LMFDB - Embedded newform 63.6.e.f.46.3

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			46.3
Root			$-2.44476 - 4.23445i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.f.37.3

$q$-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	0.564884	−	0.825170i	$-0.308921\pi$
$2$	−2.44476	−	4.23445i	−0.432177	−	0.748552i	−0.997060	+	0.0766186i	$0.975588\pi$
$3$		0			0
$3$		0			0
$4$	4.04630	−	7.00840i	0.126447	−	0.219012i
$5$	21.3752	+	37.0229i	0.382371	+	0.662286i	0.991401	−	0.130861i	$-0.0417742\pi$
$5$	21.3752	+	37.0229i	0.382371	+	0.662286i	−0.609029	+	0.793148i	$0.708441\pi$
$6$		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	$0.512983\pi$
$11$	−355.439	+	615.638i	−0.885693	+	1.53407i	−0.844917	+	0.534898i	$0.820350\pi$
$12$		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	−0.680536	−	0.732714i	$-0.738253\pi$
$17$	350.659	−	607.359i	0.294281	−	0.509710i	0.974817	+	0.223005i	$0.0715865\pi$
$18$		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	0.950510	−	0.310694i	$-0.100562\pi$
$23$	523.092	+	906.022i	0.206186	+	0.357124i	−0.744324	+	0.667818i	$0.767228\pi$
$24$		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	$-0.262385\pi$
$29$	6150.88			1.35813			0.679067	+	0.734077i	$0.262385\pi$
$30$		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	$-0.812290\pi$
$41$	−17891.4			−1.66221			−0.831103	+	0.556119i	$0.812290\pi$
$42$		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	$0.0792018\pi$
$47$	10568.6	+	18305.4i	0.697870	+	1.20875i	−0.271334	+	0.962485i	$0.587465\pi$
$48$		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	−0.867333	−	0.497728i	$-0.834168\pi$
$53$	−53.6064	+	92.8490i	−0.00262136	+	0.00454033i	0.864712	+	0.502268i	$0.167501\pi$
$54$		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	$-0.520458\pi$
$59$	22249.4	−	38537.1i	0.832124	−	1.44128i	0.896351	−	0.443346i	$-0.146209\pi$
$60$		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	$-0.404486\pi$
$71$	25110.5			0.591166			0.295583	+	0.955317i	$0.404486\pi$
$72$		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	$-0.519015\pi$
$83$	−7494.03			−0.119404			−0.0597022	+	0.998216i	$0.519015\pi$
$84$		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	0.738093	−	0.674699i	$-0.235727\pi$
$89$	−16085.6	−	27861.2i	−0.215260	−	0.372841i	−0.953353	+	0.301858i	$0.902393\pi$
$90$		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	$-0.649536\pi$
$101$	55960.9	−	96927.1i	0.545860	−	0.945457i	0.998552	−	0.0537904i	$-0.0171303\pi$
$102$		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	0.524488	−	0.851418i	$-0.324257\pi$
$107$	−56266.4	−	97456.3i	−0.475105	−	0.822906i	−0.999593	+	0.0285115i	$0.990923\pi$
$108$		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	$-0.451150\pi$
$113$	41498.7			0.305730			0.152865	+	0.988247i	$0.451150\pi$
$114$		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	$-0.986086\pi$
$131$	−105547.	−	182814.i	−0.537365	−	0.930744i	0.461679	−	0.887047i	$-0.347247\pi$
$132$		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	−0.954482	−	0.298268i	$-0.903591\pi$
$137$	−48096.6	+	83305.7i	−0.218934	+	0.379204i	0.735549	+	0.677472i	$0.236924\pi$
$138$		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	0.927092	−	0.374833i	$-0.122300\pi$
$149$	37650.0	+	65211.8i	0.138931	+	0.240636i	−0.788161	+	0.615469i	$0.788967\pi$
$150$		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	$-0.256699\pi$
$167$	498852.			1.38414			0.692070	+	0.721830i	$0.256699\pi$
$168$		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	0.982719	−	0.185103i	$-0.0592618\pi$
$173$	130322.	+	225724.i	0.331056	+	0.573405i	−0.651663	+	0.758508i	$0.725928\pi$
$174$		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	$-0.619587\pi$
$179$	266709.	−	461954.i	0.622164	−	1.07762i	0.989082	−	0.147367i	$-0.0470798\pi$
$180$		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	$-0.918526\pi$
$191$	−354418.	−	613871.i	−0.702964	−	1.21757i	0.264458	−	0.964397i	$-0.414807\pi$
$192$		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	$-0.456825\pi$
$197$	147313.			0.270443			0.135222	+	0.990815i	$0.456825\pi$
$198$		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	$0.342183\pi$
$227$	−406723.	+	704464.i	−0.523882	+	0.907391i	−0.999614	+	0.0277999i	$0.991150\pi$
$228$		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	$0.101160\pi$
$233$	617850.	+	1.07015e6i	0.745578	+	1.29138i	−0.204346	+	0.978899i	$0.565507\pi$
$234$		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	$-0.335168\pi$
$239$	874240.			0.990001			0.495001	+	0.868893i	$0.335168\pi$
$240$		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	$-0.534029\pi$
$251$	−213005.			−0.213406			−0.106703	+	0.994291i	$0.534029\pi$
$252$		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	$-0.898816\pi$
$257$	−789506.	−	1.36746e6i	−0.745629	−	1.29147i	0.204272	−	0.978914i	$-0.434517\pi$
$258$		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	−0.923234	−	0.384238i	$-0.874464\pi$
$263$	−144544.	+	250357.i	−0.128857	+	0.223188i	0.794377	+	0.607425i	$0.207798\pi$
$264$		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	$-0.502855\pi$
$269$	1.02244e6	−	1.77092e6i	0.861506	−	1.49217i	0.870475	−	0.492213i	$-0.163812\pi$
$270$		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	$-0.422374\pi$
$281$	639205.			0.482919			0.241460	+	0.970411i	$0.422374\pi$
$282$		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	$-0.591054\pi$
$293$	−829294.			−0.564338			−0.282169	+	0.959365i	$0.591054\pi$
$294$		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	−0.941219	−	0.337798i	$-0.890318\pi$
$311$	−303729.	+	526074.i	−0.178068	+	0.308422i	0.763151	+	0.646220i	$0.223651\pi$
$312$		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	$0.0426231\pi$
$317$	1.09343e6	+	1.89387e6i	0.611142	+	1.05853i	−0.379906	+	0.925025i	$0.624044\pi$
$318$		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	−0.652398	−	0.757877i	$-0.726237\pi$
$347$	740499.	−	1.28258e6i	0.330142	−	0.571823i	0.982539	+	0.186054i	$0.0595701\pi$
$348$		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	−0.999757	−	0.0220418i	$-0.992983\pi$
$353$	−1.12562e6	+	1.94963e6i	−0.480790	+	0.832752i	0.518967	+	0.854794i	$0.326317\pi$
$354$		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	0.930719	−	0.365735i	$-0.119182\pi$
$359$	362932.	+	628617.i	0.148624	+	0.257424i	−0.782095	+	0.623159i	$0.785849\pi$
$360$		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	0.874934	−	0.484241i	$-0.160904\pi$
$383$	51966.3	+	90008.2i	0.0181019	+	0.0313534i	−0.856833	+	0.515595i	$0.827571\pi$
$384$		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	−0.880148	−	0.474700i	$-0.842557\pi$
$389$	−86465.6	+	149763.i	−0.0289714	+	0.0501799i	0.851176	+	0.524880i	$0.175890\pi$
$390$		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	$-0.986705\pi$
$401$	−1.72506e6	−	2.98789e6i	−0.535726	−	0.927904i	0.463402	−	0.886148i	$-0.346629\pi$
$402$		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	$-0.751143\pi$
$419$	−5.10039e6			−1.41928			−0.709641	+	0.704564i	$0.751143\pi$
$420$		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	−0.980655	−	0.195742i	$-0.937288\pi$
$431$	−1.23720e6	+	2.14290e6i	−0.320810	+	0.555659i	0.659845	+	0.751401i	$0.270622\pi$
$432$		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	$-0.916013\pi$
$443$	−2.92674e6	−	5.06927e6i	−0.708558	−	1.22726i	0.256835	−	0.966455i	$-0.417320\pi$
$444$		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	$-0.649424\pi$
$449$	−3.86497e6			−0.904754			−0.452377	+	0.891827i	$0.649424\pi$
$450$		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	$-0.458928\pi$
$461$	1.17429e6			0.257350			0.128675	+	0.991687i	$0.458928\pi$
$462$		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	0.779669	−	0.626191i	$-0.215387\pi$
$467$	−718550.	−	1.24456e6i	−0.152463	−	0.264074i	−0.932132	+	0.362118i	$0.882054\pi$
$468$		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	−0.723422	−	0.690406i	$-0.757432\pi$
$479$	1.18608e6	−	2.05436e6i	0.236198	−	0.409107i	0.959620	+	0.281299i	$0.0907652\pi$
$480$		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	$-0.145890\pi$
$491$	9.58134e6			1.79359			0.896794	+	0.442448i	$0.145890\pi$
$492$		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	$-0.351295\pi$
$503$	5.11108e6			0.900726			0.450363	+	0.892846i	$0.351295\pi$
$504$		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	$0.0406420\pi$
$509$	3.54335e6	+	6.13725e6i	0.606204	+	1.04998i	−0.385656	+	0.922643i	$0.626025\pi$
$510$		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	−0.971069	−	0.238799i	$-0.923246\pi$
$521$	−1.72694e6	+	2.99114e6i	−0.278729	+	0.482772i	0.692340	+	0.721571i	$0.256580\pi$
$522$		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	$0.563721\pi$
$557$	−6.94253e6	+	1.20248e7i	−0.948156	+	1.64225i	−0.749305	+	0.662225i	$0.769612\pi$
$558$		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	−0.703879	−	0.710320i	$-0.748550\pi$
$563$	1.97962e6	−	3.42880e6i	0.263215	−	0.455902i	0.967094	+	0.254417i	$0.0818837\pi$
$564$		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	$0.0444812\pi$
$569$	4.75540e6	+	8.23659e6i	0.615752	+	1.06651i	−0.374500	+	0.927227i	$0.622185\pi$
$570$		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	$-0.620043\pi$
$587$	−6.14848e6			−0.736499			−0.368250	+	0.929727i	$0.620043\pi$
$588$		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	$-0.883633\pi$
$593$	−6.64979e6	−	1.15178e7i	−0.776554	−	1.34503i	0.157363	−	0.987541i	$-0.449701\pi$
$594$		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	−0.966971	−	0.254885i	$-0.917962\pi$
$599$	−2.30732e6	+	3.99639e6i	−0.262748	+	0.455094i	0.704223	+	0.709979i	$0.251296\pi$
$600$		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	$-0.252305\pi$
$617$	1.32758e7			1.40394			0.701969	+	0.712208i	$0.252305\pi$
$618$		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	−0.757297	−	0.653071i	$-0.773480\pi$
$641$	1.94455e6	−	3.36806e6i	0.186928	−	0.323768i	0.944224	+	0.329303i	$0.106814\pi$
$642$		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	−0.585242	−	0.810858i	$-0.699001\pi$
$647$	4.36138e6	−	7.55413e6i	0.409603	−	0.709453i	0.994845	+	0.101405i	$0.0323339\pi$
$648$		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	0.831352	−	0.555746i	$-0.187567\pi$
$653$	−714958.	−	1.23834e6i	−0.0656141	−	0.113647i	−0.896966	+	0.442099i	$0.854234\pi$
$654$		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	$-0.635413\pi$
$659$	−9.20182e6			−0.825392			−0.412696	+	0.910869i	$0.635413\pi$
$660$		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	$0.269118\pi$
$677$	1.16835e7	+	2.02364e7i	0.979720	+	1.69692i	0.316333	+	0.948648i	$0.397548\pi$
$678$		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	$0.351077\pi$
$683$	−6.67445e6	+	1.15605e7i	−0.547474	+	0.948253i	−0.998447	+	0.0557153i	$0.982256\pi$
$684$		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	$-0.597843\pi$
$701$	−7.87304e6			−0.605128			−0.302564	+	0.953129i	$0.597843\pi$
$702$		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	0.859537	−	0.511074i	$-0.170752\pi$
$719$	−177912.	−	308153.i	−0.0128347	−	0.0222303i	−0.872371	+	0.488844i	$0.837419\pi$
$720$		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	$-0.667921\pi$
$743$	−1.51503e7			−1.00682			−0.503408	+	0.864049i	$0.667921\pi$
$744$		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	0.608105	−	0.793857i	$-0.291930\pi$
$761$	−6.12587e6	−	1.06103e7i	−0.383448	−	0.664151i	−0.991553	+	0.129706i	$0.958597\pi$
$762$		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	−0.894841	−	0.446386i	$-0.852711\pi$
$773$	−1.01072e6	+	1.75062e6i	−0.0608389	+	0.105376i	0.834002	+	0.551762i	$0.186044\pi$
$774$		0			0
$775$	1.48827e6	+	2.57777e6i	0.0890080	+	0.154166i
$776$	3.03990e7			1.81219
$777$		0			0
$778$	845550.			0.0500830
$779$	−1.12348e7	−	1.94593e7i	−0.663320	−	1.14890i
$780$		0			0
$781$	−8.92525e6	+	1.54590e7i	−0.523592	+	0.906887i
$782$	−1.79374e6	−	3.10684e6i	−0.104892	−	0.181678i
$783$		0			0
$784$	−1.09729e7	−	4.22237e6i	−0.637577	−	0.245339i
$785$	1.97086e7			1.14151
$786$		0			0
$787$	6.05566e6	−	1.04887e7i	0.348517	−	0.603650i	−0.637469	−	0.770476i	$-0.720019\pi$
$787$	6.05566e6	−	1.04887e7i	0.348517	−	0.603650i	0.985986	+	0.166826i	$0.0533519\pi$
$788$	596074.	−	1.03243e6i	0.0341967	−	0.0592305i
$789$		0			0
$790$	5.53428e6			0.315495
$791$	1.79380e6	+	5.07211e6i	0.101937	+	0.288235i
$792$		0			0
$793$	1.02787e7	+	1.78032e7i	0.580437	+	1.00535i
$794$	−6.35553e6	+	1.10081e7i	−0.357767	+	0.619671i
$795$		0			0
$796$	5749.71	+	9958.79i	0.000321635	+	0.000557088i
$797$	−2.45062e7			−1.36657			−0.683283	−	0.730154i	$-0.739448\pi$
$797$	−2.45062e7			−1.36657			−0.683283	+	0.730154i	$0.739448\pi$
$798$		0			0
$799$	1.48239e7			0.821479
$800$	1.85050e6	+	3.20516e6i	0.102227	+	0.177062i
$801$		0			0
$802$	−8.43470e6	+	1.46093e7i	−0.463056	+	0.802037i
$803$	−3.36777e6	−	5.83316e6i	−0.184312	−	0.319238i
$804$		0			0
$805$	−5.70068e6	−	1.05896e6i	−0.310054	−	0.0575957i
$806$	9.93468e6			0.538662
$807$		0			0
$808$	−1.09702e7	+	1.90010e7i	−0.591135	+	1.02388i
$809$	−2.99377e6	+	5.18536e6i	−0.160823	+	0.278553i	−0.935164	−	0.354215i	$-0.884748\pi$
$809$	−2.99377e6	+	5.18536e6i	−0.160823	+	0.278553i	0.774341	+	0.632768i	$0.218081\pi$
$810$		0			0
$811$	1.57094e7			0.838699			0.419350	−	0.907825i	$-0.362258\pi$
$811$	1.57094e7			0.838699			0.419350	+	0.907825i	$0.362258\pi$
$812$	6.34459e6	+	1.17857e6i	0.337687	+	0.0627288i
$813$		0			0
$814$	−702311.	−	1.21644e6i	−0.0371508	−	0.0643471i
$815$	−1.02268e7	+	1.77134e7i	−0.539321	+	0.934131i
$816$		0			0
$817$	−9.17104e6	−	1.58847e7i	−0.480688	−	0.832576i
$818$	−7.05435e6			−0.368615
$819$		0			0
$820$	−6.18974e6			−0.321468
$821$	−55578.8	−	96265.3i	−0.00287774	−	0.00498439i	0.864583	−	0.502490i	$-0.167583\pi$
$821$	−55578.8	−	96265.3i	−0.00287774	−	0.00498439i	−0.867461	+	0.497506i	$0.834249\pi$
$822$		0			0
$823$	−1.71946e6	+	2.97820e6i	−0.0884898	+	0.153269i	−0.906873	−	0.421404i	$-0.861537\pi$
$823$	−1.71946e6	+	2.97820e6i	−0.0884898	+	0.153269i	0.818383	+	0.574673i	$0.194871\pi$
$824$	−5.94807e6	−	1.03024e7i	−0.305182	−	0.528590i
$825$		0			0
$826$	−9.40491e6	−	2.65931e7i	−0.479628	−	1.35618i
$827$	−1.87782e7			−0.954751			−0.477375	−	0.878700i	$-0.658412\pi$
$827$	−1.87782e7			−0.954751			−0.477375	+	0.878700i	$0.658412\pi$
$828$		0			0
$829$	−3.76889e6	+	6.52791e6i	−0.190470	+	0.329904i	−0.945406	−	0.325894i	$-0.894335\pi$
$829$	−3.76889e6	+	6.52791e6i	−0.190470	+	0.329904i	0.754936	+	0.655799i	$0.227668\pi$
$830$	−783234.	+	1.35660e6i	−0.0394636	+	0.0683529i
$831$		0			0
$832$	3.21778e7			1.61156
$833$	1.83442e6	+	1.16434e7i	0.0915978	+	0.581391i
$834$		0			0
$835$	1.06631e7	+	1.84690e7i	0.529256	+	0.916698i
$836$	−3.61248e6	+	6.25700e6i	−0.178768	+	0.309635i
$837$		0			0
$838$	1.24692e7	+	2.15973e7i	0.613380	+	1.06241i
$839$	1.65147e7			0.809962			0.404981	−	0.914325i	$-0.367278\pi$
$839$	1.65147e7			0.809962			0.404981	+	0.914325i	$0.367278\pi$
$840$		0			0
$841$	1.73222e7			0.844527
$842$	−1.24253e7	−	2.15212e7i	−0.603984	−	1.04613i
$843$		0			0
$844$	−122587.	+	212328.i	−0.00592365	+	0.0102601i
$845$	8.82873e6	+	1.52918e7i	0.425360	+	0.736745i
$846$		0			0
$847$	2.90021e7	−	3.39291e7i	1.38906	−	1.62504i
$848$	−75000.3			−0.00358157
$849$		0			0
$850$	−2.22446e6	+	3.85288e6i	−0.105603	+	0.182911i
$851$	211386.	−	366131.i	0.0100058	−	0.0173306i
$852$		0			0
$853$	2.36772e7			1.11418			0.557092	−	0.830451i	$-0.311917\pi$
$853$	2.36772e7			1.11418			0.557092	+	0.830451i	$0.311917\pi$
$854$	1.44665e7	+	2.68730e6i	0.678764	+	0.126088i
$855$		0			0
$856$	1.10301e7	+	1.91047e7i	0.514511	+	0.891160i
$857$	148276.	−	256821.i	0.00689633	−	0.0119448i	−0.862557	−	0.505961i	$-0.831138\pi$
$857$	148276.	−	256821.i	0.00689633	−	0.0119448i	0.869453	+	0.494016i	$0.164471\pi$
$858$		0			0
$859$	−6.06474e6	−	1.05044e7i	−0.280433	−	0.485725i	0.691058	−	0.722799i	$-0.257145\pi$
$859$	−6.06474e6	−	1.05044e7i	−0.280433	−	0.485725i	−0.971491	+	0.237074i	$0.923811\pi$
$860$	−5.05271e6			−0.232958
$861$		0			0
$862$	1.20987e7			0.554586
$863$	−6.50899e6	−	1.12739e7i	−0.297500	−	0.515285i	0.678063	−	0.735003i	$-0.262819\pi$
$863$	−6.50899e6	−	1.12739e7i	−0.297500	−	0.515285i	−0.975563	+	0.219718i	$0.929486\pi$
$864$		0			0
$865$	−5.57130e6	+	9.64978e6i	−0.253172	+	0.438508i
$866$	811543.	+	1.40563e6i	0.0367720	+	0.0636909i
$867$		0			0
$868$	−1.56395e6	+	1.82964e6i	−0.0704569	+	0.0824264i
$869$	−1.88213e7			−0.845473
$870$		0			0
$871$	2.95414e6	−	5.11672e6i	0.131943	−	0.228532i
$872$	−747216.	+	1.29422e6i	−0.0332778	+	0.0576389i
$873$		0			0
$874$	6.42431e6			0.284478
$875$	8.17220e6	+	2.31075e7i	0.360844	+	1.02031i
$876$		0			0
$877$	1.04463e6	+	1.80935e6i	0.0458630	+	0.0794371i	0.888046	−	0.459755i	$-0.152063\pi$
$877$	1.04463e6	+	1.80935e6i	0.0458630	+	0.0794371i	−0.842183	+	0.539192i	$0.818730\pi$
$878$	1.00533e7	−	1.74129e7i	0.440123	−	0.762315i
$879$		0			0
$880$	−1.06297e7	−	1.84112e7i	−0.462717	−	0.801449i
$881$	2.84897e6			0.123665			0.0618327	−	0.998087i	$-0.480305\pi$
$881$	2.84897e6			0.123665			0.0618327	+	0.998087i	$0.480305\pi$
$882$		0			0
$883$	−1.75998e7			−0.759636			−0.379818	−	0.925061i	$-0.624013\pi$
$883$	−1.75998e7			−0.759636			−0.379818	+	0.925061i	$0.624013\pi$
$884$	−2.51317e6	−	4.35294e6i	−0.108166	−	0.187349i
$885$		0			0
$886$	−1.43104e7	+	2.47863e7i	−0.612444	+	1.06078i
$887$	1.18659e7	+	2.05523e7i	0.506397	+	0.877106i	0.999973	+	0.00740294i	$0.00235645\pi$
$887$	1.18659e7	+	2.05523e7i	0.506397	+	0.877106i	−0.493575	+	0.869703i	$0.664310\pi$
$888$		0			0
$889$	4.09764e6	+	1.15864e7i	0.173892	+	0.491692i
$890$	−6.72473e6			−0.284577
$891$		0			0
$892$	−598304.	+	1.03629e6i	−0.0251773	+	0.0436084i
$893$	−1.32731e7	+	2.29896e7i	−0.556984	+	0.964724i
$894$		0			0
$895$	2.28038e7			0.951591
$896$	7.27537e6	−	8.51134e6i	0.302751	−	0.354183i
$897$		0			0
$898$	9.44893e6	+	1.63660e7i	0.391013	+	0.677255i
$899$	−7.05579e6	+	1.22210e7i	−0.291170	+	0.504321i
$900$		0			0
$901$	37595.1	+	65116.6i	0.00154283	+	0.00267227i
$902$	−6.21878e7			−2.54501
$903$		0			0
$904$	−8.13513e6			−0.331088
$905$	3.97148e6	+	6.87880e6i	0.161187	+	0.279184i
$906$		0			0
$907$	1.23813e7	−	2.14450e7i	0.499744	−	0.865583i	−0.500256	−	0.865878i	$-0.666761\pi$
$907$	1.23813e7	−	2.14450e7i	0.499744	−	0.865583i	1.00000		0.000295096i	$9.39319e-5\pi$
$908$	3.29144e6	+	5.70095e6i	0.132486	+	0.229473i
$909$		0			0
$910$	2.35958e7	+	4.38316e6i	0.944562	+	0.175462i
$911$	1.67991e7			0.670639			0.335320	−	0.942104i	$-0.391156\pi$
$911$	1.67991e7			0.670639			0.335320	+	0.942104i	$0.391156\pi$
$912$		0			0
$913$	2.66367e6	−	4.61361e6i	0.105756	−	0.183174i
$914$	1.31784e7	−	2.28256e7i	0.521791	−	0.903768i
$915$		0			0
$916$	−1.03762e7			−0.408602
$917$	1.77817e7	−	2.08026e7i	0.698314	−	0.816947i
$918$		0			0
$919$	−7.08247e6	−	1.22672e7i	−0.276628	−	0.479133i	0.693917	−	0.720055i	$-0.255884\pi$
$919$	−7.08247e6	−	1.22672e7i	−0.276628	−	0.479133i	−0.970545	+	0.240922i	$0.922550\pi$
$920$	4.38378e6	−	7.59293e6i	0.170757	−	0.295760i
$921$		0			0
$922$	−2.87087e6	−	4.97249e6i	−0.111221	−	0.192640i
$923$	2.22384e7			0.859212
$924$		0			0
$925$	−524292.			−0.0201474
$926$	−9.86955e6	−	1.70946e7i	−0.378242	−	0.655134i
$927$		0			0
$928$	−8.77308e6	+	1.51954e7i	−0.334412	+	0.579219i
$929$	−1.47777e7	−	2.55957e7i	−0.561781	−	0.973033i	−0.997341	−	0.0728736i	$-0.976783\pi$
$929$	−1.47777e7	−	2.55957e7i	−0.561781	−	0.973033i	0.435560	−	0.900160i	$-0.356550\pi$
$930$		0			0
$931$	−1.96996e7	−	7.58040e6i	−0.744876	−	0.286628i
$932$	1.00000e7			0.377104
$933$		0			0
$934$	−3.51336e6	+	6.08532e6i	−0.131782	+	0.228253i
$935$	−1.06566e7	+	1.84578e7i	−0.398649	+	0.690481i
$936$		0			0
$937$	3.20477e7			1.19247			0.596235	−	0.802810i	$-0.296663\pi$
$937$	3.20477e7			1.19247			0.596235	+	0.802810i	$0.296663\pi$
$938$	−1.41000e6	−	3.98687e6i	−0.0523253	−	0.147953i
$939$		0			0
$940$	3.65634e6	+	6.33298e6i	0.134967	+	0.233770i
$941$	1.84473e7	−	3.19517e7i	0.679141	−	1.17631i	−0.296100	−	0.955157i	$-0.595686\pi$
$941$	1.84473e7	−	3.19517e7i	0.679141	−	1.17631i	0.975240	−	0.221149i	$-0.0709806\pi$
$942$		0			0
$943$	−9.35885e6	−	1.62100e7i	−0.342723	−	0.593613i
$944$	3.11290e7			1.13693
$945$		0			0
$946$	−5.07642e7			−1.84429
$947$	7.28703e6	+	1.26215e7i	0.264044	+	0.457337i	0.967313	−	0.253587i	$-0.0816104\pi$
$947$	7.28703e6	+	1.26215e7i	0.264044	+	0.457337i	−0.703269	+	0.710924i	$0.748277\pi$
$948$		0			0
$949$	−4.19563e6	+	7.26704e6i	−0.151228	+	0.261934i
$950$	−3.98349e6	−	6.89960e6i	−0.143204	−	0.248036i
$951$		0			0
$952$	−1.75236e7	−	3.25519e6i	−0.626658	−	0.116408i
$953$	2.34882e7			0.837757			0.418878	−	0.908042i	$-0.362423\pi$
$953$	2.34882e7			0.837757			0.418878	+	0.908042i	$0.362423\pi$
$954$		0			0
$955$	1.51515e7	−	2.62432e7i	0.537586	−	0.931126i
$956$	3.53744e6	−	6.12702e6i	0.125183	−	0.216823i
$957$		0			0
$958$	−1.15988e7			−0.408317
$959$	−1.22609e7	−	2.27759e6i	−0.430503	−	0.0799703i
$960$		0			0
$961$	1.16828e7	+	2.02352e7i	0.408074	+	0.706805i
$962$	−874950.	+	1.51546e6i	−0.0304822	+	0.0527967i
$963$		0			0
$964$	−3.96380e6	−	6.86550e6i	−0.137378	−	0.237947i
$965$	3.09301e7			1.06921
$966$		0			0
$967$	−2.25237e7			−0.774593			−0.387296	−	0.921955i	$-0.626591\pi$
$967$	−2.25237e7			−0.774593			−0.387296	+	0.921955i	$0.626591\pi$
$968$	3.37468e7	+	5.84512e7i	1.15756	+	2.00496i
$969$		0			0
$970$	−1.62071e7	+	2.80715e7i	−0.553064	+	0.957935i
$971$	−2.65863e7	−	4.60488e7i	−0.904920	−	1.56737i	−0.821025	−	0.570892i	$-0.806597\pi$
$971$	−2.65863e7	−	4.60488e7i	−0.904920	−	1.56737i	−0.0838945	−	0.996475i	$-0.526736\pi$
$972$		0			0
$973$	−1.73764e7	−	4.91331e7i	−0.588408	−	1.66377i
$974$	3.27142e6			0.110494
$975$		0			0
$976$	−8.11906e6	+	1.40626e7i	−0.272823	+	0.472544i
$977$	−1.41109e7	+	2.44408e7i	−0.472953	+	0.819178i	−0.999521	−	0.0309550i	$-0.990145\pi$
$977$	−1.41109e7	+	2.44408e7i	−0.472953	+	0.819178i	0.526568	+	0.850133i	$0.323478\pi$
$978$		0			0
$979$	2.28699e7			0.762618
$980$	−4.52176e6	+	3.65555e6i	−0.150398	+	0.121587i
$981$		0			0
$982$	−2.34241e7	−	4.05717e7i	−0.775147	−	1.34259i
$983$	−8.58072e6	+	1.48622e7i	−0.283230	+	0.490570i	−0.972179	−	0.234241i	$-0.924739\pi$
$983$	−8.58072e6	+	1.48622e7i	−0.283230	+	0.490570i	0.688948	+	0.724811i	$0.258073\pi$
$984$		0			0
$985$	3.14885e6	+	5.45397e6i	0.103410	+	0.179111i
$986$	−2.10920e7			−0.690917
$987$		0			0
$988$	9.00097e6			0.293357
$989$	−7.63966e6	−	1.32323e7i	−0.248361	−	0.430174i
$990$		0			0
$991$	−1.52871e7	+	2.64780e7i	−0.494471	+	0.856448i	−0.999980	−	0.00637296i	$-0.997971\pi$
$991$	−1.52871e7	+	2.64780e7i	−0.494471	+	0.856448i	0.505509	+	0.862821i	$0.331305\pi$
$992$	−3.27230e6	−	5.66779e6i	−0.105578	−	0.182867i
$993$		0			0
$994$	1.03423e7	−	1.20993e7i	0.332011	−	0.388414i
$995$	−60747.5			−0.00194523
$996$		0			0
$997$	−2.37741e7	+	4.11779e7i	−0.757470	+	1.31198i	0.186667	+	0.982423i	$0.440232\pi$
$997$	−2.37741e7	+	4.11779e7i	−0.757470	+	1.31198i	−0.944137	+	0.329553i	$0.893102\pi$
$998$	5.32481e6	−	9.22284e6i	0.169230	−	0.293115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.f.46.3	yes	12
3.2	odd	2	inner	63.6.e.f.46.4	yes	12
7.2	even	3	inner	63.6.e.f.37.3	✓	12
7.3	odd	6		441.6.a.bd.1.4		6
7.4	even	3		441.6.a.bc.1.4		6
21.2	odd	6	inner	63.6.e.f.37.4	yes	12
21.11	odd	6		441.6.a.bc.1.3		6
21.17	even	6		441.6.a.bd.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.e.f.37.3	✓	12	7.2	even	3	inner
63.6.e.f.37.4	yes	12	21.2	odd	6	inner
63.6.e.f.46.3	yes	12	1.1	even	1	trivial
63.6.e.f.46.4	yes	12	3.2	odd	2	inner
441.6.a.bc.1.3		6	21.11	odd	6
441.6.a.bc.1.4		6	7.4	even	3
441.6.a.bd.1.3		6	21.17	even	6
441.6.a.bd.1.4		6	7.3	odd	6

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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