LMFDB - Embedded newform 21.6.c.a.20.3

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			20.3
Root			$-12.2117 + 5.57294i$ of defining polynomial
Character	$\chi$	$=$	21.20
Dual form			21.6.c.a.20.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.57294i q^{2} +(-13.5283 - 7.74498i) q^{3} +0.942331 q^{4} -46.2136 q^{5} +(-43.1623 + 75.3925i) q^{6} +(-120.146 + 48.7024i) q^{7} -183.586i q^{8} +(123.031 + 209.553i) q^{9} +O(q^{10})$	\(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} +(2002.57 + 271.667i) 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} +(1513.98 - 11160.2i) 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} +(-24987.4 - 19185.1i) 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} +(1887.09 + 256.000i) 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	$-0.836053\pi$
$2$		−	5.57294i		−	0.985166i	0.870265	−	0.492583i	$-0.163947\pi$
$3$	−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	$-0.635640\pi$
$5$	−46.2136			−0.826693			−0.413347	+	0.910574i	$0.635640\pi$
$6$	−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	$-0.884165\pi$
$11$		−	285.677i		−	0.711858i	0.934513	−	0.355929i	$-0.115835\pi$
$12$	−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	$-0.366912\pi$
$17$	967.641			0.812067			0.406034	+	0.913858i	$0.366912\pi$
$18$	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
$21$	2002.57	+	271.667i	0.990923	+	0.134427i
$22$	−1592.06			−0.701298
$23$			1262.08i			0.497469i	0.968572	+	0.248735i	$0.0800147\pi$
$23$			1262.08i			0.497469i	−0.968572	+	0.248735i	$0.919985\pi$
$24$	−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	$-0.978967\pi$
$29$		−	598.083i		−	0.132058i	0.997818	−	0.0660292i	$-0.0210331\pi$
$30$	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	$-0.222216\pi$
$41$	16491.1			1.53211			0.766056	+	0.642774i	$0.222216\pi$
$42$	1513.98	−	11160.2i	0.132433	−	0.976224i
$43$	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	$-0.698956\pi$
$47$	−17722.5			−1.17026			−0.585128	+	0.810941i	$0.698956\pi$
$48$	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	$-0.736900\pi$
$53$		−	30085.8i		−	1.47120i	0.677415	−	0.735601i	$-0.263100\pi$
$54$	−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	$-0.768850\pi$
$59$	−39985.0			−1.49543			−0.747717	+	0.664017i	$0.768850\pi$
$60$	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
$63$	−24987.4	−	19185.1i	−0.793176	−	0.608993i
$64$	−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	$-0.828421\pi$
$71$		−	43606.5i		−	1.02661i	0.858206	−	0.513305i	$-0.171579\pi$
$72$	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	$-0.558562\pi$
$83$	−22963.5			−0.365884			−0.182942	+	0.983124i	$0.558562\pi$
$84$	1887.09	+	256.000i	0.0291806	+	0.00395860i
$85$	−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	$-0.360076\pi$
$89$	63601.9			0.851128			0.425564	+	0.904928i	$0.360076\pi$
$90$	−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	$-0.470693\pi$
$101$	18851.6			0.183884			0.0919421	+	0.995764i	$0.470693\pi$
$102$	−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
$105$	−92546.0	−	12554.7i	−0.819190	−	0.111130i
$106$	−167667.			−1.44938
$107$		−	24776.5i		−	0.209209i	−0.994514	−	0.104605i	$-0.966642\pi$
$107$		−	24776.5i		−	0.209209i	0.994514	−	0.104605i	$-0.0333577\pi$
$108$	−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	$0.208978\pi$
$113$			165698.i			1.22074i	−0.792118	+	0.610368i	$0.791022\pi$
$114$	−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
$126$	−106917.	+	139253.i	−0.599959	+	0.781410i
$127$	−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	$-0.438329\pi$
$131$	75634.1			0.385070			0.192535	+	0.981290i	$0.438329\pi$
$132$	−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	$0.0215906\pi$
$137$			29779.1i			0.135554i	−0.997701	+	0.0677768i	$0.978409\pi$
$138$	−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
$147$	−253832.	+	64890.5i	−0.968842	+	0.247678i
$148$	3911.54			0.0146789
$149$		−	478865.i		−	1.76705i	−0.468388	−	0.883523i	$-0.655165\pi$
$149$		−	478865.i		−	1.76705i	0.468388	−	0.883523i	$-0.344835\pi$
$150$	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	$-0.275427\pi$
$167$	467393.			1.29685			0.648427	+	0.761277i	$0.275427\pi$
$168$	49874.1	−	367644.i	0.136333	−	1.00497i
$169$	−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	$-0.607575\pi$
$173$	−261040.			−0.663120			−0.331560	+	0.943434i	$0.607575\pi$
$174$	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	$0.229482\pi$
$179$			565935.i			1.32018i	−0.751186	+	0.660091i	$0.770518\pi$
$180$	−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
$189$	189449.	+	453068.i	0.385779	+	0.922591i
$190$	−29004.5			−0.0582882
$191$		−	588646.i		−	1.16754i	−0.811920	−	0.583769i	$-0.801578\pi$
$191$		−	588646.i		−	1.16754i	0.811920	−	0.583769i	$-0.198422\pi$
$192$	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	$0.208090\pi$
$197$			662538.i			1.21631i	−0.793818	+	0.608156i	$0.791910\pi$
$198$	−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
$210$	−69966.5	+	515753.i	−0.109482	+	0.807038i
$211$	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	$-0.347835\pi$
$227$	714316.			0.920081			0.460040	+	0.887898i	$0.347835\pi$
$228$	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
$231$	77608.8	−	572088.i	0.0956932	−	0.705396i
$232$	−109799.			−0.133931
$233$			1.00472e6i			1.21243i	0.795302	+	0.606214i	$0.207312\pi$
$233$			1.00472e6i			1.21243i	−0.795302	+	0.606214i	$0.792688\pi$
$234$	−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	$-0.967206\pi$
$239$		−	181636.i		−	0.205687i	0.994698	−	0.102843i	$-0.0327940\pi$
$240$	−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	$-0.304537\pi$
$251$	1.15023e6			1.15239			0.576195	+	0.817313i	$0.304537\pi$
$252$	−23546.4	−	18078.7i	−0.0233573	−	0.0179335i
$253$	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	$-0.384173\pi$
$257$	753698.			0.711810			0.355905	+	0.934522i	$0.384173\pi$
$258$	−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	$0.0915219\pi$
$263$			636200.i			0.567158i	−0.958949	+	0.283579i	$0.908478\pi$
$264$	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	$-0.624750\pi$
$269$	−906619.			−0.763914			−0.381957	+	0.924180i	$0.624750\pi$
$270$	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
$273$	310114.	−	2.28599e6i	0.251834	−	1.85638i
$274$	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	$-0.975975\pi$
$281$		−	199614.i		−	0.150808i	0.997153	−	0.0754040i	$-0.0240246\pi$
$282$	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	$-0.725921\pi$
$293$	−1.91518e6			−1.30329			−0.651645	+	0.758524i	$0.725921\pi$
$294$	361631.	+	1.41459e6i	0.244004	+	0.954471i
$295$	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	$-0.458169\pi$
$311$	447026.			0.262079			0.131039	+	0.991377i	$0.458169\pi$
$312$	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
$315$	1.15476e6	+	886610.i	0.655713	+	0.503450i
$316$	−37470.8			−0.0211094
$317$		−	920013.i		−	0.514216i	−0.966383	−	0.257108i	$-0.917230\pi$
$317$		−	920013.i		−	0.514216i	0.966383	−	0.257108i	$-0.0827697\pi$
$318$	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
$336$	−1.98847e6	−	269753.i	−0.960884	−	0.130352i
$337$	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	$-0.844623\pi$
$347$		−	2.10380e6i		−	0.937951i	0.883211	−	0.468975i	$-0.155377\pi$
$348$	−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	$-0.507235\pi$
$353$	−106417.			−0.0454541			−0.0227271	+	0.999742i	$0.507235\pi$
$354$	1.72585e6	−	3.01457e6i	0.731971	−	1.27855i
$355$			2.01521e6i			0.848692i
$356$	59934.0			0.0250639
$357$	1.93777e6	+	262876.i	0.804696	+	0.109164i
$358$	3.15392e6			1.30060
$359$		−	2.24142e6i		−	0.917882i	−0.888467	−	0.458941i	$-0.848229\pi$
$359$		−	2.24142e6i		−	0.917882i	0.888467	−	0.458941i	$-0.151771\pi$
$360$	−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
$378$	2.52492e6	−	1.05579e6i	0.908905	−	0.380057i
$379$	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	$-0.730257\pi$
$383$	−3.80041e6			−1.32384			−0.661918	+	0.749577i	$0.730257\pi$
$384$	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	$0.333561\pi$
$389$			5.17147e6i			1.73277i	−0.499380	+	0.866383i	$0.666439\pi$
$390$	−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
$399$	−30594.8	+	225527.i	−0.00962088	+	0.0709197i
$400$	982340.			0.306981
$401$		−	2.60526e6i		−	0.809079i	−0.914521	−	0.404539i	$-0.867432\pi$
$401$		−	2.60526e6i		−	0.809079i	0.914521	−	0.404539i	$-0.132568\pi$
$402$	−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	$-0.287836\pi$
$419$	4.44364e6			1.23653			0.618264	+	0.785971i	$0.287836\pi$
$420$	−87209.0	−	11830.7i	−0.0241234	−	0.00327255i
$421$	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	$0.0352284\pi$
$431$			851882.i			0.220895i	−0.993882	+	0.110448i	$0.964772\pi$
$432$	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
$441$	3.93650e6	+	1.08806e6i	0.963859	+	0.266415i
$442$	−6.15579e6			−1.49875
$443$		−	891340.i		−	0.215791i	−0.994162	−	0.107896i	$-0.965589\pi$
$443$		−	891340.i		−	0.215791i	0.994162	−	0.107896i	$-0.0344113\pi$
$444$	−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	$0.187599\pi$
$449$			4.74883e6i			1.11166i	−0.831297	+	0.555829i	$0.812401\pi$
$450$	−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	$-0.606074\pi$
$461$	−2.98519e6			−0.654213			−0.327107	+	0.944987i	$0.606074\pi$
$462$	−3.18822e6	−	432509.i	−0.694933	−	0.0942737i
$463$	−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	$-0.692921\pi$
$467$	−5.36944e6			−1.13930			−0.569648	+	0.821889i	$0.692921\pi$
$468$	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	$-0.542359\pi$
$479$	−1.33255e6			−0.265366			−0.132683	+	0.991158i	$0.542359\pi$
$480$	122069.	−	213221.i	0.0241826	−	0.0422402i
$481$		−	4.73837e6i		−	0.933827i
$482$	1.08268e6			0.212267
$483$	−342864.	+	2.52740e6i	−0.0668735	+	0.492954i
$484$	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	$0.176257\pi$
$491$			5.61830e6i			1.05172i	−0.850571	+	0.525861i	$0.823743\pi$
$492$	−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	$-0.754918\pi$
$503$	−8.14783e6			−1.43589			−0.717946	+	0.696098i	$0.754918\pi$
$504$	−3.52210e6	+	4.58733e6i	−0.617626	+	0.804421i
$505$	−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	$-0.286035\pi$
$509$	7.27954e6			1.24540			0.622701	+	0.782460i	$0.286035\pi$
$510$	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	$-0.438465\pi$
$521$	2.38061e6			0.384232			0.192116	+	0.981372i	$0.438465\pi$
$522$	−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
$525$	−1.98116e6	−	268762.i	−0.313705	−	0.0425568i
$526$	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
$546$	−1.27397e7	−	1.72825e6i	−1.82884	−	0.248099i
$547$	−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	$0.0696505\pi$
$557$			3.17885e6i			0.434143i	−0.976156	+	0.217071i	$0.930350\pi$
$558$	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	$-0.332234\pi$
$563$	7.56588e6			1.00598			0.502989	+	0.864293i	$0.332234\pi$
$564$	225929.	+	129345.i	0.0299072	+	0.0171219i
$565$		−	7.65750e6i		−	1.00917i
$566$	−9.63617e6			−1.26434
$567$	946071.	−	7.59653e6i	0.123585	−	0.992334i
$568$	−8.00554e6			−1.04116
$569$		−	4.34836e6i		−	0.563047i	−0.959554	−	0.281524i	$-0.909160\pi$
$569$		−	4.34836e6i		−	0.563047i	0.959554	−	0.281524i	$-0.0908397\pi$
$570$	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	$-0.270675\pi$
$587$	1.10150e7			1.31944			0.659721	+	0.751511i	$0.270675\pi$
$588$	−239194.	+	61148.3i	−0.0285303	+	0.00729359i
$589$	−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	$-0.484527\pi$
$593$	832174.			0.0971802			0.0485901	+	0.998819i	$0.484527\pi$
$594$	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	$-0.828656\pi$
$599$		−	9.00401e6i		−	1.02534i	0.858585	−	0.512671i	$-0.171344\pi$
$600$	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
$609$	162479.	−	1.19770e6i	0.0177523	−	0.130860i
$610$	−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	$0.0831795\pi$
$617$			4.88602e6i			0.516704i	−0.966051	+	0.258352i	$0.916821\pi$
$618$	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
$630$	4.94103e6	−	6.43539e6i	0.495982	−	0.645986i
$631$	−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	$0.0617974\pi$
$641$			4.01387e6i			0.385850i	−0.981214	+	0.192925i	$0.938203\pi$
$642$	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	$-0.204915\pi$
$647$	1.70332e7			1.59969			0.799846	+	0.600205i	$0.204915\pi$
$648$	9.46621e6	+	5.28284e6i	0.885602	+	0.494231i
$649$			1.14228e7i			1.06454i
$650$	6.29362e6			0.584275
$651$	−669807.	+	4.93744e6i	−0.0619437	+	0.456614i
$652$	−41197.5			−0.00379535
$653$			4.19237e6i			0.384748i	0.981322	+	0.192374i	$0.0616186\pi$
$653$			4.19237e6i			0.384748i	−0.981322	+	0.192374i	$0.938381\pi$
$654$	−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	$-0.839523\pi$
$659$		−	1.07708e7i		−	0.966131i	0.875584	−	0.483065i	$-0.160477\pi$
$660$	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
$672$	92651.4	−	682974.i	0.00791460	−	0.0583420i
$673$	−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	$-0.574494\pi$
$677$	−5.53094e6			−0.463796			−0.231898	+	0.972740i	$0.574494\pi$
$678$	−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	$-0.672504\pi$
$683$		−	2.08889e7i		−	1.71342i	0.515796	−	0.856712i	$-0.327496\pi$
$684$	−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
$693$	−5.48073e6	+	7.13832e6i	−0.433516	+	0.564628i
$694$	−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	$-0.964927\pi$
$701$		−	2.86133e6i		−	0.219924i	0.993936	−	0.109962i	$-0.0350729\pi$
$702$	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
$714$	1.46499e6	−	1.07991e7i	0.107545	−	0.792760i
$715$	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	$-0.583220\pi$
$719$	−7.16590e6			−0.516950			−0.258475	+	0.966018i	$0.583220\pi$
$720$	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
$735$	1.17305e7	−	2.99882e6i	0.800935	−	0.204754i
$736$	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	$0.366563\pi$
$743$			2.74896e7i			1.82683i	−0.407035	+	0.913413i	$0.633437\pi$
$744$	−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
$756$	178524.	+	426940.i	0.0113604	+	0.0271683i
$757$	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	$-0.352187\pi$
$761$	1.43097e7			0.895714			0.447857	+	0.894105i	$0.352187\pi$
$762$	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	$-0.682074\pi$
$773$	−1.79858e7			−1.08263			−0.541316	+	0.840819i	$0.682074\pi$
$774$	5.96065e6	−	3.49956e6i	0.357636	−	0.209972i
$775$		−	2.43918e6i		−	0.145878i
$776$	−2.06339e7			−1.23006
$777$	8.31251e6	+	1.12766e6i	0.493946	+	0.0670081i
$778$	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	$-0.547746\pi$
$797$	−5.35963e6			−0.298875			−0.149437	+	0.988771i	$0.547746\pi$
$798$	1.25685e6	+	170503.i	0.0698677	+	0.00947817i
$799$	−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	$-0.916056\pi$
$809$		−	9.70495e6i		−	0.521341i	0.965428	−	0.260671i	$-0.0839436\pi$
$810$	−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
$819$	−2.19002e7	+	2.85237e7i	−1.14088	+	1.48592i
$820$	−718163.			−0.0372982
$821$			8.98419e6i			0.465180i	0.972575	+	0.232590i	$0.0747200\pi$
$821$			8.98419e6i			0.465180i	−0.972575	+	0.232590i	$0.925280\pi$
$822$	−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	$-0.969837\pi$
$827$		−	3.72199e6i		−	0.189239i	0.995514	−	0.0946196i	$-0.0301635\pi$
$828$	−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	$-0.285643\pi$
$839$	2.54324e7			1.24733			0.623666	+	0.781691i	$0.285643\pi$
$840$	−2.30486e6	+	1.69901e7i	−0.112706	+	0.830803i
$841$	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	$-0.497157\pi$
$857$	384054.			0.0178624			0.00893120	+	0.999960i	$0.497157\pi$
$858$	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
$861$	3.30247e7	+	4.48009e6i	1.51821	+	0.205958i
$862$	4.74749e6			0.217618
$863$		−	3.11656e7i		−	1.42445i	−0.701950	−	0.712227i	$-0.747687\pi$
$863$		−	3.11656e7i		−	1.42445i	0.701950	−	0.712227i	$-0.252313\pi$
$864$	−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	$-0.334443\pi$
$881$	2.28985e7			0.993955			0.496977	+	0.867764i	$0.334443\pi$
$882$	6.06372e6	−	2.19379e7i	0.262463	−	0.949561i
$883$	−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	$-0.508593\pi$
$887$	−1.26497e6			−0.0539846			−0.0269923	+	0.999636i	$0.508593\pi$
$888$	−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
$903$	1.02212e7	+	1.38660e6i	0.417143	+	0.0565890i
$904$	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	$-0.754727\pi$
$911$		−	3.48951e7i		−	1.39306i	0.717530	−	0.696528i	$-0.245273\pi$
$912$	−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
$924$	73133.2	−	539097.i	0.00281796	−	0.0207724i
$925$	−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	$-0.417333\pi$
$929$	1.35101e7			0.513595			0.256797	+	0.966465i	$0.417333\pi$
$930$	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	$-0.570465\pi$
$941$	−1.19282e7			−0.439136			−0.219568	+	0.975597i	$0.570465\pi$
$942$	−1.62690e7	−	9.31404e6i	−0.597358	−	0.341988i
$943$			2.08131e7i			0.762178i
$944$	3.97034e7			1.45010
$945$	−8.75513e6	−	2.09379e7i	−0.318921	−	0.762700i
$946$	−8.12596e6			−0.295221
$947$		−	1.48015e7i		−	0.536329i	−0.963373	−	0.268164i	$-0.913583\pi$
$947$		−	1.48015e7i		−	0.536329i	0.963373	−	0.268164i	$-0.0864170\pi$
$948$	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	$0.0803201\pi$
$953$			1.39997e7i			0.499327i	−0.968333	+	0.249664i	$0.919680\pi$
$954$	−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
$966$	1.40851e7	+	1.91076e6i	0.485641	+	0.0658815i
$967$	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	$-0.780068\pi$
$971$	−4.52830e7			−1.54130			−0.770649	+	0.637260i	$0.780068\pi$
$972$	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	$0.00186249\pi$
$977$			349146.i			0.0117023i	−0.999983	+	0.00585114i	$0.998138\pi$
$978$	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	$-0.209961\pi$
$983$	4.78815e7			1.58046			0.790231	+	0.612809i	$0.209961\pi$
$984$	−2.34482e7	+	4.09574e7i	−0.772007	+	1.34848i
$985$		−	3.06182e7i		−	1.00552i
$986$	−3.22523e6			−0.105650
$987$	−3.54907e7	−	4.81462e6i	−1.15963	−	0.157315i
$988$	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.20.3	✓	12
3.2	odd	2	inner	21.6.c.a.20.10	yes	12
4.3	odd	2		336.6.k.d.209.12		12
7.6	odd	2	inner	21.6.c.a.20.4	yes	12
12.11	even	2		336.6.k.d.209.2		12
21.20	even	2	inner	21.6.c.a.20.9	yes	12
28.27	even	2		336.6.k.d.209.1		12
84.83	odd	2		336.6.k.d.209.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.c.a.20.3	✓	12	1.1	even	1	trivial
21.6.c.a.20.4	yes	12	7.6	odd	2	inner
21.6.c.a.20.9	yes	12	21.20	even	2	inner
21.6.c.a.20.10	yes	12	3.2	odd	2	inner
336.6.k.d.209.1		12	28.27	even	2
336.6.k.d.209.2		12	12.11	even	2
336.6.k.d.209.11		12	84.83	odd	2
336.6.k.d.209.12		12	4.3	odd	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} +(2002.57 + 271.667i) 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} +(1513.98 - 11160.2i) 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} +(-24987.4 - 19185.1i) 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} +(1887.09 + 256.000i) 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

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