LMFDB - Embedded newform 63.6.e.f.37.4

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			37.4
Root			$2.44476 - 4.23445i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.6.e.f.46.4

$q$-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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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	$-0.691079\pi$
$2$	2.44476	−	4.23445i	0.432177	−	0.748552i	0.997060	+	0.0766186i	$0.0244124\pi$
$3$		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	$-0.958226\pi$
$5$	−21.3752	+	37.0229i	−0.382371	+	0.662286i	0.609029	+	0.793148i	$0.291559\pi$
$6$		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	0.844917	+	0.534898i	$0.179650\pi$
$11$	355.439	+	615.638i	0.885693	+	1.53407i	0.0407765	+	0.999168i	$0.487017\pi$
$12$		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	$-0.261747\pi$
$17$	−350.659	−	607.359i	−0.294281	−	0.509710i	−0.974817	+	0.223005i	$0.928413\pi$
$18$		0			0
$19$	627.946	−	1087.63i	0.399060	−	0.691192i	−0.594550	−	0.804059i	$-0.702670\pi$
$19$	627.946	−	1087.63i	0.399060	−	0.691192i	0.993610	+	0.112866i	$0.0360031\pi$
$20$	−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	$-0.899438\pi$
$23$	−523.092	+	906.022i	−0.206186	+	0.357124i	0.744324	+	0.667818i	$0.232772\pi$
$24$		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	0.738694	−	0.674041i	$-0.235443\pi$
$31$	−1147.12	−	1986.87i	−0.214390	−	0.371334i	−0.953084	+	0.302707i	$0.902110\pi$
$32$	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	−0.877902	−	0.478839i	$-0.841058\pi$
$37$	−202.054	+	349.968i	−0.0242641	+	0.0420266i	0.853638	+	0.520866i	$0.174391\pi$
$38$	−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	0.271334	+	0.962485i	$0.412535\pi$
$47$	−10568.6	+	18305.4i	−0.697870	+	1.20875i	−0.969204	+	0.246260i	$0.920798\pi$
$48$		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	$-0.165832\pi$
$53$	53.6064	+	92.8490i	0.00262136	+	0.00454033i	−0.864712	+	0.502268i	$0.832499\pi$
$54$		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	−0.896351	−	0.443346i	$-0.853791\pi$
$59$	−22249.4	−	38537.1i	−0.832124	−	1.44128i	0.0642267	−	0.997935i	$-0.479542\pi$
$60$		0			0
$61$	11606.2	−	20102.5i	0.399360	−	0.691712i	−0.594287	−	0.804253i	$-0.702566\pi$
$61$	11606.2	−	20102.5i	0.399360	−	0.691712i	0.993647	+	0.112541i	$0.0358990\pi$
$62$	−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	0.907840	−	0.419317i	$-0.137730\pi$
$67$	3335.66	+	5777.53i	0.0907809	+	0.157237i	−0.817059	+	0.576554i	$0.804397\pi$
$68$	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	0.809300	−	0.587396i	$-0.199847\pi$
$73$	−4737.49	−	8205.57i	−0.104050	−	0.180219i	−0.913350	+	0.407176i	$0.866513\pi$
$74$	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	−0.721679	−	0.692228i	$-0.756629\pi$
$79$	13238.1	−	22929.0i	0.238647	−	0.413349i	0.960326	+	0.278879i	$0.0899627\pi$
$80$	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	−0.738093	−	0.674699i	$-0.764273\pi$
$89$	16085.6	−	27861.2i	0.215260	−	0.372841i	0.953353	+	0.301858i	$0.0976067\pi$
$90$		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	−0.998552	−	0.0537904i	$-0.982870\pi$
$101$	−55960.9	−	96927.1i	−0.545860	−	0.945457i	0.452692	−	0.891667i	$-0.350464\pi$
$102$		0			0
$103$	30342.1	−	52554.1i	0.281808	−	0.488105i	−0.690022	−	0.723788i	$-0.742399\pi$
$103$	30342.1	−	52554.1i	0.281808	−	0.488105i	0.971830	+	0.235683i	$0.0757326\pi$
$104$	173612.			1.57397
$105$		0			0
$106$	524.219			0.00453156
$107$	56266.4	−	97456.3i	0.475105	−	0.822906i	−0.524488	−	0.851418i	$-0.675743\pi$
$107$	56266.4	−	97456.3i	0.475105	−	0.822906i	0.999593	+	0.0285115i	$0.00907672\pi$
$108$		0			0
$109$	3811.67	+	6602.01i	0.0307291	+	0.0532243i	0.880981	−	0.473152i	$-0.156884\pi$
$109$	3811.67	+	6602.01i	0.0307291	+	0.0532243i	−0.850252	+	0.526376i	$0.823550\pi$
$110$	−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	−0.461679	−	0.887047i	$-0.652753\pi$
$131$	105547.	−	182814.i	0.537365	−	0.930744i	0.999045	−	0.0436972i	$-0.0139137\pi$
$132$		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	$-0.0964088\pi$
$137$	48096.6	+	83305.7i	0.218934	+	0.379204i	−0.735549	+	0.677472i	$0.763076\pi$
$138$		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	$-0.877700\pi$
$149$	−37650.0	+	65211.8i	−0.138931	+	0.240636i	0.788161	+	0.615469i	$0.211033\pi$
$150$		0			0
$151$	245297.	+	424867.i	0.875488	+	1.51639i	0.856242	+	0.516574i	$0.172793\pi$
$151$	245297.	+	424867.i	0.875488	+	1.51639i	0.0192454	+	0.999815i	$0.493874\pi$
$152$	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	0.949567	+	0.313566i	$0.101524\pi$
$157$	230508.	+	399251.i	0.746339	+	1.29270i	−0.203228	+	0.979132i	$0.565143\pi$
$158$	−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	−0.261376	−	0.965237i	$-0.584176\pi$
$163$	239222.	−	414344.i	0.705232	−	1.22150i	0.966608	−	0.256260i	$-0.0824904\pi$
$164$	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	−0.982719	−	0.185103i	$-0.940738\pi$
$173$	−130322.	+	225724.i	−0.331056	+	0.573405i	0.651663	+	0.758508i	$0.274072\pi$
$174$		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	−0.989082	−	0.147367i	$-0.952920\pi$
$179$	−266709.	−	461954.i	−0.622164	−	1.07762i	0.366918	−	0.930253i	$-0.380413\pi$
$180$		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	−0.264458	−	0.964397i	$-0.585193\pi$
$191$	354418.	−	613871.i	0.702964	−	1.21757i	0.967421	−	0.253171i	$-0.0814736\pi$
$192$		0			0
$193$	361752.	+	626573.i	0.699065	+	1.21082i	0.968791	+	0.247879i	$0.0797337\pi$
$193$	361752.	+	626573.i	0.699065	+	1.21082i	−0.269726	+	0.962937i	$0.586933\pi$
$194$	−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	0.865389	−	0.501101i	$-0.167071\pi$
$199$	−710.490	−	1230.60i	−0.00127182	−	0.00220285i	−0.866661	+	0.498898i	$0.833738\pi$
$200$	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	0.999614	+	0.0277999i	$0.00885012\pi$
$227$	406723.	+	704464.i	0.523882	+	0.907391i	−0.475731	+	0.879591i	$0.657817\pi$
$228$		0			0
$229$	−641094.	+	1.11041e6i	−0.807854	+	1.39924i	0.106493	+	0.994313i	$0.466038\pi$
$229$	−641094.	+	1.11041e6i	−0.807854	+	1.39924i	−0.914347	+	0.404931i	$0.867295\pi$
$230$	−218683.			−0.272581
$231$		0			0
$232$	−1.20578e6			−1.47078
$233$	−617850.	+	1.07015e6i	−0.745578	+	1.29138i	0.204346	+	0.978899i	$0.434493\pi$
$233$	−617850.	+	1.07015e6i	−0.745578	+	1.29138i	−0.949924	+	0.312481i	$0.898840\pi$
$234$		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	0.998716	+	0.0506545i	$0.0161307\pi$
$241$	489805.	+	848367.i	0.543226	+	0.940895i	−0.455490	+	0.890241i	$0.650536\pi$
$242$	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	−0.204272	−	0.978914i	$-0.565483\pi$
$257$	789506.	−	1.36746e6i	0.745629	−	1.29147i	0.949900	−	0.312553i	$-0.101184\pi$
$258$		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	$-0.125536\pi$
$263$	144544.	+	250357.i	0.128857	+	0.223188i	−0.794377	+	0.607425i	$0.792202\pi$
$264$		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	−0.870475	−	0.492213i	$-0.836188\pi$
$269$	−1.02244e6	−	1.77092e6i	−0.861506	−	1.49217i	0.00896851	−	0.999960i	$-0.497145\pi$
$270$		0			0
$271$	302981.	−	524779.i	0.250607	−	0.434063i	−0.713086	−	0.701076i	$-0.752703\pi$
$271$	302981.	−	524779.i	0.250607	−	0.434063i	0.963693	+	0.267013i	$0.0860366\pi$
$272$	−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	0.520953	−	0.853585i	$-0.325576\pi$
$277$	−611375.	−	1.05893e6i	−0.478750	−	0.829219i	−0.999703	+	0.0243664i	$0.992243\pi$
$278$	−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	0.764652	−	0.644444i	$-0.222911\pi$
$283$	−236827.	−	410197.i	−0.175779	−	0.304457i	−0.940430	+	0.339986i	$0.889578\pi$
$284$	−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	0.941219	−	0.337798i	$-0.109682\pi$
$311$	303729.	+	526074.i	0.178068	+	0.308422i	−0.763151	+	0.646220i	$0.776349\pi$
$312$		0			0
$313$	−789012.	+	1.36661e6i	−0.455222	+	0.788467i	−0.998701	−	0.0509555i	$-0.983773\pi$
$313$	−789012.	+	1.36661e6i	−0.455222	+	0.788467i	0.543479	+	0.839423i	$0.317107\pi$
$314$	2.25414e6			1.29020
$315$		0			0
$316$	214261.			0.120705
$317$	−1.09343e6	+	1.89387e6i	−0.611142	+	1.05853i	0.379906	+	0.925025i	$0.375956\pi$
$317$	−1.09343e6	+	1.89387e6i	−0.611142	+	1.05853i	−0.991048	+	0.133505i	$0.957377\pi$
$318$		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	−0.275845	−	0.961202i	$-0.588958\pi$
$331$	1.38434e6	−	2.39775e6i	0.694503	−	1.20291i	0.970348	−	0.241712i	$-0.0777090\pi$
$332$	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	$-0.273763\pi$
$347$	−740499.	−	1.28258e6i	−0.330142	−	0.571823i	−0.982539	+	0.186054i	$0.940430\pi$
$348$		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	$-0.00701668\pi$
$353$	1.12562e6	+	1.94963e6i	0.480790	+	0.832752i	−0.518967	+	0.854794i	$0.673683\pi$
$354$		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	$-0.880818\pi$
$359$	−362932.	+	628617.i	−0.148624	+	0.257424i	0.782095	+	0.623159i	$0.214151\pi$
$360$		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	−0.979501	−	0.201440i	$-0.935438\pi$
$367$	−1.71382e6	−	2.96843e6i	−0.664202	−	1.15043i	0.315298	−	0.948993i	$-0.397895\pi$
$368$	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	−0.746227	−	0.665692i	$-0.768136\pi$
$373$	546522.	−	946604.i	0.203393	−	0.352287i	0.949619	+	0.313405i	$0.101470\pi$
$374$	−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	$-0.839096\pi$
$383$	−51966.3	+	90008.2i	−0.0181019	+	0.0313534i	0.856833	+	0.515595i	$0.172429\pi$
$384$		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	$-0.157443\pi$
$389$	86465.6	+	149763.i	0.0289714	+	0.0501799i	−0.851176	+	0.524880i	$0.824110\pi$
$390$		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	−0.995314	−	0.0966990i	$-0.969172\pi$
$397$	−1.29983e6	+	2.25137e6i	−0.413913	+	0.716918i	0.581401	+	0.813617i	$0.302505\pi$
$398$	−6947.91			−0.00219860
$399$		0			0
$400$	907594.			0.283623
$401$	1.72506e6	−	2.98789e6i	0.535726	−	0.927904i	−0.463402	−	0.886148i	$-0.653371\pi$
$401$	1.72506e6	−	2.98789e6i	0.535726	−	0.927904i	0.999128	−	0.0417559i	$-0.0132952\pi$
$402$		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	0.952724	−	0.303837i	$-0.0982677\pi$
$409$	721374.	+	1.24946e6i	0.213232	+	0.369329i	−0.739492	+	0.673165i	$0.764934\pi$
$410$	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	0.980655	−	0.195742i	$-0.0627115\pi$
$431$	1.23720e6	+	2.14290e6i	0.320810	+	0.555659i	−0.659845	+	0.751401i	$0.729378\pi$
$432$		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	−0.490750	−	0.871300i	$-0.663277\pi$
$439$	2.05610e6	−	3.56127e6i	0.509193	−	0.881948i	0.999943	−	0.0106480i	$-0.00338942\pi$
$440$	−5.95752e6			−1.46701
$441$		0			0
$442$	−3.03690e6			−0.739391
$443$	2.92674e6	−	5.06927e6i	0.708558	−	1.22726i	−0.256835	−	0.966455i	$-0.582680\pi$
$443$	2.92674e6	−	5.06927e6i	0.708558	−	1.22726i	0.965392	−	0.260802i	$-0.0839871\pi$
$444$		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	−0.388581	−	0.921415i	$-0.627035\pi$
$457$	2.69523e6	−	4.66828e6i	0.603678	−	1.04560i	0.992259	−	0.124186i	$-0.0396321\pi$
$458$	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	−0.779669	−	0.626191i	$-0.784613\pi$
$467$	718550.	−	1.24456e6i	0.152463	−	0.264074i	0.932132	+	0.362118i	$0.117946\pi$
$468$		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	$-0.242568\pi$
$479$	−1.18608e6	−	2.05436e6i	−0.236198	−	0.409107i	−0.959620	+	0.281299i	$0.909235\pi$
$480$		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	0.832296	−	0.554332i	$-0.187026\pi$
$487$	−334534.	−	579430.i	−0.0639172	−	0.110708i	−0.896213	+	0.443624i	$0.853693\pi$
$488$	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	−0.751370	−	0.659881i	$-0.770607\pi$
$499$	1.08902e6	−	1.88625e6i	0.195788	−	0.339115i	0.947159	+	0.320766i	$0.103940\pi$
$500$	−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	0.385656	+	0.922643i	$0.373975\pi$
$509$	−3.54335e6	+	6.13725e6i	−0.606204	+	1.04998i	−0.991860	+	0.127334i	$0.959358\pi$
$510$		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	$-0.0767536\pi$
$521$	1.72694e6	+	2.99114e6i	0.278729	+	0.482772i	−0.692340	+	0.721571i	$0.743420\pi$
$522$		0			0
$523$	278599.	−	482548.i	0.0445375	−	0.0771413i	−0.842897	−	0.538074i	$-0.819152\pi$
$523$	278599.	−	482548.i	0.0445375	−	0.0771413i	0.887435	+	0.460933i	$0.152485\pi$
$524$	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	−0.986532	−	0.163566i	$-0.947700\pi$
$541$	−2.39364e6	+	4.14591e6i	−0.351614	+	0.609013i	0.634919	+	0.772579i	$0.281034\pi$
$542$	−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	0.749305	+	0.662225i	$0.230388\pi$
$557$	6.94253e6	+	1.20248e7i	0.948156	+	1.64225i	0.198851	+	0.980030i	$0.436279\pi$
$558$		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	$-0.251450\pi$
$563$	−1.97962e6	−	3.42880e6i	−0.263215	−	0.455902i	−0.967094	+	0.254417i	$0.918116\pi$
$564$		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	0.374500	+	0.927227i	$0.377815\pi$
$569$	−4.75540e6	+	8.23659e6i	−0.615752	+	1.06651i	−0.990252	+	0.139287i	$0.955519\pi$
$570$		0			0
$571$	4.53978e6	+	7.86313e6i	0.582699	+	1.00926i	0.995158	+	0.0982881i	$0.0313367\pi$
$571$	4.53978e6	+	7.86313e6i	0.582699	+	1.00926i	−0.412459	+	0.910976i	$0.635330\pi$
$572$	−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	0.956040	−	0.293237i	$-0.0947326\pi$
$577$	1.79193e6	+	3.10371e6i	0.224069	+	0.388099i	−0.731971	+	0.681336i	$0.761399\pi$
$578$	−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	−0.157363	−	0.987541i	$-0.550299\pi$
$593$	6.64979e6	−	1.15178e7i	0.776554	−	1.34503i	0.933917	−	0.357490i	$-0.116367\pi$
$594$		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	$-0.0820377\pi$
$599$	2.30732e6	+	3.99639e6i	0.262748	+	0.455094i	−0.704223	+	0.709979i	$0.748704\pi$
$600$		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	−0.720217	−	0.693749i	$-0.755958\pi$
$607$	2.18494e6	−	3.78443e6i	0.240696	−	0.416897i	0.960913	+	0.276852i	$0.0892911\pi$
$608$	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	0.681629	−	0.731698i	$-0.261272\pi$
$613$	−2.72460e6	−	4.71914e6i	−0.292854	−	0.507238i	−0.974483	+	0.224460i	$0.927938\pi$
$614$	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	0.959004	−	0.283394i	$-0.0914605\pi$
$619$	2.23142e6	+	3.86494e6i	0.234075	+	0.405430i	−0.724928	+	0.688824i	$0.758127\pi$
$620$	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	$-0.226520\pi$
$641$	−1.94455e6	−	3.36806e6i	−0.186928	−	0.323768i	−0.944224	+	0.329303i	$0.893186\pi$
$642$		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	$-0.300999\pi$
$647$	−4.36138e6	−	7.55413e6i	−0.409603	−	0.709453i	−0.994845	+	0.101405i	$0.967666\pi$
$648$		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	$-0.812433\pi$
$653$	714958.	−	1.23834e6i	0.0656141	−	0.113647i	0.896966	+	0.442099i	$0.145766\pi$
$654$		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	0.832317	−	0.554300i	$-0.187014\pi$
$661$	−717566.	−	1.24286e6i	−0.0638790	−	0.110642i	−0.896196	+	0.443658i	$0.853681\pi$
$662$	−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	−0.316333	+	0.948648i	$0.602452\pi$
$677$	−1.16835e7	+	2.02364e7i	−0.979720	+	1.69692i	−0.663387	+	0.748276i	$0.730882\pi$
$678$		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	0.998447	+	0.0557153i	$0.0177439\pi$
$683$	6.67445e6	+	1.15605e7i	0.547474	+	0.948253i	−0.450972	+	0.892538i	$0.648923\pi$
$684$		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	0.475901	+	0.879499i	$0.342122\pi$
$691$	−6.57343e6	+	1.13855e7i	−0.523717	+	0.907105i	−0.999619	+	0.0276066i	$0.991211\pi$
$692$	−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	−0.439332	−	0.898325i	$-0.644785\pi$
$709$	7.47288e6	−	1.29434e7i	0.558306	−	0.967014i	0.997638	−	0.0686895i	$-0.0218818\pi$
$710$	−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	$-0.829248\pi$
$719$	177912.	−	308153.i	0.0128347	−	0.0222303i	0.872371	+	0.488844i	$0.162581\pi$
$720$		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	0.459668	+	0.888091i	$0.347968\pi$
$733$	−7.84459e6	+	1.35872e7i	−0.539275	+	0.934052i	−0.998943	+	0.0459613i	$0.985365\pi$
$734$	−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	−0.999988	−	0.00485312i	$-0.998455\pi$
$739$	−7.48534e6	−	1.29650e7i	−0.504197	−	0.873295i	0.495791	−	0.868442i	$-0.334878\pi$
$740$	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	0.280034	+	0.959990i	$0.409654\pi$
$751$	−1.06857e7	+	1.85082e7i	−0.691359	+	1.19747i	−0.971393	+	0.237478i	$0.923679\pi$
$752$	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	$-0.708070\pi$
$761$	6.12587e6	−	1.06103e7i	0.383448	−	0.664151i	0.991553	+	0.129706i	$0.0414033\pi$
$762$		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	$-0.147289\pi$
$773$	1.01072e6	+	1.75062e6i	0.0608389	+	0.105376i	−0.834002	+	0.551762i	$0.813956\pi$
$774$		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	0.985986	−	0.166826i	$-0.0533519\pi$
$787$	6.05566e6	+	1.04887e7i	0.348517	+	0.603650i	−0.637469	+	0.770476i	$0.720019\pi$
$788$	−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	$-0.260552\pi$
$797$	2.45062e7			1.36657			0.683283	+	0.730154i	$0.260552\pi$
$798$		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	$-0.115252\pi$
$809$	2.99377e6	+	5.18536e6i	0.160823	+	0.278553i	−0.774341	+	0.632768i	$0.781919\pi$
$810$		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	$-0.832417\pi$
$821$	55578.8	−	96265.3i	0.00287774	−	0.00498439i	0.867461	+	0.497506i	$0.165751\pi$
$822$		0			0
$823$	−1.71946e6	−	2.97820e6i	−0.0884898	−	0.153269i	0.818383	−	0.574673i	$-0.194871\pi$
$823$	−1.71946e6	−	2.97820e6i	−0.0884898	−	0.153269i	−0.906873	+	0.421404i	$0.861537\pi$
$824$	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	$-0.341588\pi$
$827$	1.87782e7			0.954751			0.477375	+	0.878700i	$0.341588\pi$
$828$		0			0
$829$	−3.76889e6	−	6.52791e6i	−0.190470	−	0.329904i	0.754936	−	0.655799i	$-0.227668\pi$
$829$	−3.76889e6	−	6.52791e6i	−0.190470	−	0.329904i	−0.945406	+	0.325894i	$0.894335\pi$
$830$	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	$-0.632722\pi$
$839$	−1.65147e7			−0.809962			−0.404981	+	0.914325i	$0.632722\pi$
$840$		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	$-0.168862\pi$
$857$	−148276.	−	256821.i	−0.00689633	−	0.0119448i	−0.869453	+	0.494016i	$0.835529\pi$
$858$		0			0
$859$	−6.06474e6	+	1.05044e7i	−0.280433	+	0.485725i	−0.971491	−	0.237074i	$-0.923811\pi$
$859$	−6.06474e6	+	1.05044e7i	−0.280433	+	0.485725i	0.691058	+	0.722799i	$0.257145\pi$
$860$	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	$-0.737181\pi$
$863$	6.50899e6	−	1.12739e7i	0.297500	−	0.515285i	0.975563	+	0.219718i	$0.0705139\pi$
$864$		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	−0.842183	−	0.539192i	$-0.818730\pi$
$877$	1.04463e6	−	1.80935e6i	0.0458630	−	0.0794371i	0.888046	+	0.459755i	$0.152063\pi$
$878$	−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	$-0.519695\pi$
$881$	−2.84897e6			−0.123665			−0.0618327	+	0.998087i	$0.519695\pi$
$882$		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	0.493575	+	0.869703i	$0.335690\pi$
$887$	−1.18659e7	+	2.05523e7i	−0.506397	+	0.877106i	−0.999973	+	0.00740294i	$0.997644\pi$
$888$		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	1.00000		0.000295096i	$-9.39319e-5\pi$
$907$	1.23813e7	+	2.14450e7i	0.499744	+	0.865583i	−0.500256	+	0.865878i	$0.666761\pi$
$908$	−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	$-0.608844\pi$
$911$	−1.67991e7			−0.670639			−0.335320	+	0.942104i	$0.608844\pi$
$912$		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	−0.970545	−	0.240922i	$-0.922550\pi$
$919$	−7.08247e6	+	1.22672e7i	−0.276628	+	0.479133i	0.693917	+	0.720055i	$0.255884\pi$
$920$	−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	−0.435560	−	0.900160i	$-0.643450\pi$
$929$	1.47777e7	−	2.55957e7i	0.561781	−	0.973033i	0.997341	−	0.0728736i	$-0.0232170\pi$
$930$		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	−0.975240	−	0.221149i	$-0.929019\pi$
$941$	−1.84473e7	−	3.19517e7i	−0.679141	−	1.17631i	0.296100	−	0.955157i	$-0.404314\pi$
$942$		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	$-0.918390\pi$
$947$	−7.28703e6	+	1.26215e7i	−0.264044	+	0.457337i	0.703269	+	0.710924i	$0.251723\pi$
$948$		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	$-0.637577\pi$
$953$	−2.34882e7			−0.837757			−0.418878	+	0.908042i	$0.637577\pi$
$954$		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	0.0838945	−	0.996475i	$-0.473264\pi$
$971$	2.65863e7	−	4.60488e7i	0.904920	−	1.56737i	0.821025	−	0.570892i	$-0.193403\pi$
$972$		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	$-0.00985486\pi$
$977$	1.41109e7	+	2.44408e7i	0.472953	+	0.819178i	−0.526568	+	0.850133i	$0.676522\pi$
$978$		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	$-0.0752605\pi$
$983$	8.58072e6	+	1.48622e7i	0.283230	+	0.490570i	−0.688948	+	0.724811i	$0.741927\pi$
$984$		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	0.505509	−	0.862821i	$-0.331305\pi$
$991$	−1.52871e7	−	2.64780e7i	−0.494471	−	0.856448i	−0.999980	+	0.00637296i	$0.997971\pi$
$992$	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	−0.944137	−	0.329553i	$-0.893102\pi$
$997$	−2.37741e7	−	4.11779e7i	−0.757470	−	1.31198i	0.186667	−	0.982423i	$-0.440232\pi$
$998$	−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.37.4	yes	12
3.2	odd	2	inner	63.6.e.f.37.3	✓	12
7.2	even	3		441.6.a.bc.1.3		6
7.4	even	3	inner	63.6.e.f.46.4	yes	12
7.5	odd	6		441.6.a.bd.1.3		6
21.2	odd	6		441.6.a.bc.1.4		6
21.5	even	6		441.6.a.bd.1.4		6
21.11	odd	6	inner	63.6.e.f.46.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.e.f.37.3	✓	12	3.2	odd	2	inner
63.6.e.f.37.4	yes	12	1.1	even	1	trivial
63.6.e.f.46.3	yes	12	21.11	odd	6	inner
63.6.e.f.46.4	yes	12	7.4	even	3	inner
441.6.a.bc.1.3		6	7.2	even	3
441.6.a.bc.1.4		6	21.2	odd	6
441.6.a.bd.1.3		6	7.5	odd	6
441.6.a.bd.1.4		6	21.5	even	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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