LMFDB - Embedded newform 184.4.p.a.13.2

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			13.2
Character	$\chi$	$=$	184.13
Dual form			184.4.p.a.85.2

$q$-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 $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.79214	+	0.451587i	−0.987172	+	0.159660i
$2$	−2.79214	+	0.451587i	−0.987172	+	0.159660i
$3$	−0.319292	+	0.496829i	−0.0614479	+	0.0956147i	−0.870618	−	0.491960i	$-0.836281\pi$
$3$	−0.319292	+	0.496829i	−0.0614479	+	0.0956147i	0.809170	+	0.587574i	$0.199917\pi$
$4$	7.59214	−	2.52179i	0.949017	−	0.315224i
$5$	−11.7845	−	5.38181i	−1.05404	−	0.481364i	−0.188432	−	0.982086i	$-0.560340\pi$
$5$	−11.7845	−	5.38181i	−1.05404	−	0.481364i	−0.865608	+	0.500722i	$0.833068\pi$
$6$	0.667149	−	1.53141i	0.0453937	−	0.104199i
$7$	16.5509	+	4.85977i	0.893662	+	0.262403i	0.696149	−	0.717897i	$-0.254895\pi$
$7$	16.5509	+	4.85977i	0.893662	+	0.262403i	0.197513	+	0.980300i	$0.436713\pi$
$8$	−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	0.249225	−	0.968445i	$-0.419824\pi$
$11$	−24.5856	−	21.3035i	−0.673894	−	0.583933i	−0.923120	+	0.384513i	$0.874369\pi$
$12$	−1.17121	+	4.57718i	−0.0281750	+	0.110110i
$13$	−1.84672	−	6.28935i	−0.0393991	−	0.134181i	0.937445	−	0.348133i	$-0.113184\pi$
$13$	−1.84672	−	6.28935i	−0.0393991	−	0.134181i	−0.976844	+	0.213953i	$0.931366\pi$
$14$	−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	0.978218	−	0.207581i	$-0.0665590\pi$
$17$	−1.32178	−	9.19320i	−0.0188576	−	0.131158i	−0.997075	+	0.0764234i	$0.975650\pi$
$18$	−41.8604	−	62.6897i	−0.548144	−	0.820895i
$19$	10.2692	+	1.47649i	0.123995	+	0.0178279i	0.204033	−	0.978964i	$-0.434595\pi$
$19$	10.2692	+	1.47649i	0.123995	+	0.0178279i	−0.0800377	+	0.996792i	$0.525504\pi$
$20$	−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	0.121624	−	0.992576i	$-0.461190\pi$
$29$	80.8901	−	11.6302i	0.517962	−	0.0744718i	0.396338	+	0.918104i	$0.370281\pi$
$30$	−16.1038	+	14.4564i	−0.0980044	+	0.0879790i
$31$	189.593	−	121.844i	1.09845	−	0.705930i	0.139702	−	0.990194i	$-0.455386\pi$
$31$	189.593	−	121.844i	1.09845	−	0.705930i	0.958746	+	0.284264i	$0.0917492\pi$
$32$	−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	0.268956	−	0.963152i	$-0.413321\pi$
$37$	263.995	−	120.562i	1.17299	−	0.535685i	0.904031	+	0.427467i	$0.140594\pi$
$38$	−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	−0.100555	−	0.994932i	$-0.532062\pi$
$41$	188.289	−	412.295i	0.717214	−	1.57048i	0.817768	−	0.575547i	$-0.195211\pi$
$42$	18.4842	−	22.1039i	0.0679088	−	0.0812072i
$43$	135.387	−	210.666i	0.480145	−	0.747121i	−0.513691	−	0.857975i	$-0.671722\pi$
$43$	135.387	−	210.666i	0.480145	−	0.747121i	0.993837	+	0.110854i	$0.0353587\pi$
$44$	−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	−0.641344	−	0.767254i	$-0.721623\pi$
$53$	120.769	−	411.301i	0.312998	−	1.06597i	0.954341	−	0.298718i	$-0.0965590\pi$
$54$	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	0.999208	+	0.0398007i	$0.0126723\pi$
$59$	81.6366	+	278.029i	0.180139	+	0.613496i	−0.819069	+	0.573695i	$0.805510\pi$
$60$	38.4357	−	47.6367i	0.0827005	−	0.102498i
$61$	−97.9082	−	152.348i	−0.205506	−	0.319774i	0.723167	−	0.690673i	$-0.242686\pi$
$61$	−97.9082	−	152.348i	−0.205506	−	0.319774i	−0.928673	+	0.370900i	$0.879049\pi$
$62$	−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	−0.986961	−	0.160961i	$-0.948541\pi$
$67$	−530.923	+	460.047i	−0.968098	+	0.838862i	0.0188630	+	0.999822i	$0.493995\pi$
$68$	−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	0.997163	+	0.0752695i	$0.0239817\pi$
$71$	556.232	+	641.926i	0.929755	+	1.07300i	−0.0674077	+	0.997726i	$0.521473\pi$
$72$	−475.901	−	370.386i	−0.778964	−	0.606255i
$73$	39.4464	−	274.356i	0.0632445	−	0.439875i	−0.933455	−	0.358695i	$-0.883222\pi$
$73$	39.4464	−	274.356i	0.0632445	−	0.439875i	0.996699	−	0.0811805i	$-0.0258690\pi$
$74$	−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	−0.803502	−	0.595302i	$-0.797033\pi$
$79$	−812.834	+	238.670i	−1.15761	+	0.339904i	−0.354105	+	0.935206i	$0.615214\pi$
$80$	−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	−0.660032	−	0.751238i	$-0.729457\pi$
$83$	−396.619	+	181.130i	−0.524513	+	0.239537i	0.135519	+	0.990775i	$0.456730\pi$
$84$	−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	0.377925	−	0.925836i	$-0.376638\pi$
$89$	−257.975	−	165.790i	−0.307250	−	0.197458i	−0.685175	+	0.728379i	$0.740274\pi$
$90$	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	−0.936046	−	0.351878i	$-0.885543\pi$
$97$	−54.5825	+	119.519i	−0.0571342	+	0.125106i	0.878912	+	0.476985i	$0.158270\pi$
$98$	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	0.699476	−	0.714656i	$-0.253417\pi$
$101$	1723.16	−	786.943i	1.69764	−	0.775284i	0.998160	−	0.0606279i	$-0.0193103\pi$
$102$	−14.9603	−	4.10905i	−0.0145225	−	0.00398879i
$103$	555.638	−	641.241i	0.531540	−	0.613430i	−0.424942	−	0.905221i	$-0.639706\pi$
$103$	555.638	−	641.241i	0.531540	−	0.613430i	0.956482	+	0.291790i	$0.0942510\pi$
$104$	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	0.518389	−	0.855145i	$-0.326532\pi$
$107$	−525.544	−	817.762i	−0.474824	−	0.738841i	−0.993214	+	0.116303i	$0.962895\pi$
$108$	−249.483	+	44.8555i	−0.222283	+	0.0399650i
$109$	588.426	−	84.6029i	0.517073	−	0.0743439i	0.121162	−	0.992633i	$-0.461338\pi$
$109$	588.426	−	84.6029i	0.517073	−	0.0743439i	0.395911	+	0.918289i	$0.370429\pi$
$110$	−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	0.424501	−	0.905427i	$-0.360450\pi$
$113$	−639.190	−	737.664i	−0.532123	−	0.614103i	−0.956624	+	0.291325i	$0.905904\pi$
$114$	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	−0.751490	−	0.659745i	$-0.770664\pi$
$127$	12.1480	−	14.0195i	0.00848788	−	0.00979553i	0.759978	+	0.649949i	$0.225210\pi$
$128$	−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	0.811604	+	0.584208i	$0.198595\pi$
$131$	−280.393	+	954.929i	−0.187008	+	0.636890i	−0.998611	+	0.0526814i	$0.983223\pi$
$132$	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	$0.263390\pi$
$139$			2413.00i			1.47243i	−0.676745	+	0.736217i	$0.736610\pi$
$140$	−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	0.984544	−	0.175138i	$-0.0560373\pi$
$149$	1730.21	+	1499.23i	0.951303	+	0.824309i	−0.0332406	+	0.999447i	$0.510583\pi$
$150$	68.2958	−	21.3620i	0.0371755	−	0.0116280i
$151$	1784.79	−	524.063i	0.961884	−	0.282435i	0.237157	−	0.971471i	$-0.423784\pi$
$151$	1784.79	−	524.063i	0.961884	−	0.282435i	0.724726	+	0.689037i	$0.241966\pi$
$152$	−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	−0.00543628	−	0.999985i	$-0.501730\pi$
$157$	−575.173	−	82.6973i	−0.292381	−	0.0420380i	−0.286944	+	0.957947i	$0.592640\pi$
$158$	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	−0.890945	−	0.454111i	$-0.849957\pi$
$163$	−1182.56	+	1024.69i	−0.568252	+	0.492393i	0.322694	+	0.946503i	$0.395412\pi$
$164$	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	0.987942	−	0.154825i	$-0.0494815\pi$
$167$	−7.77091	−	54.0479i	−0.00360079	−	0.0250440i	−0.991543	+	0.129781i	$0.958572\pi$
$168$	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	0.293924	−	0.955829i	$-0.405039\pi$
$173$	−1388.82	−	1203.42i	−0.610347	−	0.528868i	−0.904270	+	0.426960i	$0.859584\pi$
$174$	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	0.917717	−	0.397234i	$-0.130030\pi$
$179$	2918.10	+	1332.65i	1.21849	+	0.556464i	0.300768	+	0.953697i	$0.402757\pi$
$180$	−870.708	−	2621.36i	−0.360549	−	1.08547i
$181$	2129.82	−	3314.07i	0.874633	−	1.36096i	−0.0573121	−	0.998356i	$-0.518253\pi$
$181$	2129.82	−	3314.07i	0.874633	−	1.36096i	0.931945	−	0.362599i	$-0.118111\pi$
$182$	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	0.0131328	−	0.999914i	$-0.495820\pi$
$191$	−1363.16	−	400.261i	−0.516413	−	0.151633i	−0.529546	+	0.848281i	$0.677638\pi$
$192$	115.207	+	279.571i	0.0433037	+	0.105085i
$193$	1537.51	+	3366.67i	0.573431	+	1.25564i	0.944950	+	0.327214i	$0.106110\pi$
$193$	1537.51	+	3366.67i	0.573431	+	1.25564i	−0.371519	+	0.928425i	$0.621163\pi$
$194$	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	0.966388	+	0.257089i	$0.0827634\pi$
$197$	808.503	+	2753.51i	0.292403	+	0.995835i	−0.673984	+	0.738746i	$0.735418\pi$
$198$	−306.349	+	2433.04i	−0.109956	+	0.873276i
$199$	−649.489	+	417.401i	−0.231362	+	0.148687i	−0.651186	−	0.758918i	$-0.725728\pi$
$199$	−649.489	+	417.401i	−0.231362	+	0.148687i	0.419824	+	0.907606i	$0.362092\pi$
$200$	−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	−0.179249	−	0.983804i	$-0.557367\pi$
$211$	−1926.04	−	276.922i	−0.628407	−	0.0903513i	−0.449158	+	0.893452i	$0.648276\pi$
$212$	−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	−0.758536	−	0.651632i	$-0.774085\pi$
$223$	−5824.20	−	1710.14i	−1.74895	−	0.513539i	−0.990419	+	0.138092i	$0.955903\pi$
$224$	−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	−0.529868	−	0.848080i	$-0.677759\pi$
$227$	1579.02	−	2457.00i	0.461687	−	0.718400i	0.991556	+	0.129680i	$0.0413951\pi$
$228$	−18.7856	+	45.2747i	−0.00545660	+	0.0131508i
$229$			694.960i			0.200543i	0.994960	+	0.100271i	$0.0319711\pi$
$229$			694.960i			0.200543i	−0.994960	+	0.100271i	$0.968029\pi$
$230$	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	0.141590	−	0.989925i	$-0.454779\pi$
$233$	−2489.82	−	1600.11i	−0.700059	−	0.449901i	−0.841649	+	0.540025i	$0.818415\pi$
$234$	−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	0.897311	−	0.441400i	$-0.145518\pi$
$239$	−88.2723	−	193.289i	−0.0238906	−	0.0523132i	−0.921201	+	0.389087i	$0.872791\pi$
$240$	171.679	−	458.591i	0.0461744	−	0.123341i
$241$	4293.54	−	4955.00i	1.14760	−	1.32440i	0.209587	−	0.977790i	$-0.432788\pi$
$241$	4293.54	−	4955.00i	1.14760	−	1.32440i	0.938010	−	0.346608i	$-0.112667\pi$
$242$	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	−0.567595	−	0.823308i	$-0.692126\pi$
$251$	662.322	−	573.905i	0.166555	−	0.144321i	0.734150	+	0.678987i	$0.237581\pi$
$252$	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	0.769432	+	0.638728i	$0.220539\pi$
$257$	−612.990	+	4263.44i	−0.148783	+	1.03481i	−0.918215	+	0.396081i	$0.870370\pi$
$258$	−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	−0.798083	−	0.602548i	$-0.794152\pi$
$263$	−4878.09	+	1432.34i	−1.14371	+	0.335824i	−0.345628	+	0.938372i	$0.612334\pi$
$264$	−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	−0.769926	−	0.638134i	$-0.779707\pi$
$269$	982.881	−	3347.39i	0.222778	−	0.758713i	0.992704	−	0.120579i	$-0.0384752\pi$
$270$	−1064.43	−	463.712i	−0.239922	−	0.104521i
$271$	−1767.88	+	3871.11i	−0.396277	+	0.867725i	0.601358	+	0.798980i	$0.294627\pi$
$271$	−1767.88	+	3871.11i	−0.396277	+	0.867725i	−0.997634	+	0.0687449i	$0.978101\pi$
$272$	−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	$-0.892616\pi$
$277$		−	3051.89i		−	0.661987i	0.943633	−	0.330993i	$-0.107384\pi$
$278$	−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	0.118988	+	0.992896i	$0.462035\pi$
$281$	−3341.16	+	7316.12i	−0.709313	+	1.55318i	−0.828301	+	0.560283i	$0.810692\pi$
$282$	−29.5536	+	67.8388i	−0.00624076	+	0.0143253i
$283$	1969.56	−	6707.70i	0.413704	−	1.40894i	−0.444566	−	0.895746i	$-0.646642\pi$
$283$	1969.56	−	6707.70i	0.413704	−	1.40894i	0.858270	−	0.513199i	$-0.171540\pi$
$284$	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	−0.332709	−	0.943029i	$-0.607963\pi$
$293$	−1937.23	+	278.531i	−0.386260	+	0.0555357i	−0.0535502	+	0.998565i	$0.517054\pi$
$294$	−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	0.982541	−	0.186044i	$-0.0595668\pi$
$307$	2179.32	+	3391.08i	0.405147	+	0.630421i	−0.577394	+	0.816465i	$0.695930\pi$
$308$	−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	−0.548821	−	0.835940i	$-0.684923\pi$
$311$	1956.42	−	2257.83i	0.356716	−	0.411672i	0.905537	+	0.424268i	$0.139469\pi$
$312$	−85.9273	+	17.0108i	−0.0155919	+	0.00308668i
$313$	1353.11	+	2962.90i	0.244353	+	0.535058i	0.991578	−	0.129513i	$-0.0413415\pi$
$313$	1353.11	+	2962.90i	0.244353	+	0.535058i	−0.747225	+	0.664571i	$0.768614\pi$
$314$	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	−0.291596	−	0.956541i	$-0.594186\pi$
$317$	−6803.63	−	3107.11i	−1.20546	−	0.550514i	−0.913861	+	0.406028i	$0.866914\pi$
$318$	−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	−0.791381	+	0.611324i	$0.790637\pi$
$331$	−10668.8	+	4872.28i	−1.77163	+	0.809077i	−0.980252	+	0.197754i	$0.936635\pi$
$332$	−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	−0.476546	−	0.879149i	$-0.658111\pi$
$337$	774.500	−	497.741i	0.125192	−	0.0804560i	0.601738	+	0.798693i	$0.294475\pi$
$338$	−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	−0.0407021	−	0.999171i	$-0.512959\pi$
$347$	6092.26	−	5278.98i	0.942507	−	0.816687i	0.983209	+	0.182485i	$0.0584140\pi$
$348$	−41.5058	+	383.870i	−0.00639352	+	0.0591310i
$349$	2121.32	+	304.999i	0.325362	+	0.0467800i	0.303061	−	0.952971i	$-0.401992\pi$
$349$	2121.32	+	304.999i	0.325362	+	0.0467800i	0.0223015	+	0.999751i	$0.492901\pi$
$350$	−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	−0.432859	−	0.901462i	$-0.642495\pi$
$353$	1375.03	−	883.676i	0.207324	−	0.133239i	0.640182	+	0.768223i	$0.278859\pi$
$354$	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	−0.995113	−	0.0987414i	$-0.968518\pi$
$359$	−2843.79	−	6227.03i	−0.418076	−	0.915460i	0.577037	−	0.816718i	$-0.304209\pi$
$360$	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	−0.302729	−	0.953077i	$-0.597898\pi$
$373$	−8797.76	−	4017.80i	−1.22126	−	0.557731i	−0.918533	+	0.395345i	$0.870625\pi$
$374$	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	0.607726	−	0.794146i	$-0.292082\pi$
$379$	−677.688	−	587.220i	−0.0918483	−	0.0795870i	−0.699575	+	0.714559i	$0.746627\pi$
$380$	−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	−0.876554	−	0.481303i	$-0.840164\pi$
$383$	−6017.95	+	3867.50i	−0.802879	+	0.515979i	0.0736752	+	0.997282i	$0.476527\pi$
$384$	−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	−0.748039	−	0.663655i	$-0.769004\pi$
$389$	−1516.01	+	1313.63i	−0.197596	+	0.171218i	0.550443	+	0.834873i	$0.314459\pi$
$390$	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	−0.616467	−	0.787381i	$-0.711437\pi$
$397$	−7800.48	+	1121.54i	−0.986133	+	0.141784i	−0.369665	+	0.929165i	$0.620528\pi$
$398$	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	0.639717	−	0.768611i	$-0.279052\pi$
$401$	12795.2	−	3757.02i	1.59342	−	0.467871i	0.953706	+	0.300739i	$0.0972334\pi$
$402$	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	−0.0608757	−	0.998145i	$-0.519389\pi$
$409$	6065.81	−	13282.3i	0.733337	−	1.60578i	0.794213	−	0.607639i	$-0.207883\pi$
$410$	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	0.633625	−	0.773640i	$-0.281566\pi$
$419$	3978.59	+	1816.96i	0.463883	+	0.211848i	−0.169742	+	0.985489i	$0.554294\pi$
$420$	867.647	−	601.639i	0.100802	−	0.0698975i
$421$	−3877.44	+	13205.3i	−0.448871	+	1.52871i	0.355552	+	0.934657i	$0.384293\pi$
$421$	−3877.44	+	13205.3i	−0.448871	+	1.52871i	−0.804423	+	0.594057i	$0.797525\pi$
$422$	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	0.718324	+	0.695709i	$0.244910\pi$
$431$	2014.16	+	14008.8i	0.225101	+	1.56561i	−0.493223	+	0.869903i	$0.664181\pi$
$432$	−1780.99	+	969.694i	−0.198352	+	0.107996i
$433$	310.023	−	2156.26i	0.0344082	−	0.239315i	−0.965358	−	0.260928i	$-0.915971\pi$
$433$	310.023	−	2156.26i	0.0344082	−	0.239315i	0.999766	+	0.0216138i	$0.00688044\pi$
$434$	−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	0.843695	−	0.536824i	$-0.180376\pi$
$439$	1768.47	+	2040.92i	0.192265	+	0.221885i	−0.651430	+	0.758709i	$0.725830\pi$
$440$	−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	0.275799	−	0.961215i	$-0.411058\pi$
$443$	7563.98	−	1087.54i	0.811231	−	0.116637i	0.535433	+	0.844578i	$0.320149\pi$
$444$	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	−0.998767	−	0.0496444i	$-0.984191\pi$
$449$	−7682.56	+	8866.14i	−0.807488	+	0.931891i	0.191278	+	0.981536i	$0.438737\pi$
$450$	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	0.516275	−	0.856423i	$-0.327318\pi$
$457$	−471.729	−	303.162i	−0.0482857	−	0.0310313i	−0.564561	+	0.825391i	$0.690955\pi$
$458$	−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	$-0.787633\pi$
$461$		−	12249.2i		−	1.23753i	0.785576	−	0.618765i	$-0.212367\pi$
$462$	−925.335	+	149.659i	−0.0931829	+	0.0150709i
$463$	−6950.98	−	4467.12i	−0.697709	−	0.448390i	0.143110	−	0.989707i	$-0.454290\pi$
$463$	−6950.98	−	4467.12i	−0.697709	−	0.448390i	−0.840819	+	0.541316i	$0.817926\pi$
$464$	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	0.724095	+	0.689701i	$0.242258\pi$
$467$	−2603.05	+	8865.16i	−0.257933	+	0.878438i	−0.982028	+	0.188738i	$0.939560\pi$
$468$	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	−0.412064	−	0.911155i	$-0.635192\pi$
$479$	2516.13	−	17500.1i	0.240011	−	1.66931i	0.652074	−	0.758155i	$-0.273899\pi$
$480$	−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	0.927720	+	0.373277i	$0.121766\pi$
$487$	−726.347	+	5051.85i	−0.0675851	+	0.470064i	−0.995305	+	0.0967876i	$0.969143\pi$
$488$	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	0.999972	+	0.00744014i	$0.00236829\pi$
$491$	6433.64	+	10010.9i	0.591337	+	0.920138i	−0.408636	+	0.912698i	$0.633995\pi$
$492$	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	0.818878	+	0.573967i	$0.194596\pi$
$499$	−2009.95	+	6845.25i	−0.180316	+	0.614100i	−0.999194	+	0.0401326i	$0.987222\pi$
$500$	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	0.642968	−	0.765893i	$-0.277703\pi$
$503$	2407.22	+	1547.03i	0.213385	+	0.137134i	−0.429583	+	0.903027i	$0.641339\pi$
$504$	−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	−0.543946	−	0.839120i	$-0.683070\pi$
$509$	5113.72	−	7957.11i	0.445308	−	0.692913i	0.989254	+	0.146208i	$0.0467068\pi$
$510$	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	−0.134958	−	0.990851i	$-0.543090\pi$
$521$	8446.79	−	5428.42i	0.710289	−	0.456475i	0.845247	+	0.534376i	$0.179454\pi$
$522$	−4115.19	−	4584.13i	−0.345052	−	0.384371i
$523$	−11727.0	+	1686.08i	−0.980468	+	0.140970i	−0.613868	−	0.789409i	$-0.710387\pi$
$523$	−11727.0	+	1686.08i	−0.980468	+	0.140970i	−0.366600	+	0.930379i	$0.619478\pi$
$524$	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	0.989229	−	0.146373i	$-0.0467599\pi$
$541$	12396.2	+	10741.4i	0.985129	+	0.853619i	−0.00410096	+	0.999992i	$0.501305\pi$
$542$	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	0.204592	−	0.978847i	$-0.434413\pi$
$547$	−5132.55	−	2343.96i	−0.401192	−	0.183218i	−0.605784	+	0.795629i	$0.707140\pi$
$548$	−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	0.895985	−	0.444084i	$-0.146471\pi$
$557$	15079.6	+	6886.62i	1.14711	+	0.523869i	0.251129	+	0.967954i	$0.419198\pi$
$558$	−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	0.974095	−	0.226137i	$-0.0726098\pi$
$563$	11874.3	+	10289.2i	0.888888	+	0.770226i	−0.0852073	+	0.996363i	$0.527155\pi$
$564$	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	0.948172	+	0.317759i	$0.102930\pi$
$569$	1736.37	+	12076.7i	0.127931	+	0.889777i	−0.820241	+	0.572018i	$0.806161\pi$
$570$	−186.717	+	124.679i	−0.0137206	+	0.00916178i
$571$	−18483.0	−	2657.45i	−1.35462	−	0.194765i	−0.573531	−	0.819184i	$-0.694427\pi$
$571$	−18483.0	−	2657.45i	−1.35462	−	0.194765i	−0.781090	+	0.624419i	$0.785336\pi$
$572$	−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	0.995927	+	0.0901630i	$0.0287388\pi$
$577$	13076.1	+	15090.6i	0.943437	+	1.08878i	−0.0524899	+	0.998621i	$0.516716\pi$
$578$	−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	0.999606	+	0.0280586i	$0.00893251\pi$
$587$	16634.5	+	14413.8i	1.16964	+	1.01350i	0.170032	+	0.985439i	$0.445613\pi$
$588$	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	−0.975822	−	0.218567i	$-0.929862\pi$
$593$	−2478.17	+	5426.44i	−0.171613	+	0.375779i	0.804209	+	0.594346i	$0.202589\pi$
$594$	−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	−0.0509163	−	0.998703i	$-0.516214\pi$
$601$	−14446.7	−	9284.32i	−0.980520	−	0.630142i	−0.929604	+	0.368561i	$0.879851\pi$
$602$	−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	0.812151	−	0.583447i	$-0.198296\pi$
$607$	−2402.27	−	5260.25i	−0.160635	−	0.351741i	−0.972786	+	0.231706i	$0.925569\pi$
$608$	−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	0.592366	−	0.805669i	$-0.298194\pi$
$613$	−5867.10	−	9129.38i	−0.386574	−	0.601521i	−0.978940	+	0.204148i	$0.934558\pi$
$614$	−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	−0.588564	−	0.808451i	$-0.700306\pi$
$617$	3125.36	−	21737.4i	0.203926	−	1.41834i	0.792490	−	0.609885i	$-0.208784\pi$
$618$	−611.306	−	1278.71i	−0.0397902	−	0.0832318i
$619$	−6004.11	+	5202.59i	−0.389863	+	0.337819i	−0.827634	−	0.561268i	$-0.810314\pi$
$619$	−6004.11	+	5202.59i	−0.389863	+	0.337819i	0.437771	+	0.899087i	$0.355768\pi$
$620$	−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	0.481981	−	0.876182i	$-0.339918\pi$
$631$	21574.9	−	6334.97i	1.36115	−	0.399669i	0.879168	+	0.476513i	$0.158099\pi$
$632$	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	0.983682	−	0.179915i	$-0.0575822\pi$
$641$	19939.7	+	12814.5i	1.22866	+	0.789613i	0.244980	+	0.969528i	$0.421219\pi$
$642$	−1602.94	+	259.252i	−0.0985406	+	0.0159375i
$643$		−	18926.5i		−	1.16079i	−0.814336	−	0.580394i	$-0.802898\pi$
$643$		−	18926.5i		−	1.16079i	0.814336	−	0.580394i	$-0.197102\pi$
$644$	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	0.941858	−	0.336012i	$-0.109078\pi$
$647$	16909.3	+	10867.0i	1.02747	+	0.660316i	0.0856145	+	0.996328i	$0.472715\pi$
$648$	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	0.0253394	−	0.999679i	$-0.491933\pi$
$653$	13306.6	−	6076.93i	0.797440	−	0.364179i	0.772101	+	0.635500i	$0.219206\pi$
$654$	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	−0.989624	−	0.143681i	$-0.954106\pi$
$659$	−11997.9	−	18669.2i	−0.709216	−	1.10356i	0.280408	−	0.959881i	$-0.409530\pi$
$660$	−1959.79	+	352.359i	−0.115583	+	0.0207811i
$661$	3301.95	−	474.749i	0.194298	−	0.0279358i	−0.0444787	−	0.999010i	$-0.514163\pi$
$661$	3301.95	−	474.749i	0.194298	−	0.0279358i	0.238777	+	0.971074i	$0.423254\pi$
$662$	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	0.992627	+	0.121207i	$0.0386766\pi$
$673$	1298.20	+	9029.17i	0.0743564	+	0.517160i	−0.918271	+	0.395953i	$0.870414\pi$
$674$	−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	−0.874503	−	0.485020i	$-0.838812\pi$
$677$	−7064.43	−	24059.2i	−0.401046	−	1.36584i	0.473457	−	0.880817i	$-0.343006\pi$
$678$	−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	0.123390	+	0.992358i	$0.460623\pi$
$683$	−9226.90	+	31423.9i	−0.516922	+	1.76047i	−0.640312	+	0.768115i	$0.721195\pi$
$684$	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	$0.214276\pi$
$691$			22649.5i			1.24693i	−0.781851	+	0.623465i	$0.785724\pi$
$692$	−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	0.276995	−	0.960871i	$-0.410662\pi$
$701$	−11779.6	−	10207.1i	−0.634676	−	0.549950i	−0.911671	+	0.410921i	$0.865207\pi$
$702$	−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	0.402115	−	0.915589i	$-0.368275\pi$
$709$	10005.5	+	1438.57i	0.529990	+	0.0762011i	0.127875	+	0.991790i	$0.459184\pi$
$710$	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	0.635838	+	0.771822i	$0.280655\pi$
$719$	4688.81	+	32611.4i	0.243203	+	1.69152i	−0.392635	+	0.919694i	$0.628436\pi$
$720$	−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	0.996708	−	0.0810705i	$-0.0258339\pi$
$727$	5542.17	+	12135.7i	0.282734	+	0.619102i	−0.713974	+	0.700172i	$0.753107\pi$
$728$	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	−0.715630	−	0.698480i	$-0.753860\pi$
$733$	4306.67	−	6701.32i	0.217013	−	0.337679i	0.932643	+	0.360801i	$0.117497\pi$
$734$	−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	−0.799221	−	0.601037i	$-0.794754\pi$
$739$	1597.30	−	2485.44i	0.0795095	−	0.123719i	0.878731	+	0.477318i	$0.158391\pi$
$740$	−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	0.825426	−	0.564510i	$-0.190935\pi$
$743$	24599.4	+	7223.04i	1.21462	+	0.356645i	0.389196	+	0.921155i	$0.372753\pi$
$744$	−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	−0.646806	−	0.762654i	$-0.723896\pi$
$751$	−4564.07	+	2933.15i	−0.221765	+	0.142519i	0.425042	+	0.905174i	$0.360259\pi$
$752$	−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	−0.602689	−	0.797976i	$-0.705904\pi$
$757$	2111.79	−	1829.88i	0.101393	−	0.0878575i	0.704082	+	0.710119i	$0.251359\pi$
$758$	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	0.613820	−	0.789446i	$-0.289632\pi$
$761$	−5352.12	−	6176.68i	−0.254946	−	0.294224i	−0.868766	+	0.495222i	$0.835087\pi$
$762$	−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	0.122307	−	0.992492i	$-0.460971\pi$
$769$	16245.0	−	4769.96i	0.761781	−	0.223679i	0.639473	+	0.768813i	$0.279152\pi$
$770$	−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	0.351484	−	0.936194i	$-0.385677\pi$
$773$	27706.7	−	12653.2i	1.28919	−	0.588751i	0.937701	+	0.347442i	$0.112950\pi$
$774$	−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	0.610458	−	0.792048i	$-0.290985\pi$
$787$	9088.09	+	4150.39i	0.411633	+	0.187987i	−0.198825	+	0.980035i	$0.563713\pi$
$788$	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	−0.863859	−	0.503733i	$-0.831959\pi$
$797$	−21672.5	−	33723.1i	−0.963211	−	1.49879i	−0.0993517	−	0.995052i	$-0.531677\pi$
$798$	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	0.758714	+	0.651424i	$0.225828\pi$
$809$	−3515.84	+	24453.2i	−0.152794	+	1.06271i	−0.911508	+	0.411282i	$0.865081\pi$
$810$	−21358.1	+	14261.7i	−0.926479	+	0.618647i
$811$	−17972.2	+	2584.01i	−0.778162	+	0.111883i	−0.519940	−	0.854203i	$-0.674046\pi$
$811$	−17972.2	+	2584.01i	−0.778162	+	0.111883i	−0.258222	+	0.966086i	$0.583137\pi$
$812$	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	0.709776	+	0.704427i	$0.248796\pi$
$821$	−6308.43	+	21484.5i	−0.268168	+	0.913295i	−0.977944	+	0.208868i	$0.933022\pi$
$822$	−916.950	+	2104.81i	−0.0389079	+	0.0893111i
$823$	−8866.57	+	19415.1i	−0.375540	+	0.822317i	0.623636	+	0.781715i	$0.285655\pi$
$823$	−8866.57	+	19415.1i	−0.375540	+	0.822317i	−0.999175	+	0.0406022i	$0.987072\pi$
$824$	−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	$-0.785701\pi$
$827$		−	29657.9i		−	1.24704i	0.781806	−	0.623522i	$-0.214299\pi$
$828$	20455.3	−	11604.8i	0.858540	−	0.487072i
$829$			24905.0i			1.04341i	0.853126	+	0.521705i	$0.174704\pi$
$829$			24905.0i			1.04341i	−0.853126	+	0.521705i	$0.825296\pi$
$830$	−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	−0.976503	−	0.215504i	$-0.930860\pi$
$839$	−15169.9	+	17506.9i	−0.624221	+	0.720390i	0.352282	+	0.935894i	$0.385406\pi$
$840$	−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	−0.318002	−	0.948090i	$-0.603012\pi$
$853$	14329.4	−	12416.5i	0.575181	−	0.498397i	0.893183	+	0.449693i	$0.148467\pi$
$854$	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	0.907578	+	0.419883i	$0.137929\pi$
$857$	3890.14	+	27056.5i	0.155058	+	1.07845i	−0.752520	+	0.658569i	$0.771162\pi$
$858$	237.947	+	265.062i	0.00946782	+	0.0105467i
$859$	−16742.1	−	26051.3i	−0.664999	−	1.03476i	−0.995844	−	0.0910738i	$-0.970970\pi$
$859$	−16742.1	−	26051.3i	−0.664999	−	1.03476i	0.330845	−	0.943685i	$-0.392666\pi$
$860$	−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	−0.959704	−	0.281012i	$-0.909330\pi$
$863$	−13816.3	+	15944.8i	−0.544973	+	0.628932i	0.414732	+	0.909944i	$0.363875\pi$
$864$	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	−0.755465	−	0.655189i	$-0.772589\pi$
$877$	4008.65	−	6237.58i	0.154347	−	0.240169i	0.909812	+	0.415020i	$0.136225\pi$
$878$	−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	0.810430	−	0.585836i	$-0.199234\pi$
$881$	30738.2	+	9025.56i	1.17548	+	0.345152i	0.365050	+	0.930988i	$0.381052\pi$
$882$	60.1156	+	3425.68i	0.00229501	+	0.130781i
$883$	2568.38	−	1172.94i	0.0978856	−	0.0447029i	−0.365870	−	0.930666i	$-0.619229\pi$
$883$	2568.38	−	1172.94i	0.0978856	−	0.0447029i	0.463756	+	0.885963i	$0.346501\pi$
$884$	−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	−0.238641	−	0.971108i	$-0.576702\pi$
$887$	2261.90	−	664.155i	0.0856226	−	0.0251411i	0.324263	+	0.945967i	$0.394884\pi$
$888$	−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	0.956338	+	0.292263i	$0.0944082\pi$
$907$	8463.05	+	28822.5i	0.309825	+	1.05517i	−0.646513	+	0.762903i	$0.723774\pi$
$908$	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	0.724792	−	0.688968i	$-0.241936\pi$
$911$	−7438.72	−	16288.5i	−0.270533	−	0.592385i	−0.995325	+	0.0965829i	$0.969209\pi$
$912$	−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	0.962897	−	0.269871i	$-0.0869809\pi$
$929$	3635.11	+	7959.77i	0.128379	+	0.281111i	−0.834518	+	0.550981i	$0.814254\pi$
$930$	−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	0.934306	+	0.356471i	$0.116020\pi$
$937$	3966.02	+	27584.3i	0.138275	+	0.961727i	−0.796031	+	0.605256i	$0.793071\pi$
$938$	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	−0.618997	+	0.785393i	$0.712461\pi$
$941$	−42851.0	+	37130.6i	−1.48449	+	1.28632i	−0.865492	+	0.500923i	$0.832994\pi$
$942$	−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	0.190051	−	0.981774i	$-0.439135\pi$
$947$	2792.02	+	401.432i	0.0958062	+	0.0137748i	−0.0942450	+	0.995549i	$0.530044\pi$
$948$	−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	−0.966618	−	0.256221i	$-0.917522\pi$
$953$	−48285.7	+	14177.9i	−1.64127	+	0.481919i	−0.674647	+	0.738140i	$0.735704\pi$
$954$	−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	0.914966	−	0.403530i	$-0.132217\pi$
$971$	36586.2	+	16708.4i	1.20917	+	0.552211i	0.294208	+	0.955742i	$0.404944\pi$
$972$	−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	−0.949847	−	0.312714i	$-0.898762\pi$
$977$	−15426.0	+	17802.5i	−0.505139	+	0.582961i	0.444709	+	0.895675i	$0.353307\pi$
$978$	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	−0.864446	−	0.502726i	$-0.832330\pi$
$983$	−5444.34	−	37866.2i	−0.176650	−	1.22863i	0.687795	−	0.725905i	$-0.258579\pi$
$984$	−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	0.950043	−	0.312120i	$-0.101039\pi$
$991$	15782.3	+	18213.7i	0.505894	+	0.583833i	−0.444148	+	0.895953i	$0.646494\pi$
$992$	−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	0.561333	−	0.827590i	$-0.310289\pi$
$997$	−13368.4	−	20801.6i	−0.424656	−	0.660777i	−0.985989	+	0.166813i	$0.946652\pi$
$998$	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.13.2	✓	700
8.5	even	2	inner	184.4.p.a.13.42	yes	700
23.16	even	11	inner	184.4.p.a.85.42	yes	700
184.85	even	22	inner	184.4.p.a.85.2	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.p.a.13.2	✓	700	1.1	even	1	trivial
184.4.p.a.13.42	yes	700	8.5	even	2	inner
184.4.p.a.85.2	yes	700	184.85	even	22	inner
184.4.p.a.85.42	yes	700	23.16	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.79214 + 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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