LMFDB - Embedded newform 108.5.d.b.55.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(55,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.55");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.d (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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 1016x^{12} + 13512x^{10} + 130640x^{8} + 569472x^{6} + 1783808x^{4} + 352256x^{2} + 65536 $ x^16 + 38x^14 + 1016x^12 + 13512x^10 + 130640x^8 + 569472x^6 + 1783808x^4 + 352256*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.11
Root			$-1.78073 - 3.08431i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.5.d.b.55.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54696 - 3.08431i) q^{2} +(-3.02598 - 15.7113i) q^{4} -3.58334 q^{5} -16.2605i q^{7} +(-56.1655 - 30.6829i) q^{8} +O(q^{10})$	\(q+(2.54696 - 3.08431i) q^{2} +(-3.02598 - 15.7113i) q^{4} -3.58334 q^{5} -16.2605i q^{7} +(-56.1655 - 30.6829i) q^{8} +(-9.12663 + 11.0521i) q^{10} -144.712i q^{11} -223.658 q^{13} +(-50.1524 - 41.4148i) q^{14} +(-237.687 + 95.0838i) q^{16} +1.80372 q^{17} +70.1406i q^{19} +(10.8431 + 56.2988i) q^{20} +(-446.338 - 368.577i) q^{22} -251.394i q^{23} -612.160 q^{25} +(-569.647 + 689.830i) q^{26} +(-255.473 + 49.2039i) q^{28} +1641.50 q^{29} -1047.19i q^{31} +(-312.111 + 975.276i) q^{32} +(4.59401 - 5.56324i) q^{34} +58.2669i q^{35} -690.791 q^{37} +(216.336 + 178.645i) q^{38} +(201.260 + 109.947i) q^{40} +993.138 q^{41} +1983.63i q^{43} +(-2273.61 + 437.896i) q^{44} +(-775.377 - 640.290i) q^{46} -3199.12i q^{47} +2136.60 q^{49} +(-1559.15 + 1888.09i) q^{50} +(676.783 + 3513.94i) q^{52} +2863.25 q^{53} +518.553i q^{55} +(-498.919 + 913.278i) q^{56} +(4180.85 - 5062.91i) q^{58} -5577.97i q^{59} +2838.27 q^{61} +(-3229.85 - 2667.14i) q^{62} +(2213.12 + 3446.64i) q^{64} +801.442 q^{65} -5289.13i q^{67} +(-5.45802 - 28.3387i) q^{68} +(179.713 + 148.403i) q^{70} +1873.59i q^{71} +4523.42 q^{73} +(-1759.42 + 2130.62i) q^{74} +(1102.00 - 212.244i) q^{76} -2353.09 q^{77} +7360.48i q^{79} +(851.713 - 340.718i) q^{80} +(2529.48 - 3063.15i) q^{82} +5006.55i q^{83} -6.46335 q^{85} +(6118.15 + 5052.24i) q^{86} +(-4440.19 + 8127.83i) q^{88} +11438.5 q^{89} +3636.78i q^{91} +(-3949.71 + 760.712i) q^{92} +(-9867.10 - 8148.04i) q^{94} -251.338i q^{95} -9022.44 q^{97} +(5441.83 - 6589.93i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{4}+O(q^{10}) $ 16 * q + 28 * q^4	$ 16 q + 28 q^{4} + 176 q^{10} + 176 q^{13} + 88 q^{16} + 384 q^{22} + 2736 q^{25} + 1812 q^{28} + 1520 q^{34} + 80 q^{37} - 688 q^{40} - 1824 q^{46} - 7904 q^{49} - 5236 q^{52} - 11584 q^{58} - 1648 q^{61} + 5056 q^{64} + 26688 q^{70} + 80 q^{73} - 8388 q^{76} - 38464 q^{82} - 16832 q^{85} - 29520 q^{88} - 4512 q^{94} + 14864 q^{97}+O(q^{100}) $ 16 * q + 28 * q^4 + 176 * q^10 + 176 * q^13 + 88 * q^16 + 384 * q^22 + 2736 * q^25 + 1812 * q^28 + 1520 * q^34 + 80 * q^37 - 688 * q^40 - 1824 * q^46 - 7904 * q^49 - 5236 * q^52 - 11584 * q^58 - 1648 * q^61 + 5056 * q^64 + 26688 * q^70 + 80 * q^73 - 8388 * q^76 - 38464 * q^82 - 16832 * q^85 - 29520 * q^88 - 4512 * q^94 + 14864 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.54696	−	3.08431i	0.636740	−	0.771078i
$2$	2.54696	−	3.08431i	0.636740	−	0.771078i
$3$		0			0
$3$		0			0
$4$	−3.02598	−	15.7113i	−0.189124	−	0.981953i
$5$	−3.58334			−0.143334			−0.0716668	−	0.997429i	$-0.522832\pi$
$5$	−3.58334			−0.143334			−0.0716668	+	0.997429i	$0.522832\pi$
$6$		0			0
$7$		−	16.2605i		−	0.331847i	−0.986139	−	0.165923i	$-0.946940\pi$
$7$		−	16.2605i		−	0.331847i	0.986139	−	0.165923i	$-0.0530604\pi$
$8$	−56.1655	−	30.6829i	−0.877586	−	0.479420i
$9$		0			0
$10$	−9.12663	+	11.0521i	−0.0912663	+	0.110521i
$11$		−	144.712i		−	1.19597i	−0.801508	−	0.597985i	$-0.795968\pi$
$11$		−	144.712i		−	1.19597i	0.801508	−	0.597985i	$-0.204032\pi$
$12$		0			0
$13$	−223.658			−1.32342			−0.661709	−	0.749761i	$-0.730169\pi$
$13$	−223.658			−1.32342			−0.661709	+	0.749761i	$0.730169\pi$
$14$	−50.1524	−	41.4148i	−0.255880	−	0.211300i
$15$		0			0
$16$	−237.687	+	95.0838i	−0.928464	+	0.371421i
$17$	1.80372			0.00624125			0.00312062	−	0.999995i	$-0.499007\pi$
$17$	1.80372			0.00624125			0.00312062	+	0.999995i	$0.499007\pi$
$18$		0			0
$19$			70.1406i			0.194295i	0.995270	+	0.0971476i	$0.0309719\pi$
$19$			70.1406i			0.194295i	−0.995270	+	0.0971476i	$0.969028\pi$
$20$	10.8431	+	56.2988i	0.0271078	+	0.140747i
$21$		0			0
$22$	−446.338	−	368.577i	−0.922186	−	0.761522i
$23$		−	251.394i		−	0.475225i	−0.971360	−	0.237612i	$-0.923635\pi$
$23$		−	251.394i		−	0.475225i	0.971360	−	0.237612i	$-0.0763648\pi$
$24$		0			0
$25$	−612.160			−0.979455
$26$	−569.647	+	689.830i	−0.842674	+	1.02046i
$27$		0			0
$28$	−255.473	+	49.2039i	−0.325858	+	0.0627601i
$29$	1641.50			1.95185			0.975924	−	0.218110i	$-0.0699891\pi$
$29$	1641.50			1.95185			0.975924	+	0.218110i	$0.0699891\pi$
$30$		0			0
$31$		−	1047.19i		−	1.08968i	−0.838539	−	0.544842i	$-0.816590\pi$
$31$		−	1047.19i		−	1.08968i	0.838539	−	0.544842i	$-0.183410\pi$
$32$	−312.111	+	975.276i	−0.304796	+	0.952418i
$33$		0			0
$34$	4.59401	−	5.56324i	0.00397405	−	0.00481249i
$35$			58.2669i			0.0475648i
$36$		0			0
$37$	−690.791			−0.504596			−0.252298	−	0.967650i	$-0.581186\pi$
$37$	−690.791			−0.504596			−0.252298	+	0.967650i	$0.581186\pi$
$38$	216.336	+	178.645i	0.149817	+	0.123716i
$39$		0			0
$40$	201.260	+	109.947i	0.125788	+	0.0687170i
$41$	993.138			0.590802			0.295401	−	0.955373i	$-0.404547\pi$
$41$	993.138			0.590802			0.295401	+	0.955373i	$0.404547\pi$
$42$		0			0
$43$			1983.63i			1.07281i	0.843959	+	0.536407i	$0.180219\pi$
$43$			1983.63i			1.07281i	−0.843959	+	0.536407i	$0.819781\pi$
$44$	−2273.61	+	437.896i	−1.17439	+	0.226186i
$45$		0			0
$46$	−775.377	−	640.290i	−0.366435	−	0.302595i
$47$		−	3199.12i		−	1.44822i	−0.689683	−	0.724111i	$-0.742250\pi$
$47$		−	3199.12i		−	1.44822i	0.689683	−	0.724111i	$-0.257750\pi$
$48$		0			0
$49$	2136.60			0.889878
$50$	−1559.15	+	1888.09i	−0.623659	+	0.755237i
$51$		0			0
$52$	676.783	+	3513.94i	0.250290	+	1.29953i
$53$	2863.25			1.01931			0.509657	−	0.860378i	$-0.329772\pi$
$53$	2863.25			1.01931			0.509657	+	0.860378i	$0.329772\pi$
$54$		0			0
$55$			518.553i			0.171423i
$56$	−498.919	+	913.278i	−0.159094	+	0.291224i
$57$		0			0
$58$	4180.85	−	5062.91i	1.24282	−	1.50503i
$59$		−	5577.97i		−	1.60241i	−0.598393	−	0.801203i	$-0.704194\pi$
$59$		−	5577.97i		−	1.60241i	0.598393	−	0.801203i	$-0.295806\pi$
$60$		0			0
$61$	2838.27			0.762770			0.381385	−	0.924416i	$-0.375447\pi$
$61$	2838.27			0.762770			0.381385	+	0.924416i	$0.375447\pi$
$62$	−3229.85	−	2667.14i	−0.840232	−	0.693846i
$63$		0			0
$64$	2213.12	+	3446.64i	0.540313	+	0.841464i
$65$	801.442			0.189690
$66$		0			0
$67$		−	5289.13i		−	1.17824i	−0.808045	−	0.589121i	$-0.799474\pi$
$67$		−	5289.13i		−	1.17824i	0.808045	−	0.589121i	$-0.200526\pi$
$68$	−5.45802	−	28.3387i	−0.00118037	−	0.00612861i
$69$		0			0
$70$	179.713	+	148.403i	0.0366762	+	0.0302864i
$71$			1873.59i			0.371671i	0.982581	+	0.185835i	$0.0594991\pi$
$71$			1873.59i			0.371671i	−0.982581	+	0.185835i	$0.940501\pi$
$72$		0			0
$73$	4523.42			0.848830			0.424415	−	0.905468i	$-0.360480\pi$
$73$	4523.42			0.848830			0.424415	+	0.905468i	$0.360480\pi$
$74$	−1759.42	+	2130.62i	−0.321296	+	0.389083i
$75$		0			0
$76$	1102.00	−	212.244i	0.190789	−	0.0367458i
$77$	−2353.09			−0.396879
$78$		0			0
$79$			7360.48i			1.17937i	0.807632	+	0.589687i	$0.200749\pi$
$79$			7360.48i			1.17937i	−0.807632	+	0.589687i	$0.799251\pi$
$80$	851.713	−	340.718i	0.133080	−	0.0532371i
$81$		0			0
$82$	2529.48	−	3063.15i	0.376187	−	0.455555i
$83$			5006.55i			0.726745i	0.931644	+	0.363372i	$0.118375\pi$
$83$			5006.55i			0.726745i	−0.931644	+	0.363372i	$0.881625\pi$
$84$		0			0
$85$	−6.46335			−0.000894581
$86$	6118.15	+	5052.24i	0.827224	+	0.683104i
$87$		0			0
$88$	−4440.19	+	8127.83i	−0.573372	+	1.04957i
$89$	11438.5			1.44407			0.722034	−	0.691858i	$-0.243208\pi$
$89$	11438.5			1.44407			0.722034	+	0.691858i	$0.243208\pi$
$90$		0			0
$91$			3636.78i			0.439172i
$92$	−3949.71	+	760.712i	−0.466648	+	0.0898762i
$93$		0			0
$94$	−9867.10	−	8148.04i	−1.11669	−	0.922142i
$95$		−	251.338i		−	0.0278490i
$96$		0			0
$97$	−9022.44			−0.958916			−0.479458	−	0.877565i	$-0.659167\pi$
$97$	−9022.44			−0.958916			−0.479458	+	0.877565i	$0.659167\pi$
$98$	5441.83	−	6589.93i	0.566621	−	0.686165i
$99$		0			0
$100$	1852.38	+	9617.80i	0.185238	+	0.961780i
$101$	−14876.5			−1.45833			−0.729167	−	0.684336i	$-0.760092\pi$
$101$	−14876.5			−1.45833			−0.729167	+	0.684336i	$0.760092\pi$
$102$		0			0
$103$		−	12827.6i		−	1.20912i	−0.796558	−	0.604562i	$-0.793348\pi$
$103$		−	12827.6i		−	1.20912i	0.796558	−	0.604562i	$-0.206652\pi$
$104$	12561.8	+	6862.46i	1.16141	+	0.634473i
$105$		0			0
$106$	7292.59	−	8831.17i	0.649038	−	0.785971i
$107$			18333.9i			1.60136i	0.599095	+	0.800678i	$0.295527\pi$
$107$			18333.9i			1.60136i	−0.599095	+	0.800678i	$0.704473\pi$
$108$		0			0
$109$	−10407.4			−0.875974			−0.437987	−	0.898981i	$-0.644308\pi$
$109$	−10407.4			−0.875974			−0.437987	+	0.898981i	$0.644308\pi$
$110$	1599.38	+	1320.74i	0.132180	+	0.109152i
$111$		0			0
$112$	1546.11	+	3864.91i	0.123255	+	0.308108i
$113$	−21057.9			−1.64914			−0.824572	−	0.565758i	$-0.808584\pi$
$113$	−21057.9			−1.64914			−0.824572	+	0.565758i	$0.808584\pi$
$114$		0			0
$115$			900.829i			0.0681156i
$116$	−4967.16	−	25790.1i	−0.369141	−	1.91662i
$117$		0			0
$118$	−17204.2	−	14206.9i	−1.23558	−	1.02032i
$119$		−	29.3294i		−	0.00207114i
$120$		0			0
$121$	−6300.65			−0.430343
$122$	7228.95	−	8754.10i	0.485686	−	0.588155i
$123$		0			0
$124$	−16452.6	+	3168.76i	−1.07002	+	0.206085i
$125$	4433.16			0.283723
$126$		0			0
$127$		−	8341.04i		−	0.517145i	−0.965992	−	0.258573i	$-0.916748\pi$
$127$		−	8341.04i		−	0.517145i	0.965992	−	0.258573i	$-0.0832521\pi$
$128$	16267.2	+	1952.49i	0.992874	+	0.119171i
$129$		0			0
$130$	2041.24	−	2471.90i	0.120783	−	0.146266i
$131$		−	17537.0i		−	1.02191i	−0.859608	−	0.510955i	$-0.829292\pi$
$131$		−	17537.0i		−	1.02191i	0.859608	−	0.510955i	$-0.170708\pi$
$132$		0			0
$133$	1140.52			0.0644762
$134$	−16313.3	−	13471.2i	−0.908516	−	0.750234i
$135$		0			0
$136$	−101.307	−	55.3434i	−0.00547723	−	0.00299218i
$137$	−15233.4			−0.811627			−0.405814	−	0.913956i	$-0.633012\pi$
$137$	−15233.4			−0.811627			−0.405814	+	0.913956i	$0.633012\pi$
$138$		0			0
$139$			29455.9i			1.52455i	0.647250	+	0.762277i	$0.275919\pi$
$139$			29455.9i			1.52455i	−0.647250	+	0.762277i	$0.724081\pi$
$140$	915.445	−	176.314i	0.0467064	−	0.00899563i
$141$		0			0
$142$	5778.75	+	4771.97i	0.286587	+	0.236658i
$143$			32366.0i			1.58277i
$144$		0			0
$145$	−5882.07			−0.279766
$146$	11521.0	−	13951.6i	0.540484	−	0.654515i
$147$		0			0
$148$	2090.32	+	10853.2i	0.0954309	+	0.495489i
$149$	−25630.4			−1.15447			−0.577234	−	0.816579i	$-0.695868\pi$
$149$	−25630.4			−1.15447			−0.577234	+	0.816579i	$0.695868\pi$
$150$		0			0
$151$		−	26662.5i		−	1.16936i	−0.811265	−	0.584679i	$-0.801220\pi$
$151$		−	26662.5i		−	1.16936i	0.811265	−	0.584679i	$-0.198780\pi$
$152$	2152.11	−	3939.48i	0.0931490	−	0.170511i
$153$		0			0
$154$	−5993.24	+	7257.68i	−0.252709	+	0.306024i
$155$			3752.43i			0.156188i
$156$		0			0
$157$	4902.53			0.198894			0.0994468	−	0.995043i	$-0.468293\pi$
$157$	4902.53			0.198894			0.0994468	+	0.995043i	$0.468293\pi$
$158$	22702.0	+	18746.8i	0.909390	+	0.750955i
$159$		0			0
$160$	1118.40	−	3494.74i	0.0436875	−	0.136513i
$161$	−4087.79			−0.157702
$162$		0			0
$163$			5606.70i			0.211024i	0.994418	+	0.105512i	$0.0336481\pi$
$163$			5606.70i			0.211024i	−0.994418	+	0.105512i	$0.966352\pi$
$164$	−3005.21	−	15603.4i	−0.111735	−	0.580140i
$165$		0			0
$166$	15441.8	+	12751.5i	0.560377	+	0.462748i
$167$		−	8055.50i		−	0.288842i	−0.989516	−	0.144421i	$-0.953868\pi$
$167$		−	8055.50i		−	0.288842i	0.989516	−	0.144421i	$-0.0461319\pi$
$168$		0			0
$169$	21461.8			0.751436
$170$	−16.4619	+	19.9350i	−0.000569616	+	0.000689792i
$171$		0			0
$172$	31165.4	−	6002.43i	1.05345	−	0.202894i
$173$	37584.7			1.25580			0.627898	−	0.778296i	$-0.283915\pi$
$173$	37584.7			1.25580			0.627898	+	0.778296i	$0.283915\pi$
$174$		0			0
$175$			9954.02i			0.325029i
$176$	13759.8	+	34396.2i	0.444208	+	1.11042i
$177$		0			0
$178$	29133.3	−	35279.8i	0.919496	−	1.11349i
$179$			34709.7i			1.08329i	0.840608	+	0.541645i	$0.182198\pi$
$179$			34709.7i			1.08329i	−0.840608	+	0.541645i	$0.817802\pi$
$180$		0			0
$181$	45374.3			1.38501			0.692504	−	0.721414i	$-0.256507\pi$
$181$	45374.3			1.38501			0.692504	+	0.721414i	$0.256507\pi$
$182$	11217.0	+	9262.75i	0.338636	+	0.279638i
$183$		0			0
$184$	−7713.49	+	14119.7i	−0.227832	+	0.417050i
$185$	2475.34			0.0723255
$186$		0			0
$187$		−	261.021i		−	0.00746434i
$188$	−50262.2	+	9680.48i	−1.42209	+	0.273893i
$189$		0			0
$190$	−775.204	−	640.147i	−0.0214738	−	0.0177326i
$191$		−	24475.4i		−	0.670907i	−0.942057	−	0.335454i	$-0.891110\pi$
$191$		−	24475.4i		−	0.670907i	0.942057	−	0.335454i	$-0.108890\pi$
$192$		0			0
$193$	13113.8			0.352058			0.176029	−	0.984385i	$-0.443675\pi$
$193$	13113.8			0.352058			0.176029	+	0.984385i	$0.443675\pi$
$194$	−22979.8	+	27828.0i	−0.610581	+	0.739400i
$195$		0			0
$196$	−6465.29	−	33568.6i	−0.168297	−	0.873818i
$197$	32666.7			0.841730			0.420865	−	0.907123i	$-0.361727\pi$
$197$	32666.7			0.841730			0.420865	+	0.907123i	$0.361727\pi$
$198$		0			0
$199$		−	8800.86i		−	0.222238i	−0.993807	−	0.111119i	$-0.964556\pi$
$199$		−	8800.86i		−	0.222238i	0.993807	−	0.111119i	$-0.0354435\pi$
$200$	34382.2	+	18782.8i	0.859556	+	0.469571i
$201$		0			0
$202$	−37889.8	+	45883.7i	−0.928580	+	1.12449i
$203$		−	26691.7i		−	0.647715i
$204$		0			0
$205$	−3558.75			−0.0846818
$206$	−39564.3	−	32671.4i	−0.932329	−	0.769898i
$207$		0			0
$208$	53160.5	−	21266.2i	1.22875	−	0.491546i
$209$	10150.2			0.232371
$210$		0			0
$211$			49061.2i			1.10198i	0.834513	+	0.550989i	$0.185749\pi$
$211$			49061.2i			1.10198i	−0.834513	+	0.550989i	$0.814251\pi$
$212$	−8664.14	−	44985.3i	−0.192776	−	1.00092i
$213$		0			0
$214$	56547.6	+	46695.8i	1.23477	+	1.01965i
$215$		−	7108.03i		−	0.153770i
$216$		0			0
$217$	−17027.8			−0.361608
$218$	−26507.4	+	32099.8i	−0.557768	+	0.675445i
$219$		0			0
$220$	8147.12	−	1569.13i	0.168329	−	0.0324201i
$221$	−403.416			−0.00825978
$222$		0			0
$223$		−	47153.5i		−	0.948210i	−0.880468	−	0.474105i	$-0.842772\pi$
$223$		−	47153.5i		−	0.948210i	0.880468	−	0.474105i	$-0.157228\pi$
$224$	15858.5	+	5075.08i	0.316057	+	0.101146i
$225$		0			0
$226$	−53633.7	+	64949.2i	−1.05008	+	1.27162i
$227$		−	61125.3i		−	1.18623i	−0.805117	−	0.593116i	$-0.797898\pi$
$227$		−	61125.3i		−	1.18623i	0.805117	−	0.593116i	$-0.202102\pi$
$228$		0			0
$229$	−42983.0			−0.819645			−0.409823	−	0.912165i	$-0.634409\pi$
$229$	−42983.0			−0.819645			−0.409823	+	0.912165i	$0.634409\pi$
$230$	2778.44	+	2294.38i	0.0525225	+	0.0433720i
$231$		0			0
$232$	−92195.9	−	50366.1i	−1.71291	−	0.935755i
$233$	63194.6			1.16404			0.582020	−	0.813175i	$-0.302263\pi$
$233$	63194.6			1.16404			0.582020	+	0.813175i	$0.302263\pi$
$234$		0			0
$235$			11463.5i			0.207579i
$236$	−87637.0	+	16878.8i	−1.57349	+	0.303053i
$237$		0			0
$238$	−90.4610	−	74.7008i	−0.00159701	−	0.00131878i
$239$		−	67281.6i		−	1.17788i	−0.808177	−	0.588940i	$-0.799546\pi$
$239$		−	67281.6i		−	1.17788i	0.808177	−	0.588940i	$-0.200454\pi$
$240$		0			0
$241$	14307.7			0.246341			0.123171	−	0.992386i	$-0.460694\pi$
$241$	14307.7			0.246341			0.123171	+	0.992386i	$0.460694\pi$
$242$	−16047.5	+	19433.2i	−0.274016	+	0.331828i
$243$		0			0
$244$	−8588.53	−	44592.7i	−0.144258	−	0.749004i
$245$	−7656.15			−0.127549
$246$		0			0
$247$		−	15687.5i		−	0.257134i
$248$	−32130.7	+	58815.8i	−0.522417	+	0.956291i
$249$		0			0
$250$	11291.1	−	13673.3i	0.180658	−	0.218772i
$251$		−	92024.1i		−	1.46068i	−0.683085	−	0.730339i	$-0.739362\pi$
$251$		−	92024.1i		−	1.46068i	0.683085	−	0.730339i	$-0.260638\pi$
$252$		0			0
$253$	−36379.8			−0.568354
$254$	−25726.4	−	21244.3i	−0.398760	−	0.329287i
$255$		0			0
$256$	47454.1	−	45200.4i	0.724093	−	0.689703i
$257$	47095.9			0.713045			0.356523	−	0.934287i	$-0.383962\pi$
$257$	47095.9			0.713045			0.356523	+	0.934287i	$0.383962\pi$
$258$		0			0
$259$			11232.6i			0.167448i
$260$	−2425.14	−	12591.7i	−0.0358749	−	0.186267i
$261$		0			0
$262$	−54089.5	−	44666.0i	−0.787972	−	0.650691i
$263$			64791.0i			0.936706i	0.883542	+	0.468353i	$0.155152\pi$
$263$			64791.0i			0.936706i	−0.883542	+	0.468353i	$0.844848\pi$
$264$		0			0
$265$	−10260.0			−0.146102
$266$	2904.86	−	3517.72i	0.0410546	−	0.0497162i
$267$		0			0
$268$	−83098.8	+	16004.8i	−1.15698	+	0.222833i
$269$	−13020.2			−0.179934			−0.0899669	−	0.995945i	$-0.528676\pi$
$269$	−13020.2			−0.179934			−0.0899669	+	0.995945i	$0.528676\pi$
$270$		0			0
$271$		−	86544.0i		−	1.17842i	−0.807981	−	0.589208i	$-0.799440\pi$
$271$		−	86544.0i		−	1.17842i	0.807981	−	0.589208i	$-0.200560\pi$
$272$	−428.721	+	171.505i	−0.00579478	+	0.00231813i
$273$		0			0
$274$	−38799.0	+	46984.7i	−0.516796	+	0.625828i
$275$			88587.0i			1.17140i
$276$		0			0
$277$	−71659.6			−0.933931			−0.466966	−	0.884275i	$-0.654653\pi$
$277$	−71659.6			−0.933931			−0.466966	+	0.884275i	$0.654653\pi$
$278$	90851.3	+	75023.1i	1.17555	+	0.970745i
$279$		0			0
$280$	1787.80	−	3272.59i	0.0228035	−	0.0417422i
$281$	15636.0			0.198022			0.0990110	−	0.995086i	$-0.468432\pi$
$281$	15636.0			0.198022			0.0990110	+	0.995086i	$0.468432\pi$
$282$		0			0
$283$			34109.5i			0.425895i	0.977064	+	0.212947i	$0.0683063\pi$
$283$			34109.5i			0.425895i	−0.977064	+	0.212947i	$0.931694\pi$
$284$	29436.5	−	5669.45i	0.364964	−	0.0702918i
$285$		0			0
$286$	99826.9	+	82435.0i	1.22044	+	1.00781i
$287$		−	16148.9i		−	0.196056i
$288$		0			0
$289$	−83517.7			−0.999961
$290$	−14981.4	+	18142.1i	−0.178138	+	0.215721i
$291$		0			0
$292$	−13687.8	−	71068.5i	−0.160534	−	0.833512i
$293$	82967.5			0.966436			0.483218	−	0.875500i	$-0.339468\pi$
$293$	82967.5			0.966436			0.483218	+	0.875500i	$0.339468\pi$
$294$		0			0
$295$			19987.8i			0.229679i
$296$	38798.6	+	21195.5i	0.442826	+	0.241913i
$297$		0			0
$298$	−65279.5	+	79052.1i	−0.735097	+	0.890186i
$299$			56226.1i			0.628921i
$300$		0			0
$301$	32254.8			0.356010
$302$	−82235.6	−	67908.4i	−0.901667	−	0.744577i
$303$		0			0
$304$	−6669.23	−	16671.5i	−0.0721654	−	0.180396i
$305$	−10170.5			−0.109331
$306$		0			0
$307$			156067.i			1.65590i	0.560802	+	0.827950i	$0.310493\pi$
$307$			156067.i			1.65590i	−0.560802	+	0.827950i	$0.689507\pi$
$308$	7120.41	+	36970.0i	0.0750591	+	0.389716i
$309$		0			0
$310$	11573.7	+	9557.29i	0.120434	+	0.0994515i
$311$			23137.2i			0.239216i	0.992821	+	0.119608i	$0.0381638\pi$
$311$			23137.2i			0.239216i	−0.992821	+	0.119608i	$0.961836\pi$
$312$		0			0
$313$	21035.4			0.214715			0.107358	−	0.994220i	$-0.465761\pi$
$313$	21035.4			0.214715			0.107358	+	0.994220i	$0.465761\pi$
$314$	12486.5	−	15120.9i	0.126644	−	0.153363i
$315$		0			0
$316$	115642.	−	22272.6i	1.15809	−	0.223048i
$317$	−106440.			−1.05922			−0.529611	−	0.848240i	$-0.677662\pi$
$317$	−106440.			−1.05922			−0.529611	+	0.848240i	$0.677662\pi$
$318$		0			0
$319$		−	237546.i		−	2.33435i
$320$	−7930.37	−	12350.5i	−0.0774450	−	0.120610i
$321$		0			0
$322$	−10411.4	+	12608.0i	−0.100415	+	0.121600i
$323$			126.514i			0.00121264i
$324$		0			0
$325$	136914.			1.29623
$326$	17292.8	+	14280.0i	0.162716	+	0.134367i
$327$		0			0
$328$	−55780.1	−	30472.3i	−0.518479	−	0.283242i
$329$	−52019.3			−0.480588
$330$		0			0
$331$			194535.i			1.77559i	0.460239	+	0.887795i	$0.347764\pi$
$331$			194535.i			1.77559i	−0.460239	+	0.887795i	$0.652236\pi$
$332$	78659.1	−	15149.7i	0.713630	−	0.137445i
$333$		0			0
$334$	−24845.7	−	20517.1i	−0.222720	−	0.183917i
$335$			18952.7i			0.168882i
$336$		0			0
$337$	81272.1			0.715618			0.357809	−	0.933795i	$-0.383524\pi$
$337$	81272.1			0.715618			0.357809	+	0.933795i	$0.383524\pi$
$338$	54662.2	−	66194.8i	0.478469	−	0.579416i
$339$		0			0
$340$	19.5579	+	101.547i	0.000169186	+	0.000878436i
$341$	−151541.			−1.30323
$342$		0			0
$343$		−	73783.5i		−	0.627150i
$344$	60863.6	−	111412.i	0.514328	−	0.941486i
$345$		0			0
$346$	95726.8	−	115923.i	0.799616	−	0.968317i
$347$			113947.i			0.946331i	0.880974	+	0.473165i	$0.156889\pi$
$347$			113947.i			0.946331i	−0.880974	+	0.473165i	$0.843111\pi$
$348$		0			0
$349$	25419.8			0.208700			0.104350	−	0.994541i	$-0.466724\pi$
$349$	25419.8			0.208700			0.104350	+	0.994541i	$0.466724\pi$
$350$	30701.3	+	25352.5i	0.250623	+	0.206959i
$351$		0			0
$352$	141134.	+	45166.3i	1.13906	+	0.364527i
$353$	−39576.0			−0.317601			−0.158801	−	0.987311i	$-0.550763\pi$
$353$	−39576.0			−0.317601			−0.158801	+	0.987311i	$0.550763\pi$
$354$		0			0
$355$		−	6713.72i		−	0.0532729i
$356$	−34612.5	−	179712.i	−0.273107	−	1.41801i
$357$		0			0
$358$	107056.	+	88404.2i	0.835301	+	0.689774i
$359$		−	120831.i		−	0.937541i	−0.883320	−	0.468771i	$-0.844697\pi$
$359$		−	120831.i		−	0.937541i	0.883320	−	0.468771i	$-0.155303\pi$
$360$		0			0
$361$	125401.			0.962249
$362$	115566.	−	139948.i	0.881891	−	1.06795i
$363$		0			0
$364$	57138.4	−	11004.8i	0.431246	−	0.0830578i
$365$	−16208.9			−0.121666
$366$		0			0
$367$		−	113429.i		−	0.842156i	−0.907024	−	0.421078i	$-0.861652\pi$
$367$		−	113429.i		−	0.842156i	0.907024	−	0.421078i	$-0.138348\pi$
$368$	23903.5	+	59753.0i	0.176508	+	0.441229i
$369$		0			0
$370$	6304.60	−	7634.73i	0.0460526	−	0.0557686i
$371$		−	46557.9i		−	0.338256i
$372$		0			0
$373$	−23277.7			−0.167310			−0.0836551	−	0.996495i	$-0.526659\pi$
$373$	−23277.7			−0.167310			−0.0836551	+	0.996495i	$0.526659\pi$
$374$	−805.069	−	664.809i	−0.00575559	−	0.00475285i
$375$		0			0
$376$	−98158.3	+	179680.i	−0.694307	+	1.27094i
$377$	−367135.			−2.58311
$378$		0			0
$379$			89977.3i			0.626404i	0.949686	+	0.313202i	$0.101402\pi$
$379$			89977.3i			0.626404i	−0.949686	+	0.313202i	$0.898598\pi$
$380$	−3948.83	+	760.542i	−0.0273465	+	0.00526691i
$381$		0			0
$382$	−75489.7	−	62337.8i	−0.517322	−	0.427194i
$383$			242067.i			1.65020i	0.564984	+	0.825102i	$0.308882\pi$
$383$			242067.i			1.65020i	−0.564984	+	0.825102i	$0.691118\pi$
$384$		0			0
$385$	8431.93			0.0568860
$386$	33400.3	−	40447.1i	0.224169	−	0.271464i
$387$		0			0
$388$	27301.7	+	141754.i	0.181354	+	0.941611i
$389$	229775.			1.51846			0.759230	−	0.650823i	$-0.225576\pi$
$389$	229775.			1.51846			0.759230	+	0.650823i	$0.225576\pi$
$390$		0			0
$391$		−	453.444i		−	0.00296599i
$392$	−120003.	−	65556.9i	−0.780944	−	0.426625i
$393$		0			0
$394$	83200.8	−	100754.i	0.535963	−	0.649040i
$395$		−	26375.1i		−	0.169044i
$396$		0			0
$397$	−78709.5			−0.499397			−0.249699	−	0.968324i	$-0.580332\pi$
$397$	−78709.5			−0.499397			−0.249699	+	0.968324i	$0.580332\pi$
$398$	−27144.6	−	22415.4i	−0.171363	−	0.141508i
$399$		0			0
$400$	145502.	−	58206.5i	0.909390	−	0.363791i
$401$	42894.9			0.266757			0.133379	−	0.991065i	$-0.457417\pi$
$401$	42894.9			0.266757			0.133379	+	0.991065i	$0.457417\pi$
$402$		0			0
$403$			234211.i			1.44211i
$404$	45015.9	+	233728.i	0.275805	+	1.43202i
$405$		0			0
$406$	−82325.5	−	67982.6i	−0.499439	−	0.412426i
$407$			99966.0i			0.603481i
$408$		0			0
$409$	−7021.98			−0.0419771			−0.0209886	−	0.999780i	$-0.506681\pi$
$409$	−7021.98			−0.0419771			−0.0209886	+	0.999780i	$0.506681\pi$
$410$	−9064.00	+	10976.3i	−0.0539203	+	0.0652963i
$411$		0			0
$412$	−201538.	+	38816.0i	−1.18730	+	0.228674i
$413$	−90700.6			−0.531753
$414$		0			0
$415$		−	17940.2i		−	0.104167i
$416$	69806.0	−	218128.i	0.403372	−	1.26045i
$417$		0			0
$418$	25852.2	−	31306.4i	0.147960	−	0.179176i
$419$			93841.8i			0.534525i	0.963624	+	0.267263i	$0.0861191\pi$
$419$			93841.8i			0.534525i	−0.963624	+	0.267263i	$0.913881\pi$
$420$		0			0
$421$	131807.			0.743662			0.371831	−	0.928300i	$-0.378730\pi$
$421$	131807.			0.743662			0.371831	+	0.928300i	$0.378730\pi$
$422$	151320.	+	124957.i	0.849711	+	0.701674i
$423$		0			0
$424$	−160816.	−	87852.8i	−0.894535	−	0.488679i
$425$	−1104.17			−0.00611302
$426$		0			0
$427$		−	46151.6i		−	0.253123i
$428$	288049.	−	55478.1i	1.57246	−	0.302854i
$429$		0			0
$430$	−21923.4	−	18103.9i	−0.118569	−	0.0979117i
$431$		−	14141.6i		−	0.0761279i	−0.999275	−	0.0380640i	$-0.987881\pi$
$431$		−	14141.6i		−	0.0761279i	0.999275	−	0.0380640i	$-0.0121191\pi$
$432$		0			0
$433$	−224082.			−1.19517			−0.597586	−	0.801805i	$-0.703873\pi$
$433$	−224082.			−1.19517			−0.597586	+	0.801805i	$0.703873\pi$
$434$	−43369.1	+	52519.0i	−0.230251	+	0.278828i
$435$		0			0
$436$	31492.7	+	163514.i	0.165667	+	0.860166i
$437$	17632.9			0.0923338
$438$		0			0
$439$		−	168793.i		−	0.875842i	−0.899013	−	0.437921i	$-0.855715\pi$
$439$		−	168793.i		−	0.875842i	0.899013	−	0.437921i	$-0.144285\pi$
$440$	15910.7	−	29124.8i	0.0821834	−	0.150438i
$441$		0			0
$442$	−1027.48	+	1244.26i	−0.00525934	+	0.00636894i
$443$			129808.i			0.661446i	0.943728	+	0.330723i	$0.107293\pi$
$443$			129808.i			0.661446i	−0.943728	+	0.330723i	$0.892707\pi$
$444$		0			0
$445$	−40987.9			−0.206983
$446$	−145436.	−	120098.i	−0.731144	−	0.603764i
$447$		0			0
$448$	56044.0	−	35986.4i	0.279237	−	0.179301i
$449$	107176.			0.531623			0.265811	−	0.964025i	$-0.414360\pi$
$449$	107176.			0.531623			0.265811	+	0.964025i	$0.414360\pi$
$450$		0			0
$451$		−	143719.i		−	0.706581i
$452$	63720.8	+	330846.i	0.311892	+	1.61938i
$453$		0			0
$454$	−188530.	−	155684.i	−0.914677	−	0.755321i
$455$		−	13031.8i		−	0.0629481i
$456$		0			0
$457$	−345116.			−1.65247			−0.826234	−	0.563327i	$-0.809521\pi$
$457$	−345116.			−1.65247			−0.826234	+	0.563327i	$0.809521\pi$
$458$	−109476.	+	132573.i	−0.521901	+	0.632011i
$459$		0			0
$460$	14153.2	−	2725.89i	0.0668864	−	0.0128823i
$461$	−26097.1			−0.122798			−0.0613988	−	0.998113i	$-0.519556\pi$
$461$	−26097.1			−0.122798			−0.0613988	+	0.998113i	$0.519556\pi$
$462$		0			0
$463$		−	6582.77i		−	0.0307077i	−0.999882	−	0.0153538i	$-0.995113\pi$
$463$		−	6582.77i		−	0.0307077i	0.999882	−	0.0153538i	$-0.00488747\pi$
$464$	−390164.	+	156081.i	−1.81222	+	0.724958i
$465$		0			0
$466$	160954.	−	194912.i	0.741191	−	0.897566i
$467$		−	107337.i		−	0.492171i	−0.969248	−	0.246085i	$-0.920856\pi$
$467$		−	107337.i		−	0.492171i	0.969248	−	0.246085i	$-0.0791443\pi$
$468$		0			0
$469$	−86003.8			−0.390996
$470$	35357.2	+	29197.2i	0.160060	+	0.132174i
$471$		0			0
$472$	−171148.	+	313290.i	−0.768225	+	1.40625i
$473$	287056.			1.28305
$474$		0			0
$475$		−	42937.2i		−	0.190304i
$476$	−460.801	+	88.7501i	−0.00203376	+	0.000391701i
$477$		0			0
$478$	−207518.	−	171364.i	−0.908237	−	0.750003i
$479$		−	348828.i		−	1.52034i	−0.649724	−	0.760170i	$-0.725116\pi$
$479$		−	348828.i		−	1.52034i	0.649724	−	0.760170i	$-0.274884\pi$
$480$		0			0
$481$	154501.			0.667791
$482$	36441.3	−	44129.6i	0.156855	−	0.189948i
$483$		0			0
$484$	19065.6	+	98991.0i	0.0813880	+	0.422576i
$485$	32330.5			0.137445
$486$		0			0
$487$		−	104528.i		−	0.440732i	−0.975417	−	0.220366i	$-0.929275\pi$
$487$		−	104528.i		−	0.440732i	0.975417	−	0.220366i	$-0.0707251\pi$
$488$	−159413.	−	87086.2i	−0.669396	−	0.365687i
$489$		0			0
$490$	−19499.9	+	23614.0i	−0.0812158	+	0.0983506i
$491$		−	181720.i		−	0.753770i	−0.926260	−	0.376885i	$-0.876995\pi$
$491$		−	181720.i		−	0.753770i	0.926260	−	0.376885i	$-0.123005\pi$
$492$		0			0
$493$	2960.82			0.0121820
$494$	−48385.1	−	39955.4i	−0.198270	−	0.163727i
$495$		0			0
$496$	99570.5	+	248903.i	0.404732	+	1.01173i
$497$	30465.5			0.123338
$498$		0			0
$499$			329701.i			1.32409i	0.749462	+	0.662047i	$0.230312\pi$
$499$			329701.i			1.32409i	−0.749462	+	0.662047i	$0.769688\pi$
$500$	−13414.7	−	69650.6i	−0.0536586	−	0.278602i
$501$		0			0
$502$	−283831.	−	234382.i	−1.12630	−	0.930072i
$503$		−	225559.i		−	0.891507i	−0.895156	−	0.445753i	$-0.852936\pi$
$503$		−	225559.i		−	0.891507i	0.895156	−	0.445753i	$-0.147064\pi$
$504$		0			0
$505$	53307.4			0.209028
$506$	−92657.9	+	112207.i	−0.361894	+	0.438245i
$507$		0			0
$508$	−131048.	+	25239.8i	−0.507813	+	0.0978044i
$509$	71361.2			0.275440			0.137720	−	0.990471i	$-0.456023\pi$
$509$	71361.2			0.275440			0.137720	+	0.990471i	$0.456023\pi$
$510$		0			0
$511$		−	73553.0i		−	0.281682i
$512$	−18548.2	−	261487.i	−0.0707559	−	0.997494i
$513$		0			0
$514$	119952.	−	145259.i	0.454025	−	0.549814i
$515$			45965.6i			0.173308i
$516$		0			0
$517$	−462952.			−1.73203
$518$	34644.9	+	28609.0i	0.129116	+	0.106621i
$519$		0			0
$520$	−45013.3	−	24590.5i	−0.166469	−	0.0909413i
$521$	254162.			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$521$	254162.			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$522$		0			0
$523$			449711.i			1.64411i	0.569410	+	0.822054i	$0.307172\pi$
$523$			449711.i			1.64411i	−0.569410	+	0.822054i	$0.692828\pi$
$524$	−275528.	+	53066.5i	−1.00347	+	0.193267i
$525$		0			0
$526$	199836.	+	165020.i	0.722273	+	0.596438i
$527$		−	1888.83i		−	0.00680099i
$528$		0			0
$529$	216642.			0.774162
$530$	−26131.8	+	31645.1i	−0.0930290	+	0.112656i
$531$		0			0
$532$	−3451.19	−	17919.0i	−0.0121940	−	0.0633126i
$533$	−222123.			−0.781878
$534$		0			0
$535$		−	65696.7i		−	0.229528i
$536$	−162286.	+	297066.i	−0.564873	+	1.03401i
$537$		0			0
$538$	−33161.9	+	40158.4i	−0.114571	+	0.138743i
$539$		−	309192.i		−	1.06427i
$540$		0			0
$541$	479811.			1.63936			0.819682	−	0.572819i	$-0.194150\pi$
$541$	479811.			1.63936			0.819682	+	0.572819i	$0.194150\pi$
$542$	−266929.	−	220424.i	−0.908651	−	0.750345i
$543$		0			0
$544$	−562.961	+	1759.13i	−0.00190231	+	0.00594428i
$545$	37293.4			0.125557
$546$		0			0
$547$		−	352931.i		−	1.17955i	−0.807569	−	0.589773i	$-0.799217\pi$
$547$		−	352931.i		−	1.17955i	0.807569	−	0.589773i	$-0.200783\pi$
$548$	46096.0	+	239336.i	0.153498	+	0.796980i
$549$		0			0
$550$	273230.	+	225628.i	0.903240	+	0.745877i
$551$			115136.i			0.379235i
$552$		0			0
$553$	119685.			0.391372
$554$	−182514.	+	221021.i	−0.594672	+	0.720134i
$555$		0			0
$556$	462789.	−	89133.0i	1.49704	−	0.288329i
$557$	360746.			1.16276			0.581382	−	0.813631i	$-0.302512\pi$
$557$	360746.			1.16276			0.581382	+	0.813631i	$0.302512\pi$
$558$		0			0
$559$		−	443655.i		−	1.41978i
$560$	−5540.24	−	13849.3i	−0.0176666	−	0.0441622i
$561$		0			0
$562$	39824.3	−	48226.4i	0.126089	−	0.152691i
$563$		−	466715.i		−	1.47243i	−0.676747	−	0.736216i	$-0.736611\pi$
$563$		−	466715.i		−	1.47243i	0.676747	−	0.736216i	$-0.263389\pi$
$564$		0			0
$565$	75457.6			0.236378
$566$	105204.	+	86875.6i	0.328398	+	0.271184i
$567$		0			0
$568$	57487.2	−	105231.i	0.178187	−	0.326173i
$569$	264863.			0.818083			0.409041	−	0.912516i	$-0.365863\pi$
$569$	264863.			0.818083			0.409041	+	0.912516i	$0.365863\pi$
$570$		0			0
$571$			605767.i			1.85795i	0.370146	+	0.928974i	$0.379308\pi$
$571$			605767.i			1.85795i	−0.370146	+	0.928974i	$0.620692\pi$
$572$	508511.	−	97938.9i	1.55420	−	0.299339i
$573$		0			0
$574$	−49808.3	−	41130.7i	−0.151174	−	0.124837i
$575$			153893.i			0.465461i
$576$		0			0
$577$	−160301.			−0.481488			−0.240744	−	0.970589i	$-0.577391\pi$
$577$	−160301.			−0.481488			−0.240744	+	0.970589i	$0.577391\pi$
$578$	−212716.	+	257595.i	−0.636715	+	0.771048i
$579$		0			0
$580$	17799.0	+	92414.7i	0.0529103	+	0.274717i
$581$	81408.9			0.241168
$582$		0			0
$583$		−	414348.i		−	1.21907i
$584$	−254060.	−	138791.i	−0.744921	−	0.406946i
$585$		0			0
$586$	211315.	−	255898.i	0.615369	−	0.745198i
$587$			64997.1i			0.188633i	0.995542	+	0.0943165i	$0.0300665\pi$
$587$			64997.1i			0.188633i	−0.995542	+	0.0943165i	$0.969933\pi$
$588$		0			0
$589$	73450.3			0.211721
$590$	61648.6	+	50908.1i	0.177100	+	0.146246i
$591$		0			0
$592$	164192.	−	65683.1i	0.468499	−	0.187417i
$593$	150269.			0.427326			0.213663	−	0.976907i	$-0.431461\pi$
$593$	150269.			0.427326			0.213663	+	0.976907i	$0.431461\pi$
$594$		0			0
$595$			105.097i			0.000296864i
$596$	77556.9	+	402685.i	0.218337	+	1.13363i
$597$		0			0
$598$	173419.	+	143206.i	0.484947	+	0.400459i
$599$			133110.i			0.370985i	0.982646	+	0.185492i	$0.0593880\pi$
$599$			133110.i			0.370985i	−0.982646	+	0.185492i	$0.940612\pi$
$600$		0			0
$601$	462021.			1.27913			0.639563	−	0.768739i	$-0.279115\pi$
$601$	462021.			1.27913			0.639563	+	0.768739i	$0.279115\pi$
$602$	82151.8	−	99484.0i	0.226686	−	0.274511i
$603$		0			0
$604$	−418902.	+	80680.3i	−1.14826	+	0.221153i
$605$	22577.4			0.0616826
$606$		0			0
$607$			223633.i			0.606959i	0.952838	+	0.303479i	$0.0981484\pi$
$607$			223633.i			0.606959i	−0.952838	+	0.303479i	$0.901852\pi$
$608$	−68406.4	−	21891.6i	−0.185050	−	0.0592204i
$609$		0			0
$610$	−25903.8	+	31368.9i	−0.0696152	+	0.0843024i
$611$			715508.i			1.91660i
$612$		0			0
$613$	383985.			1.02187			0.510933	−	0.859621i	$-0.329300\pi$
$613$	383985.			1.02187			0.510933	+	0.859621i	$0.329300\pi$
$614$	481359.	+	397496.i	1.27683	+	1.05438i
$615$		0			0
$616$	132163.	+	72199.7i	0.348295	+	0.190272i
$617$	−608003.			−1.59711			−0.798555	−	0.601921i	$-0.794402\pi$
$617$	−608003.			−1.59711			−0.798555	+	0.601921i	$0.794402\pi$
$618$		0			0
$619$			573813.i			1.49758i	0.662810	+	0.748788i	$0.269364\pi$
$619$			573813.i			1.49758i	−0.662810	+	0.748788i	$0.730636\pi$
$620$	58955.3	−	11354.8i	0.153370	−	0.0295389i
$621$		0			0
$622$	71362.5	+	58929.6i	0.184454	+	0.152319i
$623$		−	185995.i		−	0.479209i
$624$		0			0
$625$	366714.			0.938789
$626$	53576.5	−	64879.9i	0.136718	−	0.165562i
$627$		0			0
$628$	−14834.9	−	77024.8i	−0.0376155	−	0.195304i
$629$	−1245.99			−0.00314931
$630$		0			0
$631$			367125.i			0.922053i	0.887386	+	0.461026i	$0.152519\pi$
$631$			367125.i			0.922053i	−0.887386	+	0.461026i	$0.847481\pi$
$632$	225841.	−	413405.i	0.565416	−	1.03500i
$633$		0			0
$634$	−271099.	+	328295.i	−0.674450	+	0.816744i
$635$			29888.8i			0.0741243i
$636$		0			0
$637$	−477866.			−1.17768
$638$	−732666.	−	605020.i	−1.79997	−	1.48638i
$639$		0			0
$640$	−58291.1	−	6996.44i	−0.142312	−	0.0170812i
$641$	−161096.			−0.392075			−0.196037	−	0.980596i	$-0.562807\pi$
$641$	−161096.			−0.392075			−0.196037	+	0.980596i	$0.562807\pi$
$642$		0			0
$643$		−	658474.i		−	1.59264i	−0.604878	−	0.796318i	$-0.706778\pi$
$643$		−	658474.i		−	1.59264i	0.604878	−	0.796318i	$-0.293222\pi$
$644$	12369.6	+	64224.2i	0.0298251	+	0.154856i
$645$		0			0
$646$	390.209	+	322.226i	0.000935044	+	0.000772140i
$647$			410472.i			0.980563i	0.871564	+	0.490281i	$0.163106\pi$
$647$			410472.i			0.980563i	−0.871564	+	0.490281i	$0.836894\pi$
$648$		0			0
$649$	−807201.			−1.91643
$650$	348715.	−	422286.i	0.825361	−	0.999494i
$651$		0			0
$652$	88088.2	−	16965.7i	0.207216	−	0.0399096i
$653$	23202.5			0.0544136			0.0272068	−	0.999630i	$-0.491339\pi$
$653$	23202.5			0.0544136			0.0272068	+	0.999630i	$0.491339\pi$
$654$		0			0
$655$			62841.0i			0.146474i
$656$	−236056.	+	94431.4i	−0.548539	+	0.219436i
$657$		0			0
$658$	−132491.	+	160444.i	−0.306010	+	0.370571i
$659$		−	210220.i		−	0.484064i	−0.970268	−	0.242032i	$-0.922186\pi$
$659$		−	210220.i		−	0.484064i	0.970268	−	0.242032i	$-0.0778139\pi$
$660$		0			0
$661$	−21515.2			−0.0492428			−0.0246214	−	0.999697i	$-0.507838\pi$
$661$	−21515.2			−0.0492428			−0.0246214	+	0.999697i	$0.507838\pi$
$662$	600008.	+	495474.i	1.36912	+	1.13059i
$663$		0			0
$664$	153615.	−	281195.i	0.348416	−	0.637781i
$665$	−4086.87			−0.00924161
$666$		0			0
$667$		−	412664.i		−	0.927566i
$668$	−126562.	+	24375.8i	−0.283629	+	0.0546268i
$669$		0			0
$670$	58456.2	+	48271.9i	0.130221	+	0.107534i
$671$		−	410732.i		−	0.912249i
$672$		0			0
$673$	79154.4			0.174761			0.0873806	−	0.996175i	$-0.472150\pi$
$673$	79154.4			0.174761			0.0873806	+	0.996175i	$0.472150\pi$
$674$	206997.	−	250668.i	0.455663	−	0.551798i
$675$		0			0
$676$	−64942.8	−	337191.i	−0.142114	−	0.737875i
$677$	−94999.9			−0.207274			−0.103637	−	0.994615i	$-0.533048\pi$
$677$	−94999.9			−0.207274			−0.103637	+	0.994615i	$0.533048\pi$
$678$		0			0
$679$			146709.i			0.318213i
$680$	363.017	+	198.314i	0.000785071	+	0.000428880i
$681$		0			0
$682$	−385969.	+	467399.i	−0.829819	+	1.00489i
$683$			265559.i			0.569272i	0.958636	+	0.284636i	$0.0918727\pi$
$683$			265559.i			0.569272i	−0.958636	+	0.284636i	$0.908127\pi$
$684$		0			0
$685$	54586.6			0.116333
$686$	−227572.	−	187924.i	−0.483582	−	0.399332i
$687$		0			0
$688$	−188611.	−	471484.i	−0.398466	−	0.996070i
$689$	−640388.			−1.34898
$690$		0			0
$691$		−	497888.i		−	1.04274i	−0.853331	−	0.521369i	$-0.825421\pi$
$691$		−	497888.i		−	1.04274i	0.853331	−	0.521369i	$-0.174579\pi$
$692$	−113731.	−	590503.i	−0.237501	−	1.23313i
$693$		0			0
$694$	351448.	+	290218.i	0.729695	+	0.602567i
$695$		−	105551.i		−	0.218520i
$696$		0			0
$697$	1791.34			0.00368734
$698$	64743.3	−	78402.8i	0.132888	−	0.160924i
$699$		0			0
$700$	156390.	−	30120.6i	0.319163	−	0.0614707i
$701$	−102403.			−0.208389			−0.104195	−	0.994557i	$-0.533226\pi$
$701$	−102403.			−0.208389			−0.104195	+	0.994557i	$0.533226\pi$
$702$		0			0
$703$		−	48452.5i		−	0.0980405i
$704$	498771.	−	320266.i	1.00637	−	0.646198i
$705$		0			0
$706$	−100798.	+	122065.i	−0.202230	+	0.244896i
$707$			241899.i			0.483943i
$708$		0			0
$709$	−557443.			−1.10894			−0.554470	−	0.832204i	$-0.687079\pi$
$709$	−557443.			−1.10894			−0.554470	+	0.832204i	$0.687079\pi$
$710$	−20707.2	−	17099.6i	−0.0410776	−	0.0339210i
$711$		0			0
$712$	−642446.	−	350965.i	−1.26729	−	0.692315i
$713$	−263256.			−0.517845
$714$		0			0
$715$		−	115978.i		−	0.226864i
$716$	545332.	−	105031.i	1.06374	−	0.204876i
$717$		0			0
$718$	−372682.	−	307753.i	−0.722918	−	0.596970i
$719$			665001.i			1.28637i	0.765713	+	0.643183i	$0.222386\pi$
$719$			665001.i			1.28637i	−0.765713	+	0.643183i	$0.777614\pi$
$720$		0			0
$721$	−208583.			−0.401244
$722$	319392.	−	386777.i	0.612703	−	0.741970i
$723$		0			0
$724$	−137302.	−	712887.i	−0.261938	−	1.36001i
$725$	−1.00486e6			−1.91175
$726$		0			0
$727$			903006.i			1.70853i	0.519841	+	0.854263i	$0.325991\pi$
$727$			903006.i			1.70853i	−0.519841	+	0.854263i	$0.674009\pi$
$728$	111587.	−	204262.i	0.210548	−	0.385411i
$729$		0			0
$730$	−41283.5	+	49993.5i	−0.0774696	+	0.0938140i
$731$			3577.92i			0.00669570i
$732$		0			0
$733$	−633281.			−1.17866			−0.589330	−	0.807893i	$-0.700608\pi$
$733$	−633281.			−1.17866			−0.589330	+	0.807893i	$0.700608\pi$
$734$	−349851.	−	288900.i	−0.649368	−	0.536235i
$735$		0			0
$736$	245178.	+	78462.8i	0.452612	+	0.144846i
$737$	−765401.			−1.40914
$738$		0			0
$739$			72439.1i			0.132643i	0.997798	+	0.0663215i	$0.0211263\pi$
$739$			72439.1i			0.132643i	−0.997798	+	0.0663215i	$0.978874\pi$
$740$	−7490.33	−	38890.7i	−0.0136785	−	0.0710203i
$741$		0			0
$742$	−143599.	−	118581.i	−0.260822	−	0.215381i
$743$		−	600017.i		−	1.08689i	−0.839444	−	0.543446i	$-0.817119\pi$
$743$		−	600017.i		−	1.08689i	0.839444	−	0.543446i	$-0.182881\pi$
$744$		0			0
$745$	91842.3			0.165474
$746$	−59287.4	+	71795.7i	−0.106533	+	0.129009i
$747$		0			0
$748$	−4100.96	+	789.843i	−0.00732963	+	0.00141168i
$749$	298119.			0.531405
$750$		0			0
$751$		−	710454.i		−	1.25967i	−0.776730	−	0.629834i	$-0.783123\pi$
$751$		−	710454.i		−	1.25967i	0.776730	−	0.629834i	$-0.216877\pi$
$752$	304185.	+	760390.i	0.537900	+	1.34462i
$753$		0			0
$754$	−935079.	+	1.13236e6i	−1.64477	+	1.99178i
$755$			95540.9i			0.167608i
$756$		0			0
$757$	577805.			1.00830			0.504150	−	0.863616i	$-0.331806\pi$
$757$	577805.			1.00830			0.504150	+	0.863616i	$0.331806\pi$
$758$	277518.	+	229169.i	0.483007	+	0.398857i
$759$		0			0
$760$	−7711.76	+	14116.5i	−0.0133514	+	0.0244399i
$761$	751658.			1.29793			0.648965	−	0.760818i	$-0.275202\pi$
$761$	751658.			1.29793			0.648965	+	0.760818i	$0.275202\pi$
$762$		0			0
$763$			169230.i			0.290689i
$764$	−384539.	+	74061.9i	−0.658800	+	0.126884i
$765$		0			0
$766$	746610.	+	616535.i	1.27244	+	1.05075i
$767$			1.24756e6i			2.12065i
$768$		0			0
$769$	−416567.			−0.704421			−0.352211	−	0.935921i	$-0.614570\pi$
$769$	−416567.			−0.704421			−0.352211	+	0.935921i	$0.614570\pi$
$770$	21475.8	−	26006.7i	0.0362216	−	0.0438636i
$771$		0			0
$772$	−39682.1	−	206034.i	−0.0665824	−	0.345704i
$773$	611604.			1.02356			0.511778	−	0.859118i	$-0.328987\pi$
$773$	611604.			1.02356			0.511778	+	0.859118i	$0.328987\pi$
$774$		0			0
$775$			641046.i			1.06730i
$776$	506750.	+	276835.i	0.841531	+	0.459724i
$777$		0			0
$778$	585228.	−	708698.i	0.966864	−	1.17085i
$779$			69659.3i			0.114790i
$780$		0			0
$781$	271132.			0.444507
$782$	−1398.56	−	1154.90i	−0.00228701	−	0.00188857i
$783$		0			0
$784$	−507841.	+	203156.i	−0.826220	+	0.330519i
$785$	−17567.4			−0.0285081
$786$		0			0
$787$		−	462322.i		−	0.746440i	−0.927743	−	0.373220i	$-0.878254\pi$
$787$		−	462322.i		−	0.746440i	0.927743	−	0.373220i	$-0.121746\pi$
$788$	−98848.7	−	513235.i	−0.159191	−	0.826540i
$789$		0			0
$790$	−81349.0	−	67176.3i	−0.130346	−	0.107637i
$791$			342412.i			0.547263i
$792$		0			0
$793$	−634800.			−1.00946
$794$	−200470.	+	242765.i	−0.317986	+	0.385075i
$795$		0			0
$796$	−138272.	+	26631.2i	−0.218228	+	0.0420305i
$797$	−515899.			−0.812173			−0.406086	−	0.913835i	$-0.633107\pi$
$797$	−515899.			−0.812173			−0.406086	+	0.913835i	$0.633107\pi$
$798$		0			0
$799$		−	5770.33i		−	0.00903872i
$800$	191062.	−	597024.i	0.298534	−	0.932851i
$801$		0			0
$802$	109252.	−	132301.i	0.169855	−	0.205691i
$803$		−	654594.i		−	1.01517i
$804$		0			0
$805$	14647.9			0.0226040
$806$	722381.	+	596527.i	1.11198	+	0.918248i
$807$		0			0
$808$	835544.	+	456453.i	1.27981	+	0.699155i
$809$	1.06734e6			1.63081			0.815406	−	0.578889i	$-0.196513\pi$
$809$	1.06734e6			1.63081			0.815406	+	0.578889i	$0.196513\pi$
$810$		0			0
$811$		−	255259.i		−	0.388096i	−0.980992	−	0.194048i	$-0.937838\pi$
$811$		−	255259.i		−	0.388096i	0.980992	−	0.194048i	$-0.0621618\pi$
$812$	−419360.	+	80768.4i	−0.636025	+	0.122498i
$813$		0			0
$814$	308326.	+	254609.i	0.465331	+	0.384261i
$815$		−	20090.7i		−	0.0302468i
$816$		0			0
$817$	−139133.			−0.208443
$818$	−17884.7	+	21658.0i	−0.0267285	+	0.0323677i
$819$		0			0
$820$	10768.7	+	55912.5i	0.0160153	+	0.0831536i
$821$	−509001.			−0.755148			−0.377574	−	0.925979i	$-0.623242\pi$
$821$	−509001.			−0.755148			−0.377574	+	0.925979i	$0.623242\pi$
$822$		0			0
$823$			29019.0i			0.0428432i	0.999771	+	0.0214216i	$0.00681923\pi$
$823$			29019.0i			0.0428432i	−0.999771	+	0.0214216i	$0.993181\pi$
$824$	−393588.	+	720468.i	−0.579678	+	1.06111i
$825$		0			0
$826$	−231011.	+	279749.i	−0.338589	+	0.410023i
$827$			934276.i			1.36604i	0.730399	+	0.683021i	$0.239334\pi$
$827$			934276.i			1.36604i	−0.730399	+	0.683021i	$0.760666\pi$
$828$		0			0
$829$	1.06294e6			1.54667			0.773336	−	0.633996i	$-0.218586\pi$
$829$	1.06294e6			1.54667			0.773336	+	0.633996i	$0.218586\pi$
$830$	−55333.1	−	45692.9i	−0.0803209	−	0.0663273i
$831$		0			0
$832$	−494982.	−	770867.i	−0.715060	−	1.11361i
$833$	3853.82			0.00555395
$834$		0			0
$835$			28865.6i			0.0414007i
$836$	−30714.3	−	159472.i	−0.0439469	−	0.228178i
$837$		0			0
$838$	289438.	+	239011.i	0.412161	+	0.340354i
$839$		−	532910.i		−	0.757060i	−0.925589	−	0.378530i	$-0.876430\pi$
$839$		−	532910.i		−	0.757060i	0.925589	−	0.378530i	$-0.123570\pi$
$840$		0			0
$841$	1.98726e6			2.80971
$842$	335708.	−	406535.i	0.473519	−	0.573421i
$843$		0			0
$844$	770812.	−	148458.i	1.08209	−	0.208410i
$845$	−76904.8			−0.107706
$846$		0			0
$847$			102452.i			0.142808i
$848$	−680558.	+	272249.i	−0.946397	+	0.378595i
$849$		0			0
$850$	−2812.27	+	3405.59i	−0.00389241	+	0.00471362i
$851$			173661.i			0.239796i
$852$		0			0
$853$	154337.			0.212115			0.106057	−	0.994360i	$-0.466177\pi$
$853$	154337.			0.212115			0.106057	+	0.994360i	$0.466177\pi$
$854$	−142346.	−	117546.i	−0.195177	−	0.161173i
$855$		0			0
$856$	562538.	−	1.02973e6i	0.767722	−	1.40533i
$857$	−614991.			−0.837350			−0.418675	−	0.908136i	$-0.637505\pi$
$857$	−614991.			−0.837350			−0.418675	+	0.908136i	$0.637505\pi$
$858$		0			0
$859$		−	371191.i		−	0.503049i	−0.967851	−	0.251525i	$-0.919068\pi$
$859$		−	371191.i		−	0.503049i	0.967851	−	0.251525i	$-0.0809320\pi$
$860$	−111676.	+	21508.8i	−0.150995	+	0.0290816i
$861$		0			0
$862$	−43617.1	−	36018.1i	−0.0587006	−	0.0484737i
$863$		−	1.25171e6i		−	1.68067i	−0.542067	−	0.840335i	$-0.682358\pi$
$863$		−	1.25171e6i		−	1.68067i	0.542067	−	0.840335i	$-0.317642\pi$
$864$		0			0
$865$	−134679.			−0.179998
$866$	−570727.	+	691138.i	−0.761014	+	0.921571i
$867$		0			0
$868$	51525.7	+	267528.i	0.0683887	+	0.355082i
$869$	1.06515e6			1.41050
$870$		0			0
$871$			1.18295e6i			1.55931i
$872$	584539.	+	319331.i	0.768742	+	0.419960i
$873$		0			0
$874$	44910.3	−	54385.4i	0.0587927	−	0.0711966i
$875$		−	72085.4i		−	0.0941524i
$876$		0			0
$877$	−413992.			−0.538261			−0.269130	−	0.963104i	$-0.586736\pi$
$877$	−413992.			−0.538261			−0.269130	+	0.963104i	$0.586736\pi$
$878$	−520611.	−	429910.i	−0.675343	−	0.557684i
$879$		0			0
$880$	−49306.0	−	123253.i	−0.0636700	−	0.159160i
$881$	974575.			1.25563			0.627817	−	0.778361i	$-0.283948\pi$
$881$	974575.			1.25563			0.627817	+	0.778361i	$0.283948\pi$
$882$		0			0
$883$		−	269401.i		−	0.345524i	−0.984964	−	0.172762i	$-0.944731\pi$
$883$		−	269401.i		−	0.345524i	0.984964	−	0.172762i	$-0.0552691\pi$
$884$	1220.73	+	6338.17i	0.00156212	+	0.00811072i
$885$		0			0
$886$	400369.	+	330616.i	0.510027	+	0.421170i
$887$		−	609409.i		−	0.774572i	−0.921960	−	0.387286i	$-0.873413\pi$
$887$		−	609409.i		−	0.774572i	0.921960	−	0.387286i	$-0.126587\pi$
$888$		0			0
$889$	−135629.			−0.171613
$890$	−104395.	+	126419.i	−0.131795	+	0.159600i
$891$		0			0
$892$	−740841.	+	142686.i	−0.931098	+	0.179329i
$893$	224388.			0.281383
$894$		0			0
$895$		−	124377.i		−	0.155272i
$896$	31748.5	−	264513.i	0.0395464	−	0.329482i
$897$		0			0
$898$	272972.	−	330563.i	0.338506	−	0.409923i
$899$		−	1.71896e6i		−	2.12690i
$900$		0			0
$901$	5164.51			0.00636179
$902$	−443275.	−	366047.i	−0.544829	−	0.449909i
$903$		0			0
$904$	1.18273e6	+	646117.i	1.44726	+	0.790632i
$905$	−162591.			−0.198518
$906$		0			0
$907$		−	379792.i		−	0.461669i	−0.972993	−	0.230835i	$-0.925854\pi$
$907$		−	379792.i		−	0.461669i	0.972993	−	0.230835i	$-0.0741456\pi$
$908$	−960355.	+	184964.i	−1.16482	+	0.224344i
$909$		0			0
$910$	−40194.3	−	33191.6i	−0.0485379	−	0.0400816i
$911$		−	659379.i		−	0.794509i	−0.917709	−	0.397254i	$-0.869963\pi$
$911$		−	659379.i		−	0.794509i	0.917709	−	0.397254i	$-0.130037\pi$
$912$		0			0
$913$	724509.			0.869165
$914$	−878998.	+	1.06445e6i	−1.05219	+	1.27418i
$915$		0			0
$916$	130066.	+	675317.i	0.155014	+	0.804853i
$917$	−285160.			−0.339117
$918$		0			0
$919$			404939.i			0.479466i	0.970839	+	0.239733i	$0.0770600\pi$
$919$			404939.i			0.479466i	−0.970839	+	0.239733i	$0.922940\pi$
$920$	27640.0	−	50595.5i	0.0326560	−	0.0597773i
$921$		0			0
$922$	−66468.2	+	80491.5i	−0.0781902	+	0.0946866i
$923$		−	419044.i		−	0.491876i
$924$		0			0
$925$	422875.			0.494229
$926$	−20303.3	−	16766.1i	−0.0236780	−	0.0195528i
$927$		0			0
$928$	−512332.	+	1.60092e6i	−0.594915	+	1.85898i
$929$	1.39702e6			1.61872			0.809361	−	0.587312i	$-0.199814\pi$
$929$	1.39702e6			1.61872			0.809361	+	0.587312i	$0.199814\pi$
$930$		0			0
$931$			149862.i			0.172899i
$932$	−191225.	−	992866.i	−0.220147	−	1.14303i
$933$		0			0
$934$	−331061.	−	273383.i	−0.379502	−	0.313385i
$935$			935.325i			0.00106989i
$936$		0			0
$937$	−1.10888e6			−1.26301			−0.631506	−	0.775371i	$-0.717563\pi$
$937$	−1.10888e6			−1.26301			−0.631506	+	0.775371i	$0.717563\pi$
$938$	−219048.	+	265263.i	−0.248963	+	0.301488i
$939$		0			0
$940$	180107.	−	34688.4i	0.203833	−	0.0392581i
$941$	163801.			0.184986			0.0924928	−	0.995713i	$-0.470516\pi$
$941$	163801.			0.184986			0.0924928	+	0.995713i	$0.470516\pi$
$942$		0			0
$943$		−	249669.i		−	0.280764i
$944$	530375.	+	1.32581e6i	0.595167	+	1.48778i
$945$		0			0
$946$	731121.	−	885371.i	0.816971	−	0.989334i
$947$			1.36349e6i			1.52038i	0.649701	+	0.760190i	$0.274894\pi$
$947$			1.36349e6i			1.52038i	−0.649701	+	0.760190i	$0.725106\pi$
$948$		0			0
$949$	−1.01170e6			−1.12336
$950$	−132432.	−	109359.i	−0.146739	−	0.121174i
$951$		0			0
$952$	−899.910	+	1647.30i	−0.000992945	+	0.00181760i
$953$	−814580.			−0.896908			−0.448454	−	0.893806i	$-0.648025\pi$
$953$	−814580.			−0.896908			−0.448454	+	0.893806i	$0.648025\pi$
$954$		0			0
$955$			87703.6i			0.0961636i
$956$	−1.05708e6	+	203593.i	−1.15662	+	0.222765i
$957$		0			0
$958$	−1.07590e6	−	888452.i	−1.17230	−	0.968062i
$959$			247703.i			0.269336i
$960$		0			0
$961$	−173079.			−0.187413
$962$	393507.	−	476529.i	0.425209	−	0.514919i
$963$		0			0
$964$	−43294.9	−	224793.i	−0.0465890	−	0.241896i
$965$	−46991.2			−0.0504617
$966$		0			0
$967$			1.64661e6i			1.76091i	0.474131	+	0.880454i	$0.342762\pi$
$967$			1.64661e6i			1.76091i	−0.474131	+	0.880454i	$0.657238\pi$
$968$	353879.	+	193322.i	0.377662	+	0.206315i
$969$		0			0
$970$	82344.5	−	99717.4i	0.0875167	−	0.105981i
$971$		−	804225.i		−	0.852981i	−0.904492	−	0.426490i	$-0.859750\pi$
$971$		−	804225.i		−	0.852981i	0.904492	−	0.426490i	$-0.140250\pi$
$972$		0			0
$973$	478968.			0.505919
$974$	−322397.	−	266228.i	−0.339839	−	0.280632i
$975$		0			0
$976$	−674619.	+	269873.i	−0.708205	+	0.283309i
$977$	772285.			0.809074			0.404537	−	0.914522i	$-0.367433\pi$
$977$	772285.			0.809074			0.404537	+	0.914522i	$0.367433\pi$
$978$		0			0
$979$		−	1.65529e6i		−	1.72706i
$980$	23167.4	+	120288.i	0.0241226	+	0.125248i
$981$		0			0
$982$	−560480.	−	462833.i	−0.581216	−	0.479956i
$983$			366034.i			0.378804i	0.981900	+	0.189402i	$0.0606550\pi$
$983$			366034.i			0.378804i	−0.981900	+	0.189402i	$0.939345\pi$
$984$		0			0
$985$	−117056.			−0.120648
$986$	7541.08	−	9132.08i	0.00775675	−	0.00939325i
$987$		0			0
$988$	−246470.	+	47470.0i	−0.252493	+	0.0486301i
$989$	498673.			0.509827
$990$		0			0
$991$		−	518534.i		−	0.527996i	−0.964523	−	0.263998i	$-0.914959\pi$
$991$		−	518534.i		−	0.527996i	0.964523	−	0.263998i	$-0.0850412\pi$
$992$	1.02130e6	+	326839.i	1.03783	+	0.332131i
$993$		0			0
$994$	77594.6	−	93965.3i	0.0785341	−	0.0951031i
$995$			31536.5i			0.0318542i
$996$		0			0
$997$	399223.			0.401629			0.200814	−	0.979629i	$-0.435641\pi$
$997$	399223.			0.401629			0.200814	+	0.979629i	$0.435641\pi$
$998$	1.01690e6	+	839735.i	1.02098	+	0.843104i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.d.b.55.11	yes	16
3.2	odd	2	inner	108.5.d.b.55.6	yes	16
4.3	odd	2	inner	108.5.d.b.55.12	yes	16
12.11	even	2	inner	108.5.d.b.55.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.d.b.55.5	✓	16	12.11	even	2	inner
108.5.d.b.55.6	yes	16	3.2	odd	2	inner
108.5.d.b.55.11	yes	16	1.1	even	1	trivial
108.5.d.b.55.12	yes	16	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.54696 - 3.08431i) q^{2} +(-3.02598 - 15.7113i) q^{4} -3.58334 q^{5} -16.2605i q^{7} +(-56.1655 - 30.6829i) q^{8} +O(q^{10})\)	\(q+(2.54696 - 3.08431i) q^{2} +(-3.02598 - 15.7113i) q^{4} -3.58334 q^{5} -16.2605i q^{7} +(-56.1655 - 30.6829i) q^{8} +(-9.12663 + 11.0521i) q^{10} -144.712i q^{11} -223.658 q^{13} +(-50.1524 - 41.4148i) q^{14} +(-237.687 + 95.0838i) q^{16} +1.80372 q^{17} +70.1406i q^{19} +(10.8431 + 56.2988i) q^{20} +(-446.338 - 368.577i) q^{22} -251.394i q^{23} -612.160 q^{25} +(-569.647 + 689.830i) q^{26} +(-255.473 + 49.2039i) q^{28} +1641.50 q^{29} -1047.19i q^{31} +(-312.111 + 975.276i) q^{32} +(4.59401 - 5.56324i) q^{34} +58.2669i q^{35} -690.791 q^{37} +(216.336 + 178.645i) q^{38} +(201.260 + 109.947i) q^{40} +993.138 q^{41} +1983.63i q^{43} +(-2273.61 + 437.896i) q^{44} +(-775.377 - 640.290i) q^{46} -3199.12i q^{47} +2136.60 q^{49} +(-1559.15 + 1888.09i) q^{50} +(676.783 + 3513.94i) q^{52} +2863.25 q^{53} +518.553i q^{55} +(-498.919 + 913.278i) q^{56} +(4180.85 - 5062.91i) q^{58} -5577.97i q^{59} +2838.27 q^{61} +(-3229.85 - 2667.14i) q^{62} +(2213.12 + 3446.64i) q^{64} +801.442 q^{65} -5289.13i q^{67} +(-5.45802 - 28.3387i) q^{68} +(179.713 + 148.403i) q^{70} +1873.59i q^{71} +4523.42 q^{73} +(-1759.42 + 2130.62i) q^{74} +(1102.00 - 212.244i) q^{76} -2353.09 q^{77} +7360.48i q^{79} +(851.713 - 340.718i) q^{80} +(2529.48 - 3063.15i) q^{82} +5006.55i q^{83} -6.46335 q^{85} +(6118.15 + 5052.24i) q^{86} +(-4440.19 + 8127.83i) q^{88} +11438.5 q^{89} +3636.78i q^{91} +(-3949.71 + 760.712i) q^{92} +(-9867.10 - 8148.04i) q^{94} -251.338i q^{95} -9022.44 q^{97} +(5441.83 - 6589.93i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{4}+O(q^{10}) \) 16 * q + 28 * q^4	\( 16 q + 28 q^{4} + 176 q^{10} + 176 q^{13} + 88 q^{16} + 384 q^{22} + 2736 q^{25} + 1812 q^{28} + 1520 q^{34} + 80 q^{37} - 688 q^{40} - 1824 q^{46} - 7904 q^{49} - 5236 q^{52} - 11584 q^{58} - 1648 q^{61} + 5056 q^{64} + 26688 q^{70} + 80 q^{73} - 8388 q^{76} - 38464 q^{82} - 16832 q^{85} - 29520 q^{88} - 4512 q^{94} + 14864 q^{97}+O(q^{100}) \) 16 * q + 28 * q^4 + 176 * q^10 + 176 * q^13 + 88 * q^16 + 384 * q^22 + 2736 * q^25 + 1812 * q^28 + 1520 * q^34 + 80 * q^37 - 688 * q^40 - 1824 * q^46 - 7904 * q^49 - 5236 * q^52 - 11584 * q^58 - 1648 * q^61 + 5056 * q^64 + 26688 * q^70 + 80 * q^73 - 8388 * q^76 - 38464 * q^82 - 16832 * q^85 - 29520 * q^88 - 4512 * q^94 + 14864 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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