LMFDB - Embedded newform 63.4.e.c.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,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, 4, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.3
Root			$2.65415 + 4.59712i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.4.e.c.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(2.78070 + 4.81631i) q^{5} +(9.67799 - 15.7904i) q^{7} -64.6443 q^{8} +O(q^{10})$	\(q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(2.78070 + 4.81631i) q^{5} +(9.67799 - 15.7904i) q^{7} -64.6443 q^{8} +(-14.7608 + 25.5664i) q^{10} +(-6.95869 + 12.0528i) q^{11} +38.6718 q^{13} +(98.2771 + 2.58082i) q^{14} +(-90.8636 - 157.380i) q^{16} +(21.7394 - 37.6537i) q^{17} +(54.5139 + 94.4208i) q^{19} -112.218 q^{20} -73.8775 q^{22} +(-37.4389 - 64.8461i) q^{23} +(47.0354 - 81.4677i) q^{25} +(102.641 + 177.779i) q^{26} +(178.290 + 328.429i) q^{28} +72.3589 q^{29} +(-32.0215 + 55.4629i) q^{31} +(223.754 - 387.553i) q^{32} +230.798 q^{34} +(102.963 + 2.70387i) q^{35} +(-94.3636 - 163.443i) q^{37} +(-289.376 + 501.213i) q^{38} +(-179.756 - 311.347i) q^{40} +24.7923 q^{41} -243.881 q^{43} +(-140.412 - 243.201i) q^{44} +(198.737 - 344.222i) q^{46} +(-310.274 - 537.411i) q^{47} +(-155.673 - 305.638i) q^{49} +499.356 q^{50} +(-390.159 + 675.776i) q^{52} +(-143.919 + 249.276i) q^{53} -77.4001 q^{55} +(-625.627 + 1020.76i) q^{56} +(192.051 + 332.642i) q^{58} +(262.526 - 454.708i) q^{59} +(191.718 + 332.065i) q^{61} -339.960 q^{62} +921.681 q^{64} +(107.535 + 186.255i) q^{65} +(-99.0583 + 171.574i) q^{67} +(438.657 + 759.776i) q^{68} +(260.849 + 480.510i) q^{70} -785.432 q^{71} +(165.570 - 286.776i) q^{73} +(500.910 - 867.602i) q^{74} -2199.96 q^{76} +(122.972 + 226.527i) q^{77} +(-218.823 - 379.013i) q^{79} +(505.329 - 875.255i) q^{80} +(65.8024 + 113.973i) q^{82} -241.241 q^{83} +241.803 q^{85} +(-647.297 - 1121.15i) q^{86} +(449.840 - 779.145i) q^{88} +(792.772 + 1373.12i) q^{89} +(374.265 - 610.643i) q^{91} +1510.88 q^{92} +(1647.03 - 2852.73i) q^{94} +(-303.173 + 525.112i) q^{95} +79.2754 q^{97} +(991.877 - 1526.86i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8}+O(q^{10}) $ 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8	$ 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8} + 55 q^{10} + 35 q^{11} + 124 q^{13} + 326 q^{14} - 241 q^{16} + 48 q^{17} + 202 q^{19} - 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} + 274 q^{26} - 201 q^{28} - 106 q^{29} + 95 q^{31} + 683 q^{32} - 48 q^{34} - 56 q^{35} - 262 q^{37} - 398 q^{38} - 21 q^{40} - 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} - 210 q^{47} - 303 q^{49} + 2756 q^{50} - 324 q^{52} + 393 q^{53} - 2062 q^{55} - 1299 q^{56} + 1249 q^{58} + 1143 q^{59} + 70 q^{61} - 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} + 1944 q^{68} + 3251 q^{70} - 636 q^{71} - 988 q^{73} + 1002 q^{74} - 4680 q^{76} - 1073 q^{77} - 861 q^{79} + 175 q^{80} - 124 q^{82} - 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} + 1766 q^{89} - 654 q^{91} + 1344 q^{92} + 3294 q^{94} - 736 q^{95} + 38 q^{97} + 4267 q^{98}+O(q^{100}) $ 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8 + 55 * q^10 + 35 * q^11 + 124 * q^13 + 326 * q^14 - 241 * q^16 + 48 * q^17 + 202 * q^19 - 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 + 274 * q^26 - 201 * q^28 - 106 * q^29 + 95 * q^31 + 683 * q^32 - 48 * q^34 - 56 * q^35 - 262 * q^37 - 398 * q^38 - 21 * q^40 - 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 - 210 * q^47 - 303 * q^49 + 2756 * q^50 - 324 * q^52 + 393 * q^53 - 2062 * q^55 - 1299 * q^56 + 1249 * q^58 + 1143 * q^59 + 70 * q^61 - 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 + 1944 * q^68 + 3251 * q^70 - 636 * q^71 - 988 * q^73 + 1002 * q^74 - 4680 * q^76 - 1073 * q^77 - 861 * q^79 + 175 * q^80 - 124 * q^82 - 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 + 1766 * q^89 - 654 * q^91 + 1344 * q^92 + 3294 * q^94 - 736 * q^95 + 38 * q^97 + 4267 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.65415	+	4.59712i	0.938383	+	1.62533i	0.768488	+	0.639864i	$0.221009\pi$
$2$	2.65415	+	4.59712i	0.938383	+	1.62533i	0.169895	+	0.985462i	$0.445657\pi$
$3$		0			0
$3$		0			0
$4$	−10.0890	+	17.4746i	−1.26112	+	2.18433i
$5$	2.78070	+	4.81631i	0.248713	+	0.430784i	0.963169	−	0.268897i	$-0.0866590\pi$
$5$	2.78070	+	4.81631i	0.248713	+	0.430784i	−0.714456	+	0.699681i	$0.753326\pi$
$6$		0			0
$7$	9.67799	−	15.7904i	0.522562	−	0.852601i
$7$	9.67799	−	15.7904i	0.522562	−	0.852601i
$8$	−64.6443			−2.85690
$9$		0			0
$10$	−14.7608	+	25.5664i	−0.466777	+	0.808481i
$11$	−6.95869	+	12.0528i	−0.190738	+	0.330369i	−0.945495	−	0.325636i	$-0.894422\pi$
$11$	−6.95869	+	12.0528i	−0.190738	+	0.330369i	0.754757	+	0.656005i	$0.227755\pi$
$12$		0			0
$13$	38.6718			0.825048			0.412524	−	0.910947i	$-0.364647\pi$
$13$	38.6718			0.825048			0.412524	+	0.910947i	$0.364647\pi$
$14$	98.2771	+	2.58082i	1.87612	+	0.0492680i
$15$		0			0
$16$	−90.8636	−	157.380i	−1.41974	−	2.45907i
$17$	21.7394	−	37.6537i	0.310152	−	0.537198i	−0.668243	−	0.743943i	$-0.732954\pi$
$17$	21.7394	−	37.6537i	0.310152	−	0.537198i	0.978395	+	0.206744i	$0.0662869\pi$
$18$		0			0
$19$	54.5139	+	94.4208i	0.658228	+	1.14009i	0.981074	+	0.193633i	$0.0620273\pi$
$19$	54.5139	+	94.4208i	0.658228	+	1.14009i	−0.322845	+	0.946452i	$0.604639\pi$
$20$	−112.218			−1.25463
$21$		0			0
$22$	−73.8775			−0.715943
$23$	−37.4389	−	64.8461i	−0.339415	−	0.587885i	0.644907	−	0.764261i	$-0.276896\pi$
$23$	−37.4389	−	64.8461i	−0.339415	−	0.587885i	−0.984323	+	0.176376i	$0.943563\pi$
$24$		0			0
$25$	47.0354	−	81.4677i	0.376283	−	0.651742i
$26$	102.641	+	177.779i	0.774211	+	1.34097i
$27$		0			0
$28$	178.290	+	328.429i	1.20335	+	2.21668i
$29$	72.3589			0.463335			0.231667	−	0.972795i	$-0.425582\pi$
$29$	72.3589			0.463335			0.231667	+	0.972795i	$0.425582\pi$
$30$		0			0
$31$	−32.0215	+	55.4629i	−0.185524	+	0.321337i	−0.943753	−	0.330652i	$-0.892732\pi$
$31$	−32.0215	+	55.4629i	−0.185524	+	0.321337i	0.758229	+	0.651988i	$0.226065\pi$
$32$	223.754	−	387.553i	1.23608	−	2.14095i
$33$		0			0
$34$	230.798			1.16416
$35$	102.963	+	2.70387i	0.497255	+	0.0130582i
$36$		0			0
$37$	−94.3636	−	163.443i	−0.419278	−	0.726211i	0.576589	−	0.817034i	$-0.304383\pi$
$37$	−94.3636	−	163.443i	−0.419278	−	0.726211i	−0.995867	+	0.0908235i	$0.971050\pi$
$38$	−289.376	+	501.213i	−1.23534	+	2.13967i
$39$		0			0
$40$	−179.756	−	311.347i	−0.710550	−	1.23071i
$41$	24.7923			0.0944367			0.0472184	−	0.998885i	$-0.484964\pi$
$41$	24.7923			0.0944367			0.0472184	+	0.998885i	$0.484964\pi$
$42$		0			0
$43$	−243.881			−0.864920			−0.432460	−	0.901653i	$-0.642354\pi$
$43$	−243.881			−0.864920			−0.432460	+	0.901653i	$0.642354\pi$
$44$	−140.412	−	243.201i	−0.481090	−	0.833272i
$45$		0			0
$46$	198.737	−	344.222i	0.637003	−	1.10332i
$47$	−310.274	−	537.411i	−0.962940	−	1.66786i	−0.715052	−	0.699071i	$-0.753597\pi$
$47$	−310.274	−	537.411i	−0.962940	−	1.66786i	−0.247888	−	0.968789i	$-0.579736\pi$
$48$		0			0
$49$	−155.673	−	305.638i	−0.453857	−	0.891074i
$50$	499.356			1.41239
$51$		0			0
$52$	−390.159	+	675.776i	−1.04049	+	1.80218i
$53$	−143.919	+	249.276i	−0.372997	+	0.646050i	−0.990025	−	0.140891i	$-0.955003\pi$
$53$	−143.919	+	249.276i	−0.372997	+	0.646050i	0.617028	+	0.786941i	$0.288337\pi$
$54$		0			0
$55$	−77.4001			−0.189757
$56$	−625.627	+	1020.76i	−1.49291	+	2.43580i
$57$		0			0
$58$	192.051	+	332.642i	0.434785	+	0.753070i
$59$	262.526	−	454.708i	0.579287	−	1.00335i	−0.416275	−	0.909239i	$-0.636664\pi$
$59$	262.526	−	454.708i	0.579287	−	1.00335i	0.995561	−	0.0941152i	$-0.0300022\pi$
$60$		0			0
$61$	191.718	+	332.065i	0.402409	+	0.696993i	0.994016	−	0.109234i	$-0.0348397\pi$
$61$	191.718	+	332.065i	0.402409	+	0.696993i	−0.591607	+	0.806226i	$0.701506\pi$
$62$	−339.960			−0.696369
$63$		0			0
$64$	921.681			1.80016
$65$	107.535	+	186.255i	0.205200	+	0.355417i
$66$		0			0
$67$	−99.0583	+	171.574i	−0.180625	+	0.312852i	−0.942094	−	0.335350i	$-0.891145\pi$
$67$	−99.0583	+	171.574i	−0.180625	+	0.312852i	0.761468	+	0.648202i	$0.224479\pi$
$68$	438.657	+	759.776i	0.782279	+	1.35495i
$69$		0			0
$70$	260.849	+	480.510i	0.445392	+	0.820456i
$71$	−785.432			−1.31287			−0.656434	−	0.754384i	$-0.727936\pi$
$71$	−785.432			−1.31287			−0.656434	+	0.754384i	$0.727936\pi$
$72$		0			0
$73$	165.570	−	286.776i	0.265459	−	0.459789i	−0.702224	−	0.711956i	$-0.747810\pi$
$73$	165.570	−	286.776i	0.265459	−	0.459789i	0.967684	+	0.252166i	$0.0811430\pi$
$74$	500.910	−	867.602i	0.786887	−	1.36293i
$75$		0			0
$76$	−2199.96			−3.32043
$77$	122.972	+	226.527i	0.182000	+	0.335262i
$78$		0			0
$79$	−218.823	−	379.013i	−0.311640	−	0.539776i	0.667078	−	0.744988i	$-0.267545\pi$
$79$	−218.823	−	379.013i	−0.311640	−	0.539776i	−0.978718	+	0.205212i	$0.934212\pi$
$80$	505.329	−	875.255i	0.706219	−	1.22321i
$81$		0			0
$82$	65.8024	+	113.973i	0.0886178	+	0.153491i
$83$	−241.241			−0.319032			−0.159516	−	0.987195i	$-0.550993\pi$
$83$	−241.241			−0.319032			−0.159516	+	0.987195i	$0.550993\pi$
$84$		0			0
$85$	241.803			0.308555
$86$	−647.297	−	1121.15i	−0.811626	−	1.40578i
$87$		0			0
$88$	449.840	−	779.145i	0.544921	−	0.943831i
$89$	792.772	+	1373.12i	0.944198	+	1.63540i	0.757349	+	0.653010i	$0.226494\pi$
$89$	792.772	+	1373.12i	0.944198	+	1.63540i	0.186849	+	0.982389i	$0.440172\pi$
$90$		0			0
$91$	374.265	−	610.643i	0.431139	−	0.703437i
$92$	1510.88			1.71218
$93$		0			0
$94$	1647.03	−	2852.73i	1.80721	−	3.13018i
$95$	−303.173	+	525.112i	−0.327420	+	0.567109i
$96$		0			0
$97$	79.2754			0.0829814			0.0414907	−	0.999139i	$-0.486789\pi$
$97$	79.2754			0.0829814			0.0414907	+	0.999139i	$0.486789\pi$
$98$	991.877	−	1526.86i	1.02239	−	1.57384i
$99$		0			0
$100$	949.080	+	1643.85i	0.949080	+	1.64385i
$101$	577.487	−	1000.24i	0.568931	−	0.985418i	−0.427741	−	0.903902i	$-0.640690\pi$
$101$	577.487	−	1000.24i	0.568931	−	0.985418i	0.996672	−	0.0815165i	$-0.0259763\pi$
$102$		0			0
$103$	722.430	+	1251.28i	0.691098	+	1.19702i	0.971478	+	0.237128i	$0.0762061\pi$
$103$	722.430	+	1251.28i	0.691098	+	1.19702i	−0.280380	+	0.959889i	$0.590461\pi$
$104$	−2499.91			−2.35708
$105$		0			0
$106$	−1527.93			−1.40006
$107$	495.480	+	858.197i	0.447662	+	0.775374i	0.998233	−	0.0594143i	$-0.0189233\pi$
$107$	495.480	+	858.197i	0.447662	+	0.775374i	−0.550571	+	0.834788i	$0.685590\pi$
$108$		0			0
$109$	−976.585	+	1691.49i	−0.858164	+	1.48638i	0.0155145	+	0.999880i	$0.495061\pi$
$109$	−976.585	+	1691.49i	−0.858164	+	1.48638i	−0.873678	+	0.486504i	$0.838272\pi$
$110$	−205.431	−	355.817i	−0.178064	−	0.308417i
$111$		0			0
$112$	−3364.48	−	88.3533i	−2.83851	−	0.0745410i
$113$	−672.882			−0.560172			−0.280086	−	0.959975i	$-0.590363\pi$
$113$	−672.882			−0.560172			−0.280086	+	0.959975i	$0.590363\pi$
$114$		0			0
$115$	208.213	−	360.635i	0.168834	−	0.292430i
$116$	−730.028	+	1264.45i	−0.584323	+	1.01208i
$117$		0			0
$118$	2787.13			2.17437
$119$	−384.174	−	707.686i	−0.295942	−	0.545155i
$120$		0			0
$121$	568.653	+	984.936i	0.427238	+	0.739997i
$122$	−1017.69	+	1762.70i	−0.755227	+	1.30809i
$123$		0			0
$124$	−646.130	−	1119.13i	−0.467937	−	0.810491i
$125$	1218.34			0.871773
$126$		0			0
$127$	175.815			0.122843			0.0614216	−	0.998112i	$-0.480437\pi$
$127$	175.815			0.122843			0.0614216	+	0.998112i	$0.480437\pi$
$128$	656.249	+	1136.66i	0.453163	+	0.784900i
$129$		0			0
$130$	−570.825	+	988.698i	−0.385113	+	0.667035i
$131$	562.965	+	975.085i	0.375470	+	0.650332i	0.990397	−	0.138251i	$-0.0441481\pi$
$131$	562.965	+	975.085i	0.375470	+	0.650332i	−0.614928	+	0.788584i	$0.710815\pi$
$132$		0			0
$133$	2018.53	+	53.0078i	1.31600	+	0.0345591i
$134$	−1051.66			−0.677983
$135$		0			0
$136$	−1405.33	+	2434.10i	−0.886073	+	1.53472i
$137$	934.350	−	1618.34i	0.582678	−	1.00923i	−0.412483	−	0.910966i	$-0.635338\pi$
$137$	934.350	−	1618.34i	0.582678	−	1.00923i	0.995161	−	0.0982624i	$-0.0313285\pi$
$138$		0			0
$139$	−2817.19			−1.71907			−0.859537	−	0.511074i	$-0.829248\pi$
$139$	−2817.19			−1.71907			−0.859537	+	0.511074i	$0.829248\pi$
$140$	−1086.04	+	1771.96i	−0.655624	+	1.06970i
$141$		0			0
$142$	−2084.65	−	3610.72i	−1.23197	−	2.13384i
$143$	−269.105	+	466.103i	−0.157368	+	0.272570i
$144$		0			0
$145$	201.208	+	348.503i	0.115238	+	0.199597i
$146$	1757.79			0.996410
$147$		0			0
$148$	3808.14			2.11505
$149$	900.163	+	1559.13i	0.494928	+	0.857240i	0.999983	−	0.00584714i	$-0.00186121\pi$
$149$	900.163	+	1559.13i	0.494928	+	0.857240i	−0.505055	+	0.863087i	$0.668528\pi$
$150$		0			0
$151$	226.492	−	392.296i	0.122064	−	0.211421i	−0.798517	−	0.601972i	$-0.794382\pi$
$151$	226.492	−	392.296i	0.122064	−	0.211421i	0.920581	+	0.390551i	$0.127715\pi$
$152$	−3524.01	−	6103.77i	−1.88050	−	3.25711i
$153$		0			0
$154$	−714.986	+	1166.56i	−0.374125	+	0.610414i
$155$	−356.169			−0.184569
$156$		0			0
$157$	931.829	−	1613.98i	0.473682	−	0.820441i	−0.525864	−	0.850569i	$-0.676258\pi$
$157$	931.829	−	1613.98i	0.473682	−	0.820441i	0.999546	+	0.0301273i	$0.00959128\pi$
$158$	1161.58	−	2011.91i	0.584875	−	1.01303i
$159$		0			0
$160$	2488.77			1.22971
$161$	−1386.28	−	36.4046i	−0.678597	−	0.0178204i
$162$		0			0
$163$	−1160.57	−	2010.16i	−0.557686	−	0.965940i	−0.997689	−	0.0679437i	$-0.978356\pi$
$163$	−1160.57	−	2010.16i	−0.557686	−	0.965940i	0.440004	−	0.897996i	$-0.354977\pi$
$164$	−250.129	+	433.237i	−0.119096	+	0.206281i
$165$		0			0
$166$	−640.290	−	1109.01i	−0.299374	−	0.518531i
$167$	−3211.62			−1.48816			−0.744079	−	0.668092i	$-0.767111\pi$
$167$	−3211.62			−1.48816			−0.744079	+	0.668092i	$0.767111\pi$
$168$		0			0
$169$	−701.494			−0.319296
$170$	641.780	+	1111.60i	0.289543	+	0.501503i
$171$		0			0
$172$	2460.52	−	4261.74i	1.09077	−	1.88927i
$173$	107.139	+	185.569i	0.0470844	+	0.0815525i	0.888607	−	0.458669i	$-0.151674\pi$
$173$	107.139	+	185.569i	0.0470844	+	0.0815525i	−0.841523	+	0.540222i	$0.818340\pi$
$174$		0			0
$175$	−831.199	−	1531.15i	−0.359044	−	0.661395i
$176$	2529.17			1.08320
$177$		0			0
$178$	−4208.27	+	7288.93i	−1.77204	+	3.06926i
$179$	−1218.61	+	2110.70i	−0.508845	+	0.881345i	0.491102	+	0.871102i	$0.336594\pi$
$179$	−1218.61	+	2110.70i	−0.508845	+	0.881345i	−0.999948	+	0.0102437i	$0.996739\pi$
$180$		0			0
$181$	−248.631			−0.102103			−0.0510514	−	0.998696i	$-0.516257\pi$
$181$	−248.631			−0.102103			−0.0510514	+	0.998696i	$0.516257\pi$
$182$	3800.55	+	99.8048i	1.54789	+	0.0406485i
$183$		0			0
$184$	2420.21	+	4191.93i	0.969677	+	1.67953i
$185$	524.794	−	908.970i	0.208560	−	0.361237i
$186$		0			0
$187$	302.555	+	524.041i	0.118316	+	0.204929i
$188$	12521.4			4.85755
$189$		0			0
$190$	−3218.67			−1.22898
$191$	−2156.54	−	3735.24i	−0.816972	−	1.41504i	−0.907903	−	0.419180i	$-0.862317\pi$
$191$	−2156.54	−	3735.24i	−0.816972	−	1.41504i	0.0909306	−	0.995857i	$-0.471016\pi$
$192$		0			0
$193$	−1030.43	+	1784.75i	−0.384309	+	0.665643i	−0.991673	−	0.128781i	$-0.958894\pi$
$193$	−1030.43	+	1784.75i	−0.384309	+	0.665643i	0.607364	+	0.794424i	$0.292227\pi$
$194$	210.409	+	364.438i	0.0778683	+	0.134872i
$195$		0			0
$196$	6911.51	+	363.252i	2.51877	+	0.132380i
$197$	1666.09			0.602557			0.301279	−	0.953536i	$-0.402587\pi$
$197$	1666.09			0.602557			0.301279	+	0.953536i	$0.402587\pi$
$198$		0			0
$199$	543.767	−	941.832i	0.193702	−	0.335501i	−0.752773	−	0.658281i	$-0.771284\pi$
$199$	543.767	−	941.832i	0.193702	−	0.335501i	0.946474	+	0.322780i	$0.104617\pi$
$200$	−3040.57	+	5266.43i	−1.07501	+	1.86196i
$201$		0			0
$202$	6130.94			2.13550
$203$	700.288	−	1142.58i	0.242121	−	0.395040i
$204$		0			0
$205$	68.9399	+	119.407i	0.0234877	+	0.0406818i
$206$	−3834.87	+	6642.19i	−1.29703	+	2.24652i
$207$		0			0
$208$	−3513.86	−	6086.18i	−1.17136	−	2.02885i
$209$	−1517.38			−0.502198
$210$		0			0
$211$	−4676.47			−1.52579			−0.762895	−	0.646522i	$-0.776223\pi$
$211$	−4676.47			−1.52579			−0.762895	+	0.646522i	$0.776223\pi$
$212$	−2904.01	−	5029.88i	−0.940792	−	1.62950i
$213$		0			0
$214$	−2630.15	+	4555.56i	−0.840157	+	1.45520i
$215$	−678.161	−	1174.61i	−0.215117	−	0.372594i
$216$		0			0
$217$	565.878	+	1042.40i	0.177024	+	0.326096i
$218$	−10368.0			−3.22114
$219$		0			0
$220$	780.889	−	1352.54i	0.239307	−	0.414492i
$221$	840.701	−	1456.14i	0.255890	−	0.443214i
$222$		0			0
$223$	3246.03			0.974754			0.487377	−	0.873192i	$-0.337954\pi$
$223$	3246.03			0.974754			0.487377	+	0.873192i	$0.337954\pi$
$224$	−3954.12	−	7283.89i	−1.17945	−	2.17266i
$225$		0			0
$226$	−1785.93	−	3093.32i	−0.525656	−	0.910463i
$227$	2569.08	−	4449.77i	0.751171	−	1.30107i	−0.196085	−	0.980587i	$-0.562823\pi$
$227$	2569.08	−	4449.77i	0.751171	−	1.30107i	0.947256	−	0.320479i	$-0.103844\pi$
$228$		0			0
$229$	−307.403	−	532.438i	−0.0887064	−	0.153644i	0.818258	−	0.574851i	$-0.194940\pi$
$229$	−307.403	−	532.438i	−0.0887064	−	0.153644i	−0.906965	+	0.421207i	$0.861607\pi$
$230$	2210.51			0.633725
$231$		0			0
$232$	−4677.59			−1.32370
$233$	1413.71	+	2448.61i	0.397490	+	0.688472i	0.993415	−	0.114567i	$-0.0365482\pi$
$233$	1413.71	+	2448.61i	0.397490	+	0.688472i	−0.595926	+	0.803039i	$0.703215\pi$
$234$		0			0
$235$	1725.56	−	2988.76i	0.478992	−	0.829638i
$236$	5297.24	+	9175.09i	1.46111	+	2.53071i
$237$		0			0
$238$	2233.66	−	3644.39i	0.608348	−	0.992567i
$239$	3432.45			0.928983			0.464491	−	0.885578i	$-0.346237\pi$
$239$	3432.45			0.928983			0.464491	+	0.885578i	$0.346237\pi$
$240$		0			0
$241$	1318.06	−	2282.94i	0.352296	−	0.610195i	−0.634355	−	0.773042i	$-0.718734\pi$
$241$	1318.06	−	2282.94i	0.352296	−	0.610195i	0.986651	+	0.162847i	$0.0520675\pi$
$242$	−3018.58	+	5228.33i	−0.801825	+	1.38880i
$243$		0			0
$244$	−7736.96			−2.02995
$245$	1039.17	−	1599.66i	0.270980	−	0.417137i
$246$		0			0
$247$	2108.15	+	3651.42i	0.543070	+	0.940625i
$248$	2070.01	−	3585.37i	0.530024	−	0.918028i
$249$		0			0
$250$	3233.65	+	5600.85i	0.818057	+	1.41692i
$251$	−2057.57			−0.517422			−0.258711	−	0.965955i	$-0.583298\pi$
$251$	−2057.57			−0.517422			−0.258711	+	0.965955i	$0.583298\pi$
$252$		0			0
$253$	1042.10			0.258958
$254$	466.639	+	808.243i	0.115274	+	0.199660i
$255$		0			0
$256$	203.161	−	351.885i	0.0495998	−	0.0859093i
$257$	1075.10	+	1862.13i	0.260946	+	0.451972i	0.966494	−	0.256691i	$-0.0826322\pi$
$257$	1075.10	+	1862.13i	0.260946	+	0.451972i	−0.705548	+	0.708663i	$0.749299\pi$
$258$		0			0
$259$	−3494.07	−	91.7566i	−0.838267	−	0.0220134i
$260$	−4339.66			−1.03513
$261$		0			0
$262$	−2988.39	+	5176.04i	−0.704668	+	1.22052i
$263$	−2295.08	+	3975.19i	−0.538100	+	0.932017i	0.460906	+	0.887449i	$0.347525\pi$
$263$	−2295.08	+	3975.19i	−0.538100	+	0.932017i	−0.999006	+	0.0445683i	$0.985809\pi$
$264$		0			0
$265$	−1600.79			−0.371078
$266$	5113.78	+	9420.09i	1.17874	+	2.17136i
$267$		0			0
$268$	−1998.80	−	3462.02i	−0.455582	−	0.789091i
$269$	−189.689	+	328.551i	−0.0429945	+	0.0744687i	−0.886722	−	0.462303i	$-0.847023\pi$
$269$	−189.689	+	328.551i	−0.0429945	+	0.0744687i	0.843727	+	0.536772i	$0.180356\pi$
$270$		0			0
$271$	2684.42	+	4649.55i	0.601723	+	1.04221i	0.992560	+	0.121755i	$0.0388521\pi$
$271$	2684.42	+	4649.55i	0.601723	+	1.04221i	−0.390837	+	0.920460i	$0.627815\pi$
$272$	−7901.28			−1.76134
$273$		0			0
$274$	9919.61			2.18710
$275$	654.610	+	1133.82i	0.143543	+	0.248624i
$276$		0			0
$277$	2390.80	−	4140.99i	0.518590	−	0.898224i	−0.481177	−	0.876624i	$-0.659791\pi$
$277$	2390.80	−	4140.99i	0.518590	−	0.898224i	0.999767	−	0.0216003i	$-0.00687613\pi$
$278$	−7477.25	−	12951.0i	−1.61315	−	2.79406i
$279$		0			0
$280$	−6655.98	−	174.790i	−1.42061	−	0.0373061i
$281$	2076.57			0.440845			0.220423	−	0.975404i	$-0.429256\pi$
$281$	2076.57			0.440845			0.220423	+	0.975404i	$0.429256\pi$
$282$		0			0
$283$	−1278.81	+	2214.96i	−0.268612	+	0.465250i	−0.968504	−	0.248999i	$-0.919898\pi$
$283$	−1278.81	+	2214.96i	−0.268612	+	0.465250i	0.699892	+	0.714249i	$0.253232\pi$
$284$	7924.21	−	13725.1i	1.65569	−	2.86774i
$285$		0			0
$286$	−2856.97			−0.590687
$287$	239.940	−	391.480i	0.0493491	−	0.0805169i
$288$		0			0
$289$	1511.30	+	2617.65i	0.307612	+	0.532800i
$290$	−1068.07	+	1849.96i	−0.216274	+	0.374597i
$291$		0			0
$292$	3340.88	+	5786.57i	0.669555	+	1.15970i
$293$	−560.049			−0.111667			−0.0558335	−	0.998440i	$-0.517782\pi$
$293$	−560.049			−0.111667			−0.0558335	+	0.998440i	$0.517782\pi$
$294$		0			0
$295$	2920.02			0.576305
$296$	6100.08	+	10565.6i	1.19784	+	2.07471i
$297$		0			0
$298$	−4778.33	+	8276.31i	−0.928863	+	1.60884i
$299$	−1447.83	−	2507.71i	−0.280034	−	0.485033i
$300$		0			0
$301$	−2360.28	+	3850.98i	−0.451975	+	0.737432i
$302$	2404.57			0.458171
$303$		0			0
$304$	9906.66	−	17158.8i	1.86903	−	3.23726i
$305$	−1066.22	+	1846.75i	−0.200169	+	0.346703i
$306$		0			0
$307$	3653.02			0.679117			0.339558	−	0.940585i	$-0.389722\pi$
$307$	3653.02			0.679117			0.339558	+	0.940585i	$0.389722\pi$
$308$	−5199.15	−	136.533i	−0.961848	−	0.0252587i
$309$		0			0
$310$	−945.325	−	1637.35i	−0.173196	−	0.299985i
$311$	1746.13	−	3024.39i	0.318374	−	0.551439i	−0.661775	−	0.749702i	$-0.730197\pi$
$311$	1746.13	−	3024.39i	0.318374	−	0.551439i	0.980149	+	0.198263i	$0.0635300\pi$
$312$		0			0
$313$	−4356.05	−	7544.90i	−0.786640	−	1.36250i	−0.928014	−	0.372544i	$-0.878485\pi$
$313$	−4356.05	−	7544.90i	−0.786640	−	1.36250i	0.141374	−	0.989956i	$-0.454848\pi$
$314$	9892.85			1.77798
$315$		0			0
$316$	8830.83			1.57207
$317$	970.165	+	1680.37i	0.171892	+	0.297726i	0.939081	−	0.343695i	$-0.111679\pi$
$317$	970.165	+	1680.37i	0.171892	+	0.297726i	−0.767189	+	0.641421i	$0.778345\pi$
$318$		0			0
$319$	−503.523	+	872.127i	−0.0883758	+	0.153071i
$320$	2562.92	+	4439.11i	0.447724	+	0.775480i
$321$		0			0
$322$	−3512.03	−	6469.51i	−0.607820	−	1.11966i
$323$	4740.39			0.816602
$324$		0			0
$325$	1818.94	−	3150.50i	0.310452	−	0.537718i
$326$	6160.64	−	10670.5i	1.04665	−	1.81284i
$327$		0			0
$328$	−1602.68			−0.269797
$329$	−11488.8	−	301.702i	−1.92522	−	0.0505574i
$330$		0			0
$331$	2865.75	+	4963.63i	0.475879	+	0.824247i	0.999618	−	0.0276315i	$-0.00879650\pi$
$331$	2865.75	+	4963.63i	0.475879	+	0.824247i	−0.523739	+	0.851879i	$0.675463\pi$
$332$	2433.88	−	4215.61i	0.402339	−	0.696872i
$333$		0			0
$334$	−8524.10	−	14764.2i	−1.39646	−	2.41874i
$335$	−1101.81			−0.179696
$336$		0			0
$337$	2403.74			0.388547			0.194273	−	0.980947i	$-0.437765\pi$
$337$	2403.74			0.388547			0.194273	+	0.980947i	$0.437765\pi$
$338$	−1861.87	−	3224.85i	−0.299622	−	0.518960i
$339$		0			0
$340$	−2439.55	+	4225.42i	−0.389127	+	0.673987i
$341$	−445.656	−	771.898i	−0.0707731	−	0.122583i
$342$		0			0
$343$	−6332.75	−	499.826i	−0.996900	−	0.0786824i
$344$	15765.6			2.47099
$345$		0			0
$346$	−568.723	+	985.057i	−0.0883663	+	0.153055i
$347$	−1668.22	+	2889.45i	−0.258083	+	0.447013i	−0.965728	−	0.259555i	$-0.916424\pi$
$347$	−1668.22	+	2889.45i	−0.258083	+	0.447013i	0.707645	+	0.706568i	$0.249758\pi$
$348$		0			0
$349$	−2424.54			−0.371870			−0.185935	−	0.982562i	$-0.559531\pi$
$349$	−2424.54			−0.371870			−0.185935	+	0.982562i	$0.559531\pi$
$350$	4832.76	−	7885.02i	0.738062	−	1.20421i
$351$		0			0
$352$	3114.06	+	5393.71i	0.471534	+	0.816721i
$353$	−6201.56	+	10741.4i	−0.935059	+	1.61957i	−0.160531	+	0.987031i	$0.551321\pi$
$353$	−6201.56	+	10741.4i	−0.935059	+	1.61957i	−0.774528	+	0.632540i	$0.782013\pi$
$354$		0			0
$355$	−2184.05	−	3782.88i	−0.326528	−	0.565562i
$356$	−31993.1			−4.76300
$357$		0			0
$358$	−12937.5			−1.90997
$359$	676.921	+	1172.46i	0.0995168	+	0.172368i	0.911485	−	0.411334i	$-0.134937\pi$
$359$	676.921	+	1172.46i	0.0995168	+	0.172368i	−0.811968	+	0.583702i	$0.801604\pi$
$360$		0			0
$361$	−2514.03	+	4354.42i	−0.366529	+	0.634848i
$362$	−659.903	−	1142.99i	−0.0958114	−	0.165950i
$363$		0			0
$364$	6894.81	+	12700.9i	0.992819	+	1.82887i
$365$	1841.61			0.264093
$366$		0			0
$367$	689.031	−	1193.44i	0.0980031	−	0.169746i	−0.812855	−	0.582466i	$-0.802088\pi$
$367$	689.031	−	1193.44i	0.0980031	−	0.169746i	0.910858	+	0.412720i	$0.135421\pi$
$368$	−6803.67	+	11784.3i	−0.963766	+	1.66929i
$369$		0			0
$370$	5571.52			0.782837
$371$	2543.31	+	4685.03i	0.355909	+	0.655619i
$372$		0			0
$373$	−2728.46	−	4725.83i	−0.378752	−	0.656017i	0.612129	−	0.790758i	$-0.290313\pi$
$373$	−2728.46	−	4725.83i	−0.378752	−	0.656017i	−0.990881	+	0.134741i	$0.956980\pi$
$374$	−1606.05	+	2781.76i	−0.222051	+	0.384603i
$375$		0			0
$376$	20057.5	+	34740.6i	2.75103	+	4.76492i
$377$	2798.25			0.382273
$378$		0			0
$379$	554.675			0.0751761			0.0375881	−	0.999293i	$-0.488033\pi$
$379$	554.675			0.0751761			0.0375881	+	0.999293i	$0.488033\pi$
$380$	−6117.43	−	10595.7i	−0.825836	−	1.43039i
$381$		0			0
$382$	11447.5	−	19827.7i	1.53327	−	2.65569i
$383$	2930.33	+	5075.48i	0.390948	+	0.677141i	0.992575	−	0.121636i	$-0.0388140\pi$
$383$	2930.33	+	5075.48i	0.390948	+	0.677141i	−0.601627	+	0.798777i	$0.705481\pi$
$384$		0			0
$385$	−749.077	+	1222.18i	−0.0991597	+	0.161787i
$386$	−10939.6			−1.44252
$387$		0			0
$388$	−799.809	+	1385.31i	−0.104650	+	0.181259i
$389$	3889.43	−	6736.69i	0.506946	−	0.878056i	−0.493022	−	0.870017i	$-0.664108\pi$
$389$	3889.43	−	6736.69i	0.506946	−	0.878056i	0.999968	−	0.00803932i	$-0.00255902\pi$
$390$		0			0
$391$	−3255.60			−0.421081
$392$	10063.4	+	19757.8i	1.29663	+	2.54571i
$393$		0			0
$394$	4422.04	+	7659.20i	0.565429	+	0.979352i
$395$	1216.96	−	2107.84i	0.155018	−	0.268499i
$396$		0			0
$397$	−4013.94	−	6952.35i	−0.507440	−	0.878912i	−0.999963	−	0.00861270i	$-0.997258\pi$
$397$	−4013.94	−	6952.35i	−0.507440	−	0.878912i	0.492523	−	0.870300i	$-0.336075\pi$
$398$	5772.95			0.727065
$399$		0			0
$400$	−17095.2			−2.13690
$401$	389.990	+	675.482i	0.0485665	+	0.0841196i	0.889287	−	0.457350i	$-0.151201\pi$
$401$	389.990	+	675.482i	0.0485665	+	0.0841196i	−0.840720	+	0.541470i	$0.817868\pi$
$402$		0			0
$403$	−1238.33	+	2144.85i	−0.153066	+	0.265118i
$404$	11652.5	+	20182.8i	1.43499	+	2.48547i
$405$		0			0
$406$	7111.22	+	186.745i	0.869271	+	0.0228276i
$407$	2626.59			0.319890
$408$		0			0
$409$	−7346.25	+	12724.1i	−0.888139	+	1.53830i	−0.0460654	+	0.998938i	$0.514668\pi$
$409$	−7346.25	+	12724.1i	−0.888139	+	1.53830i	−0.842073	+	0.539363i	$0.818665\pi$
$410$	−365.953	+	633.850i	−0.0440809	+	0.0763503i
$411$		0			0
$412$	−29154.4			−3.48624
$413$	−4639.29	−	8546.04i	−0.552748	−	1.01822i
$414$		0			0
$415$	−670.820	−	1161.89i	−0.0793476	−	0.137434i
$416$	8652.95	−	14987.3i	1.01982	−	1.76638i
$417$		0			0
$418$	−4027.35	−	6975.57i	−0.471254	−	0.816236i
$419$	−3370.31			−0.392960			−0.196480	−	0.980508i	$-0.562951\pi$
$419$	−3370.31			−0.392960			−0.196480	+	0.980508i	$0.562951\pi$
$420$		0			0
$421$	15651.0			1.81184			0.905919	−	0.423450i	$-0.139181\pi$
$421$	15651.0			1.81184			0.905919	+	0.423450i	$0.139181\pi$
$422$	−12412.0	−	21498.3i	−1.43178	−	2.47991i
$423$		0			0
$424$	9303.58	−	16114.3i	1.06562	−	1.84570i
$425$	−2045.04	−	3542.12i	−0.233410	−	0.404277i
$426$		0			0
$427$	7098.88	+	186.421i	0.804541	+	0.0211277i
$428$	−19995.6			−2.25823
$429$		0			0
$430$	3599.88	−	6235.17i	0.403724	−	0.699271i
$431$	2444.06	−	4233.24i	0.273147	−	0.473104i	−0.696519	−	0.717538i	$-0.745269\pi$
$431$	2444.06	−	4233.24i	0.273147	−	0.473104i	0.969666	+	0.244434i	$0.0786022\pi$
$432$		0			0
$433$	−5255.73			−0.583313			−0.291656	−	0.956523i	$-0.594206\pi$
$433$	−5255.73			−0.583313			−0.291656	+	0.956523i	$0.594206\pi$
$434$	−3290.12	+	5368.10i	−0.363896	+	0.593725i
$435$		0			0
$436$	−19705.5	−	34131.0i	−2.16450	−	3.74903i
$437$	4081.88	−	7070.03i	0.446826	−	0.773925i
$438$		0			0
$439$	412.488	+	714.451i	0.0448451	+	0.0776740i	0.887577	−	0.460660i	$-0.152387\pi$
$439$	412.488	+	714.451i	0.0448451	+	0.0776740i	−0.842732	+	0.538334i	$0.819054\pi$
$440$	5003.48			0.542117
$441$		0			0
$442$	8925.37			0.960490
$443$	6513.64	+	11281.9i	0.698583	+	1.20998i	0.968958	+	0.247226i	$0.0795190\pi$
$443$	6513.64	+	11281.9i	0.698583	+	1.20998i	−0.270375	+	0.962755i	$0.587148\pi$
$444$		0			0
$445$	−4408.92	+	7636.47i	−0.469669	+	0.813491i
$446$	8615.44	+	14922.4i	0.914693	+	1.58429i
$447$		0			0
$448$	8920.02	−	14553.7i	0.940695	−	1.53482i
$449$	−16526.1			−1.73700			−0.868500	−	0.495689i	$-0.834916\pi$
$449$	−16526.1			−1.73700			−0.868500	+	0.495689i	$0.834916\pi$
$450$		0			0
$451$	−172.522	+	298.817i	−0.0180127	+	0.0311989i
$452$	6788.71	−	11758.4i	0.706447	−	1.22360i
$453$		0			0
$454$	27274.9			2.81954
$455$	3981.76	+	104.564i	0.410259	+	0.0107737i
$456$		0			0
$457$	1855.41	+	3213.67i	0.189918	+	0.328947i	0.945223	−	0.326426i	$-0.105844\pi$
$457$	1855.41	+	3213.67i	0.189918	+	0.328947i	−0.755305	+	0.655374i	$0.772511\pi$
$458$	1631.79	−	2826.34i	0.166481	−	0.288354i
$459$		0			0
$460$	4201.31	+	7276.89i	0.425842	+	0.737580i
$461$	9714.00			0.981401			0.490701	−	0.871328i	$-0.336741\pi$
$461$	9714.00			0.981401			0.490701	+	0.871328i	$0.336741\pi$
$462$		0			0
$463$	−43.2780			−0.00434406			−0.00217203	−	0.999998i	$-0.500691\pi$
$463$	−43.2780			−0.00434406			−0.00217203	+	0.999998i	$0.500691\pi$
$464$	−6574.79	−	11387.9i	−0.657817	−	1.13937i
$465$		0			0
$466$	−7504.38	+	12998.0i	−0.745995	+	1.29210i
$467$	−766.618	−	1327.82i	−0.0759633	−	0.131572i	0.825541	−	0.564341i	$-0.190870\pi$
$467$	−766.618	−	1327.82i	−0.0759633	−	0.131572i	−0.901505	+	0.432769i	$0.857537\pi$
$468$		0			0
$469$	1750.54	+	3224.66i	0.172350	+	0.317486i
$470$	18319.6			1.79791
$471$		0			0
$472$	−16970.8	+	29394.3i	−1.65497	+	2.86649i
$473$	1697.09	−	2939.45i	0.164974	−	0.285743i
$474$		0			0
$475$	10256.3			0.990722
$476$	16242.5	+	426.538i	1.56402	+	0.0410721i
$477$		0			0
$478$	9110.23	+	15779.4i	0.871741	+	1.50990i
$479$	−3517.69	+	6092.81i	−0.335547	+	0.581185i	−0.983590	−	0.180419i	$-0.942255\pi$
$479$	−3517.69	+	6092.81i	−0.335547	+	0.581185i	0.648042	+	0.761604i	$0.275588\pi$
$480$		0			0
$481$	−3649.21	−	6320.62i	−0.345924	−	0.599159i
$482$	13993.3			1.32236
$483$		0			0
$484$	−22948.6			−2.15520
$485$	220.441	+	381.815i	0.0206386	+	0.0357471i
$486$		0			0
$487$	7685.64	−	13311.9i	0.715132	−	1.23865i	−0.247776	−	0.968817i	$-0.579700\pi$
$487$	7685.64	−	13311.9i	0.715132	−	1.23865i	0.962908	−	0.269828i	$-0.0869669\pi$
$488$	−12393.5	−	21466.1i	−1.14964	−	1.99124i
$489$		0			0
$490$	10111.9	+	531.458i	0.932266	+	0.0489976i
$491$	2393.35			0.219980			0.109990	−	0.993933i	$-0.464918\pi$
$491$	2393.35			0.219980			0.109990	+	0.993933i	$0.464918\pi$
$492$		0			0
$493$	1573.04	−	2724.58i	0.143704	−	0.248903i
$494$	−11190.7	+	19382.8i	−1.01921	+	1.76533i
$495$		0			0
$496$	11638.4			1.05359
$497$	−7601.40	+	12402.3i	−0.686055	+	1.11935i
$498$		0			0
$499$	−346.760	−	600.606i	−0.0311084	−	0.0538814i	0.850052	−	0.526699i	$-0.176570\pi$
$499$	−346.760	−	600.606i	−0.0311084	−	0.0538814i	−0.881160	+	0.472817i	$0.843237\pi$
$500$	−12291.8	+	21290.1i	−1.09941	+	1.90424i
$501$		0			0
$502$	−5461.10	−	9458.91i	−0.485540	−	0.840979i
$503$	8646.95			0.766498			0.383249	−	0.923645i	$-0.374805\pi$
$503$	8646.95			0.766498			0.383249	+	0.923645i	$0.374805\pi$
$504$		0			0
$505$	6423.27			0.566003
$506$	2765.89	+	4790.67i	0.243002	+	0.420892i
$507$		0			0
$508$	−1773.80	+	3072.31i	−0.154920	+	0.268330i
$509$	−7750.44	−	13424.1i	−0.674916	−	1.16899i	−0.976494	−	0.215546i	$-0.930847\pi$
$509$	−7750.44	−	13424.1i	−0.674916	−	1.16899i	0.301578	−	0.953441i	$-0.402487\pi$
$510$		0			0
$511$	−2925.92	−	5389.84i	−0.253298	−	0.466600i
$512$	12656.9			1.09250
$513$		0			0
$514$	−5706.96	+	9884.75i	−0.489734	+	0.848245i
$515$	−4017.72	+	6958.89i	−0.343771	+	0.595428i
$516$		0			0
$517$	8636.41			0.734678
$518$	−8851.97	−	16306.2i	−0.750836	−	1.38311i
$519$		0			0
$520$	−6951.50	−	12040.4i	−0.586238	−	1.01539i
$521$	432.354	−	748.858i	0.0363565	−	0.0629714i	−0.847275	−	0.531155i	$-0.821758\pi$
$521$	432.354	−	748.858i	0.0363565	−	0.0629714i	0.883631	+	0.468184i	$0.155091\pi$
$522$		0			0
$523$	3127.81	+	5417.52i	0.261509	+	0.452947i	0.966643	−	0.256127i	$-0.0824465\pi$
$523$	3127.81	+	5417.52i	0.261509	+	0.452947i	−0.705134	+	0.709074i	$0.749113\pi$
$524$	−22719.0			−1.89406
$525$		0			0
$526$	−24365.9			−2.01978
$527$	1392.26	+	2411.46i	0.115081	+	0.199326i
$528$		0			0
$529$	3280.15	−	5681.39i	0.269594	−	0.466951i
$530$	−4248.72	−	7359.01i	−0.348213	−	0.603122i
$531$		0			0
$532$	−21291.2	+	34738.2i	−1.73513	+	2.83100i
$533$	958.762			0.0779148
$534$		0			0
$535$	−2755.56	+	4772.78i	−0.222679	+	0.385692i
$536$	6403.56	−	11091.3i	0.516029	−	0.893789i
$537$		0			0
$538$	−2013.85			−0.161381
$539$	4767.08	+	250.546i	0.380951	+	0.0200218i
$540$		0			0
$541$	−71.9353	−	124.596i	−0.00571671	−	0.00990164i	0.863153	−	0.504943i	$-0.168486\pi$
$541$	−71.9353	−	124.596i	−0.00571671	−	0.00990164i	−0.868870	+	0.495041i	$0.835153\pi$
$542$	−14249.7	+	24681.2i	−1.12929	+	1.95599i
$543$		0			0
$544$	−9728.53	−	16850.3i	−0.766741	−	1.32804i
$545$	−10862.4			−0.853747
$546$		0			0
$547$	5455.65			0.426448			0.213224	−	0.977003i	$-0.431604\pi$
$547$	5455.65			0.426448			0.213224	+	0.977003i	$0.431604\pi$
$548$	18853.3	+	32654.9i	1.46966	+	2.54552i
$549$		0			0
$550$	−3474.86	+	6018.63i	−0.269397	+	0.466610i
$551$	3944.56	+	6832.18i	0.304980	+	0.528241i
$552$		0			0
$553$	−8102.54	−	212.778i	−0.623065	−	0.0163621i
$554$	25382.2			1.94654
$555$		0			0
$556$	28422.7	−	49229.5i	2.16797	−	3.75503i
$557$	12404.9	−	21486.0i	0.943652	−	1.63445i	0.185223	−	0.982696i	$-0.440699\pi$
$557$	12404.9	−	21486.0i	0.943652	−	1.63445i	0.758428	−	0.651756i	$-0.225968\pi$
$558$		0			0
$559$	−9431.33			−0.713600
$560$	−8930.06	−	16450.1i	−0.673864	−	1.24132i
$561$		0			0
$562$	5511.51	+	9546.22i	0.413682	+	0.716517i
$563$	8184.91	−	14176.7i	0.612705	−	1.06124i	−0.378077	−	0.925774i	$-0.623415\pi$
$563$	8184.91	−	14176.7i	0.612705	−	1.06124i	0.990782	−	0.135462i	$-0.0432520\pi$
$564$		0			0
$565$	−1871.08	−	3240.81i	−0.139322	−	0.241313i
$566$	−13576.6			−1.00824
$567$		0			0
$568$	50773.7			3.75074
$569$	−9225.29	−	15978.7i	−0.679691	−	1.17726i	−0.975074	−	0.221881i	$-0.928781\pi$
$569$	−9225.29	−	15978.7i	−0.679691	−	1.17726i	0.295383	−	0.955379i	$-0.404553\pi$
$570$		0			0
$571$	3554.34	−	6156.30i	0.260499	−	0.451197i	−0.705876	−	0.708335i	$-0.749446\pi$
$571$	3554.34	−	6156.30i	0.260499	−	0.451197i	0.966374	+	0.257139i	$0.0827797\pi$
$572$	−5429.99	−	9405.02i	−0.396922	−	0.687489i
$573$		0			0
$574$	2436.52	+	63.9844i	0.177175	+	0.00465271i
$575$	−7043.82			−0.510865
$576$		0			0
$577$	−3797.09	+	6576.75i	−0.273960	+	0.474512i	−0.969872	−	0.243615i	$-0.921667\pi$
$577$	−3797.09	+	6576.75i	−0.273960	+	0.474512i	0.695912	+	0.718127i	$0.255000\pi$
$578$	−8022.42	+	13895.2i	−0.577316	+	0.999940i
$579$		0			0
$580$	−8119.96			−0.581315
$581$	−2334.73	+	3809.30i	−0.166714	+	0.272007i
$582$		0			0
$583$	−2002.98	−	3469.26i	−0.142290	−	0.246453i
$584$	−10703.2	+	18538.5i	−0.758392	+	1.31357i
$585$		0			0
$586$	−1486.45	−	2574.61i	−0.104786	−	0.181495i
$587$	1763.34			0.123988			0.0619939	−	0.998077i	$-0.480254\pi$
$587$	1763.34			0.123988			0.0619939	+	0.998077i	$0.480254\pi$
$588$		0			0
$589$	−6982.47			−0.488468
$590$	7750.16	+	13423.7i	0.540795	+	0.936684i
$591$		0			0
$592$	−17148.4	+	29702.0i	−1.19054	+	2.06207i
$593$	−6158.07	−	10666.1i	−0.426445	−	0.738624i	0.570109	−	0.821569i	$-0.306901\pi$
$593$	−6158.07	−	10666.1i	−0.426445	−	0.738624i	−0.996554	+	0.0829448i	$0.973567\pi$
$594$		0			0
$595$	2340.16	−	3818.16i	0.161239	−	0.263075i
$596$	−36327.0			−2.49666
$597$		0			0
$598$	7685.50	−	13311.7i	0.525558	−	0.910293i
$599$	−4451.70	+	7710.57i	−0.303659	+	0.525952i	−0.976962	−	0.213414i	$-0.931542\pi$
$599$	−4451.70	+	7710.57i	−0.303659	+	0.525952i	0.673303	+	0.739367i	$0.264875\pi$
$600$		0			0
$601$	−19157.1			−1.30022			−0.650112	−	0.759838i	$-0.725278\pi$
$601$	−19157.1			−1.30022			−0.650112	+	0.759838i	$0.725278\pi$
$602$	−23968.0	−	629.413i	−1.62269	−	0.0426129i
$603$		0			0
$604$	4570.15	+	7915.74i	0.307876	+	0.533256i
$605$	−3162.51	+	5477.62i	−0.212519	+	0.368094i
$606$		0			0
$607$	3784.96	+	6555.75i	0.253092	+	0.438369i	0.964376	−	0.264537i	$-0.0852191\pi$
$607$	3784.96	+	6555.75i	0.253092	+	0.438369i	−0.711283	+	0.702905i	$0.751886\pi$
$608$	48790.7			3.25448
$609$		0			0
$610$	−11319.6			−0.751340
$611$	−11998.9	−	20782.6i	−0.794471	−	1.37606i
$612$		0			0
$613$	−1453.56	+	2517.65i	−0.0957730	+	0.165884i	−0.909931	−	0.414760i	$-0.863866\pi$
$613$	−1453.56	+	2517.65i	−0.0957730	+	0.165884i	0.814158	+	0.580643i	$0.197199\pi$
$614$	9695.65	+	16793.4i	0.637272	+	1.10379i
$615$		0			0
$616$	−7949.47	−	14643.7i	−0.519956	−	0.957811i
$617$	12510.9			0.816320			0.408160	−	0.912910i	$-0.366171\pi$
$617$	12510.9			0.816320			0.408160	+	0.912910i	$0.366171\pi$
$618$		0			0
$619$	−5032.78	+	8717.03i	−0.326792	+	0.566021i	−0.981873	−	0.189538i	$-0.939301\pi$
$619$	−5032.78	+	8717.03i	−0.326792	+	0.566021i	0.655081	+	0.755558i	$0.272634\pi$
$620$	3593.39	−	6223.93i	0.232764	−	0.403160i
$621$		0			0
$622$	18538.0			1.19503
$623$	29354.6	+	770.869i	1.88775	+	0.0495734i
$624$		0			0
$625$	−2491.59	−	4315.56i	−0.159462	−	0.276196i
$626$	23123.2	−	40050.5i	1.47634	−	2.55709i
$627$		0			0
$628$	18802.4	+	32566.8i	1.19474	+	2.06936i
$629$	−8205.63			−0.520159
$630$		0			0
$631$	−25146.6			−1.58648			−0.793242	−	0.608907i	$-0.791608\pi$
$631$	−25146.6			−1.58648			−0.793242	+	0.608907i	$0.791608\pi$
$632$	14145.7	+	24501.1i	0.890325	+	1.54209i
$633$		0			0
$634$	−5149.92	+	8919.92i	−0.322602	+	0.558762i
$635$	488.889	+	846.781i	0.0305527	+	0.0529189i
$636$		0			0
$637$	−6020.16	−	11819.6i	−0.374454	−	0.735179i
$638$	−5345.70			−0.331721
$639$		0			0
$640$	−3649.66	+	6321.41i	−0.225415	+	0.390430i
$641$	−14479.5	+	25079.1i	−0.892206	+	1.54535i	−0.0549809	+	0.998487i	$0.517510\pi$
$641$	−14479.5	+	25079.1i	−0.892206	+	1.54535i	−0.837225	+	0.546859i	$0.815824\pi$
$642$		0			0
$643$	7341.90			0.450290			0.225145	−	0.974325i	$-0.427714\pi$
$643$	7341.90			0.450290			0.225145	+	0.974325i	$0.427714\pi$
$644$	14622.3	−	23857.5i	0.894721	−	1.45981i
$645$		0			0
$646$	12581.7	+	21792.1i	0.766285	+	1.32725i
$647$	3035.99	−	5258.49i	0.184478	−	0.319525i	−0.758923	−	0.651181i	$-0.774274\pi$
$647$	3035.99	−	5258.49i	0.184478	−	0.319525i	0.943400	+	0.331656i	$0.107607\pi$
$648$		0			0
$649$	3653.67	+	6328.34i	0.220985	+	0.382756i
$650$	19311.0			1.16529
$651$		0			0
$652$	46835.9			2.81324
$653$	13131.1	+	22743.7i	0.786920	+	1.36298i	0.927846	+	0.372965i	$0.121659\pi$
$653$	13131.1	+	22743.7i	0.786920	+	1.36298i	−0.140926	+	0.990020i	$0.545008\pi$
$654$		0			0
$655$	−3130.88	+	5422.84i	−0.186769	+	0.323493i
$656$	−2252.72	−	3901.82i	−0.134076	−	0.232226i
$657$		0			0
$658$	−29105.9	−	53615.9i	−1.72442	−	3.17655i
$659$	−26130.1			−1.54459			−0.772296	−	0.635263i	$-0.780892\pi$
$659$	−26130.1			−1.54459			−0.772296	+	0.635263i	$0.780892\pi$
$660$		0			0
$661$	5962.75	−	10327.8i	0.350868	−	0.607722i	−0.635533	−	0.772073i	$-0.719220\pi$
$661$	5962.75	−	10327.8i	0.350868	−	0.607722i	0.986402	+	0.164351i	$0.0525531\pi$
$662$	−15212.3	+	26348.4i	−0.893114	+	1.54692i
$663$		0			0
$664$	15594.9			0.911444
$665$	5357.61	+	9869.25i	0.312420	+	0.575509i
$666$		0			0
$667$	−2709.04	−	4692.19i	−0.157263	−	0.272387i
$668$	32402.0	−	56121.9i	1.87675	−	3.25063i
$669$		0			0
$670$	−2924.35	−	5065.13i	−0.168623	−	0.292064i
$671$	−5336.42			−0.307019
$672$		0			0
$673$	−6359.85			−0.364271			−0.182135	−	0.983273i	$-0.558301\pi$
$673$	−6359.85			−0.364271			−0.182135	+	0.983273i	$0.558301\pi$
$674$	6379.89	+	11050.3i	0.364606	+	0.631516i
$675$		0			0
$676$	7077.36	−	12258.4i	0.402672	−	0.697449i
$677$	4280.81	+	7414.57i	0.243020	+	0.420924i	0.961573	−	0.274549i	$-0.0885285\pi$
$677$	4280.81	+	7414.57i	0.243020	+	0.420924i	−0.718553	+	0.695472i	$0.755195\pi$
$678$		0			0
$679$	767.226	−	1251.79i	0.0433629	−	0.0707500i
$680$	−15631.2			−0.881513
$681$		0			0
$682$	2365.67	−	4097.46i	0.132824	−	0.230059i
$683$	−3352.94	+	5807.47i	−0.187843	+	0.325354i	−0.944531	−	0.328423i	$-0.893483\pi$
$683$	−3352.94	+	5807.47i	−0.187843	+	0.325354i	0.756688	+	0.653776i	$0.226816\pi$
$684$		0			0
$685$	10392.6			0.579679
$686$	−14510.3	−	30439.0i	−0.807589	−	1.69412i
$687$		0			0
$688$	22160.0	+	38382.2i	1.22797	+	2.12690i
$689$	−5565.62	+	9639.94i	−0.307741	+	0.533022i
$690$		0			0
$691$	12665.3	+	21937.0i	0.697267	+	1.20770i	0.969410	+	0.245445i	$0.0789342\pi$
$691$	12665.3	+	21937.0i	0.697267	+	1.20770i	−0.272143	+	0.962257i	$0.587732\pi$
$692$	−4323.68			−0.237517
$693$		0			0
$694$	−17710.8			−0.968723
$695$	−7833.77	−	13568.5i	−0.427557	−	0.740550i
$696$		0			0
$697$	538.969	−	933.522i	0.0292897	−	0.0507312i
$698$	−6435.08	−	11145.9i	−0.348956	−	0.604410i
$699$		0			0
$700$	35142.3	+	922.859i	1.89751	+	0.0498297i
$701$	27184.1			1.46467			0.732333	−	0.680947i	$-0.238432\pi$
$701$	27184.1			1.46467			0.732333	+	0.680947i	$0.238432\pi$
$702$		0			0
$703$	10288.3	−	17819.8i	0.551961	−	0.956025i
$704$	−6413.69	+	11108.8i	−0.343360	+	0.594716i
$705$		0			0
$706$	−65839.5			−3.50977
$707$	−10205.2	−	18799.0i	−0.542867	−	1.00001i
$708$		0			0
$709$	−8072.75	−	13982.4i	−0.427614	−	0.740649i	0.569047	−	0.822305i	$-0.307312\pi$
$709$	−8072.75	−	13982.4i	−0.427614	−	0.740649i	−0.996661	+	0.0816561i	$0.973979\pi$
$710$	11593.6	−	20080.7i	0.612816	−	1.06143i
$711$		0			0
$712$	−51248.2	−	88764.5i	−2.69748	−	4.67218i
$713$	4795.41			0.251879
$714$		0			0
$715$	−2993.20			−0.156558
$716$	−24589.1	−	42589.6i	−1.28343	−	2.22297i
$717$		0			0
$718$	−3593.30	+	6223.77i	−0.186770	+	0.323494i
$719$	8648.74	+	14980.0i	0.448600	+	0.776998i	0.998295	−	0.0583673i	$-0.0185895\pi$
$719$	8648.74	+	14980.0i	0.448600	+	0.776998i	−0.549695	+	0.835365i	$0.685256\pi$
$720$		0			0
$721$	26749.9	+	702.470i	1.38172	+	0.0362848i
$722$	−26690.4			−1.37578
$723$		0			0
$724$	2508.44	−	4344.74i	0.128764	−	0.223026i
$725$	3403.43	−	5894.91i	0.174345	−	0.301975i
$726$		0			0
$727$	3514.71			0.179303			0.0896516	−	0.995973i	$-0.471425\pi$
$727$	3514.71			0.179303			0.0896516	+	0.995973i	$0.471425\pi$
$728$	−24194.1	+	39474.6i	−1.23172	+	2.00965i
$729$		0			0
$730$	4887.89	+	8466.08i	0.247821	+	0.429238i
$731$	−5301.83	+	9183.04i	−0.268256	+	0.464633i
$732$		0			0
$733$	13755.6	+	23825.4i	0.693144	+	1.20056i	0.970802	+	0.239881i	$0.0771083\pi$
$733$	13755.6	+	23825.4i	0.693144	+	1.20056i	−0.277658	+	0.960680i	$0.589558\pi$
$734$	7315.16			0.367858
$735$		0			0
$736$	−33508.4			−1.67817
$737$	−1378.63	−	2387.86i	−0.0689044	−	0.119346i
$738$		0			0
$739$	−8050.80	+	13944.4i	−0.400749	+	0.694117i	−0.993816	−	0.111035i	$-0.964583\pi$
$739$	−8050.80	+	13944.4i	−0.400749	+	0.694117i	0.593068	+	0.805153i	$0.297917\pi$
$740$	10589.3	+	18341.2i	0.526040	+	0.911129i
$741$		0			0
$742$	−14787.3	+	24126.7i	−0.731617	+	1.19369i
$743$	−14682.4			−0.724961			−0.362480	−	0.931991i	$-0.618070\pi$
$743$	−14682.4			−0.724961			−0.362480	+	0.931991i	$0.618070\pi$
$744$		0			0
$745$	−5006.17	+	8670.93i	−0.246190	+	0.426414i
$746$	14483.5	−	25086.1i	0.710828	−	1.23119i
$747$		0			0
$748$	−12209.9			−0.596843
$749$	18346.5	+	481.791i	0.895016	+	0.0235037i
$750$		0			0
$751$	3636.53	+	6298.66i	0.176696	+	0.306047i	0.940747	−	0.339109i	$-0.110126\pi$
$751$	3636.53	+	6298.66i	0.176696	+	0.306047i	−0.764051	+	0.645156i	$0.776792\pi$
$752$	−56385.3	+	97662.2i	−2.73426	+	4.73587i
$753$		0			0
$754$	7426.96	+	12863.9i	0.358719	+	0.621319i
$755$	2519.23			0.121436
$756$		0			0
$757$	8505.93			0.408393			0.204196	−	0.978930i	$-0.434542\pi$
$757$	8505.93			0.408393			0.204196	+	0.978930i	$0.434542\pi$
$758$	1472.19	+	2549.91i	0.0705440	+	0.122186i
$759$		0			0
$760$	19598.4	−	33945.5i	0.935408	−	1.62017i
$761$	7108.86	+	12312.9i	0.338628	+	0.586521i	0.984175	−	0.177200i	$-0.0567038\pi$
$761$	7108.86	+	12312.9i	0.338628	+	0.586521i	−0.645547	+	0.763721i	$0.723370\pi$
$762$		0			0
$763$	17258.0	+	31790.9i	0.818848	+	1.50840i
$764$	87029.3			4.12121
$765$		0			0
$766$	−15555.1	+	26942.2i	−0.733717	+	1.27084i
$767$	10152.3	−	17584.4i	0.477939	−	0.827815i
$768$		0			0
$769$	16379.1			0.768068			0.384034	−	0.923319i	$-0.374534\pi$
$769$	16379.1			0.768068			0.384034	+	0.923319i	$0.374534\pi$
$770$	−7606.66	−	199.756i	−0.356006	−	0.00934895i
$771$		0			0
$772$	−20791.9	−	36012.6i	−0.969323	−	1.67892i
$773$	−19948.3	+	34551.6i	−0.928192	+	1.60768i	−0.141846	+	0.989889i	$0.545304\pi$
$773$	−19948.3	+	34551.6i	−0.928192	+	1.60768i	−0.786346	+	0.617787i	$0.788030\pi$
$774$		0			0
$775$	3012.29	+	5217.45i	0.139619	+	0.241827i
$776$	−5124.70			−0.237070
$777$		0			0
$778$	41292.5			1.90284
$779$	1351.52	+	2340.91i	0.0621609	+	0.107666i
$780$		0			0
$781$	5465.57	−	9466.65i	0.250414	−	0.433730i
$782$	−8640.83	−	14966.4i	−0.395135	−	0.684394i
$783$		0			0
$784$	−33956.5	+	52271.3i	−1.54685	+	2.38116i
$785$	10364.5			0.471244
$786$		0			0
$787$	16564.3	−	28690.2i	0.750257	−	1.29948i	−0.197440	−	0.980315i	$-0.563263\pi$
$787$	16564.3	−	28690.2i	0.750257	−	1.29948i	0.947698	−	0.319169i	$-0.103404\pi$
$788$	−16809.1	+	29114.3i	−0.759899	+	1.31618i
$789$		0			0
$790$	12920.0			0.581865
$791$	−6512.15	+	10625.1i	−0.292725	+	0.477603i
$792$		0			0
$793$	7414.07	+	12841.5i	0.332007	+	0.575052i
$794$	21307.2	−	36905.1i	0.952346	−	1.64951i
$795$		0			0
$796$	10972.1	+	19004.3i	0.488563	+	0.846216i
$797$	17851.5			0.793390			0.396695	−	0.917951i	$-0.370157\pi$
$797$	17851.5			0.793390			0.396695	+	0.917951i	$0.370157\pi$
$798$		0			0
$799$	−26980.7			−1.19463
$800$	−21048.7	−	36457.4i	−0.930229	−	1.61120i
$801$		0			0
$802$	−2070.18	+	3585.66i	−0.0911479	+	0.157873i
$803$	2304.30	+	3991.17i	0.101267	+	0.175399i
$804$		0			0
$805$	−3679.49	−	6777.98i	−0.161099	−	0.296761i
$806$	−13146.8			−0.574538
$807$		0			0
$808$	−37331.2	+	64659.6i	−1.62538	+	2.81524i
$809$	−2528.52	+	4379.52i	−0.109886	+	0.190328i	−0.915724	−	0.401808i	$-0.868382\pi$
$809$	−2528.52	+	4379.52i	−0.109886	+	0.190328i	0.805838	+	0.592136i	$0.201715\pi$
$810$		0			0
$811$	−17535.4			−0.759251			−0.379626	−	0.925140i	$-0.623947\pi$
$811$	−17535.4			−0.759251			−0.379626	+	0.925140i	$0.623947\pi$
$812$	12900.9	+	23764.7i	0.557553	+	1.02707i
$813$		0			0
$814$	6971.35	+	12074.7i	0.300179	+	0.519925i
$815$	6454.39	−	11179.3i	0.277408	−	0.480484i
$816$		0			0
$817$	−13294.9	−	23027.5i	−0.569315	−	0.986083i
$818$	−77992.1			−3.33366
$819$		0			0
$820$	−2782.14			−0.118484
$821$	−9350.39	−	16195.3i	−0.397480	−	0.688455i	0.595935	−	0.803033i	$-0.296782\pi$
$821$	−9350.39	−	16195.3i	−0.397480	−	0.688455i	−0.993414	+	0.114578i	$0.963448\pi$
$822$		0			0
$823$	−11111.3	+	19245.4i	−0.470615	+	0.815129i	−0.999435	−	0.0336046i	$-0.989301\pi$
$823$	−11111.3	+	19245.4i	−0.470615	+	0.815129i	0.528820	+	0.848734i	$0.322635\pi$
$824$	−46701.0	−	80888.5i	−1.97440	−	3.41976i
$825$		0			0
$826$	26973.8	−	44009.8i	1.13624	−	1.85387i
$827$	−25178.9			−1.05872			−0.529358	−	0.848399i	$-0.677567\pi$
$827$	−25178.9			−1.05872			−0.529358	+	0.848399i	$0.677567\pi$
$828$		0			0
$829$	−6139.45	+	10633.8i	−0.257216	+	0.445511i	−0.965495	−	0.260421i	$-0.916139\pi$
$829$	−6139.45	+	10633.8i	−0.257216	+	0.445511i	0.708279	+	0.705933i	$0.249472\pi$
$830$	3560.91	−	6167.67i	0.148917	−	0.257931i
$831$		0			0
$832$	35643.1			1.48522
$833$	−14892.7	−	782.721i	−0.619448	−	0.0325566i
$834$		0			0
$835$	−8930.54	−	15468.2i	−0.370125	−	0.641075i
$836$	15308.8	−	26515.7i	0.633334	−	1.09697i
$837$		0			0
$838$	−8945.30	−	15493.7i	−0.368747	−	0.638689i
$839$	25765.0			1.06020			0.530098	−	0.847936i	$-0.322155\pi$
$839$	25765.0			1.06020			0.530098	+	0.847936i	$0.322155\pi$
$840$		0			0
$841$	−19153.2			−0.785321
$842$	41540.1	+	71949.6i	1.70020	+	2.94483i
$843$		0			0
$844$	47180.9	−	81719.7i	1.92421	−	3.33283i
$845$	−1950.64	−	3378.61i	−0.0794132	−	0.137548i
$846$		0			0
$847$	21056.0	+	552.943i	0.854181	+	0.0224313i
$848$	52308.2			2.11824
$849$		0			0
$850$	10855.7	−	18802.6i	0.438055	−	0.758734i
$851$	−7065.75	+	12238.2i	−0.284619	+	0.492974i
$852$		0			0
$853$	37864.5			1.51988			0.759939	−	0.649995i	$-0.225229\pi$
$853$	37864.5			1.51988			0.759939	+	0.649995i	$0.225229\pi$
$854$	17984.5	+	33129.2i	0.720627	+	1.32747i
$855$		0			0
$856$	−32030.0	−	55477.6i	−1.27893	−	2.21517i
$857$	−14604.4	+	25295.5i	−0.582118	+	1.00826i	0.413110	+	0.910681i	$0.364443\pi$
$857$	−14604.4	+	25295.5i	−0.582118	+	1.00826i	−0.995228	+	0.0975771i	$0.968891\pi$
$858$		0			0
$859$	−17451.5	−	30226.8i	−0.693173	−	1.20061i	−0.970793	−	0.239920i	$-0.922879\pi$
$859$	−17451.5	−	30226.8i	−0.693173	−	1.20061i	0.277619	−	0.960691i	$-0.410455\pi$
$860$	27367.8			1.08516
$861$		0			0
$862$	25947.6			1.02527
$863$	−6794.67	−	11768.7i	−0.268011	−	0.464208i	0.700337	−	0.713812i	$-0.253033\pi$
$863$	−6794.67	−	11768.7i	−0.268011	−	0.464208i	−0.968348	+	0.249604i	$0.919700\pi$
$864$		0			0
$865$	−595.840	+	1032.03i	−0.0234210	+	0.0405664i
$866$	−13949.5	−	24161.2i	−0.547371	−	0.948074i
$867$		0			0
$868$	−23924.8	−	628.279i	−0.935552	−	0.0245682i
$869$	6090.89			0.237767
$870$		0			0
$871$	−3830.76	+	6635.07i	−0.149025	+	0.258118i
$872$	63130.7	−	109346.i	2.45169	−	4.24645i
$873$		0			0
$874$	43335.7			1.67717
$875$	11791.1	−	19238.1i	0.455556	−	0.743275i
$876$		0			0
$877$	1189.87	+	2060.92i	0.0458144	+	0.0793528i	0.888023	−	0.459799i	$-0.152078\pi$
$877$	1189.87	+	2060.92i	0.0458144	+	0.0793528i	−0.842209	+	0.539151i	$0.818745\pi$
$878$	−2189.61	+	3792.51i	−0.0841637	+	0.145776i
$879$		0			0
$880$	7032.85	+	12181.3i	0.269406	+	0.466625i
$881$	24235.5			0.926803			0.463401	−	0.886148i	$-0.346629\pi$
$881$	24235.5			0.926803			0.463401	+	0.886148i	$0.346629\pi$
$882$		0			0
$883$	−9844.13			−0.375177			−0.187589	−	0.982248i	$-0.560067\pi$
$883$	−9844.13			−0.375177			−0.187589	+	0.982248i	$0.560067\pi$
$884$	16963.6	+	29381.9i	0.645418	+	1.11790i
$885$		0			0
$886$	−34576.3	+	59887.9i	−1.31108	+	2.27085i
$887$	14304.9	+	24776.9i	0.541502	+	0.937910i	0.998818	+	0.0486051i	$0.0154776\pi$
$887$	14304.9	+	24776.9i	0.541502	+	0.937910i	−0.457316	+	0.889304i	$0.651189\pi$
$888$		0			0
$889$	1701.54	−	2776.19i	0.0641932	−	0.104736i
$890$	−46807.7			−1.76292
$891$		0			0
$892$	−32749.2	+	56723.2i	−1.22929	+	2.12919i
$893$	33828.5	−	58592.7i	1.26767	−	2.19567i
$894$		0			0
$895$	−13554.4			−0.506226
$896$	24299.4	+	638.118i	0.906013	+	0.0237925i
$897$		0			0
$898$	−43862.6	−	75972.2i	−1.62997	−	2.82319i
$899$	−2317.04	+	4013.24i	−0.0859596	+	0.148886i
$900$		0			0
$901$	6257.44	+	10838.2i	0.231371	+	0.400747i
$902$	−1831.59			−0.0676113
$903$		0			0
$904$	43498.0			1.60036
$905$	−691.368	−	1197.48i	−0.0253943	−	0.0439842i
$906$		0			0
$907$	−22289.2	+	38606.0i	−0.815986	+	1.41333i	0.0926313	+	0.995700i	$0.470472\pi$
$907$	−22289.2	+	38606.0i	−0.815986	+	1.41333i	−0.908618	+	0.417629i	$0.862861\pi$
$908$	51838.8	+	89787.5i	1.89464	+	3.28161i
$909$		0			0
$910$	10087.5	+	18582.2i	0.367470	+	0.676915i
$911$	−45870.6			−1.66823			−0.834116	−	0.551589i	$-0.814022\pi$
$911$	−45870.6			−1.66823			−0.834116	+	0.551589i	$0.814022\pi$
$912$		0			0
$913$	1678.72	−	2907.63i	0.0608517	−	0.105398i
$914$	−9849.07	+	17059.1i	−0.356431	+	0.617357i
$915$		0			0
$916$	12405.6			0.447479
$917$	20845.3	+	547.412i	0.750680	+	0.0197133i
$918$		0			0
$919$	−15544.1	−	26923.3i	−0.557948	−	0.966394i	−0.997668	−	0.0682590i	$-0.978256\pi$
$919$	−15544.1	−	26923.3i	−0.557948	−	0.966394i	0.439720	−	0.898135i	$-0.355078\pi$
$920$	−13459.8	+	23313.0i	−0.482343	+	0.835443i
$921$		0			0
$922$	25782.4	+	44656.4i	0.920930	+	1.59510i
$923$	−30374.0			−1.08318
$924$		0			0
$925$	−17753.7			−0.631069
$926$	−114.866	−	198.954i	−0.00407639	−	0.00706052i
$927$		0			0
$928$	16190.6	−	28042.9i	0.572717	−	0.991975i
$929$	−21047.3	−	36454.9i	−0.743313	−	1.28746i	−0.950979	−	0.309257i	$-0.899920\pi$
$929$	−21047.3	−	36454.9i	−0.743313	−	1.28746i	0.207665	−	0.978200i	$-0.433414\pi$
$930$		0			0
$931$	20372.3	−	31360.3i	0.717159	−	1.10397i
$932$	−57051.5			−2.00513
$933$		0			0
$934$	4069.43	−	7048.47i	0.142565	−	0.246930i
$935$	−1682.63	+	2914.40i	−0.0588534	+	0.101937i
$936$		0			0
$937$	−44385.1			−1.54749			−0.773745	−	0.633497i	$-0.781619\pi$
$937$	−44385.1			−1.54749			−0.773745	+	0.633497i	$0.781619\pi$
$938$	−10178.0	+	16606.1i	−0.354288	+	0.578049i
$939$		0			0
$940$	34818.3	+	60307.1i	1.20814	+	2.09255i
$941$	20495.8	−	35499.8i	0.710036	−	1.22982i	−0.254807	−	0.966992i	$-0.582012\pi$
$941$	20495.8	−	35499.8i	0.710036	−	1.22982i	0.964843	−	0.262827i	$-0.0846547\pi$
$942$		0			0
$943$	−928.197	−	1607.68i	−0.0320533	−	0.0555179i
$944$	−95416.1			−3.28976
$945$		0			0
$946$	18017.4			0.619233
$947$	−26311.2	−	45572.4i	−0.902851	−	1.56378i	−0.823777	−	0.566914i	$-0.808137\pi$
$947$	−26311.2	−	45572.4i	−0.902851	−	1.56378i	−0.0790737	−	0.996869i	$-0.525196\pi$
$948$		0			0
$949$	6402.90	−	11090.1i	0.219017	−	0.379348i
$950$	27221.8	+	47149.6i	0.929676	+	1.61025i
$951$		0			0
$952$	24834.7	+	45747.9i	0.845479	+	1.55746i
$953$	10798.1			0.367035			0.183517	−	0.983016i	$-0.441252\pi$
$953$	10798.1			0.367035			0.183517	+	0.983016i	$0.441252\pi$
$954$		0			0
$955$	11993.4	−	20773.1i	0.406384	−	0.703877i
$956$	−34630.0	+	59980.9i	−1.17156	+	2.02921i
$957$		0			0
$958$	−37345.8			−1.25949
$959$	−16511.6	−	30416.0i	−0.555983	−	1.02418i
$960$		0			0
$961$	12844.7	+	22247.7i	0.431162	+	0.746794i
$962$	19371.1	−	33551.7i	0.649219	−	1.12448i
$963$		0			0
$964$	26595.7	+	46065.1i	0.888579	+	1.53906i
$965$	−11461.2			−0.382331
$966$		0			0
$967$	15648.9			0.520408			0.260204	−	0.965554i	$-0.416210\pi$
$967$	15648.9			0.520408			0.260204	+	0.965554i	$0.416210\pi$
$968$	−36760.2	−	63670.6i	−1.22058	−	2.11410i
$969$		0			0
$970$	−1170.17	+	2026.79i	−0.0387338	+	0.0670889i
$971$	23629.9	+	40928.2i	0.780968	+	1.35268i	0.931379	+	0.364052i	$0.118607\pi$
$971$	23629.9	+	40928.2i	0.780968	+	1.35268i	−0.150411	+	0.988624i	$0.548060\pi$
$972$		0			0
$973$	−27264.8	+	44484.6i	−0.898323	+	1.46568i
$974$	81595.2			2.68427
$975$		0			0
$976$	34840.4	−	60345.3i	1.14264	−	1.97910i
$977$	−24483.2	+	42406.2i	−0.801728	+	1.38863i	0.116749	+	0.993161i	$0.462753\pi$
$977$	−24483.2	+	42406.2i	−0.801728	+	1.38863i	−0.918478	+	0.395473i	$0.870581\pi$
$978$		0			0
$979$	−22066.6			−0.720380
$980$	17469.3	+	34298.1i	0.569425	+	1.11797i
$981$		0			0
$982$	6352.29	+	11002.5i	0.206426	+	0.357540i
$983$	−9555.64	+	16550.9i	−0.310049	+	0.537020i	−0.978373	−	0.206850i	$-0.933679\pi$
$983$	−9555.64	+	16550.9i	−0.310049	+	0.537020i	0.668324	+	0.743870i	$0.267012\pi$
$984$		0			0
$985$	4632.89	+	8024.39i	0.149864	+	0.259572i
$986$	16700.3			0.539397
$987$		0			0
$988$	−85076.4			−2.73951
$989$	9130.65	+	15814.8i	0.293567	+	0.508473i
$990$		0			0
$991$	27051.3	−	46854.1i	0.867115	−	1.50189i	0.00218424	−	0.999998i	$-0.499305\pi$
$991$	27051.3	−	46854.1i	0.867115	−	1.50189i	0.864931	−	0.501890i	$-0.167362\pi$
$992$	14329.9	+	24820.1i	0.458643	+	0.794393i
$993$		0			0
$994$	−77189.9	−	2027.06i	−2.46309	−	0.0646824i
$995$	6048.21			0.192705
$996$		0			0
$997$	−4596.40	+	7961.20i	−0.146008	+	0.252892i	−0.929748	−	0.368196i	$-0.879976\pi$
$997$	−4596.40	+	7961.20i	−0.146008	+	0.252892i	0.783741	+	0.621088i	$0.213309\pi$
$998$	1840.70	−	3188.19i	0.0583832	−	0.101123i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.e.c.46.3		6
3.2	odd	2		21.4.e.b.4.1	✓	6
7.2	even	3	inner	63.4.e.c.37.3		6
7.3	odd	6		441.4.a.t.1.1		3
7.4	even	3		441.4.a.s.1.1		3
7.5	odd	6		441.4.e.w.226.3		6
7.6	odd	2		441.4.e.w.361.3		6
12.11	even	2		336.4.q.k.193.2		6
21.2	odd	6		21.4.e.b.16.1	yes	6
21.5	even	6		147.4.e.n.79.1		6
21.11	odd	6		147.4.a.l.1.3		3
21.17	even	6		147.4.a.m.1.3		3
21.20	even	2		147.4.e.n.67.1		6
84.11	even	6		2352.4.a.ci.1.2		3
84.23	even	6		336.4.q.k.289.2		6
84.59	odd	6		2352.4.a.cg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.1	✓	6	3.2	odd	2
21.4.e.b.16.1	yes	6	21.2	odd	6
63.4.e.c.37.3		6	7.2	even	3	inner
63.4.e.c.46.3		6	1.1	even	1	trivial
147.4.a.l.1.3		3	21.11	odd	6
147.4.a.m.1.3		3	21.17	even	6
147.4.e.n.67.1		6	21.20	even	2
147.4.e.n.79.1		6	21.5	even	6
336.4.q.k.193.2		6	12.11	even	2
336.4.q.k.289.2		6	84.23	even	6
441.4.a.s.1.1		3	7.4	even	3
441.4.a.t.1.1		3	7.3	odd	6
441.4.e.w.226.3		6	7.5	odd	6
441.4.e.w.361.3		6	7.6	odd	2
2352.4.a.cg.1.2		3	84.59	odd	6
2352.4.a.ci.1.2		3	84.11	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(2.78070 + 4.81631i) q^{5} +(9.67799 - 15.7904i) q^{7} -64.6443 q^{8} +O(q^{10})\)	\(q+(2.65415 + 4.59712i) q^{2} +(-10.0890 + 17.4746i) q^{4} +(2.78070 + 4.81631i) q^{5} +(9.67799 - 15.7904i) q^{7} -64.6443 q^{8} +(-14.7608 + 25.5664i) q^{10} +(-6.95869 + 12.0528i) q^{11} +38.6718 q^{13} +(98.2771 + 2.58082i) q^{14} +(-90.8636 - 157.380i) q^{16} +(21.7394 - 37.6537i) q^{17} +(54.5139 + 94.4208i) q^{19} -112.218 q^{20} -73.8775 q^{22} +(-37.4389 - 64.8461i) q^{23} +(47.0354 - 81.4677i) q^{25} +(102.641 + 177.779i) q^{26} +(178.290 + 328.429i) q^{28} +72.3589 q^{29} +(-32.0215 + 55.4629i) q^{31} +(223.754 - 387.553i) q^{32} +230.798 q^{34} +(102.963 + 2.70387i) q^{35} +(-94.3636 - 163.443i) q^{37} +(-289.376 + 501.213i) q^{38} +(-179.756 - 311.347i) q^{40} +24.7923 q^{41} -243.881 q^{43} +(-140.412 - 243.201i) q^{44} +(198.737 - 344.222i) q^{46} +(-310.274 - 537.411i) q^{47} +(-155.673 - 305.638i) q^{49} +499.356 q^{50} +(-390.159 + 675.776i) q^{52} +(-143.919 + 249.276i) q^{53} -77.4001 q^{55} +(-625.627 + 1020.76i) q^{56} +(192.051 + 332.642i) q^{58} +(262.526 - 454.708i) q^{59} +(191.718 + 332.065i) q^{61} -339.960 q^{62} +921.681 q^{64} +(107.535 + 186.255i) q^{65} +(-99.0583 + 171.574i) q^{67} +(438.657 + 759.776i) q^{68} +(260.849 + 480.510i) q^{70} -785.432 q^{71} +(165.570 - 286.776i) q^{73} +(500.910 - 867.602i) q^{74} -2199.96 q^{76} +(122.972 + 226.527i) q^{77} +(-218.823 - 379.013i) q^{79} +(505.329 - 875.255i) q^{80} +(65.8024 + 113.973i) q^{82} -241.241 q^{83} +241.803 q^{85} +(-647.297 - 1121.15i) q^{86} +(449.840 - 779.145i) q^{88} +(792.772 + 1373.12i) q^{89} +(374.265 - 610.643i) q^{91} +1510.88 q^{92} +(1647.03 - 2852.73i) q^{94} +(-303.173 + 525.112i) q^{95} +79.2754 q^{97} +(991.877 - 1526.86i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8}+O(q^{10}) \) 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8	\( 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8} + 55 q^{10} + 35 q^{11} + 124 q^{13} + 326 q^{14} - 241 q^{16} + 48 q^{17} + 202 q^{19} - 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} + 274 q^{26} - 201 q^{28} - 106 q^{29} + 95 q^{31} + 683 q^{32} - 48 q^{34} - 56 q^{35} - 262 q^{37} - 398 q^{38} - 21 q^{40} - 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} - 210 q^{47} - 303 q^{49} + 2756 q^{50} - 324 q^{52} + 393 q^{53} - 2062 q^{55} - 1299 q^{56} + 1249 q^{58} + 1143 q^{59} + 70 q^{61} - 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} + 1944 q^{68} + 3251 q^{70} - 636 q^{71} - 988 q^{73} + 1002 q^{74} - 4680 q^{76} - 1073 q^{77} - 861 q^{79} + 175 q^{80} - 124 q^{82} - 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} + 1766 q^{89} - 654 q^{91} + 1344 q^{92} + 3294 q^{94} - 736 q^{95} + 38 q^{97} + 4267 q^{98}+O(q^{100}) \) 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8 + 55 * q^10 + 35 * q^11 + 124 * q^13 + 326 * q^14 - 241 * q^16 + 48 * q^17 + 202 * q^19 - 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 + 274 * q^26 - 201 * q^28 - 106 * q^29 + 95 * q^31 + 683 * q^32 - 48 * q^34 - 56 * q^35 - 262 * q^37 - 398 * q^38 - 21 * q^40 - 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 - 210 * q^47 - 303 * q^49 + 2756 * q^50 - 324 * q^52 + 393 * q^53 - 2062 * q^55 - 1299 * q^56 + 1249 * q^58 + 1143 * q^59 + 70 * q^61 - 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 + 1944 * q^68 + 3251 * q^70 - 636 * q^71 - 988 * q^73 + 1002 * q^74 - 4680 * q^76 - 1073 * q^77 - 861 * q^79 + 175 * q^80 - 124 * q^82 - 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 + 1766 * q^89 - 654 * q^91 + 1344 * q^92 + 3294 * q^94 - 736 * q^95 + 38 * q^97 + 4267 * q^98

Introduction

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