LMFDB - Embedded newform 147.4.c.b.146.10

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			146.10
Character	$\chi$	$=$	147.146
Dual form			147.4.c.b.146.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.05015i q^{2} +(4.50851 - 2.58329i) q^{3} +6.89718 q^{4} +10.2305 q^{5} +(-2.71285 - 4.73462i) q^{6} -15.6443i q^{8} +(13.6533 - 23.2935i) q^{9} +O(q^{10})$	\(q-1.05015i q^{2} +(4.50851 - 2.58329i) q^{3} +6.89718 q^{4} +10.2305 q^{5} +(-2.71285 - 4.73462i) q^{6} -15.6443i q^{8} +(13.6533 - 23.2935i) q^{9} -10.7436i q^{10} +24.0632i q^{11} +(31.0960 - 17.8174i) q^{12} +49.4354i q^{13} +(46.1243 - 26.4283i) q^{15} +38.7485 q^{16} -125.761 q^{17} +(-24.4618 - 14.3380i) q^{18} +95.5681i q^{19} +70.5616 q^{20} +25.2700 q^{22} -185.716i q^{23} +(-40.4138 - 70.5325i) q^{24} -20.3367 q^{25} +51.9147 q^{26} +(1.38202 - 140.289i) q^{27} -40.6873i q^{29} +(-27.7538 - 48.4376i) q^{30} +37.5677i q^{31} -165.846i q^{32} +(62.1620 + 108.489i) q^{33} +132.069i q^{34} +(94.1690 - 160.660i) q^{36} +283.290 q^{37} +100.361 q^{38} +(127.706 + 222.880i) q^{39} -160.049i q^{40} -166.685 q^{41} -411.667 q^{43} +165.968i q^{44} +(139.680 - 238.305i) q^{45} -195.030 q^{46} -15.1056 q^{47} +(174.698 - 100.098i) q^{48} +21.3567i q^{50} +(-566.996 + 324.878i) q^{51} +340.964i q^{52} +190.230i q^{53} +(-147.325 - 1.45133i) q^{54} +246.178i q^{55} +(246.880 + 430.869i) q^{57} -42.7279 q^{58} +94.7330 q^{59} +(318.128 - 182.281i) q^{60} -412.161i q^{61} +39.4518 q^{62} +135.824 q^{64} +505.749i q^{65} +(113.930 - 65.2797i) q^{66} -88.7656 q^{67} -867.398 q^{68} +(-479.756 - 837.300i) q^{69} +1064.80i q^{71} +(-364.411 - 213.596i) q^{72} +828.400i q^{73} -297.497i q^{74} +(-91.6883 + 52.5356i) q^{75} +659.150i q^{76} +(234.058 - 134.111i) q^{78} +256.515 q^{79} +396.417 q^{80} +(-356.177 - 636.065i) q^{81} +175.045i q^{82} -97.2939 q^{83} -1286.60 q^{85} +432.314i q^{86} +(-105.107 - 183.439i) q^{87} +376.452 q^{88} +899.046 q^{89} +(-250.256 - 146.685i) q^{90} -1280.91i q^{92} +(97.0480 + 169.374i) q^{93} +15.8632i q^{94} +977.710i q^{95} +(-428.429 - 747.720i) q^{96} +398.892i q^{97} +(560.516 + 328.541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.05015i		−	0.371285i	−0.982617	−	0.185643i	$-0.940563\pi$
$2$		−	1.05015i		−	0.371285i	0.982617	−	0.185643i	$-0.0594367\pi$
$3$	4.50851	−	2.58329i	0.867663	−	0.497154i
$3$	4.50851	−	2.58329i	0.867663	−	0.497154i
$4$	6.89718			0.862147
$5$	10.2305			0.915044			0.457522	−	0.889198i	$-0.348737\pi$
$5$	10.2305			0.915044			0.457522	+	0.889198i	$0.348737\pi$
$6$	−2.71285	−	4.73462i	−0.184586	−	0.322150i
$7$		0			0
$7$		0			0
$8$		−	15.6443i		−	0.691388i
$9$	13.6533	−	23.2935i	0.505677	−	0.862723i
$10$		−	10.7436i		−	0.339742i
$11$			24.0632i			0.659574i	0.944055	+	0.329787i	$0.106977\pi$
$11$			24.0632i			0.659574i	−0.944055	+	0.329787i	$0.893023\pi$
$12$	31.0960	−	17.8174i	0.748053	−	0.428620i
$13$			49.4354i			1.05468i	0.849653	+	0.527342i	$0.176811\pi$
$13$			49.4354i			1.05468i	−0.849653	+	0.527342i	$0.823189\pi$
$14$		0			0
$15$	46.1243	−	26.4283i	0.793950	−	0.454918i
$16$	38.7485			0.605445
$17$	−125.761			−1.79421			−0.897106	−	0.441815i	$-0.854335\pi$
$17$	−125.761			−1.79421			−0.897106	+	0.441815i	$0.854335\pi$
$18$	−24.4618	−	14.3380i	−0.320316	−	0.187750i
$19$			95.5681i			1.15394i	0.816766	+	0.576969i	$0.195765\pi$
$19$			95.5681i			1.15394i	−0.816766	+	0.576969i	$0.804235\pi$
$20$	70.5616			0.788903
$21$		0			0
$22$	25.2700			0.244890
$23$		−	185.716i		−	1.68367i	−0.539736	−	0.841834i	$-0.681476\pi$
$23$		−	185.716i		−	1.68367i	0.539736	−	0.841834i	$-0.318524\pi$
$24$	−40.4138	−	70.5325i	−0.343726	−	0.599891i
$25$	−20.3367			−0.162694
$26$	51.9147			0.391589
$27$	1.38202	−	140.289i	0.00985074	−	0.999951i
$28$		0			0
$29$		−	40.6873i		−	0.260533i	−0.991479	−	0.130266i	$-0.958417\pi$
$29$		−	40.6873i		−	0.260533i	0.991479	−	0.130266i	$-0.0415832\pi$
$30$	−27.7538	−	48.4376i	−0.168904	−	0.294782i
$31$			37.5677i			0.217656i	0.994061	+	0.108828i	$0.0347098\pi$
$31$			37.5677i			0.217656i	−0.994061	+	0.108828i	$0.965290\pi$
$32$		−	165.846i		−	0.916181i
$33$	62.1620	+	108.489i	0.327910	+	0.572288i
$34$			132.069i			0.666165i
$35$		0			0
$36$	94.1690	−	160.660i	0.435968	−	0.743794i
$37$	283.290			1.25872			0.629358	−	0.777115i	$-0.283318\pi$
$37$	283.290			1.25872			0.629358	+	0.777115i	$0.283318\pi$
$38$	100.361			0.428440
$39$	127.706	+	222.880i	0.524340	+	0.915110i
$40$		−	160.049i		−	0.632651i
$41$	−166.685			−0.634923			−0.317462	−	0.948271i	$-0.602830\pi$
$41$	−166.685			−0.634923			−0.317462	+	0.948271i	$0.602830\pi$
$42$		0			0
$43$	−411.667			−1.45997			−0.729984	−	0.683464i	$-0.760473\pi$
$43$	−411.667			−1.45997			−0.729984	+	0.683464i	$0.760473\pi$
$44$			165.968i			0.568650i
$45$	139.680	−	238.305i	0.462716	−	0.789430i
$46$	−195.030			−0.625121
$47$	−15.1056			−0.0468805			−0.0234402	−	0.999725i	$-0.507462\pi$
$47$	−15.1056			−0.0468805			−0.0234402	+	0.999725i	$0.507462\pi$
$48$	174.698	−	100.098i	0.525322	−	0.300999i
$49$		0			0
$50$			21.3567i			0.0604058i
$51$	−566.996	+	324.878i	−1.55677	+	0.891999i
$52$			340.964i			0.909293i
$53$			190.230i			0.493020i	0.969140	+	0.246510i	$0.0792838\pi$
$53$			190.230i			0.493020i	−0.969140	+	0.246510i	$0.920716\pi$
$54$	−147.325	−	1.45133i	−0.371267	−	0.00365744i
$55$			246.178i			0.603540i
$56$		0			0
$57$	246.880	+	430.869i	0.573684	+	1.00123i
$58$	−42.7279			−0.0967320
$59$	94.7330			0.209037			0.104519	−	0.994523i	$-0.466670\pi$
$59$	94.7330			0.209037			0.104519	+	0.994523i	$0.466670\pi$
$60$	318.128	−	182.281i	0.684502	−	0.392206i
$61$		−	412.161i		−	0.865111i	−0.901607	−	0.432555i	$-0.857612\pi$
$61$		−	412.161i		−	0.865111i	0.901607	−	0.432555i	$-0.142388\pi$
$62$	39.4518			0.0808126
$63$		0			0
$64$	135.824			0.265281
$65$			505.749i			0.965083i
$66$	113.930	−	65.2797i	0.212482	−	0.121748i
$67$	−88.7656			−0.161857			−0.0809287	−	0.996720i	$-0.525789\pi$
$67$	−88.7656			−0.161857			−0.0809287	+	0.996720i	$0.525789\pi$
$68$	−867.398			−1.54688
$69$	−479.756	−	837.300i	−0.837042	−	1.46086i
$70$		0			0
$71$			1064.80i			1.77984i	0.456118	+	0.889920i	$0.349240\pi$
$71$			1064.80i			1.77984i	−0.456118	+	0.889920i	$0.650760\pi$
$72$	−364.411	−	213.596i	−0.596476	−	0.349619i
$73$			828.400i			1.32818i	0.747654	+	0.664088i	$0.231180\pi$
$73$			828.400i			1.32818i	−0.747654	+	0.664088i	$0.768820\pi$
$74$		−	297.497i		−	0.467343i
$75$	−91.6883	+	52.5356i	−0.141163	+	0.0808839i
$76$			659.150i			0.994864i
$77$		0			0
$78$	234.058	−	134.111i	0.339767	−	0.194680i
$79$	256.515			0.365319			0.182659	−	0.983176i	$-0.441529\pi$
$79$	256.515			0.365319			0.182659	+	0.983176i	$0.441529\pi$
$80$	396.417			0.554009
$81$	−356.177	−	636.065i	−0.488582	−	0.872518i
$82$			175.045i			0.235738i
$83$	−97.2939			−0.128667			−0.0643337	−	0.997928i	$-0.520492\pi$
$83$	−97.2939			−0.128667			−0.0643337	+	0.997928i	$0.520492\pi$
$84$		0			0
$85$	−1286.60			−1.64178
$86$			432.314i			0.542065i
$87$	−105.107	−	183.439i	−0.129525	−	0.226054i
$88$	376.452			0.456022
$89$	899.046			1.07077			0.535386	−	0.844608i	$-0.320166\pi$
$89$	899.046			1.07077			0.535386	+	0.844608i	$0.320166\pi$
$90$	−250.256	−	146.685i	−0.293104	−	0.171800i
$91$		0			0
$92$		−	1280.91i		−	1.45157i
$93$	97.0480	+	169.374i	0.108209	+	0.188852i
$94$			15.8632i			0.0174060i
$95$			977.710i			1.05590i
$96$	−428.429	−	747.720i	−0.455483	−	0.794936i
$97$			398.892i			0.417540i	0.977965	+	0.208770i	$0.0669460\pi$
$97$			398.892i			0.417540i	−0.977965	+	0.208770i	$0.933054\pi$
$98$		0			0
$99$	560.516	+	328.541i	0.569030	+	0.333531i
$100$	−140.266			−0.140266
$101$	57.2539			0.0564057			0.0282028	−	0.999602i	$-0.491022\pi$
$101$	57.2539			0.0564057			0.0282028	+	0.999602i	$0.491022\pi$
$102$	341.171	+	595.433i	0.331186	+	0.578006i
$103$			740.200i			0.708098i	0.935227	+	0.354049i	$0.115195\pi$
$103$			740.200i			0.708098i	−0.935227	+	0.354049i	$0.884805\pi$
$104$	773.383			0.729196
$105$		0			0
$106$	199.770			0.183051
$107$		−	862.638i		−	0.779386i	−0.920945	−	0.389693i	$-0.872581\pi$
$107$		−	862.638i		−	0.779386i	0.920945	−	0.389693i	$-0.127419\pi$
$108$	9.53205	−	967.600i	0.00849279	−	0.862105i
$109$	−657.058			−0.577383			−0.288691	−	0.957422i	$-0.593220\pi$
$109$	−657.058			−0.577383			−0.288691	+	0.957422i	$0.593220\pi$
$110$	258.525			0.224085
$111$	1277.21	−	731.818i	1.09214	−	0.625776i
$112$		0			0
$113$		−	884.317i		−	0.736190i	−0.929788	−	0.368095i	$-0.880010\pi$
$113$		−	884.317i		−	0.736190i	0.929788	−	0.368095i	$-0.119990\pi$
$114$	452.479	−	259.262i	0.371742	−	0.213001i
$115$		−	1899.96i		−	1.54063i
$116$		−	280.628i		−	0.224618i
$117$	1151.52	+	674.954i	0.909901	+	0.533329i
$118$		−	99.4842i		−	0.0776124i
$119$		0			0
$120$	−413.453	−	721.584i	−0.314524	−	0.548927i
$121$	751.964			0.564962
$122$	−432.832			−0.321203
$123$	−751.501	+	430.595i	−0.550899	+	0.315654i
$124$			259.111i			0.187652i
$125$	−1486.87			−1.06392
$126$		0			0
$127$	1004.76			0.702028			0.351014	−	0.936370i	$-0.385837\pi$
$127$	1004.76			0.702028			0.351014	+	0.936370i	$0.385837\pi$
$128$		−	1469.41i		−	1.01468i
$129$	−1856.00	+	1063.45i	−1.26676	+	0.725829i
$130$	531.114			0.358321
$131$	712.639			0.475294			0.237647	−	0.971352i	$-0.423624\pi$
$131$	712.639			0.475294			0.237647	+	0.971352i	$0.423624\pi$
$132$	428.743	+	748.268i	0.282706	+	0.493396i
$133$		0			0
$134$			93.2175i			0.0600953i
$135$	14.1388	−	1435.23i	0.00901387	−	0.915000i
$136$			1967.45i			1.24050i
$137$		−	1359.68i		−	0.847921i	−0.905681	−	0.423961i	$-0.860639\pi$
$137$		−	1359.68i		−	0.847921i	0.905681	−	0.423961i	$-0.139361\pi$
$138$	−879.293	+	503.818i	−0.542394	+	0.310781i
$139$		−	213.266i		−	0.130137i	−0.997881	−	0.0650684i	$-0.979273\pi$
$139$		−	213.266i		−	0.130137i	0.997881	−	0.0650684i	$-0.0207266\pi$
$140$		0			0
$141$	−68.1039	+	39.0222i	−0.0406765	+	0.0233068i
$142$	1118.20			0.660828
$143$	−1189.57			−0.695643
$144$	529.043	−	902.589i	0.306159	−	0.522331i
$145$		−	416.252i		−	0.238399i
$146$	869.947			0.493132
$147$		0			0
$148$	1953.90			1.08520
$149$		−	1522.90i		−	0.837319i	−0.908143	−	0.418660i	$-0.862500\pi$
$149$		−	1522.90i		−	0.837319i	0.908143	−	0.418660i	$-0.137500\pi$
$150$	55.1704	+	96.2868i	0.0300310	+	0.0524119i
$151$	410.715			0.221348			0.110674	−	0.993857i	$-0.464699\pi$
$151$	410.715			0.221348			0.110674	+	0.993857i	$0.464699\pi$
$152$	1495.10			0.797819
$153$	−1717.05	+	2929.43i	−0.907291	+	1.54791i
$154$		0			0
$155$			384.336i			0.199165i
$156$	880.809	+	1537.24i	0.452059	+	0.788960i
$157$		−	2184.75i		−	1.11059i	−0.831655	−	0.555293i	$-0.812606\pi$
$157$		−	2184.75i		−	1.11059i	0.831655	−	0.555293i	$-0.187394\pi$
$158$		−	269.380i		−	0.135637i
$159$	491.417	+	857.651i	0.245107	+	0.427775i
$160$		−	1696.69i		−	0.838346i
$161$		0			0
$162$	−667.966	+	374.040i	−0.323953	+	0.181403i
$163$	−1593.25			−0.765600			−0.382800	−	0.923831i	$-0.625040\pi$
$163$	−1593.25			−0.765600			−0.382800	+	0.923831i	$0.625040\pi$
$164$	−1149.66			−0.547397
$165$	635.949	+	1109.90i	0.300052	+	0.523669i
$166$			102.173i			0.0477723i
$167$	1297.31			0.601129			0.300564	−	0.953762i	$-0.402825\pi$
$167$	1297.31			0.601129			0.300564	+	0.953762i	$0.402825\pi$
$168$		0			0
$169$	−246.854			−0.112360
$170$			1351.13i			0.609570i
$171$	2226.12	+	1304.82i	0.995529	+	0.583519i
$172$	−2839.34			−1.25871
$173$	−3229.49			−1.41927			−0.709635	−	0.704570i	$-0.751140\pi$
$173$	−3229.49			−1.41927			−0.709635	+	0.704570i	$0.751140\pi$
$174$	−192.639	+	110.378i	−0.0839307	+	0.0480906i
$175$		0			0
$176$			932.411i			0.399336i
$177$	427.104	−	244.722i	0.181374	−	0.103924i
$178$		−	944.136i		−	0.397562i
$179$			3521.41i			1.47040i	0.677848	+	0.735202i	$0.262913\pi$
$179$			3521.41i			1.47040i	−0.677848	+	0.735202i	$0.737087\pi$
$180$	963.397	−	1643.63i	0.398930	−	0.680605i
$181$		−	3143.01i		−	1.29071i	−0.763883	−	0.645354i	$-0.776710\pi$
$181$		−	3143.01i		−	1.29071i	0.763883	−	0.645354i	$-0.223290\pi$
$182$		0			0
$183$	−1064.73	−	1858.23i	−0.430093	−	0.750624i
$184$	−2905.39			−1.16407
$185$	2898.20			1.15178
$186$	177.869	−	101.915i	0.0701181	−	0.0401763i
$187$		−	3026.22i		−	1.18342i
$188$	−104.186			−0.0404179
$189$		0			0
$190$	1026.75			0.392042
$191$			4480.24i			1.69727i	0.528978	+	0.848636i	$0.322576\pi$
$191$			4480.24i			1.69727i	−0.528978	+	0.848636i	$0.677424\pi$
$192$	612.362	−	350.871i	0.230174	−	0.131885i
$193$	5217.77			1.94603			0.973013	−	0.230751i	$-0.0741182\pi$
$193$	5217.77			1.94603			0.973013	+	0.230751i	$0.0741182\pi$
$194$	418.898			0.155026
$195$	1306.49	+	2280.17i	0.479795	+	0.837367i
$196$		0			0
$197$			474.082i			0.171457i	0.996319	+	0.0857283i	$0.0273217\pi$
$197$			474.082i			0.171457i	−0.996319	+	0.0857283i	$0.972678\pi$
$198$	345.018	−	588.628i	0.123835	−	0.211272i
$199$		−	1055.13i		−	0.375860i	−0.982182	−	0.187930i	$-0.939822\pi$
$199$		−	1055.13i		−	0.375860i	0.982182	−	0.187930i	$-0.0601778\pi$
$200$			318.154i			0.112485i
$201$	−400.200	+	229.307i	−0.140438	+	0.0804680i
$202$		−	60.1253i		−	0.0209426i
$203$		0			0
$204$	−3910.67	+	2240.74i	−1.34217	+	0.769035i
$205$	−1705.27			−0.580983
$206$	777.324			0.262906
$207$	−4325.97	−	2535.62i	−1.45254	−	0.851392i
$208$			1915.55i			0.638554i
$209$	−2299.67			−0.761108
$210$		0			0
$211$	−1367.40			−0.446141			−0.223070	−	0.974802i	$-0.571608\pi$
$211$	−1367.40			−0.446141			−0.223070	+	0.974802i	$0.571608\pi$
$212$			1312.05i			0.425056i
$213$	2750.68	+	4800.66i	0.884853	+	1.54430i
$214$	−905.902			−0.289375
$215$	−4211.56			−1.33594
$216$	−2194.73	−	21.6208i	−0.691354	−	0.00681069i
$217$		0			0
$218$			690.012i			0.214374i
$219$	2139.99	+	3734.85i	0.660308	+	1.15241i
$220$			1697.94i			0.520340i
$221$		−	6217.06i		−	1.89233i
$222$	−768.521	−	1341.27i	−0.232341	−	0.405496i
$223$		−	1165.04i		−	0.349852i	−0.984582	−	0.174926i	$-0.944031\pi$
$223$		−	1165.04i		−	0.349852i	0.984582	−	0.174926i	$-0.0559686\pi$
$224$		0			0
$225$	−277.663	+	473.714i	−0.0822705	+	0.140360i
$226$	−928.668			−0.273337
$227$	−1508.20			−0.440981			−0.220491	−	0.975389i	$-0.570766\pi$
$227$	−1508.20			−0.440981			−0.220491	+	0.975389i	$0.570766\pi$
$228$	1702.77	+	2971.78i	0.494600	+	0.863207i
$229$			2678.95i			0.773056i	0.922278	+	0.386528i	$0.126326\pi$
$229$			2678.95i			0.773056i	−0.922278	+	0.386528i	$0.873674\pi$
$230$	−1995.25			−0.572014
$231$		0			0
$232$	−636.526			−0.180129
$233$		−	1651.83i		−	0.464443i	−0.972663	−	0.232221i	$-0.925401\pi$
$233$		−	1651.83i		−	0.464443i	0.972663	−	0.232221i	$-0.0745994\pi$
$234$	708.805	−	1209.28i	0.198017	−	0.337833i
$235$	−154.538			−0.0428977
$236$	653.390			0.180221
$237$	1156.50	−	662.651i	0.316973	−	0.181620i
$238$		0			0
$239$			1945.85i			0.526638i	0.964709	+	0.263319i	$0.0848172\pi$
$239$			1945.85i			0.526638i	−0.964709	+	0.263319i	$0.915183\pi$
$240$	1787.25	−	1024.06i	0.480693	−	0.275428i
$241$		−	480.849i		−	0.128524i	−0.997933	−	0.0642618i	$-0.979531\pi$
$241$		−	480.849i		−	0.128524i	0.997933	−	0.0642618i	$-0.0204693\pi$
$242$		−	789.678i		−	0.209762i
$243$	−3248.96	−	1947.60i	−0.857700	−	0.514151i
$244$		−	2842.74i		−	0.745853i
$245$		0			0
$246$	452.191	+	789.192i	0.117198	+	0.204541i
$247$	−4724.44			−1.21704
$248$	587.720			0.150485
$249$	−438.650	+	251.338i	−0.111640	+	0.0639674i
$250$			1561.44i			0.395017i
$251$	5108.84			1.28473			0.642364	−	0.766400i	$-0.277954\pi$
$251$	5108.84			1.28473			0.642364	+	0.766400i	$0.277954\pi$
$252$		0			0
$253$	4468.90			1.11050
$254$		−	1055.15i		−	0.260653i
$255$	−5800.66	+	3323.66i	−1.42451	+	0.816219i
$256$	−456.513			−0.111453
$257$	1656.10			0.401963			0.200982	−	0.979595i	$-0.435587\pi$
$257$	1656.10			0.401963			0.200982	+	0.979595i	$0.435587\pi$
$258$	1116.79	+	1949.09i	0.269489	+	0.470329i
$259$		0			0
$260$			3488.24i			0.832044i
$261$	−947.751	−	555.515i	−0.224768	−	0.131745i
$262$		−	748.380i		−	0.176470i
$263$			1496.85i			0.350950i	0.984484	+	0.175475i	$0.0561462\pi$
$263$			1496.85i			0.350950i	−0.984484	+	0.175475i	$0.943854\pi$
$264$	1697.24	−	972.483i	0.395673	−	0.226713i
$265$			1946.15i			0.451135i
$266$		0			0
$267$	4053.35	−	2322.49i	0.929068	−	0.532338i
$268$	−612.232			−0.139545
$269$	2373.66			0.538009			0.269005	−	0.963139i	$-0.413305\pi$
$269$	2373.66			0.538009			0.269005	+	0.963139i	$0.413305\pi$
$270$	−1507.21	−	14.8479i	−0.339726	−	0.00334672i
$271$		−	5846.44i		−	1.31050i	−0.755412	−	0.655251i	$-0.772563\pi$
$271$		−	5846.44i		−	1.31050i	0.755412	−	0.655251i	$-0.227437\pi$
$272$	−4873.06			−1.08630
$273$		0			0
$274$	−1427.87			−0.314821
$275$		−	489.366i		−	0.107309i
$276$	−3308.97	−	5775.01i	−0.721653	−	1.25947i
$277$	2501.87			0.542681			0.271341	−	0.962483i	$-0.412533\pi$
$277$	2501.87			0.542681			0.271341	+	0.962483i	$0.412533\pi$
$278$	−223.962			−0.0483179
$279$	875.083	+	512.921i	0.187777	+	0.110064i
$280$		0			0
$281$		−	8088.74i		−	1.71720i	−0.512645	−	0.858601i	$-0.671334\pi$
$281$		−	8088.74i		−	1.71720i	0.512645	−	0.858601i	$-0.328666\pi$
$282$	40.9793	+	71.5195i	0.00865347	+	0.0151026i
$283$		−	4331.83i		−	0.909895i	−0.890518	−	0.454947i	$-0.849658\pi$
$283$		−	4331.83i		−	0.909895i	0.890518	−	0.454947i	$-0.150342\pi$
$284$			7344.12i			1.53448i
$285$	2525.70	+	4408.01i	0.524947	+	0.916169i
$286$			1249.23i			0.258282i
$287$		0			0
$288$	−3863.15	−	2264.35i	−0.790410	−	0.463291i
$289$	10902.9			2.21920
$290$	−437.128			−0.0885140
$291$	1030.45	+	1798.41i	0.207581	+	0.362284i
$292$			5713.62i			1.14508i
$293$	4715.26			0.940164			0.470082	−	0.882623i	$-0.344224\pi$
$293$	4715.26			0.940164			0.470082	+	0.882623i	$0.344224\pi$
$294$		0			0
$295$	969.166			0.191278
$296$		−	4431.87i		−	0.870261i
$297$	3375.81	+	33.2558i	0.659542	+	0.00649730i
$298$	−1599.28			−0.310884
$299$	9180.91			1.77574
$300$	−632.391	+	362.347i	−0.121704	+	0.0697338i
$301$		0			0
$302$		−	431.314i		−	0.0821832i
$303$	258.129	−	147.903i	0.0489411	−	0.0280423i
$304$			3703.12i			0.698646i
$305$		−	4216.61i		−	0.791615i
$306$	3076.35	+	1803.17i	0.574716	+	0.336864i
$307$			4540.05i			0.844020i	0.906591	+	0.422010i	$0.138675\pi$
$307$			4540.05i			0.844020i	−0.906591	+	0.422010i	$0.861325\pi$
$308$		0			0
$309$	1912.15	+	3337.20i	0.352033	+	0.614390i
$310$	403.612			0.0739471
$311$	−5248.33			−0.956932			−0.478466	−	0.878106i	$-0.658807\pi$
$311$	−5248.33			−0.956932			−0.478466	+	0.878106i	$0.658807\pi$
$312$	3486.80	−	1997.87i	0.632696	−	0.362522i
$313$		−	6079.22i		−	1.09782i	−0.835881	−	0.548910i	$-0.815043\pi$
$313$		−	6079.22i		−	1.09782i	0.835881	−	0.548910i	$-0.184957\pi$
$314$	−2294.32			−0.412344
$315$		0			0
$316$	1769.23			0.314959
$317$		−	4335.82i		−	0.768215i	−0.923288	−	0.384107i	$-0.874509\pi$
$317$		−	4335.82i		−	0.768215i	0.923288	−	0.384107i	$-0.125491\pi$
$318$	900.666	−	516.064i	0.158826	−	0.0910044i
$319$	979.066			0.171841
$320$	1389.55			0.242744
$321$	−2228.44	−	3889.21i	−0.387475	−	0.676244i
$322$		0			0
$323$		−	12018.8i		−	2.07041i
$324$	−2456.61	−	4387.06i	−0.421230	−	0.752239i
$325$		−	1005.35i		−	0.171591i
$326$			1673.16i			0.284256i
$327$	−2962.35	+	1697.37i	−0.500974	+	0.287048i
$328$			2607.68i			0.438978i
$329$		0			0
$330$	1165.56	−	667.844i	0.194431	−	0.111405i
$331$	6270.17			1.04121			0.520603	−	0.853799i	$-0.325707\pi$
$331$	6270.17			1.04121			0.520603	+	0.853799i	$0.325707\pi$
$332$	−671.053			−0.110930
$333$	3867.83	−	6598.81i	0.636504	−	1.08592i
$334$		−	1362.37i		−	0.223190i
$335$	−908.117			−0.148107
$336$		0			0
$337$	−5320.37			−0.859997			−0.429999	−	0.902830i	$-0.641486\pi$
$337$	−5320.37			−0.859997			−0.429999	+	0.902830i	$0.641486\pi$
$338$			259.235i			0.0417175i
$339$	−2284.44	−	3986.95i	−0.366000	−	0.638765i
$340$	−8873.93			−1.41546
$341$	−903.997			−0.143561
$342$	1370.26	−	2337.76i	0.216652	−	0.369625i
$343$		0			0
$344$			6440.25i			1.00940i
$345$	−4908.15	−	8566.00i	−0.765930	−	1.33675i
$346$			3391.46i			0.526954i
$347$			4815.66i			0.745009i	0.928030	+	0.372504i	$0.121501\pi$
$347$			4815.66i			0.745009i	−0.928030	+	0.372504i	$0.878499\pi$
$348$	−724.942	−	1265.21i	−0.111669	−	0.194892i
$349$		−	5201.69i		−	0.797822i	−0.916990	−	0.398911i	$-0.869388\pi$
$349$		−	5201.69i		−	0.797822i	0.916990	−	0.398911i	$-0.130612\pi$
$350$		0			0
$351$	6935.25	+	68.3207i	1.05463	+	0.0103894i
$352$	3990.79			0.604289
$353$	−637.734			−0.0961563			−0.0480782	−	0.998844i	$-0.515310\pi$
$353$	−637.734			−0.0961563			−0.0480782	+	0.998844i	$0.515310\pi$
$354$	−256.996	−	448.525i	−0.0385853	−	0.0673413i
$355$			10893.4i			1.62863i
$356$	6200.88			0.923163
$357$		0			0
$358$	3698.02			0.545939
$359$			5518.37i			0.811277i	0.914034	+	0.405638i	$0.132951\pi$
$359$			5518.37i			0.811277i	−0.914034	+	0.405638i	$0.867049\pi$
$360$	−3728.11	−	2185.20i	−0.545802	−	0.319917i
$361$	−2274.26			−0.331573
$362$	−3300.64			−0.479221
$363$	3390.23	−	1942.54i	0.490196	−	0.280873i
$364$		0			0
$365$			8474.95i			1.21534i
$366$	−1951.42	+	1118.13i	−0.278696	+	0.159687i
$367$			2594.14i			0.368973i	0.982835	+	0.184486i	$0.0590622\pi$
$367$			2594.14i			0.368973i	−0.982835	+	0.184486i	$0.940938\pi$
$368$		−	7196.20i		−	1.01937i
$369$	−2275.80	+	3882.69i	−0.321066	+	0.547763i
$370$		−	3043.55i		−	0.427640i
$371$		0			0
$372$	669.357	+	1168.20i	0.0932918	+	0.162819i
$373$	−5173.83			−0.718206			−0.359103	−	0.933298i	$-0.616917\pi$
$373$	−5173.83			−0.718206			−0.359103	+	0.933298i	$0.616917\pi$
$374$	−3177.99			−0.439385
$375$	−6703.56	+	3841.01i	−0.923120	+	0.528930i
$376$			236.317i			0.0324126i
$377$	2011.39			0.274780
$378$		0			0
$379$	−14088.2			−1.90940			−0.954700	−	0.297568i	$-0.903824\pi$
$379$	−14088.2			−1.90940			−0.954700	+	0.297568i	$0.903824\pi$
$380$			6743.44i			0.910345i
$381$	4529.95	−	2595.57i	0.609124	−	0.349016i
$382$	4704.94			0.630172
$383$	−7732.32			−1.03160			−0.515801	−	0.856709i	$-0.672505\pi$
$383$	−7732.32			−1.03160			−0.515801	+	0.856709i	$0.672505\pi$
$384$	−3795.90	−	6624.83i	−0.504450	−	0.880396i
$385$		0			0
$386$		−	5479.45i		−	0.722531i
$387$	−5620.60	+	9589.18i	−0.738272	+	1.25955i
$388$			2751.23i			0.359981i
$389$			731.955i			0.0954025i	0.998862	+	0.0477013i	$0.0151895\pi$
$389$			731.955i			0.0954025i	−0.998862	+	0.0477013i	$0.984810\pi$
$390$	2394.53	−	1372.02i	0.310902	−	0.178141i
$391$			23355.8i			3.02086i
$392$		0			0
$393$	3212.94	−	1840.95i	0.412395	−	0.236294i
$394$	497.859			0.0636593
$395$	2624.28			0.334283
$396$	3865.98	+	2266.00i	0.490588	+	0.287553i
$397$		−	14564.1i		−	1.84119i	−0.390518	−	0.920595i	$-0.627704\pi$
$397$		−	14564.1i		−	1.84119i	0.390518	−	0.920595i	$-0.372296\pi$
$398$	−1108.05			−0.139551
$399$		0			0
$400$	−788.018			−0.0985022
$401$		−	5909.89i		−	0.735975i	−0.929831	−	0.367988i	$-0.880047\pi$
$401$		−	5909.89i		−	0.735975i	0.929831	−	0.367988i	$-0.119953\pi$
$402$	240.807	+	420.272i	0.0298766	+	0.0521424i
$403$	−1857.17			−0.229559
$404$	394.890			0.0486300
$405$	−3643.87	−	6507.27i	−0.447075	−	0.798392i
$406$		0			0
$407$			6816.84i			0.830217i
$408$	5082.49	+	8870.27i	0.616717	+	1.07633i
$409$			8054.46i			0.973759i	0.873469	+	0.486880i	$0.161865\pi$
$409$			8054.46i			0.973759i	−0.873469	+	0.486880i	$0.838135\pi$
$410$			1790.80i			0.215710i
$411$	−3512.44	−	6130.12i	−0.421547	−	0.735709i
$412$			5105.29i			0.610485i
$413$		0			0
$414$	−2662.79	+	4542.93i	−0.316109	+	0.539307i
$415$	−995.366			−0.117736
$416$	8198.68			0.966282
$417$	−550.928	−	961.513i	−0.0646980	−	0.112915i
$418$			2415.01i			0.282588i
$419$	−13850.2			−1.61486			−0.807428	−	0.589966i	$-0.799141\pi$
$419$	−13850.2			−1.61486			−0.807428	+	0.589966i	$0.799141\pi$
$420$		0			0
$421$	−2365.25			−0.273813			−0.136906	−	0.990584i	$-0.543716\pi$
$421$	−2365.25			−0.273813			−0.136906	+	0.990584i	$0.543716\pi$
$422$			1435.98i			0.165645i
$423$	−206.241	+	351.863i	−0.0237064	+	0.0404449i
$424$	2976.01			0.340868
$425$	2557.58			0.291907
$426$	5041.43	−	2888.64i	0.573376	−	0.328533i
$427$		0			0
$428$		−	5949.77i		−	0.671946i
$429$	−5363.19	+	3073.00i	−0.603583	+	0.345841i
$430$			4422.79i			0.496013i
$431$			194.891i			0.0217809i	0.999941	+	0.0108905i	$0.00346661\pi$
$431$			194.891i			0.0217809i	−0.999941	+	0.0108905i	$0.996533\pi$
$432$	53.5512	−	5436.00i	0.00596409	−	0.605416i
$433$		−	7716.01i		−	0.856369i	−0.903691	−	0.428185i	$-0.859153\pi$
$433$		−	7716.01i		−	0.856369i	0.903691	−	0.428185i	$-0.140847\pi$
$434$		0			0
$435$	−1075.30	−	1876.68i	−0.118521	−	0.206850i
$436$	−4531.85			−0.497789
$437$	17748.5			1.94285
$438$	3922.16	−	2247.32i	0.427873	−	0.245163i
$439$			7595.59i			0.825781i	0.910781	+	0.412891i	$0.135481\pi$
$439$			7595.59i			0.825781i	−0.910781	+	0.412891i	$0.864519\pi$
$440$	3851.29			0.417280
$441$		0			0
$442$	−6528.86			−0.702594
$443$			10116.7i			1.08501i	0.840053	+	0.542505i	$0.182524\pi$
$443$			10116.7i			1.08501i	−0.840053	+	0.542505i	$0.817476\pi$
$444$	8809.16	−	5047.48i	0.941587	−	0.539511i
$445$	9197.69			0.979803
$446$	−1223.47			−0.129895
$447$	−3934.08	−	6865.99i	−0.416276	−	0.726511i
$448$		0			0
$449$			18315.5i			1.92509i	0.271131	+	0.962543i	$0.412602\pi$
$449$			18315.5i			1.92509i	−0.271131	+	0.962543i	$0.587398\pi$
$450$	497.473	+	291.589i	0.0521135	+	0.0305458i
$451$		−	4010.97i		−	0.418779i
$452$		−	6099.29i		−	0.634705i
$453$	1851.71	−	1061.00i	0.192055	−	0.110044i
$454$			1583.84i			0.163730i
$455$		0			0
$456$	6740.66	−	3862.26i	0.692237	−	0.396638i
$457$	5171.83			0.529383			0.264692	−	0.964333i	$-0.414730\pi$
$457$	5171.83			0.529383			0.264692	+	0.964333i	$0.414730\pi$
$458$	2813.31			0.287024
$459$	−173.805	+	17643.0i	−0.0176743	+	1.79413i
$460$		−	13104.4i		−	1.32825i
$461$	−7960.73			−0.804269			−0.402135	−	0.915581i	$-0.631732\pi$
$461$	−7960.73			−0.804269			−0.402135	+	0.915581i	$0.631732\pi$
$462$		0			0
$463$	1659.53			0.166577			0.0832883	−	0.996525i	$-0.473458\pi$
$463$	1659.53			0.166577			0.0832883	+	0.996525i	$0.473458\pi$
$464$		−	1576.57i		−	0.157738i
$465$	992.850	+	1732.78i	0.0990157	+	0.172808i
$466$	−1734.68			−0.172441
$467$	−6925.40			−0.686230			−0.343115	−	0.939293i	$-0.611482\pi$
$467$	−6925.40			−0.686230			−0.343115	+	0.939293i	$0.611482\pi$
$468$	7942.26	+	4655.28i	0.784468	+	0.459808i
$469$		0			0
$470$			162.289i			0.0159273i
$471$	−5643.83	−	9849.95i	−0.552131	−	0.963613i
$472$		−	1482.03i		−	0.144526i
$473$		−	9906.01i		−	0.962958i
$474$	−695.885	−	1214.50i	−0.0674327	−	0.117688i
$475$		−	1943.54i		−	0.187739i
$476$		0			0
$477$	4431.12	+	2597.26i	0.425339	+	0.249309i
$478$	2043.44			0.195533
$479$	−19425.3			−1.85295			−0.926474	−	0.376358i	$-0.877176\pi$
$479$	−19425.3			−1.85295			−0.926474	+	0.376358i	$0.877176\pi$
$480$	−4383.04	−	7649.55i	−0.416787	−	0.727401i
$481$			14004.5i			1.32755i
$482$	−504.965			−0.0477190
$483$		0			0
$484$	5186.43			0.487080
$485$			4080.87i			0.382067i
$486$	−2045.28	+	3411.91i	−0.190897	+	0.318451i
$487$	−9624.35			−0.895525			−0.447763	−	0.894152i	$-0.647779\pi$
$487$	−9624.35			−0.895525			−0.447763	+	0.894152i	$0.647779\pi$
$488$	−6447.97			−0.598127
$489$	−7183.17	+	4115.82i	−0.664283	+	0.380621i
$490$		0			0
$491$			448.247i			0.0411998i	0.999788	+	0.0205999i	$0.00655762\pi$
$491$			448.247i			0.0411998i	−0.999788	+	0.0205999i	$0.993442\pi$
$492$	−5183.24	+	2969.89i	−0.474956	+	0.272141i
$493$			5116.89i			0.467451i
$494$			4961.39i			0.451869i
$495$	5734.36	+	3361.14i	0.520688	+	0.305196i
$496$			1455.69i			0.131779i
$497$		0			0
$498$	263.943	+	460.650i	0.0237502	+	0.0414502i
$499$	−13858.2			−1.24324			−0.621620	−	0.783319i	$-0.713525\pi$
$499$	−13858.2			−1.24324			−0.621620	+	0.783319i	$0.713525\pi$
$500$	−10255.2			−0.917253
$501$	5848.91	−	3351.31i	0.521577	−	0.298853i
$502$		−	5365.06i		−	0.477001i
$503$	17853.2			1.58258			0.791288	−	0.611443i	$-0.209411\pi$
$503$	17853.2			1.58258			0.791288	+	0.611443i	$0.209411\pi$
$504$		0			0
$505$	585.736			0.0516137
$506$		−	4693.04i		−	0.412314i
$507$	−1112.94	+	637.695i	−0.0974903	+	0.0558600i
$508$	6929.98			0.605252
$509$	9982.92			0.869322			0.434661	−	0.900594i	$-0.356868\pi$
$509$	9982.92			0.869322			0.434661	+	0.900594i	$0.356868\pi$
$510$	3490.35	+	6091.58i	0.303050	+	0.528901i
$511$		0			0
$512$		−	11275.8i		−	0.973295i
$513$	13407.2	+	132.077i	1.15388	+	0.0113671i
$514$		−	1739.16i		−	0.149243i
$515$			7572.62i			0.647941i
$516$	−12801.2	+	7334.83i	−1.09213	+	0.625771i
$517$		−	363.489i		−	0.0309212i
$518$		0			0
$519$	−14560.2	+	8342.70i	−1.23145	+	0.705595i
$520$	7912.10			0.667247
$521$	−12630.5			−1.06210			−0.531048	−	0.847342i	$-0.678202\pi$
$521$	−12630.5			−1.06210			−0.531048	+	0.847342i	$0.678202\pi$
$522$	−583.376	+	995.284i	−0.0489151	+	0.0834529i
$523$		−	11669.0i		−	0.975622i	−0.872949	−	0.487811i	$-0.837795\pi$
$523$		−	11669.0i		−	0.975622i	0.872949	−	0.487811i	$-0.162205\pi$
$524$	4915.20			0.409774
$525$		0			0
$526$	1571.93			0.130303
$527$		−	4724.56i		−	0.390522i
$528$	2408.68	+	4203.78i	0.198531	+	0.346489i
$529$	−22323.3			−1.83474
$530$	2043.75			0.167500
$531$	1293.41	−	2206.67i	0.105705	−	0.180341i
$532$		0			0
$533$		−	8240.14i		−	0.669644i
$534$	−2438.97	−	4256.64i	−0.197649	−	0.344949i
$535$		−	8825.22i		−	0.713173i
$536$			1388.68i			0.111906i
$537$	9096.80	+	15876.3i	0.731016	+	1.27581i
$538$		−	2492.71i		−	0.199755i
$539$		0			0
$540$	97.5177	−	9899.04i	0.00777128	−	0.788865i
$541$	19740.4			1.56877			0.784385	−	0.620274i	$-0.212979\pi$
$541$	19740.4			1.56877			0.784385	+	0.620274i	$0.212979\pi$
$542$	−6139.66			−0.486570
$543$	−8119.30	−	14170.3i	−0.641680	−	1.11990i
$544$			20857.1i			1.64382i
$545$	−6722.04			−0.528331
$546$		0			0
$547$	7949.55			0.621386			0.310693	−	0.950510i	$-0.399439\pi$
$547$	7949.55			0.621386			0.310693	+	0.950510i	$0.399439\pi$
$548$		−	9377.95i		−	0.731033i
$549$	−9600.67	−	5627.34i	−0.746351	−	0.437466i
$550$	−513.910			−0.0398421
$551$	3888.41			0.300639
$552$	−13099.0	+	7505.46i	−1.01002	+	0.578721i
$553$		0			0
$554$		−	2627.34i		−	0.201489i
$555$	13066.5	−	7486.87i	0.999358	−	0.572612i
$556$		−	1470.94i		−	0.112197i
$557$			9866.11i			0.750522i	0.926919	+	0.375261i	$0.122447\pi$
$557$			9866.11i			0.750522i	−0.926919	+	0.375261i	$0.877553\pi$
$558$	538.646	−	918.971i	0.0408651	−	0.0697189i
$559$		−	20350.9i		−	1.53981i
$560$		0			0
$561$	−7817.58	−	13643.7i	−0.588340	−	1.02681i
$562$	−8494.42			−0.637572
$563$	9237.69			0.691514			0.345757	−	0.938324i	$-0.387622\pi$
$563$	9237.69			0.691514			0.345757	+	0.938324i	$0.387622\pi$
$564$	−469.724	+	269.143i	−0.0350691	+	0.0200939i
$565$		−	9047.01i		−	0.673647i
$566$	−4549.08			−0.337831
$567$		0			0
$568$	16658.1			1.23056
$569$		−	12586.1i		−	0.927308i	−0.886016	−	0.463654i	$-0.846538\pi$
$569$		−	12586.1i		−	0.927308i	0.886016	−	0.463654i	$-0.153462\pi$
$570$	4629.09	−	2652.38i	0.340160	−	0.194905i
$571$	20675.9			1.51534			0.757669	−	0.652640i	$-0.226338\pi$
$571$	20675.9			1.51534			0.757669	+	0.652640i	$0.226338\pi$
$572$	−8204.68			−0.599747
$573$	11573.7	+	20199.2i	0.843805	+	1.47266i
$574$		0			0
$575$			3776.85i			0.273923i
$576$	1854.44	−	3163.81i	0.134146	−	0.228864i
$577$		−	15543.6i		−	1.12147i	−0.827996	−	0.560734i	$-0.810519\pi$
$577$		−	15543.6i		−	1.12147i	0.827996	−	0.560734i	$-0.189481\pi$
$578$		−	11449.7i		−	0.823955i
$579$	23524.3	−	13479.0i	1.68849	−	0.967474i
$580$		−	2870.96i		−	0.205535i
$581$		0			0
$582$	1888.60	−	1082.13i	0.134511	−	0.0770719i
$583$	−4577.53			−0.325183
$584$	12959.8			0.918285
$585$	11780.7	+	6905.12i	0.832600	+	0.488020i
$586$		−	4951.74i		−	0.349069i
$587$	13650.3			0.959811			0.479905	−	0.877320i	$-0.340671\pi$
$587$	13650.3			0.959811			0.479905	+	0.877320i	$0.340671\pi$
$588$		0			0
$589$	−3590.27			−0.251162
$590$		−	1017.77i		−	0.0710188i
$591$	1224.69	+	2137.40i	0.0852402	+	0.148766i
$592$	10977.0			0.762084
$593$	24799.6			1.71736			0.858682	−	0.512508i	$-0.171284\pi$
$593$	24799.6			1.71736			0.858682	+	0.512508i	$0.171284\pi$
$594$	34.9237	−	3545.11i	0.00241235	−	0.244878i
$595$		0			0
$596$		−	10503.7i		−	0.721892i
$597$	−2725.70	−	4757.06i	−0.186860	−	0.326120i
$598$		−	9641.37i		−	0.659306i
$599$			7543.35i			0.514545i	0.966339	+	0.257273i	$0.0828239\pi$
$599$			7543.35i			0.514545i	−0.966339	+	0.257273i	$0.917176\pi$
$600$	821.884	+	1434.40i	0.0559221	+	0.0975987i
$601$		−	17481.2i		−	1.18648i	−0.805027	−	0.593239i	$-0.797849\pi$
$601$		−	17481.2i		−	1.18648i	0.805027	−	0.593239i	$-0.202151\pi$
$602$		0			0
$603$	−1211.94	+	2067.66i	−0.0818475	+	0.139638i
$604$	2832.78			0.190835
$605$	7692.97			0.516965
$606$	−155.321	−	271.075i	−0.0104117	−	0.0181711i
$607$			25695.5i			1.71820i	0.511806	+	0.859101i	$0.328977\pi$
$607$			25695.5i			1.71820i	−0.511806	+	0.859101i	$0.671023\pi$
$608$	15849.6			1.05722
$609$		0			0
$610$	−4428.09			−0.293915
$611$		−	746.752i		−	0.0494441i
$612$	−11842.8	+	20204.8i	−0.782219	+	1.33452i
$613$	−7168.60			−0.472328			−0.236164	−	0.971713i	$-0.575890\pi$
$613$	−7168.60			−0.472328			−0.236164	+	0.971713i	$0.575890\pi$
$614$	4767.75			0.313372
$615$	−7688.24	+	4405.21i	−0.504097	+	0.288838i
$616$		0			0
$617$		−	10280.7i		−	0.670805i	−0.942075	−	0.335402i	$-0.891128\pi$
$617$		−	10280.7i		−	0.670805i	0.942075	−	0.335402i	$-0.108872\pi$
$618$	3504.57	−	2008.05i	0.228114	−	0.130705i
$619$		−	4548.35i		−	0.295337i	−0.989037	−	0.147668i	$-0.952823\pi$
$619$		−	4548.35i		−	0.295337i	0.989037	−	0.147668i	$-0.0471769\pi$
$620$			2650.83i			0.171710i
$621$	−26053.9	−	256.663i	−1.68359	−	0.0165854i
$622$			5511.56i			0.355295i
$623$		0			0
$624$	4948.40	+	8636.25i	0.317459	+	0.554049i
$625$	−12669.3			−0.810837
$626$	−6384.11			−0.407605
$627$	−10368.1	+	5940.71i	−0.660385	+	0.378388i
$628$		−	15068.6i		−	0.957488i
$629$	−35626.9			−2.25840
$630$		0			0
$631$	18015.7			1.13660			0.568298	−	0.822823i	$-0.307602\pi$
$631$	18015.7			1.13660			0.568298	+	0.822823i	$0.307602\pi$
$632$		−	4013.00i		−	0.252577i
$633$	−6164.93	+	3532.38i	−0.387099	+	0.221800i
$634$	−4553.28			−0.285227
$635$	10279.2			0.642387
$636$	3389.39	+	5915.37i	0.211318	+	0.368805i
$637$		0			0
$638$		−	1028.17i		−	0.0638019i
$639$	24803.0	+	14538.0i	1.53551	+	0.900023i
$640$		−	15032.8i		−	0.928473i
$641$		−	1117.06i		−	0.0688321i	−0.999408	−	0.0344161i	$-0.989043\pi$
$641$		−	1117.06i		−	0.0688321i	0.999408	−	0.0344161i	$-0.0109571\pi$
$642$	−4084.27	+	2340.20i	−0.251080	+	0.143864i
$643$			11689.0i			0.716907i	0.933548	+	0.358453i	$0.116696\pi$
$643$			11689.0i			0.716907i	−0.933548	+	0.358453i	$0.883304\pi$
$644$		0			0
$645$	−18987.9	+	10879.7i	−1.15914	+	0.664165i
$646$	−12621.6			−0.768713
$647$	−10088.7			−0.613025			−0.306513	−	0.951867i	$-0.599162\pi$
$647$	−10088.7			−0.613025			−0.306513	+	0.951867i	$0.599162\pi$
$648$	−9950.81	+	5572.14i	−0.603248	+	0.337800i
$649$			2279.58i			0.137875i
$650$	−1055.78			−0.0637091
$651$		0			0
$652$	−10988.9			−0.660060
$653$			20037.7i			1.20082i	0.799693	+	0.600409i	$0.204995\pi$
$653$			20037.7i			1.20082i	−0.799693	+	0.600409i	$0.795005\pi$
$654$	1782.50	+	3110.92i	0.106577	+	0.186004i
$655$	7290.66			0.434915
$656$	−6458.80			−0.384411
$657$	19296.4	+	11310.4i	1.14585	+	0.671628i
$658$		0			0
$659$			11752.2i			0.694691i	0.937737	+	0.347345i	$0.112917\pi$
$659$			11752.2i			0.694691i	−0.937737	+	0.347345i	$0.887083\pi$
$660$	4386.25	+	7655.16i	0.258689	+	0.451480i
$661$			22013.0i			1.29532i	0.761930	+	0.647659i	$0.224252\pi$
$661$			22013.0i			1.29532i	−0.761930	+	0.647659i	$0.775748\pi$
$662$		−	6584.64i		−	0.386585i
$663$	−16060.4	−	28029.6i	−0.940778	−	1.64190i
$664$			1522.10i			0.0889590i
$665$		0			0
$666$	−6929.76	−	4061.81i	−0.403188	−	0.236324i
$667$	−7556.27			−0.438651
$668$	8947.75			0.518262
$669$	−3009.63	−	5252.60i	−0.173930	−	0.303553i
$670$			953.662i			0.0549898i
$671$	9917.89			0.570605
$672$		0			0
$673$	24243.2			1.38857			0.694283	−	0.719702i	$-0.255721\pi$
$673$	24243.2			1.38857			0.694283	+	0.719702i	$0.255721\pi$
$674$			5587.20i			0.319304i
$675$	−28.1058	+	2853.03i	−0.00160266	+	0.162686i
$676$	−1702.60			−0.0968706
$677$	−29061.2			−1.64979			−0.824897	−	0.565283i	$-0.808767\pi$
$677$	−29061.2			−1.64979			−0.824897	+	0.565283i	$0.808767\pi$
$678$	−4186.91	+	2399.02i	−0.237164	+	0.135890i
$679$		0			0
$680$			20128.0i			1.13511i
$681$	−6799.73	+	3896.11i	−0.382623	+	0.219235i
$682$			949.335i			0.0533019i
$683$		−	12078.4i		−	0.676673i	−0.941025	−	0.338337i	$-0.890136\pi$
$683$		−	12078.4i		−	0.676673i	0.941025	−	0.338337i	$-0.109864\pi$
$684$	15353.9	+	8999.55i	0.858293	+	0.503080i
$685$		−	13910.2i		−	0.775886i
$686$		0			0
$687$	6920.49	+	12078.1i	0.384328	+	0.670752i
$688$	−15951.5			−0.883931
$689$	−9404.07			−0.519980
$690$	−8995.62	+	5154.31i	−0.496315	+	0.284379i
$691$			5338.80i			0.293918i	0.989143	+	0.146959i	$0.0469486\pi$
$691$			5338.80i			0.293918i	−0.989143	+	0.146959i	$0.953051\pi$
$692$	−22274.4			−1.22362
$693$		0			0
$694$	5057.18			0.276611
$695$		−	2181.82i		−	0.119081i
$696$	−2869.78	+	1644.33i	−0.156291	+	0.0895518i
$697$	20962.6			1.13919
$698$	−5462.57			−0.296220
$699$	−4267.16	−	7447.30i	−0.230899	−	0.402980i
$700$		0			0
$701$			11322.3i			0.610038i	0.952346	+	0.305019i	$0.0986628\pi$
$701$			11322.3i			0.610038i	−0.952346	+	0.305019i	$0.901337\pi$
$702$	71.7472	−	7283.08i	0.00385744	−	0.391570i
$703$			27073.4i			1.45248i
$704$			3268.35i			0.174972i
$705$	−696.737	+	399.217i	−0.0372208	+	0.0213268i
$706$			669.719i			0.0357014i
$707$		0			0
$708$	2945.81	−	1687.89i	0.156371	−	0.0895974i
$709$	−16036.7			−0.849466			−0.424733	−	0.905319i	$-0.639632\pi$
$709$	−16036.7			−0.849466			−0.424733	+	0.905319i	$0.639632\pi$
$710$	11439.8			0.604687
$711$	3502.27	−	5975.14i	0.184733	−	0.315169i
$712$		−	14065.0i		−	0.740318i
$713$	6976.90			0.366461
$714$		0			0
$715$	−12169.9			−0.636544
$716$			24287.8i			1.26770i
$717$	5026.68	+	8772.87i	0.261820	+	0.456944i
$718$	5795.13			0.301215
$719$	−20243.8			−1.05002			−0.525011	−	0.851096i	$-0.675939\pi$
$719$	−20243.8			−1.05002			−0.525011	+	0.851096i	$0.675939\pi$
$720$	5412.38	−	9233.94i	0.280149	−	0.477956i
$721$		0			0
$722$			2388.32i			0.123108i
$723$	−1242.17	−	2167.91i	−0.0638960	−	0.111515i
$724$		−	21677.9i		−	1.11278i
$725$			827.448i			0.0423871i
$726$	−2039.96	−	3560.27i	−0.104284	−	0.182003i
$727$		−	23697.2i		−	1.20892i	−0.796637	−	0.604458i	$-0.793390\pi$
$727$		−	23697.2i		−	1.20892i	0.796637	−	0.604458i	$-0.206610\pi$
$728$		0			0
$729$	−19679.2	−	387.766i	−0.999806	−	0.0197005i
$730$	8900.00			0.451238
$731$	51771.8			2.61949
$732$	−7343.62	−	12816.5i	−0.370803	−	0.647148i
$733$			7895.50i			0.397854i	0.980014	+	0.198927i	$0.0637457\pi$
$733$			7895.50i			0.397854i	−0.980014	+	0.198927i	$0.936254\pi$
$734$	2724.24			0.136994
$735$		0			0
$736$	−30800.3			−1.54254
$737$		−	2135.98i		−	0.106757i
$738$	4077.42	+	2389.94i	0.203376	+	0.119207i
$739$	−23190.3			−1.15436			−0.577178	−	0.816619i	$-0.695846\pi$
$739$	−23190.3			−1.15436			−0.577178	+	0.816619i	$0.695846\pi$
$740$	19989.4			0.993005
$741$	−21300.2	+	12204.6i	−1.05598	+	0.605056i
$742$		0			0
$743$		−	24811.0i		−	1.22507i	−0.790443	−	0.612536i	$-0.790150\pi$
$743$		−	24811.0i		−	1.22507i	0.790443	−	0.612536i	$-0.209850\pi$
$744$	2649.74	−	1518.25i	0.130570	−	0.0748142i
$745$		−	15580.0i		−	0.766184i
$746$			5433.32i			0.266659i
$747$	−1328.38	+	2266.32i	−0.0650641	+	0.111004i
$748$		−	20872.4i		−	1.02028i
$749$		0			0
$750$	4033.65	+	7039.76i	0.196384	+	0.342741i
$751$	−26673.5			−1.29605			−0.648023	−	0.761621i	$-0.724404\pi$
$751$	−26673.5			−1.29605			−0.648023	+	0.761621i	$0.724404\pi$
$752$	−585.321			−0.0283836
$753$	23033.2	−	13197.6i	1.11471	−	0.638707i
$754$		−	2112.27i		−	0.102022i
$755$	4201.83			0.202543
$756$		0			0
$757$	−1543.03			−0.0740853			−0.0370426	−	0.999314i	$-0.511794\pi$
$757$	−1543.03			−0.0740853			−0.0370426	+	0.999314i	$0.511794\pi$
$758$			14794.8i			0.708932i
$759$	20148.1	−	11544.5i	0.963543	−	0.552091i
$760$	15295.6			0.730039
$761$	−15291.5			−0.728405			−0.364202	−	0.931320i	$-0.618658\pi$
$761$	−15291.5			−0.728405			−0.364202	+	0.931320i	$0.618658\pi$
$762$	−2725.75	−	4757.14i	−0.129584	−	0.226159i
$763$		0			0
$764$			30901.0i			1.46330i
$765$	−17566.3	+	29969.5i	−0.830212	+	1.41640i
$766$			8120.13i			0.383018i
$767$			4683.16i			0.220468i
$768$	−2058.19	+	1179.30i	−0.0967039	+	0.0554095i
$769$			30749.1i			1.44193i	0.692973	+	0.720963i	$0.256300\pi$
$769$			30749.1i			1.44193i	−0.692973	+	0.720963i	$0.743700\pi$
$770$		0			0
$771$	7466.53	−	4278.17i	0.348768	−	0.199837i
$772$	35987.9			1.67776
$773$	−16417.4			−0.763899			−0.381949	−	0.924183i	$-0.624747\pi$
$773$	−16417.4			−0.763899			−0.381949	+	0.924183i	$0.624747\pi$
$774$	10070.1	+	5902.49i	0.467652	+	0.274109i
$775$		−	764.003i		−	0.0354114i
$776$	6240.40			0.288682
$777$		0			0
$778$	768.665			0.0354216
$779$		−	15929.8i		−	0.732662i
$780$	9011.12	+	15726.7i	0.413654	+	0.721933i
$781$	−25622.5			−1.17394
$782$	24527.2			1.12160
$783$	−5708.00	−	56.2308i	−0.260520	−	0.00256644i
$784$		0			0
$785$		−	22351.1i		−	1.01623i
$786$	−1933.28	−	3374.08i	−0.0877326	−	0.153116i
$787$		−	4625.39i		−	0.209501i	−0.994499	−	0.104751i	$-0.966596\pi$
$787$		−	4625.39i		−	0.209501i	0.994499	−	0.104751i	$-0.0334044\pi$
$788$			3269.83i			0.147821i
$789$	3866.80	+	6748.57i	0.174476	+	0.304506i
$790$		−	2755.89i		−	0.124114i
$791$		0			0
$792$	5139.80	−	8768.89i	0.230599	−	0.393420i
$793$	20375.3			0.912419
$794$	−15294.6			−0.683607
$795$	5027.45	+	8774.21i	0.224283	+	0.391433i
$796$		−	7277.42i		−	0.324047i
$797$	10959.4			0.487079			0.243539	−	0.969891i	$-0.421691\pi$
$797$	10959.4			0.487079			0.243539	+	0.969891i	$0.421691\pi$
$798$		0			0
$799$	1899.71			0.0841136
$800$			3372.78i			0.149057i
$801$	12274.9	−	20941.9i	0.541464	−	0.923779i
$802$	−6206.29			−0.273257
$803$	−19933.9			−0.876031
$804$	−2760.25	+	1581.57i	−0.121078	+	0.0693752i
$805$		0			0
$806$			1950.31i			0.0852318i
$807$	10701.7	−	6131.84i	0.466811	−	0.267473i
$808$		−	895.698i		−	0.0389982i
$809$			24280.4i			1.05519i	0.849495	+	0.527597i	$0.176907\pi$
$809$			24280.4i			1.05519i	−0.849495	+	0.527597i	$0.823093\pi$
$810$	−6833.63	+	3826.62i	−0.296431	+	0.165992i
$811$			14278.5i			0.618233i	0.951024	+	0.309116i	$0.100033\pi$
$811$			14278.5i			0.618233i	−0.951024	+	0.309116i	$0.899967\pi$
$812$		0			0
$813$	−15103.0	−	26358.7i	−0.651520	−	1.13707i
$814$	7158.73			0.308247
$815$	−16299.7			−0.700558
$816$	−21970.2	+	12588.5i	−0.942539	+	0.540056i
$817$		−	39342.2i		−	1.68471i
$818$	8458.42			0.361542
$819$		0			0
$820$	−11761.6			−0.500893
$821$			13397.3i			0.569514i	0.958600	+	0.284757i	$0.0919128\pi$
$821$			13397.3i			0.569514i	−0.958600	+	0.284757i	$0.908087\pi$
$822$	−6437.57	+	3688.60i	−0.273158	+	0.156514i
$823$	13534.6			0.573252			0.286626	−	0.958043i	$-0.407466\pi$
$823$	13534.6			0.573252			0.286626	+	0.958043i	$0.407466\pi$
$824$	11579.9			0.489570
$825$	−1264.17	−	2206.31i	−0.0533489	−	0.0931078i
$826$		0			0
$827$		−	9455.93i		−	0.397600i	−0.980040	−	0.198800i	$-0.936296\pi$
$827$		−	9455.93i		−	0.397600i	0.980040	−	0.198800i	$-0.0637044\pi$
$828$	−29837.0	−	17488.7i	−1.25230	−	0.734025i
$829$			39689.0i			1.66279i	0.555680	+	0.831396i	$0.312458\pi$
$829$			39689.0i			1.66279i	−0.555680	+	0.831396i	$0.687542\pi$
$830$			1045.29i			0.0437138i
$831$	11279.7	−	6463.04i	0.470864	−	0.269796i
$832$			6714.49i			0.279787i
$833$		0			0
$834$	−1009.74	+	578.559i	−0.0419236	+	0.0240214i
$835$	13272.1			0.550060
$836$	−15861.2			−0.656187
$837$	5270.34	+	51.9193i	0.217646	+	0.00214408i
$838$			14544.8i			0.599573i
$839$	−2668.41			−0.109802			−0.0549009	−	0.998492i	$-0.517484\pi$
$839$	−2668.41			−0.109802			−0.0549009	+	0.998492i	$0.517484\pi$
$840$		0			0
$841$	22733.5			0.932123
$842$			2483.88i			0.101663i
$843$	−20895.5	−	36468.1i	−0.853713	−	1.48995i
$844$	−9431.20			−0.384639
$845$	−2525.44			−0.102814
$846$	369.511	+	216.585i	0.0150166	+	0.00880183i
$847$		0			0
$848$			7371.11i			0.298496i
$849$	−11190.3	−	19530.1i	−0.452358	−	0.789482i
$850$		−	2685.85i		−	0.108381i
$851$		−	52611.3i		−	2.11926i
$852$	18972.0	+	33111.0i	0.762874	+	1.33141i
$853$			22152.8i			0.889211i	0.895726	+	0.444606i	$0.146656\pi$
$853$			22152.8i			0.889211i	−0.895726	+	0.444606i	$0.853344\pi$
$854$		0			0
$855$	22774.3	+	13348.9i	0.910953	+	0.533946i
$856$	−13495.4			−0.538858
$857$	−22498.6			−0.896778			−0.448389	−	0.893839i	$-0.648002\pi$
$857$	−22498.6			−0.896778			−0.448389	+	0.893839i	$0.648002\pi$
$858$	3227.12	+	5632.17i	0.128406	+	0.224102i
$859$			31093.1i			1.23502i	0.786563	+	0.617511i	$0.211859\pi$
$859$			31093.1i			1.23502i	−0.786563	+	0.617511i	$0.788141\pi$
$860$	−29047.9			−1.15177
$861$		0			0
$862$	204.665			0.00808693
$863$		−	31827.4i		−	1.25541i	−0.778451	−	0.627705i	$-0.783994\pi$
$863$		−	31827.4i		−	1.25541i	0.778451	−	0.627705i	$-0.216006\pi$
$864$	−23266.5	−	229.203i	−0.916136	−	0.00902506i
$865$	−33039.3			−1.29869
$866$	−8103.00			−0.317957
$867$	49155.9	−	28165.4i	1.92551	−	1.10328i
$868$		0			0
$869$			6172.56i			0.240955i
$870$	−1970.80	+	1129.23i	−0.0768003	+	0.0440051i
$871$		−	4388.16i		−	0.170708i
$872$			10279.2i			0.399196i
$873$	9291.60	+	5446.18i	0.360221	+	0.211140i
$874$		−	18638.6i		−	0.721351i
$875$		0			0
$876$	14759.9	+	25759.9i	0.569283	+	0.993546i
$877$	26294.3			1.01242			0.506212	−	0.862409i	$-0.331045\pi$
$877$	26294.3			1.01242			0.506212	+	0.862409i	$0.331045\pi$
$878$	7976.54			0.306600
$879$	21258.8	−	12180.9i	0.815745	−	0.467406i
$880$			9539.04i			0.365410i
$881$	30578.4			1.16937			0.584684	−	0.811261i	$-0.301219\pi$
$881$	30578.4			1.16937			0.584684	+	0.811261i	$0.301219\pi$
$882$		0			0
$883$	15673.3			0.597336			0.298668	−	0.954357i	$-0.403458\pi$
$883$	15673.3			0.597336			0.298668	+	0.954357i	$0.403458\pi$
$884$		−	42880.1i		−	1.63147i
$885$	4369.49	−	2503.63i	0.165965	−	0.0950946i
$886$	10624.1			0.402848
$887$	28236.5			1.06887			0.534436	−	0.845209i	$-0.320524\pi$
$887$	28236.5			1.06887			0.534436	+	0.845209i	$0.320524\pi$
$888$	−11448.8	−	19981.1i	−0.432654	−	0.755093i
$889$		0			0
$890$		−	9658.99i		−	0.363787i
$891$	15305.7	−	8570.74i	0.575490	−	0.322256i
$892$		−	8035.50i		−	0.301624i
$893$		−	1443.62i		−	0.0540972i
$894$	−7210.34	+	4131.38i	−0.269743	+	0.154557i
$895$			36025.8i			1.34548i
$896$		0			0
$897$	41392.2	−	23716.9i	1.54074	−	0.882815i
$898$	19234.1			0.714756
$899$	1528.53			0.0567066
$900$	−1915.09	+	3267.29i	−0.0709293	+	0.121011i
$901$		−	23923.5i		−	0.884582i
$902$	−4212.14			−0.155487
$903$		0			0
$904$	−13834.5			−0.508993
$905$		−	32154.6i		−	1.18106i
$906$	−1114.21	−	1944.58i	−0.0408577	−	0.0713073i
$907$	44831.2			1.64123			0.820615	−	0.571482i	$-0.193631\pi$
$907$	44831.2			1.64123			0.820615	+	0.571482i	$0.193631\pi$
$908$	−10402.3			−0.380191
$909$	781.702	−	1333.64i	0.0285230	−	0.0486625i
$910$		0			0
$911$			3062.53i			0.111379i	0.998448	+	0.0556895i	$0.0177357\pi$
$911$			3062.53i			0.111379i	−0.998448	+	0.0556895i	$0.982264\pi$
$912$	9566.21	+	16695.5i	0.347334	+	0.606189i
$913$		−	2341.20i		−	0.0848657i
$914$		−	5431.22i		−	0.196552i
$915$	−10892.7	−	19010.6i	−0.393554	−	0.686854i
$916$			18477.2i			0.666488i
$917$		0			0
$918$	18527.8	+	182.522i	0.666132	+	0.00656222i
$919$	8419.65			0.302218			0.151109	−	0.988517i	$-0.451715\pi$
$919$	8419.65			0.302218			0.151109	+	0.988517i	$0.451715\pi$
$920$	−29723.7			−1.06517
$921$	11728.2	+	20468.8i	0.419608	+	0.732325i
$922$			8359.99i			0.298613i
$923$	−52638.8			−1.87717
$924$		0			0
$925$	−5761.19			−0.204786
$926$		−	1742.76i		−	0.0618475i
$927$	17241.9	+	10106.2i	0.610892	+	0.358069i
$928$	−6747.85			−0.238695
$929$	35888.4			1.26745			0.633725	−	0.773558i	$-0.281525\pi$
$929$	35888.4			1.26745			0.633725	+	0.773558i	$0.281525\pi$
$930$	1819.69	−	1042.64i	0.0641612	−	0.0367631i
$931$		0			0
$932$		−	11393.0i		−	0.400418i
$933$	−23662.2	+	13557.9i	−0.830294	+	0.475742i
$934$			7272.73i			0.254787i
$935$		−	30959.7i		−	1.08288i
$936$	10559.2	−	18014.8i	0.368737	−	0.629094i
$937$			1758.68i			0.0613165i	0.999530	+	0.0306583i	$0.00976035\pi$
$937$			1758.68i			0.0613165i	−0.999530	+	0.0306583i	$0.990240\pi$
$938$		0			0
$939$	−15704.4	−	27408.2i	−0.545785	−	0.952538i
$940$	−1065.88			−0.0369842
$941$	−2698.83			−0.0934957			−0.0467478	−	0.998907i	$-0.514886\pi$
$941$	−2698.83			−0.0934957			−0.0467478	+	0.998907i	$0.514886\pi$
$942$	−10344.0	+	5926.89i	−0.357775	+	0.204998i
$943$			30956.0i			1.06900i
$944$	3670.76			0.126560
$945$		0			0
$946$	−10402.8			−0.357532
$947$		−	6850.74i		−	0.235078i	−0.993068	−	0.117539i	$-0.962499\pi$
$947$		−	6850.74i		−	0.235078i	0.993068	−	0.117539i	$-0.0375005\pi$
$948$	7976.58	−	4570.42i	0.273278	−	0.156583i
$949$	−40952.3			−1.40081
$950$	−2041.02			−0.0697046
$951$	−11200.7	−	19548.1i	−0.381921	−	0.666551i
$952$		0			0
$953$		−	24475.9i		−	0.831953i	−0.909375	−	0.415977i	$-0.863440\pi$
$953$		−	24475.9i		−	0.831953i	0.909375	−	0.415977i	$-0.136560\pi$
$954$	2727.52	−	4653.35i	0.0925646	−	0.157922i
$955$			45835.1i			1.55308i
$956$			13420.9i			0.454040i
$957$	4414.13	−	2529.21i	0.149100	−	0.0854312i
$958$			20399.5i			0.687973i
$959$		0			0
$960$	6264.78	−	3589.59i	0.210620	−	0.120681i
$961$	28379.7			0.952626
$962$	14706.9			0.492899
$963$	−20093.9	−	11777.8i	−0.672395	−	0.394117i
$964$		−	3316.50i		−	0.110806i
$965$	53380.4			1.78070
$966$		0			0
$967$	−49080.8			−1.63220			−0.816098	−	0.577914i	$-0.803867\pi$
$967$	−49080.8			−1.63220			−0.816098	+	0.577914i	$0.803867\pi$
$968$		−	11764.0i		−	0.390608i
$969$	−31047.9	−	54186.7i	−1.02931	−	1.79642i
$970$	4285.54			0.141856
$971$	14730.9			0.486855			0.243427	−	0.969919i	$-0.421728\pi$
$971$	14730.9			0.486855			0.243427	+	0.969919i	$0.421728\pi$
$972$	−22408.7	−	13432.9i	−0.739464	−	0.443273i
$973$		0			0
$974$			10107.0i			0.332495i
$975$	−2597.12	−	4532.64i	−0.0853070	−	0.148883i
$976$		−	15970.6i		−	0.523777i
$977$			38879.7i			1.27315i	0.771213	+	0.636577i	$0.219650\pi$
$977$			38879.7i			1.27315i	−0.771213	+	0.636577i	$0.780350\pi$
$978$	4322.24	+	7543.43i	0.141319	+	0.246638i
$979$			21633.9i			0.706253i
$980$		0			0
$981$	−8970.99	+	15305.2i	−0.291969	+	0.498122i
$982$	470.728			0.0152969
$983$	36156.1			1.17314			0.586572	−	0.809897i	$-0.300477\pi$
$983$	36156.1			1.17314			0.586572	+	0.809897i	$0.300477\pi$
$984$	6736.37	+	11756.7i	0.218240	+	0.380885i
$985$			4850.10i			0.156890i
$986$	5373.52			0.173558
$987$		0			0
$988$	−32585.3			−1.04927
$989$			76453.0i			2.45810i
$990$	3529.71	−	6021.96i	0.113315	−	0.193324i
$991$	15576.7			0.499305			0.249652	−	0.968336i	$-0.419684\pi$
$991$	15576.7			0.499305			0.249652	+	0.968336i	$0.419684\pi$
$992$	6230.46			0.199413
$993$	28269.1	−	16197.6i	0.903416	−	0.517640i
$994$		0			0
$995$		−	10794.5i		−	0.343929i
$996$	−3025.45	+	1733.52i	−0.0962500	+	0.0551493i
$997$		−	23135.4i		−	0.734910i	−0.930041	−	0.367455i	$-0.880229\pi$
$997$		−	23135.4i		−	0.734910i	0.930041	−	0.367455i	$-0.119771\pi$
$998$			14553.2i			0.461597i
$999$	391.512	−	39742.5i	0.0123993	−	1.25866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.c.b.146.10	yes	24
3.2	odd	2	inner	147.4.c.b.146.15	yes	24
7.2	even	3		147.4.g.e.80.9		48
7.3	odd	6		147.4.g.e.68.16		48
7.4	even	3		147.4.g.e.68.15		48
7.5	odd	6		147.4.g.e.80.10		48
7.6	odd	2	inner	147.4.c.b.146.9	✓	24
21.2	odd	6		147.4.g.e.80.16		48
21.5	even	6		147.4.g.e.80.15		48
21.11	odd	6		147.4.g.e.68.10		48
21.17	even	6		147.4.g.e.68.9		48
21.20	even	2	inner	147.4.c.b.146.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.c.b.146.9	✓	24	7.6	odd	2	inner
147.4.c.b.146.10	yes	24	1.1	even	1	trivial
147.4.c.b.146.15	yes	24	3.2	odd	2	inner
147.4.c.b.146.16	yes	24	21.20	even	2	inner
147.4.g.e.68.9		48	21.17	even	6
147.4.g.e.68.10		48	21.11	odd	6
147.4.g.e.68.15		48	7.4	even	3
147.4.g.e.68.16		48	7.3	odd	6
147.4.g.e.80.9		48	7.2	even	3
147.4.g.e.80.10		48	7.5	odd	6
147.4.g.e.80.15		48	21.5	even	6
147.4.g.e.80.16		48	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.05015i q^{2} +(4.50851 - 2.58329i) q^{3} +6.89718 q^{4} +10.2305 q^{5} +(-2.71285 - 4.73462i) q^{6} -15.6443i q^{8} +(13.6533 - 23.2935i) q^{9} +O(q^{10})\)	\(q-1.05015i q^{2} +(4.50851 - 2.58329i) q^{3} +6.89718 q^{4} +10.2305 q^{5} +(-2.71285 - 4.73462i) q^{6} -15.6443i q^{8} +(13.6533 - 23.2935i) q^{9} -10.7436i q^{10} +24.0632i q^{11} +(31.0960 - 17.8174i) q^{12} +49.4354i q^{13} +(46.1243 - 26.4283i) q^{15} +38.7485 q^{16} -125.761 q^{17} +(-24.4618 - 14.3380i) q^{18} +95.5681i q^{19} +70.5616 q^{20} +25.2700 q^{22} -185.716i q^{23} +(-40.4138 - 70.5325i) q^{24} -20.3367 q^{25} +51.9147 q^{26} +(1.38202 - 140.289i) q^{27} -40.6873i q^{29} +(-27.7538 - 48.4376i) q^{30} +37.5677i q^{31} -165.846i q^{32} +(62.1620 + 108.489i) q^{33} +132.069i q^{34} +(94.1690 - 160.660i) q^{36} +283.290 q^{37} +100.361 q^{38} +(127.706 + 222.880i) q^{39} -160.049i q^{40} -166.685 q^{41} -411.667 q^{43} +165.968i q^{44} +(139.680 - 238.305i) q^{45} -195.030 q^{46} -15.1056 q^{47} +(174.698 - 100.098i) q^{48} +21.3567i q^{50} +(-566.996 + 324.878i) q^{51} +340.964i q^{52} +190.230i q^{53} +(-147.325 - 1.45133i) q^{54} +246.178i q^{55} +(246.880 + 430.869i) q^{57} -42.7279 q^{58} +94.7330 q^{59} +(318.128 - 182.281i) q^{60} -412.161i q^{61} +39.4518 q^{62} +135.824 q^{64} +505.749i q^{65} +(113.930 - 65.2797i) q^{66} -88.7656 q^{67} -867.398 q^{68} +(-479.756 - 837.300i) q^{69} +1064.80i q^{71} +(-364.411 - 213.596i) q^{72} +828.400i q^{73} -297.497i q^{74} +(-91.6883 + 52.5356i) q^{75} +659.150i q^{76} +(234.058 - 134.111i) q^{78} +256.515 q^{79} +396.417 q^{80} +(-356.177 - 636.065i) q^{81} +175.045i q^{82} -97.2939 q^{83} -1286.60 q^{85} +432.314i q^{86} +(-105.107 - 183.439i) q^{87} +376.452 q^{88} +899.046 q^{89} +(-250.256 - 146.685i) q^{90} -1280.91i q^{92} +(97.0480 + 169.374i) q^{93} +15.8632i q^{94} +977.710i q^{95} +(-428.429 - 747.720i) q^{96} +398.892i q^{97} +(560.516 + 328.541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) 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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