LMFDB - Embedded newform 39.5.g.a.34.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,5,Mod(31,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("39.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	39.g (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:	$4.03142856027$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.9
Root			$-4.67933 - 4.67933i$ of defining polynomial
Character	$\chi$	$=$	39.34
Dual form			39.5.g.a.31.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.67933 + 4.67933i) q^{2} -5.19615 q^{3} +27.7923i q^{4} +(13.1418 + 13.1418i) q^{5} +(-24.3145 - 24.3145i) q^{6} +(-30.2175 + 30.2175i) q^{7} +(-55.1800 + 55.1800i) q^{8} +27.0000 q^{9} +122.989i q^{10} +(58.8012 - 58.8012i) q^{11} -144.413i q^{12} +(120.640 - 118.351i) q^{13} -282.795 q^{14} +(-68.2867 - 68.2867i) q^{15} -71.7343 q^{16} -257.703i q^{17} +(126.342 + 126.342i) q^{18} +(336.208 + 336.208i) q^{19} +(-365.240 + 365.240i) q^{20} +(157.015 - 157.015i) q^{21} +550.300 q^{22} +486.231i q^{23} +(286.724 - 286.724i) q^{24} -279.587i q^{25} +(1118.32 + 10.7102i) q^{26} -140.296 q^{27} +(-839.813 - 839.813i) q^{28} -771.373 q^{29} -639.072i q^{30} +(-1304.18 - 1304.18i) q^{31} +(547.211 + 547.211i) q^{32} +(-305.540 + 305.540i) q^{33} +(1205.88 - 1205.88i) q^{34} -794.223 q^{35} +750.392i q^{36} +(1053.22 - 1053.22i) q^{37} +3146.45i q^{38} +(-626.864 + 614.971i) q^{39} -1450.33 q^{40} +(-1126.29 - 1126.29i) q^{41} +1469.45 q^{42} +1930.35i q^{43} +(1634.22 + 1634.22i) q^{44} +(354.828 + 354.828i) q^{45} +(-2275.24 + 2275.24i) q^{46} +(-65.7645 + 65.7645i) q^{47} +372.742 q^{48} +574.806i q^{49} +(1308.28 - 1308.28i) q^{50} +1339.06i q^{51} +(3289.25 + 3352.86i) q^{52} -5040.23 q^{53} +(-656.492 - 656.492i) q^{54} +1545.50 q^{55} -3334.80i q^{56} +(-1746.99 - 1746.99i) q^{57} +(-3609.51 - 3609.51i) q^{58} +(-206.279 + 206.279i) q^{59} +(1897.84 - 1897.84i) q^{60} +6998.83 q^{61} -12205.4i q^{62} +(-815.872 + 815.872i) q^{63} +6268.91i q^{64} +(3140.77 + 30.0794i) q^{65} -2859.44 q^{66} +(-939.648 - 939.648i) q^{67} +7162.15 q^{68} -2526.53i q^{69} +(-3716.43 - 3716.43i) q^{70} +(-3049.34 - 3049.34i) q^{71} +(-1489.86 + 1489.86i) q^{72} +(-840.175 + 840.175i) q^{73} +9856.69 q^{74} +1452.78i q^{75} +(-9343.97 + 9343.97i) q^{76} +3553.65i q^{77} +(-5810.95 - 55.6521i) q^{78} +4044.54 q^{79} +(-942.716 - 942.716i) q^{80} +729.000 q^{81} -10540.5i q^{82} +(2060.82 + 2060.82i) q^{83} +(4363.80 + 4363.80i) q^{84} +(3386.67 - 3386.67i) q^{85} +(-9032.76 + 9032.76i) q^{86} +4008.17 q^{87} +6489.30i q^{88} +(6032.18 - 6032.18i) q^{89} +3320.71i q^{90} +(-69.1630 + 7221.71i) q^{91} -13513.5 q^{92} +(6776.74 + 6776.74i) q^{93} -615.468 q^{94} +8836.73i q^{95} +(-2843.39 - 2843.39i) q^{96} +(5575.10 + 5575.10i) q^{97} +(-2689.71 + 2689.71i) q^{98} +(1587.63 - 1587.63i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 24 q^{5} - 24 q^{7} + 540 q^{9} + 372 q^{11} - 224 q^{13} + 480 q^{14} - 252 q^{15} - 2328 q^{16} - 840 q^{19} + 228 q^{20} + 936 q^{21} + 3536 q^{22} - 1404 q^{24} - 828 q^{26} - 1984 q^{28} - 5064 q^{29}+ \cdots + 10044 q^{99}+O(q^{100}) $ 20 * q + 24 * q^5 - 24 * q^7 + 540 * q^9 + 372 * q^11 - 224 * q^13 + 480 * q^14 - 252 * q^15 - 2328 * q^16 - 840 * q^19 + 228 * q^20 + 936 * q^21 + 3536 * q^22 - 1404 * q^24 - 828 * q^26 - 1984 * q^28 - 5064 * q^29 + 1712 * q^31 - 7260 * q^32 - 540 * q^33 + 8040 * q^34 + 5976 * q^35 - 868 * q^37 - 2952 * q^39 + 6336 * q^40 - 6000 * q^41 + 648 * q^42 + 20868 * q^44 + 648 * q^45 - 1992 * q^46 + 1692 * q^47 + 2592 * q^48 + 8952 * q^50 - 12416 * q^52 - 18816 * q^53 - 3280 * q^55 - 9360 * q^57 + 1256 * q^58 - 6588 * q^59 + 9036 * q^60 - 5512 * q^61 - 648 * q^63 + 33048 * q^65 + 13464 * q^66 - 4704 * q^67 - 28296 * q^68 - 31096 * q^70 + 9756 * q^71 + 13692 * q^73 - 28296 * q^74 - 17072 * q^76 - 23868 * q^78 - 5056 * q^79 + 42228 * q^80 + 14580 * q^81 + 24708 * q^83 + 26496 * q^84 - 4752 * q^85 - 77424 * q^86 + 5256 * q^87 + 36000 * q^89 + 19104 * q^91 + 12912 * q^92 - 18432 * q^93 + 112832 * q^94 - 52344 * q^96 + 50012 * q^97 + 11544 * q^98 + 10044 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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	0.982249	+	0.187584i	$0.0600658\pi$
$2$	4.67933	+	4.67933i	1.16983	+	1.16983i	0.187584	+	0.982249i	$0.439934\pi$
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$			27.7923i			1.73702i
$5$	13.1418	+	13.1418i	0.525671	+	0.525671i	0.919279	−	0.393608i	$-0.128773\pi$
$5$	13.1418	+	13.1418i	0.525671	+	0.525671i	−0.393608	+	0.919279i	$0.628773\pi$
$6$	−24.3145	−	24.3145i	−0.675403	−	0.675403i
$7$	−30.2175	+	30.2175i	−0.616684	+	0.616684i	−0.944679	−	0.327996i	$-0.893627\pi$
$7$	−30.2175	+	30.2175i	−0.616684	+	0.616684i	0.327996	+	0.944679i	$0.393627\pi$
$8$	−55.1800	+	55.1800i	−0.862187	+	0.862187i
$9$	27.0000			0.333333
$10$			122.989i			1.22989i
$11$	58.8012	−	58.8012i	0.485960	−	0.485960i	−0.421069	−	0.907029i	$-0.638345\pi$
$11$	58.8012	−	58.8012i	0.485960	−	0.485960i	0.907029	+	0.421069i	$0.138345\pi$
$12$		−	144.413i		−	1.00287i
$13$	120.640	−	118.351i	0.713846	−	0.700303i
$13$	120.640	−	118.351i	0.713846	−	0.700303i
$14$	−282.795			−1.44283
$15$	−68.2867	−	68.2867i	−0.303496	−	0.303496i
$16$	−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	$-0.147100\pi$
$18$	126.342	+	126.342i	0.389944	+	0.389944i
$19$	336.208	+	336.208i	0.931323	+	0.931323i	0.997789	−	0.0664659i	$-0.0211724\pi$
$19$	336.208	+	336.208i	0.931323	+	0.931323i	−0.0664659	+	0.997789i	$0.521172\pi$
$20$	−365.240	+	365.240i	−0.913100	+	0.913100i
$21$	157.015	−	157.015i	0.356042	−	0.356042i
$22$	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	$0.848001\pi$
$24$	286.724	−	286.724i	0.497784	−	0.497784i
$25$		−	279.587i		−	0.447340i
$26$	1118.32	+	10.7102i	1.65432	+	0.0158436i
$27$	−140.296			−0.192450
$28$	−839.813	−	839.813i	−1.07119	−	1.07119i
$29$	−771.373			−0.917209			−0.458604	−	0.888641i	$-0.651650\pi$
$29$	−771.373			−0.917209			−0.458604	+	0.888641i	$0.651650\pi$
$30$		−	639.072i		−	0.710080i
$31$	−1304.18	−	1304.18i	−1.35711	−	1.35711i	−0.877458	−	0.479654i	$-0.840762\pi$
$31$	−1304.18	−	1304.18i	−1.35711	−	1.35711i	−0.479654	−	0.877458i	$-0.659238\pi$
$32$	547.211	+	547.211i	0.534386	+	0.534386i
$33$	−305.540	+	305.540i	−0.280569	+	0.280569i
$34$	1205.88	−	1205.88i	1.04315	−	1.04315i
$35$	−794.223			−0.648345
$36$			750.392i			0.579006i
$37$	1053.22	−	1053.22i	0.769333	−	0.769333i	−0.208656	−	0.977989i	$-0.566909\pi$
$37$	1053.22	−	1053.22i	0.769333	−	0.769333i	0.977989	+	0.208656i	$0.0669091\pi$
$38$			3146.45i			2.17898i
$39$	−626.864	+	614.971i	−0.412139	+	0.404320i
$40$	−1450.33			−0.906454
$41$	−1126.29	−	1126.29i	−0.670010	−	0.670010i	0.287708	−	0.957718i	$-0.407107\pi$
$41$	−1126.29	−	1126.29i	−0.670010	−	0.670010i	−0.957718	+	0.287708i	$0.907107\pi$
$42$	1469.45			0.833020
$43$			1930.35i			1.04400i	0.852946	+	0.521999i	$0.174814\pi$
$43$			1930.35i			1.04400i	−0.852946	+	0.521999i	$0.825186\pi$
$44$	1634.22	+	1634.22i	0.844121	+	0.844121i
$45$	354.828	+	354.828i	0.175224	+	0.175224i
$46$	−2275.24	+	2275.24i	−1.07525	+	1.07525i
$47$	−65.7645	+	65.7645i	−0.0297712	+	0.0297712i	−0.721836	−	0.692064i	$-0.756701\pi$
$47$	−65.7645	+	65.7645i	−0.0297712	+	0.0297712i	0.692064	+	0.721836i	$0.256701\pi$
$48$	372.742			0.161781
$49$			574.806i			0.239403i
$50$	1308.28	−	1308.28i	0.523313	−	0.523313i
$51$			1339.06i			0.514827i
$52$	3289.25	+	3352.86i	1.21644	+	1.23996i
$53$	−5040.23			−1.79432			−0.897158	−	0.441710i	$-0.854372\pi$
$53$	−5040.23			−1.79432			−0.897158	+	0.441710i	$0.854372\pi$
$54$	−656.492	−	656.492i	−0.225134	−	0.225134i
$55$	1545.50			0.510910
$56$		−	3334.80i		−	1.06339i
$57$	−1746.99	−	1746.99i	−0.537699	−	0.537699i
$58$	−3609.51	−	3609.51i	−1.07298	−	1.07298i
$59$	−206.279	+	206.279i	−0.0592586	+	0.0592586i	−0.736115	−	0.676856i	$-0.763342\pi$
$59$	−206.279	+	206.279i	−0.0592586	+	0.0592586i	0.676856	+	0.736115i	$0.263342\pi$
$60$	1897.84	−	1897.84i	0.527178	−	0.527178i
$61$	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
$63$	−815.872	+	815.872i	−0.205561	+	0.205561i
$64$			6268.91i			1.53050i
$65$	3140.77	+	30.0794i	0.743377	+	0.00711939i
$66$	−2859.44			−0.656438
$67$	−939.648	−	939.648i	−0.209322	−	0.209322i	0.594657	−	0.803979i	$-0.297288\pi$
$67$	−939.648	−	939.648i	−0.209322	−	0.209322i	−0.803979	+	0.594657i	$0.797288\pi$
$68$	7162.15			1.54891
$69$		−	2526.53i		−	0.530672i
$70$	−3716.43	−	3716.43i	−0.758456	−	0.758456i
$71$	−3049.34	−	3049.34i	−0.604908	−	0.604908i	0.336703	−	0.941611i	$-0.390688\pi$
$71$	−3049.34	−	3049.34i	−0.604908	−	0.604908i	−0.941611	+	0.336703i	$0.890688\pi$
$72$	−1489.86	+	1489.86i	−0.287396	+	0.287396i
$73$	−840.175	+	840.175i	−0.157661	+	0.157661i	−0.781529	−	0.623869i	$-0.785560\pi$
$73$	−840.175	+	840.175i	−0.157661	+	0.157661i	0.623869	+	0.781529i	$0.285560\pi$
$74$	9856.69			1.79998
$75$			1452.78i			0.258272i
$76$	−9343.97	+	9343.97i	−1.61772	+	1.61772i
$77$			3553.65i			0.599367i
$78$	−5810.95	−	55.6521i	−0.955121	−	0.00914728i
$79$	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
$81$	729.000			0.111111
$82$		−	10540.5i		−	1.56760i
$83$	2060.82	+	2060.82i	0.299147	+	0.299147i	0.840680	−	0.541533i	$-0.182156\pi$
$83$	2060.82	+	2060.82i	0.299147	+	0.299147i	−0.541533	+	0.840680i	$0.682156\pi$
$84$	4363.80	+	4363.80i	0.618452	+	0.618452i
$85$	3386.67	−	3386.67i	0.468744	−	0.468744i
$86$	−9032.76	+	9032.76i	−1.22130	+	1.22130i
$87$	4008.17			0.529551
$88$			6489.30i			0.837977i
$89$	6032.18	−	6032.18i	0.761543	−	0.761543i	−0.215059	−	0.976601i	$-0.568994\pi$
$89$	6032.18	−	6032.18i	0.761543	−	0.761543i	0.976601	+	0.215059i	$0.0689942\pi$
$90$			3320.71i			0.409965i
$91$	−69.1630	+	7221.71i	−0.00835202	+	0.872082i
$92$	−13513.5			−1.59658
$93$	6776.74	+	6776.74i	0.783529	+	0.783529i
$94$	−615.468			−0.0696546
$95$			8836.73i			0.979139i
$96$	−2843.39	−	2843.39i	−0.308528	−	0.308528i
$97$	5575.10	+	5575.10i	0.592528	+	0.592528i	0.938314	−	0.345785i	$-0.112387\pi$
$97$	5575.10	+	5575.10i	0.592528	+	0.592528i	−0.345785	+	0.938314i	$0.612387\pi$
$98$	−2689.71	+	2689.71i	−0.280061	+	0.280061i
$99$	1587.63	−	1587.63i	0.161987	−	0.161987i
$100$	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	$-0.253665\pi$
$102$	−6265.92	+	6265.92i	−0.602261	+	0.602261i
$103$		−	13071.3i		−	1.23210i	−0.787708	−	0.616048i	$-0.788733\pi$
$103$		−	13071.3i		−	1.23210i	0.787708	−	0.616048i	$-0.211267\pi$
$104$	−126.298	+	13187.5i	−0.0116770	+	1.21926i
$105$	4126.90			0.374322
$106$	−23584.9	−	23584.9i	−2.09905	−	2.09905i
$107$	−14255.0			−1.24509			−0.622545	−	0.782584i	$-0.713901\pi$
$107$	−14255.0			−1.24509			−0.622545	+	0.782584i	$0.713901\pi$
$108$		−	3899.15i		−	0.334289i
$109$	−4886.68	−	4886.68i	−0.411302	−	0.411302i	0.470890	−	0.882192i	$-0.343933\pi$
$109$	−4886.68	−	4886.68i	−0.411302	−	0.411302i	−0.882192	+	0.470890i	$0.843933\pi$
$110$	7231.92	+	7231.92i	0.597680	+	0.597680i
$111$	−5472.67	+	5472.67i	−0.444174	+	0.444174i
$112$	2167.63	−	2167.63i	0.172802	−	0.172802i
$113$	−3433.45			−0.268890			−0.134445	−	0.990921i	$-0.542925\pi$
$113$	−3433.45			−0.268890			−0.134445	+	0.990921i	$0.542925\pi$
$114$		−	16349.4i		−	1.25804i
$115$	−6389.94	+	6389.94i	−0.483171	+	0.483171i
$116$		−	21438.2i		−	1.59321i
$117$	3257.28	−	3195.48i	0.237949	−	0.233434i
$118$	−1930.50			−0.138645
$119$	7787.14	+	7787.14i	0.549900	+	0.549900i
$120$	7536.11			0.523341
$121$			7725.84i			0.527685i
$122$	32749.8	+	32749.8i	2.20034	+	2.20034i
$123$	5852.36	+	5852.36i	0.386831	+	0.386831i
$124$	36246.3	−	36246.3i	2.35733	−	2.35733i
$125$	11887.9	−	11887.9i	0.760825	−	0.760825i
$126$	−7635.47			−0.480944
$127$			21948.2i			1.36079i	0.732846	+	0.680395i	$0.238192\pi$
$127$			21948.2i			1.36079i	−0.732846	+	0.680395i	$0.761808\pi$
$128$	−20578.9	+	20578.9i	−1.25604	+	1.25604i
$129$		−	10030.4i		−	0.602753i
$130$	14555.9	+	14837.4i	0.861298	+	0.877955i
$131$	−1658.15			−0.0966231			−0.0483116	−	0.998832i	$-0.515384\pi$
$131$	−1658.15			−0.0966231			−0.0483116	+	0.998832i	$0.515384\pi$
$132$	−8491.65	−	8491.65i	−0.487354	−	0.487354i
$133$	−20318.7			−1.14866
$134$		−	8793.84i		−	0.489744i
$135$	−1843.74	−	1843.74i	−0.101165	−	0.101165i
$136$	14220.0	+	14220.0i	0.768817	+	0.768817i
$137$	−21604.3	+	21604.3i	−1.15106	+	1.15106i	−0.164724	+	0.986340i	$0.552673\pi$
$137$	−21604.3	+	21604.3i	−1.15106	+	1.15106i	−0.986340	+	0.164724i	$0.947327\pi$
$138$	11822.5	−	11822.5i	0.620798	−	0.620798i
$139$	−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
$141$	341.723	−	341.723i	0.0171884	−	0.0171884i
$142$		−	28537.8i		−	1.41528i
$143$	134.587	−	14053.0i	0.00658157	−	0.687220i
$144$	−1936.83			−0.0934040
$145$	−10137.2	−	10137.2i	−0.482150	−	0.482150i
$146$	−7862.91			−0.368874
$147$		−	2986.78i		−	0.138219i
$148$	29271.3	+	29271.3i	1.33634	+	1.33634i
$149$	393.889	+	393.889i	0.0177420	+	0.0177420i	0.715922	−	0.698180i	$-0.246007\pi$
$149$	393.889	+	393.889i	0.0177420	+	0.0177420i	−0.698180	+	0.715922i	$0.746007\pi$
$150$	−6798.04	+	6798.04i	−0.302135	+	0.302135i
$151$	−7620.89	+	7620.89i	−0.334235	+	0.334235i	−0.854192	−	0.519957i	$-0.825948\pi$
$151$	−7620.89	+	7620.89i	−0.334235	+	0.334235i	0.519957	+	0.854192i	$0.325948\pi$
$152$	−37103.8			−1.60595
$153$		−	6957.98i		−	0.297235i
$154$	−16628.7	+	16628.7i	−0.701159	+	0.701159i
$155$		−	34278.6i		−	1.42679i
$156$	−17091.4	−	17422.0i	−0.702311	−	0.715893i
$157$	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
$159$	26189.8			1.03595
$160$			14382.7i			0.561822i
$161$	−14692.7	−	14692.7i	−0.566826	−	0.566826i
$162$	3411.23	+	3411.23i	0.129981	+	0.129981i
$163$	−16600.8	+	16600.8i	−0.624820	+	0.624820i	−0.946760	−	0.321940i	$-0.895665\pi$
$163$	−16600.8	+	16600.8i	−0.624820	+	0.624820i	0.321940	+	0.946760i	$0.395665\pi$
$164$	31302.1	−	31302.1i	1.16382	−	1.16382i
$165$	−8030.67			−0.294974
$166$			19286.6i			0.699904i
$167$	−37894.4	+	37894.4i	−1.35876	+	1.35876i	−0.483307	+	0.875451i	$0.660565\pi$
$167$	−37894.4	+	37894.4i	−1.35876	+	1.35876i	−0.875451	+	0.483307i	$0.839435\pi$
$168$			17328.1i			0.613950i
$169$	547.013	−	28555.8i	0.0191524	−	0.999817i
$170$	31694.7			1.09670
$171$	9077.60	+	9077.60i	0.310441	+	0.310441i
$172$	−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	$-0.00911002\pi$
$174$	18755.6	+	18755.6i	0.619486	+	0.619486i
$175$	8448.43	+	8448.43i	0.275867	+	0.275867i
$176$	−4218.06	+	4218.06i	−0.136172	+	0.136172i
$177$	1071.86	−	1071.86i	0.0342130	−	0.0342130i
$178$	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	$0.986582\pi$
$180$	−9861.48	+	9861.48i	−0.304367	+	0.304367i
$181$		−	31325.6i		−	0.956186i	−0.878309	−	0.478093i	$-0.841328\pi$
$181$		−	31325.6i		−	0.956186i	0.878309	−	0.478093i	$-0.158672\pi$
$182$	−34116.4	+	33469.1i	−1.02996	+	1.01042i
$183$	−36367.0			−1.08594
$184$	−26830.2	−	26830.2i	−0.792481	−	0.792481i
$185$	27682.3			0.808832
$186$			63421.2i			1.83320i
$187$	−15153.2	−	15153.2i	−0.433333	−	0.433333i
$188$	−1827.75	−	1827.75i	−0.0517131	−	0.0517131i
$189$	4239.40	−	4239.40i	0.118681	−	0.118681i
$190$	−41350.0	+	41350.0i	−1.14543	+	1.14543i
$191$	52778.0			1.44672			0.723362	−	0.690469i	$-0.242596\pi$
$191$	52778.0			1.44672			0.723362	+	0.690469i	$0.242596\pi$
$192$		−	32574.2i		−	0.883632i
$193$	1405.79	−	1405.79i	0.0377403	−	0.0377403i	−0.687985	−	0.725725i	$-0.741504\pi$
$193$	1405.79	−	1405.79i	0.0377403	−	0.0377403i	0.725725	+	0.687985i	$0.241504\pi$
$194$			52175.5i			1.38632i
$195$	−16319.9	−	156.297i	−0.429189	−	0.00411038i
$196$	−15975.2			−0.415847
$197$	10175.2	+	10175.2i	0.262188	+	0.262188i	0.825942	−	0.563755i	$-0.190644\pi$
$197$	10175.2	+	10175.2i	0.262188	+	0.262188i	−0.563755	+	0.825942i	$0.690644\pi$
$198$	14858.1			0.378995
$199$			7439.54i			0.187862i	0.995579	+	0.0939312i	$0.0299434\pi$
$199$			7439.54i			0.187862i	−0.995579	+	0.0939312i	$0.970057\pi$
$200$	15427.6	+	15427.6i	0.385691	+	0.385691i
$201$	4882.55	+	4882.55i	0.120852	+	0.120852i
$202$	68278.5	−	68278.5i	1.67333	−	1.67333i
$203$	23308.9	−	23308.9i	0.565627	−	0.565627i
$204$	−37215.6			−0.894263
$205$		−	29602.8i		−	0.704410i
$206$	61165.0	−	61165.0i	1.44135	−	1.44135i
$207$			13128.2i			0.306384i
$208$	−8654.02	+	8489.84i	−0.200028	+	0.196233i
$209$	39538.8			0.905172
$210$	19311.1	+	19311.1i	0.437895	+	0.437895i
$211$	−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
$213$	15844.9	+	15844.9i	0.349244	+	0.349244i
$214$	−66704.1	−	66704.1i	−1.45655	−	1.45655i
$215$	−25368.3	+	25368.3i	−0.548800	+	0.548800i
$216$	7741.54	−	7741.54i	0.165928	−	0.165928i
$217$	78818.4			1.67382
$218$		−	45732.8i		−	0.962309i
$219$	4365.67	−	4365.67i	0.0910255	−	0.0910255i
$220$			42953.1i			0.887460i
$221$	−30499.4	−	31089.3i	−0.624464	−	0.636541i
$222$	−51216.9			−1.03922
$223$	26187.3	+	26187.3i	0.526601	+	0.526601i	0.919557	−	0.392956i	$-0.128548\pi$
$223$	26187.3	+	26187.3i	0.526601	+	0.526601i	−0.392956	+	0.919557i	$0.628548\pi$
$224$	−33070.7			−0.659094
$225$		−	7548.86i		−	0.149113i
$226$	−16066.3	−	16066.3i	−0.314556	−	0.314556i
$227$	−20418.0	−	20418.0i	−0.396244	−	0.396244i	0.480662	−	0.876906i	$-0.340396\pi$
$227$	−20418.0	−	20418.0i	−0.396244	−	0.396244i	−0.876906	+	0.480662i	$0.840396\pi$
$228$	48552.7	−	48552.7i	0.933993	−	0.933993i
$229$	−52109.2	+	52109.2i	−0.993672	+	0.993672i	−0.999980	−	0.00630803i	$-0.997992\pi$
$229$	−52109.2	+	52109.2i	−0.993672	+	0.993672i	0.00630803	+	0.999980i	$0.497992\pi$
$230$	−59801.3			−1.13046
$231$		−	18465.3i		−	0.346045i
$232$	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	$0.861450\pi$
$234$	30194.6	+	289.177i	0.551439	+	0.00528119i
$235$	−1728.53			−0.0312997
$236$	−5732.97	−	5732.97i	−0.102933	−	0.102933i
$237$	−21016.0			−0.374157
$238$			72877.2i			1.28658i
$239$	−54954.6	−	54954.6i	−0.962073	−	0.962073i	0.0372339	−	0.999307i	$-0.488145\pi$
$239$	−54954.6	−	54954.6i	−0.962073	−	0.962073i	−0.999307	+	0.0372339i	$0.988145\pi$
$240$	4898.50	+	4898.50i	0.0850433	+	0.0850433i
$241$	23474.0	−	23474.0i	0.404159	−	0.404159i	−0.475537	−	0.879696i	$-0.657746\pi$
$241$	23474.0	−	23474.0i	0.404159	−	0.404159i	0.879696	+	0.475537i	$0.157746\pi$
$242$	−36151.8	+	36151.8i	−0.617304	+	0.617304i
$243$	−3788.00			−0.0641500
$244$			194513.i			3.26716i
$245$	−7553.98	+	7553.98i	−0.125847	+	0.125847i
$246$			54770.3i			0.905054i
$247$	80350.6	+	769.526i	1.31703	+	0.0126133i
$248$	143930.			2.34017
$249$	−10708.4	−	10708.4i	−0.172713	−	0.172713i
$250$	111255.			1.78008
$251$			51668.4i			0.820120i	0.912059	+	0.410060i	$0.134492\pi$
$251$			51668.4i			0.820120i	−0.912059	+	0.410060i	$0.865508\pi$
$252$	−22674.9	−	22674.9i	−0.357063	−	0.357063i
$253$	28591.0	+	28591.0i	0.446671	+	0.446671i
$254$	−102703.	+	102703.i	−1.59190	+	1.59190i
$255$	−17597.7	+	17597.7i	−0.270629	+	0.270629i
$256$	−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	$0.767996\pi$
$258$	46935.6	−	46935.6i	0.705120	−	0.705120i
$259$			63651.1i			0.948869i
$260$	−835.976	+	87289.1i	−0.0123665	+	1.29126i
$261$	−20827.1			−0.305736
$262$	−7759.03	−	7759.03i	−0.113033	−	0.113033i
$263$	113585.			1.64214			0.821068	−	0.570831i	$-0.193379\pi$
$263$	113585.			1.64214			0.821068	+	0.570831i	$0.193379\pi$
$264$		−	33719.4i		−	0.483806i
$265$	−66237.6	−	66237.6i	−0.943220	−	0.943220i
$266$	−95077.9	−	95077.9i	−1.34374	−	1.34374i
$267$	−31344.1	+	31344.1i	−0.439677	+	0.439677i
$268$	26114.9	−	26114.9i	0.363596	−	0.363596i
$269$	5647.94			0.0780523			0.0390262	−	0.999238i	$-0.487574\pi$
$269$	5647.94			0.0780523			0.0390262	+	0.999238i	$0.487574\pi$
$270$		−	17254.9i		−	0.236693i
$271$	−3722.39	+	3722.39i	−0.0506854	+	0.0506854i	−0.731995	−	0.681310i	$-0.761411\pi$
$271$	−3722.39	+	3722.39i	−0.0506854	+	0.0506854i	0.681310	+	0.731995i	$0.261411\pi$
$272$			18486.1i			0.249867i
$273$	359.382	−	37525.1i	0.00482204	−	0.503497i
$274$	−202187.			−2.69310
$275$	−16440.1	−	16440.1i	−0.217389	−	0.217389i
$276$	70218.1			0.921787
$277$		−	31673.1i		−	0.412792i	−0.978469	−	0.206396i	$-0.933826\pi$
$277$		−	31673.1i		−	0.412792i	0.978469	−	0.206396i	$-0.0661736\pi$
$278$	−21797.1	−	21797.1i	−0.282039	−	0.282039i
$279$	−35213.0	−	35213.0i	−0.452371	−	0.452371i
$280$	43825.2	−	43825.2i	0.558995	−	0.558995i
$281$	−10897.2	+	10897.2i	−0.138007	+	0.138007i	−0.772736	−	0.634728i	$-0.781112\pi$
$281$	−10897.2	+	10897.2i	−0.138007	+	0.138007i	0.634728	+	0.772736i	$0.281112\pi$
$282$	3198.07			0.0402151
$283$		−	30994.4i		−	0.387000i	−0.981100	−	0.193500i	$-0.938016\pi$
$283$		−	30994.4i		−	0.387000i	0.981100	−	0.193500i	$-0.0619839\pi$
$284$	84748.2	−	84748.2i	1.05074	−	1.05074i
$285$		−	45917.0i		−	0.565306i
$286$	66388.2	−	65128.7i	0.811632	−	0.796233i
$287$	68067.2			0.826369
$288$	14774.7	+	14774.7i	0.178129	+	0.178129i
$289$	17110.2			0.204861
$290$		−	94870.7i		−	1.12807i
$291$	−28969.1	−	28969.1i	−0.342096	−	0.342096i
$292$	−23350.4	−	23350.4i	−0.273860	−	0.273860i
$293$	−113536.	+	113536.i	−1.32251	+	1.32251i	−0.410765	+	0.911741i	$0.634738\pi$
$293$	−113536.	+	113536.i	−1.32251	+	1.32251i	−0.911741	+	0.410765i	$0.865262\pi$
$294$	13976.1	−	13976.1i	0.161694	−	0.161694i
$295$	−5421.75			−0.0623011
$296$			116233.i			1.32662i
$297$	−8249.58	+	8249.58i	−0.0935231	+	0.0935231i
$298$			3686.28i			0.0415103i
$299$	57546.0	+	58658.9i	0.643684	+	0.656133i
$300$	−40376.0			−0.448623
$301$	−58330.4	−	58330.4i	−0.643817	−	0.643817i
$302$	−71321.3			−0.781998
$303$			75819.7i			0.825842i
$304$	−24117.6	−	24117.6i	−0.260968	−	0.260968i
$305$	91977.0	+	91977.0i	0.988735	+	0.988735i
$306$	32558.7	−	32558.7i	0.347716	−	0.347716i
$307$	75222.4	−	75222.4i	0.798124	−	0.798124i	−0.184675	−	0.982800i	$-0.559123\pi$
$307$	75222.4	−	75222.4i	0.798124	−	0.798124i	0.982800	+	0.184675i	$0.0591233\pi$
$308$	−98764.0			−1.04111
$309$			67920.5i			0.711351i
$310$	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	$-0.283577\pi$
$312$	656.265	−	68524.4i	0.00674171	−	0.703941i
$313$	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
$315$	−21444.0			−0.216115
$316$			112407.i			1.12569i
$317$	−42350.8	−	42350.8i	−0.421447	−	0.421447i	0.464255	−	0.885702i	$-0.346322\pi$
$317$	−42350.8	−	42350.8i	−0.421447	−	0.421447i	−0.885702	+	0.464255i	$0.846322\pi$
$318$	122551.	+	122551.i	1.21189	+	1.21189i
$319$	−45357.6	+	45357.6i	−0.445727	+	0.445727i
$320$	−82384.6	+	82384.6i	−0.804537	+	0.804537i
$321$	74071.4			0.718853
$322$		−	137504.i		−	1.32618i
$323$	86641.7	−	86641.7i	0.830466	−	0.830466i
$324$			20260.6i			0.193002i
$325$	−33089.5	−	33729.4i	−0.313273	−	0.319332i
$326$	−155362.			−1.46187
$327$	25391.9	+	25391.9i	0.237465	+	0.237465i
$328$	124297.			1.15535
$329$		−	3974.48i		−	0.0367188i
$330$	−37578.2	−	37578.2i	−0.345070	−	0.345070i
$331$	23593.9	+	23593.9i	0.215349	+	0.215349i	0.806535	−	0.591186i	$-0.201340\pi$
$331$	23593.9	+	23593.9i	0.215349	+	0.215349i	−0.591186	+	0.806535i	$0.701340\pi$
$332$	−57275.0	+	57275.0i	−0.519624	+	0.519624i
$333$	28436.8	−	28436.8i	0.256444	−	0.256444i
$334$	−354641.			−3.17904
$335$		−	24697.3i		−	0.220069i
$336$	−11263.3	+	11263.3i	−0.0997674	+	0.0997674i
$337$			114863.i			1.01139i	0.862711	+	0.505697i	$0.168765\pi$
$337$			114863.i			1.01139i	−0.862711	+	0.505697i	$0.831235\pi$
$338$	136182.	−	131062.i	1.19202	−	1.14721i
$339$	17840.7			0.155244
$340$	94123.4	+	94123.4i	0.814216	+	0.814216i
$341$	−153375.			−1.31900
$342$			84954.2i			0.726328i
$343$	−89921.4	−	89921.4i	−0.764319	−	0.764319i
$344$	−106517.	−	106517.i	−0.900122	−	0.900122i
$345$	33203.1	−	33203.1i	0.278959	−	0.278959i
$346$	8015.22	−	8015.22i	0.0669520	−	0.0669520i
$347$	93409.6			0.775769			0.387885	−	0.921708i	$-0.373206\pi$
$347$	93409.6			0.775769			0.387885	+	0.921708i	$0.373206\pi$
$348$			111396.i			0.919839i
$349$	−14479.3	+	14479.3i	−0.118877	+	0.118877i	−0.764043	−	0.645166i	$-0.776788\pi$
$349$	−14479.3	+	14479.3i	−0.118877	+	0.118877i	0.645166	+	0.764043i	$0.276788\pi$
$350$			79066.0i			0.645437i
$351$	−16925.3	+	16604.2i	−0.137380	+	0.134773i
$352$	64353.3			0.519380
$353$	127078.	+	127078.i	1.01981	+	1.01981i	0.999800	+	0.0200140i	$0.00637109\pi$
$353$	127078.	+	127078.i	1.01981	+	1.01981i	0.0200140	+	0.999800i	$0.493629\pi$
$354$	10031.2			0.0800469
$355$		−	80147.6i		−	0.635966i
$356$	167648.	+	167648.i	1.32281	+	1.32281i
$357$	−40463.2	−	40463.2i	−0.317485	−	0.317485i
$358$	−12636.2	+	12636.2i	−0.0985939	+	0.0985939i
$359$	40565.6	−	40565.6i	0.314752	−	0.314752i	−0.531995	−	0.846747i	$-0.678558\pi$
$359$	40565.6	−	40565.6i	0.314752	−	0.314752i	0.846747	+	0.531995i	$0.178558\pi$
$360$	−39158.8			−0.302151
$361$			95750.0i			0.734724i
$362$	146583.	−	146583.i	1.11858	−	1.11858i
$363$		−	40144.7i		−	0.304659i
$364$	−200708.	−	1922.20i	−1.51482	−	0.0145076i
$365$	−22082.8			−0.165755
$366$	−170173.	−	170173.i	−1.27037	−	1.27037i
$367$	−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
$369$	−30409.8	−	30409.8i	−0.223337	−	0.223337i
$370$	129534.	+	129534.i	0.946198	+	0.946198i
$371$	152303.	−	152303.i	1.10652	−	1.10652i
$372$	−188341.	+	188341.i	−1.36100	+	1.36100i
$373$	−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
$375$	−61771.3	+	61771.3i	−0.439262	+	0.439262i
$376$		−	7257.77i		−	0.0513367i
$377$	−93058.4	+	91292.8i	−0.654746	+	0.642324i
$378$	39675.1			0.277673
$379$	−27066.7	−	27066.7i	−0.188433	−	0.188433i	0.606585	−	0.795018i	$-0.292539\pi$
$379$	−27066.7	−	27066.7i	−0.188433	−	0.188433i	−0.795018	+	0.606585i	$0.792539\pi$
$380$	−245593.			−1.70078
$381$		−	114046.i		−	0.785652i
$382$	246966.	+	246966.i	1.69243	+	1.69243i
$383$	−166419.	−	166419.i	−1.13451	−	1.13451i	−0.989419	−	0.145087i	$-0.953654\pi$
$383$	−166419.	−	166419.i	−1.13451	−	1.13451i	−0.145087	−	0.989419i	$-0.546346\pi$
$384$	106931.	−	106931.i	0.725174	−	0.725174i
$385$	−46701.2	+	46701.2i	−0.315070	+	0.315070i
$386$	13156.3			0.0882997
$387$			52119.5i			0.347999i
$388$	−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	$-0.0173364\pi$
$390$	−75634.9	−	77097.6i	−0.497271	−	0.506888i
$391$	125303.			0.819613
$392$	−31717.8	−	31717.8i	−0.206410	−	0.206410i
$393$	8616.00			0.0557854
$394$			95226.6i			0.613431i
$395$	53152.4	+	53152.4i	0.340666	+	0.340666i
$396$	44123.9	+	44123.9i	0.281374	+	0.281374i
$397$	−155869.	+	155869.i	−0.988957	+	0.988957i	−0.999940	−	0.0109822i	$-0.996504\pi$
$397$	−155869.	+	155869.i	−0.988957	+	0.988957i	0.0109822	+	0.999940i	$0.496504\pi$
$398$	−34812.1	+	34812.1i	−0.219768	+	0.219768i
$399$	105579.			0.663181
$400$			20056.0i			0.125350i
$401$	−142185.	+	142185.i	−0.884230	+	0.884230i	−0.993961	−	0.109732i	$-0.965001\pi$
$401$	−142185.	+	142185.i	−0.884230	+	0.884230i	0.109732	+	0.993961i	$0.465001\pi$
$402$			45694.2i			0.282754i
$403$	−311689.	−	2985.07i	−1.91916	−	0.0183800i
$404$	405531.			2.48463
$405$	9580.35	+	9580.35i	0.0584079	+	0.0584079i
$406$	218141.			1.32338
$407$		−	123861.i		−	0.747730i
$408$	−73889.5	−	73889.5i	−0.443877	−	0.443877i
$409$	9949.25	+	9949.25i	0.0594763	+	0.0594763i	0.736219	−	0.676743i	$-0.236609\pi$
$409$	9949.25	+	9949.25i	0.0594763	+	0.0594763i	−0.676743	+	0.736219i	$0.736609\pi$
$410$	138521.	−	138521.i	0.824042	−	0.824042i
$411$	112259.	−	112259.i	0.664567	−	0.664567i
$412$	363282.			2.14017
$413$		−	12466.5i		−	0.0730876i
$414$	−61431.4	+	61431.4i	−0.358418	+	0.358418i
$415$			54165.8i			0.314506i
$416$	130779.	+	1252.48i	0.755701	+	0.00723742i
$417$	24204.6			0.139195
$418$	185015.	+	185015.i	1.05890	+	1.05890i
$419$	−17793.2			−0.101351			−0.0506753	−	0.998715i	$-0.516137\pi$
$419$	−17793.2			−0.101351			−0.0506753	+	0.998715i	$0.516137\pi$
$420$			114696.i			0.650204i
$421$	−123242.	−	123242.i	−0.695334	−	0.695334i	0.268066	−	0.963400i	$-0.413615\pi$
$421$	−123242.	−	123242.i	−0.695334	−	0.695334i	−0.963400	+	0.268066i	$0.913615\pi$
$422$	−214671.	−	214671.i	−1.20545	−	1.20545i
$423$	−1775.64	+	1775.64i	−0.00992373	+	0.00992373i
$424$	278120.	−	278120.i	1.54704	−	1.54704i
$425$	−72050.5			−0.398896
$426$			148287.i			0.817114i
$427$	−211487.	+	211487.i	−1.15992	+	1.15992i
$428$		−	396180.i		−	2.16274i
$429$	−699.332	+	73021.3i	−0.00379987	+	0.396767i
$430$	−237413.			−1.28401
$431$	−81585.7	−	81585.7i	−0.439197	−	0.439197i	0.452545	−	0.891742i	$-0.350516\pi$
$431$	−81585.7	−	81585.7i	−0.439197	−	0.439197i	−0.891742	+	0.452545i	$0.850516\pi$
$432$	10064.0			0.0539268
$433$			60799.1i			0.324281i	0.986768	+	0.162141i	$0.0518398\pi$
$433$			60799.1i			0.324281i	−0.986768	+	0.162141i	$0.948160\pi$
$434$	368817.	+	368817.i	1.95809	+	1.95809i
$435$	52674.5	+	52674.5i	0.278369	+	0.278369i
$436$	135812.	−	135812.i	0.714439	−	0.714439i
$437$	−163475.	+	163475.i	−0.856027	+	0.856027i
$438$	40856.9			0.212969
$439$		−	275044.i		−	1.42716i	−0.700572	−	0.713581i	$-0.747072\pi$
$439$		−	275044.i		−	1.42716i	0.700572	−	0.713581i	$-0.252928\pi$
$440$	−85280.9	+	85280.9i	−0.440500	+	0.440500i
$441$			15519.8i			0.0798010i
$442$	2760.06	−	288194.i	0.0141278	−	1.47516i
$443$	−8716.50			−0.0444155			−0.0222077	−	0.999753i	$-0.507070\pi$
$443$	−8716.50			−0.0444155			−0.0222077	+	0.999753i	$0.507070\pi$
$444$	−152098.	−	152098.i	−0.771539	−	0.771539i
$445$	158547.			0.800642
$446$			245078.i			1.23207i
$447$	−2046.71	−	2046.71i	−0.0102433	−	0.0102433i
$448$	−189431.	−	189431.i	−0.943832	−	0.943832i
$449$	246638.	−	246638.i	1.22340	−	1.22340i	0.256982	−	0.966416i	$-0.417272\pi$
$449$	246638.	−	246638.i	1.22340	−	1.22340i	0.966416	−	0.256982i	$-0.0827280\pi$
$450$	35323.6	−	35323.6i	0.174438	−	0.174438i
$451$	−132454.			−0.651197
$452$		−	95423.5i		−	0.467066i
$453$	39599.3	−	39599.3i	0.192971	−	0.192971i
$454$		−	191086.i		−	0.927078i
$455$	−95815.0	+	93997.2i	−0.462819	+	0.454038i
$456$	192797.			0.927195
$457$	55246.3	+	55246.3i	0.264527	+	0.264527i	0.826890	−	0.562363i	$-0.190108\pi$
$457$	55246.3	+	55246.3i	0.264527	+	0.264527i	−0.562363	+	0.826890i	$0.690108\pi$
$458$	−487672.			−2.32486
$459$			36154.7i			0.171609i
$460$	−177591.	−	177591.i	−0.839277	−	0.839277i
$461$	−31473.0	−	31473.0i	−0.148093	−	0.148093i	0.629172	−	0.777266i	$-0.283394\pi$
$461$	−31473.0	−	31473.0i	−0.148093	−	0.148093i	−0.777266	+	0.629172i	$0.783394\pi$
$462$	86405.2	−	86405.2i	0.404815	−	0.404815i
$463$	134703.	−	134703.i	0.628371	−	0.628371i	−0.319287	−	0.947658i	$-0.603443\pi$
$463$	134703.	−	134703.i	0.628371	−	0.628371i	0.947658	+	0.319287i	$0.103443\pi$
$464$	55333.9			0.257013
$465$			178117.i			0.823757i
$466$	−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	$-0.0787410\pi$
$468$	88809.7	+	90527.2i	0.405479	+	0.413321i
$469$	56787.6			0.258171
$470$	−8088.34	−	8088.34i	−0.0366154	−	0.0366154i
$471$	−132956.			−0.599329
$472$		−	22765.0i		−	0.102184i
$473$	113507.	+	113507.i	0.507342	+	0.507342i
$474$	−98341.0	−	98341.0i	−0.437701	−	0.437701i
$475$	93999.4	−	93999.4i	0.416618	−	0.416618i
$476$	−216422.	+	216422.i	−0.955186	+	0.955186i
$477$	−136086.			−0.598105
$478$		−	514301.i		−	2.25093i
$479$	69279.4	−	69279.4i	0.301949	−	0.301949i	−0.539827	−	0.841776i	$-0.681510\pi$
$479$	69279.4	−	69279.4i	0.301949	−	0.301949i	0.841776	+	0.539827i	$0.181510\pi$
$480$		−	74734.4i		−	0.324368i
$481$	2410.64	−	251709.i	0.0104194	−	1.08795i
$482$	219685.			0.945597
$483$	76345.4	+	76345.4i	0.327257	+	0.327257i
$484$	−214719.			−0.916599
$485$			146533.i			0.622950i
$486$	−17725.3	−	17725.3i	−0.0750448	−	0.0750448i
$487$	334191.	+	334191.i	1.40908	+	1.40908i	0.764713	+	0.644372i	$0.222881\pi$
$487$	334191.	+	334191.i	1.40908	+	1.40908i	0.644372	+	0.764713i	$0.277119\pi$
$488$	−386195.	+	386195.i	−1.62169	+	1.62169i
$489$	86260.5	−	86260.5i	0.360740	−	0.360740i
$490$	−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	$0.860679\pi$
$492$	−162650.	+	162650.i	−0.671932	+	0.671932i
$493$			198785.i			0.817880i
$494$	372386.	+	379588.i	1.52595	+	1.55546i
$495$	41728.6			0.170303
$496$	93554.7	+	93554.7i	0.380279	+	0.380279i
$497$	184287.			0.746074
$498$		−	100216.i		−	0.404090i
$499$	263314.	+	263314.i	1.05748	+	1.05748i	0.998244	+	0.0592381i	$0.0188671\pi$
$499$	263314.	+	263314.i	1.05748	+	1.05748i	0.0592381	+	0.998244i	$0.481133\pi$
$500$	330391.	+	330391.i	1.32157	+	1.32157i
$501$	196905.	−	196905.i	0.784479	−	0.784479i
$502$	−241773.	+	241773.i	−0.959403	+	0.959403i
$503$	120971.			0.478131			0.239065	−	0.971003i	$-0.423159\pi$
$503$	120971.			0.478131			0.239065	+	0.971003i	$0.423159\pi$
$504$		−	90039.6i		−	0.354464i
$505$	191758.	−	191758.i	0.751920	−	0.751920i
$506$			267573.i			1.04506i
$507$	−2842.36	+	148380.i	−0.0110577	+	0.577244i
$508$	−609990.			−2.36371
$509$	−50199.3	−	50199.3i	−0.193759	−	0.193759i	0.603559	−	0.797318i	$-0.293749\pi$
$509$	−50199.3	−	50199.3i	−0.193759	−	0.193759i	−0.797318	+	0.603559i	$0.793749\pi$
$510$	−164691.			−0.633182
$511$		−	50775.9i		−	0.194454i
$512$	−102587.	−	102587.i	−0.391337	−	0.391337i
$513$	−47168.6	−	47168.6i	−0.179233	−	0.179233i
$514$	−411688.	+	411688.i	−1.55827	+	1.55827i
$515$	171780.	−	171780.i	0.647677	−	0.647677i
$516$	278768.			1.04699
$517$			7734.07i			0.0289352i
$518$	−297845.	+	297845.i	−1.11002	+	1.11002i
$519$			8900.49i			0.0330430i
$520$	−174967.	+	171648.i	−0.647068	+	0.634792i
$521$	−307242.			−1.13189			−0.565946	−	0.824443i	$-0.691489\pi$
$521$	−307242.			−1.13189			−0.565946	+	0.824443i	$0.691489\pi$
$522$	−97456.7	−	97456.7i	−0.357660	−	0.357660i
$523$	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
$525$	−43899.3	−	43899.3i	−0.159272	−	0.159272i
$526$	531501.	+	531501.i	1.92102	+	1.92102i
$527$	−336092.	+	336092.i	−1.21014	+	1.21014i
$528$	21917.7	−	21917.7i	0.0786189	−	0.0786189i
$529$	43420.3			0.155161
$530$		−	619895.i		−	2.20682i
$531$	−5569.54	+	5569.54i	−0.0197529	+	0.0197529i
$532$		−	564703.i		−	1.99525i
$533$	−269173.	−	2577.89i	−0.947494	−	0.00907424i
$534$	−293339.			−1.02870
$535$	−187337.	−	187337.i	−0.654508	−	0.654508i
$536$	103699.			0.360950
$537$		−	14031.8i		−	0.0486593i
$538$	26428.6	+	26428.6i	0.0913081	+	0.0913081i
$539$	33799.3	+	33799.3i	0.116340	+	0.116340i
$540$	51241.7	−	51241.7i	0.175726	−	0.175726i
$541$	184394.	−	184394.i	0.630017	−	0.630017i	−0.318055	−	0.948072i	$-0.603030\pi$
$541$	184394.	−	184394.i	0.630017	−	0.630017i	0.948072	+	0.318055i	$0.103030\pi$
$542$	−34836.6			−0.118587
$543$			162773.i			0.552054i
$544$	141018.	−	141018.i	0.476515	−	0.476515i
$545$		−	128439.i		−	0.432419i
$546$	177274.	−	173911.i	0.594648	−	0.583366i
$547$	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
$549$	188968.			0.626967
$550$		−	153857.i		−	0.508619i
$551$	−259341.	−	259341.i	−0.854217	−	0.854217i
$552$	139414.	+	139414.i	0.457539	+	0.457539i
$553$	−122216.	+	122216.i	−0.399647	+	0.399647i
$554$	148209.	−	148209.i	0.482898	−	0.482898i
$555$	−143841.			−0.466979
$556$		−	129461.i		−	0.418784i
$557$	200107.	−	200107.i	0.644987	−	0.644987i	−0.306790	−	0.951777i	$-0.599255\pi$
$557$	200107.	−	200107.i	0.644987	−	0.644987i	0.951777	+	0.306790i	$0.0992550\pi$
$558$		−	329546.i		−	1.05840i
$559$	228460.	+	232878.i	0.731115	+	0.745254i
$560$	56973.0			0.181674
$561$	78738.5	+	78738.5i	0.250185	+	0.250185i
$562$	−101983.			−0.322891
$563$		−	488676.i		−	1.54172i	−0.637007	−	0.770858i	$-0.719828\pi$
$563$		−	488676.i		−	1.54172i	0.637007	−	0.770858i	$-0.280172\pi$
$564$	9497.25	+	9497.25i	0.0298566	+	0.0298566i
$565$	−45121.7	−	45121.7i	−0.141348	−	0.141348i
$566$	145033.	−	145033.i	0.452725	−	0.452725i
$567$	−22028.6	+	22028.6i	−0.0685204	+	0.0685204i
$568$	336525.			1.04309
$569$			562947.i			1.73877i	0.494132	+	0.869387i	$0.335486\pi$
$569$			562947.i			1.73877i	−0.494132	+	0.869387i	$0.664514\pi$
$570$	214861.	−	214861.i	0.661314	−	0.661314i
$571$			183359.i			0.562380i	0.959652	+	0.281190i	$0.0907291\pi$
$571$			183359.i			0.562380i	−0.959652	+	0.281190i	$0.909271\pi$
$572$	390564.	+	3740.47i	1.19371	+	0.0114323i
$573$	−274242.			−0.835267
$574$	318509.	+	318509.i	0.966713	+	0.966713i
$575$	135944.			0.411173
$576$			169261.i			0.510165i
$577$	196407.	+	196407.i	0.589938	+	0.589938i	0.937614	−	0.347677i	$-0.113029\pi$
$577$	196407.	+	196407.i	0.589938	+	0.589938i	−0.347677	+	0.937614i	$0.613029\pi$
$578$	80064.2	+	80064.2i	0.239653	+	0.239653i
$579$	−7304.69	+	7304.69i	−0.0217894	+	0.0217894i
$580$	281736.	−	281736.i	0.837503	−	0.837503i
$581$	−124546.			−0.368958
$582$		−	271112.i		−	0.800391i
$583$	−296372.	+	296372.i	−0.871966	+	0.871966i
$584$		−	92721.6i		−	0.271866i
$585$	84800.7	+	812.145i	0.247792	+	0.00237313i
$586$	−1.06254e6			−3.09422
$587$	−127057.	−	127057.i	−0.368742	−	0.368742i	0.498276	−	0.867018i	$-0.333966\pi$
$587$	−127057.	−	127057.i	−0.368742	−	0.368742i	−0.867018	+	0.498276i	$0.833966\pi$
$588$	83009.5			0.240089
$589$		−	876953.i		−	2.52782i
$590$	−25370.2	−	25370.2i	−0.0728818	−	0.0728818i
$591$	−52872.1	−	52872.1i	−0.151374	−	0.151374i
$592$	−75551.7	+	75551.7i	−0.215576	+	0.215576i
$593$	168617.	−	168617.i	0.479503	−	0.479503i	−0.425470	−	0.904973i	$-0.639891\pi$
$593$	168617.	−	168617.i	0.479503	−	0.479503i	0.904973	+	0.425470i	$0.139891\pi$
$594$	−77205.0			−0.218813
$595$			204674.i			0.578133i
$596$	−10947.1	+	10947.1i	−0.0308181	+	0.0308181i
$597$		−	38657.0i		−	0.108462i
$598$	−5207.65	+	543761.i	−0.0145626	+	1.52057i
$599$	−22624.2			−0.0630550			−0.0315275	−	0.999503i	$-0.510037\pi$
$599$	−22624.2			−0.0630550			−0.0315275	+	0.999503i	$0.510037\pi$
$600$	−80164.3	−	80164.3i	−0.222679	−	0.222679i
$601$	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
$603$	−25370.5	−	25370.5i	−0.0697741	−	0.0697741i
$604$	−211802.	−	211802.i	−0.580572	−	0.580572i
$605$	−101531.	+	101531.i	−0.277389	+	0.277389i
$606$	−354786.	+	354786.i	−0.966097	+	0.966097i
$607$	−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
$609$	−121117.	+	121117.i	−0.326565	+	0.326565i
$610$			860782.i			2.31331i
$611$	−150.525	+	15717.1i	−0.000403204	+	0.0421009i
$612$	193378.			0.516303
$613$	−230276.	−	230276.i	−0.612812	−	0.612812i	0.330866	−	0.943678i	$-0.392659\pi$
$613$	−230276.	−	230276.i	−0.612812	−	0.612812i	−0.943678	+	0.330866i	$0.892659\pi$
$614$	703981.			1.86734
$615$			153821.i			0.406691i
$616$	−196090.	−	196090.i	−0.516767	−	0.516767i
$617$	34766.2	+	34766.2i	0.0913244	+	0.0913244i	0.751293	−	0.659969i	$-0.229430\pi$
$617$	34766.2	+	34766.2i	0.0913244	+	0.0913244i	−0.659969	+	0.751293i	$0.729430\pi$
$618$	−317823.	+	317823.i	−0.832162	+	0.832162i
$619$	−420362.	+	420362.i	−1.09709	+	1.09709i	−0.102339	+	0.994750i	$0.532633\pi$
$619$	−420362.	+	420362.i	−1.09709	+	1.09709i	−0.994750	+	0.102339i	$0.967367\pi$
$620$	952680.			2.47836
$621$		−	68216.3i		−	0.176891i
$622$	703892.	−	703892.i	1.81939	−	1.81939i
$623$			364555.i			0.939262i
$624$	44967.6	−	44114.5i	0.115486	−	0.113295i
$625$	137714.			0.352547
$626$	592423.	+	592423.i	1.51176	+	1.51176i
$627$	−205450.			−0.522601
$628$			711130.i			1.80314i
$629$	−271417.	−	271417.i	−0.686018	−	0.686018i
$630$	−100344.	−	100344.i	−0.252819	−	0.252819i
$631$	93922.3	−	93922.3i	0.235890	−	0.235890i	−0.579256	−	0.815146i	$-0.696657\pi$
$631$	93922.3	−	93922.3i	0.235890	−	0.235890i	0.815146	+	0.579256i	$0.196657\pi$
$632$	−223177.	+	223177.i	−0.558748	+	0.558748i
$633$	238380.			0.594926
$634$		−	396347.i		−	0.986045i
$635$	−288438.	+	288438.i	−0.715327	+	0.715327i
$636$			727875.i			1.79946i
$637$	68029.0	+	69344.6i	0.167654	+	0.170897i
$638$	−424487.			−1.04285
$639$	−82332.3	−	82332.3i	−0.201636	−	0.201636i
$640$	−540888.			−1.32053
$641$			123299.i			0.300084i	0.988680	+	0.150042i	$0.0479409\pi$
$641$			123299.i			0.300084i	−0.988680	+	0.150042i	$0.952059\pi$
$642$	346605.	+	346605.i	0.840938	+	0.840938i
$643$	−280732.	−	280732.i	−0.678999	−	0.678999i	0.280774	−	0.959774i	$-0.409409\pi$
$643$	−280732.	−	280732.i	−0.678999	−	0.678999i	−0.959774	+	0.280774i	$0.909409\pi$
$644$	408343.	−	408343.i	0.984586	−	0.984586i
$645$	131817.	−	131817.i	0.316850	−	0.316850i
$646$	810850.			1.94301
$647$			45435.6i			0.108539i	0.998526	+	0.0542697i	$0.0172831\pi$
$647$			45435.6i			0.108539i	−0.998526	+	0.0542697i	$0.982717\pi$
$648$	−40226.2	+	40226.2i	−0.0957986	+	0.0957986i
$649$			24258.9i			0.0575946i
$650$	2994.45	−	312668.i	0.00708746	−	0.740042i
$651$	−409552.			−0.966379
$652$	−461375.	−	461375.i	−1.08532	−	1.08532i
$653$	−378723.			−0.888168			−0.444084	−	0.895985i	$-0.646471\pi$
$653$	−378723.			−0.888168			−0.444084	+	0.895985i	$0.646471\pi$
$654$			237635.i			0.555590i
$655$	−21791.0	−	21791.0i	−0.0507920	−	0.0507920i
$656$	80793.4	+	80793.4i	0.187745	+	0.187745i
$657$	−22684.7	+	22684.7i	−0.0525536	+	0.0525536i
$658$	18597.9	−	18597.9i	0.0429548	−	0.0429548i
$659$	289116.			0.665735			0.332867	−	0.942974i	$-0.391984\pi$
$659$	289116.			0.665735			0.332867	+	0.942974i	$0.391984\pi$
$660$		−	223191.i		−	0.512375i
$661$	−168774.	+	168774.i	−0.386281	+	0.386281i	−0.873359	−	0.487078i	$-0.838063\pi$
$661$	−168774.	+	168774.i	−0.386281	+	0.386281i	0.487078	+	0.873359i	$0.338063\pi$
$662$			220807.i			0.503845i
$663$	158480.	+	161545.i	0.360534	+	0.367507i
$664$	−227433.			−0.515842
$665$	−267024.	−	267024.i	−0.603819	−	0.603819i
$666$	266131.			0.599994
$667$		−	375065.i		−	0.843054i
$668$	−1.05317e6	−	1.05317e6i	−2.36019	−	2.36019i
$669$	−136073.	−	136073.i	−0.304033	−	0.304033i
$670$	115567.	−	115567.i	0.257444	−	0.257444i
$671$	411539.	−	411539.i	0.914043	−	0.914043i
$672$	171840.			0.380528
$673$		−	163719.i		−	0.361467i	−0.983532	−	0.180734i	$-0.942153\pi$
$673$		−	163719.i		−	0.361467i	0.983532	−	0.180734i	$-0.0578472\pi$
$674$	−537482.	+	537482.i	−1.18316	+	1.18316i
$675$			39225.0i			0.0860906i
$676$	793630.	+	15202.7i	1.73670	+	0.0332681i
$677$	462025.			1.00806			0.504032	−	0.863685i	$-0.331849\pi$
$677$	462025.			1.00806			0.504032	+	0.863685i	$0.331849\pi$
$678$	83482.8	+	83482.8i	0.181609	+	0.181609i
$679$	−336931.			−0.730805
$680$			373753.i			0.808290i
$681$	106095.	+	106095.i	0.228771	+	0.228771i
$682$	−717693.	−	717693.i	−1.54301	−	1.54301i
$683$	−213724.	+	213724.i	−0.458155	+	0.458155i	−0.898049	−	0.439895i	$-0.855016\pi$
$683$	−213724.	+	213724.i	−0.458155	+	0.458155i	0.439895	+	0.898049i	$0.355016\pi$
$684$	−252287.	+	252287.i	−0.539241	+	0.539241i
$685$	−567838.			−1.21016
$686$		−	841544.i		−	1.78825i
$687$	270767.	−	270767.i	0.573697	−	0.573697i
$688$		−	138473.i		−	0.292541i
$689$	−608054.	+	596517.i	−1.28087	+	1.25656i
$690$	310737.			0.652671
$691$	−344817.	−	344817.i	−0.722159	−	0.722159i	0.246886	−	0.969045i	$-0.420593\pi$
$691$	−344817.	−	344817.i	−0.722159	−	0.722159i	−0.969045	+	0.246886i	$0.920593\pi$
$692$	47605.4			0.0994132
$693$			95948.5i			0.199789i
$694$	437094.	+	437094.i	0.907520	+	0.907520i
$695$	−61216.6	−	61216.6i	−0.126736	−	0.126736i
$696$	−221171.	+	221171.i	−0.456572	+	0.456572i
$697$	−290248.	+	290248.i	−0.597452	+	0.597452i
$698$	−135507.			−0.278132
$699$		−	237892.i		−	0.486884i
$700$	−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	$0.972895\pi$
$702$	−156896.	−	1502.61i	−0.318374	−	0.00304909i
$703$	708198.			1.43299
$704$	368619.	+	368619.i	0.743760	+	0.743760i
$705$	8981.68			0.0180709
$706$			1.18928e6i			2.38602i
$707$	440919.	+	440919.i	0.882104	+	0.882104i
$708$	29789.4	+	29789.4i	0.0594285	+	0.0594285i
$709$	507737.	−	507737.i	1.01006	−	1.01006i	0.0101092	−	0.999949i	$-0.496782\pi$
$709$	507737.	−	507737.i	1.01006	−	1.01006i	0.999949	−	0.0101092i	$-0.00321793\pi$
$710$	375037.	−	375037.i	0.743973	−	0.743973i
$711$	109203.			0.216020
$712$			665711.i			1.31318i
$713$	634135.	−	634135.i	1.24739	−	1.24739i
$714$		−	378681.i		−	0.742809i
$715$	186450.	−	182912.i	0.364711	−	0.357792i
$716$	−75051.0			−0.146396
$717$	285552.	+	285552.i	0.555453	+	0.555453i
$718$	379640.			0.736415
$719$		−	50596.5i		−	0.0978729i	−0.998802	−	0.0489364i	$-0.984417\pi$
$719$		−	50596.5i		−	0.0978729i	0.998802	−	0.0489364i	$-0.0155832\pi$
$720$	−25453.3	−	25453.3i	−0.0490998	−	0.0490998i
$721$	394982.	+	394982.i	0.759814	+	0.759814i
$722$	−448046.	+	448046.i	−0.859505	+	0.859505i
$723$	−121974.	+	121974.i	−0.233341	+	0.233341i
$724$	870610.			1.66091
$725$			215666.i			0.410304i
$726$	187850.	−	187850.i	0.356400	−	0.356400i
$727$			891410.i			1.68659i	0.537453	+	0.843294i	$0.319387\pi$
$727$			891410.i			1.68659i	−0.537453	+	0.843294i	$0.680613\pi$
$728$	−394678.	−	402310.i	−0.744697	−	0.759099i
$729$	19683.0			0.0370370
$730$	−103333.	−	103333.i	−0.193906	−	0.193906i
$731$	497458.			0.930939
$732$		−	1.01072e6i		−	1.88629i
$733$	−439182.	−	439182.i	−0.817404	−	0.817404i	0.168327	−	0.985731i	$-0.446164\pi$
$733$	−439182.	−	439182.i	−0.817404	−	0.817404i	−0.985731	+	0.168327i	$0.946164\pi$
$734$	−190672.	−	190672.i	−0.353912	−	0.353912i
$735$	39251.6	−	39251.6i	0.0726579	−	0.0726579i
$736$	−266071.	+	266071.i	−0.491182	+	0.491182i
$737$	−110505.			−0.203445
$738$		−	284595.i		−	0.522533i
$739$	83855.7	−	83855.7i	0.153548	−	0.153548i	−0.626153	−	0.779701i	$-0.715371\pi$
$739$	83855.7	−	83855.7i	0.153548	−	0.153548i	0.779701	+	0.626153i	$0.215371\pi$
$740$			769353.i			1.40495i
$741$	−417514.	−	3998.57i	−0.760387	−	0.00728230i
$742$	1.42535e6			2.58890
$743$	−153273.	−	153273.i	−0.277643	−	0.277643i	0.554524	−	0.832167i	$-0.312900\pi$
$743$	−153273.	−	153273.i	−0.277643	−	0.277643i	−0.832167	+	0.554524i	$0.812900\pi$
$744$	−747881.			−1.35110
$745$			10352.8i			0.0186529i
$746$	−207543.	−	207543.i	−0.372933	−	0.372933i
$747$	55642.3	+	55642.3i	0.0997157	+	0.0997157i
$748$	421143.	−	421143.i	0.752708	−	0.752708i
$749$	430752.	−	430752.i	0.767827	−	0.767827i
$750$	−578096.			−1.02773
$751$			208551.i			0.369771i	0.982760	+	0.184886i	$0.0591915\pi$
$751$			208551.i			0.369771i	−0.982760	+	0.184886i	$0.940808\pi$
$752$	4717.57	−	4717.57i	0.00834225	−	0.00834225i
$753$		−	268477.i		−	0.473497i
$754$	−862640.	−	8261.59i	−1.51735	−	0.0145319i
$755$	−200304.			−0.351395
$756$	117822.	+	117822.i	0.206151	+	0.206151i
$757$	−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
$759$	−148563.	−	148563.i	−0.257886	−	0.257886i
$760$	−487610.	−	487610.i	−0.844201	−	0.844201i
$761$	790313.	−	790313.i	1.36468	−	1.36468i	0.496826	−	0.867850i	$-0.334499\pi$
$761$	790313.	−	790313.i	1.36468	−	1.36468i	0.867850	−	0.496826i	$-0.165501\pi$
$762$	533659.	−	533659.i	0.919082	−	0.919082i
$763$	295326.			0.507287
$764$			1.46682e6i			2.51299i
$765$	91440.2	−	91440.2i	0.156248	−	0.156248i
$766$		−	1.55746e6i		−	2.65436i
$767$	−472.140	+	49298.9i	−0.000802565	+	0.0838005i
$768$	479546.			0.813033
$769$	170652.	+	170652.i	0.288574	+	0.288574i	0.836516	−	0.547942i	$-0.184589\pi$
$769$	170652.	+	170652.i	0.288574	+	0.288574i	−0.547942	+	0.836516i	$0.684589\pi$
$770$	−437061.			−0.737158
$771$		−	457158.i		−	0.769056i
$772$	39070.1	+	39070.1i	0.0655555	+	0.0655555i
$773$	238774.	+	238774.i	0.399602	+	0.399602i	0.878093	−	0.478490i	$-0.158816\pi$
$773$	238774.	+	238774.i	0.399602	+	0.399602i	−0.478490	+	0.878093i	$0.658816\pi$
$774$	−243885.	+	243885.i	−0.407101	+	0.407101i
$775$	−364634.	+	364634.i	−0.607090	+	0.607090i
$776$	−615268.			−1.02174
$777$		−	330741.i		−	0.547830i
$778$	77091.7	−	77091.7i	0.127365	−	0.127365i
$779$		−	757333.i		−	1.24799i
$780$	4343.86	−	453567.i	0.00713981	−	0.745509i
$781$	−358610.			−0.587923
$782$	586335.	+	586335.i	0.958810	+	0.958810i
$783$	108221.			0.176517
$784$		−	41233.3i		−	0.0670836i
$785$	336263.	+	336263.i	0.545682	+	0.545682i
$786$	40317.1	+	40317.1i	0.0652596	+	0.0652596i
$787$	−460701.	+	460701.i	−0.743823	+	0.743823i	−0.973311	−	0.229488i	$-0.926295\pi$
$787$	−460701.	+	460701.i	−0.743823	+	0.743823i	0.229488	+	0.973311i	$0.426295\pi$
$788$	−282793.	+	282793.i	−0.455424	+	0.455424i
$789$	−590204.			−0.948087
$790$			497435.i			0.797044i
$791$	103750.	−	103750.i	0.165820	−	0.165820i
$792$			175211.i			0.279326i
$793$	844339.	−	828320.i	1.34267	−	1.31720i
$794$	−1.45872e6			−2.31383
$795$	344181.	+	344181.i	0.544568	+	0.544568i
$796$	−206762.			−0.326320
$797$			940096.i			1.47998i	0.672618	+	0.739989i	$0.265170\pi$
$797$			940096.i			1.47998i	−0.672618	+	0.739989i	$0.734830\pi$
$798$	494039.	+	494039.i	0.775811	+	0.775811i
$799$	16947.7	+	16947.7i	0.0265471	+	0.0265471i
$800$	152993.	−	152993.i	0.239052	−	0.239052i
$801$	162869.	−	162869.i	0.253848	−	0.253848i
$802$	−1.33066e6			−2.06880
$803$			98806.5i			0.153234i
$804$	−135697.	+	135697.i	−0.209922	+	0.209922i
$805$		−	386176.i		−	0.595928i
$806$	−1.44453e6	−	1.47246e6i	−2.22359	−	2.26660i
$807$	−29347.6			−0.0450635
$808$	805159.	+	805159.i	1.23327	+	1.23327i
$809$	612686.			0.936140			0.468070	−	0.883691i	$-0.344950\pi$
$809$	612686.			0.936140			0.468070	+	0.883691i	$0.344950\pi$
$810$			89659.3i			0.136655i
$811$	431732.	+	431732.i	0.656406	+	0.656406i	0.954528	−	0.298121i	$-0.0963601\pi$
$811$	431732.	+	431732.i	0.656406	+	0.656406i	−0.298121	+	0.954528i	$0.596360\pi$
$812$	647809.	+	647809.i	0.982505	+	0.982505i
$813$	19342.1	−	19342.1i	0.0292633	−	0.0292633i
$814$	579585.	−	579585.i	0.874719	−	0.874719i
$815$	−436329.			−0.656900
$816$		−	96056.8i		−	0.144261i
$817$	−648999.	+	648999.i	−0.972300	+	0.972300i
$818$			93111.7i			0.139155i
$819$	−1867.40	+	194986.i	−0.00278401	+	0.290694i
$820$	822730.			1.22357
$821$	−193284.	−	193284.i	−0.286754	−	0.286754i	0.549041	−	0.835795i	$-0.314993\pi$
$821$	−193284.	−	193284.i	−0.286754	−	0.286754i	−0.835795	+	0.549041i	$0.814993\pi$
$822$	1.05060e6			1.55486
$823$		−	547967.i		−	0.809011i	−0.914536	−	0.404506i	$-0.867444\pi$
$823$		−	547967.i		−	0.809011i	0.914536	−	0.404506i	$-0.132556\pi$
$824$	721275.	+	721275.i	1.06230	+	1.06230i
$825$	85425.1	+	85425.1i	0.125510	+	0.125510i
$826$	58334.8	−	58334.8i	0.0855003	−	0.0855003i
$827$	−859953.	+	859953.i	−1.25737	+	1.25737i	−0.305029	+	0.952343i	$0.598666\pi$
$827$	−859953.	+	859953.i	−1.25737	+	1.25737i	−0.952343	+	0.305029i	$0.901334\pi$
$828$	−364864.			−0.532194
$829$			726172.i			1.05665i	0.849043	+	0.528324i	$0.177179\pi$
$829$			726172.i			1.05665i	−0.849043	+	0.528324i	$0.822821\pi$
$830$	−253460.	+	253460.i	−0.367919	+	0.367919i
$831$			164578.i			0.238326i
$832$	741933.	+	756282.i	1.07181	+	1.09254i
$833$	148129.			0.213477
$834$	113261.	+	113261.i	0.162835	+	0.162835i
$835$	−995999.			−1.42852
$836$			1.09887e6i			1.57230i
$837$	182972.	+	182972.i	0.261176	+	0.261176i
$838$	−83260.3	−	83260.3i	−0.118563	−	0.118563i
$839$	−507389.	+	507389.i	−0.720804	+	0.720804i	−0.968769	−	0.247965i	$-0.920238\pi$
$839$	−507389.	+	507389.i	−0.720804	+	0.720804i	0.247965	+	0.968769i	$0.420238\pi$
$840$	−227722.	+	227722.i	−0.322736	+	0.322736i
$841$	−112265.			−0.158728
$842$		−	1.15338e6i		−	1.62685i
$843$	56623.5	−	56623.5i	0.0796786	−	0.0796786i
$844$		−	1.27501e6i		−	1.78990i
$845$	382462.	−	368085.i	0.535642	−	0.515507i
$846$	−16617.6			−0.0232182
$847$	−233456.	−	233456.i	−0.325415	−	0.325415i
$848$	361557.			0.502789
$849$			161052.i			0.223434i
$850$	−337148.	−	337148.i	−0.466641	−	0.466641i
$851$	512107.	+	512107.i	0.707133	+	0.707133i
$852$	−440365.	+	440365.i	−0.606643	+	0.606643i
$853$	192677.	−	192677.i	0.264808	−	0.264808i	−0.562196	−	0.827004i	$-0.690043\pi$
$853$	192677.	−	192677.i	0.264808	−	0.264808i	0.827004	+	0.562196i	$0.190043\pi$
$854$	−1.97924e6			−2.71383
$855$			238592.i			0.326380i
$856$	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	$-0.0209990\pi$
$858$	−344963.	+	338419.i	−0.468596	+	0.459705i
$859$	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
$861$	−353687.			−0.477104
$862$		−	763533.i		−	1.02757i
$863$	1.02273e6	+	1.02273e6i	1.37321	+	1.37321i	0.855640	+	0.517571i	$0.173164\pi$
$863$	1.02273e6	+	1.02273e6i	1.37321	+	1.37321i	0.517571	+	0.855640i	$0.326836\pi$
$864$	−76771.6	−	76771.6i	−0.102843	−	0.102843i
$865$	22510.5	−	22510.5i	0.0300853	−	0.0300853i
$866$	−284499.	+	284499.i	−0.379355	+	0.379355i
$867$	−88907.1			−0.118276
$868$			2.19054e6i			2.90745i
$869$	237824.	−	237824.i	0.314931	−	0.314931i
$870$			492962.i			0.651291i
$871$	−224567.	−	2150.70i	−0.296013	−	0.00283494i
$872$	539294.			0.709239
$873$	150528.	+	150528.i	0.197509	+	0.197509i
$874$	−1.52990e6			−2.00282
$875$			718444.i			0.938376i
$876$	121332.	+	121332.i	0.158113	+	0.158113i
$877$	263404.	+	263404.i	0.342470	+	0.342470i	0.857295	−	0.514825i	$-0.172143\pi$
$877$	263404.	+	263404.i	0.342470	+	0.342470i	−0.514825	+	0.857295i	$0.672143\pi$
$878$	1.28702e6	−	1.28702e6i	1.66954	−	1.66954i
$879$	589949.	−	589949.i	0.763549	−	0.763549i
$880$	−110866.			−0.143163
$881$		−	580702.i		−	0.748171i	−0.927394	−	0.374086i	$-0.877957\pi$
$881$		−	580702.i		−	0.748171i	0.927394	−	0.374086i	$-0.122043\pi$
$882$	−72622.2	+	72622.2i	−0.0933538	+	0.0933538i
$883$		−	1.28367e6i		−	1.64638i	−0.567763	−	0.823192i	$-0.692191\pi$
$883$		−	1.28367e6i		−	1.64638i	0.567763	−	0.823192i	$-0.307809\pi$
$884$	864042.	−	847649.i	1.10568	−	1.08470i
$885$	28172.2			0.0359695
$886$	−40787.4	−	40787.4i	−0.0519587	−	0.0519587i
$887$	166700.			0.211879			0.105940	−	0.994373i	$-0.466215\pi$
$887$	166700.			0.211879			0.105940	+	0.994373i	$0.466215\pi$
$888$		−	603964.i		−	0.765923i
$889$	−663219.	−	663219.i	−0.839176	−	0.839176i
$890$	741894.	+	741894.i	0.936617	+	0.936617i
$891$	42866.1	−	42866.1i	0.0539956	−	0.0539956i
$892$	−727805.	+	727805.i	−0.914714	+	0.914714i
$893$	−44221.1			−0.0554532
$894$		−	19154.5i		−	0.0239660i
$895$	−35488.4	+	35488.4i	−0.0443037	+	0.0443037i
$896$		−	1.24369e6i		−	1.54916i
$897$	−299018.	−	304801.i	−0.371631	−	0.378818i
$898$	2.30820e6			2.86234
$899$	1.00601e6	+	1.00601e6i	1.24475	+	1.24475i
$900$	209800.			0.259012
$901$			1.29888e6i			1.60000i
$902$	−619796.	−	619796.i	−0.761791	−	0.761791i
$903$	303094.	+	303094.i	0.371708	+	0.371708i
$904$	189458.	−	189458.i	0.231833	−	0.231833i
$905$	411674.	−	411674.i	0.502639	−	0.502639i
$906$	370596.			0.451486
$907$		−	1.06525e6i		−	1.29490i	−0.762108	−	0.647450i	$-0.775836\pi$
$907$		−	1.06525e6i		−	1.29490i	0.762108	−	0.647450i	$-0.224164\pi$
$908$	567464.	−	567464.i	0.688282	−	0.688282i
$909$		−	393971.i		−	0.476800i
$910$	−888194.	−	8506.32i	−1.07257	−	0.0102721i
$911$	−794671.			−0.957526			−0.478763	−	0.877944i	$-0.658915\pi$
$911$	−794671.			−0.957526			−0.478763	+	0.877944i	$0.658915\pi$
$912$	125319.	+	125319.i	0.150670	+	0.150670i
$913$	242358.			0.290747
$914$			517031.i			0.618905i
$915$	−477927.	−	477927.i	−0.570846	−	0.570846i
$916$	−1.44823e6	−	1.44823e6i	−1.72603	−	1.72603i
$917$	50105.1	−	50105.1i	0.0595859	−	0.0595859i
$918$	−169180.	+	169180.i	−0.200754	+	0.200754i
$919$	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
$921$	−390867.	+	390867.i	−0.460797	+	0.460797i
$922$		−	294545.i		−	0.346489i
$923$	−728766.	−	6979.46i	−0.855431	−	0.00819254i
$924$	513193.			0.601086
$925$	−294466.	−	294466.i	−0.344153	−	0.344153i
$926$	1.26064e6			1.47018
$927$		−	352925.i		−	0.410699i
$928$	−422104.	−	422104.i	−0.490143	−	0.490143i
$929$	−746377.	−	746377.i	−0.864823	−	0.864823i	0.127071	−	0.991894i	$-0.459442\pi$
$929$	−746377.	−	746377.i	−0.864823	−	0.864823i	−0.991894	+	0.127071i	$0.959442\pi$
$930$	−833468.	+	833468.i	−0.963658	+	0.963658i
$931$	−193254.	+	193254.i	−0.222961	+	0.222961i
$932$	−1.27240e6			−1.46484
$933$			781635.i			0.897926i
$934$	499758.	−	499758.i	0.572884	−	0.572884i
$935$		−	398281.i		−	0.455582i
$936$	−3410.05	+	356063.i	−0.00389233	+	0.406420i
$937$	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
$939$	−657854.			−0.746103
$940$		−	48039.7i		−	0.0543681i
$941$	−906449.	−	906449.i	−1.02368	−	1.02368i	−0.999713	−	0.0239676i	$-0.992370\pi$
$941$	−906449.	−	906449.i	−1.02368	−	1.02368i	−0.0239676	−	0.999713i	$-0.507630\pi$
$942$	−622143.	−	622143.i	−0.701114	−	0.701114i
$943$	547636.	−	547636.i	0.615841	−	0.615841i
$944$	14797.3	−	14797.3i	0.0166050	−	0.0166050i
$945$	111426.			0.124774
$946$			1.06227e6i			1.18701i
$947$	290385.	−	290385.i	0.323798	−	0.323798i	−0.526424	−	0.850222i	$-0.676468\pi$
$947$	290385.	−	290385.i	0.323798	−	0.323798i	0.850222	+	0.526424i	$0.176468\pi$
$948$		−	584083.i		−	0.649918i
$949$	−1923.03	+	200794.i	−0.00213527	+	0.222956i
$950$	879709.			0.974747
$951$	220061.	+	220061.i	0.243323	+	0.243323i
$952$	−859388.			−0.948234
$953$			1.13841e6i			1.25347i	0.779234	+	0.626733i	$0.215608\pi$
$953$			1.13841e6i			1.25347i	−0.779234	+	0.626733i	$0.784392\pi$
$954$	−636793.	−	636793.i	−0.699683	−	0.699683i
$955$	693596.	+	693596.i	0.760501	+	0.760501i
$956$	1.52731e6	−	1.52731e6i	1.67114	−	1.67114i
$957$	235685.	−	235685.i	0.257341	−	0.257341i
$958$	648362.			0.706459
$959$		−	1.30566e6i		−	1.41968i
$960$	428083.	−	428083.i	0.464500	−	0.464500i
$961$			2.47827e6i			2.68350i
$962$	1.18911e6	−	1.16655e6i	1.28491	−	1.26053i
$963$	−384886.			−0.415030
$964$	652395.	+	652395.i	0.702032	+	0.702032i
$965$	36949.1			0.0396780
$966$			714491.i			0.765672i
$967$	19218.1	+	19218.1i	0.0205521	+	0.0205521i	0.717308	−	0.696756i	$-0.245374\pi$
$967$	19218.1	+	19218.1i	0.0205521	+	0.0205521i	−0.696756	+	0.717308i	$0.745374\pi$
$968$	−426312.	−	426312.i	−0.454964	−	0.454964i
$969$	−450203.	+	450203.i	−0.479470	+	0.479470i
$970$	−685678.	+	685678.i	−0.728747	+	0.728747i
$971$	416812.			0.442080			0.221040	−	0.975265i	$-0.429055\pi$
$971$	416812.			0.442080			0.221040	+	0.975265i	$0.429055\pi$
$972$		−	105277.i		−	0.111430i
$973$	140758.	−	140758.i	0.148678	−	0.148678i
$974$			3.12758e6i			3.29679i
$975$	171938.	+	175263.i	0.180868	+	0.184366i
$976$	−502056.			−0.527051
$977$	394416.	+	394416.i	0.413205	+	0.413205i	0.882853	−	0.469649i	$-0.155619\pi$
$977$	394416.	+	394416.i	0.413205	+	0.413205i	−0.469649	+	0.882853i	$0.655619\pi$
$978$	807283.			0.844011
$979$		−	709399.i		−	0.740159i
$980$	−209942.	−	209942.i	−0.218599	−	0.218599i
$981$	−131940.	−	131940.i	−0.137101	−	0.137101i
$982$	−956284.	+	956284.i	−0.991663	+	0.991663i
$983$	−159479.	+	159479.i	−0.165043	+	0.165043i	−0.784796	−	0.619754i	$-0.787233\pi$
$983$	−159479.	+	159479.i	−0.165043	+	0.165043i	0.619754	+	0.784796i	$0.287233\pi$
$984$	−645866.			−0.667041
$985$			267441.i			0.275649i
$986$	−930181.	+	930181.i	−0.956783	+	0.956783i
$987$			20652.0i			0.0211996i
$988$	−21386.9	+	2.23313e6i	−0.0219095	+	2.28770i
$989$	−938598.			−0.959593
$990$	195262.	+	195262.i	0.199227	+	0.199227i
$991$	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
$993$	−122597.	−	122597.i	−0.124332	−	0.124332i
$994$	862340.	+	862340.i	0.872782	+	0.872782i
$995$	−97768.8	+	97768.8i	−0.0987539	+	0.0987539i
$996$	297610.	−	297610.i	0.300005	−	0.300005i
$997$	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
$999$	−147762.	+	147762.i	−0.148058	+	0.148058i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.5.g.a.31.9	✓	20	13.5	odd	4	inner
39.5.g.a.34.9	yes	20	1.1	even	1	trivial
117.5.j.b.73.2		20	3.2	odd	2
117.5.j.b.109.2		20	39.5	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	39.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.67933 + 4.67933i) q^{2} -5.19615 q^{3} +27.7923i q^{4} +(13.1418 + 13.1418i) q^{5} +(-24.3145 - 24.3145i) q^{6} +(-30.2175 + 30.2175i) q^{7} +(-55.1800 + 55.1800i) q^{8} +27.0000 q^{9} +122.989i q^{10} +(58.8012 - 58.8012i) q^{11} -144.413i q^{12} +(120.640 - 118.351i) q^{13} -282.795 q^{14} +(-68.2867 - 68.2867i) q^{15} -71.7343 q^{16} -257.703i q^{17} +(126.342 + 126.342i) q^{18} +(336.208 + 336.208i) q^{19} +(-365.240 + 365.240i) q^{20} +(157.015 - 157.015i) q^{21} +550.300 q^{22} +486.231i q^{23} +(286.724 - 286.724i) q^{24} -279.587i q^{25} +(1118.32 + 10.7102i) q^{26} -140.296 q^{27} +(-839.813 - 839.813i) q^{28} -771.373 q^{29} -639.072i q^{30} +(-1304.18 - 1304.18i) q^{31} +(547.211 + 547.211i) q^{32} +(-305.540 + 305.540i) q^{33} +(1205.88 - 1205.88i) q^{34} -794.223 q^{35} +750.392i q^{36} +(1053.22 - 1053.22i) q^{37} +3146.45i q^{38} +(-626.864 + 614.971i) q^{39} -1450.33 q^{40} +(-1126.29 - 1126.29i) q^{41} +1469.45 q^{42} +1930.35i q^{43} +(1634.22 + 1634.22i) q^{44} +(354.828 + 354.828i) q^{45} +(-2275.24 + 2275.24i) q^{46} +(-65.7645 + 65.7645i) q^{47} +372.742 q^{48} +574.806i q^{49} +(1308.28 - 1308.28i) q^{50} +1339.06i q^{51} +(3289.25 + 3352.86i) q^{52} -5040.23 q^{53} +(-656.492 - 656.492i) q^{54} +1545.50 q^{55} -3334.80i q^{56} +(-1746.99 - 1746.99i) q^{57} +(-3609.51 - 3609.51i) q^{58} +(-206.279 + 206.279i) q^{59} +(1897.84 - 1897.84i) q^{60} +6998.83 q^{61} -12205.4i q^{62} +(-815.872 + 815.872i) q^{63} +6268.91i q^{64} +(3140.77 + 30.0794i) q^{65} -2859.44 q^{66} +(-939.648 - 939.648i) q^{67} +7162.15 q^{68} -2526.53i q^{69} +(-3716.43 - 3716.43i) q^{70} +(-3049.34 - 3049.34i) q^{71} +(-1489.86 + 1489.86i) q^{72} +(-840.175 + 840.175i) q^{73} +9856.69 q^{74} +1452.78i q^{75} +(-9343.97 + 9343.97i) q^{76} +3553.65i q^{77} +(-5810.95 - 55.6521i) q^{78} +4044.54 q^{79} +(-942.716 - 942.716i) q^{80} +729.000 q^{81} -10540.5i q^{82} +(2060.82 + 2060.82i) q^{83} +(4363.80 + 4363.80i) q^{84} +(3386.67 - 3386.67i) q^{85} +(-9032.76 + 9032.76i) q^{86} +4008.17 q^{87} +6489.30i q^{88} +(6032.18 - 6032.18i) q^{89} +3320.71i q^{90} +(-69.1630 + 7221.71i) q^{91} -13513.5 q^{92} +(6776.74 + 6776.74i) q^{93} -615.468 q^{94} +8836.73i q^{95} +(-2843.39 - 2843.39i) q^{96} +(5575.10 + 5575.10i) q^{97} +(-2689.71 + 2689.71i) q^{98} +(1587.63 - 1587.63i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{5} - 24 q^{7} + 540 q^{9} + 372 q^{11} - 224 q^{13} + 480 q^{14} - 252 q^{15} - 2328 q^{16} - 840 q^{19} + 228 q^{20} + 936 q^{21} + 3536 q^{22} - 1404 q^{24} - 828 q^{26} - 1984 q^{28} - 5064 q^{29}+ \cdots + 10044 q^{99}+O(q^{100}) \) 20 * q + 24 * q^5 - 24 * q^7 + 540 * q^9 + 372 * q^11 - 224 * q^13 + 480 * q^14 - 252 * q^15 - 2328 * q^16 - 840 * q^19 + 228 * q^20 + 936 * q^21 + 3536 * q^22 - 1404 * q^24 - 828 * q^26 - 1984 * q^28 - 5064 * q^29 + 1712 * q^31 - 7260 * q^32 - 540 * q^33 + 8040 * q^34 + 5976 * q^35 - 868 * q^37 - 2952 * q^39 + 6336 * q^40 - 6000 * q^41 + 648 * q^42 + 20868 * q^44 + 648 * q^45 - 1992 * q^46 + 1692 * q^47 + 2592 * q^48 + 8952 * q^50 - 12416 * q^52 - 18816 * q^53 - 3280 * q^55 - 9360 * q^57 + 1256 * q^58 - 6588 * q^59 + 9036 * q^60 - 5512 * q^61 - 648 * q^63 + 33048 * q^65 + 13464 * q^66 - 4704 * q^67 - 28296 * q^68 - 31096 * q^70 + 9756 * q^71 + 13692 * q^73 - 28296 * q^74 - 17072 * q^76 - 23868 * q^78 - 5056 * q^79 + 42228 * q^80 + 14580 * q^81 + 24708 * q^83 + 26496 * q^84 - 4752 * q^85 - 77424 * q^86 + 5256 * q^87 + 36000 * q^89 + 19104 * q^91 + 12912 * q^92 - 18432 * q^93 + 112832 * q^94 - 52344 * q^96 + 50012 * q^97 + 11544 * q^98 + 10044 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more