LMFDB - Embedded newform 147.4.c.b.146.21

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			146.21
Character	$\chi$	$=$	147.146
Dual form			147.4.c.b.146.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.84485i q^{2} +(-5.11673 - 0.905040i) q^{3} -15.4725 q^{4} -17.3012 q^{5} +(4.38478 - 24.7898i) q^{6} -36.2033i q^{8} +(25.3618 + 9.26169i) q^{9} +O(q^{10})$	\(q+4.84485i q^{2} +(-5.11673 - 0.905040i) q^{3} -15.4725 q^{4} -17.3012 q^{5} +(4.38478 - 24.7898i) q^{6} -36.2033i q^{8} +(25.3618 + 9.26169i) q^{9} -83.8216i q^{10} +27.8490i q^{11} +(79.1688 + 14.0033i) q^{12} +16.3036i q^{13} +(88.5254 + 15.6583i) q^{15} +51.6191 q^{16} +40.8263 q^{17} +(-44.8715 + 122.874i) q^{18} -68.1627i q^{19} +267.693 q^{20} -134.924 q^{22} -71.7749i q^{23} +(-32.7654 + 185.242i) q^{24} +174.331 q^{25} -78.9883 q^{26} +(-121.387 - 70.3430i) q^{27} -216.426i q^{29} +(-75.8619 + 428.892i) q^{30} +157.351i q^{31} -39.5396i q^{32} +(25.2044 - 142.496i) q^{33} +197.797i q^{34} +(-392.412 - 143.302i) q^{36} -348.489 q^{37} +330.238 q^{38} +(14.7554 - 83.4209i) q^{39} +626.360i q^{40} +153.371 q^{41} +427.584 q^{43} -430.894i q^{44} +(-438.789 - 160.238i) q^{45} +347.738 q^{46} +16.8103 q^{47} +(-264.121 - 46.7174i) q^{48} +844.606i q^{50} +(-208.897 - 36.9495i) q^{51} -252.258i q^{52} +192.526i q^{53} +(340.801 - 588.103i) q^{54} -481.820i q^{55} +(-61.6899 + 348.770i) q^{57} +1048.55 q^{58} -287.422 q^{59} +(-1369.71 - 242.273i) q^{60} -224.297i q^{61} -762.340 q^{62} +604.516 q^{64} -282.071i q^{65} +(690.370 + 122.112i) q^{66} -172.206 q^{67} -631.687 q^{68} +(-64.9591 + 367.252i) q^{69} -1068.78i q^{71} +(335.304 - 918.181i) q^{72} -1078.22i q^{73} -1688.38i q^{74} +(-892.004 - 157.776i) q^{75} +1054.65i q^{76} +(404.161 + 71.4875i) q^{78} +52.0336 q^{79} -893.072 q^{80} +(557.442 + 469.786i) q^{81} +743.059i q^{82} -1023.07 q^{83} -706.344 q^{85} +2071.58i q^{86} +(-195.874 + 1107.39i) q^{87} +1008.23 q^{88} +668.570 q^{89} +(776.329 - 2125.87i) q^{90} +1110.54i q^{92} +(142.409 - 805.121i) q^{93} +81.4431i q^{94} +1179.29i q^{95} +(-35.7849 + 202.313i) q^{96} +1358.39i q^{97} +(-257.929 + 706.300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			4.84485i			1.71291i	0.516220	+	0.856456i	$0.327339\pi$
$2$			4.84485i			1.71291i	−0.516220	+	0.856456i	$0.672661\pi$
$3$	−5.11673	−	0.905040i	−0.984715	−	0.174175i
$3$	−5.11673	−	0.905040i	−0.984715	−	0.174175i
$4$	−15.4725			−1.93407
$5$	−17.3012			−1.54746			−0.773732	−	0.633513i	$-0.781612\pi$
$5$	−17.3012			−1.54746			−0.773732	+	0.633513i	$0.781612\pi$
$6$	4.38478	−	24.7898i	0.298346	−	1.68673i
$7$		0			0
$7$		0			0
$8$		−	36.2033i		−	1.59998i
$9$	25.3618	+	9.26169i	0.939326	+	0.343025i
$10$		−	83.8216i		−	2.65067i
$11$			27.8490i			0.763344i	0.924298	+	0.381672i	$0.124652\pi$
$11$			27.8490i			0.763344i	−0.924298	+	0.381672i	$0.875348\pi$
$12$	79.1688	+	14.0033i	1.90450	+	0.336866i
$13$			16.3036i			0.347830i	0.984761	+	0.173915i	$0.0556419\pi$
$13$			16.3036i			0.347830i	−0.984761	+	0.173915i	$0.944358\pi$
$14$		0			0
$15$	88.5254	+	15.6583i	1.52381	+	0.269530i
$16$	51.6191			0.806549
$17$	40.8263			0.582461			0.291231	−	0.956653i	$-0.405935\pi$
$17$	40.8263			0.582461			0.291231	+	0.956653i	$0.405935\pi$
$18$	−44.8715	+	122.874i	−0.587572	+	1.60898i
$19$		−	68.1627i		−	0.823031i	−0.911403	−	0.411515i	$-0.865000\pi$
$19$		−	68.1627i		−	0.823031i	0.911403	−	0.411515i	$-0.135000\pi$
$20$	267.693			2.99290
$21$		0			0
$22$	−134.924			−1.30754
$23$		−	71.7749i		−	0.650700i	−0.945594	−	0.325350i	$-0.894518\pi$
$23$		−	71.7749i		−	0.650700i	0.945594	−	0.325350i	$-0.105482\pi$
$24$	−32.7654	+	185.242i	−0.278676	+	1.57552i
$25$	174.331			1.39465
$26$	−78.9883			−0.595803
$27$	−121.387	−	70.3430i	−0.865222	−	0.501389i
$28$		0			0
$29$		−	216.426i		−	1.38584i	−0.721014	−	0.692920i	$-0.756324\pi$
$29$		−	216.426i		−	1.38584i	0.721014	−	0.692920i	$-0.243676\pi$
$30$	−75.8619	+	428.892i	−0.461681	+	2.61015i
$31$			157.351i			0.911646i	0.890070	+	0.455823i	$0.150655\pi$
$31$			157.351i			0.911646i	−0.890070	+	0.455823i	$0.849345\pi$
$32$		−	39.5396i		−	0.218428i
$33$	25.2044	−	142.496i	0.132955	−	0.751676i
$34$			197.797i			0.997705i
$35$		0			0
$36$	−392.412	−	143.302i	−1.81672	−	0.663434i
$37$	−348.489			−1.54841			−0.774207	−	0.632933i	$-0.781851\pi$
$37$	−348.489			−1.54841			−0.774207	+	0.632933i	$0.781851\pi$
$38$	330.238			1.40978
$39$	14.7554	−	83.4209i	0.0605834	−	0.342514i
$40$			626.360i			2.47590i
$41$	153.371			0.584208			0.292104	−	0.956387i	$-0.405645\pi$
$41$	153.371			0.584208			0.292104	+	0.956387i	$0.405645\pi$
$42$		0			0
$43$	427.584			1.51642			0.758208	−	0.652012i	$-0.226075\pi$
$43$	427.584			1.51642			0.758208	+	0.652012i	$0.226075\pi$
$44$		−	430.894i		−	1.47636i
$45$	−438.789	−	160.238i	−1.45357	−	0.530820i
$46$	347.738			1.11459
$47$	16.8103			0.0521708			0.0260854	−	0.999660i	$-0.491696\pi$
$47$	16.8103			0.0521708			0.0260854	+	0.999660i	$0.491696\pi$
$48$	−264.121	−	46.7174i	−0.794221	−	0.140481i
$49$		0			0
$50$			844.606i			2.38891i
$51$	−208.897	−	36.9495i	−0.573558	−	0.101450i
$52$		−	252.258i		−	0.672727i
$53$			192.526i			0.498971i	0.968379	+	0.249486i	$0.0802615\pi$
$53$			192.526i			0.498971i	−0.968379	+	0.249486i	$0.919738\pi$
$54$	340.801	−	588.103i	0.858836	−	1.48205i
$55$		−	481.820i		−	1.18125i
$56$		0			0
$57$	−61.6899	+	348.770i	−0.143351	+	0.810451i
$58$	1048.55			2.37382
$59$	−287.422			−0.634224			−0.317112	−	0.948388i	$-0.602713\pi$
$59$	−287.422			−0.634224			−0.317112	+	0.948388i	$0.602713\pi$
$60$	−1369.71	−	242.273i	−2.94715	−	0.521289i
$61$		−	224.297i		−	0.470792i	−0.971900	−	0.235396i	$-0.924361\pi$
$61$		−	224.297i		−	0.470792i	0.971900	−	0.235396i	$-0.0756387\pi$
$62$	−762.340			−1.56157
$63$		0			0
$64$	604.516			1.18070
$65$		−	282.071i		−	0.538255i
$66$	690.370	+	122.112i	1.28755	+	0.227741i
$67$	−172.206			−0.314004			−0.157002	−	0.987598i	$-0.550183\pi$
$67$	−172.206			−0.314004			−0.157002	+	0.987598i	$0.550183\pi$
$68$	−631.687			−1.12652
$69$	−64.9591	+	367.252i	−0.113336	+	0.640754i
$70$		0			0
$71$		−	1068.78i		−	1.78649i	−0.449569	−	0.893246i	$-0.648422\pi$
$71$		−	1068.78i		−	1.78649i	0.449569	−	0.893246i	$-0.351578\pi$
$72$	335.304	−	918.181i	0.548832	−	1.50290i
$73$		−	1078.22i		−	1.72871i	−0.502881	−	0.864356i	$-0.667726\pi$
$73$		−	1078.22i		−	1.72871i	0.502881	−	0.864356i	$-0.332274\pi$
$74$		−	1688.38i		−	2.65230i
$75$	−892.004	−	157.776i	−1.37333	−	0.242913i
$76$			1054.65i			1.59180i
$77$		0			0
$78$	404.161	+	71.4875i	0.586696	+	0.103774i
$79$	52.0336			0.0741043			0.0370521	−	0.999313i	$-0.488203\pi$
$79$	52.0336			0.0741043			0.0370521	+	0.999313i	$0.488203\pi$
$80$	−893.072			−1.24811
$81$	557.442	+	469.786i	0.764667	+	0.644426i
$82$			743.059i			1.00070i
$83$	−1023.07			−1.35298			−0.676488	−	0.736454i	$-0.736499\pi$
$83$	−1023.07			−1.35298			−0.676488	+	0.736454i	$0.736499\pi$
$84$		0			0
$85$	−706.344			−0.901338
$86$			2071.58i			2.59749i
$87$	−195.874	+	1107.39i	−0.241379	+	1.36466i
$88$	1008.23			1.22133
$89$	668.570			0.796272			0.398136	−	0.917326i	$-0.369657\pi$
$89$	668.570			0.796272			0.398136	+	0.917326i	$0.369657\pi$
$90$	776.329	−	2125.87i	0.909247	−	2.48984i
$91$		0			0
$92$			1110.54i			1.25850i
$93$	142.409	−	805.121i	0.158786	−	0.897711i
$94$			81.4431i			0.0893640i
$95$			1179.29i			1.27361i
$96$	−35.7849	+	202.313i	−0.0380446	+	0.215089i
$97$			1358.39i			1.42190i	0.703244	+	0.710949i	$0.251734\pi$
$97$			1358.39i			1.42190i	−0.703244	+	0.710949i	$0.748266\pi$
$98$		0			0
$99$	−257.929	+	706.300i	−0.261846	+	0.717029i
$100$	−2697.34			−2.69734
$101$	29.0959			0.0286649			0.0143324	−	0.999897i	$-0.495438\pi$
$101$	29.0959			0.0286649			0.0143324	+	0.999897i	$0.495438\pi$
$102$	179.015	−	1012.08i	0.173775	−	0.982455i
$103$			300.909i			0.287859i	0.989588	+	0.143929i	$0.0459738\pi$
$103$			300.909i			0.287859i	−0.989588	+	0.143929i	$0.954026\pi$
$104$	590.243			0.556520
$105$		0			0
$106$	−932.759			−0.854694
$107$		−	523.431i		−	0.472916i	−0.971642	−	0.236458i	$-0.924013\pi$
$107$		−	523.431i		−	0.472916i	0.971642	−	0.236458i	$-0.0759866\pi$
$108$	1878.17	+	1088.38i	1.67340	+	0.969721i
$109$	−62.6812			−0.0550805			−0.0275402	−	0.999621i	$-0.508767\pi$
$109$	−62.6812			−0.0550805			−0.0275402	+	0.999621i	$0.508767\pi$
$110$	2334.35			2.02337
$111$	1783.13	+	315.397i	1.52475	+	0.269695i
$112$		0			0
$113$			84.9426i			0.0707144i	0.999375	+	0.0353572i	$0.0112569\pi$
$113$			84.9426i			0.0707144i	−0.999375	+	0.0353572i	$0.988743\pi$
$114$	−1689.74	−	298.878i	−1.38823	−	0.245548i
$115$			1241.79i			1.00693i
$116$			3348.66i			2.68031i
$117$	−150.998	+	413.488i	−0.119315	+	0.326726i
$118$		−	1392.52i		−	1.08637i
$119$		0			0
$120$	566.881	−	3204.91i	0.431241	−	2.43806i
$121$	555.434			0.417306
$122$	1086.69			0.806425
$123$	−784.758	−	138.807i	−0.575278	−	0.101754i
$124$		−	2434.62i		−	1.76318i
$125$	−853.482			−0.610702
$126$		0			0
$127$	−1842.84			−1.28760			−0.643802	−	0.765192i	$-0.722644\pi$
$127$	−1842.84			−1.28760			−0.643802	+	0.765192i	$0.722644\pi$
$128$			2612.47i			1.80400i
$129$	−2187.83	−	386.981i	−1.49324	−	0.264122i
$130$	1366.59			0.921984
$131$	−97.8698			−0.0652742			−0.0326371	−	0.999467i	$-0.510391\pi$
$131$	−97.8698			−0.0652742			−0.0326371	+	0.999467i	$0.510391\pi$
$132$	−389.977	+	2204.77i	−0.257145	+	1.45379i
$133$		0			0
$134$		−	834.310i		−	0.537861i
$135$	2100.14	+	1217.02i	1.33890	+	0.775882i
$136$		−	1478.05i		−	0.931924i
$137$		−	1693.85i		−	1.05631i	−0.849147	−	0.528157i	$-0.822883\pi$
$137$		−	1693.85i		−	1.05631i	0.849147	−	0.528157i	$-0.177117\pi$
$138$	−1779.28	−	314.717i	−1.09755	−	0.194134i
$139$		−	1821.25i		−	1.11134i	−0.831402	−	0.555672i	$-0.812461\pi$
$139$		−	1821.25i		−	1.11134i	0.831402	−	0.555672i	$-0.187539\pi$
$140$		0			0
$141$	−86.0135	−	15.2139i	−0.0513733	−	0.00908685i
$142$	5178.08			3.06010
$143$	−454.038			−0.265514
$144$	1309.15	+	478.080i	0.757613	+	0.276667i
$145$			3744.43i			2.14454i
$146$	5223.80			2.96113
$147$		0			0
$148$	5392.02			2.99474
$149$		−	1798.00i		−	0.988574i	−0.869299	−	0.494287i	$-0.835429\pi$
$149$		−	1798.00i		−	0.988574i	0.869299	−	0.494287i	$-0.164571\pi$
$150$	764.402	−	4321.62i	0.416088	−	2.35239i
$151$	−2089.84			−1.12628			−0.563141	−	0.826361i	$-0.690407\pi$
$151$	−2089.84			−1.12628			−0.563141	+	0.826361i	$0.690407\pi$
$152$	−2467.71			−1.31683
$153$	1035.43	+	378.121i	0.547121	+	0.199799i
$154$		0			0
$155$		−	2722.35i		−	1.41074i
$156$	−228.303	+	1290.73i	−0.117172	+	0.662445i
$157$			1090.34i			0.554258i	0.960833	+	0.277129i	$0.0893829\pi$
$157$			1090.34i			0.554258i	−0.960833	+	0.277129i	$0.910617\pi$
$158$			252.095i			0.126934i
$159$	174.244	−	985.103i	0.0869083	−	0.491344i
$160$			684.082i			0.338009i
$161$		0			0
$162$	−2276.04	+	2700.72i	−1.10384	+	1.30981i
$163$	−1940.53			−0.932478			−0.466239	−	0.884659i	$-0.654391\pi$
$163$	−1940.53			−0.932478			−0.466239	+	0.884659i	$0.654391\pi$
$164$	−2373.04			−1.12990
$165$	−436.067	+	2465.34i	−0.205744	+	1.16319i
$166$		−	4956.64i		−	2.31753i
$167$	−2664.87			−1.23481			−0.617406	−	0.786645i	$-0.711816\pi$
$167$	−2664.87			−1.23481			−0.617406	+	0.786645i	$0.711816\pi$
$168$		0			0
$169$	1931.19			0.879014
$170$		−	3422.13i		−	1.54391i
$171$	631.301	−	1728.73i	0.282320	−	0.773094i
$172$	−6615.81			−2.93285
$173$	3096.19			1.36069			0.680343	−	0.732894i	$-0.261831\pi$
$173$	3096.19			1.36069			0.680343	+	0.732894i	$0.261831\pi$
$174$	−5365.16	−	948.982i	−2.33754	−	0.413461i
$175$		0			0
$176$			1437.54i			0.615674i
$177$	1470.66	+	260.129i	0.624529	+	0.110466i
$178$			3239.12i			1.36394i
$179$		−	902.641i		−	0.376908i	−0.982082	−	0.188454i	$-0.939652\pi$
$179$		−	902.641i		−	0.376908i	0.982082	−	0.188454i	$-0.0603476\pi$
$180$	6789.18	+	2479.29i	2.81131	+	1.02664i
$181$		−	3496.01i		−	1.43567i	−0.696213	−	0.717835i	$-0.745133\pi$
$181$		−	3496.01i		−	1.43567i	0.696213	−	0.717835i	$-0.254867\pi$
$182$		0			0
$183$	−202.998	+	1147.67i	−0.0820002	+	0.463596i
$184$	−2598.49			−1.04110
$185$	6029.28			2.39612
$186$	3900.69	+	689.948i	1.53770	+	0.271986i
$187$			1136.97i			0.444618i
$188$	−260.097			−0.100902
$189$		0			0
$190$	−5713.50			−2.18158
$191$		−	354.514i		−	0.134302i	−0.997743	−	0.0671512i	$-0.978609\pi$
$191$		−	354.514i		−	0.134302i	0.997743	−	0.0671512i	$-0.0213910\pi$
$192$	−3093.15	−	547.112i	−1.16265	−	0.205648i
$193$	2839.88			1.05917			0.529584	−	0.848258i	$-0.322348\pi$
$193$	2839.88			1.05917			0.529584	+	0.848258i	$0.322348\pi$
$194$	−6581.21			−2.43559
$195$	−255.285	+	1443.28i	−0.0937506	+	0.530028i
$196$		0			0
$197$			3058.25i			1.10605i	0.833165	+	0.553024i	$0.186526\pi$
$197$			3058.25i			1.10605i	−0.833165	+	0.553024i	$0.813474\pi$
$198$	−3421.92	−	1249.62i	−1.22821	−	0.448520i
$199$		−	1839.48i		−	0.655264i	−0.944805	−	0.327632i	$-0.893749\pi$
$199$		−	1839.48i		−	0.655264i	0.944805	−	0.327632i	$-0.106251\pi$
$200$		−	6311.35i		−	2.23140i
$201$	881.129	+	155.853i	0.309204	+	0.0546916i
$202$			140.965i			0.0491004i
$203$		0			0
$204$	3232.17	+	571.702i	1.10930	+	0.196212i
$205$	−2653.50			−0.904041
$206$	−1457.86			−0.493077
$207$	664.756	−	1820.34i	0.223207	−	0.611219i
$208$			841.576i			0.280542i
$209$	1898.26			0.628256
$210$		0			0
$211$	−644.694			−0.210344			−0.105172	−	0.994454i	$-0.533539\pi$
$211$	−644.694			−0.210344			−0.105172	+	0.994454i	$0.533539\pi$
$212$		−	2978.86i		−	0.965044i
$213$	−967.289	+	5468.66i	−0.311162	+	1.75918i
$214$	2535.94			0.810063
$215$	−7397.71			−2.34660
$216$	−2546.65	+	4394.62i	−0.802210	+	1.38433i
$217$		0			0
$218$		−	303.681i		−	0.0943480i
$219$	−975.831	+	5516.95i	−0.301098	+	1.70229i
$220$			7454.98i			2.28461i
$221$			665.615i			0.202598i
$222$	−1528.05	+	8638.97i	−0.461964	+	2.61176i
$223$			3760.55i			1.12926i	0.825344	+	0.564630i	$0.190981\pi$
$223$			3760.55i			1.12926i	−0.825344	+	0.564630i	$0.809019\pi$
$224$		0			0
$225$	4421.35	+	1614.60i	1.31003	+	0.478399i
$226$	−411.534			−0.121128
$227$	−2836.86			−0.829467			−0.414733	−	0.909943i	$-0.636125\pi$
$227$	−2836.86			−0.829467			−0.414733	+	0.909943i	$0.636125\pi$
$228$	954.500	−	5396.35i	0.277251	−	1.56747i
$229$		−	5207.86i		−	1.50282i	−0.659837	−	0.751409i	$-0.729375\pi$
$229$		−	5207.86i		−	1.50282i	0.659837	−	0.751409i	$-0.270625\pi$
$230$	−6016.28			−1.72479
$231$		0			0
$232$	−7835.35			−2.21731
$233$			2185.90i			0.614604i	0.951612	+	0.307302i	$0.0994262\pi$
$233$			2185.90i			0.614604i	−0.951612	+	0.307302i	$0.900574\pi$
$234$	−2003.28	−	731.565i	−0.559653	−	0.204376i
$235$	−290.837			−0.0807325
$236$	4447.15			1.22663
$237$	−266.242	−	47.0925i	−0.0729716	−	0.0129071i
$238$		0			0
$239$		−	1921.87i		−	0.520148i	−0.965589	−	0.260074i	$-0.916253\pi$
$239$		−	1921.87i		−	0.520148i	0.965589	−	0.260074i	$-0.0837469\pi$
$240$	4569.61	+	808.266i	1.22903	+	0.217389i
$241$		−	4476.26i		−	1.19644i	−0.801333	−	0.598218i	$-0.795876\pi$
$241$		−	4476.26i		−	1.19644i	0.801333	−	0.598218i	$-0.204124\pi$
$242$			2690.99i			0.714809i
$243$	−2427.11	−	2908.28i	−0.640736	−	0.767761i
$244$			3470.45i			0.910543i
$245$		0			0
$246$	672.498	−	3802.03i	0.174296	−	0.985401i
$247$	1111.29			0.286275
$248$	5696.62			1.45861
$249$	5234.79	+	925.923i	1.33230	+	0.235655i
$250$		−	4134.99i		−	1.04608i
$251$	3296.51			0.828980			0.414490	−	0.910054i	$-0.363960\pi$
$251$	3296.51			0.828980			0.414490	+	0.910054i	$0.363960\pi$
$252$		0			0
$253$	1998.86			0.496708
$254$		−	8928.28i		−	2.20555i
$255$	3614.17	+	639.270i	0.887561	+	0.156991i
$256$	−7820.90			−1.90940
$257$	7110.67			1.72588			0.862940	−	0.505307i	$-0.168621\pi$
$257$	7110.67			1.72588			0.862940	+	0.505307i	$0.168621\pi$
$258$	1874.86	−	10599.7i	0.452418	−	2.55779i
$259$		0			0
$260$			4364.35i			1.04102i
$261$	2004.47	−	5488.96i	0.475378	−	1.30176i
$262$		−	474.164i		−	0.111809i
$263$		−	6808.88i		−	1.59640i	−0.602391	−	0.798201i	$-0.705785\pi$
$263$		−	6808.88i		−	1.59640i	0.602391	−	0.798201i	$-0.294215\pi$
$264$	−5158.81	−	912.484i	−1.20266	−	0.212725i
$265$		−	3330.93i		−	0.772140i
$266$		0			0
$267$	−3420.89	−	605.082i	−0.784101	−	0.138691i
$268$	2664.46			0.607305
$269$	3603.91			0.816856			0.408428	−	0.912791i	$-0.366077\pi$
$269$	3603.91			0.816856			0.408428	+	0.912791i	$0.366077\pi$
$270$	−5896.26	+	10174.9i	−1.32902	+	2.29342i
$271$		−	3376.15i		−	0.756777i	−0.925647	−	0.378388i	$-0.876478\pi$
$271$		−	3376.15i		−	0.756777i	0.925647	−	0.378388i	$-0.123522\pi$
$272$	2107.42			0.469784
$273$		0			0
$274$	8206.42			1.80937
$275$			4854.94i			1.06460i
$276$	1005.08	−	5682.33i	0.219199	−	1.23926i
$277$	−6940.10			−1.50538			−0.752690	−	0.658375i	$-0.771244\pi$
$277$	−6940.10			−1.50538			−0.752690	+	0.658375i	$0.771244\pi$
$278$	8823.70			1.90363
$279$	−1457.33	+	3990.70i	−0.312718	+	0.856333i
$280$		0			0
$281$			3834.00i			0.813940i	0.913441	+	0.406970i	$0.133415\pi$
$281$			3834.00i			0.813940i	−0.913441	+	0.406970i	$0.866585\pi$
$282$	73.7093	−	416.722i	0.0155650	−	0.0879980i
$283$		−	6443.70i		−	1.35349i	−0.736217	−	0.676746i	$-0.763390\pi$
$283$		−	6443.70i		−	1.35349i	0.736217	−	0.676746i	$-0.236610\pi$
$284$			16536.7i			3.45519i
$285$	1067.31	−	6034.13i	0.221831	−	1.25414i
$286$		−	2199.74i		−	0.454802i
$287$		0			0
$288$	366.203	−	1002.80i	0.0749262	−	0.205175i
$289$	−3246.21			−0.660739
$290$	−18141.2			−3.67341
$291$	1229.40	−	6950.54i	0.247659	−	1.40016i
$292$			16682.8i			3.34344i
$293$	1443.22			0.287760			0.143880	−	0.989595i	$-0.454042\pi$
$293$	1443.22			0.287760			0.143880	+	0.989595i	$0.454042\pi$
$294$		0			0
$295$	4972.74			0.981439
$296$			12616.5i			2.47742i
$297$	1958.98	−	3380.51i	0.382733	−	0.660462i
$298$	8711.01			1.69334
$299$	1170.19			0.226333
$300$	13801.6	+	2441.20i	2.65611	+	0.469809i
$301$		0			0
$302$		−	10124.9i		−	1.92922i
$303$	−148.876	−	26.3330i	−0.0282267	−	0.00499271i
$304$		−	3518.50i		−	0.663815i
$305$			3880.61i			0.728534i
$306$	−1831.94	+	5016.50i	−0.342238	+	0.937170i
$307$		−	5504.32i		−	1.02328i	−0.859199	−	0.511642i	$-0.829038\pi$
$307$		−	5504.32i		−	1.02328i	0.859199	−	0.511642i	$-0.170962\pi$
$308$		0			0
$309$	272.335	−	1539.67i	0.0501378	−	0.283459i
$310$	13189.4			2.41647
$311$	−2419.45			−0.441140			−0.220570	−	0.975371i	$-0.570792\pi$
$311$	−2419.45			−0.441140			−0.220570	+	0.975371i	$0.570792\pi$
$312$	−3020.11	−	534.193i	−0.548013	−	0.0969319i
$313$			1190.38i			0.214966i	0.994207	+	0.107483i	$0.0342791\pi$
$313$			1190.38i			0.214966i	−0.994207	+	0.107483i	$0.965721\pi$
$314$	−5282.52			−0.949395
$315$		0			0
$316$	−805.092			−0.143323
$317$			6628.17i			1.17437i	0.809453	+	0.587185i	$0.199764\pi$
$317$			6628.17i			1.17437i	−0.809453	+	0.587185i	$0.800236\pi$
$318$	4772.67	+	844.184i	0.841629	+	0.148866i
$319$	6027.25			1.05787
$320$	−10458.8			−1.82709
$321$	−473.726	+	2678.25i	−0.0823701	+	0.465687i
$322$		0			0
$323$		−	2782.83i		−	0.479384i
$324$	−8625.05	−	7268.78i	−1.47892	−	1.24636i
$325$			2842.21i			0.485101i
$326$		−	9401.56i		−	1.59725i
$327$	320.723	+	56.7290i	0.0542385	+	0.00959364i
$328$		−	5552.54i		−	0.934718i
$329$		0			0
$330$	−11944.2	−	2112.68i	−1.99245	−	0.352421i
$331$	−7185.16			−1.19315			−0.596574	−	0.802558i	$-0.703472\pi$
$331$	−7185.16			−1.19315			−0.596574	+	0.802558i	$0.703472\pi$
$332$	15829.6			2.61675
$333$	−8838.32	−	3227.60i	−1.45447	−	0.531145i
$334$		−	12910.9i		−	2.11512i
$335$	2979.36			0.485910
$336$		0			0
$337$	−7214.56			−1.16618			−0.583090	−	0.812408i	$-0.698156\pi$
$337$	−7214.56			−1.16618			−0.583090	+	0.812408i	$0.698156\pi$
$338$			9356.34i			1.50567i
$339$	76.8764	−	434.628i	0.0123167	−	0.0696335i
$340$	10928.9			1.74325
$341$	−4382.06			−0.695899
$342$	8375.42	+	3058.56i	1.32424	+	0.483590i
$343$		0			0
$344$		−	15479.9i		−	2.42623i
$345$	1123.87	−	6353.90i	0.175383	−	0.991543i
$346$			15000.6i			2.33074i
$347$			8151.04i			1.26101i	0.776185	+	0.630505i	$0.217152\pi$
$347$			8151.04i			1.26101i	−0.776185	+	0.630505i	$0.782848\pi$
$348$	3030.68	−	17134.2i	0.466843	−	2.63934i
$349$			491.916i			0.0754489i	0.999288	+	0.0377245i	$0.0120109\pi$
$349$			491.916i			0.0754489i	−0.999288	+	0.0377245i	$0.987989\pi$
$350$		0			0
$351$	1146.84	−	1979.04i	0.174398	−	0.300950i
$352$	1101.14			0.166735
$353$	−2923.64			−0.440820			−0.220410	−	0.975407i	$-0.570740\pi$
$353$	−2923.64			−0.440820			−0.220410	+	0.975407i	$0.570740\pi$
$354$	−1260.28	+	7125.13i	−0.189218	+	1.06976i
$355$			18491.2i			2.76453i
$356$	−10344.5			−1.54004
$357$		0			0
$358$	4373.16			0.645610
$359$			4802.16i			0.705985i	0.935626	+	0.352992i	$0.114836\pi$
$359$			4802.16i			0.705985i	−0.935626	+	0.352992i	$0.885164\pi$
$360$	−5801.15	+	15885.6i	−0.849298	+	2.32568i
$361$	2212.85			0.322620
$362$	16937.6			2.45918
$363$	−2842.01	−	502.690i	−0.410927	−	0.0726843i
$364$		0			0
$365$			18654.5i			2.67512i
$366$	−5560.27	−	983.494i	−0.794099	−	0.140459i
$367$			8957.91i			1.27411i	0.770817	+	0.637056i	$0.219848\pi$
$367$			8957.91i			1.27411i	−0.770817	+	0.637056i	$0.780152\pi$
$368$		−	3704.96i		−	0.524821i
$369$	3889.77	+	1420.47i	0.548762	+	0.200398i
$370$			29210.9i			4.10434i
$371$		0			0
$372$	−2203.42	+	12457.3i	−0.307103	+	1.73623i
$373$	−5072.83			−0.704186			−0.352093	−	0.935965i	$-0.614530\pi$
$373$	−5072.83			−0.704186			−0.352093	+	0.935965i	$0.614530\pi$
$374$	−5508.45			−0.761592
$375$	4367.04	+	772.435i	0.601367	+	0.106369i
$376$		−	608.587i		−	0.0834720i
$377$	3528.52			0.482037
$378$		0			0
$379$	−855.835			−0.115993			−0.0579964	−	0.998317i	$-0.518471\pi$
$379$	−855.835			−0.115993			−0.0579964	+	0.998317i	$0.518471\pi$
$380$		−	18246.7i		−	2.46325i
$381$	9429.31	+	1667.84i	1.26792	+	0.224268i
$382$	1717.57			0.230048
$383$	−7080.61			−0.944653			−0.472326	−	0.881424i	$-0.656586\pi$
$383$	−7080.61			−0.944653			−0.472326	+	0.881424i	$0.656586\pi$
$384$	2364.39	−	13367.3i	0.314212	−	1.77643i
$385$		0			0
$386$			13758.8i			1.81426i
$387$	10844.3	+	3960.15i	1.42441	+	0.520170i
$388$		−	21017.8i		−	2.75005i
$389$			2073.59i			0.270270i	0.990827	+	0.135135i	$0.0431468\pi$
$389$			2073.59i			0.270270i	−0.990827	+	0.135135i	$0.956853\pi$
$390$	−6992.47	−	1236.82i	−0.907891	−	0.160587i
$391$		−	2930.31i		−	0.379007i
$392$		0			0
$393$	500.773	+	88.5761i	0.0642765	+	0.0113691i
$394$	−14816.8			−1.89456
$395$	−900.243			−0.114674
$396$	3990.81	−	10928.3i	0.506429	−	1.38678i
$397$		−	5722.06i		−	0.723380i	−0.932298	−	0.361690i	$-0.882200\pi$
$397$		−	5722.06i		−	0.723380i	0.932298	−	0.361690i	$-0.117800\pi$
$398$	8912.01			1.12241
$399$		0			0
$400$	8998.81			1.12485
$401$		−	11728.9i		−	1.46064i	−0.683107	−	0.730319i	$-0.739372\pi$
$401$		−	11728.9i		−	1.46064i	0.683107	−	0.730319i	$-0.260628\pi$
$402$	−755.084	+	4268.94i	−0.0936820	+	0.529640i
$403$	−2565.38			−0.317098
$404$	−450.188			−0.0554398
$405$	−9644.41	−	8127.86i	−1.18330	−	0.997226i
$406$		0			0
$407$		−	9705.08i		−	1.18197i
$408$	−1337.69	+	7562.77i	−0.162318	+	0.917679i
$409$		−	2623.53i		−	0.317176i	−0.987345	−	0.158588i	$-0.949306\pi$
$409$		−	2623.53i		−	0.317176i	0.987345	−	0.158588i	$-0.0506942\pi$
$410$		−	12855.8i		−	1.54854i
$411$	−1533.00	+	8666.95i	−0.183983	+	1.04017i
$412$		−	4655.83i		−	0.556738i
$413$		0			0
$414$	8819.27	+	3220.64i	1.04696	+	0.382333i
$415$	17700.4			2.09368
$416$	644.637			0.0759757
$417$	−1648.31	+	9318.86i	−0.193568	+	1.09436i
$418$			9196.78i			1.07615i
$419$	−2183.62			−0.254598			−0.127299	−	0.991864i	$-0.540631\pi$
$419$	−2183.62			−0.254598			−0.127299	+	0.991864i	$0.540631\pi$
$420$		0			0
$421$	−12921.5			−1.49586			−0.747929	−	0.663778i	$-0.768952\pi$
$421$	−12921.5			−1.49586			−0.747929	+	0.663778i	$0.768952\pi$
$422$		−	3123.44i		−	0.360300i
$423$	426.338	+	155.691i	0.0490054	+	0.0178959i
$424$	6970.07			0.798341
$425$	7117.29			0.812328
$426$	−26494.8	−	4686.37i	−3.01333	−	0.532993i
$427$		0			0
$428$			8098.81i			0.914651i
$429$	2323.19	+	410.922i	0.261456	+	0.0462459i
$430$		−	35840.8i		−	4.01952i
$431$		−	12619.8i		−	1.41038i	−0.709018	−	0.705190i	$-0.750862\pi$
$431$		−	12619.8i		−	1.41038i	0.709018	−	0.705190i	$-0.249138\pi$
$432$	−6265.91	−	3631.04i	−0.697844	−	0.404395i
$433$			14180.4i			1.57382i	0.617066	+	0.786912i	$0.288321\pi$
$433$			14180.4i			1.57382i	−0.617066	+	0.786912i	$0.711679\pi$
$434$		0			0
$435$	3388.86	−	19159.2i	0.373525	−	2.11176i
$436$	969.837			0.106529
$437$	−4892.36			−0.535546
$438$	−26728.8	−	4727.75i	−2.91587	−	0.515755i
$439$			7467.03i			0.811804i	0.913917	+	0.405902i	$0.133043\pi$
$439$			7467.03i			0.811804i	−0.913917	+	0.405902i	$0.866957\pi$
$440$	−17443.5			−1.88997
$441$		0			0
$442$	−3224.80			−0.347032
$443$		−	363.788i		−	0.0390160i	−0.999810	−	0.0195080i	$-0.993790\pi$
$443$		−	363.788i		−	0.0390160i	0.999810	−	0.0195080i	$-0.00620998\pi$
$444$	−27589.5	−	4879.99i	−2.94896	−	0.521608i
$445$	−11567.0			−1.23220
$446$	−18219.3			−1.93432
$447$	−1627.26	+	9199.85i	−0.172185	+	0.973463i
$448$		0			0
$449$		−	5444.69i		−	0.572273i	−0.958189	−	0.286136i	$-0.907629\pi$
$449$		−	5444.69i		−	0.572273i	0.958189	−	0.286136i	$-0.0923711\pi$
$450$	−7822.48	+	21420.7i	−0.819456	+	2.24396i
$451$			4271.23i			0.445952i
$452$		−	1314.28i		−	0.136766i
$453$	10693.1	+	1891.39i	1.10907	+	0.196170i
$454$		−	13744.1i		−	1.42080i
$455$		0			0
$456$	12626.6	+	2233.38i	1.29670	+	0.229359i
$457$	2305.66			0.236005			0.118003	−	0.993013i	$-0.462351\pi$
$457$	2305.66			0.236005			0.118003	+	0.993013i	$0.462351\pi$
$458$	25231.3			2.57419
$459$	−4955.80	−	2871.85i	−0.503958	−	0.292040i
$460$		−	19213.6i		−	1.94748i
$461$	585.754			0.0591785			0.0295892	−	0.999562i	$-0.490580\pi$
$461$	585.754			0.0591785			0.0295892	+	0.999562i	$0.490580\pi$
$462$		0			0
$463$	11321.6			1.13641			0.568205	−	0.822887i	$-0.307638\pi$
$463$	11321.6			1.13641			0.568205	+	0.822887i	$0.307638\pi$
$464$		−	11171.7i		−	1.11775i
$465$	−2463.84	+	13929.5i	−0.245716	+	1.38918i
$466$	−10590.3			−1.05276
$467$	−9958.30			−0.986756			−0.493378	−	0.869815i	$-0.664238\pi$
$467$	−9958.30			−0.986756			−0.493378	+	0.869815i	$0.664238\pi$
$468$	2336.33	−	6397.71i	0.230763	−	0.631910i
$469$		0			0
$470$		−	1409.06i		−	0.138288i
$471$	986.800	−	5578.97i	0.0965379	−	0.545786i
$472$			10405.6i			1.01474i
$473$			11907.8i			1.15755i
$474$	228.156	−	1289.90i	0.0221088	−	0.124994i
$475$		−	11882.9i		−	1.14784i
$476$		0			0
$477$	−1783.11	+	4882.81i	−0.171160	+	0.468697i
$478$	9311.16			0.890967
$479$	−13832.0			−1.31942			−0.659709	−	0.751521i	$-0.729320\pi$
$479$	−13832.0			−1.31942			−0.659709	+	0.751521i	$0.729320\pi$
$480$	619.122	−	3500.26i	0.0588727	−	0.332842i
$481$		−	5681.62i		−	0.538585i
$482$	21686.8			2.04939
$483$		0			0
$484$	−8593.98			−0.807098
$485$		−	23501.8i		−	2.20034i
$486$	14090.1	−	11759.0i	1.31511	−	1.09752i
$487$	456.178			0.0424464			0.0212232	−	0.999775i	$-0.493244\pi$
$487$	456.178			0.0424464			0.0212232	+	0.999775i	$0.493244\pi$
$488$	−8120.30			−0.753256
$489$	9929.15	+	1756.26i	0.918224	+	0.162414i
$490$		0			0
$491$			17039.5i			1.56616i	0.621922	+	0.783079i	$0.286352\pi$
$491$			17039.5i			1.56616i	−0.621922	+	0.783079i	$0.713648\pi$
$492$	12142.2	+	2147.70i	1.11263	+	0.196800i
$493$		−	8835.90i		−	0.807198i
$494$			5384.05i			0.490364i
$495$	4462.47	−	12219.8i	0.405198	−	1.10958i
$496$			8122.31i			0.735287i
$497$		0			0
$498$	−4485.96	+	25361.8i	−0.403656	+	2.28210i
$499$	−1855.54			−0.166463			−0.0832317	−	0.996530i	$-0.526524\pi$
$499$	−1855.54			−0.166463			−0.0832317	+	0.996530i	$0.526524\pi$
$500$	13205.5			1.18114
$501$	13635.4	+	2411.81i	1.21594	+	0.215073i
$502$			15971.1i			1.41997i
$503$	5860.64			0.519509			0.259754	−	0.965675i	$-0.416358\pi$
$503$	5860.64			0.519509			0.259754	+	0.965675i	$0.416358\pi$
$504$		0			0
$505$	−503.394			−0.0443579
$506$			9684.15i			0.850816i
$507$	−9881.39	−	1747.81i	−0.865578	−	0.153102i
$508$	28513.4			2.49031
$509$	5456.88			0.475191			0.237595	−	0.971364i	$-0.423641\pi$
$509$	5456.88			0.475191			0.237595	+	0.971364i	$0.423641\pi$
$510$	−3097.16	+	17510.1i	−0.268911	+	1.52031i
$511$		0			0
$512$		−	16991.3i		−	1.46663i
$513$	−4794.76	+	8274.08i	−0.412659	+	0.712104i
$514$			34450.1i			2.95628i
$515$		−	5206.08i		−	0.445451i
$516$	33851.3	+	5987.57i	2.88802	+	0.510830i
$517$			468.148i			0.0398243i
$518$		0			0
$519$	−15842.4	−	2802.17i	−1.33989	−	0.236998i
$520$	−10211.9			−0.861195
$521$	−7285.24			−0.612614			−0.306307	−	0.951933i	$-0.599093\pi$
$521$	−7285.24			−0.612614			−0.306307	+	0.951933i	$0.599093\pi$
$522$	26593.2	+	9711.36i	2.22979	+	0.814281i
$523$			3415.29i			0.285545i	0.989756	+	0.142772i	$0.0456017\pi$
$523$			3415.29i			0.285545i	−0.989756	+	0.142772i	$0.954398\pi$
$524$	1514.29			0.126245
$525$		0			0
$526$	32988.0			2.73450
$527$			6424.06i			0.530999i
$528$	1301.03	−	7355.50i	0.107235	−	0.606264i
$529$	7015.37			0.576590
$530$	16137.8			1.32261
$531$	−7289.55	−	2662.01i	−0.595743	−	0.217555i
$532$		0			0
$533$			2500.49i			0.203205i
$534$	2931.53	−	16573.7i	0.237565	−	1.34310i
$535$			9055.98i			0.731821i
$536$			6234.41i			0.502398i
$537$	−816.926	+	4618.57i	−0.0656480	+	0.371147i
$538$			17460.4i			1.39920i
$539$		0			0
$540$	−32494.5	−	18830.3i	−2.58952	−	1.50061i
$541$	−2381.89			−0.189289			−0.0946447	−	0.995511i	$-0.530172\pi$
$541$	−2381.89			−0.189289			−0.0946447	+	0.995511i	$0.530172\pi$
$542$	16356.9			1.29629
$543$	−3164.03	+	17888.1i	−0.250058	+	1.41373i
$544$		−	1614.26i		−	0.127226i
$545$	1084.46			0.0852351
$546$		0			0
$547$	−1376.55			−0.107600			−0.0537998	−	0.998552i	$-0.517133\pi$
$547$	−1376.55			−0.107600			−0.0537998	+	0.998552i	$0.517133\pi$
$548$			26208.1i			2.04298i
$549$	2077.37	−	5688.58i	0.161494	−	0.442227i
$550$	−23521.4			−1.82356
$551$	−14752.2			−1.14059
$552$	13295.8	+	2351.73i	1.02519	+	0.181334i
$553$		0			0
$554$		−	33623.7i		−	2.57858i
$555$	−30850.2	−	5456.74i	−2.35949	−	0.417344i
$556$			28179.4i			2.14941i
$557$		−	2037.41i		−	0.154987i	−0.996993	−	0.0774935i	$-0.975308\pi$
$557$		−	2037.41i		−	0.154987i	0.996993	−	0.0774935i	$-0.0246917\pi$
$558$	−19334.3	−	7060.56i	−1.46682	−	0.535658i
$559$			6971.14i			0.527456i
$560$		0			0
$561$	1029.01	−	5817.58i	0.0774414	−	0.437822i
$562$	−18575.1			−1.39421
$563$	2394.19			0.179224			0.0896118	−	0.995977i	$-0.471437\pi$
$563$	2394.19			0.179224			0.0896118	+	0.995977i	$0.471437\pi$
$564$	1330.85	+	235.398i	0.0993595	+	0.0175746i
$565$		−	1469.61i		−	0.109428i
$566$	31218.7			2.31841
$567$		0			0
$568$	−38693.4			−2.85834
$569$			7635.14i			0.562534i	0.959630	+	0.281267i	$0.0907546\pi$
$569$			7635.14i			0.562534i	−0.959630	+	0.281267i	$0.909245\pi$
$570$	29234.4	+	5170.95i	2.14824	+	0.379977i
$571$	2512.52			0.184143			0.0920715	−	0.995752i	$-0.470651\pi$
$571$	2512.52			0.184143			0.0920715	+	0.995752i	$0.470651\pi$
$572$	7025.11			0.513522
$573$	−320.850	+	1813.95i	−0.0233921	+	0.132249i
$574$		0			0
$575$		−	12512.6i		−	0.907496i
$576$	15331.6	+	5598.84i	1.10906	+	0.405009i
$577$		−	10906.9i		−	0.786929i	−0.919340	−	0.393465i	$-0.871276\pi$
$577$		−	10906.9i		−	0.786929i	0.919340	−	0.393465i	$-0.128724\pi$
$578$		−	15727.4i		−	1.13179i
$579$	−14530.9	−	2570.21i	−1.04298	−	0.184480i
$580$		−	57935.9i		−	4.14768i
$581$		0			0
$582$	33674.3	+	5956.26i	2.39836	+	0.424218i
$583$	−5361.65			−0.380887
$584$	−39035.1			−2.76590
$585$	2612.45	−	7153.83i	0.184635	−	0.505597i
$586$			6992.18i			0.492908i
$587$	−25367.7			−1.78371			−0.891855	−	0.452321i	$-0.850596\pi$
$587$	−25367.7			−1.78371			−0.891855	+	0.452321i	$0.850596\pi$
$588$		0			0
$589$	10725.4			0.750313
$590$			24092.2i			1.68112i
$591$	2767.84	−	15648.2i	0.192646	−	1.08914i
$592$	−17988.7			−1.24887
$593$	−9834.38			−0.681028			−0.340514	−	0.940239i	$-0.610601\pi$
$593$	−9834.38			−0.681028			−0.340514	+	0.940239i	$0.610601\pi$
$594$	16378.1	+	9490.96i	1.13131	+	0.655587i
$595$		0			0
$596$			27819.5i			1.91197i
$597$	−1664.81	+	9412.13i	−0.114131	+	0.645248i
$598$			5669.37i			0.387689i
$599$			6922.43i			0.472192i	0.971730	+	0.236096i	$0.0758679\pi$
$599$			6922.43i			0.472192i	−0.971730	+	0.236096i	$0.924132\pi$
$600$	−5712.03	+	32293.5i	−0.388654	+	2.19729i
$601$		−	15144.9i		−	1.02791i	−0.857817	−	0.513955i	$-0.828180\pi$
$601$		−	15144.9i		−	1.02791i	0.857817	−	0.513955i	$-0.171820\pi$
$602$		0			0
$603$	−4367.44	−	1594.91i	−0.294952	−	0.107711i
$604$	32335.1			2.17830
$605$	−9609.67			−0.645766
$606$	127.579	−	721.281i	0.00855207	−	0.0483499i
$607$		−	27601.0i		−	1.84562i	−0.385259	−	0.922809i	$-0.625888\pi$
$607$		−	27601.0i		−	1.84562i	0.385259	−	0.922809i	$-0.374112\pi$
$608$	−2695.12			−0.179773
$609$		0			0
$610$	−18800.9			−1.24791
$611$			274.067i			0.0181466i
$612$	−16020.7	−	5850.49i	−1.05817	−	0.386425i
$613$	12162.1			0.801342			0.400671	−	0.916222i	$-0.368777\pi$
$613$	12162.1			0.801342			0.400671	+	0.916222i	$0.368777\pi$
$614$	26667.6			1.75279
$615$	13577.2	+	2401.52i	0.890223	+	0.157461i
$616$		0			0
$617$		−	17715.1i		−	1.15589i	−0.816077	−	0.577944i	$-0.803855\pi$
$617$		−	17715.1i		−	1.15589i	0.816077	−	0.577944i	$-0.196145\pi$
$618$	7459.46	+	1319.42i	0.485540	+	0.0858816i
$619$		−	4569.82i		−	0.296731i	−0.988933	−	0.148366i	$-0.952599\pi$
$619$		−	4569.82i		−	0.296731i	0.988933	−	0.148366i	$-0.0474013\pi$
$620$			42121.7i			2.72847i
$621$	−5048.86	+	8712.55i	−0.326254	+	0.563000i
$622$		−	11721.9i		−	0.755634i
$623$		0			0
$624$	761.660	−	4306.11i	0.0488635	−	0.276254i
$625$	−7025.11			−0.449607
$626$	−5767.21			−0.368218
$627$	−9712.88	−	1718.00i	−0.618652	−	0.109426i
$628$		−	16870.3i		−	1.07197i
$629$	−14227.6			−0.901891
$630$		0			0
$631$	−1677.26			−0.105817			−0.0529086	−	0.998599i	$-0.516849\pi$
$631$	−1677.26			−0.105817			−0.0529086	+	0.998599i	$0.516849\pi$
$632$		−	1883.79i		−	0.118565i
$633$	3298.72	+	583.474i	0.207129	+	0.0366366i
$634$	−32112.5			−2.01159
$635$	31883.3			1.99252
$636$	−2695.99	+	15242.0i	−0.168087	+	0.950293i
$637$		0			0
$638$			29201.1i			1.81204i
$639$	9898.71	−	27106.2i	0.612812	−	1.67810i
$640$		−	45198.9i		−	2.79163i
$641$			27279.5i			1.68093i	0.541868	+	0.840464i	$0.317717\pi$
$641$			27279.5i			1.68093i	−0.541868	+	0.840464i	$0.682283\pi$
$642$	−12975.7	−	2295.13i	−0.797681	−	0.141093i
$643$			19330.9i			1.18559i	0.805353	+	0.592796i	$0.201976\pi$
$643$			19330.9i			1.18559i	−0.805353	+	0.592796i	$0.798024\pi$
$644$		0			0
$645$	37852.0	+	6695.22i	2.31073	+	0.408719i
$646$	13482.4			0.821142
$647$	19942.3			1.21177			0.605884	−	0.795553i	$-0.292819\pi$
$647$	19942.3			1.21177			0.605884	+	0.795553i	$0.292819\pi$
$648$	17007.8	−	20181.3i	1.03106	−	1.22345i
$649$		−	8004.42i		−	0.484131i
$650$	−13770.1			−0.830935
$651$		0			0
$652$	30024.9			1.80347
$653$		−	12834.9i		−	0.769171i	−0.923089	−	0.384586i	$-0.874344\pi$
$653$		−	12834.9i		−	0.769171i	0.923089	−	0.384586i	$-0.125656\pi$
$654$	−274.843	+	1553.85i	−0.0164331	+	0.0929059i
$655$	1693.26			0.101010
$656$	7916.88			0.471193
$657$	9986.12	−	27345.6i	0.592992	−	1.62382i
$658$		0			0
$659$			11112.6i			0.656880i	0.944525	+	0.328440i	$0.106523\pi$
$659$			11112.6i			0.656880i	−0.944525	+	0.328440i	$0.893477\pi$
$660$	6747.06	−	38145.1i	0.397922	−	2.24969i
$661$		−	3297.94i		−	0.194062i	−0.995281	−	0.0970312i	$-0.969065\pi$
$661$		−	3297.94i		−	0.194062i	0.995281	−	0.0970312i	$-0.0309346\pi$
$662$		−	34811.0i		−	2.04376i
$663$	602.408	−	3405.77i	0.0352875	−	0.199501i
$664$			37038.7i			2.16473i
$665$		0			0
$666$	15637.2	−	42820.3i	0.909805	−	2.49137i
$667$	−15534.0			−0.901766
$668$	41232.2			2.38821
$669$	3403.45	−	19241.7i	0.196689	−	1.11200i
$670$			14434.5i			0.832321i
$671$	6246.45			0.359376
$672$		0			0
$673$	527.753			0.0302279			0.0151140	−	0.999886i	$-0.495189\pi$
$673$	527.753			0.0302279			0.0151140	+	0.999886i	$0.495189\pi$
$674$		−	34953.5i		−	1.99756i
$675$	−21161.5	−	12263.0i	−1.20668	−	0.699261i
$676$	−29880.5			−1.70007
$677$	214.998			0.0122054			0.00610269	−	0.999981i	$-0.498057\pi$
$677$	214.998			0.0122054			0.00610269	+	0.999981i	$0.498057\pi$
$678$	2105.71	+	372.454i	0.119276	+	0.0210974i
$679$		0			0
$680$			25572.0i			1.44212i
$681$	14515.4	+	2567.47i	0.816788	+	0.144472i
$682$		−	21230.4i		−	1.19201i
$683$		−	7314.04i		−	0.409757i	−0.978787	−	0.204878i	$-0.934320\pi$
$683$		−	7314.04i		−	0.409757i	0.978787	−	0.204878i	$-0.0656799\pi$
$684$	−9767.83	+	26747.8i	−0.546027	+	1.49522i
$685$			29305.5i			1.63461i
$686$		0			0
$687$	−4713.32	+	26647.2i	−0.261753	+	1.47985i
$688$	22071.5			1.22306
$689$	−3138.86			−0.173557
$690$	30783.7	+	5444.98i	1.69843	+	0.300415i
$691$		−	31412.9i		−	1.72938i	−0.502302	−	0.864692i	$-0.667514\pi$
$691$		−	31412.9i		−	1.72938i	0.502302	−	0.864692i	$-0.332486\pi$
$692$	−47905.9			−2.63166
$693$		0			0
$694$	−39490.5			−2.16000
$695$			31509.9i			1.71977i
$696$	40091.3	+	7091.30i	2.18342	+	0.386200i
$697$	6261.58			0.340279
$698$	−2383.26			−0.129237
$699$	1978.32	−	11184.6i	0.107049	−	0.605210i
$700$		0			0
$701$		−	11496.6i		−	0.619430i	−0.950829	−	0.309715i	$-0.899766\pi$
$701$		−	11496.6i		−	0.619430i	0.950829	−	0.309715i	$-0.100234\pi$
$702$	9588.17	+	5556.27i	0.515502	+	0.298729i
$703$			23754.0i			1.27439i
$704$			16835.2i			0.901277i
$705$	1488.13	+	263.219i	0.0794984	+	0.0140616i
$706$		−	14164.6i		−	0.755087i
$707$		0			0
$708$	−22754.9	−	4024.85i	−1.20788	−	0.213649i
$709$	21068.2			1.11598			0.557992	−	0.829847i	$-0.311572\pi$
$709$	21068.2			1.11598			0.557992	+	0.829847i	$0.311572\pi$
$710$	−89586.8			−4.73540
$711$	1319.67	+	481.919i	0.0696081	+	0.0254197i
$712$		−	24204.4i		−	1.27402i
$713$	11293.8			0.593208
$714$		0			0
$715$	7855.39			0.410874
$716$			13966.1i			0.728966i
$717$	−1739.37	+	9833.68i	−0.0905968	+	0.512197i
$718$	−23265.7			−1.20929
$719$	−7492.00			−0.388602			−0.194301	−	0.980942i	$-0.562244\pi$
$719$	−7492.00			−0.388602			−0.194301	+	0.980942i	$0.562244\pi$
$720$	−22649.9	−	8271.35i	−1.17238	−	0.428132i
$721$		0			0
$722$			10720.9i			0.552620i
$723$	−4051.19	+	22903.8i	−0.208389	+	1.17815i
$724$			54092.1i			2.77668i
$725$		−	37729.8i		−	1.93276i
$726$	2435.46	−	13769.1i	0.124502	−	0.703882i
$727$		−	19637.5i		−	1.00181i	−0.865503	−	0.500904i	$-0.833001\pi$
$727$		−	19637.5i		−	1.00181i	0.865503	−	0.500904i	$-0.166999\pi$
$728$		0			0
$729$	9786.73	+	17077.5i	0.497217	+	0.867626i
$730$	−90378.0			−4.58225
$731$	17456.7			0.883254
$732$	3140.89	−	17757.3i	0.158594	−	0.896626i
$733$			28892.7i			1.45590i	0.685629	+	0.727951i	$0.259527\pi$
$733$			28892.7i			1.45590i	−0.685629	+	0.727951i	$0.740473\pi$
$734$	−43399.7			−2.18244
$735$		0			0
$736$	−2837.95			−0.142131
$737$		−	4795.75i		−	0.239693i
$738$	−6881.98	+	18845.3i	−0.343265	+	0.939981i
$739$	−4114.53			−0.204811			−0.102406	−	0.994743i	$-0.532654\pi$
$739$	−4114.53			−0.204811			−0.102406	+	0.994743i	$0.532654\pi$
$740$	−93288.3			−4.63425
$741$	−5686.19	−	1005.77i	−0.281899	−	0.0498620i
$742$		0			0
$743$		−	19095.9i		−	0.942881i	−0.881898	−	0.471441i	$-0.843734\pi$
$743$		−	19095.9i		−	0.942881i	0.881898	−	0.471441i	$-0.156266\pi$
$744$	−29148.0	−	5155.67i	−1.43632	−	0.254054i
$745$			31107.4i			1.52978i
$746$		−	24577.1i		−	1.20621i
$747$	−25947.0	−	9475.40i	−1.27089	−	0.464105i
$748$		−	17591.8i		−	0.859922i
$749$		0			0
$750$	−3742.33	+	21157.6i	−0.182201	+	1.03009i
$751$	27352.7			1.32905			0.664524	−	0.747267i	$-0.268634\pi$
$751$	27352.7			1.32905			0.664524	+	0.747267i	$0.268634\pi$
$752$	867.731			0.0420783
$753$	−16867.3	−	2983.47i	−0.816308	−	0.144388i
$754$			17095.1i			0.825687i
$755$	36156.7			1.74288
$756$		0			0
$757$	2016.86			0.0968349			0.0484174	−	0.998827i	$-0.484582\pi$
$757$	2016.86			0.0968349			0.0484174	+	0.998827i	$0.484582\pi$
$758$		−	4146.39i		−	0.198686i
$759$	−10227.6	−	1809.05i	−0.489115	−	0.0865141i
$760$	42694.4			2.03775
$761$	28904.7			1.37687			0.688434	−	0.725299i	$-0.258299\pi$
$761$	28904.7			1.37687			0.688434	+	0.725299i	$0.258299\pi$
$762$	−8080.45	+	45683.6i	−0.384152	+	2.17184i
$763$		0			0
$764$			5485.23i			0.259750i
$765$	−17914.2	−	6541.94i	−0.846651	−	0.309182i
$766$		−	34304.4i		−	1.61811i
$767$		−	4686.01i		−	0.220602i
$768$	40017.4	+	7078.23i	1.88021	+	0.332570i
$769$			16726.1i			0.784343i	0.919892	+	0.392171i	$0.128276\pi$
$769$			16726.1i			0.784343i	−0.919892	+	0.392171i	$0.871724\pi$
$770$		0			0
$771$	−36383.3	−	6435.44i	−1.69950	−	0.300605i
$772$	−43940.2			−2.04850
$773$	15197.6			0.707139			0.353570	−	0.935408i	$-0.384968\pi$
$773$	15197.6			0.707139			0.353570	+	0.935408i	$0.384968\pi$
$774$	−19186.3	+	52539.0i	−0.891005	+	2.43989i
$775$			27431.1i			1.27142i
$776$	49178.4			2.27500
$777$		0			0
$778$	−10046.2			−0.462949
$779$		−	10454.2i		−	0.480821i
$780$	3949.91	−	22331.2i	0.181320	−	1.02511i
$781$	29764.4			1.36371
$782$	14196.9			0.649206
$783$	−15224.1	+	26271.4i	−0.694845	+	1.19906i
$784$		0			0
$785$		−	18864.1i		−	0.857694i
$786$	−429.138	+	2426.17i	−0.0194743	+	0.110100i
$787$			13333.2i			0.603910i	0.953322	+	0.301955i	$0.0976393\pi$
$787$			13333.2i			0.603910i	−0.953322	+	0.301955i	$0.902361\pi$
$788$		−	47318.9i		−	2.13917i
$789$	−6162.31	+	34839.2i	−0.278053	+	1.57200i
$790$		−	4361.54i		−	0.196426i
$791$		0			0
$792$	25570.4	+	9337.86i	1.14723	+	0.418948i
$793$	3656.84			0.163756
$794$	27722.5			1.23909
$795$	−3014.62	+	17043.4i	−0.134488	+	0.760338i
$796$			28461.5i			1.26732i
$797$	−31995.7			−1.42202			−0.711008	−	0.703183i	$-0.751761\pi$
$797$	−31995.7			−1.42202			−0.711008	+	0.703183i	$0.751761\pi$
$798$		0			0
$799$	686.301			0.0303875
$800$		−	6892.97i		−	0.304629i
$801$	16956.1	+	6192.08i	0.747959	+	0.273142i
$802$	56824.9			2.50194
$803$	30027.3			1.31960
$804$	−13633.3	−	2411.44i	−0.598022	−	0.105777i
$805$		0			0
$806$		−	12428.9i		−	0.543161i
$807$	−18440.2	−	3261.68i	−0.804370	−	0.142276i
$808$		−	1053.37i		−	0.0458631i
$809$		−	5450.03i		−	0.236852i	−0.992963	−	0.118426i	$-0.962215\pi$
$809$		−	5450.03i		−	0.236852i	0.992963	−	0.118426i	$-0.0377848\pi$
$810$	39378.2	−	46725.7i	1.70816	−	2.02688i
$811$		−	39222.9i		−	1.69828i	−0.528171	−	0.849138i	$-0.677122\pi$
$811$		−	39222.9i		−	1.69828i	0.528171	−	0.849138i	$-0.322878\pi$
$812$		0			0
$813$	−3055.55	+	17274.8i	−0.131812	+	0.745209i
$814$	47019.6			2.02461
$815$	33573.4			1.44298
$816$	−10783.1	−	1907.30i	−0.462603	−	0.0818246i
$817$		−	29145.3i		−	1.24806i
$818$	12710.6			0.543295
$819$		0			0
$820$	41056.4			1.74848
$821$			14897.1i			0.633267i	0.948548	+	0.316634i	$0.102553\pi$
$821$			14897.1i			0.633267i	−0.948548	+	0.316634i	$0.897447\pi$
$822$	−41990.0	−	7427.14i	−1.78172	−	0.315147i
$823$	−33975.1			−1.43900			−0.719500	−	0.694492i	$-0.755629\pi$
$823$	−33975.1			−1.43900			−0.719500	+	0.694492i	$0.755629\pi$
$824$	10893.9			0.460567
$825$	4393.91	−	24841.4i	0.185426	−	1.04832i
$826$		0			0
$827$			5008.85i			0.210610i	0.994440	+	0.105305i	$0.0335819\pi$
$827$			5008.85i			0.210610i	−0.994440	+	0.105305i	$0.966418\pi$
$828$	−10285.5	+	28165.3i	−0.431696	+	1.18214i
$829$		−	33961.3i		−	1.42283i	−0.702773	−	0.711414i	$-0.748055\pi$
$829$		−	33961.3i		−	1.42283i	0.702773	−	0.711414i	$-0.251945\pi$
$830$			85755.7i			3.58629i
$831$	35510.6	+	6281.07i	1.48237	+	0.262199i
$832$			9855.77i			0.410682i
$833$		0			0
$834$	−45148.5	−	7985.80i	−1.87454	−	0.331566i
$835$	46105.3			1.91083
$836$	−29370.9			−1.21509
$837$	11068.5	−	19100.4i	0.457090	−	0.788776i
$838$		−	10579.3i		−	0.436104i
$839$	−31564.7			−1.29885			−0.649426	−	0.760425i	$-0.724991\pi$
$839$	−31564.7			−1.29885			−0.649426	+	0.760425i	$0.724991\pi$
$840$		0			0
$841$	−22451.4			−0.920553
$842$		−	62602.8i		−	2.56227i
$843$	3469.92	−	19617.5i	0.141768	−	0.801499i
$844$	9975.05			0.406819
$845$	−33411.9			−1.36024
$846$	−754.300	+	2065.54i	−0.0306541	+	0.0839419i
$847$		0			0
$848$			9938.02i			0.402445i
$849$	−5831.80	+	32970.6i	−0.235744	+	1.33280i
$850$			34482.2i			1.39145i
$851$			25012.8i			1.00755i
$852$	14966.4	−	84614.0i	0.601809	−	3.40238i
$853$			26673.5i			1.07067i	0.844639	+	0.535336i	$0.179815\pi$
$853$			26673.5i			1.07067i	−0.844639	+	0.535336i	$0.820185\pi$
$854$		0			0
$855$	−10922.3	+	29909.0i	−0.436881	+	1.19634i
$856$	−18949.9			−0.756654
$857$	28604.9			1.14017			0.570084	−	0.821586i	$-0.306911\pi$
$857$	28604.9			1.14017			0.570084	+	0.821586i	$0.306911\pi$
$858$	−1990.86	+	11255.5i	−0.0792152	+	0.447851i
$859$			42152.2i			1.67429i	0.546980	+	0.837146i	$0.315777\pi$
$859$			42152.2i			1.67429i	−0.546980	+	0.837146i	$0.684223\pi$
$860$	114461.			4.53849
$861$		0			0
$862$	61141.0			2.41586
$863$		−	33862.3i		−	1.33567i	−0.744308	−	0.667836i	$-0.767221\pi$
$863$		−	33862.3i		−	1.33567i	0.744308	−	0.667836i	$-0.232779\pi$
$864$	−2781.33	+	4799.60i	−0.109517	+	0.188988i
$865$	−53567.7			−2.10561
$866$	−68701.8			−2.69582
$867$	16610.0	+	2937.95i	0.650639	+	0.115084i
$868$		0			0
$869$			1449.08i			0.0565671i
$870$	92823.6	+	16418.5i	3.61726	+	0.639816i
$871$		−	2807.56i		−	0.109220i
$872$			2269.27i			0.0881274i
$873$	−12581.0	+	34451.3i	−0.487747	+	1.33563i
$874$		−	23702.8i		−	0.917343i
$875$		0			0
$876$	15098.6	−	85361.2i	0.582345	−	3.29234i
$877$	14209.4			0.547111			0.273556	−	0.961856i	$-0.411800\pi$
$877$	14209.4			0.547111			0.273556	+	0.961856i	$0.411800\pi$
$878$	−36176.6			−1.39055
$879$	−7384.56	−	1306.17i	−0.283362	−	0.0501207i
$880$		−	24871.1i		−	0.952734i
$881$	40320.8			1.54193			0.770966	−	0.636877i	$-0.219774\pi$
$881$	40320.8			1.54193			0.770966	+	0.636877i	$0.219774\pi$
$882$		0			0
$883$	44671.9			1.70252			0.851262	−	0.524741i	$-0.175838\pi$
$883$	44671.9			1.70252			0.851262	+	0.524741i	$0.175838\pi$
$884$		−	10298.8i		−	0.391838i
$885$	−25444.2	−	4500.53i	−0.966437	−	0.170942i
$886$	1762.50			0.0668309
$887$	−6917.18			−0.261845			−0.130922	−	0.991393i	$-0.541794\pi$
$887$	−6917.18			−0.261845			−0.130922	+	0.991393i	$0.541794\pi$
$888$	11418.4	−	64555.0i	0.431505	−	2.43956i
$889$		0			0
$890$		−	56040.6i		−	2.11066i
$891$	−13083.1	+	15524.2i	−0.491918	+	0.583704i
$892$		−	58185.3i		−	2.18407i
$893$		−	1145.83i		−	0.0429382i
$894$	−44571.9	−	7883.81i	−1.66746	−	0.294938i
$895$			15616.8i			0.583252i
$896$		0			0
$897$	−5987.52	−	1059.07i	−0.222874	−	0.0394216i
$898$	26378.7			0.980253
$899$	34054.8			1.26340
$900$	−68409.4	−	24981.9i	−2.53368	−	0.925257i
$901$			7860.13i			0.290631i
$902$	−20693.4			−0.763876
$903$		0			0
$904$	3075.20			0.113141
$905$			60485.1i			2.22165i
$906$	−9163.48	+	51806.6i	−0.336022	+	1.89973i
$907$	3716.85			0.136071			0.0680353	−	0.997683i	$-0.478327\pi$
$907$	3716.85			0.136071			0.0680353	+	0.997683i	$0.478327\pi$
$908$	43893.4			1.60424
$909$	737.925	+	269.477i	0.0269257	+	0.00983278i
$910$		0			0
$911$			47943.1i			1.74361i	0.489855	+	0.871804i	$0.337050\pi$
$911$			47943.1i			1.74361i	−0.489855	+	0.871804i	$0.662950\pi$
$912$	−3184.38	+	18003.2i	−0.115620	+	0.653668i
$913$		−	28491.6i		−	1.03279i
$914$			11170.6i			0.404256i
$915$	3512.10	−	19856.0i	0.126892	−	0.717398i
$916$			80578.8i			2.90655i
$917$		0			0
$918$	13913.7	−	24010.1i	0.500239	−	0.863236i
$919$	−7853.69			−0.281904			−0.140952	−	0.990016i	$-0.545016\pi$
$919$	−7853.69			−0.281904			−0.140952	+	0.990016i	$0.545016\pi$
$920$	44956.9			1.61107
$921$	−4981.63	+	28164.1i	−0.178230	+	1.00764i
$922$			2837.89i			0.101367i
$923$	17424.9			0.621396
$924$		0			0
$925$	−60752.5			−2.15949
$926$			54851.2i			1.94657i
$927$	−2786.93	+	7631.60i	−0.0987429	+	0.270393i
$928$	−8557.41			−0.302706
$929$	−19541.9			−0.690148			−0.345074	−	0.938575i	$-0.612146\pi$
$929$	−19541.9			−0.690148			−0.345074	+	0.938575i	$0.612146\pi$
$930$	−67486.5	−	11936.9i	−2.37954	−	0.420889i
$931$		0			0
$932$		−	33821.4i		−	1.18869i
$933$	12379.7	+	2189.70i	0.434397	+	0.0768355i
$934$		−	48246.4i		−	1.69023i
$935$		−	19671.0i		−	0.688031i
$936$	14969.6	+	5466.64i	0.522754	+	0.190900i
$937$		−	8670.27i		−	0.302290i	−0.988512	−	0.151145i	$-0.951704\pi$
$937$		−	8670.27i		−	0.302290i	0.988512	−	0.151145i	$-0.0482960\pi$
$938$		0			0
$939$	1077.34	−	6090.86i	0.0374417	−	0.211680i
$940$	4499.99			0.156142
$941$	−49486.9			−1.71437			−0.857187	−	0.515006i	$-0.827790\pi$
$941$	−49486.9			−1.71437			−0.857187	+	0.515006i	$0.827790\pi$
$942$	27029.2	+	4780.89i	0.934883	+	0.165361i
$943$		−	11008.2i		−	0.380144i
$944$	−14836.5			−0.511532
$945$		0			0
$946$	−57691.3			−1.98278
$947$		−	34057.1i		−	1.16865i	−0.811521	−	0.584323i	$-0.801360\pi$
$947$		−	34057.1i		−	1.16865i	0.811521	−	0.584323i	$-0.198640\pi$
$948$	4119.44	+	728.641i	0.141132	+	0.0249632i
$949$	17578.8			0.601298
$950$	57570.6			1.96614
$951$	5998.76	−	33914.6i	0.204546	−	1.15642i
$952$		0			0
$953$		−	28600.5i		−	0.972152i	−0.873917	−	0.486076i	$-0.838428\pi$
$953$		−	28600.5i		−	0.972152i	0.873917	−	0.486076i	$-0.161572\pi$
$954$	−23656.4	−	8638.92i	−0.802836	−	0.293182i
$955$			6133.51i			0.207828i
$956$			29736.2i			1.00600i
$957$	−30839.8	−	5454.90i	−1.04170	−	0.184255i
$958$		−	67014.0i		−	2.26005i
$959$		0			0
$960$	53515.1	+	9465.68i	1.79916	+	0.318233i
$961$	5031.75			0.168902
$962$	27526.6			0.922549
$963$	4847.86	−	13275.2i	0.162222	−	0.444222i
$964$			69259.1i			2.31399i
$965$	−49133.3			−1.63902
$966$		0			0
$967$	10889.4			0.362131			0.181065	−	0.983471i	$-0.442045\pi$
$967$	10889.4			0.362131			0.181065	+	0.983471i	$0.442045\pi$
$968$		−	20108.6i		−	0.667679i
$969$	−2518.57	+	14239.0i	−0.0834967	+	0.472056i
$970$	113863.			3.76898
$971$	45497.2			1.50368			0.751841	−	0.659344i	$-0.229166\pi$
$971$	45497.2			1.50368			0.751841	+	0.659344i	$0.229166\pi$
$972$	37553.5	+	44998.4i	1.23923	+	1.48490i
$973$		0			0
$974$			2210.11i			0.0727069i
$975$	2572.32	−	14542.8i	0.0844924	−	0.477686i
$976$		−	11578.0i		−	0.379717i
$977$		−	27429.6i		−	0.898210i	−0.893479	−	0.449105i	$-0.851743\pi$
$977$		−	27429.6i		−	0.898210i	0.893479	−	0.449105i	$-0.148257\pi$
$978$	−8508.79	+	48105.2i	−0.278201	+	1.57284i
$979$			18619.0i			0.607830i
$980$		0			0
$981$	−1589.71	−	580.534i	−0.0517385	−	0.0188940i
$982$	−82553.9			−2.68269
$983$	−25943.6			−0.841783			−0.420892	−	0.907111i	$-0.638283\pi$
$983$	−25943.6			−0.841783			−0.420892	+	0.907111i	$0.638283\pi$
$984$	−5025.27	+	28410.8i	−0.162805	+	0.920431i
$985$		−	52911.4i		−	1.71157i
$986$	42808.6			1.38266
$987$		0			0
$988$	−17194.5			−0.553675
$989$		−	30689.8i		−	0.986732i
$990$	59203.2	+	21620.0i	1.90061	+	0.694069i
$991$	53486.9			1.71450			0.857250	−	0.514901i	$-0.172171\pi$
$991$	53486.9			1.71450			0.857250	+	0.514901i	$0.172171\pi$
$992$	6221.59			0.199129
$993$	36764.5	+	6502.86i	1.17491	+	0.207817i
$994$		0			0
$995$			31825.2i			1.01400i
$996$	−80995.5	−	14326.4i	−2.57675	−	0.455772i
$997$		−	797.622i		−	0.0253369i	−0.999920	−	0.0126685i	$-0.995967\pi$
$997$		−	797.622i		−	0.0253369i	0.999920	−	0.0126685i	$-0.00403261\pi$
$998$		−	8989.79i		−	0.285137i
$999$	42302.2	+	24513.8i	1.33972	+	0.776358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.c.b.146.21	yes	24
3.2	odd	2	inner	147.4.c.b.146.4	yes	24
7.2	even	3		147.4.g.e.80.22		48
7.3	odd	6		147.4.g.e.68.3		48
7.4	even	3		147.4.g.e.68.4		48
7.5	odd	6		147.4.g.e.80.21		48
7.6	odd	2	inner	147.4.c.b.146.22	yes	24
21.2	odd	6		147.4.g.e.80.3		48
21.5	even	6		147.4.g.e.80.4		48
21.11	odd	6		147.4.g.e.68.21		48
21.17	even	6		147.4.g.e.68.22		48
21.20	even	2	inner	147.4.c.b.146.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.c.b.146.3	✓	24	21.20	even	2	inner
147.4.c.b.146.4	yes	24	3.2	odd	2	inner
147.4.c.b.146.21	yes	24	1.1	even	1	trivial
147.4.c.b.146.22	yes	24	7.6	odd	2	inner
147.4.g.e.68.3		48	7.3	odd	6
147.4.g.e.68.4		48	7.4	even	3
147.4.g.e.68.21		48	21.11	odd	6
147.4.g.e.68.22		48	21.17	even	6
147.4.g.e.80.3		48	21.2	odd	6
147.4.g.e.80.4		48	21.5	even	6
147.4.g.e.80.21		48	7.5	odd	6
147.4.g.e.80.22		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)

\(f(q)\)	\(=\)	\(q+4.84485i q^{2} +(-5.11673 - 0.905040i) q^{3} -15.4725 q^{4} -17.3012 q^{5} +(4.38478 - 24.7898i) q^{6} -36.2033i q^{8} +(25.3618 + 9.26169i) q^{9} +O(q^{10})\)	\(q+4.84485i q^{2} +(-5.11673 - 0.905040i) q^{3} -15.4725 q^{4} -17.3012 q^{5} +(4.38478 - 24.7898i) q^{6} -36.2033i q^{8} +(25.3618 + 9.26169i) q^{9} -83.8216i q^{10} +27.8490i q^{11} +(79.1688 + 14.0033i) q^{12} +16.3036i q^{13} +(88.5254 + 15.6583i) q^{15} +51.6191 q^{16} +40.8263 q^{17} +(-44.8715 + 122.874i) q^{18} -68.1627i q^{19} +267.693 q^{20} -134.924 q^{22} -71.7749i q^{23} +(-32.7654 + 185.242i) q^{24} +174.331 q^{25} -78.9883 q^{26} +(-121.387 - 70.3430i) q^{27} -216.426i q^{29} +(-75.8619 + 428.892i) q^{30} +157.351i q^{31} -39.5396i q^{32} +(25.2044 - 142.496i) q^{33} +197.797i q^{34} +(-392.412 - 143.302i) q^{36} -348.489 q^{37} +330.238 q^{38} +(14.7554 - 83.4209i) q^{39} +626.360i q^{40} +153.371 q^{41} +427.584 q^{43} -430.894i q^{44} +(-438.789 - 160.238i) q^{45} +347.738 q^{46} +16.8103 q^{47} +(-264.121 - 46.7174i) q^{48} +844.606i q^{50} +(-208.897 - 36.9495i) q^{51} -252.258i q^{52} +192.526i q^{53} +(340.801 - 588.103i) q^{54} -481.820i q^{55} +(-61.6899 + 348.770i) q^{57} +1048.55 q^{58} -287.422 q^{59} +(-1369.71 - 242.273i) q^{60} -224.297i q^{61} -762.340 q^{62} +604.516 q^{64} -282.071i q^{65} +(690.370 + 122.112i) q^{66} -172.206 q^{67} -631.687 q^{68} +(-64.9591 + 367.252i) q^{69} -1068.78i q^{71} +(335.304 - 918.181i) q^{72} -1078.22i q^{73} -1688.38i q^{74} +(-892.004 - 157.776i) q^{75} +1054.65i q^{76} +(404.161 + 71.4875i) q^{78} +52.0336 q^{79} -893.072 q^{80} +(557.442 + 469.786i) q^{81} +743.059i q^{82} -1023.07 q^{83} -706.344 q^{85} +2071.58i q^{86} +(-195.874 + 1107.39i) q^{87} +1008.23 q^{88} +668.570 q^{89} +(776.329 - 2125.87i) q^{90} +1110.54i q^{92} +(142.409 - 805.121i) q^{93} +81.4431i q^{94} +1179.29i q^{95} +(-35.7849 + 202.313i) q^{96} +1358.39i q^{97} +(-257.929 + 706.300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) 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

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