LMFDB - Embedded newform 201.3.h.a.97.2

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			97.2
Character	$\chi$	$=$	201.97
Dual form			201.3.h.a.172.2

$q$-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 $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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	−0.976284	−	0.216495i	$-0.930537\pi$
$2$	−2.55387	+	1.47448i	−1.27694	+	0.737239i	−0.300651	+	0.953734i	$0.597204\pi$
$3$		−	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	$-0.604806\pi$
$5$		−	9.46283i		−	1.89257i	0.323340	−	0.946283i	$-0.395194\pi$
$6$	2.55387	+	4.42343i	0.425645	+	0.737239i
$7$	−6.24108	−	3.60329i	−0.891582	−	0.514755i	−0.0171226	−	0.999853i	$-0.505451\pi$
$7$	−6.24108	−	3.60329i	−0.891582	−	0.514755i	−0.874460	+	0.485098i	$0.838784\pi$
$8$			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	0.516543	−	0.856261i	$-0.327218\pi$
$11$	0.365987	+	0.211302i	0.0332715	+	0.0192093i	−0.483272	+	0.875470i	$0.660552\pi$
$12$	−7.04451	−	4.06715i	−0.587042	−	0.338929i
$13$	−15.7858	+	9.11393i	−1.21429	+	0.701071i	−0.963691	−	0.267020i	$-0.913961\pi$
$13$	−15.7858	+	9.11393i	−1.21429	+	0.701071i	−0.250600	+	0.968091i	$0.580628\pi$
$14$	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	0.958979	+	0.283477i	$0.0914878\pi$
$17$	12.3248	+	21.3472i	0.724988	+	1.25572i	−0.233992	+	0.972239i	$0.575179\pi$
$18$	7.66161	−	4.42343i	0.425645	−	0.245746i
$19$	9.32619	+	16.1534i	0.490852	+	0.850181i	0.999945	−	0.0105308i	$-0.00335213\pi$
$19$	9.32619	+	16.1534i	0.490852	+	0.850181i	−0.509092	+	0.860712i	$0.670019\pi$
$20$	−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	−0.999885	−	0.0151843i	$-0.995167\pi$
$23$	−11.8011	−	20.4401i	−0.513092	−	0.888702i	0.486792	−	0.873518i	$-0.338167\pi$
$24$	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	−0.415405	−	0.909636i	$-0.636360\pi$
$29$	16.8219	−	29.1364i	0.580066	−	1.00470i	0.995471	−	0.0950668i	$-0.0303065\pi$
$30$	41.8582	−	24.1668i	1.39527	−	0.805561i
$31$	10.8231	+	6.24870i	0.349131	+	0.201571i	0.664303	−	0.747464i	$-0.268729\pi$
$31$	10.8231	+	6.24870i	0.349131	+	0.201571i	−0.315171	+	0.949035i	$0.602062\pi$
$32$	−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	0.952242	−	0.305344i	$-0.0987715\pi$
$37$	7.83235	+	13.5660i	0.211685	+	0.366649i	−0.740557	+	0.671994i	$0.765438\pi$
$38$	−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	0.213831	−	0.976871i	$-0.431406\pi$
$41$	−21.5351	−	12.4333i	−0.525248	−	0.303252i	−0.739079	+	0.673619i	$0.764739\pi$
$42$		−	36.8093i		−	0.876412i
$43$		−	10.0856i		−	0.234549i	−0.993100	−	0.117274i	$-0.962584\pi$
$43$		−	10.0856i		−	0.234549i	0.993100	−	0.117274i	$-0.0374157\pi$
$44$	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	−0.999788	−	0.0205943i	$-0.993444\pi$
$47$	−22.6568	+	39.2427i	−0.482059	+	0.834950i	0.517729	+	0.855545i	$0.326777\pi$
$48$	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	$-0.796937\pi$
$53$		−	63.1275i		−	1.19108i	0.803324	−	0.595542i	$-0.203063\pi$
$54$	−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	0.0872794	−	0.996184i	$-0.472183\pi$
$61$	60.6120	−	34.9944i	0.993640	−	0.573678i	0.906360	+	0.422506i	$0.138849\pi$
$62$	−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	0.122400	+	0.992481i	$0.460941\pi$
$71$	−56.6803	+	98.1731i	−0.798313	+	1.38272i	−0.920714	+	0.390239i	$0.872392\pi$
$72$		−	6.16041i		−	0.0855612i
$73$	−39.6351	−	68.6499i	−0.542946	−	0.940410i	−0.998733	−	0.0503212i	$-0.983975\pi$
$73$	−39.6351	−	68.6499i	−0.542946	−	0.940410i	0.455787	−	0.890089i	$-0.349358\pi$
$74$	−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	0.481876	−	0.876239i	$-0.339956\pi$
$79$	−2.84650	−	1.64343i	−0.0360316	−	0.0208029i	−0.517908	+	0.855437i	$0.673289\pi$
$80$	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	0.842989	−	0.537930i	$-0.180794\pi$
$83$	−3.68244	−	6.37817i	−0.0443667	−	0.0768454i	−0.887356	+	0.461085i	$0.847460\pi$
$84$	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	−0.681338	+	0.731969i	$0.738602\pi$
$97$	−160.623	+	92.7359i	−1.65591	+	0.956041i	−0.974573	+	0.224072i	$0.928065\pi$
$98$	−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	−0.998012	−	0.0630262i	$-0.979925\pi$
$101$	−156.712	−	90.4775i	−1.55160	−	0.895817i	−0.553588	−	0.832791i	$-0.686742\pi$
$102$	−62.9518	+	109.036i	−0.617175	+	1.06898i
$103$	51.8398	−	89.7892i	0.503299	−	0.871740i	−0.496693	−	0.867926i	$-0.665453\pi$
$103$	51.8398	−	89.7892i	0.503299	−	0.871740i	0.999993	−	0.00381405i	$-0.00121405\pi$
$104$	−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	$0.0365642\pi$
$109$			24.9866i			0.229235i	−0.993410	+	0.114617i	$0.963436\pi$
$110$			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	0.165827	−	0.986155i	$-0.446971\pi$
$113$	−68.3983	−	39.4898i	−0.605295	−	0.349467i	−0.771122	+	0.636688i	$0.780304\pi$
$114$	−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	−0.658872	−	0.752255i	$-0.728966\pi$
$127$	40.8985	−	70.8383i	0.322035	−	0.557782i	0.980908	+	0.194473i	$0.0622997\pi$
$128$	−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	$-0.844779\pi$
$137$		−	128.381i		−	0.937084i	0.883441	−	0.468542i	$-0.155221\pi$
$138$	60.2771	−	104.403i	0.436790	−	0.756543i
$139$			147.825i			1.06349i	0.846904	+	0.531746i	$0.178464\pi$
$139$			147.825i			1.06349i	−0.846904	+	0.531746i	$0.821536\pi$
$140$	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	0.656256	+	0.754539i	$0.272139\pi$
$151$	148.218	+	256.721i	0.981577	+	1.70014i	0.325322	+	0.945603i	$0.394527\pi$
$152$	−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	0.653243	−	0.757148i	$-0.273408\pi$
$157$	−51.6668	−	89.4895i	−0.329088	−	0.569997i	−0.982331	+	0.187151i	$0.940075\pi$
$158$	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	0.346879	+	0.937910i	$0.387242\pi$
$163$	−104.127	+	180.353i	−0.638814	+	1.10646i	−0.985693	+	0.168549i	$0.946092\pi$
$164$	−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	−0.198211	−	0.980159i	$-0.563513\pi$
$167$	125.206	−	216.863i	0.749738	−	1.29858i	0.947948	−	0.318424i	$-0.103154\pi$
$168$	−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	0.954681	+	0.297631i	$0.0961964\pi$
$173$	127.172	+	220.268i	0.735096	+	1.27322i	−0.219585	+	0.975593i	$0.570470\pi$
$174$	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	$-0.904500\pi$
$179$		−	105.804i		−	0.591083i	0.955330	−	0.295541i	$-0.0955000\pi$
$180$	115.460	+	66.6610i	0.641445	+	0.370339i
$181$	71.9540	−	124.628i	0.397536	−	0.688553i	−0.595885	−	0.803070i	$-0.703199\pi$
$181$	71.9540	−	124.628i	0.397536	−	0.688553i	0.993421	+	0.114517i	$0.0365320\pi$
$182$	−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	0.167175	−	0.985927i	$-0.446535\pi$
$191$	210.979	−	121.809i	1.10460	−	0.637742i	0.937426	+	0.348185i	$0.113202\pi$
$192$		−	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	0.482053	−	0.876142i	$-0.339891\pi$
$197$	−7.02922	−	4.05832i	−0.0356813	−	0.0206006i	−0.517735	+	0.855541i	$0.673225\pi$
$198$	3.73873			0.0188825
$199$	−97.6486	−	169.132i	−0.490697	−	0.849911i	0.509246	−	0.860621i	$-0.329924\pi$
$199$	−97.6486	−	169.132i	−0.490697	−	0.849911i	−0.999943	+	0.0107095i	$0.996591\pi$
$200$		−	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	0.972924	−	0.231125i	$-0.0742405\pi$
$211$	60.4098	+	104.633i	0.286302	+	0.495890i	−0.686622	+	0.727015i	$0.740907\pi$
$212$	−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	−0.501635	−	0.865079i	$-0.667268\pi$
$227$	113.128	−	195.944i	0.498363	−	0.863190i	0.999998	+	0.00188921i	$0.000601355\pi$
$228$		−	151.724i		−	0.665456i
$229$	−184.804	+	106.697i	−0.807004	+	0.465924i	−0.845914	−	0.533319i	$-0.820945\pi$
$229$	−184.804	+	106.697i	−0.807004	+	0.465924i	0.0389106	+	0.999243i	$0.487611\pi$
$230$	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	0.177803	−	0.984066i	$-0.443101\pi$
$233$	−136.427	−	78.7660i	−0.585522	−	0.338051i	−0.763325	+	0.646015i	$0.776434\pi$
$234$	−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	0.625501	−	0.780223i	$-0.284895\pi$
$239$	62.7515	+	36.2296i	0.262559	+	0.151588i	−0.362942	+	0.931812i	$0.618228\pi$
$240$	−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	−0.423253	−	0.906012i	$-0.639112\pi$
$251$	37.5873	−	21.7010i	0.149750	−	0.0864584i	0.573003	+	0.819553i	$0.305778\pi$
$252$	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	−0.894349	−	0.447370i	$-0.852361\pi$
$257$	−15.3533	+	26.5927i	−0.0597404	+	0.103473i	0.834608	+	0.550844i	$0.185694\pi$
$258$	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	$-0.803691\pi$
$271$		−	313.474i		−	1.15673i	0.815778	−	0.578364i	$-0.196309\pi$
$272$	−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	−0.555415	−	0.831573i	$-0.687441\pi$
$281$	−31.7414	+	18.3259i	−0.112959	+	0.0652167i	0.442456	+	0.896790i	$0.354107\pi$
$282$	−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	0.931368	−	0.364080i	$-0.118617\pi$
$307$	46.1670	+	79.9636i	0.150381	+	0.260468i	−0.780987	+	0.624548i	$0.785283\pi$
$308$	−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	$0.0808439\pi$
$311$			156.282i			0.502514i	−0.967920	+	0.251257i	$0.919156\pi$
$312$	−56.1455	+	32.4156i	−0.179953	+	0.103896i
$313$		−	463.234i		−	1.47998i	−0.672618	−	0.739990i	$-0.734830\pi$
$313$		−	463.234i		−	1.47998i	0.672618	−	0.739990i	$-0.265170\pi$
$314$	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	0.536782	−	0.843721i	$-0.319640\pi$
$317$	−146.547	−	253.827i	−0.462293	−	0.800715i	−0.999075	+	0.0430064i	$0.986306\pi$
$318$	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	0.870279	−	0.492560i	$-0.163939\pi$
$331$	290.899	+	167.951i	0.878849	+	0.507403i	0.00856996	+	0.999963i	$0.497272\pi$
$332$	−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	−0.257100	−	0.966385i	$-0.582767\pi$
$337$	152.076	−	87.8009i	0.451263	−	0.260537i	0.708364	+	0.705848i	$0.249434\pi$
$338$			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	−0.0850110	−	0.996380i	$-0.527093\pi$
$347$	−343.671	−	198.419i	−0.990407	−	0.571812i	−0.905396	+	0.424568i	$0.860426\pi$
$348$	−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	0.131924	−	0.991260i	$-0.457884\pi$
$353$	372.889	−	215.288i	1.05634	−	0.609880i	0.924418	+	0.381380i	$0.124551\pi$
$354$	−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	−0.272941	−	0.962031i	$-0.587996\pi$
$367$	−456.018	−	263.282i	−1.24255	−	0.717389i	−0.969614	+	0.244641i	$0.921330\pi$
$368$	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	0.796003	−	0.605293i	$-0.206944\pi$
$373$	249.837	+	144.244i	0.669806	+	0.386712i	−0.126197	+	0.992005i	$0.540277\pi$
$374$	−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	−0.730864	−	0.682523i	$-0.760883\pi$
$379$	−191.476	+	110.549i	−0.505213	+	0.291685i	0.225651	+	0.974208i	$0.427549\pi$
$380$		−	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	−0.480916	−	0.876767i	$-0.659696\pi$
$383$	14.5269	−	8.38709i	0.0379292	−	0.0218984i	0.518845	+	0.854869i	$0.326362\pi$
$384$	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	−0.998947	−	0.0458702i	$-0.985394\pi$
$389$	−209.748	−	363.295i	−0.539198	−	0.933919i	0.459749	−	0.888049i	$-0.347939\pi$
$390$	−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	$0.118202\pi$
$401$			291.018i			0.725732i	−0.931841	+	0.362866i	$0.881798\pi$
$402$	−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	−0.00861573	−	0.999963i	$-0.502743\pi$
$409$	−359.477	−	207.544i	−0.878917	−	0.507443i	−0.870301	+	0.492520i	$0.836076\pi$
$410$		−	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	−0.999452	−	0.0331104i	$-0.989459\pi$
$419$	−221.400	−	383.476i	−0.528400	−	0.915216i	0.471051	−	0.882106i	$-0.343875\pi$
$420$	480.397	−	277.357i	1.14380	−	0.660375i
$421$	−235.642	−	408.143i	−0.559719	−	0.969462i	−0.997520	−	0.0703898i	$-0.977576\pi$
$421$	−235.642	−	408.143i	−0.559719	−	0.969462i	0.437800	−	0.899072i	$-0.355758\pi$
$422$	−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	−0.619761	−	0.784791i	$-0.712770\pi$
$431$	159.370	−	276.037i	0.369768	−	0.640458i	0.989529	+	0.144333i	$0.0461037\pi$
$432$	−57.2839	+	33.0729i	−0.132602	+	0.0765576i
$433$	539.981	+	311.758i	1.24707	+	0.719996i	0.970524	−	0.241005i	$-0.0774770\pi$
$433$	539.981	+	311.758i	1.24707	+	0.719996i	0.276545	+	0.961001i	$0.410810\pi$
$434$	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	0.956268	−	0.292493i	$-0.0944848\pi$
$439$	98.6993	+	170.952i	0.224828	+	0.389413i	−0.731440	+	0.681906i	$0.761151\pi$
$440$	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	0.995035	−	0.0995237i	$-0.0317319\pi$
$443$	623.019	+	359.700i	1.40636	+	0.811964i	0.411328	+	0.911488i	$0.365065\pi$
$444$		−	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	−0.603895	−	0.797064i	$-0.706385\pi$
$449$	174.360	−	302.001i	0.388330	−	0.672607i	0.992225	+	0.124457i	$0.0397188\pi$
$450$	−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	−0.784818	−	0.619726i	$-0.787244\pi$
$457$	65.9402	−	114.212i	0.144289	−	0.249916i	0.929108	+	0.369810i	$0.120577\pi$
$458$	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	−0.676078	−	0.736830i	$-0.736322\pi$
$463$	−174.089	+	100.511i	−0.376003	+	0.217085i	0.300075	+	0.953916i	$0.402988\pi$
$464$	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	0.998824	+	0.0484783i	$0.0154372\pi$
$467$	252.832	+	437.917i	0.541396	+	0.937725i	−0.457429	+	0.889246i	$0.651230\pi$
$468$		−	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	0.669995	−	0.742365i	$-0.266296\pi$
$479$	−147.489	−	255.458i	−0.307909	−	0.533315i	−0.977905	+	0.209050i	$0.932963\pi$
$480$	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	−0.898489	−	0.438996i	$-0.855334\pi$
$487$	−471.197	+	272.046i	−0.967551	+	0.558616i	−0.0690623	+	0.997612i	$0.522001\pi$
$488$	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	−0.665830	−	0.746103i	$-0.731922\pi$
$499$	−175.948	+	101.584i	−0.352601	+	0.203574i	0.313229	+	0.949678i	$0.398589\pi$
$500$	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	0.970756	−	0.240068i	$-0.0771699\pi$
$503$	627.859	+	362.495i	1.24823	+	0.720665i	0.277473	+	0.960734i	$0.410503\pi$
$504$	−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	$-0.686403\pi$
$521$		−	868.381i		−	1.66676i	0.552702	−	0.833379i	$-0.313597\pi$
$522$		−	297.642i		−	0.570196i
$523$	141.729	+	245.481i	0.270992	+	0.469371i	0.969116	−	0.246605i	$-0.0793151\pi$
$523$	141.729	+	245.481i	0.270992	+	0.469371i	−0.698124	+	0.715976i	$0.745982\pi$
$524$	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	$-0.904954\pi$
$541$		−	318.302i		−	0.588359i	0.955750	−	0.294180i	$-0.0950464\pi$
$542$	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	0.999483	−	0.0321385i	$-0.0102318\pi$
$547$	804.852	+	464.681i	1.47139	+	0.849509i	0.471909	+	0.881647i	$0.343565\pi$
$548$	−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	−0.918061	−	0.396439i	$-0.870246\pi$
$557$	−64.4474	+	111.626i	−0.115704	+	0.200406i	0.802357	+	0.596845i	$0.203579\pi$
$558$	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	$-0.655479\pi$
$563$		−	994.326i		−	1.76612i	0.469259	−	0.883061i	$-0.344521\pi$
$564$	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	−0.999889	−	0.0149300i	$-0.995247\pi$
$569$	−277.111	+	479.971i	−0.487015	+	0.843534i	0.512874	+	0.858464i	$0.328581\pi$
$570$	780.755	+	450.769i	1.36975	+	0.790823i
$571$	−192.986	+	334.262i	−0.337980	+	0.585398i	−0.984053	−	0.177878i	$-0.943077\pi$
$571$	−192.986	+	334.262i	−0.337980	+	0.585398i	0.646073	+	0.763276i	$0.276410\pi$
$572$	−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	0.401857	−	0.915702i	$-0.368365\pi$
$577$	−109.766	−	63.3733i	−0.190235	−	0.109832i	−0.592093	+	0.805870i	$0.701698\pi$
$578$		−	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	−0.803755	−	0.594960i	$-0.797168\pi$
$587$	−405.255	+	233.974i	−0.690383	+	0.398593i	0.113373	+	0.993553i	$0.463835\pi$
$588$		−	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	−0.446282	−	0.894892i	$-0.647252\pi$
$593$	62.6063	−	36.1458i	0.105576	−	0.0609541i	0.551858	+	0.833938i	$0.313919\pi$
$594$		−	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	0.739201	−	0.673485i	$-0.235204\pi$
$599$	314.802	+	181.751i	0.525545	+	0.303424i	−0.213655	+	0.976909i	$0.568537\pi$
$600$	−229.568			−0.382614
$601$	−238.202	−	412.578i	−0.396343	−	0.686485i	0.596929	−	0.802294i	$-0.296387\pi$
$601$	−238.202	−	412.578i	−0.396343	−	0.686485i	−0.993272	+	0.115809i	$0.963054\pi$
$602$		−	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	−0.151598	−	0.988442i	$-0.548442\pi$
$607$	473.592	−	820.285i	0.780217	−	1.35138i	0.931815	−	0.362933i	$-0.118225\pi$
$608$		−	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	0.570190	−	0.821513i	$-0.306870\pi$
$613$	−261.356	−	452.682i	−0.426356	−	0.738470i	−0.996546	+	0.0830427i	$0.973536\pi$
$614$	−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	0.547283	−	0.836948i	$-0.315662\pi$
$619$	−279.278	−	483.724i	−0.451177	−	0.781461i	−0.998459	+	0.0554868i	$0.982329\pi$
$620$	−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	−0.0108557	−	0.999941i	$-0.503456\pi$
$631$	536.155	−	309.549i	0.849691	−	0.490569i	0.860547	+	0.509372i	$0.170122\pi$
$632$	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	0.395585	−	0.918429i	$-0.370542\pi$
$641$	−129.485	−	74.7583i	−0.202005	−	0.116628i	−0.597590	+	0.801802i	$0.703875\pi$
$642$	−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	−0.988496	−	0.151248i	$-0.951671\pi$
$647$	−874.588	+	504.944i	−1.35176	+	0.780439i	−0.363263	+	0.931687i	$0.618337\pi$
$648$			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	−0.922357	−	0.386338i	$-0.873740\pi$
$653$	−684.970	+	395.467i	−1.04896	+	0.605616i	−0.126600	+	0.991954i	$0.540407\pi$
$654$	−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	0.201434	+	0.979502i	$0.435440\pi$
$659$	−492.640	+	853.277i	−0.747557	+	1.29481i	−0.948991	+	0.315304i	$0.897894\pi$
$660$	−28.1713	+	16.2647i	−0.0426837	+	0.0246435i
$661$		−	415.876i		−	0.629161i	−0.949231	−	0.314581i	$-0.898136\pi$
$661$		−	415.876i		−	0.629161i	0.949231	−	0.314581i	$-0.101864\pi$
$662$	−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	$0.196298\pi$
$673$			778.441i			1.15667i	−0.815798	+	0.578336i	$0.803702\pi$
$674$	−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	0.999991	−	0.00426617i	$-0.00135797\pi$
$677$	1012.99	+	584.850i	1.49629	+	0.863884i	0.496301	+	0.868151i	$0.334691\pi$
$678$		−	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	−0.533951	−	0.845515i	$-0.679293\pi$
$683$	−46.9149	+	27.0863i	−0.0686894	+	0.0396578i	0.465262	+	0.885173i	$0.345960\pi$
$684$	−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	−0.927791	−	0.373101i	$-0.878295\pi$
$691$	−97.2794	+	168.493i	−0.140781	+	0.243839i	0.787010	+	0.616940i	$0.211628\pi$
$692$	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	−0.960124	−	0.279575i	$-0.909807\pi$
$701$	−1179.30	−	680.867i	−1.68230	−	0.971279i	−0.722181	−	0.691704i	$-0.756860\pi$
$702$	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	0.930054	−	0.367423i	$-0.119760\pi$
$709$	104.102	+	180.310i	0.146829	+	0.254316i	−0.783225	+	0.621739i	$0.786427\pi$
$710$	−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	0.617513	−	0.786560i	$-0.288140\pi$
$719$	−267.773	−	463.797i	−0.372425	−	0.645058i	−0.989938	+	0.141502i	$0.954807\pi$
$720$	−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	0.263386	−	0.964690i	$-0.415161\pi$
$727$	894.592	−	516.493i	1.23053	−	0.710444i	0.967140	+	0.254246i	$0.0818273\pi$
$728$			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	0.109767	−	0.993957i	$-0.464990\pi$
$733$	−510.272	−	294.606i	−0.696142	−	0.401918i	−0.805909	+	0.592039i	$0.798323\pi$
$734$	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	−0.575457	−	0.817832i	$-0.695176\pi$
$739$	−114.488	+	66.0996i	−0.154923	+	0.0894446i	0.420535	+	0.907277i	$0.361843\pi$
$740$		−	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	0.533407	−	0.845859i	$-0.320912\pi$
$743$	−346.113	−	599.486i	−0.465832	−	0.806845i	−0.999239	+	0.0390143i	$0.987578\pi$
$744$	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	0.470651	−	0.882320i	$-0.344019\pi$
$757$	−44.0085	−	25.4083i	−0.0581353	−	0.0335645i	−0.528786	+	0.848755i	$0.677353\pi$
$758$	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	−0.404209	−	0.914667i	$-0.632453\pi$
$769$	−1075.40	−	620.882i	−1.39844	−	0.807388i	−0.994229	+	0.107279i	$0.965786\pi$
$770$	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	−0.396310	−	0.918117i	$-0.629709\pi$
$773$	461.448	−	799.252i	0.596958	−	1.03396i	0.993267	−	0.115844i	$-0.0369573\pi$
$774$	−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	0.314987	−	0.949096i	$-0.398000\pi$
$787$	1018.71	−	588.152i	1.29442	−	0.747335i	0.979435	+	0.201761i	$0.0646665\pi$
$788$	−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	−0.354798	−	0.934943i	$-0.615450\pi$
$797$	503.932	−	872.835i	0.632286	−	1.09515i	0.987083	−	0.160208i	$-0.0512164\pi$
$798$	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	$0.118885\pi$
$809$			590.352i			0.729731i	−0.931060	+	0.364865i	$0.881115\pi$
$810$	125.575	+	217.502i	0.155030	+	0.268520i
$811$	−766.689	−	442.648i	−0.945362	−	0.545805i	−0.0537251	−	0.998556i	$-0.517109\pi$
$811$	−766.689	−	442.648i	−0.945362	−	0.545805i	−0.891637	+	0.452751i	$0.850443\pi$
$812$			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	0.816567	+	0.577251i	$0.195874\pi$
$821$	745.630	+	1291.47i	0.908197	+	1.57304i	0.0916301	+	0.995793i	$0.470792\pi$
$822$	567.883	−	327.867i	0.690855	−	0.398865i
$823$	−355.994	−	616.600i	−0.432557	−	0.749211i	0.564536	−	0.825409i	$-0.309055\pi$
$823$	−355.994	−	616.600i	−0.432557	−	0.749211i	−0.997093	+	0.0761979i	$0.975722\pi$
$824$	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	0.984140	−	0.177392i	$-0.0567659\pi$
$827$	279.894	+	484.790i	0.338445	+	0.586203i	−0.645696	+	0.763595i	$0.723433\pi$
$828$	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	−0.999515	−	0.0311458i	$-0.990084\pi$
$839$	−396.666	+	687.046i	−0.472784	+	0.818887i	0.526730	+	0.850032i	$0.323418\pi$
$840$	−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	0.996438	+	0.0843249i	$0.0268734\pi$
$853$	487.273	+	843.982i	0.571247	+	0.989428i	−0.425192	+	0.905103i	$0.639793\pi$
$854$	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	$0.379229\pi$
$857$			1592.10i			1.85776i	−0.370376	+	0.928882i	$0.620771\pi$
$858$	−19.6729	−	34.0745i	−0.0229288	−	0.0397139i
$859$	584.353	−	1012.13i	0.680271	−	1.17826i	−0.294627	−	0.955612i	$-0.595195\pi$
$859$	584.353	−	1012.13i	0.680271	−	1.17826i	0.974898	−	0.222652i	$-0.0714714\pi$
$860$	−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	0.946738	−	0.322005i	$-0.104357\pi$
$877$	170.580	+	295.454i	0.194504	+	0.336891i	−0.752234	+	0.658896i	$0.771024\pi$
$878$	−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	0.579550	−	0.814936i	$-0.303228\pi$
$881$	−366.479	−	634.760i	−0.415981	−	0.720499i	−0.995531	+	0.0944370i	$0.969895\pi$
$882$	22.4847	+	12.9815i	0.0254928	+	0.0147183i
$883$	315.829	+	182.344i	0.357678	+	0.206505i	0.668062	−	0.744106i	$-0.267124\pi$
$883$	315.829	+	182.344i	0.357678	+	0.206505i	−0.310384	+	0.950611i	$0.600458\pi$
$884$	−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	−0.969437	−	0.245342i	$-0.921100\pi$
$887$	−618.408	−	1071.11i	−0.697191	−	1.20757i	0.272246	−	0.962228i	$-0.412234\pi$
$888$	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	−0.606480	−	0.795099i	$-0.707419\pi$
$907$	349.499	−	605.350i	0.385335	−	0.667420i	0.991816	+	0.127678i	$0.0407524\pi$
$908$	−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	−0.707113	−	0.707100i	$-0.750003\pi$
$919$	−411.991	+	237.863i	−0.448304	+	0.258828i	0.258810	+	0.965928i	$0.416670\pi$
$920$	−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	$0.175558\pi$
$929$			973.577i			1.04798i	−0.851723	+	0.523992i	$0.824442\pi$
$930$	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	$-0.860379\pi$
$937$		−	795.890i		−	0.849403i	0.905334	−	0.424701i	$-0.139621\pi$
$938$	−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	$-0.971583\pi$
$941$		−	167.791i		−	0.178311i	0.996018	−	0.0891555i	$-0.0284168\pi$
$942$	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	−0.793483	−	0.608593i	$-0.791734\pi$
$967$	126.015	−	218.264i	0.130315	−	0.225713i	0.923798	+	0.382880i	$0.125068\pi$
$968$	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	−0.913036	−	0.407880i	$-0.866268\pi$
$971$	−100.289	+	173.705i	−0.103284	+	0.178893i	0.809752	+	0.586772i	$0.199602\pi$
$972$	−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	1.00000		0.000198997i	$6.33427e-5\pi$
$977$	488.668	+	846.398i	0.500172	+	0.866324i	−0.499828	+	0.866125i	$0.666603\pi$
$978$	−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	$-0.732944\pi$
$983$		−	1462.63i		−	1.48793i	0.668220	−	0.743963i	$-0.267056\pi$
$984$	−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	$0.188647\pi$
$991$			1107.07i			1.11713i	−0.829462	+	0.558564i	$0.811353\pi$
$992$	−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.97.2	✓	22
67.38	odd	6	inner	201.3.h.a.172.2	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.2	✓	22	1.1	even	1	trivial
201.3.h.a.172.2	yes	22	67.38	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
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

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