LMFDB - Embedded newform 252.4.b.f.55.12

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 $ x^12 - x^11 - 2x^10 - 6x^9 + 56x^7 - 448x^6 + 448x^5 - 3072x^3 - 8192x^2 - 32768x + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.12
Root			$-2.78362 + 0.501431i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.f.55.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.78362 + 0.501431i) q^{2} +(7.49713 + 2.79159i) q^{4} +4.57514i q^{5} +(2.93118 + 18.2868i) q^{7} +(19.4694 + 11.5300i) q^{8} +O(q^{10})$	\(q+(2.78362 + 0.501431i) q^{2} +(7.49713 + 2.79159i) q^{4} +4.57514i q^{5} +(2.93118 + 18.2868i) q^{7} +(19.4694 + 11.5300i) q^{8} +(-2.29411 + 12.7355i) q^{10} +26.0206i q^{11} -75.0905i q^{13} +(-1.01026 + 52.3735i) q^{14} +(48.4141 + 41.8578i) q^{16} +115.976i q^{17} -119.051 q^{19} +(-12.7719 + 34.3004i) q^{20} +(-13.0475 + 72.4315i) q^{22} +61.4339i q^{23} +104.068 q^{25} +(37.6527 - 209.024i) q^{26} +(-29.0738 + 145.281i) q^{28} +71.9146 q^{29} +231.587 q^{31} +(113.778 + 140.793i) q^{32} +(-58.1538 + 322.833i) q^{34} +(-83.6647 + 13.4106i) q^{35} +13.3306 q^{37} +(-331.392 - 59.6956i) q^{38} +(-52.7515 + 89.0753i) q^{40} -144.133i q^{41} -288.638i q^{43} +(-72.6387 + 195.080i) q^{44} +(-30.8049 + 171.009i) q^{46} +343.549 q^{47} +(-325.816 + 107.204i) q^{49} +(289.687 + 52.1829i) q^{50} +(209.622 - 562.963i) q^{52} -142.666 q^{53} -119.048 q^{55} +(-153.779 + 389.831i) q^{56} +(200.183 + 36.0602i) q^{58} -403.919 q^{59} -21.7765i q^{61} +(644.651 + 116.125i) q^{62} +(246.117 + 448.966i) q^{64} +343.549 q^{65} -598.674i q^{67} +(-323.757 + 869.486i) q^{68} +(-239.616 - 4.62208i) q^{70} -589.524i q^{71} +6.85314i q^{73} +(37.1075 + 6.68439i) q^{74} +(-892.538 - 332.340i) q^{76} +(-475.834 + 76.2711i) q^{77} -972.231i q^{79} +(-191.505 + 221.501i) q^{80} +(72.2726 - 401.212i) q^{82} +429.745 q^{83} -530.605 q^{85} +(144.732 - 803.461i) q^{86} +(-300.018 + 506.605i) q^{88} -1083.91i q^{89} +(1373.17 - 220.104i) q^{91} +(-171.498 + 460.578i) q^{92} +(956.312 + 172.266i) q^{94} -544.673i q^{95} +1031.01i q^{97} +(-960.706 + 135.042i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8}+O(q^{10}) $ 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8	$ 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8} + 56 q^{10} - 69 q^{14} + 41 q^{16} - 84 q^{19} - 172 q^{20} - 182 q^{22} - 216 q^{25} - 300 q^{26} + 309 q^{28} - 200 q^{29} - 384 q^{31} + 159 q^{32} - 164 q^{34} - 84 q^{35} - 244 q^{37} - 268 q^{38} - 316 q^{40} - 190 q^{44} + 894 q^{46} - 280 q^{47} - 424 q^{49} + 1771 q^{50} - 796 q^{52} + 16 q^{53} + 212 q^{55} + 7 q^{56} - 570 q^{58} - 1168 q^{59} + 384 q^{62} + 2705 q^{64} - 280 q^{65} - 1552 q^{68} + 968 q^{70} - 1622 q^{74} - 788 q^{76} - 968 q^{77} + 3060 q^{80} - 2540 q^{82} + 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} + 1648 q^{91} - 4298 q^{92} + 4256 q^{94} - 97 q^{98}+O(q^{100}) $ 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8 + 56 * q^10 - 69 * q^14 + 41 * q^16 - 84 * q^19 - 172 * q^20 - 182 * q^22 - 216 * q^25 - 300 * q^26 + 309 * q^28 - 200 * q^29 - 384 * q^31 + 159 * q^32 - 164 * q^34 - 84 * q^35 - 244 * q^37 - 268 * q^38 - 316 * q^40 - 190 * q^44 + 894 * q^46 - 280 * q^47 - 424 * q^49 + 1771 * q^50 - 796 * q^52 + 16 * q^53 + 212 * q^55 + 7 * q^56 - 570 * q^58 - 1168 * q^59 + 384 * q^62 + 2705 * q^64 - 280 * q^65 - 1552 * q^68 + 968 * q^70 - 1622 * q^74 - 788 * q^76 - 968 * q^77 + 3060 * q^80 - 2540 * q^82 + 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 + 1648 * q^91 - 4298 * q^92 + 4256 * q^94 - 97 * q^98

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 $

$2$	2.78362	+	0.501431i	0.984160	+	0.177282i
$2$	2.78362	+	0.501431i	0.984160	+	0.177282i
$3$		0			0
$3$		0			0
$4$	7.49713	+	2.79159i	0.937142	+	0.348949i
$5$			4.57514i			0.409213i	0.978844	+	0.204606i	$0.0655914\pi$
$5$			4.57514i			0.409213i	−0.978844	+	0.204606i	$0.934409\pi$
$6$		0			0
$7$	2.93118	+	18.2868i	0.158269	+	0.987396i
$7$	2.93118	+	18.2868i	0.158269	+	0.987396i
$8$	19.4694	+	11.5300i	0.860435	+	0.509560i
$9$		0			0
$10$	−2.29411	+	12.7355i	−0.0725462	+	0.402731i
$11$			26.0206i			0.713227i	0.934252	+	0.356613i	$0.116069\pi$
$11$			26.0206i			0.713227i	−0.934252	+	0.356613i	$0.883931\pi$
$12$		0			0
$13$		−	75.0905i		−	1.60203i	−0.598647	−	0.801013i	$-0.704295\pi$
$13$		−	75.0905i		−	1.60203i	0.598647	−	0.801013i	$-0.295705\pi$
$14$	−1.01026	+	52.3735i	−0.0192859	+	0.999814i
$15$		0			0
$16$	48.4141	+	41.8578i	0.756470	+	0.654029i
$17$			115.976i			1.65460i	0.561758	+	0.827302i	$0.310125\pi$
$17$			115.976i			1.65460i	−0.561758	+	0.827302i	$0.689875\pi$
$18$		0			0
$19$	−119.051			−1.43748			−0.718739	−	0.695280i	$-0.755280\pi$
$19$	−119.051			−1.43748			−0.718739	+	0.695280i	$0.755280\pi$
$20$	−12.7719	+	34.3004i	−0.142794	+	0.383490i
$21$		0			0
$22$	−13.0475	+	72.4315i	−0.126443	+	0.701929i
$23$			61.4339i			0.556950i	0.960443	+	0.278475i	$0.0898290\pi$
$23$			61.4339i			0.556950i	−0.960443	+	0.278475i	$0.910171\pi$
$24$		0			0
$25$	104.068			0.832545
$26$	37.6527	−	209.024i	0.284011	−	1.57665i
$27$		0			0
$28$	−29.0738	+	145.281i	−0.196230	+	0.980558i
$29$	71.9146			0.460490			0.230245	−	0.973133i	$-0.426047\pi$
$29$	71.9146			0.460490			0.230245	+	0.973133i	$0.426047\pi$
$30$		0			0
$31$	231.587			1.34175			0.670875	−	0.741571i	$-0.265919\pi$
$31$	231.587			1.34175			0.670875	+	0.741571i	$0.265919\pi$
$32$	113.778	+	140.793i	0.628539	+	0.777778i
$33$		0			0
$34$	−58.1538	+	322.833i	−0.293332	+	1.62839i
$35$	−83.6647	+	13.4106i	−0.404055	+	0.0647657i
$36$		0			0
$37$	13.3306			0.0592309			0.0296155	−	0.999561i	$-0.490572\pi$
$37$	13.3306			0.0592309			0.0296155	+	0.999561i	$0.490572\pi$
$38$	−331.392	−	59.6956i	−1.41471	−	0.254840i
$39$		0			0
$40$	−52.7515	+	89.0753i	−0.208518	+	0.352101i
$41$		−	144.133i		−	0.549018i	−0.961584	−	0.274509i	$-0.911485\pi$
$41$		−	144.133i		−	0.549018i	0.961584	−	0.274509i	$-0.0885154\pi$
$42$		0			0
$43$		−	288.638i		−	1.02365i	−0.859090	−	0.511825i	$-0.828970\pi$
$43$		−	288.638i		−	1.02365i	0.859090	−	0.511825i	$-0.171030\pi$
$44$	−72.6387	+	195.080i	−0.248880	+	0.668395i
$45$		0			0
$46$	−30.8049	+	171.009i	−0.0987376	+	0.548128i
$47$	343.549			1.06621			0.533104	−	0.846050i	$-0.321025\pi$
$47$	343.549			1.06621			0.533104	+	0.846050i	$0.321025\pi$
$48$		0			0
$49$	−325.816	+	107.204i	−0.949902	+	0.312548i
$50$	289.687	+	52.1829i	0.819357	+	0.147596i
$51$		0			0
$52$	209.622	−	562.963i	0.559025	−	1.50133i
$53$	−142.666			−0.369749			−0.184875	−	0.982762i	$-0.559188\pi$
$53$	−142.666			−0.369749			−0.184875	+	0.982762i	$0.559188\pi$
$54$		0			0
$55$	−119.048			−0.291861
$56$	−153.779	+	389.831i	−0.366957	+	0.930238i
$57$		0			0
$58$	200.183	+	36.0602i	0.453196	+	0.0816368i
$59$	−403.919			−0.891284			−0.445642	−	0.895211i	$-0.647025\pi$
$59$	−403.919			−0.891284			−0.445642	+	0.895211i	$0.647025\pi$
$60$		0			0
$61$		−	21.7765i		−	0.0457082i	−0.999739	−	0.0228541i	$-0.992725\pi$
$61$		−	21.7765i		−	0.0457082i	0.999739	−	0.0228541i	$-0.00727532\pi$
$62$	644.651	+	116.125i	1.32050	+	0.237869i
$63$		0			0
$64$	246.117	+	448.966i	0.480697	+	0.876887i
$65$	343.549			0.655570
$66$		0			0
$67$		−	598.674i		−	1.09164i	−0.837904	−	0.545818i	$-0.816219\pi$
$67$		−	598.674i		−	1.09164i	0.837904	−	0.545818i	$-0.183781\pi$
$68$	−323.757	+	869.486i	−0.577372	+	1.55060i
$69$		0			0
$70$	−239.616	−	4.62208i	−0.409137	−	0.00789205i
$71$		−	589.524i		−	0.985403i	−0.870198	−	0.492701i	$-0.836009\pi$
$71$		−	589.524i		−	0.985403i	0.870198	−	0.492701i	$-0.163991\pi$
$72$		0			0
$73$			6.85314i			0.0109877i	0.999985	+	0.00549383i	$0.00174875\pi$
$73$			6.85314i			0.0109877i	−0.999985	+	0.00549383i	$0.998251\pi$
$74$	37.1075	+	6.68439i	0.0582927	+	0.0105006i
$75$		0			0
$76$	−892.538	−	332.340i	−1.34712	−	0.501606i
$77$	−475.834	+	76.2711i	−0.704237	+	0.112882i
$78$		0			0
$79$		−	972.231i		−	1.38461i	−0.721603	−	0.692307i	$-0.756594\pi$
$79$		−	972.231i		−	1.38461i	0.721603	−	0.692307i	$-0.243406\pi$
$80$	−191.505	+	221.501i	−0.267637	+	0.309557i
$81$		0			0
$82$	72.2726	−	401.212i	0.0973313	−	0.540322i
$83$	429.745			0.568321			0.284161	−	0.958777i	$-0.408285\pi$
$83$	429.745			0.568321			0.284161	+	0.958777i	$0.408285\pi$
$84$		0			0
$85$	−530.605			−0.677085
$86$	144.732	−	803.461i	0.181475	−	1.00743i
$87$		0			0
$88$	−300.018	+	506.605i	−0.363432	+	0.613685i
$89$		−	1083.91i		−	1.29095i	−0.763781	−	0.645476i	$-0.776659\pi$
$89$		−	1083.91i		−	1.29095i	0.763781	−	0.645476i	$-0.223341\pi$
$90$		0			0
$91$	1373.17	−	220.104i	1.58183	−	0.253551i
$92$	−171.498	+	460.578i	−0.194347	+	0.521942i
$93$		0			0
$94$	956.312	+	172.266i	1.04932	+	0.189020i
$95$		−	544.673i		−	0.588234i
$96$		0			0
$97$			1031.01i			1.07921i	0.841920	+	0.539603i	$0.181426\pi$
$97$			1031.01i			1.07921i	−0.841920	+	0.539603i	$0.818574\pi$
$98$	−960.706	+	135.042i	−0.990265	+	0.139197i
$99$		0			0
$100$	780.213	+	290.515i	0.780213	+	0.290515i
$101$			207.988i			0.204907i	0.994738	+	0.102454i	$0.0326693\pi$
$101$			207.988i			0.204907i	−0.994738	+	0.102454i	$0.967331\pi$
$102$		0			0
$103$	−1229.81			−1.17647			−0.588237	−	0.808689i	$-0.700178\pi$
$103$	−1229.81			−1.17647			−0.588237	+	0.808689i	$0.700178\pi$
$104$	865.795	−	1461.97i	0.816329	−	1.37844i
$105$		0			0
$106$	−397.129	−	71.5372i	−0.363892	−	0.0655500i
$107$		−	1502.68i		−	1.35766i	−0.734294	−	0.678832i	$-0.762487\pi$
$107$		−	1502.68i		−	1.35766i	0.734294	−	0.678832i	$-0.237513\pi$
$108$		0			0
$109$	579.301			0.509055			0.254527	−	0.967066i	$-0.418080\pi$
$109$	579.301			0.509055			0.254527	+	0.967066i	$0.418080\pi$
$110$	−331.384	−	59.6941i	−0.287238	−	0.0517419i
$111$		0			0
$112$	−623.537	+	1008.03i	−0.526060	+	0.850448i
$113$	−614.637			−0.511683			−0.255842	−	0.966719i	$-0.582353\pi$
$113$	−614.637			−0.511683			−0.255842	+	0.966719i	$0.582353\pi$
$114$		0			0
$115$	−281.069			−0.227911
$116$	539.153	+	200.756i	0.431544	+	0.160687i
$117$		0			0
$118$	−1124.36	−	202.537i	−0.877166	−	0.158009i
$119$	−2120.83	+	339.946i	−1.63375	+	0.261873i
$120$		0			0
$121$	653.930			0.491308
$122$	10.9194	−	60.6177i	0.00810327	−	0.0449842i
$123$		0			0
$124$	1736.24	+	646.496i	1.25741	+	0.468202i
$125$			1048.02i			0.749901i
$126$		0			0
$127$			273.874i			0.191358i	0.995412	+	0.0956788i	$0.0305022\pi$
$127$			273.874i			0.191358i	−0.995412	+	0.0956788i	$0.969498\pi$
$128$	459.972	+	1373.16i	0.317626	+	0.948216i
$129$		0			0
$130$	956.312	+	172.266i	0.645185	+	0.116221i
$131$	2187.84			1.45918			0.729591	−	0.683884i	$-0.239710\pi$
$131$	2187.84			1.45918			0.729591	+	0.683884i	$0.239710\pi$
$132$		0			0
$133$	−348.959	−	2177.06i	−0.227508	−	1.41936i
$134$	300.193	−	1666.48i	0.193528	−	1.07434i
$135$		0			0
$136$	−1337.20	+	2257.98i	−0.843120	+	1.42368i
$137$	2535.39			1.58112			0.790558	−	0.612388i	$-0.209791\pi$
$137$	2535.39			1.58112			0.790558	+	0.612388i	$0.209791\pi$
$138$		0			0
$139$	1007.32			0.614675			0.307338	−	0.951601i	$-0.400562\pi$
$139$	1007.32			0.614675			0.307338	+	0.951601i	$0.400562\pi$
$140$	−664.683	−	133.017i	−0.401257	−	0.0802998i
$141$		0			0
$142$	295.605	−	1641.01i	0.174695	−	0.969794i
$143$	1953.90			1.14261
$144$		0			0
$145$			329.019i			0.188438i
$146$	−3.43637	+	19.0766i	−0.00194792	+	0.0108136i
$147$		0			0
$148$	99.9416	+	37.2137i	0.0555078	+	0.0206686i
$149$	−2342.59			−1.28800			−0.644002	−	0.765024i	$-0.722727\pi$
$149$	−2342.59			−1.28800			−0.644002	+	0.765024i	$0.722727\pi$
$150$		0			0
$151$		−	561.022i		−	0.302353i	−0.988507	−	0.151177i	$-0.951694\pi$
$151$		−	561.022i		−	0.302353i	0.988507	−	0.151177i	$-0.0483062\pi$
$152$	−2317.85	−	1372.66i	−1.23686	−	0.732481i
$153$		0			0
$154$	−1362.79	−	26.2875i	−0.713094	−	0.0137553i
$155$			1059.54i			0.549061i
$156$		0			0
$157$		−	459.220i		−	0.233438i	−0.993165	−	0.116719i	$-0.962762\pi$
$157$		−	459.220i		−	0.233438i	0.993165	−	0.116719i	$-0.0372377\pi$
$158$	487.506	−	2706.33i	0.245468	−	1.36268i
$159$		0			0
$160$	−644.146	+	520.549i	−0.318277	+	0.257206i
$161$	−1123.43	+	180.074i	−0.549931	+	0.0881480i
$162$		0			0
$163$		−	558.186i		−	0.268224i	−0.990966	−	0.134112i	$-0.957182\pi$
$163$		−	558.186i		−	0.268224i	0.990966	−	0.134112i	$-0.0428182\pi$
$164$	402.359	−	1080.58i	0.191579	−	0.514508i
$165$		0			0
$166$	1196.25	+	215.487i	0.559319	+	0.100753i
$167$	−2494.32			−1.15579			−0.577893	−	0.816113i	$-0.696125\pi$
$167$	−2494.32			−1.15579			−0.577893	+	0.816113i	$0.696125\pi$
$168$		0			0
$169$	−3441.58			−1.56649
$170$	−1477.01	−	266.062i	−0.666360	−	0.120035i
$171$		0			0
$172$	805.760	−	2163.96i	0.357201	−	0.959305i
$173$			2881.62i			1.26639i	0.773993	+	0.633195i	$0.218257\pi$
$173$			2881.62i			1.26639i	−0.773993	+	0.633195i	$0.781743\pi$
$174$		0			0
$175$	305.043	+	1903.08i	0.131766	+	0.822052i
$176$	−1089.16	+	1259.76i	−0.466471	+	0.539534i
$177$		0			0
$178$	543.508	−	3017.21i	0.228863	−	1.27050i
$179$		−	2072.63i		−	0.865452i	−0.901525	−	0.432726i	$-0.857552\pi$
$179$		−	2072.63i		−	0.865452i	0.901525	−	0.432726i	$-0.142448\pi$
$180$		0			0
$181$		−	2764.12i		−	1.13511i	−0.823335	−	0.567556i	$-0.807889\pi$
$181$		−	2764.12i		−	1.13511i	0.823335	−	0.567556i	$-0.192111\pi$
$182$	3932.75	+	75.8609i	1.60173	+	0.0308966i
$183$		0			0
$184$	−708.335	+	1196.08i	−0.283800	+	0.479220i
$185$			60.9895i			0.0242380i
$186$		0			0
$187$	−3017.76			−1.18011
$188$	2575.63	+	959.048i	0.999188	+	0.372052i
$189$		0			0
$190$	273.115	−	1516.16i	0.104284	−	0.578916i
$191$			4118.94i			1.56040i	0.625530	+	0.780200i	$0.284883\pi$
$191$			4118.94i			1.56040i	−0.625530	+	0.780200i	$0.715117\pi$
$192$		0			0
$193$	4537.82			1.69243			0.846216	−	0.532840i	$-0.178875\pi$
$193$	4537.82			1.69243			0.846216	+	0.532840i	$0.178875\pi$
$194$	−516.979	+	2869.94i	−0.191324	+	1.06211i
$195$		0			0
$196$	−2741.96	−	105.822i	−0.999256	−	0.0385647i
$197$	−846.178			−0.306029			−0.153014	−	0.988224i	$-0.548898\pi$
$197$	−846.178			−0.306029			−0.153014	+	0.988224i	$0.548898\pi$
$198$		0			0
$199$	−1218.87			−0.434188			−0.217094	−	0.976151i	$-0.569658\pi$
$199$	−1218.87			−0.434188			−0.217094	+	0.976151i	$0.569658\pi$
$200$	2026.15	+	1199.91i	0.716351	+	0.424232i
$201$		0			0
$202$	−104.292	+	578.962i	−0.0363265	+	0.201661i
$203$	210.795	+	1315.09i	0.0728813	+	0.454686i
$204$		0			0
$205$	659.427			0.224665
$206$	−3423.33	−	616.664i	−1.15784	−	0.208568i
$207$		0			0
$208$	3143.12	−	3635.43i	1.04777	−	1.21188i
$209$		−	3097.76i		−	1.02525i
$210$		0			0
$211$			5064.81i			1.65249i	0.563308	+	0.826247i	$0.309528\pi$
$211$			5064.81i			1.65249i	−0.563308	+	0.826247i	$0.690472\pi$
$212$	−1069.59	−	398.265i	−0.346507	−	0.129023i
$213$		0			0
$214$	753.492	−	4182.91i	0.240690	−	1.33616i
$215$	1320.56			0.418890
$216$		0			0
$217$	678.824	+	4234.99i	0.212357	+	1.32484i
$218$	1612.56	+	290.479i	0.500992	+	0.0902465i
$219$		0			0
$220$	−892.516	−	332.332i	−0.273516	−	0.101845i
$221$	8708.67			2.65072
$222$		0			0
$223$	3894.06			1.16935			0.584676	−	0.811267i	$-0.301222\pi$
$223$	3894.06			1.16935			0.584676	+	0.811267i	$0.301222\pi$
$224$	−2241.15	+	2493.32i	−0.668496	+	0.743715i
$225$		0			0
$226$	−1710.92	−	308.198i	−0.503578	−	0.0907124i
$227$	−1165.95			−0.340910			−0.170455	−	0.985365i	$-0.554524\pi$
$227$	−1165.95			−0.340910			−0.170455	+	0.985365i	$0.554524\pi$
$228$		0			0
$229$			2537.92i			0.732361i	0.930544	+	0.366181i	$0.119335\pi$
$229$			2537.92i			0.732361i	−0.930544	+	0.366181i	$0.880665\pi$
$230$	−782.390	−	140.936i	−0.224301	−	0.0404047i
$231$		0			0
$232$	1400.14	+	829.177i	0.396221	+	0.234647i
$233$	−1345.53			−0.378321			−0.189160	−	0.981946i	$-0.560577\pi$
$233$	−1345.53			−0.378321			−0.189160	+	0.981946i	$0.560577\pi$
$234$		0			0
$235$			1571.78i			0.436306i
$236$	−3028.24	−	1127.58i	−0.835260	−	0.311012i
$237$		0			0
$238$	−6074.05	−	117.166i	−1.65430	−	0.0319106i
$239$			6239.81i			1.68878i	0.535725	+	0.844392i	$0.320038\pi$
$239$			6239.81i			1.68878i	−0.535725	+	0.844392i	$0.679962\pi$
$240$		0			0
$241$			4546.01i			1.21508i	0.794289	+	0.607540i	$0.207844\pi$
$241$			4546.01i			1.21508i	−0.794289	+	0.607540i	$0.792156\pi$
$242$	1820.30	+	327.901i	0.483525	+	0.0871002i
$243$		0			0
$244$	60.7912	−	163.262i	0.0159498	−	0.0428351i
$245$	−490.474	−	1490.65i	−0.127899	−	0.388712i
$246$		0			0
$247$			8939.56i			2.30288i
$248$	4508.86	+	2670.20i	1.15449	+	0.683702i
$249$		0			0
$250$	−525.508	+	2917.29i	−0.132944	+	0.738022i
$251$	−6775.91			−1.70395			−0.851976	−	0.523582i	$-0.824596\pi$
$251$	−6775.91			−1.70395			−0.851976	+	0.523582i	$0.824596\pi$
$252$		0			0
$253$	−1598.55			−0.397232
$254$	−137.329	+	762.363i	−0.0339243	+	0.188326i
$255$		0			0
$256$	591.842	+	4053.02i	0.144493	+	0.989506i
$257$		−	7170.16i		−	1.74032i	−0.492770	−	0.870160i	$-0.664016\pi$
$257$		−	7170.16i		−	1.74032i	0.492770	−	0.870160i	$-0.335984\pi$
$258$		0			0
$259$	39.0746	+	243.775i	0.00937442	+	0.0584844i
$260$	2575.63	+	959.048i	0.614362	+	0.228760i
$261$		0			0
$262$	6090.14	+	1097.05i	1.43607	+	0.258687i
$263$			2093.31i			0.490795i	0.969422	+	0.245398i	$0.0789185\pi$
$263$			2093.31i			0.490795i	−0.969422	+	0.245398i	$0.921081\pi$
$264$		0			0
$265$		−	652.717i		−	0.151306i
$266$	120.272	−	6235.09i	0.0277231	−	1.43721i
$267$		0			0
$268$	1671.25	−	4488.34i	0.380925	−	1.02302i
$269$		−	1573.92i		−	0.356742i	−0.983963	−	0.178371i	$-0.942917\pi$
$269$		−	1573.92i		−	0.356742i	0.983963	−	0.178371i	$-0.0570828\pi$
$270$		0			0
$271$	−1974.18			−0.442519			−0.221260	−	0.975215i	$-0.571017\pi$
$271$	−1974.18			−0.442519			−0.221260	+	0.975215i	$0.571017\pi$
$272$	−4854.50	+	5614.86i	−1.08216	+	1.25166i
$273$		0			0
$274$	7057.57	+	1271.32i	1.55607	+	0.280304i
$275$			2707.91i			0.593793i
$276$		0			0
$277$	4758.46			1.03216			0.516079	−	0.856541i	$-0.327391\pi$
$277$	4758.46			1.03216			0.516079	+	0.856541i	$0.327391\pi$
$278$	2804.00	+	505.102i	0.604939	+	0.108971i
$279$		0			0
$280$	−1783.53	−	703.561i	−0.380665	−	0.150164i
$281$	−1753.46			−0.372252			−0.186126	−	0.982526i	$-0.559593\pi$
$281$	−1753.46			−0.372252			−0.186126	+	0.982526i	$0.559593\pi$
$282$		0			0
$283$	−3603.19			−0.756846			−0.378423	−	0.925633i	$-0.623534\pi$
$283$	−3603.19			−0.756846			−0.378423	+	0.925633i	$0.623534\pi$
$284$	1645.71	−	4419.74i	0.343855	−	0.923462i
$285$		0			0
$286$	5438.91	+	979.743i	1.12451	+	0.202564i
$287$	2635.73	−	422.480i	0.542099	−	0.0868926i
$288$		0			0
$289$	−8537.38			−1.73771
$290$	−164.980	+	915.865i	−0.0334068	+	0.185453i
$291$		0			0
$292$	−19.1311	+	51.3789i	−0.00383413	+	0.0102970i
$293$			8854.04i			1.76539i	0.469949	+	0.882693i	$0.344272\pi$
$293$			8854.04i			1.76539i	−0.469949	+	0.882693i	$0.655728\pi$
$294$		0			0
$295$		−	1847.98i		−	0.364725i
$296$	259.540	+	153.703i	0.0509644	+	0.0301817i
$297$		0			0
$298$	−6520.90	−	1174.65i	−1.26760	−	0.228341i
$299$	4613.10			0.892249
$300$		0			0
$301$	5278.28	−	846.052i	1.01075	−	0.162012i
$302$	281.314	−	1561.68i	0.0536019	−	0.297564i
$303$		0			0
$304$	−5763.72	−	4983.20i	−1.08741	−	0.940152i
$305$	99.6307			0.0187044
$306$		0			0
$307$	4372.30			0.812836			0.406418	−	0.913687i	$-0.366778\pi$
$307$	4372.30			0.812836			0.406418	+	0.913687i	$0.366778\pi$
$308$	−3780.31	−	756.518i	−0.699360	−	0.139956i
$309$		0			0
$310$	−531.287	+	2949.37i	−0.0973389	+	0.540364i
$311$	1956.21			0.356676			0.178338	−	0.983969i	$-0.442928\pi$
$311$	1956.21			0.356676			0.178338	+	0.983969i	$0.442928\pi$
$312$		0			0
$313$		−	6314.07i		−	1.14023i	−0.821565	−	0.570115i	$-0.806899\pi$
$313$		−	6314.07i		−	1.14023i	0.821565	−	0.570115i	$-0.193101\pi$
$314$	230.267	−	1278.30i	0.0413844	−	0.229740i
$315$		0			0
$316$	2714.07	−	7288.95i	0.483159	−	1.29758i
$317$	−4962.78			−0.879298			−0.439649	−	0.898170i	$-0.644897\pi$
$317$	−4962.78			−0.879298			−0.439649	+	0.898170i	$0.644897\pi$
$318$		0			0
$319$			1871.26i			0.328434i
$320$	−2054.08	+	1126.02i	−0.358833	+	0.196707i
$321$		0			0
$322$	−3217.51	−	62.0642i	−0.556847	−	0.0107413i
$323$		−	13807.0i		−	2.37846i
$324$		0			0
$325$		−	7814.52i		−	1.33376i
$326$	279.892	−	1553.78i	0.0475514	−	0.263976i
$327$		0			0
$328$	1661.86	−	2806.18i	0.279758	−	0.472395i
$329$	1007.01	+	6282.42i	0.168748	+	1.05277i
$330$		0			0
$331$		−	6941.96i		−	1.15276i	−0.817181	−	0.576381i	$-0.804464\pi$
$331$		−	6941.96i		−	1.15276i	0.817181	−	0.576381i	$-0.195536\pi$
$332$	3221.86	+	1199.67i	0.532598	+	0.198315i
$333$		0			0
$334$	−6943.25	−	1250.73i	−1.13748	−	0.204900i
$335$	2739.01			0.446711
$336$		0			0
$337$	−1809.91			−0.292558			−0.146279	−	0.989243i	$-0.546730\pi$
$337$	−1809.91			−0.292558			−0.146279	+	0.989243i	$0.546730\pi$
$338$	−9580.06	−	1725.71i	−1.54168	−	0.277711i
$339$		0			0
$340$	−3978.02	−	1481.23i	−0.634524	−	0.236268i
$341$			6026.02i			0.956972i
$342$		0			0
$343$	−2915.45	−	5643.91i	−0.458949	−	0.888463i
$344$	3328.01	−	5619.62i	0.521611	−	0.880784i
$345$		0			0
$346$	−1444.93	+	8021.34i	−0.224509	+	1.24633i
$347$		−	3542.86i		−	0.548100i	−0.961716	−	0.274050i	$-0.911637\pi$
$347$		−	3542.86i		−	0.548100i	0.961716	−	0.274050i	$-0.0883633\pi$
$348$		0			0
$349$			1318.04i			0.202158i	0.994878	+	0.101079i	$0.0322295\pi$
$349$			1318.04i			0.202158i	−0.994878	+	0.101079i	$0.967771\pi$
$350$	−105.136	+	5450.41i	−0.0160564	+	0.832390i
$351$		0			0
$352$	−3663.51	+	2960.56i	−0.554732	+	0.448291i
$353$		−	1254.21i		−	0.189107i	−0.995520	−	0.0945534i	$-0.969858\pi$
$353$		−	1254.21i		−	0.189107i	0.995520	−	0.0945534i	$-0.0301423\pi$
$354$		0			0
$355$	2697.15			0.403239
$356$	3025.84	−	8126.25i	0.450476	−	1.20980i
$357$		0			0
$358$	1039.28	−	5769.44i	0.153430	−	0.851743i
$359$		−	2350.70i		−	0.345585i	−0.984958	−	0.172793i	$-0.944721\pi$
$359$		−	2350.70i		−	0.345585i	0.984958	−	0.172793i	$-0.0552791\pi$
$360$		0			0
$361$	7314.03			1.06634
$362$	1386.01	−	7694.26i	0.201235	−	1.11713i
$363$		0			0
$364$	10909.3	+	2183.17i	1.57088	+	0.314366i
$365$	−31.3540			−0.00449629
$366$		0			0
$367$	2941.18			0.418333			0.209167	−	0.977880i	$-0.432925\pi$
$367$	2941.18			0.418333			0.209167	+	0.977880i	$0.432925\pi$
$368$	−2571.49	+	2974.27i	−0.364262	+	0.421316i
$369$		0			0
$370$	−30.5820	+	169.772i	−0.00429698	+	0.0238541i
$371$	−418.181	−	2608.91i	−0.0585198	−	0.365089i
$372$		0			0
$373$	−7367.26			−1.02269			−0.511343	−	0.859377i	$-0.670852\pi$
$373$	−7367.26			−1.02269			−0.511343	+	0.859377i	$0.670852\pi$
$374$	−8400.30	−	1513.19i	−1.16141	−	0.209212i
$375$		0			0
$376$	6688.70	+	3961.13i	0.917403	+	0.543297i
$377$		−	5400.10i		−	0.737717i
$378$		0			0
$379$		−	8022.57i		−	1.08731i	−0.839308	−	0.543657i	$-0.817039\pi$
$379$		−	8022.57i		−	1.08731i	0.839308	−	0.543657i	$-0.182961\pi$
$380$	1520.50	−	4083.48i	0.205263	−	0.551259i
$381$		0			0
$382$	−2065.36	+	11465.6i	−0.276632	+	1.53568i
$383$	−13469.5			−1.79702			−0.898511	−	0.438950i	$-0.855350\pi$
$383$	−13469.5			−1.79702			−0.898511	+	0.438950i	$0.855350\pi$
$384$		0			0
$385$	−348.950	−	2177.00i	−0.0461926	−	0.288183i
$386$	12631.6	+	2275.40i	1.66562	+	0.300039i
$387$		0			0
$388$	−2878.15	+	7729.61i	−0.376588	+	1.01137i
$389$	642.221			0.0837067			0.0418533	−	0.999124i	$-0.486674\pi$
$389$	642.221			0.0837067			0.0418533	+	0.999124i	$0.486674\pi$
$390$		0			0
$391$	−7124.85			−0.921532
$392$	−7579.52	−	1669.47i	−0.976591	−	0.215104i
$393$		0			0
$394$	−2355.44	−	424.299i	−0.301181	−	0.0542535i
$395$	4448.09			0.566602
$396$		0			0
$397$			6101.12i			0.771301i	0.922645	+	0.385650i	$0.126023\pi$
$397$			6101.12i			0.771301i	−0.922645	+	0.385650i	$0.873977\pi$
$398$	−3392.88	−	611.179i	−0.427311	−	0.0769740i
$399$		0			0
$400$	5038.36	+	4356.07i	0.629795	+	0.544508i
$401$	−6300.98			−0.784679			−0.392339	−	0.919821i	$-0.628334\pi$
$401$	−6300.98			−0.784679			−0.392339	+	0.919821i	$0.628334\pi$
$402$		0			0
$403$		−	17390.0i		−	2.14952i
$404$	−580.618	+	1559.32i	−0.0715021	+	0.192027i
$405$		0			0
$406$	−72.6524	+	3766.41i	−0.00888098	+	0.460404i
$407$			346.871i			0.0422451i
$408$		0			0
$409$		−	897.858i		−	0.108548i	−0.998526	−	0.0542741i	$-0.982716\pi$
$409$		−	897.858i		−	0.108548i	0.998526	−	0.0542741i	$-0.0172845\pi$
$410$	1835.60	+	330.657i	0.221107	+	0.0398292i
$411$		0			0
$412$	−9220.05	−	3433.12i	−1.10252	−	0.410529i
$413$	−1183.96	−	7386.40i	−0.141063	−	0.880051i
$414$		0			0
$415$			1966.14i			0.232564i
$416$	10572.2	−	8543.63i	1.24602	−	1.00694i
$417$		0			0
$418$	1553.31	−	8623.01i	0.181758	−	1.00901i
$419$	8654.42			1.00906			0.504530	−	0.863394i	$-0.331666\pi$
$419$	8654.42			1.00906			0.504530	+	0.863394i	$0.331666\pi$
$420$		0			0
$421$	−13325.5			−1.54263			−0.771313	−	0.636456i	$-0.780400\pi$
$421$	−13325.5			−1.54263			−0.771313	+	0.636456i	$0.780400\pi$
$422$	−2539.65	+	14098.5i	−0.292958	+	1.62632i
$423$		0			0
$424$	−2777.63	−	1644.94i	−0.318145	−	0.188409i
$425$			12069.4i			1.37753i
$426$		0			0
$427$	398.224	−	63.8311i	0.0451321	−	0.00723420i
$428$	4194.88	−	11265.8i	0.473755	−	1.27232i
$429$		0			0
$430$	3675.94	+	662.169i	0.412255	+	0.0742619i
$431$		−	4512.65i		−	0.504332i	−0.967684	−	0.252166i	$-0.918857\pi$
$431$		−	4512.65i		−	0.504332i	0.967684	−	0.252166i	$-0.0811428\pi$
$432$		0			0
$433$			4597.71i			0.510282i	0.966904	+	0.255141i	$0.0821219\pi$
$433$			4597.71i			0.510282i	−0.966904	+	0.255141i	$0.917878\pi$
$434$	−233.963	+	12129.0i	−0.0258769	+	1.34150i
$435$		0			0
$436$	4343.10	+	1617.17i	0.477057	+	0.177634i
$437$		−	7313.74i		−	0.800604i
$438$		0			0
$439$	14584.7			1.58562			0.792811	−	0.609467i	$-0.208617\pi$
$439$	14584.7			1.58562			0.792811	+	0.609467i	$0.208617\pi$
$440$	−2317.79	−	1372.62i	−0.251128	−	0.148721i
$441$		0			0
$442$	24241.7	+	4366.80i	2.60873	+	0.469926i
$443$		−	10578.3i		−	1.13452i	−0.823539	−	0.567259i	$-0.808004\pi$
$443$		−	10578.3i		−	1.13452i	0.823539	−	0.567259i	$-0.191996\pi$
$444$		0			0
$445$	4959.06			0.528274
$446$	10839.6	+	1952.60i	1.15083	+	0.207306i
$447$		0			0
$448$	−7488.75	+	5816.70i	−0.789755	+	0.613422i
$449$	833.584			0.0876152			0.0438076	−	0.999040i	$-0.486051\pi$
$449$	833.584			0.0876152			0.0438076	+	0.999040i	$0.486051\pi$
$450$		0			0
$451$	3750.42			0.391575
$452$	−4608.02	−	1715.81i	−0.479520	−	0.178551i
$453$		0			0
$454$	−3245.56	−	584.642i	−0.335510	−	0.0604375i
$455$	1007.01	+	6282.42i	0.103756	+	0.647307i
$456$		0			0
$457$	−6462.47			−0.661492			−0.330746	−	0.943720i	$-0.607300\pi$
$457$	−6462.47			−0.661492			−0.330746	+	0.943720i	$0.607300\pi$
$458$	−1272.59	+	7064.63i	−0.129835	+	0.720761i
$459$		0			0
$460$	−2107.21	−	784.628i	−0.213585	−	0.0795293i
$461$		−	10142.3i		−	1.02467i	−0.858786	−	0.512334i	$-0.828781\pi$
$461$		−	10142.3i		−	1.02467i	0.858786	−	0.512334i	$-0.171219\pi$
$462$		0			0
$463$		−	1428.43i		−	0.143380i	−0.997427	−	0.0716898i	$-0.977161\pi$
$463$		−	1428.43i		−	0.143380i	0.997427	−	0.0716898i	$-0.0228391\pi$
$464$	3481.68	+	3010.19i	0.348346	+	0.301173i
$465$		0			0
$466$	−3745.46	−	674.691i	−0.372328	−	0.0670697i
$467$	−2039.86			−0.202128			−0.101064	−	0.994880i	$-0.532225\pi$
$467$	−2039.86			−0.202128			−0.101064	+	0.994880i	$0.532225\pi$
$468$		0			0
$469$	10947.8	−	1754.82i	1.07788	−	0.172772i
$470$	−788.141	+	4375.26i	−0.0773494	+	0.429395i
$471$		0			0
$472$	−7864.07	−	4657.20i	−0.766892	−	0.454163i
$473$	7510.53			0.730094
$474$		0			0
$475$	−12389.4			−1.19676
$476$	−16849.1	−	3371.86i	−1.62243	−	0.324683i
$477$		0			0
$478$	−3128.83	+	17369.3i	−0.299392	+	1.66203i
$479$	−13044.0			−1.24425			−0.622126	−	0.782917i	$-0.713731\pi$
$479$	−13044.0			−1.24425			−0.622126	+	0.782917i	$0.713731\pi$
$480$		0			0
$481$		−	1001.00i		−	0.0948895i
$482$	−2279.51	+	12654.4i	−0.215412	+	1.19583i
$483$		0			0
$484$	4902.60	+	1825.51i	0.460425	+	0.171441i
$485$	−4717.00			−0.441625
$486$		0			0
$487$			6444.14i			0.599614i	0.954000	+	0.299807i	$0.0969223\pi$
$487$			6444.14i			0.599614i	−0.954000	+	0.299807i	$0.903078\pi$
$488$	251.084	−	423.977i	0.0232911	−	0.0393289i
$489$		0			0
$490$	−617.835	−	4395.36i	−0.0569611	−	0.405229i
$491$			8032.35i			0.738279i	0.929374	+	0.369140i	$0.120348\pi$
$491$			8032.35i			0.738279i	−0.929374	+	0.369140i	$0.879652\pi$
$492$		0			0
$493$			8340.35i			0.761928i
$494$	−4482.57	+	24884.4i	−0.408260	+	2.26640i
$495$		0			0
$496$	11212.1	+	9693.73i	1.01499	+	0.877543i
$497$	10780.5	−	1728.00i	0.972983	−	0.155959i
$498$		0			0
$499$			1184.12i			0.106230i	0.998588	+	0.0531148i	$0.0169149\pi$
$499$			1184.12i			0.106230i	−0.998588	+	0.0531148i	$0.983085\pi$
$500$	−2925.64	+	7857.13i	−0.261677	+	0.702763i
$501$		0			0
$502$	−18861.6	−	3397.65i	−1.67696	−	0.302081i
$503$	19759.9			1.75159			0.875794	−	0.482684i	$-0.160338\pi$
$503$	19759.9			1.75159			0.875794	+	0.482684i	$0.160338\pi$
$504$		0			0
$505$	−951.576			−0.0838506
$506$	−4449.75	−	801.560i	−0.390940	−	0.0704223i
$507$		0			0
$508$	−764.544	+	2053.27i	−0.0667740	+	0.179329i
$509$		−	14150.4i		−	1.23223i	−0.787654	−	0.616117i	$-0.788705\pi$
$509$		−	14150.4i		−	1.23223i	0.787654	−	0.616117i	$-0.211295\pi$
$510$		0			0
$511$	−125.322	+	20.0878i	−0.0108492	+	0.00173901i
$512$	−384.840	+	11578.8i	−0.0332182	+	0.999448i
$513$		0			0
$514$	3595.34	−	19959.0i	0.308528	−	1.71275i
$515$		−	5626.55i		−	0.481428i
$516$		0			0
$517$			8939.34i			0.760448i
$518$	−13.4674	+	698.172i	−0.00114232	+	0.0592199i
$519$		0			0
$520$	6688.70	+	3961.13i	0.564075	+	0.334052i
$521$			18031.5i			1.51626i	0.652101	+	0.758132i	$0.273888\pi$
$521$			18031.5i			1.51626i	−0.652101	+	0.758132i	$0.726112\pi$
$522$		0			0
$523$	5733.64			0.479378			0.239689	−	0.970850i	$-0.422955\pi$
$523$	5733.64			0.479378			0.239689	+	0.970850i	$0.422955\pi$
$524$	16402.6	+	6107.56i	1.36746	+	0.509180i
$525$		0			0
$526$	−1049.65	+	5827.00i	−0.0870094	+	0.483021i
$527$			26858.5i			2.22006i
$528$		0			0
$529$	8392.87			0.689806
$530$	327.292	−	1816.92i	0.0268239	−	0.148909i
$531$		0			0
$532$	3461.26	−	17295.8i	0.282076	−	1.40953i
$533$	−10823.0			−0.879542
$534$		0			0
$535$	6874.99			0.555573
$536$	6902.73	−	11655.8i	0.556254	−	0.939282i
$537$		0			0
$538$	789.213	−	4381.21i	0.0632442	−	0.351092i
$539$	−2789.51	−	8477.92i	−0.222918	−	0.677495i
$540$		0			0
$541$	−3887.89			−0.308971			−0.154486	−	0.987995i	$-0.549372\pi$
$541$	−3887.89			−0.308971			−0.154486	+	0.987995i	$0.549372\pi$
$542$	−5495.37	−	989.913i	−0.435510	−	0.0784509i
$543$		0			0
$544$	−16328.6	+	13195.5i	−1.28691	+	1.03998i
$545$			2650.38i			0.208312i
$546$		0			0
$547$			4722.04i			0.369104i	0.982823	+	0.184552i	$0.0590834\pi$
$547$			4722.04i			0.369104i	−0.982823	+	0.184552i	$0.940917\pi$
$548$	19008.1	+	7077.76i	1.48173	+	0.551728i
$549$		0			0
$550$	−1357.83	+	7537.81i	−0.105269	+	0.584388i
$551$	−8561.47			−0.661943
$552$		0			0
$553$	17779.0	−	2849.79i	1.36716	−	0.219142i
$554$	13245.8	+	2386.04i	1.01581	+	0.182984i
$555$		0			0
$556$	7552.02	+	2812.03i	0.576038	+	0.214490i
$557$	13987.0			1.06400			0.532000	−	0.846745i	$-0.321441\pi$
$557$	13987.0			1.06400			0.532000	+	0.846745i	$0.321441\pi$
$558$		0			0
$559$	−21674.0			−1.63991
$560$	−4611.89	−	2852.77i	−0.348014	−	0.215270i
$561$		0			0
$562$	−4880.98	−	879.240i	−0.366356	−	0.0659938i
$563$	−6757.50			−0.505852			−0.252926	−	0.967486i	$-0.581393\pi$
$563$	−6757.50			−0.505852			−0.252926	+	0.967486i	$0.581393\pi$
$564$		0			0
$565$		−	2812.05i		−	0.209387i
$566$	−10029.9	−	1806.75i	−0.744858	−	0.134176i
$567$		0			0
$568$	6797.23	−	11477.7i	0.502122	−	0.847875i
$569$	7220.86			0.532011			0.266005	−	0.963972i	$-0.414296\pi$
$569$	7220.86			0.532011			0.266005	+	0.963972i	$0.414296\pi$
$570$		0			0
$571$		−	365.261i		−	0.0267700i	−0.999910	−	0.0133850i	$-0.995739\pi$
$571$		−	365.261i		−	0.0267700i	0.999910	−	0.0133850i	$-0.00426071\pi$
$572$	14648.6	+	5454.48i	1.07079	+	0.398712i
$573$		0			0
$574$	7548.73	+	145.612i	0.548916	+	0.0105883i
$575$			6393.31i			0.463686i
$576$		0			0
$577$			2258.22i			0.162931i	0.996676	+	0.0814653i	$0.0259600\pi$
$577$			2258.22i			0.162931i	−0.996676	+	0.0814653i	$0.974040\pi$
$578$	−23764.9	−	4280.90i	−1.71019	−	0.308066i
$579$		0			0
$580$	−918.486	+	2466.70i	−0.0657553	+	0.176593i
$581$	1259.66	+	7858.68i	0.0899477	+	0.561158i
$582$		0			0
$583$		−	3712.25i		−	0.263715i
$584$	−79.0169	+	133.427i	−0.00559887	+	0.00945417i
$585$		0			0
$586$	−4439.69	+	24646.3i	−0.312972	+	1.73742i
$587$	−1086.09			−0.0763677			−0.0381839	−	0.999271i	$-0.512157\pi$
$587$	−1086.09			−0.0763677			−0.0381839	+	0.999271i	$0.512157\pi$
$588$		0			0
$589$	−27570.6			−1.92873
$590$	926.636	−	5144.10i	0.0646593	−	0.358948i
$591$		0			0
$592$	645.391	+	557.992i	0.0448064	+	0.0387387i
$593$		−	7013.68i		−	0.485695i	−0.970064	−	0.242848i	$-0.921919\pi$
$593$		−	7013.68i		−	0.485695i	0.970064	−	0.242848i	$-0.0780815\pi$
$594$		0			0
$595$	−1555.30	−	9703.08i	−0.107162	−	0.668551i
$596$	−17562.7	−	6539.56i	−1.20704	−	0.449447i
$597$		0			0
$598$	12841.1	+	2313.15i	0.878116	+	0.158180i
$599$			25452.7i			1.73618i	0.496409	+	0.868089i	$0.334652\pi$
$599$			25452.7i			1.73618i	−0.496409	+	0.868089i	$0.665348\pi$
$600$		0			0
$601$		−	26422.8i		−	1.79336i	−0.442682	−	0.896679i	$-0.645973\pi$
$601$		−	26422.8i		−	1.79336i	0.442682	−	0.896679i	$-0.354027\pi$
$602$	15117.0	+	291.600i	1.02346	+	0.0197421i
$603$		0			0
$604$	1566.14	−	4206.06i	0.105506	−	0.283348i
$605$			2991.82i			0.201049i
$606$		0			0
$607$	6179.28			0.413195			0.206597	−	0.978426i	$-0.433761\pi$
$607$	6179.28			0.413195			0.206597	+	0.978426i	$0.433761\pi$
$608$	−13545.3	−	16761.5i	−0.903511	−	1.11804i
$609$		0			0
$610$	277.334	+	49.9579i	0.0184081	+	0.00331596i
$611$		−	25797.3i		−	1.70809i
$612$		0			0
$613$	−6512.10			−0.429072			−0.214536	−	0.976716i	$-0.568824\pi$
$613$	−6512.10			−0.429072			−0.214536	+	0.976716i	$0.568824\pi$
$614$	12170.9	+	2192.41i	0.799960	+	0.144102i
$615$		0			0
$616$	−10143.6	−	4001.42i	−0.663470	−	0.261724i
$617$	−15211.8			−0.992551			−0.496275	−	0.868165i	$-0.665299\pi$
$617$	−15211.8			−0.992551			−0.496275	+	0.868165i	$0.665299\pi$
$618$		0			0
$619$	11712.0			0.760496			0.380248	−	0.924885i	$-0.375839\pi$
$619$	11712.0			0.760496			0.380248	+	0.924885i	$0.375839\pi$
$620$	−2957.81	+	7943.53i	−0.191594	+	0.514548i
$621$		0			0
$622$	5445.35	+	980.902i	0.351027	+	0.0632325i
$623$	19821.4	−	3177.15i	1.27468	−	0.204318i
$624$		0			0
$625$	8213.69			0.525676
$626$	3166.07	−	17576.0i	0.202143	−	1.12217i
$627$		0			0
$628$	1281.95	−	3442.83i	0.0814578	−	0.218764i
$629$			1546.03i			0.0980037i
$630$		0			0
$631$			16130.7i			1.01768i	0.860862	+	0.508839i	$0.169925\pi$
$631$			16130.7i			1.01768i	−0.860862	+	0.508839i	$0.830075\pi$
$632$	11209.9	−	18928.8i	0.705544	−	1.19137i
$633$		0			0
$634$	−13814.5	−	2488.49i	−0.865370	−	0.155884i
$635$	−1253.01			−0.0783059
$636$		0			0
$637$	8050.01	+	24465.7i	0.500711	+	1.52177i
$638$	−938.306	+	5208.88i	−0.0582255	+	0.323231i
$639$		0			0
$640$	−6282.41	+	2104.43i	−0.388022	+	0.129977i
$641$	−20295.1			−1.25056			−0.625280	−	0.780401i	$-0.715015\pi$
$641$	−20295.1			−1.25056			−0.625280	+	0.780401i	$0.715015\pi$
$642$		0			0
$643$	10255.3			0.628976			0.314488	−	0.949262i	$-0.398167\pi$
$643$	10255.3			0.628976			0.314488	+	0.949262i	$0.398167\pi$
$644$	−8925.21	−	1786.12i	−0.546122	−	0.109290i
$645$		0			0
$646$	6923.24	−	38433.5i	0.421658	−	2.34078i
$647$	−15162.9			−0.921352			−0.460676	−	0.887568i	$-0.652393\pi$
$647$	−15162.9			−0.921352			−0.460676	+	0.887568i	$0.652393\pi$
$648$		0			0
$649$		−	10510.2i		−	0.635688i
$650$	3918.44	−	21752.7i	0.236452	−	1.31263i
$651$		0			0
$652$	1558.23	−	4184.80i	0.0935965	−	0.251364i
$653$	7126.05			0.427050			0.213525	−	0.976938i	$-0.431505\pi$
$653$	7126.05			0.427050			0.213525	+	0.976938i	$0.431505\pi$
$654$		0			0
$655$			10009.7i			0.597116i
$656$	6033.09	−	6978.05i	0.359074	−	0.415316i
$657$		0			0
$658$	−347.074	+	17992.9i	−0.0205628	+	1.06601i
$659$			2646.23i			0.156422i	0.996937	+	0.0782112i	$0.0249208\pi$
$659$			2646.23i			0.156422i	−0.996937	+	0.0782112i	$0.975079\pi$
$660$		0			0
$661$		−	13839.8i		−	0.814381i	−0.913343	−	0.407191i	$-0.866508\pi$
$661$		−	13839.8i		−	0.814381i	0.913343	−	0.407191i	$-0.133492\pi$
$662$	3480.91	−	19323.8i	0.204365	−	1.13450i
$663$		0			0
$664$	8366.89	+	4954.98i	0.489004	+	0.289594i
$665$	9960.33	−	1596.54i	0.580820	−	0.0930992i
$666$		0			0
$667$			4417.99i			0.256470i
$668$	−18700.2	−	6963.11i	−1.08313	−	0.403310i
$669$		0			0
$670$	7624.39	+	1373.43i	0.439636	+	0.0791941i
$671$	566.638			0.0326003
$672$		0			0
$673$	−32235.3			−1.84633			−0.923165	−	0.384404i	$-0.874407\pi$
$673$	−32235.3			−1.84633			−0.923165	+	0.384404i	$0.874407\pi$
$674$	−5038.11	−	907.544i	−0.287924	−	0.0518654i
$675$		0			0
$676$	−25802.0	−	9607.47i	−1.46802	−	0.546624i
$677$			9.30221i			0.000528084i	1.00000		0.000264042i	$8.40472e-5\pi$
$677$			9.30221i			0.000528084i	−1.00000		0.000264042i	$0.999916\pi$
$678$		0			0
$679$	−18853.9	+	3022.07i	−1.06560	+	0.170805i
$680$	−10330.6	−	6117.89i	−0.582587	−	0.345015i
$681$		0			0
$682$	−3021.63	+	16774.2i	−0.169654	+	0.941813i
$683$		−	26622.3i		−	1.49147i	−0.666244	−	0.745734i	$-0.732099\pi$
$683$		−	26622.3i		−	1.49147i	0.666244	−	0.745734i	$-0.267901\pi$
$684$		0			0
$685$			11599.7i			0.647012i
$686$	−5285.49	−	17172.4i	−0.294171	−	0.955753i
$687$		0			0
$688$	12081.8	−	13974.2i	0.669496	−	0.774360i
$689$			10712.9i			0.592348i
$690$		0			0
$691$	−20064.5			−1.10462			−0.552309	−	0.833639i	$-0.686253\pi$
$691$	−20064.5			−1.10462			−0.552309	+	0.833639i	$0.686253\pi$
$692$	−8044.29	+	21603.9i	−0.441905	+	1.18679i
$693$		0			0
$694$	1776.50	−	9861.98i	0.0971684	−	0.539418i
$695$			4608.63i			0.251533i
$696$		0			0
$697$	16715.9			0.908408
$698$	−660.906	+	3668.93i	−0.0358390	+	0.198956i
$699$		0			0
$700$	−3025.66	+	15119.2i	−0.163370	+	0.816359i
$701$	−32384.8			−1.74487			−0.872436	−	0.488728i	$-0.837461\pi$
$701$	−32384.8			−1.74487			−0.872436	+	0.488728i	$0.837461\pi$
$702$		0			0
$703$	−1587.02			−0.0851431
$704$	−11682.3	+	6404.10i	−0.625419	+	0.342846i
$705$		0			0
$706$	628.898	−	3491.24i	0.0335253	−	0.186111i
$707$	−3803.45	+	609.652i	−0.202325	+	0.0324305i
$708$		0			0
$709$	34258.5			1.81468			0.907338	−	0.420403i	$-0.138111\pi$
$709$	34258.5			1.81468			0.907338	+	0.420403i	$0.138111\pi$
$710$	7507.86	+	1352.43i	0.396852	+	0.0714873i
$711$		0			0
$712$	12497.6	−	21103.2i	0.657818	−	1.11078i
$713$			14227.3i			0.747288i
$714$		0			0
$715$			8939.34i			0.467570i
$716$	5785.94	−	15538.8i	0.301998	−	0.811051i
$717$		0			0
$718$	1178.71	−	6543.46i	0.0612662	−	0.340111i
$719$	−10303.7			−0.534443			−0.267221	−	0.963635i	$-0.586105\pi$
$719$	−10303.7			−0.534443			−0.267221	+	0.963635i	$0.586105\pi$
$720$		0			0
$721$	−3604.80	−	22489.3i	−0.186199	−	1.16165i
$722$	20359.5	+	3667.48i	1.04945	+	0.189044i
$723$		0			0
$724$	7716.28	−	20722.9i	0.396095	−	1.06376i
$725$	7484.01			0.383378
$726$		0			0
$727$	−1468.60			−0.0749209			−0.0374605	−	0.999298i	$-0.511927\pi$
$727$	−1468.60			−0.0749209			−0.0374605	+	0.999298i	$0.511927\pi$
$728$	29272.6	+	11547.4i	1.49027	+	0.587876i
$729$		0			0
$730$	−87.2779	−	15.7219i	−0.00442507	−	0.000797113i
$731$	33475.1			1.69373
$732$		0			0
$733$		−	5917.44i		−	0.298179i	−0.988824	−	0.149090i	$-0.952366\pi$
$733$		−	5917.44i		−	0.298179i	0.988824	−	0.149090i	$-0.0476343\pi$
$734$	8187.14	+	1474.80i	0.411707	+	0.0741631i
$735$		0			0
$736$	−8649.46	+	6989.82i	−0.433184	+	0.350065i
$737$	15577.8			0.778584
$738$		0			0
$739$			8120.94i			0.404240i	0.979361	+	0.202120i	$0.0647831\pi$
$739$			8120.94i			0.404240i	−0.979361	+	0.202120i	$0.935217\pi$
$740$	−170.258	+	457.247i	−0.00845783	+	0.0227145i
$741$		0			0
$742$	144.130	−	7471.92i	0.00713096	−	0.369680i
$743$			7975.20i			0.393784i	0.980425	+	0.196892i	$0.0630849\pi$
$743$			7975.20i			0.393784i	−0.980425	+	0.196892i	$0.936915\pi$
$744$		0			0
$745$		−	10717.7i		−	0.527068i
$746$	−20507.7	−	3694.17i	−1.00649	−	0.181304i
$747$		0			0
$748$	−22624.5	−	8424.33i	−1.10593	−	0.411797i
$749$	27479.3	−	4404.65i	1.34055	−	0.214876i
$750$		0			0
$751$			7417.00i			0.360387i	0.983631	+	0.180193i	$0.0576723\pi$
$751$			7417.00i			0.360387i	−0.983631	+	0.180193i	$0.942328\pi$
$752$	16632.6	+	14380.2i	0.806554	+	0.697331i
$753$		0			0
$754$	2707.77	−	15031.8i	0.130784	−	0.726031i
$755$	2566.75			0.123727
$756$		0			0
$757$	2056.45			0.0987358			0.0493679	−	0.998781i	$-0.484279\pi$
$757$	2056.45			0.0987358			0.0493679	+	0.998781i	$0.484279\pi$
$758$	4022.76	−	22331.8i	0.192762	−	1.07009i
$759$		0			0
$760$	6280.09	−	10604.5i	0.299741	−	0.506137i
$761$			28244.9i			1.34544i	0.739898	+	0.672719i	$0.234874\pi$
$761$			28244.9i			1.34544i	−0.739898	+	0.672719i	$0.765126\pi$
$762$		0			0
$763$	1698.04	+	10593.6i	0.0805676	+	0.502639i
$764$	−11498.4	+	30880.3i	−0.544499	+	1.46232i
$765$		0			0
$766$	−37494.1	−	6754.02i	−1.76856	−	0.318581i
$767$			30330.5i			1.42786i
$768$		0			0
$769$			27026.1i			1.26734i	0.773603	+	0.633671i	$0.218453\pi$
$769$			27026.1i			1.26734i	−0.773603	+	0.633671i	$0.781547\pi$
$770$	120.269	−	6234.94i	0.00562882	−	0.291807i
$771$		0			0
$772$	34020.6	+	12667.7i	1.58605	+	0.590572i
$773$		−	21487.5i		−	0.999810i	−0.866080	−	0.499905i	$-0.833368\pi$
$773$		−	21487.5i		−	0.999810i	0.866080	−	0.499905i	$-0.166632\pi$
$774$		0			0
$775$	24100.8			1.11707
$776$	−11887.6	+	20073.1i	−0.549921	+	0.928587i
$777$		0			0
$778$	1787.70	+	322.029i	0.0823808	+	0.0148397i
$779$			17159.1i			0.789202i
$780$		0			0
$781$	15339.7			0.702816
$782$	−19832.9	−	3572.62i	−0.906935	−	0.163372i
$783$		0			0
$784$	−20261.4	−	8447.78i	−0.922988	−	0.384830i
$785$	2100.99			0.0955257
$786$		0			0
$787$	−13905.7			−0.629843			−0.314921	−	0.949118i	$-0.601978\pi$
$787$	−13905.7			−0.629843			−0.314921	+	0.949118i	$0.601978\pi$
$788$	−6343.91	−	2362.18i	−0.286792	−	0.106788i
$789$		0			0
$790$	12381.8	+	2230.41i	0.557627	+	0.100449i
$791$	−1801.61	−	11239.8i	−0.0809836	−	0.505234i
$792$		0			0
$793$	−1635.21			−0.0732258
$794$	−3059.29	+	16983.2i	−0.136738	+	0.759083i
$795$		0			0
$796$	−9138.04	−	3402.59i	−0.406896	−	0.151509i
$797$		−	21571.7i		−	0.958730i	−0.877616	−	0.479365i	$-0.840867\pi$
$797$		−	21571.7i		−	0.958730i	0.877616	−	0.479365i	$-0.159133\pi$
$798$		0			0
$799$			39843.4i			1.76415i
$800$	11840.6	+	14652.0i	0.523287	+	0.647535i
$801$		0			0
$802$	−17539.6	−	3159.51i	−0.772249	−	0.139110i
$803$	−178.323			−0.00783669
$804$		0			0
$805$	−823.864	−	5139.85i	−0.0360713	−	0.225039i
$806$	8719.86	−	48407.2i	0.381072	−	2.11547i
$807$		0			0
$808$	−2398.11	+	4049.42i	−0.104413	+	0.176309i
$809$	−33518.7			−1.45668			−0.728339	−	0.685217i	$-0.759708\pi$
$809$	−33518.7			−1.45668			−0.728339	+	0.685217i	$0.759708\pi$
$810$		0			0
$811$	35133.3			1.52120			0.760602	−	0.649218i	$-0.224904\pi$
$811$	35133.3			1.52120			0.760602	+	0.649218i	$0.224904\pi$
$812$	−2090.83	+	10447.9i	−0.0903619	+	0.451537i
$813$		0			0
$814$	−173.932	+	965.558i	−0.00748931	+	0.0415759i
$815$	2553.78			0.109761
$816$		0			0
$817$			34362.5i			1.47147i
$818$	450.214	−	2499.30i	0.0192437	−	0.106829i
$819$		0			0
$820$	4943.81	+	1840.85i	0.210543	+	0.0783967i
$821$	21025.2			0.893768			0.446884	−	0.894592i	$-0.352534\pi$
$821$	21025.2			0.893768			0.446884	+	0.894592i	$0.352534\pi$
$822$		0			0
$823$		−	20491.2i		−	0.867894i	−0.900938	−	0.433947i	$-0.857120\pi$
$823$		−	20491.2i		−	0.867894i	0.900938	−	0.433947i	$-0.142880\pi$
$824$	−23943.7	−	14179.7i	−1.01228	−	0.599484i
$825$		0			0
$826$	408.063	−	21154.6i	0.0171893	−	0.891119i
$827$		−	18080.6i		−	0.760245i	−0.924936	−	0.380122i	$-0.875882\pi$
$827$		−	18080.6i		−	0.760245i	0.924936	−	0.380122i	$-0.124118\pi$
$828$		0			0
$829$			38666.1i			1.61994i	0.586471	+	0.809970i	$0.300517\pi$
$829$			38666.1i			1.61994i	−0.586471	+	0.809970i	$0.699483\pi$
$830$	−985.885	+	5473.01i	−0.0412296	+	0.228881i
$831$		0			0
$832$	33713.1	−	18481.0i	1.40480	−	0.770089i
$833$	−12433.1	−	37786.8i	−0.517144	−	1.57171i
$834$		0			0
$835$		−	11411.8i		−	0.472962i
$836$	8647.68	−	23224.3i	0.357759	−	0.960802i
$837$		0			0
$838$	24090.6	+	4339.59i	0.993076	+	0.178889i
$839$	−36214.5			−1.49018			−0.745091	−	0.666962i	$-0.767594\pi$
$839$	−36214.5			−1.49018			−0.745091	+	0.666962i	$0.767594\pi$
$840$		0			0
$841$	−19217.3			−0.787949
$842$	−37093.2	−	6681.82i	−1.51819	−	0.273481i
$843$		0			0
$844$	−14138.9	+	37971.6i	−0.576635	+	1.54862i
$845$		−	15745.7i		−	0.641027i
$846$		0			0
$847$	1916.79	+	11958.3i	0.0777588	+	0.485115i
$848$	−6907.05	−	5971.70i	−0.279704	−	0.241827i
$849$		0			0
$850$	−6051.96	+	33596.6i	−0.244212	+	1.35571i
$851$			818.954i			0.0329887i
$852$		0			0
$853$		−	1180.57i		−	0.0473881i	−0.999719	−	0.0236941i	$-0.992457\pi$
$853$		−	1180.57i		−	0.0473881i	0.999719	−	0.0236941i	$-0.00754276\pi$
$854$	1140.51	+	22.0000i	0.0456997	+	0.000881526i
$855$		0			0
$856$	17326.0	−	29256.4i	0.691811	−	1.16818i
$857$		−	29570.1i		−	1.17864i	−0.807900	−	0.589320i	$-0.799396\pi$
$857$		−	29570.1i		−	1.17864i	0.807900	−	0.589320i	$-0.200604\pi$
$858$		0			0
$859$	−18516.7			−0.735483			−0.367742	−	0.929928i	$-0.619869\pi$
$859$	−18516.7			−0.735483			−0.367742	+	0.929928i	$0.619869\pi$
$860$	9900.41	+	3686.46i	0.392560	+	0.146171i
$861$		0			0
$862$	2262.78	−	12561.5i	0.0894092	−	0.496343i
$863$		−	35215.9i		−	1.38907i	−0.719461	−	0.694533i	$-0.755611\pi$
$863$		−	35215.9i		−	1.38907i	0.719461	−	0.694533i	$-0.244389\pi$
$864$		0			0
$865$	−13183.8			−0.518223
$866$	−2305.43	+	12798.3i	−0.0904640	+	0.502199i
$867$		0			0
$868$	−6733.12	+	33645.3i	−0.263292	+	1.31566i
$869$	25298.0			0.987544
$870$		0			0
$871$	−44954.7			−1.74883
$872$	11278.7	+	6679.36i	0.438009	+	0.259394i
$873$		0			0
$874$	3667.33	−	20358.7i	0.141933	−	0.787922i
$875$	−19164.9	+	3071.93i	−0.740449	+	0.118686i
$876$		0			0
$877$	−20910.2			−0.805115			−0.402558	−	0.915395i	$-0.631879\pi$
$877$	−20910.2			−0.805115			−0.402558	+	0.915395i	$0.631879\pi$
$878$	40598.3	+	7313.20i	1.56051	+	0.281103i
$879$		0			0
$880$	−5763.58	−	4983.08i	−0.220784	−	0.190886i
$881$			19841.3i			0.758762i	0.925241	+	0.379381i	$0.123863\pi$
$881$			19841.3i			0.758762i	−0.925241	+	0.379381i	$0.876137\pi$
$882$		0			0
$883$		−	37682.4i		−	1.43614i	−0.695971	−	0.718070i	$-0.745026\pi$
$883$		−	37682.4i		−	1.43614i	0.695971	−	0.718070i	$-0.254974\pi$
$884$	65290.1	+	24311.0i	2.48410	+	0.924965i
$885$		0			0
$886$	5304.30	−	29446.1i	0.201130	−	1.11655i
$887$	16665.2			0.630850			0.315425	−	0.948950i	$-0.397853\pi$
$887$	16665.2			0.630850			0.315425	+	0.948950i	$0.397853\pi$
$888$		0			0
$889$	−5008.29	+	802.776i	−0.188946	+	0.0302860i
$890$	13804.2	+	2486.62i	0.519906	+	0.0936537i
$891$		0			0
$892$	29194.3	+	10870.6i	1.09585	+	0.408044i
$893$	−40899.7			−1.53265
$894$		0			0
$895$	9482.58			0.354154
$896$	−23762.5	+	12436.4i	−0.885994	+	0.463696i
$897$		0			0
$898$	2320.38	+	417.984i	0.0862274	+	0.0155326i
$899$	16654.5			0.617862
$900$		0			0
$901$		−	16545.8i		−	0.611788i
$902$	10439.7	+	1880.57i	0.385372	+	0.0694193i
$903$		0			0
$904$	−11966.6	−	7086.78i	−0.440270	−	0.260733i
$905$	12646.2			0.464502
$906$		0			0
$907$			20577.7i			0.753331i	0.926349	+	0.376665i	$0.122929\pi$
$907$			20577.7i			0.753331i	−0.926349	+	0.376665i	$0.877071\pi$
$908$	−8741.27	−	3254.85i	−0.319481	−	0.118960i
$909$		0			0
$910$	−347.074	+	17992.9i	−0.0126433	+	0.655448i
$911$			35684.4i			1.29778i	0.760883	+	0.648889i	$0.224766\pi$
$911$			35684.4i			1.29778i	−0.760883	+	0.648889i	$0.775234\pi$
$912$		0			0
$913$			11182.2i			0.405342i
$914$	−17989.1	−	3240.48i	−0.651013	−	0.117271i
$915$		0			0
$916$	−7084.84	+	19027.2i	−0.255556	+	0.686326i
$917$	6412.97	+	40008.7i	0.230943	+	1.44079i
$918$		0			0
$919$		−	2549.71i		−	0.0915205i	−0.998952	−	0.0457602i	$-0.985429\pi$
$919$		−	2549.71i		−	0.0915205i	0.998952	−	0.0457602i	$-0.0145710\pi$
$920$	−5472.24	−	3240.73i	−0.196103	−	0.116134i
$921$		0			0
$922$	5085.64	−	28232.2i	0.181656	−	1.00844i
$923$	−44267.6			−1.57864
$924$		0			0
$925$	1387.30			0.0493124
$926$	716.258	−	3976.21i	0.0254187	−	0.141108i
$927$		0			0
$928$	8182.28	+	10125.1i	0.289436	+	0.358159i
$929$		−	24991.8i		−	0.882620i	−0.897355	−	0.441310i	$-0.854514\pi$
$929$		−	24991.8i		−	0.882620i	0.897355	−	0.441310i	$-0.145486\pi$
$930$		0			0
$931$	38788.6	−	12762.7i	1.36546	−	0.449281i
$932$	−10087.6	−	3756.18i	−0.354540	−	0.132015i
$933$		0			0
$934$	−5678.21	−	1022.85i	−0.198926	−	0.0358337i
$935$		−	13806.6i		−	0.482915i
$936$		0			0
$937$		−	36329.3i		−	1.26662i	−0.773896	−	0.633312i	$-0.781695\pi$
$937$		−	36329.3i		−	1.26662i	0.773896	−	0.633312i	$-0.218305\pi$
$938$	31354.6	+	604.816i	1.09143	+	0.0210532i
$939$		0			0
$940$	−4387.78	+	11783.9i	−0.152248	+	0.408881i
$941$			21505.5i			0.745015i	0.928029	+	0.372507i	$0.121502\pi$
$941$			21505.5i			0.745015i	−0.928029	+	0.372507i	$0.878498\pi$
$942$		0			0
$943$	8854.64			0.305776
$944$	−19555.4	−	16907.2i	−0.674230	−	0.582926i
$945$		0			0
$946$	20906.5	+	3766.01i	0.718530	+	0.129433i
$947$		−	17365.5i		−	0.595886i	−0.954584	−	0.297943i	$-0.903699\pi$
$947$		−	17365.5i		−	0.595886i	0.954584	−	0.297943i	$-0.0963005\pi$
$948$		0			0
$949$	514.605			0.0176025
$950$	−34487.4	−	6212.41i	−1.17781	−	0.212165i
$951$		0			0
$952$	−45210.9	−	17834.7i	−1.53917	−	0.607169i
$953$	−22686.6			−0.771133			−0.385566	−	0.922680i	$-0.625994\pi$
$953$	−22686.6			−0.771133			−0.385566	+	0.922680i	$0.625994\pi$
$954$		0			0
$955$	−18844.7			−0.638535
$956$	−17419.0	+	46780.7i	−0.589299	+	1.58263i
$957$		0			0
$958$	−36309.7	−	6540.68i	−1.22454	−	0.220584i
$959$	7431.69	+	46364.2i	0.250242	+	1.56119i
$960$		0			0
$961$	23841.5			0.800293
$962$	501.934	−	2786.42i	0.0168222	−	0.0933865i
$963$		0			0
$964$	−12690.6	+	34082.1i	−0.424001	+	1.13870i
$965$			20761.1i			0.692565i
$966$		0			0
$967$		−	30178.5i		−	1.00359i	−0.864985	−	0.501797i	$-0.832672\pi$
$967$		−	30178.5i		−	1.00359i	0.864985	−	0.501797i	$-0.167328\pi$
$968$	12731.6	+	7539.84i	0.422738	+	0.250351i
$969$		0			0
$970$	−13130.4	−	2365.25i	−0.434630	−	0.0782924i
$971$	54731.9			1.80889			0.904445	−	0.426591i	$-0.140286\pi$
$971$	54731.9			1.80889			0.904445	+	0.426591i	$0.140286\pi$
$972$		0			0
$973$	2952.64	+	18420.7i	0.0972841	+	0.606928i
$974$	−3231.29	+	17938.1i	−0.106301	+	0.590116i
$975$		0			0
$976$	911.519	−	1054.29i	0.0298945	−	0.0345769i
$977$	29860.7			0.977817			0.488908	−	0.872335i	$-0.337395\pi$
$977$	29860.7			0.977817			0.488908	+	0.872335i	$0.337395\pi$
$978$		0			0
$979$	28204.1			0.920741
$980$	484.148	−	12544.8i	0.0157812	−	0.408908i
$981$		0			0
$982$	−4027.67	+	22359.1i	−0.130884	+	0.726585i
$983$	10417.7			0.338018			0.169009	−	0.985615i	$-0.445943\pi$
$983$	10417.7			0.338018			0.169009	+	0.985615i	$0.445943\pi$
$984$		0			0
$985$		−	3871.38i		−	0.125231i
$986$	−4182.11	+	23216.4i	−0.135076	+	0.749859i
$987$		0			0
$988$	−24955.6	+	67021.1i	−0.803586	+	2.15812i
$989$	17732.2			0.570122
$990$		0			0
$991$			3803.09i			0.121906i	0.998141	+	0.0609531i	$0.0194140\pi$
$991$			3803.09i			0.121906i	−0.998141	+	0.0609531i	$0.980586\pi$
$992$	26349.4	+	32605.8i	0.843343	+	1.04358i
$993$		0			0
$994$	30875.4	+	595.572i	0.985220	+	0.0190044i
$995$		−	5576.50i		−	0.177675i
$996$		0			0
$997$		−	53386.9i		−	1.69587i	−0.530103	−	0.847933i	$-0.677847\pi$
$997$		−	53386.9i		−	1.69587i	0.530103	−	0.847933i	$-0.322153\pi$
$998$	−593.755	+	3296.15i	−0.0188327	+	0.104547i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.f.55.12		12
3.2	odd	2		84.4.b.a.55.1	✓	12
4.3	odd	2		252.4.b.e.55.11		12
7.6	odd	2		252.4.b.e.55.12		12
12.11	even	2		84.4.b.b.55.2	yes	12
21.20	even	2		84.4.b.b.55.1	yes	12
24.5	odd	2		1344.4.b.h.895.8		12
24.11	even	2		1344.4.b.g.895.8		12
28.27	even	2	inner	252.4.b.f.55.11		12
84.83	odd	2		84.4.b.a.55.2	yes	12
168.83	odd	2		1344.4.b.h.895.5		12
168.125	even	2		1344.4.b.g.895.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.b.a.55.1	✓	12	3.2	odd	2
84.4.b.a.55.2	yes	12	84.83	odd	2
84.4.b.b.55.1	yes	12	21.20	even	2
84.4.b.b.55.2	yes	12	12.11	even	2
252.4.b.e.55.11		12	4.3	odd	2
252.4.b.e.55.12		12	7.6	odd	2
252.4.b.f.55.11		12	28.27	even	2	inner
252.4.b.f.55.12		12	1.1	even	1	trivial
1344.4.b.g.895.5		12	168.125	even	2
1344.4.b.g.895.8		12	24.11	even	2
1344.4.b.h.895.5		12	168.83	odd	2
1344.4.b.h.895.8		12	24.5	odd	2

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)

\(f(q)\)	\(=\)	\(q+(2.78362 + 0.501431i) q^{2} +(7.49713 + 2.79159i) q^{4} +4.57514i q^{5} +(2.93118 + 18.2868i) q^{7} +(19.4694 + 11.5300i) q^{8} +O(q^{10})\)	\(q+(2.78362 + 0.501431i) q^{2} +(7.49713 + 2.79159i) q^{4} +4.57514i q^{5} +(2.93118 + 18.2868i) q^{7} +(19.4694 + 11.5300i) q^{8} +(-2.29411 + 12.7355i) q^{10} +26.0206i q^{11} -75.0905i q^{13} +(-1.01026 + 52.3735i) q^{14} +(48.4141 + 41.8578i) q^{16} +115.976i q^{17} -119.051 q^{19} +(-12.7719 + 34.3004i) q^{20} +(-13.0475 + 72.4315i) q^{22} +61.4339i q^{23} +104.068 q^{25} +(37.6527 - 209.024i) q^{26} +(-29.0738 + 145.281i) q^{28} +71.9146 q^{29} +231.587 q^{31} +(113.778 + 140.793i) q^{32} +(-58.1538 + 322.833i) q^{34} +(-83.6647 + 13.4106i) q^{35} +13.3306 q^{37} +(-331.392 - 59.6956i) q^{38} +(-52.7515 + 89.0753i) q^{40} -144.133i q^{41} -288.638i q^{43} +(-72.6387 + 195.080i) q^{44} +(-30.8049 + 171.009i) q^{46} +343.549 q^{47} +(-325.816 + 107.204i) q^{49} +(289.687 + 52.1829i) q^{50} +(209.622 - 562.963i) q^{52} -142.666 q^{53} -119.048 q^{55} +(-153.779 + 389.831i) q^{56} +(200.183 + 36.0602i) q^{58} -403.919 q^{59} -21.7765i q^{61} +(644.651 + 116.125i) q^{62} +(246.117 + 448.966i) q^{64} +343.549 q^{65} -598.674i q^{67} +(-323.757 + 869.486i) q^{68} +(-239.616 - 4.62208i) q^{70} -589.524i q^{71} +6.85314i q^{73} +(37.1075 + 6.68439i) q^{74} +(-892.538 - 332.340i) q^{76} +(-475.834 + 76.2711i) q^{77} -972.231i q^{79} +(-191.505 + 221.501i) q^{80} +(72.2726 - 401.212i) q^{82} +429.745 q^{83} -530.605 q^{85} +(144.732 - 803.461i) q^{86} +(-300.018 + 506.605i) q^{88} -1083.91i q^{89} +(1373.17 - 220.104i) q^{91} +(-171.498 + 460.578i) q^{92} +(956.312 + 172.266i) q^{94} -544.673i q^{95} +1031.01i q^{97} +(-960.706 + 135.042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8}+O(q^{10}) \) 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8	\( 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8} + 56 q^{10} - 69 q^{14} + 41 q^{16} - 84 q^{19} - 172 q^{20} - 182 q^{22} - 216 q^{25} - 300 q^{26} + 309 q^{28} - 200 q^{29} - 384 q^{31} + 159 q^{32} - 164 q^{34} - 84 q^{35} - 244 q^{37} - 268 q^{38} - 316 q^{40} - 190 q^{44} + 894 q^{46} - 280 q^{47} - 424 q^{49} + 1771 q^{50} - 796 q^{52} + 16 q^{53} + 212 q^{55} + 7 q^{56} - 570 q^{58} - 1168 q^{59} + 384 q^{62} + 2705 q^{64} - 280 q^{65} - 1552 q^{68} + 968 q^{70} - 1622 q^{74} - 788 q^{76} - 968 q^{77} + 3060 q^{80} - 2540 q^{82} + 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} + 1648 q^{91} - 4298 q^{92} + 4256 q^{94} - 97 q^{98}+O(q^{100}) \) 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8 + 56 * q^10 - 69 * q^14 + 41 * q^16 - 84 * q^19 - 172 * q^20 - 182 * q^22 - 216 * q^25 - 300 * q^26 + 309 * q^28 - 200 * q^29 - 384 * q^31 + 159 * q^32 - 164 * q^34 - 84 * q^35 - 244 * q^37 - 268 * q^38 - 316 * q^40 - 190 * q^44 + 894 * q^46 - 280 * q^47 - 424 * q^49 + 1771 * q^50 - 796 * q^52 + 16 * q^53 + 212 * q^55 + 7 * q^56 - 570 * q^58 - 1168 * q^59 + 384 * q^62 + 2705 * q^64 - 280 * q^65 - 1552 * q^68 + 968 * q^70 - 1622 * q^74 - 788 * q^76 - 968 * q^77 + 3060 * q^80 - 2540 * q^82 + 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 + 1648 * q^91 - 4298 * q^92 + 4256 * q^94 - 97 * q^98

Introduction

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