LMFDB - Embedded newform 201.4.e.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, 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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	201.37
Dual form			201.4.e.b.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83140 - 3.17208i) q^{2} -3.00000 q^{3} +(-2.70808 + 4.69053i) q^{4} +12.9712 q^{5} +(5.49421 + 9.51625i) q^{6} +(1.64155 - 2.84325i) q^{7} -9.46413 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-1.83140 - 3.17208i) q^{2} -3.00000 q^{3} +(-2.70808 + 4.69053i) q^{4} +12.9712 q^{5} +(5.49421 + 9.51625i) q^{6} +(1.64155 - 2.84325i) q^{7} -9.46413 q^{8} +9.00000 q^{9} +(-23.7555 - 41.1456i) q^{10} +(-15.4916 + 26.8323i) q^{11} +(8.12423 - 14.0716i) q^{12} +(34.7677 + 60.2194i) q^{13} -12.0254 q^{14} -38.9135 q^{15} +(38.9973 + 67.5452i) q^{16} +(41.6567 + 72.1515i) q^{17} +(-16.4826 - 28.5488i) q^{18} +(29.9396 + 51.8569i) q^{19} +(-35.1269 + 60.8416i) q^{20} +(-4.92465 + 8.52974i) q^{21} +113.486 q^{22} +(-40.5529 - 70.2397i) q^{23} +28.3924 q^{24} +43.2513 q^{25} +(127.347 - 220.572i) q^{26} -27.0000 q^{27} +(8.89088 + 15.3995i) q^{28} +(100.602 - 174.248i) q^{29} +(71.2664 + 123.437i) q^{30} +(-24.4702 + 42.3837i) q^{31} +(104.983 - 181.836i) q^{32} +(46.4749 - 80.4969i) q^{33} +(152.580 - 264.277i) q^{34} +(21.2928 - 36.8802i) q^{35} +(-24.3727 + 42.2147i) q^{36} +(81.7150 + 141.535i) q^{37} +(109.663 - 189.942i) q^{38} +(-104.303 - 180.658i) q^{39} -122.761 q^{40} +(24.7672 - 42.8981i) q^{41} +36.0761 q^{42} +47.5235 q^{43} +(-83.9051 - 145.328i) q^{44} +116.741 q^{45} +(-148.537 + 257.274i) q^{46} +(29.0357 - 50.2912i) q^{47} +(-116.992 - 202.636i) q^{48} +(166.111 + 287.712i) q^{49} +(-79.2107 - 137.197i) q^{50} +(-124.970 - 216.455i) q^{51} -376.614 q^{52} +538.502 q^{53} +(49.4479 + 85.6463i) q^{54} +(-200.945 + 348.047i) q^{55} +(-15.5358 + 26.9089i) q^{56} +(-89.8188 - 155.571i) q^{57} -736.971 q^{58} +85.8731 q^{59} +(105.381 - 182.525i) q^{60} +(-405.730 - 702.745i) q^{61} +179.260 q^{62} +(14.7739 - 25.5892i) q^{63} -145.108 q^{64} +(450.978 + 781.116i) q^{65} -340.457 q^{66} +(222.946 + 501.057i) q^{67} -451.238 q^{68} +(121.659 + 210.719i) q^{69} -155.983 q^{70} +(261.752 - 453.368i) q^{71} -85.1772 q^{72} +(444.865 + 770.528i) q^{73} +(299.306 - 518.414i) q^{74} -129.754 q^{75} -324.315 q^{76} +(50.8606 + 88.0931i) q^{77} +(-382.042 + 661.716i) q^{78} +(-188.123 + 325.839i) q^{79} +(505.840 + 876.141i) q^{80} +81.0000 q^{81} -181.435 q^{82} +(-318.132 - 551.021i) q^{83} +(-26.6726 - 46.1984i) q^{84} +(540.336 + 935.890i) q^{85} +(-87.0346 - 150.748i) q^{86} +(-301.806 + 522.743i) q^{87} +(146.615 - 253.945i) q^{88} -873.216 q^{89} +(-213.799 - 370.311i) q^{90} +228.292 q^{91} +439.282 q^{92} +(73.4107 - 127.151i) q^{93} -212.704 q^{94} +(388.352 + 672.645i) q^{95} +(-314.949 + 545.507i) q^{96} +(399.697 + 692.296i) q^{97} +(608.431 - 1053.83i) q^{98} +(-139.425 + 241.491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.83140	−	3.17208i	−0.647499	−	1.12150i	−0.983718	−	0.179717i	$-0.942482\pi$
$2$	−1.83140	−	3.17208i	−0.647499	−	1.12150i	0.336219	−	0.941784i	$-0.390852\pi$
$3$	−3.00000			−0.577350
$3$	−3.00000			−0.577350
$4$	−2.70808	+	4.69053i	−0.338510	+	0.586316i
$5$	12.9712			1.16018			0.580089	−	0.814553i	$-0.303018\pi$
$5$	12.9712			1.16018			0.580089	+	0.814553i	$0.303018\pi$
$6$	5.49421	+	9.51625i	0.373834	+	0.647499i
$7$	1.64155	−	2.84325i	0.0886353	−	0.153521i	−0.818299	−	0.574793i	$-0.805083\pi$
$7$	1.64155	−	2.84325i	0.0886353	−	0.153521i	0.906935	+	0.421272i	$0.138416\pi$
$8$	−9.46413			−0.418259
$9$	9.00000			0.333333
$10$	−23.7555	−	41.1456i	−0.751213	−	1.30114i
$11$	−15.4916	+	26.8323i	−0.424628	+	0.735477i	−0.996386	−	0.0849455i	$-0.972928\pi$
$11$	−15.4916	+	26.8323i	−0.424628	+	0.735477i	0.571758	+	0.820422i	$0.306262\pi$
$12$	8.12423	−	14.0716i	0.195439	−	0.338510i
$13$	34.7677	+	60.2194i	0.741756	+	1.28476i	0.951695	+	0.307044i	$0.0993399\pi$
$13$	34.7677	+	60.2194i	0.741756	+	1.28476i	−0.209940	+	0.977714i	$0.567327\pi$
$14$	−12.0254			−0.229565
$15$	−38.9135			−0.669829
$16$	38.9973	+	67.5452i	0.609332	+	1.05539i
$17$	41.6567	+	72.1515i	0.594308	+	1.02937i	0.993644	+	0.112567i	$0.0359072\pi$
$17$	41.6567	+	72.1515i	0.594308	+	1.02937i	−0.399336	+	0.916804i	$0.630759\pi$
$18$	−16.4826	−	28.5488i	−0.215833	−	0.373834i
$19$	29.9396	+	51.8569i	0.361506	+	0.626147i	0.988209	−	0.153111i	$-0.0489293\pi$
$19$	29.9396	+	51.8569i	0.361506	+	0.626147i	−0.626703	+	0.779258i	$0.715596\pi$
$20$	−35.1269	+	60.8416i	−0.392731	+	0.680230i
$21$	−4.92465	+	8.52974i	−0.0511736	+	0.0886353i
$22$	113.486			1.09978
$23$	−40.5529	−	70.2397i	−0.367646	−	0.636782i	0.621551	−	0.783374i	$-0.286503\pi$
$23$	−40.5529	−	70.2397i	−0.367646	−	0.636782i	−0.989197	+	0.146592i	$0.953170\pi$
$24$	28.3924			0.241482
$25$	43.2513			0.346011
$26$	127.347	−	220.572i	0.960572	−	1.66376i
$27$	−27.0000			−0.192450
$28$	8.89088	+	15.3995i	0.0600078	+	0.103937i
$29$	100.602	−	174.248i	0.644184	−	1.11576i	−0.340306	−	0.940315i	$-0.610531\pi$
$29$	100.602	−	174.248i	0.644184	−	1.11576i	0.984489	−	0.175444i	$-0.0561360\pi$
$30$	71.2664	+	123.437i	0.433713	+	0.751213i
$31$	−24.4702	+	42.3837i	−0.141774	+	0.245559i	−0.928165	−	0.372170i	$-0.878614\pi$
$31$	−24.4702	+	42.3837i	−0.141774	+	0.245559i	0.786391	+	0.617729i	$0.211947\pi$
$32$	104.983	−	181.836i	0.579954	−	1.00451i
$33$	46.4749	−	80.4969i	0.245159	−	0.424628i
$34$	152.580	−	264.277i	0.769627	−	1.33303i
$35$	21.2928	−	36.8802i	0.102833	−	0.178111i
$36$	−24.3727	+	42.2147i	−0.112837	+	0.195439i
$37$	81.7150	+	141.535i	0.363077	+	0.628868i	0.988466	−	0.151445i	$-0.0483928\pi$
$37$	81.7150	+	141.535i	0.363077	+	0.628868i	−0.625388	+	0.780314i	$0.715059\pi$
$38$	109.663	−	189.942i	0.468150	−	0.810859i
$39$	−104.303	−	180.658i	−0.428253	−	0.741756i
$40$	−122.761			−0.485255
$41$	24.7672	−	42.8981i	0.0943413	−	0.163404i	−0.814992	−	0.579472i	$-0.803259\pi$
$41$	24.7672	−	42.8981i	0.0943413	−	0.163404i	0.909333	+	0.416068i	$0.136592\pi$
$42$	36.0761			0.132539
$43$	47.5235			0.168541			0.0842705	−	0.996443i	$-0.473144\pi$
$43$	47.5235			0.168541			0.0842705	+	0.996443i	$0.473144\pi$
$44$	−83.9051	−	145.328i	−0.287481	−	0.497932i
$45$	116.741			0.386726
$46$	−148.537	+	257.274i	−0.476101	+	0.824631i
$47$	29.0357	−	50.2912i	0.0901125	−	0.156079i	−0.817446	−	0.576005i	$-0.804611\pi$
$47$	29.0357	−	50.2912i	0.0901125	−	0.156079i	0.907558	+	0.419926i	$0.137944\pi$
$48$	−116.992	−	202.636i	−0.351798	−	0.609332i
$49$	166.111	+	287.712i	0.484288	+	0.838811i
$50$	−79.2107	−	137.197i	−0.224042	−	0.388051i
$51$	−124.970	−	216.455i	−0.343124	−	0.594308i
$52$	−376.614			−1.00437
$53$	538.502			1.39564			0.697820	−	0.716273i	$-0.254153\pi$
$53$	538.502			1.39564			0.697820	+	0.716273i	$0.254153\pi$
$54$	49.4479	+	85.6463i	0.124611	+	0.215833i
$55$	−200.945	+	348.047i	−0.492643	+	0.853283i
$56$	−15.5358	+	26.9089i	−0.0370726	+	0.0642116i
$57$	−89.8188	−	155.571i	−0.208716	−	0.361506i
$58$	−736.971			−1.66843
$59$	85.8731			0.189487			0.0947435	−	0.995502i	$-0.469797\pi$
$59$	85.8731			0.189487			0.0947435	+	0.995502i	$0.469797\pi$
$60$	105.381	−	182.525i	0.226743	−	0.392731i
$61$	−405.730	−	702.745i	−0.851613	−	1.47504i	−0.879752	−	0.475434i	$-0.842291\pi$
$61$	−405.730	−	702.745i	−0.851613	−	1.47504i	0.0281383	−	0.999604i	$-0.491042\pi$
$62$	179.260			0.367193
$63$	14.7739	−	25.5892i	0.0295451	−	0.0511736i
$64$	−145.108			−0.283414
$65$	450.978	+	781.116i	0.860568	+	1.49055i
$66$	−340.457			−0.634961
$67$	222.946	+	501.057i	0.406525	+	0.913640i
$67$	222.946	+	501.057i	0.406525	+	0.913640i
$68$	−451.238			−0.804715
$69$	121.659	+	210.719i	0.212261	+	0.367646i
$70$	−155.983			−0.266336
$71$	261.752	−	453.368i	0.437524	−	0.757815i	−0.559973	−	0.828511i	$-0.689189\pi$
$71$	261.752	−	453.368i	0.437524	−	0.757815i	0.997498	+	0.0706959i	$0.0225220\pi$
$72$	−85.1772			−0.139420
$73$	444.865	+	770.528i	0.713253	+	1.23539i	0.963630	+	0.267242i	$0.0861122\pi$
$73$	444.865	+	770.528i	0.713253	+	1.23539i	−0.250377	+	0.968148i	$0.580554\pi$
$74$	299.306	−	518.414i	0.470184	−	0.814383i
$75$	−129.754			−0.199769
$76$	−324.315			−0.489493
$77$	50.8606	+	88.0931i	0.0752741	+	0.130378i
$78$	−382.042	+	661.716i	−0.554586	+	0.960572i
$79$	−188.123	+	325.839i	−0.267918	+	0.464047i	−0.968324	−	0.249697i	$-0.919669\pi$
$79$	−188.123	+	325.839i	−0.267918	+	0.464047i	0.700406	+	0.713745i	$0.253002\pi$
$80$	505.840	+	876.141i	0.706933	+	1.22444i
$81$	81.0000			0.111111
$82$	−181.435			−0.244343
$83$	−318.132	−	551.021i	−0.420718	−	0.728704i	0.575292	−	0.817948i	$-0.304888\pi$
$83$	−318.132	−	551.021i	−0.420718	−	0.728704i	−0.996010	+	0.0892437i	$0.971555\pi$
$84$	−26.6726	−	46.1984i	−0.0346455	−	0.0600078i
$85$	540.336	+	935.890i	0.689502	+	1.19425i
$86$	−87.0346	−	150.748i	−0.109130	−	0.189019i
$87$	−301.806	+	522.743i	−0.371920	+	0.644184i
$88$	146.615	−	253.945i	0.177605	−	0.307620i
$89$	−873.216			−1.04001			−0.520004	−	0.854164i	$-0.674070\pi$
$89$	−873.216			−1.04001			−0.520004	+	0.854164i	$0.674070\pi$
$90$	−213.799	−	370.311i	−0.250404	−	0.433713i
$91$	228.292			0.262983
$92$	439.282			0.497807
$93$	73.4107	−	127.151i	0.0818531	−	0.141774i
$94$	−212.704			−0.233391
$95$	388.352	+	672.645i	0.419411	+	0.726441i
$96$	−314.949	+	545.507i	−0.334837	+	0.579954i
$97$	399.697	+	692.296i	0.418383	+	0.724660i	0.995777	−	0.0918056i	$-0.0292638\pi$
$97$	399.697	+	692.296i	0.418383	+	0.724660i	−0.577394	+	0.816465i	$0.695930\pi$
$98$	608.431	−	1053.83i	0.627151	−	1.08626i
$99$	−139.425	+	241.491i	−0.141543	+	0.245159i
$100$	−117.128	+	202.872i	−0.117128	+	0.202872i
$101$	−117.057	+	202.748i	−0.115322	+	0.199744i	−0.917909	−	0.396792i	$-0.870123\pi$
$101$	−117.057	+	202.748i	−0.115322	+	0.199744i	0.802586	+	0.596536i	$0.203457\pi$
$102$	−457.741	+	792.831i	−0.444344	+	0.769627i
$103$	−190.197	+	329.430i	−0.181948	+	0.315143i	−0.942544	−	0.334083i	$-0.891574\pi$
$103$	−190.197	+	329.430i	−0.181948	+	0.315143i	0.760596	+	0.649225i	$0.224907\pi$
$104$	−329.046	−	569.924i	−0.310246	−	0.537362i
$105$	−63.8785	+	110.641i	−0.0593705	+	0.102833i
$106$	−986.214	−	1708.17i	−0.903676	−	1.56521i
$107$	−998.506			−0.902142			−0.451071	−	0.892488i	$-0.648958\pi$
$107$	−998.506			−0.902142			−0.451071	+	0.892488i	$0.648958\pi$
$108$	73.1181	−	126.644i	0.0651462	−	0.112837i
$109$	−1524.99			−1.34007			−0.670033	−	0.742332i	$-0.733720\pi$
$109$	−1524.99			−1.34007			−0.670033	+	0.742332i	$0.733720\pi$
$110$	1472.04			1.27594
$111$	−245.145	−	424.604i	−0.209623	−	0.363077i
$112$	256.064			0.216033
$113$	−633.384	+	1097.05i	−0.527289	+	0.913292i	0.472205	+	0.881489i	$0.343458\pi$
$113$	−633.384	+	1097.05i	−0.527289	+	0.913292i	−0.999494	+	0.0318032i	$0.989875\pi$
$114$	−328.989	+	569.826i	−0.270286	+	0.468150i
$115$	−526.019	−	911.091i	−0.426535	−	0.738780i
$116$	544.876	+	943.753i	0.436125	+	0.755390i
$117$	312.909	+	541.975i	0.247252	+	0.428253i
$118$	−157.268	−	272.397i	−0.122693	−	0.212510i
$119$	273.526			0.210707
$120$	368.283			0.280162
$121$	185.518	+	321.327i	0.139382	+	0.241417i
$122$	−1486.11	+	2574.02i	−1.10284	+	1.91017i
$123$	−74.3017	+	128.694i	−0.0544680	+	0.0943413i
$124$	−132.535	−	229.557i	−0.0959835	−	0.166248i
$125$	−1060.38			−0.758743
$126$	−108.228			−0.0765217
$127$	399.904	−	692.653i	0.279415	−	0.483961i	−0.691824	−	0.722066i	$-0.743193\pi$
$127$	399.904	−	692.653i	0.279415	−	0.483961i	0.971239	+	0.238105i	$0.0765261\pi$
$128$	−574.112	−	994.391i	−0.396444	−	0.686661i
$129$	−142.570			−0.0973071
$130$	1651.84	−	2861.08i	1.11443	−	1.93026i
$131$	−1139.68			−0.760107			−0.380053	−	0.924965i	$-0.624094\pi$
$131$	−1139.68			−0.760107			−0.380053	+	0.924965i	$0.624094\pi$
$132$	251.715	+	435.984i	0.165977	+	0.287481i
$133$	196.589			0.128169
$134$	1181.09	−	1624.84i	0.761424	−	1.04750i
$135$	−350.222			−0.223276
$136$	−394.244	−	682.851i	−0.248575	−	0.430544i
$137$	2321.56			1.44777			0.723884	−	0.689922i	$-0.242355\pi$
$137$	2321.56			1.44777			0.723884	+	0.689922i	$0.242355\pi$
$138$	445.612	−	771.823i	0.274877	−	0.476101i
$139$	2536.82			1.54799			0.773994	−	0.633193i	$-0.218256\pi$
$139$	2536.82			1.54799			0.773994	+	0.633193i	$0.218256\pi$
$140$	115.325	+	199.749i	0.0696197	+	0.120585i
$141$	−87.1070	+	150.874i	−0.0520265	+	0.0901125i
$142$	−1917.49			−1.13319
$143$	−2154.43			−1.25988
$144$	350.975	+	607.907i	0.203111	+	0.351798i
$145$	1304.93	−	2260.20i	0.747367	−	1.29448i
$146$	1629.45	−	2822.30i	0.923661	−	1.59983i
$147$	−498.332	−	863.136i	−0.279604	−	0.484288i
$148$	−885.162			−0.491621
$149$	2479.84			1.36347			0.681734	−	0.731600i	$-0.261226\pi$
$149$	2479.84			1.36347			0.681734	+	0.731600i	$0.261226\pi$
$150$	237.632	+	411.591i	0.129350	+	0.224042i
$151$	413.182	+	715.653i	0.222678	+	0.385689i	0.955620	−	0.294602i	$-0.0951870\pi$
$151$	413.182	+	715.653i	0.222678	+	0.385689i	−0.732943	+	0.680290i	$0.761854\pi$
$152$	−283.352	−	490.781i	−0.151203	−	0.261892i
$153$	374.910	+	649.364i	0.198103	+	0.343124i
$154$	186.293	−	322.668i	0.0974797	−	0.168840i
$155$	−317.408	+	549.766i	−0.164483	+	0.284892i
$156$	1129.84			0.579871
$157$	−451.916	−	782.741i	−0.229725	−	0.397895i	0.728002	−	0.685575i	$-0.240449\pi$
$157$	−451.916	−	782.741i	−0.229725	−	0.397895i	−0.957727	+	0.287680i	$0.907116\pi$
$158$	1378.12			0.693906
$159$	−1615.51			−0.805773
$160$	1361.75	−	2358.62i	0.672849	−	1.16541i
$161$	−266.278			−0.130346
$162$	−148.344	−	256.939i	−0.0719443	−	0.124611i
$163$	−1524.56	+	2640.61i	−0.732592	+	1.26889i	0.223180	+	0.974777i	$0.428356\pi$
$163$	−1524.56	+	2640.61i	−0.732592	+	1.26889i	−0.955772	+	0.294109i	$0.904977\pi$
$164$	134.143	+	232.343i	0.0638708	+	0.110628i
$165$	602.834	−	1044.14i	0.284428	−	0.492643i
$166$	−1165.26	+	2018.29i	−0.544828	+	0.943670i
$167$	−285.208	+	493.995i	−0.132156	+	0.228901i	−0.924507	−	0.381164i	$-0.875523\pi$
$167$	−285.208	+	493.995i	−0.132156	+	0.228901i	0.792351	+	0.610065i	$0.208857\pi$
$168$	46.6075	−	80.7266i	0.0214039	−	0.0370726i
$169$	−1319.09	+	2284.72i	−0.600403	+	1.03993i
$170$	1979.15	−	3427.98i	0.892904	−	1.54655i
$171$	269.456	+	466.712i	0.120502	+	0.208716i
$172$	−128.697	+	222.910i	−0.0570527	+	0.0988182i
$173$	−62.2308	−	107.787i	−0.0273487	−	0.0473693i	0.852027	−	0.523498i	$-0.175373\pi$
$173$	−62.2308	−	107.787i	−0.0273487	−	0.0473693i	−0.879376	+	0.476128i	$0.842040\pi$
$174$	2210.91			0.963270
$175$	70.9992	−	122.974i	0.0306688	−	0.0531199i
$176$	−2416.53			−1.03496
$177$	−257.619			−0.109400
$178$	1599.21	+	2769.91i	0.673404	+	1.16637i
$179$	3437.70			1.43545			0.717726	−	0.696325i	$-0.245183\pi$
$179$	3437.70			1.43545			0.717726	+	0.696325i	$0.245183\pi$
$180$	−316.142	+	547.575i	−0.130910	+	0.226743i
$181$	2176.71	−	3770.17i	0.893887	−	1.54826i	0.0587102	−	0.998275i	$-0.481301\pi$
$181$	2176.71	−	3770.17i	0.893887	−	1.54826i	0.835176	−	0.549982i	$-0.185365\pi$
$182$	−418.094	−	724.160i	−0.170281	−	0.294936i
$183$	1217.19	+	2108.24i	0.491679	+	0.851613i
$184$	383.798	+	664.758i	0.153772	+	0.266340i
$185$	1059.94	+	1835.87i	0.421234	+	0.729599i
$186$	−537.779			−0.211999
$187$	−2581.32			−1.00944
$188$	157.262	+	272.385i	0.0610079	+	0.105669i
$189$	−44.3218	+	76.7677i	−0.0170579	+	0.0295451i
$190$	1422.46	−	2463.77i	0.543136	−	0.940740i
$191$	−894.834	−	1549.90i	−0.338994	−	0.587155i	0.645250	−	0.763972i	$-0.276753\pi$
$191$	−894.834	−	1549.90i	−0.338994	−	0.587155i	−0.984244	+	0.176817i	$0.943420\pi$
$192$	435.324			0.163629
$193$	3582.57			1.33616			0.668081	−	0.744088i	$-0.267116\pi$
$193$	3582.57			1.33616			0.668081	+	0.744088i	$0.267116\pi$
$194$	1464.01	−	2535.75i	0.541804	−	0.938433i
$195$	−1352.93	−	2343.35i	−0.496849	−	0.860568i
$196$	−1799.36			−0.655744
$197$	−1932.19	+	3346.65i	−0.698796	+	1.21035i	0.270088	+	0.962836i	$0.412947\pi$
$197$	−1932.19	+	3346.65i	−0.698796	+	1.21035i	−0.968884	+	0.247515i	$0.920386\pi$
$198$	1021.37			0.366595
$199$	−1811.22	−	3137.12i	−0.645195	−	1.11751i	−0.984256	−	0.176747i	$-0.943443\pi$
$199$	−1811.22	−	3137.12i	−0.645195	−	1.11751i	0.339061	−	0.940764i	$-0.389891\pi$
$200$	−409.336			−0.144722
$201$	−668.837	−	1503.17i	−0.234707	−	0.527490i
$202$	857.512			0.298685
$203$	−330.286	−	572.073i	−0.114195	−	0.197791i
$204$	1353.71			0.464603
$205$	321.260	−	556.439i	0.109453	−	0.189577i
$206$	1393.31			0.471244
$207$	−364.976	−	632.157i	−0.122549	−	0.212261i
$208$	−2711.69	+	4696.78i	−0.903951	+	1.56569i
$209$	−1855.25			−0.614022
$210$	467.949			0.153769
$211$	−503.539	−	872.155i	−0.164289	−	0.284557i	0.772113	−	0.635485i	$-0.219200\pi$
$211$	−503.539	−	872.155i	−0.164289	−	0.284557i	−0.936403	+	0.350927i	$0.885866\pi$
$212$	−1458.30	+	2525.86i	−0.472438	+	0.818286i
$213$	−785.256	+	1360.10i	−0.252605	+	0.437524i
$214$	1828.67	+	3167.35i	0.584136	+	1.01175i
$215$	616.435			0.195537
$216$	255.532			0.0804941
$217$	80.3382	+	139.150i	0.0251323	+	0.0435305i
$218$	2792.86	+	4837.38i	0.867691	+	1.50288i
$219$	−1334.59	−	2311.58i	−0.411797	−	0.713253i
$220$	−1088.35	−	1885.07i	−0.333529	−	0.577689i
$221$	−2896.61	+	5017.08i	−0.881662	+	1.52708i
$222$	−897.919	+	1555.24i	−0.271461	+	0.470184i
$223$	1306.65			0.392376			0.196188	−	0.980566i	$-0.437144\pi$
$223$	1306.65			0.392376			0.196188	+	0.980566i	$0.437144\pi$
$224$	−344.669	−	596.984i	−0.102809	−	0.178070i
$225$	389.262			0.115337
$226$	4639.92			1.36568
$227$	−110.971	+	192.207i	−0.0324467	+	0.0561993i	−0.881793	−	0.471637i	$-0.843663\pi$
$227$	−110.971	+	192.207i	−0.0324467	+	0.0561993i	0.849346	+	0.527836i	$0.176997\pi$
$228$	972.945			0.282609
$229$	−1212.52	−	2100.15i	−0.349894	−	0.606034i	0.636336	−	0.771412i	$-0.280449\pi$
$229$	−1212.52	−	2100.15i	−0.349894	−	0.606034i	−0.986230	+	0.165378i	$0.947116\pi$
$230$	−1926.71	+	3337.15i	−0.552362	+	0.956718i
$231$	−152.582	−	264.279i	−0.0434595	−	0.0752741i
$232$	−952.111	+	1649.10i	−0.269436	+	0.466677i
$233$	973.562	−	1686.26i	0.273735	−	0.474122i	−0.696080	−	0.717964i	$-0.745074\pi$
$233$	973.562	−	1686.26i	0.273735	−	0.474122i	0.969815	+	0.243842i	$0.0784077\pi$
$234$	1146.13	−	1985.15i	0.320191	−	0.554586i
$235$	376.627	−	652.336i	0.104546	−	0.181080i
$236$	−232.551	+	402.790i	−0.0641431	+	0.111099i
$237$	564.370	−	977.517i	0.154682	−	0.267918i
$238$	−500.937	−	867.648i	−0.136432	−	0.236308i
$239$	−1787.92	+	3096.76i	−0.483894	+	0.838129i	−0.999829	−	0.0184986i	$-0.994111\pi$
$239$	−1787.92	+	3096.76i	−0.483894	+	0.838129i	0.515935	+	0.856628i	$0.327445\pi$
$240$	−1517.52	−	2628.42i	−0.408148	−	0.706933i
$241$	562.633			0.150383			0.0751917	−	0.997169i	$-0.476043\pi$
$241$	562.633			0.150383			0.0751917	+	0.997169i	$0.476043\pi$
$242$	679.517	−	1176.96i	0.180500	−	0.312635i
$243$	−243.000			−0.0641500
$244$	4394.99			1.15312
$245$	2154.65	+	3731.96i	0.561859	+	0.973169i
$246$	544.305			0.141072
$247$	−2081.86	+	3605.89i	−0.536298	+	0.928896i
$248$	231.590	−	401.125i	0.0592982	−	0.102708i
$249$	954.397	+	1653.06i	0.242901	+	0.420718i
$250$	1941.98	+	3363.60i	0.491285	+	0.850931i
$251$	−3943.43	−	6830.22i	−0.991662	−	1.71761i	−0.607431	−	0.794373i	$-0.707800\pi$
$251$	−3943.43	−	6830.22i	−0.991662	−	1.71761i	−0.384232	−	0.923237i	$-0.625534\pi$
$252$	80.0179	+	138.595i	0.0200026	+	0.0346455i
$253$	2512.92			0.624451
$254$	−2929.54			−0.723684
$255$	−1621.01	−	2807.67i	−0.398084	−	0.689502i
$256$	−2683.29	+	4647.60i	−0.655101	+	1.13467i
$257$	835.406	−	1446.97i	0.202767	−	0.351203i	−0.746652	−	0.665215i	$-0.768340\pi$
$257$	835.406	−	1446.97i	0.202767	−	0.351203i	0.949419	+	0.314012i	$0.101673\pi$
$258$	261.104	+	452.245i	0.0630063	+	0.109130i
$259$	536.557			0.128726
$260$	−4885.13			−1.16524
$261$	905.418	−	1568.23i	0.214728	−	0.371920i
$262$	2087.21	+	3615.15i	0.492168	+	0.852460i
$263$	249.168			0.0584197			0.0292098	−	0.999573i	$-0.490701\pi$
$263$	249.168			0.0584197			0.0292098	+	0.999573i	$0.490701\pi$
$264$	−439.845	+	761.834i	−0.102540	+	0.177605i
$265$	6985.00			1.61919
$266$	−360.034	−	623.598i	−0.0829892	−	0.143742i
$267$	2619.65			0.600449
$268$	−2953.98	−	311.168i	−0.673294	−	0.0709240i
$269$	2622.63			0.594440			0.297220	−	0.954809i	$-0.403940\pi$
$269$	2622.63			0.594440			0.297220	+	0.954809i	$0.403940\pi$
$270$	641.397	+	1110.93i	0.144571	+	0.250404i
$271$	−2634.76			−0.590592			−0.295296	−	0.955406i	$-0.595418\pi$
$271$	−2634.76			−0.590592			−0.295296	+	0.955406i	$0.595418\pi$
$272$	−3248.99	+	5627.42i	−0.724262	+	1.25446i
$273$	−684.875			−0.151833
$274$	−4251.71	−	7364.18i	−0.937428	−	1.62367i
$275$	−670.034	+	1160.53i	−0.146926	+	0.254483i
$276$	−1317.84			−0.287409
$277$	−7492.36			−1.62517			−0.812586	−	0.582842i	$-0.801941\pi$
$277$	−7492.36			−1.62517			−0.812586	+	0.582842i	$0.801941\pi$
$278$	−4645.94	−	8047.01i	−1.00232	−	1.73607i
$279$	−220.232	+	381.453i	−0.0472579	+	0.0818531i
$280$	−201.518	+	349.040i	−0.0430107	+	0.0744968i
$281$	−2230.55	−	3863.43i	−0.473536	−	0.820189i	0.526005	−	0.850482i	$-0.323689\pi$
$281$	−2230.55	−	3863.43i	−0.473536	−	0.820189i	−0.999541	+	0.0302927i	$0.990356\pi$
$282$	638.112			0.134748
$283$	8370.47			1.75821			0.879104	−	0.476630i	$-0.158142\pi$
$283$	8370.47			1.75821			0.879104	+	0.476630i	$0.158142\pi$
$284$	1417.69	+	2455.51i	0.296212	+	0.513055i
$285$	−1165.06	−	2017.94i	−0.242147	−	0.419411i
$286$	3945.64	+	6834.05i	0.815771	+	1.41296i
$287$	−81.3133	−	140.839i	−0.0167239	−	0.0289667i
$288$	944.846	−	1636.52i	0.193318	−	0.334837i
$289$	−1014.06	+	1756.40i	−0.206403	+	0.357501i
$290$	−9559.38			−1.93568
$291$	−1199.09	−	2076.89i	−0.241553	−	0.418383i
$292$	−4818.91			−0.965772
$293$	−2894.46			−0.577119			−0.288560	−	0.957462i	$-0.593176\pi$
$293$	−2894.46			−0.577119			−0.288560	+	0.957462i	$0.593176\pi$
$294$	−1825.29	+	3161.50i	−0.362086	+	0.627151i
$295$	1113.88			0.219838
$296$	−773.361	−	1339.50i	−0.151861	−	0.263030i
$297$	418.274	−	724.472i	0.0817197	−	0.141543i
$298$	−4541.59	−	7866.27i	−0.882844	−	1.52913i
$299$	2819.86	−	4884.14i	0.545407	−	0.944673i
$300$	351.384	−	608.615i	0.0676238	−	0.117128i
$301$	78.0121	−	135.121i	0.0149387	−	0.0258746i
$302$	1513.41	−	2621.30i	0.288367	−	0.499466i
$303$	351.170	−	608.244i	0.0665815	−	0.115322i
$304$	−2335.13	+	4044.56i	−0.440555	+	0.763063i
$305$	−5262.80	−	9115.43i	−0.988022	−	1.71130i
$306$	1373.22	−	2378.49i	0.256542	−	0.444344i
$307$	−1674.21	−	2899.81i	−0.311245	−	0.539092i	0.667387	−	0.744711i	$-0.267413\pi$
$307$	−1674.21	−	2899.81i	−0.311245	−	0.539092i	−0.978632	+	0.205619i	$0.934079\pi$
$308$	−550.937			−0.101924
$309$	570.590	−	988.290i	0.105048	−	0.181948i
$310$	2325.21			0.426009
$311$	−9546.91			−1.74069			−0.870347	−	0.492439i	$-0.836106\pi$
$311$	−9546.91			−1.74069			−0.870347	+	0.492439i	$0.836106\pi$
$312$	987.138	+	1709.77i	0.179121	+	0.310246i
$313$	−6264.38			−1.13126			−0.565629	−	0.824660i	$-0.691366\pi$
$313$	−6264.38			−1.13126			−0.565629	+	0.824660i	$0.691366\pi$
$314$	−1655.28	+	2867.03i	−0.297493	+	0.515273i
$315$	191.635	−	331.922i	0.0342776	−	0.0593705i
$316$	−1018.90	−	1764.79i	−0.181386	−	0.314169i
$317$	1530.93	+	2651.65i	0.271248	+	0.469815i	0.969182	−	0.246347i	$-0.0792304\pi$
$317$	1530.93	+	2651.65i	0.271248	+	0.469815i	−0.697934	+	0.716162i	$0.745897\pi$
$318$	2958.64	+	5124.52i	0.521737	+	0.903676i
$319$	3116.98	+	5398.77i	0.547077	+	0.947564i
$320$	−1882.22			−0.328810
$321$	2995.52			0.520852
$322$	487.663	+	844.657i	0.0843988	+	0.146183i
$323$	−2494.37	+	4320.38i	−0.429692	+	0.744248i
$324$	−219.354	+	379.933i	−0.0376122	+	0.0651462i
$325$	1503.75	+	2604.57i	0.256655	+	0.444540i
$326$	11168.3			1.89741
$327$	4574.96			0.773687
$328$	−234.400	+	405.993i	−0.0394591	+	0.0683452i
$329$	−95.3269	−	165.111i	−0.0159743	−	0.0276683i
$330$	−4416.13			−0.736667
$331$	3523.61	−	6103.07i	0.585121	−	1.01346i	−0.409739	−	0.912203i	$-0.634380\pi$
$331$	3523.61	−	6103.07i	0.585121	−	1.01346i	0.994860	−	0.101257i	$-0.0322864\pi$
$332$	3446.11			0.569668
$333$	735.435	+	1273.81i	0.121026	+	0.209623i
$334$	2089.33			0.342284
$335$	2891.87	+	6499.30i	0.471641	+	1.05998i
$336$	−768.191			−0.124727
$337$	2761.09	+	4782.34i	0.446309	+	0.773029i	0.998142	−	0.0609248i	$-0.0194050\pi$
$337$	2761.09	+	4782.34i	0.446309	+	0.773029i	−0.551834	+	0.833954i	$0.686072\pi$
$338$	9663.11			1.55504
$339$	1900.15	−	3291.16i	0.304431	−	0.527289i
$340$	−5853.09			−0.933612
$341$	−758.169	−	1313.19i	−0.120402	−	0.208543i
$342$	986.967	−	1709.48i	0.156050	−	0.270286i
$343$	2216.82			0.348971
$344$	−449.768			−0.0704938
$345$	1578.06	+	2733.27i	0.246260	+	0.426535i
$346$	−227.939	+	394.803i	−0.0354165	+	0.0613431i
$347$	−5021.18	+	8696.94i	−0.776804	+	1.34546i	0.156970	+	0.987603i	$0.449827\pi$
$347$	−5021.18	+	8696.94i	−0.776804	+	1.34546i	−0.933775	+	0.357861i	$0.883506\pi$
$348$	−1634.63	−	2831.26i	−0.251797	−	0.436125i
$349$	−4301.19			−0.659706			−0.329853	−	0.944032i	$-0.606999\pi$
$349$	−4301.19			−0.659706			−0.329853	+	0.944032i	$0.606999\pi$
$350$	−520.113			−0.0794320
$351$	−938.728	−	1625.92i	−0.142751	−	0.247252i
$352$	3252.71	+	5633.87i	0.492529	+	0.853086i
$353$	2745.65	+	4755.60i	0.413983	+	0.717040i	0.995321	−	0.0966224i	$-0.0308039\pi$
$353$	2745.65	+	4755.60i	0.413983	+	0.717040i	−0.581338	+	0.813662i	$0.697471\pi$
$354$	471.805	+	817.190i	0.0708366	+	0.122693i
$355$	3395.23	−	5880.71i	0.507606	−	0.879199i
$356$	2364.74	−	4095.84i	0.352053	−	0.609773i
$357$	−820.578			−0.121652
$358$	−6295.82	−	10904.7i	−0.929454	−	1.60986i
$359$	2859.41			0.420373			0.210187	−	0.977661i	$-0.432593\pi$
$359$	2859.41			0.420373			0.210187	+	0.977661i	$0.432593\pi$
$360$	−1104.85			−0.161752
$361$	1636.74	−	2834.92i	0.238627	−	0.413313i
$362$	−15945.7			−2.31516
$363$	−556.554	−	963.980i	−0.0804725	−	0.139382i
$364$	−618.231	+	1070.81i	−0.0890223	+	0.154191i
$365$	5770.41	+	9994.65i	0.827500	+	1.43327i
$366$	4458.33	−	7722.06i	0.636723	−	1.10284i
$367$	−1749.44	+	3030.13i	−0.248829	+	0.430985i	−0.963201	−	0.268781i	$-0.913379\pi$
$367$	−1749.44	+	3030.13i	−0.248829	+	0.430985i	0.714372	+	0.699766i	$0.246712\pi$
$368$	3162.90	−	5478.31i	0.448037	−	0.776024i
$369$	222.905	−	386.083i	0.0314471	−	0.0544680i
$370$	3882.35	−	6724.43i	0.545497	−	0.944829i
$371$	883.978	−	1531.09i	0.123703	−	0.214260i
$372$	397.604	+	688.670i	0.0554161	+	0.0959835i
$373$	2459.58	−	4260.12i	0.341427	−	0.591369i	−0.643271	−	0.765639i	$-0.722423\pi$
$373$	2459.58	−	4260.12i	0.341427	−	0.591369i	0.984698	+	0.174269i	$0.0557564\pi$
$374$	4727.44	+	8188.17i	0.653610	+	1.13209i
$375$	3181.13			0.438061
$376$	−274.797	+	475.963i	−0.0376904	+	0.0652817i
$377$	13990.8			1.91131
$378$	324.685			0.0441798
$379$	5357.71	+	9279.82i	0.726140	+	1.25771i	0.958503	+	0.285082i	$0.0920208\pi$
$379$	5357.71	+	9279.82i	0.726140	+	1.25771i	−0.232363	+	0.972629i	$0.574646\pi$
$380$	−4206.75			−0.567899
$381$	−1199.71	+	2077.96i	−0.161320	+	0.279415i
$382$	−3277.60	+	5676.98i	−0.438997	+	0.760365i
$383$	517.798	+	896.852i	0.0690815	+	0.119653i	0.898497	−	0.438979i	$-0.144660\pi$
$383$	517.798	+	896.852i	0.0690815	+	0.119653i	−0.829416	+	0.558632i	$0.811326\pi$
$384$	1722.34	+	2983.17i	0.228887	+	0.396444i
$385$	659.722	+	1142.67i	0.0873312	+	0.151262i
$386$	−6561.14	−	11364.2i	−0.865164	−	1.49851i
$387$	427.711			0.0561803
$388$	−4329.64			−0.566506
$389$	45.1097	+	78.1323i	0.00587957	+	0.0101837i	0.868950	−	0.494899i	$-0.164795\pi$
$389$	45.1097	+	78.1323i	0.00587957	+	0.0101837i	−0.863071	+	0.505083i	$0.831462\pi$
$390$	−4955.53	+	8583.24i	−0.643418	+	1.11443i
$391$	3378.60	−	5851.91i	0.436990	−	0.756889i
$392$	−1572.09	−	2722.94i	−0.202558	−	0.350841i
$393$	3419.03			0.438848
$394$	14154.5			1.80988
$395$	−2440.18	+	4226.51i	−0.310832	+	0.538377i
$396$	−755.146	−	1307.95i	−0.0958271	−	0.165977i
$397$	−1486.89			−0.187972			−0.0939859	−	0.995574i	$-0.529961\pi$
$397$	−1486.89			−0.187972			−0.0939859	+	0.995574i	$0.529961\pi$
$398$	−6634.14	+	11490.7i	−0.835526	+	1.44717i
$399$	−589.768			−0.0739983
$400$	1686.68	+	2921.42i	0.210835	+	0.365178i
$401$	333.120			0.0414843			0.0207422	−	0.999785i	$-0.493397\pi$
$401$	333.120			0.0414843			0.0207422	+	0.999785i	$0.493397\pi$
$402$	−3543.27	+	4874.52i	−0.439608	+	0.604774i
$403$	−3403.10			−0.420646
$404$	−633.997	−	1098.11i	−0.0780755	−	0.135231i
$405$	1050.67			0.128909
$406$	−1209.77	+	2095.39i	−0.147882	+	0.256139i
$407$	−5063.60			−0.616691
$408$	1182.73	+	2048.55i	0.143515	+	0.248575i
$409$	−5124.21	+	8875.40i	−0.619501	+	1.07301i	0.370076	+	0.929002i	$0.379332\pi$
$409$	−5124.21	+	8875.40i	−0.619501	+	1.07301i	−0.989577	+	0.144006i	$0.954002\pi$
$410$	−2353.43			−0.283482
$411$	−6964.68			−0.835869
$412$	−1030.13	−	1784.24i	−0.123182	−	0.213358i
$413$	140.965	−	244.158i	0.0167952	−	0.0290902i
$414$	−1336.84	+	2315.47i	−0.158700	+	0.274877i
$415$	−4126.55	−	7147.39i	−0.488107	−	0.845426i
$416$	14600.1			1.72074
$417$	−7610.46			−0.893731
$418$	3397.72	+	5885.02i	0.397579	+	0.688627i
$419$	7112.53	+	12319.3i	0.829284	+	1.43636i	0.898601	+	0.438767i	$0.144585\pi$
$419$	7112.53	+	12319.3i	0.829284	+	1.43636i	−0.0693167	+	0.997595i	$0.522082\pi$
$420$	−345.976	−	599.247i	−0.0401949	−	0.0696197i
$421$	−2561.16	−	4436.06i	−0.296493	−	0.513540i	0.678838	−	0.734288i	$-0.262484\pi$
$421$	−2561.16	−	4436.06i	−0.296493	−	0.513540i	−0.975331	+	0.220747i	$0.929150\pi$
$422$	−1844.37	+	3194.53i	−0.212754	+	0.368501i
$423$	261.321	−	452.621i	0.0300375	−	0.0520265i
$424$	−5096.45			−0.583740
$425$	1801.71	+	3120.65i	0.205637	+	0.356174i
$426$	5752.48			0.654245
$427$	−2664.10			−0.301932
$428$	2704.03	−	4683.52i	0.305384	−	0.528940i
$429$	6463.30			0.727392
$430$	−1128.94	−	1955.38i	−0.126610	−	0.219295i
$431$	4966.33	−	8601.93i	0.555034	−	0.961347i	−0.442867	−	0.896587i	$-0.646039\pi$
$431$	4966.33	−	8601.93i	0.555034	−	0.961347i	0.997901	−	0.0647596i	$-0.0206281\pi$
$432$	−1052.93	−	1823.72i	−0.117266	−	0.203111i
$433$	4526.66	−	7840.41i	0.502396	−	0.870175i	−0.497600	−	0.867407i	$-0.665785\pi$
$433$	4526.66	−	7840.41i	0.502396	−	0.870175i	0.999996	−	0.00276890i	$-0.000881368\pi$
$434$	294.263	−	509.679i	0.0325463	−	0.0563718i
$435$	−3914.78	+	6780.59i	−0.431493	+	0.747367i
$436$	4129.78	−	7152.98i	0.453625	−	0.785701i
$437$	2428.28	−	4205.90i	0.265813	−	0.460401i
$438$	−4888.36	+	8466.89i	−0.533276	+	0.923661i
$439$	−8690.62	−	15052.6i	−0.944830	−	1.63649i	−0.756091	−	0.654467i	$-0.772893\pi$
$439$	−8690.62	−	15052.6i	−0.944830	−	1.63649i	−0.188740	−	0.982027i	$-0.560440\pi$
$440$	1901.77	−	3293.96i	0.206053	−	0.356894i
$441$	1495.00	+	2589.41i	0.161429	+	0.279604i
$442$	21219.5			2.28350
$443$	6817.56	−	11808.4i	0.731178	−	1.26644i	−0.225202	−	0.974312i	$-0.572304\pi$
$443$	6817.56	−	11808.4i	0.731178	−	1.26644i	0.956380	−	0.292125i	$-0.0943624\pi$
$444$	2655.49			0.283837
$445$	−11326.6			−1.20659
$446$	−2393.00	−	4144.81i	−0.254063	−	0.440050i
$447$	−7439.53			−0.787198
$448$	−238.202	+	412.578i	−0.0251205	+	0.0435100i
$449$	7318.21	−	12675.5i	0.769193	−	1.33228i	−0.168809	−	0.985649i	$-0.553992\pi$
$449$	7318.21	−	12675.5i	0.769193	−	1.33228i	0.938001	−	0.346632i	$-0.112675\pi$
$450$	−712.896	−	1234.77i	−0.0746805	−	0.129350i
$451$	767.370	+	1329.12i	0.0801198	+	0.138772i
$452$	−3430.50	−	5941.80i	−0.356985	−	0.618316i
$453$	−1239.55	−	2146.96i	−0.128563	−	0.222678i
$454$	812.929			0.0840367
$455$	2961.21			0.305107
$456$	850.057	+	1472.34i	0.0872973	+	0.151203i
$457$	9417.86	−	16312.2i	0.964002	−	1.66970i	0.251731	−	0.967797i	$-0.419000\pi$
$457$	9417.86	−	16312.2i	0.964002	−	1.66970i	0.712272	−	0.701904i	$-0.247666\pi$
$458$	−4441.23	+	7692.44i	−0.453112	+	0.784813i
$459$	−1124.73	−	1948.09i	−0.114375	−	0.198103i
$460$	5698.00			0.577544
$461$	−9344.92			−0.944113			−0.472057	−	0.881568i	$-0.656488\pi$
$461$	−9344.92			−0.944113			−0.472057	+	0.881568i	$0.656488\pi$
$462$	−558.878	+	968.004i	−0.0562799	+	0.0974797i
$463$	−7077.40	−	12258.4i	−0.710399	−	1.23045i	−0.964707	−	0.263324i	$-0.915181\pi$
$463$	−7077.40	−	12258.4i	−0.710399	−	1.23045i	0.254308	−	0.967123i	$-0.418152\pi$
$464$	15692.8			1.57009
$465$	952.223	−	1649.30i	0.0949641	−	0.164483i
$466$	−7131.94			−0.708971
$467$	3513.09	+	6084.85i	0.348108	+	0.602941i	0.985913	−	0.167257i	$-0.0534909\pi$
$467$	3513.09	+	6084.85i	0.348108	+	0.602941i	−0.637805	+	0.770198i	$0.720158\pi$
$468$	−3389.53			−0.334789
$469$	1790.61	+	188.620i	0.176295	+	0.0185707i
$470$	−2759.02			−0.270775
$471$	1355.75	+	2348.22i	0.132632	+	0.229725i
$472$	−812.715			−0.0792547
$473$	−736.216	+	1275.16i	−0.0715672	+	0.123958i
$474$	−4134.35			−0.400627
$475$	1294.93	+	2242.88i	0.125085	+	0.216654i
$476$	−740.730	+	1282.98i	−0.0713262	+	0.123541i
$477$	4846.52			0.465213
$478$	13097.6			1.25328
$479$	−8303.13	−	14381.4i	−0.792024	−	1.37183i	−0.924712	−	0.380668i	$-0.875694\pi$
$479$	−8303.13	−	14381.4i	−0.792024	−	1.37183i	0.132687	−	0.991158i	$-0.457639\pi$
$480$	−4085.25	+	7075.87i	−0.388470	+	0.672849i
$481$	−5682.08	+	9841.66i	−0.538629	+	0.932933i
$482$	−1030.41	−	1784.72i	−0.0973731	−	0.168655i
$483$	798.835			0.0752552
$484$	−2009.59			−0.188729
$485$	5184.54	+	8979.89i	0.485398	+	0.840734i
$486$	445.031	+	770.816i	0.0415371	+	0.0719443i
$487$	−2402.83	−	4161.83i	−0.223579	−	0.387250i	0.732313	−	0.680968i	$-0.238441\pi$
$487$	−2402.83	−	4161.83i	−0.223579	−	0.387250i	−0.955892	+	0.293718i	$0.905107\pi$
$488$	3839.88	+	6650.87i	0.356195	+	0.616948i
$489$	4573.67	−	7921.83i	0.422962	−	0.732592i
$490$	7892.07	−	13669.5i	0.727607	−	1.26025i
$491$	9289.33			0.853812			0.426906	−	0.904296i	$-0.359604\pi$
$491$	9289.33			0.853812			0.426906	+	0.904296i	$0.359604\pi$
$492$	−402.429	−	697.028i	−0.0368758	−	0.0638708i
$493$	16763.0			1.53137
$494$	15250.9			1.38901
$495$	−1808.50	+	3132.42i	−0.164214	+	0.284428i
$496$	−3817.09			−0.345549
$497$	−859.357	−	1488.45i	−0.0775603	−	0.134338i
$498$	3495.77	−	6054.86i	0.314557	−	0.544828i
$499$	−7343.83	−	12719.9i	−0.658828	−	1.14112i	−0.980919	−	0.194414i	$-0.937719\pi$
$499$	−7343.83	−	12719.9i	−0.658828	−	1.14112i	0.322092	−	0.946708i	$-0.395614\pi$
$500$	2871.58	−	4973.72i	0.256842	−	0.444863i
$501$	855.625	−	1481.99i	0.0763004	−	0.132156i
$502$	−14444.0	+	25017.8i	−1.28420	+	2.22430i
$503$	−9290.43	+	16091.5i	−0.823538	+	1.42641i	0.0794935	+	0.996835i	$0.474670\pi$
$503$	−9290.43	+	16091.5i	−0.823538	+	1.42641i	−0.903032	+	0.429574i	$0.858664\pi$
$504$	−139.823	+	242.180i	−0.0123575	+	0.0214039i
$505$	−1518.36	+	2629.88i	−0.133794	+	0.231739i
$506$	−4602.18	−	7971.21i	−0.404332	−	0.700323i
$507$	3957.26	−	6854.17i	0.346643	−	0.600403i
$508$	2165.94	+	3751.52i	0.189169	+	0.327651i
$509$	10248.7			0.892471			0.446235	−	0.894916i	$-0.352764\pi$
$509$	10248.7			0.892471			0.446235	+	0.894916i	$0.352764\pi$
$510$	−5937.44	+	10283.9i	−0.515518	+	0.892904i
$511$	2921.07			0.252878
$512$	10471.0			0.903820
$513$	−808.369	−	1400.14i	−0.0695719	−	0.120502i
$514$	−6119.86			−0.525166
$515$	−2467.07	+	4273.09i	−0.211092	+	0.365621i
$516$	386.091	−	668.730i	0.0329394	−	0.0570527i
$517$	899.620	+	1558.19i	0.0765285	+	0.132551i
$518$	−982.652	−	1702.00i	−0.0833499	−	0.144366i
$519$	186.692	+	323.361i	0.0157898	+	0.0273487i
$520$	−4268.11	−	7392.59i	−0.359941	−	0.623436i
$521$	17525.0			1.47367			0.736837	−	0.676070i	$-0.236318\pi$
$521$	17525.0			1.47367			0.736837	+	0.676070i	$0.236318\pi$
$522$	−6632.74			−0.556144
$523$	−6105.72	−	10575.4i	−0.510487	−	0.884189i	−0.999926	−	0.0121518i	$-0.996132\pi$
$523$	−6105.72	−	10575.4i	−0.510487	−	0.884189i	0.489439	−	0.872037i	$-0.337201\pi$
$524$	3086.33	−	5345.68i	0.257303	−	0.445663i
$525$	−212.998	+	368.923i	−0.0177066	+	0.0306688i
$526$	−456.328	−	790.383i	−0.0378267	−	0.0655177i
$527$	−4077.40			−0.337029
$528$	7249.58			0.597533
$529$	2794.42	−	4840.08i	0.229672	−	0.397804i
$530$	−12792.4	−	22157.0i	−1.04842	−	1.81592i
$531$	772.858			0.0631623
$532$	−532.379	+	922.108i	−0.0433864	+	0.0751474i
$533$	3444.40			0.279913
$534$	−4797.63	−	8309.74i	−0.388790	−	0.673404i
$535$	−12951.8			−1.04664
$536$	−2109.99	−	4742.07i	−0.170033	−	0.382139i
$537$	−10313.1			−0.828759
$538$	−4803.09	−	8319.19i	−0.384899	−	0.666665i
$539$	−10293.3			−0.822568
$540$	948.427	−	1642.72i	0.0755811	−	0.130910i
$541$	−2327.73			−0.184985			−0.0924926	−	0.995713i	$-0.529483\pi$
$541$	−2327.73			−0.184985			−0.0924926	+	0.995713i	$0.529483\pi$
$542$	4825.31	+	8357.69i	0.382408	+	0.662349i
$543$	−6530.13	+	11310.5i	−0.516086	+	0.893887i
$544$	17493.0			1.37868
$545$	−19780.9			−1.55471
$546$	1254.28	+	2172.48i	0.0983119	+	0.170281i
$547$	−8949.31	+	15500.7i	−0.699534	+	1.21163i	0.269094	+	0.963114i	$0.413276\pi$
$547$	−8949.31	+	15500.7i	−0.699534	+	1.21163i	−0.968628	+	0.248514i	$0.920058\pi$
$548$	−6286.96	+	10889.3i	−0.490083	+	0.848849i
$549$	−3651.57	−	6324.71i	−0.283871	−	0.491679i
$550$	4908.41			0.380537
$551$	12047.9			0.931505
$552$	−1151.39	−	1994.27i	−0.0887801	−	0.153772i
$553$	617.627	+	1069.76i	0.0474940	+	0.0822620i
$554$	13721.5	+	23766.4i	1.05230	+	1.82263i
$555$	−3179.82	−	5507.61i	−0.243200	−	0.421234i
$556$	−6869.91	+	11899.0i	−0.524009	+	0.907610i
$557$	4373.91	−	7575.84i	0.332726	−	0.576299i	−0.650319	−	0.759661i	$-0.725365\pi$
$557$	4373.91	−	7575.84i	0.332726	−	0.576299i	0.983045	+	0.183362i	$0.0586982\pi$
$558$	1613.34			0.122398
$559$	1652.28	+	2861.83i	0.125016	+	0.216534i
$560$	3321.45			0.250637
$561$	7743.97			0.582800
$562$	−8170.09	+	14151.0i	−0.613228	+	1.06214i
$563$	−25569.4			−1.91407			−0.957037	−	0.289967i	$-0.906356\pi$
$563$	−25569.4			−1.91407			−0.957037	+	0.289967i	$0.906356\pi$
$564$	−471.785	−	817.155i	−0.0352229	−	0.0610079i
$565$	−8215.73	+	14230.1i	−0.611749	+	1.05958i
$566$	−15329.7	−	26551.8i	−1.13844	−	1.97183i
$567$	132.965	−	230.303i	0.00984837	−	0.0170579i
$568$	−2477.25	+	4290.73i	−0.182999	+	0.316963i
$569$	−4922.45	+	8525.94i	−0.362671	+	0.628165i	−0.988400	−	0.151876i	$-0.951469\pi$
$569$	−4922.45	+	8525.94i	−0.362671	+	0.628165i	0.625728	+	0.780041i	$0.284802\pi$
$570$	−4267.37	+	7391.31i	−0.313580	+	0.543136i
$571$	619.263	−	1072.59i	0.0453859	−	0.0786107i	−0.842440	−	0.538790i	$-0.818882\pi$
$571$	619.263	−	1072.59i	0.0453859	−	0.0786107i	0.887826	+	0.460179i	$0.152215\pi$
$572$	5834.37	−	10105.4i	0.426482	−	0.738688i
$573$	2684.50	+	4649.69i	0.195718	+	0.338994i
$574$	−297.835	+	515.865i	−0.0216575	+	0.0375118i
$575$	−1753.97	−	3037.96i	−0.127210	−	0.220333i
$576$	−1305.97			−0.0944713
$577$	115.272	−	199.657i	0.00831689	−	0.0144053i	−0.861837	−	0.507185i	$-0.830686\pi$
$577$	115.272	−	199.657i	0.00831689	−	0.0144053i	0.870154	+	0.492780i	$0.164019\pi$
$578$	7428.61			0.534584
$579$	−10747.7			−0.771434
$580$	7067.68	+	12241.6i	0.505982	+	0.876386i
$581$	−2088.92			−0.149162
$582$	−4392.04	+	7607.24i	−0.312811	+	0.541804i
$583$	−8342.28	+	14449.3i	−0.592628	+	1.02646i
$584$	−4210.26	−	7292.38i	−0.298325	−	0.516714i
$585$	4058.80	+	7030.05i	0.286856	+	0.496849i
$586$	5300.92	+	9181.46i	0.373684	+	0.647240i
$587$	2755.85	+	4773.26i	0.193775	+	0.335628i	0.946498	−	0.322709i	$-0.104594\pi$
$587$	2755.85	+	4773.26i	0.193775	+	0.335628i	−0.752723	+	0.658337i	$0.771260\pi$
$588$	5398.08			0.378594
$589$	−2930.52			−0.205008
$590$	−2039.95	−	3533.31i	−0.142345	−	0.246549i
$591$	5796.57	−	10040.0i	0.403450	−	0.698796i
$592$	−6373.32	+	11038.9i	−0.442469	+	0.766379i
$593$	−6445.21	−	11163.4i	−0.446329	−	0.773064i	0.551815	−	0.833967i	$-0.313936\pi$
$593$	−6445.21	−	11163.4i	−0.446329	−	0.773064i	−0.998144	+	0.0609024i	$0.980602\pi$
$594$	−3064.12			−0.211654
$595$	3547.95			0.244457
$596$	−6715.60	+	11631.8i	−0.461547	+	0.799422i
$597$	5433.66	+	9411.37i	0.372504	+	0.645195i
$598$	−20657.2			−1.41260
$599$	1939.15	−	3358.71i	0.132273	−	0.229103i	−0.792279	−	0.610158i	$-0.791106\pi$
$599$	1939.15	−	3358.71i	0.132273	−	0.229103i	0.924552	+	0.381055i	$0.124439\pi$
$600$	1228.01			0.0835554
$601$	8886.24	+	15391.4i	0.603123	+	1.04464i	0.992345	+	0.123496i	$0.0394107\pi$
$601$	8886.24	+	15391.4i	0.603123	+	1.04464i	−0.389222	+	0.921144i	$0.627256\pi$
$602$	−571.486			−0.0386911
$603$	2006.51	+	4509.51i	0.135508	+	0.304547i
$604$	−4475.72			−0.301514
$605$	2406.39	+	4167.98i	0.161708	+	0.280087i
$606$	−2572.53			−0.172446
$607$	−4821.36	+	8350.84i	−0.322394	+	0.558402i	−0.980981	−	0.194102i	$-0.937821\pi$
$607$	−4821.36	+	8350.84i	−0.322394	+	0.558402i	0.658588	+	0.752504i	$0.271154\pi$
$608$	12572.6			0.838628
$609$	990.859	+	1716.22i	0.0659304	+	0.114195i
$610$	−19276.6	+	33388.1i	−1.27949	+	2.21614i
$611$	4038.01			0.267366
$612$	−4061.14			−0.268238
$613$	798.051	+	1382.27i	0.0525824	+	0.0910753i	0.891119	−	0.453771i	$-0.149921\pi$
$613$	798.051	+	1382.27i	0.0525824	+	0.0910753i	−0.838536	+	0.544846i	$0.816588\pi$
$614$	−6132.30	+	10621.5i	−0.403061	+	0.698123i
$615$	−963.780	+	1669.32i	−0.0631925	+	0.109453i
$616$	−481.351	−	833.725i	−0.0314841	−	0.0545320i
$617$	−4187.36			−0.273220			−0.136610	−	0.990625i	$-0.543621\pi$
$617$	−4187.36			−0.273220			−0.136610	+	0.990625i	$0.543621\pi$
$618$	−4179.92			−0.272073
$619$	−3348.11	−	5799.09i	−0.217402	−	0.376551i	0.736611	−	0.676317i	$-0.236425\pi$
$619$	−3348.11	−	5799.09i	−0.217402	−	0.376551i	−0.954013	+	0.299765i	$0.903092\pi$
$620$	−1719.13	−	2977.62i	−0.111358	−	0.192878i
$621$	1094.93	+	1896.47i	0.0707536	+	0.122549i
$622$	17484.3	+	30283.6i	1.12710	+	1.95219i
$623$	−1433.43	+	2482.77i	−0.0921815	+	0.159663i
$624$	8135.07	−	14090.4i	0.521896	−	0.903951i
$625$	−19160.7			−1.22629
$626$	11472.6	+	19871.1i	0.732488	+	1.26871i
$627$	5565.76			0.354506
$628$	4895.29			0.311056
$629$	−6807.95	+	11791.7i	−0.431559	+	0.747483i
$630$	−1403.85			−0.0887787
$631$	−9440.76	−	16351.9i	−0.595611	−	1.03163i	−0.993460	−	0.114178i	$-0.963576\pi$
$631$	−9440.76	−	16351.9i	−0.595611	−	1.03163i	0.397849	−	0.917451i	$-0.369757\pi$
$632$	1780.42	−	3083.78i	0.112059	−	0.194092i
$633$	1510.62	+	2616.46i	0.0948525	+	0.164289i
$634$	5607.50	−	9712.47i	0.351265	−	0.608409i
$635$	5187.22	−	8984.53i	0.324171	−	0.561480i
$636$	4374.91	−	7577.57i	0.272762	−	0.472438i
$637$	−11550.6	+	20006.2i	−0.718446	+	1.24439i
$638$	11416.9	−	19774.6i	0.708463	−	1.22709i
$639$	2355.77	−	4080.31i	0.145841	−	0.252605i
$640$	−7446.91	−	12898.4i	−0.459945	−	0.796648i
$641$	−8054.98	+	13951.6i	−0.496338	+	0.859682i	−0.999991	−	0.00422384i	$-0.998656\pi$
$641$	−8054.98	+	13951.6i	−0.496338	+	0.859682i	0.503653	+	0.863906i	$0.331989\pi$
$642$	−5486.00	−	9502.04i	−0.337251	−	0.584136i
$643$	16755.9			1.02766			0.513832	−	0.857891i	$-0.328225\pi$
$643$	16755.9			1.02766			0.513832	+	0.857891i	$0.328225\pi$
$644$	721.102	−	1248.99i	0.0441233	−	0.0764238i
$645$	−1849.31			−0.112894
$646$	18272.8			1.11290
$647$	−3227.70	−	5590.54i	−0.196127	−	0.339702i	0.751143	−	0.660140i	$-0.229503\pi$
$647$	−3227.70	−	5590.54i	−0.196127	−	0.339702i	−0.947269	+	0.320438i	$0.896170\pi$
$648$	−766.595			−0.0464733
$649$	−1330.32	+	2304.17i	−0.0804614	+	0.139363i
$650$	5507.94	−	9540.04i	0.332368	−	0.575679i
$651$	−241.015	−	417.450i	−0.0145102	−	0.0251323i
$652$	−8257.23	−	14301.9i	−0.495979	−	0.859060i
$653$	−13240.0	−	22932.4i	−0.793448	−	1.37429i	−0.923820	−	0.382827i	$-0.874950\pi$
$653$	−13240.0	−	22932.4i	−0.793448	−	1.37429i	0.130372	−	0.991465i	$-0.458383\pi$
$654$	−8378.59	−	14512.1i	−0.500961	−	0.867691i
$655$	−14782.9			−0.881858
$656$	3863.42			0.229941
$657$	4003.78	+	6934.75i	0.237751	+	0.411797i
$658$	−349.164	+	604.770i	−0.0206867	+	0.0358304i
$659$	12310.5	−	21322.4i	0.727692	−	1.26040i	−0.230164	−	0.973152i	$-0.573926\pi$
$659$	12310.5	−	21322.4i	0.727692	−	1.26040i	0.957856	−	0.287248i	$-0.0927405\pi$
$660$	3265.04	+	5655.22i	0.192563	+	0.333529i
$661$	−4408.23			−0.259395			−0.129698	−	0.991554i	$-0.541401\pi$
$661$	−4408.23			−0.259395			−0.129698	+	0.991554i	$0.541401\pi$
$662$	−25812.6			−1.51546
$663$	8689.84	−	15051.3i	0.509028	−	0.881662i
$664$	3010.85	+	5214.94i	0.175969	+	0.304787i
$665$	2549.99			0.148699
$666$	2693.76	−	4665.72i	0.156728	−	0.271461i
$667$	−16318.8			−0.947327
$668$	−1544.73	−	2675.55i	−0.0894723	−	0.154970i
$669$	−3919.95			−0.226538
$670$	15320.1	−	21076.1i	0.883386	−	1.21528i
$671$	25141.7			1.44647
$672$	1034.01	+	1790.95i	0.0593567	+	0.102809i
$673$	21237.1			1.21639			0.608196	−	0.793787i	$-0.291894\pi$
$673$	21237.1			1.21639			0.608196	+	0.793787i	$0.291894\pi$
$674$	10113.3	−	17516.8i	0.577969	−	1.00107i
$675$	−1167.79			−0.0665898
$676$	−7144.37	−	12374.4i	−0.406484	−	0.704051i
$677$	−10440.1	+	18082.7i	−0.592680	+	1.02655i	0.401190	+	0.915995i	$0.368597\pi$
$677$	−10440.1	+	18082.7i	−0.592680	+	1.02655i	−0.993870	+	0.110557i	$0.964737\pi$
$678$	−13919.8			−0.788474
$679$	2624.49			0.148334
$680$	−5113.81	−	8857.38i	−0.288391	−	0.499508i
$681$	332.912	−	576.621i	0.0187331	−	0.0324467i
$682$	−2777.02	+	4809.95i	−0.155920	+	0.270062i
$683$	2838.56	+	4916.53i	0.159026	+	0.275440i	0.934518	−	0.355917i	$-0.115831\pi$
$683$	2838.56	+	4916.53i	0.159026	+	0.275440i	−0.775492	+	0.631357i	$0.782498\pi$
$684$	−2918.84			−0.163164
$685$	30113.4			1.67967
$686$	−4059.89	−	7031.93i	−0.225958	−	0.391371i
$687$	3637.57	+	6300.45i	0.202011	+	0.349894i
$688$	1853.28	+	3209.98i	0.102697	+	0.177877i
$689$	18722.5	+	32428.3i	1.03522	+	1.79306i
$690$	5780.12	−	10011.5i	0.318906	−	0.552362i
$691$	−12408.7	+	21492.5i	−0.683141	+	1.18323i	0.290876	+	0.956761i	$0.406053\pi$
$691$	−12408.7	+	21492.5i	−0.683141	+	1.18323i	−0.974017	+	0.226474i	$0.927280\pi$
$692$	674.103			0.0370312
$693$	457.745	+	792.838i	0.0250914	+	0.0434595i
$694$	36783.2			2.01192
$695$	32905.5			1.79594
$696$	2856.33	−	4947.31i	0.155559	−	0.269436i
$697$	4126.88			0.224271
$698$	7877.21	+	13643.7i	0.427159	+	0.739861i
$699$	−2920.69	+	5058.78i	−0.158041	+	0.273735i
$700$	384.543	+	666.047i	0.0207633	+	0.0359632i
$701$	−6320.10	+	10946.7i	−0.340523	+	0.589804i	−0.984530	−	0.175216i	$-0.943938\pi$
$701$	−6320.10	+	10946.7i	−0.340523	+	0.589804i	0.644007	+	0.765020i	$0.277271\pi$
$702$	−3438.38	+	5955.45i	−0.184862	+	0.320191i
$703$	−4893.03	+	8474.97i	−0.262509	+	0.454680i
$704$	2247.96	−	3893.58i	0.120345	−	0.208444i
$705$	−1129.88	+	1957.01i	−0.0603599	+	0.104546i
$706$	10056.8	−	17418.8i	0.536107	−	0.928565i
$707$	384.308	+	665.642i	0.0204433	+	0.0354088i
$708$	697.653	−	1208.37i	0.0370331	−	0.0641431i
$709$	−781.382	−	1353.39i	−0.0413898	−	0.0716893i	0.844588	−	0.535416i	$-0.179845\pi$
$709$	−781.382	−	1353.39i	−0.0413898	−	0.0716893i	−0.885978	+	0.463727i	$0.846512\pi$
$710$	−24872.1			−1.31470
$711$	−1693.11	+	2932.55i	−0.0893060	+	0.154682i
$712$	8264.23			0.434993
$713$	3969.36			0.208490
$714$	1502.81	+	2602.94i	0.0787692	+	0.136432i
$715$	−27945.5			−1.46168
$716$	−9309.57	+	16124.6i	−0.485915	+	0.841629i
$717$	5363.75	−	9290.29i	0.279376	−	0.483894i
$718$	−5236.74	−	9070.30i	−0.272191	−	0.471449i
$719$	3159.70	+	5472.76i	0.163890	+	0.283866i	0.936261	−	0.351306i	$-0.114262\pi$
$719$	3159.70	+	5472.76i	0.163890	+	0.283866i	−0.772371	+	0.635172i	$0.780929\pi$
$720$	4552.56	+	7885.27i	0.235644	+	0.408148i
$721$	624.434	+	1081.55i	0.0322540	+	0.0558656i
$722$	−11990.1			−0.618042
$723$	−1687.90			−0.0868239
$724$	11789.4	+	20419.8i	0.605178	+	1.04820i
$725$	4351.17	−	7536.45i	0.222894	−	0.386064i
$726$	−2038.55	+	3530.87i	−0.104212	+	0.180500i
$727$	−12560.4	−	21755.3i	−0.640770	−	1.10985i	−0.985261	−	0.171057i	$-0.945282\pi$
$727$	−12560.4	−	21755.3i	−0.640770	−	1.10985i	0.344491	−	0.938790i	$-0.388052\pi$
$728$	−2160.58			−0.109995
$729$	729.000			0.0370370
$730$	21135.9	−	36608.5i	1.07161	−	1.85608i
$731$	1979.67	+	3428.89i	0.100165	+	0.173491i
$732$	−13185.0			−0.665752
$733$	14428.4	−	24990.7i	0.727046	−	1.25928i	−0.231080	−	0.972935i	$-0.574226\pi$
$733$	14428.4	−	24990.7i	0.727046	−	1.25928i	0.958126	−	0.286346i	$-0.0924408\pi$
$734$	12815.8			0.644466
$735$	−6463.95	−	11195.9i	−0.324390	−	0.561859i
$736$	−17029.4			−0.852872
$737$	−16898.3	−	1780.05i	−0.844583	−	0.0889674i
$738$	−1632.92			−0.0814478
$739$	2098.15	+	3634.10i	0.104441	+	0.180896i	0.913510	−	0.406817i	$-0.133361\pi$
$739$	2098.15	+	3634.10i	0.104441	+	0.180896i	−0.809069	+	0.587714i	$0.800028\pi$
$740$	−11481.6			−0.570367
$741$	6245.59	−	10817.7i	0.309632	−	0.536298i
$742$	−6475.68			−0.320390
$743$	−3861.73	−	6688.71i	−0.190677	−	0.330262i	0.754798	−	0.655958i	$-0.227735\pi$
$743$	−3861.73	−	6688.71i	−0.190677	−	0.330262i	−0.945475	+	0.325695i	$0.894402\pi$
$744$	−694.769	+	1203.37i	−0.0342358	+	0.0592982i
$745$	32166.5			1.58186
$746$	−18018.0			−0.884295
$747$	−2863.19	−	4959.19i	−0.140239	−	0.242901i
$748$	6990.42	−	12107.8i	0.341705	−	0.591850i
$749$	−1639.10	+	2839.00i	−0.0799617	+	0.138498i
$750$	−5825.93	−	10090.8i	−0.283644	−	0.491285i
$751$	32160.0			1.56263			0.781316	−	0.624136i	$-0.214549\pi$
$751$	32160.0			1.56263			0.781316	+	0.624136i	$0.214549\pi$
$752$	4529.24			0.219634
$753$	11830.3	+	20490.7i	0.572536	+	0.991662i
$754$	−25622.8	−	44380.0i	−1.23757	−	2.14353i
$755$	5359.46	+	9282.86i	0.258345	+	0.447467i
$756$	−240.054	−	415.785i	−0.0115485	−	0.0200026i
$757$	−5880.91	+	10186.0i	−0.282359	+	0.489059i	−0.971965	−	0.235125i	$-0.924450\pi$
$757$	−5880.91	+	10186.0i	−0.282359	+	0.489059i	0.689607	+	0.724184i	$0.257783\pi$
$758$	19624.3	−	33990.2i	0.940349	−	1.62873i
$759$	−7538.77			−0.360527
$760$	−3675.41	−	6366.00i	−0.175423	−	0.303841i
$761$	−4380.24			−0.208651			−0.104326	−	0.994543i	$-0.533268\pi$
$761$	−4380.24			−0.208651			−0.104326	+	0.994543i	$0.533268\pi$
$762$	8788.62			0.417819
$763$	−2503.34	+	4335.91i	−0.118777	+	0.205728i
$764$	9693.11			0.459011
$765$	4863.03	+	8423.01i	0.229834	+	0.398084i
$766$	1896.59	−	3285.00i	0.0894604	−	0.154950i
$767$	2985.61	+	5171.23i	0.140553	+	0.243445i
$768$	8049.88	−	13942.8i	0.378223	−	0.655101i
$769$	4580.44	−	7933.55i	0.214792	−	0.372030i	−0.738416	−	0.674345i	$-0.764426\pi$
$769$	4580.44	−	7933.55i	0.214792	−	0.372030i	0.953208	+	0.302315i	$0.0977594\pi$
$770$	2416.43	−	4185.38i	0.113094	−	0.195884i
$771$	−2506.22	+	4340.90i	−0.117068	+	0.202767i
$772$	−9701.88	+	16804.2i	−0.452304	+	0.783413i
$773$	5780.56	−	10012.2i	0.268968	−	0.465866i	−0.699628	−	0.714508i	$-0.746651\pi$
$773$	5780.56	−	10012.2i	0.268968	−	0.465866i	0.968596	+	0.248641i	$0.0799841\pi$
$774$	−783.312	−	1356.74i	−0.0363767	−	0.0630063i
$775$	−1058.37	+	1833.15i	−0.0490552	+	0.0849661i
$776$	−3782.79	−	6551.98i	−0.174992	−	0.303096i
$777$	−1609.67			−0.0743199
$778$	165.228	−	286.184i	0.00761403	−	0.0131879i
$779$	2966.08			0.136420
$780$	14655.4			0.672753
$781$	8109.93	+	14046.8i	0.371570	+	0.643578i
$782$	−24750.3			−1.13180
$783$	−2716.25	+	4704.69i	−0.123973	+	0.214728i
$784$	−12955.7	+	22440.0i	−0.590184	+	1.02223i
$785$	−5861.88	−	10153.1i	−0.266521	−	0.461629i
$786$	−6261.62	−	10845.4i	−0.284153	−	0.492168i
$787$	−8025.21	−	13900.1i	−0.363492	−	0.629586i	0.625041	−	0.780592i	$-0.285082\pi$
$787$	−8025.21	−	13900.1i	−0.363492	−	0.629586i	−0.988533	+	0.151006i	$0.951749\pi$
$788$	−10465.0	−	18126.0i	−0.473099	−	0.819431i
$789$	−747.505			−0.0337286
$790$	17875.8			0.805054
$791$	2079.46	+	3601.73i	0.0934730	+	0.161900i
$792$	1319.53	−	2285.50i	0.0592015	−	0.102540i
$793$	28212.6	−	48865.7i	1.26338	−	2.18823i
$794$	2723.09	+	4716.54i	0.121712	+	0.210811i
$795$	−20955.0			−0.934840
$796$	19619.7			0.873619
$797$	14504.1	−	25121.8i	0.644617	−	1.11651i	−0.339772	−	0.940508i	$-0.610350\pi$
$797$	14504.1	−	25121.8i	0.644617	−	1.11651i	0.984390	−	0.176002i	$-0.0563166\pi$
$798$	1080.10	+	1870.79i	0.0479138	+	0.0829892i
$799$	4838.12			0.214218
$800$	4540.65	−	7864.64i	0.200670	−	0.347571i
$801$	−7858.94			−0.346669
$802$	−610.077	−	1056.68i	−0.0268610	−	0.0465247i
$803$	−27566.7			−1.21147
$804$	8861.93	+	933.505i	0.388726	+	0.0409480i
$805$	−3453.94			−0.151224
$806$	6232.44	+	10794.9i	0.272368	+	0.471755i
$807$	−7867.88			−0.343200
$808$	1107.84	−	1918.83i	0.0482347	−	0.0835450i
$809$	−15698.1			−0.682219			−0.341109	−	0.940024i	$-0.610803\pi$
$809$	−15698.1			−0.682219			−0.341109	+	0.940024i	$0.610803\pi$
$810$	−1924.19	−	3332.80i	−0.0834681	−	0.144571i
$811$	3291.77	−	5701.51i	0.142527	−	0.246865i	−0.785920	−	0.618328i	$-0.787810\pi$
$811$	3291.77	−	5701.51i	0.142527	−	0.246865i	0.928448	+	0.371463i	$0.121144\pi$
$812$	3577.76			0.154624
$813$	7904.29			0.340978
$814$	9273.49	+	16062.2i	0.399307	+	0.691619i
$815$	−19775.3	+	34251.8i	−0.849936	+	1.47213i
$816$	9746.98	−	16882.3i	0.418153	−	0.724262i
$817$	1422.83	+	2464.42i	0.0609286	+	0.105531i
$818$	37538.0			1.60451
$819$	2054.62			0.0876610
$820$	1739.99	+	3013.76i	0.0741015	+	0.128348i
$821$	3317.69	+	5746.41i	0.141033	+	0.244277i	0.927886	−	0.372864i	$-0.121624\pi$
$821$	3317.69	+	5746.41i	0.141033	+	0.244277i	−0.786853	+	0.617141i	$0.788291\pi$
$822$	12755.1	+	22092.5i	0.541224	+	0.937428i
$823$	−1599.51	−	2770.44i	−0.0677468	−	0.117341i	0.830162	−	0.557522i	$-0.188248\pi$
$823$	−1599.51	−	2770.44i	−0.0677468	−	0.117341i	−0.897909	+	0.440181i	$0.854914\pi$
$824$	1800.04	−	3117.77i	0.0761014	−	0.131811i
$825$	2010.10	−	3481.60i	0.0848276	−	0.146926i
$826$	−1032.65			−0.0434996
$827$	9417.92	+	16312.3i	0.396001	+	0.685895i	0.993228	−	0.116178i	$-0.0370642\pi$
$827$	9417.92	+	16312.3i	0.396001	+	0.685895i	−0.597227	+	0.802072i	$0.703731\pi$
$828$	3953.53			0.165936
$829$	−4099.81			−0.171764			−0.0858820	−	0.996305i	$-0.527371\pi$
$829$	−4099.81			−0.171764			−0.0858820	+	0.996305i	$0.527371\pi$
$830$	−15114.8	+	26179.5i	−0.632097	+	1.09482i
$831$	22477.1			0.938293
$832$	−5045.07	−	8738.31i	−0.210224	−	0.364118i
$833$	−13839.2	+	23970.3i	−0.575632	+	0.997023i
$834$	13937.8	+	24141.0i	0.578690	+	1.00232i
$835$	−3699.49	+	6407.70i	−0.153325	+	0.265566i
$836$	5024.17	−	8702.12i	0.207852	−	0.360011i
$837$	660.697	−	1144.36i	0.0272844	−	0.0472579i
$838$	26051.8	−	45123.1i	1.07392	−	1.86009i
$839$	14031.7	−	24303.5i	0.577386	−	1.00006i	−0.418392	−	0.908266i	$-0.637406\pi$
$839$	14031.7	−	24303.5i	0.577386	−	1.00006i	0.995778	−	0.0917949i	$-0.0292604\pi$
$840$	604.554	−	1047.12i	0.0248323	−	0.0430107i
$841$	−8047.03	−	13937.9i	−0.329945	−	0.571481i
$842$	−9381.04	+	16248.4i	−0.383957	+	0.665034i
$843$	6691.66	+	11590.3i	0.273396	+	0.473536i
$844$	5454.49			0.222454
$845$	−17110.1	+	29635.5i	−0.696574	+	1.20650i
$846$	−1914.34			−0.0777970
$847$	1218.15			0.0494168
$848$	21000.1	+	36373.2i	0.850409	+	1.47295i
$849$	−25111.4			−1.01510
$850$	6599.31	−	11430.3i	0.266299	−	0.461244i
$851$	6627.56	−	11479.3i	0.266968	−	0.462402i
$852$	−4253.07	−	7366.53i	−0.171018	−	0.296212i
$853$	11022.1	+	19090.8i	0.442426	+	0.766305i	0.997869	−	0.0652501i	$-0.0207845\pi$
$853$	11022.1	+	19090.8i	0.442426	+	0.766305i	−0.555443	+	0.831555i	$0.687451\pi$
$854$	4879.05	+	8450.76i	0.195501	+	0.338617i
$855$	3495.17	+	6053.81i	0.139804	+	0.242147i
$856$	9449.99			0.377330
$857$	−13015.2			−0.518774			−0.259387	−	0.965773i	$-0.583521\pi$
$857$	−13015.2			−0.518774			−0.259387	+	0.965773i	$0.583521\pi$
$858$	−11836.9	−	20502.1i	−0.470986	−	0.815771i
$859$	−1577.32	+	2731.99i	−0.0626512	+	0.108515i	−0.895650	−	0.444760i	$-0.853289\pi$
$859$	−1577.32	+	2731.99i	−0.0626512	+	0.108515i	0.832998	+	0.553275i	$0.186622\pi$
$860$	−1669.35	+	2891.40i	−0.0661912	+	0.114647i
$861$	243.940	+	422.516i	0.00965557	+	0.0167239i
$862$	−36381.4			−1.43754
$863$	−732.970			−0.0289115			−0.0144557	−	0.999896i	$-0.504602\pi$
$863$	−732.970			−0.0289115			−0.0144557	+	0.999896i	$0.504602\pi$
$864$	−2834.54	+	4909.56i	−0.111612	+	0.193318i
$865$	−807.207	−	1398.12i	−0.0317293	−	0.0549568i
$866$	−33160.6			−1.30120
$867$	3042.18	−	5269.21i	0.119167	−	0.206403i
$868$	−870.248			−0.0340301
$869$	−5828.67	−	10095.6i	−0.227531	−	0.394095i
$870$	28678.2			1.11756
$871$	−22422.1	+	30846.3i	−0.872265	+	1.19998i
$872$	14432.7			0.560495
$873$	3597.28	+	6230.66i	0.139461	+	0.241553i
$874$	−17788.6			−0.688454
$875$	−1740.66	+	3014.91i	−0.0672515	+	0.116483i
$876$	14456.7			0.557588
$877$	−2918.16	−	5054.41i	−0.112360	−	0.194612i	0.804362	−	0.594140i	$-0.202508\pi$
$877$	−2918.16	−	5054.41i	−0.112360	−	0.194612i	−0.916721	+	0.399528i	$0.869174\pi$
$878$	−31832.0	+	55134.7i	−1.22355	+	2.11926i
$879$	8683.37			0.333200
$880$	−31345.2			−1.20073
$881$	−8183.70	−	14174.6i	−0.312958	−	0.542059i	0.666043	−	0.745913i	$-0.267987\pi$
$881$	−8183.70	−	14174.6i	−0.312958	−	0.542059i	−0.979001	+	0.203854i	$0.934653\pi$
$882$	5475.88	−	9484.50i	0.209050	−	0.362086i
$883$	5380.55	−	9319.39i	0.205062	−	0.355178i	−0.745090	−	0.666964i	$-0.767594\pi$
$883$	5380.55	−	9319.39i	0.205062	−	0.355178i	0.950153	+	0.311785i	$0.100927\pi$
$884$	−15688.5	−	27173.3i	−0.596902	−	1.03387i
$885$	−3341.63			−0.126924
$886$	−49942.8			−1.89375
$887$	12482.4	+	21620.1i	0.472510	+	0.818411i	0.999505	−	0.0314570i	$-0.0100147\pi$
$887$	12482.4	+	21620.1i	0.472510	+	0.818411i	−0.526995	+	0.849868i	$0.676681\pi$
$888$	2320.08	+	4018.50i	0.0876767	+	0.151861i
$889$	−1312.92	−	2274.05i	−0.0495321	−	0.0857921i
$890$	20743.6	+	35929.0i	0.781268	+	1.35320i
$891$	−1254.82	+	2173.42i	−0.0471809	+	0.0817197i
$892$	−3538.51	+	6128.88i	−0.132823	+	0.230056i
$893$	3477.26			0.130305
$894$	13624.8	+	23598.8i	0.509710	+	0.882844i
$895$	44591.1			1.66538
$896$	−3769.73			−0.140556
$897$	−8459.59	+	14652.4i	−0.314891	+	0.545407i
$898$	−53610.3			−1.99221
$899$	4923.51	+	8527.77i	0.182657	+	0.316371i
$900$	−1054.15	+	1825.84i	−0.0390426	+	0.0676238i
$901$	22432.2	+	38853.7i	0.829440	+	1.43663i
$902$	2810.73	−	4868.32i	0.103755	−	0.179709i
$903$	−234.036	+	405.363i	−0.00862485	+	0.0149387i
$904$	5994.43	−	10382.6i	0.220544	−	0.381993i
$905$	28234.5	−	48903.5i	1.03707	−	1.79625i
$906$	−4540.22	+	7863.89i	−0.166489	+	0.288367i
$907$	9525.91	−	16499.4i	0.348735	−	0.604026i	−0.637290	−	0.770624i	$-0.719945\pi$
$907$	9525.91	−	16499.4i	0.348735	−	0.604026i	0.986025	+	0.166597i	$0.0532780\pi$
$908$	−601.035	−	1041.02i	−0.0219670	−	0.0380480i
$909$	−1053.51	+	1824.73i	−0.0384408	+	0.0665815i
$910$	−5423.17	−	9393.20i	−0.197556	−	0.342178i
$911$	182.869			0.00665061			0.00332530	−	0.999994i	$-0.498942\pi$
$911$	182.869			0.00665061			0.00332530	+	0.999994i	$0.498942\pi$
$912$	7005.38	−	12133.7i	0.254354	−	0.440555i
$913$	19713.6			0.714594
$914$	−68991.6			−2.49676
$915$	15788.4	+	27346.3i	0.570435	+	0.988022i
$916$	13134.4			0.473770
$917$	−1870.83	+	3240.38i	−0.0673723	+	0.116692i
$918$	−4119.67	+	7135.48i	−0.148115	+	0.256542i
$919$	1394.86	+	2415.96i	0.0500676	+	0.0867196i	0.889973	−	0.456013i	$-0.150723\pi$
$919$	1394.86	+	2415.96i	0.0500676	+	0.0867196i	−0.839905	+	0.542733i	$0.817390\pi$
$920$	4978.31	+	8622.69i	0.178402	+	0.309002i
$921$	5022.63	+	8699.44i	0.179697	+	0.311245i
$922$	17114.3	+	29642.9i	0.611312	+	1.05882i
$923$	36402.0			1.29815
$924$	1652.81			0.0588458
$925$	3534.28	+	6121.56i	0.125629	+	0.217595i
$926$	−25923.2	+	44900.2i	−0.919965	+	1.59343i
$927$	−1711.77	+	2964.87i	−0.0606493	+	0.105048i
$928$	−21123.0	−	36586.1i	−0.747194	−	1.29418i
$929$	−35427.4			−1.25117			−0.625584	−	0.780157i	$-0.715139\pi$
$929$	−35427.4			−1.25117			−0.625584	+	0.780157i	$0.715139\pi$
$930$	−6975.62			−0.245957
$931$	−9946.57	+	17228.0i	−0.350146	+	0.606470i
$932$	5272.96	+	9133.04i	0.185324	+	0.320990i
$933$	28640.7			1.00499
$934$	12867.8	−	22287.6i	0.450799	−	0.780807i
$935$	−33482.8			−1.17113
$936$	−2961.41	−	5129.32i	−0.103415	−	0.179121i
$937$	54461.5			1.89880			0.949402	−	0.314063i	$-0.101690\pi$
$937$	54461.5			1.89880			0.949402	+	0.314063i	$0.101690\pi$
$938$	−2681.00	−	6025.39i	−0.0933239	−	0.209740i
$939$	18793.1			0.653132
$940$	2039.87	+	3533.15i	0.0707799	+	0.122594i
$941$	−47512.1			−1.64596			−0.822982	−	0.568068i	$-0.807691\pi$
$941$	−47512.1			−1.64596			−0.822982	+	0.568068i	$0.807691\pi$
$942$	4965.84	−	8601.09i	0.171758	−	0.297493i
$943$	−4017.53			−0.138737
$944$	3348.82	+	5800.32i	0.115460	+	0.199983i
$945$	−574.906	+	995.767i	−0.0197902	+	0.0342776i
$946$	5393.24			0.185359
$947$	−20239.0			−0.694488			−0.347244	−	0.937775i	$-0.612882\pi$
$947$	−20239.0			−0.694488			−0.347244	+	0.937775i	$0.612882\pi$
$948$	3056.71	+	5294.38i	0.104723	+	0.181386i
$949$	−30933.8	+	53579.0i	−1.05812	+	1.83272i
$950$	4743.07	−	8215.24i	0.161985	−	0.280566i
$951$	−4592.79	−	7954.94i	−0.156605	−	0.271248i
$952$	−2588.69			−0.0881301
$953$	31965.6			1.08653			0.543267	−	0.839560i	$-0.317187\pi$
$953$	31965.6			1.08653			0.543267	+	0.839560i	$0.317187\pi$
$954$	−8875.93	−	15373.6i	−0.301225	−	0.521737i
$955$	−11607.0	−	20104.0i	−0.393293	−	0.681204i
$956$	−9683.63	−	16772.5i	−0.327606	−	0.567430i
$957$	−9350.94	−	16196.3i	−0.315855	−	0.547077i
$958$	−30412.8	+	52676.4i	−1.02567	+	1.77651i
$959$	3810.95	−	6600.77i	0.128323	−	0.222263i
$960$	5646.66			0.189839
$961$	13697.9	+	23725.5i	0.459800	+	0.796398i
$962$	41624.7			1.39505
$963$	−8986.56			−0.300714
$964$	−1523.65	+	2639.05i	−0.0509062	+	0.0881721i
$965$	46470.2			1.55018
$966$	−1462.99	−	2533.97i	−0.0487277	−	0.0843988i
$967$	−15813.3	+	27389.5i	−0.525876	+	0.910843i	0.473670	+	0.880702i	$0.342929\pi$
$967$	−15813.3	+	27389.5i	−0.525876	+	0.910843i	−0.999546	+	0.0301410i	$0.990404\pi$
$968$	−1755.77	−	3041.08i	−0.0582980	−	0.100975i
$969$	7483.11	−	12961.1i	0.248083	−	0.429692i
$970$	18990.0	−	32891.6i	0.628589	−	1.08875i
$971$	−20562.0	+	35614.5i	−0.679575	+	1.17706i	0.295534	+	0.955332i	$0.404502\pi$
$971$	−20562.0	+	35614.5i	−0.679575	+	1.17706i	−0.975109	+	0.221726i	$0.928831\pi$
$972$	658.063	−	1139.80i	0.0217154	−	0.0376122i
$973$	4164.32	−	7212.81i	0.137206	−	0.237649i
$974$	−8801.12	+	15244.0i	−0.289534	+	0.501488i
$975$	−4511.25	−	7813.71i	−0.148180	−	0.256655i
$976$	31644.7	−	54810.3i	1.03783	−	1.79758i
$977$	−24766.0	−	42896.0i	−0.810988	−	1.40467i	−0.912173	−	0.409805i	$-0.865597\pi$
$977$	−24766.0	−	42896.0i	−0.810988	−	1.40467i	0.101184	−	0.994868i	$-0.467737\pi$
$978$	−33504.9			−1.09547
$979$	13527.6	−	23430.4i	0.441616	−	0.764902i
$980$	−23339.8			−0.760779
$981$	−13724.9			−0.446688
$982$	−17012.5	−	29466.5i	−0.552842	−	0.957551i
$983$	49131.7			1.59416			0.797079	−	0.603875i	$-0.206377\pi$
$983$	49131.7			1.59416			0.797079	+	0.603875i	$0.206377\pi$
$984$	703.201	−	1217.98i	0.0227817	−	0.0394591i
$985$	−25062.8	+	43410.0i	−0.810727	+	1.40422i
$986$	−30699.8	−	53173.6i	−0.991562	−	1.71744i
$987$	285.981	+	495.333i	0.00922276	+	0.0159743i
$988$	−11275.7	−	19530.1i	−0.363084	−	0.628881i
$989$	−1927.21	−	3338.03i	−0.0619634	−	0.107324i
$990$	13248.4			0.425315
$991$	8806.31			0.282282			0.141141	−	0.989989i	$-0.454923\pi$
$991$	8806.31			0.282282			0.141141	+	0.989989i	$0.454923\pi$
$992$	5137.91	+	8899.13i	0.164444	+	0.284826i
$993$	−10570.8	+	18309.2i	−0.337820	+	0.585121i
$994$	−3147.66	+	5451.91i	−0.100440	+	0.173968i
$995$	−23493.6	−	40692.2i	−0.748541	−	1.29651i
$996$	−10338.3			−0.328898
$997$	−27249.1			−0.865584			−0.432792	−	0.901494i	$-0.642472\pi$
$997$	−27249.1			−0.865584			−0.432792	+	0.901494i	$0.642472\pi$
$998$	−26899.0	+	46590.5i	−0.853180	+	1.47775i
$999$	−2206.30	−	3821.43i	−0.0698743	−	0.121026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.b.37.4	✓	36
67.29	even	3	inner	201.4.e.b.163.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.b.37.4	✓	36	1.1	even	1	trivial
201.4.e.b.163.4	yes	36	67.29	even	3	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83140 - 3.17208i) q^{2} -3.00000 q^{3} +(-2.70808 + 4.69053i) q^{4} +12.9712 q^{5} +(5.49421 + 9.51625i) q^{6} +(1.64155 - 2.84325i) q^{7} -9.46413 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-1.83140 - 3.17208i) q^{2} -3.00000 q^{3} +(-2.70808 + 4.69053i) q^{4} +12.9712 q^{5} +(5.49421 + 9.51625i) q^{6} +(1.64155 - 2.84325i) q^{7} -9.46413 q^{8} +9.00000 q^{9} +(-23.7555 - 41.1456i) q^{10} +(-15.4916 + 26.8323i) q^{11} +(8.12423 - 14.0716i) q^{12} +(34.7677 + 60.2194i) q^{13} -12.0254 q^{14} -38.9135 q^{15} +(38.9973 + 67.5452i) q^{16} +(41.6567 + 72.1515i) q^{17} +(-16.4826 - 28.5488i) q^{18} +(29.9396 + 51.8569i) q^{19} +(-35.1269 + 60.8416i) q^{20} +(-4.92465 + 8.52974i) q^{21} +113.486 q^{22} +(-40.5529 - 70.2397i) q^{23} +28.3924 q^{24} +43.2513 q^{25} +(127.347 - 220.572i) q^{26} -27.0000 q^{27} +(8.89088 + 15.3995i) q^{28} +(100.602 - 174.248i) q^{29} +(71.2664 + 123.437i) q^{30} +(-24.4702 + 42.3837i) q^{31} +(104.983 - 181.836i) q^{32} +(46.4749 - 80.4969i) q^{33} +(152.580 - 264.277i) q^{34} +(21.2928 - 36.8802i) q^{35} +(-24.3727 + 42.2147i) q^{36} +(81.7150 + 141.535i) q^{37} +(109.663 - 189.942i) q^{38} +(-104.303 - 180.658i) q^{39} -122.761 q^{40} +(24.7672 - 42.8981i) q^{41} +36.0761 q^{42} +47.5235 q^{43} +(-83.9051 - 145.328i) q^{44} +116.741 q^{45} +(-148.537 + 257.274i) q^{46} +(29.0357 - 50.2912i) q^{47} +(-116.992 - 202.636i) q^{48} +(166.111 + 287.712i) q^{49} +(-79.2107 - 137.197i) q^{50} +(-124.970 - 216.455i) q^{51} -376.614 q^{52} +538.502 q^{53} +(49.4479 + 85.6463i) q^{54} +(-200.945 + 348.047i) q^{55} +(-15.5358 + 26.9089i) q^{56} +(-89.8188 - 155.571i) q^{57} -736.971 q^{58} +85.8731 q^{59} +(105.381 - 182.525i) q^{60} +(-405.730 - 702.745i) q^{61} +179.260 q^{62} +(14.7739 - 25.5892i) q^{63} -145.108 q^{64} +(450.978 + 781.116i) q^{65} -340.457 q^{66} +(222.946 + 501.057i) q^{67} -451.238 q^{68} +(121.659 + 210.719i) q^{69} -155.983 q^{70} +(261.752 - 453.368i) q^{71} -85.1772 q^{72} +(444.865 + 770.528i) q^{73} +(299.306 - 518.414i) q^{74} -129.754 q^{75} -324.315 q^{76} +(50.8606 + 88.0931i) q^{77} +(-382.042 + 661.716i) q^{78} +(-188.123 + 325.839i) q^{79} +(505.840 + 876.141i) q^{80} +81.0000 q^{81} -181.435 q^{82} +(-318.132 - 551.021i) q^{83} +(-26.6726 - 46.1984i) q^{84} +(540.336 + 935.890i) q^{85} +(-87.0346 - 150.748i) q^{86} +(-301.806 + 522.743i) q^{87} +(146.615 - 253.945i) q^{88} -873.216 q^{89} +(-213.799 - 370.311i) q^{90} +228.292 q^{91} +439.282 q^{92} +(73.4107 - 127.151i) q^{93} -212.704 q^{94} +(388.352 + 672.645i) q^{95} +(-314.949 + 545.507i) q^{96} +(399.697 + 692.296i) q^{97} +(608.431 - 1053.83i) q^{98} +(-139.425 + 241.491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

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