LMFDB - Embedded newform 252.4.b.d.55.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 30x^{6} + 84x^{5} + 493x^{4} - 464x^{3} - 3172x^{2} + 1072x + 8978 $ x^8 - 4x^7 - 30x^6 + 84x^5 + 493x^4 - 464x^3 - 3172x^2 + 1072*x + 8978
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.7
Root			$2.19234 - 0.736813i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.d.55.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41421 + 1.47363i) q^{2} +(3.65685 + 7.11529i) q^{4} -17.0728i q^{5} +(-18.3722 - 2.33686i) q^{7} +(-1.65685 + 22.5667i) q^{8} +O(q^{10})$	\(q+(2.41421 + 1.47363i) q^{2} +(3.65685 + 7.11529i) q^{4} -17.0728i q^{5} +(-18.3722 - 2.33686i) q^{7} +(-1.65685 + 22.5667i) q^{8} +(25.1589 - 41.2174i) q^{10} -41.4710i q^{11} -45.3599i q^{13} +(-40.9109 - 32.7155i) q^{14} +(-37.2548 + 52.0392i) q^{16} -28.2871i q^{17} +41.5434 q^{19} +(121.478 - 62.4327i) q^{20} +(61.1127 - 100.120i) q^{22} -93.9291i q^{23} -166.480 q^{25} +(66.8435 - 109.509i) q^{26} +(-50.5572 - 139.269i) q^{28} -27.8234 q^{29} -81.4400 q^{31} +(-166.627 + 70.7340i) q^{32} +(41.6846 - 68.2912i) q^{34} +(-39.8967 + 313.665i) q^{35} +94.8040 q^{37} +(100.295 + 61.2194i) q^{38} +(385.276 + 28.2871i) q^{40} -227.302i q^{41} +171.988i q^{43} +(295.078 - 151.653i) q^{44} +(138.416 - 226.765i) q^{46} +286.005 q^{47} +(332.078 + 85.8665i) q^{49} +(-401.919 - 245.330i) q^{50} +(322.749 - 165.875i) q^{52} +575.921 q^{53} -708.025 q^{55} +(83.1752 - 410.728i) q^{56} +(-67.1716 - 41.0012i) q^{58} -411.999 q^{59} +778.987i q^{61} +(-196.614 - 120.012i) q^{62} +(-506.510 - 74.7794i) q^{64} -774.420 q^{65} +198.773i q^{67} +(201.271 - 103.442i) q^{68} +(-558.544 + 698.463i) q^{70} -197.762i q^{71} -255.589i q^{73} +(228.877 + 139.706i) q^{74} +(151.918 + 295.593i) q^{76} +(-96.9117 + 761.915i) q^{77} -1178.49i q^{79} +(888.454 + 636.044i) q^{80} +(334.958 - 548.756i) q^{82} -938.514 q^{83} -482.940 q^{85} +(-253.446 + 415.215i) q^{86} +(935.862 + 68.7114i) q^{88} +1166.81i q^{89} +(-106.000 + 833.363i) q^{91} +(668.333 - 343.485i) q^{92} +(690.476 + 421.464i) q^{94} -709.261i q^{95} +656.635i q^{97} +(675.173 + 696.659i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8	$ 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8} + 152 q^{14} + 64 q^{16} + 240 q^{22} - 472 q^{25} - 48 q^{28} + 592 q^{29} - 1152 q^{32} + 1392 q^{37} + 1184 q^{44} - 816 q^{46} + 1480 q^{49} - 1688 q^{50} + 1168 q^{53} - 800 q^{56} - 560 q^{58} - 3328 q^{64} - 448 q^{65} - 3200 q^{70} + 496 q^{74} - 368 q^{77} + 1024 q^{85} - 240 q^{86} + 3776 q^{88} + 3808 q^{92} + 3144 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8 + 152 * q^14 + 64 * q^16 + 240 * q^22 - 472 * q^25 - 48 * q^28 + 592 * q^29 - 1152 * q^32 + 1392 * q^37 + 1184 * q^44 - 816 * q^46 + 1480 * q^49 - 1688 * q^50 + 1168 * q^53 - 800 * q^56 - 560 * q^58 - 3328 * q^64 - 448 * q^65 - 3200 * q^70 + 496 * q^74 - 368 * q^77 + 1024 * q^85 - 240 * q^86 + 3776 * q^88 + 3808 * q^92 + 3144 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.41421	+	1.47363i	0.853553	+	0.521005i
$2$	2.41421	+	1.47363i	0.853553	+	0.521005i
$3$		0			0
$3$		0			0
$4$	3.65685	+	7.11529i	0.457107	+	0.889412i
$5$		−	17.0728i		−	1.52704i	−0.645786	−	0.763518i	$-0.723470\pi$
$5$		−	17.0728i		−	1.52704i	0.645786	−	0.763518i	$-0.276530\pi$
$6$		0			0
$7$	−18.3722	−	2.33686i	−0.992008	−	0.126178i
$7$	−18.3722	−	2.33686i	−0.992008	−	0.126178i
$8$	−1.65685	+	22.5667i	−0.0732233	+	0.997316i
$9$		0			0
$10$	25.1589	−	41.2174i	0.795594	−	1.30341i
$11$		−	41.4710i		−	1.13672i	−0.822778	−	0.568362i	$-0.807577\pi$
$11$		−	41.4710i		−	1.13672i	0.822778	−	0.568362i	$-0.192423\pi$
$12$		0			0
$13$		−	45.3599i		−	0.967737i	−0.875141	−	0.483868i	$-0.839231\pi$
$13$		−	45.3599i		−	0.967737i	0.875141	−	0.483868i	$-0.160769\pi$
$14$	−40.9109	−	32.7155i	−0.780992	−	0.624541i
$15$		0			0
$16$	−37.2548	+	52.0392i	−0.582107	+	0.813112i
$17$		−	28.2871i		−	0.403567i	−0.979430	−	0.201783i	$-0.935326\pi$
$17$		−	28.2871i		−	0.403567i	0.979430	−	0.201783i	$-0.0646737\pi$
$18$		0			0
$19$	41.5434			0.501616			0.250808	−	0.968037i	$-0.419304\pi$
$19$	41.5434			0.501616			0.250808	+	0.968037i	$0.419304\pi$
$20$	121.478	−	62.4327i	1.35816	−	0.698019i
$21$		0			0
$22$	61.1127	−	100.120i	0.592240	−	0.970255i
$23$		−	93.9291i		−	0.851546i	−0.904830	−	0.425773i	$-0.860002\pi$
$23$		−	93.9291i		−	0.851546i	0.904830	−	0.425773i	$-0.139998\pi$
$24$		0			0
$25$	−166.480			−1.33184
$26$	66.8435	−	109.509i	0.504196	−	0.826015i
$27$		0			0
$28$	−50.5572	−	139.269i	−0.341229	−	0.939980i
$29$	−27.8234			−0.178161			−0.0890805	−	0.996024i	$-0.528393\pi$
$29$	−27.8234			−0.178161			−0.0890805	+	0.996024i	$0.528393\pi$
$30$		0			0
$31$	−81.4400			−0.471841			−0.235920	−	0.971772i	$-0.575810\pi$
$31$	−81.4400			−0.471841			−0.235920	+	0.971772i	$0.575810\pi$
$32$	−166.627	+	70.7340i	−0.920495	+	0.390754i
$33$		0			0
$34$	41.6846	−	68.2912i	0.210260	−	0.344466i
$35$	−39.8967	+	313.665i	−0.192679	+	1.51483i
$36$		0			0
$37$	94.8040			0.421235			0.210617	−	0.977569i	$-0.432453\pi$
$37$	94.8040			0.421235			0.210617	+	0.977569i	$0.432453\pi$
$38$	100.295	+	61.2194i	0.428156	+	0.261345i
$39$		0			0
$40$	385.276	+	28.2871i	1.52294	+	0.111815i
$41$		−	227.302i		−	0.865820i	−0.901437	−	0.432910i	$-0.857487\pi$
$41$		−	227.302i		−	0.865820i	0.901437	−	0.432910i	$-0.142513\pi$
$42$		0			0
$43$			171.988i			0.609951i	0.952360	+	0.304976i	$0.0986483\pi$
$43$			171.988i			0.609951i	−0.952360	+	0.304976i	$0.901352\pi$
$44$	295.078	−	151.653i	1.01102	−	0.519604i
$45$		0			0
$46$	138.416	−	226.765i	0.443660	−	0.726840i
$47$	286.005			0.887619			0.443809	−	0.896121i	$-0.353627\pi$
$47$	286.005			0.887619			0.443809	+	0.896121i	$0.353627\pi$
$48$		0			0
$49$	332.078	+	85.8665i	0.968158	+	0.250340i
$50$	−401.919	−	245.330i	−1.13680	−	0.693897i
$51$		0			0
$52$	322.749	−	165.875i	0.860717	−	0.442359i
$53$	575.921			1.49262			0.746310	−	0.665599i	$-0.231824\pi$
$53$	575.921			1.49262			0.746310	+	0.665599i	$0.231824\pi$
$54$		0			0
$55$	−708.025			−1.73582
$56$	83.1752	−	410.728i	0.198478	−	0.980105i
$57$		0			0
$58$	−67.1716	−	41.0012i	−0.152070	−	0.0928229i
$59$	−411.999			−0.909114			−0.454557	−	0.890718i	$-0.650202\pi$
$59$	−411.999			−0.909114			−0.454557	+	0.890718i	$0.650202\pi$
$60$		0			0
$61$			778.987i			1.63507i	0.575881	+	0.817534i	$0.304659\pi$
$61$			778.987i			1.63507i	−0.575881	+	0.817534i	$0.695341\pi$
$62$	−196.614	−	120.012i	−0.402741	−	0.245832i
$63$		0			0
$64$	−506.510	−	74.7794i	−0.989277	−	0.146053i
$65$	−774.420			−1.47777
$66$		0			0
$67$			198.773i			0.362448i	0.983442	+	0.181224i	$0.0580060\pi$
$67$			198.773i			0.362448i	−0.983442	+	0.181224i	$0.941994\pi$
$68$	201.271	−	103.442i	0.358937	−	0.184473i
$69$		0			0
$70$	−558.544	+	698.463i	−0.953698	+	1.19260i
$71$		−	197.762i		−	0.330564i	−0.986246	−	0.165282i	$-0.947147\pi$
$71$		−	197.762i		−	0.330564i	0.986246	−	0.165282i	$-0.0528534\pi$
$72$		0			0
$73$		−	255.589i		−	0.409787i	−0.978784	−	0.204894i	$-0.934315\pi$
$73$		−	255.589i		−	0.409787i	0.978784	−	0.204894i	$-0.0656848\pi$
$74$	228.877	+	139.706i	0.359546	+	0.219466i
$75$		0			0
$76$	151.918	+	295.593i	0.229292	+	0.446143i
$77$	−96.9117	+	761.915i	−0.143430	+	1.12764i
$78$		0			0
$79$		−	1178.49i		−	1.67836i	−0.543856	−	0.839179i	$-0.683036\pi$
$79$		−	1178.49i		−	1.67836i	0.543856	−	0.839179i	$-0.316964\pi$
$80$	888.454	+	636.044i	1.24165	+	0.888899i
$81$		0			0
$82$	334.958	−	548.756i	0.451097	−	0.739024i
$83$	−938.514			−1.24115			−0.620574	−	0.784148i	$-0.713100\pi$
$83$	−938.514			−1.24115			−0.620574	+	0.784148i	$0.713100\pi$
$84$		0			0
$85$	−482.940			−0.616261
$86$	−253.446	+	415.215i	−0.317788	+	0.520626i
$87$		0			0
$88$	935.862	+	68.7114i	1.13367	+	0.0832347i
$89$			1166.81i			1.38968i	0.719165	+	0.694840i	$0.244525\pi$
$89$			1166.81i			1.38968i	−0.719165	+	0.694840i	$0.755475\pi$
$90$		0			0
$91$	−106.000	+	833.363i	−0.122107	+	0.960002i
$92$	668.333	−	343.485i	0.757375	−	0.389248i
$93$		0			0
$94$	690.476	+	421.464i	0.757630	+	0.462454i
$95$		−	709.261i		−	0.765986i
$96$		0			0
$97$			656.635i			0.687332i	0.939092	+	0.343666i	$0.111669\pi$
$97$			656.635i			0.687332i	−0.939092	+	0.343666i	$0.888331\pi$
$98$	675.173	+	696.659i	0.695946	+	0.718094i
$99$		0			0
$100$	−608.794	−	1184.56i	−0.608794	−	1.18456i
$101$		−	999.426i		−	0.984620i	−0.870420	−	0.492310i	$-0.836153\pi$
$101$		−	999.426i		−	0.984620i	0.870420	−	0.492310i	$-0.163847\pi$
$102$		0			0
$103$	−958.932			−0.917344			−0.458672	−	0.888606i	$-0.651675\pi$
$103$	−958.932			−0.917344			−0.458672	+	0.888606i	$0.651675\pi$
$104$	1023.62	+	75.1548i	0.965139	+	0.0708609i
$105$		0			0
$106$	1390.40	+	848.692i	1.27403	+	0.777663i
$107$			685.893i			0.619699i	0.950786	+	0.309849i	$0.100279\pi$
$107$			685.893i			0.619699i	−0.950786	+	0.309849i	$0.899721\pi$
$108$		0			0
$109$	1127.80			0.991045			0.495523	−	0.868595i	$-0.334977\pi$
$109$	1127.80			0.991045			0.495523	+	0.868595i	$0.334977\pi$
$110$	−1709.32	−	1043.36i	−1.48162	−	0.904372i
$111$		0			0
$112$	806.063	−	869.017i	0.680052	−	0.733164i
$113$	10.0488			0.00836557			0.00418278	−	0.999991i	$-0.498669\pi$
$113$	10.0488			0.00836557			0.00418278	+	0.999991i	$0.498669\pi$
$114$		0			0
$115$	−1603.63			−1.30034
$116$	−101.746	−	197.972i	−0.0814386	−	0.158459i
$117$		0			0
$118$	−994.654	−	607.132i	−0.775977	−	0.473653i
$119$	−66.1029	+	519.698i	−0.0509214	+	0.400341i
$120$		0			0
$121$	−388.842			−0.292143
$122$	−1147.94	+	1880.64i	−0.851879	+	1.39562i
$123$		0			0
$124$	−297.814	−	579.470i	−0.215682	−	0.419661i
$125$			708.183i			0.506735i
$126$		0			0
$127$			1347.06i			0.941198i	0.882347	+	0.470599i	$0.155962\pi$
$127$			1347.06i			0.941198i	−0.882347	+	0.470599i	$0.844038\pi$
$128$	−1112.63	−	926.939i	−0.768306	−	0.640083i
$129$		0			0
$130$	−1869.62	−	1141.21i	−1.26136	−	0.769926i
$131$	480.265			0.320313			0.160156	−	0.987092i	$-0.448800\pi$
$131$	480.265			0.320313			0.160156	+	0.987092i	$0.448800\pi$
$132$		0			0
$133$	−763.245	−	97.0809i	−0.497607	−	0.0632931i
$134$	−292.918	+	479.881i	−0.188838	+	0.309369i
$135$		0			0
$136$	638.346	+	46.8676i	0.402483	+	0.0295505i
$137$	247.803			0.154535			0.0772674	−	0.997010i	$-0.475380\pi$
$137$	247.803			0.154535			0.0772674	+	0.997010i	$0.475380\pi$
$138$		0			0
$139$	1842.35			1.12422			0.562109	−	0.827063i	$-0.309990\pi$
$139$	1842.35			1.12422			0.562109	+	0.827063i	$0.309990\pi$
$140$	−2377.72	+	863.152i	−1.43538	+	0.521069i
$141$		0			0
$142$	291.427	−	477.440i	0.172226	−	0.282154i
$143$	−1881.12			−1.10005
$144$		0			0
$145$			475.023i			0.272059i
$146$	376.643	−	617.047i	0.213501	−	0.349775i
$147$		0			0
$148$	346.685	+	674.559i	0.192549	+	0.374651i
$149$	2200.82			1.21006			0.605028	−	0.796204i	$-0.293162\pi$
$149$	2200.82			1.21006			0.605028	+	0.796204i	$0.293162\pi$
$150$		0			0
$151$		−	3208.96i		−	1.72941i	−0.502279	−	0.864706i	$-0.667505\pi$
$151$		−	3208.96i		−	1.72941i	0.502279	−	0.864706i	$-0.332495\pi$
$152$	−68.8313	+	937.496i	−0.0367300	+	0.500269i
$153$		0			0
$154$	−1356.74	+	1696.61i	−0.709931	+	0.887773i
$155$			1390.41i			0.720518i
$156$		0			0
$157$		−	636.547i		−	0.323579i	−0.986825	−	0.161790i	$-0.948273\pi$
$157$		−	636.547i		−	0.323579i	0.986825	−	0.161790i	$-0.0517266\pi$
$158$	1736.65	−	2845.12i	0.874433	−	1.43257i
$159$		0			0
$160$	1207.63	+	2844.80i	0.596696	+	1.40563i
$161$	−219.499	+	1725.69i	−0.107447	+	0.844740i
$162$		0			0
$163$			2460.38i			1.18228i	0.806568	+	0.591141i	$0.201323\pi$
$163$			2460.38i			1.18228i	−0.806568	+	0.591141i	$0.798677\pi$
$164$	1617.32	−	831.211i	0.770071	−	0.395772i
$165$		0			0
$166$	−2265.77	−	1383.02i	−1.05939	−	0.646645i
$167$	2133.16			0.988435			0.494218	−	0.869338i	$-0.335455\pi$
$167$	2133.16			0.988435			0.494218	+	0.869338i	$0.335455\pi$
$168$		0			0
$169$	139.478			0.0634855
$170$	−1165.92	−	711.673i	−0.526012	−	0.321076i
$171$		0			0
$172$	−1223.74	+	628.935i	−0.542498	+	0.278813i
$173$		−	1462.73i		−	0.642829i	−0.946939	−	0.321415i	$-0.895842\pi$
$173$		−	1462.73i		−	0.642829i	0.946939	−	0.321415i	$-0.104158\pi$
$174$		0			0
$175$	3058.61	+	389.040i	1.32120	+	0.168050i
$176$	2158.12	+	1544.99i	0.924285	+	0.661695i
$177$		0			0
$178$	−1719.44	+	2816.92i	−0.724030	+	1.18617i
$179$		−	3038.97i		−	1.26896i	−0.772941	−	0.634478i	$-0.781215\pi$
$179$		−	3038.97i		−	1.26896i	0.772941	−	0.634478i	$-0.218785\pi$
$180$		0			0
$181$		−	384.978i		−	0.158095i	−0.996871	−	0.0790475i	$-0.974812\pi$
$181$		−	384.978i		−	0.158095i	0.996871	−	0.0790475i	$-0.0251879\pi$
$182$	−1483.97	+	1855.71i	−0.604392	+	0.755795i
$183$		0			0
$184$	2119.67	+	155.627i	0.849260	+	0.0623530i
$185$		−	1618.57i		−	0.643241i
$186$		0			0
$187$	−1173.09			−0.458744
$188$	1045.88	+	2035.01i	0.405736	+	0.789459i
$189$		0			0
$190$	1045.19	−	1712.31i	0.399083	−	0.653810i
$191$		−	505.605i		−	0.191541i	−0.995403	−	0.0957704i	$-0.969469\pi$
$191$		−	505.605i		−	0.191541i	0.995403	−	0.0957704i	$-0.0305314\pi$
$192$		0			0
$193$	1921.91			0.716798			0.358399	−	0.933569i	$-0.383323\pi$
$193$	1921.91			0.716798			0.358399	+	0.933569i	$0.383323\pi$
$194$	−967.634	+	1585.26i	−0.358103	+	0.586674i
$195$		0			0
$196$	603.396	+	2676.84i	0.219896	+	0.975523i
$197$	−1603.63			−0.579968			−0.289984	−	0.957031i	$-0.593650\pi$
$197$	−1603.63			−0.579968			−0.289984	+	0.957031i	$0.593650\pi$
$198$		0			0
$199$	2558.75			0.911484			0.455742	−	0.890112i	$-0.349374\pi$
$199$	2558.75			0.911484			0.455742	+	0.890112i	$0.349374\pi$
$200$	275.833	−	3756.91i	0.0975219	−	1.32827i
$201$		0			0
$202$	1472.78	−	2412.83i	0.512992	−	0.840426i
$203$	511.178	+	65.0192i	0.176737	+	0.0224801i
$204$		0			0
$205$	−3880.68			−1.32214
$206$	−2315.07	−	1413.11i	−0.783002	−	0.477941i
$207$		0			0
$208$	2360.49	+	1689.88i	0.786879	+	0.563326i
$209$		−	1722.84i		−	0.570199i
$210$		0			0
$211$			381.389i			0.124436i	0.998063	+	0.0622178i	$0.0198173\pi$
$211$			381.389i			0.124436i	−0.998063	+	0.0622178i	$0.980183\pi$
$212$	2106.06	+	4097.85i	0.682286	+	1.32755i
$213$		0			0
$214$	−1010.75	+	1655.89i	−0.322866	+	0.528946i
$215$	2936.31			0.931418
$216$		0			0
$217$	1496.24	+	190.314i	0.468070	+	0.0595361i
$218$	2722.76	+	1661.96i	0.845910	+	0.516340i
$219$		0			0
$220$	−2589.15	−	5037.81i	−0.793455	−	1.54386i
$221$	−1283.10			−0.390546
$222$		0			0
$223$	2943.88			0.884023			0.442011	−	0.897009i	$-0.354265\pi$
$223$	2943.88			0.884023			0.442011	+	0.897009i	$0.354265\pi$
$224$	3226.61	−	910.158i	0.962443	−	0.271484i
$225$		0			0
$226$	24.2599	+	14.8081i	0.00714046	+	0.00435851i
$227$	5786.10			1.69179			0.845897	−	0.533346i	$-0.179066\pi$
$227$	5786.10			1.69179			0.845897	+	0.533346i	$0.179066\pi$
$228$		0			0
$229$		−	4303.85i		−	1.24195i	−0.783830	−	0.620975i	$-0.786737\pi$
$229$		−	4303.85i		−	1.24195i	0.783830	−	0.620975i	$-0.213263\pi$
$230$	−3871.51	−	2363.15i	−1.10991	−	0.677486i
$231$		0			0
$232$	46.0993	−	627.881i	0.0130455	−	0.177683i
$233$	−5133.92			−1.44349			−0.721747	−	0.692157i	$-0.756660\pi$
$233$	−5133.92			−1.44349			−0.721747	+	0.692157i	$0.756660\pi$
$234$		0			0
$235$		−	4882.90i		−	1.35543i
$236$	−1506.62	−	2931.49i	−0.415562	−	0.808576i
$237$		0			0
$238$	−925.427	+	1157.25i	−0.252044	+	0.315182i
$239$			468.448i			0.126784i	0.997989	+	0.0633920i	$0.0201919\pi$
$239$			468.448i			0.126784i	−0.997989	+	0.0633920i	$0.979808\pi$
$240$		0			0
$241$		−	389.501i		−	0.104108i	−0.998644	−	0.0520539i	$-0.983423\pi$
$241$		−	389.501i		−	0.104108i	0.998644	−	0.0520539i	$-0.0165768\pi$
$242$	−938.747	−	573.007i	−0.249359	−	0.152208i
$243$		0			0
$244$	−5542.72	+	2848.64i	−1.45425	+	0.747400i
$245$	1465.98	−	5669.50i	0.382278	−	1.47841i
$246$		0			0
$247$		−	1884.40i		−	0.485432i
$248$	134.934	−	1837.83i	0.0345497	−	0.470574i
$249$		0			0
$250$	−1043.60	+	1709.71i	−0.264012	+	0.432525i
$251$	−4690.59			−1.17955			−0.589776	−	0.807567i	$-0.700784\pi$
$251$	−4690.59			−1.17955			−0.589776	+	0.807567i	$0.700784\pi$
$252$		0			0
$253$	−3895.33			−0.967974
$254$	−1985.06	+	3252.09i	−0.490369	+	0.803363i
$255$		0			0
$256$	−1320.15	−	3877.42i	−0.322303	−	0.946636i
$257$		−	5223.27i		−	1.26778i	−0.773425	−	0.633888i	$-0.781458\pi$
$257$		−	5223.27i		−	1.26778i	0.773425	−	0.633888i	$-0.218542\pi$
$258$		0			0
$259$	−1741.76	−	221.543i	−0.417868	−	0.0531507i
$260$	−2831.94	−	5510.23i	−0.675499	−	1.31435i
$261$		0			0
$262$	1159.46	+	707.731i	0.273404	+	0.166885i
$263$		−	4704.80i		−	1.10308i	−0.834148	−	0.551541i	$-0.814040\pi$
$263$		−	4704.80i		−	1.10308i	0.834148	−	0.551541i	$-0.185960\pi$
$264$		0			0
$265$		−	9832.58i		−	2.27928i
$266$	−1699.57	−	1359.11i	−0.391758	−	0.313280i
$267$		0			0
$268$	−1414.33	+	726.885i	−0.322366	+	0.165678i
$269$			3444.53i			0.780730i	0.920660	+	0.390365i	$0.127651\pi$
$269$			3444.53i			0.780730i	−0.920660	+	0.390365i	$0.872349\pi$
$270$		0			0
$271$	5251.78			1.17721			0.588603	−	0.808422i	$-0.299678\pi$
$271$	5251.78			1.17721			0.588603	+	0.808422i	$0.299678\pi$
$272$	1472.04	+	1053.83i	0.328145	+	0.234919i
$273$		0			0
$274$	598.250	+	365.169i	0.131904	+	0.0805134i
$275$			6904.10i			1.51394i
$276$		0			0
$277$	6003.19			1.30215			0.651077	−	0.759012i	$-0.274317\pi$
$277$	6003.19			1.30215			0.651077	+	0.759012i	$0.274317\pi$
$278$	4447.84	+	2714.94i	0.959581	+	0.585724i
$279$		0			0
$280$	−7012.28	−	1420.03i	−1.49666	−	0.303083i
$281$	1870.63			0.397125			0.198563	−	0.980088i	$-0.436373\pi$
$281$	1870.63			0.397125			0.198563	+	0.980088i	$0.436373\pi$
$282$		0			0
$283$	3963.42			0.832512			0.416256	−	0.909248i	$-0.363342\pi$
$283$	3963.42			0.832512			0.416256	+	0.909248i	$0.363342\pi$
$284$	1407.14	−	723.187i	0.294007	−	0.151103i
$285$		0			0
$286$	−4541.43	−	2772.07i	−0.938952	−	0.573132i
$287$	−531.172	+	4176.05i	−0.109248	+	0.858900i
$288$		0			0
$289$	4112.84			0.837134
$290$	−700.006	+	1146.81i	−0.141744	+	0.232216i
$291$		0			0
$292$	1818.59	−	934.653i	0.364470	−	0.187317i
$293$			4654.67i			0.928084i	0.885813	+	0.464042i	$0.153601\pi$
$293$			4654.67i			0.928084i	−0.885813	+	0.464042i	$0.846399\pi$
$294$		0			0
$295$			7033.97i			1.38825i
$296$	−157.076	+	2139.41i	−0.0308442	+	0.420104i
$297$		0			0
$298$	5313.26	+	3243.19i	1.03285	+	0.630446i
$299$	−4260.62			−0.824073
$300$		0			0
$301$	401.911	−	3159.80i	0.0769626	−	0.605076i
$302$	4728.80	−	7747.10i	0.901033	−	1.47614i
$303$		0			0
$304$	−1547.69	+	2161.88i	−0.291994	+	0.407870i
$305$	13299.5			2.49681
$306$		0			0
$307$	−2828.15			−0.525769			−0.262884	−	0.964827i	$-0.584674\pi$
$307$	−2828.15			−0.525769			−0.262884	+	0.964827i	$0.584674\pi$
$308$	−5775.64	+	2096.66i	−1.06850	+	0.387883i
$309$		0			0
$310$	−2048.94	+	3356.74i	−0.375394	+	0.615001i
$311$	6559.10			1.19592			0.597962	−	0.801524i	$-0.295977\pi$
$311$	6559.10			1.19592			0.597962	+	0.801524i	$0.295977\pi$
$312$		0			0
$313$			6217.17i			1.12273i	0.827568	+	0.561366i	$0.189724\pi$
$313$			6217.17i			1.12273i	−0.827568	+	0.561366i	$0.810276\pi$
$314$	938.031	−	1536.76i	0.168587	−	0.276192i
$315$		0			0
$316$	8385.29	−	4309.56i	1.49275	−	0.767189i
$317$	−3254.84			−0.576687			−0.288344	−	0.957527i	$-0.593105\pi$
$317$	−3254.84			−0.576687			−0.288344	+	0.957527i	$0.593105\pi$
$318$		0			0
$319$			1153.86i			0.202520i
$320$	−1276.69	+	8647.53i	−0.223029	+	1.51066i
$321$		0			0
$322$	−3072.93	+	3842.72i	−0.531826	+	0.665051i
$323$		−	1175.14i		−	0.202436i
$324$		0			0
$325$			7551.53i			1.28887i
$326$	−3625.68	+	5939.89i	−0.615976	+	1.00914i
$327$		0			0
$328$	5129.45	+	376.607i	0.863496	+	0.0633982i
$329$	−5254.55	−	668.352i	−0.880524	−	0.111998i
$330$		0			0
$331$			4385.31i			0.728212i	0.931357	+	0.364106i	$0.118625\pi$
$331$			4385.31i			0.728212i	−0.931357	+	0.364106i	$0.881375\pi$
$332$	−3432.01	−	6677.80i	−0.567337	−	1.10389i
$333$		0			0
$334$	5149.90	+	3143.48i	0.843682	+	0.514980i
$335$	3393.62			0.553472
$336$		0			0
$337$	−9569.41			−1.54682			−0.773411	−	0.633905i	$-0.781451\pi$
$337$	−9569.41			−1.54682			−0.773411	+	0.633905i	$0.781451\pi$
$338$	336.729	+	205.538i	0.0541883	+	0.0330763i
$339$		0			0
$340$	−1766.04	−	3436.26i	−0.281697	−	0.548110i
$341$			3377.40i			0.536353i
$342$		0			0
$343$	−5900.36	−	2353.58i	−0.928833	−	0.370500i
$344$	−3881.19	−	284.959i	−0.608314	−	0.0446626i
$345$		0			0
$346$	2155.52	−	3531.35i	0.334917	−	0.548689i
$347$		−	10409.6i		−	1.61043i	−0.592985	−	0.805214i	$-0.702050\pi$
$347$		−	10409.6i		−	1.61043i	0.592985	−	0.805214i	$-0.297950\pi$
$348$		0			0
$349$			12612.4i			1.93446i	0.253895	+	0.967232i	$0.418288\pi$
$349$			12612.4i			1.93446i	−0.253895	+	0.967232i	$0.581712\pi$
$350$	6810.85	+	5446.48i	1.04016	+	0.831790i
$351$		0			0
$352$	2933.41	+	6910.20i	0.444180	+	1.04635i
$353$			10352.1i			1.56087i	0.625236	+	0.780435i	$0.285003\pi$
$353$			10352.1i			1.56087i	−0.625236	+	0.780435i	$0.714997\pi$
$354$		0			0
$355$	−3376.35			−0.504783
$356$	−8302.18	+	4266.85i	−1.23600	+	0.635232i
$357$		0			0
$358$	4478.30	−	7336.72i	0.661133	−	1.08312i
$359$			3721.83i			0.547161i	0.961849	+	0.273580i	$0.0882080\pi$
$359$			3721.83i			0.547161i	−0.961849	+	0.273580i	$0.911792\pi$
$360$		0			0
$361$	−5133.15			−0.748381
$362$	567.313	−	929.419i	0.0823683	−	0.134942i
$363$		0			0
$364$	−6317.25	+	2293.27i	−0.909653	+	0.330220i
$365$	−4363.62			−0.625760
$366$		0			0
$367$	−4676.11			−0.665097			−0.332549	−	0.943086i	$-0.607909\pi$
$367$	−4676.11			−0.665097			−0.332549	+	0.943086i	$0.607909\pi$
$368$	4887.99	+	3499.31i	0.692403	+	0.495691i
$369$		0			0
$370$	2385.17	−	3907.57i	0.335132	−	0.549041i
$371$	−10581.0	−	1345.84i	−1.48069	−	0.188336i
$372$		0			0
$373$	−6601.94			−0.916448			−0.458224	−	0.888837i	$-0.651514\pi$
$373$	−6601.94			−0.916448			−0.458224	+	0.888837i	$0.651514\pi$
$374$	−2832.10	−	1728.70i	−0.391563	−	0.239008i
$375$		0			0
$376$	−473.868	+	6454.18i	−0.0649944	+	0.885236i
$377$			1262.07i			0.172413i
$378$		0			0
$379$		−	12756.2i		−	1.72887i	−0.502747	−	0.864434i	$-0.667677\pi$
$379$		−	12756.2i		−	1.72887i	0.502747	−	0.864434i	$-0.332323\pi$
$380$	5046.60	−	2593.67i	0.681277	−	0.350137i
$381$		0			0
$382$	745.072	−	1220.64i	0.0997938	−	0.163490i
$383$	1573.51			0.209929			0.104965	−	0.994476i	$-0.466527\pi$
$383$	1573.51			0.209929			0.104965	+	0.994476i	$0.466527\pi$
$384$		0			0
$385$	13008.0	+	1654.55i	1.72195	+	0.219023i
$386$	4639.89	+	2832.17i	0.611825	+	0.373455i
$387$		0			0
$388$	−4672.15	+	2401.22i	−0.611321	+	0.314184i
$389$	4022.95			0.524349			0.262174	−	0.965021i	$-0.415560\pi$
$389$	4022.95			0.524349			0.262174	+	0.965021i	$0.415560\pi$
$390$		0			0
$391$	−2656.98			−0.343656
$392$	−2487.93	+	7351.63i	−0.320559	+	0.947228i
$393$		0			0
$394$	−3871.50	−	2363.15i	−0.495034	−	0.302167i
$395$	−20120.1			−2.56291
$396$		0			0
$397$		−	3987.32i		−	0.504075i	−0.967717	−	0.252038i	$-0.918899\pi$
$397$		−	3987.32i		−	0.504075i	0.967717	−	0.252038i	$-0.0811007\pi$
$398$	6177.38	+	3770.65i	0.778000	+	0.474888i
$399$		0			0
$400$	6202.19	−	8663.50i	0.775274	−	1.08294i
$401$	−4624.46			−0.575897			−0.287948	−	0.957646i	$-0.592973\pi$
$401$	−4624.46			−0.575897			−0.287948	+	0.957646i	$0.592973\pi$
$402$		0			0
$403$			3694.11i			0.456618i
$404$	7111.21	−	3654.76i	0.875733	−	0.450076i
$405$		0			0
$406$	1138.28	+	910.255i	0.139142	+	0.111269i
$407$		−	3931.62i		−	0.478828i
$408$		0			0
$409$		−	633.029i		−	0.0765312i	−0.999268	−	0.0382656i	$-0.987817\pi$
$409$		−	633.029i		−	0.0765312i	0.999268	−	0.0382656i	$-0.0121833\pi$
$410$	−9368.80	−	5718.67i	−1.12852	−	0.688842i
$411$		0			0
$412$	−3506.68	−	6823.09i	−0.419324	−	0.815896i
$413$	7569.34	+	962.782i	0.901848	+	0.114710i
$414$		0			0
$415$			16023.1i			1.89528i
$416$	3208.49	+	7558.21i	0.378147	+	0.890797i
$417$		0			0
$418$	2538.83	−	4159.31i	0.297077	−	0.486695i
$419$	3197.39			0.372799			0.186399	−	0.982474i	$-0.440318\pi$
$419$	3197.39			0.372799			0.186399	+	0.982474i	$0.440318\pi$
$420$		0			0
$421$	−5489.09			−0.635444			−0.317722	−	0.948184i	$-0.602918\pi$
$421$	−5489.09			−0.635444			−0.317722	+	0.948184i	$0.602918\pi$
$422$	−562.025	+	920.755i	−0.0648316	+	0.106212i
$423$		0			0
$424$	−954.217	+	12996.6i	−0.109295	+	1.48861i
$425$			4709.25i			0.537487i
$426$		0			0
$427$	1820.38	−	14311.7i	0.206310	−	1.62200i
$428$	−4880.33	+	2508.21i	−0.551167	+	0.283268i
$429$		0			0
$430$	7088.89	+	4327.03i	0.795015	+	0.485274i
$431$			4178.34i			0.466968i	0.972361	+	0.233484i	$0.0750127\pi$
$431$			4178.34i			0.466968i	−0.972361	+	0.233484i	$0.924987\pi$
$432$		0			0
$433$			9306.18i			1.03286i	0.856331	+	0.516428i	$0.172739\pi$
$433$			9306.18i			1.03286i	−0.856331	+	0.516428i	$0.827261\pi$
$434$	3331.78	+	2664.35i	0.368504	+	0.294684i
$435$		0			0
$436$	4124.21	+	8024.65i	0.453014	+	0.881448i
$437$		−	3902.13i		−	0.427149i
$438$		0			0
$439$	−2931.42			−0.318700			−0.159350	−	0.987222i	$-0.550940\pi$
$439$	−2931.42			−0.318700			−0.159350	+	0.987222i	$0.550940\pi$
$440$	1173.09	−	15977.8i	0.127103	−	1.73116i
$441$		0			0
$442$	−3097.68	−	1890.81i	−0.333352	−	0.203477i
$443$			5884.29i			0.631086i	0.948911	+	0.315543i	$0.102187\pi$
$443$			5884.29i			0.631086i	−0.948911	+	0.315543i	$0.897813\pi$
$444$		0			0
$445$	19920.7			2.12209
$446$	7107.17	+	4338.18i	0.754561	+	0.460581i
$447$		0			0
$448$	9130.97	+	2557.50i	0.962941	+	0.269711i
$449$	−12856.4			−1.35129			−0.675646	−	0.737227i	$-0.736135\pi$
$449$	−12856.4			−1.35129			−0.675646	+	0.737227i	$0.736135\pi$
$450$		0			0
$451$	−9426.44			−0.984199
$452$	36.7469	+	71.5000i	0.00382396	+	0.00744043i
$453$		0			0
$454$	13968.9	+	8526.55i	1.44404	+	0.881434i
$455$	14227.8	+	1809.71i	1.46596	+	0.186463i
$456$		0			0
$457$	1831.12			0.187431			0.0937157	−	0.995599i	$-0.470126\pi$
$457$	1831.12			0.187431			0.0937157	+	0.995599i	$0.470126\pi$
$458$	6342.27	−	10390.4i	0.647063	−	1.06007i
$459$		0			0
$460$	−5864.25	−	11410.3i	−0.594395	−	1.15654i
$461$			609.925i			0.0616205i	0.999525	+	0.0308102i	$0.00980875\pi$
$461$			609.925i			0.0616205i	−0.999525	+	0.0308102i	$0.990191\pi$
$462$		0			0
$463$			7896.96i			0.792663i	0.918107	+	0.396332i	$0.129717\pi$
$463$			7896.96i			0.792663i	−0.918107	+	0.396332i	$0.870283\pi$
$464$	1036.56	−	1447.91i	0.103709	−	0.144865i
$465$		0			0
$466$	−12394.4	−	7565.47i	−1.23210	−	0.752068i
$467$	−14588.0			−1.44551			−0.722755	−	0.691104i	$-0.757125\pi$
$467$	−14588.0			−1.44551			−0.722755	+	0.691104i	$0.757125\pi$
$468$		0			0
$469$	464.505	−	3651.91i	0.0457331	−	0.359551i
$470$	7195.57	−	11788.4i	0.706184	−	1.15693i
$471$		0			0
$472$	682.622	−	9297.45i	0.0665683	−	0.906673i
$473$	7132.50			0.693347
$474$		0			0
$475$	−6916.15			−0.668073
$476$	−3939.53	+	1430.12i	−0.379345	+	0.137709i
$477$		0			0
$478$	−690.317	+	1130.93i	−0.0660552	+	0.108217i
$479$	18352.1			1.75058			0.875289	−	0.483599i	$-0.160671\pi$
$479$	18352.1			1.75058			0.875289	+	0.483599i	$0.160671\pi$
$480$		0			0
$481$		−	4300.30i		−	0.407644i
$482$	573.979	−	940.339i	0.0542407	−	0.0888615i
$483$		0			0
$484$	−1421.94	−	2766.72i	−0.133540	−	0.259835i
$485$	11210.6			1.04958
$486$		0			0
$487$		−	14673.5i		−	1.36534i	−0.730729	−	0.682668i	$-0.760820\pi$
$487$		−	14673.5i		−	1.36534i	0.730729	−	0.682668i	$-0.239180\pi$
$488$	−17579.2	−	1290.67i	−1.63068	−	0.119725i
$489$		0			0
$490$	11893.9	−	11527.1i	1.09656	−	1.06274i
$491$		−	3216.95i		−	0.295680i	−0.989011	−	0.147840i	$-0.952768\pi$
$491$		−	3216.95i		−	0.295680i	0.989011	−	0.147840i	$-0.0472321\pi$
$492$		0			0
$493$			787.043i			0.0718999i
$494$	2776.91	−	4549.35i	0.252913	−	0.414342i
$495$		0			0
$496$	3034.03	−	4238.07i	0.274662	−	0.383659i
$497$	−462.141	+	3633.33i	−0.0417100	+	0.327922i
$498$		0			0
$499$			8857.13i			0.794589i	0.917691	+	0.397294i	$0.130051\pi$
$499$			8857.13i			0.794589i	−0.917691	+	0.397294i	$0.869949\pi$
$500$	−5038.93	+	2589.72i	−0.450696	+	0.231632i
$501$		0			0
$502$	−11324.1	−	6912.18i	−1.00681	−	0.614553i
$503$	−5037.58			−0.446550			−0.223275	−	0.974756i	$-0.571675\pi$
$503$	−5037.58			−0.446550			−0.223275	+	0.974756i	$0.571675\pi$
$504$		0			0
$505$	−17063.0			−1.50355
$506$	−9404.16	−	5740.26i	−0.826217	−	0.504319i
$507$		0			0
$508$	−9584.72	+	4926.00i	−0.837113	+	0.430228i
$509$		−	10689.6i		−	0.930860i	−0.885085	−	0.465430i	$-0.845900\pi$
$509$		−	10689.6i		−	0.930860i	0.885085	−	0.465430i	$-0.154100\pi$
$510$		0			0
$511$	−597.275	+	4695.75i	−0.0517063	+	0.406512i
$512$	2526.73	−	11306.3i	0.218100	−	0.975927i
$513$		0			0
$514$	7697.14	−	12610.1i	0.660518	−	1.08212i
$515$			16371.7i			1.40082i
$516$		0			0
$517$		−	11860.9i		−	1.00898i
$518$	−3878.51	−	3101.56i	−0.328981	−	0.263079i
$519$		0			0
$520$	1283.10	−	17476.1i	0.108207	−	1.47380i
$521$		−	13501.9i		−	1.13537i	−0.823246	−	0.567685i	$-0.807839\pi$
$521$		−	13501.9i		−	1.13537i	0.823246	−	0.567685i	$-0.192161\pi$
$522$		0			0
$523$	−13819.9			−1.15546			−0.577728	−	0.816229i	$-0.696061\pi$
$523$	−13819.9			−1.15546			−0.577728	+	0.816229i	$0.696061\pi$
$524$	1756.26	+	3417.23i	0.146417	+	0.284890i
$525$		0			0
$526$	6933.12	−	11358.4i	0.574711	−	0.941539i
$527$			2303.70i			0.190419i
$528$		0			0
$529$	3344.33			0.274869
$530$	14489.5	−	23737.9i	1.18752	−	1.94549i
$531$		0			0
$532$	−2100.32	−	5785.72i	−0.171166	−	0.471509i
$533$	−10310.4			−0.837886
$534$		0			0
$535$	11710.1			0.946303
$536$	−4485.65	−	329.339i	−0.361475	−	0.0265397i
$537$		0			0
$538$	−5075.94	+	8315.82i	−0.406765	+	0.666395i
$539$	3560.97	−	13771.6i	0.284567	−	1.10053i
$540$		0			0
$541$	−1383.46			−0.109944			−0.0549720	−	0.998488i	$-0.517507\pi$
$541$	−1383.46			−0.109944			−0.0549720	+	0.998488i	$0.517507\pi$
$542$	12678.9	+	7739.16i	1.00481	+	0.613331i
$543$		0			0
$544$	2000.86	+	4713.41i	0.157695	+	0.371481i
$545$		−	19254.7i		−	1.51336i
$546$		0			0
$547$			19306.3i			1.50910i	0.656243	+	0.754550i	$0.272145\pi$
$547$			19306.3i			1.50910i	−0.656243	+	0.754550i	$0.727855\pi$
$548$	906.180	+	1763.19i	0.0706389	+	0.137445i
$549$		0			0
$550$	−10174.1	+	16668.0i	−0.788769	+	1.29223i
$551$	−1155.88			−0.0893684
$552$		0			0
$553$	−2753.96	+	21651.5i	−0.211772	+	1.66494i
$554$	14493.0	+	8846.46i	1.11146	+	0.678429i
$555$		0			0
$556$	6737.22	+	13108.9i	0.513888	+	0.999893i
$557$	−25149.0			−1.91310			−0.956551	−	0.291564i	$-0.905825\pi$
$557$	−25149.0			−1.91310			−0.956551	+	0.291564i	$0.905825\pi$
$558$		0			0
$559$	7801.36			0.590272
$560$	−14836.5	−	13761.7i	−1.11957	−	1.03846i
$561$		0			0
$562$	4516.09	+	2756.60i	0.338968	+	0.206904i
$563$	−11127.2			−0.832956			−0.416478	−	0.909146i	$-0.636736\pi$
$563$	−11127.2			−0.832956			−0.416478	+	0.909146i	$0.636736\pi$
$564$		0			0
$565$		−	171.561i		−	0.0127745i
$566$	9568.54	+	5840.60i	0.710593	+	0.433743i
$567$		0			0
$568$	4462.83	+	327.663i	0.329677	+	0.0242050i
$569$	2444.10			0.180074			0.0900368	−	0.995938i	$-0.471302\pi$
$569$	2444.10			0.180074			0.0900368	+	0.995938i	$0.471302\pi$
$570$		0			0
$571$		−	7744.79i		−	0.567617i	−0.958881	−	0.283809i	$-0.908402\pi$
$571$		−	7744.79i		−	0.567617i	0.958881	−	0.283809i	$-0.0915980\pi$
$572$	−6878.98	−	13384.7i	−0.502840	−	0.978398i
$573$		0			0
$574$	−7436.30	+	9299.13i	−0.540741	+	0.676199i
$575$			15637.3i			1.13413i
$576$		0			0
$577$		−	27283.3i		−	1.96849i	−0.176805	−	0.984246i	$-0.556576\pi$
$577$		−	27283.3i		−	1.96849i	0.176805	−	0.984246i	$-0.443424\pi$
$578$	9929.27	+	6060.78i	0.714538	+	0.436151i
$579$		0			0
$580$	−3379.93	+	1737.09i	−0.241972	+	0.124360i
$581$	17242.6	+	2193.17i	1.23123	+	0.156606i
$582$		0			0
$583$		−	23884.0i		−	1.69670i
$584$	5767.80	+	423.474i	0.408687	+	0.0300060i
$585$		0			0
$586$	−6859.24	+	11237.4i	−0.483537	+	0.792169i
$587$	3068.80			0.215780			0.107890	−	0.994163i	$-0.465591\pi$
$587$	3068.80			0.215780			0.107890	+	0.994163i	$0.465591\pi$
$588$		0			0
$589$	−3383.29			−0.236683
$590$	−10365.4	+	16981.5i	−0.723286	+	1.18495i
$591$		0			0
$592$	−3531.91	+	4933.53i	−0.245204	+	0.342511i
$593$			21823.7i			1.51129i	0.654984	+	0.755643i	$0.272675\pi$
$593$			21823.7i			1.51129i	−0.654984	+	0.755643i	$0.727325\pi$
$594$		0			0
$595$	8872.69	+	1128.56i	0.611336	+	0.0777589i
$596$	8048.09	+	15659.5i	0.553125	+	1.07624i
$597$		0			0
$598$	−10286.0	−	6278.55i	−0.703390	−	0.429346i
$599$		−	19352.6i		−	1.32007i	−0.751233	−	0.660037i	$-0.770541\pi$
$599$		−	19352.6i		−	1.32007i	0.751233	−	0.660037i	$-0.229459\pi$
$600$		0			0
$601$			8218.83i			0.557826i	0.960316	+	0.278913i	$0.0899740\pi$
$601$			8218.83i			0.557826i	−0.960316	+	0.278913i	$0.910026\pi$
$602$	5626.66	−	7036.17i	0.380940	−	0.476367i
$603$		0			0
$604$	22832.7	−	11734.7i	1.53816	−	0.790526i
$605$			6638.62i			0.446113i
$606$		0			0
$607$	23793.3			1.59101			0.795503	−	0.605950i	$-0.207207\pi$
$607$	23793.3			1.59101			0.795503	+	0.605950i	$0.207207\pi$
$608$	−6922.27	+	2938.53i	−0.461735	+	0.196008i
$609$		0			0
$610$	32107.8	+	19598.5i	2.13116	+	1.30085i
$611$		−	12973.2i		−	0.858981i
$612$		0			0
$613$	19490.1			1.28417			0.642087	−	0.766632i	$-0.278069\pi$
$613$	19490.1			1.28417			0.642087	+	0.766632i	$0.278069\pi$
$614$	−6827.76	−	4167.63i	−0.448772	−	0.273928i
$615$		0			0
$616$	−17033.3	−	3449.36i	−1.11411	−	0.225614i
$617$	12532.4			0.817724			0.408862	−	0.912596i	$-0.365926\pi$
$617$	12532.4			0.817724			0.408862	+	0.912596i	$0.365926\pi$
$618$		0			0
$619$	−3577.14			−0.232274			−0.116137	−	0.993233i	$-0.537051\pi$
$619$	−3577.14			−0.232274			−0.116137	+	0.993233i	$0.537051\pi$
$620$	−9893.17	+	5084.52i	−0.640837	+	0.329354i
$621$		0			0
$622$	15835.1	+	9665.66i	1.02078	+	0.623083i
$623$	2726.66	−	21436.9i	0.175347	−	1.37857i
$624$		0			0
$625$	−8719.36			−0.558039
$626$	−9161.78	+	15009.6i	−0.584949	+	0.958312i
$627$		0			0
$628$	4529.22	−	2327.76i	0.287795	−	0.147910i
$629$		−	2681.73i		−	0.169996i
$630$		0			0
$631$			2950.67i			0.186156i	0.995659	+	0.0930779i	$0.0296706\pi$
$631$			2950.67i			0.186156i	−0.995659	+	0.0930779i	$0.970329\pi$
$632$	26594.6	+	1952.58i	1.67385	+	0.122895i
$633$		0			0
$634$	−7857.87	−	4796.41i	−0.492233	−	0.300457i
$635$	22998.1			1.43724
$636$		0			0
$637$	3894.90	−	15063.0i	0.242263	−	0.936922i
$638$	−1700.36	+	2785.67i	−0.105514	+	0.172862i
$639$		0			0
$640$	−15825.4	+	18995.6i	−0.977430	+	1.17323i
$641$	2474.02			0.152446			0.0762229	−	0.997091i	$-0.475714\pi$
$641$	2474.02			0.152446			0.0762229	+	0.997091i	$0.475714\pi$
$642$		0			0
$643$	−20855.1			−1.27907			−0.639537	−	0.768760i	$-0.720874\pi$
$643$	−20855.1			−1.27907			−0.639537	+	0.768760i	$0.720874\pi$
$644$	−13081.4	+	4748.79i	−0.800437	+	0.290572i
$645$		0			0
$646$	1731.72	−	2837.05i	0.105470	−	0.172790i
$647$	−24529.0			−1.49047			−0.745237	−	0.666800i	$-0.767663\pi$
$647$	−24529.0			−1.49047			−0.745237	+	0.666800i	$0.767663\pi$
$648$		0			0
$649$			17086.0i			1.03341i
$650$	−11128.1	+	18231.0i	−0.671509	+	1.10012i
$651$		0			0
$652$	−17506.4	+	8997.26i	−1.05154	+	0.540430i
$653$	−8840.01			−0.529765			−0.264882	−	0.964281i	$-0.585333\pi$
$653$	−8840.01			−0.529765			−0.264882	+	0.964281i	$0.585333\pi$
$654$		0			0
$655$		−	8199.47i		−	0.489129i
$656$	11828.6	+	8468.10i	0.704009	+	0.504000i
$657$		0			0
$658$	−11700.7	−	9356.78i	−0.693223	−	0.554354i
$659$			26347.9i			1.55746i	0.627356	+	0.778732i	$0.284137\pi$
$659$			26347.9i			1.55746i	−0.627356	+	0.778732i	$0.715863\pi$
$660$		0			0
$661$			22699.6i			1.33572i	0.744286	+	0.667861i	$0.232790\pi$
$661$			22699.6i			1.33572i	−0.744286	+	0.667861i	$0.767210\pi$
$662$	−6462.30	+	10587.1i	−0.379403	+	0.621568i
$663$		0			0
$664$	1554.98	−	21179.1i	0.0908809	−	1.23782i
$665$	−1657.44	+	13030.7i	−0.0966509	+	0.759864i
$666$		0			0
$667$			2613.42i			0.151712i
$668$	7800.65	+	15178.0i	0.451820	+	0.879126i
$669$		0			0
$670$	8192.92	+	5000.92i	0.472418	+	0.288362i
$671$	32305.4			1.85862
$672$		0			0
$673$	−5208.40			−0.298319			−0.149160	−	0.988813i	$-0.547657\pi$
$673$	−5208.40			−0.298319			−0.149160	+	0.988813i	$0.547657\pi$
$674$	−23102.6	−	14101.7i	−1.32029	−	0.805902i
$675$		0			0
$676$	510.049	+	992.424i	0.0290196	+	0.0564647i
$677$			3144.71i			0.178524i	0.996008	+	0.0892622i	$0.0284509\pi$
$677$			3144.71i			0.178524i	−0.996008	+	0.0892622i	$0.971549\pi$
$678$		0			0
$679$	1534.46	−	12063.9i	0.0867264	−	0.681838i
$680$	800.162	−	10898.4i	0.0451247	−	0.614607i
$681$		0			0
$682$	−4977.02	+	8153.76i	−0.279443	+	0.457806i
$683$			11895.3i			0.666415i	0.942854	+	0.333208i	$0.108131\pi$
$683$			11895.3i			0.666415i	−0.942854	+	0.333208i	$0.891869\pi$
$684$		0			0
$685$		−	4230.69i		−	0.235980i
$686$	−10776.4	−	14377.0i	−0.599776	−	0.800168i
$687$		0			0
$688$	−8950.11	−	6407.38i	−0.495959	−	0.355057i
$689$		−	26123.7i		−	1.44446i
$690$		0			0
$691$	24606.5			1.35467			0.677333	−	0.735676i	$-0.263136\pi$
$691$	24606.5			1.35467			0.677333	+	0.735676i	$0.263136\pi$
$692$	10407.8	−	5349.00i	0.571740	−	0.293842i
$693$		0			0
$694$	15339.9	−	25131.1i	0.839042	−	1.37459i
$695$		−	31454.1i		−	1.71672i
$696$		0			0
$697$	−6429.73			−0.349416
$698$	−18586.0	+	30449.1i	−1.00787	+	1.65117i
$699$		0			0
$700$	8416.77	+	23185.6i	0.454463	+	1.25191i
$701$	1627.77			0.0877033			0.0438516	−	0.999038i	$-0.486037\pi$
$701$	1627.77			0.0877033			0.0438516	+	0.999038i	$0.486037\pi$
$702$		0			0
$703$	3938.48			0.211298
$704$	−3101.17	+	21005.5i	−0.166023	+	1.12454i
$705$		0			0
$706$	−15255.1	+	24992.2i	−0.813222	+	1.33229i
$707$	−2335.51	+	18361.7i	−0.124238	+	0.976750i
$708$		0			0
$709$	−27634.3			−1.46379			−0.731896	−	0.681416i	$-0.761364\pi$
$709$	−27634.3			−1.46379			−0.731896	+	0.681416i	$0.761364\pi$
$710$	−8151.23	−	4975.48i	−0.430860	−	0.262995i
$711$		0			0
$712$	−26331.0	−	1933.23i	−1.38595	−	0.101757i
$713$			7649.59i			0.401794i
$714$		0			0
$715$			32116.0i			1.67982i
$716$	21623.1	−	11113.1i	1.12862	−	0.580048i
$717$		0			0
$718$	−5484.59	+	8985.30i	−0.285074	+	0.467031i
$719$	5943.23			0.308269			0.154134	−	0.988050i	$-0.450741\pi$
$719$	5943.23			0.308269			0.154134	+	0.988050i	$0.450741\pi$
$720$		0			0
$721$	17617.7	+	2240.89i	0.910012	+	0.115749i
$722$	−12392.5	−	7564.34i	−0.638783	−	0.389911i
$723$		0			0
$724$	2739.23	−	1407.81i	0.140612	−	0.0722663i
$725$	4632.04			0.237282
$726$		0			0
$727$	20574.9			1.04963			0.524816	−	0.851216i	$-0.324134\pi$
$727$	20574.9			1.04963			0.524816	+	0.851216i	$0.324134\pi$
$728$	−18630.6	−	3772.82i	−0.948484	−	0.192074i
$729$		0			0
$730$	−10534.7	−	6430.35i	−0.534120	−	0.326024i
$731$	4865.04			0.246156
$732$		0			0
$733$		−	16226.5i		−	0.817655i	−0.912612	−	0.408828i	$-0.865938\pi$
$733$		−	16226.5i		−	0.817655i	0.912612	−	0.408828i	$-0.134062\pi$
$734$	−11289.1	−	6890.83i	−0.567696	−	0.346519i
$735$		0			0
$736$	6643.98	+	15651.2i	0.332745	+	0.783844i
$737$	8243.33			0.412004
$738$		0			0
$739$			27285.1i			1.35818i	0.734054	+	0.679092i	$0.237626\pi$
$739$			27285.1i			1.35818i	−0.734054	+	0.679092i	$0.762374\pi$
$740$	11516.6	−	5918.87i	0.572106	−	0.294030i
$741$		0			0
$742$	−23561.4	−	18841.5i	−1.16572	−	0.932202i
$743$			15043.5i			0.742791i	0.928475	+	0.371396i	$0.121121\pi$
$743$			15043.5i			0.742791i	−0.928475	+	0.371396i	$0.878879\pi$
$744$		0			0
$745$		−	37574.2i		−	1.84780i
$746$	−15938.5	−	9728.78i	−0.782238	−	0.477475i
$747$		0			0
$748$	−4289.84	−	8346.92i	−0.209695	−	0.408013i
$749$	1602.83	−	12601.4i	0.0781926	−	0.614746i
$750$		0			0
$751$		−	17941.4i		−	0.871757i	−0.900006	−	0.435879i	$-0.856438\pi$
$751$		−	17941.4i		−	0.871757i	0.900006	−	0.435879i	$-0.143562\pi$
$752$	−10655.1	+	14883.5i	−0.516689	+	0.721734i
$753$		0			0
$754$	−1859.81	+	3046.90i	−0.0898281	+	0.147164i
$755$	−54785.8			−2.64088
$756$		0			0
$757$	−12961.3			−0.622305			−0.311152	−	0.950360i	$-0.600715\pi$
$757$	−12961.3			−0.622305			−0.311152	+	0.950360i	$0.600715\pi$
$758$	18797.8	−	30796.1i	0.900749	−	1.47568i
$759$		0			0
$760$	16005.7	+	1175.14i	0.763930	+	0.0560880i
$761$			8866.11i			0.422334i	0.977450	+	0.211167i	$0.0677264\pi$
$761$			8866.11i			0.422334i	−0.977450	+	0.211167i	$0.932274\pi$
$762$		0			0
$763$	−20720.3	−	2635.51i	−0.983125	−	0.125048i
$764$	3597.53	−	1848.92i	0.170359	−	0.0875546i
$765$		0			0
$766$	3798.80	+	2318.77i	0.179186	+	0.109374i
$767$			18688.2i			0.879783i
$768$		0			0
$769$		−	31664.2i		−	1.48484i	−0.669937	−	0.742418i	$-0.733679\pi$
$769$		−	31664.2i		−	1.48484i	0.669937	−	0.742418i	$-0.266321\pi$
$770$	28965.9	+	23163.4i	1.35566	+	1.08409i
$771$		0			0
$772$	7028.14	+	13674.9i	0.327653	+	0.637528i
$773$			19253.1i			0.895842i	0.894073	+	0.447921i	$0.147835\pi$
$773$			19253.1i			0.895842i	−0.894073	+	0.447921i	$0.852165\pi$
$774$		0			0
$775$	13558.2			0.628417
$776$	−14818.1	−	1087.95i	−0.685487	−	0.0503287i
$777$		0			0
$778$	9712.26	+	5928.32i	0.447559	+	0.273188i
$779$		−	9442.90i		−	0.434309i
$780$		0			0
$781$	−8201.39			−0.375760
$782$	−6414.53	−	3915.40i	−0.293329	−	0.179047i
$783$		0			0
$784$	−16839.9	+	14082.1i	−0.767126	+	0.641497i
$785$	−10867.6			−0.494118
$786$		0			0
$787$	1284.72			0.0581897			0.0290949	−	0.999577i	$-0.490738\pi$
$787$	1284.72			0.0581897			0.0290949	+	0.999577i	$0.490738\pi$
$788$	−5864.23	−	11410.3i	−0.265108	−	0.515831i
$789$		0			0
$790$	−48574.2	−	29649.5i	−2.18758	−	1.33529i
$791$	−184.618	−	23.4825i	−0.00829871	−	0.00105555i
$792$		0			0
$793$	35334.8			1.58231
$794$	5875.82	−	9626.25i	0.262626	−	0.430255i
$795$		0			0
$796$	9356.99	+	18206.3i	0.416645	+	0.810684i
$797$			2593.21i			0.115253i	0.998338	+	0.0576263i	$0.0183532\pi$
$797$			2593.21i			0.115253i	−0.998338	+	0.0576263i	$0.981647\pi$
$798$		0			0
$799$		−	8090.25i		−	0.358213i
$800$	27740.2	−	11775.8i	1.22595	−	0.520423i
$801$		0			0
$802$	−11164.4	−	6814.72i	−0.491559	−	0.300045i
$803$	−10599.5			−0.465815
$804$		0			0
$805$	29462.3	+	3747.46i	1.28995	+	0.164075i
$806$	−5443.74	+	8918.38i	−0.237900	+	0.389747i
$807$		0			0
$808$	22553.7	+	1655.90i	0.981977	+	0.0720971i
$809$	11424.8			0.496508			0.248254	−	0.968695i	$-0.420143\pi$
$809$	11424.8			0.496508			0.248254	+	0.968695i	$0.420143\pi$
$810$		0			0
$811$	32094.4			1.38962			0.694812	−	0.719191i	$-0.255487\pi$
$811$	32094.4			1.38962			0.694812	+	0.719191i	$0.255487\pi$
$812$	1406.67	+	3874.95i	0.0607937	+	0.167468i
$813$		0			0
$814$	5793.73	−	9491.76i	0.249472	−	0.408705i
$815$	42005.6			1.80539
$816$		0			0
$817$			7144.96i			0.305961i
$818$	932.847	−	1528.27i	0.0398732	−	0.0653234i
$819$		0			0
$820$	−14191.1	−	27612.2i	−0.604359	−	1.17593i
$821$	−3861.07			−0.164132			−0.0820660	−	0.996627i	$-0.526152\pi$
$821$	−3861.07			−0.164132			−0.0820660	+	0.996627i	$0.526152\pi$
$822$		0			0
$823$			4840.43i			0.205014i	0.994732	+	0.102507i	$0.0326865\pi$
$823$			4840.43i			0.205014i	−0.994732	+	0.102507i	$0.967314\pi$
$824$	1588.81	−	21639.9i	0.0671709	−	0.914881i
$825$		0			0
$826$	16855.2	+	13478.7i	0.710010	+	0.567779i
$827$			831.897i			0.0349793i	0.999847	+	0.0174897i	$0.00556741\pi$
$827$			831.897i			0.0349793i	−0.999847	+	0.0174897i	$0.994433\pi$
$828$		0			0
$829$			24696.3i			1.03467i	0.855784	+	0.517333i	$0.173075\pi$
$829$			24696.3i			1.03467i	−0.855784	+	0.517333i	$0.826925\pi$
$830$	−23612.0	+	38683.1i	−0.987450	+	1.61772i
$831$		0			0
$832$	−3391.99	+	22975.2i	−0.141341	+	0.957359i
$833$	2428.92	−	9393.54i	0.101029	−	0.390716i
$834$		0			0
$835$		−	36419.0i		−	1.50938i
$836$	12258.5	−	6300.19i	0.507142	−	0.260642i
$837$		0			0
$838$	7719.18	+	4711.75i	0.318203	+	0.194230i
$839$	20023.0			0.823922			0.411961	−	0.911202i	$-0.364844\pi$
$839$	20023.0			0.823922			0.411961	+	0.911202i	$0.364844\pi$
$840$		0			0
$841$	−23614.9			−0.968259
$842$	−13251.8	−	8088.87i	−0.542385	−	0.331070i
$843$		0			0
$844$	−2713.70	+	1394.68i	−0.110674	+	0.0568803i
$845$		−	2381.27i		−	0.0969447i
$846$		0			0
$847$	7143.89	+	908.667i	0.289808	+	0.0368621i
$848$	−21455.8	+	29970.5i	−0.868864	+	1.21367i
$849$		0			0
$850$	−6939.67	+	11369.1i	−0.280034	+	0.458774i
$851$		−	8904.86i		−	0.358701i
$852$		0			0
$853$			25542.4i			1.02527i	0.858606	+	0.512636i	$0.171331\pi$
$853$			25542.4i			1.02527i	−0.858606	+	0.512636i	$0.828669\pi$
$854$	25484.9	−	31869.0i	1.02117	−	1.27697i
$855$		0			0
$856$	−15478.3	−	1136.42i	−0.618035	−	0.0453764i
$857$		−	25923.2i		−	1.03328i	−0.856204	−	0.516638i	$-0.827183\pi$
$857$		−	25923.2i		−	1.03328i	0.856204	−	0.516638i	$-0.172817\pi$
$858$		0			0
$859$	−25807.8			−1.02509			−0.512544	−	0.858661i	$-0.671297\pi$
$859$	−25807.8			−1.02509			−0.512544	+	0.858661i	$0.671297\pi$
$860$	10737.7	+	20892.7i	0.425758	+	0.828414i
$861$		0			0
$862$	−6157.30	+	10087.4i	−0.243293	+	0.398582i
$863$			1101.05i			0.0434302i	0.999764	+	0.0217151i	$0.00691267\pi$
$863$			1101.05i			0.0434302i	−0.999764	+	0.0217151i	$0.993087\pi$
$864$		0			0
$865$	−24972.9			−0.981624
$866$	−13713.8	+	22467.1i	−0.538123	+	0.881597i
$867$		0			0
$868$	4117.38	+	11342.1i	0.161006	+	0.443521i
$869$	−48873.0			−1.90783
$870$		0			0
$871$	9016.35			0.350755
$872$	−1868.61	+	25450.8i	−0.0725676	+	0.988385i
$873$		0			0
$874$	5750.28	−	9420.58i	0.222547	−	0.364595i
$875$	1654.92	−	13010.9i	0.0639390	−	0.502685i
$876$		0			0
$877$	43509.3			1.67526			0.837631	−	0.546237i	$-0.183940\pi$
$877$	43509.3			1.67526			0.837631	+	0.546237i	$0.183940\pi$
$878$	−7077.08	−	4319.82i	−0.272027	−	0.166044i
$879$		0			0
$880$	26377.4	−	36845.1i	1.01043	−	1.41142i
$881$			39281.4i			1.50219i	0.660197	+	0.751093i	$0.270473\pi$
$881$			39281.4i			1.50219i	−0.660197	+	0.751093i	$0.729527\pi$
$882$		0			0
$883$			4217.95i			0.160754i	0.996765	+	0.0803768i	$0.0256123\pi$
$883$			4217.95i			0.160754i	−0.996765	+	0.0803768i	$0.974388\pi$
$884$	−4692.12	−	9129.65i	−0.178521	−	0.347357i
$885$		0			0
$886$	−8671.25	+	14205.9i	−0.328799	+	0.538666i
$887$	7206.54			0.272798			0.136399	−	0.990654i	$-0.456447\pi$
$887$	7206.54			0.272798			0.136399	+	0.990654i	$0.456447\pi$
$888$		0			0
$889$	3147.88	−	24748.5i	0.118759	−	0.933675i
$890$	48092.8	+	29355.6i	1.81132	+	1.10562i
$891$		0			0
$892$	10765.4	+	20946.6i	0.404093	+	0.786260i
$893$	11881.6			0.445244
$894$		0			0
$895$	−51883.7			−1.93774
$896$	18275.3	+	19630.0i	0.681401	+	0.731911i
$897$		0			0
$898$	−31038.0	−	18945.5i	−1.15340	−	0.704030i
$899$	2265.94			0.0840636
$900$		0			0
$901$		−	16291.1i		−	0.602372i
$902$	−22757.4	−	13891.0i	−0.840067	−	0.512773i
$903$		0			0
$904$	−16.6494	+	226.767i	−0.000612554	+	0.00834311i
$905$	−6572.65			−0.241417
$906$		0			0
$907$		−	28116.4i		−	1.02932i	−0.857395	−	0.514659i	$-0.827919\pi$
$907$		−	28116.4i		−	1.02932i	0.857395	−	0.514659i	$-0.172081\pi$
$908$	21158.9	+	41169.8i	0.773331	+	1.50470i
$909$		0			0
$910$	31682.2	+	25335.5i	1.15413	+	0.922928i
$911$		−	36758.1i		−	1.33683i	−0.743790	−	0.668414i	$-0.766974\pi$
$911$		−	36758.1i		−	1.33683i	0.743790	−	0.668414i	$-0.233026\pi$
$912$		0			0
$913$			38921.1i			1.41084i
$914$	4420.71	+	2698.38i	0.159983	+	0.0976527i
$915$		0			0
$916$	30623.2	−	15738.6i	1.10460	−	0.567704i
$917$	−8823.55	−	1122.31i	−0.317753	−	0.0404165i
$918$		0			0
$919$		−	4560.64i		−	0.163702i	−0.996645	−	0.0818508i	$-0.973917\pi$
$919$		−	4560.64i		−	0.163702i	0.996645	−	0.0818508i	$-0.0260831\pi$
$920$	2656.98	−	36188.6i	0.0952154	−	1.29685i
$921$		0			0
$922$	−898.801	+	1472.49i	−0.0321046	+	0.0525964i
$923$	−8970.47			−0.319899
$924$		0			0
$925$	−15783.0			−0.561018
$926$	−11637.2	+	19065.0i	−0.412982	+	0.676580i
$927$		0			0
$928$	4636.14	−	1968.06i	0.163996	−	0.0696172i
$929$		−	47031.3i		−	1.66098i	−0.557037	−	0.830488i	$-0.688062\pi$
$929$		−	47031.3i		−	1.66098i	0.557037	−	0.830488i	$-0.311938\pi$
$930$		0			0
$931$	13795.6	+	3567.19i	0.485644	+	0.125574i
$932$	−18774.0	−	36529.3i	−0.659831	−	1.28386i
$933$		0			0
$934$	−35218.6	−	21497.3i	−1.23382	−	0.753119i
$935$			20028.0i			0.700520i
$936$		0			0
$937$			958.545i			0.0334197i	0.999860	+	0.0167099i	$0.00531916\pi$
$937$			958.545i			0.0334197i	−0.999860	+	0.0167099i	$0.994681\pi$
$938$	6502.97	−	8131.99i	0.226364	−	0.283069i
$939$		0			0
$940$	34743.3	−	17856.1i	1.20553	−	0.619575i
$941$			26664.8i			0.923748i	0.886945	+	0.461874i	$0.152823\pi$
$941$			26664.8i			0.923748i	−0.886945	+	0.461874i	$0.847177\pi$
$942$		0			0
$943$	−21350.3			−0.737286
$944$	15349.0	−	21440.1i	0.529201	−	0.739212i
$945$		0			0
$946$	17219.4	+	10510.6i	0.591808	+	0.361237i
$947$			3408.56i			0.116962i	0.998289	+	0.0584812i	$0.0186258\pi$
$947$			3408.56i			0.116962i	−0.998289	+	0.0584812i	$0.981374\pi$
$948$		0			0
$949$	−11593.5			−0.396566
$950$	−16697.1	−	10191.8i	−0.570236	−	0.348070i
$951$		0			0
$952$	−11618.3	−	2352.79i	−0.395538	−	0.0800990i
$953$	30025.2			1.02058			0.510290	−	0.860002i	$-0.329538\pi$
$953$	30025.2			1.02058			0.510290	+	0.860002i	$0.329538\pi$
$954$		0			0
$955$	−8632.09			−0.292490
$956$	−3333.15	+	1713.05i	−0.112763	+	0.0579539i
$957$		0			0
$958$	44305.8	+	27044.1i	1.49421	+	0.912061i
$959$	−4552.70	−	579.080i	−0.153300	−	0.0194989i
$960$		0			0
$961$	−23158.5			−0.777366
$962$	6337.04	−	10381.9i	0.212385	−	0.347946i
$963$		0			0
$964$	2771.42	−	1424.35i	0.0925947	−	0.0475884i
$965$		−	32812.3i		−	1.09458i
$966$		0			0
$967$			21764.9i			0.723798i	0.932217	+	0.361899i	$0.117872\pi$
$967$			21764.9i			0.723798i	−0.932217	+	0.361899i	$0.882128\pi$
$968$	644.254	−	8774.87i	0.0213916	−	0.291358i
$969$		0			0
$970$	27064.8	+	16520.2i	0.895873	+	0.546837i
$971$	−21876.6			−0.723021			−0.361511	−	0.932368i	$-0.617739\pi$
$971$	−21876.6			−0.723021			−0.361511	+	0.932368i	$0.617739\pi$
$972$		0			0
$973$	−33848.2	−	4305.31i	−1.11523	−	0.141852i
$974$	21623.2	−	35424.9i	0.711347	−	1.16539i
$975$		0			0
$976$	−40537.9	−	29021.0i	−1.32949	−	0.951784i
$977$	−33945.5			−1.11158			−0.555789	−	0.831323i	$-0.687584\pi$
$977$	−33945.5			−1.11158			−0.555789	+	0.831323i	$0.687584\pi$
$978$		0			0
$979$	48388.7			1.57968
$980$	45701.1	−	10301.7i	1.48966	−	0.335790i
$981$		0			0
$982$	4740.58	−	7766.41i	0.154051	−	0.252379i
$983$	−23428.5			−0.760176			−0.380088	−	0.924950i	$-0.624106\pi$
$983$	−23428.5			−0.760176			−0.380088	+	0.924950i	$0.624106\pi$
$984$		0			0
$985$			27378.4i			0.885633i
$986$	−1159.81	+	1900.09i	−0.0374602	+	0.0613704i
$987$		0			0
$988$	13408.1	−	6890.99i	0.431749	−	0.221894i
$989$	16154.7			0.519402
$990$		0			0
$991$			54992.8i			1.76277i	0.472399	+	0.881385i	$0.343388\pi$
$991$			54992.8i			1.76277i	−0.472399	+	0.881385i	$0.656612\pi$
$992$	13570.1	−	5760.58i	0.434327	−	0.184374i
$993$		0			0
$994$	−6469.88	+	8090.61i	−0.206451	+	0.258168i
$995$		−	43685.1i		−	1.39187i
$996$		0			0
$997$		−	1381.20i		−	0.0438747i	−0.999759	−	0.0219374i	$-0.993017\pi$
$997$		−	1381.20i		−	0.0438747i	0.999759	−	0.0219374i	$-0.00698344\pi$
$998$	−13052.1	+	21383.0i	−0.413985	+	0.678224i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.d.55.7		8
3.2	odd	2		28.4.d.b.27.1	✓	8
4.3	odd	2	inner	252.4.b.d.55.5		8
7.6	odd	2	inner	252.4.b.d.55.8		8
12.11	even	2		28.4.d.b.27.4	yes	8
21.2	odd	6		196.4.f.c.31.4		16
21.5	even	6		196.4.f.c.31.3		16
21.11	odd	6		196.4.f.c.19.8		16
21.17	even	6		196.4.f.c.19.7		16
21.20	even	2		28.4.d.b.27.2	yes	8
24.5	odd	2		448.4.f.d.447.5		8
24.11	even	2		448.4.f.d.447.3		8
28.27	even	2	inner	252.4.b.d.55.6		8
84.11	even	6		196.4.f.c.19.3		16
84.23	even	6		196.4.f.c.31.7		16
84.47	odd	6		196.4.f.c.31.8		16
84.59	odd	6		196.4.f.c.19.4		16
84.83	odd	2		28.4.d.b.27.3	yes	8
168.83	odd	2		448.4.f.d.447.6		8
168.125	even	2		448.4.f.d.447.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.d.b.27.1	✓	8	3.2	odd	2
28.4.d.b.27.2	yes	8	21.20	even	2
28.4.d.b.27.3	yes	8	84.83	odd	2
28.4.d.b.27.4	yes	8	12.11	even	2
196.4.f.c.19.3		16	84.11	even	6
196.4.f.c.19.4		16	84.59	odd	6
196.4.f.c.19.7		16	21.17	even	6
196.4.f.c.19.8		16	21.11	odd	6
196.4.f.c.31.3		16	21.5	even	6
196.4.f.c.31.4		16	21.2	odd	6
196.4.f.c.31.7		16	84.23	even	6
196.4.f.c.31.8		16	84.47	odd	6
252.4.b.d.55.5		8	4.3	odd	2	inner
252.4.b.d.55.6		8	28.27	even	2	inner
252.4.b.d.55.7		8	1.1	even	1	trivial
252.4.b.d.55.8		8	7.6	odd	2	inner
448.4.f.d.447.3		8	24.11	even	2
448.4.f.d.447.4		8	168.125	even	2
448.4.f.d.447.5		8	24.5	odd	2
448.4.f.d.447.6		8	168.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.41421 + 1.47363i) q^{2} +(3.65685 + 7.11529i) q^{4} -17.0728i q^{5} +(-18.3722 - 2.33686i) q^{7} +(-1.65685 + 22.5667i) q^{8} +O(q^{10})\)	\(q+(2.41421 + 1.47363i) q^{2} +(3.65685 + 7.11529i) q^{4} -17.0728i q^{5} +(-18.3722 - 2.33686i) q^{7} +(-1.65685 + 22.5667i) q^{8} +(25.1589 - 41.2174i) q^{10} -41.4710i q^{11} -45.3599i q^{13} +(-40.9109 - 32.7155i) q^{14} +(-37.2548 + 52.0392i) q^{16} -28.2871i q^{17} +41.5434 q^{19} +(121.478 - 62.4327i) q^{20} +(61.1127 - 100.120i) q^{22} -93.9291i q^{23} -166.480 q^{25} +(66.8435 - 109.509i) q^{26} +(-50.5572 - 139.269i) q^{28} -27.8234 q^{29} -81.4400 q^{31} +(-166.627 + 70.7340i) q^{32} +(41.6846 - 68.2912i) q^{34} +(-39.8967 + 313.665i) q^{35} +94.8040 q^{37} +(100.295 + 61.2194i) q^{38} +(385.276 + 28.2871i) q^{40} -227.302i q^{41} +171.988i q^{43} +(295.078 - 151.653i) q^{44} +(138.416 - 226.765i) q^{46} +286.005 q^{47} +(332.078 + 85.8665i) q^{49} +(-401.919 - 245.330i) q^{50} +(322.749 - 165.875i) q^{52} +575.921 q^{53} -708.025 q^{55} +(83.1752 - 410.728i) q^{56} +(-67.1716 - 41.0012i) q^{58} -411.999 q^{59} +778.987i q^{61} +(-196.614 - 120.012i) q^{62} +(-506.510 - 74.7794i) q^{64} -774.420 q^{65} +198.773i q^{67} +(201.271 - 103.442i) q^{68} +(-558.544 + 698.463i) q^{70} -197.762i q^{71} -255.589i q^{73} +(228.877 + 139.706i) q^{74} +(151.918 + 295.593i) q^{76} +(-96.9117 + 761.915i) q^{77} -1178.49i q^{79} +(888.454 + 636.044i) q^{80} +(334.958 - 548.756i) q^{82} -938.514 q^{83} -482.940 q^{85} +(-253.446 + 415.215i) q^{86} +(935.862 + 68.7114i) q^{88} +1166.81i q^{89} +(-106.000 + 833.363i) q^{91} +(668.333 - 343.485i) q^{92} +(690.476 + 421.464i) q^{94} -709.261i q^{95} +656.635i q^{97} +(675.173 + 696.659i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8	\( 8 q + 8 q^{2} - 16 q^{4} + 32 q^{8} + 152 q^{14} + 64 q^{16} + 240 q^{22} - 472 q^{25} - 48 q^{28} + 592 q^{29} - 1152 q^{32} + 1392 q^{37} + 1184 q^{44} - 816 q^{46} + 1480 q^{49} - 1688 q^{50} + 1168 q^{53} - 800 q^{56} - 560 q^{58} - 3328 q^{64} - 448 q^{65} - 3200 q^{70} + 496 q^{74} - 368 q^{77} + 1024 q^{85} - 240 q^{86} + 3776 q^{88} + 3808 q^{92} + 3144 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^4 + 32 * q^8 + 152 * q^14 + 64 * q^16 + 240 * q^22 - 472 * q^25 - 48 * q^28 + 592 * q^29 - 1152 * q^32 + 1392 * q^37 + 1184 * q^44 - 816 * q^46 + 1480 * q^49 - 1688 * q^50 + 1168 * q^53 - 800 * q^56 - 560 * q^58 - 3328 * q^64 - 448 * q^65 - 3200 * q^70 + 496 * q^74 - 368 * q^77 + 1024 * q^85 - 240 * q^86 + 3776 * q^88 + 3808 * q^92 + 3144 * q^98

Introduction

L-functions

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