LMFDB - Embedded newform 169.4.c.g.146.2

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			146.2
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.4.c.g.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780776 + 1.35234i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(2.78078 - 4.81645i) q^{4} -3.56155 q^{5} +(6.78078 - 11.7446i) q^{6} +(13.5885 - 23.5360i) q^{7} +21.1771 q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.780776	+	1.35234i	0.276046	+	0.478126i	0.970399	−	0.241509i	$-0.0776424\pi$
$2$	0.780776	+	1.35234i	0.276046	+	0.478126i	−0.694352	+	0.719635i	$0.744309\pi$
$3$	−4.34233	−	7.52113i	−0.835682	−	1.44744i	−0.893474	−	0.449114i	$-0.851740\pi$
$3$	−4.34233	−	7.52113i	−0.835682	−	1.44744i	0.0577926	−	0.998329i	$-0.481594\pi$
$4$	2.78078	−	4.81645i	0.347597	−	0.602056i
$5$	−3.56155			−0.318555			−0.159277	−	0.987234i	$-0.550916\pi$
$5$	−3.56155			−0.318555			−0.159277	+	0.987234i	$0.550916\pi$
$6$	6.78078	−	11.7446i	0.461373	−	0.799122i
$7$	13.5885	−	23.5360i	0.733712	−	1.27083i	−0.221574	−	0.975144i	$-0.571119\pi$
$7$	13.5885	−	23.5360i	0.733712	−	1.27083i	0.955286	−	0.295683i	$-0.0955473\pi$
$8$	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	$-0.233739\pi$
$11$	−7.63068	−	13.2167i	−0.209158	−	0.362272i	−0.951450	+	0.307805i	$0.900406\pi$
$12$	−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	−0.980022	−	0.198890i	$-0.936266\pi$
$17$	−22.2732	+	38.5783i	−0.317767	+	0.550389i	0.662255	+	0.749279i	$0.269600\pi$
$18$	−75.6155			−0.990153
$19$	−11.9848	+	20.7584i	−0.144711	+	0.250647i	−0.929265	−	0.369413i	$-0.879559\pi$
$19$	−11.9848	+	20.7584i	−0.144711	+	0.250647i	0.784554	+	0.620061i	$0.212892\pi$
$20$	−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	−0.997796	−	0.0663568i	$-0.978862\pi$
$23$	−61.3693	−	106.295i	−0.556365	−	0.963652i	0.441431	−	0.897295i	$-0.354471\pi$
$24$	−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	0.967026	+	0.254678i	$0.0819694\pi$
$29$	109.955	+	190.447i	0.704071	+	1.21949i	−0.262955	+	0.964808i	$0.584697\pi$
$30$	−24.1501	+	41.8292i	−0.146973	+	0.254564i
$31$	27.0928			0.156968			0.0784840	−	0.996915i	$-0.474992\pi$
$31$	27.0928			0.156968			0.0784840	+	0.996915i	$0.474992\pi$
$32$	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	$-0.233772\pi$
$37$	−47.0961	−	81.5729i	−0.209258	−	0.362446i	−0.951481	+	0.307707i	$0.900438\pi$
$38$	−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	$-0.0678752\pi$
$41$	80.1771	+	138.871i	0.305404	+	0.528975i	−0.671947	+	0.740599i	$0.734542\pi$
$42$	−184.282	−	319.185i	−0.677031	−	1.17265i
$43$	75.6510	−	131.031i	0.268295	−	0.464700i	−0.700127	−	0.714018i	$-0.746873\pi$
$43$	75.6510	−	131.031i	0.268295	−	0.464700i	0.968422	+	0.249318i	$0.0802066\pi$
$44$	−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	$-0.242030\pi$
$47$	466.948			1.44918			0.724589	+	0.689181i	$0.242030\pi$
$48$	−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	$-0.672137\pi$
$59$	219.816	−	380.733i	0.485045	−	0.840122i	0.999852	+	0.0171836i	$0.00546997\pi$
$60$	172.024			0.370136
$61$	68.6525	−	118.910i	0.144099	−	0.249587i	−0.784937	−	0.619575i	$-0.787305\pi$
$61$	68.6525	−	118.910i	0.144099	−	0.249587i	0.929037	+	0.369988i	$0.120638\pi$
$62$	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	$-0.321351\pi$
$67$	−256.140	−	443.648i	−0.467052	−	0.808958i	−0.999292	+	0.0376358i	$0.988017\pi$
$68$	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	$-0.944866\pi$
$71$	−205.359	+	355.693i	−0.343263	+	0.594549i	0.641774	+	0.766894i	$0.278199\pi$
$72$	−512.732	+	888.078i	−0.839251	+	1.45362i
$73$	−308.004			−0.493823			−0.246912	−	0.969038i	$-0.579416\pi$
$73$	−308.004			−0.493823			−0.246912	+	0.969038i	$0.579416\pi$
$74$	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	$-0.146861\pi$
$83$	1354.20			1.79088			0.895440	+	0.445182i	$0.146861\pi$
$84$	−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	$-0.251033\pi$
$89$	−219.941	−	380.949i	−0.261952	−	0.453714i	−0.966761	+	0.255683i	$0.917700\pi$
$90$	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	−0.134414	−	0.990925i	$-0.542915\pi$
$97$	755.634	−	1308.80i	0.790959	−	1.36998i	0.925374	−	0.379056i	$-0.123751\pi$
$98$	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	0.771243	−	0.636541i	$-0.219635\pi$
$101$	−168.130	−	291.209i	−0.165639	−	0.286895i	−0.936882	+	0.349646i	$0.886302\pi$
$102$	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	−0.983580	−	0.180471i	$-0.942238\pi$
$107$	−717.309	−	1242.42i	−0.648083	−	1.12251i	0.335498	−	0.942041i	$-0.391096\pi$
$108$	517.375	−	896.119i	0.460967	−	0.798417i
$109$	849.147			0.746179			0.373089	−	0.927795i	$-0.378298\pi$
$109$	849.147			0.746179			0.373089	+	0.927795i	$0.378298\pi$
$110$	−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	0.305280	+	0.952263i	$0.401250\pi$
$113$	−807.263	+	1398.22i	−0.672044	+	1.16401i	−0.977324	+	0.211751i	$0.932083\pi$
$114$	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	0.674394	−	0.738371i	$-0.264405\pi$
$127$	−432.587	−	749.263i	−0.302251	−	0.523514i	−0.976646	+	0.214857i	$0.931071\pi$
$128$	−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	−0.0793428	−	0.996847i	$-0.525282\pi$
$137$	1320.72	−	2287.55i	0.823624	−	1.42656i	0.902967	−	0.429711i	$-0.141384\pi$
$138$	−1664.53			−1.02677
$139$	999.318	−	1730.87i	0.609791	−	1.05619i	−0.381483	−	0.924376i	$-0.624587\pi$
$139$	999.318	−	1730.87i	0.609791	−	1.05619i	0.991274	−	0.131814i	$-0.0420801\pi$
$140$	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	$-0.673276\pi$
$149$	876.491	−	1518.13i	0.481912	−	0.834696i	0.999784	+	0.0207617i	$0.00660911\pi$
$150$	−761.585	+	1319.10i	−0.414554	+	0.718029i
$151$	−2794.64			−1.50613			−0.753063	−	0.657949i	$-0.771424\pi$
$151$	−2794.64			−1.50613			−0.753063	+	0.657949i	$0.771424\pi$
$152$	−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	0.138517	+	0.990360i	$0.455766\pi$
$163$	−1640.73	+	2841.83i	−0.788418	+	1.36558i	−0.926936	+	0.375221i	$0.877567\pi$
$164$	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	0.959235	+	0.282608i	$0.0911996\pi$
$167$	1563.26	+	2707.65i	0.724364	+	1.25463i	−0.234872	+	0.972026i	$0.575467\pi$
$168$	−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	−0.876546	−	0.481318i	$-0.840158\pi$
$173$	−48.7849	+	84.4980i	−0.0214396	+	0.0371345i	0.855107	+	0.518452i	$0.173492\pi$
$174$	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	0.869627	−	0.493710i	$-0.164360\pi$
$179$	17.3575	+	30.0640i	0.00724782	+	0.0125536i	−0.862379	+	0.506264i	$0.831026\pi$
$180$	−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	0.101407	+	0.994845i	$0.467666\pi$
$191$	−2140.40	+	3707.28i	−0.810858	+	1.40445i	−0.912265	+	0.409602i	$0.865668\pi$
$192$	−872.903	−	1511.91i	−0.328106	−	0.568296i
$193$	−236.160	−	409.041i	−0.0880786	−	0.152557i	0.818620	−	0.574335i	$-0.194739\pi$
$193$	−236.160	−	409.041i	−0.0880786	−	0.152557i	−0.906699	+	0.421778i	$0.861406\pi$
$194$	2359.93			0.873365
$195$		0			0
$196$	−2200.12			−0.801791
$197$	2242.18	+	3883.58i	0.810908	+	1.40453i	0.912229	+	0.409681i	$0.134360\pi$
$197$	2242.18	+	3883.58i	0.810908	+	1.40453i	−0.101321	+	0.994854i	$0.532307\pi$
$198$	576.998	+	999.390i	0.207098	+	0.358705i
$199$	183.120	−	317.173i	0.0652314	−	0.112984i	−0.831565	−	0.555427i	$-0.812555\pi$
$199$	183.120	−	317.173i	0.0652314	−	0.112984i	0.896797	+	0.442443i	$0.145888\pi$
$200$	−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	0.639320	−	0.768941i	$-0.279216\pi$
$211$	−1061.28	−	1838.19i	−0.346262	−	0.599744i	−0.985582	+	0.169197i	$0.945883\pi$
$212$	−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	0.840081	+	0.542461i	$0.182507\pi$
$223$	2963.21	+	5132.43i	0.889826	+	1.54122i	0.0497449	+	0.998762i	$0.484159\pi$
$224$	−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	$-0.791534\pi$
$227$	447.830	−	775.665i	0.130941	−	0.226796i	0.924039	+	0.382297i	$0.124867\pi$
$228$	578.870	−	1002.63i	0.168143	−	0.291232i
$229$	627.717			0.181138			0.0905692	−	0.995890i	$-0.471131\pi$
$229$	627.717			0.181138			0.0905692	+	0.995890i	$0.471131\pi$
$230$	−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	$-0.476519\pi$
$239$	544.622			0.147400			0.0737001	+	0.997280i	$0.476519\pi$
$240$	176.666	−	305.995i	0.0475156	−	0.0822995i
$241$	−2713.05	+	4699.14i	−0.725157	+	1.25601i	0.233752	+	0.972296i	$0.424900\pi$
$241$	−2713.05	+	4699.14i	−0.725157	+	1.25601i	−0.958909	+	0.283713i	$0.908434\pi$
$242$	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	−0.325022	−	0.945706i	$-0.605372\pi$
$251$	2610.61	−	4521.71i	0.656494	−	1.13708i	0.981517	−	0.191375i	$-0.0612948\pi$
$252$	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	0.823319	−	0.567579i	$-0.192120\pi$
$257$	−329.103	−	570.023i	−0.0798789	−	0.138354i	−0.903198	+	0.429225i	$0.858787\pi$
$258$	−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	0.610565	−	0.791966i	$-0.290942\pi$
$263$	−1623.23	−	2811.51i	−0.380580	−	0.659184i	−0.991145	+	0.132782i	$0.957609\pi$
$264$	−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	−0.681482	−	0.731835i	$-0.738664\pi$
$269$	1292.90	−	2239.37i	0.293047	−	0.507572i	0.974529	+	0.224263i	$0.0719976\pi$
$270$	−517.375	−	896.119i	−0.116616	−	0.201985i
$271$	−494.466	−	856.441i	−0.110836	−	0.191974i	0.805271	−	0.592907i	$-0.202020\pi$
$271$	−494.466	−	856.441i	−0.110836	−	0.191974i	−0.916108	+	0.400932i	$0.868686\pi$
$272$	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	−0.0351939	+	0.999381i	$0.511205\pi$
$277$	−4071.20	+	7051.53i	−0.883086	+	1.52955i	−0.847892	+	0.530169i	$0.822128\pi$
$278$	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	$-0.447930\pi$
$281$	1534.21			0.325705			0.162853	+	0.986650i	$0.447930\pi$
$282$	3166.27	−	5484.14i	0.668612	−	1.15807i
$283$	3482.50	+	6031.87i	0.731495	+	1.26699i	0.956244	+	0.292570i	$0.0945105\pi$
$283$	3482.50	+	6031.87i	0.731495	+	1.26699i	−0.224749	+	0.974417i	$0.572156\pi$
$284$	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	$-0.853658\pi$
$293$	−320.015	+	554.281i	−0.0638070	+	0.110517i	0.832357	+	0.554240i	$0.186991\pi$
$294$	−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	$-0.502971\pi$
$307$	−100.406			−0.0186660			−0.00933299	+	0.999956i	$0.502971\pi$
$308$	−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	$-0.372338\pi$
$317$	4406.81			0.780791			0.390396	+	0.920647i	$0.372338\pi$
$318$	−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	$-0.721879\pi$
$331$	2065.75	−	3577.98i	0.343032	−	0.594149i	0.984994	+	0.172587i	$0.0552127\pi$
$332$	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	0.153683	+	0.988120i	$0.450887\pi$
$347$	−5034.70	+	8720.36i	−0.778896	+	1.34909i	−0.932579	+	0.360967i	$0.882447\pi$
$348$	−5310.82	−	9198.62i	−0.818075	−	1.41695i
$349$	−2939.66	−	5091.64i	−0.450878	−	0.780944i	0.547563	−	0.836765i	$-0.315556\pi$
$349$	−2939.66	−	5091.64i	−0.450878	−	0.780944i	−0.998441	+	0.0558207i	$0.982222\pi$
$350$	−4766.49			−0.727942
$351$		0			0
$352$	−2857.76			−0.432725
$353$	4571.28	+	7917.69i	0.689249	+	1.19381i	0.972081	+	0.234644i	$0.0753925\pi$
$353$	4571.28	+	7917.69i	0.689249	+	1.19381i	−0.282833	+	0.959169i	$0.591274\pi$
$354$	−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	$-0.564894\pi$
$359$	−2754.32			−0.404924			−0.202462	+	0.979290i	$0.564894\pi$
$360$	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	0.737438	−	0.675415i	$-0.236036\pi$
$367$	−1520.09	−	2632.88i	−0.216208	−	0.374483i	−0.953646	+	0.300932i	$0.902702\pi$
$368$	−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	−0.616397	−	0.787435i	$-0.711408\pi$
$373$	2692.36	−	4663.31i	0.373740	−	0.647337i	0.990138	+	0.140098i	$0.0447418\pi$
$374$	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	$-0.0921239\pi$
$379$	1712.13	+	2965.50i	0.232049	+	0.401920i	−0.726362	+	0.687312i	$0.758791\pi$
$380$	−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	$-0.825200\pi$
$383$	191.493	−	331.675i	0.0255478	−	0.0442501i	0.878517	+	0.477712i	$0.158534\pi$
$384$	−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	$-0.682048\pi$
$397$	3619.58	−	6269.30i	0.457586	−	0.792562i	0.998833	+	0.0483020i	$0.0153810\pi$
$398$	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	$-0.252321\pi$
$401$	−2134.81	−	3697.60i	−0.265854	−	0.460472i	−0.967787	+	0.251770i	$0.918987\pi$
$402$	−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	0.0859711	+	0.996298i	$0.472601\pi$
$409$	−6781.26	+	11745.5i	−0.819834	+	1.41999i	−0.905805	+	0.423696i	$0.860733\pi$
$410$	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	0.881392	+	0.472386i	$0.156607\pi$
$419$	7288.44	+	12624.0i	0.849794	+	1.47189i	−0.0315973	+	0.999501i	$0.510059\pi$
$420$	2337.55	−	4048.76i	0.271573	−	0.470379i
$421$	15848.4			1.83469			0.917343	−	0.398099i	$-0.130330\pi$
$421$	15848.4			1.83469			0.917343	+	0.398099i	$0.130330\pi$
$422$	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	−0.993172	−	0.116662i	$-0.962781\pi$
$431$	−5347.36	−	9261.90i	−0.597618	−	1.03510i	0.395554	−	0.918443i	$-0.370553\pi$
$432$	−1062.67	−	1840.61i	−0.118352	−	0.204991i
$433$	8039.50	−	13924.8i	0.892272	−	1.54546i	0.0551273	−	0.998479i	$-0.482444\pi$
$433$	8039.50	−	13924.8i	0.892272	−	1.54546i	0.837145	−	0.546981i	$-0.184223\pi$
$434$	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	0.654034	−	0.756465i	$-0.273075\pi$
$439$	−3017.90	−	5227.16i	−0.328101	−	0.568288i	−0.982135	+	0.188177i	$0.939742\pi$
$440$	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	$-0.734345\pi$
$449$	2911.27	−	5042.47i	0.305994	−	0.529997i	0.977482	+	0.211018i	$0.0676779\pi$
$450$	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	$-0.242677\pi$
$457$	−2310.80	−	4002.42i	−0.236531	−	0.409684i	−0.959717	+	0.280970i	$0.909344\pi$
$458$	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	$-0.916736\pi$
$461$	−2563.88	+	4440.78i	−0.259028	+	0.448650i	0.706954	+	0.707260i	$0.250069\pi$
$462$	−2812.39	+	4871.20i	−0.283213	+	0.490539i
$463$	6486.27			0.651064			0.325532	−	0.945531i	$-0.394457\pi$
$463$	6486.27			0.651064			0.325532	+	0.945531i	$0.394457\pi$
$464$	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	$-0.0773084\pi$
$479$	2904.48	+	5030.71i	0.277055	+	0.479873i	−0.693597	+	0.720363i	$0.743975\pi$
$480$	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	$-0.752695\pi$
$487$	2693.57	−	4665.40i	0.250631	−	0.434106i	0.963700	+	0.266989i	$0.0860286\pi$
$488$	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	−0.968026	−	0.250849i	$-0.919290\pi$
$491$	−7629.53	−	13214.7i	−0.701255	−	1.21461i	0.266772	−	0.963760i	$-0.414043\pi$
$492$	−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	$-0.473469\pi$
$499$	1856.04			0.166509			0.0832544	+	0.996528i	$0.473469\pi$
$500$	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	−0.888345	−	0.459176i	$-0.848145\pi$
$503$	−524.732	+	908.862i	−0.0465142	+	0.0805649i	0.841831	+	0.539741i	$0.181478\pi$
$504$	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	$-0.159028\pi$
$509$	275.553	+	477.272i	0.0239954	+	0.0415613i	−0.853778	+	0.520637i	$0.825695\pi$
$510$	−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	0.804958	−	0.593332i	$-0.202188\pi$
$523$	−1331.96	−	2307.02i	−0.111362	−	0.192885i	−0.916320	+	0.400448i	$0.868855\pi$
$524$	−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	$-0.578832\pi$
$541$	−6169.23			−0.490270			−0.245135	+	0.969489i	$0.578832\pi$
$542$	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	$-0.200370\pi$
$557$	−1389.28	−	2406.30i	−0.105683	−	0.183049i	−0.914017	+	0.405675i	$0.867036\pi$
$558$	−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	−0.943115	−	0.332468i	$-0.892119\pi$
$563$	−2453.07	+	4248.85i	−0.183632	+	0.318059i	0.759483	+	0.650527i	$0.225452\pi$
$564$	−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	0.985340	−	0.170602i	$-0.0545713\pi$
$569$	4681.58	+	8108.73i	0.344924	+	0.597426i	−0.640416	+	0.768028i	$0.721238\pi$
$570$	−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	$-0.635534\pi$
$577$	−11449.6			−0.826086			−0.413043	+	0.910711i	$0.635534\pi$
$578$	−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	$-0.105418\pi$
$587$	2719.70	+	4710.65i	0.191233	+	0.331226i	−0.754426	+	0.656385i	$0.772085\pi$
$588$	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	$-0.942180\pi$
$593$	−28405.8			−1.96709			−0.983547	+	0.180651i	$0.942180\pi$
$594$	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	0.806616	−	0.591076i	$-0.201297\pi$
$601$	−1599.77	−	2770.88i	−0.108579	−	0.188064i	−0.915195	+	0.403012i	$0.867963\pi$
$602$	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	−0.990951	−	0.134224i	$-0.957146\pi$
$607$	−5671.40	+	9823.15i	−0.379234	+	0.656853i	0.611717	+	0.791077i	$0.290479\pi$
$608$	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	$-0.323826\pi$
$613$	−7192.70	−	12458.1i	−0.473916	−	0.820846i	−0.999554	+	0.0298622i	$0.990493\pi$
$614$	−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	0.241575	+	0.970382i	$0.422336\pi$
$617$	−11028.4	+	19101.7i	−0.719588	+	1.24636i	−0.961163	+	0.275981i	$0.910997\pi$
$618$	2188.24	−	3790.14i	0.142433	−	0.246702i
$619$	13621.4			0.884477			0.442238	−	0.896898i	$-0.354185\pi$
$619$	13621.4			0.884477			0.442238	+	0.896898i	$0.354185\pi$
$620$	−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	−0.403021	−	0.915191i	$-0.632040\pi$
$631$	9368.74	−	16227.1i	0.591068	−	1.02376i	0.994089	−	0.108569i	$-0.0346267\pi$
$632$	−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	−0.115753	+	0.993278i	$0.536928\pi$
$641$	−14899.4	+	25806.5i	−0.918081	+	1.59016i	−0.802327	+	0.596884i	$0.796405\pi$
$642$	−19455.6			−1.19603
$643$	11491.8	−	19904.3i	0.704807	−	1.22076i	−0.261955	−	0.965080i	$-0.584367\pi$
$643$	11491.8	−	19904.3i	0.704807	−	1.22076i	0.966761	−	0.255681i	$-0.0822996\pi$
$644$	−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	0.944539	+	0.328400i	$0.106509\pi$
$647$	12452.7	+	21568.7i	0.756672	+	1.31059i	−0.187866	+	0.982195i	$0.560157\pi$
$648$	−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	0.674610	−	0.738175i	$-0.264312\pi$
$653$	−5038.92	−	8727.67i	−0.301973	−	0.523033i	−0.976583	+	0.215142i	$0.930979\pi$
$654$	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	−0.988705	−	0.149874i	$-0.952113\pi$
$659$	−6167.30	+	10682.1i	−0.364558	+	0.631433i	0.624147	+	0.781307i	$0.285447\pi$
$660$	−1312.66	−	2273.59i	−0.0774169	−	0.134090i
$661$	6374.56	+	11041.1i	0.375101	+	0.649694i	0.990342	−	0.138645i	$-0.0442747\pi$
$661$	6374.56	+	11041.1i	0.375101	+	0.649694i	−0.615241	+	0.788339i	$0.710941\pi$
$662$	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	0.992450	−	0.122654i	$-0.0391404\pi$
$673$	6809.12	+	11793.7i	0.390004	+	0.675506i	−0.602446	+	0.798160i	$0.705807\pi$
$674$	−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	$-0.984431\pi$
$683$	−8158.38	+	14130.7i	−0.457060	+	0.791650i	0.541744	+	0.840543i	$0.317764\pi$
$684$	−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	$-0.187279\pi$
$691$	−1175.42	−	2035.89i	−0.0647106	−	0.112082i	−0.896566	+	0.442911i	$0.853946\pi$
$692$	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	$-0.715818\pi$
$709$	6812.44	−	11799.5i	0.360856	−	0.625021i	0.988102	+	0.153801i	$0.0491513\pi$
$710$	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	−0.996044	−	0.0888616i	$-0.971677\pi$
$719$	−8117.89	+	14060.6i	−0.421066	+	0.729307i	0.574978	+	0.818169i	$0.305010\pi$
$720$	−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	$-0.475486\pi$
$733$	3053.70			0.153876			0.0769379	+	0.997036i	$0.475486\pi$
$734$	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	$-0.102590\pi$
$739$	4016.81	+	6957.32i	0.199947	+	0.346318i	−0.748564	+	0.663062i	$0.769256\pi$
$740$	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	$-0.0362128\pi$
$743$	8069.81	+	13977.3i	0.398456	+	0.690146i	−0.595080	+	0.803667i	$0.702880\pi$
$744$	−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	0.998336	−	0.0576584i	$-0.0183634\pi$
$751$	9245.56	+	16013.8i	0.449235	+	0.778097i	−0.549102	+	0.835755i	$0.685030\pi$
$752$	−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	0.864091	−	0.503336i	$-0.167894\pi$
$757$	−80.3149	−	139.109i	−0.00385613	−	0.00667902i	−0.867947	+	0.496657i	$0.834561\pi$
$758$	−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	0.347528	+	0.937670i	$0.387021\pi$
$761$	−13399.5	+	23208.7i	−0.638282	+	1.10554i	−0.985810	+	0.167867i	$0.946312\pi$
$762$	−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	$-0.128168\pi$
$769$	2572.91	+	4456.41i	0.120652	+	0.208976i	−0.799373	+	0.600835i	$0.794835\pi$
$770$	1153.35	+

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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