LMFDB - Embedded newform 63.4.p.a.26.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(17,63)]

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([3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.p (of order $6$, 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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 $ x^16 - 48x^14 + 1647x^12 - 27620x^10 + 336765x^8 - 1200006x^6 + 3242464x^4 - 1762200*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.6
Root			$1.57646 + 0.910170i$ of defining polynomial
Character	$\chi$	$=$	63.26
Dual form			63.4.p.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57646 + 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +(16.2919 + 8.80760i) q^{7} -23.0935i q^{8} +O(q^{10})$	\(q+(1.57646 + 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +(16.2919 + 8.80760i) q^{7} -23.0935i q^{8} +(23.7848 - 13.7321i) q^{10} +(8.56529 - 4.94517i) q^{11} +67.8891i q^{13} +(17.6671 + 28.7132i) q^{14} +(2.27356 - 3.93792i) q^{16} +(-35.0687 - 60.7407i) q^{17} +(-53.2242 - 30.7290i) q^{19} -70.7052 q^{20} +18.0038 q^{22} +(113.895 + 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} +(-61.7906 + 107.025i) q^{26} +(-2.42915 - 86.7586i) q^{28} +158.738i q^{29} +(-66.2349 + 38.2407i) q^{31} +(-152.828 + 88.2353i) q^{32} -127.674i q^{34} +(237.983 - 146.430i) q^{35} +(-174.341 + 301.967i) q^{37} +(-55.9372 - 96.8861i) q^{38} +(-301.742 - 174.211i) q^{40} -138.909 q^{41} +539.651 q^{43} +(-40.1400 - 23.1749i) q^{44} +(119.701 + 207.328i) q^{46} +(-111.821 + 193.680i) q^{47} +(187.852 + 286.985i) q^{49} -186.823i q^{50} +(275.529 - 159.076i) q^{52} +(459.003 - 265.005i) q^{53} -149.220i q^{55} +(203.398 - 376.237i) q^{56} +(-144.479 + 250.245i) q^{58} +(-271.438 - 470.145i) q^{59} +(-116.218 - 67.0983i) q^{61} -139.222 q^{62} -357.614 q^{64} +(887.046 + 512.136i) q^{65} +(-160.290 - 277.630i) q^{67} +(-164.344 + 284.653i) q^{68} +(508.446 - 14.2359i) q^{70} -416.958i q^{71} +(472.510 - 272.804i) q^{73} +(-549.683 + 317.360i) q^{74} +288.014i q^{76} +(183.100 - 5.12660i) q^{77} +(161.369 - 279.499i) q^{79} +(-34.3022 - 59.4132i) q^{80} +(-218.984 - 126.431i) q^{82} -885.170 q^{83} -1058.19 q^{85} +(850.739 + 491.174i) q^{86} +(-114.201 - 197.802i) q^{88} +(-812.312 + 1406.97i) q^{89} +(-597.940 + 1106.04i) q^{91} -616.327i q^{92} +(-352.564 + 203.553i) q^{94} +(-803.017 + 463.622i) q^{95} -739.155i q^{97} +(34.9363 + 623.398i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 56 q^{7}+O(q^{10}) $ 16 * q + 32 * q^4 + 56 * q^7	$ 16 q + 32 q^{4} + 56 q^{7} - 72 q^{10} - 188 q^{16} - 612 q^{19} + 528 q^{22} - 20 q^{25} + 1036 q^{28} + 1128 q^{31} - 1196 q^{37} - 3204 q^{40} + 328 q^{43} - 1392 q^{46} + 784 q^{49} + 4452 q^{52} - 3372 q^{58} - 1632 q^{61} + 5432 q^{64} + 308 q^{67} + 3612 q^{70} + 4068 q^{73} - 2176 q^{79} - 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 924 q^{91} - 2916 q^{94}+O(q^{100}) $ 16 * q + 32 * q^4 + 56 * q^7 - 72 * q^10 - 188 * q^16 - 612 * q^19 + 528 * q^22 - 20 * q^25 + 1036 * q^28 + 1128 * q^31 - 1196 * q^37 - 3204 * q^40 + 328 * q^43 - 1392 * q^46 + 784 * q^49 + 4452 * q^52 - 3372 * q^58 - 1632 * q^61 + 5432 * q^64 + 308 * q^67 + 3612 * q^70 + 4068 * q^73 - 2176 * q^79 - 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 924 * q^91 - 2916 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.57646	+	0.910170i	0.557363	+	0.321794i	0.752086	−	0.659064i	$-0.229048\pi$
$2$	1.57646	+	0.910170i	0.557363	+	0.321794i	−0.194723	+	0.980858i	$0.562381\pi$
$3$		0			0
$3$		0			0
$4$	−2.34318	−	4.05851i	−0.292898	−	0.507314i
$5$	7.54372	−	13.0661i	0.674731	−	1.16867i	−0.301817	−	0.953366i	$-0.597593\pi$
$5$	7.54372	−	13.0661i	0.674731	−	1.16867i	0.976547	−	0.215302i	$-0.0690736\pi$
$6$		0			0
$7$	16.2919	+	8.80760i	0.879680	+	0.475566i
$7$	16.2919	+	8.80760i	0.879680	+	0.475566i
$8$		−	23.0935i		−	1.02060i
$9$		0			0
$10$	23.7848	−	13.7321i	0.752140	−	0.434248i
$11$	8.56529	−	4.94517i	0.234776	−	0.135548i	−0.377998	−	0.925807i	$-0.623387\pi$
$11$	8.56529	−	4.94517i	0.234776	−	0.135548i	0.612773	+	0.790259i	$0.290054\pi$
$12$		0			0
$13$			67.8891i			1.44839i	0.689596	+	0.724194i	$0.257788\pi$
$13$			67.8891i			1.44839i	−0.689596	+	0.724194i	$0.742212\pi$
$14$	17.6671	+	28.7132i	0.337267	+	0.548138i
$15$		0			0
$16$	2.27356	−	3.93792i	0.0355244	−	0.0615300i
$17$	−35.0687	−	60.7407i	−0.500318	−	0.866575i	−1.00000		0.000366661i	$-0.999883\pi$
$17$	−35.0687	−	60.7407i	−0.500318	−	0.866575i	0.499682	−	0.866209i	$-0.333450\pi$
$18$		0			0
$19$	−53.2242	−	30.7290i	−0.642656	−	0.371038i	0.142981	−	0.989725i	$-0.454331\pi$
$19$	−53.2242	−	30.7290i	−0.642656	−	0.371038i	−0.785637	+	0.618688i	$0.787665\pi$
$20$	−70.7052			−0.790508
$21$		0			0
$22$	18.0038			0.174474
$23$	113.895	+	65.7575i	1.03256	+	0.596147i	0.917716	−	0.397236i	$-0.130031\pi$
$23$	113.895	+	65.7575i	1.03256	+	0.596147i	0.114841	+	0.993384i	$0.463364\pi$
$24$		0			0
$25$	−51.3154	−	88.8809i	−0.410523	−	0.711047i
$26$	−61.7906	+	107.025i	−0.466082	+	0.807278i
$27$		0			0
$28$	−2.42915	−	86.7586i	−0.0163952	−	0.585566i
$29$			158.738i			1.01645i	0.861225	+	0.508223i	$0.169698\pi$
$29$			158.738i			1.01645i	−0.861225	+	0.508223i	$0.830302\pi$
$30$		0			0
$31$	−66.2349	+	38.2407i	−0.383746	+	0.221556i	−0.679447	−	0.733725i	$-0.737780\pi$
$31$	−66.2349	+	38.2407i	−0.383746	+	0.221556i	0.295701	+	0.955281i	$0.404447\pi$
$32$	−152.828	+	88.2353i	−0.844264	+	0.487436i
$33$		0			0
$34$		−	127.674i		−	0.643996i
$35$	237.983	−	146.430i	1.14933	−	0.707175i
$36$		0			0
$37$	−174.341	+	301.967i	−0.774634	+	1.34171i	0.160366	+	0.987058i	$0.448733\pi$
$37$	−174.341	+	301.967i	−0.774634	+	1.34171i	−0.935000	+	0.354648i	$0.884601\pi$
$38$	−55.9372	−	96.8861i	−0.238795	−	0.413605i
$39$		0			0
$40$	−301.742	−	174.211i	−1.19274	−	0.688629i
$41$	−138.909			−0.529120			−0.264560	−	0.964369i	$-0.585227\pi$
$41$	−138.909			−0.529120			−0.264560	+	0.964369i	$0.585227\pi$
$42$		0			0
$43$	539.651			1.91386			0.956931	−	0.290316i	$-0.0937604\pi$
$43$	539.651			1.91386			0.956931	+	0.290316i	$0.0937604\pi$
$44$	−40.1400	−	23.1749i	−0.137530	−	0.0794032i
$45$		0			0
$46$	119.701	+	207.328i	0.383673	+	0.664541i
$47$	−111.821	+	193.680i	−0.347039	+	0.601089i	−0.985722	−	0.168381i	$-0.946146\pi$
$47$	−111.821	+	193.680i	−0.347039	+	0.601089i	0.638683	+	0.769470i	$0.279480\pi$
$48$		0			0
$49$	187.852	+	286.985i	0.547674	+	0.836692i
$50$		−	186.823i		−	0.528415i
$51$		0			0
$52$	275.529	−	159.076i	0.734787	−	0.424230i
$53$	459.003	−	265.005i	1.18960	−	0.686817i	0.231386	−	0.972862i	$-0.425674\pi$
$53$	459.003	−	265.005i	1.18960	−	0.686817i	0.958216	+	0.286045i	$0.0923407\pi$
$54$		0			0
$55$		−	149.220i		−	0.365833i
$56$	203.398	−	376.237i	0.485362	−	0.897800i
$57$		0			0
$58$	−144.479	+	250.245i	−0.327086	+	0.566530i
$59$	−271.438	−	470.145i	−0.598953	−	1.03742i	−0.992976	−	0.118317i	$-0.962250\pi$
$59$	−271.438	−	470.145i	−0.598953	−	1.03742i	0.394023	−	0.919101i	$-0.371083\pi$
$60$		0			0
$61$	−116.218	−	67.0983i	−0.243937	−	0.140837i	0.373048	−	0.927812i	$-0.378313\pi$
$61$	−116.218	−	67.0983i	−0.243937	−	0.140837i	−0.616985	+	0.786975i	$0.711646\pi$
$62$	−139.222			−0.285181
$63$		0			0
$64$	−357.614			−0.698464
$65$	887.046	+	512.136i	1.69269	+	0.977272i
$66$		0			0
$67$	−160.290	−	277.630i	−0.292276	−	0.506238i	0.682071	−	0.731286i	$-0.261079\pi$
$67$	−160.290	−	277.630i	−0.292276	−	0.506238i	−0.974348	+	0.225048i	$0.927746\pi$
$68$	−164.344	+	284.653i	−0.293084	+	0.507636i
$69$		0			0
$70$	508.446	−	14.2359i	0.868156	−	0.0243074i
$71$		−	416.958i		−	0.696955i	−0.937317	−	0.348478i	$-0.886699\pi$
$71$		−	416.958i		−	0.696955i	0.937317	−	0.348478i	$-0.113301\pi$
$72$		0			0
$73$	472.510	−	272.804i	0.757577	−	0.437387i	−0.0708484	−	0.997487i	$-0.522571\pi$
$73$	472.510	−	272.804i	0.757577	−	0.437387i	0.828425	+	0.560100i	$0.189237\pi$
$74$	−549.683	+	317.360i	−0.863505	+	0.498545i
$75$		0			0
$76$			288.014i			0.434704i
$77$	183.100	−	5.12660i	0.270989	−	0.00758740i
$78$		0			0
$79$	161.369	−	279.499i	0.229815	−	0.398052i	−0.727938	−	0.685643i	$-0.759521\pi$
$79$	161.369	−	279.499i	0.229815	−	0.398052i	0.957753	+	0.287591i	$0.0928545\pi$
$80$	−34.3022	−	59.4132i	−0.0479388	−	0.0830324i
$81$		0			0
$82$	−218.984	−	126.431i	−0.294912	−	0.170267i
$83$	−885.170			−1.17060			−0.585301	−	0.810816i	$-0.699024\pi$
$83$	−885.170			−1.17060			−0.585301	+	0.810816i	$0.699024\pi$
$84$		0			0
$85$	−1058.19			−1.35032
$86$	850.739	+	491.174i	1.06672	+	0.615869i
$87$		0			0
$88$	−114.201	−	197.802i	−0.138340	−	0.239612i
$89$	−812.312	+	1406.97i	−0.967471	+	1.67571i	−0.264645	+	0.964346i	$0.585255\pi$
$89$	−812.312	+	1406.97i	−0.967471	+	1.67571i	−0.702826	+	0.711362i	$0.748079\pi$
$90$		0			0
$91$	−597.940	+	1106.04i	−0.688804	+	1.27412i
$92$		−	616.327i		−	0.698441i
$93$		0			0
$94$	−352.564	+	203.553i	−0.386853	+	0.223350i
$95$	−803.017	+	463.622i	−0.867240	+	0.500701i
$96$		0			0
$97$		−	739.155i		−	0.773710i	−0.922141	−	0.386855i	$-0.873561\pi$
$97$		−	739.155i		−	0.773710i	0.922141	−	0.386855i	$-0.126439\pi$
$98$	34.9363	+	623.398i	0.0360112	+	0.642579i
$99$		0			0
$100$	−240.483	+	416.528i	−0.240483	+	0.416528i
$101$	−119.758	−	207.427i	−0.117984	−	0.204354i	0.800985	−	0.598685i	$-0.204310\pi$
$101$	−119.758	−	207.427i	−0.117984	−	0.204354i	−0.918969	+	0.394331i	$0.870976\pi$
$102$		0			0
$103$	−44.2852	−	25.5681i	−0.0423645	−	0.0244592i	0.478668	−	0.877996i	$-0.341120\pi$
$103$	−44.2852	−	25.5681i	−0.0423645	−	0.0244592i	−0.521033	+	0.853537i	$0.674453\pi$
$104$	1567.80			1.47822
$105$		0			0
$106$	964.800			0.884054
$107$	−1031.43	−	595.495i	−0.931886	−	0.538025i	−0.0444785	−	0.999010i	$-0.514163\pi$
$107$	−1031.43	−	595.495i	−0.931886	−	0.538025i	−0.887408	+	0.460986i	$0.847496\pi$
$108$		0			0
$109$	−194.585	−	337.031i	−0.170989	−	0.296162i	0.767777	−	0.640718i	$-0.221363\pi$
$109$	−194.585	−	337.031i	−0.170989	−	0.296162i	−0.938766	+	0.344555i	$0.888030\pi$
$110$	135.816	−	235.239i	0.117723	−	0.203902i
$111$		0			0
$112$	71.7243	−	44.1316i	0.0605117	−	0.0372326i
$113$			718.545i			0.598186i	0.954224	+	0.299093i	$0.0966841\pi$
$113$			718.545i			0.598186i	−0.954224	+	0.299093i	$0.903316\pi$
$114$		0			0
$115$	1718.39	−	992.113i	1.39340	−	0.804478i
$116$	644.240	−	371.952i	0.515657	−	0.297715i
$117$		0			0
$118$		−	988.220i		−	0.770958i
$119$	−36.3552	−	1298.45i	−0.0280057	−	1.00024i
$120$		0			0
$121$	−616.591	+	1067.97i	−0.463254	+	0.802379i
$122$	−122.142	−	211.556i	−0.0906409	−	0.156995i
$123$		0			0
$124$	310.401	+	179.210i	0.224797	+	0.129786i
$125$	337.493			0.241490
$126$		0			0
$127$	−179.456			−0.125387			−0.0626934	−	0.998033i	$-0.519969\pi$
$127$	−179.456			−0.125387			−0.0626934	+	0.998033i	$0.519969\pi$
$128$	658.861	+	380.393i	0.454966	+	0.262675i
$129$		0			0
$130$	932.263	+	1614.73i	0.628960	+	1.08939i
$131$	1223.43	−	2119.05i	0.815968	−	1.41330i	−0.0926619	−	0.995698i	$-0.529538\pi$
$131$	1223.43	−	2119.05i	0.815968	−	1.41330i	0.908630	−	0.417601i	$-0.137129\pi$
$132$		0			0
$133$	−596.474	−	969.411i	−0.388879	−	0.632020i
$134$		−	583.564i		−	0.376211i
$135$		0			0
$136$	−1402.71	+	809.858i	−0.884425	+	0.510623i
$137$	443.021	−	255.778i	0.276276	−	0.159508i	−0.355460	−	0.934691i	$-0.615676\pi$
$137$	443.021	−	255.778i	0.276276	−	0.159508i	0.631736	+	0.775183i	$0.282342\pi$
$138$		0			0
$139$		−	599.427i		−	0.365775i	−0.983134	−	0.182888i	$-0.941456\pi$
$139$		−	599.427i		−	0.365775i	0.983134	−	0.182888i	$-0.0585444\pi$
$140$	−1151.92	−	622.743i	−0.695394	−	0.375939i
$141$		0			0
$142$	379.503	−	657.318i	0.224276	−	0.388457i
$143$	335.723	+	581.490i	0.196326	+	0.340046i
$144$		0			0
$145$	2074.09	+	1197.48i	1.18789	+	0.685828i
$146$	993.191			0.562994
$147$		0			0
$148$	1634.05			0.907554
$149$	−1899.63	−	1096.75i	−1.04445	−	0.603016i	−0.123362	−	0.992362i	$-0.539368\pi$
$149$	−1899.63	−	1096.75i	−1.04445	−	0.603016i	−0.921092	+	0.389346i	$0.872701\pi$
$150$		0			0
$151$	358.683	+	621.257i	0.193306	+	0.334816i	0.946344	−	0.323161i	$-0.104746\pi$
$151$	358.683	+	621.257i	0.193306	+	0.334816i	−0.753038	+	0.657977i	$0.771412\pi$
$152$	−709.640	+	1229.13i	−0.378680	+	0.655893i
$153$		0			0
$154$	293.316	+	158.570i	0.153481	+	0.0829737i
$155$			1153.91i			0.597963i
$156$		0			0
$157$	−1561.39	+	901.471i	−0.793712	+	0.458250i	−0.841268	−	0.540619i	$-0.818190\pi$
$157$	−1561.39	+	901.471i	−0.793712	+	0.458250i	0.0475556	+	0.998869i	$0.484857\pi$
$158$	508.783	−	293.746i	0.256181	−	0.147906i
$159$		0			0
$160$			2662.49i			1.31555i
$161$	1276.41	+	2074.46i	0.624813	+	1.01547i
$162$		0			0
$163$	1453.90	−	2518.24i	0.698642	−	1.21008i	−0.270296	−	0.962777i	$-0.587122\pi$
$163$	1453.90	−	2518.24i	0.698642	−	1.21008i	0.968938	−	0.247305i	$-0.0795451\pi$
$164$	325.489	+	563.763i	0.154978	+	0.268430i
$165$		0			0
$166$	−1395.44	−	805.655i	−0.652451	−	0.376693i
$167$	−3491.37			−1.61779			−0.808893	−	0.587956i	$-0.799933\pi$
$167$	−3491.37			−1.61779			−0.808893	+	0.587956i	$0.799933\pi$
$168$		0			0
$169$	−2411.93			−1.09783
$170$	−1668.20	−	963.135i	−0.752618	−	0.434524i
$171$		0			0
$172$	−1264.50	−	2190.18i	−0.560566	−	0.970928i
$173$	877.377	−	1519.66i	0.385583	−	0.667848i	−0.606267	−	0.795261i	$-0.707334\pi$
$173$	877.377	−	1519.66i	0.385583	−	0.667848i	0.991850	+	0.127412i	$0.0406672\pi$
$174$		0			0
$175$	−53.1981	−	1900.01i	−0.0229794	−	0.820725i
$176$		−	44.9726i		−	0.0192610i
$177$		0			0
$178$	−2561.16	+	1478.68i	−1.07846	+	0.622652i
$179$	685.639	−	395.854i	0.286296	−	0.165293i	−0.349974	−	0.936759i	$-0.613810\pi$
$179$	685.639	−	395.854i	0.286296	−	0.165293i	0.636270	+	0.771466i	$0.280476\pi$
$180$		0			0
$181$			2522.19i			1.03576i	0.855452	+	0.517882i	$0.173279\pi$
$181$			2522.19i			1.03576i	−0.855452	+	0.517882i	$0.826721\pi$
$182$	−1949.32	+	1199.41i	−0.793917	+	0.488494i
$183$		0			0
$184$	1518.57	−	2630.24i	0.608427	−	1.05383i
$185$	2630.36	+	4555.91i	1.04534	+	1.81058i
$186$		0			0
$187$	−600.746	−	346.841i	−0.234925	−	0.135634i
$188$	1048.07			0.406588
$189$		0			0
$190$	−1687.90			−0.644490
$191$	782.266	+	451.642i	0.296350	+	0.171098i	0.640802	−	0.767706i	$-0.278602\pi$
$191$	782.266	+	451.642i	0.296350	+	0.171098i	−0.344452	+	0.938804i	$0.611935\pi$
$192$		0			0
$193$	99.4374	+	172.231i	0.0370863	+	0.0642354i	0.883973	−	0.467538i	$-0.154859\pi$
$193$	99.4374	+	172.231i	0.0370863	+	0.0642354i	−0.846886	+	0.531774i	$0.821526\pi$
$194$	672.757	−	1165.25i	0.248975	−	0.431237i
$195$		0			0
$196$	724.560	−	1434.86i	0.264053	−	0.522908i
$197$			3220.69i			1.16480i	0.812904	+	0.582398i	$0.197886\pi$
$197$			3220.69i			1.16480i	−0.812904	+	0.582398i	$0.802114\pi$
$198$		0			0
$199$	2468.10	−	1424.96i	0.879191	−	0.507601i	0.00879944	−	0.999961i	$-0.497199\pi$
$199$	2468.10	−	1424.96i	0.879191	−	0.507601i	0.870392	+	0.492360i	$0.163866\pi$
$200$	−2052.57	+	1185.05i	−0.725694	+	0.418979i
$201$		0			0
$202$		−	436.000i		−	0.151866i
$203$	−1398.10	+	2586.15i	−0.483387	+	0.894148i
$204$		0			0
$205$	−1047.89	+	1815.00i	−0.357014	+	0.618366i
$206$	−46.5426	−	80.6141i	−0.0157416	−	0.0272653i
$207$		0			0
$208$	267.342	+	154.350i	0.0891194	+	0.0514531i
$209$	−607.841			−0.201173
$210$		0			0
$211$	1204.50			0.392993			0.196496	−	0.980505i	$-0.437044\pi$
$211$	1204.50			0.392993			0.196496	+	0.980505i	$0.437044\pi$
$212$	−2151.05	−	1241.91i	−0.696863	−	0.402334i
$213$		0			0
$214$	−1084.00	−	1877.55i	−0.346266	−	0.599750i
$215$	4070.98	−	7051.14i	1.29134	−	2.23667i
$216$		0			0
$217$	−1415.90	+	39.6437i	−0.442938	+	0.0124018i
$218$		−	708.421i		−	0.220093i
$219$		0			0
$220$	−605.611	+	349.649i	−0.185592	+	0.107152i
$221$	4123.63	−	2380.78i	1.25514	−	0.724654i
$222$		0			0
$223$			3377.73i			1.01430i	0.861857	+	0.507151i	$0.169301\pi$
$223$			3377.73i			1.01430i	−0.861857	+	0.507151i	$0.830699\pi$
$224$	−3267.00	+	91.4725i	−0.974490	+	0.0272846i
$225$		0			0
$226$	−653.998	+	1132.76i	−0.192493	+	0.333407i
$227$	−2261.98	−	3917.86i	−0.661378	−	1.14554i	−0.980254	−	0.197744i	$-0.936638\pi$
$227$	−2261.98	−	3917.86i	−0.661378	−	1.14554i	0.318875	−	0.947797i	$-0.396695\pi$
$228$		0			0
$229$	3389.61	+	1956.99i	0.978131	+	0.564724i	0.901705	−	0.432351i	$-0.142316\pi$
$229$	3389.61	+	1956.99i	0.978131	+	0.564724i	0.0764258	+	0.997075i	$0.475649\pi$
$230$	3611.96			1.03550
$231$		0			0
$232$	3665.82			1.03738
$233$	−3783.80	−	2184.58i	−1.06388	−	0.614234i	−0.137381	−	0.990518i	$-0.543868\pi$
$233$	−3783.80	−	2184.58i	−1.06388	−	0.614234i	−0.926504	+	0.376284i	$0.877202\pi$
$234$		0			0
$235$	1687.10	+	2922.14i	0.468316	+	0.811147i
$236$	−1272.06	+	2203.27i	−0.350864	+	0.607714i
$237$		0			0
$238$	1124.50	−	2080.05i	0.306263	−	0.566511i
$239$			1945.23i			0.526471i	0.964732	+	0.263235i	$0.0847896\pi$
$239$			1945.23i			0.526471i	−0.964732	+	0.263235i	$0.915210\pi$
$240$		0			0
$241$	−3499.81	+	2020.61i	−0.935446	+	0.540080i	−0.888530	−	0.458819i	$-0.848273\pi$
$241$	−3499.81	+	2020.61i	−0.935446	+	0.540080i	−0.0469158	+	0.998899i	$0.514939\pi$
$242$	−1944.06	+	1122.40i	−0.516401	+	0.298144i
$243$		0			0
$244$			628.894i			0.165003i
$245$	5166.88	−	289.561i	1.34735	−	0.0755077i
$246$		0			0
$247$	2086.16	−	3613.34i	0.537407	−	0.930816i
$248$	883.112	+	1529.59i	0.226120	+	0.391651i
$249$		0			0
$250$	532.045	+	307.176i	0.134598	+	0.0777101i
$251$	4415.70			1.11042			0.555212	−	0.831709i	$-0.312637\pi$
$251$	4415.70			1.11042			0.555212	+	0.831709i	$0.312637\pi$
$252$		0			0
$253$	1300.73			0.323226
$254$	−282.905	−	163.335i	−0.0698860	−	0.0403487i
$255$		0			0
$256$	2122.90	+	3676.97i	0.518286	+	0.897698i
$257$	348.800	−	604.139i	0.0846597	−	0.146635i	−0.820586	−	0.571522i	$-0.806353\pi$
$257$	348.800	−	604.139i	0.0846597	−	0.146635i	0.905246	+	0.424888i	$0.139686\pi$
$258$		0			0
$259$	−5499.95	+	3384.10i	−1.31950	+	0.811882i
$260$		−	4800.11i		−	1.14496i
$261$		0			0
$262$	3857.39	−	2227.06i	0.909581	−	0.525147i
$263$	−690.664	+	398.755i	−0.161932	+	0.0934915i	−0.578776	−	0.815487i	$-0.696469\pi$
$263$	−690.664	+	398.755i	−0.161932	+	0.0934915i	0.416844	+	0.908978i	$0.363136\pi$
$264$		0			0
$265$		−	7996.51i		−	1.85367i
$266$	−57.9894	−	2071.13i	−0.0133668	−	0.477403i
$267$		0			0
$268$	−751.176	+	1301.08i	−0.171214	+	0.296552i
$269$	−205.351	−	355.679i	−0.0465446	−	0.0806176i	0.841815	−	0.539767i	$-0.181488\pi$
$269$	−205.351	−	355.679i	−0.0465446	−	0.0806176i	−0.888359	+	0.459149i	$0.848154\pi$
$270$		0			0
$271$	3283.42	+	1895.69i	0.735992	+	0.424925i	0.820610	−	0.571488i	$-0.193634\pi$
$271$	3283.42	+	1895.69i	0.735992	+	0.424925i	−0.0846182	+	0.996413i	$0.526967\pi$
$272$	−318.923			−0.0710939
$273$		0			0
$274$	931.207			0.205315
$275$	−879.063	−	507.527i	−0.192762	−	0.111291i
$276$		0			0
$277$	−1623.31	−	2811.66i	−0.352113	−	0.609877i	0.634507	−	0.772917i	$-0.281203\pi$
$277$	−1623.31	−	2811.66i	−0.352113	−	0.609877i	−0.986619	+	0.163040i	$0.947870\pi$
$278$	545.581	−	944.973i	0.117704	−	0.203870i
$279$		0			0
$280$	−3381.57	−	5495.85i	−0.721741	−	1.17300i
$281$			1599.58i			0.339583i	0.985480	+	0.169791i	$0.0543094\pi$
$281$			1599.58i			0.339583i	−0.985480	+	0.169791i	$0.945691\pi$
$282$		0			0
$283$	−3694.70	+	2133.13i	−0.776067	+	0.448062i	−0.835034	−	0.550198i	$-0.814552\pi$
$283$	−3694.70	+	2133.13i	−0.776067	+	0.448062i	0.0589678	+	0.998260i	$0.481219\pi$
$284$	−1692.23	+	977.008i	−0.353575	+	0.204137i
$285$		0			0
$286$			1222.26i			0.252706i
$287$	−2263.09	−	1223.45i	−0.465456	−	0.251631i
$288$		0			0
$289$	−3.12079	+	5.40536i	−0.000635210	+	0.00110022i
$290$	2179.82	+	3775.55i	0.441390	+	0.764510i
$291$		0			0
$292$	−2214.35	−	1278.46i	−0.443785	−	0.256219i
$293$	−2926.77			−0.583562			−0.291781	−	0.956485i	$-0.594248\pi$
$293$	−2926.77			−0.583562			−0.291781	+	0.956485i	$0.594248\pi$
$294$		0			0
$295$	−8190.62			−1.61653
$296$	6973.48	+	4026.14i	1.36934	+	0.790590i
$297$		0			0
$298$	−1996.46	−	3457.97i	−0.388093	−	0.672198i
$299$	−4464.22	+	7732.25i	−0.863453	+	1.49554i
$300$		0			0
$301$	8791.95	+	4753.03i	1.68359	+	0.910167i
$302$			1305.85i			0.248819i
$303$		0			0
$304$	−242.017	+	139.728i	−0.0456599	+	0.0263618i
$305$	−1753.43	+	1012.34i	−0.329183	+	0.190054i
$306$		0			0
$307$		−	3571.36i		−	0.663935i	−0.943291	−	0.331968i	$-0.892288\pi$
$307$		−	3571.36i		−	0.663935i	0.943291	−	0.331968i	$-0.107712\pi$
$308$	−449.843	−	731.100i	−0.0832213	−	0.135254i
$309$		0			0
$310$	−1050.25	+	1819.09i	−0.192421	+	0.333282i
$311$	−1286.71	−	2228.64i	−0.234606	−	0.406349i	0.724552	−	0.689220i	$-0.242047\pi$
$311$	−1286.71	−	2228.64i	−0.234606	−	0.406349i	−0.959158	+	0.282871i	$0.908713\pi$
$312$		0			0
$313$	−1278.56	−	738.176i	−0.230889	−	0.133304i	0.380093	−	0.924948i	$-0.375892\pi$
$313$	−1278.56	−	738.176i	−0.230889	−	0.133304i	−0.610982	+	0.791644i	$0.709225\pi$
$314$	−3281.97			−0.589848
$315$		0			0
$316$	−1512.46			−0.269249
$317$	2188.36	+	1263.45i	0.387730	+	0.223856i	0.681176	−	0.732120i	$-0.261469\pi$
$317$	2188.36	+	1263.45i	0.387730	+	0.223856i	−0.293446	+	0.955976i	$0.594802\pi$
$318$		0			0
$319$	784.988	+	1359.64i	0.137777	+	0.238637i
$320$	−2697.74	+	4672.62i	−0.471275	+	0.816273i
$321$		0			0
$322$	124.093	+	4432.05i	0.0214764	+	0.767045i
$323$			4310.50i			0.742546i
$324$		0			0
$325$	6034.05	−	3483.76i	1.02987	−	0.594597i
$326$	4584.05	−	2646.60i	0.778794	−	0.449637i
$327$		0			0
$328$			3207.89i			0.540019i
$329$	−3527.64	+	2170.54i	−0.591141	+	0.363726i
$330$		0			0
$331$	−737.778	+	1277.87i	−0.122513	+	0.212200i	−0.920758	−	0.390134i	$-0.872429\pi$
$331$	−737.778	+	1277.87i	−0.122513	+	0.212200i	0.798245	+	0.602333i	$0.205762\pi$
$332$	2074.11	+	3592.47i	0.342867	+	0.593863i
$333$		0			0
$334$	−5504.01	−	3177.74i	−0.901694	−	0.520593i
$335$	−4836.73			−0.788832
$336$		0			0
$337$	−6727.28			−1.08741			−0.543706	−	0.839275i	$-0.682979\pi$
$337$	−6727.28			−1.08741			−0.543706	+	0.839275i	$0.682979\pi$
$338$	−3802.32	−	2195.27i	−0.611890	−	0.353275i
$339$		0			0
$340$	2479.54	+	4294.68i	0.395505	+	0.685035i
$341$	−378.214	+	655.086i	−0.0600629	+	0.104032i
$342$		0			0
$343$	532.819	+	6330.06i	0.0838761	+	0.996476i
$344$		−	12462.4i		−	1.95328i
$345$		0			0
$346$	2766.30	−	1597.13i	0.429819	−	0.248156i
$347$	−466.060	+	269.080i	−0.0721021	+	0.0416281i	−0.535618	−	0.844461i	$-0.679921\pi$
$347$	−466.060	+	269.080i	−0.0721021	+	0.0416281i	0.463516	+	0.886089i	$0.346588\pi$
$348$		0			0
$349$		−	6975.93i		−	1.06995i	−0.844867	−	0.534976i	$-0.820321\pi$
$349$		−	6975.93i		−	1.06995i	0.844867	−	0.534976i	$-0.179679\pi$
$350$	1645.46	−	3043.70i	0.251296	−	0.464837i
$351$		0			0
$352$	−872.678	+	1511.52i	−0.132142	+	0.228876i
$353$	−4438.40	−	7687.53i	−0.669213	−	1.15911i	−0.978125	−	0.208020i	$-0.933298\pi$
$353$	−4438.40	−	7687.53i	−0.669213	−	1.15911i	0.308912	−	0.951091i	$-0.400035\pi$
$354$		0			0
$355$	−5448.02	−	3145.42i	−0.814509	−	0.470257i
$356$	7613.57			1.13348
$357$		0			0
$358$	1441.18			0.212761
$359$	9565.96	+	5522.91i	1.40633	+	0.811944i	0.995032	−	0.0995575i	$-0.0317427\pi$
$359$	9565.96	+	5522.91i	1.40633	+	0.811944i	0.411297	+	0.911502i	$0.365076\pi$
$360$		0			0
$361$	−1540.96	−	2669.02i	−0.224662	−	0.389126i
$362$	−2295.62	+	3976.14i	−0.333302	+	0.577296i
$363$		0			0
$364$	5889.97	−	164.913i	0.848127	−	0.0237466i
$365$		−	8231.82i		−	1.18047i
$366$		0			0
$367$	7210.59	−	4163.04i	1.02559	−	0.592122i	0.109868	−	0.993946i	$-0.464957\pi$
$367$	7210.59	−	4163.04i	1.02559	−	0.592122i	0.915717	+	0.401824i	$0.131624\pi$
$368$	517.896	−	299.007i	0.0733619	−	0.0423555i
$369$		0			0
$370$			9576.29i			1.34553i
$371$	9812.09	−	274.728i	1.37310	−	0.0384452i
$372$		0			0
$373$	2272.66	−	3936.36i	0.315479	−	0.546426i	−0.664060	−	0.747679i	$-0.731168\pi$
$373$	2272.66	−	3936.36i	0.315479	−	0.546426i	0.979539	+	0.201253i	$0.0645014\pi$
$374$	−631.369	−	1093.56i	−0.0872922	−	0.151195i
$375$		0			0
$376$	4472.76	+	2582.35i	0.613470	+	0.354187i
$377$	−10776.6			−1.47221
$378$		0			0
$379$	11527.2			1.56230			0.781151	−	0.624343i	$-0.214633\pi$
$379$	11527.2			1.56230			0.781151	+	0.624343i	$0.214633\pi$
$380$	3763.23	+	2172.70i	0.508025	+	0.293308i
$381$		0			0
$382$	822.141	+	1423.99i	0.110116	+	0.190727i
$383$	1960.23	−	3395.22i	0.261522	−	0.452970i	−0.705124	−	0.709084i	$-0.749109\pi$
$383$	1960.23	−	3395.22i	0.261522	−	0.452970i	0.966647	+	0.256114i	$0.0824422\pi$
$384$		0			0
$385$	1314.27	−	2431.08i	0.173978	−	0.321816i
$386$			362.020i			0.0477366i
$387$		0			0
$388$	−2999.87	+	1731.97i	−0.392513	+	0.226618i
$389$	689.734	−	398.218i	0.0898995	−	0.0519035i	−0.454376	−	0.890810i	$-0.650138\pi$
$389$	689.734	−	398.218i	0.0898995	−	0.0519035i	0.544276	+	0.838906i	$0.316805\pi$
$390$		0			0
$391$		−	9224.11i		−	1.19305i
$392$	6627.49	−	4338.16i	0.853926	−	0.558955i
$393$		0			0
$394$	−2931.38	+	5077.30i	−0.374824	+	0.649214i
$395$	−2434.64	−	4216.92i	−0.310127	−	0.537155i
$396$		0			0
$397$	3338.59	+	1927.54i	0.422063	+	0.243678i	0.695960	−	0.718081i	$-0.254979\pi$
$397$	3338.59	+	1927.54i	0.422063	+	0.243678i	−0.273896	+	0.961759i	$0.588313\pi$
$398$	5187.82			0.653371
$399$		0			0
$400$	−466.675			−0.0583344
$401$	4031.65	+	2327.68i	0.502073	+	0.289872i	0.729569	−	0.683907i	$-0.239721\pi$
$401$	4031.65	+	2327.68i	0.502073	+	0.289872i	−0.227496	+	0.973779i	$0.573054\pi$
$402$		0			0
$403$	−2596.13	−	4496.63i	−0.320899	−	0.555814i
$404$	−561.229	+	972.077i	−0.0691143	+	0.119709i
$405$		0			0
$406$	−4557.89	+	2804.45i	−0.557153	+	0.342814i
$407$			3448.58i			0.420000i
$408$		0			0
$409$	−8478.82	+	4895.25i	−1.02506	+	0.591821i	−0.915566	−	0.402167i	$-0.868257\pi$
$409$	−8478.82	+	4895.25i	−1.02506	+	0.591821i	−0.109497	+	0.993987i	$0.534924\pi$
$410$	−3303.91	+	1907.52i	−0.397972	+	0.229769i
$411$		0			0
$412$			239.642i			0.0286561i
$413$	−281.397	−	10050.3i	−0.0335269	−	1.19744i
$414$		0			0
$415$	−6677.47	+	11565.7i	−0.789842	+	1.36805i
$416$	−5990.22	−	10375.4i	−0.705997	−	1.22282i
$417$		0			0
$418$	−958.237	−	553.238i	−0.112127	−	0.0647363i
$419$	3007.46			0.350654			0.175327	−	0.984510i	$-0.443902\pi$
$419$	3007.46			0.350654			0.175327	+	0.984510i	$0.443902\pi$
$420$		0			0
$421$	7646.06			0.885145			0.442573	−	0.896733i	$-0.354066\pi$
$421$	7646.06			0.885145			0.442573	+	0.896733i	$0.354066\pi$
$422$	1898.85	+	1096.30i	0.219040	+	0.126463i
$423$		0			0
$424$	−6119.90	−	10600.0i	−0.700964	−	1.21411i
$425$	−3599.13	+	6233.87i	−0.410784	+	0.711499i
$426$		0			0
$427$	−1302.43	−	2116.76i	−0.147609	−	0.239899i
$428$			5581.41i			0.630345i
$429$		0			0
$430$	12835.5	−	7410.57i	1.43949	−	0.831091i
$431$	−12983.1	+	7495.81i	−1.45099	+	0.837727i	−0.998537	−	0.0540641i	$-0.982782\pi$
$431$	−12983.1	+	7495.81i	−1.45099	+	0.837727i	−0.452448	+	0.891791i	$0.649449\pi$
$432$		0			0
$433$			5666.63i			0.628916i	0.949271	+	0.314458i	$0.101823\pi$
$433$			5666.63i			0.628916i	−0.949271	+	0.314458i	$0.898177\pi$
$434$	−2268.20	−	1226.21i	−0.250868	−	0.135623i
$435$		0			0
$436$	−911.895	+	1579.45i	−0.100165	+	0.173491i
$437$	−4041.32	−	6999.78i	−0.442386	−	0.766235i
$438$		0			0
$439$	−4790.07	−	2765.55i	−0.520769	−	0.300666i	0.216480	−	0.976287i	$-0.430542\pi$
$439$	−4790.07	−	2765.55i	−0.520769	−	0.300666i	−0.737249	+	0.675621i	$0.763876\pi$
$440$	−3446.01			−0.373368
$441$		0			0
$442$	8667.66			0.932757
$443$	−349.200	−	201.611i	−0.0374515	−	0.0216226i	0.481157	−	0.876634i	$-0.340217\pi$
$443$	−349.200	−	201.611i	−0.0374515	−	0.0216226i	−0.518609	+	0.855012i	$0.673550\pi$
$444$		0			0
$445$	12255.7	+	21227.5i	1.30556	+	2.26130i
$446$	−3074.31	+	5324.85i	−0.326396	+	0.565334i
$447$		0			0
$448$	−5826.21	−	3149.72i	−0.614425	−	0.332166i
$449$			8429.03i			0.885948i	0.896534	+	0.442974i	$0.146077\pi$
$449$			8429.03i			0.885948i	−0.896534	+	0.442974i	$0.853923\pi$
$450$		0			0
$451$	−1189.79	+	686.928i	−0.124224	+	0.0717210i
$452$	2916.22	−	1683.68i	0.303468	−	0.175207i
$453$		0			0
$454$		−	8235.15i		−	0.851310i
$455$	9940.98	+	16156.4i	1.02426	+	1.66467i
$456$		0			0
$457$	−342.830	+	593.799i	−0.0350917	+	0.0607807i	−0.883038	−	0.469302i	$-0.844506\pi$
$457$	−342.830	+	593.799i	−0.0350917	+	0.0607807i	0.847946	+	0.530082i	$0.177839\pi$
$458$	3562.40	+	6170.25i	0.363449	+	0.629513i
$459$		0			0
$460$	−8052.99	−	4649.40i	−0.816245	−	0.471259i
$461$	−4864.48			−0.491456			−0.245728	−	0.969339i	$-0.579027\pi$
$461$	−4864.48			−0.491456			−0.245728	+	0.969339i	$0.579027\pi$
$462$		0			0
$463$	−8354.23			−0.838562			−0.419281	−	0.907857i	$-0.637718\pi$
$463$	−8354.23			−0.838562			−0.419281	+	0.907857i	$0.637718\pi$
$464$	625.099	+	360.901i	0.0625420	+	0.0361086i
$465$		0			0
$466$	−3976.68	−	6887.81i	−0.395313	−	0.684703i
$467$	−501.469	+	868.570i	−0.0496900	+	0.0860656i	−0.889801	−	0.456350i	$-0.849157\pi$
$467$	−501.469	+	868.570i	−0.0496900	+	0.0860656i	0.840111	+	0.542415i	$0.182490\pi$
$468$		0			0
$469$	−166.170	−	5934.89i	−0.0163604	−	0.584324i
$470$			6142.19i			0.602804i
$471$		0			0
$472$	−10857.3	+	6268.46i	−1.05879	+	0.611290i
$473$	4622.27	−	2668.67i	0.449328	−	0.259420i
$474$		0			0
$475$			6307.49i			0.609279i
$476$	−5184.59	+	3190.06i	−0.499234	+	0.307176i
$477$		0			0
$478$	−1770.49	+	3066.58i	−0.169415	+	0.293435i
$479$	3026.38	+	5241.84i	0.288682	+	0.500012i	0.973495	−	0.228706i	$-0.0734496\pi$
$479$	3026.38	+	5241.84i	0.288682	+	0.500012i	−0.684813	+	0.728719i	$0.740116\pi$
$480$		0			0
$481$	−20500.3	−	11835.8i	−1.94331	−	1.12197i
$482$	−7356.41			−0.695177
$483$		0			0
$484$	5779.13			0.542743
$485$	−9657.88	−	5575.98i	−0.904210	−	0.522046i
$486$		0			0
$487$	−7654.72	−	13258.4i	−0.712255	−	1.23366i	−0.964009	−	0.265871i	$-0.914340\pi$
$487$	−7654.72	−	13258.4i	−0.712255	−	1.23366i	0.251753	−	0.967791i	$-0.418993\pi$
$488$	−1549.53	+	2683.87i	−0.143738	+	0.248961i
$489$		0			0
$490$	8408.94	+	4246.26i	0.775260	+	0.391483i
$491$		−	4291.01i		−	0.394400i	−0.980363	−	0.197200i	$-0.936815\pi$
$491$		−	4291.01i		−	0.394400i	0.980363	−	0.197200i	$-0.0631848\pi$
$492$		0			0
$493$	9641.87	−	5566.74i	0.880828	−	0.508546i
$494$	6577.51	−	3797.53i	0.599061	−	0.345868i
$495$		0			0
$496$			347.770i			0.0314826i
$497$	3672.40	−	6793.04i	0.331448	−	0.613098i
$498$		0			0
$499$	−3445.77	+	5968.24i	−0.309126	+	0.535421i	−0.978171	−	0.207800i	$-0.933370\pi$
$499$	−3445.77	+	5968.24i	−0.309126	+	0.535421i	0.669046	+	0.743221i	$0.266703\pi$
$500$	−790.807	−	1369.72i	−0.0707319	−	0.122511i
$501$		0			0
$502$	6961.17	+	4019.03i	0.618909	+	0.357327i
$503$	13534.6			1.19975			0.599877	−	0.800092i	$-0.295216\pi$
$503$	13534.6			1.19975			0.599877	+	0.800092i	$0.295216\pi$
$504$		0			0
$505$	−3613.68			−0.318429
$506$	2050.55	+	1183.88i	0.180154	+	0.104012i
$507$		0			0
$508$	420.498	+	728.323i	0.0367255	+	0.0636105i
$509$	6043.91	−	10468.4i	0.526310	−	0.911595i	−0.473221	−	0.880944i	$-0.656909\pi$
$509$	6043.91	−	10468.4i	0.526310	−	0.911595i	0.999530	−	0.0306510i	$-0.00975805\pi$
$510$		0			0
$511$	10100.8	−	282.812i	0.874431	−	0.0244831i
$512$			1642.50i			0.141776i
$513$		0			0
$514$	1099.74	−	634.934i	0.0943724	−	0.0544859i
$515$	−668.150	+	385.757i	−0.0571693	+	0.0330067i
$516$		0			0
$517$			2211.91i			0.188161i
$518$	−11750.6	+	329.003i	−0.996699	+	0.0279065i
$519$		0			0
$520$	11827.0	−	20485.0i	0.997402	−	1.72755i
$521$	3812.94	+	6604.20i	0.320629	+	0.555346i	0.980618	−	0.195930i	$-0.0627724\pi$
$521$	3812.94	+	6604.20i	0.320629	+	0.555346i	−0.659989	+	0.751275i	$0.729439\pi$
$522$		0			0
$523$	13328.7	+	7695.34i	1.11439	+	0.643392i	0.939962	−	0.341279i	$-0.110860\pi$
$523$	13328.7	+	7695.34i	1.11439	+	0.643392i	0.174425	+	0.984670i	$0.444193\pi$
$524$	−11466.9			−0.955981
$525$		0			0
$526$	−1451.74			−0.120340
$527$	4645.54	+	2682.10i	0.383990	+	0.221697i
$528$		0			0
$529$	2564.60	+	4442.02i	0.210783	+	0.365088i
$530$	7278.18	−	12606.2i	0.596498	−	1.03317i
$531$		0			0
$532$	−2536.72	+	4692.30i	−0.206730	+	0.382401i
$533$		−	9430.40i		−	0.766371i
$534$		0			0
$535$	−15561.6	+	8984.49i	−1.25754	+	0.726044i
$536$	−6411.45	+	3701.65i	−0.516665	+	0.298297i
$537$		0			0
$538$		−	747.619i		−	0.0599110i
$539$	3028.20	+	1529.15i	0.241992	+	0.122199i
$540$		0			0
$541$	6850.44	−	11865.3i	0.544406	−	0.942939i	−0.454238	−	0.890880i	$-0.650088\pi$
$541$	6850.44	−	11865.3i	0.544406	−	0.942939i	0.998644	−	0.0520584i	$-0.0165782\pi$
$542$	3450.79	+	5976.95i	0.273477	+	0.473675i
$543$		0			0
$544$	10718.9	+	6188.59i	0.844800	+	0.487745i
$545$	−5871.58			−0.461487
$546$		0			0
$547$	−6139.00			−0.479863			−0.239931	−	0.970790i	$-0.577125\pi$
$547$	−6139.00			−0.479863			−0.239931	+	0.970790i	$0.577125\pi$
$548$	−2076.16	−	1198.67i	−0.161841	−	0.0934391i
$549$		0			0
$550$	−923.872	−	1600.19i	−0.0716255	−	0.124059i
$551$	4877.87	−	8448.71i	0.377140	−	0.653226i
$552$		0			0
$553$	5090.72	−	3132.30i	0.391464	−	0.240866i
$554$		−	5909.95i		−	0.453231i
$555$		0			0
$556$	−2432.78	+	1404.57i	−0.185563	+	0.107135i
$557$	19687.1	−	11366.4i	1.49761	−	0.864646i	0.497615	−	0.867398i	$-0.334209\pi$
$557$	19687.1	−	11366.4i	1.49761	−	0.864646i	0.999996	+	0.00275234i	$0.000876098\pi$
$558$		0			0
$559$			36636.4i			2.77202i
$560$	−35.5607	−	1270.07i	−0.00268341	−	0.0958400i
$561$		0			0
$562$	−1455.89	+	2521.67i	−0.109276	+	0.189271i
$563$	4958.81	+	8588.90i	0.371206	+	0.642947i	0.989751	−	0.142802i	$-0.0456112\pi$
$563$	4958.81	+	8588.90i	0.371206	+	0.642947i	−0.618546	+	0.785749i	$0.712278\pi$
$564$		0			0
$565$	9388.59	+	5420.51i	0.699081	+	0.403615i
$566$	−7766.06			−0.576735
$567$		0			0
$568$	−9629.02			−0.711311
$569$	−4448.79	−	2568.51i	−0.327773	−	0.189240i	0.327079	−	0.944997i	$-0.393936\pi$
$569$	−4448.79	−	2568.51i	−0.327773	−	0.189240i	−0.654852	+	0.755757i	$0.727269\pi$
$570$		0			0
$571$	9093.02	+	15749.6i	0.666429	+	1.15429i	0.978896	+	0.204360i	$0.0655114\pi$
$571$	9093.02	+	15749.6i	0.666429	+	1.15429i	−0.312467	+	0.949929i	$0.601155\pi$
$572$	1573.32	−	2725.07i	0.115007	−	0.199198i
$573$		0			0
$574$	−2454.12	−	3988.52i	−0.178455	−	0.290031i
$575$		−	13497.5i		−	0.978930i
$576$		0			0
$577$	10737.5	−	6199.32i	0.774713	−	0.447281i	−0.0598401	−	0.998208i	$-0.519059\pi$
$577$	10737.5	−	6199.32i	0.774713	−	0.447281i	0.834553	+	0.550927i	$0.185726\pi$
$578$	−9.83959	+	5.68089i	−0.000708085	+	0.000408813i
$579$		0			0
$580$		−	11223.6i		−	0.803509i
$581$	−14421.1	−	7796.23i	−1.02976	−	0.556699i
$582$		0			0
$583$	2621.00	−	4539.70i	0.186193	−	0.322496i
$584$	−6299.99	−	10911.9i	−0.446396	−	0.773181i
$585$		0			0
$586$	−4613.94	−	2663.86i	−0.325256	−	0.187787i
$587$	18977.6			1.33439			0.667195	−	0.744883i	$-0.267495\pi$
$587$	18977.6			1.33439			0.667195	+	0.744883i	$0.267495\pi$
$588$		0			0
$589$	4700.40			0.328822
$590$	−12912.2	−	7454.85i	−0.900994	−	0.520189i
$591$		0			0
$592$	792.749	+	1373.08i	0.0550368	+	0.0953265i
$593$	−5364.44	+	9291.48i	−0.371486	+	0.643432i	−0.989794	−	0.142503i	$-0.954485\pi$
$593$	−5364.44	+	9291.48i	−0.371486	+	0.643432i	0.618308	+	0.785936i	$0.287818\pi$
$594$		0			0
$595$	−17240.0	−	9320.14i	−1.18785	−	0.642165i
$596$			10279.5i			0.706488i
$597$		0			0
$598$	−14075.3	+	8126.40i	−0.962514	+	0.555708i
$599$	1577.36	−	910.687i	0.107594	−	0.0621196i	−0.445237	−	0.895413i	$-0.646881\pi$
$599$	1577.36	−	910.687i	0.107594	−	0.0621196i	0.552832	+	0.833293i	$0.313547\pi$
$600$		0			0
$601$		−	18933.3i		−	1.28503i	−0.766273	−	0.642516i	$-0.777891\pi$
$601$		−	18933.3i		−	1.28503i	0.766273	−	0.642516i	$-0.222109\pi$
$602$	9534.09	+	15495.1i	0.645483	+	1.04906i
$603$		0			0
$604$	1680.92	−	2911.43i	0.113238	−	0.196133i
$605$	9302.77	+	16112.9i	0.625143	+	1.08278i
$606$		0			0
$607$	13323.3	+	7692.20i	0.890898	+	0.514360i	0.874236	−	0.485501i	$-0.161363\pi$
$607$	13323.3	+	7692.20i	0.890898	+	0.514360i	0.0166621	+	0.999861i	$0.494696\pi$
$608$	10845.5			0.723428
$609$		0			0
$610$	−3685.61			−0.244633
$611$	−13148.8	−	7591.46i	−0.870611	−	0.502647i
$612$		0			0
$613$	2753.60	+	4769.38i	0.181431	+	0.314247i	0.942368	−	0.334578i	$-0.108594\pi$
$613$	2753.60	+	4769.38i	0.181431	+	0.314247i	−0.760937	+	0.648825i	$0.775261\pi$
$614$	3250.54	−	5630.10i	0.213650	−	0.370053i
$615$		0			0
$616$	−118.391	−	4228.42i	−0.00774369	−	0.276571i
$617$			18134.0i			1.18322i	0.806224	+	0.591610i	$0.201507\pi$
$617$			18134.0i			1.18322i	−0.806224	+	0.591610i	$0.798493\pi$
$618$		0			0
$619$	3148.73	−	1817.92i	0.204456	−	0.118043i	−0.394276	−	0.918992i	$-0.629005\pi$
$619$	3148.73	−	1817.92i	0.204456	−	0.118043i	0.598732	+	0.800949i	$0.295671\pi$
$620$	4683.15	−	2703.82i	0.303355	−	0.175142i
$621$		0			0
$622$		−	4684.49i		−	0.301979i
$623$	−25626.1	+	15767.6i	−1.64797	+	1.01399i
$624$		0			0
$625$	8960.38	−	15519.8i	0.573464	−	0.993270i
$626$	−1343.73	−	2327.41i	−0.0857928	−	0.148597i
$627$		0			0
$628$	7317.26	+	4224.62i	0.464953	+	0.268441i
$629$	24455.6			1.55025
$630$		0			0
$631$	−5912.59			−0.373021			−0.186511	−	0.982453i	$-0.559718\pi$
$631$	−5912.59			−0.373021			−0.186511	+	0.982453i	$0.559718\pi$
$632$	−6454.60	−	3726.57i	−0.406251	−	0.234549i
$633$		0			0
$634$	2299.90	+	3983.55i	0.144071	+	0.249538i
$635$	−1353.76	+	2344.79i	−0.0846024	+	0.146536i
$636$		0			0
$637$	−19483.2	+	12753.1i	−1.21185	+	0.793245i
$638$			2857.89i			0.177343i
$639$		0			0
$640$	9940.52	−	5739.16i	0.613959	−	0.354469i
$641$	−23786.7	+	13733.3i	−1.46571	+	0.846227i	−0.999265	−	0.0383236i	$-0.987798\pi$
$641$	−23786.7	+	13733.3i	−1.46571	+	0.846227i	−0.466443	+	0.884551i	$0.654465\pi$
$642$		0			0
$643$		−	28474.0i		−	1.74635i	−0.487403	−	0.873177i	$-0.662056\pi$
$643$		−	28474.0i		−	1.74635i	0.487403	−	0.873177i	$-0.337944\pi$
$644$	5428.36	−	10041.1i	0.332154	−	0.614404i
$645$		0			0
$646$	−3923.29	+	6795.33i	−0.238947	+	0.413868i
$647$	−661.681	−	1146.06i	−0.0402061	−	0.0696390i	0.845222	−	0.534415i	$-0.179468\pi$
$647$	−661.681	−	1146.06i	−0.0402061	−	0.0696390i	−0.885428	+	0.464776i	$0.846135\pi$
$648$		0			0
$649$	−4649.89	−	2684.62i	−0.281239	−	0.162374i
$650$	12683.3			0.765351
$651$		0			0
$652$	−13627.0			−0.818522
$653$	3331.38	+	1923.37i	0.199643	+	0.115264i	0.596489	−	0.802621i	$-0.296562\pi$
$653$	3331.38	+	1923.37i	0.199643	+	0.115264i	−0.396846	+	0.917885i	$0.629895\pi$
$654$		0			0
$655$	−18458.5	−	31971.0i	−1.10112	−	1.90719i
$656$	−315.818	+	547.012i	−0.0187967	+	0.0325568i
$657$		0			0
$658$	−7536.76	+	211.021i	−0.446525	+	0.0125022i
$659$			6796.84i			0.401771i	0.979615	+	0.200886i	$0.0643819\pi$
$659$			6796.84i			0.401771i	−0.979615	+	0.200886i	$0.935618\pi$
$660$		0			0
$661$	−26902.5	+	15532.2i	−1.58304	+	0.913966i	−0.588623	+	0.808408i	$0.700330\pi$
$661$	−26902.5	+	15532.2i	−1.58304	+	0.913966i	−0.994413	+	0.105559i	$0.966337\pi$
$662$	−2326.16	+	1343.01i	−0.136569	+	0.0788481i
$663$		0			0
$664$			20441.7i			1.19471i
$665$	−17166.1	+	480.631i	−1.00101	+	0.0280272i
$666$		0			0
$667$	−10438.2	+	18079.5i	−0.605952	+	1.04954i
$668$	8180.91	+	14169.7i	0.473846	+	0.820725i
$669$		0			0
$670$	−7624.91	−	4402.24i	−0.439666	−	0.253841i
$671$	−1327.25			−0.0763605
$672$		0			0
$673$	15508.2			0.888259			0.444129	−	0.895963i	$-0.353513\pi$
$673$	15508.2			0.888259			0.444129	+	0.895963i	$0.353513\pi$
$674$	−10605.3	−	6122.97i	−0.606084	−	0.349923i
$675$		0			0
$676$	5651.59	+	9788.84i	0.321552	+	0.556944i
$677$	15337.4	−	26565.2i	0.870701	−	1.50810i	0.00942744	−	0.999956i	$-0.496999\pi$
$677$	15337.4	−	26565.2i	0.870701	−	1.50810i	0.861273	−	0.508142i	$-0.169668\pi$
$678$		0			0
$679$	6510.19	−	12042.2i	0.367950	−	0.680617i
$680$			24437.4i			1.37813i
$681$		0			0
$682$	−1192.48	+	688.478i	−0.0669536	+	0.0386557i
$683$	−15292.8	+	8829.33i	−0.856756	+	0.494648i	−0.862925	−	0.505333i	$-0.831370\pi$
$683$	−15292.8	+	8829.33i	−0.856756	+	0.494648i	0.00616869	+	0.999981i	$0.498036\pi$
$684$		0			0
$685$		−	7718.08i		−	0.430500i
$686$	−4921.47	+	10464.1i	−0.273910	+	0.582390i
$687$		0			0
$688$	1226.93	−	2125.10i	0.0679887	−	0.117760i
$689$	17991.0	+	31161.3i	0.994778	+	1.72301i
$690$		0			0
$691$	11402.3	+	6583.11i	0.627733	+	0.362422i	0.779874	−	0.625937i	$-0.215283\pi$
$691$	11402.3	+	6583.11i	0.627733	+	0.362422i	−0.152141	+	0.988359i	$0.548617\pi$
$692$	−8223.42			−0.451745
$693$		0			0
$694$	−979.634			−0.0535827
$695$	−7832.18	−	4521.91i	−0.427470	−	0.246800i
$696$		0			0
$697$	4871.35	+	8437.42i	0.264728	+	0.458522i
$698$	6349.29	−	10997.3i	0.344304	−	0.596352i
$699$		0			0
$700$	−7586.54	+	4667.96i	−0.409634	+	0.252046i
$701$		−	25910.0i		−	1.39602i	−0.716090	−	0.698008i	$-0.754070\pi$
$701$		−	25910.0i		−	1.39602i	0.716090	−	0.698008i	$-0.245930\pi$
$702$		0			0
$703$	18558.3	−	10714.6i	0.995646	−	0.574837i
$704$	−3063.06	+	1768.46i	−0.163982	+	0.0946752i
$705$		0			0
$706$		−	16158.8i		−	0.861394i
$707$	−124.152	−	4434.16i	−0.00660424	−	0.235875i
$708$		0			0
$709$	−3104.25	+	5376.71i	−0.164432	+	0.284805i	−0.936454	−	0.350792i	$-0.885913\pi$
$709$	−3104.25	+	5376.71i	−0.164432	+	0.284805i	0.772021	+	0.635597i	$0.219246\pi$
$710$	−5725.73	−	9917.25i	−0.302652	−	0.524208i
$711$		0			0
$712$	32491.7	+	18759.1i	1.71022	+	0.987398i
$713$	−10058.5			−0.528320
$714$		0			0
$715$	10130.4			0.529868
$716$	−3213.15	−	1855.11i	−0.167711	−	0.0968280i
$717$		0			0
$718$	10053.6	+	17413.3i	0.522557	+	0.905095i
$719$	−14379.4	+	24905.9i	−0.745843	+	1.29184i	0.203957	+	0.978980i	$0.434620\pi$
$719$	−14379.4	+	24905.9i	−0.745843	+	1.29184i	−0.949800	+	0.312858i	$0.898713\pi$
$720$		0			0
$721$	−496.296	−	806.599i	−0.0256353	−	0.0416634i
$722$		−	5610.13i		−	0.289180i
$723$		0			0
$724$	10236.3	−	5909.95i	0.525457	−	0.303373i
$725$	14108.8	−	8145.72i	0.722742	−	0.417275i
$726$		0			0
$727$			35275.7i			1.79959i	0.436312	+	0.899795i	$0.356284\pi$
$727$			35275.7i			1.79959i	−0.436312	+	0.899795i	$0.643716\pi$
$728$	25542.4	+	13808.5i	1.30036	+	0.702992i
$729$		0			0
$730$	7492.35	−	12977.1i	0.379869	−	0.657953i
$731$	−18924.8	−	32778.8i	−0.957539	−	1.65851i
$732$		0			0
$733$	−6885.15	−	3975.14i	−0.346942	−	0.200307i	0.316395	−	0.948627i	$-0.397527\pi$
$733$	−6885.15	−	3975.14i	−0.346942	−	0.200307i	−0.663338	+	0.748320i	$0.730861\pi$
$734$	15156.3			0.762164
$735$		0			0
$736$	−23208.5			−1.16233
$737$	−2745.86	−	1585.32i	−0.137239	−	0.0792348i
$738$		0			0
$739$	−16676.8	−	28885.1i	−0.830130	−	1.43783i	−0.897935	−	0.440129i	$-0.854933\pi$
$739$	−16676.8	−	28885.1i	−0.830130	−	1.43783i	0.0678046	−	0.997699i	$-0.478401\pi$
$740$	12326.8	−	21350.6i	0.612354	−	1.06063i
$741$		0			0
$742$	15718.4	+	8497.58i	0.777684	+	0.420426i
$743$		−	32933.6i		−	1.62613i	−0.582171	−	0.813066i	$-0.697797\pi$
$743$		−	32933.6i		−	1.62613i	0.582171	−	0.813066i	$-0.302203\pi$
$744$		0			0
$745$	−28660.5	+	16547.2i	−1.40945	+	0.813747i
$746$	7165.51	−	4137.01i	0.351673	−	0.203039i
$747$		0			0
$748$			3250.85i			0.158907i
$749$	−11559.0	−	18786.1i	−0.563895	−	0.916463i
$750$		0			0
$751$	19818.3	−	34326.3i	0.962956	−	1.66789i	0.247945	−	0.968774i	$-0.420245\pi$
$751$	19818.3	−	34326.3i	0.962956	−	1.66789i	0.715010	−	0.699114i	$-0.246422\pi$
$752$	508.466	+	880.688i	0.0246567	+	0.0427066i
$753$		0			0
$754$	−16988.9	−	9808.54i	−0.820555	−	0.473748i
$755$	10823.2			0.521718
$756$		0			0
$757$	−3996.51			−0.191883			−0.0959417	−	0.995387i	$-0.530586\pi$
$757$	−3996.51			−0.191883			−0.0959417	+	0.995387i	$0.530586\pi$
$758$	18172.2	+	10491.7i	0.870769	+	0.502739i
$759$		0			0
$760$	10706.6	+	18544.5i	0.511014	+	0.885103i
$761$	−13117.8	+	22720.8i	−0.624863	+	1.08230i	0.363704	+	0.931515i	$0.381512\pi$
$761$	−13117.8	+	22720.8i	−0.624863	+	1.08230i	−0.988567	+	0.150781i	$0.951821\pi$
$762$		0			0
$763$	−201.724	−	7204.70i	−0.00957128	−	0.341845i
$764$		−	4233.11i		−	0.200456i
$765$		0			0
$766$	6180.45	−	3568.28i	0.291526	−	0.168312i
$767$	31917.7	−	18427.7i	1.50258	−	0.867517i
$768$		0			0
$769$			36456.9i			1.70958i	0.518971	+	0.854792i	$0.326315\pi$
$769$			36456.9i			1.70958i	−0.518971	+	0.854792i	$0.673685\pi$
$770$	4284.59	−	2636.29i	0.200527	−	0.123383i
$771$		0			0
$772$	466.000	−	807.135i	0.0217250	−	0.0376288i
$773$	4732.74	+	8197.34i	0.220213	+	0.381420i	0.954873	−	0.297016i	$-0.0959914\pi$
$773$	4732.74	+	8197.34i	0.220213	+	0.381420i	−0.734660	+	0.678436i	$0.762658\pi$
$774$		0			0
$775$	6797.74	+	3924.68i	0.315074	+	0.181908i
$776$	−17069.7			−0.789646
$777$		0			0
$778$	1449.79			0.0668089
$779$	7393.31	+	4268.53i	0.340042	+	0.196323i
$780$		0			0
$781$	−2061.93	−	3571.37i	−0.0944707	−	0.163628i
$782$	8395.51	−	14541.4i	0.383917	−	0.664963i
$783$		0			0
$784$	1557.22	−	87.2692i	0.0709374	−	0.00397546i
$785$			27201.8i			1.23678i
$786$		0			0
$787$	21665.9	−	12508.8i	0.981330	−	0.566571i	0.0786582	−	0.996902i	$-0.474936\pi$
$787$	21665.9	−	12508.8i	0.981330	−	0.566571i	0.902671	+	0.430331i	$0.141603\pi$
$788$	13071.2	−	7546.67i	0.590917	−	0.341166i
$789$		0			0
$790$		−	8863.75i		−	0.399187i
$791$	−6328.66	+	11706.5i	−0.284477	+	0.526213i
$792$		0			0
$793$	4555.24	−	7889.91i	0.203987	−	0.353315i
$794$	3508.77	+	6077.37i	0.156828	+	0.271635i
$795$		0			0
$796$	−11566.4	−	6677.87i	−0.515026	−	0.297350i
$797$	−38893.5			−1.72858			−0.864290	−	0.502994i	$-0.832232\pi$
$797$	−38893.5			−1.72858			−0.864290	+	0.502994i	$0.832232\pi$
$798$		0			0
$799$	15685.7			0.694519
$800$	15684.9	+	9055.67i	0.693180	+	0.400208i
$801$		0			0
$802$	4237.16	+	7338.98i	0.186558	+	0.323128i
$803$	2698.12	−	4673.28i	0.118574	−	0.205376i
$804$		0			0
$805$	36734.0	−	1028.51i	1.60833	−	0.0450314i
$806$		−	9451.67i		−	0.413053i
$807$		0			0
$808$	−4790.21	+	2765.63i	−0.208563	+	0.120414i
$809$	6072.26	−	3505.82i	0.263893	−	0.152359i	−0.362216	−	0.932094i	$-0.617980\pi$
$809$	6072.26	−	3505.82i	0.263893	−	0.152359i	0.626109	+	0.779735i	$0.284646\pi$
$810$		0			0
$811$		−	5013.82i		−	0.217089i	−0.994092	−	0.108544i	$-0.965381\pi$
$811$		−	5013.82i		−	0.217089i	0.994092	−	0.108544i	$-0.0346189\pi$
$812$	13771.9	−	385.598i	0.595196	−	0.0166648i
$813$		0			0
$814$	−3138.80	+	5436.55i	−0.135153	+	0.234092i
$815$	−21935.7	−	37993.7i	−0.942790	−	1.63296i
$816$		0			0
$817$	−28722.5	−	16582.9i	−1.22995	−	0.710115i
$818$	−17822.0			−0.761776
$819$		0			0
$820$	9821.58			0.418274
$821$	603.281	+	348.304i	0.0256451	+	0.0148062i	0.512768	−	0.858527i	$-0.328620\pi$
$821$	603.281	+	348.304i	0.0256451	+	0.0148062i	−0.487123	+	0.873334i	$0.661954\pi$
$822$		0			0
$823$	−3206.57	−	5553.95i	−0.135813	−	0.235235i	0.790095	−	0.612985i	$-0.210031\pi$
$823$	−3206.57	−	5553.95i	−0.135813	−	0.235235i	−0.925908	+	0.377750i	$0.876698\pi$
$824$	−590.456	+	1022.70i	−0.0249630	+	0.0432372i
$825$		0			0
$826$	8703.85	−	16100.0i	0.366641	−	0.678196i
$827$			16718.9i			0.702989i	0.936190	+	0.351494i	$0.114326\pi$
$827$			16718.9i			0.702989i	−0.936190	+	0.351494i	$0.885674\pi$
$828$		0			0
$829$	−12606.9	+	7278.59i	−0.528173	+	0.304941i	−0.740272	−	0.672307i	$-0.765303\pi$
$829$	−12606.9	+	7278.59i	−0.528173	+	0.304941i	0.212099	+	0.977248i	$0.431970\pi$
$830$	−21053.6	+	12155.3i	−0.880457	+	0.508332i
$831$		0			0
$832$		−	24278.1i		−	1.01165i
$833$	10844.0	−	21474.5i	0.451045	−	0.893212i
$834$		0			0
$835$	−26337.9	+	45618.6i	−1.09157	+	1.89065i
$836$	1424.28	+	2466.93i	0.0589232	+	0.102058i
$837$		0			0
$838$	4741.15	+	2737.30i	0.195442	+	0.112838i
$839$	19467.0			0.801045			0.400523	−	0.916287i	$-0.368829\pi$
$839$	19467.0			0.801045			0.400523	+	0.916287i	$0.368829\pi$
$840$		0			0
$841$	−808.829			−0.0331637
$842$	12053.7	+	6959.22i	0.493347	+	0.284834i
$843$		0			0
$844$	−2822.37	−	4888.49i	−0.115107	−	0.199371i
$845$	−18194.9	+	31514.6i	−0.740740	+	1.28300i
$846$		0			0
$847$	−19451.7	+	11968.5i	−0.789099	+	0.485529i
$848$		−	2410.02i		−	0.0975950i
$849$		0			0
$850$	−11347.8	+	6551.63i	−0.457912	+	0.264376i
$851$	−39713.2	+	22928.4i	−1.59971	+	0.923592i
$852$		0			0
$853$			22345.3i			0.896938i	0.893798	+	0.448469i	$0.148031\pi$
$853$			22345.3i			0.896938i	−0.893798	+	0.448469i	$0.851969\pi$
$854$	−126.623	−	4522.42i	−0.00507370	−	0.181211i
$855$		0			0
$856$	−13752.1	+	23819.3i	−0.549107	+	0.951081i
$857$	24039.8	+	41638.2i	0.958209	+	1.65967i	0.726847	+	0.686800i	$0.240985\pi$
$857$	24039.8	+	41638.2i	0.958209	+	1.65967i	0.231363	+	0.972868i	$0.425682\pi$
$858$		0			0
$859$	−22612.6	−	13055.4i	−0.898173	−	0.518560i	−0.0215659	−	0.999767i	$-0.506865\pi$
$859$	−22612.6	−	13055.4i	−0.898173	−	0.518560i	−0.876607	+	0.481207i	$0.840199\pi$
$860$	−38156.2			−1.51292
$861$		0			0
$862$	−27289.8			−1.07830
$863$	−2536.20	−	1464.27i	−0.100038	−	0.0577572i	0.449146	−	0.893458i	$-0.351728\pi$
$863$	−2536.20	−	1464.27i	−0.100038	−	0.0577572i	−0.549185	+	0.835701i	$0.685062\pi$
$864$		0			0
$865$	−13237.4	−	22927.8i	−0.520329	−	0.901236i
$866$	−5157.59	+	8933.22i	−0.202381	+	0.350535i
$867$		0			0
$868$	3478.61	+	5653.55i	0.136027	+	0.221076i
$869$		−	3191.98i		−	0.124604i
$870$		0			0
$871$	18848.1	−	10881.9i	0.733229	−	0.423330i
$872$	−7783.22	+	4493.64i	−0.302263	+	0.174511i
$873$		0			0
$874$		−	14713.2i		−	0.569428i
$875$	5498.40	+	2972.50i	0.212434	+	0.114845i
$876$		0			0
$877$	−6545.28	+	11336.8i	−0.252016	+	0.436505i	−0.964081	−	0.265609i	$-0.914427\pi$
$877$	−6545.28	+	11336.8i	−0.252016	+	0.436505i	0.712064	+	0.702114i	$0.247760\pi$
$878$	−5034.24	−	8719.56i	−0.193505	−	0.335160i
$879$		0			0
$880$	−587.617	−	339.261i	−0.0225097	−	0.0129960i
$881$	7888.79			0.301680			0.150840	−	0.988558i	$-0.451802\pi$
$881$	7888.79			0.301680			0.150840	+	0.988558i	$0.451802\pi$
$882$		0			0
$883$	45061.9			1.71739			0.858694	−	0.512489i	$-0.171276\pi$
$883$	45061.9			1.71739			0.858694	+	0.512489i	$0.171276\pi$
$884$	−19324.8	−	11157.2i	−0.735254	−	0.424499i
$885$		0			0
$886$	−367.000	−	635.663i	−0.0139160	−	0.0241033i
$887$	−1773.29	+	3071.43i	−0.0671266	+	0.116267i	−0.897635	−	0.440739i	$-0.854716\pi$
$887$	−1773.29	+	3071.43i	−0.0671266	+	0.116267i	0.830509	+	0.557006i	$0.188050\pi$
$888$		0			0
$889$	−2923.68	−	1580.58i	−0.110300	−	0.0596297i
$890$			44619.1i			1.68049i
$891$		0			0
$892$	13708.5	−	7914.62i	0.514569	−	0.297087i
$893$	11903.2	−	6872.32i	0.446053	−	0.257529i
$894$		0			0
$895$		−	11944.8i		−	0.446114i
$896$	7383.74	+	12000.3i	0.275305	+	0.447436i
$897$		0			0
$898$	−7671.85	+	13288.0i	−0.285092	+	0.493795i
$899$	−6070.26	−	10514.0i	−0.225200	−	0.390058i
$900$		0			0
$901$	−32193.2	−	18586.8i	−1.19036	−	0.687253i
$902$	−2500.89			−0.0923175
$903$		0			0
$904$	16593.7			0.610508
$905$	32955.2	+	19026.7i	1.21046	+	0.698861i
$906$		0			0
$907$	7339.77	+	12712.9i	0.268703	+	0.465406i	0.968527	−	0.248908i	$-0.0800718\pi$
$907$	7339.77	+	12712.9i	0.268703	+	0.465406i	−0.699825	+	0.714315i	$0.746738\pi$
$908$	−10600.5	+	18360.5i	−0.387432	+	0.671052i
$909$		0			0
$910$	966.465	+	34518.0i	0.0352066	+	1.25743i
$911$		−	12355.2i		−	0.449336i	−0.974435	−	0.224668i	$-0.927870\pi$
$911$		−	12355.2i		−	0.449336i	0.974435	−	0.224668i	$-0.0721297\pi$
$912$		0			0
$913$	−7581.74	+	4377.32i	−0.274829	+	0.158673i
$914$	−1080.92	+	624.068i	−0.0391177	+	0.0225846i
$915$		0			0
$916$		−	18342.4i		−	0.661626i
$917$	38595.8	−	23747.8i	1.38991	−	0.855204i
$918$		0			0
$919$	1535.18	−	2659.01i	0.0551044	−	0.0954437i	−0.837157	−	0.546962i	$-0.815784\pi$
$919$	1535.18	−	2659.01i	0.0551044	−	0.0954437i	0.892262	+	0.451518i	$0.149117\pi$
$920$	−22911.3	−	39683.6i	−0.821049	−	1.42210i
$921$		0			0
$922$	−7668.66	−	4427.50i	−0.273920	−	0.158148i
$923$	28306.9			1.00946
$924$		0			0
$925$	35785.5			1.27202
$926$	−13170.1	−	7603.77i	−0.467383	−	0.269844i
$927$		0			0
$928$	−14006.3	−	24259.7i	−0.495453	−	0.858149i
$929$	−15264.3	+	26438.6i	−0.539082	+	0.933717i	0.459872	+	0.887985i	$0.347895\pi$
$929$	−15264.3	+	26438.6i	−0.539082	+	0.933717i	−0.998954	+	0.0457316i	$0.985438\pi$
$930$		0			0
$931$	−1179.51	−	21047.1i	−0.0415220	−	0.740913i
$932$			20475.5i			0.719631i
$933$		0			0
$934$	−1581.09	+	912.844i	−0.0553907	+	0.0319798i
$935$	−9063.72	+	5232.94i	−0.317022	+	0.183033i
$936$		0			0
$937$		−	18235.1i		−	0.635769i	−0.948129	−	0.317885i	$-0.897028\pi$
$937$		−	18235.1i		−	0.635769i	0.948129	−	0.317885i	$-0.102972\pi$
$938$	5139.80	−	9507.37i	0.178913	−	0.330945i
$939$		0			0
$940$	7906.36	−	13694.2i	0.274337	−	0.475166i
$941$	−6686.17	−	11580.8i	−0.231629	−	0.401193i	0.726659	−	0.686999i	$-0.241072\pi$
$941$	−6686.17	−	11580.8i	−0.231629	−	0.401193i	−0.958288	+	0.285806i	$0.907739\pi$
$942$		0			0
$943$	−15821.1	−	9134.30i	−0.546347	−	0.315433i
$944$	−2468.52			−0.0851098
$945$		0			0
$946$	9715.77			0.333919
$947$	4431.54	+	2558.55i	0.152065	+	0.0877948i	0.574102	−	0.818784i	$-0.305351\pi$
$947$	4431.54	+	2558.55i	0.152065	+	0.0877948i	−0.422037	+	0.906579i	$0.638685\pi$
$948$		0			0
$949$	18520.4	+	32078.3i	0.633506	+	1.09727i
$950$	−5740.89	+	9943.50i	−0.196062	+	0.339589i
$951$		0			0
$952$	−29985.8	+	839.569i	−1.02085	+	0.0285826i
$953$		−	35456.7i		−	1.20520i	−0.798044	−	0.602599i	$-0.794132\pi$
$953$		−	35456.7i		−	1.20520i	0.798044	−	0.602599i	$-0.205868\pi$
$954$		0			0
$955$	11802.4	−	6814.12i	0.399913	−	0.230890i
$956$	7894.73	−	4558.03i	0.267086	−	0.154202i
$957$		0			0
$958$			11018.1i			0.371584i
$959$	9470.45	−	265.162i	0.318891	−	0.00892861i
$960$		0			0
$961$	−11970.8	+	20734.0i	−0.401826	+	0.695983i
$962$	−21545.3	−	37317.5i	−0.722086	−	1.25069i
$963$		0			0
$964$	16401.4	+	9469.33i	0.547980	+	0.316376i
$965$	3000.51			0.100093
$966$		0			0
$967$	−2804.92			−0.0932784			−0.0466392	−	0.998912i	$-0.514851\pi$
$967$	−2804.92			−0.0932784			−0.0466392	+	0.998912i	$0.514851\pi$
$968$	24663.1	+	14239.2i	0.818906	+	0.472796i
$969$		0			0
$970$	−10150.2	−	17580.6i	−0.335982	−	0.581938i
$971$	13683.8	−	23701.0i	0.452248	−	0.783316i	−0.546278	−	0.837604i	$-0.683956\pi$
$971$	13683.8	−	23701.0i	0.452248	−	0.783316i	0.998525	+	0.0542881i	$0.0172889\pi$
$972$		0			0
$973$	5279.52	−	9765.81i	0.173950	−	0.321765i
$974$		−	27868.4i		−	0.916797i
$975$		0			0
$976$	−528.455	+	305.104i	−0.0173314	+	0.0100063i
$977$	20868.5	−	12048.4i	0.683359	−	0.394537i	−0.117761	−	0.993042i	$-0.537572\pi$
$977$	20868.5	−	12048.4i	0.683359	−	0.394537i	0.801119	+	0.598505i	$0.204238\pi$
$978$		0			0
$979$			16068.1i			0.524554i
$980$	−13282.1	−	20291.4i	−0.432941	−	0.661412i
$981$		0			0
$982$	3905.55	−	6764.60i	0.126915	−	0.219824i
$983$	−4655.36	−	8063.32i	−0.151051	−	0.261628i	0.780563	−	0.625077i	$-0.214932\pi$
$983$	−4655.36	−	8063.32i	−0.151051	−	0.261628i	−0.931614	+	0.363449i	$0.881599\pi$
$984$		0			0
$985$	42081.9	+	24296.0i	1.36126	+	0.785924i
$986$	20266.7			0.654588
$987$		0			0
$988$	−19553.0			−0.629621
$989$	61463.8	+	35486.1i	1.97617	+	1.14094i
$990$		0			0
$991$	12095.2	+	20949.6i	0.387707	+	0.671528i	0.992141	−	0.125127i	$-0.0399339\pi$
$991$	12095.2	+	20949.6i	0.387707	+	0.671528i	−0.604434	+	0.796655i	$0.706601\pi$
$992$	6748.36	−	11688.5i	0.215989	−	0.374103i
$993$		0			0
$994$	11972.2	−	7366.45i	0.382028	−	0.235060i
$995$		−	42998.0i		−	1.36998i
$996$		0			0
$997$	42319.8	−	24433.4i	1.34431	−	0.776140i	0.356877	−	0.934151i	$-0.383841\pi$
$997$	42319.8	−	24433.4i	1.34431	−	0.776140i	0.987437	+	0.158011i	$0.0505081\pi$
$998$	−10864.2	+	6272.47i	−0.344590	+	0.198949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.p.a.26.6	yes	16
3.2	odd	2	inner	63.4.p.a.26.3	yes	16
4.3	odd	2		1008.4.bt.a.593.8		16
7.2	even	3		441.4.c.a.440.5		16
7.3	odd	6	inner	63.4.p.a.17.3	✓	16
7.4	even	3		441.4.p.c.80.3		16
7.5	odd	6		441.4.c.a.440.6		16
7.6	odd	2		441.4.p.c.215.6		16
12.11	even	2		1008.4.bt.a.593.1		16
21.2	odd	6		441.4.c.a.440.12		16
21.5	even	6		441.4.c.a.440.11		16
21.11	odd	6		441.4.p.c.80.6		16
21.17	even	6	inner	63.4.p.a.17.6	yes	16
21.20	even	2		441.4.p.c.215.3		16
28.3	even	6		1008.4.bt.a.17.1		16
84.59	odd	6		1008.4.bt.a.17.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.3	✓	16	7.3	odd	6	inner
63.4.p.a.17.6	yes	16	21.17	even	6	inner
63.4.p.a.26.3	yes	16	3.2	odd	2	inner
63.4.p.a.26.6	yes	16	1.1	even	1	trivial
441.4.c.a.440.5		16	7.2	even	3
441.4.c.a.440.6		16	7.5	odd	6
441.4.c.a.440.11		16	21.5	even	6
441.4.c.a.440.12		16	21.2	odd	6
441.4.p.c.80.3		16	7.4	even	3
441.4.p.c.80.6		16	21.11	odd	6
441.4.p.c.215.3		16	21.20	even	2
441.4.p.c.215.6		16	7.6	odd	2
1008.4.bt.a.17.1		16	28.3	even	6
1008.4.bt.a.17.8		16	84.59	odd	6
1008.4.bt.a.593.1		16	12.11	even	2
1008.4.bt.a.593.8		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.57646 + 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +(16.2919 + 8.80760i) q^{7} -23.0935i q^{8} +O(q^{10})\)	\(q+(1.57646 + 0.910170i) q^{2} +(-2.34318 - 4.05851i) q^{4} +(7.54372 - 13.0661i) q^{5} +(16.2919 + 8.80760i) q^{7} -23.0935i q^{8} +(23.7848 - 13.7321i) q^{10} +(8.56529 - 4.94517i) q^{11} +67.8891i q^{13} +(17.6671 + 28.7132i) q^{14} +(2.27356 - 3.93792i) q^{16} +(-35.0687 - 60.7407i) q^{17} +(-53.2242 - 30.7290i) q^{19} -70.7052 q^{20} +18.0038 q^{22} +(113.895 + 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} +(-61.7906 + 107.025i) q^{26} +(-2.42915 - 86.7586i) q^{28} +158.738i q^{29} +(-66.2349 + 38.2407i) q^{31} +(-152.828 + 88.2353i) q^{32} -127.674i q^{34} +(237.983 - 146.430i) q^{35} +(-174.341 + 301.967i) q^{37} +(-55.9372 - 96.8861i) q^{38} +(-301.742 - 174.211i) q^{40} -138.909 q^{41} +539.651 q^{43} +(-40.1400 - 23.1749i) q^{44} +(119.701 + 207.328i) q^{46} +(-111.821 + 193.680i) q^{47} +(187.852 + 286.985i) q^{49} -186.823i q^{50} +(275.529 - 159.076i) q^{52} +(459.003 - 265.005i) q^{53} -149.220i q^{55} +(203.398 - 376.237i) q^{56} +(-144.479 + 250.245i) q^{58} +(-271.438 - 470.145i) q^{59} +(-116.218 - 67.0983i) q^{61} -139.222 q^{62} -357.614 q^{64} +(887.046 + 512.136i) q^{65} +(-160.290 - 277.630i) q^{67} +(-164.344 + 284.653i) q^{68} +(508.446 - 14.2359i) q^{70} -416.958i q^{71} +(472.510 - 272.804i) q^{73} +(-549.683 + 317.360i) q^{74} +288.014i q^{76} +(183.100 - 5.12660i) q^{77} +(161.369 - 279.499i) q^{79} +(-34.3022 - 59.4132i) q^{80} +(-218.984 - 126.431i) q^{82} -885.170 q^{83} -1058.19 q^{85} +(850.739 + 491.174i) q^{86} +(-114.201 - 197.802i) q^{88} +(-812.312 + 1406.97i) q^{89} +(-597.940 + 1106.04i) q^{91} -616.327i q^{92} +(-352.564 + 203.553i) q^{94} +(-803.017 + 463.622i) q^{95} -739.155i q^{97} +(34.9363 + 623.398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 56 q^{7}+O(q^{10}) \) 16 * q + 32 * q^4 + 56 * q^7	\( 16 q + 32 q^{4} + 56 q^{7} - 72 q^{10} - 188 q^{16} - 612 q^{19} + 528 q^{22} - 20 q^{25} + 1036 q^{28} + 1128 q^{31} - 1196 q^{37} - 3204 q^{40} + 328 q^{43} - 1392 q^{46} + 784 q^{49} + 4452 q^{52} - 3372 q^{58} - 1632 q^{61} + 5432 q^{64} + 308 q^{67} + 3612 q^{70} + 4068 q^{73} - 2176 q^{79} - 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 924 q^{91} - 2916 q^{94}+O(q^{100}) \) 16 * q + 32 * q^4 + 56 * q^7 - 72 * q^10 - 188 * q^16 - 612 * q^19 + 528 * q^22 - 20 * q^25 + 1036 * q^28 + 1128 * q^31 - 1196 * q^37 - 3204 * q^40 + 328 * q^43 - 1392 * q^46 + 784 * q^49 + 4452 * q^52 - 3372 * q^58 - 1632 * q^61 + 5432 * q^64 + 308 * q^67 + 3612 * q^70 + 4068 * q^73 - 2176 * q^79 - 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 924 * q^91 - 2916 * q^94

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