LMFDB - Embedded newform 252.4.bm.a.173.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (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			173.4
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.40362 + 2.75828i) q^{3} +3.45780 q^{5} +(13.4196 + 12.7638i) q^{7} +(11.7838 - 24.2928i) q^{9} +O(q^{10})$	\(q+(-4.40362 + 2.75828i) q^{3} +3.45780 q^{5} +(13.4196 + 12.7638i) q^{7} +(11.7838 - 24.2928i) q^{9} -31.0970i q^{11} +(2.16207 - 1.24827i) q^{13} +(-15.2268 + 9.53756i) q^{15} +(-0.621716 - 1.07684i) q^{17} +(76.0352 + 43.8990i) q^{19} +(-94.3009 - 19.1920i) q^{21} +49.7252i q^{23} -113.044 q^{25} +(15.1150 + 139.480i) q^{27} +(228.650 + 132.011i) q^{29} +(222.606 + 128.522i) q^{31} +(85.7741 + 136.939i) q^{33} +(46.4022 + 44.1346i) q^{35} +(-47.7268 + 82.6653i) q^{37} +(-6.07787 + 11.4605i) q^{39} +(-93.9702 - 162.761i) q^{41} +(-133.204 + 230.716i) q^{43} +(40.7460 - 83.9997i) q^{45} +(285.924 + 495.236i) q^{47} +(17.1705 + 342.570i) q^{49} +(5.70804 + 3.02715i) q^{51} +(-167.674 + 96.8064i) q^{53} -107.527i q^{55} +(-455.916 + 16.4118i) q^{57} +(145.530 - 252.065i) q^{59} +(-137.596 + 79.4410i) q^{61} +(468.203 - 175.594i) q^{63} +(7.47601 - 4.31628i) q^{65} +(221.989 - 384.496i) q^{67} +(-137.156 - 218.971i) q^{69} -405.345i q^{71} +(-505.536 + 291.872i) q^{73} +(497.802 - 311.806i) q^{75} +(396.916 - 417.309i) q^{77} +(643.560 + 1114.68i) q^{79} +(-451.284 - 572.524i) q^{81} +(610.720 - 1057.80i) q^{83} +(-2.14977 - 3.72351i) q^{85} +(-1371.01 + 49.3530i) q^{87} +(406.886 - 704.748i) q^{89} +(44.9468 + 10.8450i) q^{91} +(-1334.77 + 48.0483i) q^{93} +(262.914 + 151.794i) q^{95} +(-496.443 - 286.621i) q^{97} +(-755.434 - 366.441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−4.40362	+	2.75828i	−0.847478	+	0.530831i
$3$	−4.40362	+	2.75828i	−0.847478	+	0.530831i
$4$		0			0
$5$	3.45780			0.309275			0.154637	−	0.987971i	$-0.450579\pi$
$5$	3.45780			0.309275			0.154637	+	0.987971i	$0.450579\pi$
$6$		0			0
$7$	13.4196	+	12.7638i	0.724589	+	0.689181i
$7$	13.4196	+	12.7638i	0.724589	+	0.689181i
$8$		0			0
$9$	11.7838	−	24.2928i	0.436437	−	0.899735i
$10$		0			0
$11$		−	31.0970i		−	0.852372i	−0.904636	−	0.426186i	$-0.859857\pi$
$11$		−	31.0970i		−	0.852372i	0.904636	−	0.426186i	$-0.140143\pi$
$12$		0			0
$13$	2.16207	−	1.24827i	0.0461270	−	0.0266314i	−0.476759	−	0.879034i	$-0.658189\pi$
$13$	2.16207	−	1.24827i	0.0461270	−	0.0266314i	0.522886	+	0.852403i	$0.324855\pi$
$14$		0			0
$15$	−15.2268	+	9.53756i	−0.262103	+	0.164173i
$16$		0			0
$17$	−0.621716	−	1.07684i	−0.00886990	−	0.0153631i	0.861556	−	0.507662i	$-0.169490\pi$
$17$	−0.621716	−	1.07684i	−0.00886990	−	0.0153631i	−0.870426	+	0.492299i	$0.836157\pi$
$18$		0			0
$19$	76.0352	+	43.8990i	0.918088	+	0.530059i	0.883025	−	0.469326i	$-0.155503\pi$
$19$	76.0352	+	43.8990i	0.918088	+	0.530059i	0.0350638	+	0.999385i	$0.488837\pi$
$20$		0			0
$21$	−94.3009	−	19.1920i	−0.979912	−	0.199431i
$22$		0			0
$23$			49.7252i			0.450801i	0.974266	+	0.225401i	$0.0723691\pi$
$23$			49.7252i			0.450801i	−0.974266	+	0.225401i	$0.927631\pi$
$24$		0			0
$25$	−113.044			−0.904349
$26$		0			0
$27$	15.1150	+	139.480i	0.107736	+	0.994180i
$28$		0			0
$29$	228.650	+	132.011i	1.46411	+	0.845307i	0.999198	−	0.0400471i	$-0.0127508\pi$
$29$	228.650	+	132.011i	1.46411	+	0.845307i	0.464917	+	0.885354i	$0.346084\pi$
$30$		0			0
$31$	222.606	+	128.522i	1.28972	+	0.744618i	0.978603	−	0.205755i	$-0.0659651\pi$
$31$	222.606	+	128.522i	1.28972	+	0.744618i	0.311112	+	0.950373i	$0.399298\pi$
$32$		0			0
$33$	85.7741	+	136.939i	0.452465	+	0.722366i
$34$		0			0
$35$	46.4022	+	44.1346i	0.224097	+	0.213146i
$36$		0			0
$37$	−47.7268	+	82.6653i	−0.212061	+	0.367300i	−0.952359	−	0.304978i	$-0.901351\pi$
$37$	−47.7268	+	82.6653i	−0.212061	+	0.367300i	0.740299	+	0.672278i	$0.234684\pi$
$38$		0			0
$39$	−6.07787	+	11.4605i	−0.0249548	+	0.0470552i
$40$		0			0
$41$	−93.9702	−	162.761i	−0.357944	−	0.619976i	0.629674	−	0.776860i	$-0.283189\pi$
$41$	−93.9702	−	162.761i	−0.357944	−	0.619976i	−0.987617	+	0.156883i	$0.949855\pi$
$42$		0			0
$43$	−133.204	+	230.716i	−0.472405	+	0.818230i	−0.999501	−	0.0315755i	$-0.989948\pi$
$43$	−133.204	+	230.716i	−0.472405	+	0.818230i	0.527096	+	0.849806i	$0.323281\pi$
$44$		0			0
$45$	40.7460	−	83.9997i	0.134979	−	0.278265i
$46$		0			0
$47$	285.924	+	495.236i	0.887369	+	1.53697i	0.842974	+	0.537955i	$0.180803\pi$
$47$	285.924	+	495.236i	0.887369	+	1.53697i	0.0443956	+	0.999014i	$0.485864\pi$
$48$		0			0
$49$	17.1705	+	342.570i	0.0500599	+	0.998746i
$50$		0			0
$51$	5.70804	+	3.02715i	0.0156723	+	0.00831149i
$52$		0			0
$53$	−167.674	+	96.8064i	−0.434561	+	0.250894i	−0.701288	−	0.712878i	$-0.747391\pi$
$53$	−167.674	+	96.8064i	−0.434561	+	0.250894i	0.266727	+	0.963772i	$0.414058\pi$
$54$		0			0
$55$		−	107.527i		−	0.263617i
$56$		0			0
$57$	−455.916	+	16.4118i	−1.05943	+	0.0381368i
$58$		0			0
$59$	145.530	−	252.065i	0.321125	−	0.556205i	−0.659595	−	0.751621i	$-0.729272\pi$
$59$	145.530	−	252.065i	0.321125	−	0.556205i	0.980720	+	0.195416i	$0.0626056\pi$
$60$		0			0
$61$	−137.596	+	79.4410i	−0.288809	+	0.166744i	−0.637404	−	0.770529i	$-0.719992\pi$
$61$	−137.596	+	79.4410i	−0.288809	+	0.166744i	0.348596	+	0.937273i	$0.386659\pi$
$62$		0			0
$63$	468.203	−	175.594i	0.936318	−	0.351154i
$64$		0			0
$65$	7.47601	−	4.31628i	0.0142659	−	0.00823643i
$66$		0			0
$67$	221.989	−	384.496i	0.404780	−	0.701099i	−0.589516	−	0.807757i	$-0.700682\pi$
$67$	221.989	−	384.496i	0.404780	−	0.701099i	0.994296	+	0.106658i	$0.0340149\pi$
$68$		0			0
$69$	−137.156	−	218.971i	−0.239299	−	0.382044i
$70$		0			0
$71$		−	405.345i		−	0.677543i	−0.940869	−	0.338772i	$-0.889989\pi$
$71$		−	405.345i		−	0.677543i	0.940869	−	0.338772i	$-0.110011\pi$
$72$		0			0
$73$	−505.536	+	291.872i	−0.810528	+	0.467959i	−0.847139	−	0.531371i	$-0.821677\pi$
$73$	−505.536	+	291.872i	−0.810528	+	0.467959i	0.0366111	+	0.999330i	$0.488344\pi$
$74$		0			0
$75$	497.802	−	311.806i	0.766416	−	0.480056i
$76$		0			0
$77$	396.916	−	417.309i	0.587438	−	0.617620i
$78$		0			0
$79$	643.560	+	1114.68i	0.916533	+	1.58748i	0.804641	+	0.593761i	$0.202358\pi$
$79$	643.560	+	1114.68i	0.916533	+	1.58748i	0.111892	+	0.993720i	$0.464309\pi$
$80$		0			0
$81$	−451.284	−	572.524i	−0.619045	−	0.785355i
$82$		0			0
$83$	610.720	−	1057.80i	0.807653	−	1.39890i	−0.106832	−	0.994277i	$-0.534071\pi$
$83$	610.720	−	1057.80i	0.807653	−	1.39890i	0.914485	−	0.404619i	$-0.132596\pi$
$84$		0			0
$85$	−2.14977	−	3.72351i	−0.00274324	−	0.00475142i
$86$		0			0
$87$	−1371.01	+	49.3530i	−1.68952	+	0.0608184i
$88$		0			0
$89$	406.886	−	704.748i	0.484605	−	0.839361i	−0.515238	−	0.857047i	$-0.672297\pi$
$89$	406.886	−	704.748i	0.484605	−	0.839361i	0.999844	+	0.0176859i	$0.00562989\pi$
$90$		0			0
$91$	44.9468	+	10.8450i	0.0517770	+	0.0124930i
$92$		0			0
$93$	−1334.77	+	48.0483i	−1.48827	+	0.0535740i
$94$		0			0
$95$	262.914	+	151.794i	0.283942	+	0.163934i
$96$		0			0
$97$	−496.443	−	286.621i	−0.519651	−	0.300021i	0.217141	−	0.976140i	$-0.430327\pi$
$97$	−496.443	−	286.621i	−0.519651	−	0.300021i	−0.736792	+	0.676120i	$0.763660\pi$
$98$		0			0
$99$	−755.434	−	366.441i	−0.766909	−	0.372007i
$100$		0			0
$101$	1014.98			0.999940			0.499970	−	0.866043i	$-0.333344\pi$
$101$	1014.98			0.999940			0.499970	+	0.866043i	$0.333344\pi$
$102$		0			0
$103$			790.590i			0.756302i	0.925744	+	0.378151i	$0.123440\pi$
$103$			790.590i			0.756302i	−0.925744	+	0.378151i	$0.876560\pi$
$104$		0			0
$105$	−326.073	−	66.3622i	−0.303062	−	0.0616789i
$106$		0			0
$107$	−739.624	−	427.022i	−0.668244	−	0.385811i	0.127167	−	0.991881i	$-0.459412\pi$
$107$	−739.624	−	427.022i	−0.668244	−	0.385811i	−0.795411	+	0.606070i	$0.792745\pi$
$108$		0			0
$109$	−51.1159	−	88.5354i	−0.0449176	−	0.0777996i	0.842693	−	0.538395i	$-0.180969\pi$
$109$	−51.1159	−	88.5354i	−0.0449176	−	0.0777996i	−0.887610	+	0.460596i	$0.847636\pi$
$110$		0			0
$111$	−17.8429	−	495.671i	−0.0152574	−	0.423847i
$112$		0			0
$113$	−459.268	+	265.159i	−0.382339	+	0.220743i	−0.678835	−	0.734290i	$-0.737515\pi$
$113$	−459.268	+	265.159i	−0.382339	+	0.220743i	0.296496	+	0.955034i	$0.404182\pi$
$114$		0			0
$115$			171.940i			0.139421i
$116$		0			0
$117$	−4.84666	−	67.2323i	−0.00382969	−	0.0531250i
$118$		0			0
$119$	5.40145	−	22.3863i	0.00416093	−	0.0172449i
$120$		0			0
$121$	363.978			0.273462
$122$		0			0
$123$	862.750	+	457.543i	0.632452	+	0.335409i
$124$		0			0
$125$	−823.106			−0.588967
$126$		0			0
$127$	−2163.65			−1.51176			−0.755878	−	0.654713i	$-0.772790\pi$
$127$	−2163.65			−1.51176			−0.755878	+	0.654713i	$0.772790\pi$
$128$		0			0
$129$	−49.7989	−	1383.40i	−0.0339888	−	0.944199i
$130$		0			0
$131$	2570.55			1.71443			0.857215	−	0.514959i	$-0.172193\pi$
$131$	2570.55			1.71443			0.857215	+	0.514959i	$0.172193\pi$
$132$		0			0
$133$	460.044	+	1559.61i	0.299931	+	1.01680i
$134$		0			0
$135$	52.2645	+	482.292i	0.0333201	+	0.307475i
$136$		0			0
$137$		−	618.994i		−	0.386016i	−0.981197	−	0.193008i	$-0.938176\pi$
$137$		−	618.994i		−	0.386016i	0.981197	−	0.193008i	$-0.0618244\pi$
$138$		0			0
$139$	977.790	−	564.527i	0.596655	−	0.344479i	−0.171070	−	0.985259i	$-0.554722\pi$
$139$	977.790	−	564.527i	0.596655	−	0.344479i	0.767724	+	0.640780i	$0.221389\pi$
$140$		0			0
$141$	−2625.10	−	1392.17i	−1.56790	−	0.831504i
$142$		0			0
$143$	−38.8175	−	67.2339i	−0.0226999	−	0.0393174i
$144$		0			0
$145$	790.627	+	456.469i	0.452814	+	0.261432i
$146$		0			0
$147$	−1020.52	−	1461.19i	−0.572590	−	0.819842i
$148$		0			0
$149$		−	1349.08i		−	0.741751i	−0.928683	−	0.370875i	$-0.879058\pi$
$149$		−	1349.08i		−	0.741751i	0.928683	−	0.370875i	$-0.120942\pi$
$150$		0			0
$151$	−424.315			−0.228677			−0.114339	−	0.993442i	$-0.536475\pi$
$151$	−424.315			−0.228677			−0.114339	+	0.993442i	$0.536475\pi$
$152$		0			0
$153$	−33.4858	+	2.41393i	−0.0176939	+	0.00127552i
$154$		0			0
$155$	769.726	+	444.401i	0.398876	+	0.230291i
$156$		0			0
$157$	878.260	+	507.063i	0.446451	+	0.257758i	0.706330	−	0.707883i	$-0.250349\pi$
$157$	878.260	+	507.063i	0.446451	+	0.257758i	−0.259879	+	0.965641i	$0.583683\pi$
$158$		0			0
$159$	471.353	−	888.790i	0.235099	−	0.443306i
$160$		0			0
$161$	−634.683	+	667.292i	−0.310683	+	0.326646i
$162$		0			0
$163$	−40.6443	+	70.3980i	−0.0195307	+	0.0338282i	−0.875626	−	0.482991i	$-0.839551\pi$
$163$	−40.6443	+	70.3980i	−0.0195307	+	0.0338282i	0.856095	+	0.516819i	$0.172884\pi$
$164$		0			0
$165$	296.589	+	473.508i	0.139936	+	0.223410i
$166$		0			0
$167$	−240.081	−	415.832i	−0.111245	−	0.192683i	0.805027	−	0.593238i	$-0.202151\pi$
$167$	−240.081	−	415.832i	−0.111245	−	0.192683i	−0.916273	+	0.400555i	$0.868817\pi$
$168$		0			0
$169$	−1095.38	+	1897.26i	−0.498582	+	0.863569i
$170$		0			0
$171$	1962.41	−	1329.82i	0.877600	−	0.594699i
$172$		0			0
$173$	445.983	+	772.465i	0.195997	+	0.339477i	0.947227	−	0.320564i	$-0.103872\pi$
$173$	445.983	+	772.465i	0.195997	+	0.339477i	−0.751230	+	0.660041i	$0.770539\pi$
$174$		0			0
$175$	−1517.00	−	1442.87i	−0.655282	−	0.623260i
$176$		0			0
$177$	54.4070	+	1511.41i	0.0231044	+	0.641835i
$178$		0			0
$179$	−777.039	+	448.624i	−0.324462	+	0.187328i	−0.653380	−	0.757031i	$-0.726649\pi$
$179$	−777.039	+	448.624i	−0.324462	+	0.187328i	0.328918	+	0.944359i	$0.393316\pi$
$180$		0			0
$181$		−	2318.80i		−	0.952240i	−0.879380	−	0.476120i	$-0.842043\pi$
$181$		−	2318.80i		−	0.952240i	0.879380	−	0.476120i	$-0.157957\pi$
$182$		0			0
$183$	386.800	−	729.355i	0.156246	−	0.294620i
$184$		0			0
$185$	−165.030	+	285.840i	−0.0655850	+	0.113596i
$186$		0			0
$187$	−33.4866	+	19.3335i	−0.0130951	+	0.00756045i
$188$		0			0
$189$	−1577.45	+	2064.68i	−0.607105	+	0.794622i
$190$		0			0
$191$	1769.04	−	1021.36i	0.670174	−	0.386925i	−0.125969	−	0.992034i	$-0.540204\pi$
$191$	1769.04	−	1021.36i	0.670174	−	0.386925i	0.796142	+	0.605109i	$0.206871\pi$
$192$		0			0
$193$	−242.764	+	420.480i	−0.0905417	+	0.156823i	−0.907739	−	0.419535i	$-0.862193\pi$
$193$	−242.764	+	420.480i	−0.0905417	+	0.156823i	0.817197	+	0.576358i	$0.195527\pi$
$194$		0			0
$195$	−21.0160	+	39.6282i	−0.00771790	+	0.0145530i
$196$		0			0
$197$		−	2212.99i		−	0.800351i	−0.916439	−	0.400175i	$-0.868949\pi$
$197$		−	2212.99i		−	0.800351i	0.916439	−	0.400175i	$-0.131051\pi$
$198$		0			0
$199$	930.187	−	537.044i	0.331353	−	0.191307i	−0.325089	−	0.945684i	$-0.605394\pi$
$199$	930.187	−	537.044i	0.331353	−	0.191307i	0.656442	+	0.754377i	$0.272061\pi$
$200$		0			0
$201$	82.9914	+	2305.48i	0.0291232	+	0.809035i
$202$		0			0
$203$	1383.43	+	4689.99i	0.478313	+	1.62154i
$204$		0			0
$205$	−324.930	−	562.795i	−0.110703	−	0.191743i
$206$		0			0
$207$	1207.97	+	585.952i	0.405601	+	0.196746i
$208$		0			0
$209$	1365.13	−	2364.47i	0.451807	−	0.782553i
$210$		0			0
$211$	1512.38	+	2619.51i	0.493442	+	0.854666i	0.999971	−	0.00755635i	$-0.00240528\pi$
$211$	1512.38	+	2619.51i	0.493442	+	0.854666i	−0.506530	+	0.862223i	$0.669072\pi$
$212$		0			0
$213$	1118.05	+	1784.99i	0.359661	+	0.574203i
$214$		0			0
$215$	−460.593	+	797.770i	−0.146103	+	0.253058i
$216$		0			0
$217$	1346.85	+	4566.00i	0.421338	+	1.42839i
$218$		0			0
$219$	1421.13	−	2679.70i	0.438498	−	0.826838i
$220$		0			0
$221$	−2.68839	−	1.55214i	−0.000818284	−	0.000472437i
$222$		0			0
$223$	1185.83	+	684.638i	0.356094	+	0.205591i	0.667366	−	0.744730i	$-0.267422\pi$
$223$	1185.83	+	684.638i	0.356094	+	0.205591i	−0.311272	+	0.950321i	$0.600755\pi$
$224$		0			0
$225$	−1332.08	+	2746.15i	−0.394692	+	0.813674i
$226$		0			0
$227$	6038.25			1.76552			0.882760	−	0.469825i	$-0.155683\pi$
$227$	6038.25			1.76552			0.882760	+	0.469825i	$0.155683\pi$
$228$		0			0
$229$			2591.85i			0.747921i	0.927445	+	0.373961i	$0.122000\pi$
$229$			2591.85i			0.747921i	−0.927445	+	0.373961i	$0.878000\pi$
$230$		0			0
$231$	−596.815	+	2932.47i	−0.169989	+	0.835249i
$232$		0			0
$233$	−1457.96	−	841.752i	−0.409931	−	0.236674i	0.280829	−	0.959758i	$-0.409391\pi$
$233$	−1457.96	−	841.752i	−0.409931	−	0.236674i	−0.690760	+	0.723084i	$0.742724\pi$
$234$		0			0
$235$	988.668	+	1712.42i	0.274441	+	0.475346i
$236$		0			0
$237$	−5908.59	−	3133.51i	−1.61943	−	0.858831i
$238$		0			0
$239$	−3631.74	+	2096.79i	−0.982920	+	0.567489i	−0.903150	−	0.429324i	$-0.858752\pi$
$239$	−3631.74	+	2096.79i	−0.982920	+	0.567489i	−0.0797694	+	0.996813i	$0.525418\pi$
$240$		0			0
$241$		−	3788.07i		−	1.01249i	−0.862389	−	0.506246i	$-0.831033\pi$
$241$		−	3788.07i		−	1.01249i	0.862389	−	0.506246i	$-0.168967\pi$
$242$		0			0
$243$	3566.47	+	1276.41i	0.941518	+	0.336963i
$244$		0			0
$245$	59.3722	+	1184.54i	0.0154823	+	0.308887i
$246$		0			0
$247$	219.192			0.0564649
$248$		0			0
$249$	228.320	+	6342.68i	0.0581093	+	1.61426i
$250$		0			0
$251$	−3435.63			−0.863966			−0.431983	−	0.901882i	$-0.642186\pi$
$251$	−3435.63			−0.863966			−0.431983	+	0.901882i	$0.642186\pi$
$252$		0			0
$253$	1546.30			0.384250
$254$		0			0
$255$	19.7372	+	10.4673i	0.00484703	+	0.00257053i
$256$		0			0
$257$	−3331.12			−0.808520			−0.404260	−	0.914644i	$-0.632471\pi$
$257$	−3331.12			−0.808520			−0.404260	+	0.914644i	$0.632471\pi$
$258$		0			0
$259$	−1695.60	+	500.158i	−0.406793	+	0.119993i
$260$		0			0
$261$	5901.30	−	3998.97i	1.39955	−	0.948392i
$262$		0			0
$263$			5911.11i			1.38591i	0.720980	+	0.692956i	$0.243692\pi$
$263$			5911.11i			1.38591i	−0.720980	+	0.692956i	$0.756308\pi$
$264$		0			0
$265$	−579.781	+	334.737i	−0.134399	+	0.0775952i
$266$		0			0
$267$	152.116	+	4225.75i	0.0348665	+	0.968583i
$268$		0			0
$269$	−460.264	−	797.201i	−0.104323	−	0.180692i	0.809139	−	0.587618i	$-0.199934\pi$
$269$	−460.264	−	797.201i	−0.104323	−	0.180692i	−0.913461	+	0.406926i	$0.866601\pi$
$270$		0			0
$271$	−2199.30	−	1269.77i	−0.492981	−	0.284623i	0.232829	−	0.972518i	$-0.425202\pi$
$271$	−2199.30	−	1269.77i	−0.492981	−	0.284623i	−0.725810	+	0.687895i	$0.758535\pi$
$272$		0			0
$273$	−227.842	+	76.2187i	−0.0505115	+	0.0168973i
$274$		0			0
$275$			3515.32i			0.770842i
$276$		0			0
$277$	2879.16			0.624520			0.312260	−	0.949997i	$-0.398914\pi$
$277$	2879.16			0.624520			0.312260	+	0.949997i	$0.398914\pi$
$278$		0			0
$279$	5745.30	−	3893.26i	1.23284	−	0.835423i
$280$		0			0
$281$	−6811.30	−	3932.50i	−1.44601	−	0.834852i	−0.447767	−	0.894150i	$-0.647780\pi$
$281$	−6811.30	−	3932.50i	−1.44601	−	0.834852i	−0.998240	+	0.0592980i	$0.981114\pi$
$282$		0			0
$283$	−4729.76	−	2730.73i	−0.993481	−	0.573586i	−0.0871678	−	0.996194i	$-0.527782\pi$
$283$	−4729.76	−	2730.73i	−0.993481	−	0.573586i	−0.906313	+	0.422607i	$0.861115\pi$
$284$		0			0
$285$	−1576.47	+	56.7487i	−0.327655	+	0.0117948i
$286$		0			0
$287$	816.411	−	3383.61i	0.167914	−	0.695916i
$288$		0			0
$289$	2455.73	−	4253.44i	0.499843	−	0.865753i
$290$		0			0
$291$	2976.73	−	107.155i	0.599653	−	0.0215860i
$292$		0			0
$293$	411.644	+	712.989i	0.0820768	+	0.142161i	0.904142	−	0.427232i	$-0.140511\pi$
$293$	411.644	+	712.989i	0.0820768	+	0.142161i	−0.822065	+	0.569394i	$0.807178\pi$
$294$		0			0
$295$	503.213	−	871.590i	0.0993159	−	0.172020i
$296$		0			0
$297$	4337.39	−	470.030i	0.847411	−	0.0918313i
$298$		0			0
$299$	62.0707	+	107.510i	0.0120055	+	0.0207941i
$300$		0			0
$301$	−4732.36	+	1395.93i	−0.906209	+	0.267308i
$302$		0			0
$303$	−4469.57	+	2799.59i	−0.847427	+	0.530799i
$304$		0			0
$305$	−475.778	+	274.691i	−0.0893212	+	0.0515696i
$306$		0			0
$307$		−	9015.37i		−	1.67601i	−0.545665	−	0.838004i	$-0.683723\pi$
$307$		−	9015.37i		−	1.67601i	0.545665	−	0.838004i	$-0.316277\pi$
$308$		0			0
$309$	−2180.67	−	3481.46i	−0.401469	−	0.640950i
$310$		0			0
$311$	−5320.73	+	9215.78i	−0.970132	+	1.68032i	−0.274986	+	0.961448i	$0.588673\pi$
$311$	−5320.73	+	9215.78i	−0.970132	+	1.68032i	−0.695145	+	0.718869i	$0.744660\pi$
$312$		0			0
$313$	6755.41	−	3900.24i	1.21993	−	0.704328i	0.255028	−	0.966934i	$-0.417915\pi$
$313$	6755.41	−	3900.24i	1.21993	−	0.704328i	0.964903	+	0.262606i	$0.0845819\pi$
$314$		0			0
$315$	1618.95	−	607.167i	0.289579	−	0.108603i
$316$		0			0
$317$	6756.97	−	3901.14i	1.19719	−	0.691198i	0.237263	−	0.971446i	$-0.423750\pi$
$317$	6756.97	−	3901.14i	1.19719	−	0.691198i	0.959928	+	0.280247i	$0.0904164\pi$
$318$		0			0
$319$	4105.16	−	7110.34i	0.720516	−	1.24797i
$320$		0			0
$321$	4434.87	−	159.644i	0.771122	−	0.0277584i
$322$		0			0
$323$		−	109.171i		−	0.0188063i
$324$		0			0
$325$	−244.409	+	141.109i	−0.0417149	+	0.0240841i
$326$		0			0
$327$	469.301	+	248.885i	0.0793651	+	0.0420897i
$328$		0			0
$329$	−2484.10	+	10295.3i	−0.416271	+	1.72523i
$330$		0			0
$331$	−3616.94	−	6264.73i	−0.600620	−	1.04030i	−0.992727	−	0.120384i	$-0.961587\pi$
$331$	−3616.94	−	6264.73i	−0.600620	−	1.04030i	0.392108	−	0.919919i	$-0.371746\pi$
$332$		0			0
$333$	1445.77	+	2133.53i	0.237921	+	0.351101i
$334$		0			0
$335$	767.591	−	1329.51i	0.125188	−	0.216832i
$336$		0			0
$337$	−3328.34	−	5764.85i	−0.538001	−	0.931844i	−0.999012	−	0.0444499i	$-0.985846\pi$
$337$	−3328.34	−	5764.85i	−0.538001	−	0.931844i	0.461011	−	0.887394i	$-0.347487\pi$
$338$		0			0
$339$	1291.06	−	2434.45i	0.206846	−	0.390033i
$340$		0			0
$341$	3996.63	−	6922.37i	0.634691	−	1.09932i
$342$		0			0
$343$	−4142.07	+	4816.31i	−0.652044	+	0.758181i
$344$		0			0
$345$	−474.257	−	757.158i	−0.0740092	−	0.118157i
$346$		0			0
$347$	−4286.13	−	2474.60i	−0.663088	−	0.382834i	0.130364	−	0.991466i	$-0.458385\pi$
$347$	−4286.13	−	2474.60i	−0.663088	−	0.382834i	−0.793453	+	0.608632i	$0.791719\pi$
$348$		0			0
$349$	−4149.53	−	2395.73i	−0.636444	−	0.367451i	0.146799	−	0.989166i	$-0.453103\pi$
$349$	−4149.53	−	2395.73i	−0.636444	−	0.367451i	−0.783244	+	0.621715i	$0.786436\pi$
$350$		0			0
$351$	206.788	+	282.697i	0.0314460	+	0.0429894i
$352$		0			0
$353$	−8960.92			−1.35111			−0.675555	−	0.737310i	$-0.736096\pi$
$353$	−8960.92			−1.35111			−0.675555	+	0.737310i	$0.736096\pi$
$354$		0			0
$355$		−	1401.60i		−	0.209547i
$356$		0			0
$357$	37.9616	+	113.479i	0.00562784	+	0.0168234i
$358$		0			0
$359$	−11505.1	−	6642.48i	−1.69141	−	0.976536i	−0.953382	−	0.301767i	$-0.902424\pi$
$359$	−11505.1	−	6642.48i	−1.69141	−	0.976536i	−0.738029	−	0.674769i	$-0.764243\pi$
$360$		0			0
$361$	424.739	+	735.669i	0.0619243	+	0.107256i
$362$		0			0
$363$	−1602.82	+	1003.95i	−0.231753	+	0.145162i
$364$		0			0
$365$	−1748.04	+	1009.23i	−0.250676	+	0.144728i
$366$		0			0
$367$		−	7040.04i		−	1.00133i	−0.865642	−	0.500664i	$-0.833089\pi$
$367$		−	7040.04i		−	1.00133i	0.865642	−	0.500664i	$-0.166911\pi$
$368$		0			0
$369$	−5061.26	+	364.858i	−0.714034	+	0.0514735i
$370$		0			0
$371$	−3485.73	−	841.052i	−0.487790	−	0.117696i
$372$		0			0
$373$	2535.77			0.352003			0.176001	−	0.984390i	$-0.443684\pi$
$373$	2535.77			0.352003			0.176001	+	0.984390i	$0.443684\pi$
$374$		0			0
$375$	3624.65	−	2270.36i	0.499136	−	0.312642i
$376$		0			0
$377$	659.145			0.0900470
$378$		0			0
$379$	−5227.61			−0.708507			−0.354254	−	0.935149i	$-0.615265\pi$
$379$	−5227.61			−0.708507			−0.354254	+	0.935149i	$0.615265\pi$
$380$		0			0
$381$	9527.91	−	5967.95i	1.28118	−	0.802487i
$382$		0			0
$383$	3573.80			0.476795			0.238398	−	0.971168i	$-0.423378\pi$
$383$	3573.80			0.476795			0.238398	+	0.971168i	$0.423378\pi$
$384$		0			0
$385$	1372.45	−	1442.97i	0.181680	−	0.191014i
$386$		0			0
$387$	4035.10	+	5954.62i	0.530015	+	0.782146i
$388$		0			0
$389$		−	10614.3i		−	1.38346i	−0.722158	−	0.691728i	$-0.756850\pi$
$389$		−	10614.3i		−	1.38346i	0.722158	−	0.691728i	$-0.243150\pi$
$390$		0			0
$391$	53.5463	−	30.9150i	0.00692571	−	0.00399856i
$392$		0			0
$393$	−11319.7	+	7090.30i	−1.45294	+	0.910072i
$394$		0			0
$395$	2225.30	+	3854.33i	0.283460	+	0.490968i
$396$		0			0
$397$	12393.1	+	7155.16i	1.56673	+	0.904552i	0.996547	+	0.0830338i	$0.0264610\pi$
$397$	12393.1	+	7155.16i	1.56673	+	0.904552i	0.570183	+	0.821518i	$0.306872\pi$
$398$		0			0
$399$	−6327.68	−	5598.99i	−0.793936	−	0.702506i
$400$		0			0
$401$			11677.9i			1.45428i	0.686487	+	0.727142i	$0.259152\pi$
$401$			11677.9i			1.45428i	−0.686487	+	0.727142i	$0.740848\pi$
$402$		0			0
$403$	641.720			0.0793210
$404$		0			0
$405$	−1560.45	−	1979.67i	−0.191455	−	0.242891i
$406$		0			0
$407$	2570.64	+	1484.16i	0.313076	+	0.180754i
$408$		0			0
$409$	−7362.28	−	4250.62i	−0.890077	−	0.513886i	−0.0161093	−	0.999870i	$-0.505128\pi$
$409$	−7362.28	−	4250.62i	−0.890077	−	0.513886i	−0.873968	+	0.485984i	$0.838461\pi$
$410$		0			0
$411$	1707.36	+	2725.82i	0.204909	+	0.327140i
$412$		0			0
$413$	5170.26	−	1525.10i	0.616010	−	0.181707i
$414$		0			0
$415$	2111.74	−	3657.65i	0.249787	−	0.432643i
$416$		0			0
$417$	−2748.69	+	5182.98i	−0.322792	+	0.608661i
$418$		0			0
$419$	−2317.23	−	4013.55i	−0.270176	−	0.467959i	0.698730	−	0.715385i	$-0.253749\pi$
$419$	−2317.23	−	4013.55i	−0.270176	−	0.467959i	−0.968907	+	0.247426i	$0.920415\pi$
$420$		0			0
$421$	3934.88	−	6815.41i	0.455521	−	0.788985i	−0.543197	−	0.839605i	$-0.682786\pi$
$421$	3934.88	−	6815.41i	0.455521	−	0.788985i	0.998718	+	0.0506201i	$0.0161198\pi$
$422$		0			0
$423$	15400.0	−	1110.16i	1.77015	−	0.127607i
$424$		0			0
$425$	70.2811	+	121.730i	0.00802149	+	0.0138936i
$426$		0			0
$427$	−2860.45	−	690.181i	−0.324184	−	0.0782206i
$428$		0			0
$429$	356.388	+	189.003i	0.0401085	+	0.0212708i
$430$		0			0
$431$	−14037.4	+	8104.49i	−1.56881	+	0.905753i	−0.572502	+	0.819903i	$0.694027\pi$
$431$	−14037.4	+	8104.49i	−1.56881	+	0.905753i	−0.996308	+	0.0858498i	$0.972639\pi$
$432$		0			0
$433$			12760.5i			1.41624i	0.706094	+	0.708118i	$0.250455\pi$
$433$			12760.5i			1.41624i	−0.706094	+	0.708118i	$0.749545\pi$
$434$		0			0
$435$	−4740.69	+	170.653i	−0.522526	+	0.0188096i
$436$		0			0
$437$	−2182.89	+	3780.87i	−0.238951	+	0.413875i
$438$		0			0
$439$	−4901.84	+	2830.08i	−0.532921	+	0.307682i	−0.742205	−	0.670173i	$-0.766220\pi$
$439$	−4901.84	+	2830.08i	−0.532921	+	0.307682i	0.209284	+	0.977855i	$0.432887\pi$
$440$		0			0
$441$	8524.33	+	3619.66i	0.920455	+	0.390849i
$442$		0			0
$443$	−5138.56	+	2966.75i	−0.551107	+	0.318182i	−0.749568	−	0.661927i	$-0.769739\pi$
$443$	−5138.56	+	2966.75i	−0.551107	+	0.318182i	0.198462	+	0.980109i	$0.436405\pi$
$444$		0			0
$445$	1406.93	−	2436.87i	0.149876	−	0.259593i
$446$		0			0
$447$	3721.14	+	5940.84i	0.393744	+	0.628617i
$448$		0			0
$449$		−	11706.5i		−	1.23043i	−0.788358	−	0.615216i	$-0.789069\pi$
$449$		−	11706.5i		−	1.23043i	0.788358	−	0.615216i	$-0.210931\pi$
$450$		0			0
$451$	−5061.38	+	2922.19i	−0.528451	+	0.305101i
$452$		0			0
$453$	1868.52	−	1170.38i	0.193799	−	0.121389i
$454$		0			0
$455$	155.417	+	37.4997i	0.0160133	+	0.00386376i
$456$		0			0
$457$	7421.67	+	12854.7i	0.759675	+	1.31580i	0.943017	+	0.332746i	$0.107975\pi$
$457$	7421.67	+	12854.7i	0.759675	+	1.31580i	−0.183342	+	0.983049i	$0.558692\pi$
$458$		0			0
$459$	140.800	−	102.993i	0.0143181	−	0.0104734i
$460$		0			0
$461$	4515.51	−	7821.10i	0.456200	−	0.790162i	−0.542556	−	0.840020i	$-0.682543\pi$
$461$	4515.51	−	7821.10i	0.456200	−	0.790162i	0.998756	+	0.0498575i	$0.0158767\pi$
$462$		0			0
$463$	7326.56	+	12690.0i	0.735408	+	1.27376i	0.954544	+	0.298070i	$0.0963429\pi$
$463$	7326.56	+	12690.0i	0.735408	+	1.27376i	−0.219136	+	0.975694i	$0.570324\pi$
$464$		0			0
$465$	−4615.36	+	166.141i	−0.460285	+	0.0165691i
$466$		0			0
$467$	−3535.45	+	6123.57i	−0.350323	+	0.606778i	−0.986306	−	0.164926i	$-0.947262\pi$
$467$	−3535.45	+	6123.57i	−0.350323	+	0.606778i	0.635983	+	0.771703i	$0.280595\pi$
$468$		0			0
$469$	7886.62	−	2326.35i	0.776483	−	0.229043i
$470$		0			0
$471$	−5266.15	+	189.568i	−0.515183	+	0.0185453i
$472$		0			0
$473$	7174.58	+	4142.24i	0.697437	+	0.402665i
$474$		0			0
$475$	−8595.30	−	4962.50i	−0.830273	−	0.479358i
$476$		0			0
$477$	375.870	+	5214.02i	0.0360794	+	0.500489i
$478$		0			0
$479$	13137.1			1.25313			0.626564	−	0.779370i	$-0.284461\pi$
$479$	13137.1			1.25313			0.626564	+	0.779370i	$0.284461\pi$
$480$		0			0
$481$			238.305i			0.0225899i
$482$		0			0
$483$	954.329	−	4689.13i	0.0899036	−	0.441745i
$484$		0			0
$485$	−1716.60	−	991.079i	−0.160715	−	0.0927888i
$486$		0			0
$487$	−10134.9	−	17554.1i	−0.943027	−	1.63337i	−0.759654	−	0.650328i	$-0.774632\pi$
$487$	−10134.9	−	17554.1i	−0.943027	−	1.63337i	−0.183374	−	0.983043i	$-0.558702\pi$
$488$		0			0
$489$	−15.1950	−	422.114i	−0.00140520	−	0.0390361i
$490$		0			0
$491$	3894.03	−	2248.22i	0.357913	−	0.206641i	−0.310252	−	0.950654i	$-0.600413\pi$
$491$	3894.03	−	2248.22i	0.357913	−	0.206641i	0.668165	+	0.744013i	$0.267080\pi$
$492$		0			0
$493$		−	328.295i		−	0.0299912i
$494$		0			0
$495$	−2612.14	−	1267.08i	−0.237185	−	0.115052i
$496$		0			0
$497$	5173.74	−	5439.56i	0.466950	−	0.490941i
$498$		0			0
$499$	−5561.35			−0.498918			−0.249459	−	0.968385i	$-0.580253\pi$
$499$	−5561.35			−0.498918			−0.249459	+	0.968385i	$0.580253\pi$
$500$		0			0
$501$	2204.20	+	1168.96i	0.196560	+	0.104242i
$502$		0			0
$503$	−6642.04			−0.588775			−0.294388	−	0.955686i	$-0.595116\pi$
$503$	−6642.04			−0.588775			−0.294388	+	0.955686i	$0.595116\pi$
$504$		0			0
$505$	3509.58			0.309256
$506$		0			0
$507$	−409.514	−	11376.2i	−0.0358721	−	0.996518i
$508$		0			0
$509$	3532.48			0.307612			0.153806	−	0.988101i	$-0.450847\pi$
$509$	3532.48			0.307612			0.153806	+	0.988101i	$0.450847\pi$
$510$		0			0
$511$	−10509.5	−	2535.77i	−0.909808	−	0.219522i
$512$		0			0
$513$	−4973.74	+	11268.9i	−0.428062	+	0.969851i
$514$		0			0
$515$			2733.70i			0.233905i
$516$		0			0
$517$	15400.3	−	8891.38i	1.31007	−	0.756369i
$518$		0			0
$519$	−4094.62	−	2171.50i	−0.346308	−	0.183658i
$520$		0			0
$521$	5551.90	+	9616.17i	0.466858	+	0.808622i	0.999283	−	0.0378554i	$-0.0120526\pi$
$521$	5551.90	+	9616.17i	0.466858	+	0.808622i	−0.532425	+	0.846477i	$0.678719\pi$
$522$		0			0
$523$	2636.38	+	1522.11i	0.220422	+	0.127261i	0.606146	−	0.795354i	$-0.292715\pi$
$523$	2636.38	+	1522.11i	0.220422	+	0.127261i	−0.385724	+	0.922614i	$0.626048\pi$
$524$		0			0
$525$	10660.1	+	2169.54i	0.886183	+	0.180355i
$526$		0			0
$527$		−	319.616i		−	0.0264187i
$528$		0			0
$529$	9694.40			0.796778
$530$		0			0
$531$	−4408.49	−	6505.62i	−0.360286	−	0.531676i
$532$		0			0
$533$	−406.341	−	234.601i	−0.0330217	−	0.0190651i
$534$		0			0
$535$	−2557.47	−	1476.55i	−0.206671	−	0.119322i
$536$		0			0
$537$	2184.36	−	4118.86i	0.175535	−	0.330991i
$538$		0			0
$539$	10652.9	−	533.952i	0.851303	−	0.0426696i
$540$		0			0
$541$	1771.35	−	3068.07i	0.140770	−	0.243820i	−0.787017	−	0.616931i	$-0.788376\pi$
$541$	1771.35	−	3068.07i	0.140770	−	0.243820i	0.927787	+	0.373111i	$0.121709\pi$
$542$		0			0
$543$	6395.91	+	10211.1i	0.505478	+	0.807002i
$544$		0			0
$545$	−176.748	−	306.137i	−0.0138919	−	0.0240614i
$546$		0			0
$547$	−8883.45	+	15386.6i	−0.694385	+	1.20271i	0.276002	+	0.961157i	$0.410990\pi$
$547$	−8883.45	+	15386.6i	−0.694385	+	1.20271i	−0.970387	+	0.241554i	$0.922343\pi$
$548$		0			0
$549$	308.445	+	4278.71i	0.0239783	+	0.332624i
$550$		0			0
$551$	11590.3	+	20075.0i	0.896125	+	1.55213i
$552$		0			0
$553$	−5591.23	+	23172.8i	−0.429952	+	1.78193i
$554$		0			0
$555$	−61.6970	−	1713.93i	−0.00471873	−	0.131085i
$556$		0			0
$557$	−18571.9	+	10722.5i	−1.41277	+	0.815665i	−0.995649	−	0.0931845i	$-0.970295\pi$
$557$	−18571.9	+	10722.5i	−1.41277	+	0.815665i	−0.417124	+	0.908849i	$0.636962\pi$
$558$		0			0
$559$			665.101i			0.0503234i
$560$		0			0
$561$	94.1352	−	177.503i	0.00708448	−	0.0133586i
$562$		0			0
$563$	−4515.29	+	7820.71i	−0.338005	+	0.585441i	−0.984057	−	0.177852i	$-0.943085\pi$
$563$	−4515.29	+	7820.71i	−0.338005	+	0.585441i	0.646053	+	0.763293i	$0.276419\pi$
$564$		0			0
$565$	−1588.06	+	916.864i	−0.118248	+	0.0682704i
$566$		0			0
$567$	1251.54	−	13443.1i	0.0926981	−	0.995694i
$568$		0			0
$569$	9362.28	−	5405.32i	0.689784	−	0.398247i	−0.113747	−	0.993510i	$-0.536285\pi$
$569$	9362.28	−	5405.32i	0.689784	−	0.398247i	0.803531	+	0.595263i	$0.202952\pi$
$570$		0			0
$571$	5520.27	−	9561.40i	0.404582	−	0.700757i	−0.589691	−	0.807629i	$-0.700750\pi$
$571$	5520.27	−	9561.40i	0.404582	−	0.700757i	0.994273	+	0.106873i	$0.0340837\pi$
$572$		0			0
$573$	−4973.00	+	9377.17i	−0.362566	+	0.683659i
$574$		0			0
$575$		−	5621.12i		−	0.407682i
$576$		0			0
$577$	−11806.0	+	6816.19i	−0.851802	+	0.491788i	−0.861258	−	0.508167i	$-0.830323\pi$
$577$	−11806.0	+	6816.19i	−0.851802	+	0.491788i	0.00945662	+	0.999955i	$0.496990\pi$
$578$		0			0
$579$	−90.7585	−	2521.25i	−0.00651432	−	0.180966i
$580$		0			0
$581$	21697.1	−	6400.10i	1.54931	−	0.457007i
$582$		0			0
$583$	3010.39	+	5214.14i	0.213855	+	0.370408i
$584$		0			0
$585$	−16.7588	−	232.476i	−0.00118443	−	0.0164302i
$586$		0			0
$587$	−7427.33	+	12864.5i	−0.522247	+	0.904558i	0.477418	+	0.878676i	$0.341573\pi$
$587$	−7427.33	+	12864.5i	−0.522247	+	0.904558i	−0.999665	+	0.0258815i	$0.991761\pi$
$588$		0			0
$589$	11283.9	+	19544.3i	0.789382	+	1.36725i
$590$		0			0
$591$	6104.04	+	9745.18i	0.424851	+	0.678279i
$592$		0			0
$593$	5557.23	−	9625.41i	0.384837	−	0.666557i	−0.606910	−	0.794771i	$-0.707591\pi$
$593$	5557.23	−	9625.41i	0.384837	−	0.666557i	0.991747	+	0.128214i	$0.0409244\pi$
$594$		0			0
$595$	18.6771	−	77.4071i	0.00128687	−	0.00533342i
$596$		0			0
$597$	−2614.88	+	4930.65i	−0.179263	+	0.338021i
$598$		0			0
$599$	−23353.6	−	13483.2i	−1.59299	−	0.919713i	−0.992791	−	0.119861i	$-0.961755\pi$
$599$	−23353.6	−	13483.2i	−1.59299	−	0.919713i	−0.600198	−	0.799851i	$-0.704912\pi$
$600$		0			0
$601$	10479.2	+	6050.20i	0.711244	+	0.410637i	0.811521	−	0.584323i	$-0.198640\pi$
$601$	10479.2	+	6050.20i	0.711244	+	0.410637i	−0.100278	+	0.994959i	$0.531973\pi$
$602$		0			0
$603$	−6724.62	−	9923.55i	−0.454142	−	0.670180i
$604$		0			0
$605$	1258.56			0.0845749
$606$		0			0
$607$			14091.0i			0.942235i	0.882071	+	0.471117i	$0.156149\pi$
$607$			14091.0i			0.942235i	−0.882071	+	0.471117i	$0.843851\pi$
$608$		0			0
$609$	−19028.4	−	16837.1i	−1.26612	−	1.12032i
$610$		0			0
$611$	1236.38	+	713.824i	0.0818634	+	0.0472639i
$612$		0			0
$613$	−1054.90	−	1827.14i	−0.0695059	−	0.120388i	0.829178	−	0.558985i	$-0.188809\pi$
$613$	−1054.90	−	1827.14i	−0.0695059	−	0.120388i	−0.898684	+	0.438597i	$0.855476\pi$
$614$		0			0
$615$	2983.21	+	1582.09i	0.195601	+	0.103733i
$616$		0			0
$617$	19738.2	−	11395.8i	1.28789	−	0.743565i	0.309614	−	0.950862i	$-0.399800\pi$
$617$	19738.2	−	11395.8i	1.28789	−	0.743565i	0.978278	+	0.207297i	$0.0664668\pi$
$618$		0			0
$619$			20201.8i			1.31176i	0.754866	+	0.655879i	$0.227702\pi$
$619$			20201.8i			1.31176i	−0.754866	+	0.655879i	$0.772298\pi$
$620$		0			0
$621$	−6935.65	+	751.595i	−0.448177	+	0.0485676i
$622$		0			0
$623$	14455.5	−	4264.01i	0.929611	−	0.274212i
$624$		0			0
$625$	11284.3			0.722197
$626$		0			0
$627$	510.358	+	14177.6i	0.0325067	+	0.903029i
$628$		0			0
$629$	118.690			0.00752383
$630$		0			0
$631$	16687.2			1.05278			0.526392	−	0.850242i	$-0.323544\pi$
$631$	16687.2			1.05278			0.526392	+	0.850242i	$0.323544\pi$
$632$		0			0
$633$	−13885.3	−	7363.79i	−0.871864	−	0.462376i
$634$		0			0
$635$	−7481.46			−0.467548
$636$		0			0
$637$	464.745	+	719.228i	0.0289072	+	0.0447360i
$638$		0			0
$639$	−9846.97	−	4776.50i	−0.609609	−	0.295705i
$640$		0			0
$641$			3948.37i			0.243294i	0.992573	+	0.121647i	$0.0388175\pi$
$641$			3948.37i			0.243294i	−0.992573	+	0.121647i	$0.961182\pi$
$642$		0			0
$643$	−6034.19	+	3483.84i	−0.370086	+	0.213669i	−0.673496	−	0.739191i	$-0.735208\pi$
$643$	−6034.19	+	3483.84i	−0.370086	+	0.213669i	0.303410	+	0.952860i	$0.401875\pi$
$644$		0			0
$645$	−172.195	−	4783.52i	−0.0105119	−	0.292017i
$646$		0			0
$647$	799.396	+	1384.60i	0.0485742	+	0.0841330i	0.889290	−	0.457343i	$-0.151199\pi$
$647$	799.396	+	1384.60i	0.0485742	+	0.0841330i	−0.840716	+	0.541476i	$0.817866\pi$
$648$		0			0
$649$	−7838.47	−	4525.54i	−0.474094	−	0.273718i
$650$		0			0
$651$	−18525.3	−	16392.0i	−1.11531	−	0.986869i
$652$		0			0
$653$		−	21943.9i		−	1.31506i	−0.753430	−	0.657528i	$-0.771602\pi$
$653$		−	21943.9i		−	1.31506i	0.753430	−	0.657528i	$-0.228398\pi$
$654$		0			0
$655$	8888.45			0.530230
$656$		0			0
$657$	1133.25	+	15720.3i	0.0672941	+	0.933495i
$658$		0			0
$659$	15961.3	+	9215.25i	0.943495	+	0.544727i	0.891054	−	0.453897i	$-0.149966\pi$
$659$	15961.3	+	9215.25i	0.943495	+	0.544727i	0.0524411	+	0.998624i	$0.483300\pi$
$660$		0			0
$661$	−16970.7	−	9798.05i	−0.998615	−	0.576551i	−0.0907766	−	0.995871i	$-0.528935\pi$
$661$	−16970.7	−	9798.05i	−0.998615	−	0.576551i	−0.907838	+	0.419321i	$0.862268\pi$
$662$		0			0
$663$	16.1199	−	0.580276i	0.000944262	−	3.39910e-5i
$664$		0			0
$665$	1590.74	+	5392.80i	0.0927611	+	0.314472i
$666$		0			0
$667$	−6564.30	+	11369.7i	−0.381065	+	0.660025i
$668$		0			0
$669$	−7110.36	+	255.955i	−0.410916	+	0.0147919i
$670$		0			0
$671$	2470.37	+	4278.81i	0.142128	+	0.246172i
$672$		0			0
$673$	−4893.95	+	8476.57i	−0.280309	+	0.485510i	−0.971461	−	0.237200i	$-0.923770\pi$
$673$	−4893.95	+	8476.57i	−0.280309	+	0.485510i	0.691152	+	0.722710i	$0.257104\pi$
$674$		0			0
$675$	−1708.65	−	15767.3i	−0.0974312	−	0.899085i
$676$		0			0
$677$	−13770.8	−	23851.7i	−0.781764	−	1.35405i	−0.930913	−	0.365240i	$-0.880987\pi$
$677$	−13770.8	−	23851.7i	−0.781764	−	1.35405i	0.149149	−	0.988815i	$-0.452347\pi$
$678$		0			0
$679$	−3003.68	−	10182.8i	−0.169765	−	0.575525i
$680$		0			0
$681$	−26590.2	+	16655.2i	−1.49624	+	0.937192i
$682$		0			0
$683$	20518.2	−	11846.2i	1.14950	−	0.663663i	0.200733	−	0.979646i	$-0.435668\pi$
$683$	20518.2	−	11846.2i	1.14950	−	0.663663i	0.948765	+	0.315983i	$0.102334\pi$
$684$		0			0
$685$		−	2140.36i		−	0.119385i
$686$		0			0
$687$	−7149.03	−	11413.5i	−0.397020	−	0.633847i
$688$		0			0
$689$	−241.682	+	418.605i	−0.0133633	+	0.0231460i
$690$		0			0
$691$	−10342.6	+	5971.29i	−0.569392	+	0.328739i	−0.756907	−	0.653523i	$-0.773290\pi$
$691$	−10342.6	+	5971.29i	−0.569392	+	0.328739i	0.187514	+	0.982262i	$0.439957\pi$
$692$		0			0
$693$	−5460.43	−	14559.7i	−0.299314	−	0.798091i
$694$		0			0
$695$	3381.00	−	1952.02i	0.184530	−	0.106539i
$696$		0			0
$697$	−116.846	+	202.383i	−0.00634985	+	0.0109983i
$698$		0			0
$699$	8742.08	−	314.693i	0.473041	−	0.0170283i
$700$		0			0
$701$		−	23013.5i		−	1.23995i	−0.784620	−	0.619977i	$-0.787142\pi$
$701$		−	23013.5i		−	1.23995i	0.784620	−	0.619977i	$-0.212858\pi$
$702$		0			0
$703$	−7257.84	+	4190.32i	−0.389381	+	0.224809i
$704$		0			0
$705$	−9077.06	−	4813.85i	−0.484911	−	0.257163i
$706$		0			0
$707$	13620.6	+	12955.0i	0.724546	+	0.689139i
$708$		0			0
$709$	−3830.42	−	6634.48i	−0.202898	−	0.351429i	0.746563	−	0.665315i	$-0.231703\pi$
$709$	−3830.42	−	6634.48i	−0.202898	−	0.351429i	−0.949461	+	0.313885i	$0.898369\pi$
$710$		0			0
$711$	34662.3	−	2498.74i	1.82832	−	0.131801i
$712$		0			0
$713$	−6390.76	+	11069.1i	−0.335675	+	0.581405i
$714$		0			0
$715$	−134.223	−	232.481i	−0.00702050	−	0.0121599i
$716$		0			0
$717$	10209.3	−	19250.8i	0.531762	−	1.00270i
$718$		0			0
$719$	12056.5	−	20882.5i	0.625358	−	1.08315i	−0.363114	−	0.931745i	$-0.618286\pi$
$719$	12056.5	−	20882.5i	0.625358	−	1.08315i	0.988472	−	0.151406i	$-0.0483802\pi$
$720$		0			0
$721$	−10090.9	+	10609.4i	−0.521229	+	0.548009i
$722$		0			0
$723$	10448.5	+	16681.2i	0.537462	+	0.858065i
$724$		0			0
$725$	−25847.5	−	14923.1i	−1.32407	−	0.764453i
$726$		0			0
$727$	19496.3	+	11256.2i	0.994606	+	0.574236i	0.906648	−	0.421888i	$-0.138632\pi$
$727$	19496.3	+	11256.2i	0.994606	+	0.574236i	0.0879583	+	0.996124i	$0.471966\pi$
$728$		0			0
$729$	−19226.1	+	4216.46i	−0.976786	+	0.214218i
$730$		0			0
$731$	331.261			0.0167608
$732$		0			0
$733$		−	9572.15i		−	0.482340i	−0.970483	−	0.241170i	$-0.922469\pi$
$733$		−	9572.15i		−	0.482340i	0.970483	−	0.241170i	$-0.0775312\pi$
$734$		0			0
$735$	−3528.74	−	5052.49i	−0.177088	−	0.253556i
$736$		0			0
$737$	−11956.6	−	6903.18i	−0.597597	−	0.345023i
$738$		0			0
$739$	−17009.8	−	29461.8i	−0.846705	−	1.46654i	−0.884132	−	0.467237i	$-0.845249\pi$
$739$	−17009.8	−	29461.8i	−0.846705	−	1.46654i	0.0374266	−	0.999299i	$-0.488084\pi$
$740$		0			0
$741$	−965.238	+	604.592i	−0.0478528	+	0.0299733i
$742$		0			0
$743$	27100.0	−	15646.2i	1.33809	−	0.772548i	0.351568	−	0.936163i	$-0.385649\pi$
$743$	27100.0	−	15646.2i	1.33809	−	0.772548i	0.986524	+	0.163615i	$0.0523154\pi$
$744$		0			0
$745$		−	4664.84i		−	0.229405i
$746$		0			0
$747$	−18500.3	−	27301.0i	−0.906146	−	1.33720i
$748$		0			0
$749$	−4475.02	−	15170.9i	−0.218309	−	0.740095i
$750$		0			0
$751$	26136.2			1.26994			0.634969	−	0.772538i	$-0.281013\pi$
$751$	26136.2			1.26994			0.634969	+	0.772538i	$0.281013\pi$
$752$		0			0
$753$	15129.2	−	9476.44i	0.732192	−	0.458620i
$754$		0			0
$755$	−1467.20			−0.0707241
$756$		0			0
$757$	19034.4			0.913893			0.456946	−	0.889494i	$-0.348943\pi$
$757$	19034.4			0.913893			0.456946	+	0.889494i	$0.348943\pi$
$758$		0			0
$759$	−6809.34	+	4265.14i	−0.325643	+	0.203972i
$760$		0			0
$761$	−1982.94			−0.0944565			−0.0472283	−	0.998884i	$-0.515039\pi$
$761$	−1982.94			−0.0944565			−0.0472283	+	0.998884i	$0.515039\pi$
$762$		0			0
$763$	444.094	−	1840.54i	0.0210711	−	0.0873291i
$764$		0			0
$765$	−115.787	+	8.34689i	−0.00547227	+	0.000394487i
$766$		0			0
$767$		−	726.645i		−	0.0342081i
$768$		0			0
$769$	6456.22	−	3727.50i	0.302753	−	0.174795i	−0.340926	−	0.940090i	$-0.610740\pi$
$769$	6456.22	−	3727.50i	0.302753	−	0.174795i	0.643679	+	0.765295i	$0.277407\pi$
$770$		0			0
$771$	14669.0	−	9188.16i	0.685203	−	0.429187i
$772$		0			0
$773$	18980.1	+	32874.5i	0.883139	+	1.52964i	0.847832	+	0.530265i	$0.177908\pi$
$773$	18980.1	+	32874.5i	0.883139	+	1.52964i	0.0353072	+	0.999377i	$0.488759\pi$
$774$		0			0
$775$	−25164.2	−	14528.5i	−1.16635	−	0.673394i
$776$		0			0
$777$	6087.20	−	6879.44i	0.281052	−	0.317630i
$778$		0			0
$779$		−	16500.8i		−	0.758924i
$780$		0			0
$781$	−12605.0			−0.577519
$782$		0			0
$783$	−14956.8	+	33887.4i	−0.682649	+	1.54666i
$784$		0			0
$785$	3036.84	+	1753.32i	0.138076	+	0.0797181i
$786$		0			0
$787$	−29316.6	−	16926.0i	−1.32786	−	0.766640i	−0.342891	−	0.939375i	$-0.611406\pi$
$787$	−29316.6	−	16926.0i	−1.32786	−	0.766640i	−0.984968	+	0.172736i	$0.944739\pi$
$788$		0			0
$789$	−16304.5	−	26030.3i	−0.735685	−	1.17453i
$790$		0			0
$791$	−9547.62	−	2303.69i	−0.429171	−	0.103552i
$792$		0			0
$793$	−198.328	+	343.514i	−0.00888126	+	0.0153828i
$794$		0			0
$795$	1629.84	−	3073.25i	0.0727101	−	0.137103i
$796$		0			0
$797$	1396.19	+	2418.28i	0.0620523	+	0.107478i	0.895383	−	0.445298i	$-0.146902\pi$
$797$	1396.19	+	2418.28i	0.0620523	+	0.107478i	−0.833330	+	0.552775i	$0.813569\pi$
$798$		0			0
$799$	355.528	−	615.792i	0.0157418	−	0.0272655i
$800$		0			0
$801$	−12325.7	−	18189.0i	−0.543703	−	0.802345i
$802$		0			0
$803$	9076.32	+	15720.7i	0.398875	+	0.690871i
$804$		0			0
$805$	−2194.60	+	2307.36i	−0.0960865	+	0.101023i
$806$		0			0
$807$	4225.73	+	2241.04i	0.184328	+	0.0977549i
$808$		0			0
$809$	−25463.7	+	14701.5i	−1.10662	+	0.638909i	−0.937952	−	0.346764i	$-0.887280\pi$
$809$	−25463.7	+	14701.5i	−1.10662	+	0.638909i	−0.168670	+	0.985673i	$0.553947\pi$
$810$		0			0
$811$			42354.1i			1.83385i	0.399059	+	0.916925i	$0.369337\pi$
$811$			42354.1i			1.83385i	−0.399059	+	0.916925i	$0.630663\pi$
$812$		0			0
$813$	13187.2	−	474.707i	0.568877	−	0.0204781i
$814$		0			0
$815$	−140.540	+	243.422i	−0.00604036	+	0.0104622i
$816$		0			0
$817$	−20256.4	+	11695.0i	−0.867420	+	0.500805i
$818$		0			0
$819$	793.100	−	964.091i	0.0338378	−	0.0411332i
$820$		0			0
$821$	−5045.57	+	2913.06i	−0.214484	+	0.123833i	−0.603394	−	0.797443i	$-0.706185\pi$
$821$	−5045.57	+	2913.06i	−0.214484	+	0.123833i	0.388909	+	0.921276i	$0.372852\pi$
$822$		0			0
$823$	19722.1	−	34159.7i	0.835322	−	1.44682i	−0.0584456	−	0.998291i	$-0.518614\pi$
$823$	19722.1	−	34159.7i	0.835322	−	1.44682i	0.893768	−	0.448530i	$-0.148052\pi$
$824$		0			0
$825$	−9696.22	−	15480.1i	−0.409187	−	0.653271i
$826$		0			0
$827$		−	8871.60i		−	0.373030i	−0.982452	−	0.186515i	$-0.940281\pi$
$827$		−	8871.60i		−	0.373030i	0.982452	−	0.186515i	$-0.0597193\pi$
$828$		0			0
$829$	−11452.9	+	6612.31i	−0.479824	+	0.277027i	−0.720343	−	0.693618i	$-0.756016\pi$
$829$	−11452.9	+	6612.31i	−0.479824	+	0.277027i	0.240519	+	0.970644i	$0.422682\pi$
$830$		0			0
$831$	−12678.7	+	7941.53i	−0.529267	+	0.331514i
$832$		0			0
$833$	358.219	−	231.471i	0.0148998	−	0.00962786i
$834$		0			0
$835$	−830.150	−	1437.86i	−0.0344054	−	0.0595919i
$836$		0			0
$837$	−14561.4	+	32991.6i	−0.601335	+	1.36243i
$838$		0			0
$839$	−7504.38	+	12998.0i	−0.308796	+	0.534850i	−0.978099	−	0.208139i	$-0.933259\pi$
$839$	−7504.38	+	12998.0i	−0.308796	+	0.534850i	0.669303	+	0.742989i	$0.266593\pi$
$840$		0			0
$841$	22659.5	+	39247.5i	0.929088	+	1.60923i
$842$		0			0
$843$	40841.3	−	1470.18i	1.66862	−	0.0600662i
$844$		0			0
$845$	−3787.61	+	6560.34i	−0.154199	+	0.267080i
$846$		0			0
$847$	4884.44	+	4645.75i	0.198148	+	0.188465i
$848$		0			0
$849$	28360.2	−	1020.89i	1.14643	−	0.0412686i
$850$		0			0
$851$	−4110.55	−	2373.23i	−0.165579	−	0.0955971i
$852$		0			0
$853$	−817.893	−	472.211i	−0.0328302	−	0.0189545i	0.483495	−	0.875347i	$-0.339367\pi$
$853$	−817.893	−	472.211i	−0.0328302	−	0.0189545i	−0.516325	+	0.856393i	$0.672700\pi$
$854$		0			0
$855$	6785.63	−	4598.23i	0.271419	−	0.183925i
$856$		0			0
$857$	−33806.6			−1.34750			−0.673752	−	0.738958i	$-0.735318\pi$
$857$	−33806.6			−1.34750			−0.673752	+	0.738958i	$0.735318\pi$
$858$		0			0
$859$			21779.3i			0.865075i	0.901616	+	0.432537i	$0.142382\pi$
$859$			21779.3i			0.865075i	−0.901616	+	0.432537i	$0.857618\pi$
$860$		0			0
$861$	5737.76	+	17152.0i	0.227111	+	0.678907i
$862$		0			0
$863$	−8670.13	−	5005.70i	−0.341987	−	0.197446i	0.319163	−	0.947700i	$-0.396598\pi$
$863$	−8670.13	−	5005.70i	−0.341987	−	0.197446i	−0.661150	+	0.750253i	$0.729931\pi$
$864$		0			0
$865$	1542.12	+	2671.03i	0.0606169	+	0.104992i
$866$		0			0
$867$	918.084	+	25504.1i	0.0359628	+	0.999038i
$868$		0			0
$869$	34663.1	−	20012.8i	1.35312	−	0.781227i
$870$		0			0
$871$		−	1108.41i		−	0.0431195i
$872$		0			0
$873$	−12812.8	+	8682.52i	−0.496734	+	0.336608i
$874$		0			0
$875$	−11045.7	−	10506.0i	−0.426759	−	0.405905i
$876$		0			0
$877$	6096.29			0.234729			0.117364	−	0.993089i	$-0.462555\pi$
$877$	6096.29			0.234729			0.117364	+	0.993089i	$0.462555\pi$
$878$		0			0
$879$	−3779.35	−	2004.30i	−0.145022	−	0.0769096i
$880$		0			0
$881$	27623.6			1.05637			0.528185	−	0.849130i	$-0.322873\pi$
$881$	27623.6			1.05637			0.528185	+	0.849130i	$0.322873\pi$
$882$		0			0
$883$	45677.7			1.74086			0.870428	−	0.492295i	$-0.163842\pi$
$883$	45677.7			1.74086			0.870428	+	0.492295i	$0.163842\pi$
$884$		0			0
$885$	188.128	+	5226.16i	0.00714561	+	0.198503i
$886$		0			0
$887$	−22848.5			−0.864913			−0.432456	−	0.901655i	$-0.642353\pi$
$887$	−22848.5			−0.864913			−0.432456	+	0.901655i	$0.642353\pi$
$888$		0			0
$889$	−29035.3	−	27616.4i	−1.09540	−	1.04187i
$890$		0			0
$891$	−17803.8	+	14033.6i	−0.669415	+	0.527657i
$892$		0			0
$893$			50207.1i			1.88143i
$894$		0			0
$895$	−2686.84	+	1551.25i	−0.100348	+	0.0579358i
$896$		0			0
$897$	−569.877	−	302.223i	−0.0212125	−	0.0112497i
$898$		0			0
$899$	33932.6	+	58773.0i	1.25886	+	2.18041i
$900$		0			0
$901$	208.491	+	120.372i	0.00770903	+	0.00445081i
$902$		0			0
$903$	16989.2	−	19200.3i	0.626096	−	0.707581i
$904$		0			0
$905$		−	8017.95i		−	0.294504i
$906$		0			0
$907$	36814.3			1.34774			0.673869	−	0.738851i	$-0.264631\pi$
$907$	36814.3			1.34774			0.673869	+	0.738851i	$0.264631\pi$
$908$		0			0
$909$	11960.3	−	24656.7i	0.436411	−	0.899681i
$910$		0			0
$911$	−18246.8	−	10534.8i	−0.663604	−	0.383132i	0.130045	−	0.991508i	$-0.458488\pi$
$911$	−18246.8	−	10534.8i	−0.663604	−	0.383132i	−0.793649	+	0.608376i	$0.791821\pi$
$912$		0			0
$913$	−32894.3	−	18991.5i	−1.19238	−	0.688421i
$914$		0			0
$915$	1337.47	−	2521.96i	0.0483230	−	0.0911186i
$916$		0			0
$917$	34495.8	+	32810.0i	1.24226	+	1.18155i
$918$		0			0
$919$	15269.0	−	26446.7i	0.548073	−	0.949289i	−0.450334	−	0.892860i	$-0.648695\pi$
$919$	15269.0	−	26446.7i	0.548073	−	0.949289i	0.998407	−	0.0564293i	$-0.0179716\pi$
$920$		0			0
$921$	24866.9	+	39700.3i	0.889676	+	1.42038i
$922$		0			0
$923$	−505.981	−	876.385i	−0.0180440	−	0.0312530i
$924$		0			0
$925$	5395.21	−	9344.78i	0.191777	−	0.332167i
$926$		0			0
$927$	19205.7	+	9316.16i	0.680472	+	0.330078i
$928$		0			0
$929$	−19782.2	−	34263.8i	−0.698637	−	1.21007i	−0.968939	−	0.247299i	$-0.920457\pi$
$929$	−19782.2	−	34263.8i	−0.698637	−	1.21007i	0.270303	−	0.962775i	$-0.412876\pi$
$930$		0			0
$931$	−13732.9	+	26801.2i	−0.483435	+	0.943472i
$932$		0			0
$933$	−1989.18	−	55258.9i	−0.0697993	−	1.93901i
$934$		0			0
$935$	−115.790	+	66.8513i	−0.00404998	+	0.00233826i
$936$		0			0
$937$		−	17421.8i		−	0.607412i	−0.952766	−	0.303706i	$-0.901776\pi$
$937$		−	17421.8i		−	0.607412i	0.952766	−	0.303706i	$-0.0982241\pi$
$938$		0			0
$939$	−18990.4	+	35808.5i	−0.659986	+	1.24448i
$940$		0			0
$941$	−2739.18	+	4744.40i	−0.0948935	+	0.164360i	−0.909564	−	0.415564i	$-0.863584\pi$
$941$	−2739.18	+	4744.40i	−0.0948935	+	0.164360i	0.814671	+	0.579924i	$0.196918\pi$
$942$		0			0
$943$	8093.34	−	4672.69i	0.279486	−	0.161361i
$944$		0			0
$945$	−5454.51	+	7139.25i	−0.187762	+	0.245756i
$946$		0			0
$947$	−8809.34	+	5086.07i	−0.302286	+	0.174525i	−0.643469	−	0.765472i	$-0.722506\pi$
$947$	−8809.34	+	5086.07i	−0.302286	+	0.174525i	0.341183	+	0.939997i	$0.389172\pi$
$948$		0			0
$949$	−728.671	+	1262.10i	−0.0249248	+	0.0431711i
$950$		0			0
$951$	−18994.7	+	35816.8i	−0.647683	+	1.22128i
$952$		0			0
$953$			34572.9i			1.17516i	0.809166	+	0.587580i	$0.199919\pi$
$953$			34572.9i			1.17516i	−0.809166	+	0.587580i	$0.800081\pi$
$954$		0			0
$955$	6116.98	−	3531.64i	0.207268	−	0.119666i
$956$		0			0
$957$	1534.73	+	42634.4i	0.0518399	+	1.44010i
$958$		0			0
$959$	7900.72	−	8306.65i	0.266035	−	0.279703i
$960$		0			0
$961$	18140.1	+	31419.5i	0.608911	+	1.05467i
$962$		0			0
$963$	−19089.2	+	12935.6i	−0.638774	+	0.432860i
$964$		0			0
$965$	−839.429	+	1453.93i	−0.0280023	+	0.0485014i
$966$		0			0
$967$	2296.74	+	3978.07i	0.0763787	+	0.132292i	0.901685	−	0.432394i	$-0.142331\pi$
$967$	2296.74	+	3978.07i	0.0763787	+	0.132292i	−0.825306	+	0.564685i	$0.808998\pi$
$968$		0			0
$969$	301.123	+	480.747i	0.00998295	+	0.0159379i
$970$		0			0
$971$	16400.0	−	28405.6i	0.542018	−	0.938803i	−0.456770	−	0.889585i	$-0.650994\pi$
$971$	16400.0	−	28405.6i	0.542018	−	0.938803i	0.998788	−	0.0492181i	$-0.0156729\pi$
$972$		0			0
$973$	20327.0	+	4904.60i	0.669738	+	0.161597i
$974$		0			0
$975$	687.065	−	1295.54i	0.0225679	−	0.0425543i
$976$		0			0
$977$	−9723.16	−	5613.67i	−0.318395	−	0.183825i	0.332282	−	0.943180i	$-0.392181\pi$
$977$	−9723.16	−	5613.67i	−0.318395	−	0.183825i	−0.650677	+	0.759355i	$0.725515\pi$
$978$		0			0
$979$	−21915.5	−	12652.9i	−0.715448	−	0.413064i
$980$		0			0
$981$	−2753.12	+	198.467i	−0.0896027	+	0.00645930i
$982$		0			0
$983$	−16168.6			−0.524615			−0.262308	−	0.964984i	$-0.584484\pi$
$983$	−16168.6			−0.524615			−0.262308	+	0.964984i	$0.584484\pi$
$984$		0			0
$985$		−	7652.07i		−	0.247528i
$986$		0			0
$987$	−17458.4	−	52188.6i	−0.563025	−	1.68306i
$988$		0			0
$989$	−11472.4	−	6623.60i	−0.368859	−	0.212961i
$990$		0			0
$991$	8490.45	+	14705.9i	0.272158	+	0.471391i	0.969414	−	0.245431i	$-0.0789295\pi$
$991$	8490.45	+	14705.9i	0.272158	+	0.471391i	−0.697257	+	0.716822i	$0.745596\pi$
$992$		0			0
$993$	33207.5	+	17611.0i	1.06124	+	0.562807i
$994$		0			0
$995$	3216.40	−	1856.99i	0.102479	−	0.0591663i
$996$		0			0
$997$		−	35959.0i		−	1.14226i	−0.820859	−	0.571130i	$-0.806505\pi$
$997$		−	35959.0i		−	1.14226i	0.820859	−	0.571130i	$-0.193495\pi$
$998$		0			0
$999$	−12251.5	−	5407.43i	−0.388008	−	0.171255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.4	yes	48
3.2	odd	2		756.4.bm.a.89.11		48
7.3	odd	6		252.4.w.a.101.5	yes	48
9.4	even	3		756.4.w.a.341.11		48
9.5	odd	6		252.4.w.a.5.5	✓	48
21.17	even	6		756.4.w.a.521.11		48
63.31	odd	6		756.4.bm.a.17.11		48
63.59	even	6	inner	252.4.bm.a.185.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.5	✓	48	9.5	odd	6
252.4.w.a.101.5	yes	48	7.3	odd	6
252.4.bm.a.173.4	yes	48	1.1	even	1	trivial
252.4.bm.a.185.4	yes	48	63.59	even	6	inner
756.4.w.a.341.11		48	9.4	even	3
756.4.w.a.521.11		48	21.17	even	6
756.4.bm.a.17.11		48	63.31	odd	6
756.4.bm.a.89.11		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-4.40362 + 2.75828i) q^{3} +3.45780 q^{5} +(13.4196 + 12.7638i) q^{7} +(11.7838 - 24.2928i) q^{9} +O(q^{10})\)	\(q+(-4.40362 + 2.75828i) q^{3} +3.45780 q^{5} +(13.4196 + 12.7638i) q^{7} +(11.7838 - 24.2928i) q^{9} -31.0970i q^{11} +(2.16207 - 1.24827i) q^{13} +(-15.2268 + 9.53756i) q^{15} +(-0.621716 - 1.07684i) q^{17} +(76.0352 + 43.8990i) q^{19} +(-94.3009 - 19.1920i) q^{21} +49.7252i q^{23} -113.044 q^{25} +(15.1150 + 139.480i) q^{27} +(228.650 + 132.011i) q^{29} +(222.606 + 128.522i) q^{31} +(85.7741 + 136.939i) q^{33} +(46.4022 + 44.1346i) q^{35} +(-47.7268 + 82.6653i) q^{37} +(-6.07787 + 11.4605i) q^{39} +(-93.9702 - 162.761i) q^{41} +(-133.204 + 230.716i) q^{43} +(40.7460 - 83.9997i) q^{45} +(285.924 + 495.236i) q^{47} +(17.1705 + 342.570i) q^{49} +(5.70804 + 3.02715i) q^{51} +(-167.674 + 96.8064i) q^{53} -107.527i q^{55} +(-455.916 + 16.4118i) q^{57} +(145.530 - 252.065i) q^{59} +(-137.596 + 79.4410i) q^{61} +(468.203 - 175.594i) q^{63} +(7.47601 - 4.31628i) q^{65} +(221.989 - 384.496i) q^{67} +(-137.156 - 218.971i) q^{69} -405.345i q^{71} +(-505.536 + 291.872i) q^{73} +(497.802 - 311.806i) q^{75} +(396.916 - 417.309i) q^{77} +(643.560 + 1114.68i) q^{79} +(-451.284 - 572.524i) q^{81} +(610.720 - 1057.80i) q^{83} +(-2.14977 - 3.72351i) q^{85} +(-1371.01 + 49.3530i) q^{87} +(406.886 - 704.748i) q^{89} +(44.9468 + 10.8450i) q^{91} +(-1334.77 + 48.0483i) q^{93} +(262.914 + 151.794i) q^{95} +(-496.443 - 286.621i) q^{97} +(-755.434 - 366.441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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