LMFDB - Embedded newform 201.3.h.a.172.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (of order $6$, degree $2$, 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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			172.2
Character	$\chi$	$=$	201.172
Dual form			201.3.h.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55387 - 1.47448i) q^{2} +1.73205i q^{3} +(2.34817 + 4.06715i) q^{4} +9.46283i q^{5} +(2.55387 - 4.42343i) q^{6} +(-6.24108 + 3.60329i) q^{7} -2.05347i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-2.55387 - 1.47448i) q^{2} +1.73205i q^{3} +(2.34817 + 4.06715i) q^{4} +9.46283i q^{5} +(2.55387 - 4.42343i) q^{6} +(-6.24108 + 3.60329i) q^{7} -2.05347i q^{8} -3.00000 q^{9} +(13.9527 - 24.1668i) q^{10} +(0.365987 - 0.211302i) q^{11} +(-7.04451 + 4.06715i) q^{12} +(-15.7858 - 9.11393i) q^{13} +21.2519 q^{14} -16.3901 q^{15} +(6.36488 - 11.0243i) q^{16} +(12.3248 - 21.3472i) q^{17} +(7.66161 + 4.42343i) q^{18} +(9.32619 - 16.1534i) q^{19} +(-38.4867 + 22.2203i) q^{20} +(-6.24108 - 10.8099i) q^{21} -1.24624 q^{22} +(-11.8011 + 20.4401i) q^{23} +3.55671 q^{24} -64.5451 q^{25} +(26.8766 + 46.5516i) q^{26} -5.19615i q^{27} +(-29.3102 - 16.9223i) q^{28} +(16.8219 + 29.1364i) q^{29} +(41.8582 + 24.1668i) q^{30} +(10.8231 - 6.24870i) q^{31} +(-39.6236 + 22.8767i) q^{32} +(0.365987 + 0.633907i) q^{33} +(-62.9518 + 36.3452i) q^{34} +(-34.0973 - 59.0582i) q^{35} +(-7.04451 - 12.2014i) q^{36} +(7.83235 - 13.5660i) q^{37} +(-47.6358 + 27.5025i) q^{38} +(15.7858 - 27.3418i) q^{39} +19.4316 q^{40} +(-21.5351 + 12.4333i) q^{41} +36.8093i q^{42} +10.0856i q^{43} +(1.71880 + 0.992348i) q^{44} -28.3885i q^{45} +(60.2771 - 34.8010i) q^{46} +(-22.6568 - 39.2427i) q^{47} +(19.0946 + 11.0243i) q^{48} +(1.46736 - 2.54154i) q^{49} +(164.840 + 95.1704i) q^{50} +(36.9744 + 21.3472i) q^{51} -85.6041i q^{52} +63.1275i q^{53} +(-7.66161 + 13.2703i) q^{54} +(1.99952 + 3.46327i) q^{55} +(7.39924 + 12.8159i) q^{56} +(27.9786 + 16.1534i) q^{57} -99.2141i q^{58} -7.36117 q^{59} +(-38.4867 - 66.6610i) q^{60} +(60.6120 + 34.9944i) q^{61} -36.8543 q^{62} +(18.7232 - 10.8099i) q^{63} +84.0056 q^{64} +(86.2435 - 149.378i) q^{65} -2.15856i q^{66} +(-54.1867 - 39.4057i) q^{67} +115.763 q^{68} +(-35.4034 - 20.4401i) q^{69} +201.103i q^{70} +(-56.6803 - 98.1731i) q^{71} +6.16041i q^{72} +(-39.6351 + 68.6499i) q^{73} +(-40.0056 + 23.0972i) q^{74} -111.795i q^{75} +87.5979 q^{76} +(-1.52277 + 2.63751i) q^{77} +(-80.6297 + 46.5516i) q^{78} +(-2.84650 + 1.64343i) q^{79} +(104.321 + 60.2298i) q^{80} +9.00000 q^{81} +73.3306 q^{82} +(-3.68244 + 6.37817i) q^{83} +(29.3102 - 50.7668i) q^{84} +(202.005 + 116.627i) q^{85} +(14.8710 - 25.7573i) q^{86} +(-50.4657 + 29.1364i) q^{87} +(-0.433903 - 0.751542i) q^{88} -90.8678 q^{89} +(-41.8582 + 72.5005i) q^{90} +131.360 q^{91} -110.844 q^{92} +(10.8231 + 18.7461i) q^{93} +133.628i q^{94} +(152.857 + 88.2522i) q^{95} +(-39.6236 - 68.6301i) q^{96} +(-160.623 - 92.7359i) q^{97} +(-7.49489 + 4.32718i) q^{98} +(-1.09796 + 0.633907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.55387	−	1.47448i	−1.27694	−	0.737239i	−0.300651	−	0.953734i	$-0.597204\pi$
$2$	−2.55387	−	1.47448i	−1.27694	−	0.737239i	−0.976284	+	0.216495i	$0.930537\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	2.34817	+	4.06715i	0.587042	+	1.01679i
$5$			9.46283i			1.89257i	0.323340	+	0.946283i	$0.395194\pi$
$5$			9.46283i			1.89257i	−0.323340	+	0.946283i	$0.604806\pi$
$6$	2.55387	−	4.42343i	0.425645	−	0.737239i
$7$	−6.24108	+	3.60329i	−0.891582	+	0.514755i	−0.874460	−	0.485098i	$-0.838784\pi$
$7$	−6.24108	+	3.60329i	−0.891582	+	0.514755i	−0.0171226	+	0.999853i	$0.505451\pi$
$8$		−	2.05347i		−	0.256684i
$9$	−3.00000			−0.333333
$10$	13.9527	−	24.1668i	1.39527	−	2.41668i
$11$	0.365987	−	0.211302i	0.0332715	−	0.0192093i	−0.483272	−	0.875470i	$-0.660552\pi$
$11$	0.365987	−	0.211302i	0.0332715	−	0.0192093i	0.516543	+	0.856261i	$0.327218\pi$
$12$	−7.04451	+	4.06715i	−0.587042	+	0.338929i
$13$	−15.7858	−	9.11393i	−1.21429	−	0.701071i	−0.250600	−	0.968091i	$-0.580628\pi$
$13$	−15.7858	−	9.11393i	−1.21429	−	0.701071i	−0.963691	+	0.267020i	$0.913961\pi$
$14$	21.2519			1.51799
$15$	−16.3901			−1.09267
$16$	6.36488	−	11.0243i	0.397805	−	0.689019i
$17$	12.3248	−	21.3472i	0.724988	−	1.25572i	−0.233992	−	0.972239i	$-0.575179\pi$
$17$	12.3248	−	21.3472i	0.724988	−	1.25572i	0.958979	−	0.283477i	$-0.0914878\pi$
$18$	7.66161	+	4.42343i	0.425645	+	0.245746i
$19$	9.32619	−	16.1534i	0.490852	−	0.850181i	−0.509092	−	0.860712i	$-0.670019\pi$
$19$	9.32619	−	16.1534i	0.490852	−	0.850181i	0.999945	+	0.0105308i	$0.00335213\pi$
$20$	−38.4867	+	22.2203i	−1.92434	+	1.11102i
$21$	−6.24108	−	10.8099i	−0.297194	−	0.514755i
$22$	−1.24624			−0.0566474
$23$	−11.8011	+	20.4401i	−0.513092	+	0.888702i	0.486792	+	0.873518i	$0.338167\pi$
$23$	−11.8011	+	20.4401i	−0.513092	+	0.888702i	−0.999885	+	0.0151843i	$0.995167\pi$
$24$	3.55671			0.148196
$25$	−64.5451			−2.58181
$26$	26.8766	+	46.5516i	1.03371	+	1.79044i
$27$		−	5.19615i		−	0.192450i
$28$	−29.3102	−	16.9223i	−1.04679	−	0.604366i
$29$	16.8219	+	29.1364i	0.580066	+	1.00470i	0.995471	+	0.0950668i	$0.0303065\pi$
$29$	16.8219	+	29.1364i	0.580066	+	1.00470i	−0.415405	+	0.909636i	$0.636360\pi$
$30$	41.8582	+	24.1668i	1.39527	+	0.805561i
$31$	10.8231	−	6.24870i	0.349131	−	0.201571i	−0.315171	−	0.949035i	$-0.602062\pi$
$31$	10.8231	−	6.24870i	0.349131	−	0.201571i	0.664303	+	0.747464i	$0.268729\pi$
$32$	−39.6236	+	22.8767i	−1.23824	+	0.714897i
$33$	0.365987	+	0.633907i	0.0110905	+	0.0192093i
$34$	−62.9518	+	36.3452i	−1.85152	+	1.06898i
$35$	−34.0973	−	59.0582i	−0.974208	−	1.68738i
$36$	−7.04451	−	12.2014i	−0.195681	−	0.338929i
$37$	7.83235	−	13.5660i	0.211685	−	0.366649i	−0.740557	−	0.671994i	$-0.765438\pi$
$37$	7.83235	−	13.5660i	0.211685	−	0.366649i	0.952242	+	0.305344i	$0.0987715\pi$
$38$	−47.6358	+	27.5025i	−1.25357	+	0.723751i
$39$	15.7858	−	27.3418i	0.404764	−	0.701071i
$40$	19.4316			0.485791
$41$	−21.5351	+	12.4333i	−0.525248	+	0.303252i	−0.739079	−	0.673619i	$-0.764739\pi$
$41$	−21.5351	+	12.4333i	−0.525248	+	0.303252i	0.213831	+	0.976871i	$0.431406\pi$
$42$			36.8093i			0.876412i
$43$			10.0856i			0.234549i	0.993100	+	0.117274i	$0.0374157\pi$
$43$			10.0856i			0.234549i	−0.993100	+	0.117274i	$0.962584\pi$
$44$	1.71880	+	0.992348i	0.0390636	+	0.0225534i
$45$		−	28.3885i		−	0.630855i
$46$	60.2771	−	34.8010i	1.31037	−	0.756543i
$47$	−22.6568	−	39.2427i	−0.482059	−	0.834950i	0.517729	−	0.855545i	$-0.326777\pi$
$47$	−22.6568	−	39.2427i	−0.482059	−	0.834950i	−0.999788	+	0.0205943i	$0.993444\pi$
$48$	19.0946	+	11.0243i	0.397805	+	0.229673i
$49$	1.46736	−	2.54154i	0.0299461	−	0.0518682i
$50$	164.840	+	95.1704i	3.29680	+	1.90341i
$51$	36.9744	+	21.3472i	0.724988	+	0.418572i
$52$		−	85.6041i		−	1.64623i
$53$			63.1275i			1.19108i	0.803324	+	0.595542i	$0.203063\pi$
$53$			63.1275i			1.19108i	−0.803324	+	0.595542i	$0.796937\pi$
$54$	−7.66161	+	13.2703i	−0.141882	+	0.245746i
$55$	1.99952	+	3.46327i	0.0363549	+	0.0629685i
$56$	7.39924	+	12.8159i	0.132129	+	0.228855i
$57$	27.9786	+	16.1534i	0.490852	+	0.283394i
$58$		−	99.2141i		−	1.71059i
$59$	−7.36117			−0.124766			−0.0623828	−	0.998052i	$-0.519870\pi$
$59$	−7.36117			−0.124766			−0.0623828	+	0.998052i	$0.519870\pi$
$60$	−38.4867	−	66.6610i	−0.641445	−	1.11102i
$61$	60.6120	+	34.9944i	0.993640	+	0.573678i	0.906360	−	0.422506i	$-0.138849\pi$
$61$	60.6120	+	34.9944i	0.993640	+	0.573678i	0.0872794	+	0.996184i	$0.472183\pi$
$62$	−36.8543			−0.594424
$63$	18.7232	−	10.8099i	0.297194	−	0.171585i
$64$	84.0056			1.31259
$65$	86.2435	−	149.378i	1.32682	−	2.29813i
$66$		−	2.15856i		−	0.0327054i
$67$	−54.1867	−	39.4057i	−0.808756	−	0.588144i
$67$	−54.1867	−	39.4057i	−0.808756	−	0.588144i
$68$	115.763			1.70239
$69$	−35.4034	−	20.4401i	−0.513092	−	0.296234i
$70$			201.103i			2.87290i
$71$	−56.6803	−	98.1731i	−0.798313	−	1.38272i	−0.920714	−	0.390239i	$-0.872392\pi$
$71$	−56.6803	−	98.1731i	−0.798313	−	1.38272i	0.122400	−	0.992481i	$-0.460941\pi$
$72$			6.16041i			0.0855612i
$73$	−39.6351	+	68.6499i	−0.542946	+	0.940410i	0.455787	+	0.890089i	$0.349358\pi$
$73$	−39.6351	+	68.6499i	−0.542946	+	0.940410i	−0.998733	+	0.0503212i	$0.983975\pi$
$74$	−40.0056	+	23.0972i	−0.540616	+	0.312125i
$75$		−	111.795i		−	1.49061i
$76$	87.5979			1.15260
$77$	−1.52277	+	2.63751i	−0.0197762	+	0.0342534i
$78$	−80.6297	+	46.5516i	−1.03371	+	0.596815i
$79$	−2.84650	+	1.64343i	−0.0360316	+	0.0208029i	−0.517908	−	0.855437i	$-0.673289\pi$
$79$	−2.84650	+	1.64343i	−0.0360316	+	0.0208029i	0.481876	+	0.876239i	$0.339956\pi$
$80$	104.321	+	60.2298i	1.30401	+	0.752872i
$81$	9.00000			0.111111
$82$	73.3306			0.894276
$83$	−3.68244	+	6.37817i	−0.0443667	+	0.0768454i	−0.887356	−	0.461085i	$-0.847460\pi$
$83$	−3.68244	+	6.37817i	−0.0443667	+	0.0768454i	0.842989	+	0.537930i	$0.180794\pi$
$84$	29.3102	−	50.7668i	0.348931	−	0.604366i
$85$	202.005	+	116.627i	2.37652	+	1.37209i
$86$	14.8710	−	25.7573i	0.172918	−	0.299503i
$87$	−50.4657	+	29.1364i	−0.580066	+	0.334901i
$88$	−0.433903	−	0.751542i	−0.00493072	−	0.00854025i
$89$	−90.8678			−1.02099			−0.510493	−	0.859882i	$-0.670537\pi$
$89$	−90.8678			−1.02099			−0.510493	+	0.859882i	$0.670537\pi$
$90$	−41.8582	+	72.5005i	−0.465091	+	0.805561i
$91$	131.360			1.44352
$92$	−110.844			−1.20483
$93$	10.8231	+	18.7461i	0.116377	+	0.201571i
$94$			133.628i			1.42157i
$95$	152.857	+	88.2522i	1.60902	+	0.928970i
$96$	−39.6236	−	68.6301i	−0.412746	−	0.714897i
$97$	−160.623	−	92.7359i	−1.65591	−	0.956041i	−0.974573	−	0.224072i	$-0.928065\pi$
$97$	−160.623	−	92.7359i	−1.65591	−	0.956041i	−0.681338	−	0.731969i	$-0.738602\pi$
$98$	−7.49489	+	4.32718i	−0.0764785	+	0.0441549i
$99$	−1.09796	+	0.633907i	−0.0110905	+	0.00640311i
$100$	−151.563	−	262.515i	−1.51563	−	2.62515i
$101$	−156.712	+	90.4775i	−1.55160	+	0.895817i	−0.553588	+	0.832791i	$0.686742\pi$
$101$	−156.712	+	90.4775i	−1.55160	+	0.895817i	−0.998012	+	0.0630262i	$0.979925\pi$
$102$	−62.9518	−	109.036i	−0.617175	−	1.06898i
$103$	51.8398	+	89.7892i	0.503299	+	0.871740i	0.999993	+	0.00381405i	$0.00121405\pi$
$103$	51.8398	+	89.7892i	0.503299	+	0.871740i	−0.496693	+	0.867926i	$0.665453\pi$
$104$	−18.7152	+	32.4156i	−0.179953	+	0.311689i
$105$	102.292	−	59.0582i	0.974208	−	0.562460i
$106$	93.0801	−	161.219i	0.878114	−	1.52094i
$107$	−123.760			−1.15664			−0.578320	−	0.815810i	$-0.696291\pi$
$107$	−123.760			−1.15664			−0.578320	+	0.815810i	$0.696291\pi$
$108$	21.1335	−	12.2014i	0.195681	−	0.112976i
$109$		−	24.9866i		−	0.229235i	−0.993410	−	0.114617i	$-0.963436\pi$
$109$		−	24.9866i		−	0.229235i	0.993410	−	0.114617i	$-0.0365642\pi$
$110$		−	11.7930i		−	0.107209i
$111$	23.4970	+	13.5660i	0.211685	+	0.122216i
$112$			91.7380i			0.819089i
$113$	−68.3983	+	39.4898i	−0.605295	+	0.349467i	−0.771122	−	0.636688i	$-0.780304\pi$
$113$	−68.3983	+	39.4898i	−0.605295	+	0.349467i	0.165827	+	0.986155i	$0.446971\pi$
$114$	−47.6358	−	82.5076i	−0.417858	−	0.723751i
$115$	−193.422	−	111.672i	−1.68193	−	0.971061i
$116$	−79.0013	+	136.834i	−0.681046	+	1.17961i
$117$	47.3573	+	27.3418i	0.404764	+	0.233690i
$118$	18.7995	+	10.8539i	0.159318	+	0.0919821i
$119$			177.639i			1.49276i
$120$			33.6566i			0.280471i
$121$	−60.4107	+	104.634i	−0.499262	+	0.864747i
$122$	−103.197	−	178.742i	−0.845876	−	1.46510i
$123$	−21.5351	−	37.3000i	−0.175083	−	0.303252i
$124$	50.8288	+	29.3460i	0.409909	+	0.236661i
$125$		−	374.209i		−	2.99367i
$126$	−63.7556			−0.505997
$127$	40.8985	+	70.8383i	0.322035	+	0.557782i	0.980908	−	0.194473i	$-0.0622997\pi$
$127$	40.8985	+	70.8383i	0.322035	+	0.557782i	−0.658872	+	0.752255i	$0.728966\pi$
$128$	−56.0451	−	32.3576i	−0.437852	−	0.252794i
$129$	−17.4688			−0.135417
$130$	−440.510	+	254.328i	−3.38854	+	1.95637i
$131$	164.038			1.25220			0.626098	−	0.779744i	$-0.284651\pi$
$131$	164.038			1.25220			0.626098	+	0.779744i	$0.284651\pi$
$132$	−1.71880	+	2.97704i	−0.0130212	+	0.0225534i
$133$			134.420i			1.01068i
$134$	80.2829	+	180.534i	0.599126	+	1.34727i
$135$	49.1703			0.364224
$136$	−43.8357	−	25.3086i	−0.322321	−	0.186092i
$137$			128.381i			0.937084i	0.883441	+	0.468542i	$0.155221\pi$
$137$			128.381i			0.937084i	−0.883441	+	0.468542i	$0.844779\pi$
$138$	60.2771	+	104.403i	0.436790	+	0.756543i
$139$		−	147.825i		−	1.06349i	−0.846904	−	0.531746i	$-0.821536\pi$
$139$		−	147.825i		−	1.06349i	0.846904	−	0.531746i	$-0.178464\pi$
$140$	160.132	−	277.357i	1.14380	−	1.98112i
$141$	67.9703	−	39.2427i	0.482059	−	0.278317i
$142$			334.295i			2.35419i
$143$	−7.70318			−0.0538684
$144$	−19.0946	+	33.0729i	−0.132602	+	0.229673i
$145$	−275.713	+	159.183i	−1.90147	+	1.09781i
$146$	202.446	−	116.882i	1.38661	−	0.800562i
$147$	4.40208	+	2.54154i	0.0299461	+	0.0172894i
$148$	73.5667			0.497072
$149$	−60.8716			−0.408534			−0.204267	−	0.978915i	$-0.565481\pi$
$149$	−60.8716			−0.408534			−0.204267	+	0.978915i	$0.565481\pi$
$150$	−164.840	+	285.511i	−1.09893	+	1.90341i
$151$	148.218	−	256.721i	0.981577	−	1.70014i	0.325322	−	0.945603i	$-0.394527\pi$
$151$	148.218	−	256.721i	0.981577	−	1.70014i	0.656256	−	0.754539i	$-0.272139\pi$
$152$	−33.1706	−	19.1510i	−0.218228	−	0.125994i
$153$	−36.9744	+	64.0415i	−0.241663	+	0.418572i
$154$	7.77790	−	4.49057i	0.0505058	−	0.0291596i
$155$	59.1304	+	102.417i	0.381486	+	0.660754i
$156$	148.271			0.950453
$157$	−51.6668	+	89.4895i	−0.329088	+	0.569997i	−0.982331	−	0.187151i	$-0.940075\pi$
$157$	−51.6668	+	89.4895i	−0.329088	+	0.569997i	0.653243	+	0.757148i	$0.273408\pi$
$158$	9.69278			0.0613467
$159$	−109.340			−0.687673
$160$	−216.478	−	374.951i	−1.35299	−	2.34345i
$161$		−	170.091i		−	1.05647i
$162$	−22.9848	−	13.2703i	−0.141882	−	0.0819154i
$163$	−104.127	−	180.353i	−0.638814	−	1.10646i	−0.985693	−	0.168549i	$-0.946092\pi$
$163$	−104.127	−	180.353i	−0.638814	−	1.10646i	0.346879	−	0.937910i	$-0.387242\pi$
$164$	−101.136	−	58.3911i	−0.616685	−	0.356043i
$165$	−5.99856	+	3.46327i	−0.0363549	+	0.0209895i
$166$	18.8089	−	10.8593i	0.113307	−	0.0654178i
$167$	125.206	+	216.863i	0.749738	+	1.29858i	0.947948	+	0.318424i	$0.103154\pi$
$167$	125.206	+	216.863i	0.749738	+	1.29858i	−0.198211	+	0.980159i	$0.563513\pi$
$168$	−22.1977	+	12.8159i	−0.132129	+	0.0762848i
$169$	81.6273	+	141.383i	0.483002	+	0.836583i
$170$	−343.929	−	595.702i	−2.02311	−	3.50413i
$171$	−27.9786	+	48.4603i	−0.163617	+	0.283394i
$172$	−41.0196	+	23.6827i	−0.238486	+	0.137690i
$173$	127.172	−	220.268i	0.735096	−	1.27322i	−0.219585	−	0.975593i	$-0.570470\pi$
$173$	127.172	−	220.268i	0.735096	−	1.27322i	0.954681	−	0.297631i	$-0.0961964\pi$
$174$	171.844			0.987608
$175$	402.831	−	232.575i	2.30189	−	1.32900i
$176$		−	5.37966i		−	0.0305663i
$177$		−	12.7499i		−	0.0720335i
$178$	232.064	+	133.982i	1.30373	+	0.752711i
$179$			105.804i			0.591083i	0.955330	+	0.295541i	$0.0955000\pi$
$179$			105.804i			0.591083i	−0.955330	+	0.295541i	$0.904500\pi$
$180$	115.460	−	66.6610i	0.641445	−	0.370339i
$181$	71.9540	+	124.628i	0.397536	+	0.688553i	0.993421	−	0.114517i	$-0.0365320\pi$
$181$	71.9540	+	124.628i	0.397536	+	0.688553i	−0.595885	+	0.803070i	$0.703199\pi$
$182$	−335.477	−	193.688i	−1.84328	−	1.06422i
$183$	−60.6120	+	104.983i	−0.331213	+	0.573678i
$184$	41.9732	+	24.2332i	0.228115	+	0.131702i
$185$	128.373	+	74.1162i	0.693908	+	0.400628i
$186$		−	63.8335i		−	0.343191i
$187$		−	10.4170i		−	0.0557061i
$188$	106.404	−	184.297i	0.565978	−	0.980302i
$189$	18.7232	+	32.4296i	0.0990647	+	0.171585i
$190$	−260.252	−	450.769i	−1.36975	−	2.37247i
$191$	210.979	+	121.809i	1.10460	+	0.637742i	0.937426	−	0.348185i	$-0.113202\pi$
$191$	210.979	+	121.809i	1.10460	+	0.637742i	0.167175	+	0.985927i	$0.446535\pi$
$192$			145.502i			0.757823i
$193$	−9.39454			−0.0486764			−0.0243382	−	0.999704i	$-0.507748\pi$
$193$	−9.39454			−0.0486764			−0.0243382	+	0.999704i	$0.507748\pi$
$194$	273.474	+	473.671i	1.40966	+	2.44160i
$195$	258.731	+	149.378i	1.32682	+	0.766042i
$196$	13.7824			0.0703185
$197$	−7.02922	+	4.05832i	−0.0356813	+	0.0206006i	−0.517735	−	0.855541i	$-0.673225\pi$
$197$	−7.02922	+	4.05832i	−0.0356813	+	0.0206006i	0.482053	+	0.876142i	$0.339891\pi$
$198$	3.73873			0.0188825
$199$	−97.6486	+	169.132i	−0.490697	+	0.849911i	−0.999943	−	0.0107095i	$-0.996591\pi$
$199$	−97.6486	+	169.132i	−0.490697	+	0.849911i	0.509246	+	0.860621i	$0.329924\pi$
$200$			132.541i			0.662707i
$201$	68.2526	−	93.8540i	0.339565	−	0.466936i
$202$	533.628			2.64172
$203$	−209.974	−	121.228i	−1.03435	−	0.597184i
$204$			200.507i			0.982877i
$205$	−117.654	−	203.783i	−0.573924	−	0.994066i
$206$		−	305.747i		−	1.48421i
$207$	35.4034	−	61.3204i	0.171031	−	0.296234i
$208$	−200.949	+	116.018i	−0.966102	+	0.557779i
$209$		−	7.88259i		−	0.0377157i
$210$	−348.320			−1.65867
$211$	60.4098	−	104.633i	0.286302	−	0.495890i	−0.686622	−	0.727015i	$-0.740907\pi$
$211$	60.4098	−	104.633i	0.286302	−	0.495890i	0.972924	+	0.231125i	$0.0742405\pi$
$212$	−256.749	+	148.234i	−1.21108	+	0.699217i
$213$	170.041	−	98.1731i	0.798313	−	0.460907i
$214$	316.068	+	182.482i	1.47695	+	0.852720i
$215$	−95.4382			−0.443899
$216$	−10.6701			−0.0493988
$217$	−45.0317	+	77.9972i	−0.207519	+	0.359434i
$218$	−36.8422	+	63.8125i	−0.169001	+	0.292718i
$219$	−118.905	−	68.6499i	−0.542946	−	0.313470i
$220$	−9.39042	+	16.2647i	−0.0426837	+	0.0739304i
$221$	−389.113	+	224.654i	−1.76069	+	1.01654i
$222$	−40.0056	−	69.2917i	−0.180205	−	0.312125i
$223$	−15.8632			−0.0711356			−0.0355678	−	0.999367i	$-0.511324\pi$
$223$	−15.8632			−0.0711356			−0.0355678	+	0.999367i	$0.511324\pi$
$224$	164.863	−	285.550i	0.735994	−	1.27478i
$225$	193.635			0.860602
$226$	232.907			1.03056
$227$	113.128	+	195.944i	0.498363	+	0.863190i	0.999998	−	0.00188921i	$-0.000601355\pi$
$227$	113.128	+	195.944i	0.498363	+	0.863190i	−0.501635	+	0.865079i	$0.667268\pi$
$228$			151.724i			0.665456i
$229$	−184.804	−	106.697i	−0.807004	−	0.465924i	0.0389106	−	0.999243i	$-0.487611\pi$
$229$	−184.804	−	106.697i	−0.807004	−	0.465924i	−0.845914	+	0.533319i	$0.820945\pi$
$230$	329.316	+	570.392i	1.43181	+	2.47996i
$231$	−4.56830	−	2.63751i	−0.0197762	−	0.0114178i
$232$	59.8307	−	34.5433i	0.257891	−	0.148893i
$233$	−136.427	+	78.7660i	−0.585522	+	0.338051i	−0.763325	−	0.646015i	$-0.776434\pi$
$233$	−136.427	+	78.7660i	−0.585522	+	0.338051i	0.177803	+	0.984066i	$0.443101\pi$
$234$	−80.6297	−	139.655i	−0.344571	−	0.596815i
$235$	371.347	−	214.397i	1.58020	−	0.912328i
$236$	−17.2853	−	29.9390i	−0.0732427	−	0.126860i
$237$	−2.84650	−	4.93028i	−0.0120105	−	0.0208029i
$238$	261.925	−	453.667i	1.10052	−	1.90616i
$239$	62.7515	−	36.2296i	0.262559	−	0.151588i	−0.362942	−	0.931812i	$-0.618228\pi$
$239$	62.7515	−	36.2296i	0.262559	−	0.151588i	0.625501	+	0.780223i	$0.284895\pi$
$240$	−104.321	+	180.689i	−0.434671	+	0.752872i
$241$	389.323			1.61545			0.807724	−	0.589561i	$-0.200699\pi$
$241$	389.323			1.61545			0.807724	+	0.589561i	$0.200699\pi$
$242$	308.562	−	178.148i	1.27505	−	0.736151i
$243$			15.5885i			0.0641500i
$244$			328.691i			1.34709i
$245$	24.0502	+	13.8854i	0.0981640	+	0.0566750i
$246$			127.012i			0.516310i
$247$	−294.443	+	169.996i	−1.19208	+	0.688245i
$248$	−12.8315	−	22.2248i	−0.0517400	−	0.0896162i
$249$	−11.0473	−	6.37817i	−0.0443667	−	0.0256151i
$250$	−551.763	+	955.681i	−2.20705	+	3.82273i
$251$	37.5873	+	21.7010i	0.149750	+	0.0864584i	0.573003	−	0.819553i	$-0.305778\pi$
$251$	37.5873	+	21.7010i	0.149750	+	0.0864584i	−0.423253	+	0.906012i	$0.639112\pi$
$252$	87.9306	+	50.7668i	0.348931	+	0.201455i
$253$			9.97443i			0.0394246i
$254$		−	241.216i		−	0.949668i
$255$	−202.005	+	349.882i	−0.792175	+	1.37209i
$256$	−72.5900	−	125.730i	−0.283555	−	0.491131i
$257$	−15.3533	−	26.5927i	−0.0597404	−	0.103473i	0.834608	−	0.550844i	$-0.185694\pi$
$257$	−15.3533	−	26.5927i	−0.0597404	−	0.103473i	−0.894349	+	0.447370i	$0.852361\pi$
$258$	44.6129	+	25.7573i	0.172918	+	0.0998345i
$259$			112.889i			0.435864i
$260$	810.057			3.11561
$261$	−50.4657	−	87.4092i	−0.193355	−	0.334901i
$262$	−418.931	−	241.870i	−1.59897	−	0.923167i
$263$	−306.659			−1.16600			−0.583002	−	0.812471i	$-0.698122\pi$
$263$	−306.659			−1.16600			−0.583002	+	0.812471i	$0.698122\pi$
$264$	1.30171	−	0.751542i	0.00493072	−	0.00284675i
$265$	−597.365			−2.25421
$266$	198.199	−	343.291i	0.745109	−	1.29057i
$267$		−	157.388i		−	0.589467i
$268$	33.0293	−	312.916i	0.123243	−	1.16760i
$269$	−324.825			−1.20753			−0.603764	−	0.797163i	$-0.706333\pi$
$269$	−324.825			−1.20753			−0.603764	+	0.797163i	$0.706333\pi$
$270$	−125.575	−	72.5005i	−0.465091	−	0.268520i
$271$			313.474i			1.15673i	0.815778	+	0.578364i	$0.196309\pi$
$271$			313.474i			1.15673i	−0.815778	+	0.578364i	$0.803691\pi$
$272$	−156.892	−	271.744i	−0.576807	−	0.999060i
$273$			227.523i			0.833417i
$274$	189.294	−	327.867i	0.690855	−	1.19660i
$275$	−23.6227	+	13.6385i	−0.0859006	+	0.0495947i
$276$		−	191.988i		−	0.695607i
$277$	−160.316			−0.578757			−0.289379	−	0.957215i	$-0.593449\pi$
$277$	−160.316			−0.578757			−0.289379	+	0.957215i	$0.593449\pi$
$278$	−217.965	+	377.527i	−0.784047	+	1.35801i
$279$	−32.4692	+	18.7461i	−0.116377	+	0.0671903i
$280$	−121.274	+	70.0177i	−0.433122	+	0.250063i
$281$	−31.7414	−	18.3259i	−0.112959	−	0.0652167i	0.442456	−	0.896790i	$-0.354107\pi$
$281$	−31.7414	−	18.3259i	−0.112959	−	0.0652167i	−0.555415	+	0.831573i	$0.687441\pi$
$282$	−231.450			−0.820744
$283$	40.4768			0.143027			0.0715137	−	0.997440i	$-0.477217\pi$
$283$	40.4768			0.143027			0.0715137	+	0.997440i	$0.477217\pi$
$284$	266.190	−	461.054i	0.937287	−	1.62343i
$285$	−152.857	+	264.757i	−0.536341	+	0.928970i
$286$	19.6729	+	11.3582i	0.0687864	+	0.0397139i
$287$	89.6017	−	155.195i	0.312201	−	0.540748i
$288$	118.871	−	68.6301i	0.412746	−	0.238299i
$289$	−159.301	−	275.917i	−0.551214	−	0.954730i
$290$	938.846			3.23740
$291$	160.623	−	278.208i	0.551970	−	0.956041i
$292$	−372.279			−1.27493
$293$	−26.7511			−0.0913006			−0.0456503	−	0.998957i	$-0.514536\pi$
$293$	−26.7511			−0.0913006			−0.0456503	+	0.998957i	$0.514536\pi$
$294$	−7.49489	−	12.9815i	−0.0254928	−	0.0441549i
$295$		−	69.6575i		−	0.236127i
$296$	−27.8574	−	16.0835i	−0.0941129	−	0.0543361i
$297$	−1.09796	−	1.90172i	−0.00369683	−	0.00640311i
$298$	155.458	+	89.7539i	0.521672	+	0.301187i
$299$	372.580	−	215.109i	1.24609	−	0.719428i
$300$	454.689	−	262.515i	1.51563	−	0.875049i
$301$	−36.3413	−	62.9449i	−0.120735	−	0.209119i
$302$	−757.060	+	437.089i	−2.50682	+	1.44731i
$303$	−156.712	−	271.432i	−0.517200	−	0.895817i
$304$	−118.720	−	205.629i	−0.390527	−	0.676413i
$305$	−331.146	+	573.561i	−1.08572	+	1.88053i
$306$	188.855	−	109.036i	0.617175	−	0.356326i
$307$	46.1670	−	79.9636i	0.150381	−	0.260468i	−0.780987	−	0.624548i	$-0.785283\pi$
$307$	46.1670	−	79.9636i	0.150381	−	0.260468i	0.931368	+	0.364080i	$0.118617\pi$
$308$	−14.3029			−0.0464378
$309$	−155.520	+	89.7892i	−0.503299	+	0.290580i
$310$		−	348.746i		−	1.12499i
$311$		−	156.282i		−	0.502514i	−0.967920	−	0.251257i	$-0.919156\pi$
$311$		−	156.282i		−	0.502514i	0.967920	−	0.251257i	$-0.0808439\pi$
$312$	−56.1455	−	32.4156i	−0.179953	−	0.103896i
$313$			463.234i			1.47998i	0.672618	+	0.739990i	$0.265170\pi$
$313$			463.234i			1.47998i	−0.672618	+	0.739990i	$0.734830\pi$
$314$	263.900	−	152.363i	0.840447	−	0.485232i
$315$	102.292	+	177.175i	0.324736	+	0.562460i
$316$	−13.3681	−	7.71809i	−0.0423042	−	0.0244243i
$317$	−146.547	+	253.827i	−0.462293	+	0.800715i	−0.999075	−	0.0430064i	$-0.986306\pi$
$317$	−146.547	+	253.827i	−0.462293	+	0.800715i	0.536782	+	0.843721i	$0.319640\pi$
$318$	279.240	+	161.219i	0.878114	+	0.506979i
$319$	12.3132	+	7.10902i	0.0385993	+	0.0222853i
$320$			794.931i			2.48416i
$321$		−	214.359i		−	0.667786i
$322$	−250.796	+	434.391i	−0.778869	+	1.34904i
$323$	−229.887	−	398.175i	−0.711724	−	1.23274i
$324$	21.1335	+	36.6043i	0.0652269	+	0.112976i
$325$	1018.90	+	588.260i	3.13506	+	1.81003i
$326$			614.130i			1.88384i
$327$	43.2781			0.132349
$328$	25.5314	+	44.2217i	0.0778397	+	0.134822i
$329$	282.805	+	163.278i	0.859590	+	0.496285i
$330$	20.4261			0.0618971
$331$	290.899	−	167.951i	0.878849	−	0.507403i	0.00856996	−	0.999963i	$-0.497272\pi$
$331$	290.899	−	167.951i	0.878849	−	0.507403i	0.870279	+	0.492560i	$0.163939\pi$
$332$	−34.5879			−0.104181
$333$	−23.4970	+	40.6981i	−0.0705617	+	0.122216i
$334$		−	738.455i		−	2.21094i
$335$	372.889	−	512.759i	1.11310	−	1.53062i
$336$	−158.895			−0.472901
$337$	152.076	+	87.8009i	0.451263	+	0.260537i	0.708364	−	0.705848i	$-0.249434\pi$
$337$	152.076	+	87.8009i	0.451263	+	0.260537i	−0.257100	+	0.966385i	$0.582767\pi$
$338$		−	481.430i		−	1.42435i
$339$	−68.3983	−	118.469i	−0.201765	−	0.349467i
$340$			1095.44i			3.22189i
$341$	2.64073	−	4.57388i	0.00774408	−	0.0134131i
$342$	142.907	−	82.5076i	0.417858	−	0.241250i
$343$		−	331.973i		−	0.967851i
$344$	20.7104			0.0602048
$345$	193.422	−	335.016i	0.560642	−	0.971061i
$346$	−649.560	+	375.023i	−1.87734	+	1.08388i
$347$	−343.671	+	198.419i	−0.990407	+	0.571812i	−0.905396	−	0.424568i	$-0.860426\pi$
$347$	−343.671	+	198.419i	−0.990407	+	0.571812i	−0.0850110	+	0.996380i	$0.527093\pi$
$348$	−237.004	−	136.834i	−0.681046	−	0.393202i
$349$	353.558			1.01306			0.506530	−	0.862223i	$-0.330928\pi$
$349$	353.558			1.01306			0.506530	+	0.862223i	$0.330928\pi$
$350$	−1371.70			−3.91916
$351$	−47.3573	+	82.0253i	−0.134921	+	0.233690i
$352$	−9.66780	+	16.7451i	−0.0274653	+	0.0475714i
$353$	372.889	+	215.288i	1.05634	+	0.609880i	0.924418	−	0.381380i	$-0.124551\pi$
$353$	372.889	+	215.288i	1.05634	+	0.609880i	0.131924	+	0.991260i	$0.457884\pi$
$354$	−18.7995	+	32.5616i	−0.0531059	+	0.0919821i
$355$	928.995	−	536.356i	2.61689	−	1.51086i
$356$	−213.373	−	369.573i	−0.599362	−	1.03813i
$357$	−307.680			−0.861848
$358$	156.005	−	270.209i	0.435769	−	0.754774i
$359$	58.9796			0.164288			0.0821442	−	0.996620i	$-0.473823\pi$
$359$	58.9796			0.164288			0.0821442	+	0.996620i	$0.473823\pi$
$360$	−58.2949			−0.161930
$361$	6.54421	+	11.3349i	0.0181280	+	0.0313986i
$362$		−	424.378i		−	1.17232i
$363$	−181.232	−	104.634i	−0.499262	−	0.288249i
$364$	308.456	+	534.262i	0.847407	+	1.46775i
$365$	−649.623	−	375.060i	−1.77979	−	1.02756i
$366$	309.590	−	178.742i	0.845876	−	0.488366i
$367$	−456.018	+	263.282i	−1.24255	+	0.717389i	−0.969614	−	0.244641i	$-0.921330\pi$
$367$	−456.018	+	263.282i	−1.24255	+	0.717389i	−0.272941	+	0.962031i	$0.587996\pi$
$368$	150.226	+	260.198i	0.408221	+	0.707060i
$369$	64.6054	−	37.3000i	0.175083	−	0.101084i
$370$	−218.565	−	378.566i	−0.590717	−	1.02315i
$371$	−227.466	−	393.983i	−0.613117	−	1.06195i
$372$	−50.8288	+	88.0380i	−0.136636	+	0.236661i
$373$	249.837	−	144.244i	0.669806	−	0.386712i	−0.126197	−	0.992005i	$-0.540277\pi$
$373$	249.837	−	144.244i	0.669806	−	0.386712i	0.796003	+	0.605293i	$0.206944\pi$
$374$	−15.3597	+	26.6037i	−0.0410687	+	0.0711330i
$375$	648.149			1.72840
$376$	−80.5836	+	46.5249i	−0.214318	+	0.123737i
$377$		−	613.254i		−	1.62667i
$378$		−	110.428i		−	0.292137i
$379$	−191.476	−	110.549i	−0.505213	−	0.291685i	0.225651	−	0.974208i	$-0.427549\pi$
$379$	−191.476	−	110.549i	−0.505213	−	0.291685i	−0.730864	+	0.682523i	$0.760883\pi$
$380$			828.924i			2.18138i
$381$	−122.695	+	70.8383i	−0.322035	+	0.185927i
$382$	−359.208	−	622.167i	−0.940336	−	1.62871i
$383$	14.5269	+	8.38709i	0.0379292	+	0.0218984i	0.518845	−	0.854869i	$-0.326362\pi$
$383$	14.5269	+	8.38709i	0.0379292	+	0.0218984i	−0.480916	+	0.876767i	$0.659696\pi$
$384$	56.0451	−	97.0729i	0.145951	−	0.252794i
$385$	−24.9583	−	14.4097i	−0.0648268	−	0.0374278i
$386$	23.9924	+	13.8520i	0.0621566	+	0.0358861i
$387$		−	30.2568i		−	0.0781829i
$388$		−	871.039i		−	2.24494i
$389$	−209.748	+	363.295i	−0.539198	+	0.933919i	0.459749	+	0.888049i	$0.347939\pi$
$389$	−209.748	+	363.295i	−0.539198	+	0.933919i	−0.998947	+	0.0458702i	$0.985394\pi$
$390$	−440.510	−	762.985i	−1.12951	−	1.95637i
$391$	290.893	+	503.841i	0.743971	+	1.28860i
$392$	−5.21898	−	3.01318i	−0.0133137	−	0.00768668i
$393$			284.122i			0.722956i
$394$	23.9356			0.0607503
$395$	−15.5515	−	26.9359i	−0.0393708	−	0.0681922i
$396$	−5.15639	−	2.97704i	−0.0130212	−	0.00751779i
$397$	150.349			0.378714			0.189357	−	0.981908i	$-0.439360\pi$
$397$	150.349			0.378714			0.189357	+	0.981908i	$0.439360\pi$
$398$	498.764	−	287.961i	1.25318	−	0.723521i
$399$	−232.822			−0.583514
$400$	−410.822	+	711.565i	−1.02706	+	1.77891i
$401$		−	291.018i		−	0.725732i	−0.931841	−	0.362866i	$-0.881798\pi$
$401$		−	291.018i		−	0.725732i	0.931841	−	0.362866i	$-0.118202\pi$
$402$	−312.694	+	139.054i	−0.777846	+	0.345906i
$403$	−227.801			−0.565262
$404$	−735.971	−	424.913i	−1.82171	−	1.05176i
$405$			85.1655i			0.210285i
$406$	357.497	+	619.203i	0.880534	+	1.52513i
$407$		−	6.61998i		−	0.0162653i
$408$	43.8357	−	75.9257i	0.107440	−	0.186092i
$409$	−359.477	+	207.544i	−0.878917	+	0.507443i	−0.870301	−	0.492520i	$-0.836076\pi$
$409$	−359.477	+	207.544i	−0.878917	+	0.507443i	−0.00861573	+	0.999963i	$0.502743\pi$
$410$			693.915i			1.69248i
$411$	−222.362			−0.541026
$412$	−243.457	+	421.681i	−0.590916	+	1.02350i
$413$	45.9416	−	26.5244i	0.111239	−	0.0642238i
$414$	−180.831	+	104.403i	−0.436790	+	0.252181i
$415$	−60.3555	−	34.8463i	−0.145435	−	0.0839670i
$416$	833.986			2.00477
$417$	256.041			0.614007
$418$	−11.6227	+	20.1311i	−0.0278055	+	0.0481606i
$419$	−221.400	+	383.476i	−0.528400	+	0.915216i	0.471051	+	0.882106i	$0.343875\pi$
$419$	−221.400	+	383.476i	−0.528400	+	0.915216i	−0.999452	+	0.0331104i	$0.989459\pi$
$420$	480.397	+	277.357i	1.14380	+	0.660375i
$421$	−235.642	+	408.143i	−0.559719	+	0.969462i	0.437800	+	0.899072i	$0.355758\pi$
$421$	−235.642	+	408.143i	−0.559719	+	0.969462i	−0.997520	+	0.0703898i	$0.977576\pi$
$422$	−308.557	+	178.146i	−0.731179	+	0.422146i
$423$	67.9703	+	117.728i	0.160686	+	0.278317i
$424$	129.630			0.305732
$425$	−795.505	+	1377.86i	−1.87178	+	3.24201i
$426$	−579.016			−1.35919
$427$	−504.379			−1.18122
$428$	−290.610	−	503.352i	−0.678996	−	1.17606i
$429$		−	13.3423i		−	0.0311009i
$430$	243.737	+	140.722i	0.566830	+	0.327259i
$431$	159.370	+	276.037i	0.369768	+	0.640458i	0.989529	−	0.144333i	$-0.0461037\pi$
$431$	159.370	+	276.037i	0.369768	+	0.640458i	−0.619761	+	0.784791i	$0.712770\pi$
$432$	−57.2839	−	33.0729i	−0.132602	−	0.0765576i
$433$	539.981	−	311.758i	1.24707	−	0.719996i	0.276545	−	0.961001i	$-0.410810\pi$
$433$	539.981	−	311.758i	1.24707	−	0.719996i	0.970524	+	0.241005i	$0.0774770\pi$
$434$	230.010	−	132.797i	0.529978	−	0.305983i
$435$	−275.713	−	477.548i	−0.633822	−	1.09781i
$436$	101.624	−	58.6728i	0.233083	−	0.134571i
$437$	220.119	+	381.258i	0.503705	+	0.872443i
$438$	202.446	+	350.646i	0.462205	+	0.800562i
$439$	98.6993	−	170.952i	0.224828	−	0.389413i	−0.731440	−	0.681906i	$-0.761151\pi$
$439$	98.6993	−	170.952i	0.224828	−	0.389413i	0.956268	+	0.292493i	$0.0944848\pi$
$440$	7.11171	−	4.10595i	0.0161630	−	0.00933170i
$441$	−4.40208	+	7.62463i	−0.00998204	+	0.0172894i
$442$	1324.99			2.99772
$443$	623.019	−	359.700i	1.40636	−	0.811964i	0.411328	−	0.911488i	$-0.365065\pi$
$443$	623.019	−	359.700i	1.40636	−	0.811964i	0.995035	+	0.0995237i	$0.0317319\pi$
$444$			127.421i			0.286985i
$445$		−	859.866i		−	1.93228i
$446$	40.5127	+	23.3900i	0.0908356	+	0.0524439i
$447$		−	105.433i		−	0.235867i
$448$	−524.285	+	302.696i	−1.17028	+	0.675662i
$449$	174.360	+	302.001i	0.388330	+	0.672607i	0.992225	−	0.124457i	$-0.0397188\pi$
$449$	174.360	+	302.001i	0.388330	+	0.672607i	−0.603895	+	0.797064i	$0.706385\pi$
$450$	−494.520	−	285.511i	−1.09893	−	0.634469i
$451$	−5.25438	+	9.10086i	−0.0116505	+	0.0201793i
$452$	−321.221	−	185.457i	−0.710667	−	0.410304i
$453$	444.655	+	256.721i	0.981577	+	0.566714i
$454$		−	667.221i		−	1.46965i
$455$			1243.04i			2.73196i
$456$	33.1706	−	57.4531i	0.0727425	−	0.125994i
$457$	65.9402	+	114.212i	0.144289	+	0.249916i	0.929108	−	0.369810i	$-0.120577\pi$
$457$	65.9402	+	114.212i	0.144289	+	0.249916i	−0.784818	+	0.619726i	$0.787244\pi$
$458$	314.643	+	544.978i	0.686994	+	1.18991i
$459$	−110.923	−	64.0415i	−0.241663	−	0.139524i
$460$		−	1048.90i		−	2.28022i
$461$	−157.396			−0.341423			−0.170712	−	0.985321i	$-0.554607\pi$
$461$	−157.396			−0.341423			−0.170712	+	0.985321i	$0.554607\pi$
$462$	7.77790	+	13.4717i	0.0168353	+	0.0291596i
$463$	−174.089	−	100.511i	−0.376003	−	0.217085i	0.300075	−	0.953916i	$-0.402988\pi$
$463$	−174.089	−	100.511i	−0.376003	−	0.217085i	−0.676078	+	0.736830i	$0.736322\pi$
$464$	428.278			0.923012
$465$	−177.391	+	102.417i	−0.381486	+	0.220251i
$466$	464.555			0.996898
$467$	252.832	−	437.917i	0.541396	−	0.937725i	−0.457429	−	0.889246i	$-0.651230\pi$
$467$	252.832	−	437.917i	0.541396	−	0.937725i	0.998824	−	0.0484783i	$-0.0154372\pi$
$468$			256.812i			0.548745i
$469$	480.173	+	50.6837i	1.02382	+	0.108068i
$470$	−1264.49			−2.69041
$471$	−155.000	−	89.4895i	−0.329088	−	0.189999i
$472$			15.1159i			0.0320253i
$473$	2.13111	+	3.69119i	0.00450552	+	0.00780379i
$474$			16.7884i			0.0354186i
$475$	−601.961	+	1042.63i	−1.26729	+	2.19500i
$476$	−722.484	+	417.126i	−1.51782	+	0.876316i
$477$		−	189.382i		−	0.397028i
$478$	−213.679			−0.447027
$479$	−147.489	+	255.458i	−0.307909	+	0.533315i	−0.977905	−	0.209050i	$-0.932963\pi$
$479$	−147.489	+	255.458i	−0.307909	+	0.533315i	0.669995	+	0.742365i	$0.266296\pi$
$480$	649.435	−	374.951i	1.35299	−	0.781148i
$481$	−247.279	+	142.767i	−0.514095	+	0.296813i
$482$	−994.280	−	574.048i	−2.06282	−	1.19097i
$483$	294.607			0.609952
$484$	−567.418			−1.17235
$485$	877.544	−	1519.95i	1.80937	−	3.13392i
$486$	22.9848	−	39.8109i	0.0472939	−	0.0819154i
$487$	−471.197	−	272.046i	−0.967551	−	0.558616i	−0.0690623	−	0.997612i	$-0.522001\pi$
$487$	−471.197	−	272.046i	−0.967551	−	0.558616i	−0.898489	+	0.438996i	$0.855334\pi$
$488$	71.8598	−	124.465i	0.147254	−	0.255051i
$489$	312.380	−	180.353i	0.638814	−	0.368820i
$490$	−40.9474	−	70.9229i	−0.0835660	−	0.144741i
$491$	−531.161			−1.08179			−0.540897	−	0.841089i	$-0.681915\pi$
$491$	−531.161			−1.08179			−0.540897	+	0.841089i	$0.681915\pi$
$492$	101.136	−	175.173i	0.205562	−	0.356043i
$493$	829.306			1.68216
$494$	1002.62			2.02960
$495$	−5.99856	−	10.3898i	−0.0121183	−	0.0209895i
$496$		−	159.089i		−	0.320744i
$497$	707.492	+	408.471i	1.42352	+	0.821872i
$498$	18.8089	+	32.5780i	0.0377690	+	0.0654178i
$499$	−175.948	−	101.584i	−0.352601	−	0.203574i	0.313229	−	0.949678i	$-0.398589\pi$
$499$	−175.948	−	101.584i	−0.352601	−	0.203574i	−0.665830	+	0.746103i	$0.731922\pi$
$500$	1521.96	−	878.706i	3.04393	−	1.75741i
$501$	−375.619	+	216.863i	−0.749738	+	0.432861i
$502$	−63.9954	−	110.843i	−0.127481	−	0.220803i
$503$	627.859	−	362.495i	1.24823	−	0.720665i	0.277473	−	0.960734i	$-0.410503\pi$
$503$	627.859	−	362.495i	1.24823	−	0.720665i	0.970756	+	0.240068i	$0.0771699\pi$
$504$	−22.1977	−	38.4476i	−0.0440431	−	0.0762848i
$505$	−856.173	−	1482.94i	−1.69539	−	2.93651i
$506$	14.7071	−	25.4734i	0.0290654	−	0.0503427i
$507$	−244.882	+	141.383i	−0.483002	+	0.278861i
$508$	−192.073	+	332.680i	−0.378097	+	0.654883i
$509$	−52.0612			−0.102281			−0.0511406	−	0.998691i	$-0.516286\pi$
$509$	−52.0612			−0.102281			−0.0511406	+	0.998691i	$0.516286\pi$
$510$	1031.79	−	595.702i	2.02311	−	1.16804i
$511$		−	571.266i		−	1.11794i
$512$			686.990i			1.34178i
$513$	−83.9357	−	48.4603i	−0.163617	−	0.0944646i
$514$			90.5522i			0.176172i
$515$	−849.660	+	490.552i	−1.64983	+	0.952527i
$516$	−41.0196	−	71.0480i	−0.0794953	−	0.137690i
$517$	−16.5841	−	9.57486i	−0.0320776	−	0.0185200i
$518$	166.452	−	288.303i	0.321336	−	0.556570i
$519$	381.515	+	220.268i	0.735096	+	0.424408i
$520$	−306.743	−	177.098i	−0.589891	−	0.340574i
$521$			868.381i			1.66676i	0.552702	+	0.833379i	$0.313597\pi$
$521$			868.381i			1.66676i	−0.552702	+	0.833379i	$0.686403\pi$
$522$			297.642i			0.570196i
$523$	141.729	−	245.481i	0.270992	−	0.469371i	−0.698124	−	0.715976i	$-0.745982\pi$
$523$	141.729	−	245.481i	0.270992	−	0.469371i	0.969116	+	0.246605i	$0.0793151\pi$
$524$	385.188	+	667.165i	0.735092	+	1.27322i
$525$	402.831	+	697.724i	0.767298	+	1.32900i
$526$	783.168	+	452.162i	1.48891	+	0.859624i
$527$		−	308.056i		−	0.584546i
$528$	9.31785			0.0176474
$529$	−14.0330	−	24.3059i	−0.0265274	−	0.0459469i
$530$	1525.59	+	880.801i	2.87848	+	1.66189i
$531$	22.0835			0.0415885
$532$	−546.705	+	315.640i	−1.02764	+	0.593309i
$533$	453.266			0.850404
$534$	−232.064	+	401.947i	−0.434578	+	0.752711i
$535$		−	1171.12i		−	2.18902i
$536$	−80.9183	+	111.271i	−0.150967	+	0.207594i
$537$	−183.258			−0.341262
$538$	829.561	+	478.947i	1.54193	+	0.890236i
$539$		−	1.24023i		−	0.00230098i
$540$	115.460	+	199.983i	0.213815	+	0.370339i
$541$			318.302i			0.588359i	0.955750	+	0.294180i	$0.0950464\pi$
$541$			318.302i			0.588359i	−0.955750	+	0.294180i	$0.904954\pi$
$542$	462.210	−	800.571i	0.852785	−	1.47707i
$543$	−215.862	+	124.628i	−0.397536	+	0.229518i
$544$			1127.80i			2.07316i
$545$	236.444			0.433842
$546$	335.477	−	581.064i	0.614427	−	1.06422i
$547$	804.852	−	464.681i	1.47139	−	0.849509i	0.471909	−	0.881647i	$-0.343565\pi$
$547$	804.852	−	464.681i	1.47139	−	0.849509i	0.999483	+	0.0321385i	$0.0102318\pi$
$548$	−522.143	+	301.459i	−0.952815	+	0.550108i
$549$	−181.836	−	104.983i	−0.331213	−	0.191226i
$550$	80.4389			0.146253
$551$	627.537			1.13891
$552$	−41.9732	+	72.6997i	−0.0760384	+	0.131702i
$553$	11.8435	−	20.5135i	0.0214168	−	0.0370949i
$554$	409.426	+	236.382i	0.739035	+	0.426682i
$555$	−128.373	+	222.349i	−0.231303	+	0.400628i
$556$	601.227	−	347.119i	1.08134	−	0.624314i
$557$	−64.4474	−	111.626i	−0.115704	−	0.200406i	0.802357	−	0.596845i	$-0.203579\pi$
$557$	−64.4474	−	111.626i	−0.115704	−	0.200406i	−0.918061	+	0.396439i	$0.870246\pi$
$558$	110.563			0.198141
$559$	91.9193	−	159.209i	0.164435	−	0.284810i
$560$	−868.101			−1.55018
$561$	18.0428			0.0321619
$562$	54.0422	+	93.6038i	0.0961605	+	0.166555i
$563$			994.326i			1.76612i	0.469259	+	0.883061i	$0.344521\pi$
$563$			994.326i			1.76612i	−0.469259	+	0.883061i	$0.655479\pi$
$564$	319.211	+	184.297i	0.565978	+	0.326767i
$565$	−373.685	−	647.241i	−0.661389	−	1.14556i
$566$	−103.372	−	59.6821i	−0.182637	−	0.105445i
$567$	−56.1697	+	32.4296i	−0.0990647	+	0.0571950i
$568$	−201.595	+	116.391i	−0.354921	+	0.204914i
$569$	−277.111	−	479.971i	−0.487015	−	0.843534i	0.512874	−	0.858464i	$-0.328581\pi$
$569$	−277.111	−	479.971i	−0.487015	−	0.843534i	−0.999889	+	0.0149300i	$0.995247\pi$
$570$	780.755	−	450.769i	1.36975	−	0.790823i
$571$	−192.986	−	334.262i	−0.337980	−	0.585398i	0.646073	−	0.763276i	$-0.276410\pi$
$571$	−192.986	−	334.262i	−0.337980	−	0.585398i	−0.984053	+	0.177878i	$0.943077\pi$
$572$	−18.0884	−	31.3300i	−0.0316230	−	0.0547727i
$573$	−210.979	+	365.426i	−0.368200	+	0.637742i
$574$	−457.662	+	264.231i	−0.797321	+	0.460333i
$575$	761.705	−	1319.31i	1.32470	−	2.29446i
$576$	−252.017			−0.437529
$577$	−109.766	+	63.3733i	−0.190235	+	0.109832i	−0.592093	−	0.805870i	$-0.701698\pi$
$577$	−109.766	+	63.3733i	−0.190235	+	0.109832i	0.401857	+	0.915702i	$0.368365\pi$
$578$			939.542i			1.62550i
$579$		−	16.2718i		−	0.0281033i
$580$	−1294.84	−	747.576i	−2.23248	−	1.28892i
$581$		−	53.0755i		−	0.0913520i
$582$	−820.422	+	473.671i	−1.40966	+	0.813868i
$583$	13.3390	+	23.1038i	0.0228799	+	0.0396292i
$584$	140.970	+	81.3893i	0.241388	+	0.139365i
$585$	−258.731	+	448.135i	−0.442275	+	0.766042i
$586$	68.3188	+	39.4439i	0.116585	+	0.0673103i
$587$	−405.255	−	233.974i	−0.690383	−	0.398593i	0.113373	−	0.993553i	$-0.463835\pi$
$587$	−405.255	−	233.974i	−0.690383	−	0.398593i	−0.803755	+	0.594960i	$0.797168\pi$
$588$			23.8719i			0.0405984i
$589$		−	233.106i		−	0.395766i
$590$	−102.708	+	177.896i	−0.174082	+	0.301519i
$591$	−7.02922	−	12.1750i	−0.0118938	−	0.0206006i
$592$	−99.7039	−	172.692i	−0.168419	−	0.291710i
$593$	62.6063	+	36.1458i	0.105576	+	0.0609541i	0.551858	−	0.833938i	$-0.313919\pi$
$593$	62.6063	+	36.1458i	0.105576	+	0.0609541i	−0.446282	+	0.894892i	$0.647252\pi$
$594$			6.47567i			0.0109018i
$595$	−1680.97			−2.82516
$596$	−142.937	−	247.574i	−0.239827	−	0.415392i
$597$	−292.946	−	169.132i	−0.490697	−	0.283304i
$598$	−1268.69			−2.12156
$599$	314.802	−	181.751i	0.525545	−	0.303424i	−0.213655	−	0.976909i	$-0.568537\pi$
$599$	314.802	−	181.751i	0.525545	−	0.303424i	0.739201	+	0.673485i	$0.235204\pi$
$600$	−229.568			−0.382614
$601$	−238.202	+	412.578i	−0.396343	+	0.686485i	−0.993272	−	0.115809i	$-0.963054\pi$
$601$	−238.202	+	412.578i	−0.396343	+	0.686485i	0.596929	+	0.802294i	$0.296387\pi$
$602$			214.338i			0.356043i
$603$	162.560	+	118.217i	0.269585	+	0.196048i
$604$	1392.17			2.30491
$605$	−990.138	−	571.656i	−1.63659	−	0.944886i
$606$			924.271i			1.52520i
$607$	473.592	+	820.285i	0.780217	+	1.35138i	0.931815	+	0.362933i	$0.118225\pi$
$607$	473.592	+	820.285i	0.780217	+	1.35138i	−0.151598	+	0.988442i	$0.548442\pi$
$608$			853.410i			1.40363i
$609$	209.974	−	363.685i	0.344784	−	0.597184i
$610$	1691.41	−	976.534i	2.77280	−	1.60088i
$611$			825.968i			1.35183i
$612$	−347.288			−0.567464
$613$	−261.356	+	452.682i	−0.426356	+	0.738470i	−0.996546	−	0.0830427i	$-0.973536\pi$
$613$	−261.356	+	452.682i	−0.426356	+	0.738470i	0.570190	+	0.821513i	$0.306870\pi$
$614$	−235.809	+	136.144i	−0.384054	+	0.221733i
$615$	352.963	−	203.783i	0.573924	−	0.331355i
$616$	5.41604	+	3.12695i	0.00879228	+	0.00507622i
$617$	500.341			0.810926			0.405463	−	0.914111i	$-0.367110\pi$
$617$	500.341			0.810926			0.405463	+	0.914111i	$0.367110\pi$
$618$	529.569			0.856908
$619$	−279.278	+	483.724i	−0.451177	+	0.781461i	−0.998459	−	0.0554868i	$-0.982329\pi$
$619$	−279.278	+	483.724i	−0.451177	+	0.781461i	0.547283	+	0.836948i	$0.315662\pi$
$620$	−277.696	+	480.984i	−0.447897	+	0.775781i
$621$	106.210	+	61.3204i	0.171031	+	0.0987447i
$622$	−230.434	+	399.123i	−0.370473	+	0.641678i
$623$	567.113	−	327.423i	0.910293	−	0.525558i
$624$	−200.949	−	348.054i	−0.322034	−	0.557779i
$625$	1927.45			3.08392
$626$	683.028	−	1183.04i	1.09110	−	1.88984i
$627$	13.6530			0.0217752
$628$	−485.289			−0.772753
$629$	−193.064	−	334.397i	−0.306938	−	0.531632i
$630$		−	603.308i		−	0.957632i
$631$	536.155	+	309.549i	0.849691	+	0.490569i	0.860547	−	0.509372i	$-0.170122\pi$
$631$	536.155	+	309.549i	0.849691	+	0.490569i	−0.0108557	+	0.999941i	$0.503456\pi$
$632$	3.37473	+	5.84520i	0.00533976	+	0.00924873i
$633$	181.229	+	104.633i	0.286302	+	0.165297i
$634$	748.523	−	432.160i	1.18064	−	0.681640i
$635$	−670.330	+	387.015i	−1.05564	+	0.609473i
$636$	−256.749	−	444.702i	−0.403693	−	0.699217i
$637$	−46.3268	+	26.7468i	−0.0727266	+	0.0419887i
$638$	−20.9642	−	36.3110i	−0.0328592	−	0.0569138i
$639$	170.041	+	294.519i	0.266104	+	0.460907i
$640$	306.195	−	530.345i	0.478430	−	0.828664i
$641$	−129.485	+	74.7583i	−0.202005	+	0.116628i	−0.597590	−	0.801802i	$-0.703875\pi$
$641$	−129.485	+	74.7583i	−0.202005	+	0.116628i	0.395585	+	0.918429i	$0.370542\pi$
$642$	−316.068	+	547.446i	−0.492318	+	0.852720i
$643$	−843.958			−1.31253			−0.656266	−	0.754530i	$-0.727865\pi$
$643$	−843.958			−1.31253			−0.656266	+	0.754530i	$0.727865\pi$
$644$	691.787	−	399.403i	1.07420	−	0.620191i
$645$		−	165.304i		−	0.256285i
$646$			1355.85i			2.09884i
$647$	−874.588	−	504.944i	−1.35176	−	0.780439i	−0.363263	−	0.931687i	$-0.618337\pi$
$647$	−874.588	−	504.944i	−1.35176	−	0.780439i	−0.988496	+	0.151248i	$0.951671\pi$
$648$		−	18.4812i		−	0.0285204i
$649$	−2.69409	+	1.55543i	−0.00415114	+	0.00239666i
$650$	−1734.75	−	3004.68i	−2.66885	−	4.62258i
$651$	−135.095	−	77.9972i	−0.207519	−	0.119811i
$652$	489.014	−	846.998i	0.750022	−	1.29908i
$653$	−684.970	−	395.467i	−1.04896	−	0.605616i	−0.126600	−	0.991954i	$-0.540407\pi$
$653$	−684.970	−	395.467i	−1.04896	−	0.605616i	−0.922357	+	0.386338i	$0.873740\pi$
$654$	−110.527	−	63.8125i	−0.169001	−	0.0975727i
$655$			1552.26i			2.36986i
$656$			316.547i			0.482540i
$657$	118.905	−	205.950i	0.180982	−	0.313470i
$658$	−481.498	−	833.980i	−0.731761	−	1.26745i
$659$	−492.640	−	853.277i	−0.747557	−	1.29481i	−0.948991	−	0.315304i	$-0.897894\pi$
$659$	−492.640	−	853.277i	−0.747557	−	1.29481i	0.201434	−	0.979502i	$-0.435440\pi$
$660$	−28.1713	−	16.2647i	−0.0426837	−	0.0246435i
$661$			415.876i			0.629161i	0.949231	+	0.314581i	$0.101864\pi$
$661$			415.876i			0.629161i	−0.949231	+	0.314581i	$0.898136\pi$
$662$	−990.557			−1.49631
$663$	−389.113	−	673.963i	−0.586897	−	1.01654i
$664$	13.0974	+	7.56177i	0.0197250	+	0.0113882i
$665$	−1271.99			−1.91277
$666$	120.017	−	69.2917i	0.180205	−	0.104042i
$667$	−794.070			−1.19051
$668$	−588.011	+	1018.46i	−0.880255	+	1.52465i
$669$		−	27.4759i		−	0.0410702i
$670$	−1708.36	+	759.704i	−2.54979	+	1.13389i
$671$	29.5776			0.0440799
$672$	494.588	+	285.550i	0.735994	+	0.424926i
$673$		−	778.441i		−	1.15667i	−0.815798	−	0.578336i	$-0.803702\pi$
$673$		−	778.441i		−	1.15667i	0.815798	−	0.578336i	$-0.196298\pi$
$674$	−258.921	−	448.464i	−0.384156	−	0.665377i
$675$			335.386i			0.496869i
$676$	−383.349	+	663.980i	−0.567085	+	0.982220i
$677$	1012.99	−	584.850i	1.49629	−	0.863884i	0.496301	−	0.868151i	$-0.334691\pi$
$677$	1012.99	−	584.850i	1.49629	−	0.863884i	0.999991	+	0.00426617i	$0.00135797\pi$
$678$			403.407i			0.594996i
$679$	1336.62			1.96851
$680$	239.491	−	414.810i	0.352192	−	0.610015i
$681$	−339.385	+	195.944i	−0.498363	+	0.287730i
$682$	−13.4882	+	7.78740i	−0.0197774	+	0.0114185i
$683$	−46.9149	−	27.0863i	−0.0686894	−	0.0396578i	0.465262	−	0.885173i	$-0.345960\pi$
$683$	−46.9149	−	27.0863i	−0.0686894	−	0.0396578i	−0.533951	+	0.845515i	$0.679293\pi$
$684$	−262.794			−0.384201
$685$	−1214.84			−1.77349
$686$	−489.487	+	847.816i	−0.713537	+	1.23588i
$687$	184.804	−	320.090i	0.269001	−	0.465924i
$688$	111.187	+	64.1936i	0.161608	+	0.0933046i
$689$	575.339	−	996.517i	0.835035	−	1.44632i
$690$	−987.947	+	570.392i	−1.43181	+	0.826655i
$691$	−97.2794	−	168.493i	−0.140781	−	0.243839i	0.787010	−	0.616940i	$-0.211628\pi$
$691$	−97.2794	−	168.493i	−0.140781	−	0.243839i	−0.927791	+	0.373101i	$0.878295\pi$
$692$	1194.48			1.72613
$693$	4.56830	−	7.91253i	0.00659207	−	0.0114178i
$694$	1170.26			1.68625
$695$	1398.85			2.01273
$696$	59.8307	+	103.630i	0.0859636	+	0.148893i
$697$			612.952i			0.879415i
$698$	−902.940	−	521.313i	−1.29361	−	0.746867i
$699$	−136.427	−	236.298i	−0.195174	−	0.338051i
$700$	1891.83	+	1092.25i	2.70262	+	1.56036i
$701$	−1179.30	+	680.867i	−1.68230	+	0.971279i	−0.722181	+	0.691704i	$0.756860\pi$
$701$	−1179.30	+	680.867i	−1.68230	+	0.971279i	−0.960124	+	0.279575i	$0.909807\pi$
$702$	241.889	−	139.655i	0.344571	−	0.198938i
$703$	−146.092	−	253.039i	−0.207812	−	0.359941i
$704$	30.7449	−	17.7506i	0.0436718	−	0.0252139i
$705$	371.347	+	643.191i	0.526733	+	0.912328i
$706$	−634.873	−	1099.63i	−0.899254	−	1.55755i
$707$	652.033	−	1129.35i	0.922253	−	1.59739i
$708$	51.8558	−	29.9390i	0.0732427	−	0.0422867i
$709$	104.102	−	180.310i	0.146829	−	0.254316i	−0.783225	−	0.621739i	$-0.786427\pi$
$709$	104.102	−	180.310i	0.146829	−	0.254316i	0.930054	+	0.367423i	$0.119760\pi$
$710$	−3163.38			−4.45546
$711$	8.53950	−	4.93028i	0.0120105	−	0.00693429i
$712$			186.594i			0.262070i
$713$			294.967i			0.413698i
$714$	785.774	+	453.667i	1.10052	+	0.635388i
$715$		−	72.8939i		−	0.101949i
$716$	−430.320	+	248.445i	−0.601005	+	0.346991i
$717$	62.7515	+	108.689i	0.0875196	+	0.151588i
$718$	−150.626	−	86.9641i	−0.209786	−	0.121120i
$719$	−267.773	+	463.797i	−0.372425	+	0.645058i	−0.989938	−	0.141502i	$-0.954807\pi$
$719$	−267.773	+	463.797i	−0.372425	+	0.645058i	0.617513	+	0.786560i	$0.288140\pi$
$720$	−312.963	−	180.689i	−0.434671	−	0.250957i
$721$	−647.073	−	373.588i	−0.897466	−	0.518152i
$722$		−	38.5972i		−	0.0534587i
$723$			674.327i			0.932679i
$724$	−337.920	+	585.295i	−0.466741	+	0.808419i
$725$	−1085.77	−	1880.61i	−1.49762	−	2.59395i
$726$	308.562	+	534.445i	0.425017	+	0.736151i
$727$	894.592	+	516.493i	1.23053	+	0.710444i	0.967140	−	0.254246i	$-0.0818273\pi$
$727$	894.592	+	516.493i	1.23053	+	0.710444i	0.263386	+	0.964690i	$0.415161\pi$
$728$		−	269.744i		−	0.370528i
$729$	−27.0000			−0.0370370
$730$	1106.03	+	1915.71i	1.51512	+	2.62426i
$731$	215.299	+	124.303i	0.294526	+	0.170045i
$732$	−569.309			−0.777745
$733$	−510.272	+	294.606i	−0.696142	+	0.401918i	−0.805909	−	0.592039i	$-0.798323\pi$
$733$	−510.272	+	294.606i	−0.696142	+	0.401918i	0.109767	+	0.993957i	$0.464990\pi$
$734$	1552.81			2.11555
$735$	−24.0502	+	41.6561i	−0.0327213	+	0.0566750i
$736$		−	1079.88i		−	1.46723i
$737$	−28.1581	−	2.97217i	−0.0382064	−	0.00403280i
$738$	−219.992			−0.298092
$739$	−114.488	−	66.0996i	−0.154923	−	0.0894446i	0.420535	−	0.907277i	$-0.361843\pi$
$739$	−114.488	−	66.0996i	−0.154923	−	0.0894446i	−0.575457	+	0.817832i	$0.695176\pi$
$740$			696.149i			0.940742i
$741$	−294.443	−	509.989i	−0.397358	−	0.688245i
$742$			1341.58i			1.80806i
$743$	−346.113	+	599.486i	−0.465832	+	0.806845i	−0.999239	−	0.0390143i	$-0.987578\pi$
$743$	−346.113	+	599.486i	−0.465832	+	0.806845i	0.533407	+	0.845859i	$0.320912\pi$
$744$	38.4945	−	22.2248i	0.0517400	−	0.0298721i
$745$		−	576.018i		−	0.773178i
$746$	−850.737			−1.14040
$747$	11.0473	−	19.1345i	0.0147889	−	0.0256151i
$748$	42.3676	−	24.4609i	0.0566412	−	0.0327018i
$749$	772.399	−	445.945i	1.03124	−	0.595387i
$750$	−1655.29	−	955.681i	−2.20705	−	1.27424i
$751$	68.6022			0.0913477			0.0456739	−	0.998956i	$-0.485456\pi$
$751$	68.6022			0.0913477			0.0456739	+	0.998956i	$0.485456\pi$
$752$	−576.830			−0.767062
$753$	−37.5873	+	65.1031i	−0.0499168	+	0.0864584i
$754$	−904.230	+	1566.17i	−1.19924	+	2.07715i
$755$	2429.31	+	1402.56i	3.21763	+	1.85770i
$756$	−87.9306	+	152.300i	−0.116310	+	0.201455i
$757$	−44.0085	+	25.4083i	−0.0581353	+	0.0335645i	−0.528786	−	0.848755i	$-0.677353\pi$
$757$	−44.0085	+	25.4083i	−0.0581353	+	0.0335645i	0.470651	+	0.882320i	$0.344019\pi$
$758$	326.003	+	564.654i	0.430083	+	0.744926i
$759$	−17.2762			−0.0227618
$760$	181.223	−	313.888i	0.238451	−	0.413010i
$761$	511.392			0.672000			0.336000	−	0.941862i	$-0.390926\pi$
$761$	511.392			0.672000			0.336000	+	0.941862i	$0.390926\pi$
$762$	417.798			0.548291
$763$	90.0339	+	155.943i	0.118000	+	0.204382i
$764$			1144.11i			1.49753i
$765$	−606.014	−	349.882i	−0.792175	−	0.457362i
$766$	−24.7332	−	42.8391i	−0.0322887	−	0.0559257i
$767$	116.202	+	67.0892i	0.151502	+	0.0874696i
$768$	217.770	−	125.730i	0.283555	−	0.163710i
$769$	−1075.40	+	620.882i	−1.39844	+	0.807388i	−0.994229	−	0.107279i	$-0.965786\pi$
$769$	−1075.40	+	620.882i	−1.39844	+	0.807388i	−0.404209	+	0.914667i	$0.632453\pi$
$770$	42.4935	+	73.6009i	0.0551864	+	0.0955856i
$771$	46.0598	−	26.5927i	0.0597404	−	0.0344911i
$772$	−22.0600	−	38.2090i	−0.0285751	−	0.0494935i
$773$	461.448	+	799.252i	0.596958	+	1.03396i	0.993267	+	0.115844i	$0.0369573\pi$
$773$	461.448	+	799.252i	0.596958	+	1.03396i	−0.396310	+	0.918117i	$0.629709\pi$
$774$	−44.6129	+	77.2719i	−0.0576395	+	0.0998345i
$775$	−698.576	+	403.323i	−0.901389	+	0.520417i
$776$	−190.430	+	329.835i	−0.245400	+	0.425045i
$777$	−195.529			−0.251646
$778$	1071.34	−	618.538i	1.37704	−	0.795036i
$779$			463.822i			0.595407i
$780$			1403.06i			1.79880i
$781$	−41.4884	−	23.9534i	−0.0531222	−	0.0306701i
$782$		−	1715.66i		−	2.19394i
$783$	151.397	−	87.4092i	0.193355	−	0.111634i
$784$	−18.6791	−	32.3532i	−0.0238254	−	0.0412669i
$785$	−846.824	−	488.914i	−1.07876	−	0.622820i
$786$	418.931	−	725.610i	0.532991	−	0.923167i
$787$	1018.71	+	588.152i	1.29442	+	0.747335i	0.979435	−	0.201761i	$-0.0646665\pi$
$787$	1018.71	+	588.152i	1.29442	+	0.747335i	0.314987	+	0.949096i	$0.398000\pi$
$788$	−33.0116	−	19.0593i	−0.0418929	−	0.0241869i
$789$		−	531.149i		−	0.673193i
$790$			91.7212i			0.116103i
$791$	284.586	−	492.917i	0.359780	−	0.623157i
$792$	1.30171	+	2.25463i	0.00164357	+	0.00284675i
$793$	−637.872	−	1104.83i	−0.804378	−	1.39322i
$794$	−383.973	−	221.687i	−0.483593	−	0.279202i
$795$		−	1034.67i		−	1.30147i
$796$	−917.182			−1.15224
$797$	503.932	+	872.835i	0.632286	+	1.09515i	0.987083	+	0.160208i	$0.0512164\pi$
$797$	503.932	+	872.835i	0.632286	+	1.09515i	−0.354798	+	0.934943i	$0.615450\pi$
$798$	594.597	+	343.291i	0.745109	+	0.430189i
$799$	−1116.96			−1.39795
$800$	2557.51	−	1476.58i	3.19689	−	1.84572i
$801$	272.603			0.340329
$802$	−429.100	+	743.223i	−0.535038	+	0.926713i
$803$			33.4999i			0.0417185i
$804$	541.987	+	57.2083i	0.674113	+	0.0711547i
$805$	1609.55			1.99944
$806$	581.774	+	335.887i	0.721803	+	0.416733i
$807$		−	562.613i		−	0.697167i
$808$	185.793	+	321.802i	0.229941	+	0.398270i
$809$		−	590.352i		−	0.729731i	−0.931060	−	0.364865i	$-0.881115\pi$
$809$		−	590.352i		−	0.729731i	0.931060	−	0.364865i	$-0.118885\pi$
$810$	125.575	−	217.502i	0.155030	−	0.268520i
$811$	−766.689	+	442.648i	−0.945362	+	0.545805i	−0.891637	−	0.452751i	$-0.850443\pi$
$811$	−766.689	+	442.648i	−0.945362	+	0.545805i	−0.0537251	+	0.998556i	$0.517109\pi$
$812$		−	1138.66i		−	1.40229i
$813$	−542.952			−0.667838
$814$	−9.76101	+	16.9066i	−0.0119914	+	0.0207697i
$815$	1706.65	−	985.334i	2.09405	−	1.20900i
$816$	470.675	−	271.744i	0.576807	−	0.333020i
$817$	162.917	+	94.0602i	0.199409	+	0.115129i
$818$	1224.08			1.49643
$819$	−394.081			−0.481174
$820$	552.545	−	957.036i	0.673835	−	1.16712i
$821$	745.630	−	1291.47i	0.908197	−	1.57304i	0.0916301	−	0.995793i	$-0.470792\pi$
$821$	745.630	−	1291.47i	0.908197	−	1.57304i	0.816567	−	0.577251i	$-0.195874\pi$
$822$	567.883	+	327.867i	0.690855	+	0.398865i
$823$	−355.994	+	616.600i	−0.432557	+	0.749211i	−0.997093	−	0.0761979i	$-0.975722\pi$
$823$	−355.994	+	616.600i	−0.432557	+	0.749211i	0.564536	+	0.825409i	$0.309055\pi$
$824$	184.379	−	106.451i	0.223761	−	0.129189i
$825$	−23.6227	−	40.9156i	−0.0286335	−	0.0495947i
$826$	−156.439			−0.189393
$827$	279.894	−	484.790i	0.338445	−	0.586203i	−0.645696	−	0.763595i	$-0.723433\pi$
$827$	279.894	−	484.790i	0.338445	−	0.586203i	0.984140	+	0.177392i	$0.0567659\pi$
$828$	332.532			0.401609
$829$	−309.387			−0.373206			−0.186603	−	0.982435i	$-0.559748\pi$
$829$	−309.387			−0.373206			−0.186603	+	0.982435i	$0.559748\pi$
$830$	102.760	+	177.986i	0.123807	+	0.214441i
$831$		−	277.675i		−	0.334146i
$832$	−1326.09	−	765.621i	−1.59386	−	0.920217i
$833$	−36.1698	−	62.6479i	−0.0434211	−	0.0752076i
$834$	−653.895	−	377.527i	−0.784047	−	0.452670i
$835$	−2052.14	+	1184.80i	−2.45766	+	1.41893i
$836$	32.0597	−	18.5097i	0.0383489	−	0.0221407i
$837$	−32.4692	−	56.2383i	−0.0387924	−	0.0671903i
$838$	1130.85	−	652.898i	1.34947	−	0.779114i
$839$	−396.666	−	687.046i	−0.472784	−	0.818887i	0.526730	−	0.850032i	$-0.323418\pi$
$839$	−396.666	−	687.046i	−0.472784	−	0.818887i	−0.999515	+	0.0311458i	$0.990084\pi$
$840$	−121.274	−	210.053i	−0.144374	−	0.250063i
$841$	−145.453	+	251.932i	−0.172952	+	0.299562i
$842$	1203.60	−	694.897i	1.42945	−	0.825293i
$843$	31.7414	−	54.9776i	0.0376529	−	0.0652167i
$844$	567.409			0.672286
$845$	−1337.88	+	772.425i	−1.58329	+	0.914112i
$846$		−	400.883i		−	0.473857i
$847$		−	870.708i		−	1.02799i
$848$	695.936	+	401.799i	0.820680	+	0.473820i
$849$			70.1078i			0.0825769i
$850$	4063.23	−	2345.91i	4.78028	−	2.75989i
$851$	184.861	+	320.189i	0.217228	+	0.376250i
$852$	798.569	+	461.054i	0.937287	+	0.541143i
$853$	487.273	−	843.982i	0.571247	−	0.989428i	−0.425192	−	0.905103i	$-0.639793\pi$
$853$	487.273	−	843.982i	0.571247	−	0.989428i	0.996438	−	0.0843249i	$-0.0268734\pi$
$854$	1288.12	+	743.696i	1.50834	+	0.870838i
$855$	−458.572	−	264.757i	−0.536341	−	0.309657i
$856$			254.138i			0.296890i
$857$		−	1592.10i		−	1.85776i	−0.370376	−	0.928882i	$-0.620771\pi$
$857$		−	1592.10i		−	1.85776i	0.370376	−	0.928882i	$-0.379229\pi$
$858$	−19.6729	+	34.0745i	−0.0229288	+	0.0397139i
$859$	584.353	+	1012.13i	0.680271	+	1.17826i	0.974898	+	0.222652i	$0.0714714\pi$
$859$	584.353	+	1012.13i	0.680271	+	1.17826i	−0.294627	+	0.955612i	$0.595195\pi$
$860$	−224.105	−	388.161i	−0.260587	−	0.451350i
$861$	268.805	+	155.195i	0.312201	+	0.180249i
$862$		−	939.951i		−	1.09043i
$863$	768.984			0.891059			0.445529	−	0.895267i	$-0.353016\pi$
$863$	768.984			0.891059			0.445529	+	0.895267i	$0.353016\pi$
$864$	118.871	+	205.890i	0.137582	+	0.238299i
$865$	2084.36	+	1203.40i	2.40966	+	1.39122i
$866$	−1838.72			−2.12324
$867$	477.902	−	275.917i	0.551214	−	0.318243i
$868$	−422.968			−0.487291
$869$	−0.694520	+	1.20294i	−0.000799218	+	0.00138429i
$870$			1626.13i			1.86911i
$871$	496.238	+	1115.90i	0.569734	+	1.28117i
$872$	−51.3092			−0.0588408
$873$	481.870	+	278.208i	0.551970	+	0.318680i
$874$		−	1298.24i		−	1.48540i
$875$	1348.38	+	2335.47i	1.54101	+	2.66911i
$876$		−	644.807i		−	0.736081i
$877$	170.580	−	295.454i	0.194504	−	0.336891i	−0.752234	−	0.658896i	$-0.771024\pi$
$877$	170.580	−	295.454i	0.194504	−	0.336891i	0.946738	+	0.322005i	$0.104357\pi$
$878$	−504.130	+	291.060i	−0.574180	+	0.331503i
$879$		−	46.3342i		−	0.0527124i
$880$	50.9068			0.0578487
$881$	−366.479	+	634.760i	−0.415981	+	0.720499i	−0.995531	−	0.0944370i	$-0.969895\pi$
$881$	−366.479	+	634.760i	−0.415981	+	0.720499i	0.579550	+	0.814936i	$0.303228\pi$
$882$	22.4847	−	12.9815i	0.0254928	−	0.0147183i
$883$	315.829	−	182.344i	0.357678	−	0.206505i	−0.310384	−	0.950611i	$-0.600458\pi$
$883$	315.829	−	182.344i	0.357678	−	0.206505i	0.668062	+	0.744106i	$0.267124\pi$
$884$	−1827.41	−	1055.05i	−2.06720	−	1.19350i
$885$	120.650			0.136328
$886$	−2121.48			−2.39445
$887$	−618.408	+	1071.11i	−0.697191	+	1.20757i	0.272246	+	0.962228i	$0.412234\pi$
$887$	−618.408	+	1071.11i	−0.697191	+	1.20757i	−0.969437	+	0.245342i	$0.921100\pi$
$888$	27.8574	−	48.2504i	0.0313710	−	0.0543361i
$889$	−510.501	−	294.738i	−0.574242	−	0.331539i
$890$	−1267.85	+	2195.99i	−1.42455	+	2.46740i
$891$	3.29388	−	1.90172i	0.00369683	−	0.00213437i
$892$	−37.2496	−	64.5181i	−0.0417596	−	0.0723298i
$893$	−845.205			−0.946479
$894$	−155.458	+	269.262i	−0.173891	+	0.301187i
$895$	−1001.20			−1.11866
$896$	466.376			0.520508
$897$	372.580	+	645.327i	0.415362	+	0.719428i
$898$		−	1028.36i		−	1.14517i
$899$	364.129	+	210.230i	0.405038	+	0.233849i
$900$	454.689	+	787.544i	0.505210	+	0.875049i
$901$	1347.59	+	778.033i	1.49566	+	0.863521i
$902$	26.8380	−	15.4949i	0.0297539	−	0.0171784i
$903$	109.024	−	62.9449i	0.120735	−	0.0697065i
$904$	81.0910	+	140.454i	0.0897024	+	0.155369i
$905$	−1179.33	+	680.889i	−1.30313	+	0.752363i
$906$	−757.060	−	1311.27i	−0.835607	−	1.44731i
$907$	349.499	+	605.350i	0.385335	+	0.667420i	0.991816	−	0.127678i	$-0.0407524\pi$
$907$	349.499	+	605.350i	0.385335	+	0.667420i	−0.606480	+	0.795099i	$0.707419\pi$
$908$	−531.289	+	920.220i	−0.585120	+	1.01346i
$909$	470.135	−	271.432i	0.517200	−	0.298606i
$910$	1832.84	−	3174.57i	2.01411	−	3.48853i
$911$	186.384			0.204593			0.102297	−	0.994754i	$-0.467381\pi$
$911$	186.384			0.204593			0.102297	+	0.994754i	$0.467381\pi$
$912$	356.161	−	205.629i	0.390527	−	0.225471i
$913$			3.11243i			0.00340902i
$914$		−	388.909i		−	0.425502i
$915$	−993.437	−	573.561i	−1.08572	−	0.626843i
$916$		−	1002.17i		−	1.09407i
$917$	−1023.77	+	591.075i	−1.11644	+	0.644574i
$918$	188.855	+	327.107i	0.205725	+	0.356326i
$919$	−411.991	−	237.863i	−0.448304	−	0.258828i	0.258810	−	0.965928i	$-0.416670\pi$
$919$	−411.991	−	237.863i	−0.448304	−	0.258828i	−0.707113	+	0.707100i	$0.750003\pi$
$920$	−229.315	+	397.185i	−0.249255	+	0.431723i
$921$	138.501	+	79.9636i	0.150381	+	0.0868225i
$922$	401.969	+	232.077i	0.435975	+	0.251711i
$923$			2066.32i			2.23870i
$924$		−	24.7733i		−	0.0268109i
$925$	−505.540	+	875.621i	−0.546530	+	0.946617i
$926$	296.401	+	513.382i	0.320087	+	0.554408i
$927$	−155.520	−	269.368i	−0.167766	−	0.290580i
$928$	−1333.09	−	769.659i	−1.43652	−	0.829374i
$929$		−	973.577i		−	1.04798i	−0.851723	−	0.523992i	$-0.824442\pi$
$929$		−	973.577i		−	1.04798i	0.851723	−	0.523992i	$-0.175558\pi$
$930$	604.045			0.649511
$931$	−27.3698	−	47.4058i	−0.0293982	−	0.0509193i
$932$	−640.706	−	369.912i	−0.687452	−	0.396901i
$933$	270.688			0.290126
$934$	−1291.40	+	745.589i	−1.38265	+	0.798276i
$935$	98.5746			0.105427
$936$	56.1455	−	97.2468i	0.0599845	−	0.103896i
$937$			795.890i			0.849403i	0.905334	+	0.424701i	$0.139621\pi$
$937$			795.890i			0.849403i	−0.905334	+	0.424701i	$0.860379\pi$
$938$	−1151.57	−	837.444i	−1.22768	−	0.892797i
$939$	−802.344			−0.854467
$940$	1743.97	+	1006.88i	1.85529	+	1.07115i
$941$			167.791i			0.178311i	0.996018	+	0.0891555i	$0.0284168\pi$
$941$			167.791i			0.178311i	−0.996018	+	0.0891555i	$0.971583\pi$
$942$	263.900	+	457.089i	0.280149	+	0.485232i
$943$		−	586.909i		−	0.622385i
$944$	−46.8530	+	81.1518i	−0.0496324	+	0.0859658i
$945$	−306.876	+	177.175i	−0.324736	+	0.187487i
$946$		−	12.5691i		−	0.0132866i
$947$	−101.406			−0.107081			−0.0535405	−	0.998566i	$-0.517051\pi$
$947$	−101.406			−0.107081			−0.0535405	+	0.998566i	$0.517051\pi$
$948$	13.3681	−	23.1543i	0.0141014	−	0.0244243i
$949$	1251.34	−	722.462i	1.31859	−	0.761288i
$950$	3074.66	−	1775.15i	3.23648	−	1.86858i
$951$	−439.640	−	253.827i	−0.462293	−	0.266905i
$952$	364.776			0.383168
$953$	−83.7346			−0.0878642			−0.0439321	−	0.999035i	$-0.513989\pi$
$953$	−83.7346			−0.0878642			−0.0439321	+	0.999035i	$0.513989\pi$
$954$	−279.240	+	483.658i	−0.292705	+	0.506979i
$955$	−1152.65	+	1996.46i	−1.20697	+	2.09053i
$956$	294.702	+	170.147i	0.308266	+	0.177978i
$957$	−12.3132	+	21.3271i	−0.0128664	+	0.0222853i
$958$	753.334	−	434.937i	0.786361	−	0.454006i
$959$	−462.592	−	801.233i	−0.482369	−	0.835488i
$960$	−1376.86			−1.43423
$961$	−402.407	+	696.990i	−0.418738	+	0.725276i
$962$	842.026			0.875287
$963$	371.281			0.385547
$964$	914.196	+	1583.43i	0.948336	+	1.64257i
$965$		−	88.8990i		−	0.0921233i
$966$	−752.388	−	434.391i	−0.778869	−	0.449680i
$967$	126.015	+	218.264i	0.130315	+	0.225713i	0.923798	−	0.382880i	$-0.125068\pi$
$967$	126.015	+	218.264i	0.130315	+	0.225713i	−0.793483	+	0.608593i	$0.791734\pi$
$968$	214.863	+	124.051i	0.221966	+	0.128152i
$969$	689.660	−	398.175i	0.711724	−	0.410914i
$970$	−4482.27	+	2587.84i	−4.62090	+	2.66788i
$971$	−100.289	−	173.705i	−0.103284	−	0.178893i	0.809752	−	0.586772i	$-0.199602\pi$
$971$	−100.289	−	173.705i	−0.103284	−	0.178893i	−0.913036	+	0.407880i	$0.866268\pi$
$972$	−63.4006	+	36.6043i	−0.0652269	+	0.0376588i
$973$	532.657	+	922.589i	0.547438	+	0.948190i
$974$	802.251	+	1389.54i	0.823667	+	1.42663i
$975$	−1018.90	+	1764.78i	−1.04502	+	1.81003i
$976$	771.577	−	445.470i	0.790550	−	0.456424i
$977$	488.668	−	846.398i	0.500172	−	0.866324i	−0.499828	−	0.866125i	$-0.666603\pi$
$977$	488.668	−	846.398i	0.500172	−	0.866324i	1.00000		0.000198997i	$-6.33427e-5\pi$
$978$	−1063.70			−1.08763
$979$	−33.2564	+	19.2006i	−0.0339697	+	0.0196124i
$980$			130.421i			0.133082i
$981$			74.9598i			0.0764116i
$982$	1356.52	+	783.185i	1.38138	+	0.797541i
$983$			1462.63i			1.48793i	0.668220	+	0.743963i	$0.267056\pi$
$983$			1462.63i			1.48793i	−0.668220	+	0.743963i	$0.732944\pi$
$984$	−76.5943	+	44.2217i	−0.0778397	+	0.0449408i
$985$	−38.4032	−	66.5163i	−0.0389880	−	0.0675293i
$986$	−2117.94	−	1222.79i	−2.14801	−	1.24015i
$987$	−282.805	+	489.833i	−0.286530	+	0.496285i
$988$	−1382.80	−	798.361i	−1.39960	−	0.808058i
$989$	−206.151	−	119.021i	−0.208444	−	0.120345i
$990$			35.3790i			0.0357363i
$991$		−	1107.07i		−	1.11713i	−0.829462	−	0.558564i	$-0.811353\pi$
$991$		−	1107.07i		−	1.11713i	0.829462	−	0.558564i	$-0.188647\pi$
$992$	−285.899	+	495.192i	−0.288205	+	0.499185i
$993$	290.899	+	503.852i	0.292950	+	0.507403i
$994$	−1204.56	−	2086.36i	−1.21183	−	2.09896i
$995$	−1600.47	−	924.032i	−1.60851	−	0.928676i
$996$		−	59.9081i		−	0.0601487i
$997$	−684.646			−0.686706			−0.343353	−	0.939206i	$-0.611563\pi$
$997$	−684.646			−0.686706			−0.343353	+	0.939206i	$0.611563\pi$
$998$	299.565	+	518.862i	0.300166	+	0.519902i
$999$	−70.4911	−	40.6981i	−0.0705617	−	0.0407388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.a.172.2	yes	22
67.30	odd	6	inner	201.3.h.a.97.2	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.2	✓	22	67.30	odd	6	inner
201.3.h.a.172.2	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55387 - 1.47448i) q^{2} +1.73205i q^{3} +(2.34817 + 4.06715i) q^{4} +9.46283i q^{5} +(2.55387 - 4.42343i) q^{6} +(-6.24108 + 3.60329i) q^{7} -2.05347i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-2.55387 - 1.47448i) q^{2} +1.73205i q^{3} +(2.34817 + 4.06715i) q^{4} +9.46283i q^{5} +(2.55387 - 4.42343i) q^{6} +(-6.24108 + 3.60329i) q^{7} -2.05347i q^{8} -3.00000 q^{9} +(13.9527 - 24.1668i) q^{10} +(0.365987 - 0.211302i) q^{11} +(-7.04451 + 4.06715i) q^{12} +(-15.7858 - 9.11393i) q^{13} +21.2519 q^{14} -16.3901 q^{15} +(6.36488 - 11.0243i) q^{16} +(12.3248 - 21.3472i) q^{17} +(7.66161 + 4.42343i) q^{18} +(9.32619 - 16.1534i) q^{19} +(-38.4867 + 22.2203i) q^{20} +(-6.24108 - 10.8099i) q^{21} -1.24624 q^{22} +(-11.8011 + 20.4401i) q^{23} +3.55671 q^{24} -64.5451 q^{25} +(26.8766 + 46.5516i) q^{26} -5.19615i q^{27} +(-29.3102 - 16.9223i) q^{28} +(16.8219 + 29.1364i) q^{29} +(41.8582 + 24.1668i) q^{30} +(10.8231 - 6.24870i) q^{31} +(-39.6236 + 22.8767i) q^{32} +(0.365987 + 0.633907i) q^{33} +(-62.9518 + 36.3452i) q^{34} +(-34.0973 - 59.0582i) q^{35} +(-7.04451 - 12.2014i) q^{36} +(7.83235 - 13.5660i) q^{37} +(-47.6358 + 27.5025i) q^{38} +(15.7858 - 27.3418i) q^{39} +19.4316 q^{40} +(-21.5351 + 12.4333i) q^{41} +36.8093i q^{42} +10.0856i q^{43} +(1.71880 + 0.992348i) q^{44} -28.3885i q^{45} +(60.2771 - 34.8010i) q^{46} +(-22.6568 - 39.2427i) q^{47} +(19.0946 + 11.0243i) q^{48} +(1.46736 - 2.54154i) q^{49} +(164.840 + 95.1704i) q^{50} +(36.9744 + 21.3472i) q^{51} -85.6041i q^{52} +63.1275i q^{53} +(-7.66161 + 13.2703i) q^{54} +(1.99952 + 3.46327i) q^{55} +(7.39924 + 12.8159i) q^{56} +(27.9786 + 16.1534i) q^{57} -99.2141i q^{58} -7.36117 q^{59} +(-38.4867 - 66.6610i) q^{60} +(60.6120 + 34.9944i) q^{61} -36.8543 q^{62} +(18.7232 - 10.8099i) q^{63} +84.0056 q^{64} +(86.2435 - 149.378i) q^{65} -2.15856i q^{66} +(-54.1867 - 39.4057i) q^{67} +115.763 q^{68} +(-35.4034 - 20.4401i) q^{69} +201.103i q^{70} +(-56.6803 - 98.1731i) q^{71} +6.16041i q^{72} +(-39.6351 + 68.6499i) q^{73} +(-40.0056 + 23.0972i) q^{74} -111.795i q^{75} +87.5979 q^{76} +(-1.52277 + 2.63751i) q^{77} +(-80.6297 + 46.5516i) q^{78} +(-2.84650 + 1.64343i) q^{79} +(104.321 + 60.2298i) q^{80} +9.00000 q^{81} +73.3306 q^{82} +(-3.68244 + 6.37817i) q^{83} +(29.3102 - 50.7668i) q^{84} +(202.005 + 116.627i) q^{85} +(14.8710 - 25.7573i) q^{86} +(-50.4657 + 29.1364i) q^{87} +(-0.433903 - 0.751542i) q^{88} -90.8678 q^{89} +(-41.8582 + 72.5005i) q^{90} +131.360 q^{91} -110.844 q^{92} +(10.8231 + 18.7461i) q^{93} +133.628i q^{94} +(152.857 + 88.2522i) q^{95} +(-39.6236 - 68.6301i) q^{96} +(-160.623 - 92.7359i) q^{97} +(-7.49489 + 4.32718i) q^{98} +(-1.09796 + 0.633907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more