LMFDB - Embedded newform 147.4.c.b.146.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.20
Character	$\chi$	$=$	147.146
Dual form			147.4.c.b.146.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.20022i q^{2} +(0.930073 - 5.11224i) q^{3} -2.24142 q^{4} -11.9763 q^{5} +(16.3603 + 2.97644i) q^{6} +18.4287i q^{8} +(-25.2699 - 9.50951i) q^{9} +O(q^{10})$	\(q+3.20022i q^{2} +(0.930073 - 5.11224i) q^{3} -2.24142 q^{4} -11.9763 q^{5} +(16.3603 + 2.97644i) q^{6} +18.4287i q^{8} +(-25.2699 - 9.50951i) q^{9} -38.3267i q^{10} +60.3470i q^{11} +(-2.08468 + 11.4587i) q^{12} +3.46204i q^{13} +(-11.1388 + 61.2255i) q^{15} -76.9074 q^{16} -32.4937 q^{17} +(30.4325 - 80.8694i) q^{18} +142.952i q^{19} +26.8438 q^{20} -193.124 q^{22} +89.8989i q^{23} +(94.2120 + 17.1401i) q^{24} +18.4309 q^{25} -11.0793 q^{26} +(-72.1177 + 120.341i) q^{27} -247.795i q^{29} +(-195.935 - 35.6466i) q^{30} -207.886i q^{31} -98.6909i q^{32} +(308.508 + 56.1271i) q^{33} -103.987i q^{34} +(56.6405 + 21.3148i) q^{36} +98.3044 q^{37} -457.477 q^{38} +(17.6988 + 3.21995i) q^{39} -220.707i q^{40} -150.249 q^{41} +59.4615 q^{43} -135.263i q^{44} +(302.639 + 113.888i) q^{45} -287.696 q^{46} -232.849 q^{47} +(-71.5295 + 393.169i) q^{48} +58.9830i q^{50} +(-30.2215 + 166.115i) q^{51} -7.75989i q^{52} +292.851i q^{53} +(-385.119 - 230.793i) q^{54} -722.731i q^{55} +(730.803 + 132.956i) q^{57} +792.998 q^{58} +465.699 q^{59} +(24.9667 - 137.232i) q^{60} +13.1309i q^{61} +665.282 q^{62} -299.427 q^{64} -41.4623i q^{65} +(-179.619 + 987.294i) q^{66} +481.684 q^{67} +72.8320 q^{68} +(459.584 + 83.6125i) q^{69} +550.199i q^{71} +(175.248 - 465.693i) q^{72} +372.298i q^{73} +314.596i q^{74} +(17.1421 - 94.2231i) q^{75} -320.415i q^{76} +(-10.3046 + 56.6400i) q^{78} +879.193 q^{79} +921.063 q^{80} +(548.139 + 480.609i) q^{81} -480.832i q^{82} -1119.54 q^{83} +389.153 q^{85} +190.290i q^{86} +(-1266.78 - 230.467i) q^{87} -1112.12 q^{88} +21.2955 q^{89} +(-364.468 + 968.513i) q^{90} -201.501i q^{92} +(-1062.76 - 193.349i) q^{93} -745.169i q^{94} -1712.03i q^{95} +(-504.531 - 91.7897i) q^{96} -612.931i q^{97} +(573.870 - 1524.96i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) $ 24 * q - 96 * q^4 - 64 * q^9	$ 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) $ 24 * q - 96 * q^4 - 64 * q^9 + 256 * q^15 + 864 * q^16 - 32 * q^18 - 384 * q^22 + 744 * q^25 - 1704 * q^30 + 584 * q^36 + 432 * q^37 - 2368 * q^39 - 624 * q^43 + 3744 * q^46 - 2160 * q^51 + 2032 * q^57 + 6384 * q^58 - 5832 * q^60 - 3504 * q^64 + 3792 * q^67 - 7472 * q^72 + 2248 * q^78 + 2784 * q^79 - 1968 * q^81 - 3744 * q^85 - 624 * q^88 - 3232 * q^93 + 1320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			3.20022i			1.13145i	0.824594	+	0.565725i	$0.191403\pi$
$2$			3.20022i			1.13145i	−0.824594	+	0.565725i	$0.808597\pi$
$3$	0.930073	−	5.11224i	0.178993	−	0.983850i
$3$	0.930073	−	5.11224i	0.178993	−	0.983850i
$4$	−2.24142			−0.280177
$5$	−11.9763			−1.07119			−0.535595	−	0.844475i	$-0.679913\pi$
$5$	−11.9763			−1.07119			−0.535595	+	0.844475i	$0.679913\pi$
$6$	16.3603	+	2.97644i	1.11318	+	0.202521i
$7$		0			0
$7$		0			0
$8$			18.4287i			0.814443i
$9$	−25.2699	−	9.50951i	−0.935923	−	0.352204i
$10$		−	38.3267i		−	1.21200i
$11$			60.3470i			1.65412i	0.562115	+	0.827059i	$0.309988\pi$
$11$			60.3470i			1.65412i	−0.562115	+	0.827059i	$0.690012\pi$
$12$	−2.08468	+	11.4587i	−0.0501497	+	0.275653i
$13$			3.46204i			0.0738613i	0.999318	+	0.0369307i	$0.0117581\pi$
$13$			3.46204i			0.0738613i	−0.999318	+	0.0369307i	$0.988242\pi$
$14$		0			0
$15$	−11.1388	+	61.2255i	−0.191735	+	1.05389i
$16$	−76.9074			−1.20168
$17$	−32.4937			−0.463581			−0.231790	−	0.972766i	$-0.574458\pi$
$17$	−32.4937			−0.463581			−0.231790	+	0.972766i	$0.574458\pi$
$18$	30.4325	−	80.8694i	0.398501	−	1.05895i
$19$			142.952i			1.72607i	0.505142	+	0.863036i	$0.331440\pi$
$19$			142.952i			1.72607i	−0.505142	+	0.863036i	$0.668560\pi$
$20$	26.8438			0.300123
$21$		0			0
$22$	−193.124			−1.87155
$23$			89.8989i			0.815009i	0.913203	+	0.407505i	$0.133601\pi$
$23$			89.8989i			0.815009i	−0.913203	+	0.407505i	$0.866399\pi$
$24$	94.2120	+	17.1401i	0.801290	+	0.145779i
$25$	18.4309			0.147447
$26$	−11.0793			−0.0835703
$27$	−72.1177	+	120.341i	−0.514039	+	0.857767i
$28$		0			0
$29$		−	247.795i		−	1.58670i	−0.608766	−	0.793350i	$-0.708335\pi$
$29$		−	247.795i		−	1.58670i	0.608766	−	0.793350i	$-0.291665\pi$
$30$	−195.935	−	35.6466i	−1.19242	−	0.216938i
$31$		−	207.886i		−	1.20443i	−0.798332	−	0.602217i	$-0.794284\pi$
$31$		−	207.886i		−	1.20443i	0.798332	−	0.602217i	$-0.205716\pi$
$32$		−	98.6909i		−	0.545195i
$33$	308.508	+	56.1271i	1.62740	+	0.296075i
$34$		−	103.987i		−	0.524518i
$35$		0			0
$36$	56.6405	+	21.3148i	0.262225	+	0.0986796i
$37$	98.3044			0.436787			0.218394	−	0.975861i	$-0.429918\pi$
$37$	98.3044			0.436787			0.218394	+	0.975861i	$0.429918\pi$
$38$	−457.477			−1.95296
$39$	17.6988	+	3.21995i	0.0726685	+	0.0132206i
$40$		−	220.707i		−	0.872423i
$41$	−150.249			−0.572318			−0.286159	−	0.958182i	$-0.592378\pi$
$41$	−150.249			−0.572318			−0.286159	+	0.958182i	$0.592378\pi$
$42$		0			0
$43$	59.4615			0.210879			0.105439	−	0.994426i	$-0.466375\pi$
$43$	59.4615			0.210879			0.105439	+	0.994426i	$0.466375\pi$
$44$		−	135.263i		−	0.463447i
$45$	302.639	+	113.888i	1.00255	+	0.377277i
$46$	−287.696			−0.922142
$47$	−232.849			−0.722649			−0.361325	−	0.932440i	$-0.617675\pi$
$47$	−232.849			−0.722649			−0.361325	+	0.932440i	$0.617675\pi$
$48$	−71.5295	+	393.169i	−0.215092	+	1.18227i
$49$		0			0
$50$			58.9830i			0.166829i
$51$	−30.2215	+	166.115i	−0.0829775	+	0.456094i
$52$		−	7.75989i		−	0.0206943i
$53$			292.851i			0.758984i	0.925195	+	0.379492i	$0.123901\pi$
$53$			292.851i			0.758984i	−0.925195	+	0.379492i	$0.876099\pi$
$54$	−385.119	−	230.793i	−0.970519	−	0.581609i
$55$		−	722.731i		−	1.77187i
$56$		0			0
$57$	730.803	+	132.956i	1.69820	+	0.308954i
$58$	792.998			1.79527
$59$	465.699			1.02761			0.513804	−	0.857908i	$-0.328236\pi$
$59$	465.699			1.02761			0.513804	+	0.857908i	$0.328236\pi$
$60$	24.9667	−	137.232i	0.0537198	−	0.295276i
$61$			13.1309i			0.0275612i	0.999905	+	0.0137806i	$0.00438664\pi$
$61$			13.1309i			0.0275612i	−0.999905	+	0.0137806i	$0.995613\pi$
$62$	665.282			1.36276
$63$		0			0
$64$	−299.427			−0.584817
$65$		−	41.4623i		−	0.0791195i
$66$	−179.619	+	987.294i	−0.334994	+	1.84133i
$67$	481.684			0.878315			0.439157	−	0.898410i	$-0.355277\pi$
$67$	481.684			0.878315			0.439157	+	0.898410i	$0.355277\pi$
$68$	72.8320			0.129885
$69$	459.584	+	83.6125i	0.801847	+	0.145881i
$70$		0			0
$71$			550.199i			0.919671i	0.888004	+	0.459836i	$0.152092\pi$
$71$			550.199i			0.919671i	−0.888004	+	0.459836i	$0.847908\pi$
$72$	175.248	−	465.693i	0.286850	−	0.762256i
$73$			372.298i			0.596907i	0.954424	+	0.298453i	$0.0964707\pi$
$73$			372.298i			0.596907i	−0.954424	+	0.298453i	$0.903529\pi$
$74$			314.596i			0.494203i
$75$	17.1421	−	94.2231i	0.0263920	−	0.145066i
$76$		−	320.415i		−	0.483607i
$77$		0			0
$78$	−10.3046	+	56.6400i	−0.0149585	+	0.0822207i
$79$	879.193			1.25211			0.626056	−	0.779778i	$-0.284668\pi$
$79$	879.193			1.25211			0.626056	+	0.779778i	$0.284668\pi$
$80$	921.063			1.28723
$81$	548.139	+	480.609i	0.751905	+	0.659272i
$82$		−	480.832i		−	0.647548i
$83$	−1119.54			−1.48055			−0.740275	−	0.672304i	$-0.765305\pi$
$83$	−1119.54			−1.48055			−0.740275	+	0.672304i	$0.765305\pi$
$84$		0			0
$85$	389.153			0.496583
$86$			190.290i			0.238599i
$87$	−1266.78	−	230.467i	−1.56108	−	0.284008i
$88$	−1112.12			−1.34718
$89$	21.2955			0.0253631			0.0126816	−	0.999920i	$-0.495963\pi$
$89$	21.2955			0.0253631			0.0126816	+	0.999920i	$0.495963\pi$
$90$	−364.468	+	968.513i	−0.426870	+	1.13434i
$91$		0			0
$92$		−	201.501i		−	0.228347i
$93$	−1062.76	−	193.349i	−1.18498	−	0.215585i
$94$		−	745.169i		−	0.817641i
$95$		−	1712.03i		−	1.84895i
$96$	−504.531	−	91.7897i	−0.536390	−	0.0975859i
$97$		−	612.931i		−	0.641585i	−0.947150	−	0.320792i	$-0.896051\pi$
$97$		−	612.931i		−	0.641585i	0.947150	−	0.320792i	$-0.103949\pi$
$98$		0			0
$99$	573.870	−	1524.96i	0.582587	−	1.54813i
$100$	−41.3114			−0.0413114
$101$	−341.044			−0.335992			−0.167996	−	0.985788i	$-0.553730\pi$
$101$	−341.044			−0.335992			−0.167996	+	0.985788i	$0.553730\pi$
$102$	−531.606	−	96.7155i	−0.516047	−	0.0938849i
$103$			595.559i			0.569730i	0.958568	+	0.284865i	$0.0919488\pi$
$103$			595.559i			0.569730i	−0.958568	+	0.284865i	$0.908051\pi$
$104$	−63.8010			−0.0601558
$105$		0			0
$106$	−937.188			−0.858752
$107$		−	27.6358i		−	0.0249687i	−0.999922	−	0.0124844i	$-0.996026\pi$
$107$		−	27.6358i		−	0.0249687i	0.999922	−	0.0124844i	$-0.00397400\pi$
$108$	161.646	−	269.735i	0.144022	−	0.240327i
$109$	362.610			0.318640			0.159320	−	0.987227i	$-0.449070\pi$
$109$	362.610			0.318640			0.159320	+	0.987227i	$0.449070\pi$
$110$	2312.90			2.00479
$111$	91.4302	−	502.555i	0.0781817	−	0.429734i
$112$		0			0
$113$		−	557.806i		−	0.464371i	−0.972672	−	0.232186i	$-0.925412\pi$
$113$		−	557.806i		−	0.464371i	0.972672	−	0.232186i	$-0.0745876\pi$
$114$	−425.487	+	2338.73i	−0.349566	+	1.92142i
$115$		−	1076.65i		−	0.873030i
$116$			555.412i			0.444558i
$117$	32.9223	−	87.4855i	0.0260142	−	0.0691285i
$118$			1490.34i			1.16269i
$119$		0			0
$120$	−1128.31	−	205.274i	−0.858333	−	0.156157i
$121$	−2310.76			−1.73611
$122$	−42.0217			−0.0311841
$123$	−139.743	+	768.111i	−0.102441	+	0.563075i
$124$			465.960i			0.337455i
$125$	1276.30			0.913246
$126$		0			0
$127$	−1038.78			−0.725804			−0.362902	−	0.931827i	$-0.618214\pi$
$127$	−1038.78			−0.725804			−0.362902	+	0.931827i	$0.618214\pi$
$128$		−	1747.76i		−	1.20689i
$129$	55.3035	−	303.981i	0.0377458	−	0.207473i
$130$	132.689			0.0895197
$131$	−825.411			−0.550508			−0.275254	−	0.961372i	$-0.588762\pi$
$131$	−825.411			−0.550508			−0.275254	+	0.961372i	$0.588762\pi$
$132$	−691.496	−	125.804i	−0.455962	−	0.0829535i
$133$		0			0
$134$			1541.50i			0.993769i
$135$	863.701	−	1441.24i	0.550634	−	0.918831i
$136$		−	598.817i		−	0.377560i
$137$		−	1890.23i		−	1.17878i	−0.807847	−	0.589392i	$-0.799367\pi$
$137$		−	1890.23i		−	1.17878i	0.807847	−	0.589392i	$-0.200633\pi$
$138$	−267.579	+	1470.77i	−0.165057	+	0.907250i
$139$		−	201.550i		−	0.122987i	−0.998107	−	0.0614936i	$-0.980414\pi$
$139$		−	201.550i		−	0.122987i	0.998107	−	0.0614936i	$-0.0195864\pi$
$140$		0			0
$141$	−216.567	+	1190.38i	−0.129349	+	0.710979i
$142$	−1760.76			−1.04056
$143$	−208.924			−0.122175
$144$	1943.44	+	731.351i	1.12468	+	0.423236i
$145$			2967.65i			1.69966i
$146$	−1191.44			−0.675369
$147$		0			0
$148$	−220.341			−0.122378
$149$			2151.81i			1.18311i	0.806265	+	0.591554i	$0.201485\pi$
$149$			2151.81i			1.18311i	−0.806265	+	0.591554i	$0.798515\pi$
$150$	301.535	+	54.8585i	0.164135	+	0.0298612i
$151$	1803.04			0.971718			0.485859	−	0.874037i	$-0.338507\pi$
$151$	1803.04			0.971718			0.485859	+	0.874037i	$0.338507\pi$
$152$	−2634.42			−1.40579
$153$	821.113	+	308.999i	0.433876	+	0.163275i
$154$		0			0
$155$			2489.70i			1.29018i
$156$	−39.6704	−	7.21726i	−0.0203601	−	0.00370412i
$157$			2626.82i			1.33531i	0.744472	+	0.667654i	$0.232701\pi$
$157$			2626.82i			1.33531i	−0.744472	+	0.667654i	$0.767299\pi$
$158$			2813.61i			1.41670i
$159$	1497.12	+	272.373i	0.746727	+	0.135853i
$160$			1181.95i			0.584007i
$161$		0			0
$162$	−1538.06	+	1754.17i	−0.745933	+	0.850742i
$163$	1445.35			0.694531			0.347265	−	0.937767i	$-0.387110\pi$
$163$	1445.35			0.694531			0.347265	+	0.937767i	$0.387110\pi$
$164$	336.772			0.160350
$165$	−3694.77	−	672.193i	−1.74326	−	0.317152i
$166$		−	3582.78i		−	1.67517i
$167$	2634.85			1.22090			0.610452	−	0.792054i	$-0.290988\pi$
$167$	2634.85			1.22090			0.610452	+	0.792054i	$0.290988\pi$
$168$		0			0
$169$	2185.01			0.994545
$170$			1245.38i			0.561858i
$171$	1359.40	−	3612.38i	0.607930	−	1.61547i
$172$	−133.278			−0.0590835
$173$	−593.511			−0.260831			−0.130416	−	0.991459i	$-0.541631\pi$
$173$	−593.511			−0.260831			−0.130416	+	0.991459i	$0.541631\pi$
$174$	737.546	−	4053.99i	0.321340	−	1.76628i
$175$		0			0
$176$		−	4641.13i		−	1.98772i
$177$	433.134	−	2380.76i	0.183934	−	1.01101i
$178$			68.1503i			0.0286971i
$179$			2639.12i			1.10199i	0.834508	+	0.550996i	$0.185752\pi$
$179$			2639.12i			1.10199i	−0.834508	+	0.550996i	$0.814248\pi$
$180$	−678.342	−	255.272i	−0.280892	−	0.105705i
$181$			1778.65i			0.730421i	0.930925	+	0.365211i	$0.119003\pi$
$181$			1778.65i			0.730421i	−0.930925	+	0.365211i	$0.880997\pi$
$182$		0			0
$183$	67.1281	+	12.2127i	0.0271161	+	0.00493326i
$184$	−1656.72			−0.663778
$185$	−1177.32			−0.467882
$186$	618.761	−	3401.08i	0.243923	−	1.34075i
$187$		−	1960.89i		−	0.766817i
$188$	521.912			0.202470
$189$		0			0
$190$	5478.87			2.09199
$191$		−	1407.33i		−	0.533147i	−0.963815	−	0.266574i	$-0.914108\pi$
$191$		−	1407.33i		−	0.533147i	0.963815	−	0.266574i	$-0.0858916\pi$
$192$	−278.489	+	1530.74i	−0.104678	+	0.575373i
$193$	−1993.13			−0.743362			−0.371681	−	0.928360i	$-0.621219\pi$
$193$	−1993.13			−0.743362			−0.371681	+	0.928360i	$0.621219\pi$
$194$	1961.52			0.725921
$195$	−211.965	−	38.5630i	−0.0778417	−	0.0141618i
$196$		0			0
$197$		−	3336.46i		−	1.20666i	−0.797490	−	0.603332i	$-0.793840\pi$
$197$		−	3336.46i		−	1.20666i	0.797490	−	0.603332i	$-0.206160\pi$
$198$	4880.22	+	1836.51i	1.75163	+	0.659167i
$199$			2628.45i			0.936312i	0.883646	+	0.468156i	$0.155082\pi$
$199$			2628.45i			0.936312i	−0.883646	+	0.468156i	$0.844918\pi$
$200$			339.658i			0.120087i
$201$	448.001	−	2462.48i	0.157212	−	0.864130i
$202$		−	1091.42i		−	0.380158i
$203$		0			0
$204$	67.7390	−	372.334i	0.0232484	−	0.127787i
$205$	1799.43			0.613061
$206$	−1905.92			−0.644621
$207$	854.894	−	2271.74i	0.287050	−	0.762786i
$208$		−	266.256i		−	0.0887575i
$209$	−8626.71			−2.85513
$210$		0			0
$211$	−2000.49			−0.652698			−0.326349	−	0.945249i	$-0.605818\pi$
$211$	−2000.49			−0.652698			−0.326349	+	0.945249i	$0.605818\pi$
$212$		−	656.402i		−	0.212650i
$213$	2812.75	+	511.726i	0.904819	+	0.164614i
$214$	88.4406			0.0282508
$215$	−712.126			−0.225891
$216$	−2217.74	−	1329.04i	−0.698602	−	0.418656i
$217$		0			0
$218$			1160.43i			0.360525i
$219$	1903.28	+	346.264i	0.587267	+	0.106842i
$220$			1619.94i			0.496439i
$221$		−	112.494i		−	0.0342407i
$222$	1608.29	+	292.597i	0.486222	+	0.0884587i
$223$			5476.01i			1.64440i	0.569200	+	0.822199i	$0.307253\pi$
$223$			5476.01i			1.64440i	−0.569200	+	0.822199i	$0.692747\pi$
$224$		0			0
$225$	−465.748	−	175.269i	−0.137999	−	0.0519315i
$226$	1785.10			0.525412
$227$	−3873.17			−1.13247			−0.566236	−	0.824243i	$-0.691601\pi$
$227$	−3873.17			−1.13247			−0.566236	+	0.824243i	$0.691601\pi$
$228$	−1638.04	−	298.009i	−0.475797	−	0.0865621i
$229$		−	1923.73i		−	0.555124i	−0.960708	−	0.277562i	$-0.910474\pi$
$229$		−	1923.73i		−	0.555124i	0.960708	−	0.277562i	$-0.0895265\pi$
$230$	3445.53			0.987789
$231$		0			0
$232$	4566.54			1.29228
$233$			1976.75i			0.555800i	0.960610	+	0.277900i	$0.0896383\pi$
$233$			1976.75i			0.555800i	−0.960610	+	0.277900i	$0.910362\pi$
$234$	279.973	+	105.359i	0.0782154	+	0.0294338i
$235$	2788.66			0.774095
$236$	−1043.83			−0.287913
$237$	817.713	−	4494.64i	0.224119	−	1.23189i
$238$		0			0
$239$		−	1168.46i		−	0.316241i	−0.987420	−	0.158121i	$-0.949457\pi$
$239$		−	1168.46i		−	0.316241i	0.987420	−	0.158121i	$-0.0505434\pi$
$240$	856.656	−	4708.69i	0.230404	−	1.26644i
$241$			6244.92i			1.66917i	0.550877	+	0.834587i	$0.314293\pi$
$241$			6244.92i			1.66917i	−0.550877	+	0.834587i	$0.685707\pi$
$242$		−	7394.93i		−	1.96432i
$243$	2966.80	−	2355.21i	0.783210	−	0.621757i
$244$		−	29.4318i		−	0.00772204i
$245$		0			0
$246$	−2458.12	−	447.208i	−0.637091	−	0.115906i
$247$	−494.905			−0.127490
$248$	3831.08			0.980943
$249$	−1041.26	+	5723.36i	−0.265007	+	1.45664i
$250$			4084.44i			1.03329i
$251$	3590.31			0.902862			0.451431	−	0.892306i	$-0.350914\pi$
$251$	3590.31			0.902862			0.451431	+	0.892306i	$0.350914\pi$
$252$		0			0
$253$	−5425.13			−1.34812
$254$		−	3324.34i		−	0.821211i
$255$	361.941	−	1989.44i	0.0888847	−	0.488563i
$256$	3197.80			0.780713
$257$	−952.226			−0.231121			−0.115561	−	0.993300i	$-0.536866\pi$
$257$	−952.226			−0.231121			−0.115561	+	0.993300i	$0.536866\pi$
$258$	972.807	+	176.984i	0.234745	+	0.0427074i
$259$		0			0
$260$			92.9344i			0.0221675i
$261$	−2356.40	+	6261.75i	−0.558842	+	1.48503i
$262$		−	2641.50i		−	0.622871i
$263$			5149.06i			1.20724i	0.797271	+	0.603621i	$0.206276\pi$
$263$			5149.06i			1.20724i	−0.797271	+	0.603621i	$0.793724\pi$
$264$	−1034.35	+	5685.41i	−0.241136	+	1.32543i
$265$		−	3507.26i		−	0.813016i
$266$		0			0
$267$	19.8064	−	108.868i	0.00453981	−	0.0249535i
$268$	−1079.66			−0.246084
$269$	7121.96			1.61425			0.807126	−	0.590380i	$-0.201022\pi$
$269$	7121.96			1.61425			0.807126	+	0.590380i	$0.201022\pi$
$270$	4612.29	+	2764.03i	1.03961	+	0.623014i
$271$		−	806.788i		−	0.180845i	−0.995904	−	0.0904223i	$-0.971178\pi$
$271$		−	806.788i		−	0.180845i	0.995904	−	0.0904223i	$-0.0288217\pi$
$272$	2499.00			0.557075
$273$		0			0
$274$	6049.16			1.33373
$275$			1112.25i			0.243895i
$276$	−1030.12	−	187.411i	−0.224660	−	0.0408725i
$277$	−5533.95			−1.20037			−0.600185	−	0.799861i	$-0.704906\pi$
$277$	−5533.95			−1.20037			−0.600185	+	0.799861i	$0.704906\pi$
$278$	645.003			0.139154
$279$	−1976.90	+	5253.27i	−0.424207	+	1.12726i
$280$		0			0
$281$			8052.89i			1.70959i	0.518965	+	0.854796i	$0.326318\pi$
$281$			8052.89i			1.70959i	−0.518965	+	0.854796i	$0.673682\pi$
$282$	−3809.48	−	693.061i	−0.804437	−	0.146352i
$283$		−	4273.39i		−	0.897622i	−0.893627	−	0.448811i	$-0.851848\pi$
$283$		−	4273.39i		−	0.897622i	0.893627	−	0.448811i	$-0.148152\pi$
$284$		−	1233.23i		−	0.257671i
$285$	−8752.29	−	1592.31i	−1.81909	−	0.330949i
$286$		−	668.602i		−	0.138235i
$287$		0			0
$288$	−938.501	+	2493.91i	−0.192020	+	0.510261i
$289$	−3857.16			−0.785093
$290$	−9497.15			−1.92308
$291$	−3133.45	−	570.071i	−0.631223	−	0.114839i
$292$		−	834.476i		−	0.167240i
$293$	5195.28			1.03588			0.517938	−	0.855418i	$-0.326700\pi$
$293$	5195.28			1.03588			0.517938	+	0.855418i	$0.326700\pi$
$294$		0			0
$295$	−5577.34			−1.10076
$296$			1811.62i			0.355738i
$297$	−7262.23	−	4352.09i	−1.41885	−	0.850282i
$298$	−6886.27			−1.33863
$299$	−311.234			−0.0601977
$300$	−38.4226	+	211.194i	−0.00739443	+	0.0406442i
$301$		0			0
$302$			5770.13i			1.09945i
$303$	−317.196	+	1743.50i	−0.0601401	+	0.330566i
$304$		−	10994.0i		−	2.07418i
$305$		−	157.259i		−	0.0295233i
$306$	−988.865	+	2627.74i	−0.184737	+	0.490909i
$307$			5359.28i			0.996320i	0.867085	+	0.498160i	$0.165991\pi$
$307$			5359.28i			0.996320i	−0.867085	+	0.498160i	$0.834009\pi$
$308$		0			0
$309$	3044.64	+	553.914i	0.560529	+	0.101977i
$310$	−7967.59			−1.45977
$311$	9042.99			1.64881			0.824406	−	0.565998i	$-0.191509\pi$
$311$	9042.99			1.64881			0.824406	+	0.565998i	$0.191509\pi$
$312$	−59.3396	+	326.166i	−0.0107674	+	0.0591843i
$313$			4146.30i			0.748764i	0.927275	+	0.374382i	$0.122145\pi$
$313$			4146.30i			0.748764i	−0.927275	+	0.374382i	$0.877855\pi$
$314$	−8406.42			−1.51083
$315$		0			0
$316$	−1970.64			−0.350814
$317$		−	6742.06i		−	1.19455i	−0.802037	−	0.597274i	$-0.796250\pi$
$317$		−	6742.06i		−	1.19455i	0.802037	−	0.597274i	$-0.203750\pi$
$318$	−871.653	+	4791.12i	−0.153710	+	0.844883i
$319$	14953.7			2.62459
$320$	3586.01			0.626450
$321$	−141.281	−	25.7033i	−0.0245655	−	0.00446922i
$322$		0			0
$323$		−	4645.03i		−	0.800174i
$324$	−1228.61	−	1077.25i	−0.210667	−	0.184713i
$325$			63.8085i			0.0108906i
$326$			4625.44i			0.785826i
$327$	337.254	−	1853.75i	0.0570342	−	0.313494i
$328$		−	2768.91i		−	0.466120i
$329$		0			0
$330$	2151.17	−	11824.1i	0.358842	−	1.97241i
$331$	1435.92			0.238445			0.119223	−	0.992868i	$-0.461960\pi$
$331$	1435.92			0.238445			0.119223	+	0.992868i	$0.461960\pi$
$332$	2509.36			0.414817
$333$	−2484.14	−	934.826i	−0.408800	−	0.153838i
$334$			8432.10i			1.38139i
$335$	−5768.78			−0.940842
$336$		0			0
$337$	−10555.0			−1.70613			−0.853066	−	0.521804i	$-0.825259\pi$
$337$	−10555.0			−1.70613			−0.853066	+	0.521804i	$0.825259\pi$
$338$			6992.53i			1.12528i
$339$	−2851.63	−	518.800i	−0.456872	−	0.0831190i
$340$	−872.255			−0.139131
$341$	12545.3			1.99228
$342$	11560.4	+	4350.38i	1.82782	+	0.687842i
$343$		0			0
$344$			1095.80i			0.171749i
$345$	−5504.10	−	1001.37i	−0.858930	−	0.156266i
$346$		−	1899.37i		−	0.295117i
$347$		−	10123.3i		−	1.56614i	−0.621936	−	0.783068i	$-0.713654\pi$
$347$		−	10123.3i		−	1.56614i	0.621936	−	0.783068i	$-0.286346\pi$
$348$	2839.40	+	516.573i	0.437378	+	0.0795725i
$349$		−	8986.21i		−	1.37828i	−0.724627	−	0.689141i	$-0.757988\pi$
$349$		−	8986.21i		−	1.37828i	0.724627	−	0.689141i	$-0.242012\pi$
$350$		0			0
$351$	−416.626	−	249.674i	−0.0633558	−	0.0379676i
$352$	5955.69			0.901817
$353$	−121.541			−0.0183257			−0.00916286	−	0.999958i	$-0.502917\pi$
$353$	−121.541			−0.0183257			−0.00916286	+	0.999958i	$0.502917\pi$
$354$	7618.97	+	1386.13i	1.14391	+	0.208112i
$355$		−	6589.33i		−	0.985142i
$356$	−47.7321			−0.00710617
$357$		0			0
$358$	−8445.75			−1.24685
$359$			1227.13i			0.180405i	0.995923	+	0.0902025i	$0.0287514\pi$
$359$			1227.13i			0.180405i	−0.995923	+	0.0902025i	$0.971249\pi$
$360$	−2098.82	+	5577.26i	−0.307271	+	0.816521i
$361$	−13576.2			−1.97933
$362$	−5692.08			−0.826434
$363$	−2149.17	+	11813.1i	−0.310750	+	1.70807i
$364$		0			0
$365$		−	4458.74i		−	0.639400i
$366$	−39.0832	+	214.825i	−0.00558173	+	0.0306805i
$367$			4743.63i			0.674702i	0.941379	+	0.337351i	$0.109531\pi$
$367$			4743.63i			0.674702i	−0.941379	+	0.337351i	$0.890469\pi$
$368$		−	6913.89i		−	0.979379i
$369$	3796.79	+	1428.80i	0.535645	+	0.201572i
$370$		−	3767.68i		−	0.529385i
$371$		0			0
$372$	2382.10	+	433.377i	0.332006	+	0.0604020i
$373$	3990.87			0.553993			0.276996	−	0.960871i	$-0.410661\pi$
$373$	3990.87			0.553993			0.276996	+	0.960871i	$0.410661\pi$
$374$	6275.30			0.867615
$375$	1187.05	−	6524.75i	0.163464	−	0.898497i
$376$		−	4291.11i		−	0.588557i
$377$	857.875			0.117196
$378$		0			0
$379$	11239.6			1.52332			0.761659	−	0.647978i	$-0.224385\pi$
$379$	11239.6			1.52332			0.761659	+	0.647978i	$0.224385\pi$
$380$			3837.37i			0.518035i
$381$	−966.145	+	5310.51i	−0.129914	+	0.714083i
$382$	4503.78			0.603229
$383$	−2856.23			−0.381061			−0.190530	−	0.981681i	$-0.561021\pi$
$383$	−2856.23			−0.381061			−0.190530	+	0.981681i	$0.561021\pi$
$384$	−8934.95	−	1625.54i	−1.18740	−	0.216024i
$385$		0			0
$386$		−	6378.47i		−	0.841077i
$387$	−1502.59	−	565.449i	−0.197366	−	0.0742724i
$388$			1373.84i			0.179758i
$389$			5117.16i			0.666967i	0.942756	+	0.333483i	$0.108224\pi$
$389$			5117.16i			0.666967i	−0.942756	+	0.333483i	$0.891776\pi$
$390$	123.410	−	678.335i	0.0160234	−	0.0880740i
$391$		−	2921.15i		−	0.377823i
$392$		0			0
$393$	−767.692	+	4219.70i	−0.0985368	+	0.541617i
$394$	10677.4			1.36528
$395$	−10529.4			−1.34125
$396$	−1286.28	+	3418.08i	−0.163228	+	0.433750i
$397$			11770.8i			1.48806i	0.668145	+	0.744031i	$0.267089\pi$
$397$			11770.8i			1.48806i	−0.668145	+	0.744031i	$0.732911\pi$
$398$	−8411.63			−1.05939
$399$		0			0
$400$	−1417.47			−0.177184
$401$		−	7064.59i		−	0.879773i	−0.898053	−	0.439886i	$-0.855019\pi$
$401$		−	7064.59i		−	0.879773i	0.898053	−	0.439886i	$-0.144981\pi$
$402$	7880.49	+	1433.70i	0.977720	+	0.177877i
$403$	719.711			0.0889611
$404$	764.424			0.0941374
$405$	−6564.65	−	5755.90i	−0.805433	−	0.706205i
$406$		0			0
$407$			5932.37i			0.722498i
$408$	−3061.30	−	556.944i	−0.371463	−	0.0675805i
$409$		−	116.430i		−	0.0140760i	−0.999975	−	0.00703800i	$-0.997760\pi$
$409$		−	116.430i		−	0.0140760i	0.999975	−	0.00703800i	$-0.00224028\pi$
$410$			5758.57i			0.693647i
$411$	−9663.31	−	1758.05i	−1.15975	−	0.210994i
$412$		−	1334.90i		−	0.159626i
$413$		0			0
$414$	7270.07	+	2735.85i	0.863054	+	0.324782i
$415$	13407.9			1.58595
$416$	341.672			0.0402688
$417$	−1030.37	−	187.456i	−0.121001	−	0.0220138i
$418$		−	27607.4i		−	3.23043i
$419$	15827.8			1.84544			0.922721	−	0.385469i	$-0.125960\pi$
$419$	15827.8			1.84544			0.922721	+	0.385469i	$0.125960\pi$
$420$		0			0
$421$	9126.46			1.05652			0.528262	−	0.849082i	$-0.322844\pi$
$421$	9126.46			1.05652			0.528262	+	0.849082i	$0.322844\pi$
$422$		−	6402.00i		−	0.738494i
$423$	5884.08	+	2214.28i	0.676344	+	0.254520i
$424$	−5396.87			−0.618149
$425$	−598.888			−0.0683537
$426$	−1637.64	+	9001.42i	−0.186253	+	1.02376i
$427$		0			0
$428$			61.9434i			0.00699567i
$429$	−194.314	+	1068.07i	−0.0218685	+	0.120202i
$430$		−	2278.96i		−	0.255584i
$431$			7030.17i			0.785688i	0.919605	+	0.392844i	$0.128509\pi$
$431$			7030.17i			0.785688i	−0.919605	+	0.392844i	$0.871491\pi$
$432$	5546.39	−	9255.14i	0.617710	−	1.03076i
$433$		−	3219.72i		−	0.357344i	−0.983909	−	0.178672i	$-0.942820\pi$
$433$		−	3219.72i		−	0.357344i	0.983909	−	0.178672i	$-0.0571801\pi$
$434$		0			0
$435$	15171.3	+	2760.13i	1.67221	+	0.304226i
$436$	−812.762			−0.0892758
$437$	−12851.2			−1.40677
$438$	−1108.12	+	6090.90i	−0.120886	+	0.664463i
$439$			8192.20i			0.890643i	0.895371	+	0.445322i	$0.146911\pi$
$439$			8192.20i			0.890643i	−0.895371	+	0.445322i	$0.853089\pi$
$440$	13319.0			1.44309
$441$		0			0
$442$	360.007			0.0387416
$443$		−	8513.16i		−	0.913030i	−0.889716	−	0.456515i	$-0.849097\pi$
$443$		−	8513.16i		−	0.913030i	0.889716	−	0.456515i	$-0.150903\pi$
$444$	−204.934	+	1126.44i	−0.0219048	+	0.120402i
$445$	−255.040			−0.0271687
$446$	−17524.5			−1.86055
$447$	11000.6	+	2001.34i	1.16400	+	0.211768i
$448$		0			0
$449$		−	7522.13i		−	0.790627i	−0.918546	−	0.395313i	$-0.870636\pi$
$449$		−	7522.13i		−	0.790627i	0.918546	−	0.395313i	$-0.129364\pi$
$450$	560.899	−	1490.50i	0.0587578	−	0.156139i
$451$		−	9067.10i		−	0.946681i
$452$			1250.28i			0.130106i
$453$	1676.96	−	9217.57i	0.173930	−	0.956025i
$454$		−	12395.0i		−	1.28133i
$455$		0			0
$456$	−2450.20	+	13467.8i	−0.251626	+	1.38308i
$457$	2743.19			0.280790			0.140395	−	0.990096i	$-0.455163\pi$
$457$	2743.19			0.280790			0.140395	+	0.990096i	$0.455163\pi$
$458$	6156.35			0.628095
$459$	2343.37	−	3910.33i	0.238299	−	0.397644i
$460$			2413.23i			0.244603i
$461$	5771.24			0.583066			0.291533	−	0.956561i	$-0.405835\pi$
$461$	5771.24			0.583066			0.291533	+	0.956561i	$0.405835\pi$
$462$		0			0
$463$	−7850.41			−0.787990			−0.393995	−	0.919113i	$-0.628907\pi$
$463$	−7850.41			−0.787990			−0.393995	+	0.919113i	$0.628907\pi$
$464$			19057.2i			1.90670i
$465$	12727.9	+	2315.60i	1.26934	+	0.230932i
$466$	−6326.04			−0.628859
$467$	−8750.90			−0.867117			−0.433558	−	0.901125i	$-0.642742\pi$
$467$	−8750.90			−0.867117			−0.433558	+	0.901125i	$0.642742\pi$
$468$	−73.7927	+	196.092i	−0.00728861	+	0.0193683i
$469$		0			0
$470$			8924.34i			0.875849i
$471$	13428.9	+	2443.14i	1.31374	+	0.239010i
$472$			8582.25i			0.836928i
$473$			3588.32i			0.348818i
$474$	14383.8	+	2616.86i	1.39382	+	0.253579i
$475$			2634.73i			0.254505i
$476$		0			0
$477$	2784.87	−	7400.32i	0.267317	−	0.710351i
$478$	3739.34			0.357811
$479$	−3902.82			−0.372285			−0.186143	−	0.982523i	$-0.559599\pi$
$479$	−3902.82			−0.372285			−0.186143	+	0.982523i	$0.559599\pi$
$480$	6042.40	+	1099.30i	0.574576	+	0.104533i
$481$			340.334i			0.0322617i
$482$	−19985.1			−1.88858
$483$		0			0
$484$	5179.38			0.486418
$485$			7340.62i			0.687259i
$486$	7537.20	+	9494.41i	0.703487	+	0.886163i
$487$	9800.27			0.911895			0.455947	−	0.890007i	$-0.349300\pi$
$487$	9800.27			0.911895			0.455947	+	0.890007i	$0.349300\pi$
$488$	−241.985			−0.0224470
$489$	1344.28	−	7388.97i	0.124316	−	0.683314i
$490$		0			0
$491$		−	4021.32i		−	0.369612i	−0.982775	−	0.184806i	$-0.940834\pi$
$491$		−	4021.32i		−	0.369612i	0.982775	−	0.184806i	$-0.0591657\pi$
$492$	313.223	−	1721.66i	0.0287016	−	0.157761i
$493$			8051.76i			0.735564i
$494$		−	1583.81i		−	0.144248i
$495$	−6872.82	+	18263.4i	−0.624061	+	1.65834i
$496$			15988.0i			1.44734i
$497$		0			0
$498$	−18316.0	−	3332.25i	−1.64811	−	0.299842i
$499$	−14860.6			−1.33317			−0.666585	−	0.745429i	$-0.732245\pi$
$499$	−14860.6			−1.33317			−0.666585	+	0.745429i	$0.732245\pi$
$500$	−2860.72			−0.255871
$501$	2450.60	−	13470.0i	0.218533	−	1.20119i
$502$			11489.8i			1.02154i
$503$	−12436.1			−1.10238			−0.551191	−	0.834379i	$-0.685826\pi$
$503$	−12436.1			−1.10238			−0.551191	+	0.834379i	$0.685826\pi$
$504$		0			0
$505$	4084.44			0.359911
$506$		−	17361.6i		−	1.52533i
$507$	2032.22	−	11170.3i	0.178016	−	0.978483i
$508$	2328.35			0.203354
$509$	1508.79			0.131387			0.0656935	−	0.997840i	$-0.479074\pi$
$509$	1508.79			0.131387			0.0656935	+	0.997840i	$0.479074\pi$
$510$	6366.65	+	1158.29i	0.552785	+	0.100569i
$511$		0			0
$512$		−	3748.39i		−	0.323549i
$513$	−17203.0	−	10309.4i	−1.48057	−	0.887269i
$514$		−	3047.33i		−	0.261502i
$515$		−	7132.57i		−	0.610289i
$516$	−123.958	+	681.349i	−0.0105755	+	0.0581293i
$517$		−	14051.7i		−	1.19535i
$518$		0			0
$519$	−552.008	+	3034.17i	−0.0466869	+	0.256619i
$520$	764.098			0.0644383
$521$	−5041.89			−0.423971			−0.211986	−	0.977273i	$-0.567993\pi$
$521$	−5041.89			−0.423971			−0.211986	+	0.977273i	$0.567993\pi$
$522$	−20039.0	−	7541.02i	−1.68024	−	0.632301i
$523$		−	11320.9i		−	0.946520i	−0.880923	−	0.473260i	$-0.843077\pi$
$523$		−	11320.9i		−	0.946520i	0.880923	−	0.473260i	$-0.156923\pi$
$524$	1850.09			0.154240
$525$		0			0
$526$	−16478.1			−1.36593
$527$			6754.99i			0.558353i
$528$	−23726.5	−	4316.59i	−1.95562	−	0.355787i
$529$	4085.19			0.335760
$530$	11224.0			0.919886
$531$	−11768.2	−	4428.57i	−0.961762	−	0.361928i
$532$		0			0
$533$		−	520.170i		−	0.0422721i
$534$	348.400	+	63.3847i	0.0282336	+	0.00513657i
$535$			330.973i			0.0267462i
$536$			8876.83i			0.715337i
$537$	13491.8	+	2454.57i	1.08420	+	0.197249i
$538$			22791.9i			1.82644i
$539$		0			0
$540$	−1935.92	+	3230.42i	−0.154275	+	0.257436i
$541$	−2725.44			−0.216591			−0.108295	−	0.994119i	$-0.534539\pi$
$541$	−2725.44			−0.216591			−0.108295	+	0.994119i	$0.534539\pi$
$542$	2581.90			0.204616
$543$	9092.89	+	1654.28i	0.718625	+	0.130740i
$544$			3206.83i			0.252742i
$545$	−4342.72			−0.341324
$546$		0			0
$547$	−2794.16			−0.218409			−0.109204	−	0.994019i	$-0.534830\pi$
$547$	−2794.16			−0.218409			−0.109204	+	0.994019i	$0.534830\pi$
$548$			4236.80i			0.330269i
$549$	124.868	−	331.816i	0.00970717	−	0.0257952i
$550$	−3559.44			−0.275955
$551$	35422.7			2.73876
$552$	−1540.87	+	8469.56i	−0.118811	+	0.653059i
$553$		0			0
$554$		−	17709.9i		−	1.35816i
$555$	−1094.99	+	6018.73i	−0.0837475	+	0.460326i
$556$			451.757i			0.0344582i
$557$			9812.66i			0.746455i	0.927740	+	0.373228i	$0.121749\pi$
$557$			9812.66i			0.746455i	−0.927740	+	0.373228i	$0.878251\pi$
$558$	−16811.6	−	6326.50i	−1.27544	−	0.479968i
$559$			205.858i			0.0155758i
$560$		0			0
$561$	−10024.6	−	1823.78i	−0.754433	−	0.137255i
$562$	−25771.0			−1.93432
$563$	7765.81			0.581332			0.290666	−	0.956825i	$-0.406123\pi$
$563$	7765.81			0.581332			0.290666	+	0.956825i	$0.406123\pi$
$564$	485.417	−	2668.14i	0.0362407	−	0.199200i
$565$			6680.43i			0.497429i
$566$	13675.8			1.01561
$567$		0			0
$568$	−10139.5			−0.749020
$569$			17119.1i			1.26128i	0.776074	+	0.630642i	$0.217208\pi$
$569$			17119.1i			1.26128i	−0.776074	+	0.630642i	$0.782792\pi$
$570$	5095.75	−	28009.3i	0.374452	−	2.05821i
$571$	9591.66			0.702974			0.351487	−	0.936193i	$-0.385676\pi$
$571$	9591.66			0.702974			0.351487	+	0.936193i	$0.385676\pi$
$572$	468.286			0.0342308
$573$	−7194.63	−	1308.92i	−0.524537	−	0.0954295i
$574$		0			0
$575$			1656.92i			0.120171i
$576$	7566.49	+	2847.40i	0.547344	+	0.205975i
$577$		−	12488.1i		−	0.901015i	−0.892773	−	0.450508i	$-0.851243\pi$
$577$		−	12488.1i		−	0.901015i	0.892773	−	0.450508i	$-0.148757\pi$
$578$		−	12343.8i		−	0.888293i
$579$	−1853.76	+	10189.4i	−0.133056	+	0.731357i
$580$		−	6651.76i		−	0.476206i
$581$		0			0
$582$	1824.35	−	10027.7i	0.129934	−	0.714197i
$583$	−17672.7			−1.25545
$584$	−6860.98			−0.486146
$585$	−394.286	+	1047.75i	−0.0278662	+	0.0740498i
$586$			16626.0i			1.17204i
$587$	−7385.70			−0.519319			−0.259660	−	0.965700i	$-0.583610\pi$
$587$	−7385.70			−0.519319			−0.259660	+	0.965700i	$0.583610\pi$
$588$		0			0
$589$	29717.7			2.07894
$590$		−	17848.7i		−	1.24546i
$591$	−17056.8	−	3103.15i	−1.18718	−	0.215984i
$592$	−7560.33			−0.524878
$593$	−26052.0			−1.80409			−0.902047	−	0.431638i	$-0.857936\pi$
$593$	−26052.0			−1.80409			−0.902047	+	0.431638i	$0.857936\pi$
$594$	13927.6	−	23240.8i	0.962051	−	1.60535i
$595$		0			0
$596$		−	4823.11i		−	0.331480i
$597$	13437.3	+	2444.65i	0.921191	+	0.167593i
$598$		−	996.016i		−	0.0681106i
$599$		−	15788.5i		−	1.07696i	−0.842638	−	0.538480i	$-0.818999\pi$
$599$		−	15788.5i		−	1.07696i	0.842638	−	0.538480i	$-0.181001\pi$
$600$	1736.41	+	315.907i	0.118148	+	0.0214947i
$601$			27175.5i			1.84445i	0.386658	+	0.922223i	$0.373629\pi$
$601$			27175.5i			1.84445i	−0.386658	+	0.922223i	$0.626371\pi$
$602$		0			0
$603$	−12172.1	−	4580.58i	−0.822035	−	0.309346i
$604$	−4041.37			−0.272253
$605$	27674.2			1.85970
$606$	−5579.59	−	1015.10i	−0.374019	−	0.0680455i
$607$		−	17900.4i		−	1.19696i	−0.801138	−	0.598480i	$-0.795772\pi$
$607$		−	17900.4i		−	1.19696i	0.801138	−	0.598480i	$-0.204228\pi$
$608$	14108.0			0.941047
$609$		0			0
$610$	503.263			0.0334041
$611$		−	806.133i		−	0.0533758i
$612$	−1840.46	−	692.596i	−0.121562	−	0.0457460i
$613$	−14607.7			−0.962478			−0.481239	−	0.876589i	$-0.659813\pi$
$613$	−14607.7			−0.962478			−0.481239	+	0.876589i	$0.659813\pi$
$614$	−17150.9			−1.12729
$615$	1673.60	−	9199.10i	0.109733	−	0.603160i
$616$		0			0
$617$			23934.5i			1.56170i	0.624721	+	0.780848i	$0.285213\pi$
$617$			23934.5i			1.56170i	−0.624721	+	0.780848i	$0.714787\pi$
$618$	−1772.65	+	9743.52i	−0.115382	+	0.634210i
$619$		−	20858.7i		−	1.35441i	−0.735793	−	0.677207i	$-0.763190\pi$
$619$		−	20858.7i		−	1.35441i	0.735793	−	0.677207i	$-0.236810\pi$
$620$		−	5580.46i		−	0.361479i
$621$	−10818.6	−	6483.30i	−0.699088	−	0.418947i
$622$			28939.6i			1.86555i
$623$		0			0
$624$	−1361.17	−	247.638i	−0.0873241	−	0.0158869i
$625$	−17589.2			−1.12571
$626$	−13269.1			−0.847188
$627$	−8023.47	+	44101.8i	−0.511047	+	2.80902i
$628$		−	5887.82i		−	0.374123i
$629$	−3194.27			−0.202486
$630$		0			0
$631$	2986.73			0.188431			0.0942155	−	0.995552i	$-0.469966\pi$
$631$	2986.73			0.188431			0.0942155	+	0.995552i	$0.469966\pi$
$632$			16202.4i			1.01977i
$633$	−1860.60	+	10227.0i	−0.116828	+	0.642157i
$634$	21576.1			1.35157
$635$	12440.8			0.777474
$636$	−3355.68	−	610.501i	−0.209216	−	0.0380628i
$637$		0			0
$638$			47855.0i			2.96959i
$639$	5232.13	−	13903.5i	0.323912	−	0.860742i
$640$			20931.6i			1.29280i
$641$			64.5977i			0.00398043i	0.999998	+	0.00199021i	$0.000633505\pi$
$641$			64.5977i			0.00398043i	−0.999998	+	0.00199021i	$0.999366\pi$
$642$	82.2562	−	452.129i	0.00505669	−	0.0277946i
$643$		−	18370.0i		−	1.12666i	−0.826232	−	0.563330i	$-0.809520\pi$
$643$		−	18370.0i		−	1.12666i	0.826232	−	0.563330i	$-0.190480\pi$
$644$		0			0
$645$	−662.329	+	3640.56i	−0.0404329	+	0.222243i
$646$	14865.1			0.905357
$647$	13583.6			0.825389			0.412694	−	0.910870i	$-0.364588\pi$
$647$	13583.6			0.825389			0.412694	+	0.910870i	$0.364588\pi$
$648$	−8857.02	+	10101.5i	−0.536939	+	0.612383i
$649$			28103.5i			1.69978i
$650$	−204.201			−0.0123222
$651$		0			0
$652$	−3239.63			−0.194592
$653$		−	18842.8i		−	1.12922i	−0.825359	−	0.564608i	$-0.809028\pi$
$653$		−	18842.8i		−	1.12922i	0.825359	−	0.564608i	$-0.190972\pi$
$654$	5932.41	+	1079.29i	0.354703	+	0.0645313i
$655$	9885.34			0.589698
$656$	11555.3			0.687741
$657$	3540.37	−	9407.94i	0.210233	−	0.558659i
$658$		0			0
$659$		−	7348.15i		−	0.434360i	−0.976132	−	0.217180i	$-0.930314\pi$
$659$		−	7348.15i		−	0.434360i	0.976132	−	0.217180i	$-0.0696859\pi$
$660$	8281.54	+	1506.67i	0.488422	+	0.0888590i
$661$			24656.9i			1.45090i	0.688276	+	0.725449i	$0.258368\pi$
$661$			24656.9i			1.45090i	−0.688276	+	0.725449i	$0.741632\pi$
$662$			4595.27i			0.269789i
$663$	−575.098	−	104.628i	−0.0336877	−	0.00612883i
$664$		−	20631.7i		−	1.20582i
$665$		0			0
$666$	2991.65	−	7949.81i	0.174060	−	0.462536i
$667$	22276.5			1.29318
$668$	−5905.80			−0.342070
$669$	27994.7	+	5093.09i	1.61784	+	0.294335i
$670$		−	18461.4i		−	1.06451i
$671$	−792.408			−0.0455895
$672$		0			0
$673$	4465.46			0.255767			0.127883	−	0.991789i	$-0.459182\pi$
$673$	4465.46			0.255767			0.127883	+	0.991789i	$0.459182\pi$
$674$		−	33778.3i		−	1.93040i
$675$	−1329.19	+	2218.00i	−0.0757937	+	0.126475i
$676$	−4897.53			−0.278649
$677$	−12986.1			−0.737218			−0.368609	−	0.929585i	$-0.620166\pi$
$677$	−12986.1			−0.737218			−0.368609	+	0.929585i	$0.620166\pi$
$678$	1660.27	−	9125.86i	0.0940449	−	0.516927i
$679$		0			0
$680$			7171.59i			0.404438i
$681$	−3602.33	+	19800.5i	−0.202704	+	1.11418i
$682$			40147.8i			2.25416i
$683$			6369.97i			0.356867i	0.983952	+	0.178433i	$0.0571029\pi$
$683$			6369.97i			0.356867i	−0.983952	+	0.178433i	$0.942897\pi$
$684$	−3046.99	+	8096.86i	−0.170328	+	0.452619i
$685$			22637.9i			1.26270i
$686$		0			0
$687$	−9834.55	−	1789.21i	−0.546159	−	0.0993632i
$688$	−4573.03			−0.253408
$689$	−1013.86			−0.0560596
$690$	3204.59	−	17614.4i	0.176807	−	0.971836i
$691$		−	5802.65i		−	0.319455i	−0.987161	−	0.159727i	$-0.948938\pi$
$691$		−	5802.65i		−	0.319455i	0.987161	−	0.159727i	$-0.0510615\pi$
$692$	1330.31			0.0730790
$693$		0			0
$694$	32396.9			1.77200
$695$			2413.81i			0.131743i
$696$	4247.22	−	23345.2i	0.231308	−	1.27141i
$697$	4882.16			0.265315
$698$	28757.9			1.55946
$699$	10105.6	+	1838.52i	0.546824	+	0.0994840i
$700$		0			0
$701$			1479.34i			0.0797058i	0.999206	+	0.0398529i	$0.0126889\pi$
$701$			1479.34i			0.0797058i	−0.999206	+	0.0398529i	$0.987311\pi$
$702$	799.014	−	1333.30i	0.0429584	−	0.0716838i
$703$			14052.8i			0.753927i
$704$		−	18069.5i		−	0.967357i
$705$	2593.66	−	14256.3i	0.138557	−	0.761593i
$706$		−	388.958i		−	0.0207346i
$707$		0			0
$708$	−970.836	+	5336.29i	−0.0515342	+	0.283263i
$709$	20247.8			1.07253			0.536264	−	0.844050i	$-0.319835\pi$
$709$	20247.8			1.07253			0.536264	+	0.844050i	$0.319835\pi$
$710$	21087.3			1.11464
$711$	−22217.1	−	8360.69i	−1.17188	−	0.440999i
$712$			392.449i			0.0206568i
$713$	18688.7			0.981625
$714$		0			0
$715$	2502.12			0.130873
$716$		−	5915.37i		−	0.308754i
$717$	−5973.46	−	1086.76i	−0.311134	−	0.0566048i
$718$	−3927.08			−0.204119
$719$	−20722.0			−1.07482			−0.537412	−	0.843320i	$-0.680598\pi$
$719$	−20722.0			−1.07482			−0.537412	+	0.843320i	$0.680598\pi$
$720$	−23275.2	−	8758.86i	−1.20474	−	0.453366i
$721$		0			0
$722$		−	43446.9i		−	2.23951i
$723$	31925.5	+	5808.23i	1.64222	+	0.298770i
$724$		−	3986.71i		−	0.204648i
$725$		−	4567.08i		−	0.233954i
$726$	−37804.7	−	6877.83i	−1.93259	−	0.351598i
$727$		−	6251.88i		−	0.318940i	−0.987203	−	0.159470i	$-0.949021\pi$
$727$		−	6251.88i		−	0.318940i	0.987203	−	0.159470i	$-0.0509785\pi$
$728$		0			0
$729$	−9281.07	−	17357.5i	−0.471527	−	0.881852i
$730$	14269.0			0.723449
$731$	−1932.12			−0.0977594
$732$	−150.462	−	27.3737i	−0.00759733	−	0.00138219i
$733$		−	36709.5i		−	1.84979i	−0.380220	−	0.924896i	$-0.624152\pi$
$733$		−	36709.5i		−	1.84979i	0.380220	−	0.924896i	$-0.375848\pi$
$734$	−15180.7			−0.763391
$735$		0			0
$736$	8872.20			0.444339
$737$			29068.2i			1.45284i
$738$	−4572.47	+	12150.6i	−0.228069	+	0.606055i
$739$	−26973.7			−1.34268			−0.671341	−	0.741148i	$-0.734282\pi$
$739$	−26973.7			−1.34268			−0.671341	+	0.741148i	$0.734282\pi$
$740$	2638.87			0.131090
$741$	−460.298	+	2530.07i	−0.0228198	+	0.125431i
$742$		0			0
$743$		−	14303.4i		−	0.706246i	−0.935577	−	0.353123i	$-0.885120\pi$
$743$		−	14303.4i		−	0.706246i	0.935577	−	0.353123i	$-0.114880\pi$
$744$	3563.18	−	19585.4i	0.175582	−	0.965101i
$745$		−	25770.6i		−	1.26733i
$746$			12771.7i			0.626815i
$747$	28290.7	+	10646.3i	1.38568	+	0.521455i
$748$			4395.19i			0.214845i
$749$		0			0
$750$	20880.6	+	3798.83i	1.01660	+	0.184952i
$751$	−3720.67			−0.180784			−0.0903921	−	0.995906i	$-0.528812\pi$
$751$	−3720.67			−0.180784			−0.0903921	+	0.995906i	$0.528812\pi$
$752$	17907.8			0.868392
$753$	3339.25	−	18354.5i	0.161606	−	0.888281i
$754$			2745.39i			0.132601i
$755$	−21593.7			−1.04089
$756$		0			0
$757$	107.033			0.00513896			0.00256948	−	0.999997i	$-0.499182\pi$
$757$	107.033			0.00513896			0.00256948	+	0.999997i	$0.499182\pi$
$758$			35969.1i			1.72356i
$759$	−5045.76	+	27734.5i	−0.241304	+	1.32635i
$760$	31550.5			1.50586
$761$	15183.9			0.723279			0.361639	−	0.932318i	$-0.382217\pi$
$761$	15183.9			0.723279			0.361639	+	0.932318i	$0.382217\pi$
$762$	−16994.8	−	3091.88i	−0.807949	−	0.146991i
$763$		0			0
$764$			3154.43i			0.149376i
$765$	−9833.86	−	3700.65i	−0.464764	−	0.174898i
$766$		−	9140.55i		−	0.431151i
$767$			1612.27i			0.0759005i
$768$	2974.19	−	16347.9i	0.139742	−	0.768105i
$769$			23780.6i			1.11515i	0.830126	+	0.557576i	$0.188268\pi$
$769$			23780.6i			1.11515i	−0.830126	+	0.557576i	$0.811732\pi$
$770$		0			0
$771$	−885.639	+	4868.00i	−0.0413690	+	0.227389i
$772$	4467.45			0.208273
$773$	−24377.3			−1.13427			−0.567135	−	0.823625i	$-0.691948\pi$
$773$	−24377.3			−1.13427			−0.567135	+	0.823625i	$0.691948\pi$
$774$	1809.56	−	4808.61i	0.0840354	−	0.223310i
$775$		−	3831.53i		−	0.177591i
$776$	11295.5			0.522534
$777$		0			0
$778$	−16376.0			−0.754639
$779$		−	21478.4i		−	0.987862i
$780$	475.103	+	86.4358i	0.0218095	+	0.00396782i
$781$	−33202.9			−1.52124
$782$	9348.31			0.427487
$783$	29819.9	+	17870.4i	1.36102	+	0.815626i
$784$		0			0
$785$		−	31459.5i		−	1.43037i
$786$	−13504.0	−	2456.79i	−0.612812	−	0.111489i
$787$		−	4388.52i		−	0.198772i	−0.995049	−	0.0993862i	$-0.968312\pi$
$787$		−	4388.52i		−	0.198772i	0.995049	−	0.0993862i	$-0.0316879\pi$
$788$			7478.40i			0.338080i
$789$	26323.2	+	4789.00i	1.18775	+	0.216087i
$790$		−	33696.5i		−	1.51756i
$791$		0			0
$792$	28103.1	+	10575.7i	1.26086	+	0.474484i
$793$	−45.4596			−0.00203571
$794$	−37669.3			−1.68367
$795$	−17929.9	−	3262.01i	−0.799886	−	0.145524i
$796$		−	5891.47i		−	0.262334i
$797$	−38506.3			−1.71137			−0.855685	−	0.517497i	$-0.826864\pi$
$797$	−38506.3			−1.71137			−0.855685	+	0.517497i	$0.826864\pi$
$798$		0			0
$799$	7566.12			0.335006
$800$		−	1818.96i		−	0.0803875i
$801$	−538.135	−	202.510i	−0.0237379	−	0.00893299i
$802$	22608.3			0.995418
$803$	−22467.1			−0.987354
$804$	−1004.16	+	5519.46i	−0.0440472	+	0.242110i
$805$		0			0
$806$			2303.23i			0.100655i
$807$	6623.94	−	36409.1i	0.288939	−	1.58818i
$808$		−	6285.02i		−	0.273646i
$809$		−	12120.4i		−	0.526737i	−0.964695	−	0.263369i	$-0.915166\pi$
$809$		−	12120.4i		−	0.526737i	0.964695	−	0.263369i	$-0.0848336\pi$
$810$	18420.2	−	21008.3i	0.799035	−	0.911306i
$811$		−	28763.6i		−	1.24541i	−0.782458	−	0.622703i	$-0.786034\pi$
$811$		−	28763.6i		−	1.24541i	0.782458	−	0.622703i	$-0.213966\pi$
$812$		0			0
$813$	−4124.49	−	750.372i	−0.177924	−	0.0323698i
$814$	−18984.9			−0.817470
$815$	−17309.9			−0.743974
$816$	2324.26	−	12775.5i	0.0997123	−	0.548078i
$817$			8500.12i			0.363992i
$818$	372.601			0.0159263
$819$		0			0
$820$	−4033.27			−0.171766
$821$		−	11399.6i		−	0.484590i	−0.970203	−	0.242295i	$-0.922100\pi$
$821$		−	11399.6i		−	0.484590i	0.970203	−	0.242295i	$-0.0779002\pi$
$822$	5626.16	−	30924.7i	0.238729	−	1.31219i
$823$	−19367.9			−0.820318			−0.410159	−	0.912014i	$-0.634527\pi$
$823$	−19367.9			−0.820318			−0.410159	+	0.912014i	$0.634527\pi$
$824$	−10975.4			−0.464012
$825$	5686.08	+	1034.47i	0.239956	+	0.0436554i
$826$		0			0
$827$			20414.5i			0.858382i	0.903214	+	0.429191i	$0.141201\pi$
$827$			20414.5i			0.858382i	−0.903214	+	0.429191i	$0.858799\pi$
$828$	−1916.18	+	5091.92i	−0.0804248	+	0.213716i
$829$		−	406.747i		−	0.0170409i	−0.999964	−	0.00852045i	$-0.997288\pi$
$829$		−	406.747i		−	0.0170409i	0.999964	−	0.00852045i	$-0.00271218\pi$
$830$			42908.3i			1.79442i
$831$	−5146.97	+	28290.8i	−0.214857	+	1.18098i
$832$		−	1036.63i		−	0.0431954i
$833$		0			0
$834$	599.900	−	3297.41i	0.0249075	−	0.136906i
$835$	−31555.7			−1.30782
$836$	19336.1			0.799943
$837$	25017.3	+	14992.3i	1.03312	+	0.619127i
$838$			50652.6i			2.08802i
$839$	22418.0			0.922475			0.461238	−	0.887277i	$-0.347406\pi$
$839$	22418.0			0.922475			0.461238	+	0.887277i	$0.347406\pi$
$840$		0			0
$841$	−37013.2			−1.51762
$842$			29206.7i			1.19540i
$843$	41168.3	+	7489.78i	1.68198	+	0.306004i
$844$	4483.93			0.182871
$845$	−26168.3			−1.06535
$846$	−7086.19	+	18830.4i	−0.287976	+	0.765249i
$847$		0			0
$848$		−	22522.4i		−	0.912054i
$849$	−21846.6	−	3974.57i	−0.883125	−	0.160668i
$850$		−	1916.57i		−	0.0773387i
$851$			8837.45i			0.355986i
$852$	−6304.55	−	1146.99i	−0.253510	−	0.0461212i
$853$			43457.5i			1.74438i	0.489167	+	0.872190i	$0.337301\pi$
$853$			43457.5i			1.74438i	−0.489167	+	0.872190i	$0.662699\pi$
$854$		0			0
$855$	−16280.5	+	43262.8i	−0.651208	+	1.73048i
$856$	509.293			0.0203356
$857$	29746.2			1.18566			0.592830	−	0.805328i	$-0.298011\pi$
$857$	29746.2			1.18566			0.592830	+	0.805328i	$0.298011\pi$
$858$	−3418.05	−	621.849i	−0.136003	−	0.0247431i
$859$		−	33883.6i		−	1.34586i	−0.739705	−	0.672931i	$-0.765035\pi$
$859$		−	33883.6i		−	1.34586i	0.739705	−	0.672931i	$-0.234965\pi$
$860$	1596.17			0.0632896
$861$		0			0
$862$	−22498.1			−0.888966
$863$		−	4716.58i		−	0.186042i	−0.995664	−	0.0930211i	$-0.970348\pi$
$863$		−	4716.58i		−	0.186042i	0.995664	−	0.0930211i	$-0.0296524\pi$
$864$	11876.6	+	7117.36i	0.467650	+	0.280252i
$865$	7108.04			0.279400
$866$	10303.8			0.404317
$867$	−3587.44	+	19718.7i	−0.140526	+	0.772414i
$868$		0			0
$869$			53056.6i			2.07114i
$870$	−8833.04	+	48551.7i	−0.344216	+	1.89202i
$871$			1667.61i			0.0648735i
$872$			6682.45i			0.259514i
$873$	−5828.67	+	15488.7i	−0.225969	+	0.600474i
$874$		−	41126.7i		−	1.59168i
$875$		0			0
$876$	−4266.04	−	776.124i	−0.164539	−	0.0299347i
$877$	44155.6			1.70015			0.850073	−	0.526665i	$-0.176558\pi$
$877$	44155.6			1.70015			0.850073	+	0.526665i	$0.176558\pi$
$878$	−26216.9			−1.00772
$879$	4831.99	−	26559.5i	0.185414	−	1.01915i
$880$			55583.4i			2.12922i
$881$	42589.0			1.62867			0.814336	−	0.580393i	$-0.197101\pi$
$881$	42589.0			1.62867			0.814336	+	0.580393i	$0.197101\pi$
$882$		0			0
$883$	−30605.4			−1.16643			−0.583213	−	0.812319i	$-0.698205\pi$
$883$	−30605.4			−1.16643			−0.583213	+	0.812319i	$0.698205\pi$
$884$			252.147i			0.00959347i
$885$	−5187.33	+	28512.7i	−0.197028	+	1.08299i
$886$	27244.0			1.03305
$887$	−24997.4			−0.946257			−0.473128	−	0.880993i	$-0.656875\pi$
$887$	−24997.4			−0.946257			−0.473128	+	0.880993i	$0.656875\pi$
$888$	9261.46	+	1684.94i	0.349993	+	0.0636745i
$889$		0			0
$890$		−	816.186i		−	0.0307400i
$891$	−29003.3	+	33078.5i	−1.09051	+	1.24374i
$892$		−	12274.0i		−	0.460723i
$893$		−	33286.2i		−	1.24735i
$894$	−6404.73	+	35204.2i	−0.239604	+	1.31701i
$895$		−	31606.7i		−	1.18044i
$896$		0			0
$897$	−289.470	+	1591.10i	−0.0107749	+	0.0592255i
$898$	24072.5			0.894554
$899$	−51513.1			−1.91108
$900$	1043.94	+	392.851i	0.0386643	+	0.0145500i
$901$		−	9515.80i		−	0.351850i
$902$	29016.7			1.07112
$903$		0			0
$904$	10279.6			0.378204
$905$		−	21301.6i		−	0.782419i
$906$	29498.3	+	5366.64i	1.08169	+	0.196793i
$907$	−1336.70			−0.0489355			−0.0244677	−	0.999701i	$-0.507789\pi$
$907$	−1336.70			−0.0489355			−0.0244677	+	0.999701i	$0.507789\pi$
$908$	8681.39			0.317293
$909$	8618.17	+	3243.16i	0.314463	+	0.118338i
$910$		0			0
$911$			4107.48i			0.149382i	0.997207	+	0.0746909i	$0.0237970\pi$
$911$			4107.48i			0.149382i	−0.997207	+	0.0746909i	$0.976203\pi$
$912$	−56204.2	−	10225.3i	−2.04069	−	0.371264i
$913$		−	67560.9i		−	2.44900i
$914$			8778.81i			0.317700i
$915$	−803.944	−	146.262i	−0.0290465	−	0.00528445i
$916$			4311.88i			0.155533i
$917$		0			0
$918$	12513.9	+	7499.30i	0.449914	+	0.269623i
$919$	−39927.8			−1.43318			−0.716592	−	0.697492i	$-0.754299\pi$
$919$	−39927.8			−1.43318			−0.716592	+	0.697492i	$0.754299\pi$
$920$	19841.3			0.711033
$921$	27397.9	+	4984.52i	0.980230	+	0.178334i
$922$			18469.3i			0.659710i
$923$	−1904.81			−0.0679281
$924$		0			0
$925$	1811.84			0.0644031
$926$		−	25123.0i		−	0.891571i
$927$	5663.47	−	15049.7i	0.200661	−	0.533224i
$928$	−24455.1			−0.865061
$929$	18802.6			0.664041			0.332020	−	0.943272i	$-0.392270\pi$
$929$	18802.6			0.664041			0.332020	+	0.943272i	$0.392270\pi$
$930$	−7410.44	+	40732.2i	−0.261288	+	1.43620i
$931$		0			0
$932$		−	4430.73i		−	0.155723i
$933$	8410.64	−	46229.9i	0.295125	−	1.62219i
$934$		−	28004.8i		−	0.981099i
$935$			23484.2i			0.821407i
$936$	1612.25	+	606.716i	0.0563012	+	0.0211871i
$937$			4022.67i			0.140251i	0.997538	+	0.0701254i	$0.0223400\pi$
$937$			4022.67i			0.140251i	−0.997538	+	0.0701254i	$0.977660\pi$
$938$		0			0
$939$	21196.9	+	3856.37i	0.736671	+	0.134023i
$940$	−6250.56			−0.216884
$941$	−21484.8			−0.744299			−0.372150	−	0.928173i	$-0.621379\pi$
$941$	−21484.8			−0.744299			−0.372150	+	0.928173i	$0.621379\pi$
$942$	−7818.58	+	42975.6i	−0.270428	+	1.48643i
$943$		−	13507.3i		−	0.466444i
$944$	−35815.7			−1.23485
$945$		0			0
$946$	−11483.4			−0.394670
$947$			56097.0i			1.92493i	0.271405	+	0.962465i	$0.412512\pi$
$947$			56097.0i			1.92493i	−0.271405	+	0.962465i	$0.587488\pi$
$948$	−1832.84	+	10074.4i	−0.0627931	+	0.345148i
$949$	−1288.91			−0.0440883
$950$	−8431.72			−0.287959
$951$	−34467.0	−	6270.61i	−1.17526	−	0.213815i
$952$		0			0
$953$		−	31294.8i		−	1.06373i	−0.846828	−	0.531866i	$-0.821491\pi$
$953$		−	31294.8i		−	1.06373i	0.846828	−	0.531866i	$-0.178509\pi$
$954$	23682.7	+	8912.19i	0.803726	+	0.302456i
$955$			16854.6i			0.571102i
$956$			2619.02i			0.0886036i
$957$	13908.0	−	76446.6i	0.469782	−	2.58220i
$958$		−	12489.9i		−	0.421222i
$959$		0			0
$960$	3335.25	−	18332.5i	0.112130	−	0.616333i
$961$	−13425.7			−0.450663
$962$	−1089.14			−0.0365025
$963$	−262.803	+	698.354i	−0.00879408	+	0.0233688i
$964$		−	13997.5i		−	0.467665i
$965$	23870.3			0.796282
$966$		0			0
$967$	−25395.3			−0.844527			−0.422263	−	0.906473i	$-0.638764\pi$
$967$	−25395.3			−0.844527			−0.422263	+	0.906473i	$0.638764\pi$
$968$		−	42584.3i		−	1.41396i
$969$	−23746.5	−	4320.22i	−0.787252	−	0.143225i
$970$	−23491.6			−0.777599
$971$	12397.5			0.409737			0.204868	−	0.978790i	$-0.434323\pi$
$971$	12397.5			0.409737			0.204868	+	0.978790i	$0.434323\pi$
$972$	−6649.84	+	5279.02i	−0.219438	+	0.174202i
$973$		0			0
$974$			31363.1i			1.03176i
$975$	326.204	+	59.3466i	0.0107148	+	0.00194935i
$976$		−	1009.86i		−	0.0331197i
$977$		−	9705.95i		−	0.317831i	−0.987292	−	0.158916i	$-0.949200\pi$
$977$		−	9705.95i		−	0.317831i	0.987292	−	0.158916i	$-0.0507998\pi$
$978$	23646.3	+	4301.99i	0.773135	+	0.140657i
$979$			1285.12i			0.0419536i
$980$		0			0
$981$	−9163.14	−	3448.25i	−0.298223	−	0.112226i
$982$	12869.1			0.418197
$983$	50242.8			1.63021			0.815105	−	0.579313i	$-0.196679\pi$
$983$	50242.8			1.63021			0.815105	+	0.579313i	$0.196679\pi$
$984$	−14155.3	−	2575.29i	−0.458592	−	0.0834320i
$985$			39958.3i			1.29257i
$986$	−25767.4			−0.832253
$987$		0			0
$988$	1109.29			0.0357198
$989$			5345.52i			0.171868i
$990$	−58446.8	−	21994.5i	−1.87633	−	0.706093i
$991$	−24755.2			−0.793518			−0.396759	−	0.917923i	$-0.629865\pi$
$991$	−24755.2			−0.793518			−0.396759	+	0.917923i	$0.629865\pi$
$992$	−20516.5			−0.656652
$993$	1335.51	−	7340.77i	0.0426799	−	0.234594i
$994$		0			0
$995$		−	31479.1i		−	1.00297i
$996$	2333.89	−	12828.5i	0.0742491	−	0.408118i
$997$			8353.89i			0.265367i	0.991158	+	0.132683i	$0.0423593\pi$
$997$			8353.89i			0.265367i	−0.991158	+	0.132683i	$0.957641\pi$
$998$		−	47557.2i		−	1.50841i
$999$	−7089.49	+	11830.1i	−0.224526	+	0.374662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.c.b.146.20	yes	24
3.2	odd	2	inner	147.4.c.b.146.5	✓	24
7.2	even	3		147.4.g.e.80.20		48
7.3	odd	6		147.4.g.e.68.6		48
7.4	even	3		147.4.g.e.68.5		48
7.5	odd	6		147.4.g.e.80.19		48
7.6	odd	2	inner	147.4.c.b.146.19	yes	24
21.2	odd	6		147.4.g.e.80.6		48
21.5	even	6		147.4.g.e.80.5		48
21.11	odd	6		147.4.g.e.68.19		48
21.17	even	6		147.4.g.e.68.20		48
21.20	even	2	inner	147.4.c.b.146.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.c.b.146.5	✓	24	3.2	odd	2	inner
147.4.c.b.146.6	yes	24	21.20	even	2	inner
147.4.c.b.146.19	yes	24	7.6	odd	2	inner
147.4.c.b.146.20	yes	24	1.1	even	1	trivial
147.4.g.e.68.5		48	7.4	even	3
147.4.g.e.68.6		48	7.3	odd	6
147.4.g.e.68.19		48	21.11	odd	6
147.4.g.e.68.20		48	21.17	even	6
147.4.g.e.80.5		48	21.5	even	6
147.4.g.e.80.6		48	21.2	odd	6
147.4.g.e.80.19		48	7.5	odd	6
147.4.g.e.80.20		48	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.20022i q^{2} +(0.930073 - 5.11224i) q^{3} -2.24142 q^{4} -11.9763 q^{5} +(16.3603 + 2.97644i) q^{6} +18.4287i q^{8} +(-25.2699 - 9.50951i) q^{9} +O(q^{10})\)	\(q+3.20022i q^{2} +(0.930073 - 5.11224i) q^{3} -2.24142 q^{4} -11.9763 q^{5} +(16.3603 + 2.97644i) q^{6} +18.4287i q^{8} +(-25.2699 - 9.50951i) q^{9} -38.3267i q^{10} +60.3470i q^{11} +(-2.08468 + 11.4587i) q^{12} +3.46204i q^{13} +(-11.1388 + 61.2255i) q^{15} -76.9074 q^{16} -32.4937 q^{17} +(30.4325 - 80.8694i) q^{18} +142.952i q^{19} +26.8438 q^{20} -193.124 q^{22} +89.8989i q^{23} +(94.2120 + 17.1401i) q^{24} +18.4309 q^{25} -11.0793 q^{26} +(-72.1177 + 120.341i) q^{27} -247.795i q^{29} +(-195.935 - 35.6466i) q^{30} -207.886i q^{31} -98.6909i q^{32} +(308.508 + 56.1271i) q^{33} -103.987i q^{34} +(56.6405 + 21.3148i) q^{36} +98.3044 q^{37} -457.477 q^{38} +(17.6988 + 3.21995i) q^{39} -220.707i q^{40} -150.249 q^{41} +59.4615 q^{43} -135.263i q^{44} +(302.639 + 113.888i) q^{45} -287.696 q^{46} -232.849 q^{47} +(-71.5295 + 393.169i) q^{48} +58.9830i q^{50} +(-30.2215 + 166.115i) q^{51} -7.75989i q^{52} +292.851i q^{53} +(-385.119 - 230.793i) q^{54} -722.731i q^{55} +(730.803 + 132.956i) q^{57} +792.998 q^{58} +465.699 q^{59} +(24.9667 - 137.232i) q^{60} +13.1309i q^{61} +665.282 q^{62} -299.427 q^{64} -41.4623i q^{65} +(-179.619 + 987.294i) q^{66} +481.684 q^{67} +72.8320 q^{68} +(459.584 + 83.6125i) q^{69} +550.199i q^{71} +(175.248 - 465.693i) q^{72} +372.298i q^{73} +314.596i q^{74} +(17.1421 - 94.2231i) q^{75} -320.415i q^{76} +(-10.3046 + 56.6400i) q^{78} +879.193 q^{79} +921.063 q^{80} +(548.139 + 480.609i) q^{81} -480.832i q^{82} -1119.54 q^{83} +389.153 q^{85} +190.290i q^{86} +(-1266.78 - 230.467i) q^{87} -1112.12 q^{88} +21.2955 q^{89} +(-364.468 + 968.513i) q^{90} -201.501i q^{92} +(-1062.76 - 193.349i) q^{93} -745.169i q^{94} -1712.03i q^{95} +(-504.531 - 91.7897i) q^{96} -612.931i q^{97} +(573.870 - 1524.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) 24 * q - 96 * q^4 - 64 * q^9	\( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) 24 * q - 96 * q^4 - 64 * q^9 + 256 * q^15 + 864 * q^16 - 32 * q^18 - 384 * q^22 + 744 * q^25 - 1704 * q^30 + 584 * q^36 + 432 * q^37 - 2368 * q^39 - 624 * q^43 + 3744 * q^46 - 2160 * q^51 + 2032 * q^57 + 6384 * q^58 - 5832 * q^60 - 3504 * q^64 + 3792 * q^67 - 7472 * q^72 + 2248 * q^78 + 2784 * q^79 - 1968 * q^81 - 3744 * q^85 - 624 * q^88 - 3232 * q^93 + 1320 * q^99

Introduction

L-functions

Modular forms

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Database

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