LMFDB - Embedded newform 630.4.k.b.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,4,Mod(361,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.361"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,-4,-5,0,17] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$37.1712033036$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.361
Dual form			630.4.k.b.541.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(8.50000 + 16.4545i) q^{7} +8.00000 q^{8} +(-5.00000 + 8.66025i) q^{10} +(-1.00000 + 1.73205i) q^{11} -8.00000 q^{13} +(20.0000 - 31.1769i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-26.0000 + 45.0333i) q^{17} +(-13.0000 - 22.5167i) q^{19} +20.0000 q^{20} +4.00000 q^{22} +(33.5000 + 58.0237i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(8.00000 + 13.8564i) q^{26} +(-74.0000 - 3.46410i) q^{28} -69.0000 q^{29} +(166.000 - 287.520i) q^{31} +(-16.0000 + 27.7128i) q^{32} +104.000 q^{34} +(50.0000 - 77.9423i) q^{35} +(-98.0000 - 169.741i) q^{37} +(-26.0000 + 45.0333i) q^{38} +(-20.0000 - 34.6410i) q^{40} -353.000 q^{41} -369.000 q^{43} +(-4.00000 - 6.92820i) q^{44} +(67.0000 - 116.047i) q^{46} +(44.0000 + 76.2102i) q^{47} +(-198.500 + 279.726i) q^{49} +50.0000 q^{50} +(16.0000 - 27.7128i) q^{52} +(291.000 - 504.027i) q^{53} +10.0000 q^{55} +(68.0000 + 131.636i) q^{56} +(69.0000 + 119.512i) q^{58} +(-175.000 + 303.109i) q^{59} +(233.500 + 404.434i) q^{61} -664.000 q^{62} +64.0000 q^{64} +(20.0000 + 34.6410i) q^{65} +(-145.500 + 252.013i) q^{67} +(-104.000 - 180.133i) q^{68} +(-185.000 - 8.66025i) q^{70} -770.000 q^{71} +(-314.000 + 543.864i) q^{73} +(-196.000 + 339.482i) q^{74} +104.000 q^{76} +(-37.0000 - 1.73205i) q^{77} +(-585.000 - 1013.25i) q^{79} +(-40.0000 + 69.2820i) q^{80} +(353.000 + 611.414i) q^{82} -525.000 q^{83} +260.000 q^{85} +(369.000 + 639.127i) q^{86} +(-8.00000 + 13.8564i) q^{88} +(44.5000 + 77.0763i) q^{89} +(-68.0000 - 131.636i) q^{91} -268.000 q^{92} +(88.0000 - 152.420i) q^{94} +(-65.0000 + 112.583i) q^{95} -290.000 q^{97} +(683.000 + 64.0859i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} - 5 q^{5} + 17 q^{7} + 16 q^{8} - 10 q^{10} - 2 q^{11} - 16 q^{13} + 40 q^{14} - 16 q^{16} - 52 q^{17} - 26 q^{19} + 40 q^{20} + 8 q^{22} + 67 q^{23} - 25 q^{25} + 16 q^{26} - 148 q^{28}+ \cdots + 1366 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 - 5 * q^5 + 17 * q^7 + 16 * q^8 - 10 * q^10 - 2 * q^11 - 16 * q^13 + 40 * q^14 - 16 * q^16 - 52 * q^17 - 26 * q^19 + 40 * q^20 + 8 * q^22 + 67 * q^23 - 25 * q^25 + 16 * q^26 - 148 * q^28 - 138 * q^29 + 332 * q^31 - 32 * q^32 + 208 * q^34 + 100 * q^35 - 196 * q^37 - 52 * q^38 - 40 * q^40 - 706 * q^41 - 738 * q^43 - 8 * q^44 + 134 * q^46 + 88 * q^47 - 397 * q^49 + 100 * q^50 + 32 * q^52 + 582 * q^53 + 20 * q^55 + 136 * q^56 + 138 * q^58 - 350 * q^59 + 467 * q^61 - 1328 * q^62 + 128 * q^64 + 40 * q^65 - 291 * q^67 - 208 * q^68 - 370 * q^70 - 1540 * q^71 - 628 * q^73 - 392 * q^74 + 208 * q^76 - 74 * q^77 - 1170 * q^79 - 80 * q^80 + 706 * q^82 - 1050 * q^83 + 520 * q^85 + 738 * q^86 - 16 * q^88 + 89 * q^89 - 136 * q^91 - 536 * q^92 + 176 * q^94 - 130 * q^95 - 580 * q^97 + 1366 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	8.50000	+	16.4545i	0.458957	+	0.888459i
$7$	8.50000	+	16.4545i	0.458957	+	0.888459i
$8$	8.00000			0.353553
$9$		0			0
$10$	−5.00000	+	8.66025i	−0.158114	+	0.273861i
$11$	−1.00000	+	1.73205i	−0.0274101	+	0.0474757i	−0.879405	−	0.476074i	$-0.842059\pi$
$11$	−1.00000	+	1.73205i	−0.0274101	+	0.0474757i	0.851995	+	0.523550i	$0.175393\pi$
$12$		0			0
$13$	−8.00000			−0.170677			−0.0853385	−	0.996352i	$-0.527197\pi$
$13$	−8.00000			−0.170677			−0.0853385	+	0.996352i	$0.527197\pi$
$14$	20.0000	−	31.1769i	0.381802	−	0.595170i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−26.0000	+	45.0333i	−0.370937	+	0.642481i	−0.989710	−	0.143088i	$-0.954297\pi$
$17$	−26.0000	+	45.0333i	−0.370937	+	0.642481i	0.618773	+	0.785570i	$0.287630\pi$
$18$		0			0
$19$	−13.0000	−	22.5167i	−0.156969	−	0.271878i	0.776805	−	0.629741i	$-0.216839\pi$
$19$	−13.0000	−	22.5167i	−0.156969	−	0.271878i	−0.933774	+	0.357863i	$0.883505\pi$
$20$	20.0000			0.223607
$21$		0			0
$22$	4.00000			0.0387638
$23$	33.5000	+	58.0237i	0.303706	+	0.526034i	0.976972	−	0.213366i	$-0.0684427\pi$
$23$	33.5000	+	58.0237i	0.303706	+	0.526034i	−0.673267	+	0.739400i	$0.735109\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	8.00000	+	13.8564i	0.0603434	+	0.104518i
$27$		0			0
$28$	−74.0000	−	3.46410i	−0.499453	−	0.0233805i
$29$	−69.0000			−0.441827			−0.220913	−	0.975293i	$-0.570904\pi$
$29$	−69.0000			−0.441827			−0.220913	+	0.975293i	$0.570904\pi$
$30$		0			0
$31$	166.000	−	287.520i	0.961757	−	1.66581i	0.243672	−	0.969858i	$-0.421648\pi$
$31$	166.000	−	287.520i	0.961757	−	1.66581i	0.718085	−	0.695955i	$-0.245019\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	104.000			0.524584
$35$	50.0000	−	77.9423i	0.241473	−	0.376419i
$36$		0			0
$37$	−98.0000	−	169.741i	−0.435435	−	0.754196i	0.561896	−	0.827208i	$-0.310072\pi$
$37$	−98.0000	−	169.741i	−0.435435	−	0.754196i	−0.997331	+	0.0730121i	$0.976739\pi$
$38$	−26.0000	+	45.0333i	−0.110994	+	0.192247i
$39$		0			0
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−353.000			−1.34462			−0.672309	−	0.740271i	$-0.734697\pi$
$41$	−353.000			−1.34462			−0.672309	+	0.740271i	$0.734697\pi$
$42$		0			0
$43$	−369.000			−1.30865			−0.654325	−	0.756213i	$-0.727047\pi$
$43$	−369.000			−1.30865			−0.654325	+	0.756213i	$0.727047\pi$
$44$	−4.00000	−	6.92820i	−0.0137051	−	0.0237379i
$45$		0			0
$46$	67.0000	−	116.047i	0.214752	−	0.371962i
$47$	44.0000	+	76.2102i	0.136554	+	0.236519i	0.926190	−	0.377057i	$-0.123064\pi$
$47$	44.0000	+	76.2102i	0.136554	+	0.236519i	−0.789636	+	0.613576i	$0.789730\pi$
$48$		0			0
$49$	−198.500	+	279.726i	−0.578717	+	0.815528i
$50$	50.0000			0.141421
$51$		0			0
$52$	16.0000	−	27.7128i	0.0426692	−	0.0739053i
$53$	291.000	−	504.027i	0.754187	−	1.30629i	−0.191590	−	0.981475i	$-0.561364\pi$
$53$	291.000	−	504.027i	0.754187	−	1.30629i	0.945777	−	0.324816i	$-0.105302\pi$
$54$		0			0
$55$	10.0000			0.0245164
$56$	68.0000	+	131.636i	0.162266	+	0.314118i
$57$		0			0
$58$	69.0000	+	119.512i	0.156209	+	0.270563i
$59$	−175.000	+	303.109i	−0.386154	+	0.668838i	−0.991928	−	0.126798i	$-0.959530\pi$
$59$	−175.000	+	303.109i	−0.386154	+	0.668838i	0.605775	+	0.795636i	$0.292863\pi$
$60$		0			0
$61$	233.500	+	404.434i	0.490108	+	0.848893i	0.999935	−	0.0113844i	$-0.00362386\pi$
$61$	233.500	+	404.434i	0.490108	+	0.848893i	−0.509827	+	0.860277i	$0.670291\pi$
$62$	−664.000			−1.36013
$63$		0			0
$64$	64.0000			0.125000
$65$	20.0000	+	34.6410i	0.0381645	+	0.0661029i
$66$		0			0
$67$	−145.500	+	252.013i	−0.265308	+	0.459527i	−0.967644	−	0.252318i	$-0.918807\pi$
$67$	−145.500	+	252.013i	−0.265308	+	0.459527i	0.702336	+	0.711846i	$0.252140\pi$
$68$	−104.000	−	180.133i	−0.185468	−	0.321241i
$69$		0			0
$70$	−185.000	−	8.66025i	−0.315882	−	0.0147871i
$71$	−770.000			−1.28707			−0.643537	−	0.765415i	$-0.722534\pi$
$71$	−770.000			−1.28707			−0.643537	+	0.765415i	$0.722534\pi$
$72$		0			0
$73$	−314.000	+	543.864i	−0.503437	+	0.871979i	0.496555	+	0.868005i	$0.334598\pi$
$73$	−314.000	+	543.864i	−0.503437	+	0.871979i	−0.999992	+	0.00397357i	$0.998735\pi$
$74$	−196.000	+	339.482i	−0.307899	+	0.533297i
$75$		0			0
$76$	104.000			0.156969
$77$	−37.0000	−	1.73205i	−0.0547603	−	0.00256345i
$78$		0			0
$79$	−585.000	−	1013.25i	−0.833135	−	1.44303i	−0.895540	−	0.444981i	$-0.853211\pi$
$79$	−585.000	−	1013.25i	−0.833135	−	1.44303i	0.0624054	−	0.998051i	$-0.480123\pi$
$80$	−40.0000	+	69.2820i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	353.000	+	611.414i	0.475394	+	0.823407i
$83$	−525.000			−0.694292			−0.347146	−	0.937811i	$-0.612849\pi$
$83$	−525.000			−0.694292			−0.347146	+	0.937811i	$0.612849\pi$
$84$		0			0
$85$	260.000			0.331776
$86$	369.000	+	639.127i	0.462678	+	0.801382i
$87$		0			0
$88$	−8.00000	+	13.8564i	−0.00969094	+	0.0167852i
$89$	44.5000	+	77.0763i	0.0529999	+	0.0917985i	0.891308	−	0.453398i	$-0.149788\pi$
$89$	44.5000	+	77.0763i	0.0529999	+	0.0917985i	−0.838308	+	0.545197i	$0.816455\pi$
$90$		0			0
$91$	−68.0000	−	131.636i	−0.0783334	−	0.151639i
$92$	−268.000			−0.303706
$93$		0			0
$94$	88.0000	−	152.420i	0.0965586	−	0.167244i
$95$	−65.0000	+	112.583i	−0.0701985	+	0.121587i
$96$		0			0
$97$	−290.000			−0.303557			−0.151779	−	0.988415i	$-0.548500\pi$
$97$	−290.000			−0.303557			−0.151779	+	0.988415i	$0.548500\pi$
$98$	683.000	+	64.0859i	0.704014	+	0.0660577i
$99$		0			0
$100$	−50.0000	−	86.6025i	−0.0500000	−	0.0866025i
$101$	−616.500	+	1067.81i	−0.607367	+	1.05199i	0.384306	+	0.923206i	$0.374441\pi$
$101$	−616.500	+	1067.81i	−0.607367	+	1.05199i	−0.991673	+	0.128784i	$0.958893\pi$
$102$		0			0
$103$	−776.500	−	1344.94i	−0.742823	−	1.28661i	−0.951205	−	0.308560i	$-0.900153\pi$
$103$	−776.500	−	1344.94i	−0.742823	−	1.28661i	0.208381	−	0.978048i	$-0.433181\pi$
$104$	−64.0000			−0.0603434
$105$		0			0
$106$	−1164.00			−1.06658
$107$	915.500	+	1585.69i	0.827147	+	1.43266i	0.900267	+	0.435337i	$0.143371\pi$
$107$	915.500	+	1585.69i	0.827147	+	1.43266i	−0.0731204	+	0.997323i	$0.523296\pi$
$108$		0			0
$109$	−405.500	+	702.347i	−0.356329	+	0.617180i	−0.987344	−	0.158590i	$-0.949305\pi$
$109$	−405.500	+	702.347i	−0.356329	+	0.617180i	0.631016	+	0.775770i	$0.282638\pi$
$110$	−10.0000	−	17.3205i	−0.00866784	−	0.0150131i
$111$		0			0
$112$	160.000	−	249.415i	0.134987	−	0.210424i
$113$	−2170.00			−1.80652			−0.903259	−	0.429097i	$-0.858832\pi$
$113$	−2170.00			−1.80652			−0.903259	+	0.429097i	$0.858832\pi$
$114$		0			0
$115$	167.500	−	290.119i	0.135821	−	0.235249i
$116$	138.000	−	239.023i	0.110457	−	0.191317i
$117$		0			0
$118$	700.000			0.546104
$119$	−962.000	−	45.0333i	−0.741062	−	0.0346907i
$120$		0			0
$121$	663.500	+	1149.22i	0.498497	+	0.863423i
$122$	467.000	−	808.868i	0.346559	−	0.600258i
$123$		0			0
$124$	664.000	+	1150.08i	0.480879	+	0.832906i
$125$	125.000			0.0894427
$126$		0			0
$127$	48.0000			0.0335379			0.0167689	−	0.999859i	$-0.494662\pi$
$127$	48.0000			0.0335379			0.0167689	+	0.999859i	$0.494662\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	40.0000	−	69.2820i	0.0269864	−	0.0467418i
$131$	−396.000	−	685.892i	−0.264112	−	0.457456i	0.703219	−	0.710974i	$-0.251746\pi$
$131$	−396.000	−	685.892i	−0.264112	−	0.457456i	−0.967331	+	0.253518i	$0.918412\pi$
$132$		0			0
$133$	260.000	−	405.300i	0.169510	−	0.264240i
$134$	582.000			0.375203
$135$		0			0
$136$	−208.000	+	360.267i	−0.131146	+	0.227151i
$137$	542.000	−	938.772i	0.338001	−	0.585436i	−0.646055	−	0.763291i	$-0.723582\pi$
$137$	542.000	−	938.772i	0.338001	−	0.585436i	0.984057	+	0.177855i	$0.0569158\pi$
$138$		0			0
$139$	−46.0000			−0.0280696			−0.0140348	−	0.999902i	$-0.504468\pi$
$139$	−46.0000			−0.0280696			−0.0140348	+	0.999902i	$0.504468\pi$
$140$	170.000	+	329.090i	0.102626	+	0.198665i
$141$		0			0
$142$	770.000	+	1333.68i	0.455049	+	0.788168i
$143$	8.00000	−	13.8564i	0.00467828	−	0.00810301i
$144$		0			0
$145$	172.500	+	298.779i	0.0987955	+	0.171119i
$146$	1256.00			0.711968
$147$		0			0
$148$	784.000			0.435435
$149$	−184.500	−	319.563i	−0.101442	−	0.175702i	0.810837	−	0.585272i	$-0.199012\pi$
$149$	−184.500	−	319.563i	−0.101442	−	0.175702i	−0.912279	+	0.409570i	$0.865679\pi$
$150$		0			0
$151$	−1240.00	+	2147.74i	−0.668277	+	1.15749i	0.310109	+	0.950701i	$0.399634\pi$
$151$	−1240.00	+	2147.74i	−0.668277	+	1.15749i	−0.978386	+	0.206788i	$0.933699\pi$
$152$	−104.000	−	180.133i	−0.0554968	−	0.0961233i
$153$		0			0
$154$	34.0000	+	65.8179i	0.0177909	+	0.0344400i
$155$	−1660.00			−0.860222
$156$		0			0
$157$	−613.000	+	1061.75i	−0.311610	+	0.539724i	−0.978711	−	0.205243i	$-0.934201\pi$
$157$	−613.000	+	1061.75i	−0.311610	+	0.539724i	0.667101	+	0.744967i	$0.267535\pi$
$158$	−1170.00	+	2026.50i	−0.589115	+	1.02038i
$159$		0			0
$160$	160.000			0.0790569
$161$	−670.000	+	1044.43i	−0.327971	+	0.511257i
$162$		0			0
$163$	330.000	+	571.577i	0.158574	+	0.274659i	0.934355	−	0.356344i	$-0.115977\pi$
$163$	330.000	+	571.577i	0.158574	+	0.274659i	−0.775781	+	0.631003i	$0.782644\pi$
$164$	706.000	−	1222.83i	0.336154	−	0.582237i
$165$		0			0
$166$	525.000	+	909.327i	0.245469	+	0.425165i
$167$	949.000			0.439735			0.219868	−	0.975530i	$-0.429437\pi$
$167$	949.000			0.439735			0.219868	+	0.975530i	$0.429437\pi$
$168$		0			0
$169$	−2133.00			−0.970869
$170$	−260.000	−	450.333i	−0.117301	−	0.203170i
$171$		0			0
$172$	738.000	−	1278.25i	0.327163	−	0.566662i
$173$	1696.00	+	2937.56i	0.745344	+	1.29097i	0.950034	+	0.312147i	$0.101048\pi$
$173$	1696.00	+	2937.56i	0.745344	+	1.29097i	−0.204690	+	0.978827i	$0.565619\pi$
$174$		0			0
$175$	−462.500	−	21.6506i	−0.199781	−	0.00935220i
$176$	32.0000			0.0137051
$177$		0			0
$178$	89.0000	−	154.153i	0.0374766	−	0.0649113i
$179$	134.000	−	232.095i	0.0559532	−	0.0969139i	−0.836692	−	0.547674i	$-0.815514\pi$
$179$	134.000	−	232.095i	0.0559532	−	0.0969139i	0.892645	+	0.450760i	$0.148847\pi$
$180$		0			0
$181$	−4093.00			−1.68083			−0.840415	−	0.541943i	$-0.817689\pi$
$181$	−4093.00			−1.68083			−0.840415	+	0.541943i	$0.817689\pi$
$182$	−160.000	+	249.415i	−0.0651648	+	0.101582i
$183$		0			0
$184$	268.000	+	464.190i	0.107376	+	0.185981i
$185$	−490.000	+	848.705i	−0.194733	+	0.337287i
$186$		0			0
$187$	−52.0000	−	90.0666i	−0.0203348	−	0.0352210i
$188$	−352.000			−0.136554
$189$		0			0
$190$	260.000			0.0992757
$191$	−989.000	−	1713.00i	−0.374668	−	0.648943i	0.615610	−	0.788051i	$-0.288910\pi$
$191$	−989.000	−	1713.00i	−0.374668	−	0.648943i	−0.990277	+	0.139108i	$0.955577\pi$
$192$		0			0
$193$	1999.00	−	3462.37i	0.745550	−	1.29133i	−0.204387	−	0.978890i	$-0.565520\pi$
$193$	1999.00	−	3462.37i	0.745550	−	1.29133i	0.949937	−	0.312441i	$-0.101146\pi$
$194$	290.000	+	502.295i	0.107324	+	0.185890i
$195$		0			0
$196$	−572.000	−	1247.08i	−0.208455	−	0.454474i
$197$	3030.00			1.09583			0.547915	−	0.836534i	$-0.315422\pi$
$197$	3030.00			1.09583			0.547915	+	0.836534i	$0.315422\pi$
$198$		0			0
$199$	−178.000	+	308.305i	−0.0634075	+	0.109825i	−0.895986	−	0.444081i	$-0.853530\pi$
$199$	−178.000	+	308.305i	−0.0634075	+	0.109825i	0.832579	+	0.553906i	$0.186863\pi$
$200$	−100.000	+	173.205i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	2466.00			0.858946
$203$	−586.500	−	1135.36i	−0.202779	−	0.392545i
$204$		0			0
$205$	882.500	+	1528.53i	0.300666	+	0.520768i
$206$	−1553.00	+	2689.87i	−0.525256	+	0.909769i
$207$		0			0
$208$	64.0000	+	110.851i	0.0213346	+	0.0369527i
$209$	52.0000			0.0172101
$210$		0			0
$211$	−2602.00			−0.848953			−0.424476	−	0.905439i	$-0.639542\pi$
$211$	−2602.00			−0.848953			−0.424476	+	0.905439i	$0.639542\pi$
$212$	1164.00	+	2016.11i	0.377094	+	0.653145i
$213$		0			0
$214$	1831.00	−	3171.39i	0.584881	−	1.01304i
$215$	922.500	+	1597.82i	0.292623	+	0.506838i
$216$		0			0
$217$	6142.00	+	287.520i	1.92141	+	0.0899454i
$218$	1622.00			0.503925
$219$		0			0
$220$	−20.0000	+	34.6410i	−0.00612909	+	0.0106159i
$221$	208.000	−	360.267i	0.0633104	−	0.109657i
$222$		0			0
$223$	−3156.00			−0.947719			−0.473860	−	0.880600i	$-0.657140\pi$
$223$	−3156.00			−0.947719			−0.473860	+	0.880600i	$0.657140\pi$
$224$	−592.000	−	27.7128i	−0.176583	−	0.00826625i
$225$		0			0
$226$	2170.00	+	3758.55i	0.638700	+	1.10626i
$227$	2118.00	−	3668.48i	0.619280	−	1.07262i	−0.370337	−	0.928897i	$-0.620758\pi$
$227$	2118.00	−	3668.48i	0.619280	−	1.07262i	0.989617	−	0.143727i	$-0.0459088\pi$
$228$		0			0
$229$	−3167.00	−	5485.40i	−0.913892	−	1.58291i	−0.808516	−	0.588475i	$-0.799729\pi$
$229$	−3167.00	−	5485.40i	−0.913892	−	1.58291i	−0.105376	−	0.994432i	$-0.533605\pi$
$230$	−670.000			−0.192080
$231$		0			0
$232$	−552.000			−0.156209
$233$	−2344.00	−	4059.93i	−0.659058	−	1.14152i	−0.980860	−	0.194715i	$-0.937622\pi$
$233$	−2344.00	−	4059.93i	−0.659058	−	1.14152i	0.321802	−	0.946807i	$-0.395712\pi$
$234$		0			0
$235$	220.000	−	381.051i	0.0610690	−	0.105775i
$236$	−700.000	−	1212.44i	−0.193077	−	0.334419i
$237$		0			0
$238$	884.000	+	1711.27i	0.240761	+	0.466071i
$239$	−1856.00			−0.502321			−0.251160	−	0.967945i	$-0.580812\pi$
$239$	−1856.00			−0.502321			−0.251160	+	0.967945i	$0.580812\pi$
$240$		0			0
$241$	2403.00	−	4162.12i	0.642286	−	1.11247i	−0.342636	−	0.939468i	$-0.611320\pi$
$241$	2403.00	−	4162.12i	0.642286	−	1.11247i	0.984921	−	0.173003i	$-0.0553470\pi$
$242$	1327.00	−	2298.43i	0.352491	−	0.610532i
$243$		0			0
$244$	−1868.00			−0.490108
$245$	1707.50	+	160.215i	0.445258	+	0.0417785i
$246$		0			0
$247$	104.000	+	180.133i	0.0267909	+	0.0464033i
$248$	1328.00	−	2300.16i	0.340033	−	0.588954i
$249$		0			0
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	3200.00			0.804710			0.402355	−	0.915484i	$-0.368192\pi$
$251$	3200.00			0.804710			0.402355	+	0.915484i	$0.368192\pi$
$252$		0			0
$253$	−134.000			−0.0332984
$254$	−48.0000	−	83.1384i	−0.0118574	−	0.0205377i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−560.000	−	969.948i	−0.135922	−	0.235423i	0.790028	−	0.613071i	$-0.210066\pi$
$257$	−560.000	−	969.948i	−0.135922	−	0.235423i	−0.925949	+	0.377648i	$0.876733\pi$
$258$		0			0
$259$	1960.00	−	3055.34i	0.470226	−	0.733009i
$260$	−160.000			−0.0381645
$261$		0			0
$262$	−792.000	+	1371.78i	−0.186755	+	0.323470i
$263$	3202.50	−	5546.89i	0.750854	−	1.30052i	−0.196555	−	0.980493i	$-0.562975\pi$
$263$	3202.50	−	5546.89i	0.750854	−	1.30052i	0.947409	−	0.320025i	$-0.103691\pi$
$264$		0			0
$265$	−2910.00			−0.674566
$266$	−962.000	−	45.0333i	−0.221744	−	0.0103803i
$267$		0			0
$268$	−582.000	−	1008.05i	−0.132654	−	0.229764i
$269$	2467.50	−	4273.84i	0.559279	−	0.968700i	−0.438277	−	0.898840i	$-0.644411\pi$
$269$	2467.50	−	4273.84i	0.559279	−	0.968700i	0.997557	−	0.0698604i	$-0.0222554\pi$
$270$		0			0
$271$	723.000	+	1252.27i	0.162063	+	0.280702i	0.935608	−	0.353039i	$-0.114852\pi$
$271$	723.000	+	1252.27i	0.162063	+	0.280702i	−0.773545	+	0.633741i	$0.781518\pi$
$272$	832.000			0.185468
$273$		0			0
$274$	−2168.00			−0.478006
$275$	−25.0000	−	43.3013i	−0.00548202	−	0.00949514i
$276$		0			0
$277$	4010.00	−	6945.52i	0.869811	−	1.50656i	0.00762078	−	0.999971i	$-0.497574\pi$
$277$	4010.00	−	6945.52i	0.869811	−	1.50656i	0.862190	−	0.506585i	$-0.169092\pi$
$278$	46.0000	+	79.6743i	0.00992409	+	0.0171890i
$279$		0			0
$280$	400.000	−	623.538i	0.0853735	−	0.133084i
$281$	−4978.00			−1.05681			−0.528403	−	0.848994i	$-0.677209\pi$
$281$	−4978.00			−1.05681			−0.528403	+	0.848994i	$0.677209\pi$
$282$		0			0
$283$	−2926.00	+	5067.98i	−0.614603	+	1.06452i	0.375851	+	0.926680i	$0.377350\pi$
$283$	−2926.00	+	5067.98i	−0.614603	+	1.06452i	−0.990454	+	0.137844i	$0.955983\pi$
$284$	1540.00	−	2667.36i	0.321768	−	0.557319i
$285$		0			0
$286$	−32.0000			−0.00661608
$287$	−3000.50	−	5808.43i	−0.617122	−	1.19464i
$288$		0			0
$289$	1104.50	+	1913.05i	0.224812	+	0.389385i
$290$	345.000	−	597.558i	0.0698590	−	0.120999i
$291$		0			0
$292$	−1256.00	−	2175.46i	−0.251719	−	0.435989i
$293$	3012.00			0.600556			0.300278	−	0.953852i	$-0.402921\pi$
$293$	3012.00			0.600556			0.300278	+	0.953852i	$0.402921\pi$
$294$		0			0
$295$	1750.00			0.345386
$296$	−784.000	−	1357.93i	−0.153950	−	0.266648i
$297$		0			0
$298$	−369.000	+	639.127i	−0.0717302	+	0.124240i
$299$	−268.000	−	464.190i	−0.0518356	−	0.0897819i
$300$		0			0
$301$	−3136.50	−	6071.70i	−0.600614	−	1.16268i
$302$	4960.00			0.945086
$303$		0			0
$304$	−208.000	+	360.267i	−0.0392422	+	0.0679694i
$305$	1167.50	−	2022.17i	0.219183	−	0.379636i
$306$		0			0
$307$	9443.00			1.75551			0.877753	−	0.479113i	$-0.159042\pi$
$307$	9443.00			1.75551			0.877753	+	0.479113i	$0.159042\pi$
$308$	80.0000	−	124.708i	0.0148001	−	0.0230710i
$309$		0			0
$310$	1660.00	+	2875.20i	0.304134	+	0.526776i
$311$	−4997.00	+	8655.06i	−0.911106	+	1.57808i	−0.0986008	+	0.995127i	$0.531437\pi$
$311$	−4997.00	+	8655.06i	−0.911106	+	1.57808i	−0.812505	+	0.582954i	$0.801897\pi$
$312$		0			0
$313$	−728.000	−	1260.93i	−0.131466	−	0.227707i	0.792776	−	0.609514i	$-0.208635\pi$
$313$	−728.000	−	1260.93i	−0.131466	−	0.227707i	−0.924242	+	0.381807i	$0.875302\pi$
$314$	2452.00			0.440683
$315$		0			0
$316$	4680.00			0.833135
$317$	3436.00	+	5951.33i	0.608785	+	1.05445i	0.991441	+	0.130556i	$0.0416763\pi$
$317$	3436.00	+	5951.33i	0.608785	+	1.05445i	−0.382655	+	0.923891i	$0.624990\pi$
$318$		0			0
$319$	69.0000	−	119.512i	0.0121105	−	0.0209760i
$320$	−160.000	−	277.128i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	2479.00	+	116.047i	0.429035	+	0.0200841i
$323$	1352.00			0.232902
$324$		0			0
$325$	100.000	−	173.205i	0.0170677	−	0.0295621i
$326$	660.000	−	1143.15i	0.112129	−	0.194213i
$327$		0			0
$328$	−2824.00			−0.475394
$329$	−880.000	+	1371.78i	−0.147465	+	0.229875i
$330$		0			0
$331$	196.000	+	339.482i	0.0325472	+	0.0563735i	0.881840	−	0.471548i	$-0.156305\pi$
$331$	196.000	+	339.482i	0.0325472	+	0.0563735i	−0.849293	+	0.527922i	$0.822971\pi$
$332$	1050.00	−	1818.65i	0.173573	−	0.300637i
$333$		0			0
$334$	−949.000	−	1643.72i	−0.155470	−	0.269282i
$335$	1455.00			0.237299
$336$		0			0
$337$	3926.00			0.634608			0.317304	−	0.948324i	$-0.397222\pi$
$337$	3926.00			0.634608			0.317304	+	0.948324i	$0.397222\pi$
$338$	2133.00	+	3694.46i	0.343254	+	0.594534i
$339$		0			0
$340$	−520.000	+	900.666i	−0.0829440	+	0.143663i
$341$	332.000	+	575.041i	0.0527238	+	0.0913203i
$342$		0			0
$343$	−6290.00	−	888.542i	−0.990169	−	0.139874i
$344$	−2952.00			−0.462678
$345$		0			0
$346$	3392.00	−	5875.12i	0.527038	−	0.912856i
$347$	−892.500	+	1545.86i	−0.138075	+	0.239152i	−0.926768	−	0.375635i	$-0.877425\pi$
$347$	−892.500	+	1545.86i	−0.138075	+	0.239152i	0.788693	+	0.614787i	$0.210758\pi$
$348$		0			0
$349$	−1591.00			−0.244024			−0.122012	−	0.992529i	$-0.538935\pi$
$349$	−1591.00			−0.244024			−0.122012	+	0.992529i	$0.538935\pi$
$350$	425.000	+	822.724i	0.0649063	+	0.125647i
$351$		0			0
$352$	−32.0000	−	55.4256i	−0.00484547	−	0.00839260i
$353$	843.000	−	1460.12i	0.127106	−	0.220154i	−0.795448	−	0.606021i	$-0.792765\pi$
$353$	843.000	−	1460.12i	0.127106	−	0.220154i	0.922554	+	0.385868i	$0.126098\pi$
$354$		0			0
$355$	1925.00	+	3334.20i	0.287798	+	0.498481i
$356$	−356.000			−0.0529999
$357$		0			0
$358$	−536.000			−0.0791298
$359$	3686.00	+	6384.34i	0.541893	+	0.938586i	0.998795	+	0.0490695i	$0.0156256\pi$
$359$	3686.00	+	6384.34i	0.541893	+	0.938586i	−0.456902	+	0.889517i	$0.651041\pi$
$360$		0			0
$361$	3091.50	−	5354.64i	0.450722	−	0.780673i
$362$	4093.00	+	7089.28i	0.594263	+	1.02929i
$363$		0			0
$364$	592.000	+	27.7128i	0.0852451	+	0.00399051i
$365$	3140.00			0.450288
$366$		0			0
$367$	−3318.50	+	5747.81i	−0.472001	+	0.817529i	−0.999487	−	0.0320344i	$-0.989801\pi$
$367$	−3318.50	+	5747.81i	−0.472001	+	0.817529i	0.527486	+	0.849564i	$0.323135\pi$
$368$	536.000	−	928.379i	0.0759264	−	0.131508i
$369$		0			0
$370$	1960.00			0.275393
$371$	10767.0	+	504.027i	1.50672	+	0.0705331i
$372$		0			0
$373$	−1738.00	−	3010.30i	−0.241261	−	0.417876i	0.719813	−	0.694168i	$-0.244228\pi$
$373$	−1738.00	−	3010.30i	−0.241261	−	0.417876i	−0.961074	+	0.276292i	$0.910894\pi$
$374$	−104.000	+	180.133i	−0.0143789	+	0.0249050i
$375$		0			0
$376$	352.000	+	609.682i	0.0482793	+	0.0836222i
$377$	552.000			0.0754097
$378$		0			0
$379$	−2378.00			−0.322295			−0.161147	−	0.986930i	$-0.551519\pi$
$379$	−2378.00			−0.322295			−0.161147	+	0.986930i	$0.551519\pi$
$380$	−260.000	−	450.333i	−0.0350993	−	0.0607937i
$381$		0			0
$382$	−1978.00	+	3426.00i	−0.264930	+	0.458872i
$383$	−1228.50	−	2127.82i	−0.163899	−	0.283882i	0.772365	−	0.635179i	$-0.219074\pi$
$383$	−1228.50	−	2127.82i	−0.163899	−	0.283882i	−0.936264	+	0.351298i	$0.885741\pi$
$384$		0			0
$385$	85.0000	+	164.545i	0.0112520	+	0.0217818i
$386$	−7996.00			−1.05437
$387$		0			0
$388$	580.000	−	1004.59i	0.0758893	−	0.131444i
$389$	4281.00	−	7414.91i	0.557983	−	0.966455i	−0.439682	−	0.898154i	$-0.644909\pi$
$389$	4281.00	−	7414.91i	0.557983	−	0.966455i	0.997665	−	0.0683010i	$-0.0217578\pi$
$390$		0			0
$391$	−3484.00			−0.450623
$392$	−1588.00	+	2237.81i	−0.204607	+	0.288333i
$393$		0			0
$394$	−3030.00	−	5248.11i	−0.387435	−	0.671056i
$395$	−2925.00	+	5066.25i	−0.372589	+	0.645343i
$396$		0			0
$397$	4921.00	+	8523.42i	0.622111	+	1.07753i	0.989092	+	0.147299i	$0.0470579\pi$
$397$	4921.00	+	8523.42i	0.622111	+	1.07753i	−0.366981	+	0.930228i	$0.619609\pi$
$398$	712.000			0.0896717
$399$		0			0
$400$	400.000			0.0500000
$401$	−4048.50	−	7012.21i	−0.504171	−	0.873249i	−0.999988	−	0.00482260i	$-0.998465\pi$
$401$	−4048.50	−	7012.21i	−0.504171	−	0.873249i	0.495818	−	0.868427i	$-0.334868\pi$
$402$		0			0
$403$	−1328.00	+	2300.16i	−0.164150	+	0.284316i
$404$	−2466.00	−	4271.24i	−0.303683	−	0.525995i
$405$		0			0
$406$	−1380.00	+	2151.21i	−0.168690	+	0.262962i
$407$	392.000			0.0477413
$408$		0			0
$409$	−7629.50	+	13214.7i	−0.922383	+	1.59761i	−0.126665	+	0.991946i	$0.540427\pi$
$409$	−7629.50	+	13214.7i	−0.922383	+	1.59761i	−0.795717	+	0.605668i	$0.792906\pi$
$410$	1765.00	−	3057.07i	0.212603	−	0.368239i
$411$		0			0
$412$	6212.00			0.742823
$413$	−6475.00	−	303.109i	−0.771462	−	0.0361138i
$414$		0			0
$415$	1312.50	+	2273.32i	0.155248	+	0.268898i
$416$	128.000	−	221.703i	0.0150859	−	0.0261295i
$417$		0			0
$418$	−52.0000	−	90.0666i	−0.00608470	−	0.0105390i
$419$	−16224.0			−1.89163			−0.945817	−	0.324701i	$-0.894736\pi$
$419$	−16224.0			−1.89163			−0.945817	+	0.324701i	$0.894736\pi$
$420$		0			0
$421$	2977.00			0.344632			0.172316	−	0.985042i	$-0.444875\pi$
$421$	2977.00			0.344632			0.172316	+	0.985042i	$0.444875\pi$
$422$	2602.00	+	4506.80i	0.300150	+	0.519875i
$423$		0			0
$424$	2328.00	−	4032.21i	0.266645	−	0.461843i
$425$	−650.000	−	1125.83i	−0.0741874	−	0.128496i
$426$		0			0
$427$	−4670.00	+	7279.81i	−0.529267	+	0.825046i
$428$	−7324.00			−0.827147
$429$		0			0
$430$	1845.00	−	3195.63i	0.206916	−	0.358389i
$431$	7101.00	−	12299.3i	0.793604	−	1.37456i	−0.130119	−	0.991498i	$-0.541536\pi$
$431$	7101.00	−	12299.3i	0.793604	−	1.37456i	0.923722	−	0.383063i	$-0.125131\pi$
$432$		0			0
$433$	14310.0			1.58821			0.794105	−	0.607781i	$-0.207940\pi$
$433$	14310.0			1.58821			0.794105	+	0.607781i	$0.207940\pi$
$434$	−5644.00	−	10925.8i	−0.624241	−	1.20842i
$435$		0			0
$436$	−1622.00	−	2809.39i	−0.178164	−	0.308590i
$437$	871.000	−	1508.62i	0.0953446	−	0.165142i
$438$		0			0
$439$	1178.00	+	2040.36i	0.128070	+	0.221824i	0.922929	−	0.384970i	$-0.125788\pi$
$439$	1178.00	+	2040.36i	0.128070	+	0.221824i	−0.794859	+	0.606795i	$0.792455\pi$
$440$	80.0000			0.00866784
$441$		0			0
$442$	−832.000			−0.0895344
$443$	4145.50	+	7180.22i	0.444602	+	0.770073i	0.998024	−	0.0628276i	$-0.0200118\pi$
$443$	4145.50	+	7180.22i	0.444602	+	0.770073i	−0.553422	+	0.832901i	$0.686678\pi$
$444$		0			0
$445$	222.500	−	385.381i	0.0237023	−	0.0410535i
$446$	3156.00	+	5466.35i	0.335069	+	0.580357i
$447$		0			0
$448$	544.000	+	1053.09i	0.0573696	+	0.111057i
$449$	3521.00			0.370081			0.185040	−	0.982731i	$-0.440758\pi$
$449$	3521.00			0.370081			0.185040	+	0.982731i	$0.440758\pi$
$450$		0			0
$451$	353.000	−	611.414i	0.0368561	−	0.0638367i
$452$	4340.00	−	7517.10i	0.451629	−	0.782245i
$453$		0			0
$454$	−8472.00			−0.875794
$455$	−400.000	+	623.538i	−0.0412138	+	0.0642460i
$456$		0			0
$457$	2716.00	+	4704.25i	0.278007	+	0.481522i	0.970889	−	0.239529i	$-0.0769929\pi$
$457$	2716.00	+	4704.25i	0.278007	+	0.481522i	−0.692882	+	0.721051i	$0.743660\pi$
$458$	−6334.00	+	10970.8i	−0.646219	+	1.11928i
$459$		0			0
$460$	670.000	+	1160.47i	0.0679107	+	0.117625i
$461$	5350.00			0.540508			0.270254	−	0.962789i	$-0.412892\pi$
$461$	5350.00			0.540508			0.270254	+	0.962789i	$0.412892\pi$
$462$		0			0
$463$	−10123.0			−1.01610			−0.508052	−	0.861327i	$-0.669634\pi$
$463$	−10123.0			−1.01610			−0.508052	+	0.861327i	$0.669634\pi$
$464$	552.000	+	956.092i	0.0552284	+	0.0956583i
$465$		0			0
$466$	−4688.00	+	8119.85i	−0.466024	+	0.807178i
$467$	3231.50	+	5597.12i	0.320206	+	0.554612i	0.980530	−	0.196368i	$-0.0629147\pi$
$467$	3231.50	+	5597.12i	0.320206	+	0.554612i	−0.660325	+	0.750980i	$0.729581\pi$
$468$		0			0
$469$	−5383.50	−	252.013i	−0.530036	−	0.0248121i
$470$	−880.000			−0.0863646
$471$		0			0
$472$	−1400.00	+	2424.87i	−0.136526	+	0.236470i
$473$	369.000	−	639.127i	0.0358703	−	0.0621291i
$474$		0			0
$475$	650.000			0.0627875
$476$	2080.00	−	3242.40i	0.200287	−	0.312217i
$477$		0			0
$478$	1856.00	+	3214.69i	0.177597	+	0.307607i
$479$	−8820.00	+	15276.7i	−0.841328	+	1.45722i	0.0474444	+	0.998874i	$0.484892\pi$
$479$	−8820.00	+	15276.7i	−0.841328	+	1.45722i	−0.888772	+	0.458349i	$0.848441\pi$
$480$		0			0
$481$	784.000	+	1357.93i	0.0743188	+	0.128724i
$482$	−9612.00			−0.908329
$483$		0			0
$484$	−5308.00			−0.498497
$485$	725.000	+	1255.74i	0.0678774	+	0.117567i
$486$		0			0
$487$	5016.00	−	8687.97i	0.466728	−	0.808397i	−0.532549	−	0.846399i	$-0.678766\pi$
$487$	5016.00	−	8687.97i	0.466728	−	0.808397i	0.999278	+	0.0380019i	$0.0120993\pi$
$488$	1868.00	+	3235.47i	0.173279	+	0.300129i
$489$		0			0
$490$	−1430.00	−	3117.69i	−0.131838	−	0.287435i
$491$	−5916.00			−0.543758			−0.271879	−	0.962331i	$-0.587645\pi$
$491$	−5916.00			−0.543758			−0.271879	+	0.962331i	$0.587645\pi$
$492$		0			0
$493$	1794.00	−	3107.30i	0.163890	−	0.283866i
$494$	208.000	−	360.267i	0.0189441	−	0.0328121i
$495$		0			0
$496$	−5312.00			−0.480879
$497$	−6545.00	−	12670.0i	−0.590711	−	1.14351i
$498$		0			0
$499$	−6947.00	−	12032.6i	−0.623227	−	1.07946i	−0.988881	−	0.148710i	$-0.952488\pi$
$499$	−6947.00	−	12032.6i	−0.623227	−	1.07946i	0.365653	−	0.930751i	$-0.380846\pi$
$500$	−250.000	+	433.013i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	−3200.00	−	5542.56i	−0.284508	−	0.492782i
$503$	−18427.0			−1.63344			−0.816719	−	0.577036i	$-0.804209\pi$
$503$	−18427.0			−1.63344			−0.816719	+	0.577036i	$0.804209\pi$
$504$		0			0
$505$	6165.00			0.543245
$506$	134.000	+	232.095i	0.0117728	+	0.0203911i
$507$		0			0
$508$	−96.0000	+	166.277i	−0.00838447	+	0.0145223i
$509$	9278.50	+	16070.8i	0.807981	+	1.39946i	0.914260	+	0.405128i	$0.132773\pi$
$509$	9278.50	+	16070.8i	0.807981	+	1.39946i	−0.106279	+	0.994336i	$0.533894\pi$
$510$		0			0
$511$	−11618.0	−	543.864i	−1.00577	−	0.0470824i
$512$	512.000			0.0441942
$513$		0			0
$514$	−1120.00	+	1939.90i	−0.0961111	+	0.166469i
$515$	−3882.50	+	6724.69i	−0.332201	+	0.575389i
$516$		0			0
$517$	−176.000			−0.0149719
$518$	−7252.00	−	339.482i	−0.615125	−	0.0287953i
$519$		0			0
$520$	160.000	+	277.128i	0.0134932	+	0.0233709i
$521$	−4965.00	+	8599.63i	−0.417506	+	0.723142i	−0.995688	−	0.0927663i	$-0.970429\pi$
$521$	−4965.00	+	8599.63i	−0.417506	+	0.723142i	0.578182	+	0.815908i	$0.303762\pi$
$522$		0			0
$523$	3962.00	+	6862.39i	0.331255	+	0.573750i	0.982758	−	0.184896i	$-0.0591948\pi$
$523$	3962.00	+	6862.39i	0.331255	+	0.573750i	−0.651504	+	0.758646i	$0.725861\pi$
$524$	3168.00			0.264112
$525$		0			0
$526$	−12810.0			−1.06187
$527$	8632.00	+	14951.1i	0.713503	+	1.23582i
$528$		0			0
$529$	3839.00	−	6649.34i	0.315526	−	0.546506i
$530$	2910.00	+	5040.27i	0.238495	+	0.413085i
$531$		0			0
$532$	884.000	+	1711.27i	0.0720418	+	0.139460i
$533$	2824.00			0.229495
$534$		0			0
$535$	4577.50	−	7928.46i	0.369911	−	0.640705i
$536$	−1164.00	+	2016.11i	−0.0938006	+	0.162467i
$537$		0			0
$538$	−9870.00			−0.790940
$539$	−286.000	−	623.538i	−0.0228551	−	0.0498287i
$540$		0			0
$541$	11748.5	+	20349.0i	0.933655	+	1.61714i	0.777015	+	0.629483i	$0.216733\pi$
$541$	11748.5	+	20349.0i	0.933655	+	1.61714i	0.156641	+	0.987656i	$0.449934\pi$
$542$	1446.00	−	2504.55i	0.114596	−	0.198486i
$543$		0			0
$544$	−832.000	−	1441.07i	−0.0655730	−	0.113576i
$545$	4055.00			0.318710
$546$		0			0
$547$	11131.0			0.870068			0.435034	−	0.900414i	$-0.356736\pi$
$547$	11131.0			0.870068			0.435034	+	0.900414i	$0.356736\pi$
$548$	2168.00	+	3755.09i	0.169001	+	0.292718i
$549$		0			0
$550$	−50.0000	+	86.6025i	−0.00387638	+	0.00671408i
$551$	897.000	+	1553.65i	0.0693530	+	0.120123i
$552$		0			0
$553$	11700.0	−	18238.5i	0.899701	−	1.40249i
$554$	−16040.0			−1.23010
$555$		0			0
$556$	92.0000	−	159.349i	0.00701739	−	0.0121545i
$557$	−5989.00	+	10373.3i	−0.455587	+	0.789100i	−0.998722	−	0.0505455i	$-0.983904\pi$
$557$	−5989.00	+	10373.3i	−0.455587	+	0.789100i	0.543135	+	0.839646i	$0.317237\pi$
$558$		0			0
$559$	2952.00			0.223357
$560$	−1480.00	−	69.2820i	−0.111681	−	0.00522804i
$561$		0			0
$562$	4978.00	+	8622.15i	0.373637	+	0.647159i
$563$	−5029.50	+	8711.35i	−0.376498	+	0.652113i	−0.990550	−	0.137152i	$-0.956205\pi$
$563$	−5029.50	+	8711.35i	−0.376498	+	0.652113i	0.614052	+	0.789265i	$0.289538\pi$
$564$		0			0
$565$	5425.00	+	9396.38i	0.403949	+	0.699661i
$566$	11704.0			0.869180
$567$		0			0
$568$	−6160.00			−0.455049
$569$	−7833.00	−	13567.2i	−0.577111	−	0.999586i	−0.995809	−	0.0914605i	$-0.970846\pi$
$569$	−7833.00	−	13567.2i	−0.577111	−	0.999586i	0.418697	−	0.908126i	$-0.362487\pi$
$570$		0			0
$571$	−1265.00	+	2191.04i	−0.0927121	+	0.160582i	−0.908651	−	0.417555i	$-0.862887\pi$
$571$	−1265.00	+	2191.04i	−0.0927121	+	0.160582i	0.815939	+	0.578138i	$0.196220\pi$
$572$	32.0000	+	55.4256i	0.00233914	+	0.00405151i
$573$		0			0
$574$	−7060.00	+	11005.5i	−0.513378	+	0.800276i
$575$	−1675.00			−0.121482
$576$		0			0
$577$	−6409.00	+	11100.7i	−0.462409	+	0.800916i	−0.999080	−	0.0428751i	$-0.986348\pi$
$577$	−6409.00	+	11100.7i	−0.462409	+	0.800916i	0.536671	+	0.843791i	$0.319682\pi$
$578$	2209.00	−	3826.10i	0.158966	−	0.275337i
$579$		0			0
$580$	−1380.00			−0.0987955
$581$	−4462.50	−	8638.60i	−0.318650	−	0.616850i
$582$		0			0
$583$	582.000	+	1008.05i	0.0413447	+	0.0716112i
$584$	−2512.00	+	4350.91i	−0.177992	+	0.308291i
$585$		0			0
$586$	−3012.00	−	5216.94i	−0.212329	−	0.367764i
$587$	15228.0			1.07074			0.535372	−	0.844616i	$-0.320171\pi$
$587$	15228.0			1.07074			0.535372	+	0.844616i	$0.320171\pi$
$588$		0			0
$589$	−8632.00			−0.603863
$590$	−1750.00	−	3031.09i	−0.122112	−	0.211505i
$591$		0			0
$592$	−1568.00	+	2715.86i	−0.108859	+	0.188549i
$593$	−1299.00	−	2249.93i	−0.0899554	−	0.155807i	0.817537	−	0.575877i	$-0.195339\pi$
$593$	−1299.00	−	2249.93i	−0.0899554	−	0.155807i	−0.907492	+	0.420069i	$0.862006\pi$
$594$		0			0
$595$	2210.00	+	4278.17i	0.152271	+	0.294769i
$596$	1476.00			0.101442
$597$		0			0
$598$	−536.000	+	928.379i	−0.0366533	+	0.0634854i
$599$	−1274.00	+	2206.63i	−0.0869019	+	0.150518i	−0.906200	−	0.422849i	$-0.861030\pi$
$599$	−1274.00	+	2206.63i	−0.0869019	+	0.150518i	0.819298	+	0.573368i	$0.194363\pi$
$600$		0			0
$601$	1706.00			0.115789			0.0578945	−	0.998323i	$-0.481561\pi$
$601$	1706.00			0.115789			0.0578945	+	0.998323i	$0.481561\pi$
$602$	−7380.00	+	11504.3i	−0.499645	+	0.778870i
$603$		0			0
$604$	−4960.00	−	8590.97i	−0.334138	−	0.578745i
$605$	3317.50	−	5746.08i	0.222935	−	0.386134i
$606$		0			0
$607$	6283.50	+	10883.3i	0.420164	+	0.727745i	0.995955	−	0.0898517i	$-0.0286393\pi$
$607$	6283.50	+	10883.3i	0.420164	+	0.727745i	−0.575791	+	0.817597i	$0.695306\pi$
$608$	832.000			0.0554968
$609$		0			0
$610$	−4670.00			−0.309972
$611$	−352.000	−	609.682i	−0.0233067	−	0.0403684i
$612$		0			0
$613$	4814.00	−	8338.09i	0.317187	−	0.549384i	−0.662713	−	0.748874i	$-0.730595\pi$
$613$	4814.00	−	8338.09i	0.317187	−	0.549384i	0.979900	+	0.199490i	$0.0639284\pi$
$614$	−9443.00	−	16355.8i	−0.620665	−	1.07502i
$615$		0			0
$616$	−296.000	−	13.8564i	−0.0193607	−	0.000906316i
$617$	4316.00			0.281614			0.140807	−	0.990037i	$-0.455030\pi$
$617$	4316.00			0.281614			0.140807	+	0.990037i	$0.455030\pi$
$618$		0			0
$619$	−8201.00	+	14204.5i	−0.532514	+	0.922341i	0.466766	+	0.884381i	$0.345419\pi$
$619$	−8201.00	+	14204.5i	−0.532514	+	0.922341i	−0.999279	+	0.0379598i	$0.987914\pi$
$620$	3320.00	−	5750.41i	0.215055	−	0.372487i
$621$		0			0
$622$	19988.0			1.28850
$623$	−890.000	+	1387.37i	−0.0572345	+	0.0892198i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−1456.00	+	2521.87i	−0.0929608	+	0.161013i
$627$		0			0
$628$	−2452.00	−	4246.99i	−0.155805	−	0.269862i
$629$	10192.0			0.646076
$630$		0			0
$631$	8490.00			0.535628			0.267814	−	0.963471i	$-0.413699\pi$
$631$	8490.00			0.535628			0.267814	+	0.963471i	$0.413699\pi$
$632$	−4680.00	−	8106.00i	−0.294558	−	0.510189i
$633$		0			0
$634$	6872.00	−	11902.7i	0.430476	−	0.745607i
$635$	−120.000	−	207.846i	−0.00749930	−	0.0129892i
$636$		0			0
$637$	1588.00	−	2237.81i	0.0987737	−	0.139192i
$638$	−276.000			−0.0171269
$639$		0			0
$640$	−320.000	+	554.256i	−0.0197642	+	0.0342327i
$641$	−61.5000	+	106.521i	−0.00378955	+	0.00656370i	−0.867914	−	0.496715i	$-0.834540\pi$
$641$	−61.5000	+	106.521i	−0.00378955	+	0.00656370i	0.864124	+	0.503278i	$0.167873\pi$
$642$		0			0
$643$	−23924.0			−1.46729			−0.733647	−	0.679530i	$-0.762184\pi$
$643$	−23924.0			−1.46729			−0.733647	+	0.679530i	$0.762184\pi$
$644$	−2278.00	−	4409.80i	−0.139388	−	0.269830i
$645$		0			0
$646$	−1352.00	−	2341.73i	−0.0823432	−	0.142623i
$647$	90.5000	−	156.751i	0.00549911	−	0.00952473i	−0.863263	−	0.504755i	$-0.831583\pi$
$647$	90.5000	−	156.751i	0.00549911	−	0.00952473i	0.868762	+	0.495230i	$0.164916\pi$
$648$		0			0
$649$	−350.000	−	606.218i	−0.0211690	−	0.0366658i
$650$	−400.000			−0.0241374
$651$		0			0
$652$	−2640.00			−0.158574
$653$	−8906.00	−	15425.6i	−0.533719	−	0.924429i	−0.999224	−	0.0393836i	$-0.987461\pi$
$653$	−8906.00	−	15425.6i	−0.533719	−	0.924429i	0.465505	−	0.885045i	$-0.345873\pi$
$654$		0			0
$655$	−1980.00	+	3429.46i	−0.118115	+	0.204580i
$656$	2824.00	+	4891.31i	0.168077	+	0.291118i
$657$		0			0
$658$	3256.00	+	152.420i	0.192906	+	0.00903035i
$659$	−15334.0			−0.906416			−0.453208	−	0.891405i	$-0.649720\pi$
$659$	−15334.0			−0.906416			−0.453208	+	0.891405i	$0.649720\pi$
$660$		0			0
$661$	−668.500	+	1157.88i	−0.0393368	+	0.0681334i	−0.885024	−	0.465546i	$-0.845858\pi$
$661$	−668.500	+	1157.88i	−0.0393368	+	0.0681334i	0.845687	+	0.533680i	$0.179191\pi$
$662$	392.000	−	678.964i	0.0230144	−	0.0398621i
$663$		0			0
$664$	−4200.00			−0.245469
$665$	−2405.00	−	112.583i	−0.140243	−	0.00656510i
$666$		0			0
$667$	−2311.50	−	4003.64i	−0.134185	−	0.232416i
$668$	−1898.00	+	3287.43i	−0.109934	+	0.190411i
$669$		0			0
$670$	−1455.00	−	2520.13i	−0.0838978	−	0.145315i
$671$	−934.000			−0.0537357
$672$		0			0
$673$	−15112.0			−0.865564			−0.432782	−	0.901499i	$-0.642468\pi$
$673$	−15112.0			−0.865564			−0.432782	+	0.901499i	$0.642468\pi$
$674$	−3926.00	−	6800.03i	−0.224368	−	0.388616i
$675$		0			0
$676$	4266.00	−	7388.93i	0.242717	−	0.420399i
$677$	12696.0	+	21990.1i	0.720749	+	1.24837i	0.960700	+	0.277589i	$0.0895352\pi$
$677$	12696.0	+	21990.1i	0.720749	+	1.24837i	−0.239951	+	0.970785i	$0.577131\pi$
$678$		0			0
$679$	−2465.00	−	4771.80i	−0.139320	−	0.269698i
$680$	2080.00			0.117301
$681$		0			0
$682$	664.000	−	1150.08i	0.0372813	−	0.0645732i
$683$	14615.5	−	25314.8i	0.818809	−	1.41822i	−0.0877512	−	0.996142i	$-0.527968\pi$
$683$	14615.5	−	25314.8i	0.818809	−	1.41822i	0.906560	−	0.422076i	$-0.138699\pi$
$684$		0			0
$685$	−5420.00			−0.302318
$686$	4751.00	+	11783.1i	0.264423	+	0.655805i
$687$		0			0
$688$	2952.00	+	5113.01i	0.163581	+	0.283331i
$689$	−2328.00	+	4032.21i	−0.128722	+	0.222954i
$690$		0			0
$691$	3769.00	+	6528.10i	0.207496	+	0.359393i	0.950925	−	0.309421i	$-0.100135\pi$
$691$	3769.00	+	6528.10i	0.207496	+	0.359393i	−0.743429	+	0.668814i	$0.766802\pi$
$692$	−13568.0			−0.745344
$693$		0			0
$694$	3570.00			0.195267
$695$	115.000	+	199.186i	0.00627654	+	0.0108713i
$696$		0			0
$697$	9178.00	−	15896.8i	0.498768	−	0.863892i
$698$	1591.00	+	2755.69i	0.0862754	+	0.149433i
$699$		0			0
$700$	1000.00	−	1558.85i	0.0539949	−	0.0841698i
$701$	−22125.0			−1.19208			−0.596041	−	0.802954i	$-0.703261\pi$
$701$	−22125.0			−1.19208			−0.596041	+	0.802954i	$0.703261\pi$
$702$		0			0
$703$	−2548.00	+	4413.27i	−0.136699	+	0.236770i
$704$	−64.0000	+	110.851i	−0.00342627	+	0.00593447i
$705$		0			0
$706$	−3372.00			−0.179755
$707$	−22810.5	−	1067.81i	−1.21340	−	0.0568021i
$708$		0			0
$709$	2219.50	+	3844.29i	0.117567	+	0.203632i	0.918803	−	0.394716i	$-0.129157\pi$
$709$	2219.50	+	3844.29i	0.117567	+	0.203632i	−0.801236	+	0.598349i	$0.795824\pi$
$710$	3850.00	−	6668.40i	0.203504	−	0.352479i
$711$		0			0
$712$	356.000	+	616.610i	0.0187383	+	0.0324557i
$713$	22244.0			1.16837
$714$		0			0
$715$	−80.0000			−0.00418438
$716$	536.000	+	928.379i	0.0279766	+	0.0484569i
$717$		0			0
$718$	7372.00	−	12768.7i	0.383176	−	0.663681i
$719$	6825.00	+	11821.2i	0.354005	+	0.613155i	0.986947	−	0.161045i	$-0.0514863\pi$
$719$	6825.00	+	11821.2i	0.354005	+	0.613155i	−0.632942	+	0.774199i	$0.718153\pi$
$720$		0			0
$721$	15530.0	−	24208.9i	0.802174	−	1.25047i
$722$	−12366.0			−0.637417
$723$		0			0
$724$	8186.00	−	14178.6i	0.420208	−	0.727821i
$725$	862.500	−	1493.89i	0.0441827	−	0.0765267i
$726$		0			0
$727$	−11397.0			−0.581419			−0.290709	−	0.956811i	$-0.593891\pi$
$727$	−11397.0			−0.581419			−0.290709	+	0.956811i	$0.593891\pi$
$728$	−544.000	−	1053.09i	−0.0276950	−	0.0536126i
$729$		0			0
$730$	−3140.00	−	5438.64i	−0.159201	−	0.275744i
$731$	9594.00	−	16617.3i	0.485427	−	0.840784i
$732$		0			0
$733$	−8343.00	−	14450.5i	−0.420403	−	0.728160i	0.575575	−	0.817749i	$-0.304778\pi$
$733$	−8343.00	−	14450.5i	−0.420403	−	0.728160i	−0.995979	+	0.0895886i	$0.971445\pi$
$734$	13274.0			0.667510
$735$		0			0
$736$	−2144.00			−0.107376
$737$	−291.000	−	504.027i	−0.0145443	−	0.0251914i
$738$		0			0
$739$	−11235.0	+	19459.6i	−0.559251	+	0.968650i	0.438309	+	0.898825i	$0.355578\pi$
$739$	−11235.0	+	19459.6i	−0.559251	+	0.968650i	−0.997559	+	0.0698258i	$0.977756\pi$
$740$	−1960.00	−	3394.82i	−0.0973663	−	0.168643i
$741$		0			0
$742$	−9894.00	−	19153.0i	−0.489515	−	0.947614i
$743$	−5625.00			−0.277741			−0.138870	−	0.990311i	$-0.544347\pi$
$743$	−5625.00			−0.277741			−0.138870	+	0.990311i	$0.544347\pi$
$744$		0			0
$745$	−922.500	+	1597.82i	−0.0453662	+	0.0785765i
$746$	−3476.00	+	6020.61i	−0.170597	+	0.295483i
$747$		0			0
$748$	416.000			0.0203348
$749$	−18310.0	+	28542.5i	−0.893235	+	1.39242i
$750$		0			0
$751$	−8810.00	−	15259.4i	−0.428071	−	0.741441i	0.568631	−	0.822593i	$-0.307473\pi$
$751$	−8810.00	−	15259.4i	−0.428071	−	0.741441i	−0.996702	+	0.0811520i	$0.974140\pi$
$752$	704.000	−	1219.36i	0.0341386	−	0.0591298i
$753$		0			0
$754$	−552.000	−	956.092i	−0.0266613	−	0.0461788i
$755$	12400.0			0.597725
$756$		0			0
$757$	39056.0			1.87518			0.937592	−	0.347737i	$-0.113050\pi$
$757$	39056.0			1.87518			0.937592	+	0.347737i	$0.113050\pi$
$758$	2378.00	+	4118.82i	0.113948	+	0.197364i
$759$		0			0
$760$	−520.000	+	900.666i	−0.0248189	+	0.0429876i
$761$	14869.0	+	25753.9i	0.708280	+	1.22678i	0.965495	+	0.260422i	$0.0838618\pi$
$761$	14869.0	+	25753.9i	0.708280	+	1.22678i	−0.257215	+	0.966354i	$0.582805\pi$
$762$		0			0
$763$	−15003.5	−	702.347i	−0.711878	−	0.0333246i
$764$	7912.00			0.374668
$765$		0			0
$766$	−2457.00	+	4255.65i	−0.115894	+	0.200735i
$767$	1400.00	−	2424.87i	0.0659075	−	0.114155i
$768$		0			0
$769$	−1118.00			−0.0524267			−0.0262133	−	0.999656i	$-0.508345\pi$
$769$	−1118.00			−0.0524267			−0.0262133	+	0.999656i	$0.508345\pi$
$770$	200.000	−	311.769i	0.00936039	−	0.0145914i
$771$		0			0
$772$	7996.00	+	13849.5i	0.372775	+	0.645665i
$773$	6716.00	−	11632.5i	0.312494	−	0.541255i	−0.666408	−	0.745587i	$-0.732169\pi$
$773$	6716.00	−	11632.5i	0.312494	−	0.541255i	0.978902	+	0.204332i	$0.0655023\pi$
$774$		0			0
$775$	4150.00	+	7188.01i	0.192351	+	0.333163i
$776$	−2320.00			−0.107324
$777$		0			0
$778$	−17124.0			−0.789107
$779$	4589.00	+	7948.38i	0.211063	+	0.365572i
$780$		0			0
$781$	770.000	−	1333.68i	0.0352788	−	0.0611047i
$782$	3484.00	+	6034.47i	0.159319	+	0.275949i
$783$		0			0
$784$	5464.00	+	512.687i	0.248907	+	0.0233549i
$785$	6130.00			0.278712
$786$		0			0
$787$	4674.50	−	8096.47i	0.211725	−	0.366719i	−0.740529	−	0.672024i	$-0.765425\pi$
$787$	4674.50	−	8096.47i	0.211725	−	0.366719i	0.952255	+	0.305305i	$0.0987584\pi$
$788$	−6060.00	+	10496.2i	−0.273958	+	0.474508i
$789$		0			0
$790$	11700.0			0.526921
$791$	−18445.0	−	35706.2i	−0.829113	−	1.60502i
$792$		0			0
$793$	−1868.00	−	3235.47i	−0.0836502	−	0.144886i
$794$	9842.00	−	17046.8i	0.439899	−	0.761927i
$795$		0			0
$796$	−712.000	−	1233.22i	−0.0317037	−	0.0549125i
$797$	28008.0			1.24479			0.622393	−	0.782705i	$-0.286161\pi$
$797$	28008.0			1.24479			0.622393	+	0.782705i	$0.286161\pi$
$798$		0			0
$799$	−4576.00			−0.202612
$800$	−400.000	−	692.820i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−8097.00	+	14024.4i	−0.356503	+	0.617480i
$803$	−628.000	−	1087.73i	−0.0275986	−	0.0478021i
$804$		0			0
$805$	6197.50	+	290.119i	0.271346	+	0.0127023i
$806$	5312.00			0.232143
$807$		0			0
$808$	−4932.00	+	8542.47i	−0.214737	+	0.371935i
$809$	9834.50	−	17033.9i	0.427395	−	0.740270i	−0.569246	−	0.822167i	$-0.692765\pi$
$809$	9834.50	−	17033.9i	0.427395	−	0.740270i	0.996641	+	0.0818975i	$0.0260980\pi$
$810$		0			0
$811$	31860.0			1.37948			0.689739	−	0.724059i	$-0.257725\pi$
$811$	31860.0			1.37948			0.689739	+	0.724059i	$0.257725\pi$
$812$	5106.00	+	239.023i	0.220672	+	0.0103301i
$813$		0			0
$814$	−392.000	−	678.964i	−0.0168791	−	0.0292355i
$815$	1650.00	−	2857.88i	0.0709165	−	0.122831i
$816$		0			0
$817$	4797.00	+	8308.65i	0.205417	+	0.355793i
$818$	30518.0			1.30445
$819$		0			0
$820$	−7060.00			−0.300666
$821$	1115.00	+	1931.24i	0.0473980	+	0.0820958i	0.888751	−	0.458390i	$-0.151574\pi$
$821$	1115.00	+	1931.24i	0.0473980	+	0.0820958i	−0.841353	+	0.540486i	$0.818240\pi$
$822$		0			0
$823$	−7401.50	+	12819.8i	−0.313487	+	0.542976i	−0.979115	−	0.203308i	$-0.934831\pi$
$823$	−7401.50	+	12819.8i	−0.313487	+	0.542976i	0.665627	+	0.746284i	$0.268164\pi$
$824$	−6212.00	−	10759.5i	−0.262628	−	0.454885i
$825$		0			0
$826$	5950.00	+	11518.1i	0.250638	+	0.485190i
$827$	−13257.0			−0.557426			−0.278713	−	0.960374i	$-0.589908\pi$
$827$	−13257.0			−0.557426			−0.278713	+	0.960374i	$0.589908\pi$
$828$		0			0
$829$	10787.0	−	18683.6i	0.451928	−	0.782762i	−0.546578	−	0.837408i	$-0.684070\pi$
$829$	10787.0	−	18683.6i	0.451928	−	0.782762i	0.998506	+	0.0546465i	$0.0174032\pi$
$830$	2625.00	−	4546.63i	0.109777	−	0.190140i
$831$		0			0
$832$	−512.000			−0.0213346
$833$	−7436.00	−	16212.0i	−0.309294	−	0.674325i
$834$		0			0
$835$	−2372.50	−	4109.29i	−0.0983278	−	0.170309i
$836$	−104.000	+	180.133i	−0.00430253	+	0.00745220i
$837$		0			0
$838$	16224.0	+	28100.8i	0.668793	+	1.15838i
$839$	−12990.0			−0.534523			−0.267261	−	0.963624i	$-0.586119\pi$
$839$	−12990.0			−0.534523			−0.267261	+	0.963624i	$0.586119\pi$
$840$		0			0
$841$	−19628.0			−0.804789
$842$	−2977.00	−	5156.32i	−0.121846	−	0.211043i
$843$		0			0
$844$	5204.00	−	9013.59i	0.212238	−	0.367607i
$845$	5332.50	+	9236.16i	0.217093	+	0.376016i
$846$		0			0
$847$	−13270.0	+	20685.9i	−0.538327	+	0.839168i
$848$	−9312.00			−0.377094
$849$		0			0
$850$	−1300.00	+	2251.67i	−0.0524584	+	0.0908606i
$851$	6566.00	−	11372.6i	0.264488	−	0.458107i
$852$		0			0
$853$	24838.0			0.996995			0.498498	−	0.866891i	$-0.333885\pi$
$853$	24838.0			0.996995			0.498498	+	0.866891i	$0.333885\pi$
$854$	17279.0	+	808.868i	0.692360	+	0.0324109i
$855$		0			0
$856$	7324.00	+	12685.5i	0.292441	+	0.506522i
$857$	−8513.00	+	14744.9i	−0.339322	+	0.587722i	−0.984305	−	0.176474i	$-0.943531\pi$
$857$	−8513.00	+	14744.9i	−0.339322	+	0.587722i	0.644984	+	0.764196i	$0.276864\pi$
$858$		0			0
$859$	−3364.00	−	5826.62i	−0.133618	−	0.231434i	0.791450	−	0.611233i	$-0.209326\pi$
$859$	−3364.00	−	5826.62i	−0.133618	−	0.231434i	−0.925069	+	0.379800i	$0.875993\pi$
$860$	−7380.00			−0.292623
$861$		0			0
$862$	−28404.0			−1.12232
$863$	−15049.5	−	26066.5i	−0.593616	−	1.02817i	−0.993741	−	0.111713i	$-0.964366\pi$
$863$	−15049.5	−	26066.5i	−0.593616	−	1.02817i	0.400124	−	0.916461i	$-0.368967\pi$
$864$		0			0
$865$	8480.00	−	14687.8i	0.333328	−	0.577341i
$866$	−14310.0	−	24785.6i	−0.561517	−	0.972576i
$867$		0			0
$868$	−13280.0	+	20701.5i	−0.519300	+	0.809509i
$869$	2340.00			0.0913453
$870$		0			0
$871$	1164.00	−	2016.11i	0.0452820	−	0.0784308i
$872$	−3244.00	+	5618.77i	−0.125981	+	0.218206i
$873$		0			0
$874$	−3484.00			−0.134838
$875$	1062.50	+	2056.81i	0.0410503	+	0.0794661i
$876$		0			0
$877$	2813.00	+	4872.26i	0.108310	+	0.187599i	0.915086	−	0.403259i	$-0.132123\pi$
$877$	2813.00	+	4872.26i	0.108310	+	0.187599i	−0.806775	+	0.590858i	$0.798789\pi$
$878$	2356.00	−	4080.71i	0.0905594	−	0.156853i
$879$		0			0
$880$	−80.0000	−	138.564i	−0.00306454	−	0.00530795i
$881$	15927.0			0.609074			0.304537	−	0.952500i	$-0.401498\pi$
$881$	15927.0			0.609074			0.304537	+	0.952500i	$0.401498\pi$
$882$		0			0
$883$	39124.0			1.49108			0.745542	−	0.666458i	$-0.232191\pi$
$883$	39124.0			1.49108			0.745542	+	0.666458i	$0.232191\pi$
$884$	832.000	+	1441.07i	0.0316552	+	0.0548284i
$885$		0			0
$886$	8291.00	−	14360.4i	0.314381	−	0.544524i
$887$	−12665.5	−	21937.3i	−0.479443	−	0.830419i	0.520279	−	0.853996i	$-0.325828\pi$
$887$	−12665.5	−	21937.3i	−0.479443	−	0.830419i	−0.999722	+	0.0235768i	$0.992495\pi$
$888$		0			0
$889$	408.000	+	789.815i	0.0153924	+	0.0297970i
$890$	−890.000			−0.0335201
$891$		0			0
$892$	6312.00	−	10932.7i	0.236930	−	0.410374i
$893$	1144.00	−	1981.47i	0.0428695	−	0.0742522i
$894$		0			0
$895$	−1340.00			−0.0500461
$896$	1280.00	−	1995.32i	0.0477252	−	0.0743963i
$897$		0			0
$898$	−3521.00	−	6098.55i	−0.130843	−	0.226627i
$899$	−11454.0	+	19838.9i	−0.424930	+	0.736001i
$900$		0			0
$901$	15132.0	+	26209.4i	0.559512	+	0.969103i
$902$	−1412.00			−0.0521225
$903$		0			0
$904$	−17360.0			−0.638700
$905$	10232.5	+	17723.2i	0.375845	+	0.650983i
$906$		0			0
$907$	−13192.5	+	22850.1i	−0.482966	+	0.836521i	−0.999809	−	0.0195592i	$-0.993774\pi$
$907$	−13192.5	+	22850.1i	−0.482966	+	0.836521i	0.516843	+	0.856080i	$0.327107\pi$
$908$	8472.00	+	14673.9i	0.309640	+	0.536312i
$909$		0			0
$910$	1480.00	+	69.2820i	0.0539138	+	0.00252382i
$911$	40770.0			1.48273			0.741367	−	0.671100i	$-0.234178\pi$
$911$	40770.0			1.48273			0.741367	+	0.671100i	$0.234178\pi$
$912$		0			0
$913$	525.000	−	909.327i	0.0190306	−	0.0329620i
$914$	5432.00	−	9408.50i	0.196581	−	0.340487i
$915$		0			0
$916$	25336.0			0.913892
$917$	7920.00	−	12346.1i	0.285214	−	0.444605i
$918$		0			0
$919$	7309.00	+	12659.6i	0.262352	+	0.454407i	0.966867	−	0.255282i	$-0.0821685\pi$
$919$	7309.00	+	12659.6i	0.262352	+	0.454407i	−0.704514	+	0.709690i	$0.748835\pi$
$920$	1340.00	−	2320.95i	0.0480201	−	0.0831733i
$921$		0			0
$922$	−5350.00	−	9266.47i	−0.191099	−	0.330992i
$923$	6160.00			0.219674
$924$		0			0
$925$	4900.00			0.174174
$926$	10123.0	+	17533.6i	0.359247	+	0.622233i
$927$		0			0
$928$	1104.00	−	1912.18i	0.0390523	−	0.0676406i
$929$	20661.5	+	35786.8i	0.729690	+	1.26386i	0.957014	+	0.290041i	$0.0936689\pi$
$929$	20661.5	+	35786.8i	0.729690	+	1.26386i	−0.227324	+	0.973819i	$0.572998\pi$
$930$		0			0
$931$	8879.00	+	833.116i	0.312564	+	0.0293279i
$932$	18752.0			0.659058
$933$		0			0
$934$	6463.00	−	11194.2i	0.226420	−	0.392170i
$935$	−260.000	+	450.333i	−0.00909402	+	0.0157513i
$936$		0			0
$937$	−22620.0			−0.788648			−0.394324	−	0.918971i	$-0.629021\pi$
$937$	−22620.0			−0.788648			−0.394324	+	0.918971i	$0.629021\pi$
$938$	4947.00	+	9576.51i	0.172202	+	0.333352i
$939$		0			0
$940$	880.000	+	1524.20i	0.0305345	+	0.0528873i
$941$	25989.0	−	45014.3i	0.900337	−	1.55943i	0.0732801	−	0.997311i	$-0.476653\pi$
$941$	25989.0	−	45014.3i	0.900337	−	1.55943i	0.827057	−	0.562118i	$-0.190013\pi$
$942$		0			0
$943$	−11825.5	−	20482.4i	−0.408368	−	0.707315i
$944$	5600.00			0.193077
$945$		0			0
$946$	−1476.00			−0.0507282
$947$	4993.50	+	8649.00i	0.171348	+	0.296784i	0.938892	−	0.344213i	$-0.111854\pi$
$947$	4993.50	+	8649.00i	0.171348	+	0.296784i	−0.767543	+	0.640997i	$0.778521\pi$
$948$		0			0
$949$	2512.00	−	4350.91i	0.0859252	−	0.148827i
$950$	−650.000	−	1125.83i	−0.0221987	−	0.0384493i
$951$		0			0
$952$	−7696.00	−	360.267i	−0.262005	−	0.0122650i
$953$	−6588.00			−0.223931			−0.111966	−	0.993712i	$-0.535715\pi$
$953$	−6588.00			−0.223931			−0.111966	+	0.993712i	$0.535715\pi$
$954$		0			0
$955$	−4945.00	+	8564.99i	−0.167556	+	0.290216i
$956$	3712.00	−	6429.37i	0.125580	−	0.217511i
$957$		0			0
$958$	35280.0			1.18982
$959$	20054.0	+	938.772i	0.675263	+	0.0316105i
$960$		0			0
$961$	−40216.5	−	69657.0i	−1.34995	−	2.33819i
$962$	1568.00	−	2715.86i	0.0525513	−	0.0910215i
$963$		0			0
$964$	9612.00	+	16648.5i	0.321143	+	0.556236i
$965$	−19990.0			−0.666840
$966$		0			0
$967$	−4091.00			−0.136047			−0.0680236	−	0.997684i	$-0.521669\pi$
$967$	−4091.00			−0.136047			−0.0680236	+	0.997684i	$0.521669\pi$
$968$	5308.00	+	9193.73i	0.176245	+	0.305266i
$969$		0			0
$970$	1450.00	−	2511.47i	0.0479966	−	0.0831325i
$971$	11820.0	+	20472.8i	0.390651	+	0.676627i	0.992536	−	0.121956i	$-0.0389167\pi$
$971$	11820.0	+	20472.8i	0.390651	+	0.676627i	−0.601885	+	0.798583i	$0.705583\pi$
$972$		0			0
$973$	−391.000	−	756.906i	−0.0128827	−	0.0249386i
$974$	−20064.0			−0.660053
$975$		0			0
$976$	3736.00	−	6470.94i	0.122527	−	0.212223i
$977$	18333.0	−	31753.7i	0.600332	−	1.03981i	−0.392438	−	0.919778i	$-0.628368\pi$
$977$	18333.0	−	31753.7i	0.600332	−	1.03981i	0.992771	−	0.120028i	$-0.0382983\pi$
$978$		0			0
$979$	−178.000			−0.00581093
$980$	−3970.00	+	5594.52i	−0.129405	+	0.182358i
$981$		0			0
$982$	5916.00	+	10246.8i	0.192248	+	0.332983i
$983$	−20535.5	+	35568.5i	−0.666308	+	1.15408i	0.312621	+	0.949878i	$0.398793\pi$
$983$	−20535.5	+	35568.5i	−0.666308	+	1.15408i	−0.978929	+	0.204201i	$0.934540\pi$
$984$		0			0
$985$	−7575.00	−	13120.3i	−0.245035	−	0.424413i
$986$	−7176.00			−0.231775
$987$		0			0
$988$	−832.000			−0.0267909
$989$	−12361.5	−	21410.7i	−0.397445	−	0.688394i
$990$		0			0
$991$	−15992.0	+	27699.0i	−0.512616	+	0.887877i	0.487277	+	0.873248i	$0.337990\pi$
$991$	−15992.0	+	27699.0i	−0.512616	+	0.887877i	−0.999893	+	0.0146297i	$0.995343\pi$
$992$	5312.00	+	9200.65i	0.170016	+	0.294477i
$993$		0			0
$994$	−15400.0	+	24006.2i	−0.491407	+	0.766027i
$995$	1780.00			0.0567134
$996$		0			0
$997$	21947.0	−	38013.3i	0.697160	−	1.20752i	−0.272287	−	0.962216i	$-0.587780\pi$
$997$	21947.0	−	38013.3i	0.697160	−	1.20752i	0.969447	−	0.245300i	$-0.0788866\pi$
$998$	−13894.0	+	24065.1i	−0.440688	+	0.763294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.k.b.361.1		2
3.2	odd	2		70.4.e.c.11.1	✓	2
7.2	even	3	inner	630.4.k.b.541.1		2
12.11	even	2		560.4.q.d.81.1		2
15.2	even	4		350.4.j.e.249.1		4
15.8	even	4		350.4.j.e.249.2		4
15.14	odd	2		350.4.e.a.151.1		2
21.2	odd	6		70.4.e.c.51.1	yes	2
21.5	even	6		490.4.e.m.471.1		2
21.11	odd	6		490.4.a.c.1.1		1
21.17	even	6		490.4.a.e.1.1		1
21.20	even	2		490.4.e.m.361.1		2
84.23	even	6		560.4.q.d.401.1		2
105.2	even	12		350.4.j.e.149.2		4
105.23	even	12		350.4.j.e.149.1		4
105.44	odd	6		350.4.e.a.51.1		2
105.59	even	6		2450.4.a.be.1.1		1
105.74	odd	6		2450.4.a.bg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.c.11.1	✓	2	3.2	odd	2
70.4.e.c.51.1	yes	2	21.2	odd	6
350.4.e.a.51.1		2	105.44	odd	6
350.4.e.a.151.1		2	15.14	odd	2
350.4.j.e.149.1		4	105.23	even	12
350.4.j.e.149.2		4	105.2	even	12
350.4.j.e.249.1		4	15.2	even	4
350.4.j.e.249.2		4	15.8	even	4
490.4.a.c.1.1		1	21.11	odd	6
490.4.a.e.1.1		1	21.17	even	6
490.4.e.m.361.1		2	21.20	even	2
490.4.e.m.471.1		2	21.5	even	6
560.4.q.d.81.1		2	12.11	even	2
560.4.q.d.401.1		2	84.23	even	6
630.4.k.b.361.1		2	1.1	even	1	trivial
630.4.k.b.541.1		2	7.2	even	3	inner
2450.4.a.be.1.1		1	105.59	even	6
2450.4.a.bg.1.1		1	105.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(8.50000 + 16.4545i) q^{7} +8.00000 q^{8} +(-5.00000 + 8.66025i) q^{10} +(-1.00000 + 1.73205i) q^{11} -8.00000 q^{13} +(20.0000 - 31.1769i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-26.0000 + 45.0333i) q^{17} +(-13.0000 - 22.5167i) q^{19} +20.0000 q^{20} +4.00000 q^{22} +(33.5000 + 58.0237i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(8.00000 + 13.8564i) q^{26} +(-74.0000 - 3.46410i) q^{28} -69.0000 q^{29} +(166.000 - 287.520i) q^{31} +(-16.0000 + 27.7128i) q^{32} +104.000 q^{34} +(50.0000 - 77.9423i) q^{35} +(-98.0000 - 169.741i) q^{37} +(-26.0000 + 45.0333i) q^{38} +(-20.0000 - 34.6410i) q^{40} -353.000 q^{41} -369.000 q^{43} +(-4.00000 - 6.92820i) q^{44} +(67.0000 - 116.047i) q^{46} +(44.0000 + 76.2102i) q^{47} +(-198.500 + 279.726i) q^{49} +50.0000 q^{50} +(16.0000 - 27.7128i) q^{52} +(291.000 - 504.027i) q^{53} +10.0000 q^{55} +(68.0000 + 131.636i) q^{56} +(69.0000 + 119.512i) q^{58} +(-175.000 + 303.109i) q^{59} +(233.500 + 404.434i) q^{61} -664.000 q^{62} +64.0000 q^{64} +(20.0000 + 34.6410i) q^{65} +(-145.500 + 252.013i) q^{67} +(-104.000 - 180.133i) q^{68} +(-185.000 - 8.66025i) q^{70} -770.000 q^{71} +(-314.000 + 543.864i) q^{73} +(-196.000 + 339.482i) q^{74} +104.000 q^{76} +(-37.0000 - 1.73205i) q^{77} +(-585.000 - 1013.25i) q^{79} +(-40.0000 + 69.2820i) q^{80} +(353.000 + 611.414i) q^{82} -525.000 q^{83} +260.000 q^{85} +(369.000 + 639.127i) q^{86} +(-8.00000 + 13.8564i) q^{88} +(44.5000 + 77.0763i) q^{89} +(-68.0000 - 131.636i) q^{91} -268.000 q^{92} +(88.0000 - 152.420i) q^{94} +(-65.0000 + 112.583i) q^{95} -290.000 q^{97} +(683.000 + 64.0859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} - 5 q^{5} + 17 q^{7} + 16 q^{8} - 10 q^{10} - 2 q^{11} - 16 q^{13} + 40 q^{14} - 16 q^{16} - 52 q^{17} - 26 q^{19} + 40 q^{20} + 8 q^{22} + 67 q^{23} - 25 q^{25} + 16 q^{26} - 148 q^{28}+ \cdots + 1366 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 - 5 * q^5 + 17 * q^7 + 16 * q^8 - 10 * q^10 - 2 * q^11 - 16 * q^13 + 40 * q^14 - 16 * q^16 - 52 * q^17 - 26 * q^19 + 40 * q^20 + 8 * q^22 + 67 * q^23 - 25 * q^25 + 16 * q^26 - 148 * q^28 - 138 * q^29 + 332 * q^31 - 32 * q^32 + 208 * q^34 + 100 * q^35 - 196 * q^37 - 52 * q^38 - 40 * q^40 - 706 * q^41 - 738 * q^43 - 8 * q^44 + 134 * q^46 + 88 * q^47 - 397 * q^49 + 100 * q^50 + 32 * q^52 + 582 * q^53 + 20 * q^55 + 136 * q^56 + 138 * q^58 - 350 * q^59 + 467 * q^61 - 1328 * q^62 + 128 * q^64 + 40 * q^65 - 291 * q^67 - 208 * q^68 - 370 * q^70 - 1540 * q^71 - 628 * q^73 - 392 * q^74 + 208 * q^76 - 74 * q^77 - 1170 * q^79 - 80 * q^80 + 706 * q^82 - 1050 * q^83 + 520 * q^85 + 738 * q^86 - 16 * q^88 + 89 * q^89 - 136 * q^91 - 536 * q^92 + 176 * q^94 - 130 * q^95 - 580 * q^97 + 1366 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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