LMFDB - Embedded newform 1368.2.e.g.379.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.9
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.g.379.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939794 - 1.05678i) q^{2} +(-0.233575 + 1.98631i) q^{4} +1.70737i q^{5} +4.15645i q^{7} +(2.31861 - 1.61989i) q^{8} +O(q^{10})$	\(q+(-0.939794 - 1.05678i) q^{2} +(-0.233575 + 1.98631i) q^{4} +1.70737i q^{5} +4.15645i q^{7} +(2.31861 - 1.61989i) q^{8} +(1.80431 - 1.60457i) q^{10} +2.55988 q^{11} +6.69724 q^{13} +(4.39246 - 3.90620i) q^{14} +(-3.89089 - 0.927907i) q^{16} +3.18831 q^{17} +(-4.14166 + 1.35892i) q^{19} +(-3.39136 - 0.398798i) q^{20} +(-2.40576 - 2.70524i) q^{22} -2.96695i q^{23} +2.08490 q^{25} +(-6.29403 - 7.07753i) q^{26} +(-8.25600 - 0.970842i) q^{28} -5.33562 q^{29} -2.28480 q^{31} +(2.67603 + 4.98386i) q^{32} +(-2.99636 - 3.36935i) q^{34} -7.09657 q^{35} +4.67640 q^{37} +(5.32839 + 3.09973i) q^{38} +(2.76574 + 3.95872i) q^{40} +2.45906i q^{41} +10.7093 q^{43} +(-0.597925 + 5.08473i) q^{44} +(-3.13542 + 2.78832i) q^{46} +6.90120i q^{47} -10.2760 q^{49} +(-1.95938 - 2.20329i) q^{50} +(-1.56431 + 13.3028i) q^{52} -0.126777 q^{53} +4.37066i q^{55} +(6.73297 + 9.63719i) q^{56} +(5.01438 + 5.63858i) q^{58} -0.727966i q^{59} +5.65631i q^{61} +(2.14724 + 2.41454i) q^{62} +(2.75193 - 7.51178i) q^{64} +11.4346i q^{65} -3.07580i q^{67} +(-0.744710 + 6.33299i) q^{68} +(6.66931 + 7.49953i) q^{70} -6.20693 q^{71} -4.97655 q^{73} +(-4.39485 - 4.94193i) q^{74} +(-1.73185 - 8.54404i) q^{76} +10.6400i q^{77} +7.98062 q^{79} +(1.58428 - 6.64316i) q^{80} +(2.59869 - 2.31101i) q^{82} -17.8223 q^{83} +5.44361i q^{85} +(-10.0645 - 11.3174i) q^{86} +(5.93538 - 4.14672i) q^{88} -10.6502i q^{89} +27.8367i q^{91} +(5.89330 + 0.693007i) q^{92} +(7.29307 - 6.48571i) q^{94} +(-2.32017 - 7.07132i) q^{95} -8.04606i q^{97} +(9.65736 + 10.8595i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4}+O(q^{10}) $ 40 * q - 4 * q^4	$ 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−0.939794	−	1.05678i	−0.664535	−	0.747258i
$2$	−0.939794	−	1.05678i	−0.664535	−	0.747258i
$3$		0			0
$3$		0			0
$4$	−0.233575	+	1.98631i	−0.116788	+	0.993157i
$5$			1.70737i			0.763557i	0.924254	+	0.381778i	$0.124688\pi$
$5$			1.70737i			0.763557i	−0.924254	+	0.381778i	$0.875312\pi$
$6$		0			0
$7$			4.15645i			1.57099i	0.618869	+	0.785494i	$0.287591\pi$
$7$			4.15645i			1.57099i	−0.618869	+	0.785494i	$0.712409\pi$
$8$	2.31861	−	1.61989i	0.819753	−	0.572717i
$9$		0			0
$10$	1.80431	−	1.60457i	0.570574	−	0.507410i
$11$	2.55988			0.771834			0.385917	−	0.922534i	$-0.373885\pi$
$11$	2.55988			0.771834			0.385917	+	0.922534i	$0.373885\pi$
$12$		0			0
$13$	6.69724			1.85748			0.928741	−	0.370730i	$-0.120892\pi$
$13$	6.69724			1.85748			0.928741	+	0.370730i	$0.120892\pi$
$14$	4.39246	−	3.90620i	1.17393	−	1.04398i
$15$		0			0
$16$	−3.89089	−	0.927907i	−0.972721	−	0.231977i
$17$	3.18831			0.773279			0.386640	−	0.922231i	$-0.373636\pi$
$17$	3.18831			0.773279			0.386640	+	0.922231i	$0.373636\pi$
$18$		0			0
$19$	−4.14166	+	1.35892i	−0.950162	+	0.311757i
$19$	−4.14166	+	1.35892i	−0.950162	+	0.311757i
$20$	−3.39136	−	0.398798i	−0.758332	−	0.0891740i
$21$		0			0
$22$	−2.40576	−	2.70524i	−0.512910	−	0.576759i
$23$		−	2.96695i		−	0.618653i	−0.950956	−	0.309326i	$-0.899896\pi$
$23$		−	2.96695i		−	0.618653i	0.950956	−	0.309326i	$-0.100104\pi$
$24$		0			0
$25$	2.08490			0.416981
$26$	−6.29403	−	7.07753i	−1.23436	−	1.38802i
$27$		0			0
$28$	−8.25600	−	0.970842i	−1.56024	−	0.183472i
$29$	−5.33562			−0.990800			−0.495400	−	0.868665i	$-0.664978\pi$
$29$	−5.33562			−0.990800			−0.495400	+	0.868665i	$0.664978\pi$
$30$		0			0
$31$	−2.28480			−0.410363			−0.205181	−	0.978724i	$-0.565778\pi$
$31$	−2.28480			−0.410363			−0.205181	+	0.978724i	$0.565778\pi$
$32$	2.67603	+	4.98386i	0.473061	+	0.881030i
$33$		0			0
$34$	−2.99636	−	3.36935i	−0.513871	−	0.577839i
$35$	−7.09657			−1.19954
$36$		0			0
$37$	4.67640			0.768795			0.384397	−	0.923168i	$-0.374409\pi$
$37$	4.67640			0.768795			0.384397	+	0.923168i	$0.374409\pi$
$38$	5.32839	+	3.09973i	0.864378	+	0.502842i
$39$		0			0
$40$	2.76574	+	3.95872i	0.437302	+	0.625928i
$41$			2.45906i			0.384041i	0.981391	+	0.192021i	$0.0615041\pi$
$41$			2.45906i			0.384041i	−0.981391	+	0.192021i	$0.938496\pi$
$42$		0			0
$43$	10.7093			1.63315			0.816574	−	0.577241i	$-0.195871\pi$
$43$	10.7093			1.63315			0.816574	+	0.577241i	$0.195871\pi$
$44$	−0.597925	+	5.08473i	−0.0901406	+	0.766552i
$45$		0			0
$46$	−3.13542	+	2.78832i	−0.462293	+	0.411116i
$47$			6.90120i			1.00664i	0.864099	+	0.503322i	$0.167889\pi$
$47$			6.90120i			1.00664i	−0.864099	+	0.503322i	$0.832111\pi$
$48$		0			0
$49$	−10.2760			−1.46801
$50$	−1.95938	−	2.20329i	−0.277098	−	0.311592i
$51$		0			0
$52$	−1.56431	+	13.3028i	−0.216931	+	1.84477i
$53$	−0.126777			−0.0174142			−0.00870709	−	0.999962i	$-0.502772\pi$
$53$	−0.126777			−0.0174142			−0.00870709	+	0.999962i	$0.502772\pi$
$54$		0			0
$55$			4.37066i			0.589339i
$56$	6.73297	+	9.63719i	0.899731	+	1.28782i
$57$		0			0
$58$	5.01438	+	5.63858i	0.658421	+	0.740382i
$59$		−	0.727966i		−	0.0947732i	−0.998877	−	0.0473866i	$-0.984911\pi$
$59$		−	0.727966i		−	0.0947732i	0.998877	−	0.0473866i	$-0.0150893\pi$
$60$		0			0
$61$			5.65631i			0.724216i	0.932136	+	0.362108i	$0.117943\pi$
$61$			5.65631i			0.724216i	−0.932136	+	0.362108i	$0.882057\pi$
$62$	2.14724	+	2.41454i	0.272700	+	0.306647i
$63$		0			0
$64$	2.75193	−	7.51178i	0.343991	−	0.938973i
$65$			11.4346i			1.41829i
$66$		0			0
$67$		−	3.07580i		−	0.375769i	−0.982191	−	0.187884i	$-0.939837\pi$
$67$		−	3.07580i		−	0.375769i	0.982191	−	0.187884i	$-0.0601631\pi$
$68$	−0.744710	+	6.33299i	−0.0903094	+	0.767988i
$69$		0			0
$70$	6.66931	+	7.49953i	0.797135	+	0.896365i
$71$	−6.20693			−0.736627			−0.368313	−	0.929702i	$-0.620065\pi$
$71$	−6.20693			−0.736627			−0.368313	+	0.929702i	$0.620065\pi$
$72$		0			0
$73$	−4.97655			−0.582461			−0.291230	−	0.956653i	$-0.594065\pi$
$73$	−4.97655			−0.582461			−0.291230	+	0.956653i	$0.594065\pi$
$74$	−4.39485	−	4.94193i	−0.510891	−	0.574488i
$75$		0			0
$76$	−1.73185	−	8.54404i	−0.198657	−	0.980069i
$77$			10.6400i			1.21254i
$78$		0			0
$79$	7.98062			0.897890			0.448945	−	0.893559i	$-0.351800\pi$
$79$	7.98062			0.897890			0.448945	+	0.893559i	$0.351800\pi$
$80$	1.58428	−	6.64316i	0.177127	−	0.742728i
$81$		0			0
$82$	2.59869	−	2.31101i	0.286978	−	0.255209i
$83$	−17.8223			−1.95625			−0.978127	−	0.208010i	$-0.933301\pi$
$83$	−17.8223			−1.95625			−0.978127	+	0.208010i	$0.933301\pi$
$84$		0			0
$85$			5.44361i			0.590443i
$86$	−10.0645	−	11.3174i	−1.08528	−	1.22038i
$87$		0			0
$88$	5.93538	−	4.14672i	0.632713	−	0.442042i
$89$		−	10.6502i		−	1.12892i	−0.825461	−	0.564459i	$-0.809085\pi$
$89$		−	10.6502i		−	1.12892i	0.825461	−	0.564459i	$-0.190915\pi$
$90$		0			0
$91$			27.8367i			2.91808i
$92$	5.89330	+	0.693007i	0.614419	+	0.0722509i
$93$		0			0
$94$	7.29307	−	6.48571i	0.752222	−	0.668950i
$95$	−2.32017	−	7.07132i	−0.238045	−	0.725503i
$96$		0			0
$97$		−	8.04606i		−	0.816954i	−0.912769	−	0.408477i	$-0.866060\pi$
$97$		−	8.04606i		−	0.816954i	0.912769	−	0.408477i	$-0.133940\pi$
$98$	9.65736	+	10.8595i	0.975540	+	1.09698i
$99$		0			0
$100$	−0.486982	+	4.14127i	−0.0486982	+	0.414127i
$101$			9.95393i			0.990453i	0.868764	+	0.495226i	$0.164915\pi$
$101$			9.95393i			0.990453i	−0.868764	+	0.495226i	$0.835085\pi$
$102$		0			0
$103$	2.45993			0.242384			0.121192	−	0.992629i	$-0.461328\pi$
$103$	2.45993			0.242384			0.121192	+	0.992629i	$0.461328\pi$
$104$	15.5283	−	10.8488i	1.52268	−	1.06381i
$105$		0			0
$106$	0.119144	+	0.133976i	0.0115723	+	0.0130129i
$107$			13.5433i			1.30928i	0.755940	+	0.654641i	$0.227180\pi$
$107$			13.5433i			1.30928i	−0.755940	+	0.654641i	$0.772820\pi$
$108$		0			0
$109$	12.1893			1.16753			0.583763	−	0.811924i	$-0.301580\pi$
$109$	12.1893			1.16753			0.583763	+	0.811924i	$0.301580\pi$
$110$	4.61883	−	4.10752i	0.440388	−	0.391636i
$111$		0			0
$112$	3.85680	−	16.1723i	0.364433	−	1.52813i
$113$		−	20.2162i		−	1.90178i	−0.309523	−	0.950892i	$-0.600169\pi$
$113$		−	20.2162i		−	1.90178i	0.309523	−	0.950892i	$-0.399831\pi$
$114$		0			0
$115$	5.06567			0.472376
$116$	1.24627	−	10.5982i	0.115713	−	0.984019i
$117$		0			0
$118$	−0.769302	+	0.684138i	−0.0708200	+	0.0629800i
$119$			13.2520i			1.21481i
$120$		0			0
$121$	−4.44700			−0.404273
$122$	5.97748	−	5.31576i	0.541176	−	0.481267i
$123$		0			0
$124$	0.533673	−	4.53834i	0.0479253	−	0.407555i
$125$			12.0965i			1.08195i
$126$		0			0
$127$	−19.1981			−1.70355			−0.851777	−	0.523905i	$-0.824475\pi$
$127$	−19.1981			−1.70355			−0.851777	+	0.523905i	$0.824475\pi$
$128$	−10.5246	+	4.15134i	−0.930249	+	0.366930i
$129$		0			0
$130$	12.0839	−	10.7462i	1.05983	−	0.942505i
$131$	16.3577			1.42918			0.714592	−	0.699542i	$-0.246613\pi$
$131$	16.3577			1.42918			0.714592	+	0.699542i	$0.246613\pi$
$132$		0			0
$133$	−5.64827	−	17.2146i	−0.489767	−	1.49269i
$134$	−3.25045	+	2.89062i	−0.280796	+	0.249711i
$135$		0			0
$136$	7.39246	−	5.16471i	0.633898	−	0.442870i
$137$	7.47670			0.638778			0.319389	−	0.947624i	$-0.396522\pi$
$137$	7.47670			0.638778			0.319389	+	0.947624i	$0.396522\pi$
$138$		0			0
$139$	−10.8542			−0.920645			−0.460323	−	0.887752i	$-0.652266\pi$
$139$	−10.8542			−0.920645			−0.460323	+	0.887752i	$0.652266\pi$
$140$	1.65758	−	14.0960i	0.140091	−	1.19133i
$141$		0			0
$142$	5.83323	+	6.55937i	0.489514	+	0.550450i
$143$	17.1442			1.43367
$144$		0			0
$145$		−	9.10985i		−	0.756532i
$146$	4.67693	+	5.25912i	0.387065	+	0.435248i
$147$		0			0
$148$	−1.09229	+	9.28879i	−0.0897857	+	0.763534i
$149$			8.97462i			0.735230i	0.929978	+	0.367615i	$0.119826\pi$
$149$			8.97462i			0.735230i	−0.929978	+	0.367615i	$0.880174\pi$
$150$		0			0
$151$	−3.45834			−0.281436			−0.140718	−	0.990050i	$-0.544941\pi$
$151$	−3.45834			−0.281436			−0.140718	+	0.990050i	$0.544941\pi$
$152$	−7.40161	+	9.85983i	−0.600350	+	0.799738i
$153$		0			0
$154$	11.2442	−	9.99942i	0.906081	−	0.805776i
$155$		−	3.90099i		−	0.313335i
$156$		0			0
$157$			11.1948i			0.893441i	0.894673	+	0.446721i	$0.147408\pi$
$157$			11.1948i			0.893441i	−0.894673	+	0.446721i	$0.852592\pi$
$158$	−7.50014	−	8.43378i	−0.596679	−	0.670955i
$159$		0			0
$160$	−8.50927	+	4.56897i	−0.672717	+	0.361209i
$161$	12.3320			0.971896
$162$		0			0
$163$	−4.50485			−0.352847			−0.176424	−	0.984314i	$-0.556453\pi$
$163$	−4.50485			−0.352847			−0.176424	+	0.984314i	$0.556453\pi$
$164$	−4.88447	−	0.574376i	−0.381413	−	0.0448513i
$165$		0			0
$166$	16.7493	+	18.8343i	1.30000	+	1.46182i
$167$	−17.5886			−1.36104			−0.680522	−	0.732728i	$-0.738247\pi$
$167$	−17.5886			−1.36104			−0.680522	+	0.732728i	$0.738247\pi$
$168$		0			0
$169$	31.8531			2.45024
$170$	5.75271	−	5.11587i	0.441213	−	0.392370i
$171$		0			0
$172$	−2.50142	+	21.2720i	−0.190731	+	1.62197i
$173$	14.2210			1.08121			0.540603	−	0.841278i	$-0.318196\pi$
$173$	14.2210			1.08121			0.540603	+	0.841278i	$0.318196\pi$
$174$		0			0
$175$			8.66579i			0.655072i
$176$	−9.96021	−	2.37533i	−0.750779	−	0.179048i
$177$		0			0
$178$	−11.2549	+	10.0090i	−0.843593	+	0.750205i
$179$			22.7963i			1.70388i	0.523641	+	0.851939i	$0.324573\pi$
$179$			22.7963i			1.70388i	−0.523641	+	0.851939i	$0.675427\pi$
$180$		0			0
$181$	−11.7529			−0.873588			−0.436794	−	0.899562i	$-0.643886\pi$
$181$	−11.7529			−0.873588			−0.436794	+	0.899562i	$0.643886\pi$
$182$	29.4173	−	26.1608i	2.18056	−	1.93917i
$183$		0			0
$184$	−4.80613	−	6.87922i	−0.354313	−	0.507143i
$185$			7.98432i			0.587019i
$186$		0			0
$187$	8.16171			0.596843
$188$	−13.7080	−	1.61195i	−0.999755	−	0.117564i
$189$		0			0
$190$	−5.29236	+	9.09750i	−0.383948	+	0.660002i
$191$		−	9.93237i		−	0.718681i	−0.933206	−	0.359341i	$-0.883002\pi$
$191$		−	9.93237i		−	0.718681i	0.933206	−	0.359341i	$-0.116998\pi$
$192$		0			0
$193$		−	14.0805i		−	1.01354i	−0.862082	−	0.506769i	$-0.830840\pi$
$193$		−	14.0805i		−	1.01354i	0.862082	−	0.506769i	$-0.169160\pi$
$194$	−8.50293	+	7.56164i	−0.610475	+	0.542894i
$195$		0			0
$196$	2.40023	−	20.4114i	0.171445	−	1.45796i
$197$		−	9.70037i		−	0.691123i	−0.938396	−	0.345561i	$-0.887688\pi$
$197$		−	9.70037i		−	0.691123i	0.938396	−	0.345561i	$-0.112312\pi$
$198$		0			0
$199$			1.41713i			0.100457i	0.998738	+	0.0502287i	$0.0159950\pi$
$199$			1.41713i			0.100457i	−0.998738	+	0.0502287i	$0.984005\pi$
$200$	4.83408	−	3.37731i	0.341821	−	0.238812i
$201$		0			0
$202$	10.5191	−	9.35464i	0.740123	−	0.658190i
$203$		−	22.1772i		−	1.55653i
$204$		0			0
$205$	−4.19852			−0.293237
$206$	−2.31183	−	2.59961i	−0.161073	−	0.181123i
$207$		0			0
$208$	−26.0582	−	6.21442i	−1.80681	−	0.430893i
$209$	−10.6022	+	3.47867i	−0.733367	+	0.240625i
$210$		0			0
$211$		−	3.90200i		−	0.268625i	−0.990939	−	0.134312i	$-0.957117\pi$
$211$		−	3.90200i		−	0.268625i	0.990939	−	0.134312i	$-0.0428825\pi$
$212$	0.0296120	−	0.251819i	0.00203376	−	0.0172950i
$213$		0			0
$214$	14.3123	−	12.7279i	0.978370	−	0.870063i
$215$			18.2846i			1.24700i
$216$		0			0
$217$		−	9.49666i		−	0.644675i
$218$	−11.4555	−	12.8815i	−0.775861	−	0.872443i
$219$		0			0
$220$	−8.68149	−	1.02088i	−0.585306	−	0.0688275i
$221$	21.3529			1.43635
$222$		0			0
$223$	−10.3623			−0.693913			−0.346957	−	0.937881i	$-0.612785\pi$
$223$	−10.3623			−0.693913			−0.346957	+	0.937881i	$0.612785\pi$
$224$	−20.7151	+	11.1228i	−1.38409	+	0.743173i
$225$		0			0
$226$	−21.3642	+	18.9991i	−1.42112	+	1.26380i
$227$			4.71228i			0.312765i	0.987697	+	0.156383i	$0.0499833\pi$
$227$			4.71228i			0.312765i	−0.987697	+	0.156383i	$0.950017\pi$
$228$		0			0
$229$		−	22.0069i		−	1.45426i	−0.686500	−	0.727130i	$-0.740854\pi$
$229$		−	22.0069i		−	1.45426i	0.686500	−	0.727130i	$-0.259146\pi$
$230$	−4.76069	−	5.35331i	−0.313911	−	0.352987i
$231$		0			0
$232$	−12.3712	+	8.64310i	−0.812211	+	0.567447i
$233$	28.1404			1.84354			0.921770	−	0.387738i	$-0.126743\pi$
$233$	28.1404			1.84354			0.921770	+	0.387738i	$0.126743\pi$
$234$		0			0
$235$	−11.7829			−0.768630
$236$	1.44597	+	0.170035i	0.0941246	+	0.0110683i
$237$		0			0
$238$	14.0045	−	12.4542i	0.907778	−	0.807285i
$239$		−	20.6711i		−	1.33710i	−0.743667	−	0.668550i	$-0.766915\pi$
$239$		−	20.6711i		−	1.33710i	0.743667	−	0.668550i	$-0.233085\pi$
$240$		0			0
$241$			0.308647i			0.0198817i	0.999951	+	0.00994085i	$0.00316432\pi$
$241$			0.308647i			0.0198817i	−0.999951	+	0.00994085i	$0.996836\pi$
$242$	4.17926	+	4.69951i	0.268653	+	0.302096i
$243$		0			0
$244$	−11.2352	−	1.32117i	−0.719260	−	0.0845794i
$245$		−	17.5449i		−	1.12091i
$246$		0			0
$247$	−27.7377	+	9.10102i	−1.76491	+	0.579084i
$248$	−5.29757	+	3.70112i	−0.336396	+	0.235022i
$249$		0			0
$250$	12.7834	−	11.3682i	0.808492	−	0.718990i
$251$	17.0918			1.07882			0.539411	−	0.842043i	$-0.318647\pi$
$251$	17.0918			1.07882			0.539411	+	0.842043i	$0.318647\pi$
$252$		0			0
$253$		−	7.59505i		−	0.477497i
$254$	18.0422	+	20.2882i	1.13207	+	1.27299i
$255$		0			0
$256$	14.2780	+	7.22076i	0.892374	+	0.451298i
$257$			0.574779i			0.0358537i	0.999839	+	0.0179269i	$0.00570661\pi$
$257$			0.574779i			0.0358537i	−0.999839	+	0.0179269i	$0.994293\pi$
$258$		0			0
$259$			19.4372i			1.20777i
$260$	−22.7128	−	2.67085i	−1.40859	−	0.165639i
$261$		0			0
$262$	−15.3729	−	17.2866i	−0.949742	−	1.06797i
$263$			20.3184i			1.25288i	0.779468	+	0.626442i	$0.215489\pi$
$263$			20.3184i			1.25288i	−0.779468	+	0.626442i	$0.784511\pi$
$264$		0			0
$265$		−	0.216455i		−	0.0132967i
$266$	−12.8838	+	22.1471i	−0.789959	+	1.35793i
$267$		0			0
$268$	6.10951	+	0.718431i	0.373198	+	0.0438851i
$269$	−15.7637			−0.961132			−0.480566	−	0.876959i	$-0.659569\pi$
$269$	−15.7637			−0.961132			−0.480566	+	0.876959i	$0.659569\pi$
$270$		0			0
$271$		−	26.3680i		−	1.60174i	−0.598835	−	0.800872i	$-0.704370\pi$
$271$		−	26.3680i		−	1.60174i	0.598835	−	0.800872i	$-0.295630\pi$
$272$	−12.4054	−	2.95846i	−0.752185	−	0.179383i
$273$		0			0
$274$	−7.02656	−	7.90124i	−0.424490	−	0.477332i
$275$	5.33711			0.321840
$276$		0			0
$277$			27.4804i			1.65114i	0.564301	+	0.825569i	$0.309146\pi$
$277$			27.4804i			1.65114i	−0.564301	+	0.825569i	$0.690854\pi$
$278$	10.2008	+	11.4706i	0.611801	+	0.687959i
$279$		0			0
$280$	−16.4542	+	11.4956i	−0.983326	+	0.686996i
$281$		−	2.25225i		−	0.134358i	−0.997741	−	0.0671789i	$-0.978600\pi$
$281$		−	2.25225i		−	0.134358i	0.997741	−	0.0671789i	$-0.0213998\pi$
$282$		0			0
$283$	−1.57719			−0.0937541			−0.0468770	−	0.998901i	$-0.514927\pi$
$283$	−1.57719			−0.0937541			−0.0468770	+	0.998901i	$0.514927\pi$
$284$	1.44978	−	12.3289i	0.0860289	−	0.731586i
$285$		0			0
$286$	−16.1120	−	18.1176i	−0.952721	−	1.07132i
$287$	−10.2210			−0.603325
$288$		0			0
$289$	−6.83467			−0.402039
$290$	−9.62712	+	8.56138i	−0.565324	+	0.502742i
$291$		0			0
$292$	1.16240	−	9.88498i	0.0680242	−	0.578475i
$293$	−16.4526			−0.961172			−0.480586	−	0.876947i	$-0.659576\pi$
$293$	−16.4526			−0.961172			−0.480586	+	0.876947i	$0.659576\pi$
$294$		0			0
$295$	1.24290			0.0723647
$296$	10.8428	−	7.57524i	0.630222	−	0.440302i
$297$		0			0
$298$	9.48422	−	8.43429i	0.549406	−	0.488586i
$299$		−	19.8704i		−	1.14914i
$300$		0			0
$301$			44.5125i			2.56566i
$302$	3.25012	+	3.65471i	0.187024	+	0.210305i
$303$		0			0
$304$	17.3757	−	1.44432i	0.996563	−	0.0828377i
$305$	−9.65738			−0.552980
$306$		0			0
$307$		−	27.2838i		−	1.55717i	−0.627540	−	0.778584i	$-0.715938\pi$
$307$		−	27.2838i		−	1.55717i	0.627540	−	0.778584i	$-0.284062\pi$
$308$	−21.1344	−	2.48524i	−1.20424	−	0.141610i
$309$		0			0
$310$	−4.12250	+	3.66613i	−0.234142	+	0.208222i
$311$			6.99438i			0.396615i	0.980140	+	0.198307i	$0.0635444\pi$
$311$			6.99438i			0.396615i	−0.980140	+	0.198307i	$0.936456\pi$
$312$		0			0
$313$	9.96963			0.563517			0.281758	−	0.959485i	$-0.409082\pi$
$313$	9.96963			0.563517			0.281758	+	0.959485i	$0.409082\pi$
$314$	11.8304	−	10.5208i	0.667631	−	0.593723i
$315$		0			0
$316$	−1.86408	+	15.8520i	−0.104862	+	0.891746i
$317$	20.2728			1.13863			0.569317	−	0.822118i	$-0.307208\pi$
$317$	20.2728			1.13863			0.569317	+	0.822118i	$0.307208\pi$
$318$		0			0
$319$	−13.6586			−0.764733
$320$	12.8254	+	4.69855i	0.716959	+	0.262657i
$321$		0			0
$322$	−11.5895	−	13.0322i	−0.645859	−	0.726257i
$323$	−13.2049	+	4.33266i	−0.734740	+	0.241076i
$324$		0			0
$325$	13.9631			0.774534
$326$	4.23363	+	4.76065i	0.234479	+	0.263668i
$327$		0			0
$328$	3.98341	+	5.70162i	0.219947	+	0.314819i
$329$	−28.6845			−1.58143
$330$		0			0
$331$			34.9272i			1.91977i	0.280387	+	0.959887i	$0.409537\pi$
$331$			34.9272i			1.91977i	−0.280387	+	0.959887i	$0.590463\pi$
$332$	4.16285	−	35.4007i	0.228466	−	1.94287i
$333$		0			0
$334$	16.5296	+	18.5873i	0.904460	+	1.01705i
$335$	5.25152			0.286921
$336$		0			0
$337$			29.8823i			1.62779i	0.581009	+	0.813897i	$0.302658\pi$
$337$			29.8823i			1.62779i	−0.581009	+	0.813897i	$0.697342\pi$
$338$	−29.9353	−	33.6618i	−1.62827	−	1.83096i
$339$		0			0
$340$	−10.8127	−	1.27149i	−0.586402	−	0.0689564i
$341$	−5.84883			−0.316732
$342$		0			0
$343$		−	13.6167i		−	0.735231i
$344$	24.8306	−	17.3478i	1.33878	−	0.935331i
$345$		0			0
$346$	−13.3648	−	15.0285i	−0.718498	−	0.807939i
$347$	−6.83014			−0.366661			−0.183331	−	0.983051i	$-0.558688\pi$
$347$	−6.83014			−0.366661			−0.183331	+	0.983051i	$0.558688\pi$
$348$		0			0
$349$		−	14.0932i		−	0.754394i	−0.926133	−	0.377197i	$-0.876888\pi$
$349$		−	14.0932i		−	0.754394i	0.926133	−	0.377197i	$-0.123112\pi$
$350$	9.15785	−	8.14405i	0.489507	−	0.435318i
$351$		0			0
$352$	6.85034	+	12.7581i	0.365124	+	0.680009i
$353$	−21.9193			−1.16664			−0.583322	−	0.812241i	$-0.698248\pi$
$353$	−21.9193			−1.16664			−0.583322	+	0.812241i	$0.698248\pi$
$354$		0			0
$355$		−	10.5975i		−	0.562457i
$356$	21.1546	+	2.48762i	1.12119	+	0.131844i
$357$		0			0
$358$	24.0907	−	21.4238i	1.27324	−	1.13229i
$359$		−	14.4813i		−	0.764293i	−0.924102	−	0.382146i	$-0.875185\pi$
$359$		−	14.4813i		−	0.764293i	0.924102	−	0.382146i	$-0.124815\pi$
$360$		0			0
$361$	15.3067	−	11.2564i	0.805615	−	0.592440i
$362$	11.0453	+	12.4203i	0.580529	+	0.652795i
$363$		0			0
$364$	−55.2925	−	6.50197i	−2.89811	−	0.340796i
$365$		−	8.49678i		−	0.444742i
$366$		0			0
$367$		−	14.6158i		−	0.762937i	−0.924382	−	0.381468i	$-0.875419\pi$
$367$		−	14.6158i		−	0.762937i	0.924382	−	0.381468i	$-0.124581\pi$
$368$	−2.75306	+	11.5441i	−0.143513	+	0.601777i
$369$		0			0
$370$	8.43768	−	7.50361i	0.438654	−	0.390094i
$371$		−	0.526942i		−	0.0273575i
$372$		0			0
$373$	−11.5518			−0.598129			−0.299064	−	0.954233i	$-0.596675\pi$
$373$	−11.5518			−0.598129			−0.299064	+	0.954233i	$0.596675\pi$
$374$	−7.67032	−	8.62514i	−0.396623	−	0.445995i
$375$		0			0
$376$	11.1792	+	16.0012i	0.576522	+	0.825200i
$377$	−35.7339			−1.84039
$378$		0			0
$379$		−	19.5608i		−	1.00477i	−0.864644	−	0.502384i	$-0.832456\pi$
$379$		−	19.5608i		−	1.00477i	0.864644	−	0.502384i	$-0.167544\pi$
$380$	14.5878	−	2.95690i	0.748339	−	0.151686i
$381$		0			0
$382$	−10.4964	+	9.33438i	−0.537040	+	0.477589i
$383$	−25.2759			−1.29154			−0.645768	−	0.763534i	$-0.723463\pi$
$383$	−25.2759			−1.29154			−0.645768	+	0.763534i	$0.723463\pi$
$384$		0			0
$385$	−18.1664			−0.925845
$386$	−14.8800	+	13.2328i	−0.757374	+	0.673531i
$387$		0			0
$388$	15.9820	+	1.87936i	0.811363	+	0.0954101i
$389$		−	20.4996i		−	1.03937i	−0.854358	−	0.519685i	$-0.826049\pi$
$389$		−	20.4996i		−	1.03937i	0.854358	−	0.519685i	$-0.173951\pi$
$390$		0			0
$391$		−	9.45957i		−	0.478391i
$392$	−23.8261	+	16.6460i	−1.20340	+	0.840751i
$393$		0			0
$394$	−10.2512	+	9.11635i	−0.516447	+	0.459275i
$395$			13.6258i			0.685590i
$396$		0			0
$397$		−	2.40053i		−	0.120479i	−0.998184	−	0.0602396i	$-0.980814\pi$
$397$		−	2.40053i		−	0.120479i	0.998184	−	0.0602396i	$-0.0191865\pi$
$398$	1.49759	−	1.33181i	0.0750675	−	0.0667574i
$399$		0			0
$400$	−8.11212	−	1.93460i	−0.405606	−	0.0967299i
$401$		−	9.70252i		−	0.484521i	−0.970211	−	0.242260i	$-0.922111\pi$
$401$		−	9.70252i		−	0.484521i	0.970211	−	0.242260i	$-0.0778888\pi$
$402$		0			0
$403$	−15.3019			−0.762241
$404$	−19.7716	−	2.32499i	−0.983675	−	0.115673i
$405$		0			0
$406$	−23.4365	+	20.8420i	−1.16313	+	1.03437i
$407$	11.9710			0.593382
$408$		0			0
$409$		−	24.2154i		−	1.19738i	−0.800982	−	0.598688i	$-0.795689\pi$
$409$		−	24.2154i		−	1.19738i	0.800982	−	0.598688i	$-0.204311\pi$
$410$	3.94574	+	4.43692i	0.194866	+	0.219124i
$411$		0			0
$412$	−0.574579	+	4.88620i	−0.0283075	+	0.240726i
$413$	3.02575			0.148888
$414$		0			0
$415$		−	30.4292i		−	1.49371i
$416$	17.9221	+	33.3781i	0.878701	+	1.63650i
$417$		0			0
$418$	13.6400	+	7.93493i	0.667157	+	0.388110i
$419$	8.73494			0.426730			0.213365	−	0.976973i	$-0.431558\pi$
$419$	8.73494			0.426730			0.213365	+	0.976973i	$0.431558\pi$
$420$		0			0
$421$	39.2056			1.91076			0.955381	−	0.295377i	$-0.0954452\pi$
$421$	39.2056			1.91076			0.955381	+	0.295377i	$0.0954452\pi$
$422$	−4.12356	+	3.66707i	−0.200732	+	0.178510i
$423$		0			0
$424$	−0.293947	+	0.205365i	−0.0142753	+	0.00997339i
$425$	6.64732			0.322443
$426$		0			0
$427$	−23.5101			−1.13774
$428$	−26.9013	−	3.16338i	−1.30032	−	0.152908i
$429$		0			0
$430$	19.3229	−	17.1838i	0.931831	−	0.828676i
$431$	−4.08225			−0.196635			−0.0983175	−	0.995155i	$-0.531346\pi$
$431$	−4.08225			−0.196635			−0.0983175	+	0.995155i	$0.531346\pi$
$432$		0			0
$433$		−	22.0583i		−	1.06006i	−0.847980	−	0.530028i	$-0.822181\pi$
$433$		−	22.0583i		−	1.06006i	0.847980	−	0.530028i	$-0.177819\pi$
$434$	−10.0359	+	8.92490i	−0.481738	+	0.428409i
$435$		0			0
$436$	−2.84712	+	24.2118i	−0.136353	+	1.15954i
$437$	4.03185	+	12.2881i	0.192870	+	0.587820i
$438$		0			0
$439$	8.52763			0.407001			0.203501	−	0.979075i	$-0.434768\pi$
$439$	8.52763			0.407001			0.203501	+	0.979075i	$0.434768\pi$
$440$	7.07997	+	10.1339i	0.337524	+	0.483113i
$441$		0			0
$442$	−20.0673	−	22.5654i	−0.954506	−	1.07332i
$443$	−16.1402			−0.766842			−0.383421	−	0.923574i	$-0.625254\pi$
$443$	−16.1402			−0.766842			−0.383421	+	0.923574i	$0.625254\pi$
$444$		0			0
$445$	18.1838			0.861994
$446$	9.73846	+	10.9507i	0.461129	+	0.518532i
$447$		0			0
$448$	31.2223	+	11.4382i	1.47512	+	0.540406i
$449$		−	23.3900i		−	1.10384i	−0.833897	−	0.551921i	$-0.813895\pi$
$449$		−	23.3900i		−	1.10384i	0.833897	−	0.551921i	$-0.186105\pi$
$450$		0			0
$451$			6.29492i			0.296416i
$452$	40.1558	+	4.72201i	1.88877	+	0.222105i
$453$		0			0
$454$	4.97985	−	4.42857i	0.233716	−	0.207843i
$455$	−47.5275			−2.22812
$456$		0			0
$457$	1.64919			0.0771460			0.0385730	−	0.999256i	$-0.487719\pi$
$457$	1.64919			0.0771460			0.0385730	+	0.999256i	$0.487719\pi$
$458$	−23.2565	+	20.6820i	−1.08671	+	0.966406i
$459$		0			0
$460$	−1.18322	+	10.0620i	−0.0551677	+	0.469144i
$461$			14.4519i			0.673094i	0.941667	+	0.336547i	$0.109259\pi$
$461$			14.4519i			0.673094i	−0.941667	+	0.336547i	$0.890741\pi$
$462$		0			0
$463$			23.7653i			1.10447i	0.833689	+	0.552235i	$0.186225\pi$
$463$			23.7653i			1.10447i	−0.833689	+	0.552235i	$0.813775\pi$
$464$	20.7603	+	4.95096i	0.963772	+	0.229842i
$465$		0			0
$466$	−26.4462	−	29.7383i	−1.22510	−	1.37760i
$467$	8.32898			0.385419			0.192710	−	0.981256i	$-0.438272\pi$
$467$	8.32898			0.385419			0.192710	+	0.981256i	$0.438272\pi$
$468$		0			0
$469$	12.7844			0.590329
$470$	11.0735	+	12.4519i	0.510781	+	0.574365i
$471$		0			0
$472$	−1.17922	−	1.68787i	−0.0542782	−	0.0776906i
$473$	27.4145			1.26052
$474$		0			0
$475$	−8.63496	+	2.83322i	−0.396199	+	0.129997i
$476$	−26.3227	−	3.09535i	−1.20650	−	0.141875i
$477$		0			0
$478$	−21.8448	+	19.4265i	−0.999158	+	0.888550i
$479$		−	20.7962i		−	0.950203i	−0.879931	−	0.475101i	$-0.842411\pi$
$479$		−	20.7962i		−	0.950203i	0.879931	−	0.475101i	$-0.157589\pi$
$480$		0			0
$481$	31.3190			1.42802
$482$	0.326173	−	0.290065i	0.0148568	−	0.0132121i
$483$		0			0
$484$	1.03871	−	8.83313i	0.0472140	−	0.401506i
$485$	13.7376			0.623791
$486$		0			0
$487$	1.42813			0.0647148			0.0323574	−	0.999476i	$-0.489699\pi$
$487$	1.42813			0.0647148			0.0323574	+	0.999476i	$0.489699\pi$
$488$	9.16258	+	13.1148i	0.414771	+	0.593678i
$489$		0			0
$490$	−18.5412	+	16.4886i	−0.837605	+	0.744881i
$491$	13.3271			0.601442			0.300721	−	0.953712i	$-0.402773\pi$
$491$	13.3271			0.601442			0.300721	+	0.953712i	$0.402773\pi$
$492$		0			0
$493$	−17.0116			−0.766165
$494$	35.6855	+	20.7596i	1.60557	+	0.934019i
$495$		0			0
$496$	8.88991	+	2.12009i	0.399169	+	0.0951946i
$497$		−	25.7988i		−	1.15723i
$498$		0			0
$499$	35.9721			1.61033			0.805166	−	0.593049i	$-0.202076\pi$
$499$	35.9721			1.61033			0.805166	+	0.593049i	$0.202076\pi$
$500$	−24.0275	−	2.82545i	−1.07454	−	0.126358i
$501$		0			0
$502$	−16.0627	−	18.0623i	−0.716914	−	0.806158i
$503$			10.7695i			0.480190i	0.970749	+	0.240095i	$0.0771786\pi$
$503$			10.7695i			0.480190i	−0.970749	+	0.240095i	$0.922821\pi$
$504$		0			0
$505$	−16.9950			−0.756267
$506$	−8.02631	+	7.13779i	−0.356813	+	0.317313i
$507$		0			0
$508$	4.48419	−	38.1334i	0.198954	−	1.69190i
$509$	−17.4092			−0.771651			−0.385825	−	0.922572i	$-0.626083\pi$
$509$	−17.4092			−0.771651			−0.385825	+	0.922572i	$0.626083\pi$
$510$		0			0
$511$		−	20.6847i		−	0.915039i
$512$	−5.78759	−	21.8747i	−0.255778	−	0.966736i
$513$		0			0
$514$	0.607416	−	0.540174i	0.0267920	−	0.0238261i
$515$			4.20000i			0.185074i
$516$		0			0
$517$			17.6663i			0.776962i
$518$	20.5409	−	18.2669i	0.902514	−	0.802603i
$519$		0			0
$520$	18.5228	+	26.5125i	0.812280	+	1.16265i
$521$		−	32.4161i		−	1.42017i	−0.704114	−	0.710086i	$-0.748656\pi$
$521$		−	32.4161i		−	1.42017i	0.704114	−	0.710086i	$-0.251344\pi$
$522$		0			0
$523$			7.71738i			0.337458i	0.985663	+	0.168729i	$0.0539662\pi$
$523$			7.71738i			0.337458i	−0.985663	+	0.168729i	$0.946034\pi$
$524$	−3.82076	+	32.4916i	−0.166911	+	1.41940i
$525$		0			0
$526$	21.4721	−	19.0951i	0.936227	−	0.832584i
$527$	−7.28467			−0.317325
$528$		0			0
$529$	14.1972			0.617269
$530$	−0.228746	+	0.203423i	−0.00993607	+	0.00883613i
$531$		0			0
$532$	35.5129	−	7.19835i	1.53968	−	0.312088i
$533$			16.4690i			0.713350i
$534$		0			0
$535$	−23.1234			−0.999711
$536$	−4.98245	−	7.13159i	−0.215209	−	0.308038i
$537$		0			0
$538$	14.8147	+	16.6588i	0.638705	+	0.718213i
$539$	−26.3055			−1.13306
$540$		0			0
$541$		−	7.57735i		−	0.325776i	−0.986645	−	0.162888i	$-0.947919\pi$
$541$		−	7.57735i		−	0.325776i	0.986645	−	0.162888i	$-0.0520809\pi$
$542$	−27.8653	+	24.7805i	−1.19692	+	1.06441i
$543$		0			0
$544$	8.53203	+	15.8901i	0.365808	+	0.681282i
$545$			20.8116i			0.891473i
$546$		0			0
$547$		−	31.2474i		−	1.33604i	−0.744142	−	0.668022i	$-0.767141\pi$
$547$		−	31.2474i		−	1.33604i	0.744142	−	0.668022i	$-0.232859\pi$
$548$	−1.74637	+	14.8511i	−0.0746013	+	0.634407i
$549$		0			0
$550$	−5.01578	−	5.64016i	−0.213874	−	0.240497i
$551$	22.0983	−	7.25068i	0.941420	−	0.308889i
$552$		0			0
$553$			33.1710i			1.41058i
$554$	29.0408	−	25.8259i	1.23383	−	1.09724i
$555$		0			0
$556$	2.53528	−	21.5599i	0.107520	−	0.914345i
$557$		−	38.3210i		−	1.62371i	−0.583856	−	0.811857i	$-0.698457\pi$
$557$		−	38.3210i		−	1.62371i	0.583856	−	0.811857i	$-0.301543\pi$
$558$		0			0
$559$	71.7226			3.03354
$560$	27.6119	+	6.58496i	1.16682	+	0.278265i
$561$		0			0
$562$	−2.38013	+	2.11665i	−0.100400	+	0.0892854i
$563$			25.1039i			1.05800i	0.848621	+	0.529001i	$0.177433\pi$
$563$			25.1039i			1.05800i	−0.848621	+	0.529001i	$0.822567\pi$
$564$		0			0
$565$	34.5165			1.45212
$566$	1.48223	+	1.66674i	0.0623028	+	0.0700584i
$567$		0			0
$568$	−14.3915	+	10.0545i	−0.603852	+	0.421879i
$569$			40.1028i			1.68120i	0.541658	+	0.840599i	$0.317797\pi$
$569$			40.1028i			1.68120i	−0.541658	+	0.840599i	$0.682203\pi$
$570$		0			0
$571$	12.1764			0.509568			0.254784	−	0.966998i	$-0.417996\pi$
$571$	12.1764			0.509568			0.254784	+	0.966998i	$0.417996\pi$
$572$	−4.00445	+	34.0537i	−0.167435	+	1.42386i
$573$		0			0
$574$	9.60560	+	10.8013i	0.400930	+	0.450839i
$575$		−	6.18581i		−	0.257966i
$576$		0			0
$577$	−4.25085			−0.176965			−0.0884827	−	0.996078i	$-0.528202\pi$
$577$	−4.25085			−0.176965			−0.0884827	+	0.996078i	$0.528202\pi$
$578$	6.42318	+	7.22275i	0.267169	+	0.300427i
$579$		0			0
$580$	18.0950	+	2.12783i	0.751355	+	0.0883535i
$581$		−	74.0775i		−	3.07325i
$582$		0			0
$583$	−0.324535			−0.0134409
$584$	−11.5387	+	8.06145i	−0.477474	+	0.333585i
$585$		0			0
$586$	15.4621	+	17.3868i	0.638732	+	0.718243i
$587$	46.1030			1.90287			0.951437	−	0.307843i	$-0.0996070\pi$
$587$	46.1030			1.90287			0.951437	+	0.307843i	$0.0996070\pi$
$588$		0			0
$589$	9.46288	−	3.10486i	0.389911	−	0.127934i
$590$	−1.16807	−	1.31348i	−0.0480889	−	0.0540751i
$591$		0			0
$592$	−18.1953	−	4.33926i	−0.747823	−	0.178343i
$593$	−4.66707			−0.191653			−0.0958267	−	0.995398i	$-0.530549\pi$
$593$	−4.66707			−0.191653			−0.0958267	+	0.995398i	$0.530549\pi$
$594$		0			0
$595$	−22.6261			−0.927579
$596$	−17.8264	−	2.09625i	−0.730198	−	0.0858657i
$597$		0			0
$598$	−20.9987	+	18.6741i	−0.858700	+	0.763640i
$599$	25.9970			1.06221			0.531104	−	0.847307i	$-0.321777\pi$
$599$	25.9970			1.06221			0.531104	+	0.847307i	$0.321777\pi$
$600$		0			0
$601$			30.7149i			1.25289i	0.779467	+	0.626443i	$0.215490\pi$
$601$			30.7149i			1.25289i	−0.779467	+	0.626443i	$0.784510\pi$
$602$	47.0400	−	41.8326i	1.91721	−	1.70497i
$603$		0			0
$604$	0.807782	−	6.86934i	0.0328682	−	0.279510i
$605$		−	7.59265i		−	0.308685i
$606$		0			0
$607$	22.4845			0.912617			0.456309	−	0.889822i	$-0.349171\pi$
$607$	22.4845			0.912617			0.456309	+	0.889822i	$0.349171\pi$
$608$	−17.8559	−	17.0049i	−0.724152	−	0.689641i
$609$		0			0
$610$	9.07595	+	10.2057i	0.367474	+	0.413219i
$611$			46.2191i			1.86982i
$612$		0			0
$613$		−	39.1691i		−	1.58202i	−0.611800	−	0.791012i	$-0.709554\pi$
$613$		−	39.1691i		−	1.58202i	0.611800	−	0.791012i	$-0.290446\pi$
$614$	−28.8330	+	25.6411i	−1.16361	+	1.03479i
$615$		0			0
$616$	17.2356	+	24.6701i	0.694443	+	0.993985i
$617$	14.9585			0.602208			0.301104	−	0.953591i	$-0.402645\pi$
$617$	14.9585			0.602208			0.301104	+	0.953591i	$0.402645\pi$
$618$		0			0
$619$	−18.6781			−0.750736			−0.375368	−	0.926876i	$-0.622484\pi$
$619$	−18.6781			−0.750736			−0.375368	+	0.926876i	$0.622484\pi$
$620$	7.74860	+	0.911175i	0.311191	+	0.0365937i
$621$		0			0
$622$	7.39153	−	6.57327i	0.296373	−	0.263564i
$623$	44.2670			1.77352
$624$		0			0
$625$	−10.2287			−0.409146
$626$	−9.36940	−	10.5357i	−0.374476	−	0.421092i
$627$		0			0
$628$	−22.2364	−	2.61482i	−0.887328	−	0.104343i
$629$	14.9098			0.594493
$630$		0			0
$631$			17.2968i			0.688573i	0.938865	+	0.344287i	$0.111879\pi$
$631$			17.2968i			0.688573i	−0.938865	+	0.344287i	$0.888121\pi$
$632$	18.5040	−	12.9277i	0.736049	−	0.514237i
$633$		0			0
$634$	−19.0523	−	21.4239i	−0.756662	−	0.850853i
$635$		−	32.7781i		−	1.30076i
$636$		0			0
$637$	−68.8211			−2.72679
$638$	12.8362	+	14.4341i	0.508191	+	0.571452i
$639$		0			0
$640$	−7.08785	−	17.9693i	−0.280172	−	0.710298i
$641$			36.8143i			1.45408i	0.686596	+	0.727039i	$0.259104\pi$
$641$			36.8143i			1.45408i	−0.686596	+	0.727039i	$0.740896\pi$
$642$		0			0
$643$	−10.8105			−0.426324			−0.213162	−	0.977017i	$-0.568376\pi$
$643$	−10.8105			−0.426324			−0.213162	+	0.977017i	$0.568376\pi$
$644$	−2.88044	+	24.4952i	−0.113505	+	0.965245i
$645$		0			0
$646$	16.9886	+	9.88289i	0.668406	+	0.388837i
$647$		−	35.7578i		−	1.40578i	−0.711297	−	0.702892i	$-0.751892\pi$
$647$		−	35.7578i		−	1.40578i	0.711297	−	0.702892i	$-0.248108\pi$
$648$		0			0
$649$		−	1.86351i		−	0.0731491i
$650$	−13.1224	−	14.7560i	−0.514705	−	0.578776i
$651$		0			0
$652$	1.05222	−	8.94805i	0.0412082	−	0.350433i
$653$			10.6898i			0.418322i	0.977881	+	0.209161i	$0.0670733\pi$
$653$			10.6898i			0.418322i	−0.977881	+	0.209161i	$0.932927\pi$
$654$		0			0
$655$			27.9287i			1.09126i
$656$	2.28178	−	9.56794i	0.0890887	−	0.373565i
$657$		0			0
$658$	26.9575	+	30.3132i	1.05091	+	1.18173i
$659$			16.4833i			0.642099i	0.947062	+	0.321049i	$0.104036\pi$
$659$			16.4833i			0.642099i	−0.947062	+	0.321049i	$0.895964\pi$
$660$		0			0
$661$	−10.4550			−0.406653			−0.203326	−	0.979111i	$-0.565175\pi$
$661$	−10.4550			−0.406653			−0.203326	+	0.979111i	$0.565175\pi$
$662$	36.9105	−	32.8244i	1.43457	−	1.27576i
$663$		0			0
$664$	−41.3230	+	28.8701i	−1.60365	+	1.12038i
$665$	29.3916	−	9.64367i	1.13976	−	0.373965i
$666$		0			0
$667$			15.8305i			0.612961i
$668$	4.10825	−	34.9364i	0.158953	−	1.35173i
$669$		0			0
$670$	−4.93534	−	5.54971i	−0.190669	−	0.214404i
$671$			14.4795i			0.558974i
$672$		0			0
$673$		−	37.2894i		−	1.43740i	−0.695320	−	0.718701i	$-0.744737\pi$
$673$		−	37.2894i		−	1.43740i	0.695320	−	0.718701i	$-0.255263\pi$
$674$	31.5791	−	28.0832i	1.21638	−	1.08173i
$675$		0			0
$676$	−7.44009	+	63.2702i	−0.286157	+	2.43347i
$677$	8.74230			0.335994			0.167997	−	0.985788i	$-0.446270\pi$
$677$	8.74230			0.335994			0.167997	+	0.985788i	$0.446270\pi$
$678$		0			0
$679$	33.4430			1.28343
$680$	8.81804	+	12.6216i	0.338156	+	0.484017i
$681$		0			0
$682$	5.49669	+	6.18094i	0.210479	+	0.236680i
$683$		−	9.95444i		−	0.380896i	−0.981697	−	0.190448i	$-0.939006\pi$
$683$		−	9.95444i		−	0.380896i	0.981697	−	0.190448i	$-0.0609940\pi$
$684$		0			0
$685$			12.7655i			0.487743i
$686$	−14.3898	+	12.7969i	−0.549407	+	0.488586i
$687$		0			0
$688$	−41.6685	−	9.93720i	−1.58860	−	0.378852i
$689$	−0.849057			−0.0323465
$690$		0			0
$691$	12.3232			0.468798			0.234399	−	0.972140i	$-0.424688\pi$
$691$	12.3232			0.468798			0.234399	+	0.972140i	$0.424688\pi$
$692$	−3.32168	+	28.2474i	−0.126271	+	1.07381i
$693$		0			0
$694$	6.41892	+	7.21796i	0.243659	+	0.273990i
$695$		−	18.5322i		−	0.702965i
$696$		0			0
$697$			7.84027i			0.296971i
$698$	−14.8935	+	13.2447i	−0.563726	+	0.501321i
$699$		0			0
$700$	−17.2130	−	2.02411i	−0.650589	−	0.0765043i
$701$		−	23.5557i		−	0.889687i	−0.895608	−	0.444844i	$-0.853259\pi$
$701$		−	23.5557i		−	0.889687i	0.895608	−	0.444844i	$-0.146741\pi$
$702$		0			0
$703$	−19.3680	+	6.35485i	−0.730479	+	0.239678i
$704$	7.04462	−	19.2293i	0.265504	−	0.724731i
$705$		0			0
$706$	20.5996	+	23.1639i	0.775276	+	0.871784i
$707$	−41.3729			−1.55599
$708$		0			0
$709$		−	0.175430i		−	0.00658841i	−0.999995	−	0.00329420i	$-0.998951\pi$
$709$		−	0.175430i		−	0.00658841i	0.999995	−	0.00329420i	$-0.00104858\pi$
$710$	−11.1992	+	9.95946i	−0.420300	+	0.373772i
$711$		0			0
$712$	−17.2521	−	24.6937i	−0.646551	−	0.925435i
$713$			6.77891i			0.253872i
$714$		0			0
$715$			29.2714i			1.09469i
$716$	−45.2807	−	5.32466i	−1.69222	−	0.198992i
$717$		0			0
$718$	−15.3036	+	13.6094i	−0.571124	+	0.507899i
$719$			3.73038i			0.139120i	0.997578	+	0.0695599i	$0.0221595\pi$
$719$			3.73038i			0.139120i	−0.997578	+	0.0695599i	$0.977841\pi$
$720$		0			0
$721$			10.2246i			0.380783i
$722$	−26.2806	−	5.59716i	−0.978064	−	0.208305i
$723$		0			0
$724$	2.74519	−	23.3450i	0.102024	−	0.867610i
$725$	−11.1243			−0.413144
$726$		0			0
$727$			29.5101i			1.09447i	0.836979	+	0.547234i	$0.184319\pi$
$727$			29.5101i			1.09447i	−0.836979	+	0.547234i	$0.815681\pi$
$728$	45.0924	+	64.5426i	1.67123	+	2.39211i
$729$		0			0
$730$	−8.97925	+	7.98522i	−0.332337	+	0.295546i
$731$	34.1445			1.26288
$732$		0			0
$733$		−	24.1339i		−	0.891404i	−0.895181	−	0.445702i	$-0.852954\pi$
$733$		−	24.1339i		−	0.891404i	0.895181	−	0.445702i	$-0.147046\pi$
$734$	−15.4457	+	13.7358i	−0.570110	+	0.506998i
$735$		0			0
$736$	14.7869	−	7.93967i	0.545051	−	0.292660i
$737$		−	7.87369i		−	0.290031i
$738$		0			0
$739$	12.3479			0.454225			0.227113	−	0.973869i	$-0.427071\pi$
$739$	12.3479			0.454225			0.227113	+	0.973869i	$0.427071\pi$
$740$	−15.8594	−	1.86494i	−0.583002	−	0.0685565i
$741$		0			0
$742$	−0.556863	+	0.495217i	−0.0204431	+	0.0181800i
$743$	−2.44280			−0.0896178			−0.0448089	−	0.998996i	$-0.514268\pi$
$743$	−2.44280			−0.0896178			−0.0448089	+	0.998996i	$0.514268\pi$
$744$		0			0
$745$	−15.3230			−0.561390
$746$	10.8563	+	12.2077i	0.397477	+	0.446956i
$747$		0			0
$748$	−1.90637	+	16.2117i	−0.0697039	+	0.592759i
$749$	−56.2920			−2.05687
$750$		0			0
$751$	7.29453			0.266181			0.133091	−	0.991104i	$-0.457510\pi$
$751$	7.29453			0.266181			0.133091	+	0.991104i	$0.457510\pi$
$752$	6.40368	−	26.8518i	0.233518	−	0.979184i
$753$		0			0
$754$	33.5825	+	37.7630i	1.22300	+	1.37525i
$755$		−	5.90465i		−	0.214892i
$756$		0			0
$757$		−	29.4139i		−	1.06906i	−0.845148	−	0.534532i	$-0.820488\pi$
$757$		−	29.4139i		−	1.06906i	0.845148	−	0.534532i	$-0.179512\pi$
$758$	−20.6715	+	18.3831i	−0.750821	+	0.667704i
$759$		0			0
$760$	−16.8343	−	12.6372i	−0.610645	−	0.458401i
$761$	31.4314			1.13939			0.569693	−	0.821858i	$-0.307062\pi$
$761$	31.4314			1.13939			0.569693	+	0.821858i	$0.307062\pi$
$762$		0			0
$763$			50.6643i			1.83417i
$764$	19.7288	+	2.31996i	0.713763	+	0.0839330i
$765$		0			0
$766$	23.7541	+	26.7111i	0.858270	+	0.965110i
$767$		−	4.87537i		−	0.176039i
$768$		0			0
$769$	35.7321			1.28853			0.644266	−	0.764802i	$-0.277163\pi$
$769$	35.7321			1.28853			0.644266	+	0.764802i	$0.277163\pi$
$770$	17.0727	+	19.1979i	0.615256	+	0.691845i
$771$		0			0
$772$	27.9683	+	3.28886i	1.00660	+	0.118369i
$773$	46.5592			1.67462			0.837308	−	0.546731i	$-0.184128\pi$
$773$	46.5592			1.67462			0.837308	+	0.546731i	$0.184128\pi$
$774$		0			0
$775$	−4.76360			−0.171113
$776$	−13.0337	−	18.6557i	−0.467883	−	0.669701i
$777$		0			0
$778$	−21.6636	+	19.2654i	−0.776676	+	0.690697i
$779$	−3.34167	−	10.1846i	−0.119728	−	0.364901i
$780$		0			0
$781$	−15.8890			−0.568554
$782$	−9.99670	+	8.89005i	−0.357481	+	0.317908i
$783$		0			0
$784$	39.9829	+	9.53521i	1.42796	+	0.340543i
$785$	−19.1136			−0.682193
$786$		0			0
$787$			14.0965i			0.502487i	0.967924	+	0.251244i	$0.0808395\pi$
$787$			14.0965i			0.502487i	−0.967924	+	0.251244i	$0.919160\pi$
$788$	19.2680	+	2.26577i	0.686393	+	0.0807146i
$789$		0			0
$790$	14.3995	−	12.8055i	0.512313	−	0.455599i
$791$	84.0277			2.98768
$792$		0			0
$793$			37.8817i			1.34522i
$794$	−2.53684	+	2.25600i	−0.0900290	+	0.0800626i
$795$		0			0
$796$	−2.81486	−	0.331005i	−0.0997699	−	0.0117322i
$797$	−3.03101			−0.107364			−0.0536820	−	0.998558i	$-0.517096\pi$
$797$	−3.03101			−0.107364			−0.0536820	+	0.998558i	$0.517096\pi$
$798$		0			0
$799$			22.0032i			0.778417i
$800$	5.57927	+	10.3909i	0.197257	+	0.367373i
$801$		0			0
$802$	−10.2534	+	9.11837i	−0.362062	+	0.321981i
$803$	−12.7394			−0.449563
$804$		0			0
$805$			21.0552i			0.742098i
$806$	14.3806	+	16.1708i	0.506536	+	0.569591i
$807$		0			0
$808$	16.1242	+	23.0793i	0.567249	+	0.811927i
$809$	32.0795			1.12785			0.563927	−	0.825824i	$-0.309290\pi$
$809$	32.0795			1.12785			0.563927	+	0.825824i	$0.309290\pi$
$810$		0			0
$811$		−	20.9982i		−	0.737348i	−0.929559	−	0.368674i	$-0.879812\pi$
$811$		−	20.9982i		−	0.737348i	0.929559	−	0.368674i	$-0.120188\pi$
$812$	44.0509	+	5.18004i	1.54588	+	0.181784i
$813$		0			0
$814$	−11.2503	−	12.6508i	−0.394323	−	0.443409i
$815$		−	7.69143i		−	0.269419i
$816$		0			0
$817$	−44.3541	+	14.5530i	−1.55175	+	0.509146i
$818$	−25.5904	+	22.7575i	−0.894749	+	0.795698i
$819$		0			0
$820$	0.980670	−	8.33958i	0.0342465	−	0.291231i
$821$			27.5469i			0.961392i	0.876887	+	0.480696i	$0.159616\pi$
$821$			27.5469i			0.961392i	−0.876887	+	0.480696i	$0.840384\pi$
$822$		0			0
$823$		−	8.60456i		−	0.299936i	−0.988691	−	0.149968i	$-0.952083\pi$
$823$		−	8.60456i		−	0.299936i	0.988691	−	0.149968i	$-0.0479171\pi$
$824$	5.70363	−	3.98481i	0.198695	−	0.138818i
$825$		0			0
$826$	−2.84358	−	3.19756i	−0.0989409	−	0.111257i
$827$		−	40.9232i		−	1.42304i	−0.702667	−	0.711519i	$-0.748007\pi$
$827$		−	40.9232i		−	1.42304i	0.702667	−	0.711519i	$-0.251993\pi$
$828$		0			0
$829$	−23.9874			−0.833115			−0.416558	−	0.909109i	$-0.636764\pi$
$829$	−23.9874			−0.833115			−0.416558	+	0.909109i	$0.636764\pi$
$830$	−32.1570	+	28.5972i	−1.11619	+	0.992622i
$831$		0			0
$832$	18.4303	−	50.3083i	0.638957	−	1.74412i
$833$	−32.7632			−1.13518
$834$		0			0
$835$		−	30.0301i		−	1.03923i
$836$	−4.43334	−	21.8718i	−0.153330	−	0.756450i
$837$		0			0
$838$	−8.20904	−	9.23092i	−0.283577	−	0.318877i
$839$	−6.32625			−0.218406			−0.109203	−	0.994019i	$-0.534830\pi$
$839$	−6.32625			−0.218406			−0.109203	+	0.994019i	$0.534830\pi$
$840$		0			0
$841$	−0.531170			−0.0183162
$842$	−36.8451	−	41.4317i	−1.26977	−	1.42783i
$843$		0			0
$844$	7.75059	+	0.911410i	0.266786	+	0.0313720i
$845$			54.3849i			1.87090i
$846$		0			0
$847$		−	18.4837i		−	0.635108i
$848$	0.493275	+	0.117637i	0.0169391	+	0.00403968i
$849$		0			0
$850$	−6.24711	−	7.02477i	−0.214274	−	0.240948i
$851$		−	13.8746i		−	0.475617i
$852$		0			0
$853$		−	8.05958i		−	0.275955i	−0.990435	−	0.137977i	$-0.955940\pi$
$853$		−	8.05958i		−	0.275955i	0.990435	−	0.137977i	$-0.0440601\pi$
$854$	22.0947	+	24.8451i	0.756064	+	0.850181i
$855$		0			0
$856$	21.9386	+	31.4017i	0.749847	+	1.07329i
$857$			6.37004i			0.217597i	0.994064	+	0.108798i	$0.0347003\pi$
$857$			6.37004i			0.217597i	−0.994064	+	0.108798i	$0.965300\pi$
$858$		0			0
$859$	24.5126			0.836358			0.418179	−	0.908365i	$-0.362669\pi$
$859$	24.5126			0.836358			0.418179	+	0.908365i	$0.362669\pi$
$860$	−36.3190	−	4.27084i	−1.23847	−	0.145634i
$861$		0			0
$862$	3.83647	+	4.31405i	0.130671	+	0.146937i
$863$	−12.3375			−0.419974			−0.209987	−	0.977704i	$-0.567342\pi$
$863$	−12.3375			−0.419974			−0.209987	+	0.977704i	$0.567342\pi$
$864$		0			0
$865$			24.2805i			0.825562i
$866$	−23.3109	+	20.7303i	−0.792135	+	0.704444i
$867$		0			0
$868$	18.8633	+	2.21818i	0.640264	+	0.0752901i
$869$	20.4295			0.693022
$870$		0			0
$871$		−	20.5994i		−	0.697984i
$872$	28.2623	−	19.7453i	0.957083	−	0.668662i
$873$		0			0
$874$	9.19674	−	15.8091i	0.311084	−	0.534750i
$875$	−50.2785			−1.69972
$876$		0			0
$877$	20.1694			0.681072			0.340536	−	0.940231i	$-0.389391\pi$
$877$	20.1694			0.681072			0.340536	+	0.940231i	$0.389391\pi$
$878$	−8.01421	−	9.01184i	−0.270466	−	0.304135i
$879$		0			0
$880$	4.05556	−	17.0057i	0.136713	−	0.573263i
$881$	−28.5176			−0.960782			−0.480391	−	0.877054i	$-0.659505\pi$
$881$	−28.5176			−0.960782			−0.480391	+	0.877054i	$0.659505\pi$
$882$		0			0
$883$	7.92729			0.266774			0.133387	−	0.991064i	$-0.457415\pi$
$883$	7.92729			0.266774			0.133387	+	0.991064i	$0.457415\pi$
$884$	−4.98751	+	42.4136i	−0.167748	+	1.42652i
$885$		0			0
$886$	15.1684	+	17.0566i	0.509593	+	0.573028i
$887$	10.8245			0.363451			0.181726	−	0.983349i	$-0.441832\pi$
$887$	10.8245			0.363451			0.181726	+	0.983349i	$0.441832\pi$
$888$		0			0
$889$		−	79.7957i		−	2.67626i
$890$	−17.0890	−	19.2163i	−0.572825	−	0.644131i
$891$		0			0
$892$	2.42038	−	20.5829i	0.0810405	−	0.689165i
$893$	−9.37818	−	28.5824i	−0.313829	−	0.956475i
$894$		0			0
$895$	−38.9217			−1.30101
$896$	−17.2548	−	43.7448i	−0.576443	−	1.46141i
$897$		0			0
$898$	−24.7181	+	21.9818i	−0.824854	+	0.733541i
$899$	12.1908			0.406587
$900$		0			0
$901$	−0.404205			−0.0134660
$902$	6.65235	−	5.91592i	0.221499	−	0.196979i
$903$		0			0
$904$	−32.7480	−	46.8736i	−1.08918	−	1.55899i
$905$		−	20.0665i		−	0.667034i
$906$		0			0
$907$		−	20.0044i		−	0.664235i	−0.943238	−	0.332118i	$-0.892237\pi$
$907$		−	20.0044i		−	0.664235i	0.943238	−	0.332118i	$-0.107763\pi$
$908$	−9.36007	−	1.10067i	−0.310625	−	0.0365271i
$909$		0			0
$910$	44.6660	+	50.2262i	1.48066	+	1.66498i
$911$	6.84236			0.226698			0.113349	−	0.993555i	$-0.463842\pi$
$911$	6.84236			0.226698			0.113349	+	0.993555i	$0.463842\pi$
$912$		0			0
$913$	−45.6230			−1.50990
$914$	−1.54990	−	1.74284i	−0.0512662	−	0.0576479i
$915$		0			0
$916$	43.7127	+	5.14028i	1.44431	+	0.169839i
$917$			67.9901i			2.24523i
$918$		0			0
$919$		−	12.2104i		−	0.402785i	−0.979511	−	0.201392i	$-0.935453\pi$
$919$		−	12.2104i		−	0.402785i	0.979511	−	0.201392i	$-0.0645466\pi$
$920$	11.7453	−	8.20582i	0.387232	−	0.270538i
$921$		0			0
$922$	15.2725	−	13.5818i	0.502974	−	0.447294i
$923$	−41.5693			−1.36827
$924$		0			0
$925$	9.74984			0.320573
$926$	25.1148	−	22.3345i	0.825323	−	0.733958i
$927$		0			0
$928$	−14.2783	−	26.5920i	−0.468708	−	0.872924i
$929$	−19.5233			−0.640539			−0.320269	−	0.947326i	$-0.603773\pi$
$929$	−19.5233			−0.640539			−0.320269	+	0.947326i	$0.603773\pi$
$930$		0			0
$931$	42.5598	−	13.9643i	1.39484	−	0.457662i
$932$	−6.57290	+	55.8957i	−0.215303	+	1.83092i
$933$		0			0
$934$	−7.82752	−	8.80191i	−0.256124	−	0.288007i
$935$			13.9350i			0.455724i
$936$		0			0
$937$	−23.2904			−0.760864			−0.380432	−	0.924809i	$-0.624225\pi$
$937$	−23.2904			−0.760864			−0.380432	+	0.924809i	$0.624225\pi$
$938$	−12.0147	−	13.5103i	−0.392294	−	0.441128i
$939$		0			0
$940$	2.75219	−	23.4045i	0.0897664	−	0.763370i
$941$	−19.9893			−0.651633			−0.325816	−	0.945433i	$-0.605639\pi$
$941$	−19.9893			−0.651633			−0.325816	+	0.945433i	$0.605639\pi$
$942$		0			0
$943$	7.29593			0.237588
$944$	−0.675485	+	2.83243i	−0.0219852	+	0.0921879i
$945$		0			0
$946$	−25.7640	−	28.9711i	−0.837658	−	0.941932i
$947$	37.1453			1.20706			0.603530	−	0.797340i	$-0.293760\pi$
$947$	37.1453			1.20706			0.603530	+	0.797340i	$0.293760\pi$
$948$		0			0
$949$	−33.3292			−1.08191
$950$	11.1092	+	6.46263i	0.360429	+	0.209675i
$951$		0			0
$952$	21.4668	+	30.7264i	0.695744	+	0.995847i
$953$			7.44803i			0.241266i	0.992697	+	0.120633i	$0.0384923\pi$
$953$			7.44803i			0.241266i	−0.992697	+	0.120633i	$0.961508\pi$
$954$		0			0
$955$	16.9582			0.548754
$956$	41.0592	+	4.82825i	1.32795	+	0.156157i
$957$		0			0
$958$	−21.9771	+	19.5441i	−0.710046	+	0.631443i
$959$			31.0765i			1.00351i
$960$		0			0
$961$	−25.7797			−0.831602
$962$	−29.4334	−	33.0973i	−0.948970	−	1.06710i
$963$		0			0
$964$	−0.613070	−	0.0720923i	−0.0197457	−	0.00232194i
$965$	24.0406			0.773894
$966$		0			0
$967$		−	39.7937i		−	1.27968i	−0.768509	−	0.639839i	$-0.779001\pi$
$967$		−	39.7937i		−	1.27968i	0.768509	−	0.639839i	$-0.220999\pi$
$968$	−10.3109	+	7.20364i	−0.331404	+	0.231534i
$969$		0			0
$970$	−12.9105	−	14.5176i	−0.414531	−	0.466132i
$971$		−	13.6500i		−	0.438049i	−0.975719	−	0.219025i	$-0.929713\pi$
$971$		−	13.6500i		−	0.438049i	0.975719	−	0.219025i	$-0.0702875\pi$
$972$		0			0
$973$		−	45.1151i		−	1.44632i
$974$	−1.34215	−	1.50922i	−0.0430052	−	0.0483586i
$975$		0			0
$976$	5.24853	−	22.0080i	0.168001	−	0.704460i
$977$		−	2.58415i		−	0.0826742i	−0.999145	−	0.0413371i	$-0.986838\pi$
$977$		−	2.58415i		−	0.0826742i	0.999145	−	0.0413371i	$-0.0131618\pi$
$978$		0			0
$979$		−	27.2633i		−	0.871338i
$980$	34.8498	+	4.09806i	1.11324	+	0.130908i
$981$		0			0
$982$	−12.5247	−	14.0838i	−0.399679	−	0.449432i
$983$	21.5379			0.686953			0.343476	−	0.939161i	$-0.388395\pi$
$983$	21.5379			0.686953			0.343476	+	0.939161i	$0.388395\pi$
$984$		0			0
$985$	16.5621			0.527712
$986$	15.9874	+	17.9776i	0.509143	+	0.572522i
$987$		0			0
$988$	−11.5986	−	57.2216i	−0.369002	−	1.82046i
$989$		−	31.7739i		−	1.01035i
$990$		0			0
$991$	49.3048			1.56622			0.783109	−	0.621885i	$-0.213633\pi$
$991$	49.3048			1.56622			0.783109	+	0.621885i	$0.213633\pi$
$992$	−6.11421	−	11.3871i	−0.194126	−	0.361542i
$993$		0			0
$994$	−27.2637	+	24.2455i	−0.864751	+	0.769021i
$995$	−2.41955			−0.0767049
$996$		0			0
$997$			26.9528i			0.853604i	0.904345	+	0.426802i	$0.140360\pi$
$997$			26.9528i			0.853604i	−0.904345	+	0.426802i	$0.859640\pi$
$998$	−33.8064	−	38.0147i	−1.07012	−	1.20333i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.g.379.9		40
3.2	odd	2		456.2.e.a.379.32	yes	40
4.3	odd	2		5472.2.e.g.5167.2		40
8.3	odd	2	inner	1368.2.e.g.379.31		40
8.5	even	2		5472.2.e.g.5167.35		40
12.11	even	2		1824.2.e.a.1519.5		40
19.18	odd	2	inner	1368.2.e.g.379.32		40
24.5	odd	2		1824.2.e.a.1519.39		40
24.11	even	2		456.2.e.a.379.10	yes	40
57.56	even	2		456.2.e.a.379.9	✓	40
76.75	even	2		5472.2.e.g.5167.36		40
152.37	odd	2		5472.2.e.g.5167.1		40
152.75	even	2	inner	1368.2.e.g.379.10		40
228.227	odd	2		1824.2.e.a.1519.40		40
456.227	odd	2		456.2.e.a.379.31	yes	40
456.341	even	2		1824.2.e.a.1519.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.9	✓	40	57.56	even	2
456.2.e.a.379.10	yes	40	24.11	even	2
456.2.e.a.379.31	yes	40	456.227	odd	2
456.2.e.a.379.32	yes	40	3.2	odd	2
1368.2.e.g.379.9		40	1.1	even	1	trivial
1368.2.e.g.379.10		40	152.75	even	2	inner
1368.2.e.g.379.31		40	8.3	odd	2	inner
1368.2.e.g.379.32		40	19.18	odd	2	inner
1824.2.e.a.1519.5		40	12.11	even	2
1824.2.e.a.1519.6		40	456.341	even	2
1824.2.e.a.1519.39		40	24.5	odd	2
1824.2.e.a.1519.40		40	228.227	odd	2
5472.2.e.g.5167.1		40	152.37	odd	2
5472.2.e.g.5167.2		40	4.3	odd	2
5472.2.e.g.5167.35		40	8.5	even	2
5472.2.e.g.5167.36		40	76.75	even	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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939794 - 1.05678i) q^{2} +(-0.233575 + 1.98631i) q^{4} +1.70737i q^{5} +4.15645i q^{7} +(2.31861 - 1.61989i) q^{8} +O(q^{10})\)	\(q+(-0.939794 - 1.05678i) q^{2} +(-0.233575 + 1.98631i) q^{4} +1.70737i q^{5} +4.15645i q^{7} +(2.31861 - 1.61989i) q^{8} +(1.80431 - 1.60457i) q^{10} +2.55988 q^{11} +6.69724 q^{13} +(4.39246 - 3.90620i) q^{14} +(-3.89089 - 0.927907i) q^{16} +3.18831 q^{17} +(-4.14166 + 1.35892i) q^{19} +(-3.39136 - 0.398798i) q^{20} +(-2.40576 - 2.70524i) q^{22} -2.96695i q^{23} +2.08490 q^{25} +(-6.29403 - 7.07753i) q^{26} +(-8.25600 - 0.970842i) q^{28} -5.33562 q^{29} -2.28480 q^{31} +(2.67603 + 4.98386i) q^{32} +(-2.99636 - 3.36935i) q^{34} -7.09657 q^{35} +4.67640 q^{37} +(5.32839 + 3.09973i) q^{38} +(2.76574 + 3.95872i) q^{40} +2.45906i q^{41} +10.7093 q^{43} +(-0.597925 + 5.08473i) q^{44} +(-3.13542 + 2.78832i) q^{46} +6.90120i q^{47} -10.2760 q^{49} +(-1.95938 - 2.20329i) q^{50} +(-1.56431 + 13.3028i) q^{52} -0.126777 q^{53} +4.37066i q^{55} +(6.73297 + 9.63719i) q^{56} +(5.01438 + 5.63858i) q^{58} -0.727966i q^{59} +5.65631i q^{61} +(2.14724 + 2.41454i) q^{62} +(2.75193 - 7.51178i) q^{64} +11.4346i q^{65} -3.07580i q^{67} +(-0.744710 + 6.33299i) q^{68} +(6.66931 + 7.49953i) q^{70} -6.20693 q^{71} -4.97655 q^{73} +(-4.39485 - 4.94193i) q^{74} +(-1.73185 - 8.54404i) q^{76} +10.6400i q^{77} +7.98062 q^{79} +(1.58428 - 6.64316i) q^{80} +(2.59869 - 2.31101i) q^{82} -17.8223 q^{83} +5.44361i q^{85} +(-10.0645 - 11.3174i) q^{86} +(5.93538 - 4.14672i) q^{88} -10.6502i q^{89} +27.8367i q^{91} +(5.89330 + 0.693007i) q^{92} +(7.29307 - 6.48571i) q^{94} +(-2.32017 - 7.07132i) q^{95} -8.04606i q^{97} +(9.65736 + 10.8595i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4}+O(q^{10}) \) 40 * q - 4 * q^4	\( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more