LMFDB - Embedded newform 108.5.d.a.55.4

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} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} + \cdots + 2924100 $ x^16 - 2x^15 + 6x^14 - 22x^13 + 19x^12 + 18x^11 + 1423x^10 + 660x^9 - 7353x^8 - 22934x^7 - 36353x^6 - 16248x^5 + 360646x^4 + 1077384x^3 + 2005641x^2 + 2990790*x + 2924100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{26} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.4
Root			$-1.81633 - 0.757118i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.5.d.a.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.36416 + 2.16389i) q^{2} +(6.63513 - 14.5594i) q^{4} +43.0579 q^{5} -14.1139i q^{7} +(9.18328 + 63.3377i) q^{8} +O(q^{10})$	\(q+(-3.36416 + 2.16389i) q^{2} +(6.63513 - 14.5594i) q^{4} +43.0579 q^{5} -14.1139i q^{7} +(9.18328 + 63.3377i) q^{8} +(-144.853 + 93.1726i) q^{10} -209.481i q^{11} -195.703 q^{13} +(30.5409 + 47.4813i) q^{14} +(-167.950 - 193.207i) q^{16} +303.688 q^{17} -274.792i q^{19} +(285.694 - 626.895i) q^{20} +(453.296 + 704.729i) q^{22} +466.347i q^{23} +1228.98 q^{25} +(658.376 - 423.480i) q^{26} +(-205.489 - 93.6473i) q^{28} +439.835 q^{29} -1220.96i q^{31} +(983.089 + 286.551i) q^{32} +(-1021.65 + 657.148i) q^{34} -607.713i q^{35} +624.147 q^{37} +(594.620 + 924.443i) q^{38} +(395.412 + 2727.19i) q^{40} +203.592 q^{41} -419.418i q^{43} +(-3049.92 - 1389.94i) q^{44} +(-1009.12 - 1568.86i) q^{46} -1995.53i q^{47} +2201.80 q^{49} +(-4134.48 + 2659.38i) q^{50} +(-1298.51 + 2849.31i) q^{52} +206.451 q^{53} -9019.82i q^{55} +(893.940 - 129.612i) q^{56} +(-1479.67 + 951.756i) q^{58} +2321.87i q^{59} -1392.10 q^{61} +(2642.02 + 4107.49i) q^{62} +(-3927.33 + 1163.30i) q^{64} -8426.55 q^{65} +7348.27i q^{67} +(2015.01 - 4421.50i) q^{68} +(1315.03 + 2044.44i) q^{70} +8546.65i q^{71} -3245.43 q^{73} +(-2099.73 + 1350.59i) q^{74} +(-4000.79 - 1823.28i) q^{76} -2956.59 q^{77} -6157.41i q^{79} +(-7231.57 - 8319.06i) q^{80} +(-684.915 + 440.551i) q^{82} -213.990i q^{83} +13076.2 q^{85} +(907.576 + 1410.99i) q^{86} +(13268.1 - 1923.73i) q^{88} +8439.35 q^{89} +2762.12i q^{91} +(6789.71 + 3094.27i) q^{92} +(4318.11 + 6713.28i) q^{94} -11831.9i q^{95} -1022.49 q^{97} +(-7407.20 + 4764.46i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{4}+O(q^{10}) $ 16 * q - 14 * q^4	$ 16 q - 14 q^{4} - 202 q^{10} - 352 q^{13} - 206 q^{16} + 738 q^{22} + 1632 q^{25} + 342 q^{28} - 2536 q^{34} + 3200 q^{37} - 2854 q^{40} + 36 q^{46} - 896 q^{49} + 2288 q^{52} + 2492 q^{58} - 2752 q^{61} + 682 q^{64} - 14166 q^{70} + 8240 q^{73} - 33084 q^{76} + 68 q^{82} + 8800 q^{85} + 48294 q^{88} + 52596 q^{94} - 6928 q^{97}+O(q^{100}) $ 16 * q - 14 * q^4 - 202 * q^10 - 352 * q^13 - 206 * q^16 + 738 * q^22 + 1632 * q^25 + 342 * q^28 - 2536 * q^34 + 3200 * q^37 - 2854 * q^40 + 36 * q^46 - 896 * q^49 + 2288 * q^52 + 2492 * q^58 - 2752 * q^61 + 682 * q^64 - 14166 * q^70 + 8240 * q^73 - 33084 * q^76 + 68 * q^82 + 8800 * q^85 + 48294 * q^88 + 52596 * q^94 - 6928 * 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 $

$2$	−3.36416	+	2.16389i	−0.841040	+	0.540973i
$2$	−3.36416	+	2.16389i	−0.841040	+	0.540973i
$3$		0			0
$3$		0			0
$4$	6.63513	−	14.5594i	0.414696	−	0.909960i
$5$	43.0579			1.72231			0.861157	−	0.508339i	$-0.169740\pi$
$5$	43.0579			1.72231			0.861157	+	0.508339i	$0.169740\pi$
$6$		0			0
$7$		−	14.1139i		−	0.288038i	−0.989575	−	0.144019i	$-0.953997\pi$
$7$		−	14.1139i		−	0.288038i	0.989575	−	0.144019i	$-0.0460027\pi$
$8$	9.18328	+	63.3377i	0.143489	+	0.989652i
$9$		0			0
$10$	−144.853	+	93.1726i	−1.44853	+	0.931726i
$11$		−	209.481i		−	1.73125i	−0.500691	−	0.865626i	$-0.666921\pi$
$11$		−	209.481i		−	1.73125i	0.500691	−	0.865626i	$-0.333079\pi$
$12$		0			0
$13$	−195.703			−1.15801			−0.579003	−	0.815326i	$-0.696558\pi$
$13$	−195.703			−1.15801			−0.579003	+	0.815326i	$0.696558\pi$
$14$	30.5409	+	47.4813i	0.155821	+	0.242252i
$15$		0			0
$16$	−167.950	−	193.207i	−0.656055	−	0.754713i
$17$	303.688			1.05082			0.525412	−	0.850848i	$-0.323911\pi$
$17$	303.688			1.05082			0.525412	+	0.850848i	$0.323911\pi$
$18$		0			0
$19$		−	274.792i		−	0.761196i	−0.924741	−	0.380598i	$-0.875718\pi$
$19$		−	274.792i		−	0.761196i	0.924741	−	0.380598i	$-0.124282\pi$
$20$	285.694	−	626.895i	0.714236	−	1.56724i
$21$		0			0
$22$	453.296	+	704.729i	0.936561	+	1.45605i
$23$			466.347i			0.881563i	0.897614	+	0.440782i	$0.145299\pi$
$23$			466.347i			0.881563i	−0.897614	+	0.440782i	$0.854701\pi$
$24$		0			0
$25$	1228.98			1.96637
$26$	658.376	−	423.480i	0.973928	−	0.626450i
$27$		0			0
$28$	−205.489	−	93.6473i	−0.262103	−	0.119448i
$29$	439.835			0.522990			0.261495	−	0.965205i	$-0.415784\pi$
$29$	439.835			0.522990			0.261495	+	0.965205i	$0.415784\pi$
$30$		0			0
$31$		−	1220.96i		−	1.27051i	−0.772304	−	0.635253i	$-0.780896\pi$
$31$		−	1220.96i		−	1.27051i	0.772304	−	0.635253i	$-0.219104\pi$
$32$	983.089	+	286.551i	0.960048	+	0.279835i
$33$		0			0
$34$	−1021.65	+	657.148i	−0.883784	+	0.568467i
$35$		−	607.713i		−	0.496092i
$36$		0			0
$37$	624.147			0.455914			0.227957	−	0.973671i	$-0.426795\pi$
$37$	624.147			0.455914			0.227957	+	0.973671i	$0.426795\pi$
$38$	594.620	+	924.443i	0.411787	+	0.640196i
$39$		0			0
$40$	395.412	+	2727.19i	0.247133	+	1.70449i
$41$	203.592			0.121114			0.0605568	−	0.998165i	$-0.480712\pi$
$41$	203.592			0.121114			0.0605568	+	0.998165i	$0.480712\pi$
$42$		0			0
$43$		−	419.418i		−	0.226835i	−0.993547	−	0.113418i	$-0.963820\pi$
$43$		−	419.418i		−	0.226835i	0.993547	−	0.113418i	$-0.0361798\pi$
$44$	−3049.92	−	1389.94i	−1.57537	−	0.717943i
$45$		0			0
$46$	−1009.12	−	1568.86i	−0.476902	−	0.741430i
$47$		−	1995.53i		−	0.903364i	−0.892179	−	0.451682i	$-0.850824\pi$
$47$		−	1995.53i		−	0.903364i	0.892179	−	0.451682i	$-0.149176\pi$
$48$		0			0
$49$	2201.80			0.917034
$50$	−4134.48	+	2659.38i	−1.65379	+	1.06375i
$51$		0			0
$52$	−1298.51	+	2849.31i	−0.480220	+	1.05374i
$53$	206.451			0.0734962			0.0367481	−	0.999325i	$-0.488300\pi$
$53$	206.451			0.0734962			0.0367481	+	0.999325i	$0.488300\pi$
$54$		0			0
$55$		−	9019.82i		−	2.98176i
$56$	893.940	−	129.612i	0.285057	−	0.0413302i
$57$		0			0
$58$	−1479.67	+	951.756i	−0.439856	+	0.282924i
$59$			2321.87i			0.667011i	0.942748	+	0.333505i	$0.108232\pi$
$59$			2321.87i			0.667011i	−0.942748	+	0.333505i	$0.891768\pi$
$60$		0			0
$61$	−1392.10			−0.374120			−0.187060	−	0.982349i	$-0.559896\pi$
$61$	−1392.10			−0.374120			−0.187060	+	0.982349i	$0.559896\pi$
$62$	2642.02	+	4107.49i	0.687310	+	1.06855i
$63$		0			0
$64$	−3927.33	+	1163.30i	−0.958822	+	0.284008i
$65$	−8426.55			−1.99445
$66$		0			0
$67$			7348.27i			1.63695i	0.574542	+	0.818475i	$0.305180\pi$
$67$			7348.27i			1.63695i	−0.574542	+	0.818475i	$0.694820\pi$
$68$	2015.01	−	4421.50i	0.435772	−	0.956207i
$69$		0			0
$70$	1315.03	+	2044.44i	0.268373	+	0.417233i
$71$			8546.65i			1.69543i	0.530453	+	0.847714i	$0.322022\pi$
$71$			8546.65i			1.69543i	−0.530453	+	0.847714i	$0.677978\pi$
$72$		0			0
$73$	−3245.43			−0.609012			−0.304506	−	0.952510i	$-0.598491\pi$
$73$	−3245.43			−0.609012			−0.304506	+	0.952510i	$0.598491\pi$
$74$	−2099.73	+	1350.59i	−0.383442	+	0.246638i
$75$		0			0
$76$	−4000.79	−	1823.28i	−0.692658	−	0.315665i
$77$	−2956.59			−0.498667
$78$		0			0
$79$		−	6157.41i		−	0.986606i	−0.869858	−	0.493303i	$-0.835789\pi$
$79$		−	6157.41i		−	0.986606i	0.869858	−	0.493303i	$-0.164211\pi$
$80$	−7231.57	−	8319.06i	−1.12993	−	1.29985i
$81$		0			0
$82$	−684.915	+	440.551i	−0.101861	+	0.0655192i
$83$		−	213.990i		−	0.0310626i	−0.999879	−	0.0155313i	$-0.995056\pi$
$83$		−	213.990i		−	0.0310626i	0.999879	−	0.0155313i	$-0.00494397\pi$
$84$		0			0
$85$	13076.2			1.80985
$86$	907.576	+	1410.99i	0.122712	+	0.190777i
$87$		0			0
$88$	13268.1	−	1923.73i	1.71334	−	0.248415i
$89$	8439.35			1.06544			0.532720	−	0.846292i	$-0.321170\pi$
$89$	8439.35			1.06544			0.532720	+	0.846292i	$0.321170\pi$
$90$		0			0
$91$			2762.12i			0.333550i
$92$	6789.71	+	3094.27i	0.802187	+	0.365580i
$93$		0			0
$94$	4318.11	+	6713.28i	0.488696	+	0.759765i
$95$		−	11831.9i		−	1.31102i
$96$		0			0
$97$	−1022.49			−0.108672			−0.0543358	−	0.998523i	$-0.517304\pi$
$97$	−1022.49			−0.108672			−0.0543358	+	0.998523i	$0.517304\pi$
$98$	−7407.20	+	4764.46i	−0.771262	+	0.496091i
$99$		0			0
$100$	8154.44	−	17893.2i	0.815444	−	1.78932i
$101$	−2374.52			−0.232773			−0.116387	−	0.993204i	$-0.537131\pi$
$101$	−2374.52			−0.232773			−0.116387	+	0.993204i	$0.537131\pi$
$102$		0			0
$103$			8481.02i			0.799418i	0.916642	+	0.399709i	$0.130889\pi$
$103$			8481.02i			0.799418i	−0.916642	+	0.399709i	$0.869111\pi$
$104$	−1797.19	−	12395.4i	−0.166161	−	1.14602i
$105$		0			0
$106$	−694.533	+	446.738i	−0.0618132	+	0.0397595i
$107$		−	9579.93i		−	0.836748i	−0.908275	−	0.418374i	$-0.862600\pi$
$107$		−	9579.93i		−	0.836748i	0.908275	−	0.418374i	$-0.137400\pi$
$108$		0			0
$109$	−11549.9			−0.972130			−0.486065	−	0.873923i	$-0.661568\pi$
$109$	−11549.9			−0.972130			−0.486065	+	0.873923i	$0.661568\pi$
$110$	19517.9	+	30344.1i	1.61305	+	2.50778i
$111$		0			0
$112$	−2726.89	+	2370.43i	−0.217386	+	0.188969i
$113$	21853.8			1.71147			0.855735	−	0.517414i	$-0.173105\pi$
$113$	21853.8			1.71147			0.855735	+	0.517414i	$0.173105\pi$
$114$		0			0
$115$			20079.9i			1.51833i
$116$	2918.36	−	6403.71i	0.216882	−	0.475900i
$117$		0			0
$118$	−5024.27	−	7811.12i	−0.360835	−	0.560983i
$119$		−	4286.21i		−	0.302677i
$120$		0			0
$121$	−29241.5			−1.99723
$122$	4683.25	−	3012.36i	0.314650	−	0.202389i
$123$		0			0
$124$	−17776.4	−	8101.21i	−1.15611	−	0.526874i
$125$	26006.0			1.66439
$126$		0			0
$127$			7358.63i			0.456236i	0.973634	+	0.228118i	$0.0732572\pi$
$127$			7358.63i			0.456236i	−0.973634	+	0.228118i	$0.926743\pi$
$128$	10694.9	−	12411.8i	0.652767	−	0.757559i
$129$		0			0
$130$	28348.2	−	18234.2i	1.67741	−	1.07894i
$131$			8567.97i			0.499270i	0.968340	+	0.249635i	$0.0803106\pi$
$131$			8567.97i			0.499270i	−0.968340	+	0.249635i	$0.919689\pi$
$132$		0			0
$133$	−3878.37			−0.219253
$134$	−15900.9	−	24720.7i	−0.885546	−	1.37674i
$135$		0			0
$136$	2788.85	+	19234.9i	0.150781	+	1.03995i
$137$	−33585.2			−1.78940			−0.894699	−	0.446669i	$-0.852610\pi$
$137$	−33585.2			−1.78940			−0.894699	+	0.446669i	$0.852610\pi$
$138$		0			0
$139$		−	8638.51i		−	0.447104i	−0.974692	−	0.223552i	$-0.928235\pi$
$139$		−	8638.51i		−	0.447104i	0.974692	−	0.223552i	$-0.0717653\pi$
$140$	−8847.91	−	4032.25i	−0.451424	−	0.205727i
$141$		0			0
$142$	−18494.1	−	28752.3i	−0.917182	−	1.42592i
$143$			40996.1i			2.00480i
$144$		0			0
$145$	18938.3			0.900754
$146$	10918.1	−	7022.75i	0.512203	−	0.329459i
$147$		0			0
$148$	4141.29	−	9087.18i	0.189066	−	0.414864i
$149$	−24096.5			−1.08538			−0.542689	−	0.839934i	$-0.682594\pi$
$149$	−24096.5			−1.08538			−0.542689	+	0.839934i	$0.682594\pi$
$150$		0			0
$151$			26512.7i			1.16279i	0.813623	+	0.581393i	$0.197492\pi$
$151$			26512.7i			1.16279i	−0.813623	+	0.581393i	$0.802508\pi$
$152$	17404.7	−	2523.49i	0.753319	−	0.109223i
$153$		0			0
$154$	9946.45	−	6397.75i	0.419398	−	0.269765i
$155$		−	52571.8i		−	2.18821i
$156$		0			0
$157$	−33191.1			−1.34655			−0.673274	−	0.739393i	$-0.735113\pi$
$157$	−33191.1			−1.34655			−0.673274	+	0.739393i	$0.735113\pi$
$158$	13324.0	+	20714.5i	0.533727	+	0.829775i
$159$		0			0
$160$	42329.7	+	12338.3i	1.65350	+	0.481964i
$161$	6581.96			0.253924
$162$		0			0
$163$			22135.9i			0.833146i	0.909102	+	0.416573i	$0.136769\pi$
$163$			22135.9i			0.833146i	−0.909102	+	0.416573i	$0.863231\pi$
$164$	1350.86	−	2964.17i	0.0502252	−	0.110208i
$165$		0			0
$166$	463.052	+	719.897i	0.0168040	+	0.0261249i
$167$			31233.9i			1.11993i	0.828515	+	0.559967i	$0.189186\pi$
$167$			31233.9i			1.11993i	−0.828515	+	0.559967i	$0.810814\pi$
$168$		0			0
$169$	9738.62			0.340976
$170$	−43990.3	+	28295.4i	−1.52215	+	0.979080i
$171$		0			0
$172$	−6106.46	−	2782.89i	−0.206411	−	0.0940675i
$173$	−19702.2			−0.658298			−0.329149	−	0.944278i	$-0.606762\pi$
$173$	−19702.2			−0.658298			−0.329149	+	0.944278i	$0.606762\pi$
$174$		0			0
$175$		−	17345.6i		−	0.566388i
$176$	−40473.2	+	35182.4i	−1.30660	+	1.13580i
$177$		0			0
$178$	−28391.3	+	18261.9i	−0.896077	+	0.576375i
$179$		−	931.868i		−	0.0290836i	−0.999894	−	0.0145418i	$-0.995371\pi$
$179$		−	931.868i		−	0.0290836i	0.999894	−	0.0145418i	$-0.00462896\pi$
$180$		0			0
$181$	8201.99			0.250358			0.125179	−	0.992134i	$-0.460049\pi$
$181$	8201.99			0.250358			0.125179	+	0.992134i	$0.460049\pi$
$182$	−5976.94	−	9292.23i	−0.180441	−	0.280529i
$183$		0			0
$184$	−29537.3	+	4282.59i	−0.872441	+	0.126494i
$185$	26874.4			0.785228
$186$		0			0
$187$		−	63617.0i		−	1.81924i
$188$	−29053.6	−	13240.6i	−0.822025	−	0.374621i
$189$		0			0
$190$	25603.1	+	39804.5i	0.709226	+	1.10262i
$191$		−	3283.65i		−	0.0900099i	−0.998987	−	0.0450049i	$-0.985670\pi$
$191$		−	3283.65i		−	0.0900099i	0.998987	−	0.0450049i	$-0.0143304\pi$
$192$		0			0
$193$	70666.2			1.89713			0.948565	−	0.316583i	$-0.102536\pi$
$193$	70666.2			1.89713			0.948565	+	0.316583i	$0.102536\pi$
$194$	3439.82	−	2212.56i	0.0913971	−	0.0587884i
$195$		0			0
$196$	14609.2	−	32056.8i	0.380290	−	0.834464i
$197$	14865.2			0.383034			0.191517	−	0.981489i	$-0.438659\pi$
$197$	14865.2			0.383034			0.191517	+	0.981489i	$0.438659\pi$
$198$		0			0
$199$			63878.1i			1.61304i	0.591205	+	0.806521i	$0.298652\pi$
$199$			63878.1i			1.61304i	−0.591205	+	0.806521i	$0.701348\pi$
$200$	11286.1	+	77840.7i	0.282151	+	1.94602i
$201$		0			0
$202$	7988.26	−	5138.21i	0.195771	−	0.125924i
$203$		−	6207.77i		−	0.150641i
$204$		0			0
$205$	8766.23			0.208596
$206$	−18352.0	−	28531.5i	−0.432464	−	0.672342i
$207$		0			0
$208$	32868.3	+	37811.1i	0.759715	+	0.873962i
$209$	−57563.8			−1.31782
$210$		0			0
$211$		−	66608.9i		−	1.49612i	−0.663629	−	0.748062i	$-0.730985\pi$
$211$		−	66608.9i		−	1.49612i	0.663629	−	0.748062i	$-0.269015\pi$
$212$	1369.83	−	3005.79i	0.0304786	−	0.0668786i
$213$		0			0
$214$	20729.9	+	32228.4i	0.452658	+	0.703738i
$215$		−	18059.2i		−	0.390681i
$216$		0			0
$217$	−17232.4			−0.365954
$218$	38855.6	−	24992.7i	0.817600	−	0.525896i
$219$		0			0
$220$	−131323.	−	59847.7i	−2.71328	−	1.23652i
$221$	−59432.6			−1.21686
$222$		0			0
$223$		−	48074.2i		−	0.966723i	−0.875421	−	0.483361i	$-0.839416\pi$
$223$		−	48074.2i		−	0.966723i	0.875421	−	0.483361i	$-0.160584\pi$
$224$	4044.35	−	13875.2i	0.0806032	−	0.276530i
$225$		0			0
$226$	−73519.5	+	47289.2i	−1.43941	+	0.925860i
$227$			18940.2i			0.367564i	0.982967	+	0.183782i	$0.0588341\pi$
$227$			18940.2i			0.367564i	−0.982967	+	0.183782i	$0.941166\pi$
$228$		0			0
$229$	349.738			0.00666917			0.00333458	−	0.999994i	$-0.498939\pi$
$229$	349.738			0.00666917			0.00333458	+	0.999994i	$0.498939\pi$
$230$	−43450.8	−	67552.0i	−0.821375	−	1.27697i
$231$		0			0
$232$	4039.13	+	27858.1i	0.0750432	+	0.517578i
$233$	−7529.14			−0.138686			−0.0693432	−	0.997593i	$-0.522090\pi$
$233$	−7529.14			−0.138686			−0.0693432	+	0.997593i	$0.522090\pi$
$234$		0			0
$235$		−	85923.3i		−	1.55588i
$236$	33804.9	+	15405.9i	0.606953	+	0.276607i
$237$		0			0
$238$	9274.91	+	14419.5i	0.163740	+	0.254564i
$239$			53394.8i			0.934766i	0.884055	+	0.467383i	$0.154803\pi$
$239$			53394.8i			0.934766i	−0.884055	+	0.467383i	$0.845197\pi$
$240$		0			0
$241$	−88157.7			−1.51784			−0.758920	−	0.651184i	$-0.774273\pi$
$241$	−88157.7			−1.51784			−0.758920	+	0.651184i	$0.774273\pi$
$242$	98373.0	−	63275.5i	1.67975	−	1.08045i
$243$		0			0
$244$	−9236.76	+	20268.1i	−0.155146	+	0.340434i
$245$	94804.7			1.57942
$246$		0			0
$247$			53777.5i			0.881469i
$248$	77332.6	−	11212.4i	1.25736	−	0.182303i
$249$		0			0
$250$	−87488.4	+	56274.3i	−1.39982	+	0.900389i
$251$			23284.3i			0.369587i	0.982777	+	0.184793i	$0.0591616\pi$
$251$			23284.3i			0.369587i	−0.982777	+	0.184793i	$0.940838\pi$
$252$		0			0
$253$	97691.0			1.52621
$254$	−15923.3	−	24755.6i	−0.246811	−	0.383712i
$255$		0			0
$256$	−9121.53	+	64898.1i	−0.139183	+	0.990267i
$257$	118409.			1.79274			0.896369	−	0.443308i	$-0.146195\pi$
$257$	118409.			1.79274			0.896369	+	0.443308i	$0.146195\pi$
$258$		0			0
$259$		−	8809.12i		−	0.131321i
$260$	−55911.2	+	122685.i	−0.827089	+	1.81487i
$261$		0			0
$262$	−18540.2	−	28824.0i	−0.270092	−	0.419906i
$263$			44424.6i			0.642262i	0.947035	+	0.321131i	$0.104063\pi$
$263$			44424.6i			0.642262i	−0.947035	+	0.321131i	$0.895937\pi$
$264$		0			0
$265$	8889.33			0.126584
$266$	13047.5	−	8392.39i	0.184401	−	0.118610i
$267$		0			0
$268$	106986.	+	48756.7i	1.48956	+	0.678836i
$269$	55818.5			0.771390			0.385695	−	0.922626i	$-0.373962\pi$
$269$	55818.5			0.771390			0.385695	+	0.922626i	$0.373962\pi$
$270$		0			0
$271$		−	98301.7i		−	1.33851i	−0.743032	−	0.669256i	$-0.766613\pi$
$271$		−	98301.7i		−	1.33851i	0.743032	−	0.669256i	$-0.233387\pi$
$272$	−51004.4	−	58674.5i	−0.689398	−	0.793070i
$273$		0			0
$274$	112986.	−	72674.8i	1.50496	−	0.968017i
$275$		−	257448.i		−	3.40428i
$276$		0			0
$277$	111306.			1.45063			0.725317	−	0.688415i	$-0.241693\pi$
$277$	111306.			1.45063			0.725317	+	0.688415i	$0.241693\pi$
$278$	18692.8	+	29061.3i	0.241872	+	0.376033i
$279$		0			0
$280$	38491.2	−	5580.80i	0.490959	−	0.0711836i
$281$	−24996.7			−0.316571			−0.158285	−	0.987393i	$-0.550597\pi$
$281$	−24996.7			−0.316571			−0.158285	+	0.987393i	$0.550597\pi$
$282$		0			0
$283$		−	30559.7i		−	0.381571i	−0.981632	−	0.190786i	$-0.938896\pi$
$283$		−	30559.7i		−	0.381571i	0.981632	−	0.190786i	$-0.0611035\pi$
$284$	124434.	+	56708.2i	1.54277	+	0.703087i
$285$		0			0
$286$	−88711.3	−	137917.i	−1.08454	−	1.68612i
$287$		−	2873.47i		−	0.0348853i
$288$		0			0
$289$	8705.37			0.104230
$290$	−63711.6	+	40980.6i	−0.757570	+	0.487284i
$291$		0			0
$292$	−21533.8	+	47251.3i	−0.252555	+	0.554177i
$293$	−49225.1			−0.573392			−0.286696	−	0.958022i	$-0.592557\pi$
$293$	−49225.1			−0.573392			−0.286696	+	0.958022i	$0.592557\pi$
$294$		0			0
$295$			99974.5i			1.14880i
$296$	5731.71	+	39532.0i	0.0654186	+	0.451197i
$297$		0			0
$298$	81064.4	−	52142.2i	0.912846	−	0.587160i
$299$		−	91265.4i		−	1.02085i
$300$		0			0
$301$	−5919.61			−0.0653372
$302$	−57370.7	−	89192.9i	−0.629037	−	0.977950i
$303$		0			0
$304$	−53091.5	+	46151.3i	−0.574484	+	0.499386i
$305$	−59940.8			−0.644352
$306$		0			0
$307$			143871.i			1.52650i	0.646105	+	0.763249i	$0.276397\pi$
$307$			143871.i			1.52650i	−0.646105	+	0.763249i	$0.723603\pi$
$308$	−19617.4	+	43046.1i	−0.206795	+	0.453767i
$309$		0			0
$310$	113760.	+	176860.i	1.18376	+	1.84037i
$311$			144670.i			1.49575i	0.663842	+	0.747873i	$0.268925\pi$
$311$			144670.i			1.49575i	−0.663842	+	0.747873i	$0.731075\pi$
$312$		0			0
$313$	80345.4			0.820111			0.410055	−	0.912061i	$-0.365509\pi$
$313$	80345.4			0.820111			0.410055	+	0.912061i	$0.365509\pi$
$314$	111660.	−	71821.9i	1.13250	−	0.728447i
$315$		0			0
$316$	−89647.9	−	40855.2i	−0.897772	−	0.409141i
$317$	144593.			1.43889			0.719445	−	0.694549i	$-0.244396\pi$
$317$	144593.			1.43889			0.719445	+	0.694549i	$0.244396\pi$
$318$		0			0
$319$		−	92137.2i		−	0.905428i
$320$	−169103.	+	50089.0i	−1.65139	+	0.489151i
$321$		0			0
$322$	−22142.8	+	14242.7i	−0.213560	+	0.137366i
$323$		−	83450.9i		−	0.799882i
$324$		0			0
$325$	−240515.			−2.27706
$326$	−47899.6	−	74468.5i	−0.450710	−	0.700709i
$327$		0			0
$328$	1869.64	+	12895.0i	0.0173784	+	0.119860i
$329$	−28164.7			−0.260203
$330$		0			0
$331$			89506.7i			0.816957i	0.912768	+	0.408479i	$0.133941\pi$
$331$			89506.7i			0.816957i	−0.912768	+	0.408479i	$0.866059\pi$
$332$	−3115.56	−	1419.85i	−0.0282657	−	0.0128815i
$333$		0			0
$334$	−67586.8	−	105076.i	−0.605855	−	0.941910i
$335$			316401.i			2.81934i
$336$		0			0
$337$	−134427.			−1.18366			−0.591830	−	0.806062i	$-0.701595\pi$
$337$	−134427.			−1.18366			−0.591830	+	0.806062i	$0.701595\pi$
$338$	−32762.3	+	21073.3i	−0.286775	+	0.184459i
$339$		0			0
$340$	86762.0	−	190380.i	0.750536	−	1.64689i
$341$	−255768.			−2.19957
$342$		0			0
$343$		−	64963.3i		−	0.552179i
$344$	26565.0	−	3851.63i	0.224488	−	0.0325483i
$345$		0			0
$346$	66281.3	−	42633.4i	0.553654	−	0.356121i
$347$			73087.9i			0.606997i	0.952832	+	0.303499i	$0.0981547\pi$
$347$			73087.9i			0.606997i	−0.952832	+	0.303499i	$0.901845\pi$
$348$		0			0
$349$	−54237.0			−0.445292			−0.222646	−	0.974899i	$-0.571469\pi$
$349$	−54237.0			−0.445292			−0.222646	+	0.974899i	$0.571469\pi$
$350$	37534.1	+	58353.5i	0.306401	+	0.476355i
$351$		0			0
$352$	60027.2	−	205939.i	0.484465	−	1.66208i
$353$	−29031.6			−0.232982			−0.116491	−	0.993192i	$-0.537165\pi$
$353$	−29031.6			−0.232982			−0.116491	+	0.993192i	$0.537165\pi$
$354$		0			0
$355$			368001.i			2.92006i
$356$	55996.2	−	122872.i	0.441833	−	0.969508i
$357$		0			0
$358$	2016.46	+	3134.95i	0.0157335	+	0.0244605i
$359$			9197.54i			0.0713646i	0.999363	+	0.0356823i	$0.0113604\pi$
$359$			9197.54i			0.0713646i	−0.999363	+	0.0356823i	$0.988640\pi$
$360$		0			0
$361$	54810.5			0.420581
$362$	−27592.8	+	17748.2i	−0.210561	+	0.135437i
$363$		0			0
$364$	40214.8	+	18327.1i	0.303517	+	0.138322i
$365$	−139741.			−1.04891
$366$		0			0
$367$		−	96131.3i		−	0.713728i	−0.934156	−	0.356864i	$-0.883846\pi$
$367$		−	96131.3i		−	0.713728i	0.934156	−	0.356864i	$-0.116154\pi$
$368$	90101.3	−	78323.0i	0.665327	−	0.578354i
$369$		0			0
$370$	−90409.8	+	58153.4i	−0.660408	+	0.424787i
$371$		−	2913.82i		−	0.0211697i
$372$		0			0
$373$	−27728.8			−0.199303			−0.0996513	−	0.995022i	$-0.531773\pi$
$373$	−27728.8			−0.199303			−0.0996513	+	0.995022i	$0.531773\pi$
$374$	137660.	+	214018.i	0.984160	+	1.53005i
$375$		0			0
$376$	126392.	−	18325.5i	0.894016	−	0.129623i
$377$	−86076.9			−0.605626
$378$		0			0
$379$		−	101903.i		−	0.709432i	−0.934974	−	0.354716i	$-0.884578\pi$
$379$		−	101903.i		−	0.709432i	0.934974	−	0.354716i	$-0.115422\pi$
$380$	−172266.	−	78506.5i	−1.19297	−	0.543674i
$381$		0			0
$382$	7105.47	+	11046.7i	0.0486930	+	0.0757019i
$383$		−	6261.76i		−	0.0426873i	−0.999772	−	0.0213437i	$-0.993206\pi$
$383$		−	6261.76i		−	0.0426873i	0.999772	−	0.0213437i	$-0.00679442\pi$
$384$		0			0
$385$	−127305.			−0.858860
$386$	−237732.	+	152914.i	−1.59556	+	1.02630i
$387$		0			0
$388$	−6784.36	+	14886.8i	−0.0450656	+	0.0988867i
$389$	147789.			0.976658			0.488329	−	0.872660i	$-0.337607\pi$
$389$	147789.			0.976658			0.488329	+	0.872660i	$0.337607\pi$
$390$		0			0
$391$			141624.i			0.926367i
$392$	20219.7	+	139457.i	0.131584	+	0.907545i
$393$		0			0
$394$	−50008.8	+	32166.6i	−0.322147	+	0.207211i
$395$		−	265125.i		−	1.69924i
$396$		0			0
$397$	−142937.			−0.906912			−0.453456	−	0.891279i	$-0.649809\pi$
$397$	−142937.			−0.906912			−0.453456	+	0.891279i	$0.649809\pi$
$398$	−138225.	−	214896.i	−0.872613	−	1.35663i
$399$		0			0
$400$	−206407.	−	237447.i	−1.29004	−	1.48404i
$401$	−18071.6			−0.112385			−0.0561923	−	0.998420i	$-0.517896\pi$
$401$	−18071.6			−0.112385			−0.0561923	+	0.998420i	$0.517896\pi$
$402$		0			0
$403$			238945.i			1.47125i
$404$	−15755.2	+	34571.5i	−0.0965300	+	0.211814i
$405$		0			0
$406$	13433.0	+	20883.9i	0.0814928	+	0.126695i
$407$		−	130747.i		−	0.789303i
$408$		0			0
$409$	166751.			0.996831			0.498416	−	0.866938i	$-0.333915\pi$
$409$	166751.			0.996831			0.498416	+	0.866938i	$0.333915\pi$
$410$	−29491.0	+	18969.2i	−0.175437	+	0.112845i
$411$		0			0
$412$	123478.	+	56272.7i	0.727438	+	0.331515i
$413$	32770.5			0.192125
$414$		0			0
$415$		−	9213.96i		−	0.0534996i
$416$	−192393.	−	56078.9i	−1.11174	−	0.324051i
$417$		0			0
$418$	193654.	−	124562.i	1.10834	−	0.712906i
$419$			24068.3i			0.137094i	0.997648	+	0.0685469i	$0.0218363\pi$
$419$			24068.3i			0.137094i	−0.997648	+	0.0685469i	$0.978164\pi$
$420$		0			0
$421$	−113463.			−0.640162			−0.320081	−	0.947390i	$-0.603710\pi$
$421$	−113463.			−0.640162			−0.320081	+	0.947390i	$0.603710\pi$
$422$	144135.	+	224083.i	0.809363	+	1.25830i
$423$		0			0
$424$	1895.90	+	13076.1i	0.0105459	+	0.0727357i
$425$	373226.			2.06630
$426$		0			0
$427$			19647.9i			0.107761i
$428$	−139478.	−	63564.1i	−0.761407	−	0.346996i
$429$		0			0
$430$	39078.3	+	60754.2i	0.211348	+	0.328579i
$431$			154439.i			0.831388i	0.909505	+	0.415694i	$0.136461\pi$
$431$			154439.i			0.831388i	−0.909505	+	0.415694i	$0.863539\pi$
$432$		0			0
$433$	124462.			0.663836			0.331918	−	0.943308i	$-0.392304\pi$
$433$	124462.			0.663836			0.331918	+	0.943308i	$0.392304\pi$
$434$	57972.6	−	37289.1i	0.307782	−	0.197972i
$435$		0			0
$436$	−76634.9	+	168159.i	−0.403138	+	0.884600i
$437$	128148.			0.671042
$438$		0			0
$439$		−	100585.i		−	0.521921i	−0.965349	−	0.260960i	$-0.915961\pi$
$439$		−	100585.i		−	0.521921i	0.965349	−	0.260960i	$-0.0840392\pi$
$440$	571295.	−	82831.5i	2.95090	−	0.427849i
$441$		0			0
$442$	199941.	−	128606.i	1.02343	−	0.658288i
$443$		−	195614.i		−	0.996764i	−0.866957	−	0.498382i	$-0.833928\pi$
$443$		−	195614.i		−	0.996764i	0.866957	−	0.498382i	$-0.166072\pi$
$444$		0			0
$445$	363380.			1.83502
$446$	104027.	+	161729.i	0.522971	+	0.813052i
$447$		0			0
$448$	16418.6	+	55429.9i	0.0818051	+	0.276177i
$449$	47139.5			0.233826			0.116913	−	0.993142i	$-0.462700\pi$
$449$	47139.5			0.233826			0.116913	+	0.993142i	$0.462700\pi$
$450$		0			0
$451$		−	42648.7i		−	0.209678i
$452$	145003.	−	318177.i	0.709739	−	1.55737i
$453$		0			0
$454$	−40984.6	−	63717.9i	−0.198842	−	0.309136i
$455$			118931.i			0.574477i
$456$		0			0
$457$	−44420.0			−0.212690			−0.106345	−	0.994329i	$-0.533915\pi$
$457$	−44420.0			−0.212690			−0.106345	+	0.994329i	$0.533915\pi$
$458$	−1176.57	+	756.796i	−0.00560904	+	0.00360784i
$459$		0			0
$460$	292350.	+	133233.i	1.38162	+	0.629644i
$461$	−189396.			−0.891187			−0.445594	−	0.895235i	$-0.647007\pi$
$461$	−189396.			−0.891187			−0.445594	+	0.895235i	$0.647007\pi$
$462$		0			0
$463$		−	146188.i		−	0.681944i	−0.940073	−	0.340972i	$-0.889244\pi$
$463$		−	146188.i		−	0.681944i	0.940073	−	0.340972i	$-0.110756\pi$
$464$	−73870.3	−	84979.0i	−0.343110	−	0.394708i
$465$		0			0
$466$	25329.2	−	16292.3i	0.116641	−	0.0750256i
$467$		−	145806.i		−	0.668563i	−0.942473	−	0.334281i	$-0.891506\pi$
$467$		−	145806.i		−	0.668563i	0.942473	−	0.334281i	$-0.108494\pi$
$468$		0			0
$469$	103712.			0.471504
$470$	185929.	+	289059.i	0.841687	+	1.30855i
$471$		0			0
$472$	−147062.	+	21322.3i	−0.660109	+	0.0957086i
$473$	−87860.3			−0.392709
$474$		0			0
$475$		−	337713.i		−	1.49679i
$476$	−62404.5	−	28439.6i	−0.275424	−	0.125519i
$477$		0			0
$478$	−115541.	−	179629.i	−0.505684	−	0.786175i
$479$			366733.i			1.59838i	0.601081	+	0.799188i	$0.294737\pi$
$479$			366733.i			1.59838i	−0.601081	+	0.799188i	$0.705263\pi$
$480$		0			0
$481$	−122147.			−0.527951
$482$	296576.	−	190764.i	1.27656	−	0.821111i
$483$		0			0
$484$	−194021.	+	425737.i	−0.828244	+	1.81740i
$485$	−44026.2			−0.187166
$486$		0			0
$487$			202033.i			0.851851i	0.904758	+	0.425926i	$0.140051\pi$
$487$			202033.i			0.851851i	−0.904758	+	0.425926i	$0.859949\pi$
$488$	−12784.0	−	88172.4i	−0.0536820	−	0.370248i
$489$		0			0
$490$	−318938.	+	205147.i	−1.32836	+	0.854425i
$491$		−	229449.i		−	0.951750i	−0.879513	−	0.475875i	$-0.842131\pi$
$491$		−	229449.i		−	0.951750i	0.879513	−	0.475875i	$-0.157869\pi$
$492$		0			0
$493$	133573.			0.549570
$494$	−116369.	−	180916.i	−0.476851	−	0.741350i
$495$		0			0
$496$	−235897.	+	205060.i	−0.958868	+	0.833523i
$497$	120626.			0.488348
$498$		0			0
$499$		−	353378.i		−	1.41918i	−0.704613	−	0.709592i	$-0.748879\pi$
$499$		−	353378.i		−	1.41918i	0.704613	−	0.709592i	$-0.251121\pi$
$500$	172553.	−	378631.i	0.690214	−	1.51453i
$501$		0			0
$502$	−50384.8	−	78332.2i	−0.199937	−	0.310837i
$503$			173765.i			0.686793i	0.939190	+	0.343397i	$0.111578\pi$
$503$			173765.i			0.686793i	−0.939190	+	0.343397i	$0.888422\pi$
$504$		0			0
$505$	−102242.			−0.400908
$506$	−328648.	+	211393.i	−1.28360	+	0.825638i
$507$		0			0
$508$	107137.	+	48825.4i	0.415156	+	0.189199i
$509$	427247.			1.64909			0.824543	−	0.565800i	$-0.191432\pi$
$509$	427247.			1.64909			0.824543	+	0.565800i	$0.191432\pi$
$510$		0			0
$511$			45805.5i			0.175419i
$512$	−109746.	−	238066.i	−0.418649	−	0.908148i
$513$		0			0
$514$	−398345.	+	256224.i	−1.50776	+	0.969824i
$515$			365175.i			1.37685i
$516$		0			0
$517$	−418027.			−1.56395
$518$	19062.0	+	29635.3i	0.0710410	+	0.110446i
$519$		0			0
$520$	−77383.3	−	533718.i	−0.286181	−	1.97381i
$521$	−238355.			−0.878111			−0.439056	−	0.898460i	$-0.644687\pi$
$521$	−238355.			−0.878111			−0.439056	+	0.898460i	$0.644687\pi$
$522$		0			0
$523$			65331.4i			0.238846i	0.992843	+	0.119423i	$0.0381045\pi$
$523$			65331.4i			0.238846i	−0.992843	+	0.119423i	$0.961895\pi$
$524$	124744.	+	56849.6i	0.454315	+	0.207045i
$525$		0			0
$526$	−96130.1	−	149451.i	−0.347446	−	0.540168i
$527$		−	370790.i		−	1.33508i
$528$		0			0
$529$	62361.6			0.222847
$530$	−29905.1	+	19235.6i	−0.106462	+	0.0684783i
$531$		0			0
$532$	−25733.5	+	56466.6i	−0.0909234	+	0.199512i
$533$	−39843.5			−0.140250
$534$		0			0
$535$		−	412491.i		−	1.44114i
$536$	−465423.	+	67481.2i	−1.62001	+	0.234884i
$537$		0			0
$538$	−187782.	+	120785.i	−0.648769	+	0.417301i
$539$		−	461236.i		−	1.58762i
$540$		0			0
$541$	343182.			1.17255			0.586273	−	0.810113i	$-0.300595\pi$
$541$	343182.			1.17255			0.586273	+	0.810113i	$0.300595\pi$
$542$	212714.	+	330703.i	0.724100	+	1.12574i
$543$		0			0
$544$	298552.	+	87022.2i	1.00884	+	0.294057i
$545$	−497313.			−1.67431
$546$		0			0
$547$		−	135514.i		−	0.452908i	−0.974022	−	0.226454i	$-0.927287\pi$
$547$		−	135514.i		−	0.452908i	0.974022	−	0.226454i	$-0.0727133\pi$
$548$	−222842.	+	488979.i	−0.742056	+	1.62828i
$549$		0			0
$550$	557091.	+	866097.i	1.84162	+	2.86313i
$551$		−	120863.i		−	0.398098i
$552$		0			0
$553$	−86904.8			−0.284180
$554$	−374450.	+	240854.i	−1.22004	+	0.784755i
$555$		0			0
$556$	−125771.	−	57317.6i	−0.406847	−	0.185412i
$557$	64031.9			0.206389			0.103194	−	0.994661i	$-0.467094\pi$
$557$	64031.9			0.206389			0.103194	+	0.994661i	$0.467094\pi$
$558$		0			0
$559$			82081.3i			0.262676i
$560$	−117414.	+	102065.i	−0.374407	+	0.325464i
$561$		0			0
$562$	84093.0	−	54090.3i	0.266248	−	0.171256i
$563$		−	53438.7i		−	0.168593i	−0.996441	−	0.0842964i	$-0.973136\pi$
$563$		−	53438.7i		−	0.168593i	0.996441	−	0.0842964i	$-0.0268643\pi$
$564$		0			0
$565$	940976.			2.94769
$566$	66127.9	+	102808.i	0.206420	+	0.320917i
$567$		0			0
$568$	−541326.	+	78486.3i	−1.67788	+	0.243275i
$569$	225959.			0.697919			0.348960	−	0.937138i	$-0.386535\pi$
$569$	225959.			0.697919			0.348960	+	0.937138i	$0.386535\pi$
$570$		0			0
$571$		−	472292.i		−	1.44857i	−0.689502	−	0.724284i	$-0.742171\pi$
$571$		−	472292.i		−	1.44857i	0.689502	−	0.724284i	$-0.257829\pi$
$572$	596878.	+	272015.i	1.82429	+	0.831381i
$573$		0			0
$574$	6217.88	+	9666.80i	0.0188720	+	0.0293399i
$575$			573130.i			1.73348i
$576$		0			0
$577$	376338.			1.13038			0.565192	−	0.824959i	$-0.308802\pi$
$577$	376338.			1.13038			0.565192	+	0.824959i	$0.308802\pi$
$578$	−29286.2	+	18837.5i	−0.0876613	+	0.0563855i
$579$		0			0
$580$	125658.	−	275730.i	0.373539	−	0.819650i
$581$	−3020.23			−0.00894722
$582$		0			0
$583$		−	43247.6i		−	0.127240i
$584$	−29803.6	−	205558.i	−0.0873864	−	0.602710i
$585$		0			0
$586$	165601.	−	106518.i	0.482245	−	0.310190i
$587$		−	282756.i		−	0.820608i	−0.911949	−	0.410304i	$-0.865423\pi$
$587$		−	282756.i		−	0.820608i	0.911949	−	0.410304i	$-0.134577\pi$
$588$		0			0
$589$	−335509.			−0.967104
$590$	−216334.	−	336330.i	−0.621472	−	0.966189i
$591$		0			0
$592$	−104826.	−	120589.i	−0.299105	−	0.344085i
$593$	439919.			1.25102			0.625508	−	0.780217i	$-0.284892\pi$
$593$	439919.			1.25102			0.625508	+	0.780217i	$0.284892\pi$
$594$		0			0
$595$		−	184555.i		−	0.521305i
$596$	−159883.	+	350829.i	−0.450101	+	0.987651i
$597$		0			0
$598$	197489.	+	307031.i	0.552255	+	0.858579i
$599$			384400.i			1.07135i	0.844425	+	0.535673i	$0.179942\pi$
$599$			384400.i			1.07135i	−0.844425	+	0.535673i	$0.820058\pi$
$600$		0			0
$601$	−495470.			−1.37173			−0.685864	−	0.727730i	$-0.740576\pi$
$601$	−495470.			−1.37173			−0.685864	+	0.727730i	$0.740576\pi$
$602$	19914.5	−	12809.4i	0.0549512	−	0.0353457i
$603$		0			0
$604$	386008.	+	175915.i	1.05809	+	0.482203i
$605$	−1.25908e6			−3.43986
$606$		0			0
$607$			630975.i			1.71252i	0.516549	+	0.856258i	$0.327216\pi$
$607$			630975.i			1.71252i	−0.516549	+	0.856258i	$0.672784\pi$
$608$	78741.9	−	270145.i	0.213009	−	0.730784i
$609$		0			0
$610$	201651.	−	129706.i	0.541926	−	0.348577i
$611$			390531.i			1.04610i
$612$		0			0
$613$	−256888.			−0.683634			−0.341817	−	0.939767i	$-0.611042\pi$
$613$	−256888.			−0.683634			−0.341817	+	0.939767i	$0.611042\pi$
$614$	−311321.	−	484004.i	−0.825794	−	1.28384i
$615$		0			0
$616$	−27151.2	−	187264.i	−0.0715530	−	0.493506i
$617$	−115496.			−0.303387			−0.151694	−	0.988428i	$-0.548473\pi$
$617$	−115496.			−0.303387			−0.151694	+	0.988428i	$0.548473\pi$
$618$		0			0
$619$			229059.i			0.597814i	0.954282	+	0.298907i	$0.0966221\pi$
$619$			229059.i			0.597814i	−0.954282	+	0.298907i	$0.903378\pi$
$620$	−765412.	−	348821.i	−1.99119	−	0.907442i
$621$		0			0
$622$	−313051.	−	486693.i	−0.809159	−	1.25798i
$623$		−	119112.i		−	0.306887i
$624$		0			0
$625$	351652.			0.900230
$626$	−270295.	+	173859.i	−0.689746	+	0.443658i
$627$		0			0
$628$	−220227.	+	483241.i	−0.558408	+	1.22531i
$629$	189546.			0.479085
$630$		0			0
$631$			481121.i			1.20836i	0.796849	+	0.604178i	$0.206499\pi$
$631$			481121.i			1.20836i	−0.796849	+	0.604178i	$0.793501\pi$
$632$	389996.	−	56545.2i	0.976396	−	0.141567i
$633$		0			0
$634$	−486433.	+	312883.i	−1.21016	+	0.778402i
$635$			316847.i			0.785781i
$636$		0			0
$637$	−430898.			−1.06193
$638$	199375.	+	309964.i	0.489812	+	0.761501i
$639$		0			0
$640$	460501.	−	534428.i	1.12427	−	1.30475i
$641$	−476453.			−1.15959			−0.579794	−	0.814763i	$-0.696867\pi$
$641$	−476453.			−1.15959			−0.579794	+	0.814763i	$0.696867\pi$
$642$		0			0
$643$		−	416293.i		−	1.00688i	−0.864030	−	0.503440i	$-0.832068\pi$
$643$		−	416293.i		−	1.00688i	0.864030	−	0.503440i	$-0.167932\pi$
$644$	43672.1	−	95829.1i	0.105301	−	0.231061i
$645$		0			0
$646$	180579.	+	280742.i	0.432715	+	0.672733i
$647$			18567.6i			0.0443554i	0.999754	+	0.0221777i	$0.00705996\pi$
$647$			18567.6i			0.0443554i	−0.999754	+	0.0221777i	$0.992940\pi$
$648$		0			0
$649$	486388.			1.15476
$650$	809130.	−	520448.i	1.91510	−	1.23183i
$651$		0			0
$652$	322284.	+	146874.i	0.758130	+	0.345502i
$653$	462788.			1.08531			0.542657	−	0.839954i	$-0.317418\pi$
$653$	462788.			1.08531			0.542657	+	0.839954i	$0.317418\pi$
$654$		0			0
$655$			368918.i			0.859899i
$656$	−34193.3	−	39335.3i	−0.0794571	−	0.0914059i
$657$		0			0
$658$	94750.4	−	60945.3i	0.218841	−	0.140763i
$659$		−	602985.i		−	1.38847i	−0.719749	−	0.694234i	$-0.755743\pi$
$659$		−	602985.i		−	1.38847i	0.719749	−	0.694234i	$-0.244257\pi$
$660$		0			0
$661$	412862.			0.944935			0.472468	−	0.881348i	$-0.343363\pi$
$661$	412862.			0.944935			0.472468	+	0.881348i	$0.343363\pi$
$662$	−193683.	−	301115.i	−0.441952	−	0.687094i
$663$		0			0
$664$	13553.7	−	1965.13i	0.0307412	−	0.00445713i
$665$	−166994.			−0.377623
$666$		0			0
$667$			205116.i			0.461049i
$668$	454745.	+	207241.i	1.01910	+	0.464432i
$669$		0			0
$670$	−684657.	−	1.06442e6i	−1.52519	−	2.37118i
$671$			291619.i			0.647696i
$672$		0			0
$673$	−372998.			−0.823525			−0.411763	−	0.911291i	$-0.635087\pi$
$673$	−372998.			−0.823525			−0.411763	+	0.911291i	$0.635087\pi$
$674$	452234.	−	290886.i	0.995506	−	0.640329i
$675$		0			0
$676$	64617.0	−	141788.i	0.141401	−	0.310275i
$677$	359783.			0.784989			0.392494	−	0.919754i	$-0.371612\pi$
$677$	359783.			0.784989			0.392494	+	0.919754i	$0.371612\pi$
$678$		0			0
$679$			14431.3i			0.0313015i
$680$	120082.	+	828214.i	0.259693	+	1.79112i
$681$		0			0
$682$	860444.	−	553454.i	1.84992	−	1.18991i
$683$			107389.i			0.230206i	0.993354	+	0.115103i	$0.0367199\pi$
$683$			107389.i			0.230206i	−0.993354	+	0.115103i	$0.963280\pi$
$684$		0			0
$685$	−1.44611e6			−3.08191
$686$	140574.	+	218547.i	0.298714	+	0.464404i
$687$		0			0
$688$	−81034.3	+	70441.3i	−0.171195	+	0.148816i
$689$	−40403.0			−0.0851090
$690$		0			0
$691$		−	617454.i		−	1.29315i	−0.762851	−	0.646574i	$-0.776201\pi$
$691$		−	617454.i		−	1.29315i	0.762851	−	0.646574i	$-0.223799\pi$
$692$	−130727.	+	286851.i	−0.272993	+	0.599025i
$693$		0			0
$694$	−158154.	−	245879.i	−0.328369	−	0.510509i
$695$		−	371956.i		−	0.770054i
$696$		0			0
$697$	61828.4			0.127269
$698$	182462.	−	117363.i	0.374508	−	0.240891i
$699$		0			0
$700$	−252542.	−	115091.i	−0.515391	−	0.234879i
$701$	486515.			0.990057			0.495028	−	0.868877i	$-0.335158\pi$
$701$	486515.			0.990057			0.495028	+	0.868877i	$0.335158\pi$
$702$		0			0
$703$		−	171510.i		−	0.347040i
$704$	243689.	+	822704.i	0.491689	+	1.65996i
$705$		0			0
$706$	97667.0	−	62821.3i	0.195947	−	0.126037i
$707$			33513.6i			0.0670475i
$708$		0			0
$709$	−144205.			−0.286872			−0.143436	−	0.989660i	$-0.545815\pi$
$709$	−144205.			−0.286872			−0.143436	+	0.989660i	$0.545815\pi$
$710$	−796314.	−	1.23801e6i	−1.57967	−	2.45589i
$711$		0			0
$712$	77500.9	+	534529.i	0.152879	+	1.05441i
$713$	569390.			1.12003
$714$		0			0
$715$			1.76521e6i			3.45289i
$716$	−13567.4	−	6183.06i	−0.0264649	−	0.0120608i
$717$		0			0
$718$	−19902.5	−	30942.0i	−0.0386063	−	0.0600204i
$719$		−	978439.i		−	1.89268i	−0.323179	−	0.946338i	$-0.604752\pi$
$719$		−	978439.i		−	1.89268i	0.323179	−	0.946338i	$-0.395248\pi$
$720$		0			0
$721$	119700.			0.230263
$722$	−184391.	+	118604.i	−0.353725	+	0.227523i
$723$		0			0
$724$	54421.3	−	119416.i	0.103822	−	0.227816i
$725$	540548.			1.02839
$726$		0			0
$727$			650971.i			1.23166i	0.787877	+	0.615832i	$0.211180\pi$
$727$			650971.i			1.23166i	−0.787877	+	0.615832i	$0.788820\pi$
$728$	−174947.	+	25365.4i	−0.330098	+	0.0478606i
$729$		0			0
$730$	470111.	−	302385.i	0.882175	−	0.567432i
$731$		−	127372.i		−	0.238364i
$732$		0			0
$733$	−502166.			−0.934629			−0.467315	−	0.884091i	$-0.654778\pi$
$733$	−502166.			−0.934629			−0.467315	+	0.884091i	$0.654778\pi$
$734$	208018.	+	323401.i	0.386108	+	0.600274i
$735$		0			0
$736$	−133632.	+	458461.i	−0.246692	+	0.846343i
$737$	1.53933e6			2.83397
$738$		0			0
$739$		−	143898.i		−	0.263491i	−0.991284	−	0.131745i	$-0.957942\pi$
$739$		−	143898.i		−	0.263491i	0.991284	−	0.131745i	$-0.0420581\pi$
$740$	178315.	−	391274.i	0.325631	−	0.714526i
$741$		0			0
$742$	6305.20	+	9802.55i	0.0114522	+	0.0178046i
$743$		−	639135.i		−	1.15775i	−0.815416	−	0.578876i	$-0.803492\pi$
$743$		−	639135.i		−	1.15775i	0.815416	−	0.578876i	$-0.196508\pi$
$744$		0			0
$745$	−1.03754e6			−1.86936
$746$	93284.0	−	60002.1i	0.167621	−	0.107817i
$747$		0			0
$748$	−926223.	−	422107.i	−1.65544	−	0.754431i
$749$	−135210.			−0.241015
$750$		0			0
$751$			494004.i			0.875892i	0.899001	+	0.437946i	$0.144294\pi$
$751$			494004.i			0.875892i	−0.899001	+	0.437946i	$0.855706\pi$
$752$	−385549.	+	335150.i	−0.681780	+	0.592656i
$753$		0			0
$754$	289577.	−	186261.i	0.509355	−	0.327627i
$755$			1.14158e6i			2.00268i
$756$		0			0
$757$	−207090.			−0.361382			−0.180691	−	0.983540i	$-0.557833\pi$
$757$	−207090.			−0.361382			−0.180691	+	0.983540i	$0.557833\pi$
$758$	220508.	+	342819.i	0.383784	+	0.596660i
$759$		0			0
$760$	749408.	−	108656.i	1.29745	−	0.188116i
$761$	−584487.			−1.00927			−0.504633	−	0.863334i	$-0.668372\pi$
$761$	−584487.			−1.00927			−0.504633	+	0.863334i	$0.668372\pi$
$762$		0			0
$763$			163013.i			0.280011i
$764$	−47807.9	−	21787.4i	−0.0819054	−	0.0373267i
$765$		0			0
$766$	13549.8	+	21065.6i	0.0230927	+	0.0359017i
$767$		−	454396.i		−	0.772402i
$768$		0			0
$769$	521698.			0.882200			0.441100	−	0.897458i	$-0.354588\pi$
$769$	521698.			0.882200			0.441100	+	0.897458i	$0.354588\pi$
$770$	428273.	−	275474.i	0.722336	−	0.464621i
$771$		0			0
$772$	468879.	−	1.02885e6i	0.786731	−	1.72631i
$773$	−810366.			−1.35620			−0.678098	−	0.734971i	$-0.737196\pi$
$773$	−810366.			−1.35620			−0.678098	+	0.734971i	$0.737196\pi$
$774$		0			0
$775$		−	1.50053e6i		−	2.49828i
$776$	−9389.81	−	64762.2i	−0.0155931	−	0.107547i
$777$		0			0
$778$	−497185.	+	319799.i	−0.821408	+	0.528346i
$779$		−	55945.3i		−	0.0921911i
$780$		0			0
$781$	1.79037e6			2.93521
$782$	−306459.	−	476445.i	−0.501140	−	0.779111i
$783$		0			0
$784$	−369792.	−	425402.i	−0.601625	−	0.692098i
$785$	−1.42914e6			−2.31918
$786$		0			0
$787$			380693.i			0.614646i	0.951605	+	0.307323i	$0.0994332\pi$
$787$			380693.i			0.614646i	−0.951605	+	0.307323i	$0.900567\pi$
$788$	98632.3	−	216427.i	0.158842	−	0.348546i
$789$		0			0
$790$	573702.	+	891922.i	0.919246	+	1.42913i
$791$		−	308441.i		−	0.492969i
$792$		0			0
$793$	272438.			0.433233
$794$	480864.	−	309301.i	0.762749	−	0.490615i
$795$		0			0
$796$	930024.	+	423839.i	1.46780	+	0.668921i
$797$	174404.			0.274562			0.137281	−	0.990532i	$-0.456164\pi$
$797$	174404.			0.274562			0.137281	+	0.990532i	$0.456164\pi$
$798$		0			0
$799$		−	606018.i		−	0.949276i
$800$	1.20820e6	+	352166.i	1.88781	+	0.550259i
$801$		0			0
$802$	60795.6	−	39104.9i	0.0945199	−	0.0607971i
$803$			679856.i			1.05435i
$804$		0			0
$805$	283405.			0.437337
$806$	−517051.	−	803848.i	−0.795909	−	1.23738i
$807$		0			0
$808$	−21805.9	−	150397.i	−0.0334003	−	0.230364i
$809$	−334685.			−0.511375			−0.255688	−	0.966759i	$-0.582302\pi$
$809$	−334685.			−0.511375			−0.255688	+	0.966759i	$0.582302\pi$
$810$		0			0
$811$			1.01253e6i			1.53946i	0.638372	+	0.769728i	$0.279608\pi$
$811$			1.01253e6i			1.53946i	−0.638372	+	0.769728i	$0.720392\pi$
$812$	−90381.2	−	41189.4i	−0.137077	−	0.0624702i
$813$		0			0
$814$	282923.	+	439854.i	0.426992	+	0.663835i
$815$			953122.i			1.43494i
$816$		0			0
$817$	−115253.			−0.172666
$818$	−560977.	+	360831.i	−0.838375	+	0.539259i
$819$		0			0
$820$	58165.1	−	127631.i	0.0865037	−	0.189814i
$821$	−672538.			−0.997770			−0.498885	−	0.866668i	$-0.666257\pi$
$821$	−672538.			−0.997770			−0.498885	+	0.866668i	$0.666257\pi$
$822$		0			0
$823$		−	790727.i		−	1.16742i	−0.811962	−	0.583710i	$-0.801601\pi$
$823$		−	790727.i		−	1.16742i	0.811962	−	0.583710i	$-0.198399\pi$
$824$	−537169.	+	77883.6i	−0.791145	+	0.114707i
$825$		0			0
$826$	−110245.	+	70911.9i	−0.161584	+	0.103934i
$827$			688532.i			1.00673i	0.864074	+	0.503365i	$0.167905\pi$
$827$			688532.i			1.00673i	−0.864074	+	0.503365i	$0.832095\pi$
$828$		0			0
$829$	301250.			0.438348			0.219174	−	0.975686i	$-0.429664\pi$
$829$	301250.			0.438348			0.219174	+	0.975686i	$0.429664\pi$
$830$	19938.0	+	30997.2i	0.0289418	+	0.0449953i
$831$		0			0
$832$	768591.	−	227660.i	1.11032	−	0.328883i
$833$	668660.			0.963641
$834$		0			0
$835$			1.34486e6i			1.92888i
$836$	−381943.	+	838092.i	−0.546495	+	1.19917i
$837$		0			0
$838$	−52081.3	−	80969.7i	−0.0741641	−	0.115301i
$839$		−	269219.i		−	0.382456i	−0.981546	−	0.191228i	$-0.938753\pi$
$839$		−	269219.i		−	0.382456i	0.981546	−	0.191228i	$-0.0612470\pi$
$840$		0			0
$841$	−513826.			−0.726481
$842$	381707.	−	245522.i	0.538401	−	0.346310i
$843$		0			0
$844$	−969783.	−	441959.i	−1.36141	−	0.620436i
$845$	419324.			0.587268
$846$		0			0
$847$			412710.i			0.575279i
$848$	−34673.4	−	39887.7i	−0.0482176	−	0.0554685i
$849$		0			0
$850$	−1.25559e6	+	807621.i	−1.73784	+	1.11782i
$851$			291069.i			0.401917i
$852$		0			0
$853$	379053.			0.520957			0.260478	−	0.965480i	$-0.416120\pi$
$853$	379053.			0.520957			0.260478	+	0.965480i	$0.416120\pi$
$854$	−42516.0	−	66098.7i	−0.0582957	−	0.0906311i
$855$		0			0
$856$	606771.	−	87975.1i	0.828089	−	0.120064i
$857$	818271.			1.11413			0.557064	−	0.830469i	$-0.311928\pi$
$857$	818271.			1.11413			0.557064	+	0.830469i	$0.311928\pi$
$858$		0			0
$859$		−	1.16384e6i		−	1.57727i	−0.614862	−	0.788635i	$-0.710788\pi$
$859$		−	1.16384e6i		−	1.57727i	0.614862	−	0.788635i	$-0.289212\pi$
$860$	−262931.	−	119825.i	−0.355504	−	0.162014i
$861$		0			0
$862$	−334191.	−	519559.i	−0.449759	−	0.699230i
$863$			1.11517e6i			1.49734i	0.662945	+	0.748668i	$0.269306\pi$
$863$			1.11517e6i			1.49734i	−0.662945	+	0.748668i	$0.730694\pi$
$864$		0			0
$865$	−848334.			−1.13380
$866$	−418710.	+	269322.i	−0.558313	+	0.359118i
$867$		0			0
$868$	−114339.	+	250893.i	−0.151760	+	0.333004i
$869$	−1.28986e6			−1.70806
$870$		0			0
$871$		−	1.43808e6i		−	1.89560i
$872$	−106066.	−	731543.i	−0.139490	−	0.962070i
$873$		0			0
$874$	−431111.	+	277299.i	−0.564373	+	0.363016i
$875$		−	367046.i		−	0.479407i
$876$		0			0
$877$	−573209.			−0.745270			−0.372635	−	0.927978i	$-0.621546\pi$
$877$	−573209.			−0.745270			−0.372635	+	0.927978i	$0.621546\pi$
$878$	217655.	+	338384.i	0.282345	+	0.438956i
$879$		0			0
$880$	−1.74269e6	+	1.51488e6i	−2.25037	+	1.95620i
$881$	−517273.			−0.666451			−0.333226	−	0.942847i	$-0.608137\pi$
$881$	−517273.			−0.666451			−0.333226	+	0.942847i	$0.608137\pi$
$882$		0			0
$883$		−	1.38647e6i		−	1.77824i	−0.457678	−	0.889118i	$-0.651319\pi$
$883$		−	1.38647e6i		−	1.77824i	0.457678	−	0.889118i	$-0.348681\pi$
$884$	−394343.	+	865301.i	−0.504626	+	1.10729i
$885$		0			0
$886$	423288.	+	658077.i	0.539223	+	0.838318i
$887$		−	1.30999e6i		−	1.66503i	−0.554005	−	0.832513i	$-0.686901\pi$
$887$		−	1.30999e6i		−	1.66503i	0.554005	−	0.832513i	$-0.313099\pi$
$888$		0			0
$889$	103859.			0.131413
$890$	−1.22247e6	+	786316.i	−1.54333	+	0.992698i
$891$		0			0
$892$	−699929.	−	318978.i	−0.879679	−	0.400896i
$893$	−548355.			−0.687637
$894$		0			0
$895$		−	40124.2i		−	0.0500911i
$896$	−175179.	−	150947.i	−0.218206	−	0.188022i
$897$		0			0
$898$	−158585.	+	102005.i	−0.196657	+	0.126494i
$899$		−	537019.i		−	0.664463i
$900$		0			0
$901$	62696.6			0.0772315
$902$	92287.3	+	143477.i	0.113430	+	0.176348i
$903$		0			0
$904$	200689.	+	1.38417e6i	0.245577	+	1.69376i
$905$	353160.			0.431196
$906$		0			0
$907$			947897.i			1.15225i	0.817362	+	0.576125i	$0.195436\pi$
$907$			947897.i			1.15225i	−0.817362	+	0.576125i	$0.804564\pi$
$908$	275758.	+	125671.i	0.334469	+	0.152427i
$909$		0			0
$910$	−257354.	−	400103.i	−0.310777	−	0.483158i
$911$			1.17071e6i			1.41062i	0.708898	+	0.705311i	$0.249193\pi$
$911$			1.17071e6i			1.41062i	−0.708898	+	0.705311i	$0.750807\pi$
$912$		0			0
$913$	−44827.0			−0.0537772
$914$	149436.	−	96120.2i	0.178880	−	0.115059i
$915$		0			0
$916$	2320.56	−	5091.96i	0.00276568	−	0.00606868i
$917$	120927.			0.143809
$918$		0			0
$919$		−	949625.i		−	1.12440i	−0.827001	−	0.562200i	$-0.809955\pi$
$919$		−	949625.i		−	1.12440i	0.827001	−	0.562200i	$-0.190045\pi$
$920$	−1.27181e6	+	184399.i	−1.50262	+	0.217863i
$921$		0			0
$922$	637158.	−	409833.i	0.749524	−	0.482108i
$923$		−	1.67261e6i		−	1.96332i
$924$		0			0
$925$	767063.			0.896495
$926$	316334.	+	491798.i	0.368913	+	0.573542i
$927$		0			0
$928$	432397.	+	126035.i	0.502096	+	0.146351i
$929$	−314076.			−0.363918			−0.181959	−	0.983306i	$-0.558244\pi$
$929$	−314076.			−0.363918			−0.181959	+	0.983306i	$0.558244\pi$
$930$		0			0
$931$		−	605036.i		−	0.698042i
$932$	−49956.8	+	109620.i	−0.0575126	+	0.126199i
$933$		0			0
$934$	315509.	+	490515.i	0.361675	+	0.562288i
$935$		−	2.73921e6i		−	3.13330i
$936$		0			0
$937$	1.50272e6			1.71159			0.855795	−	0.517315i	$-0.173069\pi$
$937$	1.50272e6			1.71159			0.855795	+	0.517315i	$0.173069\pi$
$938$	−348905.	+	224423.i	−0.396554	+	0.255071i
$939$		0			0
$940$	−1.25099e6	−	570112.i	−1.41579	−	0.645215i
$941$	71086.4			0.0802800			0.0401400	−	0.999194i	$-0.487220\pi$
$941$	71086.4			0.0802800			0.0401400	+	0.999194i	$0.487220\pi$
$942$		0			0
$943$			94944.4i			0.106769i
$944$	448600.	−	389957.i	0.503402	−	0.437596i
$945$		0			0
$946$	295576.	−	190120.i	0.330284	−	0.212445i
$947$			1.58311e6i			1.76527i	0.470058	+	0.882636i	$0.344233\pi$
$947$			1.58311e6i			1.76527i	−0.470058	+	0.882636i	$0.655767\pi$
$948$		0			0
$949$	635139.			0.705239
$950$	730775.	+	1.13612e6i	0.809723	+	1.25886i
$951$		0			0
$952$	271479.	−	39361.5i	0.299545	−	0.0434308i
$953$	−1.05600e6			−1.16273			−0.581367	−	0.813642i	$-0.697482\pi$
$953$	−1.05600e6			−1.16273			−0.581367	+	0.813642i	$0.697482\pi$
$954$		0			0
$955$		−	141387.i		−	0.155025i
$956$	777394.	+	354281.i	0.850600	+	0.387643i
$957$		0			0
$958$	−793571.	−	1.23375e6i	−0.864679	−	1.34430i
$959$			474017.i			0.515415i
$960$		0			0
$961$	−567215.			−0.614188
$962$	410923.	−	264314.i	0.444028	−	0.285608i
$963$		0			0
$964$	−584938.	+	1.28352e6i	−0.629442	+	1.38117i
$965$	3.04273e6			3.26745
$966$		0			0
$967$		−	104102.i		−	0.111328i	−0.998450	−	0.0556642i	$-0.982272\pi$
$967$		−	104102.i		−	0.111328i	0.998450	−	0.0556642i	$-0.0177276\pi$
$968$	−268533.	−	1.85209e6i	−0.286580	−	1.97657i
$969$		0			0
$970$	148111.	−	95268.1i	0.157414	−	0.101252i
$971$			865558.i			0.918032i	0.888428	+	0.459016i	$0.151798\pi$
$971$			865558.i			0.918032i	−0.888428	+	0.459016i	$0.848202\pi$
$972$		0			0
$973$	−121923.			−0.128783
$974$	−437177.	−	679670.i	−0.460829	−	0.716441i
$975$		0			0
$976$	233803.	+	268963.i	0.245443	+	0.282353i
$977$	−303107.			−0.317546			−0.158773	−	0.987315i	$-0.550754\pi$
$977$	−303107.			−0.317546			−0.158773	+	0.987315i	$0.550754\pi$
$978$		0			0
$979$		−	1.76789e6i		−	1.84454i
$980$	629042.	−	1.38030e6i	0.654979	−	1.43721i
$981$		0			0
$982$	496503.	+	771903.i	0.514872	+	0.800460i
$983$		−	769392.i		−	0.796234i	−0.917335	−	0.398117i	$-0.869664\pi$
$983$		−	769392.i		−	0.796234i	0.917335	−	0.398117i	$-0.130336\pi$
$984$		0			0
$985$	640062.			0.659705
$986$	−449359.	+	289037.i	−0.462211	+	0.297303i
$987$		0			0
$988$	782967.	+	356821.i	0.802101	+	0.365541i
$989$	195594.			0.199969
$990$		0			0
$991$			885320.i			0.901473i	0.892657	+	0.450737i	$0.148839\pi$
$991$			885320.i			0.901473i	−0.892657	+	0.450737i	$0.851161\pi$
$992$	349867.	−	1.20031e6i	0.355533	−	1.21975i
$993$		0			0
$994$	−405806.	+	261023.i	−0.410720	+	0.264183i
$995$			2.75045e6i			2.77817i
$996$		0			0
$997$	−1.24546e6			−1.25297			−0.626483	−	0.779435i	$-0.715506\pi$
$997$	−1.24546e6			−1.25297			−0.626483	+	0.779435i	$0.715506\pi$
$998$	764673.	+	1.18882e6i	0.767741	+	1.19359i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.d.a.55.4	yes	16
3.2	odd	2	inner	108.5.d.a.55.13	yes	16
4.3	odd	2	inner	108.5.d.a.55.3	✓	16
12.11	even	2	inner	108.5.d.a.55.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.d.a.55.3	✓	16	4.3	odd	2	inner
108.5.d.a.55.4	yes	16	1.1	even	1	trivial
108.5.d.a.55.13	yes	16	3.2	odd	2	inner
108.5.d.a.55.14	yes	16	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(-3.36416 + 2.16389i) q^{2} +(6.63513 - 14.5594i) q^{4} +43.0579 q^{5} -14.1139i q^{7} +(9.18328 + 63.3377i) q^{8} +O(q^{10})\)	\(q+(-3.36416 + 2.16389i) q^{2} +(6.63513 - 14.5594i) q^{4} +43.0579 q^{5} -14.1139i q^{7} +(9.18328 + 63.3377i) q^{8} +(-144.853 + 93.1726i) q^{10} -209.481i q^{11} -195.703 q^{13} +(30.5409 + 47.4813i) q^{14} +(-167.950 - 193.207i) q^{16} +303.688 q^{17} -274.792i q^{19} +(285.694 - 626.895i) q^{20} +(453.296 + 704.729i) q^{22} +466.347i q^{23} +1228.98 q^{25} +(658.376 - 423.480i) q^{26} +(-205.489 - 93.6473i) q^{28} +439.835 q^{29} -1220.96i q^{31} +(983.089 + 286.551i) q^{32} +(-1021.65 + 657.148i) q^{34} -607.713i q^{35} +624.147 q^{37} +(594.620 + 924.443i) q^{38} +(395.412 + 2727.19i) q^{40} +203.592 q^{41} -419.418i q^{43} +(-3049.92 - 1389.94i) q^{44} +(-1009.12 - 1568.86i) q^{46} -1995.53i q^{47} +2201.80 q^{49} +(-4134.48 + 2659.38i) q^{50} +(-1298.51 + 2849.31i) q^{52} +206.451 q^{53} -9019.82i q^{55} +(893.940 - 129.612i) q^{56} +(-1479.67 + 951.756i) q^{58} +2321.87i q^{59} -1392.10 q^{61} +(2642.02 + 4107.49i) q^{62} +(-3927.33 + 1163.30i) q^{64} -8426.55 q^{65} +7348.27i q^{67} +(2015.01 - 4421.50i) q^{68} +(1315.03 + 2044.44i) q^{70} +8546.65i q^{71} -3245.43 q^{73} +(-2099.73 + 1350.59i) q^{74} +(-4000.79 - 1823.28i) q^{76} -2956.59 q^{77} -6157.41i q^{79} +(-7231.57 - 8319.06i) q^{80} +(-684.915 + 440.551i) q^{82} -213.990i q^{83} +13076.2 q^{85} +(907.576 + 1410.99i) q^{86} +(13268.1 - 1923.73i) q^{88} +8439.35 q^{89} +2762.12i q^{91} +(6789.71 + 3094.27i) q^{92} +(4318.11 + 6713.28i) q^{94} -11831.9i q^{95} -1022.49 q^{97} +(-7407.20 + 4764.46i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{4}+O(q^{10}) \) 16 * q - 14 * q^4	\( 16 q - 14 q^{4} - 202 q^{10} - 352 q^{13} - 206 q^{16} + 738 q^{22} + 1632 q^{25} + 342 q^{28} - 2536 q^{34} + 3200 q^{37} - 2854 q^{40} + 36 q^{46} - 896 q^{49} + 2288 q^{52} + 2492 q^{58} - 2752 q^{61} + 682 q^{64} - 14166 q^{70} + 8240 q^{73} - 33084 q^{76} + 68 q^{82} + 8800 q^{85} + 48294 q^{88} + 52596 q^{94} - 6928 q^{97}+O(q^{100}) \) 16 * q - 14 * q^4 - 202 * q^10 - 352 * q^13 - 206 * q^16 + 738 * q^22 + 1632 * q^25 + 342 * q^28 - 2536 * q^34 + 3200 * q^37 - 2854 * q^40 + 36 * q^46 - 896 * q^49 + 2288 * q^52 + 2492 * q^58 - 2752 * q^61 + 682 * q^64 - 14166 * q^70 + 8240 * q^73 - 33084 * q^76 + 68 * q^82 + 8800 * q^85 + 48294 * q^88 + 52596 * q^94 - 6928 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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