LMFDB - Embedded newform 490.4.c.g.99.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(99,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.c (of order $2$, degree $1$, 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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 438 x^{18} + 80439 x^{16} + 8097428 x^{14} + 488971671 x^{12} + 18162509334 x^{10} + \cdots + 9871083181584 $ x^20 + 438x^18 + 80439x^16 + 8097428x^14 + 488971671x^12 + 18162509334x^10 + 407198911753x^8 + 5129420990112x^6 + 30509282328120x^4 + 52488428698656*x^2 + 9871083181584
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{23}\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.5
Root			$-0.462233i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.g.99.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -0.537767i q^{3} -4.00000 q^{4} +(-8.93458 + 6.72110i) q^{5} -1.07553 q^{6} +8.00000i q^{8} +26.7108 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -0.537767i q^{3} -4.00000 q^{4} +(-8.93458 + 6.72110i) q^{5} -1.07553 q^{6} +8.00000i q^{8} +26.7108 q^{9} +(13.4422 + 17.8692i) q^{10} +14.1793 q^{11} +2.15107i q^{12} -13.9177i q^{13} +(3.61439 + 4.80472i) q^{15} +16.0000 q^{16} -65.7823i q^{17} -53.4216i q^{18} -95.1968 q^{19} +(35.7383 - 26.8844i) q^{20} -28.3586i q^{22} +69.4781i q^{23} +4.30213 q^{24} +(34.6536 - 120.101i) q^{25} -27.8353 q^{26} -28.8839i q^{27} -127.840 q^{29} +(9.60944 - 7.22877i) q^{30} -98.3654 q^{31} -32.0000i q^{32} -7.62517i q^{33} -131.565 q^{34} -106.843 q^{36} +287.582i q^{37} +190.394i q^{38} -7.48445 q^{39} +(-53.7688 - 71.4767i) q^{40} -310.112 q^{41} +197.986i q^{43} -56.7173 q^{44} +(-238.650 + 179.526i) q^{45} +138.956 q^{46} +538.883i q^{47} -8.60427i q^{48} +(-240.201 - 69.3071i) q^{50} -35.3755 q^{51} +55.6706i q^{52} -314.867i q^{53} -57.7678 q^{54} +(-126.686 + 95.3006i) q^{55} +51.1937i q^{57} +255.680i q^{58} -242.143 q^{59} +(-14.4575 - 19.2189i) q^{60} -440.612 q^{61} +196.731i q^{62} -64.0000 q^{64} +(93.5420 + 124.348i) q^{65} -15.2503 q^{66} -858.375i q^{67} +263.129i q^{68} +37.3630 q^{69} +142.246 q^{71} +213.686i q^{72} +459.680i q^{73} +575.164 q^{74} +(-64.5861 - 18.6355i) q^{75} +380.787 q^{76} +14.9689i q^{78} -1193.09 q^{79} +(-142.953 + 107.538i) q^{80} +705.659 q^{81} +620.223i q^{82} -403.628i q^{83} +(442.129 + 587.737i) q^{85} +395.973 q^{86} +68.7480i q^{87} +113.435i q^{88} -1084.30 q^{89} +(359.052 + 477.300i) q^{90} -277.912i q^{92} +52.8977i q^{93} +1077.77 q^{94} +(850.544 - 639.827i) q^{95} -17.2085 q^{96} -166.723i q^{97} +378.741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) $ 20 * q - 80 * q^4 - 316 * q^9	$ 20 q - 80 q^{4} - 316 q^{9} + 104 q^{11} - 360 q^{15} + 320 q^{16} - 440 q^{25} - 216 q^{29} + 224 q^{30} + 1264 q^{36} - 504 q^{39} - 416 q^{44} + 1600 q^{46} + 952 q^{50} - 296 q^{51} + 1440 q^{60} - 1280 q^{64} + 2732 q^{65} - 1872 q^{71} - 5968 q^{74} - 6424 q^{79} + 2020 q^{81} + 428 q^{85} + 3616 q^{86} + 3568 q^{95} + 624 q^{99}+O(q^{100}) $ 20 * q - 80 * q^4 - 316 * q^9 + 104 * q^11 - 360 * q^15 + 320 * q^16 - 440 * q^25 - 216 * q^29 + 224 * q^30 + 1264 * q^36 - 504 * q^39 - 416 * q^44 + 1600 * q^46 + 952 * q^50 - 296 * q^51 + 1440 * q^60 - 1280 * q^64 + 2732 * q^65 - 1872 * q^71 - 5968 * q^74 - 6424 * q^79 + 2020 * q^81 + 428 * q^85 + 3616 * q^86 + 3568 * q^95 + 624 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$		−	0.537767i		−	0.103493i	−0.998660	−	0.0517466i	$-0.983521\pi$
$3$		−	0.537767i		−	0.103493i	0.998660	−	0.0517466i	$-0.0164788\pi$
$4$	−4.00000			−0.500000
$5$	−8.93458	+	6.72110i	−0.799133	+	0.601154i
$5$	−8.93458	+	6.72110i	−0.799133	+	0.601154i
$6$	−1.07553			−0.0731808
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	26.7108			0.989289
$10$	13.4422	+	17.8692i	0.425080	+	0.565073i
$11$	14.1793			0.388657			0.194328	−	0.980937i	$-0.437747\pi$
$11$	14.1793			0.388657			0.194328	+	0.980937i	$0.437747\pi$
$12$			2.15107i			0.0517466i
$13$		−	13.9177i		−	0.296928i	−0.988918	−	0.148464i	$-0.952567\pi$
$13$		−	13.9177i		−	0.296928i	0.988918	−	0.148464i	$-0.0474329\pi$
$14$		0			0
$15$	3.61439	+	4.80472i	0.0622154	+	0.0827049i
$16$	16.0000			0.250000
$17$		−	65.7823i		−	0.938503i	−0.883065	−	0.469251i	$-0.844524\pi$
$17$		−	65.7823i		−	0.938503i	0.883065	−	0.469251i	$-0.155476\pi$
$18$		−	53.4216i		−	0.699533i
$19$	−95.1968			−1.14945			−0.574727	−	0.818345i	$-0.694892\pi$
$19$	−95.1968			−1.14945			−0.574727	+	0.818345i	$0.694892\pi$
$20$	35.7383	−	26.8844i	0.399567	−	0.300577i
$21$		0			0
$22$		−	28.3586i		−	0.274822i
$23$			69.4781i			0.629877i	0.949112	+	0.314939i	$0.101984\pi$
$23$			69.4781i			0.629877i	−0.949112	+	0.314939i	$0.898016\pi$
$24$	4.30213			0.0365904
$25$	34.6536	−	120.101i	0.277229	−	0.960804i
$26$	−27.8353			−0.209960
$27$		−	28.8839i		−	0.205878i
$28$		0			0
$29$	−127.840			−0.818595			−0.409298	−	0.912401i	$-0.634226\pi$
$29$	−127.840			−0.818595			−0.409298	+	0.912401i	$0.634226\pi$
$30$	9.60944	−	7.22877i	0.0584812	−	0.0439929i
$31$	−98.3654			−0.569902			−0.284951	−	0.958542i	$-0.591977\pi$
$31$	−98.3654			−0.569902			−0.284951	+	0.958542i	$0.591977\pi$
$32$		−	32.0000i		−	0.176777i
$33$		−	7.62517i		−	0.0402234i
$34$	−131.565			−0.663622
$35$		0			0
$36$	−106.843			−0.494645
$37$			287.582i			1.27779i	0.769294	+	0.638895i	$0.220608\pi$
$37$			287.582i			1.27779i	−0.769294	+	0.638895i	$0.779392\pi$
$38$			190.394i			0.812787i
$39$	−7.48445			−0.0307300
$40$	−53.7688	−	71.4767i	−0.212540	−	0.282536i
$41$	−310.112			−1.18125			−0.590625	−	0.806946i	$-0.701119\pi$
$41$	−310.112			−1.18125			−0.590625	+	0.806946i	$0.701119\pi$
$42$		0			0
$43$			197.986i			0.702154i	0.936347	+	0.351077i	$0.114184\pi$
$43$			197.986i			0.702154i	−0.936347	+	0.351077i	$0.885816\pi$
$44$	−56.7173			−0.194328
$45$	−238.650	+	179.526i	−0.790574	+	0.594715i
$46$	138.956			0.445391
$47$			538.883i			1.67243i	0.548402	+	0.836215i	$0.315237\pi$
$47$			538.883i			1.67243i	−0.548402	+	0.836215i	$0.684763\pi$
$48$		−	8.60427i		−	0.0258733i
$49$		0			0
$50$	−240.201	−	69.3071i	−0.679391	−	0.196030i
$51$	−35.3755			−0.0971287
$52$			55.6706i			0.148464i
$53$		−	314.867i		−	0.816043i	−0.912972	−	0.408021i	$-0.866219\pi$
$53$		−	314.867i		−	0.816043i	0.912972	−	0.408021i	$-0.133781\pi$
$54$	−57.7678			−0.145578
$55$	−126.686	+	95.3006i	−0.310589	+	0.233642i
$56$		0			0
$57$			51.1937i			0.118961i
$58$			255.680i			0.578834i
$59$	−242.143			−0.534311			−0.267156	−	0.963653i	$-0.586084\pi$
$59$	−242.143			−0.534311			−0.267156	+	0.963653i	$0.586084\pi$
$60$	−14.4575	−	19.2189i	−0.0311077	−	0.0413525i
$61$	−440.612			−0.924830			−0.462415	−	0.886664i	$-0.653017\pi$
$61$	−440.612			−0.924830			−0.462415	+	0.886664i	$0.653017\pi$
$62$			196.731i			0.402981i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	93.5420	+	124.348i	0.178499	+	0.237285i
$66$	−15.2503			−0.0284422
$67$		−	858.375i		−	1.56518i	−0.622536	−	0.782591i	$-0.713898\pi$
$67$		−	858.375i		−	1.56518i	0.622536	−	0.782591i	$-0.286102\pi$
$68$			263.129i			0.469251i
$69$	37.3630			0.0651881
$70$		0			0
$71$	142.246			0.237768			0.118884	−	0.992908i	$-0.462068\pi$
$71$	142.246			0.237768			0.118884	+	0.992908i	$0.462068\pi$
$72$			213.686i			0.349767i
$73$			459.680i			0.737007i	0.929626	+	0.368503i	$0.120130\pi$
$73$			459.680i			0.737007i	−0.929626	+	0.368503i	$0.879870\pi$
$74$	575.164			0.903534
$75$	−64.5861	−	18.6355i	−0.0994367	−	0.0286913i
$76$	380.787			0.574727
$77$		0			0
$78$			14.9689i			0.0217294i
$79$	−1193.09			−1.69915			−0.849574	−	0.527470i	$-0.823141\pi$
$79$	−1193.09			−1.69915			−0.849574	+	0.527470i	$0.823141\pi$
$80$	−142.953	+	107.538i	−0.199783	+	0.150288i
$81$	705.659			0.967982
$82$			620.223i			0.835271i
$83$		−	403.628i		−	0.533782i	−0.963727	−	0.266891i	$-0.914004\pi$
$83$		−	403.628i		−	0.533782i	0.963727	−	0.266891i	$-0.0859964\pi$
$84$		0			0
$85$	442.129	+	587.737i	0.564184	+	0.749989i
$86$	395.973			0.496498
$87$			68.7480i			0.0847191i
$88$			113.435i			0.137411i
$89$	−1084.30			−1.29141			−0.645704	−	0.763587i	$-0.723436\pi$
$89$	−1084.30			−1.29141			−0.645704	+	0.763587i	$0.723436\pi$
$90$	359.052	+	477.300i	0.420527	+	0.559020i
$91$		0			0
$92$		−	277.912i		−	0.314939i
$93$			52.8977i			0.0589810i
$94$	1077.77			1.18259
$95$	850.544	−	639.827i	0.918568	−	0.690999i
$96$	−17.2085			−0.0182952
$97$		−	166.723i		−	0.174517i	−0.996186	−	0.0872583i	$-0.972189\pi$
$97$		−	166.723i		−	0.174517i	0.996186	−	0.0872583i	$-0.0278106\pi$
$98$		0			0
$99$	378.741			0.384494
$100$	−138.614	+	480.402i	−0.138614	+	0.480402i
$101$	−834.364			−0.822003			−0.411002	−	0.911635i	$-0.634821\pi$
$101$	−834.364			−0.822003			−0.411002	+	0.911635i	$0.634821\pi$
$102$			70.7510i			0.0686804i
$103$			1415.11i			1.35373i	0.736106	+	0.676867i	$0.236663\pi$
$103$			1415.11i			1.35373i	−0.736106	+	0.676867i	$0.763337\pi$
$104$	111.341			0.104980
$105$		0			0
$106$	−629.733			−0.577029
$107$		−	1569.05i		−	1.41763i	−0.705396	−	0.708813i	$-0.749231\pi$
$107$		−	1569.05i		−	1.41763i	0.705396	−	0.708813i	$-0.250769\pi$
$108$			115.536i			0.102939i
$109$	−750.399			−0.659405			−0.329703	−	0.944085i	$-0.606948\pi$
$109$	−750.399			−0.659405			−0.329703	+	0.944085i	$0.606948\pi$
$110$	190.601	+	253.373i	0.165210	+	0.219619i
$111$	154.652			0.132243
$112$		0			0
$113$			2017.09i			1.67922i	0.543188	+	0.839611i	$0.317217\pi$
$113$			2017.09i			1.67922i	−0.543188	+	0.839611i	$0.682783\pi$
$114$	102.387			0.0841180
$115$	−466.969	−	620.758i	−0.378653	−	0.503356i
$116$	511.359			0.409298
$117$		−	371.752i		−	0.293748i
$118$			484.287i			0.377815i
$119$		0			0
$120$	−38.4378	+	28.9151i	−0.0292406	+	0.0219964i
$121$	−1129.95			−0.848946
$122$			881.225i			0.653953i
$123$			166.768i			0.122252i
$124$	393.462			0.284951
$125$	497.593	+	1305.96i	0.356048	+	0.934468i
$126$		0			0
$127$			89.7776i			0.0627281i	0.999508	+	0.0313641i	$0.00998513\pi$
$127$			89.7776i			0.0627281i	−0.999508	+	0.0313641i	$0.990015\pi$
$128$			128.000i			0.0883883i
$129$	106.470			0.0726682
$130$	248.697	−	187.084i	0.167786	−	0.126218i
$131$	1406.47			0.938042			0.469021	−	0.883187i	$-0.344607\pi$
$131$	1406.47			0.938042			0.469021	+	0.883187i	$0.344607\pi$
$132$			30.5007i			0.0201117i
$133$		0			0
$134$	−1716.75			−1.10675
$135$	194.132	+	258.066i	0.123764	+	0.164524i
$136$	526.258			0.331811
$137$		−	646.886i		−	0.403410i	−0.979446	−	0.201705i	$-0.935352\pi$
$137$		−	646.886i		−	0.403410i	0.979446	−	0.201705i	$-0.0646483\pi$
$138$		−	74.7260i		−	0.0460949i
$139$	−1309.84			−0.799273			−0.399636	−	0.916674i	$-0.630864\pi$
$139$	−1309.84			−0.799273			−0.399636	+	0.916674i	$0.630864\pi$
$140$		0			0
$141$	289.794			0.173085
$142$		−	284.493i		−	0.168127i
$143$		−	197.343i		−	0.115403i
$144$	427.373			0.247322
$145$	1142.20	−	859.224i	0.654167	−	0.492101i
$146$	919.360			0.521142
$147$		0			0
$148$		−	1150.33i		−	0.638895i
$149$	−1457.54			−0.801385			−0.400692	−	0.916213i	$-0.631230\pi$
$149$	−1457.54			−0.801385			−0.400692	+	0.916213i	$0.631230\pi$
$150$	−37.2711	+	129.172i	−0.0202878	+	0.0703124i
$151$	−1943.86			−1.04761			−0.523804	−	0.851839i	$-0.675488\pi$
$151$	−1943.86			−1.04761			−0.523804	+	0.851839i	$0.675488\pi$
$152$		−	761.574i		−	0.406394i
$153$		−	1757.10i		−	0.928451i
$154$		0			0
$155$	878.854	−	661.124i	0.455427	−	0.342598i
$156$	29.9378			0.0153650
$157$		−	1322.67i		−	0.672361i	−0.941798	−	0.336181i	$-0.890865\pi$
$157$		−	1322.67i		−	0.672361i	0.941798	−	0.336181i	$-0.109135\pi$
$158$			2386.17i			1.20148i
$159$	−169.325			−0.0844549
$160$	215.075	+	285.907i	0.106270	+	0.141268i
$161$		0			0
$162$		−	1411.32i		−	0.684467i
$163$			1133.89i			0.544866i	0.962175	+	0.272433i	$0.0878283\pi$
$163$			1133.89i			0.544866i	−0.962175	+	0.272433i	$0.912172\pi$
$164$	1240.45			0.590625
$165$	51.2495	+	68.1277i	0.0241804	+	0.0321438i
$166$	−807.256			−0.377441
$167$			483.314i			0.223952i	0.993711	+	0.111976i	$0.0357179\pi$
$167$			483.314i			0.223952i	−0.993711	+	0.111976i	$0.964282\pi$
$168$		0			0
$169$	2003.30			0.911834
$170$	1175.47	−	884.259i	0.530322	−	0.398939i
$171$	−2542.78			−1.13714
$172$		−	791.945i		−	0.351077i
$173$		−	1289.72i		−	0.566795i	−0.959003	−	0.283398i	$-0.908538\pi$
$173$		−	1289.72i		−	0.566795i	0.959003	−	0.283398i	$-0.0914616\pi$
$174$	137.496			0.0599054
$175$		0			0
$176$	226.869			0.0971642
$177$			130.217i			0.0552976i
$178$			2168.60i			0.913164i
$179$	−2735.61			−1.14229			−0.571143	−	0.820851i	$-0.693500\pi$
$179$	−2735.61			−1.14229			−0.571143	+	0.820851i	$0.693500\pi$
$180$	954.600	−	718.104i	0.395287	−	0.297357i
$181$	−1146.35			−0.470761			−0.235380	−	0.971903i	$-0.575634\pi$
$181$	−1146.35			−0.470761			−0.235380	+	0.971903i	$0.575634\pi$
$182$		0			0
$183$			236.947i			0.0957137i
$184$	−555.825			−0.222695
$185$	−1932.87	−	2569.43i	−0.768148	−	1.02112i
$186$	105.795			0.0417059
$187$		−	932.748i		−	0.364755i
$188$		−	2155.53i		−	0.836215i
$189$		0			0
$190$	−1279.65	−	1701.09i	−0.488610	−	0.649526i
$191$	4247.74			1.60919			0.804597	−	0.593822i	$-0.202382\pi$
$191$	4247.74			1.60919			0.804597	+	0.593822i	$0.202382\pi$
$192$			34.4171i			0.0129367i
$193$			5298.59i			1.97617i	0.153903	+	0.988086i	$0.450816\pi$
$193$			5298.59i			1.97617i	−0.153903	+	0.988086i	$0.549184\pi$
$194$	−333.445			−0.123402
$195$	66.8705	−	50.3038i	0.0245574	−	0.0184735i
$196$		0			0
$197$		−	653.948i		−	0.236507i	−0.992983	−	0.118253i	$-0.962270\pi$
$197$		−	653.948i		−	0.236507i	0.992983	−	0.118253i	$-0.0377295\pi$
$198$		−	757.482i		−	0.271878i
$199$	4484.94			1.59763			0.798817	−	0.601574i	$-0.205460\pi$
$199$	4484.94			1.59763			0.798817	+	0.601574i	$0.205460\pi$
$200$	960.804	+	277.229i	0.339696	+	0.0980151i
$201$	−461.606			−0.161986
$202$			1668.73i			0.581244i
$203$		0			0
$204$	141.502			0.0485644
$205$	2770.72	−	2084.29i	0.943977	−	0.710113i
$206$	2830.21			0.957234
$207$			1855.82i			0.623131i
$208$		−	222.683i		−	0.0742320i
$209$	−1349.83			−0.446743
$210$		0			0
$211$	2160.14			0.704787			0.352394	−	0.935852i	$-0.385368\pi$
$211$	2160.14			0.704787			0.352394	+	0.935852i	$0.385368\pi$
$212$			1259.47i			0.408021i
$213$		−	76.4953i		−	0.0246074i
$214$	−3138.11			−1.00241
$215$	−1330.69	−	1768.93i	−0.422103	−	0.561115i
$216$	231.071			0.0727889
$217$		0			0
$218$			1500.80i			0.466270i
$219$	247.201			0.0762752
$220$	506.745	−	381.203i	0.155294	−	0.116821i
$221$	−915.535			−0.278668
$222$		−	309.304i		−	0.0935096i
$223$		−	6026.45i		−	1.80969i	−0.425742	−	0.904845i	$-0.639987\pi$
$223$		−	6026.45i		−	1.80969i	0.425742	−	0.904845i	$-0.360013\pi$
$224$		0			0
$225$	925.625	−	3207.98i	0.274259	−	0.950513i
$226$	4034.19			1.18739
$227$		−	4659.04i		−	1.36225i	−0.732165	−	0.681127i	$-0.761490\pi$
$227$		−	4659.04i		−	1.36225i	0.732165	−	0.681127i	$-0.238510\pi$
$228$		−	204.775i		−	0.0594804i
$229$	−356.000			−0.102730			−0.0513649	−	0.998680i	$-0.516357\pi$
$229$	−356.000			−0.102730			−0.0513649	+	0.998680i	$0.516357\pi$
$230$	−1241.52	+	933.938i	−0.355927	+	0.267748i
$231$		0			0
$232$		−	1022.72i		−	0.289417i
$233$		−	3308.76i		−	0.930318i	−0.885227	−	0.465159i	$-0.845997\pi$
$233$		−	3308.76i		−	0.930318i	0.885227	−	0.465159i	$-0.154003\pi$
$234$	−743.504			−0.207711
$235$	−3621.89	−	4814.70i	−1.00539	−	1.33649i
$236$	968.573			0.267156
$237$			641.602i			0.175850i
$238$		0			0
$239$	−985.684			−0.266772			−0.133386	−	0.991064i	$-0.542585\pi$
$239$	−985.684			−0.266772			−0.133386	+	0.991064i	$0.542585\pi$
$240$	57.8302	+	76.8756i	0.0155538	+	0.0206762i
$241$	−351.514			−0.0939544			−0.0469772	−	0.998896i	$-0.514959\pi$
$241$	−351.514			−0.0939544			−0.0469772	+	0.998896i	$0.514959\pi$
$242$			2259.89i			0.600295i
$243$		−	1159.34i		−	0.306058i
$244$	1762.45			0.462415
$245$		0			0
$246$	333.535			0.0864449
$247$			1324.92i			0.341305i
$248$		−	786.923i		−	0.201491i
$249$	−217.058			−0.0552429
$250$	2611.92	−	995.185i	0.660768	−	0.251764i
$251$	16.6514			0.00418737			0.00209368	−	0.999998i	$-0.499334\pi$
$251$	16.6514			0.00418737			0.00209368	+	0.999998i	$0.499334\pi$
$252$		0			0
$253$			985.152i			0.244806i
$254$	179.555			0.0443555
$255$	316.066	−	237.763i	0.0776188	−	0.0583893i
$256$	256.000			0.0625000
$257$		−	7095.34i		−	1.72216i	−0.508469	−	0.861081i	$-0.669788\pi$
$257$		−	7095.34i		−	1.72216i	0.508469	−	0.861081i	$-0.330212\pi$
$258$		−	212.941i		−	0.0513842i
$259$		0			0
$260$	−374.168	−	497.394i	−0.0892497	−	0.118643i
$261$	−3414.70			−0.809827
$262$		−	2812.93i		−	0.663296i
$263$			4943.46i			1.15904i	0.814959	+	0.579519i	$0.196760\pi$
$263$			4943.46i			1.15904i	−0.814959	+	0.579519i	$0.803240\pi$
$264$	61.0013			0.0142211
$265$	2116.25	+	2813.20i	0.490567	+	0.652127i
$266$		0			0
$267$			583.100i			0.133652i
$268$			3433.50i			0.782591i
$269$	2145.29			0.486248			0.243124	−	0.969995i	$-0.421828\pi$
$269$	2145.29			0.486248			0.243124	+	0.969995i	$0.421828\pi$
$270$	516.131	−	388.263i	0.116336	−	0.0875146i
$271$	8339.99			1.86944			0.934720	−	0.355385i	$-0.115650\pi$
$271$	8339.99			1.86944			0.934720	+	0.355385i	$0.115650\pi$
$272$		−	1052.52i		−	0.234626i
$273$		0			0
$274$	−1293.77			−0.285254
$275$	491.364	−	1702.94i	0.107747	−	0.373423i
$276$	−149.452			−0.0325940
$277$			1094.05i			0.237311i	0.992935	+	0.118655i	$0.0378584\pi$
$277$			1094.05i			0.237311i	−0.992935	+	0.118655i	$0.962142\pi$
$278$			2619.67i			0.565171i
$279$	−2627.42			−0.563798
$280$		0			0
$281$	−5699.48			−1.20997			−0.604987	−	0.796235i	$-0.706822\pi$
$281$	−5699.48			−1.20997			−0.604987	+	0.796235i	$0.706822\pi$
$282$		−	579.587i		−	0.122390i
$283$			6101.50i			1.28161i	0.767703	+	0.640806i	$0.221400\pi$
$283$			6101.50i			1.28161i	−0.767703	+	0.640806i	$0.778600\pi$
$284$	−568.985			−0.118884
$285$	−344.078	−	457.394i	−0.0715137	−	0.0950656i
$286$	−394.686			−0.0816023
$287$		0			0
$288$		−	854.746i		−	0.174883i
$289$	585.692			0.119213
$290$	−1718.45	−	2284.39i	−0.347968	−	0.462566i
$291$	−89.6579			−0.0180613
$292$		−	1838.72i		−	0.368503i
$293$		−	9195.72i		−	1.83351i	−0.399446	−	0.916757i	$-0.630797\pi$
$293$		−	9195.72i		−	1.83351i	0.399446	−	0.916757i	$-0.369203\pi$
$294$		0			0
$295$	2163.45	−	1627.47i	0.426986	−	0.321203i
$296$	−2300.66			−0.451767
$297$		−	409.554i		−	0.0800159i
$298$			2915.08i			0.566665i
$299$	966.972			0.187028
$300$	258.344	+	74.5422i	0.0497184	+	0.0143456i
$301$		0			0
$302$			3887.72i			0.740771i
$303$			448.693i			0.0850718i
$304$	−1523.15			−0.287364
$305$	3936.69	−	2961.40i	0.739063	−	0.555965i
$306$	−3514.20			−0.656514
$307$			7888.57i			1.46653i	0.679944	+	0.733264i	$0.262004\pi$
$307$			7888.57i			1.46653i	−0.679944	+	0.733264i	$0.737996\pi$
$308$		0			0
$309$	760.997			0.140102
$310$	−1322.25	−	1757.71i	−0.242254	−	0.322036i
$311$	1745.55			0.318267			0.159133	−	0.987257i	$-0.449130\pi$
$311$	1745.55			0.318267			0.159133	+	0.987257i	$0.449130\pi$
$312$		−	59.8756i		−	0.0108647i
$313$			7968.41i			1.43898i	0.694502	+	0.719491i	$0.255625\pi$
$313$			7968.41i			1.43898i	−0.694502	+	0.719491i	$0.744375\pi$
$314$	−2645.34			−0.475431
$315$		0			0
$316$	4772.34			0.849574
$317$		−	3587.39i		−	0.635608i	−0.948156	−	0.317804i	$-0.897055\pi$
$317$		−	3587.39i		−	0.635608i	0.948156	−	0.317804i	$-0.102945\pi$
$318$			338.650i			0.0597187i
$319$	−1812.68			−0.318153
$320$	571.813	−	430.151i	0.0998917	−	0.0751442i
$321$	−843.784			−0.146715
$322$		0			0
$323$			6262.26i			1.07877i
$324$	−2822.64			−0.483991
$325$	−1671.52	−	482.297i	−0.285290	−	0.0823169i
$326$	2267.78			0.385278
$327$			403.540i			0.0682440i
$328$		−	2480.89i		−	0.417635i
$329$		0			0
$330$	136.255	−	102.499i	0.0227291	−	0.0170981i
$331$	−1442.47			−0.239532			−0.119766	−	0.992802i	$-0.538214\pi$
$331$	−1442.47			−0.239532			−0.119766	+	0.992802i	$0.538214\pi$
$332$			1614.51i			0.266891i
$333$			7681.55i			1.26410i
$334$	966.627			0.158358
$335$	5769.23	+	7669.22i	0.940915	+	1.25079i
$336$		0			0
$337$		−	5613.50i		−	0.907380i	−0.891160	−	0.453690i	$-0.850107\pi$
$337$		−	5613.50i		−	0.907380i	0.891160	−	0.453690i	$-0.149893\pi$
$338$		−	4006.60i		−	0.644764i
$339$	1084.73			0.173788
$340$	−1768.52	−	2350.95i	−0.282092	−	0.374994i
$341$	−1394.75			−0.221496
$342$			5085.57i			0.804082i
$343$		0			0
$344$	−1583.89			−0.248249
$345$	−333.823	+	251.121i	−0.0520940	+	0.0391880i
$346$	−2579.44			−0.400785
$347$		−	11217.9i		−	1.73547i	−0.497029	−	0.867734i	$-0.665576\pi$
$347$		−	11217.9i		−	1.73547i	0.497029	−	0.867734i	$-0.334424\pi$
$348$		−	274.992i		−	0.0423595i
$349$	5462.91			0.837888			0.418944	−	0.908012i	$-0.362400\pi$
$349$	5462.91			0.837888			0.418944	+	0.908012i	$0.362400\pi$
$350$		0			0
$351$	−401.996			−0.0611309
$352$		−	453.738i		−	0.0687055i
$353$			1434.34i			0.216268i	0.994136	+	0.108134i	$0.0344875\pi$
$353$			1434.34i			0.216268i	−0.994136	+	0.108134i	$0.965513\pi$
$354$	260.433			0.0391013
$355$	−1270.91	+	956.052i	−0.190008	+	0.142935i
$356$	4337.19			0.645704
$357$		0			0
$358$			5471.22i			0.807718i
$359$	−174.484			−0.0256515			−0.0128258	−	0.999918i	$-0.504083\pi$
$359$	−174.484			−0.0256515			−0.0128258	+	0.999918i	$0.504083\pi$
$360$	−1436.21	−	1909.20i	−0.210263	−	0.279510i
$361$	2203.43			0.321246
$362$			2292.70i			0.332878i
$363$			607.648i			0.0878602i
$364$		0			0
$365$	−3089.56	−	4107.05i	−0.443054	−	0.588967i
$366$	473.893			0.0676798
$367$			12258.5i			1.74356i	0.489893	+	0.871782i	$0.337036\pi$
$367$			12258.5i			1.74356i	−0.489893	+	0.871782i	$0.662964\pi$
$368$			1111.65i			0.157469i
$369$	−8283.33			−1.16860
$370$	−5138.85	+	3865.74i	−0.722044	+	0.543163i
$371$		0			0
$372$		−	211.591i		−	0.0294905i
$373$			5921.30i			0.821966i	0.911643	+	0.410983i	$0.134814\pi$
$373$			5921.30i			0.821966i	−0.911643	+	0.410983i	$0.865186\pi$
$374$	−1865.50			−0.257921
$375$	702.301	−	267.589i	0.0967111	−	0.0368486i
$376$	−4311.07			−0.591293
$377$			1779.23i			0.243064i
$378$		0			0
$379$	6322.18			0.856857			0.428428	−	0.903576i	$-0.359067\pi$
$379$	6322.18			0.856857			0.428428	+	0.903576i	$0.359067\pi$
$380$	−3402.17	+	2559.31i	−0.459284	+	0.345499i
$381$	48.2794			0.00649194
$382$		−	8495.49i		−	1.13787i
$383$			11997.0i			1.60057i	0.599619	+	0.800285i	$0.295319\pi$
$383$			11997.0i			1.60057i	−0.599619	+	0.800285i	$0.704681\pi$
$384$	68.8341			0.00914760
$385$		0			0
$386$	10597.2			1.39736
$387$			5288.37i			0.694633i
$388$			666.891i			0.0872583i
$389$	14636.9			1.90776			0.953879	−	0.300191i	$-0.0970505\pi$
$389$	14636.9			1.90776			0.953879	+	0.300191i	$0.0970505\pi$
$390$	−100.608	−	133.741i	−0.0130627	−	0.0173647i
$391$	4570.43			0.591142
$392$		0			0
$393$		−	756.351i		−	0.0970810i
$394$	−1307.90			−0.167236
$395$	10659.7	−	8018.85i	1.35785	−	1.02145i
$396$	−1514.96			−0.192247
$397$			6298.50i			0.796254i	0.917330	+	0.398127i	$0.130340\pi$
$397$			6298.50i			0.796254i	−0.917330	+	0.398127i	$0.869660\pi$
$398$		−	8969.88i		−	1.12970i
$399$		0			0
$400$	554.457	−	1921.61i	0.0693071	−	0.240201i
$401$	−8289.93			−1.03237			−0.516183	−	0.856478i	$-0.672648\pi$
$401$	−8289.93			−1.03237			−0.516183	+	0.856478i	$0.672648\pi$
$402$			923.211i			0.114541i
$403$			1369.02i			0.169220i
$404$	3337.46			0.411002
$405$	−6304.77	+	4742.81i	−0.773547	+	0.581906i
$406$		0			0
$407$			4077.72i			0.496622i
$408$		−	283.004i		−	0.0343402i
$409$	−9522.06			−1.15119			−0.575593	−	0.817736i	$-0.695229\pi$
$409$	−9522.06			−1.15119			−0.575593	+	0.817736i	$0.695229\pi$
$410$	−4168.58	−	5541.44i	−0.502126	−	0.667493i
$411$	−347.874			−0.0417503
$412$		−	5660.42i		−	0.676867i
$413$		0			0
$414$	3711.63			0.440620
$415$	2712.82	+	3606.25i	0.320885	+	0.426563i
$416$	−445.365			−0.0524899
$417$			704.387i			0.0827194i
$418$			2699.65i			0.315895i
$419$	8936.51			1.04195			0.520975	−	0.853572i	$-0.325568\pi$
$419$	8936.51			1.04195			0.520975	+	0.853572i	$0.325568\pi$
$420$		0			0
$421$	−10741.8			−1.24352			−0.621760	−	0.783207i	$-0.713582\pi$
$421$	−10741.8			−1.24352			−0.621760	+	0.783207i	$0.713582\pi$
$422$		−	4320.28i		−	0.498360i
$423$			14394.0i			1.65452i
$424$	2518.93			0.288515
$425$	−7900.48	−	2279.59i	−0.901717	−	0.260180i
$426$	−152.991			−0.0174001
$427$		0			0
$428$			6276.21i			0.708813i
$429$	−106.124			−0.0119434
$430$	−3537.85	+	2661.37i	−0.396768	+	0.298472i
$431$	7886.50			0.881391			0.440695	−	0.897657i	$-0.354732\pi$
$431$	7886.50			0.881391			0.440695	+	0.897657i	$0.354732\pi$
$432$		−	462.142i		−	0.0514695i
$433$		−	3756.12i		−	0.416877i	−0.978035	−	0.208438i	$-0.933162\pi$
$433$		−	3756.12i		−	0.416877i	0.978035	−	0.208438i	$-0.0668381\pi$
$434$		0			0
$435$	−462.062	−	614.235i	−0.0509292	−	0.0677018i
$436$	3001.60			0.329703
$437$		−	6614.09i		−	0.724016i
$438$		−	494.401i		−	0.0539347i
$439$	6920.65			0.752402			0.376201	−	0.926538i	$-0.377230\pi$
$439$	6920.65			0.752402			0.376201	+	0.926538i	$0.377230\pi$
$440$	−762.405	−	1013.49i	−0.0826051	−	0.109810i
$441$		0			0
$442$			1831.07i			0.197048i
$443$			11618.9i			1.24611i	0.782176	+	0.623057i	$0.214110\pi$
$443$			11618.9i			1.24611i	−0.782176	+	0.623057i	$0.785890\pi$
$444$	−618.608			−0.0661213
$445$	9687.75	−	7287.68i	1.03201	−	0.776335i
$446$	−12052.9			−1.27964
$447$			783.817i			0.0829379i
$448$		0			0
$449$	−17715.7			−1.86204			−0.931018	−	0.364973i	$-0.881078\pi$
$449$	−17715.7			−1.86204			−0.931018	+	0.364973i	$0.881078\pi$
$450$	−6415.96	−	1851.25i	−0.672114	−	0.193931i
$451$	−4397.17			−0.459101
$452$		−	8068.37i		−	0.839611i
$453$			1045.34i			0.108420i
$454$	−9318.09			−0.963259
$455$		0			0
$456$	−409.549			−0.0420590
$457$		−	2724.63i		−	0.278890i	−0.990230	−	0.139445i	$-0.955468\pi$
$457$		−	2724.63i		−	0.278890i	0.990230	−	0.139445i	$-0.0445319\pi$
$458$			712.000i			0.0726410i
$459$	−1900.05			−0.193217
$460$	1867.88	+	2483.03i	0.189327	+	0.251678i
$461$	−11108.3			−1.12227			−0.561135	−	0.827724i	$-0.689635\pi$
$461$	−11108.3			−1.12227			−0.561135	+	0.827724i	$0.689635\pi$
$462$		0			0
$463$			14640.7i			1.46957i	0.678301	+	0.734784i	$0.262716\pi$
$463$			14640.7i			1.46957i	−0.678301	+	0.734784i	$0.737284\pi$
$464$	−2045.44			−0.204649
$465$	−355.531	−	472.619i	−0.0354566	−	0.0471337i
$466$	−6617.52			−0.657834
$467$			1242.76i			0.123143i	0.998103	+	0.0615716i	$0.0196113\pi$
$467$			1242.76i			0.123143i	−0.998103	+	0.0615716i	$0.980389\pi$
$468$			1487.01i			0.146874i
$469$		0			0
$470$	−9629.40	+	7243.78i	−0.945045	+	0.710916i
$471$	−711.289			−0.0695849
$472$		−	1937.15i		−	0.188908i
$473$			2807.31i			0.272897i
$474$	1283.20			0.124345
$475$	−3298.91	+	11433.2i	−0.318662	+	1.10440i
$476$		0			0
$477$		−	8410.34i		−	0.807302i
$478$			1971.37i			0.188637i
$479$	3197.61			0.305015			0.152508	−	0.988302i	$-0.451265\pi$
$479$	3197.61			0.305015			0.152508	+	0.988302i	$0.451265\pi$
$480$	153.751	−	115.660i	0.0146203	−	0.0109982i
$481$	4002.47			0.379411
$482$			703.028i			0.0664358i
$483$		0			0
$484$	4519.79			0.424473
$485$	1120.56	+	1489.60i	0.104911	+	0.139462i
$486$	−2318.69			−0.216415
$487$		−	7448.42i		−	0.693060i	−0.938039	−	0.346530i	$-0.887360\pi$
$487$		−	7448.42i		−	0.693060i	0.938039	−	0.346530i	$-0.112640\pi$
$488$		−	3524.90i		−	0.326977i
$489$	609.769			0.0563900
$490$		0			0
$491$	−20139.2			−1.85106			−0.925528	−	0.378679i	$-0.876378\pi$
$491$	−20139.2			−1.85106			−0.925528	+	0.378679i	$0.876378\pi$
$492$		−	667.071i		−	0.0611258i
$493$			8409.59i			0.768254i
$494$	2649.83			0.241339
$495$	−3383.89	+	2545.56i	−0.307262	+	0.231140i
$496$	−1573.85			−0.142475
$497$		0			0
$498$			434.115i			0.0390626i
$499$	17794.2			1.59635			0.798174	−	0.602427i	$-0.205799\pi$
$499$	17794.2			1.59635			0.798174	+	0.602427i	$0.205799\pi$
$500$	−1990.37	−	5223.83i	−0.178024	−	0.467234i
$501$	259.910			0.0231775
$502$		−	33.3029i		−	0.00296092i
$503$		−	16316.2i		−	1.44633i	−0.690674	−	0.723166i	$-0.742686\pi$
$503$		−	16316.2i		−	1.44633i	0.690674	−	0.723166i	$-0.257314\pi$
$504$		0			0
$505$	7454.70	−	5607.85i	0.656890	−	0.494150i
$506$	1970.30			0.173104
$507$		−	1077.31i		−	0.0943687i
$508$		−	359.110i		−	0.0313641i
$509$	−8586.36			−0.747709			−0.373854	−	0.927487i	$-0.621964\pi$
$509$	−8586.36			−0.747709			−0.373854	+	0.927487i	$0.621964\pi$
$510$	−475.525	−	632.131i	−0.0412875	−	0.0548848i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$			2749.65i			0.236647i
$514$	−14190.7			−1.21775
$515$	−9511.07	−	12643.4i	−0.813802	−	1.08181i
$516$	−425.882			−0.0363341
$517$			7641.00i			0.650001i
$518$		0			0
$519$	−693.568			−0.0586595
$520$	−994.788	+	748.336i	−0.0838929	+	0.0631091i
$521$	8784.84			0.738715			0.369358	−	0.929287i	$-0.379578\pi$
$521$	8784.84			0.738715			0.369358	+	0.929287i	$0.379578\pi$
$522$			6829.41i			0.572634i
$523$			6156.83i			0.514760i	0.966310	+	0.257380i	$0.0828592\pi$
$523$			6156.83i			0.514760i	−0.966310	+	0.257380i	$0.917141\pi$
$524$	−5625.86			−0.469021
$525$		0			0
$526$	9886.93			0.819564
$527$			6470.70i			0.534854i
$528$		−	122.003i		−	0.0100558i
$529$	7339.80			0.603254
$530$	5626.41	−	4232.50i	0.461124	−	0.346883i
$531$	−6467.84			−0.528588
$532$		0			0
$533$			4316.03i			0.350746i
$534$	1166.20			0.0945063
$535$	10545.8	+	14018.8i	0.852211	+	1.13287i
$536$	6867.00			0.553375
$537$			1471.12i			0.118219i
$538$		−	4290.58i		−	0.343829i
$539$		0			0
$540$	−776.526	−	1032.26i	−0.0618822	−	0.0822620i
$541$	−9921.09			−0.788431			−0.394215	−	0.919018i	$-0.628984\pi$
$541$	−9921.09			−0.788431			−0.394215	+	0.919018i	$0.628984\pi$
$542$		−	16680.0i		−	1.32189i
$543$			616.470i			0.0487206i
$544$	−2105.03			−0.165905
$545$	6704.50	−	5043.51i	0.526953	−	0.396404i
$546$		0			0
$547$		−	17559.1i		−	1.37253i	−0.727353	−	0.686264i	$-0.759249\pi$
$547$		−	17559.1i		−	1.37253i	0.727353	−	0.686264i	$-0.240751\pi$
$548$			2587.54i			0.201705i
$549$	−11769.1			−0.914924
$550$	−3405.89	−	982.728i	−0.264050	−	0.0761885i
$551$	12169.9			0.940938
$552$			298.904i			0.0230475i
$553$		0			0
$554$	2188.10			0.167804
$555$	−1381.75	+	1039.43i	−0.105679	+	0.0794981i
$556$	5239.35			0.399636
$557$			642.121i			0.0488466i	0.999702	+	0.0244233i	$0.00777495\pi$
$557$			642.121i			0.0488466i	−0.999702	+	0.0244233i	$0.992225\pi$
$558$			5254.84i			0.398665i
$559$	2755.51			0.208489
$560$		0			0
$561$	−501.601			−0.0377497
$562$			11399.0i			0.855581i
$563$			3933.27i			0.294436i	0.989104	+	0.147218i	$0.0470320\pi$
$563$			3933.27i			0.294436i	−0.989104	+	0.147218i	$0.952968\pi$
$564$	−1159.17			−0.0865426
$565$	−13557.1	−	18021.9i	−1.00947	−	1.34192i
$566$	12203.0			0.906237
$567$		0			0
$568$			1137.97i			0.0840637i
$569$	15117.4			1.11380			0.556902	−	0.830578i	$-0.311990\pi$
$569$	15117.4			1.11380			0.556902	+	0.830578i	$0.311990\pi$
$570$	−914.788	+	688.156i	−0.0672215	+	0.0505678i
$571$	−20883.6			−1.53056			−0.765282	−	0.643695i	$-0.777400\pi$
$571$	−20883.6			−1.53056			−0.765282	+	0.643695i	$0.777400\pi$
$572$			789.372i			0.0577015i
$573$		−	2284.30i		−	0.166541i
$574$		0			0
$575$	8344.35	+	2407.66i	0.605189	+	0.174620i
$576$	−1709.49			−0.123661
$577$		−	738.564i		−	0.0532874i	−0.999645	−	0.0266437i	$-0.991518\pi$
$577$		−	738.564i		−	0.0532874i	0.999645	−	0.0266437i	$-0.00848196\pi$
$578$		−	1171.38i		−	0.0842961i
$579$	2849.41			0.204520
$580$	−4568.78	+	3436.90i	−0.327083	+	0.246051i
$581$		0			0
$582$			179.316i			0.0127713i
$583$		−	4464.60i		−	0.317161i
$584$	−3677.44			−0.260571
$585$	2498.58	+	3321.45i	0.176587	+	0.234744i
$586$	−18391.4			−1.29649
$587$		−	9348.74i		−	0.657349i	−0.944443	−	0.328674i	$-0.893398\pi$
$587$		−	9348.74i		−	0.657349i	0.944443	−	0.328674i	$-0.106602\pi$
$588$		0			0
$589$	9364.07			0.655076
$590$	−3254.94	−	4326.90i	−0.227125	−	0.301925i
$591$	−351.671			−0.0244769
$592$			4601.31i			0.319447i
$593$		−	20470.1i		−	1.41755i	−0.705434	−	0.708775i	$-0.749248\pi$
$593$		−	20470.1i		−	1.41755i	0.705434	−	0.708775i	$-0.250752\pi$
$594$	−819.108			−0.0565798
$595$		0			0
$596$	5830.16			0.400692
$597$		−	2411.85i		−	0.165344i
$598$		−	1933.94i		−	0.132249i
$599$	−2394.09			−0.163306			−0.0816528	−	0.996661i	$-0.526020\pi$
$599$	−2394.09			−0.163306			−0.0816528	+	0.996661i	$0.526020\pi$
$600$	149.084	−	516.688i	0.0101439	−	0.0351562i
$601$	−5007.10			−0.339840			−0.169920	−	0.985458i	$-0.554351\pi$
$601$	−5007.10			−0.339840			−0.169920	+	0.985458i	$0.554351\pi$
$602$		0			0
$603$		−	22927.9i		−	1.54842i
$604$	7775.43			0.523804
$605$	10095.6	−	7594.49i	0.678421	−	0.510347i
$606$	897.387			0.0601549
$607$			15037.7i			1.00554i	0.864422	+	0.502768i	$0.167685\pi$
$607$			15037.7i			1.00554i	−0.864422	+	0.502768i	$0.832315\pi$
$608$			3046.30i			0.203197i
$609$		0			0
$610$	−5922.80	−	7873.37i	−0.393127	−	0.522596i
$611$	7500.00			0.496591
$612$			7028.39i			0.464225i
$613$			29396.1i			1.93687i	0.249276	+	0.968433i	$0.419807\pi$
$613$			29396.1i			1.93687i	−0.249276	+	0.968433i	$0.580193\pi$
$614$	15777.1			1.03699
$615$	−1120.86	−	1490.00i	−0.0734919	−	0.0976953i
$616$		0			0
$617$			14648.4i			0.955788i	0.878417	+	0.477894i	$0.158600\pi$
$617$			14648.4i			0.955788i	−0.878417	+	0.477894i	$0.841400\pi$
$618$		−	1521.99i		−	0.0990673i
$619$	8336.14			0.541289			0.270644	−	0.962679i	$-0.412763\pi$
$619$	8336.14			0.541289			0.270644	+	0.962679i	$0.412763\pi$
$620$	−3515.42	+	2644.50i	−0.227714	+	0.171299i
$621$	2006.80			0.129678
$622$		−	3491.10i		−	0.225049i
$623$		0			0
$624$	−119.751			−0.00768251
$625$	−13223.3	−	8323.82i	−0.846289	−	0.532725i
$626$	15936.8			1.01751
$627$			725.891i			0.0462349i
$628$			5290.69i			0.336181i
$629$	18917.8			1.19921
$630$		0			0
$631$	5599.86			0.353292			0.176646	−	0.984274i	$-0.443475\pi$
$631$	5599.86			0.353292			0.176646	+	0.984274i	$0.443475\pi$
$632$		−	9544.69i		−	0.600739i
$633$		−	1161.65i		−	0.0729407i
$634$	−7174.77			−0.449442
$635$	−603.404	−	802.125i	−0.0377092	−	0.0501282i
$636$	677.299			0.0422275
$637$		0			0
$638$			3625.36i			0.224968i
$639$	3799.51			0.235221
$640$	−860.301	−	1143.63i	−0.0531350	−	0.0706341i
$641$	18625.8			1.14770			0.573850	−	0.818960i	$-0.305449\pi$
$641$	18625.8			1.14770			0.573850	+	0.818960i	$0.305449\pi$
$642$			1687.57i			0.103743i
$643$			9741.95i			0.597489i	0.954333	+	0.298744i	$0.0965678\pi$
$643$			9741.95i			0.597489i	−0.954333	+	0.298744i	$0.903432\pi$
$644$		0			0
$645$	−951.269	+	715.599i	−0.0580716	+	0.0436848i
$646$	12524.5			0.762803
$647$		−	15071.8i		−	0.915820i	−0.888999	−	0.457910i	$-0.848598\pi$
$647$		−	15071.8i		−	0.915820i	0.888999	−	0.457910i	$-0.151402\pi$
$648$			5645.27i			0.342233i
$649$	−3433.43			−0.207664
$650$	−964.593	+	3343.04i	−0.0582068	+	0.201730i
$651$		0			0
$652$		−	4535.56i		−	0.272433i
$653$		−	22142.9i		−	1.32698i	−0.748186	−	0.663489i	$-0.769075\pi$
$653$		−	22142.9i		−	1.32698i	0.748186	−	0.663489i	$-0.230925\pi$
$654$	807.079			0.0482558
$655$	−12566.2	+	9453.00i	−0.749621	+	0.563907i
$656$	−4961.79			−0.295313
$657$			12278.4i			0.729113i
$658$		0			0
$659$	12874.3			0.761022			0.380511	−	0.924776i	$-0.375748\pi$
$659$	12874.3			0.761022			0.380511	+	0.924776i	$0.375748\pi$
$660$	−204.998	−	272.511i	−0.0120902	−	0.0160719i
$661$	−13184.1			−0.775799			−0.387899	−	0.921702i	$-0.626799\pi$
$661$	−13184.1			−0.775799			−0.387899	+	0.921702i	$0.626799\pi$
$662$			2884.94i			0.169375i
$663$			492.344i			0.0288402i
$664$	3229.02			0.188720
$665$		0			0
$666$	15363.1			0.893856
$667$		−	8882.06i		−	0.515615i
$668$		−	1933.25i		−	0.111976i
$669$	−3240.82			−0.187291
$670$	15338.4	−	11538.5i	0.884442	−	0.665327i
$671$	−6247.58			−0.359441
$672$		0			0
$673$		−	5699.50i		−	0.326448i	−0.986589	−	0.163224i	$-0.947811\pi$
$673$		−	5699.50i		−	0.326448i	0.986589	−	0.163224i	$-0.0521893\pi$
$674$	−11227.0			−0.641615
$675$	−3468.97	−	1000.93i	−0.197808	−	0.0570753i
$676$	−8013.20			−0.455917
$677$		−	23186.5i		−	1.31629i	−0.752889	−	0.658147i	$-0.771340\pi$
$677$		−	23186.5i		−	1.31629i	0.752889	−	0.658147i	$-0.228660\pi$
$678$		−	2169.45i		−	0.122887i
$679$		0			0
$680$	−4701.90	+	3537.04i	−0.265161	+	0.199469i
$681$	−2505.48			−0.140984
$682$			2789.51i			0.156621i
$683$		−	9258.04i		−	0.518666i	−0.965788	−	0.259333i	$-0.916497\pi$
$683$		−	9258.04i		−	0.518666i	0.965788	−	0.259333i	$-0.0835027\pi$
$684$	10171.1			0.568572
$685$	4347.79	+	5779.66i	0.242512	+	0.322379i
$686$		0			0
$687$			191.445i			0.0106318i
$688$			3167.78i			0.175539i
$689$	−4382.21			−0.242306
$690$	502.241	+	667.646i	0.0277101	+	0.0368360i
$691$	30149.5			1.65983			0.829913	−	0.557892i	$-0.188390\pi$
$691$	30149.5			1.65983			0.829913	+	0.557892i	$0.188390\pi$
$692$			5158.88i			0.283398i
$693$		0			0
$694$	−22435.8			−1.22716
$695$	11702.8	−	8803.55i	0.638726	−	0.480486i
$696$	−549.984			−0.0299527
$697$			20399.8i			1.10861i
$698$		−	10925.8i		−	0.592476i
$699$	−1779.34			−0.0962817
$700$		0			0
$701$	−9299.00			−0.501025			−0.250512	−	0.968113i	$-0.580599\pi$
$701$	−9299.00			−0.501025			−0.250512	+	0.968113i	$0.580599\pi$
$702$			803.992i			0.0432261i
$703$		−	27376.9i		−	1.46876i
$704$	−907.476			−0.0485821
$705$	−2589.19	+	1947.73i	−0.138318	+	0.104051i
$706$	2868.69			0.152924
$707$		0			0
$708$		−	520.867i		−	0.0276488i
$709$	−26855.2			−1.42252			−0.711262	−	0.702927i	$-0.751876\pi$
$709$	−26855.2			−1.42252			−0.711262	+	0.702927i	$0.751876\pi$
$710$	1912.10	+	2541.82i	0.101070	+	0.134356i
$711$	−31868.3			−1.68095
$712$		−	8674.39i		−	0.456582i
$713$		−	6834.24i		−	0.358968i
$714$		0			0
$715$	1326.36	+	1763.18i	0.0693750	+	0.0922225i
$716$	10942.4			0.571143
$717$			530.068i			0.0276091i
$718$			348.967i			0.0181384i
$719$	29252.7			1.51730			0.758651	−	0.651498i	$-0.225859\pi$
$719$	29252.7			1.51730			0.758651	+	0.651498i	$0.225859\pi$
$720$	−3818.40	+	2872.42i	−0.197644	+	0.148679i
$721$		0			0
$722$		−	4406.86i		−	0.227155i
$723$			189.033i			0.00972365i
$724$	4585.41			0.235380
$725$	−4430.11	+	15353.6i	−0.226938	+	0.786509i
$726$	1215.30			0.0621265
$727$		−	2271.26i		−	0.115869i	−0.998320	−	0.0579343i	$-0.981549\pi$
$727$		−	2271.26i		−	0.115869i	0.998320	−	0.0579343i	$-0.0184514\pi$
$728$		0			0
$729$	18429.3			0.936307
$730$	−8214.10	+	6179.11i	−0.416462	+	0.313287i
$731$	13024.0			0.658974
$732$		−	947.787i		−	0.0478568i
$733$		−	7665.14i		−	0.386246i	−0.981175	−	0.193123i	$-0.938138\pi$
$733$		−	7665.14i		−	0.386246i	0.981175	−	0.193123i	$-0.0618617\pi$
$734$	24517.0			1.23289
$735$		0			0
$736$	2223.30			0.111348
$737$		−	12171.2i		−	0.608319i
$738$			16566.7i			0.826324i
$739$	4464.70			0.222242			0.111121	−	0.993807i	$-0.464556\pi$
$739$	4464.70			0.222242			0.111121	+	0.993807i	$0.464556\pi$
$740$	7731.48	+	10277.7i	0.384074	+	0.510562i
$741$	712.496			0.0353228
$742$		0			0
$743$			26438.3i			1.30542i	0.757608	+	0.652710i	$0.226368\pi$
$743$			26438.3i			1.30542i	−0.757608	+	0.652710i	$0.773632\pi$
$744$	−423.181			−0.0208529
$745$	13022.5	−	9796.28i	0.640413	−	0.481755i
$746$	11842.6			0.581217
$747$		−	10781.2i		−	0.528065i
$748$			3730.99i			0.182378i
$749$		0			0
$750$	−535.177	−	1404.60i	−0.0260559	−	0.0683851i
$751$	−30714.1			−1.49238			−0.746188	−	0.665735i	$-0.768118\pi$
$751$	−30714.1			−1.49238			−0.746188	+	0.665735i	$0.768118\pi$
$752$			8622.13i			0.418108i
$753$		−	8.95459i		−	0.000433364i
$754$	3558.46			0.171872
$755$	17367.6	−	13064.9i	0.837179	−	0.629774i
$756$		0			0
$757$		−	7199.44i		−	0.345665i	−0.984951	−	0.172832i	$-0.944708\pi$
$757$		−	7199.44i		−	0.345665i	0.984951	−	0.172832i	$-0.0552919\pi$
$758$		−	12644.4i		−	0.605889i
$759$	529.782			0.0253358
$760$	5118.62	+	6804.35i	0.244305	+	0.324763i
$761$	16957.6			0.807768			0.403884	−	0.914810i	$-0.367660\pi$
$761$	16957.6			0.807768			0.403884	+	0.914810i	$0.367660\pi$
$762$		−	96.5588i		−	0.00459049i
$763$		0			0
$764$	−16991.0			−0.804597
$765$	11809.6	+	15698.9i	0.558141	+	0.741956i
$766$	23994.0			1.13177
$767$			3370.07i			0.158652i
$768$		−	137.668i		−	0.00646833i
$769$	−9879.39			−0.463277			−0.231638	−	0.972802i	$-0.574409\pi$
$769$	−9879.39			−0.463277			−0.231638	+	0.972802i	$0.574409\pi$
$770$		0			0
$771$	−3815.64			−0.178232
$772$		−	21194.4i		−	0.988086i
$773$		−	21797.7i		−	1.01424i	−0.861875	−	0.507121i	$-0.830710\pi$
$773$		−	21797.7i		−	1.01424i	0.861875	−	0.507121i	$-0.169290\pi$
$774$	10576.7			0.491180
$775$	−3408.71	+	11813.7i	−0.157993	+	0.547564i
$776$	1333.78			0.0617010
$777$		0			0
$778$		−	29273.7i		−	1.34899i
$779$	29521.6			1.35779
$780$	−267.482	+	201.215i	−0.0122787	+	0.00923674i
$781$	2016.96			0.0924102
$782$		−	9140.85i		−	0.418000i
$783$			3692.51i			0.168531i
$784$		0			0
$785$	8889.82	+	11817.5i	0.404193	+	0.537306i
$786$	−1512.70			−0.0686467
$787$			5954.44i			0.269699i	0.990866	+	0.134849i	$0.0430550\pi$
$787$			5954.44i			0.269699i	−0.990866	+	0.134849i	$0.956945\pi$
$788$			2615.79i			0.118253i
$789$	2658.43			0.119953
$790$	−16037.7	−	21319.5i	−0.722273	−	0.960142i
$791$		0			0
$792$			3029.93i			0.135939i
$793$			6132.29i			0.274608i
$794$	12597.0			0.563037
$795$	1512.85	−	1138.05i	0.0674908	−	0.0507704i
$796$	−17939.8			−0.798817
$797$		−	30426.4i		−	1.35227i	−0.736779	−	0.676134i	$-0.763654\pi$
$797$		−	30426.4i		−	1.35227i	0.736779	−	0.676134i	$-0.236346\pi$
$798$		0			0
$799$	35449.0			1.56958
$800$	−3843.22	−	1108.91i	−0.169848	−	0.0490075i
$801$	−28962.5			−1.27758
$802$			16579.9i			0.729994i
$803$			6517.95i			0.286443i
$804$	1846.42			0.0809929
$805$		0			0
$806$	2738.03			0.119656
$807$		−	1153.67i		−	0.0503234i
$808$		−	6674.91i		−	0.290622i
$809$	−12450.3			−0.541074			−0.270537	−	0.962710i	$-0.587201\pi$
$809$	−12450.3			−0.541074			−0.270537	+	0.962710i	$0.587201\pi$
$810$	9485.61	+	12609.5i	0.411470	+	0.546980i
$811$	−3330.98			−0.144225			−0.0721126	−	0.997397i	$-0.522974\pi$
$811$	−3330.98			−0.144225			−0.0721126	+	0.997397i	$0.522974\pi$
$812$		0			0
$813$		−	4484.97i		−	0.193474i
$814$	8155.44			0.351165
$815$	−7620.99	−	10130.8i	−0.327548	−	0.435421i
$816$	−566.008			−0.0242822
$817$		−	18847.7i		−	0.807094i
$818$			19044.1i			0.814012i
$819$		0			0
$820$	−11082.9	+	8337.17i	−0.471989	+	0.355057i
$821$	4257.43			0.180981			0.0904905	−	0.995897i	$-0.471157\pi$
$821$	4257.43			0.180981			0.0904905	+	0.995897i	$0.471157\pi$
$822$			695.748i			0.0295219i
$823$		−	9845.13i		−	0.416986i	−0.978024	−	0.208493i	$-0.933144\pi$
$823$		−	9845.13i		−	0.416986i	0.978024	−	0.208493i	$-0.0668559\pi$
$824$	−11320.8			−0.478617
$825$	−915.786	−	264.239i	−0.0386468	−	0.0111511i
$826$		0			0
$827$			31609.5i			1.32911i	0.747242	+	0.664553i	$0.231378\pi$
$827$			31609.5i			1.32911i	−0.747242	+	0.664553i	$0.768622\pi$
$828$		−	7423.26i		−	0.311565i
$829$	−448.283			−0.0187811			−0.00939054	−	0.999956i	$-0.502989\pi$
$829$	−448.283			−0.0187811			−0.00939054	+	0.999956i	$0.502989\pi$
$830$	7212.49	−	5425.65i	0.301626	−	0.226900i
$831$	588.344			0.0245601
$832$			890.730i			0.0371160i
$833$		0			0
$834$	1408.77			0.0584914
$835$	−3248.40	−	4318.21i	−0.134629	−	0.178967i
$836$	5399.30			0.223372
$837$			2841.18i			0.117330i
$838$		−	17873.0i		−	0.736770i
$839$	−14956.1			−0.615424			−0.307712	−	0.951480i	$-0.599563\pi$
$839$	−14956.1			−0.615424			−0.307712	+	0.951480i	$0.599563\pi$
$840$		0			0
$841$	−8045.98			−0.329902
$842$			21483.6i			0.879302i
$843$			3064.99i			0.125224i
$844$	−8640.55			−0.352394
$845$	−17898.6	+	13464.4i	−0.728677	+	0.548152i
$846$	28788.0			1.16992
$847$		0			0
$848$		−	5037.87i		−	0.204011i
$849$	3281.18			0.132638
$850$	−4559.18	+	15801.0i	−0.183975	+	0.637610i
$851$	−19980.7			−0.804851
$852$			305.981i			0.0123037i
$853$			45363.9i			1.82090i	0.413615	+	0.910452i	$0.364266\pi$
$853$			45363.9i			1.82090i	−0.413615	+	0.910452i	$0.635734\pi$
$854$		0			0
$855$	22718.7	−	17090.3i	0.908729	−	0.683598i
$856$	12552.4			0.501207
$857$		−	1714.18i		−	0.0683258i	−0.999416	−	0.0341629i	$-0.989123\pi$
$857$		−	1714.18i		−	0.0683258i	0.999416	−	0.0341629i	$-0.0108765\pi$
$858$			212.249i			0.00844529i
$859$	−34820.1			−1.38306			−0.691529	−	0.722348i	$-0.743063\pi$
$859$	−34820.1			−1.38306			−0.691529	+	0.722348i	$0.743063\pi$
$860$	5322.74	+	7075.70i	0.211051	+	0.280557i
$861$		0			0
$862$		−	15773.0i		−	0.623237i
$863$		−	7309.71i		−	0.288326i	−0.989554	−	0.144163i	$-0.953951\pi$
$863$		−	7309.71i		−	0.288326i	0.989554	−	0.144163i	$-0.0460490\pi$
$864$	−924.284			−0.0363944
$865$	8668.34	+	11523.1i	0.340731	+	0.452945i
$866$	−7512.24			−0.294776
$867$		−	314.966i		−	0.0123377i
$868$		0			0
$869$	−16917.1			−0.660385
$870$	−1228.47	+	924.125i	−0.0478724	+	0.0360124i
$871$	−11946.6			−0.464746
$872$		−	6003.19i		−	0.233135i
$873$		−	4453.30i		−	0.172647i
$874$	−13228.2			−0.511956
$875$		0			0
$876$	−988.803			−0.0381376
$877$		−	2992.90i		−	0.115237i	−0.998339	−	0.0576186i	$-0.981649\pi$
$877$		−	2992.90i		−	0.115237i	0.998339	−	0.0576186i	$-0.0183507\pi$
$878$		−	13841.3i		−	0.532029i
$879$	−4945.15			−0.189756
$880$	−2026.98	+	1524.81i	−0.0776472	+	0.0584106i
$881$	−28667.6			−1.09629			−0.548147	−	0.836382i	$-0.684667\pi$
$881$	−28667.6			−1.09629			−0.548147	+	0.836382i	$0.684667\pi$
$882$		0			0
$883$		−	23488.0i		−	0.895169i	−0.894242	−	0.447585i	$-0.852284\pi$
$883$		−	23488.0i		−	0.895169i	0.894242	−	0.447585i	$-0.147716\pi$
$884$	3662.14			0.139334
$885$	−875.199	−	1163.43i	−0.0332424	−	0.0441902i
$886$	23237.7			0.881136
$887$			22944.5i			0.868546i	0.900781	+	0.434273i	$0.142995\pi$
$887$			22944.5i			0.868546i	−0.900781	+	0.434273i	$0.857005\pi$
$888$			1237.22i			0.0467548i
$889$		0			0
$890$	−14575.4	−	19375.5i	−0.548952	−	0.729740i
$891$	10005.8			0.376213
$892$			24105.8i			0.904845i
$893$		−	51300.0i		−	1.92238i
$894$	1567.63			0.0586460
$895$	24441.5	−	18386.3i	0.912839	−	0.686689i
$896$		0			0
$897$		−	520.005i		−	0.0193562i
$898$			35431.3i			1.31666i
$899$	12575.0			0.466519
$900$	−3702.50	+	12831.9i	−0.137130	+	0.475256i
$901$	−20712.7			−0.765858
$902$			8794.34i			0.324634i
$903$		0			0
$904$	−16136.7			−0.593695
$905$	10242.2	−	7704.75i	0.376201	−	0.283000i
$906$	2090.68			0.0766648
$907$		−	14063.6i		−	0.514855i	−0.966298	−	0.257428i	$-0.917125\pi$
$907$		−	14063.6i		−	0.514855i	0.966298	−	0.257428i	$-0.0828749\pi$
$908$			18636.2i			0.681127i
$909$	−22286.5			−0.813199
$910$		0			0
$911$	−1591.22			−0.0578700			−0.0289350	−	0.999581i	$-0.509212\pi$
$911$	−1591.22			−0.0578700			−0.0289350	+	0.999581i	$0.509212\pi$
$912$			819.099i			0.0297402i
$913$		−	5723.17i		−	0.207458i
$914$	−5449.26			−0.197205
$915$	−1592.54	−	2117.02i	−0.0575386	−	0.0764880i
$916$	1424.00			0.0513649
$917$		0			0
$918$			3800.10i			0.136625i
$919$	−33319.1			−1.19597			−0.597984	−	0.801508i	$-0.704031\pi$
$919$	−33319.1			−1.19597			−0.597984	+	0.801508i	$0.704031\pi$
$920$	4966.06	−	3735.75i	0.177963	−	0.133874i
$921$	4242.21			0.151776
$922$			22216.7i			0.793565i
$923$		−	1979.74i		−	0.0706000i
$924$		0			0
$925$	34538.8	+	9965.75i	1.22771	+	0.354240i
$926$	29281.4			1.03914
$927$			37798.6i			1.33923i
$928$			4090.87i			0.144709i
$929$	−44409.8			−1.56839			−0.784197	−	0.620512i	$-0.786925\pi$
$929$	−44409.8			−1.56839			−0.784197	+	0.620512i	$0.786925\pi$
$930$	−945.237	+	711.061i	−0.0333285	+	0.0250716i
$931$		0			0
$932$			13235.0i			0.465159i
$933$		−	938.698i		−	0.0329385i
$934$	2485.51			0.0870754
$935$	6269.09	+	8333.71i	0.219274	+	0.291488i
$936$	2974.02			0.103855
$937$		−	25069.7i		−	0.874055i	−0.899448	−	0.437028i	$-0.856031\pi$
$937$		−	25069.7i		−	0.874055i	0.899448	−	0.437028i	$-0.143969\pi$
$938$		0			0
$939$	4285.15			0.148925
$940$	14487.6	+	19258.8i	0.502694	+	0.668247i
$941$	−27867.4			−0.965409			−0.482704	−	0.875783i	$-0.660345\pi$
$941$	−27867.4			−0.965409			−0.482704	+	0.875783i	$0.660345\pi$
$942$			1422.58i			0.0492039i
$943$		−	21546.0i		−	0.744043i
$944$	−3874.29			−0.133578
$945$		0			0
$946$	5614.62			0.192967
$947$			31947.8i			1.09627i	0.836391	+	0.548133i	$0.184661\pi$
$947$			31947.8i			1.09627i	−0.836391	+	0.548133i	$0.815339\pi$
$948$		−	2566.41i		−	0.0879252i
$949$	6397.67			0.218838
$950$	22866.4	+	6597.82i	0.780929	+	0.225328i
$951$	−1929.18			−0.0657811
$952$		0			0
$953$		−	13026.8i		−	0.442792i	−0.975184	−	0.221396i	$-0.928939\pi$
$953$		−	13026.8i		−	0.442792i	0.975184	−	0.221396i	$-0.0710613\pi$
$954$	−16820.7			−0.570849
$955$	−37951.8	+	28549.5i	−1.28596	+	0.967372i
$956$	3942.74			0.133386
$957$			974.800i			0.0329266i
$958$		−	6395.21i		−	0.215678i
$959$		0			0
$960$	−231.321	−	307.502i	−0.00777692	−	0.0103381i
$961$	−20115.2			−0.675212
$962$		−	8004.94i		−	0.268284i
$963$		−	41910.7i		−	1.40244i
$964$	1406.06			0.0469772
$965$	−35612.4	−	47340.7i	−1.18798	−	1.57923i
$966$		0			0
$967$			25825.8i			0.858844i	0.903104	+	0.429422i	$0.141283\pi$
$967$			25825.8i			0.858844i	−0.903104	+	0.429422i	$0.858717\pi$
$968$		−	9039.58i		−	0.300148i
$969$	3367.64			0.111645
$970$	2979.19	−	2241.12i	0.0986146	−	0.0741835i
$971$	27715.9			0.916011			0.458005	−	0.888949i	$-0.348564\pi$
$971$	27715.9			0.916011			0.458005	+	0.888949i	$0.348564\pi$
$972$			4637.38i			0.153029i
$973$		0			0
$974$	−14896.8			−0.490067
$975$	−259.363	+	898.887i	−0.00851925	+	0.0295256i
$976$	−7049.80			−0.231207
$977$		−	16522.4i		−	0.541043i	−0.962714	−	0.270521i	$-0.912804\pi$
$977$		−	16522.4i		−	0.541043i	0.962714	−	0.270521i	$-0.0871961\pi$
$978$		−	1219.54i		−	0.0398737i
$979$	−15374.6			−0.501915
$980$		0			0
$981$	−20043.8			−0.652342
$982$			40278.4i			1.30889i
$983$		−	16046.6i		−	0.520659i	−0.965520	−	0.260330i	$-0.916169\pi$
$983$		−	16046.6i		−	0.520659i	0.965520	−	0.260330i	$-0.0838312\pi$
$984$	−1334.14			−0.0432224
$985$	4395.25	+	5842.75i	0.142177	+	0.189001i
$986$	16819.2			0.543237
$987$		0			0
$988$		−	5299.67i		−	0.170653i
$989$	−13755.7			−0.442271
$990$	5091.11	+	6767.79i	0.163441	+	0.217267i
$991$	7725.20			0.247628			0.123814	−	0.992305i	$-0.460487\pi$
$991$	7725.20			0.247628			0.123814	+	0.992305i	$0.460487\pi$
$992$			3147.69i			0.100745i
$993$			775.711i			0.0247900i
$994$		0			0
$995$	−40071.1	+	30143.8i	−1.27672	+	0.960423i
$996$	868.231			0.0276214
$997$		−	11167.4i		−	0.354738i	−0.984144	−	0.177369i	$-0.943241\pi$
$997$		−	11167.4i		−	0.354738i	0.984144	−	0.177369i	$-0.0567586\pi$
$998$		−	35588.4i		−	1.12879i
$999$	8306.49			0.263069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.g.99.5	✓	20
5.2	odd	4		2450.4.a.dc.1.5		10
5.3	odd	4		2450.4.a.db.1.6		10
5.4	even	2	inner	490.4.c.g.99.16	yes	20
7.6	odd	2	inner	490.4.c.g.99.6	yes	20
35.13	even	4		2450.4.a.db.1.5		10
35.27	even	4		2450.4.a.dc.1.6		10
35.34	odd	2	inner	490.4.c.g.99.15	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.c.g.99.5	✓	20	1.1	even	1	trivial
490.4.c.g.99.6	yes	20	7.6	odd	2	inner
490.4.c.g.99.15	yes	20	35.34	odd	2	inner
490.4.c.g.99.16	yes	20	5.4	even	2	inner
2450.4.a.db.1.5		10	35.13	even	4
2450.4.a.db.1.6		10	5.3	odd	4
2450.4.a.dc.1.5		10	5.2	odd	4
2450.4.a.dc.1.6		10	35.27	even	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -0.537767i q^{3} -4.00000 q^{4} +(-8.93458 + 6.72110i) q^{5} -1.07553 q^{6} +8.00000i q^{8} +26.7108 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -0.537767i q^{3} -4.00000 q^{4} +(-8.93458 + 6.72110i) q^{5} -1.07553 q^{6} +8.00000i q^{8} +26.7108 q^{9} +(13.4422 + 17.8692i) q^{10} +14.1793 q^{11} +2.15107i q^{12} -13.9177i q^{13} +(3.61439 + 4.80472i) q^{15} +16.0000 q^{16} -65.7823i q^{17} -53.4216i q^{18} -95.1968 q^{19} +(35.7383 - 26.8844i) q^{20} -28.3586i q^{22} +69.4781i q^{23} +4.30213 q^{24} +(34.6536 - 120.101i) q^{25} -27.8353 q^{26} -28.8839i q^{27} -127.840 q^{29} +(9.60944 - 7.22877i) q^{30} -98.3654 q^{31} -32.0000i q^{32} -7.62517i q^{33} -131.565 q^{34} -106.843 q^{36} +287.582i q^{37} +190.394i q^{38} -7.48445 q^{39} +(-53.7688 - 71.4767i) q^{40} -310.112 q^{41} +197.986i q^{43} -56.7173 q^{44} +(-238.650 + 179.526i) q^{45} +138.956 q^{46} +538.883i q^{47} -8.60427i q^{48} +(-240.201 - 69.3071i) q^{50} -35.3755 q^{51} +55.6706i q^{52} -314.867i q^{53} -57.7678 q^{54} +(-126.686 + 95.3006i) q^{55} +51.1937i q^{57} +255.680i q^{58} -242.143 q^{59} +(-14.4575 - 19.2189i) q^{60} -440.612 q^{61} +196.731i q^{62} -64.0000 q^{64} +(93.5420 + 124.348i) q^{65} -15.2503 q^{66} -858.375i q^{67} +263.129i q^{68} +37.3630 q^{69} +142.246 q^{71} +213.686i q^{72} +459.680i q^{73} +575.164 q^{74} +(-64.5861 - 18.6355i) q^{75} +380.787 q^{76} +14.9689i q^{78} -1193.09 q^{79} +(-142.953 + 107.538i) q^{80} +705.659 q^{81} +620.223i q^{82} -403.628i q^{83} +(442.129 + 587.737i) q^{85} +395.973 q^{86} +68.7480i q^{87} +113.435i q^{88} -1084.30 q^{89} +(359.052 + 477.300i) q^{90} -277.912i q^{92} +52.8977i q^{93} +1077.77 q^{94} +(850.544 - 639.827i) q^{95} -17.2085 q^{96} -166.723i q^{97} +378.741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) \) 20 * q - 80 * q^4 - 316 * q^9	\( 20 q - 80 q^{4} - 316 q^{9} + 104 q^{11} - 360 q^{15} + 320 q^{16} - 440 q^{25} - 216 q^{29} + 224 q^{30} + 1264 q^{36} - 504 q^{39} - 416 q^{44} + 1600 q^{46} + 952 q^{50} - 296 q^{51} + 1440 q^{60} - 1280 q^{64} + 2732 q^{65} - 1872 q^{71} - 5968 q^{74} - 6424 q^{79} + 2020 q^{81} + 428 q^{85} + 3616 q^{86} + 3568 q^{95} + 624 q^{99}+O(q^{100}) \) 20 * q - 80 * q^4 - 316 * q^9 + 104 * q^11 - 360 * q^15 + 320 * q^16 - 440 * q^25 - 216 * q^29 + 224 * q^30 + 1264 * q^36 - 504 * q^39 - 416 * q^44 + 1600 * q^46 + 952 * q^50 - 296 * q^51 + 1440 * q^60 - 1280 * q^64 + 2732 * q^65 - 1872 * q^71 - 5968 * q^74 - 6424 * q^79 + 2020 * q^81 + 428 * q^85 + 3616 * q^86 + 3568 * q^95 + 624 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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