LMFDB - Embedded newform 169.4.c.j.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.j.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 + 1.35234i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(2.78078 + 4.81645i) q^{4} +3.56155 q^{5} +(-6.78078 - 11.7446i) q^{6} +(-13.5885 - 23.5360i) q^{7} -21.1771 q^{8} +(-24.2116 - 41.9358i) q^{9} +O(q^{10})$	\(q+(-0.780776 + 1.35234i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(2.78078 + 4.81645i) q^{4} +3.56155 q^{5} +(-6.78078 - 11.7446i) q^{6} +(-13.5885 - 23.5360i) q^{7} -21.1771 q^{8} +(-24.2116 - 41.9358i) q^{9} +(-2.78078 + 4.81645i) q^{10} +(7.63068 - 13.2167i) q^{11} -48.3002 q^{12} +42.4384 q^{14} +(-15.4654 + 26.7869i) q^{15} +(-5.71165 + 9.89286i) q^{16} +(-22.2732 - 38.5783i) q^{17} +75.6155 q^{18} +(11.9848 + 20.7584i) q^{19} +(9.90388 + 17.1540i) q^{20} +236.024 q^{21} +(11.9157 + 20.6386i) q^{22} +(-61.3693 + 106.295i) q^{23} +(91.9579 - 159.276i) q^{24} -112.315 q^{25} +186.054 q^{27} +(75.5734 - 130.897i) q^{28} +(109.955 - 190.447i) q^{29} +(-24.1501 - 41.8292i) q^{30} -27.0928 q^{31} +(-93.6274 - 162.167i) q^{32} +(66.2699 + 114.783i) q^{33} +69.5616 q^{34} +(-48.3963 - 83.8249i) q^{35} +(134.654 - 233.228i) q^{36} +(47.0961 - 81.5729i) q^{37} -37.4299 q^{38} -75.4233 q^{40} +(-80.1771 + 138.871i) q^{41} +(-184.282 + 319.185i) q^{42} +(75.6510 + 131.031i) q^{43} +84.8769 q^{44} +(-86.2311 - 149.357i) q^{45} +(-95.8314 - 165.985i) q^{46} -466.948 q^{47} +(-49.6037 - 85.9161i) q^{48} +(-197.797 + 342.594i) q^{49} +(87.6932 - 151.889i) q^{50} +386.870 q^{51} -120.847 q^{53} +(-145.267 + 251.609i) q^{54} +(27.1771 - 47.0721i) q^{55} +(287.766 + 498.425i) q^{56} -208.169 q^{57} +(171.700 + 297.393i) q^{58} +(-219.816 - 380.733i) q^{59} -172.024 q^{60} +(68.6525 + 118.910i) q^{61} +(21.1534 - 36.6388i) q^{62} +(-658.002 + 1139.69i) q^{63} +201.022 q^{64} -206.968 q^{66} +(256.140 - 443.648i) q^{67} +(123.874 - 214.555i) q^{68} +(-532.972 - 923.134i) q^{69} +151.147 q^{70} +(205.359 + 355.693i) q^{71} +(512.732 + 888.078i) q^{72} +308.004 q^{73} +(73.5431 + 127.380i) q^{74} +(487.710 - 844.739i) q^{75} +(-66.6543 + 115.449i) q^{76} -414.759 q^{77} -586.462 q^{79} +(-20.3423 + 35.2339i) q^{80} +(-154.193 + 267.070i) q^{81} +(-125.201 - 216.854i) q^{82} -1354.20 q^{83} +(656.329 + 1136.80i) q^{84} +(-79.3272 - 137.399i) q^{85} -236.266 q^{86} +(954.918 + 1653.97i) q^{87} +(-161.596 + 279.892i) q^{88} +(219.941 - 380.949i) q^{89} +269.309 q^{90} -682.617 q^{92} +(117.646 - 203.769i) q^{93} +(364.582 - 631.474i) q^{94} +(42.6847 + 73.9320i) q^{95} +1626.24 q^{96} +(-755.634 - 1308.80i) q^{97} +(-308.870 - 534.979i) q^{98} -739.006 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9}+O(q^{10}) $ 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9	\( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9} - 7 q^{10} + 80 q^{11} - 86 q^{12} + 178 q^{14} - 33 q^{15} + 39 q^{16} - 19 q^{17} + 220 q^{18} - 84 q^{19} + 19 q^{20} + 606 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 474 q^{25} + 670 q^{27} + 125 q^{28} + 44 q^{29} - 43 q^{30} + 172 q^{31} - 123 q^{32} - 106 q^{33} + 270 q^{34} - 107 q^{35} + 250 q^{36} + 209 q^{37} - 628 q^{38} - 178 q^{40} - 230 q^{41} - 197 q^{42} - 287 q^{43} + 356 q^{44} - 180 q^{45} - 4 q^{46} - 870 q^{47} - 285 q^{48} - 383 q^{49} - 144 q^{50} + 962 q^{51} - 236 q^{53} + 91 q^{54} + 18 q^{55} + 1015 q^{56} - 1212 q^{57} + 794 q^{58} - 368 q^{59} - 350 q^{60} + 1058 q^{61} + 332 q^{62} - 1560 q^{63} + 1538 q^{64} - 1636 q^{66} + 68 q^{67} + 211 q^{68} - 796 q^{69} + 250 q^{70} - 131 q^{71} + 1350 q^{72} - 912 q^{73} - 147 q^{74} + 516 q^{75} + 22 q^{76} + 1524 q^{77} - 2016 q^{79} - 69 q^{80} - 122 q^{81} - 72 q^{82} - 3916 q^{83} + 1409 q^{84} - 173 q^{85} - 2718 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 500 q^{90} - 1576 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 3726 q^{96} - 928 q^{97} - 650 q^{98} + 260 q^{99}+O(q^{100}) \) 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9 - 7 * q^10 + 80 * q^11 - 86 * q^12 + 178 * q^14 - 33 * q^15 + 39 * q^16 - 19 * q^17 + 220 * q^18 - 84 * q^19 + 19 * q^20 + 606 * q^21 - 142 * q^22 - 196 * q^23 + 273 * q^24 - 474 * q^25 + 670 * q^27 + 125 * q^28 + 44 * q^29 - 43 * q^30 + 172 * q^31 - 123 * q^32 - 106 * q^33 + 270 * q^34 - 107 * q^35 + 250 * q^36 + 209 * q^37 - 628 * q^38 - 178 * q^40 - 230 * q^41 - 197 * q^42 - 287 * q^43 + 356 * q^44 - 180 * q^45 - 4 * q^46 - 870 * q^47 - 285 * q^48 - 383 * q^49 - 144 * q^50 + 962 * q^51 - 236 * q^53 + 91 * q^54 + 18 * q^55 + 1015 * q^56 - 1212 * q^57 + 794 * q^58 - 368 * q^59 - 350 * q^60 + 1058 * q^61 + 332 * q^62 - 1560 * q^63 + 1538 * q^64 - 1636 * q^66 + 68 * q^67 + 211 * q^68 - 796 * q^69 + 250 * q^70 - 131 * q^71 + 1350 * q^72 - 912 * q^73 - 147 * q^74 + 516 * q^75 + 22 * q^76 + 1524 * q^77 - 2016 * q^79 - 69 * q^80 - 122 * q^81 - 72 * q^82 - 3916 * q^83 + 1409 * q^84 - 173 * q^85 - 2718 * q^86 + 2558 * q^87 + 1242 * q^88 - 720 * q^89 + 500 * q^90 - 1576 * q^92 + 652 * q^93 + 811 * q^94 + 146 * q^95 + 3726 * q^96 - 928 * q^97 - 650 * q^98 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.780776	+	1.35234i	−0.276046	+	0.478126i	−0.970399	−	0.241509i	$-0.922358\pi$
$2$	−0.780776	+	1.35234i	−0.276046	+	0.478126i	0.694352	+	0.719635i	$0.255691\pi$
$3$	−4.34233	+	7.52113i	−0.835682	+	1.44744i	0.0577926	+	0.998329i	$0.481594\pi$
$3$	−4.34233	+	7.52113i	−0.835682	+	1.44744i	−0.893474	+	0.449114i	$0.851740\pi$
$4$	2.78078	+	4.81645i	0.347597	+	0.602056i
$5$	3.56155			0.318555			0.159277	−	0.987234i	$-0.449084\pi$
$5$	3.56155			0.318555			0.159277	+	0.987234i	$0.449084\pi$
$6$	−6.78078	−	11.7446i	−0.461373	−	0.799122i
$7$	−13.5885	−	23.5360i	−0.733712	−	1.27083i	−0.955286	−	0.295683i	$-0.904453\pi$
$7$	−13.5885	−	23.5360i	−0.733712	−	1.27083i	0.221574	−	0.975144i	$-0.428881\pi$
$8$	−21.1771			−0.935904
$9$	−24.2116	−	41.9358i	−0.896728	−	1.55318i
$10$	−2.78078	+	4.81645i	−0.0879359	+	0.152309i
$11$	7.63068	−	13.2167i	0.209158	−	0.362272i	−0.742292	−	0.670077i	$-0.766261\pi$
$11$	7.63068	−	13.2167i	0.209158	−	0.362272i	0.951450	+	0.307805i	$0.0995944\pi$
$12$	−48.3002			−1.16192
$13$		0			0
$13$		0			0
$14$	42.4384			0.810154
$15$	−15.4654	+	26.7869i	−0.266211	+	0.461090i
$16$	−5.71165	+	9.89286i	−0.0892445	+	0.154576i
$17$	−22.2732	−	38.5783i	−0.317767	−	0.550389i	0.662255	−	0.749279i	$-0.269600\pi$
$17$	−22.2732	−	38.5783i	−0.317767	−	0.550389i	−0.980022	+	0.198890i	$0.936266\pi$
$18$	75.6155			0.990153
$19$	11.9848	+	20.7584i	0.144711	+	0.250647i	0.929265	−	0.369413i	$-0.120441\pi$
$19$	11.9848	+	20.7584i	0.144711	+	0.250647i	−0.784554	+	0.620061i	$0.787108\pi$
$20$	9.90388	+	17.1540i	0.110729	+	0.191788i
$21$	236.024			2.45260
$22$	11.9157	+	20.6386i	0.115474	+	0.200008i
$23$	−61.3693	+	106.295i	−0.556365	+	0.963652i	0.441431	+	0.897295i	$0.354471\pi$
$23$	−61.3693	+	106.295i	−0.556365	+	0.963652i	−0.997796	+	0.0663568i	$0.978862\pi$
$24$	91.9579	−	159.276i	0.782117	−	1.35467i
$25$	−112.315			−0.898523
$26$		0			0
$27$	186.054			1.32615
$28$	75.5734	−	130.897i	0.510072	−	0.883471i
$29$	109.955	−	190.447i	0.704071	−	1.21949i	−0.262955	−	0.964808i	$-0.584697\pi$
$29$	109.955	−	190.447i	0.704071	−	1.21949i	0.967026	−	0.254678i	$-0.0819694\pi$
$30$	−24.1501	−	41.8292i	−0.146973	−	0.254564i
$31$	−27.0928			−0.156968			−0.0784840	−	0.996915i	$-0.525008\pi$
$31$	−27.0928			−0.156968			−0.0784840	+	0.996915i	$0.525008\pi$
$32$	−93.6274	−	162.167i	−0.517223	−	0.895856i
$33$	66.2699	+	114.783i	0.349579	+	0.605488i
$34$	69.5616			0.350874
$35$	−48.3963	−	83.8249i	−0.233728	−	0.404828i
$36$	134.654	−	233.228i	0.623400	−	1.07976i
$37$	47.0961	−	81.5729i	0.209258	−	0.362446i	−0.742223	−	0.670153i	$-0.766228\pi$
$37$	47.0961	−	81.5729i	0.209258	−	0.362446i	0.951481	+	0.307707i	$0.0995617\pi$
$38$	−37.4299			−0.159788
$39$		0			0
$40$	−75.4233			−0.298137
$41$	−80.1771	+	138.871i	−0.305404	+	0.528975i	−0.977351	−	0.211624i	$-0.932125\pi$
$41$	−80.1771	+	138.871i	−0.305404	+	0.528975i	0.671947	+	0.740599i	$0.265458\pi$
$42$	−184.282	+	319.185i	−0.677031	+	1.17265i
$43$	75.6510	+	131.031i	0.268295	+	0.464700i	0.968422	−	0.249318i	$-0.0802066\pi$
$43$	75.6510	+	131.031i	0.268295	+	0.464700i	−0.700127	+	0.714018i	$0.746873\pi$
$44$	84.8769			0.290811
$45$	−86.2311	−	149.357i	−0.285657	−	0.494773i
$46$	−95.8314	−	165.985i	−0.307165	−	0.532025i
$47$	−466.948			−1.44918			−0.724589	−	0.689181i	$-0.757970\pi$
$47$	−466.948			−1.44918			−0.724589	+	0.689181i	$0.757970\pi$
$48$	−49.6037	−	85.9161i	−0.149160	−	0.258353i
$49$	−197.797	+	342.594i	−0.576667	+	0.998817i
$50$	87.6932	−	151.889i	0.248034	−	0.429607i
$51$	386.870			1.06221
$52$		0			0
$53$	−120.847			−0.313199			−0.156600	−	0.987662i	$-0.550053\pi$
$53$	−120.847			−0.313199			−0.156600	+	0.987662i	$0.550053\pi$
$54$	−145.267	+	251.609i	−0.366079	+	0.634068i
$55$	27.1771	−	47.0721i	0.0666283	−	0.115404i
$56$	287.766	+	498.425i	0.686684	+	1.18937i
$57$	−208.169			−0.483730
$58$	171.700	+	297.393i	0.388712	+	0.673269i
$59$	−219.816	−	380.733i	−0.485045	−	0.840122i	0.514808	−	0.857306i	$-0.327863\pi$
$59$	−219.816	−	380.733i	−0.485045	−	0.840122i	−0.999852	+	0.0171836i	$0.994530\pi$
$60$	−172.024			−0.370136
$61$	68.6525	+	118.910i	0.144099	+	0.249587i	0.929037	−	0.369988i	$-0.120638\pi$
$61$	68.6525	+	118.910i	0.144099	+	0.249587i	−0.784937	+	0.619575i	$0.787305\pi$
$62$	21.1534	−	36.6388i	0.0433304	−	0.0750505i
$63$	−658.002	+	1139.69i	−1.31588	+	2.27917i
$64$	201.022			0.392621
$65$		0			0
$66$	−206.968			−0.386000
$67$	256.140	−	443.648i	0.467052	−	0.808958i	−0.532239	−	0.846594i	$-0.678649\pi$
$67$	256.140	−	443.648i	0.467052	−	0.808958i	0.999292	+	0.0376358i	$0.0119827\pi$
$68$	123.874	−	214.555i	0.220910	−	0.382627i
$69$	−532.972	−	923.134i	−0.929887	−	1.61061i
$70$	151.147			0.258078
$71$	205.359	+	355.693i	0.343263	+	0.594549i	0.985037	−	0.172345i	$-0.0551345\pi$
$71$	205.359	+	355.693i	0.343263	+	0.594549i	−0.641774	+	0.766894i	$0.721801\pi$
$72$	512.732	+	888.078i	0.839251	+	1.45362i
$73$	308.004			0.493823			0.246912	−	0.969038i	$-0.420584\pi$
$73$	308.004			0.493823			0.246912	+	0.969038i	$0.420584\pi$
$74$	73.5431	+	127.380i	0.115530	+	0.200104i
$75$	487.710	−	844.739i	0.750879	−	1.30056i
$76$	−66.6543	+	115.449i	−0.100602	+	0.174248i
$77$	−414.759			−0.613847
$78$		0			0
$79$	−586.462			−0.835217			−0.417608	−	0.908627i	$-0.637132\pi$
$79$	−586.462			−0.835217			−0.417608	+	0.908627i	$0.637132\pi$
$80$	−20.3423	+	35.2339i	−0.0284293	+	0.0492409i
$81$	−154.193	+	267.070i	−0.211513	+	0.366352i
$82$	−125.201	−	216.854i	−0.168611	−	0.292043i
$83$	−1354.20			−1.79088			−0.895440	−	0.445182i	$-0.853139\pi$
$83$	−1354.20			−1.79088			−0.895440	+	0.445182i	$0.853139\pi$
$84$	656.329	+	1136.80i	0.852516	+	1.47660i
$85$	−79.3272	−	137.399i	−0.101226	−	0.175329i
$86$	−236.266			−0.296247
$87$	954.918	+	1653.97i	1.17676	+	2.03820i
$88$	−161.596	+	279.892i	−0.195752	+	0.339052i
$89$	219.941	−	380.949i	0.261952	−	0.453714i	−0.704809	−	0.709398i	$-0.748967\pi$
$89$	219.941	−	380.949i	0.261952	−	0.453714i	0.966761	+	0.255683i	$0.0823005\pi$
$90$	269.309			0.315418
$91$		0			0
$92$	−682.617			−0.773563
$93$	117.646	−	203.769i	0.131175	−	0.227202i
$94$	364.582	−	631.474i	0.400040	−	0.692889i
$95$	42.6847	+	73.9320i	0.0460985	+	0.0798449i
$96$	1626.24			1.72894
$97$	−755.634	−	1308.80i	−0.790959	−	1.36998i	−0.925374	−	0.379056i	$-0.876249\pi$
$97$	−755.634	−	1308.80i	−0.790959	−	1.36998i	0.134414	−	0.990925i	$-0.457085\pi$
$98$	−308.870	−	534.979i	−0.318374	−	0.551439i
$99$	−739.006			−0.750231
$100$	−312.324	−	540.961i	−0.312324	−	0.540961i
$101$	−168.130	+	291.209i	−0.165639	+	0.286895i	−0.936882	−	0.349646i	$-0.886302\pi$
$101$	−168.130	+	291.209i	−0.165639	+	0.286895i	0.771243	+	0.636541i	$0.219635\pi$
$102$	−302.059	+	523.182i	−0.293219	+	0.507870i
$103$	322.712			0.308716			0.154358	−	0.988015i	$-0.450669\pi$
$103$	322.712			0.308716			0.154358	+	0.988015i	$0.450669\pi$
$104$		0			0
$105$	840.611			0.781288
$106$	94.3542	−	163.426i	0.0864574	−	0.149749i
$107$	−717.309	+	1242.42i	−0.648083	+	1.12251i	0.335498	+	0.942041i	$0.391096\pi$
$107$	−717.309	+	1242.42i	−0.648083	+	1.12251i	−0.983580	+	0.180471i	$0.942238\pi$
$108$	517.375	+	896.119i	0.460967	+	0.798417i
$109$	−849.147			−0.746179			−0.373089	−	0.927795i	$-0.621702\pi$
$109$	−849.147			−0.746179			−0.373089	+	0.927795i	$0.621702\pi$
$110$	42.4384	+	73.5055i	0.0367850	+	0.0637134i
$111$	409.014	+	708.433i	0.349747	+	0.605779i
$112$	310.452			0.261919
$113$	−807.263	−	1398.22i	−0.672044	−	1.16401i	−0.977324	−	0.211751i	$-0.932083\pi$
$113$	−807.263	−	1398.22i	−0.672044	−	1.16401i	0.305280	−	0.952263i	$-0.401250\pi$
$114$	162.533	−	281.516i	0.133532	−	0.231284i
$115$	−218.570	+	378.574i	−0.177233	+	0.306976i
$116$	1223.04			0.978931
$117$		0			0
$118$	686.509			0.535579
$119$	−605.321	+	1048.45i	−0.466300	+	0.807654i
$120$	327.513	−	567.269i	0.249147	−	0.431536i
$121$	549.045	+	950.974i	0.412506	+	0.714481i
$122$	−214.409			−0.159112
$123$	−696.311	−	1206.05i	−0.510441	−	0.884109i
$124$	−75.3390	−	130.491i	−0.0545616	−	0.0945035i
$125$	−845.211			−0.604784
$126$	−1027.50	−	1779.69i	−0.726487	−	1.25831i
$127$	−432.587	+	749.263i	−0.302251	+	0.523514i	−0.976646	−	0.214857i	$-0.931071\pi$
$127$	−432.587	+	749.263i	−0.302251	+	0.523514i	0.674394	+	0.738371i	$0.264405\pi$
$128$	592.066	−	1025.49i	0.408842	−	0.708134i
$129$	−1314.01			−0.896836
$130$		0			0
$131$	−281.400			−0.187680			−0.0938400	−	0.995587i	$-0.529914\pi$
$131$	−281.400			−0.187680			−0.0938400	+	0.995587i	$0.529914\pi$
$132$	−368.563	+	638.371i	−0.243025	+	0.420932i
$133$	325.713	−	564.152i	0.212353	−	0.367806i
$134$	399.976	+	692.779i	0.257856	+	0.446620i
$135$	662.641			0.422452
$136$	471.681	+	816.976i	0.297400	+	0.515111i
$137$	−1320.72	−	2287.55i	−0.823624	−	1.42656i	−0.902967	−	0.429711i	$-0.858616\pi$
$137$	−1320.72	−	2287.55i	−0.823624	−	1.42656i	0.0793428	−	0.996847i	$-0.474718\pi$
$138$	1664.53			1.02677
$139$	999.318	+	1730.87i	0.609791	+	1.05619i	0.991274	+	0.131814i	$0.0420801\pi$
$139$	999.318	+	1730.87i	0.609791	+	1.05619i	−0.381483	+	0.924376i	$0.624587\pi$
$140$	269.159	−	466.196i	0.162486	−	0.281434i
$141$	2027.64	−	3511.98i	1.21105	−	2.09760i
$142$	−641.359			−0.379026
$143$		0			0
$144$	553.153			0.320112
$145$	391.609	−	678.286i	0.224285	−	0.388473i
$146$	−240.482	+	416.527i	−0.136318	+	0.236110i
$147$	−1717.80	−	2975.31i	−0.963820	−	1.66939i
$148$	523.855			0.290950
$149$	−876.491	−	1518.13i	−0.481912	−	0.834696i	0.517872	−	0.855458i	$-0.326724\pi$
$149$	−876.491	−	1518.13i	−0.481912	−	0.834696i	−0.999784	+	0.0207617i	$0.993391\pi$
$150$	761.585	+	1319.10i	0.414554	+	0.718029i
$151$	2794.64			1.50613			0.753063	−	0.657949i	$-0.228576\pi$
$151$	2794.64			1.50613			0.753063	+	0.657949i	$0.228576\pi$
$152$	−253.804	−	439.601i	−0.135436	−	0.234582i
$153$	−1078.54	+	1868.09i	−0.569901	+	0.987098i
$154$	323.834	−	560.898i	0.169450	−	0.293496i
$155$	−96.4924			−0.0500030
$156$		0			0
$157$	3244.87			1.64949			0.824743	−	0.565508i	$-0.191320\pi$
$157$	3244.87			1.64949			0.824743	+	0.565508i	$0.191320\pi$
$158$	457.896	−	793.099i	0.230558	−	0.399339i
$159$	524.756	−	908.903i	0.261735	−	0.453338i
$160$	−333.459	−	577.568i	−0.164764	−	0.285380i
$161$	3335.68			1.63285
$162$	−240.781	−	417.045i	−0.116775	−	0.202260i
$163$	1640.73	+	2841.83i	0.788418	+	1.36558i	0.926936	+	0.375221i	$0.122433\pi$
$163$	1640.73	+	2841.83i	0.788418	+	1.36558i	−0.138517	+	0.990360i	$0.544234\pi$
$164$	−891.818			−0.424630
$165$	236.024	+	408.805i	0.111360	+	0.192881i
$166$	1057.33	−	1831.35i	0.494366	−	0.856266i
$167$	−1563.26	+	2707.65i	−0.724364	+	1.25463i	0.234872	+	0.972026i	$0.424533\pi$
$167$	−1563.26	+	2707.65i	−0.724364	+	1.25463i	−0.959235	+	0.282608i	$0.908800\pi$
$168$	−4998.29			−2.29540
$169$		0			0
$170$	247.747			0.111773
$171$	580.346	−	1005.19i	0.259533	−	0.449524i
$172$	−420.737	+	728.738i	−0.186517	+	0.323057i
$173$	−48.7849	−	84.4980i	−0.0214396	−	0.0371345i	0.855107	−	0.518452i	$-0.173492\pi$
$173$	−48.7849	−	84.4980i	−0.0214396	−	0.0371345i	−0.876546	+	0.481318i	$0.840158\pi$
$174$	−2982.31			−1.29936
$175$	1526.20	+	2643.46i	0.659257	+	1.14187i
$176$	87.1675	+	150.979i	0.0373324	+	0.0646616i
$177$	3818.06			1.62137
$178$	343.450	+	594.873i	0.144622	+	0.250492i
$179$	17.3575	−	30.0640i	0.00724782	−	0.0125536i	−0.862379	−	0.506264i	$-0.831026\pi$
$179$	17.3575	−	30.0640i	0.00724782	−	0.0125536i	0.869627	+	0.493710i	$0.164360\pi$
$180$	479.579	−	830.654i	0.198587	−	0.343963i
$181$	−1229.35			−0.504843			−0.252422	−	0.967617i	$-0.581227\pi$
$181$	−1229.35			−0.504843			−0.252422	+	0.967617i	$0.581227\pi$
$182$		0			0
$183$	−1192.45			−0.481684
$184$	1299.62	−	2251.01i	0.520704	−	0.901885i
$185$	167.735	−	290.526i	0.0666602	−	0.115459i
$186$	183.710	+	318.195i	0.0724209	+	0.125437i
$187$	−679.839			−0.265854
$188$	−1298.48	−	2249.03i	−0.503730	−	0.872486i
$189$	−2528.20	−	4378.97i	−0.973014	−	1.68531i
$190$	−133.309			−0.0509012
$191$	−2140.40	−	3707.28i	−0.810858	−	1.40445i	−0.912265	−	0.409602i	$-0.865668\pi$
$191$	−2140.40	−	3707.28i	−0.810858	−	1.40445i	0.101407	−	0.994845i	$-0.467666\pi$
$192$	−872.903	+	1511.91i	−0.328106	+	0.568296i
$193$	236.160	−	409.041i	0.0880786	−	0.152557i	−0.818620	−	0.574335i	$-0.805261\pi$
$193$	236.160	−	409.041i	0.0880786	−	0.152557i	0.906699	+	0.421778i	$0.138594\pi$
$194$	2359.93			0.873365
$195$		0			0
$196$	−2200.12			−0.801791
$197$	−2242.18	+	3883.58i	−0.810908	+	1.40453i	0.101321	+	0.994854i	$0.467693\pi$
$197$	−2242.18	+	3883.58i	−0.810908	+	1.40453i	−0.912229	+	0.409681i	$0.865640\pi$
$198$	576.998	−	999.390i	0.207098	−	0.358705i
$199$	183.120	+	317.173i	0.0652314	+	0.112984i	0.896797	−	0.442443i	$-0.145888\pi$
$199$	183.120	+	317.173i	0.0652314	+	0.112984i	−0.831565	+	0.555427i	$0.812555\pi$
$200$	2378.51			0.840931
$201$	2224.49	+	3852.93i	0.780614	+	1.35206i
$202$	−262.543	−	454.739i	−0.0914480	−	0.158393i
$203$	−5976.49			−2.06634
$204$	1075.80	+	1863.34i	0.369221	+	0.639509i
$205$	−285.555	+	494.596i	−0.0972879	+	0.168508i
$206$	−251.966	+	436.418i	−0.0852199	+	0.147605i
$207$	5943.41			1.99563
$208$		0			0
$209$	365.810			0.121070
$210$	−656.329	+	1136.80i	−0.215671	+	0.373554i
$211$	−1061.28	+	1838.19i	−0.346262	+	0.599744i	−0.985582	−	0.169197i	$-0.945883\pi$
$211$	−1061.28	+	1838.19i	−0.346262	+	0.599744i	0.639320	+	0.768941i	$0.279216\pi$
$212$	−336.047	−	582.051i	−0.108867	−	0.188563i
$213$	−3566.95			−1.14743
$214$	−1120.12	−	1940.10i	−0.357801	−	0.619730i
$215$	269.435	+	466.675i	0.0854666	+	0.148033i
$216$	−3940.08			−1.24115
$217$	368.152	+	637.657i	0.115169	+	0.199479i
$218$	662.994	−	1148.34i	0.205980	−	0.356768i
$219$	−1337.45	+	2316.54i	−0.412679	+	0.714781i
$220$	302.294			0.0926392
$221$		0			0
$222$	−1277.39			−0.386185
$223$	−2963.21	+	5132.43i	−0.889826	+	1.54122i	−0.0497449	+	0.998762i	$0.515841\pi$
$223$	−2963.21	+	5132.43i	−0.889826	+	1.54122i	−0.840081	+	0.542461i	$0.817493\pi$
$224$	−2544.52	+	4407.24i	−0.758986	+	1.31460i
$225$	2719.34	+	4710.03i	0.805730	+	1.39557i
$226$	2521.17			0.742060
$227$	−447.830	−	775.665i	−0.130941	−	0.226796i	0.793099	−	0.609093i	$-0.208466\pi$
$227$	−447.830	−	775.665i	−0.130941	−	0.226796i	−0.924039	+	0.382297i	$0.875133\pi$
$228$	−578.870	−	1002.63i	−0.168143	−	0.291232i
$229$	−627.717			−0.181138			−0.0905692	−	0.995890i	$-0.528869\pi$
$229$	−627.717			−0.181138			−0.0905692	+	0.995890i	$0.528869\pi$
$230$	−341.309	−	591.164i	−0.0978488	−	0.169479i
$231$	1801.02	−	3119.46i	0.512981	−	0.888509i
$232$	−2328.52	+	4033.11i	−0.658942	+	1.14132i
$233$	2303.72			0.647734			0.323867	−	0.946103i	$-0.395017\pi$
$233$	2303.72			0.647734			0.323867	+	0.946103i	$0.395017\pi$
$234$		0			0
$235$	−1663.06			−0.461643
$236$	1222.52	−	2117.47i	0.337200	−	0.584048i
$237$	2546.61	−	4410.86i	0.697976	−	1.20893i
$238$	−945.240	−	1637.20i	−0.257440	−	0.445900i
$239$	−544.622			−0.147400			−0.0737001	−	0.997280i	$-0.523481\pi$
$239$	−544.622			−0.147400			−0.0737001	+	0.997280i	$0.523481\pi$
$240$	−176.666	−	305.995i	−0.0475156	−	0.0822995i
$241$	2713.05	+	4699.14i	0.725157	+	1.25601i	0.958909	+	0.283713i	$0.0915662\pi$
$241$	2713.05	+	4699.14i	0.725157	+	1.25601i	−0.233752	+	0.972296i	$0.575100\pi$
$242$	−1714.73			−0.455483
$243$	1172.61	+	2031.03i	0.309561	+	0.536175i
$244$	−381.814	+	661.322i	−0.100177	+	0.173511i
$245$	−704.464	+	1220.17i	−0.183700	+	0.318178i
$246$	2174.65			0.563621
$247$		0			0
$248$	573.746			0.146907
$249$	5880.39	−	10185.1i	1.49661	−	2.59220i
$250$	659.921	−	1143.02i	0.166948	−	0.289163i
$251$	2610.61	+	4521.71i	0.656494	+	1.13708i	0.981517	+	0.191375i	$0.0612948\pi$
$251$	2610.61	+	4521.71i	0.656494	+	1.13708i	−0.325022	+	0.945706i	$0.605372\pi$
$252$	−7319.02			−1.82958
$253$	936.580	+	1622.20i	0.232736	+	0.403111i
$254$	−675.508	−	1170.01i	−0.166871	−	0.289028i
$255$	1377.86			0.338372
$256$	1728.63	+	2994.07i	0.422029	+	0.730975i
$257$	−329.103	+	570.023i	−0.0798789	+	0.138354i	−0.903198	−	0.429225i	$-0.858787\pi$
$257$	−329.103	+	570.023i	−0.0798789	+	0.138354i	0.823319	+	0.567579i	$0.192120\pi$
$258$	1025.95	−	1776.99i	0.247568	−	0.428801i
$259$	−2559.87			−0.614141
$260$		0			0
$261$	−10648.7			−2.52544
$262$	219.711	−	380.550i	0.0518083	−	0.0897346i
$263$	−1623.23	+	2811.51i	−0.380580	+	0.659184i	−0.991145	−	0.132782i	$-0.957609\pi$
$263$	−1623.23	+	2811.51i	−0.380580	+	0.659184i	0.610565	+	0.791966i	$0.290942\pi$
$264$	−1403.40	−	2430.76i	−0.327172	−	0.566679i
$265$	−430.401			−0.0997711
$266$	508.618	+	880.953i	0.117238	+	0.203063i
$267$	1910.11	+	3308.42i	0.437817	+	0.758321i
$268$	2849.07			0.649384
$269$	1292.90	+	2239.37i	0.293047	+	0.507572i	0.974529	−	0.224263i	$-0.0719976\pi$
$269$	1292.90	+	2239.37i	0.293047	+	0.507572i	−0.681482	+	0.731835i	$0.738664\pi$
$270$	−517.375	+	896.119i	−0.116616	+	0.201985i
$271$	494.466	−	856.441i	0.110836	−	0.191974i	−0.805271	−	0.592907i	$-0.797980\pi$
$271$	494.466	−	856.441i	0.110836	−	0.191974i	0.916108	+	0.400932i	$0.131314\pi$
$272$	508.867			0.113436
$273$		0			0
$274$	4124.74			0.909433
$275$	−857.043	+	1484.44i	−0.187933	+	0.325510i
$276$	2964.15	−	5134.06i	0.646452	−	1.11969i
$277$	−4071.20	−	7051.53i	−0.883086	−	1.52955i	−0.847892	−	0.530169i	$-0.822128\pi$
$277$	−4071.20	−	7051.53i	−0.883086	−	1.52955i	−0.0351939	−	0.999381i	$-0.511205\pi$
$278$	−3120.97			−0.673322
$279$	655.961	+	1136.16i	0.140758	+	0.243799i
$280$	1024.89	+	1775.17i	0.218747	+	0.378880i
$281$	−1534.21			−0.325705			−0.162853	−	0.986650i	$-0.552070\pi$
$281$	−1534.21			−0.325705			−0.162853	+	0.986650i	$0.552070\pi$
$282$	3166.27	+	5484.14i	0.668612	+	1.15807i
$283$	3482.50	−	6031.87i	0.731495	−	1.26699i	−0.224749	−	0.974417i	$-0.572156\pi$
$283$	3482.50	−	6031.87i	0.731495	−	1.26699i	0.956244	−	0.292570i	$-0.0945105\pi$
$284$	−1142.12	+	1978.20i	−0.238634	+	0.413327i
$285$	−741.403			−0.154095
$286$		0			0
$287$	4357.96			0.896314
$288$	−4533.75	+	7852.68i	−0.927616	+	1.60668i
$289$	1464.31	−	2536.26i	0.298048	−	0.516234i
$290$	611.518	+	1059.18i	0.123826	+	0.214473i
$291$	13124.9			2.64396
$292$	856.490	+	1483.48i	0.171652	+	0.297309i
$293$	320.015	+	554.281i	0.0638070	+	0.110517i	0.896164	−	0.443723i	$-0.146342\pi$
$293$	320.015	+	554.281i	0.0638070	+	0.110517i	−0.832357	+	0.554240i	$0.813009\pi$
$294$	5364.87			1.06424
$295$	−782.887	−	1356.00i	−0.154513	−	0.267625i
$296$	−997.358	+	1727.48i	−0.195846	+	0.339214i
$297$	1419.72	−	2459.03i	0.277375	−	0.480428i
$298$	2737.37			0.532120
$299$		0			0
$300$	5424.85			1.04401
$301$	2055.97	−	3561.05i	0.393702	−	0.681912i
$302$	−2181.99	+	3779.32i	−0.415760	+	0.720118i
$303$	−1460.15	−	2529.05i	−0.276843	−	0.479506i
$304$	−273.813			−0.0516587
$305$	244.509	+	423.503i	0.0459035	+	0.0795072i
$306$	−1684.20	−	2917.12i	−0.314638	−	0.544969i
$307$	100.406			0.0186660			0.00933299	−	0.999956i	$-0.497029\pi$
$307$	100.406			0.0186660			0.00933299	+	0.999956i	$0.497029\pi$
$308$	−1153.35	−	1997.67i	−0.213371	−	0.369570i
$309$	−1401.32	+	2427.16i	−0.257988	+	0.446849i
$310$	75.3390	−	130.491i	0.0138031	−	0.0239077i
$311$	−3878.92			−0.707245			−0.353623	−	0.935388i	$-0.615050\pi$
$311$	−3878.92			−0.707245			−0.353623	+	0.935388i	$0.615050\pi$
$312$		0			0
$313$	−3789.39			−0.684311			−0.342155	−	0.939643i	$-0.611157\pi$
$313$	−3789.39			−0.684311			−0.342155	+	0.939643i	$0.611157\pi$
$314$	−2533.52	+	4388.19i	−0.455334	+	0.788662i
$315$	−2343.51	+	4059.08i	−0.419180	+	0.726041i
$316$	−1630.82	−	2824.66i	−0.290319	−	0.502847i
$317$	−4406.81			−0.780791			−0.390396	−	0.920647i	$-0.627662\pi$
$317$	−4406.81			−0.780791			−0.390396	+	0.920647i	$0.627662\pi$
$318$	819.434	+	1419.30i	0.144502	+	0.250284i
$319$	−1678.06	−	2906.48i	−0.294524	−	0.510130i
$320$	715.950			0.125071
$321$	−6229.58	−	10790.0i	−1.08318	−	1.87613i
$322$	−2604.42	+	4510.99i	−0.450741	+	0.780706i
$323$	533.882	−	924.710i	0.0919690	−	0.159295i
$324$	−1715.11			−0.294086
$325$		0			0
$326$	−5124.19			−0.870559
$327$	3687.27	−	6386.55i	0.623568	−	1.08005i
$328$	1697.92	−	2940.88i	0.285829	−	0.495070i
$329$	6345.14	+	10990.1i	1.06328	+	1.84165i
$330$	−737.127			−0.122962
$331$	−2065.75	−	3577.98i	−0.343032	−	0.594149i	0.641962	−	0.766736i	$-0.278121\pi$
$331$	−2065.75	−	3577.98i	−0.343032	−	0.594149i	−0.984994	+	0.172587i	$0.944787\pi$
$332$	−3765.73	−	6522.44i	−0.622505	−	1.07821i
$333$	−4561.10			−0.750591
$334$	−2441.11	−	4228.13i	−0.399916	−	0.692674i
$335$	912.257	−	1580.07i	0.148782	−	0.257698i
$336$	−1348.08	+	2334.95i	−0.218881	+	0.379113i
$337$	−4560.82			−0.737221			−0.368611	−	0.929584i	$-0.620166\pi$
$337$	−4560.82			−0.737221			−0.368611	+	0.929584i	$0.620166\pi$
$338$		0			0
$339$	14021.6			2.24646
$340$	441.182	−	764.150i	0.0703720	−	0.121888i
$341$	−206.737	+	358.078i	−0.0328311	+	0.0568652i
$342$	906.240	+	1569.65i	0.143286	+	0.248179i
$343$	1429.34			0.225007
$344$	−1602.07	−	2774.86i	−0.251098	−	0.434914i
$345$	−1898.21	−	3287.79i	−0.296220	−	0.513069i
$346$	152.360			0.0236733
$347$	−5034.70	−	8720.36i	−0.778896	−	1.34909i	−0.932579	−	0.360967i	$-0.882447\pi$
$347$	−5034.70	−	8720.36i	−0.778896	−	1.34909i	0.153683	−	0.988120i	$-0.450887\pi$
$348$	−5310.82	+	9198.62i	−0.818075	+	1.41695i
$349$	2939.66	−	5091.64i	0.450878	−	0.780944i	−0.547563	−	0.836765i	$-0.684444\pi$
$349$	2939.66	−	5091.64i	0.450878	−	0.780944i	0.998441	+	0.0558207i	$0.0177775\pi$
$350$	−4766.49			−0.727942
$351$		0			0
$352$	−2857.76			−0.432725
$353$	−4571.28	+	7917.69i	−0.689249	+	1.19381i	0.282833	+	0.959169i	$0.408726\pi$
$353$	−4571.28	+	7917.69i	−0.689249	+	1.19381i	−0.972081	+	0.234644i	$0.924607\pi$
$354$	−2981.05	+	5163.33i	−0.447574	+	0.775220i
$355$	731.398	+	1266.82i	0.109348	+	0.189397i
$356$	2446.43			0.364215
$357$	−5257.00	−	9105.39i	−0.779356	−	1.34988i
$358$	27.1046	+	46.9466i	0.00400146	+	0.00693074i
$359$	2754.32			0.404924			0.202462	−	0.979290i	$-0.435106\pi$
$359$	2754.32			0.404924			0.202462	+	0.979290i	$0.435106\pi$
$360$	1826.12	+	3162.94i	0.267347	+	0.463059i
$361$	3142.23	−	5442.50i	0.458117	−	0.793483i
$362$	959.845	−	1662.50i	0.139360	−	0.241379i
$363$	−9536.54			−1.37889
$364$		0			0
$365$	1096.97			0.157310
$366$	931.034	−	1612.60i	0.132967	−	0.230306i
$367$	−1520.09	+	2632.88i	−0.216208	+	0.374483i	−0.953646	−	0.300932i	$-0.902702\pi$
$367$	−1520.09	+	2632.88i	−0.216208	+	0.374483i	0.737438	+	0.675415i	$0.236036\pi$
$368$	−701.040	−	1214.24i	−0.0993049	−	0.172001i
$369$	7764.88			1.09546
$370$	261.928	+	453.672i	0.0368026	+	0.0637440i
$371$	1642.13	+	2844.25i	0.229798	+	0.398022i
$372$	1308.59			0.182385
$373$	2692.36	+	4663.31i	0.373740	+	0.647337i	0.990138	−	0.140098i	$-0.0447418\pi$
$373$	2692.36	+	4663.31i	0.373740	+	0.647337i	−0.616397	+	0.787435i	$0.711408\pi$
$374$	530.802	−	919.376i	0.0733880	−	0.127112i
$375$	3670.18	−	6356.95i	0.505407	−	0.875390i
$376$	9888.59			1.35629
$377$		0			0
$378$	7895.84			1.07439
$379$	−1712.13	+	2965.50i	−0.232049	+	0.401920i	−0.958411	−	0.285392i	$-0.907876\pi$
$379$	−1712.13	+	2965.50i	−0.232049	+	0.401920i	0.726362	+	0.687312i	$0.241209\pi$
$380$	−237.393	+	411.177i	−0.0320474	+	0.0555077i
$381$	−3756.87	−	6507.09i	−0.505171	−	0.874983i
$382$	6684.69			0.895336
$383$	−191.493	−	331.675i	−0.0255478	−	0.0442501i	0.852969	−	0.521962i	$-0.174800\pi$
$383$	−191.493	−	331.675i	−0.0255478	−	0.0442501i	−0.878517	+	0.477712i	$0.841466\pi$
$384$	5141.89	+	8906.01i	0.683323	+	1.18355i
$385$	−1477.19			−0.195544
$386$	368.776	+	638.739i	0.0486275	+	0.0842253i
$387$	3663.27	−	6344.97i	0.481175	−	0.833419i
$388$	4202.50	−	7278.94i	0.549870	−	0.952403i
$389$	8588.34			1.11940			0.559699	−	0.828696i	$-0.310917\pi$
$389$	8588.34			1.11940			0.559699	+	0.828696i	$0.310917\pi$
$390$		0			0
$391$	5467.56			0.707178
$392$	4188.76	−	7255.15i	0.539705	−	0.934796i
$393$	1221.93	−	2116.45i	0.156841	−	0.271656i
$394$	−3501.29	−	6064.41i	−0.447696	−	0.775433i
$395$	−2088.72			−0.266063
$396$	−2055.01	−	3559.38i	−0.260778	−	0.451681i
$397$	−3619.58	−	6269.30i	−0.457586	−	0.792562i	0.541247	−	0.840864i	$-0.317952\pi$
$397$	−3619.58	−	6269.30i	−0.457586	−	0.792562i	−0.998833	+	0.0483020i	$0.984619\pi$
$398$	−571.904			−0.0720275
$399$	2828.71	+	4899.46i	0.354918	+	0.614737i
$400$	641.505	−	1111.12i	0.0801882	−	0.138890i
$401$	2134.81	−	3697.60i	0.265854	−	0.460472i	−0.701933	−	0.712243i	$-0.747679\pi$
$401$	2134.81	−	3697.60i	0.265854	−	0.460472i	0.967787	+	0.251770i	$0.0810128\pi$
$402$	−6947.32			−0.861942
$403$		0			0
$404$	−1870.12			−0.230302
$405$	−549.167	+	951.185i	−0.0673786	+	0.116703i
$406$	4666.30	−	8082.27i	0.570405	−	0.987971i
$407$	−718.751	−	1244.91i	−0.0875360	−	0.151617i
$408$	−8192.78			−0.994125
$409$	6781.26	+	11745.5i	0.819834	+	1.41999i	0.905805	+	0.423696i	$0.139267\pi$
$409$	6781.26	+	11745.5i	0.819834	+	1.41999i	−0.0859711	+	0.996298i	$0.527399\pi$
$410$	−445.909	−	772.337i	−0.0537119	−	0.0930317i
$411$	22939.9			2.75315
$412$	897.390	+	1554.33i	0.107309	+	0.185864i
$413$	−5973.96	+	10347.2i	−0.711767	+	1.23282i
$414$	−4640.47	+	8037.54i	−0.550886	+	0.954163i
$415$	−4823.06			−0.570494
$416$		0			0
$417$	−17357.5			−2.03837
$418$	−285.616	+	494.701i	−0.0334209	+	0.0578867i
$419$	7288.44	−	12624.0i	0.849794	−	1.47189i	−0.0315973	−	0.999501i	$-0.510059\pi$
$419$	7288.44	−	12624.0i	0.849794	−	1.47189i	0.881392	−	0.472386i	$-0.156607\pi$
$420$	2337.55	+	4048.76i	0.271573	+	0.470379i
$421$	−15848.4			−1.83469			−0.917343	−	0.398099i	$-0.869670\pi$
$421$	−15848.4			−1.83469			−0.917343	+	0.398099i	$0.869670\pi$
$422$	−1657.24	−	2870.42i	−0.191169	−	0.331114i
$423$	11305.6	+	19581.8i	1.29952	+	2.25083i
$424$	2559.18			0.293124
$425$	2501.62	+	4332.94i	0.285521	+	0.494537i
$426$	2784.99	−	4823.75i	0.316745	−	0.548618i
$427$	1865.77	−	3231.62i	0.211455	−	0.366250i
$428$	−7978.70			−0.901087
$429$		0			0
$430$	−841.474			−0.0943709
$431$	5347.36	−	9261.90i	0.597618	−	1.03510i	−0.395554	−	0.918443i	$-0.629447\pi$
$431$	5347.36	−	9261.90i	0.597618	−	1.03510i	0.993172	−	0.116662i	$-0.0372193\pi$
$432$	−1062.67	+	1840.61i	−0.118352	+	0.204991i
$433$	8039.50	+	13924.8i	0.892272	+	1.54546i	0.837145	+	0.546981i	$0.184223\pi$
$433$	8039.50	+	13924.8i	0.892272	+	1.54546i	0.0551273	+	0.998479i	$0.482444\pi$
$434$	−1149.78			−0.127168
$435$	3400.99	+	5890.69i	0.374862	+	0.649280i
$436$	−2361.29	−	4089.87i	−0.259370	−	0.449241i
$437$	−2942.01			−0.322049
$438$	−2088.50	−	3617.40i	−0.227837	−	0.394625i
$439$	−3017.90	+	5227.16i	−0.328101	+	0.568288i	−0.982135	−	0.188177i	$-0.939742\pi$
$439$	−3017.90	+	5227.16i	−0.328101	+	0.568288i	0.654034	+	0.756465i	$0.273075\pi$
$440$	−575.531	+	996.849i	−0.0623577	+	0.108007i
$441$	19156.0			2.06845
$442$		0			0
$443$	10201.3			1.09409			0.547043	−	0.837105i	$-0.315753\pi$
$443$	10201.3			1.09409			0.547043	+	0.837105i	$0.315753\pi$
$444$	−2274.75	+	3939.98i	−0.243142	+	0.421134i
$445$	783.332	−	1356.77i	0.0834461	−	0.144533i
$446$	−4627.21	−	8014.56i	−0.491266	−	0.850897i
$447$	15224.0			1.61090
$448$	−2731.59	−	4731.26i	−0.288071	−	0.498953i
$449$	−2911.27	−	5042.47i	−0.305994	−	0.529997i	0.671488	−	0.741015i	$-0.265655\pi$
$449$	−2911.27	−	5042.47i	−0.305994	−	0.529997i	−0.977482	+	0.211018i	$0.932322\pi$
$450$	−8492.78			−0.889675
$451$	1223.61	+	2119.36i	0.127755	+	0.221279i
$452$	4489.64	−	7776.28i	0.467201	−	0.809216i
$453$	−12135.3	+	21018.9i	−1.25864	+	2.18003i
$454$	1398.62			0.144583
$455$		0			0
$456$	4408.40			0.452724
$457$	2310.80	−	4002.42i	0.236531	−	0.409684i	−0.723186	−	0.690654i	$-0.757323\pi$
$457$	2310.80	−	4002.42i	0.236531	−	0.409684i	0.959717	+	0.280970i	$0.0906562\pi$
$458$	490.106	−	848.889i	0.0500026	−	0.0866070i
$459$	−4144.02	−	7177.65i	−0.421408	−	0.729900i
$460$	−2431.18			−0.246422
$461$	2563.88	+	4440.78i	0.259028	+	0.448650i	0.965982	−	0.258610i	$-0.0832644\pi$
$461$	2563.88	+	4440.78i	0.259028	+	0.448650i	−0.706954	+	0.707260i	$0.749931\pi$
$462$	2812.39	+	4871.20i	0.283213	+	0.490539i
$463$	−6486.27			−0.651064			−0.325532	−	0.945531i	$-0.605543\pi$
$463$	−6486.27			−0.651064			−0.325532	+	0.945531i	$0.605543\pi$
$464$	1256.04	+	2175.53i	0.125669	+	0.217665i
$465$	419.002	−	725.733i	0.0417866	−	0.0723764i
$466$	−1798.69	+	3115.43i	−0.178804	+	0.309698i
$467$	12978.0			1.28598			0.642990	−	0.765875i	$-0.277694\pi$
$467$	12978.0			1.28598			0.642990	+	0.765875i	$0.277694\pi$
$468$		0			0
$469$	−13922.3			−1.37073
$470$	1298.48	−	2249.03i	0.127435	−	0.220723i
$471$	−14090.3	+	24405.1i	−1.37844	+	2.38754i
$472$	4655.07	+	8062.81i	0.453955	+	0.786273i
$473$	2309.08			0.224464
$474$	3976.67	+	6887.79i	0.385347	+	0.667440i
$475$	−1346.08	−	2331.48i	−0.130026	−	0.225212i
$476$	−6733.04			−0.648337
$477$	2925.89	+	5067.80i	0.280854	+	0.486454i
$478$	425.228	−	736.516i	0.0406893	−	0.0704759i
$479$	−2904.48	+	5030.71i	−0.277055	+	0.479873i	−0.970651	−	0.240491i	$-0.922692\pi$
$479$	−2904.48	+	5030.71i	−0.277055	+	0.479873i	0.693597	+	0.720363i	$0.256025\pi$
$480$	5791.95			0.550761
$481$		0			0
$482$	−8473.14			−0.800707
$483$	−14484.6	+	25088.1i	−1.36454	+	2.36345i
$484$	−3053.54	+	5288.89i	−0.286772	+	0.496703i
$485$	−2691.23	−	4661.35i	−0.251964	−	0.436414i
$486$	−3662.20			−0.341812
$487$	−2693.57	−	4665.40i	−0.250631	−	0.434106i	0.713069	−	0.701094i	$-0.247305\pi$
$487$	−2693.57	−	4665.40i	−0.250631	−	0.434106i	−0.963700	+	0.266989i	$0.913971\pi$
$488$	−1453.86	−	2518.16i	−0.134863	−	0.233589i
$489$	−28498.4			−2.63547
$490$	−1100.06	−	1905.36i	−0.101419	−	0.175664i
$491$	−7629.53	+	13214.7i	−0.701255	+	1.21461i	0.266772	+	0.963760i	$0.414043\pi$
$491$	−7629.53	+	13214.7i	−0.701255	+	1.21461i	−0.968026	+	0.250849i	$0.919290\pi$
$492$	3872.57	−	6707.48i	0.354855	−	0.614628i
$493$	−9796.16			−0.894922
$494$		0			0
$495$	−2632.01			−0.238990
$496$	154.744	−	268.025i	0.0140085	−	0.0242635i
$497$	5581.07	−	9666.69i	0.503712	−	0.872456i
$498$	9182.55	+	15904.6i	0.826264	+	1.43113i
$499$	−1856.04			−0.166509			−0.0832544	−	0.996528i	$-0.526531\pi$
$499$	−1856.04			−0.166509			−0.0832544	+	0.996528i	$0.526531\pi$
$500$	−2350.34	−	4070.91i	−0.210221	−	0.364114i
$501$	−13576.4	−	23515.0i	−1.21067	−	2.09695i
$502$	−8153.20			−0.724891
$503$	−524.732	−	908.862i	−0.0465142	−	0.0805649i	0.841831	−	0.539741i	$-0.181478\pi$
$503$	−524.732	−	908.862i	−0.0465142	−	0.0805649i	−0.888345	+	0.459176i	$0.848145\pi$
$504$	13934.6	−	24135.4i	1.23154	−	2.13308i
$505$	−598.803	+	1037.16i	−0.0527651	+	0.0913919i
$506$	−2925.04			−0.256984
$507$		0			0
$508$	−4811.71			−0.420246
$509$	−275.553	+	477.272i	−0.0239954	+	0.0415613i	−0.877774	−	0.479075i	$-0.840972\pi$
$509$	−275.553	+	477.272i	−0.0239954	+	0.0415613i	0.853778	+	0.520637i	$0.174305\pi$
$510$	−1075.80	+	1863.34i	−0.0934063	+	0.161784i
$511$	−4185.32	−	7249.19i	−0.362324	−	0.627564i
$512$	4074.36			0.351686
$513$	2229.83	+	3862.18i	0.191909	+	0.332396i
$514$	−513.911	−	890.121i	−0.0441005	−	0.0763843i
$515$	1149.36			0.0983431
$516$	−3653.96	−	6328.84i	−0.311738	−	0.539945i
$517$	−3563.13	+	6171.52i	−0.303107	+	0.524997i
$518$	1998.69	−	3461.83i	0.169531	−	0.293637i
$519$	847.361			0.0716667
$520$		0			0
$521$	−8995.30			−0.756413			−0.378206	−	0.925721i	$-0.623459\pi$
$521$	−8995.30			−0.756413			−0.378206	+	0.925721i	$0.623459\pi$
$522$	8314.27	−	14400.7i	0.697137	−	1.20748i
$523$	−1331.96	+	2307.02i	−0.111362	+	0.192885i	−0.916320	−	0.400448i	$-0.868855\pi$
$523$	−1331.96	+	2307.02i	−0.111362	+	0.192885i	0.804958	+	0.593332i	$0.202188\pi$
$524$	−782.512	−	1355.35i	−0.0652370	−	0.112994i
$525$	−26509.1			−2.20372
$526$	−2534.76	−	4390.32i	−0.210115	−	0.363930i
$527$	603.443	+	1045.19i	0.0498793	+	0.0863935i
$528$	−1514.04			−0.124792
$529$	−1448.89	−	2509.54i	−0.119083	−	0.206258i
$530$	336.047	−	582.051i	0.0275414	−	0.0477032i
$531$	−10644.2	+	18436.3i	−0.869906	+	1.50672i
$532$	3622.94			0.295253
$533$		0			0
$534$	−5965.49			−0.483431
$535$	−2554.73	+	4424.93i	−0.206450	+	0.357582i
$536$	−5424.30	+	9395.16i	−0.437116	+	0.757107i
$537$	150.744	+	261.096i	0.0121137	+	0.0209816i
$538$	−4037.86			−0.323577
$539$	3018.65	+	5228.46i	0.241229	+	0.417821i
$540$	1842.66	+	3191.57i	0.146843	+	0.254340i
$541$	6169.23			0.490270			0.245135	−	0.969489i	$-0.421168\pi$
$541$	6169.23			0.490270			0.245135	+	0.969489i	$0.421168\pi$
$542$	772.135	+	1337.38i	0.0611920	+	0.105988i
$543$	5338.23	−	9246.08i	0.421888	−	0.730732i
$544$	−4170.76	+	7223.97i	−0.328713	+	0.569348i
$545$	−3024.28			−0.237699
$546$		0			0
$547$	5140.42			0.401807			0.200904	−	0.979611i	$-0.435612\pi$
$547$	5140.42			0.401807			0.200904	+	0.979611i	$0.435612\pi$
$548$	7345.24	−	12722.3i	0.572578	−	0.991735i
$549$	3324.38	−	5757.99i	0.258435	−	0.447623i
$550$	−1338.32	−	2318.03i	−0.103756	−	0.179711i
$551$	5271.15			0.407547
$552$	11286.8	+	19549.3i	0.870285	+	1.50738i
$553$	7969.16	+	13803.0i	0.612809	+	1.06142i
$554$	12714.8			0.975090
$555$	1456.72	+	2523.12i	0.111413	+	0.192974i
$556$	−5557.76	+	9626.32i	−0.423923	+	0.734257i
$557$	1389.28	−	2406.30i	0.105683	−	0.183049i	−0.808334	−	0.588724i	$-0.799630\pi$
$557$	1389.28	−	2406.30i	0.105683	−	0.183049i	0.914017	+	0.405675i	$0.132964\pi$
$558$	−2048.64			−0.155422
$559$		0			0
$560$	1105.69			0.0834356
$561$	2952.08	−	5113.16i	0.222170	−	0.384809i
$562$	1197.87	−	2074.78i	0.0899097	−	0.155728i
$563$	−2453.07	−	4248.85i	−0.183632	−	0.318059i	0.759483	−	0.650527i	$-0.225452\pi$
$563$	−2453.07	−	4248.85i	−0.183632	−	0.318059i	−0.943115	+	0.332468i	$0.892119\pi$
$564$	22553.7			1.68383
$565$	−2875.11	−	4979.84i	−0.214083	−	0.370802i
$566$	5438.11	+	9419.08i	0.403853	+	0.699494i
$567$	8381.04			0.620759
$568$	−4348.91	−	7532.54i	−0.321261	−	0.556440i
$569$	4681.58	−	8108.73i	0.344924	−	0.597426i	−0.640416	−	0.768028i	$-0.721238\pi$
$569$	4681.58	−	8108.73i	0.344924	−	0.597426i	0.985340	+	0.170602i	$0.0545713\pi$
$570$	578.870	−	1002.63i	0.0425372	−	0.0736766i
$571$	7199.32			0.527640			0.263820	−	0.964572i	$-0.415018\pi$
$571$	7199.32			0.527640			0.263820	+	0.964572i	$0.415018\pi$
$572$		0			0
$573$	37177.3			2.71048
$574$	−3402.59	+	5893.46i	−0.247424	+	0.428551i
$575$	6892.72	−	11938.5i	0.499906	−	0.865863i
$576$	−4867.07	−	8430.01i	−0.352074	−	0.609810i
$577$	11449.6			0.826086			0.413043	−	0.910711i	$-0.364466\pi$
$577$	11449.6			0.826086			0.413043	+	0.910711i	$0.364466\pi$
$578$	2286.60	+	3960.50i	0.164550	+	0.285009i
$579$	2050.97	+	3552.38i	0.147211	+	0.254978i
$580$	4355.91			0.311843
$581$	18401.6	+	31872.6i	1.31399	+	2.27590i
$582$	−10247.6	+	17749.3i	−0.729855	+	1.26415i
$583$	−922.142	+	1597.20i	−0.0655081	+	0.113463i
$584$	−6522.62			−0.462171
$585$		0			0
$586$	−999.439			−0.0704547
$587$	−2719.70	+	4710.65i	−0.191233	+	0.331226i	−0.945659	−	0.325160i	$-0.894582\pi$
$587$	−2719.70	+	4710.65i	−0.191233	+	0.331226i	0.754426	+	0.656385i	$0.227915\pi$
$588$	9553.63	−	16547.4i	0.670042	−	1.16055i
$589$	−324.703	−	562.402i	−0.0227150	−	0.0393436i
$590$	2445.04			0.170611
$591$	−19472.6	−	33727.5i	−1.35532	−	2.34749i
$592$	537.993	+	931.831i	0.0373503	+	0.0646926i
$593$	28405.8			1.96709			0.983547	−	0.180651i	$-0.0578204\pi$
$593$	28405.8			1.96709			0.983547	+	0.180651i	$0.0578204\pi$
$594$	2216.97	+	3839.90i	0.153137	+	0.265241i
$595$	−2155.88	+	3734.10i	−0.148542	+	0.257282i
$596$	4874.65	−	8443.14i	0.335022	−	0.580276i
$597$	−3180.67			−0.218051
$598$		0			0
$599$	−10482.3			−0.715020			−0.357510	−	0.933909i	$-0.616374\pi$
$599$	−10482.3			−0.715020			−0.357510	+	0.933909i	$0.616374\pi$
$600$	−10328.3	+	17889.1i	−0.702750	+	1.21720i
$601$	−1599.77	+	2770.88i	−0.108579	+	0.188064i	−0.915195	−	0.403012i	$-0.867963\pi$
$601$	−1599.77	+	2770.88i	−0.108579	+	0.188064i	0.806616	+	0.591076i	$0.201297\pi$
$602$	3210.51	+	5560.77i	0.217360	+	0.376479i
$603$	−24806.3			−1.67527
$604$	7771.28	+	13460.3i	0.523525	+	0.906772i
$605$	1955.45	+	3386.95i	0.131406	+	0.227602i
$606$	4560.20			0.305686
$607$	−5671.40	−	9823.15i	−0.379234	−	0.656853i	0.611717	−	0.791077i	$-0.290479\pi$
$607$	−5671.40	−	9823.15i	−0.379234	−	0.656853i	−0.990951	+	0.134224i	$0.957146\pi$
$608$	2244.22	−	3887.10i	0.149696	−	0.259281i
$609$	25951.9	−	44950.0i	1.72680	−	2.99091i
$610$	−763.629			−0.0506859
$611$		0			0
$612$	−11996.7			−0.792384
$613$	7192.70	−	12458.1i	0.473916	−	0.820846i	−0.525638	−	0.850708i	$-0.676174\pi$
$613$	7192.70	−	12458.1i	0.473916	−	0.820846i	0.999554	+	0.0298622i	$0.00950685\pi$
$614$	−78.3944	+	135.783i	−0.00515267	+	0.00892469i
$615$	−2479.95	−	4295.39i	−0.162603	−	0.281637i
$616$	8783.39			0.574502
$617$	11028.4	+	19101.7i	0.719588	+	1.24636i	0.961163	+	0.275981i	$0.0890027\pi$
$617$	11028.4	+	19101.7i	0.719588	+	1.24636i	−0.241575	+	0.970382i	$0.577664\pi$
$618$	−2188.24	−	3790.14i	−0.142433	−	0.246702i
$619$	−13621.4			−0.884477			−0.442238	−	0.896898i	$-0.645815\pi$
$619$	−13621.4			−0.884477			−0.442238	+	0.896898i	$0.645815\pi$
$620$	−268.324	−	464.751i	−0.0173809	−	0.0301046i
$621$	−11418.0	+	19776.6i	−0.737824	+	1.27795i
$622$	3028.57	−	5245.63i	0.195232	−	0.338152i
$623$	−11954.7			−0.768789
$624$		0			0
$625$	11029.2			0.705866
$626$	2958.67	−	5124.57i	0.188901	−	0.327187i
$627$	−1588.47	+	2751.31i	−0.101176	+	0.175242i
$628$	9023.27	+	15628.8i	0.573356	+	0.993082i
$629$	−4195.92			−0.265982
$630$	−3659.51	−	6338.46i	−0.231426	−	0.400842i
$631$	−9368.74	−	16227.1i	−0.591068	−	1.02376i	−0.994089	−	0.108569i	$-0.965373\pi$
$631$	−9368.74	−	16227.1i	−0.591068	−	1.02376i	0.403021	−	0.915191i	$-0.367960\pi$
$632$	12419.6			0.781683
$633$	−9216.83	−	15964.0i	−0.578730	−	1.00239i
$634$	3440.73	−	5959.52i	0.215534	−	0.373317i
$635$	−1540.68	+	2668.54i	−0.0962836	+	0.166768i
$636$	5836.91			0.363913
$637$		0			0
$638$	5240.75			0.325209
$639$	9944.18	−	17223.8i	0.615627	−	1.06630i
$640$	2108.67	−	3652.33i	0.130239	−	0.225580i
$641$	−14899.4	−	25806.5i	−0.918081	−	1.59016i	−0.802327	−	0.596884i	$-0.796405\pi$
$641$	−14899.4	−	25806.5i	−0.918081	−	1.59016i	−0.115753	−	0.993278i	$-0.536928\pi$
$642$	19455.6			1.19603
$643$	−11491.8	−	19904.3i	−0.704807	−	1.22076i	−0.966761	−	0.255681i	$-0.917700\pi$
$643$	−11491.8	−	19904.3i	−0.704807	−	1.22076i	0.261955	−	0.965080i	$-0.415633\pi$
$644$	9275.77	+	16066.1i	0.567573	+	0.983064i
$645$	−4679.90			−0.285692
$646$	833.684	+	1443.98i	0.0507753	+	0.0879455i
$647$	12452.7	−	21568.7i	0.756672	−	1.31059i	−0.187866	−	0.982195i	$-0.560157\pi$
$647$	12452.7	−	21568.7i	0.756672	−	1.31059i	0.944539	−	0.328400i	$-0.106509\pi$
$648$	3265.36	−	5655.77i	0.197956	−	0.342870i
$649$	−6709.39			−0.405804
$650$		0			0
$651$	−6394.54			−0.384980
$652$	−9125.03	+	15805.0i	−0.548104	+	0.949344i
$653$	−5038.92	+	8727.67i	−0.301973	+	0.523033i	−0.976583	−	0.215142i	$-0.930979\pi$
$653$	−5038.92	+	8727.67i	−0.301973	+	0.523033i	0.674610	+	0.738175i	$0.264312\pi$
$654$	5757.87	+	9972.93i	0.344267	+	0.596288i
$655$	−1002.22			−0.0597864
$656$	−915.886	−	1586.36i	−0.0545112	−	0.0944162i
$657$	−7457.28	−	12916.4i	−0.442825	−	0.766996i
$658$	−19816.5			−1.17406
$659$	−6167.30	−	10682.1i	−0.364558	−	0.631433i	0.624147	−	0.781307i	$-0.285447\pi$
$659$	−6167.30	−	10682.1i	−0.364558	−	0.631433i	−0.988705	+	0.149874i	$0.952113\pi$
$660$	−1312.66	+	2273.59i	−0.0774169	+	0.134090i
$661$	−6374.56	+	11041.1i	−0.375101	+	0.649694i	−0.990342	−	0.138645i	$-0.955725\pi$
$661$	−6374.56	+	11041.1i	−0.375101	+	0.649694i	0.615241	+	0.788339i	$0.289059\pi$
$662$	6451.54			0.378771
$663$		0			0
$664$	28678.1			1.67609
$665$	1160.04	−	2009.26i	0.0676460	−	0.117166i
$666$	3561.20	−	6168.18i	0.207198	−	0.358877i
$667$	13495.7	+	23375.2i	0.783440	+	1.35696i
$668$	−17388.3			−1.00715
$669$	−25734.5	−	44573.4i	−1.48722	−	2.57594i
$670$	1424.54	+	2467.37i	0.0821413	+	0.142273i
$671$	2095.46			0.120558
$672$	−22098.3	−	38275.3i	−1.26854	−	2.19718i
$673$	6809.12	−	11793.7i	0.390004	−	0.675506i	−0.602446	−	0.798160i	$-0.705807\pi$
$673$	6809.12	−	11793.7i	0.390004	−	0.675506i	0.992450	+	0.122654i	$0.0391404\pi$
$674$	3560.98	−	6167.80i	0.203507	−	0.352485i
$675$	−20896.7			−1.19158
$676$		0			0
$677$	9655.67			0.548150			0.274075	−	0.961708i	$-0.411628\pi$
$677$	9655.67			0.548150			0.274075	+	0.961708i	$0.411628\pi$
$678$	−10947.7	+	18962.0i	−0.620126	+	1.07409i
$679$	−20535.9	+	35569.3i	−1.16067	+	2.01034i
$680$	1679.92	+	2909.70i	0.0947381	+	0.164091i
$681$	7778.51			0.437699
$682$	−322.830	−	559.158i	−0.0181258	−	0.0313948i
$683$	8158.38	+	14130.7i	0.457060	+	0.791650i	0.998804	−	0.0488929i	$-0.0155693\pi$
$683$	8158.38	+	14130.7i	0.457060	+	0.791650i	−0.541744	+	0.840543i	$0.682236\pi$
$684$	6455.25			0.360852
$685$	−4703.80	−	8147.23i	−0.262369	−	0.454437i
$686$	−1116.00	+	1932.97i	−0.0621123	+	0.107582i
$687$	2725.75	−	4721.14i	0.151374	−	0.262188i
$688$	−1728.37			−0.0957753
$689$		0			0
$690$	5928.30			0.327082
$691$	1175.42	−	2035.89i	0.0647106	−	0.112082i	−0.831855	−	0.554993i	$-0.812721\pi$
$691$	1175.42	−	2035.89i	0.0647106	−	0.112082i	0.896566	+	0.442911i	$0.146054\pi$
$692$	271.320	−	469.940i	0.0149047	−	0.0258157i
$693$	10042.0	+	17393.3i	0.550454	+	0.953414i
$694$	15723.9			0.860045
$695$	3559.12	+	6164.58i	0.194252	+	0.336455i
$696$	−20222.4	−	35026.2i	−1.10133	−	1.90756i
$697$	7143.20			0.388189
$698$	4590.44	+	7950.87i	0.248926	+	0.431153i
$699$	−10003.5	+	17326.6i	−0.541299	+	0.937558i
$700$	−8488.05	+	14701.7i	−0.458312	+	0.793819i
$701$	−8076.90			−0.435179			−0.217589	−	0.976040i	$-0.569819\pi$
$701$	−8076.90			−0.435179			−0.217589	+	0.976040i	$0.569819\pi$
$702$		0			0
$703$	2257.76			0.121128
$704$	1533.93	−	2656.85i	0.0821197	−	0.142236i
$705$	7221.55	−	12508.1i	0.385786	−	0.668202i
$706$	−7138.30	−	12363.9i	−0.380529	−	0.659095i
$707$	9138.55			0.486125
$708$	10617.2	+	18389.5i	0.563584	+	0.976156i
$709$	−6812.44	−	11799.5i	−0.360856	−	0.625021i	0.627246	−	0.778821i	$-0.284182\pi$
$709$	−6812.44	−	11799.5i	−0.360856	−	0.625021i	−0.988102	+	0.153801i	$0.950849\pi$
$710$	−2284.23			−0.120741
$711$	14199.2	+	24593.8i	0.748962	+	1.29724i
$712$	−4657.71	+	8067.40i	−0.245162	+	0.424633i
$713$	1662.67	−	2879.82i	0.0873315	−	0.151263i
$714$	16418.2			0.860553
$715$		0			0
$716$	193.069			0.0100773
$717$	2364.93	−	4096.18i	0.123180	−	0.213354i
$718$	−2150.51	+	3724.79i	−0.111778	+	0.193605i
$719$	−8117.89	−	14060.6i	−0.421066	−	0.729307i	0.574978	−	0.818169i	$-0.305010\pi$
$719$	−8117.89	−	14060.6i	−0.421066	−	0.729307i	−0.996044	+	0.0888616i	$0.971677\pi$
$720$	1970.09			0.101973
$721$	−4385.19	−	7595.36i	−0.226509	−	0.392325i
$722$	4906.75	+	8498.75i	0.252923	+	0.438076i
$723$	−47123.8			−2.42400
$724$	−3418.54	−	5921.08i	−0.175482	−	0.303944i
$725$	−12349.6	+	21390.1i	−0.632623	+	1.09574i
$726$	7445.91	−	12896.7i	0.380638	−	0.659285i
$727$	24181.2			1.23361			0.616803	−	0.787118i	$-0.288428\pi$
$727$	24181.2			1.23361			0.616803	+	0.787118i	$0.288428\pi$
$728$		0			0
$729$	−28693.9			−1.45780
$730$	−856.490	+	1483.48i	−0.0434248	+	0.0752139i
$731$	3369.98	−	5836.98i	0.170511	−	0.295333i
$732$	−3315.93	−	5743.36i	−0.167432	−	0.290001i
$733$	−3053.70			−0.153876			−0.0769379	−	0.997036i	$-0.524514\pi$
$733$	−3053.70			−0.153876			−0.0769379	+	0.997036i	$0.524514\pi$
$734$	−2373.71	−	4111.38i	−0.119367	−	0.206749i
$735$	−6118.03	−	10596.7i	−0.307030	−	0.531791i
$736$	22983.4			1.15106
$737$	−3909.05	−	6770.67i	−0.195375	−	0.338400i
$738$	−6062.63	+	10500.8i	−0.302396	+	0.523766i
$739$	−4016.81	+	6957.32i	−0.199947	+	0.346318i	−0.948511	−	0.316744i	$-0.897410\pi$
$739$	−4016.81	+	6957.32i	−0.199947	+	0.346318i	0.748564	+	0.663062i	$0.230744\pi$
$740$	1865.74			0.0926836
$741$		0			0
$742$	−5128.54			−0.253739
$743$	−8069.81	+	13977.3i	−0.398456	+	0.690146i	−0.993536	−	0.113521i	$-0.963787\pi$
$743$	−8069.81	+	13977.3i	−0.398456	+	0.690146i	0.595080	+	0.803667i	$0.297120\pi$
$744$	−2491.40	+	4315.22i	−0.122767	+	0.212639i
$745$	−3121.67	−	5406.89i	−0.153515	−	0.265897i
$746$	−8408.53			−0.412678
$747$	32787.5	+	56789.6i	1.60593	+	2.78156i
$748$	−1890.48	−	3274.41i	−0.0924102	−	0.160059i
$749$	38988.7			1.90202
$750$	5731.19	+	9926.71i	0.279031	+	0.483296i
$751$	9245.56	−	16013.8i	0.449235	−	0.778097i	−0.549102	−	0.835755i	$-0.685030\pi$
$751$	9245.56	−	16013.8i	0.449235	−	0.778097i	0.998336	+	0.0576584i	$0.0183634\pi$
$752$	2667.04	−	4619.45i	0.129331	−	0.224008i
$753$	−45344.5			−2.19448
$754$		0			0
$755$	9953.28			0.479784
$756$	14060.7	−	24353.9i	0.676434	−	1.17162i
$757$	−80.3149	+	139.109i	−0.00385613	+	0.00667902i	−0.867947	−	0.496657i	$-0.834561\pi$
$757$	−80.3149	+	139.109i	−0.00385613	+	0.00667902i	0.864091	+	0.503336i	$0.167894\pi$
$758$	−2673.59	−	4630.79i	−0.128112	−	0.221897i
$759$	−16267.7			−0.777973
$760$	−903.936	−	1565.66i	−0.0431437	−	0.0747271i
$761$	13399.5	+	23208.7i	0.638282	+	1.10554i	0.985810	+	0.167867i	$0.0536879\pi$
$761$	13399.5	+	23208.7i	0.638282	+	1.10554i	−0.347528	+	0.937670i	$0.612979\pi$
$762$	11733.1			0.557803
$763$	11538.7	+	19985.6i	0.547481	+	0.948264i
$764$	11903.9	−	20618.2i	0.563703	−	0.976363i
$765$	−3841.28	+	6653.30i	−0.181545	+	0.314445i
$766$	598.052			0.0282095
$767$		0			0
$768$	−30025.1			−1.41073
$769$	−2572.91	+	4456.41i	−0.120652	+	0.208976i	−0.920025	−	0.391860i	$-0.871832\pi$
$769$	−2572.91	+	4456.41i	−0.120652	+	0.208976i	0.799373	+	0.600835i	$0.205165\pi$
$770$	1153.35	−	1997.67i	0.0539792	−	0.0934947i
$771$	−2858.15	−	4950.45i	−0.133507	−	0.231240i
$772$	2626.83			0.122463
$773$	6405.28	+	11094.3i	0.298036	+	0.516214i	0.975687	−	0.219170i	$-0.0703351\pi$
$773$	6405.28	+	11094.3i	0.298036	+	0.516214i	−0.677650	+	0.735384i	$0.737002\pi$
$774$	5720.39	+	9908.01i	0.265653	+	0.460124i
$775$	3042.94			0.141039
$776$	16002.1	+	27716.5i	0.740262	+	1.28217i
$777$	11115.8	−	19253.1i	0.513227	−	0.888934i
$778$	−6705.57	+	11614.4i	−0.309006	+	0.535214i
$779$	−3843.64			−0.176781
$780$		0			0
$781$	6268.13			0.287185
$782$	−4268.94	+	7394.03i	−0.195214	+	0.338120i
$783$	20457.5	−	35433.4i	0.933705	−	1.61722i
$784$	−2259.49	−	3913.55i	−0.102929	−	0.178278i
$785$	11556.8			0.525452
$786$	1908.11	+	3304.95i	0.0865905	+	0.149979i
$787$	14036.5	+	24311.9i	0.635764	+	1.10118i	0.986353	+	0.164646i	$0.0526483\pi$
$787$	14036.5	+	24311.9i	0.635764	+	1.10118i	−0.350588	+	0.936530i	$0.614018\pi$
$788$	−24940.0			−1.12748
$789$	−14097.2	−	24417.0i	−0.636087	−	1.10174i
$790$	1630.82	−	2824.66i	0.0734455	−	0.127211i
$791$	−21939.1	+	37999.6i	−0.986173	+	1.70810i
$792$	15650.0			0.702144
$793$		0			0
$794$	11304.3			0.505259
$795$	1868.94	−	3237.11i	0.0833769	−	0.144413i
$796$	−1018.43	+	1763.98i	−0.0453485	+	0.0785459i
$797$	−15046.6	−	26061.4i	−0.668729	−	1.15827i	−0.978260	−	0.207383i	$-0.933505\pi$
$797$	−15046.6	−	26061.4i	−0.668729	−	1.15827i	0.309531	−	0.950889i	$-0.399828\pi$
$798$	−8834.35			−0.391896
$799$	10400.4	+	18014.1i	0.460501	+	0.797612i
$800$	10515.8	+	18213.9i	0.464737	+	0.804947i
$801$	−21300.6			−0.939598
$802$	3333.62	+	5774.00i	0.146776	+	0.254223i
$803$	2350.28	−	4070.80i	0.103287	−	0.178899i
$804$	−12371.6	+	21428.3i	−0.542678	+	0.939946i
$805$	11880.2			0.520151
$806$		0			0
$807$	−22456.8			−0.979575
$808$	3560.50	−	6166.96i	0.155022	−	0.268506i
$809$	12168.6	−	21076.6i	0.528831	−	0.915961i	−0.470604	−	0.882344i	$-0.655964\pi$
$809$	12168.6	−	21076.6i	0.528831	−	0.915961i	0.999435	−	0.0336170i	$-0.0107026\pi$
$810$	−857.553	−	1485.33i	−0.0371992	−	0.0644309i
$811$	−19078.7			−0.826071			−0.413035	−	0.910715i	$-0.635531\pi$
$811$	−19078.7			−0.826071			−0.413035	+	0.910715i	$0.635531\pi$
$812$	−16619.3	−	28785.4i	−0.718254	−	1.24405i
$813$	4294.27	+	7437.89i	0.185248	+	0.320859i
$814$	2244.74			0.0966559
$815$	5843.56	+	10121.3i	0.251155	+	0.435013i
$816$	−2209.67	+	3827.25i	−0.0947963	+	0.164192i
$817$	−1813.33	+	3140.78i	−0.0776505	+	0.134495i
$818$	−21178.6			−0.905248
$819$		0			0
$820$	−3176.26			−0.135268
$821$	1006.96	−	1744.10i	0.0428052	−	0.0741408i	−0.843829	−	0.536612i	$-0.819704\pi$
$821$	1006.96	−	1744.10i	0.0428052	−	0.0741408i	0.886634	+	0.462471i	$0.153037\pi$
$822$	−17911.0	+	31022.7i	−0.759996	+	1.31635i
$823$	3846.05	+	6661.55i	0.162898	+	0.282147i	0.935907	−	0.352248i	$-0.114583\pi$
$823$	3846.05	+	6661.55i	0.162898	+	0.282147i	−0.773009	+	0.634395i	$0.781249\pi$
$824$	−6834.10			−0.288929
$825$	−7443.12	−	12891.9i	−0.314105	−	0.544045i
$826$	−9328.66	−	16157.7i	−0.392961	−	0.680628i
$827$	4762.76			0.200263			0.100131	−	0.994974i	$-0.468074\pi$
$827$	4762.76			0.200263			0.100131	+	0.994974i	$0.468074\pi$
$828$	16527.3	+	28626.1i	0.693675	+	1.20148i
$829$	−9988.83	+	17301.2i	−0.418488	+	0.724842i	−0.995788	−	0.0916901i	$-0.970773\pi$
$829$	−9988.83	+	17301.2i	−0.418488	+	0.724842i	0.577300	+	0.816532i	$0.304106\pi$
$830$	3765.73	−	6522.44i	0.157483	−	0.272768i
$831$	70714.0			2.95191
$832$		0			0
$833$	17622.3			0.732984
$834$	13552.3	−	23473.3i	0.562683	−	0.974596i
$835$	−5567.63	+	9643.43i	−0.230750	+	0.399670i
$836$	1017.24	+	1761.91i	0.0420836	+	0.0728909i
$837$	−5040.72			−0.208164
$838$	11381.3	+	19713.0i	0.469165	+	0.812617i
$839$	−15307.9	−	26514.0i	−0.629901	−	1.09102i	−0.987571	−	0.157172i	$-0.949762\pi$
$839$	−15307.9	−	26514.0i	−0.629901	−	1.09102i	0.357670	−	0.933848i	$-0.383571\pi$
$840$	−17801.7			−0.731210
$841$	−11985.5	−	20759.5i	−0.491431	−	0.851183i
$842$	12374.0	−	21432.5i	0.506458	−	0.877211i
$843$	6662.04	−	11539.0i	0.272186	−	0.471440i
$844$	−11804.7			−0.481439
$845$		0			0
$846$	−35308.5			−1.43491
$847$	14921.4	−	25844.7i	0.605321	−	1.04845i
$848$	690.233	−	1195.52i	0.0279513	−	0.0484131i
$849$	30244.3	+	52384.7i	1.22259	+	2.11760i
$850$	−7812.83			−0.315268
$851$	5780.51	+	10012.1i	0.232848	+	0.403304i
$852$	−9918.89	−	17180.0i	−0.398845	−	0.690819i
$853$	−5660.88			−0.227227			−0.113614	−	0.993525i	$-0.536243\pi$
$853$	−5660.88			−0.227227			−0.113614	+	0.993525i	$0.536243\pi$
$854$	2913.50	+	5046.34i	0.116742	+	0.202204i
$855$	2066.93	−	3580.03i	0.0826755	−	0.143198i
$856$	15190.5	−	26310.7i	0.606543	−	1.05056i
$857$	41346.1			1.64802			0.824012	−	0.566572i	$-0.191731\pi$
$857$	41346.1			1.64802			0.824012	+	0.566572i	$0.191731\pi$
$858$		0			0
$859$	−34810.5			−1.38268			−0.691339	−	0.722530i	$-0.742979\pi$
$859$	−34810.5			−1.38268			−0.691339	+	0.722530i	$0.742979\pi$
$860$	−1498.48	+	2595.44i	−0.0594159	+	0.102911i
$861$	−18923.7	+	32776.8i	−0.749033	+	1.29736i
$862$	8350.19	+	14462.9i	0.329940	+	0.571473i
$863$	8360.51			0.329774			0.164887	−	0.986312i	$-0.447274\pi$
$863$	8360.51			0.329774			0.164887	+	0.986312i	$0.447274\pi$
$864$	−17419.7	−	30171.9i	−0.685916	−	1.18804i
$865$	−173.750	−	300.944i	−0.00682969	−	0.0118294i
$866$	−25108.2			−0.985233
$867$	12717.0	+	22026.5i	0.498146	+	0.862815i
$868$	−2047.49	+	3546.36i	−0.0800651	+	0.138677i
$869$	−4475.11	+	7751.11i	−0.174692	+	0.302576i
$870$	−10621.6			−0.413917
$871$		0			0
$872$	17982.4			0.698352
$873$	−36590.3	+	63376.3i	−1.41855	+	2.45700i
$874$	2297.05	−	3978.61i	0.0889003	−	0.153980i
$875$	11485.2	+	19892.9i	0.443737	+	0.768576i
$876$	−14876.6			−0.573784
$877$	−20289.7	−	35142.7i	−0.781223	−	1.35312i	−0.931229	−	0.364434i	$-0.881263\pi$
$877$	−20289.7	−	35142.7i	−0.781223	−	1.35312i	0.150006	−	0.988685i	$-0.452071\pi$
$878$	−4712.61	−	8162.48i	−0.181142	−	0.313748i
$879$	−5558.43			−0.213289
$880$	310.452	+	537.718i	0.0118924	+	0.0205983i
$881$	−5222.62	+	9045.84i	−0.199721	+	0.345927i	−0.948438	−	0.316963i	$-0.897337\pi$
$881$	−5222.62	+	9045.84i	−0.199721	+	0.345927i	0.748717	+	0.662890i	$0.230670\pi$
$882$	−14956.5	+	25905.4i	−0.570989	+	0.988981i
$883$	18227.6			0.694685			0.347343	−	0.937738i	$-0.387084\pi$
$883$	18227.6			0.694685			0.347343	+	0.937738i	$0.387084\pi$
$884$		0			0
$885$	13598.2			0.516496
$886$	−7964.96	+	13795.7i	−0.302018	+	0.523111i
$887$	11758.8	−	20366.9i	0.445122	−	0.770974i	−0.552938	−	0.833222i	$-0.686494\pi$
$887$	11758.8	−	20366.9i	0.445122	−	0.770974i	0.998061	+	0.0622477i	$0.0198269\pi$
$888$	−8661.72	−	15002.5i	−0.327329	−	0.566950i
$889$	23512.9			0.887061
$890$	1223.21	+	2118.67i	0.0460699	+	0.0797955i
$891$	2353.20	+	4075.86i	0.0884794	+	0.153251i
$892$	−32960.1			−1.23720
$893$	−5596.30	−	9693.07i	−0.209712	−	0.363232i
$894$	−11886.6	+	20588.1i	−0.444683	+	0.770213i
$895$	61.8196	−	107.075i	0.00230883	−	0.00399901i
$896$	−32181.2			−1.19989
$897$		0			0
$898$	9092.21			0.337874
$899$	−2978.98	+	5159.74i	−0.110517	+	0.191420i
$900$	−15123.7	+	26195.1i	−0.560139	+	0.970189i
$901$	2691.64	+	4662.06i	0.0995245	+	0.172381i
$902$	−3821.47			−0.141065
$903$	17855.4	+	30926.5i	0.658019	+	1.13972i
$904$	17095.5	+	29610.2i	0.628968	+	1.08940i
$905$	−4378.38			−0.160820
$906$	−18949.9	−	32822.1i	−0.694886	−	1.20358i
$907$	15282.3	−	26469.7i	0.559471	−	0.969032i	−0.438070	−	0.898941i	$-0.644338\pi$
$907$	15282.3	−	26469.7i	0.559471	−	0.969032i	0.997541	−	0.0700908i	$-0.0223289\pi$
$908$	2490.63	−	4313.90i	0.0910292	−	0.157667i
$909$	16282.8			0.594132
$910$		0			0
$911$	−32766.5			−1.19166			−0.595831	−	0.803110i	$-0.703177\pi$
$911$	−32766.5			−1.19166			−0.595831	+	0.803110i	$0.703177\pi$
$912$	1188.99	−	2059.38i	0.0431702	−	0.0747730i
$913$	−10333.5	+	17898.1i	−0.374577	+	0.648786i
$914$	3608.44	+	6249.99i	0.130587	+	0.226183i
$915$	−4246.96			−0.153443
$916$	−1745.54	−	3023.36i	−0.0629632	−	0.109055i
$917$	3823.82	+	6623.05i	0.137703	+	0.238509i
$918$	12942.2			0.465312
$919$	−10343.4	−	17915.2i	−0.371269	−	0.643057i	0.618492	−	0.785791i	$-0.287744\pi$
$919$	−10343.4	−	17915.2i	−0.371269	−	0.643057i	−0.989761	+	0.142734i	$0.954411\pi$
$920$	4628.68	−	8017.10i	0.165873	−	0.287300i
$921$	−435.995	+	755.165i	−0.0155988	+	0.0270179i
$922$	−8007.28			−0.286015
$923$		0			0
$924$	20033.0			0.713242
$925$	−5289.62	+	9161.88i	−0.188023	+	0.325666i
$926$	5064.32	−	8771.67i	0.179724	−	0.311290i
$927$	−7813.39	−	13533.2i	−0.276834	−	0.479491i
$928$	−41179.0			−1.45665
$929$	22816.1	+	39518.6i	0.805782	+	1.39566i	0.915762	+	0.401722i	$0.131588\pi$
$929$	22816.1	+	39518.6i	0.805782	+	1.39566i	−0.109979	+	0.993934i	$0.535078\pi$
$930$	654.294	+	1133.27i	0.0230700	+	0.0399585i
$931$	−9482.26			−0.333801
$932$	6406.14	+	11095.8i	0.225150	+	0.389972i
$933$	16843.5	−	29173.9i	0.591032	−	1.02370i
$934$	−10133.0	+	17550.8i	−0.354990	+	0.614860i
$935$	−2421.28			−0.0846892
$936$		0			0
$937$	−17761.4			−0.619253			−0.309626	−	0.950858i	$-0.600204\pi$
$937$	−17761.4			−0.619253			−0.309626	+	0.950858i	$0.600204\pi$
$938$	10870.2	−	18827.7i	0.378384	−	0.655380i
$939$	16454.8	−	28500.5i	0.571866	−	0.990501i
$940$	−4624.60	−	8010.04i	−0.160466	−	0.277935i
$941$	44888.3			1.55507			0.777534	−	0.628841i	$-0.216470\pi$
$941$	44888.3			1.55507			0.777534	+	0.628841i	$0.216470\pi$
$942$	−22002.8	−	38109.9i	−0.761029	−	1.31814i
$943$	−9840.83	−	17044.8i	−0.339832	−	0.588606i
$944$	5022.05			0.173150
$945$	−9004.32	−	15595.9i	−0.309958	−	0.536864i
$946$	−1802.87	+	3122.67i	−0.0619624	+	0.107322i
$947$	8034.78	−	13916.6i	0.275708	−	0.477540i	−0.694606	−	0.719391i	$-0.744421\pi$
$947$	8034.78	−	13916.6i	0.275708	−	0.477540i	0.970313	+	0.241851i	$0.0777545\pi$
$948$	28326.2			0.970457
$949$		0			0
$950$	4203.96			0.143573
$951$	19135.8	−	33144.2i	0.652493	−	1.13015i
$952$	12818.9	−	22203.0i	0.436411	−	0.755887i
$953$	−1756.02	−	3041.51i	−0.0596883	−	0.103383i	0.834637	−	0.550800i	$-0.185677\pi$
$953$	−1756.02	−	3041.51i	−0.0596883	−	0.103383i	−0.894325	+	0.447417i	$0.852344\pi$
$954$	−9137.88			−0.310115
$955$	−7623.14	−	13203.7i	−0.258303	−	0.447393i
$956$	−1514.47	−	2623.14i	−0.0512359	−	0.0887432i
$957$	29146.7			0.984513
$958$	−4535.50	−	7855.72i	−0.152960	−	0.264934i
$959$	−35893.2	+	62168.9i	−1.20861	+	2.09337i
$960$	−3108.89	+	5384.75i	−0.104520	+	0.181034i
$961$	−29057.0			−0.975361
$962$		0			0
$963$	69468.9			2.32461
$964$	−15088.8	+	26134.5i	−0.504125	+	0.873170i
$965$	841.097	−	1456.82i	0.0280579	−	0.0485977i
$966$	−22618.5	−	39176.4i	−0.753352	−	1.30484i
$967$	37011.9			1.23084			0.615421	−	0.788199i	$-0.288986\pi$
$967$	37011.9			1.23084			0.615421	+	0.788199i	$0.288986\pi$
$968$	−11627.2	−	20138.9i	−0.386066	−	0.668685i
$969$	4636.58	+	8030.79i	0.153714	+	0.266240i
$970$	8405.00			0.278215
$971$	−9766.15	−	16915.5i	−0.322771	−	0.559056i	0.658288	−	0.752766i	$-0.271281\pi$
$971$	−9766.15	−	16915.5i	−0.322771	−	0.559056i	−0.981059	+	0.193711i	$0.937948\pi$
$972$	−6521.55	+	11295.7i	−0.215205	+	0.372745i
$973$	27158.5	−	47040.0i	0.894823	−	1.54988i
$974$	8412.30			0.276743
$975$		0			0
$976$	−1568.47			−0.0514402
$977$	15100.6	−	26155.0i	0.494485	−	0.856473i	−0.505495	−	0.862830i	$-0.668690\pi$
$977$	15100.6	−	26155.0i	0.494485	−	0.856473i	0.999980	+	0.00635674i	$0.00202343\pi$
$978$	22250.9	−	38539.7i	0.727511	−	1.26009i
$979$	−3356.60	−	5813.81i	−0.109579	−	0.189796i
$980$	−7835.83			−0.255415
$981$	20559.2	+	35609.7i	0.669119	+	1.15895i
$982$	−11913.9	−	20635.5i	−0.387157	−	0.670576i
$983$	38774.9			1.25812			0.629058	−	0.777359i	$-0.283441\pi$
$983$	38774.9			1.25812			0.629058	+	0.777359i	$0.283441\pi$
$984$	14745.8	+	25540.5i	0.477723	+	0.827441i
$985$	−7985.65	+	13831.6i	−0.258319	+	0.447421i
$986$	7648.61	−	13247.8i	0.247040	−	0.427886i
$987$	−110211.			−3.55425
$988$		0			0
$989$	−18570.6			−0.597079
$990$	2055.01	−	3559.38i	0.0659722	−	0.114267i
$991$	13864.5	−	24014.0i	0.444419	−	0.769757i	−0.553592	−	0.832788i	$-0.686743\pi$
$991$	13864.5	−	24014.0i	0.444419	−	0.769757i	0.998012	+	0.0630311i	$0.0200767\pi$
$992$	2536.63	+	4393.57i	0.0811875	+	0.140621i
$993$	35880.6			1.14666
$994$	8715.13	+	15095.1i	0.278096	+	0.481676i
$995$	652.192	+	1129.63i	0.0207798	+	0.0359916i
$996$	65408.2			2.08086
$997$	24459.1	+	42364.4i	0.776958	+	1.34573i	0.933687	+	0.358090i	$0.116572\pi$
$997$	24459.1	+	42364.4i	0.776958	+	1.34573i	−0.156729	+	0.987642i	$0.550095\pi$
$998$	1449.16	−	2510.01i	0.0459641	−	0.0796122i
$999$	8762.42	−	15177.0i	0.277508	−	0.480658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.j.22.1		4
13.2	odd	12		169.4.e.f.23.2		8
13.3	even	3	inner	169.4.c.j.146.1		4
13.4	even	6		13.4.a.b.1.1	✓	2
13.5	odd	4		169.4.e.f.147.3		8
13.6	odd	12		169.4.b.f.168.2		4
13.7	odd	12		169.4.b.f.168.3		4
13.8	odd	4		169.4.e.f.147.2		8
13.9	even	3		169.4.a.g.1.2		2
13.10	even	6		169.4.c.g.146.2		4
13.11	odd	12		169.4.e.f.23.3		8
13.12	even	2		169.4.c.g.22.2		4
39.17	odd	6		117.4.a.d.1.2		2
39.35	odd	6		1521.4.a.r.1.1		2
52.43	odd	6		208.4.a.h.1.1		2
65.4	even	6		325.4.a.f.1.2		2
65.17	odd	12		325.4.b.e.274.2		4
65.43	odd	12		325.4.b.e.274.3		4
91.69	odd	6		637.4.a.b.1.1		2
104.43	odd	6		832.4.a.z.1.2		2
104.69	even	6		832.4.a.s.1.1		2
143.43	odd	6		1573.4.a.b.1.2		2
156.95	even	6		1872.4.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.b.1.1	✓	2	13.4	even	6
117.4.a.d.1.2		2	39.17	odd	6
169.4.a.g.1.2		2	13.9	even	3
169.4.b.f.168.2		4	13.6	odd	12
169.4.b.f.168.3		4	13.7	odd	12
169.4.c.g.22.2		4	13.12	even	2
169.4.c.g.146.2		4	13.10	even	6
169.4.c.j.22.1		4	1.1	even	1	trivial
169.4.c.j.146.1		4	13.3	even	3	inner
169.4.e.f.23.2		8	13.2	odd	12
169.4.e.f.23.3		8	13.11	odd	12
169.4.e.f.147.2		8	13.8	odd	4
169.4.e.f.147.3		8	13.5	odd	4
208.4.a.h.1.1		2	52.43	odd	6
325.4.a.f.1.2		2	65.4	even	6
325.4.b.e.274.2		4	65.17	odd	12
325.4.b.e.274.3		4	65.43	odd	12
637.4.a.b.1.1		2	91.69	odd	6
832.4.a.s.1.1		2	104.69	even	6
832.4.a.z.1.2		2	104.43	odd	6
1521.4.a.r.1.1		2	39.35	odd	6
1573.4.a.b.1.2		2	143.43	odd	6
1872.4.a.bb.1.2		2	156.95	even	6

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 + 1.35234i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(2.78078 + 4.81645i) q^{4} +3.56155 q^{5} +(-6.78078 - 11.7446i) q^{6} +(-13.5885 - 23.5360i) q^{7} -21.1771 q^{8} +(-24.2116 - 41.9358i) q^{9} +O(q^{10})\)	\(q+(-0.780776 + 1.35234i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(2.78078 + 4.81645i) q^{4} +3.56155 q^{5} +(-6.78078 - 11.7446i) q^{6} +(-13.5885 - 23.5360i) q^{7} -21.1771 q^{8} +(-24.2116 - 41.9358i) q^{9} +(-2.78078 + 4.81645i) q^{10} +(7.63068 - 13.2167i) q^{11} -48.3002 q^{12} +42.4384 q^{14} +(-15.4654 + 26.7869i) q^{15} +(-5.71165 + 9.89286i) q^{16} +(-22.2732 - 38.5783i) q^{17} +75.6155 q^{18} +(11.9848 + 20.7584i) q^{19} +(9.90388 + 17.1540i) q^{20} +236.024 q^{21} +(11.9157 + 20.6386i) q^{22} +(-61.3693 + 106.295i) q^{23} +(91.9579 - 159.276i) q^{24} -112.315 q^{25} +186.054 q^{27} +(75.5734 - 130.897i) q^{28} +(109.955 - 190.447i) q^{29} +(-24.1501 - 41.8292i) q^{30} -27.0928 q^{31} +(-93.6274 - 162.167i) q^{32} +(66.2699 + 114.783i) q^{33} +69.5616 q^{34} +(-48.3963 - 83.8249i) q^{35} +(134.654 - 233.228i) q^{36} +(47.0961 - 81.5729i) q^{37} -37.4299 q^{38} -75.4233 q^{40} +(-80.1771 + 138.871i) q^{41} +(-184.282 + 319.185i) q^{42} +(75.6510 + 131.031i) q^{43} +84.8769 q^{44} +(-86.2311 - 149.357i) q^{45} +(-95.8314 - 165.985i) q^{46} -466.948 q^{47} +(-49.6037 - 85.9161i) q^{48} +(-197.797 + 342.594i) q^{49} +(87.6932 - 151.889i) q^{50} +386.870 q^{51} -120.847 q^{53} +(-145.267 + 251.609i) q^{54} +(27.1771 - 47.0721i) q^{55} +(287.766 + 498.425i) q^{56} -208.169 q^{57} +(171.700 + 297.393i) q^{58} +(-219.816 - 380.733i) q^{59} -172.024 q^{60} +(68.6525 + 118.910i) q^{61} +(21.1534 - 36.6388i) q^{62} +(-658.002 + 1139.69i) q^{63} +201.022 q^{64} -206.968 q^{66} +(256.140 - 443.648i) q^{67} +(123.874 - 214.555i) q^{68} +(-532.972 - 923.134i) q^{69} +151.147 q^{70} +(205.359 + 355.693i) q^{71} +(512.732 + 888.078i) q^{72} +308.004 q^{73} +(73.5431 + 127.380i) q^{74} +(487.710 - 844.739i) q^{75} +(-66.6543 + 115.449i) q^{76} -414.759 q^{77} -586.462 q^{79} +(-20.3423 + 35.2339i) q^{80} +(-154.193 + 267.070i) q^{81} +(-125.201 - 216.854i) q^{82} -1354.20 q^{83} +(656.329 + 1136.80i) q^{84} +(-79.3272 - 137.399i) q^{85} -236.266 q^{86} +(954.918 + 1653.97i) q^{87} +(-161.596 + 279.892i) q^{88} +(219.941 - 380.949i) q^{89} +269.309 q^{90} -682.617 q^{92} +(117.646 - 203.769i) q^{93} +(364.582 - 631.474i) q^{94} +(42.6847 + 73.9320i) q^{95} +1626.24 q^{96} +(-755.634 - 1308.80i) q^{97} +(-308.870 - 534.979i) q^{98} -739.006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9}+O(q^{10}) \) 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9	\( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9} - 7 q^{10} + 80 q^{11} - 86 q^{12} + 178 q^{14} - 33 q^{15} + 39 q^{16} - 19 q^{17} + 220 q^{18} - 84 q^{19} + 19 q^{20} + 606 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 474 q^{25} + 670 q^{27} + 125 q^{28} + 44 q^{29} - 43 q^{30} + 172 q^{31} - 123 q^{32} - 106 q^{33} + 270 q^{34} - 107 q^{35} + 250 q^{36} + 209 q^{37} - 628 q^{38} - 178 q^{40} - 230 q^{41} - 197 q^{42} - 287 q^{43} + 356 q^{44} - 180 q^{45} - 4 q^{46} - 870 q^{47} - 285 q^{48} - 383 q^{49} - 144 q^{50} + 962 q^{51} - 236 q^{53} + 91 q^{54} + 18 q^{55} + 1015 q^{56} - 1212 q^{57} + 794 q^{58} - 368 q^{59} - 350 q^{60} + 1058 q^{61} + 332 q^{62} - 1560 q^{63} + 1538 q^{64} - 1636 q^{66} + 68 q^{67} + 211 q^{68} - 796 q^{69} + 250 q^{70} - 131 q^{71} + 1350 q^{72} - 912 q^{73} - 147 q^{74} + 516 q^{75} + 22 q^{76} + 1524 q^{77} - 2016 q^{79} - 69 q^{80} - 122 q^{81} - 72 q^{82} - 3916 q^{83} + 1409 q^{84} - 173 q^{85} - 2718 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 500 q^{90} - 1576 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 3726 q^{96} - 928 q^{97} - 650 q^{98} + 260 q^{99}+O(q^{100}) \) 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9 - 7 * q^10 + 80 * q^11 - 86 * q^12 + 178 * q^14 - 33 * q^15 + 39 * q^16 - 19 * q^17 + 220 * q^18 - 84 * q^19 + 19 * q^20 + 606 * q^21 - 142 * q^22 - 196 * q^23 + 273 * q^24 - 474 * q^25 + 670 * q^27 + 125 * q^28 + 44 * q^29 - 43 * q^30 + 172 * q^31 - 123 * q^32 - 106 * q^33 + 270 * q^34 - 107 * q^35 + 250 * q^36 + 209 * q^37 - 628 * q^38 - 178 * q^40 - 230 * q^41 - 197 * q^42 - 287 * q^43 + 356 * q^44 - 180 * q^45 - 4 * q^46 - 870 * q^47 - 285 * q^48 - 383 * q^49 - 144 * q^50 + 962 * q^51 - 236 * q^53 + 91 * q^54 + 18 * q^55 + 1015 * q^56 - 1212 * q^57 + 794 * q^58 - 368 * q^59 - 350 * q^60 + 1058 * q^61 + 332 * q^62 - 1560 * q^63 + 1538 * q^64 - 1636 * q^66 + 68 * q^67 + 211 * q^68 - 796 * q^69 + 250 * q^70 - 131 * q^71 + 1350 * q^72 - 912 * q^73 - 147 * q^74 + 516 * q^75 + 22 * q^76 + 1524 * q^77 - 2016 * q^79 - 69 * q^80 - 122 * q^81 - 72 * q^82 - 3916 * q^83 + 1409 * q^84 - 173 * q^85 - 2718 * q^86 + 2558 * q^87 + 1242 * q^88 - 720 * q^89 + 500 * q^90 - 1576 * q^92 + 652 * q^93 + 811 * q^94 + 146 * q^95 + 3726 * q^96 - 928 * q^97 - 650 * q^98 + 260 * q^99

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