LMFDB - Embedded newform 441.4.e.y.361.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.5922408960000.19
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 54x^{6} + 176x^{5} + 1307x^{4} - 2912x^{3} - 15314x^{2} + 16800x + 86044 $ x^8 - 4x^7 - 54x^6 + 176x^5 + 1307x^4 - 2912x^3 - 15314x^2 + 16800*x + 86044
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-4.23824 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.y.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76556 - 3.05805i) q^{2} +(-2.23444 + 3.87016i) q^{4} +(1.03865 + 1.79899i) q^{5} -12.4689 q^{8} +O(q^{10})$	\(q+(-1.76556 - 3.05805i) q^{2} +(-2.23444 + 3.87016i) q^{4} +(1.03865 + 1.79899i) q^{5} -12.4689 q^{8} +(3.66760 - 6.35247i) q^{10} +(24.5934 - 42.5970i) q^{11} +44.8559 q^{13} +(39.8901 + 69.0916i) q^{16} +(-13.2589 + 22.9652i) q^{17} +(38.8675 + 67.3205i) q^{19} -9.28317 q^{20} -173.685 q^{22} +(27.8755 + 48.2818i) q^{23} +(60.3424 - 104.516i) q^{25} +(-79.1960 - 137.171i) q^{26} -121.436 q^{29} +(152.776 - 264.616i) q^{31} +(90.9815 - 157.585i) q^{32} +93.6380 q^{34} +(-38.5934 - 66.8457i) q^{37} +(137.246 - 237.717i) q^{38} +(-12.9508 - 22.4314i) q^{40} +248.720 q^{41} -147.179 q^{43} +(109.905 + 190.360i) q^{44} +(98.4319 - 170.489i) q^{46} +(-134.925 - 233.698i) q^{47} -426.154 q^{50} +(-100.228 + 173.599i) q^{52} +(-70.5603 + 122.214i) q^{53} +102.176 q^{55} +(214.403 + 371.356i) q^{58} +(212.417 - 367.917i) q^{59} +(-293.998 - 509.220i) q^{61} -1078.95 q^{62} -4.29373 q^{64} +(46.5895 + 80.6954i) q^{65} +(89.8171 - 155.568i) q^{67} +(-59.2525 - 102.628i) q^{68} -674.872 q^{71} +(118.744 - 205.671i) q^{73} +(-136.278 + 236.041i) q^{74} -347.388 q^{76} +(-247.926 - 429.421i) q^{79} +(-82.8636 + 143.524i) q^{80} +(-439.131 - 760.598i) q^{82} -24.4406 q^{83} -55.0855 q^{85} +(259.854 + 450.080i) q^{86} +(-306.652 + 531.136i) q^{88} +(-536.144 - 928.628i) q^{89} -249.144 q^{92} +(-476.439 + 825.216i) q^{94} +(-80.7393 + 139.845i) q^{95} -1667.43 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8	$ 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8} + 100 q^{11} + 174 q^{16} - 680 q^{22} + 352 q^{23} + 128 q^{25} - 520 q^{29} - 30 q^{32} - 212 q^{37} + 1080 q^{43} + 460 q^{44} - 696 q^{46} - 2732 q^{50} + 16 q^{53} + 780 q^{58} - 3356 q^{64} - 756 q^{65} + 1944 q^{67} - 4496 q^{71} - 284 q^{74} + 1048 q^{79} - 6568 q^{85} + 4820 q^{86} - 1260 q^{88} - 7024 q^{92} + 2192 q^{95}+O(q^{100}) $ 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8 + 100 * q^11 + 174 * q^16 - 680 * q^22 + 352 * q^23 + 128 * q^25 - 520 * q^29 - 30 * q^32 - 212 * q^37 + 1080 * q^43 + 460 * q^44 - 696 * q^46 - 2732 * q^50 + 16 * q^53 + 780 * q^58 - 3356 * q^64 - 756 * q^65 + 1944 * q^67 - 4496 * q^71 - 284 * q^74 + 1048 * q^79 - 6568 * q^85 + 4820 * q^86 - 1260 * q^88 - 7024 * q^92 + 2192 * q^95

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 $

$2$	−1.76556	−	3.05805i	−0.624221	−	1.08118i	−0.988691	−	0.149968i	$-0.952083\pi$
$2$	−1.76556	−	3.05805i	−0.624221	−	1.08118i	0.364470	−	0.931215i	$-0.381250\pi$
$3$		0			0
$3$		0			0
$4$	−2.23444	+	3.87016i	−0.279304	+	0.483769i
$5$	1.03865	+	1.79899i	0.0928996	+	0.160907i	0.908730	−	0.417384i	$-0.137053\pi$
$5$	1.03865	+	1.79899i	0.0928996	+	0.160907i	−0.815830	+	0.578291i	$0.803720\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−12.4689			−0.551051
$9$		0			0
$10$	3.66760	−	6.35247i	0.115980	−	0.200883i
$11$	24.5934	−	42.5970i	0.674108	−	1.16759i	−0.302621	−	0.953111i	$-0.597862\pi$
$11$	24.5934	−	42.5970i	0.674108	−	1.16759i	0.976729	−	0.214478i	$-0.0688050\pi$
$12$		0			0
$13$	44.8559			0.956983			0.478492	−	0.878092i	$-0.341184\pi$
$13$	44.8559			0.956983			0.478492	+	0.878092i	$0.341184\pi$
$14$		0			0
$15$		0			0
$16$	39.8901	+	69.0916i	0.623282	+	1.07956i
$17$	−13.2589	+	22.9652i	−0.189163	+	0.327639i	−0.944971	−	0.327153i	$-0.893911\pi$
$17$	−13.2589	+	22.9652i	−0.189163	+	0.327639i	0.755809	+	0.654793i	$0.227244\pi$
$18$		0			0
$19$	38.8675	+	67.3205i	0.469306	+	0.812862i	0.999384	−	0.0350869i	$-0.0111708\pi$
$19$	38.8675	+	67.3205i	0.469306	+	0.812862i	−0.530078	+	0.847949i	$0.677837\pi$
$20$	−9.28317			−0.103789
$21$		0			0
$22$	−173.685			−1.68317
$23$	27.8755	+	48.2818i	0.252715	+	0.437715i	0.964272	−	0.264913i	$-0.0853432\pi$
$23$	27.8755	+	48.2818i	0.252715	+	0.437715i	−0.711558	+	0.702628i	$0.752010\pi$
$24$		0			0
$25$	60.3424	−	104.516i	0.482739	−	0.836129i
$26$	−79.1960	−	137.171i	−0.597369	−	1.03467i
$27$		0			0
$28$		0			0
$29$	−121.436			−0.777588			−0.388794	−	0.921325i	$-0.627108\pi$
$29$	−121.436			−0.777588			−0.388794	+	0.921325i	$0.627108\pi$
$30$		0			0
$31$	152.776	−	264.616i	0.885143	−	1.53311i	0.0395940	−	0.999216i	$-0.487394\pi$
$31$	152.776	−	264.616i	0.885143	−	1.53311i	0.845549	−	0.533897i	$-0.179273\pi$
$32$	90.9815	−	157.585i	0.502607	−	0.870540i
$33$		0			0
$34$	93.6380			0.472317
$35$		0			0
$36$		0			0
$37$	−38.5934	−	66.8457i	−0.171479	−	0.297010i	0.767458	−	0.641099i	$-0.221521\pi$
$37$	−38.5934	−	66.8457i	−0.171479	−	0.297010i	−0.938937	+	0.344089i	$0.888188\pi$
$38$	137.246	−	237.717i	0.585902	−	1.01481i
$39$		0			0
$40$	−12.9508	−	22.4314i	−0.0511924	−	0.0886679i
$41$	248.720			0.947403			0.473702	−	0.880685i	$-0.342917\pi$
$41$	248.720			0.947403			0.473702	+	0.880685i	$0.342917\pi$
$42$		0			0
$43$	−147.179			−0.521967			−0.260984	−	0.965343i	$-0.584047\pi$
$43$	−147.179			−0.521967			−0.260984	+	0.965343i	$0.584047\pi$
$44$	109.905	+	190.360i	0.376563	+	0.652226i
$45$		0			0
$46$	98.4319	−	170.489i	0.315500	−	0.546462i
$47$	−134.925	−	233.698i	−0.418742	−	0.725283i	0.577071	−	0.816694i	$-0.304196\pi$
$47$	−134.925	−	233.698i	−0.418742	−	0.725283i	−0.995813	+	0.0914112i	$0.970862\pi$
$48$		0			0
$49$		0			0
$50$	−426.154			−1.20534
$51$		0			0
$52$	−100.228	+	173.599i	−0.267290	+	0.462959i
$53$	−70.5603	+	122.214i	−0.182872	+	0.316743i	−0.942857	−	0.333197i	$-0.891873\pi$
$53$	−70.5603	+	122.214i	−0.182872	+	0.316743i	0.759986	+	0.649940i	$0.225206\pi$
$54$		0			0
$55$	102.176			0.250497
$56$		0			0
$57$		0			0
$58$	214.403	+	371.356i	0.485387	+	0.840715i
$59$	212.417	−	367.917i	0.468717	−	0.811842i	−0.530643	−	0.847595i	$-0.678050\pi$
$59$	212.417	−	367.917i	0.468717	−	0.811842i	0.999361	+	0.0357532i	$0.0113830\pi$
$60$		0			0
$61$	−293.998	−	509.220i	−0.617092	−	1.06883i	−0.990014	−	0.140972i	$-0.954977\pi$
$61$	−293.998	−	509.220i	−0.617092	−	1.06883i	0.372922	−	0.927863i	$-0.378356\pi$
$62$	−1078.95			−2.21010
$63$		0			0
$64$	−4.29373			−0.00838618
$65$	46.5895	+	80.6954i	0.0889033	+	0.153985i
$66$		0			0
$67$	89.8171	−	155.568i	0.163775	−	0.283666i	−0.772445	−	0.635082i	$-0.780966\pi$
$67$	89.8171	−	155.568i	0.163775	−	0.283666i	0.936219	+	0.351416i	$0.114300\pi$
$68$	−59.2525	−	102.628i	−0.105668	−	0.183022i
$69$		0			0
$70$		0			0
$71$	−674.872			−1.12806			−0.564032	−	0.825753i	$-0.690750\pi$
$71$	−674.872			−1.12806			−0.564032	+	0.825753i	$0.690750\pi$
$72$		0			0
$73$	118.744	−	205.671i	0.190383	−	0.329754i	−0.754994	−	0.655732i	$-0.772360\pi$
$73$	118.744	−	205.671i	0.190383	−	0.329754i	0.945377	+	0.325978i	$0.105694\pi$
$74$	−136.278	+	236.041i	−0.214081	+	0.370800i
$75$		0			0
$76$	−347.388			−0.524317
$77$		0			0
$78$		0			0
$79$	−247.926	−	429.421i	−0.353087	−	0.611564i	0.633702	−	0.773578i	$-0.281535\pi$
$79$	−247.926	−	429.421i	−0.353087	−	0.611564i	−0.986789	+	0.162013i	$0.948201\pi$
$80$	−82.8636	+	143.524i	−0.115805	+	0.200581i
$81$		0			0
$82$	−439.131	−	760.598i	−0.591389	−	1.02432i
$83$	−24.4406			−0.0323217			−0.0161609	−	0.999869i	$-0.505144\pi$
$83$	−24.4406			−0.0323217			−0.0161609	+	0.999869i	$0.505144\pi$
$84$		0			0
$85$	−55.0855			−0.0702925
$86$	259.854	+	450.080i	0.325823	+	0.564342i
$87$		0			0
$88$	−306.652	+	531.136i	−0.371468	+	0.643402i
$89$	−536.144	−	928.628i	−0.638552	−	1.10600i	−0.985751	−	0.168213i	$-0.946200\pi$
$89$	−536.144	−	928.628i	−0.638552	−	1.10600i	0.347199	−	0.937792i	$-0.387133\pi$
$90$		0			0
$91$		0			0
$92$	−249.144			−0.282337
$93$		0			0
$94$	−476.439	+	825.216i	−0.522776	+	0.905474i
$95$	−80.7393	+	139.845i	−0.0871966	+	0.151029i
$96$		0			0
$97$	−1667.43			−1.74538			−0.872690	−	0.488275i	$-0.837626\pi$
$97$	−1667.43			−1.74538			−0.872690	+	0.488275i	$0.837626\pi$
$98$		0			0
$99$		0			0
$100$	269.662	+	467.069i	0.269662	+	0.467069i
$101$	38.5593	−	66.7867i	0.0379881	−	0.0657973i	−0.846406	−	0.532538i	$-0.821238\pi$
$101$	38.5593	−	66.7867i	0.0379881	−	0.0657973i	0.884394	+	0.466740i	$0.154572\pi$
$102$		0			0
$103$	82.3463	+	142.628i	0.0787749	+	0.136442i	0.902722	−	0.430225i	$-0.141566\pi$
$103$	82.3463	+	142.628i	0.0787749	+	0.136442i	−0.823947	+	0.566667i	$0.808232\pi$
$104$	−559.302			−0.527347
$105$		0			0
$106$	498.315			0.456610
$107$	511.311	+	885.617i	0.461966	+	0.800148i	0.999059	−	0.0433749i	$-0.0138110\pi$
$107$	511.311	+	885.617i	0.461966	+	0.800148i	−0.537093	+	0.843523i	$0.680478\pi$
$108$		0			0
$109$	−681.259	+	1179.97i	−0.598649	+	1.03689i	0.394372	+	0.918951i	$0.370962\pi$
$109$	−681.259	+	1179.97i	−0.598649	+	1.03689i	−0.993021	+	0.117940i	$0.962371\pi$
$110$	−180.398	−	312.458i	−0.156366	−	0.270833i
$111$		0			0
$112$		0			0
$113$	1538.41			1.28072			0.640360	−	0.768075i	$-0.278785\pi$
$113$	1538.41			1.28072			0.640360	+	0.768075i	$0.278785\pi$
$114$		0			0
$115$	−57.9057	+	100.296i	−0.0469542	+	0.0813270i
$116$	271.340	−	469.975i	0.217184	−	0.376174i
$117$		0			0
$118$	−1500.14			−1.17033
$119$		0			0
$120$		0			0
$121$	−544.169	−	942.529i	−0.408842	−	0.708136i
$122$	−1038.15	+	1798.12i	−0.770404	+	1.33438i
$123$		0			0
$124$	682.738	+	1182.54i	0.494449	+	0.856411i
$125$	510.360			0.365184
$126$		0			0
$127$	−170.358			−0.119030			−0.0595151	−	0.998227i	$-0.518955\pi$
$127$	−170.358			−0.119030			−0.0595151	+	0.998227i	$0.518955\pi$
$128$	−720.271	−	1247.55i	−0.497372	−	0.861473i
$129$		0			0
$130$	164.514	−	284.946i	0.110991	−	0.192242i
$131$	375.968	+	651.195i	0.250751	+	0.434314i	0.963733	−	0.266869i	$-0.0859890\pi$
$131$	375.968	+	651.195i	0.250751	+	0.434314i	−0.712981	+	0.701183i	$0.752656\pi$
$132$		0			0
$133$		0			0
$134$	−634.312			−0.408927
$135$		0			0
$136$	165.324	−	286.350i	0.104238	−	0.180546i
$137$	259.311	−	449.140i	0.161711	−	0.280092i	−0.773771	−	0.633465i	$-0.781632\pi$
$137$	259.311	−	449.140i	0.161711	−	0.280092i	0.935483	+	0.353373i	$0.114965\pi$
$138$		0			0
$139$	2975.72			1.81581			0.907905	−	0.419177i	$-0.137681\pi$
$139$	2975.72			1.81581			0.907905	+	0.419177i	$0.137681\pi$
$140$		0			0
$141$		0			0
$142$	1191.53	+	2063.79i	0.704161	+	1.21964i
$143$	1103.16	−	1910.73i	0.645110	−	1.11736i
$144$		0			0
$145$	−126.129	−	218.462i	−0.0722376	−	0.125119i
$146$	−838.604			−0.475365
$147$		0			0
$148$	344.938			0.191579
$149$	−1358.97	−	2353.80i	−0.747188	−	1.29417i	−0.949165	−	0.314778i	$-0.898070\pi$
$149$	−1358.97	−	2353.80i	−0.747188	−	1.29417i	0.201977	−	0.979390i	$-0.435263\pi$
$150$		0			0
$151$	−353.825	+	612.843i	−0.190688	+	0.330281i	−0.945478	−	0.325685i	$-0.894405\pi$
$151$	−353.825	+	612.843i	−0.190688	+	0.330281i	0.754791	+	0.655966i	$0.227738\pi$
$152$	−484.634	−	839.410i	−0.258612	−	0.447929i
$153$		0			0
$154$		0			0
$155$	634.724			0.328918
$156$		0			0
$157$	1558.96	−	2700.19i	0.792473	−	1.37260i	−0.131958	−	0.991255i	$-0.542126\pi$
$157$	1558.96	−	2700.19i	0.792473	−	1.37260i	0.924431	−	0.381349i	$-0.124540\pi$
$158$	−875.459	+	1516.34i	−0.440809	+	0.763503i
$159$		0			0
$160$	377.991			0.186768
$161$		0			0
$162$		0			0
$163$	−904.387	−	1566.44i	−0.434583	−	0.752720i	0.562678	−	0.826676i	$-0.309771\pi$
$163$	−904.387	−	1566.44i	−0.434583	−	0.752720i	−0.997262	+	0.0739557i	$0.976438\pi$
$164$	−555.749	+	962.585i	−0.264614	+	0.458325i
$165$		0			0
$166$	43.1514	+	74.7404i	0.0201759	+	0.0349457i
$167$	3147.38			1.45839			0.729197	−	0.684303i	$-0.239894\pi$
$167$	3147.38			1.45839			0.729197	+	0.684303i	$0.239894\pi$
$168$		0			0
$169$	−184.949			−0.0841827
$170$	97.2570	+	168.454i	0.0438781	+	0.0759991i
$171$		0			0
$172$	328.862	−	569.606i	0.145788	−	0.252512i
$173$	1642.18	+	2844.34i	0.721691	+	1.25001i	0.960322	+	0.278895i	$0.0899681\pi$
$173$	1642.18	+	2844.34i	0.721691	+	1.25001i	−0.238631	+	0.971110i	$0.576699\pi$
$174$		0			0
$175$		0			0
$176$	3924.13			1.68064
$177$		0			0
$178$	−1893.19	+	3279.11i	−0.797196	+	1.38078i
$179$	1399.41	−	2423.85i	0.584341	−	1.01211i	−0.410616	−	0.911808i	$-0.634686\pi$
$179$	1399.41	−	2423.85i	0.584341	−	1.01211i	0.994957	−	0.100300i	$-0.0319802\pi$
$180$		0			0
$181$	3723.04			1.52890			0.764451	−	0.644682i	$-0.223010\pi$
$181$	3723.04			1.52890			0.764451	+	0.644682i	$0.223010\pi$
$182$		0			0
$183$		0			0
$184$	−347.576	−	602.019i	−0.139259	−	0.241203i
$185$	80.1699	−	138.858i	0.0318606	−	0.0551842i
$186$		0			0
$187$	652.164	+	1129.58i	0.255032	+	0.441728i
$188$	1205.93			0.467826
$189$		0			0
$190$	570.202			0.217720
$191$	479.825	+	831.081i	0.181774	+	0.314842i	0.942485	−	0.334249i	$-0.108483\pi$
$191$	479.825	+	831.081i	0.181774	+	0.314842i	−0.760710	+	0.649091i	$0.775149\pi$
$192$		0			0
$193$	1895.12	−	3282.45i	0.706808	−	1.22423i	−0.259227	−	0.965816i	$-0.583468\pi$
$193$	1895.12	−	3282.45i	0.706808	−	1.22423i	0.966035	−	0.258411i	$-0.0831988\pi$
$194$	2943.95	+	5099.08i	1.08950	+	1.88707i
$195$		0			0
$196$		0			0
$197$	−5117.99			−1.85097			−0.925487	−	0.378779i	$-0.876344\pi$
$197$	−5117.99			−1.85097			−0.925487	+	0.378779i	$0.876344\pi$
$198$		0			0
$199$	432.427	−	748.986i	0.154040	−	0.266805i	−0.778669	−	0.627435i	$-0.784105\pi$
$199$	432.427	−	748.986i	0.154040	−	0.266805i	0.932709	+	0.360630i	$0.117438\pi$
$200$	−752.402	+	1303.20i	−0.266014	+	0.460750i
$201$		0			0
$202$	−272.316			−0.0948519
$203$		0			0
$204$		0			0
$205$	258.333	+	447.445i	0.0880134	+	0.152444i
$206$	290.775	−	503.637i	0.0983460	−	0.170340i
$207$		0			0
$208$	1789.30	+	3099.17i	0.596471	+	1.03312i
$209$	3823.53			1.26545
$210$		0			0
$211$	−1344.61			−0.438707			−0.219353	−	0.975645i	$-0.570395\pi$
$211$	−1344.61			−0.438707			−0.219353	+	0.975645i	$0.570395\pi$
$212$	−315.325	−	546.159i	−0.102154	−	0.176936i
$213$		0			0
$214$	1805.51	−	3127.23i	0.576738	−	0.998939i
$215$	−152.867	−	264.774i	−0.0484905	−	0.0839881i
$216$		0			0
$217$		0			0
$218$	4811.23			1.49476
$219$		0			0
$220$	−228.305	+	395.435i	−0.0699650	+	0.121183i
$221$	−594.741	+	1030.12i	−0.181026	+	0.313545i
$222$		0			0
$223$	864.916			0.259727			0.129863	−	0.991532i	$-0.458546\pi$
$223$	864.916			0.259727			0.129863	+	0.991532i	$0.458546\pi$
$224$		0			0
$225$		0			0
$226$	−2716.16	−	4704.53i	−0.799452	−	1.38469i
$227$	−857.672	+	1485.53i	−0.250774	+	0.434353i	−0.963739	−	0.266846i	$-0.914018\pi$
$227$	−857.672	+	1485.53i	−0.250774	+	0.434353i	0.712965	+	0.701200i	$0.247352\pi$
$228$		0			0
$229$	522.729	+	905.394i	0.150842	+	0.261267i	0.931537	−	0.363646i	$-0.118468\pi$
$229$	522.729	+	905.394i	0.150842	+	0.261267i	−0.780695	+	0.624912i	$0.785135\pi$
$230$	408.945			0.117239
$231$		0			0
$232$	1514.17			0.428491
$233$	724.335	+	1254.58i	0.203660	+	0.352749i	0.949705	−	0.313146i	$-0.101383\pi$
$233$	724.335	+	1254.58i	0.203660	+	0.352749i	−0.746045	+	0.665895i	$0.768050\pi$
$234$		0			0
$235$	280.280	−	485.459i	0.0778019	−	0.134757i
$236$	949.263	+	1644.17i	0.261830	+	0.453502i
$237$		0			0
$238$		0			0
$239$	3153.12			0.853383			0.426691	−	0.904397i	$-0.359679\pi$
$239$	3153.12			0.853383			0.426691	+	0.904397i	$0.359679\pi$
$240$		0			0
$241$	190.506	−	329.966i	0.0509194	−	0.0881950i	−0.839442	−	0.543449i	$-0.817118\pi$
$241$	190.506	−	329.966i	0.0509194	−	0.0881950i	0.890362	+	0.455254i	$0.150451\pi$
$242$	−1921.53	+	3328.19i	−0.510416	+	0.884067i
$243$		0			0
$244$	2627.68			0.689426
$245$		0			0
$246$		0			0
$247$	1743.44	+	3019.72i	0.449118	+	0.777895i
$248$	−1904.95	+	3299.47i	−0.487759	+	0.844824i
$249$		0			0
$250$	−901.074	−	1560.71i	−0.227956	−	0.394831i
$251$	−3776.23			−0.949617			−0.474808	−	0.880089i	$-0.657483\pi$
$251$	−3776.23			−0.949617			−0.474808	+	0.880089i	$0.657483\pi$
$252$		0			0
$253$	2742.21			0.681428
$254$	300.778	+	520.963i	0.0743012	+	0.128693i
$255$		0			0
$256$	−2560.55	+	4435.00i	−0.625133	+	1.08276i
$257$	2129.21	+	3687.90i	0.516795	+	0.895116i	0.999810	+	0.0195034i	$0.00620851\pi$
$257$	2129.21	+	3687.90i	0.516795	+	0.895116i	−0.483014	+	0.875612i	$0.660458\pi$
$258$		0			0
$259$		0			0
$260$	−416.405			−0.0993244
$261$		0			0
$262$	1327.59	−	2299.45i	0.313049	−	0.542216i
$263$	2099.41	−	3636.29i	0.492226	−	0.852560i	−0.507734	−	0.861514i	$-0.669517\pi$
$263$	2099.41	−	3636.29i	0.492226	−	0.852560i	0.999960	+	0.00895400i	$0.00285018\pi$
$264$		0			0
$265$	−293.150			−0.0679548
$266$		0			0
$267$		0			0
$268$	401.381	+	695.212i	0.0914860	+	0.158458i
$269$	1870.29	−	3239.44i	0.423917	−	0.734247i	−0.572401	−	0.819974i	$-0.693988\pi$
$269$	1870.29	−	3239.44i	0.423917	−	0.734247i	0.996319	+	0.0857271i	$0.0273213\pi$
$270$		0			0
$271$	−2178.15	−	3772.66i	−0.488240	−	0.845656i	0.511669	−	0.859183i	$-0.329028\pi$
$271$	−2178.15	−	3772.66i	−0.488240	−	0.845656i	−0.999909	+	0.0135265i	$0.995694\pi$
$272$	−2115.60			−0.471607
$273$		0			0
$274$	−1831.32			−0.403775
$275$	−2968.05	−	5140.81i	−0.650837	−	1.12728i
$276$		0			0
$277$	672.152	−	1164.20i	0.145797	−	0.252527i	−0.783873	−	0.620921i	$-0.786759\pi$
$277$	672.152	−	1164.20i	0.145797	−	0.252527i	0.929670	+	0.368394i	$0.120092\pi$
$278$	−5253.83	−	9099.90i	−1.13347	−	1.96322i
$279$		0			0
$280$		0			0
$281$	−4205.54			−0.892817			−0.446408	−	0.894829i	$-0.647297\pi$
$281$	−4205.54			−0.892817			−0.446408	+	0.894829i	$0.647297\pi$
$282$		0			0
$283$	−2376.02	+	4115.38i	−0.499079	+	0.864431i	−0.999999	−	0.00106280i	$-0.999662\pi$
$283$	−2376.02	+	4115.38i	−0.499079	+	0.864431i	0.500920	+	0.865494i	$0.332995\pi$
$284$	1507.96	−	2611.86i	0.315073	−	0.545723i
$285$		0			0
$286$	−7790.79			−1.61077
$287$		0			0
$288$		0			0
$289$	2104.90	+	3645.80i	0.428435	+	0.742071i
$290$	−445.378	+	771.418i	−0.0901845	+	0.156204i
$291$		0			0
$292$	530.654	+	919.119i	0.106350	+	0.184203i
$293$	4961.17			0.989196			0.494598	−	0.869122i	$-0.335315\pi$
$293$	4961.17			0.989196			0.494598	+	0.869122i	$0.335315\pi$
$294$		0			0
$295$	882.506			0.174174
$296$	481.216	+	833.490i	0.0944936	+	0.163668i
$297$		0			0
$298$	−4798.69	+	8311.58i	−0.932822	+	1.61569i
$299$	1250.38	+	2165.72i	0.241844	+	0.418886i
$300$		0			0
$301$		0			0
$302$	2498.80			0.476126
$303$		0			0
$304$	−3100.85	+	5370.84i	−0.585020	+	1.01329i
$305$	610.722	−	1057.80i	0.114655	−	0.198589i
$306$		0			0
$307$	−4234.00			−0.787124			−0.393562	−	0.919298i	$-0.628757\pi$
$307$	−4234.00			−0.787124			−0.393562	+	0.919298i	$0.628757\pi$
$308$		0			0
$309$		0			0
$310$	−1120.65	−	1941.02i	−0.205317	−	0.355620i
$311$	−342.350	+	592.968i	−0.0624209	+	0.108116i	−0.895547	−	0.444967i	$-0.853215\pi$
$311$	−342.350	+	592.968i	−0.0624209	+	0.108116i	0.833126	+	0.553083i	$0.186549\pi$
$312$		0			0
$313$	2972.04	+	5147.72i	0.536707	+	0.929604i	0.999079	+	0.0429180i	$0.0136654\pi$
$313$	2972.04	+	5147.72i	0.536707	+	0.929604i	−0.462371	+	0.886686i	$0.653001\pi$
$314$	−11009.8			−1.97872
$315$		0			0
$316$	2215.90			0.394475
$317$	−1411.95	−	2445.56i	−0.250166	−	0.433301i	0.713405	−	0.700752i	$-0.247152\pi$
$317$	−1411.95	−	2445.56i	−0.250166	−	0.433301i	−0.963571	+	0.267451i	$0.913819\pi$
$318$		0			0
$319$	−2986.52	+	5172.80i	−0.524178	+	0.907904i
$320$	−4.45967	−	7.72438i	−0.000779073	−	0.00134939i
$321$		0			0
$322$		0			0
$323$	−2061.37			−0.355101
$324$		0			0
$325$	2706.71	−	4688.16i	0.461974	−	0.800162i
$326$	−3193.51	+	5531.32i	−0.542552	+	0.939728i
$327$		0			0
$328$	−3101.26			−0.522068
$329$		0			0
$330$		0			0
$331$	1406.48	+	2436.10i	0.233557	+	0.404533i	0.958852	−	0.283905i	$-0.0916301\pi$
$331$	1406.48	+	2436.10i	0.233557	+	0.404533i	−0.725295	+	0.688438i	$0.758297\pi$
$332$	54.6109	−	94.5888i	0.00902760	−	0.0156363i
$333$		0			0
$334$	−5556.91	−	9624.85i	−0.910361	−	1.57679i
$335$	373.154			0.0608584
$336$		0			0
$337$	4260.10			0.688612			0.344306	−	0.938857i	$-0.388114\pi$
$337$	4260.10			0.688612			0.344306	+	0.938857i	$0.388114\pi$
$338$	326.540	+	565.584i	0.0525486	+	0.0910169i
$339$		0			0
$340$	123.085	−	213.190i	0.0196330	−	0.0340054i
$341$	−7514.58	−	13015.6i	−1.19336	−	2.06697i
$342$		0			0
$343$		0			0
$344$	1835.16			0.287631
$345$		0			0
$346$	5798.74	−	10043.7i	0.900990	−	1.56056i
$347$	18.0292	−	31.2275i	0.00278922	−	0.00483106i	−0.864627	−	0.502414i	$-0.832445\pi$
$347$	18.0292	−	31.2275i	0.00278922	−	0.00483106i	0.867417	+	0.497583i	$0.165779\pi$
$348$		0			0
$349$	−242.692			−0.0372236			−0.0186118	−	0.999827i	$-0.505925\pi$
$349$	−242.692			−0.0372236			−0.0186118	+	0.999827i	$0.505925\pi$
$350$		0			0
$351$		0			0
$352$	−4475.09	−	7751.08i	−0.677622	−	1.17368i
$353$	−54.9949	+	95.2539i	−0.00829201	+	0.0143622i	−0.870142	−	0.492802i	$-0.835973\pi$
$353$	−54.9949	+	95.2539i	−0.00829201	+	0.0143622i	0.861850	+	0.507164i	$0.169306\pi$
$354$		0			0
$355$	−700.955	−	1214.09i	−0.104797	−	0.181513i
$356$	4791.92			0.713402
$357$		0			0
$358$	−9883.01			−1.45903
$359$	6202.23	+	10742.6i	0.911814	+	1.57931i	0.811500	+	0.584352i	$0.198651\pi$
$359$	6202.23	+	10742.6i	0.911814	+	1.57931i	0.100314	+	0.994956i	$0.468015\pi$
$360$		0			0
$361$	408.136	−	706.913i	0.0595038	−	0.103064i
$362$	−6573.26	−	11385.2i	−0.954373	−	1.65302i
$363$		0			0
$364$		0			0
$365$	493.335			0.0707461
$366$		0			0
$367$	−6929.81	+	12002.8i	−0.985649	+	1.70719i	−0.346634	+	0.938001i	$0.612675\pi$
$367$	−6929.81	+	12002.8i	−0.985649	+	1.70719i	−0.639015	+	0.769194i	$0.720658\pi$
$368$	−2223.91	+	3851.93i	−0.315025	+	0.545640i
$369$		0			0
$370$	−566.181			−0.0795523
$371$		0			0
$372$		0			0
$373$	−2449.03	−	4241.85i	−0.339963	−	0.588832i	0.644463	−	0.764636i	$-0.277081\pi$
$373$	−2449.03	−	4241.85i	−0.339963	−	0.588832i	−0.984425	+	0.175803i	$0.943748\pi$
$374$	2302.88	−	3988.70i	0.318393	−	0.551472i
$375$		0			0
$376$	1682.37	+	2913.94i	0.230748	+	0.399668i
$377$	−5447.11			−0.744139
$378$		0			0
$379$	−9806.25			−1.32906			−0.664530	−	0.747262i	$-0.731368\pi$
$379$	−9806.25			−1.32906			−0.664530	+	0.747262i	$0.731368\pi$
$380$	−360.814	−	624.948i	−0.0487088	−	0.0843662i
$381$		0			0
$382$	1694.32	−	2934.65i	0.226935	−	0.393063i
$383$	5364.84	+	9292.18i	0.715746	+	1.23971i	0.962671	+	0.270673i	$0.0872463\pi$
$383$	5364.84	+	9292.18i	0.715746	+	1.23971i	−0.246926	+	0.969034i	$0.579420\pi$
$384$		0			0
$385$		0			0
$386$	−13383.8			−1.76482
$387$		0			0
$388$	3725.76	−	6453.21i	0.487492	−	0.844361i
$389$	2632.03	−	4558.80i	0.343057	−	0.594191i	−0.641942	−	0.766753i	$-0.721871\pi$
$389$	2632.03	−	4558.80i	0.343057	−	0.594191i	0.984999	+	0.172562i	$0.0552044\pi$
$390$		0			0
$391$	−1478.40			−0.191217
$392$		0			0
$393$		0			0
$394$	9036.15	+	15651.1i	1.15542	+	2.00124i
$395$	515.016	−	892.034i	0.0656032	−	0.113628i
$396$		0			0
$397$	−607.450	−	1052.13i	−0.0767935	−	0.133010i	0.825071	−	0.565029i	$-0.191135\pi$
$397$	−607.450	−	1052.13i	−0.0767935	−	0.133010i	−0.901865	+	0.432018i	$0.857802\pi$
$398$	−3053.91			−0.384620
$399$		0			0
$400$	9628.26			1.20353
$401$	1147.73	+	1987.92i	0.142929	+	0.247561i	0.928599	−	0.371086i	$-0.121014\pi$
$401$	1147.73	+	1987.92i	0.142929	+	0.247561i	−0.785669	+	0.618647i	$0.787681\pi$
$402$		0			0
$403$	6852.92	−	11869.6i	0.847067	−	1.46716i
$404$	172.317	+	298.461i	0.0212205	+	0.0367550i
$405$		0			0
$406$		0			0
$407$	−3796.57			−0.462381
$408$		0			0
$409$	−2323.27	+	4024.03i	−0.280876	+	0.486492i	−0.971601	−	0.236626i	$-0.923958\pi$
$409$	−2323.27	+	4024.03i	−0.280876	+	0.486492i	0.690724	+	0.723118i	$0.257292\pi$
$410$	912.206	−	1579.99i	0.109880	−	0.190317i
$411$		0			0
$412$	−735.990			−0.0880087
$413$		0			0
$414$		0			0
$415$	−25.3852	−	43.9684i	−0.00300267	−	0.00520078i
$416$	4081.06	−	7068.60i	0.480986	−	0.833093i
$417$		0			0
$418$	−6750.69	−	11692.5i	−0.789922	−	1.36818i
$419$	−7541.24			−0.879269			−0.439634	−	0.898177i	$-0.644892\pi$
$419$	−7541.24			−0.879269			−0.439634	+	0.898177i	$0.644892\pi$
$420$		0			0
$421$	−6243.63			−0.722794			−0.361397	−	0.932412i	$-0.617700\pi$
$421$	−6243.63			−0.722794			−0.361397	+	0.932412i	$0.617700\pi$
$422$	2374.00	+	4111.90i	0.273850	+	0.474322i
$423$		0			0
$424$	879.808	−	1523.87i	0.100772	−	0.174542i
$425$	1600.15	+	2771.55i	0.182632	+	0.316329i
$426$		0			0
$427$		0			0
$428$	−4569.97			−0.516116
$429$		0			0
$430$	−539.794	+	934.951i	−0.0605376	+	0.104854i
$431$	5732.90	−	9929.68i	0.640706	−	1.10974i	−0.344570	−	0.938761i	$-0.611975\pi$
$431$	5732.90	−	9929.68i	0.640706	−	1.10974i	0.985275	−	0.170974i	$-0.0546915\pi$
$432$		0			0
$433$	5156.40			0.572289			0.286144	−	0.958187i	$-0.407626\pi$
$433$	5156.40			0.572289			0.286144	+	0.958187i	$0.407626\pi$
$434$		0			0
$435$		0			0
$436$	−3044.46	−	5273.16i	−0.334411	−	0.579216i
$437$	−2166.90	+	3753.18i	−0.237201	+	0.410844i
$438$		0			0
$439$	2532.12	+	4385.77i	0.275289	+	0.476814i	0.970208	−	0.242274i	$-0.0778932\pi$
$439$	2532.12	+	4385.77i	0.275289	+	0.476814i	−0.694919	+	0.719088i	$0.744560\pi$
$440$	−1274.01			−0.138037
$441$		0			0
$442$	4200.22			0.452000
$443$	6351.82	+	11001.7i	0.681228	+	1.17992i	0.974606	+	0.223925i	$0.0718871\pi$
$443$	6351.82	+	11001.7i	0.681228	+	1.17992i	−0.293378	+	0.955996i	$0.594780\pi$
$444$		0			0
$445$	1113.73	−	1929.04i	0.118642	−	0.205495i
$446$	−1527.06	−	2644.95i	−0.162127	−	0.280812i
$447$		0			0
$448$		0			0
$449$	−13942.2			−1.46542			−0.732709	−	0.680542i	$-0.761744\pi$
$449$	−13942.2			−1.46542			−0.732709	+	0.680542i	$0.761744\pi$
$450$		0			0
$451$	6116.87	−	10594.7i	0.638652	−	1.10618i
$452$	−3437.48	+	5953.88i	−0.357711	+	0.619573i
$453$		0			0
$454$	6057.10			0.626154
$455$		0			0
$456$		0			0
$457$	7607.01	+	13175.7i	0.778646	+	1.34865i	0.932722	+	0.360595i	$0.117426\pi$
$457$	7607.01	+	13175.7i	0.778646	+	1.34865i	−0.154077	+	0.988059i	$0.549240\pi$
$458$	1845.82	−	3197.06i	0.188318	−	0.326177i
$459$		0			0
$460$	−258.773	−	448.208i	−0.0262290	−	0.0454300i
$461$	11430.2			1.15479			0.577394	−	0.816465i	$-0.304070\pi$
$461$	11430.2			1.15479			0.577394	+	0.816465i	$0.304070\pi$
$462$		0			0
$463$	−9347.88			−0.938300			−0.469150	−	0.883119i	$-0.655440\pi$
$463$	−9347.88			−0.938300			−0.469150	+	0.883119i	$0.655440\pi$
$464$	−4844.08	−	8390.20i	−0.484657	−	0.839451i
$465$		0			0
$466$	2557.72	−	4430.10i	0.254258	−	0.440387i
$467$	1815.42	+	3144.40i	0.179888	+	0.311575i	0.941842	−	0.336056i	$-0.109093\pi$
$467$	1815.42	+	3144.40i	0.179888	+	0.311575i	−0.761954	+	0.647631i	$0.775760\pi$
$468$		0			0
$469$		0			0
$470$	−1979.41			−0.194262
$471$		0			0
$472$	−2648.60	+	4587.51i	−0.258287	+	0.447367i
$473$	−3619.63	+	6269.38i	−0.351862	+	0.609443i
$474$		0			0
$475$	9381.43			0.906210
$476$		0			0
$477$		0			0
$478$	−5567.04	−	9642.39i	−0.532700	−	0.922663i
$479$	3260.62	−	5647.57i	0.311027	−	0.538714i	−0.667558	−	0.744557i	$-0.732661\pi$
$479$	3260.62	−	5647.57i	0.311027	−	0.538714i	0.978585	+	0.205844i	$0.0659939\pi$
$480$		0			0
$481$	−1731.14	−	2998.42i	−0.164102	−	0.284234i
$482$	−1345.40			−0.127140
$483$		0			0
$484$	4863.65			0.456766
$485$	−1731.87	−	2999.69i	−0.162145	−	0.280843i
$486$		0			0
$487$	1833.14	−	3175.10i	0.170570	−	0.295436i	−0.768049	−	0.640391i	$-0.778772\pi$
$487$	1833.14	−	3175.10i	0.170570	−	0.295436i	0.938619	+	0.344955i	$0.112106\pi$
$488$	3665.83	+	6349.40i	0.340049	+	0.588983i
$489$		0			0
$490$		0			0
$491$	12470.7			1.14623			0.573113	−	0.819476i	$-0.305736\pi$
$491$	12470.7			1.14623			0.573113	+	0.819476i	$0.305736\pi$
$492$		0			0
$493$	1610.11	−	2788.79i	0.147091	−	0.254768i
$494$	6156.30	−	10663.0i	0.560698	−	0.971158i
$495$		0			0
$496$	24377.0			2.20678
$497$		0			0
$498$		0			0
$499$	1151.97	+	1995.26i	0.103345	+	0.178998i	0.913061	−	0.407824i	$-0.133712\pi$
$499$	1151.97	+	1995.26i	0.103345	+	0.178998i	−0.809716	+	0.586822i	$0.800379\pi$
$500$	−1140.37	+	1975.17i	−0.101998	+	0.176665i
$501$		0			0
$502$	6667.18	+	11547.9i	0.592771	+	1.02671i
$503$	10520.4			0.932570			0.466285	−	0.884635i	$-0.345592\pi$
$503$	10520.4			0.932570			0.466285	+	0.884635i	$0.345592\pi$
$504$		0			0
$505$	160.198			0.0141163
$506$	−4841.55	−	8385.81i	−0.425362	−	0.736748i
$507$		0			0
$508$	380.654	−	659.312i	0.0332457	−	0.0575832i
$509$	−4831.11	−	8367.73i	−0.420698	−	0.728670i	0.575310	−	0.817935i	$-0.304881\pi$
$509$	−4831.11	−	8367.73i	−0.420698	−	0.728670i	−0.996008	+	0.0892655i	$0.971548\pi$
$510$		0			0
$511$		0			0
$512$	6558.89			0.566142
$513$		0			0
$514$	7518.51	−	13022.4i	0.645189	−	1.11750i
$515$	−171.058	+	296.281i	−0.0146363	+	0.0253508i
$516$		0			0
$517$	−13273.1			−1.12911
$518$		0			0
$519$		0			0
$520$	−580.919	−	1006.18i	−0.0489903	−	0.0848537i
$521$	4303.90	−	7454.58i	0.361914	−	0.626854i	−0.626361	−	0.779533i	$-0.715457\pi$
$521$	4303.90	−	7454.58i	0.361914	−	0.626854i	0.988276	+	0.152679i	$0.0487899\pi$
$522$		0			0
$523$	5241.36	+	9078.30i	0.438219	+	0.759018i	0.997552	−	0.0699250i	$-0.0222760\pi$
$523$	5241.36	+	9078.30i	0.438219	+	0.759018i	−0.559333	+	0.828943i	$0.688943\pi$
$524$	−3360.30			−0.280144
$525$		0			0
$526$	−14826.6			−1.22903
$527$	4051.30	+	7017.06i	0.334872	+	0.580015i
$528$		0			0
$529$	4529.41	−	7845.18i	0.372270	−	0.644791i
$530$	517.574	+	896.465i	0.0424189	+	0.0734716i
$531$		0			0
$532$		0			0
$533$	11156.6			0.906649
$534$		0			0
$535$	−1062.15	+	1839.69i	−0.0858328	+	0.148667i
$536$	−1119.92	+	1939.75i	−0.0902483	+	0.156315i
$537$		0			0
$538$	−13208.5			−1.05847
$539$		0			0
$540$		0			0
$541$	−10361.3	−	17946.3i	−0.823416	−	1.42620i	−0.903124	−	0.429380i	$-0.858732\pi$
$541$	−10361.3	−	17946.3i	−0.823416	−	1.42620i	0.0797082	−	0.996818i	$-0.474601\pi$
$542$	−7691.32	+	13321.8i	−0.609540	+	1.05575i
$543$		0			0
$544$	2412.64	+	4178.81i	0.190149	+	0.329347i
$545$	−2830.35			−0.222457
$546$		0			0
$547$	−4175.09			−0.326351			−0.163176	−	0.986597i	$-0.552174\pi$
$547$	−4175.09			−0.326351			−0.163176	+	0.986597i	$0.552174\pi$
$548$	1158.83	+	2007.15i	0.0903334	+	0.156462i
$549$		0			0
$550$	−10480.6	+	18152.9i	−0.812532	+	1.40735i
$551$	−4719.91	−	8175.12i	−0.364927	−	0.632072i
$552$		0			0
$553$		0			0
$554$	−4746.91			−0.364038
$555$		0			0
$556$	−6649.06	+	11516.5i	−0.507164	+	0.878433i
$557$	−5080.87	+	8800.33i	−0.386505	+	0.669447i	−0.991977	−	0.126420i	$-0.959651\pi$
$557$	−5080.87	+	8800.33i	−0.386505	+	0.669447i	0.605472	+	0.795867i	$0.292985\pi$
$558$		0			0
$559$	−6601.85			−0.499514
$560$		0			0
$561$		0			0
$562$	7425.15	+	12860.7i	0.557315	+	0.965298i
$563$	−8552.22	+	14812.9i	−0.640201	+	1.10886i	0.345187	+	0.938534i	$0.387816\pi$
$563$	−8552.22	+	14812.9i	−0.640201	+	1.10886i	−0.985388	+	0.170326i	$0.945518\pi$
$564$		0			0
$565$	1597.87	+	2767.59i	0.118978	+	0.206076i
$566$	16780.0			1.24614
$567$		0			0
$568$	8414.89			0.621621
$569$	−9128.79	−	15811.5i	−0.672581	−	1.16495i	−0.977170	−	0.212461i	$-0.931852\pi$
$569$	−9128.79	−	15811.5i	−0.672581	−	1.16495i	0.304588	−	0.952484i	$-0.401481\pi$
$570$		0			0
$571$	−6815.25	+	11804.4i	−0.499491	+	0.865143i	−1.00000		0.000587868i	$-0.999813\pi$
$571$	−6815.25	+	11804.4i	−0.499491	+	0.865143i	0.500509	+	0.865731i	$0.333146\pi$
$572$	4929.87	+	8538.79i	0.360364	+	0.624169i
$573$		0			0
$574$		0			0
$575$	6728.30			0.487981
$576$		0			0
$577$	−2221.04	+	3846.96i	−0.160248	+	0.277558i	−0.934958	−	0.354759i	$-0.884563\pi$
$577$	−2221.04	+	3846.96i	−0.160248	+	0.277558i	0.774709	+	0.632317i	$0.217896\pi$
$578$	7432.68	−	12873.8i	0.534877	−	0.926433i
$579$		0			0
$580$	1127.31			0.0807052
$581$		0			0
$582$		0			0
$583$	3470.63	+	6011.32i	0.246551	+	0.427038i
$584$	−1480.61	+	2564.49i	−0.104911	+	0.181711i
$585$		0			0
$586$	−8759.26	−	15171.5i	−0.617477	−	1.06950i
$587$	−3103.38			−0.218211			−0.109106	−	0.994030i	$-0.534799\pi$
$587$	−3103.38			−0.218211			−0.109106	+	0.994030i	$0.534799\pi$
$588$		0			0
$589$	23752.1			1.66161
$590$	−1558.12	−	2698.74i	−0.108723	−	0.188314i
$591$		0			0
$592$	3078.99	−	5332.96i	0.213759	−	0.370242i
$593$	2968.86	+	5142.21i	0.205592	+	0.356096i	0.950321	−	0.311271i	$-0.100755\pi$
$593$	2968.86	+	5142.21i	0.205592	+	0.356096i	−0.744729	+	0.667367i	$0.767421\pi$
$594$		0			0
$595$		0			0
$596$	12146.1			0.834772
$597$		0			0
$598$	4415.25	−	7647.44i	0.301928	−	0.522955i
$599$	−1300.16	+	2251.95i	−0.0886866	+	0.153610i	−0.906956	−	0.421225i	$-0.861600\pi$
$599$	−1300.16	+	2251.95i	−0.0886866	+	0.153610i	0.818270	+	0.574835i	$0.194934\pi$
$600$		0			0
$601$	−13881.4			−0.942156			−0.471078	−	0.882092i	$-0.656135\pi$
$601$	−13881.4			−0.942156			−0.471078	+	0.882092i	$0.656135\pi$
$602$		0			0
$603$		0			0
$604$	−1581.20	−	2738.71i	−0.106520	−	0.184498i
$605$	1130.40	−	1957.91i	0.0759626	−	0.131571i
$606$		0			0
$607$	6142.28	+	10638.7i	0.410721	+	0.711389i	0.994969	−	0.100186i	$-0.0319438\pi$
$607$	6142.28	+	10638.7i	0.410721	+	0.711389i	−0.584248	+	0.811575i	$0.698610\pi$
$608$	14144.9			0.943505
$609$		0			0
$610$	−4313.07			−0.286281
$611$	−6052.20	−	10482.7i	−0.400729	−	0.694084i
$612$		0			0
$613$	−11031.0	+	19106.2i	−0.726815	+	1.25888i	0.231408	+	0.972857i	$0.425667\pi$
$613$	−11031.0	+	19106.2i	−0.726815	+	1.25888i	−0.958223	+	0.286023i	$0.907666\pi$
$614$	7475.40	+	12947.8i	0.491340	+	0.851025i
$615$		0			0
$616$		0			0
$617$	12182.2			0.794871			0.397436	−	0.917630i	$-0.369900\pi$
$617$	12182.2			0.794871			0.397436	+	0.917630i	$0.369900\pi$
$618$		0			0
$619$	−11624.3	+	20133.9i	−0.754799	+	1.30735i	0.190675	+	0.981653i	$0.438932\pi$
$619$	−11624.3	+	20133.9i	−0.754799	+	1.30735i	−0.945474	+	0.325698i	$0.894401\pi$
$620$	−1418.25	+	2456.48i	−0.0918682	+	0.159120i
$621$		0			0
$622$	2417.76			0.155858
$623$		0			0
$624$		0			0
$625$	−7012.72	−	12146.4i	−0.448814	−	0.777368i
$626$	10494.6	−	18177.3i	0.670048	−	1.16056i
$627$		0			0
$628$	6966.78	+	12066.8i	0.442683	+	0.766749i
$629$	2046.83			0.129749
$630$		0			0
$631$	19184.4			1.21033			0.605165	−	0.796100i	$-0.293107\pi$
$631$	19184.4			1.21033			0.605165	+	0.796100i	$0.293107\pi$
$632$	3091.36	+	5354.39i	0.194569	+	0.337004i
$633$		0			0
$634$	−4985.76	+	8635.59i	−0.312318	+	0.540951i
$635$	−176.942	−	306.473i	−0.0110579	−	0.0191528i
$636$		0			0
$637$		0			0
$638$	21091.6			1.30881
$639$		0			0
$640$	1496.22	−	2591.53i	0.0924113	−	0.160061i
$641$	−9716.68	+	16829.8i	−0.598730	+	1.03703i	0.394279	+	0.918991i	$0.370994\pi$
$641$	−9716.68	+	16829.8i	−0.598730	+	1.03703i	−0.993009	+	0.118040i	$0.962339\pi$
$642$		0			0
$643$	5777.47			0.354341			0.177170	−	0.984180i	$-0.443306\pi$
$643$	5777.47			0.354341			0.177170	+	0.984180i	$0.443306\pi$
$644$		0			0
$645$		0			0
$646$	3639.48	+	6303.76i	0.221661	+	0.383929i
$647$	−14615.7	+	25315.2i	−0.888106	+	1.53824i	−0.0459932	+	0.998942i	$0.514645\pi$
$647$	−14615.7	+	25315.2i	−0.888106	+	1.53824i	−0.842112	+	0.539302i	$0.818688\pi$
$648$		0			0
$649$	−10448.1	−	18096.6i	−0.631932	−	1.09454i
$650$	−19115.5			−1.15349
$651$		0			0
$652$	8083.18			0.485524
$653$	−3546.63	−	6142.95i	−0.212543	−	0.368135i	0.739967	−	0.672643i	$-0.234841\pi$
$653$	−3546.63	−	6142.95i	−0.212543	−	0.368135i	−0.952510	+	0.304508i	$0.901508\pi$
$654$		0			0
$655$	−780.997	+	1352.73i	−0.0465894	+	0.0806952i
$656$	9921.46	+	17184.5i	0.590500	+	1.02278i
$657$		0			0
$658$		0			0
$659$	−19014.2			−1.12396			−0.561980	−	0.827151i	$-0.689960\pi$
$659$	−19014.2			−1.12396			−0.561980	+	0.827151i	$0.689960\pi$
$660$		0			0
$661$	10529.2	−	18237.1i	0.619573	−	1.07313i	−0.369990	−	0.929036i	$-0.620639\pi$
$661$	10529.2	−	18237.1i	0.619573	−	1.07313i	0.989564	−	0.144097i	$-0.0460277\pi$
$662$	4966.48	−	8602.19i	0.291583	−	0.505036i
$663$		0			0
$664$	304.746			0.0178109
$665$		0			0
$666$		0			0
$667$	−3385.08	−	5863.13i	−0.196508	−	0.340362i
$668$	−7032.63	+	12180.9i	−0.407336	+	0.705527i
$669$		0			0
$670$	−658.827	−	1141.12i	−0.0379891	−	0.0657991i
$671$	−28921.6			−1.66395
$672$		0			0
$673$	9634.87			0.551853			0.275926	−	0.961179i	$-0.411015\pi$
$673$	9634.87			0.551853			0.275926	+	0.961179i	$0.411015\pi$
$674$	−7521.48	−	13027.6i	−0.429846	−	0.744516i
$675$		0			0
$676$	413.257	−	715.783i	0.0235126	−	0.0407250i
$677$	4185.66	+	7249.77i	0.237619	+	0.411568i	0.960030	−	0.279895i	$-0.0902998\pi$
$677$	4185.66	+	7249.77i	0.237619	+	0.411568i	−0.722412	+	0.691463i	$0.756966\pi$
$678$		0			0
$679$		0			0
$680$	686.854			0.0387348
$681$		0			0
$682$	−26534.9	+	45959.9i	−1.48985	+	2.58049i
$683$	−6034.42	+	10451.9i	−0.338069	+	0.585552i	−0.984069	−	0.177785i	$-0.943107\pi$
$683$	−6034.42	+	10451.9i	−0.338069	+	0.585552i	0.646001	+	0.763337i	$0.276440\pi$
$684$		0			0
$685$	1077.33			0.0600917
$686$		0			0
$687$		0			0
$688$	−5870.98	−	10168.8i	−0.325333	−	0.563493i
$689$	−3165.05	+	5482.02i	−0.175005	+	0.303118i
$690$		0			0
$691$	−1490.64	−	2581.87i	−0.0820648	−	0.142140i	0.822072	−	0.569384i	$-0.192818\pi$
$691$	−1490.64	−	2581.87i	−0.0820648	−	0.142140i	−0.904137	+	0.427243i	$0.859485\pi$
$692$	−14677.4			−0.806286
$693$		0			0
$694$	−127.327			−0.00696435
$695$	3090.73	+	5353.30i	0.168688	+	0.292176i
$696$		0			0
$697$	−3297.76	+	5711.89i	−0.179213	+	0.310407i
$698$	428.489	+	742.165i	0.0232357	+	0.0402455i
$699$		0			0
$700$		0			0
$701$	28978.0			1.56132			0.780660	−	0.624956i	$-0.214883\pi$
$701$	28978.0			1.56132			0.780660	+	0.624956i	$0.214883\pi$
$702$		0			0
$703$	3000.06	−	5196.25i	0.160952	−	0.278777i
$704$	−105.597	+	182.900i	−0.00565319	+	0.00979161i
$705$		0			0
$706$	388.388			0.0207042
$707$		0			0
$708$		0			0
$709$	8186.22	+	14178.9i	0.433625	+	0.751060i	0.997182	−	0.0750169i	$-0.0239011\pi$
$709$	8186.22	+	14178.9i	0.433625	+	0.751060i	−0.563558	+	0.826077i	$0.690568\pi$
$710$	−2475.16	+	4287.10i	−0.130833	+	0.226609i
$711$		0			0
$712$	6685.11	+	11578.9i	0.351875	+	0.609465i
$713$	17034.9			0.894755
$714$		0			0
$715$	4583.18			0.239722
$716$	6253.79	+	10831.9i	0.326418	+	0.565373i
$717$		0			0
$718$	21900.9	−	37933.4i	1.13835	−	1.97168i
$719$	11505.3	+	19927.7i	0.596765	+	1.03363i	0.993295	+	0.115605i	$0.0368808\pi$
$719$	11505.3	+	19927.7i	0.596765	+	1.03363i	−0.396530	+	0.918022i	$0.629786\pi$
$720$		0			0
$721$		0			0
$722$	−2882.36			−0.148574
$723$		0			0
$724$	−8318.89	+	14408.7i	−0.427029	+	0.739636i
$725$	−7327.73	+	12692.0i	−0.375372	+	0.650164i
$726$		0			0
$727$	−24636.8			−1.25685			−0.628423	−	0.777872i	$-0.716299\pi$
$727$	−24636.8			−1.25685			−0.628423	+	0.777872i	$0.716299\pi$
$728$		0			0
$729$		0			0
$730$	−871.015	−	1508.64i	−0.0441612	−	0.0764895i
$731$	1951.44	−	3379.99i	0.0987367	−	0.171017i
$732$		0			0
$733$	−3452.38	−	5979.70i	−0.173965	−	0.301317i	0.765837	−	0.643034i	$-0.222325\pi$
$733$	−3452.38	−	5979.70i	−0.173965	−	0.301317i	−0.939803	+	0.341718i	$0.888991\pi$
$734$	48940.1			2.46105
$735$		0			0
$736$	10144.6			0.508065
$737$	−4417.81	−	7651.88i	−0.220804	−	0.382443i
$738$		0			0
$739$	4617.44	−	7997.65i	0.229845	−	0.398103i	−0.727917	−	0.685665i	$-0.759511\pi$
$739$	4617.44	−	7997.65i	0.229845	−	0.398103i	0.957762	+	0.287562i	$0.0928448\pi$
$740$	358.269	+	620.540i	0.0177976	+	0.0308264i
$741$		0			0
$742$		0			0
$743$	−20216.9			−0.998232			−0.499116	−	0.866535i	$-0.666342\pi$
$743$	−20216.9			−0.998232			−0.499116	+	0.866535i	$0.666342\pi$
$744$		0			0
$745$	2822.98	−	4889.55i	0.138827	−	0.240455i
$746$	−8647.84	+	14978.5i	−0.424424	+	0.735123i
$747$		0			0
$748$	−5828.88			−0.284926
$749$		0			0
$750$		0			0
$751$	−12027.5	−	20832.2i	−0.584405	−	1.01222i	−0.994949	−	0.100378i	$-0.967995\pi$
$751$	−12027.5	−	20832.2i	−0.584405	−	1.01222i	0.410544	−	0.911841i	$-0.365339\pi$
$752$	10764.4	−	18644.4i	0.521989	−	0.904112i
$753$		0			0
$754$	9617.23	+	16657.5i	0.464508	+	0.804551i
$755$	−1470.00			−0.0708593
$756$		0			0
$757$	−30328.2			−1.45614			−0.728069	−	0.685504i	$-0.759582\pi$
$757$	−30328.2			−1.45614			−0.728069	+	0.685504i	$0.759582\pi$
$758$	17313.6	+	29988.0i	0.829627	+	1.43696i
$759$		0			0
$760$	1006.73	−	1743.70i	0.0480498	−	0.0832248i
$761$	−16917.1	−	29301.2i	−0.805839	−	1.39575i	−0.915723	−	0.401810i	$-0.868381\pi$
$761$	−16917.1	−	29301.2i	−0.805839	−	1.39575i	0.109884	−	0.993944i	$-0.464952\pi$
$762$		0			0
$763$		0			0
$764$	−4288.55			−0.203082
$765$		0			0
$766$	18943.9	−	32811.9i	0.893567	−	1.54770i
$767$	9528.14	−	16503.2i	0.448555	−	0.776919i
$768$		0			0
$769$	31738.1			1.48830			0.744151	−	0.668011i	$-0.232854\pi$
$769$	31738.1			1.48830			0.744151	+	0.668011i	$0.232854\pi$
$770$		0			0
$771$		0			0
$772$	8469.06	+	14668.8i	0.394829	+	0.683864i
$773$	13747.1	−	23810.7i	0.639650	−	1.10791i	−0.345860	−	0.938286i	$-0.612413\pi$
$773$	13747.1	−	23810.7i	0.639650	−	1.10791i	0.985510	−	0.169619i	$-0.0542538\pi$
$774$		0			0
$775$	−18437.8	−	31935.2i	−0.854587	−	1.48019i
$776$	20791.0			0.961794
$777$		0			0
$778$	−18588.0			−0.856573
$779$	9667.12	+	16743.9i	0.444622	+	0.770108i
$780$		0			0
$781$	−16597.4	+	28747.5i	−0.760436	+	1.31711i
$782$	2610.21	+	4521.01i	0.119362	+	0.206740i
$783$		0			0
$784$		0			0
$785$	6476.84			0.294482
$786$		0			0
$787$	234.178	−	405.608i	0.0106068	−	0.0183715i	−0.860673	−	0.509158i	$-0.829957\pi$
$787$	234.178	−	405.608i	0.0106068	−	0.0183715i	0.871280	+	0.490786i	$0.163290\pi$
$788$	11435.8	−	19807.4i	0.516985	−	0.895445i
$789$		0			0
$790$	−3637.18			−0.163804
$791$		0			0
$792$		0			0
$793$	−13187.6	−	22841.5i	−0.590547	−	1.02286i
$794$	−2144.98	+	3715.22i	−0.0958723	+	0.166056i
$795$		0			0
$796$	1932.46	+	3347.12i	0.0860481	+	0.149040i
$797$	−37723.8			−1.67659			−0.838297	−	0.545214i	$-0.816449\pi$
$797$	−37723.8			−1.67659			−0.838297	+	0.545214i	$0.816449\pi$
$798$		0			0
$799$	7155.87			0.316841
$800$	−10980.1	−	19018.1i	−0.485256	−	0.840488i
$801$		0			0
$802$	4052.77	−	7019.60i	0.178439	−	0.309066i
$803$	−5840.66	−	10116.3i	−0.256678	−	0.444579i
$804$		0			0
$805$		0			0
$806$	−48397.1			−2.11503
$807$		0			0
$808$	−480.791	+	832.755i	−0.0209334	+	0.0362577i
$809$	−3898.57	+	6752.51i	−0.169427	+	0.293456i	−0.938218	−	0.346043i	$-0.887525\pi$
$809$	−3898.57	+	6752.51i	−0.169427	+	0.293456i	0.768792	+	0.639499i	$0.220858\pi$
$810$		0			0
$811$	16925.9			0.732860			0.366430	−	0.930446i	$-0.380580\pi$
$811$	16925.9			0.732860			0.366430	+	0.930446i	$0.380580\pi$
$812$		0			0
$813$		0			0
$814$	6703.09	+	11610.1i	0.288628	+	0.499918i
$815$	1878.68	−	3253.97i	0.0807452	−	0.139855i
$816$		0			0
$817$	−5720.48	−	9908.16i	−0.244962	−	0.424287i
$818$	16407.5			0.701316
$819$		0			0
$820$	−2308.91			−0.0983301
$821$	−15004.7	−	25988.8i	−0.637840	−	1.10477i	−0.985906	−	0.167301i	$-0.946495\pi$
$821$	−15004.7	−	25988.8i	−0.637840	−	1.10477i	0.348066	−	0.937470i	$-0.386838\pi$
$822$		0			0
$823$	11692.8	−	20252.5i	0.495243	−	0.857786i	−0.504742	−	0.863270i	$-0.668412\pi$
$823$	11692.8	−	20252.5i	0.495243	−	0.857786i	0.999985	+	0.00548398i	$0.00174562\pi$
$824$	−1026.76	−	1778.41i	−0.0434090	−	0.0751867i
$825$		0			0
$826$		0			0
$827$	37325.9			1.56947			0.784734	−	0.619833i	$-0.212800\pi$
$827$	37325.9			1.56947			0.784734	+	0.619833i	$0.212800\pi$
$828$		0			0
$829$	12335.7	−	21366.0i	0.516809	−	0.895140i	−0.483000	−	0.875620i	$-0.660453\pi$
$829$	12335.7	−	21366.0i	0.516809	−	0.895140i	0.999809	−	0.0195199i	$-0.00621377\pi$
$830$	−89.6383	+	155.258i	−0.00374866	+	0.00649288i
$831$		0			0
$832$	−192.599			−0.00802544
$833$		0			0
$834$		0			0
$835$	3269.03	+	5662.12i	0.135484	+	0.234666i
$836$	−8543.44	+	14797.7i	−0.353446	+	0.612187i
$837$		0			0
$838$	13314.5	+	23061.5i	0.548858	+	0.950650i
$839$	−14147.4			−0.582147			−0.291074	−	0.956701i	$-0.594013\pi$
$839$	−14147.4			−0.582147			−0.291074	+	0.956701i	$0.594013\pi$
$840$		0			0
$841$	−9642.35			−0.395356
$842$	11023.5	+	19093.3i	0.451183	+	0.781472i
$843$		0			0
$844$	3004.46	−	5203.87i	0.122533	−	0.212233i
$845$	−192.097	−	332.723i	−0.00782054	−	0.0135456i
$846$		0			0
$847$		0			0
$848$	−11258.6			−0.455923
$849$		0			0
$850$	5650.35	−	9786.69i	0.228006	−	0.394918i
$851$	2151.62	−	3726.71i	0.0866704	−	0.150118i
$852$		0			0
$853$	27963.6			1.12246			0.561229	−	0.827661i	$-0.310329\pi$
$853$	27963.6			1.12246			0.561229	+	0.827661i	$0.310329\pi$
$854$		0			0
$855$		0			0
$856$	−6375.47	−	11042.6i	−0.254567	−	0.440923i
$857$	16927.9	−	29320.0i	0.674734	−	1.16867i	−0.301813	−	0.953367i	$-0.597592\pi$
$857$	16927.9	−	29320.0i	0.674734	−	1.16867i	0.976547	−	0.215306i	$-0.0690748\pi$
$858$		0			0
$859$	12141.3	+	21029.4i	0.482255	+	0.835291i	0.999793	−	0.0203699i	$-0.00648439\pi$
$859$	12141.3	+	21029.4i	0.482255	+	0.835291i	−0.517537	+	0.855661i	$0.673151\pi$
$860$	1366.29			0.0541745
$861$		0			0
$862$	−40487.2			−1.59977
$863$	−9833.49	−	17032.1i	−0.387875	−	0.671819i	0.604289	−	0.796765i	$-0.293457\pi$
$863$	−9833.49	−	17032.1i	−0.387875	−	0.671819i	−0.992163	+	0.124947i	$0.960124\pi$
$864$		0			0
$865$	−3411.29	+	5908.53i	−0.134090	+	0.232250i
$866$	−9103.96	−	15768.5i	−0.357235	−	0.618749i
$867$		0			0
$868$		0			0
$869$	−24389.4			−0.952075
$870$		0			0
$871$	4028.83	−	6978.13i	0.156730	−	0.271464i
$872$	8494.53	−	14713.0i	0.329887	−	0.571380i
$873$		0			0
$874$	15303.2			0.592264
$875$		0			0
$876$		0			0
$877$	18030.5	+	31229.8i	0.694238	+	1.20246i	0.970437	+	0.241355i	$0.0775919\pi$
$877$	18030.5	+	31229.8i	0.694238	+	1.20246i	−0.276199	+	0.961101i	$0.589075\pi$
$878$	8941.26	−	15486.7i	0.343682	−	0.595275i
$879$		0			0
$880$	4075.79	+	7059.48i	0.156131	+	0.270426i
$881$	15889.7			0.607646			0.303823	−	0.952728i	$-0.401737\pi$
$881$	15889.7			0.607646			0.303823	+	0.952728i	$0.401737\pi$
$882$		0			0
$883$	14861.3			0.566390			0.283195	−	0.959062i	$-0.408606\pi$
$883$	14861.3			0.566390			0.283195	+	0.959062i	$0.408606\pi$
$884$	−2657.82	−	4603.48i	−0.101122	−	0.175149i
$885$		0			0
$886$	22429.1	−	38848.3i	0.850474	−	1.47306i
$887$	−19094.9	−	33073.4i	−0.722824	−	1.25197i	−0.959863	−	0.280468i	$-0.909510\pi$
$887$	−19094.9	−	33073.4i	−0.722824	−	1.25197i	0.237039	−	0.971500i	$-0.423823\pi$
$888$		0			0
$889$		0			0
$890$	−7865.45			−0.296237
$891$		0			0
$892$	−1932.60	+	3347.36i	−0.0725428	+	0.125648i
$893$	10488.4	−	18166.5i	0.393036	−	0.680759i
$894$		0			0
$895$	5813.99			0.217140
$896$		0			0
$897$		0			0
$898$	24615.8	+	42635.9i	0.914745	+	1.58438i
$899$	−18552.5	+	32133.9i	−0.688277	+	1.19213i
$900$		0			0
$901$	−1871.11	−	3240.86i	−0.0691850	−	0.119832i
$902$	−43198.9			−1.59464
$903$		0			0
$904$	−19182.2			−0.705742
$905$	3866.93	+	6697.72i	0.142034	+	0.246011i
$906$		0			0
$907$	−8432.75	+	14606.0i	−0.308715	+	0.534711i	−0.978082	−	0.208222i	$-0.933232\pi$
$907$	−8432.75	+	14606.0i	−0.308715	+	0.534711i	0.669366	+	0.742933i	$0.266566\pi$
$908$	−3832.83	−	6638.65i	−0.140085	−	0.242634i
$909$		0			0
$910$		0			0
$911$	−26754.1			−0.973000			−0.486500	−	0.873681i	$-0.661727\pi$
$911$	−26754.1			−0.973000			−0.486500	+	0.873681i	$0.661727\pi$
$912$		0			0
$913$	−601.077	+	1041.10i	−0.0217883	+	0.0377385i
$914$	26861.3	−	46525.2i	0.972095	−	1.68372i
$915$		0			0
$916$	−4672.02			−0.168524
$917$		0			0
$918$		0			0
$919$	20763.8	+	35963.9i	0.745303	+	1.29090i	0.950053	+	0.312088i	$0.101028\pi$
$919$	20763.8	+	35963.9i	0.745303	+	1.29090i	−0.204750	+	0.978814i	$0.565638\pi$
$920$	722.018	−	1250.57i	0.0258742	−	0.0448154i
$921$		0			0
$922$	−20180.8	−	34954.1i	−0.720844	−	1.24854i
$923$	−30272.0			−1.07954
$924$		0			0
$925$	−9315.27			−0.331118
$926$	16504.3	+	28586.2i	0.585707	+	1.01447i
$927$		0			0
$928$	−11048.4	+	19136.4i	−0.390821	+	0.676922i
$929$	2292.34	+	3970.45i	0.0809572	+	0.140222i	0.903661	−	0.428248i	$-0.140869\pi$
$929$	2292.34	+	3970.45i	0.0809572	+	0.140222i	−0.822704	+	0.568470i	$0.807536\pi$
$930$		0			0
$931$		0			0
$932$	−6473.92			−0.227532
$933$		0			0
$934$	6410.48	−	11103.3i	0.224580	−	0.388983i
$935$	−1354.74	+	2346.48i	−0.0473847	+	0.0820727i
$936$		0			0
$937$	−6928.18			−0.241552			−0.120776	−	0.992680i	$-0.538538\pi$
$937$	−6928.18			−0.241552			−0.120776	+	0.992680i	$0.538538\pi$
$938$		0			0
$939$		0			0
$940$	1252.54	+	2169.45i	0.0434609	+	0.0752764i
$941$	10472.5	−	18138.9i	0.362798	−	0.628384i	−0.625622	−	0.780126i	$-0.715155\pi$
$941$	10472.5	−	18138.9i	0.362798	−	0.628384i	0.988420	+	0.151742i	$0.0484882\pi$
$942$		0			0
$943$	6933.19	+	12008.6i	0.239423	+	0.414693i
$944$	33893.3			1.16857
$945$		0			0
$946$	25562.8			0.878559
$947$	14639.5	+	25356.3i	0.502342	+	0.870082i	0.999996	+	0.00270685i	$0.000861617\pi$
$947$	14639.5	+	25356.3i	0.502342	+	0.870082i	−0.497654	+	0.867376i	$0.665805\pi$
$948$		0			0
$949$	5326.39	−	9225.57i	0.182194	−	0.315569i
$950$	−16563.5	−	28688.9i	−0.565676	−	0.979779i
$951$		0			0
$952$		0			0
$953$	−2136.81			−0.0726316			−0.0363158	−	0.999340i	$-0.511562\pi$
$953$	−2136.81			−0.0726316			−0.0363158	+	0.999340i	$0.511562\pi$
$954$		0			0
$955$	−996.739	+	1726.40i	−0.0337735	+	0.0584975i
$956$	−7045.45	+	12203.1i	−0.238354	+	0.412840i
$957$		0			0
$958$	−23027.4			−0.776597
$959$		0			0
$960$		0			0
$961$	−31785.7	−	55054.5i	−1.06696	−	1.84802i
$962$	−6112.88	+	10587.8i	−0.204872	+	0.354849i
$963$		0			0
$964$	851.348	+	1474.58i	0.0284440	+	0.0492665i
$965$	7873.47			0.262649
$966$		0			0
$967$	−3921.32			−0.130405			−0.0652023	−	0.997872i	$-0.520769\pi$
$967$	−3921.32			−0.130405			−0.0652023	+	0.997872i	$0.520769\pi$
$968$	6785.18	+	11752.3i	0.225293	+	0.390219i
$969$		0			0
$970$	−6115.47	+	10592.3i	−0.202429	+	0.350617i
$971$	23904.5	+	41403.9i	0.790045	+	1.36840i	0.925939	+	0.377674i	$0.123276\pi$
$971$	23904.5	+	41403.9i	0.790045	+	1.36840i	−0.135894	+	0.990723i	$0.543391\pi$
$972$		0			0
$973$		0			0
$974$	−12946.1			−0.425894
$975$		0			0
$976$	23455.2	−	40625.6i	0.769245	−	1.33237i
$977$	−25664.6	+	44452.3i	−0.840411	+	1.45563i	0.0491363	+	0.998792i	$0.484353\pi$
$977$	−25664.6	+	44452.3i	−0.840411	+	1.45563i	−0.889547	+	0.456843i	$0.848980\pi$
$978$		0			0
$979$	−52742.4			−1.72181
$980$		0			0
$981$		0			0
$982$	−22017.9	−	38136.1i	−0.715499	−	1.23928i
$983$	−8163.16	+	14139.0i	−0.264867	+	0.458763i	−0.967529	−	0.252761i	$-0.918661\pi$
$983$	−8163.16	+	14139.0i	−0.264867	+	0.458763i	0.702662	+	0.711524i	$0.251995\pi$
$984$		0			0
$985$	−5315.80	−	9207.23i	−0.171955	−	0.297834i
$986$	−11371.0			−0.367268
$987$		0			0
$988$	−15582.4			−0.501763
$989$	−4102.69	−	7106.06i	−0.131909	−	0.228473i
$990$		0			0
$991$	−16885.0	+	29245.7i	−0.541242	+	0.937458i	0.457592	+	0.889163i	$0.348712\pi$
$991$	−16885.0	+	29245.7i	−0.541242	+	0.937458i	−0.998833	+	0.0482954i	$0.984621\pi$
$992$	−27799.7	−	48150.4i	−0.889758	−	1.54111i
$993$		0			0
$994$		0			0
$995$	1796.56			0.0572410
$996$		0			0
$997$	−25347.7	+	43903.5i	−0.805185	+	1.39462i	0.110981	+	0.993823i	$0.464601\pi$
$997$	−25347.7	+	43903.5i	−0.805185	+	1.39462i	−0.916166	+	0.400799i	$0.868733\pi$
$998$	4067.74	−	7045.53i	0.129020	−	0.223469i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.y.361.2		8
3.2	odd	2		49.4.c.e.18.3		8
7.2	even	3	inner	441.4.e.y.226.2		8
7.3	odd	6		441.4.a.u.1.4		4
7.4	even	3		441.4.a.u.1.3		4
7.5	odd	6	inner	441.4.e.y.226.1		8
7.6	odd	2	inner	441.4.e.y.361.1		8
21.2	odd	6		49.4.c.e.30.3		8
21.5	even	6		49.4.c.e.30.4		8
21.11	odd	6		49.4.a.e.1.2	yes	4
21.17	even	6		49.4.a.e.1.1	✓	4
21.20	even	2		49.4.c.e.18.4		8
84.11	even	6		784.4.a.bf.1.1		4
84.59	odd	6		784.4.a.bf.1.4		4
105.59	even	6		1225.4.a.bb.1.4		4
105.74	odd	6		1225.4.a.bb.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.a.e.1.1	✓	4	21.17	even	6
49.4.a.e.1.2	yes	4	21.11	odd	6
49.4.c.e.18.3		8	3.2	odd	2
49.4.c.e.18.4		8	21.20	even	2
49.4.c.e.30.3		8	21.2	odd	6
49.4.c.e.30.4		8	21.5	even	6
441.4.a.u.1.3		4	7.4	even	3
441.4.a.u.1.4		4	7.3	odd	6
441.4.e.y.226.1		8	7.5	odd	6	inner
441.4.e.y.226.2		8	7.2	even	3	inner
441.4.e.y.361.1		8	7.6	odd	2	inner
441.4.e.y.361.2		8	1.1	even	1	trivial
784.4.a.bf.1.1		4	84.11	even	6
784.4.a.bf.1.4		4	84.59	odd	6
1225.4.a.bb.1.3		4	105.74	odd	6
1225.4.a.bb.1.4		4	105.59	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.76556 - 3.05805i) q^{2} +(-2.23444 + 3.87016i) q^{4} +(1.03865 + 1.79899i) q^{5} -12.4689 q^{8} +O(q^{10})\)	\(q+(-1.76556 - 3.05805i) q^{2} +(-2.23444 + 3.87016i) q^{4} +(1.03865 + 1.79899i) q^{5} -12.4689 q^{8} +(3.66760 - 6.35247i) q^{10} +(24.5934 - 42.5970i) q^{11} +44.8559 q^{13} +(39.8901 + 69.0916i) q^{16} +(-13.2589 + 22.9652i) q^{17} +(38.8675 + 67.3205i) q^{19} -9.28317 q^{20} -173.685 q^{22} +(27.8755 + 48.2818i) q^{23} +(60.3424 - 104.516i) q^{25} +(-79.1960 - 137.171i) q^{26} -121.436 q^{29} +(152.776 - 264.616i) q^{31} +(90.9815 - 157.585i) q^{32} +93.6380 q^{34} +(-38.5934 - 66.8457i) q^{37} +(137.246 - 237.717i) q^{38} +(-12.9508 - 22.4314i) q^{40} +248.720 q^{41} -147.179 q^{43} +(109.905 + 190.360i) q^{44} +(98.4319 - 170.489i) q^{46} +(-134.925 - 233.698i) q^{47} -426.154 q^{50} +(-100.228 + 173.599i) q^{52} +(-70.5603 + 122.214i) q^{53} +102.176 q^{55} +(214.403 + 371.356i) q^{58} +(212.417 - 367.917i) q^{59} +(-293.998 - 509.220i) q^{61} -1078.95 q^{62} -4.29373 q^{64} +(46.5895 + 80.6954i) q^{65} +(89.8171 - 155.568i) q^{67} +(-59.2525 - 102.628i) q^{68} -674.872 q^{71} +(118.744 - 205.671i) q^{73} +(-136.278 + 236.041i) q^{74} -347.388 q^{76} +(-247.926 - 429.421i) q^{79} +(-82.8636 + 143.524i) q^{80} +(-439.131 - 760.598i) q^{82} -24.4406 q^{83} -55.0855 q^{85} +(259.854 + 450.080i) q^{86} +(-306.652 + 531.136i) q^{88} +(-536.144 - 928.628i) q^{89} -249.144 q^{92} +(-476.439 + 825.216i) q^{94} +(-80.7393 + 139.845i) q^{95} -1667.43 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8	\( 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8} + 100 q^{11} + 174 q^{16} - 680 q^{22} + 352 q^{23} + 128 q^{25} - 520 q^{29} - 30 q^{32} - 212 q^{37} + 1080 q^{43} + 460 q^{44} - 696 q^{46} - 2732 q^{50} + 16 q^{53} + 780 q^{58} - 3356 q^{64} - 756 q^{65} + 1944 q^{67} - 4496 q^{71} - 284 q^{74} + 1048 q^{79} - 6568 q^{85} + 4820 q^{86} - 1260 q^{88} - 7024 q^{92} + 2192 q^{95}+O(q^{100}) \) 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8 + 100 * q^11 + 174 * q^16 - 680 * q^22 + 352 * q^23 + 128 * q^25 - 520 * q^29 - 30 * q^32 - 212 * q^37 + 1080 * q^43 + 460 * q^44 - 696 * q^46 - 2732 * q^50 + 16 * q^53 + 780 * q^58 - 3356 * q^64 - 756 * q^65 + 1944 * q^67 - 4496 * q^71 - 284 * q^74 + 1048 * q^79 - 6568 * q^85 + 4820 * q^86 - 1260 * q^88 - 7024 * q^92 + 2192 * q^95

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