LMFDB - Embedded newform 252.4.x.a.41.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, degree $2$, 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.7
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.07854 - 3.21955i) q^{3} +(0.330097 - 0.571745i) q^{5} +(-15.6440 - 9.91296i) q^{7} +(6.26899 + 26.2621i) q^{9} +O(q^{10})$	\(q+(-4.07854 - 3.21955i) q^{3} +(0.330097 - 0.571745i) q^{5} +(-15.6440 - 9.91296i) q^{7} +(6.26899 + 26.2621i) q^{9} +(21.4150 - 12.3640i) q^{11} +(-43.5283 - 25.1311i) q^{13} +(-3.18708 + 1.26912i) q^{15} -67.5530 q^{17} +62.9647i q^{19} +(31.8892 + 90.7969i) q^{21} +(135.811 + 78.4107i) q^{23} +(62.2821 + 107.876i) q^{25} +(58.9839 - 127.295i) q^{27} +(-129.859 + 74.9743i) q^{29} +(139.518 + 80.5507i) q^{31} +(-127.149 - 18.5198i) q^{33} +(-10.8317 + 5.67211i) q^{35} -16.2664 q^{37} +(96.6211 + 242.639i) q^{39} +(-134.901 + 233.655i) q^{41} +(188.088 + 325.779i) q^{43} +(17.0846 + 5.08479i) q^{45} +(-31.3735 - 54.3405i) q^{47} +(146.467 + 310.156i) q^{49} +(275.518 + 217.490i) q^{51} -136.820i q^{53} -16.3253i q^{55} +(202.718 - 256.804i) q^{57} +(-358.829 + 621.509i) q^{59} +(23.9682 - 13.8380i) q^{61} +(162.264 - 472.988i) q^{63} +(-28.7371 + 16.5914i) q^{65} +(-163.773 + 283.664i) q^{67} +(-301.465 - 757.052i) q^{69} -246.304i q^{71} +261.253i q^{73} +(93.2913 - 640.496i) q^{75} +(-457.579 - 18.8649i) q^{77} +(-391.980 - 678.930i) q^{79} +(-650.399 + 329.274i) q^{81} +(-599.424 - 1038.23i) q^{83} +(-22.2990 + 38.6231i) q^{85} +(771.020 + 112.303i) q^{87} -968.771 q^{89} +(431.831 + 824.643i) q^{91} +(-309.692 - 777.714i) q^{93} +(35.9997 + 20.7845i) q^{95} +(1106.79 - 639.005i) q^{97} +(458.955 + 484.895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	−4.07854	−	3.21955i	−0.784916	−	0.619603i
$3$	−4.07854	−	3.21955i	−0.784916	−	0.619603i
$4$		0			0
$5$	0.330097	−	0.571745i	0.0295248	−	0.0511384i	−0.850885	−	0.525351i	$-0.823934\pi$
$5$	0.330097	−	0.571745i	0.0295248	−	0.0511384i	0.880410	+	0.474213i	$0.157267\pi$
$6$		0			0
$7$	−15.6440	−	9.91296i	−0.844694	−	0.535249i
$7$	−15.6440	−	9.91296i	−0.844694	−	0.535249i
$8$		0			0
$9$	6.26899	+	26.2621i	0.232185	+	0.972672i
$10$		0			0
$11$	21.4150	−	12.3640i	0.586989	−	0.338898i	−0.176917	−	0.984226i	$-0.556612\pi$
$11$	21.4150	−	12.3640i	0.586989	−	0.338898i	0.763906	+	0.645328i	$0.223279\pi$
$12$		0			0
$13$	−43.5283	−	25.1311i	−0.928659	−	0.536162i	−0.0422718	−	0.999106i	$-0.513460\pi$
$13$	−43.5283	−	25.1311i	−0.928659	−	0.536162i	−0.886387	+	0.462945i	$0.846793\pi$
$14$		0			0
$15$	−3.18708	+	1.26912i	−0.0548600	+	0.0218457i
$16$		0			0
$17$	−67.5530			−0.963765			−0.481882	−	0.876236i	$-0.660047\pi$
$17$	−67.5530			−0.963765			−0.481882	+	0.876236i	$0.660047\pi$
$18$		0			0
$19$			62.9647i			0.760268i	0.924932	+	0.380134i	$0.124122\pi$
$19$			62.9647i			0.760268i	−0.924932	+	0.380134i	$0.875878\pi$
$20$		0			0
$21$	31.8892	+	90.7969i	0.331372	+	0.943500i
$22$		0			0
$23$	135.811	+	78.4107i	1.23124	+	0.710859i	0.967289	−	0.253676i	$-0.0816398\pi$
$23$	135.811	+	78.4107i	1.23124	+	0.710859i	0.263954	+	0.964535i	$0.414973\pi$
$24$		0			0
$25$	62.2821	+	107.876i	0.498257	+	0.863006i
$26$		0			0
$27$	58.9839	−	127.295i	0.420424	−	0.907328i
$28$		0			0
$29$	−129.859	+	74.9743i	−0.831527	+	0.480082i	−0.854375	−	0.519657i	$-0.826060\pi$
$29$	−129.859	+	74.9743i	−0.831527	+	0.480082i	0.0228484	+	0.999739i	$0.492727\pi$
$30$		0			0
$31$	139.518	+	80.5507i	0.808327	+	0.466688i	0.846375	−	0.532588i	$-0.178780\pi$
$31$	139.518	+	80.5507i	0.808327	+	0.466688i	−0.0380475	+	0.999276i	$0.512114\pi$
$32$		0			0
$33$	−127.149	−	18.5198i	−0.670719	−	0.0976934i
$34$		0			0
$35$	−10.8317	+	5.67211i	−0.0523112	+	0.0273932i
$36$		0			0
$37$	−16.2664			−0.0722753			−0.0361377	−	0.999347i	$-0.511505\pi$
$37$	−16.2664			−0.0722753			−0.0361377	+	0.999347i	$0.511505\pi$
$38$		0			0
$39$	96.6211	+	242.639i	0.396712	+	0.996241i
$40$		0			0
$41$	−134.901	+	233.655i	−0.513853	+	0.890019i	0.486018	+	0.873949i	$0.338449\pi$
$41$	−134.901	+	233.655i	−0.513853	+	0.890019i	−0.999871	+	0.0160703i	$0.994884\pi$
$42$		0			0
$43$	188.088	+	325.779i	0.667051	+	1.15537i	0.978725	+	0.205178i	$0.0657772\pi$
$43$	188.088	+	325.779i	0.667051	+	1.15537i	−0.311673	+	0.950189i	$0.600889\pi$
$44$		0			0
$45$	17.0846	+	5.08479i	0.0565961	+	0.0168444i
$46$		0			0
$47$	−31.3735	−	54.3405i	−0.0973679	−	0.168646i	0.813226	−	0.581947i	$-0.197709\pi$
$47$	−31.3735	−	54.3405i	−0.0973679	−	0.168646i	−0.910594	+	0.413301i	$0.864376\pi$
$48$		0			0
$49$	146.467	+	310.156i	0.427016	+	0.904244i
$50$		0			0
$51$	275.518	+	217.490i	0.756474	+	0.597151i
$52$		0			0
$53$		−	136.820i		−	0.354597i	−0.984157	−	0.177299i	$-0.943264\pi$
$53$		−	136.820i		−	0.354597i	0.984157	−	0.177299i	$-0.0567358\pi$
$54$		0			0
$55$		−	16.3253i		−	0.0400236i
$56$		0			0
$57$	202.718	−	256.804i	0.471064	−	0.596746i
$58$		0			0
$59$	−358.829	+	621.509i	−0.791788	+	1.37142i	0.133070	+	0.991107i	$0.457516\pi$
$59$	−358.829	+	621.509i	−0.791788	+	1.37142i	−0.924859	+	0.380311i	$0.875817\pi$
$60$		0			0
$61$	23.9682	−	13.8380i	0.0503083	−	0.0290455i	−0.474635	−	0.880183i	$-0.657420\pi$
$61$	23.9682	−	13.8380i	0.0503083	−	0.0290455i	0.524943	+	0.851137i	$0.324087\pi$
$62$		0			0
$63$	162.264	−	472.988i	0.324497	−	0.945887i
$64$		0			0
$65$	−28.7371	+	16.5914i	−0.0548369	+	0.0316601i
$66$		0			0
$67$	−163.773	+	283.664i	−0.298628	+	0.517239i	−0.975822	−	0.218565i	$-0.929862\pi$
$67$	−163.773	+	283.664i	−0.298628	+	0.517239i	0.677194	+	0.735804i	$0.263196\pi$
$68$		0			0
$69$	−301.465	−	757.052i	−0.525972	−	1.32085i
$70$		0			0
$71$		−	246.304i		−	0.411703i	−0.978583	−	0.205852i	$-0.934004\pi$
$71$		−	246.304i		−	0.411703i	0.978583	−	0.205852i	$-0.0659965\pi$
$72$		0			0
$73$			261.253i			0.418868i	0.977823	+	0.209434i	$0.0671622\pi$
$73$			261.253i			0.418868i	−0.977823	+	0.209434i	$0.932838\pi$
$74$		0			0
$75$	93.2913	−	640.496i	0.143631	−	0.986108i
$76$		0			0
$77$	−457.579	−	18.8649i	−0.677221	−	0.0279201i
$78$		0			0
$79$	−391.980	−	678.930i	−0.558244	−	0.966906i	−0.997643	−	0.0686145i	$-0.978142\pi$
$79$	−391.980	−	678.930i	−0.558244	−	0.966906i	0.439400	−	0.898292i	$-0.355191\pi$
$80$		0			0
$81$	−650.399	+	329.274i	−0.892180	+	0.451679i
$82$		0			0
$83$	−599.424	−	1038.23i	−0.792715	−	1.37302i	−0.924280	−	0.381715i	$-0.875334\pi$
$83$	−599.424	−	1038.23i	−0.792715	−	1.37302i	0.131565	−	0.991308i	$-0.458000\pi$
$84$		0			0
$85$	−22.2990	+	38.6231i	−0.0284550	+	0.0492854i
$86$		0			0
$87$	771.020	+	112.303i	0.950139	+	0.138392i
$88$		0			0
$89$	−968.771			−1.15381			−0.576907	−	0.816810i	$-0.695741\pi$
$89$	−968.771			−1.15381			−0.576907	+	0.816810i	$0.695741\pi$
$90$		0			0
$91$	431.831	+	824.643i	0.497453	+	0.949957i
$92$		0			0
$93$	−309.692	−	777.714i	−0.345307	−	0.867152i
$94$		0			0
$95$	35.9997	+	20.7845i	0.0388789	+	0.0224467i
$96$		0			0
$97$	1106.79	−	639.005i	1.15853	−	0.668878i	0.207579	−	0.978218i	$-0.433442\pi$
$97$	1106.79	−	639.005i	1.15853	−	0.668878i	0.950951	+	0.309340i	$0.100108\pi$
$98$		0			0
$99$	458.955	+	484.895i	0.465927	+	0.492260i
$100$		0			0
$101$	285.125	+	493.852i	0.280901	+	0.486535i	0.971607	−	0.236601i	$-0.0760333\pi$
$101$	285.125	+	493.852i	0.280901	+	0.486535i	−0.690706	+	0.723136i	$0.742700\pi$
$102$		0			0
$103$	1559.24	+	900.228i	1.49162	+	0.861186i	0.999954	−	0.00959990i	$-0.00305579\pi$
$103$	1559.24	+	900.228i	1.49162	+	0.861186i	0.491663	+	0.870785i	$0.336389\pi$
$104$		0			0
$105$	62.4392	+	11.7393i	0.0580328	+	0.0109108i
$106$		0			0
$107$		−	2038.95i		−	1.84218i	−0.389350	−	0.921090i	$-0.627300\pi$
$107$		−	2038.95i		−	1.84218i	0.389350	−	0.921090i	$-0.372700\pi$
$108$		0			0
$109$	−1189.58			−1.04533			−0.522666	−	0.852538i	$-0.675062\pi$
$109$	−1189.58			−1.04533			−0.522666	+	0.852538i	$0.675062\pi$
$110$		0			0
$111$	66.3434	+	52.3706i	0.0567300	+	0.0447820i
$112$		0			0
$113$	−646.454	−	373.230i	−0.538171	−	0.310713i	0.206167	−	0.978517i	$-0.433901\pi$
$113$	−646.454	−	373.230i	−0.538171	−	0.310713i	−0.744337	+	0.667804i	$0.767234\pi$
$114$		0			0
$115$	89.6618	−	51.7663i	0.0727044	−	0.0419759i
$116$		0			0
$117$	387.117	−	1300.69i	0.305889	−	1.02777i
$118$		0			0
$119$	1056.80	+	669.650i	0.814086	+	0.515854i
$120$		0			0
$121$	−359.764	+	623.130i	−0.270296	+	0.468167i
$122$		0			0
$123$	1302.46	−	518.652i	0.954789	−	0.380205i
$124$		0			0
$125$	164.761			0.117893
$126$		0			0
$127$	−1832.75			−1.28055			−0.640277	−	0.768144i	$-0.721180\pi$
$127$	−1832.75			−1.28055			−0.640277	+	0.768144i	$0.721180\pi$
$128$		0			0
$129$	281.735	−	1934.26i	0.192289	−	1.32017i
$130$		0			0
$131$	−235.639	+	408.138i	−0.157159	+	0.272208i	−0.933843	−	0.357683i	$-0.883567\pi$
$131$	−235.639	+	408.138i	−0.157159	+	0.272208i	0.776684	+	0.629890i	$0.216900\pi$
$132$		0			0
$133$	624.166	−	985.016i	0.406933	−	0.642194i
$134$		0			0
$135$	−53.3096	−	75.7433i	−0.0339864	−	0.0482885i
$136$		0			0
$137$	−2271.58	+	1311.50i	−1.41660	+	0.817874i	−0.995998	−	0.0893720i	$-0.971514\pi$
$137$	−2271.58	+	1311.50i	−1.41660	+	0.817874i	−0.420601	+	0.907246i	$0.638181\pi$
$138$		0			0
$139$	164.415	+	94.9252i	0.100328	+	0.0579241i	0.549324	−	0.835609i	$-0.314885\pi$
$139$	164.415	+	94.9252i	0.100328	+	0.0579241i	−0.448997	+	0.893533i	$0.648219\pi$
$140$		0			0
$141$	−46.9938	+	322.638i	−0.0280680	+	0.192702i
$142$		0			0
$143$	−1242.88			−0.726817
$144$		0			0
$145$			98.9953i			0.0566973i
$146$		0			0
$147$	401.192	−	1736.54i	0.225100	−	0.974336i
$148$		0			0
$149$	−383.974	−	221.687i	−0.211117	−	0.121888i	0.390714	−	0.920512i	$-0.372228\pi$
$149$	−383.974	−	221.687i	−0.211117	−	0.121888i	−0.601830	+	0.798624i	$0.705562\pi$
$150$		0			0
$151$	943.459	+	1634.12i	0.508461	+	0.880680i	0.999952	+	0.00979739i	$0.00311865\pi$
$151$	943.459	+	1634.12i	0.508461	+	0.880680i	−0.491491	+	0.870883i	$0.663548\pi$
$152$		0			0
$153$	−423.489	−	1774.09i	−0.223772	−	0.937427i
$154$		0			0
$155$	92.1089	−	53.1791i	0.0477314	−	0.0275577i
$156$		0			0
$157$	2133.22	+	1231.62i	1.08439	+	0.626075i	0.932078	−	0.362257i	$-0.117994\pi$
$157$	2133.22	+	1231.62i	1.08439	+	0.626075i	0.152316	+	0.988332i	$0.451327\pi$
$158$		0			0
$159$	−440.498	+	558.025i	−0.219709	+	0.278329i
$160$		0			0
$161$	−1347.34	−	2572.94i	−0.659537	−	1.25948i
$162$		0			0
$163$	2514.36			1.20822			0.604111	−	0.796900i	$-0.293528\pi$
$163$	2514.36			1.20822			0.604111	+	0.796900i	$0.293528\pi$
$164$		0			0
$165$	−52.5600	+	66.5832i	−0.0247987	+	0.0314151i
$166$		0			0
$167$	−1415.81	+	2452.25i	−0.656038	+	1.13629i	0.325594	+	0.945510i	$0.394436\pi$
$167$	−1415.81	+	2452.25i	−0.656038	+	1.13629i	−0.981632	+	0.190782i	$0.938898\pi$
$168$		0			0
$169$	164.640	+	285.164i	0.0749385	+	0.129797i
$170$		0			0
$171$	−1653.59	+	394.725i	−0.739491	+	0.176523i
$172$		0			0
$173$	−667.439	−	1156.04i	−0.293320	−	0.508046i	0.681272	−	0.732030i	$-0.261427\pi$
$173$	−667.439	−	1156.04i	−0.293320	−	0.508046i	−0.974593	+	0.223984i	$0.928094\pi$
$174$		0			0
$175$	95.0295	−	2305.00i	0.0410489	−	0.995667i
$176$		0			0
$177$	3464.48	−	1379.58i	1.47122	−	0.585853i
$178$		0			0
$179$			1431.23i			0.597626i	0.954312	+	0.298813i	$0.0965907\pi$
$179$			1431.23i			0.597626i	−0.954312	+	0.298813i	$0.903409\pi$
$180$		0			0
$181$			262.769i			0.107909i	0.998543	+	0.0539543i	$0.0171825\pi$
$181$			262.769i			0.107909i	−0.998543	+	0.0539543i	$0.982817\pi$
$182$		0			0
$183$	−142.307	−	20.7278i	−0.0574845	−	0.00837289i
$184$		0			0
$185$	−5.36951	+	9.30026i	−0.00213391	+	0.00369605i
$186$		0			0
$187$	−1446.65	+	835.223i	−0.565719	+	0.326618i
$188$		0			0
$189$	−2184.61	+	1406.68i	−0.840777	+	0.541382i
$190$		0			0
$191$	−97.8990	+	56.5220i	−0.0370876	+	0.0214125i	−0.518429	−	0.855121i	$-0.673483\pi$
$191$	−97.8990	+	56.5220i	−0.0370876	+	0.0214125i	0.481342	+	0.876533i	$0.340150\pi$
$192$		0			0
$193$	−2091.54	+	3622.65i	−0.780063	+	1.35111i	0.151842	+	0.988405i	$0.451480\pi$
$193$	−2091.54	+	3622.65i	−0.780063	+	1.35111i	−0.931905	+	0.362704i	$0.881854\pi$
$194$		0			0
$195$	170.622	+	24.8520i	0.0626591	+	0.00912659i
$196$		0			0
$197$			314.320i			0.113677i	0.998383	+	0.0568385i	$0.0181020\pi$
$197$			314.320i			0.113677i	−0.998383	+	0.0568385i	$0.981898\pi$
$198$		0			0
$199$			1407.97i			0.501550i	0.968045	+	0.250775i	$0.0806855\pi$
$199$			1407.97i			0.501550i	−0.968045	+	0.250775i	$0.919314\pi$
$200$		0			0
$201$	1581.23	−	629.658i	0.554881	−	0.220958i
$202$		0			0
$203$	2774.73	+	114.395i	0.959349	+	0.0395516i
$204$		0			0
$205$	89.0607	+	154.258i	0.0303428	+	0.0525552i
$206$		0			0
$207$	−1207.83	+	4058.25i	−0.405556	+	1.36265i
$208$		0			0
$209$	778.494	+	1348.39i	0.257653	+	0.446269i
$210$		0			0
$211$	−73.9358	+	128.061i	−0.0241230	+	0.0417822i	−0.877835	−	0.478963i	$-0.841013\pi$
$211$	−73.9358	+	128.061i	−0.0241230	+	0.0417822i	0.853712	+	0.520746i	$0.174346\pi$
$212$		0			0
$213$	−792.989	+	1004.56i	−0.255093	+	0.323152i
$214$		0			0
$215$	248.350			0.0787782
$216$		0			0
$217$	−1384.12	−	2643.16i	−0.432995	−	0.826865i
$218$		0			0
$219$	841.118	−	1065.53i	0.259532	−	0.328776i
$220$		0			0
$221$	2940.46	+	1697.68i	0.895009	+	0.516734i
$222$		0			0
$223$	−2005.48	+	1157.86i	−0.602228	+	0.347696i	−0.769917	−	0.638143i	$-0.779703\pi$
$223$	−2005.48	+	1157.86i	−0.602228	+	0.347696i	0.167690	+	0.985840i	$0.446369\pi$
$224$		0			0
$225$	−2442.60	+	2311.93i	−0.723734	+	0.685017i
$226$		0			0
$227$	−2233.35	−	3868.27i	−0.653006	−	1.13104i	−0.982390	−	0.186843i	$-0.940174\pi$
$227$	−2233.35	−	3868.27i	−0.653006	−	1.13104i	0.329384	−	0.944196i	$-0.393159\pi$
$228$		0			0
$229$	−1016.15	−	586.677i	−0.293229	−	0.169296i	0.346168	−	0.938172i	$-0.387483\pi$
$229$	−1016.15	−	586.677i	−0.293229	−	0.169296i	−0.639397	+	0.768877i	$0.720816\pi$
$230$		0			0
$231$	1805.52	+	1550.14i	0.514262	+	0.441523i
$232$		0			0
$233$		−	1751.08i		−	0.492347i	−0.969226	−	0.246173i	$-0.920827\pi$
$233$		−	1751.08i		−	0.492347i	0.969226	−	0.246173i	$-0.0791733\pi$
$234$		0			0
$235$	−41.4252			−0.0114991
$236$		0			0
$237$	−587.141	+	4031.04i	−0.160924	+	1.10483i
$238$		0			0
$239$	5007.40	+	2891.03i	1.35524	+	0.782447i	0.988978	−	0.148065i	$-0.0473045\pi$
$239$	5007.40	+	2891.03i	1.35524	+	0.782447i	0.366261	+	0.930512i	$0.380638\pi$
$240$		0			0
$241$	230.468	−	133.061i	0.0616005	−	0.0355651i	−0.468883	−	0.883260i	$-0.655344\pi$
$241$	230.468	−	133.061i	0.0616005	−	0.0355651i	0.530484	+	0.847695i	$0.322010\pi$
$242$		0			0
$243$	3712.80	+	751.035i	0.980148	+	0.198267i
$244$		0			0
$245$	225.678	+	18.6400i	0.0588492	+	0.00486067i
$246$		0			0
$247$	1582.37	−	2740.74i	0.407626	−	0.706029i
$248$		0			0
$249$	−897.867	+	6164.35i	−0.228514	+	1.56887i
$250$		0			0
$251$	7212.14			1.81365			0.906826	−	0.421506i	$-0.138498\pi$
$251$	7212.14			1.81365			0.906826	+	0.421506i	$0.138498\pi$
$252$		0			0
$253$	3877.87			0.963635
$254$		0			0
$255$	215.297	−	85.7329i	0.0528721	−	0.0210541i
$256$		0			0
$257$	−2752.31	+	4767.14i	−0.668033	+	1.15707i	0.310421	+	0.950599i	$0.399530\pi$
$257$	−2752.31	+	4767.14i	−0.668033	+	1.15707i	−0.978453	+	0.206468i	$0.933803\pi$
$258$		0			0
$259$	254.471	+	161.249i	0.0610505	+	0.0386853i
$260$		0			0
$261$	−2783.07	−	2940.37i	−0.660030	−	0.697335i
$262$		0			0
$263$	−4088.19	+	2360.32i	−0.958511	+	0.553396i	−0.895714	−	0.444630i	$-0.853335\pi$
$263$	−4088.19	+	2360.32i	−0.958511	+	0.553396i	−0.0627964	+	0.998026i	$0.520002\pi$
$264$		0			0
$265$	−78.2261	−	45.1639i	−0.0181336	−	0.0104694i
$266$		0			0
$267$	3951.17	+	3119.01i	0.905647	+	0.714907i
$268$		0			0
$269$	3595.18			0.814877			0.407439	−	0.913233i	$-0.366422\pi$
$269$	3595.18			0.814877			0.407439	+	0.913233i	$0.366422\pi$
$270$		0			0
$271$			3673.66i			0.823466i	0.911305	+	0.411733i	$0.135076\pi$
$271$			3673.66i			0.823466i	−0.911305	+	0.411733i	$0.864924\pi$
$272$		0			0
$273$	893.739	−	4753.64i	0.198137	−	1.05386i
$274$		0			0
$275$	2667.55	+	1540.11i	0.584942	+	0.337716i
$276$		0			0
$277$	880.297	+	1524.72i	0.190946	+	0.330727i	0.945564	−	0.325437i	$-0.105511\pi$
$277$	880.297	+	1524.72i	0.190946	+	0.330727i	−0.754618	+	0.656164i	$0.772178\pi$
$278$		0			0
$279$	−1240.80	+	4169.01i	−0.266253	+	0.894595i
$280$		0			0
$281$	−6960.95	+	4018.91i	−1.47778	+	0.853195i	−0.999685	−	0.0251141i	$-0.992005\pi$
$281$	−6960.95	+	4018.91i	−1.47778	+	0.853195i	−0.478093	+	0.878309i	$0.658672\pi$
$282$		0			0
$283$	−6519.11	−	3763.81i	−1.36933	−	0.790584i	−0.378488	−	0.925606i	$-0.623556\pi$
$283$	−6519.11	−	3763.81i	−1.36933	−	0.790584i	−0.990843	+	0.135022i	$0.956889\pi$
$284$		0			0
$285$	−79.9098	−	200.673i	−0.0166086	−	0.0417083i
$286$		0			0
$287$	4426.59	−	2318.02i	0.910430	−	0.476754i
$288$		0			0
$289$	−349.597			−0.0711575
$290$		0			0
$291$	−6571.40	−	957.156i	−1.32379	−	0.192816i
$292$		0			0
$293$	−105.807	+	183.262i	−0.0210965	+	0.0365403i	−0.876381	−	0.481619i	$-0.840049\pi$
$293$	−105.807	+	183.262i	−0.0210965	+	0.0365403i	0.855284	+	0.518159i	$0.173382\pi$
$294$		0			0
$295$	236.897	+	410.317i	0.0467548	+	0.0809816i
$296$		0			0
$297$	−310.724	−	3455.29i	−0.0607072	−	0.675072i
$298$		0			0
$299$	−3941.08	−	6826.16i	−0.762270	−	1.32029i
$300$		0			0
$301$	286.984	−	6960.98i	0.0549551	−	1.33297i
$302$		0			0
$303$	427.085	−	2932.17i	0.0809748	−	0.555937i
$304$		0			0
$305$		−	18.2716i		−	0.00343025i
$306$		0			0
$307$		−	2701.00i		−	0.502131i	−0.967970	−	0.251065i	$-0.919219\pi$
$307$		−	2701.00i		−	0.502131i	0.967970	−	0.251065i	$-0.0807809\pi$
$308$		0			0
$309$	−3461.10	−	8691.67i	−0.637201	−	1.60017i
$310$		0			0
$311$	3234.86	−	5602.95i	0.589815	−	1.02159i	−0.404442	−	0.914564i	$-0.632534\pi$
$311$	3234.86	−	5602.95i	0.589815	−	1.02159i	0.994256	−	0.107025i	$-0.0341325\pi$
$312$		0			0
$313$	−1476.26	+	852.319i	−0.266592	+	0.153917i	−0.627338	−	0.778747i	$-0.715855\pi$
$313$	−1476.26	+	852.319i	−0.266592	+	0.153917i	0.360746	+	0.932664i	$0.382522\pi$
$314$		0			0
$315$	−216.866	−	248.905i	−0.0387905	−	0.0445214i
$316$		0			0
$317$	1247.17	−	720.056i	0.220972	−	0.127578i	−0.385428	−	0.922738i	$-0.625946\pi$
$317$	1247.17	−	720.056i	0.220972	−	0.127578i	0.606400	+	0.795159i	$0.292613\pi$
$318$		0			0
$319$	−1853.96	+	3211.16i	−0.325398	+	0.563606i
$320$		0			0
$321$	−6564.52	+	8315.96i	−1.14142	+	1.44596i
$322$		0			0
$323$		−	4253.45i		−	0.732719i
$324$		0			0
$325$		−	6260.86i		−	1.06858i
$326$		0			0
$327$	4851.75	+	3829.91i	0.820497	+	0.647690i
$328$		0			0
$329$	−47.8694	+	1161.10i	−0.00802166	+	0.194571i
$330$		0			0
$331$	−5661.53	−	9806.05i	−0.940138	−	1.62837i	−0.765205	−	0.643786i	$-0.777363\pi$
$331$	−5661.53	−	9806.05i	−0.940138	−	1.62837i	−0.174932	−	0.984580i	$-0.555971\pi$
$332$		0			0
$333$	−101.974	−	427.191i	−0.0167812	−	0.0703002i
$334$		0			0
$335$	108.122	+	187.273i	0.0176339	+	0.0305428i
$336$		0			0
$337$	−1069.77	+	1852.89i	−0.172920	+	0.299505i	−0.939439	−	0.342715i	$-0.888653\pi$
$337$	−1069.77	+	1852.89i	−0.172920	+	0.299505i	0.766520	+	0.642221i	$0.221987\pi$
$338$		0			0
$339$	1434.96	+	3603.53i	0.229900	+	0.577335i
$340$		0			0
$341$	3983.71			0.632639
$342$		0			0
$343$	783.244	−	6303.98i	0.123298	−	0.992370i
$344$		0			0
$345$	−532.354	−	77.5399i	−0.0830752	−	0.0121003i
$346$		0			0
$347$	3237.97	+	1869.44i	0.500931	+	0.289213i	0.729098	−	0.684409i	$-0.239940\pi$
$347$	3237.97	+	1869.44i	0.500931	+	0.289213i	−0.228167	+	0.973622i	$0.573273\pi$
$348$		0			0
$349$	5644.28	−	3258.72i	0.865705	−	0.499815i	−0.000213394	−	1.00000i	$-0.500068\pi$
$349$	5644.28	−	3258.72i	0.865705	−	0.499815i	0.865919	+	0.500185i	$0.166735\pi$
$350$		0			0
$351$	−5766.51	+	4058.58i	−0.876905	+	0.617183i
$352$		0			0
$353$	1772.88	+	3070.72i	0.267312	+	0.462998i	0.968167	−	0.250306i	$-0.0805313\pi$
$353$	1772.88	+	3070.72i	0.267312	+	0.462998i	−0.700855	+	0.713304i	$0.747198\pi$
$354$		0			0
$355$	−140.823	−	81.3044i	−0.0210539	−	0.0121555i
$356$		0			0
$357$	−2154.21	−	6133.60i	−0.319364	−	0.909312i
$358$		0			0
$359$		−	6414.84i		−	0.943071i	−0.881847	−	0.471535i	$-0.843700\pi$
$359$		−	6414.84i		−	0.943071i	0.881847	−	0.471535i	$-0.156300\pi$
$360$		0			0
$361$	2894.45			0.421993
$362$		0			0
$363$	3473.51	−	1383.18i	0.502237	−	0.199995i
$364$		0			0
$365$	149.370	+	86.2390i	0.0214203	+	0.0123670i
$366$		0			0
$367$	−6771.55	+	3909.55i	−0.963139	+	0.556068i	−0.897138	−	0.441751i	$-0.854357\pi$
$367$	−6771.55	+	3909.55i	−0.963139	+	0.556068i	−0.0660011	+	0.997820i	$0.521024\pi$
$368$		0			0
$369$	−6981.97	−	2078.00i	−0.985005	−	0.293161i
$370$		0			0
$371$	−1356.29	+	2140.40i	−0.189798	+	0.299526i
$372$		0			0
$373$	5548.13	−	9609.65i	0.770165	−	1.33396i	−0.167307	−	0.985905i	$-0.553507\pi$
$373$	5548.13	−	9609.65i	0.770165	−	1.33396i	0.937472	−	0.348060i	$-0.113159\pi$
$374$		0			0
$375$	−671.984	−	530.456i	−0.0925363	−	0.0730470i
$376$		0			0
$377$	7536.74			1.02961
$378$		0			0
$379$	−5192.03			−0.703686			−0.351843	−	0.936059i	$-0.614445\pi$
$379$	−5192.03			−0.703686			−0.351843	+	0.936059i	$0.614445\pi$
$380$		0			0
$381$	7474.95	+	5900.63i	1.00513	+	0.793435i
$382$		0			0
$383$	6875.13	−	11908.1i	0.917240	−	1.58871i	0.113652	−	0.993521i	$-0.463745\pi$
$383$	6875.13	−	11908.1i	0.917240	−	1.58871i	0.803588	−	0.595186i	$-0.202922\pi$
$384$		0			0
$385$	−161.832	+	255.392i	−0.0214226	+	0.0338077i
$386$		0			0
$387$	−7376.52	+	6981.91i	−0.968913	+	0.917081i
$388$		0			0
$389$	−8425.29	+	4864.34i	−1.09815	+	0.634016i	−0.935734	−	0.352707i	$-0.885261\pi$
$389$	−8425.29	+	4864.34i	−1.09815	+	0.634016i	−0.162413	+	0.986723i	$0.551928\pi$
$390$		0			0
$391$	−9174.45	−	5296.87i	−1.18663	−	0.685101i
$392$		0			0
$393$	2275.08	−	905.958i	0.292017	−	0.116284i
$394$		0			0
$395$	−517.567			−0.0659281
$396$		0			0
$397$			9192.44i			1.16210i	0.813866	+	0.581052i	$0.197359\pi$
$397$			9192.44i			1.16210i	−0.813866	+	0.581052i	$0.802641\pi$
$398$		0			0
$399$	−5717.00	+	2007.90i	−0.717313	+	0.251931i
$400$		0			0
$401$	7796.50	+	4501.31i	0.970919	+	0.560560i	0.899516	−	0.436887i	$-0.143919\pi$
$401$	7796.50	+	4501.31i	0.970919	+	0.560560i	0.0714027	+	0.997448i	$0.477252\pi$
$402$		0			0
$403$	−4048.65	−	7012.46i	−0.500440	−	0.866788i
$404$		0			0
$405$	−26.4341	+	480.555i	−0.00324326	+	0.0589604i
$406$		0			0
$407$	−348.346	+	201.118i	−0.0424248	+	0.0244940i
$408$		0			0
$409$	4580.39	+	2644.49i	0.553755	+	0.319711i	0.750635	−	0.660717i	$-0.229748\pi$
$409$	4580.39	+	2644.49i	0.553755	+	0.319711i	−0.196880	+	0.980428i	$0.563081\pi$
$410$		0			0
$411$	13487.2	+	1964.47i	1.61867	+	0.235767i
$412$		0			0
$413$	11774.5	−	6165.81i	1.40287	−	0.734624i
$414$		0			0
$415$	−791.473			−0.0936190
$416$		0			0
$417$	−364.958	−	916.500i	−0.0428587	−	0.107629i
$418$		0			0
$419$	2805.44	−	4859.17i	0.327100	−	0.566554i	−0.654835	−	0.755772i	$-0.727262\pi$
$419$	2805.44	−	4859.17i	0.327100	−	0.566554i	0.981935	+	0.189218i	$0.0605953\pi$
$420$		0			0
$421$	−641.365	−	1110.88i	−0.0742475	−	0.128600i	0.826511	−	0.562920i	$-0.190322\pi$
$421$	−641.365	−	1110.88i	−0.0742475	−	0.128600i	−0.900759	+	0.434320i	$0.856989\pi$
$422$		0			0
$423$	1230.42	−	1164.59i	0.141430	−	0.133864i
$424$		0			0
$425$	−4207.34	−	7287.32i	−0.480202	−	0.831734i
$426$		0			0
$427$	−512.133	−	21.1140i	−0.0580418	−	0.00239292i
$428$		0			0
$429$	5069.13	+	4001.51i	0.570490	+	0.450338i
$430$		0			0
$431$			7183.17i			0.802787i	0.915906	+	0.401393i	$0.131474\pi$
$431$			7183.17i			0.802787i	−0.915906	+	0.401393i	$0.868526\pi$
$432$		0			0
$433$		−	15271.9i		−	1.69497i	−0.530820	−	0.847485i	$-0.678116\pi$
$433$		−	15271.9i		−	1.69497i	0.530820	−	0.847485i	$-0.321884\pi$
$434$		0			0
$435$	318.720	−	403.756i	0.0351298	−	0.0445026i
$436$		0			0
$437$	−4937.10	+	8551.31i	−0.540443	+	0.936075i
$438$		0			0
$439$	−5050.88	+	2916.13i	−0.549123	+	0.317037i	−0.748768	−	0.662832i	$-0.769354\pi$
$439$	−5050.88	+	2916.13i	−0.549123	+	0.317037i	0.199645	+	0.979868i	$0.436021\pi$
$440$		0			0
$441$	−7227.15	+	5790.89i	−0.780386	+	0.625298i
$442$		0			0
$443$	2636.52	−	1522.20i	0.282765	−	0.163255i	−0.351909	−	0.936034i	$-0.614467\pi$
$443$	2636.52	−	1522.20i	0.282765	−	0.163255i	0.634675	+	0.772780i	$0.281134\pi$
$444$		0			0
$445$	−319.788	+	553.890i	−0.0340661	+	0.0590043i
$446$		0			0
$447$	852.319	+	2140.38i	0.0901864	+	0.226480i
$448$		0			0
$449$			1445.89i			0.151973i	0.997109	+	0.0759863i	$0.0242105\pi$
$449$			1445.89i			0.151973i	−0.997109	+	0.0759863i	$0.975789\pi$
$450$		0			0
$451$			6671.64i			0.696575i
$452$		0			0
$453$	1413.19	−	9702.33i	0.146573	−	1.00630i
$454$		0			0
$455$	614.032	+	25.3150i	0.0632665	+	0.00260832i
$456$		0			0
$457$	8001.23	+	13858.5i	0.818998	+	1.41855i	0.906422	+	0.422374i	$0.138803\pi$
$457$	8001.23	+	13858.5i	0.818998	+	1.41855i	−0.0874239	+	0.996171i	$0.527863\pi$
$458$		0			0
$459$	−3984.54	+	8599.12i	−0.405190	+	0.874450i
$460$		0			0
$461$	6375.19	+	11042.2i	0.644083	+	1.11559i	0.984512	+	0.175315i	$0.0560943\pi$
$461$	6375.19	+	11042.2i	0.644083	+	1.11559i	−0.340429	+	0.940270i	$0.610572\pi$
$462$		0			0
$463$	3779.86	−	6546.91i	0.379406	−	0.657151i	−0.611570	−	0.791191i	$-0.709462\pi$
$463$	3779.86	−	6546.91i	0.379406	−	0.657151i	0.990976	+	0.134040i	$0.0427949\pi$
$464$		0			0
$465$	−546.883	−	79.6561i	−0.0545399	−	0.00794401i
$466$		0			0
$467$	−15808.4			−1.56643			−0.783217	−	0.621749i	$-0.786423\pi$
$467$	−15808.4			−1.56643			−0.783217	+	0.621749i	$0.786423\pi$
$468$		0			0
$469$	5374.01	−	2814.14i	0.529102	−	0.277068i
$470$		0			0
$471$	−4735.19	−	11891.2i	−0.463240	−	1.16331i
$472$		0			0
$473$	8055.84	+	4651.04i	0.783103	+	0.452125i
$474$		0			0
$475$	−6792.36	+	3921.57i	−0.656115	+	0.378808i
$476$		0			0
$477$	3593.18	−	857.723i	0.344907	−	0.0823321i
$478$		0			0
$479$	−4236.78	−	7338.32i	−0.404141	−	0.699992i	0.590080	−	0.807345i	$-0.299096\pi$
$479$	−4236.78	−	7338.32i	−0.404141	−	0.699992i	−0.994221	+	0.107352i	$0.965763\pi$
$480$		0			0
$481$	708.050	+	408.793i	0.0671191	+	0.0387512i
$482$		0			0
$483$	−2788.53	+	14831.7i	−0.262696	+	1.39724i
$484$		0			0
$485$		−	843.735i		−	0.0789939i
$486$		0			0
$487$	−5933.46			−0.552096			−0.276048	−	0.961144i	$-0.589025\pi$
$487$	−5933.46			−0.552096			−0.276048	+	0.961144i	$0.589025\pi$
$488$		0			0
$489$	−10254.9	−	8095.12i	−0.948352	−	0.748618i
$490$		0			0
$491$	232.094	+	133.999i	0.0213325	+	0.0123163i	0.510628	−	0.859802i	$-0.329413\pi$
$491$	232.094	+	133.999i	0.0213325	+	0.0123163i	−0.489296	+	0.872118i	$0.662746\pi$
$492$		0			0
$493$	8772.38	−	5064.74i	0.801396	−	0.462686i
$494$		0			0
$495$	428.736	−	102.343i	0.0389298	−	0.00929287i
$496$		0			0
$497$	−2441.60	+	3853.17i	−0.220364	+	0.347763i
$498$		0			0
$499$	−5365.31	+	9292.98i	−0.481331	+	0.833689i	−0.999770	−	0.0214248i	$-0.993180\pi$
$499$	−5365.31	+	9292.98i	−0.481331	+	0.833689i	0.518440	+	0.855114i	$0.326513\pi$
$500$		0			0
$501$	13669.6	−	5443.34i	1.21898	−	0.485410i
$502$		0			0
$503$	−1490.98			−0.132166			−0.0660830	−	0.997814i	$-0.521050\pi$
$503$	−1490.98			−0.132166			−0.0660830	+	0.997814i	$0.521050\pi$
$504$		0			0
$505$	376.476			0.0331742
$506$		0			0
$507$	246.611	−	1693.12i	0.0216023	−	0.148312i
$508$		0			0
$509$	−5918.88	+	10251.8i	−0.515422	+	0.892736i	0.484418	+	0.874837i	$0.339031\pi$
$509$	−5918.88	+	10251.8i	−0.515422	+	0.892736i	−0.999840	+	0.0178998i	$0.994302\pi$
$510$		0			0
$511$	2589.79	−	4087.04i	0.224199	−	0.353816i
$512$		0			0
$513$	8015.06	+	3713.90i	0.689812	+	0.319635i
$514$		0			0
$515$	1029.40	−	594.326i	0.0880794	−	0.0508526i
$516$		0			0
$517$	−1343.73	−	775.802i	−0.114308	−	0.0659956i
$518$		0			0
$519$	−999.746	+	6863.80i	−0.0845549	+	0.580515i
$520$		0			0
$521$	−5868.12			−0.493449			−0.246724	−	0.969086i	$-0.579354\pi$
$521$	−5868.12			−0.493449			−0.246724	+	0.969086i	$0.579354\pi$
$522$		0			0
$523$			20680.0i			1.72901i	0.502622	+	0.864507i	$0.332369\pi$
$523$			20680.0i			1.72901i	−0.502622	+	0.864507i	$0.667631\pi$
$524$		0			0
$525$	−7808.65	+	9095.09i	−0.649138	+	0.756081i
$526$		0			0
$527$	−9424.84	−	5441.44i	−0.779037	−	0.449777i
$528$		0			0
$529$	6212.96	+	10761.2i	0.510640	+	0.884455i
$530$		0			0
$531$	−18571.7	−	5527.37i	−1.51778	−	0.451728i
$532$		0			0
$533$	11744.0	−	6780.40i	0.954388	−	0.551016i
$534$		0			0
$535$	−1165.76	−	673.053i	−0.0942062	−	0.0543900i
$536$		0			0
$537$	4607.91	−	5837.33i	0.370291	−	0.469086i
$538$		0			0
$539$	6971.35	+	4831.09i	0.557100	+	0.386066i
$540$		0			0
$541$	7401.95			0.588234			0.294117	−	0.955769i	$-0.404974\pi$
$541$	7401.95			0.588234			0.294117	+	0.955769i	$0.404974\pi$
$542$		0			0
$543$	845.997	−	1071.71i	0.0668604	−	0.0846991i
$544$		0			0
$545$	−392.677	+	680.137i	−0.0308632	+	0.0534566i
$546$		0			0
$547$	5185.72	+	8981.93i	0.405348	+	0.702083i	0.994362	−	0.106040i	$-0.0338171\pi$
$547$	5185.72	+	8981.93i	0.405348	+	0.702083i	−0.589014	+	0.808123i	$0.700484\pi$
$548$		0			0
$549$	513.672	+	542.705i	0.0399326	+	0.0421896i
$550$		0			0
$551$	−4720.73	−	8176.55i	−0.364991	−	0.632183i
$552$		0			0
$553$	−598.081	+	14506.8i	−0.0459909	+	1.11554i
$554$		0			0
$555$	51.8424	−	20.6441i	0.00396502	−	0.00157891i
$556$		0			0
$557$		−	23317.1i		−	1.77375i	−0.462014	−	0.886873i	$-0.652873\pi$
$557$		−	23317.1i		−	1.77375i	0.462014	−	0.886873i	$-0.347127\pi$
$558$		0			0
$559$		−	18907.4i		−	1.43059i
$560$		0			0
$561$	8589.26	+	1251.07i	0.646415	+	0.0941535i
$562$		0			0
$563$	−4168.16	+	7219.47i	−0.312020	+	0.540434i	−0.978799	−	0.204821i	$-0.934339\pi$
$563$	−4168.16	+	7219.47i	−0.312020	+	0.540434i	0.666780	+	0.745255i	$0.267672\pi$
$564$		0			0
$565$	−426.785	+	246.405i	−0.0317788	+	0.0183475i
$566$		0			0
$567$	13438.9	+	1296.23i	0.995381	+	0.0960081i
$568$		0			0
$569$	−19760.4	+	11408.7i	−1.45589	+	0.840556i	−0.998805	−	0.0488697i	$-0.984438\pi$
$569$	−19760.4	+	11408.7i	−1.45589	+	0.840556i	−0.457080	+	0.889425i	$0.651105\pi$
$570$		0			0
$571$	4072.82	−	7054.34i	0.298498	−	0.517014i	−0.677295	−	0.735712i	$-0.736848\pi$
$571$	4072.82	−	7054.34i	0.298498	−	0.517014i	0.975793	+	0.218698i	$0.0701810\pi$
$572$		0			0
$573$	581.261	+	84.6634i	0.0423779	+	0.00617254i
$574$		0			0
$575$			19534.3i			1.41676i
$576$		0			0
$577$			19823.7i			1.43028i	0.698982	+	0.715140i	$0.253637\pi$
$577$			19823.7i			1.43028i	−0.698982	+	0.715140i	$0.746363\pi$
$578$		0			0
$579$	20193.7	−	8041.31i	1.44943	−	0.577177i
$580$		0			0
$581$	−914.597	+	22184.1i	−0.0653079	+	1.58408i
$582$		0			0
$583$	−1691.64	−	2930.00i	−0.120172	−	0.208145i
$584$		0			0
$585$	−615.878	−	650.687i	−0.0435272	−	0.0459873i
$586$		0			0
$587$	−349.569	−	605.472i	−0.0245797	−	0.0425732i	0.853474	−	0.521136i	$-0.174491\pi$
$587$	−349.569	−	605.472i	−0.0245797	−	0.0425732i	−0.878054	+	0.478562i	$0.841158\pi$
$588$		0			0
$589$	−5071.84	+	8784.69i	−0.354808	+	0.614545i
$590$		0			0
$591$	1011.97	−	1281.97i	0.0704345	−	0.0892268i
$592$		0			0
$593$	−22770.8			−1.57687			−0.788434	−	0.615119i	$-0.789108\pi$
$593$	−22770.8			−1.57687			−0.788434	+	0.615119i	$0.789108\pi$
$594$		0			0
$595$	731.714	−	383.168i	0.0504157	−	0.0264006i
$596$		0			0
$597$	4533.04	−	5742.47i	0.310762	−	0.393675i
$598$		0			0
$599$	−1737.23	−	1002.99i	−0.118500	−	0.0684159i	0.439579	−	0.898204i	$-0.355128\pi$
$599$	−1737.23	−	1002.99i	−0.118500	−	0.0684159i	−0.558078	+	0.829788i	$0.688461\pi$
$600$		0			0
$601$	12437.9	−	7181.05i	0.844184	−	0.487390i	−0.0145004	−	0.999895i	$-0.504616\pi$
$601$	12437.9	−	7181.05i	0.844184	−	0.487390i	0.858684	+	0.512505i	$0.171282\pi$
$602$		0			0
$603$	−8476.31	−	2522.75i	−0.572441	−	0.170372i
$604$		0			0
$605$	237.514	+	411.387i	0.0159609	+	0.0276450i
$606$		0			0
$607$	13864.4	+	8004.64i	0.927085	+	0.535253i	0.885888	−	0.463898i	$-0.153550\pi$
$607$	13864.4	+	8004.64i	0.927085	+	0.535253i	0.0411965	+	0.999151i	$0.486883\pi$
$608$		0			0
$609$	−10948.6	−	9399.95i	−0.728502	−	0.625460i
$610$		0			0
$611$			3153.79i			0.208820i
$612$		0			0
$613$	721.073			0.0475104			0.0237552	−	0.999718i	$-0.492438\pi$
$613$	721.073			0.0475104			0.0237552	+	0.999718i	$0.492438\pi$
$614$		0			0
$615$	133.403	−	915.882i	0.00874685	−	0.0600519i
$616$		0			0
$617$	−7798.16	−	4502.27i	−0.508820	−	0.293767i	0.223528	−	0.974697i	$-0.428242\pi$
$617$	−7798.16	−	4502.27i	−0.508820	−	0.293767i	−0.732349	+	0.680930i	$0.761576\pi$
$618$		0			0
$619$	−9685.79	+	5592.09i	−0.628925	+	0.363110i	−0.780336	−	0.625361i	$-0.784952\pi$
$619$	−9685.79	+	5592.09i	−0.628925	+	0.363110i	0.151411	+	0.988471i	$0.451618\pi$
$620$		0			0
$621$	17991.9	−	12663.1i	1.16263	−	0.818279i
$622$		0			0
$623$	15155.4	+	9603.38i	0.974620	+	0.617578i
$624$		0			0
$625$	−7730.87	+	13390.3i	−0.494776	+	0.856977i
$626$		0			0
$627$	1166.09	−	8005.87i	0.0742732	−	0.509926i
$628$		0			0
$629$	1098.85			0.0696564
$630$		0			0
$631$	8969.76			0.565897			0.282948	−	0.959135i	$-0.408688\pi$
$631$	8969.76			0.565897			0.282948	+	0.959135i	$0.408688\pi$
$632$		0			0
$633$	713.847	−	284.260i	0.0448229	−	0.0178489i
$634$		0			0
$635$	−604.986	+	1047.87i	−0.0378081	+	0.0654855i
$636$		0			0
$637$	1419.11	−	17181.4i	0.0882684	−	1.06868i
$638$		0			0
$639$	6468.48	−	1544.08i	0.400452	−	0.0955913i
$640$		0			0
$641$	−1495.77	+	863.586i	−0.0921678	+	0.0532131i	−0.545375	−	0.838192i	$-0.683613\pi$
$641$	−1495.77	+	863.586i	−0.0921678	+	0.0532131i	0.453208	+	0.891405i	$0.350280\pi$
$642$		0			0
$643$	15392.5	+	8886.86i	0.944045	+	0.545045i	0.891226	−	0.453560i	$-0.149846\pi$
$643$	15392.5	+	8886.86i	0.944045	+	0.545045i	0.0528189	+	0.998604i	$0.483179\pi$
$644$		0			0
$645$	−1012.90	−	799.575i	−0.0618342	−	0.0488112i
$646$		0			0
$647$	7518.12			0.456828			0.228414	−	0.973564i	$-0.426646\pi$
$647$	7518.12			0.456828			0.228414	+	0.973564i	$0.426646\pi$
$648$		0			0
$649$			17746.2i			1.07334i
$650$		0			0
$651$	−2864.63	+	15236.5i	−0.172464	+	0.917304i
$652$		0			0
$653$	5483.68	+	3166.00i	0.328626	+	0.189732i	0.655231	−	0.755429i	$-0.272571\pi$
$653$	5483.68	+	3166.00i	0.328626	+	0.189732i	−0.326605	+	0.945161i	$0.605905\pi$
$654$		0			0
$655$	155.567	+	269.451i	0.00928018	+	0.0160737i
$656$		0			0
$657$	−6861.07	+	1637.80i	−0.407421	+	0.0972549i
$658$		0			0
$659$	5478.28	−	3162.89i	0.323829	−	0.186963i	−0.329269	−	0.944236i	$-0.606802\pi$
$659$	5478.28	−	3162.89i	0.323829	−	0.186963i	0.653098	+	0.757273i	$0.273469\pi$
$660$		0			0
$661$	18882.2	+	10901.7i	1.11110	+	0.641491i	0.939113	−	0.343608i	$-0.111649\pi$
$661$	18882.2	+	10901.7i	1.11110	+	0.641491i	0.171983	+	0.985100i	$0.444983\pi$
$662$		0			0
$663$	−6527.04	−	16391.0i	−0.382337	−	0.960142i
$664$		0			0
$665$	−357.143	−	682.015i	−0.0208262	−	0.0397705i
$666$		0			0
$667$	−23515.1			−1.36508
$668$		0			0
$669$	11907.2	+	1734.35i	0.688132	+	0.100230i
$670$		0			0
$671$	342.186	−	592.684i	0.0196870	−	0.0340988i
$672$		0			0
$673$	−12150.3	−	21044.9i	−0.695926	−	1.20538i	−0.969868	−	0.243632i	$-0.921661\pi$
$673$	−12150.3	−	21044.9i	−0.695926	−	1.20538i	0.273942	−	0.961746i	$-0.411672\pi$
$674$		0			0
$675$	17405.6	−	1565.23i	0.992508	−	0.0892532i
$676$		0			0
$677$	−15606.5	−	27031.3i	−0.885979	−	1.53456i	−0.844587	−	0.535418i	$-0.820154\pi$
$677$	−15606.5	−	27031.3i	−0.885979	−	1.53456i	−0.0413922	−	0.999143i	$-0.513179\pi$
$678$		0			0
$679$	−23649.0	−	974.990i	−1.33662	−	0.0551056i
$680$		0			0
$681$	−3345.29	+	22967.3i	−0.188241	+	1.29237i
$682$		0			0
$683$		−	32330.6i		−	1.81127i	−0.424063	−	0.905633i	$-0.639397\pi$
$683$		−	32330.6i		−	1.81127i	0.424063	−	0.905633i	$-0.360603\pi$
$684$		0			0
$685$			1731.69i			0.0965902i
$686$		0			0
$687$	2255.59	+	5664.35i	0.125264	+	0.314568i
$688$		0			0
$689$	−3438.43	+	5955.53i	−0.190121	+	0.329300i
$690$		0			0
$691$	−10098.5	+	5830.40i	−0.555958	+	0.320982i	−0.751521	−	0.659709i	$-0.770680\pi$
$691$	−10098.5	+	5830.40i	−0.555958	+	0.320982i	0.195564	+	0.980691i	$0.437346\pi$
$692$		0			0
$693$	−2373.13	−	12135.3i	−0.130083	−	0.665196i
$694$		0			0
$695$	108.546	−	62.6691i	0.00592430	−	0.00342040i
$696$		0			0
$697$	9112.95	−	15784.1i	0.495233	−	0.857769i
$698$		0			0
$699$	−5637.68	+	7141.84i	−0.305060	+	0.386451i
$700$		0			0
$701$		−	35502.0i		−	1.91283i	−0.292015	−	0.956414i	$-0.594326\pi$
$701$		−	35502.0i		−	1.91283i	0.292015	−	0.956414i	$-0.405674\pi$
$702$		0			0
$703$		−	1024.21i		−	0.0549486i
$704$		0			0
$705$	168.954	+	133.370i	0.00902580	+	0.00712485i
$706$		0			0
$707$	435.042	−	10552.2i	0.0231421	−	0.561326i
$708$		0			0
$709$	6912.86	+	11973.4i	0.366175	+	0.634233i	0.988964	−	0.148156i	$-0.0473339\pi$
$709$	6912.86	+	11973.4i	0.366175	+	0.634233i	−0.622789	+	0.782390i	$0.714001\pi$
$710$		0			0
$711$	15372.8	−	14550.4i	0.810867	−	0.767489i
$712$		0			0
$713$	12632.1	+	21879.4i	0.663498	+	1.14921i
$714$		0			0
$715$	−410.271	+	710.610i	−0.0214591	+	0.0371683i
$716$		0			0
$717$	−11115.1	−	27912.8i	−0.578941	−	1.45386i
$718$		0			0
$719$	−35196.0			−1.82558			−0.912788	−	0.408434i	$-0.866075\pi$
$719$	−35196.0			−1.82558			−0.912788	+	0.408434i	$0.866075\pi$
$720$		0			0
$721$	−15468.8	−	29539.8i	−0.799011	−	1.52583i
$722$		0			0
$723$	−1368.37	−	199.309i	−0.0703874	−	0.0102523i
$724$		0			0
$725$	−16175.8	−	9339.11i	−0.828627	−	0.478408i
$726$		0			0
$727$	27427.8	−	15835.4i	1.39923	−	0.807846i	0.404918	−	0.914353i	$-0.367300\pi$
$727$	27427.8	−	15835.4i	1.39923	−	0.807846i	0.994312	+	0.106507i	$0.0339667\pi$
$728$		0			0
$729$	−12724.8	−	15016.7i	−0.646487	−	0.762925i
$730$		0			0
$731$	−12705.9	−	22007.3i	−0.642881	−	1.11350i
$732$		0			0
$733$	33629.6	+	19416.1i	1.69460	+	0.978375i	0.950717	+	0.310060i	$0.100349\pi$
$733$	33629.6	+	19416.1i	1.69460	+	0.978375i	0.743878	+	0.668315i	$0.232984\pi$
$734$		0			0
$735$	−860.425	−	802.606i	−0.0431800	−	0.0402783i
$736$		0			0
$737$			8099.56i			0.404818i
$738$		0			0
$739$	−63.2905			−0.00315044			−0.00157522	−	0.999999i	$-0.500501\pi$
$739$	−63.2905			−0.00315044			−0.00157522	+	0.999999i	$0.500501\pi$
$740$		0			0
$741$	−15277.7	+	6083.72i	−0.757410	+	0.301607i
$742$		0			0
$743$	−17506.0	−	10107.1i	−0.864376	−	0.499048i	0.00109946	−	0.999999i	$-0.499650\pi$
$743$	−17506.0	−	10107.1i	−0.864376	−	0.499048i	−0.865475	+	0.500952i	$0.832983\pi$
$744$		0			0
$745$	−253.497	+	146.357i	−0.0124663	+	0.00719745i
$746$		0			0
$747$	23508.4	−	22250.8i	1.15144	−	1.08985i
$748$		0			0
$749$	−20212.1	+	31897.3i	−0.986025	+	1.55608i
$750$		0			0
$751$	2887.55	−	5001.39i	0.140304	−	0.243014i	−0.787307	−	0.616561i	$-0.788525\pi$
$751$	2887.55	−	5001.39i	0.140304	−	0.243014i	0.927611	+	0.373547i	$0.121859\pi$
$752$		0			0
$753$	−29415.0	−	23219.9i	−1.42356	−	1.12374i
$754$		0			0
$755$	1245.73			0.0600488
$756$		0			0
$757$	−10392.0			−0.498949			−0.249474	−	0.968381i	$-0.580258\pi$
$757$	−10392.0			−0.498949			−0.249474	+	0.968381i	$0.580258\pi$
$758$		0			0
$759$	−15816.1	−	12485.0i	−0.756372	−	0.597071i
$760$		0			0
$761$	−4343.28	+	7522.79i	−0.206891	+	0.358345i	−0.950733	−	0.310009i	$-0.899668\pi$
$761$	−4343.28	+	7522.79i	−0.206891	+	0.358345i	0.743843	+	0.668355i	$0.233001\pi$
$762$		0			0
$763$	18609.7	+	11792.3i	0.882985	+	0.559513i
$764$		0			0
$765$	−1154.12	−	343.493i	−0.0545453	−	0.0162340i
$766$		0			0
$767$	31238.4	−	18035.5i	1.47060	−	0.849053i
$768$		0			0
$769$	−24932.6	−	14394.8i	−1.16917	−	0.675021i	−0.215687	−	0.976463i	$-0.569199\pi$
$769$	−24932.6	−	14394.8i	−1.16917	−	0.675021i	−0.953485	+	0.301441i	$0.902532\pi$
$770$		0			0
$771$	26573.5	−	10581.8i	1.24127	−	0.494285i
$772$		0			0
$773$	−12521.5			−0.582622			−0.291311	−	0.956628i	$-0.594091\pi$
$773$	−12521.5			−0.582622			−0.291311	+	0.956628i	$0.594091\pi$
$774$		0			0
$775$			20067.4i			0.930121i
$776$		0			0
$777$	−518.724	−	1476.94i	−0.0239500	−	0.0681918i
$778$		0			0
$779$	−14712.0	−	8493.98i	−0.676653	−	0.390666i
$780$		0			0
$781$	−3045.30	−	5274.62i	−0.139526	−	0.241665i
$782$		0			0
$783$	1884.21	+	20952.7i	0.0859976	+	0.956305i
$784$		0			0
$785$	1408.34	−	813.107i	0.0640330	−	0.0369695i
$786$		0			0
$787$	15973.1	+	9222.08i	0.723482	+	0.417702i	0.816033	−	0.578006i	$-0.196169\pi$
$787$	15973.1	+	9222.08i	0.723482	+	0.417702i	−0.0925512	+	0.995708i	$0.529502\pi$
$788$		0			0
$789$	24273.0	+	3535.48i	1.09524	+	0.159526i
$790$		0			0
$791$	6413.28	+	12247.1i	0.288281	+	0.550513i
$792$		0			0
$793$	−1391.06			−0.0622924
$794$		0			0
$795$	173.641	+	436.056i	0.00774643	+	0.0194532i
$796$		0			0
$797$	−4810.14	+	8331.41i	−0.213782	+	0.370281i	−0.952895	−	0.303300i	$-0.901911\pi$
$797$	−4810.14	+	8331.41i	−0.213782	+	0.370281i	0.739113	+	0.673581i	$0.235245\pi$
$798$		0			0
$799$	2119.37	+	3670.86i	0.0938398	+	0.162535i
$800$		0			0
$801$	−6073.22	−	25442.0i	−0.267898	−	1.12228i
$802$		0			0
$803$	3230.13	+	5594.75i	0.141954	+	0.245871i
$804$		0			0
$805$	−1915.82	−	78.9846i	−0.0838806	−	0.00345819i
$806$		0			0
$807$	−14663.1	−	11574.9i	−0.639610	−	0.504900i
$808$		0			0
$809$			18955.4i			0.823776i	0.911234	+	0.411888i	$0.135131\pi$
$809$			18955.4i			0.823776i	−0.911234	+	0.411888i	$0.864869\pi$
$810$		0			0
$811$			16233.0i			0.702857i	0.936215	+	0.351428i	$0.114304\pi$
$811$			16233.0i			0.702857i	−0.936215	+	0.351428i	$0.885696\pi$
$812$		0			0
$813$	11827.5	−	14983.2i	0.510222	−	0.646351i
$814$		0			0
$815$	829.984	−	1437.58i	0.0356725	−	0.0617866i
$816$		0			0
$817$	−20512.5	+	11842.9i	−0.878388	+	0.507138i
$818$		0			0
$819$	−18949.7	+	16510.5i	−0.808495	+	0.704424i
$820$		0			0
$821$	15840.8	−	9145.67i	0.673382	−	0.388777i	−0.123975	−	0.992285i	$-0.539564\pi$
$821$	15840.8	−	9145.67i	0.673382	−	0.388777i	0.797357	+	0.603508i	$0.206231\pi$
$822$		0			0
$823$	9144.29	−	15838.4i	0.387302	−	0.670827i	−0.604783	−	0.796390i	$-0.706740\pi$
$823$	9144.29	−	15838.4i	0.387302	−	0.670827i	0.992086	+	0.125563i	$0.0400737\pi$
$824$		0			0
$825$	−5921.24	−	14869.7i	−0.249880	−	0.627511i
$826$		0			0
$827$			26216.6i			1.10234i	0.834392	+	0.551172i	$0.185819\pi$
$827$			26216.6i			1.10234i	−0.834392	+	0.551172i	$0.814181\pi$
$828$		0			0
$829$		−	7768.92i		−	0.325483i	−0.986669	−	0.162742i	$-0.947966\pi$
$829$		−	7768.92i		−	0.325483i	0.986669	−	0.162742i	$-0.0520337\pi$
$830$		0			0
$831$	1318.58	−	9052.79i	0.0550435	−	0.377904i
$832$		0			0
$833$	−9894.25	−	20951.9i	−0.411543	−	0.871478i
$834$		0			0
$835$	934.708	+	1618.96i	0.0387388	+	0.0670976i
$836$		0			0
$837$	18483.0	−	13008.7i	0.763279	−	0.537210i
$838$		0			0
$839$	22208.7	+	38466.7i	0.913863	+	1.58286i	0.808558	+	0.588416i	$0.200248\pi$
$839$	22208.7	+	38466.7i	0.913863	+	1.58286i	0.105304	+	0.994440i	$0.466418\pi$
$840$		0			0
$841$	−952.198	+	1649.26i	−0.0390421	+	0.0676229i
$842$		0			0
$843$	41329.6	+	6019.85i	1.68857	+	0.245949i
$844$		0			0
$845$	217.389			0.00885017
$846$		0			0
$847$	11805.2	−	6181.89i	0.478903	−	0.250782i
$848$		0			0
$849$	14470.7	+	36339.4i	0.584961	+	1.46898i
$850$		0			0
$851$	−2209.17	−	1275.46i	−0.0889885	−	0.0513775i
$852$		0			0
$853$	1982.58	−	1144.64i	0.0795806	−	0.0459459i	−0.459682	−	0.888084i	$-0.652036\pi$
$853$	1982.58	−	1144.64i	0.0795806	−	0.0459459i	0.539262	+	0.842138i	$0.318703\pi$
$854$		0			0
$855$	−320.162	+	1075.73i	−0.0128062	+	0.0430282i
$856$		0			0
$857$	−10021.5	−	17357.7i	−0.399448	−	0.691864i	0.594210	−	0.804310i	$-0.297465\pi$
$857$	−10021.5	−	17357.7i	−0.399448	−	0.691864i	−0.993658	+	0.112446i	$0.964132\pi$
$858$		0			0
$859$	−2786.72	−	1608.91i	−0.110689	−	0.0639062i	0.443634	−	0.896208i	$-0.353689\pi$
$859$	−2786.72	−	1608.91i	−0.110689	−	0.0639062i	−0.554322	+	0.832302i	$0.687023\pi$
$860$		0			0
$861$	−25517.0	−	4797.49i	−1.01001	−	0.189893i
$862$		0			0
$863$			30086.4i			1.18674i	0.804931	+	0.593368i	$0.202202\pi$
$863$			30086.4i			1.18674i	−0.804931	+	0.593368i	$0.797798\pi$
$864$		0			0
$865$	−881.279			−0.0346409
$866$		0			0
$867$	1425.84	+	1125.54i	0.0558526	+	0.0440894i
$868$		0			0
$869$	−16788.6	−	9692.87i	−0.655365	−	0.378375i
$870$		0			0
$871$	14257.5	−	8231.59i	0.554648	−	0.320226i
$872$		0			0
$873$	23720.1	+	25060.7i	0.919592	+	0.971566i
$874$		0			0
$875$	−2577.51	−	1633.27i	−0.0995837	−	0.0631023i
$876$		0			0
$877$	−13897.7	+	24071.6i	−0.535112	+	0.926841i	0.464046	+	0.885811i	$0.346397\pi$
$877$	−13897.7	+	24071.6i	−0.535112	+	0.926841i	−0.999158	+	0.0410299i	$0.986936\pi$
$878$		0			0
$879$	1021.56	−	406.793i	0.0391995	−	0.0156096i
$880$		0			0
$881$	43478.8			1.66270			0.831349	−	0.555751i	$-0.187569\pi$
$881$	43478.8			1.66270			0.831349	+	0.555751i	$0.187569\pi$
$882$		0			0
$883$	18034.0			0.687308			0.343654	−	0.939096i	$-0.388335\pi$
$883$	18034.0			0.687308			0.343654	+	0.939096i	$0.388335\pi$
$884$		0			0
$885$	354.844	−	2436.20i	0.0134779	−	0.0925331i
$886$		0			0
$887$	4520.21	−	7829.24i	0.171109	−	0.296370i	−0.767699	−	0.640811i	$-0.778598\pi$
$887$	4520.21	−	7829.24i	0.171109	−	0.296370i	0.938808	+	0.344441i	$0.111932\pi$
$888$		0			0
$889$	28671.5	+	18168.0i	1.08168	+	0.685416i
$890$		0			0
$891$	−9857.19	+	15092.9i	−0.370627	+	0.567489i
$892$		0			0
$893$	3421.53	−	1975.42i	0.128216	−	0.0740257i
$894$		0			0
$895$	818.298	+	472.445i	0.0305617	+	0.0176448i
$896$		0			0
$897$	−5903.29	+	40529.3i	−0.219738	+	1.50862i
$898$		0			0
$899$	−24156.9			−0.896194
$900$		0			0
$901$			9242.59i			0.341748i
$902$		0			0
$903$	−23581.7	+	27466.7i	−0.869047	+	1.01222i
$904$		0			0
$905$	150.237	+	86.7392i	0.00551827	+	0.00318598i
$906$		0			0
$907$	−20675.3	−	35810.7i	−0.756905	−	1.31100i	−0.944422	−	0.328737i	$-0.893377\pi$
$907$	−20675.3	−	35810.7i	−0.756905	−	1.31100i	0.187516	−	0.982261i	$-0.439956\pi$
$908$		0			0
$909$	−11182.2	+	10584.0i	−0.408018	+	0.386191i
$910$		0			0
$911$	36143.5	−	20867.5i	1.31448	−	0.758913i	0.331642	−	0.943405i	$-0.392398\pi$
$911$	36143.5	−	20867.5i	1.31448	−	0.758913i	0.982834	+	0.184493i	$0.0590642\pi$
$912$		0			0
$913$	−25673.4	−	14822.5i	−0.930630	−	0.537299i
$914$		0			0
$915$	−58.8262	+	74.5214i	−0.00212539	+	0.00269246i
$916$		0			0
$917$	7732.18	−	4049.02i	0.278450	−	0.145813i
$918$		0			0
$919$	−4424.74			−0.158824			−0.0794118	−	0.996842i	$-0.525304\pi$
$919$	−4424.74			−0.158824			−0.0794118	+	0.996842i	$0.525304\pi$
$920$		0			0
$921$	−8696.00	+	11016.1i	−0.311122	+	0.394130i
$922$		0			0
$923$	−6189.89	+	10721.2i	−0.220740	+	0.382332i
$924$		0			0
$925$	−1013.11	−	1754.75i	−0.0360117	−	0.0623740i
$926$		0			0
$927$	−13867.0	+	46592.5i	−0.491320	+	1.65081i
$928$		0			0
$929$	−16928.2	−	29320.5i	−0.597843	−	1.03550i	−0.993139	−	0.116941i	$-0.962691\pi$
$929$	−16928.2	−	29320.5i	−0.597843	−	1.03550i	0.395295	−	0.918554i	$-0.370642\pi$
$930$		0			0
$931$	−19528.8	+	9222.22i	−0.687467	+	0.324647i
$932$		0			0
$933$	−31232.5	+	12437.1i	−1.09593	+	0.436410i
$934$		0			0
$935$			1102.82i			0.0385733i
$936$		0			0
$937$		−	26589.0i		−	0.927026i	−0.886090	−	0.463513i	$-0.846589\pi$
$937$		−	26589.0i		−	0.927026i	0.886090	−	0.463513i	$-0.153411\pi$
$938$		0			0
$939$	8765.07	+	1276.68i	0.304619	+	0.0443692i
$940$		0			0
$941$	19164.6	−	33194.1i	0.663919	−	1.14994i	−0.315658	−	0.948873i	$-0.602225\pi$
$941$	19164.6	−	33194.1i	0.663919	−	1.14994i	0.979577	−	0.201069i	$-0.0644415\pi$
$942$		0			0
$943$	−36642.1	+	21155.3i	−1.26536	+	0.730553i
$944$		0			0
$945$	83.1324	+	1713.38i	0.00286169	+	0.0589802i
$946$		0			0
$947$	27807.6	−	16054.7i	0.954196	−	0.550906i	0.0598145	−	0.998210i	$-0.480949\pi$
$947$	27807.6	−	16054.7i	0.954196	−	0.550906i	0.894382	+	0.447304i	$0.147616\pi$
$948$		0			0
$949$	6565.57	−	11371.9i	0.224581	−	0.388986i
$950$		0			0
$951$	−7404.91	−	1078.56i	−0.252493	−	0.0367768i
$952$		0			0
$953$			40510.3i			1.37697i	0.725249	+	0.688487i	$0.241725\pi$
$953$			40510.3i			1.37697i	−0.725249	+	0.688487i	$0.758275\pi$
$954$		0			0
$955$			74.6311i			0.00252880i
$956$		0			0
$957$	17899.9	−	7127.91i	0.604622	−	0.240766i
$958$		0			0
$959$	48537.3	+	2001.07i	1.63436	+	0.0673806i
$960$		0			0
$961$	−1918.68	−	3323.26i	−0.0644048	−	0.111552i
$962$		0			0
$963$	53547.3	−	12782.2i	1.79184	−	0.427726i
$964$		0			0
$965$	1380.82	+	2391.65i	0.0460624	+	0.0797824i
$966$		0			0
$967$	−2453.20	+	4249.08i	−0.0815820	+	0.141304i	−0.903930	−	0.427681i	$-0.859331\pi$
$967$	−2453.20	+	4249.08i	−0.0815820	+	0.141304i	0.822348	+	0.568985i	$0.192664\pi$
$968$		0			0
$969$	−13694.2	+	17347.9i	−0.453995	+	0.575123i
$970$		0			0
$971$	−41704.4			−1.37833			−0.689165	−	0.724604i	$-0.742023\pi$
$971$	−41704.4			−1.37833			−0.689165	+	0.724604i	$0.742023\pi$
$972$		0			0
$973$	−1631.12	−	3114.85i	−0.0537422	−	0.102628i
$974$		0			0
$975$	−20157.1	+	25535.2i	−0.662098	+	0.838748i
$976$		0			0
$977$	39726.6	+	22936.2i	1.30089	+	0.751067i	0.980556	−	0.196239i	$-0.0628727\pi$
$977$	39726.6	+	22936.2i	1.30089	+	0.751067i	0.320330	+	0.947306i	$0.396206\pi$
$978$		0			0
$979$	−20746.3	+	11977.9i	−0.677276	+	0.391026i
$980$		0			0
$981$	−7457.47	−	31240.9i	−0.242710	−	1.01676i
$982$		0			0
$983$	29949.7	+	51874.3i	0.971766	+	1.68315i	0.690219	+	0.723600i	$0.257514\pi$
$983$	29949.7	+	51874.3i	0.971766	+	1.68315i	0.281546	+	0.959548i	$0.409153\pi$
$984$		0			0
$985$	179.711	+	103.756i	0.00581326	+	0.00335629i
$986$		0			0
$987$	3933.47	−	4581.49i	0.126853	−	0.147751i
$988$		0			0
$989$			58992.5i			1.89672i
$990$		0			0
$991$	37752.2			1.21013			0.605065	−	0.796176i	$-0.293147\pi$
$991$	37752.2			1.21013			0.605065	+	0.796176i	$0.293147\pi$
$992$		0			0
$993$	−8480.31	+	58222.0i	−0.271012	+	1.86064i
$994$		0			0
$995$	805.002	+	464.768i	0.0256485	+	0.0148082i
$996$		0			0
$997$	−42235.3	+	24384.6i	−1.34163	+	0.774591i	−0.987047	−	0.160433i	$-0.948711\pi$
$997$	−42235.3	+	24384.6i	−1.34163	+	0.774591i	−0.354585	+	0.935024i	$0.615378\pi$
$998$		0			0
$999$	−959.459	+	2070.63i	−0.0303863	+	0.0655774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.41.7	✓	48
3.2	odd	2		756.4.x.a.125.12		48
7.6	odd	2	inner	252.4.x.a.41.18	yes	48
9.2	odd	6	inner	252.4.x.a.209.18	yes	48
9.4	even	3		2268.4.f.a.1133.23		48
9.5	odd	6		2268.4.f.a.1133.26		48
9.7	even	3		756.4.x.a.629.13		48
21.20	even	2		756.4.x.a.125.13		48
63.13	odd	6		2268.4.f.a.1133.25		48
63.20	even	6	inner	252.4.x.a.209.7	yes	48
63.34	odd	6		756.4.x.a.629.12		48
63.41	even	6		2268.4.f.a.1133.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.7	✓	48	1.1	even	1	trivial
252.4.x.a.41.18	yes	48	7.6	odd	2	inner
252.4.x.a.209.7	yes	48	63.20	even	6	inner
252.4.x.a.209.18	yes	48	9.2	odd	6	inner
756.4.x.a.125.12		48	3.2	odd	2
756.4.x.a.125.13		48	21.20	even	2
756.4.x.a.629.12		48	63.34	odd	6
756.4.x.a.629.13		48	9.7	even	3
2268.4.f.a.1133.23		48	9.4	even	3
2268.4.f.a.1133.24		48	63.41	even	6
2268.4.f.a.1133.25		48	63.13	odd	6
2268.4.f.a.1133.26		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.07854 - 3.21955i) q^{3} +(0.330097 - 0.571745i) q^{5} +(-15.6440 - 9.91296i) q^{7} +(6.26899 + 26.2621i) q^{9} +O(q^{10})\)	\(q+(-4.07854 - 3.21955i) q^{3} +(0.330097 - 0.571745i) q^{5} +(-15.6440 - 9.91296i) q^{7} +(6.26899 + 26.2621i) q^{9} +(21.4150 - 12.3640i) q^{11} +(-43.5283 - 25.1311i) q^{13} +(-3.18708 + 1.26912i) q^{15} -67.5530 q^{17} +62.9647i q^{19} +(31.8892 + 90.7969i) q^{21} +(135.811 + 78.4107i) q^{23} +(62.2821 + 107.876i) q^{25} +(58.9839 - 127.295i) q^{27} +(-129.859 + 74.9743i) q^{29} +(139.518 + 80.5507i) q^{31} +(-127.149 - 18.5198i) q^{33} +(-10.8317 + 5.67211i) q^{35} -16.2664 q^{37} +(96.6211 + 242.639i) q^{39} +(-134.901 + 233.655i) q^{41} +(188.088 + 325.779i) q^{43} +(17.0846 + 5.08479i) q^{45} +(-31.3735 - 54.3405i) q^{47} +(146.467 + 310.156i) q^{49} +(275.518 + 217.490i) q^{51} -136.820i q^{53} -16.3253i q^{55} +(202.718 - 256.804i) q^{57} +(-358.829 + 621.509i) q^{59} +(23.9682 - 13.8380i) q^{61} +(162.264 - 472.988i) q^{63} +(-28.7371 + 16.5914i) q^{65} +(-163.773 + 283.664i) q^{67} +(-301.465 - 757.052i) q^{69} -246.304i q^{71} +261.253i q^{73} +(93.2913 - 640.496i) q^{75} +(-457.579 - 18.8649i) q^{77} +(-391.980 - 678.930i) q^{79} +(-650.399 + 329.274i) q^{81} +(-599.424 - 1038.23i) q^{83} +(-22.2990 + 38.6231i) q^{85} +(771.020 + 112.303i) q^{87} -968.771 q^{89} +(431.831 + 824.643i) q^{91} +(-309.692 - 777.714i) q^{93} +(35.9997 + 20.7845i) q^{95} +(1106.79 - 639.005i) q^{97} +(458.955 + 484.895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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