LMFDB - Embedded newform 161.4.o.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(5,161)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("161.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.o (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$46$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	161.33
Dual form			161.4.o.a.122.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.24626 + 1.01113i) q^{2} +(9.78230 + 0.465988i) q^{3} +(19.0739 - 7.63605i) q^{4} +(-7.00146 - 9.83217i) q^{5} +(-51.7917 + 7.44652i) q^{6} +(16.3937 + 8.61668i) q^{7} +(-56.3885 + 36.2387i) q^{8} +(68.5985 + 6.55036i) q^{9} +(46.6731 + 44.5027i) q^{10} +(0.611352 - 3.17200i) q^{11} +(190.145 - 65.8099i) q^{12} +(16.5556 + 56.3833i) q^{13} +(-94.7182 - 28.6291i) q^{14} +(-63.9087 - 99.4438i) q^{15} +(140.230 - 133.709i) q^{16} +(1.99973 - 1.57260i) q^{17} +(-366.509 + 34.9974i) q^{18} +(-32.6935 - 25.7104i) q^{19} +(-208.624 - 134.075i) q^{20} +(156.353 + 91.9302i) q^{21} +17.2593i q^{22} +(69.2444 - 85.8616i) q^{23} +(-568.496 + 328.221i) q^{24} +(-6.76769 + 19.5540i) q^{25} +(-143.866 - 279.062i) q^{26} +(406.268 + 58.4126i) q^{27} +(378.489 + 39.1709i) q^{28} +(8.25391 + 57.4072i) q^{29} +(435.833 + 457.088i) q^{30} +(128.884 - 250.000i) q^{31} +(-289.439 + 406.460i) q^{32} +(7.45854 - 30.7445i) q^{33} +(-8.90099 + 10.2723i) q^{34} +(-30.0590 - 221.515i) q^{35} +(1358.46 - 398.880i) q^{36} +(-26.9113 + 281.828i) q^{37} +(197.515 + 101.826i) q^{38} +(135.678 + 559.273i) q^{39} +(751.106 + 300.698i) q^{40} +(-44.2342 - 20.2011i) q^{41} +(-913.221 - 324.196i) q^{42} +(-35.1637 + 54.7158i) q^{43} +(-12.5606 - 65.1707i) q^{44} +(-415.885 - 720.334i) q^{45} +(-276.457 + 520.468i) q^{46} +(-11.5992 - 6.69679i) q^{47} +(1434.08 - 1242.63i) q^{48} +(194.506 + 282.518i) q^{49} +(15.7334 - 109.428i) q^{50} +(20.2948 - 14.4518i) q^{51} +(746.326 + 949.031i) q^{52} +(463.643 - 112.478i) q^{53} +(-2190.45 + 104.344i) q^{54} +(-35.4680 + 16.1977i) q^{55} +(-1236.67 + 108.204i) q^{56} +(-307.837 - 266.742i) q^{57} +(-101.349 - 292.827i) q^{58} +(-229.150 + 240.326i) q^{59} +(-1978.35 - 1408.77i) q^{60} +(-26.0595 - 547.056i) q^{61} +(-423.375 + 1441.88i) q^{62} +(1068.14 + 698.475i) q^{63} +(463.565 - 1015.07i) q^{64} +(438.457 - 557.543i) q^{65} +(-8.04262 + 168.835i) q^{66} +(-772.113 - 267.231i) q^{67} +(26.1342 - 45.2658i) q^{68} +(717.380 - 807.657i) q^{69} +(381.679 + 1131.73i) q^{70} +(68.0442 + 78.5272i) q^{71} +(-4105.54 + 2116.55i) q^{72} +(264.596 + 660.929i) q^{73} +(-143.782 - 1505.75i) q^{74} +(-75.3155 + 188.129i) q^{75} +(-819.919 - 240.750i) q^{76} +(37.3544 - 46.7329i) q^{77} +(-1277.30 - 2796.90i) q^{78} +(-63.0147 - 15.2872i) q^{79} +(-2296.46 - 442.607i) q^{80} +(2120.06 + 408.607i) q^{81} +(252.490 + 61.2534i) q^{82} +(265.126 + 580.545i) q^{83} +(3684.24 + 559.553i) q^{84} +(-29.4631 - 8.65116i) q^{85} +(129.153 - 322.608i) q^{86} +(53.9911 + 565.420i) q^{87} +(80.4757 + 201.019i) q^{88} +(-639.139 + 329.499i) q^{89} +(2910.20 + 3358.55i) q^{90} +(-214.429 + 1066.98i) q^{91} +(665.119 - 2166.47i) q^{92} +(1377.28 - 2385.51i) q^{93} +(67.6237 + 23.4048i) q^{94} +(-23.8874 + 501.458i) q^{95} +(-3020.79 + 3841.24i) q^{96} +(123.822 - 271.132i) q^{97} +(-1306.09 - 1285.49i) q^{98} +(62.7155 - 213.590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 11 q^{2} - 27 q^{3} + 157 q^{4} - 33 q^{5} - 22 q^{7} - 104 q^{8} - 359 q^{9} - 33 q^{10} - 11 q^{11} - 75 q^{12} - 22 q^{14} - 44 q^{15} + 1157 q^{16} - 33 q^{17} + 179 q^{18} - 33 q^{19} - 1342 q^{21}+ \cdots + 23056 q^{99}+O(q^{100}) $ 920 * q - 11 * q^2 - 27 * q^3 + 157 * q^4 - 33 * q^5 - 22 * q^7 - 104 * q^8 - 359 * q^9 - 33 * q^10 - 11 * q^11 - 75 * q^12 - 22 * q^14 - 44 * q^15 + 1157 * q^16 - 33 * q^17 + 179 * q^18 - 33 * q^19 - 1342 * q^21 - 494 * q^23 - 570 * q^24 + 1269 * q^25 - 609 * q^26 + 682 * q^28 - 348 * q^29 + 1485 * q^30 + 105 * q^31 - 1017 * q^32 - 33 * q^33 + 966 * q^35 + 4354 * q^36 - 1199 * q^37 - 33 * q^38 + 5 * q^39 - 33 * q^40 - 3652 * q^42 - 3476 * q^43 + 3388 * q^44 + 477 * q^46 - 1188 * q^47 - 1408 * q^49 - 3234 * q^50 + 649 * q^51 + 1911 * q^52 - 11 * q^53 - 1659 * q^54 + 9361 * q^56 + 7612 * q^57 - 4198 * q^58 - 915 * q^59 - 11 * q^60 - 33 * q^61 - 2112 * q^63 - 5064 * q^64 - 4323 * q^65 + 858 * q^66 - 11 * q^67 - 2478 * q^70 + 1732 * q^71 - 9181 * q^72 - 3987 * q^73 + 2354 * q^74 + 2871 * q^75 + 2164 * q^77 - 24268 * q^78 + 1837 * q^79 + 12144 * q^80 + 3035 * q^81 + 5823 * q^82 + 11330 * q^84 + 13676 * q^85 + 5225 * q^86 - 24657 * q^87 - 12342 * q^88 - 33 * q^89 + 9810 * q^92 - 1440 * q^93 - 15858 * q^94 - 4187 * q^95 + 2439 * q^96 - 11284 * q^98 + 23056 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−5.24626	+	1.01113i	−1.85483	+	0.357490i	−0.989596	−	0.143872i	$-0.954044\pi$
$2$	−5.24626	+	1.01113i	−1.85483	+	0.357490i	−0.865237	+	0.501362i	$0.832832\pi$
$3$	9.78230	+	0.465988i	1.88260	+	0.0896795i	0.957222	−	0.289355i	$-0.0934409\pi$
$3$	9.78230	+	0.465988i	1.88260	+	0.0896795i	0.925382	+	0.379035i	$0.123744\pi$
$4$	19.0739	−	7.63605i	2.38424	−	0.954506i
$5$	−7.00146	−	9.83217i	−0.626229	−	0.879416i	0.372590	−	0.927996i	$-0.378470\pi$
$5$	−7.00146	−	9.83217i	−0.626229	−	0.879416i	−0.998819	+	0.0485800i	$0.984530\pi$
$6$	−51.7917	+	7.44652i	−3.52398	+	0.506671i
$7$	16.3937	+	8.61668i	0.885176	+	0.465257i
$7$	16.3937	+	8.61668i	0.885176	+	0.465257i
$8$	−56.3885	+	36.2387i	−2.49204	+	1.60154i
$9$	68.5985	+	6.55036i	2.54068	+	0.242606i
$10$	46.6731	+	44.5027i	1.47593	+	1.40730i
$11$	0.611352	−	3.17200i	0.0167572	−	0.0869448i	−0.972587	−	0.232538i	$-0.925297\pi$
$11$	0.611352	−	3.17200i	0.0167572	−	0.0869448i	0.989345	+	0.145593i	$0.0465091\pi$
$12$	190.145	−	65.8099i	4.57418	−	1.58314i
$13$	16.5556	+	56.3833i	0.353208	+	1.20292i	0.924183	+	0.381949i	$0.124747\pi$
$13$	16.5556	+	56.3833i	0.353208	+	1.20292i	−0.570975	+	0.820967i	$0.693435\pi$
$14$	−94.7182	−	28.6291i	−1.80818	−	0.546533i
$15$	−63.9087	−	99.4438i	−1.10008	−	1.71175i
$16$	140.230	−	133.709i	2.19109	−	2.08920i
$17$	1.99973	−	1.57260i	0.0285297	−	0.0224360i	−0.603792	−	0.797142i	$-0.706344\pi$
$17$	1.99973	−	1.57260i	0.0285297	−	0.0224360i	0.632322	+	0.774706i	$0.282102\pi$
$18$	−366.509	+	34.9974i	−4.79928	+	0.458275i
$19$	−32.6935	−	25.7104i	−0.394758	−	0.310441i	0.400975	−	0.916089i	$-0.368672\pi$
$19$	−32.6935	−	25.7104i	−0.394758	−	0.310441i	−0.795733	+	0.605648i	$0.792914\pi$
$20$	−208.624	−	134.075i	−2.33249	−	1.49900i
$21$	156.353	+	91.9302i	1.62471	+	0.955277i
$22$			17.2593i			0.167259i
$23$	69.2444	−	85.8616i	0.627759	−	0.778408i
$23$	69.2444	−	85.8616i	0.627759	−	0.778408i
$24$	−568.496	+	328.221i	−4.83515	+	2.79158i
$25$	−6.76769	+	19.5540i	−0.0541415	+	0.156432i
$26$	−143.866	−	279.062i	−1.08517	−	2.10494i
$27$	406.268	+	58.4126i	2.89579	+	0.416352i
$28$	378.489	+	39.1709i	2.55456	+	0.264379i
$29$	8.25391	+	57.4072i	0.0528521	+	0.367595i	0.999033	+	0.0439575i	$0.0139966\pi$
$29$	8.25391	+	57.4072i	0.0528521	+	0.367595i	−0.946181	+	0.323637i	$0.895094\pi$
$30$	435.833	+	457.088i	2.65239	+	2.78175i
$31$	128.884	−	250.000i	0.746716	−	1.44843i	−0.141951	−	0.989874i	$-0.545337\pi$
$31$	128.884	−	250.000i	0.746716	−	1.44843i	0.888667	−	0.458553i	$-0.151632\pi$
$32$	−289.439	+	406.460i	−1.59894	+	2.24540i
$33$	7.45854	−	30.7445i	0.0393444	−	0.162180i
$34$	−8.90099	+	10.2723i	−0.0448973	+	0.0518142i
$35$	−30.0590	−	221.515i	−0.145169	−	1.06980i
$36$	1358.46	−	398.880i	6.28917	−	1.84667i
$37$	−26.9113	+	281.828i	−0.119573	+	1.25222i	0.714132	+	0.700011i	$0.246822\pi$
$37$	−26.9113	+	281.828i	−0.119573	+	1.25222i	−0.833705	+	0.552211i	$0.813784\pi$
$38$	197.515	+	101.826i	0.843190	+	0.434695i
$39$	135.678	+	559.273i	0.557074	+	2.29629i
$40$	751.106	+	300.698i	2.96901	+	1.18861i
$41$	−44.2342	−	20.2011i	−0.168493	−	0.0769482i	0.329383	−	0.944196i	$-0.393159\pi$
$41$	−44.2342	−	20.2011i	−0.168493	−	0.0769482i	−0.497876	+	0.867248i	$0.665887\pi$
$42$	−913.221	−	324.196i	−3.35507	−	1.19106i
$43$	−35.1637	+	54.7158i	−0.124707	+	0.194048i	−0.897993	−	0.440009i	$-0.854975\pi$
$43$	−35.1637	+	54.7158i	−0.124707	+	0.194048i	0.773286	+	0.634057i	$0.218612\pi$
$44$	−12.5606	−	65.1707i	−0.0430360	−	0.223292i
$45$	−415.885	−	720.334i	−1.37770	−	2.38625i
$46$	−276.457	+	520.468i	−0.886115	+	1.66823i
$47$	−11.5992	−	6.69679i	−0.0359982	−	0.0207836i	0.481893	−	0.876230i	$-0.339949\pi$
$47$	−11.5992	−	6.69679i	−0.0359982	−	0.0207836i	−0.517891	+	0.855447i	$0.673283\pi$
$48$	1434.08	−	1242.63i	4.31231	−	3.73664i
$49$	194.506	+	282.518i	0.567072	+	0.823668i
$50$	15.7334	−	109.428i	0.0445008	−	0.309510i
$51$	20.2948	−	14.4518i	0.0557223	−	0.0396796i
$52$	746.326	+	949.031i	1.99032	+	2.53090i
$53$	463.643	−	112.478i	1.20163	−	0.291511i	0.415509	−	0.909589i	$-0.363603\pi$
$53$	463.643	−	112.478i	1.20163	−	0.291511i	0.786117	+	0.618077i	$0.212088\pi$
$54$	−2190.45	+	104.344i	−5.52005	+	0.262952i
$55$	−35.4680	+	16.1977i	−0.0869545	+	0.0397108i
$56$	−1236.67	+	108.204i	−2.95102	+	0.258203i
$57$	−307.837	−	266.742i	−0.715333	−	0.619839i
$58$	−101.349	−	292.827i	−0.229443	−	0.662933i
$59$	−229.150	+	240.326i	−0.505641	+	0.530301i	−0.926234	−	0.376949i	$-0.876973\pi$
$59$	−229.150	+	240.326i	−0.505641	+	0.530301i	0.420594	+	0.907249i	$0.361822\pi$
$60$	−1978.35	−	1408.77i	−4.25673	−	3.03120i
$61$	−26.0595	−	547.056i	−0.0546980	−	1.14825i	−0.844732	−	0.535189i	$-0.820240\pi$
$61$	−26.0595	−	547.056i	−0.0546980	−	1.14825i	0.790034	−	0.613063i	$-0.210063\pi$
$62$	−423.375	+	1441.88i	−0.867236	+	2.95353i
$63$	1068.14	+	698.475i	2.13608	+	1.39682i
$64$	463.565	−	1015.07i	0.905400	−	1.98255i
$65$	438.457	−	557.543i	0.836675	−	1.06392i
$66$	−8.04262	+	168.835i	−0.0149997	+	0.314882i
$67$	−772.113	−	267.231i	−1.40789	−	0.487275i	−0.485738	−	0.874104i	$-0.661449\pi$
$67$	−772.113	−	267.231i	−1.40789	−	0.487275i	−0.922151	+	0.386829i	$0.873570\pi$
$68$	26.1342	−	45.2658i	0.0466064	−	0.0807247i
$69$	717.380	−	807.657i	1.25163	−	1.40914i
$70$	381.679	+	1131.73i	0.651705	+	1.93240i
$71$	68.0442	+	78.5272i	0.113737	+	0.131260i	0.809763	−	0.586757i	$-0.199596\pi$
$71$	68.0442	+	78.5272i	0.113737	+	0.131260i	−0.696026	+	0.718017i	$0.745050\pi$
$72$	−4105.54	+	2116.55i	−6.72003	+	3.46442i
$73$	264.596	+	660.929i	0.424228	+	1.05967i	0.974441	+	0.224646i	$0.0721225\pi$
$73$	264.596	+	660.929i	0.424228	+	1.05967i	−0.550212	+	0.835025i	$0.685453\pi$
$74$	−143.782	−	1505.75i	−0.225869	−	2.36541i
$75$	−75.3155	+	188.129i	−0.115956	+	0.289643i
$76$	−819.919	−	240.750i	−1.23752	−	0.363367i
$77$	37.3544	−	46.7329i	0.0552848	−	0.0691650i
$78$	−1277.30	−	2796.90i	−1.85418	−	4.06009i
$79$	−63.0147	−	15.2872i	−0.0897432	−	0.0217715i	0.190636	−	0.981661i	$-0.438945\pi$
$79$	−63.0147	−	15.2872i	−0.0897432	−	0.0217715i	−0.280379	+	0.959889i	$0.590460\pi$
$80$	−2296.46	−	442.607i	−3.20940	−	0.618561i
$81$	2120.06	+	408.607i	2.90817	+	0.560504i
$82$	252.490	+	61.2534i	0.340035	+	0.0824916i
$83$	265.126	+	580.545i	0.350619	+	0.767748i	0.999974	+	0.00726276i	$0.00231183\pi$
$83$	265.126	+	580.545i	0.350619	+	0.767748i	−0.649355	+	0.760486i	$0.724961\pi$
$84$	3684.24	+	559.553i	4.78552	+	0.726813i
$85$	−29.4631	−	8.65116i	−0.0375968	−	0.0110394i
$86$	129.153	−	322.608i	0.161941	−	0.404509i
$87$	53.9911	+	565.420i	0.0665340	+	0.696775i
$88$	80.4757	+	201.019i	0.0974857	+	0.243507i
$89$	−639.139	+	329.499i	−0.761221	+	0.392436i	−0.794700	−	0.607003i	$-0.792372\pi$
$89$	−639.139	+	329.499i	−0.761221	+	0.392436i	0.0334790	+	0.999439i	$0.489341\pi$
$90$	2910.20	+	3358.55i	3.40846	+	3.93358i
$91$	−214.429	+	1066.98i	−0.247014	+	1.22912i
$92$	665.119	−	2166.47i	0.753733	−	2.45511i
$93$	1377.28	−	2385.51i	1.53567	−	2.65985i
$94$	67.6237	+	23.4048i	0.0742005	+	0.0256811i
$95$	−23.8874	+	501.458i	−0.0257979	+	0.541564i
$96$	−3020.79	+	3841.24i	−3.21154	+	4.08380i
$97$	123.822	−	271.132i	0.129610	−	0.283807i	−0.833690	−	0.552233i	$-0.813776\pi$
$97$	123.822	−	271.132i	0.129610	−	0.283807i	0.963300	+	0.268425i	$0.0865033\pi$
$98$	−1306.09	−	1285.49i	−1.34628	−	1.32504i
$99$	62.7155	−	213.590i	0.0636682	−	0.216834i
$100$	20.2285	+	424.649i	0.0202285	+	0.424649i
$101$	−750.162	−	534.188i	−0.739048	−	0.526274i	0.147414	−	0.989075i	$-0.452905\pi$
$101$	−750.162	−	534.188i	−0.739048	−	0.526274i	−0.886462	+	0.462801i	$0.846845\pi$
$102$	−91.8589	+	96.3388i	−0.0891705	+	0.0935193i
$103$	−424.804	−	1227.39i	−0.406381	−	1.17416i	−0.943706	−	0.330785i	$-0.892687\pi$
$103$	−424.804	−	1227.39i	−0.406381	−	1.17416i	0.537326	−	0.843375i	$-0.319435\pi$
$104$	−2976.80	−	2579.41i	−2.80673	−	2.43204i
$105$	−190.823	−	2180.93i	−0.177356	−	2.02702i
$106$	−2318.66	+	1058.90i	−2.12460	+	0.970275i
$107$	−883.393	+	42.0812i	−0.798139	+	0.0380200i	−0.442689	−	0.896675i	$-0.645975\pi$
$107$	−883.393	+	42.0812i	−0.798139	+	0.0380200i	−0.355450	+	0.934695i	$0.615672\pi$
$108$	8195.17	−	1988.13i	7.30167	−	1.77137i
$109$	−1073.09	−	1364.54i	−0.942966	−	1.19908i	−0.979845	−	0.199759i	$-0.935984\pi$
$109$	−1073.09	−	1364.54i	−0.942966	−	1.19908i	0.0368790	−	0.999320i	$-0.488258\pi$
$110$	169.696	−	120.840i	0.147090	−	0.104742i
$111$	−394.583	+	2744.38i	−0.337407	+	2.34671i
$112$	3451.01	−	983.665i	2.91151	−	0.829890i
$113$	−1232.33	+	1067.82i	−1.02591	+	0.888959i	−0.993873	−	0.110528i	$-0.964746\pi$
$113$	−1232.33	+	1067.82i	−1.02591	+	0.888959i	−0.0320400	+	0.999487i	$0.510200\pi$
$114$	1884.70	+	1088.13i	1.54841	+	0.893975i
$115$	−1329.02	−	79.6664i	−1.07767	−	0.0645994i
$116$	595.799	+	1031.95i	0.476884	+	0.825987i
$117$	766.360	+	3976.25i	0.605556	+	3.14192i
$118$	959.180	−	1492.51i	0.748302	−	1.16438i
$119$	46.3336	−	8.54976i	0.0356924	−	0.00658618i
$120$	7207.42	+	3291.52i	5.48287	+	2.50394i
$121$	1225.97	+	490.804i	0.921089	+	0.368749i
$122$	689.862	+	2843.65i	0.511944	+	2.11026i
$123$	−423.298	−	218.225i	−0.310305	−	0.159973i
$124$	549.310	−	5752.64i	0.397819	−	4.16614i
$125$	−1208.03	+	354.709i	−0.864395	+	0.253809i
$126$	−6309.99	−	2584.35i	−4.46142	−	1.82724i
$127$	306.461	−	353.675i	0.214126	−	0.247115i	−0.638518	−	0.769607i	$-0.720452\pi$
$127$	306.461	−	353.675i	0.214126	−	0.247115i	0.852644	+	0.522492i	$0.174998\pi$
$128$	−464.497	+	1914.68i	−0.320751	+	1.32215i
$129$	−369.479	+	518.860i	−0.252177	+	0.354132i
$130$	−1736.51	+	3368.35i	−1.17155	+	2.27249i
$131$	449.443	+	471.362i	0.299756	+	0.314375i	0.856336	−	0.516419i	$-0.172735\pi$
$131$	449.443	+	471.362i	0.299756	+	0.314375i	−0.556580	+	0.830794i	$0.687887\pi$
$132$	−92.5030	−	643.373i	−0.0609951	−	0.424230i
$133$	−314.428	−	703.198i	−0.204995	−	0.458459i
$134$	4320.91	+	621.254i	2.78560	+	0.400508i
$135$	−2270.15	−	4403.47i	−1.44728	−	2.80734i
$136$	−55.7726	+	161.144i	−0.0351651	+	0.101603i
$137$	420.281	−	242.649i	0.262095	−	0.151321i	−0.363195	−	0.931713i	$-0.618314\pi$
$137$	420.281	−	242.649i	0.262095	−	0.151321i	0.625290	+	0.780393i	$0.284981\pi$
$138$	−2946.91	+	4962.55i	−1.81781	+	3.06116i
$139$			2409.55i			1.47032i	0.677891	+	0.735162i	$0.262894\pi$
$139$			2409.55i			1.47032i	−0.677891	+	0.735162i	$0.737106\pi$
$140$	−2264.84	−	3995.63i	−1.36724	−	2.41209i
$141$	−110.346	−	70.9151i	−0.0659064	−	0.0423555i
$142$	−436.379	−	343.172i	−0.257888	−	0.202806i
$143$	188.969	−	18.0443i	0.110506	−	0.0105521i
$144$	10495.4	−	8253.67i	6.07372	−	4.77643i
$145$	506.648	−	483.088i	0.290171	−	0.276678i
$146$	−2056.43	−	3199.87i	−1.16569	−	1.81386i
$147$	1771.06	+	2854.31i	0.993706	+	1.60150i
$148$	1638.75	+	5581.06i	0.910163	+	3.09973i
$149$	−728.747	+	252.222i	−0.400680	+	0.138677i	−0.519974	−	0.854182i	$-0.674058\pi$
$149$	−728.747	+	252.222i	−0.400680	+	0.138677i	0.119294	+	0.992859i	$0.461937\pi$
$150$	204.901	−	1063.13i	0.111534	−	0.578693i
$151$	−1356.59	−	1293.50i	−0.731110	−	0.697112i	0.230027	−	0.973184i	$-0.426119\pi$
$151$	−1356.59	−	1293.50i	−0.731110	−	0.697112i	−0.961137	+	0.276072i	$0.910967\pi$
$152$	2775.25	+	265.004i	1.48094	+	0.141412i
$153$	147.480	−	94.7793i	0.0779282	−	0.0500814i
$154$	−148.718	+	282.943i	−0.0778182	+	0.148053i
$155$	−3360.41	+	483.154i	−1.74139	+	0.250373i
$156$	6858.55	+	9631.49i	3.52002	+	4.94318i
$157$	−306.305	+	122.626i	−0.155706	+	0.0623351i	−0.448206	−	0.893930i	$-0.647937\pi$
$157$	−306.305	+	122.626i	−0.155706	+	0.0623351i	0.292501	+	0.956265i	$0.405513\pi$
$158$	346.049	+	16.4844i	0.174242	+	0.00830016i
$159$	4587.90	−	884.246i	2.28833	−	0.441039i
$160$	6022.88			2.97594
$161$	1875.01	−	810.931i	0.917837	−	0.396959i
$162$	−11535.5			−5.59455
$163$	27.0326	−	5.21011i	0.0129899	−	0.00250360i	−0.182752	−	0.983159i	$-0.558501\pi$
$163$	27.0326	−	5.21011i	0.0129899	−	0.00250360i	0.195742	+	0.980655i	$0.437288\pi$
$164$	−997.976	−	47.5394i	−0.475176	−	0.0226354i
$165$	−354.506	+	141.923i	−0.167262	+	0.0669617i
$166$	−1977.93	−	2777.61i	−0.924802	−	1.29870i
$167$	−2626.71	+	377.664i	−1.21713	+	0.174997i	−0.720804	−	0.693138i	$-0.756227\pi$
$167$	−2626.71	+	377.664i	−1.21713	+	0.174997i	−0.496327	+	0.868136i	$0.665318\pi$
$168$	−12147.9	+	482.209i	−5.57876	+	0.221448i
$169$	−1056.75	+	679.134i	−0.480998	+	0.309119i
$170$	163.319	+	15.5951i	0.0736822	+	0.00703580i
$171$	−2074.31	−	1977.85i	−0.927640	−	0.884503i
$172$	−252.897	+	1312.16i	−0.112112	+	0.581692i
$173$	33.8987	−	11.7324i	0.0148975	−	0.00515608i	−0.319609	−	0.947549i	$-0.603552\pi$
$173$	33.8987	−	11.7324i	0.0148975	−	0.00515608i	0.334507	+	0.942393i	$0.391430\pi$
$174$	−854.967	−	2911.75i	−0.372499	−	1.26862i
$175$	−279.437	+	262.246i	−0.120706	+	0.113280i
$176$	−338.394	−	526.551i	−0.144928	−	0.225513i
$177$	−2353.60	+	2244.16i	−0.999478	+	0.953000i
$178$	3019.92	−	2374.89i	1.27165	−	1.00003i
$179$	−2934.27	+	280.188i	−1.22524	+	0.116996i	−0.687543	−	0.726144i	$-0.741311\pi$
$179$	−2934.27	+	280.188i	−1.22524	+	0.116996i	−0.537694	+	0.843140i	$0.680704\pi$
$180$	−13433.1	−	10563.9i	−5.56245	−	4.37436i
$181$	−1139.42	−	732.260i	−0.467914	−	0.300710i	0.285356	−	0.958422i	$-0.407888\pi$
$181$	−1139.42	−	732.260i	−0.467914	−	0.300710i	−0.753270	+	0.657712i	$0.771524\pi$
$182$	46.0861	−	5814.50i	0.0187699	−	2.36813i
$183$		−	5363.61i		−	2.16661i
$184$	−793.075	+	7350.93i	−0.317752	+	2.94520i
$185$	2959.40	−	1708.61i	1.17610	−	0.679024i
$186$	−4813.48	+	13907.6i	−1.89753	+	5.48256i
$187$	−3.76576	−	7.30455i	−0.00147262	−	0.00285648i
$188$	−272.379	−	39.1622i	−0.105666	−	0.0151925i
$189$	6156.91	+	4458.28i	2.36957	+	1.71583i
$190$	−381.722	−	2654.94i	−0.145753	−	1.01373i
$191$	486.701	+	510.437i	0.184379	+	0.193371i	0.809436	−	0.587208i	$-0.199773\pi$
$191$	486.701	+	510.437i	0.184379	+	0.193371i	−0.625057	+	0.780579i	$0.714924\pi$
$192$	5007.74	−	9713.66i	1.88230	−	3.65116i
$193$	122.728	−	172.348i	0.0457729	−	0.0642790i	−0.791055	−	0.611745i	$-0.790468\pi$
$193$	122.728	−	172.348i	0.0457729	−	0.0642790i	0.836828	+	0.547466i	$0.184407\pi$
$194$	−375.451	+	1547.63i	−0.138948	+	0.572750i
$195$	4548.92	−	5249.74i	1.67054	−	1.92790i
$196$	5867.31	+	3903.48i	2.13823	+	1.42255i
$197$	4730.31	−	1388.94i	1.71077	−	0.502326i	0.727749	−	0.685844i	$-0.240567\pi$
$197$	4730.31	−	1388.94i	1.71077	−	0.502326i	0.983016	+	0.183518i	$0.0587485\pi$
$198$	−113.054	+	1183.96i	−0.0405779	+	0.424951i
$199$	−1921.68	−	990.695i	−0.684544	−	0.352907i	0.0806178	−	0.996745i	$-0.474311\pi$
$199$	−1921.68	−	990.695i	−0.684544	−	0.352907i	−0.765162	+	0.643838i	$0.777341\pi$
$200$	−326.990	−	1347.87i	−0.115608	−	0.476544i
$201$	−7428.51	−	2973.93i	−2.60680	−	1.04361i
$202$	4475.68	+	2043.98i	1.55895	+	0.711948i
$203$	−359.347	+	1012.24i	−0.124243	+	0.349976i
$204$	276.746	−	430.625i	0.0949808	−	0.147793i
$205$	111.083	+	576.355i	0.0378458	+	0.196363i
$206$	3469.69	+	6009.68i	1.17352	+	2.03259i
$207$	5312.48	−	5436.40i	1.78378	−	1.82539i
$208$	9860.54	+	5692.98i	3.28704	+	1.89778i
$209$	−101.541	+	87.9855i	−0.0336063	+	0.0291200i
$210$	3206.32	+	11248.8i	1.05361	+	3.69638i
$211$	−510.208	+	3548.58i	−0.166465	+	1.15779i	0.719653	+	0.694333i	$0.244301\pi$
$211$	−510.208	+	3548.58i	−0.166465	+	1.15779i	−0.886119	+	0.463458i	$0.846608\pi$
$212$	7984.59	−	5685.80i	2.58672	−	1.84199i
$213$	629.036	+	799.884i	0.202351	+	0.257311i
$214$	4591.96	−	1114.00i	1.46682	−	0.355847i
$215$	784.172	−	37.3547i	0.248745	−	0.0118492i
$216$	−25025.6	+	11428.8i	−7.88324	+	3.60015i
$217$	4267.04	−	2987.86i	1.33487	−	0.934698i
$218$	7009.44	+	6073.72i	2.17770	+	1.88699i
$219$	2280.37	+	6588.71i	0.703623	+	2.03298i
$220$	−552.827	+	579.788i	−0.169416	+	0.177679i
$221$	121.775	+	86.7159i	0.0370656	+	0.0263943i
$222$	−704.855	−	14796.7i	−0.213094	−	4.47339i
$223$	999.490	−	3403.95i	0.300138	−	1.02218i	−0.661975	−	0.749526i	$-0.730281\pi$
$223$	999.490	−	3403.95i	0.300138	−	1.02218i	0.962113	−	0.272651i	$-0.0879004\pi$
$224$	−8247.31	+	4169.38i	−2.46003	+	1.24365i
$225$	−592.339	+	1297.04i	−0.175508	+	0.384308i
$226$	5385.43	−	6848.13i	1.58510	−	2.01562i
$227$	−50.8011	+	1066.45i	−0.0148537	+	0.311818i	0.979198	+	0.202908i	$0.0650391\pi$
$227$	−50.8011	+	1066.45i	−0.0148537	+	0.311818i	−0.994052	+	0.108910i	$0.965264\pi$
$228$	−7908.51	−	2737.16i	−2.29717	−	0.795057i
$229$	−2455.48	+	4253.01i	−0.708570	+	1.22728i	0.256818	+	0.966460i	$0.417326\pi$
$229$	−2455.48	+	4253.01i	−0.708570	+	1.22728i	−0.965388	+	0.260819i	$0.916007\pi$
$230$	7052.93	−	925.864i	2.02198	−	0.265433i
$231$	387.189	−	439.748i	0.110282	−	0.125252i
$232$	−2545.79	−	2937.99i	−0.720427	−	0.831417i
$233$	−3494.34	+	1801.46i	−0.982496	+	0.506512i	−0.873129	−	0.487490i	$-0.837913\pi$
$233$	−3494.34	+	1801.46i	−0.982496	+	0.506512i	−0.109367	+	0.994001i	$0.534882\pi$
$234$	−8041.05	−	20085.6i	−2.24641	−	5.61126i
$235$	15.3672	+	160.932i	0.00426572	+	0.0446726i
$236$	−2535.65	+	6333.75i	−0.699394	+	1.74700i
$237$	−609.305	−	178.908i	−0.166998	−	0.0490352i
$238$	−234.433	+	91.7037i	−0.0638489	+	0.0249759i
$239$	1418.47	+	3106.01i	0.383904	+	0.840632i	0.998652	+	0.0519087i	$0.0165305\pi$
$239$	1418.47	+	3106.01i	0.383904	+	0.840632i	−0.614748	+	0.788724i	$0.710742\pi$
$240$	−22258.4	−	5399.83i	−5.98656	−	1.45232i
$241$	−4647.58	−	895.748i	−1.24223	−	0.239420i	−0.474534	−	0.880237i	$-0.657384\pi$
$241$	−4647.58	−	895.748i	−1.24223	−	0.239420i	−0.767694	+	0.640817i	$0.778596\pi$
$242$	−6928.03	−	1335.27i	−1.84029	−	0.354687i
$243$	9778.97	+	2372.35i	2.58157	+	0.626282i
$244$	−4674.40	−	10235.5i	−1.22643	−	2.68550i
$245$	1415.94	−	3890.45i	0.369230	−	1.01450i
$246$	2441.39	+	716.856i	0.632753	+	0.185793i
$247$	908.378	−	2269.02i	0.234003	−	0.584511i
$248$	1792.09	+	18767.7i	0.458863	+	4.80543i
$249$	2323.02	+	5802.61i	0.591225	+	1.47681i
$250$	5978.98	−	3082.38i	1.51257	−	0.779786i
$251$	3221.72	+	3718.06i	0.810171	+	0.934987i	0.998893	−	0.0470433i	$-0.0149799\pi$
$251$	3221.72	+	3718.06i	0.810171	+	0.934987i	−0.188722	+	0.982031i	$0.560434\pi$
$252$	25707.2	+	5166.31i	6.42620	+	1.29146i
$253$	−230.020	−	272.135i	−0.0571590	−	0.0676243i
$254$	−1250.16	+	2165.34i	−0.308827	+	0.534905i
$255$	−284.186	−	98.3577i	−0.0697898	−	0.0241545i
$256$	76.0950	−	1597.43i	0.0185779	−	0.389998i
$257$	−2003.15	+	2547.21i	−0.486198	+	0.618251i	−0.965817	−	0.259226i	$-0.916533\pi$
$257$	−2003.15	+	2547.21i	−0.486198	+	0.618251i	0.479619	+	0.877477i	$0.340775\pi$
$258$	1413.74	−	3095.67i	0.341147	−	0.747007i
$259$	−2869.59	+	4388.31i	−0.688448	+	1.05280i
$260$	4105.67	−	13982.6i	0.979317	−	3.33525i
$261$	190.168	+	3992.11i	0.0450999	+	0.946764i
$262$	−2834.50	−	2018.44i	−0.668383	−	0.475953i
$263$	2825.76	−	2963.57i	0.662524	−	0.694835i	−0.303633	−	0.952789i	$-0.598200\pi$
$263$	2825.76	−	2963.57i	0.662524	−	0.694835i	0.966157	+	0.257954i	$0.0830482\pi$
$264$	693.565	+	2003.92i	0.161689	+	0.467171i
$265$	−4352.08	−	3771.10i	−1.00885	−	0.874177i
$266$	2360.60	+	3371.23i	0.544126	+	0.777081i
$267$	−6405.79	+	2925.43i	−1.46827	+	0.670537i
$268$	−16767.8	+	798.749i	−3.82186	+	0.182057i
$269$	−6305.52	+	1529.70i	−1.42920	+	0.346720i	−0.874376	−	0.485248i	$-0.838729\pi$
$269$	−6305.52	+	1529.70i	−1.42920	+	0.346720i	−0.554823	+	0.831968i	$0.687214\pi$
$270$	16362.3	+	20806.3i	3.68806	+	4.68975i
$271$	−12.7731	+	9.09566i	−0.00286313	+	0.00203883i	−0.581488	−	0.813555i	$-0.697529\pi$
$271$	−12.7731	+	9.09566i	−0.00286313	+	0.00203883i	0.578624	+	0.815594i	$0.303590\pi$
$272$	70.1505	−	487.907i	0.0156379	−	0.108764i
$273$	−2594.81	+	10337.6i	−0.575257	+	2.29180i
$274$	−1959.55	+	1697.96i	−0.432047	+	0.374371i
$275$	57.8876	+	33.4214i	0.0126937	+	0.00732868i
$276$	7515.94	−	20883.1i	1.63915	−	4.55441i
$277$	−1026.28	−	1777.57i	−0.222611	−	0.385573i	0.732989	−	0.680240i	$-0.238125\pi$
$277$	−1026.28	−	1777.57i	−0.222611	−	0.385573i	−0.955600	+	0.294667i	$0.904791\pi$
$278$	−2436.37	−	12641.1i	−0.525626	−	2.72721i
$279$	10478.8	−	16305.4i	2.24857	−	3.49884i
$280$	9722.38	+	11401.6i	2.07508	+	2.43348i
$281$	−1310.46	−	598.466i	−0.278204	−	0.127052i	0.271427	−	0.962459i	$-0.412504\pi$
$281$	−1310.46	−	598.466i	−0.278204	−	0.127052i	−0.549631	+	0.835407i	$0.685232\pi$
$282$	650.609	+	260.464i	0.137387	+	0.0550015i
$283$	−1305.35	−	5380.74i	−0.274188	−	1.13022i	−0.927708	−	0.373308i	$-0.878224\pi$
$283$	−1305.35	−	5380.74i	−0.274188	−	1.13022i	0.653520	−	0.756909i	$-0.273292\pi$
$284$	1897.51	+	978.233i	0.396466	+	0.204393i
$285$	−467.348	+	4894.29i	−0.0971343	+	1.01724i
$286$	−973.135	+	285.738i	−0.201198	+	0.0590771i
$287$	−551.095	−	712.321i	−0.113345	−	0.146505i
$288$	−22517.5	+	25986.6i	−4.60715	+	5.31693i
$289$	−1156.76	+	4768.22i	−0.235448	+	0.970531i
$290$	−2169.54	+	3046.69i	−0.439310	+	0.616924i
$291$	1337.61	−	2594.60i	0.269457	−	0.522673i
$292$	10093.8	+	10586.1i	2.02292	+	2.12158i
$293$	−83.5385	−	581.023i	−0.0166566	−	0.115849i	0.979797	−	0.199995i	$-0.0640927\pi$
$293$	−83.5385	−	581.023i	−0.0166566	−	0.115849i	−0.996453	+	0.0841465i	$0.973184\pi$
$294$	−12177.6	−	13183.7i	−2.41568	−	2.61527i
$295$	3967.31	+	570.413i	0.783002	+	0.112579i
$296$	−8695.58	−	16867.1i	−1.70750	−	3.31209i
$297$	433.657	−	1252.97i	0.0847251	−	0.244797i
$298$	3568.17	−	2060.08i	0.693619	−	0.400461i
$299$	5987.54	+	2482.73i	1.15809	+	0.480201i
$300$			4163.47i			0.801260i
$301$	−1047.93	+	593.999i	−0.200670	+	0.113746i
$302$	8424.92	+	5414.37i	1.60530	+	1.03166i
$303$	−7089.38	−	5575.15i	−1.34414	−	1.05704i
$304$	−8022.31	+	766.038i	−1.51352	+	0.144524i
$305$	−5196.30	+	4086.41i	−0.975538	+	0.767171i
$306$	−677.882	+	646.359i	−0.126640	+	0.120751i
$307$	−340.083	−	529.180i	−0.0632234	−	0.0983775i	0.808203	−	0.588905i	$-0.200441\pi$
$307$	−340.083	−	529.180i	−0.0632234	−	0.0983775i	−0.871426	+	0.490527i	$0.836804\pi$
$308$	355.640	−	1176.62i	0.0657938	−	0.217676i
$309$	−3583.61	−	12204.7i	−0.659756	−	2.24692i
$310$	17141.1	−	5932.58i	3.14047	−	1.08693i
$311$	−1271.53	+	6597.34i	−0.231839	+	1.20290i	0.660253	+	0.751043i	$0.270449\pi$
$311$	−1271.53	+	6597.34i	−0.231839	+	1.20290i	−0.892092	+	0.451853i	$0.850763\pi$
$312$	−27918.0	−	26619.7i	−5.06585	−	4.83028i
$313$	2799.05	+	267.277i	0.505469	+	0.0482664i	0.344676	−	0.938722i	$-0.387989\pi$
$313$	2799.05	+	267.277i	0.505469	+	0.0482664i	0.160793	+	0.986988i	$0.448595\pi$
$314$	1482.96	−	953.042i	0.266524	−	0.171284i
$315$	−611.001	−	15392.5i	−0.109289	−	2.75323i
$316$	−1318.67	+	189.596i	−0.234750	+	0.0337520i
$317$	−220.082	−	309.061i	−0.0389937	−	0.0547590i	0.794619	−	0.607109i	$-0.207671\pi$
$317$	−220.082	−	309.061i	−0.0389937	−	0.0547590i	−0.833613	+	0.552350i	$0.813731\pi$
$318$	−23175.3	+	9277.97i	−4.08680	+	1.63611i
$319$	187.141	+	8.91464i	0.0328461	+	0.00156465i
$320$	−13225.9	+	2549.09i	−2.31048	+	0.445308i
$321$	−8661.22			−1.50599
$322$	−9016.85	+	6150.25i	−1.56053	+	1.06441i
$323$	−105.810			−0.0182274
$324$	43558.0	−	8395.11i	7.46879	−	1.43949i
$325$	−1214.56	−	57.8566i	−0.207297	−	0.00987479i
$326$	−136.552	+	54.6672i	−0.0231992	+	0.00928754i
$327$	−9861.42	−	13848.4i	−1.66770	−	2.34196i
$328$	3226.36	−	463.880i	0.543127	−	0.0780899i
$329$	−132.449	−	209.731i	−0.0221950	−	0.0351455i
$330$	1716.33	−	1103.02i	0.286305	−	0.183997i
$331$	−492.530	−	47.0309i	−0.0817882	−	0.00780983i	0.0540817	−	0.998537i	$-0.482777\pi$
$331$	−492.530	−	47.0309i	−0.0817882	−	0.00780983i	−0.135870	+	0.990727i	$0.543383\pi$
$332$	9490.07	+	9048.76i	1.56878	+	1.49583i
$333$	−3692.15	+	19156.7i	−0.607593	+	3.15249i
$334$	13398.5	−	4637.28i	2.19502	−	0.759703i
$335$	2778.46	+	9462.55i	0.453144	+	1.54327i
$336$	34217.2	−	8014.38i	5.55565	−	1.30125i
$337$	1242.53	+	1933.41i	0.200845	+	0.312521i	0.927036	−	0.374972i	$-0.122348\pi$
$337$	1242.53	+	1933.41i	0.200845	+	0.312521i	−0.726191	+	0.687493i	$0.758711\pi$
$338$	4857.31	−	4631.43i	0.781665	−	0.745316i
$339$	−12552.6	+	9871.51i	−2.01111	+	1.58155i
$340$	−628.038	+	59.9704i	−0.100177	+	0.00956574i
$341$	−714.204	−	561.656i	−0.113420	−	0.0891947i
$342$	12882.2	+	8278.92i	2.03682	+	1.30898i
$343$	754.297	+	6307.51i	0.118741	+	0.992925i
$344$		−	4359.62i		−	0.683300i
$345$	−12963.7	−	1398.63i	−2.02302	−	0.218260i
$346$	−165.978	+	95.8276i	−0.0257891	+	0.0148894i
$347$	1005.14	−	2904.15i	0.155500	−	0.449289i	−0.840161	−	0.542337i	$-0.817540\pi$
$347$	1005.14	−	2904.15i	0.155500	−	0.449289i	0.995662	+	0.0930480i	$0.0296610\pi$
$348$	5347.40	+	10372.5i	0.823709	+	1.59777i
$349$	−4452.82	−	640.219i	−0.682963	−	0.0981953i	−0.207904	−	0.978149i	$-0.566664\pi$
$349$	−4452.82	−	640.219i	−0.682963	−	0.0981953i	−0.475059	+	0.879954i	$0.657573\pi$
$350$	1200.84	−	1658.36i	0.183393	−	0.253266i
$351$	3432.53	+	23873.8i	0.521980	+	3.63045i
$352$	1112.34	+	1166.59i	0.168432	+	0.176646i
$353$	4709.83	−	9135.79i	0.710138	−	1.37748i	−0.206775	−	0.978389i	$-0.566297\pi$
$353$	4709.83	−	9135.79i	0.710138	−	1.37748i	0.916913	−	0.399088i	$-0.130673\pi$
$354$	10078.5	−	14153.2i	1.51318	−	2.12496i
$355$	295.684	−	1218.83i	0.0442065	−	0.182222i
$356$	−9674.82	+	11165.3i	−1.44035	+	1.66225i
$357$	457.233	−	62.0454i	0.0677852	−	0.00919829i
$358$	15110.6	−	4436.88i	2.23079	−	0.655018i
$359$	762.525	−	7985.52i	0.112102	−	1.17398i	−0.747943	−	0.663763i	$-0.768958\pi$
$359$	762.525	−	7985.52i	0.112102	−	1.17398i	0.860044	−	0.510219i	$-0.170436\pi$
$360$	49555.1	+	25547.4i	7.25495	+	3.74019i
$361$	−1209.23	−	4984.53i	−0.176299	−	0.726713i
$362$	6718.10	+	2689.52i	0.975403	+	0.390492i
$363$	11764.1	+	5372.48i	1.70098	+	0.776810i
$364$	4057.54	+	21989.0i	0.584267	+	3.16631i
$365$	4645.81	−	7229.02i	0.666227	−	1.03667i
$366$	5423.33	+	28138.9i	0.774541	+	4.01870i
$367$	2263.15	+	3919.89i	0.321895	+	0.557538i	0.980879	−	0.194618i	$-0.0623469\pi$
$367$	2263.15	+	3919.89i	0.321895	+	0.557538i	−0.658984	+	0.752157i	$0.729014\pi$
$368$	−1770.33	−	21298.9i	−0.250774	−	3.01708i
$369$	−2902.07	−	1675.51i	−0.409420	−	0.236379i
$370$	−13798.1	+	11956.2i	−1.93873	+	1.67992i
$371$	8570.00	+	2151.12i	1.19928	+	0.301026i
$372$	8054.18	−	56018.0i	1.12255	−	7.80752i
$373$	4857.18	−	3458.78i	0.674250	−	0.480131i	−0.190923	−	0.981605i	$-0.561148\pi$
$373$	4857.18	−	3458.78i	0.674250	−	0.480131i	0.865173	+	0.501474i	$0.167209\pi$
$374$	27.1420	+	34.5139i	0.00375262	+	0.00477185i
$375$	−11982.6	+	2906.94i	−1.65008	+	0.400304i
$376$	896.742	−	42.7171i	0.122995	−	0.00585895i
$377$	−3100.16	+	1415.79i	−0.423518	+	0.193414i
$378$	−36808.7	−	17163.8i	−5.00856	−	2.33548i
$379$	−6420.38	−	5563.29i	−0.870166	−	0.754003i	0.100372	−	0.994950i	$-0.467997\pi$
$379$	−6420.38	−	5563.29i	−0.870166	−	0.754003i	−0.970538	+	0.240947i	$0.922542\pi$
$380$	3373.53	+	9747.19i	0.455418	+	1.31584i
$381$	3162.70	−	3316.95i	0.425276	−	0.446017i
$382$	−3069.48	−	2185.77i	−0.411121	−	0.292758i
$383$	−430.448	−	9036.23i	−0.0574279	−	1.20556i	−0.825201	−	0.564839i	$-0.808938\pi$
$383$	−430.448	−	9036.23i	−0.0574279	−	1.20556i	0.767773	−	0.640721i	$-0.221365\pi$
$384$	−5436.06	+	18513.5i	−0.722416	+	2.46032i
$385$	−721.021	−	40.0764i	−0.0954458	−	0.00530515i
$386$	−469.598	+	1028.28i	−0.0619220	+	0.135590i
$387$	−2770.58	+	3523.08i	−0.363919	+	0.462761i
$388$	291.392	−	6117.07i	0.0381267	−	0.800379i
$389$	13784.8	+	4770.96i	1.79670	+	0.621843i	0.999844	+	0.0176729i	$0.00562574\pi$
$389$	13784.8	+	4770.96i	1.79670	+	0.621843i	0.796855	+	0.604171i	$0.206495\pi$
$390$	−18556.7	+	32141.1i	−2.40937	+	4.17314i
$391$	3.44371	−	280.594i	0.000445411	−	0.0362922i
$392$	−21206.0	−	8882.14i	−2.73230	−	1.14443i
$393$	4176.93	+	4820.44i	0.536128	+	0.618725i
$394$	−23412.0	+	12069.7i	−2.99361	+	1.54331i
$395$	290.888	+	726.604i	0.0370536	+	0.0925555i
$396$	−434.748	−	4552.89i	−0.0551690	−	0.577756i
$397$	2081.89	−	5200.32i	0.263192	−	0.657422i	−0.736630	−	0.676296i	$-0.763584\pi$
$397$	2081.89	−	5200.32i	0.263192	−	0.657422i	0.999822	+	0.0188743i	$0.00600825\pi$
$398$	11083.4	+	3254.37i	1.39588	+	0.409866i
$399$	−2748.15	−	7025.41i	−0.344811	−	0.881480i
$400$	1665.50	+	3646.95i	0.208188	+	0.455868i
$401$	9008.42	+	2185.42i	1.12184	+	0.272156i	0.753444	−	0.657512i	$-0.228391\pi$
$401$	9008.42	+	2185.42i	1.12184	+	0.272156i	0.368398	+	0.929668i	$0.379906\pi$
$402$	41979.0	+	8090.78i	5.20826	+	1.00381i
$403$	16229.5	+	3127.99i	2.00608	+	0.386641i
$404$	−18387.6	−	4460.79i	−2.26440	−	0.549338i
$405$	−10826.0	−	23705.6i	−1.32827	−	2.90850i
$406$	861.723	−	5673.81i	0.105336	−	0.693562i
$407$	877.504	+	257.659i	0.106870	+	0.0313800i
$408$	−620.675	+	1550.37i	−0.0753137	+	0.188125i
$409$	501.187	+	5248.67i	0.0605920	+	0.634548i	0.973854	+	0.227175i	$0.0729489\pi$
$409$	501.187	+	5248.67i	0.0605920	+	0.634548i	−0.913262	+	0.407373i	$0.866445\pi$
$410$	−1165.54	−	2911.39i	−0.140395	−	0.350691i
$411$	4224.38	−	2177.82i	0.506991	−	0.261372i
$412$	−17475.1	−	20167.3i	−2.08965	−	2.41159i
$413$	−5827.42	+	1965.31i	−0.694307	+	0.234156i
$414$	−22373.8	+	33892.4i	−2.65606	+	4.02348i
$415$	3851.75	−	6671.43i	0.455602	−	0.789127i
$416$	−27709.4	−	9590.32i	−3.26578	−	1.13030i
$417$	−1122.82	+	23570.9i	−0.131858	+	2.76804i
$418$	443.744	−	564.266i	0.0519240	−	0.0660267i
$419$	4247.37	−	9300.44i	0.495221	−	1.08438i	−0.482772	−	0.875746i	$-0.660370\pi$
$419$	4247.37	−	9300.44i	0.495221	−	1.08438i	0.977993	−	0.208637i	$-0.0669026\pi$
$420$	−20293.4	−	40141.8i	−2.35766	−	4.66362i
$421$	−2950.76	+	10049.4i	−0.341594	+	1.16336i	0.592271	+	0.805739i	$0.298231\pi$
$421$	−2950.76	+	10049.4i	−0.341594	+	1.16336i	−0.933866	+	0.357624i	$0.883587\pi$
$422$	−911.400	−	19132.6i	−0.105133	−	2.20702i
$423$	−751.820	−	535.368i	−0.0864178	−	0.0615378i
$424$	−22068.0	+	23144.3i	−2.52764	+	2.65091i
$425$	17.2171	+	49.7455i	0.00196506	+	0.00567767i
$426$	−4108.88	−	3560.36i	−0.467314	−	0.404930i
$427$	4286.60	−	9192.81i	0.485815	−	1.04185i
$428$	−16528.4	+	7548.29i	−1.86666	+	0.852477i
$429$	1856.96	−	88.4578i	0.208986	−	0.00995521i
$430$	−4076.20	+	988.875i	−0.457144	+	0.110902i
$431$	2072.75	+	2635.71i	0.231649	+	0.294566i	0.887956	−	0.459928i	$-0.152125\pi$
$431$	2072.75	+	2635.71i	0.231649	+	0.294566i	−0.656307	+	0.754494i	$0.727882\pi$
$432$	64781.2	−	46130.5i	7.21478	−	5.13762i
$433$	231.494	−	1610.08i	0.0256926	−	0.178696i	−0.972934	−	0.231082i	$-0.925773\pi$
$433$	231.494	−	1610.08i	0.0256926	−	0.178696i	0.998627	+	0.0523857i	$0.0166825\pi$
$434$	−19364.9	+	19989.7i	−2.14181	+	2.21091i
$435$	5181.29	−	4489.62i	0.571090	−	0.494852i
$436$	−30887.7	−	17833.0i	−3.39279	−	1.95883i
$437$	−4471.38	+	1026.81i	−0.489462	+	0.112401i
$438$	−18625.5	−	32260.3i	−2.03187	−	3.51931i
$439$	−131.842	−	684.062i	−0.0143337	−	0.0743702i	0.974058	−	0.226301i	$-0.0726632\pi$
$439$	−131.842	−	684.062i	−0.0143337	−	0.0743702i	−0.988391	+	0.151930i	$0.951451\pi$
$440$	1413.00	−	2198.67i	0.153096	−	0.238222i
$441$	11492.2	+	20654.4i	1.24092	+	2.23026i
$442$	−726.547	−	331.803i	−0.0781862	−	0.0357065i
$443$	6898.05	+	2761.56i	0.739811	+	0.296176i	0.710791	−	0.703403i	$-0.248337\pi$
$443$	6898.05	+	2761.56i	0.739811	+	0.296176i	0.0290202	+	0.999579i	$0.490761\pi$
$444$	13430.0	+	55359.2i	1.43549	+	5.91719i
$445$	7714.60	+	3977.15i	0.821814	+	0.423674i
$446$	−1801.74	+	18868.6i	−0.191289	+	2.00326i
$447$	−7246.35	+	2127.72i	−0.766758	+	0.225140i
$448$	16346.0	−	12646.3i	1.72383	−	1.33366i
$449$	6039.55	−	6970.01i	0.634797	−	0.732595i	−0.343649	−	0.939098i	$-0.611663\pi$
$449$	6039.55	−	6970.01i	0.634797	−	0.732595i	0.978446	+	0.206503i	$0.0662085\pi$
$450$	1796.08	−	7403.55i	0.188151	−	0.775570i
$451$	−91.1203	+	127.961i	−0.00951372	+	0.0133602i
$452$	−15351.5	+	29777.7i	−1.59751	+	3.09873i
$453$	−12667.8	−	13285.6i	−1.31387	−	1.37795i
$454$	−811.805	−	5646.23i	−0.0839205	−	0.583680i
$455$	11992.1	−	5362.14i	1.23560	−	0.552486i
$456$	27024.8	+	3885.58i	2.77533	+	0.399033i
$457$	7675.12	+	14887.7i	0.785617	+	1.52388i	0.850490	+	0.525991i	$0.176305\pi$
$457$	7675.12	+	14887.7i	0.785617	+	1.52388i	−0.0648736	+	0.997893i	$0.520664\pi$
$458$	8581.71	−	24795.2i	0.875539	−	2.52971i
$459$	904.286	−	522.090i	0.0919575	−	0.0530917i
$460$	−25957.9	+	8628.89i	−2.63107	+	0.874618i
$461$		−	9173.37i		−	0.926782i	−0.886154	−	0.463391i	$-0.846633\pi$
$461$		−	9173.37i		−	0.926782i	0.886154	−	0.463391i	$-0.153367\pi$
$462$	−1586.65	+	2698.53i	−0.159778	+	0.271747i
$463$	−10290.7	−	6613.40i	−1.03293	−	0.663825i	−0.0897027	−	0.995969i	$-0.528592\pi$
$463$	−10290.7	−	6613.40i	−1.03293	−	0.663825i	−0.943229	+	0.332144i	$0.892228\pi$
$464$	8833.29	+	6946.58i	0.883783	+	0.695015i
$465$	−33097.7	+	3160.45i	−3.30079	+	0.315188i
$466$	16510.7	−	12984.1i	1.64129	−	1.29073i
$467$	7605.97	−	7252.28i	0.753667	−	0.718620i	−0.212323	−	0.977199i	$-0.568103\pi$
$467$	7605.97	−	7252.28i	0.753667	−	0.718620i	0.965990	+	0.258580i	$0.0832545\pi$
$468$	44980.4	+	69990.8i	4.44277	+	6.91309i
$469$	−10355.1	−	11033.9i	−1.01952	−	1.08635i
$470$	−243.344	−	828.755i	−0.0238822	−	0.0813354i
$471$	−3053.51	+	1056.83i	−0.298722	+	0.103389i
$472$	4212.34	−	21855.7i	0.410781	−	2.13133i
$473$	152.061	+	144.990i	0.0147817	+	0.0140944i
$474$	3377.47	+	322.510i	0.327284	+	0.0312518i
$475$	724.000	−	465.287i	0.0699356	−	0.0449449i
$476$	818.477	−	516.883i	0.0788126	−	0.0497716i
$477$	32541.9	−	4678.83i	3.12368	−	0.449117i
$478$	−10582.2	−	14860.7i	−1.01260	−	1.42199i
$479$	12525.9	−	5014.63i	1.19483	−	0.478338i	0.312932	−	0.949776i	$-0.398689\pi$
$479$	12525.9	−	5014.63i	1.19483	−	0.478338i	0.881900	+	0.471437i	$0.156265\pi$
$480$	58917.6	+	2806.59i	5.60252	+	0.266881i
$481$	−16335.9	+	3148.49i	−1.54855	+	0.298459i
$482$	25288.1			2.38972
$483$	18719.8	−	7059.04i	1.76352	−	0.665005i
$484$	27131.9			2.54807
$485$	−3532.75	+	680.882i	−0.330751	+	0.0637469i
$486$	−53701.8	−	2558.13i	−5.01227	−	0.238764i
$487$	−684.665	+	274.098i	−0.0637066	+	0.0255043i	−0.403297	−	0.915069i	$-0.632136\pi$
$487$	−684.665	+	274.098i	−0.0637066	+	0.0255043i	0.339590	+	0.940573i	$0.389712\pi$
$488$	21294.0	+	29903.3i	1.97528	+	2.77389i
$489$	266.869	−	38.3700i	0.0246794	−	0.00354837i
$490$	−3494.64	+	21842.0i	−0.322187	+	2.01372i
$491$	1074.15	−	690.317i	0.0987289	−	0.0634492i	−0.490345	−	0.871529i	$-0.663129\pi$
$491$	1074.15	−	690.317i	0.0987289	−	0.0634492i	0.589074	+	0.808079i	$0.299493\pi$
$492$	−9740.34	−	930.090i	−0.892538	−	0.0852270i
$493$	106.784	+	101.819i	0.00975523	+	0.00930159i
$494$	−2471.31	+	12822.4i	−0.225080	+	1.16782i
$495$	−2539.15	+	878.808i	−0.230558	+	0.0797969i
$496$	−15353.8	−	52290.3i	−1.38993	−	4.73367i
$497$	438.852	+	1873.67i	0.0396080	+	0.169105i
$498$	−18054.4	−	28093.1i	−1.62457	−	2.52788i
$499$	−9977.36	+	9513.39i	−0.895086	+	0.853462i	−0.989861	−	0.142036i	$-0.954635\pi$
$499$	−9977.36	+	9513.39i	−0.895086	+	0.853462i	0.0947758	+	0.995499i	$0.469787\pi$
$500$	−20333.3	+	15990.3i	−1.81866	+	1.43021i
$501$	−25871.3	+	2470.41i	−2.30707	+	0.220299i
$502$	−20661.4	−	16248.3i	−1.83698	−	1.44462i
$503$	−8661.99	−	5566.73i	−0.767831	−	0.493455i	0.0971435	−	0.995270i	$-0.469029\pi$
$503$	−8661.99	−	5566.73i	−0.767831	−	0.493455i	−0.864975	+	0.501815i	$0.832666\pi$
$504$	−85542.6	−	678.016i	−7.56025	−	0.0599231i
$505$			11115.8i			0.979499i
$506$	1481.91	+	1195.11i	0.130195	+	0.104998i
$507$	−10653.9	+	6151.05i	−0.933251	+	0.538812i
$508$	3144.74	−	9086.12i	0.274656	−	0.793566i
$509$	7528.74	+	14603.7i	0.655610	+	1.27171i	0.948868	+	0.315672i	$0.102230\pi$
$509$	7528.74	+	14603.7i	0.655610	+	1.27171i	−0.293259	+	0.956033i	$0.594740\pi$
$510$	1590.37	+	228.660i	0.138084	+	0.0198534i
$511$	−1357.31	+	13115.0i	−0.117503	+	1.13537i
$512$	−1027.13	−	7143.83i	−0.0886583	−	0.616632i
$513$	−11780.5	−	12355.0i	−1.01388	−	1.06333i
$514$	7933.47	−	15388.8i	0.680798	−	1.32056i
$515$	−9093.67	+	12770.3i	−0.778087	+	1.09267i
$516$	−3085.37	+	12718.1i	−0.263228	+	1.08504i
$517$	−28.3334	+	32.6984i	−0.00241025	+	0.00278158i
$518$	10617.5	−	25923.8i	0.900589	−	2.19889i
$519$	337.074	−	98.9739i	0.0285085	−	0.00837085i
$520$	−4519.28	+	47328.1i	−0.381122	+	3.99130i
$521$	−9091.66	−	4687.07i	−0.764516	−	0.394135i	0.0314278	−	0.999506i	$-0.489995\pi$
$521$	−9091.66	−	4687.07i	−0.764516	−	0.394135i	−0.795944	+	0.605371i	$0.793025\pi$
$522$	−5034.23	−	20751.4i	−0.422112	−	1.73997i
$523$	−1947.95	−	779.842i	−0.162864	−	0.0652009i	0.288798	−	0.957390i	$-0.406744\pi$
$523$	−1947.95	−	779.842i	−0.162864	−	0.0652009i	−0.451662	+	0.892189i	$0.649169\pi$
$524$	12172.0	+	5558.76i	1.01476	+	0.463427i
$525$	−2855.74	+	2435.16i	−0.237400	+	0.202436i
$526$	−11828.1	+	18404.9i	−0.980475	+	1.52565i
$527$	−135.418	−	702.615i	−0.0111933	−	0.0580766i
$528$	−3064.90	−	5308.57i	−0.252619	−	0.437549i
$529$	−2577.43	−	11890.9i	−0.211838	−	0.977305i
$530$	26645.2	+	15383.6i	2.18377	+	1.26080i
$531$	−17293.6	+	14985.0i	−1.41333	+	1.22465i
$532$	−11367.0	−	11011.8i	−0.926360	−	0.897407i
$533$	406.678	−	2828.51i	0.0330491	−	0.229862i
$534$	30648.5	−	21824.7i	2.48369	−	1.76863i
$535$	6598.79	+	8391.04i	0.533253	+	0.678087i
$536$	53222.4	−	12911.6i	4.28891	−	1.04048i
$537$	−28834.4	+	1373.55i	−2.31713	+	0.110378i
$538$	31533.7	−	14401.0i	2.52698	−	1.15403i
$539$	1015.06	−	444.253i	0.0811162	−	0.0355016i
$540$	−76925.8	−	66656.5i	−6.13029	−	5.31193i
$541$	3297.41	+	9527.25i	0.262046	+	0.757132i	0.996883	+	0.0788888i	$0.0251372\pi$
$541$	3297.41	+	9527.25i	0.262046	+	0.757132i	−0.734837	+	0.678243i	$0.762742\pi$
$542$	57.8139	−	60.6335i	0.00458177	−	0.00480522i
$543$	−10804.9	−	7694.14i	−0.853929	−	0.608080i
$544$	60.4015	+	1267.98i	0.00476047	+	0.0999345i
$545$	−5903.24	+	20104.6i	−0.463976	+	1.58016i
$546$	3160.31	−	56857.7i	0.247709	−	4.45656i
$547$	−976.405	+	2138.03i	−0.0763219	+	0.167122i	−0.943947	−	0.330098i	$-0.892918\pi$
$547$	−976.405	+	2138.03i	−0.0763219	+	0.167122i	0.867625	+	0.497219i	$0.165646\pi$
$548$	6163.52	−	7837.56i	0.480461	−	0.610956i
$549$	1795.77	−	37697.9i	0.139602	−	2.93062i
$550$	−337.487	−	116.805i	−0.0261645	−	0.00905564i
$551$	1206.12	−	2089.05i	0.0932527	−	0.161518i
$552$	−11183.5	+	71539.4i	−0.862325	+	5.51616i
$553$	−901.319	−	793.591i	−0.0693092	−	0.0610252i
$554$	7181.49	+	8287.88i	0.550744	+	0.635592i
$555$	29745.9	−	15335.1i	2.27503	−	1.17286i
$556$	18399.4	+	45959.5i	1.40343	+	3.50561i
$557$	2144.45	+	22457.7i	0.163130	+	1.70837i	0.592771	+	0.805371i	$0.298034\pi$
$557$	2144.45	+	22457.7i	0.163130	+	1.70837i	−0.429642	+	0.903000i	$0.641360\pi$
$558$	−38487.7	+	96137.6i	−2.91992	+	7.29360i
$559$	−3667.21	−	1076.79i	−0.277471	−	0.0814730i
$560$	−33833.7	−	27043.8i	−2.55309	−	2.04073i
$561$	−33.4339	−	73.2101i	−0.00251619	−	0.00550968i
$562$	7480.14	+	1814.66i	0.561442	+	0.136204i
$563$	13270.8	+	2557.74i	0.993426	+	0.191467i	0.659965	−	0.751297i	$-0.270571\pi$
$563$	13270.8	+	2557.74i	0.993426	+	0.191467i	0.333461	+	0.942764i	$0.391783\pi$
$564$	−2646.24	−	510.021i	−0.197565	−	0.0380776i
$565$	19127.1	+	4640.20i	1.42422	+	0.345512i
$566$	12288.9	+	26908.9i	0.912614	+	1.99835i
$567$	31234.7	+	24966.4i	2.31346	+	1.84919i
$568$	−6682.63	−	1962.20i	−0.493657	−	0.144951i
$569$	4026.06	−	10056.6i	0.296628	−	0.740941i	−0.702931	−	0.711258i	$-0.748126\pi$
$569$	4026.06	−	10056.6i	0.296628	−	0.740941i	0.999559	−	0.0296831i	$-0.00944982\pi$
$570$	−2496.95	−	26149.3i	−0.183484	−	1.92153i
$571$	−5570.08	−	13913.4i	−0.408232	−	1.01971i	−0.979946	−	0.199262i	$-0.936146\pi$
$571$	−5570.08	−	13913.4i	−0.408232	−	1.01971i	0.571714	−	0.820453i	$-0.306279\pi$
$572$	3466.59	−	1787.15i	0.253401	−	0.130637i
$573$	4523.20	+	5220.05i	0.329772	+	0.380577i
$574$	3611.44	+	3179.79i	0.262611	+	0.231223i
$575$	1210.31	+	1935.09i	0.0877798	+	0.140346i
$576$	38448.9	−	66595.4i	2.78132	−	4.81738i
$577$	−3365.94	−	1164.96i	−0.242852	−	0.0840521i	0.202930	−	0.979193i	$-0.434953\pi$
$577$	−3365.94	−	1164.96i	−0.242852	−	0.0840521i	−0.445783	+	0.895141i	$0.647075\pi$
$578$	1247.34	−	26185.0i	0.0897624	−	1.88434i
$579$	1280.88	−	1628.77i	0.0919368	−	0.116907i
$580$	5974.88	−	13083.2i	0.427747	−	0.936636i
$581$	−655.978	+	11801.8i	−0.0468409	+	0.842720i
$582$	−4393.95	+	14964.4i	−0.312947	+	1.06580i
$583$	−73.3324	−	1539.44i	−0.00520946	−	0.109360i
$584$	−38871.4	−	27680.2i	−2.75430	−	1.96133i
$585$	33729.6	−	35374.5i	2.38384	−	2.50010i
$586$	1025.76	+	2963.73i	0.0723100	+	0.208926i
$587$	4956.62	+	4294.93i	0.348520	+	0.301995i	0.811475	−	0.584388i	$-0.198665\pi$
$587$	4956.62	+	4294.93i	0.348520	+	0.301995i	−0.462954	+	0.886382i	$0.653211\pi$
$588$	55576.8	+	40919.1i	3.89787	+	2.86985i
$589$	−10641.3	+	4859.70i	−0.744423	+	0.339967i
$590$	−21390.3	+	1018.95i	−1.49258	+	0.0711005i
$591$	46920.5	−	11382.8i	3.26574	−	0.792260i
$592$	33909.1	+	43118.9i	2.35415	+	2.99354i
$593$	−546.878	+	389.430i	−0.0378711	+	0.0269679i	−0.598836	−	0.800872i	$-0.704370\pi$
$593$	−546.878	+	389.430i	−0.0378711	+	0.0269679i	0.560965	+	0.827840i	$0.310430\pi$
$594$	−1008.16	+	7011.90i	−0.0696385	+	0.484346i
$595$	−408.465	−	395.699i	−0.0281436	−	0.0272640i
$596$	−11974.1	+	10375.6i	−0.822949	+	0.713090i
$597$	−18336.8	−	10586.7i	−1.25708	−	0.725774i
$598$	−33922.6	−	6970.86i	−2.31973	−	0.476689i
$599$	6362.11	+	11019.5i	0.433971	+	0.751661i	0.997211	−	0.0746330i	$-0.0237785\pi$
$599$	6362.11	+	11019.5i	0.433971	+	0.751661i	−0.563240	+	0.826294i	$0.690445\pi$
$600$	−2570.62	−	13337.6i	−0.174908	−	0.907511i
$601$	8415.16	−	13094.2i	0.571151	−	0.888728i	−0.428741	−	0.903427i	$-0.641043\pi$
$601$	8415.16	−	13094.2i	0.571151	−	0.888728i	0.999892	+	0.0146996i	$0.00467920\pi$
$602$	4897.11	−	4175.87i	0.331547	−	0.282717i
$603$	−51215.3	−	23389.2i	−3.45879	−	1.57958i
$604$	−35752.7	−	14313.2i	−2.40854	−	0.964234i
$605$	−3757.90	−	15490.3i	−0.252530	−	1.04094i
$606$	42830.0	+	22080.4i	2.87104	+	1.48012i
$607$	1854.67	−	19423.0i	0.124018	−	1.29877i	−0.692486	−	0.721431i	$-0.743484\pi$
$607$	1854.67	−	19423.0i	0.124018	−	1.29877i	0.816504	−	0.577340i	$-0.195909\pi$
$608$	19913.0	−	5847.00i	1.32826	−	0.390012i
$609$	−3986.93	+	9734.55i	−0.265285	+	0.647724i
$610$	23129.2	−	26692.5i	1.53520	−	1.77172i
$611$	185.555	−	764.869i	0.0122860	−	0.0506437i
$612$	2089.27	−	2933.97i	0.137997	−	0.193789i
$613$	−8110.63	+	15732.4i	−0.534397	+	1.03659i	0.454882	+	0.890551i	$0.349681\pi$
$613$	−8110.63	+	15732.4i	−0.534397	+	1.03659i	−0.989280	+	0.146034i	$0.953349\pi$
$614$	2319.24	+	2432.35i	0.152438	+	0.159872i
$615$	818.075	+	5689.84i	0.0536390	+	0.373067i
$616$	−412.819	+	3988.87i	−0.0270016	+	0.260903i
$617$	7426.62	+	1067.79i	0.484578	+	0.0696718i	0.380274	−	0.924874i	$-0.375830\pi$
$617$	7426.62	+	1067.79i	0.484578	+	0.0696718i	0.104303	+	0.994546i	$0.466739\pi$
$618$	31141.1	+	60405.3i	2.02699	+	3.93181i
$619$	8264.76	−	23879.5i	0.536654	−	1.55056i	−0.272013	−	0.962294i	$-0.587689\pi$
$619$	8264.76	−	23879.5i	0.536654	−	1.55056i	0.808667	−	0.588267i	$-0.200189\pi$
$620$	−60406.9	+	34875.9i	−3.91290	+	2.25911i
$621$	33147.2	−	30838.1i	2.14195	−	1.99274i
$622$		−	35897.0i		−	2.31405i
$623$	−13317.0	−	105.552i	−0.856398	−	0.00678787i
$624$	93805.8	+	60285.4i	6.01801	+	3.86754i
$625$	13978.7	+	10992.9i	0.894634	+	0.703548i
$626$	−14954.8	+	1428.01i	−0.954815	+	0.0911738i
$627$	−1034.30	+	813.383i	−0.0658788	+	0.0518077i
$628$	−4906.05	+	4677.91i	−0.311740	+	0.297244i
$629$	389.388	+	605.900i	0.0246835	+	0.0384083i
$630$	18769.3	+	80135.2i	1.18697	+	5.06772i
$631$	5996.15	+	20421.0i	0.378293	+	1.28835i	0.900249	+	0.435375i	$0.143384\pi$
$631$	5996.15	+	20421.0i	0.378293	+	1.28835i	−0.521956	+	0.852972i	$0.674797\pi$
$632$	4107.29	−	1421.55i	0.258512	−	0.0894717i
$633$	−6644.60	+	34475.5i	−0.417218	+	2.16473i
$634$	1467.11	+	1398.88i	0.0919027	+	0.0876291i
$635$	−5623.07	−	536.938i	−0.351409	−	0.0335555i
$636$	80757.2	−	51899.5i	5.03495	−	3.23577i
$637$	−12709.1	+	15644.1i	−0.790509	+	0.973066i
$638$	−990.807	+	142.457i	−0.0614834	+	0.00883998i
$639$	4153.35	+	5832.56i	0.257127	+	0.361084i
$640$	22077.6	−	8838.55i	1.36359	−	0.545897i
$641$	−26702.2	−	1271.98i	−1.64536	−	0.0783780i	−0.795692	−	0.605701i	$-0.792893\pi$
$641$	−26702.2	−	1271.98i	−1.64536	−	0.0783780i	−0.849665	+	0.527323i	$0.823196\pi$
$642$	45439.1	−	8757.66i	2.79336	−	0.538376i
$643$	13107.9			0.803925			0.401963	−	0.915656i	$-0.368328\pi$
$643$	13107.9			0.803925			0.401963	+	0.915656i	$0.368328\pi$
$644$	29571.5	−	29785.3i	1.80944	−	1.82253i
$645$	7688.41			0.469350
$646$	555.109	−	106.989i	0.0338088	−	0.00651611i
$647$	−32795.4	−	1562.24i	−1.99277	−	0.0949273i	−0.993032	−	0.117843i	$-0.962402\pi$
$647$	−32795.4	−	1562.24i	−1.99277	−	0.0949273i	−0.999737	+	0.0229155i	$0.992705\pi$
$648$	−134354.	+	53787.3i	−8.14495	+	3.26075i
$649$	622.221	+	873.786i	0.0376337	+	0.0528492i
$650$	6430.40	−	924.552i	0.388032	−	0.0557906i
$651$	43133.8	−	27239.8i	2.59685	−	1.63996i
$652$	475.834	−	305.800i	0.0285814	−	0.0183682i
$653$	15194.0	+	1450.85i	0.910547	+	0.0869467i	0.539806	−	0.841789i	$-0.318498\pi$
$653$	15194.0	+	1450.85i	0.910547	+	0.0869467i	0.370741	+	0.928736i	$0.379104\pi$
$654$	65738.2	+	62681.2i	3.93053	+	3.74775i
$655$	1487.76	−	7719.22i	0.0887504	−	0.460481i
$656$	−8904.01	+	3081.71i	−0.529944	+	0.183415i
$657$	13821.6	+	47072.0i	0.820747	+	2.79521i
$658$	906.930	+	966.382i	0.0537322	+	0.0572545i
$659$	−2643.72	−	4113.70i	−0.156274	−	0.243167i	0.754284	−	0.656548i	$-0.227984\pi$
$659$	−2643.72	−	4113.70i	−0.156274	−	0.243167i	−0.910558	+	0.413381i	$0.864348\pi$
$660$	−5678.09	+	5414.05i	−0.334878	+	0.319306i
$661$	17391.6	−	13676.9i	1.02338	−	0.804795i	0.0424384	−	0.999099i	$-0.486487\pi$
$661$	17391.6	−	13676.9i	1.02338	−	0.804795i	0.980941	+	0.194304i	$0.0622450\pi$
$662$	2631.50	−	251.277i	0.154495	−	0.0147525i
$663$	1150.83	+	905.026i	0.0674128	+	0.0530140i
$664$	−35988.2	−	23128.2i	−2.10334	−	1.35173i
$665$	−4712.51	+	8014.92i	−0.274802	+	0.467376i
$666$		−	104234.i		−	6.06456i
$667$	5500.61	+	3266.43i	0.319317	+	0.189620i
$668$	−47217.8	+	27261.2i	−2.73490	+	1.57899i
$669$	11363.5	−	32832.7i	0.656710	−	1.89744i
$670$	−24144.4	−	46833.6i	−1.39221	−	2.70051i
$671$	−1751.19	−	251.783i	−0.100751	−	0.0144858i
$672$	−82620.5	+	36943.0i	−4.74279	+	2.12069i
$673$	3319.01	+	23084.2i	0.190102	+	1.32219i	0.831734	+	0.555175i	$0.187349\pi$
$673$	3319.01	+	23084.2i	0.190102	+	1.32219i	−0.641632	+	0.767013i	$0.721742\pi$
$674$	−8473.55	−	8886.80i	−0.484257	−	0.507874i
$675$	−3891.69	+	7548.83i	−0.221913	+	0.430451i
$676$	−14970.5	+	21023.2i	−0.851760	+	1.19613i
$677$	3789.59	−	15620.9i	0.215134	−	0.886794i	−0.757197	−	0.653187i	$-0.773432\pi$
$677$	3789.59	−	15620.9i	0.215134	−	0.886794i	0.972331	−	0.233608i	$-0.0750531\pi$
$678$	55873.0	−	64480.9i	3.16488	−	3.65247i
$679$	4366.16	−	3377.92i	0.246771	−	0.190917i
$680$	1974.89	−	579.879i	0.111373	−	0.0327020i
$681$	−993.904	+	10408.6i	−0.0559273	+	0.585697i
$682$	4314.81	+	2224.44i	0.242262	+	0.124895i
$683$	−17.9191	−	73.8637i	−0.00100389	−	0.00413809i	0.971307	−	0.237827i	$-0.0764353\pi$
$683$	−17.9191	−	73.8637i	−0.00100389	−	0.00413809i	−0.972311	+	0.233689i	$0.924920\pi$
$684$	−54668.2	−	21885.9i	−3.05598	−	1.22343i
$685$	−5328.35	−	2433.37i	−0.297205	−	0.135729i
$686$	−10335.0	−	32328.1i	−0.575206	−	1.79926i
$687$	−26002.1	+	40460.0i	−1.44402	+	2.24694i
$688$	2384.98	+	12374.5i	0.132161	+	0.685716i
$689$	14017.8	+	24279.5i	0.775088	+	1.34249i
$690$	69425.3	−	5770.50i	3.83040	−	0.318375i
$691$	10861.7	+	6270.98i	0.597970	+	0.345238i	0.768242	−	0.640159i	$-0.221132\pi$
$691$	10861.7	+	6270.98i	0.597970	+	0.345238i	−0.170273	+	0.985397i	$0.554465\pi$
$692$	556.991	−	482.636i	0.0305977	−	0.0265131i
$693$	2868.57	−	2961.12i	0.157241	−	0.162314i
$694$	−2336.72	+	16252.3i	−0.127811	+	0.888945i
$695$	23691.1	−	16870.3i	1.29303	−	0.920760i
$696$	−23534.6	−	29926.6i	−1.28172	−	1.62984i
$697$	−120.225	+	29.1662i	−0.00653348	+	0.00158500i
$698$	24008.0	−	1143.64i	1.30189	−	0.0620165i
$699$	−35022.1	+	15994.1i	−1.89507	+	0.865452i
$700$	−3327.44	+	7135.87i	−0.179665	+	0.385301i
$701$	−18144.1	−	15722.0i	−0.977594	−	0.847090i	0.0106552	−	0.999943i	$-0.496608\pi$
$701$	−18144.1	−	15722.0i	−0.977594	−	0.847090i	−0.988249	+	0.152854i	$0.951154\pi$
$702$	−42147.6	−	121777.i	−2.26604	−	6.54728i
$703$	8125.74	−	8522.03i	0.435943	−	0.457204i
$704$	−2936.38	−	2090.99i	−0.157200	−	0.111942i
$705$	75.3337	+	1581.45i	0.00402444	+	0.0844834i
$706$	−15471.5	+	52691.0i	−0.824755	+	2.80886i
$707$	−7694.99	−	15221.2i	−0.409335	−	0.809692i
$708$	−27756.0	+	60777.1i	−1.47335	+	3.22619i
$709$	18984.7	−	24141.1i	1.00562	−	1.27875i	0.0455622	−	0.998962i	$-0.485492\pi$
$709$	18984.7	−	24141.1i	1.00562	−	1.27875i	0.960061	−	0.279792i	$-0.0902655\pi$
$710$	−318.839	+	6693.26i	−0.0168533	+	0.353794i
$711$	−4222.58	−	1461.45i	−0.222727	−	0.0770866i
$712$	24099.5	−	41741.5i	1.26849	−	2.19709i
$713$	−12540.9	−	28377.2i	−0.658709	−	1.49051i
$714$	−2336.03	+	787.830i	−0.122442	+	0.0412938i
$715$	−1500.47	−	1731.64i	−0.0784818	−	0.0905728i
$716$	−53828.5	+	27750.5i	−2.80959	+	1.44844i
$717$	12428.5	+	31044.9i	0.647352	+	1.61701i
$718$	4074.03	+	42665.1i	0.211757	+	2.21762i
$719$	8567.92	−	21401.6i	0.444408	−	1.11008i	−0.521973	−	0.852962i	$-0.674804\pi$
$719$	8567.92	−	21401.6i	0.444408	−	1.11008i	0.966381	−	0.257115i	$-0.0827720\pi$
$720$	−154634.	−	45404.8i	−8.00401	−	2.35019i
$721$	3611.93	−	23781.9i	0.186568	−	1.22841i
$722$	11384.0	+	24927.4i	0.586798	+	1.28491i
$723$	−45046.6	−	10928.2i	−2.31715	−	0.562135i
$724$	−27324.8	−	5266.42i	−1.40265	−	0.270338i
$725$	−1178.40	−	227.117i	−0.0603649	−	0.0116344i
$726$	−67149.8	−	16290.4i	−3.43273	−	0.832772i
$727$	14667.1	+	32116.4i	0.748242	+	1.63842i	0.769500	+	0.638647i	$0.220506\pi$
$727$	14667.1	+	32116.4i	0.748242	+	1.63842i	−0.0212582	+	0.999774i	$0.506767\pi$
$728$	−26574.8	−	67936.2i	−1.35292	−	3.45863i
$729$	38621.6	+	11340.3i	1.96218	+	0.576149i
$730$	−17063.6	+	42622.9i	−0.865142	+	2.16102i
$731$	15.7284	+	164.715i	0.000795809	+	0.00833408i
$732$	−40956.8	−	102305.i	−2.06804	−	5.16572i
$733$	−4606.40	+	2374.77i	−0.232117	+	0.119664i	−0.570362	−	0.821394i	$-0.693197\pi$
$733$	−4606.40	+	2374.77i	−0.232117	+	0.119664i	0.338245	+	0.941058i	$0.390167\pi$
$734$	−15836.6	−	18276.4i	−0.796376	−	0.919067i
$735$	15664.1	−	37397.8i	0.786093	−	1.87678i
$736$	14857.3	+	52996.8i	0.744086	+	2.65420i
$737$	−1319.69	+	2285.77i	−0.0659584	+	0.114243i
$738$	16919.2	+	5855.79i	0.843908	+	0.292079i
$739$	−224.631	+	4715.58i	−0.0111816	+	0.234730i	0.986358	+	0.164617i	$0.0526389\pi$
$739$	−224.631	+	4715.58i	−0.0111816	+	0.234730i	−0.997539	+	0.0701125i	$0.977664\pi$
$740$	43400.3	−	55188.0i	2.15598	−	2.74156i
$741$	9943.36	−	21772.9i	0.492953	−	1.07942i
$742$	−47135.5	−	2619.93i	−2.33208	−	0.129624i
$743$	5218.82	−	17773.7i	0.257685	−	0.877594i	−0.724436	−	0.689342i	$-0.757900\pi$
$743$	5218.82	−	17773.7i	0.257685	−	0.877594i	0.982121	−	0.188252i	$-0.0602822\pi$
$744$	8785.29	+	184426.i	0.432909	+	9.08788i
$745$	7582.18	+	5399.25i	0.372872	+	0.265521i
$746$	−21984.8	+	23056.9i	−1.07898	+	1.13160i
$747$	14384.5	+	41561.2i	0.704552	+	2.03567i
$748$	−127.606	−	110.571i	−0.00623760	−	0.00540491i
$749$	−14844.7	−	6922.05i	−0.724182	−	0.337685i
$750$	59924.5	−	27366.6i	2.91751	−	1.33238i
$751$	8987.21	−	428.113i	0.436681	−	0.0208017i	0.171909	−	0.985113i	$-0.445006\pi$
$751$	8987.21	−	428.113i	0.436681	−	0.0208017i	0.264772	+	0.964311i	$0.414703\pi$
$752$	−2521.97	+	611.823i	−0.122296	+	0.0296687i
$753$	29783.2	+	37872.4i	1.44138	+	1.83287i
$754$	14832.7	−	10562.3i	0.716412	−	0.510154i
$755$	−3219.86	+	22394.6i	−0.155209	+	1.07950i
$756$	151480.	+	38022.4i	7.28741	+	1.82918i
$757$	−11613.0	+	10062.7i	−0.557571	+	0.483138i	−0.887462	−	0.460881i	$-0.847533\pi$
$757$	−11613.0	+	10062.7i	−0.557571	+	0.483138i	0.329891	+	0.944019i	$0.392988\pi$
$758$	39308.2	+	22694.6i	1.88356	+	1.08747i
$759$	−2123.31	−	2769.29i	−0.101543	−	0.132436i
$760$	−16825.2	−	29142.1i	−0.803046	−	1.39092i
$761$	−1410.28	−	7317.20i	−0.0671780	−	0.348552i	0.932750	−	0.360523i	$-0.117402\pi$
$761$	−1410.28	−	7317.20i	−0.0671780	−	0.348552i	−0.999928	+	0.0119704i	$0.996190\pi$
$762$	−13238.5	+	20599.5i	−0.629370	+	0.979318i
$763$	−5834.05	−	31616.4i	−0.276811	−	1.50012i
$764$	13181.0	+	6019.57i	0.624179	+	0.285053i
$765$	−1964.46	−	786.450i	−0.0928433	−	0.0371689i
$766$	11395.1	+	46971.2i	0.537495	+	2.21558i
$767$	−17344.1	−	8941.49i	−0.816503	−	0.420937i
$768$	1488.77	−	15591.1i	0.0699496	−	0.732545i
$769$	−14323.3	+	4205.69i	−0.671665	+	0.197219i	−0.599744	−	0.800192i	$-0.704731\pi$
$769$	−14323.3	+	4205.69i	−0.671665	+	0.197219i	−0.0719208	+	0.997410i	$0.522913\pi$
$770$	3823.19	−	518.797i	0.178933	−	0.0242807i
$771$	−20782.4	+	23984.1i	−0.970763	+	1.12032i
$772$	1024.85	−	4224.51i	0.0477789	−	0.196947i
$773$	18646.4	−	26185.2i	0.867612	−	1.21839i	−0.106949	−	0.994265i	$-0.534108\pi$
$773$	18646.4	−	26185.2i	0.867612	−	1.21839i	0.974560	−	0.224126i	$-0.0719526\pi$
$774$	10972.9	−	21284.4i	0.509577	−	0.988441i
$775$	4016.23	+	4212.11i	0.186151	+	0.195230i
$776$	2843.34	+	19775.9i	0.131533	+	0.914836i
$777$	−30116.1	+	41590.6i	−1.39049	+	1.92027i
$778$	−77142.6	−	11091.4i	−3.55488	−	0.511115i
$779$	926.791	+	1797.72i	0.0426261	+	0.0826831i
$780$	46678.6	−	134869.i	2.14277	−	6.19113i
$781$	290.687	−	167.828i	0.0133183	−	0.00768933i
$782$	265.652	+	1475.55i	0.0121479	+	0.0674752i
$783$			23804.8i			1.08648i
$784$	65050.7	+	13610.3i	2.96331	+	0.620004i
$785$	3350.26	+	2153.08i	0.152326	+	0.0978939i
$786$	−26787.4	−	21065.8i	−1.21562	−	0.955972i
$787$	−8884.03	+	848.322i	−0.402391	+	0.0384237i	−0.294290	−	0.955716i	$-0.595083\pi$
$787$	−8884.03	+	848.322i	−0.402391	+	0.0384237i	−0.108101	+	0.994140i	$0.534477\pi$
$788$	79619.6	−	62613.5i	3.59940	−	2.83060i
$789$	29023.4	−	27673.8i	1.30958	−	1.24868i
$790$	−2260.77	−	3517.83i	−0.101816	−	0.158429i
$791$	−29403.6	+	6886.93i	−1.32171	+	0.309572i
$792$	4203.77	+	14316.7i	0.188604	+	0.642326i
$793$	30413.4	−	10526.2i	1.36193	−	0.471369i
$794$	−5663.94	+	29387.3i	−0.253156	+	1.31350i
$795$	−40816.1	−	38918.0i	−1.82088	−	1.73620i
$796$	−44219.0	−	4222.40i	−1.96897	−	0.188014i
$797$	−35497.5	+	22812.8i	−1.57765	+	1.01389i	−0.600945	+	0.799291i	$0.705209\pi$
$797$	−35497.5	+	22812.8i	−1.57765	+	1.01389i	−0.976702	+	0.214601i	$0.931155\pi$
$798$	21521.1	+	34078.4i	0.954687	+	1.51173i
$799$	−33.7266	+	4.84916i	−0.00149332	+	0.000214707i
$800$	−5989.07	−	8410.47i	−0.264682	−	0.371694i
$801$	−46002.3	+	18416.6i	−2.02923	+	0.812381i
$802$	−49470.3	−	2356.56i	−2.17812	−	0.103757i
$803$	2258.23	−	435.238i	0.0992417	−	0.0191273i
$804$	−164400.			−7.21137
$805$	−21101.0	−	12757.7i	−0.923868	−	0.558573i
$806$	−88307.3			−3.85917
$807$	−62395.3	+	12025.7i	−2.72171	+	0.524567i
$808$	61658.7	+	2937.17i	2.68459	+	0.127883i
$809$	10940.7	−	4379.98i	0.475468	−	0.190349i	−0.121536	−	0.992587i	$-0.538782\pi$
$809$	10940.7	−	4379.98i	0.475468	−	0.190349i	0.597004	+	0.802239i	$0.296358\pi$
$810$	80765.5	+	113419.i	3.50347	+	4.91994i
$811$	−16498.4	+	2372.11i	−0.714350	+	0.102708i	−0.489901	−	0.871778i	$-0.662967\pi$
$811$	−16498.4	+	2372.11i	−0.714350	+	0.102708i	−0.224448	+	0.974486i	$0.572058\pi$
$812$	875.323	+	22051.3i	0.0378298	+	0.953017i
$813$	−129.188	+	83.0243i	−0.00557298	+	0.00358154i
$814$	−4864.15	−	464.470i	−0.209445	−	0.0199996i
$815$	−240.495	−	229.311i	−0.0103364	−	0.00985573i
$816$	913.592	−	4740.17i	0.0391938	−	0.203357i
$817$	2556.39	−	884.775i	0.109470	−	0.0378878i
$818$	−7936.47	−	27029.1i	−0.339232	−	1.15532i
$819$	−21698.6	+	71788.9i	−0.925777	+	3.06289i
$820$	6519.87	+	10145.1i	0.277663	+	0.432052i
$821$	10405.3	−	9921.47i	0.442325	−	0.421756i	−0.435906	−	0.899992i	$-0.643572\pi$
$821$	10405.3	−	9921.47i	0.442325	−	0.421756i	0.878231	+	0.478236i	$0.158724\pi$
$822$	−19960.2	+	15696.8i	−0.846947	+	0.666046i
$823$	19646.5	−	1876.01i	0.832119	−	0.0794577i	0.329704	−	0.944084i	$-0.393051\pi$
$823$	19646.5	−	1876.01i	0.832119	−	0.0794577i	0.502415	+	0.864627i	$0.332445\pi$
$824$	68433.1	+	53816.4i	2.89318	+	2.27522i
$825$	550.700	+	353.913i	0.0232399	+	0.0149354i
$826$	28585.0	−	16202.8i	1.20411	−	0.682529i
$827$			33384.4i			1.40374i	0.712307	+	0.701868i	$0.247650\pi$
$827$			33384.4i			1.40374i	−0.712307	+	0.701868i	$0.752350\pi$
$828$	59817.3	−	144260.i	2.51062	−	6.05480i
$829$	15605.8	−	9010.02i	0.653815	−	0.377480i	−0.136101	−	0.990695i	$-0.543457\pi$
$829$	15605.8	−	9010.02i	0.653815	−	0.377480i	0.789916	+	0.613215i	$0.210124\pi$
$830$	−13461.6	+	38894.7i	−0.562962	+	1.62657i
$831$	−9211.04	−	17866.9i	−0.384510	−	0.745845i
$832$	64907.4	+	9332.27i	2.70464	+	0.388868i
$833$	833.248	+	259.079i	0.0346583	+	0.0107762i
$834$	−17942.7	−	124794.i	−0.744971	−	5.18139i
$835$	22104.1	+	23182.1i	0.916099	+	0.960777i
$836$	−1264.92	+	2453.60i	−0.0523302	+	0.101507i
$837$	66964.5	−	94038.4i	2.76539	−	3.88345i
$838$	−12878.8	+	53087.2i	−0.530897	+	2.18839i
$839$	11975.6	−	13820.6i	0.492782	−	0.568700i	−0.453825	−	0.891091i	$-0.649941\pi$
$839$	11975.6	−	13820.6i	0.492782	−	0.568700i	0.946607	+	0.322390i	$0.104486\pi$
$840$	89794.3	+	116064.i	3.68833	+	4.76737i
$841$	20173.6	−	5923.51i	0.827160	−	0.242876i
$842$	5319.20	−	55705.2i	0.217710	−	2.27996i
$843$	−12540.4	−	6465.04i	−0.512355	−	0.264137i
$844$	17365.4	+	71581.3i	0.708226	+	2.91935i
$845$	14076.2	+	5635.25i	0.573059	+	0.229418i
$846$	4485.57	+	2048.49i	0.182290	+	0.0832489i
$847$	15869.1	+	18609.9i	0.643763	+	0.754950i
$848$	49977.1	−	77765.9i	2.02385	−	3.14917i
$849$	−10262.0	−	53244.2i	−0.414830	−	2.15234i
$850$	−140.625	−	243.569i	−0.00567458	−	0.00982865i
$851$	22334.7	+	21825.6i	0.899677	+	0.879170i
$852$	18106.1	+	10453.6i	0.728059	+	0.420345i
$853$	12925.8	−	11200.3i	0.518841	−	0.449578i	−0.355651	−	0.934619i	$-0.615741\pi$
$853$	12925.8	−	11200.3i	0.518841	−	0.449578i	0.874492	+	0.485041i	$0.161195\pi$
$854$	−13193.4	+	52562.2i	−0.528654	+	2.10614i
$855$	−4923.37	+	34242.8i	−0.196931	+	1.36968i
$856$	48288.2	−	34385.9i	1.92810	−	1.37300i
$857$	1908.61	+	2426.99i	0.0760755	+	0.0967379i	0.822601	−	0.568619i	$-0.192522\pi$
$857$	1908.61	+	2426.99i	0.0760755	+	0.0967379i	−0.746526	+	0.665357i	$0.768280\pi$
$858$	−9652.65	+	2341.71i	−0.384075	+	0.0931755i
$859$	−25619.8	+	1220.42i	−1.01762	+	0.0484753i	−0.549757	−	0.835325i	$-0.685280\pi$
$859$	−25619.8	+	1220.42i	−1.01762	+	0.0484753i	−0.467865	+	0.883800i	$0.654977\pi$
$860$	14672.0	−	6700.48i	0.581757	−	0.265679i
$861$	−5059.04	−	7224.94i	−0.200246	−	0.285976i
$862$	−13539.2	−	11731.8i	−0.534975	−	0.463558i
$863$	10984.0	+	31736.2i	0.433255	+	1.25181i	0.924632	+	0.380862i	$0.124373\pi$
$863$	10984.0	+	31736.2i	0.433255	+	1.25181i	−0.491377	+	0.870947i	$0.663506\pi$
$864$	−141332.	+	148225.i	−5.56507	+	5.83648i
$865$	−352.695	−	251.153i	−0.0138636	−	0.00987222i
$866$	413.525	+	8680.97i	0.0162265	+	0.340637i
$867$	−13537.7	+	46105.1i	−0.530293	+	1.80601i
$868$	58573.8	−	89573.7i	2.29047	−	3.50268i
$869$	−87.0151	+	190.537i	−0.00339676	+	0.00743787i
$870$	−22642.8	+	28792.7i	−0.882372	+	1.12203i
$871$	2284.54	−	47958.4i	0.0888734	−	1.86568i
$872$	109959.	+	38057.2i	4.27028	+	1.47796i
$873$	10270.0	−	17788.2i	0.398153	−	0.689620i
$874$	22419.8	−	9908.08i	0.867689	−	0.383462i
$875$	−22860.5	−	4594.20i	−0.883228	−	0.177500i
$876$	93807.4	+	108259.i	3.61810	+	4.17551i
$877$	33852.1	−	17452.0i	1.30343	−	0.671964i	0.340125	−	0.940380i	$-0.389531\pi$
$877$	33852.1	−	17452.0i	1.30343	−	0.671964i	0.963303	+	0.268417i	$0.0865005\pi$
$878$	1383.36	+	3455.46i	0.0531732	+	0.132820i
$879$	−546.449	−	5722.67i	−0.0209684	−	0.219591i
$880$	−2807.89	+	7013.78i	−0.107561	+	0.268675i
$881$	−23269.3	−	6832.49i	−0.889856	−	0.261285i	−0.195317	−	0.980740i	$-0.562574\pi$
$881$	−23269.3	−	6832.49i	−0.889856	−	0.261285i	−0.694539	+	0.719455i	$0.744392\pi$
$882$	−81175.5	−	96738.2i	−3.09900	−	3.69314i
$883$	1715.16	+	3755.67i	0.0653676	+	0.143135i	0.939496	−	0.342560i	$-0.111294\pi$
$883$	1715.16	+	3755.67i	0.0653676	+	0.143135i	−0.874128	+	0.485695i	$0.838567\pi$
$884$	2984.90	+	724.129i	0.113567	+	0.0275510i
$885$	38543.6	+	7428.66i	1.46399	+	0.282160i
$886$	−38981.3	−	7513.03i	−1.47811	−	0.284882i
$887$	−36431.4	−	8838.17i	−1.37908	−	0.334562i	−0.523412	−	0.852080i	$-0.675341\pi$
$887$	−36431.4	−	8838.17i	−1.37908	−	0.334562i	−0.855673	+	0.517518i	$0.826856\pi$
$888$	−77202.9	−	169051.i	−2.91752	−	6.38848i
$889$	8071.53	−	3157.36i	0.304511	−	0.119116i
$890$	−44494.2	−	13064.7i	−1.67579	−	0.492055i
$891$	2592.20	−	6475.01i	0.0974658	−	0.243458i
$892$	−6928.53	−	72558.9i	−0.260072	−	2.72360i
$893$	207.040	+	517.161i	0.00775849	+	0.0193798i
$894$	35864.9	−	18489.6i	1.34172	−	0.691706i
$895$	23299.0	+	26888.5i	0.870167	+	1.00423i
$896$	−24113.0	+	27386.3i	−0.899061	+	1.02111i
$897$	57415.0	+	27077.0i	2.13716	+	1.00789i
$898$	−24637.4	+	42673.3i	−0.915547	+	1.58577i
$899$	15415.6	+	5335.38i	0.571900	+	0.197936i
$900$	−1393.96	+	29262.8i	−0.0516281	+	1.08381i
$901$	750.276	−	954.053i	0.0277417	−	0.0352765i
$902$	348.656	−	763.450i	0.0128703	−	0.0281819i
$903$	−10528.0	+	5322.35i	−0.387983	+	0.196143i
$904$	30792.9	−	104871.i	1.13292	−	3.85836i
$905$	777.887	+	16329.9i	0.0285722	+	0.599804i
$906$	79892.1	+	56890.9i	2.92962	+	2.08617i
$907$	9592.47	−	10060.3i	0.351172	−	0.368298i	−0.524328	−	0.851516i	$-0.675684\pi$
$907$	9592.47	−	10060.3i	0.351172	−	0.368298i	0.875500	+	0.483218i	$0.160532\pi$
$908$	7174.47	+	20729.3i	0.262217	+	0.757626i
$909$	−47960.8	−	41558.3i	−1.75001	−	1.51639i
$910$	−57491.8	+	40256.8i	−2.09432	+	1.46648i
$911$	3818.02	−	1743.63i	0.138855	−	0.0634127i	−0.344776	−	0.938685i	$-0.612045\pi$
$911$	3818.02	−	1743.63i	0.138855	−	0.0634127i	0.483631	+	0.875272i	$0.339318\pi$
$912$	−78833.6	+	3755.31i	−2.86233	+	0.136349i
$913$	2003.57	−	486.061i	0.0726271	−	0.0176192i
$914$	−55319.1	−	70344.0i	−2.00196	−	2.54570i
$915$	−52735.9	+	37553.1i	−1.90535	+	1.35679i
$916$	−14359.4	+	99871.8i	−0.517956	+	3.60246i
$917$	3306.45	+	11600.1i	0.119071	+	0.417740i
$918$	−4216.22	+	3653.38i	−0.151586	+	0.131350i
$919$	−27074.8	−	15631.6i	−0.971834	−	0.561089i	−0.0720391	−	0.997402i	$-0.522951\pi$
$919$	−27074.8	−	15631.6i	−0.971834	−	0.561089i	−0.899795	+	0.436313i	$0.856284\pi$
$920$	77828.3	−	43669.6i	2.78905	−	1.56494i
$921$	−3080.20	−	5335.07i	−0.110202	−	0.190876i
$922$	9275.50	+	48125.9i	0.331315	+	1.71903i
$923$	−3301.11	+	5136.62i	−0.117722	+	0.183179i
$924$	4027.27	−	11344.3i	0.143385	−	0.403897i
$925$	−5328.72	−	2433.55i	−0.189413	−	0.0865021i
$926$	60674.5	+	24290.4i	2.15323	+	0.862022i
$927$	−21101.1	−	86979.8i	−0.747627	−	3.08176i
$928$	−25722.7	−	13261.0i	−0.909904	−	0.469088i
$929$	1151.46	−	12058.7i	0.0406656	−	0.425869i	−0.952099	−	0.305791i	$-0.901079\pi$
$929$	1151.46	−	12058.7i	0.0406656	−	0.425869i	0.992764	−	0.120079i	$-0.0383147\pi$
$930$	170444.	−	50046.7i	6.00975	−	1.76462i
$931$	904.597	−	14237.3i	0.0318442	−	0.501192i
$932$	−52894.7	+	61043.8i	−1.85904	+	2.14544i
$933$	−15512.8	+	63944.6i	−0.544336	+	2.24379i
$934$	−32569.9	+	45738.0i	−1.14103	+	1.60235i
$935$	−45.4538	+	88.1680i	−0.00158984	+	0.00308385i
$936$	−187308.	−	196443.i	−6.54098	−	6.85998i
$937$	−3074.80	−	21385.7i	−0.107203	−	0.745614i	−0.970532	−	0.240972i	$-0.922534\pi$
$937$	−3074.80	−	21385.7i	−0.107203	−	0.745614i	0.863329	−	0.504642i	$-0.168375\pi$
$938$	65482.5	+	47416.5i	2.27940	+	1.65054i
$939$	27256.6	+	3918.91i	0.947269	+	0.136197i
$940$	1522.00	+	2952.27i	0.0528108	+	0.102439i
$941$	−13806.1	+	39890.1i	−0.478285	+	1.38191i	0.405532	+	0.914081i	$0.367086\pi$
$941$	−13806.1	+	39890.1i	−0.478285	+	1.38191i	−0.883817	+	0.467833i	$0.845035\pi$
$942$	14950.9	−	8631.90i	0.517119	−	0.298559i
$943$	−4797.46	+	2399.21i	−0.165670	+	0.0828514i
$944$			64340.2i			2.21832i
$945$	727.219	−	91750.3i	0.0250333	−	3.15834i
$946$	−944.355	−	606.900i	−0.0324563	−	0.0208584i
$947$	31248.1	+	24573.7i	1.07226	+	0.843231i	0.988191	−	0.153230i	$-0.0489674\pi$
$947$	31248.1	+	24573.7i	1.07226	+	0.843231i	0.0840645	+	0.996460i	$0.473210\pi$
$948$	−12988.0	+	1240.20i	−0.444969	+	0.0424894i
$949$	−32884.8	+	25860.9i	−1.12485	+	0.884595i
$950$	−3327.83	+	3173.08i	−0.113652	+	0.108367i
$951$	−2008.89	−	3125.89i	−0.0684990	−	0.106587i
$952$	−2302.85	+	2161.17i	−0.0783988	+	0.0735757i
$953$	8549.92	+	29118.3i	0.290618	+	0.989754i	0.967333	+	0.253509i	$0.0815847\pi$
$953$	8549.92	+	29118.3i	0.290618	+	0.989754i	−0.676715	+	0.736245i	$0.736597\pi$
$954$	−165993.	+	57450.6i	−5.63334	+	1.94972i
$955$	1611.09	−	8359.13i	0.0545902	−	0.283241i
$956$	50773.4	+	48412.3i	1.71771	+	1.63783i
$957$	1826.52	+	174.411i	0.0616959	+	0.00589124i
$958$	−60643.9	+	38973.4i	−2.04521	+	1.31438i
$959$	8980.78	−	356.490i	0.302403	−	0.0120038i
$960$	−130568.	+	18772.8i	−4.38965	+	0.631136i
$961$	−28608.3	−	40174.7i	−0.960299	−	1.34855i
$962$	82518.9	−	33035.6i	2.76561	−	1.10718i
$963$	−60875.1	−	2899.84i	−2.03704	−	0.0970363i
$964$	−95487.6	+	18403.7i	−3.19030	+	0.614880i
$965$	−2553.83			−0.0851924
$966$	−91071.4	+	55961.8i	−3.03331	+	1.86391i
$967$	55399.1			1.84231			0.921156	−	0.389193i	$-0.127246\pi$
$967$	55399.1			1.84231			0.921156	+	0.389193i	$0.127246\pi$
$968$	−86916.7	+	16751.8i	−2.88596	+	0.556223i
$969$	−1035.07	−	49.3064i	−0.0343150	−	0.00163462i
$970$	17845.3	−	7144.17i	0.590698	−	0.236480i
$971$	−16192.2	−	22738.7i	−0.535151	−	0.751515i	0.455156	−	0.890412i	$-0.349584\pi$
$971$	−16192.2	−	22738.7i	−0.535151	−	0.751515i	−0.990307	+	0.138897i	$0.955644\pi$
$972$	204639.	−	29422.6i	6.75287	−	0.970916i
$973$	−20762.3	+	39501.3i	−0.684078	+	1.30150i
$974$	3314.78	−	2130.28i	0.109048	−	0.0700806i
$975$	−11854.2	−	1131.94i	−0.389373	−	0.0371806i
$976$	−76800.6	−	73229.2i	−2.51878	−	2.40165i
$977$	3335.89	−	17308.2i	0.109237	−	0.566775i	−0.885528	−	0.464586i	$-0.846203\pi$
$977$	3335.89	−	17308.2i	0.109237	−	0.566775i	0.994765	−	0.102189i	$-0.0325846\pi$
$978$	−1361.27	+	471.139i	−0.0445077	+	0.0154043i
$979$	654.431	+	2228.79i	0.0213644	+	0.0727603i
$980$	−2700.08	−	85018.4i	−0.0880111	−	2.77124i
$981$	−64674.0	−	100635.i	−2.10488	−	3.27525i
$982$	−4937.29	+	4707.70i	−0.160443	+	0.152982i
$983$	12991.8	−	10216.9i	0.421541	−	0.331504i	−0.384752	−	0.923020i	$-0.625713\pi$
$983$	12991.8	−	10216.9i	0.421541	−	0.331504i	0.806293	+	0.591516i	$0.201470\pi$
$984$	31777.3	−	3034.37i	1.02950	−	0.0983050i
$985$	−46775.4	−	36784.6i	−1.51308	−	1.18990i
$986$	−663.171	−	426.194i	−0.0214195	−	0.0137655i
$987$	−1197.92	−	2113.37i	−0.0386326	−	0.0681555i
$988$		−	50215.5i		−	1.61697i
$989$	2263.09	+	6807.97i	0.0727626	+	0.218889i
$990$	12432.4	−	7177.88i	0.399120	−	0.230432i
$991$	13031.2	−	37651.1i	0.417708	−	1.20689i	−0.518388	−	0.855145i	$-0.673468\pi$
$991$	13031.2	−	37651.1i	0.417708	−	1.20689i	0.936096	−	0.351743i	$-0.114411\pi$
$992$	64310.9	+	124746.i	2.05834	+	3.99262i
$993$	−4796.16	−	689.584i	−0.153274	−	0.0220375i
$994$	−4196.86	−	9386.00i	−0.133920	−	0.299503i
$995$	3713.88	+	25830.6i	0.118329	+	0.823000i
$996$	88618.1	+	92940.0i	2.81925	+	2.95674i
$997$	−26007.6	+	50447.7i	−0.826148	+	1.60250i	−0.0283344	+	0.999598i	$0.509020\pi$
$997$	−26007.6	+	50447.7i	−0.826148	+	1.60250i	−0.797813	+	0.602905i	$0.794010\pi$
$998$	42724.5	−	59998.2i	1.35513	−	1.90302i
$999$	−27395.5	+	112926.i	−0.867622	+	3.57639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.o.a.33.2	yes	920
7.3	odd	6	inner	161.4.o.a.10.45	✓	920
23.7	odd	22	inner	161.4.o.a.145.45	yes	920
161.122	even	66	inner	161.4.o.a.122.2	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.o.a.10.45	✓	920	7.3	odd	6	inner
161.4.o.a.33.2	yes	920	1.1	even	1	trivial
161.4.o.a.122.2	yes	920	161.122	even	66	inner
161.4.o.a.145.45	yes	920	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.24626 + 1.01113i) q^{2} +(9.78230 + 0.465988i) q^{3} +(19.0739 - 7.63605i) q^{4} +(-7.00146 - 9.83217i) q^{5} +(-51.7917 + 7.44652i) q^{6} +(16.3937 + 8.61668i) q^{7} +(-56.3885 + 36.2387i) q^{8} +(68.5985 + 6.55036i) q^{9} +(46.6731 + 44.5027i) q^{10} +(0.611352 - 3.17200i) q^{11} +(190.145 - 65.8099i) q^{12} +(16.5556 + 56.3833i) q^{13} +(-94.7182 - 28.6291i) q^{14} +(-63.9087 - 99.4438i) q^{15} +(140.230 - 133.709i) q^{16} +(1.99973 - 1.57260i) q^{17} +(-366.509 + 34.9974i) q^{18} +(-32.6935 - 25.7104i) q^{19} +(-208.624 - 134.075i) q^{20} +(156.353 + 91.9302i) q^{21} +17.2593i q^{22} +(69.2444 - 85.8616i) q^{23} +(-568.496 + 328.221i) q^{24} +(-6.76769 + 19.5540i) q^{25} +(-143.866 - 279.062i) q^{26} +(406.268 + 58.4126i) q^{27} +(378.489 + 39.1709i) q^{28} +(8.25391 + 57.4072i) q^{29} +(435.833 + 457.088i) q^{30} +(128.884 - 250.000i) q^{31} +(-289.439 + 406.460i) q^{32} +(7.45854 - 30.7445i) q^{33} +(-8.90099 + 10.2723i) q^{34} +(-30.0590 - 221.515i) q^{35} +(1358.46 - 398.880i) q^{36} +(-26.9113 + 281.828i) q^{37} +(197.515 + 101.826i) q^{38} +(135.678 + 559.273i) q^{39} +(751.106 + 300.698i) q^{40} +(-44.2342 - 20.2011i) q^{41} +(-913.221 - 324.196i) q^{42} +(-35.1637 + 54.7158i) q^{43} +(-12.5606 - 65.1707i) q^{44} +(-415.885 - 720.334i) q^{45} +(-276.457 + 520.468i) q^{46} +(-11.5992 - 6.69679i) q^{47} +(1434.08 - 1242.63i) q^{48} +(194.506 + 282.518i) q^{49} +(15.7334 - 109.428i) q^{50} +(20.2948 - 14.4518i) q^{51} +(746.326 + 949.031i) q^{52} +(463.643 - 112.478i) q^{53} +(-2190.45 + 104.344i) q^{54} +(-35.4680 + 16.1977i) q^{55} +(-1236.67 + 108.204i) q^{56} +(-307.837 - 266.742i) q^{57} +(-101.349 - 292.827i) q^{58} +(-229.150 + 240.326i) q^{59} +(-1978.35 - 1408.77i) q^{60} +(-26.0595 - 547.056i) q^{61} +(-423.375 + 1441.88i) q^{62} +(1068.14 + 698.475i) q^{63} +(463.565 - 1015.07i) q^{64} +(438.457 - 557.543i) q^{65} +(-8.04262 + 168.835i) q^{66} +(-772.113 - 267.231i) q^{67} +(26.1342 - 45.2658i) q^{68} +(717.380 - 807.657i) q^{69} +(381.679 + 1131.73i) q^{70} +(68.0442 + 78.5272i) q^{71} +(-4105.54 + 2116.55i) q^{72} +(264.596 + 660.929i) q^{73} +(-143.782 - 1505.75i) q^{74} +(-75.3155 + 188.129i) q^{75} +(-819.919 - 240.750i) q^{76} +(37.3544 - 46.7329i) q^{77} +(-1277.30 - 2796.90i) q^{78} +(-63.0147 - 15.2872i) q^{79} +(-2296.46 - 442.607i) q^{80} +(2120.06 + 408.607i) q^{81} +(252.490 + 61.2534i) q^{82} +(265.126 + 580.545i) q^{83} +(3684.24 + 559.553i) q^{84} +(-29.4631 - 8.65116i) q^{85} +(129.153 - 322.608i) q^{86} +(53.9911 + 565.420i) q^{87} +(80.4757 + 201.019i) q^{88} +(-639.139 + 329.499i) q^{89} +(2910.20 + 3358.55i) q^{90} +(-214.429 + 1066.98i) q^{91} +(665.119 - 2166.47i) q^{92} +(1377.28 - 2385.51i) q^{93} +(67.6237 + 23.4048i) q^{94} +(-23.8874 + 501.458i) q^{95} +(-3020.79 + 3841.24i) q^{96} +(123.822 - 271.132i) q^{97} +(-1306.09 - 1285.49i) q^{98} +(62.7155 - 213.590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 11 q^{2} - 27 q^{3} + 157 q^{4} - 33 q^{5} - 22 q^{7} - 104 q^{8} - 359 q^{9} - 33 q^{10} - 11 q^{11} - 75 q^{12} - 22 q^{14} - 44 q^{15} + 1157 q^{16} - 33 q^{17} + 179 q^{18} - 33 q^{19} - 1342 q^{21}+ \cdots + 23056 q^{99}+O(q^{100}) \) 920 * q - 11 * q^2 - 27 * q^3 + 157 * q^4 - 33 * q^5 - 22 * q^7 - 104 * q^8 - 359 * q^9 - 33 * q^10 - 11 * q^11 - 75 * q^12 - 22 * q^14 - 44 * q^15 + 1157 * q^16 - 33 * q^17 + 179 * q^18 - 33 * q^19 - 1342 * q^21 - 494 * q^23 - 570 * q^24 + 1269 * q^25 - 609 * q^26 + 682 * q^28 - 348 * q^29 + 1485 * q^30 + 105 * q^31 - 1017 * q^32 - 33 * q^33 + 966 * q^35 + 4354 * q^36 - 1199 * q^37 - 33 * q^38 + 5 * q^39 - 33 * q^40 - 3652 * q^42 - 3476 * q^43 + 3388 * q^44 + 477 * q^46 - 1188 * q^47 - 1408 * q^49 - 3234 * q^50 + 649 * q^51 + 1911 * q^52 - 11 * q^53 - 1659 * q^54 + 9361 * q^56 + 7612 * q^57 - 4198 * q^58 - 915 * q^59 - 11 * q^60 - 33 * q^61 - 2112 * q^63 - 5064 * q^64 - 4323 * q^65 + 858 * q^66 - 11 * q^67 - 2478 * q^70 + 1732 * q^71 - 9181 * q^72 - 3987 * q^73 + 2354 * q^74 + 2871 * q^75 + 2164 * q^77 - 24268 * q^78 + 1837 * q^79 + 12144 * q^80 + 3035 * q^81 + 5823 * q^82 + 11330 * q^84 + 13676 * q^85 + 5225 * q^86 - 24657 * q^87 - 12342 * q^88 - 33 * q^89 + 9810 * q^92 - 1440 * q^93 - 15858 * q^94 - 4187 * q^95 + 2439 * q^96 - 11284 * q^98 + 23056 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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