LMFDB - Embedded newform 108.5.d.a.55.10

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			55.10
Root			$0.229644 - 3.68150i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.5.d.a.55.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35962 + 3.76184i) q^{2} +(-12.3029 + 10.2293i) q^{4} -2.66014 q^{5} -88.8835i q^{7} +(-55.2083 - 32.3735i) q^{8} +O(q^{10})$	\(q+(1.35962 + 3.76184i) q^{2} +(-12.3029 + 10.2293i) q^{4} -2.66014 q^{5} -88.8835i q^{7} +(-55.2083 - 32.3735i) q^{8} +(-3.61678 - 10.0070i) q^{10} -72.9595i q^{11} -173.728 q^{13} +(334.365 - 120.848i) q^{14} +(46.7216 - 251.700i) q^{16} +423.661 q^{17} +153.339i q^{19} +(32.7274 - 27.2115i) q^{20} +(274.462 - 99.1971i) q^{22} -723.430i q^{23} -617.924 q^{25} +(-236.203 - 653.536i) q^{26} +(909.218 + 1093.52i) q^{28} -366.864 q^{29} -642.635i q^{31} +(1010.38 - 166.457i) q^{32} +(576.017 + 1593.74i) q^{34} +236.443i q^{35} -535.717 q^{37} +(-576.836 + 208.482i) q^{38} +(146.862 + 86.1181i) q^{40} +2141.50 q^{41} -615.945i q^{43} +(746.327 + 897.612i) q^{44} +(2721.43 - 983.589i) q^{46} -330.667i q^{47} -5499.27 q^{49} +(-840.140 - 2324.53i) q^{50} +(2137.35 - 1777.12i) q^{52} -4628.97 q^{53} +194.083i q^{55} +(-2877.47 + 4907.11i) q^{56} +(-498.795 - 1380.08i) q^{58} +3469.85i q^{59} -4646.40 q^{61} +(2417.49 - 873.738i) q^{62} +(1999.92 + 3574.57i) q^{64} +462.141 q^{65} -6670.10i q^{67} +(-5212.25 + 4333.77i) q^{68} +(-889.460 + 321.472i) q^{70} +6445.22i q^{71} +4735.78 q^{73} +(-728.370 - 2015.28i) q^{74} +(-1568.55 - 1886.51i) q^{76} -6484.89 q^{77} -2085.24i q^{79} +(-124.286 + 669.559i) q^{80} +(2911.62 + 8055.98i) q^{82} -9294.47i q^{83} -1127.00 q^{85} +(2317.09 - 837.450i) q^{86} +(-2361.95 + 4027.97i) q^{88} +5704.72 q^{89} +15441.5i q^{91} +(7400.21 + 8900.27i) q^{92} +(1243.92 - 449.581i) q^{94} -407.903i q^{95} +6975.60 q^{97} +(-7476.91 - 20687.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.35962	+	3.76184i	0.339904	+	0.940460i
$2$	1.35962	+	3.76184i	0.339904	+	0.940460i
$3$		0			0
$3$		0			0
$4$	−12.3029	+	10.2293i	−0.768930	+	0.639333i
$5$	−2.66014			−0.106406			−0.0532029	−	0.998584i	$-0.516943\pi$
$5$	−2.66014			−0.106406			−0.0532029	+	0.998584i	$0.516943\pi$
$6$		0			0
$7$		−	88.8835i		−	1.81395i	−0.421186	−	0.906974i	$-0.638386\pi$
$7$		−	88.8835i		−	1.81395i	0.421186	−	0.906974i	$-0.361614\pi$
$8$	−55.2083	−	32.3735i	−0.862630	−	0.505836i
$9$		0			0
$10$	−3.61678	−	10.0070i	−0.0361678	−	0.100070i
$11$		−	72.9595i		−	0.602971i	−0.953471	−	0.301486i	$-0.902517\pi$
$11$		−	72.9595i		−	0.602971i	0.953471	−	0.301486i	$-0.0974825\pi$
$12$		0			0
$13$	−173.728			−1.02797			−0.513987	−	0.857798i	$-0.671832\pi$
$13$	−173.728			−1.02797			−0.513987	+	0.857798i	$0.671832\pi$
$14$	334.365	−	120.848i	1.70595	−	0.616569i
$15$		0			0
$16$	46.7216	−	251.700i	0.182506	−	0.983205i
$17$	423.661			1.46595			0.732977	−	0.680253i	$-0.238130\pi$
$17$	423.661			1.46595			0.732977	+	0.680253i	$0.238130\pi$
$18$		0			0
$19$			153.339i			0.424761i	0.977187	+	0.212381i	$0.0681216\pi$
$19$			153.339i			0.424761i	−0.977187	+	0.212381i	$0.931878\pi$
$20$	32.7274	−	27.2115i	0.0818186	−	0.0680287i
$21$		0			0
$22$	274.462	−	99.1971i	0.567070	−	0.204953i
$23$		−	723.430i		−	1.36754i	−0.729696	−	0.683771i	$-0.760339\pi$
$23$		−	723.430i		−	1.36754i	0.729696	−	0.683771i	$-0.239661\pi$
$24$		0			0
$25$	−617.924			−0.988678
$26$	−236.203	−	653.536i	−0.349413	−	0.966769i
$27$		0			0
$28$	909.218	+	1093.52i	1.15972	+	1.39480i
$29$	−366.864			−0.436223			−0.218112	−	0.975924i	$-0.569990\pi$
$29$	−366.864			−0.436223			−0.218112	+	0.975924i	$0.569990\pi$
$30$		0			0
$31$		−	642.635i		−	0.668715i	−0.942446	−	0.334357i	$-0.891481\pi$
$31$		−	642.635i		−	0.668715i	0.942446	−	0.334357i	$-0.108519\pi$
$32$	1010.38	−	166.457i	0.986699	−	0.162556i
$33$		0			0
$34$	576.017	+	1593.74i	0.498284	+	1.37867i
$35$			236.443i			0.193015i
$36$		0			0
$37$	−535.717			−0.391320			−0.195660	−	0.980672i	$-0.562685\pi$
$37$	−535.717			−0.391320			−0.195660	+	0.980672i	$0.562685\pi$
$38$	−576.836	+	208.482i	−0.399471	+	0.144378i
$39$		0			0
$40$	146.862	+	86.1181i	0.0917888	+	0.0538238i
$41$	2141.50			1.27394			0.636972	−	0.770887i	$-0.280187\pi$
$41$	2141.50			1.27394			0.636972	+	0.770887i	$0.280187\pi$
$42$		0			0
$43$		−	615.945i		−	0.333123i	−0.986031	−	0.166562i	$-0.946734\pi$
$43$		−	615.945i		−	0.333123i	0.986031	−	0.166562i	$-0.0532665\pi$
$44$	746.327	+	897.612i	0.385499	+	0.463643i
$45$		0			0
$46$	2721.43	−	983.589i	1.28612	−	0.464834i
$47$		−	330.667i		−	0.149691i	−0.997195	−	0.0748454i	$-0.976154\pi$
$47$		−	330.667i		−	0.149691i	0.997195	−	0.0748454i	$-0.0238463\pi$
$48$		0			0
$49$	−5499.27			−2.29041
$50$	−840.140	−	2324.53i	−0.336056	−	0.929812i
$51$		0			0
$52$	2137.35	−	1777.12i	0.790440	−	0.657218i
$53$	−4628.97			−1.64791			−0.823953	−	0.566659i	$-0.808236\pi$
$53$	−4628.97			−1.64791			−0.823953	+	0.566659i	$0.808236\pi$
$54$		0			0
$55$			194.083i			0.0641596i
$56$	−2877.47	+	4907.11i	−0.917560	+	1.56477i
$57$		0			0
$58$	−498.795	−	1380.08i	−0.148274	−	0.410250i
$59$			3469.85i			0.996797i	0.866948	+	0.498399i	$0.166078\pi$
$59$			3469.85i			0.996797i	−0.866948	+	0.498399i	$0.833922\pi$
$60$		0			0
$61$	−4646.40			−1.24870			−0.624348	−	0.781146i	$-0.714635\pi$
$61$	−4646.40			−1.24870			−0.624348	+	0.781146i	$0.714635\pi$
$62$	2417.49	−	873.738i	0.628899	−	0.227299i
$63$		0			0
$64$	1999.92	+	3574.57i	0.488261	+	0.872698i
$65$	462.141			0.109382
$66$		0			0
$67$		−	6670.10i		−	1.48588i	−0.669360	−	0.742938i	$-0.733432\pi$
$67$		−	6670.10i		−	1.48588i	0.669360	−	0.742938i	$-0.266568\pi$
$68$	−5212.25	+	4333.77i	−1.12722	+	0.937233i
$69$		0			0
$70$	−889.460	+	321.472i	−0.181522	+	0.0656065i
$71$			6445.22i			1.27856i	0.768974	+	0.639280i	$0.220768\pi$
$71$			6445.22i			1.27856i	−0.768974	+	0.639280i	$0.779232\pi$
$72$		0			0
$73$	4735.78			0.888682			0.444341	−	0.895858i	$-0.353438\pi$
$73$	4735.78			0.888682			0.444341	+	0.895858i	$0.353438\pi$
$74$	−728.370	−	2015.28i	−0.133011	−	0.368021i
$75$		0			0
$76$	−1568.55	−	1886.51i	−0.271564	−	0.326611i
$77$	−6484.89			−1.09376
$78$		0			0
$79$		−	2085.24i		−	0.334119i	−0.985947	−	0.167059i	$-0.946573\pi$
$79$		−	2085.24i		−	0.334119i	0.985947	−	0.167059i	$-0.0534272\pi$
$80$	−124.286	+	669.559i	−0.0194197	+	0.104619i
$81$		0			0
$82$	2911.62	+	8055.98i	0.433019	+	1.19809i
$83$		−	9294.47i		−	1.34917i	−0.738195	−	0.674587i	$-0.764322\pi$
$83$		−	9294.47i		−	1.34917i	0.738195	−	0.674587i	$-0.235678\pi$
$84$		0			0
$85$	−1127.00			−0.155986
$86$	2317.09	−	837.450i	0.313289	−	0.113230i
$87$		0			0
$88$	−2361.95	+	4027.97i	−0.305004	+	0.520141i
$89$	5704.72			0.720202			0.360101	−	0.932913i	$-0.382742\pi$
$89$	5704.72			0.720202			0.360101	+	0.932913i	$0.382742\pi$
$90$		0			0
$91$			15441.5i			1.86469i
$92$	7400.21	+	8900.27i	0.874315	+	1.05154i
$93$		0			0
$94$	1243.92	−	449.581i	0.140778	−	0.0508805i
$95$		−	407.903i		−	0.0451970i
$96$		0			0
$97$	6975.60			0.741376			0.370688	−	0.928758i	$-0.379122\pi$
$97$	6975.60			0.741376			0.370688	+	0.928758i	$0.379122\pi$
$98$	−7476.91	−	20687.4i	−0.778520	−	2.15404i
$99$		0			0
$100$	7602.24	−	6320.94i	0.760224	−	0.632094i
$101$	14821.3			1.45293			0.726463	−	0.687206i	$-0.241163\pi$
$101$	14821.3			1.45293			0.726463	+	0.687206i	$0.241163\pi$
$102$		0			0
$103$			8686.29i			0.818766i	0.912363	+	0.409383i	$0.134256\pi$
$103$			8686.29i			0.818766i	−0.912363	+	0.409383i	$0.865744\pi$
$104$	9591.21	+	5624.17i	0.886761	+	0.519986i
$105$		0			0
$106$	−6293.62	−	17413.4i	−0.560130	−	1.54979i
$107$			10919.9i			0.953790i	0.878960	+	0.476895i	$0.158238\pi$
$107$			10919.9i			0.953790i	−0.878960	+	0.476895i	$0.841762\pi$
$108$		0			0
$109$	12531.6			1.05476			0.527379	−	0.849630i	$-0.323175\pi$
$109$	12531.6			1.05476			0.527379	+	0.849630i	$0.323175\pi$
$110$	−730.108	+	263.878i	−0.0603395	+	0.0218081i
$111$		0			0
$112$	−22372.0	−	4152.78i	−1.78348	−	0.331057i
$113$	−12299.0			−0.963194			−0.481597	−	0.876393i	$-0.659943\pi$
$113$	−12299.0			−0.963194			−0.481597	+	0.876393i	$0.659943\pi$
$114$		0			0
$115$			1924.43i			0.145514i
$116$	4513.48	−	3752.77i	0.335425	−	0.278892i
$117$		0			0
$118$	−13053.0	+	4717.67i	−0.937448	+	0.338816i
$119$		−	37656.4i		−	2.65916i
$120$		0			0
$121$	9317.91			0.636426
$122$	−6317.33	−	17479.0i	−0.424438	−	1.17435i
$123$		0			0
$124$	6573.72	+	7906.26i	0.427532	+	0.514195i
$125$	3306.36			0.211607
$126$		0			0
$127$		−	22807.9i		−	1.41409i	−0.707167	−	0.707047i	$-0.750027\pi$
$127$		−	22807.9i		−	1.41409i	0.707167	−	0.707047i	$-0.249973\pi$
$128$	−10727.8	+	12383.4i	−0.654775	+	0.755824i
$129$		0			0
$130$	628.335	+	1738.50i	0.0371796	+	0.102870i
$131$			6242.75i			0.363775i	0.983319	+	0.181888i	$0.0582207\pi$
$131$			6242.75i			0.363775i	−0.983319	+	0.181888i	$0.941779\pi$
$132$		0			0
$133$	13629.3			0.770495
$134$	25091.8	−	9068.78i	1.39741	−	0.505056i
$135$		0			0
$136$	−23389.6	−	13715.4i	−1.26458	−	0.741532i
$137$	9530.74			0.507791			0.253896	−	0.967232i	$-0.418288\pi$
$137$	9530.74			0.507791			0.253896	+	0.967232i	$0.418288\pi$
$138$		0			0
$139$		−	11582.2i		−	0.599462i	−0.954024	−	0.299731i	$-0.903103\pi$
$139$		−	11582.2i		−	0.599462i	0.954024	−	0.299731i	$-0.0968970\pi$
$140$	−2418.65	−	2908.93i	−0.123401	−	0.148415i
$141$		0			0
$142$	−24245.9	+	8763.04i	−1.20243	+	0.434588i
$143$			12675.1i			0.619839i
$144$		0			0
$145$	975.910			0.0464167
$146$	6438.86	+	17815.3i	0.302067	+	0.835769i
$147$		0			0
$148$	6590.86	−	5480.03i	0.300898	−	0.250184i
$149$	38532.6			1.73562			0.867811	−	0.496894i	$-0.165526\pi$
$149$	38532.6			1.73562			0.867811	+	0.496894i	$0.165526\pi$
$150$		0			0
$151$			22912.5i			1.00489i	0.864610	+	0.502444i	$0.167566\pi$
$151$			22912.5i			1.00489i	−0.864610	+	0.502444i	$0.832434\pi$
$152$	4964.11	−	8465.57i	0.214859	−	0.366412i
$153$		0			0
$154$	−8816.98	−	24395.1i	−0.371773	−	1.02864i
$155$			1709.50i			0.0711551i
$156$		0			0
$157$	25755.8			1.04490			0.522451	−	0.852669i	$-0.325018\pi$
$157$	25755.8			1.04490			0.522451	+	0.852669i	$0.325018\pi$
$158$	7844.33	−	2835.12i	0.314226	−	0.113569i
$159$		0			0
$160$	−2687.76	+	442.800i	−0.104990	+	0.0172969i
$161$	−64301.0			−2.48065
$162$		0			0
$163$			21920.6i			0.825045i	0.910947	+	0.412522i	$0.135352\pi$
$163$			21920.6i			0.825045i	−0.910947	+	0.412522i	$0.864648\pi$
$164$	−26346.6	+	21906.1i	−0.979573	+	0.814474i
$165$		0			0
$166$	34964.3	−	12636.9i	1.26884	−	0.458591i
$167$		−	3716.35i		−	0.133255i	−0.997778	−	0.0666275i	$-0.978776\pi$
$167$		−	3716.35i		−	0.133255i	0.997778	−	0.0666275i	$-0.0212239\pi$
$168$		0			0
$169$	1620.29			0.0567309
$170$	−1532.29	−	4239.59i	−0.0530203	−	0.146699i
$171$		0			0
$172$	6300.71	+	7577.90i	0.212977	+	0.256148i
$173$	−23829.7			−0.796208			−0.398104	−	0.917340i	$-0.630332\pi$
$173$	−23829.7			−0.796208			−0.398104	+	0.917340i	$0.630332\pi$
$174$		0			0
$175$			54923.2i			1.79341i
$176$	−18363.9	−	3408.79i	−0.592844	−	0.110046i
$177$		0			0
$178$	7756.24	+	21460.3i	0.244800	+	0.677322i
$179$			53055.1i			1.65585i	0.560838	+	0.827926i	$0.310479\pi$
$179$			53055.1i			1.65585i	−0.560838	+	0.827926i	$0.689521\pi$
$180$		0			0
$181$	−38125.2			−1.16374			−0.581869	−	0.813283i	$-0.697678\pi$
$181$	−38125.2			−1.16374			−0.581869	+	0.813283i	$0.697678\pi$
$182$	−58088.5	+	20994.6i	−1.75367	+	0.633817i
$183$		0			0
$184$	−23419.9	+	39939.4i	−0.691752	+	1.17968i
$185$	1425.08			0.0416387
$186$		0			0
$187$		−	30910.1i		−	0.883928i
$188$	3382.50	+	4068.15i	0.0957022	+	0.115102i
$189$		0			0
$190$	1534.47	−	554.592i	0.0425060	−	0.0153627i
$191$		−	19578.7i		−	0.536683i	−0.963324	−	0.268341i	$-0.913525\pi$
$191$		−	19578.7i		−	0.536683i	0.963324	−	0.268341i	$-0.0864755\pi$
$192$		0			0
$193$	10489.3			0.281600			0.140800	−	0.990038i	$-0.455033\pi$
$193$	10489.3			0.281600			0.140800	+	0.990038i	$0.455033\pi$
$194$	9484.15	+	26241.1i	0.251997	+	0.697234i
$195$		0			0
$196$	67656.9	−	56253.9i	1.76116	−	1.46433i
$197$	18533.1			0.477547			0.238773	−	0.971075i	$-0.423255\pi$
$197$	18533.1			0.477547			0.238773	+	0.971075i	$0.423255\pi$
$198$		0			0
$199$		−	66138.9i		−	1.67013i	−0.550150	−	0.835066i	$-0.685430\pi$
$199$		−	66138.9i		−	1.67013i	0.550150	−	0.835066i	$-0.314570\pi$
$200$	34114.5	+	20004.3i	0.852863	+	0.500108i
$201$		0			0
$202$	20151.3	+	55755.4i	0.493856	+	1.36642i
$203$			32608.1i			0.791286i
$204$		0			0
$205$	−5696.69			−0.135555
$206$	−32676.4	+	11810.0i	−0.770017	+	0.278302i
$207$		0			0
$208$	−8116.84	+	43727.3i	−0.187612	+	1.01071i
$209$	11187.5			0.256119
$210$		0			0
$211$		−	25222.6i		−	0.566533i	−0.959041	−	0.283267i	$-0.908582\pi$
$211$		−	25222.6i		−	0.566533i	0.959041	−	0.283267i	$-0.0914182\pi$
$212$	56949.6	−	47351.2i	1.26712	−	1.05356i
$213$		0			0
$214$	−41079.1	+	14846.9i	−0.897001	+	0.324198i
$215$			1638.50i			0.0354462i
$216$		0			0
$217$	−57119.6			−1.21301
$218$	17038.2	+	47141.8i	0.358517	+	0.991958i
$219$		0			0
$220$	−1985.34	−	2387.78i	−0.0410194	−	0.0493342i
$221$	−73601.6			−1.50696
$222$		0			0
$223$		−	14958.0i		−	0.300791i	−0.988626	−	0.150395i	$-0.951945\pi$
$223$		−	14958.0i		−	0.300791i	0.988626	−	0.150395i	$-0.0480547\pi$
$224$	−14795.3	−	89806.1i	−0.294868	−	1.78982i
$225$		0			0
$226$	−16722.0	−	46267.0i	−0.327394	−	0.905845i
$227$		−	26750.1i		−	0.519126i	−0.965726	−	0.259563i	$-0.916421\pi$
$227$		−	26750.1i		−	0.519126i	0.965726	−	0.259563i	$-0.0835785\pi$
$228$		0			0
$229$	−54043.1			−1.03055			−0.515275	−	0.857025i	$-0.672310\pi$
$229$	−54043.1			−1.03055			−0.515275	+	0.857025i	$0.672310\pi$
$230$	−7239.39	+	2616.49i	−0.136850	+	0.0494610i
$231$		0			0
$232$	20253.9	+	11876.7i	0.376299	+	0.220657i
$233$	89436.5			1.64742			0.823708	−	0.567015i	$-0.191902\pi$
$233$	89436.5			1.64742			0.823708	+	0.567015i	$0.191902\pi$
$234$		0			0
$235$			879.621i			0.0159280i
$236$	−35494.2	−	42689.2i	−0.637285	−	0.766467i
$237$		0			0
$238$	141657.	−	51198.4i	2.50084	−	0.903862i
$239$		−	64893.0i		−	1.13606i	−0.823007	−	0.568031i	$-0.807705\pi$
$239$		−	64893.0i		−	1.13606i	0.823007	−	0.568031i	$-0.192295\pi$
$240$		0			0
$241$	−93131.9			−1.60348			−0.801742	−	0.597671i	$-0.796093\pi$
$241$	−93131.9			−1.60348			−0.801742	+	0.597671i	$0.796093\pi$
$242$	12668.8	+	35052.5i	0.216324	+	0.598533i
$243$		0			0
$244$	57164.1	−	47529.6i	0.960160	−	0.798333i
$245$	14628.9			0.243713
$246$		0			0
$247$		−	26639.2i		−	0.436643i
$248$	−20804.3	+	35478.8i	−0.338260	+	0.576853i
$249$		0			0
$250$	4495.38	+	12438.0i	0.0719261	+	0.199008i
$251$			13729.0i			0.217917i	0.994046	+	0.108958i	$0.0347515\pi$
$251$			13729.0i			0.217917i	−0.994046	+	0.108958i	$0.965249\pi$
$252$		0			0
$253$	−52781.1			−0.824589
$254$	85799.7	−	31010.1i	1.32990	−	0.480657i
$255$		0			0
$256$	−61170.2	−	23519.7i	−0.933383	−	0.358882i
$257$	24255.6			0.367237			0.183618	−	0.982998i	$-0.441219\pi$
$257$	24255.6			0.367237			0.183618	+	0.982998i	$0.441219\pi$
$258$		0			0
$259$			47616.4i			0.709834i
$260$	−5685.66	+	4727.39i	−0.0841074	+	0.0699318i
$261$		0			0
$262$	−23484.2	+	8487.75i	−0.342116	+	0.123649i
$263$		−	34613.8i		−	0.500423i	−0.968191	−	0.250212i	$-0.919500\pi$
$263$		−	34613.8i		−	0.500423i	0.968191	−	0.250212i	$-0.0805002\pi$
$264$		0			0
$265$	12313.7			0.175347
$266$	18530.6	+	51271.2i	0.261895	+	0.724619i
$267$		0			0
$268$	68230.6	+	82061.4i	0.949970	+	1.14253i
$269$	−67272.9			−0.929684			−0.464842	−	0.885394i	$-0.653889\pi$
$269$	−67272.9			−0.929684			−0.464842	+	0.885394i	$0.653889\pi$
$270$		0			0
$271$		−	7814.00i		−	0.106398i	−0.998584	−	0.0531992i	$-0.983058\pi$
$271$		−	7814.00i		−	0.106398i	0.998584	−	0.0531992i	$-0.0169418\pi$
$272$	19794.1	−	106636.i	0.267546	−	1.44133i
$273$		0			0
$274$	12958.2	+	35853.1i	0.172601	+	0.477557i
$275$			45083.4i			0.596144i
$276$		0			0
$277$	50559.4			0.658935			0.329467	−	0.944167i	$-0.393131\pi$
$277$	50559.4			0.658935			0.329467	+	0.944167i	$0.393131\pi$
$278$	43570.4	−	15747.4i	0.563770	−	0.203760i
$279$		0			0
$280$	7654.48	−	13053.6i	0.0976336	−	0.166500i
$281$	81351.4			1.03027			0.515136	−	0.857108i	$-0.327741\pi$
$281$	81351.4			1.03027			0.515136	+	0.857108i	$0.327741\pi$
$282$		0			0
$283$		−	2795.45i		−	0.0349043i	−0.999848	−	0.0174522i	$-0.994445\pi$
$283$		−	2795.45i		−	0.0349043i	0.999848	−	0.0174522i	$-0.00555548\pi$
$284$	−65930.3	−	79294.8i	−0.817426	−	0.983123i
$285$		0			0
$286$	−47681.6	+	17233.3i	−0.582934	+	0.210686i
$287$		−	190344.i		−	2.31087i
$288$		0			0
$289$	95967.4			1.14902
$290$	1326.87	+	3671.22i	0.0157772	+	0.0436530i
$291$		0			0
$292$	−58263.8	+	48443.9i	−0.683334	+	0.568164i
$293$	48302.8			0.562648			0.281324	−	0.959613i	$-0.409226\pi$
$293$	48302.8			0.562648			0.281324	+	0.959613i	$0.409226\pi$
$294$		0			0
$295$		−	9230.30i		−	0.106065i
$296$	29576.0	+	17343.0i	0.337564	+	0.197944i
$297$		0			0
$298$	52389.6	+	144953.i	0.589946	+	1.63228i
$299$			125680.i			1.40580i
$300$		0			0
$301$	−54747.3			−0.604269
$302$	−86193.0	+	31152.2i	−0.945057	+	0.341566i
$303$		0			0
$304$	38595.4	+	7164.23i	0.417627	+	0.0775216i
$305$	12360.1			0.132869
$306$		0			0
$307$		−	1578.26i		−	0.0167457i	−0.999965	−	0.00837284i	$-0.997335\pi$
$307$		−	1578.26i		−	0.0167457i	0.999965	−	0.00837284i	$-0.00266519\pi$
$308$	79782.9	−	66336.1i	0.841024	−	0.699276i
$309$		0			0
$310$	−6430.87	+	2324.27i	−0.0669185	+	0.0241859i
$311$			2640.95i			0.0273049i	0.999907	+	0.0136524i	$0.00434584\pi$
$311$			2640.95i			0.0273049i	−0.999907	+	0.0136524i	$0.995654\pi$
$312$		0			0
$313$	52927.9			0.540252			0.270126	−	0.962825i	$-0.412935\pi$
$313$	52927.9			0.540252			0.270126	+	0.962825i	$0.412935\pi$
$314$	35018.1	+	96889.2i	0.355167	+	0.982689i
$315$		0			0
$316$	21330.6	+	25654.4i	0.213613	+	0.256914i
$317$	−40687.1			−0.404891			−0.202446	−	0.979293i	$-0.564889\pi$
$317$	−40687.1			−0.404891			−0.202446	+	0.979293i	$0.564889\pi$
$318$		0			0
$319$			26766.2i			0.263030i
$320$	−5320.06	−	9508.87i	−0.0519538	−	0.0928601i
$321$		0			0
$322$	−87424.8	−	241890.i	−0.843185	−	2.33295i
$323$			64963.6i			0.622680i
$324$		0			0
$325$	107350.			1.01634
$326$	−82461.8	+	29803.7i	−0.775922	+	0.280436i
$327$		0			0
$328$	−118229.	−	69327.8i	−1.09894	−	0.644406i
$329$	−29390.8			−0.271531
$330$		0			0
$331$		−	44484.1i		−	0.406021i	−0.979177	−	0.203011i	$-0.934927\pi$
$331$		−	44484.1i		−	0.406021i	0.979177	−	0.203011i	$-0.0650726\pi$
$332$	95076.2	+	114349.i	0.862572	+	1.03742i
$333$		0			0
$334$	13980.3	−	5052.82i	0.125321	−	0.0452940i
$335$			17743.4i			0.158106i
$336$		0			0
$337$	−1175.77			−0.0103529			−0.00517645	−	0.999987i	$-0.501648\pi$
$337$	−1175.77			−0.0103529			−0.00517645	+	0.999987i	$0.501648\pi$
$338$	2202.98	+	6095.27i	0.0192831	+	0.0533531i
$339$		0			0
$340$	13865.3	−	11528.4i	0.119942	−	0.0997270i
$341$	−46886.3			−0.403216
$342$		0			0
$343$			275385.i			2.34073i
$344$	−19940.3	+	34005.3i	−0.168506	+	0.287362i
$345$		0			0
$346$	−32399.3	−	89643.6i	−0.270635	−	0.748802i
$347$			80258.8i			0.666551i	0.942829	+	0.333276i	$0.108154\pi$
$347$			80258.8i			0.666551i	−0.942829	+	0.333276i	$0.891846\pi$
$348$		0			0
$349$	−11160.8			−0.0916318			−0.0458159	−	0.998950i	$-0.514589\pi$
$349$	−11160.8			−0.0916318			−0.0458159	+	0.998950i	$0.514589\pi$
$350$	−206612.	+	74674.6i	−1.68663	+	0.609588i
$351$		0			0
$352$	−12144.6	−	73716.8i	−0.0980164	−	0.594951i
$353$	−235353.			−1.88873			−0.944366	−	0.328895i	$-0.893324\pi$
$353$	−235353.			−1.88873			−0.944366	+	0.328895i	$0.893324\pi$
$354$		0			0
$355$		−	17145.2i		−	0.136046i
$356$	−70184.5	+	58355.5i	−0.553785	+	0.460449i
$357$		0			0
$358$	−199585.	+	72134.7i	−1.55726	+	0.562831i
$359$		−	141216.i		−	1.09571i	−0.836573	−	0.547855i	$-0.815444\pi$
$359$		−	141216.i		−	1.09571i	0.836573	−	0.547855i	$-0.184556\pi$
$360$		0			0
$361$	106808.			0.819578
$362$	−51835.7	−	143421.i	−0.395560	−	1.09445i
$363$		0			0
$364$	−157956.	−	189975.i	−1.19216	−	1.43382i
$365$	−12597.9			−0.0945608
$366$		0			0
$367$		−	63764.0i		−	0.473417i	−0.971581	−	0.236708i	$-0.923931\pi$
$367$		−	63764.0i		−	0.473417i	0.971581	−	0.236708i	$-0.0760686\pi$
$368$	−182088.	−	33799.8i	−1.34457	−	0.249585i
$369$		0			0
$370$	1937.57	+	5360.94i	0.0141532	+	0.0391595i
$371$			411438.i			2.98921i
$372$		0			0
$373$	119610.			0.859708			0.429854	−	0.902898i	$-0.358565\pi$
$373$	119610.			0.859708			0.429854	+	0.902898i	$0.358565\pi$
$374$	116279.	−	42025.9i	0.831299	−	0.300451i
$375$		0			0
$376$	−10704.8	+	18255.6i	−0.0757189	+	0.129128i
$377$	63734.4			0.448426
$378$		0			0
$379$		−	40019.5i		−	0.278608i	−0.990250	−	0.139304i	$-0.955514\pi$
$379$		−	40019.5i		−	0.278608i	0.990250	−	0.139304i	$-0.0444865\pi$
$380$	4172.58	+	5018.38i	0.0288960	+	0.0347533i
$381$		0			0
$382$	73652.0	−	26619.6i	0.504729	−	0.182421i
$383$		−	195988.i		−	1.33608i	−0.744125	−	0.668040i	$-0.767133\pi$
$383$		−	195988.i		−	1.33608i	0.744125	−	0.668040i	$-0.232867\pi$
$384$		0			0
$385$	17250.8			0.116382
$386$	14261.4	+	39459.1i	0.0957170	+	0.264833i
$387$		0			0
$388$	−85820.0	+	71355.7i	−0.570066	+	0.473986i
$389$	29348.7			0.193950			0.0969751	−	0.995287i	$-0.469083\pi$
$389$	29348.7			0.193950			0.0969751	+	0.995287i	$0.469083\pi$
$390$		0			0
$391$		−	306489.i		−	2.00475i
$392$	303605.	+	178031.i	1.97577	+	1.15857i
$393$		0			0
$394$	25198.0	+	69718.6i	0.162320	+	0.449114i
$395$			5547.03i			0.0355522i
$396$		0			0
$397$	190863.			1.21099			0.605495	−	0.795849i	$-0.292975\pi$
$397$	190863.			1.21099			0.605495	+	0.795849i	$0.292975\pi$
$398$	248804.	−	89923.6i	1.57069	−	0.567685i
$399$		0			0
$400$	−28870.4	+	155532.i	−0.180440	+	0.972073i
$401$	35070.1			0.218096			0.109048	−	0.994036i	$-0.465220\pi$
$401$	35070.1			0.218096			0.109048	+	0.994036i	$0.465220\pi$
$402$		0			0
$403$			111643.i			0.687422i
$404$	−182345.	+	151612.i	−1.11720	+	0.928904i
$405$		0			0
$406$	−122667.	+	44334.6i	−0.744173	+	0.268962i
$407$			39085.7i			0.235955i
$408$		0			0
$409$	−106623.			−0.637388			−0.318694	−	0.947858i	$-0.603244\pi$
$409$	−106623.			−0.637388			−0.318694	+	0.947858i	$0.603244\pi$
$410$	−7745.33	−	21430.1i	−0.0460757	−	0.127484i
$411$		0			0
$412$	−88855.0	−	106866.i	−0.523465	−	0.629574i
$413$	308412.			1.80814
$414$		0			0
$415$			24724.6i			0.143560i
$416$	−175531.	+	28918.2i	−1.01430	+	0.167103i
$417$		0			0
$418$	15210.8	+	42085.7i	0.0870559	+	0.240869i
$419$		−	150952.i		−	0.859826i	−0.902870	−	0.429913i	$-0.858544\pi$
$419$		−	150952.i		−	0.859826i	0.902870	−	0.429913i	$-0.141456\pi$
$420$		0			0
$421$	188580.			1.06397			0.531987	−	0.846752i	$-0.321445\pi$
$421$	188580.			1.06397			0.531987	+	0.846752i	$0.321445\pi$
$422$	94883.5	−	34293.1i	0.532802	−	0.192567i
$423$		0			0
$424$	255557.	+	149856.i	1.42153	+	0.833569i
$425$	−261790.			−1.44936
$426$		0			0
$427$			412988.i			2.26507i
$428$	−111704.	−	134347.i	−0.609790	−	0.733398i
$429$		0			0
$430$	−6163.78	+	2227.74i	−0.0333358	+	0.0120483i
$431$		−	111824.i		−	0.601975i	−0.953628	−	0.300988i	$-0.902684\pi$
$431$		−	111824.i		−	0.601975i	0.953628	−	0.300988i	$-0.0973163\pi$
$432$		0			0
$433$	86904.0			0.463515			0.231758	−	0.972774i	$-0.425552\pi$
$433$	86904.0			0.463515			0.231758	+	0.972774i	$0.425552\pi$
$434$	−77660.9	−	214875.i	−0.412309	−	1.14079i
$435$		0			0
$436$	−154175.	+	128190.i	−0.811035	+	0.674342i
$437$	110930.			0.580879
$438$		0			0
$439$			200474.i			1.04023i	0.854096	+	0.520115i	$0.174111\pi$
$439$			200474.i			1.04023i	−0.854096	+	0.520115i	$0.825889\pi$
$440$	6283.14	−	10715.0i	0.0324542	−	0.0553460i
$441$		0			0
$442$	−100070.	−	276877.i	−0.512223	−	1.41724i
$443$			40063.7i			0.204147i	0.994777	+	0.102074i	$0.0325477\pi$
$443$			40063.7i			0.204147i	−0.994777	+	0.102074i	$0.967452\pi$
$444$		0			0
$445$	−15175.4			−0.0766337
$446$	56269.7	−	20337.2i	0.282882	−	0.102240i
$447$		0			0
$448$	317720.	−	177759.i	1.58303	−	0.885680i
$449$	−95081.8			−0.471634			−0.235817	−	0.971798i	$-0.575777\pi$
$449$	−95081.8			−0.471634			−0.235817	+	0.971798i	$0.575777\pi$
$450$		0			0
$451$		−	156243.i		−	0.768151i
$452$	151313.	−	125811.i	0.740629	−	0.615802i
$453$		0			0
$454$	100629.	−	36369.8i	0.488217	−	0.176453i
$455$		−	41076.7i		−	0.198414i
$456$		0			0
$457$	−132420.			−0.634047			−0.317024	−	0.948418i	$-0.602683\pi$
$457$	−132420.			−0.634047			−0.317024	+	0.948418i	$0.602683\pi$
$458$	−73477.9	−	203301.i	−0.350289	−	0.969191i
$459$		0			0
$460$	−19685.6	−	23676.0i	−0.0930322	−	0.111890i
$461$	85031.6			0.400109			0.200055	−	0.979785i	$-0.435888\pi$
$461$	85031.6			0.400109			0.200055	+	0.979785i	$0.435888\pi$
$462$		0			0
$463$		−	23890.7i		−	0.111447i	−0.998446	−	0.0557234i	$-0.982254\pi$
$463$		−	23890.7i		−	0.111447i	0.998446	−	0.0557234i	$-0.0177465\pi$
$464$	−17140.5	+	92339.7i	−0.0796135	+	0.428897i
$465$		0			0
$466$	121599.	+	336446.i	0.559964	+	1.54933i
$467$		−	233452.i		−	1.07044i	−0.844712	−	0.535221i	$-0.820228\pi$
$467$		−	233452.i		−	1.07044i	0.844712	−	0.535221i	$-0.179772\pi$
$468$		0			0
$469$	−592861.			−2.69530
$470$	−3308.99	+	1195.95i	−0.0149796	+	0.00541398i
$471$		0			0
$472$	112331.	−	191565.i	0.504215	−	0.859867i
$473$	−44939.1			−0.200864
$474$		0			0
$475$		−	94751.6i		−	0.419952i
$476$	385200.	+	463283.i	1.70009	+	2.04471i
$477$		0			0
$478$	244117.	−	88229.7i	1.06842	−	0.386153i
$479$		−	97384.4i		−	0.424442i	−0.977222	−	0.212221i	$-0.931930\pi$
$479$		−	97384.4i		−	0.424442i	0.977222	−	0.212221i	$-0.0680696\pi$
$480$		0			0
$481$	93068.8			0.402267
$482$	−126624.	−	350347.i	−0.545031	−	1.50801i
$483$		0			0
$484$	−114637.	+	95316.0i	−0.489367	+	0.406888i
$485$	−18556.1			−0.0788866
$486$		0			0
$487$			42812.3i			0.180514i	0.995919	+	0.0902570i	$0.0287689\pi$
$487$			42812.3i			0.180514i	−0.995919	+	0.0902570i	$0.971231\pi$
$488$	256520.	+	150420.i	1.07716	+	0.631635i
$489$		0			0
$490$	19889.6	+	55031.4i	0.0828390	+	0.229202i
$491$			376010.i			1.55968i	0.625976	+	0.779842i	$0.284701\pi$
$491$			376010.i			1.55968i	−0.625976	+	0.779842i	$0.715299\pi$
$492$		0			0
$493$	−155426.			−0.639483
$494$	100212.	−	36219.1i	0.410646	−	0.148417i
$495$		0			0
$496$	−161751.	−	30024.9i	−0.657484	−	0.122045i
$497$	572874.			2.31924
$498$		0			0
$499$		−	239303.i		−	0.961051i	−0.876981	−	0.480525i	$-0.840446\pi$
$499$		−	239303.i		−	0.961051i	0.876981	−	0.480525i	$-0.159554\pi$
$500$	−40677.7	+	33821.8i	−0.162711	+	0.135287i
$501$		0			0
$502$	−51646.1	+	18666.1i	−0.204942	+	0.0740708i
$503$		−	297365.i		−	1.17531i	−0.809111	−	0.587656i	$-0.800051\pi$
$503$		−	297365.i		−	1.17531i	0.809111	−	0.587656i	$-0.199949\pi$
$504$		0			0
$505$	−39426.8			−0.154600
$506$	−71762.1	−	198554.i	−0.280281	−	0.775493i
$507$		0			0
$508$	233310.	+	280603.i	0.904077	+	1.08734i
$509$	189362.			0.730897			0.365449	−	0.930831i	$-0.380916\pi$
$509$	189362.			0.730897			0.365449	+	0.930831i	$0.380916\pi$
$510$		0			0
$511$		−	420933.i		−	1.61202i
$512$	5309.28	−	262090.i	0.0202533	−	0.999795i
$513$		0			0
$514$	32978.4	+	91245.8i	0.124825	+	0.345372i
$515$		−	23106.8i		−	0.0871215i
$516$		0			0
$517$	−24125.3			−0.0902592
$518$	−179125.	+	64740.1i	−0.667571	+	0.241276i
$519$		0			0
$520$	−25514.0	−	14961.1i	−0.0943565	−	0.0553295i
$521$	−347810.			−1.28135			−0.640673	−	0.767814i	$-0.721345\pi$
$521$	−347810.			−1.28135			−0.640673	+	0.767814i	$0.721345\pi$
$522$		0			0
$523$		−	465334.i		−	1.70122i	−0.525794	−	0.850612i	$-0.676232\pi$
$523$		−	465334.i		−	1.70122i	0.525794	−	0.850612i	$-0.323768\pi$
$524$	−63859.1	−	76803.7i	−0.232573	−	0.279718i
$525$		0			0
$526$	130212.	−	47061.5i	0.470628	−	0.170096i
$527$		−	272259.i		−	0.980305i
$528$		0			0
$529$	−243510.			−0.870173
$530$	16741.9	+	46322.2i	0.0596011	+	0.164906i
$531$		0			0
$532$	−167679.	+	139418.i	−0.592456	+	0.492603i
$533$	−372038.			−1.30958
$534$		0			0
$535$		−	29048.6i		−	0.101489i
$536$	−215934.	+	368245.i	−0.751609	+	1.28176i
$537$		0			0
$538$	−91465.4	−	253070.i	−0.316004	−	0.874331i
$539$			401224.i			1.38105i
$540$		0			0
$541$	−340727.			−1.16416			−0.582080	−	0.813132i	$-0.697761\pi$
$541$	−340727.			−1.16416			−0.582080	+	0.813132i	$0.697761\pi$
$542$	29395.0	−	10624.1i	0.100063	−	0.0361653i
$543$		0			0
$544$	428058.	−	70521.3i	1.44646	−	0.238299i
$545$	−33335.8			−0.112232
$546$		0			0
$547$			87443.4i			0.292248i	0.989266	+	0.146124i	$0.0466799\pi$
$547$			87443.4i			0.292248i	−0.989266	+	0.146124i	$0.953320\pi$
$548$	−117255.	+	97493.1i	−0.390456	+	0.324648i
$549$		0			0
$550$	−169597.	+	61296.2i	−0.560650	+	0.202632i
$551$		−	56254.4i		−	0.185291i
$552$		0			0
$553$	−185343.			−0.606075
$554$	68741.5	+	190196.i	0.223975	+	0.619702i
$555$		0			0
$556$	118478.	+	142495.i	0.383256	+	0.460944i
$557$	−82261.1			−0.265146			−0.132573	−	0.991173i	$-0.542324\pi$
$557$	−82261.1			−0.265146			−0.132573	+	0.991173i	$0.542324\pi$
$558$		0			0
$559$			107007.i			0.342442i
$560$	59512.8	+	11047.0i	0.189773	+	0.0352264i
$561$		0			0
$562$	110607.	+	306031.i	0.350194	+	0.968930i
$563$			440276.i			1.38902i	0.719483	+	0.694510i	$0.244379\pi$
$563$			440276.i			1.38902i	−0.719483	+	0.694510i	$0.755621\pi$
$564$		0			0
$565$	32717.2			0.102489
$566$	10516.0	−	3800.75i	0.0328261	−	0.0118641i
$567$		0			0
$568$	208654.	−	355830.i	0.646741	−	1.10292i
$569$	124980.			0.386026			0.193013	−	0.981196i	$-0.438174\pi$
$569$	124980.			0.386026			0.193013	+	0.981196i	$0.438174\pi$
$570$		0			0
$571$			404239.i			1.23984i	0.784665	+	0.619921i	$0.212835\pi$
$571$			404239.i			1.23984i	−0.784665	+	0.619921i	$0.787165\pi$
$572$	−129658.	−	155940.i	−0.396283	−	0.476613i
$573$		0			0
$574$	716043.	−	258795.i	2.17328	−	0.785474i
$575$			447025.i			1.35206i
$576$		0			0
$577$	−118286.			−0.355290			−0.177645	−	0.984095i	$-0.556848\pi$
$577$	−118286.			−0.355290			−0.177645	+	0.984095i	$0.556848\pi$
$578$	130479.	+	361014.i	0.390558	+	1.08061i
$579$		0			0
$580$	−12006.5	+	9982.91i	−0.0356912	+	0.0296757i
$581$	−826124.			−2.44733
$582$		0			0
$583$			337727.i			0.993639i
$584$	−261455.	−	153314.i	−0.766603	−	0.449527i
$585$		0			0
$586$	65673.3	+	181707.i	0.191247	+	0.529148i
$587$			47852.6i			0.138877i	0.997586	+	0.0694383i	$0.0221207\pi$
$587$			47852.6i			0.138877i	−0.997586	+	0.0694383i	$0.977879\pi$
$588$		0			0
$589$	98540.8			0.284044
$590$	34722.9	−	12549.7i	0.0997498	−	0.0360520i
$591$		0			0
$592$	−25029.6	+	134840.i	−0.0714184	+	0.384748i
$593$	633658.			1.80196			0.900981	−	0.433859i	$-0.142848\pi$
$593$	633658.			1.80196			0.900981	+	0.433859i	$0.142848\pi$
$594$		0			0
$595$			100172.i			0.282950i
$596$	−474061.	+	394162.i	−1.33457	+	1.10964i
$597$		0			0
$598$	−472787.	+	170877.i	−1.32210	+	0.477837i
$599$		−	158241.i		−	0.441027i	−0.975384	−	0.220513i	$-0.929227\pi$
$599$		−	158241.i		−	0.441027i	0.975384	−	0.220513i	$-0.0707733\pi$
$600$		0			0
$601$	−84042.2			−0.232674			−0.116337	−	0.993210i	$-0.537115\pi$
$601$	−84042.2			−0.232674			−0.116337	+	0.993210i	$0.537115\pi$
$602$	−74435.5	−	205951.i	−0.205394	−	0.568290i
$603$		0			0
$604$	−234379.	−	281889.i	−0.642458	−	0.772689i
$605$	−24787.0			−0.0677194
$606$		0			0
$607$			504787.i			1.37003i	0.728528	+	0.685016i	$0.240205\pi$
$607$			504787.i			1.37003i	−0.728528	+	0.685016i	$0.759795\pi$
$608$	25524.3	+	154930.i	0.0690474	+	0.419111i
$609$		0			0
$610$	16805.0	+	46496.7i	0.0451626	+	0.124958i
$611$			57446.0i			0.153878i
$612$		0			0
$613$	−30449.3			−0.0810320			−0.0405160	−	0.999179i	$-0.512900\pi$
$613$	−30449.3			−0.0810320			−0.0405160	+	0.999179i	$0.512900\pi$
$614$	5937.18	−	2145.84i	0.0157486	−	0.00569193i
$615$		0			0
$616$	358020.	+	209939.i	0.943509	+	0.553262i
$617$	−147465.			−0.387364			−0.193682	−	0.981064i	$-0.562043\pi$
$617$	−147465.			−0.387364			−0.193682	+	0.981064i	$0.562043\pi$
$618$		0			0
$619$		−	264366.i		−	0.689960i	−0.938610	−	0.344980i	$-0.887886\pi$
$619$		−	264366.i		−	0.689960i	0.938610	−	0.344980i	$-0.112114\pi$
$620$	−17487.1	−	21031.8i	−0.0454918	−	0.0547133i
$621$		0			0
$622$	−9934.84	+	3590.69i	−0.0256791	+	0.00928104i
$623$		−	507056.i		−	1.30641i
$624$		0			0
$625$	377407.			0.966162
$626$	71961.8	+	199106.i	0.183634	+	0.508085i
$627$		0			0
$628$	−316871.	+	263465.i	−0.803457	+	0.668041i
$629$	−226962.			−0.573657
$630$		0			0
$631$		−	455734.i		−	1.14460i	−0.820045	−	0.572299i	$-0.806052\pi$
$631$		−	455734.i		−	1.14460i	0.820045	−	0.572299i	$-0.193948\pi$
$632$	−67506.4	+	115122.i	−0.169009	+	0.288221i
$633$		0			0
$634$	−55318.9	−	153058.i	−0.137624	−	0.380784i
$635$			60672.3i			0.150468i
$636$		0			0
$637$	955375.			2.35448
$638$	−100690.	+	36391.8i	−0.247369	+	0.0894051i
$639$		0			0
$640$	28537.6	−	32941.7i	0.0696719	−	0.0804240i
$641$	−42568.5			−0.103603			−0.0518015	−	0.998657i	$-0.516496\pi$
$641$	−42568.5			−0.103603			−0.0518015	+	0.998657i	$0.516496\pi$
$642$		0			0
$643$		−	397515.i		−	0.961461i	−0.876868	−	0.480730i	$-0.840372\pi$
$643$		−	397515.i		−	0.961461i	0.876868	−	0.480730i	$-0.159628\pi$
$644$	791087.	−	657756.i	1.90745	−	1.58596i
$645$		0			0
$646$	−244383.	+	88325.7i	−0.585606	+	0.211652i
$647$			454122.i			1.08483i	0.840109	+	0.542417i	$0.182491\pi$
$647$			454122.i			1.08483i	−0.840109	+	0.542417i	$0.817509\pi$
$648$		0			0
$649$	253159.			0.601040
$650$	145956.	+	403835.i	0.345457	+	0.955823i
$651$		0			0
$652$	−224233.	−	269687.i	−0.527478	−	0.634402i
$653$	351238.			0.823712			0.411856	−	0.911249i	$-0.364881\pi$
$653$	351238.			0.823712			0.411856	+	0.911249i	$0.364881\pi$
$654$		0			0
$655$		−	16606.6i		−	0.0387078i
$656$	100054.	−	539016.i	0.232503	−	1.25255i
$657$		0			0
$658$	−39960.3	−	110564.i	−0.0922947	−	0.255364i
$659$		−	636361.i		−	1.46532i	−0.680595	−	0.732660i	$-0.738279\pi$
$659$		−	636361.i		−	1.46532i	0.680595	−	0.732660i	$-0.261721\pi$
$660$		0			0
$661$	−194949.			−0.446188			−0.223094	−	0.974797i	$-0.571616\pi$
$661$	−194949.			−0.446188			−0.223094	+	0.974797i	$0.571616\pi$
$662$	167342.	−	60481.4i	0.381847	−	0.138009i
$663$		0			0
$664$	−300894.	+	513132.i	−0.682461	+	1.16384i
$665$	−36255.8			−0.0819851
$666$		0			0
$667$			265400.i			0.596554i
$668$	38015.8	+	45721.8i	0.0851944	+	0.102464i
$669$		0			0
$670$	−66747.9	+	24124.3i	−0.148692	+	0.0537409i
$671$			338999.i			0.752928i
$672$		0			0
$673$	−771557.			−1.70348			−0.851742	−	0.523962i	$-0.824453\pi$
$673$	−771557.			−1.70348			−0.851742	+	0.523962i	$0.824453\pi$
$674$	−1598.59	−	4423.05i	−0.00351899	−	0.00973648i
$675$		0			0
$676$	−19934.2	+	16574.5i	−0.0436220	+	0.0362699i
$677$	334198.			0.729166			0.364583	−	0.931171i	$-0.381212\pi$
$677$	334198.			0.729166			0.364583	+	0.931171i	$0.381212\pi$
$678$		0			0
$679$		−	620016.i		−	1.34482i
$680$	62219.7	+	36484.9i	0.134558	+	0.0789032i
$681$		0			0
$682$	−63747.5	−	176379.i	−0.137055	−	0.379208i
$683$			452549.i			0.970117i	0.874482	+	0.485059i	$0.161202\pi$
$683$			452549.i			0.970117i	−0.874482	+	0.485059i	$0.838798\pi$
$684$		0			0
$685$	−25353.1			−0.0540319
$686$	−1.03595e6	+	374418.i	−2.20137	+	0.795626i
$687$		0			0
$688$	−155034.	−	28778.0i	−0.327528	−	0.0607971i
$689$	804179.			1.69400
$690$		0			0
$691$			864703.i			1.81097i	0.424379	+	0.905485i	$0.360492\pi$
$691$			864703.i			1.81097i	−0.424379	+	0.905485i	$0.639508\pi$
$692$	293174.	−	243762.i	0.612228	−	0.509042i
$693$		0			0
$694$	−301921.	+	109121.i	−0.626865	+	0.226564i
$695$			30810.3i			0.0637862i
$696$		0			0
$697$	907269.			1.86754
$698$	−15174.5	−	41985.3i	−0.0311461	−	0.0861761i
$699$		0			0
$700$	−561827.	−	675713.i	−1.14659	−	1.37901i
$701$	−576160.			−1.17249			−0.586243	−	0.810136i	$-0.699393\pi$
$701$	−576160.			−1.17249			−0.586243	+	0.810136i	$0.699393\pi$
$702$		0			0
$703$		−	82146.2i		−	0.166217i
$704$	260799.	−	145913.i	0.526212	−	0.294407i
$705$		0			0
$706$	−319990.	−	885361.i	−0.641989	−	1.77628i
$707$		−	1.31737e6i		−	2.63553i
$708$		0			0
$709$	506535.			1.00767			0.503834	−	0.863801i	$-0.331922\pi$
$709$	506535.			1.00767			0.503834	+	0.863801i	$0.331922\pi$
$710$	64497.6	−	23310.9i	0.127946	−	0.0462427i
$711$		0			0
$712$	−314948.	−	184682.i	−0.621268	−	0.364304i
$713$	−464901.			−0.914496
$714$		0			0
$715$		−	33717.5i		−	0.0659544i
$716$	−542719.	−	652731.i	−1.05864	−	1.27323i
$717$		0			0
$718$	531233.	−	192000.i	1.03047	−	0.372437i
$719$		−	521745.i		−	1.00925i	−0.863338	−	0.504627i	$-0.831630\pi$
$719$		−	521745.i		−	1.00925i	0.863338	−	0.504627i	$-0.168370\pi$
$720$		0			0
$721$	772068.			1.48520
$722$	145218.	+	401795.i	0.278578	+	0.770780i
$723$		0			0
$724$	469050.	−	389995.i	0.894833	−	0.744016i
$725$	226694.			0.431284
$726$		0			0
$727$		−	26945.2i		−	0.0509815i	−0.999675	−	0.0254908i	$-0.991885\pi$
$727$		−	26945.2i		−	0.0509815i	0.999675	−	0.0254908i	$-0.00811484\pi$
$728$	499896.	−	852500.i	0.943228	−	1.60854i
$729$		0			0
$730$	−17128.3	−	47391.2i	−0.0321417	−	0.0889307i
$731$		−	260952.i		−	0.488344i
$732$		0			0
$733$	−672594.			−1.25183			−0.625914	−	0.779892i	$-0.715274\pi$
$733$	−672594.			−1.25183			−0.625914	+	0.779892i	$0.715274\pi$
$734$	239870.	−	86694.7i	0.445229	−	0.160916i
$735$		0			0
$736$	−120420.	−	730939.i	−0.222302	−	1.34935i
$737$	−486647.			−0.895940
$738$		0			0
$739$			846279.i			1.54962i	0.632196	+	0.774809i	$0.282154\pi$
$739$			846279.i			1.54962i	−0.632196	+	0.774809i	$0.717846\pi$
$740$	−17532.6	+	14577.7i	−0.0320172	+	0.0266210i
$741$		0			0
$742$	−1.54777e6	+	559399.i	−2.81124	+	1.01605i
$743$			713156.i			1.29183i	0.763407	+	0.645917i	$0.223525\pi$
$743$			713156.i			1.29183i	−0.763407	+	0.645917i	$0.776475\pi$
$744$		0			0
$745$	−102502.			−0.184680
$746$	162624.	+	449955.i	0.292219	+	0.808521i
$747$		0			0
$748$	316189.	+	380283.i	0.565124	+	0.679679i
$749$	970602.			1.73013
$750$		0			0
$751$			1.09057e6i			1.93364i	0.255461	+	0.966819i	$0.417773\pi$
$751$			1.09057e6i			1.93364i	−0.255461	+	0.966819i	$0.582227\pi$
$752$	−83229.0	−	15449.3i	−0.147177	−	0.0273195i
$753$		0			0
$754$	86654.4	+	239758.i	0.152422	+	0.421727i
$755$		−	60950.4i		−	0.106926i
$756$		0			0
$757$	727090.			1.26881			0.634405	−	0.773001i	$-0.281245\pi$
$757$	727090.			1.26881			0.634405	+	0.773001i	$0.281245\pi$
$758$	150547.	−	54411.2i	0.262019	−	0.0947000i
$759$		0			0
$760$	−13205.2	+	22519.6i	−0.0228623	+	0.0389883i
$761$	377157.			0.651258			0.325629	−	0.945498i	$-0.394424\pi$
$761$	377157.			0.651258			0.325629	+	0.945498i	$0.394424\pi$
$762$		0			0
$763$		−	1.11385e6i		−	1.91328i
$764$	200277.	+	240875.i	0.343119	+	0.412671i
$765$		0			0
$766$	737276.	−	266469.i	1.25653	−	0.454140i
$767$		−	602809.i		−	1.02468i
$768$		0			0
$769$	−508831.			−0.860440			−0.430220	−	0.902724i	$-0.641564\pi$
$769$	−508831.			−0.860440			−0.430220	+	0.902724i	$0.641564\pi$
$770$	23454.4	+	64894.6i	0.0395588	+	0.109453i
$771$		0			0
$772$	−129049.	+	107299.i	−0.216530	+	0.180036i
$773$	569650.			0.953344			0.476672	−	0.879081i	$-0.341843\pi$
$773$	569650.			0.953344			0.476672	+	0.879081i	$0.341843\pi$
$774$		0			0
$775$			397099.i			0.661143i
$776$	−385111.	−	225825.i	−0.639533	−	0.375014i
$777$		0			0
$778$	39903.1	+	110405.i	0.0659246	+	0.182402i
$779$			328375.i			0.541122i
$780$		0			0
$781$	470240.			0.770935
$782$	1.15296e6	−	416708.i	1.88539	−	0.681425i
$783$		0			0
$784$	−256935.	+	1.38417e6i	−0.418014	+	2.25194i
$785$	−68514.2			−0.111184
$786$		0			0
$787$		−	911291.i		−	1.47132i	−0.677350	−	0.735661i	$-0.736872\pi$
$787$		−	911291.i		−	1.47132i	0.677350	−	0.735661i	$-0.263128\pi$
$788$	−228011.	+	189581.i	−0.367200	+	0.305312i
$789$		0			0
$790$	−20867.0	+	7541.84i	−0.0334354	+	0.0120843i
$791$			1.09318e6i			1.74718i
$792$		0			0
$793$	807208.			1.28363
$794$	259500.	+	717995.i	0.411621	+	1.13889i
$795$		0			0
$796$	676556.	+	813699.i	1.06777	+	1.28421i
$797$	229990.			0.362069			0.181035	−	0.983477i	$-0.442055\pi$
$797$	229990.			0.362069			0.181035	+	0.983477i	$0.442055\pi$
$798$		0			0
$799$		−	140091.i		−	0.219440i
$800$	−624338.	+	102858.i	−0.975528	+	0.160715i
$801$		0			0
$802$	47682.0	+	131928.i	0.0741320	+	0.205111i
$803$		−	345521.i		−	0.535849i
$804$		0			0
$805$	171050.			0.263956
$806$	−419985.	+	151792.i	−0.646492	+	0.233658i
$807$		0			0
$808$	−818259.	−	479817.i	−1.25334	−	0.734942i
$809$	−642259.			−0.981326			−0.490663	−	0.871350i	$-0.663245\pi$
$809$	−642259.			−0.981326			−0.490663	+	0.871350i	$0.663245\pi$
$810$		0			0
$811$			878969.i			1.33639i	0.743988	+	0.668193i	$0.232932\pi$
$811$			878969.i			1.33639i	−0.743988	+	0.668193i	$0.767068\pi$
$812$	−333559.	−	401174.i	−0.505896	−	0.608444i
$813$		0			0
$814$	−147034.	+	53141.6i	−0.221906	+	0.0802020i
$815$		−	58312.0i		−	0.0877895i
$816$		0			0
$817$	94448.2			0.141498
$818$	−144966.	−	401098.i	−0.216651	−	0.599438i
$819$		0			0
$820$	70085.7	−	58273.4i	0.104232	−	0.0866647i
$821$	−322494.			−0.478448			−0.239224	−	0.970964i	$-0.576893\pi$
$821$	−322494.			−0.478448			−0.239224	+	0.970964i	$0.576893\pi$
$822$		0			0
$823$		−	172131.i		−	0.254133i	−0.991894	−	0.127066i	$-0.959444\pi$
$823$		−	172131.i		−	0.254133i	0.991894	−	0.127066i	$-0.0405561\pi$
$824$	281206.	−	479556.i	0.414161	−	0.706292i
$825$		0			0
$826$	419323.	+	1.16020e6i	0.614594	+	1.70048i
$827$		−	25110.9i		−	0.0367156i	−0.999831	−	0.0183578i	$-0.994156\pi$
$827$		−	25110.9i		−	0.0367156i	0.999831	−	0.0183578i	$-0.00584381\pi$
$828$		0			0
$829$	−757576.			−1.10234			−0.551172	−	0.834392i	$-0.685819\pi$
$829$	−757576.			−1.10234			−0.551172	+	0.834392i	$0.685819\pi$
$830$	−93010.0	+	33616.0i	−0.135012	+	0.0487967i
$831$		0			0
$832$	−347441.	−	621002.i	−0.501919	−	0.897111i
$833$	−2.32983e6			−3.35763
$834$		0			0
$835$			9886.03i			0.0141791i
$836$	−137639.	+	114441.i	−0.196937	+	0.163745i
$837$		0			0
$838$	567857.	−	205237.i	0.808632	−	0.292259i
$839$			224257.i			0.318583i	0.987232	+	0.159292i	$0.0509210\pi$
$839$			224257.i			0.318583i	−0.987232	+	0.159292i	$0.949079\pi$
$840$		0			0
$841$	−572692.			−0.809709
$842$	256397.	+	709408.i	0.361650	+	1.00063i
$843$		0			0
$844$	258011.	+	310311.i	0.362204	+	0.435624i
$845$	−4310.20			−0.00603649
$846$		0			0
$847$		−	828208.i		−	1.15444i
$848$	−216273.	+	1.16511e6i	−0.300753	+	1.62023i
$849$		0			0
$850$	−355934.	−	984812.i	−0.492643	−	1.36306i
$851$			387554.i			0.535147i
$852$		0			0
$853$	−337460.			−0.463794			−0.231897	−	0.972740i	$-0.574493\pi$
$853$	−337460.			−0.463794			−0.231897	+	0.972740i	$0.574493\pi$
$854$	−1.55360e6	+	561506.i	−2.13021	+	0.769908i
$855$		0			0
$856$	353517.	−	602872.i	0.482461	−	0.822768i
$857$	370777.			0.504837			0.252418	−	0.967618i	$-0.418774\pi$
$857$	370777.			0.504837			0.252418	+	0.967618i	$0.418774\pi$
$858$		0			0
$859$		−	240459.i		−	0.325877i	−0.986636	−	0.162939i	$-0.947903\pi$
$859$		−	240459.i		−	0.325877i	0.986636	−	0.162939i	$-0.0520973\pi$
$860$	−16760.8	−	20158.3i	−0.0226620	−	0.0272557i
$861$		0			0
$862$	420662.	−	152037.i	0.566134	−	0.204614i
$863$			5184.93i			0.00696179i	0.999994	+	0.00348090i	$0.00110801\pi$
$863$			5184.93i			0.00696179i	−0.999994	+	0.00348090i	$0.998892\pi$
$864$		0			0
$865$	63390.5			0.0847211
$866$	118156.	+	326919.i	0.157551	+	0.435917i
$867$		0			0
$868$	702736.	−	584295.i	0.932723	−	0.775520i
$869$	−152138.			−0.201464
$870$		0			0
$871$			1.15878e6i			1.52744i
$872$	−691848.	−	405691.i	−0.909866	−	0.533534i
$873$		0			0
$874$	150822.	+	417300.i	0.197443	+	0.546293i
$875$		−	293880.i		−	0.383844i
$876$		0			0
$877$	261506.			0.340003			0.170001	−	0.985444i	$-0.445623\pi$
$877$	261506.			0.340003			0.170001	+	0.985444i	$0.445623\pi$
$878$	−754152.	+	272568.i	−0.978295	+	0.353579i
$879$		0			0
$880$	48850.7	+	9067.86i	0.0630820	+	0.0117095i
$881$	1.02303e6			1.31807			0.659035	−	0.752113i	$-0.270965\pi$
$881$	1.02303e6			1.31807			0.659035	+	0.752113i	$0.270965\pi$
$882$		0			0
$883$		−	223764.i		−	0.286991i	−0.989651	−	0.143496i	$-0.954166\pi$
$883$		−	223764.i		−	0.286991i	0.989651	−	0.143496i	$-0.0458343\pi$
$884$	905511.	−	752895.i	1.15875	−	0.963451i
$885$		0			0
$886$	−150713.	+	54471.3i	−0.191992	+	0.0693906i
$887$			1.14417e6i			1.45426i	0.686500	+	0.727129i	$0.259146\pi$
$887$			1.14417e6i			1.45426i	−0.686500	+	0.727129i	$0.740854\pi$
$888$		0			0
$889$	−2.02725e6			−2.56509
$890$	−20632.7	−	57087.4i	−0.0260481	−	0.0720709i
$891$		0			0
$892$	153011.	+	184027.i	0.192306	+	0.231287i
$893$	50704.0			0.0635828
$894$		0			0
$895$		−	141134.i		−	0.176192i
$896$	1.10068e6	+	953528.i	1.37102	+	1.18773i
$897$		0			0
$898$	−129275.	−	357683.i	−0.160310	−	0.443553i
$899$			235759.i			0.291709i
$900$		0			0
$901$	−1.96111e6			−2.41575
$902$	587760.	−	212430.i	0.722415	−	0.261098i
$903$		0			0
$904$	679008.	+	398162.i	0.830880	+	0.487218i
$905$	101419.			0.123828
$906$		0			0
$907$			326996.i			0.397492i	0.980051	+	0.198746i	$0.0636868\pi$
$907$			326996.i			0.397492i	−0.980051	+	0.198746i	$0.936313\pi$
$908$	273635.	+	329103.i	0.331895	+	0.399172i
$909$		0			0
$910$	154524.	−	55848.6i	0.186600	−	0.0674418i
$911$			1.40153e6i			1.68875i	0.535752	+	0.844375i	$0.320028\pi$
$911$			1.40153e6i			1.68875i	−0.535752	+	0.844375i	$0.679972\pi$
$912$		0			0
$913$	−678120.			−0.813514
$914$	−180041.	−	498143.i	−0.215515	−	0.596296i
$915$		0			0
$916$	664885.	−	552824.i	0.792421	−	0.658865i
$917$	554877.			0.659869
$918$		0			0
$919$		−	1.18092e6i		−	1.39826i	−0.714995	−	0.699130i	$-0.753571\pi$
$919$		−	1.18092e6i		−	1.39826i	0.714995	−	0.699130i	$-0.246429\pi$
$920$	62300.4	−	106244.i	0.0736064	−	0.125525i
$921$		0			0
$922$	115610.	+	319875.i	0.135999	+	0.376287i
$923$		−	1.11971e6i		−	1.31433i
$924$		0			0
$925$	331032.			0.386889
$926$	89873.1	−	32482.3i	0.104811	−	0.0378812i
$927$		0			0
$928$	−370672.	+	61067.1i	−0.430421	+	0.0709106i
$929$	−569778.			−0.660198			−0.330099	−	0.943946i	$-0.607082\pi$
$929$	−569778.			−0.660198			−0.330099	+	0.943946i	$0.607082\pi$
$930$		0			0
$931$		−	843251.i		−	0.972876i
$932$	−1.10033e6	+	914876.i	−1.26675	+	1.05325i
$933$		0			0
$934$	878208.	−	317405.i	1.00671	−	0.363848i
$935$			82225.3i			0.0940550i
$936$		0			0
$937$	1.25337e6			1.42758			0.713791	−	0.700359i	$-0.246977\pi$
$937$	1.25337e6			1.42758			0.713791	+	0.700359i	$0.246977\pi$
$938$	−806065.	−	2.23025e6i	−0.916145	−	2.53482i
$939$		0			0
$940$	−8997.94	−	10821.9i	−0.0101833	−	0.0122475i
$941$	−1.13681e6			−1.28383			−0.641914	−	0.766776i	$-0.721860\pi$
$941$	−1.13681e6			−1.28383			−0.641914	+	0.766776i	$0.721860\pi$
$942$		0			0
$943$		−	1.54922e6i		−	1.74217i
$944$	873363.	+	162117.i	0.980056	+	0.181922i
$945$		0			0
$946$	−61099.9	−	169054.i	−0.0682745	−	0.188904i
$947$		−	939587.i		−	1.04770i	−0.851811	−	0.523850i	$-0.824495\pi$
$947$		−	939587.i		−	1.04770i	0.851811	−	0.523850i	$-0.175505\pi$
$948$		0			0
$949$	−822737.			−0.913542
$950$	356440.	−	128826.i	0.394948	−	0.142744i
$951$		0			0
$952$	−1.21907e6	+	2.07895e6i	−1.34510	+	2.29388i
$953$	103408.			0.113859			0.0569296	−	0.998378i	$-0.481869\pi$
$953$	103408.			0.113859			0.0569296	+	0.998378i	$0.481869\pi$
$954$		0			0
$955$			52082.2i			0.0571061i
$956$	663812.	+	798371.i	0.726322	+	0.873552i
$957$		0			0
$958$	366344.	−	132406.i	0.399171	−	0.144270i
$959$		−	847125.i		−	0.921107i
$960$		0			0
$961$	510541.			0.552821
$962$	126538.	+	350110.i	0.136732	+	0.378316i
$963$		0			0
$964$	1.14579e6	−	952677.i	1.23297	−	1.02516i
$965$	−27903.1			−0.0299638
$966$		0			0
$967$			568578.i			0.608047i	0.952665	+	0.304023i	$0.0983301\pi$
$967$			568578.i			0.608047i	−0.952665	+	0.304023i	$0.901670\pi$
$968$	−514426.	−	301653.i	−0.549000	−	0.321927i
$969$		0			0
$970$	−25229.2	−	69805.1i	−0.0268139	−	0.0741897i
$971$		−	1.25649e6i		−	1.33267i	−0.745653	−	0.666334i	$-0.767863\pi$
$971$		−	1.25649e6i		−	1.33267i	0.745653	−	0.666334i	$-0.232137\pi$
$972$		0			0
$973$	−1.02947e6			−1.08739
$974$	−161053.	+	58208.4i	−0.169766	+	0.0613575i
$975$		0			0
$976$	−217087.	+	1.16950e6i	−0.227895	+	1.22772i
$977$	1.34062e6			1.40448			0.702241	−	0.711939i	$-0.252183\pi$
$977$	1.34062e6			1.40448			0.702241	+	0.711939i	$0.252183\pi$
$978$		0			0
$979$		−	416214.i		−	0.434261i
$980$	−179977.	+	149643.i	−0.187398	+	0.155814i
$981$		0			0
$982$	−1.41449e6	+	511230.i	−1.46682	+	0.530144i
$983$			1.08955e6i			1.12757i	0.825923	+	0.563783i	$0.190654\pi$
$983$			1.08955e6i			1.12757i	−0.825923	+	0.563783i	$0.809346\pi$
$984$		0			0
$985$	−49300.8			−0.0508137
$986$	−211320.	−	584687.i	−0.217363	−	0.601408i
$987$		0			0
$988$	272501.	+	327739.i	0.279161	+	0.335748i
$989$	−445593.			−0.455560
$990$		0			0
$991$			114312.i			0.116398i	0.998305	+	0.0581990i	$0.0185358\pi$
$991$			114312.i			0.116398i	−0.998305	+	0.0581990i	$0.981464\pi$
$992$	−106971.	−	649306.i	−0.108703	−	0.659820i
$993$		0			0
$994$	778889.	+	2.15506e6i	0.788321	+	2.18115i
$995$			175939.i			0.177712i
$996$		0			0
$997$	1.31273e6			1.32065			0.660323	−	0.750981i	$-0.270419\pi$
$997$	1.31273e6			1.32065			0.660323	+	0.750981i	$0.270419\pi$
$998$	900218.	−	325360.i	0.903830	−	0.326666i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.d.a.55.10	yes	16
3.2	odd	2	inner	108.5.d.a.55.7	✓	16
4.3	odd	2	inner	108.5.d.a.55.9	yes	16
12.11	even	2	inner	108.5.d.a.55.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.d.a.55.7	✓	16	3.2	odd	2	inner
108.5.d.a.55.8	yes	16	12.11	even	2	inner
108.5.d.a.55.9	yes	16	4.3	odd	2	inner
108.5.d.a.55.10	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.35962 + 3.76184i) q^{2} +(-12.3029 + 10.2293i) q^{4} -2.66014 q^{5} -88.8835i q^{7} +(-55.2083 - 32.3735i) q^{8} +O(q^{10})\)	\(q+(1.35962 + 3.76184i) q^{2} +(-12.3029 + 10.2293i) q^{4} -2.66014 q^{5} -88.8835i q^{7} +(-55.2083 - 32.3735i) q^{8} +(-3.61678 - 10.0070i) q^{10} -72.9595i q^{11} -173.728 q^{13} +(334.365 - 120.848i) q^{14} +(46.7216 - 251.700i) q^{16} +423.661 q^{17} +153.339i q^{19} +(32.7274 - 27.2115i) q^{20} +(274.462 - 99.1971i) q^{22} -723.430i q^{23} -617.924 q^{25} +(-236.203 - 653.536i) q^{26} +(909.218 + 1093.52i) q^{28} -366.864 q^{29} -642.635i q^{31} +(1010.38 - 166.457i) q^{32} +(576.017 + 1593.74i) q^{34} +236.443i q^{35} -535.717 q^{37} +(-576.836 + 208.482i) q^{38} +(146.862 + 86.1181i) q^{40} +2141.50 q^{41} -615.945i q^{43} +(746.327 + 897.612i) q^{44} +(2721.43 - 983.589i) q^{46} -330.667i q^{47} -5499.27 q^{49} +(-840.140 - 2324.53i) q^{50} +(2137.35 - 1777.12i) q^{52} -4628.97 q^{53} +194.083i q^{55} +(-2877.47 + 4907.11i) q^{56} +(-498.795 - 1380.08i) q^{58} +3469.85i q^{59} -4646.40 q^{61} +(2417.49 - 873.738i) q^{62} +(1999.92 + 3574.57i) q^{64} +462.141 q^{65} -6670.10i q^{67} +(-5212.25 + 4333.77i) q^{68} +(-889.460 + 321.472i) q^{70} +6445.22i q^{71} +4735.78 q^{73} +(-728.370 - 2015.28i) q^{74} +(-1568.55 - 1886.51i) q^{76} -6484.89 q^{77} -2085.24i q^{79} +(-124.286 + 669.559i) q^{80} +(2911.62 + 8055.98i) q^{82} -9294.47i q^{83} -1127.00 q^{85} +(2317.09 - 837.450i) q^{86} +(-2361.95 + 4027.97i) q^{88} +5704.72 q^{89} +15441.5i q^{91} +(7400.21 + 8900.27i) q^{92} +(1243.92 - 449.581i) q^{94} -407.903i q^{95} +6975.60 q^{97} +(-7476.91 - 20687.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{4}+O(q^{10}) \) 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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