LMFDB - Embedded newform 63.6.e.f.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} + 187x^{10} + 25399x^{8} + 1518438x^{6} + 66232188x^{4} + 1297462320x^{2} + 18380851776 $ x^12 + 187x^10 + 25399x^8 + 1518438x^6 + 66232188x^4 + 1297462320*x^2 + 18380851776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.4
Root			$2.44476 + 4.23445i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.f.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44476 + 4.23445i) q^{2} +(4.04630 - 7.00840i) q^{4} +(-21.3752 - 37.0229i) q^{5} +(43.2256 + 122.223i) q^{7} +196.034 q^{8} +O(q^{10})$	\(q+(2.44476 + 4.23445i) q^{2} +(4.04630 - 7.00840i) q^{4} +(-21.3752 - 37.0229i) q^{5} +(43.2256 + 122.223i) q^{7} +196.034 q^{8} +(104.514 - 181.024i) q^{10} +(355.439 - 615.638i) q^{11} +885.624 q^{13} +(-411.872 + 481.843i) q^{14} +(349.773 + 605.825i) q^{16} +(-350.659 + 607.359i) q^{17} +(627.946 + 1087.63i) q^{19} -345.962 q^{20} +3475.85 q^{22} +(-523.092 - 906.022i) q^{23} +(648.701 - 1123.58i) q^{25} +(2165.14 + 3750.13i) q^{26} +(1031.49 + 191.611i) q^{28} -6150.88 q^{29} +(-1147.12 + 1986.87i) q^{31} +(1426.31 - 2470.45i) q^{32} -3429.10 q^{34} +(3601.11 - 4212.89i) q^{35} +(-202.054 - 349.968i) q^{37} +(-3070.35 + 5318.01i) q^{38} +(-4190.26 - 7257.74i) q^{40} +17891.4 q^{41} -14604.8 q^{43} +(-2876.43 - 4982.11i) q^{44} +(2557.67 - 4430.01i) q^{46} +(-10568.6 - 18305.4i) q^{47} +(-13070.1 + 10566.3i) q^{49} +6343.67 q^{50} +(3583.50 - 6206.80i) q^{52} +(53.6064 - 92.8490i) q^{53} -30390.3 q^{55} +(8473.66 + 23959.9i) q^{56} +(-15037.4 - 26045.6i) q^{58} +(-22249.4 + 38537.1i) q^{59} +(11606.2 + 20102.5i) q^{61} -11217.7 q^{62} +36333.5 q^{64} +(-18930.4 - 32788.4i) q^{65} +(3335.66 - 5777.53i) q^{67} +(2837.74 + 4915.11i) q^{68} +(26643.1 + 4949.23i) q^{70} -25110.5 q^{71} +(-4737.49 + 8205.57i) q^{73} +(987.948 - 1711.18i) q^{74} +10163.4 q^{76} +(90609.5 + 16831.6i) q^{77} +(13238.1 + 22929.0i) q^{79} +(14953.0 - 25899.3i) q^{80} +(43740.2 + 75760.2i) q^{82} +7494.03 q^{83} +29981.6 q^{85} +(-35705.3 - 61843.3i) q^{86} +(69678.0 - 120686. i) q^{88} +(16085.6 + 27861.2i) q^{89} +(38281.6 + 108244. i) q^{91} -8466.35 q^{92} +(51675.5 - 89504.7i) q^{94} +(26845.0 - 46496.8i) q^{95} -155070. q^{97} +(-76695.9 - 29512.5i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) $ 12 * q - 182 * q^4 + 142 * q^7	$ 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) $ 12 * q - 182 * q^4 + 142 * q^7 + 686 * q^10 + 308 * q^13 - 1898 * q^16 + 9422 * q^19 - 18292 * q^22 - 7526 * q^25 + 37074 * q^28 + 23422 * q^31 - 55608 * q^34 - 18182 * q^37 + 69258 * q^40 - 87372 * q^43 + 25332 * q^46 + 30354 * q^49 + 34272 * q^52 - 96320 * q^55 - 89782 * q^58 - 16156 * q^61 + 380580 * q^64 + 144650 * q^67 - 187262 * q^70 - 100058 * q^73 - 685440 * q^76 + 101994 * q^79 + 75712 * q^82 + 602352 * q^85 + 752310 * q^88 - 282306 * q^91 - 120456 * q^94 - 866096 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.44476	+	4.23445i	0.432177	+	0.748552i	0.997060	−	0.0766186i	$-0.0244124\pi$
$2$	2.44476	+	4.23445i	0.432177	+	0.748552i	−0.564884	+	0.825170i	$0.691079\pi$
$3$		0			0
$3$		0			0
$4$	4.04630	−	7.00840i	0.126447	−	0.219012i
$5$	−21.3752	−	37.0229i	−0.382371	−	0.662286i	0.609029	−	0.793148i	$-0.291559\pi$
$5$	−21.3752	−	37.0229i	−0.382371	−	0.662286i	−0.991401	+	0.130861i	$0.958226\pi$
$6$		0			0
$7$	43.2256	+	122.223i	0.333423	+	0.942777i
$7$	43.2256	+	122.223i	0.333423	+	0.942777i
$8$	196.034			1.08294
$9$		0			0
$10$	104.514	−	181.024i	0.330504	−	0.572449i
$11$	355.439	−	615.638i	0.885693	−	1.53407i	0.0407765	−	0.999168i	$-0.487017\pi$
$11$	355.439	−	615.638i	0.885693	−	1.53407i	0.844917	−	0.534898i	$-0.179650\pi$
$12$		0			0
$13$	885.624			1.45342			0.726709	−	0.686945i	$-0.241049\pi$
$13$	885.624			1.45342			0.726709	+	0.686945i	$0.241049\pi$
$14$	−411.872	+	481.843i	−0.561620	+	0.657031i
$15$		0			0
$16$	349.773	+	605.825i	0.341576	+	0.591626i
$17$	−350.659	+	607.359i	−0.294281	+	0.509710i	−0.974817	−	0.223005i	$-0.928413\pi$
$17$	−350.659	+	607.359i	−0.294281	+	0.509710i	0.680536	+	0.732714i	$0.261747\pi$
$18$		0			0
$19$	627.946	+	1087.63i	0.399060	+	0.691192i	0.993610	−	0.112866i	$-0.0360031\pi$
$19$	627.946	+	1087.63i	0.399060	+	0.691192i	−0.594550	+	0.804059i	$0.702670\pi$
$20$	−345.962			−0.193399
$21$		0			0
$22$	3475.85			1.53110
$23$	−523.092	−	906.022i	−0.206186	−	0.357124i	0.744324	−	0.667818i	$-0.232772\pi$
$23$	−523.092	−	906.022i	−0.206186	−	0.357124i	−0.950510	+	0.310694i	$0.899438\pi$
$24$		0			0
$25$	648.701	−	1123.58i	0.207584	−	0.359547i
$26$	2165.14	+	3750.13i	0.628134	+	1.08796i
$27$		0			0
$28$	1031.49	+	191.611i	0.248640	+	0.0461875i
$29$	−6150.88			−1.35813			−0.679067	−	0.734077i	$-0.737615\pi$
$29$	−6150.88			−1.35813			−0.679067	+	0.734077i	$0.737615\pi$
$30$		0			0
$31$	−1147.12	+	1986.87i	−0.214390	+	0.371334i	−0.953084	−	0.302707i	$-0.902110\pi$
$31$	−1147.12	+	1986.87i	−0.214390	+	0.371334i	0.738694	+	0.674041i	$0.235443\pi$
$32$	1426.31	−	2470.45i	0.246229	−	0.426482i
$33$		0			0
$34$	−3429.10			−0.508725
$35$	3601.11	−	4212.89i	0.496897	−	0.581312i
$36$		0			0
$37$	−202.054	−	349.968i	−0.0242641	−	0.0420266i	0.853638	−	0.520866i	$-0.174391\pi$
$37$	−202.054	−	349.968i	−0.0242641	−	0.0420266i	−0.877902	+	0.478839i	$0.841058\pi$
$38$	−3070.35	+	5318.01i	−0.344929	+	0.597434i
$39$		0			0
$40$	−4190.26	−	7257.74i	−0.414086	−	0.717218i
$41$	17891.4			1.66221			0.831103	−	0.556119i	$-0.187710\pi$
$41$	17891.4			1.66221			0.831103	+	0.556119i	$0.187710\pi$
$42$		0			0
$43$	−14604.8			−1.20455			−0.602275	−	0.798289i	$-0.705739\pi$
$43$	−14604.8			−1.20455			−0.602275	+	0.798289i	$0.705739\pi$
$44$	−2876.43	−	4982.11i	−0.223986	−	0.387956i
$45$		0			0
$46$	2557.67	−	4430.01i	0.178217	−	0.308681i
$47$	−10568.6	−	18305.4i	−0.697870	−	1.20875i	−0.969204	−	0.246260i	$-0.920798\pi$
$47$	−10568.6	−	18305.4i	−0.697870	−	1.20875i	0.271334	−	0.962485i	$-0.412535\pi$
$48$		0			0
$49$	−13070.1	+	10566.3i	−0.777658	+	0.628687i
$50$	6343.67			0.358852
$51$		0			0
$52$	3583.50	−	6206.80i	0.183780	−	0.318317i
$53$	53.6064	−	92.8490i	0.00262136	−	0.00454033i	−0.864712	−	0.502268i	$-0.832499\pi$
$53$	53.6064	−	92.8490i	0.00262136	−	0.00454033i	0.867333	+	0.497728i	$0.165832\pi$
$54$		0			0
$55$	−30390.3			−1.35465
$56$	8473.66	+	23959.9i	0.361078	+	1.02097i
$57$		0			0
$58$	−15037.4	−	26045.6i	−0.586953	−	1.01663i
$59$	−22249.4	+	38537.1i	−0.832124	+	1.44128i	0.0642267	+	0.997935i	$0.479542\pi$
$59$	−22249.4	+	38537.1i	−0.832124	+	1.44128i	−0.896351	+	0.443346i	$0.853791\pi$
$60$		0			0
$61$	11606.2	+	20102.5i	0.399360	+	0.691712i	0.993647	−	0.112541i	$-0.0358990\pi$
$61$	11606.2	+	20102.5i	0.399360	+	0.691712i	−0.594287	+	0.804253i	$0.702566\pi$
$62$	−11217.7			−0.370617
$63$		0			0
$64$	36333.5			1.10881
$65$	−18930.4	−	32788.4i	−0.555746	−	0.962580i
$66$		0			0
$67$	3335.66	−	5777.53i	0.0907809	−	0.157237i	−0.817059	−	0.576554i	$-0.804397\pi$
$67$	3335.66	−	5777.53i	0.0907809	−	0.157237i	0.907840	+	0.419317i	$0.137730\pi$
$68$	2837.74	+	4915.11i	0.0744218	+	0.128902i
$69$		0			0
$70$	26643.1	+	4949.23i	0.649890	+	0.120724i
$71$	−25110.5			−0.591166			−0.295583	−	0.955317i	$-0.595514\pi$
$71$	−25110.5			−0.591166			−0.295583	+	0.955317i	$0.595514\pi$
$72$		0			0
$73$	−4737.49	+	8205.57i	−0.104050	+	0.180219i	−0.913350	−	0.407176i	$-0.866513\pi$
$73$	−4737.49	+	8205.57i	−0.104050	+	0.180219i	0.809300	+	0.587396i	$0.199847\pi$
$74$	987.948	−	1711.18i	0.0209727	−	0.0363258i
$75$		0			0
$76$	10163.4			0.201840
$77$	90609.5	+	16831.6i	1.74159	+	0.323519i
$78$		0			0
$79$	13238.1	+	22929.0i	0.238647	+	0.413349i	0.960326	−	0.278879i	$-0.0899627\pi$
$79$	13238.1	+	22929.0i	0.238647	+	0.413349i	−0.721679	+	0.692228i	$0.756629\pi$
$80$	14953.0	−	25899.3i	0.261217	−	0.452442i
$81$		0			0
$82$	43740.2	+	75760.2i	0.718366	+	1.24425i
$83$	7494.03			0.119404			0.0597022	−	0.998216i	$-0.480985\pi$
$83$	7494.03			0.119404			0.0597022	+	0.998216i	$0.480985\pi$
$84$		0			0
$85$	29981.6			0.450098
$86$	−35705.3	−	61843.3i	−0.520578	−	0.901668i
$87$		0			0
$88$	69678.0	−	120686.i	0.959155	−	1.66131i
$89$	16085.6	+	27861.2i	0.215260	+	0.372841i	0.953353	−	0.301858i	$-0.0976067\pi$
$89$	16085.6	+	27861.2i	0.215260	+	0.372841i	−0.738093	+	0.674699i	$0.764273\pi$
$90$		0			0
$91$	38281.6	+	108244.i	0.484603	+	1.37025i
$92$	−8466.35			−0.104286
$93$		0			0
$94$	51675.5	−	89504.7i	0.603206	−	1.04478i
$95$	26845.0	−	46496.8i	0.305178	−	0.528584i
$96$		0			0
$97$	−155070.			−1.67340			−0.836699	−	0.547664i	$-0.815517\pi$
$97$	−155070.			−1.67340			−0.836699	+	0.547664i	$0.815517\pi$
$98$	−76695.9	−	29512.5i	−0.806691	−	0.310414i
$99$		0			0
$100$	−5249.68	−	9092.71i	−0.0524968	−	0.0909271i
$101$	−55960.9	+	96927.1i	−0.545860	+	0.945457i	0.452692	+	0.891667i	$0.350464\pi$
$101$	−55960.9	+	96927.1i	−0.545860	+	0.945457i	−0.998552	+	0.0537904i	$0.982870\pi$
$102$		0			0
$103$	30342.1	+	52554.1i	0.281808	+	0.488105i	0.971830	−	0.235683i	$-0.0757326\pi$
$103$	30342.1	+	52554.1i	0.281808	+	0.488105i	−0.690022	+	0.723788i	$0.742399\pi$
$104$	173612.			1.57397
$105$		0			0
$106$	524.219			0.00453156
$107$	56266.4	+	97456.3i	0.475105	+	0.822906i	0.999593	−	0.0285115i	$-0.00907672\pi$
$107$	56266.4	+	97456.3i	0.475105	+	0.822906i	−0.524488	+	0.851418i	$0.675743\pi$
$108$		0			0
$109$	3811.67	−	6602.01i	0.0307291	−	0.0532243i	−0.850252	−	0.526376i	$-0.823550\pi$
$109$	3811.67	−	6602.01i	0.0307291	−	0.0532243i	0.880981	+	0.473152i	$0.156884\pi$
$110$	−74297.0	−	128686.i	−0.585450	−	1.01403i
$111$		0			0
$112$	−58926.9	+	68937.6i	−0.443883	+	0.519291i
$113$	−41498.7			−0.305730			−0.152865	−	0.988247i	$-0.548850\pi$
$113$	−41498.7			−0.305730			−0.152865	+	0.988247i	$0.548850\pi$
$114$		0			0
$115$	−22362.4	+	38732.8i	−0.157679	+	0.273108i
$116$	−24888.3	+	43107.8i	−0.171732	+	0.297448i
$117$		0			0
$118$	−217578.			−1.43850
$119$	−89390.8	−	16605.3i	−0.578663	−	0.107493i
$120$		0			0
$121$	−172148.	−	298170.i	−1.06891	−	1.85140i
$122$	−56748.6	+	98291.5i	−0.345188	+	0.597883i
$123$		0			0
$124$	9283.17	+	16078.9i	0.0542178	+	0.0939080i
$125$	−189060.			−1.08224
$126$		0			0
$127$	94796.7			0.521535			0.260768	−	0.965402i	$-0.416024\pi$
$127$	94796.7			0.521535			0.260768	+	0.965402i	$0.416024\pi$
$128$	43184.6	+	74797.9i	0.232972	+	0.403519i
$129$		0			0
$130$	92560.5	−	160319.i	0.480360	−	0.832009i
$131$	105547.	+	182814.i	0.537365	+	0.930744i	0.999045	+	0.0436972i	$0.0139137\pi$
$131$	105547.	+	182814.i	0.537365	+	0.930744i	−0.461679	+	0.887047i	$0.652753\pi$
$132$		0			0
$133$	−105791.	+	123763.i	−0.518585	+	0.606684i
$134$	32619.5			0.156934
$135$		0			0
$136$	−68740.8	+	119063.i	−0.318689	+	0.551986i
$137$	48096.6	−	83305.7i	0.218934	−	0.379204i	−0.735549	−	0.677472i	$-0.763076\pi$
$137$	48096.6	−	83305.7i	0.218934	−	0.379204i	0.954482	+	0.298268i	$0.0964088\pi$
$138$		0			0
$139$	−401994.			−1.76475			−0.882375	−	0.470548i	$-0.844056\pi$
$139$	−401994.			−1.76475			−0.882375	+	0.470548i	$0.844056\pi$
$140$	−14954.4	−	42284.6i	−0.0644835	−	0.182332i
$141$		0			0
$142$	−61389.1	−	106329.i	−0.255488	−	0.442518i
$143$	314785.	−	545224.i	1.28728	−	2.22964i
$144$		0			0
$145$	131476.	+	227724.i	0.519311	+	0.899474i
$146$	−46328.1			−0.179871
$147$		0			0
$148$	−3270.29			−0.0122725
$149$	−37650.0	−	65211.8i	−0.138931	−	0.240636i	0.788161	−	0.615469i	$-0.211033\pi$
$149$	−37650.0	−	65211.8i	−0.138931	−	0.240636i	−0.927092	+	0.374833i	$0.877700\pi$
$150$		0			0
$151$	245297.	−	424867.i	0.875488	−	1.51639i	0.0192454	−	0.999815i	$-0.493874\pi$
$151$	245297.	−	424867.i	0.875488	−	1.51639i	0.856242	−	0.516574i	$-0.172793\pi$
$152$	123098.	+	213213.i	0.432159	+	0.748522i
$153$		0			0
$154$	150246.	+	424830.i	0.510505	+	1.44349i
$155$	98079.6			0.327906
$156$		0			0
$157$	230508.	−	399251.i	0.746339	−	1.29270i	−0.203228	−	0.979132i	$-0.565143\pi$
$157$	230508.	−	399251.i	0.746339	−	1.29270i	0.949567	−	0.313566i	$-0.101524\pi$
$158$	−64727.7	+	112112.i	−0.206276	+	0.357280i
$159$		0			0
$160$	−121951.			−0.376604
$161$	88126.1	−	103097.i	0.267941	−	0.313461i
$162$		0			0
$163$	239222.	+	414344.i	0.705232	+	1.22150i	0.966608	+	0.256260i	$0.0824904\pi$
$163$	239222.	+	414344.i	0.705232	+	1.22150i	−0.261376	+	0.965237i	$0.584176\pi$
$164$	72393.9	−	125390.i	0.210181	−	0.364043i
$165$		0			0
$166$	18321.1	+	31733.1i	0.0516038	+	0.0893803i
$167$	−498852.			−1.38414			−0.692070	−	0.721830i	$-0.743301\pi$
$167$	−498852.			−1.38414			−0.692070	+	0.721830i	$0.743301\pi$
$168$		0			0
$169$	413036.			1.11243
$170$	73297.8	+	126956.i	0.194522	+	0.336922i
$171$		0			0
$172$	−59095.5	+	102356.i	−0.152312	+	0.263811i
$173$	−130322.	−	225724.i	−0.331056	−	0.573405i	0.651663	−	0.758508i	$-0.274072\pi$
$173$	−130322.	−	225724.i	−0.331056	−	0.573405i	−0.982719	+	0.185103i	$0.940738\pi$
$174$		0			0
$175$	165369.	+	30718.9i	0.408186	+	0.0758248i
$176$	497292.			1.21012
$177$		0			0
$178$	−78651.1	+	136228.i	−0.186061	+	0.322267i
$179$	−266709.	+	461954.i	−0.622164	+	1.07762i	0.366918	+	0.930253i	$0.380413\pi$
$179$	−266709.	+	461954.i	−0.622164	+	1.07762i	−0.989082	+	0.147367i	$0.952920\pi$
$180$		0			0
$181$	185798.			0.421546			0.210773	−	0.977535i	$-0.432402\pi$
$181$	185798.			0.421546			0.210773	+	0.977535i	$0.432402\pi$
$182$	−364764.	+	426732.i	−0.816269	+	0.954941i
$183$		0			0
$184$	−102544.	−	177611.i	−0.223287	−	0.386745i
$185$	−8637.90	+	14961.3i	−0.0185558	+	0.0321395i
$186$		0			0
$187$	249275.	+	431758.i	0.521285	+	0.902893i
$188$	−171055.			−0.352974
$189$		0			0
$190$	262518.			0.527564
$191$	354418.	+	613871.i	0.702964	+	1.21757i	0.967421	+	0.253171i	$0.0814736\pi$
$191$	354418.	+	613871.i	0.702964	+	1.21757i	−0.264458	+	0.964397i	$0.585193\pi$
$192$		0			0
$193$	361752.	−	626573.i	0.699065	−	1.21082i	−0.269726	−	0.962937i	$-0.586933\pi$
$193$	361752.	−	626573.i	0.699065	−	1.21082i	0.968791	−	0.247879i	$-0.0797337\pi$
$194$	−379109.	−	656637.i	−0.723203	−	1.25262i
$195$		0			0
$196$	21167.6	+	134355.i	0.0393578	+	0.249812i
$197$	−147313.			−0.270443			−0.135222	−	0.990815i	$-0.543175\pi$
$197$	−147313.			−0.270443			−0.135222	+	0.990815i	$0.543175\pi$
$198$		0			0
$199$	−710.490	+	1230.60i	−0.00127182	+	0.00220285i	−0.866661	−	0.498898i	$-0.833738\pi$
$199$	−710.490	+	1230.60i	−0.00127182	+	0.00220285i	0.865389	+	0.501101i	$0.167071\pi$
$200$	127167.	−	220260.i	0.224802	−	0.389368i
$201$		0			0
$202$	−547244.			−0.943632
$203$	−265875.	−	751782.i	−0.452833	−	1.28042i
$204$		0			0
$205$	−382432.	−	662392.i	−0.635579	−	1.10086i
$206$	−148358.	+	256964.i	−0.243581	+	0.421895i
$207$		0			0
$208$	309768.	+	536533.i	0.496452	+	0.859881i
$209$	892786.			1.41378
$210$		0			0
$211$	−30296.2			−0.0468470			−0.0234235	−	0.999726i	$-0.507457\pi$
$211$	−30296.2			−0.0468470			−0.0234235	+	0.999726i	$0.507457\pi$
$212$	−433.815	−	751.389i	−0.000662926	−	0.00114822i
$213$		0			0
$214$	−275116.	+	476514.i	−0.410659	+	0.711281i
$215$	312181.	+	540713.i	0.460585	+	0.797757i
$216$		0			0
$217$	−292427.	−	54321.2i	−0.421568	−	0.0783106i
$218$	37274.5			0.0531215
$219$		0			0
$220$	−122968.	+	212987.i	−0.171292	+	0.296686i
$221$	−310552.	+	537891.i	−0.427714	+	0.740822i
$222$		0			0
$223$	−147864.			−0.199114			−0.0995570	−	0.995032i	$-0.531743\pi$
$223$	−147864.			−0.199114			−0.0995570	+	0.995032i	$0.531743\pi$
$224$	363599.	+	67542.4i	0.484176	+	0.0899407i
$225$		0			0
$226$	−101454.	−	175724.i	−0.132129	−	0.228855i
$227$	406723.	−	704464.i	0.523882	−	0.907391i	−0.475731	−	0.879591i	$-0.657817\pi$
$227$	406723.	−	704464.i	0.523882	−	0.907391i	0.999614	−	0.0277999i	$-0.00885012\pi$
$228$		0			0
$229$	−641094.	−	1.11041e6i	−0.807854	−	1.39924i	−0.914347	−	0.404931i	$-0.867295\pi$
$229$	−641094.	−	1.11041e6i	−0.807854	−	1.39924i	0.106493	−	0.994313i	$-0.466038\pi$
$230$	−218683.			−0.272581
$231$		0			0
$232$	−1.20578e6			−1.47078
$233$	−617850.	−	1.07015e6i	−0.745578	−	1.29138i	−0.949924	−	0.312481i	$-0.898840\pi$
$233$	−617850.	−	1.07015e6i	−0.745578	−	1.29138i	0.204346	−	0.978899i	$-0.434493\pi$
$234$		0			0
$235$	−451813.	+	782564.i	−0.533691	+	0.924379i
$236$	180055.	+	311865.i	0.210439	+	0.364491i
$237$		0			0
$238$	−148225.	−	419117.i	−0.169621	−	0.479615i
$239$	−874240.			−0.990001			−0.495001	−	0.868893i	$-0.664832\pi$
$239$	−874240.			−0.990001			−0.495001	+	0.868893i	$0.664832\pi$
$240$		0			0
$241$	489805.	−	848367.i	0.543226	−	0.940895i	−0.455490	−	0.890241i	$-0.650536\pi$
$241$	489805.	−	848367.i	0.543226	−	0.940895i	0.998716	−	0.0506545i	$-0.0161307\pi$
$242$	841722.	−	1.45791e6i	0.923912	−	1.60026i
$243$		0			0
$244$	187848.			0.201991
$245$	670573.	+	258036.i	0.713725	+	0.274641i
$246$		0			0
$247$	556124.	+	963235.i	0.580002	+	1.00459i
$248$	−224874.	+	389493.i	−0.232172	+	0.402133i
$249$		0			0
$250$	−462205.	−	800563.i	−0.467719	−	0.810113i
$251$	213005.			0.213406			0.106703	−	0.994291i	$-0.465971\pi$
$251$	213005.			0.213406			0.106703	+	0.994291i	$0.465971\pi$
$252$		0			0
$253$	−743709.			−0.730469
$254$	231755.	+	401412.i	0.225395	+	0.390396i
$255$		0			0
$256$	370184.	−	641177.i	0.353035	−	0.611474i
$257$	789506.	+	1.36746e6i	0.745629	+	1.29147i	0.949900	+	0.312553i	$0.101184\pi$
$257$	789506.	+	1.36746e6i	0.745629	+	1.29147i	−0.204272	+	0.978914i	$0.565483\pi$
$258$		0			0
$259$	34040.4	−	39823.3i	0.0315315	−	0.0368883i
$260$	−306392.			−0.281089
$261$		0			0
$262$	−516076.	+	893871.i	−0.464473	+	0.804492i
$263$	144544.	−	250357.i	0.128857	−	0.223188i	−0.794377	−	0.607425i	$-0.792202\pi$
$263$	144544.	−	250357.i	0.128857	−	0.223188i	0.923234	+	0.384238i	$0.125536\pi$
$264$		0			0
$265$	−4583.39			−0.00400933
$266$	−782703.	−	145395.i	−0.678255	−	0.125993i
$267$		0			0
$268$	−26994.2	−	46755.2i	−0.0229579	−	0.0397643i
$269$	−1.02244e6	+	1.77092e6i	−0.861506	+	1.49217i	0.00896851	+	0.999960i	$0.497145\pi$
$269$	−1.02244e6	+	1.77092e6i	−0.861506	+	1.49217i	−0.870475	+	0.492213i	$0.836188\pi$
$270$		0			0
$271$	302981.	+	524779.i	0.250607	+	0.434063i	0.963693	−	0.267013i	$-0.0860366\pi$
$271$	302981.	+	524779.i	0.250607	+	0.434063i	−0.713086	+	0.701076i	$0.752703\pi$
$272$	−490604.			−0.402077
$273$		0			0
$274$	470338.			0.378472
$275$	−461147.	−	798731.i	−0.367712	−	0.636896i
$276$		0			0
$277$	−611375.	+	1.05893e6i	−0.478750	+	0.829219i	−0.999703	−	0.0243664i	$-0.992243\pi$
$277$	−611375.	+	1.05893e6i	−0.478750	+	0.829219i	0.520953	+	0.853585i	$0.325576\pi$
$278$	−982780.	−	1.70222e6i	−0.762683	−	1.32101i
$279$		0			0
$280$	705939.	−	825867.i	0.538111	−	0.629528i
$281$	−639205.			−0.482919			−0.241460	−	0.970411i	$-0.577626\pi$
$281$	−639205.			−0.482919			−0.241460	+	0.970411i	$0.577626\pi$
$282$		0			0
$283$	−236827.	+	410197.i	−0.175779	+	0.304457i	−0.940430	−	0.339986i	$-0.889578\pi$
$283$	−236827.	+	410197.i	−0.175779	+	0.304457i	0.764652	+	0.644444i	$0.222911\pi$
$284$	−101605.	+	175984.i	−0.0747511	+	0.129473i
$285$		0			0
$286$	3.07830e6			2.22533
$287$	773365.	+	2.18675e6i	0.554217	+	1.56709i
$288$		0			0
$289$	464006.	+	803681.i	0.326797	+	0.566030i
$290$	−642856.	+	1.11346e6i	−0.448868	+	0.777463i
$291$		0			0
$292$	38338.6	+	66404.3i	0.0263135	+	0.0455763i
$293$	829294.			0.564338			0.282169	−	0.959365i	$-0.408946\pi$
$293$	829294.			0.564338			0.282169	+	0.959365i	$0.408946\pi$
$294$		0			0
$295$	1.90234e6			1.27272
$296$	−39609.4	−	68605.5i	−0.0262766	−	0.0455124i
$297$		0			0
$298$	184091.	−	318854.i	0.120086	−	0.207994i
$299$	−463263.	−	802394.i	−0.299674	−	0.519051i
$300$		0			0
$301$	−631301.	−	1.78505e6i	−0.401625	−	1.13562i
$302$	2.39877e6			1.51346
$303$		0			0
$304$	−439278.	+	760851.i	−0.272618	+	0.472189i
$305$	496169.	−	859390.i	0.305408	−	0.528981i
$306$		0			0
$307$	1.63715e6			0.991385			0.495693	−	0.868498i	$-0.334914\pi$
$307$	1.63715e6			0.991385			0.495693	+	0.868498i	$0.334914\pi$
$308$	484596.	−	566921.i	0.291074	−	0.340522i
$309$		0			0
$310$	239781.	+	415313.i	0.141713	+	0.245455i
$311$	303729.	−	526074.i	0.178068	−	0.308422i	−0.763151	−	0.646220i	$-0.776349\pi$
$311$	303729.	−	526074.i	0.178068	−	0.308422i	0.941219	+	0.337798i	$0.109682\pi$
$312$		0			0
$313$	−789012.	−	1.36661e6i	−0.455222	−	0.788467i	0.543479	−	0.839423i	$-0.317107\pi$
$313$	−789012.	−	1.36661e6i	−0.455222	−	0.788467i	−0.998701	+	0.0509555i	$0.983773\pi$
$314$	2.25414e6			1.29020
$315$		0			0
$316$	214261.			0.120705
$317$	−1.09343e6	−	1.89387e6i	−0.611142	−	1.05853i	−0.991048	−	0.133505i	$-0.957377\pi$
$317$	−1.09343e6	−	1.89387e6i	−0.611142	−	1.05853i	0.379906	−	0.925025i	$-0.375956\pi$
$318$		0			0
$319$	−2.18626e6	+	3.78672e6i	−1.20289	+	2.08347i
$320$	−776635.	−	1.34517e6i	−0.423977	−	0.734349i
$321$		0			0
$322$	652008.	+	121117.i	0.350439	+	0.0650977i
$323$	−880779.			−0.469743
$324$		0			0
$325$	574505.	−	995072.i	0.301707	−	0.522572i
$326$	−1.16968e6	+	2.02595e6i	−0.609569	+	1.05580i
$327$		0			0
$328$	3.50731e6			1.80007
$329$	1.78051e6	−	2.08300e6i	0.906892	−	1.06096i
$330$		0			0
$331$	1.38434e6	+	2.39775e6i	0.694503	+	1.20291i	0.970348	+	0.241712i	$0.0777090\pi$
$331$	1.38434e6	+	2.39775e6i	0.694503	+	1.20291i	−0.275845	+	0.961202i	$0.588958\pi$
$332$	30323.1	−	52521.1i	0.0150983	−	0.0261510i
$333$		0			0
$334$	−1.21957e6	−	2.11236e6i	−0.598193	−	1.03610i
$335$	−285202.			−0.138848
$336$		0			0
$337$	−2.45187e6			−1.17604			−0.588021	−	0.808846i	$-0.700093\pi$
$337$	−2.45187e6			−1.17604			−0.588021	+	0.808846i	$0.700093\pi$
$338$	1.00977e6	+	1.74898e6i	0.480765	+	0.832709i
$339$		0			0
$340$	121315.	−	210123.i	0.0569135	−	0.0985771i
$341$	815461.	+	1.41242e6i	0.379767	+	0.657776i
$342$		0			0
$343$	−1.85642e6	−	1.14074e6i	−0.852001	−	0.523540i
$344$	−2.86303e6			−1.30446
$345$		0			0
$346$	637210.	−	1.10368e6i	0.286149	−	0.495625i
$347$	−740499.	+	1.28258e6i	−0.330142	+	0.571823i	−0.982539	−	0.186054i	$-0.940430\pi$
$347$	−740499.	+	1.28258e6i	−0.330142	+	0.571823i	0.652398	+	0.757877i	$0.273763\pi$
$348$		0			0
$349$	−1.28643e6			−0.565357			−0.282678	−	0.959215i	$-0.591223\pi$
$349$	−1.28643e6			−0.565357			−0.282678	+	0.959215i	$0.591223\pi$
$350$	274209.	+	775345.i	0.119650	+	0.338318i
$351$		0			0
$352$	−1.01393e6	−	1.75619e6i	−0.436167	−	0.755464i
$353$	1.12562e6	−	1.94963e6i	0.480790	−	0.832752i	−0.518967	−	0.854794i	$-0.673683\pi$
$353$	1.12562e6	−	1.94963e6i	0.480790	−	0.832752i	0.999757	+	0.0220418i	$0.00701668\pi$
$354$		0			0
$355$	536742.	+	929664.i	0.226045	+	0.391521i
$356$	260349.			0.108876
$357$		0			0
$358$	−2.60816e6			−1.07554
$359$	−362932.	−	628617.i	−0.148624	−	0.257424i	0.782095	−	0.623159i	$-0.214151\pi$
$359$	−362932.	−	628617.i	−0.148624	−	0.257424i	−0.930719	+	0.365735i	$0.880818\pi$
$360$		0			0
$361$	449417.	−	778413.i	0.181502	−	0.314371i
$362$	454232.	+	786753.i	0.182182	+	0.315549i
$363$		0			0
$364$	913515.	+	169695.i	0.361378	+	0.0671298i
$365$	405059.			0.159142
$366$		0			0
$367$	−1.71382e6	+	2.96843e6i	−0.664202	+	1.15043i	0.315298	+	0.948993i	$0.397895\pi$
$367$	−1.71382e6	+	2.96843e6i	−0.664202	+	1.15043i	−0.979501	+	0.201440i	$0.935438\pi$
$368$	365927.	−	633805.i	0.140856	−	0.243970i
$369$		0			0
$370$	−84470.4			−0.0320775
$371$	13665.5	+	2538.50i	0.00515454	+	0.000957509i
$372$		0			0
$373$	546522.	+	946604.i	0.203393	+	0.352287i	0.949619	−	0.313405i	$-0.101470\pi$
$373$	546522.	+	946604.i	0.203393	+	0.352287i	−0.746227	+	0.665692i	$0.768136\pi$
$374$	−1.21884e6	+	2.11109e6i	−0.450575	+	0.780418i
$375$		0			0
$376$	−2.07181e6	−	3.58847e6i	−0.755753	−	1.30900i
$377$	−5.44737e6			−1.97394
$378$		0			0
$379$	−2.92579e6			−1.04627			−0.523137	−	0.852249i	$-0.675238\pi$
$379$	−2.92579e6			−1.04627			−0.523137	+	0.852249i	$0.675238\pi$
$380$	−217245.	−	376280.i	−0.0771777	−	0.133676i
$381$		0			0
$382$	−1.73294e6	+	3.00153e6i	−0.607609	+	1.05241i
$383$	−51966.3	−	90008.2i	−0.0181019	−	0.0313534i	0.856833	−	0.515595i	$-0.172429\pi$
$383$	−51966.3	−	90008.2i	−0.0181019	−	0.0313534i	−0.874934	+	0.484241i	$0.839096\pi$
$384$		0			0
$385$	−1.31364e6	−	3.71441e6i	−0.451673	−	1.27714i
$386$	3.53759e6			1.20848
$387$		0			0
$388$	−627460.	+	1.08679e6i	−0.211596	+	0.366495i
$389$	86465.6	−	149763.i	0.0289714	−	0.0501799i	−0.851176	−	0.524880i	$-0.824110\pi$
$389$	86465.6	−	149763.i	0.0289714	−	0.0501799i	0.880148	+	0.474700i	$0.157443\pi$
$390$		0			0
$391$	733707.			0.242706
$392$	−2.56218e6	+	2.07136e6i	−0.842159	+	0.680832i
$393$		0			0
$394$	−360146.	−	623791.i	−0.116879	−	0.202441i
$395$	565932.	−	980224.i	0.182504	−	0.316106i
$396$		0			0
$397$	−1.29983e6	−	2.25137e6i	−0.413913	−	0.716918i	0.581401	−	0.813617i	$-0.302505\pi$
$397$	−1.29983e6	−	2.25137e6i	−0.413913	−	0.716918i	−0.995314	+	0.0966990i	$0.969172\pi$
$398$	−6947.91			−0.00219860
$399$		0			0
$400$	907594.			0.283623
$401$	1.72506e6	+	2.98789e6i	0.535726	+	0.927904i	0.999128	+	0.0417559i	$0.0132952\pi$
$401$	1.72506e6	+	2.98789e6i	0.535726	+	0.927904i	−0.463402	+	0.886148i	$0.653371\pi$
$402$		0			0
$403$	−1.01592e6	+	1.75962e6i	−0.311598	+	0.539704i
$404$	452869.	+	784392.i	0.138045	+	0.239100i
$405$		0			0
$406$	2.53338e6	−	2.96376e6i	0.762755	−	0.892335i
$407$	−287272.			−0.0859621
$408$		0			0
$409$	721374.	−	1.24946e6i	0.213232	−	0.369329i	−0.739492	−	0.673165i	$-0.764934\pi$
$409$	721374.	−	1.24946e6i	0.213232	−	0.369329i	0.952724	+	0.303837i	$0.0982677\pi$
$410$	1.86991e6	−	3.23878e6i	0.549365	−	0.951528i
$411$		0			0
$412$	491093.			0.142535
$413$	−5.67187e6	−	1.05361e6i	−1.63626	−	0.303952i
$414$		0			0
$415$	−160186.	−	277451.i	−0.0456568	−	0.0790799i
$416$	1.26318e6	−	2.18789e6i	0.357874	−	0.619857i
$417$		0			0
$418$	2.18265e6	+	3.78046e6i	0.611002	+	1.05829i
$419$	5.10039e6			1.41928			0.709641	−	0.704564i	$-0.248857\pi$
$419$	5.10039e6			1.41928			0.709641	+	0.704564i	$0.248857\pi$
$420$		0			0
$421$	5.08241e6			1.39754			0.698771	−	0.715346i	$-0.253731\pi$
$421$	5.08241e6			1.39754			0.698771	+	0.715346i	$0.253731\pi$
$422$	−74066.9	−	128288.i	−0.0202462	−	0.0350674i
$423$		0			0
$424$	10508.6	−	18201.5i	0.00283878	−	0.00491692i
$425$	454945.	+	787988.i	0.122176	+	0.211616i
$426$		0			0
$427$	−1.95531e6	+	2.28749e6i	−0.518974	+	0.607140i
$428$	910683.			0.240302
$429$		0			0
$430$	−1.52641e6	+	2.64383e6i	−0.398109	+	0.689544i
$431$	1.23720e6	−	2.14290e6i	0.320810	−	0.555659i	−0.659845	−	0.751401i	$-0.729378\pi$
$431$	1.23720e6	−	2.14290e6i	0.320810	−	0.555659i	0.980655	+	0.195742i	$0.0627115\pi$
$432$		0			0
$433$	−331952.			−0.0850855			−0.0425428	−	0.999095i	$-0.513546\pi$
$433$	−331952.			−0.0850855			−0.0425428	+	0.999095i	$0.513546\pi$
$434$	−484892.	−	1.37107e6i	−0.123572	−	0.349409i
$435$		0			0
$436$	−30846.3	−	53427.4i	−0.00777119	−	0.0134601i
$437$	656947.	−	1.13787e6i	0.164561	−	0.285028i
$438$		0			0
$439$	2.05610e6	+	3.56127e6i	0.509193	+	0.881948i	0.999943	+	0.0106480i	$0.00338942\pi$
$439$	2.05610e6	+	3.56127e6i	0.509193	+	0.881948i	−0.490750	+	0.871300i	$0.663277\pi$
$440$	−5.95752e6			−1.46701
$441$		0			0
$442$	−3.03690e6			−0.739391
$443$	2.92674e6	+	5.06927e6i	0.708558	+	1.22726i	0.965392	+	0.260802i	$0.0839871\pi$
$443$	2.92674e6	+	5.06927e6i	0.708558	+	1.22726i	−0.256835	+	0.966455i	$0.582680\pi$
$444$		0			0
$445$	687668.	−	1.19108e6i	0.164619	−	0.285128i
$446$	−361493.	−	626124.i	−0.0860524	−	0.149047i
$447$		0			0
$448$	1.57053e6	+	4.44080e6i	0.369702	+	1.04536i
$449$	3.86497e6			0.904754			0.452377	−	0.891827i	$-0.350576\pi$
$449$	3.86497e6			0.904754			0.452377	+	0.891827i	$0.350576\pi$
$450$		0			0
$451$	6.35930e6	−	1.10146e7i	1.47220	−	2.54993i
$452$	−167916.	+	290839.i	−0.0386586	+	0.0669586i
$453$		0			0
$454$	3.97736e6			0.905638
$455$	3.18923e6	−	3.73103e6i	0.722200	−	0.844891i
$456$		0			0
$457$	2.69523e6	+	4.66828e6i	0.603678	+	1.04560i	0.992259	+	0.124186i	$0.0396321\pi$
$457$	2.69523e6	+	4.66828e6i	0.603678	+	1.04560i	−0.388581	+	0.921415i	$0.627035\pi$
$458$	3.13464e6	−	5.42936e6i	0.698271	−	1.20944i
$459$		0			0
$460$	180970.	+	313449.i	0.0398760	+	0.0690673i
$461$	−1.17429e6			−0.257350			−0.128675	−	0.991687i	$-0.541072\pi$
$461$	−1.17429e6			−0.257350			−0.128675	+	0.991687i	$0.541072\pi$
$462$		0			0
$463$	4.03702e6			0.875203			0.437601	−	0.899169i	$-0.355828\pi$
$463$	4.03702e6			0.875203			0.437601	+	0.899169i	$0.355828\pi$
$464$	−2.15141e6	−	3.72636e6i	−0.463905	−	0.803507i
$465$		0			0
$466$	3.02099e6	−	5.23251e6i	0.644443	−	1.11621i
$467$	718550.	+	1.24456e6i	0.152463	+	0.264074i	0.932132	−	0.362118i	$-0.117946\pi$
$467$	718550.	+	1.24456e6i	0.152463	+	0.264074i	−0.779669	+	0.626191i	$0.784613\pi$
$468$		0			0
$469$	850335.	+	157959.i	0.178508	+	0.0331597i
$470$	−4.41830e6			−0.922594
$471$		0			0
$472$	−4.36163e6	+	7.55456e6i	−0.901143	+	1.56082i
$473$	−5.19112e6	+	8.99129e6i	−1.06686	+	1.84786i
$474$		0			0
$475$	1.62940e6			0.331355
$476$	−478078.	+	559296.i	−0.0967123	+	0.113142i
$477$		0			0
$478$	−2.13731e6	−	3.70192e6i	−0.427855	−	0.741067i
$479$	−1.18608e6	+	2.05436e6i	−0.236198	+	0.409107i	−0.959620	−	0.281299i	$-0.909235\pi$
$479$	−1.18608e6	+	2.05436e6i	−0.236198	+	0.409107i	0.723422	+	0.690406i	$0.242568\pi$
$480$		0			0
$481$	−178944.	−	309940.i	−0.0352659	−	0.0610823i
$482$	4.78982e6			0.939079
$483$		0			0
$484$	−2.78625e6			−0.540639
$485$	3.31466e6	+	5.74116e6i	0.639859	+	1.10827i
$486$		0			0
$487$	−334534.	+	579430.i	−0.0639172	+	0.110708i	−0.896213	−	0.443624i	$-0.853693\pi$
$487$	−334534.	+	579430.i	−0.0639172	+	0.110708i	0.832296	+	0.554332i	$0.187026\pi$
$488$	2.27520e6	+	3.94076e6i	0.432484	+	0.749084i
$489$		0			0
$490$	546751.	+	3.47034e6i	0.102873	+	0.652954i
$491$	−9.58134e6			−1.79359			−0.896794	−	0.442448i	$-0.854110\pi$
$491$	−9.58134e6			−1.79359			−0.896794	+	0.442448i	$0.854110\pi$
$492$		0			0
$493$	2.15686e6	−	3.73579e6i	0.399673	−	0.692254i
$494$	−2.71918e6	+	4.70976e6i	−0.501326	+	0.868322i
$495$		0			0
$496$	−1.60493e6			−0.292921
$497$	−1.08541e6	−	3.06909e6i	−0.197108	−	0.557338i
$498$		0			0
$499$	1.08902e6	+	1.88625e6i	0.195788	+	0.339115i	0.947159	−	0.320766i	$-0.103940\pi$
$499$	1.08902e6	+	1.88625e6i	0.195788	+	0.339115i	−0.751370	+	0.659881i	$0.770607\pi$
$500$	−764991.	+	1.32500e6i	−0.136846	+	0.237024i
$501$		0			0
$502$	520746.	+	901959.i	0.0922289	+	0.159745i
$503$	−5.11108e6			−0.900726			−0.450363	−	0.892846i	$-0.648705\pi$
$503$	−5.11108e6			−0.900726			−0.450363	+	0.892846i	$0.648705\pi$
$504$		0			0
$505$	4.78470e6			0.834885
$506$	−1.81819e6	−	3.14920e6i	−0.315692	−	0.546794i
$507$		0			0
$508$	383576.	−	664373.i	0.0659465	−	0.114223i
$509$	−3.54335e6	−	6.13725e6i	−0.606204	−	1.04998i	−0.991860	−	0.127334i	$-0.959358\pi$
$509$	−3.54335e6	−	6.13725e6i	−0.606204	−	1.04998i	0.385656	−	0.922643i	$-0.373975\pi$
$510$		0			0
$511$	−1.20769e6	−	224341.i	−0.204599	−	0.0380064i
$512$	6.38385e6			1.07624
$513$		0			0
$514$	−3.86031e6	+	6.68624e6i	−0.644487	+	1.11628i
$515$	1.29714e6	−	2.24671e6i	0.215510	−	0.373275i
$516$		0			0
$517$	−1.50260e7			−2.47239
$518$	251850.	+	46783.8i	0.0412400	+	0.00766075i
$519$		0			0
$520$	−3.71099e6	−	6.42762e6i	−0.601841	−	1.04242i
$521$	1.72694e6	−	2.99114e6i	0.278729	−	0.482772i	−0.692340	−	0.721571i	$-0.743420\pi$
$521$	1.72694e6	−	2.99114e6i	0.278729	−	0.482772i	0.971069	+	0.238799i	$0.0767536\pi$
$522$		0			0
$523$	278599.	+	482548.i	0.0445375	+	0.0771413i	0.887435	−	0.460933i	$-0.152485\pi$
$523$	278599.	+	482548.i	0.0445375	+	0.0771413i	−0.842897	+	0.538074i	$0.819152\pi$
$524$	1.70831e6			0.271793
$525$		0			0
$526$	1.41350e6			0.222757
$527$	−804494.	−	1.39342e6i	−0.126182	−	0.218553i
$528$		0			0
$529$	2.67092e6	−	4.62617e6i	0.414975	−	0.718758i
$530$	−11205.3	−	19408.1i	−0.00173274	−	0.00300119i
$531$		0			0
$532$	439320.	+	1.24221e6i	0.0672979	+	0.190290i
$533$	1.58450e7			2.41588
$534$		0			0
$535$	2.40541e6	−	4.16629e6i	0.363333	−	0.629311i
$536$	653901.	−	1.13259e6i	0.0983106	−	0.170279i
$537$		0			0
$538$	−9.99851e6			−1.48929
$539$	1.85942e6	+	1.18021e7i	0.275681	+	1.74980i
$540$		0			0
$541$	−2.39364e6	−	4.14591e6i	−0.351614	−	0.609013i	0.634919	−	0.772579i	$-0.281034\pi$
$541$	−2.39364e6	−	4.14591e6i	−0.351614	−	0.609013i	−0.986532	+	0.163566i	$0.947700\pi$
$542$	−1.48143e6	+	2.56592e6i	−0.216613	+	0.375184i
$543$		0			0
$544$	1.00030e6	+	1.73257e6i	0.144921	+	0.251011i
$545$	−325901.			−0.0469997
$546$		0			0
$547$	2.30360e6			0.329184			0.164592	−	0.986362i	$-0.447369\pi$
$547$	2.30360e6			0.329184			0.164592	+	0.986362i	$0.447369\pi$
$548$	−389226.	−	674159.i	−0.0553669	−	0.0958984i
$549$		0			0
$550$	2.25479e6	−	3.90541e6i	0.317833	−	0.550503i
$551$	−3.86242e6	−	6.68991e6i	−0.541977	−	0.938732i
$552$		0			0
$553$	−2.23024e6	+	2.60912e6i	−0.310126	+	0.362811i
$554$	−5.97866e6			−0.827617
$555$		0			0
$556$	−1.62659e6	+	2.81734e6i	−0.223147	+	0.386502i
$557$	6.94253e6	−	1.20248e7i	0.948156	−	1.64225i	0.198851	−	0.980030i	$-0.436279\pi$
$557$	6.94253e6	−	1.20248e7i	0.948156	−	1.64225i	0.749305	−	0.662225i	$-0.230388\pi$
$558$		0			0
$559$	−1.29344e7			−1.75072
$560$	3.81185e6	+	708090.i	0.513648	+	0.0954154i
$561$		0			0
$562$	−1.56270e6	−	2.70668e6i	−0.208706	−	0.361490i
$563$	−1.97962e6	+	3.42880e6i	−0.263215	+	0.455902i	−0.967094	−	0.254417i	$-0.918116\pi$
$563$	−1.97962e6	+	3.42880e6i	−0.263215	+	0.455902i	0.703879	+	0.710320i	$0.251450\pi$
$564$		0			0
$565$	887042.	+	1.53640e6i	0.116902	+	0.202481i
$566$	−2.31595e6			−0.303870
$567$		0			0
$568$	−4.92250e6			−0.640199
$569$	−4.75540e6	−	8.23659e6i	−0.615752	−	1.06651i	−0.990252	−	0.139287i	$-0.955519\pi$
$569$	−4.75540e6	−	8.23659e6i	−0.615752	−	1.06651i	0.374500	−	0.927227i	$-0.377815\pi$
$570$		0			0
$571$	4.53978e6	−	7.86313e6i	0.582699	−	1.00926i	−0.412459	−	0.910976i	$-0.635330\pi$
$571$	4.53978e6	−	7.86313e6i	0.582699	−	1.00926i	0.995158	−	0.0982881i	$-0.0313367\pi$
$572$	−2.54743e6	−	4.41228e6i	−0.325546	−	0.563862i
$573$		0			0
$574$	−7.36897e6	+	8.62085e6i	−0.933528	+	1.09212i
$575$	−1.35732e6			−0.171204
$576$		0			0
$577$	1.79193e6	−	3.10371e6i	0.224069	−	0.388099i	−0.731971	−	0.681336i	$-0.761399\pi$
$577$	1.79193e6	−	3.10371e6i	0.224069	−	0.388099i	0.956040	+	0.293237i	$0.0947326\pi$
$578$	−2.26876e6	+	3.92962e6i	−0.282468	+	0.489250i
$579$		0			0
$580$	2.12797e6			0.262661
$581$	323934.	+	915945.i	0.0398121	+	0.112572i
$582$		0			0
$583$	−38107.6	−	66004.3i	−0.00464344	−	0.00804268i
$584$	−928706.	+	1.60857e6i	−0.112680	+	0.195167i
$585$		0			0
$586$	2.02742e6	+	3.51160e6i	0.243894	+	0.422436i
$587$	6.14848e6			0.736499			0.368250	−	0.929727i	$-0.379957\pi$
$587$	6.14848e6			0.736499			0.368250	+	0.929727i	$0.379957\pi$
$588$		0			0
$589$	−2.88131e6			−0.342218
$590$	4.65077e6	+	8.05536e6i	0.550040	+	0.952698i
$591$		0			0
$592$	141346.	−	244819.i	0.0165760	−	0.0287105i
$593$	6.64979e6	+	1.15178e7i	0.776554	+	1.34503i	0.933917	+	0.357490i	$0.116367\pi$
$593$	6.64979e6	+	1.15178e7i	0.776554	+	1.34503i	−0.157363	+	0.987541i	$0.550299\pi$
$594$		0			0
$595$	1.29597e6	+	3.66445e6i	0.150073	+	0.424343i
$596$	−609373.			−0.0702697
$597$		0			0
$598$	2.26513e6	−	3.92332e6i	0.259024	−	0.448643i
$599$	2.30732e6	−	3.99639e6i	0.262748	−	0.455094i	−0.704223	−	0.709979i	$-0.748704\pi$
$599$	2.30732e6	−	3.99639e6i	0.262748	−	0.455094i	0.966971	+	0.254885i	$0.0820377\pi$
$600$		0			0
$601$	8.17563e6			0.923284			0.461642	−	0.887066i	$-0.347260\pi$
$601$	8.17563e6			0.923284			0.461642	+	0.887066i	$0.347260\pi$
$602$	6.01532e6	−	7.03723e6i	0.676500	−	0.791426i
$603$		0			0
$604$	−1.98509e6	−	3.43828e6i	−0.221405	−	0.383485i
$605$	−7.35941e6	+	1.27469e7i	−0.817437	+	1.41584i
$606$		0			0
$607$	2.18494e6	+	3.78443e6i	0.240696	+	0.416897i	0.960913	−	0.276852i	$-0.0892911\pi$
$607$	2.18494e6	+	3.78443e6i	0.240696	+	0.416897i	−0.720217	+	0.693749i	$0.755958\pi$
$608$	3.58259e6			0.393041
$609$		0			0
$610$	4.85205e6			0.527960
$611$	−9.35983e6	−	1.62117e7i	−1.01430	−	1.75681i
$612$		0			0
$613$	−2.72460e6	+	4.71914e6i	−0.292854	+	0.507238i	−0.974483	−	0.224460i	$-0.927938\pi$
$613$	−2.72460e6	+	4.71914e6i	−0.292854	+	0.507238i	0.681629	+	0.731698i	$0.261272\pi$
$614$	4.00244e6	+	6.93243e6i	0.428453	+	0.742103i
$615$		0			0
$616$	1.77625e7	+	3.29957e6i	1.88605	+	0.350352i
$617$	−1.32758e7			−1.40394			−0.701969	−	0.712208i	$-0.747695\pi$
$617$	−1.32758e7			−1.40394			−0.701969	+	0.712208i	$0.747695\pi$
$618$		0			0
$619$	2.23142e6	−	3.86494e6i	0.234075	−	0.405430i	−0.724928	−	0.688824i	$-0.758127\pi$
$619$	2.23142e6	−	3.86494e6i	0.234075	−	0.405430i	0.959004	+	0.283394i	$0.0914605\pi$
$620$	396859.	−	687381.i	0.0414627	−	0.0718155i
$621$		0			0
$622$	2.97018e6			0.307827
$623$	−2.70997e6	+	3.17036e6i	−0.279734	+	0.327256i
$624$		0			0
$625$	2.01399e6	+	3.48834e6i	0.206233	+	0.357206i
$626$	3.85789e6	−	6.68206e6i	0.393472	−	0.681514i
$627$		0			0
$628$	−1.86541e6	−	3.23098e6i	−0.188744	−	0.326915i
$629$	283408.			0.0285618
$630$		0			0
$631$	8.00421e6			0.800286			0.400143	−	0.916453i	$-0.368960\pi$
$631$	8.00421e6			0.800286			0.400143	+	0.916453i	$0.368960\pi$
$632$	2.59510e6	+	4.49485e6i	0.258441	+	0.447634i
$633$		0			0
$634$	5.34634e6	−	9.26014e6i	0.528243	−	0.914943i
$635$	−2.02630e6	−	3.50965e6i	−0.199420	−	0.345406i
$636$		0			0
$637$	−1.15752e7	+	9.35780e6i	−1.13026	+	0.913746i
$638$	−2.13796e7			−2.07944
$639$		0			0
$640$	1.84616e6	−	3.19764e6i	0.178164	−	0.308588i
$641$	−1.94455e6	+	3.36806e6i	−0.186928	+	0.323768i	−0.944224	−	0.329303i	$-0.893186\pi$
$641$	−1.94455e6	+	3.36806e6i	−0.186928	+	0.323768i	0.757297	+	0.653071i	$0.226520\pi$
$642$		0			0
$643$	−1.77478e7			−1.69285			−0.846423	−	0.532511i	$-0.821249\pi$
$643$	−1.77478e7			−1.69285			−0.846423	+	0.532511i	$0.821249\pi$
$644$	−365962.	−	1.03479e6i	−0.0347714	−	0.0983186i
$645$		0			0
$646$	−2.15329e6	−	3.72961e6i	−0.203012	−	0.351627i
$647$	−4.36138e6	+	7.55413e6i	−0.409603	+	0.709453i	−0.994845	−	0.101405i	$-0.967666\pi$
$647$	−4.36138e6	+	7.55413e6i	−0.409603	+	0.709453i	0.585242	+	0.810858i	$0.300999\pi$
$648$		0			0
$649$	1.58166e7	+	2.73952e7i	1.47401	+	2.55307i
$650$	5.61811e6			0.521563
$651$		0			0
$652$	3.87185e6			0.356697
$653$	714958.	+	1.23834e6i	0.0656141	+	0.113647i	0.896966	−	0.442099i	$-0.145766\pi$
$653$	714958.	+	1.23834e6i	0.0656141	+	0.113647i	−0.831352	+	0.555746i	$0.812433\pi$
$654$		0			0
$655$	4.51220e6	−	7.81536e6i	0.410946	−	0.711780i
$656$	6.25793e6	+	1.08391e7i	0.567769	+	0.983404i
$657$		0			0
$658$	1.31733e7	+	2.44707e6i	1.18612	+	0.220334i
$659$	9.20182e6			0.825392			0.412696	−	0.910869i	$-0.364587\pi$
$659$	9.20182e6			0.825392			0.412696	+	0.910869i	$0.364587\pi$
$660$		0			0
$661$	−717566.	+	1.24286e6i	−0.0638790	+	0.110642i	−0.896196	−	0.443658i	$-0.853681\pi$
$661$	−717566.	+	1.24286e6i	−0.0638790	+	0.110642i	0.832317	+	0.554300i	$0.187014\pi$
$662$	−6.76878e6	+	1.17239e7i	−0.600296	+	1.03974i
$663$		0			0
$664$	1.46908e6			0.129308
$665$	6.84339e6	+	1.27123e6i	0.600091	+	0.111473i
$666$		0			0
$667$	3.21748e6	+	5.57283e6i	0.280028	+	0.485022i
$668$	−2.01850e6	+	3.49615e6i	−0.175020	+	0.303144i
$669$		0			0
$670$	−697249.	−	1.20767e6i	−0.0600069	−	0.103935i
$671$	1.65012e7			1.41484
$672$		0			0
$673$	2.10985e7			1.79562			0.897808	−	0.440388i	$-0.145159\pi$
$673$	2.10985e7			1.79562			0.897808	+	0.440388i	$0.145159\pi$
$674$	−5.99423e6	−	1.03823e7i	−0.508258	−	0.880328i
$675$		0			0
$676$	1.67127e6	−	2.89472e6i	0.140663	−	0.243635i
$677$	−1.16835e7	−	2.02364e7i	−0.979720	−	1.69692i	−0.663387	−	0.748276i	$-0.730882\pi$
$677$	−1.16835e7	−	2.02364e7i	−0.979720	−	1.69692i	−0.316333	−	0.948648i	$-0.602452\pi$
$678$		0			0
$679$	−6.70300e6	−	1.89532e7i	−0.557949	−	1.57764i
$680$	5.87740e6			0.487431
$681$		0			0
$682$	−3.98721e6	+	6.90606e6i	−0.328253	+	0.568551i
$683$	6.67445e6	−	1.15605e7i	0.547474	−	0.948253i	−0.450972	−	0.892538i	$-0.648923\pi$
$683$	6.67445e6	−	1.15605e7i	0.547474	−	0.948253i	0.998447	−	0.0557153i	$-0.0177439\pi$
$684$		0			0
$685$	−4.11229e6			−0.334856
$686$	291894.	−	1.06497e7i	0.0236818	−	0.864029i
$687$		0			0
$688$	−5.10838e6	−	8.84797e6i	−0.411445	−	0.712644i
$689$	47475.1	−	82229.2i	0.00380993	−	0.00659900i
$690$		0			0
$691$	−6.57343e6	−	1.13855e7i	−0.523717	−	0.907105i	−0.999619	−	0.0276066i	$-0.991211\pi$
$691$	−6.57343e6	−	1.13855e7i	−0.523717	−	0.907105i	0.475901	−	0.879499i	$-0.342122\pi$
$692$	−2.10928e6			−0.167444
$693$		0			0
$694$	−7.24137e6			−0.570718
$695$	8.59271e6	+	1.48830e7i	0.674789	+	1.16877i
$696$		0			0
$697$	−6.27377e6	+	1.08665e7i	−0.489155	+	0.847242i
$698$	−3.14501e6	−	5.44732e6i	−0.244334	−	0.423199i
$699$		0			0
$700$	884421.	−	1.03467e6i	0.0682204	−	0.0798100i
$701$	7.87304e6			0.605128			0.302564	−	0.953129i	$-0.402157\pi$
$701$	7.87304e6			0.605128			0.302564	+	0.953129i	$0.402157\pi$
$702$		0			0
$703$	253758.	−	439522.i	0.0193657	−	0.0335423i
$704$	1.29143e7	−	2.23683e7i	0.982065	−	1.70099i
$705$		0			0
$706$	1.10075e7			0.831144
$707$	−1.42657e7	−	2.65000e6i	−1.07336	−	0.199387i
$708$		0			0
$709$	7.47288e6	+	1.29434e7i	0.558306	+	0.967014i	0.997638	+	0.0686895i	$0.0218818\pi$
$709$	7.47288e6	+	1.29434e7i	0.558306	+	0.967014i	−0.439332	+	0.898325i	$0.644785\pi$
$710$	−2.62441e6	+	4.54561e6i	−0.195383	+	0.338413i
$711$		0			0
$712$	3.15333e6	+	5.46172e6i	0.233114	+	0.403766i
$713$	2.40019e6			0.176816
$714$		0			0
$715$	−2.69144e7			−1.96888
$716$	2.15837e6	+	3.73840e6i	0.157341	+	0.272523i
$717$		0			0
$718$	1.77456e6	−	3.07363e6i	0.128464	−	0.222506i
$719$	177912.	+	308153.i	0.0128347	+	0.0222303i	0.872371	−	0.488844i	$-0.162581\pi$
$719$	177912.	+	308153.i	0.0128347	+	0.0222303i	−0.859537	+	0.511074i	$0.829248\pi$
$720$		0			0
$721$	−5.11178e6	+	5.98020e6i	−0.366214	+	0.428428i
$722$	4.39487e6			0.313764
$723$		0			0
$724$	751795.	−	1.30215e6i	0.0533032	−	0.0923238i
$725$	−3.99009e6	+	6.91103e6i	−0.281927	+	0.488312i
$726$		0			0
$727$	−1.16451e7			−0.817160			−0.408580	−	0.912722i	$-0.633976\pi$
$727$	−1.16451e7			−0.817160			−0.408580	+	0.912722i	$0.633976\pi$
$728$	7.50447e6	+	2.12194e7i	0.524797	+	1.48390i
$729$		0			0
$730$	990272.	+	1.71520e6i	0.0687776	+	0.119126i
$731$	5.12130e6	−	8.87036e6i	0.354476	−	0.613971i
$732$		0			0
$733$	−7.84459e6	−	1.35872e7i	−0.539275	−	0.934052i	−0.998943	−	0.0459613i	$-0.985365\pi$
$733$	−7.84459e6	−	1.35872e7i	−0.539275	−	0.934052i	0.459668	−	0.888091i	$-0.347968\pi$
$734$	−1.67595e7			−1.14821
$735$		0			0
$736$	−2.98437e6			−0.203076
$737$	−2.37125e6	−	4.10712e6i	−0.160808	−	0.278528i
$738$		0			0
$739$	−7.48534e6	+	1.29650e7i	−0.504197	+	0.873295i	0.495791	+	0.868442i	$0.334878\pi$
$739$	−7.48534e6	+	1.29650e7i	−0.504197	+	0.873295i	−0.999988	+	0.00485312i	$0.998455\pi$
$740$	69903.1	+	121076.i	0.00469264	+	0.00812789i
$741$		0			0
$742$	22659.6	+	64071.8i	0.00151093	+	0.00427225i
$743$	1.51503e7			1.00682			0.503408	−	0.864049i	$-0.332079\pi$
$743$	1.51503e7			1.00682			0.503408	+	0.864049i	$0.332079\pi$
$744$		0			0
$745$	−1.60955e6	+	2.78783e6i	−0.106247	+	0.184025i
$746$	−2.67223e6	+	4.62844e6i	−0.175803	+	0.304500i
$747$		0			0
$748$	4.03457e6			0.263660
$749$	−9.47929e6	+	1.10897e7i	−0.617406	+	0.722294i
$750$		0			0
$751$	−1.06857e7	−	1.85082e7i	−0.691359	−	1.19747i	−0.971393	−	0.237478i	$-0.923679\pi$
$751$	−1.06857e7	−	1.85082e7i	−0.691359	−	1.19747i	0.280034	−	0.959990i	$-0.409654\pi$
$752$	7.39325e6	−	1.28055e7i	0.476750	−	0.825756i
$753$		0			0
$754$	−1.33175e7	−	2.30666e7i	−0.853089	−	1.47759i
$755$	−2.09731e7			−1.33905
$756$		0			0
$757$	−1.74578e7			−1.10726			−0.553632	−	0.832762i	$-0.686758\pi$
$757$	−1.74578e7			−1.10726			−0.553632	+	0.832762i	$0.686758\pi$
$758$	−7.15286e6	−	1.23891e7i	−0.452175	−	0.783190i
$759$		0			0
$760$	5.26251e6	−	9.11494e6i	0.330491	−	0.572426i
$761$	6.12587e6	+	1.06103e7i	0.383448	+	0.664151i	0.991553	−	0.129706i	$-0.0414033\pi$
$761$	6.12587e6	+	1.06103e7i	0.383448	+	0.664151i	−0.608105	+	0.793857i	$0.708070\pi$
$762$		0			0
$763$	971682.	+	180500.i	0.0604245	+	0.0112245i
$764$	5.73633e6			0.355550
$765$		0			0
$766$	254090.	−	440097.i	0.0156465	−	0.0271004i
$767$	−1.97046e7	+	3.41293e7i	−1.20942	+	2.09479i
$768$		0			0
$769$	7.26941e6			0.443285			0.221643	−	0.975128i	$-0.428858\pi$
$769$	7.26941e6			0.443285			0.221643	+	0.975128i	$0.428858\pi$
$770$	1.25169e7	−	1.46434e7i	0.760801	−	0.890050i
$771$		0			0
$772$	−2.92751e6	−	5.07060e6i	−0.176789	−	0.306208i
$773$	1.01072e6	−	1.75062e6i	0.0608389	−	0.105376i	−0.834002	−	0.551762i	$-0.813956\pi$
$773$	1.01072e6	−	1.75062e6i	0.0608389	−	0.105376i	0.894841	+	0.446386i	$0.147289\pi$
$774$		0			0
$775$	1.48827e6	+	2.57777e6i	0.0890080	+	0.154166i
$776$	−3.03990e7			−1.81219

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44476 + 4.23445i) q^{2} +(4.04630 - 7.00840i) q^{4} +(-21.3752 - 37.0229i) q^{5} +(43.2256 + 122.223i) q^{7} +196.034 q^{8} +O(q^{10})\)	\(q+(2.44476 + 4.23445i) q^{2} +(4.04630 - 7.00840i) q^{4} +(-21.3752 - 37.0229i) q^{5} +(43.2256 + 122.223i) q^{7} +196.034 q^{8} +(104.514 - 181.024i) q^{10} +(355.439 - 615.638i) q^{11} +885.624 q^{13} +(-411.872 + 481.843i) q^{14} +(349.773 + 605.825i) q^{16} +(-350.659 + 607.359i) q^{17} +(627.946 + 1087.63i) q^{19} -345.962 q^{20} +3475.85 q^{22} +(-523.092 - 906.022i) q^{23} +(648.701 - 1123.58i) q^{25} +(2165.14 + 3750.13i) q^{26} +(1031.49 + 191.611i) q^{28} -6150.88 q^{29} +(-1147.12 + 1986.87i) q^{31} +(1426.31 - 2470.45i) q^{32} -3429.10 q^{34} +(3601.11 - 4212.89i) q^{35} +(-202.054 - 349.968i) q^{37} +(-3070.35 + 5318.01i) q^{38} +(-4190.26 - 7257.74i) q^{40} +17891.4 q^{41} -14604.8 q^{43} +(-2876.43 - 4982.11i) q^{44} +(2557.67 - 4430.01i) q^{46} +(-10568.6 - 18305.4i) q^{47} +(-13070.1 + 10566.3i) q^{49} +6343.67 q^{50} +(3583.50 - 6206.80i) q^{52} +(53.6064 - 92.8490i) q^{53} -30390.3 q^{55} +(8473.66 + 23959.9i) q^{56} +(-15037.4 - 26045.6i) q^{58} +(-22249.4 + 38537.1i) q^{59} +(11606.2 + 20102.5i) q^{61} -11217.7 q^{62} +36333.5 q^{64} +(-18930.4 - 32788.4i) q^{65} +(3335.66 - 5777.53i) q^{67} +(2837.74 + 4915.11i) q^{68} +(26643.1 + 4949.23i) q^{70} -25110.5 q^{71} +(-4737.49 + 8205.57i) q^{73} +(987.948 - 1711.18i) q^{74} +10163.4 q^{76} +(90609.5 + 16831.6i) q^{77} +(13238.1 + 22929.0i) q^{79} +(14953.0 - 25899.3i) q^{80} +(43740.2 + 75760.2i) q^{82} +7494.03 q^{83} +29981.6 q^{85} +(-35705.3 - 61843.3i) q^{86} +(69678.0 - 120686. i) q^{88} +(16085.6 + 27861.2i) q^{89} +(38281.6 + 108244. i) q^{91} -8466.35 q^{92} +(51675.5 - 89504.7i) q^{94} +(26845.0 - 46496.8i) q^{95} -155070. q^{97} +(-76695.9 - 29512.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) \) 12 * q - 182 * q^4 + 142 * q^7	\( 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) \) 12 * q - 182 * q^4 + 142 * q^7 + 686 * q^10 + 308 * q^13 - 1898 * q^16 + 9422 * q^19 - 18292 * q^22 - 7526 * q^25 + 37074 * q^28 + 23422 * q^31 - 55608 * q^34 - 18182 * q^37 + 69258 * q^40 - 87372 * q^43 + 25332 * q^46 + 30354 * q^49 + 34272 * q^52 - 96320 * q^55 - 89782 * q^58 - 16156 * q^61 + 380580 * q^64 + 144650 * q^67 - 187262 * q^70 - 100058 * q^73 - 685440 * q^76 + 101994 * q^79 + 75712 * q^82 + 602352 * q^85 + 752310 * q^88 - 282306 * q^91 - 120456 * q^94 - 866096 * q^97

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