LMFDB - Embedded newform 441.4.e.w.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not 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:	$26.0198423125$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$2.65415 + 4.59712i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.w.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.714456	−	0.699681i	$-0.246674\pi$
$5$	−2.78070	−	4.81631i	−0.248713	−	0.430784i	−0.963169	+	0.268897i	$0.913341\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−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	$-0.635353\pi$
$13$	−38.6718			−0.825048			−0.412524	+	0.910947i	$0.635353\pi$
$14$		0			0
$15$		0			0
$16$	−90.8636	−	157.380i	−1.41974	−	2.45907i
$17$	−21.7394	+	37.6537i	−0.310152	+	0.537198i	−0.978395	−	0.206744i	$-0.933713\pi$
$17$	−21.7394	+	37.6537i	−0.310152	+	0.537198i	0.668243	+	0.743943i	$0.267046\pi$
$18$		0			0
$19$	−54.5139	−	94.4208i	−0.658228	−	1.14009i	−0.981074	−	0.193633i	$-0.937973\pi$
$19$	−54.5139	−	94.4208i	−0.658228	−	1.14009i	0.322845	−	0.946452i	$-0.395361\pi$
$20$	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
$28$		0			0
$29$	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	−0.758229	−	0.651988i	$-0.773935\pi$
$31$	32.0215	−	55.4629i	0.185524	−	0.321337i	0.943753	+	0.330652i	$0.107268\pi$
$32$	223.754	−	387.553i	1.23608	−	2.14095i
$33$		0			0
$34$	−230.798			−1.16416
$35$		0			0
$36$		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	$-0.515036\pi$
$41$	−24.7923			−0.0944367			−0.0472184	+	0.998885i	$0.515036\pi$
$42$		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	$0.246403\pi$
$47$	310.274	+	537.411i	0.962940	+	1.66786i	0.247888	+	0.968789i	$0.420264\pi$
$48$		0			0
$49$		0			0
$50$	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
$56$		0			0
$57$		0			0
$58$	192.051	+	332.642i	0.434785	+	0.753070i
$59$	−262.526	+	454.708i	−0.579287	+	1.00335i	0.416275	+	0.909239i	$0.363336\pi$
$59$	−262.526	+	454.708i	−0.579287	+	1.00335i	−0.995561	+	0.0941152i	$0.969998\pi$
$60$		0			0
$61$	−191.718	−	332.065i	−0.402409	−	0.696993i	0.591607	−	0.806226i	$-0.298494\pi$
$61$	−191.718	−	332.065i	−0.402409	−	0.696993i	−0.994016	+	0.109234i	$0.965160\pi$
$62$	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
$70$		0			0
$71$	−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	−0.967684	−	0.252166i	$-0.918857\pi$
$73$	−165.570	+	286.776i	−0.265459	+	0.459789i	0.702224	+	0.711956i	$0.252190\pi$
$74$	500.910	−	867.602i	0.786887	−	1.36293i
$75$		0			0
$76$	2199.96			3.32043
$77$		0			0
$78$		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	$-0.449007\pi$
$83$	241.241			0.319032			0.159516	+	0.987195i	$0.449007\pi$
$84$		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	$-0.773506\pi$
$89$	−792.772	−	1373.12i	−0.944198	−	1.63540i	−0.186849	−	0.982389i	$-0.559828\pi$
$90$		0			0
$91$		0			0
$92$	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	$-0.513211\pi$
$97$	−79.2754			−0.0829814			−0.0414907	+	0.999139i	$0.513211\pi$
$98$		0			0
$99$		0			0
$100$	949.080	+	1643.85i	0.949080	+	1.64385i
$101$	−577.487	+	1000.24i	−0.568931	+	0.985418i	0.427741	+	0.903902i	$0.359310\pi$
$101$	−577.487	+	1000.24i	−0.568931	+	0.985418i	−0.996672	+	0.0815165i	$0.974024\pi$
$102$		0			0
$103$	−722.430	−	1251.28i	−0.691098	−	1.19702i	−0.971478	−	0.237128i	$-0.923794\pi$
$103$	−722.430	−	1251.28i	−0.691098	−	1.19702i	0.280380	−	0.959889i	$-0.409539\pi$
$104$	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
$112$		0			0
$113$	−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
$119$		0			0
$120$		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	0.614928	−	0.788584i	$-0.289185\pi$
$131$	−562.965	−	975.085i	−0.375470	−	0.650332i	−0.990397	+	0.138251i	$0.955852\pi$
$132$		0			0
$133$		0			0
$134$	−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	$-0.170752\pi$
$139$	2817.19			1.71907			0.859537	+	0.511074i	$0.170752\pi$
$140$		0			0
$141$		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
$154$		0			0
$155$	−356.169			−0.184569
$156$		0			0
$157$	−931.829	+	1613.98i	−0.473682	+	0.820441i	−0.999546	−	0.0301273i	$-0.990409\pi$
$157$	−931.829	+	1613.98i	−0.473682	+	0.820441i	0.525864	+	0.850569i	$0.323742\pi$
$158$	1161.58	−	2011.91i	0.584875	−	1.01303i
$159$		0			0
$160$	−2488.77			−1.22971
$161$		0			0
$162$		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	$-0.232889\pi$
$167$	3211.62			1.48816			0.744079	+	0.668092i	$0.232889\pi$
$168$		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	0.841523	−	0.540222i	$-0.181660\pi$
$173$	−107.139	−	185.569i	−0.0470844	−	0.0815525i	−0.888607	+	0.458669i	$0.848326\pi$
$174$		0			0
$175$		0			0
$176$	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	$-0.483743\pi$
$181$	248.631			0.102103			0.0510514	+	0.998696i	$0.483743\pi$
$182$		0			0
$183$		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
$196$		0			0
$197$	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	−0.946474	−	0.322780i	$-0.895383\pi$
$199$	−543.767	+	941.832i	−0.193702	+	0.335501i	0.752773	+	0.658281i	$0.228716\pi$
$200$	−3040.57	+	5266.43i	−1.07501	+	1.86196i
$201$		0			0
$202$	−6130.94			−2.13550
$203$		0			0
$204$		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
$217$		0			0
$218$	−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	$-0.662046\pi$
$223$	−3246.03			−0.974754			−0.487377	+	0.873192i	$0.662046\pi$
$224$		0			0
$225$		0			0
$226$	−1785.93	−	3093.32i	−0.525656	−	0.910463i
$227$	−2569.08	+	4449.77i	−0.751171	+	1.30107i	0.196085	+	0.980587i	$0.437177\pi$
$227$	−2569.08	+	4449.77i	−0.751171	+	1.30107i	−0.947256	+	0.320479i	$0.896156\pi$
$228$		0			0
$229$	307.403	+	532.438i	0.0887064	+	0.153644i	0.906965	−	0.421207i	$-0.138393\pi$
$229$	307.403	+	532.438i	0.0887064	+	0.153644i	−0.818258	+	0.574851i	$0.805060\pi$
$230$	−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
$238$		0			0
$239$	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	−0.986651	−	0.162847i	$-0.947932\pi$
$241$	−1318.06	+	2282.94i	−0.352296	+	0.610195i	0.634355	+	0.773042i	$0.281266\pi$
$242$	−3018.58	+	5228.33i	−0.801825	+	1.38880i
$243$		0			0
$244$	7736.96			2.02995
$245$		0			0
$246$		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	$-0.416702\pi$
$251$	2057.57			0.517422			0.258711	+	0.965955i	$0.416702\pi$
$252$		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	0.705548	−	0.708663i	$-0.250701\pi$
$257$	−1075.10	−	1862.13i	−0.260946	−	0.451972i	−0.966494	+	0.256691i	$0.917368\pi$
$258$		0			0
$259$		0			0
$260$	−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
$266$		0			0
$267$		0			0
$268$	−1998.80	−	3462.02i	−0.455582	−	0.789091i
$269$	189.689	−	328.551i	0.0429945	−	0.0744687i	−0.843727	−	0.536772i	$-0.819644\pi$
$269$	189.689	−	328.551i	0.0429945	−	0.0744687i	0.886722	+	0.462303i	$0.152977\pi$
$270$		0			0
$271$	−2684.42	−	4649.55i	−0.601723	−	1.04221i	−0.992560	−	0.121755i	$-0.961148\pi$
$271$	−2684.42	−	4649.55i	−0.601723	−	1.04221i	0.390837	−	0.920460i	$-0.372185\pi$
$272$	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
$280$		0			0
$281$	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	−0.699892	−	0.714249i	$-0.746768\pi$
$283$	1278.81	−	2214.96i	0.268612	−	0.465250i	0.968504	+	0.248999i	$0.0801017\pi$
$284$	7924.21	−	13725.1i	1.65569	−	2.86774i
$285$		0			0
$286$	2856.97			0.590687
$287$		0			0
$288$		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	$-0.482218\pi$
$293$	560.049			0.111667			0.0558335	+	0.998440i	$0.482218\pi$
$294$		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
$301$		0			0
$302$	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	$-0.610278\pi$
$307$	−3653.02			−0.679117			−0.339558	+	0.940585i	$0.610278\pi$
$308$		0			0
$309$		0			0
$310$	−945.325	−	1637.35i	−0.173196	−	0.299985i
$311$	−1746.13	+	3024.39i	−0.318374	+	0.551439i	−0.980149	−	0.198263i	$-0.936470\pi$
$311$	−1746.13	+	3024.39i	−0.318374	+	0.551439i	0.661775	+	0.749702i	$0.269803\pi$
$312$		0			0
$313$	4356.05	+	7544.90i	0.786640	+	1.36250i	0.928014	+	0.372544i	$0.121515\pi$
$313$	4356.05	+	7544.90i	0.786640	+	1.36250i	−0.141374	+	0.989956i	$0.545152\pi$
$314$	−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
$322$		0			0
$323$	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
$329$		0			0
$330$		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
$343$		0			0
$344$	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	$-0.440469\pi$
$349$	2424.54			0.371870			0.185935	+	0.982562i	$0.440469\pi$
$350$		0			0
$351$		0			0
$352$	3114.06	+	5393.71i	0.471534	+	0.816721i
$353$	6201.56	−	10741.4i	0.935059	−	1.61957i	0.160531	−	0.987031i	$-0.448679\pi$
$353$	6201.56	−	10741.4i	0.935059	−	1.61957i	0.774528	−	0.632540i	$-0.217987\pi$
$354$		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
$364$		0			0
$365$	1841.61			0.264093
$366$		0			0
$367$	−689.031	+	1193.44i	−0.0980031	+	0.169746i	−0.910858	−	0.412720i	$-0.864579\pi$
$367$	−689.031	+	1193.44i	−0.0980031	+	0.169746i	0.812855	+	0.582466i	$0.197912\pi$
$368$	−6803.67	+	11784.3i	−0.963766	+	1.66929i
$369$		0			0
$370$	−5571.52			−0.782837
$371$		0			0
$372$		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	0.601627	−	0.798777i	$-0.294519\pi$
$383$	−2930.33	−	5075.48i	−0.390948	−	0.677141i	−0.992575	+	0.121636i	$0.961186\pi$
$384$		0			0
$385$		0			0
$386$	−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
$392$		0			0
$393$		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	$0.00274154\pi$
$397$	4013.94	+	6952.35i	0.507440	+	0.878912i	−0.492523	+	0.870300i	$0.663925\pi$
$398$	−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
$406$		0			0
$407$	2626.59			0.319890
$408$		0			0
$409$	7346.25	−	12724.1i	0.888139	−	1.53830i	0.0460654	−	0.998938i	$-0.485332\pi$
$409$	7346.25	−	12724.1i	0.888139	−	1.53830i	0.842073	−	0.539363i	$-0.181335\pi$
$410$	−365.953	+	633.850i	−0.0440809	+	0.0763503i
$411$		0			0
$412$	29154.4			3.48624
$413$		0			0
$414$		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	$-0.437049\pi$
$419$	3370.31			0.392960			0.196480	+	0.980508i	$0.437049\pi$
$420$		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
$427$		0			0
$428$	−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	$-0.405794\pi$
$433$	5255.73			0.583313			0.291656	+	0.956523i	$0.405794\pi$
$434$		0			0
$435$		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	0.842732	−	0.538334i	$-0.180946\pi$
$439$	−412.488	−	714.451i	−0.0448451	−	0.0776740i	−0.887577	+	0.460660i	$0.847613\pi$
$440$	−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
$448$		0			0
$449$	−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
$455$		0			0
$456$		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	$-0.663259\pi$
$461$	−9714.00			−0.981401			−0.490701	+	0.871328i	$0.663259\pi$
$462$		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	0.901505	−	0.432769i	$-0.142463\pi$
$467$	766.618	+	1327.82i	0.0759633	+	0.131572i	−0.825541	+	0.564341i	$0.809130\pi$
$468$		0			0
$469$		0			0
$470$	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
$476$		0			0
$477$		0			0
$478$	9110.23	+	15779.4i	0.871741	+	1.50990i
$479$	3517.69	−	6092.81i	0.335547	−	0.581185i	−0.648042	−	0.761604i	$-0.724412\pi$
$479$	3517.69	−	6092.81i	0.335547	−	0.581185i	0.983590	+	0.180419i	$0.0577454\pi$
$480$		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
$490$		0			0
$491$	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
$497$		0			0
$498$		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	$-0.625195\pi$
$503$	−8646.95			−0.766498			−0.383249	+	0.923645i	$0.625195\pi$
$504$		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	$0.0691533\pi$
$509$	7750.44	+	13424.1i	0.674916	+	1.16899i	−0.301578	+	0.953441i	$0.597513\pi$
$510$		0			0
$511$		0			0
$512$	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
$518$		0			0
$519$		0			0
$520$	−6951.50	−	12040.4i	−0.586238	−	1.01539i
$521$	−432.354	+	748.858i	−0.0363565	+	0.0629714i	−0.883631	−	0.468184i	$-0.844909\pi$
$521$	−432.354	+	748.858i	−0.0363565	+	0.0629714i	0.847275	+	0.531155i	$0.178242\pi$
$522$		0			0
$523$	−3127.81	−	5417.52i	−0.261509	−	0.452947i	0.705134	−	0.709074i	$-0.250887\pi$
$523$	−3127.81	−	5417.52i	−0.261509	−	0.452947i	−0.966643	+	0.256127i	$0.917554\pi$
$524$	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
$532$		0			0
$533$	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
$539$		0			0
$540$		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
$553$		0			0
$554$	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
$560$		0			0
$561$		0			0
$562$	5511.51	+	9546.22i	0.413682	+	0.716517i
$563$	−8184.91	+	14176.7i	−0.612705	+	1.06124i	0.378077	+	0.925774i	$0.376585\pi$
$563$	−8184.91	+	14176.7i	−0.612705	+	1.06124i	−0.990782	+	0.135462i	$0.956748\pi$
$564$		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
$574$		0			0
$575$	−7043.82			−0.510865
$576$		0			0
$577$	3797.09	−	6576.75i	0.273960	−	0.474512i	−0.695912	−	0.718127i	$-0.745000\pi$
$577$	3797.09	−	6576.75i	0.273960	−	0.474512i	0.969872	+	0.243615i	$0.0783332\pi$
$578$	−8022.42	+	13895.2i	−0.577316	+	0.999940i
$579$		0			0
$580$	8119.96			0.581315
$581$		0			0
$582$		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	$-0.519746\pi$
$587$	−1763.34			−0.123988			−0.0619939	+	0.998077i	$0.519746\pi$
$588$		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	0.996554	−	0.0829448i	$-0.0264325\pi$
$593$	6158.07	+	10666.1i	0.426445	+	0.738624i	−0.570109	+	0.821569i	$0.693099\pi$
$594$		0			0
$595$		0			0
$596$	−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	$-0.274722\pi$
$601$	19157.1			1.30022			0.650112	+	0.759838i	$0.274722\pi$
$602$		0			0
$603$		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	0.711283	−	0.702905i	$-0.248114\pi$
$607$	−3784.96	−	6555.75i	−0.253092	−	0.438369i	−0.964376	+	0.264537i	$0.914781\pi$
$608$	−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
$616$		0			0
$617$	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	−0.655081	−	0.755558i	$-0.727366\pi$
$619$	5032.78	−	8717.03i	0.326792	−	0.566021i	0.981873	+	0.189538i	$0.0606989\pi$
$620$	3593.39	−	6223.93i	0.232764	−	0.403160i
$621$		0			0
$622$	−18538.0			−1.19503
$623$		0			0
$624$		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
$637$		0			0
$638$	−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	$-0.572286\pi$
$643$	−7341.90			−0.450290			−0.225145	+	0.974325i	$0.572286\pi$
$644$		0			0
$645$		0			0
$646$	12581.7	+	21792.1i	0.766285	+	1.32725i
$647$	−3035.99	+	5258.49i	−0.184478	+	0.319525i	−0.943400	−	0.331656i	$-0.892393\pi$
$647$	−3035.99	+	5258.49i	−0.184478	+	0.319525i	0.758923	+	0.651181i	$0.225726\pi$
$648$		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
$658$		0			0
$659$	−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	−0.986402	−	0.164351i	$-0.947447\pi$
$661$	−5962.75	+	10327.8i	−0.350868	+	0.607722i	0.635533	+	0.772073i	$0.280780\pi$
$662$	−15212.3	+	26348.4i	−0.893114	+	1.54692i
$663$		0			0
$664$	−15594.9			−0.911444
$665$		0			0
$666$		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	0.718553	−	0.695472i	$-0.244805\pi$
$677$	−4280.81	−	7414.57i	−0.243020	−	0.420924i	−0.961573	+	0.274549i	$0.911472\pi$
$678$		0			0
$679$		0			0
$680$	−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
$686$		0			0
$687$		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	$-0.921066\pi$
$691$	−12665.3	−	21937.0i	−0.697267	−	1.20770i	0.272143	−	0.962257i	$-0.412268\pi$
$692$	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
$700$		0			0
$701$	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
$707$		0			0
$708$		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	0.549695	−	0.835365i	$-0.314744\pi$
$719$	−8648.74	−	14980.0i	−0.448600	−	0.776998i	−0.998295	+	0.0583673i	$0.981411\pi$
$720$		0			0
$721$		0			0
$722$	−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	$-0.528575\pi$
$727$	−3514.71			−0.179303			−0.0896516	+	0.995973i	$0.528575\pi$
$728$		0			0
$729$		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	$-0.922892\pi$
$733$	−13755.6	−	23825.4i	−0.693144	−	1.20056i	0.277658	−	0.960680i	$-0.410442\pi$
$734$	−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
$742$		0			0
$743$	−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
$749$		0			0
$750$		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	0.645547	−	0.763721i	$-0.276630\pi$
$761$	−7108.86	−	12312.9i	−0.338628	−	0.586521i	−0.984175	+	0.177200i	$0.943296\pi$
$762$		0			0
$763$		0			0
$764$	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	$-0.625466\pi$
$769$	−16379.1			−0.768068			−0.384034	+	0.923319i	$0.625466\pi$
$770$		0			0
$771$		0			0
$772$	−20791.9	−	36012.6i	−0.969323	−	1.67892i
$773$	19948.3	−	34551.6i	0.928192	−	1.60768i	0.141846	−	0.989889i	$-0.454696\pi$
$773$	19948.3	−	34551.6i	0.928192	−	1.60768i	0.786346	−	0.617787i	$-0.211970\pi$
$774$		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
$784$		0			0
$785$	10364.5			0.471244
$786$		0			0
$787$	−16564.3	+	28690.2i	−0.750257	+	1.29948i	0.197440	+	0.980315i	$0.436737\pi$
$787$	−16564.3	+	28690.2i	−0.750257	+	1.29948i	−0.947698	+	0.319169i	$0.896596\pi$
$788$	−16809.1	+	29114.3i	−0.759899	+	1.31618i
$789$		0			0
$790$	−12920.0			−0.581865
$791$		0			0
$792$		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	$-0.629843\pi$
$797$	−17851.5			−0.793390			−0.396695	+	0.917951i	$0.629843\pi$
$798$		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
$805$		0			0
$806$	−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	$-0.376053\pi$
$811$	17535.4			0.759251			0.379626	+	0.925140i	$0.376053\pi$
$812$		0			0
$813$		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
$826$		0			0
$827$	−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	−0.708279	−	0.705933i	$-0.750528\pi$
$829$	6139.45	−	10633.8i	0.257216	−	0.445511i	0.965495	+	0.260421i	$0.0838615\pi$
$830$	3560.91	−	6167.67i	0.148917	−	0.257931i
$831$		0			0
$832$	−35643.1			−1.48522
$833$		0			0
$834$		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	$-0.677845\pi$
$839$	−25765.0			−1.06020			−0.530098	+	0.847936i	$0.677845\pi$
$840$		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
$847$		0			0
$848$	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	$-0.774771\pi$
$853$	−37864.5			−1.51988			−0.759939	+	0.649995i	$0.774771\pi$
$854$		0			0
$855$		0			0
$856$	−32030.0	−	55477.6i	−1.27893	−	2.21517i
$857$	14604.4	−	25295.5i	0.582118	−	1.00826i	−0.413110	−	0.910681i	$-0.635557\pi$
$857$	14604.4	−	25295.5i	0.582118	−	1.00826i	0.995228	−	0.0975771i	$-0.0311093\pi$
$858$		0			0
$859$	17451.5	+	30226.8i	0.693173	+	1.20061i	0.970793	+	0.239920i	$0.0771213\pi$
$859$	17451.5	+	30226.8i	0.693173	+	1.20061i	−0.277619	+	0.960691i	$0.589545\pi$
$860$	−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
$868$		0			0
$869$	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
$875$		0			0
$876$		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	$-0.653371\pi$
$881$	−24235.5			−0.926803			−0.463401	+	0.886148i	$0.653371\pi$
$882$		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	$-0.984522\pi$
$887$	−14304.9	−	24776.9i	−0.541502	−	0.937910i	0.457316	−	0.889304i	$-0.348811\pi$
$888$		0			0
$889$		0			0
$890$	−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
$896$		0			0
$897$		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
$910$		0			0
$911$	−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
$917$		0			0
$918$		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	$0.100080\pi$
$929$	21047.3	+	36454.9i	0.743313	+	1.28746i	−0.207665	+	0.978200i	$0.566586\pi$
$930$		0			0
$931$		0			0
$932$	−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	$-0.218381\pi$
$937$	44385.1			1.54749			0.773745	+	0.633497i	$0.218381\pi$
$938$		0			0
$939$		0			0
$940$	34818.3	+	60307.1i	1.20814	+	2.09255i
$941$	−20495.8	+	35499.8i	−0.710036	+	1.22982i	0.254807	+	0.966992i	$0.417988\pi$
$941$	−20495.8	+	35499.8i	−0.710036	+	1.22982i	−0.964843	+	0.262827i	$0.915345\pi$
$942$		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
$952$		0			0
$953$	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
$959$		0			0
$960$		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	$-0.881393\pi$
$971$	−23629.9	−	40928.2i	−0.780968	−	1.35268i	0.150411	−	0.988624i	$-0.451940\pi$
$972$		0			0
$973$		0			0
$974$	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
$980$		0			0
$981$		0			0
$982$	6352.29	+	11002.5i	0.206426	+	0.357540i
$983$	9555.64	−	16550.9i	0.310049	−	0.537020i	−0.668324	−	0.743870i	$-0.732988\pi$
$983$	9555.64	−	16550.9i	0.310049	−	0.537020i	0.978373	+	0.206850i	$0.0663214\pi$
$984$		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
$994$		0			0
$995$	6048.21			0.192705
$996$		0			0
$997$	4596.40	−	7961.20i	0.146008	−	0.252892i	−0.783741	−	0.621088i	$-0.786691\pi$
$997$	4596.40	−	7961.20i	0.146008	−	0.252892i	0.929748	+	0.368196i	$0.120024\pi$
$998$	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	441.4.e.w.361.3		6
3.2	odd	2		147.4.e.n.67.1		6
7.2	even	3	inner	441.4.e.w.226.3		6
7.3	odd	6		441.4.a.s.1.1		3
7.4	even	3		441.4.a.t.1.1		3
7.5	odd	6		63.4.e.c.37.3		6
7.6	odd	2		63.4.e.c.46.3		6
21.2	odd	6		147.4.e.n.79.1		6
21.5	even	6		21.4.e.b.16.1	yes	6
21.11	odd	6		147.4.a.m.1.3		3
21.17	even	6		147.4.a.l.1.3		3
21.20	even	2		21.4.e.b.4.1	✓	6
84.11	even	6		2352.4.a.cg.1.2		3
84.47	odd	6		336.4.q.k.289.2		6
84.59	odd	6		2352.4.a.ci.1.2		3
84.83	odd	2		336.4.q.k.193.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.1	✓	6	21.20	even	2
21.4.e.b.16.1	yes	6	21.5	even	6
63.4.e.c.37.3		6	7.5	odd	6
63.4.e.c.46.3		6	7.6	odd	2
147.4.a.l.1.3		3	21.17	even	6
147.4.a.m.1.3		3	21.11	odd	6
147.4.e.n.67.1		6	3.2	odd	2
147.4.e.n.79.1		6	21.2	odd	6
336.4.q.k.193.2		6	84.83	odd	2
336.4.q.k.289.2		6	84.47	odd	6
441.4.a.s.1.1		3	7.3	odd	6
441.4.a.t.1.1		3	7.4	even	3
441.4.e.w.226.3		6	7.2	even	3	inner
441.4.e.w.361.3		6	1.1	even	1	trivial
2352.4.a.cg.1.2		3	84.11	even	6
2352.4.a.ci.1.2		3	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

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

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