LMFDB - Embedded newform 252.4.b.g.55.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.b (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 358 x^{14} - 2828 x^{13} + 52557 x^{12} - 549972 x^{11} + 4434734 x^{10} + \cdots + 52705588025 $ x^16 - 4x^15 + 358x^14 - 2828x^13 + 52557x^12 - 549972x^11 + 4434734x^10 - 37785264x^9 + 272741368x^8 - 1739202044x^7 + 9778426658x^6 - 39463975388x^5 + 101978126949x^4 - 176540053420x^3 + 219245087130x^2 - 139977817400*x + 52705588025
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{26} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.14
Root			$-4.46104 - 12.9280i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.g.55.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.69547 - 0.856992i) q^{2} +(6.53113 - 4.62000i) q^{4} +10.3049i q^{5} +(16.6272 + 8.15690i) q^{7} +(13.6452 - 18.0502i) q^{8} +O(q^{10})$	\(q+(2.69547 - 0.856992i) q^{2} +(6.53113 - 4.62000i) q^{4} +10.3049i q^{5} +(16.6272 + 8.15690i) q^{7} +(13.6452 - 18.0502i) q^{8} +(8.83121 + 27.7765i) q^{10} -18.0502i q^{11} +49.0412i q^{13} +(51.8086 + 7.73727i) q^{14} +(21.3113 - 60.3476i) q^{16} +46.6928i q^{17} +48.8465 q^{19} +(47.6085 + 67.3025i) q^{20} +(-15.4689 - 48.6538i) q^{22} +33.7962i q^{23} +18.8094 q^{25} +(42.0280 + 132.189i) q^{26} +(146.279 - 23.5440i) q^{28} +48.1829 q^{29} +152.751 q^{31} +(5.72657 - 180.929i) q^{32} +(40.0153 + 125.859i) q^{34} +(-84.0559 + 171.342i) q^{35} +37.6848 q^{37} +(131.664 - 41.8611i) q^{38} +(186.005 + 140.612i) q^{40} -409.288i q^{41} -470.799i q^{43} +(-83.3918 - 117.888i) q^{44} +(28.9631 + 91.0966i) q^{46} -548.980 q^{47} +(209.930 + 271.253i) q^{49} +(50.7001 - 16.1195i) q^{50} +(226.570 + 320.295i) q^{52} -203.157 q^{53} +186.005 q^{55} +(374.115 - 188.823i) q^{56} +(129.875 - 41.2923i) q^{58} -717.092 q^{59} +493.466i q^{61} +(411.735 - 130.906i) q^{62} +(-139.619 - 492.596i) q^{64} -505.364 q^{65} +240.375i q^{67} +(215.720 + 304.956i) q^{68} +(-79.7317 + 533.882i) q^{70} +995.648i q^{71} -790.766i q^{73} +(101.578 - 32.2956i) q^{74} +(319.023 - 225.671i) q^{76} +(147.234 - 300.125i) q^{77} +214.111i q^{79} +(621.875 + 219.610i) q^{80} +(-350.757 - 1103.23i) q^{82} -885.204 q^{83} -481.164 q^{85} +(-403.471 - 1269.03i) q^{86} +(-325.809 - 246.298i) q^{88} +67.3025i q^{89} +(-400.024 + 815.420i) q^{91} +(156.138 + 220.727i) q^{92} +(-1479.76 + 470.472i) q^{94} +503.358i q^{95} -934.837i q^{97} +(798.322 + 551.247i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{4}+O(q^{10}) $ 16 * q + 40 * q^4	$ 16 q + 40 q^{4} - 304 q^{16} - 312 q^{22} - 1376 q^{25} - 816 q^{28} - 816 q^{37} - 2568 q^{46} - 640 q^{49} + 2336 q^{58} + 1120 q^{64} - 424 q^{70} + 5072 q^{85} - 3536 q^{88}+O(q^{100}) $ 16 * q + 40 * q^4 - 304 * q^16 - 312 * q^22 - 1376 * q^25 - 816 * q^28 - 816 * q^37 - 2568 * q^46 - 640 * q^49 + 2336 * q^58 + 1120 * q^64 - 424 * q^70 + 5072 * q^85 - 3536 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	2.69547	−	0.856992i	0.952993	−	0.302992i
$2$	2.69547	−	0.856992i	0.952993	−	0.302992i
$3$		0			0
$3$		0			0
$4$	6.53113	−	4.62000i	0.816391	−	0.577499i
$5$			10.3049i			0.921697i	0.887479	+	0.460848i	$0.152455\pi$
$5$			10.3049i			0.921697i	−0.887479	+	0.460848i	$0.847545\pi$
$6$		0			0
$7$	16.6272	+	8.15690i	0.897786	+	0.440431i
$7$	16.6272	+	8.15690i	0.897786	+	0.440431i
$8$	13.6452	−	18.0502i	0.603037	−	0.797713i
$9$		0			0
$10$	8.83121	+	27.7765i	0.279267	+	0.878371i
$11$		−	18.0502i		−	0.494758i	−0.968919	−	0.247379i	$-0.920431\pi$
$11$		−	18.0502i		−	0.494758i	0.968919	−	0.247379i	$-0.0795693\pi$
$12$		0			0
$13$			49.0412i			1.04628i	0.852248	+	0.523138i	$0.175239\pi$
$13$			49.0412i			1.04628i	−0.852248	+	0.523138i	$0.824761\pi$
$14$	51.8086	+	7.73727i	0.989031	+	0.147705i
$15$		0			0
$16$	21.3113	−	60.3476i	0.332989	−	0.942931i
$17$			46.6928i			0.666156i	0.942899	+	0.333078i	$0.108087\pi$
$17$			46.6928i			0.666156i	−0.942899	+	0.333078i	$0.891913\pi$
$18$		0			0
$19$	48.8465			0.589798			0.294899	−	0.955528i	$-0.404714\pi$
$19$	48.8465			0.589798			0.294899	+	0.955528i	$0.404714\pi$
$20$	47.6085	+	67.3025i	0.532279	+	0.752465i
$21$		0			0
$22$	−15.4689	−	48.6538i	−0.149908	−	0.471501i
$23$			33.7962i			0.306391i	0.988196	+	0.153195i	$0.0489564\pi$
$23$			33.7962i			0.306391i	−0.988196	+	0.153195i	$0.951044\pi$
$24$		0			0
$25$	18.8094			0.150475
$26$	42.0280	+	132.189i	0.317014	+	0.997094i
$27$		0			0
$28$	146.279	−	23.5440i	0.987294	−	0.158907i
$29$	48.1829			0.308529			0.154264	−	0.988030i	$-0.450699\pi$
$29$	48.1829			0.308529			0.154264	+	0.988030i	$0.450699\pi$
$30$		0			0
$31$	152.751			0.884994			0.442497	−	0.896770i	$-0.354093\pi$
$31$	152.751			0.884994			0.442497	+	0.896770i	$0.354093\pi$
$32$	5.72657	−	180.929i	0.0316351	−	0.999499i
$33$		0			0
$34$	40.0153	+	125.859i	0.201840	+	0.634842i
$35$	−84.0559	+	171.342i	−0.405944	+	0.827487i
$36$		0			0
$37$	37.6848			0.167442			0.0837209	−	0.996489i	$-0.473320\pi$
$37$	37.6848			0.167442			0.0837209	+	0.996489i	$0.473320\pi$
$38$	131.664	−	41.8611i	0.562073	−	0.178704i
$39$		0			0
$40$	186.005	+	140.612i	0.735250	+	0.555817i
$41$		−	409.288i		−	1.55903i	−0.626385	−	0.779514i	$-0.715466\pi$
$41$		−	409.288i		−	1.55903i	0.626385	−	0.779514i	$-0.284534\pi$
$42$		0			0
$43$		−	470.799i		−	1.66968i	−0.550494	−	0.834839i	$-0.685560\pi$
$43$		−	470.799i		−	1.66968i	0.550494	−	0.834839i	$-0.314440\pi$
$44$	−83.3918	−	117.888i	−0.285722	−	0.403916i
$45$		0			0
$46$	28.9631	+	91.0966i	0.0928341	+	0.291988i
$47$	−548.980			−1.70377			−0.851883	−	0.523733i	$-0.824539\pi$
$47$	−548.980			−1.70377			−0.851883	+	0.523733i	$0.824539\pi$
$48$		0			0
$49$	209.930	+	271.253i	0.612041	+	0.790826i
$50$	50.7001	−	16.1195i	0.143401	−	0.0455927i
$51$		0			0
$52$	226.570	+	320.295i	0.604224	+	0.854171i
$53$	−203.157			−0.526523			−0.263262	−	0.964724i	$-0.584798\pi$
$53$	−203.157			−0.526523			−0.263262	+	0.964724i	$0.584798\pi$
$54$		0			0
$55$	186.005			0.456017
$56$	374.115	−	188.823i	0.892736	−	0.450580i
$57$		0			0
$58$	129.875	−	41.2923i	0.294026	−	0.0934819i
$59$	−717.092			−1.58233			−0.791164	−	0.611604i	$-0.790525\pi$
$59$	−717.092			−1.58233			−0.791164	+	0.611604i	$0.790525\pi$
$60$		0			0
$61$			493.466i			1.03577i	0.855451	+	0.517884i	$0.173280\pi$
$61$			493.466i			1.03577i	−0.855451	+	0.517884i	$0.826720\pi$
$62$	411.735	−	130.906i	0.843393	−	0.268147i
$63$		0			0
$64$	−139.619	−	492.596i	−0.272693	−	0.962101i
$65$	−505.364			−0.964350
$66$		0			0
$67$			240.375i			0.438305i	0.975691	+	0.219152i	$0.0703292\pi$
$67$			240.375i			0.438305i	−0.975691	+	0.219152i	$0.929671\pi$
$68$	215.720	+	304.956i	0.384705	+	0.543844i
$69$		0			0
$70$	−79.7317	+	533.882i	−0.136139	+	0.911587i
$71$			995.648i			1.66425i	0.554589	+	0.832125i	$0.312876\pi$
$71$			995.648i			1.66425i	−0.554589	+	0.832125i	$0.687124\pi$
$72$		0			0
$73$		−	790.766i		−	1.26784i	−0.773399	−	0.633919i	$-0.781445\pi$
$73$		−	790.766i		−	1.26784i	0.773399	−	0.633919i	$-0.218555\pi$
$74$	101.578	−	32.2956i	0.159571	−	0.0507336i
$75$		0			0
$76$	319.023	−	225.671i	0.481506	−	0.340608i
$77$	147.234	−	300.125i	0.217907	−	0.444187i
$78$		0			0
$79$			214.111i			0.304928i	0.988309	+	0.152464i	$0.0487209\pi$
$79$			214.111i			0.304928i	−0.988309	+	0.152464i	$0.951279\pi$
$80$	621.875	+	219.610i	0.869096	+	0.306915i
$81$		0			0
$82$	−350.757	−	1103.23i	−0.472373	−	1.48574i
$83$	−885.204			−1.17065			−0.585324	−	0.810800i	$-0.699033\pi$
$83$	−885.204			−1.17065			−0.585324	+	0.810800i	$0.699033\pi$
$84$		0			0
$85$	−481.164			−0.613994
$86$	−403.471	−	1269.03i	−0.505900	−	1.59119i
$87$		0			0
$88$	−325.809	−	246.298i	−0.394675	−	0.298357i
$89$			67.3025i			0.0801579i	0.999197	+	0.0400790i	$0.0127609\pi$
$89$			67.3025i			0.0801579i	−0.999197	+	0.0400790i	$0.987239\pi$
$90$		0			0
$91$	−400.024	+	815.420i	−0.460813	+	0.939333i
$92$	156.138	+	220.727i	0.176941	+	0.250135i
$93$		0			0
$94$	−1479.76	+	470.472i	−1.62368	+	0.516228i
$95$			503.358i			0.543615i
$96$		0			0
$97$		−	934.837i		−	0.978539i	−0.872133	−	0.489269i	$-0.837263\pi$
$97$		−	934.837i		−	0.978539i	0.872133	−	0.489269i	$-0.162737\pi$
$98$	798.322	+	551.247i	0.822885	+	0.568208i
$99$		0			0
$100$	122.846	−	86.8991i	0.122846	−	0.0868991i
$101$		−	643.394i		−	0.633862i	−0.948449	−	0.316931i	$-0.897348\pi$
$101$		−	643.394i		−	0.633862i	0.948449	−	0.316931i	$-0.102652\pi$
$102$		0			0
$103$	−834.403			−0.798215			−0.399108	−	0.916904i	$-0.630680\pi$
$103$	−834.403			−0.798215			−0.399108	+	0.916904i	$0.630680\pi$
$104$	885.204	+	669.176i	0.834628	+	0.630943i
$105$		0			0
$106$	−547.603	+	174.104i	−0.501773	+	0.159533i
$107$		−	1511.02i		−	1.36520i	−0.730793	−	0.682599i	$-0.760850\pi$
$107$		−	1511.02i		−	1.36520i	0.730793	−	0.682599i	$-0.239150\pi$
$108$		0			0
$109$	−1347.35			−1.18397			−0.591983	−	0.805950i	$-0.701655\pi$
$109$	−1347.35			−1.18397			−0.591983	+	0.805950i	$0.701655\pi$
$110$	501.371	−	159.405i	0.434581	−	0.138170i
$111$		0			0
$112$	846.597	−	829.579i	0.714249	−	0.699892i
$113$	1677.23			1.39629			0.698145	−	0.715956i	$-0.254009\pi$
$113$	1677.23			1.39629			0.698145	+	0.715956i	$0.254009\pi$
$114$		0			0
$115$	−348.266			−0.282400
$116$	314.688	−	222.605i	0.251880	−	0.178175i
$117$		0			0
$118$	−1932.90	+	614.542i	−1.50795	+	0.479434i
$119$	−380.868	+	776.372i	−0.293396	+	0.598066i
$120$		0			0
$121$	1005.19			0.755215
$122$	422.896	+	1330.12i	0.313830	+	0.987079i
$123$		0			0
$124$	997.634	−	705.707i	0.722502	−	0.511084i
$125$			1481.94i			1.06039i
$126$		0			0
$127$			401.212i			0.280329i	0.990128	+	0.140164i	$0.0447631\pi$
$127$			401.212i			0.280329i	−0.990128	+	0.140164i	$0.955237\pi$
$128$	−798.489	−	1208.13i	−0.551384	−	0.834252i
$129$		0			0
$130$	−1362.19	+	433.093i	−0.919018	+	0.292191i
$131$	44.6445			0.0297756			0.0148878	−	0.999889i	$-0.495261\pi$
$131$	44.6445			0.0297756			0.0148878	+	0.999889i	$0.495261\pi$
$132$		0			0
$133$	812.183	+	398.436i	0.529513	+	0.259765i
$134$	205.999	+	647.923i	0.132803	+	0.417702i
$135$		0			0
$136$	842.813	+	637.131i	0.531402	+	0.401717i
$137$	−1481.82			−0.924089			−0.462044	−	0.886857i	$-0.652884\pi$
$137$	−1481.82			−0.924089			−0.462044	+	0.886857i	$0.652884\pi$
$138$		0			0
$139$	−1197.16			−0.730517			−0.365259	−	0.930906i	$-0.619019\pi$
$139$	−1197.16			−0.730517			−0.365259	+	0.930906i	$0.619019\pi$
$140$	242.618	+	1507.39i	0.146464	+	0.909985i
$141$		0			0
$142$	853.263	+	2683.74i	0.504255	+	1.58602i
$143$	885.204			0.517653
$144$		0			0
$145$			496.519i			0.284370i
$146$	−677.680	−	2131.49i	−0.384145	−	1.20824i
$147$		0			0
$148$	246.125	−	174.104i	0.136698	−	0.0966976i
$149$	−1198.40			−0.658907			−0.329453	−	0.944172i	$-0.606864\pi$
$149$	−1198.40			−0.658907			−0.329453	+	0.944172i	$0.606864\pi$
$150$		0			0
$151$		−	3058.27i		−	1.64820i	−0.566444	−	0.824100i	$-0.691681\pi$
$151$		−	3058.27i		−	1.64820i	0.566444	−	0.824100i	$-0.308319\pi$
$152$	666.519	−	881.689i	0.355670	−	0.470490i
$153$		0			0
$154$	139.659	−	935.156i	0.0730783	−	0.489331i
$155$			1574.08i			0.815697i
$156$		0			0
$157$		−	2265.06i		−	1.15141i	−0.817658	−	0.575704i	$-0.804728\pi$
$157$		−	2265.06i		−	1.15141i	0.817658	−	0.575704i	$-0.195272\pi$
$158$	183.491	+	577.129i	0.0923910	+	0.290595i
$159$		0			0
$160$	1864.45	+	59.0116i	0.921236	+	0.0291580i
$161$	−275.672	+	561.937i	−0.134944	+	0.275074i
$162$		0			0
$163$			1497.01i			0.719357i	0.933076	+	0.359678i	$0.117114\pi$
$163$			1497.01i			0.719357i	−0.933076	+	0.359678i	$0.882886\pi$
$164$	−1890.91	−	2673.12i	−0.900337	−	1.27278i
$165$		0			0
$166$	−2386.04	+	758.613i	−1.11562	+	0.354697i
$167$	672.447			0.311590			0.155795	−	0.987789i	$-0.450206\pi$
$167$	672.447			0.311590			0.155795	+	0.987789i	$0.450206\pi$
$168$		0			0
$169$	−208.043			−0.0946940
$170$	−1296.96	+	412.353i	−0.585132	+	0.186036i
$171$		0			0
$172$	−2175.09	−	3074.85i	−0.964239	−	1.36311i
$173$		−	2008.77i		−	0.882798i	−0.897311	−	0.441399i	$-0.854482\pi$
$173$		−	2008.77i		−	0.882798i	0.897311	−	0.441399i	$-0.145518\pi$
$174$		0			0
$175$	312.748	+	153.426i	0.135094	+	0.0662738i
$176$	−1089.29	−	384.673i	−0.466522	−	0.164749i
$177$		0			0
$178$	57.6777	+	181.412i	0.0242872	+	0.0763899i
$179$		−	3724.04i		−	1.55502i	−0.628872	−	0.777509i	$-0.716483\pi$
$179$		−	3724.04i		−	1.55502i	0.628872	−	0.777509i	$-0.283517\pi$
$180$		0			0
$181$			2010.69i			0.825710i	0.910797	+	0.412855i	$0.135468\pi$
$181$			2010.69i			0.825710i	−0.910797	+	0.412855i	$0.864532\pi$
$182$	−379.446	+	2540.76i	−0.154541	+	1.03480i
$183$		0			0
$184$	610.027	+	461.155i	0.244412	+	0.184765i
$185$			388.338i			0.154331i
$186$		0			0
$187$	842.813			0.329586
$188$	−3585.46	+	2536.28i	−1.39094	+	0.983923i
$189$		0			0
$190$	431.374	+	1356.79i	0.164711	+	0.518061i
$191$		−	1167.67i		−	0.442355i	−0.975234	−	0.221178i	$-0.929010\pi$
$191$		−	1167.67i		−	0.442355i	0.975234	−	0.221178i	$-0.0709901\pi$
$192$		0			0
$193$	−4481.71			−1.67150			−0.835752	−	0.549106i	$-0.814968\pi$
$193$	−4481.71			−1.67150			−0.835752	+	0.549106i	$0.814968\pi$
$194$	−801.148	−	2519.83i	−0.296490	−	0.932541i
$195$		0			0
$196$	2624.27	+	801.715i	0.956366	+	0.292170i
$197$	4433.60			1.60346			0.801728	−	0.597689i	$-0.203914\pi$
$197$	4433.60			1.60346			0.801728	+	0.597689i	$0.203914\pi$
$198$		0			0
$199$	2895.34			1.03138			0.515691	−	0.856775i	$-0.327535\pi$
$199$	2895.34			1.03138			0.515691	+	0.856775i	$0.327535\pi$
$200$	256.657	−	339.512i	0.0907419	−	0.120036i
$201$		0			0
$202$	−551.383	−	1734.25i	−0.192055	−	0.604066i
$203$	801.148	+	393.023i	0.276993	+	0.135886i
$204$		0			0
$205$	4217.67			1.43695
$206$	−2249.11	+	715.077i	−0.760693	+	0.241853i
$207$		0			0
$208$	2959.52	+	1045.13i	0.986566	+	0.348398i
$209$		−	881.689i		−	0.291807i
$210$		0			0
$211$			2313.24i			0.754740i	0.926063	+	0.377370i	$0.123172\pi$
$211$			2313.24i			0.754740i	−0.926063	+	0.377370i	$0.876828\pi$
$212$	−1326.84	+	938.583i	−0.429849	+	0.304067i
$213$		0			0
$214$	−1294.94	−	4072.92i	−0.413645	−	1.30102i
$215$	4851.53			1.53894
$216$		0			0
$217$	2539.82	+	1245.97i	0.794536	+	0.389779i
$218$	−3631.73	+	1154.67i	−1.12831	+	0.358733i
$219$		0			0
$220$	1214.82	−	859.343i	0.372288	−	0.263349i
$221$	−2289.87			−0.696984
$222$		0			0
$223$	4169.23			1.25198			0.625992	−	0.779830i	$-0.284694\pi$
$223$	4169.23			1.25198			0.625992	+	0.779830i	$0.284694\pi$
$224$	1571.03	−	2961.63i	0.468612	−	0.883404i
$225$		0			0
$226$	4520.93	−	1437.38i	1.33066	−	0.423066i
$227$	3461.99			1.01225			0.506124	−	0.862461i	$-0.331078\pi$
$227$	3461.99			1.01225			0.506124	+	0.862461i	$0.331078\pi$
$228$		0			0
$229$		−	303.407i		−	0.0875533i	−0.999041	−	0.0437766i	$-0.986061\pi$
$229$		−	303.407i		−	0.0875533i	0.999041	−	0.0437766i	$-0.0139390\pi$
$230$	−938.740	+	298.461i	−0.269125	+	0.0855649i
$231$		0			0
$232$	657.463	−	869.710i	0.186054	−	0.246117i
$233$	2216.24			0.623137			0.311569	−	0.950224i	$-0.399146\pi$
$233$	2216.24			0.623137			0.311569	+	0.950224i	$0.399146\pi$
$234$		0			0
$235$		−	5657.18i		−	1.57035i
$236$	−4683.42	+	3312.96i	−1.29180	+	0.913794i
$237$		0			0
$238$	−361.275	+	2419.09i	−0.0983948	+	0.658850i
$239$		−	1062.67i		−	0.287609i	−0.989606	−	0.143805i	$-0.954066\pi$
$239$		−	1062.67i		−	0.287609i	0.989606	−	0.143805i	$-0.0459337\pi$
$240$		0			0
$241$			7334.62i			1.96043i	0.197926	+	0.980217i	$0.436579\pi$
$241$			7334.62i			1.96043i	−0.197926	+	0.980217i	$0.563421\pi$
$242$	2709.46	−	861.441i	0.719714	−	0.228824i
$243$		0			0
$244$	2279.81	+	3222.89i	0.598155	+	0.845591i
$245$	−2795.23	+	2163.30i	−0.728902	+	0.564116i
$246$		0			0
$247$			2395.49i			0.617092i
$248$	2084.31	−	2757.18i	0.533684	−	0.705972i
$249$		0			0
$250$	1270.01	+	3994.52i	0.321290	+	1.01054i
$251$	5904.85			1.48490			0.742451	−	0.669900i	$-0.233663\pi$
$251$	5904.85			1.48490			0.742451	+	0.669900i	$0.233663\pi$
$252$		0			0
$253$	610.027			0.151589
$254$	343.835	+	1081.45i	0.0849375	+	0.267151i
$255$		0			0
$256$	−3187.66	−	2572.17i	−0.778237	−	0.627971i
$257$			5814.10i			1.41118i	0.708620	+	0.705591i	$0.249318\pi$
$257$			5814.10i			1.41118i	−0.708620	+	0.705591i	$0.750682\pi$
$258$		0			0
$259$	626.595	+	307.391i	0.150327	+	0.0737466i
$260$	−3300.60	+	2334.78i	−0.787286	+	0.556911i
$261$		0			0
$262$	120.338	−	38.2600i	0.0283760	−	0.00902180i
$263$		−	1699.79i		−	0.398530i	−0.979946	−	0.199265i	$-0.936144\pi$
$263$		−	1699.79i		−	0.398530i	0.979946	−	0.199265i	$-0.0638555\pi$
$264$		0			0
$265$		−	2093.51i		−	0.485295i
$266$	2530.67	+	377.939i	0.583329	+	0.0871163i
$267$		0			0
$268$	1110.53	+	1569.92i	0.253121	+	0.357828i
$269$			5550.40i			1.25804i	0.777387	+	0.629022i	$0.216545\pi$
$269$			5550.40i			1.25804i	−0.777387	+	0.629022i	$0.783455\pi$
$270$		0			0
$271$	3741.78			0.838733			0.419367	−	0.907817i	$-0.362252\pi$
$271$	3741.78			0.838733			0.419367	+	0.907817i	$0.362252\pi$
$272$	2817.79	+	995.083i	0.628139	+	0.221823i
$273$		0			0
$274$	−3994.19	+	1269.91i	−0.880650	+	0.279992i
$275$		−	339.512i		−	0.0744486i
$276$		0			0
$277$	−5697.37			−1.23582			−0.617910	−	0.786249i	$-0.712020\pi$
$277$	−5697.37			−1.23582			−0.617910	+	0.786249i	$0.712020\pi$
$278$	−3226.91	+	1025.96i	−0.696178	+	0.221341i
$279$		0			0
$280$	1945.79	+	3855.21i	0.415298	+	0.822832i
$281$	6405.15			1.35978			0.679892	−	0.733312i	$-0.262027\pi$
$281$	6405.15			1.35978			0.679892	+	0.733312i	$0.262027\pi$
$282$		0			0
$283$	−7258.60			−1.52466			−0.762330	−	0.647188i	$-0.775945\pi$
$283$	−7258.60			−1.52466			−0.762330	+	0.647188i	$0.775945\pi$
$284$	4599.89	+	6502.71i	0.961103	+	1.35868i
$285$		0			0
$286$	2386.04	−	758.613i	0.493320	−	0.156845i
$287$	3338.52	−	6805.34i	0.686644	−	1.39967i
$288$		0			0
$289$	2732.79			0.556236
$290$	425.513	+	1338.35i	0.0861619	+	0.271003i
$291$		0			0
$292$	−3653.34	−	5164.60i	−0.732176	−	1.03505i
$293$		−	2353.32i		−	0.469224i	−0.972089	−	0.234612i	$-0.924618\pi$
$293$		−	2353.32i		−	0.469224i	0.972089	−	0.234612i	$-0.0753819\pi$
$294$		0			0
$295$		−	7389.55i		−	1.45843i
$296$	514.216	−	680.218i	0.100974	−	0.133571i
$297$		0			0
$298$	−3230.27	+	1027.02i	−0.627934	+	0.199644i
$299$	−1657.41			−0.320569
$300$		0			0
$301$	3840.26	−	7828.09i	0.735379	−	1.49901i
$302$	−2620.91	−	8243.47i	−0.499392	−	1.57072i
$303$		0			0
$304$	1040.98	−	2947.77i	0.196396	−	0.556139i
$305$	−5085.11			−0.954663
$306$		0			0
$307$	−5602.21			−1.04148			−0.520741	−	0.853714i	$-0.674344\pi$
$307$	−5602.21			−1.04148			−0.520741	+	0.853714i	$0.674344\pi$
$308$	−424.974	−	2640.37i	−0.0786205	−	0.488471i
$309$		0			0
$310$	1348.97	+	4242.88i	0.247150	+	0.777353i
$311$	−3081.12			−0.561783			−0.280891	−	0.959740i	$-0.590630\pi$
$311$	−3081.12			−0.561783			−0.280891	+	0.959740i	$0.590630\pi$
$312$		0			0
$313$		−	5032.74i		−	0.908841i	−0.890787	−	0.454420i	$-0.849846\pi$
$313$		−	5032.74i		−	0.908841i	0.890787	−	0.454420i	$-0.150154\pi$
$314$	−1941.14	−	6105.39i	−0.348868	−	1.09728i
$315$		0			0
$316$	989.190	+	1398.38i	0.176096	+	0.248941i
$317$	6446.37			1.14216			0.571079	−	0.820895i	$-0.306525\pi$
$317$	6446.37			1.14216			0.571079	+	0.820895i	$0.306525\pi$
$318$		0			0
$319$		−	869.710i		−	0.152647i
$320$	5076.14	−	1438.75i	0.886766	−	0.251340i
$321$		0			0
$322$	−261.490	+	1750.93i	−0.0452555	+	0.303030i
$323$			2280.78i			0.392898i
$324$		0			0
$325$			922.434i			0.157438i
$326$	1282.93	+	4035.16i	0.217960	+	0.685542i
$327$		0			0
$328$	−7387.73	−	5584.81i	−1.24366	−	0.940151i
$329$	−9128.02	−	4477.97i	−1.52962	−	0.750391i
$330$		0			0
$331$			8175.39i			1.35758i	0.734331	+	0.678791i	$0.237496\pi$
$331$			8175.39i			1.35758i	−0.734331	+	0.678791i	$0.762504\pi$
$332$	−5781.38	+	4089.64i	−0.955706	+	0.676048i
$333$		0			0
$334$	1812.56	−	576.282i	0.296943	−	0.0944094i
$335$	−2477.03			−0.403984
$336$		0			0
$337$	−5692.64			−0.920172			−0.460086	−	0.887874i	$-0.652181\pi$
$337$	−5692.64			−0.920172			−0.460086	+	0.887874i	$0.652181\pi$
$338$	−560.773	+	178.291i	−0.0902427	+	0.0286916i
$339$		0			0
$340$	−3142.54	+	2222.97i	−0.501259	+	0.354581i
$341$		−	2757.18i		−	0.437858i
$342$		0			0
$343$	1277.97	+	6222.57i	0.201177	+	0.979555i
$344$	−8498.01	−	6424.13i	−1.33192	−	1.00688i
$345$		0			0
$346$	−1721.50	−	5414.58i	−0.267481	−	0.841300i
$347$			6701.89i			1.03682i	0.855132	+	0.518410i	$0.173476\pi$
$347$			6701.89i			1.03682i	−0.855132	+	0.518410i	$0.826524\pi$
$348$		0			0
$349$			3914.14i			0.600341i	0.953886	+	0.300171i	$0.0970436\pi$
$349$			3914.14i			0.600341i	−0.953886	+	0.300171i	$0.902956\pi$
$350$	974.487	+	145.533i	0.148824	+	0.0222259i
$351$		0			0
$352$	−3265.80	−	103.366i	−0.494510	−	0.0156517i
$353$		−	9853.62i		−	1.48571i	−0.669453	−	0.742854i	$-0.733472\pi$
$353$		−	9853.62i		−	1.48571i	0.669453	−	0.742854i	$-0.266528\pi$
$354$		0			0
$355$	−10260.0			−1.53393
$356$	310.937	+	439.561i	0.0462911	+	0.0654402i
$357$		0			0
$358$	−3191.48	−	10038.1i	−0.471159	−	1.48192i
$359$			10120.4i			1.48784i	0.668270	+	0.743919i	$0.267035\pi$
$359$			10120.4i			1.48784i	−0.668270	+	0.743919i	$0.732965\pi$
$360$		0			0
$361$	−4473.02			−0.652138
$362$	1723.15	+	5419.76i	0.250184	+	0.786896i
$363$		0			0
$364$	1154.63	+	7173.73i	0.166261	+	1.03298i
$365$	8148.75			1.16856
$366$		0			0
$367$	4458.69			0.634173			0.317086	−	0.948397i	$-0.397295\pi$
$367$	4458.69			0.634173			0.317086	+	0.948397i	$0.397295\pi$
$368$	2039.52	+	720.240i	0.288905	+	0.102025i
$369$		0			0
$370$	332.803	+	1046.75i	0.0467610	+	0.147076i
$371$	−3377.94	−	1657.13i	−0.472705	−	0.231897i
$372$		0			0
$373$	829.392			0.115132			0.0575661	−	0.998342i	$-0.481666\pi$
$373$	829.392			0.115132			0.0575661	+	0.998342i	$0.481666\pi$
$374$	2271.78	−	722.284i	0.314093	−	0.0998621i
$375$		0			0
$376$	−7490.92	+	9909.19i	−1.02743	+	1.35912i
$377$			2362.95i			0.322806i
$378$		0			0
$379$			521.296i			0.0706521i	0.999376	+	0.0353261i	$0.0112470\pi$
$379$			521.296i			0.0706521i	−0.999376	+	0.0353261i	$0.988753\pi$
$380$	2325.51	+	3287.50i	0.313937	+	0.443803i
$381$		0			0
$382$	−1000.69	−	3147.43i	−0.134030	−	0.421562i
$383$	−12605.6			−1.68177			−0.840883	−	0.541217i	$-0.817964\pi$
$383$	−12605.6			−1.68177			−0.840883	+	0.541217i	$0.817964\pi$
$384$		0			0
$385$	3092.75	+	1517.23i	0.409406	+	0.200844i
$386$	−12080.3	+	3840.79i	−1.59293	+	0.506453i
$387$		0			0
$388$	−4318.94	−	6105.54i	−0.565106	−	0.798871i
$389$	−11263.9			−1.46812			−0.734062	−	0.679082i	$-0.762378\pi$
$389$	−11263.9			−1.46812			−0.734062	+	0.679082i	$0.762378\pi$
$390$		0			0
$391$	−1578.04			−0.204104
$392$	7760.71	−	87.9778i	0.999936	−	0.0113356i
$393$		0			0
$394$	11950.6	−	3799.56i	1.52808	−	0.485835i
$395$	−2206.39			−0.281051
$396$		0			0
$397$		−	3304.08i		−	0.417701i	−0.977948	−	0.208850i	$-0.933028\pi$
$397$		−	3304.08i		−	0.417701i	0.977948	−	0.208850i	$-0.0669721\pi$
$398$	7804.30	−	2481.28i	0.982900	−	0.312501i
$399$		0			0
$400$	400.852	−	1135.10i	0.0501064	−	0.141887i
$401$	5752.87			0.716420			0.358210	−	0.933641i	$-0.383387\pi$
$401$	5752.87			0.716420			0.358210	+	0.933641i	$0.383387\pi$
$402$		0			0
$403$			7491.08i			0.925949i
$404$	−2972.48	−	4202.09i	−0.366055	−	0.517479i
$405$		0			0
$406$	2496.29	+	372.804i	0.305145	+	0.0455713i
$407$		−	680.218i		−	0.0828432i
$408$		0			0
$409$		−	1731.71i		−	0.209358i	−0.994506	−	0.104679i	$-0.966618\pi$
$409$		−	1731.71i		−	0.209358i	0.994506	−	0.104679i	$-0.0333815\pi$
$410$	11368.6	−	3614.51i	1.36940	−	0.435385i
$411$		0			0
$412$	−5449.59	+	3854.94i	−0.651656	+	0.460969i
$413$	−11923.3	−	5849.25i	−1.42059	−	0.696907i
$414$		0			0
$415$		−	9121.92i		−	1.07898i
$416$	8872.97	+	280.838i	1.04575	+	0.0330991i
$417$		0			0
$418$	−755.601	−	2376.57i	−0.0884154	−	0.278090i
$419$	−13882.1			−1.61859			−0.809293	−	0.587406i	$-0.800149\pi$
$419$	−13882.1			−1.61859			−0.809293	+	0.587406i	$0.800149\pi$
$420$		0			0
$421$	−3343.52			−0.387062			−0.193531	−	0.981094i	$-0.561994\pi$
$421$	−3343.52			−0.387062			−0.193531	+	0.981094i	$0.561994\pi$
$422$	1982.43	+	6235.28i	0.228681	+	0.719262i
$423$		0			0
$424$	−2772.11	+	3667.02i	−0.317513	+	0.420014i
$425$			878.261i			0.100240i
$426$		0			0
$427$	−4025.15	+	8204.97i	−0.456184	+	0.929898i
$428$	−6980.92	−	9868.69i	−0.788401	−	1.11454i
$429$		0			0
$430$	13077.2	−	4157.72i	1.46660	−	0.466287i
$431$		−	7075.93i		−	0.790802i	−0.918509	−	0.395401i	$-0.870606\pi$
$431$		−	7075.93i		−	0.790802i	0.918509	−	0.395401i	$-0.129394\pi$
$432$		0			0
$433$		−	4910.23i		−	0.544967i	−0.962160	−	0.272483i	$-0.912155\pi$
$433$		−	4910.23i		−	0.544967i	0.962160	−	0.272483i	$-0.0878450\pi$
$434$	7913.80	+	1181.87i	0.875287	+	0.130718i
$435$		0			0
$436$	−8799.69	+	6224.73i	−0.966580	+	0.683740i
$437$			1650.83i			0.180709i
$438$		0			0
$439$	13445.2			1.46174			0.730868	−	0.682518i	$-0.239115\pi$
$439$	13445.2			1.46174			0.730868	+	0.682518i	$0.239115\pi$
$440$	2538.07	−	3357.43i	0.274995	−	0.363771i
$441$		0			0
$442$	−6172.28	+	1962.40i	−0.664220	+	0.211181i
$443$			14965.5i			1.60504i	0.596629	+	0.802518i	$0.296507\pi$
$443$			14965.5i			1.60504i	−0.596629	+	0.802518i	$0.703493\pi$
$444$		0			0
$445$	−693.545			−0.0738813
$446$	11238.0	−	3573.00i	1.19313	−	0.379342i
$447$		0			0
$448$	1696.58	−	9329.36i	0.178919	−	0.983864i
$449$	10908.7			1.14658			0.573291	−	0.819352i	$-0.305666\pi$
$449$	10908.7			1.14658			0.573291	+	0.819352i	$0.305666\pi$
$450$		0			0
$451$	−7387.73			−0.771341
$452$	10954.2	−	7748.81i	1.13992	−	0.806357i
$453$		0			0
$454$	9331.70	−	2966.90i	0.964666	−	0.306704i
$455$	−8402.81	−	4122.21i	−0.865780	−	0.424730i
$456$		0			0
$457$	4804.83			0.491817			0.245908	−	0.969293i	$-0.420914\pi$
$457$	4804.83			0.491817			0.245908	+	0.969293i	$0.420914\pi$
$458$	−260.017	−	817.825i	−0.0265280	−	0.0834376i
$459$		0			0
$460$	−2274.57	+	1608.99i	−0.230548	+	0.163086i
$461$			6090.11i			0.615281i	0.951503	+	0.307641i	$0.0995394\pi$
$461$			6090.11i			0.615281i	−0.951503	+	0.307641i	$0.900461\pi$
$462$		0			0
$463$		−	4149.32i		−	0.416491i	−0.978077	−	0.208246i	$-0.933225\pi$
$463$		−	4149.32i		−	0.416491i	0.978077	−	0.208246i	$-0.0667753\pi$
$464$	1026.84	−	2907.72i	0.102737	−	0.290921i
$465$		0			0
$466$	5973.82	−	1899.30i	0.593845	−	0.188806i
$467$	6598.23			0.653810			0.326905	−	0.945057i	$-0.393994\pi$
$467$	6598.23			0.653810			0.326905	+	0.945057i	$0.393994\pi$
$468$		0			0
$469$	−1960.71	+	3996.77i	−0.193043	+	0.393504i
$470$	−4848.15	−	15248.8i	−0.475806	−	1.49654i
$471$		0			0
$472$	−9784.84	+	12943.6i	−0.954203	+	1.26224i
$473$	−8498.01			−0.826087
$474$		0			0
$475$	918.772			0.0887498
$476$	1099.33	+	6830.19i	0.105857	+	0.657692i
$477$		0			0
$478$	−910.703	−	2864.41i	−0.0871435	−	0.274090i
$479$	−4494.37			−0.428712			−0.214356	−	0.976756i	$-0.568765\pi$
$479$	−4494.37			−0.428712			−0.214356	+	0.976756i	$0.568765\pi$
$480$		0			0
$481$			1848.11i			0.175190i
$482$	6285.71	+	19770.3i	0.593997	+	1.86828i
$483$		0			0
$484$	6565.03	−	4643.98i	0.616550	−	0.436136i
$485$	9633.38			0.901916
$486$		0			0
$487$		−	12562.5i		−	1.16892i	−0.811424	−	0.584458i	$-0.801307\pi$
$487$		−	12562.5i		−	1.16892i	0.811424	−	0.584458i	$-0.198693\pi$
$488$	8907.15	+	6733.42i	0.826245	+	0.624606i
$489$		0			0
$490$	−5680.54	+	8226.62i	−0.523716	+	0.758451i
$491$			12172.0i			1.11877i	0.828909	+	0.559383i	$0.188962\pi$
$491$			12172.0i			1.11877i	−0.828909	+	0.559383i	$0.811038\pi$
$492$		0			0
$493$			2249.79i			0.205528i
$494$	2052.92	+	6456.99i	0.186974	+	0.588084i
$495$		0			0
$496$	3255.31	−	9218.13i	0.294693	−	0.834488i
$497$	−8121.40	+	16554.9i	−0.732987	+	1.49414i
$498$		0			0
$499$		−	3482.57i		−	0.312427i	−0.987723	−	0.156214i	$-0.950071\pi$
$499$		−	3482.57i		−	0.312427i	0.987723	−	0.156214i	$-0.0499288\pi$
$500$	6846.55	+	9678.73i	0.612374	+	0.865692i
$501$		0			0
$502$	15916.3	−	5060.41i	1.41510	−	0.449914i
$503$	−480.623			−0.0426043			−0.0213021	−	0.999773i	$-0.506781\pi$
$503$	−480.623			−0.0426043			−0.0213021	+	0.999773i	$0.506781\pi$
$504$		0			0
$505$	6630.10			0.584229
$506$	1644.31	−	522.789i	0.144464	−	0.0459304i
$507$		0			0
$508$	1853.60	+	2620.36i	0.161890	+	0.228858i
$509$		−	13977.8i		−	1.21720i	−0.793476	−	0.608602i	$-0.791731\pi$
$509$		−	13977.8i		−	1.21720i	0.793476	−	0.608602i	$-0.208269\pi$
$510$		0			0
$511$	6450.20	−	13148.3i	0.558395	−	1.13825i
$512$	−10796.6	−	4201.41i	−0.931925	−	0.362652i
$513$		0			0
$514$	4982.64	+	15671.7i	0.427577	+	1.34485i
$515$		−	8598.43i		−	0.735712i
$516$		0			0
$517$			9909.19i			0.842951i
$518$	1952.40	+	291.578i	0.165605	+	0.0247320i
$519$		0			0
$520$	−6895.78	+	9121.92i	−0.581538	+	0.769274i
$521$		−	1574.54i		−	0.132403i	−0.997806	−	0.0662015i	$-0.978912\pi$
$521$		−	1574.54i		−	0.132403i	0.997806	−	0.0662015i	$-0.0210880\pi$
$522$		0			0
$523$	−8049.27			−0.672982			−0.336491	−	0.941687i	$-0.609240\pi$
$523$	−8049.27			−0.672982			−0.336491	+	0.941687i	$0.609240\pi$
$524$	291.579	−	206.257i	0.0243086	−	0.0171954i
$525$		0			0
$526$	−1456.71	−	4581.73i	−0.120752	−	0.379797i
$527$			7132.35i			0.589545i
$528$		0			0
$529$	11024.8			0.906125
$530$	−1794.12	−	5642.99i	−0.147041	−	0.462483i
$531$		0			0
$532$	7145.24	−	1150.04i	0.582304	−	0.0937231i
$533$	20072.0			1.63117
$534$		0			0
$535$	15570.9			1.25830
$536$	4338.81	+	3279.95i	0.349642	+	0.264314i
$537$		0			0
$538$	4756.65	+	14961.0i	0.381178	+	1.19891i
$539$	4896.18	−	3789.28i	0.391268	−	0.302812i
$540$		0			0
$541$	−4564.27			−0.362723			−0.181362	−	0.983416i	$-0.558050\pi$
$541$	−4564.27			−0.362723			−0.181362	+	0.983416i	$0.558050\pi$
$542$	10085.9	−	3206.67i	0.799307	−	0.254130i
$543$		0			0
$544$	8448.06	+	267.389i	0.665823	+	0.0210739i
$545$		−	13884.2i		−	1.09126i
$546$		0			0
$547$			3464.95i			0.270842i	0.990788	+	0.135421i	$0.0432387\pi$
$547$			3464.95i			0.270842i	−0.990788	+	0.135421i	$0.956761\pi$
$548$	−9677.94	+	6845.99i	−0.754418	+	0.533661i
$549$		0			0
$550$	−290.959	−	915.146i	−0.0225574	−	0.0709490i
$551$	2353.57			0.181970
$552$		0			0
$553$	−1746.48	+	3560.07i	−0.134300	+	0.273760i
$554$	−15357.1	+	4882.60i	−1.17773	+	0.374444i
$555$		0			0
$556$	−7818.81	+	5530.88i	−0.596388	+	0.421873i
$557$	−14056.1			−1.06926			−0.534629	−	0.845087i	$-0.679549\pi$
$557$	−14056.1			−1.06926			−0.534629	+	0.845087i	$0.679549\pi$
$558$		0			0
$559$	23088.6			1.74695
$560$	8548.72	+	8724.08i	0.645088	+	0.658321i
$561$		0			0
$562$	17264.9	−	5489.17i	1.29586	−	0.412004i
$563$	−13614.3			−1.01914			−0.509568	−	0.860430i	$-0.670195\pi$
$563$	−13614.3			−1.01914			−0.509568	+	0.860430i	$0.670195\pi$
$564$		0			0
$565$			17283.7i			1.28696i
$566$	−19565.3	+	6220.56i	−1.45299	+	0.461961i
$567$		0			0
$568$	17971.6	+	13585.8i	1.32759	+	1.00360i
$569$	2692.70			0.198390			0.0991950	−	0.995068i	$-0.468373\pi$
$569$	2692.70			0.198390			0.0991950	+	0.995068i	$0.468373\pi$
$570$		0			0
$571$			8780.97i			0.643559i	0.946815	+	0.321779i	$0.104281\pi$
$571$			8780.97i			0.643559i	−0.946815	+	0.321779i	$0.895719\pi$
$572$	5781.38	−	4089.64i	0.422608	−	0.298945i
$573$		0			0
$574$	3166.78	−	21204.7i	0.230276	−	1.54193i
$575$			635.684i			0.0461041i
$576$		0			0
$577$		−	4486.99i		−	0.323736i	−0.986812	−	0.161868i	$-0.948248\pi$
$577$		−	4486.99i		−	0.323736i	0.986812	−	0.161868i	$-0.0517519\pi$
$578$	7366.15	−	2341.98i	0.530089	−	0.168535i
$579$		0			0
$580$	2293.91	+	3242.83i	0.164223	+	0.232157i
$581$	−14718.5	−	7220.52i	−1.05099	−	0.515589i
$582$		0			0
$583$			3667.02i			0.260502i
$584$	−14273.5	−	10790.1i	−1.01137	−	0.764553i
$585$		0			0
$586$	−2016.78	−	6343.31i	−0.142171	−	0.447167i
$587$	5983.67			0.420737			0.210368	−	0.977622i	$-0.432534\pi$
$587$	5983.67			0.420737			0.210368	+	0.977622i	$0.432534\pi$
$588$		0			0
$589$	7461.34			0.521968
$590$	−6332.78	−	19918.3i	−0.441893	−	1.38987i
$591$		0			0
$592$	803.112	−	2274.19i	0.0557563	−	0.157886i
$593$			594.936i			0.0411992i	0.999788	+	0.0205996i	$0.00655751\pi$
$593$			594.936i			0.0411992i	−0.999788	+	0.0205996i	$0.993442\pi$
$594$		0			0
$595$	−8000.42	−	3924.80i	−0.551236	−	0.270422i
$596$	−7826.94	+	5536.62i	−0.537926	+	0.380518i
$597$		0			0
$598$	−4467.49	+	1420.38i	−0.305500	+	0.0971301i
$599$			13607.8i			0.928213i	0.885779	+	0.464107i	$0.153625\pi$
$599$			13607.8i			0.928213i	−0.885779	+	0.464107i	$0.846375\pi$
$600$		0			0
$601$		−	12594.1i		−	0.854779i	−0.904068	−	0.427390i	$-0.859433\pi$
$601$		−	12594.1i		−	0.854779i	0.904068	−	0.427390i	$-0.140567\pi$
$602$	3642.70	−	24391.5i	0.246620	−	1.65136i
$603$		0			0
$604$	−14129.2	−	19973.9i	−0.951834	−	1.34558i
$605$			10358.4i			0.696079i
$606$		0			0
$607$	10949.8			0.732187			0.366094	−	0.930578i	$-0.380695\pi$
$607$	10949.8			0.732187			0.366094	+	0.930578i	$0.380695\pi$
$608$	279.723	−	8837.74i	0.0186583	−	0.589503i
$609$		0			0
$610$	−13706.8	+	4357.90i	−0.909787	+	0.289256i
$611$		−	26922.7i		−	1.78261i
$612$		0			0
$613$	3150.93			0.207610			0.103805	−	0.994598i	$-0.466898\pi$
$613$	3150.93			0.207610			0.103805	+	0.994598i	$0.466898\pi$
$614$	−15100.6	+	4801.05i	−0.992526	+	0.315562i
$615$		0			0
$616$	−3408.28	−	6752.85i	−0.222928	−	0.441688i
$617$	25804.8			1.68373			0.841865	−	0.539688i	$-0.181458\pi$
$617$	25804.8			1.68373			0.841865	+	0.539688i	$0.181458\pi$
$618$		0			0
$619$	−727.458			−0.0472359			−0.0236179	−	0.999721i	$-0.507519\pi$
$619$	−727.458			−0.0472359			−0.0236179	+	0.999721i	$0.507519\pi$
$620$	7272.23	+	10280.5i	0.471064	+	0.665927i
$621$		0			0
$622$	−8305.08	+	2640.50i	−0.535375	+	0.170216i
$623$	−548.980	+	1119.06i	−0.0353040	+	0.0719647i
$624$		0			0
$625$	−12920.0			−0.826883
$626$	−4313.02	−	13565.6i	−0.275372	−	0.866119i
$627$		0			0
$628$	−10464.5	−	14793.4i	−0.664938	−	0.940000i
$629$			1759.61i			0.111542i
$630$		0			0
$631$			21044.9i			1.32771i	0.747862	+	0.663854i	$0.231080\pi$
$631$			21044.9i			1.32771i	−0.747862	+	0.663854i	$0.768920\pi$
$632$	3864.74	+	2921.58i	0.243245	+	0.183883i
$633$		0			0
$634$	17376.0	−	5524.49i	1.08847	−	0.346066i
$635$	−4134.44			−0.258378
$636$		0			0
$637$	−13302.6	+	10295.2i	−0.827423	+	0.640364i
$638$	−745.334	−	2344.28i	−0.0462509	−	0.145472i
$639$		0			0
$640$	12449.6	−	8228.34i	0.768927	−	0.508209i
$641$	−22930.9			−1.41297			−0.706486	−	0.707727i	$-0.749721\pi$
$641$	−22930.9			−1.41297			−0.706486	+	0.707727i	$0.749721\pi$
$642$		0			0
$643$	−26817.0			−1.64473			−0.822364	−	0.568962i	$-0.807345\pi$
$643$	−26817.0			−1.64473			−0.822364	+	0.568962i	$0.807345\pi$
$644$	795.697	+	4943.69i	0.0486877	+	0.302498i
$645$		0			0
$646$	1954.61	+	6147.78i	0.119045	+	0.374429i
$647$	27901.0			1.69537			0.847683	−	0.530503i	$-0.177997\pi$
$647$	27901.0			1.69537			0.847683	+	0.530503i	$0.177997\pi$
$648$		0			0
$649$			12943.6i			0.782870i
$650$	790.519	+	2486.39i	0.0477026	+	0.150038i
$651$		0			0
$652$	6916.19	+	9777.19i	0.415428	+	0.587276i
$653$	−9804.28			−0.587552			−0.293776	−	0.955874i	$-0.594912\pi$
$653$	−9804.28			−0.587552			−0.293776	+	0.955874i	$0.594912\pi$
$654$		0			0
$655$			460.057i			0.0274441i
$656$	−24699.6	−	8722.46i	−1.47005	−	0.519139i
$657$		0			0
$658$	−28441.9	−	4247.61i	−1.68508	−	0.251655i
$659$			6511.96i			0.384931i	0.981304	+	0.192466i	$0.0616484\pi$
$659$			6511.96i			0.384931i	−0.981304	+	0.192466i	$0.938352\pi$
$660$		0			0
$661$		−	30763.5i		−	1.81023i	−0.425165	−	0.905116i	$-0.639784\pi$
$661$		−	30763.5i		−	1.81023i	0.425165	−	0.905116i	$-0.360216\pi$
$662$	7006.24	+	22036.5i	0.411337	+	1.29377i
$663$		0			0
$664$	−12078.8	+	15978.1i	−0.705944	+	0.933841i
$665$	−4105.84	+	8369.45i	−0.239425	+	0.488050i
$666$		0			0
$667$			1628.40i			0.0945304i
$668$	4391.84	−	3106.70i	0.254379	−	0.179943i
$669$		0			0
$670$	−6676.77	+	2122.80i	−0.384994	+	0.122404i
$671$	8907.15			0.512454
$672$		0			0
$673$	−2596.57			−0.148723			−0.0743615	−	0.997231i	$-0.523692\pi$
$673$	−2596.57			−0.148723			−0.0743615	+	0.997231i	$0.523692\pi$
$674$	−15344.3	+	4878.55i	−0.876917	+	0.278805i
$675$		0			0
$676$	−1358.75	+	961.156i	−0.0773073	+	0.0546857i
$677$			15954.7i			0.905744i	0.891576	+	0.452872i	$0.149601\pi$
$677$			15954.7i			0.905744i	−0.891576	+	0.452872i	$0.850399\pi$
$678$		0			0
$679$	7625.37	−	15543.8i	0.430979	−	0.878519i
$680$	−6565.56	+	8685.09i	−0.370261	+	0.489791i
$681$		0			0
$682$	−2362.88	−	7431.89i	−0.132668	−	0.417276i
$683$		−	17296.4i		−	0.969002i	−0.874791	−	0.484501i	$-0.839001\pi$
$683$		−	17296.4i		−	0.969002i	0.874791	−	0.484501i	$-0.160999\pi$
$684$		0			0
$685$		−	15270.0i		−	0.851730i
$686$	8777.42	+	15677.6i	0.488518	+	0.872554i
$687$		0			0
$688$	−28411.6	−	10033.3i	−1.57439	−	0.555985i
$689$		−	9963.06i		−	0.550889i
$690$		0			0
$691$	−30696.5			−1.68994			−0.844970	−	0.534814i	$-0.820382\pi$
$691$	−30696.5			−1.68994			−0.844970	+	0.534814i	$0.820382\pi$
$692$	−9280.51	−	13119.5i	−0.509815	−	0.720708i
$693$		0			0
$694$	5743.47	+	18064.7i	0.314148	+	0.988081i
$695$		−	12336.6i		−	0.673315i
$696$		0			0
$697$	19110.8			1.03856
$698$	3354.39	+	10550.4i	0.181899	+	0.572121i
$699$		0			0
$700$	2751.42	−	442.847i	0.148563	−	0.0239115i
$701$	27695.1			1.49219			0.746097	−	0.665837i	$-0.231925\pi$
$701$	27695.1			1.49219			0.746097	+	0.665837i	$0.231925\pi$
$702$		0			0
$703$	1840.77			0.0987569
$704$	−8891.45	+	2520.14i	−0.476007	+	0.134917i
$705$		0			0
$706$	−8444.47	−	26560.1i	−0.450158	−	1.41587i
$707$	5248.10	−	10697.9i	0.279173	−	0.569073i
$708$		0			0
$709$	−10901.1			−0.577433			−0.288716	−	0.957415i	$-0.593228\pi$
$709$	−10901.1			−0.577433			−0.288716	+	0.957415i	$0.593228\pi$
$710$	−27655.6	+	8792.77i	−1.46183	+	0.464770i
$711$		0			0
$712$	1214.82	+	918.354i	0.0639430	+	0.0483382i
$713$			5162.39i			0.271154i
$714$		0			0
$715$			9121.92i			0.477120i
$716$	−17205.1	−	24322.2i	−0.898022	−	1.26950i
$717$		0			0
$718$	8673.10	+	27279.2i	0.450804	+	1.41790i
$719$	28539.3			1.48030			0.740150	−	0.672442i	$-0.234755\pi$
$719$	28539.3			1.48030			0.740150	+	0.672442i	$0.234755\pi$
$720$		0			0
$721$	−13873.8	−	6806.14i	−0.716627	−	0.351559i
$722$	−12056.9	+	3833.34i	−0.621483	+	0.197593i
$723$		0			0
$724$	9289.38	+	13132.1i	0.476847	+	0.674102i
$725$	906.288			0.0464258
$726$		0			0
$727$	−1103.93			−0.0563169			−0.0281584	−	0.999603i	$-0.508964\pi$
$727$	−1103.93			−0.0563169			−0.0281584	+	0.999603i	$0.508964\pi$
$728$	9260.09	+	18347.1i	0.471431	+	0.934049i
$729$		0			0
$730$	21964.7	−	6983.42i	1.11363	−	0.354066i
$731$	21982.9			1.11227
$732$		0			0
$733$		−	12729.3i		−	0.641431i	−0.947176	−	0.320716i	$-0.896077\pi$
$733$		−	12729.3i		−	0.641431i	0.947176	−	0.320716i	$-0.103923\pi$
$734$	12018.3	−	3821.06i	0.604362	−	0.192150i
$735$		0			0
$736$	6114.70	+	193.536i	0.306238	+	0.00969271i
$737$	4338.81			0.216855
$738$		0			0
$739$			20655.8i			1.02819i	0.857732	+	0.514097i	$0.171873\pi$
$739$			20655.8i			1.02819i	−0.857732	+	0.514097i	$0.828127\pi$
$740$	1794.12	+	2536.28i	0.0891259	+	0.125994i
$741$		0			0
$742$	−10525.3	−	1571.88i	−0.520748	−	0.0777702i
$743$			30656.9i			1.51372i	0.653577	+	0.756860i	$0.273268\pi$
$743$			30656.9i			1.51372i	−0.653577	+	0.756860i	$0.726732\pi$
$744$		0			0
$745$		−	12349.4i		−	0.607312i
$746$	2235.60	−	710.783i	0.109720	−	0.0348842i
$747$		0			0
$748$	5504.52	−	3893.79i	0.269071	−	0.190336i
$749$	12325.3	−	25124.2i	0.601276	−	1.22566i
$750$		0			0
$751$		−	18986.0i		−	0.922513i	−0.887267	−	0.461257i	$-0.847399\pi$
$751$		−	18986.0i		−	0.922513i	0.887267	−	0.461257i	$-0.152601\pi$
$752$	−11699.5	+	33129.6i	−0.567335	+	1.60653i
$753$		0			0
$754$	2025.03	+	6369.25i	0.0978079	+	0.307632i
$755$	31515.1			1.51914
$756$		0			0
$757$	22252.7			1.06841			0.534206	−	0.845354i	$-0.320611\pi$
$757$	22252.7			1.06841			0.534206	+	0.845354i	$0.320611\pi$
$758$	446.746	+	1405.14i	0.0214071	+	0.0673310i
$759$		0			0
$760$	9085.71	+	6868.40i	0.433649	+	0.327820i
$761$			21595.4i			1.02869i	0.857583	+	0.514346i	$0.171965\pi$
$761$			21595.4i			1.02869i	−0.857583	+	0.514346i	$0.828035\pi$
$762$		0			0
$763$	−22402.6	−	10990.2i	−1.06295	−	0.521456i
$764$	−5394.65	−	7626.23i	−0.255460	−	0.361135i
$765$		0			0
$766$	−33978.0	+	10802.9i	−1.60271	+	0.509562i
$767$		−	35167.1i		−	1.65555i
$768$		0			0
$769$			37574.2i			1.76198i	0.473139	+	0.880988i	$0.343121\pi$
$769$			37574.2i			1.76198i	−0.473139	+	0.880988i	$0.656879\pi$
$770$	9636.67	+	1439.17i	0.451015	+	0.0673561i
$771$		0			0
$772$	−29270.6	+	20705.5i	−1.36460	+	0.965293i
$773$			31649.2i			1.47263i	0.676638	+	0.736315i	$0.263436\pi$
$773$			31649.2i			1.47263i	−0.676638	+	0.736315i	$0.736564\pi$
$774$		0			0
$775$	2873.14			0.133169
$776$	−16874.0	−	12756.0i	−0.780593	−	0.590095i
$777$		0			0
$778$	−30361.4	+	9653.04i	−1.39911	+	0.444831i
$779$		−	19992.3i		−	0.919511i
$780$		0			0
$781$	17971.6			0.823401
$782$	−4253.55	+	1352.37i	−0.194510	+	0.0618420i
$783$		0			0
$784$	20843.4	−	6888.01i	0.949497	−	0.313776i
$785$	23341.1			1.06125
$786$		0			0
$787$	−13129.8			−0.594698			−0.297349	−	0.954769i	$-0.596103\pi$
$787$	−13129.8			−0.594698			−0.297349	+	0.954769i	$0.596103\pi$
$788$	28956.4	−	20483.2i	1.30905	−	0.925995i
$789$		0			0
$790$	−5947.25	+	1890.86i	−0.267840	+	0.0851565i
$791$	27887.8	+	13681.0i	1.25357	+	0.614970i
$792$		0			0
$793$	−24200.2			−1.08370
$794$	−2831.57	−	8906.06i	−0.126560	−	0.398066i
$795$		0			0
$796$	18909.8	−	13376.4i	0.842011	−	0.595623i
$797$			14391.2i			0.639603i	0.947485	+	0.319802i	$0.103616\pi$
$797$			14391.2i			0.639603i	−0.947485	+	0.319802i	$0.896384\pi$
$798$		0			0
$799$		−	25633.4i		−	1.13497i
$800$	107.713	−	3403.15i	0.00476029	−	0.150399i
$801$		0			0
$802$	15506.7	−	4930.16i	0.682744	−	0.217070i
$803$	−14273.5			−0.627273
$804$		0			0
$805$	−5790.70	−	2840.77i	−0.253534	−	0.124378i
$806$	6419.80	+	20192.0i	0.280555	+	0.882423i
$807$		0			0
$808$	−11613.4	−	8779.22i	−0.505640	−	0.382242i
$809$	−5116.40			−0.222352			−0.111176	−	0.993801i	$-0.535462\pi$
$809$	−5116.40			−0.222352			−0.111176	+	0.993801i	$0.535462\pi$
$810$		0			0
$811$	−9442.84			−0.408857			−0.204429	−	0.978881i	$-0.565534\pi$
$811$	−9442.84			−0.408857			−0.204429	+	0.978881i	$0.565534\pi$
$812$	7048.16	−	1134.42i	0.304608	−	0.0490274i
$813$		0			0
$814$	−582.942	−	1833.51i	−0.0251009	−	0.0789490i
$815$	−15426.5			−0.663029
$816$		0			0
$817$		−	22996.9i		−	0.984773i
$818$	−1484.06	−	4667.77i	−0.0634340	−	0.199517i
$819$		0			0
$820$	27546.1	−	19485.6i	1.17311	−	0.829838i
$821$	−8380.02			−0.356230			−0.178115	−	0.984010i	$-0.557000\pi$
$821$	−8380.02			−0.356230			−0.178115	+	0.984010i	$0.557000\pi$
$822$		0			0
$823$			30980.2i			1.31215i	0.754694	+	0.656077i	$0.227785\pi$
$823$			30980.2i			1.31215i	−0.754694	+	0.656077i	$0.772215\pi$
$824$	−11385.6	+	15061.1i	−0.481353	+	0.636747i
$825$		0			0
$826$	−37151.5	−	5548.34i	−1.56497	−	0.233718i
$827$		−	21707.7i		−	0.912760i	−0.889785	−	0.456380i	$-0.849146\pi$
$827$		−	21707.7i		−	0.912760i	0.889785	−	0.456380i	$-0.150854\pi$
$828$		0			0
$829$			40210.4i			1.68464i	0.538980	+	0.842319i	$0.318810\pi$
$829$			40210.4i			1.68464i	−0.538980	+	0.842319i	$0.681190\pi$
$830$	−7817.41	−	24587.9i	−0.326923	−	1.02826i
$831$		0			0
$832$	24157.5	−	6847.07i	1.00662	−	0.285312i
$833$	−12665.6	+	9802.21i	−0.526814	+	0.407715i
$834$		0			0
$835$			6929.49i			0.287192i
$836$	−4073.40	−	5758.43i	−0.168519	−	0.238229i
$837$		0			0
$838$	−37418.9	+	11896.9i	−1.54250	+	0.490419i
$839$	−1008.67			−0.0415056			−0.0207528	−	0.999785i	$-0.506606\pi$
$839$	−1008.67			−0.0415056			−0.0207528	+	0.999785i	$0.506606\pi$
$840$		0			0
$841$	−22067.4			−0.904810
$842$	−9012.37	+	2865.37i	−0.368868	+	0.117277i
$843$		0			0
$844$	10687.2	+	15108.1i	0.435862	+	0.616163i
$845$		−	2143.86i		−	0.0872791i
$846$		0			0
$847$	16713.5	+	8199.24i	0.678021	+	0.332620i
$848$	−4329.53	+	12260.0i	−0.175326	+	0.496475i
$849$		0			0
$850$	752.662	+	2367.33i	0.0303719	+	0.0955278i
$851$			1273.60i			0.0513027i
$852$		0			0
$853$		−	41994.2i		−	1.68564i	−0.538193	−	0.842821i	$-0.680893\pi$
$853$		−	41994.2i		−	1.68564i	0.538193	−	0.842821i	$-0.319107\pi$
$854$	−3818.08	+	25565.8i	−0.152988	+	1.02441i
$855$		0			0
$856$	−27274.3	−	20618.2i	−1.08904	−	0.823265i
$857$		−	43337.5i		−	1.72740i	−0.504007	−	0.863700i	$-0.668141\pi$
$857$		−	43337.5i		−	1.72740i	0.504007	−	0.863700i	$-0.331859\pi$
$858$		0			0
$859$	25845.0			1.02657			0.513283	−	0.858219i	$-0.328429\pi$
$859$	25845.0			1.02657			0.513283	+	0.858219i	$0.328429\pi$
$860$	31686.0	−	22414.0i	1.25638	−	0.888736i
$861$		0			0
$862$	−6064.02	−	19073.0i	−0.239607	−	0.753629i
$863$		−	4759.33i		−	0.187728i	−0.995585	−	0.0938641i	$-0.970078\pi$
$863$		−	4759.33i		−	0.187728i	0.995585	−	0.0938641i	$-0.0299219\pi$
$864$		0			0
$865$	20700.2			0.813672
$866$	−4208.03	−	13235.4i	−0.165121	−	0.519349i
$867$		0			0
$868$	22344.3	−	3596.36i	0.873749	−	0.140632i
$869$	3864.74			0.150866
$870$		0			0
$871$	−11788.3			−0.458588
$872$	−18384.8	+	24319.9i	−0.713976	+	0.944466i
$873$		0			0
$874$	1414.74	+	4449.75i	0.0547534	+	0.172214i
$875$	−12088.0	+	24640.5i	−0.467028	+	0.952003i
$876$		0			0
$877$	−4600.79			−0.177147			−0.0885734	−	0.996070i	$-0.528231\pi$
$877$	−4600.79			−0.177147			−0.0885734	+	0.996070i	$0.528231\pi$
$878$	36241.0	−	11522.4i	1.39302	−	0.442895i
$879$		0			0
$880$	3964.01	−	11225.0i	0.151849	−	0.429992i
$881$			12349.2i			0.472253i	0.971722	+	0.236127i	$0.0758780\pi$
$881$			12349.2i			0.472253i	−0.971722	+	0.236127i	$0.924122\pi$
$882$		0			0
$883$			20446.6i			0.779257i	0.920972	+	0.389629i	$0.127397\pi$
$883$			20446.6i			0.779257i	−0.920972	+	0.389629i	$0.872603\pi$
$884$	−14955.4	+	10579.2i	−0.569011	+	0.402508i
$885$		0			0
$886$	12825.3	+	40339.0i	0.486314	+	1.52959i
$887$	−12482.1			−0.472502			−0.236251	−	0.971692i	$-0.575919\pi$
$887$	−12482.1			−0.472502			−0.236251	+	0.971692i	$0.575919\pi$
$888$		0			0
$889$	−3272.64	+	6671.04i	−0.123466	+	0.251675i
$890$	−1869.43	+	594.362i	−0.0704084	+	0.0223855i
$891$		0			0
$892$	27229.8	−	19261.8i	1.02211	−	0.723020i
$893$	−26815.8			−1.00488
$894$		0			0
$895$	38375.9			1.43326
$896$	−3422.11	−	26601.0i	−0.127594	−	0.991826i
$897$		0			0
$898$	29404.2	−	9348.71i	1.09269	−	0.347406i
$899$	7359.96			0.273046
$900$		0			0
$901$		−	9485.95i		−	0.350747i
$902$	−19913.4	+	6331.23i	−0.735083	+	0.233711i
$903$		0			0
$904$	22886.1	−	30274.4i	0.842015	−	1.11384i
$905$	−20719.9			−0.761054
$906$		0			0
$907$			16244.3i			0.594690i	0.954770	+	0.297345i	$0.0961011\pi$
$907$			16244.3i			0.594690i	−0.954770	+	0.297345i	$0.903899\pi$
$908$	22610.7	−	15994.4i	0.826391	−	0.584573i
$909$		0			0
$910$	−26182.2	−	3910.14i	−0.953772	−	0.142440i
$911$			18806.3i			0.683953i	0.939709	+	0.341976i	$0.111096\pi$
$911$			18806.3i			0.683953i	−0.939709	+	0.341976i	$0.888904\pi$
$912$		0			0
$913$			15978.1i			0.579187i
$914$	12951.3	−	4117.70i	0.468698	−	0.149017i
$915$		0			0
$916$	−1401.74	−	1981.59i	−0.0505620	−	0.0714777i
$917$	742.315	+	364.161i	0.0267322	+	0.0131141i
$918$		0			0
$919$		−	42382.0i		−	1.52128i	−0.649176	−	0.760639i	$-0.724886\pi$
$919$		−	42382.0i		−	1.52128i	0.649176	−	0.760639i	$-0.275114\pi$
$920$	−4752.14	+	6286.26i	−0.170297	+	0.225274i
$921$		0			0
$922$	5219.17	+	16415.7i	0.186426	+	0.586358i
$923$	−48827.8			−1.74126
$924$		0			0
$925$	708.827			0.0251958
$926$	−3555.94	−	11184.4i	−0.126194	−	0.396913i
$927$		0			0
$928$	275.922	−	8717.66i	0.00976034	−	0.308374i
$929$		−	14960.7i		−	0.528357i	−0.964474	−	0.264178i	$-0.914899\pi$
$929$		−	14960.7i		−	0.528357i	0.964474	−	0.264178i	$-0.0851008\pi$
$930$		0			0
$931$	10254.4	+	13249.8i	0.360980	+	0.466428i
$932$	14474.6	−	10239.0i	0.508724	−	0.359861i
$933$		0			0
$934$	17785.3	−	5654.63i	0.623077	−	0.198100i
$935$			8685.09i			0.303779i
$936$		0			0
$937$			24321.2i			0.847961i	0.905671	+	0.423980i	$0.139367\pi$
$937$			24321.2i			0.847961i	−0.905671	+	0.423980i	$0.860633\pi$
$938$	−1859.84	+	12453.5i	−0.0647399	+	0.433497i
$939$		0			0
$940$	−26136.1	−	36947.7i	−0.906879	−	1.28202i
$941$			7556.97i			0.261796i	0.991396	+	0.130898i	$0.0417861\pi$
$941$			7556.97i			0.261796i	−0.991396	+	0.130898i	$0.958214\pi$
$942$		0			0
$943$	13832.4			0.477672
$944$	−15282.1	+	43274.7i	−0.526898	+	1.49203i
$945$		0			0
$946$	−22906.1	+	7282.73i	−0.787255	+	0.250298i
$947$			35766.4i			1.22730i	0.789579	+	0.613649i	$0.210299\pi$
$947$			35766.4i			1.22730i	−0.789579	+	0.613649i	$0.789701\pi$
$948$		0			0
$949$	38780.1			1.32651
$950$	2476.52	−	787.380i	0.0845779	−	0.0268905i
$951$		0			0
$952$	8816.64	+	17468.5i	0.300157	+	0.594702i
$953$	−7503.23			−0.255040			−0.127520	−	0.991836i	$-0.540702\pi$
$953$	−7503.23			−0.255040			−0.127520	+	0.991836i	$0.540702\pi$
$954$		0			0
$955$	12032.7			0.407718
$956$	−4909.55	−	6940.46i	−0.166094	−	0.234802i
$957$		0			0
$958$	−12114.5	+	3851.64i	−0.408560	+	0.129897i
$959$	−24638.5	−	12087.0i	−0.829634	−	0.406998i
$960$		0			0
$961$	−6458.24			−0.216785
$962$	1583.82	+	4981.53i	0.0530814	+	0.166955i
$963$		0			0
$964$	33885.9	+	47903.4i	1.13215	+	1.60048i
$965$		−	46183.5i		−	1.54062i
$966$		0			0
$967$		−	41391.4i		−	1.37648i	−0.725482	−	0.688241i	$-0.758383\pi$
$967$		−	41391.4i		−	1.37648i	0.725482	−	0.688241i	$-0.241617\pi$
$968$	13716.0	−	18143.9i	0.455422	−	0.602445i
$969$		0			0
$970$	25966.5	−	8255.73i	0.859520	−	0.273274i
$971$	18250.3			0.603171			0.301586	−	0.953439i	$-0.402484\pi$
$971$	18250.3			0.603171			0.301586	+	0.953439i	$0.402484\pi$
$972$		0			0
$973$	−19905.5	−	9765.12i	−0.655848	−	0.321742i
$974$	−10766.0	−	33861.9i	−0.354173	−	1.11397i
$975$		0			0
$976$	29779.4	+	10516.4i	0.976657	+	0.344899i
$977$	17959.5			0.588102			0.294051	−	0.955790i	$-0.404996\pi$
$977$	17959.5			0.588102			0.294051	+	0.955790i	$0.404996\pi$
$978$		0			0
$979$	1214.82			0.0396588
$980$	−8261.58	+	27042.8i	−0.269292	+	0.881480i
$981$		0			0
$982$	10431.3	+	32809.2i	0.338978	+	1.06618i
$983$	−47801.0			−1.55098			−0.775491	−	0.631359i	$-0.782498\pi$
$983$	−47801.0			−1.55098			−0.775491	+	0.631359i	$0.782498\pi$
$984$		0			0
$985$			45687.7i			1.47790i
$986$	1928.05	+	6064.24i	0.0622735	+	0.195867i
$987$		0			0
$988$	11067.2	+	15645.3i	0.356370	+	0.503788i
$989$	15911.2			0.511574
$990$		0			0
$991$		−	5324.87i		−	0.170686i	−0.996352	−	0.0853431i	$-0.972801\pi$
$991$		−	5324.87i		−	0.170686i	0.996352	−	0.0853431i	$-0.0271986\pi$
$992$	874.737	−	27637.0i	0.0279969	−	0.884551i
$993$		0			0
$994$	−7703.60	+	51583.2i	−0.245818	+	1.64599i
$995$			29836.1i			0.950622i
$996$		0			0
$997$			33227.4i			1.05549i	0.849403	+	0.527745i	$0.176962\pi$
$997$			33227.4i			1.05549i	−0.849403	+	0.527745i	$0.823038\pi$
$998$	−2984.53	−	9387.16i	−0.0946631	−	0.297741i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.g.55.14	yes	16
3.2	odd	2	inner	252.4.b.g.55.3	yes	16
4.3	odd	2	inner	252.4.b.g.55.16	yes	16
7.6	odd	2	inner	252.4.b.g.55.13	yes	16
12.11	even	2	inner	252.4.b.g.55.1	✓	16
21.20	even	2	inner	252.4.b.g.55.4	yes	16
28.27	even	2	inner	252.4.b.g.55.15	yes	16
84.83	odd	2	inner	252.4.b.g.55.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.b.g.55.1	✓	16	12.11	even	2	inner
252.4.b.g.55.2	yes	16	84.83	odd	2	inner
252.4.b.g.55.3	yes	16	3.2	odd	2	inner
252.4.b.g.55.4	yes	16	21.20	even	2	inner
252.4.b.g.55.13	yes	16	7.6	odd	2	inner
252.4.b.g.55.14	yes	16	1.1	even	1	trivial
252.4.b.g.55.15	yes	16	28.27	even	2	inner
252.4.b.g.55.16	yes	16	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.69547 - 0.856992i) q^{2} +(6.53113 - 4.62000i) q^{4} +10.3049i q^{5} +(16.6272 + 8.15690i) q^{7} +(13.6452 - 18.0502i) q^{8} +O(q^{10})\)	\(q+(2.69547 - 0.856992i) q^{2} +(6.53113 - 4.62000i) q^{4} +10.3049i q^{5} +(16.6272 + 8.15690i) q^{7} +(13.6452 - 18.0502i) q^{8} +(8.83121 + 27.7765i) q^{10} -18.0502i q^{11} +49.0412i q^{13} +(51.8086 + 7.73727i) q^{14} +(21.3113 - 60.3476i) q^{16} +46.6928i q^{17} +48.8465 q^{19} +(47.6085 + 67.3025i) q^{20} +(-15.4689 - 48.6538i) q^{22} +33.7962i q^{23} +18.8094 q^{25} +(42.0280 + 132.189i) q^{26} +(146.279 - 23.5440i) q^{28} +48.1829 q^{29} +152.751 q^{31} +(5.72657 - 180.929i) q^{32} +(40.0153 + 125.859i) q^{34} +(-84.0559 + 171.342i) q^{35} +37.6848 q^{37} +(131.664 - 41.8611i) q^{38} +(186.005 + 140.612i) q^{40} -409.288i q^{41} -470.799i q^{43} +(-83.3918 - 117.888i) q^{44} +(28.9631 + 91.0966i) q^{46} -548.980 q^{47} +(209.930 + 271.253i) q^{49} +(50.7001 - 16.1195i) q^{50} +(226.570 + 320.295i) q^{52} -203.157 q^{53} +186.005 q^{55} +(374.115 - 188.823i) q^{56} +(129.875 - 41.2923i) q^{58} -717.092 q^{59} +493.466i q^{61} +(411.735 - 130.906i) q^{62} +(-139.619 - 492.596i) q^{64} -505.364 q^{65} +240.375i q^{67} +(215.720 + 304.956i) q^{68} +(-79.7317 + 533.882i) q^{70} +995.648i q^{71} -790.766i q^{73} +(101.578 - 32.2956i) q^{74} +(319.023 - 225.671i) q^{76} +(147.234 - 300.125i) q^{77} +214.111i q^{79} +(621.875 + 219.610i) q^{80} +(-350.757 - 1103.23i) q^{82} -885.204 q^{83} -481.164 q^{85} +(-403.471 - 1269.03i) q^{86} +(-325.809 - 246.298i) q^{88} +67.3025i q^{89} +(-400.024 + 815.420i) q^{91} +(156.138 + 220.727i) q^{92} +(-1479.76 + 470.472i) q^{94} +503.358i q^{95} -934.837i q^{97} +(798.322 + 551.247i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{4}+O(q^{10}) \) 16 * q + 40 * q^4	\( 16 q + 40 q^{4} - 304 q^{16} - 312 q^{22} - 1376 q^{25} - 816 q^{28} - 816 q^{37} - 2568 q^{46} - 640 q^{49} + 2336 q^{58} + 1120 q^{64} - 424 q^{70} + 5072 q^{85} - 3536 q^{88}+O(q^{100}) \) 16 * q + 40 * q^4 - 304 * q^16 - 312 * q^22 - 1376 * q^25 - 816 * q^28 - 816 * q^37 - 2568 * q^46 - 640 * q^49 + 2336 * q^58 + 1120 * q^64 - 424 * q^70 + 5072 * q^85 - 3536 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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