LMFDB - Embedded newform 21.6.c.a.20.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 484x^{10} + 194194x^{8} - 39867800x^{6} + 5398720873x^{4} - 310089434788x^{2} + 9371104623076 $ x^12 - 484x^10 + 194194x^8 - 39867800x^6 + 5398720873x^4 - 310089434788*x^2 + 9371104623076
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.10
Root			$12.2117 - 5.57294i$ of defining polynomial
Character	$\chi$	$=$	21.20
Dual form			21.6.c.a.20.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.57294i q^{2} +(13.5283 - 7.74498i) q^{3} +0.942331 q^{4} +46.2136 q^{5} +(43.1623 + 75.3925i) q^{6} +(-120.146 + 48.7024i) q^{7} +183.586i q^{8} +(123.031 - 209.553i) q^{9} +O(q^{10})$	\(q+5.57294i q^{2} +(13.5283 - 7.74498i) q^{3} +0.942331 q^{4} +46.2136 q^{5} +(43.1623 + 75.3925i) q^{6} +(-120.146 + 48.7024i) q^{7} +183.586i q^{8} +(123.031 - 209.553i) q^{9} +257.545i q^{10} +285.677i q^{11} +(12.7482 - 7.29833i) q^{12} -1141.52i q^{13} +(-271.416 - 669.567i) q^{14} +(625.192 - 357.923i) q^{15} -992.957 q^{16} -967.641 q^{17} +(1167.83 + 685.643i) q^{18} +112.619i q^{19} +43.5485 q^{20} +(-1248.17 + 1589.39i) q^{21} -1592.06 q^{22} -1262.08i q^{23} +(1421.87 + 2483.61i) q^{24} -989.307 q^{25} +6361.65 q^{26} +(41.4161 - 3787.77i) q^{27} +(-113.217 + 45.8938i) q^{28} +598.083i q^{29} +(1994.68 + 3484.16i) q^{30} +2465.55i q^{31} +341.048i q^{32} +(2212.56 + 3864.73i) q^{33} -5392.61i q^{34} +(-5552.38 + 2250.71i) q^{35} +(115.936 - 197.468i) q^{36} +4150.91 q^{37} -627.618 q^{38} +(-8841.08 - 15442.9i) q^{39} +8484.15i q^{40} -16491.1 q^{41} +(-8857.58 - 6956.01i) q^{42} +5104.06 q^{43} +269.202i q^{44} +(5685.69 - 9684.19i) q^{45} +7033.48 q^{46} +17722.5 q^{47} +(-13433.0 + 7690.43i) q^{48} +(12063.2 - 11702.8i) q^{49} -5513.35i q^{50} +(-13090.6 + 7494.36i) q^{51} -1075.69i q^{52} +30085.8i q^{53} +(21109.0 + 230.810i) q^{54} +13202.1i q^{55} +(-8941.06 - 22057.1i) q^{56} +(872.230 + 1523.54i) q^{57} -3333.08 q^{58} +39985.0 q^{59} +(589.138 - 337.282i) q^{60} +36958.1i q^{61} -13740.4 q^{62} +(-4575.92 + 31168.9i) q^{63} -33675.3 q^{64} -52753.9i q^{65} +(-21537.9 + 12330.5i) q^{66} +34620.1 q^{67} -911.838 q^{68} +(-9774.75 - 17073.8i) q^{69} +(-12543.1 - 30943.1i) q^{70} +43606.5i q^{71} +(38470.9 + 22586.7i) q^{72} -31725.9i q^{73} +23132.8i q^{74} +(-13383.7 + 7662.16i) q^{75} +106.124i q^{76} +(-13913.1 - 34322.9i) q^{77} +(86062.4 - 49270.8i) q^{78} -39763.9 q^{79} -45888.1 q^{80} +(-28775.9 - 51562.9i) q^{81} -91904.0i q^{82} +22963.5 q^{83} +(-1176.19 + 1497.73i) q^{84} -44718.1 q^{85} +28444.6i q^{86} +(4632.14 + 8091.05i) q^{87} -52446.1 q^{88} -63601.9 q^{89} +(53969.4 + 31686.0i) q^{90} +(55595.0 + 137150. i) q^{91} -1189.29i q^{92} +(19095.6 + 33354.7i) q^{93} +98766.6i q^{94} +5204.52i q^{95} +(2641.41 + 4613.81i) q^{96} -112394. i q^{97} +(65219.0 + 67227.2i) q^{98} +(59864.4 + 35147.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9}+O(q^{10}) $ 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9	$ 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9} + 1392 q^{15} + 4868 q^{16} - 3804 q^{18} + 4116 q^{21} - 8752 q^{22} + 7812 q^{25} - 8204 q^{28} - 27876 q^{30} + 54864 q^{36} + 27464 q^{37} - 16080 q^{39} - 3444 q^{42} - 73840 q^{43} + 59144 q^{46} + 6972 q^{49} + 23760 q^{51} + 103968 q^{57} - 71512 q^{58} - 152676 q^{60} - 120624 q^{63} - 198788 q^{64} + 79344 q^{67} + 368760 q^{70} + 226644 q^{72} + 394644 q^{78} - 247104 q^{79} - 248868 q^{81} - 608076 q^{84} - 320112 q^{85} + 595456 q^{88} + 310128 q^{91} + 397272 q^{93} + 696576 q^{99}+O(q^{100}) $ 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9 + 1392 * q^15 + 4868 * q^16 - 3804 * q^18 + 4116 * q^21 - 8752 * q^22 + 7812 * q^25 - 8204 * q^28 - 27876 * q^30 + 54864 * q^36 + 27464 * q^37 - 16080 * q^39 - 3444 * q^42 - 73840 * q^43 + 59144 * q^46 + 6972 * q^49 + 23760 * q^51 + 103968 * q^57 - 71512 * q^58 - 152676 * q^60 - 120624 * q^63 - 198788 * q^64 + 79344 * q^67 + 368760 * q^70 + 226644 * q^72 + 394644 * q^78 - 247104 * q^79 - 248868 * q^81 - 608076 * q^84 - 320112 * q^85 + 595456 * q^88 + 310128 * q^91 + 397272 * q^93 + 696576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			5.57294i			0.985166i	0.870265	+	0.492583i	$0.163947\pi$
$2$			5.57294i			0.985166i	−0.870265	+	0.492583i	$0.836053\pi$
$3$	13.5283	−	7.74498i	0.867842	−	0.496840i
$3$	13.5283	−	7.74498i	0.867842	−	0.496840i
$4$	0.942331			0.0294478
$5$	46.2136			0.826693			0.413347	−	0.910574i	$-0.364360\pi$
$5$	46.2136			0.826693			0.413347	+	0.910574i	$0.364360\pi$
$6$	43.1623	+	75.3925i	0.489470	+	0.854968i
$7$	−120.146	+	48.7024i	−0.926754	+	0.375669i
$7$	−120.146	+	48.7024i	−0.926754	+	0.375669i
$8$			183.586i			1.01418i
$9$	123.031	−	209.553i	0.506299	−	0.862358i
$10$			257.545i			0.814430i
$11$			285.677i			0.711858i	0.934513	+	0.355929i	$0.115835\pi$
$11$			285.677i			0.711858i	−0.934513	+	0.355929i	$0.884165\pi$
$12$	12.7482	−	7.29833i	0.0255561	−	0.0146309i
$13$		−	1141.52i		−	1.87338i	−0.350154	−	0.936692i	$-0.613871\pi$
$13$		−	1141.52i		−	1.87338i	0.350154	−	0.936692i	$-0.386129\pi$
$14$	−271.416	−	669.567i	−0.370096	−	0.913006i
$15$	625.192	−	357.923i	0.717439	−	0.410735i
$16$	−992.957			−0.969685
$17$	−967.641			−0.812067			−0.406034	−	0.913858i	$-0.633088\pi$
$17$	−967.641			−0.812067			−0.406034	+	0.913858i	$0.633088\pi$
$18$	1167.83	+	685.643i	0.849566	+	0.498789i
$19$			112.619i			0.0715693i	0.999360	+	0.0357847i	$0.0113930\pi$
$19$			112.619i			0.0715693i	−0.999360	+	0.0357847i	$0.988607\pi$
$20$	43.5485			0.0243443
$21$	−1248.17	+	1589.39i	−0.617628	+	0.786470i
$22$	−1592.06			−0.701298
$23$		−	1262.08i		−	0.497469i	−0.968572	−	0.248735i	$-0.919985\pi$
$23$		−	1262.08i		−	0.497469i	0.968572	−	0.248735i	$-0.0800147\pi$
$24$	1421.87	+	2483.61i	0.503884	+	0.880145i
$25$	−989.307			−0.316578
$26$	6361.65			1.84559
$27$	41.4161	−	3787.77i	0.0109335	−	0.999940i
$28$	−113.217	+	45.8938i	−0.0272909	+	0.0110626i
$29$			598.083i			0.132058i	0.997818	+	0.0660292i	$0.0210331\pi$
$29$			598.083i			0.132058i	−0.997818	+	0.0660292i	$0.978967\pi$
$30$	1994.68	+	3484.16i	0.404642	+	0.706797i
$31$			2465.55i			0.460797i	0.973096	+	0.230398i	$0.0740029\pi$
$31$			2465.55i			0.460797i	−0.973096	+	0.230398i	$0.925997\pi$
$32$			341.048i			0.0588764i
$33$	2212.56	+	3864.73i	0.353680	+	0.617780i
$34$		−	5392.61i		−	0.800021i
$35$	−5552.38	+	2250.71i	−0.766141	+	0.310563i
$36$	115.936	−	197.468i	0.0149094	−	0.0253946i
$37$	4150.91			0.498471			0.249235	−	0.968443i	$-0.419821\pi$
$37$	4150.91			0.498471			0.249235	+	0.968443i	$0.419821\pi$
$38$	−627.618			−0.0705077
$39$	−8841.08	−	15442.9i	−0.930773	−	1.62580i
$40$			8484.15i			0.838413i
$41$	−16491.1			−1.53211			−0.766056	−	0.642774i	$-0.777784\pi$
$41$	−16491.1			−1.53211			−0.766056	+	0.642774i	$0.777784\pi$
$42$	−8857.58	−	6956.01i	−0.774804	−	0.608467i
$43$	5104.06			0.420963			0.210482	−	0.977598i	$-0.432497\pi$
$43$	5104.06			0.420963			0.210482	+	0.977598i	$0.432497\pi$
$44$			269.202i			0.0209627i
$45$	5685.69	−	9684.19i	0.418554	−	0.712905i
$46$	7033.48			0.490090
$47$	17722.5			1.17026			0.585128	−	0.810941i	$-0.301044\pi$
$47$	17722.5			1.17026			0.585128	+	0.810941i	$0.301044\pi$
$48$	−13433.0	+	7690.43i	−0.841533	+	0.481779i
$49$	12063.2	−	11702.8i	0.717746	−	0.696305i
$50$		−	5513.35i		−	0.311882i
$51$	−13090.6	+	7494.36i	−0.704746	+	0.403468i
$52$		−	1075.69i		−	0.0551671i
$53$			30085.8i			1.47120i	0.677415	+	0.735601i	$0.263100\pi$
$53$			30085.8i			1.47120i	−0.677415	+	0.735601i	$0.736900\pi$
$54$	21109.0	+	230.810i	0.985107	+	0.0107713i
$55$			13202.1i			0.588488i
$56$	−8941.06	−	22057.1i	−0.380995	−	0.939893i
$57$	872.230	+	1523.54i	0.0355585	+	0.0621109i
$58$	−3333.08			−0.130100
$59$	39985.0			1.49543			0.747717	−	0.664017i	$-0.231150\pi$
$59$	39985.0			1.49543			0.747717	+	0.664017i	$0.231150\pi$
$60$	589.138	−	337.282i	0.0211270	−	0.0120952i
$61$			36958.1i			1.27170i	0.771812	+	0.635851i	$0.219351\pi$
$61$			36958.1i			1.27170i	−0.771812	+	0.635851i	$0.780649\pi$
$62$	−13740.4			−0.453961
$63$	−4575.92	+	31168.9i	−0.145254	+	0.989394i
$64$	−33675.3			−1.02769
$65$		−	52753.9i		−	1.54871i
$66$	−21537.9	+	12330.5i	−0.608616	+	0.348433i
$67$	34620.1			0.942196			0.471098	−	0.882081i	$-0.343858\pi$
$67$	34620.1			0.942196			0.471098	+	0.882081i	$0.343858\pi$
$68$	−911.838			−0.0239136
$69$	−9774.75	−	17073.8i	−0.247163	−	0.431725i
$70$	−12543.1	−	30943.1i	−0.305956	−	0.754776i
$71$			43606.5i			1.02661i	0.858206	+	0.513305i	$0.171579\pi$
$71$			43606.5i			1.02661i	−0.858206	+	0.513305i	$0.828421\pi$
$72$	38470.9	+	22586.7i	0.874584	+	0.513477i
$73$		−	31725.9i		−	0.696798i	−0.937346	−	0.348399i	$-0.886725\pi$
$73$		−	31725.9i		−	0.696798i	0.937346	−	0.348399i	$-0.113275\pi$
$74$			23132.8i			0.491076i
$75$	−13383.7	+	7662.16i	−0.274740	+	0.157289i
$76$			106.124i			0.00210756i
$77$	−13913.1	−	34322.9i	−0.267423	−	0.659717i
$78$	86062.4	−	49270.8i	1.60168	−	0.916966i
$79$	−39763.9			−0.716839			−0.358420	−	0.933561i	$-0.616684\pi$
$79$	−39763.9			−0.716839			−0.358420	+	0.933561i	$0.616684\pi$
$80$	−45888.1			−0.801632
$81$	−28775.9	−	51562.9i	−0.487322	−	0.873222i
$82$		−	91904.0i		−	1.50938i
$83$	22963.5			0.365884			0.182942	−	0.983124i	$-0.441438\pi$
$83$	22963.5			0.365884			0.182942	+	0.983124i	$0.441438\pi$
$84$	−1176.19	+	1497.73i	−0.0181878	+	0.0231599i
$85$	−44718.1			−0.671331
$86$			28444.6i			0.414719i
$87$	4632.14	+	8091.05i	0.0656120	+	0.114606i
$88$	−52446.1			−0.721950
$89$	−63601.9			−0.851128			−0.425564	−	0.904928i	$-0.639924\pi$
$89$	−63601.9			−0.851128			−0.425564	+	0.904928i	$0.639924\pi$
$90$	53969.4	+	31686.0i	0.702330	+	0.412345i
$91$	55595.0	+	137150.i	0.703772	+	1.73617i
$92$		−	1189.29i		−	0.0146494i
$93$	19095.6	+	33354.7i	0.228942	+	0.399899i
$94$			98766.6i			1.15290i
$95$			5204.52i			0.0591659i
$96$	2641.41	+	4613.81i	0.0292521	+	0.0510954i
$97$		−	112394.i		−	1.21286i	−0.795135	−	0.606432i	$-0.792600\pi$
$97$		−	112394.i		−	1.21286i	0.795135	−	0.606432i	$-0.207400\pi$
$98$	65219.0	+	67227.2i	0.685976	+	0.707099i
$99$	59864.4	+	35147.0i	0.613876	+	0.360413i
$100$	−932.255			−0.00932255
$101$	−18851.6			−0.183884			−0.0919421	−	0.995764i	$-0.529307\pi$
$101$	−18851.6			−0.183884			−0.0919421	+	0.995764i	$0.529307\pi$
$102$	−41765.6	−	72952.9i	−0.397483	−	0.694292i
$103$		−	34021.1i		−	0.315976i	−0.987441	−	0.157988i	$-0.949499\pi$
$103$		−	34021.1i		−	0.315976i	0.987441	−	0.157988i	$-0.0505008\pi$
$104$	209568.			1.89994
$105$	−57682.6	+	73451.4i	−0.510589	+	0.650169i
$106$	−167667.			−1.44938
$107$			24776.5i			0.209209i	0.994514	+	0.104605i	$0.0333577\pi$
$107$			24776.5i			0.209209i	−0.994514	+	0.104605i	$0.966642\pi$
$108$	39.0277	−	3569.33i	0.000321969	−	0.0294461i
$109$	152937.			1.23295			0.616476	−	0.787374i	$-0.288560\pi$
$109$	152937.			1.23295			0.616476	+	0.787374i	$0.288560\pi$
$110$	−73574.7			−0.579758
$111$	56154.9	−	32148.7i	0.432594	−	0.247660i
$112$	119300.	−	48359.4i	0.898659	−	0.364281i
$113$		−	165698.i		−	1.22074i	−0.792118	−	0.610368i	$-0.791022\pi$
$113$		−	165698.i		−	1.22074i	0.792118	−	0.610368i	$-0.208978\pi$
$114$	−8490.62	+	4860.89i	−0.0611895	+	0.0350311i
$115$		−	58325.1i		−	0.411254i
$116$			563.592i			0.00388884i
$117$	−239210.	−	140443.i	−1.61553	−	0.948493i
$118$			222834.i			1.47325i
$119$	116258.	−	47126.5i	0.752587	−	0.305068i
$120$	65709.5	+	114776.i	0.416558	+	0.727610i
$121$	79439.8			0.493259
$122$	−205965.			−1.25284
$123$	−223097.	+	127723.i	−1.32963	+	0.761215i
$124$			2323.36i			0.0135695i
$125$	−190137.			−1.08841
$126$	−173702.	−	25501.3i	−0.974718	−	0.143099i
$127$	−29830.5			−0.164116			−0.0820582	−	0.996628i	$-0.526149\pi$
$127$	−29830.5			−0.164116			−0.0820582	+	0.996628i	$0.526149\pi$
$128$		−	176757.i		−	0.953567i
$129$	69049.3	−	39530.8i	0.365330	−	0.209152i
$130$	293994.			1.52574
$131$	−75634.1			−0.385070			−0.192535	−	0.981290i	$-0.561671\pi$
$131$	−75634.1			−0.385070			−0.192535	+	0.981290i	$0.561671\pi$
$132$	2084.96	+	3641.85i	0.0104151	+	0.0181923i
$133$	−5484.81	−	13530.7i	−0.0268864	−	0.0663272i
$134$			192936.i			0.928219i
$135$	1913.99	−	175046.i	0.00903867	−	0.826644i
$136$		−	177645.i		−	0.823580i
$137$		−	29779.1i		−	0.135554i	−0.997701	−	0.0677768i	$-0.978409\pi$
$137$		−	29779.1i		−	0.135554i	0.997701	−	0.0677768i	$-0.0215906\pi$
$138$	95151.1	−	54474.1i	0.425320	−	0.243496i
$139$			119702.i			0.525492i	0.964865	+	0.262746i	$0.0846281\pi$
$139$			119702.i			0.525492i	−0.964865	+	0.262746i	$0.915372\pi$
$140$	−5232.18	+	2120.92i	−0.0225612	+	0.00914541i
$141$	239756.	−	137261.i	1.01560	−	0.581431i
$142$	−243017.			−1.01138
$143$	326107.			1.33358
$144$	−122164.	+	208077.i	−0.490951	+	0.836215i
$145$			27639.5i			0.109172i
$146$	176807.			0.686461
$147$	72556.2	−	251748.i	0.276937	−	0.960888i
$148$	3911.54			0.0146789
$149$			478865.i			1.76705i	0.468388	+	0.883523i	$0.344835\pi$
$149$			478865.i			1.76705i	−0.468388	+	0.883523i	$0.655165\pi$
$150$	−42700.8	−	74586.4i	−0.154956	−	0.270664i
$151$	−51677.8			−0.184443			−0.0922214	−	0.995739i	$-0.529397\pi$
$151$	−51677.8			−0.184443			−0.0922214	+	0.995739i	$0.529397\pi$
$152$	−20675.2			−0.0725840
$153$	−119050.	+	202772.i	−0.411149	+	0.700293i
$154$	191280.	−	77537.1i	0.649931	−	0.263456i
$155$			113942.i			0.380937i
$156$	−8331.22	−	14552.3i	−0.0274093	−	0.0478764i
$157$			215791.i			0.698690i	0.936994	+	0.349345i	$0.113596\pi$
$157$			215791.i			0.698690i	−0.936994	+	0.349345i	$0.886404\pi$
$158$		−	221602.i		−	0.706206i
$159$	233014.	+	407011.i	0.730953	+	1.27677i
$160$			15761.1i			0.0486727i
$161$	61466.2	+	151634.i	0.186884	+	0.461031i
$162$	287357.	−	160366.i	0.860269	−	0.480093i
$163$	−43718.7			−0.128884			−0.0644419	−	0.997921i	$-0.520527\pi$
$163$	−43718.7			−0.128884			−0.0644419	+	0.997921i	$0.520527\pi$
$164$	−15540.1			−0.0451174
$165$	102250.	+	178603.i	0.292385	+	0.510714i
$166$			127974.i			0.360456i
$167$	−467393.			−1.29685			−0.648427	−	0.761277i	$-0.724573\pi$
$167$	−467393.			−1.29685			−0.648427	+	0.761277i	$0.724573\pi$
$168$	−291789.	−	229147.i	−0.797620	−	0.626385i
$169$	−931785.			−2.50957
$170$		−	249212.i		−	0.661372i
$171$	23599.6	+	13855.6i	0.0617184	+	0.0362355i
$172$	4809.71			0.0123965
$173$	261040.			0.663120			0.331560	−	0.943434i	$-0.392425\pi$
$173$	261040.			0.663120			0.331560	+	0.943434i	$0.392425\pi$
$174$	−45091.0	+	25814.6i	−0.112906	+	0.0646387i
$175$	118861.	−	48181.6i	0.293390	−	0.118929i
$176$		−	283665.i		−	0.690278i
$177$	540930.	−	309683.i	1.29780	−	0.742992i
$178$		−	354450.i		−	0.838503i
$179$		−	565935.i		−	1.32018i	−0.751186	−	0.660091i	$-0.770518\pi$
$179$		−	565935.i		−	1.32018i	0.751186	−	0.660091i	$-0.229482\pi$
$180$	5357.80	−	9125.71i	0.0123255	−	0.0209935i
$181$		−	615493.i		−	1.39645i	−0.715877	−	0.698227i	$-0.753973\pi$
$181$		−	615493.i		−	1.39645i	0.715877	−	0.698227i	$-0.246027\pi$
$182$	−764327.	+	309828.i	−1.71041	+	0.693333i
$183$	286240.	+	499981.i	0.631833	+	1.10364i
$184$	231699.			0.504522
$185$	191829.			0.412082
$186$	−185884.	+	106419.i	−0.393967	+	0.225546i
$187$		−	276433.i		−	0.578076i
$188$	16700.5			0.0344615
$189$	179497.	+	457103.i	0.365514	+	0.930806i
$190$	−29004.5			−0.0582882
$191$			588646.i			1.16754i	0.811920	+	0.583769i	$0.198422\pi$
$191$			588646.i			1.16754i	−0.811920	+	0.583769i	$0.801578\pi$
$192$	−455570.	+	260814.i	−0.891871	+	0.510597i
$193$	102554.			0.198179			0.0990896	−	0.995079i	$-0.468407\pi$
$193$	102554.			0.198179			0.0990896	+	0.995079i	$0.468407\pi$
$194$	626363.			1.19487
$195$	−408578.	−	713672.i	−0.769464	−	1.34404i
$196$	11367.5	−	11027.9i	0.0211361	−	0.0205047i
$197$		−	662538.i		−	1.21631i	−0.793818	−	0.608156i	$-0.791910\pi$
$197$		−	662538.i		−	1.21631i	0.793818	−	0.608156i	$-0.208090\pi$
$198$	−195872.	+	333621.i	−0.355067	+	0.604770i
$199$			697611.i			1.24877i	0.781119	+	0.624383i	$0.214649\pi$
$199$			697611.i			1.24877i	−0.781119	+	0.624383i	$0.785351\pi$
$200$		−	181623.i		−	0.321066i
$201$	468352.	−	268132.i	0.817677	−	0.468121i
$202$		−	105059.i		−	0.181157i
$203$	−29128.1	−	71857.3i	−0.0496103	−	0.122386i
$204$	−12335.6	+	7062.17i	−0.0207533	+	0.0118813i
$205$	−762113.			−1.26659
$206$	189597.			0.311289
$207$	−264472.	−	155274.i	−0.428996	−	0.251868i
$208$			1.13349e6i			1.81659i
$209$	−32172.6			−0.0509472
$210$	−409340.	−	321462.i	−0.640525	−	0.503015i
$211$	743288.			1.14935			0.574673	−	0.818383i	$-0.305129\pi$
$211$	743288.			1.14935			0.574673	+	0.818383i	$0.305129\pi$
$212$			28350.8i			0.0433237i
$213$	337732.	+	589923.i	0.510062	+	0.890936i
$214$	−138078.			−0.206106
$215$	235877.			0.348008
$216$	695380.	+	7603.41i	1.01412	+	0.0110885i
$217$	−120078.	−	296226.i	−0.173107	−	0.427045i
$218$			852309.i			1.21466i
$219$	−245716.	−	429198.i	−0.346197	−	0.604710i
$220$			12440.8i			0.0173297i
$221$			1.10459e6i			1.52131i
$222$	179163.	+	312948.i	0.243987	+	0.426177i
$223$		−	337580.i		−	0.454584i	−0.973827	−	0.227292i	$-0.927013\pi$
$223$		−	337580.i		−	0.454584i	0.973827	−	0.227292i	$-0.0729872\pi$
$224$	−16609.9	−	40975.6i	−0.0221180	−	0.0545639i
$225$	−121715.	+	207312.i	−0.160283	+	0.273004i
$226$	923426.			1.20263
$227$	−714316.			−0.920081			−0.460040	−	0.887898i	$-0.652165\pi$
$227$	−714316.			−0.920081			−0.460040	+	0.887898i	$0.652165\pi$
$228$	821.930	+	1435.68i	0.00104712	+	0.00182903i
$229$		−	195949.i		−	0.246920i	−0.992350	−	0.123460i	$-0.960601\pi$
$229$		−	195949.i		−	0.246920i	0.992350	−	0.123460i	$-0.0393990\pi$
$230$	325042.			0.405154
$231$	−454052.	−	356575.i	−0.559855	−	0.439663i
$232$	−109799.			−0.133931
$233$		−	1.00472e6i		−	1.21243i	−0.795302	−	0.606214i	$-0.792688\pi$
$233$		−	1.00472e6i		−	1.21243i	0.795302	−	0.606214i	$-0.207312\pi$
$234$	782678.	−	1.33310e6i	0.934423	−	1.59156i
$235$	819021.			0.967443
$236$	37679.1			0.0440373
$237$	−537939.	+	307971.i	−0.622103	+	0.356155i
$238$	262633.	+	647900.i	0.300543	+	0.741423i
$239$			181636.i			0.205687i	0.994698	+	0.102843i	$0.0327940\pi$
$239$			181636.i			0.205687i	−0.994698	+	0.102843i	$0.967206\pi$
$240$	−620789.	+	355402.i	−0.695690	+	0.398283i
$241$			194274.i			0.215463i	0.994180	+	0.107731i	$0.0343587\pi$
$241$			194274.i			0.215463i	−0.994180	+	0.107731i	$0.965641\pi$
$242$			442713.i			0.485942i
$243$	−788643.	−	474691.i	−0.856771	−	0.515698i
$244$			34826.8i			0.0374489i
$245$	557481.	−	540828.i	0.593355	−	0.575631i
$246$	−711794.	−	1.24331e6i	−0.749923	−	1.30991i
$247$	128557.			0.134077
$248$	−452639.			−0.467329
$249$	310658.	−	177852.i	0.317529	−	0.181786i
$250$		−	1.05962e6i		−	1.07226i
$251$	−1.15023e6			−1.15239			−0.576195	−	0.817313i	$-0.695463\pi$
$251$	−1.15023e6			−1.15239			−0.576195	+	0.817313i	$0.695463\pi$
$252$	−4312.03	+	29371.4i	−0.00427741	+	0.0291355i
$253$	360546.			0.354127
$254$		−	166244.i		−	0.161682i
$255$	−604961.	+	346341.i	−0.582609	+	0.333544i
$256$	−92553.8			−0.0882662
$257$	−753698.			−0.711810			−0.355905	−	0.934522i	$-0.615827\pi$
$257$	−753698.			−0.711810			−0.355905	+	0.934522i	$0.615827\pi$
$258$	220303.	+	384808.i	0.206049	+	0.359910i
$259$	−498716.	+	202160.i	−0.461960	+	0.187260i
$260$		−	49711.6i		−	0.0456063i
$261$	125330.	+	73582.6i	0.113882	+	0.0668611i
$262$		−	421504.i		−	0.379358i
$263$		−	636200.i		−	0.567158i	−0.958949	−	0.283579i	$-0.908478\pi$
$263$		−	636200.i		−	0.567158i	0.958949	−	0.283579i	$-0.0915219\pi$
$264$	−709508.	+	406194.i	−0.626538	+	0.358694i
$265$			1.39037e6i			1.21623i
$266$	75405.8	−	30566.5i	0.0653433	−	0.0264876i
$267$	−860426.	+	492595.i	−0.738645	+	0.422875i
$268$	32623.6			0.0277456
$269$	906619.			0.763914			0.381957	−	0.924180i	$-0.375250\pi$
$269$	906619.			0.763914			0.381957	+	0.924180i	$0.375250\pi$
$270$	975522.	+	10666.5i	0.814381	+	0.00890459i
$271$		−	64809.8i		−	0.0536065i	−0.999641	−	0.0268032i	$-0.991467\pi$
$271$		−	64809.8i		−	0.0536065i	0.999641	−	0.0268032i	$-0.00853276\pi$
$272$	960826.			0.787449
$273$	1.81433e6	+	1.42482e6i	1.47336	+	1.15706i
$274$	165957.			0.133543
$275$		−	282622.i		−	0.225359i
$276$	−9211.05	−	16089.1i	−0.00727841	−	0.0127134i
$277$	−1.20323e6			−0.942215			−0.471108	−	0.882076i	$-0.656146\pi$
$277$	−1.20323e6			−0.942215			−0.471108	+	0.882076i	$0.656146\pi$
$278$	−667095.			−0.517697
$279$	516663.	+	303338.i	0.397372	+	0.233301i
$280$	−413198.	−	1.01934e6i	−0.314966	−	0.777003i
$281$			199614.i			0.150808i	0.997153	+	0.0754040i	$0.0240246\pi$
$281$			199614.i			0.150808i	−0.997153	+	0.0754040i	$0.975975\pi$
$282$	764945.	+	1.33615e6i	0.572806	+	1.00053i
$283$		−	1.72910e6i		−	1.28338i	−0.766966	−	0.641688i	$-0.778234\pi$
$283$		−	1.72910e6i		−	1.28338i	0.766966	−	0.641688i	$-0.221766\pi$
$284$			41091.8i			0.0302315i
$285$	40308.9	+	70408.4i	0.0293960	+	0.0513466i
$286$			1.81737e6i			1.31380i
$287$	1.98134e6	−	803157.i	1.41989	−	0.575567i
$288$	71467.7	+	41959.4i	0.0507725	+	0.0298091i
$289$	−483528.			−0.340547
$290$	−154033.			−0.107552
$291$	−870486.	−	1.52050e6i	−0.602600	−	1.05257i
$292$		−	29896.3i		−	0.0205192i
$293$	1.91518e6			1.30329			0.651645	−	0.758524i	$-0.274079\pi$
$293$	1.91518e6			1.30329			0.651645	+	0.758524i	$0.274079\pi$
$294$	1.40298e6	+	404351.i	0.946634	+	0.272829i
$295$	1.84785e6			1.23627
$296$			762048.i			0.505537i
$297$	1.08208e6	+	11831.6i	0.711815	+	0.00778311i
$298$	−2.66869e6			−1.74083
$299$	−1.44069e6			−0.931951
$300$	−12611.8	+	7220.29i	−0.00809050	+	0.00463182i
$301$	−613232.	+	248580.i	−0.390130	+	0.158143i
$302$		−	287997.i		−	0.181707i
$303$	−255030.	+	146005.i	−0.159582	+	0.0913611i
$304$		−	111826.i		−	0.0693997i
$305$			1.70797e6i			1.05131i
$306$	−1.13004e6	−	663456.i	−0.689904	−	0.405050i
$307$			131454.i			0.0796030i	0.999208	+	0.0398015i	$0.0126726\pi$
$307$			131454.i			0.0796030i	−0.999208	+	0.0398015i	$0.987327\pi$
$308$	−13110.8	−	32343.6i	−0.00787503	−	0.0194272i
$309$	−263492.	−	460248.i	−0.156990	−	0.274218i
$310$	−634991.			−0.375287
$311$	−447026.			−0.262079			−0.131039	−	0.991377i	$-0.541831\pi$
$311$	−447026.			−0.262079			−0.131039	+	0.991377i	$0.541831\pi$
$312$	2.83510e6	−	1.62310e6i	1.64885	−	0.943969i
$313$		−	211680.i		−	0.122129i	−0.998134	−	0.0610645i	$-0.980550\pi$
$313$		−	211680.i		−	0.122129i	0.998134	−	0.0610645i	$-0.0194495\pi$
$314$	−1.20259e6			−0.688325
$315$	−211470.	+	1.44042e6i	−0.120080	+	0.817926i
$316$	−37470.8			−0.0211094
$317$			920013.i			0.514216i	0.966383	+	0.257108i	$0.0827697\pi$
$317$			920013.i			0.514216i	−0.966383	+	0.257108i	$0.917230\pi$
$318$	−2.26825e6	+	1.29857e6i	−1.25783	+	0.720110i
$319$	−170858.			−0.0940068
$320$	−1.55625e6			−0.849583
$321$	191893.	+	335184.i	0.103944	+	0.181560i
$322$	−845045.	+	342547.i	−0.454193	+	0.184112i
$323$		−	108975.i		−	0.0581191i
$324$	−27116.4	−	48589.3i	−0.0143506	−	0.0257145i
$325$			1.12932e6i			0.593073i
$326$		−	243642.i		−	0.126972i
$327$	2.06898e6	−	1.18449e6i	1.07001	−	0.612580i
$328$		−	3.02753e6i		−	1.55383i
$329$	−2.12929e6	+	863130.i	−1.08454	+	0.439629i
$330$	−995342.	+	569834.i	−0.503139	+	0.288047i
$331$	2.59767e6			1.30321			0.651605	−	0.758559i	$-0.274096\pi$
$331$	2.59767e6			1.30321			0.651605	+	0.758559i	$0.274096\pi$
$332$	21639.2			0.0107745
$333$	510690.	−	869836.i	0.252375	−	0.429860i
$334$		−	2.60475e6i		−	1.27762i
$335$	1.59992e6			0.778907
$336$	1.23938e6	−	1.57820e6i	0.598905	−	0.762628i
$337$	259510.			0.124474			0.0622372	−	0.998061i	$-0.480176\pi$
$337$	259510.			0.124474			0.0622372	+	0.998061i	$0.480176\pi$
$338$		−	5.19278e6i		−	2.47234i
$339$	−1.28333e6	−	2.24162e6i	−0.606510	−	1.05941i
$340$	−42139.3			−0.0197692
$341$	−704350.			−0.328022
$342$	−77216.3	+	131519.i	−0.0356980	+	0.0608029i
$343$	−879385.	+	1.99355e6i	−0.403593	+	0.914939i
$344$			937032.i			0.426931i
$345$	−451726.	−	789040.i	−0.204328	−	0.356904i
$346$			1.45476e6i			0.653284i
$347$			2.10380e6i			0.937951i	0.883211	+	0.468975i	$0.155377\pi$
$347$			2.10380e6i			0.937951i	−0.883211	+	0.468975i	$0.844623\pi$
$348$	4365.01	+	7624.45i	0.00193213	+	0.00337490i
$349$		−	2.10644e6i		−	0.925732i	−0.886428	−	0.462866i	$-0.846821\pi$
$349$		−	2.10644e6i		−	0.925732i	0.886428	−	0.462866i	$-0.153179\pi$
$350$	268513.	+	662407.i	0.117164	+	0.289038i
$351$	−4.32383e6	−	47277.5i	−1.87327	−	0.0204827i
$352$	−97429.5			−0.0419116
$353$	106417.			0.0454541			0.0227271	−	0.999742i	$-0.492765\pi$
$353$	106417.			0.0454541			0.0227271	+	0.999742i	$0.492765\pi$
$354$	1.72585e6	+	3.01457e6i	0.731971	+	1.27855i
$355$			2.01521e6i			0.848692i
$356$	−59934.0			−0.0250639
$357$	1.20779e6	−	1.53796e6i	0.501556	−	0.638667i
$358$	3.15392e6			1.30060
$359$			2.24142e6i			0.917882i	0.888467	+	0.458941i	$0.151771\pi$
$359$			2.24142e6i			0.917882i	−0.888467	+	0.458941i	$0.848229\pi$
$360$	1.77788e6	+	1.04381e6i	0.723012	+	0.424488i
$361$	2.46342e6			0.994878
$362$	3.43010e6			1.37574
$363$	1.07469e6	−	615259.i	0.428071	−	0.245071i
$364$	52388.9	+	129240.i	0.0207246	+	0.0511264i
$365$		−	1.46617e6i		−	0.576038i
$366$	−2.78637e6	+	1.59520e6i	−1.08726	+	0.622460i
$367$			1.72877e6i			0.669995i	0.942219	+	0.334997i	$0.108735\pi$
$367$			1.72877e6i			0.669995i	−0.942219	+	0.334997i	$0.891265\pi$
$368$			1.25319e6i			0.482388i
$369$	−2.02891e6	+	3.45576e6i	−0.775707	+	1.32123i
$370$			1.06905e6i			0.405969i
$371$	−1.46525e6	−	3.61469e6i	−0.552685	−	1.36344i
$372$	17994.4	+	31431.2i	0.00674186	+	0.0117762i
$373$	−2.66469e6			−0.991687			−0.495844	−	0.868412i	$-0.665141\pi$
$373$	−2.66469e6			−0.991687			−0.495844	+	0.868412i	$0.665141\pi$
$374$	1.54054e6			0.569501
$375$	−2.57223e6	+	1.47260e6i	−0.944565	+	0.540764i
$376$			3.25360e6i			1.18685i
$377$	682726.			0.247396
$378$	−2.54741e6	+	1.00033e6i	−0.916998	+	0.360092i
$379$	2.31059e6			0.826274			0.413137	−	0.910669i	$-0.364433\pi$
$379$	2.31059e6			0.826274			0.413137	+	0.910669i	$0.364433\pi$
$380$			4904.38i			0.00174231i
$381$	−403557.	+	231037.i	−0.142427	+	0.0815396i
$382$	−3.28049e6			−1.15022
$383$	3.80041e6			1.32384			0.661918	−	0.749577i	$-0.269743\pi$
$383$	3.80041e6			1.32384			0.661918	+	0.749577i	$0.269743\pi$
$384$	−1.36898e6	−	2.39122e6i	−0.473771	−	0.827545i
$385$	−642976.	−	1.58618e6i	−0.221077	−	0.545383i
$386$			571526.i			0.195239i
$387$	627956.	−	1.06957e6i	0.213133	−	0.363021i
$388$		−	105912.i		−	0.0357162i
$389$		−	5.17147e6i		−	1.73277i	−0.499380	−	0.866383i	$-0.666439\pi$
$389$		−	5.17147e6i		−	1.73277i	0.499380	−	0.866383i	$-0.333561\pi$
$390$	3.97725e6	−	2.27698e6i	1.32410	−	0.758049i
$391$			1.22124e6i			0.403978i
$392$	2.14847e6	+	2.21462e6i	0.706177	+	0.727921i
$393$	−1.02320e6	+	585784.i	−0.334180	+	0.191318i
$394$	3.69228e6			1.19827
$395$	−1.83763e6			−0.592606
$396$	56412.1	+	33120.1i	0.0180773	+	0.0106134i
$397$		−	2.02589e6i		−	0.645119i	−0.946549	−	0.322559i	$-0.895457\pi$
$397$		−	2.02589e6i		−	0.645119i	0.946549	−	0.322559i	$-0.104543\pi$
$398$	−3.88775e6			−1.23024
$399$	−178995.	−	140568.i	−0.0562871	−	0.0442033i
$400$	982340.			0.306981
$401$			2.60526e6i			0.809079i	0.914521	+	0.404539i	$0.132568\pi$
$401$			2.60526e6i			0.809079i	−0.914521	+	0.404539i	$0.867432\pi$
$402$	1.49428e6	+	2.61010e6i	0.461177	+	0.805548i
$403$	2.81448e6			0.863249
$404$	−17764.4			−0.00541500
$405$	−1.32984e6	−	2.38291e6i	−0.402866	−	0.721887i
$406$	400456.	−	162329.i	0.120570	−	0.0488744i
$407$			1.18582e6i			0.354840i
$408$	−1.37586e6	−	2.40324e6i	−0.409188	−	0.714737i
$409$		−	4.09861e6i		−	1.21151i	−0.795650	−	0.605756i	$-0.792871\pi$
$409$		−	4.09861e6i		−	1.21151i	0.795650	−	0.605756i	$-0.207129\pi$
$410$		−	4.24721e6i		−	1.24780i
$411$	−230639.	−	402862.i	−0.0673485	−	0.117639i
$412$		−	32059.1i		−	0.00930483i
$413$	−4.80404e6	+	1.94737e6i	−1.38590	+	0.561788i
$414$	865334.	−	1.47389e6i	0.248132	−	0.422633i
$415$	1.06123e6			0.302474
$416$	389315.			0.110298
$417$	927092.	+	1.61937e6i	0.261086	+	0.456044i
$418$		−	179296.i		−	0.0501914i
$419$	−4.44364e6			−1.23653			−0.618264	−	0.785971i	$-0.712164\pi$
$419$	−4.44364e6			−1.23653			−0.618264	+	0.785971i	$0.712164\pi$
$420$	−54356.1	+	69215.5i	−0.0150358	+	0.0191461i
$421$	518872.			0.142677			0.0713387	−	0.997452i	$-0.477273\pi$
$421$	518872.			0.142677			0.0713387	+	0.997452i	$0.477273\pi$
$422$			4.14230e6i			1.13230i
$423$	2.18042e6	−	3.71381e6i	0.592500	−	1.00918i
$424$	−5.52333e6			−1.49206
$425$	957294.			0.257083
$426$	−3.28761e6	+	1.88216e6i	−0.877720	+	0.502495i
$427$	−1.79995e6	−	4.44037e6i	−0.477739	−	1.17855i
$428$			23347.7i			0.00616076i
$429$	4.41168e6	−	2.52569e6i	1.15734	−	0.662578i
$430$			1.31453e6i			0.342845i
$431$		−	851882.i		−	0.220895i	−0.993882	−	0.110448i	$-0.964772\pi$
$431$		−	851882.i		−	0.220895i	0.993882	−	0.110448i	$-0.0352284\pi$
$432$	−41124.5	+	3.76109e6i	−0.0106021	+	0.969627i
$433$			2.57351e6i			0.659639i	0.944044	+	0.329820i	$0.106988\pi$
$433$			2.57351e6i			0.659639i	−0.944044	+	0.329820i	$0.893012\pi$
$434$	1.65085e6	−	669188.i	0.420710	−	0.170539i
$435$	214067.	+	373916.i	0.0542410	+	0.0947439i
$436$	144117.			0.0363078
$437$	142134.			0.0356035
$438$	2.39189e6	−	1.36936e6i	0.595740	−	0.341062i
$439$			7.33839e6i			1.81735i	0.417500	+	0.908677i	$0.362906\pi$
$439$			7.33839e6i			1.81735i	−0.417500	+	0.908677i	$0.637094\pi$
$440$	−2.42372e6			−0.596831
$441$	−968219.	−	3.96767e6i	−0.237070	−	0.971492i
$442$	−6.15579e6			−1.49875
$443$			891340.i			0.215791i	0.994162	+	0.107896i	$0.0344113\pi$
$443$			891340.i			0.215791i	−0.994162	+	0.107896i	$0.965589\pi$
$444$	52916.5	−	30294.8i	0.0127390	−	0.00729306i
$445$	−2.93927e6			−0.703622
$446$	1.88131e6			0.447841
$447$	3.70880e6	+	6.47824e6i	0.877939	+	1.53352i
$448$	4.04595e6	−	1.64007e6i	0.952414	−	0.386071i
$449$		−	4.74883e6i		−	1.11166i	−0.831297	−	0.555829i	$-0.812401\pi$
$449$		−	4.74883e6i		−	1.11166i	0.831297	−	0.555829i	$-0.187599\pi$
$450$	−1.15534e6	−	678311.i	−0.268954	−	0.157906i
$451$		−	4.71113e6i		−	1.09065i
$452$		−	156142.i		−	0.0359480i
$453$	−699113.	+	400243.i	−0.160067	+	0.0916386i
$454$		−	3.98084e6i		−	0.906432i
$455$	2.56924e6	+	6.33817e6i	0.581804	+	1.43528i
$456$	−279701.	+	160129.i	−0.0629914	+	0.0360627i
$457$	−3.14654e6			−0.704762			−0.352381	−	0.935857i	$-0.614628\pi$
$457$	−3.14654e6			−0.704762			−0.352381	+	0.935857i	$0.614628\pi$
$458$	1.09201e6			0.243257
$459$	−40076.0	+	3.66520e6i	−0.00887876	+	0.812019i
$460$		−	54961.5i		−	0.0121106i
$461$	2.98519e6			0.654213			0.327107	−	0.944987i	$-0.393926\pi$
$461$	2.98519e6			0.654213			0.327107	+	0.944987i	$0.393926\pi$
$462$	1.98717e6	−	2.53040e6i	0.433142	−	0.551550i
$463$	−2.38242e6			−0.516495			−0.258248	−	0.966079i	$-0.583145\pi$
$463$	−2.38242e6			−0.516495			−0.258248	+	0.966079i	$0.583145\pi$
$464$		−	593871.i		−	0.128055i
$465$	882476.	+	1.54144e6i	0.189265	+	0.330594i
$466$	5.59925e6			1.19444
$467$	5.36944e6			1.13930			0.569648	−	0.821889i	$-0.307079\pi$
$467$	5.36944e6			1.13930			0.569648	+	0.821889i	$0.307079\pi$
$468$	−225415.	−	132343.i	−0.0475738	−	0.0279311i
$469$	−4.15947e6	+	1.68608e6i	−0.873184	+	0.353954i
$470$			4.56436e6i			0.953092i
$471$	1.67130e6	+	2.91929e6i	0.347137	+	0.606352i
$472$			7.34068e6i			1.51664i
$473$			1.45811e6i			0.299666i
$474$	−1.71630e6	−	2.99790e6i	−0.350871	−	0.612875i
$475$		−	111415.i		−	0.0226573i
$476$	109554.	−	44408.7i	0.0221621	−	0.00898361i
$477$	6.30458e6	+	3.70148e6i	1.26870	+	0.744869i
$478$	−1.01224e6			−0.202636
$479$	1.33255e6			0.265366			0.132683	−	0.991158i	$-0.457641\pi$
$479$	1.33255e6			0.265366			0.132683	+	0.991158i	$0.457641\pi$
$480$	122069.	+	213221.i	0.0241826	+	0.0422402i
$481$		−	4.73837e6i		−	0.933827i
$482$	−1.08268e6			−0.212267
$483$	2.00593e6	+	1.57529e6i	0.391245	+	0.307251i
$484$	74858.6			0.0145254
$485$		−	5.19411e6i		−	1.00267i
$486$	2.64542e6	−	4.39506e6i	0.508048	−	0.844061i
$487$	3.86580e6			0.738612			0.369306	−	0.929308i	$-0.379595\pi$
$487$	3.86580e6			0.738612			0.369306	+	0.929308i	$0.379595\pi$
$488$	−6.78498e6			−1.28973
$489$	−591440.	+	338600.i	−0.111851	+	0.0640346i
$490$	3.01400e6	+	3.10681e6i	0.567092	+	0.584554i
$491$		−	5.61830e6i		−	1.05172i	−0.850571	−	0.525861i	$-0.823743\pi$
$491$		−	5.61830e6i		−	1.05172i	0.850571	−	0.525861i	$-0.176257\pi$
$492$	−210231.	+	120358.i	−0.0391548	+	0.0224161i
$493$		−	578729.i		−	0.107240i
$494$			716441.i			0.132088i
$495$	2.76655e6	+	1.62427e6i	0.507487	+	0.297951i
$496$		−	2.44818e6i		−	0.446828i
$497$	−2.12374e6	−	5.23915e6i	−0.385666	−	0.951415i
$498$	991158.	+	1.73128e6i	0.179089	+	0.312819i
$499$	−1.06142e7			−1.90826			−0.954130	−	0.299394i	$-0.903216\pi$
$499$	−1.06142e7			−1.90826			−0.954130	+	0.299394i	$0.903216\pi$
$500$	−179172.			−0.0320512
$501$	−6.32304e6	+	3.61995e6i	−1.12546	+	0.644329i
$502$		−	6.41015e6i		−	1.13529i
$503$	8.14783e6			1.43589			0.717946	−	0.696098i	$-0.245082\pi$
$503$	8.14783e6			1.43589			0.717946	+	0.696098i	$0.245082\pi$
$504$	−5.72215e6	−	840074.i	−1.00342	−	0.147313i
$505$	−871199.			−0.152016
$506$			2.00930e6i			0.348874i
$507$	−1.26055e7	+	7.21665e6i	−2.17791	+	1.24685i
$508$	−28110.2			−0.00483287
$509$	−7.27954e6			−1.24540			−0.622701	−	0.782460i	$-0.713965\pi$
$509$	−7.27954e6			−1.24540			−0.622701	+	0.782460i	$0.713965\pi$
$510$	−1.93014e6	−	3.37141e6i	−0.328596	−	0.573966i
$511$	1.54513e6	+	3.81174e6i	0.261765	+	0.645760i
$512$		−	6.17201e6i		−	1.04052i
$513$	426574.	+	4664.24i	0.0715651	+	0.000782505i
$514$		−	4.20031e6i		−	0.701251i
$515$		−	1.57223e6i		−	0.261216i
$516$	65067.3	−	37251.1i	0.0107582	−	0.00615907i
$517$			5.06291e6i			0.833056i
$518$	−1.12662e6	−	2.77931e6i	−0.184482	−	0.455107i
$519$	3.53144e6	−	2.02175e6i	0.575484	−	0.329465i
$520$	9.68486e6			1.57067
$521$	−2.38061e6			−0.384232			−0.192116	−	0.981372i	$-0.561535\pi$
$521$	−2.38061e6			−0.384232			−0.192116	+	0.981372i	$0.561535\pi$
$522$	−410071.	+	698457.i	−0.0658693	+	0.112192i
$523$			1.14144e6i			0.182473i	0.995829	+	0.0912363i	$0.0290818\pi$
$523$			1.14144e6i			0.182473i	−0.995829	+	0.0912363i	$0.970918\pi$
$524$	−71272.4			−0.0113395
$525$	1.23483e6	−	1.57239e6i	0.195528	−	0.248979i
$526$	3.54550e6			0.558745
$527$		−	2.38577e6i		−	0.374198i
$528$	−2.19698e6	−	3.83751e6i	−0.342958	−	0.599052i
$529$	4.84351e6			0.752524
$530$	−7.74847e6			−1.19819
$531$	4.91939e6	−	8.37898e6i	0.757137	−	1.28960i
$532$	−5168.51	−	12750.4i	−0.000791746	−	0.00195319i
$533$			1.88250e7i			2.87023i
$534$	−2.74520e6	−	4.79511e6i	−0.416602	−	0.727688i
$535$			1.14501e6i			0.172952i
$536$			6.35575e6i			0.955553i
$537$	−4.38315e6	−	7.65614e6i	−0.655920	−	1.14571i
$538$			5.05254e6i			0.752582i
$539$	3.34322e6	+	3.44616e6i	0.495670	+	0.510933i
$540$	1803.61	−	164952.i	0.000266169	−	0.0243429i
$541$	7.55281e6			1.10947			0.554735	−	0.832027i	$-0.312820\pi$
$541$	7.55281e6			1.10947			0.554735	+	0.832027i	$0.312820\pi$
$542$	361181.			0.0528113
$543$	−4.76698e6	−	8.32658e6i	−0.693814	−	1.21190i
$544$		−	330012.i		−	0.0478116i
$545$	7.06776e6			1.01927
$546$	−7.94045e6	+	1.01111e7i	−1.13989	+	1.45150i
$547$	−7.39779e6			−1.05714			−0.528571	−	0.848889i	$-0.677272\pi$
$547$	−7.39779e6			−1.05714			−0.528571	+	0.848889i	$0.677272\pi$
$548$		−	28061.8i		−	0.00399176i
$549$	7.74468e6	+	4.54698e6i	1.09666	+	0.643862i
$550$	1.57504e6			0.222016
$551$	−67355.4			−0.00945134
$552$	3.13450e6	−	1.79450e6i	0.437845	−	0.250667i
$553$	4.77748e6	−	1.93660e6i	0.664334	−	0.269294i
$554$		−	6.70554e6i		−	0.928239i
$555$	2.59512e6	−	1.48571e6i	0.357622	−	0.204739i
$556$			112799.i			0.0154746i
$557$		−	3.17885e6i		−	0.434143i	−0.976156	−	0.217071i	$-0.930350\pi$
$557$		−	3.17885e6i		−	0.434143i	0.976156	−	0.217071i	$-0.0696505\pi$
$558$	−1.69049e6	+	2.87933e6i	−0.229840	+	0.391477i
$559$		−	5.82641e6i		−	0.788626i
$560$	5.51327e6	−	2.23486e6i	0.742916	−	0.301148i
$561$	−2.14096e6	−	3.73967e6i	−0.287212	−	0.501679i
$562$	−1.11243e6			−0.148571
$563$	−7.56588e6			−1.00598			−0.502989	−	0.864293i	$-0.667766\pi$
$563$	−7.56588e6			−1.00598			−0.502989	+	0.864293i	$0.667766\pi$
$564$	225929.	−	129345.i	0.0299072	−	0.0171219i
$565$		−	7.65750e6i		−	1.00917i
$566$	9.63617e6			1.26434
$567$	5.96855e6	+	4.79362e6i	0.779670	+	0.626190i
$568$	−8.00554e6			−1.04116
$569$			4.34836e6i			0.563047i	0.959554	+	0.281524i	$0.0908397\pi$
$569$			4.34836e6i			0.563047i	−0.959554	+	0.281524i	$0.909160\pi$
$570$	−392382.	+	224639.i	−0.0505850	+	0.0289599i
$571$	5.84474e6			0.750196			0.375098	−	0.926985i	$-0.377609\pi$
$571$	5.84474e6			0.750196			0.375098	+	0.926985i	$0.377609\pi$
$572$	307301.			0.0392711
$573$	4.55905e6	+	7.96339e6i	0.580080	+	1.01324i
$574$	4.47595e6	+	1.10419e7i	0.567029	+	1.39883i
$575$			1.24858e6i			0.157488i
$576$	−4.14309e6	+	7.05675e6i	−0.520318	+	0.886235i
$577$			1.37469e7i			1.71896i	0.511173	+	0.859478i	$0.329211\pi$
$577$			1.37469e7i			1.71896i	−0.511173	+	0.859478i	$0.670789\pi$
$578$		−	2.69467e6i		−	0.335495i
$579$	1.38738e6	−	794276.i	0.171988	−	0.0984635i
$580$			26045.6i			0.00321488i
$581$	−2.75898e6	+	1.11838e6i	−0.339084	+	0.137451i
$582$	8.47364e6	−	4.85116e6i	1.03696	−	0.593661i
$583$	−8.59482e6			−1.04729
$584$	5.82442e6			0.706676
$585$	−1.10547e7	−	6.49035e6i	−1.33555	−	0.784113i
$586$			1.06732e7i			1.28396i
$587$	−1.10150e7			−1.31944			−0.659721	−	0.751511i	$-0.729325\pi$
$587$	−1.10150e7			−1.31944			−0.659721	+	0.751511i	$0.729325\pi$
$588$	68372.0	−	237230.i	0.00815520	−	0.0282961i
$589$	−277667.			−0.0329789
$590$			1.02980e7i			1.21793i
$591$	−5.13134e6	−	8.96302e6i	−0.604313	−	1.05557i
$592$	−4.12168e6			−0.483359
$593$	−832174.			−0.0971802			−0.0485901	−	0.998819i	$-0.515473\pi$
$593$	−832174.			−0.0971802			−0.0485901	+	0.998819i	$0.515473\pi$
$594$	−65936.9	+	6.03035e6i	−0.00766766	+	0.701256i
$595$	5.37271e6	−	2.17788e6i	0.622158	−	0.252198i
$596$			451250.i			0.0520357i
$597$	5.40298e6	+	9.43751e6i	0.620437	+	1.08373i
$598$		−	8.02889e6i		−	0.918126i
$599$			9.00401e6i			1.02534i	0.858585	+	0.512671i	$0.171344\pi$
$599$			9.00401e6i			1.02534i	−0.858585	+	0.512671i	$0.828656\pi$
$600$	−1.40666e6	−	2.45705e6i	−0.159519	−	0.278635i
$601$			1.57084e6i			0.177397i	0.996059	+	0.0886984i	$0.0282707\pi$
$601$			1.57084e6i			0.177397i	−0.996059	+	0.0886984i	$0.971729\pi$
$602$	−1.38532e6	−	3.41751e6i	−0.155797	−	0.384342i
$603$	4.25933e6	−	7.25474e6i	0.477033	−	0.812510i
$604$	−48697.6			−0.00543144
$605$	3.67120e6			0.407774
$606$	−813678.	−	1.42127e6i	−0.0900059	−	0.157215i
$607$		−	9.46468e6i		−	1.04264i	−0.853361	−	0.521320i	$-0.825440\pi$
$607$		−	9.46468e6i		−	1.04264i	0.853361	−	0.521320i	$-0.174560\pi$
$608$	−38408.5			−0.00421374
$609$	−950587.	−	746512.i	−0.103860	−	0.0815631i
$610$	−9.51839e6			−1.03571
$611$		−	2.02307e7i		−	2.19234i
$612$	−112184.	+	191078.i	−0.0121075	+	0.0206221i
$613$	9.55862e6			1.02741			0.513705	−	0.857967i	$-0.328273\pi$
$613$	9.55862e6			1.02741			0.513705	+	0.857967i	$0.328273\pi$
$614$	−732588.			−0.0784222
$615$	−1.03101e7	+	5.90255e6i	−1.09920	+	0.629291i
$616$	6.30120e6	−	2.55425e6i	0.669070	−	0.271214i
$617$		−	4.88602e6i		−	0.516704i	−0.966051	−	0.258352i	$-0.916821\pi$
$617$		−	4.88602e6i		−	0.516704i	0.966051	−	0.258352i	$-0.0831795\pi$
$618$	2.56493e6	−	1.46843e6i	0.270150	−	0.154661i
$619$		−	9.76741e6i		−	1.02460i	−0.858808	−	0.512298i	$-0.828794\pi$
$619$		−	9.76741e6i		−	1.02460i	0.858808	−	0.512298i	$-0.171206\pi$
$620$			107371.i			0.0112178i
$621$	−4.78045e6	−	52270.3i	−0.497439	−	0.00543909i
$622$		−	2.49125e6i		−	0.258191i
$623$	7.64152e6	−	3.09756e6i	0.788786	−	0.319742i
$624$	8.77881e6	+	1.53341e7i	0.902557	+	1.57652i
$625$	−5.69531e6			−0.583200
$626$	1.17968e6			0.120317
$627$	−435241.	+	249176.i	−0.0442141	+	0.0253126i
$628$			203347.i			0.0205749i
$629$	−4.01660e6			−0.404792
$630$	−8.02740e6	−	1.17851e6i	−0.805793	−	0.118299i
$631$	−899670.			−0.0899518			−0.0449759	−	0.998988i	$-0.514321\pi$
$631$	−899670.			−0.0899518			−0.0449759	+	0.998988i	$0.514321\pi$
$632$		−	7.30009e6i		−	0.727002i
$633$	1.00554e7	−	5.75675e6i	0.997451	−	0.571042i
$634$	−5.12718e6			−0.506588
$635$	−1.37858e6			−0.135674
$636$	219576.	+	383539.i	0.0215250	+	0.0375982i
$637$	−1.33590e7	−	1.37704e7i	−1.30445	−	1.34461i
$638$		−	952183.i		−	0.0926123i
$639$	9.13788e6	+	5.36494e6i	0.885306	+	0.519772i
$640$		−	8.16856e6i		−	0.788307i
$641$		−	4.01387e6i		−	0.385850i	−0.981214	−	0.192925i	$-0.938203\pi$
$641$		−	4.01387e6i		−	0.385850i	0.981214	−	0.192925i	$-0.0617974\pi$
$642$	−1.86796e6	+	1.06941e6i	−0.178867	+	0.102402i
$643$			7.33239e6i			0.699388i	0.936864	+	0.349694i	$0.113714\pi$
$643$			7.33239e6i			0.699388i	−0.936864	+	0.349694i	$0.886286\pi$
$644$	57921.5	+	142889.i	0.00550332	+	0.0135764i
$645$	3.19101e6	−	1.82686e6i	0.302016	−	0.172904i
$646$	607309.			0.0572570
$647$	−1.70332e7			−1.59969			−0.799846	−	0.600205i	$-0.795085\pi$
$647$	−1.70332e7			−1.59969			−0.799846	+	0.600205i	$0.795085\pi$
$648$	9.46621e6	−	5.28284e6i	0.885602	−	0.494231i
$649$			1.14228e7i			1.06454i
$650$	−6.29362e6			−0.584275
$651$	−3.91872e6	−	3.07744e6i	−0.362403	−	0.284601i
$652$	−41197.5			−0.00379535
$653$		−	4.19237e6i		−	0.384748i	−0.981322	−	0.192374i	$-0.938381\pi$
$653$		−	4.19237e6i		−	0.384748i	0.981322	−	0.192374i	$-0.0616186\pi$
$654$	6.60111e6	+	1.15303e7i	0.603493	+	1.05414i
$655$	−3.49532e6			−0.318335
$656$	1.63750e7			1.48567
$657$	−6.64825e6	−	3.90326e6i	−0.600889	−	0.352788i
$658$	−4.81017e6	−	1.18664e7i	−0.433108	−	1.06845i
$659$			1.07708e7i			0.966131i	0.875584	+	0.483065i	$0.160477\pi$
$659$			1.07708e7i			0.966131i	−0.875584	+	0.483065i	$0.839523\pi$
$660$	96353.6	+	168303.i	0.00861010	+	0.0150394i
$661$			9.47459e6i			0.843445i	0.906725	+	0.421723i	$0.138574\pi$
$661$			9.47459e6i			0.843445i	−0.906725	+	0.421723i	$0.861426\pi$
$662$			1.44767e7i			1.28388i
$663$	8.55499e6	+	1.49432e7i	0.755850	+	1.32026i
$664$			4.21577e6i			0.371071i
$665$	−253473.	−	625302.i	−0.0222268	−	0.0548322i
$666$	4.84755e6	+	2.84605e6i	0.423483	+	0.248632i
$667$	754826.			0.0656950
$668$	−440439.			−0.0381895
$669$	−2.61455e6	−	4.56689e6i	−0.225856	−	0.394507i
$670$			8.91625e6i			0.767353i
$671$	−1.05581e7			−0.905270
$672$	−542059.	−	425688.i	−0.0463045	−	0.0363637i
$673$	−2.97586e6			−0.253265			−0.126632	−	0.991950i	$-0.540417\pi$
$673$	−2.97586e6			−0.253265			−0.126632	+	0.991950i	$0.540417\pi$
$674$			1.44624e6i			0.122628i
$675$	−40973.3	+	3.74727e6i	−0.00346132	+	0.316559i
$676$	−878050.			−0.0739014
$677$	5.53094e6			0.463796			0.231898	−	0.972740i	$-0.425506\pi$
$677$	5.53094e6			0.463796			0.231898	+	0.972740i	$0.425506\pi$
$678$	1.24924e7	−	7.15191e6i	1.04369	−	0.597514i
$679$	5.47384e6	+	1.35036e7i	0.455636	+	1.12403i
$680$		−	8.20961e6i		−	0.680848i
$681$	−9.66350e6	+	5.53236e6i	−0.798485	+	0.457133i
$682$		−	3.92530e6i		−	0.323156i
$683$			2.08889e7i			1.71342i	0.515796	+	0.856712i	$0.327496\pi$
$683$			2.08889e7i			1.71342i	−0.515796	+	0.856712i	$0.672504\pi$
$684$	22238.6	+	13056.5i	0.00181747	+	0.00106706i
$685$		−	1.37620e6i		−	0.112061i
$686$	−1.11099e7	−	4.90076e6i	−0.901366	−	0.397606i
$687$	−1.51762e6	−	2.65087e6i	−0.122680	−	0.214287i
$688$	−5.06811e6			−0.408202
$689$	3.43437e7			2.75613
$690$	4.39727e6	−	2.51744e6i	0.351610	−	0.201297i
$691$		−	2.76828e6i		−	0.220554i	−0.993901	−	0.110277i	$-0.964826\pi$
$691$		−	2.76828e6i		−	0.220554i	0.993901	−	0.110277i	$-0.0351738\pi$
$692$	245986.			0.0195275
$693$	−8.90422e6	−	1.30723e6i	−0.704308	−	0.103400i
$694$	−1.17243e7			−0.924037
$695$			5.53188e6i			0.434421i
$696$	−1.48540e6	+	850394.i	−0.116231	+	0.0665422i
$697$	1.59575e7			1.24418
$698$	1.17391e7			0.912000
$699$	−7.78154e6	−	1.35922e7i	−0.602383	−	1.05220i
$700$	112007.	−	45403.1i	0.00863971	−	0.00350219i
$701$			2.86133e6i			0.219924i	0.993936	+	0.109962i	$0.0350729\pi$
$701$			2.86133e6i			0.219924i	−0.993936	+	0.109962i	$0.964927\pi$
$702$	263475.	−	2.40965e7i	0.0201789	−	1.84548i
$703$			467471.i			0.0356752i
$704$		−	9.62024e6i		−	0.731568i
$705$	1.10800e7	−	6.34330e6i	0.839588	−	0.480665i
$706$			593054.i			0.0447798i
$707$	2.26494e6	−	918118.i	0.170415	−	0.0690796i
$708$	509735.	−	291824.i	0.0382174	−	0.0218795i
$709$	3.16019e6			0.236101			0.118050	−	0.993008i	$-0.462336\pi$
$709$	3.16019e6			0.236101			0.118050	+	0.993008i	$0.462336\pi$
$710$	−1.12307e7			−0.836103
$711$	−4.89219e6	+	8.33265e6i	−0.362935	+	0.618172i
$712$		−	1.16764e7i		−	0.863195i
$713$	3.11171e6			0.229232
$714$	8.57095e6	+	6.73092e6i	0.629193	+	0.494116i
$715$	1.50706e7			1.10246
$716$		−	533298.i		−	0.0388765i
$717$	1.40676e6	+	2.45722e6i	0.102193	+	0.178504i
$718$	−1.24913e7			−0.904266
$719$	7.16590e6			0.516950			0.258475	−	0.966018i	$-0.416780\pi$
$719$	7.16590e6			0.516950			0.258475	+	0.966018i	$0.416780\pi$
$720$	−5.64565e6	+	9.61599e6i	−0.405866	+	0.691294i
$721$	1.65691e6	+	4.08750e6i	0.118703	+	0.292832i
$722$			1.37285e7i			0.980120i
$723$	1.50465e6	+	2.62820e6i	0.107051	+	0.186988i
$724$		−	579998.i		−	0.0411225i
$725$		−	591688.i		−	0.0418069i
$726$	3.42880e6	+	5.98917e6i	0.241435	+	0.421721i
$727$		−	2.11535e7i		−	1.48439i	−0.670186	−	0.742194i	$-0.733785\pi$
$727$		−	2.11535e7i		−	1.48439i	0.670186	−	0.742194i	$-0.266215\pi$
$728$	−2.51787e7	+	1.02064e7i	−1.76078	+	0.713750i
$729$	−1.43455e7	−	313749.i	−0.999761	−	0.0218657i
$730$	8.17086e6			0.567493
$731$	−4.93890e6			−0.341851
$732$	269733.	+	471148.i	0.0186061	+	0.0324997i
$733$			1.58013e7i			1.08626i	0.839648	+	0.543130i	$0.182761\pi$
$733$			1.58013e7i			1.08626i	−0.839648	+	0.543130i	$0.817239\pi$
$734$	−9.63431e6			−0.660056
$735$	3.35308e6	−	1.16342e7i	0.228942	−	0.794360i
$736$	430429.			0.0292892
$737$			9.89015e6i			0.670709i
$738$	−1.92588e7	−	1.13070e7i	−1.30163	−	0.764200i
$739$	1.13985e7			0.767781			0.383890	−	0.923379i	$-0.374584\pi$
$739$	1.13985e7			0.767781			0.383890	+	0.923379i	$0.374584\pi$
$740$	180766.			0.0121349
$741$	1.73916e6	−	995672.i	0.116358	−	0.0666148i
$742$	2.01445e7	−	8.16577e6i	1.34322	−	0.544487i
$743$		−	2.74896e7i		−	1.82683i	−0.407035	−	0.913413i	$-0.633437\pi$
$743$		−	2.74896e7i		−	1.82683i	0.407035	−	0.913413i	$-0.366563\pi$
$744$	−6.12345e6	+	3.50568e6i	−0.405568	+	0.232188i
$745$			2.21301e7i			1.46080i
$746$		−	1.48502e7i		−	0.976977i
$747$	2.82522e6	−	4.81207e6i	0.185247	−	0.315523i
$748$		−	260491.i		−	0.0170231i
$749$	−1.20668e6	−	2.97680e6i	−0.0785934	−	0.193885i
$750$	−8.20674e6	−	1.43349e7i	−0.532743	−	0.930553i
$751$	−7.32522e6			−0.473937			−0.236969	−	0.971517i	$-0.576154\pi$
$751$	−7.32522e6			−0.473937			−0.236969	+	0.971517i	$0.576154\pi$
$752$	−1.75977e7			−1.13478
$753$	−1.55606e7	+	8.90848e6i	−1.00009	+	0.572554i
$754$			3.80479e6i			0.243726i
$755$	−2.38821e6			−0.152478
$756$	169146.	+	430742.i	0.0107636	+	0.0274102i
$757$	1.29529e7			0.821536			0.410768	−	0.911740i	$-0.365261\pi$
$757$	1.29529e7			0.821536			0.410768	+	0.911740i	$0.365261\pi$
$758$			1.28768e7i			0.814017i
$759$	4.87758e6	−	2.79242e6i	0.307326	−	0.175945i
$760$	−955475.			−0.0600047
$761$	−1.43097e7			−0.895714			−0.447857	−	0.894105i	$-0.647813\pi$
$761$	−1.43097e7			−0.895714			−0.447857	+	0.894105i	$0.647813\pi$
$762$	−1.28755e6	−	2.24900e6i	−0.0803301	−	0.140314i
$763$	−1.83748e7	+	7.44840e6i	−1.14264	+	0.463182i
$764$			554699.i			0.0343815i
$765$	−5.50170e6	+	9.37082e6i	−0.339894	+	0.578927i
$766$			2.11795e7i			1.30420i
$767$		−	4.56439e7i		−	2.80152i
$768$	−1.25210e6	+	716827.i	−0.0766011	+	0.0438542i
$769$		−	2.84449e7i		−	1.73456i	−0.497822	−	0.867279i	$-0.665867\pi$
$769$		−	2.84449e7i		−	1.73456i	0.497822	−	0.867279i	$-0.334133\pi$
$770$	8.83971e6	−	3.58327e6i	0.537293	−	0.217797i
$771$	−1.01963e7	+	5.83737e6i	−0.617739	+	0.353656i
$772$	96639.6			0.00583595
$773$	1.79858e7			1.08263			0.541316	−	0.840819i	$-0.317926\pi$
$773$	1.79858e7			1.08263			0.541316	+	0.840819i	$0.317926\pi$
$774$	5.96065e6	+	3.49956e6i	0.357636	+	0.209972i
$775$		−	2.43918e6i		−	0.145878i
$776$	2.06339e7			1.23006
$777$	−5.18107e6	+	6.59742e6i	−0.307870	+	0.392032i
$778$	2.88203e7			1.70706
$779$		−	1.85721e6i		−	0.109652i
$780$	−385015.	−	672515.i	−0.0226590	−	0.0395791i
$781$	−1.24574e7			−0.730801
$782$	−6.80588e6			−0.397986
$783$	2.26540e6	+	24770.3i	0.132051	+	0.00144386i
$784$	−1.19782e7	+	1.16204e7i	−0.695987	+	0.675197i
$785$			9.97247e6i			0.577602i
$786$	−3.26454e6	−	5.70224e6i	−0.188480	−	0.329222i
$787$		−	1.53079e7i		−	0.881003i	−0.897752	−	0.440502i	$-0.854801\pi$
$787$		−	1.53079e7i		−	0.881003i	0.897752	−	0.440502i	$-0.145199\pi$
$788$		−	624330.i		−	0.0358178i
$789$	−4.92735e6	−	8.60671e6i	−0.281787	−	0.492204i
$790$		−	1.02410e7i		−	0.583815i
$791$	8.06990e6	+	1.99080e7i	0.458592	+	1.13132i
$792$	−6.45249e6	+	1.09902e7i	−0.365523	+	0.622579i
$793$	4.21886e7			2.38239
$794$	1.12902e7			0.635549
$795$	1.07684e7	+	1.88094e7i	0.604274	+	1.05550i
$796$			657381.i			0.0367735i
$797$	5.35963e6			0.298875			0.149437	−	0.988771i	$-0.452254\pi$
$797$	5.35963e6			0.298875			0.149437	+	0.988771i	$0.452254\pi$
$798$	783377.	−	997530.i	0.0435475	−	0.0554522i
$799$	−1.71490e7			−0.950327
$800$		−	337401.i		−	0.0186390i
$801$	−7.82499e6	+	1.33280e7i	−0.430926	+	0.733977i
$802$	−1.45190e7			−0.797077
$803$	9.06335e6			0.496021
$804$	441342.	−	252669.i	0.0240788	−	0.0137852i
$805$	2.84057e6	+	7.00753e6i	0.154496	+	0.381132i
$806$			1.56850e7i			0.850444i
$807$	1.22650e7	−	7.02175e6i	0.662956	−	0.379543i
$808$		−	3.46088e6i		−	0.186491i
$809$			9.70495e6i			0.521341i	0.965428	+	0.260671i	$0.0839436\pi$
$809$			9.70495e6i			0.521341i	−0.965428	+	0.260671i	$0.916056\pi$
$810$	1.32798e7	−	7.41110e6i	0.711179	−	0.396890i
$811$			3.08898e7i			1.64916i	0.565746	+	0.824579i	$0.308588\pi$
$811$			3.08898e7i			1.64916i	−0.565746	+	0.824579i	$0.691412\pi$
$812$	−27448.3	−	67713.4i	−0.00146092	−	0.00360400i
$813$	−501950.	−	876767.i	−0.0266339	−	0.0465220i
$814$	−6.60850e6			−0.349576
$815$	−2.02040e6			−0.106547
$816$	1.29984e7	−	7.44158e6i	0.683382	−	0.391237i
$817$			574813.i			0.0301281i
$818$	2.28413e7			1.19354
$819$	3.55800e7	+	5.22353e6i	1.85352	+	0.272116i
$820$	−718163.			−0.0372982
$821$		−	8.98419e6i		−	0.465180i	−0.972575	−	0.232590i	$-0.925280\pi$
$821$		−	8.98419e6i		−	0.465180i	0.972575	−	0.232590i	$-0.0747200\pi$
$822$	2.24512e6	−	1.28534e6i	0.115894	−	0.0663494i
$823$	−2.18846e7			−1.12626			−0.563132	−	0.826367i	$-0.690404\pi$
$823$	−2.18846e7			−1.12626			−0.563132	+	0.826367i	$0.690404\pi$
$824$	6.24578e6			0.320456
$825$	−2.18890e6	−	3.82340e6i	−0.111967	−	0.195576i
$826$	−1.08526e7	−	2.67727e7i	−0.553455	−	1.36534i
$827$			3.72199e6i			0.189239i	0.995514	+	0.0946196i	$0.0301635\pi$
$827$			3.72199e6i			0.189239i	−0.995514	+	0.0946196i	$0.969837\pi$
$828$	−249220.	−	146320.i	−0.0126330	−	0.00741698i
$829$		−	2.09659e7i		−	1.05956i	−0.848135	−	0.529781i	$-0.822274\pi$
$829$		−	2.09659e7i		−	1.05956i	0.848135	−	0.529781i	$-0.177726\pi$
$830$			5.91415e6i			0.297987i
$831$	−1.62777e7	+	9.31901e6i	−0.817694	+	0.468131i
$832$			3.84412e7i			1.92525i
$833$	−1.16728e7	+	1.13241e7i	−0.582858	+	0.565447i
$834$	−9.02467e6	+	5.16663e6i	−0.449279	+	0.257213i
$835$	−2.15999e7			−1.07210
$836$	−30317.2			−0.00150028
$837$	9.33893e6	+	102113.i	0.460769	+	0.00503813i
$838$		−	2.47641e7i		−	1.21818i
$839$	−2.54324e7			−1.24733			−0.623666	−	0.781691i	$-0.714357\pi$
$839$	−2.54324e7			−1.24733			−0.623666	+	0.781691i	$0.714357\pi$
$840$	−1.34846e7	−	1.05897e7i	−0.659387	−	0.517828i
$841$	2.01534e7			0.982561
$842$			2.89165e6i			0.140561i
$843$	1.54600e6	+	2.70044e6i	0.0749275	+	0.130877i
$844$	700423.			0.0338458
$845$	−4.30611e7			−2.07464
$846$	2.06968e7	+	1.21513e7i	0.994210	+	0.583711i
$847$	−9.54438e6	+	3.86891e6i	−0.457129	+	0.185302i
$848$		−	2.98740e7i		−	1.42660i
$849$	−1.33918e7	−	2.33918e7i	−0.637633	−	1.11377i
$850$			5.33494e6i			0.253269i
$851$		−	5.23877e6i		−	0.247974i
$852$	318255.	+	555903.i	0.0150202	+	0.0262361i
$853$			1.95954e7i			0.922110i	0.887372	+	0.461055i	$0.152529\pi$
$853$			1.95954e7i			0.922110i	−0.887372	+	0.461055i	$0.847471\pi$
$854$	2.47459e7	−	1.00310e7i	1.16107	−	0.470652i
$855$	1.09062e6	+	640315.i	0.0510222	+	0.0299556i
$856$	−4.54861e6			−0.212175
$857$	−384054.			−0.0178624			−0.00893120	−	0.999960i	$-0.502843\pi$
$857$	−384054.			−0.0178624			−0.00893120	+	0.999960i	$0.502843\pi$
$858$	1.40755e7	+	2.45860e7i	0.652749	+	1.14017i
$859$			4.78621e6i			0.221314i	0.993859	+	0.110657i	$0.0352955\pi$
$859$			4.78621e6i			0.221314i	−0.993859	+	0.110657i	$0.964705\pi$
$860$	222274.			0.0102481
$861$	2.05838e7	−	2.62108e7i	0.946276	−	1.20496i
$862$	4.74749e6			0.217618
$863$			3.11656e7i			1.42445i	0.701950	+	0.712227i	$0.252313\pi$
$863$			3.11656e7i			1.42445i	−0.701950	+	0.712227i	$0.747687\pi$
$864$	1.29181e6	+	14124.9i	0.0588728	+	0.000643726i
$865$	1.20636e7			0.548197
$866$	−1.43420e7			−0.649854
$867$	−6.54132e6	+	3.74491e6i	−0.295541	+	0.169197i
$868$	−113153.	−	279143.i	−0.00509763	−	0.0125756i
$869$		−	1.13596e7i		−	0.510287i
$870$	−2.08381e6	+	1.19299e6i	−0.0933385	+	0.0534364i
$871$		−	3.95197e7i		−	1.76509i
$872$			2.80770e7i			1.25043i
$873$	−2.35524e7	−	1.38279e7i	−1.04592	−	0.614072i
$874$			792102.i			0.0350754i
$875$	2.28442e7	−	9.26012e6i	1.00868	−	0.408881i
$876$	−231546.	−	404447.i	−0.0101948	−	0.0178074i
$877$	−4.19059e7			−1.83982			−0.919912	−	0.392125i	$-0.871740\pi$
$877$	−4.19059e7			−1.83982			−0.919912	+	0.392125i	$0.871740\pi$
$878$	−4.08964e7			−1.79040
$879$	2.59092e7	−	1.48330e7i	1.13105	−	0.647527i
$880$		−	1.31092e7i		−	0.570648i
$881$	−2.28985e7			−0.993955			−0.496977	−	0.867764i	$-0.665557\pi$
$881$	−2.28985e7			−0.993955			−0.496977	+	0.867764i	$0.665557\pi$
$882$	2.21116e7	−	5.39583e6i	0.957081	−	0.233554i
$883$	−5.01973e6			−0.216660			−0.108330	−	0.994115i	$-0.534550\pi$
$883$	−5.01973e6			−0.216660			−0.108330	+	0.994115i	$0.534550\pi$
$884$			1.04089e6i			0.0447994i
$885$	2.49983e7	−	1.43116e7i	1.07288	−	0.614227i
$886$	−4.96739e6			−0.212590
$887$	1.26497e6			0.0539846			0.0269923	−	0.999636i	$-0.491407\pi$
$887$	1.26497e6			0.0539846			0.0269923	+	0.999636i	$0.491407\pi$
$888$	5.90205e6	+	1.03092e7i	0.251171	+	0.438727i
$889$	3.58402e6	−	1.45282e6i	0.152095	−	0.0616534i
$890$		−	1.63804e7i		−	0.693184i
$891$	1.47303e7	−	8.22060e6i	0.621610	−	0.346904i
$892$		−	318112.i		−	0.0133865i
$893$			1.99589e6i			0.0837545i
$894$	−3.61029e7	+	2.06689e7i	−1.51077	+	0.864916i
$895$		−	2.61539e7i		−	1.09139i
$896$	8.60848e6	+	2.12366e7i	0.358226	+	0.883722i
$897$	−1.94901e7	+	1.11581e7i	−0.808786	+	0.463031i
$898$	2.64650e7			1.09517
$899$	−1.47460e6			−0.0608521
$900$	−114696.	+	195357.i	−0.00472000	+	0.00803937i
$901$		−	2.91123e7i		−	1.19472i
$902$	2.62548e7			1.07447
$903$	−6.37076e6	+	8.11234e6i	−0.259999	+	0.331075i
$904$	3.04198e7			1.23804
$905$		−	2.84441e7i		−	1.15444i
$906$	−2.23053e6	−	3.89612e6i	−0.0902792	−	0.157693i
$907$	−1.39026e7			−0.561148			−0.280574	−	0.959832i	$-0.590525\pi$
$907$	−1.39026e7			−0.561148			−0.280574	+	0.959832i	$0.590525\pi$
$908$	−673123.			−0.0270944
$909$	−2.31932e6	+	3.95041e6i	−0.0931005	+	0.158574i
$910$	−3.53223e7	+	1.43182e7i	−1.41399	+	0.573173i
$911$			3.48951e7i			1.39306i	0.717530	+	0.696528i	$0.245273\pi$
$911$			3.48951e7i			1.39306i	−0.717530	+	0.696528i	$0.754727\pi$
$912$	−866087.	−	1.51281e6i	−0.0344806	−	0.0602280i
$913$			6.56014e6i			0.260457i
$914$		−	1.75355e7i		−	0.694308i
$915$	1.32282e7	+	2.31059e7i	0.522332	+	0.912368i
$916$		−	184649.i		−	0.00727125i
$917$	9.08714e6	−	3.68356e6i	0.356865	−	0.144659i
$918$	−2.04259e7	−	223341.i	−0.799973	−	0.00874705i
$919$	2.31882e7			0.905686			0.452843	−	0.891590i	$-0.350410\pi$
$919$	2.31882e7			0.905686			0.452843	+	0.891590i	$0.350410\pi$
$920$	1.07076e7			0.417085
$921$	1.01811e6	+	1.77836e6i	0.0395500	+	0.0690828i
$922$			1.66363e7i			0.644509i
$923$	4.97779e7			1.92324
$924$	−427867.	−	336011.i	−0.0164865	−	0.0129471i
$925$	−4.10653e6			−0.157805
$926$		−	1.32771e7i		−	0.508834i
$927$	−7.12921e6	−	4.18563e6i	−0.272485	−	0.159979i
$928$	−203975.			−0.00777512
$929$	−1.35101e7			−0.513595			−0.256797	−	0.966465i	$-0.582667\pi$
$929$	−1.35101e7			−0.513595			−0.256797	+	0.966465i	$0.582667\pi$
$930$	−8.59036e6	+	4.91799e6i	−0.325690	+	0.186458i
$931$	1.31796e6	+	1.35854e6i	0.0498341	+	0.0513686i
$932$		−	946780.i		−	0.0357034i
$933$	−6.04751e6	+	3.46221e6i	−0.227443	+	0.130211i
$934$			2.99236e7i			1.12240i
$935$		−	1.27749e7i		−	0.477892i
$936$	2.57832e7	−	4.39155e7i	0.961940	−	1.63843i
$937$			1.67971e7i			0.625008i	0.949916	+	0.312504i	$0.101168\pi$
$937$			1.67971e7i			0.625008i	−0.949916	+	0.312504i	$0.898832\pi$
$938$	−9.39643e6	−	2.31805e7i	−0.348703	−	0.860231i
$939$	−1.63946e6	−	2.86367e6i	−0.0606786	−	0.105989i
$940$	771789.			0.0284891
$941$	1.19282e7			0.439136			0.219568	−	0.975597i	$-0.429535\pi$
$941$	1.19282e7			0.439136			0.219568	+	0.975597i	$0.429535\pi$
$942$	−1.62690e7	+	9.31404e6i	−0.597358	+	0.341988i
$943$			2.08131e7i			0.762178i
$944$	−3.97034e7			−1.45010
$945$	8.29522e6	+	2.11243e7i	0.302168	+	0.769491i
$946$	−8.12596e6			−0.295221
$947$			1.48015e7i			0.536329i	0.963373	+	0.268164i	$0.0864170\pi$
$947$			1.48015e7i			0.536329i	−0.963373	+	0.268164i	$0.913583\pi$
$948$	−506917.	+	290210.i	−0.0183196	+	0.0104880i
$949$	−3.62159e7			−1.30537
$950$	620907.			0.0223212
$951$	7.12548e6	+	1.24462e7i	0.255483	+	0.446258i
$952$	8.65174e6	+	2.13433e7i	0.309393	+	0.763256i
$953$		−	1.39997e7i		−	0.499327i	−0.968333	−	0.249664i	$-0.919680\pi$
$953$		−	1.39997e7i		−	0.499327i	0.968333	−	0.249664i	$-0.0803201\pi$
$954$	−2.06281e7	+	3.51350e7i	−0.733819	+	1.24988i
$955$			2.72034e7i			0.965195i
$956$			171161.i			0.00605703i
$957$	−2.31143e6	+	1.32329e6i	−0.0815831	+	0.0467064i
$958$			7.42624e6i			0.261430i
$959$	1.45032e6	+	3.57785e6i	0.0509233	+	0.125625i
$960$	−2.10535e7	+	1.20532e7i	−0.737303	+	0.422107i
$961$	2.25502e7			0.787666
$962$	2.64067e7			0.919975
$963$	5.19199e6	+	3.04827e6i	0.180413	+	0.105922i
$964$			183071.i			0.00634492i
$965$	4.73937e6			0.163833
$966$	−8.77901e6	+	1.11789e7i	−0.302693	+	0.385441i
$967$	4.96805e7			1.70852			0.854260	−	0.519846i	$-0.174011\pi$
$967$	4.96805e7			1.70852			0.854260	+	0.519846i	$0.174011\pi$
$968$			1.45840e7i			0.500252i
$969$	−844006.	−	1.47424e6i	−0.0288759	−	0.0504382i
$970$	2.89465e7			0.987793
$971$	4.52830e7			1.54130			0.770649	−	0.637260i	$-0.219932\pi$
$971$	4.52830e7			1.54130			0.770649	+	0.637260i	$0.219932\pi$
$972$	−743163.	−	447316.i	−0.0252301	−	0.0151862i
$973$	−5.82980e6	−	1.43818e7i	−0.197411	−	0.487002i
$974$			2.15438e7i			0.727656i
$975$	8.74654e6	+	1.52778e7i	0.294663	+	0.514693i
$976$		−	3.66978e7i		−	1.23315i
$977$		−	349146.i		−	0.0117023i	−0.999983	−	0.00585114i	$-0.998138\pi$
$977$		−	349146.i		−	0.0117023i	0.999983	−	0.00585114i	$-0.00186249\pi$
$978$	−1.88700e6	−	3.29606e6i	−0.0630848	−	0.110192i
$979$		−	1.81696e7i		−	0.605882i
$980$	525332.	−	509639.i	0.0174730	−	0.0169511i
$981$	1.88159e7	−	3.20484e7i	0.624243	−	1.06325i
$982$	3.13104e7			1.03612
$983$	−4.78815e7			−1.58046			−0.790231	−	0.612809i	$-0.790039\pi$
$983$	−4.78815e7			−1.58046			−0.790231	+	0.612809i	$0.790039\pi$
$984$	−2.34482e7	−	4.09574e7i	−0.772007	−	1.34848i
$985$		−	3.06182e7i		−	1.00552i
$986$	3.22523e6			0.105650
$987$	−2.21208e7	+	2.81680e7i	−0.722783	+	0.920372i
$988$	121143.			0.00394828
$989$		−	6.44171e6i		−	0.209416i
$990$	−9.05195e6	+	1.54178e7i	−0.293531	+	0.499959i
$991$	−2.48785e7			−0.804711			−0.402356	−	0.915483i	$-0.631808\pi$
$991$	−2.48785e7			−0.804711			−0.402356	+	0.915483i	$0.631808\pi$
$992$	−840871.			−0.0271300
$993$	3.51421e7	−	2.01189e7i	1.13098	−	0.647487i
$994$	2.91975e7	−	1.18355e7i	0.937302	−	0.379945i
$995$			3.22391e7i			1.03235i
$996$	292743.	−	167595.i	0.00935056	−	0.00535320i
$997$			2.95568e7i			0.941714i	0.882209	+	0.470857i	$0.156055\pi$
$997$			2.95568e7i			0.941714i	−0.882209	+	0.470857i	$0.843945\pi$
$998$		−	5.91525e7i		−	1.87995i
$999$	171915.	−	1.57227e7i	0.00545004	−	0.498441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.c.a.20.10	yes	12
3.2	odd	2	inner	21.6.c.a.20.3	✓	12
4.3	odd	2		336.6.k.d.209.2		12
7.6	odd	2	inner	21.6.c.a.20.9	yes	12
12.11	even	2		336.6.k.d.209.12		12
21.20	even	2	inner	21.6.c.a.20.4	yes	12
28.27	even	2		336.6.k.d.209.11		12
84.83	odd	2		336.6.k.d.209.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.c.a.20.3	✓	12	3.2	odd	2	inner
21.6.c.a.20.4	yes	12	21.20	even	2	inner
21.6.c.a.20.9	yes	12	7.6	odd	2	inner
21.6.c.a.20.10	yes	12	1.1	even	1	trivial
336.6.k.d.209.1		12	84.83	odd	2
336.6.k.d.209.2		12	4.3	odd	2
336.6.k.d.209.11		12	28.27	even	2
336.6.k.d.209.12		12	12.11	even	2

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.57294i q^{2} +(13.5283 - 7.74498i) q^{3} +0.942331 q^{4} +46.2136 q^{5} +(43.1623 + 75.3925i) q^{6} +(-120.146 + 48.7024i) q^{7} +183.586i q^{8} +(123.031 - 209.553i) q^{9} +O(q^{10})\)	\(q+5.57294i q^{2} +(13.5283 - 7.74498i) q^{3} +0.942331 q^{4} +46.2136 q^{5} +(43.1623 + 75.3925i) q^{6} +(-120.146 + 48.7024i) q^{7} +183.586i q^{8} +(123.031 - 209.553i) q^{9} +257.545i q^{10} +285.677i q^{11} +(12.7482 - 7.29833i) q^{12} -1141.52i q^{13} +(-271.416 - 669.567i) q^{14} +(625.192 - 357.923i) q^{15} -992.957 q^{16} -967.641 q^{17} +(1167.83 + 685.643i) q^{18} +112.619i q^{19} +43.5485 q^{20} +(-1248.17 + 1589.39i) q^{21} -1592.06 q^{22} -1262.08i q^{23} +(1421.87 + 2483.61i) q^{24} -989.307 q^{25} +6361.65 q^{26} +(41.4161 - 3787.77i) q^{27} +(-113.217 + 45.8938i) q^{28} +598.083i q^{29} +(1994.68 + 3484.16i) q^{30} +2465.55i q^{31} +341.048i q^{32} +(2212.56 + 3864.73i) q^{33} -5392.61i q^{34} +(-5552.38 + 2250.71i) q^{35} +(115.936 - 197.468i) q^{36} +4150.91 q^{37} -627.618 q^{38} +(-8841.08 - 15442.9i) q^{39} +8484.15i q^{40} -16491.1 q^{41} +(-8857.58 - 6956.01i) q^{42} +5104.06 q^{43} +269.202i q^{44} +(5685.69 - 9684.19i) q^{45} +7033.48 q^{46} +17722.5 q^{47} +(-13433.0 + 7690.43i) q^{48} +(12063.2 - 11702.8i) q^{49} -5513.35i q^{50} +(-13090.6 + 7494.36i) q^{51} -1075.69i q^{52} +30085.8i q^{53} +(21109.0 + 230.810i) q^{54} +13202.1i q^{55} +(-8941.06 - 22057.1i) q^{56} +(872.230 + 1523.54i) q^{57} -3333.08 q^{58} +39985.0 q^{59} +(589.138 - 337.282i) q^{60} +36958.1i q^{61} -13740.4 q^{62} +(-4575.92 + 31168.9i) q^{63} -33675.3 q^{64} -52753.9i q^{65} +(-21537.9 + 12330.5i) q^{66} +34620.1 q^{67} -911.838 q^{68} +(-9774.75 - 17073.8i) q^{69} +(-12543.1 - 30943.1i) q^{70} +43606.5i q^{71} +(38470.9 + 22586.7i) q^{72} -31725.9i q^{73} +23132.8i q^{74} +(-13383.7 + 7662.16i) q^{75} +106.124i q^{76} +(-13913.1 - 34322.9i) q^{77} +(86062.4 - 49270.8i) q^{78} -39763.9 q^{79} -45888.1 q^{80} +(-28775.9 - 51562.9i) q^{81} -91904.0i q^{82} +22963.5 q^{83} +(-1176.19 + 1497.73i) q^{84} -44718.1 q^{85} +28444.6i q^{86} +(4632.14 + 8091.05i) q^{87} -52446.1 q^{88} -63601.9 q^{89} +(53969.4 + 31686.0i) q^{90} +(55595.0 + 137150. i) q^{91} -1189.29i q^{92} +(19095.6 + 33354.7i) q^{93} +98766.6i q^{94} +5204.52i q^{95} +(2641.41 + 4613.81i) q^{96} -112394. i q^{97} +(65219.0 + 67227.2i) q^{98} +(59864.4 + 35147.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9}+O(q^{10}) \) 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9	\( 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9} + 1392 q^{15} + 4868 q^{16} - 3804 q^{18} + 4116 q^{21} - 8752 q^{22} + 7812 q^{25} - 8204 q^{28} - 27876 q^{30} + 54864 q^{36} + 27464 q^{37} - 16080 q^{39} - 3444 q^{42} - 73840 q^{43} + 59144 q^{46} + 6972 q^{49} + 23760 q^{51} + 103968 q^{57} - 71512 q^{58} - 152676 q^{60} - 120624 q^{63} - 198788 q^{64} + 79344 q^{67} + 368760 q^{70} + 226644 q^{72} + 394644 q^{78} - 247104 q^{79} - 248868 q^{81} - 608076 q^{84} - 320112 q^{85} + 595456 q^{88} + 310128 q^{91} + 397272 q^{93} + 696576 q^{99}+O(q^{100}) \) 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9 + 1392 * q^15 + 4868 * q^16 - 3804 * q^18 + 4116 * q^21 - 8752 * q^22 + 7812 * q^25 - 8204 * q^28 - 27876 * q^30 + 54864 * q^36 + 27464 * q^37 - 16080 * q^39 - 3444 * q^42 - 73840 * q^43 + 59144 * q^46 + 6972 * q^49 + 23760 * q^51 + 103968 * q^57 - 71512 * q^58 - 152676 * q^60 - 120624 * q^63 - 198788 * q^64 + 79344 * q^67 + 368760 * q^70 + 226644 * q^72 + 394644 * q^78 - 247104 * q^79 - 248868 * q^81 - 608076 * q^84 - 320112 * q^85 + 595456 * q^88 + 310128 * q^91 + 397272 * q^93 + 696576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more