.576804i
$327$	−145.847	−	319.360i	−0.0246647	−	0.0540081i
$328$	539.628	−	10241.8i	0.0908413	−	1.72411i
$329$	−733.176	+	215.280i	−0.122861	+	0.0360753i
$330$	703.894	+	12.3523i	0.117418	+	0.00206052i
$331$	−10668.8	−	4872.28i	−1.77163	−	0.809077i	−0.980252	−	0.197754i	$-0.936635\pi$
$331$	−10668.8	−	4872.28i	−1.77163	−	0.809077i	−0.791381	−	0.611324i	$-0.790637\pi$
$332$	−2554.41	−	2375.35i	−0.422264	−	0.392664i
$333$	5845.54	−	5065.19i	0.961963	−	0.833546i
$334$	46.1049	−	147.400i	0.00755313	−	0.0241479i
$335$	8732.56	+	2564.11i	1.42421	+	0.418186i
$336$	−139.362	−	636.918i	−0.0226275	−	0.103413i
$337$	774.500	+	497.741i	0.125192	+	0.0804560i	0.601738	−	0.798693i	$-0.294475\pi$
$337$	774.500	+	497.741i	0.125192	+	0.0804560i	−0.476546	+	0.879149i	$0.658111\pi$
$338$	−4533.71	−	4069.93i	−0.729590	−	0.654956i
$339$	570.581	+	82.0372i	0.0914151	+	0.0131435i
$340$	33.7740	−	962.007i	0.00538722	−	0.153448i
$341$	−7256.96	+	1043.39i	−1.15245	+	0.165698i
$342$	−337.312	+	705.579i	−0.0533326	+	0.111559i
$343$	−4387.98	+	5064.00i	−0.690754	+	0.797173i
$344$	−510.181	−	5643.31i	−0.0799625	−	0.884497i
$345$	−279.979	+	796.158i	−0.0436914	+	0.124243i
$346$	4421.23	−	2732.95i	0.686957	−	0.424636i
$347$	6092.26	+	5278.98i	0.942507	+	0.816687i	0.983209	−	0.182485i	$-0.0584140\pi$
$347$	6092.26	+	5278.98i	0.942507	+	0.816687i	−0.0407021	+	0.999171i	$0.512959\pi$
$348$	−41.5058	−	383.870i	−0.00639352	−	0.0591310i
$349$	2121.32	−	304.999i	0.325362	−	0.0467800i	0.0223015	−	0.999751i	$-0.492901\pi$
$349$	2121.32	−	304.999i	0.325362	−	0.0467800i	0.303061	+	0.952971i	$0.401992\pi$
$350$	−1160.66	+	1738.18i	−0.177256	+	0.265457i
$351$	29.5579	−	205.580i	0.00449482	−	0.0312622i
$352$	5866.16	+	515.985i	0.888260	+	0.0781309i
$353$	1375.03	+	883.676i	0.207324	+	0.133239i	0.640182	−	0.768223i	$-0.278859\pi$
$353$	1375.03	+	883.676i	0.207324	+	0.133239i	−0.432859	+	0.901462i	$0.642495\pi$
$354$	480.238	−	60.4678i	0.0721028	−	0.00907861i
$355$	−3100.21	+	10558.3i	−0.463498	+	1.57853i
$356$	−2376.67	+	608.144i	−0.353829	+	0.0905382i
$357$	71.5066	−	61.9608i	0.0106009	−	0.00918575i
$358$	−8749.56	+	2403.18i	−1.29170	+	0.354782i
$359$	−2843.79	+	6227.03i	−0.418076	+	0.915460i	0.577037	+	0.816718i	$0.304209\pi$
$359$	−2843.79	+	6227.03i	−0.418076	+	0.915460i	−0.995113	+	0.0987414i	$0.968518\pi$
$360$	3614.92	−	6926.03i	0.529230	−	1.01398i
$361$	−6477.89	+	1902.08i	−0.944436	+	0.277311i
$362$	−4450.18	−	10215.2i	−0.646123	−	1.48314i
$363$	146.502	−	66.9051i	0.0211828	−	0.00967385i
$364$	−285.136	+	858.433i	−0.0410582	+	0.123610i
$365$	−1941.39	−	3020.86i	−0.278402	−	0.433202i
$366$	−298.626	−	48.2983i	−0.0426488	−	0.00689779i
$367$	7221.50			1.02714			0.513568	−	0.858049i	$-0.328323\pi$
$367$	7221.50			1.02714			0.513568	+	0.858049i	$0.328323\pi$
$368$	−2803.23	+	6479.04i	−0.397088	+	0.917781i
$369$	12079.8			1.70420
$370$	10498.2	+	1697.92i	1.47507	+	0.238570i
$371$	3997.65	+	6220.47i	0.559428	+	0.870487i
$372$	335.648	−	1010.51i	0.0467811	−	0.140840i
$373$	−8797.76	+	4017.80i	−1.22126	+	0.557731i	−0.918533	−	0.395345i	$-0.870625\pi$
$373$	−8797.76	+	4017.80i	−1.22126	+	0.557731i	−0.302729	+	0.953077i	$0.597898\pi$
$374$	341.315	+	783.471i	0.0471898	+	0.108322i
$375$	−603.163	+	177.105i	−0.0830592	+	0.0243884i
$376$	888.605	+	463.792i	0.121878	+	0.0636123i
$377$	−222.528	+	487.268i	−0.0303999	+	0.0665665i
$378$	1490.70	−	409.439i	0.202839	−	0.0557124i
$379$	−677.688	+	587.220i	−0.0918483	+	0.0795870i	−0.699575	−	0.714559i	$-0.746627\pi$
$379$	−677.688	+	587.220i	−0.0918483	+	0.0795870i	0.607726	+	0.794146i	$0.292082\pi$
$380$	−1041.70	+	266.552i	−0.140627	+	0.0359837i
$381$	3.08655	−	10.5118i	0.000415035	−	0.00141348i
$382$	3986.90	−	501.999i	0.533999	−	0.0672369i
$383$	−6017.95	−	3867.50i	−0.802879	−	0.515979i	0.0736752	−	0.997282i	$-0.476527\pi$
$383$	−6017.95	−	3867.50i	−0.802879	−	0.515979i	−0.876554	+	0.481303i	$0.840164\pi$
$384$	−447.924	+	728.576i	−0.0595261	+	0.0968229i
$385$	1034.61	−	7195.89i	0.136958	−	0.952563i
$386$	−5813.29	+	8705.91i	−0.766551	+	1.14798i
$387$	6606.03	−	949.803i	0.867709	−	0.124758i
$388$	−112.996	−	1045.05i	−0.0147848	−	0.136738i
$389$	−1516.01	−	1313.63i	−0.197596	−	0.171218i	0.550443	−	0.834873i	$-0.314459\pi$
$389$	−1516.01	−	1313.63i	−0.197596	−	0.171218i	−0.748039	+	0.663655i	$0.769004\pi$
$390$	120.661	−	74.5853i	0.0156664	−	0.00968403i
$391$	−1020.31	+	92.3275i	−0.131967	+	0.0119417i
$392$	1024.28	−	92.5996i	0.131974	−	0.0119311i
$393$	−384.909	+	444.209i	−0.0494048	+	0.0570162i
$394$	−3500.91	+	7323.09i	−0.447648	+	0.936375i
$395$	10863.3	−	1561.91i	1.38378	−	0.198958i
$396$	−243.359	+	6931.74i	−0.0308819	+	0.879629i
$397$	−7800.48	−	1121.54i	−0.986133	−	0.141784i	−0.369665	−	0.929165i	$-0.620528\pi$
$397$	−7800.48	−	1121.54i	−0.986133	−	0.141784i	−0.616467	+	0.787381i	$0.711437\pi$
$398$	1624.97	+	1458.74i	0.204655	+	0.183719i
$399$	−88.9129	−	57.1408i	−0.0111559	−	0.00716947i
$400$	2678.32	−	586.036i	0.334790	−	0.0732545i
$401$	12795.2	+	3757.02i	1.59342	+	0.467871i	0.953706	−	0.300739i	$-0.0972334\pi$
$401$	12795.2	+	3757.02i	1.59342	+	0.467871i	0.639717	+	0.768611i	$0.279052\pi$
$402$	350.314	−	1119.98i	0.0434629	−	0.138954i
$403$	−1116.44	+	967.404i	−0.138000	+	0.119578i
$404$	11098.0	+	10320.0i	1.36670	+	1.27089i
$405$	8259.42	+	3771.95i	1.01337	+	0.462789i
$406$	−3986.53	−	69.9578i	−0.487311	−	0.00855159i
$407$	−9058.88	+	2659.93i	−1.10327	+	0.323950i
$408$	−123.943	−	6.53043i	−0.0150395	−	0.000792413i
$409$	6065.81	+	13282.3i	0.733337	+	1.60578i	0.794213	+	0.607639i	$0.207883\pi$
$409$	6065.81	+	13282.3i	0.733337	+	1.60578i	−0.0608757	+	0.998145i	$0.519389\pi$
$410$	10654.4	+	12740.9i	1.28338	+	1.53470i
$411$	438.845	+	682.857i	0.0526682	+	0.0819534i
$412$	2601.41	+	6269.59i	0.311073	+	0.749710i
$413$		−	4998.35i		−	0.595527i
$414$	−7794.35	−	2895.63i	−0.925293	−	0.343749i
$415$	5648.77			0.668162
$416$	1050.57	−	551.571i	0.123818	−	0.0650072i
$417$	−1198.85	+	770.454i	−0.140786	+	0.0904779i
$418$	732.306	−	612.384i	0.0856896	−	0.0716571i
$419$	3978.59	−	1816.96i	0.463883	−	0.211848i	−0.169742	−	0.985489i	$-0.554294\pi$
$419$	3978.59	−	1816.96i	0.463883	−	0.211848i	0.633625	+	0.773640i	$0.281566\pi$
$420$	867.647	+	601.639i	0.100802	+	0.0698975i
$421$	−3877.44	−	13205.3i	−0.448871	−	1.52871i	−0.804423	−	0.594057i	$-0.797525\pi$
$421$	−3877.44	−	13205.3i	−0.448871	−	1.52871i	0.355552	−	0.934657i	$-0.384293\pi$
$422$	5502.83	+	96.5666i	0.634771	+	0.0111393i
$423$	−490.441	+	1073.92i	−0.0563737	+	0.123441i
$424$	1883.64	−	9514.92i	0.215749	−	1.08982i
$425$	260.553	+	300.694i	0.0297381	+	0.0343196i
$426$	1354.14	+	423.557i	0.154010	+	0.0481723i
$427$	−880.088	+	2997.30i	−0.0997434	+	0.339695i
$428$	−6052.23	+	4883.25i	−0.683517	+	0.551497i
$429$	−68.0856	+	105.943i	−0.00766248	+	0.0119231i
$430$	6828.33	+	6129.81i	0.765793	+	0.687456i
$431$	2014.16	−	14008.8i	0.225101	−	1.56561i	−0.493223	−	0.869903i	$-0.664181\pi$
$431$	2014.16	−	14008.8i	0.225101	−	1.56561i	0.718324	−	0.695709i	$-0.244910\pi$
$432$	−1780.99	−	969.694i	−0.198352	−	0.107996i
$433$	310.023	+	2156.26i	0.0344082	+	0.239315i	0.999766	−	0.0216138i	$-0.00688044\pi$
$433$	310.023	+	2156.26i	0.0344082	+	0.239315i	−0.965358	+	0.260928i	$0.915971\pi$
$434$	−9920.26	−	4742.52i	−1.09721	−	0.524536i
$435$	472.544	+	409.462i	0.0520845	+	0.0451315i
$436$	4254.06	+	2126.20i	0.467276	+	0.233548i
$437$	420.054	+	1064.50i	0.0459815	+	0.116526i
$438$	−393.833	+	243.445i	−0.0429636	+	0.0265576i
$439$	1768.47	−	2040.92i	0.192265	−	0.221885i	−0.651430	−	0.758709i	$-0.725830\pi$
$439$	1768.47	−	2040.92i	0.192265	−	0.221885i	0.843695	+	0.536824i	$0.180376\pi$
$440$	−7525.73	+	5857.15i	−0.815398	+	0.634610i
$441$	172.393	+	1199.02i	0.0186149	+	0.129469i
$442$	143.203	+	95.6226i	0.0154106	+	0.0102903i
$443$	7563.98	+	1087.54i	0.811231	+	0.116637i	0.535433	−	0.844578i	$-0.320149\pi$
$443$	7563.98	+	1087.54i	0.811231	+	0.116637i	0.275799	+	0.961215i	$0.411058\pi$
$444$	242.642	−	1349.56i	0.0259353	−	0.144250i
$445$	2147.86	−	3342.13i	0.228805	−	0.356028i
$446$	17034.3	−	2144.82i	1.80851	−	0.227713i
$447$	−1297.31	−	380.923i	−0.137272	−	0.0403066i
$448$	6886.87	+	5529.15i	0.726281	+	0.583098i
$449$	−7682.56	−	8866.14i	−0.807488	−	0.931891i	0.191278	−	0.981536i	$-0.438737\pi$
$449$	−7682.56	−	8866.14i	−0.807488	−	0.931891i	−0.998767	+	0.0496444i	$0.984191\pi$
$450$	855.276	+	3113.91i	0.0895958	+	0.326203i
$451$	−13412.5	−	6125.30i	−1.40038	−	0.639532i
$452$	−6713.05	+	3988.55i	−0.698574	+	0.415056i
$453$	−309.502	−	1054.07i	−0.0321008	−	0.109325i
$454$	−3299.29	−	7573.36i	−0.341065	−	0.782897i
$455$	−608.514	−	1332.46i	−0.0626980	−	0.137290i
$456$	32.0065	+	134.897i	0.00328694	+	0.0138533i
$457$	−471.729	+	303.162i	−0.0482857	+	0.0310313i	−0.564561	−	0.825391i	$-0.690955\pi$
$457$	−471.729	+	303.162i	−0.0482857	+	0.0310313i	0.516275	+	0.856423i	$0.327318\pi$
$458$	−313.835	+	1940.43i	−0.0320187	+	0.197970i
$459$		−	294.286i		−	0.0299261i
$460$	−3820.56	−	10774.9i	−0.387249	−	1.09213i
$461$			12249.2i			1.23753i	0.785576	+	0.618765i	$0.212367\pi$
$461$			12249.2i			1.23753i	−0.785576	+	0.618765i	$0.787633\pi$
$462$	−925.335	−	149.659i	−0.0931829	−	0.0150709i
$463$	−6950.98	+	4467.12i	−0.697709	+	0.448390i	−0.840819	−	0.541316i	$-0.817926\pi$
$463$	−6950.98	+	4467.12i	−0.697709	+	0.448390i	0.143110	+	0.989707i	$0.454290\pi$
$464$	3702.79	+	3693.82i	0.370470	+	0.369572i
$465$	716.314	+	1568.51i	0.0714371	+	0.156425i
$466$	7674.54	−	3343.37i	0.762910	−	0.332358i
$467$	−2603.05	−	8865.16i	−0.257933	−	0.878438i	−0.982028	−	0.188738i	$-0.939560\pi$
$467$	−2603.05	−	8865.16i	−0.257933	−	0.878438i	0.724095	−	0.689701i	$-0.242258\pi$
$468$	713.862	+	1201.49i	0.0705092	+	0.118673i
$469$	−11023.0	−	5034.01i	−1.08527	−	0.495627i
$470$	−1565.26	+	429.918i	−0.153617	+	0.0421929i
$471$	224.735	+	259.358i	0.0219856	+	0.0253728i
$472$	−4548.47	+	4722.41i	−0.443560	+	0.460523i
$473$	−7816.48	−	2295.13i	−0.759835	−	0.223108i
$474$	−176.781	−	1404.01i	−0.0171305	−	0.136051i
$475$	240.285	−	373.890i	0.0232105	−	0.0361163i
$476$	−226.801	+	1261.45i	−0.0218391	+	0.121467i
$477$	11308.1	+	1625.87i	1.08546	+	0.156066i
$478$	333.756	−	499.829i	0.0319365	−	0.0478277i
$479$	2516.13	+	17500.1i	0.240011	+	1.66931i	0.652074	+	0.758155i	$0.273899\pi$
$479$	2516.13	+	17500.1i	0.240011	+	1.66931i	−0.412064	+	0.911155i	$0.635192\pi$
$480$	−272.260	−	1357.98i	−0.0258894	−	0.129131i
$481$	−1245.78	+	1437.71i	−0.118093	+	0.136287i
$482$	−9750.55	−	15774.0i	−0.921422	−	1.49063i
$483$	519.852	−	996.220i	0.0489733	−	0.0938501i
$484$	−975.366	+	1951.49i	−0.0916008	+	0.183273i
$485$	1286.46	+	1114.72i	0.120443	+	0.104365i
$486$	1548.62	−	3239.34i	0.144540	−	0.302345i
$487$	−726.347	−	5051.85i	−0.0675851	−	0.470064i	−0.995305	−	0.0967876i	$-0.969143\pi$
$487$	−726.347	−	5051.85i	−0.0675851	−	0.470064i	0.927720	−	0.373277i	$-0.121766\pi$
$488$	3559.04	−	2030.96i	0.330143	−	0.188396i
$489$	−131.515	+	914.705i	−0.0121622	+	0.0845897i
$490$	−1112.58	+	1239.36i	−0.102574	+	0.114263i
$491$	6433.64	−	10010.9i	0.591337	−	0.920138i	−0.408636	−	0.912698i	$-0.633995\pi$
$491$	6433.64	−	10010.9i	0.591337	−	0.920138i	0.999972	−	0.00744014i	$-0.00236829\pi$
$492$	1666.62	−	1344.72i	0.152718	−	0.123221i
$493$	−213.838	+	728.266i	−0.0195351	+	0.0665303i
$494$	57.4206	−	183.578i	0.00522971	−	0.0167197i
$495$	−7355.55	−	8488.75i	−0.667893	−	0.770790i
$496$	5056.94	+	13508.1i	0.457788	+	1.22285i
$497$	6086.51	−	13327.6i	0.549330	−	1.20287i
$498$	12.7793	−	728.225i	0.00114991	−	0.0655272i
$499$	−2009.95	−	6845.25i	−0.180316	−	0.614100i	−0.999194	−	0.0401326i	$-0.987222\pi$
$499$	−2009.95	−	6845.25i	−0.180316	−	0.614100i	0.818878	−	0.573967i	$-0.194596\pi$
$500$	4852.26	−	6997.63i	0.433999	−	0.625887i
$501$	29.3337	−	13.3963i	0.00261584	−	0.00119461i
$502$	−1590.13	−	1901.52i	−0.141376	−	0.169062i
$503$	2407.22	−	1547.03i	0.213385	−	0.137134i	−0.429583	−	0.903027i	$-0.641339\pi$
$503$	2407.22	−	1547.03i	0.213385	−	0.137134i	0.642968	+	0.765893i	$0.277703\pi$
$504$	−6076.58	+	8442.97i	−0.537048	+	0.746190i
$505$	−24541.8			−2.16257
$506$	7186.00	+	7167.38i	0.631338	+	0.629701i
$507$		−	1272.13i		−	0.111435i
$508$	56.8749	+	137.073i	0.00496735	+	0.0119717i
$509$	5113.72	+	7957.11i	0.445308	+	0.692913i	0.989254	−	0.146208i	$-0.0467068\pi$
$509$	5113.72	+	7957.11i	0.445308	+	0.692913i	−0.543946	+	0.839120i	$0.683070\pi$
$510$	154.186	−	128.937i	0.0133872	−	0.0111949i
$511$	1986.18	+	4349.12i	0.171944	+	0.376504i
$512$	−1475.17	−	11490.9i	−0.127332	−	0.991860i
$513$	−315.414	+	92.6138i	−0.0271459	+	0.00797076i
$514$	−213.758	+	12181.0i	−0.0183433	+	1.04529i
$515$	−9998.96	−	4566.37i	−0.855548	−	0.390715i
$516$	805.688	−	866.423i	0.0687373	−	0.0739189i
$517$	1089.10	−	943.713i	0.0926473	−	0.0802794i
$518$	−13514.0	−	4227.01i	−1.14628	−	0.358541i
$519$	1041.33	+	305.763i	0.0880721	+	0.0258603i
$520$	−637.612	+	1812.65i	−0.0537714	+	0.152865i
$521$	8446.79	+	5428.42i	0.710289	+	0.456475i	0.845247	−	0.534376i	$-0.179454\pi$
$521$	8446.79	+	5428.42i	0.710289	+	0.456475i	−0.134958	+	0.990851i	$0.543090\pi$
$522$	−4115.19	+	4584.13i	−0.345052	+	0.384371i
$523$	−11727.0	−	1686.08i	−0.980468	−	0.140970i	−0.366600	−	0.930379i	$-0.619478\pi$
$523$	−11727.0	−	1686.08i	−0.980468	−	0.140970i	−0.613868	+	0.789409i	$0.710387\pi$
$524$	279.355	−	7957.05i	0.0232895	−	0.663369i
$525$	−431.969	+	62.1078i	−0.0359099	+	0.00516306i
$526$	12973.5	+	6202.17i	1.07542	+	0.514121i
$527$	−1370.74	+	1581.91i	−0.113302	+	0.130758i
$528$	738.063	+	983.448i	0.0608335	+	0.0810589i
$529$	−10869.2	+	5467.79i	−0.893333	+	0.449395i
$530$	8258.99	+	13361.0i	0.676882	+	1.09503i
$531$	−5836.37	−	5057.24i	−0.476981	−	0.413306i
$532$	1423.39	−	153.904i	0.116000	−	0.0125424i
$533$	−2940.78	+	422.821i	−0.238986	+	0.0343610i
$534$	−426.000	−	284.457i	−0.0345222	−	0.0230518i
$535$	1792.24	−	12465.3i	0.144832	−	1.00733i
$536$	5833.50	+	14786.9i	0.470091	+	1.19160i
$537$	−1593.83	−	1024.29i	−0.128079	−	0.0823117i
$538$	−1232.71	−	9790.24i	−0.0987842	−	0.784549i
$539$	416.573	−	1418.72i	0.0332896	−	0.113374i
$540$	3181.44	−	814.070i	0.253532	−	0.0648741i
$541$	12396.2	−	10741.4i	0.985129	−	0.853619i	−0.00410096	−	0.999992i	$-0.501305\pi$
$541$	12396.2	−	10741.4i	0.985129	−	0.853619i	0.989229	+	0.146373i	$0.0467599\pi$
$542$	3188.03	+	11607.1i	0.252652	+	0.919863i
$543$	966.489	−	2116.32i	0.0763831	−	0.167256i
$544$	1362.19	−	985.424i	0.107360	−	0.0776649i
$545$	−7389.63	+	2169.79i	−0.580802	+	0.170539i
$546$	−173.154	+	75.4337i	−0.0135720	+	0.00591257i
$547$	−5132.55	+	2343.96i	−0.401192	+	0.183218i	−0.605784	−	0.795629i	$-0.707140\pi$
$547$	−5132.55	+	2343.96i	−0.401192	+	0.183218i	0.204592	+	0.978847i	$0.434413\pi$
$548$	−10434.9	−	3466.03i	−0.813422	−	0.270185i
$549$	2609.37	+	4060.26i	0.202851	+	0.315643i
$550$	629.335	−	3891.15i	0.0487908	−	0.301672i
$551$	847.847			0.0655527
$552$	−1397.71	+	468.160i	−0.107773	+	0.0360982i
$553$	−14613.0			−1.12370
$554$	1378.19	−	8521.32i	0.105693	−	0.653495i
$555$	1200.51	+	1868.03i	0.0918175	+	0.142871i
$556$	6085.10	−	18319.9i	0.464147	−	1.39737i
$557$	15079.6	−	6886.62i	1.14711	−	0.523869i	0.251129	−	0.967954i	$-0.419198\pi$
$557$	15079.6	−	6886.62i	1.14711	−	0.523869i	0.895985	+	0.444084i	$0.146471\pi$
$558$	−15574.8	+	6785.08i	−1.18160	+	0.514759i
$559$	−1574.97	+	462.453i	−0.119167	+	0.0349905i
$560$	−14264.6	+	1037.61i	−1.07641	+	0.0782986i
$561$	−74.1267	+	162.315i	−0.00557866	+	0.0122156i
$562$	6025.14	+	21936.5i	0.452233	+	1.64650i
$563$	11874.3	−	10289.2i	0.888888	−	0.770226i	−0.0852073	−	0.996363i	$-0.527155\pi$
$563$	11874.3	−	10289.2i	0.888888	−	0.770226i	0.974095	+	0.226137i	$0.0726098\pi$
$564$	51.8829	+	202.762i	0.00387352	+	0.0151380i
$565$	3562.58	−	12133.0i	0.265272	−	0.903434i
$566$	−2470.18	−	19618.3i	−0.183444	−	1.45692i
$567$	−10170.5	−	6536.19i	−0.753301	−	0.484117i
$568$	−17878.6	+	7053.15i	−1.32072	+	0.521027i
$569$	1736.37	−	12076.7i	0.127931	−	0.889777i	−0.820241	−	0.572018i	$-0.806161\pi$
$569$	1736.37	−	12076.7i	0.127931	−	0.889777i	0.948172	−	0.317759i	$-0.102930\pi$
$570$	−186.717	−	124.679i	−0.0137206	−	0.00916178i
$571$	−18483.0	+	2657.45i	−1.35462	+	0.194765i	−0.781090	−	0.624419i	$-0.785336\pi$
$571$	−18483.0	+	2657.45i	−1.35462	+	0.194765i	−0.573531	+	0.819184i	$0.694427\pi$
$572$	−183.382	−	1696.03i	−0.0134049	−	0.123976i
$573$	634.108	+	549.458i	0.0462308	+	0.0400592i
$574$	−11627.4	−	18810.3i	−0.845505	−	1.36782i
$575$	4189.23	+	2186.05i	0.303831	+	0.158547i
$576$	13424.2	−	2447.22i	0.971078	−	0.177027i
$577$	13076.1	−	15090.6i	0.943437	−	1.08878i	−0.0524899	−	0.998621i	$-0.516716\pi$
$577$	13076.1	−	15090.6i	0.943437	−	1.08878i	0.995927	−	0.0901630i	$-0.0287388\pi$
$578$	−12316.9	−	5888.30i	−0.886362	−	0.423738i
$579$	−2163.57	+	311.075i	−0.155294	+	0.0223279i
$580$	−8464.61	−	297.175i	−0.605990	−	0.0212750i
$581$	−7444.63	−	1070.38i	−0.531593	−	0.0764315i
$582$	146.618	−	163.325i	0.0104424	−	0.0116324i
$583$	−11731.3	−	7539.27i	−0.833383	−	0.535583i
$584$	2081.15	−	5916.44i	0.147463	−	0.419219i
$585$	−2171.55	−	637.623i	−0.153474	−	0.0450641i
$586$	5283.24	+	1652.53i	0.372438	+	0.116494i
$587$	16634.5	−	14413.8i	1.16964	−	1.01350i	0.170032	−	0.985439i	$-0.445613\pi$
$587$	16634.5	−	14413.8i	1.16964	−	1.01350i	0.999606	−	0.0280586i	$-0.00893251\pi$
$588$	157.259	+	146.235i	0.0110293	+	0.0102562i
$589$	2126.87	+	971.307i	0.148788	+	0.0679491i
$590$	186.300	−	10616.3i	0.0129997	−	0.740788i
$591$	−1626.17	+	477.487i	−0.113184	+	0.0332338i
$592$	8921.43	+	16291.4i	0.619372	+	1.13103i
$593$	−2478.17	−	5426.44i	−0.171613	−	0.375779i	0.804209	−	0.594346i	$-0.202589\pi$
$593$	−2478.17	−	5426.44i	−0.171613	−	0.375779i	−0.975822	+	0.218567i	$0.929862\pi$
$594$	−2236.52	+	1870.27i	−0.154487	+	0.129189i
$595$	−1122.13	−	1746.07i	−0.0773157	−	0.120306i
$596$	16916.7	−	7019.16i	1.16265	−	0.482410i
$597$			455.958i			0.0312581i
$598$	1998.86	+	432.110i	0.136688	+	0.0295490i
$599$	9489.72			0.647311			0.323656	−	0.946175i	$-0.395088\pi$
$599$	9489.72			0.647311			0.323656	+	0.946175i	$0.395088\pi$
$600$	464.640	+	334.411i	0.0316148	+	0.0227538i
$601$	−14446.7	+	9284.32i	−0.980520	+	0.630142i	−0.929604	−	0.368561i	$-0.879851\pi$
$601$	−14446.7	+	9284.32i	−0.980520	+	0.630142i	−0.0509163	+	0.998703i	$0.516214\pi$
$602$	−7837.66	−	9372.50i	−0.530630	−	0.634542i
$603$	−17030.8	+	7777.73i	−1.15017	+	0.525263i
$604$	12228.8	+	8479.64i	0.823814	+	0.571244i
$605$	−995.361	−	3389.89i	−0.0668879	−	0.227799i
$606$	−55.5213	+	3163.87i	−0.00372178	+	0.212085i
$607$	−2402.27	+	5260.25i	−0.160635	+	0.351741i	−0.972786	−	0.231706i	$-0.925569\pi$
$607$	−2402.27	+	5260.25i	−0.160635	+	0.351741i	0.812151	+	0.583447i	$0.198296\pi$
$608$	−1484.86	−	1149.87i	−0.0990447	−	0.0766998i
$609$	−545.187	−	629.180i	−0.0362760	−	0.0418648i
$610$	−1980.99	+	6333.34i	−0.131488	+	0.420376i
$611$	81.8067	−	278.608i	0.00541660	−	0.0184473i
$612$	1243.47	+	1541.14i	0.0821312	+	0.101792i
$613$	−5867.10	+	9129.38i	−0.386574	+	0.601521i	−0.978940	−	0.204148i	$-0.934558\pi$
$613$	−5867.10	+	9129.38i	−0.386574	+	0.601521i	0.592366	+	0.805669i	$0.298194\pi$
$614$	−7616.33	+	8484.24i	−0.500603	+	0.557648i
$615$	−493.536	+	3432.62i	−0.0323598	+	0.225067i
$616$	11028.2	−	6293.22i	0.721328	−	0.411625i
$617$	3125.36	+	21737.4i	0.203926	+	1.41834i	0.792490	+	0.609885i	$0.208784\pi$
$617$	3125.36	+	21737.4i	0.203926	+	1.41834i	−0.588564	+	0.808451i	$0.700306\pi$
$618$	−611.306	+	1278.71i	−0.0397902	+	0.0832318i
$619$	−6004.11	−	5202.59i	−0.389863	−	0.337819i	0.437771	−	0.899087i	$-0.355768\pi$
$619$	−6004.11	−	5202.59i	−0.389863	−	0.337819i	−0.827634	+	0.561268i	$0.810314\pi$
$620$	−20893.4	−	10442.7i	−1.35339	−	0.676432i
$621$	−1282.88	−	3251.07i	−0.0828987	−	0.210082i
$622$	−4443.01	−	7187.69i	−0.286412	−	0.463344i
$623$	−3464.00	+	3997.67i	−0.222765	+	0.257084i
$624$	232.239	+	86.3001i	0.0148991	+	0.00553649i
$625$	2724.57	+	18949.8i	0.174373	+	1.21279i
$626$	−5116.09	+	7661.80i	−0.326646	+	0.489181i
$627$	197.296	+	28.3669i	0.0125666	+	0.00180680i
$628$	−4575.34	−	822.617i	−0.290726	−	0.0522707i
$629$	−1457.30	+	2267.60i	−0.0923788	+	0.143744i
$630$	−2104.45	−	16713.6i	−0.133085	−	1.05696i
$631$	21574.9	+	6334.97i	1.36115	+	0.399669i	0.879168	−	0.476513i	$-0.158099\pi$
$631$	21574.9	+	6334.97i	1.36115	+	0.399669i	0.481981	+	0.876182i	$0.339918\pi$
$632$	13806.3	+	13297.7i	0.868962	+	0.836956i
$633$	752.552	+	868.492i	0.0472532	+	0.0545331i
$634$	20399.8	−	5603.08i	1.27789	−	0.350988i
$635$	−218.609	−	99.8353i	−0.0136618	−	0.00623912i
$636$	1741.15	−	1034.50i	0.108555	−	0.0644979i
$637$	−83.9367	−	285.862i	−0.00522087	−	0.0177807i
$638$	6893.69	−	3003.20i	0.427780	−	0.186360i
$639$	−9403.87	−	20591.6i	−0.582177	−	1.27479i
$640$	14421.3	+	12000.4i	0.890708	+	0.741182i
$641$	19939.7	−	12814.5i	1.22866	−	0.789613i	0.244980	−	0.969528i	$-0.421219\pi$
$641$	19939.7	−	12814.5i	1.22866	−	0.789613i	0.983682	+	0.179915i	$0.0575822\pi$
$642$	−1602.94	−	259.252i	−0.0985406	−	0.0159375i
$643$			18926.5i			1.16079i	0.814336	+	0.580394i	$0.197102\pi$
$643$			18926.5i			1.16079i	−0.814336	+	0.580394i	$0.802898\pi$
$644$	2993.48	+	14924.4i	0.183167	+	0.913202i
$645$			1915.99i			0.116964i
$646$	43.5142	−	269.046i	0.00265022	−	0.0163862i
$647$	16909.3	−	10867.0i	1.02747	−	0.660316i	0.0856145	−	0.996328i	$-0.472715\pi$
$647$	16909.3	−	10867.0i	1.02747	−	0.660316i	0.941858	+	0.336012i	$0.109078\pi$
$648$	3661.14	+	15430.5i	0.221950	+	0.935443i
$649$	3915.91	+	8574.65i	0.236846	+	0.518620i
$650$	−317.208	−	728.135i	−0.0191414	−	0.0439382i
$651$	−646.831	−	2202.90i	−0.0389421	−	0.132625i
$652$	−6394.08	−	10761.8i	−0.384066	−	0.646416i
$653$	13306.6	+	6076.93i	0.797440	+	0.364179i	0.772101	−	0.635500i	$-0.219206\pi$
$653$	13306.6	+	6076.93i	0.797440	+	0.364179i	0.0253394	+	0.999679i	$0.491933\pi$
$654$	263.006	+	957.561i	0.0157253	+	0.0572532i
$655$	8443.54	+	9744.37i	0.503689	+	0.581288i
$656$	−6131.77	+	28352.8i	−0.364947	+	1.68749i
$657$	7087.87	+	2081.19i	0.420889	+	0.123584i
$658$	2144.35	−	270.000i	0.127045	−	0.0159965i
$659$	−11997.9	+	18669.2i	−0.709216	+	1.10356i	0.280408	+	0.959881i	$0.409530\pi$
$659$	−11997.9	+	18669.2i	−0.709216	+	1.10356i	−0.989624	+	0.143681i	$0.954106\pi$
$660$	−1959.79	−	352.359i	−0.115583	−	0.0207811i
$661$	3301.95	+	474.749i	0.194298	+	0.0279358i	0.238777	−	0.971074i	$-0.423254\pi$
$661$	3301.95	+	474.749i	0.194298	+	0.0279358i	−0.0444787	+	0.999010i	$0.514163\pi$
$662$	27588.6	+	18422.0i	1.61973	+	1.08156i
$663$	5.11686	+	35.5885i	0.000299732	+	0.00208468i
$664$	6059.61	+	7785.87i	0.354154	+	0.455046i
$665$	−1518.28	+	1752.19i	−0.0885362	+	0.102176i
$666$	−18609.0	+	11503.0i	−1.08271	+	0.669266i
$667$	812.381	+	8977.58i	0.0471597	+	0.521159i
$668$	−195.295	+	390.742i	−0.0113117	+	0.0226322i
$669$	2709.27	+	2347.59i	0.156571	+	0.135670i
$670$	−23224.6	−	11102.9i	−1.33917	−	0.640211i
$671$	−838.423	−	5831.36i	−0.0482369	−	0.335495i
$672$	101.496	+	1841.30i	0.00582631	+	0.105699i
$673$	1298.20	−	9029.17i	0.0743564	−	0.517160i	−0.918271	−	0.395953i	$-0.870414\pi$
$673$	1298.20	−	9029.17i	0.0743564	−	0.517160i	0.992627	−	0.121207i	$-0.0386766\pi$
$674$	−1937.74	−	1739.52i	−0.110740	−	0.0994121i
$675$	−733.848	+	1141.89i	−0.0418456	+	0.0651131i
$676$	10820.9	+	13411.2i	0.615661	+	0.763041i
$677$	−7064.43	+	24059.2i	−0.401046	+	1.36584i	0.473457	+	0.880817i	$0.343006\pi$
$677$	−7064.43	+	24059.2i	−0.401046	+	1.36584i	−0.874503	+	0.485020i	$0.838812\pi$
$678$	−1556.10	−	486.727i	−0.0881440	−	0.0275703i
$679$	−1484.22	−	1712.88i	−0.0838870	−	0.0968107i
$680$	−528.732	+	2670.81i	−0.0298176	+	0.150619i
$681$	716.539	−	1569.00i	0.0403199	−	0.0882883i
$682$	20733.7	+	363.846i	1.16412	+	0.0204287i
$683$	−9226.90	−	31423.9i	−0.516922	−	1.76047i	−0.640312	−	0.768115i	$-0.721195\pi$
$683$	−9226.90	−	31423.9i	−0.516922	−	1.76047i	0.123390	−	0.992358i	$-0.460623\pi$
$684$	1260.45	−	1817.75i	0.0704601	−	0.101613i
$685$	16197.0	−	7396.93i	0.903439	−	0.412587i
$686$	14538.7	−	12157.9i	0.809170	−	0.676661i
$687$	−345.276	+	221.896i	−0.0191748	+	0.0123229i
$688$	−1123.95	+	15987.3i	−0.0622822	+	0.885917i
$689$	−2809.84			−0.155365
$690$	1141.28	−	2096.55i	0.0629675	−	0.115673i
$691$		−	22649.5i		−	1.24693i	−0.781851	−	0.623465i	$-0.785724\pi$
$691$		−	22649.5i		−	1.24693i	0.781851	−	0.623465i	$-0.214276\pi$
$692$	−13578.9	+	5634.21i	−0.745942	+	0.309509i
$693$	8085.51	+	12581.3i	0.443208	+	0.689645i
$694$	−14626.6	−	17490.8i	−0.800024	−	0.956691i
$695$	12986.3	+	28436.1i	0.708777	+	1.55200i
$696$	−57.4606	+	1090.56i	−0.00312937	+	0.0593933i
$697$	−4039.18	+	1186.01i	−0.219505	+	0.0644525i
$698$	−6060.75	−	106.357i	−0.328657	−	0.00576746i
$699$	1589.96	+	726.112i	0.0860343	+	0.0392906i
$700$	4025.66	−	4329.12i	0.217365	−	0.233751i
$701$	−11779.6	+	10207.1i	−0.634676	+	0.549950i	−0.911671	−	0.410921i	$-0.865207\pi$
$701$	−11779.6	+	10207.1i	−0.634676	+	0.549950i	0.276995	+	0.960871i	$0.410662\pi$
$702$	−175.367	+	560.660i	−0.00942849	+	0.0301435i
$703$	2889.02	+	848.294i	0.154995	+	0.0455107i
$704$	−16146.2	−	4089.79i	−0.864391	−	0.218948i
$705$	−285.129	−	183.241i	−0.0152320	−	0.00978902i
$706$	−3440.22	−	3088.30i	−0.183391	−	0.164631i
$707$	32344.2	+	4650.39i	1.72055	+	0.247378i
$708$	−1368.20	−	48.0347i	−0.0726273	−	0.00254979i
$709$	10005.5	−	1438.57i	0.529990	−	0.0762011i	0.127875	−	0.991790i	$-0.459184\pi$
$709$	10005.5	−	1438.57i	0.529990	−	0.0762011i	0.402115	+	0.915589i	$0.368275\pi$
$710$	13424.2	−	28080.4i	0.709581	−	1.48428i
$711$	−14785.2	+	17063.0i	−0.779869	+	0.900017i
$712$	6910.64	−	624.753i	0.363746	−	0.0328843i
$713$	−8246.96	+	23451.4i	−0.433171	+	1.23178i
$714$	−227.637	+	140.712i	−0.0119315	+	0.00737537i
$715$	2087.81	+	1809.10i	0.109202	+	0.0946243i
$716$	25515.3	−	2758.83i	1.33177	−	0.143998i
$717$	124.216	−	17.8596i	0.00646994	−	0.000930237i
$718$	10752.3	−	16102.5i	0.558876	−	0.836966i
$719$	4688.81	−	32611.4i	0.243203	−	1.69152i	−0.392635	−	0.919694i	$-0.628436\pi$
$719$	4688.81	−	32611.4i	0.243203	−	1.69152i	0.635838	−	0.771822i	$-0.280655\pi$
$720$	−13221.1	+	17706.0i	−0.684334	+	0.916478i
$721$	12312.6	+	7912.81i	0.635983	+	0.408722i
$722$	18946.1	−	2385.55i	0.976596	−	0.122965i
$723$	1090.90	−	3715.25i	0.0561146	−	0.191109i
$724$	7812.52	+	30531.9i	0.401036	+	1.56728i
$725$	2645.78	−	2292.58i	0.135534	−	0.117441i
$726$	−439.268	+	120.650i	−0.0224556	+	0.00616771i
$727$	5542.17	−	12135.7i	0.282734	−	0.619102i	−0.713974	−	0.700172i	$-0.753107\pi$
$727$	5542.17	−	12135.7i	0.282734	−	0.619102i	0.996708	+	0.0810705i	$0.0258339\pi$
$728$	1183.80	−	2268.11i	0.0602671	−	0.115469i
$729$	−17437.6	+	5120.15i	−0.885923	+	0.260130i
$730$	4056.45	+	9311.37i	0.205666	+	0.472095i
$731$	−2115.64	+	966.181i	−0.107045	+	0.0488858i
$732$	811.997	+	269.712i	0.0410004	+	0.0136186i
$733$	4306.67	+	6701.32i	0.217013	+	0.337679i	0.932643	−	0.360801i	$-0.117497\pi$
$733$	4306.67	+	6701.32i	0.217013	+	0.337679i	−0.715630	+	0.698480i	$0.753860\pi$
$734$	−20163.5	−	3261.14i	−1.01396	−	0.163993i
$735$	−347.758			−0.0174520
$736$	10752.9	−	16824.5i	0.538527	−	0.842608i
$737$	22853.7			1.14223
$738$	−33728.5	−	5455.08i	−1.68233	−	0.272092i
$739$	1597.30	+	2485.44i	0.0795095	+	0.123719i	0.878731	−	0.477318i	$-0.158391\pi$
$739$	1597.30	+	2485.44i	0.0795095	+	0.123719i	−0.799221	+	0.601037i	$0.794754\pi$
$740$	−28545.7	−	9481.69i	−1.41805	−	0.471019i
$741$	36.5333	−	16.6842i	0.00181118	−	0.000827138i
$742$	−8352.94	−	19173.7i	−0.413270	−	0.948639i
$743$	24599.4	−	7223.04i	1.21462	−	0.356645i	0.389196	−	0.921155i	$-0.372753\pi$
$743$	24599.4	−	7223.04i	1.21462	−	0.356645i	0.825426	+	0.564510i	$0.190935\pi$
$744$	−1393.51	+	2669.91i	−0.0686674	+	0.131564i
$745$	−12321.1	+	26979.4i	−0.605919	+	1.32678i
$746$	26379.0	−	7245.32i	1.29464	−	0.355590i
$747$	−8782.18	+	7609.81i	−0.430152	+	0.372729i
$748$	−599.196	−	2341.70i	−0.0292898	−	0.114467i
$749$	−4724.06	+	16088.7i	−0.230459	+	0.784870i
$750$	1764.10	−	222.121i	0.0858875	−	0.0108143i
$751$	−4564.07	−	2933.15i	−0.221765	−	0.142519i	0.425042	−	0.905174i	$-0.360259\pi$
$751$	−4564.07	−	2933.15i	−0.221765	−	0.142519i	−0.646806	+	0.762654i	$0.723896\pi$
$752$	−2271.67	−	1696.26i	−0.110159	−	0.0822555i
$753$	73.6582	−	512.304i	0.00356475	−	0.0247934i
$754$	841.374	−	1260.03i	0.0406380	−	0.0608590i
$755$	−23853.3	+	3429.59i	−1.14982	+	0.165319i
$756$	−4347.15	+	470.033i	−0.209132	+	0.0226124i
$757$	2111.79	+	1829.88i	0.101393	+	0.0878575i	0.704082	−	0.710119i	$-0.251359\pi$
$757$	2111.79	+	1829.88i	0.101393	+	0.0878575i	−0.602689	+	0.797976i	$0.705904\pi$
$758$	2157.38	−	1333.57i	0.103377	−	0.0639016i
$759$	−111.325	+	2116.29i	−0.00532390	+	0.101207i
$760$	3028.96	−	273.831i	0.144568	−	0.0130696i
$761$	−5352.12	+	6176.68i	−0.254946	+	0.294224i	−0.868766	−	0.495222i	$-0.835087\pi$
$761$	−5352.12	+	6176.68i	−0.254946	+	0.294224i	0.613820	+	0.789446i	$0.289632\pi$
$762$	−13.3651	+	27.9566i	−0.000635388	+	0.00132908i
$763$	10150.1	−	1459.36i	0.481597	−	0.0692432i
$764$	−11358.7	−	398.780i	−0.537884	−	0.0188840i
$765$	−3174.17	−	456.376i	−0.150016	−	0.0215690i
$766$	15056.5	+	13516.2i	0.710198	+	0.637548i
$767$	1597.86	+	1026.88i	0.0752221	+	0.0483423i
$768$	1579.68	−	1832.01i	0.0742212	−	0.0860769i
$769$	16245.0	+	4769.96i	0.761781	+	0.223679i	0.639473	−	0.768813i	$-0.279152\pi$
$769$	16245.0	+	4769.96i	0.761781	+	0.223679i	0.122307	+	0.992492i	$0.460971\pi$
$770$	−6138.36	+	19624.7i	−0.287287	+	0.918476i
$771$	−1922.48	+	1665.84i	−0.0898007	+	0.0778127i
$772$	20163.0	−	21683.0i	0.940004	−	1.01086i
$773$	27706.7	+	12653.2i	1.28919	+	0.588751i	0.937701	−	0.347442i	$-0.112950\pi$
$773$	27706.7	+	12653.2i	1.28919	+	0.588751i	0.351484	+	0.936194i	$0.385677\pi$
$774$	−18873.9	−	331.209i	−0.876497	−	0.0153812i
$775$	9263.49	−	2720.01i	0.429360	−	0.126072i
$776$	−156.431	+	2968.96i	−0.00723654	+	0.137345i
$777$	−1228.20	−	2689.39i	−0.0567073	−	0.124172i
$778$	3639.71	+	4352.47i	0.167725	+	0.200570i
$779$	2542.32	+	3955.93i	0.116930	+	0.181946i
$780$	−370.584	+	153.764i	−0.0170116	+	0.00705851i
$781$			27631.9i			1.26600i
$782$	2890.54	+	202.966i	0.132181	+	0.00928138i
$783$	−2589.39			−0.118183
$784$	−2901.75	−	204.000i	−0.132186	−	0.00929302i
$785$	6333.07	−	4070.02i	0.287945	−	0.185051i
$786$	1275.32	−	1066.48i	0.0578743	−	0.0483968i
$787$	9088.09	−	4150.39i	0.411633	−	0.187987i	−0.198825	−	0.980035i	$-0.563713\pi$
$787$	9088.09	−	4150.39i	0.411633	−	0.187987i	0.610458	+	0.792048i	$0.290985\pi$
$788$	13082.1	−	18866.1i	0.591407	−	0.852892i
$789$	845.911	+	2880.91i	0.0381689	+	0.129991i
$790$	−31037.3	−	544.660i	−1.39780	−	0.0245293i
$791$	−6994.26	+	15315.3i	−0.314396	+	0.688431i
$792$	3809.78	−	19244.5i	0.170927	−	0.863415i
$793$	−777.362	−	897.123i	−0.0348108	−	0.0401737i
$794$	21273.6	+	6654.09i	0.950845	+	0.297412i
$795$	−924.019	+	3146.92i	−0.0412221	+	0.140390i
$796$	−3878.41	−	4806.84i	−0.172697	−	0.214038i
$797$	−21672.5	+	33723.1i	−0.963211	+	1.49879i	−0.0993517	+	0.995052i	$0.531677\pi$
$797$	−21672.5	+	33723.1i	−0.963211	+	1.49879i	−0.863859	+	0.503733i	$0.831959\pi$
$798$	222.454	+	199.697i	0.00986813	+	0.00885866i
$799$	58.5528	−	407.244i	0.00259255	−	0.0180316i
$800$	−7742.90	+	426.802i	−0.342191	+	0.0188622i
$801$	1163.10	+	8089.55i	0.0513061	+	0.356842i
$802$	−34029.5	−	16268.3i	−1.49828	−	0.716276i
$803$	−6814.56	−	5904.85i	−0.299478	−	0.259499i
$804$	−1483.90	+	2968.94i	−0.0650908	+	0.130232i
$805$	−20008.2	−	14397.7i	−0.876020	−	0.630376i
$806$	3554.14	−	2196.96i	0.155322	−	0.0960107i
$807$	1349.25	−	1557.12i	0.0588549	−	0.0679222i
$808$	−26326.8	−	33826.8i	−1.14625	−	1.47280i
$809$	−3515.84	−	24453.2i	−0.152794	−	1.06271i	−0.911508	−	0.411282i	$-0.865081\pi$
$809$	−3515.84	−	24453.2i	−0.152794	−	1.06271i	0.758714	−	0.651424i	$-0.225828\pi$
$810$	−21358.1	−	14261.7i	−0.926479	−	0.618647i
$811$	−17972.2	−	2584.01i	−0.778162	−	0.111883i	−0.258222	−	0.966086i	$-0.583137\pi$
$811$	−17972.2	−	2584.01i	−0.778162	−	0.111883i	−0.519940	+	0.854203i	$0.674046\pi$
$812$	11099.4	+	1995.60i	0.479694	+	0.0862460i
$813$	−1358.81	+	2114.35i	−0.0586169	+	0.0912097i
$814$	26494.9	−	3336.03i	1.14084	−	0.143646i
$815$	19450.6	+	5711.20i	0.835980	+	0.245466i
$816$	343.118	+	74.2050i	0.0147200	+	0.00318345i
$817$	1701.35	+	1963.47i	0.0728554	+	0.0840796i
$818$	−10938.5	−	39825.3i	−0.467550	−	1.70227i
$819$	2741.10	+	1251.82i	0.116950	+	0.0534092i
$820$	−23995.1	−	40385.7i	−1.02188	−	1.71991i
$821$	−6308.43	−	21484.5i	−0.268168	−	0.913295i	−0.977944	−	0.208868i	$-0.933022\pi$
$821$	−6308.43	−	21484.5i	−0.268168	−	0.913295i	0.709776	−	0.704427i	$-0.248796\pi$
$822$	−916.950	−	2104.81i	−0.0389079	−	0.0893111i
$823$	−8866.57	−	19415.1i	−0.375540	−	0.822317i	−0.999175	−	0.0406022i	$-0.987072\pi$
$823$	−8866.57	−	19415.1i	−0.375540	−	0.822317i	0.623636	−	0.781715i	$-0.285655\pi$
$824$	−4432.23	−	18680.4i	−0.187384	−	0.789759i
$825$	692.384	−	444.968i	0.0292191	−	0.0187780i
$826$	−2257.19	+	13956.1i	−0.0950819	+	0.587887i
$827$			29657.9i			1.24704i	0.781806	+	0.623522i	$0.214299\pi$
$827$			29657.9i			1.24704i	−0.781806	+	0.623522i	$0.785701\pi$
$828$	20455.3	+	11604.8i	0.858540	+	0.487072i
$829$		−	24905.0i		−	1.04341i	−0.853126	−	0.521705i	$-0.825296\pi$
$829$		−	24905.0i		−	1.04341i	0.853126	−	0.521705i	$-0.174704\pi$
$830$	−15772.2	−	2550.91i	−0.659591	−	0.106679i
$831$	1516.27	−	974.446i	0.0632957	−	0.0406777i
$832$	−3182.41	+	1065.64i	−0.132609	+	0.0444045i
$833$	−175.365	−	383.996i	−0.00729416	−	0.0159720i
$834$	3695.29	−	1609.83i	0.153426	−	0.0668393i
$835$	−199.299	−	678.750i	−0.00825991	−	0.0281307i
$836$	−2321.25	+	1379.16i	−0.0960311	+	0.0570567i
$837$	−6495.61	−	2966.45i	−0.268245	−	0.122504i
$838$	−11929.3	+	3276.54i	−0.491756	+	0.135067i
$839$	−15169.9	−	17506.9i	−0.624221	−	0.720390i	0.352282	−	0.935894i	$-0.385406\pi$
$839$	−15169.9	−	17506.9i	−0.624221	−	0.720390i	−0.976503	+	0.215504i	$0.930860\pi$
$840$	−2150.90	−	2071.68i	−0.0883491	−	0.0850950i
$841$	−16993.1	−	4989.63i	−0.696754	−	0.204585i
$842$	4863.00	+	38622.2i	0.199038	+	1.58077i
$843$	−2568.05	+	3995.97i	−0.104921	+	0.163260i
$844$	−15321.1	−	2754.64i	−0.624850	−	0.112344i
$845$	−27622.0	−	3971.45i	−1.12453	−	0.161683i
$846$	1854.35	−	2777.05i	0.0753592	−	0.112857i
$847$	669.462	+	4656.21i	0.0271582	+	0.188889i
$848$	−9556.20	+	25716.4i	−0.386983	+	1.04140i
$849$	2703.71	−	3120.25i	0.109295	−	0.126133i
$850$	−591.712	−	957.244i	−0.0238771	−	0.0386273i
$851$	−6214.14	+	31403.7i	−0.250315	+	1.26499i
$852$	−3589.68	−	1794.14i	−0.144343	−	0.0721436i
$853$	14329.4	+	12416.5i	0.575181	+	0.498397i	0.893183	−	0.449693i	$-0.148467\pi$
$853$	14329.4	+	12416.5i	0.575181	+	0.498397i	−0.318002	+	0.948090i	$0.603012\pi$
$854$	3810.88	−	7971.47i	0.152700	−	0.319412i
$855$	509.792	+	3545.68i	0.0203912	+	0.141824i
$856$	19103.9	−	10901.6i	0.762801	−	0.435292i
$857$	3890.14	−	27056.5i	0.155058	−	1.07845i	−0.752520	−	0.658569i	$-0.771162\pi$
$857$	3890.14	−	27056.5i	0.155058	−	1.07845i	0.907578	−	0.419883i	$-0.137929\pi$
$858$	237.947	−	265.062i	0.00946782	−	0.0105467i
$859$	−16742.1	+	26051.3i	−0.664999	+	1.03476i	0.330845	+	0.943685i	$0.392666\pi$
$859$	−16742.1	+	26051.3i	−0.664999	+	1.03476i	−0.995844	+	0.0910738i	$0.970970\pi$
$860$	−16297.5	−	20198.9i	−0.646210	−	0.800904i
$861$	1300.88	−	4430.40i	0.0514912	−	0.175363i
$862$	−11950.0	+	38204.9i	−0.472179	+	1.50959i
$863$	−13816.3	−	15944.8i	−0.544973	−	0.628932i	0.414732	−	0.909944i	$-0.363875\pi$
$863$	−13816.3	−	15944.8i	−0.544973	−	0.628932i	−0.959704	+	0.281012i	$0.909330\pi$
$864$	4534.89	+	3511.80i	0.178565	+	0.138280i
$865$	9890.00	−	21656.1i	0.388752	−	0.851247i
$866$	108.109	−	6160.59i	0.00424215	−	0.241738i
$867$	−803.102	−	2735.11i	−0.0314588	−	0.107139i
$868$	25557.1	+	17721.7i	0.999384	+	0.692987i
$869$	25068.5	−	11448.4i	0.978586	−	0.446905i
$870$	−1134.50	−	1356.67i	−0.0442107	−	0.0528684i
$871$	3873.86	−	2489.58i	0.150701	−	0.0968499i
$872$	−10917.8	−	7857.75i	−0.423994	−	0.305157i
$873$	−3501.78			−0.135759
$874$	−692.135	−	3161.93i	−0.0267870	−	0.122373i
$875$		−	18360.8i		−	0.709381i
$876$	1209.58	−	501.882i	0.0466527	−	0.0193573i
$877$	4008.65	+	6237.58i	0.154347	+	0.240169i	0.909812	−	0.415020i	$-0.136225\pi$
$877$	4008.65	+	6237.58i	0.154347	+	0.240169i	−0.755465	+	0.655189i	$0.772589\pi$
$878$	−5859.46	+	4899.92i	−0.225225	+	0.188342i
$879$	480.160	+	1051.40i	0.0184248	+	0.0403447i
$880$	23657.9	−	12955.5i	0.906260	−	0.496283i
$881$	30738.2	−	9025.56i	1.17548	−	0.345152i	0.365050	−	0.930988i	$-0.381052\pi$
$881$	30738.2	−	9025.56i	1.17548	−	0.345152i	0.810430	+	0.585836i	$0.199234\pi$
$882$	60.1156	−	3425.68i	0.00229501	−	0.130781i
$883$	2568.38	+	1172.94i	0.0978856	+	0.0447029i	0.463756	−	0.885963i	$-0.346501\pi$
$883$	2568.38	+	1172.94i	0.0978856	+	0.0447029i	−0.365870	+	0.930666i	$0.619229\pi$
$884$	−356.662	−	331.661i	−0.0135700	−	0.0126187i
$885$	1675.53	−	1451.85i	0.0636410	−	0.0551452i
$886$	−20628.6	−	6452.35i	−0.782203	−	0.244663i
$887$	2261.90	+	664.155i	0.0856226	+	0.0251411i	0.324263	−	0.945967i	$-0.394884\pi$
$887$	2261.90	+	664.155i	0.0856226	+	0.0251411i	−0.238641	+	0.971108i	$0.576702\pi$
$888$	−1286.93	+	3658.59i	−0.0486337	+	0.138259i
$889$	269.192	+	172.999i	0.0101557	+	0.00652665i
$890$	−7506.39	+	8361.77i	−0.282713	+	0.314929i
$891$	22568.2	+	3244.82i	0.848556	+	0.122004i
$892$	−48530.7	−	1703.81i	−1.82167	−	0.0639549i
$893$	−454.909	+	65.4060i	−0.0170470	+	0.00245098i
$894$	3450.24	+	1649.44i	0.129075	+	0.0617064i
$895$	−27216.3	+	31409.3i	−1.01647	+	1.17307i
$896$	−16732.2	−	18548.2i	−0.623867	−	0.691576i
$897$	211.669	+	370.853i	0.00787894	+	0.0138043i
$898$	17447.0	+	28224.9i	0.648344	+	1.04886i
$899$	13919.1	+	12061.0i	0.516383	+	0.447448i
$900$	−981.850	−	9080.73i	−0.0363648	−	0.336323i
$901$	−3940.80	+	566.601i	−0.145713	+	0.0209503i
$902$	34683.6	+	23159.6i	1.28031	+	0.854913i
$903$	363.057	−	2525.12i	0.0133796	−	0.0930573i
$904$	20545.0	−	8105.06i	0.755881	−	0.298197i
$905$	−42934.7	−	27592.4i	−1.57701	−	1.01348i
$906$	388.171	+	3082.87i	0.0142341	+	0.113048i
$907$	8463.05	−	28822.5i	0.309825	−	1.05517i	−0.646513	−	0.762903i	$-0.723774\pi$
$907$	8463.05	−	28822.5i	0.309825	−	1.05517i	0.956338	−	0.292263i	$-0.0944082\pi$
$908$	5792.07	+	22635.8i	0.211692	+	0.827309i
$909$	38155.4	−	33061.8i	1.39223	−	1.20637i
$910$	1097.34	+	3995.22i	0.0399741	+	0.145539i
$911$	−7438.72	+	16288.5i	−0.270533	+	0.592385i	−0.995325	−	0.0965829i	$-0.969209\pi$
$911$	−7438.72	+	16288.5i	−0.270533	+	0.592385i	0.724792	+	0.688968i	$0.241936\pi$
$912$	−28.4492	−	391.105i	−0.00103295	−	0.0142004i
$913$	13609.8	−	3996.20i	0.493340	−	0.144858i
$914$	1454.04	−	633.445i	0.0526208	−	0.0229240i
$915$	−1260.38	+	575.597i	−0.0455376	+	0.0207963i
$916$	1752.55	−	5276.23i	0.0632159	−	0.190318i
$917$	−9281.47	−	14442.3i	−0.334243	−	0.520093i
$918$	−132.896	+	821.688i	−0.00477801	+	0.0295422i
$919$	24002.8			0.861567			0.430783	−	0.902455i	$-0.358237\pi$
$919$	24002.8			0.861567			0.430783	+	0.902455i	$0.358237\pi$
$920$	5801.76	+	31810.3i	0.207911	+	1.13995i
$921$	−2380.63			−0.0851730
$922$	5531.57	−	34201.5i	0.197584	−	1.22165i
$923$	3010.09	+	4683.80i	0.107344	+	0.167030i
$924$	2516.09	+	835.739i	0.0895813	+	0.0297552i
$925$	11309.2	−	5164.76i	0.401995	−	0.183585i
$926$	21425.4	−	9333.87i	0.760349	−	0.331242i
$927$	21697.1	−	6370.85i	0.768745	−	0.225724i
$928$	−8670.65	−	11985.8i	−0.306711	−	0.423980i
$929$	3635.11	−	7959.77i	0.128379	−	0.281111i	−0.834518	−	0.550981i	$-0.814254\pi$
$929$	3635.11	−	7959.77i	0.128379	−	0.281111i	0.962897	+	0.269871i	$0.0869809\pi$
$930$	−1291.73	−	4702.98i	−0.0455458	−	0.165825i
$931$	−356.376	+	308.802i	−0.0125454	+	0.0108706i
$932$	−22938.2	+	5869.46i	−0.806188	+	0.206288i
$933$	497.085	−	1692.92i	0.0174425	−	0.0594037i
$934$	3264.69	+	25928.3i	0.114372	+	0.908351i
$935$	3292.95	+	2116.25i	0.115178	+	0.0740202i
$936$	−1450.63	−	3677.10i	−0.0506574	−	0.128408i
$937$	3966.02	−	27584.3i	0.138275	−	0.961727i	−0.796031	−	0.605256i	$-0.793071\pi$
$937$	3966.02	−	27584.3i	0.138275	−	0.961727i	0.934306	−	0.356471i	$-0.116020\pi$
$938$	28504.4	+	19033.5i	0.992218	+	0.662544i
$939$	−1904.09	+	273.767i	−0.0661744	+	0.00951444i
$940$	4564.57	−	493.543i	0.158383	−	0.0171251i
$941$	−42851.0	−	37130.6i	−1.48449	−	1.28632i	−0.865492	−	0.500923i	$-0.832994\pi$
$941$	−42851.0	−	37130.6i	−1.48449	−	1.28632i	−0.618997	−	0.785393i	$-0.712461\pi$
$942$	−510.369	−	825.651i	−0.0176526	−	0.0285575i
$943$	−39452.1	+	30710.2i	−1.36239	+	1.06051i
$944$	14832.6	−	11131.6i	0.511397	−	0.383796i
$945$	4636.96	−	5351.34i	0.159619	−	0.184211i
$946$	20788.3	+	9938.14i	0.714467	+	0.341561i
$947$	2792.02	−	401.432i	0.0958062	−	0.0137748i	−0.0942450	−	0.995549i	$-0.530044\pi$
$947$	2792.02	−	401.432i	0.0958062	−	0.0137748i	0.190051	+	0.981774i	$0.439135\pi$
$948$	−140.432	+	4000.02i	−0.00481121	+	0.137041i
$949$	−1798.36	−	258.566i	−0.0615146	−	0.00884447i
$950$	−839.753	+	935.445i	−0.0286791	+	0.0319472i
$951$	3716.05	+	2388.16i	0.126710	+	0.0814316i
$952$	1202.91	−	3419.73i	0.0409524	−	0.116422i
$953$	−48285.7	−	14177.9i	−1.64127	−	0.481919i	−0.674647	−	0.738140i	$-0.735704\pi$
$953$	−48285.7	−	14177.9i	−1.64127	−	0.481919i	−0.966618	+	0.256221i	$0.917522\pi$
$954$	−30839.8	−	9646.27i	−1.04662	−	0.327368i
$955$	13910.1	−	12053.2i	0.471330	−	0.408410i
$956$	−1157.61	+	1244.88i	−0.0391630	+	0.0421152i
$957$	1428.19	+	652.234i	0.0482413	+	0.0220311i
$958$	877.410	−	49999.0i	0.0295906	−	1.68622i
$959$	−22748.0	+	6679.42i	−0.765976	+	0.224911i
$960$	146.943	+	3914.63i	0.00494016	+	0.131608i
$961$	8723.88	+	19102.6i	0.292836	+	0.641222i
$962$	4127.66	−	3451.72i	0.138338	−	0.115684i
$963$	14006.4	+	21794.3i	0.468691	+	0.729297i
$964$	20101.6	+	48446.5i	0.671608	+	1.61863i
$965$			47949.2i			1.59952i
$966$	−1901.38	+	2546.83i	−0.0633292	+	0.0848271i
$967$	−23350.0			−0.776511			−0.388255	−	0.921552i	$-0.626922\pi$
$967$	−23350.0			−0.776511			−0.388255	+	0.921552i	$0.626922\pi$
$968$	3604.63	−	5008.37i	0.119687	−	0.166297i
$969$	47.8736	−	30.7665i	0.00158712	−	0.00101998i
$970$	−3088.58	−	3693.41i	−0.102235	−	0.122256i
$971$	36586.2	−	16708.4i	1.20917	−	0.552211i	0.294208	−	0.955742i	$-0.404944\pi$
$971$	36586.2	−	16708.4i	1.20917	−	0.552211i	0.914966	+	0.403530i	$0.132217\pi$
$972$	−5786.80	+	8345.38i	−0.190959	+	0.275389i
$973$	−11726.6	−	39937.3i	−0.386371	−	1.31586i
$974$	−253.287	+	14433.5i	−0.00833249	+	0.474825i
$975$	68.8912	−	150.851i	0.00226285	−	0.00495496i
$976$	−10854.5	+	4063.52i	−0.355988	+	0.133269i
$977$	−15426.0	−	17802.5i	−0.505139	−	0.582961i	0.444709	−	0.895675i	$-0.353307\pi$
$977$	−15426.0	−	17802.5i	−0.505139	−	0.582961i	−0.949847	+	0.312714i	$0.898762\pi$
$978$	780.277	−	2494.60i	0.0255118	−	0.0815628i
$979$	2810.54	−	9571.83i	0.0917522	−	0.312479i
$980$	3666.17	−	2958.06i	0.119502	−	0.0964200i
$981$	8565.66	−	13328.4i	0.278777	−	0.433786i
$982$	−22484.5	+	25046.7i	−0.730660	+	0.813921i
$983$	−5444.34	+	37866.2i	−0.176650	+	1.22863i	0.687795	+	0.725905i	$0.258579\pi$
$983$	−5444.34	+	37866.2i	−0.176650	+	1.22863i	−0.864446	+	0.502726i	$0.832330\pi$
$984$	−5260.71	+	3002.02i	−0.170432	+	0.0972570i
$985$	5291.04	+	36800.0i	0.171154	+	1.19040i
$986$	925.942	−	1936.86i	0.0299067	−	0.0625579i
$987$	341.055	+	295.526i	0.0109989	+	0.00953059i
$988$	−243.228	+	486.644i	−0.00783210	+	0.0156703i
$989$	−19160.3	+	19896.4i	−0.616040	+	0.639706i
$990$	16704.3	+	27023.5i	0.536261	+	0.867538i
$991$	15782.3	−	18213.7i	0.505894	−	0.583833i	−0.444148	−	0.895953i	$-0.646494\pi$
$991$	15782.3	−	18213.7i	0.505894	−	0.583833i	0.950043	+	0.312120i	$0.101039\pi$
$992$	−8019.60	−	40000.2i	−0.256676	−	1.28025i
$993$	985.780	+	6856.25i	0.0315033	+	0.219110i
$994$	−23013.0	+	34464.0i	−0.734333	+	1.09973i
$995$	9900.29	+	1423.45i	0.315437	+	0.0453530i
$996$	−364.539	+	2027.54i	−0.0115972	+	0.0645030i
$997$	−13368.4	+	20801.6i	−0.424656	+	0.660777i	−0.985989	−	0.166813i	$-0.946652\pi$
$997$	−13368.4	+	20801.6i	−0.424656	+	0.660777i	0.561333	+	0.827590i	$0.310289\pi$
$998$	2520.84	+	20020.6i	0.0799556	+	0.635011i
$999$	−8823.30	−	2590.76i	−0.279436	−	0.0820499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.p.a.85.2	yes	700
8.5	even	2	inner	184.4.p.a.85.42	yes	700
23.13	even	11	inner	184.4.p.a.13.42	yes	700
184.13	even	22	inner	184.4.p.a.13.2	✓	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.p.a.13.2	✓	700	184.13	even	22	inner
184.4.p.a.13.42	yes	700	23.13	even	11	inner
184.4.p.a.85.2	yes	700	1.1	even	1	trivial
184.4.p.a.85.42	yes	700	8.5	even	2	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+(-2.79214 - 0.451587i) q^{2} +(-0.319292 - 0.496829i) q^{3} +(7.59214 + 2.52179i) q^{4} +(-11.7845 + 5.38181i) q^{5} +(0.667149 + 1.53141i) q^{6} +(16.5509 - 4.85977i) q^{7} +(-20.0595 - 10.4697i) q^{8} +(11.0713 - 24.2428i) q^{9} +(35.3344 - 9.70505i) q^{10} +(-24.5856 + 21.3035i) q^{11} +(-1.17121 - 4.57718i) q^{12} +(-1.84672 + 6.28935i) q^{13} +(-48.4070 + 6.09502i) q^{14} +(6.43655 + 4.13652i) q^{15} +(51.2811 + 38.2916i) q^{16} +(-1.32178 + 9.19320i) q^{17} +(-41.8604 + 62.6897i) q^{18} +(10.2692 - 1.47649i) q^{19} +(-103.042 + 11.1413i) q^{20} +(-7.69904 - 6.67125i) q^{21} +(78.2669 - 48.3800i) q^{22} +(25.4736 + 107.322i) q^{23} +(1.20320 + 13.3091i) q^{24} +(28.0535 - 32.3754i) q^{25} +(7.99650 - 16.7268i) q^{26} +(-31.3629 + 4.50930i) q^{27} +(137.912 + 4.84179i) q^{28} +(80.8901 + 11.6302i) q^{29} +(-16.1038 - 14.4564i) q^{30} +(189.593 + 121.844i) q^{31} +(-125.892 - 130.074i) q^{32} +(18.4342 + 5.41277i) q^{33} +(7.84214 - 25.0718i) q^{34} +(-168.890 + 146.344i) q^{35} +(145.190 - 156.135i) q^{36} +(263.995 + 120.562i) q^{37} +(-29.3398 - 0.514871i) q^{38} +(3.71437 - 1.09064i) q^{39} +(292.738 + 15.4240i) q^{40} +(188.289 + 412.295i) q^{41} +(18.4842 + 22.1039i) q^{42} +(135.387 + 210.666i) q^{43} +(-240.380 + 99.7396i) q^{44} +345.273i q^{45} +(-22.6607 - 311.163i) q^{46} -44.2984 q^{47} +(2.65069 - 37.7042i) q^{48} +(-38.2365 + 24.5731i) q^{49} +(-92.9497 + 77.7283i) q^{50} +(4.98948 - 2.27862i) q^{51} +(-29.8810 + 43.0926i) q^{52} +(120.769 + 411.301i) q^{53} +(89.6061 + 1.57246i) q^{54} +(175.078 - 383.367i) q^{55} +(-382.883 - 75.7981i) q^{56} +(-4.01244 - 4.63060i) q^{57} +(-220.605 - 69.0022i) q^{58} +(81.6366 - 278.029i) q^{59} +(38.4357 + 47.6367i) q^{60} +(-97.9082 + 152.348i) q^{61} +(-474.347 - 425.824i) q^{62} +(65.4253 - 455.043i) q^{63} +(292.770 + 420.035i) q^{64} +(-12.0854 - 84.0557i) q^{65} +(-49.0266 - 23.4379i) q^{66} +(-530.923 - 460.047i) q^{67} +(-33.2185 + 66.4628i) q^{68} +(45.1873 - 46.9233i) q^{69} +(537.651 - 332.344i) q^{70} +(556.232 - 641.926i) q^{71} +(-475.901 + 370.386i) q^{72} +(39.4464 + 274.356i) q^{73} +(-682.668 - 455.845i) q^{74} +(-25.0423 - 3.60054i) q^{75} +(81.6885 + 14.6871i) q^{76} +(-303.382 + 472.072i) q^{77} +(-10.8636 + 1.36786i) q^{78} +(-812.834 - 238.670i) q^{79} +(-810.402 - 175.263i) q^{80} +(-458.972 - 529.682i) q^{81} +(-339.542 - 1236.22i) q^{82} +(-396.619 - 181.130i) q^{83} +(-41.6286 - 70.0645i) q^{84} +(-33.8995 - 115.451i) q^{85} +(-282.885 - 649.347i) q^{86} +(-20.0494 - 43.9020i) q^{87} +(716.218 - 169.935i) q^{88} +(-257.975 + 165.790i) q^{89} +(155.921 - 964.053i) q^{90} +113.069i q^{91} +(-77.2454 + 879.046i) q^{92} -133.099i q^{93} +(123.687 + 20.0046i) q^{94} +(-113.071 + 72.6665i) q^{95} +(-24.4278 + 104.078i) q^{96} +(-54.5825 - 119.519i) q^{97} +(117.859 - 51.3445i) q^{98} +(244.263 + 831.882i) 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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