LMFDB - Embedded newform 201.4.e.a.37.16

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			37.16
Character	$\chi$	$=$	201.37
Dual form			201.4.e.a.163.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.53918 + 4.39800i) q^{2} +3.00000 q^{3} +(-8.89492 + 15.4064i) q^{4} -17.1999 q^{5} +(7.61755 + 13.1940i) q^{6} +(0.556661 - 0.964165i) q^{7} -49.7164 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(2.53918 + 4.39800i) q^{2} +3.00000 q^{3} +(-8.89492 + 15.4064i) q^{4} -17.1999 q^{5} +(7.61755 + 13.1940i) q^{6} +(0.556661 - 0.964165i) q^{7} -49.7164 q^{8} +9.00000 q^{9} +(-43.6738 - 75.6453i) q^{10} +(-17.0971 + 29.6130i) q^{11} +(-26.6847 + 46.2193i) q^{12} +(-10.1057 - 17.5036i) q^{13} +5.65386 q^{14} -51.5998 q^{15} +(-55.0797 - 95.4009i) q^{16} +(-8.81433 - 15.2669i) q^{17} +(22.8527 + 39.5820i) q^{18} +(11.5544 + 20.0128i) q^{19} +(152.992 - 264.990i) q^{20} +(1.66998 - 2.89249i) q^{21} -173.651 q^{22} +(-37.7195 - 65.3320i) q^{23} -149.149 q^{24} +170.838 q^{25} +(51.3205 - 88.8898i) q^{26} +27.0000 q^{27} +(9.90290 + 17.1523i) q^{28} +(-77.9248 + 134.970i) q^{29} +(-131.021 - 226.936i) q^{30} +(-128.881 + 223.228i) q^{31} +(80.8496 - 140.036i) q^{32} +(-51.2913 + 88.8391i) q^{33} +(44.7624 - 77.5308i) q^{34} +(-9.57453 + 16.5836i) q^{35} +(-80.0542 + 138.658i) q^{36} +(32.4077 + 56.1318i) q^{37} +(-58.6776 + 101.633i) q^{38} +(-30.3171 - 52.5108i) q^{39} +855.119 q^{40} +(-103.583 + 179.412i) q^{41} +16.9616 q^{42} +341.366 q^{43} +(-304.154 - 526.811i) q^{44} -154.799 q^{45} +(191.553 - 331.780i) q^{46} +(-266.039 + 460.793i) q^{47} +(-165.239 - 286.203i) q^{48} +(170.880 + 295.973i) q^{49} +(433.789 + 751.345i) q^{50} +(-26.4430 - 45.8006i) q^{51} +359.558 q^{52} +597.847 q^{53} +(68.5580 + 118.746i) q^{54} +(294.069 - 509.342i) q^{55} +(-27.6752 + 47.9348i) q^{56} +(34.6632 + 60.0385i) q^{57} -791.462 q^{58} -589.164 q^{59} +(458.976 - 794.970i) q^{60} +(-266.273 - 461.199i) q^{61} -1309.01 q^{62} +(5.00995 - 8.67748i) q^{63} -60.1069 q^{64} +(173.818 + 301.061i) q^{65} -520.952 q^{66} +(514.175 - 190.755i) q^{67} +313.611 q^{68} +(-113.158 - 195.996i) q^{69} -97.2460 q^{70} +(395.299 - 684.677i) q^{71} -447.447 q^{72} +(281.059 + 486.809i) q^{73} +(-164.578 + 285.058i) q^{74} +512.514 q^{75} -411.102 q^{76} +(19.0346 + 32.9688i) q^{77} +(153.962 - 266.669i) q^{78} +(629.549 - 1090.41i) q^{79} +(947.368 + 1640.89i) q^{80} +81.0000 q^{81} -1052.07 q^{82} +(444.076 + 769.161i) q^{83} +(29.7087 + 51.4570i) q^{84} +(151.606 + 262.589i) q^{85} +(866.792 + 1501.33i) q^{86} +(-233.774 + 404.909i) q^{87} +(850.005 - 1472.25i) q^{88} -1123.83 q^{89} +(-393.064 - 680.808i) q^{90} -22.5018 q^{91} +1342.05 q^{92} +(-386.642 + 669.683i) q^{93} -2702.09 q^{94} +(-198.735 - 344.220i) q^{95} +(242.549 - 420.107i) q^{96} +(480.446 + 832.157i) q^{97} +(-867.793 + 1503.06i) q^{98} +(-153.874 + 266.517i) 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 $

$2$	2.53918	+	4.39800i	0.897737	+	1.55493i	0.830380	+	0.557198i	$0.188123\pi$
$2$	2.53918	+	4.39800i	0.897737	+	1.55493i	0.0673574	+	0.997729i	$0.478543\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	−8.89492	+	15.4064i	−1.11186	+	1.92581i
$5$	−17.1999			−1.53841			−0.769205	−	0.639002i	$-0.779347\pi$
$5$	−17.1999			−1.53841			−0.769205	+	0.639002i	$0.779347\pi$
$6$	7.61755	+	13.1940i	0.518309	+	0.897737i
$7$	0.556661	−	0.964165i	0.0300569	−	0.0520600i	−0.850606	−	0.525804i	$-0.823764\pi$
$7$	0.556661	−	0.964165i	0.0300569	−	0.0520600i	0.880663	+	0.473744i	$0.157098\pi$
$8$	−49.7164			−2.19717
$9$	9.00000			0.333333
$10$	−43.6738	−	75.6453i	−1.38109	−	2.39211i
$11$	−17.0971	+	29.6130i	−0.468633	+	0.811696i	−0.999357	−	0.0358482i	$-0.988587\pi$
$11$	−17.0971	+	29.6130i	−0.468633	+	0.811696i	0.530724	+	0.847545i	$0.321920\pi$
$12$	−26.6847	+	46.2193i	−0.641935	+	1.11186i
$13$	−10.1057	−	17.5036i	−0.215602	−	0.373433i	0.737857	−	0.674957i	$-0.235838\pi$
$13$	−10.1057	−	17.5036i	−0.215602	−	0.373433i	−0.953458	+	0.301524i	$0.902505\pi$
$14$	5.65386			0.107933
$15$	−51.5998			−0.888201
$16$	−55.0797	−	95.4009i	−0.860621	−	1.49064i
$17$	−8.81433	−	15.2669i	−0.125752	−	0.217809i	0.796274	−	0.604935i	$-0.206801\pi$
$17$	−8.81433	−	15.2669i	−0.125752	−	0.217809i	−0.922027	+	0.387126i	$0.873468\pi$
$18$	22.8527	+	39.5820i	0.299246	+	0.518309i
$19$	11.5544	+	20.0128i	0.139514	+	0.241645i	0.927313	−	0.374287i	$-0.122113\pi$
$19$	11.5544	+	20.0128i	0.139514	+	0.241645i	−0.787799	+	0.615933i	$0.788779\pi$
$20$	152.992	−	264.990i	1.71050	−	2.96268i
$21$	1.66998	−	2.89249i	0.0173533	−	0.0300569i
$22$	−173.651			−1.68284
$23$	−37.7195	−	65.3320i	−0.341959	−	0.592290i	0.642838	−	0.766002i	$-0.277757\pi$
$23$	−37.7195	−	65.3320i	−0.341959	−	0.592290i	−0.984796	+	0.173713i	$0.944424\pi$
$24$	−149.149			−1.26854
$25$	170.838			1.36670
$26$	51.3205	−	88.8898i	0.387107	−	0.670489i
$27$	27.0000			0.192450
$28$	9.90290	+	17.1523i	0.0668383	+	0.115767i
$29$	−77.9248	+	134.970i	−0.498975	+	0.864250i	−0.999999	−	0.00118312i	$-0.999623\pi$
$29$	−77.9248	+	134.970i	−0.498975	+	0.864250i	0.501024	+	0.865433i	$0.332957\pi$
$30$	−131.021	−	226.936i	−0.797371	−	1.38109i
$31$	−128.881	+	223.228i	−0.746698	+	1.29332i	0.202700	+	0.979241i	$0.435028\pi$
$31$	−128.881	+	223.228i	−0.746698	+	1.29332i	−0.949397	+	0.314077i	$0.898305\pi$
$32$	80.8496	−	140.036i	0.446635	−	0.773595i
$33$	−51.2913	+	88.8391i	−0.270565	+	0.468633i
$34$	44.7624	−	77.5308i	0.225785	−	0.391071i
$35$	−9.57453	+	16.5836i	−0.0462398	+	0.0800896i
$36$	−80.0542	+	138.658i	−0.370621	+	0.641935i
$37$	32.4077	+	56.1318i	0.143994	+	0.249406i	0.928997	−	0.370086i	$-0.120672\pi$
$37$	32.4077	+	56.1318i	0.143994	+	0.249406i	−0.785003	+	0.619492i	$0.787339\pi$
$38$	−58.6776	+	101.633i	−0.250494	+	0.433868i
$39$	−30.3171	−	52.5108i	−0.124478	−	0.215602i
$40$	855.119			3.38015
$41$	−103.583	+	179.412i	−0.394561	+	0.683399i	−0.993045	−	0.117735i	$-0.962437\pi$
$41$	−103.583	+	179.412i	−0.394561	+	0.683399i	0.598484	+	0.801135i	$0.295770\pi$
$42$	16.9616			0.0623149
$43$	341.366			1.21065			0.605324	−	0.795979i	$-0.293043\pi$
$43$	341.366			1.21065			0.605324	+	0.795979i	$0.293043\pi$
$44$	−304.154	−	526.811i	−1.04211	−	1.80499i
$45$	−154.799			−0.512803
$46$	191.553	−	331.780i	0.613978	−	1.06344i
$47$	−266.039	+	460.793i	−0.825655	+	1.43008i	0.0757624	+	0.997126i	$0.475861\pi$
$47$	−266.039	+	460.793i	−0.825655	+	1.43008i	−0.901418	+	0.432951i	$0.857472\pi$
$48$	−165.239	−	286.203i	−0.496880	−	0.860621i
$49$	170.880	+	295.973i	0.498193	+	0.862896i
$50$	433.789	+	751.345i	1.22694	+	2.12512i
$51$	−26.4430	−	45.8006i	−0.0726031	−	0.125752i
$52$	359.558			0.958879
$53$	597.847			1.54944			0.774722	−	0.632302i	$-0.217890\pi$
$53$	597.847			1.54944			0.774722	+	0.632302i	$0.217890\pi$
$54$	68.5580	+	118.746i	0.172770	+	0.299246i
$55$	294.069	−	509.342i	0.720950	−	1.24872i
$56$	−27.6752	+	47.9348i	−0.0660401	+	0.114385i
$57$	34.6632	+	60.0385i	0.0805484	+	0.139514i
$58$	−791.462			−1.79179
$59$	−589.164			−1.30004			−0.650022	−	0.759915i	$-0.725240\pi$
$59$	−589.164			−1.30004			−0.650022	+	0.759915i	$0.725240\pi$
$60$	458.976	−	794.970i	0.987559	−	1.71050i
$61$	−266.273	−	461.199i	−0.558898	−	0.968040i	−0.997589	−	0.0694020i	$-0.977891\pi$
$61$	−266.273	−	461.199i	−0.558898	−	0.968040i	0.438690	−	0.898638i	$-0.355442\pi$
$62$	−1309.01			−2.68135
$63$	5.00995	−	8.67748i	0.0100190	−	0.0173533i
$64$	−60.1069			−0.117396
$65$	173.818	+	301.061i	0.331683	+	0.574493i
$66$	−520.952			−0.971587
$67$	514.175	−	190.755i	0.937559	−	0.347828i
$67$	514.175	−	190.755i	0.937559	−	0.347828i
$68$	313.611			0.559278
$69$	−113.158	−	195.996i	−0.197430	−	0.341959i
$70$	−97.2460			−0.166045
$71$	395.299	−	684.677i	0.660751	−	1.14445i	−0.319668	−	0.947530i	$-0.603571\pi$
$71$	395.299	−	684.677i	0.660751	−	1.14445i	0.980419	−	0.196925i	$-0.0630954\pi$
$72$	−447.447			−0.732391
$73$	281.059	+	486.809i	0.450624	+	0.780503i	0.998425	−	0.0561055i	$-0.0178683\pi$
$73$	281.059	+	486.809i	0.450624	+	0.780503i	−0.547801	+	0.836609i	$0.684535\pi$
$74$	−164.578	+	285.058i	−0.258538	+	0.447802i
$75$	512.514			0.789067
$76$	−411.102			−0.620482
$77$	19.0346	+	32.9688i	0.0281713	+	0.0487941i
$78$	153.962	−	266.669i	0.223496	−	0.387107i
$79$	629.549	−	1090.41i	0.896580	−	1.55292i	0.0647429	−	0.997902i	$-0.479377\pi$
$79$	629.549	−	1090.41i	0.896580	−	1.55292i	0.831837	−	0.555020i	$-0.187289\pi$
$80$	947.368	+	1640.89i	1.32399	+	2.29321i
$81$	81.0000			0.111111
$82$	−1052.07			−1.41685
$83$	444.076	+	769.161i	0.587273	+	1.01719i	0.994588	+	0.103898i	$0.0331316\pi$
$83$	444.076	+	769.161i	0.587273	+	1.01719i	−0.407315	+	0.913288i	$0.633535\pi$
$84$	29.7087	+	51.4570i	0.0385891	+	0.0668383i
$85$	151.606	+	262.589i	0.193459	+	0.335080i
$86$	866.792	+	1501.33i	1.08684	+	1.88247i
$87$	−233.774	+	404.909i	−0.288083	+	0.498975i
$88$	850.005	−	1472.25i	1.02967	−	1.78344i
$89$	−1123.83			−1.33850			−0.669249	−	0.743039i	$-0.733384\pi$
$89$	−1123.83			−1.33850			−0.669249	+	0.743039i	$0.733384\pi$
$90$	−393.064	−	680.808i	−0.460363	−	0.797371i
$91$	−22.5018			−0.0259212
$92$	1342.05			1.52085
$93$	−386.642	+	669.683i	−0.431106	+	0.746698i
$94$	−2702.09			−2.96489
$95$	−198.735	−	344.220i	−0.214630	−	0.371749i
$96$	242.549	−	420.107i	0.257865	−	0.446635i
$97$	480.446	+	832.157i	0.502906	+	0.871059i	0.999994	+	0.00335897i	$0.00106919\pi$
$97$	480.446	+	832.157i	0.502906	+	0.871059i	−0.497088	+	0.867700i	$0.665597\pi$
$98$	−867.793	+	1503.06i	−0.894493	+	1.54931i
$99$	−153.874	+	266.517i	−0.156211	+	0.270565i
$100$	−1519.59	+	2632.01i	−1.51959	+	2.63201i
$101$	−306.374	+	530.655i	−0.301835	+	0.522793i	−0.976552	−	0.215284i	$-0.930932\pi$
$101$	−306.374	+	530.655i	−0.301835	+	0.522793i	0.674717	+	0.738077i	$0.264266\pi$
$102$	134.287	−	232.592i	0.130357	−	0.225785i
$103$	115.027	−	199.232i	0.110038	−	0.190591i	−0.805747	−	0.592259i	$-0.798236\pi$
$103$	115.027	−	199.232i	0.110038	−	0.190591i	0.915785	+	0.401668i	$0.131569\pi$
$104$	502.419	+	870.216i	0.473714	+	0.820497i
$105$	−28.7236	+	49.7507i	−0.0266965	+	0.0462398i
$106$	1518.04	+	2629.33i	1.39099	+	2.40927i
$107$	−778.111			−0.703017			−0.351509	−	0.936185i	$-0.614331\pi$
$107$	−778.111			−0.703017			−0.351509	+	0.936185i	$0.614331\pi$
$108$	−240.163	+	415.974i	−0.213978	+	0.370621i
$109$	−1201.24			−1.05558			−0.527789	−	0.849376i	$-0.676979\pi$
$109$	−1201.24			−1.05558			−0.527789	+	0.849376i	$0.676979\pi$
$110$	2986.78			2.58889
$111$	97.2231	+	168.395i	0.0831352	+	0.143994i
$112$	−122.643			−0.103470
$113$	306.293	−	530.516i	0.254988	−	0.441652i	−0.709904	−	0.704298i	$-0.751262\pi$
$113$	306.293	−	530.516i	0.254988	−	0.441652i	0.964892	+	0.262646i	$0.0845951\pi$
$114$	−176.033	+	304.898i	−0.144623	+	0.250494i
$115$	648.772	+	1123.71i	0.526073	+	0.911184i
$116$	−1386.27	−	2401.09i	−1.10959	−	1.92186i
$117$	−90.9514	−	157.532i	−0.0718672	−	0.124478i
$118$	−1496.00	−	2591.14i	−1.16710	−	2.02147i
$119$	−19.6264			−0.0151189
$120$	2565.36			1.95153
$121$	80.8794	+	140.087i	0.0607659	+	0.105250i
$122$	1352.23	−	2342.14i	1.00349	−	1.73809i
$123$	−310.750	+	538.235i	−0.227800	+	0.394561i
$124$	−2292.76	−	3971.18i	−1.66045	−	2.87599i
$125$	−788.412			−0.564141
$126$	50.8847			0.0359775
$127$	205.635	−	356.170i	0.143678	−	0.248858i	−0.785201	−	0.619241i	$-0.787440\pi$
$127$	205.635	−	356.170i	0.143678	−	0.248858i	0.928879	+	0.370383i	$0.120774\pi$
$128$	−799.420	−	1384.64i	−0.552026	−	0.956138i
$129$	1024.10			0.698968
$130$	−882.710	+	1528.90i	−0.595529	+	1.03149i
$131$	2280.60			1.52105			0.760523	−	0.649311i	$-0.224943\pi$
$131$	2280.60			1.52105			0.760523	+	0.649311i	$0.224943\pi$
$132$	−912.463	−	1580.43i	−0.601664	−	1.04211i
$133$	25.7276			0.0167734
$134$	2144.52	+	1776.98i	1.38253	+	1.14558i
$135$	−464.398			−0.296067
$136$	438.216	+	759.013i	0.276300	+	0.478565i
$137$	2.39001			0.00149046			0.000745229	−	1.00000i	$-0.499763\pi$
$137$	2.39001			0.00149046			0.000745229		1.00000i	$0.499763\pi$
$138$	574.660	−	995.340i	0.354480	−	0.613978i
$139$	−1410.99			−0.860997			−0.430498	−	0.902591i	$-0.641662\pi$
$139$	−1410.99			−0.860997			−0.430498	+	0.902591i	$0.641662\pi$
$140$	−170.329	−	295.019i	−0.102825	−	0.178098i
$141$	−798.117	+	1382.38i	−0.476692	+	0.825655i
$142$	4014.95			2.37272
$143$	691.113			0.404152
$144$	−495.717	−	858.608i	−0.286874	−	0.496880i
$145$	1340.30	−	2321.47i	0.767628	−	1.32957i
$146$	−1427.32	+	2472.20i	−0.809083	+	1.40137i
$147$	512.641	+	887.920i	0.287632	+	0.498193i
$148$	−1153.06			−0.640409
$149$	−363.911			−0.200085			−0.100043	−	0.994983i	$-0.531898\pi$
$149$	−363.911			−0.200085			−0.100043	+	0.994983i	$0.531898\pi$
$150$	1301.37	+	2254.04i	0.708375	+	1.22694i
$151$	−1575.57	−	2728.96i	−0.849124	−	1.47073i	−0.881991	−	0.471266i	$-0.843797\pi$
$151$	−1575.57	−	2728.96i	−0.849124	−	1.47073i	0.0328668	−	0.999460i	$-0.489536\pi$
$152$	−574.444	−	994.966i	−0.306536	−	0.530937i
$153$	−79.3290	−	137.402i	−0.0419174	−	0.0726031i
$154$	−96.6645	+	167.428i	−0.0505808	+	0.0876085i
$155$	2216.74	−	3839.50i	1.14873	−	1.98965i
$156$	1078.67			0.553609
$157$	388.832	+	673.477i	0.197657	+	0.342352i	0.947768	−	0.318960i	$-0.103333\pi$
$157$	388.832	+	673.477i	0.197657	+	0.342352i	−0.750111	+	0.661312i	$0.770000\pi$
$158$	6394.17			3.21957
$159$	1793.54			0.894572
$160$	−1390.61	+	2408.61i	−0.687108	+	1.19011i
$161$	−83.9878			−0.0411128
$162$	205.674	+	356.238i	0.0997486	+	0.172770i
$163$	1294.35	−	2241.88i	0.621972	−	1.07729i	−0.367147	−	0.930163i	$-0.619665\pi$
$163$	1294.35	−	2241.88i	0.621972	−	1.07729i	0.989118	−	0.147123i	$-0.0470014\pi$
$164$	−1842.73	−	3191.70i	−0.877396	−	1.51970i
$165$	882.207	−	1528.03i	0.416241	−	0.720950i
$166$	−2255.18	+	3906.09i	−1.05443	+	1.82633i
$167$	261.513	−	452.954i	0.121177	−	0.209884i	−0.799055	−	0.601258i	$-0.794667\pi$
$167$	261.513	−	452.954i	0.121177	−	0.209884i	0.920232	+	0.391373i	$0.128000\pi$
$168$	−83.0255	+	143.804i	−0.0381283	+	0.0660401i
$169$	894.249	−	1548.89i	0.407032	−	0.705000i
$170$	−769.911	+	1333.52i	−0.347350	+	0.601628i
$171$	103.990	+	180.115i	0.0465046	+	0.0805484i
$172$	−3036.43	+	5259.24i	−1.34608	+	2.33147i
$173$	919.941	+	1593.38i	0.404288	+	0.700247i	0.994238	−	0.107192i	$-0.0341861\pi$
$173$	919.941	+	1593.38i	0.404288	+	0.700247i	−0.589950	+	0.807439i	$0.700853\pi$
$174$	−2374.39			−1.03449
$175$	95.0988	−	164.716i	0.0410788	−	0.0711506i
$176$	3766.81			1.61326
$177$	−1767.49			−0.750581
$178$	−2853.62	−	4942.62i	−1.20162	−	2.08126i
$179$	−1190.64			−0.497165			−0.248583	−	0.968611i	$-0.579965\pi$
$179$	−1190.64			−0.497165			−0.248583	+	0.968611i	$0.579965\pi$
$180$	1376.93	−	2384.91i	0.570168	−	0.987559i
$181$	−48.3947	+	83.8220i	−0.0198737	+	0.0344223i	−0.875791	−	0.482690i	$-0.839660\pi$
$181$	−48.3947	+	83.8220i	−0.0198737	+	0.0344223i	0.855917	+	0.517112i	$0.172993\pi$
$182$	−57.1362	−	98.9629i	−0.0232704	−	0.0403056i
$183$	−798.820	−	1383.60i	−0.322680	−	0.558898i
$184$	1875.27	+	3248.07i	0.751343	+	1.30136i
$185$	−557.411	−	965.464i	−0.221522	−	0.383688i
$186$	−3927.02			−1.54808
$187$	602.797			0.235727
$188$	−4732.79	−	8197.43i	−1.83603	−	3.18010i
$189$	15.0298	−	26.0324i	0.00578444	−	0.0100190i
$190$	1009.25	−	1748.07i	0.385362	−	0.667466i
$191$	1686.35	+	2920.85i	0.638849	+	1.10652i	0.985686	+	0.168594i	$0.0539225\pi$
$191$	1686.35	+	2920.85i	0.638849	+	1.10652i	−0.346837	+	0.937926i	$0.612744\pi$
$192$	−180.321			−0.0677787
$193$	2559.30			0.954521			0.477260	−	0.878762i	$-0.341630\pi$
$193$	2559.30			0.954521			0.477260	+	0.878762i	$0.341630\pi$
$194$	−2439.88	+	4226.00i	−0.902955	+	1.56396i
$195$	521.453	+	903.183i	0.191498	+	0.331683i
$196$	−6079.86			−2.21569
$197$	−982.895	+	1702.42i	−0.355474	+	0.615699i	−0.987199	−	0.159493i	$-0.949014\pi$
$197$	−982.895	+	1702.42i	−0.355474	+	0.615699i	0.631725	+	0.775193i	$0.282347\pi$
$198$	−1562.86			−0.560946
$199$	−1188.23	−	2058.07i	−0.423273	−	0.733130i	0.572985	−	0.819566i	$-0.305785\pi$
$199$	−1188.23	−	2058.07i	−0.423273	−	0.733130i	−0.996257	+	0.0864361i	$0.972452\pi$
$200$	−8493.45			−3.00289
$201$	1542.52	−	572.265i	0.541300	−	0.200818i
$202$	−3111.76			−1.08387
$203$	86.7554	+	150.265i	0.0299952	+	0.0519533i
$204$	940.832			0.322899
$205$	1781.63	−	3085.87i	0.606996	−	1.05135i
$206$	1168.29			0.395141
$207$	−339.475	−	587.988i	−0.113986	−	0.197430i
$208$	−1113.24	+	1928.19i	−0.371102	+	0.642768i
$209$	−790.187			−0.261523
$210$	−291.738			−0.0958659
$211$	1785.17	+	3092.00i	0.582445	+	1.00882i	0.995189	+	0.0979776i	$0.0312373\pi$
$211$	1785.17	+	3092.00i	0.582445	+	1.00882i	−0.412743	+	0.910847i	$0.635429\pi$
$212$	−5317.80	+	9210.69i	−1.72277	+	2.98393i
$213$	1185.90	−	2054.03i	0.381485	−	0.660751i
$214$	−1975.77	−	3422.13i	−0.631125	−	1.09314i
$215$	−5871.48			−1.86247
$216$	−1342.34			−0.422846
$217$	143.485	+	248.524i	0.0448868	+	0.0777462i
$218$	−3050.17	−	5283.05i	−0.947631	−	1.64135i
$219$	843.178	+	1460.43i	0.260168	+	0.450624i
$220$	5231.44	+	9061.11i	1.60320	+	2.77682i
$221$	−178.150	+	308.565i	−0.0542248	+	0.0939200i
$222$	−493.735	+	855.174i	−0.149267	+	0.258538i
$223$	−337.975			−0.101491			−0.0507454	−	0.998712i	$-0.516160\pi$
$223$	−337.975			−0.101491			−0.0507454	+	0.998712i	$0.516160\pi$
$224$	−90.0117	−	155.905i	−0.0268489	−	0.0465037i
$225$	1537.54			0.455568
$226$	3110.94			0.915650
$227$	−3381.11	+	5856.25i	−0.988598	+	1.71230i	−0.363897	+	0.931439i	$0.618554\pi$
$227$	−3381.11	+	5856.25i	−0.988598	+	1.71230i	−0.624702	+	0.780863i	$0.714779\pi$
$228$	−1233.31			−0.358236
$229$	1936.96	+	3354.91i	0.558942	+	0.968116i	0.997585	+	0.0694544i	$0.0221258\pi$
$229$	1936.96	+	3354.91i	0.558942	+	0.968116i	−0.438643	+	0.898661i	$0.644541\pi$
$230$	−3294.71	+	5706.60i	−0.944550	+	1.63601i
$231$	57.1037	+	98.9064i	0.0162647	+	0.0281713i
$232$	3874.14	−	6710.21i	1.09634	−	1.89891i
$233$	1603.04	−	2776.55i	0.450724	−	0.780677i	−0.547707	−	0.836670i	$-0.684499\pi$
$233$	1603.04	−	2776.55i	0.450724	−	0.780677i	0.998431	+	0.0559935i	$0.0178326\pi$
$234$	461.885	−	800.008i	0.129036	−	0.223496i
$235$	4575.86	−	7925.62i	1.27020	−	2.20004i
$236$	5240.56	−	9076.92i	1.44547	−	2.50363i
$237$	1888.65	−	3271.23i	0.517641	−	0.896580i
$238$	−49.8350	−	86.3167i	−0.0135728	−	0.0235087i
$239$	−2687.04	+	4654.10i	−0.727240	+	1.25962i	0.230805	+	0.973000i	$0.425864\pi$
$239$	−2687.04	+	4654.10i	−0.727240	+	1.25962i	−0.958045	+	0.286617i	$0.907469\pi$
$240$	2842.10	+	4922.67i	0.764404	+	1.32399i
$241$	3183.12			0.850799			0.425400	−	0.905006i	$-0.360134\pi$
$241$	3183.12			0.850799			0.425400	+	0.905006i	$0.360134\pi$
$242$	−410.735	+	711.414i	−0.109104	+	0.188973i
$243$	243.000			0.0641500
$244$	9473.91			2.48568
$245$	−2939.13	−	5090.72i	−0.766425	−	1.32749i
$246$	−3156.21			−0.818018
$247$	233.531	−	404.488i	0.0601588	−	0.104198i
$248$	6407.47	−	11098.1i	1.64062	−	2.84165i
$249$	1332.23	+	2307.48i	0.339062	+	0.587273i
$250$	−2001.92	−	3467.43i	−0.506451	−	0.877199i
$251$	1829.03	+	3167.98i	0.459950	+	0.796657i	0.998958	−	0.0456441i	$-0.0145340\pi$
$251$	1829.03	+	3167.98i	0.459950	+	0.796657i	−0.539008	+	0.842301i	$0.681201\pi$
$252$	89.1261	+	154.371i	0.0222794	+	0.0385891i
$253$	2579.57			0.641013
$254$	2088.58			0.515941
$255$	454.818	+	787.768i	0.111693	+	0.193459i
$256$	3819.32	−	6615.26i	0.932451	−	1.61505i
$257$	1797.94	−	3114.13i	0.436391	−	0.755852i	−0.561017	−	0.827805i	$-0.689590\pi$
$257$	1797.94	−	3114.13i	0.436391	−	0.755852i	0.997408	+	0.0719524i	$0.0229230\pi$
$258$	2600.38	+	4503.99i	0.627490	+	1.08684i
$259$	72.1604			0.0173121
$260$	−6184.37			−1.47515
$261$	−701.323	+	1214.73i	−0.166325	+	0.288083i
$262$	5790.87	+	10030.1i	1.36550	+	2.36511i
$263$	−2476.59			−0.580658			−0.290329	−	0.956927i	$-0.593765\pi$
$263$	−2476.59			−0.580658			−0.290329	+	0.956927i	$0.593765\pi$
$264$	2550.02	−	4416.76i	0.594480	−	1.02967i
$265$	−10282.9			−2.38368
$266$	65.3270	+	113.150i	0.0150581	+	0.0260814i
$267$	−3371.50			−0.772782
$268$	−1634.68	+	9618.35i	−0.372590	+	2.19229i
$269$	5966.65			1.35239			0.676195	−	0.736723i	$-0.263628\pi$
$269$	5966.65			1.35239			0.676195	+	0.736723i	$0.263628\pi$
$270$	−1179.19	−	2042.42i	−0.265790	−	0.460363i
$271$	899.695			0.201670			0.100835	−	0.994903i	$-0.467849\pi$
$271$	899.695			0.201670			0.100835	+	0.994903i	$0.467849\pi$
$272$	−970.981	+	1681.79i	−0.216450	+	0.374902i
$273$	−67.5054			−0.0149656
$274$	6.06869	+	10.5113i	0.00133804	+	0.00231755i
$275$	−2920.83	+	5059.03i	−0.640483	+	1.10935i
$276$	4026.14			0.878061
$277$	−6146.04			−1.33314			−0.666570	−	0.745442i	$-0.732238\pi$
$277$	−6146.04			−1.33314			−0.666570	+	0.745442i	$0.732238\pi$
$278$	−3582.76	−	6205.53i	−0.772949	−	1.33879i
$279$	−1159.92	+	2009.05i	−0.248899	+	0.431106i
$280$	476.011	−	824.475i	0.101597	−	0.175971i
$281$	−1489.06	−	2579.12i	−0.316120	−	0.547536i	0.663555	−	0.748128i	$-0.269047\pi$
$281$	−1489.06	−	2579.12i	−0.316120	−	0.547536i	−0.979675	+	0.200592i	$0.935714\pi$
$282$	−8106.27			−1.71178
$283$	−7211.76			−1.51482			−0.757411	−	0.652938i	$-0.773536\pi$
$283$	−7211.76			−1.51482			−0.757411	+	0.652938i	$0.773536\pi$
$284$	7032.30	+	12180.3i	1.46933	+	2.54496i
$285$	−596.206	−	1032.66i	−0.123916	−	0.214630i
$286$	1754.86	+	3039.51i	0.362822	+	0.628427i
$287$	115.322	+	199.743i	0.0237185	+	0.0410817i
$288$	727.647	−	1260.32i	0.148878	−	0.257865i
$289$	2301.12	−	3985.65i	0.468373	−	0.811245i
$290$	13613.1			2.75651
$291$	1441.34	+	2496.47i	0.290353	+	0.502906i
$292$	−10000.0			−2.00413
$293$	5847.34			1.16589			0.582944	−	0.812512i	$-0.301901\pi$
$293$	5847.34			1.16589			0.582944	+	0.812512i	$0.301901\pi$
$294$	−2603.38	+	4509.18i	−0.516436	+	0.894493i
$295$	10133.6			2.00000
$296$	−1611.19	−	2790.67i	−0.316381	−	0.547988i
$297$	−461.621	+	799.552i	−0.0901885	+	0.156211i
$298$	−924.036	−	1600.48i	−0.179624	−	0.311118i
$299$	−762.364	+	1320.45i	−0.147454	+	0.255397i
$300$	−4558.77	+	7896.02i	−0.877336	+	1.51959i
$301$	190.025	−	329.134i	0.0363883	−	0.0630264i
$302$	8001.31	−	13858.7i	1.52458	−	2.64065i
$303$	−919.121	+	1591.96i	−0.174264	+	0.301835i
$304$	1272.83	−	2204.60i	0.240137	−	0.415930i
$305$	4579.88	+	7932.59i	0.859815	+	1.48924i
$306$	402.862	−	697.777i	0.0752617	−	0.130357i
$307$	2808.64	+	4864.71i	0.522142	+	0.904377i	0.999668	+	0.0257590i	$0.00820025\pi$
$307$	2808.64	+	4864.71i	0.522142	+	0.904377i	−0.477526	+	0.878618i	$0.658466\pi$
$308$	−677.243			−0.125291
$309$	345.080	−	597.696i	0.0635304	−	0.110038i
$310$	22514.8			4.12502
$311$	−5729.22			−1.04461			−0.522306	−	0.852758i	$-0.674928\pi$
$311$	−5729.22			−1.04461			−0.522306	+	0.852758i	$0.674928\pi$
$312$	1507.26	+	2610.65i	0.273499	+	0.473714i
$313$	−5873.64			−1.06070			−0.530348	−	0.847780i	$-0.677939\pi$
$313$	−5873.64			−1.06070			−0.530348	+	0.847780i	$0.677939\pi$
$314$	−1974.63	+	3420.16i	−0.354888	+	0.614685i
$315$	−86.1708	+	149.252i	−0.0154133	+	0.0266965i
$316$	11199.6	+	19398.2i	1.99375	+	3.45328i
$317$	−3277.71	−	5677.16i	−0.580740	−	1.00587i	−0.995392	−	0.0958906i	$-0.969430\pi$
$317$	−3277.71	−	5677.16i	−0.580740	−	1.00587i	0.414652	−	0.909980i	$-0.363903\pi$
$318$	4554.13	+	7887.98i	0.803091	+	1.39099i
$319$	−2664.57	−	4615.18i	−0.467673	−	0.810033i
$320$	1033.83			0.180603
$321$	−2334.33			−0.405887
$322$	−213.260	−	369.378i	−0.0369085	−	0.0639274i
$323$	203.689	−	352.799i	0.0350884	−	0.0607749i
$324$	−720.488	+	1247.92i	−0.123540	+	0.213978i
$325$	−1726.44	−	2990.28i	−0.294664	−	0.510372i
$326$	13146.4			2.23347
$327$	−3603.72			−0.609438
$328$	5149.79	−	8919.69i	0.866919	−	1.50155i
$329$	296.187	+	513.011i	0.0496332	+	0.0859672i
$330$	8960.34			1.49470
$331$	−4986.86	+	8637.50i	−0.828105	+	1.43432i	0.0714174	+	0.997447i	$0.477248\pi$
$331$	−4986.86	+	8637.50i	−0.828105	+	1.43432i	−0.899523	+	0.436874i	$0.856086\pi$
$332$	−15800.1			−2.61187
$333$	291.669	+	505.186i	0.0479982	+	0.0831352i
$334$	2656.12			0.435139
$335$	−8843.77	+	3280.98i	−1.44235	+	0.535101i
$336$	−367.929			−0.0597386
$337$	3619.77	+	6269.62i	0.585108	+	1.01344i	0.994862	+	0.101241i	$0.0322812\pi$
$337$	3619.77	+	6269.62i	0.585108	+	1.01344i	−0.409754	+	0.912196i	$0.634385\pi$
$338$	9082.66			1.46163
$339$	918.880	−	1591.55i	0.147217	−	0.254988i
$340$	−5394.09			−0.860399
$341$	−4406.96	−	7633.08i	−0.699855	−	1.21218i
$342$	−528.098	+	914.693i	−0.0834979	+	0.144623i
$343$	762.359			0.120010
$344$	−16971.5			−2.66001
$345$	1946.32	+	3371.12i	0.303728	+	0.526073i
$346$	−4671.80	+	8091.79i	−0.725889	+	1.25728i
$347$	2059.97	−	3567.97i	0.318689	−	0.551985i	−0.661526	−	0.749922i	$-0.730091\pi$
$347$	2059.97	−	3567.97i	0.318689	−	0.551985i	0.980215	+	0.197937i	$0.0634242\pi$
$348$	−4158.81	−	7203.27i	−0.640619	−	1.10959i
$349$	1114.26			0.170902			0.0854511	−	0.996342i	$-0.472767\pi$
$349$	1114.26			0.170902			0.0854511	+	0.996342i	$0.472767\pi$
$350$	965.894			0.147512
$351$	−272.854	−	472.597i	−0.0414925	−	0.0718672i
$352$	2764.59	+	4788.40i	0.418616	+	0.725065i
$353$	−5268.11	−	9124.64i	−0.794315	−	1.37579i	−0.923273	−	0.384144i	$-0.874497\pi$
$353$	−5268.11	−	9124.64i	−0.794315	−	1.37579i	0.128958	−	0.991650i	$-0.458837\pi$
$354$	−4487.99	−	7773.42i	−0.673824	−	1.16710i
$355$	−6799.12	+	11776.4i	−1.01651	+	1.76064i
$356$	9996.42	−	17314.3i	1.48823	−	2.57769i
$357$	−58.8791			−0.00872888
$358$	−3023.25	−	5236.43i	−0.446324	−	0.773055i
$359$	−5305.59			−0.779996			−0.389998	−	0.920816i	$-0.627524\pi$
$359$	−5305.59			−0.779996			−0.389998	+	0.920816i	$0.627524\pi$
$360$	7696.07			1.12672
$361$	3162.49	−	5477.60i	0.461072	−	0.798600i
$362$	−491.532			−0.0713656
$363$	242.638	+	420.262i	0.0350832	+	0.0607659i
$364$	200.152	−	346.673i	0.0288209	−	0.0499192i
$365$	−4834.21	−	8373.09i	−0.693244	−	1.20073i
$366$	4056.70	−	7026.41i	0.579364	−	1.00349i
$367$	−665.624	+	1152.89i	−0.0946738	+	0.163980i	−0.909472	−	0.415764i	$-0.863514\pi$
$367$	−665.624	+	1152.89i	−0.0946738	+	0.163980i	0.814799	+	0.579744i	$0.196847\pi$
$368$	−4155.15	+	7196.94i	−0.588593	+	1.01947i
$369$	−932.250	+	1614.70i	−0.131520	+	0.227800i
$370$	2830.74	−	4902.98i	0.397738	−	0.688902i
$371$	332.798	−	576.423i	0.0465714	−	0.0806641i
$372$	−6878.29	−	11913.5i	−0.958663	−	1.66045i
$373$	−5144.22	+	8910.06i	−0.714096	+	1.23685i	0.249211	+	0.968449i	$0.419829\pi$
$373$	−5144.22	+	8910.06i	−0.714096	+	1.23685i	−0.963307	+	0.268402i	$0.913505\pi$
$374$	1530.61	+	2651.10i	0.211621	+	0.366538i
$375$	−2365.24			−0.325707
$376$	13226.5	−	22909.0i	1.81411	−	3.14213i
$377$	3149.94			0.430319
$378$	152.654			0.0207716
$379$	5343.03	+	9254.41i	0.724151	+	1.25427i	0.959323	+	0.282312i	$0.0911014\pi$
$379$	5343.03	+	9254.41i	0.724151	+	1.25427i	−0.235172	+	0.971954i	$0.575565\pi$
$380$	7070.93			0.954556
$381$	616.904	−	1068.51i	0.0829527	−	0.143678i
$382$	−8563.92	+	14833.1i	−1.14704	+	1.98673i
$383$	−518.698	−	898.411i	−0.0692016	−	0.119861i	0.829348	−	0.558732i	$-0.188712\pi$
$383$	−518.698	−	898.411i	−0.0692016	−	0.119861i	−0.898550	+	0.438871i	$0.855379\pi$
$384$	−2398.26	−	4153.91i	−0.318713	−	0.552026i
$385$	−327.393	−	567.062i	−0.0433390	−	0.0750653i
$386$	6498.54	+	11255.8i	0.856909	+	1.48421i
$387$	3072.30			0.403550
$388$	−17094.1			−2.23665
$389$	5068.25	+	8778.47i	0.660593	+	1.14418i	0.980460	+	0.196718i	$0.0630284\pi$
$389$	5068.25	+	8778.47i	0.660593	+	1.14418i	−0.319867	+	0.947462i	$0.603638\pi$
$390$	−2648.13	+	4586.70i	−0.343829	+	0.595529i
$391$	−664.943	+	1151.72i	−0.0860042	+	0.148964i
$392$	−8495.55	−	14714.7i	−1.09462	−	1.89593i
$393$	6841.80			0.878176
$394$	−9983.01			−1.27649
$395$	−10828.2	+	18755.0i	−1.37931	+	2.38903i
$396$	−2737.39	−	4741.30i	−0.347371	−	0.601664i
$397$	−9577.91			−1.21083			−0.605417	−	0.795908i	$-0.706994\pi$
$397$	−9577.91			−1.21083			−0.605417	+	0.795908i	$0.706994\pi$
$398$	6034.26	−	10451.6i	0.759976	−	1.31632i
$399$	77.1827			0.00968413
$400$	−9409.71	−	16298.1i	−1.17621	−	2.03726i
$401$	−14536.1			−1.81022			−0.905110	−	0.425177i	$-0.860212\pi$
$401$	−14536.1			−1.81022			−0.905110	+	0.425177i	$0.860212\pi$
$402$	6433.57	+	5330.93i	0.798203	+	0.661399i
$403$	5209.72			0.643957
$404$	−5450.33	−	9440.26i	−0.671199	−	1.16255i
$405$	−1393.20			−0.170934
$406$	−440.576	+	763.100i	−0.0538557	+	0.0932808i
$407$	−2216.31			−0.269922
$408$	1314.65	+	2277.04i	0.159522	+	0.276300i
$409$	4516.84	−	7823.40i	0.546072	−	0.945824i	−0.452467	−	0.891781i	$-0.649456\pi$
$409$	4516.84	−	7823.40i	0.546072	−	0.945824i	0.998539	−	0.0540428i	$-0.0172107\pi$
$410$	18095.5			2.17969
$411$	7.17004			0.000860516
$412$	2046.30	+	3544.30i	0.244694	+	0.423823i
$413$	−327.964	+	568.051i	−0.0390752	+	0.0676803i
$414$	1723.98	−	2986.02i	0.204659	−	0.354480i
$415$	−7638.07	−	13229.5i	−0.903466	−	1.56485i
$416$	−3268.17			−0.385181
$417$	−4232.97			−0.497097
$418$	−2006.43	−	3475.24i	−0.234779	−	0.406650i
$419$	3858.73	+	6683.52i	0.449908	+	0.779263i	0.998380	−	0.0569062i	$-0.0181236\pi$
$419$	3858.73	+	6683.52i	0.449908	+	0.779263i	−0.548472	+	0.836169i	$0.684790\pi$
$420$	−510.988	−	885.057i	−0.0593659	−	0.102825i
$421$	3436.48	+	5952.17i	0.397824	+	0.689052i	0.993457	−	0.114205i	$-0.0364321\pi$
$421$	3436.48	+	5952.17i	0.397824	+	0.689052i	−0.595633	+	0.803257i	$0.703099\pi$
$422$	−9065.74	+	15702.3i	−1.04577	+	1.81132i
$423$	−2394.35	+	4147.14i	−0.275218	+	0.476692i
$424$	−29722.8			−3.40440
$425$	−1505.82	−	2608.16i	−0.171866	−	0.297681i
$426$	12044.8			1.36989
$427$	−592.895			−0.0671949
$428$	6921.23	−	11987.9i	0.781660	−	1.35387i
$429$	2073.34			0.233337
$430$	−14908.8	−	25822.8i	−1.67201	−	2.89601i
$431$	−1009.48	+	1748.47i	−0.112819	+	0.195408i	−0.916906	−	0.399104i	$-0.869321\pi$
$431$	−1009.48	+	1748.47i	−0.112819	+	0.195408i	0.804087	+	0.594512i	$0.202655\pi$
$432$	−1487.15	−	2575.82i	−0.165627	−	0.286874i
$433$	−3477.16	+	6022.63i	−0.385917	+	0.668427i	−0.991896	−	0.127053i	$-0.959448\pi$
$433$	−3477.16	+	6022.63i	−0.385917	+	0.668427i	0.605979	+	0.795480i	$0.292781\pi$
$434$	−728.672	+	1262.10i	−0.0805930	+	0.139591i
$435$	4020.91	−	6964.42i	0.443190	−	0.767628i
$436$	10684.9	−	18506.8i	1.17366	−	2.03284i
$437$	871.652	−	1509.75i	0.0954160	−	0.165265i
$438$	−4281.97	+	7416.59i	−0.467124	+	0.809083i
$439$	−4341.46	−	7519.63i	−0.471997	−	0.817523i	0.527490	−	0.849561i	$-0.323133\pi$
$439$	−4341.46	−	7519.63i	−0.471997	−	0.817523i	−0.999487	+	0.0320388i	$0.989800\pi$
$440$	−14620.0	+	25322.7i	−1.58405	+	2.74366i
$441$	1537.92	+	2663.76i	0.166064	+	0.287632i
$442$	−1809.42			−0.194718
$443$	−2761.06	+	4782.30i	−0.296122	+	0.512899i	−0.975245	−	0.221126i	$-0.929027\pi$
$443$	−2761.06	+	4782.30i	−0.296122	+	0.512899i	0.679123	+	0.734024i	$0.262360\pi$
$444$	−3459.17			−0.369740
$445$	19329.9			2.05916
$446$	−858.180	−	1486.41i	−0.0911121	−	0.157811i
$447$	−1091.73			−0.115519
$448$	−33.4591	+	57.9529i	−0.00352856	+	0.00611165i
$449$	4760.15	−	8244.82i	0.500323	−	0.866586i	−0.499677	−	0.866212i	$-0.666548\pi$
$449$	4760.15	−	8244.82i	0.500323	−	0.866586i	1.00000		0.000373453i	$-0.000118874\pi$
$450$	3904.10	+	6762.11i	0.408980	+	0.708375i
$451$	−3541.95	−	6134.83i	−0.369809	−	0.640527i
$452$	5448.91	+	9437.79i	0.567025	+	0.982115i
$453$	−4726.70	−	8186.88i	−0.490242	−	0.849124i
$454$	−34341.0			−3.55001
$455$	387.030			0.0398775
$456$	−1723.33	−	2984.90i	−0.176979	−	0.306536i
$457$	−7209.54	+	12487.3i	−0.737961	+	1.27819i	0.215451	+	0.976515i	$0.430878\pi$
$457$	−7209.54	+	12487.3i	−0.737961	+	1.27819i	−0.953412	+	0.301671i	$0.902456\pi$
$458$	−9836.58	+	17037.5i	−1.00357	+	1.73823i
$459$	−237.987	−	412.205i	−0.0242010	−	0.0419174i
$460$	−23083.1			−2.33969
$461$	8353.52			0.843952			0.421976	−	0.906607i	$-0.361337\pi$
$461$	8353.52			0.843952			0.421976	+	0.906607i	$0.361337\pi$
$462$	−289.993	+	502.283i	−0.0292028	+	0.0505808i
$463$	−740.219	−	1282.10i	−0.0742999	−	0.128691i	0.826482	−	0.562964i	$-0.190339\pi$
$463$	−740.219	−	1282.10i	−0.0742999	−	0.128691i	−0.900782	+	0.434272i	$0.857006\pi$
$464$	17168.3			1.71771
$465$	6650.21	−	11518.5i	0.663218	−	1.14873i
$466$	16281.7			1.61853
$467$	2889.09	+	5004.04i	0.286276	+	0.495845i	0.972918	−	0.231151i	$-0.0742492\pi$
$467$	2889.09	+	5004.04i	0.286276	+	0.495845i	−0.686642	+	0.726996i	$0.740916\pi$
$468$	3236.02			0.319626
$469$	102.301	−	601.935i	0.0100722	−	0.0592639i
$470$	46475.8			4.56121
$471$	1166.50	+	2020.43i	0.114117	+	0.197657i
$472$	29291.1			2.85642
$473$	−5836.37	+	10108.9i	−0.567350	+	0.982679i
$474$	19182.5			1.85882
$475$	1973.93	+	3418.95i	0.190674	+	0.330258i
$476$	174.575	−	302.372i	0.0168101	−	0.0291160i
$477$	5380.62			0.516481
$478$	−27291.6			−2.61148
$479$	−3385.48	−	5863.82i	−0.322936	−	0.559342i	0.658156	−	0.752881i	$-0.271337\pi$
$479$	−3385.48	−	5863.82i	−0.322936	−	0.559342i	−0.981093	+	0.193539i	$0.938003\pi$
$480$	−4171.83	+	7225.82i	−0.396702	+	0.687108i
$481$	655.006	−	1134.50i	0.0620908	−	0.107545i
$482$	8082.52	+	13999.3i	0.763794	+	1.32293i
$483$	−251.963			−0.0237365
$484$	−2877.66			−0.270254
$485$	−8263.64	−	14313.0i	−0.773676	−	1.34005i
$486$	617.022	+	1068.71i	0.0575899	+	0.0997486i
$487$	3798.35	+	6578.94i	0.353429	+	0.612157i	0.986848	−	0.161652i	$-0.0516823\pi$
$487$	3798.35	+	6578.94i	0.353429	+	0.612157i	−0.633419	+	0.773809i	$0.718349\pi$
$488$	13238.1	+	22929.1i	1.22800	+	2.12695i
$489$	3883.05	−	6725.64i	0.359095	−	0.621972i
$490$	14926.0	−	25852.6i	1.37610	−	2.38347i
$491$	17895.7			1.64485			0.822427	−	0.568871i	$-0.192620\pi$
$491$	17895.7			1.64485			0.822427	+	0.568871i	$0.192620\pi$
$492$	−5528.19	−	9575.10i	−0.506565	−	0.877396i
$493$	2747.42			0.250989
$494$	2371.91			0.216027
$495$	2646.62	−	4584.08i	0.240317	−	0.416241i
$496$	28394.8			2.57049
$497$	−440.095	−	762.266i	−0.0397202	−	0.0687974i
$498$	−6765.54	+	11718.3i	−0.608777	+	1.05443i
$499$	2739.23	+	4744.49i	0.245741	+	0.425636i	0.962340	−	0.271850i	$-0.0876353\pi$
$499$	2739.23	+	4744.49i	0.245741	+	0.425636i	−0.716599	+	0.697486i	$0.754302\pi$
$500$	7012.86	−	12146.6i	0.627249	−	1.08643i
$501$	784.539	−	1358.86i	0.0699614	−	0.121177i
$502$	−9288.50	+	16088.1i	−0.825828	+	1.43038i
$503$	5620.96	−	9735.79i	0.498263	−	0.863017i	−0.501735	−	0.865021i	$-0.667305\pi$
$503$	5620.96	−	9735.79i	0.498263	−	0.863017i	0.999998	+	0.00200457i	$0.000638075\pi$
$504$	−249.076	+	431.413i	−0.0220134	+	0.0381283i
$505$	5269.61	−	9127.23i	0.464346	−	0.804270i
$506$	6550.01	+	11344.9i	0.575461	+	0.996728i
$507$	2682.75	−	4646.66i	0.235000	−	0.407032i
$508$	3658.21	+	6336.20i	0.319502	+	0.553393i
$509$	−6585.97			−0.573513			−0.286756	−	0.958004i	$-0.592577\pi$
$509$	−6585.97			−0.573513			−0.286756	+	0.958004i	$0.592577\pi$
$510$	−2309.73	+	4000.57i	−0.200543	+	0.347350i
$511$	625.819			0.0541773
$512$	26001.1			2.24433
$513$	311.969	+	540.346i	0.0268495	+	0.0465046i
$514$	18261.2			1.56706
$515$	−1978.45	+	3426.78i	−0.169283	+	0.293207i
$516$	−9109.28	+	15777.7i	−0.777158	+	1.34608i
$517$	−9096.99	−	15756.4i	−0.773859	−	1.34036i
$518$	183.229	+	317.361i	0.0155417	+	0.0269190i
$519$	2759.82	+	4780.15i	0.233416	+	0.404288i
$520$	−8641.58	−	14967.7i	−0.728766	−	1.26226i
$521$	−3391.61			−0.285200			−0.142600	−	0.989780i	$-0.545546\pi$
$521$	−3391.61			−0.285200			−0.142600	+	0.989780i	$0.545546\pi$
$522$	−7123.16			−0.597265
$523$	11222.2	+	19437.5i	0.938268	+	1.62513i	0.768700	+	0.639610i	$0.220904\pi$
$523$	11222.2	+	19437.5i	0.938268	+	1.62513i	0.169569	+	0.985518i	$0.445763\pi$
$524$	−20285.7	+	35135.9i	−1.69120	+	2.92924i
$525$	285.297	−	494.148i	0.0237169	−	0.0410788i
$526$	−6288.52	−	10892.0i	−0.521278	−	0.902880i
$527$	4543.98			0.375596
$528$	11300.4			0.931417
$529$	3237.99	−	5608.36i	0.266129	−	0.460948i
$530$	−26110.3	−	45224.3i	−2.13992	−	3.70645i
$531$	−5302.47			−0.433348
$532$	−228.844	+	396.370i	−0.0186497	+	0.0323023i
$533$	4187.13			0.340272
$534$	−8560.87	−	14827.9i	−0.693755	−	1.20162i
$535$	13383.5			1.08153
$536$	−25562.9	+	9483.65i	−2.05998	+	0.764238i
$537$	−3571.92			−0.287038
$538$	15150.4	+	26241.3i	1.21409	+	2.10287i
$539$	−11686.2			−0.933879
$540$	4130.79	−	7154.73i	0.329186	−	0.570168i
$541$	8860.83			0.704172			0.352086	−	0.935968i	$-0.385472\pi$
$541$	8860.83			0.704172			0.352086	+	0.935968i	$0.385472\pi$
$542$	2284.49	+	3956.86i	0.181047	+	0.313582i
$543$	−145.184	+	251.466i	−0.0114741	+	0.0198737i
$544$	−2850.54			−0.224662
$545$	20661.3			1.62391
$546$	−171.409	−	296.889i	−0.0134352	−	0.0232704i
$547$	3682.05	−	6377.50i	0.287812	−	0.498505i	−0.685475	−	0.728096i	$-0.740406\pi$
$547$	3682.05	−	6377.50i	0.287812	−	0.498505i	0.973287	+	0.229591i	$0.0737389\pi$
$548$	−21.2590	+	36.8216i	−0.00165719	+	0.00287033i
$549$	−2396.46	−	4150.79i	−0.186299	−	0.322680i
$550$	−29666.1			−2.29994
$551$	−3601.50			−0.278456
$552$	5625.82	+	9744.21i	0.433788	+	0.751343i
$553$	−700.891	−	1213.98i	−0.0538967	−	0.0933519i
$554$	−15605.9	−	27030.3i	−1.19681	−	2.07294i
$555$	−1672.23	−	2896.39i	−0.127896	−	0.221522i
$556$	12550.6	−	21738.3i	0.957312	−	1.65811i
$557$	5268.42	−	9125.17i	0.400772	−	0.694158i	−0.593047	−	0.805168i	$-0.702075\pi$
$557$	5268.42	−	9125.17i	0.400772	−	0.694158i	0.993819	+	0.111010i	$0.0354086\pi$
$558$	−11781.1			−0.893784
$559$	−3449.75	−	5975.14i	−0.261018	−	0.452096i
$560$	2109.45			0.159180
$561$	1808.39			0.136097
$562$	7561.98	−	13097.7i	0.567585	−	0.983087i
$563$	−13242.3			−0.991291			−0.495646	−	0.868525i	$-0.665068\pi$
$563$	−13242.3			−0.991291			−0.495646	+	0.868525i	$0.665068\pi$
$564$	−14198.4	−	24592.3i	−1.06003	−	1.83603i
$565$	−5268.23	+	9124.84i	−0.392276	+	0.679442i
$566$	−18312.0	−	31717.3i	−1.35991	−	2.35544i
$567$	45.0895	−	78.0973i	0.00333965	−	0.00578444i
$568$	−19652.8	+	34039.7i	−1.45179	+	2.51457i
$569$	2737.17	−	4740.92i	0.201666	−	0.349296i	−0.747399	−	0.664375i	$-0.768698\pi$
$569$	2737.17	−	4740.92i	0.201666	−	0.349296i	0.949065	+	0.315079i	$0.102031\pi$
$570$	3027.75	−	5244.22i	0.222489	−	0.385362i
$571$	−6941.68	+	12023.3i	−0.508757	+	0.881194i	0.491191	+	0.871052i	$0.336562\pi$
$571$	−6941.68	+	12023.3i	−0.508757	+	0.881194i	−0.999949	+	0.0101418i	$0.996772\pi$
$572$	−6147.39	+	10647.6i	−0.449362	+	0.778318i
$573$	5059.06	+	8762.54i	0.368840	+	0.638849i
$574$	−585.645	+	1014.37i	−0.0425860	+	0.0737611i
$575$	−6443.92	−	11161.2i	−0.467356	−	0.809485i
$576$	−540.962			−0.0391321
$577$	−8223.59	+	14243.7i	−0.593332	+	1.02768i	0.400448	+	0.916319i	$0.368854\pi$
$577$	−8223.59	+	14243.7i	−0.593332	+	1.02768i	−0.993780	+	0.111361i	$0.964479\pi$
$578$	23371.8			1.68190
$579$	7677.90			0.551093
$580$	23843.8	+	41298.6i	1.70700	+	2.95660i
$581$	988.798			0.0706063
$582$	−7319.65	+	12678.0i	−0.521321	+	0.902955i
$583$	−10221.4	+	17704.0i	−0.726121	+	1.25768i
$584$	−13973.3	−	24202.4i	−0.990099	−	1.71490i
$585$	1564.36	+	2709.55i	0.110561	+	0.191498i
$586$	14847.5	+	25716.6i	1.04666	+	1.81287i
$587$	−8358.07	−	14476.6i	−0.587691	−	1.01791i	−0.994534	−	0.104412i	$-0.966704\pi$
$587$	−8358.07	−	14476.6i	−0.587691	−	1.01791i	0.406843	−	0.913498i	$-0.366630\pi$
$588$	−18239.6			−1.27923
$589$	−5956.56			−0.416699
$590$	25731.0	+	44567.5i	1.79547	+	3.10985i
$591$	−2948.69	+	5107.27i	−0.205233	+	0.355474i
$592$	3570.02	−	6183.45i	0.247849	−	0.429287i
$593$	4375.74	+	7579.00i	0.303019	+	0.524844i	0.976818	−	0.214070i	$-0.0686722\pi$
$593$	4375.74	+	7579.00i	0.303019	+	0.524844i	−0.673800	+	0.738914i	$0.735339\pi$
$594$	−4688.57			−0.323862
$595$	337.572			0.0232590
$596$	3236.95	−	5606.57i	0.222468	−	0.385325i
$597$	−3564.69	−	6174.22i	−0.244377	−	0.423273i
$598$	−7743.13			−0.529498
$599$	−5088.13	+	8812.89i	−0.347070	+	0.601144i	−0.985728	−	0.168348i	$-0.946157\pi$
$599$	−5088.13	+	8812.89i	−0.347070	+	0.601144i	0.638657	+	0.769491i	$0.279490\pi$
$600$	−25480.3			−1.73372
$601$	8859.14	+	15344.5i	0.601284	+	1.04145i	0.992627	+	0.121210i	$0.0386774\pi$
$601$	8859.14	+	15344.5i	0.601284	+	1.04145i	−0.391343	+	0.920245i	$0.627989\pi$
$602$	1930.04			0.130669
$603$	4627.57	−	1716.80i	0.312520	−	0.115943i
$604$	56058.1			3.77644
$605$	−1391.12	−	2409.49i	−0.0934828	−	0.161917i
$606$	−9335.27			−0.625775
$607$	7808.08	−	13524.0i	0.522109	−	0.904320i	−0.477560	−	0.878599i	$-0.658479\pi$
$607$	7808.08	−	13524.0i	0.522109	−	0.904320i	0.999669	−	0.0257206i	$-0.00818803\pi$
$608$	3736.68			0.249247
$609$	260.266	+	450.794i	0.0173178	+	0.0299952i
$610$	−23258.3	+	40284.6i	−1.54378	+	2.67390i
$611$	10754.1			0.712050
$612$	2822.50			0.186426
$613$	−1037.40	−	1796.84i	−0.0683530	−	0.118391i	0.829823	−	0.558026i	$-0.188441\pi$
$613$	−1037.40	−	1796.84i	−0.0683530	−	0.118391i	−0.898176	+	0.439635i	$0.855108\pi$
$614$	−14263.3	+	24704.8i	−0.937493	+	1.62379i
$615$	5344.88	−	9257.61i	0.350449	−	0.606996i
$616$	−946.329	−	1639.09i	−0.0618972	−	0.107209i
$617$	26190.4			1.70889			0.854446	−	0.519540i	$-0.173897\pi$
$617$	26190.4			1.70889			0.854446	+	0.519540i	$0.173897\pi$
$618$	3504.88			0.228134
$619$	−10842.6	−	18780.0i	−0.704043	−	1.21944i	−0.967036	−	0.254640i	$-0.918043\pi$
$619$	−10842.6	−	18780.0i	−0.704043	−	1.21944i	0.262993	−	0.964798i	$-0.415290\pi$
$620$	39435.4	+	68304.1i	2.55446	+	4.42445i
$621$	−1018.43	−	1763.96i	−0.0658100	−	0.113986i
$622$	−14547.5	−	25197.1i	−0.937787	−	1.62429i
$623$	−625.595	+	1083.56i	−0.0402310	+	0.0696822i
$624$	−3339.72	+	5784.56i	−0.214256	+	0.371102i
$625$	−7794.12			−0.498824
$626$	−14914.3	−	25832.3i	−0.952226	−	1.64930i
$627$	−2370.56			−0.150991
$628$	−13834.5			−0.879072
$629$	571.304	−	989.528i	0.0362153	−	0.0627267i
$630$	−875.214			−0.0553482
$631$	−2054.75	−	3558.93i	−0.129633	−	0.224530i	0.793902	−	0.608046i	$-0.208046\pi$
$631$	−2054.75	−	3558.93i	−0.129633	−	0.224530i	−0.923534	+	0.383516i	$0.874713\pi$
$632$	−31298.9	+	54211.3i	−1.96994	+	3.41204i
$633$	5355.50	+	9276.00i	0.336275	+	0.582445i
$634$	16645.4	−	28830.7i	1.04270	−	1.80601i
$635$	−3536.91	+	6126.10i	−0.221036	+	0.382846i
$636$	−15953.4	+	27632.1i	−0.994643	+	1.72277i
$637$	3453.73	−	5982.04i	0.214822	−	0.372083i
$638$	13531.7	−	23437.6i	0.839694	−	1.45439i
$639$	3557.69	−	6162.10i	0.220250	−	0.381485i
$640$	13750.0	+	23815.6i	0.849243	+	1.47093i
$641$	−6244.78	+	10816.3i	−0.384795	+	0.666485i	−0.991741	−	0.128258i	$-0.959061\pi$
$641$	−6244.78	+	10816.3i	−0.384795	+	0.666485i	0.606945	+	0.794744i	$0.292395\pi$
$642$	−5927.30	−	10266.4i	−0.364380	−	0.631125i
$643$	5310.86			0.325723			0.162861	−	0.986649i	$-0.447928\pi$
$643$	5310.86			0.325723			0.162861	+	0.986649i	$0.447928\pi$
$644$	747.064	−	1293.95i	0.0457119	−	0.0791753i
$645$	−17614.5			−1.07530
$646$	2068.81			0.126001
$647$	−8831.16	−	15296.0i	−0.536613	−	0.929442i	−0.999083	−	0.0428067i	$-0.986370\pi$
$647$	−8831.16	−	15296.0i	−0.536613	−	0.929442i	0.462470	−	0.886635i	$-0.346963\pi$
$648$	−4027.03			−0.244130
$649$	10073.0	−	17446.9i	0.609244	−	1.05524i
$650$	8767.50	−	15185.8i	0.529061	−	0.916360i
$651$	430.456	+	745.572i	0.0259154	+	0.0448868i
$652$	23026.3	+	39882.7i	1.38310	+	2.39559i
$653$	−9667.48	−	16744.6i	−0.579353	−	1.00347i	−0.995554	−	0.0941965i	$-0.969972\pi$
$653$	−9667.48	−	16744.6i	−0.579353	−	1.00347i	0.416200	−	0.909273i	$-0.363362\pi$
$654$	−9150.51	−	15849.2i	−0.547115	−	0.947631i
$655$	−39226.2			−2.33999
$656$	22821.4			1.35827
$657$	2529.54	+	4381.28i	0.150208	+	0.260168i
$658$	−1504.15	+	2605.26i	−0.0891151	+	0.154352i
$659$	4519.74	−	7828.43i	0.267169	−	0.462750i	−0.700961	−	0.713200i	$-0.747245\pi$
$659$	4519.74	−	7828.43i	0.267169	−	0.462750i	0.968130	+	0.250450i	$0.0805786\pi$
$660$	15694.3	+	27183.3i	0.925606	+	1.60320i
$661$	8067.53			0.474721			0.237361	−	0.971422i	$-0.423718\pi$
$661$	8067.53			0.474721			0.237361	+	0.971422i	$0.423718\pi$
$662$	−50650.3			−2.97368
$663$	−534.450	+	925.695i	−0.0313067	+	0.0542248i
$664$	−22077.8	−	38239.9i	−1.29034	−	2.23493i
$665$	−442.513			−0.0258044
$666$	−1481.20	+	2565.52i	−0.0861795	+	0.149267i
$667$	11757.1			0.682515
$668$	4652.28	+	8057.98i	0.269464	+	0.466725i
$669$	−1013.92			−0.0585958
$670$	−36885.7	−	30563.9i	−2.12689	−	1.76237i
$671$	18210.0			1.04767
$672$	−270.035	−	467.714i	−0.0155012	−	0.0268489i
$673$	−9183.43			−0.525996			−0.262998	−	0.964796i	$-0.584711\pi$
$673$	−9183.43			−0.525996			−0.262998	+	0.964796i	$0.584711\pi$
$674$	−18382.5	+	31839.5i	−1.05055	+	1.81960i
$675$	4612.63			0.263022
$676$	15908.5	+	27554.4i	0.905129	+	1.56773i
$677$	8625.91	−	14940.5i	0.489691	−	0.848169i	−0.510239	−	0.860033i	$-0.670443\pi$
$677$	8625.91	−	14940.5i	0.489691	−	0.848169i	0.999930	+	0.0118637i	$0.00377641\pi$
$678$	9332.83			0.528651
$679$	1069.78			0.0604631
$680$	−7537.30	−	13055.0i	−0.425062	−	0.736229i
$681$	−10143.3	+	17568.7i	−0.570768	+	0.988598i
$682$	22380.2	−	38763.6i	1.25657	−	2.17644i
$683$	−768.017	−	1330.24i	−0.0430269	−	0.0745248i	0.843710	−	0.536799i	$-0.180367\pi$
$683$	−768.017	−	1330.24i	−0.0430269	−	0.0745248i	−0.886737	+	0.462275i	$0.847033\pi$
$684$	−3699.92			−0.206827
$685$	−41.1081			−0.00229293
$686$	1935.77	+	3352.85i	0.107738	+	0.186607i
$687$	5810.87	+	10064.7i	0.322705	+	0.558942i
$688$	−18802.4	−	32566.7i	−1.04191	−	1.80464i
$689$	−6041.66	−	10464.5i	−0.334063	−	0.578613i
$690$	−9884.12	+	17119.8i	−0.545336	+	0.944550i
$691$	8841.18	−	15313.4i	0.486735	−	0.843051i	−0.513148	−	0.858300i	$-0.671521\pi$
$691$	8841.18	−	15313.4i	0.486735	−	0.843051i	0.999884	+	0.0152494i	$0.00485423\pi$
$692$	−32731.2			−1.79805
$693$	171.311	+	296.719i	0.00939043	+	0.0162647i
$694$	20922.6			1.14440
$695$	24268.9			1.32457
$696$	11622.4	−	20130.6i	0.632969	−	1.09634i
$697$	3652.07			0.198468
$698$	2829.31	+	4900.51i	0.153425	+	0.265741i
$699$	4809.12	−	8329.64i	0.260226	−	0.450724i
$700$	1691.79	+	2930.27i	0.0913482	+	0.158220i
$701$	14931.9	−	25862.8i	0.804521	−	1.39347i	−0.112093	−	0.993698i	$-0.535756\pi$
$701$	14931.9	−	25862.8i	0.804521	−	1.39347i	0.916614	−	0.399773i	$-0.130911\pi$
$702$	1385.65	−	2400.02i	0.0744988	−	0.129036i
$703$	−748.904	+	1297.14i	−0.0401785	+	0.0695911i
$704$	1027.65	−	1779.95i	0.0550158	−	0.0952901i
$705$	13727.6	−	23776.9i	0.733348	−	1.27020i
$706$	26753.4	−	46338.3i	1.42617	−	2.47020i
$707$	341.092	+	590.789i	0.0181444	+	0.0314270i
$708$	15721.7	−	27230.8i	0.834544	−	1.44547i
$709$	1691.82	+	2930.32i	0.0896159	+	0.155219i	0.907349	−	0.420379i	$-0.138103\pi$
$709$	1691.82	+	2930.32i	0.0896159	+	0.155219i	−0.817733	+	0.575598i	$0.804769\pi$
$710$	−69056.8			−3.65022
$711$	5665.94	−	9813.70i	0.298860	−	0.517641i
$712$	55873.0			2.94091
$713$	19445.2			1.02136
$714$	−149.505	−	258.950i	−0.00783625	−	0.0135728i
$715$	−11887.1			−0.621752
$716$	10590.6	−	18343.5i	0.552780	−	0.957443i
$717$	−8061.13	+	13962.3i	−0.419872	+	0.727240i
$718$	−13471.9	−	23334.0i	−0.700231	−	1.21284i
$719$	−2067.83	−	3581.58i	−0.107256	−	0.185773i	0.807402	−	0.590002i	$-0.200873\pi$
$719$	−2067.83	−	3581.58i	−0.107256	−	0.185773i	−0.914658	+	0.404229i	$0.867540\pi$
$720$	8526.31	+	14768.0i	0.441329	+	0.764404i
$721$	−128.062	−	221.809i	−0.00661479	−	0.0114571i
$722$	32120.6			1.65569
$723$	9549.35			0.491209
$724$	−860.933	−	1491.18i	−0.0441938	−	0.0765459i
$725$	−13312.5	+	23058.0i	−0.681951	+	1.18117i
$726$	−1232.21	+	2134.24i	−0.0629910	+	0.109104i
$727$	15477.9	+	26808.6i	0.789607	+	1.36764i	0.926208	+	0.377014i	$0.123049\pi$
$727$	15477.9	+	26808.6i	0.789607	+	1.36764i	−0.136600	+	0.990626i	$0.543618\pi$
$728$	1118.71			0.0569534
$729$	729.000			0.0370370
$730$	24549.9	−	42521.7i	1.24470	−	2.15589i
$731$	−3008.92	−	5211.60i	−0.152242	−	0.263691i
$732$	28421.7			1.43511
$733$	6866.86	−	11893.8i	0.346021	−	0.599326i	−0.639518	−	0.768776i	$-0.720866\pi$
$733$	6866.86	−	11893.8i	0.346021	−	0.599326i	0.985539	+	0.169450i	$0.0541993\pi$
$734$	−6760.57			−0.339969
$735$	−8817.39	−	15272.2i	−0.442496	−	0.766425i
$736$	−12198.4			−0.610923
$737$	−3142.05	+	18487.6i	−0.157041	+	0.924017i
$738$	−9468.62			−0.472283
$739$	15324.0	+	26542.0i	0.762792	+	1.32120i	0.941406	+	0.337276i	$0.109505\pi$
$739$	15324.0	+	26542.0i	0.762792	+	1.32120i	−0.178614	+	0.983919i	$0.557161\pi$
$740$	19832.5			0.985212
$741$	700.593	−	1213.46i	0.0347327	−	0.0601588i
$742$	3380.14			0.167236
$743$	5096.18	+	8826.84i	0.251629	+	0.435835i	0.963975	−	0.265994i	$-0.0857003\pi$
$743$	5096.18	+	8826.84i	0.251629	+	0.435835i	−0.712345	+	0.701829i	$0.752367\pi$
$744$	19222.4	−	33294.2i	0.947215	−	1.64062i
$745$	6259.24			0.307813
$746$	−52248.5			−2.56428
$747$	3996.68	+	6922.45i	0.195758	+	0.339062i
$748$	−5361.83	+	9286.96i	−0.262096	+	0.453964i
$749$	−433.144	+	750.227i	−0.0211305	+	0.0365991i
$750$	−6005.77	−	10402.3i	−0.292400	−	0.506451i
$751$	−13568.0			−0.659258			−0.329629	−	0.944111i	$-0.606924\pi$
$751$	−13568.0			−0.659258			−0.329629	+	0.944111i	$0.606924\pi$
$752$	58613.4			2.84230
$753$	5487.09	+	9503.93i	0.265552	+	0.459950i
$754$	7998.29	+	13853.4i	0.386314	+	0.669115i
$755$	27099.6	+	46938.0i	1.30630	+	2.26258i
$756$	267.378	+	463.113i	0.0128630	+	0.0222794i
$757$	256.911	−	444.983i	0.0123350	−	0.0213649i	−0.859792	−	0.510644i	$-0.829407\pi$
$757$	256.911	−	444.983i	0.0123350	−	0.0213649i	0.872127	+	0.489280i	$0.162740\pi$
$758$	−27133.9	+	46997.3i	−1.30019	+	2.25200i
$759$	7738.71			0.370089
$760$	9880.40	+	17113.3i	0.471579	+	0.816798i
$761$	−11499.0			−0.547749			−0.273875	−	0.961765i	$-0.588305\pi$
$761$	−11499.0			−0.547749			−0.273875	+	0.961765i	$0.588305\pi$
$762$	6265.74			0.297879
$763$	−668.683	+	1158.19i	−0.0317273	+	0.0549534i
$764$	−59999.8			−2.84125
$765$	1364.45	+	2363.30i	0.0644862	+	0.111693i
$766$	2634.14	−	4562.46i	0.124250	−	0.215207i
$767$	5953.92	+	10312.5i	0.280291	+	0.485479i
$768$	11458.0	−	19845.8i	0.538351	−	0.932451i
$769$	9050.66	−	15676.2i	0.424415	−	0.735108i	−0.571951	−	0.820288i	$-0.693813\pi$
$769$	9050.66	−	15676.2i	0.424415	−	0.735108i	0.996366	+	0.0851799i	$0.0271465\pi$
$770$	1662.62	−	2879.75i	0.0778140	−	0.134778i
$771$	5393.83	−	9342.39i	0.251951	−	0.436391i
$772$	−22764.8	+	39429.7i	−1.06130	+	1.83822i
$773$	20302.8	−	35165.5i	0.944685	−	1.63624i	0.188306	−	0.982110i	$-0.439700\pi$
$773$	20302.8	−	35165.5i	0.944685	−	1.63624i	0.756380	−	0.654133i	$-0.226966\pi$
$774$	7801.13	+	13512.0i	0.362282	+	0.627490i
$775$	−22017.7	+	38135.8i	−1.02051	+	1.76758i
$776$	−23886.0	−	41371.8i	−1.10497	−	1.91387i
$777$	216.481			0.00999514
$778$	−25738.5	+	44580.3i	−1.18608	+	2.05435i
$779$	−4787.38			−0.220187
$780$	−18553.1			−0.851677
$781$	13516.9	+	23412.0i	0.619300	+	1.07266i
$782$	−6753.65			−0.308837
$783$	−2103.97	+	3644.18i	−0.0960278	+	0.166325i
$784$	18824.1	−	32604.3i	0.857511	−	1.48525i
$785$	−6687.89	−	11583.8i	−0.304078	−	0.526678i
$786$	17372.6	+	30090.2i	0.788371	+	1.36550i
$787$	402.585	+	697.297i	0.0182346	+	0.0315832i	0.874999	−	0.484125i	$-0.160862\pi$
$787$	402.585	+	697.297i	0.0182346	+	0.0315832i	−0.856764	+	0.515708i	$0.827529\pi$
$788$	−17485.5	−	30285.8i	−0.790478	−	1.36915i
$789$	−7429.77			−0.335243
$790$	−109979.			−4.95302
$791$	−341.003	−	590.635i	−0.0153283	−	0.0265494i
$792$	7650.05	−	13250.3i	0.343223	−	0.594480i
$793$	−5381.76	+	9321.48i	−0.240999	+	0.417422i
$794$	−24320.1	−	42123.6i	−1.08701	−	1.88276i
$795$	−30848.8			−1.37622
$796$	42276.8			1.88249
$797$	6366.44	−	11027.0i	0.282950	−	0.490083i	−0.689160	−	0.724609i	$-0.742020\pi$
$797$	6366.44	−	11027.0i	0.282950	−	0.490083i	0.972110	+	0.234526i	$0.0753538\pi$
$798$	195.981	+	339.449i	0.00869380	+	0.0150581i
$799$	9379.82			0.415312
$800$	13812.2	−	23923.4i	0.610419	−	1.05728i
$801$	−10114.5			−0.446166
$802$	−36909.9	−	63929.7i	−1.62510	−	2.81476i
$803$	−19221.2			−0.844709
$804$	−4904.04	+	28855.1i	−0.215115	+	1.26572i
$805$	1444.58			0.0632483
$806$	13228.4	+	22912.3i	0.578104	+	1.00131i
$807$	17899.9			0.780803
$808$	15231.8	−	26382.2i	0.663184	−	1.14867i
$809$	38031.7			1.65281			0.826405	−	0.563076i	$-0.190382\pi$
$809$	38031.7			1.65281			0.826405	+	0.563076i	$0.190382\pi$
$810$	−3537.58	−	6127.27i	−0.153454	−	0.265790i
$811$	−9474.80	+	16410.8i	−0.410241	+	0.710558i	−0.994916	−	0.100710i	$-0.967889\pi$
$811$	−9474.80	+	16410.8i	−0.410241	+	0.710558i	0.584675	+	0.811268i	$0.301222\pi$
$812$	−3086.73			−0.133403
$813$	2699.09			0.116434
$814$	−5627.62	−	9747.32i	−0.242319	−	0.419709i
$815$	−22262.8	+	38560.2i	−0.956847	+	1.65731i
$816$	−2912.94	+	5045.37i	−0.124967	+	0.216450i
$817$	3944.29	+	6831.71i	0.168902	+	0.292547i
$818$	45876.4			1.96092
$819$	−202.516			−0.00864041
$820$	31694.8	+	54897.1i	1.34980	+	2.33791i
$821$	−3767.41	−	6525.35i	−0.160151	−	0.277389i	0.774772	−	0.632241i	$-0.217865\pi$
$821$	−3767.41	−	6525.35i	−0.160151	−	0.277389i	−0.934923	+	0.354852i	$0.884531\pi$
$822$	18.2061	+	31.5338i	0.000772517	+	0.00133804i
$823$	−16610.6	−	28770.5i	−0.703537	−	1.21856i	−0.967217	−	0.253951i	$-0.918270\pi$
$823$	−16610.6	−	28770.5i	−0.703537	−	1.21856i	0.263681	−	0.964610i	$-0.415064\pi$
$824$	−5718.70	+	9905.09i	−0.241772	+	0.418762i
$825$	−8762.50	+	15177.1i	−0.369783	+	0.640483i
$826$	−3331.05			−0.140317
$827$	10558.0	+	18287.1i	0.443941	+	0.768928i	0.997978	−	0.0635638i	$-0.0202466\pi$
$827$	10558.0	+	18287.1i	0.443941	+	0.768928i	−0.554037	+	0.832492i	$0.686913\pi$
$828$	12078.4			0.506949
$829$	−3224.29			−0.135084			−0.0675418	−	0.997716i	$-0.521516\pi$
$829$	−3224.29			−0.135084			−0.0675418	+	0.997716i	$0.521516\pi$
$830$	38789.0	−	67184.4i	1.62215	−	2.80965i
$831$	−18438.1			−0.769689
$832$	607.423	+	1052.09i	0.0253108	+	0.0438396i
$833$	3012.39	−	5217.61i	0.125298	−	0.217022i
$834$	−10748.3	−	18616.6i	−0.446262	−	0.772949i
$835$	−4498.01	+	7790.78i	−0.186419	+	0.322888i
$836$	7028.65	−	12174.0i	0.290779	−	0.503643i
$837$	−3479.77	+	6027.15i	−0.143702	+	0.248899i
$838$	−19596.1	+	33941.4i	−0.807798	+	1.39915i
$839$	−8120.70	+	14065.5i	−0.334157	+	0.578777i	−0.983323	−	0.181870i	$-0.941785\pi$
$839$	−8120.70	+	14065.5i	−0.334157	+	0.578777i	0.649165	+	0.760647i	$0.275118\pi$
$840$	1428.03	−	2473.43i	0.0586569	−	0.101597i
$841$	49.9442	+	86.5059i	0.00204782	+	0.00354692i
$842$	−17451.7	+	30227.3i	−0.714283	+	1.23717i
$843$	−4467.17	−	7737.37i	−0.182512	−	0.316120i
$844$	−63515.6			−2.59040
$845$	−15381.0	+	26640.7i	−0.626182	+	1.08458i
$846$	−24318.8			−0.988295
$847$	180.089			0.00730572
$848$	−32929.2	−	57035.1i	−1.33348	−	2.30966i
$849$	−21635.3			−0.874583
$850$	7647.12	−	13245.2i	0.308581	−	0.534479i
$851$	2444.80	−	4234.52i	0.0984803	−	0.170573i
$852$	21096.9	+	36540.9i	0.848319	+	1.46933i
$853$	−12933.7	−	22401.9i	−0.519160	−	0.899211i	−0.999752	−	0.0222667i	$-0.992912\pi$
$853$	−12933.7	−	22401.9i	−0.519160	−	0.899211i	0.480592	−	0.876944i	$-0.340422\pi$
$854$	−1505.47	−	2607.55i	−0.0603234	−	0.104483i
$855$	−1788.62	−	3097.98i	−0.0715432	−	0.123916i
$856$	38684.9			1.54465
$857$	−46214.6			−1.84208			−0.921038	−	0.389473i	$-0.872657\pi$
$857$	−46214.6			−1.84208			−0.921038	+	0.389473i	$0.872657\pi$
$858$	5264.59	+	9118.53i	0.209476	+	0.362822i
$859$	−8415.29	+	14575.7i	−0.334256	+	0.578949i	−0.983342	−	0.181767i	$-0.941818\pi$
$859$	−8415.29	+	14575.7i	−0.334256	+	0.578949i	0.649086	+	0.760715i	$0.275152\pi$
$860$	52226.4	−	90458.7i	2.07082	−	3.58676i
$861$	345.965	+	599.228i	0.0136939	+	0.0237185i
$862$	−10253.0			−0.405128
$863$	21043.2			0.830033			0.415017	−	0.909814i	$-0.363776\pi$
$863$	21043.2			0.830033			0.415017	+	0.909814i	$0.363776\pi$
$864$	2182.94	−	3780.96i	0.0859550	−	0.148878i
$865$	−15822.9	−	27406.1i	−0.621960	−	1.07727i
$866$	−35316.6			−1.38581
$867$	6903.35	−	11956.9i	0.270415	−	0.468373i
$868$	−5105.16			−0.199632
$869$	21526.9	+	37285.7i	0.840334	+	1.45550i
$870$	40839.3			1.59147
$871$	−8535.00	−	7072.19i	−0.332029	−	0.275123i
$872$	59721.3			2.31929
$873$	4324.01	+	7489.41i	0.167635	+	0.290353i
$874$	8853.14			0.342634
$875$	−438.878	+	760.159i	−0.0169563	+	0.0293692i
$876$	−30000.0			−1.15708
$877$	1798.54	+	3115.15i	0.0692500	+	0.119944i	0.898571	−	0.438827i	$-0.144606\pi$
$877$	1798.54	+	3115.15i	0.0692500	+	0.119944i	−0.829321	+	0.558772i	$0.811273\pi$
$878$	22047.5	−	38187.5i	0.847458	−	1.46784i
$879$	17542.0			0.673126
$880$	−64788.9			−2.48186
$881$	4165.46	+	7214.78i	0.159294	+	0.275905i	0.934614	−	0.355663i	$-0.115745\pi$
$881$	4165.46	+	7214.78i	0.159294	+	0.275905i	−0.775320	+	0.631568i	$0.782412\pi$
$882$	−7810.14	+	13527.6i	−0.298164	+	0.516436i
$883$	−19687.4	+	34099.6i	−0.750321	+	1.29959i	0.197346	+	0.980334i	$0.436768\pi$
$883$	−19687.4	+	34099.6i	−0.750321	+	1.29959i	−0.947667	+	0.319260i	$0.896566\pi$
$884$	−3169.26	−	5489.32i	−0.120581	−	0.208853i
$885$	30400.8			1.15470
$886$	−28043.4			−1.06336
$887$	2828.72	+	4899.49i	0.107079	+	0.185466i	0.914586	−	0.404392i	$-0.132517\pi$
$887$	2828.72	+	4899.49i	0.107079	+	0.185466i	−0.807507	+	0.589858i	$0.799184\pi$
$888$	−4833.58	−	8372.01i	−0.182663	−	0.316381i
$889$	−228.938	−	396.532i	−0.00863703	−	0.0149598i
$890$	49082.2	+	85012.8i	1.84858	+	3.20184i
$891$	−1384.86	+	2398.65i	−0.0520704	+	0.0901885i
$892$	3006.26	−	5206.99i	0.112844	−	0.195452i
$893$	−12295.7			−0.460762
$894$	−2772.11	−	4801.43i	−0.103706	−	0.179624i
$895$	20478.9			0.764843
$896$	−1780.02			−0.0663687
$897$	−2287.09	+	3961.36i	−0.0851324	+	0.147454i
$898$	48347.6			1.79664
$899$	−20086.0	−	34789.9i	−0.745167	−	1.29067i
$900$	−13676.3	+	23688.1i	−0.506530	+	0.877336i
$901$	−5269.62	−	9127.24i	−0.194846	−	0.337483i
$902$	17987.3	−	31154.9i	0.663982	−	1.15005i
$903$	570.076	−	987.401i	0.0210088	−	0.0363883i
$904$	−15227.8	+	26375.3i	−0.560253	+	0.970387i
$905$	832.385	−	1441.73i	0.0305740	−	0.0529556i
$906$	24003.9	−	41576.0i	0.880217	−	1.52458i
$907$	25814.8	−	44712.5i	0.945056	−	1.63688i	0.189416	−	0.981897i	$-0.439340\pi$
$907$	25814.8	−	44712.5i	0.945056	−	1.63688i	0.755640	−	0.654988i	$-0.227326\pi$
$908$	−60149.3	−	104182.i	−2.19837	−	3.80770i
$909$	−2757.36	+	4775.89i	−0.100612	+	0.174264i
$910$	982.740	+	1702.16i	0.0357995	+	0.0620065i
$911$	−4990.55			−0.181498			−0.0907489	−	0.995874i	$-0.528926\pi$
$911$	−4990.55			−0.181498			−0.0907489	+	0.995874i	$0.528926\pi$
$912$	3818.48	−	6613.81i	0.138643	−	0.240137i
$913$	−30369.6			−1.10086
$914$	−73225.4			−2.64998
$915$	13739.7	+	23797.8i	0.496414	+	0.859815i
$916$	−68916.2			−2.48587
$917$	1269.52	−	2198.87i	0.0457179	−	0.0791856i
$918$	1208.59	−	2093.33i	0.0434523	−	0.0752617i
$919$	13152.5	+	22780.8i	0.472101	+	0.817704i	0.999490	−	0.0319203i	$-0.0101623\pi$
$919$	13152.5	+	22780.8i	0.472101	+	0.817704i	−0.527389	+	0.849624i	$0.676829\pi$
$920$	−32254.6	−	55866.6i	−1.15587	−	2.00203i
$921$	8425.92	+	14594.1i	0.301459	+	0.522142i
$922$	21211.1	+	36738.7i	0.757648	+	1.31228i
$923$	−15979.1			−0.569836
$924$	−2031.73			−0.0723366
$925$	5536.47	+	9589.45i	0.196798	+	0.340864i
$926$	3759.10	−	6510.96i	0.133404	−	0.231062i
$927$	1035.24	−	1793.09i	0.0366793	−	0.0635304i
$928$	12600.4	+	21824.5i	0.445720	+	0.772009i
$929$	36340.3			1.28341			0.641704	−	0.766952i	$-0.278228\pi$
$929$	36340.3			1.28341			0.641704	+	0.766952i	$0.278228\pi$
$930$	67544.5			2.38158
$931$	−3948.84	+	6839.60i	−0.139010	+	0.240772i
$932$	28517.8	+	49394.3i	1.00229	+	1.73601i
$933$	−17187.7			−0.603107
$934$	−14671.8	+	25412.4i	−0.514002	+	0.890277i
$935$	−10368.1			−0.362644
$936$	4521.77	+	7831.94i	0.157905	+	0.273499i
$937$	−5685.70			−0.198232			−0.0991162	−	0.995076i	$-0.531602\pi$
$937$	−5685.70			−0.198232			−0.0991162	+	0.995076i	$0.531602\pi$
$938$	2907.07	−	1078.50i	0.101193	−	0.0375420i
$939$	−17620.9			−0.612393
$940$	81403.7	+	140995.i	2.82457	+	4.89230i
$941$	−16281.4			−0.564038			−0.282019	−	0.959409i	$-0.591004\pi$
$941$	−16281.4			−0.564038			−0.282019	+	0.959409i	$0.591004\pi$
$942$	−5923.90	+	10260.5i	−0.204895	+	0.354888i
$943$	15628.4			0.539694
$944$	32451.0	+	56206.7i	1.11884	+	1.93790i
$945$	−258.512	+	447.757i	−0.00889885	+	0.0154133i
$946$	−59278.5			−2.03733
$947$	21486.0			0.737277			0.368639	−	0.929573i	$-0.379824\pi$
$947$	21486.0			0.737277			0.368639	+	0.929573i	$0.379824\pi$
$948$	33598.7	+	58194.7i	1.15109	+	1.99375i
$949$	5680.61	−	9839.11i	0.194310	−	0.336555i
$950$	−10024.4	+	17362.7i	−0.342351	+	0.592969i
$951$	−9833.13	−	17031.5i	−0.335290	−	0.580740i
$952$	975.752			0.0332188
$953$	27105.3			0.921328			0.460664	−	0.887574i	$-0.347611\pi$
$953$	27105.3			0.921328			0.460664	+	0.887574i	$0.347611\pi$
$954$	13662.4	+	23663.9i	0.463665	+	0.803091i
$955$	−29005.2	−	50238.4i	−0.982812	−	1.70228i
$956$	−47802.0	−	82795.6i	−1.61718	−	2.80105i
$957$	−7993.72	−	13845.5i	−0.270011	−	0.467673i
$958$	17192.7	−	29778.7i	0.579824	−	1.00428i
$959$	1.33043	−	2.30437i	4.47985e−5	−	7.75932e-5i
$960$	3101.50			0.104271
$961$	−18324.9	−	31739.6i	−0.615115	−	1.06541i
$962$	6652.72			0.222965
$963$	−7003.00			−0.234339
$964$	−28313.6	+	49040.5i	−0.945973	+	1.63847i
$965$	−44019.8			−1.46844
$966$	−639.781	−	1108.13i	−0.0213091	−	0.0369085i
$967$	20820.6	−	36062.3i	0.692394	−	1.19926i	−0.278658	−	0.960390i	$-0.589890\pi$
$967$	20820.6	−	36062.3i	0.692394	−	1.19926i	0.971051	−	0.238870i	$-0.0767771\pi$
$968$	−4021.03	−	6964.63i	−0.133513	−	0.231252i
$969$	611.066	−	1058.40i	0.0202583	−	0.0350884i
$970$	41965.8	−	72686.9i	1.38911	−	2.40602i
$971$	479.278	−	830.133i	0.0158401	−	0.0274359i	−0.857997	−	0.513655i	$-0.828291\pi$
$971$	479.278	−	830.133i	0.0158401	−	0.0274359i	0.873837	+	0.486219i	$0.161624\pi$
$972$	−2161.46	+	3743.77i	−0.0713261	+	0.123540i
$973$	−785.442	+	1360.43i	−0.0258789	+	0.0448235i
$974$	−19289.4	+	33410.3i	−0.634572	+	1.09911i
$975$	−5179.32	−	8970.84i	−0.170124	−	0.294664i
$976$	−29332.5	+	50805.4i	−0.961999	+	1.66623i
$977$	8571.68	+	14846.6i	0.280688	+	0.486166i	0.971554	−	0.236817i	$-0.0761040\pi$
$977$	8571.68	+	14846.6i	0.280688	+	0.486166i	−0.690866	+	0.722982i	$0.742771\pi$
$978$	39439.1			1.28949
$979$	19214.3	−	33280.1i	0.627264	−	1.08645i
$980$	104573.			3.40864
$981$	−10811.2			−0.351859
$982$	45440.6	+	78705.4i	1.47665	+	2.55763i
$983$	−25911.2			−0.840730			−0.420365	−	0.907355i	$-0.638098\pi$
$983$	−25911.2			−0.840730			−0.420365	+	0.907355i	$0.638098\pi$
$984$	15449.4	−	26759.1i	0.500516	−	0.866919i
$985$	16905.7	−	29281.6i	0.546865	−	0.947198i
$986$	6976.21	+	12083.1i	0.225322	+	0.390269i
$987$	888.561	+	1539.03i	0.0286557	+	0.0496332i
$988$	4154.48	+	7195.77i	0.133777	+	0.231708i
$989$	−12876.2	−	22302.2i	−0.413992	−	0.717055i
$990$	26881.0			0.862965
$991$	−8162.12			−0.261633			−0.130816	−	0.991407i	$-0.541760\pi$
$991$	−8162.12			−0.261633			−0.130816	+	0.991407i	$0.541760\pi$
$992$	20839.9	+	36095.7i	0.667003	+	1.15528i
$993$	−14960.6	+	25912.5i	−0.478107	+	0.828105i
$994$	2234.96	−	3871.07i	0.0713166	−	0.123524i
$995$	20437.5	+	35398.7i	0.651167	+	1.12785i
$996$	−47400.2			−1.50796
$997$	31902.0			1.01339			0.506694	−	0.862126i	$-0.330867\pi$
$997$	31902.0			1.01339			0.506694	+	0.862126i	$0.330867\pi$
$998$	−13910.8	+	24094.3i	−0.441222	+	0.764219i
$999$	875.008	+	1515.56i	0.0277117	+	0.0479982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.37.16	✓	32
67.29	even	3	inner	201.4.e.a.163.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.16	✓	32	1.1	even	1	trivial
201.4.e.a.163.16	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)

\(f(q)\)	\(=\)	\(q+(2.53918 + 4.39800i) q^{2} +3.00000 q^{3} +(-8.89492 + 15.4064i) q^{4} -17.1999 q^{5} +(7.61755 + 13.1940i) q^{6} +(0.556661 - 0.964165i) q^{7} -49.7164 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(2.53918 + 4.39800i) q^{2} +3.00000 q^{3} +(-8.89492 + 15.4064i) q^{4} -17.1999 q^{5} +(7.61755 + 13.1940i) q^{6} +(0.556661 - 0.964165i) q^{7} -49.7164 q^{8} +9.00000 q^{9} +(-43.6738 - 75.6453i) q^{10} +(-17.0971 + 29.6130i) q^{11} +(-26.6847 + 46.2193i) q^{12} +(-10.1057 - 17.5036i) q^{13} +5.65386 q^{14} -51.5998 q^{15} +(-55.0797 - 95.4009i) q^{16} +(-8.81433 - 15.2669i) q^{17} +(22.8527 + 39.5820i) q^{18} +(11.5544 + 20.0128i) q^{19} +(152.992 - 264.990i) q^{20} +(1.66998 - 2.89249i) q^{21} -173.651 q^{22} +(-37.7195 - 65.3320i) q^{23} -149.149 q^{24} +170.838 q^{25} +(51.3205 - 88.8898i) q^{26} +27.0000 q^{27} +(9.90290 + 17.1523i) q^{28} +(-77.9248 + 134.970i) q^{29} +(-131.021 - 226.936i) q^{30} +(-128.881 + 223.228i) q^{31} +(80.8496 - 140.036i) q^{32} +(-51.2913 + 88.8391i) q^{33} +(44.7624 - 77.5308i) q^{34} +(-9.57453 + 16.5836i) q^{35} +(-80.0542 + 138.658i) q^{36} +(32.4077 + 56.1318i) q^{37} +(-58.6776 + 101.633i) q^{38} +(-30.3171 - 52.5108i) q^{39} +855.119 q^{40} +(-103.583 + 179.412i) q^{41} +16.9616 q^{42} +341.366 q^{43} +(-304.154 - 526.811i) q^{44} -154.799 q^{45} +(191.553 - 331.780i) q^{46} +(-266.039 + 460.793i) q^{47} +(-165.239 - 286.203i) q^{48} +(170.880 + 295.973i) q^{49} +(433.789 + 751.345i) q^{50} +(-26.4430 - 45.8006i) q^{51} +359.558 q^{52} +597.847 q^{53} +(68.5580 + 118.746i) q^{54} +(294.069 - 509.342i) q^{55} +(-27.6752 + 47.9348i) q^{56} +(34.6632 + 60.0385i) q^{57} -791.462 q^{58} -589.164 q^{59} +(458.976 - 794.970i) q^{60} +(-266.273 - 461.199i) q^{61} -1309.01 q^{62} +(5.00995 - 8.67748i) q^{63} -60.1069 q^{64} +(173.818 + 301.061i) q^{65} -520.952 q^{66} +(514.175 - 190.755i) q^{67} +313.611 q^{68} +(-113.158 - 195.996i) q^{69} -97.2460 q^{70} +(395.299 - 684.677i) q^{71} -447.447 q^{72} +(281.059 + 486.809i) q^{73} +(-164.578 + 285.058i) q^{74} +512.514 q^{75} -411.102 q^{76} +(19.0346 + 32.9688i) q^{77} +(153.962 - 266.669i) q^{78} +(629.549 - 1090.41i) q^{79} +(947.368 + 1640.89i) q^{80} +81.0000 q^{81} -1052.07 q^{82} +(444.076 + 769.161i) q^{83} +(29.7087 + 51.4570i) q^{84} +(151.606 + 262.589i) q^{85} +(866.792 + 1501.33i) q^{86} +(-233.774 + 404.909i) q^{87} +(850.005 - 1472.25i) q^{88} -1123.83 q^{89} +(-393.064 - 680.808i) q^{90} -22.5018 q^{91} +1342.05 q^{92} +(-386.642 + 669.683i) q^{93} -2702.09 q^{94} +(-198.735 - 344.220i) q^{95} +(242.549 - 420.107i) q^{96} +(480.446 + 832.157i) q^{97} +(-867.793 + 1503.06i) q^{98} +(-153.874 + 266.517i) 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

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