LMFDB - Embedded newform 441.4.e.r.226.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 19x^{2} + 361 $ x^4 + 19*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$2.17945 - 3.77492i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.r.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17945 - 3.77492i) q^{2} +(-5.50000 - 9.52628i) q^{4} +(4.35890 - 7.54983i) q^{5} -13.0767 q^{8} +O(q^{10})$	\(q+(2.17945 - 3.77492i) q^{2} +(-5.50000 - 9.52628i) q^{4} +(4.35890 - 7.54983i) q^{5} -13.0767 q^{8} +(-19.0000 - 32.9090i) q^{10} +(-21.7945 - 37.7492i) q^{11} +82.0000 q^{13} +(15.5000 - 26.8468i) q^{16} +(-39.2301 - 67.9485i) q^{17} +(10.0000 - 17.3205i) q^{19} -95.8958 q^{20} -190.000 q^{22} +(-65.3835 + 113.248i) q^{23} +(24.5000 + 42.4352i) q^{25} +(178.715 - 309.543i) q^{26} -244.098 q^{29} +(-78.0000 - 135.100i) q^{31} +(-119.870 - 207.620i) q^{32} -342.000 q^{34} +(-93.0000 + 161.081i) q^{37} +(-43.5890 - 75.4983i) q^{38} +(-57.0000 + 98.7269i) q^{40} +165.638 q^{41} +164.000 q^{43} +(-239.739 + 415.241i) q^{44} +(285.000 + 493.634i) q^{46} +(235.381 - 407.691i) q^{47} +213.586 q^{50} +(-451.000 - 781.155i) q^{52} +(-78.4602 - 135.897i) q^{53} -380.000 q^{55} +(-532.000 + 921.451i) q^{58} +(78.4602 + 135.897i) q^{59} +(-395.000 + 684.160i) q^{61} -679.988 q^{62} -797.000 q^{64} +(357.430 - 619.086i) q^{65} +(22.0000 + 38.1051i) q^{67} +(-431.531 + 747.434i) q^{68} -444.608 q^{71} +(-63.0000 - 109.119i) q^{73} +(405.378 + 702.135i) q^{74} -220.000 q^{76} +(356.000 - 616.610i) q^{79} +(-135.126 - 234.045i) q^{80} +(361.000 - 625.270i) q^{82} +1464.59 q^{83} -684.000 q^{85} +(357.430 - 619.086i) q^{86} +(285.000 + 493.634i) q^{88} +(-727.936 + 1260.82i) q^{89} +1438.44 q^{92} +(-1026.00 - 1777.08i) q^{94} +(-87.1780 - 150.997i) q^{95} +798.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 22 q^{4}+O(q^{10}) $ 4 * q - 22 * q^4	$ 4 q - 22 q^{4} - 76 q^{10} + 328 q^{13} + 62 q^{16} + 40 q^{19} - 760 q^{22} + 98 q^{25} - 312 q^{31} - 1368 q^{34} - 372 q^{37} - 228 q^{40} + 656 q^{43} + 1140 q^{46} - 1804 q^{52} - 1520 q^{55} - 2128 q^{58} - 1580 q^{61} - 3188 q^{64} + 88 q^{67} - 252 q^{73} - 880 q^{76} + 1424 q^{79} + 1444 q^{82} - 2736 q^{85} + 1140 q^{88} - 4104 q^{94} + 3192 q^{97}+O(q^{100}) $ 4 * q - 22 * q^4 - 76 * q^10 + 328 * q^13 + 62 * q^16 + 40 * q^19 - 760 * q^22 + 98 * q^25 - 312 * q^31 - 1368 * q^34 - 372 * q^37 - 228 * q^40 + 656 * q^43 + 1140 * q^46 - 1804 * q^52 - 1520 * q^55 - 2128 * q^58 - 1580 * q^61 - 3188 * q^64 + 88 * q^67 - 252 * q^73 - 880 * q^76 + 1424 * q^79 + 1444 * q^82 - 2736 * q^85 + 1140 * q^88 - 4104 * q^94 + 3192 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.17945	−	3.77492i	0.770552	−	1.33463i	−0.166709	−	0.986006i	$-0.553314\pi$
$2$	2.17945	−	3.77492i	0.770552	−	1.33463i	0.937261	−	0.348629i	$-0.113353\pi$
$3$		0			0
$3$		0			0
$4$	−5.50000	−	9.52628i	−0.687500	−	1.19078i
$5$	4.35890	−	7.54983i	0.389872	−	0.675278i	−0.602560	−	0.798073i	$-0.705853\pi$
$5$	4.35890	−	7.54983i	0.389872	−	0.675278i	0.992432	+	0.122796i	$0.0391860\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−13.0767			−0.577914
$9$		0			0
$10$	−19.0000	−	32.9090i	−0.600833	−	1.04067i
$11$	−21.7945	−	37.7492i	−0.597390	−	1.03471i	−0.993205	−	0.116379i	$-0.962871\pi$
$11$	−21.7945	−	37.7492i	−0.597390	−	1.03471i	0.395815	−	0.918330i	$-0.370462\pi$
$12$		0			0
$13$	82.0000			1.74944			0.874720	−	0.484629i	$-0.161046\pi$
$13$	82.0000			1.74944			0.874720	+	0.484629i	$0.161046\pi$
$14$		0			0
$15$		0			0
$16$	15.5000	−	26.8468i	0.242188	−	0.419481i
$17$	−39.2301	−	67.9485i	−0.559688	−	0.969408i	−0.997522	−	0.0703522i	$-0.977588\pi$
$17$	−39.2301	−	67.9485i	−0.559688	−	0.969408i	0.437834	−	0.899056i	$-0.355746\pi$
$18$		0			0
$19$	10.0000	−	17.3205i	0.120745	−	0.209137i	−0.799317	−	0.600910i	$-0.794805\pi$
$19$	10.0000	−	17.3205i	0.120745	−	0.209137i	0.920062	+	0.391773i	$0.128138\pi$
$20$	−95.8958			−1.07215
$21$		0			0
$22$	−190.000			−1.84128
$23$	−65.3835	+	113.248i	−0.592756	+	1.02668i	0.401103	+	0.916033i	$0.368627\pi$
$23$	−65.3835	+	113.248i	−0.592756	+	1.02668i	−0.993859	+	0.110651i	$0.964706\pi$
$24$		0			0
$25$	24.5000	+	42.4352i	0.196000	+	0.339482i
$26$	178.715	−	309.543i	1.34803	−	2.33486i
$27$		0			0
$28$		0			0
$29$	−244.098			−1.56303			−0.781516	−	0.623885i	$-0.785553\pi$
$29$	−244.098			−1.56303			−0.781516	+	0.623885i	$0.785553\pi$
$30$		0			0
$31$	−78.0000	−	135.100i	−0.451910	−	0.782731i	0.546595	−	0.837397i	$-0.315924\pi$
$31$	−78.0000	−	135.100i	−0.451910	−	0.782731i	−0.998505	+	0.0546661i	$0.982591\pi$
$32$	−119.870	−	207.620i	−0.662193	−	1.14695i
$33$		0			0
$34$	−342.000			−1.72507
$35$		0			0
$36$		0			0
$37$	−93.0000	+	161.081i	−0.413219	+	0.715716i	−0.995240	−	0.0974576i	$-0.968929\pi$
$37$	−93.0000	+	161.081i	−0.413219	+	0.715716i	0.582021	+	0.813174i	$0.302262\pi$
$38$	−43.5890	−	75.4983i	−0.186081	−	0.322301i
$39$		0			0
$40$	−57.0000	+	98.7269i	−0.225312	+	0.390252i
$41$	165.638			0.630935			0.315467	−	0.948936i	$-0.397839\pi$
$41$	165.638			0.630935			0.315467	+	0.948936i	$0.397839\pi$
$42$		0			0
$43$	164.000			0.581622			0.290811	−	0.956780i	$-0.406075\pi$
$43$	164.000			0.581622			0.290811	+	0.956780i	$0.406075\pi$
$44$	−239.739	+	415.241i	−0.821411	+	1.42273i
$45$		0			0
$46$	285.000	+	493.634i	0.913499	+	1.58223i
$47$	235.381	−	407.691i	0.730506	−	1.26527i	−0.226161	−	0.974090i	$-0.572618\pi$
$47$	235.381	−	407.691i	0.730506	−	1.26527i	0.956667	−	0.291184i	$-0.0940490\pi$
$48$		0			0
$49$		0			0
$50$	213.586			0.604113
$51$		0			0
$52$	−451.000	−	781.155i	−1.20274	−	2.08321i
$53$	−78.4602	−	135.897i	−0.203346	−	0.352205i	0.746259	−	0.665656i	$-0.231848\pi$
$53$	−78.4602	−	135.897i	−0.203346	−	0.352205i	−0.949604	+	0.313451i	$0.898515\pi$
$54$		0			0
$55$	−380.000			−0.931622
$56$		0			0
$57$		0			0
$58$	−532.000	+	921.451i	−1.20440	+	2.08608i
$59$	78.4602	+	135.897i	0.173130	+	0.299869i	0.939512	−	0.342515i	$-0.111279\pi$
$59$	78.4602	+	135.897i	0.173130	+	0.299869i	−0.766383	+	0.642384i	$0.777945\pi$
$60$		0			0
$61$	−395.000	+	684.160i	−0.829091	+	1.43603i	0.0696607	+	0.997571i	$0.477808\pi$
$61$	−395.000	+	684.160i	−0.829091	+	1.43603i	−0.898752	+	0.438457i	$0.855525\pi$
$62$	−679.988			−1.39288
$63$		0			0
$64$	−797.000			−1.55664
$65$	357.430	−	619.086i	0.682057	−	1.18136i
$66$		0			0
$67$	22.0000	+	38.1051i	0.0401153	+	0.0694818i	0.885386	−	0.464857i	$-0.153894\pi$
$67$	22.0000	+	38.1051i	0.0401153	+	0.0694818i	−0.845271	+	0.534338i	$0.820561\pi$
$68$	−431.531	+	747.434i	−0.769571	+	1.33294i
$69$		0			0
$70$		0			0
$71$	−444.608			−0.743172			−0.371586	−	0.928398i	$-0.621186\pi$
$71$	−444.608			−0.743172			−0.371586	+	0.928398i	$0.621186\pi$
$72$		0			0
$73$	−63.0000	−	109.119i	−0.101008	−	0.174951i	0.811092	−	0.584918i	$-0.198873\pi$
$73$	−63.0000	−	109.119i	−0.101008	−	0.174951i	−0.912100	+	0.409967i	$0.865540\pi$
$74$	405.378	+	702.135i	0.636813	+	1.10299i
$75$		0			0
$76$	−220.000			−0.332049
$77$		0			0
$78$		0			0
$79$	356.000	−	616.610i	0.507002	−	0.878153i	−0.492966	−	0.870049i	$-0.664087\pi$
$79$	356.000	−	616.610i	0.507002	−	0.878153i	0.999967	−	0.00810375i	$-0.00257953\pi$
$80$	−135.126	−	234.045i	−0.188844	−	0.327088i
$81$		0			0
$82$	361.000	−	625.270i	0.486168	−	0.842068i
$83$	1464.59			1.93686			0.968432	−	0.249280i	$-0.0801938\pi$
$83$	1464.59			1.93686			0.968432	+	0.249280i	$0.0801938\pi$
$84$		0			0
$85$	−684.000			−0.872826
$86$	357.430	−	619.086i	0.448170	−	0.776254i
$87$		0			0
$88$	285.000	+	493.634i	0.345240	+	0.597973i
$89$	−727.936	+	1260.82i	−0.866978	+	1.50165i	−0.00190909	+	0.999998i	$0.500608\pi$
$89$	−727.936	+	1260.82i	−0.866978	+	1.50165i	−0.865069	+	0.501652i	$0.832726\pi$
$90$		0			0
$91$		0			0
$92$	1438.44			1.63008
$93$		0			0
$94$	−1026.00	−	1777.08i	−1.12579	−	1.94992i
$95$	−87.1780	−	150.997i	−0.0941502	−	0.163073i
$96$		0			0
$97$	798.000			0.835305			0.417653	−	0.908607i	$-0.362853\pi$
$97$	798.000			0.835305			0.417653	+	0.908607i	$0.362853\pi$
$98$		0			0
$99$		0			0
$100$	269.500	−	466.788i	0.269500	−	0.466788i
$101$	204.868	+	354.842i	0.201833	+	0.349585i	0.949119	−	0.314917i	$-0.101977\pi$
$101$	204.868	+	354.842i	0.201833	+	0.349585i	−0.747286	+	0.664503i	$0.768643\pi$
$102$		0			0
$103$	458.000	−	793.279i	0.438137	−	0.758875i	−0.559409	−	0.828892i	$-0.688972\pi$
$103$	458.000	−	793.279i	0.438137	−	0.758875i	0.997546	+	0.0700167i	$0.0223052\pi$
$104$	−1072.29			−1.01103
$105$		0			0
$106$	−684.000			−0.626754
$107$	448.967	−	777.633i	0.405638	−	0.702585i	−0.588758	−	0.808310i	$-0.700383\pi$
$107$	448.967	−	777.633i	0.405638	−	0.702585i	0.994395	+	0.105724i	$0.0337161\pi$
$108$		0			0
$109$	171.000	+	296.181i	0.150264	+	0.260266i	0.931325	−	0.364190i	$-0.118654\pi$
$109$	171.000	+	296.181i	0.150264	+	0.260266i	−0.781060	+	0.624456i	$0.785321\pi$
$110$	−828.191	+	1434.47i	−0.717863	+	1.24337i
$111$		0			0
$112$		0			0
$113$	488.197			0.406422			0.203211	−	0.979135i	$-0.434862\pi$
$113$	488.197			0.406422			0.203211	+	0.979135i	$0.434862\pi$
$114$		0			0
$115$	570.000	+	987.269i	0.462198	+	0.800550i
$116$	1342.54	+	2325.35i	1.07458	+	1.86123i
$117$		0			0
$118$	684.000			0.533621
$119$		0			0
$120$		0			0
$121$	−284.500	+	492.768i	−0.213749	+	0.370224i
$122$	1721.77	+	2982.18i	1.27772	+	2.21307i
$123$		0			0
$124$	−858.000	+	1486.10i	−0.621376	+	1.07626i
$125$	1516.90			1.08540
$126$		0			0
$127$	456.000			0.318610			0.159305	−	0.987229i	$-0.449075\pi$
$127$	456.000			0.318610			0.159305	+	0.987229i	$0.449075\pi$
$128$	−778.063	+	1347.65i	−0.537279	+	0.930595i
$129$		0			0
$130$	−1558.00	−	2698.54i	−1.05112	−	1.82059i
$131$	749.731	−	1298.57i	0.500033	−	0.866082i	−0.499967	−	0.866044i	$-0.666655\pi$
$131$	749.731	−	1298.57i	0.500033	−	0.866082i	1.00000		3.76230e-5i	$-1.19758e-5\pi$
$132$		0			0
$133$		0			0
$134$	191.792			0.123644
$135$		0			0
$136$	513.000	+	888.542i	0.323451	+	0.560234i
$137$	−444.608	−	770.083i	−0.277266	−	0.480238i	0.693439	−	0.720516i	$-0.256095\pi$
$137$	−444.608	−	770.083i	−0.277266	−	0.480238i	−0.970704	+	0.240278i	$0.922762\pi$
$138$		0			0
$139$	−768.000			−0.468640			−0.234320	−	0.972160i	$-0.575286\pi$
$139$	−768.000			−0.468640			−0.234320	+	0.972160i	$0.575286\pi$
$140$		0			0
$141$		0			0
$142$	−969.000	+	1678.36i	−0.572653	+	0.991863i
$143$	−1787.15	−	3095.43i	−1.04510	−	1.81016i
$144$		0			0
$145$	−1064.00	+	1842.90i	−0.609382	+	1.05548i
$146$	−549.221			−0.311328
$147$		0			0
$148$	2046.00			1.13635
$149$	496.914	−	860.681i	0.273214	−	0.473220i	−0.696469	−	0.717587i	$-0.745247\pi$
$149$	496.914	−	860.681i	0.273214	−	0.473220i	0.969683	+	0.244367i	$0.0785801\pi$
$150$		0			0
$151$	1748.00	+	3027.62i	0.942054	+	1.63169i	0.761544	+	0.648113i	$0.224442\pi$
$151$	1748.00	+	3027.62i	0.942054	+	1.63169i	0.180510	+	0.983573i	$0.442225\pi$
$152$	−130.767	+	226.495i	−0.0697803	+	0.120863i
$153$		0			0
$154$		0			0
$155$	−1359.98			−0.704748
$156$		0			0
$157$	253.000	+	438.209i	0.128609	+	0.222757i	0.923138	−	0.384469i	$-0.125615\pi$
$157$	253.000	+	438.209i	0.128609	+	0.222757i	−0.794529	+	0.607226i	$0.792282\pi$
$158$	−1551.77	−	2687.74i	−0.781342	−	1.35332i
$159$		0			0
$160$	−2090.00			−1.03268
$161$		0			0
$162$		0			0
$163$	1282.00	−	2220.49i	0.616037	−	1.06701i	−0.374165	−	0.927362i	$-0.622071\pi$
$163$	1282.00	−	2220.49i	0.616037	−	1.06701i	0.990202	−	0.139645i	$-0.0445961\pi$
$164$	−911.010	−	1577.92i	−0.433768	−	0.751308i
$165$		0			0
$166$	3192.00	−	5528.71i	1.49245	−	2.58500i
$167$	645.117			0.298926			0.149463	−	0.988767i	$-0.452245\pi$
$167$	645.117			0.298926			0.149463	+	0.988767i	$0.452245\pi$
$168$		0			0
$169$	4527.00			2.06054
$170$	−1490.74	+	2582.04i	−0.672558	+	1.16490i
$171$		0			0
$172$	−902.000	−	1562.31i	−0.399865	−	0.692587i
$173$	1930.99	−	3344.58i	0.848616	−	1.46985i	−0.0338270	−	0.999428i	$-0.510770\pi$
$173$	1930.99	−	3344.58i	0.848616	−	1.46985i	0.882443	−	0.470419i	$-0.155897\pi$
$174$		0			0
$175$		0			0
$176$	−1351.26			−0.578721
$177$		0			0
$178$	3173.00	+	5495.80i	1.33610	+	2.31420i
$179$	−135.126	−	234.045i	−0.0564234	−	0.0977281i	0.836434	−	0.548068i	$-0.184636\pi$
$179$	−135.126	−	234.045i	−0.0564234	−	0.0977281i	−0.892857	+	0.450339i	$0.851303\pi$
$180$		0			0
$181$	418.000			0.171656			0.0858279	−	0.996310i	$-0.472646\pi$
$181$	418.000			0.171656			0.0858279	+	0.996310i	$0.472646\pi$
$182$		0			0
$183$		0			0
$184$	855.000	−	1480.90i	0.342562	−	0.593335i
$185$	810.755	+	1404.27i	0.322205	+	0.558075i
$186$		0			0
$187$	−1710.00	+	2961.81i	−0.668704	+	1.15823i
$188$	−5178.37			−2.00889
$189$		0			0
$190$	−760.000			−0.290191
$191$	762.807	−	1321.22i	0.288978	−	0.500525i	−0.684588	−	0.728930i	$-0.740018\pi$
$191$	762.807	−	1321.22i	0.288978	−	0.500525i	0.973566	+	0.228406i	$0.0733512\pi$
$192$		0			0
$193$	−679.000	−	1176.06i	−0.253241	−	0.438626i	0.711175	−	0.703015i	$-0.248163\pi$
$193$	−679.000	−	1176.06i	−0.253241	−	0.438626i	−0.964416	+	0.264389i	$0.914830\pi$
$194$	1739.20	−	3012.38i	0.643646	−	1.11483i
$195$		0			0
$196$		0			0
$197$	−3748.65			−1.35574			−0.677869	−	0.735183i	$-0.737096\pi$
$197$	−3748.65			−1.35574			−0.677869	+	0.735183i	$0.737096\pi$
$198$		0			0
$199$	528.000	+	914.523i	0.188085	+	0.325773i	0.944612	−	0.328190i	$-0.106439\pi$
$199$	528.000	+	914.523i	0.188085	+	0.325773i	−0.756527	+	0.653963i	$0.773105\pi$
$200$	−320.379	−	554.913i	−0.113271	−	0.196191i
$201$		0			0
$202$	1786.00			0.622092
$203$		0			0
$204$		0			0
$205$	722.000	−	1250.54i	0.245984	−	0.426056i
$206$	−1996.38	−	3457.82i	−0.675214	−	1.16950i
$207$		0			0
$208$	1271.00	−	2201.44i	0.423692	−	0.733857i
$209$	−871.780			−0.288528
$210$		0			0
$211$	−3620.00			−1.18110			−0.590548	−	0.807003i	$-0.701088\pi$
$211$	−3620.00			−1.18110			−0.590548	+	0.807003i	$0.701088\pi$
$212$	−863.062	+	1494.87i	−0.279601	+	0.484283i
$213$		0			0
$214$	−1957.00	−	3389.62i	−0.625130	−	1.08276i
$215$	714.859	−	1238.17i	0.226758	−	0.392757i
$216$		0			0
$217$		0			0
$218$	1490.74			0.463146
$219$		0			0
$220$	2090.00	+	3619.99i	0.640490	+	1.10936i
$221$	−3216.87	−	5571.78i	−0.979140	−	1.69592i
$222$		0			0
$223$	5368.00			1.61196			0.805982	−	0.591940i	$-0.201638\pi$
$223$	5368.00			1.61196			0.805982	+	0.591940i	$0.201638\pi$
$224$		0			0
$225$		0			0
$226$	1064.00	−	1842.90i	0.313169	−	0.542425i
$227$	810.755	+	1404.27i	0.237056	+	0.410593i	0.959868	−	0.280451i	$-0.0904842\pi$
$227$	810.755	+	1404.27i	0.237056	+	0.410593i	−0.722812	+	0.691045i	$0.757151\pi$
$228$		0			0
$229$	−1093.00	+	1893.13i	−0.315404	+	0.546295i	−0.979523	−	0.201331i	$-0.935473\pi$
$229$	−1093.00	+	1893.13i	−0.315404	+	0.546295i	0.664119	+	0.747626i	$0.268807\pi$
$230$	4969.14			1.42459
$231$		0			0
$232$	3192.00			0.903298
$233$	−2066.12	+	3578.62i	−0.580927	+	1.00619i	0.414443	+	0.910075i	$0.363976\pi$
$233$	−2066.12	+	3578.62i	−0.580927	+	1.00619i	−0.995370	+	0.0961192i	$0.969357\pi$
$234$		0			0
$235$	−2052.00	−	3554.17i	−0.569607	−	0.986589i
$236$	863.062	−	1494.87i	0.238053	−	0.412320i
$237$		0			0
$238$		0			0
$239$	4838.38			1.30949			0.654746	−	0.755849i	$-0.272776\pi$
$239$	4838.38			1.30949			0.654746	+	0.755849i	$0.272776\pi$
$240$		0			0
$241$	−643.000	−	1113.71i	−0.171864	−	0.297678i	0.767207	−	0.641399i	$-0.221646\pi$
$241$	−643.000	−	1113.71i	−0.171864	−	0.297678i	−0.939072	+	0.343722i	$0.888312\pi$
$242$	1240.11	+	2147.93i	0.329409	+	0.570554i
$243$		0			0
$244$	8690.00			2.28000
$245$		0			0
$246$		0			0
$247$	820.000	−	1420.28i	0.211236	−	0.365872i
$248$	1019.98	+	1766.66i	0.261165	+	0.452351i
$249$		0			0
$250$	3306.00	−	5726.16i	0.836359	−	1.44862i
$251$	1795.87			0.451610			0.225805	−	0.974173i	$-0.427499\pi$
$251$	1795.87			0.451610			0.225805	+	0.974173i	$0.427499\pi$
$252$		0			0
$253$	5700.00			1.41643
$254$	993.829	−	1721.36i	0.245505	−	0.425228i
$255$		0			0
$256$	203.500	+	352.472i	0.0496826	+	0.0860528i
$257$	−972.034	+	1683.61i	−0.235929	+	0.408642i	−0.959542	−	0.281564i	$-0.909147\pi$
$257$	−972.034	+	1683.61i	−0.235929	+	0.408642i	0.723613	+	0.690206i	$0.242480\pi$
$258$		0			0
$259$		0			0
$260$	−7863.45			−1.87566
$261$		0			0
$262$	−3268.00	−	5660.34i	−0.770602	−	1.33472i
$263$	2672.01	+	4628.05i	0.626475	+	1.08509i	0.988254	+	0.152822i	$0.0488362\pi$
$263$	2672.01	+	4628.05i	0.626475	+	1.08509i	−0.361779	+	0.932264i	$0.617830\pi$
$264$		0			0
$265$	−1368.00			−0.317115
$266$		0			0
$267$		0			0
$268$	242.000	−	419.156i	0.0551586	−	0.0955375i
$269$	−2000.73	−	3465.37i	−0.453483	−	0.785456i	0.545117	−	0.838360i	$-0.316485\pi$
$269$	−2000.73	−	3465.37i	−0.453483	−	0.785456i	−0.998600	+	0.0529046i	$0.983152\pi$
$270$		0			0
$271$	−1394.00	+	2414.48i	−0.312470	+	0.541215i	−0.978897	−	0.204356i	$-0.934490\pi$
$271$	−1394.00	+	2414.48i	−0.312470	+	0.541215i	0.666426	+	0.745571i	$0.267823\pi$
$272$	−2432.27			−0.542198
$273$		0			0
$274$	−3876.00			−0.854590
$275$	1067.93	−	1849.71i	0.234177	−	0.405606i
$276$		0			0
$277$	2281.00	+	3950.81i	0.494773	+	0.856971i	0.999982	−	0.00602561i	$-0.00191802\pi$
$277$	2281.00	+	3950.81i	0.494773	+	0.856971i	−0.505209	+	0.862997i	$0.668585\pi$
$278$	−1673.82	+	2899.14i	−0.361111	+	0.625463i
$279$		0			0
$280$		0			0
$281$	1551.77			0.329433			0.164717	−	0.986341i	$-0.447329\pi$
$281$	1551.77			0.329433			0.164717	+	0.986341i	$0.447329\pi$
$282$		0			0
$283$	3394.00	+	5878.58i	0.712906	+	1.23479i	0.963762	+	0.266765i	$0.0859547\pi$
$283$	3394.00	+	5878.58i	0.712906	+	1.23479i	−0.250856	+	0.968024i	$0.580712\pi$
$284$	2445.34	+	4235.46i	0.510931	+	0.884958i
$285$		0			0
$286$	−15580.0			−3.22121
$287$		0			0
$288$		0			0
$289$	−621.500	+	1076.47i	−0.126501	+	0.219106i
$290$	4637.87	+	8033.02i	0.939121	+	1.62660i
$291$		0			0
$292$	−693.000	+	1200.31i	−0.138886	+	0.240558i
$293$	−1142.03			−0.227707			−0.113854	−	0.993498i	$-0.536319\pi$
$293$	−1142.03			−0.227707			−0.113854	+	0.993498i	$0.536319\pi$
$294$		0			0
$295$	1368.00			0.269993
$296$	1216.13	−	2106.40i	0.238805	−	0.413622i
$297$		0			0
$298$	−2166.00	−	3751.62i	−0.421050	−	0.729281i
$299$	−5361.45	+	9286.30i	−1.03699	+	1.79612i
$300$		0			0
$301$		0			0
$302$	15238.7			2.90361
$303$		0			0
$304$	−310.000	−	536.936i	−0.0584859	−	0.101301i
$305$	3443.53	+	5964.37i	0.646479	+	1.11973i
$306$		0			0
$307$	532.000			0.0989018			0.0494509	−	0.998777i	$-0.484253\pi$
$307$	532.000			0.0989018			0.0494509	+	0.998777i	$0.484253\pi$
$308$		0			0
$309$		0			0
$310$	−2964.00	+	5133.80i	−0.543045	+	0.940581i
$311$	3269.17	+	5662.38i	0.596070	+	1.03242i	0.993395	+	0.114746i	$0.0366054\pi$
$311$	3269.17	+	5662.38i	0.596070	+	1.03242i	−0.397325	+	0.917678i	$0.630061\pi$
$312$		0			0
$313$	−2497.00	+	4324.93i	−0.450923	+	0.781021i	−0.998444	−	0.0557711i	$-0.982238\pi$
$313$	−2497.00	+	4324.93i	−0.450923	+	0.781021i	0.547521	+	0.836792i	$0.315572\pi$
$314$	2205.60			0.396399
$315$		0			0
$316$	−7832.00			−1.39425
$317$	−235.381	+	407.691i	−0.0417044	+	0.0722341i	−0.886124	−	0.463448i	$-0.846612\pi$
$317$	−235.381	+	407.691i	−0.0417044	+	0.0722341i	0.844420	+	0.535682i	$0.179945\pi$
$318$		0			0
$319$	5320.00	+	9214.51i	0.933739	+	1.61728i
$320$	−3474.04	+	6017.22i	−0.606890	+	1.05116i
$321$		0			0
$322$		0			0
$323$	−1569.20			−0.270318
$324$		0			0
$325$	2009.00	+	3479.69i	0.342890	+	0.593903i
$326$	−5588.11	−	9678.89i	−0.949376	−	1.64437i
$327$		0			0
$328$	−2166.00			−0.364626
$329$		0			0
$330$		0			0
$331$	−1294.00	+	2241.27i	−0.214878	+	0.372180i	−0.953235	−	0.302230i	$-0.902269\pi$
$331$	−1294.00	+	2241.27i	−0.214878	+	0.372180i	0.738357	+	0.674410i	$0.235602\pi$
$332$	−8055.25	−	13952.1i	−1.33159	−	2.30639i
$333$		0			0
$334$	1406.00	−	2435.26i	0.230338	−	0.398957i
$335$	383.583			0.0625594
$336$		0			0
$337$	238.000			0.0384709			0.0192354	−	0.999815i	$-0.493877\pi$
$337$	238.000			0.0384709			0.0192354	+	0.999815i	$0.493877\pi$
$338$	9866.37	−	17089.1i	1.58775	−	2.75006i
$339$		0			0
$340$	3762.00	+	6515.98i	0.600068	+	1.03935i
$341$	−3399.94	+	5888.87i	−0.539933	+	0.935191i
$342$		0			0
$343$		0			0
$344$	−2144.58			−0.336128
$345$		0			0
$346$	−8417.00	−	14578.7i	−1.30781	−	2.26519i
$347$	3526.35	+	6107.82i	0.545546	+	0.944913i	0.998572	+	0.0534159i	$0.0170109\pi$
$347$	3526.35	+	6107.82i	0.545546	+	0.944913i	−0.453027	+	0.891497i	$0.649656\pi$
$348$		0			0
$349$	−10850.0			−1.66415			−0.832073	−	0.554666i	$-0.812846\pi$
$349$	−10850.0			−1.66415			−0.832073	+	0.554666i	$0.812846\pi$
$350$		0			0
$351$		0			0
$352$	−5225.00	+	9049.97i	−0.791175	+	1.37035i
$353$	2645.85	+	4582.75i	0.398936	+	0.690978i	0.993595	−	0.113000i	$-0.0360462\pi$
$353$	2645.85	+	4582.75i	0.398936	+	0.690978i	−0.594659	+	0.803978i	$0.702713\pi$
$354$		0			0
$355$	−1938.00	+	3356.71i	−0.289742	+	0.501848i
$356$	16014.6			2.38419
$357$		0			0
$358$	−1178.00			−0.173908
$359$	−2410.47	+	4175.06i	−0.354373	+	0.613792i	−0.987010	−	0.160656i	$-0.948639\pi$
$359$	−2410.47	+	4175.06i	−0.354373	+	0.613792i	0.632638	+	0.774448i	$0.281972\pi$
$360$		0			0
$361$	3229.50	+	5593.66i	0.470841	+	0.815521i
$362$	911.010	−	1577.92i	0.132270	−	0.229098i
$363$		0			0
$364$		0			0
$365$	−1098.44			−0.157521
$366$		0			0
$367$	−5856.00	−	10142.9i	−0.832917	−	1.44266i	−0.895715	−	0.444629i	$-0.853336\pi$
$367$	−5856.00	−	10142.9i	−0.832917	−	1.44266i	0.0627973	−	0.998026i	$-0.479998\pi$
$368$	2026.89	+	3510.67i	0.287116	+	0.497300i
$369$		0			0
$370$	7068.00			0.993102
$371$		0			0
$372$		0			0
$373$	5225.00	−	9049.97i	0.725309	−	1.25627i	−0.233538	−	0.972348i	$-0.575030\pi$
$373$	5225.00	−	9049.97i	0.725309	−	1.25627i	0.958847	−	0.283924i	$-0.0916364\pi$
$374$	7453.72	+	12910.2i	1.03054	+	1.78495i
$375$		0			0
$376$	−3078.00	+	5331.25i	−0.422169	+	0.731219i
$377$	−20016.1			−2.73443
$378$		0			0
$379$	−756.000			−0.102462			−0.0512310	−	0.998687i	$-0.516314\pi$
$379$	−756.000			−0.102462			−0.0512310	+	0.998687i	$0.516314\pi$
$380$	−958.958	+	1660.96i	−0.129457	+	0.224225i
$381$		0			0
$382$	−3325.00	−	5759.07i	−0.445345	−	0.771360i
$383$	3190.71	−	5526.48i	0.425686	−	0.737310i	−0.570798	−	0.821091i	$-0.693366\pi$
$383$	3190.71	−	5526.48i	0.425686	−	0.737310i	0.996484	+	0.0837802i	$0.0266994\pi$
$384$		0			0
$385$		0			0
$386$	−5919.38			−0.780541
$387$		0			0
$388$	−4389.00	−	7601.97i	−0.574272	−	0.994669i
$389$	−209.227	−	362.392i	−0.0272705	−	0.0472339i	0.852068	−	0.523431i	$-0.175348\pi$
$389$	−209.227	−	362.392i	−0.0272705	−	0.0472339i	−0.879339	+	0.476197i	$0.842015\pi$
$390$		0			0
$391$	10260.0			1.32703
$392$		0			0
$393$		0			0
$394$	−8170.00	+	14150.9i	−1.04467	+	1.80942i
$395$	−3103.54	−	5375.48i	−0.395331	−	0.684734i
$396$		0			0
$397$	2901.00	−	5024.68i	0.366743	−	0.635218i	−0.622311	−	0.782770i	$-0.713806\pi$
$397$	2901.00	−	5024.68i	0.366743	−	0.635218i	0.989054	+	0.147552i	$0.0471395\pi$
$398$	4603.00			0.579717
$399$		0			0
$400$	1519.00			0.189875
$401$	−2066.12	+	3578.62i	−0.257299	+	0.445655i	−0.965517	−	0.260338i	$-0.916166\pi$
$401$	−2066.12	+	3578.62i	−0.257299	+	0.445655i	0.708218	+	0.705994i	$0.249499\pi$
$402$		0			0
$403$	−6396.00	−	11078.2i	−0.790589	−	1.36934i
$404$	2253.55	−	3903.26i	0.277521	−	0.480680i
$405$		0			0
$406$		0			0
$407$	8107.55			0.987411
$408$		0			0
$409$	665.000	+	1151.81i	0.0803964	+	0.139251i	0.903420	−	0.428756i	$-0.141048\pi$
$409$	665.000	+	1151.81i	0.0803964	+	0.139251i	−0.823024	+	0.568007i	$0.807715\pi$
$410$	−3147.13	−	5450.98i	−0.379086	−	0.656597i
$411$		0			0
$412$	−10076.0			−1.20488
$413$		0			0
$414$		0			0
$415$	6384.00	−	11057.4i	0.755128	−	1.30792i
$416$	−9829.32	−	17024.9i	−1.15847	−	2.00652i
$417$		0			0
$418$	−1900.00	+	3290.90i	−0.222325	+	0.385079i
$419$	−10409.1			−1.21364			−0.606820	−	0.794839i	$-0.707555\pi$
$419$	−10409.1			−1.21364			−0.606820	+	0.794839i	$0.707555\pi$
$420$		0			0
$421$	−12274.0			−1.42090			−0.710449	−	0.703749i	$-0.751508\pi$
$421$	−12274.0			−1.42090			−0.710449	+	0.703749i	$0.751508\pi$
$422$	−7889.61	+	13665.2i	−0.910095	+	1.57633i
$423$		0			0
$424$	1026.00	+	1777.08i	0.117516	+	0.203544i
$425$	1922.27	−	3329.48i	0.219398	−	0.380008i
$426$		0			0
$427$		0			0
$428$	−9877.27			−1.11550
$429$		0			0
$430$	−3116.00	−	5397.07i	−0.349458	−	0.605279i
$431$	−2340.73	−	4054.26i	−0.261598	−	0.453102i	0.705068	−	0.709139i	$-0.250916\pi$
$431$	−2340.73	−	4054.26i	−0.261598	−	0.453102i	−0.966667	+	0.256037i	$0.917583\pi$
$432$		0			0
$433$	5770.00			0.640389			0.320195	−	0.947352i	$-0.396252\pi$
$433$	5770.00			0.640389			0.320195	+	0.947352i	$0.396252\pi$
$434$		0			0
$435$		0			0
$436$	1881.00	−	3257.99i	0.206614	−	0.357865i
$437$	1307.67	+	2264.95i	0.143145	+	0.247934i
$438$		0			0
$439$	936.000	−	1621.20i	0.101760	−	0.176254i	−0.810650	−	0.585532i	$-0.800886\pi$
$439$	936.000	−	1621.20i	0.101760	−	0.176254i	0.912410	+	0.409277i	$0.134219\pi$
$440$	4969.14			0.538397
$441$		0			0
$442$	−28044.0			−3.01791
$443$	−5557.60	+	9626.04i	−0.596048	+	1.03239i	0.397350	+	0.917667i	$0.369930\pi$
$443$	−5557.60	+	9626.04i	−0.596048	+	1.03239i	−0.993398	+	0.114719i	$0.963403\pi$
$444$		0			0
$445$	6346.00	+	10991.6i	0.676021	+	1.17090i
$446$	11699.3	−	20263.8i	1.24210	−	2.15138i
$447$		0			0
$448$		0			0
$449$	7636.79			0.802678			0.401339	−	0.915930i	$-0.368545\pi$
$449$	7636.79			0.802678			0.401339	+	0.915930i	$0.368545\pi$
$450$		0			0
$451$	−3610.00	−	6252.70i	−0.376914	−	0.652834i
$452$	−2685.08	−	4650.70i	−0.279415	−	0.483961i
$453$		0			0
$454$	7068.00			0.730656
$455$		0			0
$456$		0			0
$457$	−7571.00	+	13113.4i	−0.774959	+	1.34227i	0.159858	+	0.987140i	$0.448896\pi$
$457$	−7571.00	+	13113.4i	−0.774959	+	1.34227i	−0.934817	+	0.355129i	$0.884437\pi$
$458$	4764.28	+	8251.97i	0.486070	+	0.841898i
$459$		0			0
$460$	6270.00	−	10860.0i	0.635522	−	1.10076i
$461$	13190.0			1.33258			0.666292	−	0.745691i	$-0.267881\pi$
$461$	13190.0			1.33258			0.666292	+	0.745691i	$0.267881\pi$
$462$		0			0
$463$	9328.00			0.936304			0.468152	−	0.883648i	$-0.344920\pi$
$463$	9328.00			0.936304			0.468152	+	0.883648i	$0.344920\pi$
$464$	−3783.52	+	6553.26i	−0.378547	+	0.655662i
$465$		0			0
$466$	9006.00	+	15598.8i	0.895268	+	1.55065i
$467$	1699.97	−	2944.44i	0.168448	−	0.291761i	−0.769426	−	0.638736i	$-0.779458\pi$
$467$	1699.97	−	2944.44i	0.168448	−	0.291761i	0.937874	+	0.346975i	$0.112791\pi$
$468$		0			0
$469$		0			0
$470$	−17888.9			−1.75565
$471$		0			0
$472$	−1026.00	−	1777.08i	−0.100054	−	0.173299i
$473$	−3574.30	−	6190.86i	−0.347455	−	0.601810i
$474$		0			0
$475$	980.000			0.0946642
$476$		0			0
$477$		0			0
$478$	10545.0	−	18264.5i	1.00903	−	1.74769i
$479$	1787.15	+	3095.43i	0.170474	+	0.295269i	0.938586	−	0.345047i	$-0.112137\pi$
$479$	1787.15	+	3095.43i	0.170474	+	0.295269i	−0.768112	+	0.640316i	$0.778804\pi$
$480$		0			0
$481$	−7626.00	+	13208.6i	−0.722902	+	1.25210i
$482$	−5605.54			−0.529721
$483$		0			0
$484$	6259.00			0.587810
$485$	3478.40	−	6024.77i	0.325662	−	0.564063i
$486$		0			0
$487$	−4484.00	−	7766.52i	−0.417227	−	0.722658i	0.578433	−	0.815730i	$-0.303665\pi$
$487$	−4484.00	−	7766.52i	−0.417227	−	0.722658i	−0.995659	+	0.0930722i	$0.970331\pi$
$488$	5165.30	−	8946.55i	0.479143	−	0.829901i
$489$		0			0
$490$		0			0
$491$	−5169.65			−0.475159			−0.237580	−	0.971368i	$-0.576354\pi$
$491$	−5169.65			−0.475159			−0.237580	+	0.971368i	$0.576354\pi$
$492$		0			0
$493$	9576.00	+	16586.1i	0.874810	+	1.51522i
$494$	−3574.30	−	6190.86i	−0.325537	−	0.563846i
$495$		0			0
$496$	−4836.00			−0.437788
$497$		0			0
$498$		0			0
$499$	−1970.00	+	3412.14i	−0.176732	+	0.306109i	−0.940759	−	0.339075i	$-0.889886\pi$
$499$	−1970.00	+	3412.14i	−0.176732	+	0.306109i	0.764027	+	0.645184i	$0.223219\pi$
$500$	−8342.93	−	14450.4i	−0.746215	−	1.29248i
$501$		0			0
$502$	3914.00	−	6779.25i	0.347989	−	0.602734i
$503$	−10252.1			−0.908787			−0.454394	−	0.890801i	$-0.650144\pi$
$503$	−10252.1			−0.908787			−0.454394	+	0.890801i	$0.650144\pi$
$504$		0			0
$505$	3572.00			0.314756
$506$	12422.9	−	21517.0i	1.09143	−	1.89041i
$507$		0			0
$508$	−2508.00	−	4343.98i	−0.219044	−	0.379396i
$509$	4886.33	−	8463.36i	0.425506	−	0.736998i	−0.570961	−	0.820977i	$-0.693429\pi$
$509$	4886.33	−	8463.36i	0.425506	−	0.736998i	0.996468	+	0.0839787i	$0.0267628\pi$
$510$		0			0
$511$		0			0
$512$	−10674.9			−0.921426
$513$		0			0
$514$	4237.00	+	7338.70i	0.363592	+	0.629759i
$515$	−3992.75	−	6915.65i	−0.341634	−	0.591728i
$516$		0			0
$517$	−20520.0			−1.74559
$518$		0			0
$519$		0			0
$520$	−4674.00	+	8095.61i	−0.394170	+	0.682723i
$521$	−3700.71	−	6409.81i	−0.311192	−	0.539000i	0.667429	−	0.744673i	$-0.267395\pi$
$521$	−3700.71	−	6409.81i	−0.311192	−	0.539000i	−0.978621	+	0.205674i	$0.934061\pi$
$522$		0			0
$523$	1384.00	−	2397.16i	0.115713	−	0.200421i	−0.802351	−	0.596852i	$-0.796418\pi$
$523$	1384.00	−	2397.16i	0.115713	−	0.200421i	0.918065	+	0.396431i	$0.129751\pi$
$524$	−16494.1			−1.37509
$525$		0			0
$526$	23294.0			1.93093
$527$	−6119.89	+	10600.0i	−0.505857	+	0.876170i
$528$		0			0
$529$	−2466.50	−	4272.10i	−0.202720	−	0.351122i
$530$	−2981.49	+	5164.09i	−0.244354	+	0.423233i
$531$		0			0
$532$		0			0
$533$	13582.3			1.10378
$534$		0			0
$535$	−3914.00	−	6779.25i	−0.316293	−	0.547836i
$536$	−287.687	−	498.289i	−0.0231832	−	0.0401545i
$537$		0			0
$538$	−17442.0			−1.39773
$539$		0			0
$540$		0			0
$541$	−8155.00	+	14124.9i	−0.648079	+	1.12251i	0.335502	+	0.942040i	$0.391094\pi$
$541$	−8155.00	+	14124.9i	−0.648079	+	1.12251i	−0.983581	+	0.180467i	$0.942239\pi$
$542$	6076.31	+	10524.5i	0.481549	+	0.834068i
$543$		0			0
$544$	−9405.00	+	16289.9i	−0.741243	+	1.28387i
$545$	2981.49			0.234336
$546$		0			0
$547$	11140.0			0.870771			0.435386	−	0.900244i	$-0.356612\pi$
$547$	11140.0			0.870771			0.435386	+	0.900244i	$0.356612\pi$
$548$	−4890.68	+	8470.91i	−0.381240	+	0.660328i
$549$		0			0
$550$	−4655.00	−	8062.70i	−0.360891	−	0.625081i
$551$	−2440.98	+	4227.91i	−0.188728	+	0.326887i
$552$		0			0
$553$		0			0
$554$	19885.3			1.52499
$555$		0			0
$556$	4224.00	+	7316.18i	0.322190	+	0.558049i
$557$	11394.2	+	19735.3i	0.866761	+	1.50127i	0.865287	+	0.501276i	$0.167136\pi$
$557$	11394.2	+	19735.3i	0.866761	+	1.50127i	0.00147399	+	0.999999i	$0.499531\pi$
$558$		0			0
$559$	13448.0			1.01751
$560$		0			0
$561$		0			0
$562$	3382.00	−	5857.80i	0.253845	−	0.439673i
$563$	−5762.46	−	9980.88i	−0.431366	−	0.747147i	0.565625	−	0.824662i	$-0.308635\pi$
$563$	−5762.46	−	9980.88i	−0.431366	−	0.747147i	−0.996991	+	0.0775149i	$0.975301\pi$
$564$		0			0
$565$	2128.00	−	3685.80i	0.158452	−	0.274448i
$566$	29588.2			2.19732
$567$		0			0
$568$	5814.00			0.429489
$569$	−845.626	+	1464.67i	−0.0623032	+	0.107912i	−0.895495	−	0.445073i	$-0.853178\pi$
$569$	−845.626	+	1464.67i	−0.0623032	+	0.107912i	0.833191	+	0.552985i	$0.186511\pi$
$570$		0			0
$571$	−5614.00	−	9723.73i	−0.411451	−	0.712654i	0.583598	−	0.812043i	$-0.301645\pi$
$571$	−5614.00	−	9723.73i	−0.411451	−	0.712654i	−0.995049	+	0.0993888i	$0.968311\pi$
$572$	−19658.6	+	34049.8i	−1.43701	+	2.48897i
$573$		0			0
$574$		0			0
$575$	−6407.58			−0.464721
$576$		0			0
$577$	−1025.00	−	1775.35i	−0.0739537	−	0.128092i	0.826677	−	0.562677i	$-0.190228\pi$
$577$	−1025.00	−	1775.35i	−0.0739537	−	0.128092i	−0.900631	+	0.434585i	$0.856895\pi$
$578$	2709.06	+	4692.22i	0.194951	+	0.337666i
$579$		0			0
$580$	23408.0			1.67580
$581$		0			0
$582$		0			0
$583$	−3420.00	+	5923.61i	−0.242954	+	0.420808i
$584$	823.832	+	1426.92i	0.0583740	+	0.101107i
$585$		0			0
$586$	−2489.00	+	4311.07i	−0.175460	+	0.303906i
$587$	−18394.6			−1.29340			−0.646699	−	0.762745i	$-0.723851\pi$
$587$	−18394.6			−1.29340			−0.646699	+	0.762745i	$0.723851\pi$
$588$		0			0
$589$	−3120.00			−0.218264
$590$	2981.49	−	5164.09i	0.208044	−	0.360343i
$591$		0			0
$592$	2883.00	+	4993.50i	0.200153	+	0.346675i
$593$	−6316.04	+	10939.7i	−0.437384	+	0.757572i	−0.997487	−	0.0708515i	$-0.977428\pi$
$593$	−6316.04	+	10939.7i	−0.437384	+	0.757572i	0.560103	+	0.828423i	$0.310762\pi$
$594$		0			0
$595$		0			0
$596$	−10932.1			−0.751337
$597$		0			0
$598$	23370.0	+	40478.0i	1.59811	+	2.76801i
$599$	−4799.15	−	8312.37i	−0.327359	−	0.567002i	0.654628	−	0.755951i	$-0.272825\pi$
$599$	−4799.15	−	8312.37i	−0.327359	−	0.567002i	−0.981987	+	0.188949i	$0.939492\pi$
$600$		0			0
$601$	−10758.0			−0.730163			−0.365082	−	0.930976i	$-0.618959\pi$
$601$	−10758.0			−0.730163			−0.365082	+	0.930976i	$0.618959\pi$
$602$		0			0
$603$		0			0
$604$	19228.0	−	33303.9i	1.29532	−	2.24357i
$605$	2480.21	+	4295.86i	0.166669	+	0.288680i
$606$		0			0
$607$	10676.0	−	18491.4i	0.713881	−	1.23648i	−0.249509	−	0.968372i	$-0.580269\pi$
$607$	10676.0	−	18491.4i	0.713881	−	1.23648i	0.963390	−	0.268105i	$-0.0863974\pi$
$608$	−4794.79			−0.319826
$609$		0			0
$610$	30020.0			1.99258
$611$	19301.2	−	33430.7i	1.27798	−	2.21352i
$612$		0			0
$613$	2857.00	+	4948.47i	0.188243	+	0.326047i	0.944665	−	0.328038i	$-0.106387\pi$
$613$	2857.00	+	4948.47i	0.188243	+	0.326047i	−0.756421	+	0.654085i	$0.773054\pi$
$614$	1159.47	−	2008.26i	0.0762089	−	0.131998i
$615$		0			0
$616$		0			0
$617$	−6747.58			−0.440271			−0.220135	−	0.975469i	$-0.570650\pi$
$617$	−6747.58			−0.440271			−0.220135	+	0.975469i	$0.570650\pi$
$618$		0			0
$619$	940.000	+	1628.13i	0.0610368	+	0.105719i	0.894929	−	0.446208i	$-0.147226\pi$
$619$	940.000	+	1628.13i	0.0610368	+	0.105719i	−0.833892	+	0.551927i	$0.813893\pi$
$620$	7479.87	+	12955.5i	0.484514	+	0.839203i
$621$		0			0
$622$	28500.0			1.83721
$623$		0			0
$624$		0			0
$625$	3549.50	−	6147.91i	0.227168	−	0.393467i
$626$	10884.2	+	18851.9i	0.694918	+	1.20363i
$627$		0			0
$628$	2783.00	−	4820.30i	0.176837	−	0.306291i
$629$	14593.6			0.925095
$630$		0			0
$631$	−28888.0			−1.82252			−0.911262	−	0.411826i	$-0.864891\pi$
$631$	−28888.0			−1.82252			−0.911262	+	0.411826i	$0.864891\pi$
$632$	−4655.30	+	8063.22i	−0.293003	+	0.507497i
$633$		0			0
$634$	1026.00	+	1777.08i	0.0642708	+	0.111320i
$635$	1987.66	−	3442.72i	0.124217	−	0.215150i
$636$		0			0
$637$		0			0
$638$	46378.7			2.87798
$639$		0			0
$640$	6783.00	+	11748.5i	0.418940	+	0.725625i
$641$	12998.2	+	22513.6i	0.800935	+	1.38726i	0.919001	+	0.394255i	$0.128997\pi$
$641$	12998.2	+	22513.6i	0.800935	+	1.38726i	−0.118066	+	0.993006i	$0.537669\pi$
$642$		0			0
$643$	24788.0			1.52029			0.760143	−	0.649756i	$-0.225129\pi$
$643$	24788.0			1.52029			0.760143	+	0.649756i	$0.225129\pi$
$644$		0			0
$645$		0			0
$646$	−3420.00	+	5923.61i	−0.208294	+	0.360776i
$647$	14236.2	+	24657.8i	0.865041	+	1.49829i	0.867007	+	0.498296i	$0.166041\pi$
$647$	14236.2	+	24657.8i	0.865041	+	1.49829i	−0.00196599	+	0.999998i	$0.500626\pi$
$648$		0			0
$649$	3420.00	−	5923.61i	0.206852	−	0.358278i
$650$	17514.1			1.05686
$651$		0			0
$652$	−28204.0			−1.69410
$653$	1621.51	−	2808.54i	0.0971740	−	0.168310i	−0.813340	−	0.581789i	$-0.802353\pi$
$653$	1621.51	−	2808.54i	0.0971740	−	0.168310i	0.910514	+	0.413479i	$0.135686\pi$
$654$		0			0
$655$	−6536.00	−	11320.7i	−0.389897	−	0.675322i
$656$	2567.39	−	4446.85i	0.152805	−	0.264665i
$657$		0			0
$658$		0			0
$659$	−1176.90			−0.0695685			−0.0347842	−	0.999395i	$-0.511074\pi$
$659$	−1176.90			−0.0695685			−0.0347842	+	0.999395i	$0.511074\pi$
$660$		0			0
$661$	−5795.00	−	10037.2i	−0.340998	−	0.590625i	0.643621	−	0.765345i	$-0.277431\pi$
$661$	−5795.00	−	10037.2i	−0.340998	−	0.590625i	−0.984618	+	0.174720i	$0.944098\pi$
$662$	5640.42	+	9769.49i	0.331149	+	0.573568i
$663$		0			0
$664$	−19152.0			−1.11934
$665$		0			0
$666$		0			0
$667$	15960.0	−	27643.5i	0.926497	−	1.60474i
$668$	−3548.14	−	6145.57i	−0.205512	−	0.355957i
$669$		0			0
$670$	836.000	−	1447.99i	0.0482052	−	0.0834939i
$671$	34435.3			1.98116
$672$		0			0
$673$	23062.0			1.32091			0.660457	−	0.750864i	$-0.270363\pi$
$673$	23062.0			1.32091			0.660457	+	0.750864i	$0.270363\pi$
$674$	518.709	−	898.430i	0.0296438	−	0.0513446i
$675$		0			0
$676$	−24898.5	−	43125.5i	−1.41662	−	2.45366i
$677$	−11442.1	+	19818.3i	−0.649566	+	1.12508i	0.333661	+	0.942693i	$0.391716\pi$
$677$	−11442.1	+	19818.3i	−0.649566	+	1.12508i	−0.983227	+	0.182388i	$0.941617\pi$
$678$		0			0
$679$		0			0
$680$	8944.46			0.504418
$681$		0			0
$682$	14820.0	+	25669.0i	0.832093	+	1.44123i
$683$	−12357.5	−	21403.8i	−0.692307	−	1.19911i	−0.971080	−	0.238754i	$-0.923261\pi$
$683$	−12357.5	−	21403.8i	−0.692307	−	1.19911i	0.278773	−	0.960357i	$-0.410072\pi$
$684$		0			0
$685$	−7752.00			−0.432392
$686$		0			0
$687$		0			0
$688$	2542.00	−	4402.87i	0.140862	−	0.243980i
$689$	−6433.73	−	11143.6i	−0.355741	−	0.616162i
$690$		0			0
$691$	5300.00	−	9179.87i	0.291782	−	0.505382i	−0.682449	−	0.730933i	$-0.739085\pi$
$691$	5300.00	−	9179.87i	0.291782	−	0.505382i	0.974231	+	0.225552i	$0.0724184\pi$
$692$	−42481.8			−2.33369
$693$		0			0
$694$	30742.0			1.68148
$695$	−3347.63	+	5798.27i	−0.182709	+	0.316462i
$696$		0			0
$697$	−6498.00	−	11254.9i	−0.353127	−	0.611633i
$698$	−23647.0	+	40957.9i	−1.28231	+	2.22103i
$699$		0			0
$700$		0			0
$701$	−12449.0			−0.670746			−0.335373	−	0.942085i	$-0.608862\pi$
$701$	−12449.0			−0.670746			−0.335373	+	0.942085i	$0.608862\pi$
$702$		0			0
$703$	1860.00	+	3221.61i	0.0997884	+	0.172839i
$704$	17370.2	+	30086.1i	0.929921	+	1.61067i
$705$		0			0
$706$	23066.0			1.22960
$707$		0			0
$708$		0			0
$709$	6855.00	−	11873.2i	0.363110	−	0.628925i	−0.625361	−	0.780336i	$-0.715048\pi$
$709$	6855.00	−	11873.2i	0.363110	−	0.628925i	0.988471	+	0.151411i	$0.0483816\pi$
$710$	8447.55	+	14631.6i	0.446522	+	0.773399i
$711$		0			0
$712$	9519.00	−	16487.4i	0.501039	−	0.867825i
$713$	20399.6			1.07149
$714$		0			0
$715$	−31160.0			−1.62982
$716$	−1486.38	+	2574.49i	−0.0775821	+	0.134376i
$717$		0			0
$718$	10507.0	+	18198.7i	0.546125	+	0.945916i
$719$	−1255.36	+	2174.35i	−0.0651142	+	0.112781i	−0.896745	−	0.442548i	$-0.854075\pi$
$719$	−1255.36	+	2174.35i	−0.0651142	+	0.112781i	0.831630	+	0.555329i	$0.187408\pi$
$720$		0			0
$721$		0			0
$722$	28154.1			1.45123
$723$		0			0
$724$	−2299.00	−	3981.98i	−0.118013	−	0.204405i
$725$	−5980.41	−	10358.4i	−0.306354	−	0.530621i
$726$		0			0
$727$	620.000			0.0316293			0.0158147	−	0.999875i	$-0.494966\pi$
$727$	620.000			0.0316293			0.0158147	+	0.999875i	$0.494966\pi$
$728$		0			0
$729$		0			0
$730$	−2394.00	+	4146.53i	−0.121378	+	0.210233i
$731$	−6433.73	−	11143.6i	−0.325527	−	0.563829i
$732$		0			0
$733$	10107.0	−	17505.8i	0.509291	−	0.882119i	−0.490651	−	0.871356i	$-0.663241\pi$
$733$	10107.0	−	17505.8i	0.509291	−	0.882119i	0.999942	−	0.0107622i	$-0.00342577\pi$
$734$	−51051.4			−2.56722
$735$		0			0
$736$	31350.0			1.57008
$737$	958.958	−	1660.96i	0.0479290	−	0.0830154i
$738$		0			0
$739$	6162.00	+	10672.9i	0.306729	+	0.531270i	0.977645	−	0.210263i	$-0.0674321\pi$
$739$	6162.00	+	10672.9i	0.306729	+	0.531270i	−0.670916	+	0.741534i	$0.734099\pi$
$740$	8918.31	−	15447.0i	0.443032	−	0.767353i
$741$		0			0
$742$		0			0
$743$	−29736.4			−1.46827			−0.734134	−	0.679005i	$-0.762412\pi$
$743$	−29736.4			−1.46827			−0.734134	+	0.679005i	$0.762412\pi$
$744$		0			0
$745$	−4332.00	−	7503.24i	−0.213037	−	0.368990i
$746$	−22775.2	−	39447.9i	−1.11778	−	1.93605i
$747$		0			0
$748$	37620.0			1.83894
$749$		0			0
$750$		0			0
$751$	−9668.00	+	16745.5i	−0.469761	+	0.813650i	−0.999402	−	0.0345721i	$-0.988993\pi$
$751$	−9668.00	+	16745.5i	−0.469761	+	0.813650i	0.529641	+	0.848222i	$0.322326\pi$
$752$	−7296.80	−	12638.4i	−0.353839	−	0.612867i
$753$		0			0
$754$	−43624.0	+	75559.0i	−2.10702	+	3.64946i
$755$	30477.4			1.46912
$756$		0			0
$757$	15986.0			0.767531			0.383766	−	0.923431i	$-0.374627\pi$
$757$	15986.0			0.767531			0.383766	+	0.923431i	$0.374627\pi$
$758$	−1647.66	+	2853.84i	−0.0789523	+	0.136749i
$759$		0			0
$760$	1140.00	+	1974.54i	0.0544107	+	0.0942421i
$761$	18503.5	−	32049.0i	0.881409	−	1.52665i	0.0316342	−	0.999500i	$-0.489929\pi$
$761$	18503.5	−	32049.0i	0.881409	−	1.52665i	0.849775	−	0.527146i	$-0.176738\pi$
$762$		0			0
$763$		0			0
$764$	−16781.8			−0.794690
$765$		0			0
$766$	−13908.0	−	24089.4i	−0.656027	−	1.13627i
$767$	6433.73	+	11143.6i	0.302880	+	0.524603i
$768$		0			0
$769$	−36070.0			−1.69144			−0.845720	−	0.533627i	$-0.820829\pi$
$769$	−36070.0			−1.69144			−0.845720	+	0.533627i	$0.820829\pi$
$770$		0			0
$771$		0			0
$772$	−7469.00	+	12936.7i	−0.348206	+	0.603111i
$773$	−265.893	−	460.540i	−0.0123719	−	0.0214288i	0.859773	−	0.510676i	$-0.170605\pi$
$773$	−265.893	−	460.540i	−0.0123719	−	0.0214288i	−0.872145	+	0.489247i	$0.837272\pi$
$774$		0			0
$775$	3822.00	−	6619.90i	0.177149	−	0.306831i
$776$	−10435.2			−0.482735
$777$		0			0
$778$	−1824.00			−0.0840534
$779$	1656.38	−	2868.94i	0.0761823	−	0.131952i
$780$		0			0
$781$	9690.00	+	16783.6i	0.443963	+	0.768967i
$782$	22361.2	−	38730.7i	1.02255	−	1.77111i
$783$		0			0
$784$		0			0
$785$	4411.21			0.200564
$786$		0			0
$787$	568.000	+	983.805i	0.0257268	+	0.0445602i	0.878602	−	0.477554i	$-0.158477\pi$
$787$	568.000	+	983.805i	0.0257268	+	0.0445602i	−0.852875	+	0.522115i	$0.825143\pi$
$788$	20617.6	+	35710.7i	0.932070	+	1.61439i
$789$		0			0
$790$	−27056.0			−1.21849
$791$		0			0
$792$		0			0
$793$	−32390.0	+	56101.1i	−1.45044	+	2.51224i
$794$	−12645.2	−	21902.1i	−0.565189	−	0.978936i
$795$		0			0
$796$	5808.00	−	10059.8i	0.258617	−	0.447938i
$797$	−18054.6			−0.802416			−0.401208	−	0.915987i	$-0.631409\pi$
$797$	−18054.6			−0.802416			−0.401208	+	0.915987i	$0.631409\pi$
$798$		0			0
$799$	−36936.0			−1.63542
$800$	5873.62	−	10173.4i	0.259580	−	0.449605i
$801$		0			0
$802$	9006.00	+	15598.8i	0.396525	+	0.686801i
$803$	−2746.11	+	4756.40i	−0.120682	+	0.209028i
$804$		0			0
$805$		0			0
$806$	−55759.0			−2.43676
$807$		0			0
$808$	−2679.00	−	4640.16i	−0.116642	−	0.202030i
$809$	−19353.5	−	33521.3i	−0.841079	−	1.45679i	−0.888983	−	0.457940i	$-0.848587\pi$
$809$	−19353.5	−	33521.3i	−0.841079	−	1.45679i	0.0479036	−	0.998852i	$-0.484746\pi$
$810$		0			0
$811$	17936.0			0.776595			0.388297	−	0.921534i	$-0.373063\pi$
$811$	17936.0			0.776595			0.388297	+	0.921534i	$0.373063\pi$
$812$		0			0
$813$		0			0
$814$	17670.0	−	30605.3i	0.760852	−	1.31783i
$815$	−11176.2	−	19357.8i	−0.480351	−	0.831992i
$816$		0			0
$817$	1640.00	−	2840.56i	0.0702281	−	0.121639i
$818$	5797.34			0.247798
$819$		0			0
$820$	−15884.0			−0.676455
$821$	12457.7	−	21577.4i	0.529571	−	0.917244i	−0.469834	−	0.882755i	$-0.655686\pi$
$821$	12457.7	−	21577.4i	0.529571	−	0.917244i	0.999405	−	0.0344893i	$-0.0109805\pi$
$822$		0			0
$823$	−11712.0	−	20285.8i	−0.496057	−	0.859195i	0.503933	−	0.863743i	$-0.331886\pi$
$823$	−11712.0	−	20285.8i	−0.496057	−	0.859195i	−0.999990	+	0.00454737i	$0.998553\pi$
$824$	−5989.13	+	10373.5i	−0.253205	+	0.438564i
$825$		0			0
$826$		0			0
$827$	26650.3			1.12058			0.560291	−	0.828296i	$-0.310689\pi$
$827$	26650.3			1.12058			0.560291	+	0.828296i	$0.310689\pi$
$828$		0			0
$829$	13127.0	+	22736.6i	0.549963	+	0.952564i	0.998276	+	0.0586877i	$0.0186916\pi$
$829$	13127.0	+	22736.6i	0.549963	+	0.952564i	−0.448313	+	0.893877i	$0.647975\pi$
$830$	−27827.2	−	48198.1i	−1.16373	−	2.01564i
$831$		0			0
$832$	−65354.0			−2.72325
$833$		0			0
$834$		0			0
$835$	2812.00	−	4870.53i	0.116543	−	0.201858i
$836$	4794.79	+	8304.82i	0.198363	+	0.343574i
$837$		0			0
$838$	−22686.0	+	39293.3i	−0.935173	+	1.61977i
$839$	6189.64			0.254696			0.127348	−	0.991858i	$-0.459353\pi$
$839$	6189.64			0.254696			0.127348	+	0.991858i	$0.459353\pi$
$840$		0			0
$841$	35195.0			1.44307
$842$	−26750.6	+	46333.3i	−1.09488	+	1.89638i
$843$		0			0
$844$	19910.0	+	34485.1i	0.812003	+	1.40643i
$845$	19732.7	−	34178.1i	0.803345	−	1.39143i
$846$		0			0
$847$		0			0
$848$	−4864.53			−0.196991
$849$		0			0
$850$	−8379.00	−	14512.9i	−0.338115	−	0.585632i
$851$	−12161.3	−	21064.0i	−0.489877	−	0.848491i
$852$		0			0
$853$	−45322.0			−1.81922			−0.909611	−	0.415462i	$-0.863620\pi$
$853$	−45322.0			−1.81922			−0.909611	+	0.415462i	$0.863620\pi$
$854$		0			0
$855$		0			0
$856$	−5871.00	+	10168.9i	−0.234424	+	0.406034i
$857$	4345.82	+	7527.18i	0.173221	+	0.300028i	0.939544	−	0.342428i	$-0.111249\pi$
$857$	4345.82	+	7527.18i	0.173221	+	0.300028i	−0.766323	+	0.642455i	$0.777916\pi$
$858$		0			0
$859$	21626.0	−	37457.3i	0.858987	−	1.48781i	−0.0139098	−	0.999903i	$-0.504428\pi$
$859$	21626.0	−	37457.3i	0.858987	−	1.48781i	0.872897	−	0.487905i	$-0.162239\pi$
$860$	−15726.9			−0.623585
$861$		0			0
$862$	−20406.0			−0.806301
$863$	−14659.0	+	25390.1i	−0.578212	+	1.00149i	0.417472	+	0.908690i	$0.362916\pi$
$863$	−14659.0	+	25390.1i	−0.578212	+	1.00149i	−0.995684	+	0.0928036i	$0.970417\pi$
$864$		0			0
$865$	−16834.0	−	29157.3i	−0.661703	−	1.14610i
$866$	12575.4	−	21781.3i	0.493453	−	0.854686i
$867$		0			0
$868$		0			0
$869$	−31035.4			−1.21151
$870$		0			0
$871$	1804.00	+	3124.62i	0.0701793	+	0.121554i
$872$	−2236.12	−	3873.07i	−0.0868399	−	0.150411i
$873$		0			0
$874$	11400.0			0.441202
$875$		0			0
$876$		0			0
$877$	−23555.0	+	40798.5i	−0.906951	+	1.57088i	−0.0886738	+	0.996061i	$0.528263\pi$
$877$	−23555.0	+	40798.5i	−0.906951	+	1.57088i	−0.818277	+	0.574824i	$0.805070\pi$
$878$	−4079.93	−	7066.65i	−0.156823	−	0.271626i
$879$		0			0
$880$	−5890.00	+	10201.8i	−0.225627	+	0.390798i
$881$	42133.1			1.61124			0.805619	−	0.592434i	$-0.201833\pi$
$881$	42133.1			1.61124			0.805619	+	0.592434i	$0.201833\pi$
$882$		0			0
$883$	−22732.0			−0.866356			−0.433178	−	0.901308i	$-0.642608\pi$
$883$	−22732.0			−0.866356			−0.433178	+	0.901308i	$0.642608\pi$
$884$	−35385.5	+	61289.6i	−1.34632	+	2.33189i
$885$		0			0
$886$	24225.0	+	41958.9i	0.918572	+	1.59101i
$887$	10731.6	−	18587.7i	0.406237	−	0.703623i	−0.588228	−	0.808695i	$-0.700174\pi$
$887$	10731.6	−	18587.7i	0.406237	−	0.703623i	0.994465	+	0.105072i	$0.0335074\pi$
$888$		0			0
$889$		0			0
$890$	55323.1			2.08364
$891$		0			0
$892$	−29524.0	−	51137.1i	−1.10822	−	1.91950i
$893$	−4707.61	−	8153.82i	−0.176410	−	0.305551i
$894$		0			0
$895$	−2356.00			−0.0879915
$896$		0			0
$897$		0			0
$898$	16644.0	−	28828.3i	0.618505	−	1.07128i
$899$	19039.7	+	32977.7i	0.706350	+	1.22343i
$900$		0			0
$901$	−6156.00	+	10662.5i	−0.227621	+	0.394250i
$902$	−31471.3			−1.16173
$903$		0			0
$904$	−6384.00			−0.234877
$905$	1822.02	−	3155.83i	0.0669237	−	0.115915i
$906$		0			0
$907$	3458.00	+	5989.43i	0.126594	+	0.219268i	0.922355	−	0.386343i	$-0.126262\pi$
$907$	3458.00	+	5989.43i	0.126594	+	0.219268i	−0.795761	+	0.605611i	$0.792929\pi$
$908$	8918.31	−	15447.0i	0.325952	−	0.564565i
$909$		0			0
$910$		0			0
$911$	−38210.1			−1.38963			−0.694817	−	0.719186i	$-0.744515\pi$
$911$	−38210.1			−1.38963			−0.694817	+	0.719186i	$0.744515\pi$
$912$		0			0
$913$	−31920.0	−	55287.1i	−1.15706	−	2.00409i
$914$	33001.2	+	57159.8i	1.19429	+	2.06858i
$915$		0			0
$916$	24046.0			0.867360
$917$		0			0
$918$		0			0
$919$	23816.0	−	41250.5i	0.854861	−	1.48066i	−0.0219127	−	0.999760i	$-0.506976\pi$
$919$	23816.0	−	41250.5i	0.854861	−	1.48066i	0.876774	−	0.480903i	$-0.159691\pi$
$920$	−7453.72	−	12910.2i	−0.267111	−	0.462649i
$921$		0			0
$922$	28747.0	−	49791.3i	1.02682	−	1.77851i
$923$	−36457.8			−1.30013
$924$		0			0
$925$	−9114.00			−0.323964
$926$	20329.9	−	35212.4i	0.721471	−	1.24962i
$927$		0			0
$928$	29260.0	+	50679.8i	1.03503	+	1.79272i
$929$	−1652.02	+	2861.39i	−0.0583435	+	0.101054i	−0.893722	−	0.448621i	$-0.851915\pi$
$929$	−1652.02	+	2861.39i	−0.0583435	+	0.101054i	0.835378	+	0.549675i	$0.185249\pi$
$930$		0			0
$931$		0			0
$932$	45454.6			1.59755
$933$		0			0
$934$	−7410.00	−	12834.5i	−0.259596	−	0.449633i
$935$	14907.4	+	25820.4i	0.521417	+	0.903121i
$936$		0			0
$937$	21858.0			0.762081			0.381040	−	0.924558i	$-0.375566\pi$
$937$	21858.0			0.762081			0.381040	+	0.924558i	$0.375566\pi$
$938$		0			0
$939$		0			0
$940$	−22572.0	+	39095.9i	−0.783210	+	1.35656i
$941$	−25190.1	−	43630.5i	−0.872660	−	1.51149i	−0.859235	−	0.511582i	$-0.829060\pi$
$941$	−25190.1	−	43630.5i	−0.872660	−	1.51149i	−0.0134252	−	0.999910i	$-0.504274\pi$
$942$		0			0
$943$	−10830.0	+	18758.1i	−0.373991	+	0.647771i
$944$	4864.53			0.167719
$945$		0			0
$946$	−31160.0			−1.07093
$947$	15530.8	−	26900.1i	0.532927	−	0.923056i	−0.466334	−	0.884609i	$-0.654425\pi$
$947$	15530.8	−	26900.1i	0.532927	−	0.923056i	0.999261	−	0.0384476i	$-0.0122413\pi$
$948$		0			0
$949$	−5166.00	−	8947.77i	−0.176708	−	0.306066i
$950$	2135.86	−	3699.42i	0.0729436	−	0.126342i
$951$		0			0
$952$		0			0
$953$	−22770.9			−0.773999			−0.387000	−	0.922080i	$-0.626489\pi$
$953$	−22770.9			−0.773999			−0.387000	+	0.922080i	$0.626489\pi$
$954$		0			0
$955$	−6650.00	−	11518.1i	−0.225329	−	0.390281i
$956$	−26611.1	−	46091.7i	−0.900276	−	1.55932i
$957$		0			0
$958$	15580.0			0.525435
$959$		0			0
$960$		0			0
$961$	2727.50	−	4724.17i	0.0915545	−	0.158577i
$962$	33241.0	+	57575.0i	1.11407	+	1.92962i
$963$		0			0
$964$	−7073.00	+	12250.8i	−0.236313	+	0.409307i
$965$	−11838.8			−0.394926
$966$		0			0
$967$	−36416.0			−1.21102			−0.605512	−	0.795836i	$-0.707032\pi$
$967$	−36416.0			−1.21102			−0.605512	+	0.795836i	$0.707032\pi$
$968$	3720.32	−	6443.78i	0.123529	−	0.213958i
$969$		0			0
$970$	−15162.0	−	26261.4i	−0.501879	−	0.869280i
$971$	−9310.61	+	16126.4i	−0.307715	+	0.532979i	−0.977862	−	0.209250i	$-0.932898\pi$
$971$	−9310.61	+	16126.4i	−0.307715	+	0.532979i	0.670147	+	0.742229i	$0.266231\pi$
$972$		0			0
$973$		0			0
$974$	−39090.6			−1.28598
$975$		0			0
$976$	12245.0	+	21209.0i	0.401591	+	0.695576i
$977$	−2903.03	−	5028.19i	−0.0950625	−	0.164653i	0.814572	−	0.580062i	$-0.196972\pi$
$977$	−2903.03	−	5028.19i	−0.0950625	−	0.164653i	−0.909635	+	0.415409i	$0.863638\pi$
$978$		0			0
$979$	63460.0			2.07170
$980$		0			0
$981$		0			0
$982$	−11267.0	+	19515.0i	−0.366135	+	0.634164i
$983$	−1621.51	−	2808.54i	−0.0526126	−	0.0911276i	0.838520	−	0.544871i	$-0.183422\pi$
$983$	−1621.51	−	2808.54i	−0.0526126	−	0.0911276i	−0.891132	+	0.453744i	$0.850088\pi$
$984$		0			0
$985$	−16340.0	+	28301.7i	−0.528564	+	0.915500i
$986$	83481.6			2.69635
$987$		0			0
$988$	−18040.0			−0.580900
$989$	−10722.9	+	18572.6i	−0.344760	+	0.597143i
$990$		0			0
$991$	−24724.0	−	42823.2i	−0.792516	−	1.37268i	−0.924404	−	0.381414i	$-0.875437\pi$
$991$	−24724.0	−	42823.2i	−0.792516	−	1.37268i	0.131888	−	0.991265i	$-0.457896\pi$
$992$	−18699.7	+	32388.8i	−0.598503	+	1.03664i
$993$		0			0
$994$		0			0
$995$	9205.99			0.293316
$996$		0			0
$997$	−8147.00	−	14111.0i	−0.258794	−	0.448245i	0.707125	−	0.707089i	$-0.249992\pi$
$997$	−8147.00	−	14111.0i	−0.258794	−	0.448245i	−0.965919	+	0.258844i	$0.916659\pi$
$998$	8587.03	+	14873.2i	0.272362	+	0.471746i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.r.226.2		4
3.2	odd	2	inner	441.4.e.r.226.1		4
7.2	even	3		63.4.a.d.1.1	✓	2
7.3	odd	6		441.4.e.s.361.2		4
7.4	even	3	inner	441.4.e.r.361.2		4
7.5	odd	6		441.4.a.q.1.1		2
7.6	odd	2		441.4.e.s.226.2		4
21.2	odd	6		63.4.a.d.1.2	yes	2
21.5	even	6		441.4.a.q.1.2		2
21.11	odd	6	inner	441.4.e.r.361.1		4
21.17	even	6		441.4.e.s.361.1		4
21.20	even	2		441.4.e.s.226.1		4
28.23	odd	6		1008.4.a.be.1.1		2
35.9	even	6		1575.4.a.t.1.2		2
84.23	even	6		1008.4.a.be.1.2		2
105.44	odd	6		1575.4.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.a.d.1.1	✓	2	7.2	even	3
63.4.a.d.1.2	yes	2	21.2	odd	6
441.4.a.q.1.1		2	7.5	odd	6
441.4.a.q.1.2		2	21.5	even	6
441.4.e.r.226.1		4	3.2	odd	2	inner
441.4.e.r.226.2		4	1.1	even	1	trivial
441.4.e.r.361.1		4	21.11	odd	6	inner
441.4.e.r.361.2		4	7.4	even	3	inner
441.4.e.s.226.1		4	21.20	even	2
441.4.e.s.226.2		4	7.6	odd	2
441.4.e.s.361.1		4	21.17	even	6
441.4.e.s.361.2		4	7.3	odd	6
1008.4.a.be.1.1		2	28.23	odd	6
1008.4.a.be.1.2		2	84.23	even	6
1575.4.a.t.1.1		2	105.44	odd	6
1575.4.a.t.1.2		2	35.9	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)

\(f(q)\)	\(=\)	\(q+(2.17945 - 3.77492i) q^{2} +(-5.50000 - 9.52628i) q^{4} +(4.35890 - 7.54983i) q^{5} -13.0767 q^{8} +O(q^{10})\)	\(q+(2.17945 - 3.77492i) q^{2} +(-5.50000 - 9.52628i) q^{4} +(4.35890 - 7.54983i) q^{5} -13.0767 q^{8} +(-19.0000 - 32.9090i) q^{10} +(-21.7945 - 37.7492i) q^{11} +82.0000 q^{13} +(15.5000 - 26.8468i) q^{16} +(-39.2301 - 67.9485i) q^{17} +(10.0000 - 17.3205i) q^{19} -95.8958 q^{20} -190.000 q^{22} +(-65.3835 + 113.248i) q^{23} +(24.5000 + 42.4352i) q^{25} +(178.715 - 309.543i) q^{26} -244.098 q^{29} +(-78.0000 - 135.100i) q^{31} +(-119.870 - 207.620i) q^{32} -342.000 q^{34} +(-93.0000 + 161.081i) q^{37} +(-43.5890 - 75.4983i) q^{38} +(-57.0000 + 98.7269i) q^{40} +165.638 q^{41} +164.000 q^{43} +(-239.739 + 415.241i) q^{44} +(285.000 + 493.634i) q^{46} +(235.381 - 407.691i) q^{47} +213.586 q^{50} +(-451.000 - 781.155i) q^{52} +(-78.4602 - 135.897i) q^{53} -380.000 q^{55} +(-532.000 + 921.451i) q^{58} +(78.4602 + 135.897i) q^{59} +(-395.000 + 684.160i) q^{61} -679.988 q^{62} -797.000 q^{64} +(357.430 - 619.086i) q^{65} +(22.0000 + 38.1051i) q^{67} +(-431.531 + 747.434i) q^{68} -444.608 q^{71} +(-63.0000 - 109.119i) q^{73} +(405.378 + 702.135i) q^{74} -220.000 q^{76} +(356.000 - 616.610i) q^{79} +(-135.126 - 234.045i) q^{80} +(361.000 - 625.270i) q^{82} +1464.59 q^{83} -684.000 q^{85} +(357.430 - 619.086i) q^{86} +(285.000 + 493.634i) q^{88} +(-727.936 + 1260.82i) q^{89} +1438.44 q^{92} +(-1026.00 - 1777.08i) q^{94} +(-87.1780 - 150.997i) q^{95} +798.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 22 q^{4}+O(q^{10}) \) 4 * q - 22 * q^4	\( 4 q - 22 q^{4} - 76 q^{10} + 328 q^{13} + 62 q^{16} + 40 q^{19} - 760 q^{22} + 98 q^{25} - 312 q^{31} - 1368 q^{34} - 372 q^{37} - 228 q^{40} + 656 q^{43} + 1140 q^{46} - 1804 q^{52} - 1520 q^{55} - 2128 q^{58} - 1580 q^{61} - 3188 q^{64} + 88 q^{67} - 252 q^{73} - 880 q^{76} + 1424 q^{79} + 1444 q^{82} - 2736 q^{85} + 1140 q^{88} - 4104 q^{94} + 3192 q^{97}+O(q^{100}) \) 4 * q - 22 * q^4 - 76 * q^10 + 328 * q^13 + 62 * q^16 + 40 * q^19 - 760 * q^22 + 98 * q^25 - 312 * q^31 - 1368 * q^34 - 372 * q^37 - 228 * q^40 + 656 * q^43 + 1140 * q^46 - 1804 * q^52 - 1520 * q^55 - 2128 * q^58 - 1580 * q^61 - 3188 * q^64 + 88 * q^67 - 252 * q^73 - 880 * q^76 + 1424 * q^79 + 1444 * q^82 - 2736 * q^85 + 1140 * q^88 - 4104 * q^94 + 3192 * q^97

Introduction

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