LMFDB - Embedded newform 117.5.j.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,5,Mod(73,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("117.73");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	117.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0942856808$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 $ x^20 + 5446x^16 - 1452x^15 + 106320x^13 + 8376897x^12 - 1643220x^11 + 1054152x^10 + 232107192x^9 + 3337033804x^8 + 3105930144x^7 + 2297014848x^6 + 21034904256x^5 + 158658808624x^4 + 235144077504x^3 + 177846480000x^2 + 27353289600*x + 2103506496
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.2
Root			$-4.67933 + 4.67933i$ of defining polynomial
Character	$\chi$	$=$	117.109
Dual form			117.5.j.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.67933 + 4.67933i) q^{2} -27.7923i q^{4} +(-13.1418 + 13.1418i) q^{5} +(-30.2175 - 30.2175i) q^{7} +(55.1800 + 55.1800i) q^{8} -122.989i q^{10} +(-58.8012 - 58.8012i) q^{11} +(120.640 + 118.351i) q^{13} +282.795 q^{14} -71.7343 q^{16} -257.703i q^{17} +(336.208 - 336.208i) q^{19} +(365.240 + 365.240i) q^{20} +550.300 q^{22} +486.231i q^{23} +279.587i q^{25} +(-1118.32 + 10.7102i) q^{26} +(-839.813 + 839.813i) q^{28} +771.373 q^{29} +(-1304.18 + 1304.18i) q^{31} +(-547.211 + 547.211i) q^{32} +(1205.88 + 1205.88i) q^{34} +794.223 q^{35} +(1053.22 + 1053.22i) q^{37} +3146.45i q^{38} -1450.33 q^{40} +(1126.29 - 1126.29i) q^{41} -1930.35i q^{43} +(-1634.22 + 1634.22i) q^{44} +(-2275.24 - 2275.24i) q^{46} +(65.7645 + 65.7645i) q^{47} -574.806i q^{49} +(-1308.28 - 1308.28i) q^{50} +(3289.25 - 3352.86i) q^{52} +5040.23 q^{53} +1545.50 q^{55} -3334.80i q^{56} +(-3609.51 + 3609.51i) q^{58} +(206.279 + 206.279i) q^{59} +6998.83 q^{61} -12205.4i q^{62} -6268.91i q^{64} +(-3140.77 + 30.0794i) q^{65} +(-939.648 + 939.648i) q^{67} -7162.15 q^{68} +(-3716.43 + 3716.43i) q^{70} +(3049.34 - 3049.34i) q^{71} +(-840.175 - 840.175i) q^{73} -9856.69 q^{74} +(-9343.97 - 9343.97i) q^{76} +3553.65i q^{77} +4044.54 q^{79} +(942.716 - 942.716i) q^{80} +10540.5i q^{82} +(-2060.82 + 2060.82i) q^{83} +(3386.67 + 3386.67i) q^{85} +(9032.76 + 9032.76i) q^{86} -6489.30i q^{88} +(-6032.18 - 6032.18i) q^{89} +(-69.1630 - 7221.71i) q^{91} +13513.5 q^{92} -615.468 q^{94} +8836.73i q^{95} +(5575.10 - 5575.10i) q^{97} +(2689.71 + 2689.71i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{5} - 24 q^{7} - 372 q^{11} - 224 q^{13} - 480 q^{14} - 2328 q^{16} - 840 q^{19} - 228 q^{20} + 3536 q^{22} + 828 q^{26} - 1984 q^{28} + 5064 q^{29} + 1712 q^{31} + 7260 q^{32} + 8040 q^{34}+ \cdots - 11544 q^{98}+O(q^{100}) $ 20 * q - 24 * q^5 - 24 * q^7 - 372 * q^11 - 224 * q^13 - 480 * q^14 - 2328 * q^16 - 840 * q^19 - 228 * q^20 + 3536 * q^22 + 828 * q^26 - 1984 * q^28 + 5064 * q^29 + 1712 * q^31 + 7260 * q^32 + 8040 * q^34 - 5976 * q^35 - 868 * q^37 + 6336 * q^40 + 6000 * q^41 - 20868 * q^44 - 1992 * q^46 - 1692 * q^47 - 8952 * q^50 - 12416 * q^52 + 18816 * q^53 - 3280 * q^55 + 1256 * q^58 + 6588 * q^59 - 5512 * q^61 - 33048 * q^65 - 4704 * q^67 + 28296 * q^68 - 31096 * q^70 - 9756 * q^71 + 13692 * q^73 + 28296 * q^74 - 17072 * q^76 - 5056 * q^79 - 42228 * q^80 - 24708 * q^83 - 4752 * q^85 + 77424 * q^86 - 36000 * q^89 + 19104 * q^91 - 12912 * q^92 + 112832 * q^94 + 50012 * q^97 - 11544 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−4.67933	+	4.67933i	−1.16983	+	1.16983i	−0.187584	+	0.982249i	$0.560066\pi$
$2$	−4.67933	+	4.67933i	−1.16983	+	1.16983i	−0.982249	+	0.187584i	$0.939934\pi$
$3$		0			0
$3$		0			0
$4$		−	27.7923i		−	1.73702i
$5$	−13.1418	+	13.1418i	−0.525671	+	0.525671i	−0.919279	−	0.393608i	$-0.871227\pi$
$5$	−13.1418	+	13.1418i	−0.525671	+	0.525671i	0.393608	+	0.919279i	$0.371227\pi$
$6$		0			0
$7$	−30.2175	−	30.2175i	−0.616684	−	0.616684i	0.327996	−	0.944679i	$-0.393627\pi$
$7$	−30.2175	−	30.2175i	−0.616684	−	0.616684i	−0.944679	+	0.327996i	$0.893627\pi$
$8$	55.1800	+	55.1800i	0.862187	+	0.862187i
$9$		0			0
$10$		−	122.989i		−	1.22989i
$11$	−58.8012	−	58.8012i	−0.485960	−	0.485960i	0.421069	−	0.907029i	$-0.361655\pi$
$11$	−58.8012	−	58.8012i	−0.485960	−	0.485960i	−0.907029	+	0.421069i	$0.861655\pi$
$12$		0			0
$13$	120.640	+	118.351i	0.713846	+	0.700303i
$13$	120.640	+	118.351i	0.713846	+	0.700303i
$14$	282.795			1.44283
$15$		0			0
$16$	−71.7343			−0.280212
$17$		−	257.703i		−	0.891706i	−0.895106	−	0.445853i	$-0.852900\pi$
$17$		−	257.703i		−	0.891706i	0.895106	−	0.445853i	$-0.147100\pi$
$18$		0			0
$19$	336.208	−	336.208i	0.931323	−	0.931323i	−0.0664659	−	0.997789i	$-0.521172\pi$
$19$	336.208	−	336.208i	0.931323	−	0.931323i	0.997789	+	0.0664659i	$0.0211724\pi$
$20$	365.240	+	365.240i	0.913100	+	0.913100i
$21$		0			0
$22$	550.300			1.13698
$23$			486.231i			0.919151i	0.888139	+	0.459576i	$0.151999\pi$
$23$			486.231i			0.919151i	−0.888139	+	0.459576i	$0.848001\pi$
$24$		0			0
$25$			279.587i			0.447340i
$26$	−1118.32	+	10.7102i	−1.65432	+	0.0158436i
$27$		0			0
$28$	−839.813	+	839.813i	−1.07119	+	1.07119i
$29$	771.373			0.917209			0.458604	−	0.888641i	$-0.348350\pi$
$29$	771.373			0.917209			0.458604	+	0.888641i	$0.348350\pi$
$30$		0			0
$31$	−1304.18	+	1304.18i	−1.35711	+	1.35711i	−0.479654	+	0.877458i	$0.659238\pi$
$31$	−1304.18	+	1304.18i	−1.35711	+	1.35711i	−0.877458	+	0.479654i	$0.840762\pi$
$32$	−547.211	+	547.211i	−0.534386	+	0.534386i
$33$		0			0
$34$	1205.88	+	1205.88i	1.04315	+	1.04315i
$35$	794.223			0.648345
$36$		0			0
$37$	1053.22	+	1053.22i	0.769333	+	0.769333i	0.977989	−	0.208656i	$-0.0669091\pi$
$37$	1053.22	+	1053.22i	0.769333	+	0.769333i	−0.208656	+	0.977989i	$0.566909\pi$
$38$			3146.45i			2.17898i
$39$		0			0
$40$	−1450.33			−0.906454
$41$	1126.29	−	1126.29i	0.670010	−	0.670010i	−0.287708	−	0.957718i	$-0.592893\pi$
$41$	1126.29	−	1126.29i	0.670010	−	0.670010i	0.957718	+	0.287708i	$0.0928932\pi$
$42$		0			0
$43$		−	1930.35i		−	1.04400i	−0.852946	−	0.521999i	$-0.825186\pi$
$43$		−	1930.35i		−	1.04400i	0.852946	−	0.521999i	$-0.174814\pi$
$44$	−1634.22	+	1634.22i	−0.844121	+	0.844121i
$45$		0			0
$46$	−2275.24	−	2275.24i	−1.07525	−	1.07525i
$47$	65.7645	+	65.7645i	0.0297712	+	0.0297712i	0.721836	−	0.692064i	$-0.243299\pi$
$47$	65.7645	+	65.7645i	0.0297712	+	0.0297712i	−0.692064	+	0.721836i	$0.743299\pi$
$48$		0			0
$49$		−	574.806i		−	0.239403i
$50$	−1308.28	−	1308.28i	−0.523313	−	0.523313i
$51$		0			0
$52$	3289.25	−	3352.86i	1.21644	−	1.23996i
$53$	5040.23			1.79432			0.897158	−	0.441710i	$-0.145628\pi$
$53$	5040.23			1.79432			0.897158	+	0.441710i	$0.145628\pi$
$54$		0			0
$55$	1545.50			0.510910
$56$		−	3334.80i		−	1.06339i
$57$		0			0
$58$	−3609.51	+	3609.51i	−1.07298	+	1.07298i
$59$	206.279	+	206.279i	0.0592586	+	0.0592586i	0.736115	−	0.676856i	$-0.236658\pi$
$59$	206.279	+	206.279i	0.0592586	+	0.0592586i	−0.676856	+	0.736115i	$0.736658\pi$
$60$		0			0
$61$	6998.83			1.88090			0.940450	−	0.339932i	$-0.110404\pi$
$61$	6998.83			1.88090			0.940450	+	0.339932i	$0.110404\pi$
$62$		−	12205.4i		−	3.17519i
$63$		0			0
$64$		−	6268.91i		−	1.53050i
$65$	−3140.77	+	30.0794i	−0.743377	+	0.00711939i
$66$		0			0
$67$	−939.648	+	939.648i	−0.209322	+	0.209322i	−0.803979	−	0.594657i	$-0.797288\pi$
$67$	−939.648	+	939.648i	−0.209322	+	0.209322i	0.594657	+	0.803979i	$0.297288\pi$
$68$	−7162.15			−1.54891
$69$		0			0
$70$	−3716.43	+	3716.43i	−0.758456	+	0.758456i
$71$	3049.34	−	3049.34i	0.604908	−	0.604908i	−0.336703	−	0.941611i	$-0.609312\pi$
$71$	3049.34	−	3049.34i	0.604908	−	0.604908i	0.941611	+	0.336703i	$0.109312\pi$
$72$		0			0
$73$	−840.175	−	840.175i	−0.157661	−	0.157661i	0.623869	−	0.781529i	$-0.285560\pi$
$73$	−840.175	−	840.175i	−0.157661	−	0.157661i	−0.781529	+	0.623869i	$0.785560\pi$
$74$	−9856.69			−1.79998
$75$		0			0
$76$	−9343.97	−	9343.97i	−1.61772	−	1.61772i
$77$			3553.65i			0.599367i
$78$		0			0
$79$	4044.54			0.648059			0.324030	−	0.946047i	$-0.394962\pi$
$79$	4044.54			0.648059			0.324030	+	0.946047i	$0.394962\pi$
$80$	942.716	−	942.716i	0.147299	−	0.147299i
$81$		0			0
$82$			10540.5i			1.56760i
$83$	−2060.82	+	2060.82i	−0.299147	+	0.299147i	−0.840680	−	0.541533i	$-0.817844\pi$
$83$	−2060.82	+	2060.82i	−0.299147	+	0.299147i	0.541533	+	0.840680i	$0.317844\pi$
$84$		0			0
$85$	3386.67	+	3386.67i	0.468744	+	0.468744i
$86$	9032.76	+	9032.76i	1.22130	+	1.22130i
$87$		0			0
$88$		−	6489.30i		−	0.837977i
$89$	−6032.18	−	6032.18i	−0.761543	−	0.761543i	0.215059	−	0.976601i	$-0.431006\pi$
$89$	−6032.18	−	6032.18i	−0.761543	−	0.761543i	−0.976601	+	0.215059i	$0.931006\pi$
$90$		0			0
$91$	−69.1630	−	7221.71i	−0.00835202	−	0.872082i
$92$	13513.5			1.59658
$93$		0			0
$94$	−615.468			−0.0696546
$95$			8836.73i			0.979139i
$96$		0			0
$97$	5575.10	−	5575.10i	0.592528	−	0.592528i	−0.345785	−	0.938314i	$-0.612387\pi$
$97$	5575.10	−	5575.10i	0.592528	−	0.592528i	0.938314	+	0.345785i	$0.112387\pi$
$98$	2689.71	+	2689.71i	0.280061	+	0.280061i
$99$		0			0
$100$	7770.37			0.777037
$101$		−	14591.5i		−	1.43040i	−0.698920	−	0.715200i	$-0.746335\pi$
$101$		−	14591.5i		−	1.43040i	0.698920	−	0.715200i	$-0.253665\pi$
$102$		0			0
$103$			13071.3i			1.23210i	0.787708	+	0.616048i	$0.211267\pi$
$103$			13071.3i			1.23210i	−0.787708	+	0.616048i	$0.788733\pi$
$104$	126.298	+	13187.5i	0.0116770	+	1.21926i
$105$		0			0
$106$	−23584.9	+	23584.9i	−2.09905	+	2.09905i
$107$	14255.0			1.24509			0.622545	−	0.782584i	$-0.286099\pi$
$107$	14255.0			1.24509			0.622545	+	0.782584i	$0.286099\pi$
$108$		0			0
$109$	−4886.68	+	4886.68i	−0.411302	+	0.411302i	−0.882192	−	0.470890i	$-0.843933\pi$
$109$	−4886.68	+	4886.68i	−0.411302	+	0.411302i	0.470890	+	0.882192i	$0.343933\pi$
$110$	−7231.92	+	7231.92i	−0.597680	+	0.597680i
$111$		0			0
$112$	2167.63	+	2167.63i	0.172802	+	0.172802i
$113$	3433.45			0.268890			0.134445	−	0.990921i	$-0.457075\pi$
$113$	3433.45			0.268890			0.134445	+	0.990921i	$0.457075\pi$
$114$		0			0
$115$	−6389.94	−	6389.94i	−0.483171	−	0.483171i
$116$		−	21438.2i		−	1.59321i
$117$		0			0
$118$	−1930.50			−0.138645
$119$	−7787.14	+	7787.14i	−0.549900	+	0.549900i
$120$		0			0
$121$		−	7725.84i		−	0.527685i
$122$	−32749.8	+	32749.8i	−2.20034	+	2.20034i
$123$		0			0
$124$	36246.3	+	36246.3i	2.35733	+	2.35733i
$125$	−11887.9	−	11887.9i	−0.760825	−	0.760825i
$126$		0			0
$127$		−	21948.2i		−	1.36079i	−0.732846	−	0.680395i	$-0.761808\pi$
$127$		−	21948.2i		−	1.36079i	0.732846	−	0.680395i	$-0.238192\pi$
$128$	20578.9	+	20578.9i	1.25604	+	1.25604i
$129$		0			0
$130$	14555.9	−	14837.4i	0.861298	−	0.877955i
$131$	1658.15			0.0966231			0.0483116	−	0.998832i	$-0.484616\pi$
$131$	1658.15			0.0966231			0.0483116	+	0.998832i	$0.484616\pi$
$132$		0			0
$133$	−20318.7			−1.14866
$134$		−	8793.84i		−	0.489744i
$135$		0			0
$136$	14220.0	−	14220.0i	0.768817	−	0.768817i
$137$	21604.3	+	21604.3i	1.15106	+	1.15106i	0.986340	+	0.164724i	$0.0526732\pi$
$137$	21604.3	+	21604.3i	1.15106	+	1.15106i	0.164724	+	0.986340i	$0.447327\pi$
$138$		0			0
$139$	−4658.17			−0.241094			−0.120547	−	0.992708i	$-0.538465\pi$
$139$	−4658.17			−0.241094			−0.120547	+	0.992708i	$0.538465\pi$
$140$		−	22073.3i		−	1.12619i
$141$		0			0
$142$			28537.8i			1.41528i
$143$	−134.587	−	14053.0i	−0.00658157	−	0.687220i
$144$		0			0
$145$	−10137.2	+	10137.2i	−0.482150	+	0.482150i
$146$	7862.91			0.368874
$147$		0			0
$148$	29271.3	−	29271.3i	1.33634	−	1.33634i
$149$	−393.889	+	393.889i	−0.0177420	+	0.0177420i	−0.715922	−	0.698180i	$-0.753993\pi$
$149$	−393.889	+	393.889i	−0.0177420	+	0.0177420i	0.698180	+	0.715922i	$0.253993\pi$
$150$		0			0
$151$	−7620.89	−	7620.89i	−0.334235	−	0.334235i	0.519957	−	0.854192i	$-0.325948\pi$
$151$	−7620.89	−	7620.89i	−0.334235	−	0.334235i	−0.854192	+	0.519957i	$0.825948\pi$
$152$	37103.8			1.60595
$153$		0			0
$154$	−16628.7	−	16628.7i	−0.701159	−	0.701159i
$155$		−	34278.6i		−	1.42679i
$156$		0			0
$157$	25587.3			1.03807			0.519034	−	0.854754i	$-0.326292\pi$
$157$	25587.3			1.03807			0.519034	+	0.854754i	$0.326292\pi$
$158$	−18925.7	+	18925.7i	−0.758121	+	0.758121i
$159$		0			0
$160$		−	14382.7i		−	0.561822i
$161$	14692.7	−	14692.7i	0.566826	−	0.566826i
$162$		0			0
$163$	−16600.8	−	16600.8i	−0.624820	−	0.624820i	0.321940	−	0.946760i	$-0.395665\pi$
$163$	−16600.8	−	16600.8i	−0.624820	−	0.624820i	−0.946760	+	0.321940i	$0.895665\pi$
$164$	−31302.1	−	31302.1i	−1.16382	−	1.16382i
$165$		0			0
$166$		−	19286.6i		−	0.699904i
$167$	37894.4	+	37894.4i	1.35876	+	1.35876i	0.875451	+	0.483307i	$0.160565\pi$
$167$	37894.4	+	37894.4i	1.35876	+	1.35876i	0.483307	+	0.875451i	$0.339435\pi$
$168$		0			0
$169$	547.013	+	28555.8i	0.0191524	+	0.999817i
$170$	−31694.7			−1.09670
$171$		0			0
$172$	−53648.9			−1.81344
$173$		−	1712.90i		−	0.0572321i	−0.999590	−	0.0286161i	$-0.990890\pi$
$173$		−	1712.90i		−	0.0572321i	0.999590	−	0.0286161i	$-0.00911002\pi$
$174$		0			0
$175$	8448.43	−	8448.43i	0.275867	−	0.275867i
$176$	4218.06	+	4218.06i	0.136172	+	0.136172i
$177$		0			0
$178$	56453.1			1.78176
$179$			2700.43i			0.0842803i	0.999112	+	0.0421401i	$0.0134176\pi$
$179$			2700.43i			0.0842803i	−0.999112	+	0.0421401i	$0.986582\pi$
$180$		0			0
$181$			31325.6i			0.956186i	0.878309	+	0.478093i	$0.158672\pi$
$181$			31325.6i			0.956186i	−0.878309	+	0.478093i	$0.841328\pi$
$182$	34116.4	+	33469.1i	1.02996	+	1.01042i
$183$		0			0
$184$	−26830.2	+	26830.2i	−0.792481	+	0.792481i
$185$	−27682.3			−0.808832
$186$		0			0
$187$	−15153.2	+	15153.2i	−0.433333	+	0.433333i
$188$	1827.75	−	1827.75i	0.0517131	−	0.0517131i
$189$		0			0
$190$	−41350.0	−	41350.0i	−1.14543	−	1.14543i
$191$	−52778.0			−1.44672			−0.723362	−	0.690469i	$-0.757404\pi$
$191$	−52778.0			−1.44672			−0.723362	+	0.690469i	$0.757404\pi$
$192$		0			0
$193$	1405.79	+	1405.79i	0.0377403	+	0.0377403i	0.725725	−	0.687985i	$-0.241504\pi$
$193$	1405.79	+	1405.79i	0.0377403	+	0.0377403i	−0.687985	+	0.725725i	$0.741504\pi$
$194$			52175.5i			1.38632i
$195$		0			0
$196$	−15975.2			−0.415847
$197$	−10175.2	+	10175.2i	−0.262188	+	0.262188i	−0.825942	−	0.563755i	$-0.809356\pi$
$197$	−10175.2	+	10175.2i	−0.262188	+	0.262188i	0.563755	+	0.825942i	$0.309356\pi$
$198$		0			0
$199$		−	7439.54i		−	0.187862i	−0.995579	−	0.0939312i	$-0.970057\pi$
$199$		−	7439.54i		−	0.187862i	0.995579	−	0.0939312i	$-0.0299434\pi$
$200$	−15427.6	+	15427.6i	−0.385691	+	0.385691i
$201$		0			0
$202$	68278.5	+	68278.5i	1.67333	+	1.67333i
$203$	−23308.9	−	23308.9i	−0.565627	−	0.565627i
$204$		0			0
$205$			29602.8i			0.704410i
$206$	−61165.0	−	61165.0i	−1.44135	−	1.44135i
$207$		0			0
$208$	−8654.02	−	8489.84i	−0.200028	−	0.196233i
$209$	−39538.8			−0.905172
$210$		0			0
$211$	−45876.3			−1.03044			−0.515221	−	0.857057i	$-0.672290\pi$
$211$	−45876.3			−1.03044			−0.515221	+	0.857057i	$0.672290\pi$
$212$		−	140080.i		−	3.11676i
$213$		0			0
$214$	−66704.1	+	66704.1i	−1.45655	+	1.45655i
$215$	25368.3	+	25368.3i	0.548800	+	0.548800i
$216$		0			0
$217$	78818.4			1.67382
$218$		−	45732.8i		−	0.962309i
$219$		0			0
$220$		−	42953.1i		−	0.887460i
$221$	30499.4	−	31089.3i	0.624464	−	0.636541i
$222$		0			0
$223$	26187.3	−	26187.3i	0.526601	−	0.526601i	−0.392956	−	0.919557i	$-0.628548\pi$
$223$	26187.3	−	26187.3i	0.526601	−	0.526601i	0.919557	+	0.392956i	$0.128548\pi$
$224$	33070.7			0.659094
$225$		0			0
$226$	−16066.3	+	16066.3i	−0.314556	+	0.314556i
$227$	20418.0	−	20418.0i	0.396244	−	0.396244i	−0.480662	−	0.876906i	$-0.659604\pi$
$227$	20418.0	−	20418.0i	0.396244	−	0.396244i	0.876906	+	0.480662i	$0.159604\pi$
$228$		0			0
$229$	−52109.2	−	52109.2i	−0.993672	−	0.993672i	0.00630803	−	0.999980i	$-0.497992\pi$
$229$	−52109.2	−	52109.2i	−0.993672	−	0.993672i	−0.999980	+	0.00630803i	$0.997992\pi$
$230$	59801.3			1.13046
$231$		0			0
$232$	42564.3	+	42564.3i	0.790806	+	0.790806i
$233$			45782.3i			0.843308i	0.906757	+	0.421654i	$0.138550\pi$
$233$			45782.3i			0.843308i	−0.906757	+	0.421654i	$0.861450\pi$
$234$		0			0
$235$	−1728.53			−0.0312997
$236$	5732.97	−	5732.97i	0.102933	−	0.102933i
$237$		0			0
$238$		−	72877.2i		−	1.28658i
$239$	54954.6	−	54954.6i	0.962073	−	0.962073i	−0.0372339	−	0.999307i	$-0.511855\pi$
$239$	54954.6	−	54954.6i	0.962073	−	0.962073i	0.999307	+	0.0372339i	$0.0118546\pi$
$240$		0			0
$241$	23474.0	+	23474.0i	0.404159	+	0.404159i	0.879696	−	0.475537i	$-0.157746\pi$
$241$	23474.0	+	23474.0i	0.404159	+	0.404159i	−0.475537	+	0.879696i	$0.657746\pi$
$242$	36151.8	+	36151.8i	0.617304	+	0.617304i
$243$		0			0
$244$		−	194513.i		−	3.26716i
$245$	7553.98	+	7553.98i	0.125847	+	0.125847i
$246$		0			0
$247$	80350.6	−	769.526i	1.31703	−	0.0126133i
$248$	−143930.			−2.34017
$249$		0			0
$250$	111255.			1.78008
$251$			51668.4i			0.820120i	0.912059	+	0.410060i	$0.134492\pi$
$251$			51668.4i			0.820120i	−0.912059	+	0.410060i	$0.865508\pi$
$252$		0			0
$253$	28591.0	−	28591.0i	0.446671	−	0.446671i
$254$	102703.	+	102703.i	1.59190	+	1.59190i
$255$		0			0
$256$	−92288.7			−1.40821
$257$			87980.2i			1.33204i	0.745932	+	0.666022i	$0.232004\pi$
$257$			87980.2i			1.33204i	−0.745932	+	0.666022i	$0.767996\pi$
$258$		0			0
$259$		−	63651.1i		−	0.948869i
$260$	835.976	+	87289.1i	0.0123665	+	1.29126i
$261$		0			0
$262$	−7759.03	+	7759.03i	−0.113033	+	0.113033i
$263$	−113585.			−1.64214			−0.821068	−	0.570831i	$-0.806621\pi$
$263$	−113585.			−1.64214			−0.821068	+	0.570831i	$0.806621\pi$
$264$		0			0
$265$	−66237.6	+	66237.6i	−0.943220	+	0.943220i
$266$	95077.9	−	95077.9i	1.34374	−	1.34374i
$267$		0			0
$268$	26114.9	+	26114.9i	0.363596	+	0.363596i
$269$	−5647.94			−0.0780523			−0.0390262	−	0.999238i	$-0.512426\pi$
$269$	−5647.94			−0.0780523			−0.0390262	+	0.999238i	$0.512426\pi$
$270$		0			0
$271$	−3722.39	−	3722.39i	−0.0506854	−	0.0506854i	0.681310	−	0.731995i	$-0.261411\pi$
$271$	−3722.39	−	3722.39i	−0.0506854	−	0.0506854i	−0.731995	+	0.681310i	$0.761411\pi$
$272$			18486.1i			0.249867i
$273$		0			0
$274$	−202187.			−2.69310
$275$	16440.1	−	16440.1i	0.217389	−	0.217389i
$276$		0			0
$277$			31673.1i			0.412792i	0.978469	+	0.206396i	$0.0661736\pi$
$277$			31673.1i			0.412792i	−0.978469	+	0.206396i	$0.933826\pi$
$278$	21797.1	−	21797.1i	0.282039	−	0.282039i
$279$		0			0
$280$	43825.2	+	43825.2i	0.558995	+	0.558995i
$281$	10897.2	+	10897.2i	0.138007	+	0.138007i	0.772736	−	0.634728i	$-0.218888\pi$
$281$	10897.2	+	10897.2i	0.138007	+	0.138007i	−0.634728	+	0.772736i	$0.718888\pi$
$282$		0			0
$283$			30994.4i			0.387000i	0.981100	+	0.193500i	$0.0619839\pi$
$283$			30994.4i			0.387000i	−0.981100	+	0.193500i	$0.938016\pi$
$284$	−84748.2	−	84748.2i	−1.05074	−	1.05074i
$285$		0			0
$286$	66388.2	+	65128.7i	0.811632	+	0.796233i
$287$	−68067.2			−0.826369
$288$		0			0
$289$	17110.2			0.204861
$290$		−	94870.7i		−	1.12807i
$291$		0			0
$292$	−23350.4	+	23350.4i	−0.273860	+	0.273860i
$293$	113536.	+	113536.i	1.32251	+	1.32251i	0.911741	+	0.410765i	$0.134738\pi$
$293$	113536.	+	113536.i	1.32251	+	1.32251i	0.410765	+	0.911741i	$0.365262\pi$
$294$		0			0
$295$	−5421.75			−0.0623011
$296$			116233.i			1.32662i
$297$		0			0
$298$		−	3686.28i		−	0.0415103i
$299$	−57546.0	+	58658.9i	−0.643684	+	0.656133i
$300$		0			0
$301$	−58330.4	+	58330.4i	−0.643817	+	0.643817i
$302$	71321.3			0.781998
$303$		0			0
$304$	−24117.6	+	24117.6i	−0.260968	+	0.260968i
$305$	−91977.0	+	91977.0i	−0.988735	+	0.988735i
$306$		0			0
$307$	75222.4	+	75222.4i	0.798124	+	0.798124i	0.982800	−	0.184675i	$-0.0591233\pi$
$307$	75222.4	+	75222.4i	0.798124	+	0.798124i	−0.184675	+	0.982800i	$0.559123\pi$
$308$	98764.0			1.04111
$309$		0			0
$310$	160401.	+	160401.i	1.66910	+	1.66910i
$311$		−	150426.i		−	1.55525i	−0.628726	−	0.777627i	$-0.716423\pi$
$311$		−	150426.i		−	1.55525i	0.628726	−	0.777627i	$-0.283577\pi$
$312$		0			0
$313$	126604.			1.29229			0.646144	−	0.763216i	$-0.276381\pi$
$313$	126604.			1.29229			0.646144	+	0.763216i	$0.276381\pi$
$314$	−119732.	+	119732.i	−1.21437	+	1.21437i
$315$		0			0
$316$		−	112407.i		−	1.12569i
$317$	42350.8	−	42350.8i	0.421447	−	0.421447i	−0.464255	−	0.885702i	$-0.653678\pi$
$317$	42350.8	−	42350.8i	0.421447	−	0.421447i	0.885702	+	0.464255i	$0.153678\pi$
$318$		0			0
$319$	−45357.6	−	45357.6i	−0.445727	−	0.445727i
$320$	82384.6	+	82384.6i	0.804537	+	0.804537i
$321$		0			0
$322$			137504.i			1.32618i
$323$	−86641.7	−	86641.7i	−0.830466	−	0.830466i
$324$		0			0
$325$	−33089.5	+	33729.4i	−0.313273	+	0.319332i
$326$	155362.			1.46187
$327$		0			0
$328$	124297.			1.15535
$329$		−	3974.48i		−	0.0367188i
$330$		0			0
$331$	23593.9	−	23593.9i	0.215349	−	0.215349i	−0.591186	−	0.806535i	$-0.701340\pi$
$331$	23593.9	−	23593.9i	0.215349	−	0.215349i	0.806535	+	0.591186i	$0.201340\pi$
$332$	57275.0	+	57275.0i	0.519624	+	0.519624i
$333$		0			0
$334$	−354641.			−3.17904
$335$		−	24697.3i		−	0.220069i
$336$		0			0
$337$		−	114863.i		−	1.01139i	−0.862711	−	0.505697i	$-0.831235\pi$
$337$		−	114863.i		−	1.01139i	0.862711	−	0.505697i	$-0.168765\pi$
$338$	−136182.	−	131062.i	−1.19202	−	1.14721i
$339$		0			0
$340$	94123.4	−	94123.4i	0.814216	−	0.814216i
$341$	153375.			1.31900
$342$		0			0
$343$	−89921.4	+	89921.4i	−0.764319	+	0.764319i
$344$	106517.	−	106517.i	0.900122	−	0.900122i
$345$		0			0
$346$	8015.22	+	8015.22i	0.0669520	+	0.0669520i
$347$	−93409.6			−0.775769			−0.387885	−	0.921708i	$-0.626794\pi$
$347$	−93409.6			−0.775769			−0.387885	+	0.921708i	$0.626794\pi$
$348$		0			0
$349$	−14479.3	−	14479.3i	−0.118877	−	0.118877i	0.645166	−	0.764043i	$-0.276788\pi$
$349$	−14479.3	−	14479.3i	−0.118877	−	0.118877i	−0.764043	+	0.645166i	$0.776788\pi$
$350$			79066.0i			0.645437i
$351$		0			0
$352$	64353.3			0.519380
$353$	−127078.	+	127078.i	−1.01981	+	1.01981i	−0.0200140	+	0.999800i	$0.506371\pi$
$353$	−127078.	+	127078.i	−1.01981	+	1.01981i	−0.999800	+	0.0200140i	$0.993629\pi$
$354$		0			0
$355$			80147.6i			0.635966i
$356$	−167648.	+	167648.i	−1.32281	+	1.32281i
$357$		0			0
$358$	−12636.2	−	12636.2i	−0.0985939	−	0.0985939i
$359$	−40565.6	−	40565.6i	−0.314752	−	0.314752i	0.531995	−	0.846747i	$-0.321442\pi$
$359$	−40565.6	−	40565.6i	−0.314752	−	0.314752i	−0.846747	+	0.531995i	$0.821442\pi$
$360$		0			0
$361$		−	95750.0i		−	0.734724i
$362$	−146583.	−	146583.i	−1.11858	−	1.11858i
$363$		0			0
$364$	−200708.	+	1922.20i	−1.51482	+	0.0145076i
$365$	22082.8			0.165755
$366$		0			0
$367$	−40747.7			−0.302532			−0.151266	−	0.988493i	$-0.548335\pi$
$367$	−40747.7			−0.302532			−0.151266	+	0.988493i	$0.548335\pi$
$368$		−	34879.4i		−	0.257557i
$369$		0			0
$370$	129534.	−	129534.i	0.946198	−	0.946198i
$371$	−152303.	−	152303.i	−1.10652	−	1.10652i
$372$		0			0
$373$	−44353.1			−0.318791			−0.159396	−	0.987215i	$-0.550955\pi$
$373$	−44353.1			−0.318791			−0.159396	+	0.987215i	$0.550955\pi$
$374$		−	141814.i		−	1.01386i
$375$		0			0
$376$			7257.77i			0.0513367i
$377$	93058.4	+	91292.8i	0.654746	+	0.642324i
$378$		0			0
$379$	−27066.7	+	27066.7i	−0.188433	+	0.188433i	−0.795018	−	0.606585i	$-0.792539\pi$
$379$	−27066.7	+	27066.7i	−0.188433	+	0.188433i	0.606585	+	0.795018i	$0.292539\pi$
$380$	245593.			1.70078
$381$		0			0
$382$	246966.	−	246966.i	1.69243	−	1.69243i
$383$	166419.	−	166419.i	1.13451	−	1.13451i	0.145087	−	0.989419i	$-0.453654\pi$
$383$	166419.	−	166419.i	1.13451	−	1.13451i	0.989419	−	0.145087i	$-0.0463461\pi$
$384$		0			0
$385$	−46701.2	−	46701.2i	−0.315070	−	0.315070i
$386$	−13156.3			−0.0882997
$387$		0			0
$388$	−154945.	−	154945.i	−1.02923	−	1.02923i
$389$		−	16474.9i		−	0.108874i	−0.998517	−	0.0544371i	$-0.982664\pi$
$389$		−	16474.9i		−	0.108874i	0.998517	−	0.0544371i	$-0.0173364\pi$
$390$		0			0
$391$	125303.			0.819613
$392$	31717.8	−	31717.8i	0.206410	−	0.206410i
$393$		0			0
$394$		−	95226.6i		−	0.613431i
$395$	−53152.4	+	53152.4i	−0.340666	+	0.340666i
$396$		0			0
$397$	−155869.	−	155869.i	−0.988957	−	0.988957i	0.0109822	−	0.999940i	$-0.496504\pi$
$397$	−155869.	−	155869.i	−0.988957	−	0.988957i	−0.999940	+	0.0109822i	$0.996504\pi$
$398$	34812.1	+	34812.1i	0.219768	+	0.219768i
$399$		0			0
$400$		−	20056.0i		−	0.125350i
$401$	142185.	+	142185.i	0.884230	+	0.884230i	0.993961	−	0.109732i	$-0.0349991\pi$
$401$	142185.	+	142185.i	0.884230	+	0.884230i	−0.109732	+	0.993961i	$0.534999\pi$
$402$		0			0
$403$	−311689.	+	2985.07i	−1.91916	+	0.0183800i
$404$	−405531.			−2.48463
$405$		0			0
$406$	218141.			1.32338
$407$		−	123861.i		−	0.747730i
$408$		0			0
$409$	9949.25	−	9949.25i	0.0594763	−	0.0594763i	−0.676743	−	0.736219i	$-0.736609\pi$
$409$	9949.25	−	9949.25i	0.0594763	−	0.0594763i	0.736219	+	0.676743i	$0.236609\pi$
$410$	−138521.	−	138521.i	−0.824042	−	0.824042i
$411$		0			0
$412$	363282.			2.14017
$413$		−	12466.5i		−	0.0730876i
$414$		0			0
$415$		−	54165.8i		−	0.314506i
$416$	−130779.	+	1252.48i	−0.755701	+	0.00723742i
$417$		0			0
$418$	185015.	−	185015.i	1.05890	−	1.05890i
$419$	17793.2			0.101351			0.0506753	−	0.998715i	$-0.483863\pi$
$419$	17793.2			0.101351			0.0506753	+	0.998715i	$0.483863\pi$
$420$		0			0
$421$	−123242.	+	123242.i	−0.695334	+	0.695334i	−0.963400	−	0.268066i	$-0.913615\pi$
$421$	−123242.	+	123242.i	−0.695334	+	0.695334i	0.268066	+	0.963400i	$0.413615\pi$
$422$	214671.	−	214671.i	1.20545	−	1.20545i
$423$		0			0
$424$	278120.	+	278120.i	1.54704	+	1.54704i
$425$	72050.5			0.398896
$426$		0			0
$427$	−211487.	−	211487.i	−1.15992	−	1.15992i
$428$		−	396180.i		−	2.16274i
$429$		0			0
$430$	−237413.			−1.28401
$431$	81585.7	−	81585.7i	0.439197	−	0.439197i	−0.452545	−	0.891742i	$-0.649484\pi$
$431$	81585.7	−	81585.7i	0.439197	−	0.439197i	0.891742	+	0.452545i	$0.149484\pi$
$432$		0			0
$433$		−	60799.1i		−	0.324281i	−0.986768	−	0.162141i	$-0.948160\pi$
$433$		−	60799.1i		−	0.324281i	0.986768	−	0.162141i	$-0.0518398\pi$
$434$	−368817.	+	368817.i	−1.95809	+	1.95809i
$435$		0			0
$436$	135812.	+	135812.i	0.714439	+	0.714439i
$437$	163475.	+	163475.i	0.856027	+	0.856027i
$438$		0			0
$439$			275044.i			1.42716i	0.700572	+	0.713581i	$0.252928\pi$
$439$			275044.i			1.42716i	−0.700572	+	0.713581i	$0.747072\pi$
$440$	85280.9	+	85280.9i	0.440500	+	0.440500i
$441$		0			0
$442$	2760.06	+	288194.i	0.0141278	+	1.47516i
$443$	8716.50			0.0444155			0.0222077	−	0.999753i	$-0.492930\pi$
$443$	8716.50			0.0444155			0.0222077	+	0.999753i	$0.492930\pi$
$444$		0			0
$445$	158547.			0.800642
$446$			245078.i			1.23207i
$447$		0			0
$448$	−189431.	+	189431.i	−0.943832	+	0.943832i
$449$	−246638.	−	246638.i	−1.22340	−	1.22340i	−0.966416	−	0.256982i	$-0.917272\pi$
$449$	−246638.	−	246638.i	−1.22340	−	1.22340i	−0.256982	−	0.966416i	$-0.582728\pi$
$450$		0			0
$451$	−132454.			−0.651197
$452$		−	95423.5i		−	0.467066i
$453$		0			0
$454$			191086.i			0.927078i
$455$	95815.0	+	93997.2i	0.462819	+	0.454038i
$456$		0			0
$457$	55246.3	−	55246.3i	0.264527	−	0.264527i	−0.562363	−	0.826890i	$-0.690108\pi$
$457$	55246.3	−	55246.3i	0.264527	−	0.264527i	0.826890	+	0.562363i	$0.190108\pi$
$458$	487672.			2.32486
$459$		0			0
$460$	−177591.	+	177591.i	−0.839277	+	0.839277i
$461$	31473.0	−	31473.0i	0.148093	−	0.148093i	−0.629172	−	0.777266i	$-0.716606\pi$
$461$	31473.0	−	31473.0i	0.148093	−	0.148093i	0.777266	+	0.629172i	$0.216606\pi$
$462$		0			0
$463$	134703.	+	134703.i	0.628371	+	0.628371i	0.947658	−	0.319287i	$-0.103443\pi$
$463$	134703.	+	134703.i	0.628371	+	0.628371i	−0.319287	+	0.947658i	$0.603443\pi$
$464$	−55333.9			−0.257013
$465$		0			0
$466$	−214231.	−	214231.i	−0.986529	−	0.986529i
$467$		−	106801.i		−	0.489714i	−0.969559	−	0.244857i	$-0.921259\pi$
$467$		−	106801.i		−	0.489714i	0.969559	−	0.244857i	$-0.0787410\pi$
$468$		0			0
$469$	56787.6			0.258171
$470$	8088.34	−	8088.34i	0.0366154	−	0.0366154i
$471$		0			0
$472$			22765.0i			0.102184i
$473$	−113507.	+	113507.i	−0.507342	+	0.507342i
$474$		0			0
$475$	93999.4	+	93999.4i	0.416618	+	0.416618i
$476$	216422.	+	216422.i	0.955186	+	0.955186i
$477$		0			0
$478$			514301.i			2.25093i
$479$	−69279.4	−	69279.4i	−0.301949	−	0.301949i	0.539827	−	0.841776i	$-0.318490\pi$
$479$	−69279.4	−	69279.4i	−0.301949	−	0.301949i	−0.841776	+	0.539827i	$0.818490\pi$
$480$		0			0
$481$	2410.64	+	251709.i	0.0104194	+	1.08795i
$482$	−219685.			−0.945597
$483$		0			0
$484$	−214719.			−0.916599
$485$			146533.i			0.622950i
$486$		0			0
$487$	334191.	−	334191.i	1.40908	−	1.40908i	0.644372	−	0.764713i	$-0.277119\pi$
$487$	334191.	−	334191.i	1.40908	−	1.40908i	0.764713	−	0.644372i	$-0.222881\pi$
$488$	386195.	+	386195.i	1.62169	+	1.62169i
$489$		0			0
$490$	−70695.1			−0.294440
$491$			204363.i			0.847696i	0.905733	+	0.423848i	$0.139321\pi$
$491$			204363.i			0.847696i	−0.905733	+	0.423848i	$0.860679\pi$
$492$		0			0
$493$		−	198785.i		−	0.817880i
$494$	−372386.	+	379588.i	−1.52595	+	1.55546i
$495$		0			0
$496$	93554.7	−	93554.7i	0.380279	−	0.380279i
$497$	−184287.			−0.746074
$498$		0			0
$499$	263314.	−	263314.i	1.05748	−	1.05748i	0.0592381	−	0.998244i	$-0.481133\pi$
$499$	263314.	−	263314.i	1.05748	−	1.05748i	0.998244	−	0.0592381i	$-0.0188671\pi$
$500$	−330391.	+	330391.i	−1.32157	+	1.32157i
$501$		0			0
$502$	−241773.	−	241773.i	−0.959403	−	0.959403i
$503$	−120971.			−0.478131			−0.239065	−	0.971003i	$-0.576841\pi$
$503$	−120971.			−0.478131			−0.239065	+	0.971003i	$0.576841\pi$
$504$		0			0
$505$	191758.	+	191758.i	0.751920	+	0.751920i
$506$			267573.i			1.04506i
$507$		0			0
$508$	−609990.			−2.36371
$509$	50199.3	−	50199.3i	0.193759	−	0.193759i	−0.603559	−	0.797318i	$-0.706251\pi$
$509$	50199.3	−	50199.3i	0.193759	−	0.193759i	0.797318	+	0.603559i	$0.206251\pi$
$510$		0			0
$511$			50775.9i			0.194454i
$512$	102587.	−	102587.i	0.391337	−	0.391337i
$513$		0			0
$514$	−411688.	−	411688.i	−1.55827	−	1.55827i
$515$	−171780.	−	171780.i	−0.647677	−	0.647677i
$516$		0			0
$517$		−	7734.07i		−	0.0289352i
$518$	297845.	+	297845.i	1.11002	+	1.11002i
$519$		0			0
$520$	−174967.	−	171648.i	−0.647068	−	0.634792i
$521$	307242.			1.13189			0.565946	−	0.824443i	$-0.308511\pi$
$521$	307242.			1.13189			0.565946	+	0.824443i	$0.308511\pi$
$522$		0			0
$523$	271249.			0.991664			0.495832	−	0.868418i	$-0.334863\pi$
$523$	271249.			0.991664			0.495832	+	0.868418i	$0.334863\pi$
$524$		−	46083.7i		−	0.167836i
$525$		0			0
$526$	531501.	−	531501.i	1.92102	−	1.92102i
$527$	336092.	+	336092.i	1.21014	+	1.21014i
$528$		0			0
$529$	43420.3			0.155161
$530$		−	619895.i		−	2.20682i
$531$		0			0
$532$			564703.i			1.99525i
$533$	269173.	−	2577.89i	0.947494	−	0.00907424i
$534$		0			0
$535$	−187337.	+	187337.i	−0.654508	+	0.654508i
$536$	−103699.			−0.360950
$537$		0			0
$538$	26428.6	−	26428.6i	0.0913081	−	0.0913081i
$539$	−33799.3	+	33799.3i	−0.116340	+	0.116340i
$540$		0			0
$541$	184394.	+	184394.i	0.630017	+	0.630017i	0.948072	−	0.318055i	$-0.103030\pi$
$541$	184394.	+	184394.i	0.630017	+	0.630017i	−0.318055	+	0.948072i	$0.603030\pi$
$542$	34836.6			0.118587
$543$		0			0
$544$	141018.	+	141018.i	0.476515	+	0.476515i
$545$		−	128439.i		−	0.432419i
$546$		0			0
$547$	373290.			1.24759			0.623795	−	0.781588i	$-0.285590\pi$
$547$	373290.			1.24759			0.623795	+	0.781588i	$0.285590\pi$
$548$	600433.	−	600433.i	1.99942	−	1.99942i
$549$		0			0
$550$			153857.i			0.508619i
$551$	259341.	−	259341.i	0.854217	−	0.854217i
$552$		0			0
$553$	−122216.	−	122216.i	−0.399647	−	0.399647i
$554$	−148209.	−	148209.i	−0.482898	−	0.482898i
$555$		0			0
$556$			129461.i			0.418784i
$557$	−200107.	−	200107.i	−0.644987	−	0.644987i	0.306790	−	0.951777i	$-0.400745\pi$
$557$	−200107.	−	200107.i	−0.644987	−	0.644987i	−0.951777	+	0.306790i	$0.900745\pi$
$558$		0			0
$559$	228460.	−	232878.i	0.731115	−	0.745254i
$560$	−56973.0			−0.181674
$561$		0			0
$562$	−101983.			−0.322891
$563$		−	488676.i		−	1.54172i	−0.637007	−	0.770858i	$-0.719828\pi$
$563$		−	488676.i		−	1.54172i	0.637007	−	0.770858i	$-0.280172\pi$
$564$		0			0
$565$	−45121.7	+	45121.7i	−0.141348	+	0.141348i
$566$	−145033.	−	145033.i	−0.452725	−	0.452725i
$567$		0			0
$568$	336525.			1.04309
$569$			562947.i			1.73877i	0.494132	+	0.869387i	$0.335486\pi$
$569$			562947.i			1.73877i	−0.494132	+	0.869387i	$0.664514\pi$
$570$		0			0
$571$		−	183359.i		−	0.562380i	−0.959652	−	0.281190i	$-0.909271\pi$
$571$		−	183359.i		−	0.562380i	0.959652	−	0.281190i	$-0.0907291\pi$
$572$	−390564.	+	3740.47i	−1.19371	+	0.0114323i
$573$		0			0
$574$	318509.	−	318509.i	0.966713	−	0.966713i
$575$	−135944.			−0.411173
$576$		0			0
$577$	196407.	−	196407.i	0.589938	−	0.589938i	−0.347677	−	0.937614i	$-0.613029\pi$
$577$	196407.	−	196407.i	0.589938	−	0.589938i	0.937614	+	0.347677i	$0.113029\pi$
$578$	−80064.2	+	80064.2i	−0.239653	+	0.239653i
$579$		0			0
$580$	281736.	+	281736.i	0.837503	+	0.837503i
$581$	124546.			0.368958
$582$		0			0
$583$	−296372.	−	296372.i	−0.871966	−	0.871966i
$584$		−	92721.6i		−	0.271866i
$585$		0			0
$586$	−1.06254e6			−3.09422
$587$	127057.	−	127057.i	0.368742	−	0.368742i	−0.498276	−	0.867018i	$-0.666034\pi$
$587$	127057.	−	127057.i	0.368742	−	0.368742i	0.867018	+	0.498276i	$0.166034\pi$
$588$		0			0
$589$			876953.i			2.52782i
$590$	25370.2	−	25370.2i	0.0728818	−	0.0728818i
$591$		0			0
$592$	−75551.7	−	75551.7i	−0.215576	−	0.215576i
$593$	−168617.	−	168617.i	−0.479503	−	0.479503i	0.425470	−	0.904973i	$-0.360109\pi$
$593$	−168617.	−	168617.i	−0.479503	−	0.479503i	−0.904973	+	0.425470i	$0.860109\pi$
$594$		0			0
$595$		−	204674.i		−	0.578133i
$596$	10947.1	+	10947.1i	0.0308181	+	0.0308181i
$597$		0			0
$598$	−5207.65	−	543761.i	−0.0145626	−	1.52057i
$599$	22624.2			0.0630550			0.0315275	−	0.999503i	$-0.489963\pi$
$599$	22624.2			0.0630550			0.0315275	+	0.999503i	$0.489963\pi$
$600$		0			0
$601$	621958.			1.72192			0.860958	−	0.508675i	$-0.169865\pi$
$601$	621958.			1.72192			0.860958	+	0.508675i	$0.169865\pi$
$602$		−	545895.i		−	1.50632i
$603$		0			0
$604$	−211802.	+	211802.i	−0.580572	+	0.580572i
$605$	101531.	+	101531.i	0.277389	+	0.277389i
$606$		0			0
$607$	−600769.			−1.63054			−0.815268	−	0.579084i	$-0.803410\pi$
$607$	−600769.			−1.63054			−0.815268	+	0.579084i	$0.803410\pi$
$608$			367953.i			0.995371i
$609$		0			0
$610$		−	860782.i		−	2.31331i
$611$	150.525	+	15717.1i	0.000403204	+	0.0421009i
$612$		0			0
$613$	−230276.	+	230276.i	−0.612812	+	0.612812i	−0.943678	−	0.330866i	$-0.892659\pi$
$613$	−230276.	+	230276.i	−0.612812	+	0.612812i	0.330866	+	0.943678i	$0.392659\pi$
$614$	−703981.			−1.86734
$615$		0			0
$616$	−196090.	+	196090.i	−0.516767	+	0.516767i
$617$	−34766.2	+	34766.2i	−0.0913244	+	0.0913244i	−0.751293	−	0.659969i	$-0.770570\pi$
$617$	−34766.2	+	34766.2i	−0.0913244	+	0.0913244i	0.659969	+	0.751293i	$0.270570\pi$
$618$		0			0
$619$	−420362.	−	420362.i	−1.09709	−	1.09709i	−0.994750	−	0.102339i	$-0.967367\pi$
$619$	−420362.	−	420362.i	−1.09709	−	1.09709i	−0.102339	−	0.994750i	$-0.532633\pi$
$620$	−952680.			−2.47836
$621$		0			0
$622$	703892.	+	703892.i	1.81939	+	1.81939i
$623$			364555.i			0.939262i
$624$		0			0
$625$	137714.			0.352547
$626$	−592423.	+	592423.i	−1.51176	+	1.51176i
$627$		0			0
$628$		−	711130.i		−	1.80314i
$629$	271417.	−	271417.i	0.686018	−	0.686018i
$630$		0			0
$631$	93922.3	+	93922.3i	0.235890	+	0.235890i	0.815146	−	0.579256i	$-0.196657\pi$
$631$	93922.3	+	93922.3i	0.235890	+	0.235890i	−0.579256	+	0.815146i	$0.696657\pi$
$632$	223177.	+	223177.i	0.558748	+	0.558748i
$633$		0			0
$634$			396347.i			0.986045i
$635$	288438.	+	288438.i	0.715327	+	0.715327i
$636$		0			0
$637$	68029.0	−	69344.6i	0.167654	−	0.170897i
$638$	424487.			1.04285
$639$		0			0
$640$	−540888.			−1.32053
$641$			123299.i			0.300084i	0.988680	+	0.150042i	$0.0479409\pi$
$641$			123299.i			0.300084i	−0.988680	+	0.150042i	$0.952059\pi$
$642$		0			0
$643$	−280732.	+	280732.i	−0.678999	+	0.678999i	−0.959774	−	0.280774i	$-0.909409\pi$
$643$	−280732.	+	280732.i	−0.678999	+	0.678999i	0.280774	+	0.959774i	$0.409409\pi$
$644$	−408343.	−	408343.i	−0.984586	−	0.984586i
$645$		0			0
$646$	810850.			1.94301
$647$			45435.6i			0.108539i	0.998526	+	0.0542697i	$0.0172831\pi$
$647$			45435.6i			0.108539i	−0.998526	+	0.0542697i	$0.982717\pi$
$648$		0			0
$649$		−	24258.9i		−	0.0575946i
$650$	−2994.45	−	312668.i	−0.00708746	−	0.740042i
$651$		0			0
$652$	−461375.	+	461375.i	−1.08532	+	1.08532i
$653$	378723.			0.888168			0.444084	−	0.895985i	$-0.353529\pi$
$653$	378723.			0.888168			0.444084	+	0.895985i	$0.353529\pi$
$654$		0			0
$655$	−21791.0	+	21791.0i	−0.0507920	+	0.0507920i
$656$	−80793.4	+	80793.4i	−0.187745	+	0.187745i
$657$		0			0
$658$	18597.9	+	18597.9i	0.0429548	+	0.0429548i
$659$	−289116.			−0.665735			−0.332867	−	0.942974i	$-0.608016\pi$
$659$	−289116.			−0.665735			−0.332867	+	0.942974i	$0.608016\pi$
$660$		0			0
$661$	−168774.	−	168774.i	−0.386281	−	0.386281i	0.487078	−	0.873359i	$-0.338063\pi$
$661$	−168774.	−	168774.i	−0.386281	−	0.386281i	−0.873359	+	0.487078i	$0.838063\pi$
$662$			220807.i			0.503845i
$663$		0			0
$664$	−227433.			−0.515842
$665$	267024.	−	267024.i	0.603819	−	0.603819i
$666$		0			0
$667$			375065.i			0.843054i
$668$	1.05317e6	−	1.05317e6i	2.36019	−	2.36019i
$669$		0			0
$670$	115567.	+	115567.i	0.257444	+	0.257444i
$671$	−411539.	−	411539.i	−0.914043	−	0.914043i
$672$		0			0
$673$			163719.i			0.361467i	0.983532	+	0.180734i	$0.0578472\pi$
$673$			163719.i			0.361467i	−0.983532	+	0.180734i	$0.942153\pi$
$674$	537482.	+	537482.i	1.18316	+	1.18316i
$675$		0			0
$676$	793630.	−	15202.7i	1.73670	−	0.0332681i
$677$	−462025.			−1.00806			−0.504032	−	0.863685i	$-0.668151\pi$
$677$	−462025.			−1.00806			−0.504032	+	0.863685i	$0.668151\pi$
$678$		0			0
$679$	−336931.			−0.730805
$680$			373753.i			0.808290i
$681$		0			0
$682$	−717693.	+	717693.i	−1.54301	+	1.54301i
$683$	213724.	+	213724.i	0.458155	+	0.458155i	0.898049	−	0.439895i	$-0.144984\pi$
$683$	213724.	+	213724.i	0.458155	+	0.458155i	−0.439895	+	0.898049i	$0.644984\pi$
$684$		0			0
$685$	−567838.			−1.21016
$686$		−	841544.i		−	1.78825i
$687$		0			0
$688$			138473.i			0.292541i
$689$	608054.	+	596517.i	1.28087	+	1.25656i
$690$		0			0
$691$	−344817.	+	344817.i	−0.722159	+	0.722159i	−0.969045	−	0.246886i	$-0.920593\pi$
$691$	−344817.	+	344817.i	−0.722159	+	0.722159i	0.246886	+	0.969045i	$0.420593\pi$
$692$	−47605.4			−0.0994132
$693$		0			0
$694$	437094.	−	437094.i	0.907520	−	0.907520i
$695$	61216.6	−	61216.6i	0.126736	−	0.126736i
$696$		0			0
$697$	−290248.	−	290248.i	−0.597452	−	0.597452i
$698$	135507.			0.278132
$699$		0			0
$700$	−234801.	−	234801.i	−0.479186	−	0.479186i
$701$			83587.3i			0.170100i	0.996377	+	0.0850500i	$0.0271050\pi$
$701$			83587.3i			0.170100i	−0.996377	+	0.0850500i	$0.972895\pi$
$702$		0			0
$703$	708198.			1.43299
$704$	−368619.	+	368619.i	−0.743760	+	0.743760i
$705$		0			0
$706$		−	1.18928e6i		−	2.38602i
$707$	−440919.	+	440919.i	−0.882104	+	0.882104i
$708$		0			0
$709$	507737.	+	507737.i	1.01006	+	1.01006i	0.999949	+	0.0101092i	$0.00321793\pi$
$709$	507737.	+	507737.i	1.01006	+	1.01006i	0.0101092	+	0.999949i	$0.496782\pi$
$710$	−375037.	−	375037.i	−0.743973	−	0.743973i
$711$		0			0
$712$		−	665711.i		−	1.31318i
$713$	−634135.	−	634135.i	−1.24739	−	1.24739i
$714$		0			0
$715$	186450.	+	182912.i	0.364711	+	0.357792i
$716$	75051.0			0.146396
$717$		0			0
$718$	379640.			0.736415
$719$		−	50596.5i		−	0.0978729i	−0.998802	−	0.0489364i	$-0.984417\pi$
$719$		−	50596.5i		−	0.0978729i	0.998802	−	0.0489364i	$-0.0155832\pi$
$720$		0			0
$721$	394982.	−	394982.i	0.759814	−	0.759814i
$722$	448046.	+	448046.i	0.859505	+	0.859505i
$723$		0			0
$724$	870610.			1.66091
$725$			215666.i			0.410304i
$726$		0			0
$727$		−	891410.i		−	1.68659i	−0.537453	−	0.843294i	$-0.680613\pi$
$727$		−	891410.i		−	1.68659i	0.537453	−	0.843294i	$-0.319387\pi$
$728$	394678.	−	402310.i	0.744697	−	0.759099i
$729$		0			0
$730$	−103333.	+	103333.i	−0.193906	+	0.193906i
$731$	−497458.			−0.930939
$732$		0			0
$733$	−439182.	+	439182.i	−0.817404	+	0.817404i	−0.985731	−	0.168327i	$-0.946164\pi$
$733$	−439182.	+	439182.i	−0.817404	+	0.817404i	0.168327	+	0.985731i	$0.446164\pi$
$734$	190672.	−	190672.i	0.353912	−	0.353912i
$735$		0			0
$736$	−266071.	−	266071.i	−0.491182	−	0.491182i
$737$	110505.			0.203445
$738$		0			0
$739$	83855.7	+	83855.7i	0.153548	+	0.153548i	0.779701	−	0.626153i	$-0.215371\pi$
$739$	83855.7	+	83855.7i	0.153548	+	0.153548i	−0.626153	+	0.779701i	$0.715371\pi$
$740$			769353.i			1.40495i
$741$		0			0
$742$	1.42535e6			2.58890
$743$	153273.	−	153273.i	0.277643	−	0.277643i	−0.554524	−	0.832167i	$-0.687100\pi$
$743$	153273.	−	153273.i	0.277643	−	0.277643i	0.832167	+	0.554524i	$0.187100\pi$
$744$		0			0
$745$		−	10352.8i		−	0.0186529i
$746$	207543.	−	207543.i	0.372933	−	0.372933i
$747$		0			0
$748$	421143.	+	421143.i	0.752708	+	0.752708i
$749$	−430752.	−	430752.i	−0.767827	−	0.767827i
$750$		0			0
$751$		−	208551.i		−	0.369771i	−0.982760	−	0.184886i	$-0.940808\pi$
$751$		−	208551.i		−	0.369771i	0.982760	−	0.184886i	$-0.0591915\pi$
$752$	−4717.57	−	4717.57i	−0.00834225	−	0.00834225i
$753$		0			0
$754$	−862640.	+	8261.59i	−1.51735	+	0.0145319i
$755$	200304.			0.351395
$756$		0			0
$757$	−762290.			−1.33024			−0.665118	−	0.746739i	$-0.731619\pi$
$757$	−762290.			−1.33024			−0.665118	+	0.746739i	$0.731619\pi$
$758$		−	253308.i		−	0.440870i
$759$		0			0
$760$	−487610.	+	487610.i	−0.844201	+	0.844201i
$761$	−790313.	−	790313.i	−1.36468	−	1.36468i	−0.867850	−	0.496826i	$-0.834499\pi$
$761$	−790313.	−	790313.i	−1.36468	−	1.36468i	−0.496826	−	0.867850i	$-0.665501\pi$
$762$		0			0
$763$	295326.			0.507287
$764$			1.46682e6i			2.51299i
$765$		0			0
$766$			1.55746e6i			2.65436i
$767$	472.140	+	49298.9i	0.000802565	+	0.0838005i
$768$		0			0
$769$	170652.	−	170652.i	0.288574	−	0.288574i	−0.547942	−	0.836516i	$-0.684589\pi$
$769$	170652.	−	170652.i	0.288574	−	0.288574i	0.836516	+	0.547942i	$0.184589\pi$
$770$	437061.			0.737158
$771$		0			0
$772$	39070.1	−	39070.1i	0.0655555	−	0.0655555i
$773$	−238774.	+	238774.i	−0.399602	+	0.399602i	−0.878093	−	0.478490i	$-0.841184\pi$
$773$	−238774.	+	238774.i	−0.399602	+	0.399602i	0.478490	+	0.878093i	$0.341184\pi$
$774$		0			0
$775$	−364634.	−	364634.i	−0.607090	−	0.607090i
$776$	615268.			1.02174
$777$		0			0
$778$	77091.7	+	77091.7i	0.127365	+	0.127365i
$779$		−	757333.i		−	1.24799i
$780$		0			0
$781$	−358610.			−0.587923
$782$	−586335.	+	586335.i	−0.958810	+	0.958810i
$783$		0			0
$784$			41233.3i			0.0670836i
$785$	−336263.	+	336263.i	−0.545682	+	0.545682i
$786$		0			0
$787$	−460701.	−	460701.i	−0.743823	−	0.743823i	0.229488	−	0.973311i	$-0.426295\pi$
$787$	−460701.	−	460701.i	−0.743823	−	0.743823i	−0.973311	+	0.229488i	$0.926295\pi$
$788$	282793.	+	282793.i	0.455424	+	0.455424i
$789$		0			0
$790$		−	497435.i		−	0.797044i
$791$	−103750.	−	103750.i	−0.165820	−	0.165820i
$792$		0			0
$793$	844339.	+	828320.i	1.34267	+	1.31720i
$794$	1.45872e6			2.31383
$795$		0			0
$796$	−206762.			−0.326320
$797$			940096.i			1.47998i	0.672618	+	0.739989i	$0.265170\pi$
$797$			940096.i			1.47998i	−0.672618	+	0.739989i	$0.734830\pi$
$798$		0			0
$799$	16947.7	−	16947.7i	0.0265471	−	0.0265471i
$800$	−152993.	−	152993.i	−0.239052	−	0.239052i
$801$		0			0
$802$	−1.33066e6			−2.06880
$803$			98806.5i			0.153234i
$804$		0			0
$805$			386176.i			0.595928i
$806$	1.44453e6	−	1.47246e6i	2.22359	−	2.26660i
$807$		0			0
$808$	805159.	−	805159.i	1.23327	−	1.23327i
$809$	−612686.			−0.936140			−0.468070	−	0.883691i	$-0.655050\pi$
$809$	−612686.			−0.936140			−0.468070	+	0.883691i	$0.655050\pi$
$810$		0			0
$811$	431732.	−	431732.i	0.656406	−	0.656406i	−0.298121	−	0.954528i	$-0.596360\pi$
$811$	431732.	−	431732.i	0.656406	−	0.656406i	0.954528	+	0.298121i	$0.0963601\pi$
$812$	−647809.	+	647809.i	−0.982505	+	0.982505i
$813$		0			0
$814$	579585.	+	579585.i	0.874719	+	0.874719i
$815$	436329.			0.656900
$816$		0			0
$817$	−648999.	−	648999.i	−0.972300	−	0.972300i
$818$			93111.7i			0.139155i
$819$		0			0
$820$	822730.			1.22357
$821$	193284.	−	193284.i	0.286754	−	0.286754i	−0.549041	−	0.835795i	$-0.685007\pi$
$821$	193284.	−	193284.i	0.286754	−	0.286754i	0.835795	+	0.549041i	$0.185007\pi$
$822$		0			0
$823$			547967.i			0.809011i	0.914536	+	0.404506i	$0.132556\pi$
$823$			547967.i			0.809011i	−0.914536	+	0.404506i	$0.867444\pi$
$824$	−721275.	+	721275.i	−1.06230	+	1.06230i
$825$		0			0
$826$	58334.8	+	58334.8i	0.0855003	+	0.0855003i
$827$	859953.	+	859953.i	1.25737	+	1.25737i	0.952343	+	0.305029i	$0.0986660\pi$
$827$	859953.	+	859953.i	1.25737	+	1.25737i	0.305029	+	0.952343i	$0.401334\pi$
$828$		0			0
$829$		−	726172.i		−	1.05665i	−0.849043	−	0.528324i	$-0.822821\pi$
$829$		−	726172.i		−	1.05665i	0.849043	−	0.528324i	$-0.177179\pi$
$830$	253460.	+	253460.i	0.367919	+	0.367919i
$831$		0			0
$832$	741933.	−	756282.i	1.07181	−	1.09254i
$833$	−148129.			−0.213477
$834$		0			0
$835$	−995999.			−1.42852
$836$			1.09887e6i			1.57230i
$837$		0			0
$838$	−83260.3	+	83260.3i	−0.118563	+	0.118563i
$839$	507389.	+	507389.i	0.720804	+	0.720804i	0.968769	−	0.247965i	$-0.0797618\pi$
$839$	507389.	+	507389.i	0.720804	+	0.720804i	−0.247965	+	0.968769i	$0.579762\pi$
$840$		0			0
$841$	−112265.			−0.158728
$842$		−	1.15338e6i		−	1.62685i
$843$		0			0
$844$			1.27501e6i			1.78990i
$845$	−382462.	−	368085.i	−0.535642	−	0.515507i
$846$		0			0
$847$	−233456.	+	233456.i	−0.325415	+	0.325415i
$848$	−361557.			−0.502789
$849$		0			0
$850$	−337148.	+	337148.i	−0.466641	+	0.466641i
$851$	−512107.	+	512107.i	−0.707133	+	0.707133i
$852$		0			0
$853$	192677.	+	192677.i	0.264808	+	0.264808i	0.827004	−	0.562196i	$-0.190043\pi$
$853$	192677.	+	192677.i	0.264808	+	0.264808i	−0.562196	+	0.827004i	$0.690043\pi$
$854$	1.97924e6			2.71383
$855$		0			0
$856$	786593.	+	786593.i	1.07350	+	1.07350i
$857$		−	96833.2i		−	0.131845i	−0.997825	−	0.0659223i	$-0.979001\pi$
$857$		−	96833.2i		−	0.131845i	0.997825	−	0.0659223i	$-0.0209990\pi$
$858$		0			0
$859$	248211.			0.336383			0.168192	−	0.985754i	$-0.446207\pi$
$859$	248211.			0.336383			0.168192	+	0.985754i	$0.446207\pi$
$860$	705042.	−	705042.i	0.953275	−	0.953275i
$861$		0			0
$862$			763533.i			1.02757i
$863$	−1.02273e6	+	1.02273e6i	−1.37321	+	1.37321i	−0.517571	+	0.855640i	$0.673164\pi$
$863$	−1.02273e6	+	1.02273e6i	−1.37321	+	1.37321i	−0.855640	+	0.517571i	$0.826836\pi$
$864$		0			0
$865$	22510.5	+	22510.5i	0.0300853	+	0.0300853i
$866$	284499.	+	284499.i	0.379355	+	0.379355i
$867$		0			0
$868$		−	2.19054e6i		−	2.90745i
$869$	−237824.	−	237824.i	−0.314931	−	0.314931i
$870$		0			0
$871$	−224567.	+	2150.70i	−0.296013	+	0.00283494i
$872$	−539294.			−0.709239
$873$		0			0
$874$	−1.52990e6			−2.00282
$875$			718444.i			0.938376i
$876$		0			0
$877$	263404.	−	263404.i	0.342470	−	0.342470i	−0.514825	−	0.857295i	$-0.672143\pi$
$877$	263404.	−	263404.i	0.342470	−	0.342470i	0.857295	+	0.514825i	$0.172143\pi$
$878$	−1.28702e6	−	1.28702e6i	−1.66954	−	1.66954i
$879$		0			0
$880$	−110866.			−0.143163
$881$		−	580702.i		−	0.748171i	−0.927394	−	0.374086i	$-0.877957\pi$
$881$		−	580702.i		−	0.748171i	0.927394	−	0.374086i	$-0.122043\pi$
$882$		0			0
$883$			1.28367e6i			1.64638i	0.567763	+	0.823192i	$0.307809\pi$
$883$			1.28367e6i			1.64638i	−0.567763	+	0.823192i	$0.692191\pi$
$884$	−864042.	−	847649.i	−1.10568	−	1.08470i
$885$		0			0
$886$	−40787.4	+	40787.4i	−0.0519587	+	0.0519587i
$887$	−166700.			−0.211879			−0.105940	−	0.994373i	$-0.533785\pi$
$887$	−166700.			−0.211879			−0.105940	+	0.994373i	$0.533785\pi$
$888$		0			0
$889$	−663219.	+	663219.i	−0.839176	+	0.839176i
$890$	−741894.	+	741894.i	−0.936617	+	0.936617i
$891$		0			0
$892$	−727805.	−	727805.i	−0.914714	−	0.914714i
$893$	44221.1			0.0554532
$894$		0			0
$895$	−35488.4	−	35488.4i	−0.0443037	−	0.0443037i
$896$		−	1.24369e6i		−	1.54916i
$897$		0			0
$898$	2.30820e6			2.86234
$899$	−1.00601e6	+	1.00601e6i	−1.24475	+	1.24475i
$900$		0			0
$901$		−	1.29888e6i		−	1.60000i
$902$	619796.	−	619796.i	0.761791	−	0.761791i
$903$		0			0
$904$	189458.	+	189458.i	0.231833	+	0.231833i
$905$	−411674.	−	411674.i	−0.502639	−	0.502639i
$906$		0			0
$907$			1.06525e6i			1.29490i	0.762108	+	0.647450i	$0.224164\pi$
$907$			1.06525e6i			1.29490i	−0.762108	+	0.647450i	$0.775836\pi$
$908$	−567464.	−	567464.i	−0.688282	−	0.688282i
$909$		0			0
$910$	−888194.	+	8506.32i	−1.07257	+	0.0102721i
$911$	794671.			0.957526			0.478763	−	0.877944i	$-0.341085\pi$
$911$	794671.			0.957526			0.478763	+	0.877944i	$0.341085\pi$
$912$		0			0
$913$	242358.			0.290747
$914$			517031.i			0.618905i
$915$		0			0
$916$	−1.44823e6	+	1.44823e6i	−1.72603	+	1.72603i
$917$	−50105.1	−	50105.1i	−0.0595859	−	0.0595859i
$918$		0			0
$919$	514196.			0.608833			0.304416	−	0.952539i	$-0.401539\pi$
$919$	514196.			0.608833			0.304416	+	0.952539i	$0.401539\pi$
$920$		−	705193.i		−	0.833168i
$921$		0			0
$922$			294545.i			0.346489i
$923$	728766.	−	6979.46i	0.855431	−	0.00819254i
$924$		0			0
$925$	−294466.	+	294466.i	−0.344153	+	0.344153i
$926$	−1.26064e6			−1.47018
$927$		0			0
$928$	−422104.	+	422104.i	−0.490143	+	0.490143i
$929$	746377.	−	746377.i	0.864823	−	0.864823i	−0.127071	−	0.991894i	$-0.540558\pi$
$929$	746377.	−	746377.i	0.864823	−	0.864823i	0.991894	+	0.127071i	$0.0405576\pi$
$930$		0			0
$931$	−193254.	−	193254.i	−0.222961	−	0.222961i
$932$	1.27240e6			1.46484
$933$		0			0
$934$	499758.	+	499758.i	0.572884	+	0.572884i
$935$		−	398281.i		−	0.455582i
$936$		0			0
$937$	379998.			0.432815			0.216408	−	0.976303i	$-0.430566\pi$
$937$	379998.			0.432815			0.216408	+	0.976303i	$0.430566\pi$
$938$	−265728.	+	265728.i	−0.302017	+	0.302017i
$939$		0			0
$940$			48039.7i			0.0543681i
$941$	906449.	−	906449.i	1.02368	−	1.02368i	0.0239676	−	0.999713i	$-0.492370\pi$
$941$	906449.	−	906449.i	1.02368	−	1.02368i	0.999713	−	0.0239676i	$-0.00762984\pi$
$942$		0			0
$943$	547636.	+	547636.i	0.615841	+	0.615841i
$944$	−14797.3	−	14797.3i	−0.0166050	−	0.0166050i
$945$		0			0
$946$		−	1.06227e6i		−	1.18701i
$947$	−290385.	−	290385.i	−0.323798	−	0.323798i	0.526424	−	0.850222i	$-0.323532\pi$
$947$	−290385.	−	290385.i	−0.323798	−	0.323798i	−0.850222	+	0.526424i	$0.823532\pi$
$948$		0			0
$949$	−1923.03	−	200794.i	−0.00213527	−	0.222956i
$950$	−879709.			−0.974747
$951$		0			0
$952$	−859388.			−0.948234
$953$			1.13841e6i			1.25347i	0.779234	+	0.626733i	$0.215608\pi$
$953$			1.13841e6i			1.25347i	−0.779234	+	0.626733i	$0.784392\pi$
$954$		0			0
$955$	693596.	−	693596.i	0.760501	−	0.760501i
$956$	−1.52731e6	−	1.52731e6i	−1.67114	−	1.67114i
$957$		0			0
$958$	648362.			0.706459
$959$		−	1.30566e6i		−	1.41968i
$960$		0			0
$961$		−	2.47827e6i		−	2.68350i
$962$	−1.18911e6	−	1.16655e6i	−1.28491	−	1.26053i
$963$		0			0
$964$	652395.	−	652395.i	0.702032	−	0.702032i
$965$	−36949.1			−0.0396780
$966$		0			0
$967$	19218.1	−	19218.1i	0.0205521	−	0.0205521i	−0.696756	−	0.717308i	$-0.745374\pi$
$967$	19218.1	−	19218.1i	0.0205521	−	0.0205521i	0.717308	+	0.696756i	$0.245374\pi$
$968$	426312.	−	426312.i	0.454964	−	0.454964i
$969$		0			0
$970$	−685678.	−	685678.i	−0.728747	−	0.728747i
$971$	−416812.			−0.442080			−0.221040	−	0.975265i	$-0.570945\pi$
$971$	−416812.			−0.442080			−0.221040	+	0.975265i	$0.570945\pi$
$972$		0			0
$973$	140758.	+	140758.i	0.148678	+	0.148678i
$974$			3.12758e6i			3.29679i
$975$		0			0
$976$	−502056.			−0.527051
$977$	−394416.	+	394416.i	−0.413205	+	0.413205i	−0.882853	−	0.469649i	$-0.844381\pi$
$977$	−394416.	+	394416.i	−0.413205	+	0.413205i	0.469649	+	0.882853i	$0.344381\pi$
$978$		0			0
$979$			709399.i			0.740159i
$980$	209942.	−	209942.i	0.218599	−	0.218599i
$981$		0			0
$982$	−956284.	−	956284.i	−0.991663	−	0.991663i
$983$	159479.	+	159479.i	0.165043	+	0.165043i	0.784796	−	0.619754i	$-0.212767\pi$
$983$	159479.	+	159479.i	0.165043	+	0.165043i	−0.619754	+	0.784796i	$0.712767\pi$
$984$		0			0
$985$		−	267441.i		−	0.275649i
$986$	930181.	+	930181.i	0.956783	+	0.956783i
$987$		0			0
$988$	−21386.9	−	2.23313e6i	−0.0219095	−	2.28770i
$989$	938598.			0.959593
$990$		0			0
$991$	869851.			0.885722			0.442861	−	0.896590i	$-0.353964\pi$
$991$	869851.			0.885722			0.442861	+	0.896590i	$0.353964\pi$
$992$		−	1.42733e6i		−	1.45044i
$993$		0			0
$994$	862340.	−	862340.i	0.872782	−	0.872782i
$995$	97768.8	+	97768.8i	0.0987539	+	0.0987539i
$996$		0			0
$997$	798123.			0.802934			0.401467	−	0.915874i	$-0.368501\pi$
$997$	798123.			0.802934			0.401467	+	0.915874i	$0.368501\pi$
$998$			2.46427e6i			2.47415i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.5.j.b.109.2		20
3.2	odd	2		39.5.g.a.31.9	✓	20
13.8	odd	4	inner	117.5.j.b.73.2		20
39.8	even	4		39.5.g.a.34.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.5.g.a.31.9	✓	20	3.2	odd	2
39.5.g.a.34.9	yes	20	39.8	even	4
117.5.j.b.73.2		20	13.8	odd	4	inner
117.5.j.b.109.2		20	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	117.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.67933 + 4.67933i) q^{2} -27.7923i q^{4} +(-13.1418 + 13.1418i) q^{5} +(-30.2175 - 30.2175i) q^{7} +(55.1800 + 55.1800i) q^{8} -122.989i q^{10} +(-58.8012 - 58.8012i) q^{11} +(120.640 + 118.351i) q^{13} +282.795 q^{14} -71.7343 q^{16} -257.703i q^{17} +(336.208 - 336.208i) q^{19} +(365.240 + 365.240i) q^{20} +550.300 q^{22} +486.231i q^{23} +279.587i q^{25} +(-1118.32 + 10.7102i) q^{26} +(-839.813 + 839.813i) q^{28} +771.373 q^{29} +(-1304.18 + 1304.18i) q^{31} +(-547.211 + 547.211i) q^{32} +(1205.88 + 1205.88i) q^{34} +794.223 q^{35} +(1053.22 + 1053.22i) q^{37} +3146.45i q^{38} -1450.33 q^{40} +(1126.29 - 1126.29i) q^{41} -1930.35i q^{43} +(-1634.22 + 1634.22i) q^{44} +(-2275.24 - 2275.24i) q^{46} +(65.7645 + 65.7645i) q^{47} -574.806i q^{49} +(-1308.28 - 1308.28i) q^{50} +(3289.25 - 3352.86i) q^{52} +5040.23 q^{53} +1545.50 q^{55} -3334.80i q^{56} +(-3609.51 + 3609.51i) q^{58} +(206.279 + 206.279i) q^{59} +6998.83 q^{61} -12205.4i q^{62} -6268.91i q^{64} +(-3140.77 + 30.0794i) q^{65} +(-939.648 + 939.648i) q^{67} -7162.15 q^{68} +(-3716.43 + 3716.43i) q^{70} +(3049.34 - 3049.34i) q^{71} +(-840.175 - 840.175i) q^{73} -9856.69 q^{74} +(-9343.97 - 9343.97i) q^{76} +3553.65i q^{77} +4044.54 q^{79} +(942.716 - 942.716i) q^{80} +10540.5i q^{82} +(-2060.82 + 2060.82i) q^{83} +(3386.67 + 3386.67i) q^{85} +(9032.76 + 9032.76i) q^{86} -6489.30i q^{88} +(-6032.18 - 6032.18i) q^{89} +(-69.1630 - 7221.71i) q^{91} +13513.5 q^{92} -615.468 q^{94} +8836.73i q^{95} +(5575.10 - 5575.10i) q^{97} +(2689.71 + 2689.71i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{5} - 24 q^{7} - 372 q^{11} - 224 q^{13} - 480 q^{14} - 2328 q^{16} - 840 q^{19} - 228 q^{20} + 3536 q^{22} + 828 q^{26} - 1984 q^{28} + 5064 q^{29} + 1712 q^{31} + 7260 q^{32} + 8040 q^{34}+ \cdots - 11544 q^{98}+O(q^{100}) \) 20 * q - 24 * q^5 - 24 * q^7 - 372 * q^11 - 224 * q^13 - 480 * q^14 - 2328 * q^16 - 840 * q^19 - 228 * q^20 + 3536 * q^22 + 828 * q^26 - 1984 * q^28 + 5064 * q^29 + 1712 * q^31 + 7260 * q^32 + 8040 * q^34 - 5976 * q^35 - 868 * q^37 + 6336 * q^40 + 6000 * q^41 - 20868 * q^44 - 1992 * q^46 - 1692 * q^47 - 8952 * q^50 - 12416 * q^52 + 18816 * q^53 - 3280 * q^55 + 1256 * q^58 + 6588 * q^59 - 5512 * q^61 - 33048 * q^65 - 4704 * q^67 + 28296 * q^68 - 31096 * q^70 - 9756 * q^71 + 13692 * q^73 + 28296 * q^74 - 17072 * q^76 - 5056 * q^79 - 42228 * q^80 - 24708 * q^83 - 4752 * q^85 + 77424 * q^86 - 36000 * q^89 + 19104 * q^91 - 12912 * q^92 + 112832 * q^94 + 50012 * q^97 - 11544 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more