LMFDB - Embedded newform 201.4.e.a.37.2

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	201.37
Dual form			201.4.e.a.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32403 - 4.02534i) q^{2} +3.00000 q^{3} +(-6.80224 + 11.7818i) q^{4} +1.94047 q^{5} +(-6.97209 - 12.0760i) q^{6} +(-1.41925 + 2.45821i) q^{7} +26.0500 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-2.32403 - 4.02534i) q^{2} +3.00000 q^{3} +(-6.80224 + 11.7818i) q^{4} +1.94047 q^{5} +(-6.97209 - 12.0760i) q^{6} +(-1.41925 + 2.45821i) q^{7} +26.0500 q^{8} +9.00000 q^{9} +(-4.50971 - 7.81105i) q^{10} +(-29.5066 + 51.1068i) q^{11} +(-20.4067 + 35.3455i) q^{12} +(-26.7945 - 46.4094i) q^{13} +13.1935 q^{14} +5.82141 q^{15} +(-6.12299 - 10.6053i) q^{16} +(48.4352 + 83.8923i) q^{17} +(-20.9163 - 36.2281i) q^{18} +(27.3401 + 47.3544i) q^{19} +(-13.1995 + 22.8623i) q^{20} +(-4.25774 + 7.37462i) q^{21} +274.297 q^{22} +(87.8240 + 152.116i) q^{23} +78.1499 q^{24} -121.235 q^{25} +(-124.542 + 215.714i) q^{26} +27.0000 q^{27} +(-19.3081 - 33.4426i) q^{28} +(-77.2126 + 133.736i) q^{29} +(-13.5291 - 23.4331i) q^{30} +(96.1571 - 166.549i) q^{31} +(75.7398 - 131.185i) q^{32} +(-88.5197 + 153.321i) q^{33} +(225.130 - 389.937i) q^{34} +(-2.75400 + 4.77007i) q^{35} +(-61.2201 + 106.036i) q^{36} +(47.4515 + 82.1884i) q^{37} +(127.078 - 220.106i) q^{38} +(-80.3834 - 139.228i) q^{39} +50.5491 q^{40} +(-47.3075 + 81.9391i) q^{41} +39.5805 q^{42} +29.3926 q^{43} +(-401.421 - 695.282i) q^{44} +17.4642 q^{45} +(408.212 - 707.043i) q^{46} +(255.507 - 442.551i) q^{47} +(-18.3690 - 31.8160i) q^{48} +(167.471 + 290.069i) q^{49} +(281.753 + 488.010i) q^{50} +(145.306 + 251.677i) q^{51} +729.049 q^{52} -271.052 q^{53} +(-62.7488 - 108.684i) q^{54} +(-57.2566 + 99.1713i) q^{55} +(-36.9713 + 64.0362i) q^{56} +(82.0202 + 142.063i) q^{57} +717.778 q^{58} +115.227 q^{59} +(-39.5986 + 68.5868i) q^{60} +(-136.607 - 236.611i) q^{61} -893.888 q^{62} +(-12.7732 + 22.1239i) q^{63} -802.054 q^{64} +(-51.9938 - 90.0560i) q^{65} +822.890 q^{66} +(-471.583 - 279.951i) q^{67} -1317.87 q^{68} +(263.472 + 456.347i) q^{69} +25.6016 q^{70} +(-370.299 + 641.377i) q^{71} +234.450 q^{72} +(503.537 + 872.152i) q^{73} +(220.557 - 382.017i) q^{74} -363.704 q^{75} -743.895 q^{76} +(-83.7541 - 145.066i) q^{77} +(-373.627 + 647.141i) q^{78} +(55.8368 - 96.7122i) q^{79} +(-11.8815 - 20.5793i) q^{80} +81.0000 q^{81} +439.777 q^{82} +(697.074 + 1207.37i) q^{83} +(-57.9243 - 100.328i) q^{84} +(93.9871 + 162.790i) q^{85} +(-68.3093 - 118.315i) q^{86} +(-231.638 + 401.208i) q^{87} +(-768.644 + 1331.33i) q^{88} -537.282 q^{89} +(-40.5874 - 70.2994i) q^{90} +152.112 q^{91} -2389.60 q^{92} +(288.471 - 499.647i) q^{93} -2375.22 q^{94} +(53.0526 + 91.8898i) q^{95} +(227.219 - 393.555i) q^{96} +(376.970 + 652.931i) q^{97} +(778.418 - 1348.26i) q^{98} +(-265.559 + 459.962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * 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 $

$2$	−2.32403	−	4.02534i	−0.821669	−	1.42317i	−0.904439	−	0.426604i	$-0.859710\pi$
$2$	−2.32403	−	4.02534i	−0.821669	−	1.42317i	0.0827697	−	0.996569i	$-0.473623\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	−6.80224	+	11.7818i	−0.850280	+	1.47273i
$5$	1.94047			0.173561			0.0867804	−	0.996227i	$-0.472342\pi$
$5$	1.94047			0.173561			0.0867804	+	0.996227i	$0.472342\pi$
$6$	−6.97209	−	12.0760i	−0.474391	−	0.821669i
$7$	−1.41925	+	2.45821i	−0.0766321	+	0.132731i	−0.901795	−	0.432164i	$-0.857750\pi$
$7$	−1.41925	+	2.45821i	−0.0766321	+	0.132731i	0.825163	+	0.564895i	$0.191083\pi$
$8$	26.0500			1.15126
$9$	9.00000			0.333333
$10$	−4.50971	−	7.81105i	−0.142610	−	0.247007i
$11$	−29.5066	+	51.1068i	−0.808778	+	1.40084i	0.104932	+	0.994479i	$0.466537\pi$
$11$	−29.5066	+	51.1068i	−0.808778	+	1.40084i	−0.913711	+	0.406366i	$0.866796\pi$
$12$	−20.4067	+	35.3455i	−0.490909	+	0.850280i
$13$	−26.7945	−	46.4094i	−0.571650	−	0.990126i	−0.996397	−	0.0848144i	$-0.972970\pi$
$13$	−26.7945	−	46.4094i	−0.571650	−	0.990126i	0.424747	−	0.905312i	$-0.360363\pi$
$14$	13.1935			0.251865
$15$	5.82141			0.100205
$16$	−6.12299	−	10.6053i	−0.0956718	−	0.165708i
$17$	48.4352	+	83.8923i	0.691016	+	1.19687i	0.971505	+	0.237018i	$0.0761699\pi$
$17$	48.4352	+	83.8923i	0.691016	+	1.19687i	−0.280489	+	0.959857i	$0.590497\pi$
$18$	−20.9163	−	36.2281i	−0.273890	−	0.474391i
$19$	27.3401	+	47.3544i	0.330118	+	0.571781i	0.982535	−	0.186079i	$-0.0595781\pi$
$19$	27.3401	+	47.3544i	0.330118	+	0.571781i	−0.652417	+	0.757861i	$0.726245\pi$
$20$	−13.1995	+	22.8623i	−0.147575	+	0.255608i
$21$	−4.25774	+	7.37462i	−0.0442436	+	0.0766321i
$22$	274.297			2.65819
$23$	87.8240	+	152.116i	0.796199	+	1.37906i	0.922075	+	0.387011i	$0.126493\pi$
$23$	87.8240	+	152.116i	0.796199	+	1.37906i	−0.125876	+	0.992046i	$0.540174\pi$
$24$	78.1499			0.664678
$25$	−121.235			−0.969877
$26$	−124.542	+	215.714i	−0.939414	+	1.62711i
$27$	27.0000			0.192450
$28$	−19.3081	−	33.4426i	−0.130317	−	0.225716i
$29$	−77.2126	+	133.736i	−0.494414	+	0.856351i	−0.999979	−	0.00643772i	$-0.997951\pi$
$29$	−77.2126	+	133.736i	−0.494414	+	0.856351i	0.505565	+	0.862789i	$0.331284\pi$
$30$	−13.5291	−	23.4331i	−0.0823357	−	0.142610i
$31$	96.1571	−	166.549i	0.557107	−	0.964938i	−0.440629	−	0.897689i	$-0.645245\pi$
$31$	96.1571	−	166.549i	0.557107	−	0.964938i	0.997736	−	0.0672485i	$-0.0214220\pi$
$32$	75.7398	−	131.185i	0.418407	−	0.724702i
$33$	−88.5197	+	153.321i	−0.466948	+	0.808778i
$34$	225.130	−	389.937i	1.13557	−	1.96687i
$35$	−2.75400	+	4.77007i	−0.0133003	+	0.0230368i
$36$	−61.2201	+	106.036i	−0.283427	+	0.490909i
$37$	47.4515	+	82.1884i	0.210837	+	0.365181i	0.951977	−	0.306170i	$-0.0990477\pi$
$37$	47.4515	+	82.1884i	0.210837	+	0.365181i	−0.741140	+	0.671351i	$0.765714\pi$
$38$	127.078	−	220.106i	0.542496	−	0.939630i
$39$	−80.3834	−	139.228i	−0.330042	−	0.571650i
$40$	50.5491			0.199813
$41$	−47.3075	+	81.9391i	−0.180200	+	0.312115i	−0.941949	−	0.335757i	$-0.891008\pi$
$41$	−47.3075	+	81.9391i	−0.180200	+	0.312115i	0.761749	+	0.647873i	$0.224341\pi$
$42$	39.5805			0.145414
$43$	29.3926			0.104240			0.0521201	−	0.998641i	$-0.483402\pi$
$43$	29.3926			0.104240			0.0521201	+	0.998641i	$0.483402\pi$
$44$	−401.421	−	695.282i	−1.37538	−	2.38222i
$45$	17.4642			0.0578536
$46$	408.212	−	707.043i	1.30842	−	2.26626i
$47$	255.507	−	442.551i	0.792968	−	1.37346i	−0.131153	−	0.991362i	$-0.541868\pi$
$47$	255.507	−	442.551i	0.792968	−	1.37346i	0.924121	−	0.382099i	$-0.124799\pi$
$48$	−18.3690	−	31.8160i	−0.0552361	−	0.0956718i
$49$	167.471	+	290.069i	0.488255	+	0.845683i
$50$	281.753	+	488.010i	0.796918	+	1.38030i
$51$	145.306	+	251.677i	0.398958	+	0.691016i
$52$	729.049			1.94425
$53$	−271.052			−0.702487			−0.351243	−	0.936284i	$-0.614241\pi$
$53$	−271.052			−0.702487			−0.351243	+	0.936284i	$0.614241\pi$
$54$	−62.7488	−	108.684i	−0.158130	−	0.273890i
$55$	−57.2566	+	99.1713i	−0.140372	+	0.243132i
$56$	−36.9713	+	64.0362i	−0.0882232	+	0.152807i
$57$	82.0202	+	142.063i	0.190594	+	0.330118i
$58$	717.778			1.62498
$59$	115.227			0.254260			0.127130	−	0.991886i	$-0.459423\pi$
$59$	115.227			0.254260			0.127130	+	0.991886i	$0.459423\pi$
$60$	−39.5986	+	68.5868i	−0.0852026	+	0.147575i
$61$	−136.607	−	236.611i	−0.286734	−	0.496638i	0.686294	−	0.727324i	$-0.259236\pi$
$61$	−136.607	−	236.611i	−0.286734	−	0.496638i	−0.973028	+	0.230686i	$0.925903\pi$
$62$	−893.888			−1.83103
$63$	−12.7732	+	22.1239i	−0.0255440	+	0.0442436i
$64$	−802.054			−1.56651
$65$	−51.9938	−	90.0560i	−0.0992160	−	0.171847i
$66$	822.890			1.53471
$67$	−471.583	−	279.951i	−0.859896	−	0.510469i
$67$	−471.583	−	279.951i	−0.859896	−	0.510469i
$68$	−1317.87			−2.35023
$69$	263.472	+	456.347i	0.459686	+	0.796199i
$70$	25.6016			0.0437139
$71$	−370.299	+	641.377i	−0.618964	+	1.07208i	0.370711	+	0.928748i	$0.379114\pi$
$71$	−370.299	+	641.377i	−0.618964	+	1.07208i	−0.989675	+	0.143329i	$0.954219\pi$
$72$	234.450			0.383752
$73$	503.537	+	872.152i	0.807323	+	1.39832i	0.914712	+	0.404107i	$0.132418\pi$
$73$	503.537	+	872.152i	0.807323	+	1.39832i	−0.107389	+	0.994217i	$0.534249\pi$
$74$	220.557	−	382.017i	0.346477	−	0.600116i
$75$	−363.704			−0.559959
$76$	−743.895			−1.12277
$77$	−83.7541	−	145.066i	−0.123957	−	0.214699i
$78$	−373.627	+	647.141i	−0.542371	+	0.939414i
$79$	55.8368	−	96.7122i	0.0795207	−	0.137734i	−0.823523	−	0.567284i	$-0.807994\pi$
$79$	55.8368	−	96.7122i	0.0795207	−	0.137734i	0.903043	+	0.429550i	$0.141328\pi$
$80$	−11.8815	−	20.5793i	−0.0166049	−	0.0287605i
$81$	81.0000			0.111111
$82$	439.777			0.592259
$83$	697.074	+	1207.37i	0.921853	+	1.59670i	0.796545	+	0.604579i	$0.206659\pi$
$83$	697.074	+	1207.37i	0.921853	+	1.59670i	0.125308	+	0.992118i	$0.460008\pi$
$84$	−57.9243	−	100.328i	−0.0752388	−	0.130317i
$85$	93.9871	+	162.790i	0.119933	+	0.207731i
$86$	−68.3093	−	118.315i	−0.0856509	−	0.148352i
$87$	−231.638	+	401.208i	−0.285450	+	0.494414i
$88$	−768.644	+	1331.33i	−0.931111	+	1.61273i
$89$	−537.282			−0.639908			−0.319954	−	0.947433i	$-0.603667\pi$
$89$	−537.282			−0.639908			−0.319954	+	0.947433i	$0.603667\pi$
$90$	−40.5874	−	70.2994i	−0.0475365	−	0.0823357i
$91$	152.112			0.175227
$92$	−2389.60			−2.70797
$93$	288.471	−	499.647i	0.321646	−	0.557107i
$94$	−2375.22			−2.60623
$95$	53.0526	+	91.8898i	0.0572956	+	0.0992389i
$96$	227.219	−	393.555i	0.241567	−	0.418407i
$97$	376.970	+	652.931i	0.394592	+	0.683454i	0.993049	−	0.117701i	$-0.0375524\pi$
$97$	376.970	+	652.931i	0.394592	+	0.683454i	−0.598457	+	0.801155i	$0.704219\pi$
$98$	778.418	−	1348.26i	0.802368	−	1.38974i
$99$	−265.559	+	459.962i	−0.269593	+	0.466948i
$100$	824.667	−	1428.36i	0.824667	−	1.42836i
$101$	−302.586	+	524.095i	−0.298104	+	0.516330i	−0.975702	−	0.219102i	$-0.929687\pi$
$101$	−302.586	+	524.095i	−0.298104	+	0.516330i	0.677599	+	0.735432i	$0.263021\pi$
$102$	675.390	−	1169.81i	0.655623	−	1.13557i
$103$	373.147	−	646.309i	0.356964	−	0.618279i	−0.630488	−	0.776199i	$-0.717145\pi$
$103$	373.147	−	646.309i	0.356964	−	0.618279i	0.987452	+	0.157920i	$0.0504787\pi$
$104$	−697.995	−	1208.96i	−0.658115	−	1.13989i
$105$	−8.26201	+	14.3102i	−0.00767895	+	0.0133003i
$106$	629.932	+	1091.07i	0.577212	+	0.999760i
$107$	−2166.93			−1.95781			−0.978903	−	0.204324i	$-0.934500\pi$
$107$	−2166.93			−1.95781			−0.978903	+	0.204324i	$0.934500\pi$
$108$	−183.660	+	318.109i	−0.163636	+	0.283427i
$109$	−1129.81			−0.992811			−0.496405	−	0.868091i	$-0.665347\pi$
$109$	−1129.81			−0.992811			−0.496405	+	0.868091i	$0.665347\pi$
$110$	532.264			0.461358
$111$	142.354	+	246.565i	0.121727	+	0.210837i
$112$	34.7601			0.0293261
$113$	302.928	−	524.687i	0.252187	−	0.436800i	−0.711941	−	0.702239i	$-0.752184\pi$
$113$	302.928	−	524.687i	0.252187	−	0.436800i	0.964128	+	0.265439i	$0.0855170\pi$
$114$	381.235	−	660.319i	0.313210	−	0.542496i
$115$	170.420	+	295.176i	0.138189	+	0.239350i
$116$	−1050.44	−	1819.41i	−0.840781	−	1.45628i
$117$	−241.150	−	417.684i	−0.190550	−	0.330042i
$118$	−267.792	−	463.829i	−0.208917	−	0.361856i
$119$	−274.966			−0.211816
$120$	151.647			0.115362
$121$	−1075.77	−	1863.29i	−0.808244	−	1.39992i
$122$	−634.959	+	1099.78i	−0.471201	+	0.816144i
$123$	−141.923	+	245.817i	−0.104038	+	0.180200i
$124$	1308.17	+	2265.81i	0.947394	+	1.64093i
$125$	−477.811			−0.341893
$126$	118.741			0.0839549
$127$	−297.202	+	514.768i	−0.207657	+	0.359672i	−0.950976	−	0.309265i	$-0.899917\pi$
$127$	−297.202	+	514.768i	−0.207657	+	0.359672i	0.743319	+	0.668937i	$0.233250\pi$
$128$	1258.08	+	2179.06i	0.868747	+	1.50471i
$129$	88.1778			0.0601831
$130$	−241.671	+	418.586i	−0.163045	+	0.282403i
$131$	2058.37			1.37283			0.686416	−	0.727210i	$-0.259183\pi$
$131$	2058.37			1.37283			0.686416	+	0.727210i	$0.259183\pi$
$132$	−1204.26	−	2085.85i	−0.794073	−	1.37538i
$133$	−155.209			−0.101191
$134$	−30.9241	+	2548.90i	−0.0199361	+	1.64322i
$135$	52.3927			0.0334018
$136$	1261.74	+	2185.39i	0.795537	+	1.37791i
$137$	1512.51			0.943228			0.471614	−	0.881805i	$-0.343672\pi$
$137$	1512.51			0.943228			0.471614	+	0.881805i	$0.343672\pi$
$138$	1224.63	−	2121.13i	0.755419	−	1.30842i
$139$	−1418.13			−0.865353			−0.432676	−	0.901549i	$-0.642431\pi$
$139$	−1418.13			−0.865353			−0.432676	+	0.901549i	$0.642431\pi$
$140$	−37.4668	−	64.8944i	−0.0226180	−	0.0391755i
$141$	766.521	−	1327.65i	0.457820	−	0.792968i
$142$	3442.35			2.03433
$143$	3162.45			1.84935
$144$	−55.1069	−	95.4480i	−0.0318906	−	0.0552361i
$145$	−149.829	+	259.511i	−0.0858110	+	0.148629i
$146$	2340.47	−	4053.82i	1.32670	−	2.29792i
$147$	502.414	+	870.207i	0.281894	+	0.488255i
$148$	−1291.11			−0.717083
$149$	1131.96			0.622375			0.311187	−	0.950349i	$-0.399273\pi$
$149$	1131.96			0.622375			0.311187	+	0.950349i	$0.399273\pi$
$150$	845.259	+	1464.03i	0.460101	+	0.796918i
$151$	−1354.02	−	2345.23i	−0.729726	−	1.26392i	−0.956999	−	0.290091i	$-0.906314\pi$
$151$	−1354.02	−	2345.23i	−0.729726	−	1.26392i	0.227273	−	0.973831i	$-0.427019\pi$
$152$	712.208	+	1233.58i	0.380051	+	0.658267i
$153$	435.917	+	755.031i	0.230339	+	0.398958i
$154$	−389.294	+	674.277i	−0.203703	+	0.352824i
$155$	186.590	−	323.183i	0.0966920	−	0.167475i
$156$	2187.15			1.12251
$157$	−93.8976	−	162.635i	−0.0477315	−	0.0826733i	0.841173	−	0.540767i	$-0.181866\pi$
$157$	−93.8976	−	162.635i	−0.0477315	−	0.0826733i	−0.888904	+	0.458093i	$0.848533\pi$
$158$	−519.066			−0.261359
$159$	−813.155			−0.405581
$160$	146.971	−	254.561i	0.0726191	−	0.125780i
$161$	−498.576			−0.244058
$162$	−188.246	−	326.052i	−0.0912966	−	0.158130i
$163$	−568.633	+	984.901i	−0.273244	+	0.473272i	−0.969691	−	0.244336i	$-0.921430\pi$
$163$	−568.633	+	984.901i	−0.273244	+	0.473272i	0.696447	+	0.717609i	$0.254763\pi$
$164$	−643.594	−	1114.74i	−0.306441	−	0.530771i
$165$	−171.770	+	297.514i	−0.0810440	+	0.140372i
$166$	3240.04	−	5611.92i	1.51492	−	2.62391i
$167$	323.621	−	560.528i	0.149955	−	0.259730i	−0.781255	−	0.624212i	$-0.785420\pi$
$167$	323.621	−	560.528i	0.149955	−	0.259730i	0.931211	+	0.364481i	$0.118754\pi$
$168$	−110.914	+	192.108i	−0.0509357	+	0.0882232i
$169$	−337.387	+	584.371i	−0.153567	+	0.265986i
$170$	436.858	−	756.660i	0.197091	−	0.341372i
$171$	246.061	+	426.190i	0.110039	+	0.190594i
$172$	−199.935	+	346.298i	−0.0886333	+	0.153517i
$173$	356.116	+	616.811i	0.156503	+	0.271071i	0.933605	−	0.358303i	$-0.116645\pi$
$173$	356.116	+	616.811i	0.156503	+	0.271071i	−0.777102	+	0.629374i	$0.783311\pi$
$174$	2153.33			0.938183
$175$	172.062	−	298.020i	0.0743237	−	0.128732i
$176$	722.674			0.309509
$177$	345.682			0.146797
$178$	1248.66	+	2162.74i	0.525793	+	0.910699i
$179$	−2908.11			−1.21432			−0.607158	−	0.794581i	$-0.707690\pi$
$179$	−2908.11			−1.21432			−0.607158	+	0.794581i	$0.707690\pi$
$180$	−118.796	+	205.760i	−0.0491918	+	0.0852026i
$181$	121.623	−	210.657i	0.0499456	−	0.0865083i	−0.839972	−	0.542630i	$-0.817429\pi$
$181$	121.623	−	210.657i	0.0499456	−	0.0865083i	0.889917	+	0.456122i	$0.150762\pi$
$182$	−353.512	−	612.301i	−0.143978	−	0.249378i
$183$	−409.822	−	709.832i	−0.165546	−	0.286734i
$184$	2287.81	+	3962.61i	0.916629	+	1.58765i
$185$	92.0782	+	159.484i	0.0365931	+	0.0633811i
$186$	−2681.66			−1.05715
$187$	−5716.63			−2.23551
$188$	3476.04	+	6020.67i	1.34849	+	2.33565i
$189$	−38.3196	+	66.3716i	−0.0147479	+	0.0255440i
$190$	246.592	−	427.109i	0.0941560	−	0.163083i
$191$	−1275.70	−	2209.57i	−0.483278	−	0.837062i	0.516537	−	0.856265i	$-0.327221\pi$
$191$	−1275.70	−	2209.57i	−0.483278	−	0.837062i	−0.999816	+	0.0192022i	$0.993887\pi$
$192$	−2406.16			−0.904426
$193$	872.038			0.325237			0.162618	−	0.986689i	$-0.448006\pi$
$193$	872.038			0.325237			0.162618	+	0.986689i	$0.448006\pi$
$194$	1752.18	−	3034.86i	0.648449	−	1.12315i
$195$	−155.982	−	270.168i	−0.0572824	−	0.0992160i
$196$	−4556.72			−1.66061
$197$	21.4914	−	37.2243i	0.00777260	−	0.0134625i	−0.862113	−	0.506716i	$-0.830859\pi$
$197$	21.4914	−	37.2243i	0.00777260	−	0.0134625i	0.869886	+	0.493254i	$0.164193\pi$
$198$	2468.67			0.886064
$199$	−312.668	−	541.557i	−0.111379	−	0.192915i	0.804947	−	0.593346i	$-0.202193\pi$
$199$	−312.668	−	541.557i	−0.111379	−	0.192915i	−0.916327	+	0.400432i	$0.868860\pi$
$200$	−3158.16			−1.11658
$201$	−1414.75	−	839.853i	−0.496461	−	0.294720i
$202$	2812.88			0.979770
$203$	−219.167	−	379.609i	−0.0757760	−	0.131248i
$204$	−3953.62			−1.35690
$205$	−91.7988	+	159.000i	−0.0312756	+	0.0541710i
$206$	−3468.82			−1.17322
$207$	790.416	+	1369.04i	0.265400	+	0.459686i
$208$	−328.125	+	568.329i	−0.109381	+	0.189454i
$209$	−3226.85			−1.06797
$210$	76.8047			0.0252382
$211$	−798.005	−	1382.18i	−0.260364	−	0.450964i	0.705974	−	0.708237i	$-0.250509\pi$
$211$	−798.005	−	1382.18i	−0.260364	−	0.450964i	−0.966339	+	0.257273i	$0.917176\pi$
$212$	1843.76	−	3193.48i	0.597310	−	1.03457i
$213$	−1110.90	+	1924.13i	−0.357359	+	0.618964i
$214$	5036.02	+	8722.64i	1.60867	+	2.78630i
$215$	57.0354			0.0180920
$216$	703.349			0.221559
$217$	272.941	+	472.748i	0.0853845	+	0.147890i
$218$	2625.72	+	4547.88i	0.815762	+	1.41294i
$219$	1510.61	+	2616.46i	0.466108	+	0.807323i
$220$	−778.946	−	1349.17i	−0.238711	−	0.413460i
$221$	2595.59	−	4495.70i	0.790038	−	1.36839i
$222$	661.672	−	1146.05i	0.200039	−	0.346477i
$223$	6253.49			1.87787			0.938934	−	0.344098i	$-0.111815\pi$
$223$	6253.49			1.87787			0.938934	+	0.344098i	$0.111815\pi$
$224$	214.987	+	372.368i	0.0641268	+	0.111071i
$225$	−1091.11			−0.323292
$226$	−2816.06			−0.828856
$227$	911.450	−	1578.68i	0.266498	−	0.461588i	−0.701457	−	0.712712i	$-0.747467\pi$
$227$	911.450	−	1578.68i	0.266498	−	0.461588i	0.967955	+	0.251124i	$0.0808001\pi$
$228$	−2231.69			−0.648232
$229$	−2116.81	−	3666.42i	−0.610842	−	1.05801i	−0.991099	−	0.133128i	$-0.957498\pi$
$229$	−2116.81	−	3666.42i	−0.610842	−	1.05801i	0.380257	−	0.924881i	$-0.375836\pi$
$230$	792.122	−	1372.00i	0.227091	−	0.393334i
$231$	−251.262	−	435.199i	−0.0715664	−	0.123957i
$232$	−2011.38	+	3483.82i	−0.569198	+	0.985879i
$233$	−1388.15	+	2404.35i	−0.390305	+	0.676028i	−0.992490	−	0.122329i	$-0.960964\pi$
$233$	−1388.15	+	2404.35i	−0.390305	+	0.676028i	0.602185	+	0.798357i	$0.294297\pi$
$234$	−1120.88	+	1941.42i	−0.313138	+	0.542371i
$235$	495.803	−	858.756i	0.137628	−	0.238379i
$236$	−783.804	+	1357.59i	−0.216192	+	0.374456i
$237$	167.511	−	290.137i	0.0459113	−	0.0795207i
$238$	639.030	+	1106.83i	0.174043	+	0.301451i
$239$	−1588.59	+	2751.52i	−0.429948	+	0.744691i	−0.996868	−	0.0790813i	$-0.974801\pi$
$239$	−1588.59	+	2751.52i	−0.429948	+	0.744691i	0.566921	+	0.823772i	$0.308135\pi$
$240$	−35.6444	−	61.7380i	−0.00958683	−	0.0166049i
$241$	1142.58			0.305396			0.152698	−	0.988273i	$-0.451204\pi$
$241$	1142.58			0.305396			0.152698	+	0.988273i	$0.451204\pi$
$242$	−5000.26	+	8660.71i	−1.32822	+	2.30054i
$243$	243.000			0.0641500
$244$	3716.94			0.975216
$245$	324.973	+	562.870i	0.0847420	+	0.146777i
$246$	1319.33			0.341941
$247$	1465.13	−	2537.67i	0.377424	−	0.653717i
$248$	2504.89	−	4338.59i	0.641373	−	1.11089i
$249$	2091.22	+	3622.10i	0.532232	+	0.921853i
$250$	1110.45	+	1923.35i	0.280923	+	0.486573i
$251$	695.131	+	1204.00i	0.174806	+	0.302773i	0.940094	−	0.340915i	$-0.110737\pi$
$251$	695.131	+	1204.00i	0.174806	+	0.302773i	−0.765288	+	0.643688i	$0.777404\pi$
$252$	−173.773	−	300.983i	−0.0434391	−	0.0752388i
$253$	−10365.5			−2.57579
$254$	2762.82			0.682500
$255$	281.961	+	488.371i	0.0692435	+	0.119933i
$256$	2639.42	−	4571.61i	0.644389	−	1.11612i
$257$	−5.89186	+	10.2050i	−0.00143005	+	0.00247693i	−0.866740	−	0.498761i	$-0.833789\pi$
$257$	−5.89186	+	10.2050i	−0.00143005	+	0.00247693i	0.865309	+	0.501238i	$0.167122\pi$
$258$	−204.928	−	354.946i	−0.0494506	−	0.0856509i
$259$	−269.381			−0.0646276
$260$	1414.70			0.337446
$261$	−694.913	+	1203.63i	−0.164805	+	0.285450i
$262$	−4783.72	−	8285.65i	−1.12801	−	1.95378i
$263$	−7050.04			−1.65294			−0.826471	−	0.562979i	$-0.809655\pi$
$263$	−7050.04			−1.65294			−0.826471	+	0.562979i	$0.809655\pi$
$264$	−2305.93	+	3993.99i	−0.537577	+	0.931111i
$265$	−525.967			−0.121924
$266$	360.711	+	624.770i	0.0831451	+	0.144012i
$267$	−1611.85			−0.369451
$268$	6506.15	−	3651.81i	1.48293	−	0.832351i
$269$	8113.11			1.83890			0.919452	−	0.393203i	$-0.128633\pi$
$269$	8113.11			1.83890			0.919452	+	0.393203i	$0.128633\pi$
$270$	−121.762	−	210.898i	−0.0274452	−	0.0475365i
$271$	6146.89			1.37785			0.688924	−	0.724833i	$-0.258083\pi$
$271$	6146.89			1.37785			0.688924	+	0.724833i	$0.258083\pi$
$272$	593.137	−	1027.34i	0.132221	−	0.229014i
$273$	456.335			0.101167
$274$	−3515.11	−	6088.35i	−0.775021	−	1.34238i
$275$	3577.21	−	6195.92i	0.784415	−	1.35865i
$276$	−7168.80			−1.56345
$277$	5695.02			1.23531			0.617655	−	0.786449i	$-0.288083\pi$
$277$	5695.02			1.23531			0.617655	+	0.786449i	$0.288083\pi$
$278$	3295.77	+	5708.44i	0.711033	+	1.23155i
$279$	865.414	−	1498.94i	0.185702	−	0.321646i
$280$	−71.7417	+	124.260i	−0.0153121	+	0.0265213i
$281$	4170.72	+	7223.90i	0.885425	+	1.53360i	0.845226	+	0.534409i	$0.179466\pi$
$281$	4170.72	+	7223.90i	0.885425	+	1.53360i	0.0401988	+	0.999192i	$0.487201\pi$
$282$	−7125.67			−1.50471
$283$	−643.363			−0.135138			−0.0675689	−	0.997715i	$-0.521524\pi$
$283$	−643.363			−0.135138			−0.0675689	+	0.997715i	$0.521524\pi$
$284$	−5037.73	−	8725.60i	−1.05258	−	1.82313i
$285$	159.158	+	275.669i	0.0330796	+	0.0572956i
$286$	−7349.63	−	12729.9i	−1.51955	−	2.63195i
$287$	−134.282	−	232.583i	−0.0276182	−	0.0478361i
$288$	681.658	−	1180.67i	0.139469	−	0.241567i
$289$	−2235.45	+	3871.91i	−0.455006	+	0.788094i
$290$	1392.83			0.282033
$291$	1130.91	+	1958.79i	0.227818	+	0.394592i
$292$	−13700.7			−2.74580
$293$	−1175.28			−0.234337			−0.117168	−	0.993112i	$-0.537382\pi$
$293$	−1175.28			−0.234337			−0.117168	+	0.993112i	$0.537382\pi$
$294$	2335.25	−	4044.78i	0.463247	−	0.802368i
$295$	223.595			0.0441296
$296$	1236.11	+	2141.00i	0.242728	+	0.420417i
$297$	−796.677	+	1379.88i	−0.155649	+	0.269593i
$298$	−2630.71	−	4556.53i	−0.511386	−	0.885747i
$299$	4706.40	−	8151.72i	0.910294	−	1.57668i
$300$	2474.00	−	4285.09i	0.476121	−	0.824667i
$301$	−41.7153	+	72.2531i	−0.00798814	+	0.0138359i
$302$	−6293.57	+	10900.8i	−1.19919	+	2.07705i
$303$	−907.759	+	1572.28i	−0.172110	+	0.298104i
$304$	334.806	−	579.901i	0.0631660	−	0.109407i
$305$	−265.082	−	459.136i	−0.0497658	−	0.0861969i
$306$	2026.17	−	3509.43i	0.378524	−	0.655623i
$307$	2124.45	+	3679.65i	0.394947	+	0.684068i	0.993094	−	0.117318i	$-0.0374298\pi$
$307$	2124.45	+	3679.65i	0.394947	+	0.684068i	−0.598148	+	0.801386i	$0.704096\pi$
$308$	2278.86			0.421592
$309$	1119.44	−	1938.93i	0.206093	−	0.356964i
$310$	−1734.56			−0.317795
$311$	9752.03			1.77809			0.889046	−	0.457818i	$-0.151369\pi$
$311$	9752.03			1.77809			0.889046	+	0.457818i	$0.151369\pi$
$312$	−2093.98	−	3626.89i	−0.379963	−	0.658115i
$313$	−508.455			−0.0918198			−0.0459099	−	0.998946i	$-0.514619\pi$
$313$	−508.455			−0.0918198			−0.0459099	+	0.998946i	$0.514619\pi$
$314$	−436.442	+	755.939i	−0.0784390	+	0.135860i
$315$	−24.7860	+	42.9307i	−0.00443344	+	0.00767895i
$316$	759.631	+	1315.72i	0.135230	+	0.234225i
$317$	−3742.55	−	6482.28i	−0.663099	−	1.14852i	−0.979797	−	0.199995i	$-0.935907\pi$
$317$	−3742.55	−	6482.28i	−0.663099	−	1.14852i	0.316698	−	0.948527i	$-0.397426\pi$
$318$	1889.80	+	3273.22i	0.333253	+	0.577212i
$319$	−4556.55	−	7892.18i	−0.799743	−	1.38520i
$320$	−1556.36			−0.271885
$321$	−6500.80			−1.13034
$322$	1158.71	+	2006.94i	0.200535	+	0.347336i
$323$	−2648.45	+	4587.24i	−0.456234	+	0.790220i
$324$	−550.981	+	954.328i	−0.0944755	+	0.163636i
$325$	3248.42	+	5626.42i	0.554430	+	0.960301i
$326$	5286.08			0.898064
$327$	−3389.44			−0.573200
$328$	−1232.36	+	2134.51i	−0.207456	+	0.359325i
$329$	725.254	+	1256.18i	0.121534	+	0.210502i
$330$	1596.79			0.266365
$331$	5549.26	−	9611.60i	0.921496	−	1.59608i	0.124393	−	0.992233i	$-0.460302\pi$
$331$	5549.26	−	9611.60i	0.921496	−	1.59608i	0.797102	−	0.603844i	$-0.206365\pi$
$332$	−18966.7			−3.13533
$333$	427.063	+	739.696i	0.0702791	+	0.121727i
$334$	−3008.42			−0.492855
$335$	−915.092	−	543.236i	−0.149244	−	0.0885975i
$336$	104.280			0.0169314
$337$	621.225	+	1075.99i	0.100416	+	0.173926i	0.911856	−	0.410510i	$-0.134649\pi$
$337$	621.225	+	1075.99i	0.100416	+	0.173926i	−0.811440	+	0.584436i	$0.801316\pi$
$338$	3136.39			0.504725
$339$	908.785	−	1574.06i	0.145600	−	0.252187i
$340$	−2557.29			−0.407908
$341$	5674.53	+	9828.57i	0.901152	+	1.56084i
$342$	1143.71	−	1980.96i	0.180832	−	0.313210i
$343$	−1924.34			−0.302928
$344$	765.676			0.120007
$345$	511.260	+	885.528i	0.0797835	+	0.138189i
$346$	1655.25	−	2866.98i	0.257187	−	0.445461i
$347$	284.131	−	492.129i	0.0439566	−	0.0761351i	−0.843210	−	0.537584i	$-0.819337\pi$
$347$	284.131	−	492.129i	0.0439566	−	0.0761351i	0.887167	+	0.461449i	$0.152670\pi$
$348$	−3151.31	−	5458.23i	−0.485425	−	0.840781i
$349$	5450.22			0.835941			0.417971	−	0.908461i	$-0.362742\pi$
$349$	5450.22			0.835941			0.417971	+	0.908461i	$0.362742\pi$
$350$	−1599.51			−0.244278
$351$	−723.451	−	1253.05i	−0.110014	−	0.190550i
$352$	4469.64	+	7741.64i	0.676797	+	1.17225i
$353$	−2383.64	−	4128.58i	−0.359400	−	0.622499i	0.628461	−	0.777841i	$-0.283685\pi$
$353$	−2383.64	−	4128.58i	−0.359400	−	0.622499i	−0.987861	+	0.155343i	$0.950352\pi$
$354$	−803.376	−	1391.49i	−0.120619	−	0.208917i
$355$	−718.554	+	1244.57i	−0.107428	+	0.186071i
$356$	3654.72	−	6330.17i	0.544101	−	0.942410i
$357$	−824.898			−0.122292
$358$	6758.54	+	11706.1i	0.997766	+	1.72818i
$359$	−7185.31			−1.05634			−0.528170	−	0.849139i	$-0.677122\pi$
$359$	−7185.31			−1.05634			−0.528170	+	0.849139i	$0.677122\pi$
$360$	454.942			0.0666043
$361$	1934.54	−	3350.72i	0.282044	−	0.488515i
$362$	−1130.62			−0.164155
$363$	−3227.32	−	5589.88i	−0.466640	−	0.808244i
$364$	−1034.70	+	1792.15i	−0.148992	+	0.258061i
$365$	977.099	+	1692.38i	0.140120	+	0.242694i
$366$	−1904.88	+	3299.34i	−0.272048	+	0.471201i
$367$	−4133.38	+	7159.22i	−0.587903	+	1.01828i	0.406603	+	0.913605i	$0.366713\pi$
$367$	−4133.38	+	7159.22i	−0.587903	+	1.01828i	−0.994507	+	0.104674i	$0.966620\pi$
$368$	1075.49	−	1862.81i	0.152348	−	0.263874i
$369$	−425.768	+	737.451i	−0.0600666	+	0.104038i
$370$	427.985	−	741.292i	0.0601348	−	0.104157i
$371$	384.689	−	666.301i	0.0538330	−	0.0932415i
$372$	3924.50	+	6797.43i	0.546978	+	0.947394i
$373$	−1775.49	+	3075.25i	−0.246465	+	0.426891i	−0.962543	−	0.271130i	$-0.912603\pi$
$373$	−1775.49	+	3075.25i	−0.246465	+	0.426891i	0.716077	+	0.698021i	$0.245936\pi$
$374$	13285.6	+	23011.4i	1.83685	+	3.18152i
$375$	−1433.43			−0.197392
$376$	6655.94	−	11528.4i	0.912910	−	1.58121i
$377$	8275.48			1.13053
$378$	356.224			0.0484714
$379$	241.086	+	417.574i	0.0326749	+	0.0565946i	0.881900	−	0.471436i	$-0.156264\pi$
$379$	241.086	+	417.574i	0.0326749	+	0.0565946i	−0.849226	+	0.528030i	$0.822931\pi$
$380$	−1443.51			−0.194869
$381$	−891.605	+	1544.31i	−0.119891	+	0.207657i
$382$	−5929.51	+	10270.2i	−0.794189	+	1.37558i
$383$	−2630.72	−	4556.55i	−0.350976	−	0.607908i	0.635445	−	0.772146i	$-0.280817\pi$
$383$	−2630.72	−	4556.55i	−0.350976	−	0.607908i	−0.986421	+	0.164238i	$0.947483\pi$
$384$	3774.24	+	6537.18i	0.501571	+	0.868747i
$385$	−162.522	−	281.497i	−0.0215140	−	0.0372634i
$386$	−2026.64	−	3510.25i	−0.267237	−	0.462868i
$387$	264.533			0.0347467
$388$	−10256.9			−1.34206
$389$	4991.90	+	8646.23i	0.650641	+	1.12694i	0.982967	+	0.183780i	$0.0588332\pi$
$389$	4991.90	+	8646.23i	0.650641	+	1.12694i	−0.332326	+	0.943165i	$0.607833\pi$
$390$	−725.012	+	1255.76i	−0.0941343	+	0.163045i
$391$	−8507.56	+	14735.5i	−1.10037	+	1.90590i
$392$	4362.62	+	7556.29i	0.562107	+	0.973597i
$393$	6175.12			0.792604
$394$	−199.787			−0.0255460
$395$	108.350	−	187.667i	0.0138017	−	0.0239052i
$396$	−3612.79	−	6257.54i	−0.458459	−	0.794073i
$397$	10689.6			1.35137			0.675686	−	0.737190i	$-0.263848\pi$
$397$	10689.6			1.35137			0.675686	+	0.737190i	$0.263848\pi$
$398$	−1453.30	+	2517.19i	−0.183034	+	0.317024i
$399$	−465.628			−0.0584224
$400$	742.318	+	1285.73i	0.0927898	+	0.160717i
$401$	11907.5			1.48287			0.741435	−	0.671025i	$-0.234146\pi$
$401$	11907.5			1.48287			0.741435	+	0.671025i	$0.234146\pi$
$402$	−92.7723	+	7646.69i	−0.0115101	+	0.948712i
$403$	−10305.9			−1.27388
$404$	−4116.53	−	7130.04i	−0.506943	−	0.878051i
$405$	157.178			0.0192845
$406$	−1018.70	+	1764.45i	−0.124526	+	0.215685i
$407$	−5600.52			−0.682082
$408$	3785.21	+	6556.17i	0.459303	+	0.795537i
$409$	3385.09	−	5863.14i	0.409246	−	0.708835i	−0.585559	−	0.810630i	$-0.699125\pi$
$409$	3385.09	−	5863.14i	0.409246	−	0.708835i	0.994805	+	0.101794i	$0.0324583\pi$
$410$	853.373			0.102793
$411$	4537.52			0.544573
$412$	5076.47	+	8792.70i	0.607038	+	1.05142i
$413$	−163.536	+	283.253i	−0.0194845	+	0.0337481i
$414$	3673.90	−	6363.39i	0.436141	−	0.755419i
$415$	1352.65	+	2342.86i	0.159998	+	0.277124i
$416$	−8117.63			−0.956729
$417$	−4254.38			−0.499612
$418$	7499.29	+	12989.2i	0.877517	+	1.51990i
$419$	−8542.44	−	14795.9i	−0.996004	−	1.72513i	−0.575346	−	0.817910i	$-0.695132\pi$
$419$	−8542.44	−	14795.9i	−0.996004	−	1.72513i	−0.420658	−	0.907219i	$-0.638201\pi$
$420$	−112.400	−	194.683i	−0.0130585	−	0.0226180i
$421$	4891.84	+	8472.91i	0.566303	+	0.980866i	0.996927	+	0.0783344i	$0.0249602\pi$
$421$	4891.84	+	8472.91i	0.566303	+	0.980866i	−0.430624	+	0.902531i	$0.641706\pi$
$422$	−3709.17	+	6424.48i	−0.427867	+	0.741087i
$423$	2299.56	−	3982.96i	0.264323	−	0.457820i
$424$	−7060.88			−0.808742
$425$	−5872.03	−	10170.6i	−0.670200	−	1.16082i
$426$	10327.0			1.17452
$427$	775.517			0.0878921
$428$	14740.0	−	25530.4i	1.66468	−	2.88332i
$429$	9487.35			1.06772
$430$	−132.552	−	229.587i	−0.0148657	−	0.0257481i
$431$	3647.24	−	6317.21i	0.407614	−	0.706007i	−0.587008	−	0.809581i	$-0.699694\pi$
$431$	3647.24	−	6317.21i	0.407614	−	0.706007i	0.994622	+	0.103574i	$0.0330277\pi$
$432$	−165.321	−	286.344i	−0.0184120	−	0.0318906i
$433$	3982.21	−	6897.39i	0.441969	−	0.765514i	−0.555866	−	0.831272i	$-0.687613\pi$
$433$	3982.21	−	6897.39i	0.441969	−	0.765514i	0.997836	+	0.0657583i	$0.0209466\pi$
$434$	1268.65	−	2197.36i	0.140316	−	0.243034i
$435$	−449.486	+	778.533i	−0.0495430	+	0.0858110i
$436$	7685.25	−	13311.2i	0.844167	−	1.46214i
$437$	−4802.23	+	8317.71i	−0.525680	+	0.910504i
$438$	7021.42	−	12161.5i	0.765973	−	1.32670i
$439$	3949.62	+	6840.94i	0.429396	+	0.743736i	0.996820	−	0.0796901i	$-0.0253931\pi$
$439$	3949.62	+	6840.94i	0.429396	+	0.743736i	−0.567424	+	0.823426i	$0.692060\pi$
$440$	−1491.53	+	2583.41i	−0.161604	+	0.279907i
$441$	1507.24	+	2610.62i	0.162752	+	0.281894i
$442$	−24129.0			−2.59660
$443$	6805.17	−	11786.9i	0.729849	−	1.26414i	−0.227098	−	0.973872i	$-0.572924\pi$
$443$	6805.17	−	11786.9i	0.729849	−	1.26414i	0.956947	−	0.290264i	$-0.0937430\pi$
$444$	−3873.32			−0.414008
$445$	−1042.58			−0.111063
$446$	−14533.3	−	25172.4i	−1.54299	−	2.67253i
$447$	3395.88			0.359328
$448$	1138.31	−	1971.61i	0.120045	−	0.207924i
$449$	5309.93	−	9197.07i	0.558109	−	0.966674i	−0.439545	−	0.898221i	$-0.644860\pi$
$449$	5309.93	−	9197.07i	0.558109	−	0.966674i	0.997654	−	0.0684531i	$-0.0218063\pi$
$450$	2535.78	+	4392.09i	0.265639	+	0.460101i
$451$	−2791.76	−	4835.48i	−0.291483	−	0.504864i
$452$	4121.18	+	7138.09i	0.428858	+	0.742805i
$453$	−4062.06	−	7035.70i	−0.421307	−	0.729726i
$454$	−8472.95			−0.875892
$455$	295.168			0.0304125
$456$	2136.62	+	3700.74i	0.219422	+	0.380051i
$457$	−4733.64	+	8198.90i	−0.484530	+	0.839230i	−0.999842	−	0.0177721i	$-0.994343\pi$
$457$	−4733.64	+	8198.90i	−0.484530	+	0.839230i	0.515312	+	0.857003i	$0.327676\pi$
$458$	−9839.07	+	17041.8i	−1.00382	+	1.73867i
$459$	1307.75	+	2265.09i	0.132986	+	0.230339i
$460$	−4636.95			−0.469997
$461$	5719.91			0.577880			0.288940	−	0.957347i	$-0.406697\pi$
$461$	5719.91			0.577880			0.288940	+	0.957347i	$0.406697\pi$
$462$	−1167.88	+	2022.83i	−0.117608	+	0.203703i
$463$	8719.01	+	15101.8i	0.875177	+	1.51585i	0.856575	+	0.516023i	$0.172588\pi$
$463$	8719.01	+	15101.8i	0.875177	+	1.51585i	0.0186019	+	0.999827i	$0.494078\pi$
$464$	1891.09			0.189206
$465$	559.769	−	969.549i	0.0558251	−	0.0966920i
$466$	12904.5			1.28281
$467$	863.090	+	1494.92i	0.0855226	+	0.148129i	0.905614	−	0.424103i	$-0.139411\pi$
$467$	863.090	+	1494.92i	0.0855226	+	0.148129i	−0.820091	+	0.572233i	$0.806077\pi$
$468$	6561.44			0.648083
$469$	1357.47	−	761.929i	0.133651	−	0.0750162i
$470$	−4609.05			−0.452339
$471$	−281.693	−	487.906i	−0.0275578	−	0.0477315i
$472$	3001.67			0.292718
$473$	−867.274	+	1502.16i	−0.0843072	+	0.146024i
$474$	−1557.20			−0.150896
$475$	−3314.56	−	5740.99i	−0.320174	−	0.554557i
$476$	1870.39	−	3239.60i	0.180103	−	0.311947i
$477$	−2439.46			−0.234162
$478$	14767.7			1.41310
$479$	−5350.05	−	9266.56i	−0.510334	−	0.883924i	−0.999928	−	0.0119741i	$-0.996188\pi$
$479$	−5350.05	−	9266.56i	−0.510334	−	0.883924i	0.489594	−	0.871950i	$-0.337145\pi$
$480$	440.912	−	763.682i	0.0419267	−	0.0726191i
$481$	2542.87	−	4404.39i	0.241050	−	0.417511i
$482$	−2655.40	−	4599.29i	−0.250934	−	0.434631i
$483$	−1495.73			−0.140907
$484$	29270.7			2.74894
$485$	731.498	+	1266.99i	0.0684858	+	0.118621i
$486$	−564.739	−	978.157i	−0.0527101	−	0.0912966i
$487$	−10331.0	−	17893.8i	−0.961275	−	1.66498i	−0.719306	−	0.694693i	$-0.755540\pi$
$487$	−10331.0	−	17893.8i	−0.961275	−	1.66498i	−0.241969	−	0.970284i	$-0.577793\pi$
$488$	−3558.61	−	6163.70i	−0.330104	−	0.571757i
$489$	−1705.90	+	2954.70i	−0.157757	+	0.273244i
$490$	1510.50	−	2616.26i	0.139260	−	0.241205i
$491$	13031.1			1.19773			0.598863	−	0.800851i	$-0.295619\pi$
$491$	13031.1			1.19773			0.598863	+	0.800851i	$0.295619\pi$
$492$	−1930.78	−	3344.21i	−0.176924	−	0.306441i
$493$	−14959.2			−1.36659
$494$	−13620.0			−1.24047
$495$	−515.309	+	892.541i	−0.0467907	+	0.0810440i
$496$	−2355.08			−0.213198
$497$	−1051.09	−	1820.54i	−0.0948650	−	0.164311i
$498$	9720.13	−	16835.8i	0.874637	−	1.51492i
$499$	2087.79	+	3616.15i	0.187299	+	0.324411i	0.944349	−	0.328946i	$-0.106693\pi$
$499$	2087.79	+	3616.15i	0.187299	+	0.324411i	−0.757050	+	0.653357i	$0.773360\pi$
$500$	3250.18	−	5629.48i	0.290705	−	0.503516i
$501$	970.863	−	1681.58i	0.0865768	−	0.149955i
$502$	3231.01	−	5596.28i	0.287265	−	0.497558i
$503$	7977.14	−	13816.8i	0.707124	−	1.22477i	−0.258796	−	0.965932i	$-0.583326\pi$
$503$	7977.14	−	13816.8i	0.707124	−	1.22477i	0.965920	−	0.258842i	$-0.0833410\pi$
$504$	−332.742	+	576.325i	−0.0294077	+	0.0509357i
$505$	−587.159	+	1016.99i	−0.0517391	+	0.0896148i
$506$	24089.8	+	41724.8i	2.11645	+	3.66580i
$507$	−1012.16	+	1753.11i	−0.0886619	+	0.153567i
$508$	−4043.27	−	7003.16i	−0.353132	−	0.611643i
$509$	−6898.64			−0.600741			−0.300370	−	0.953823i	$-0.597110\pi$
$509$	−6898.64			−0.600741			−0.300370	+	0.953823i	$0.597110\pi$
$510$	1310.57	−	2269.98i	0.113791	−	0.197091i
$511$	−2858.57			−0.247467
$512$	−4407.08			−0.380404
$513$	738.182	+	1278.57i	0.0635313	+	0.110039i
$514$	54.7714			0.00470013
$515$	724.080	−	1254.14i	0.0619549	−	0.107309i
$516$	−599.806	+	1038.90i	−0.0511725	+	0.0886333i
$517$	15078.3	+	26116.3i	1.28267	+	2.22165i
$518$	626.051	+	1084.35i	0.0531025	+	0.0919762i
$519$	1068.35	+	1850.43i	0.0903570	+	0.156503i
$520$	−1354.44	−	2345.95i	−0.114223	−	0.197840i
$521$	−11663.3			−0.980768			−0.490384	−	0.871507i	$-0.663143\pi$
$521$	−11663.3			−0.980768			−0.490384	+	0.871507i	$0.663143\pi$
$522$	6460.00			0.541660
$523$	−794.050	−	1375.34i	−0.0663889	−	0.114989i	0.830920	−	0.556391i	$-0.187814\pi$
$523$	−794.050	−	1375.34i	−0.0663889	−	0.114989i	−0.897309	+	0.441402i	$0.854481\pi$
$524$	−14001.5	+	24251.4i	−1.16729	+	2.02181i
$525$	516.185	−	894.059i	0.0429108	−	0.0743237i
$526$	16384.5	+	28378.8i	1.35817	+	2.35242i
$527$	18629.6			1.53988
$528$	2168.02			0.178695
$529$	−9342.62	+	16181.9i	−0.767866	+	1.32998i
$530$	1222.36	+	2117.20i	0.100181	+	0.173519i
$531$	1037.05			0.0847533
$532$	1055.77	−	1828.65i	0.0860403	−	0.149026i
$533$	5070.32			0.412045
$534$	3745.98	+	6488.23i	0.303566	+	0.525793i
$535$	−4204.87			−0.339799
$536$	−12284.7	−	7292.71i	−0.989961	−	0.587681i
$537$	−8724.34			−0.701086
$538$	−18855.1	−	32658.0i	−1.51097	−	2.61708i
$539$	−19766.0			−1.57956
$540$	−356.387	+	617.281i	−0.0284009	+	0.0491918i
$541$	4403.92			0.349980			0.174990	−	0.984570i	$-0.444011\pi$
$541$	4403.92			0.349980			0.174990	+	0.984570i	$0.444011\pi$
$542$	−14285.6	−	24743.3i	−1.13214	−	1.96092i
$543$	364.868	−	631.971i	0.0288361	−	0.0499456i
$544$	14673.9			1.15650
$545$	−2192.37			−0.172313
$546$	−1060.54	−	1836.90i	−0.0831260	−	0.143978i
$547$	−4389.68	+	7603.15i	−0.343125	+	0.594310i	−0.985011	−	0.172490i	$-0.944819\pi$
$547$	−4389.68	+	7603.15i	−0.343125	+	0.594310i	0.641886	+	0.766800i	$0.278152\pi$
$548$	−10288.4	+	17820.1i	−0.802008	+	1.38912i
$549$	−1229.47	−	2129.50i	−0.0955780	−	0.165546i
$550$	−33254.2			−2.57812
$551$	−8443.99			−0.652861
$552$	6863.44	+	11887.8i	0.529216	+	0.916629i
$553$	158.492	+	274.517i	0.0121877	+	0.0211097i
$554$	−13235.4	−	22924.4i	−1.01502	−	1.75806i
$555$	276.235	+	478.452i	0.0211270	+	0.0365931i
$556$	9646.44	−	16708.1i	0.735792	−	1.27443i
$557$	−9443.10	+	16355.9i	−0.718343	+	1.24421i	0.243313	+	0.969948i	$0.421766\pi$
$557$	−9443.10	+	16355.9i	−0.718343	+	1.24421i	−0.961656	+	0.274259i	$0.911568\pi$
$558$	−8044.99			−0.610343
$559$	−787.559	−	1364.09i	−0.0595889	−	0.103211i
$560$	67.4510			0.00508986
$561$	−17149.9			−1.29068
$562$	19385.8	−	33577.1i	1.45505	−	2.52022i
$563$	10758.1			0.805329			0.402665	−	0.915348i	$-0.368084\pi$
$563$	10758.1			0.805329			0.402665	+	0.915348i	$0.368084\pi$
$564$	10428.1	+	18062.0i	0.778551	+	1.34849i
$565$	587.823	−	1018.14i	0.0437697	−	0.0758114i
$566$	1495.20	+	2589.76i	0.111039	+	0.192324i
$567$	−114.959	+	199.115i	−0.00851468	+	0.0147479i
$568$	−9646.28	+	16707.8i	−0.712586	+	1.23423i
$569$	2912.45	−	5044.51i	0.214580	−	0.371664i	−0.738562	−	0.674185i	$-0.764495\pi$
$569$	2912.45	−	5044.51i	0.214580	−	0.371664i	0.953143	+	0.302521i	$0.0978283\pi$
$570$	739.775	−	1281.33i	0.0543610	−	0.0941560i
$571$	12183.0	−	21101.6i	0.892897	−	1.54654i	0.0565108	−	0.998402i	$-0.482002\pi$
$571$	12183.0	−	21101.6i	0.892897	−	1.54654i	0.836386	−	0.548141i	$-0.184664\pi$
$572$	−21511.7	+	37259.4i	−1.57247	+	2.72359i
$573$	−3827.09	−	6628.71i	−0.279021	−	0.483278i
$574$	−624.151	+	1081.06i	−0.0453860	+	0.0786109i
$575$	−10647.3	−	18441.7i	−0.772215	−	1.33752i
$576$	−7218.49			−0.522171
$577$	−4228.30	+	7323.64i	−0.305072	+	0.528400i	−0.977277	−	0.211964i	$-0.932014\pi$
$577$	−4228.30	+	7323.64i	−0.305072	+	0.528400i	0.672205	+	0.740365i	$0.265347\pi$
$578$	20781.0			1.49546
$579$	2616.11			0.187775
$580$	−2038.34	−	3530.51i	−0.145927	−	0.252752i
$581$	−3957.28			−0.282574
$582$	5256.53	−	9104.58i	0.374382	−	0.648449i
$583$	7997.80	−	13852.6i	0.568156	−	0.984075i
$584$	13117.1	+	22719.5i	0.929436	+	1.60983i
$585$	−467.945	−	810.504i	−0.0330720	−	0.0572824i
$586$	2731.39	+	4730.91i	0.192547	+	0.333502i
$587$	3196.54	+	5536.57i	0.224762	+	0.389299i	0.956248	−	0.292557i	$-0.0945062\pi$
$587$	3196.54	+	5536.57i	0.224762	+	0.389299i	−0.731486	+	0.681856i	$0.761173\pi$
$588$	−13670.2			−0.958756
$589$	10515.8			0.735645
$590$	−519.642	−	900.047i	−0.0362599	−	0.0628040i
$591$	64.4743	−	111.673i	0.00448751	−	0.00777260i
$592$	581.090	−	1006.48i	0.0403423	−	0.0698750i
$593$	5234.32	+	9066.11i	0.362475	+	0.627825i	0.988368	−	0.152084i	$-0.0485984\pi$
$593$	5234.32	+	9066.11i	0.362475	+	0.627825i	−0.625892	+	0.779909i	$0.715265\pi$
$594$	7406.01			0.511569
$595$	−533.563			−0.0367630
$596$	−7699.87	+	13336.6i	−0.529193	+	0.916589i
$597$	−938.005	−	1624.67i	−0.0643048	−	0.111379i
$598$	−43751.2			−2.99184
$599$	−1844.54	+	3194.83i	−0.125819	+	0.217925i	−0.922053	−	0.387064i	$-0.873489\pi$
$599$	−1844.54	+	3194.83i	−0.125819	+	0.217925i	0.796234	+	0.604989i	$0.206823\pi$
$600$	−9474.47			−0.644656
$601$	−9823.40	−	17014.6i	−0.666730	−	1.15481i	−0.978813	−	0.204755i	$-0.934360\pi$
$601$	−9823.40	−	17014.6i	−0.666730	−	1.15481i	0.312083	−	0.950055i	$-0.398973\pi$
$602$	387.791			0.0262544
$603$	−4244.25	−	2519.56i	−0.286632	−	0.170156i
$604$	36841.5			2.48188
$605$	−2087.51	−	3615.67i	−0.140280	−	0.242971i
$606$	8438.64			0.565670
$607$	−4668.49	+	8086.07i	−0.312172	+	0.540698i	−0.978832	−	0.204664i	$-0.934390\pi$
$607$	−4668.49	+	8086.07i	−0.312172	+	0.540698i	0.666660	+	0.745362i	$0.267723\pi$
$608$	8282.93			0.552495
$609$	−657.502	−	1138.83i	−0.0437493	−	0.0757760i
$610$	−1232.12	+	2134.09i	−0.0817820	+	0.141651i
$611$	−27384.7			−1.81320
$612$	−11860.9			−0.783409
$613$	5128.39	+	8882.63i	0.337902	+	0.585263i	0.984038	−	0.177959i	$-0.0569495\pi$
$613$	5128.39	+	8882.63i	0.337902	+	0.585263i	−0.646136	+	0.763222i	$0.723616\pi$
$614$	9874.56	−	17103.2i	0.649031	−	1.12415i
$615$	−275.396	+	477.001i	−0.0180570	+	0.0312756i
$616$	−2181.79	−	3778.97i	−0.142706	−	0.247174i
$617$	−17211.2			−1.12301			−0.561504	−	0.827474i	$-0.689777\pi$
$617$	−17211.2			−1.12301			−0.561504	+	0.827474i	$0.689777\pi$
$618$	−10406.5			−0.677361
$619$	−7532.36	−	13046.4i	−0.489097	−	0.847140i	0.510825	−	0.859685i	$-0.329340\pi$
$619$	−7532.36	−	13046.4i	−0.489097	−	0.847140i	−0.999921	+	0.0125445i	$0.996007\pi$
$620$	2538.46	+	4396.74i	0.164430	+	0.284802i
$621$	2371.25	+	4107.12i	0.153229	+	0.265400i
$622$	−22664.0	−	39255.2i	−1.46100	−	2.53053i
$623$	762.536	−	1320.75i	0.0490375	−	0.0849354i
$624$	−984.374	+	1704.99i	−0.0631514	+	0.109381i
$625$	14227.1			0.910537
$626$	1181.67	+	2046.71i	0.0754455	+	0.130675i
$627$	−9680.54			−0.616592
$628$	2554.85			0.162340
$629$	−4596.65	+	7961.63i	−0.291384	+	0.504692i
$630$	230.414			0.0145713
$631$	10743.4	+	18608.1i	0.677794	+	1.17397i	0.975644	+	0.219360i	$0.0703971\pi$
$631$	10743.4	+	18608.1i	0.677794	+	1.17397i	−0.297850	+	0.954613i	$0.596270\pi$
$632$	1454.55	−	2519.35i	0.0915487	−	0.158567i
$633$	−2394.01	−	4146.55i	−0.150321	−	0.260364i
$634$	−17395.6	+	30130.1i	−1.08970	+	1.88741i
$635$	−576.711	+	998.892i	−0.0360411	+	0.0624249i
$636$	5531.27	−	9580.45i	0.344857	−	0.597310i
$637$	8974.62	−	15544.5i	0.558222	−	0.966868i
$638$	−21179.1	+	36683.4i	−1.31425	+	2.27634i
$639$	−3332.69	+	5772.39i	−0.206321	+	0.357359i
$640$	2441.27	+	4228.40i	0.150781	+	0.261160i
$641$	−9885.57	+	17122.3i	−0.609137	+	1.05506i	0.382247	+	0.924060i	$0.375151\pi$
$641$	−9885.57	+	17122.3i	−0.609137	+	1.05506i	−0.991383	+	0.130995i	$0.958183\pi$
$642$	15108.1	+	26167.9i	0.928765	+	1.60867i
$643$	2103.20			0.128992			0.0644962	−	0.997918i	$-0.479456\pi$
$643$	2103.20			0.128992			0.0644962	+	0.997918i	$0.479456\pi$
$644$	3391.43	−	5874.13i	0.207517	−	0.359430i
$645$	171.106			0.0104454
$646$	24620.3			1.49949
$647$	−13875.5	−	24033.1i	−0.843126	−	1.46034i	−0.887239	−	0.461310i	$-0.847380\pi$
$647$	−13875.5	−	24033.1i	−0.843126	−	1.46034i	0.0441136	−	0.999027i	$-0.485954\pi$
$648$	2110.05			0.127917
$649$	−3399.96	+	5888.91i	−0.205640	+	0.356179i
$650$	15098.8	−	26152.0i	0.911115	−	1.57810i
$651$	818.823	+	1418.24i	0.0492968	+	0.0853845i
$652$	−7735.95	−	13399.1i	−0.464668	−	0.804828i
$653$	7421.17	+	12853.8i	0.444736	+	0.770306i	0.998034	−	0.0626780i	$-0.0199641\pi$
$653$	7421.17	+	12853.8i	0.444736	+	0.770306i	−0.553298	+	0.832984i	$0.686631\pi$
$654$	7877.16	+	13643.6i	0.470980	+	0.815762i
$655$	3994.21			0.238270
$656$	1158.65			0.0689602
$657$	4531.84	+	7849.37i	0.269108	+	0.466108i
$658$	3371.03	−	5838.79i	0.199721	−	0.345927i
$659$	−6613.34	+	11454.6i	−0.390924	+	0.677101i	−0.992572	−	0.121661i	$-0.961178\pi$
$659$	−6613.34	+	11454.6i	−0.390924	+	0.677101i	0.601647	+	0.798762i	$0.294511\pi$
$660$	−2336.84	−	4047.52i	−0.137820	−	0.238711i
$661$	−5091.19			−0.299583			−0.149791	−	0.988718i	$-0.547860\pi$
$661$	−5091.19			−0.299583			−0.149791	+	0.988718i	$0.547860\pi$
$662$	−51586.6			−3.02866
$663$	7786.78	−	13487.1i	0.456129	−	0.790038i
$664$	18158.7	+	31451.9i	1.06129	+	1.83821i
$665$	−301.179			−0.0175627
$666$	1985.02	−	3438.15i	0.115492	−	0.200039i
$667$	−27124.5			−1.57461
$668$	4402.69	+	7625.69i	0.255008	+	0.441687i
$669$	18760.5			1.08419
$670$	−60.0073	+	4946.05i	−0.00346012	+	0.285198i
$671$	16123.2			0.927617
$672$	644.960	+	1117.10i	0.0370236	+	0.0641268i
$673$	−3503.13			−0.200648			−0.100324	−	0.994955i	$-0.531988\pi$
$673$	−3503.13			−0.200648			−0.100324	+	0.994955i	$0.531988\pi$
$674$	2887.49	−	5001.28i	0.165018	−	0.285819i
$675$	−3273.33			−0.186653
$676$	−4589.97	−	7950.06i	−0.261150	−	0.452325i
$677$	4620.16	−	8002.36i	0.262285	−	0.454292i	−0.704563	−	0.709641i	$-0.748857\pi$
$677$	4620.16	−	8002.36i	0.262285	−	0.454292i	0.966849	+	0.255349i	$0.0821905\pi$
$678$	−8448.17			−0.478540
$679$	−2140.05			−0.120954
$680$	2448.36	+	4240.68i	0.138074	+	0.239151i
$681$	2734.35	−	4736.03i	0.153863	−	0.266498i
$682$	26375.5	−	45683.8i	1.48090	−	2.56499i
$683$	10396.2	+	18006.7i	0.582429	+	1.00880i	0.995191	+	0.0979571i	$0.0312308\pi$
$683$	10396.2	+	18006.7i	0.582429	+	1.00880i	−0.412762	+	0.910839i	$0.635436\pi$
$684$	−6695.06			−0.374257
$685$	2934.97			0.163707
$686$	4472.22	+	7746.10i	0.248907	+	0.431119i
$687$	−6350.43	−	10999.3i	−0.352670	−	0.610842i
$688$	−179.971	−	311.718i	−0.00997284	−	0.0172735i
$689$	7262.68	+	12579.3i	0.401576	+	0.695551i
$690$	2376.37	−	4115.99i	0.131111	−	0.227091i
$691$	1410.33	−	2442.76i	0.0776430	−	0.134482i	−0.824590	−	0.565731i	$-0.808594\pi$
$691$	1410.33	−	2442.76i	0.0776430	−	0.134482i	0.902233	+	0.431250i	$0.141927\pi$
$692$	−9689.55			−0.532285
$693$	−753.787	−	1305.60i	−0.0413189	−	0.0715664i
$694$	−2641.32			−0.144471
$695$	−2751.83			−0.150191
$696$	−6034.15	+	10451.5i	−0.328626	+	0.569198i
$697$	−9165.41			−0.498084
$698$	−12666.5	−	21939.0i	−0.686867	−	1.18969i
$699$	−4164.46	+	7213.06i	−0.225343	+	0.390305i
$700$	2340.81	+	4054.40i	0.126392	+	0.218917i
$701$	−13045.3	+	22595.0i	−0.702871	+	1.21741i	0.264583	+	0.964363i	$0.414766\pi$
$701$	−13045.3	+	22595.0i	−0.702871	+	1.21741i	−0.967454	+	0.253045i	$0.918568\pi$
$702$	−3362.64	+	5824.27i	−0.180790	+	0.313138i
$703$	−2594.66	+	4494.08i	−0.139202	+	0.241106i
$704$	23665.9	−	40990.5i	1.26696	−	2.19444i
$705$	1487.41	−	2576.27i	0.0794597	−	0.137628i
$706$	−11079.3	+	19189.9i	−0.590615	+	1.02298i
$707$	−858.889	−	1487.64i	−0.0456886	−	0.0791350i
$708$	−2351.41	+	4072.77i	−0.124819	+	0.216192i
$709$	18408.2	+	31884.0i	0.975086	+	1.68890i	0.679650	+	0.733537i	$0.262132\pi$
$709$	18408.2	+	31884.0i	0.975086	+	1.68890i	0.295437	+	0.955362i	$0.404535\pi$
$710$	6679.77			0.353081
$711$	502.532	−	870.410i	0.0265069	−	0.0459113i
$712$	−13996.2			−0.736698
$713$	33779.6			1.77427
$714$	1917.09	+	3320.50i	0.100484	+	0.174043i
$715$	6136.64			0.320975
$716$	19781.7	−	34262.9i	1.03251	−	1.78836i
$717$	−4765.78	+	8254.57i	−0.248230	+	0.429948i
$718$	16698.9	+	28923.3i	0.867962	+	1.50335i
$719$	−12427.8	−	21525.6i	−0.644617	−	1.11651i	−0.984390	−	0.176002i	$-0.943684\pi$
$719$	−12427.8	−	21525.6i	−0.644617	−	1.11651i	0.339773	−	0.940508i	$-0.389650\pi$
$720$	−106.933	−	185.214i	−0.00553496	−	0.00958683i
$721$	1059.17	+	1834.54i	0.0547097	+	0.0947600i
$722$	−17983.7			−0.926987
$723$	3427.75			0.176320
$724$	1654.62	+	2865.88i	0.0849355	+	0.147113i
$725$	9360.84	−	16213.4i	0.479521	−	0.830555i
$726$	−15000.8	+	25982.1i	−0.766847	+	1.32822i
$727$	6671.18	+	11554.8i	0.340331	+	0.589470i	0.984494	−	0.175418i	$-0.0561277\pi$
$727$	6671.18	+	11554.8i	0.340331	+	0.589470i	−0.644163	+	0.764888i	$0.722794\pi$
$728$	3962.50			0.201731
$729$	729.000			0.0370370
$730$	4541.61	−	7866.31i	0.230264	−	0.398829i
$731$	1423.64	+	2465.81i	0.0720316	+	0.124762i
$732$	11150.8			0.563041
$733$	−5865.86	+	10160.0i	−0.295580	+	0.511960i	−0.975120	−	0.221679i	$-0.928846\pi$
$733$	−5865.86	+	10160.0i	−0.295580	+	0.511960i	0.679539	+	0.733639i	$0.262180\pi$
$734$	38424.4			1.93225
$735$	974.920	+	1688.61i	0.0489258	+	0.0847420i
$736$	26607.1			1.33254
$737$	28222.2	−	15840.7i	1.41055	−	0.791724i
$738$	3957.99			0.197420
$739$	−19293.1	−	33416.7i	−0.960364	−	1.66340i	−0.721586	−	0.692324i	$-0.756587\pi$
$739$	−19293.1	−	33416.7i	−0.960364	−	1.66340i	−0.238777	−	0.971074i	$-0.576747\pi$
$740$	−2505.35			−0.124457
$741$	4395.38	−	7613.02i	0.217906	−	0.377424i
$742$	−3576.12			−0.176932
$743$	−3677.95	−	6370.39i	−0.181603	−	0.314545i	0.760824	−	0.648959i	$-0.224795\pi$
$743$	−3677.95	−	6370.39i	−0.181603	−	0.314545i	−0.942426	+	0.334413i	$0.891462\pi$
$744$	7514.66	−	13015.8i	0.370297	−	0.641373i
$745$	2196.54			0.108020
$746$	16505.2			0.810052
$747$	6273.67	+	10866.3i	0.307284	+	0.532232i
$748$	38885.9	−	67352.3i	1.90081	−	3.29230i
$749$	3075.41	−	5326.77i	0.150031	−	0.259861i
$750$	3331.34	+	5770.05i	0.162191	+	0.280923i
$751$	24804.0			1.20521			0.602605	−	0.798040i	$-0.294129\pi$
$751$	24804.0			1.20521			0.602605	+	0.798040i	$0.294129\pi$
$752$	−6257.87			−0.303459
$753$	2085.39	+	3612.01i	0.100924	+	0.174806i
$754$	−19232.5	−	33311.6i	−0.928919	−	1.60894i
$755$	−2627.43	−	4550.85i	−0.126652	−	0.219367i
$756$	−521.319	−	902.950i	−0.0250796	−	0.0434391i
$757$	832.129	−	1441.29i	0.0399528	−	0.0692002i	−0.845358	−	0.534201i	$-0.820613\pi$
$757$	832.129	−	1441.29i	0.0399528	−	0.0692002i	0.885310	+	0.465001i	$0.153946\pi$
$758$	1120.58	−	1940.91i	0.0536959	−	0.0930040i
$759$	−31096.6			−1.48714
$760$	1382.02	+	2393.72i	0.0659619	+	0.114249i
$761$	−14507.8			−0.691074			−0.345537	−	0.938405i	$-0.612303\pi$
$761$	−14507.8			−0.691074			−0.345537	+	0.938405i	$0.612303\pi$
$762$	8288.47			0.394041
$763$	1603.48	−	2777.31i	0.0760812	−	0.131776i
$764$	34710.4			1.64369
$765$	845.884	+	1465.11i	0.0399778	+	0.0692435i
$766$	−12227.8	+	21179.1i	−0.576772	+	0.998998i
$767$	−3087.46	−	5347.63i	−0.145348	−	0.251749i
$768$	7918.26	−	13714.8i	0.372038	−	0.644389i
$769$	−8048.24	+	13940.0i	−0.377408	+	0.653690i	−0.990684	−	0.136179i	$-0.956518\pi$
$769$	−8048.24	+	13940.0i	−0.377408	+	0.653690i	0.613276	+	0.789868i	$0.289851\pi$
$770$	−755.414	+	1308.41i	−0.0353548	+	0.0612364i
$771$	−17.6756	+	30.6150i	−0.000825642	+	0.00143005i
$772$	−5931.81	+	10274.2i	−0.276542	+	0.478985i
$773$	15230.0	−	26379.0i	0.708646	−	1.22741i	−0.256714	−	0.966487i	$-0.582640\pi$
$773$	15230.0	−	26379.0i	0.708646	−	1.22741i	0.965360	−	0.260923i	$-0.0840269\pi$
$774$	−614.784	−	1064.84i	−0.0285503	−	0.0494506i
$775$	−11657.6	+	20191.5i	−0.540325	+	0.935870i
$776$	9820.04	+	17008.8i	0.454277	+	0.786831i
$777$	−808.144			−0.0373128
$778$	23202.7	−	40188.2i	1.06922	−	1.85195i
$779$	−5173.57			−0.237949
$780$	4244.09			0.194824
$781$	−21852.5	−	37849.6i	−1.00121	−	1.73414i
$782$	79087.3			3.61657
$783$	−2084.74	+	3610.88i	−0.0951501	+	0.164805i
$784$	2050.85	−	3552.18i	0.0934244	−	0.161816i
$785$	−182.205	−	315.589i	−0.00828432	−	0.0143489i
$786$	−14351.2	−	24856.9i	−0.651258	−	1.12801i
$787$	12057.7	+	20884.5i	0.546136	+	0.945935i	0.998534	+	0.0541195i	$0.0172352\pi$
$787$	12057.7	+	20884.5i	0.546136	+	0.945935i	−0.452398	+	0.891816i	$0.649431\pi$
$788$	292.380	+	506.417i	0.0132178	+	0.0228939i
$789$	−21150.1			−0.954327
$790$	−1007.23			−0.0453617
$791$	859.859	+	1489.32i	0.0386512	+	0.0669458i
$792$	−6917.80	+	11982.0i	−0.310370	+	0.537577i
$793$	−7320.64	+	12679.7i	−0.327823	+	0.567806i
$794$	−24842.9	−	43029.2i	−1.11038	−	1.92323i
$795$	−1577.90			−0.0703930
$796$	8507.38			0.378814
$797$	−6614.37	+	11456.4i	−0.293969	+	0.509169i	−0.974744	−	0.223323i	$-0.928309\pi$
$797$	−6614.37	+	11456.4i	−0.293969	+	0.509169i	0.680776	+	0.732492i	$0.261643\pi$
$798$	1082.13	+	1874.31i	0.0480039	+	0.0831451i
$799$	49502.2			2.19182
$800$	−9182.28	+	15904.2i	−0.405803	+	0.702872i
$801$	−4835.54			−0.213303
$802$	−27673.3	−	47931.6i	−1.21843	−	2.11038i
$803$	−59430.6			−2.61178
$804$	19518.5	−	10955.4i	0.856173	−	0.480558i
$805$	−967.471			−0.0423588
$806$	23951.2	+	41484.8i	1.04671	+	1.81295i
$807$	24339.3			1.06169
$808$	−7882.36	+	13652.6i	−0.343194	+	0.594429i
$809$	−18207.9			−0.791291			−0.395645	−	0.918403i	$-0.629479\pi$
$809$	−18207.9			−0.791291			−0.395645	+	0.918403i	$0.629479\pi$
$810$	−365.287	−	632.695i	−0.0158455	−	0.0274452i
$811$	−15856.5	+	27464.3i	−0.686558	+	1.18915i	0.286387	+	0.958114i	$0.407546\pi$
$811$	−15856.5	+	27464.3i	−0.686558	+	1.18915i	−0.972945	+	0.231039i	$0.925788\pi$
$812$	5963.31			0.257723
$813$	18440.7			0.795501
$814$	13015.8	+	22544.0i	0.560446	+	0.970721i
$815$	−1103.41	+	1911.17i	−0.0474245	+	0.0821416i
$816$	1779.41	−	3082.03i	0.0763381	−	0.132221i
$817$	803.596	+	1391.87i	0.0344116	+	0.0596026i
$818$	−31468.2			−1.34506
$819$	1369.01			0.0584090
$820$	−1248.87	−	2163.11i	−0.0531861	−	0.0921210i
$821$	7864.75	+	13622.1i	0.334326	+	0.579070i	0.983355	−	0.181694i	$-0.0581580\pi$
$821$	7864.75	+	13622.1i	0.334326	+	0.579070i	−0.649029	+	0.760764i	$0.724825\pi$
$822$	−10545.3	−	18265.1i	−0.447459	−	0.775021i
$823$	−5848.94	−	10130.7i	−0.247730	−	0.429080i	0.715166	−	0.698955i	$-0.246351\pi$
$823$	−5848.94	−	10130.7i	−0.247730	−	0.429080i	−0.962895	+	0.269875i	$0.913018\pi$
$824$	9720.46	−	16836.3i	0.410957	−	0.711798i
$825$	10731.6	−	18587.8i	0.452882	−	0.784415i
$826$	1520.25			0.0640391
$827$	15636.3	+	27082.9i	0.657471	+	1.13877i	0.981268	+	0.192646i	$0.0617069\pi$
$827$	15636.3	+	27082.9i	0.657471	+	1.13877i	−0.323798	+	0.946126i	$0.604960\pi$
$828$	−21506.4			−0.902656
$829$	948.345			0.0397315			0.0198657	−	0.999803i	$-0.493676\pi$
$829$	948.345			0.0397315			0.0198657	+	0.999803i	$0.493676\pi$
$830$	6287.20	−	10889.8i	0.262930	−	0.455408i
$831$	17085.1			0.713206
$832$	21490.6	+	37222.8i	0.895496	+	1.55105i
$833$	−16223.0	+	28099.1i	−0.674784	+	1.16876i
$834$	9887.32	+	17125.3i	0.410515	+	0.711033i
$835$	627.977	−	1087.69i	0.0260264	−	0.0450790i
$836$	21949.8	−	38018.1i	0.908073	−	1.57283i
$837$	2596.24	−	4496.82i	0.107215	−	0.185702i
$838$	−39705.8	+	68772.5i	−1.63677	+	2.83497i
$839$	−5192.76	+	8994.13i	−0.213676	+	0.370098i	−0.952862	−	0.303404i	$-0.901877\pi$
$839$	−5192.76	+	8994.13i	−0.213676	+	0.370098i	0.739186	+	0.673501i	$0.235210\pi$
$840$	−215.225	+	372.781i	−0.00884044	+	0.0153121i
$841$	270.932	+	469.268i	0.0111088	+	0.0192410i
$842$	22737.6	−	39382.6i	0.930628	−	1.61189i
$843$	12512.2	+	21671.7i	0.511200	+	0.885425i
$844$	21712.9			0.885531
$845$	−654.688	+	1133.95i	−0.0266532	+	0.0461647i
$846$	−21377.0			−0.868743
$847$	6107.15			0.247750
$848$	1659.65	+	2874.59i	0.0672082	+	0.116408i
$849$	−1930.09			−0.0780218
$850$	−27293.5	+	47273.8i	−1.10137	+	1.90762i
$851$	−8334.76	+	14436.2i	−0.335737	+	0.581513i
$852$	−15113.2	−	26176.8i	−0.607710	−	1.05258i
$853$	9398.15	+	16278.1i	0.377241	+	0.653401i	0.990660	−	0.136357i	$-0.0435395\pi$
$853$	9398.15	+	16278.1i	0.377241	+	0.653401i	−0.613419	+	0.789758i	$0.710206\pi$
$854$	−1802.33	−	3121.72i	−0.0722182	−	0.125086i
$855$	477.473	+	827.008i	0.0190985	+	0.0330796i
$856$	−56448.5			−2.25394
$857$	31833.4			1.26886			0.634428	−	0.772982i	$-0.281236\pi$
$857$	31833.4			1.26886			0.634428	+	0.772982i	$0.281236\pi$
$858$	−22048.9	−	38189.8i	−0.877315	−	1.51955i
$859$	2428.17	−	4205.72i	0.0964472	−	0.167052i	−0.813764	−	0.581195i	$-0.802585\pi$
$859$	2428.17	−	4205.72i	0.0964472	−	0.167052i	0.910212	+	0.414143i	$0.135919\pi$
$860$	−387.969	+	671.981i	−0.0153833	+	0.0266446i
$861$	−402.846	−	697.750i	−0.0159454	−	0.0276182i
$862$	−33905.2			−1.33969
$863$	21960.8			0.866226			0.433113	−	0.901340i	$-0.357415\pi$
$863$	21960.8			0.866226			0.433113	+	0.901340i	$0.357415\pi$
$864$	2044.97	−	3542.00i	0.0805225	−	0.139469i
$865$	691.033	+	1196.90i	0.0271628	+	0.0470473i
$866$	−37019.1			−1.45261
$867$	−6706.34	+	11615.7i	−0.262698	+	0.455006i
$868$	−7426.44			−0.290403
$869$	3295.11	+	5707.29i	0.128629	+	0.222792i
$870$	4178.48			0.162832
$871$	−356.533	+	29387.0i	−0.0138699	+	1.14322i
$872$	−29431.6			−1.14298
$873$	3392.73	+	5876.38i	0.131531	+	0.227818i
$874$	44642.2			1.72774
$875$	678.131	−	1174.56i	0.0262000	−	0.0453797i
$876$	−41102.2			−1.58529
$877$	−8693.50	−	15057.6i	−0.334731	−	0.579770i	0.648702	−	0.761042i	$-0.275312\pi$
$877$	−8693.50	−	15057.6i	−0.334731	−	0.579770i	−0.983433	+	0.181272i	$0.941979\pi$
$878$	18358.1	−	31797.1i	0.705643	−	1.22221i
$879$	−3525.85			−0.135295
$880$	1402.33			0.0537186
$881$	17796.0	+	30823.6i	0.680549	+	1.17875i	0.974814	+	0.223021i	$0.0715920\pi$
$881$	17796.0	+	30823.6i	0.680549	+	1.17875i	−0.294265	+	0.955724i	$0.595075\pi$
$882$	7005.76	−	12134.3i	0.267456	−	0.463247i
$883$	15322.9	−	26540.1i	0.583983	−	1.01149i	−0.411018	−	0.911627i	$-0.634827\pi$
$883$	15322.9	−	26540.1i	0.583983	−	1.01149i	0.995001	−	0.0998612i	$-0.0318399\pi$
$884$	35311.7	+	61161.6i	1.34351	+	2.32702i
$885$	670.786			0.0254782
$886$	−63261.7			−2.39878
$887$	16839.3	+	29166.5i	0.637439	+	1.10408i	0.985993	+	0.166788i	$0.0533395\pi$
$887$	16839.3	+	29166.5i	0.637439	+	1.10408i	−0.348554	+	0.937289i	$0.613327\pi$
$888$	3708.33	+	6423.01i	0.140139	+	0.242728i
$889$	−843.605	−	1461.17i	−0.0318263	−	0.0551248i
$890$	2422.99	+	4196.74i	0.0912570	+	0.158062i
$891$	−2390.03	+	4139.65i	−0.0898642	+	0.155649i
$892$	−42537.7	+	73677.5i	−1.59671	+	2.76559i
$893$	27942.3			1.04709
$894$	−7892.14	−	13669.6i	−0.295249	−	0.511386i
$895$	−5643.10			−0.210758
$896$	−7142.10			−0.266296
$897$	14119.2	−	24455.2i	0.525559	−	0.910294i
$898$	−49361.8			−1.83432
$899$	14849.1	+	25719.3i	0.550883	+	0.954158i
$900$	7422.00	−	12855.3i	0.274889	−	0.476121i
$901$	−13128.5	−	22739.1i	−0.485430	−	0.840789i
$902$	−12976.3	+	22475.6i	−0.479006	+	0.829663i
$903$	−125.146	+	216.759i	−0.00461196	+	0.00798814i
$904$	7891.27	−	13668.1i	0.290331	−	0.502869i
$905$	236.005	−	408.773i	0.00866860	−	0.0150145i
$906$	−18880.7	+	32702.3i	−0.692351	+	1.19919i
$907$	−2548.75	+	4414.57i	−0.0933076	+	0.161613i	−0.908901	−	0.417012i	$-0.863077\pi$
$907$	−2548.75	+	4414.57i	−0.0933076	+	0.161613i	0.815593	+	0.578625i	$0.196411\pi$
$908$	12399.8	+	21477.1i	0.453196	+	0.784958i
$909$	−2723.28	+	4716.85i	−0.0993678	+	0.172110i
$910$	−685.980	−	1188.15i	−0.0249890	−	0.0432823i
$911$	7646.47			0.278089			0.139044	−	0.990286i	$-0.455597\pi$
$911$	7646.47			0.278089			0.139044	+	0.990286i	$0.455597\pi$
$912$	1004.42	−	1739.70i	0.0364689	−	0.0631660i
$913$	−82273.0			−2.98230
$914$	44004.5			1.59249
$915$	−795.247	−	1377.41i	−0.0287323	−	0.0497658i
$916$	57596.2			2.07755
$917$	−2921.34	+	5059.90i	−0.105203	+	0.182217i
$918$	6078.51	−	10528.3i	0.218541	−	0.378524i
$919$	12164.2	+	21069.0i	0.436626	+	0.756258i	0.997427	−	0.0716929i	$-0.0228401\pi$
$919$	12164.2	+	21069.0i	0.436626	+	0.756258i	−0.560801	+	0.827950i	$0.689507\pi$
$920$	4439.43	+	7689.32i	0.159091	+	0.275554i
$921$	6373.34	+	11039.0i	0.228023	+	0.394947i
$922$	−13293.3	−	23024.6i	−0.474826	−	0.822424i
$923$	39687.9			1.41532
$924$	6836.59			0.243406
$925$	−5752.76	−	9964.08i	−0.204486	−	0.354180i
$926$	40526.5	−	70193.9i	1.43821	−	2.49105i
$927$	3358.32	−	5816.78i	0.118988	−	0.206093i
$928$	11696.1	+	20258.3i	0.413733	+	0.716607i
$929$	8000.37			0.282544			0.141272	−	0.989971i	$-0.454881\pi$
$929$	8000.37			0.282544			0.141272	+	0.989971i	$0.454881\pi$
$930$	−5203.69			−0.183479
$931$	−9157.37	+	15861.0i	−0.322364	+	0.558350i
$932$	−18885.1	−	32710.0i	−0.663737	−	1.14963i
$933$	29256.1			1.02658
$934$	4011.70	−	6948.46i	0.140542	−	0.243427i
$935$	−11092.9			−0.387998
$936$	−6281.95	−	10880.7i	−0.219372	−	0.379963i
$937$	−49326.3			−1.71976			−0.859882	−	0.510492i	$-0.829463\pi$
$937$	−49326.3			−1.71976			−0.859882	+	0.510492i	$0.829463\pi$
$938$	−6221.82	−	3693.53i	−0.216578	−	0.128569i
$939$	−1525.37			−0.0530122
$940$	6745.14	+	11682.9i	0.234045	+	0.405378i
$941$	−35574.9			−1.23242			−0.616210	−	0.787582i	$-0.711333\pi$
$941$	−35574.9			−1.23242			−0.616210	+	0.787582i	$0.711333\pi$
$942$	−1309.33	+	2267.82i	−0.0452867	+	0.0784390i
$943$	−16619.0			−0.573900
$944$	−705.537	−	1222.03i	−0.0243255	−	0.0421330i
$945$	−74.3581	+	128.792i	−0.00255965	+	0.00443344i
$946$	8062.29			0.277090
$947$	−54225.9			−1.86072			−0.930361	−	0.366644i	$-0.880507\pi$
$947$	−54225.9			−1.86072			−0.930361	+	0.366644i	$0.880507\pi$
$948$	2278.89	+	3947.16i	0.0780749	+	0.135230i
$949$	26984.0	−	46737.7i	0.923012	−	1.59870i
$950$	−15406.3	+	26684.5i	−0.526154	+	0.911325i
$951$	−11227.6	−	19446.9i	−0.382841	−	0.663099i
$952$	−7162.86			−0.243854
$953$	−22742.4			−0.773032			−0.386516	−	0.922283i	$-0.626322\pi$
$953$	−22742.4			−0.773032			−0.386516	+	0.922283i	$0.626322\pi$
$954$	5669.39	+	9819.67i	0.192404	+	0.333253i
$955$	−2475.45	−	4287.60i	−0.0838782	−	0.145281i
$956$	−21612.0	−	37433.0i	−0.731152	−	1.26639i
$957$	−13669.7	−	23676.6i	−0.461732	−	0.799743i
$958$	−24867.4	+	43071.5i	−0.838651	+	1.45259i
$959$	−2146.62	+	3718.05i	−0.0722815	+	0.125195i
$960$	−4669.08			−0.156973
$961$	−3596.86	−	6229.94i	−0.120736	−	0.209122i
$962$	−23638.9			−0.792254
$963$	−19502.4			−0.652602
$964$	−7772.13	+	13461.7i	−0.259672	+	0.449765i
$965$	1692.16			0.0564483
$966$	3476.12	+	6020.81i	0.115779	+	0.200535i
$967$	8278.02	−	14337.9i	0.275288	−	0.476812i	−0.694920	−	0.719087i	$-0.744560\pi$
$967$	8278.02	−	14337.9i	0.275288	−	0.476812i	0.970208	+	0.242275i	$0.0778936\pi$
$968$	−28023.8	−	48538.7i	−0.930496	−	1.61167i
$969$	−7945.34	+	13761.7i	−0.263407	+	0.456234i
$970$	3400.05	−	5889.06i	0.112545	−	0.194934i
$971$	29853.1	−	51707.1i	0.986645	−	1.70892i	0.352258	−	0.935903i	$-0.385414\pi$
$971$	29853.1	−	51707.1i	0.986645	−	1.70892i	0.634386	−	0.773016i	$-0.281253\pi$
$972$	−1652.94	+	2862.98i	−0.0545455	+	0.0944755i
$973$	2012.67	−	3486.05i	0.0663138	−	0.114859i
$974$	−48019.0	+	83171.3i	−1.57970	+	2.73612i
$975$	9745.25	+	16879.3i	0.320100	+	0.554430i
$976$	−1672.89	+	2897.53i	−0.0548647	+	0.0950284i
$977$	19075.5	+	33039.7i	0.624645	+	1.08192i	0.988609	+	0.150504i	$0.0480898\pi$
$977$	19075.5	+	33039.7i	0.624645	+	1.08192i	−0.363964	+	0.931413i	$0.618577\pi$
$978$	15858.2			0.518498
$979$	15853.3	−	27458.8i	0.517544	−	0.896412i
$980$	−8842.18			−0.288218
$981$	−10168.3			−0.330937
$982$	−30284.6	−	52454.5i	−0.984135	−	1.70457i
$983$	54921.2			1.78201			0.891004	−	0.453995i	$-0.150002\pi$
$983$	54921.2			1.78201			0.891004	+	0.453995i	$0.150002\pi$
$984$	−3697.08	+	6403.53i	−0.119775	+	0.207456i
$985$	41.7035	−	72.2326i	0.00134902	−	0.00233657i
$986$	34765.7	+	60216.0i	1.12289	+	1.94490i
$987$	2175.76	+	3768.53i	0.0701675	+	0.121534i
$988$	19932.3	+	34523.7i	0.641832	+	1.11169i
$989$	2581.38	+	4471.07i	0.0829959	+	0.143753i
$990$	4790.38			0.153786
$991$	13938.1			0.446778			0.223389	−	0.974729i	$-0.428288\pi$
$991$	13938.1			0.446778			0.223389	+	0.974729i	$0.428288\pi$
$992$	−14565.8	−	25228.8i	−0.466195	−	0.807474i
$993$	16647.8	−	28834.8i	0.532026	−	0.921496i
$994$	−4885.54	+	8462.00i	−0.155895	+	0.270018i
$995$	−606.723	−	1050.88i	−0.0193311	−	0.0334824i
$996$	−56900.0			−1.81019
$997$	5478.61			0.174031			0.0870157	−	0.996207i	$-0.472267\pi$
$997$	5478.61			0.174031			0.0870157	+	0.996207i	$0.472267\pi$
$998$	9704.16	−	16808.1i	0.307795	−	0.533117i
$999$	1281.19	+	2219.09i	0.0405756	+	0.0702791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.37.2	✓	32
67.29	even	3	inner	201.4.e.a.163.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.2	✓	32	1.1	even	1	trivial
201.4.e.a.163.2	yes	32	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)

\(f(q)\)	\(=\)	\(q+(-2.32403 - 4.02534i) q^{2} +3.00000 q^{3} +(-6.80224 + 11.7818i) q^{4} +1.94047 q^{5} +(-6.97209 - 12.0760i) q^{6} +(-1.41925 + 2.45821i) q^{7} +26.0500 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-2.32403 - 4.02534i) q^{2} +3.00000 q^{3} +(-6.80224 + 11.7818i) q^{4} +1.94047 q^{5} +(-6.97209 - 12.0760i) q^{6} +(-1.41925 + 2.45821i) q^{7} +26.0500 q^{8} +9.00000 q^{9} +(-4.50971 - 7.81105i) q^{10} +(-29.5066 + 51.1068i) q^{11} +(-20.4067 + 35.3455i) q^{12} +(-26.7945 - 46.4094i) q^{13} +13.1935 q^{14} +5.82141 q^{15} +(-6.12299 - 10.6053i) q^{16} +(48.4352 + 83.8923i) q^{17} +(-20.9163 - 36.2281i) q^{18} +(27.3401 + 47.3544i) q^{19} +(-13.1995 + 22.8623i) q^{20} +(-4.25774 + 7.37462i) q^{21} +274.297 q^{22} +(87.8240 + 152.116i) q^{23} +78.1499 q^{24} -121.235 q^{25} +(-124.542 + 215.714i) q^{26} +27.0000 q^{27} +(-19.3081 - 33.4426i) q^{28} +(-77.2126 + 133.736i) q^{29} +(-13.5291 - 23.4331i) q^{30} +(96.1571 - 166.549i) q^{31} +(75.7398 - 131.185i) q^{32} +(-88.5197 + 153.321i) q^{33} +(225.130 - 389.937i) q^{34} +(-2.75400 + 4.77007i) q^{35} +(-61.2201 + 106.036i) q^{36} +(47.4515 + 82.1884i) q^{37} +(127.078 - 220.106i) q^{38} +(-80.3834 - 139.228i) q^{39} +50.5491 q^{40} +(-47.3075 + 81.9391i) q^{41} +39.5805 q^{42} +29.3926 q^{43} +(-401.421 - 695.282i) q^{44} +17.4642 q^{45} +(408.212 - 707.043i) q^{46} +(255.507 - 442.551i) q^{47} +(-18.3690 - 31.8160i) q^{48} +(167.471 + 290.069i) q^{49} +(281.753 + 488.010i) q^{50} +(145.306 + 251.677i) q^{51} +729.049 q^{52} -271.052 q^{53} +(-62.7488 - 108.684i) q^{54} +(-57.2566 + 99.1713i) q^{55} +(-36.9713 + 64.0362i) q^{56} +(82.0202 + 142.063i) q^{57} +717.778 q^{58} +115.227 q^{59} +(-39.5986 + 68.5868i) q^{60} +(-136.607 - 236.611i) q^{61} -893.888 q^{62} +(-12.7732 + 22.1239i) q^{63} -802.054 q^{64} +(-51.9938 - 90.0560i) q^{65} +822.890 q^{66} +(-471.583 - 279.951i) q^{67} -1317.87 q^{68} +(263.472 + 456.347i) q^{69} +25.6016 q^{70} +(-370.299 + 641.377i) q^{71} +234.450 q^{72} +(503.537 + 872.152i) q^{73} +(220.557 - 382.017i) q^{74} -363.704 q^{75} -743.895 q^{76} +(-83.7541 - 145.066i) q^{77} +(-373.627 + 647.141i) q^{78} +(55.8368 - 96.7122i) q^{79} +(-11.8815 - 20.5793i) q^{80} +81.0000 q^{81} +439.777 q^{82} +(697.074 + 1207.37i) q^{83} +(-57.9243 - 100.328i) q^{84} +(93.9871 + 162.790i) q^{85} +(-68.3093 - 118.315i) q^{86} +(-231.638 + 401.208i) q^{87} +(-768.644 + 1331.33i) q^{88} -537.282 q^{89} +(-40.5874 - 70.2994i) q^{90} +152.112 q^{91} -2389.60 q^{92} +(288.471 - 499.647i) q^{93} -2375.22 q^{94} +(53.0526 + 91.8898i) q^{95} +(227.219 - 393.555i) q^{96} +(376.970 + 652.931i) q^{97} +(778.418 - 1348.26i) q^{98} +(-265.559 + 459.962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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