LMFDB - Embedded newform 490.4.e.m.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.4.e.m.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 - 22.5167i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 - 22.5167i) q^{9} +(5.00000 + 8.66025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-2.00000 + 3.46410i) q^{12} +8.00000 q^{13} +5.00000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-26.0000 - 45.0333i) q^{17} +(-26.0000 - 45.0333i) q^{18} +(13.0000 - 22.5167i) q^{19} +20.0000 q^{20} +4.00000 q^{22} +(-33.5000 + 58.0237i) q^{23} +(4.00000 + 6.92820i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(8.00000 - 13.8564i) q^{26} -53.0000 q^{27} +69.0000 q^{29} +(5.00000 - 8.66025i) q^{30} +(-166.000 - 287.520i) q^{31} +(16.0000 + 27.7128i) q^{32} +(1.00000 - 1.73205i) q^{33} -104.000 q^{34} -104.000 q^{36} +(-98.0000 + 169.741i) q^{37} +(-26.0000 - 45.0333i) q^{38} +(-4.00000 - 6.92820i) q^{39} +(20.0000 - 34.6410i) q^{40} -353.000 q^{41} -369.000 q^{43} +(4.00000 - 6.92820i) q^{44} +(65.0000 + 112.583i) q^{45} +(67.0000 + 116.047i) q^{46} +(44.0000 - 76.2102i) q^{47} +16.0000 q^{48} -50.0000 q^{50} +(-26.0000 + 45.0333i) q^{51} +(-16.0000 - 27.7128i) q^{52} +(-291.000 - 504.027i) q^{53} +(-53.0000 + 91.7987i) q^{54} -10.0000 q^{55} -26.0000 q^{57} +(69.0000 - 119.512i) q^{58} +(-175.000 - 303.109i) q^{59} +(-10.0000 - 17.3205i) q^{60} +(-233.500 + 404.434i) q^{61} -664.000 q^{62} +64.0000 q^{64} +(-20.0000 + 34.6410i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(-145.500 - 252.013i) q^{67} +(-104.000 + 180.133i) q^{68} +67.0000 q^{69} +770.000 q^{71} +(-104.000 + 180.133i) q^{72} +(314.000 + 543.864i) q^{73} +(196.000 + 339.482i) q^{74} +(-12.5000 + 21.6506i) q^{75} -104.000 q^{76} -16.0000 q^{78} +(-585.000 + 1013.25i) q^{79} +(-40.0000 - 69.2820i) q^{80} +(-324.500 - 562.050i) q^{81} +(-353.000 + 611.414i) q^{82} -525.000 q^{83} +260.000 q^{85} +(-369.000 + 639.127i) q^{86} +(-34.5000 - 59.7558i) q^{87} +(-8.00000 - 13.8564i) q^{88} +(44.5000 - 77.0763i) q^{89} +260.000 q^{90} +268.000 q^{92} +(-166.000 + 287.520i) q^{93} +(-88.0000 - 152.420i) q^{94} +(65.0000 + 112.583i) q^{95} +(16.0000 - 27.7128i) q^{96} +290.000 q^{97} +52.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} - 4 q^{4} - 5 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 - 4 * q^4 - 5 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9	\( 2 q + 2 q^{2} - q^{3} - 4 q^{4} - 5 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9} + 10 q^{10} + 2 q^{11} - 4 q^{12} + 16 q^{13} + 10 q^{15} - 16 q^{16} - 52 q^{17} - 52 q^{18} + 26 q^{19} + 40 q^{20} + 8 q^{22} - 67 q^{23} + 8 q^{24} - 25 q^{25} + 16 q^{26} - 106 q^{27} + 138 q^{29} + 10 q^{30} - 332 q^{31} + 32 q^{32} + 2 q^{33} - 208 q^{34} - 208 q^{36} - 196 q^{37} - 52 q^{38} - 8 q^{39} + 40 q^{40} - 706 q^{41} - 738 q^{43} + 8 q^{44} + 130 q^{45} + 134 q^{46} + 88 q^{47} + 32 q^{48} - 100 q^{50} - 52 q^{51} - 32 q^{52} - 582 q^{53} - 106 q^{54} - 20 q^{55} - 52 q^{57} + 138 q^{58} - 350 q^{59} - 20 q^{60} - 467 q^{61} - 1328 q^{62} + 128 q^{64} - 40 q^{65} - 4 q^{66} - 291 q^{67} - 208 q^{68} + 134 q^{69} + 1540 q^{71} - 208 q^{72} + 628 q^{73} + 392 q^{74} - 25 q^{75} - 208 q^{76} - 32 q^{78} - 1170 q^{79} - 80 q^{80} - 649 q^{81} - 706 q^{82} - 1050 q^{83} + 520 q^{85} - 738 q^{86} - 69 q^{87} - 16 q^{88} + 89 q^{89} + 520 q^{90} + 536 q^{92} - 332 q^{93} - 176 q^{94} + 130 q^{95} + 32 q^{96} + 580 q^{97} + 104 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 - 4 * q^4 - 5 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9 + 10 * q^10 + 2 * q^11 - 4 * q^12 + 16 * q^13 + 10 * q^15 - 16 * q^16 - 52 * q^17 - 52 * q^18 + 26 * q^19 + 40 * q^20 + 8 * q^22 - 67 * q^23 + 8 * q^24 - 25 * q^25 + 16 * q^26 - 106 * q^27 + 138 * q^29 + 10 * q^30 - 332 * q^31 + 32 * q^32 + 2 * q^33 - 208 * q^34 - 208 * q^36 - 196 * q^37 - 52 * q^38 - 8 * q^39 + 40 * q^40 - 706 * q^41 - 738 * q^43 + 8 * q^44 + 130 * q^45 + 134 * q^46 + 88 * q^47 + 32 * q^48 - 100 * q^50 - 52 * q^51 - 32 * q^52 - 582 * q^53 - 106 * q^54 - 20 * q^55 - 52 * q^57 + 138 * q^58 - 350 * q^59 - 20 * q^60 - 467 * q^61 - 1328 * q^62 + 128 * q^64 - 40 * q^65 - 4 * q^66 - 291 * q^67 - 208 * q^68 + 134 * q^69 + 1540 * q^71 - 208 * q^72 + 628 * q^73 + 392 * q^74 - 25 * q^75 - 208 * q^76 - 32 * q^78 - 1170 * q^79 - 80 * q^80 - 649 * q^81 - 706 * q^82 - 1050 * q^83 + 520 * q^85 - 738 * q^86 - 69 * q^87 - 16 * q^88 + 89 * q^89 + 520 * q^90 + 536 * q^92 - 332 * q^93 - 176 * q^94 + 130 * q^95 + 32 * q^96 + 580 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i	0.813894	−	0.581013i	$-0.197344\pi$
$3$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i	−0.910119	+	0.414346i	$0.864010\pi$
$4$	−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
$6$	−2.00000			−0.136083
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	13.0000	−	22.5167i	0.481481	−	0.833950i
$10$	5.00000	+	8.66025i	0.158114	+	0.273861i
$11$	1.00000	+	1.73205i	0.0274101	+	0.0474757i	0.879405	−	0.476074i	$-0.157941\pi$
$11$	1.00000	+	1.73205i	0.0274101	+	0.0474757i	−0.851995	+	0.523550i	$0.824607\pi$
$12$	−2.00000	+	3.46410i	−0.0481125	+	0.0833333i
$13$	8.00000			0.170677			0.0853385	−	0.996352i	$-0.472803\pi$
$13$	8.00000			0.170677			0.0853385	+	0.996352i	$0.472803\pi$
$14$		0			0
$15$	5.00000			0.0860663
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−26.0000	−	45.0333i	−0.370937	−	0.642481i	0.618773	−	0.785570i	$-0.287630\pi$
$17$	−26.0000	−	45.0333i	−0.370937	−	0.642481i	−0.989710	+	0.143088i	$0.954297\pi$
$18$	−26.0000	−	45.0333i	−0.340459	−	0.589692i
$19$	13.0000	−	22.5167i	0.156969	−	0.271878i	−0.776805	−	0.629741i	$-0.783161\pi$
$19$	13.0000	−	22.5167i	0.156969	−	0.271878i	0.933774	+	0.357863i	$0.116495\pi$
$20$	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	$-0.931557\pi$
$23$	−33.5000	+	58.0237i	−0.303706	+	0.526034i	0.673267	+	0.739400i	$0.264891\pi$
$24$	4.00000	+	6.92820i	0.0340207	+	0.0589256i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	8.00000	−	13.8564i	0.0603434	−	0.104518i
$27$	−53.0000			−0.377772
$28$		0			0
$29$	69.0000			0.441827			0.220913	−	0.975293i	$-0.429096\pi$
$29$	69.0000			0.441827			0.220913	+	0.975293i	$0.429096\pi$
$30$	5.00000	−	8.66025i	0.0304290	−	0.0527046i
$31$	−166.000	−	287.520i	−0.961757	−	1.66581i	−0.718085	−	0.695955i	$-0.754981\pi$
$31$	−166.000	−	287.520i	−0.961757	−	1.66581i	−0.243672	−	0.969858i	$-0.578352\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	1.00000	−	1.73205i	0.00527508	−	0.00913671i
$34$	−104.000			−0.524584
$35$		0			0
$36$	−104.000			−0.481481
$37$	−98.0000	+	169.741i	−0.435435	+	0.754196i	−0.997331	−	0.0730121i	$-0.976739\pi$
$37$	−98.0000	+	169.741i	−0.435435	+	0.754196i	0.561896	+	0.827208i	$0.310072\pi$
$38$	−26.0000	−	45.0333i	−0.110994	−	0.192247i
$39$	−4.00000	−	6.92820i	−0.0164234	−	0.0284462i
$40$	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
$45$	65.0000	+	112.583i	0.215325	+	0.372954i
$46$	67.0000	+	116.047i	0.214752	+	0.371962i
$47$	44.0000	−	76.2102i	0.136554	−	0.236519i	−0.789636	−	0.613576i	$-0.789730\pi$
$47$	44.0000	−	76.2102i	0.136554	−	0.236519i	0.926190	+	0.377057i	$0.123064\pi$
$48$	16.0000			0.0481125
$49$		0			0
$50$	−50.0000			−0.141421
$51$	−26.0000	+	45.0333i	−0.0713868	+	0.123646i
$52$	−16.0000	−	27.7128i	−0.0426692	−	0.0739053i
$53$	−291.000	−	504.027i	−0.754187	−	1.30629i	−0.945777	−	0.324816i	$-0.894698\pi$
$53$	−291.000	−	504.027i	−0.754187	−	1.30629i	0.191590	−	0.981475i	$-0.438636\pi$
$54$	−53.0000	+	91.7987i	−0.133563	+	0.231337i
$55$	−10.0000			−0.0245164
$56$		0			0
$57$	−26.0000			−0.0604173
$58$	69.0000	−	119.512i	0.156209	−	0.270563i
$59$	−175.000	−	303.109i	−0.386154	−	0.668838i	0.605775	−	0.795636i	$-0.292863\pi$
$59$	−175.000	−	303.109i	−0.386154	−	0.668838i	−0.991928	+	0.126798i	$0.959530\pi$
$60$	−10.0000	−	17.3205i	−0.0215166	−	0.0372678i
$61$	−233.500	+	404.434i	−0.490108	+	0.848893i	−0.999935	−	0.0113844i	$-0.996376\pi$
$61$	−233.500	+	404.434i	−0.490108	+	0.848893i	0.509827	+	0.860277i	$0.329709\pi$
$62$	−664.000			−1.36013
$63$		0			0
$64$	64.0000			0.125000
$65$	−20.0000	+	34.6410i	−0.0381645	+	0.0661029i
$66$	−2.00000	−	3.46410i	−0.00373005	−	0.00646063i
$67$	−145.500	−	252.013i	−0.265308	−	0.459527i	0.702336	−	0.711846i	$-0.252140\pi$
$67$	−145.500	−	252.013i	−0.265308	−	0.459527i	−0.967644	+	0.252318i	$0.918807\pi$
$68$	−104.000	+	180.133i	−0.185468	+	0.321241i
$69$	67.0000			0.116896
$70$		0			0
$71$	770.000			1.28707			0.643537	−	0.765415i	$-0.277466\pi$
$71$	770.000			1.28707			0.643537	+	0.765415i	$0.277466\pi$
$72$	−104.000	+	180.133i	−0.170229	+	0.294846i
$73$	314.000	+	543.864i	0.503437	+	0.871979i	0.999992	+	0.00397357i	$0.00126483\pi$
$73$	314.000	+	543.864i	0.503437	+	0.871979i	−0.496555	+	0.868005i	$0.665402\pi$
$74$	196.000	+	339.482i	0.307899	+	0.533297i
$75$	−12.5000	+	21.6506i	−0.0192450	+	0.0333333i
$76$	−104.000			−0.156969
$77$		0			0
$78$	−16.0000			−0.0232262
$79$	−585.000	+	1013.25i	−0.833135	+	1.44303i	0.0624054	+	0.998051i	$0.480123\pi$
$79$	−585.000	+	1013.25i	−0.833135	+	1.44303i	−0.895540	+	0.444981i	$0.853211\pi$
$80$	−40.0000	−	69.2820i	−0.0559017	−	0.0968246i
$81$	−324.500	−	562.050i	−0.445130	−	0.770988i
$82$	−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
$87$	−34.5000	−	59.7558i	−0.0425148	−	0.0736378i
$88$	−8.00000	−	13.8564i	−0.00969094	−	0.0167852i
$89$	44.5000	−	77.0763i	0.0529999	−	0.0917985i	−0.838308	−	0.545197i	$-0.816455\pi$
$89$	44.5000	−	77.0763i	0.0529999	−	0.0917985i	0.891308	+	0.453398i	$0.149788\pi$
$90$	260.000			0.304516
$91$		0			0
$92$	268.000			0.303706
$93$	−166.000	+	287.520i	−0.185090	+	0.320586i
$94$	−88.0000	−	152.420i	−0.0965586	−	0.167244i
$95$	65.0000	+	112.583i	0.0701985	+	0.121587i
$96$	16.0000	−	27.7128i	0.0170103	−	0.0294628i
$97$	290.000			0.303557			0.151779	−	0.988415i	$-0.451500\pi$
$97$	290.000			0.303557			0.151779	+	0.988415i	$0.451500\pi$
$98$		0			0
$99$	52.0000			0.0527899
$100$	−50.0000	+	86.6025i	−0.0500000	+	0.0866025i
$101$	−616.500	−	1067.81i	−0.607367	−	1.05199i	−0.991673	−	0.128784i	$-0.958893\pi$
$101$	−616.500	−	1067.81i	−0.607367	−	1.05199i	0.384306	−	0.923206i	$-0.374441\pi$
$102$	52.0000	+	90.0666i	0.0504781	+	0.0874307i
$103$	776.500	−	1344.94i	0.742823	−	1.28661i	−0.208381	−	0.978048i	$-0.566819\pi$
$103$	776.500	−	1344.94i	0.742823	−	1.28661i	0.951205	−	0.308560i	$-0.0998472\pi$
$104$	−64.0000			−0.0603434
$105$		0			0
$106$	−1164.00			−1.06658
$107$	−915.500	+	1585.69i	−0.827147	+	1.43266i	0.0731204	+	0.997323i	$0.476704\pi$
$107$	−915.500	+	1585.69i	−0.827147	+	1.43266i	−0.900267	+	0.435337i	$0.856629\pi$
$108$	106.000	+	183.597i	0.0944431	+	0.163580i
$109$	−405.500	−	702.347i	−0.356329	−	0.617180i	0.631016	−	0.775770i	$-0.282638\pi$
$109$	−405.500	−	702.347i	−0.356329	−	0.617180i	−0.987344	+	0.158590i	$0.949305\pi$
$110$	−10.0000	+	17.3205i	−0.00866784	+	0.0150131i
$111$	196.000			0.167599
$112$		0			0
$113$	2170.00			1.80652			0.903259	−	0.429097i	$-0.141168\pi$
$113$	2170.00			1.80652			0.903259	+	0.429097i	$0.141168\pi$
$114$	−26.0000	+	45.0333i	−0.0213607	+	0.0369979i
$115$	−167.500	−	290.119i	−0.135821	−	0.235249i
$116$	−138.000	−	239.023i	−0.110457	−	0.191317i
$117$	104.000	−	180.133i	0.0821778	−	0.142336i
$118$	−700.000			−0.546104
$119$		0			0
$120$	−40.0000			−0.0304290
$121$	663.500	−	1149.22i	0.498497	−	0.863423i
$122$	467.000	+	808.868i	0.346559	+	0.600258i
$123$	176.500	+	305.707i	0.129386	+	0.224103i
$124$	−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
$129$	184.500	+	319.563i	0.125925	+	0.218108i
$130$	40.0000	+	69.2820i	0.0269864	+	0.0467418i
$131$	−396.000	+	685.892i	−0.264112	+	0.457456i	−0.967331	−	0.253518i	$-0.918412\pi$
$131$	−396.000	+	685.892i	−0.264112	+	0.457456i	0.703219	+	0.710974i	$0.251746\pi$
$132$	−8.00000			−0.00527508
$133$		0			0
$134$	−582.000			−0.375203
$135$	132.500	−	229.497i	0.0844725	−	0.146311i
$136$	208.000	+	360.267i	0.131146	+	0.227151i
$137$	−542.000	−	938.772i	−0.338001	−	0.585436i	0.646055	−	0.763291i	$-0.276418\pi$
$137$	−542.000	−	938.772i	−0.338001	−	0.585436i	−0.984057	+	0.177855i	$0.943084\pi$
$138$	67.0000	−	116.047i	0.0413291	−	0.0715841i
$139$	46.0000			0.0280696			0.0140348	−	0.999902i	$-0.495532\pi$
$139$	46.0000			0.0280696			0.0140348	+	0.999902i	$0.495532\pi$
$140$		0			0
$141$	−88.0000			−0.0525598
$142$	770.000	−	1333.68i	0.455049	−	0.788168i
$143$	8.00000	+	13.8564i	0.00467828	+	0.00810301i
$144$	208.000	+	360.267i	0.120370	+	0.208488i
$145$	−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	$-0.800988\pi$
$149$	184.500	−	319.563i	0.101442	−	0.175702i	0.912279	+	0.409570i	$0.134321\pi$
$150$	25.0000	+	43.3013i	0.0136083	+	0.0235702i
$151$	−1240.00	−	2147.74i	−0.668277	−	1.15749i	−0.978386	−	0.206788i	$-0.933699\pi$
$151$	−1240.00	−	2147.74i	−0.668277	−	1.15749i	0.310109	−	0.950701i	$-0.399634\pi$
$152$	−104.000	+	180.133i	−0.0554968	+	0.0961233i
$153$	−1352.00			−0.714397
$154$		0			0
$155$	1660.00			0.860222
$156$	−16.0000	+	27.7128i	−0.00821170	+	0.0142231i
$157$	613.000	+	1061.75i	0.311610	+	0.539724i	0.978711	−	0.205243i	$-0.0657985\pi$
$157$	613.000	+	1061.75i	0.311610	+	0.539724i	−0.667101	+	0.744967i	$0.732465\pi$
$158$	1170.00	+	2026.50i	0.589115	+	1.02038i
$159$	−291.000	+	504.027i	−0.145143	+	0.251396i
$160$	−160.000			−0.0790569
$161$		0			0
$162$	−1298.00			−0.629509
$163$	330.000	−	571.577i	0.158574	−	0.274659i	−0.775781	−	0.631003i	$-0.782644\pi$
$163$	330.000	−	571.577i	0.158574	−	0.274659i	0.934355	+	0.356344i	$0.115977\pi$
$164$	706.000	+	1222.83i	0.336154	+	0.582237i
$165$	5.00000	+	8.66025i	0.00235909	+	0.00408606i
$166$	−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
$171$	−338.000	−	585.433i	−0.151155	−	0.261808i
$172$	738.000	+	1278.25i	0.327163	+	0.566662i
$173$	1696.00	−	2937.56i	0.745344	−	1.29097i	−0.204690	−	0.978827i	$-0.565619\pi$
$173$	1696.00	−	2937.56i	0.745344	−	1.29097i	0.950034	−	0.312147i	$-0.101048\pi$
$174$	−138.000			−0.0601250
$175$		0			0
$176$	−32.0000			−0.0137051
$177$	−175.000	+	303.109i	−0.0743153	+	0.128718i
$178$	−89.0000	−	154.153i	−0.0374766	−	0.0649113i
$179$	−134.000	−	232.095i	−0.0559532	−	0.0969139i	0.836692	−	0.547674i	$-0.184486\pi$
$179$	−134.000	−	232.095i	−0.0559532	−	0.0969139i	−0.892645	+	0.450760i	$0.851153\pi$
$180$	260.000	−	450.333i	0.107663	−	0.186477i
$181$	4093.00			1.68083			0.840415	−	0.541943i	$-0.182311\pi$
$181$	4093.00			1.68083			0.840415	+	0.541943i	$0.182311\pi$
$182$		0			0
$183$	467.000			0.188643
$184$	268.000	−	464.190i	0.107376	−	0.185981i
$185$	−490.000	−	848.705i	−0.194733	−	0.337287i
$186$	332.000	+	575.041i	0.130879	+	0.226688i
$187$	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	$-0.711090\pi$
$191$	989.000	−	1713.00i	0.374668	−	0.648943i	0.990277	+	0.139108i	$0.0444235\pi$
$192$	−32.0000	−	55.4256i	−0.0120281	−	0.0208333i
$193$	1999.00	+	3462.37i	0.745550	+	1.29133i	0.949937	+	0.312441i	$0.101146\pi$
$193$	1999.00	+	3462.37i	0.745550	+	1.29133i	−0.204387	+	0.978890i	$0.565520\pi$
$194$	290.000	−	502.295i	0.107324	−	0.185890i
$195$	40.0000			0.0146895
$196$		0			0
$197$	−3030.00			−1.09583			−0.547915	−	0.836534i	$-0.684578\pi$
$197$	−3030.00			−1.09583			−0.547915	+	0.836534i	$0.684578\pi$
$198$	52.0000	−	90.0666i	0.0186640	−	0.0323271i
$199$	178.000	+	308.305i	0.0634075	+	0.109825i	0.895986	−	0.444081i	$-0.146470\pi$
$199$	178.000	+	308.305i	0.0634075	+	0.109825i	−0.832579	+	0.553906i	$0.813137\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$	−145.500	+	252.013i	−0.0510586	+	0.0884361i
$202$	−2466.00			−0.858946
$203$		0			0
$204$	208.000			0.0713868
$205$	882.500	−	1528.53i	0.300666	−	0.520768i
$206$	−1553.00	−	2689.87i	−0.525256	−	0.909769i
$207$	871.000	+	1508.62i	0.292457	+	0.506551i
$208$	−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
$213$	−385.000	−	666.840i	−0.123849	−	0.214512i
$214$	1831.00	+	3171.39i	0.584881	+	1.01304i
$215$	922.500	−	1597.82i	0.292623	−	0.506838i
$216$	424.000			0.133563
$217$		0			0
$218$	−1622.00			−0.503925
$219$	314.000	−	543.864i	0.0968865	−	0.167812i
$220$	20.0000	+	34.6410i	0.00612909	+	0.0106159i
$221$	−208.000	−	360.267i	−0.0633104	−	0.109657i
$222$	196.000	−	339.482i	0.0592552	−	0.102633i
$223$	3156.00			0.947719			0.473860	−	0.880600i	$-0.342860\pi$
$223$	3156.00			0.947719			0.473860	+	0.880600i	$0.342860\pi$
$224$		0			0
$225$	−650.000			−0.192593
$226$	2170.00	−	3758.55i	0.638700	−	1.10626i
$227$	2118.00	+	3668.48i	0.619280	+	1.07262i	0.989617	+	0.143727i	$0.0459088\pi$
$227$	2118.00	+	3668.48i	0.619280	+	1.07262i	−0.370337	+	0.928897i	$0.620758\pi$
$228$	52.0000	+	90.0666i	0.0151043	+	0.0261614i
$229$	3167.00	−	5485.40i	0.913892	−	1.58291i	0.105376	−	0.994432i	$-0.466395\pi$
$229$	3167.00	−	5485.40i	0.913892	−	1.58291i	0.808516	−	0.588475i	$-0.200271\pi$
$230$	−670.000			−0.192080
$231$		0			0
$232$	−552.000			−0.156209
$233$	2344.00	−	4059.93i	0.659058	−	1.14152i	−0.321802	−	0.946807i	$-0.604288\pi$
$233$	2344.00	−	4059.93i	0.659058	−	1.14152i	0.980860	−	0.194715i	$-0.0623782\pi$
$234$	−208.000	−	360.267i	−0.0581085	−	0.100647i
$235$	220.000	+	381.051i	0.0610690	+	0.105775i
$236$	−700.000	+	1212.44i	−0.193077	+	0.334419i
$237$	1170.00			0.320674
$238$		0			0
$239$	1856.00			0.502321			0.251160	−	0.967945i	$-0.419188\pi$
$239$	1856.00			0.502321			0.251160	+	0.967945i	$0.419188\pi$
$240$	−40.0000	+	69.2820i	−0.0107583	+	0.0186339i
$241$	−2403.00	−	4162.12i	−0.642286	−	1.11247i	−0.984921	−	0.173003i	$-0.944653\pi$
$241$	−2403.00	−	4162.12i	−0.642286	−	1.11247i	0.342636	−	0.939468i	$-0.388680\pi$
$242$	−1327.00	−	2298.43i	−0.352491	−	0.610532i
$243$	−1040.00	+	1801.33i	−0.274552	+	0.475537i
$244$	1868.00			0.490108
$245$		0			0
$246$	706.000			0.182979
$247$	104.000	−	180.133i	0.0267909	−	0.0464033i
$248$	1328.00	+	2300.16i	0.340033	+	0.588954i
$249$	262.500	+	454.663i	0.0668083	+	0.115715i
$250$	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
$255$	−130.000	−	225.167i	−0.0319252	−	0.0552960i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−560.000	+	969.948i	−0.135922	+	0.235423i	−0.925949	−	0.377648i	$-0.876733\pi$
$257$	−560.000	+	969.948i	−0.135922	+	0.235423i	0.790028	+	0.613071i	$0.210066\pi$
$258$	738.000			0.178085
$259$		0			0
$260$	160.000			0.0381645
$261$	897.000	−	1553.65i	0.212731	−	0.368462i
$262$	792.000	+	1371.78i	0.186755	+	0.323470i
$263$	−3202.50	−	5546.89i	−0.750854	−	1.30052i	−0.947409	−	0.320025i	$-0.896309\pi$
$263$	−3202.50	−	5546.89i	−0.750854	−	1.30052i	0.196555	−	0.980493i	$-0.437025\pi$
$264$	−8.00000	+	13.8564i	−0.00186502	+	0.00323031i
$265$	2910.00			0.674566
$266$		0			0
$267$	−89.0000			−0.0203997
$268$	−582.000	+	1008.05i	−0.132654	+	0.229764i
$269$	2467.50	+	4273.84i	0.559279	+	0.968700i	0.997557	+	0.0698604i	$0.0222554\pi$
$269$	2467.50	+	4273.84i	0.559279	+	0.968700i	−0.438277	+	0.898840i	$0.644411\pi$
$270$	−265.000	−	458.993i	−0.0597311	−	0.103457i
$271$	−723.000	+	1252.27i	−0.162063	+	0.280702i	−0.935608	−	0.353039i	$-0.885148\pi$
$271$	−723.000	+	1252.27i	−0.162063	+	0.280702i	0.773545	+	0.633741i	$0.218482\pi$
$272$	832.000			0.185468
$273$		0			0
$274$	−2168.00			−0.478006
$275$	25.0000	−	43.3013i	0.00548202	−	0.00949514i
$276$	−134.000	−	232.095i	−0.0292241	−	0.0506176i
$277$	4010.00	+	6945.52i	0.869811	+	1.50656i	0.862190	+	0.506585i	$0.169092\pi$
$277$	4010.00	+	6945.52i	0.869811	+	1.50656i	0.00762078	+	0.999971i	$0.497574\pi$
$278$	46.0000	−	79.6743i	0.00992409	−	0.0171890i
$279$	−8632.00			−1.85227
$280$		0			0
$281$	4978.00			1.05681			0.528403	−	0.848994i	$-0.322791\pi$
$281$	4978.00			1.05681			0.528403	+	0.848994i	$0.322791\pi$
$282$	−88.0000	+	152.420i	−0.0185827	+	0.0321862i
$283$	2926.00	+	5067.98i	0.614603	+	1.06452i	0.990454	+	0.137844i	$0.0440171\pi$
$283$	2926.00	+	5067.98i	0.614603	+	1.06452i	−0.375851	+	0.926680i	$0.622650\pi$
$284$	−1540.00	−	2667.36i	−0.321768	−	0.557319i
$285$	65.0000	−	112.583i	0.0135097	−	0.0233995i
$286$	32.0000			0.00661608
$287$		0			0
$288$	832.000			0.170229
$289$	1104.50	−	1913.05i	0.224812	−	0.389385i
$290$	345.000	+	597.558i	0.0698590	+	0.120999i
$291$	−145.000	−	251.147i	−0.0292098	−	0.0505929i
$292$	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
$297$	−53.0000	−	91.7987i	−0.0103548	−	0.0179350i
$298$	−369.000	−	639.127i	−0.0717302	−	0.124240i
$299$	−268.000	+	464.190i	−0.0518356	+	0.0897819i
$300$	100.000			0.0192450
$301$		0			0
$302$	−4960.00			−0.945086
$303$	−616.500	+	1067.81i	−0.116888	+	0.202456i
$304$	208.000	+	360.267i	0.0392422	+	0.0679694i
$305$	−1167.50	−	2022.17i	−0.219183	−	0.379636i
$306$	−1352.00	+	2341.73i	−0.252577	+	0.437477i
$307$	−9443.00			−1.75551			−0.877753	−	0.479113i	$-0.840958\pi$
$307$	−9443.00			−1.75551			−0.877753	+	0.479113i	$0.840958\pi$
$308$		0			0
$309$	−1553.00			−0.285913
$310$	1660.00	−	2875.20i	0.304134	−	0.526776i
$311$	−4997.00	−	8655.06i	−0.911106	−	1.57808i	−0.812505	−	0.582954i	$-0.801897\pi$
$311$	−4997.00	−	8655.06i	−0.911106	−	1.57808i	−0.0986008	−	0.995127i	$-0.531437\pi$
$312$	32.0000	+	55.4256i	0.00580655	+	0.0100572i
$313$	728.000	−	1260.93i	0.131466	−	0.227707i	−0.792776	−	0.609514i	$-0.791365\pi$
$313$	728.000	−	1260.93i	0.131466	−	0.227707i	0.924242	+	0.381807i	$0.124698\pi$
$314$	2452.00			0.440683
$315$		0			0
$316$	4680.00			0.833135
$317$	−3436.00	+	5951.33i	−0.608785	+	1.05445i	0.382655	+	0.923891i	$0.375010\pi$
$317$	−3436.00	+	5951.33i	−0.608785	+	1.05445i	−0.991441	+	0.130556i	$0.958324\pi$
$318$	582.000	+	1008.05i	0.102632	+	0.177764i
$319$	69.0000	+	119.512i	0.0121105	+	0.0209760i
$320$	−160.000	+	277.128i	−0.0279508	+	0.0484123i
$321$	1831.00			0.318369
$322$		0			0
$323$	−1352.00			−0.232902
$324$	−1298.00	+	2248.20i	−0.222565	+	0.385494i
$325$	−100.000	−	173.205i	−0.0170677	−	0.0295621i
$326$	−660.000	−	1143.15i	−0.112129	−	0.194213i
$327$	−405.500	+	702.347i	−0.0685755	+	0.118776i
$328$	2824.00			0.475394
$329$		0			0
$330$	20.0000			0.00333625
$331$	196.000	−	339.482i	0.0325472	−	0.0563735i	−0.849293	−	0.527922i	$-0.822971\pi$
$331$	196.000	−	339.482i	0.0325472	−	0.0563735i	0.881840	+	0.471548i	$0.156305\pi$
$332$	1050.00	+	1818.65i	0.173573	+	0.300637i
$333$	2548.00	+	4413.27i	0.419308	+	0.726263i
$334$	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
$339$	−1085.00	−	1879.28i	−0.173832	−	0.301086i
$340$	−520.000	−	900.666i	−0.0829440	−	0.143663i
$341$	332.000	−	575.041i	0.0527238	−	0.0913203i
$342$	−1352.00			−0.213765
$343$		0			0
$344$	2952.00			0.462678
$345$	−167.500	+	290.119i	−0.0261388	+	0.0452738i
$346$	−3392.00	−	5875.12i	−0.527038	−	0.912856i
$347$	892.500	+	1545.86i	0.138075	+	0.239152i	0.926768	−	0.375635i	$-0.122575\pi$
$347$	892.500	+	1545.86i	0.138075	+	0.239152i	−0.788693	+	0.614787i	$0.789242\pi$
$348$	−138.000	+	239.023i	−0.0212574	+	0.0368189i
$349$	1591.00			0.244024			0.122012	−	0.992529i	$-0.461065\pi$
$349$	1591.00			0.244024			0.122012	+	0.992529i	$0.461065\pi$
$350$		0			0
$351$	−424.000			−0.0644771
$352$	−32.0000	+	55.4256i	−0.00484547	+	0.00839260i
$353$	843.000	+	1460.12i	0.127106	+	0.220154i	0.922554	−	0.385868i	$-0.126098\pi$
$353$	843.000	+	1460.12i	0.127106	+	0.220154i	−0.795448	+	0.606021i	$0.792765\pi$
$354$	350.000	+	606.218i	0.0525488	+	0.0910173i
$355$	−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	0.456902	+	0.889517i	$0.348959\pi$
$359$	−3686.00	+	6384.34i	−0.541893	+	0.938586i	−0.998795	+	0.0490695i	$0.984374\pi$
$360$	−520.000	−	900.666i	−0.0761289	−	0.131859i
$361$	3091.50	+	5354.64i	0.450722	+	0.780673i
$362$	4093.00	−	7089.28i	0.594263	−	1.02929i
$363$	−1327.00			−0.191872
$364$		0			0
$365$	−3140.00			−0.450288
$366$	467.000	−	808.868i	0.0666953	−	0.115520i
$367$	3318.50	+	5747.81i	0.472001	+	0.817529i	0.999487	−	0.0320344i	$-0.0101986\pi$
$367$	3318.50	+	5747.81i	0.472001	+	0.817529i	−0.527486	+	0.849564i	$0.676865\pi$
$368$	−536.000	−	928.379i	−0.0759264	−	0.131508i
$369$	−4589.00	+	7948.38i	−0.647409	+	1.12134i
$370$	−1960.00			−0.275393
$371$		0			0
$372$	1328.00			0.185090
$373$	−1738.00	+	3010.30i	−0.241261	+	0.417876i	−0.961074	−	0.276292i	$-0.910894\pi$
$373$	−1738.00	+	3010.30i	−0.241261	+	0.417876i	0.719813	+	0.694168i	$0.244228\pi$
$374$	−104.000	−	180.133i	−0.0143789	−	0.0249050i
$375$	−62.5000	−	108.253i	−0.00860663	−	0.0149071i
$376$	−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
$381$	−24.0000	−	41.5692i	−0.00322718	−	0.00558965i
$382$	−1978.00	−	3426.00i	−0.264930	−	0.458872i
$383$	−1228.50	+	2127.82i	−0.163899	+	0.283882i	−0.936264	−	0.351298i	$-0.885741\pi$
$383$	−1228.50	+	2127.82i	−0.163899	+	0.283882i	0.772365	+	0.635179i	$0.219074\pi$
$384$	−128.000			−0.0170103
$385$		0			0
$386$	7996.00			1.05437
$387$	−4797.00	+	8308.65i	−0.630091	+	1.09135i
$388$	−580.000	−	1004.59i	−0.0758893	−	0.131444i
$389$	−4281.00	−	7414.91i	−0.557983	−	0.966455i	−0.997665	−	0.0683010i	$-0.978242\pi$
$389$	−4281.00	−	7414.91i	−0.557983	−	0.966455i	0.439682	−	0.898154i	$-0.355091\pi$
$390$	40.0000	−	69.2820i	0.00519354	−	0.00899547i
$391$	3484.00			0.450623
$392$		0			0
$393$	792.000			0.101657
$394$	−3030.00	+	5248.11i	−0.387435	+	0.671056i
$395$	−2925.00	−	5066.25i	−0.372589	−	0.645343i
$396$	−104.000	−	180.133i	−0.0131975	−	0.0228587i
$397$	−4921.00	+	8523.42i	−0.622111	+	1.07753i	0.366981	+	0.930228i	$0.380391\pi$
$397$	−4921.00	+	8523.42i	−0.622111	+	1.07753i	−0.989092	+	0.147299i	$0.952942\pi$
$398$	712.000			0.0896717
$399$		0			0
$400$	400.000			0.0500000
$401$	4048.50	−	7012.21i	0.504171	−	0.873249i	−0.495818	−	0.868427i	$-0.665132\pi$
$401$	4048.50	−	7012.21i	0.504171	−	0.873249i	0.999988	−	0.00482260i	$-0.00153509\pi$
$402$	291.000	+	504.027i	0.0361039	+	0.0625338i
$403$	−1328.00	−	2300.16i	−0.164150	−	0.284316i
$404$	−2466.00	+	4271.24i	−0.303683	+	0.525995i
$405$	3245.00			0.398137
$406$		0			0
$407$	−392.000			−0.0477413
$408$	208.000	−	360.267i	0.0252391	−	0.0437153i
$409$	7629.50	+	13214.7i	0.922383	+	1.59761i	0.795717	+	0.605668i	$0.207094\pi$
$409$	7629.50	+	13214.7i	0.922383	+	1.59761i	0.126665	+	0.991946i	$0.459573\pi$
$410$	−1765.00	−	3057.07i	−0.212603	−	0.368239i
$411$	−542.000	+	938.772i	−0.0650484	+	0.112667i
$412$	−6212.00			−0.742823
$413$		0			0
$414$	3484.00			0.413597
$415$	1312.50	−	2273.32i	0.155248	−	0.268898i
$416$	128.000	+	221.703i	0.0150859	+	0.0261295i
$417$	−23.0000	−	39.8372i	−0.00270099	−	0.00467826i
$418$	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
$423$	−1144.00	−	1981.47i	−0.131497	−	0.227759i
$424$	2328.00	+	4032.21i	0.266645	+	0.461843i
$425$	−650.000	+	1125.83i	−0.0741874	+	0.128496i
$426$	−1540.00			−0.175148
$427$		0			0
$428$	7324.00			0.827147
$429$	8.00000	−	13.8564i	0.000900335	−	0.00155943i
$430$	−1845.00	−	3195.63i	−0.206916	−	0.358389i
$431$	−7101.00	−	12299.3i	−0.793604	−	1.37456i	−0.923722	−	0.383063i	$-0.874869\pi$
$431$	−7101.00	−	12299.3i	−0.793604	−	1.37456i	0.130119	−	0.991498i	$-0.458464\pi$
$432$	424.000	−	734.390i	0.0472215	−	0.0817901i
$433$	−14310.0			−1.58821			−0.794105	−	0.607781i	$-0.792060\pi$
$433$	−14310.0			−1.58821			−0.794105	+	0.607781i	$0.792060\pi$
$434$		0			0
$435$	345.000			0.0380264
$436$	−1622.00	+	2809.39i	−0.178164	+	0.308590i
$437$	871.000	+	1508.62i	0.0953446	+	0.165142i
$438$	−628.000	−	1087.73i	−0.0685091	−	0.118661i
$439$	−1178.00	+	2040.36i	−0.128070	+	0.221824i	−0.922929	−	0.384970i	$-0.874212\pi$
$439$	−1178.00	+	2040.36i	−0.128070	+	0.221824i	0.794859	+	0.606795i	$0.207545\pi$
$440$	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	$-0.979988\pi$
$443$	−4145.50	+	7180.22i	−0.444602	+	0.770073i	0.553422	+	0.832901i	$0.313322\pi$
$444$	−392.000	−	678.964i	−0.0418998	−	0.0725725i
$445$	222.500	+	385.381i	0.0237023	+	0.0410535i
$446$	3156.00	−	5466.35i	0.335069	−	0.580357i
$447$	−369.000			−0.0390450
$448$		0			0
$449$	−3521.00			−0.370081			−0.185040	−	0.982731i	$-0.559242\pi$
$449$	−3521.00			−0.370081			−0.185040	+	0.982731i	$0.559242\pi$
$450$	−650.000	+	1125.83i	−0.0680918	+	0.117938i
$451$	−353.000	−	611.414i	−0.0368561	−	0.0638367i
$452$	−4340.00	−	7517.10i	−0.451629	−	0.782245i
$453$	−1240.00	+	2147.74i	−0.128610	+	0.222759i
$454$	8472.00			0.875794
$455$		0			0
$456$	208.000			0.0213607
$457$	2716.00	−	4704.25i	0.278007	−	0.481522i	−0.692882	−	0.721051i	$-0.743660\pi$
$457$	2716.00	−	4704.25i	0.278007	−	0.481522i	0.970889	+	0.239529i	$0.0769929\pi$
$458$	−6334.00	−	10970.8i	−0.646219	−	1.11928i
$459$	1378.00	+	2386.77i	0.140130	+	0.242712i
$460$	−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
$465$	−830.000	−	1437.60i	−0.0827749	−	0.143370i
$466$	−4688.00	−	8119.85i	−0.466024	−	0.807178i
$467$	3231.50	−	5597.12i	0.320206	−	0.554612i	−0.660325	−	0.750980i	$-0.729581\pi$
$467$	3231.50	−	5597.12i	0.320206	−	0.554612i	0.980530	+	0.196368i	$0.0629147\pi$
$468$	−832.000			−0.0821778
$469$		0			0
$470$	880.000			0.0863646
$471$	613.000	−	1061.75i	0.0599693	−	0.103870i
$472$	1400.00	+	2424.87i	0.136526	+	0.236470i
$473$	−369.000	−	639.127i	−0.0358703	−	0.0621291i
$474$	1170.00	−	2026.50i	0.113375	−	0.196372i
$475$	−650.000			−0.0627875
$476$		0			0
$477$	−15132.0			−1.45251
$478$	1856.00	−	3214.69i	0.177597	−	0.307607i
$479$	−8820.00	−	15276.7i	−0.841328	−	1.45722i	−0.888772	−	0.458349i	$-0.848441\pi$
$479$	−8820.00	−	15276.7i	−0.841328	−	1.45722i	0.0474444	−	0.998874i	$-0.484892\pi$
$480$	80.0000	+	138.564i	0.00760726	+	0.0131762i
$481$	−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
$486$	2080.00	+	3602.67i	0.194137	+	0.336256i
$487$	5016.00	+	8687.97i	0.466728	+	0.808397i	0.999278	−	0.0380019i	$-0.0120993\pi$
$487$	5016.00	+	8687.97i	0.466728	+	0.808397i	−0.532549	+	0.846399i	$0.678766\pi$
$488$	1868.00	−	3235.47i	0.173279	−	0.300129i
$489$	−660.000			−0.0610352
$490$		0			0
$491$	5916.00			0.543758			0.271879	−	0.962331i	$-0.412355\pi$
$491$	5916.00			0.543758			0.271879	+	0.962331i	$0.412355\pi$
$492$	706.000	−	1222.83i	0.0646930	−	0.112051i
$493$	−1794.00	−	3107.30i	−0.163890	−	0.283866i
$494$	−208.000	−	360.267i	−0.0189441	−	0.0328121i
$495$	−130.000	+	225.167i	−0.0118042	+	0.0204454i
$496$	5312.00			0.480879
$497$		0			0
$498$	1050.00			0.0944812
$499$	−6947.00	+	12032.6i	−0.623227	+	1.07946i	0.365653	+	0.930751i	$0.380846\pi$
$499$	−6947.00	+	12032.6i	−0.623227	+	1.07946i	−0.988881	+	0.148710i	$0.952488\pi$
$500$	−250.000	−	433.013i	−0.0223607	−	0.0387298i
$501$	−474.500	−	821.858i	−0.0423136	−	0.0732892i
$502$	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
$507$	1066.50	+	1847.23i	0.0934219	+	0.161812i
$508$	−96.0000	−	166.277i	−0.00838447	−	0.0145223i
$509$	9278.50	−	16070.8i	0.807981	−	1.39946i	−0.106279	−	0.994336i	$-0.533894\pi$
$509$	9278.50	−	16070.8i	0.807981	−	1.39946i	0.914260	−	0.405128i	$-0.132773\pi$
$510$	−520.000			−0.0451490
$511$		0			0
$512$	−512.000			−0.0441942
$513$	−689.000	+	1193.38i	−0.0592984	+	0.102708i
$514$	1120.00	+	1939.90i	0.0961111	+	0.166469i
$515$	3882.50	+	6724.69i	0.332201	+	0.575389i
$516$	738.000	−	1278.25i	0.0629625	−	0.109054i
$517$	176.000			0.0149719
$518$		0			0
$519$	−3392.00			−0.286883
$520$	160.000	−	277.128i	0.0134932	−	0.0233709i
$521$	−4965.00	−	8599.63i	−0.417506	−	0.723142i	0.578182	−	0.815908i	$-0.303762\pi$
$521$	−4965.00	−	8599.63i	−0.417506	−	0.723142i	−0.995688	+	0.0927663i	$0.970429\pi$
$522$	−1794.00	−	3107.30i	−0.150424	−	0.260542i
$523$	−3962.00	+	6862.39i	−0.331255	+	0.573750i	−0.982758	−	0.184896i	$-0.940805\pi$
$523$	−3962.00	+	6862.39i	−0.331255	+	0.573750i	0.651504	+	0.758646i	$0.274139\pi$
$524$	3168.00			0.264112
$525$		0			0
$526$	−12810.0			−1.06187
$527$	−8632.00	+	14951.1i	−0.713503	+	1.23582i
$528$	16.0000	+	27.7128i	0.00131877	+	0.00228418i
$529$	3839.00	+	6649.34i	0.315526	+	0.546506i
$530$	2910.00	−	5040.27i	0.238495	−	0.413085i
$531$	−9100.00			−0.743703
$532$		0			0
$533$	−2824.00			−0.229495
$534$	−89.0000	+	154.153i	−0.00721237	+	0.0124922i
$535$	−4577.50	−	7928.46i	−0.369911	−	0.640705i
$536$	1164.00	+	2016.11i	0.0938006	+	0.162467i
$537$	−134.000	+	232.095i	−0.0107682	+	0.0186511i
$538$	9870.00			0.790940
$539$		0			0
$540$	−1060.00			−0.0844725
$541$	11748.5	−	20349.0i	0.933655	−	1.61714i	0.156641	−	0.987656i	$-0.449934\pi$
$541$	11748.5	−	20349.0i	0.933655	−	1.61714i	0.777015	−	0.629483i	$-0.216733\pi$
$542$	1446.00	+	2504.55i	0.114596	+	0.198486i
$543$	−2046.50	−	3544.64i	−0.161738	−	0.280138i
$544$	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
$549$	6071.00	+	10515.3i	0.471956	+	0.817452i
$550$	−50.0000	−	86.6025i	−0.00387638	−	0.00671408i
$551$	897.000	−	1553.65i	0.0693530	−	0.120123i
$552$	−536.000			−0.0413291
$553$		0			0
$554$	16040.0			1.23010
$555$	−490.000	+	848.705i	−0.0374763	+	0.0649108i
$556$	−92.0000	−	159.349i	−0.00701739	−	0.0121545i
$557$	5989.00	+	10373.3i	0.455587	+	0.789100i	0.998722	−	0.0505455i	$-0.0160960\pi$
$557$	5989.00	+	10373.3i	0.455587	+	0.789100i	−0.543135	+	0.839646i	$0.682763\pi$
$558$	−8632.00	+	14951.1i	−0.654878	+	1.13428i
$559$	−2952.00			−0.223357
$560$		0			0
$561$	−104.000			−0.00782689
$562$	4978.00	−	8622.15i	0.373637	−	0.647159i
$563$	−5029.50	−	8711.35i	−0.376498	−	0.652113i	0.614052	−	0.789265i	$-0.289538\pi$
$563$	−5029.50	−	8711.35i	−0.376498	−	0.652113i	−0.990550	+	0.137152i	$0.956205\pi$
$564$	176.000	+	304.841i	0.0131400	+	0.0227591i
$565$	−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	−0.418697	−	0.908126i	$-0.637513\pi$
$569$	7833.00	−	13567.2i	0.577111	−	0.999586i	0.995809	−	0.0914605i	$-0.0291535\pi$
$570$	−130.000	−	225.167i	−0.00955281	−	0.0165459i
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	0.815939	−	0.578138i	$-0.196220\pi$
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	−0.908651	+	0.417555i	$0.862887\pi$
$572$	32.0000	−	55.4256i	0.00233914	−	0.00405151i
$573$	−1978.00			−0.144210
$574$		0			0
$575$	1675.00			0.121482
$576$	832.000	−	1441.07i	0.0601852	−	0.104244i
$577$	6409.00	+	11100.7i	0.462409	+	0.800916i	0.999080	−	0.0428751i	$-0.0136518\pi$
$577$	6409.00	+	11100.7i	0.462409	+	0.800916i	−0.536671	+	0.843791i	$0.680318\pi$
$578$	−2209.00	−	3826.10i	−0.158966	−	0.275337i
$579$	1999.00	−	3462.37i	0.143481	−	0.248517i
$580$	1380.00			0.0987955
$581$		0			0
$582$	−580.000			−0.0413089
$583$	582.000	−	1008.05i	0.0413447	−	0.0716112i
$584$	−2512.00	−	4350.91i	−0.177992	−	0.308291i
$585$	520.000	+	900.666i	0.0367510	+	0.0636547i
$586$	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
$591$	1515.00	+	2624.06i	0.105446	+	0.182638i
$592$	−1568.00	−	2715.86i	−0.108859	−	0.188549i
$593$	−1299.00	+	2249.93i	−0.0899554	+	0.155807i	−0.907492	−	0.420069i	$-0.862006\pi$
$593$	−1299.00	+	2249.93i	−0.0899554	+	0.155807i	0.817537	+	0.575877i	$0.195339\pi$
$594$	−212.000			−0.0146439
$595$		0			0
$596$	−1476.00			−0.101442
$597$	178.000	−	308.305i	0.0122028	−	0.0211358i
$598$	536.000	+	928.379i	0.0366533	+	0.0634854i
$599$	1274.00	+	2206.63i	0.0869019	+	0.150518i	0.906200	−	0.422849i	$-0.138970\pi$
$599$	1274.00	+	2206.63i	0.0869019	+	0.150518i	−0.819298	+	0.573368i	$0.805637\pi$
$600$	100.000	−	173.205i	0.00680414	−	0.0117851i
$601$	−1706.00			−0.115789			−0.0578945	−	0.998323i	$-0.518439\pi$
$601$	−1706.00			−0.115789			−0.0578945	+	0.998323i	$0.518439\pi$
$602$		0			0
$603$	−7566.00			−0.510964
$604$	−4960.00	+	8590.97i	−0.334138	+	0.578745i
$605$	3317.50	+	5746.08i	0.222935	+	0.386134i
$606$	1233.00	+	2135.62i	0.0826521	+	0.143158i
$607$	−6283.50	+	10883.3i	−0.420164	+	0.727745i	−0.995955	−	0.0898517i	$-0.971361\pi$
$607$	−6283.50	+	10883.3i	−0.420164	+	0.727745i	0.575791	+	0.817597i	$0.304694\pi$
$608$	832.000			0.0554968
$609$		0			0
$610$	−4670.00			−0.309972
$611$	352.000	−	609.682i	0.0233067	−	0.0403684i
$612$	2704.00	+	4683.47i	0.178599	+	0.309343i
$613$	4814.00	+	8338.09i	0.317187	+	0.549384i	0.979900	−	0.199490i	$-0.0639284\pi$
$613$	4814.00	+	8338.09i	0.317187	+	0.549384i	−0.662713	+	0.748874i	$0.730595\pi$
$614$	−9443.00	+	16355.8i	−0.620665	+	1.07502i
$615$	−1765.00			−0.115726
$616$		0			0
$617$	−4316.00			−0.281614			−0.140807	−	0.990037i	$-0.544970\pi$
$617$	−4316.00			−0.281614			−0.140807	+	0.990037i	$0.544970\pi$
$618$	−1553.00	+	2689.87i	−0.101085	+	0.175085i
$619$	8201.00	+	14204.5i	0.532514	+	0.922341i	0.999279	+	0.0379598i	$0.0120859\pi$
$619$	8201.00	+	14204.5i	0.532514	+	0.922341i	−0.466766	+	0.884381i	$0.654581\pi$
$620$	−3320.00	−	5750.41i	−0.215055	−	0.372487i
$621$	1775.50	−	3075.26i	0.114732	−	0.198721i
$622$	−19988.0			−1.28850
$623$		0			0
$624$	128.000			0.00821170
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−1456.00	−	2521.87i	−0.0929608	−	0.161013i
$627$	−26.0000	−	45.0333i	−0.00165604	−	0.00286835i
$628$	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
$633$	1301.00	+	2253.40i	0.0816905	+	0.141492i
$634$	6872.00	+	11902.7i	0.430476	+	0.745607i
$635$	−120.000	+	207.846i	−0.00749930	+	0.0129892i
$636$	2328.00			0.145143
$637$		0			0
$638$	276.000			0.0171269
$639$	10010.0	−	17337.8i	0.619702	−	1.07336i
$640$	320.000	+	554.256i	0.0197642	+	0.0342327i
$641$	61.5000	+	106.521i	0.00378955	+	0.00656370i	0.867914	−	0.496715i	$-0.165460\pi$
$641$	61.5000	+	106.521i	0.00378955	+	0.00656370i	−0.864124	+	0.503278i	$0.832127\pi$
$642$	1831.00	−	3171.39i	0.112560	−	0.194960i
$643$	23924.0			1.46729			0.733647	−	0.679530i	$-0.237816\pi$
$643$	23924.0			1.46729			0.733647	+	0.679530i	$0.237816\pi$
$644$		0			0
$645$	−1845.00			−0.112631
$646$	−1352.00	+	2341.73i	−0.0823432	+	0.142623i
$647$	90.5000	+	156.751i	0.00549911	+	0.00952473i	0.868762	−	0.495230i	$-0.164916\pi$
$647$	90.5000	+	156.751i	0.00549911	+	0.00952473i	−0.863263	+	0.504755i	$0.831583\pi$
$648$	2596.00	+	4496.40i	0.157377	+	0.272586i
$649$	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	−0.465505	−	0.885045i	$-0.654127\pi$
$653$	8906.00	−	15425.6i	0.533719	−	0.924429i	0.999224	−	0.0393836i	$-0.0125394\pi$
$654$	811.000	+	1404.69i	0.0484902	+	0.0839875i
$655$	−1980.00	−	3429.46i	−0.118115	−	0.204580i
$656$	2824.00	−	4891.31i	0.168077	−	0.291118i
$657$	16328.0			0.969583
$658$		0			0
$659$	15334.0			0.906416			0.453208	−	0.891405i	$-0.350280\pi$
$659$	15334.0			0.906416			0.453208	+	0.891405i	$0.350280\pi$
$660$	20.0000	−	34.6410i	0.00117954	−	0.00204303i
$661$	668.500	+	1157.88i	0.0393368	+	0.0681334i	0.885024	−	0.465546i	$-0.154142\pi$
$661$	668.500	+	1157.88i	0.0393368	+	0.0681334i	−0.845687	+	0.533680i	$0.820809\pi$
$662$	−392.000	−	678.964i	−0.0230144	−	0.0398621i
$663$	−208.000	+	360.267i	−0.0121841	+	0.0211035i
$664$	4200.00			0.245469
$665$		0			0
$666$	10192.0			0.592991
$667$	−2311.50	+	4003.64i	−0.134185	+	0.232416i
$668$	−1898.00	−	3287.43i	−0.109934	−	0.190411i
$669$	−1578.00	−	2733.18i	−0.0911943	−	0.157953i
$670$	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
$675$	662.500	+	1147.48i	0.0377772	+	0.0654321i
$676$	4266.00	+	7388.93i	0.242717	+	0.420399i
$677$	12696.0	−	21990.1i	0.720749	−	1.24837i	−0.239951	−	0.970785i	$-0.577131\pi$
$677$	12696.0	−	21990.1i	0.720749	−	1.24837i	0.960700	−	0.277589i	$-0.0895352\pi$
$678$	−4340.00			−0.245836
$679$		0			0
$680$	−2080.00			−0.117301
$681$	2118.00	−	3668.48i	0.119181	−	0.206427i
$682$	−664.000	−	1150.08i	−0.0372813	−	0.0645732i
$683$	−14615.5	−	25314.8i	−0.818809	−	1.41822i	−0.906560	−	0.422076i	$-0.861301\pi$
$683$	−14615.5	−	25314.8i	−0.818809	−	1.41822i	0.0877512	−	0.996142i	$-0.472032\pi$
$684$	−1352.00	+	2341.73i	−0.0755775	+	0.130904i
$685$	5420.00			0.302318
$686$		0			0
$687$	−6334.00			−0.351757
$688$	2952.00	−	5113.01i	0.163581	−	0.283331i
$689$	−2328.00	−	4032.21i	−0.128722	−	0.222954i
$690$	335.000	+	580.237i	0.0184829	+	0.0320134i
$691$	−3769.00	+	6528.10i	−0.207496	+	0.359393i	−0.950925	−	0.309421i	$-0.899865\pi$
$691$	−3769.00	+	6528.10i	−0.207496	+	0.359393i	0.743429	+	0.668814i	$0.233198\pi$
$692$	−13568.0			−0.745344
$693$		0			0
$694$	3570.00			0.195267
$695$	−115.000	+	199.186i	−0.00627654	+	0.0108713i
$696$	276.000	+	478.046i	0.0150313	+	0.0260349i
$697$	9178.00	+	15896.8i	0.498768	+	0.863892i
$698$	1591.00	−	2755.69i	0.0862754	−	0.149433i
$699$	−4688.00			−0.253672
$700$		0			0
$701$	22125.0			1.19208			0.596041	−	0.802954i	$-0.296739\pi$
$701$	22125.0			1.19208			0.596041	+	0.802954i	$0.296739\pi$
$702$	−424.000	+	734.390i	−0.0227961	+	0.0394840i
$703$	2548.00	+	4413.27i	0.136699	+	0.236770i
$704$	64.0000	+	110.851i	0.00342627	+	0.00593447i
$705$	220.000	−	381.051i	0.0117527	−	0.0203563i
$706$	3372.00			0.179755
$707$		0			0
$708$	1400.00			0.0743153
$709$	2219.50	−	3844.29i	0.117567	−	0.203632i	−0.801236	−	0.598349i	$-0.795824\pi$
$709$	2219.50	−	3844.29i	0.117567	−	0.203632i	0.918803	+	0.394716i	$0.129157\pi$
$710$	3850.00	+	6668.40i	0.203504	+	0.352479i
$711$	15210.0	+	26344.5i	0.802278	+	1.38959i
$712$	−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
$717$	−928.000	−	1607.34i	−0.0483358	−	0.0837201i
$718$	7372.00	+	12768.7i	0.383176	+	0.663681i
$719$	6825.00	−	11821.2i	0.354005	−	0.613155i	−0.632942	−	0.774199i	$-0.718153\pi$
$719$	6825.00	−	11821.2i	0.354005	−	0.613155i	0.986947	+	0.161045i	$0.0514863\pi$
$720$	−2080.00			−0.107663
$721$		0			0
$722$	12366.0			0.637417
$723$	−2403.00	+	4162.12i	−0.123608	+	0.214095i
$724$	−8186.00	−	14178.6i	−0.420208	−	0.727821i
$725$	−862.500	−	1493.89i	−0.0441827	−	0.0765267i
$726$	−1327.00	+	2298.43i	−0.0678369	+	0.117497i
$727$	11397.0			0.581419			0.290709	−	0.956811i	$-0.406109\pi$
$727$	11397.0			0.581419			0.290709	+	0.956811i	$0.406109\pi$
$728$		0			0
$729$	−15443.0			−0.784586
$730$	−3140.00	+	5438.64i	−0.159201	+	0.275744i
$731$	9594.00	+	16617.3i	0.485427	+	0.840784i
$732$	−934.000	−	1617.74i	−0.0471607	−	0.0816847i
$733$	8343.00	−	14450.5i	0.420403	−	0.728160i	−0.575575	−	0.817749i	$-0.695222\pi$
$733$	8343.00	−	14450.5i	0.420403	−	0.728160i	0.995979	+	0.0895886i	$0.0285552\pi$
$734$	13274.0			0.667510
$735$		0			0
$736$	−2144.00			−0.107376
$737$	291.000	−	504.027i	0.0145443	−	0.0251914i
$738$	9178.00	+	15896.8i	0.457787	+	0.792910i
$739$	−11235.0	−	19459.6i	−0.559251	−	0.968650i	−0.997559	−	0.0698258i	$-0.977756\pi$
$739$	−11235.0	−	19459.6i	−0.559251	−	0.968650i	0.438309	−	0.898825i	$-0.355578\pi$
$740$	−1960.00	+	3394.82i	−0.0973663	+	0.168643i
$741$	−208.000			−0.0103118
$742$		0			0
$743$	5625.00			0.277741			0.138870	−	0.990311i	$-0.455653\pi$
$743$	5625.00			0.277741			0.138870	+	0.990311i	$0.455653\pi$
$744$	1328.00	−	2300.16i	0.0654393	−	0.113344i
$745$	922.500	+	1597.82i	0.0453662	+	0.0785765i
$746$	3476.00	+	6020.61i	0.170597	+	0.295483i
$747$	−6825.00	+	11821.2i	−0.334289	+	0.579005i
$748$	−416.000			−0.0203348
$749$		0			0
$750$	−250.000			−0.0121716
$751$	−8810.00	+	15259.4i	−0.428071	+	0.741441i	−0.996702	−	0.0811520i	$-0.974140\pi$
$751$	−8810.00	+	15259.4i	−0.428071	+	0.741441i	0.568631	+	0.822593i	$0.307473\pi$
$752$	704.000	+	1219.36i	0.0341386	+	0.0591298i
$753$	−1600.00	−	2771.28i	−0.0774333	−	0.134118i
$754$	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
$759$	67.0000	+	116.047i	0.00320414	+	0.00554974i
$760$	−520.000	−	900.666i	−0.0248189	−	0.0429876i
$761$	14869.0	−	25753.9i	0.708280	−	1.22678i	−0.257215	−	0.966354i	$-0.582805\pi$
$761$	14869.0	−	25753.9i	0.708280	−	1.22678i	0.965495	−	0.260422i	$-0.0838618\pi$
$762$	−96.0000			−0.00456393
$763$		0			0
$764$	−7912.00			−0.374668
$765$	3380.00	−	5854.33i	0.159744	−	0.276685i
$766$	2457.00	+	4255.65i	0.115894	+	0.200735i
$767$	−1400.00	−	2424.87i	−0.0659075	−	0.114155i
$768$	−128.000	+	221.703i	−0.00601407	+	0.0104167i
$769$	1118.00			0.0524267			0.0262133	−	0.999656i	$-0.491655\pi$
$769$	1118.00			0.0524267			0.0262133	+	0.999656i	$0.491655\pi$
$770$		0			0
$771$	1120.00			0.0523162
$772$	7996.00	−	13849.5i	0.372775	−	0.645665i
$773$	6716.00	+	11632.5i	0.312494	+	0.541255i	0.978902	−	0.204332i	$-0.0655023\pi$
$773$	6716.00	+	11632.5i	0.312494	+	0.541255i	−0.666408	+	0.745587i	$0.732169\pi$
$774$	9594.00	+	16617.3i	0.445542	+	0.771701i
$775$	−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
$780$	−80.0000	−	138.564i	−0.00367238	−	0.00636076i
$781$	770.000	+	1333.68i	0.0352788	+	0.0611047i
$782$	3484.00	−	6034.47i	0.159319	−	0.275949i
$783$	−3657.00			−0.166910
$784$		0			0
$785$	−6130.00			−0.278712
$786$	792.000	−	1371.78i	0.0359411	−	0.0622518i
$787$	−4674.50	−	8096.47i	−0.211725	−	0.366719i	0.740529	−	0.672024i	$-0.234575\pi$
$787$	−4674.50	−	8096.47i	−0.211725	−	0.366719i	−0.952255	+	0.305305i	$0.901242\pi$
$788$	6060.00	+	10496.2i	0.273958	+	0.474508i
$789$	−3202.50	+	5546.89i	−0.144502	+	0.250285i
$790$	−11700.0			−0.526921
$791$		0			0
$792$	−416.000			−0.0186640
$793$	−1868.00	+	3235.47i	−0.0836502	+	0.144886i
$794$	9842.00	+	17046.8i	0.439899	+	0.761927i
$795$	−1455.00	−	2520.13i	−0.0649101	−	0.112428i
$796$	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
$801$	−1157.00	−	2003.98i	−0.0510369	−	0.0883986i
$802$	−8097.00	−	14024.4i	−0.356503	−	0.617480i
$803$	−628.000	+	1087.73i	−0.0275986	+	0.0478021i
$804$	1164.00			0.0510586
$805$		0			0
$806$	−5312.00			−0.232143
$807$	2467.50	−	4273.84i	0.107633	−	0.186426i
$808$	4932.00	+	8542.47i	0.214737	+	0.371935i
$809$	−9834.50	−	17033.9i	−0.427395	−	0.740270i	0.569246	−	0.822167i	$-0.307235\pi$
$809$	−9834.50	−	17033.9i	−0.427395	−	0.740270i	−0.996641	+	0.0818975i	$0.973902\pi$
$810$	3245.00	−	5620.50i	0.140763	−	0.243808i
$811$	−31860.0			−1.37948			−0.689739	−	0.724059i	$-0.742275\pi$
$811$	−31860.0			−1.37948			−0.689739	+	0.724059i	$0.742275\pi$
$812$		0			0
$813$	1446.00			0.0623781
$814$	−392.000	+	678.964i	−0.0168791	+	0.0292355i
$815$	1650.00	+	2857.88i	0.0709165	+	0.122831i
$816$	−416.000	−	720.533i	−0.0178467	−	0.0309114i
$817$	−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	$-0.848426\pi$
$821$	−1115.00	+	1931.24i	−0.0473980	+	0.0820958i	0.841353	+	0.540486i	$0.181760\pi$
$822$	1084.00	+	1877.54i	0.0459962	+	0.0796677i
$823$	−7401.50	−	12819.8i	−0.313487	−	0.542976i	0.665627	−	0.746284i	$-0.268164\pi$
$823$	−7401.50	−	12819.8i	−0.313487	−	0.542976i	−0.979115	+	0.203308i	$0.934831\pi$
$824$	−6212.00	+	10759.5i	−0.262628	+	0.454885i
$825$	−50.0000			−0.00211003
$826$		0			0
$827$	13257.0			0.557426			0.278713	−	0.960374i	$-0.410092\pi$
$827$	13257.0			0.557426			0.278713	+	0.960374i	$0.410092\pi$
$828$	3484.00	−	6034.47i	0.146229	−	0.253276i
$829$	−10787.0	−	18683.6i	−0.451928	−	0.782762i	0.546578	−	0.837408i	$-0.315930\pi$
$829$	−10787.0	−	18683.6i	−0.451928	−	0.782762i	−0.998506	+	0.0546465i	$0.982597\pi$
$830$	−2625.00	−	4546.63i	−0.109777	−	0.190140i
$831$	4010.00	−	6945.52i	0.167395	−	0.289937i
$832$	512.000			0.0213346
$833$		0			0
$834$	−92.0000			−0.00381978
$835$	−2372.50	+	4109.29i	−0.0983278	+	0.170309i
$836$	−104.000	−	180.133i	−0.00430253	−	0.00745220i
$837$	8798.00	+	15238.6i	0.363325	+	0.629298i
$838$	−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
$843$	−2489.00	−	4311.07i	−0.101691	−	0.176134i
$844$	5204.00	+	9013.59i	0.212238	+	0.367607i
$845$	5332.50	−	9236.16i	0.217093	−	0.376016i
$846$	−4576.00			−0.185965
$847$		0			0
$848$	9312.00			0.377094
$849$	2926.00	−	5067.98i	0.118280	−	0.204868i
$850$	1300.00	+	2251.67i	0.0524584	+	0.0908606i
$851$	−6566.00	−	11372.6i	−0.264488	−	0.458107i
$852$	−1540.00	+	2667.36i	−0.0619243	+	0.107256i
$853$	−24838.0			−0.996995			−0.498498	−	0.866891i	$-0.666115\pi$
$853$	−24838.0			−0.996995			−0.498498	+	0.866891i	$0.666115\pi$
$854$		0			0
$855$	3380.00			0.135197
$856$	7324.00	−	12685.5i	0.292441	−	0.506522i
$857$	−8513.00	−	14744.9i	−0.339322	−	0.587722i	0.644984	−	0.764196i	$-0.276864\pi$
$857$	−8513.00	−	14744.9i	−0.339322	−	0.587722i	−0.984305	+	0.176474i	$0.943531\pi$
$858$	−16.0000	−	27.7128i	−0.000636633	−	0.00110268i
$859$	3364.00	−	5826.62i	0.133618	−	0.231434i	−0.791450	−	0.611233i	$-0.790674\pi$
$859$	3364.00	−	5826.62i	0.133618	−	0.231434i	0.925069	+	0.379800i	$0.124007\pi$
$860$	−7380.00			−0.292623
$861$		0			0
$862$	−28404.0			−1.12232
$863$	15049.5	−	26066.5i	0.593616	−	1.02817i	−0.400124	−	0.916461i	$-0.631033\pi$
$863$	15049.5	−	26066.5i	0.593616	−	1.02817i	0.993741	−	0.111713i	$-0.0356337\pi$
$864$	−848.000	−	1468.78i	−0.0333907	−	0.0578344i
$865$	8480.00	+	14687.8i	0.333328	+	0.577341i
$866$	−14310.0	+	24785.6i	−0.561517	+	0.972576i
$867$	−2209.00			−0.0865301
$868$		0			0
$869$	−2340.00			−0.0913453
$870$	345.000	−	597.558i	0.0134444	−	0.0232863i
$871$	−1164.00	−	2016.11i	−0.0452820	−	0.0784308i
$872$	3244.00	+	5618.77i	0.125981	+	0.218206i
$873$	3770.00	−	6529.83i	0.146157	−	0.253152i
$874$	3484.00			0.134838
$875$		0			0
$876$	−2512.00			−0.0968865
$877$	2813.00	−	4872.26i	0.108310	−	0.187599i	−0.806775	−	0.590858i	$-0.798789\pi$
$877$	2813.00	−	4872.26i	0.108310	−	0.187599i	0.915086	+	0.403259i	$0.132123\pi$
$878$	2356.00	+	4080.71i	0.0905594	+	0.156853i
$879$	−1506.00	−	2608.47i	−0.0577885	−	0.100093i
$880$	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
$885$	−875.000	−	1515.54i	−0.0332348	−	0.0575644i
$886$	8291.00	+	14360.4i	0.314381	+	0.544524i
$887$	−12665.5	+	21937.3i	−0.479443	+	0.830419i	−0.999722	−	0.0235768i	$-0.992495\pi$
$887$	−12665.5	+	21937.3i	−0.479443	+	0.830419i	0.520279	+	0.853996i	$0.325828\pi$
$888$	−1568.00			−0.0592552
$889$		0			0
$890$	890.000			0.0335201
$891$	649.000	−	1124.10i	0.0244022	−	0.0422658i
$892$	−6312.00	−	10932.7i	−0.236930	−	0.410374i
$893$	−1144.00	−	1981.47i	−0.0428695	−	0.0742522i
$894$	−369.000	+	639.127i	−0.0138045	+	0.0239101i
$895$	1340.00			0.0500461
$896$		0			0
$897$	536.000			0.0199515
$898$	−3521.00	+	6098.55i	−0.130843	+	0.226627i
$899$	−11454.0	−	19838.9i	−0.424930	−	0.736001i
$900$	1300.00	+	2251.67i	0.0481481	+	0.0833950i
$901$	−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
$906$	2480.00	+	4295.49i	0.0909409	+	0.157514i
$907$	−13192.5	−	22850.1i	−0.482966	−	0.836521i	0.516843	−	0.856080i	$-0.327107\pi$
$907$	−13192.5	−	22850.1i	−0.482966	−	0.836521i	−0.999809	+	0.0195592i	$0.993774\pi$
$908$	8472.00	−	14673.9i	0.309640	−	0.536312i
$909$	−32058.0			−1.16974
$910$		0			0
$911$	−40770.0			−1.48273			−0.741367	−	0.671100i	$-0.765822\pi$
$911$	−40770.0			−1.48273			−0.741367	+	0.671100i	$0.765822\pi$
$912$	208.000	−	360.267i	0.00755216	−	0.0130807i
$913$	−525.000	−	909.327i	−0.0190306	−	0.0329620i
$914$	−5432.00	−	9408.50i	−0.196581	−	0.340487i
$915$	−1167.50	+	2022.17i	−0.0421818	+	0.0730610i
$916$	−25336.0			−0.913892
$917$		0			0
$918$	5512.00			0.198173
$919$	7309.00	−	12659.6i	0.262352	−	0.454407i	−0.704514	−	0.709690i	$-0.748835\pi$
$919$	7309.00	−	12659.6i	0.262352	−	0.454407i	0.966867	+	0.255282i	$0.0821685\pi$
$920$	1340.00	+	2320.95i	0.0480201	+	0.0831733i
$921$	4721.50	+	8177.88i	0.168924	+	0.292584i
$922$	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
$927$	−20189.0	−	34968.4i	−0.715311	−	1.23896i
$928$	1104.00	+	1912.18i	0.0390523	+	0.0676406i
$929$	20661.5	−	35786.8i	0.729690	−	1.26386i	−0.227324	−	0.973819i	$-0.572998\pi$
$929$	20661.5	−	35786.8i	0.729690	−	1.26386i	0.957014	−	0.290041i	$-0.0936689\pi$
$930$	−3320.00			−0.117061
$931$		0			0
$932$	−18752.0			−0.659058
$933$	−4997.00	+	8655.06i	−0.175342	+	0.303702i
$934$	−6463.00	−	11194.2i	−0.226420	−	0.392170i
$935$	260.000	+	450.333i	0.00909402	+	0.0157513i
$936$	−832.000	+	1441.07i	−0.0290542	+	0.0503234i
$937$	22620.0			0.788648			0.394324	−	0.918971i	$-0.370979\pi$
$937$	22620.0			0.788648			0.394324	+	0.918971i	$0.370979\pi$
$938$		0			0
$939$	−1456.00			−0.0506015
$940$	880.000	−	1524.20i	0.0305345	−	0.0528873i
$941$	25989.0	+	45014.3i	0.900337	+	1.55943i	0.827057	+	0.562118i	$0.190013\pi$
$941$	25989.0	+	45014.3i	0.900337	+	1.55943i	0.0732801	+	0.997311i	$0.476653\pi$
$942$	−1226.00	−	2123.49i	−0.0424047	−	0.0734471i
$943$	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	$-0.888146\pi$
$947$	−4993.50	+	8649.00i	−0.171348	+	0.296784i	0.767543	+	0.640997i	$0.221479\pi$
$948$	−2340.00	−	4053.00i	−0.0801684	−	0.138856i
$949$	2512.00	+	4350.91i	0.0859252	+	0.148827i
$950$	−650.000	+	1125.83i	−0.0221987	+	0.0384493i
$951$	6872.00			0.234322
$952$		0			0
$953$	6588.00			0.223931			0.111966	−	0.993712i	$-0.464285\pi$
$953$	6588.00			0.223931			0.111966	+	0.993712i	$0.464285\pi$
$954$	−15132.0	+	26209.4i	−0.513539	+	0.889476i
$955$	4945.00	+	8564.99i	0.167556	+	0.290216i
$956$	−3712.00	−	6429.37i	−0.125580	−	0.217511i
$957$	69.0000	−	119.512i	0.00233067	−	0.00403684i
$958$	−35280.0			−1.18982
$959$		0			0
$960$	320.000			0.0107583
$961$	−40216.5	+	69657.0i	−1.34995	+	2.33819i
$962$	1568.00	+	2715.86i	0.0525513	+	0.0910215i
$963$	23803.0	+	41228.0i	0.796512	+	1.37960i
$964$	−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
$969$	676.000	+	1170.87i	0.0224110	+	0.0388170i
$970$	1450.00	+	2511.47i	0.0479966	+	0.0831325i
$971$	11820.0	−	20472.8i	0.390651	−	0.676627i	−0.601885	−	0.798583i	$-0.705583\pi$
$971$	11820.0	−	20472.8i	0.390651	−	0.676627i	0.992536	+	0.121956i	$0.0389167\pi$
$972$	8320.00			0.274552
$973$		0			0
$974$	20064.0			0.660053
$975$	−100.000	+	173.205i	−0.00328468	+	0.00568923i
$976$	−3736.00	−	6470.94i	−0.122527	−	0.212223i
$977$	−18333.0	−	31753.7i	−0.600332	−	1.03981i	−0.992771	−	0.120028i	$-0.961702\pi$
$977$	−18333.0	−	31753.7i	−0.600332	−	1.03981i	0.392438	−	0.919778i	$-0.371632\pi$
$978$	−660.000	+	1143.15i	−0.0215792	+	0.0373763i
$979$	178.000			0.00581093
$980$		0			0
$981$	−21086.0			−0.686263
$982$	5916.00	−	10246.8i	0.192248	−	0.332983i
$983$	−20535.5	−	35568.5i	−0.666308	−	1.15408i	−0.978929	−	0.204201i	$-0.934540\pi$
$983$	−20535.5	−	35568.5i	−0.666308	−	1.15408i	0.312621	−	0.949878i	$-0.398793\pi$
$984$	−1412.00	−	2445.66i	−0.0457448	−	0.0792324i
$985$	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
$990$	260.000	+	450.333i	0.00834681	+	0.0144571i
$991$	−15992.0	−	27699.0i	−0.512616	−	0.887877i	−0.999893	−	0.0146297i	$-0.995343\pi$
$991$	−15992.0	−	27699.0i	−0.512616	−	0.887877i	0.487277	−	0.873248i	$-0.337990\pi$
$992$	5312.00	−	9200.65i	0.170016	−	0.294477i
$993$	−392.000			−0.0125274
$994$		0			0
$995$	−1780.00			−0.0567134
$996$	1050.00	−	1818.65i	0.0334041	−	0.0578577i
$997$	−21947.0	−	38013.3i	−0.697160	−	1.20752i	−0.969447	−	0.245300i	$-0.921113\pi$
$997$	−21947.0	−	38013.3i	−0.697160	−	1.20752i	0.272287	−	0.962216i	$-0.412220\pi$
$998$	13894.0	+	24065.1i	0.440688	+	0.763294i
$999$	5194.00	−	8996.27i	0.164495	−	0.284914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.e.m.471.1		2
7.2	even	3		490.4.a.e.1.1		1
7.3	odd	6		70.4.e.c.11.1	✓	2
7.4	even	3	inner	490.4.e.m.361.1		2
7.5	odd	6		490.4.a.c.1.1		1
7.6	odd	2		70.4.e.c.51.1	yes	2
21.17	even	6		630.4.k.b.361.1		2
21.20	even	2		630.4.k.b.541.1		2
28.3	even	6		560.4.q.d.81.1		2
28.27	even	2		560.4.q.d.401.1		2
35.3	even	12		350.4.j.e.249.2		4
35.9	even	6		2450.4.a.be.1.1		1
35.13	even	4		350.4.j.e.149.1		4
35.17	even	12		350.4.j.e.249.1		4
35.19	odd	6		2450.4.a.bg.1.1		1
35.24	odd	6		350.4.e.a.151.1		2
35.27	even	4		350.4.j.e.149.2		4
35.34	odd	2		350.4.e.a.51.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.c.11.1	✓	2	7.3	odd	6
70.4.e.c.51.1	yes	2	7.6	odd	2
350.4.e.a.51.1		2	35.34	odd	2
350.4.e.a.151.1		2	35.24	odd	6
350.4.j.e.149.1		4	35.13	even	4
350.4.j.e.149.2		4	35.27	even	4
350.4.j.e.249.1		4	35.17	even	12
350.4.j.e.249.2		4	35.3	even	12
490.4.a.c.1.1		1	7.5	odd	6
490.4.a.e.1.1		1	7.2	even	3
490.4.e.m.361.1		2	7.4	even	3	inner
490.4.e.m.471.1		2	1.1	even	1	trivial
560.4.q.d.81.1		2	28.3	even	6
560.4.q.d.401.1		2	28.27	even	2
630.4.k.b.361.1		2	21.17	even	6
630.4.k.b.541.1		2	21.20	even	2
2450.4.a.be.1.1		1	35.9	even	6
2450.4.a.bg.1.1		1	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 - 22.5167i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 - 22.5167i) q^{9} +(5.00000 + 8.66025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-2.00000 + 3.46410i) q^{12} +8.00000 q^{13} +5.00000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-26.0000 - 45.0333i) q^{17} +(-26.0000 - 45.0333i) q^{18} +(13.0000 - 22.5167i) q^{19} +20.0000 q^{20} +4.00000 q^{22} +(-33.5000 + 58.0237i) q^{23} +(4.00000 + 6.92820i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(8.00000 - 13.8564i) q^{26} -53.0000 q^{27} +69.0000 q^{29} +(5.00000 - 8.66025i) q^{30} +(-166.000 - 287.520i) q^{31} +(16.0000 + 27.7128i) q^{32} +(1.00000 - 1.73205i) q^{33} -104.000 q^{34} -104.000 q^{36} +(-98.0000 + 169.741i) q^{37} +(-26.0000 - 45.0333i) q^{38} +(-4.00000 - 6.92820i) q^{39} +(20.0000 - 34.6410i) q^{40} -353.000 q^{41} -369.000 q^{43} +(4.00000 - 6.92820i) q^{44} +(65.0000 + 112.583i) q^{45} +(67.0000 + 116.047i) q^{46} +(44.0000 - 76.2102i) q^{47} +16.0000 q^{48} -50.0000 q^{50} +(-26.0000 + 45.0333i) q^{51} +(-16.0000 - 27.7128i) q^{52} +(-291.000 - 504.027i) q^{53} +(-53.0000 + 91.7987i) q^{54} -10.0000 q^{55} -26.0000 q^{57} +(69.0000 - 119.512i) q^{58} +(-175.000 - 303.109i) q^{59} +(-10.0000 - 17.3205i) q^{60} +(-233.500 + 404.434i) q^{61} -664.000 q^{62} +64.0000 q^{64} +(-20.0000 + 34.6410i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(-145.500 - 252.013i) q^{67} +(-104.000 + 180.133i) q^{68} +67.0000 q^{69} +770.000 q^{71} +(-104.000 + 180.133i) q^{72} +(314.000 + 543.864i) q^{73} +(196.000 + 339.482i) q^{74} +(-12.5000 + 21.6506i) q^{75} -104.000 q^{76} -16.0000 q^{78} +(-585.000 + 1013.25i) q^{79} +(-40.0000 - 69.2820i) q^{80} +(-324.500 - 562.050i) q^{81} +(-353.000 + 611.414i) q^{82} -525.000 q^{83} +260.000 q^{85} +(-369.000 + 639.127i) q^{86} +(-34.5000 - 59.7558i) q^{87} +(-8.00000 - 13.8564i) q^{88} +(44.5000 - 77.0763i) q^{89} +260.000 q^{90} +268.000 q^{92} +(-166.000 + 287.520i) q^{93} +(-88.0000 - 152.420i) q^{94} +(65.0000 + 112.583i) q^{95} +(16.0000 - 27.7128i) q^{96} +290.000 q^{97} +52.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} - 4 q^{4} - 5 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 - 4 * q^4 - 5 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9	\( 2 q + 2 q^{2} - q^{3} - 4 q^{4} - 5 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9} + 10 q^{10} + 2 q^{11} - 4 q^{12} + 16 q^{13} + 10 q^{15} - 16 q^{16} - 52 q^{17} - 52 q^{18} + 26 q^{19} + 40 q^{20} + 8 q^{22} - 67 q^{23} + 8 q^{24} - 25 q^{25} + 16 q^{26} - 106 q^{27} + 138 q^{29} + 10 q^{30} - 332 q^{31} + 32 q^{32} + 2 q^{33} - 208 q^{34} - 208 q^{36} - 196 q^{37} - 52 q^{38} - 8 q^{39} + 40 q^{40} - 706 q^{41} - 738 q^{43} + 8 q^{44} + 130 q^{45} + 134 q^{46} + 88 q^{47} + 32 q^{48} - 100 q^{50} - 52 q^{51} - 32 q^{52} - 582 q^{53} - 106 q^{54} - 20 q^{55} - 52 q^{57} + 138 q^{58} - 350 q^{59} - 20 q^{60} - 467 q^{61} - 1328 q^{62} + 128 q^{64} - 40 q^{65} - 4 q^{66} - 291 q^{67} - 208 q^{68} + 134 q^{69} + 1540 q^{71} - 208 q^{72} + 628 q^{73} + 392 q^{74} - 25 q^{75} - 208 q^{76} - 32 q^{78} - 1170 q^{79} - 80 q^{80} - 649 q^{81} - 706 q^{82} - 1050 q^{83} + 520 q^{85} - 738 q^{86} - 69 q^{87} - 16 q^{88} + 89 q^{89} + 520 q^{90} + 536 q^{92} - 332 q^{93} - 176 q^{94} + 130 q^{95} + 32 q^{96} + 580 q^{97} + 104 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 - 4 * q^4 - 5 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9 + 10 * q^10 + 2 * q^11 - 4 * q^12 + 16 * q^13 + 10 * q^15 - 16 * q^16 - 52 * q^17 - 52 * q^18 + 26 * q^19 + 40 * q^20 + 8 * q^22 - 67 * q^23 + 8 * q^24 - 25 * q^25 + 16 * q^26 - 106 * q^27 + 138 * q^29 + 10 * q^30 - 332 * q^31 + 32 * q^32 + 2 * q^33 - 208 * q^34 - 208 * q^36 - 196 * q^37 - 52 * q^38 - 8 * q^39 + 40 * q^40 - 706 * q^41 - 738 * q^43 + 8 * q^44 + 130 * q^45 + 134 * q^46 + 88 * q^47 + 32 * q^48 - 100 * q^50 - 52 * q^51 - 32 * q^52 - 582 * q^53 - 106 * q^54 - 20 * q^55 - 52 * q^57 + 138 * q^58 - 350 * q^59 - 20 * q^60 - 467 * q^61 - 1328 * q^62 + 128 * q^64 - 40 * q^65 - 4 * q^66 - 291 * q^67 - 208 * q^68 + 134 * q^69 + 1540 * q^71 - 208 * q^72 + 628 * q^73 + 392 * q^74 - 25 * q^75 - 208 * q^76 - 32 * q^78 - 1170 * q^79 - 80 * q^80 - 649 * q^81 - 706 * q^82 - 1050 * q^83 + 520 * q^85 - 738 * q^86 - 69 * q^87 - 16 * q^88 + 89 * q^89 + 520 * q^90 + 536 * q^92 - 332 * q^93 - 176 * q^94 + 130 * q^95 + 32 * q^96 + 580 * q^97 + 104 * q^99

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