LMFDB - Embedded newform 161.4.o.a.122.9

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			122.9
Character	$\chi$	$=$	161.122
Dual form			161.4.o.a.33.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.64593 - 0.702695i) q^{2} +(8.42807 - 0.401479i) q^{3} +(5.37207 + 2.15065i) q^{4} +(-0.808912 + 1.13596i) q^{5} +(-31.0103 - 4.45860i) q^{6} +(-17.9795 + 4.44264i) q^{7} +(6.91384 + 4.44325i) q^{8} +(43.9935 - 4.20087i) q^{9} +(3.74747 - 3.57320i) q^{10} +(8.69765 + 45.1277i) q^{11} +(46.1397 + 15.9691i) q^{12} +(-22.7808 + 77.5842i) q^{13} +(68.6739 - 3.56341i) q^{14} +(-6.36151 + 9.89870i) q^{15} +(-55.5887 - 53.0037i) q^{16} +(-22.0789 - 17.3631i) q^{17} +(-163.349 - 15.5979i) q^{18} +(107.559 - 84.5855i) q^{19} +(-6.78859 + 4.36276i) q^{20} +(-149.749 + 44.6612i) q^{21} -170.644i q^{22} +(-92.6000 + 59.9353i) q^{23} +(60.0542 + 34.6723i) q^{24} +(40.2474 + 116.287i) q^{25} +(137.575 - 266.859i) q^{26} +(143.596 - 20.6461i) q^{27} +(-106.142 - 14.8016i) q^{28} +(-1.25458 + 8.72581i) q^{29} +(30.1494 - 31.6197i) q^{30} +(92.8607 + 180.125i) q^{31} +(127.289 + 178.753i) q^{32} +(91.4222 + 376.847i) q^{33} +(68.2973 + 78.8193i) q^{34} +(9.49720 - 24.0177i) q^{35} +(245.371 + 72.0474i) q^{36} +(-11.0126 - 115.329i) q^{37} +(-451.591 + 232.811i) q^{38} +(-160.850 + 663.031i) q^{39} +(-10.6400 + 4.25963i) q^{40} +(357.866 - 163.432i) q^{41} +(577.358 - 57.6038i) q^{42} +(214.695 + 334.072i) q^{43} +(-50.3296 + 261.135i) q^{44} +(-30.8148 + 53.3729i) q^{45} +(379.729 - 153.450i) q^{46} +(-81.2312 + 46.8988i) q^{47} +(-489.785 - 424.401i) q^{48} +(303.526 - 159.753i) q^{49} +(-65.0247 - 452.257i) q^{50} +(-193.054 - 137.473i) q^{51} +(-289.237 + 367.795i) q^{52} +(-183.213 - 44.4471i) q^{53} +(-538.050 - 25.6305i) q^{54} +(-58.2988 - 26.6242i) q^{55} +(-144.047 - 49.1719i) q^{56} +(872.558 - 756.076i) q^{57} +(10.7057 - 30.9321i) q^{58} +(-558.302 - 585.530i) q^{59} +(-55.4632 + 39.4951i) q^{60} +(-31.4186 + 659.557i) q^{61} +(-211.991 - 721.975i) q^{62} +(-772.318 + 270.977i) q^{63} +(-83.2211 - 182.229i) q^{64} +(-69.7048 - 88.6368i) q^{65} +(-68.5099 - 1438.20i) q^{66} +(132.923 - 46.0052i) q^{67} +(-81.2678 - 140.760i) q^{68} +(-756.377 + 542.316i) q^{69} +(-51.5032 + 80.8931i) q^{70} +(-53.1880 + 61.3823i) q^{71} +(322.829 + 166.430i) q^{72} +(-284.553 + 710.780i) q^{73} +(-40.8902 + 428.221i) q^{74} +(385.895 + 963.919i) q^{75} +(759.730 - 223.077i) q^{76} +(-356.865 - 772.733i) q^{77} +(1052.36 - 2304.34i) q^{78} +(540.965 - 131.237i) q^{79} +(105.176 - 20.2711i) q^{80} +(30.2888 - 5.83768i) q^{81} +(-1419.60 + 344.390i) q^{82} +(352.844 - 772.621i) q^{83} +(-900.514 - 82.1349i) q^{84} +(37.5837 - 11.0356i) q^{85} +(-548.011 - 1368.87i) q^{86} +(-7.07048 + 74.0454i) q^{87} +(-140.380 + 350.651i) q^{88} +(-959.037 - 494.418i) q^{89} +(149.854 - 172.940i) q^{90} +(64.9090 - 1496.13i) q^{91} +(-626.354 + 122.826i) q^{92} +(854.953 + 1480.82i) q^{93} +(329.119 - 113.909i) q^{94} +(9.07964 + 190.605i) q^{95} +(1144.57 + 1455.44i) q^{96} +(-522.129 - 1143.30i) q^{97} +(-1218.89 + 369.161i) q^{98} +(572.215 + 1948.79i) 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 $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−3.64593	−	0.702695i	−1.28903	−	0.248440i	−0.501738	−	0.865020i	$-0.667306\pi$
$2$	−3.64593	−	0.702695i	−1.28903	−	0.248440i	−0.787293	+	0.616579i	$0.788518\pi$
$3$	8.42807	−	0.401479i	1.62198	−	0.0772646i	0.783214	−	0.621752i	$-0.213579\pi$
$3$	8.42807	−	0.401479i	1.62198	−	0.0772646i	0.838769	+	0.544487i	$0.183276\pi$
$4$	5.37207	+	2.15065i	0.671509	+	0.268832i
$5$	−0.808912	+	1.13596i	−0.0723513	+	0.101603i	−0.849166	−	0.528126i	$-0.822895\pi$
$5$	−0.808912	+	1.13596i	−0.0723513	+	0.101603i	0.776815	+	0.629729i	$0.216834\pi$
$6$	−31.0103	−	4.45860i	−2.10998	−	0.303370i
$7$	−17.9795	+	4.44264i	−0.970803	+	0.239880i
$7$	−17.9795	+	4.44264i	−0.970803	+	0.239880i
$8$	6.91384	+	4.44325i	0.305551	+	0.196366i
$9$	43.9935	−	4.20087i	1.62939	−	0.155588i
$10$	3.74747	−	3.57320i	0.118505	−	0.112995i
$11$	8.69765	+	45.1277i	0.238404	+	1.23696i	0.881874	+	0.471484i	$0.156282\pi$
$11$	8.69765	+	45.1277i	0.238404	+	1.23696i	−0.643471	+	0.765471i	$0.722506\pi$
$12$	46.1397	+	15.9691i	1.10995	+	0.384157i
$13$	−22.7808	+	77.5842i	−0.486019	+	1.65523i	0.242460	+	0.970162i	$0.422046\pi$
$13$	−22.7808	+	77.5842i	−0.486019	+	1.65523i	−0.728479	+	0.685068i	$0.759772\pi$
$14$	68.6739	−	3.56341i	1.31099	−	0.0680259i
$15$	−6.36151	+	9.89870i	−0.109502	+	0.170389i
$16$	−55.5887	−	53.0037i	−0.868573	−	0.828183i
$17$	−22.0789	−	17.3631i	−0.314996	−	0.247716i	0.448125	−	0.893971i	$-0.352092\pi$
$17$	−22.0789	−	17.3631i	−0.314996	−	0.247716i	−0.763121	+	0.646255i	$0.776334\pi$
$18$	−163.349	−	15.5979i	−2.13899	−	0.204248i
$19$	107.559	−	84.5855i	1.29873	−	1.02133i	0.301020	−	0.953618i	$-0.402673\pi$
$19$	107.559	−	84.5855i	1.29873	−	1.02133i	0.997705	−	0.0677111i	$-0.0215696\pi$
$20$	−6.78859	+	4.36276i	−0.0758987	+	0.0487772i
$21$	−149.749	+	44.6612i	−1.55609	+	0.464090i
$22$		−	170.644i		−	1.65370i
$23$	−92.6000	+	59.9353i	−0.839497	+	0.543364i
$23$	−92.6000	+	59.9353i	−0.839497	+	0.543364i
$24$	60.0542	+	34.6723i	0.510771	+	0.294894i
$25$	40.2474	+	116.287i	0.321979	+	0.930299i
$26$	137.575	−	266.859i	1.03772	−	2.01290i
$27$	143.596	−	20.6461i	1.02352	−	0.147161i
$28$	−106.142	−	14.8016i	−0.716390	−	0.0999011i
$29$	−1.25458	+	8.72581i	−0.00803345	+	0.0558739i	−0.993444	−	0.114321i	$-0.963531\pi$
$29$	−1.25458	+	8.72581i	−0.00803345	+	0.0558739i	0.985410	+	0.170195i	$0.0544398\pi$
$30$	30.1494	−	31.6197i	0.183483	−	0.192432i
$31$	92.8607	+	180.125i	0.538009	+	1.04359i	0.988558	+	0.150840i	$0.0481979\pi$
$31$	92.8607	+	180.125i	0.538009	+	1.04359i	−0.450549	+	0.892752i	$0.648772\pi$
$32$	127.289	+	178.753i	0.703181	+	0.987479i
$33$	91.4222	+	376.847i	0.482259	+	1.98790i
$34$	68.2973	+	78.8193i	0.344497	+	0.397571i
$35$	9.49720	−	24.0177i	0.0458663	−	0.115992i
$36$	245.371	+	72.0474i	1.13598	+	0.333553i
$37$	−11.0126	−	115.329i	−0.0489314	−	0.512433i	−0.986400	−	0.164363i	$-0.947443\pi$
$37$	−11.0126	−	115.329i	−0.0489314	−	0.512433i	0.937468	−	0.348070i	$-0.113163\pi$
$38$	−451.591	+	232.811i	−1.92784	+	0.993868i
$39$	−160.850	+	663.031i	−0.660425	+	2.72231i
$40$	−10.6400	+	4.25963i	−0.0420584	+	0.0168377i
$41$	357.866	−	163.432i	1.36315	−	0.622531i	0.406470	−	0.913664i	$-0.366760\pi$
$41$	357.866	−	163.432i	1.36315	−	0.622531i	0.956683	+	0.291133i	$0.0940323\pi$
$42$	577.358	−	57.6038i	2.12115	−	0.211630i
$43$	214.695	+	334.072i	0.761410	+	1.18478i	0.978018	+	0.208519i	$0.0668642\pi$
$43$	214.695	+	334.072i	0.761410	+	1.18478i	−0.216608	+	0.976259i	$0.569499\pi$
$44$	−50.3296	+	261.135i	−0.172443	+	0.894717i
$45$	−30.8148	+	53.3729i	−0.102080	+	0.176808i
$46$	379.729	−	153.450i	1.21713	−	0.491848i
$47$	−81.2312	+	46.8988i	−0.252102	+	0.145551i	−0.620726	−	0.784027i	$-0.713162\pi$
$47$	−81.2312	+	46.8988i	−0.252102	+	0.145551i	0.368624	+	0.929578i	$0.379829\pi$
$48$	−489.785	−	424.401i	−1.47280	−	1.27619i
$49$	303.526	−	159.753i	0.884915	−	0.465752i
$50$	−65.0247	−	452.257i	−0.183918	−	1.27918i
$51$	−193.054	−	137.473i	−0.530058	−	0.377452i
$52$	−289.237	+	367.795i	−0.771345	+	0.980845i
$53$	−183.213	−	44.4471i	−0.474836	−	0.115194i	−0.00880274	−	0.999961i	$-0.502802\pi$
$53$	−183.213	−	44.4471i	−0.474836	−	0.115194i	−0.466033	+	0.884767i	$0.654317\pi$
$54$	−538.050	−	25.6305i	−1.35591	−	0.0645902i
$55$	−58.2988	−	26.6242i	−0.142927	−	0.0652727i
$56$	−144.047	−	49.1719i	−0.343734	−	0.117337i
$57$	872.558	−	756.076i	2.02760	−	1.75692i
$58$	10.7057	−	30.9321i	0.0242367	−	0.0700273i
$59$	−558.302	−	585.530i	−1.23194	−	1.29203i	−0.942251	−	0.334907i	$-0.891295\pi$
$59$	−558.302	−	585.530i	−1.23194	−	1.29203i	−0.289694	−	0.957119i	$-0.593553\pi$
$60$	−55.4632	+	39.4951i	−0.119338	+	0.0849800i
$61$	−31.4186	+	659.557i	−0.0659465	+	1.38439i	0.687169	+	0.726498i	$0.258853\pi$
$61$	−31.4186	+	659.557i	−0.0659465	+	1.38439i	−0.753115	+	0.657889i	$0.771450\pi$
$62$	−211.991	−	721.975i	−0.434240	−	1.47889i
$63$	−772.318	+	270.977i	−1.54449	+	0.541902i
$64$	−83.2211	−	182.229i	−0.162541	−	0.355915i
$65$	−69.7048	−	88.6368i	−0.133012	−	0.169139i
$66$	−68.5099	−	1438.20i	−0.127773	−	2.68228i
$67$	132.923	−	46.0052i	0.242376	−	0.0838871i	−0.203179	−	0.979142i	$-0.565127\pi$
$67$	132.923	−	46.0052i	0.242376	−	0.0838871i	0.445555	+	0.895254i	$0.353006\pi$
$68$	−81.2678	−	140.760i	−0.144929	−	0.251024i
$69$	−756.377	+	542.316i	−1.31967	+	0.946191i
$70$	−51.5032	+	80.8931i	−0.0879402	+	0.138123i
$71$	−53.1880	+	61.3823i	−0.0889051	+	0.102602i	−0.798459	−	0.602049i	$-0.794351\pi$
$71$	−53.1880	+	61.3823i	−0.0889051	+	0.102602i	0.709554	+	0.704651i	$0.248897\pi$
$72$	322.829	+	166.430i	0.528414	+	0.272416i
$73$	−284.553	+	710.780i	−0.456225	+	1.13960i	0.504825	+	0.863222i	$0.331557\pi$
$73$	−284.553	+	710.780i	−0.456225	+	1.13960i	−0.961050	+	0.276374i	$0.910867\pi$
$74$	−40.8902	+	428.221i	−0.0642349	+	0.672699i
$75$	385.895	+	963.919i	0.594124	+	1.48405i
$76$	759.730	−	223.077i	1.14667	−	0.336693i
$77$	−356.865	−	772.733i	−0.528163	−	1.14365i
$78$	1052.36	−	2304.34i	1.52764	−	3.34506i
$79$	540.965	−	131.237i	0.770422	−	0.186902i	0.168764	−	0.985656i	$-0.446022\pi$
$79$	540.965	−	131.237i	0.770422	−	0.186902i	0.601657	+	0.798754i	$0.294507\pi$
$80$	105.176	−	20.2711i	0.146988	−	0.0283297i
$81$	30.2888	−	5.83768i	0.0415484	−	0.00800780i
$82$	−1419.60	+	344.390i	−1.91181	+	0.463799i
$83$	352.844	−	772.621i	0.466622	−	1.02176i	−0.519305	−	0.854589i	$-0.673809\pi$
$83$	352.844	−	772.621i	0.466622	−	1.02176i	0.985928	−	0.167172i	$-0.0534635\pi$
$84$	−900.514	−	82.1349i	−1.16969	−	0.106686i
$85$	37.5837	−	11.0356i	0.0479591	−	0.0140820i
$86$	−548.011	−	1368.87i	−0.687135	−	1.71638i
$87$	−7.07048	+	74.0454i	−0.00871305	+	0.0912472i
$88$	−140.380	+	350.651i	−0.170051	+	0.424768i
$89$	−959.037	−	494.418i	−1.14222	−	0.588856i	−0.219993	−	0.975502i	$-0.570603\pi$
$89$	−959.037	−	494.418i	−1.14222	−	0.588856i	−0.922228	+	0.386646i	$0.873634\pi$
$90$	149.854	−	172.940i	0.175511	−	0.202550i
$91$	64.9090	−	1496.13i	0.0747727	−	1.72349i
$92$	−626.354	+	122.826i	−0.709804	+	0.139191i
$93$	854.953	+	1480.82i	0.953274	+	1.65112i
$94$	329.119	−	113.909i	0.361128	−	0.124987i
$95$	9.07964	+	190.605i	0.00980580	+	0.205849i
$96$	1144.57	+	1455.44i	1.21684	+	1.54734i
$97$	−522.129	−	1143.30i	−0.546538	−	1.19675i	−0.958380	−	0.285496i	$-0.907842\pi$
$97$	−522.129	−	1143.30i	−0.546538	−	1.19675i	0.411842	−	0.911255i	$-0.364886\pi$
$98$	−1218.89	+	369.161i	−1.25639	+	0.380520i
$99$	572.215	+	1948.79i	0.580907	+	1.97839i
$100$	−33.8816	+	711.262i	−0.0338816	+	0.711262i
$101$	20.7304	−	14.7621i	0.0204233	−	0.0145434i	−0.569800	−	0.821784i	$-0.692979\pi$
$101$	20.7304	−	14.7621i	0.0204233	−	0.0145434i	0.590223	+	0.807240i	$0.299040\pi$
$102$	607.259	+	636.875i	0.589486	+	0.618235i
$103$	512.734	−	1481.45i	0.490497	−	1.41720i	−0.379984	−	0.924993i	$-0.624070\pi$
$103$	512.734	−	1481.45i	0.490497	−	1.41720i	0.870480	−	0.492204i	$-0.163808\pi$
$104$	−502.229	+	435.184i	−0.473535	+	0.410320i
$105$	70.4005	−	206.236i	0.0654322	−	0.191681i
$106$	636.750	+	290.794i	0.583459	+	0.266457i
$107$	−192.549	−	9.17224i	−0.173966	−	0.00828705i	−0.0395821	−	0.999216i	$-0.512603\pi$
$107$	−192.549	−	9.17224i	−0.173966	−	0.00828705i	−0.134384	+	0.990929i	$0.542906\pi$
$108$	815.813	+	197.914i	0.726867	+	0.176336i
$109$	709.341	−	902.000i	0.623326	−	0.792623i	−0.367172	−	0.930153i	$-0.619674\pi$
$109$	709.341	−	902.000i	0.623326	−	0.792623i	0.990498	+	0.137530i	$0.0439163\pi$
$110$	193.845	+	138.036i	0.168021	+	0.119647i
$111$	−139.117	−	967.583i	−0.118959	−	0.827377i
$112$	1234.93	+	706.020i	1.04188	+	0.595649i
$113$	659.925	+	571.828i	0.549385	+	0.476045i	0.884765	−	0.466038i	$-0.154319\pi$
$113$	659.925	+	571.828i	0.549385	+	0.476045i	−0.335379	+	0.942083i	$0.608865\pi$
$114$	−3712.57	+	2143.46i	−3.05013	+	1.76099i
$115$	6.82126	−	153.672i	0.00553118	−	0.124609i
$116$	−25.5059	+	44.1775i	−0.0204152	+	0.0353602i
$117$	−676.285	+	3508.90i	−0.534381	+	2.77263i
$118$	1624.08	+	2527.12i	1.26702	+	1.97153i
$119$	474.107	+	214.091i	0.365221	+	0.164922i
$120$	−87.9648	+	40.1722i	−0.0669171	+	0.0305600i
$121$	−725.200	+	290.326i	−0.544854	+	0.218126i
$122$	578.017	−	2382.62i	0.428944	−	1.76813i
$123$	2950.50	−	1521.09i	2.16291	−	1.11506i
$124$	111.469	+	1167.35i	0.0807274	+	0.845416i
$125$	−331.910	−	97.4577i	−0.237496	−	0.0697351i
$126$	3006.23	−	445.257i	2.12553	−	0.314814i
$127$	−901.205	−	1040.05i	−0.629677	−	0.726686i	0.347837	−	0.937555i	$-0.386916\pi$
$127$	−901.205	−	1040.05i	−0.629677	−	0.726686i	−0.977514	+	0.210869i	$0.932371\pi$
$128$	−238.518	−	983.185i	−0.164705	−	0.678922i
$129$	1943.59	+	2729.38i	1.32654	+	1.86286i
$130$	191.854	+	372.145i	0.129436	+	0.251071i
$131$	−65.9767	+	69.1943i	−0.0440031	+	0.0461491i	−0.745368	−	0.666654i	$-0.767726\pi$
$131$	−65.9767	+	69.1943i	−0.0440031	+	0.0461491i	0.701365	+	0.712803i	$0.252575\pi$
$132$	−319.342	+	2221.07i	−0.210569	+	1.46454i
$133$	−1558.08	+	1998.65i	−1.01581	+	1.30305i
$134$	−516.957	+	74.3272i	−0.333271	+	0.0479171i
$135$	−92.7039	+	179.820i	−0.0591013	+	0.114641i
$136$	−75.5017	−	218.148i	−0.0476045	−	0.137544i
$137$	−96.9301	−	55.9626i	−0.0604474	−	0.0348993i	0.469472	−	0.882948i	$-0.344444\pi$
$137$	−96.9301	−	55.9626i	−0.0604474	−	0.0348993i	−0.529919	+	0.848048i	$0.677778\pi$
$138$	3138.78	−	1445.74i	1.93616	−	0.891810i
$139$			1510.02i			0.921426i	0.887549	+	0.460713i	$0.152406\pi$
$139$			1510.02i			0.921426i	−0.887549	+	0.460713i	$0.847594\pi$
$140$	102.673	−	108.600i	0.0619820	−	0.0655596i
$141$	−665.793	+	427.879i	−0.397659	+	0.255560i
$142$	237.053	−	186.420i	0.140092	−	0.110169i
$143$	−3699.33	−	353.244i	−2.16331	−	0.206571i
$144$	−2668.20	−	2098.30i	−1.54410	−	1.21429i
$145$	−8.89731	−	8.48356i	−0.00509573	−	0.00485877i
$146$	1536.92	−	2391.50i	0.871210	−	1.35563i
$147$	2494.00	−	1468.27i	1.39933	−	0.823814i
$148$	188.873	−	643.242i	0.104900	−	0.357258i
$149$	−453.626	−	157.002i	−0.249413	−	0.0863227i	0.199501	−	0.979898i	$-0.436068\pi$
$149$	−453.626	−	157.002i	−0.249413	−	0.0863227i	−0.448914	+	0.893575i	$0.648189\pi$
$150$	−729.605	−	3785.55i	−0.397146	−	2.06059i
$151$	−497.491	+	474.357i	−0.268114	+	0.255646i	−0.812195	−	0.583387i	$-0.801727\pi$
$151$	−497.491	+	474.357i	−0.268114	+	0.255646i	0.544080	+	0.839033i	$0.316879\pi$
$152$	1119.48	−	106.898i	0.597381	−	0.0570430i
$153$	−1044.27	−	671.111i	−0.551792	−	0.354615i
$154$	758.109	+	3068.10i	0.396690	+	1.60542i
$155$	−279.730	−	40.2191i	−0.144958	−	0.0208418i
$156$	−2290.05	+	3215.92i	−1.17532	+	1.65051i
$157$	1065.57	+	426.592i	0.541669	+	0.216852i	0.626330	−	0.779558i	$-0.284556\pi$
$157$	1065.57	+	426.592i	0.541669	+	0.216852i	−0.0846606	+	0.996410i	$0.526981\pi$
$158$	−2064.54	+	98.3461i	−1.03953	+	0.0495190i
$159$	−1561.98	−	301.047i	−0.779076	−	0.150155i
$160$	−306.022			−0.151207
$161$	1398.63	−	1489.00i	0.684644	−	0.728878i
$162$	−114.533			−0.0555466
$163$	1642.87	+	316.638i	0.789446	+	0.152153i	0.568010	−	0.823022i	$-0.307714\pi$
$163$	1642.87	+	316.638i	0.789446	+	0.152153i	0.221436	+	0.975175i	$0.428926\pi$
$164$	2273.97	−	108.322i	1.08273	−	0.0515766i
$165$	−502.035	−	200.985i	−0.236869	−	0.0948281i
$166$	−1829.36	+	2568.98i	−0.855337	+	1.20115i
$167$	−831.706	−	119.581i	−0.385385	−	0.0554101i	−0.0531007	−	0.998589i	$-0.516910\pi$
$167$	−831.706	−	119.581i	−0.385385	−	0.0554101i	−0.332285	+	0.943179i	$0.607820\pi$
$168$	−1233.78	−	356.592i	−0.566597	−	0.163760i
$169$	−3652.11	−	2347.07i	−1.66232	−	1.06831i
$170$	−144.782	+	13.8250i	−0.0653192	+	0.00623723i
$171$	4376.57	−	4173.05i	1.95722	−	1.86621i
$172$	434.884	+	2256.39i	0.192788	+	1.00028i
$173$	1659.58	+	574.387i	0.729340	+	0.252427i	0.666404	−	0.745591i	$-0.267833\pi$
$173$	1659.58	+	574.387i	0.729340	+	0.252427i	0.0629355	+	0.998018i	$0.479954\pi$
$174$	77.8098	−	264.996i	0.0339009	−	0.115456i
$175$	−1240.25	−	1911.99i	−0.535738	−	0.825900i
$176$	1908.44	−	2969.59i	0.817354	−	1.27183i
$177$	−4940.49	−	4710.75i	−2.09802	−	2.00046i
$178$	3149.15	+	2476.52i	1.32606	+	1.04283i
$179$	−1539.74	−	147.027i	−0.642935	−	0.0613928i	−0.231504	−	0.972834i	$-0.574365\pi$
$179$	−1539.74	−	147.027i	−0.642935	−	0.0613928i	−0.411431	+	0.911441i	$0.634971\pi$
$180$	−280.326	+	220.451i	−0.116079	+	0.0912858i
$181$	964.614	−	619.920i	0.396128	−	0.254576i	−0.327379	−	0.944893i	$-0.606165\pi$
$181$	964.614	−	619.920i	0.396128	−	0.254576i	0.723507	+	0.690317i	$0.242529\pi$
$182$	−1287.98	+	5409.18i	−0.524568	+	2.20305i
$183$			5571.41i			2.25055i
$184$	−906.529	+	2.93769i	−0.363208	+	0.00117701i
$185$	139.918	+	80.7814i	0.0556051	+	0.0321036i
$186$	−2076.53	−	5999.74i	−0.818595	−	2.36518i
$187$	591.520	−	1147.39i	0.231317	−	0.448692i
$188$	−537.243	+	77.2439i	−0.208417	+	0.0299659i
$189$	−2490.07	+	1009.15i	−0.958339	+	0.388387i
$190$	100.834	−	701.313i	0.0385012	−	0.267782i
$191$	1055.87	−	1107.37i	0.400002	−	0.419510i	−0.492671	−	0.870216i	$-0.663979\pi$
$191$	1055.87	−	1107.37i	0.400002	−	0.419510i	0.892672	+	0.450706i	$0.148828\pi$
$192$	−774.554	−	1502.43i	−0.291139	−	0.564730i
$193$	1617.32	+	2271.20i	0.603197	+	0.847071i	0.997408	−	0.0719483i	$-0.0229217\pi$
$193$	1617.32	+	2271.20i	0.603197	+	0.847071i	−0.394212	+	0.919020i	$0.628982\pi$
$194$	1100.25	+	4535.30i	0.407183	+	1.67843i
$195$	−623.063	−	719.053i	−0.228812	−	0.264064i
$196$	1974.14	−	205.425i	0.719438	−	0.0748633i
$197$	1352.13	+	397.021i	0.489012	+	0.143587i	0.516937	−	0.856023i	$-0.327072\pi$
$197$	1352.13	+	397.021i	0.489012	+	0.143587i	−0.0279257	+	0.999610i	$0.508890\pi$
$198$	−716.853	−	7507.23i	−0.257296	−	2.69452i
$199$	2849.09	−	1468.81i	1.01491	−	0.523221i	0.131246	−	0.991350i	$-0.458102\pi$
$199$	2849.09	−	1468.81i	1.01491	−	0.523221i	0.883660	+	0.468129i	$0.155072\pi$
$200$	−238.430	+	982.821i	−0.0842977	+	0.347480i
$201$	1101.82	−	441.101i	0.386648	−	0.154791i
$202$	−85.9550	+	39.2543i	−0.0299395	+	0.0136729i
$203$	−16.2088	−	162.459i	−0.00560412	−	0.0561695i
$204$	−741.443	−	1153.71i	−0.254468	−	0.395959i
$205$	−103.830	+	538.723i	−0.0353747	+	0.183542i
$206$	−2910.40	+	5040.95i	−0.984354	+	1.70495i
$207$	−3822.02	+	3025.76i	−1.28333	+	1.01597i
$208$	5378.60	−	3105.34i	1.79298	−	1.03517i
$209$	4752.66	+	4118.20i	1.57296	+	1.36298i
$210$	−401.596	+	702.450i	−0.131966	+	0.230827i
$211$	398.425	+	2771.10i	0.129994	+	0.904127i	0.945557	+	0.325458i	$0.105518\pi$
$211$	398.425	+	2771.10i	0.129994	+	0.904127i	−0.815563	+	0.578669i	$0.803572\pi$
$212$	−888.646	−	632.802i	−0.287889	−	0.205005i
$213$	−423.629	+	538.688i	−0.136275	+	0.173288i
$214$	695.575	+	168.745i	0.222189	+	0.0539025i
$215$	−553.160	−	26.3503i	−0.175466	−	0.00835848i
$216$	1084.54	+	495.292i	0.341636	+	0.156020i
$217$	−2469.82	−	2826.01i	−0.772637	−	0.884064i
$218$	−3220.04	+	2790.18i	−1.00041	+	0.866856i
$219$	−2112.87	+	6104.75i	−0.651939	+	1.88366i
$220$	−255.926	−	268.407i	−0.0784297	−	0.0822547i
$221$	1850.08	−	1317.43i	0.563120	−	0.400996i
$222$	−172.704	+	3625.49i	−0.0522122	+	1.09607i
$223$	333.618	+	1136.20i	0.100183	+	0.341190i	0.994297	−	0.106649i	$-0.0340120\pi$
$223$	333.618	+	1136.20i	0.100183	+	0.341190i	−0.894114	+	0.447839i	$0.852194\pi$
$224$	−3082.73	−	2648.39i	−0.919526	−	0.789969i
$225$	2259.13	+	4946.81i	0.669372	+	1.46572i
$226$	−2004.22	−	2548.57i	−0.589906	−	0.750126i
$227$	119.978	+	2518.64i	0.0350802	+	0.736424i	0.946064	+	0.323981i	$0.105021\pi$
$227$	119.978	+	2518.64i	0.0350802	+	0.736424i	−0.910983	+	0.412443i	$0.864676\pi$
$228$	6313.50	−	2185.12i	1.83387	−	0.634708i
$229$	−438.553	−	759.596i	−0.126552	−	0.219194i	0.795787	−	0.605577i	$-0.207058\pi$
$229$	−438.553	−	759.596i	−0.126552	−	0.219194i	−0.922338	+	0.386383i	$0.873724\pi$
$230$	−132.855	+	555.484i	−0.0380877	+	0.159250i
$231$	−3317.92	−	6369.38i	−0.945036	−	1.81417i
$232$	−47.4449	+	54.7544i	−0.0134264	+	0.0154948i
$233$	702.136	+	361.976i	0.197418	+	0.101776i	0.554101	−	0.832449i	$-0.313062\pi$
$233$	702.136	+	361.976i	0.197418	+	0.101776i	−0.356683	+	0.934225i	$0.616092\pi$
$234$	4931.37	−	12318.0i	1.37767	−	3.44124i
$235$	12.4338	−	130.212i	0.00345144	−	0.0361451i
$236$	−1739.97	−	4346.23i	−0.479925	−	1.19879i
$237$	4506.60	−	1323.26i	1.23517	−	0.362679i
$238$	−1578.12	−	1113.71i	−0.429808	−	0.303325i
$239$	1578.71	−	3456.89i	0.427273	−	0.935597i	−0.566488	−	0.824070i	$-0.691698\pi$
$239$	1578.71	−	3456.89i	0.427273	−	0.935597i	0.993761	−	0.111528i	$-0.0355744\pi$
$240$	878.295	−	213.072i	0.236224	−	0.0573073i
$241$	3087.69	−	595.104i	0.825293	−	0.159062i	0.240918	−	0.970546i	$-0.422552\pi$
$241$	3087.69	−	595.104i	0.825293	−	0.159062i	0.584376	+	0.811483i	$0.301339\pi$
$242$	2848.04	−	548.914i	0.756524	−	0.145808i
$243$	−3553.63	+	862.101i	−0.938129	+	0.227588i
$244$	−1587.26	+	3475.62i	−0.416451	+	0.911900i
$245$	−64.0533	+	474.019i	−0.0167029	+	0.123608i
$246$	−11826.2	+	3472.48i	−3.06508	+	0.899990i
$247$	4112.22	+	10271.8i	1.05933	+	2.64607i
$248$	−158.316	+	1657.96i	−0.0405365	+	0.424517i
$249$	2663.60	−	6653.36i	0.677908	−	1.69333i
$250$	1141.64	+	588.556i	0.288814	+	0.148894i
$251$	125.357	−	144.669i	0.0315236	−	0.0363802i	−0.739769	−	0.672861i	$-0.765065\pi$
$251$	125.357	−	144.669i	0.0315236	−	0.0363802i	0.771292	+	0.636481i	$0.219611\pi$
$252$	−4731.73	−	205.284i	−1.18282	−	0.0513161i
$253$	−3510.14	−	3657.53i	−0.872256	−	0.908880i
$254$	2554.89	+	4425.21i	0.631135	+	1.09316i
$255$	312.327	−	108.098i	0.0767007	−	0.0265464i
$256$	254.998	+	5353.07i	0.0622554	+	1.30690i
$257$	−2900.73	−	3688.58i	−0.704057	−	0.895282i	0.294112	−	0.955771i	$-0.404976\pi$
$257$	−2900.73	−	3688.58i	−0.704057	−	0.895282i	−0.998169	+	0.0604895i	$0.980734\pi$
$258$	−5168.25	−	11316.9i	−1.24714	−	2.73085i
$259$	710.368	+	2024.64i	0.170425	+	0.485734i
$260$	−183.832	−	626.074i	−0.0438492	−	0.149336i
$261$	−18.5374	+	389.149i	−0.00439632	+	0.0922901i
$262$	289.169	−	205.916i	0.0681867	−	0.0485555i
$263$	686.929	+	720.430i	0.161056	+	0.168911i	0.799318	−	0.600909i	$-0.205194\pi$
$263$	686.929	+	720.430i	0.161056	+	0.168911i	−0.638261	+	0.769820i	$0.720346\pi$
$264$	−1042.35	+	3011.67i	−0.243001	+	0.702105i
$265$	198.694	−	172.169i	0.0460590	−	0.0399104i
$266$	7085.09	−	6192.09i	1.63314	−	1.42730i
$267$	−8281.33	−	3781.96i	−1.89816	−	0.866861i
$268$	813.016	+	38.7287i	0.185309	+	0.00882736i
$269$	1523.44	+	369.582i	0.345300	+	0.0837688i	0.404658	−	0.914468i	$-0.367390\pi$
$269$	1523.44	+	369.582i	0.345300	+	0.0837688i	−0.0593588	+	0.998237i	$0.518906\pi$
$270$	464.351	−	590.470i	0.104665	−	0.133092i
$271$	3544.52	+	2524.04i	0.794517	+	0.565773i	0.903659	−	0.428253i	$-0.140871\pi$
$271$	3544.52	+	2524.04i	0.794517	+	0.565773i	−0.109142	+	0.994026i	$0.534810\pi$
$272$	307.032	+	2135.46i	0.0684432	+	0.476033i
$273$	−53.6074	−	12635.6i	−0.0118845	−	2.80125i
$274$	314.075	+	272.148i	0.0692481	+	0.0600039i
$275$	−4897.72	+	2827.70i	−1.07398	+	0.620061i
$276$	−5229.65	+	1286.66i	−1.14054	+	0.280607i
$277$	−3844.72	+	6659.26i	−0.833961	+	1.44446i	0.0609130	+	0.998143i	$0.480599\pi$
$277$	−3844.72	+	6659.26i	−0.833961	+	1.44446i	−0.894874	+	0.446319i	$0.852735\pi$
$278$	1061.08	−	5505.42i	0.228919	−	1.18775i
$279$	4841.95	+	7534.22i	1.03900	+	1.61671i
$280$	172.379	−	123.856i	0.0367914	−	0.0264350i
$281$	7233.34	−	3303.36i	1.53561	−	0.701287i	0.545050	−	0.838403i	$-0.316511\pi$
$281$	7233.34	−	3303.36i	1.53561	−	0.701287i	0.990555	+	0.137116i	$0.0437833\pi$
$282$	2728.10	−	1092.17i	0.576086	−	0.230630i
$283$	−119.473	+	492.474i	−0.0250952	+	0.103444i	−0.982982	−	0.183703i	$-0.941192\pi$
$283$	−119.473	+	492.474i	−0.0250952	+	0.103444i	0.957887	+	0.287147i	$0.0927067\pi$
$284$	−417.742	+	215.361i	−0.0872832	+	0.0449976i
$285$	153.048	+	1602.79i	0.0318097	+	0.333126i
$286$	13239.3	+	3887.41i	2.73726	+	0.803731i
$287$	−5708.19	+	4528.29i	−1.17402	+	0.931347i
$288$	6350.82	+	7329.23i	1.29939	+	1.49958i
$289$	−972.280	−	4007.79i	−0.197899	−	0.815753i
$290$	26.4776	+	37.1826i	0.00536144	+	0.00752909i
$291$	−4859.56	−	9426.22i	−0.978942	−	1.89888i
$292$	−3057.28	+	3206.39i	−0.612719	+	0.642601i
$293$	366.096	−	2546.25i	0.0729950	−	0.507691i	−0.920220	−	0.391401i	$-0.871991\pi$
$293$	366.096	−	2546.25i	0.0729950	−	0.507691i	0.993215	−	0.116290i	$-0.0371003\pi$
$294$	−10124.7	+	3600.68i	−2.00845	+	0.714271i
$295$	1116.76	−	160.565i	0.220407	−	0.0316897i
$296$	436.298	−	846.300i	0.0856733	−	0.166183i
$297$	2180.66	+	6300.60i	0.426043	+	1.23097i
$298$	1543.57	+	891.178i	0.300055	+	0.173237i
$299$	−2540.53	−	8549.67i	−0.491381	−	1.65365i
$300$			6008.17i			1.15627i
$301$	−5344.26	−	5052.63i	−1.02338	−	0.967538i
$302$	2147.15	−	1379.89i	0.409120	−	0.262926i
$303$	168.791	−	132.739i	0.0320026	−	0.0251671i
$304$	−10462.4	−	999.040i	−1.97388	−	0.188483i
$305$	−723.814	−	569.214i	−0.135887	−	0.106863i
$306$	3335.75	+	3180.63i	0.623176	+	0.594197i
$307$	866.147	−	1347.75i	0.161021	−	0.250554i	−0.751363	−	0.659890i	$-0.770603\pi$
$307$	866.147	−	1347.75i	0.161021	−	0.250554i	0.912384	+	0.409335i	$0.134239\pi$
$308$	−255.225	−	4918.67i	−0.0472168	−	0.909959i
$309$	3726.59	−	12691.6i	0.686078	−	2.33657i
$310$	991.615	+	343.201i	0.181677	+	0.0628791i
$311$	1973.10	+	10237.4i	0.359757	+	1.86660i	0.485062	+	0.874480i	$0.338797\pi$
$311$	1973.10	+	10237.4i	0.359757	+	1.86660i	−0.125305	+	0.992118i	$0.539991\pi$
$312$	−4058.10	+	3869.39i	−0.736362	+	0.702120i
$313$	1574.36	−	150.333i	0.284307	−	0.0271481i	0.0480718	−	0.998844i	$-0.484692\pi$
$313$	1574.36	−	150.333i	0.284307	−	0.0271481i	0.236235	+	0.971696i	$0.424086\pi$
$314$	−3585.24	−	2304.10i	−0.644354	−	0.414101i
$315$	316.920	−	1096.52i	0.0566870	−	0.196133i
$316$	3188.35	+	458.415i	0.567591	+	0.0816072i
$317$	−1089.79	+	1530.39i	−0.193087	+	0.271153i	−0.899758	−	0.436390i	$-0.856257\pi$
$317$	−1089.79	+	1530.39i	−0.193087	+	0.271153i	0.706671	+	0.707543i	$0.250196\pi$
$318$	5483.32	+	2195.19i	0.966948	+	0.387108i
$319$	−404.687	+	19.2776i	−0.0710287	+	0.00338351i
$320$	274.323	+	52.8714i	0.0479222	+	0.00923625i
$321$	−1626.50			−0.282811
$322$	−6145.62	+	4445.96i	−1.06361	+	0.769452i
$323$	−3843.46			−0.662092
$324$	175.268	+	33.7802i	0.0300529	+	0.00579222i
$325$	−9938.93	+	473.449i	−1.69635	+	0.0808069i
$326$	−5767.29	−	2308.88i	−0.979818	−	0.392260i
$327$	5616.24	−	7886.91i	0.949782	−	1.33378i
$328$	3200.40	+	460.147i	0.538757	+	0.0774615i
$329$	1252.14	−	1204.10i	0.209826	−	0.201775i
$330$	1689.15	+	1085.55i	0.281772	+	0.181084i
$331$	7449.41	−	711.333i	1.23703	−	0.118122i	0.544034	−	0.839063i	$-0.316896\pi$
$331$	7449.41	−	711.333i	1.23703	−	0.118122i	0.692996	+	0.720941i	$0.256290\pi$
$332$	3557.14	−	3391.73i	0.588023	−	0.560679i
$333$	−968.967	−	5027.48i	−0.159457	−	0.827339i
$334$	2948.31	+	1020.42i	0.483008	+	0.167171i
$335$	−55.2633	+	188.210i	−0.00901301	+	0.0306955i
$336$	10691.6	+	5454.59i	1.73593	+	0.885632i
$337$	2179.44	−	3391.27i	0.352289	−	0.548173i	−0.619207	−	0.785228i	$-0.712546\pi$
$337$	2179.44	−	3391.27i	0.352289	−	0.548173i	0.971496	+	0.237055i	$0.0761822\pi$
$338$	11666.1	+	11123.6i	1.87737	+	1.79007i
$339$	5791.47	+	4554.46i	0.927875	+	0.729689i
$340$	225.636	+	21.5456i	0.0359907	+	0.00343669i
$341$	−7320.94	+	5757.25i	−1.16261	+	0.914289i
$342$	−18889.1	+	12139.3i	−2.98656	+	1.91934i
$343$	−4747.53	+	4220.73i	−0.747354	+	0.664426i
$344$			3263.66i			0.511525i
$345$	−4.20595	−	1297.90i	−0.000656350	−	0.202541i
$346$	−5647.10	−	3260.36i	−0.877428	−	0.506583i
$347$	3364.74	+	9721.78i	0.520544	+	1.50401i	0.832560	+	0.553936i	$0.186875\pi$
$347$	3364.74	+	9721.78i	0.520544	+	1.50401i	−0.312016	+	0.950077i	$0.601004\pi$
$348$	−197.229	+	382.571i	−0.0303810	+	0.0589310i
$349$	9384.23	−	1349.25i	1.43933	−	0.206945i	0.621957	−	0.783052i	$-0.286338\pi$
$349$	9384.23	−	1349.25i	1.43933	−	0.206945i	0.817374	+	0.576107i	$0.195429\pi$
$350$	3178.33	+	7842.48i	0.485396	+	1.19771i
$351$	−1669.43	+	11611.2i	−0.253868	+	1.76569i
$352$	−6959.58	+	7299.00i	−1.05383	+	1.10522i
$353$	−961.799	−	1865.63i	−0.145018	−	0.281296i	0.805128	−	0.593101i	$-0.202097\pi$
$353$	−961.799	−	1865.63i	−0.145018	−	0.281296i	−0.950146	+	0.311805i	$0.899066\pi$
$354$	14702.5	+	20646.7i	2.20742	+	3.09989i
$355$	−26.7032	−	110.072i	−0.00399228	−	0.0164564i
$356$	−4088.69	−	4718.61i	−0.608709	−	0.702488i
$357$	4081.76	+	1614.03i	0.605125	+	0.239282i
$358$	5510.46	+	1618.02i	0.813510	+	0.238868i
$359$	−1176.55	−	12321.4i	−0.172970	−	1.81142i	−0.499587	−	0.866264i	$-0.666515\pi$
$359$	−1176.55	−	12321.4i	−0.172970	−	1.81142i	0.326618	−	0.945157i	$-0.394091\pi$
$360$	−450.198	+	232.093i	−0.0659098	+	0.0339788i
$361$	2797.21	−	11530.3i	0.407816	−	1.68104i
$362$	−3952.53	+	1582.35i	−0.573868	+	0.229742i
$363$	−5995.48	+	2738.04i	−0.866890	+	0.395895i
$364$	3566.36	−	7897.74i	0.513539	−	1.13724i
$365$	−577.237	−	898.199i	−0.0827781	−	0.128805i
$366$	3915.00	−	20313.0i	0.559127	−	2.90102i
$367$	493.428	−	854.643i	0.0701819	−	0.121559i	−0.828799	−	0.559546i	$-0.810975\pi$
$367$	493.428	−	854.643i	0.0701819	−	0.121559i	0.898981	+	0.437988i	$0.144309\pi$
$368$	8324.30	+	1576.42i	1.17917	+	0.223306i
$369$	15057.2	−	8693.28i	2.12425	−	1.22643i
$370$	−453.365	−	392.843i	−0.0637008	−	0.0551971i
$371$	3491.55	−	14.8132i	0.488604	−	0.00207294i
$372$	1408.14	+	9793.80i	0.196259	+	1.36501i
$373$	−135.953	−	96.8117i	−0.0188723	−	0.0134389i	0.570582	−	0.821241i	$-0.306718\pi$
$373$	−135.953	−	96.8117i	−0.0188723	−	0.0134389i	−0.589454	+	0.807802i	$0.700657\pi$
$374$	−2962.91	+	3767.64i	−0.409648	+	0.520909i
$375$	−2836.49	−	688.126i	−0.390602	−	0.0947591i
$376$	−770.002	−	36.6797i	−0.105611	−	0.00503089i
$377$	−648.405	−	296.116i	−0.0885797	−	0.0404530i
$378$	9787.75	−	1929.54i	1.33182	−	0.262552i
$379$	−6078.13	+	5266.73i	−0.823780	+	0.713810i	−0.960945	−	0.276739i	$-0.910746\pi$
$379$	−6078.13	+	5266.73i	−0.823780	+	0.713810i	0.137165	+	0.990548i	$0.456201\pi$
$380$	−361.149	+	1043.47i	−0.0487541	+	0.140866i
$381$	−8012.98	−	8403.77i	−1.07747	−	1.13002i
$382$	−4627.78	+	3295.43i	−0.619837	+	0.441384i
$383$	34.2840	−	719.709i	0.00457397	−	0.0960193i	−0.995426	−	0.0955366i	$-0.969543\pi$
$383$	34.2840	−	719.709i	0.00457397	−	0.0960193i	1.00000		0.000482751i	$-0.000153664\pi$
$384$	−2404.97	−	8190.59i	−0.319605	−	1.08847i
$385$	1166.47	+	219.689i	0.154412	+	0.0290816i
$386$	−4300.66	−	9417.13i	−0.567092	−	1.24176i
$387$	10848.6	+	13795.1i	1.42497	+	1.81200i
$388$	−346.067	−	7264.83i	−0.0452806	−	0.950557i
$389$	5809.56	−	2010.71i	0.757214	−	0.262074i	0.0789361	−	0.996880i	$-0.474848\pi$
$389$	5809.56	−	2010.71i	0.757214	−	0.262074i	0.678278	+	0.734805i	$0.262726\pi$
$390$	1766.37	+	3059.44i	0.229342	+	0.397232i
$391$	3085.17	+	284.512i	0.399038	+	0.0367990i
$392$	2808.35	+	244.138i	0.361845	+	0.0314561i
$393$	−528.276	+	609.663i	−0.0678066	+	0.0782530i
$394$	−4650.79	−	2397.65i	−0.594678	−	0.306578i
$395$	−288.514	+	720.672i	−0.0367511	+	0.0917999i
$396$	−1117.18	+	11699.7i	−0.141769	+	1.48467i
$397$	1757.75	+	4390.64i	0.222214	+	0.555063i	0.997021	−	0.0771350i	$-0.0245772\pi$
$397$	1757.75	+	4390.64i	0.222214	+	0.555063i	−0.774807	+	0.632198i	$0.782153\pi$
$398$	−11419.7	+	3353.12i	−1.43823	+	0.422304i
$399$	−12329.2	+	17470.3i	−1.54695	+	2.19201i
$400$	3926.36	−	8597.52i	0.490794	−	1.07469i
$401$	2244.73	−	544.566i	0.279543	−	0.0678163i	−0.0935365	−	0.995616i	$-0.529817\pi$
$401$	2244.73	−	544.566i	0.279543	−	0.0678163i	0.373079	+	0.927800i	$0.378302\pi$
$402$	−4327.11	+	833.982i	−0.536857	+	0.103471i
$403$	−16090.3	+	3101.15i	−1.98887	+	0.383323i
$404$	143.114	−	34.7190i	0.0176242	−	0.00427558i
$405$	−17.8696	+	39.1289i	−0.00219246	+	0.00480082i
$406$	−55.0633	+	603.705i	−0.00673090	+	0.0737966i
$407$	5108.76	−	1500.07i	0.622191	−	0.182692i
$408$	−723.915	−	1808.25i	−0.0878411	−	0.219416i
$409$	565.277	−	5919.85i	0.0683402	−	0.715691i	−0.894760	−	0.446547i	$-0.852653\pi$
$409$	565.277	−	5919.85i	0.0683402	−	0.715691i	0.963100	−	0.269143i	$-0.0867405\pi$
$410$	757.116	−	1891.18i	0.0911982	−	0.227802i
$411$	−839.401	−	432.741i	−0.100741	−	0.0519357i
$412$	5940.52	−	6855.73i	0.710361	−	0.819800i
$413$	12639.3	+	8047.22i	1.50591	+	0.958784i
$414$	16061.0	−	8346.00i	1.90665	−	0.990782i
$415$	592.245	+	1025.80i	0.0700534	+	0.121336i
$416$	−16768.1	+	5803.51i	−1.97626	+	0.683992i
$417$	606.240	+	12726.6i	0.0711936	+	1.49454i
$418$	−14434.0	−	18354.3i	−1.68897	−	2.14770i
$419$	1620.37	+	3548.12i	0.188927	+	0.413692i	0.980265	−	0.197686i	$-0.0633427\pi$
$419$	1620.37	+	3548.12i	0.188927	+	0.413692i	−0.791338	+	0.611378i	$0.790615\pi$
$420$	821.738	−	956.506i	0.0954684	−	0.111126i
$421$	−394.694	−	1344.20i	−0.0456917	−	0.155612i	0.933487	−	0.358610i	$-0.116749\pi$
$421$	−394.694	−	1344.20i	−0.0456917	−	0.155612i	−0.979179	+	0.202999i	$0.934931\pi$
$422$	494.614	−	10383.2i	0.0570555	−	1.19774i
$423$	−3376.63	+	2404.48i	−0.388126	+	0.276383i
$424$	−1069.22	−	1121.36i	−0.122467	−	0.128439i
$425$	1130.48	−	3266.32i	0.129027	−	0.372800i
$426$	1923.05	−	1666.34i	0.218714	−	0.189517i
$427$	−2365.28	−	11998.1i	−0.268065	−	1.35979i
$428$	−1014.66	−	463.380i	−0.114592	−	0.0523326i
$429$	−31320.1	−	1491.96i	−3.52482	−	0.167908i
$430$	1998.27	+	484.774i	0.224105	+	0.0543672i
$431$	1487.20	−	1891.13i	0.166208	−	0.211351i	−0.695813	−	0.718223i	$-0.744956\pi$
$431$	1487.20	−	1891.13i	0.166208	−	0.211351i	0.862021	+	0.506872i	$0.169198\pi$
$432$	−9076.65	−	6463.45i	−1.01088	−	0.719845i
$433$	−750.953	−	5222.99i	−0.0833453	−	0.579679i	−0.988108	−	0.153763i	$-0.950861\pi$
$433$	−750.953	−	5222.99i	−0.0833453	−	0.579679i	0.904762	−	0.425916i	$-0.140048\pi$
$434$	7018.96	+	12039.0i	0.776316	+	1.33154i
$435$	−78.3931	−	67.9280i	−0.00864060	−	0.00748712i
$436$	5750.52	−	3320.06i	0.631651	−	0.364684i
$437$	−4890.33	+	14279.2i	−0.535323	+	1.56308i
$438$	11993.2	−	20772.8i	1.30835	−	2.26612i
$439$	364.079	−	1889.02i	0.0395821	−	0.205372i	−0.956754	−	0.290899i	$-0.906046\pi$
$439$	364.079	−	1889.02i	0.0395821	−	0.205372i	0.996336	+	0.0855278i	$0.0272576\pi$
$440$	−284.770	−	443.111i	−0.0308543	−	0.0480102i
$441$	12682.1	−	8303.16i	1.36941	−	0.896572i
$442$	−7671.00	+	3503.23i	−0.825503	+	0.376995i
$443$	6869.30	−	2750.05i	0.736727	−	0.294941i	0.0272105	−	0.999630i	$-0.491338\pi$
$443$	6869.30	−	2750.05i	0.736727	−	0.294941i	0.709517	+	0.704689i	$0.248913\pi$
$444$	1333.59	−	5497.12i	0.142543	−	0.587572i
$445$	1337.41	−	689.485i	0.142471	−	0.0734488i
$446$	−417.946	−	4376.93i	−0.0443729	−	0.464694i
$447$	−3886.23	−	1141.10i	−0.411213	−	0.120743i
$448$	2305.85	+	2906.66i	0.243172	+	0.306533i
$449$	−7862.25	−	9073.53i	−0.826376	−	0.953688i	0.173137	−	0.984898i	$-0.444610\pi$
$449$	−7862.25	−	9073.53i	−0.826376	−	0.953688i	−0.999513	+	0.0312092i	$0.990064\pi$
$450$	−4760.54	−	19623.2i	−0.498697	−	2.05566i
$451$	10487.9	+	14728.2i	1.09502	+	1.53774i
$452$	2315.36	+	4491.17i	0.240941	+	0.467361i
$453$	−4002.45	+	4197.65i	−0.415124	+	0.435370i
$454$	1332.41	−	9267.10i	0.137738	−	0.957989i
$455$	1647.04	+	1283.97i	0.169702	+	0.132294i
$456$	9392.16	−	1350.39i	0.964535	−	0.138679i
$457$	−2165.35	+	4200.19i	−0.221643	+	0.429927i	−0.973271	−	0.229660i	$-0.926238\pi$
$457$	−2165.35	+	4200.19i	−0.221643	+	0.429927i	0.751628	+	0.659587i	$0.229269\pi$
$458$	1065.17	+	3077.60i	0.108673	+	0.313989i
$459$	−3528.94	−	2037.43i	−0.358860	−	0.207188i
$460$	367.140	−	810.868i	0.0372130	−	0.0821889i
$461$		−	12956.5i		−	1.30899i	−0.756068	−	0.654494i	$-0.772882\pi$
$461$		−	12956.5i		−	1.30899i	0.756068	−	0.654494i	$-0.227118\pi$
$462$	7621.18	+	25553.8i	0.767466	+	2.57331i
$463$	−5860.21	+	3766.13i	−0.588222	+	0.378027i	−0.800635	−	0.599153i	$-0.795504\pi$
$463$	−5860.21	+	3766.13i	−0.588222	+	0.378027i	0.212413	+	0.977180i	$0.431868\pi$
$464$	532.240	−	418.559i	0.0532514	−	0.0418774i
$465$	−2373.73	−	226.664i	−0.236730	−	0.0226049i
$466$	−2305.58	−	1813.13i	−0.229193	−	0.180239i
$467$	9585.54	+	9139.80i	0.949820	+	0.905652i	0.995638	−	0.0932979i	$-0.0297409\pi$
$467$	9585.54	+	9139.80i	0.949820	+	0.905652i	−0.0458179	+	0.998950i	$0.514589\pi$
$468$	−11179.5	+	17395.6i	−1.10421	+	1.71819i
$469$	−2185.51	+	1417.68i	−0.215176	+	0.139579i
$470$	−136.832	+	466.007i	−0.0134289	+	0.0457347i
$471$	9152.00	+	3167.54i	0.895333	+	0.309878i
$472$	−1258.35	−	6528.94i	−0.122712	−	0.636692i
$473$	−13208.5	+	12594.3i	−1.28399	+	1.22429i
$474$	−17360.6	+	1657.74i	−1.68228	+	0.160638i
$475$	14165.2	+	9103.43i	1.36830	+	0.879355i
$476$	2086.50	+	2169.75i	0.200913	+	0.208929i
$477$	−8246.91	−	1185.73i	−0.791614	−	0.113817i
$478$	−8185.01	+	11494.2i	−0.783208	+	1.09986i
$479$	1600.61	+	640.789i	0.152680	+	0.0611240i	0.446744	−	0.894662i	$-0.352584\pi$
$479$	1600.61	+	640.789i	0.152680	+	0.0611240i	−0.294064	+	0.955786i	$0.595008\pi$
$480$	−2579.17	+	122.861i	−0.245255	+	0.0116830i
$481$	9198.61	+	1772.89i	0.871976	+	0.168060i
$482$	−11675.7			−1.10335
$483$	11190.0	−	13110.9i	1.05416	−	1.23513i
$484$	−4520.22			−0.424514
$485$	1721.10	+	331.715i	0.161137	+	0.0310565i
$486$	13562.1	−	646.041i	1.26582	−	0.0602984i
$487$	−4775.84	−	1911.96i	−0.444382	−	0.177904i	0.138670	−	0.990339i	$-0.455717\pi$
$487$	−4775.84	−	1911.96i	−0.444382	−	0.177904i	−0.583052	+	0.812435i	$0.698141\pi$
$488$	−3147.80	+	4420.47i	−0.291996	+	0.410052i
$489$	13973.4	+	2009.07i	1.29222	+	0.185794i
$490$	566.624	−	1683.23i	0.0522398	−	0.155185i
$491$	−5476.94	−	3519.81i	−0.503403	−	0.323517i	0.264173	−	0.964475i	$-0.414901\pi$
$491$	−5476.94	−	3519.81i	−0.503403	−	0.323517i	−0.767576	+	0.640958i	$0.778537\pi$
$492$	19121.7	−	1825.90i	1.75218	−	0.167313i
$493$	179.207	−	170.873i	0.0163713	−	0.0156100i
$494$	−7774.89	−	40340.0i	−0.708115	−	3.67405i
$495$	−2676.61	−	926.384i	−0.243040	−	0.0841169i
$496$	4385.27	−	14934.9i	0.396985	−	1.35201i
$497$	683.596	−	1339.92i	0.0616971	−	0.120933i
$498$	−14386.6	+	22386.0i	−1.29454	+	2.01434i
$499$	−242.334	−	231.065i	−0.0217402	−	0.0207292i	0.679131	−	0.734017i	$-0.262357\pi$
$499$	−242.334	−	231.065i	−0.0217402	−	0.0207292i	−0.700871	+	0.713288i	$0.747205\pi$
$500$	−1573.45	−	1237.37i	−0.140734	−	0.110674i
$501$	−7057.69	−	673.928i	−0.629370	−	0.0600975i
$502$	−558.699	+	439.366i	−0.0496733	+	0.0390635i
$503$	−1521.97	+	978.109i	−0.134913	+	0.0867032i	−0.606356	−	0.795193i	$-0.707369\pi$
$503$	−1521.97	+	978.109i	−0.134913	+	0.0867032i	0.471443	+	0.881896i	$0.343733\pi$
$504$	−6543.70	−	1558.12i	−0.578333	−	0.137707i
$505$			35.4901i			0.00312731i
$506$	10227.6	+	15801.6i	0.898562	+	1.38828i
$507$	−31722.6	−	18315.0i	−2.77879	−	1.60434i
$508$	−2604.56	−	7525.38i	−0.227478	−	0.657254i
$509$	1239.53	−	2404.35i	0.107939	−	0.209373i	−0.828679	−	0.559724i	$-0.810907\pi$
$509$	1239.53	−	2404.35i	0.107939	−	0.209373i	0.936619	+	0.350351i	$0.113938\pi$
$510$	−1214.68	+	174.645i	−0.105465	+	0.0151635i
$511$	1958.40	−	14043.6i	0.169539	−	1.21576i
$512$	1680.03	−	11684.9i	0.145015	−	1.00860i
$513$	13698.8	−	14366.9i	1.17898	−	1.23648i
$514$	7983.92	+	15486.6i	0.685127	+	1.32896i
$515$	1268.10	+	1780.80i	0.108504	+	0.152372i
$516$	4571.12	+	18842.4i	0.389986	+	1.60754i
$517$	−2822.96	−	3257.86i	−0.240142	−	0.277139i
$518$	−1167.24	−	7880.87i	−0.0990073	−	0.668466i
$519$	14217.7	+	4174.69i	1.20248	+	0.353080i
$520$	−88.0915	−	922.536i	−0.00742898	−	0.0777998i
$521$	5449.87	−	2809.60i	0.458278	−	0.236259i	−0.213599	−	0.976921i	$-0.568519\pi$
$521$	5449.87	−	2809.60i	0.458278	−	0.236259i	0.671877	+	0.740663i	$0.265488\pi$
$522$	341.039	−	1405.78i	0.0285956	−	0.117873i
$523$	−16017.0	+	6412.26i	−1.33915	+	0.536115i	−0.927021	−	0.375009i	$-0.877639\pi$
$523$	−16017.0	+	6412.26i	−1.33915	+	0.536115i	−0.412130	+	0.911125i	$0.635215\pi$
$524$	−503.245	+	229.824i	−0.0419549	+	0.0191601i
$525$	−11220.6	−	15616.4i	−0.932771	−	1.29820i
$526$	−1998.25	−	3109.34i	−0.165642	−	0.257745i
$527$	1077.25	−	5589.31i	0.0890433	−	0.462000i
$528$	14892.3	−	25794.2i	1.22747	−	2.12603i
$529$	4982.52	−	11100.0i	0.409511	−	0.912305i
$530$	−845.405	+	488.095i	−0.0692869	+	0.0400028i
$531$	−27021.4	−	23414.2i	−2.20834	−	1.91354i
$532$	−12668.5	+	7386.02i	−1.03243	+	0.601926i
$533$	4527.27	+	31487.8i	0.367913	+	2.55889i
$534$	27535.6	+	19608.0i	2.23142	+	1.58899i
$535$	166.175	−	211.308i	0.0134287	−	0.0170760i
$536$	1123.42	+	272.540i	0.0905308	+	0.0219625i
$537$	−13036.0	−	620.983i	−1.04757	−	0.0499021i
$538$	−5294.64	−	2417.98i	−0.424290	−	0.193767i
$539$	9849.24	+	12307.9i	0.787081	+	0.983564i
$540$	−884.744	+	766.635i	−0.0705061	+	0.0610939i
$541$	734.328	−	2121.70i	0.0583572	−	0.168612i	−0.912054	−	0.410070i	$-0.865504\pi$
$541$	734.328	−	2121.70i	0.0583572	−	0.168612i	0.970411	+	0.241458i	$0.0776255\pi$
$542$	−11149.4	−	11693.2i	−0.883596	−	0.926689i
$543$	7880.95	−	5612.00i	0.622844	−	0.443525i
$544$	293.285	−	6156.81i	0.0231149	−	0.485241i
$545$	450.840	+	1535.42i	0.0354346	+	0.120679i
$546$	−8683.51	+	46106.1i	−0.680623	+	3.61384i
$547$	−3276.44	−	7174.40i	−0.256107	−	0.560796i	0.737283	−	0.675584i	$-0.236108\pi$
$547$	−3276.44	−	7174.40i	−0.256107	−	0.560796i	−0.993390	+	0.114788i	$0.963381\pi$
$548$	−400.359	−	509.098i	−0.0312089	−	0.0396854i
$549$	1388.50	+	29148.2i	0.107941	+	2.26596i
$550$	19843.7	−	6867.99i	1.53844	−	0.532458i
$551$	603.135	+	1044.66i	0.0466323	+	0.0807696i
$552$	−7639.11	+	388.711i	−0.589026	+	0.0299722i
$553$	−9143.25	+	4762.88i	−0.703093	+	0.366254i
$554$	18697.0	−	21577.5i	1.43386	−	1.65477i
$555$	1211.67	+	624.658i	0.0926710	+	0.0477752i
$556$	−3247.53	+	8111.94i	−0.247709	+	0.618746i
$557$	1693.18	−	17731.8i	0.128801	−	1.34887i	−0.667791	−	0.744349i	$-0.732760\pi$
$557$	1693.18	−	17731.8i	0.128801	−	1.34887i	0.796592	−	0.604518i	$-0.206634\pi$
$558$	−12359.1	−	30871.6i	−0.937641	−	2.34211i
$559$	−30809.6	+	9046.51i	−2.33114	+	0.684484i
$560$	−1800.96	+	831.724i	−0.135901	+	0.0627621i
$561$	4524.72	−	9907.76i	0.340524	−	0.745644i
$562$	−28693.5	+	6960.97i	−2.15367	+	0.522475i
$563$	8725.77	−	1681.75i	0.653192	−	0.125893i	0.148120	−	0.988969i	$-0.452678\pi$
$563$	8725.77	−	1681.75i	0.653192	−	0.125893i	0.505073	+	0.863077i	$0.331466\pi$
$564$	−4496.91	+	866.709i	−0.335734	+	0.0647075i
$565$	−1183.39	+	287.088i	−0.0881164	+	0.0213768i
$566$	781.649	−	1711.57i	0.0580480	−	0.127107i
$567$	−518.643	+	239.521i	−0.0384144	+	0.0177406i
$568$	−640.470	+	188.059i	−0.0473126	+	0.0138922i
$569$	−5217.12	−	13031.7i	−0.384381	−	0.960138i	−0.986798	−	0.161956i	$-0.948220\pi$
$569$	−5217.12	−	13031.7i	−0.384381	−	0.960138i	0.602416	−	0.798182i	$-0.294205\pi$
$570$	568.270	−	5951.20i	0.0417583	−	0.437313i
$571$	−7020.49	+	17536.3i	−0.514533	+	1.28524i	0.412737	+	0.910850i	$0.364573\pi$
$571$	−7020.49	+	17536.3i	−0.514533	+	1.28524i	−0.927271	+	0.374392i	$0.877852\pi$
$572$	−19113.4	−	9853.64i	−1.39715	−	0.720282i
$573$	8454.39	−	9756.89i	0.616383	−	0.711343i
$574$	23993.7	−	12498.7i	1.74473	−	0.908861i
$575$	−10696.6	−	8355.96i	−0.775792	−	0.606031i
$576$	−4426.70	−	7667.27i	−0.320219	−	0.554635i
$577$	24180.0	−	8368.78i	1.74459	−	0.603807i	0.746485	−	0.665402i	$-0.231740\pi$
$577$	24180.0	−	8368.78i	1.74459	−	0.603807i	0.998101	+	0.0615949i	$0.0196187\pi$
$578$	728.607	+	15295.3i	0.0524326	+	1.10070i
$579$	14542.7	+	18492.5i	1.04382	+	1.32733i
$580$	−29.5518	−	64.7094i	−0.00211564	−	0.00463260i
$581$	−2911.49	+	15458.9i	−0.207899	+	1.10386i
$582$	11093.8	+	37782.1i	0.790127	+	2.69093i
$583$	412.268	−	8654.58i	0.0292872	−	0.614813i
$584$	−5125.53	+	3649.87i	−0.363178	+	0.258618i
$585$	−3438.91	−	3606.62i	−0.243045	−	0.254898i
$586$	−3124.00	+	9026.20i	−0.220224	+	0.636295i
$587$	1472.26	−	1275.72i	0.103521	−	0.0897010i	−0.601563	−	0.798826i	$-0.705455\pi$
$587$	1472.26	−	1275.72i	0.103521	−	0.0897010i	0.705083	+	0.709124i	$0.250910\pi$
$588$	16555.7	−	2523.91i	1.16113	−	0.177014i
$589$	25224.0	+	11519.4i	1.76458	+	0.805855i
$590$	−4184.44	−	199.329i	−0.291984	−	0.0139089i
$591$	11555.2	+	2803.27i	0.804263	+	0.195112i
$592$	−5500.70	+	6994.71i	−0.381888	+	0.485610i
$593$	20773.2	+	14792.5i	1.43854	+	1.02438i	0.991534	+	0.129845i	$0.0414479\pi$
$593$	20773.2	+	14792.5i	1.43854	+	1.02438i	0.447002	+	0.894533i	$0.352492\pi$
$594$	−3523.13	−	24503.9i	−0.243360	−	1.69260i
$595$	−626.709	+	365.384i	−0.0431808	+	0.0251753i
$596$	−2099.26	−	1819.02i	−0.144277	−	0.125017i
$597$	23422.6	−	13523.0i	1.60573	−	0.927071i
$598$	3254.79	+	32956.7i	0.222572	+	2.25368i
$599$	−5093.75	+	8822.63i	−0.347454	+	0.601808i	−0.985796	−	0.167944i	$-0.946287\pi$
$599$	−5093.75	+	8822.63i	−0.347454	+	0.601808i	0.638342	+	0.769753i	$0.279620\pi$
$600$	−1614.92	+	8379.01i	−0.109882	+	0.570120i
$601$	9580.94	+	14908.2i	0.650274	+	1.01185i	0.997260	+	0.0739757i	$0.0235687\pi$
$601$	9580.94	+	14908.2i	0.650274	+	1.01185i	−0.346986	+	0.937870i	$0.612795\pi$
$602$	15934.3	+	22176.9i	1.07880	+	1.50144i
$603$	5654.50	−	2582.32i	0.381872	−	0.174395i
$604$	−3692.74	+	1478.35i	−0.248767	+	0.0995913i
$605$	256.825	−	1058.65i	0.0172585	−	0.0711406i
$606$	−708.675	+	365.347i	−0.0475049	+	0.0244905i
$607$	714.260	+	7480.07i	0.0477610	+	0.500176i	0.987426	+	0.158080i	$0.0505305\pi$
$607$	714.260	+	7480.07i	0.0477610	+	0.500176i	−0.939665	+	0.342095i	$0.888863\pi$
$608$	28811.0	+	8459.69i	1.92178	+	0.564285i
$609$	−201.833	−	1362.71i	−0.0134297	−	0.0906731i
$610$	2238.99	+	2583.93i	0.148613	+	0.171509i
$611$	−1788.10	−	7370.65i	−0.118394	−	0.488027i
$612$	−4166.57	−	5851.12i	−0.275202	−	0.386467i
$613$	−10571.7	−	20506.3i	−0.696554	−	1.35113i	−0.925896	−	0.377780i	$-0.876688\pi$
$613$	−10571.7	−	20506.3i	−0.696554	−	1.35113i	0.229342	−	0.973346i	$-0.426343\pi$
$614$	−4104.97	+	4305.17i	−0.269809	+	0.282968i
$615$	−658.803	+	4582.08i	−0.0431960	+	0.300435i
$616$	966.141	−	6928.19i	0.0631931	−	0.453157i
$617$	−14791.4	+	2126.69i	−0.965123	+	0.138764i	−0.606818	−	0.794841i	$-0.707554\pi$
$617$	−14791.4	+	2126.69i	−0.965123	+	0.138764i	−0.358305	+	0.933604i	$0.616645\pi$
$618$	−22505.2	+	43654.0i	−1.46487	+	2.84146i
$619$	6084.64	+	17580.4i	0.395093	+	1.14155i	0.950703	+	0.310103i	$0.100363\pi$
$619$	6084.64	+	17580.4i	0.395093	+	1.14155i	−0.555610	+	0.831443i	$0.687515\pi$
$620$	−1416.23	−	817.663i	−0.0917377	−	0.0529648i
$621$	−12059.6	+	10518.3i	−0.779284	+	0.679687i
$622$		−	38711.5i		−	2.49548i
$623$	19439.5	+	4628.74i	1.25013	+	0.297667i
$624$	44084.5	−	28331.4i	2.82819	−	1.81757i
$625$	−11711.8	+	9210.26i	−0.749555	+	0.589457i
$626$	−5845.65	−	558.192i	−0.373225	−	0.0356387i
$627$	41709.1	+	32800.4i	2.65662	+	2.08919i
$628$	4806.89	+	4583.36i	0.305439	+	0.291236i
$629$	−1759.33	+	2737.56i	−0.111524	+	0.173535i
$630$	−1925.98	+	3775.13i	−0.121799	+	0.238738i
$631$	−6605.46	+	22496.1i	−0.416734	+	1.41927i	0.437426	+	0.899254i	$0.355890\pi$
$631$	−6605.46	+	22496.1i	−0.416734	+	1.41927i	−0.854160	+	0.520011i	$0.825928\pi$
$632$	4323.26	+	1496.29i	0.272105	+	0.0941763i
$633$	4470.49	+	23195.1i	0.280705	+	1.45643i
$634$	5048.69	−	4813.92i	0.316261	−	0.301554i
$635$	1910.44	−	182.425i	0.119392	−	0.0114005i
$636$	−7743.63	−	4976.53i	−0.482790	−	0.310271i
$637$	5479.74	+	27188.1i	0.340840	+	1.69110i
$638$	1489.01	+	214.087i	0.0923987	+	0.0132849i
$639$	−2082.07	+	2923.86i	−0.128897	+	0.181011i
$640$	1309.80	+	524.363i	0.0808973	+	0.0323864i
$641$	−16438.3	+	783.053i	−1.01291	+	0.0482507i	−0.547466	−	0.836828i	$-0.684407\pi$
$641$	−16438.3	+	783.053i	−1.01291	+	0.0482507i	−0.465441	+	0.885079i	$0.654104\pi$
$642$	5930.10	+	1142.93i	0.364552	+	0.0702617i
$643$	−12125.8			−0.743692			−0.371846	−	0.928294i	$-0.621275\pi$
$643$	−12125.8			−0.743692			−0.371846	+	0.928294i	$0.621275\pi$
$644$	10715.9	−	4991.02i	0.655690	−	0.305394i
$645$	−4672.65			−0.285249
$646$	14013.0	+	2700.78i	0.853457	+	0.164490i
$647$	−3072.55	+	146.364i	−0.186699	+	0.00889358i	−0.140723	−	0.990049i	$-0.544943\pi$
$647$	−3072.55	+	146.364i	−0.186699	+	0.00889358i	−0.0459760	+	0.998943i	$0.514640\pi$
$648$	235.350	+	94.2199i	0.0142676	+	0.00571189i
$649$	21567.7	−	30287.6i	1.30448	−	1.83188i
$650$	36569.3	+	5257.87i	2.20672	+	0.317278i
$651$	−21950.4	−	22826.2i	−1.32151	−	1.37424i
$652$	8144.65	+	5234.25i	0.489216	+	0.314400i
$653$	11872.9	−	1133.72i	0.711519	−	0.0679419i	0.266981	−	0.963702i	$-0.413974\pi$
$653$	11872.9	−	1133.72i	0.711519	−	0.0679419i	0.444538	+	0.895760i	$0.353368\pi$
$654$	−26018.5	+	24808.6i	−1.55566	+	1.48332i
$655$	−25.2325	−	130.919i	−0.00150522	−	0.00780981i
$656$	−28555.8	−	9883.25i	−1.69957	−	0.588226i
$657$	−9532.60	+	32465.0i	−0.566061	+	1.92783i
$658$	−5411.34	+	3510.18i	−0.320602	+	0.207965i
$659$	−12136.3	+	18884.5i	−0.717395	+	1.11629i	0.270733	+	0.962655i	$0.412734\pi$
$659$	−12136.3	+	18884.5i	−0.717395	+	1.11629i	−0.988128	+	0.153634i	$0.950902\pi$
$660$	−2264.72	−	2159.41i	−0.133567	−	0.127356i
$661$	−9798.87	−	7705.92i	−0.576599	−	0.453442i	0.286782	−	0.957996i	$-0.407415\pi$
$661$	−9798.87	−	7705.92i	−0.576599	−	0.453442i	−0.863380	+	0.504554i	$0.831657\pi$
$662$	−27659.9	−	2641.20i	−1.62392	−	0.155065i
$663$	15063.7	−	11846.2i	0.882389	−	0.693918i
$664$	5872.45	−	3774.00i	0.343216	−	0.220572i
$665$	−1010.04	−	3386.65i	−0.0588985	−	0.197487i
$666$			19010.7i			1.10608i
$667$	−406.810	−	883.204i	−0.0236158	−	0.0512710i
$668$	−4210.81	−	2431.11i	−0.243894	−	0.140812i
$669$	3267.91	+	9442.02i	0.188856	+	0.545664i
$670$	333.740	−	647.366i	0.0192440	−	0.0373282i
$671$	−30037.5	+	4318.75i	−1.72815	+	0.248470i
$672$	−27044.8	−	21083.2i	−1.55249	−	1.21027i
$673$	2004.98	−	13944.9i	0.114838	−	0.798719i	−0.848262	−	0.529577i	$-0.822351\pi$
$673$	2004.98	−	13944.9i	0.114838	−	0.798719i	0.963100	−	0.269142i	$-0.0867401\pi$
$674$	−10329.1	+	10832.9i	−0.590300	+	0.619089i
$675$	8180.26	+	15867.5i	0.466457	+	0.904800i
$676$	−14571.7	−	20463.1i	−0.829067	−	1.16426i
$677$	−6810.02	−	28071.3i	−0.386603	−	1.59360i	−0.749654	−	0.661830i	$-0.769780\pi$
$677$	−6810.02	−	28071.3i	−0.386603	−	1.59360i	0.363051	−	0.931769i	$-0.381735\pi$
$678$	−17914.9	−	20674.9i	−1.01478	−	1.17111i
$679$	14466.9	+	18236.4i	0.817657	+	1.03071i
$680$	308.881	+	90.6957i	0.0174192	+	0.00511473i
$681$	2022.36	+	21179.1i	0.113799	+	1.19176i
$682$	30737.2	−	15846.1i	1.72579	−	0.889707i
$683$	−7347.53	+	30286.9i	−0.411633	+	1.69677i	0.268163	+	0.963374i	$0.413583\pi$
$683$	−7347.53	+	30286.9i	−0.411633	+	1.69677i	−0.679796	+	0.733401i	$0.737932\pi$
$684$	32486.1	−	13005.5i	1.81599	−	0.727012i
$685$	141.979	−	64.8397i	0.00791933	−	0.00361664i
$686$	20275.0	−	12052.4i	1.12843	−	0.670793i
$687$	−4001.12	−	6225.86i	−0.222201	−	0.345751i
$688$	5772.43	−	29950.2i	0.319872	−	1.65965i
$689$	7622.13	−	13201.9i	0.421452	−	0.729976i
$690$	−896.692	+	4735.00i	−0.0494732	+	0.261244i
$691$	21931.0	−	12661.9i	1.20737	−	0.697076i	0.245187	−	0.969476i	$-0.421151\pi$
$691$	21931.0	−	12661.9i	1.20737	−	0.697076i	0.962184	+	0.272399i	$0.0878172\pi$
$692$	7680.10	+	6654.84i	0.421898	+	0.365577i
$693$	−18945.9	−	32496.1i	−1.03852	−	1.78128i
$694$	−5436.16	−	37809.3i	−0.297340	−	2.06804i
$695$	−1715.32	−	1221.47i	−0.0936198	−	0.0666664i
$696$	−377.887	+	480.522i	−0.0205801	+	0.0261697i
$697$	−10739.0	−	2605.25i	−0.583598	−	0.141579i
$698$	−35162.4	−	1674.99i	−1.90676	−	0.0908299i
$699$	6062.98	+	2768.87i	0.328073	+	0.149826i
$700$	−2550.70	−	12938.7i	−0.137725	−	0.698623i
$701$	−26128.3	+	22640.3i	−1.40778	+	1.21984i	−0.465482	+	0.885057i	$0.654119\pi$
$701$	−26128.3	+	22640.3i	−1.40778	+	1.21984i	−0.942294	+	0.334787i	$0.891336\pi$
$702$	14245.7	−	41160.3i	0.765912	−	2.21296i
$703$	−10939.7	−	11473.2i	−0.586911	−	0.615535i
$704$	7499.73	−	5340.53i	0.401501	−	0.285908i
$705$	52.5152	−	1102.43i	0.00280544	−	0.0588935i
$706$	2195.68	+	7477.81i	0.117048	+	0.398627i
$707$	−307.141	+	357.513i	−0.0163384	+	0.0190179i
$708$	−16409.5	−	35931.8i	−0.871054	−	1.90734i
$709$	−9429.33	−	11990.4i	−0.499473	−	0.635131i	0.469313	−	0.883032i	$-0.344502\pi$
$709$	−9429.33	−	11990.4i	−0.499473	−	0.635131i	−0.968785	+	0.247901i	$0.920259\pi$
$710$	20.0109	+	420.080i	0.00105774	+	0.0222047i
$711$	23247.6	−	8046.08i	1.22624	−	0.424404i
$712$	−4433.80	−	7679.57i	−0.233376	−	0.404219i
$713$	−19394.7	−	11113.9i	−1.01871	−	0.583758i
$714$	−13747.6	−	8752.87i	−0.720577	−	0.458779i
$715$	3393.71	−	3916.55i	0.177507	−	0.204854i
$716$	−7955.38	−	4101.28i	−0.415232	−	0.214067i
$717$	11917.6	−	29768.8i	0.620741	−	1.55054i
$718$	−4368.58	+	45749.8i	−0.227067	+	2.37795i
$719$	−3631.64	−	9071.41i	−0.188369	−	0.470524i	0.803879	−	0.594792i	$-0.202766\pi$
$719$	−3631.64	−	9071.41i	−0.188369	−	0.470524i	−0.992249	+	0.124269i	$0.960342\pi$
$720$	4541.91	−	1333.63i	0.235093	−	0.0690296i
$721$	−2637.18	+	28913.6i	−0.136219	+	1.49348i
$722$	−18300.7	+	40072.9i	−0.943325	+	2.06559i
$723$	25784.4	−	6255.22i	1.32632	−	0.321762i
$724$	6515.21	−	1255.70i	0.334442	−	0.0644584i
$725$	−1065.19	+	205.299i	−0.0545660	+	0.0105167i
$726$	23783.1	−	5769.72i	1.21580	−	0.294951i
$727$	−729.804	+	1598.05i	−0.0372310	+	0.0815246i	−0.927334	−	0.374235i	$-0.877905\pi$
$727$	−729.804	+	1598.05i	−0.0372310	+	0.0815246i	0.890103	+	0.455760i	$0.150632\pi$
$728$	7096.47	−	10055.6i	0.361281	−	0.511931i
$729$	−30403.2	+	8927.19i	−1.54464	+	0.453548i
$730$	1473.41	+	3680.39i	0.0747030	+	0.186599i
$731$	1060.28	−	11103.7i	0.0536467	−	0.561813i
$732$	−11982.2	+	29930.0i	−0.605019	+	1.51126i
$733$	15562.2	+	8022.87i	0.784179	+	0.404272i	0.803322	−	0.595545i	$-0.203064\pi$
$733$	15562.2	+	8022.87i	0.784179	+	0.404272i	−0.0191436	+	0.999817i	$0.506094\pi$
$734$	−2399.56	+	2769.24i	−0.120667	+	0.139257i
$735$	−349.537	+	4020.78i	−0.0175413	+	0.201781i
$736$	−22500.6	−	8923.39i	−1.12688	−	0.446903i
$737$	3232.23	+	5598.39i	0.161548	+	0.279809i
$738$	−61006.2	+	21114.5i	−3.04291	+	1.05316i
$739$	−620.753	−	13031.2i	−0.0308996	−	0.648662i	−0.960196	−	0.279327i	$-0.909889\pi$
$739$	−620.753	−	13031.2i	−0.0308996	−	0.648662i	0.929296	−	0.369335i	$-0.120414\pi$
$740$	577.915	+	734.878i	0.0287089	+	0.0365063i
$741$	38782.0	+	84920.7i	1.92266	+	4.21004i
$742$	−12740.4	−	2399.49i	−0.630341	−	0.118717i
$743$	−6330.13	−	21558.4i	−0.312557	−	1.06447i	−0.954622	−	0.297821i	$-0.903740\pi$
$743$	−6330.13	−	21558.4i	−0.312557	−	1.06447i	0.642065	−	0.766650i	$-0.278078\pi$
$744$	−668.662	+	14036.9i	−0.0329494	+	0.691692i
$745$	545.291	−	388.300i	0.0268160	−	0.0190956i
$746$	427.646	+	448.502i	0.0209882	+	0.0220118i
$747$	12277.2	−	35472.5i	0.601336	−	1.73745i
$748$	5645.33	−	4891.71i	0.275954	−	0.239116i
$749$	3502.69	−	690.513i	0.170875	−	0.0336860i
$750$	9858.11	+	4502.05i	0.479956	+	0.219189i
$751$	−10503.4	−	500.338i	−0.510352	−	0.0243111i	−0.209173	−	0.977879i	$-0.567077\pi$
$751$	−10503.4	−	500.338i	−0.510352	−	0.0243111i	−0.301179	+	0.953568i	$0.597380\pi$
$752$	7001.34	+	1698.51i	0.339512	+	0.0823646i
$753$	998.433	−	1269.61i	0.0483199	−	0.0614438i
$754$	2155.96	+	1535.25i	0.104132	+	0.0741519i
$755$	−136.423	−	948.842i	−0.00657608	−	0.0457376i
$756$	−15547.2	+	65.9601i	−0.747944	+	0.00317321i
$757$	−23162.6	−	20070.5i	−1.11210	−	0.963640i	−0.112550	−	0.993646i	$-0.535902\pi$
$757$	−23162.6	−	20070.5i	−1.11210	−	0.963640i	−0.999550	+	0.0300061i	$0.990447\pi$
$758$	25861.4	−	14931.1i	1.23922	−	0.715462i
$759$	−31052.2	−	29416.6i	−1.48501	−	1.40679i
$760$	−784.131	+	1358.16i	−0.0374256	+	0.0648230i
$761$	5485.05	−	28459.1i	0.261278	−	1.35564i	−0.579814	−	0.814749i	$-0.696875\pi$
$761$	5485.05	−	28459.1i	0.261278	−	1.35564i	0.841092	−	0.540892i	$-0.181913\pi$
$762$	23309.5	+	36270.2i	1.10815	+	1.72432i
$763$	−8746.34	+	19368.9i	−0.414992	+	0.919004i
$764$	8053.80	−	3678.04i	0.381382	−	0.174171i
$765$	1607.08	−	643.376i	0.0759529	−	0.0304070i
$766$	−630.733	+	2599.92i	−0.0297511	+	0.122636i
$767$	58146.5	−	29976.6i	2.73735	−	1.41120i
$768$	4298.29	+	45013.7i	0.201954	+	2.11496i
$769$	29790.8	+	8747.38i	1.39699	+	0.410193i	0.891649	−	0.452727i	$-0.149549\pi$
$769$	29790.8	+	8747.38i	1.39699	+	0.410193i	0.505340	+	0.862920i	$0.331367\pi$
$770$	−4098.47	−	1620.64i	−0.191817	−	0.0758492i
$771$	−25928.5	−	29923.0i	−1.21114	−	1.39773i
$772$	3803.77	+	15679.4i	0.177333	+	0.730975i
$773$	−7793.47	−	10944.4i	−0.362628	−	0.509240i	0.592445	−	0.805611i	$-0.298163\pi$
$773$	−7793.47	−	10944.4i	−0.362628	−	0.509240i	−0.955073	+	0.296371i	$0.904224\pi$
$774$	−29859.3	−	57919.0i	−1.38666	−	2.68974i
$775$	−17208.8	+	18048.1i	−0.797624	+	0.836524i
$776$	1470.07	−	10224.6i	0.0680058	−	0.472990i
$777$	6799.88	+	16778.6i	0.313957	+	0.774684i
$778$	−22594.2	+	3248.55i	−1.04118	+	0.149699i
$779$	24667.8	−	47848.9i	1.13455	−	2.20072i
$780$	−1800.71	−	5202.80i	−0.0826610	−	0.238833i
$781$	−3232.65	−	1866.37i	−0.148109	−	0.0855109i
$782$	−11048.4	−	3205.25i	−0.505230	−	0.146572i
$783$			1278.90i			0.0583704i
$784$	−25340.1	−	7207.55i	−1.15434	−	0.328332i
$785$	−1346.55	+	865.372i	−0.0612233	+	0.0393458i
$786$	2354.46	−	1851.57i	0.106846	−	0.0840246i
$787$	7953.36	+	759.454i	0.360237	+	0.0343985i	0.273606	−	0.961842i	$-0.411784\pi$
$787$	7953.36	+	759.454i	0.360237	+	0.0343985i	0.0866316	+	0.996240i	$0.472390\pi$
$788$	6409.89	+	5040.79i	0.289775	+	0.227882i
$789$	6078.72	+	5796.05i	0.274282	+	0.261527i
$790$	1558.31	−	2424.78i	0.0701801	−	0.109202i
$791$	−14405.6	−	7349.39i	−0.647538	−	0.330359i
$792$	−4702.75	+	16016.1i	−0.210991	+	0.718569i
$793$	−50455.5	−	17462.8i	−2.25943	−	0.781995i
$794$	−3323.34	−	17243.1i	−0.148540	−	0.770700i
$795$	1605.48	−	1530.82i	0.0716233	−	0.0682927i
$796$	18464.4	−	1763.14i	0.822177	−	0.0785084i
$797$	12101.0	+	7776.87i	0.537818	+	0.345635i	0.781185	−	0.624300i	$-0.214616\pi$
$797$	12101.0	+	7776.87i	0.537818	+	0.345635i	−0.243367	+	0.969934i	$0.578252\pi$
$798$	57227.7	−	55031.9i	2.53864	−	2.44124i
$799$	2607.81	+	374.946i	0.115466	+	0.0166015i
$800$	−15663.6	+	21996.5i	−0.692241	+	0.972116i
$801$	−44268.3	−	17722.4i	−1.95274	−	0.781759i
$802$	−8566.80	+	408.087i	−0.377187	+	0.0179676i
$803$	−34550.8	−	6659.12i	−1.51839	−	0.292647i
$804$	6867.71			0.301250
$805$	560.066	+	2793.25i	0.0245214	+	0.122297i
$806$	60843.1			2.65894
$807$	12988.0	+	2503.23i	0.566542	+	0.109192i
$808$	208.919	−	9.95202i	0.00909620	−	0.000433305i
$809$	−25343.0	−	10145.8i	−1.10138	−	0.440924i	−0.251473	−	0.967864i	$-0.580915\pi$
$809$	−25343.0	−	10145.8i	−1.10138	−	0.440924i	−0.849902	+	0.526940i	$0.823339\pi$
$810$	92.6470	−	130.104i	0.00401887	−	0.00564371i
$811$	−14849.1	−	2134.97i	−0.642937	−	0.0924403i	−0.186868	−	0.982385i	$-0.559834\pi$
$811$	−14849.1	−	2134.97i	−0.642937	−	0.0924403i	−0.456069	+	0.889945i	$0.650743\pi$
$812$	262.319	−	907.604i	0.0113369	−	0.0392249i
$813$	30886.8	+	19849.7i	1.33241	+	0.856286i
$814$	−19680.3	+	1879.24i	−0.847412	+	0.0809180i
$815$	−1688.63	+	1610.10i	−0.0725767	+	0.0692017i
$816$	3445.03	+	17874.5i	0.147794	+	0.766830i
$817$	51350.0	+	17772.4i	2.19891	+	0.761050i
$818$	−6220.81	+	21186.1i	−0.265899	+	0.905569i
$819$	−3429.48	−	66092.8i	−0.146320	−	2.81986i
$820$	−1716.39	+	2670.76i	−0.0730963	+	0.113740i
$821$	21073.3	+	20093.4i	0.895814	+	0.854157i	0.989952	−	0.141402i	$-0.0451611\pi$
$821$	21073.3	+	20093.4i	0.895814	+	0.854157i	−0.0941382	+	0.995559i	$0.530010\pi$
$822$	2756.31	+	2167.59i	0.116956	+	0.0919748i
$823$	8797.91	+	840.099i	0.372632	+	0.0355820i	0.279692	−	0.960090i	$-0.409768\pi$
$823$	8797.91	+	840.099i	0.372632	+	0.0355820i	0.0929396	+	0.995672i	$0.470374\pi$
$824$	10127.4	−	7964.27i	0.428161	−	0.336710i
$825$	−40143.1	+	25798.4i	−1.69406	+	1.08871i
$826$	−40427.2	−	38221.2i	−1.70296	−	1.61003i
$827$			21425.1i			0.900876i	0.892808	+	0.450438i	$0.148732\pi$
$827$			21425.1i			0.900876i	−0.892808	+	0.450438i	$0.851268\pi$
$828$	−27039.5	+	8034.79i	−1.13489	+	0.337232i
$829$	−2843.89	−	1641.92i	−0.119146	−	0.0687892i	0.439242	−	0.898369i	$-0.355247\pi$
$829$	−2843.89	−	1641.92i	−0.119146	−	0.0687892i	−0.558389	+	0.829579i	$0.688580\pi$
$830$	−1438.46	−	4156.15i	−0.0601562	−	0.173810i
$831$	−29730.1	+	57668.3i	−1.24106	+	2.40733i
$832$	16033.9	−	2305.33i	0.668120	−	0.0960612i
$833$	−9475.34	−	1742.97i	−0.394119	−	0.0724974i
$834$	6732.58	−	46826.1i	0.279533	−	1.94419i
$835$	808.617	−	848.053i	0.0335130	−	0.0351474i
$836$	16674.8	+	32344.6i	0.689845	+	1.33811i
$837$	17053.3	+	23948.1i	0.704241	+	0.988968i
$838$	−3414.51	−	14074.8i	−0.140755	−	0.580199i
$839$	28642.8	+	33055.5i	1.17862	+	1.36019i	0.918891	+	0.394511i	$0.129086\pi$
$839$	28642.8	+	33055.5i	1.17862	+	1.36019i	0.259724	+	0.965683i	$0.416368\pi$
$840$	1403.09	−	1113.07i	0.0576326	−	0.0457198i
$841$	23326.5	+	6849.28i	0.956436	+	0.280835i
$842$	494.460	+	5178.22i	0.0202378	+	0.211940i
$843$	59636.9	−	30745.0i	2.43654	−	1.25612i
$844$	−3819.32	+	15743.5i	−0.155766	+	0.642076i
$845$	5620.41	−	2250.07i	0.228814	−	0.0916034i
$846$	14000.6	−	6393.84i	0.568970	−	0.259840i
$847$	11748.9	−	8441.73i	0.476621	−	0.342457i
$848$	7828.73	+	12181.7i	0.317028	+	0.493305i
$849$	−809.209	+	4198.57i	−0.0327114	+	0.169723i
$850$	−6416.90	+	11114.4i	−0.258938	+	0.448495i
$851$	7932.07	+	10019.5i	0.319516	+	0.403599i
$852$	−3434.30	+	1982.79i	−0.138095	+	0.0797293i
$853$	−540.395	−	468.255i	−0.0216914	−	0.0187957i	0.643948	−	0.765070i	$-0.277295\pi$
$853$	−540.395	−	468.255i	−0.0216914	−	0.0187957i	−0.665639	+	0.746274i	$0.731841\pi$
$854$	192.639	+	45406.3i	0.00771895	+	1.81940i
$855$	1200.15	+	8347.23i	0.0480050	+	0.333882i
$856$	−1290.50	−	918.959i	−0.0515284	−	0.0366932i
$857$	−29882.4	+	37998.6i	−1.19109	+	1.51460i	−0.384880	+	0.922967i	$0.625757\pi$
$857$	−29882.4	+	37998.6i	−1.19109	+	1.51460i	−0.806211	+	0.591629i	$0.798485\pi$
$858$	113142.	+	27448.0i	4.50188	+	1.09215i
$859$	25653.2	+	1222.01i	1.01895	+	0.0485384i	0.550400	−	0.834901i	$-0.314475\pi$
$859$	25653.2	+	1222.01i	1.01895	+	0.0485384i	0.468546	+	0.883439i	$0.344778\pi$
$860$	−2914.95	−	1331.21i	−0.115580	−	0.0527837i
$861$	−46291.0	+	40456.5i	−1.83228	+	1.60134i
$862$	−6751.10	+	5849.86i	−0.266756	+	0.231145i
$863$	−11133.0	+	32166.7i	−0.439133	+	1.26879i	0.480839	+	0.876809i	$0.340332\pi$
$863$	−11133.0	+	32166.7i	−0.439133	+	1.26879i	−0.919972	+	0.391983i	$0.871789\pi$
$864$	21968.8	+	23040.3i	0.865041	+	0.907228i
$865$	−1994.94	+	1420.59i	−0.0784161	+	0.0558398i
$866$	−932.251	+	19570.4i	−0.0365810	+	0.767931i
$867$	−9803.49	−	33387.6i	−0.384018	−	1.30785i
$868$	−7190.29	−	20493.3i	−0.281168	−	0.801367i
$869$	10627.5	+	23271.0i	0.414861	+	0.908419i
$870$	238.083	+	302.747i	0.00927790	+	0.0117978i
$871$	541.181	+	11360.8i	0.0210531	+	0.441958i
$872$	8912.08	−	3084.50i	0.346102	−	0.119787i
$873$	−27773.2	−	48104.5i	−1.07672	−	1.86494i
$874$	27863.7	−	48624.6i	1.07838	−	1.88187i
$875$	6400.56	+	277.685i	0.247290	+	0.0107285i
$876$	−24479.7	+	28251.1i	−0.944170	+	1.08963i
$877$	4726.04	+	2436.44i	0.181969	+	0.0938117i	0.546804	−	0.837261i	$-0.315844\pi$
$877$	4726.04	+	2436.44i	0.181969	+	0.0938117i	−0.364835	+	0.931072i	$0.618875\pi$
$878$	−2654.81	+	6631.41i	−0.102045	+	0.254896i
$879$	2063.22	−	21607.0i	0.0791701	−	0.829107i
$880$	1829.57	+	4570.05i	0.0700851	+	0.175064i
$881$	−3154.07	+	926.119i	−0.120617	+	0.0354163i	−0.341484	−	0.939888i	$-0.610929\pi$
$881$	−3154.07	+	926.119i	−0.120617	+	0.0354163i	0.220867	+	0.975304i	$0.429111\pi$
$882$	−52072.5	+	21361.1i	−1.98795	+	0.815494i
$883$	−8806.52	+	19283.6i	−0.335632	+	0.734931i	−0.999921	−	0.0125442i	$-0.996007\pi$
$883$	−8806.52	+	19283.6i	−0.335632	+	0.734931i	0.664289	+	0.747475i	$0.268734\pi$
$884$	12772.1	−	3098.48i	0.485941	−	0.117888i
$885$	9347.63	−	1801.61i	0.355048	−	0.0684298i
$886$	−26977.4	+	5199.47i	−1.02294	+	0.197155i
$887$	24436.6	−	5928.26i	0.925030	−	0.224410i	0.255169	−	0.966897i	$-0.417869\pi$
$887$	24436.6	−	5928.26i	0.925030	−	0.224410i	0.669861	+	0.742487i	$0.266354\pi$
$888$	3337.38	−	7307.84i	0.126121	−	0.276166i
$889$	20823.8	+	14695.8i	0.785610	+	0.554422i
$890$	−5360.61	+	1574.02i	−0.201897	+	0.0592823i
$891$	526.882	+	1316.09i	0.0198106	+	0.0494844i
$892$	−651.349	+	6821.24i	−0.0244493	+	0.256045i
$893$	−4770.20	+	11915.4i	−0.178755	+	0.446510i
$894$	13367.1	+	6891.20i	0.500069	+	0.257804i
$895$	1412.53	−	1630.14i	0.0527549	−	0.0608824i
$896$	8656.37	+	16617.5i	0.322756	+	0.619590i
$897$	−24844.3	−	71037.3i	−0.924779	−	2.64422i
$898$	22289.3	+	38606.2i	0.828289	+	1.43464i
$899$	−1688.23	+	584.304i	−0.0626316	+	0.0216770i
$900$	1497.35	+	31433.2i	0.0554574	+	1.16419i
$901$	3273.42	+	4162.49i	0.121036	+	0.153910i
$902$	−27888.7	−	61067.7i	−1.02948	−	2.25425i
$903$	−47070.4	−	40438.4i	−1.73467	−	1.49026i
$904$	2021.84	+	6885.74i	0.0743864	+	0.253337i
$905$	−76.0851	+	1597.22i	−0.00279464	+	0.0586668i
$906$	17542.3	−	12491.8i	0.643272	−	0.458072i
$907$	1237.15	+	1297.48i	0.0452909	+	0.0474997i	0.745990	−	0.665957i	$-0.231977\pi$
$907$	1237.15	+	1297.48i	0.0452909	+	0.0474997i	−0.700699	+	0.713457i	$0.747128\pi$
$908$	−4772.20	+	13788.4i	−0.174418	+	0.503946i
$909$	849.991	−	736.521i	0.0310147	−	0.0268744i
$910$	−5102.74	−	5838.65i	−0.185884	−	0.212691i
$911$	−25978.6	−	11864.1i	−0.944798	−	0.431475i	−0.117396	−	0.993085i	$-0.537455\pi$
$911$	−25978.6	−	11864.1i	−0.944798	−	0.431475i	−0.827402	+	0.561610i	$0.810182\pi$
$912$	−88579.1	−	4219.54i	−3.21617	−	0.153205i
$913$	37935.5	+	9203.05i	1.37512	+	0.333600i
$914$	10846.2	−	13792.0i	0.392515	−	0.499124i
$915$	−6328.88	−	4506.78i	−0.228663	−	0.162830i
$916$	−722.310	−	5023.78i	−0.0260544	−	0.181212i
$917$	878.823	−	1537.19i	0.0316481	−	0.0553572i
$918$	11434.6	+	9908.10i	0.411108	+	0.356227i
$919$	4221.55	−	2437.31i	0.151530	−	0.0874859i	−0.422318	−	0.906448i	$-0.638783\pi$
$919$	4221.55	−	2437.31i	0.151530	−	0.0874859i	0.573848	+	0.818962i	$0.305450\pi$
$920$	729.965	−	1032.16i	0.0261590	−	0.0369882i
$921$	6758.85	−	11706.7i	0.241815	−	0.418836i
$922$	−9104.45	+	47238.4i	−0.325205	+	1.68732i
$923$	−3550.63	−	5524.89i	−0.126620	−	0.197025i
$924$	−4125.80	−	41352.5i	−0.146893	−	1.47229i
$925$	12968.1	−	5922.34i	0.460961	−	0.210514i
$926$	24012.3	−	9613.09i	0.852154	−	0.341151i
$927$	16333.6	−	67327.9i	0.578711	−	2.38548i
$928$	−1719.46	+	886.442i	−0.0608232	+	0.0313566i
$929$	−2601.89	−	27248.3i	−0.0918895	−	0.962310i	−0.917411	−	0.397940i	$-0.869725\pi$
$929$	−2601.89	−	27248.3i	−0.0918895	−	0.962310i	0.825522	−	0.564370i	$-0.190881\pi$
$930$	8495.19	+	2494.41i	0.299536	+	0.0879516i
$931$	19134.2	−	42856.8i	0.673576	−	1.50867i
$932$	2993.44	+	3454.61i	0.105208	+	0.121416i
$933$	20739.6	+	85489.7i	0.727742	+	2.99979i
$934$	−28525.7	−	40058.8i	−0.999347	−	1.40339i
$935$	824.898	+	1600.08i	0.0288525	+	0.0559660i
$936$	−20266.6	+	21255.0i	−0.707731	+	0.742247i
$937$	−1980.91	+	13777.6i	−0.0690647	+	0.480356i	0.925708	+	0.378239i	$0.123470\pi$
$937$	−1980.91	+	13777.6i	−0.0690647	+	0.480356i	−0.994772	+	0.102116i	$0.967439\pi$
$938$	8964.43	−	3633.02i	0.312046	−	0.126463i
$939$	13208.5	−	1899.09i	0.459044	−	0.0660006i
$940$	346.837	−	672.769i	0.0120346	−	0.0233439i
$941$	−1801.72	−	5205.74i	−0.0624171	−	0.180342i	0.909480	−	0.415747i	$-0.136480\pi$
$941$	−1801.72	−	5205.74i	−0.0624171	−	0.180342i	−0.971898	+	0.235404i	$0.924359\pi$
$942$	−31141.7	−	17979.7i	−1.07713	−	0.621879i
$943$	−23343.0	+	36582.6i	−0.806102	+	1.26330i
$944$			62140.9i			2.14249i
$945$	867.894	−	3644.93i	0.0298758	−	0.125471i
$946$	57007.3	−	36636.4i	1.95927	−	1.25915i
$947$	−2501.38	+	1967.11i	−0.0858331	+	0.0674999i	−0.660154	−	0.751131i	$-0.729509\pi$
$947$	−2501.38	+	1967.11i	−0.0858331	+	0.0674999i	0.574320	+	0.818631i	$0.305266\pi$
$948$	27055.7	+	2583.50i	0.926928	+	0.0885109i
$949$	−48662.9	−	38269.0i	−1.66456	−	1.30902i
$950$	−45248.4	−	43144.3i	−1.54532	−	1.47346i
$951$	−8570.40	+	13335.8i	−0.292234	+	0.454724i
$952$	2326.64	+	3586.77i	0.0792087	+	0.122109i
$953$	14024.1	−	47761.6i	0.476689	−	1.62345i	−0.273247	−	0.961944i	$-0.588098\pi$
$953$	14024.1	−	47761.6i	0.476689	−	1.62345i	0.749936	−	0.661510i	$-0.230084\pi$
$954$	29234.4	+	10118.1i	0.992138	+	0.343382i
$955$	403.815	+	2095.19i	0.0136829	+	0.0709935i
$956$	15915.5	−	15175.4i	0.538436	−	0.513398i
$957$	−3402.99	+	324.947i	−0.114946	+	0.0109760i
$958$	−5385.44	−	3461.01i	−0.181624	−	0.116723i
$959$	1991.38	+	575.555i	0.0670541	+	0.0193802i
$960$	2333.24	+	335.469i	0.0784427	+	0.0112784i
$961$	−6541.31	+	9185.99i	−0.219573	+	0.308348i
$962$	−32291.7	−	12927.6i	−1.08225	−	0.433268i
$963$	−8509.43	+	405.354i	−0.284748	+	0.0135642i
$964$	17867.2	+	3443.62i	0.596953	+	0.115053i
$965$	−3888.26			−0.129707
$966$	−50010.8	+	39938.2i	−1.66571	+	1.33022i
$967$	−41241.9			−1.37151			−0.685755	−	0.727832i	$-0.740528\pi$
$967$	−41241.9			−1.37151			−0.685755	+	0.727832i	$0.740528\pi$
$968$	−6303.91	−	1214.98i	−0.209313	−	0.0403418i
$969$	−32393.0	+	1543.07i	−1.07390	+	0.0511563i
$970$	−6041.92	−	2418.82i	−0.199994	−	0.0800656i
$971$	11878.9	−	16681.5i	0.392596	−	0.551324i	−0.570216	−	0.821495i	$-0.693141\pi$
$971$	11878.9	−	16681.5i	0.392596	−	0.551324i	0.962813	+	0.270170i	$0.0870800\pi$
$972$	−20944.4	−	3011.36i	−0.691145	−	0.0993717i
$973$	−6708.47	−	27149.4i	−0.221031	−	0.894523i
$974$	16068.8	+	10326.8i	0.528623	+	0.339725i
$975$	−83575.9	+	7980.53i	−2.74520	+	0.262135i
$976$	36705.5	−	34998.6i	1.20380	−	1.14783i
$977$	683.126	+	3544.40i	0.0223697	+	0.116065i	0.991397	−	0.130888i	$-0.0417828\pi$
$977$	683.126	+	3544.40i	0.0223697	+	0.116065i	−0.969028	+	0.246953i	$0.920571\pi$
$978$	−49534.1	−	17143.9i	−1.61956	−	0.560534i
$979$	13970.6	−	47579.4i	0.456079	−	1.55326i
$980$	−1363.55	+	2408.71i	−0.0444459	+	0.0785136i
$981$	27417.2	−	42662.0i	0.892317	−	1.38847i
$982$	17495.2	+	16681.6i	0.568527	+	0.542089i
$983$	17716.4	+	13932.3i	0.574838	+	0.452058i	0.862772	−	0.505592i	$-0.168726\pi$
$983$	17716.4	+	13932.3i	0.574838	+	0.452058i	−0.287934	+	0.957650i	$0.592968\pi$
$984$	27157.9	+	2593.27i	0.879840	+	0.0840145i
$985$	−1544.75	+	1214.81i	−0.0499695	+	0.0392965i
$986$	−773.447	+	497.064i	−0.0249813	+	0.0160545i
$987$	10069.7	−	10650.9i	0.324745	−	0.343488i
$988$			64025.0i			2.06164i
$989$	−39903.4	−	18067.2i	−1.28297	−	0.580894i
$990$	9107.77	+	5258.37i	0.292388	+	0.168810i
$991$	−6448.17	−	18630.8i	−0.206693	−	0.597201i	0.793238	−	0.608911i	$-0.208393\pi$
$991$	−6448.17	−	18630.8i	−0.206693	−	0.597201i	−0.999931	+	0.0117107i	$0.996272\pi$
$992$	−20377.6	+	39527.1i	−0.652208	+	1.26511i
$993$	62498.6	−	8985.94i	1.99731	−	0.287170i
$994$	−3433.90	+	4404.89i	−0.109574	+	0.140558i
$995$	−636.158	+	4424.58i	−0.0202689	+	0.140973i
$996$	28618.2	−	30013.9i	0.910443	−	0.954845i
$997$	1173.42	+	2276.13i	0.0372746	+	0.0723026i	0.906737	−	0.421696i	$-0.138565\pi$
$997$	1173.42	+	2276.13i	0.0372746	+	0.0723026i	−0.869463	+	0.493999i	$0.835535\pi$
$998$	721.163	+	1012.73i	0.0228738	+	0.0321217i
$999$	−3962.47	−	16333.5i	−0.125492	−	0.517287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.o.a.122.9	yes	920
7.5	odd	6	inner	161.4.o.a.145.38	yes	920
23.10	odd	22	inner	161.4.o.a.10.38	✓	920
161.33	even	66	inner	161.4.o.a.33.9	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.o.a.10.38	✓	920	23.10	odd	22	inner
161.4.o.a.33.9	yes	920	161.33	even	66	inner
161.4.o.a.122.9	yes	920	1.1	even	1	trivial
161.4.o.a.145.38	yes	920	7.5	odd	6	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+(-3.64593 - 0.702695i) q^{2} +(8.42807 - 0.401479i) q^{3} +(5.37207 + 2.15065i) q^{4} +(-0.808912 + 1.13596i) q^{5} +(-31.0103 - 4.45860i) q^{6} +(-17.9795 + 4.44264i) q^{7} +(6.91384 + 4.44325i) q^{8} +(43.9935 - 4.20087i) q^{9} +(3.74747 - 3.57320i) q^{10} +(8.69765 + 45.1277i) q^{11} +(46.1397 + 15.9691i) q^{12} +(-22.7808 + 77.5842i) q^{13} +(68.6739 - 3.56341i) q^{14} +(-6.36151 + 9.89870i) q^{15} +(-55.5887 - 53.0037i) q^{16} +(-22.0789 - 17.3631i) q^{17} +(-163.349 - 15.5979i) q^{18} +(107.559 - 84.5855i) q^{19} +(-6.78859 + 4.36276i) q^{20} +(-149.749 + 44.6612i) q^{21} -170.644i q^{22} +(-92.6000 + 59.9353i) q^{23} +(60.0542 + 34.6723i) q^{24} +(40.2474 + 116.287i) q^{25} +(137.575 - 266.859i) q^{26} +(143.596 - 20.6461i) q^{27} +(-106.142 - 14.8016i) q^{28} +(-1.25458 + 8.72581i) q^{29} +(30.1494 - 31.6197i) q^{30} +(92.8607 + 180.125i) q^{31} +(127.289 + 178.753i) q^{32} +(91.4222 + 376.847i) q^{33} +(68.2973 + 78.8193i) q^{34} +(9.49720 - 24.0177i) q^{35} +(245.371 + 72.0474i) q^{36} +(-11.0126 - 115.329i) q^{37} +(-451.591 + 232.811i) q^{38} +(-160.850 + 663.031i) q^{39} +(-10.6400 + 4.25963i) q^{40} +(357.866 - 163.432i) q^{41} +(577.358 - 57.6038i) q^{42} +(214.695 + 334.072i) q^{43} +(-50.3296 + 261.135i) q^{44} +(-30.8148 + 53.3729i) q^{45} +(379.729 - 153.450i) q^{46} +(-81.2312 + 46.8988i) q^{47} +(-489.785 - 424.401i) q^{48} +(303.526 - 159.753i) q^{49} +(-65.0247 - 452.257i) q^{50} +(-193.054 - 137.473i) q^{51} +(-289.237 + 367.795i) q^{52} +(-183.213 - 44.4471i) q^{53} +(-538.050 - 25.6305i) q^{54} +(-58.2988 - 26.6242i) q^{55} +(-144.047 - 49.1719i) q^{56} +(872.558 - 756.076i) q^{57} +(10.7057 - 30.9321i) q^{58} +(-558.302 - 585.530i) q^{59} +(-55.4632 + 39.4951i) q^{60} +(-31.4186 + 659.557i) q^{61} +(-211.991 - 721.975i) q^{62} +(-772.318 + 270.977i) q^{63} +(-83.2211 - 182.229i) q^{64} +(-69.7048 - 88.6368i) q^{65} +(-68.5099 - 1438.20i) q^{66} +(132.923 - 46.0052i) q^{67} +(-81.2678 - 140.760i) q^{68} +(-756.377 + 542.316i) q^{69} +(-51.5032 + 80.8931i) q^{70} +(-53.1880 + 61.3823i) q^{71} +(322.829 + 166.430i) q^{72} +(-284.553 + 710.780i) q^{73} +(-40.8902 + 428.221i) q^{74} +(385.895 + 963.919i) q^{75} +(759.730 - 223.077i) q^{76} +(-356.865 - 772.733i) q^{77} +(1052.36 - 2304.34i) q^{78} +(540.965 - 131.237i) q^{79} +(105.176 - 20.2711i) q^{80} +(30.2888 - 5.83768i) q^{81} +(-1419.60 + 344.390i) q^{82} +(352.844 - 772.621i) q^{83} +(-900.514 - 82.1349i) q^{84} +(37.5837 - 11.0356i) q^{85} +(-548.011 - 1368.87i) q^{86} +(-7.07048 + 74.0454i) q^{87} +(-140.380 + 350.651i) q^{88} +(-959.037 - 494.418i) q^{89} +(149.854 - 172.940i) q^{90} +(64.9090 - 1496.13i) q^{91} +(-626.354 + 122.826i) q^{92} +(854.953 + 1480.82i) q^{93} +(329.119 - 113.909i) q^{94} +(9.07964 + 190.605i) q^{95} +(1144.57 + 1455.44i) q^{96} +(-522.129 - 1143.30i) q^{97} +(-1218.89 + 369.161i) q^{98} +(572.215 + 1948.79i) 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

Fields

Representations

Groups

Database

Properties

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