LMFDB - Embedded newform 161.4.e.a.116.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(93,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("161.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.20
Character	$\chi$	$=$	161.116
Dual form			161.4.e.a.93.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.42180 + 4.19468i) q^{2} +(-4.52353 + 7.83499i) q^{3} +(-7.73021 + 13.3891i) q^{4} +(-7.08114 - 12.2649i) q^{5} -43.8204 q^{6} +(17.4156 - 6.30053i) q^{7} -36.1353 q^{8} +(-27.4247 - 47.5010i) q^{9} +(34.2982 - 59.4062i) q^{10} +(-24.1350 + 41.8031i) q^{11} +(-69.9358 - 121.132i) q^{12} -21.7909 q^{13} +(68.6058 + 57.7943i) q^{14} +128.127 q^{15} +(-25.6707 - 44.4630i) q^{16} +(-54.5639 + 94.5074i) q^{17} +(132.834 - 230.076i) q^{18} +(-59.9072 - 103.762i) q^{19} +218.955 q^{20} +(-29.4155 + 164.952i) q^{21} -233.801 q^{22} +(11.5000 + 19.9186i) q^{23} +(163.459 - 283.120i) q^{24} +(-37.7852 + 65.4459i) q^{25} +(-52.7731 - 91.4057i) q^{26} +251.956 q^{27} +(-50.2678 + 281.884i) q^{28} +85.5165 q^{29} +(310.298 + 537.452i) q^{30} +(36.8773 - 63.8733i) q^{31} +(-20.2026 + 34.9920i) q^{32} +(-218.351 - 378.195i) q^{33} -528.571 q^{34} +(-200.598 - 168.986i) q^{35} +847.996 q^{36} +(127.348 + 220.574i) q^{37} +(290.167 - 502.583i) q^{38} +(98.5718 - 170.731i) q^{39} +(255.879 + 443.196i) q^{40} -108.515 q^{41} +(-763.158 + 276.091i) q^{42} -447.497 q^{43} +(-373.138 - 646.294i) q^{44} +(-388.397 + 672.723i) q^{45} +(-55.7014 + 96.4776i) q^{46} +(25.3131 + 43.8436i) q^{47} +464.490 q^{48} +(263.607 - 219.455i) q^{49} -366.033 q^{50} +(-493.643 - 855.015i) q^{51} +(168.448 - 291.761i) q^{52} +(-310.913 + 538.517i) q^{53} +(610.186 + 1056.87i) q^{54} +683.614 q^{55} +(-629.318 + 227.671i) q^{56} +1083.97 q^{57} +(207.104 + 358.714i) q^{58} +(234.718 - 406.544i) q^{59} +(-990.451 + 1715.51i) q^{60} +(-87.0548 - 150.783i) q^{61} +357.237 q^{62} +(-776.900 - 654.469i) q^{63} -606.438 q^{64} +(154.304 + 267.263i) q^{65} +(1057.61 - 1831.83i) q^{66} +(-138.189 + 239.350i) q^{67} +(-843.581 - 1461.12i) q^{68} -208.083 q^{69} +(223.033 - 1250.69i) q^{70} +77.7204 q^{71} +(991.001 + 1716.46i) q^{72} +(-433.307 + 750.510i) q^{73} +(-616.823 + 1068.37i) q^{74} +(-341.845 - 592.093i) q^{75} +1852.38 q^{76} +(-156.945 + 880.089i) q^{77} +954.884 q^{78} +(197.620 + 342.287i) q^{79} +(-363.556 + 629.698i) q^{80} +(-399.264 + 691.545i) q^{81} +(-262.801 - 455.185i) q^{82} -207.255 q^{83} +(-1981.17 - 1668.96i) q^{84} +1545.50 q^{85} +(-1083.75 - 1877.11i) q^{86} +(-386.837 + 670.021i) q^{87} +(872.126 - 1510.57i) q^{88} +(494.394 + 856.315i) q^{89} -3762.48 q^{90} +(-379.501 + 137.294i) q^{91} -355.590 q^{92} +(333.631 + 577.866i) q^{93} +(-122.607 + 212.361i) q^{94} +(-848.424 + 1469.51i) q^{95} +(-182.775 - 316.575i) q^{96} -1132.16 q^{97} +(1558.95 + 574.270i) q^{98} +2647.59 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	2.42180	+	4.19468i	0.856235	+	1.48304i	0.875495	+	0.483228i	$0.160536\pi$
$2$	2.42180	+	4.19468i	0.856235	+	1.48304i	−0.0192595	+	0.999815i	$0.506131\pi$
$3$	−4.52353	+	7.83499i	−0.870555	+	1.50784i	−0.00913057	+	0.999958i	$0.502906\pi$
$3$	−4.52353	+	7.83499i	−0.870555	+	1.50784i	−0.861424	+	0.507886i	$0.830427\pi$
$4$	−7.73021	+	13.3891i	−0.966277	+	1.67364i
$5$	−7.08114	−	12.2649i	−0.633357	−	1.09701i	−0.986861	−	0.161573i	$-0.948343\pi$
$5$	−7.08114	−	12.2649i	−0.633357	−	1.09701i	0.353504	−	0.935433i	$-0.384990\pi$
$6$	−43.8204			−2.98160
$7$	17.4156	−	6.30053i	0.940354	−	0.340196i
$7$	17.4156	−	6.30053i	0.940354	−	0.340196i
$8$	−36.1353			−1.59697
$9$	−27.4247	−	47.5010i	−1.01573	−	1.75930i
$10$	34.2982	−	59.4062i	1.08460	−	1.87859i
$11$	−24.1350	+	41.8031i	−0.661544	+	1.14583i	0.318666	+	0.947867i	$0.396765\pi$
$11$	−24.1350	+	41.8031i	−0.661544	+	1.14583i	−0.980210	+	0.197961i	$0.936568\pi$
$12$	−69.9358	−	121.132i	−1.68239	−	2.91399i
$13$	−21.7909			−0.464900			−0.232450	−	0.972608i	$-0.574674\pi$
$13$	−21.7909			−0.464900			−0.232450	+	0.972608i	$0.574674\pi$
$14$	68.6058	+	57.7943i	1.30969	+	1.10330i
$15$	128.127			2.20549
$16$	−25.6707	−	44.4630i	−0.401105	−	0.694734i
$17$	−54.5639	+	94.5074i	−0.778452	+	1.34832i	0.154382	+	0.988011i	$0.450661\pi$
$17$	−54.5639	+	94.5074i	−0.778452	+	1.34832i	−0.932834	+	0.360307i	$0.882672\pi$
$18$	132.834	−	230.076i	1.73941	−	3.01274i
$19$	−59.9072	−	103.762i	−0.723351	−	1.25288i	−0.959649	−	0.281200i	$-0.909268\pi$
$19$	−59.9072	−	103.762i	−0.723351	−	1.25288i	0.236298	−	0.971681i	$-0.424066\pi$
$20$	218.955			2.44799
$21$	−29.4155	+	164.952i	−0.305666	+	1.71407i
$22$	−233.801			−2.26575
$23$	11.5000	+	19.9186i	0.104257	+	0.180579i
$23$	11.5000	+	19.9186i	0.104257	+	0.180579i
$24$	163.459	−	283.120i	1.39025	−	2.40798i
$25$	−37.7852	+	65.4459i	−0.302282	+	0.523567i
$26$	−52.7731	−	91.4057i	−0.398064	−	0.689467i
$27$	251.956			1.79589
$28$	−50.2678	+	281.884i	−0.339276	+	1.90254i
$29$	85.5165			0.547587			0.273793	−	0.961789i	$-0.411722\pi$
$29$	85.5165			0.547587			0.273793	+	0.961789i	$0.411722\pi$
$30$	310.298	+	537.452i	1.88841	+	3.27083i
$31$	36.8773	−	63.8733i	0.213657	−	0.370064i	−0.739200	−	0.673486i	$-0.764796\pi$
$31$	36.8773	−	63.8733i	0.213657	−	0.370064i	0.952856	+	0.303422i	$0.0981293\pi$
$32$	−20.2026	+	34.9920i	−0.111605	+	0.193305i
$33$	−218.351	−	378.195i	−1.15182	−	1.99501i
$34$	−528.571			−2.66615
$35$	−200.598	−	168.986i	−0.968777	−	0.816109i
$36$	847.996			3.92591
$37$	127.348	+	220.574i	0.565835	+	0.980056i	0.996971	+	0.0777688i	$0.0247796\pi$
$37$	127.348	+	220.574i	0.565835	+	0.980056i	−0.431136	+	0.902287i	$0.641887\pi$
$38$	290.167	−	502.583i	1.23872	−	2.14552i
$39$	98.5718	−	170.731i	0.404721	−	0.700997i
$40$	255.879	+	443.196i	1.01145	+	1.75189i
$41$	−108.515			−0.413346			−0.206673	−	0.978410i	$-0.566264\pi$
$41$	−108.515			−0.413346			−0.206673	+	0.978410i	$0.566264\pi$
$42$	−763.158	+	276.091i	−2.80376	+	1.01433i
$43$	−447.497			−1.58704			−0.793520	−	0.608544i	$-0.791754\pi$
$43$	−447.497			−1.58704			−0.793520	+	0.608544i	$0.791754\pi$
$44$	−373.138	−	646.294i	−1.27847	−	2.21437i
$45$	−388.397	+	672.723i	−1.28664	+	2.22853i
$46$	−55.7014	+	96.4776i	−0.178537	+	0.309236i
$47$	25.3131	+	43.8436i	0.0785595	+	0.136069i	0.902629	−	0.430420i	$-0.141635\pi$
$47$	25.3131	+	43.8436i	0.0785595	+	0.136069i	−0.824069	+	0.566489i	$0.808301\pi$
$48$	464.490			1.39674
$49$	263.607	−	219.455i	0.768533	−	0.639810i
$50$	−366.033			−1.03530
$51$	−493.643	−	855.015i	−1.35537	−	2.34757i
$52$	168.448	−	291.761i	0.449222	−	0.778076i
$53$	−310.913	+	538.517i	−0.805796	+	1.39568i	0.109957	+	0.993936i	$0.464929\pi$
$53$	−310.913	+	538.517i	−0.805796	+	1.39568i	−0.915752	+	0.401743i	$0.868405\pi$
$54$	610.186	+	1056.87i	1.53770	+	2.66338i
$55$	683.614			1.67597
$56$	−629.318	+	227.671i	−1.50172	+	0.543284i
$57$	1083.97			2.51887
$58$	207.104	+	358.714i	0.468863	+	0.812094i
$59$	234.718	−	406.544i	0.517927	−	0.897077i	−0.481856	−	0.876251i	$-0.660037\pi$
$59$	234.718	−	406.544i	0.517927	−	0.897077i	0.999783	−	0.0208261i	$-0.00662963\pi$
$60$	−990.451	+	1715.51i	−2.13111	+	3.69119i
$61$	−87.0548	−	150.783i	−0.182725	−	0.316489i	0.760083	−	0.649827i	$-0.225158\pi$
$61$	−87.0548	−	150.783i	−0.182725	−	0.316489i	−0.942808	+	0.333338i	$0.891825\pi$
$62$	357.237			0.731761
$63$	−776.900	−	654.469i	−1.55365	−	1.30881i
$64$	−606.438			−1.18445
$65$	154.304	+	267.263i	0.294448	+	0.509998i
$66$	1057.61	−	1831.83i	1.97246	−	3.41640i
$67$	−138.189	+	239.350i	−0.251976	+	0.436436i	−0.964070	−	0.265649i	$-0.914414\pi$
$67$	−138.189	+	239.350i	−0.251976	+	0.436436i	0.712093	+	0.702085i	$0.247747\pi$
$68$	−843.581	−	1461.12i	−1.50440	−	2.60570i
$69$	−208.083			−0.363046
$70$	223.033	−	1250.69i	0.380823	−	2.13552i
$71$	77.7204			0.129911			0.0649557	−	0.997888i	$-0.479309\pi$
$71$	77.7204			0.129911			0.0649557	+	0.997888i	$0.479309\pi$
$72$	991.001	+	1716.46i	1.62209	+	2.80954i
$73$	−433.307	+	750.510i	−0.694722	+	1.20329i	0.275552	+	0.961286i	$0.411139\pi$
$73$	−433.307	+	750.510i	−0.694722	+	1.20329i	−0.970274	+	0.242008i	$0.922194\pi$
$74$	−616.823	+	1068.37i	−0.968976	+	1.67832i
$75$	−341.845	−	592.093i	−0.526305	−	0.911587i
$76$	1852.38			2.79583
$77$	−156.945	+	880.089i	−0.232279	+	1.30254i
$78$	954.884			1.38615
$79$	197.620	+	342.287i	0.281442	+	0.487472i	0.971740	−	0.236053i	$-0.0758539\pi$
$79$	197.620	+	342.287i	0.281442	+	0.487472i	−0.690298	+	0.723525i	$0.742521\pi$
$80$	−363.556	+	629.698i	−0.508085	+	0.880029i
$81$	−399.264	+	691.545i	−0.547687	+	0.948621i
$82$	−262.801	−	455.185i	−0.353922	−	0.613010i
$83$	−207.255			−0.274087			−0.137044	−	0.990565i	$-0.543760\pi$
$83$	−207.255			−0.274087			−0.137044	+	0.990565i	$0.543760\pi$
$84$	−1981.17	−	1668.96i	−2.57338	−	2.16784i
$85$	1545.50			1.97215
$86$	−1083.75	−	1877.11i	−1.35888	−	2.35365i
$87$	−386.837	+	670.021i	−0.476704	+	0.825676i
$88$	872.126	−	1510.57i	1.05647	−	1.82985i
$89$	494.394	+	856.315i	0.588827	+	1.01988i	0.994386	+	0.105810i	$0.0337435\pi$
$89$	494.394	+	856.315i	0.588827	+	1.01988i	−0.405559	+	0.914069i	$0.632923\pi$
$90$	−3762.48			−4.40666
$91$	−379.501	+	137.294i	−0.437171	+	0.158157i
$92$	−355.590			−0.402965
$93$	333.631	+	577.866i	0.371999	+	0.644322i
$94$	−122.607	+	212.361i	−0.134531	+	0.233014i
$95$	−848.424	+	1469.51i	−0.916278	+	1.58704i
$96$	−182.775	−	316.575i	−0.194316	−	0.336566i
$97$	−1132.16			−1.18509			−0.592543	−	0.805539i	$-0.701876\pi$
$97$	−1132.16			−1.18509			−0.592543	+	0.805539i	$0.701876\pi$
$98$	1558.95	+	574.270i	1.60691	+	0.591939i
$99$	2647.59			2.68780
$100$	−584.175	−	1011.82i	−0.584175	−	1.01182i
$101$	219.315	−	379.865i	0.216066	−	0.374237i	−0.737536	−	0.675308i	$-0.764011\pi$
$101$	219.315	−	379.865i	0.216066	−	0.374237i	0.953602	+	0.301071i	$0.0973441\pi$
$102$	2391.01	−	4141.35i	2.32103	−	4.02014i
$103$	460.827	+	798.176i	0.440841	+	0.763560i	0.997752	−	0.0670126i	$-0.0213468\pi$
$103$	460.827	+	798.176i	0.440841	+	0.763560i	−0.556911	+	0.830572i	$0.688013\pi$
$104$	787.420			0.742432
$105$	2231.41	−	807.269i	2.07394	−	0.750299i
$106$	−3011.87			−2.75980
$107$	884.358	+	1531.75i	0.799010	+	1.38393i	0.920261	+	0.391304i	$0.127976\pi$
$107$	884.358	+	1531.75i	0.799010	+	1.38393i	−0.121251	+	0.992622i	$0.538691\pi$
$108$	−1947.67	+	3373.47i	−1.73532	+	3.00567i
$109$	−359.135	+	622.040i	−0.315586	+	0.546611i	−0.979562	−	0.201143i	$-0.935534\pi$
$109$	−359.135	+	622.040i	−0.315586	+	0.546611i	0.663976	+	0.747754i	$0.268868\pi$
$110$	1655.58	+	2867.54i	1.43503	+	2.48554i
$111$	−2304.26			−1.97036
$112$	−727.211	−	612.611i	−0.613527	−	0.516842i
$113$	1317.27			1.09662			0.548311	−	0.836274i	$-0.315271\pi$
$113$	1317.27			1.09662			0.548311	+	0.836274i	$0.315271\pi$
$114$	2625.16	+	4546.90i	2.15674	+	3.73558i
$115$	162.866	−	282.093i	0.132064	−	0.228742i
$116$	−661.061	+	1144.99i	−0.529120	+	0.916463i
$117$	597.609	+	1035.09i	0.472213	+	0.817898i
$118$	2273.76			1.77387
$119$	−354.817	+	1989.68i	−0.273328	+	1.53272i
$120$	−4629.92			−3.52210
$121$	−499.499	−	865.157i	−0.375281	−	0.650005i
$122$	421.658	−	730.334i	0.312911	−	0.541978i
$123$	490.871	−	850.214i	0.359840	−	0.623262i
$124$	570.138	+	987.508i	0.412903	+	0.715168i
$125$	−700.036			−0.500905
$126$	863.792	−	4843.84i	0.610735	−	3.42479i
$127$	1140.07			0.796575			0.398288	−	0.917261i	$-0.369605\pi$
$127$	1140.07			0.796575			0.398288	+	0.917261i	$0.369605\pi$
$128$	−1307.05	−	2263.88i	−0.902563	−	1.56328i
$129$	2024.27	−	3506.14i	1.38160	−	2.39301i
$130$	−747.388	+	1294.51i	−0.504233	+	0.873357i
$131$	389.085	+	673.915i	0.259500	+	0.449468i	0.966108	−	0.258138i	$-0.0831088\pi$
$131$	389.085	+	673.915i	0.259500	+	0.449468i	−0.706608	+	0.707605i	$0.749775\pi$
$132$	6751.61			4.45191
$133$	−1697.08	−	1429.64i	−1.10643	−	0.932070i
$134$	−1338.66			−0.863004
$135$	−1784.14	−	3090.21i	−1.13744	−	1.97010i
$136$	1971.68	−	3415.05i	1.24316	−	2.15322i
$137$	686.744	−	1189.48i	0.428266	−	0.741779i	−0.568453	−	0.822716i	$-0.692458\pi$
$137$	686.744	−	1189.48i	0.428266	−	0.741779i	0.996719	+	0.0809368i	$0.0257912\pi$
$138$	−503.934	−	872.839i	−0.310853	−	0.538413i
$139$	−1907.88			−1.16420			−0.582101	−	0.813116i	$-0.697769\pi$
$139$	−1907.88			−1.16420			−0.582101	+	0.813116i	$0.697769\pi$
$140$	3813.24	−	1379.53i	2.30198	−	0.832798i
$141$	−458.019			−0.273561
$142$	188.223	+	326.012i	0.111235	+	0.192664i
$143$	525.923	−	910.926i	0.307552	−	0.532696i
$144$	−1408.02	+	2438.77i	−0.814829	+	1.41133i
$145$	−605.555	−	1048.85i	−0.346818	−	0.600706i
$146$	−4197.53			−2.37938
$147$	526.994	+	3058.07i	0.295685	+	1.71582i
$148$	−3937.72			−2.18701
$149$	434.273	+	752.183i	0.238772	+	0.413566i	0.960362	−	0.278755i	$-0.0899218\pi$
$149$	434.273	+	752.183i	0.238772	+	0.413566i	−0.721590	+	0.692321i	$0.756588\pi$
$150$	1655.76	−	2867.86i	0.901282	−	1.56107i
$151$	1439.32	−	2492.97i	0.775694	−	1.34354i	−0.158709	−	0.987325i	$-0.550733\pi$
$151$	1439.32	−	2492.97i	0.775694	−	1.34354i	0.934404	−	0.356216i	$-0.115933\pi$
$152$	2164.77	+	3749.49i	1.15517	+	2.00081i
$153$	5985.60			3.16279
$154$	−4071.78	+	1473.07i	−2.13061	+	0.770800i
$155$	−1044.53			−0.541283
$156$	1523.96	+	2639.58i	0.782145	+	1.35472i
$157$	−124.752	+	216.077i	−0.0634160	+	0.109840i	−0.895990	−	0.444074i	$-0.853533\pi$
$157$	−124.752	+	216.077i	−0.0634160	+	0.109840i	0.832574	+	0.553913i	$0.186866\pi$
$158$	−957.190	+	1657.90i	−0.481962	+	0.834782i
$159$	−2812.85	−	4872.00i	−1.40298	−	2.43003i
$160$	572.231			0.282743
$161$	325.777	+	274.438i	0.159471	+	0.134340i
$162$	−3867.74			−1.87579
$163$	−1723.03	−	2984.37i	−0.827963	−	1.43407i	−0.899634	−	0.436645i	$-0.856167\pi$
$163$	−1723.03	−	2984.37i	−0.827963	−	1.43407i	0.0716713	−	0.997428i	$-0.477167\pi$
$164$	838.844	−	1452.92i	0.399407	−	0.691793i
$165$	−3092.35	+	5356.11i	−1.45903	+	2.52711i
$166$	−501.931	−	869.370i	−0.234683	−	0.406483i
$167$	2953.64			1.36862			0.684311	−	0.729190i	$-0.260103\pi$
$167$	2953.64			1.36862			0.684311	+	0.729190i	$0.260103\pi$
$168$	1062.94	−	5960.58i	0.488140	−	2.73732i
$169$	−1722.16			−0.783868
$170$	3742.89	+	6482.87i	1.68862	+	2.92478i
$171$	−3285.88	+	5691.31i	−1.46946	+	2.54518i
$172$	3459.25	−	5991.60i	1.53352	−	2.65613i
$173$	579.051	+	1002.95i	0.254477	+	0.440767i	0.964753	−	0.263156i	$-0.0847635\pi$
$173$	579.051	+	1002.95i	0.254477	+	0.440767i	−0.710277	+	0.703923i	$0.751430\pi$
$174$	−3747.36			−1.63268
$175$	−245.709	+	1377.85i	−0.106136	+	0.595174i
$176$	2478.25			1.06139
$177$	2123.51	+	3678.03i	0.901768	+	1.56191i
$178$	−2394.64	+	4147.64i	−1.00835	+	1.74651i
$179$	99.9028	−	173.037i	0.0417156	−	0.0722535i	−0.844414	−	0.535692i	$-0.820051\pi$
$179$	99.9028	−	173.037i	0.0417156	−	0.0722535i	0.886129	+	0.463438i	$0.153384\pi$
$180$	−6004.78	−	10400.6i	−2.48650	−	4.30674i
$181$	840.861			0.345308			0.172654	−	0.984983i	$-0.444766\pi$
$181$	840.861			0.345308			0.172654	+	0.984983i	$0.444766\pi$
$182$	−1494.98	−	1259.39i	−0.608875	−	0.512923i
$183$	1575.18			0.636288
$184$	−415.556	−	719.764i	−0.166496	−	0.288379i
$185$	1803.54	−	3123.83i	0.716751	−	1.24145i
$186$	−1615.97	+	2798.95i	−0.637038	+	1.10338i
$187$	−2633.80	−	4561.88i	−1.02996	−	1.78394i
$188$	−782.703			−0.303641
$189$	4387.96	−	1587.45i	1.68877	−	0.610954i
$190$	−8218.84			−3.13820
$191$	−339.633	−	588.262i	−0.128665	−	0.222854i	0.794495	−	0.607271i	$-0.207736\pi$
$191$	−339.633	−	588.262i	−0.128665	−	0.222854i	−0.923160	+	0.384417i	$0.874402\pi$
$192$	2743.24	−	4751.44i	1.03113	−	1.78597i
$193$	−34.0371	+	58.9540i	−0.0126945	+	0.0219876i	−0.872303	−	0.488966i	$-0.837374\pi$
$193$	−34.0371	+	58.9540i	−0.0126945	+	0.0219876i	0.859608	+	0.510953i	$0.170708\pi$
$194$	−2741.86	−	4749.04i	−1.01471	−	1.75753i
$195$	−2792.00			−1.02533
$196$	900.574	+	5225.90i	0.328197	+	1.90448i
$197$	−1230.56			−0.445046			−0.222523	−	0.974927i	$-0.571429\pi$
$197$	−1230.56			−0.445046			−0.222523	+	0.974927i	$0.571429\pi$
$198$	6411.92	+	11105.8i	2.30139	+	3.98612i
$199$	1457.70	−	2524.80i	0.519263	−	0.899390i	−0.480486	−	0.877002i	$-0.659540\pi$
$199$	1457.70	−	2524.80i	0.519263	−	0.899390i	0.999749	−	0.0223879i	$-0.00712687\pi$
$200$	1365.38	−	2364.91i	0.482735	−	0.836121i
$201$	−1250.20	−	2165.41i	−0.438719	−	0.759883i
$202$	2124.55			0.740013
$203$	1489.32	−	538.799i	0.514925	−	0.186287i
$204$	15263.9			5.23865
$205$	768.410	+	1330.93i	0.261796	+	0.453443i
$206$	−2232.06	+	3866.04i	−0.754928	+	1.30757i
$207$	630.769	−	1092.52i	0.211794	−	0.366839i
$208$	559.388	+	968.888i	0.186474	+	0.322982i
$209$	5783.45			1.91411
$210$	8790.26	+	7405.02i	2.88850	+	2.43331i
$211$	5163.14			1.68458			0.842288	−	0.539028i	$-0.181208\pi$
$211$	5163.14			1.68458			0.842288	+	0.539028i	$0.181208\pi$
$212$	−4806.85	−	8325.70i	−1.55724	−	2.69723i
$213$	−351.571	+	608.938i	−0.113095	+	0.195886i
$214$	−4283.47	+	7419.19i	−1.36828	+	2.36993i
$215$	3168.79	+	5488.51i	1.00516	+	1.74099i
$216$	−9104.50			−2.86798
$217$	239.804	−	1344.74i	0.0750184	−	0.420676i
$218$	−3479.01			−1.08086
$219$	−3920.16	−	6789.91i	−1.20959	−	2.09507i
$220$	−5284.48	+	9153.00i	−1.61945	+	2.80498i
$221$	1188.99	−	2059.40i	0.361902	−	0.626833i
$222$	−5580.44	−	9665.61i	−1.68709	−	2.92213i
$223$	459.966			0.138124			0.0690618	−	0.997612i	$-0.477999\pi$
$223$	459.966			0.138124			0.0690618	+	0.997612i	$0.477999\pi$
$224$	−131.373	+	736.694i	−0.0391863	+	0.219743i
$225$	4144.99			1.22815
$226$	3190.16	+	5525.53i	0.938967	+	1.62634i
$227$	−2401.07	+	4158.78i	−0.702048	+	1.21598i	0.265699	+	0.964056i	$0.414397\pi$
$227$	−2401.07	+	4158.78i	−0.702048	+	1.21598i	−0.967746	+	0.251926i	$0.918936\pi$
$228$	−8379.32	+	14513.4i	−2.43392	+	4.21568i
$229$	3225.29	+	5586.37i	0.930713	+	1.61204i	0.782106	+	0.623146i	$0.214146\pi$
$229$	3225.29	+	5586.37i	0.930713	+	1.61204i	0.148607	+	0.988896i	$0.452521\pi$
$230$	1577.72			0.452311
$231$	−6185.55	−	5210.77i	−1.76181	−	1.48417i
$232$	−3090.16			−0.874480
$233$	−555.409	−	961.996i	−0.156163	−	0.270483i	0.777319	−	0.629107i	$-0.216579\pi$
$233$	−555.409	−	961.996i	−0.156163	−	0.270483i	−0.933482	+	0.358624i	$0.883246\pi$
$234$	−2894.58	+	5013.55i	−0.808651	+	1.40063i
$235$	358.492	−	620.926i	0.0995124	−	0.172361i
$236$	3628.85	+	6285.35i	1.00092	+	1.73365i
$237$	−3575.76			−0.980044
$238$	−9205.38	+	3330.27i	−2.50713	+	0.907015i
$239$	−1498.95			−0.405685			−0.202843	−	0.979211i	$-0.565018\pi$
$239$	−1498.95			−0.405685			−0.202843	+	0.979211i	$0.565018\pi$
$240$	−3289.12	−	5696.92i	−0.884632	−	1.53223i
$241$	−1569.92	+	2719.19i	−0.419617	+	0.726797i	−0.995901	−	0.0904520i	$-0.971169\pi$
$241$	−1569.92	+	2719.19i	−0.419617	+	0.726797i	0.576284	+	0.817249i	$0.304502\pi$
$242$	2419.37	−	4190.47i	0.642657	−	1.11311i
$243$	−210.760	−	365.048i	−0.0556390	−	0.0963696i
$244$	2691.81			0.706252
$245$	−4558.23	−	1679.12i	−1.18863	−	0.437857i
$246$	4755.17			1.23243
$247$	1305.43	+	2261.07i	0.336286	+	0.582464i
$248$	−1332.57	+	2308.08i	−0.341203	+	0.590981i
$249$	937.527	−	1623.84i	0.238608	−	0.413281i
$250$	−1695.35	−	2936.43i	−0.428893	−	0.742864i
$251$	−3363.59			−0.845847			−0.422924	−	0.906165i	$-0.638996\pi$
$251$	−3363.59			−0.845847			−0.422924	+	0.906165i	$0.638996\pi$
$252$	14768.4	−	5342.82i	3.69174	−	1.33558i
$253$	−1110.21			−0.275883
$254$	2761.03	+	4782.24i	0.682056	+	1.18136i
$255$	−6991.12	+	12109.0i	−1.71687	+	2.97370i
$256$	3905.07	−	6763.78i	0.953386	−	1.65131i
$257$	1522.48	+	2637.01i	0.369532	+	0.640048i	0.989492	−	0.144585i	$-0.0461847\pi$
$257$	1522.48	+	2637.01i	0.369532	+	0.640048i	−0.619960	+	0.784633i	$0.712851\pi$
$258$	19609.5			4.73191
$259$	3607.58	+	3039.06i	0.865497	+	0.729105i
$260$	−4771.22			−1.13807
$261$	−2345.27	−	4062.12i	−0.556200	−	0.963367i
$262$	−1884.57	+	3264.17i	−0.444386	+	0.769700i
$263$	−2079.00	+	3600.93i	−0.487439	+	0.844269i	−0.999896	−	0.0144442i	$-0.995402\pi$
$263$	−2079.00	+	3600.93i	−0.487439	+	0.844269i	0.512457	+	0.858713i	$0.328735\pi$
$264$	7890.19	+	13666.2i	1.83942	+	3.18597i
$265$	8806.48			2.04143
$266$	1886.89	−	10581.0i	0.434934	−	2.43896i
$267$	−8945.63			−2.05042
$268$	−2136.45	−	3700.45i	−0.486958	−	0.843436i
$269$	−1390.74	+	2408.83i	−0.315222	+	0.545981i	−0.979485	−	0.201519i	$-0.935412\pi$
$269$	−1390.74	+	2408.83i	−0.315222	+	0.545981i	0.664263	+	0.747499i	$0.268746\pi$
$270$	8641.64	−	14967.8i	1.94783	−	3.37373i
$271$	354.004	+	613.153i	0.0793513	+	0.137441i	0.902970	−	0.429703i	$-0.141382\pi$
$271$	354.004	+	613.153i	0.0793513	+	0.137441i	−0.823619	+	0.567144i	$0.808048\pi$
$272$	5602.78			1.24896
$273$	640.990	−	3594.44i	0.142104	−	0.796871i
$274$	6652.62			1.46679
$275$	−1823.89	−	3159.08i	−0.399945	−	0.692725i
$276$	1608.52	−	2786.04i	0.350803	−	0.607609i
$277$	1632.29	−	2827.21i	0.354061	−	0.613251i	−0.632896	−	0.774237i	$-0.718134\pi$
$277$	1632.29	−	2827.21i	0.354061	−	0.613251i	0.986957	+	0.160985i	$0.0514672\pi$
$278$	−4620.50	−	8002.94i	−0.996831	−	1.72656i
$279$	−4045.40			−0.868070
$280$	7248.66	+	6106.35i	1.54711	+	1.30330i
$281$	4343.07			0.922014			0.461007	−	0.887396i	$-0.347488\pi$
$281$	4343.07			0.922014			0.461007	+	0.887396i	$0.347488\pi$
$282$	−1109.23	−	1921.24i	−0.234233	−	0.405703i
$283$	−2520.78	+	4366.11i	−0.529486	+	0.917097i	0.469922	+	0.882708i	$0.344282\pi$
$283$	−2520.78	+	4366.11i	−0.529486	+	0.917097i	−0.999409	+	0.0343893i	$0.989051\pi$
$284$	−600.795	+	1040.61i	−0.125530	+	0.217425i
$285$	−7675.75	−	13294.8i	−1.59534	−	2.76321i
$286$	5094.72			1.05335
$287$	−1889.85	+	683.702i	−0.388692	+	0.140619i
$288$	2216.21			0.453442
$289$	−3497.93	−	6058.60i	−0.711975	−	1.23318i
$290$	2933.06	−	5080.21i	0.593915	−	1.02869i
$291$	5121.36	−	8870.45i	1.03168	−	1.78692i
$292$	−6699.11	−	11603.2i	−1.34259	−	2.32543i
$293$	−2543.20			−0.507084			−0.253542	−	0.967324i	$-0.581596\pi$
$293$	−2543.20			−0.507084			−0.253542	+	0.967324i	$0.581596\pi$
$294$	−11551.3	+	9616.60i	−2.29146	+	1.90766i
$295$	−6648.30			−1.31213
$296$	−4601.77	−	7970.49i	−0.903622	−	1.56512i
$297$	−6080.96	+	10532.5i	−1.18806	+	2.05778i
$298$	−2103.44	+	3643.27i	−0.408890	+	0.708219i
$299$	−250.595	−	434.043i	−0.0484692	−	0.0839511i
$300$	10570.1			2.03423
$301$	−7793.44	+	2819.47i	−1.49238	+	0.539905i
$302$	13942.9			2.65671
$303$	1984.16	+	3436.66i	0.376194	+	0.651588i
$304$	−3075.72	+	5327.31i	−0.580279	+	1.00507i
$305$	−1232.90	+	2135.44i	−0.231460	+	0.400901i
$306$	14495.9	+	25107.6i	2.70809	+	4.69055i
$307$	1389.36			0.258290			0.129145	−	0.991626i	$-0.458777\pi$
$307$	1389.36			0.258290			0.129145	+	0.991626i	$0.458777\pi$
$308$	−10570.4	−	8904.63i	−1.95554	−	1.64737i
$309$	−8338.27			−1.53511
$310$	−2529.65	−	4381.48i	−0.463466	−	0.802746i
$311$	2759.62	−	4779.80i	0.503163	−	0.871504i	−0.496830	−	0.867848i	$-0.665503\pi$
$311$	2759.62	−	4779.80i	0.503163	−	0.871504i	0.999993	−	0.00365645i	$-0.00116389\pi$
$312$	−3561.92	+	6169.43i	−0.646327	+	1.11947i
$313$	−2360.75	−	4088.95i	−0.426318	−	0.738405i	0.570224	−	0.821489i	$-0.306856\pi$
$313$	−2360.75	−	4088.95i	−0.426318	−	0.738405i	−0.996543	+	0.0830839i	$0.973523\pi$
$314$	−1208.50			−0.217196
$315$	−2525.66	+	14163.0i	−0.451761	+	2.53331i
$316$	−6110.57			−1.08780
$317$	−1049.02	−	1816.95i	−0.185863	−	0.321925i	0.758004	−	0.652250i	$-0.226175\pi$
$317$	−1049.02	−	1816.95i	−0.185863	−	0.321925i	−0.943867	+	0.330326i	$0.892841\pi$
$318$	13624.3	−	23598.0i	2.40256	−	4.16135i
$319$	−2063.94	+	3574.85i	−0.362253	+	0.627440i
$320$	4294.28	+	7437.91i	0.750179	+	1.29935i
$321$	−16001.7			−2.78233
$322$	−362.213	+	2031.16i	−0.0626875	+	0.351529i
$323$	13075.1			2.25238
$324$	−6172.79	−	10691.6i	−1.05843	−	1.83326i
$325$	823.373	−	1426.12i	0.140531	−	0.243406i
$326$	8345.65	−	14455.1i	1.41786	−	2.45581i
$327$	−3249.12	−	5627.63i	−0.549470	−	0.951709i
$328$	3921.22			0.660102
$329$	717.081	+	604.077i	0.120164	+	0.101227i
$330$	−29956.2			−4.99708
$331$	−1749.16	−	3029.63i	−0.290461	−	0.503092i	0.683458	−	0.729990i	$-0.260475\pi$
$331$	−1749.16	−	3029.63i	−0.290461	−	0.503092i	−0.973919	+	0.226897i	$0.927142\pi$
$332$	1602.13	−	2774.97i	0.264844	−	0.458724i
$333$	6984.98	−	12098.3i	1.14947	−	1.99095i
$334$	7153.13	+	12389.6i	1.17186	+	2.02972i
$335$	3914.13			0.638364
$336$	8089.37	−	2926.53i	1.31343	−	0.475164i
$337$	7647.85			1.23622			0.618108	−	0.786093i	$-0.287899\pi$
$337$	7647.85			1.23622			0.618108	+	0.786093i	$0.287899\pi$
$338$	−4170.72	−	7223.90i	−0.671175	−	1.16251i
$339$	−5958.72	+	10320.8i	−0.954670	+	1.65354i
$340$	−11947.0	+	20692.9i	−1.90564	+	3.30067i
$341$	1780.07	+	3083.17i	0.282686	+	0.489627i
$342$	−31831.0			−5.03281
$343$	3208.19	−	5482.80i	0.505032	−	0.863101i
$344$	16170.5			2.53446
$345$	1473.46	+	2552.11i	0.229938	+	0.398264i
$346$	−2804.69	+	4857.87i	−0.435784	+	0.754800i
$347$	2070.92	−	3586.94i	0.320382	−	0.554919i	−0.660185	−	0.751103i	$-0.729522\pi$
$347$	2070.92	−	3586.94i	0.320382	−	0.554919i	0.980567	+	0.196185i	$0.0628553\pi$
$348$	−5980.66	−	10358.8i	−0.921256	−	1.59566i
$349$	7699.13			1.18087			0.590437	−	0.807084i	$-0.298955\pi$
$349$	7699.13			1.18087			0.590437	+	0.807084i	$0.298955\pi$
$350$	−6374.68	+	2306.20i	−0.973545	+	0.352204i
$351$	−5490.34			−0.834908
$352$	−975.182	−	1689.06i	−0.147663	−	0.255760i
$353$	971.851	−	1683.29i	0.146534	−	0.253804i	−0.783410	−	0.621505i	$-0.786522\pi$
$353$	971.851	−	1683.29i	0.146534	−	0.253804i	0.929944	+	0.367701i	$0.119855\pi$
$354$	−10285.4	+	17814.9i	−1.54425	+	2.67472i
$355$	−550.349	−	953.233i	−0.0822803	−	0.142514i
$356$	−15287.1			−2.27588
$357$	−13984.1	−	11780.4i	−2.07316	−	1.74646i
$358$	967.778			0.142873
$359$	2311.37	+	4003.41i	0.339804	+	0.588557i	0.984396	−	0.175970i	$-0.0563061\pi$
$359$	2311.37	+	4003.41i	0.339804	+	0.588557i	−0.644592	+	0.764527i	$0.722973\pi$
$360$	14034.8	−	24309.1i	2.05473	−	3.55889i
$361$	−3748.26	+	6492.17i	−0.546473	+	0.946519i
$362$	2036.40	+	3527.14i	0.295665	+	0.512106i
$363$	9037.99			1.30681
$364$	1095.38	−	6142.50i	0.157729	−	0.884491i
$365$	12273.2			1.76003
$366$	3814.77	+	6607.38i	0.544812	+	0.943643i
$367$	4570.45	−	7916.25i	0.650069	−	1.12595i	−0.333036	−	0.942914i	$-0.608073\pi$
$367$	4570.45	−	7916.25i	0.650069	−	1.12595i	0.983106	−	0.183039i	$-0.0585934\pi$
$368$	590.427	−	1022.65i	0.0836362	−	0.144862i
$369$	2975.99	+	5154.57i	0.419848	+	0.727199i
$370$	17471.3			2.45483
$371$	−2021.80	+	11337.5i	−0.282928	+	1.58656i
$372$	−10316.2			−1.43782
$373$	−1637.40	−	2836.06i	−0.227296	−	0.393688i	0.729710	−	0.683757i	$-0.239655\pi$
$373$	−1637.40	−	2836.06i	−0.227296	−	0.393688i	−0.957006	+	0.290069i	$0.906322\pi$
$374$	12757.1	−	22095.9i	1.76378	−	3.05495i
$375$	3166.64	−	5484.78i	0.436065	−	0.755287i
$376$	−914.697	−	1584.30i	−0.125457	−	0.217298i
$377$	−1863.48			−0.254573
$378$	17285.6	+	14561.6i	2.35205	+	1.98140i
$379$	4917.53			0.666482			0.333241	−	0.942842i	$-0.391858\pi$
$379$	4917.53			0.666482			0.333241	+	0.942842i	$0.391858\pi$
$380$	−13117.0	−	22719.3i	−1.77076	−	3.06704i
$381$	−5157.16	+	8932.46i	−0.693462	+	1.20111i
$382$	1645.05	−	2849.30i	0.220335	−	0.381631i
$383$	1830.06	+	3169.76i	0.244156	+	0.422890i	0.961894	−	0.273423i	$-0.0881558\pi$
$383$	1830.06	+	3169.76i	0.244156	+	0.422890i	−0.717738	+	0.696313i	$0.754823\pi$
$384$	23649.9			3.14292
$385$	11905.6	−	4307.13i	1.57601	−	0.570160i
$386$	−329.724			−0.0434780
$387$	12272.5	+	21256.6i	1.61200	+	2.79207i
$388$	8751.83	−	15158.6i	1.14512	−	1.98341i
$389$	1298.51	−	2249.08i	0.169247	−	0.293144i	−0.768909	−	0.639359i	$-0.779200\pi$
$389$	1298.51	−	2249.08i	0.169247	−	0.293144i	0.938155	+	0.346215i	$0.112533\pi$
$390$	−6761.67	−	11711.6i	−0.877924	−	1.52061i
$391$	−2509.94			−0.324637
$392$	−9525.51	+	7930.07i	−1.22732	+	1.02176i
$393$	−7040.16			−0.903637
$394$	−2980.18	−	5161.82i	−0.381064	−	0.660022i
$395$	2798.75	−	4847.57i	0.356507	−	0.617488i
$396$	−20466.4	+	35448.9i	−2.59716	+	4.49841i
$397$	−1829.24	−	3168.34i	−0.231252	−	0.400540i	0.726925	−	0.686717i	$-0.240949\pi$
$397$	−1829.24	−	3168.34i	−0.231252	−	0.400540i	−0.958177	+	0.286177i	$0.907615\pi$
$398$	14121.0			1.77845
$399$	18878.0	−	6829.58i	2.36863	−	0.856909i
$400$	3879.89			0.484987
$401$	1993.96	+	3453.64i	0.248313	+	0.430092i	0.963058	−	0.269294i	$-0.0867904\pi$
$401$	1993.96	+	3453.64i	0.248313	+	0.430092i	−0.714745	+	0.699386i	$0.753457\pi$
$402$	6055.47	−	10488.4i	0.751292	−	1.30128i
$403$	−803.588	+	1391.86i	−0.0993290	+	0.172043i
$404$	3390.70	+	5872.87i	0.417559	+	0.723233i
$405$	11309.0			1.38752
$406$	5866.92	+	4942.36i	0.717169	+	0.604151i
$407$	−12294.2			−1.49730
$408$	17837.9	+	30896.2i	2.16449	+	3.74900i
$409$	−6688.72	+	11585.2i	−0.808646	+	1.40062i	0.105156	+	0.994456i	$0.466466\pi$
$409$	−6688.72	+	11585.2i	−0.808646	+	1.40062i	−0.913802	+	0.406160i	$0.866868\pi$
$410$	−3721.87	+	6446.47i	−0.448317	+	0.776508i
$411$	6213.02	+	10761.3i	0.745658	+	1.29152i
$412$	−14249.2			−1.70390
$413$	1526.32	−	8559.06i	0.181853	−	1.01977i
$414$	6110.38			0.725383
$415$	1467.61	+	2541.97i	0.173595	+	0.300675i
$416$	440.233	−	762.506i	0.0518851	−	0.0898676i
$417$	8630.36	−	14948.2i	1.01350	−	1.75544i
$418$	14006.4	+	24259.7i	1.63893	+	2.83871i
$419$	−16050.8			−1.87144			−0.935721	−	0.352740i	$-0.885250\pi$
$419$	−16050.8			−1.87144			−0.935721	+	0.352740i	$0.885250\pi$
$420$	−6440.68	+	36117.0i	−0.748269	+	4.19602i
$421$	−16936.8			−1.96069			−0.980345	−	0.197291i	$-0.936786\pi$
$421$	−16936.8			−1.96069			−0.980345	+	0.197291i	$0.936786\pi$
$422$	12504.1	+	21657.7i	1.44239	+	2.49830i
$423$	1388.41	−	2404.80i	0.159591	−	0.276419i
$424$	11234.9	−	19459.5i	1.28683	−	2.22886i
$425$	−4123.41	−	7141.96i	−0.470623	−	0.815144i
$426$	−3405.73			−0.387344
$427$	−2466.13	−	2077.49i	−0.279495	−	0.235449i
$428$	−27345.1			−3.08826
$429$	4758.06	+	8241.21i	0.535481	+	0.927481i
$430$	−15348.4	+	26584.1i	−1.72131	+	2.98140i
$431$	5979.39	−	10356.6i	0.668253	−	1.15745i	−0.310139	−	0.950691i	$-0.600376\pi$
$431$	5979.39	−	10356.6i	0.668253	−	1.15745i	0.978392	−	0.206758i	$-0.0662911\pi$
$432$	−6467.89	−	11202.7i	−0.720339	−	1.24766i
$433$	7076.96			0.785444			0.392722	−	0.919657i	$-0.371533\pi$
$433$	7076.96			0.785444			0.392722	+	0.919657i	$0.371533\pi$
$434$	6221.50	−	2250.78i	0.688114	−	0.248942i
$435$	10957.0			1.20769
$436$	−5552.38	−	9617.00i	−0.609887	−	1.05635i
$437$	1377.87	−	2386.54i	0.150829	−	0.261244i
$438$	18987.7	−	32887.6i	2.07138	−	3.58774i
$439$	−7101.19	−	12299.6i	−0.772030	−	1.33720i	−0.936448	−	0.350805i	$-0.885908\pi$
$439$	−7101.19	−	12299.6i	−0.772030	−	1.33720i	0.164418	−	0.986391i	$-0.447425\pi$
$440$	−24702.6			−2.67648
$441$	−17653.7	−	6503.09i	−1.90624	−	0.702202i
$442$	11518.0			1.23949
$443$	−6041.18	−	10463.6i	−0.647913	−	1.12222i	−0.983621	−	0.180252i	$-0.942309\pi$
$443$	−6041.18	−	10463.6i	−0.647913	−	1.12222i	0.335708	−	0.941966i	$-0.391025\pi$
$444$	17812.4	−	30852.0i	1.90392	−	3.29768i
$445$	7001.74	−	12127.4i	0.745875	−	1.29189i
$446$	1113.94	+	1929.41i	0.118266	+	0.204843i
$447$	−7857.80			−0.831457
$448$	−10561.5	+	3820.88i	−1.11380	+	0.402946i
$449$	17576.9			1.84745			0.923724	−	0.383059i	$-0.125129\pi$
$449$	17576.9			1.84745			0.923724	+	0.383059i	$0.125129\pi$
$450$	10038.3	+	17386.9i	1.05158	+	1.82139i
$451$	2619.01	−	4536.26i	0.273447	−	0.473624i
$452$	−10182.8	+	17637.1i	−1.05964	+	1.83535i
$453$	13021.6	+	22554.0i	1.35057	+	2.33925i
$454$	−23259.7			−2.40447
$455$	4371.20	+	3682.35i	0.450385	+	0.379409i
$456$	−39169.6			−4.02255
$457$	−2414.14	−	4181.42i	−0.247109	−	0.428006i	0.715613	−	0.698497i	$-0.246147\pi$
$457$	−2414.14	−	4181.42i	−0.247109	−	0.428006i	−0.962723	+	0.270491i	$0.912814\pi$
$458$	−15622.0	+	27058.1i	−1.59382	+	2.76057i
$459$	−13747.7	+	23811.7i	−1.39801	+	2.42143i
$460$	2517.98	+	4361.27i	0.255221	+	0.442055i
$461$	−6792.64			−0.686258			−0.343129	−	0.939288i	$-0.611487\pi$
$461$	−6792.64			−0.686258			−0.343129	+	0.939288i	$0.611487\pi$
$462$	6877.37	−	38565.8i	0.692563	−	3.88365i
$463$	−17088.5			−1.71527			−0.857636	−	0.514258i	$-0.828067\pi$
$463$	−17088.5			−1.71527			−0.857636	+	0.514258i	$0.828067\pi$
$464$	−2195.27	−	3802.32i	−0.219640	−	0.380427i
$465$	4724.98	−	8183.91i	0.471217	−	0.816171i
$466$	2690.18	−	4659.52i	0.267425	−	0.463193i
$467$	5224.66	+	9049.38i	0.517705	+	0.896692i	0.999788	+	0.0205667i	$0.00654703\pi$
$467$	5224.66	+	9049.38i	0.517705	+	0.896692i	−0.482083	+	0.876126i	$0.660120\pi$
$468$	−18478.6			−1.82516
$469$	−898.609	+	5039.08i	−0.0884732	+	0.496126i
$470$	3472.78			0.340824
$471$	−1128.64	−	1954.87i	−0.110414	−	0.191243i
$472$	−8481.62	+	14690.6i	−0.827115	+	1.43260i
$473$	10800.4	−	18706.8i	1.04990	−	1.81847i
$474$	−8659.76	−	14999.1i	−0.839148	−	1.45345i
$475$	9054.43			0.874623
$476$	−23897.3	−	20131.4i	−2.30112	−	1.93849i
$477$	34106.8			3.27389
$478$	−3630.14	−	6287.59i	−0.347362	−	0.601648i
$479$	−5927.09	+	10266.0i	−0.565377	+	0.979262i	0.431637	+	0.902047i	$0.357936\pi$
$479$	−5927.09	+	10266.0i	−0.565377	+	0.979262i	−0.997014	+	0.0772149i	$0.975397\pi$
$480$	−2588.51	+	4483.42i	−0.246143	+	0.426332i
$481$	−2775.03	−	4806.49i	−0.263057	−	0.455628i
$482$	−15208.1			−1.43716
$483$	−3623.88	+	1311.03i	−0.341392	+	0.123507i
$484$	15444.9			1.45050
$485$	8016.98	+	13885.8i	0.750582	+	1.30005i
$486$	1020.84	−	1768.14i	0.0952801	−	0.165030i
$487$	−6142.93	+	10639.9i	−0.571586	+	0.990017i	0.424817	+	0.905279i	$0.360338\pi$
$487$	−6142.93	+	10639.9i	−0.571586	+	0.990017i	−0.996403	+	0.0847374i	$0.972995\pi$
$488$	3145.75	+	5448.60i	0.291806	+	0.505424i
$489$	31176.7			2.88315
$490$	−3995.76	−	23186.8i	−0.368388	−	2.13770i
$491$	−4951.05			−0.455067			−0.227534	−	0.973770i	$-0.573066\pi$
$491$	−4951.05			−0.455067			−0.227534	+	0.973770i	$0.573066\pi$
$492$	7589.08	+	13144.7i	0.695411	+	1.20449i
$493$	−4666.11	+	8081.94i	−0.426270	+	0.738321i
$494$	−6322.98	+	10951.7i	−0.575880	+	0.997453i
$495$	−18747.9	−	32472.4i	−1.70234	−	2.94853i
$496$	−3786.66			−0.342795
$497$	1353.55	−	489.679i	0.122163	−	0.0441954i
$498$	9082.01			0.817218
$499$	−8512.18	−	14743.5i	−0.763642	−	1.32267i	−0.940962	−	0.338513i	$-0.890076\pi$
$499$	−8512.18	−	14743.5i	−0.763642	−	1.32267i	0.177320	−	0.984153i	$-0.443257\pi$
$500$	5411.43	−	9372.87i	0.484013	−	0.838335i
$501$	−13360.9	+	23141.8i	−1.19146	+	2.06367i
$502$	−8145.93	−	14109.2i	−0.724244	−	1.25443i
$503$	15602.2			1.38304			0.691519	−	0.722359i	$-0.256942\pi$
$503$	15602.2			1.38304			0.691519	+	0.722359i	$0.256942\pi$
$504$	28073.5	+	23649.4i	2.48114	+	2.09014i
$505$	−6212.00			−0.547387
$506$	−2688.71	−	4656.98i	−0.236221	−	0.409146i
$507$	7790.24	−	13493.1i	0.682400	−	1.18195i
$508$	−8813.01	+	15264.6i	−0.769712	+	1.33318i
$509$	−2752.10	−	4766.77i	−0.239655	−	0.415095i	0.720960	−	0.692977i	$-0.243701\pi$
$509$	−2752.10	−	4766.77i	−0.239655	−	0.415095i	−0.960615	+	0.277881i	$0.910368\pi$
$510$	−67724.3			−5.88016
$511$	−2817.70	+	15800.6i	−0.243929	+	1.36787i
$512$	16916.4			1.46017
$513$	−15094.0	−	26143.5i	−1.29906	−	2.25003i
$514$	−7374.28	+	12772.6i	−0.632813	+	1.09606i
$515$	6526.37	−	11304.0i	0.558420	−	0.967211i
$516$	31296.1	+	54206.4i	2.67003	+	4.62462i
$517$	−2443.73			−0.207882
$518$	−4011.06	+	22492.6i	−0.340224	+	1.90785i
$519$	−10477.4			−0.886143
$520$	−5575.84	−	9657.63i	−0.470224	−	0.814452i
$521$	−8594.48	+	14886.1i	−0.722708	+	1.25177i	0.237202	+	0.971460i	$0.423770\pi$
$521$	−8594.48	+	14886.1i	−0.722708	+	1.25177i	−0.959910	+	0.280307i	$0.909564\pi$
$522$	11359.5	−	19675.3i	0.952477	−	1.64974i
$523$	−1527.65	−	2645.97i	−0.127724	−	0.221224i	0.795071	−	0.606517i	$-0.207434\pi$
$523$	−1527.65	−	2645.97i	−0.127724	−	0.221224i	−0.922794	+	0.385293i	$0.874100\pi$
$524$	−12030.8			−1.00300
$525$	−9683.94	−	8157.86i	−0.805032	−	0.678168i
$526$	−20139.6			−1.66945
$527$	4024.33	+	6970.35i	0.332643	+	0.576154i
$528$	−11210.5	+	19417.1i	−0.924002	+	1.60042i
$529$	−264.500	+	458.127i	−0.0217391	+	0.0376533i
$530$	21327.5	+	36940.3i	1.74794	+	3.02752i
$531$	−25748.3			−2.10430
$532$	32260.4	−	11671.0i	2.62907	−	0.951131i
$533$	2364.64			0.192165
$534$	−21664.5	−	37524.0i	−1.75565	−	3.04087i
$535$	12524.5	−	21693.1i	1.01212	−	1.75304i
$536$	4993.49	−	8648.97i	0.402399	−	0.696975i
$537$	903.828	+	1565.48i	0.0726314	+	0.125801i
$538$	−13472.3			−1.07962
$539$	2811.74	+	16316.1i	0.224694	+	1.30387i
$540$	55167.0			4.39632
$541$	643.290	+	1114.21i	0.0511224	+	0.0885465i	0.890454	−	0.455073i	$-0.150387\pi$
$541$	643.290	+	1114.21i	0.0511224	+	0.0885465i	−0.839332	+	0.543619i	$0.817053\pi$
$542$	−1714.65	+	2969.87i	−0.135887	+	0.235363i
$543$	−3803.66	+	6588.14i	−0.300609	+	0.520670i
$544$	−2204.67	−	3818.60i	−0.173758	−	0.300958i
$545$	10172.3			0.799514
$546$	16629.9	−	6016.27i	1.30347	−	0.471562i
$547$	15862.3			1.23990			0.619949	−	0.784642i	$-0.287153\pi$
$547$	15862.3			1.23990			0.619949	+	0.784642i	$0.287153\pi$
$548$	10617.4	+	18389.8i	0.827648	+	1.43353i
$549$	−4774.91	+	8270.38i	−0.371199	+	0.642935i
$550$	8834.20	−	15301.3i	0.684894	−	1.18627i
$551$	−5123.06	−	8873.40i	−0.396097	−	0.686061i
$552$	7519.13			0.579774
$553$	5598.26	+	4716.03i	0.430492	+	0.362651i
$554$	15812.3			1.21264
$555$	16316.8	+	28261.5i	1.24794	+	2.16150i
$556$	14748.3	−	25544.8i	1.12494	−	1.94846i
$557$	−2676.42	+	4635.69i	−0.203597	+	0.352640i	−0.949685	−	0.313207i	$-0.898596\pi$
$557$	−2676.42	+	4635.69i	−0.203597	+	0.352640i	0.746088	+	0.665847i	$0.231930\pi$
$558$	−9797.13	−	16969.1i	−0.743272	−	1.28738i
$559$	9751.36			0.737815
$560$	−2364.12	+	13257.2i	−0.178397	+	1.00039i
$561$	47656.3			3.58655
$562$	10518.0	+	18217.8i	0.789461	+	1.36739i
$563$	−2393.92	+	4146.40i	−0.179204	+	0.310391i	−0.941608	−	0.336711i	$-0.890686\pi$
$563$	−2393.92	+	4146.40i	−0.179204	+	0.310391i	0.762404	+	0.647101i	$0.224019\pi$
$564$	3540.58	−	6132.47i	0.264336	−	0.457843i
$565$	−9327.78	−	16156.2i	−0.694554	−	1.20300i
$566$	−24419.3			−1.81346
$567$	−2596.32	+	14559.2i	−0.192302	+	1.07836i
$568$	−2808.45			−0.207465
$569$	2017.77	+	3494.88i	0.148663	+	0.257492i	0.930734	−	0.365698i	$-0.119170\pi$
$569$	2017.77	+	3494.88i	0.148663	+	0.257492i	−0.782070	+	0.623190i	$0.785836\pi$
$570$	37178.2	−	64394.6i	2.73197	−	4.73192i
$571$	−237.669	+	411.654i	−0.0174188	+	0.0301702i	−0.874603	−	0.484839i	$-0.838878\pi$
$571$	−237.669	+	411.654i	−0.0174188	+	0.0301702i	0.857185	+	0.515009i	$0.172212\pi$
$572$	8131.00	+	14083.3i	0.594361	+	1.02946i
$573$	6145.37			0.448039
$574$	−7444.76	−	6271.54i	−0.541356	−	0.456044i
$575$	−1738.12			−0.126060
$576$	16631.4	+	28806.4i	1.20308	+	2.08380i
$577$	−902.039	+	1562.38i	−0.0650821	+	0.112726i	−0.896730	−	0.442577i	$-0.854064\pi$
$577$	−902.039	+	1562.38i	−0.0650821	+	0.112726i	0.831648	+	0.555303i	$0.187398\pi$
$578$	16942.6	−	29345.4i	1.21924	−	2.11178i
$579$	−307.936	−	533.361i	−0.0221026	−	0.0382828i
$580$	18724.3			1.34049
$581$	−3609.48	+	1305.82i	−0.257739	+	0.0932435i
$582$	49611.6			3.53345
$583$	−15007.8	−	25994.2i	−1.06614	−	1.84661i
$584$	15657.7	−	27119.9i	1.10945	−	1.92163i
$585$	8463.51	−	14659.2i	0.598159	−	1.03604i
$586$	−6159.12	−	10667.9i	−0.434183	−	0.752027i
$587$	−22682.5			−1.59490			−0.797451	−	0.603384i	$-0.793819\pi$
$587$	−22682.5			−1.59490			−0.797451	+	0.603384i	$0.793819\pi$
$588$	−45018.6	−	16583.5i	−3.15738	−	1.16308i
$589$	−8836.86			−0.618194
$590$	−16100.8	−	27887.5i	−1.12349	−	1.94595i
$591$	5566.50	−	9641.46i	0.387437	−	0.671060i
$592$	6538.24	−	11324.6i	0.453919	−	0.786211i
$593$	487.773	+	844.847i	0.0337781	+	0.0585054i	0.882420	−	0.470462i	$-0.155913\pi$
$593$	487.773	+	844.847i	0.0337781	+	0.0585054i	−0.848642	+	0.528967i	$0.822579\pi$
$594$	−58907.4			−4.06903
$595$	26915.8	−	9737.45i	1.85452	−	0.670919i
$596$	−13428.1			−0.922880
$597$	13187.9	+	22842.1i	0.904094	+	1.56594i
$598$	1213.78	−	2102.33i	0.0830021	−	0.143764i
$599$	−5884.26	+	10191.8i	−0.401376	+	0.695204i	−0.993892	−	0.110355i	$-0.964801\pi$
$599$	−5884.26	+	10191.8i	−0.401376	+	0.695204i	0.592516	+	0.805559i	$0.298135\pi$
$600$	12352.7	+	21395.5i	0.840494	+	1.45578i
$601$	−1113.58			−0.0755805			−0.0377902	−	0.999286i	$-0.512032\pi$
$601$	−1113.58			−0.0755805			−0.0377902	+	0.999286i	$0.512032\pi$
$602$	−30700.9	−	25862.8i	−2.07853	−	1.75098i
$603$	15159.1			1.02376
$604$	22252.4	+	38542.3i	1.49907	+	2.59647i
$605$	−7074.04	+	12252.6i	−0.475373	+	0.823370i
$606$	−9610.46	+	16645.8i	−0.644222	+	1.11582i
$607$	−1913.24	−	3313.83i	−0.127934	−	0.221589i	0.794942	−	0.606686i	$-0.207501\pi$
$607$	−1913.24	−	3313.83i	−0.127934	−	0.221589i	−0.922876	+	0.385097i	$0.874168\pi$
$608$	4841.14			0.322918
$609$	−2515.51	+	14106.1i	−0.167379	+	0.938601i
$610$	−11943.3			−0.792737
$611$	−551.595	−	955.391i	−0.0365223	−	0.0632585i
$612$	−46269.9	+	80141.9i	−3.05613	+	5.29337i
$613$	10033.5	−	17378.6i	0.661095	−	1.14505i	−0.319234	−	0.947676i	$-0.603426\pi$
$613$	10033.5	−	17378.6i	0.661095	−	1.14505i	0.980328	−	0.197373i	$-0.0632411\pi$
$614$	3364.75	+	5827.92i	0.221157	+	0.383055i
$615$	−13903.7			−0.911630
$616$	5671.24	−	31802.3i	0.370943	−	2.08012i
$617$	−3629.44			−0.236816			−0.118408	−	0.992965i	$-0.537779\pi$
$617$	−3629.44			−0.236816			−0.118408	+	0.992965i	$0.537779\pi$
$618$	−20193.6	−	34976.4i	−1.31441	−	2.27663i
$619$	7699.04	−	13335.1i	0.499920	−	0.865887i	−0.500080	−	0.865979i	$-0.666696\pi$
$619$	7699.04	−	13335.1i	0.499920	−	0.865887i	1.00000		9.23398e-5i	$2.93927e-5\pi$
$620$	8074.46	−	13985.4i	0.523029	−	0.905913i
$621$	2897.49	+	5018.60i	0.187234	+	0.324299i
$622$	26733.0			1.72330
$623$	14005.4	+	11798.3i	0.900665	+	0.758730i
$624$	−10121.6			−0.649342
$625$	9680.21	+	16766.6i	0.619533	+	1.07306i
$626$	11434.5	−	19805.2i	0.730058	−	1.26450i
$627$	−26161.6	+	45313.3i	−1.66634	+	2.88619i
$628$	−1928.72	−	3340.65i	−0.122555	−	0.212271i
$629$	−27794.4			−1.76190
$630$	−65525.8	+	23705.6i	−4.14383	+	1.49913i
$631$	−2920.89			−0.184277			−0.0921385	−	0.995746i	$-0.529370\pi$
$631$	−2920.89			−0.184277			−0.0921385	+	0.995746i	$0.529370\pi$
$632$	−7141.05	−	12368.7i	−0.449455	−	0.778479i
$633$	−23355.7	+	40453.2i	−1.46652	+	2.54008i
$634$	5081.01	−	8800.57i	0.318285	−	0.551286i
$635$	−8073.02	−	13982.9i	−0.504516	−	0.873848i
$636$	86975.8			5.42266
$637$	−5744.22	+	4782.12i	−0.357291	+	0.297448i
$638$	−19993.8			−1.24069
$639$	−2131.46	−	3691.80i	−0.131955	−	0.228553i
$640$	−18510.8	+	32061.7i	−1.14329	+	1.98023i
$641$	2652.08	−	4593.54i	0.163418	−	0.283048i	−0.772674	−	0.634803i	$-0.781081\pi$
$641$	2652.08	−	4593.54i	0.163418	−	0.283048i	0.936092	+	0.351754i	$0.114415\pi$
$642$	−38752.9	−	67121.9i	−2.38233	−	4.12631i
$643$	14449.6			0.886215			0.443107	−	0.896468i	$-0.353876\pi$
$643$	14449.6			0.886215			0.443107	+	0.896468i	$0.353876\pi$
$644$	−6192.81	+	2240.40i	−0.378930	+	0.137087i
$645$	−57336.6			−3.50019
$646$	31665.2	+	54845.8i	1.92856	+	3.34037i
$647$	−3161.66	+	5476.16i	−0.192114	+	0.332751i	−0.945951	−	0.324311i	$-0.894868\pi$
$647$	−3161.66	+	5476.16i	−0.192114	+	0.332751i	0.753837	+	0.657062i	$0.228201\pi$
$648$	14427.5	−	24989.2i	0.874639	−	1.51492i
$649$	11329.9	+	19623.9i	0.685264	+	1.18691i
$650$	7976.17			0.481309
$651$	9451.25	+	7961.84i	0.569007	+	0.479338i
$652$	53277.5			3.20016
$653$	12621.8	+	21861.5i	0.756398	+	1.31012i	0.944676	+	0.328004i	$0.106376\pi$
$653$	12621.8	+	21861.5i	0.756398	+	1.31012i	−0.188278	+	0.982116i	$0.560291\pi$
$654$	15737.4	−	27258.0i	0.940950	−	1.62977i
$655$	5510.34	−	9544.18i	0.328712	−	0.569347i
$656$	2785.66	+	4824.90i	0.165795	+	0.287166i
$657$	47533.3			2.82260
$658$	−797.282	+	4470.88i	−0.0472360	+	0.264883i
$659$	15592.3			0.921684			0.460842	−	0.887482i	$-0.347547\pi$
$659$	15592.3			0.921684			0.460842	+	0.887482i	$0.347547\pi$
$660$	−47809.1	−	82807.8i	−2.81965	−	4.88377i
$661$	−1640.83	+	2842.00i	−0.0965521	+	0.167233i	−0.910255	−	0.414047i	$-0.864115\pi$
$661$	−1640.83	+	2842.00i	−0.0965521	+	0.167233i	0.813703	+	0.581281i	$0.197448\pi$
$662$	8472.22	−	14674.3i	0.497405	−	0.861531i
$663$	10756.9	+	18631.5i	0.630112	+	1.09139i
$664$	7489.24			0.437709
$665$	−5517.11	+	30938.0i	−0.321721	+	1.80410i
$666$	67664.8			3.93688
$667$	983.440	+	1703.37i	0.0570899	+	0.0988825i
$668$	−22832.3	+	39546.7i	−1.32247	+	2.29058i
$669$	−2080.67	+	3603.83i	−0.120244	+	0.208269i
$670$	9479.24	+	16418.5i	0.546590	+	0.946721i
$671$	8404.28			0.483522
$672$	−5177.72	−	4361.77i	−0.297224	−	0.250385i
$673$	−22502.7			−1.28888			−0.644438	−	0.764656i	$-0.722909\pi$
$673$	−22502.7			−1.28888			−0.644438	+	0.764656i	$0.722909\pi$
$674$	18521.5	+	32080.3i	1.05849	+	1.83336i
$675$	−9520.20	+	16489.5i	−0.542863	+	0.940267i
$676$	13312.6	−	23058.2i	0.757433	−	1.31191i
$677$	−5696.96	−	9867.42i	−0.323415	−	0.560171i	0.657775	−	0.753214i	$-0.271498\pi$
$677$	−5696.96	−	9867.42i	−0.323415	−	0.560171i	−0.981190	+	0.193043i	$0.938164\pi$
$678$	−57723.3			−3.26969
$679$	−19717.2	+	7133.19i	−1.11440	+	0.403162i
$680$	−55847.1			−3.14947
$681$	−21722.7	−	37624.8i	−1.22234	−	2.11716i
$682$	−8621.93	+	14933.6i	−0.484092	+	0.838472i
$683$	−4729.00	+	8190.87i	−0.264935	+	0.458880i	−0.967546	−	0.252693i	$-0.918684\pi$
$683$	−4729.00	+	8190.87i	−0.264935	+	0.458880i	0.702612	+	0.711573i	$0.252017\pi$
$684$	−50801.1	−	87990.1i	−2.83981	−	4.91869i
$685$	−19451.7			−1.08498
$686$	30768.2	+	179.075i	1.71244	+	0.00996663i
$687$	−58358.9			−3.24095
$688$	11487.6	+	19897.1i	0.636570	+	1.10257i
$689$	6775.07	−	11734.8i	0.374615	−	0.648852i
$690$	−7136.86	+	12361.4i	−0.393762	+	0.682015i
$691$	−8553.21	−	14814.6i	−0.470882	−	0.815591i	0.528564	−	0.848894i	$-0.322731\pi$
$691$	−8553.21	−	14814.6i	−0.470882	−	0.815591i	−0.999445	+	0.0333027i	$0.989397\pi$
$692$	−17904.8			−0.983580
$693$	46109.3	−	16681.2i	2.52749	−	0.914381i
$694$	20061.4			1.09729
$695$	13510.0	+	23399.9i	0.737356	+	1.27714i
$696$	13978.5	−	24211.4i	0.761282	−	1.31858i
$697$	5921.00	−	10255.5i	0.321770	−	0.557322i
$698$	18645.7	+	32295.4i	1.01111	+	1.75129i
$699$	10049.6			0.543794
$700$	−16548.8	−	13940.9i	−0.893550	−	0.752736i
$701$	−5644.90			−0.304144			−0.152072	−	0.988369i	$-0.548595\pi$
$701$	−5644.90			−0.304144			−0.152072	+	0.988369i	$0.548595\pi$
$702$	−13296.5	−	23030.2i	−0.714878	−	1.23820i
$703$	15258.2	−	26427.9i	0.818595	−	1.41785i
$704$	14636.4	−	25351.0i	0.783566	−	1.35718i
$705$	3243.30	+	5617.56i	0.173262	+	0.300099i
$706$	9414.51			0.501869
$707$	1426.16	−	7997.37i	0.0758644	−	0.425420i
$708$	−65660.8			−3.48543
$709$	10608.2	+	18373.9i	0.561915	+	0.973265i	0.997329	+	0.0730351i	$0.0232685\pi$
$709$	10608.2	+	18373.9i	0.561915	+	0.973265i	−0.435414	+	0.900230i	$0.643398\pi$
$710$	2665.67	−	4617.07i	0.140902	−	0.244050i
$711$	10839.3	−	18774.3i	0.571739	−	0.990281i
$712$	−17865.1	−	30943.2i	−0.940339	−	1.62872i
$713$	1696.35			0.0891009
$714$	15548.2	−	87188.7i	0.814953	−	4.56996i
$715$	−14896.6			−0.779160
$716$	1544.54	+	2675.22i	0.0806176	+	0.139634i
$717$	6780.53	−	11744.2i	0.353171	−	0.611710i
$718$	−11195.3	+	19390.9i	−0.581903	+	1.00789i
$719$	−1010.68	−	1750.55i	−0.0524229	−	0.0907991i	0.838623	−	0.544712i	$-0.183361\pi$
$719$	−1010.68	−	1750.55i	−0.0524229	−	0.0907991i	−0.891046	+	0.453913i	$0.850028\pi$
$720$	39881.7			2.06431
$721$	13054.5	+	10997.3i	0.674307	+	0.568044i
$722$	−36310.1			−1.87164
$723$	−14203.2	−	24600.7i	−0.730598	−	1.26543i
$724$	−6500.04	+	11258.4i	−0.333663	+	0.577921i
$725$	−3231.26	+	5596.70i	−0.165525	+	0.286698i
$726$	21888.2	+	37911.5i	1.11894	+	1.93805i
$727$	22603.7			1.15313			0.576565	−	0.817051i	$-0.304393\pi$
$727$	22603.7			1.15313			0.576565	+	0.817051i	$0.304393\pi$
$728$	13713.4	−	4961.16i	0.698149	−	0.252573i
$729$	−17746.7			−0.901626
$730$	29723.3	+	51482.3i	1.50700	+	2.61020i
$731$	24417.2	−	42291.8i	1.23543	−	2.13983i
$732$	−12176.5	+	21090.3i	−0.614831	+	1.06492i
$733$	12779.9	+	22135.4i	0.643977	+	1.11540i	0.984537	+	0.175178i	$0.0560500\pi$
$733$	12779.9	+	22135.4i	0.643977	+	1.11540i	−0.340560	+	0.940223i	$0.610617\pi$
$734$	44274.8			2.22645
$735$	33775.2	−	28118.2i	1.69499	−	1.41109i
$736$	−929.321			−0.0465424
$737$	−6670.37	−	11553.4i	−0.333387	−	0.577443i
$738$	−14414.5	+	24966.7i	−0.718978	+	1.24531i
$739$	−7419.52	+	12851.0i	−0.369325	+	0.639690i	−0.989460	−	0.144805i	$-0.953745\pi$
$739$	−7419.52	+	12851.0i	−0.369325	+	0.639690i	0.620135	+	0.784495i	$0.287078\pi$
$740$	27883.5	+	48295.7i	1.38516	+	2.39917i
$741$	−23620.7			−1.17102
$742$	−52453.6	+	18976.4i	−2.59519	+	0.938875i
$743$	−29321.0			−1.44776			−0.723879	−	0.689927i	$-0.757642\pi$
$743$	−29321.0			−1.44776			−0.723879	+	0.689927i	$0.757642\pi$
$744$	−12055.9	−	20881.4i	−0.594072	−	1.02896i
$745$	6150.30	−	10652.6i	0.302456	−	0.523869i
$746$	7930.92	−	13736.7i	0.389238	−	0.674180i
$747$	5683.92	+	9844.85i	0.278399	+	0.482201i
$748$	81439.4			3.98091
$749$	25052.5	+	21104.5i	1.22216	+	1.02956i
$750$	30675.8			1.49350
$751$	−6207.57	−	10751.8i	−0.301621	−	0.522423i	0.674882	−	0.737925i	$-0.264194\pi$
$751$	−6207.57	−	10751.8i	−0.301621	−	0.522423i	−0.976503	+	0.215503i	$0.930861\pi$
$752$	1299.61	−	2250.99i	0.0630212	−	0.109156i
$753$	15215.3	−	26353.7i	0.736356	−	1.27541i
$754$	−4512.97	−	7816.70i	−0.217974	−	0.377543i
$755$	−40768.0			−1.96516
$756$	−12665.3	+	71022.4i	−0.609301	+	3.41674i
$757$	3575.68			0.171678			0.0858391	−	0.996309i	$-0.472643\pi$
$757$	3575.68			0.171678			0.0858391	+	0.996309i	$0.472643\pi$
$758$	11909.3	+	20627.5i	0.570665	+	0.988421i
$759$	5022.08	−	8698.49i	0.240171	−	0.415989i
$760$	30658.1	−	53101.3i	1.46327	−	2.53446i
$761$	−15332.0	−	26555.8i	−0.730335	−	1.26498i	−0.956740	−	0.290945i	$-0.906030\pi$
$761$	−15332.0	−	26555.8i	−0.730335	−	1.26498i	0.226404	−	0.974033i	$-0.427303\pi$
$762$	−49958.4			−2.37507
$763$	−2335.37	+	13095.9i	−0.110808	+	0.621369i
$764$	10501.7			0.497304
$765$	−42384.9	−	73412.8i	−2.00317	−	3.46960i
$766$	−8864.07	+	15353.0i	−0.418109	+	0.724187i
$767$	−5114.72	+	8858.95i	−0.240785	+	0.417051i
$768$	35329.4	+	61192.4i	1.65995	+	2.87512i
$769$	−2380.92			−0.111649			−0.0558245	−	0.998441i	$-0.517779\pi$
$769$	−2380.92			−0.111649			−0.0558245	+	0.998441i	$0.517779\pi$
$770$	46899.9	+	39509.0i	2.19501	+	1.84910i
$771$	−27548.0			−1.28679
$772$	−526.228	−	911.454i	−0.0245329	−	0.0424922i
$773$	−678.807	+	1175.73i	−0.0315847	+	0.0547064i	−0.881386	−	0.472397i	$-0.843389\pi$
$773$	−678.807	+	1175.73i	−0.0315847	+	0.0547064i	0.849801	+	0.527104i	$0.176722\pi$
$774$	−59443.0	+	102958.i	−2.76051	+	4.78134i
$775$	2786.83	+	4826.93i	0.129169	+	0.223727i
$776$	40910.9			1.89255
$777$	−40130.0	+	14518.0i	−1.85284	+	0.670310i
$778$	12578.9			0.579659
$779$	6500.84	+	11259.8i	0.298994	+	0.517873i
$780$	21582.8	−	37382.5i	0.990754	−	1.71604i
$781$	−1875.78	+	3248.95i	−0.0859421	+	0.148856i
$782$	−6078.56	−	10528.4i	−0.277965	−	0.481450i
$783$	21546.4			0.983403
$784$	−16524.6	−	6087.18i	−0.752761	−	0.277295i
$785$	3533.55			0.160660
$786$	−17049.9	−	29531.2i	−0.773725	−	1.34013i
$787$	4155.04	−	7196.74i	0.188197	−	0.325967i	−0.756452	−	0.654049i	$-0.773069\pi$
$787$	4155.04	−	7196.74i	0.188197	−	0.325967i	0.944649	+	0.328082i	$0.106402\pi$
$788$	9512.52	−	16476.2i	0.430038	−	0.744847i
$789$	−18808.8	−	32577.8i	−0.848684	−	1.46996i
$790$	27112.0			1.22101
$791$	22941.1	−	8299.50i	1.03121	−	0.373067i
$792$	−95671.3			−4.29234
$793$	1897.00	+	3285.70i	0.0849489	+	0.147136i
$794$	8860.11	−	15346.2i	0.396012	−	0.685913i
$795$	−39836.4	+	68998.7i	−1.77717	+	3.07815i
$796$	22536.6	+	39034.6i	1.00350	+	1.73812i
$797$	25096.3			1.11538			0.557690	−	0.830049i	$-0.311688\pi$
$797$	25096.3			1.11538			0.557690	+	0.830049i	$0.311688\pi$
$798$	74366.6	+	62647.2i	3.29893	+	2.77906i
$799$	−5524.73			−0.244619
$800$	−1526.72	−	2644.36i	−0.0674722	−	0.116865i
$801$	27117.2	−	46968.4i	1.19618	−	2.07184i
$802$	−9657.95	+	16728.1i	−0.425229	+	0.736519i
$803$	−20915.7	−	36227.1i	−0.919179	−	1.59206i
$804$	38657.3			1.69569
$805$	1059.08	−	5938.96i	0.0463699	−	0.260026i
$806$	−7784.51			−0.340196
$807$	−12582.1	−	21792.8i	−0.548836	−	0.950612i
$808$	−7925.01	+	13726.5i	−0.345051	+	0.597646i
$809$	3614.20	−	6259.98i	0.157069	−	0.272051i	−0.776742	−	0.629819i	$-0.783129\pi$
$809$	3614.20	−	6259.98i	0.157069	−	0.272051i	0.933810	+	0.357768i	$0.116462\pi$
$810$	27388.0	+	47437.5i	1.18805	+	2.05776i
$811$	−6413.12			−0.277676			−0.138838	−	0.990315i	$-0.544337\pi$
$811$	−6413.12			−0.277676			−0.138838	+	0.990315i	$0.544337\pi$
$812$	−4298.73	+	24105.7i	−0.185783	+	1.04181i
$813$	−6405.40			−0.276319
$814$	−29774.1	−	51570.2i	−1.28204	−	2.22056i
$815$	−24402.0	+	42265.5i	−1.04879	+	1.81656i
$816$	−25344.3	+	43897.7i	−1.08729	+	1.88324i
$817$	26808.3	+	46433.4i	1.14799	+	1.98837i
$818$	−64795.0			−2.76956
$819$	16929.3	+	14261.5i	0.722294	+	0.608468i
$820$	−23759.9			−1.01187
$821$	−6969.07	−	12070.8i	−0.296251	−	0.513122i	0.679024	−	0.734116i	$-0.262403\pi$
$821$	−6969.07	−	12070.8i	−0.296251	−	0.513122i	−0.975275	+	0.220994i	$0.929070\pi$
$822$	−30093.4	+	52123.2i	−1.27692	+	2.21169i
$823$	−9960.45	+	17252.0i	−0.421870	+	0.730701i	−0.996122	−	0.0879775i	$-0.971960\pi$
$823$	−9960.45	+	17252.0i	−0.421870	+	0.730701i	0.574252	+	0.818679i	$0.305293\pi$
$824$	−16652.1	−	28842.3i	−0.704011	−	1.21938i
$825$	33001.8			1.39270
$826$	39598.9	−	14325.9i	1.66807	−	0.603465i
$827$	−27205.3			−1.14392			−0.571959	−	0.820282i	$-0.693816\pi$
$827$	−27205.3			−1.14392			−0.571959	+	0.820282i	$0.693816\pi$
$828$	9751.95	+	16890.9i	0.409304	+	0.708936i
$829$	666.825	−	1154.97i	0.0279370	−	0.0483883i	−0.851719	−	0.523999i	$-0.824440\pi$
$829$	666.825	−	1154.97i	0.0279370	−	0.0483883i	0.879656	+	0.475611i	$0.157773\pi$
$830$	−7108.49	+	12312.3i	−0.297276	+	0.514898i
$831$	14767.4	+	25578.0i	0.616459	+	1.06774i
$832$	13214.8			0.550651
$833$	6356.72	+	36887.1i	0.264402	+	1.53429i
$834$	83603.9			3.47118
$835$	−20915.2	−	36226.2i	−0.866826	−	1.50139i
$836$	−44707.3	+	77435.3i	−1.84956	+	3.20354i
$837$	9291.44	−	16093.3i	0.383703	−	0.664593i
$838$	−38871.9	−	67328.1i	−1.60239	−	2.77543i
$839$	−40503.3			−1.66666			−0.833331	−	0.552775i	$-0.813569\pi$
$839$	−40503.3			−1.66666			−0.833331	+	0.552775i	$0.813569\pi$
$840$	−80632.8	+	29170.9i	−3.31202	+	1.19820i
$841$	−17075.9			−0.700149
$842$	−41017.6	−	71044.5i	−1.67881	−	2.90779i
$843$	−19646.0	+	34027.9i	−0.802664	+	1.39025i
$844$	−39912.2	+	69130.0i	−1.62777	+	2.81937i
$845$	12194.8	+	21122.1i	0.496468	+	0.859908i
$846$	13449.8			0.546588
$847$	−14150.0	−	11920.1i	−0.574026	−	0.483566i
$848$	31925.4			1.29283
$849$	−22805.6	−	39500.5i	−0.921893	−	1.59677i
$850$	19972.2	−	34592.8i	0.805928	−	1.39591i
$851$	−2929.01	+	5073.19i	−0.117985	+	0.204356i
$852$	−5435.43	−	9414.45i	−0.218562	−	0.378561i
$853$	−8595.25			−0.345013			−0.172506	−	0.985008i	$-0.555187\pi$
$853$	−8595.25			−0.345013			−0.172506	+	0.985008i	$0.555187\pi$
$854$	2741.95	−	15375.9i	0.109868	−	0.616103i
$855$	93071.1			3.72277
$856$	−31956.5	−	55350.3i	−1.27600	−	2.21009i
$857$	−18636.2	+	32278.8i	−0.742824	+	1.28661i	0.208380	+	0.978048i	$0.433181\pi$
$857$	−18636.2	+	32278.8i	−0.742824	+	1.28661i	−0.951204	+	0.308561i	$0.900153\pi$
$858$	−23046.1	+	39917.1i	−0.916996	+	1.58828i
$859$	14775.9	+	25592.6i	0.586900	+	1.01654i	0.994636	+	0.103440i	$0.0329850\pi$
$859$	14775.9	+	25592.6i	0.586900	+	1.01654i	−0.407736	+	0.913100i	$0.633682\pi$
$860$	−97981.8			−3.88506
$861$	3192.03	−	17899.7i	0.126346	−	0.708504i
$862$	57923.5			2.28873
$863$	6429.08	+	11135.5i	0.253590	+	0.439231i	0.964512	−	0.264040i	$-0.0850552\pi$
$863$	6429.08	+	11135.5i	0.253590	+	0.439231i	−0.710921	+	0.703271i	$0.751722\pi$
$864$	−5090.17	+	8816.44i	−0.200430	+	0.347154i
$865$	8200.69	−	14204.0i	0.322349	−	0.558325i
$866$	17139.0	+	29685.6i	0.672524	+	1.16485i
$867$	63292.1			2.47925
$868$	16151.1	+	13605.9i	0.631573	+	0.532044i
$869$	−19078.2			−0.744746
$870$	26535.6	+	45961.0i	1.03407	+	1.79106i
$871$	3011.25	−	5215.64i	0.117144	−	0.202899i
$872$	12977.4	−	22477.6i	0.503981	−	0.872921i
$873$	31049.1	+	53778.7i	1.20373	+	2.08492i
$874$	13347.7			0.516581
$875$	−12191.6	+	4410.60i	−0.471028	+	0.170406i
$876$	121215.			4.67519
$877$	14903.0	+	25812.8i	0.573818	+	0.993883i	0.996169	+	0.0874501i	$0.0278718\pi$
$877$	14903.0	+	25812.8i	0.573818	+	0.993883i	−0.422350	+	0.906433i	$0.638795\pi$
$878$	34395.3	−	59574.4i	1.32208	−	2.28991i
$879$	11504.3	−	19926.0i	0.441444	−	0.764603i
$880$	−17548.9	−	30395.5i	−0.672241	−	1.16436i
$881$	39365.3			1.50539			0.752696	−	0.658368i	$-0.228753\pi$
$881$	39365.3			1.50539			0.752696	+	0.658368i	$0.228753\pi$
$882$	−15475.3	−	89800.7i	−0.590793	−	3.42828i
$883$	−16970.4			−0.646773			−0.323386	−	0.946267i	$-0.604821\pi$
$883$	−16970.4			−0.646773			−0.323386	+	0.946267i	$0.604821\pi$
$884$	18382.4	+	31839.2i	0.699396	+	1.21139i
$885$	30073.8	−	52089.3i	1.14228	−	1.97849i
$886$	29261.1	−	50681.6i	1.10953	−	1.92176i
$887$	−10219.3	−	17700.3i	−0.386842	−	0.670031i	0.605181	−	0.796088i	$-0.293101\pi$
$887$	−10219.3	−	17700.3i	−0.386842	−	0.670031i	−0.992023	+	0.126058i	$0.959768\pi$
$888$	83265.0			3.14661
$889$	19855.1	−	7183.06i	0.749063	−	0.270992i
$890$	67827.3			2.55458
$891$	−19272.5	−	33380.9i	−0.724638	−	1.25511i
$892$	−3555.63	+	6158.54i	−0.133466	+	0.231169i
$893$	3032.88	−	5253.10i	0.113652	−	0.196851i
$894$	−19030.0	−	32960.9i	−0.711922	−	1.23309i
$895$	−2829.70			−0.105683
$896$	−37026.7	−	31191.7i	−1.38055	−	1.16299i
$897$	4534.30			0.168780
$898$	42567.7	+	73729.3i	1.58185	+	2.73984i
$899$	3153.61	−	5462.22i	0.116995	−	0.202642i
$900$	−32041.7	+	55497.9i	−1.18673	+	2.05548i
$901$	−33929.2	−	58767.1i	−1.25455	−	2.17294i
$902$	25370.9			0.936539
$903$	13163.4	−	73815.5i	0.485105	−	2.72029i
$904$	−47600.0			−1.75127
$905$	−5954.26	−	10313.1i	−0.218703	−	0.378805i
$906$	−63071.3	+	109243.i	−2.31281	+	4.00590i
$907$	13587.0	−	23533.4i	0.497408	−	0.861536i	−0.502588	−	0.864526i	$-0.667619\pi$
$907$	13587.0	−	23533.4i	0.497408	−	0.861536i	0.999996	+	0.00299040i	$0.000951874\pi$
$908$	−37121.6	−	64296.5i	−1.35674	−	2.34995i
$909$	−24058.6			−0.877859
$910$	−4860.10	+	27253.7i	−0.177045	+	0.992803i
$911$	17192.3			0.625255			0.312628	−	0.949876i	$-0.398791\pi$
$911$	17192.3			0.625255			0.312628	+	0.949876i	$0.398791\pi$
$912$	−27826.3	−	48196.5i	−1.01033	−	1.74994i
$913$	5002.12	−	8663.92i	0.181321	−	0.314057i
$914$	11693.1	−	20253.1i	0.423167	−	0.732947i
$915$	−11154.1	−	19319.4i	−0.402998	−	0.698012i
$916$	−99728.8			−3.59730
$917$	11022.2	+	9285.20i	0.396929	+	0.334378i
$918$	−133177.			−4.78810
$919$	18183.5	+	31494.7i	0.652685	+	1.13048i	0.982469	+	0.186427i	$0.0596909\pi$
$919$	18183.5	+	31494.7i	0.652685	+	1.13048i	−0.329783	+	0.944057i	$0.606976\pi$
$920$	−5885.22	+	10193.5i	−0.210902	+	0.365293i
$921$	−6284.82	+	10885.6i	−0.224855	+	0.389461i
$922$	−16450.4	−	28493.0i	−0.587598	−	1.01775i
$923$	−1693.60			−0.0603958
$924$	117583.	−	42538.7i	4.18637	−	1.51452i
$925$	−19247.5			−0.684167
$926$	−41384.9	−	71680.8i	−1.46868	−	2.54382i
$927$	25276.1	−	43779.5i	0.895552	−	1.55114i
$928$	−1727.66	+	2992.39i	−0.0611133	+	0.105851i
$929$	20852.3	+	36117.3i	0.736430	+	1.27553i	0.954093	+	0.299510i	$0.0968231\pi$
$929$	20852.3	+	36117.3i	0.736430	+	1.27553i	−0.217663	+	0.976024i	$0.569844\pi$
$930$	45771.8			1.61389
$931$	−38563.1	−	14205.5i	−1.35752	−	0.500072i
$932$	17173.7			0.603588
$933$	24966.5	+	43243.2i	0.876062	+	1.51738i
$934$	−25306.1	+	43831.5i	−0.886555	+	1.53556i
$935$	−37300.6	+	64606.6i	−1.30466	+	2.25975i
$936$	−21594.8	−	37403.3i	−0.754111	−	1.30616i
$937$	26116.7			0.910559			0.455280	−	0.890349i	$-0.349539\pi$
$937$	26116.7			0.910559			0.455280	+	0.890349i	$0.349539\pi$
$938$	−23313.6	+	8434.26i	−0.811530	+	0.293591i
$939$	42715.8			1.48453
$940$	5542.43	+	9599.78i	0.192313	+	0.333096i
$941$	−21421.3	+	37102.8i	−0.742098	+	1.28535i	0.209440	+	0.977822i	$0.432836\pi$
$941$	−21421.3	+	37102.8i	−0.742098	+	1.28535i	−0.951538	+	0.307531i	$0.900497\pi$
$942$	5466.69	−	9468.58i	0.189081	−	0.327498i
$943$	−1247.92	−	2161.47i	−0.0430943	−	0.0746416i
$944$	−24101.6			−0.830973
$945$	−50541.8	−	42577.0i	−1.73981	−	1.46564i
$946$	104625.			3.59583
$947$	−1156.58	−	2003.26i	−0.0396872	−	0.0687403i	0.845499	−	0.533976i	$-0.179303\pi$
$947$	−1156.58	−	2003.26i	−0.0396872	−	0.0687403i	−0.885187	+	0.465236i	$0.845969\pi$
$948$	27641.4	−	47876.2i	0.946993	−	1.64024i
$949$	9442.14	−	16354.3i	0.322977	−	0.559412i
$950$	21928.0	+	37980.4i	0.748882	+	1.29710i
$951$	18981.0			0.647216
$952$	12821.4	−	71897.9i	0.436496	−	2.44771i
$953$	7807.63			0.265387			0.132694	−	0.991157i	$-0.457637\pi$
$953$	7807.63			0.265387			0.132694	+	0.991157i	$0.457637\pi$
$954$	82599.8	+	143067.i	2.80322	+	4.85531i
$955$	−4809.98	+	8331.13i	−0.162982	+	0.282292i
$956$	11587.2	−	20069.6i	0.392004	−	0.678971i
$957$	−18672.6	−	32341.9i	−0.630721	−	1.09244i
$958$	−57416.9			−1.93638
$959$	4465.74	−	25042.3i	0.150372	−	0.843230i
$960$	−77701.2			−2.61229
$961$	12175.6	+	21088.8i	0.408702	+	0.707892i
$962$	13441.1	−	23280.7i	0.450477	−	0.780250i
$963$	48506.5	−	84015.8i	1.62316	−	2.81139i
$964$	−24271.7	−	42039.8i	−0.810932	−	1.40457i
$965$	964.086			0.0321607
$966$	−14275.7	−	12026.0i	−0.475478	−	0.400548i
$967$	38058.5			1.26565			0.632823	−	0.774296i	$-0.281896\pi$
$967$	38058.5			1.26565			0.632823	+	0.774296i	$0.281896\pi$
$968$	18049.5	+	31262.7i	0.599312	+	1.03804i
$969$	−59145.6	+	102443.i	−1.96082	+	3.39623i
$970$	−38831.0	+	67257.3i	−1.28535	+	2.22629i
$971$	−5816.00	−	10073.6i	−0.192219	−	0.332932i	0.753767	−	0.657142i	$-0.228235\pi$
$971$	−5816.00	−	10073.6i	−0.192219	−	0.332932i	−0.945985	+	0.324210i	$0.894902\pi$
$972$	6516.89			0.215051
$973$	−33226.9	+	12020.6i	−1.09476	+	0.396058i
$974$	−59507.7			−1.95765
$975$	7449.11	+	12902.2i	0.244679	+	0.423797i
$976$	−4469.52	+	7741.43i	−0.146584	+	0.253891i
$977$	−6417.52	+	11115.5i	−0.210148	+	0.363987i	−0.951761	−	0.306841i	$-0.900728\pi$
$977$	−6417.52	+	11115.5i	−0.210148	+	0.363987i	0.741613	+	0.670828i	$0.234061\pi$
$978$	75503.7	+	130776.i	2.46865	+	4.27583i
$979$	−47728.8			−1.55814
$980$	57718.0	−	48050.8i	1.88136	−	1.56625i
$981$	39396.7			1.28220
$982$	−11990.5	−	20768.1i	−0.389644	−	0.674884i
$983$	14550.7	−	25202.5i	0.472120	−	0.817737i	−0.527371	−	0.849635i	$-0.676822\pi$
$983$	14550.7	−	25202.5i	0.472120	−	0.817737i	0.999491	+	0.0318987i	$0.0101554\pi$
$984$	−17737.8	+	30722.8i	−0.574655	+	0.995331i
$985$	8713.80	+	15092.7i	0.281873	+	0.488218i
$986$	−45201.5			−1.45995
$987$	−7976.68	+	2885.76i	−0.257245	+	0.0930646i
$988$	−40365.1			−1.29978
$989$	−5146.22	−	8913.51i	−0.165460	−	0.286586i
$990$	90807.4	−	157283.i	2.91520	−	5.04928i
$991$	21450.0	−	37152.5i	0.687571	−	1.19091i	−0.285051	−	0.958512i	$-0.592011\pi$
$991$	21450.0	−	37152.5i	0.687571	−	1.19091i	0.972622	−	0.232395i	$-0.0746562\pi$
$992$	1490.04	+	2580.82i	0.0476902	+	0.0826018i
$993$	31649.5			1.01145
$994$	5332.07	+	4491.79i	0.170144	+	0.143331i
$995$	−41288.6			−1.31552
$996$	14494.6	+	25105.3i	0.461123	+	0.798688i
$997$	23314.9	−	40382.6i	0.740612	−	1.28278i	−0.211605	−	0.977355i	$-0.567869\pi$
$997$	23314.9	−	40382.6i	0.740612	−	1.28278i	0.952217	−	0.305422i	$-0.0987975\pi$
$998$	41229.6	−	71411.7i	1.30771	−	2.26503i
$999$	32086.1	+	55574.8i	1.01618	+	1.76007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.e.a.116.20	yes	44
7.2	even	3	inner	161.4.e.a.93.20	✓	44
7.3	odd	6		1127.4.a.k.1.3		22
7.4	even	3		1127.4.a.l.1.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.e.a.93.20	✓	44	7.2	even	3	inner
161.4.e.a.116.20	yes	44	1.1	even	1	trivial
1127.4.a.k.1.3		22	7.3	odd	6
1127.4.a.l.1.3		22	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.42180 + 4.19468i) q^{2} +(-4.52353 + 7.83499i) q^{3} +(-7.73021 + 13.3891i) q^{4} +(-7.08114 - 12.2649i) q^{5} -43.8204 q^{6} +(17.4156 - 6.30053i) q^{7} -36.1353 q^{8} +(-27.4247 - 47.5010i) q^{9} +(34.2982 - 59.4062i) q^{10} +(-24.1350 + 41.8031i) q^{11} +(-69.9358 - 121.132i) q^{12} -21.7909 q^{13} +(68.6058 + 57.7943i) q^{14} +128.127 q^{15} +(-25.6707 - 44.4630i) q^{16} +(-54.5639 + 94.5074i) q^{17} +(132.834 - 230.076i) q^{18} +(-59.9072 - 103.762i) q^{19} +218.955 q^{20} +(-29.4155 + 164.952i) q^{21} -233.801 q^{22} +(11.5000 + 19.9186i) q^{23} +(163.459 - 283.120i) q^{24} +(-37.7852 + 65.4459i) q^{25} +(-52.7731 - 91.4057i) q^{26} +251.956 q^{27} +(-50.2678 + 281.884i) q^{28} +85.5165 q^{29} +(310.298 + 537.452i) q^{30} +(36.8773 - 63.8733i) q^{31} +(-20.2026 + 34.9920i) q^{32} +(-218.351 - 378.195i) q^{33} -528.571 q^{34} +(-200.598 - 168.986i) q^{35} +847.996 q^{36} +(127.348 + 220.574i) q^{37} +(290.167 - 502.583i) q^{38} +(98.5718 - 170.731i) q^{39} +(255.879 + 443.196i) q^{40} -108.515 q^{41} +(-763.158 + 276.091i) q^{42} -447.497 q^{43} +(-373.138 - 646.294i) q^{44} +(-388.397 + 672.723i) q^{45} +(-55.7014 + 96.4776i) q^{46} +(25.3131 + 43.8436i) q^{47} +464.490 q^{48} +(263.607 - 219.455i) q^{49} -366.033 q^{50} +(-493.643 - 855.015i) q^{51} +(168.448 - 291.761i) q^{52} +(-310.913 + 538.517i) q^{53} +(610.186 + 1056.87i) q^{54} +683.614 q^{55} +(-629.318 + 227.671i) q^{56} +1083.97 q^{57} +(207.104 + 358.714i) q^{58} +(234.718 - 406.544i) q^{59} +(-990.451 + 1715.51i) q^{60} +(-87.0548 - 150.783i) q^{61} +357.237 q^{62} +(-776.900 - 654.469i) q^{63} -606.438 q^{64} +(154.304 + 267.263i) q^{65} +(1057.61 - 1831.83i) q^{66} +(-138.189 + 239.350i) q^{67} +(-843.581 - 1461.12i) q^{68} -208.083 q^{69} +(223.033 - 1250.69i) q^{70} +77.7204 q^{71} +(991.001 + 1716.46i) q^{72} +(-433.307 + 750.510i) q^{73} +(-616.823 + 1068.37i) q^{74} +(-341.845 - 592.093i) q^{75} +1852.38 q^{76} +(-156.945 + 880.089i) q^{77} +954.884 q^{78} +(197.620 + 342.287i) q^{79} +(-363.556 + 629.698i) q^{80} +(-399.264 + 691.545i) q^{81} +(-262.801 - 455.185i) q^{82} -207.255 q^{83} +(-1981.17 - 1668.96i) q^{84} +1545.50 q^{85} +(-1083.75 - 1877.11i) q^{86} +(-386.837 + 670.021i) q^{87} +(872.126 - 1510.57i) q^{88} +(494.394 + 856.315i) q^{89} -3762.48 q^{90} +(-379.501 + 137.294i) q^{91} -355.590 q^{92} +(333.631 + 577.866i) q^{93} +(-122.607 + 212.361i) q^{94} +(-848.424 + 1469.51i) q^{95} +(-182.775 - 316.575i) q^{96} -1132.16 q^{97} +(1558.95 + 574.270i) q^{98} +2647.59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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