LMFDB - Embedded newform 490.4.c.g.99.14

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			99.14
Root			$5.69313i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.g.99.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -4.69313i q^{3} -4.00000 q^{4} +(1.54203 + 11.0735i) q^{5} +9.38627 q^{6} -8.00000i q^{8} +4.97448 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -4.69313i q^{3} -4.00000 q^{4} +(1.54203 + 11.0735i) q^{5} +9.38627 q^{6} -8.00000i q^{8} +4.97448 q^{9} +(-22.1470 + 3.08406i) q^{10} +1.37696 q^{11} +18.7725i q^{12} -69.4841i q^{13} +(51.9694 - 7.23695i) q^{15} +16.0000 q^{16} +26.3126i q^{17} +9.94897i q^{18} -14.1726 q^{19} +(-6.16812 - 44.2940i) q^{20} +2.75393i q^{22} +29.6889i q^{23} -37.5451 q^{24} +(-120.244 + 34.1513i) q^{25} +138.968 q^{26} -150.061i q^{27} +75.5596 q^{29} +(14.4739 + 103.939i) q^{30} +245.058 q^{31} +32.0000i q^{32} -6.46227i q^{33} -52.6253 q^{34} -19.8979 q^{36} +245.100i q^{37} -28.3452i q^{38} -326.098 q^{39} +(88.5879 - 12.3362i) q^{40} +238.438 q^{41} +194.636i q^{43} -5.50785 q^{44} +(7.67080 + 55.0849i) q^{45} -59.3777 q^{46} -375.460i q^{47} -75.0902i q^{48} +(-68.3026 - 240.489i) q^{50} +123.489 q^{51} +277.936i q^{52} -511.930i q^{53} +300.121 q^{54} +(2.12332 + 15.2478i) q^{55} +66.5140i q^{57} +151.119i q^{58} +656.810 q^{59} +(-207.878 + 28.9478i) q^{60} +809.766 q^{61} +490.116i q^{62} -64.0000 q^{64} +(769.431 - 107.146i) q^{65} +12.9245 q^{66} -220.579i q^{67} -105.251i q^{68} +139.334 q^{69} +1106.75 q^{71} -39.7959i q^{72} -898.681i q^{73} -490.201 q^{74} +(160.277 + 564.323i) q^{75} +56.6905 q^{76} -652.197i q^{78} +708.811 q^{79} +(24.6725 + 177.176i) q^{80} -569.943 q^{81} +476.876i q^{82} +419.279i q^{83} +(-291.373 + 40.5749i) q^{85} -389.271 q^{86} -354.612i q^{87} -11.0157i q^{88} +393.760 q^{89} +(-110.170 + 15.3416i) q^{90} -118.755i q^{92} -1150.09i q^{93} +750.920 q^{94} +(-21.8546 - 156.940i) q^{95} +150.180 q^{96} +152.826i q^{97} +6.84968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	4.69313i		−	0.903194i	−0.892222	−	0.451597i	$-0.850854\pi$
$3$		−	4.69313i		−	0.903194i	0.892222	−	0.451597i	$-0.149146\pi$
$4$	−4.00000			−0.500000
$5$	1.54203	+	11.0735i	0.137923	+	0.990443i
$5$	1.54203	+	11.0735i	0.137923	+	0.990443i
$6$	9.38627			0.638655
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	4.97448			0.184240
$10$	−22.1470	+	3.08406i	−0.700349	+	0.0975265i
$11$	1.37696			0.0377427			0.0188714	−	0.999822i	$-0.493993\pi$
$11$	1.37696			0.0377427			0.0188714	+	0.999822i	$0.493993\pi$
$12$			18.7725i			0.451597i
$13$		−	69.4841i		−	1.48242i	−0.671275	−	0.741209i	$-0.734253\pi$
$13$		−	69.4841i		−	1.48242i	0.671275	−	0.741209i	$-0.265747\pi$
$14$		0			0
$15$	51.9694	−	7.23695i	0.894562	−	0.124571i
$16$	16.0000			0.250000
$17$			26.3126i			0.375397i	0.982227	+	0.187699i	$0.0601028\pi$
$17$			26.3126i			0.375397i	−0.982227	+	0.187699i	$0.939897\pi$
$18$			9.94897i			0.130277i
$19$	−14.1726			−0.171127			−0.0855637	−	0.996333i	$-0.527269\pi$
$19$	−14.1726			−0.171127			−0.0855637	+	0.996333i	$0.527269\pi$
$20$	−6.16812	−	44.2940i	−0.0689616	−	0.495221i
$21$		0			0
$22$			2.75393i			0.0266881i
$23$			29.6889i			0.269155i	0.990903	+	0.134577i	$0.0429677\pi$
$23$			29.6889i			0.269155i	−0.990903	+	0.134577i	$0.957032\pi$
$24$	−37.5451			−0.319327
$25$	−120.244	+	34.1513i	−0.961954	+	0.273210i
$26$	138.968			1.04823
$27$		−	150.061i		−	1.06960i
$28$		0			0
$29$	75.5596			0.483830			0.241915	−	0.970297i	$-0.422224\pi$
$29$	75.5596			0.483830			0.241915	+	0.970297i	$0.422224\pi$
$30$	14.4739	+	103.939i	0.0880853	+	0.632551i
$31$	245.058			1.41980			0.709898	−	0.704304i	$-0.248741\pi$
$31$	245.058			1.41980			0.709898	+	0.704304i	$0.248741\pi$
$32$			32.0000i			0.176777i
$33$		−	6.46227i		−	0.0340890i
$34$	−52.6253			−0.265446
$35$		0			0
$36$	−19.8979			−0.0921201
$37$			245.100i			1.08903i	0.838750	+	0.544517i	$0.183287\pi$
$37$			245.100i			1.08903i	−0.838750	+	0.544517i	$0.816713\pi$
$38$		−	28.3452i		−	0.121005i
$39$	−326.098			−1.33891
$40$	88.5879	−	12.3362i	0.350174	−	0.0487632i
$41$	238.438			0.908239			0.454119	−	0.890941i	$-0.349954\pi$
$41$	238.438			0.908239			0.454119	+	0.890941i	$0.349954\pi$
$42$		0			0
$43$			194.636i			0.690271i	0.938553	+	0.345136i	$0.112167\pi$
$43$			194.636i			0.690271i	−0.938553	+	0.345136i	$0.887833\pi$
$44$	−5.50785			−0.0188714
$45$	7.67080	+	55.0849i	0.0254110	+	0.182479i
$46$	−59.3777			−0.190321
$47$		−	375.460i		−	1.16524i	−0.812743	−	0.582622i	$-0.802027\pi$
$47$		−	375.460i		−	1.16524i	0.812743	−	0.582622i	$-0.197973\pi$
$48$		−	75.0902i		−	0.225799i
$49$		0			0
$50$	−68.3026	−	240.489i	−0.193189	−	0.680204i
$51$	123.489			0.339057
$52$			277.936i			0.741209i
$53$		−	511.930i		−	1.32677i	−0.748277	−	0.663387i	$-0.769118\pi$
$53$		−	511.930i		−	1.32677i	0.748277	−	0.663387i	$-0.230882\pi$
$54$	300.121			0.756321
$55$	2.12332	+	15.2478i	0.00520560	+	0.0373820i
$56$		0			0
$57$			66.5140i			0.154561i
$58$			151.119i			0.342120i
$59$	656.810			1.44931			0.724655	−	0.689111i	$-0.241999\pi$
$59$	656.810			1.44931			0.724655	+	0.689111i	$0.241999\pi$
$60$	−207.878	+	28.9478i	−0.447281	+	0.0622857i
$61$	809.766			1.69967			0.849836	−	0.527047i	$-0.176701\pi$
$61$	809.766			1.69967			0.849836	+	0.527047i	$0.176701\pi$
$62$			490.116i			1.00395i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	769.431	−	107.146i	1.46825	−	0.204460i
$66$	12.9245			0.0241046
$67$		−	220.579i		−	0.402210i	−0.979570	−	0.201105i	$-0.935547\pi$
$67$		−	220.579i		−	0.402210i	0.979570	−	0.201105i	$-0.0644532\pi$
$68$		−	105.251i		−	0.187699i
$69$	139.334			0.243099
$70$		0			0
$71$	1106.75			1.84995			0.924976	−	0.380027i	$-0.124085\pi$
$71$	1106.75			1.84995			0.924976	+	0.380027i	$0.124085\pi$
$72$		−	39.7959i		−	0.0651387i
$73$		−	898.681i		−	1.44086i	−0.693528	−	0.720429i	$-0.743945\pi$
$73$		−	898.681i		−	1.44086i	0.693528	−	0.720429i	$-0.256055\pi$
$74$	−490.201			−0.770063
$75$	160.277	+	564.323i	0.246762	+	0.868832i
$76$	56.6905			0.0855637
$77$		0			0
$78$		−	652.197i		−	0.946753i
$79$	708.811			1.00946			0.504731	−	0.863277i	$-0.331592\pi$
$79$	708.811			1.00946			0.504731	+	0.863277i	$0.331592\pi$
$80$	24.6725	+	177.176i	0.0344808	+	0.247611i
$81$	−569.943			−0.781815
$82$			476.876i			0.642222i
$83$			419.279i			0.554481i	0.960801	+	0.277240i	$0.0894198\pi$
$83$			419.279i			0.554481i	−0.960801	+	0.277240i	$0.910580\pi$
$84$		0			0
$85$	−291.373	+	40.5749i	−0.371810	+	0.0517760i
$86$	−389.271			−0.488096
$87$		−	354.612i		−	0.436993i
$88$		−	11.0157i		−	0.0133441i
$89$	393.760			0.468972			0.234486	−	0.972119i	$-0.424659\pi$
$89$	393.760			0.468972			0.234486	+	0.972119i	$0.424659\pi$
$90$	−110.170	+	15.3416i	−0.129032	+	0.0179683i
$91$		0			0
$92$		−	118.755i		−	0.134577i
$93$		−	1150.09i		−	1.28235i
$94$	750.920			0.823952
$95$	−21.8546	−	156.940i	−0.0236024	−	0.169492i
$96$	150.180			0.159664
$97$			152.826i			0.159971i	0.996796	+	0.0799853i	$0.0254873\pi$
$97$			152.826i			0.159971i	−0.996796	+	0.0799853i	$0.974513\pi$
$98$		0			0
$99$	6.84968			0.00695372
$100$	480.977	−	136.605i	0.480977	−	0.136605i
$101$	−351.090			−0.345888			−0.172944	−	0.984932i	$-0.555328\pi$
$101$	−351.090			−0.345888			−0.172944	+	0.984932i	$0.555328\pi$
$102$			246.978i			0.239749i
$103$			375.433i			0.359151i	0.983744	+	0.179576i	$0.0574724\pi$
$103$			375.433i			0.359151i	−0.983744	+	0.179576i	$0.942528\pi$
$104$	−555.873			−0.524114
$105$		0			0
$106$	1023.86			0.938170
$107$		−	514.577i		−	0.464917i	−0.972606	−	0.232458i	$-0.925323\pi$
$107$		−	514.577i		−	0.464917i	0.972606	−	0.232458i	$-0.0746769\pi$
$108$			600.242i			0.534799i
$109$	−1795.57			−1.57784			−0.788918	−	0.614499i	$-0.789358\pi$
$109$	−1795.57			−1.57784			−0.788918	+	0.614499i	$0.789358\pi$
$110$	−30.4956	+	4.24663i	−0.0264331	+	0.00368091i
$111$	1150.29			0.983609
$112$		0			0
$113$			925.436i			0.770422i	0.922828	+	0.385211i	$0.125871\pi$
$113$			925.436i			0.770422i	−0.922828	+	0.385211i	$0.874129\pi$
$114$	−133.028			−0.109291
$115$	−328.759	+	45.7811i	−0.266582	+	0.0371227i
$116$	−302.239			−0.241915
$117$		−	345.648i		−	0.273121i
$118$			1313.62i			1.02482i
$119$		0			0
$120$	−57.8956	−	415.755i	−0.0440427	−	0.316276i
$121$	−1329.10			−0.998575
$122$			1619.53i			1.20185i
$123$		−	1119.02i		−	0.820316i
$124$	−980.231			−0.709898
$125$	−563.594	−	1278.86i	−0.403275	−	0.915079i
$126$		0			0
$127$			2780.44i			1.94271i	0.237636	+	0.971354i	$0.423627\pi$
$127$			2780.44i			1.94271i	−0.237636	+	0.971354i	$0.576373\pi$
$128$		−	128.000i		−	0.0883883i
$129$	913.452			0.623449
$130$	214.293	+	1538.86i	0.144575	+	1.03821i
$131$	1747.06			1.16520			0.582601	−	0.812759i	$-0.302035\pi$
$131$	1747.06			1.16520			0.582601	+	0.812759i	$0.302035\pi$
$132$			25.8491i			0.0170445i
$133$		0			0
$134$	441.159			0.284405
$135$	1661.69	−	231.398i	1.05938	−	0.147523i
$136$	210.501			0.132723
$137$			2067.80i			1.28952i	0.764386	+	0.644759i	$0.223042\pi$
$137$			2067.80i			1.28952i	−0.764386	+	0.644759i	$0.776958\pi$
$138$			278.668i			0.171897i
$139$	−2336.91			−1.42600			−0.713001	−	0.701163i	$-0.752664\pi$
$139$	−2336.91			−1.42600			−0.713001	+	0.701163i	$0.752664\pi$
$140$		0			0
$141$	−1762.08			−1.05244
$142$			2213.49i			1.30811i
$143$		−	95.6770i		−	0.0559504i
$144$	79.5918			0.0460600
$145$	116.515	+	836.709i	0.0667314	+	0.479206i
$146$	1797.36			1.01884
$147$		0			0
$148$		−	980.401i		−	0.544517i
$149$	−2230.70			−1.22648			−0.613241	−	0.789896i	$-0.710135\pi$
$149$	−2230.70			−1.22648			−0.613241	+	0.789896i	$0.710135\pi$
$150$	−1128.65	+	320.553i	−0.614357	+	0.174487i
$151$	2572.46			1.38638			0.693192	−	0.720753i	$-0.256204\pi$
$151$	2572.46			1.38638			0.693192	+	0.720753i	$0.256204\pi$
$152$			113.381i			0.0605027i
$153$			130.892i			0.0691633i
$154$		0			0
$155$	377.886	+	2713.64i	0.195823	+	1.40623i
$156$	1304.39			0.669455
$157$		−	1083.02i		−	0.550535i	−0.961368	−	0.275268i	$-0.911234\pi$
$157$		−	1083.02i		−	0.550535i	0.961368	−	0.275268i	$-0.0887664\pi$
$158$			1417.62i			0.713797i
$159$	−2402.56			−1.19833
$160$	−354.352	+	49.3449i	−0.175087	+	0.0243816i
$161$		0			0
$162$		−	1139.89i		−	0.552827i
$163$			1368.56i			0.657633i	0.944394	+	0.328816i	$0.106650\pi$
$163$			1368.56i			0.657633i	−0.944394	+	0.328816i	$0.893350\pi$
$164$	−953.753			−0.454119
$165$	71.5599	−	9.96501i	0.0337632	−	0.00470167i
$166$	−838.559			−0.392077
$167$		−	2268.75i		−	1.05126i	−0.850712	−	0.525632i	$-0.823829\pi$
$167$		−	2268.75i		−	1.05126i	0.850712	−	0.525632i	$-0.176171\pi$
$168$		0			0
$169$	−2631.04			−1.19756
$170$	−81.1497	−	582.746i	−0.0366112	−	0.262909i
$171$	−70.5015			−0.0315285
$172$		−	778.543i		−	0.345136i
$173$		−	2365.83i		−	1.03972i	−0.854252	−	0.519859i	$-0.825985\pi$
$173$		−	2365.83i		−	1.03972i	0.854252	−	0.519859i	$-0.174015\pi$
$174$	709.223			0.309000
$175$		0			0
$176$	22.0314			0.00943568
$177$		−	3082.50i		−	1.30901i
$178$			787.521i			0.331613i
$179$	2007.64			0.838313			0.419156	−	0.907914i	$-0.362326\pi$
$179$	2007.64			0.838313			0.419156	+	0.907914i	$0.362326\pi$
$180$	−30.6832	−	220.340i	−0.0127055	−	0.0912397i
$181$	2030.01			0.833645			0.416822	−	0.908988i	$-0.363144\pi$
$181$	2030.01			0.833645			0.416822	+	0.908988i	$0.363144\pi$
$182$		0			0
$183$		−	3800.34i		−	1.53513i
$184$	237.511			0.0951605
$185$	−2714.12	+	377.952i	−1.07863	+	0.150203i
$186$	2300.18			0.906760
$187$			36.2315i			0.0141685i
$188$			1501.84i			0.582622i
$189$		0			0
$190$	313.881	−	43.7092i	0.119849	−	0.0166895i
$191$	−1509.50			−0.571849			−0.285925	−	0.958252i	$-0.592301\pi$
$191$	−1509.50			−0.571849			−0.285925	+	0.958252i	$0.592301\pi$
$192$			300.361i			0.112899i
$193$		−	4067.79i		−	1.51713i	−0.651599	−	0.758564i	$-0.725901\pi$
$193$		−	4067.79i		−	1.51713i	0.651599	−	0.758564i	$-0.274099\pi$
$194$	−305.652			−0.113116
$195$	−502.853	−	3611.05i	−0.184667	−	1.32611i
$196$		0			0
$197$		−	919.891i		−	0.332688i	−0.986068	−	0.166344i	$-0.946804\pi$
$197$		−	919.891i		−	0.332688i	0.986068	−	0.166344i	$-0.0531962\pi$
$198$			13.6994i			0.00491703i
$199$	1769.06			0.630177			0.315088	−	0.949062i	$-0.397966\pi$
$199$	1769.06			0.630177			0.315088	+	0.949062i	$0.397966\pi$
$200$	273.210	+	961.954i	0.0965944	+	0.340102i
$201$	−1035.21			−0.363274
$202$		−	702.179i		−	0.244580i
$203$		0			0
$204$	−493.955			−0.169528
$205$	367.679	+	2640.34i	0.125267	+	0.899559i
$206$	−750.867			−0.253958
$207$			147.687i			0.0495891i
$208$		−	1111.75i		−	0.370604i
$209$	−19.5152			−0.00645881
$210$		0			0
$211$	−1377.05			−0.449290			−0.224645	−	0.974441i	$-0.572122\pi$
$211$	−1377.05			−0.449290			−0.224645	+	0.974441i	$0.572122\pi$
$212$			2047.72i			0.663387i
$213$		−	5194.11i		−	1.67087i
$214$	1029.15			0.328746
$215$	−2155.30	+	300.134i	−0.683674	+	0.0952045i
$216$	−1200.48			−0.378160
$217$		0			0
$218$		−	3591.13i		−	1.11570i
$219$	−4217.63			−1.30138
$220$	−8.49326	−	60.9911i	−0.00260280	−	0.0186910i
$221$	1828.31			0.556495
$222$			2300.58i			0.695517i
$223$			5623.92i			1.68881i	0.535702	+	0.844407i	$0.320047\pi$
$223$			5623.92i			1.68881i	−0.535702	+	0.844407i	$0.679953\pi$
$224$		0			0
$225$	−598.153	+	169.885i	−0.177231	+	0.0503363i
$226$	−1850.87			−0.544771
$227$		−	2236.97i		−	0.654066i	−0.945013	−	0.327033i	$-0.893951\pi$
$227$		−	2236.97i		−	0.654066i	0.945013	−	0.327033i	$-0.106049\pi$
$228$		−	266.056i		−	0.0772806i
$229$	−5538.87			−1.59833			−0.799167	−	0.601108i	$-0.794726\pi$
$229$	−5538.87			−1.59833			−0.799167	+	0.601108i	$0.794726\pi$
$230$	−91.5622	−	657.519i	−0.0262497	−	0.188502i
$231$		0			0
$232$		−	604.477i		−	0.171060i
$233$		−	1190.21i		−	0.334649i	−0.985902	−	0.167325i	$-0.946487\pi$
$233$		−	1190.21i		−	0.334649i	0.985902	−	0.167325i	$-0.0535128\pi$
$234$	691.295			0.193126
$235$	4157.65	−	578.970i	1.15411	−	0.160714i
$236$	−2627.24			−0.724655
$237$		−	3326.55i		−	0.911740i
$238$		0			0
$239$	1602.92			0.433824			0.216912	−	0.976191i	$-0.430401\pi$
$239$	1602.92			0.433824			0.216912	+	0.976191i	$0.430401\pi$
$240$	831.510	−	115.791i	0.223641	−	0.0311429i
$241$	−4523.89			−1.20917			−0.604583	−	0.796542i	$-0.706660\pi$
$241$	−4523.89			−1.20917			−0.604583	+	0.796542i	$0.706660\pi$
$242$		−	2658.21i		−	0.706099i
$243$		−	1376.81i		−	0.363468i
$244$	−3239.07			−0.849836
$245$		0			0
$246$	2238.05			0.580051
$247$			984.771i			0.253682i
$248$		−	1960.46i		−	0.501974i
$249$	1967.74			0.500804
$250$	2557.72	−	1127.19i	0.647058	−	0.285159i
$251$	−6421.20			−1.61475			−0.807376	−	0.590038i	$-0.799113\pi$
$251$	−6421.20			−1.61475			−0.807376	+	0.590038i	$0.799113\pi$
$252$		0			0
$253$			40.8805i			0.0101586i
$254$	−5560.88			−1.37370
$255$	190.423	+	1367.45i	0.0467638	+	0.335816i
$256$	256.000			0.0625000
$257$		−	4221.71i		−	1.02468i	−0.858782	−	0.512341i	$-0.828779\pi$
$257$		−	4221.71i		−	1.02468i	0.858782	−	0.512341i	$-0.171221\pi$
$258$			1826.90i			0.440845i
$259$		0			0
$260$	−3077.73	+	428.586i	−0.734125	+	0.102230i
$261$	375.870			0.0891410
$262$			3494.12i			0.823922i
$263$		−	6969.60i		−	1.63408i	−0.576579	−	0.817041i	$-0.695613\pi$
$263$		−	6969.60i		−	1.63408i	0.576579	−	0.817041i	$-0.304387\pi$
$264$	−51.6982			−0.0120523
$265$	5668.85	−	789.411i	1.31409	−	0.182993i
$266$		0			0
$267$		−	1847.97i		−	0.423573i
$268$			882.317i			0.201105i
$269$	−757.838			−0.171770			−0.0858851	−	0.996305i	$-0.527372\pi$
$269$	−757.838			−0.171770			−0.0858851	+	0.996305i	$0.527372\pi$
$270$	462.795	+	3323.39i	0.104314	+	0.749092i
$271$	−1198.66			−0.268684			−0.134342	−	0.990935i	$-0.542892\pi$
$271$	−1198.66			−0.268684			−0.134342	+	0.990935i	$0.542892\pi$
$272$			421.002i			0.0938493i
$273$		0			0
$274$	−4135.60			−0.911828
$275$	−165.572	+	47.0250i	−0.0363068	+	0.0103117i
$276$	−557.335			−0.121549
$277$			5216.82i			1.13158i	0.824549	+	0.565791i	$0.191429\pi$
$277$			5216.82i			1.13158i	−0.824549	+	0.565791i	$0.808571\pi$
$278$		−	4673.82i		−	1.00834i
$279$	1219.04			0.261584
$280$		0			0
$281$	2533.29			0.537805			0.268902	−	0.963167i	$-0.413339\pi$
$281$	2533.29			0.537805			0.268902	+	0.963167i	$0.413339\pi$
$282$		−	3524.17i		−	0.744189i
$283$			2453.49i			0.515353i	0.966231	+	0.257676i	$0.0829569\pi$
$283$			2453.49i			0.515353i	−0.966231	+	0.257676i	$0.917043\pi$
$284$	−4426.98			−0.924976
$285$	−736.542	+	102.566i	−0.153084	+	0.0213176i
$286$	191.354			0.0395629
$287$		0			0
$288$			159.184i			0.0325694i
$289$	4220.64			0.859077
$290$	−1673.42	+	233.030i	−0.338850	+	0.0471862i
$291$	717.233			0.144484
$292$			3594.73i			0.720429i
$293$			8109.93i			1.61702i	0.588482	+	0.808510i	$0.299726\pi$
$293$			8109.93i			1.61702i	−0.588482	+	0.808510i	$0.700274\pi$
$294$		0			0
$295$	1012.82	+	7273.17i	0.199894	+	1.43546i
$296$	1960.80			0.385032
$297$		−	206.628i		−	0.0403696i
$298$		−	4461.40i		−	0.867254i
$299$	2062.90			0.398999
$300$	−641.106	−	2257.29i	−0.123381	−	0.434416i
$301$		0			0
$302$			5144.92i			0.980321i
$303$			1647.71i			0.312404i
$304$	−226.762			−0.0427819
$305$	1248.68	+	8966.94i	0.234424	+	1.68343i
$306$	−261.784			−0.0489058
$307$		−	2741.20i		−	0.509605i	−0.966993	−	0.254803i	$-0.917990\pi$
$307$		−	2741.20i		−	0.509605i	0.966993	−	0.254803i	$-0.0820105\pi$
$308$		0			0
$309$	1761.96			0.324383
$310$	−5427.29	+	755.772i	−0.994353	+	0.138468i
$311$	−5851.31			−1.06687			−0.533437	−	0.845840i	$-0.679100\pi$
$311$	−5851.31			−1.06687			−0.533437	+	0.845840i	$0.679100\pi$
$312$			2608.79i			0.473376i
$313$		−	3252.21i		−	0.587302i	−0.955913	−	0.293651i	$-0.905130\pi$
$313$		−	3252.21i		−	0.587302i	0.955913	−	0.293651i	$-0.0948704\pi$
$314$	2166.03			0.389287
$315$		0			0
$316$	−2835.24			−0.504731
$317$			9.59340i			0.00169974i	1.00000		0.000849872i	$0.000270523\pi$
$317$			9.59340i			0.00169974i	−1.00000		0.000849872i	$0.999729\pi$
$318$		−	4805.11i		−	0.847350i
$319$	104.043			0.0182611
$320$	−98.6899	−	708.703i	−0.0172404	−	0.123805i
$321$	−2414.98			−0.419910
$322$		0			0
$323$		−	372.919i		−	0.0642408i
$324$	2279.77			0.390908
$325$	2372.97	+	8355.07i	0.405012	+	1.42602i
$326$	−2737.13			−0.465017
$327$			8426.84i			1.42509i
$328$		−	1907.51i		−	0.321111i
$329$		0			0
$330$	19.9300	+	143.120i	0.00332458	+	0.0238742i
$331$	5067.12			0.841433			0.420716	−	0.907192i	$-0.361779\pi$
$331$	5067.12			0.841433			0.420716	+	0.907192i	$0.361779\pi$
$332$		−	1677.12i		−	0.277240i
$333$			1219.25i			0.200644i
$334$	4537.50			0.743355
$335$	2442.58	−	340.140i	0.398366	−	0.0554741i
$336$		0			0
$337$		−	3099.47i		−	0.501006i	−0.968116	−	0.250503i	$-0.919404\pi$
$337$		−	3099.47i		−	0.501006i	0.968116	−	0.250503i	$-0.0805960\pi$
$338$		−	5262.08i		−	0.846803i
$339$	4343.20			0.695841
$340$	1165.49	−	162.299i	0.185905	−	0.0258880i
$341$	337.435			0.0535870
$342$		−	141.003i		−	0.0222940i
$343$		0			0
$344$	1557.09			0.244048
$345$	214.857	+	1542.91i	0.0335290	+	0.240776i
$346$	4731.67			0.735191
$347$			5206.13i			0.805417i	0.915328	+	0.402709i	$0.131931\pi$
$347$			5206.13i			0.805417i	−0.915328	+	0.402709i	$0.868069\pi$
$348$			1418.45i			0.218496i
$349$	4727.17			0.725043			0.362521	−	0.931975i	$-0.381916\pi$
$349$	4727.17			0.725043			0.362521	+	0.931975i	$0.381916\pi$
$350$		0			0
$351$	−10426.8			−1.58559
$352$			44.0628i			0.00667203i
$353$		−	6737.46i		−	1.01586i	−0.861398	−	0.507930i	$-0.830411\pi$
$353$		−	6737.46i		−	1.01586i	0.861398	−	0.507930i	$-0.169589\pi$
$354$	6164.99			0.925609
$355$	1706.63	+	12255.5i	0.255151	+	1.83227i
$356$	−1575.04			−0.234486
$357$		0			0
$358$			4015.28i			0.592777i
$359$	−1429.57			−0.210167			−0.105083	−	0.994463i	$-0.533511\pi$
$359$	−1429.57			−0.210167			−0.105083	+	0.994463i	$0.533511\pi$
$360$	440.679	−	61.3664i	0.0645162	−	0.00898415i
$361$	−6658.14			−0.970715
$362$			4060.03i			0.589476i
$363$			6237.66i			0.901908i
$364$		0			0
$365$	9951.54	−	1385.79i	1.42709	−	0.198728i
$366$	7600.69			1.08550
$367$			10595.2i			1.50699i	0.657455	+	0.753493i	$0.271633\pi$
$367$			10595.2i			1.50699i	−0.657455	+	0.753493i	$0.728367\pi$
$368$			475.022i			0.0672887i
$369$	1186.11			0.167334
$370$	−755.904	−	5428.23i	−0.106210	−	0.762704i
$371$		0			0
$372$			4600.36i			0.641176i
$373$		−	12340.9i		−	1.71311i	−0.516057	−	0.856554i	$-0.672601\pi$
$373$		−	12340.9i		−	1.71311i	0.516057	−	0.856554i	$-0.327399\pi$
$374$	−72.4631			−0.0100187
$375$	−6001.87	+	2645.02i	−0.826494	+	0.364236i
$376$	−3003.68			−0.411976
$377$		−	5250.19i		−	0.717238i
$378$		0			0
$379$	2953.93			0.400352			0.200176	−	0.979760i	$-0.435849\pi$
$379$	2953.93			0.400352			0.200176	+	0.979760i	$0.435849\pi$
$380$	87.4183	+	627.761i	0.0118012	+	0.0847460i
$381$	13049.0			1.75464
$382$		−	3018.99i		−	0.404359i
$383$			2952.33i			0.393883i	0.980415	+	0.196941i	$0.0631009\pi$
$383$			2952.33i			0.393883i	−0.980415	+	0.196941i	$0.936899\pi$
$384$	−600.721			−0.0798318
$385$		0			0
$386$	8135.57			1.07277
$387$			968.213i			0.127176i
$388$		−	611.304i		−	0.0799853i
$389$	−10036.7			−1.30818			−0.654088	−	0.756418i	$-0.726948\pi$
$389$	−10036.7			−1.30818			−0.654088	+	0.756418i	$0.726948\pi$
$390$	7222.09	−	1005.71i	0.937705	−	0.130579i
$391$	−781.193			−0.101040
$392$		0			0
$393$		−	8199.19i		−	1.05240i
$394$	1839.78			0.235246
$395$	1093.01	+	7849.01i	0.139228	+	0.999814i
$396$	−27.3987			−0.00347686
$397$		−	1702.16i		−	0.215187i	−0.994195	−	0.107593i	$-0.965686\pi$
$397$		−	1702.16i		−	0.215187i	0.994195	−	0.107593i	$-0.0343144\pi$
$398$			3538.11i			0.445602i
$399$		0			0
$400$	−1923.91	+	546.420i	−0.240489	+	0.0683026i
$401$	5463.99			0.680446			0.340223	−	0.940345i	$-0.389497\pi$
$401$	5463.99			0.680446			0.340223	+	0.940345i	$0.389497\pi$
$402$		−	2070.42i		−	0.256873i
$403$		−	17027.6i		−	2.10473i
$404$	1404.36			0.172944
$405$	−878.869	−	6311.26i	−0.107831	−	0.774344i
$406$		0			0
$407$			337.494i			0.0411031i
$408$		−	987.910i		−	0.119875i
$409$	1295.75			0.156652			0.0783262	−	0.996928i	$-0.475042\pi$
$409$	1295.75			0.156652			0.0783262	+	0.996928i	$0.475042\pi$
$410$	−5280.68	+	735.357i	−0.636084	+	0.0885773i
$411$	9704.47			1.16469
$412$		−	1501.73i		−	0.179576i
$413$		0			0
$414$	−295.374			−0.0350648
$415$	−4642.89	+	646.541i	−0.549182	+	0.0764758i
$416$	2223.49			0.262057
$417$			10967.4i			1.28796i
$418$		−	39.0303i		−	0.00456707i
$419$	−1699.48			−0.198150			−0.0990750	−	0.995080i	$-0.531588\pi$
$419$	−1699.48			−0.198150			−0.0990750	+	0.995080i	$0.531588\pi$
$420$		0			0
$421$	−11127.8			−1.28820			−0.644102	−	0.764940i	$-0.722769\pi$
$421$	−11127.8			−1.28820			−0.644102	+	0.764940i	$0.722769\pi$
$422$		−	2754.10i		−	0.317696i
$423$		−	1867.72i		−	0.214685i
$424$	−4095.44			−0.469085
$425$	−898.611	−	3163.95i	−0.102562	−	0.361115i
$426$	10388.2			1.18148
$427$		0			0
$428$			2058.31i			0.232458i
$429$	−449.025			−0.0505341
$430$	−600.268	−	4310.59i	−0.0673197	−	0.483431i
$431$	−16330.1			−1.82504			−0.912519	−	0.409035i	$-0.865865\pi$
$431$	−16330.1			−1.82504			−0.912519	+	0.409035i	$0.865865\pi$
$432$		−	2400.97i		−	0.267400i
$433$			14851.9i			1.64835i	0.566334	+	0.824176i	$0.308361\pi$
$433$			14851.9i			1.64835i	−0.566334	+	0.824176i	$0.691639\pi$
$434$		0			0
$435$	3926.79	−	546.821i	0.432816	−	0.0602714i
$436$	7182.27			0.788918
$437$		−	420.769i		−	0.0460597i
$438$		−	8435.27i		−	0.920211i
$439$	10095.5			1.09757			0.548786	−	0.835963i	$-0.315090\pi$
$439$	10095.5			1.09757			0.548786	+	0.835963i	$0.315090\pi$
$440$	121.982	−	16.9865i	0.0132165	−	0.00184046i
$441$		0			0
$442$			3656.62i			0.393502i
$443$			13256.2i			1.42171i	0.703336	+	0.710857i	$0.251693\pi$
$443$			13256.2i			1.42171i	−0.703336	+	0.710857i	$0.748307\pi$
$444$	−4601.16			−0.491805
$445$	607.190	+	4360.30i	0.0646822	+	0.464490i
$446$	−11247.8			−1.19417
$447$			10469.0i			1.10775i
$448$		0			0
$449$	15773.7			1.65792			0.828962	−	0.559306i	$-0.188932\pi$
$449$	15773.7			1.65792			0.828962	+	0.559306i	$0.188932\pi$
$450$	−339.770	−	1196.31i	−0.0355931	−	0.125321i
$451$	328.320			0.0342794
$452$		−	3701.75i		−	0.385211i
$453$		−	12072.9i		−	1.25217i
$454$	4473.94			0.462494
$455$		0			0
$456$	532.112			0.0546457
$457$			7088.20i			0.725540i	0.931879	+	0.362770i	$0.118169\pi$
$457$			7088.20i			0.725540i	−0.931879	+	0.362770i	$0.881831\pi$
$458$		−	11077.7i		−	1.13019i
$459$	3948.49			0.401525
$460$	1315.04	−	183.124i	0.133291	−	0.0185613i
$461$	−17395.7			−1.75748			−0.878739	−	0.477303i	$-0.841614\pi$
$461$	−17395.7			−1.75748			−0.878739	+	0.477303i	$0.841614\pi$
$462$		0			0
$463$		−	13350.8i		−	1.34010i	−0.742316	−	0.670050i	$-0.766273\pi$
$463$		−	13350.8i		−	1.34010i	0.742316	−	0.670050i	$-0.233727\pi$
$464$	1208.95			0.120958
$465$	12735.5	−	1773.47i	1.27010	−	0.176866i
$466$	2380.42			0.236633
$467$			1522.43i			0.150856i	0.997151	+	0.0754281i	$0.0240323\pi$
$467$			1522.43i			0.150856i	−0.997151	+	0.0754281i	$0.975968\pi$
$468$			1382.59i			0.136560i
$469$		0			0
$470$	1157.94	+	8315.30i	0.113642	+	0.816077i
$471$	−5082.74			−0.497240
$472$		−	5254.48i		−	0.512409i
$473$			268.006i			0.0260527i
$474$	6653.09			0.644697
$475$	1704.18	−	484.013i	0.164617	−	0.0467538i
$476$		0			0
$477$		−	2546.59i		−	0.244445i
$478$			3205.83i			0.306760i
$479$	−15526.6			−1.48106			−0.740529	−	0.672024i	$-0.765425\pi$
$479$	−15526.6			−1.48106			−0.740529	+	0.672024i	$0.765425\pi$
$480$	231.582	+	1663.02i	0.0220213	+	0.158138i
$481$	17030.6			1.61440
$482$		−	9047.77i		−	0.855010i
$483$		0			0
$484$	5316.42			0.499288
$485$	−1692.32	+	235.662i	−0.158442	+	0.0220637i
$486$	2753.63			0.257011
$487$		−	12837.5i		−	1.19450i	−0.802055	−	0.597250i	$-0.796260\pi$
$487$		−	12837.5i		−	1.19450i	0.802055	−	0.597250i	$-0.203740\pi$
$488$		−	6478.13i		−	0.600925i
$489$	6422.85			0.593970
$490$		0			0
$491$	6619.17			0.608389			0.304194	−	0.952610i	$-0.401613\pi$
$491$	6619.17			0.608389			0.304194	+	0.952610i	$0.401613\pi$
$492$			4476.09i			0.410158i
$493$			1988.17i			0.181629i
$494$	−1969.54			−0.179380
$495$	10.5624	+	75.8498i	0.000959080	+	0.00688727i
$496$	3920.93			0.354949
$497$		0			0
$498$			3935.47i			0.354122i
$499$	16221.6			1.45527			0.727633	−	0.685966i	$-0.240620\pi$
$499$	16221.6			1.45527			0.727633	+	0.685966i	$0.240620\pi$
$500$	2254.38	+	5115.45i	0.201638	+	0.457539i
$501$	−10647.5			−0.949495
$502$		−	12842.4i		−	1.14180i
$503$			3242.95i			0.287467i	0.989616	+	0.143734i	$0.0459109\pi$
$503$			3242.95i			0.287467i	−0.989616	+	0.143734i	$0.954089\pi$
$504$		0			0
$505$	−541.390	−	3887.79i	−0.0477061	−	0.342583i
$506$	−81.7609			−0.00718323
$507$			12347.8i			1.08163i
$508$		−	11121.8i		−	0.971354i
$509$	10885.0			0.947878			0.473939	−	0.880558i	$-0.342832\pi$
$509$	10885.0			0.947878			0.473939	+	0.880558i	$0.342832\pi$
$510$	−2734.90	+	380.847i	−0.237458	+	0.0330670i
$511$		0			0
$512$			512.000i			0.0441942i
$513$			2126.75i			0.183038i
$514$	8443.42			0.724559
$515$	−4157.36	+	578.929i	−0.355719	+	0.0495353i
$516$	−3653.81			−0.311725
$517$		−	516.994i		−	0.0439795i
$518$		0			0
$519$	−11103.2			−0.939066
$520$	−857.172	−	6155.45i	−0.0722875	−	0.519105i
$521$	−16284.5			−1.36936			−0.684679	−	0.728845i	$-0.740057\pi$
$521$	−16284.5			−1.36936			−0.684679	+	0.728845i	$0.740057\pi$
$522$			751.741i			0.0630322i
$523$			2243.58i			0.187581i	0.995592	+	0.0937907i	$0.0298985\pi$
$523$			2243.58i			0.187581i	−0.995592	+	0.0937907i	$0.970102\pi$
$524$	−6988.24			−0.582601
$525$		0			0
$526$	13939.2			1.15547
$527$			6448.12i			0.532988i
$528$		−	103.396i		−	0.00852225i
$529$	11285.6			0.927556
$530$	1578.82	+	11337.7i	0.129396	+	0.929204i
$531$	3267.29			0.267021
$532$		0			0
$533$		−	16567.7i		−	1.34639i
$534$	3695.94			0.299511
$535$	5698.17	−	793.493i	0.460473	−	0.0641228i
$536$	−1764.63			−0.142203
$537$		−	9422.12i		−	0.757159i
$538$		−	1515.68i		−	0.121460i
$539$		0			0
$540$	−6646.78	+	925.591i	−0.529688	+	0.0737613i
$541$	−12207.7			−0.970147			−0.485073	−	0.874473i	$-0.661207\pi$
$541$	−12207.7			−0.970147			−0.485073	+	0.874473i	$0.661207\pi$
$542$		−	2397.32i		−	0.189988i
$543$		−	9527.13i		−	0.752943i
$544$	−842.005			−0.0663615
$545$	−2768.82	−	19883.2i	−0.217620	−	1.56276i
$546$		0			0
$547$			12789.6i			0.999716i	0.866107	+	0.499858i	$0.166614\pi$
$547$			12789.6i			0.999716i	−0.866107	+	0.499858i	$0.833386\pi$
$548$		−	8271.20i		−	0.644759i
$549$	4028.17			0.313148
$550$	−94.0501	−	331.144i	−0.00729147	−	0.0256728i
$551$	−1070.88			−0.0827966
$552$		−	1114.67i		−	0.0859484i
$553$		0			0
$554$	−10433.6			−0.800149
$555$	1773.78	+	12737.7i	0.135663	+	0.974209i
$556$	9347.64			0.713001
$557$			7623.39i			0.579917i	0.957039	+	0.289958i	$0.0936414\pi$
$557$			7623.39i			0.579917i	−0.957039	+	0.289958i	$0.906359\pi$
$558$			2438.07i			0.184967i
$559$	13524.1			1.02327
$560$		0			0
$561$	170.039			0.0127969
$562$			5066.57i			0.380285i
$563$		−	3329.24i		−	0.249220i	−0.992206	−	0.124610i	$-0.960232\pi$
$563$		−	3329.24i		−	0.249220i	0.992206	−	0.124610i	$-0.0397679\pi$
$564$	7048.34			0.526221
$565$	−10247.8	+	1427.05i	−0.763059	+	0.106259i
$566$	−4906.98			−0.364410
$567$		0			0
$568$		−	8853.96i		−	0.654056i
$569$	12728.9			0.937828			0.468914	−	0.883244i	$-0.344645\pi$
$569$	12728.9			0.937828			0.468914	+	0.883244i	$0.344645\pi$
$570$	−205.133	−	1473.08i	−0.0150738	−	0.108247i
$571$	12084.5			0.885672			0.442836	−	0.896603i	$-0.353972\pi$
$571$	12084.5			0.885672			0.442836	+	0.896603i	$0.353972\pi$
$572$			382.708i			0.0279752i
$573$			7084.26i			0.516491i
$574$		0			0
$575$	−1013.91	−	3569.92i	−0.0735358	−	0.258914i
$576$	−318.367			−0.0230300
$577$		−	1738.58i		−	0.125438i	−0.998031	−	0.0627192i	$-0.980023\pi$
$577$		−	1738.58i		−	0.125438i	0.998031	−	0.0627192i	$-0.0199773\pi$
$578$			8441.29i			0.607459i
$579$	−19090.7			−1.37026
$580$	−466.061	−	3346.84i	−0.0333657	−	0.239603i
$581$		0			0
$582$			1434.47i			0.102166i
$583$		−	704.908i		−	0.0500760i
$584$	−7189.45			−0.509421
$585$	3827.52	−	532.999i	0.270511	−	0.0376697i
$586$	−16219.9			−1.14341
$587$		−	5392.62i		−	0.379177i	−0.981864	−	0.189589i	$-0.939285\pi$
$587$		−	5392.62i		−	0.379177i	0.981864	−	0.189589i	$-0.0607154\pi$
$588$		0			0
$589$	−3473.11			−0.242966
$590$	−14546.3	+	2025.64i	−1.01502	+	0.141346i
$591$	−4317.17			−0.300482
$592$			3921.61i			0.272258i
$593$			5429.42i			0.375986i	0.982170	+	0.187993i	$0.0601982\pi$
$593$			5429.42i			0.375986i	−0.982170	+	0.187993i	$0.939802\pi$
$594$	413.256			0.0285456
$595$		0			0
$596$	8922.79			0.613241
$597$		−	8302.42i		−	0.569172i
$598$			4125.81i			0.282135i
$599$	−10220.4			−0.697151			−0.348575	−	0.937281i	$-0.613334\pi$
$599$	−10220.4			−0.697151			−0.348575	+	0.937281i	$0.613334\pi$
$600$	4514.58	−	1282.21i	0.307178	−	0.0872435i
$601$	−1659.74			−0.112649			−0.0563247	−	0.998413i	$-0.517938\pi$
$601$	−1659.74			−0.112649			−0.0563247	+	0.998413i	$0.517938\pi$
$602$		0			0
$603$		−	1097.27i		−	0.0741032i
$604$	−10289.8			−0.693192
$605$	−2049.52	−	14717.8i	−0.137727	−	0.989032i
$606$	−3295.42			−0.220903
$607$			24030.5i			1.60686i	0.595396	+	0.803432i	$0.296995\pi$
$607$			24030.5i			1.60686i	−0.595396	+	0.803432i	$0.703005\pi$
$608$		−	453.524i		−	0.0302513i
$609$		0			0
$610$	−17933.9	+	2497.37i	−1.19036	+	0.165763i
$611$	−26088.5			−1.72738
$612$		−	523.567i		−	0.0345816i
$613$			28438.2i			1.87375i	0.349666	+	0.936874i	$0.386295\pi$
$613$			28438.2i			1.87375i	−0.349666	+	0.936874i	$0.613705\pi$
$614$	5482.41			0.360345
$615$	12391.5	−	1725.57i	0.812476	−	0.113141i
$616$		0			0
$617$		−	3296.92i		−	0.215120i	−0.994199	−	0.107560i	$-0.965696\pi$
$617$		−	3296.92i		−	0.215120i	0.994199	−	0.107560i	$-0.0343038\pi$
$618$			3523.92i			0.229374i
$619$	1357.63			0.0881549			0.0440774	−	0.999028i	$-0.485965\pi$
$619$	1357.63			0.0881549			0.0440774	+	0.999028i	$0.485965\pi$
$620$	−1511.54	−	10854.6i	−0.0979115	−	0.703114i
$621$	4455.13			0.287887
$622$		−	11702.6i		−	0.754393i
$623$		0			0
$624$	−5217.57			−0.334728
$625$	13292.4	−	8212.99i	0.850712	−	0.525632i
$626$	6504.41			0.415285
$627$			91.5873i			0.00583356i
$628$			4332.06i			0.275268i
$629$	−6449.24			−0.408820
$630$		0			0
$631$	−21289.4			−1.34314			−0.671568	−	0.740943i	$-0.734379\pi$
$631$	−21289.4			−1.34314			−0.671568	+	0.740943i	$0.734379\pi$
$632$		−	5670.49i		−	0.356899i
$633$			6462.69i			0.405796i
$634$	−19.1868			−0.00120190
$635$	−30789.1	+	4287.52i	−1.92414	+	0.267945i
$636$	9610.23			0.599167
$637$		0			0
$638$			208.086i			0.0129125i
$639$	5505.49			0.340835
$640$	1417.41	−	197.380i	0.0875436	−	0.0121908i
$641$	29433.2			1.81364			0.906819	−	0.421520i	$-0.138503\pi$
$641$	29433.2			1.81364			0.906819	+	0.421520i	$0.138503\pi$
$642$		−	4829.96i		−	0.296921i
$643$		−	13351.4i		−	0.818862i	−0.912341	−	0.409431i	$-0.865727\pi$
$643$		−	13351.4i		−	0.818862i	0.912341	−	0.409431i	$-0.134273\pi$
$644$		0			0
$645$	1408.57	+	10115.1i	0.0859881	+	0.617491i
$646$	745.838			0.0454251
$647$			8985.21i			0.545974i	0.962018	+	0.272987i	$0.0880116\pi$
$647$			8985.21i			0.545974i	−0.962018	+	0.272987i	$0.911988\pi$
$648$			4559.55i			0.276413i
$649$	904.402			0.0547009
$650$	−16710.1	+	4745.94i	−1.00835	+	0.286386i
$651$		0			0
$652$		−	5474.25i		−	0.328816i
$653$		−	12069.4i		−	0.723298i	−0.932314	−	0.361649i	$-0.882214\pi$
$653$		−	12069.4i		−	0.723298i	0.932314	−	0.361649i	$-0.117786\pi$
$654$	−16853.7			−1.00769
$655$	2694.02	+	19346.1i	0.160708	+	1.15407i
$656$	3815.01			0.227060
$657$		−	4470.48i		−	0.265464i
$658$		0			0
$659$	23236.3			1.37353			0.686765	−	0.726880i	$-0.259030\pi$
$659$	23236.3			1.37353			0.686765	+	0.726880i	$0.259030\pi$
$660$	−286.240	+	39.8600i	−0.0168816	+	0.00235083i
$661$	11281.7			0.663856			0.331928	−	0.943305i	$-0.392301\pi$
$661$	11281.7			0.663856			0.331928	+	0.943305i	$0.392301\pi$
$662$			10134.2i			0.594983i
$663$		−	8580.51i		−	0.502623i
$664$	3354.24			0.196039
$665$		0			0
$666$	−2438.50			−0.141877
$667$			2243.28i			0.130225i
$668$			9074.99i			0.525632i
$669$	26393.8			1.52533
$670$	680.279	+	4885.17i	0.0392261	+	0.281687i
$671$	1115.02			0.0641502
$672$		0			0
$673$			2558.69i			0.146553i	0.997312	+	0.0732766i	$0.0233456\pi$
$673$			2558.69i			0.146553i	−0.997312	+	0.0732766i	$0.976654\pi$
$674$	6198.95			0.354265
$675$	5124.76	+	18043.9i	0.292225	+	1.02891i
$676$	10524.2			0.598780
$677$		−	9567.49i		−	0.543144i	−0.962418	−	0.271572i	$-0.912457\pi$
$677$		−	9567.49i		−	0.543144i	0.962418	−	0.271572i	$-0.0875435\pi$
$678$			8686.40i			0.492034i
$679$		0			0
$680$	324.599	+	2330.98i	0.0183056	+	0.131455i
$681$	−10498.4			−0.590749
$682$			674.871i			0.0378917i
$683$		−	26825.8i		−	1.50287i	−0.659807	−	0.751435i	$-0.729362\pi$
$683$		−	26825.8i		−	1.50287i	0.659807	−	0.751435i	$-0.270638\pi$
$684$	282.006			0.0157643
$685$	−22897.8	+	3188.61i	−1.27719	+	0.177855i
$686$		0			0
$687$			25994.7i			1.44361i
$688$			3114.17i			0.172568i
$689$	−35571.0			−1.96683
$690$	−3085.82	+	429.714i	−0.170254	+	0.0237086i
$691$	−8541.18			−0.470220			−0.235110	−	0.971969i	$-0.575545\pi$
$691$	−8541.18			−0.470220			−0.235110	+	0.971969i	$0.575545\pi$
$692$			9463.34i			0.519859i
$693$		0			0
$694$	−10412.3			−0.569516
$695$	−3603.58	−	25877.8i	−0.196679	−	1.41237i
$696$	−2836.89			−0.154500
$697$			6273.94i			0.340950i
$698$			9454.35i			0.512682i
$699$	−5585.82			−0.302253
$700$		0			0
$701$	3409.68			0.183711			0.0918557	−	0.995772i	$-0.470720\pi$
$701$	3409.68			0.183711			0.0918557	+	0.995772i	$0.470720\pi$
$702$		−	20853.6i		−	1.12118i
$703$		−	3473.71i		−	0.186364i
$704$	−88.1256			−0.00471784
$705$	−2717.18	−	19512.4i	−0.145156	−	1.04238i
$706$	13474.9			0.718322
$707$		0			0
$708$			12330.0i			0.654505i
$709$	−8364.26			−0.443056			−0.221528	−	0.975154i	$-0.571104\pi$
$709$	−8364.26			−0.443056			−0.221528	+	0.975154i	$0.571104\pi$
$710$	−24511.1	+	3413.27i	−1.29561	+	0.180419i
$711$	3525.97			0.185983
$712$		−	3150.08i		−	0.165807i
$713$			7275.49i			0.382145i
$714$		0			0
$715$	1059.48	−	147.537i	0.0554157	−	0.00771687i
$716$	−8030.56			−0.419156
$717$		−	7522.70i		−	0.391828i
$718$		−	2859.14i		−	0.148610i
$719$	−31967.1			−1.65810			−0.829049	−	0.559176i	$-0.811118\pi$
$719$	−31967.1			−1.65810			−0.829049	+	0.559176i	$0.811118\pi$
$720$	122.733	+	881.358i	0.00635275	+	0.0456198i
$721$		0			0
$722$		−	13316.3i		−	0.686399i
$723$			21231.2i			1.09211i
$724$	−8120.05			−0.416822
$725$	−9085.62	+	2580.46i	−0.465423	+	0.132187i
$726$	−12475.3			−0.637745
$727$			27903.4i			1.42349i	0.702437	+	0.711746i	$0.252095\pi$
$727$			27903.4i			1.42349i	−0.702437	+	0.711746i	$0.747905\pi$
$728$		0			0
$729$	−21850.0			−1.11010
$730$	2771.59	+	19903.1i	0.140522	+	1.00910i
$731$	−5121.38			−0.259126
$732$			15201.4i			0.767567i
$733$		−	1029.02i		−	0.0518521i	−0.999664	−	0.0259261i	$-0.991747\pi$
$733$		−	1029.02i		−	0.0518521i	0.999664	−	0.0259261i	$-0.00825345\pi$
$734$	−21190.4			−1.06560
$735$		0			0
$736$	−950.044			−0.0475803
$737$		−	303.730i		−	0.0151805i
$738$			2372.21i			0.118323i
$739$	22515.6			1.12077			0.560385	−	0.828232i	$-0.310653\pi$
$739$	22515.6			1.12077			0.560385	+	0.828232i	$0.310653\pi$
$740$	10856.5	−	1511.81i	0.539313	−	0.0751016i
$741$	4621.66			0.229124
$742$		0			0
$743$			34792.5i			1.71792i	0.512045	+	0.858958i	$0.328888\pi$
$743$			34792.5i			1.71792i	−0.512045	+	0.858958i	$0.671112\pi$
$744$	−9200.72			−0.453380
$745$	−3439.80	−	24701.6i	−0.169161	−	1.21476i
$746$	24681.9			1.21135
$747$			2085.70i			0.102158i
$748$		−	144.926i		−	0.00708426i
$749$		0			0
$750$	−5290.05	−	12003.7i	−0.257554	−	0.584419i
$751$	−8250.40			−0.400881			−0.200440	−	0.979706i	$-0.564237\pi$
$751$	−8250.40			−0.400881			−0.200440	+	0.979706i	$0.564237\pi$
$752$		−	6007.36i		−	0.291311i
$753$			30135.6i			1.45843i
$754$	10500.4			0.507164
$755$	3966.81	+	28486.1i	0.191215	+	1.37313i
$756$		0			0
$757$		−	437.145i		−	0.0209885i	−0.999945	−	0.0104943i	$-0.996660\pi$
$757$		−	437.145i		−	0.0209885i	0.999945	−	0.0104943i	$-0.00334049\pi$
$758$			5907.86i			0.283091i
$759$	191.857			0.00917521
$760$	−1255.52	+	174.837i	−0.0599244	+	0.00834473i
$761$	20973.4			0.999063			0.499531	−	0.866296i	$-0.333506\pi$
$761$	20973.4			0.999063			0.499531	+	0.866296i	$0.333506\pi$
$762$			26097.9i			1.24072i
$763$		0			0
$764$	6037.98			0.285925
$765$	−1449.43	+	201.839i	−0.0685023	+	0.00953922i
$766$	−5904.66			−0.278517
$767$		−	45637.8i		−	2.14848i
$768$		−	1201.44i		−	0.0564496i
$769$	3186.01			0.149402			0.0747012	−	0.997206i	$-0.476200\pi$
$769$	3186.01			0.149402			0.0747012	+	0.997206i	$0.476200\pi$
$770$		0			0
$771$	−19813.1			−0.925486
$772$			16271.1i			0.758564i
$773$		−	11968.5i		−	0.556894i	−0.960452	−	0.278447i	$-0.910180\pi$
$773$		−	11968.5i		−	0.556894i	0.960452	−	0.278447i	$-0.0898196\pi$
$774$	−1936.43			−0.0899268
$775$	−29466.8	+	8369.04i	−1.36578	+	0.387903i
$776$	1222.61			0.0565581
$777$		0			0
$778$		−	20073.4i		−	0.925021i
$779$	−3379.29			−0.155425
$780$	2011.41	+	14444.2i	0.0923335	+	0.663057i
$781$	1523.95			0.0698222
$782$		−	1562.39i		−	0.0714460i
$783$		−	11338.5i		−	0.517504i
$784$		0			0
$785$	11992.8	−	1670.04i	0.545274	−	0.0759316i
$786$	16398.4			0.744161
$787$		−	14961.3i		−	0.677653i	−0.940849	−	0.338827i	$-0.889970\pi$
$787$		−	14961.3i		−	0.677653i	0.940849	−	0.338827i	$-0.110030\pi$
$788$			3679.56i			0.166344i
$789$	−32709.3			−1.47589
$790$	−15698.0	+	2186.01i	−0.706975	+	0.0984492i
$791$		0			0
$792$		−	54.7974i		−	0.00245851i
$793$		−	56265.9i		−	2.51962i
$794$	3404.32			0.152160
$795$	−3704.81	−	26604.7i	−0.165278	−	1.18688i
$796$	−7076.23			−0.315088
$797$		−	23075.5i		−	1.02556i	−0.858519	−	0.512782i	$-0.828615\pi$
$797$		−	23075.5i		−	1.02556i	0.858519	−	0.512782i	$-0.171385\pi$
$798$		0			0
$799$	9879.34			0.437429
$800$	−1092.84	−	3847.82i	−0.0482972	−	0.170051i
$801$	1958.76			0.0864035
$802$			10928.0i			0.481148i
$803$		−	1237.45i		−	0.0543819i
$804$	4140.83			0.181637
$805$		0			0
$806$	34055.2			1.48827
$807$			3556.63i			0.155142i
$808$			2808.72i			0.122290i
$809$	−31847.6			−1.38405			−0.692027	−	0.721871i	$-0.743282\pi$
$809$	−31847.6			−1.38405			−0.692027	+	0.721871i	$0.743282\pi$
$810$	12622.5	−	1757.74i	0.547544	−	0.0762477i
$811$	9375.21			0.405929			0.202964	−	0.979186i	$-0.434942\pi$
$811$	9375.21			0.405929			0.202964	+	0.979186i	$0.434942\pi$
$812$		0			0
$813$			5625.48i			0.242674i
$814$	−674.988			−0.0290643
$815$	−15154.8	+	2110.36i	−0.651348	+	0.0907028i
$816$	1975.82			0.0847642
$817$		−	2758.50i		−	0.118124i
$818$			2591.50i			0.110770i
$819$		0			0
$820$	−1470.71	−	10561.4i	−0.0626336	−	0.449779i
$821$	−35109.2			−1.49247			−0.746237	−	0.665681i	$-0.768141\pi$
$821$	−35109.2			−1.49247			−0.746237	+	0.665681i	$0.768141\pi$
$822$			19408.9i			0.823557i
$823$			6387.04i			0.270520i	0.990810	+	0.135260i	$0.0431870\pi$
$823$			6387.04i			0.270520i	−0.990810	+	0.135260i	$0.956813\pi$
$824$	3003.47			0.126979
$825$	220.695	+	777.051i	0.00931346	+	0.0327921i
$826$		0			0
$827$		−	32401.5i		−	1.36241i	−0.732095	−	0.681203i	$-0.761457\pi$
$827$		−	32401.5i		−	1.36241i	0.732095	−	0.681203i	$-0.238543\pi$
$828$		−	590.747i		−	0.0247945i
$829$	38188.2			1.59991			0.799957	−	0.600057i	$-0.204855\pi$
$829$	38188.2			1.59991			0.799957	+	0.600057i	$0.204855\pi$
$830$	−1293.08	−	9285.77i	−0.0540766	−	0.388330i
$831$	24483.2			1.02204
$832$			4446.98i			0.185302i
$833$		0			0
$834$	−21934.9			−0.910723
$835$	25123.0	−	3498.47i	1.04122	−	0.144994i
$836$	78.0606			0.00322941
$837$		−	36773.5i		−	1.51861i
$838$		−	3398.95i		−	0.140113i
$839$	−11555.7			−0.475503			−0.237751	−	0.971326i	$-0.576410\pi$
$839$	−11555.7			−0.475503			−0.237751	+	0.971326i	$0.576410\pi$
$840$		0			0
$841$	−18679.7			−0.765908
$842$		−	22255.5i		−	0.910897i
$843$		−	11889.1i		−	0.485742i
$844$	5508.20			0.224645
$845$	−4057.14	−	29134.8i	−0.165171	−	1.18612i
$846$	3735.44			0.151805
$847$		0			0
$848$		−	8190.88i		−	0.331693i
$849$	11514.6			0.465464
$850$	6327.89	−	1797.22i	0.255347	−	0.0725226i
$851$	−7276.75			−0.293118
$852$			20776.4i			0.835433i
$853$		−	15910.9i		−	0.638661i	−0.947643	−	0.319331i	$-0.896542\pi$
$853$		−	15910.9i		−	0.638661i	0.947643	−	0.319331i	$-0.103458\pi$
$854$		0			0
$855$	−108.715	−	780.697i	−0.00434852	−	0.0312272i
$856$	−4116.62			−0.164373
$857$		−	18769.1i		−	0.748120i	−0.927404	−	0.374060i	$-0.877965\pi$
$857$		−	18769.1i		−	0.748120i	0.927404	−	0.374060i	$-0.122035\pi$
$858$		−	898.050i		−	0.0357330i
$859$	25394.0			1.00865			0.504327	−	0.863513i	$-0.331741\pi$
$859$	25394.0			1.00865			0.504327	+	0.863513i	$0.331741\pi$
$860$	8621.19	−	1200.54i	0.341837	−	0.0476022i
$861$		0			0
$862$		−	32660.1i		−	1.29050i
$863$			7314.11i			0.288500i	0.989541	+	0.144250i	$0.0460769\pi$
$863$			7314.11i			0.288500i	−0.989541	+	0.144250i	$0.953923\pi$
$864$	4801.94			0.189080
$865$	26198.0	−	3648.18i	1.02978	−	0.143401i
$866$	−29703.8			−1.16556
$867$		−	19808.1i		−	0.775913i
$868$		0			0
$869$	976.006			0.0380998
$870$	1093.64	+	7853.58i	0.0426183	+	0.306047i
$871$	−15326.8			−0.596243
$872$			14364.5i			0.557849i
$873$			760.231i			0.0294730i
$874$	841.538			0.0325691
$875$		0			0
$876$	16870.5			0.650688
$877$		−	823.666i		−	0.0317140i	−0.999874	−	0.0158570i	$-0.994952\pi$
$877$		−	823.666i		−	0.0317140i	0.999874	−	0.0158570i	$-0.00504766\pi$
$878$			20191.1i			0.776100i
$879$	38061.0			1.46048
$880$	33.9731	+	243.964i	0.00130140	+	0.00934550i
$881$	−14893.3			−0.569543			−0.284772	−	0.958595i	$-0.591918\pi$
$881$	−14893.3			−0.569543			−0.284772	+	0.958595i	$0.591918\pi$
$882$		0			0
$883$			25856.7i			0.985443i	0.870187	+	0.492722i	$0.163998\pi$
$883$			25856.7i			0.985443i	−0.870187	+	0.492722i	$0.836002\pi$
$884$	−7313.24			−0.278248
$885$	34134.0	−	4753.30i	1.29650	−	0.180543i
$886$	−26512.3			−1.00530
$887$			33095.8i			1.25282i	0.779495	+	0.626408i	$0.215476\pi$
$887$			33095.8i			1.25282i	−0.779495	+	0.626408i	$0.784524\pi$
$888$		−	9202.31i		−	0.347758i
$889$		0			0
$890$	−8720.60	+	1214.38i	−0.328444	+	0.0457372i
$891$	−784.791			−0.0295078
$892$		−	22495.7i		−	0.844407i
$893$			5321.25i			0.199405i
$894$	−20937.9			−0.783299
$895$	3095.84	+	22231.6i	0.115623	+	0.830301i
$896$		0			0
$897$		−	9681.49i		−	0.360374i
$898$			31547.4i			1.17233i
$899$	18516.5			0.686940
$900$	2392.61	−	679.540i	0.0886153	−	0.0251682i
$901$	13470.2			0.498067
$902$			656.641i			0.0242392i
$903$		0			0
$904$	7403.49			0.272385
$905$	3130.34	+	22479.3i	0.114979	+	0.825677i
$906$	24145.8			0.885421
$907$			21942.3i			0.803288i	0.915796	+	0.401644i	$0.131561\pi$
$907$			21942.3i			0.803288i	−0.915796	+	0.401644i	$0.868439\pi$
$908$			8947.88i			0.327033i
$909$	−1746.49			−0.0637265
$910$		0			0
$911$	24393.5			0.887150			0.443575	−	0.896237i	$-0.353710\pi$
$911$	24393.5			0.887150			0.443575	+	0.896237i	$0.353710\pi$
$912$			1064.22i			0.0386403i
$913$			577.332i			0.0209276i
$914$	−14176.4			−0.513035
$915$	42083.1	−	5860.24i	1.52046	−	0.211731i
$916$	22155.5			0.799167
$917$		0			0
$918$			7896.98i			0.283921i
$919$	3024.68			0.108569			0.0542845	−	0.998526i	$-0.482712\pi$
$919$	3024.68			0.108569			0.0542845	+	0.998526i	$0.482712\pi$
$920$	366.249	+	2630.07i	0.0131249	+	0.0942511i
$921$	−12864.8			−0.460272
$922$		−	34791.3i		−	1.24272i
$923$		−	76901.2i		−	2.74240i
$924$		0			0
$925$	−8370.49	−	29471.9i	−0.297535	−	1.04760i
$926$	26701.7			0.947594
$927$			1867.59i			0.0661701i
$928$			2417.91i			0.0855299i
$929$	10167.2			0.359068			0.179534	−	0.983752i	$-0.442541\pi$
$929$	10167.2			0.359068			0.179534	+	0.983752i	$0.442541\pi$
$930$	3546.94	+	25471.0i	0.125063	+	0.898094i
$931$		0			0
$932$			4760.84i			0.167325i
$933$			27461.0i			0.963594i
$934$	−3044.87			−0.106671
$935$	−401.209	+	55.8701i	−0.0140331	+	0.00195417i
$936$	−2765.18			−0.0965628
$937$			9820.83i			0.342404i	0.985236	+	0.171202i	$0.0547651\pi$
$937$			9820.83i			0.342404i	−0.985236	+	0.171202i	$0.945235\pi$
$938$		0			0
$939$	−15263.0			−0.530448
$940$	−16630.6	+	2315.88i	−0.577054	+	0.0803571i
$941$	−33497.1			−1.16044			−0.580220	−	0.814460i	$-0.697033\pi$
$941$	−33497.1			−1.16044			−0.580220	+	0.814460i	$0.697033\pi$
$942$		−	10165.5i		−	0.351602i
$943$			7078.96i			0.244457i
$944$	10509.0			0.362328
$945$		0			0
$946$	−536.012			−0.0184221
$947$			12844.3i			0.440742i	0.975416	+	0.220371i	$0.0707268\pi$
$947$			12844.3i			0.440742i	−0.975416	+	0.220371i	$0.929273\pi$
$948$			13306.2i			0.455870i
$949$	−62444.1			−2.13595
$950$	968.026	+	3408.35i	0.0330599	+	0.116402i
$951$	45.0231			0.00153520
$952$		0			0
$953$			42080.9i			1.43036i	0.698939	+	0.715181i	$0.253656\pi$
$953$			42080.9i			1.43036i	−0.698939	+	0.715181i	$0.746344\pi$
$954$	5093.18			0.172849
$955$	−2327.69	−	16715.4i	−0.0788713	−	0.566384i
$956$	−6411.67			−0.216912
$957$		−	488.287i		−	0.0164933i
$958$		−	31053.1i		−	1.04727i
$959$		0			0
$960$	−3326.04	+	463.165i	−0.111820	+	0.0155714i
$961$	30262.3			1.01582
$962$			34061.2i			1.14155i
$963$		−	2559.76i		−	0.0856563i
$964$	18095.5			0.604583
$965$	45044.6	−	6272.65i	1.50263	−	0.209247i
$966$		0			0
$967$			27707.6i			0.921422i	0.887550	+	0.460711i	$0.152405\pi$
$967$			27707.6i			0.921422i	−0.887550	+	0.460711i	$0.847595\pi$
$968$			10632.8i			0.353050i
$969$	−1750.16			−0.0580219
$970$	−471.325	−	3384.64i	−0.0156014	−	0.112035i
$971$	33481.8			1.10657			0.553286	−	0.832991i	$-0.313374\pi$
$971$	33481.8			1.10657			0.553286	+	0.832991i	$0.313374\pi$
$972$			5507.26i			0.181734i
$973$		0			0
$974$	25675.0			0.844640
$975$	39211.5	−	11136.7i	1.28797	−	0.365804i
$976$	12956.3			0.424918
$977$		−	15829.2i		−	0.518342i	−0.965831	−	0.259171i	$-0.916551\pi$
$977$		−	15829.2i		−	0.518342i	0.965831	−	0.259171i	$-0.0834494\pi$
$978$			12845.7i			0.420000i
$979$	542.193			0.0177003
$980$		0			0
$981$	−8932.02			−0.290701
$982$			13238.3i			0.430196i
$983$			17743.6i			0.575720i	0.957672	+	0.287860i	$0.0929438\pi$
$983$			17743.6i			0.575720i	−0.957672	+	0.287860i	$0.907056\pi$
$984$	−8952.18			−0.290025
$985$	10186.4	−	1418.50i	0.329508	−	0.0458854i
$986$	−3976.35			−0.128431
$987$		0			0
$988$		−	3939.09i		−	0.126841i
$989$	−5778.51			−0.185790
$990$	−151.700	+	21.1248i	−0.00487003	+	0.000678172i
$991$	−23864.5			−0.764966			−0.382483	−	0.923962i	$-0.624931\pi$
$991$	−23864.5			−0.764966			−0.382483	+	0.923962i	$0.624931\pi$
$992$			7841.85i			0.250987i
$993$		−	23780.7i		−	0.759977i
$994$		0			0
$995$	2727.94	+	19589.6i	0.0869160	+	0.624154i
$996$	−7870.94			−0.250402
$997$		−	9649.90i		−	0.306535i	−0.988185	−	0.153268i	$-0.951020\pi$
$997$		−	9649.90i		−	0.306535i	0.988185	−	0.153268i	$-0.0489796\pi$
$998$			32443.2i			1.02903i
$999$	36779.9			1.16483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.g.99.14	yes	20
5.2	odd	4		2450.4.a.db.1.4		10
5.3	odd	4		2450.4.a.dc.1.7		10
5.4	even	2	inner	490.4.c.g.99.7	yes	20
7.6	odd	2	inner	490.4.c.g.99.17	yes	20
35.13	even	4		2450.4.a.dc.1.4		10
35.27	even	4		2450.4.a.db.1.7		10
35.34	odd	2	inner	490.4.c.g.99.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.c.g.99.4	✓	20	35.34	odd	2	inner
490.4.c.g.99.7	yes	20	5.4	even	2	inner
490.4.c.g.99.14	yes	20	1.1	even	1	trivial
490.4.c.g.99.17	yes	20	7.6	odd	2	inner
2450.4.a.db.1.4		10	5.2	odd	4
2450.4.a.db.1.7		10	35.27	even	4
2450.4.a.dc.1.4		10	35.13	even	4
2450.4.a.dc.1.7		10	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.69313i q^{3} -4.00000 q^{4} +(1.54203 + 11.0735i) q^{5} +9.38627 q^{6} -8.00000i q^{8} +4.97448 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -4.69313i q^{3} -4.00000 q^{4} +(1.54203 + 11.0735i) q^{5} +9.38627 q^{6} -8.00000i q^{8} +4.97448 q^{9} +(-22.1470 + 3.08406i) q^{10} +1.37696 q^{11} +18.7725i q^{12} -69.4841i q^{13} +(51.9694 - 7.23695i) q^{15} +16.0000 q^{16} +26.3126i q^{17} +9.94897i q^{18} -14.1726 q^{19} +(-6.16812 - 44.2940i) q^{20} +2.75393i q^{22} +29.6889i q^{23} -37.5451 q^{24} +(-120.244 + 34.1513i) q^{25} +138.968 q^{26} -150.061i q^{27} +75.5596 q^{29} +(14.4739 + 103.939i) q^{30} +245.058 q^{31} +32.0000i q^{32} -6.46227i q^{33} -52.6253 q^{34} -19.8979 q^{36} +245.100i q^{37} -28.3452i q^{38} -326.098 q^{39} +(88.5879 - 12.3362i) q^{40} +238.438 q^{41} +194.636i q^{43} -5.50785 q^{44} +(7.67080 + 55.0849i) q^{45} -59.3777 q^{46} -375.460i q^{47} -75.0902i q^{48} +(-68.3026 - 240.489i) q^{50} +123.489 q^{51} +277.936i q^{52} -511.930i q^{53} +300.121 q^{54} +(2.12332 + 15.2478i) q^{55} +66.5140i q^{57} +151.119i q^{58} +656.810 q^{59} +(-207.878 + 28.9478i) q^{60} +809.766 q^{61} +490.116i q^{62} -64.0000 q^{64} +(769.431 - 107.146i) q^{65} +12.9245 q^{66} -220.579i q^{67} -105.251i q^{68} +139.334 q^{69} +1106.75 q^{71} -39.7959i q^{72} -898.681i q^{73} -490.201 q^{74} +(160.277 + 564.323i) q^{75} +56.6905 q^{76} -652.197i q^{78} +708.811 q^{79} +(24.6725 + 177.176i) q^{80} -569.943 q^{81} +476.876i q^{82} +419.279i q^{83} +(-291.373 + 40.5749i) q^{85} -389.271 q^{86} -354.612i q^{87} -11.0157i q^{88} +393.760 q^{89} +(-110.170 + 15.3416i) q^{90} -118.755i q^{92} -1150.09i q^{93} +750.920 q^{94} +(-21.8546 - 156.940i) q^{95} +150.180 q^{96} +152.826i q^{97} +6.84968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) \) 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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