LMFDB - Embedded newform 61.4.b.a.60.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,4,Mod(60,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("61.60");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	61.b (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:	$3.59911651035$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 75x^{12} + 2176x^{10} + 30960x^{8} + 227127x^{6} + 841453x^{4} + 1469744x^{2} + 950976 $ x^14 + 75x^12 + 2176x^10 + 30960x^8 + 227127x^6 + 841453x^4 + 1469744x^2 + 950976
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			60.2
Root			$-4.32757i$ of defining polynomial
Character	$\chi$	$=$	61.60
Dual form			61.4.b.a.60.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.32757i q^{2} +9.22345 q^{3} -10.7278 q^{4} -10.7161 q^{5} -39.9151i q^{6} -11.5740i q^{7} +11.8049i q^{8} +58.0721 q^{9} +O(q^{10})$	\(q-4.32757i q^{2} +9.22345 q^{3} -10.7278 q^{4} -10.7161 q^{5} -39.9151i q^{6} -11.5740i q^{7} +11.8049i q^{8} +58.0721 q^{9} +46.3747i q^{10} +1.50544i q^{11} -98.9477 q^{12} +31.5441 q^{13} -50.0874 q^{14} -98.8396 q^{15} -34.7362 q^{16} +131.230i q^{17} -251.311i q^{18} +94.5397 q^{19} +114.961 q^{20} -106.752i q^{21} +6.51487 q^{22} +165.409i q^{23} +108.882i q^{24} -10.1648 q^{25} -136.509i q^{26} +286.592 q^{27} +124.164i q^{28} -137.626i q^{29} +427.735i q^{30} +104.773i q^{31} +244.762i q^{32} +13.8853i q^{33} +567.906 q^{34} +124.029i q^{35} -622.988 q^{36} -422.515i q^{37} -409.127i q^{38} +290.945 q^{39} -126.503i q^{40} -326.114 q^{41} -461.978 q^{42} -155.736i q^{43} -16.1501i q^{44} -622.307 q^{45} +715.820 q^{46} -499.306 q^{47} -320.388 q^{48} +209.042 q^{49} +43.9888i q^{50} +1210.39i q^{51} -338.400 q^{52} -277.912i q^{53} -1240.24i q^{54} -16.1324i q^{55} +136.630 q^{56} +871.982 q^{57} -595.586 q^{58} +157.924i q^{59} +1060.34 q^{60} +(-239.510 + 411.844i) q^{61} +453.410 q^{62} -672.127i q^{63} +781.336 q^{64} -338.030 q^{65} +60.0896 q^{66} +134.481i q^{67} -1407.81i q^{68} +1525.64i q^{69} +536.742 q^{70} -654.077i q^{71} +685.535i q^{72} -395.378 q^{73} -1828.46 q^{74} -93.7545 q^{75} -1014.21 q^{76} +17.4239 q^{77} -1259.09i q^{78} +196.407i q^{79} +372.237 q^{80} +1075.42 q^{81} +1411.28i q^{82} +857.379 q^{83} +1145.22i q^{84} -1406.28i q^{85} -673.957 q^{86} -1269.39i q^{87} -17.7715 q^{88} +370.824i q^{89} +2693.08i q^{90} -365.092i q^{91} -1774.48i q^{92} +966.365i q^{93} +2160.78i q^{94} -1013.10 q^{95} +2257.55i q^{96} +170.152 q^{97} -904.643i q^{98} +87.4237i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9}+O(q^{10}) $ 14 * q - 2 * q^3 - 38 * q^4 - 14 * q^5 + 116 * q^9	$ 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9} - 150 q^{12} - 86 q^{13} - 8 q^{14} - 28 q^{15} - 158 q^{16} + 166 q^{19} + 54 q^{20} + 242 q^{22} + 204 q^{25} + 88 q^{27} + 824 q^{34} - 572 q^{36} + 1160 q^{39} - 64 q^{41} - 1936 q^{42} - 1310 q^{45} + 488 q^{46} - 1308 q^{47} + 230 q^{48} + 254 q^{49} - 50 q^{52} - 172 q^{56} + 1736 q^{57} - 470 q^{58} + 772 q^{60} - 630 q^{61} + 1546 q^{62} + 1098 q^{64} - 390 q^{65} - 292 q^{66} + 1390 q^{70} - 3032 q^{73} - 3806 q^{74} + 1978 q^{75} + 162 q^{76} - 82 q^{77} - 1682 q^{80} + 4238 q^{81} - 1822 q^{83} - 104 q^{86} + 3274 q^{88} - 1648 q^{95} + 3890 q^{97}+O(q^{100}) $ 14 * q - 2 * q^3 - 38 * q^4 - 14 * q^5 + 116 * q^9 - 150 * q^12 - 86 * q^13 - 8 * q^14 - 28 * q^15 - 158 * q^16 + 166 * q^19 + 54 * q^20 + 242 * q^22 + 204 * q^25 + 88 * q^27 + 824 * q^34 - 572 * q^36 + 1160 * q^39 - 64 * q^41 - 1936 * q^42 - 1310 * q^45 + 488 * q^46 - 1308 * q^47 + 230 * q^48 + 254 * q^49 - 50 * q^52 - 172 * q^56 + 1736 * q^57 - 470 * q^58 + 772 * q^60 - 630 * q^61 + 1546 * q^62 + 1098 * q^64 - 390 * q^65 - 292 * q^66 + 1390 * q^70 - 3032 * q^73 - 3806 * q^74 + 1978 * q^75 + 162 * q^76 - 82 * q^77 - 1682 * q^80 + 4238 * q^81 - 1822 * q^83 - 104 * q^86 + 3274 * q^88 - 1648 * q^95 + 3890 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	4.32757i		−	1.53003i	−0.644015	−	0.765013i	$-0.722732\pi$
$2$		−	4.32757i		−	1.53003i	0.644015	−	0.765013i	$-0.277268\pi$
$3$	9.22345			1.77505			0.887527	−	0.460756i	$-0.152422\pi$
$3$	9.22345			1.77505			0.887527	+	0.460756i	$0.152422\pi$
$4$	−10.7278			−1.34098
$5$	−10.7161			−0.958479			−0.479239	−	0.877684i	$-0.659087\pi$
$5$	−10.7161			−0.958479			−0.479239	+	0.877684i	$0.659087\pi$
$6$		−	39.9151i		−	2.71588i
$7$		−	11.5740i		−	0.624939i	−0.949928	−	0.312469i	$-0.898844\pi$
$7$		−	11.5740i		−	0.624939i	0.949928	−	0.312469i	$-0.101156\pi$
$8$			11.8049i			0.521708i
$9$	58.0721			2.15082
$10$			46.3747i			1.46650i
$11$			1.50544i			0.0412642i	0.999787	+	0.0206321i	$0.00656786\pi$
$11$			1.50544i			0.0412642i	−0.999787	+	0.0206321i	$0.993432\pi$
$12$	−98.9477			−2.38031
$13$	31.5441			0.672981			0.336491	−	0.941687i	$-0.390760\pi$
$13$	31.5441			0.672981			0.336491	+	0.941687i	$0.390760\pi$
$14$	−50.0874			−0.956172
$15$	−98.8396			−1.70135
$16$	−34.7362			−0.542753
$17$			131.230i			1.87223i	0.351692	+	0.936116i	$0.385606\pi$
$17$			131.230i			1.87223i	−0.351692	+	0.936116i	$0.614394\pi$
$18$		−	251.311i		−	3.29081i
$19$	94.5397			1.14152			0.570760	−	0.821117i	$-0.306649\pi$
$19$	94.5397			1.14152			0.570760	+	0.821117i	$0.306649\pi$
$20$	114.961			1.28530
$21$		−	106.752i		−	1.10930i
$22$	6.51487			0.0631352
$23$			165.409i			1.49957i	0.661679	+	0.749787i	$0.269844\pi$
$23$			165.409i			1.49957i	−0.661679	+	0.749787i	$0.730156\pi$
$24$			108.882i			0.926060i
$25$	−10.1648			−0.0813184
$26$		−	136.509i		−	1.02968i
$27$	286.592			2.04276
$28$			124.164i			0.838030i
$29$		−	137.626i		−	0.881260i	−0.897689	−	0.440630i	$-0.854755\pi$
$29$		−	137.626i		−	0.881260i	0.897689	−	0.440630i	$-0.145245\pi$
$30$			427.735i			2.60311i
$31$			104.773i			0.607023i	0.952828	+	0.303511i	$0.0981590\pi$
$31$			104.773i			0.607023i	−0.952828	+	0.303511i	$0.901841\pi$
$32$			244.762i			1.35213i
$33$			13.8853i			0.0732461i
$34$	567.906			2.86456
$35$			124.029i			0.598990i
$36$	−622.988			−2.88420
$37$		−	422.515i		−	1.87732i	−0.344837	−	0.938662i	$-0.612066\pi$
$37$		−	422.515i		−	1.87732i	0.344837	−	0.938662i	$-0.387934\pi$
$38$		−	409.127i		−	1.74656i
$39$	290.945			1.19458
$40$		−	126.503i		−	0.500046i
$41$	−326.114			−1.24221			−0.621103	−	0.783729i	$-0.713315\pi$
$41$	−326.114			−1.24221			−0.621103	+	0.783729i	$0.713315\pi$
$42$	−461.978			−1.69726
$43$		−	155.736i		−	0.552313i	−0.961113	−	0.276157i	$-0.910939\pi$
$43$		−	155.736i		−	0.552313i	0.961113	−	0.276157i	$-0.0890609\pi$
$44$		−	16.1501i		−	0.0553344i
$45$	−622.307			−2.06151
$46$	715.820			2.29439
$47$	−499.306			−1.54960			−0.774800	−	0.632206i	$-0.782150\pi$
$47$	−499.306			−1.54960			−0.774800	+	0.632206i	$0.782150\pi$
$48$	−320.388			−0.963416
$49$	209.042			0.609452
$50$			43.9888i			0.124419i
$51$			1210.39i			3.32331i
$52$	−338.400			−0.902454
$53$		−	277.912i		−	0.720268i	−0.932901	−	0.360134i	$-0.882731\pi$
$53$		−	277.912i		−	0.720268i	0.932901	−	0.360134i	$-0.117269\pi$
$54$		−	1240.24i		−	3.12548i
$55$		−	16.1324i		−	0.0395508i
$56$	136.630			0.326035
$57$	871.982			2.02626
$58$	−595.586			−1.34835
$59$			157.924i			0.348474i	0.984704	+	0.174237i	$0.0557460\pi$
$59$			157.924i			0.348474i	−0.984704	+	0.174237i	$0.944254\pi$
$60$	1060.34			2.28148
$61$	−239.510	+	411.844i	−0.502724	+	0.864447i
$61$	−239.510	+	411.844i	−0.502724	+	0.864447i
$62$	453.410			0.928761
$63$		−	672.127i		−	1.34413i
$64$	781.336			1.52605
$65$	−338.030			−0.645038
$66$	60.0896			0.112068
$67$			134.481i			0.245216i	0.992455	+	0.122608i	$0.0391258\pi$
$67$			134.481i			0.245216i	−0.992455	+	0.122608i	$0.960874\pi$
$68$		−	1407.81i		−	2.51062i
$69$			1525.64i			2.66183i
$70$	536.742			0.916471
$71$		−	654.077i		−	1.09330i	−0.837360	−	0.546652i	$-0.815902\pi$
$71$		−	654.077i		−	1.09330i	0.837360	−	0.546652i	$-0.184098\pi$
$72$			685.535i			1.12210i
$73$	−395.378			−0.633911			−0.316956	−	0.948440i	$-0.602661\pi$
$73$	−395.378			−0.633911			−0.316956	+	0.948440i	$0.602661\pi$
$74$	−1828.46			−2.87236
$75$	−93.7545			−0.144345
$76$	−1014.21			−1.53076
$77$	17.4239			0.0257876
$78$		−	1259.09i		−	1.82774i
$79$			196.407i			0.279716i	0.990172	+	0.139858i	$0.0446646\pi$
$79$			196.407i			0.279716i	−0.990172	+	0.139858i	$0.955335\pi$
$80$	372.237			0.520217
$81$	1075.42			1.47520
$82$			1411.28i			1.90061i
$83$	857.379			1.13385			0.566925	−	0.823770i	$-0.308133\pi$
$83$	857.379			1.13385			0.566925	+	0.823770i	$0.308133\pi$
$84$			1145.22i			1.48755i
$85$		−	1406.28i		−	1.79449i
$86$	−673.957			−0.845054
$87$		−	1269.39i		−	1.56428i
$88$	−17.7715			−0.0215278
$89$			370.824i			0.441655i	0.975313	+	0.220828i	$0.0708758\pi$
$89$			370.824i			0.441655i	−0.975313	+	0.220828i	$0.929124\pi$
$90$			2693.08i			3.15417i
$91$		−	365.092i		−	0.420572i
$92$		−	1774.48i		−	2.01090i
$93$			966.365i			1.07750i
$94$			2160.78i			2.37093i
$95$	−1013.10			−1.09412
$96$			2257.55i			2.40011i
$97$	170.152			0.178107			0.0890533	−	0.996027i	$-0.471616\pi$
$97$	170.152			0.178107			0.0890533	+	0.996027i	$0.471616\pi$
$98$		−	904.643i		−	0.932477i
$99$			87.4237i			0.0887517i
$100$	109.046			0.109046
$101$			25.7402i			0.0253589i	0.999920	+	0.0126794i	$0.00403610\pi$
$101$			25.7402i			0.0253589i	−0.999920	+	0.0126794i	$0.995964\pi$
$102$	5238.06			5.08475
$103$	−566.773			−0.542192			−0.271096	−	0.962552i	$-0.587386\pi$
$103$	−566.773			−0.542192			−0.271096	+	0.962552i	$0.587386\pi$
$104$			372.375i			0.351100i
$105$			1143.97i			1.06324i
$106$	−1202.68			−1.10203
$107$	−410.932			−0.371274			−0.185637	−	0.982618i	$-0.559435\pi$
$107$	−410.932			−0.371274			−0.185637	+	0.982618i	$0.559435\pi$
$108$	−3074.51			−2.73930
$109$	63.8086			0.0560711			0.0280356	−	0.999607i	$-0.491075\pi$
$109$	63.8086			0.0560711			0.0280356	+	0.999607i	$0.491075\pi$
$110$	−69.8141			−0.0605138
$111$		−	3897.05i		−	3.33235i
$112$			402.038i			0.339187i
$113$	−778.394			−0.648010			−0.324005	−	0.946055i	$-0.605029\pi$
$113$	−778.394			−0.648010			−0.324005	+	0.946055i	$0.605029\pi$
$114$		−	3773.56i		−	3.10023i
$115$		−	1772.55i		−	1.43731i
$116$			1476.43i			1.18175i
$117$	1831.83			1.44746
$118$	683.428			0.533175
$119$	1518.86			1.17003
$120$		−	1166.79i		−	0.887609i
$121$	1328.73			0.998297
$122$	1782.28	+	1036.50i	1.32263	+	0.769181i
$123$	−3007.90			−2.20498
$124$		−	1123.98i		−	0.814005i
$125$	1448.44			1.03642
$126$	−2908.68			−2.05655
$127$	−385.599			−0.269421			−0.134710	−	0.990885i	$-0.543010\pi$
$127$	−385.599			−0.269421			−0.134710	+	0.990885i	$0.543010\pi$
$128$		−	1423.19i		−	0.982758i
$129$		−	1436.42i		−	0.980386i
$130$			1462.85i			0.986925i
$131$	−1559.33			−1.04000			−0.519998	−	0.854168i	$-0.674067\pi$
$131$	−1559.33			−1.04000			−0.519998	+	0.854168i	$0.674067\pi$
$132$		−	148.959i		−	0.0982216i
$133$		−	1094.20i		−	0.713380i
$134$	581.975			0.375187
$135$	−3071.15			−1.95794
$136$	−1549.16			−0.976758
$137$	2260.28			1.40955			0.704777	−	0.709429i	$-0.251047\pi$
$137$	2260.28			1.40955			0.704777	+	0.709429i	$0.251047\pi$
$138$	6602.33			4.07266
$139$			1644.18i			1.00329i	0.865073	+	0.501647i	$0.167272\pi$
$139$			1644.18i			1.00329i	−0.865073	+	0.501647i	$0.832728\pi$
$140$		−	1330.56i		−	0.803234i
$141$	−4605.32			−2.75062
$142$	−2830.56			−1.67279
$143$			47.4876i			0.0277700i
$144$	−2017.20			−1.16736
$145$			1474.82i			0.844669i
$146$			1711.03i			0.969901i
$147$	1928.09			1.08181
$148$			4532.67i			2.51745i
$149$	704.372			0.387278			0.193639	−	0.981073i	$-0.437971\pi$
$149$	704.372			0.387278			0.193639	+	0.981073i	$0.437971\pi$
$150$			405.729i			0.220851i
$151$			19.0677i			0.0102762i	0.999987	+	0.00513811i	$0.00163552\pi$
$151$			19.0677i			0.0102762i	−0.999987	+	0.00513811i	$0.998364\pi$
$152$			1116.03i			0.595540i
$153$			7620.79i			4.02683i
$154$		−	75.4033i		−	0.0394556i
$155$		−	1122.76i		−	0.581818i
$156$	−3121.22			−1.60191
$157$		−	1413.97i		−	0.718772i	−0.933189	−	0.359386i	$-0.882986\pi$
$157$		−	1413.97i		−	0.718772i	0.933189	−	0.359386i	$-0.117014\pi$
$158$	849.965			0.427972
$159$		−	2563.31i		−	1.27851i
$160$		−	2622.90i		−	1.29599i
$161$	1914.45			0.937142
$162$		−	4653.95i		−	2.25709i
$163$	2239.95			1.07636			0.538180	−	0.842830i	$-0.319112\pi$
$163$	2239.95			1.07636			0.538180	+	0.842830i	$0.319112\pi$
$164$	3498.50			1.66577
$165$		−	148.797i		−	0.0702048i
$166$		−	3710.36i		−	1.73482i
$167$	−180.245			−0.0835197			−0.0417598	−	0.999128i	$-0.513296\pi$
$167$	−180.245			−0.0835197			−0.0417598	+	0.999128i	$0.513296\pi$
$168$	1260.20			0.578731
$169$	−1201.97			−0.547096
$170$	−6085.75			−2.74562
$171$	5490.11			2.45520
$172$			1670.71i			0.740641i
$173$			217.521i			0.0955942i	0.998857	+	0.0477971i	$0.0152201\pi$
$173$			217.521i			0.0955942i	−0.998857	+	0.0477971i	$0.984780\pi$
$174$	−5493.36			−2.39339
$175$			117.648i			0.0508190i
$176$		−	52.2931i		−	0.0223962i
$177$			1456.61i			0.618561i
$178$	1604.77			0.675744
$179$	−2205.91			−0.921105			−0.460552	−	0.887632i	$-0.652349\pi$
$179$	−2205.91			−0.921105			−0.460552	+	0.887632i	$0.652349\pi$
$180$	6676.01			2.76445
$181$			2733.87i			1.12269i	0.827582	+	0.561344i	$0.189716\pi$
$181$			2733.87i			1.12269i	−0.827582	+	0.561344i	$0.810284\pi$
$182$	−1579.96			−0.643486
$183$	−2209.11	+	3798.63i	−0.892362	+	1.53444i
$184$	−1952.64			−0.782340
$185$			4527.72i			1.79938i
$186$	4182.01			1.64860
$187$	−197.558			−0.0772561
$188$	5356.47			2.07798
$189$		−	3317.02i		−	1.27660i
$190$			4384.25i			1.67404i
$191$		−	3437.61i		−	1.30229i	−0.758955	−	0.651144i	$-0.774290\pi$
$191$		−	3437.61i		−	1.30229i	0.758955	−	0.651144i	$-0.225710\pi$
$192$	7206.62			2.70882
$193$		−	3341.48i		−	1.24624i	−0.782125	−	0.623122i	$-0.785864\pi$
$193$		−	3341.48i		−	1.24624i	0.782125	−	0.623122i	$-0.214136\pi$
$194$		−	736.346i		−	0.272508i
$195$	−3117.81			−1.14498
$196$	−2242.57			−0.817262
$197$	−4274.55			−1.54593			−0.772967	−	0.634446i	$-0.781228\pi$
$197$	−4274.55			−1.54593			−0.772967	+	0.634446i	$0.781228\pi$
$198$	378.332			0.135792
$199$	1736.23			0.618483			0.309241	−	0.950984i	$-0.399925\pi$
$199$	1736.23			0.618483			0.309241	+	0.950984i	$0.399925\pi$
$200$		−	119.994i		−	0.0424244i
$201$			1240.38i			0.435272i
$202$	111.393			0.0387998
$203$	−1592.89			−0.550733
$204$		−	12984.9i		−	4.45649i
$205$	3494.67			1.19063
$206$			2452.75i			0.829568i
$207$			9605.66i			3.22531i
$208$	−1095.72			−0.365263
$209$			142.323i			0.0471039i
$210$	4950.62			1.62679
$211$		−	4687.61i		−	1.52942i	−0.644373	−	0.764711i	$-0.722882\pi$
$211$		−	4687.61i		−	1.52942i	0.644373	−	0.764711i	$-0.277118\pi$
$212$			2981.40i			0.965865i
$213$		−	6032.85i		−	1.94068i
$214$			1778.34i			0.568058i
$215$			1668.88i			0.529381i
$216$			3383.19i			1.06573i
$217$	1212.64			0.379352
$218$		−	276.136i		−	0.0857903i
$219$	−3646.75			−1.12523
$220$			173.066i			0.0530369i
$221$			4139.53i			1.25998i
$222$	−16864.7			−5.09859
$223$		−	2478.59i		−	0.744299i	−0.928173	−	0.372150i	$-0.878621\pi$
$223$		−	2478.59i		−	0.744299i	0.928173	−	0.372150i	$-0.121379\pi$
$224$	2832.89			0.845001
$225$	−590.291			−0.174901
$226$			3368.55i			0.991472i
$227$		−	662.262i		−	0.193638i	−0.995302	−	0.0968191i	$-0.969133\pi$
$227$		−	662.262i		−	0.193638i	0.995302	−	0.0968191i	$-0.0308668\pi$
$228$	−9354.48			−2.71717
$229$	1442.59			0.416284			0.208142	−	0.978099i	$-0.433258\pi$
$229$	1442.59			0.416284			0.208142	+	0.978099i	$0.433258\pi$
$230$	−7670.81			−2.19912
$231$	160.709			0.0457743
$232$	1624.66			0.459760
$233$			4595.36i			1.29207i	0.763308	+	0.646035i	$0.223574\pi$
$233$			4595.36i			1.29207i	−0.763308	+	0.646035i	$0.776426\pi$
$234$		−	7927.37i		−	2.21465i
$235$	5350.62			1.48526
$236$		−	1694.19i		−	0.467297i
$237$			1811.55i			0.496510i
$238$		−	6572.96i		−	1.79018i
$239$	−3055.16			−0.826870			−0.413435	−	0.910534i	$-0.635671\pi$
$239$	−3055.16			−0.826870			−0.413435	+	0.910534i	$0.635671\pi$
$240$	3433.31			0.923414
$241$	−405.412			−0.108360			−0.0541802	−	0.998531i	$-0.517255\pi$
$241$	−405.412			−0.108360			−0.0541802	+	0.998531i	$0.517255\pi$
$242$		−	5750.18i		−	1.52742i
$243$	2181.10			0.575791
$244$	2569.43	−	4418.20i	0.674142	−	1.15921i
$245$	−2240.12			−0.584147
$246$			13016.9i			3.37368i
$247$	2982.17			0.768222
$248$	−1236.83			−0.316689
$249$	7907.99			2.01264
$250$		−	6268.23i		−	1.58575i
$251$		−	4399.21i		−	1.10628i	−0.833089	−	0.553138i	$-0.813430\pi$
$251$		−	4399.21i		−	1.10628i	0.833089	−	0.553138i	$-0.186570\pi$
$252$			7210.47i			1.80245i
$253$	−249.013			−0.0618787
$254$			1668.71i			0.412221i
$255$		−	12970.7i		−	3.18532i
$256$	91.7573			0.0224017
$257$	5476.38			1.32921			0.664606	−	0.747194i	$-0.268599\pi$
$257$	5476.38			1.32921			0.664606	+	0.747194i	$0.268599\pi$
$258$	−6216.21			−1.50002
$259$	−4890.20			−1.17321
$260$	3626.33			0.864983
$261$		−	7992.23i		−	1.89543i
$262$			6748.11i			1.59122i
$263$	4557.37			1.06851			0.534257	−	0.845322i	$-0.320591\pi$
$263$	4557.37			1.06851			0.534257	+	0.845322i	$0.320591\pi$
$264$	−163.915			−0.0382131
$265$			2978.14i			0.690362i
$266$	−4735.24			−1.09149
$267$			3420.28i			0.783962i
$268$		−	1442.69i		−	0.328830i
$269$	6267.60			1.42060			0.710302	−	0.703897i	$-0.248558\pi$
$269$	6267.60			1.42060			0.710302	+	0.703897i	$0.248558\pi$
$270$			13290.6i			2.99571i
$271$	−1135.19			−0.254458			−0.127229	−	0.991873i	$-0.540608\pi$
$271$	−1135.19			−0.254458			−0.127229	+	0.991873i	$0.540608\pi$
$272$		−	4558.43i		−	1.01616i
$273$		−	3367.41i		−	0.746538i
$274$		−	9781.52i		−	2.15665i
$275$		−	15.3024i		−	0.00335553i
$276$		−	16366.9i		−	3.56946i
$277$		−	3365.52i		−	0.730016i	−0.931004	−	0.365008i	$-0.881066\pi$
$277$		−	3365.52i		−	0.730016i	0.931004	−	0.365008i	$-0.118934\pi$
$278$	7115.31			1.53506
$279$			6084.36i			1.30559i
$280$	−1464.15			−0.312498
$281$			3563.38i			0.756490i	0.925706	+	0.378245i	$0.123472\pi$
$281$			3563.38i			0.756490i	−0.925706	+	0.378245i	$0.876528\pi$
$282$			19929.8i			4.20853i
$283$	6873.38			1.44375			0.721873	−	0.692026i	$-0.243282\pi$
$283$	6873.38			1.44375			0.721873	+	0.692026i	$0.243282\pi$
$284$			7016.83i			1.46610i
$285$	−9344.26			−1.94213
$286$	205.506			0.0424888
$287$			3774.45i			0.776302i
$288$			14213.9i			2.90819i
$289$	−12308.3			−2.50525
$290$	6382.37			1.29236
$291$	1569.39			0.316149
$292$	4241.55			0.850062
$293$	−3011.62			−0.600479			−0.300240	−	0.953864i	$-0.597067\pi$
$293$	−3011.62			−0.600479			−0.300240	+	0.953864i	$0.597067\pi$
$294$		−	8343.93i		−	1.65520i
$295$		−	1692.34i		−	0.334005i
$296$	4987.75			0.979415
$297$			431.445i			0.0842929i
$298$		−	3048.22i		−	0.592545i
$299$			5217.69i			1.00919i
$300$	1005.78			0.193563
$301$	−1802.49			−0.345162
$302$	82.5169			0.0157229
$303$			237.414i			0.0450134i
$304$	−3283.95			−0.619564
$305$	2566.62	−	4413.37i	0.481850	−	0.828554i
$306$	32979.5			6.16115
$307$			5922.30i			1.10099i	0.834839	+	0.550494i	$0.185561\pi$
$307$			5922.30i			1.10099i	−0.834839	+	0.550494i	$0.814439\pi$
$308$	−186.921			−0.0345806
$309$	−5227.60			−0.962421
$310$	−4858.80			−0.890197
$311$			5603.14i			1.02162i	0.859693	+	0.510812i	$0.170655\pi$
$311$			5603.14i			1.02162i	−0.859693	+	0.510812i	$0.829345\pi$
$312$			3434.58i			0.623221i
$313$		−	5060.46i		−	0.913847i	−0.889506	−	0.456924i	$-0.848951\pi$
$313$		−	5060.46i		−	0.913847i	0.889506	−	0.456924i	$-0.151049\pi$
$314$	−6119.06			−1.09974
$315$			7202.60i			1.28832i
$316$		−	2107.02i		−	0.375093i
$317$	2369.24			0.419778			0.209889	−	0.977725i	$-0.432690\pi$
$317$	2369.24			0.419778			0.209889	+	0.977725i	$0.432690\pi$
$318$	−11092.9			−1.95616
$319$	207.187			0.0363644
$320$	−8372.89			−1.46268
$321$	−3790.21			−0.659031
$322$		−	8284.92i		−	1.43385i
$323$			12406.4i			2.13719i
$324$	−11536.9			−1.97821
$325$	−320.639			−0.0547257
$326$		−	9693.55i		−	1.64686i
$327$	588.535			0.0995293
$328$		−	3849.74i		−	0.648068i
$329$			5778.98i			0.968405i
$330$	−643.927			−0.107415
$331$		−	1161.45i		−	0.192867i	−0.995339	−	0.0964333i	$-0.969257\pi$
$331$		−	1161.45i		−	0.192867i	0.995339	−	0.0964333i	$-0.0307435\pi$
$332$	−9197.82			−1.52047
$333$		−	24536.3i		−	4.03778i
$334$			780.023i			0.127787i
$335$		−	1441.11i		−	0.235034i
$336$			3708.17i			0.602076i
$337$			4661.02i			0.753419i	0.926332	+	0.376709i	$0.122944\pi$
$337$			4661.02i			0.753419i	−0.926332	+	0.376709i	$0.877056\pi$
$338$			5201.61i			0.837071i
$339$	−7179.48			−1.15025
$340$			15086.3i			2.40638i
$341$	−157.728			−0.0250483
$342$		−	23758.8i		−	3.75652i
$343$		−	6389.35i		−	1.00581i
$344$	1838.44			0.288146
$345$		−	16349.0i		−	2.55130i
$346$	941.335			0.146262
$347$	−8508.41			−1.31630			−0.658149	−	0.752888i	$-0.728660\pi$
$347$	−8508.41			−1.31630			−0.658149	+	0.752888i	$0.728660\pi$
$348$			13617.8i			2.09767i
$349$			7060.60i			1.08294i	0.840721	+	0.541469i	$0.182132\pi$
$349$			7060.60i			1.08294i	−0.840721	+	0.541469i	$0.817868\pi$
$350$	509.128			0.0777544
$351$	9040.27			1.37474
$352$	−368.474			−0.0557947
$353$	3269.20			0.492924			0.246462	−	0.969152i	$-0.420732\pi$
$353$	3269.20			0.492924			0.246462	+	0.969152i	$0.420732\pi$
$354$	6303.57			0.946415
$355$			7009.17i			1.04791i
$356$		−	3978.14i		−	0.592251i
$357$	14009.1			2.07687
$358$			9546.24i			1.40931i
$359$		−	1476.90i		−	0.217124i	−0.994090	−	0.108562i	$-0.965375\pi$
$359$		−	1476.90i		−	0.217124i	0.994090	−	0.108562i	$-0.0346246\pi$
$360$		−	7346.27i		−	1.07551i
$361$	2078.75			0.303069
$362$	11831.0			1.71774
$363$	12255.5			1.77203
$364$			3916.65i			0.563979i
$365$	4236.92			0.607591
$366$	16438.8	+	9560.08i	2.34773	+	1.36534i
$367$	−8425.88			−1.19844			−0.599220	−	0.800584i	$-0.704523\pi$
$367$	−8425.88			−1.19844			−0.599220	+	0.800584i	$0.704523\pi$
$368$		−	5745.69i		−	0.813899i
$369$	−18938.1			−2.67176
$370$	19594.0			2.75309
$371$	−3216.56			−0.450123
$372$		−	10367.0i		−	1.44490i
$373$			2297.45i			0.318920i	0.987204	+	0.159460i	$0.0509753\pi$
$373$			2297.45i			0.318920i	−0.987204	+	0.159460i	$0.949025\pi$
$374$			854.946i			0.118204i
$375$	13359.6			1.83970
$376$		−	5894.26i		−	0.808439i
$377$		−	4341.29i		−	0.593071i
$378$	−14354.6			−1.95323
$379$	108.802			0.0147461			0.00737304	−	0.999973i	$-0.497653\pi$
$379$	108.802			0.0147461			0.00737304	+	0.999973i	$0.497653\pi$
$380$	10868.4			1.46720
$381$	−3556.56			−0.478236
$382$	−14876.5			−1.99253
$383$		−	10786.1i		−	1.43902i	−0.694480	−	0.719512i	$-0.744365\pi$
$383$		−	10786.1i		−	1.43902i	0.694480	−	0.719512i	$-0.255635\pi$
$384$		−	13126.7i		−	1.74445i
$385$	−186.717			−0.0247168
$386$	−14460.5			−1.90679
$387$		−	9043.89i		−	1.18792i
$388$	−1825.37			−0.238837
$389$			11709.7i			1.52624i	0.646257	+	0.763120i	$0.276333\pi$
$389$			11709.7i			1.52624i	−0.646257	+	0.763120i	$0.723667\pi$
$390$			13492.5i			1.75185i
$391$	−21706.7			−2.80755
$392$			2467.72i			0.317956i
$393$	−14382.4			−1.84605
$394$			18498.4i			2.36532i
$395$		−	2104.72i		−	0.268102i
$396$		−	937.867i		−	0.119014i
$397$			10091.6i			1.27577i	0.770131	+	0.637885i	$0.220191\pi$
$397$			10091.6i			1.27577i	−0.770131	+	0.637885i	$0.779809\pi$
$398$		−	7513.65i		−	0.946295i
$399$		−	10092.3i		−	1.26629i
$400$	353.086			0.0441358
$401$		−	10326.3i		−	1.28596i	−0.765885	−	0.642978i	$-0.777699\pi$
$401$		−	10326.3i		−	1.28596i	0.765885	−	0.642978i	$-0.222301\pi$
$402$	5367.82			0.665977
$403$			3304.96i			0.408515i
$404$		−	276.137i		−	0.0340058i
$405$	−11524.3			−1.41394
$406$			6893.33i			0.842636i
$407$	636.069			0.0774662
$408$	−14288.6			−1.73380
$409$		−	7877.01i		−	0.952306i	−0.879362	−	0.476153i	$-0.842031\pi$
$409$		−	7877.01i		−	0.952306i	0.879362	−	0.476153i	$-0.157969\pi$
$410$		−	15123.4i		−	1.82169i
$411$	20847.6			2.50203
$412$	6080.25			0.727069
$413$	1827.82			0.217775
$414$	41569.1			4.93481
$415$	−9187.77			−1.08677
$416$			7720.81i			0.909961i
$417$			15165.0i			1.78090i
$418$	615.914			0.0720702
$419$		−	14103.6i		−	1.64441i	−0.569194	−	0.822203i	$-0.692745\pi$
$419$		−	14103.6i		−	1.64441i	0.569194	−	0.822203i	$-0.307255\pi$
$420$		−	12272.3i		−	1.42578i
$421$			1859.75i			0.215294i	0.994189	+	0.107647i	$0.0343317\pi$
$421$			1859.75i			0.215294i	−0.994189	+	0.107647i	$0.965668\pi$
$422$	−20285.9			−2.34006
$423$	−28995.7			−3.33291
$424$	3280.73			0.375769
$425$		−	1333.93i		−	0.152247i
$426$	−26107.6			−2.96928
$427$	4766.70	+	2772.10i	0.540226	+	0.314172i
$428$	4408.41			0.497870
$429$			437.999i			0.0492933i
$430$	7222.20			0.809966
$431$	14233.3			1.59071			0.795355	−	0.606144i	$-0.207284\pi$
$431$	14233.3			1.59071			0.795355	+	0.606144i	$0.207284\pi$
$432$	−9955.10			−1.10872
$433$		−	12327.8i		−	1.36822i	−0.729380	−	0.684109i	$-0.760191\pi$
$433$		−	12327.8i		−	1.36822i	0.729380	−	0.684109i	$-0.239809\pi$
$434$		−	5247.78i		−	0.580418i
$435$			13602.9i			1.49933i
$436$	−684.528			−0.0751903
$437$			15637.7i			1.71180i
$438$			15781.6i			1.72163i
$439$	−4833.09			−0.525447			−0.262723	−	0.964871i	$-0.584621\pi$
$439$	−4833.09			−0.525447			−0.262723	+	0.964871i	$0.584621\pi$
$440$	190.442			0.0206340
$441$	12139.5			1.31082
$442$	17914.1			1.92780
$443$	13169.5			1.41242			0.706212	−	0.708000i	$-0.250402\pi$
$443$	13169.5			1.41242			0.706212	+	0.708000i	$0.250402\pi$
$444$			41806.9i			4.46862i
$445$		−	3973.80i		−	0.423317i
$446$	−10726.3			−1.13880
$447$	6496.74			0.687439
$448$		−	9043.21i		−	0.953686i
$449$	11099.4			1.16662			0.583309	−	0.812250i	$-0.301758\pi$
$449$	11099.4			1.16662			0.583309	+	0.812250i	$0.301758\pi$
$450$			2554.52i			0.267603i
$451$		−	490.943i		−	0.0512586i
$452$	8350.48			0.868968
$453$			175.870i			0.0182408i
$454$	−2865.98			−0.296271
$455$			3912.37i			0.403109i
$456$			10293.7i			1.05712i
$457$			12858.0i			1.31613i	0.752963	+	0.658063i	$0.228624\pi$
$457$			12858.0i			1.31613i	−0.752963	+	0.658063i	$0.771376\pi$
$458$		−	6242.91i		−	0.636926i
$459$			37609.4i			3.82452i
$460$			19015.6i			1.92740i
$461$	−396.581			−0.0400664			−0.0200332	−	0.999799i	$-0.506377\pi$
$461$	−396.581			−0.0400664			−0.0200332	+	0.999799i	$0.506377\pi$
$462$		−	695.479i		−	0.0700359i
$463$	5630.42			0.565157			0.282579	−	0.959244i	$-0.408810\pi$
$463$	5630.42			0.565157			0.282579	+	0.959244i	$0.408810\pi$
$464$			4780.61i			0.478306i
$465$		−	10355.7i		−	1.03276i
$466$	19886.7			1.97690
$467$		−	10170.7i		−	1.00780i	−0.863763	−	0.503899i	$-0.831898\pi$
$467$		−	10170.7i		−	1.00780i	0.863763	−	0.503899i	$-0.168102\pi$
$468$	−19651.6			−1.94101
$469$	1556.49			0.153245
$470$		−	23155.2i		−	2.27249i
$471$		−	13041.7i		−	1.27586i
$472$	−1864.28			−0.181802
$473$	234.450			0.0227907
$474$	7839.61			0.759674
$475$	−960.977			−0.0928266
$476$	−16294.1			−1.56899
$477$		−	16138.9i		−	1.54916i
$478$			13221.4i			1.26513i
$479$	−828.408			−0.0790207			−0.0395104	−	0.999219i	$-0.512580\pi$
$479$	−828.408			−0.0790207			−0.0395104	+	0.999219i	$0.512580\pi$
$480$		−	24192.2i		−	2.30046i
$481$		−	13327.8i		−	1.26340i
$482$			1754.45i			0.165794i
$483$	17657.8			1.66348
$484$	−14254.4			−1.33870
$485$	−1823.37			−0.170711
$486$		−	9438.84i		−	0.880976i
$487$	2205.02			0.205172			0.102586	−	0.994724i	$-0.467288\pi$
$487$	2205.02			0.205172			0.102586	+	0.994724i	$0.467288\pi$
$488$	−4861.78	−	2827.40i	−0.450989	−	0.262275i
$489$	20660.1			1.91060
$490$			9694.26i			0.893760i
$491$	−10516.7			−0.966622			−0.483311	−	0.875449i	$-0.660566\pi$
$491$	−10516.7			−0.966622			−0.483311	+	0.875449i	$0.660566\pi$
$492$	32268.2			2.95684
$493$	18060.7			1.64992
$494$		−	12905.5i		−	1.17540i
$495$		−	936.843i		−	0.0850666i
$496$		−	3639.40i		−	0.329463i
$497$	−7570.30			−0.683248
$498$		−	34222.4i		−	3.07940i
$499$		−	7430.42i		−	0.666596i	−0.942822	−	0.333298i	$-0.891838\pi$
$499$		−	7430.42i		−	0.666596i	0.942822	−	0.333298i	$-0.108162\pi$
$500$	−15538.7			−1.38982
$501$	−1662.48			−0.148252
$502$	−19037.9			−1.69263
$503$	12723.7			1.12788			0.563940	−	0.825816i	$-0.309285\pi$
$503$	12723.7			1.12788			0.563940	+	0.825816i	$0.309285\pi$
$504$	7934.40			0.701243
$505$		−	275.835i		−	0.0243060i
$506$			1077.62i			0.0946760i
$507$	−11086.3			−0.971125
$508$	4136.65			0.361288
$509$			19969.6i			1.73897i	0.493957	+	0.869486i	$0.335550\pi$
$509$			19969.6i			1.73897i	−0.493957	+	0.869486i	$0.664450\pi$
$510$	−56131.6			−4.87363
$511$			4576.12i			0.396156i
$512$		−	11782.6i		−	1.01703i
$513$	27094.3			2.33186
$514$		−	23699.4i		−	2.03373i
$515$	6073.61			0.519680
$516$			15409.7i			1.31468i
$517$		−	751.672i		−	0.0639430i
$518$			21162.7i			1.79505i
$519$			2006.29i			0.169685i
$520$		−	3990.41i		−	0.336522i
$521$			17408.5i			1.46387i	0.681372	+	0.731937i	$0.261384\pi$
$521$			17408.5i			1.46387i	−0.681372	+	0.731937i	$0.738616\pi$
$522$	−34586.9			−2.90005
$523$		−	564.171i		−	0.0471692i	−0.999722	−	0.0235846i	$-0.992492\pi$
$523$		−	564.171i		−	0.0471692i	0.999722	−	0.0235846i	$-0.00750791\pi$
$524$	16728.3			1.39461
$525$			1085.12i			0.0902065i
$526$		−	19722.3i		−	1.63486i
$527$	−13749.3			−1.13649
$528$		−	482.323i		−	0.0397545i
$529$	−15193.2			−1.24872
$530$	12888.1			1.05627
$531$			9170.99i			0.749505i
$532$			11738.4i			0.956628i
$533$	−10287.0			−0.835981
$534$	14801.5			1.19948
$535$	4403.59			0.355858
$536$	−1587.53			−0.127931
$537$	−20346.1			−1.63501
$538$		−	27123.5i		−	2.17356i
$539$			314.699i			0.0251485i
$540$	32946.8			2.62556
$541$		−	5907.11i		−	0.469439i	−0.972063	−	0.234720i	$-0.924583\pi$
$541$		−	5907.11i		−	0.469439i	0.972063	−	0.234720i	$-0.0754172\pi$
$542$			4912.63i			0.389327i
$543$			25215.7i			1.99283i
$544$	−32120.2			−2.53151
$545$	−683.780			−0.0537430
$546$	−14572.7			−1.14222
$547$			6261.60i			0.489445i	0.969593	+	0.244723i	$0.0786969\pi$
$547$			6261.60i			0.489445i	−0.969593	+	0.244723i	$0.921303\pi$
$548$	−24247.9			−1.89018
$549$	−13908.9	+	23916.7i	−1.08127	+	1.85927i
$550$	−66.2223			−0.00513406
$551$		−	13011.1i		−	1.00598i
$552$	−18010.1			−1.38870
$553$	2273.22			0.174805
$554$	−14564.5			−1.11694
$555$			41761.2i			3.19399i
$556$		−	17638.5i		−	1.34540i
$557$		−	2654.05i		−	0.201895i	−0.994892	−	0.100948i	$-0.967813\pi$
$557$		−	2654.05i		−	0.201895i	0.994892	−	0.100948i	$-0.0321875\pi$
$558$	26330.5			1.99759
$559$		−	4912.54i		−	0.371697i
$560$		−	4308.28i		−	0.325104i
$561$	−1822.17			−0.137134
$562$	15420.8			1.15745
$563$	8230.70			0.616133			0.308066	−	0.951365i	$-0.400318\pi$
$563$	8230.70			0.616133			0.308066	+	0.951365i	$0.400318\pi$
$564$	49405.2			3.68853
$565$	8341.36			0.621104
$566$		−	29745.0i		−	2.20897i
$567$		−	12446.9i		−	0.921907i
$568$	7721.31			0.570386
$569$	−7132.65			−0.525512			−0.262756	−	0.964862i	$-0.584631\pi$
$569$	−7132.65			−0.525512			−0.262756	+	0.964862i	$0.584631\pi$
$570$			40437.9i			2.97151i
$571$	−3900.11			−0.285839			−0.142920	−	0.989734i	$-0.545649\pi$
$571$	−3900.11			−0.285839			−0.142920	+	0.989734i	$0.545649\pi$
$572$		−	509.439i		−	0.0372390i
$573$		−	31706.6i		−	2.31163i
$574$	16334.2			1.18776
$575$		−	1681.35i		−	0.121943i
$576$	45373.8			3.28225
$577$		−	547.579i		−	0.0395078i	−0.999805	−	0.0197539i	$-0.993712\pi$
$577$		−	547.579i		−	0.0395078i	0.999805	−	0.0197539i	$-0.00628828\pi$
$578$			53265.0i			3.83310i
$579$		−	30820.0i		−	2.21215i
$580$		−	15821.6i		−	1.13268i
$581$		−	9923.32i		−	0.708586i
$582$		−	6791.65i		−	0.483716i
$583$	418.379			0.0297212
$584$		−	4667.40i		−	0.330717i
$585$	−19630.1			−1.38736
$586$			13033.0i			0.918749i
$587$		−	16377.4i		−	1.15156i	−0.817605	−	0.575780i	$-0.804698\pi$
$587$		−	16377.4i		−	1.15156i	0.817605	−	0.575780i	$-0.195302\pi$
$588$	−20684.2			−1.45069
$589$			9905.16i			0.692929i
$590$	−7323.70			−0.511037
$591$	−39426.1			−2.74412
$592$			14676.6i			1.01892i
$593$		−	8195.73i		−	0.567552i	−0.958891	−	0.283776i	$-0.908413\pi$
$593$		−	8195.73i		−	0.567552i	0.958891	−	0.283776i	$-0.0915872\pi$
$594$	1867.11			0.128970
$595$	−16276.3			−1.12145
$596$	−7556.39			−0.519332
$597$	16014.0			1.09784
$598$	22579.9			1.54408
$599$		−	4800.05i		−	0.327420i	−0.986508	−	0.163710i	$-0.947654\pi$
$599$		−	4800.05i		−	0.327420i	0.986508	−	0.163710i	$-0.0523462\pi$
$600$		−	1106.76i		−	0.0753057i
$601$	14733.3			0.999975			0.499987	−	0.866033i	$-0.333338\pi$
$601$	14733.3			0.999975			0.499987	+	0.866033i	$0.333338\pi$
$602$			7800.39i			0.528107i
$603$			7809.59i			0.527415i
$604$		−	204.555i		−	0.0137802i
$605$	−14238.9			−0.956847
$606$	1027.42			0.0688717
$607$	−4334.33			−0.289827			−0.144914	−	0.989444i	$-0.546290\pi$
$607$	−4334.33			−0.289827			−0.144914	+	0.989444i	$0.546290\pi$
$608$			23139.8i			1.54349i
$609$	−14691.9			−0.977581
$610$	−19099.2	−	11107.2i	−1.26771	−	0.737243i
$611$	−15750.1			−1.04285
$612$		−	81754.6i		−	5.39989i
$613$	−14025.4			−0.924110			−0.462055	−	0.886851i	$-0.652888\pi$
$613$	−14025.4			−0.924110			−0.462055	+	0.886851i	$0.652888\pi$
$614$	25629.1			1.68454
$615$	32233.0			2.11343
$616$			205.688i			0.0134536i
$617$		−	28033.2i		−	1.82913i	−0.404440	−	0.914565i	$-0.632534\pi$
$617$		−	28033.2i		−	1.82913i	0.404440	−	0.914565i	$-0.367466\pi$
$618$			22622.8i			1.47253i
$619$	10093.7			0.655411			0.327706	−	0.944780i	$-0.393725\pi$
$619$	10093.7			0.655411			0.327706	+	0.944780i	$0.393725\pi$
$620$			12044.7i			0.780207i
$621$			47404.9i			3.06327i
$622$	24248.0			1.56311
$623$	4291.93			0.276007
$624$	−10106.3			−0.648361
$625$	−14251.1			−0.912069
$626$	−21899.5			−1.39821
$627$			1312.71i			0.0836119i
$628$			15168.9i			0.963859i
$629$	55446.6			3.51479
$630$	31169.7			1.97116
$631$			28309.3i			1.78602i	0.450040	+	0.893008i	$0.351410\pi$
$631$			28309.3i			1.78602i	−0.450040	+	0.893008i	$0.648590\pi$
$632$	−2318.57			−0.145930
$633$		−	43235.9i		−	2.71481i
$634$		−	10253.0i		−	0.642271i
$635$	4132.13			0.258234
$636$			27498.8i			1.71446i
$637$	6594.04			0.410150
$638$		−	896.616i		−	0.0556385i
$639$		−	37983.6i		−	2.35150i
$640$			15251.0i			0.941953i
$641$			13721.8i			0.845518i	0.906242	+	0.422759i	$0.138938\pi$
$641$			13721.8i			0.845518i	−0.906242	+	0.422759i	$0.861062\pi$
$642$			16402.4i			1.00833i
$643$		−	9176.05i		−	0.562781i	−0.959593	−	0.281390i	$-0.909204\pi$
$643$		−	9176.05i		−	0.562781i	0.959593	−	0.281390i	$-0.0907956\pi$
$644$	−20537.9			−1.25669
$645$			15392.9i			0.939679i
$646$	53689.7			3.26996
$647$		−	4384.91i		−	0.266443i	−0.991086	−	0.133222i	$-0.957468\pi$
$647$		−	4384.91i		−	0.266443i	0.991086	−	0.133222i	$-0.0425322\pi$
$648$			12695.2i			0.769622i
$649$	−237.745			−0.0143795
$650$			1387.59i			0.0837318i
$651$	11184.7			0.673370
$652$	−24029.9			−1.44338
$653$			6074.89i			0.364057i	0.983293	+	0.182028i	$0.0582663\pi$
$653$			6074.89i			0.364057i	−0.983293	+	0.182028i	$0.941734\pi$
$654$		−	2546.93i		−	0.152282i
$655$	16710.0			0.996814
$656$	11328.0			0.674211
$657$	−22960.4			−1.36343
$658$	25008.9			1.48169
$659$	−4266.70			−0.252211			−0.126106	−	0.992017i	$-0.540248\pi$
$659$	−4266.70			−0.252211			−0.126106	+	0.992017i	$0.540248\pi$
$660$			1596.27i			0.0941433i
$661$			1300.33i			0.0765159i	0.999268	+	0.0382580i	$0.0121809\pi$
$661$			1300.33i			0.0765159i	−0.999268	+	0.0382580i	$0.987819\pi$
$662$	−5026.24			−0.295091
$663$			38180.8i			2.23653i
$664$			10121.3i			0.591538i
$665$			11725.6i			0.683760i
$666$	−106183.			−6.17791
$667$	22764.6			1.32151
$668$	1933.64			0.111998
$669$		−	22861.2i		−	1.32117i
$670$	−6236.52			−0.359609
$671$	−620.005	−	360.567i	−0.0356707	−	0.0207445i
$672$	26129.0			1.49992
$673$			17828.4i			1.02115i	0.859833	+	0.510576i	$0.170568\pi$
$673$			17828.4i			1.02115i	−0.859833	+	0.510576i	$0.829432\pi$
$674$	20170.9			1.15275
$675$	−2913.15			−0.166114
$676$	12894.5			0.733645
$677$			4383.11i			0.248828i	0.992230	+	0.124414i	$0.0397051\pi$
$677$			4383.11i			0.248828i	−0.992230	+	0.124414i	$0.960295\pi$
$678$			31069.7i			1.75992i
$679$		−	1969.35i		−	0.111306i
$680$	16600.9			0.936202
$681$		−	6108.34i		−	0.343718i
$682$			682.580i			0.0383245i
$683$	−19102.6			−1.07019			−0.535094	−	0.844792i	$-0.679724\pi$
$683$	−19102.6			−1.07019			−0.535094	+	0.844792i	$0.679724\pi$
$684$	−58897.1			−3.29238
$685$	−24221.4			−1.35103
$686$	−27650.3			−1.53891
$687$	13305.7			0.738927
$688$			5409.67i			0.299770i
$689$		−	8766.49i		−	0.484727i
$690$	−70751.3			−3.90356
$691$	−25284.8			−1.39201			−0.696005	−	0.718037i	$-0.745041\pi$
$691$	−25284.8			−1.39201			−0.696005	+	0.718037i	$0.745041\pi$
$692$		−	2333.53i		−	0.128190i
$693$	1011.84			0.0554643
$694$			36820.7i			2.01397i
$695$		−	17619.3i		−	0.961635i
$696$	14985.0			0.816099
$697$		−	42795.9i		−	2.32570i
$698$	30555.2			1.65692
$699$			42385.1i			2.29349i
$700$		−	1262.10i		−	0.0681472i
$701$			10059.1i			0.541980i	0.962582	+	0.270990i	$0.0873511\pi$
$701$			10059.1i			0.541980i	−0.962582	+	0.270990i	$0.912649\pi$
$702$		−	39122.4i		−	2.10339i
$703$		−	39944.4i		−	2.14300i
$704$			1176.25i			0.0629711i
$705$	49351.2			2.63642
$706$		−	14147.7i		−	0.754187i
$707$	297.918			0.0158477
$708$		−	15626.2i		−	0.829478i
$709$			18595.8i			0.985021i	0.870306	+	0.492511i	$0.163921\pi$
$709$			18595.8i			0.985021i	−0.870306	+	0.492511i	$0.836079\pi$
$710$	30332.6			1.60333
$711$			11405.8i			0.601617i
$712$	−4377.55			−0.230415
$713$	−17330.4			−0.910276
$714$		−	60625.4i		−	3.17766i
$715$		−	508.883i		−	0.0266170i
$716$	23664.7			1.23518
$717$	−28179.1			−1.46774
$718$	−6391.37			−0.332206
$719$	−33346.7			−1.72966			−0.864828	−	0.502067i	$-0.832573\pi$
$719$	−33346.7			−1.72966			−0.864828	+	0.502067i	$0.832573\pi$
$720$	21616.6			1.11889
$721$			6559.84i			0.338837i
$722$		−	8995.94i		−	0.463704i
$723$	−3739.30			−0.192346
$724$		−	29328.5i		−	1.50550i
$725$			1398.94i			0.0716626i
$726$		−	53036.5i		−	2.71125i
$727$	24165.3			1.23280			0.616398	−	0.787435i	$-0.288591\pi$
$727$	24165.3			1.23280			0.616398	+	0.787435i	$0.288591\pi$
$728$	4309.88			0.219416
$729$	−8919.07			−0.453136
$730$		−	18335.6i		−	0.929629i
$731$	20437.2			1.03406
$732$	23699.0	−	40751.1i	1.19664	−	2.05765i
$733$	−12552.9			−0.632539			−0.316269	−	0.948669i	$-0.602430\pi$
$733$	−12552.9			−0.632539			−0.316269	+	0.948669i	$0.602430\pi$
$734$			36463.6i			1.83364i
$735$	−20661.6			−1.03689
$736$	−40486.0			−2.02763
$737$	−202.452			−0.0101186
$738$			81955.9i			4.08786i
$739$			28840.0i			1.43558i	0.696257	+	0.717792i	$0.254847\pi$
$739$			28840.0i			1.43558i	−0.696257	+	0.717792i	$0.745153\pi$
$740$		−	48572.6i		−	2.41293i
$741$	27505.9			1.36364
$742$			13919.9i			0.688700i
$743$		−	3769.36i		−	0.186117i	−0.995661	−	0.0930583i	$-0.970336\pi$
$743$		−	3769.36i		−	0.186117i	0.995661	−	0.0930583i	$-0.0296643\pi$
$744$	−11407.8			−0.562139
$745$	−7548.13			−0.371197
$746$	9942.35			0.487956
$747$	49789.7			2.43870
$748$	2119.37			0.103599
$749$			4756.13i			0.232023i
$750$		−	57814.7i		−	2.81479i
$751$	−27514.8			−1.33692			−0.668462	−	0.743746i	$-0.733047\pi$
$751$	−27514.8			−1.33692			−0.668462	+	0.743746i	$0.733047\pi$
$752$	17344.0			0.841050
$753$		−	40575.9i		−	1.96370i
$754$	−18787.2			−0.907414
$755$		−	204.332i		−	0.00984954i
$756$			35584.4i			1.71190i
$757$	38053.0			1.82703			0.913515	−	0.406806i	$-0.133357\pi$
$757$	38053.0			1.82703			0.913515	+	0.406806i	$0.133357\pi$
$758$		−	470.846i		−	0.0225619i
$759$	−2296.76			−0.109838
$760$		−	11959.5i		−	0.570813i
$761$		−	33061.0i		−	1.57485i	−0.616412	−	0.787424i	$-0.711414\pi$
$761$		−	33061.0i		−	1.57485i	0.616412	−	0.787424i	$-0.288586\pi$
$762$			15391.2i			0.731714i
$763$		−	738.522i		−	0.0350410i
$764$			36878.1i			1.74634i
$765$		−	81665.3i		−	3.85963i
$766$	−46677.8			−2.20175
$767$			4981.58i			0.234517i
$768$	846.319			0.0397642
$769$			41387.6i			1.94080i	0.241501	+	0.970400i	$0.422360\pi$
$769$			41387.6i			1.94080i	−0.241501	+	0.970400i	$0.577640\pi$
$770$			808.031i			0.0378174i
$771$	50511.2			2.35942
$772$			35846.9i			1.67119i
$773$	1049.27			0.0488224			0.0244112	−	0.999702i	$-0.492229\pi$
$773$	1049.27			0.0488224			0.0244112	+	0.999702i	$0.492229\pi$
$774$	−39138.1			−1.81756
$775$		−	1064.99i		−	0.0493621i
$776$			2008.63i			0.0929197i
$777$	−45104.5			−2.08252
$778$	50674.7			2.33519
$779$	−30830.7			−1.41800
$780$	33447.3			1.53539
$781$	984.670			0.0451143
$782$			93937.0i			4.29563i
$783$		−	39442.5i		−	1.80020i
$784$	−7261.32			−0.330782
$785$			15152.3i			0.688928i
$786$			62240.9i			2.82450i
$787$		−	18030.5i		−	0.816667i	−0.912833	−	0.408334i	$-0.866110\pi$
$787$		−	18030.5i		−	0.816667i	0.912833	−	0.408334i	$-0.133890\pi$
$788$	45856.7			2.07307
$789$	42034.7			1.89667
$790$	−9108.33			−0.410202
$791$			9009.15i			0.404966i
$792$	−1032.03			−0.0463024
$793$	−7555.14	+	12991.3i	−0.338324	+	0.581757i
$794$	43671.9			1.95196
$795$			27468.7i			1.22543i
$796$	−18626.0			−0.829373
$797$	22402.4			0.995649			0.497825	−	0.867278i	$-0.334132\pi$
$797$	22402.4			0.995649			0.497825	+	0.867278i	$0.334132\pi$
$798$	−43675.3			−1.93745
$799$		−	65523.9i		−	2.90121i
$800$		−	2487.96i		−	0.109953i
$801$			21534.5i			0.949919i
$802$	−44687.5			−1.96755
$803$		−	595.216i		−	0.0261578i
$804$		−	13306.6i		−	0.583690i
$805$	−20515.5			−0.898231
$806$	14302.4			0.625039
$807$	57808.9			2.52165
$808$	−303.861			−0.0132299
$809$	−23722.6			−1.03095			−0.515477	−	0.856903i	$-0.672385\pi$
$809$	−23722.6			−1.03095			−0.515477	+	0.856903i	$0.672385\pi$
$810$			49872.2i			2.16337i
$811$			22289.2i			0.965081i	0.875874	+	0.482541i	$0.160286\pi$
$811$			22289.2i			0.965081i	−0.875874	+	0.482541i	$0.839714\pi$
$812$	17088.2			0.738522
$813$	−10470.4			−0.451677
$814$		−	2752.63i		−	0.118525i
$815$	−24003.6			−1.03167
$816$		−	42044.4i		−	1.80374i
$817$		−	14723.2i		−	0.630477i
$818$	−34088.3			−1.45705
$819$		−	21201.7i		−	0.904573i
$820$	−37490.3			−1.59661
$821$			20824.4i			0.885232i	0.896711	+	0.442616i	$0.145950\pi$
$821$			20824.4i			0.885232i	−0.896711	+	0.442616i	$0.854050\pi$
$822$		−	90219.4i		−	3.82818i
$823$			31149.9i			1.31934i	0.751555	+	0.659671i	$0.229304\pi$
$823$			31149.9i			1.31934i	−0.751555	+	0.659671i	$0.770696\pi$
$824$		−	6690.70i		−	0.282866i
$825$		−	141.141i		−	0.00595625i
$826$		−	7910.01i		−	0.333202i
$827$	−2335.21			−0.0981901			−0.0490951	−	0.998794i	$-0.515634\pi$
$827$	−2335.21			−0.0981901			−0.0490951	+	0.998794i	$0.515634\pi$
$828$		−	103048.i		−	4.32508i
$829$	−17747.2			−0.743529			−0.371764	−	0.928327i	$-0.621247\pi$
$829$	−17747.2			−0.743529			−0.371764	+	0.928327i	$0.621247\pi$
$830$			39760.7i			1.66279i
$831$		−	31041.7i		−	1.29582i
$832$	24646.5			1.02700
$833$			27432.6i			1.14103i
$834$	65627.7			2.72482
$835$	1931.53			0.0800518
$836$		−	1526.82i		−	0.0631654i
$837$			30026.9i			1.24000i
$838$	−61034.3			−2.51599
$839$	−23997.2			−0.987455			−0.493727	−	0.869617i	$-0.664366\pi$
$839$	−23997.2			−0.987455			−0.493727	+	0.869617i	$0.664366\pi$
$840$	−13504.5			−0.554701
$841$	5448.06			0.223382
$842$	8048.21			0.329406
$843$			32866.7i			1.34281i
$844$			50287.9i			2.05092i
$845$	12880.5			0.524380
$846$			125481.i			5.09943i
$847$		−	15378.8i		−	0.623874i
$848$			9653.62i			0.390928i
$849$	63396.3			2.56273
$850$	−5772.65			−0.232942
$851$	69887.9			2.81519
$852$			64719.4i			2.60241i
$853$	−25171.1			−1.01037			−0.505183	−	0.863012i	$-0.668575\pi$
$853$	−25171.1			−1.01037			−0.505183	+	0.863012i	$0.668575\pi$
$854$	11996.4	−	20628.2i	0.480691	−	0.826560i
$855$	−58832.7			−2.35326
$856$		−	4851.01i		−	0.193696i
$857$	12233.2			0.487608			0.243804	−	0.969825i	$-0.421605\pi$
$857$	12233.2			0.487608			0.243804	+	0.969825i	$0.421605\pi$
$858$	1895.47			0.0754200
$859$	−7417.30			−0.294616			−0.147308	−	0.989091i	$-0.547061\pi$
$859$	−7417.30			−0.294616			−0.147308	+	0.989091i	$0.547061\pi$
$860$		−	17903.5i		−	0.709889i
$861$			34813.5i			1.37798i
$862$		−	61595.8i		−	2.43383i
$863$	−21283.7			−0.839518			−0.419759	−	0.907636i	$-0.637885\pi$
$863$	−21283.7			−0.839518			−0.419759	+	0.907636i	$0.637885\pi$
$864$			70146.9i			2.76209i
$865$		−	2330.98i		−	0.0916250i
$866$	−53349.6			−2.09341
$867$	−113525.			−4.44696
$868$	−13009.0			−0.508703
$869$	−295.678			−0.0115422
$870$	58867.5			2.29402
$871$			4242.08i			0.165026i
$872$			753.254i			0.0292528i
$873$	9881.09			0.383075
$874$	67673.4			2.61909
$875$		−	16764.3i		−	0.647699i
$876$	39121.8			1.50891
$877$		−	23932.8i		−	0.921497i	−0.887531	−	0.460748i	$-0.847581\pi$
$877$		−	23932.8i		−	0.921497i	0.887531	−	0.460748i	$-0.152419\pi$
$878$			20915.5i			0.803947i
$879$	−27777.5			−1.06588
$880$			560.379i			0.0214663i
$881$	17062.4			0.652492			0.326246	−	0.945285i	$-0.394216\pi$
$881$	17062.4			0.652492			0.326246	+	0.945285i	$0.394216\pi$
$882$		−	52534.5i		−	2.00559i
$883$			2803.00i			0.106827i	0.998572	+	0.0534137i	$0.0170102\pi$
$883$			2803.00i			0.106827i	−0.998572	+	0.0534137i	$0.982990\pi$
$884$		−	44408.2i		−	1.68960i
$885$		−	15609.2i		−	0.592878i
$886$		−	56992.1i		−	2.16105i
$887$			22283.7i			0.843532i	0.906705	+	0.421766i	$0.138590\pi$
$887$			22283.7i			0.843532i	−0.906705	+	0.421766i	$0.861410\pi$
$888$	46004.2			1.73852
$889$			4462.94i			0.168371i
$890$	−17196.9			−0.647686
$891$			1618.97i			0.0608727i
$892$			26589.9i			0.998090i
$893$	−47204.2			−1.76890
$894$		−	28115.1i		−	1.05180i
$895$	23638.8			0.882860
$896$	−16472.0			−0.614164
$897$			48125.1i			1.79136i
$898$		−	48033.2i		−	1.78496i
$899$	14419.4			0.534945
$900$	6332.54			0.234539
$901$	36470.4			1.34851
$902$	−2124.59			−0.0784269
$903$	−16625.2			−0.612681
$904$		−	9188.86i		−	0.338072i
$905$		−	29296.4i		−	1.07607i
$906$	761.090			0.0279090
$907$			17830.6i			0.652764i	0.945238	+	0.326382i	$0.105830\pi$
$907$			17830.6i			0.652764i	−0.945238	+	0.326382i	$0.894170\pi$
$908$			7104.64i			0.259665i
$909$			1494.79i			0.0545423i
$910$	16931.0			0.616768
$911$	−38085.1			−1.38509			−0.692544	−	0.721376i	$-0.743510\pi$
$911$	−38085.1			−1.38509			−0.692544	+	0.721376i	$0.743510\pi$
$912$	−30289.3			−1.09976
$913$			1290.73i			0.0467874i
$914$	55643.7			2.01371
$915$	23673.1	−	40706.5i	0.855310	−	1.47073i
$916$	−15475.9			−0.558229
$917$			18047.7i			0.649933i
$918$	162757.			5.85162
$919$	14731.4			0.528774			0.264387	−	0.964417i	$-0.414830\pi$
$919$	14731.4			0.528774			0.264387	+	0.964417i	$0.414830\pi$
$920$	20924.7			0.749856
$921$			54624.0i			1.95431i
$922$			1716.23i			0.0613027i
$923$		−	20632.3i		−	0.735774i
$924$	−1724.06			−0.0613824
$925$			4294.78i			0.152661i
$926$		−	24366.0i		−	0.864705i
$927$	−32913.7			−1.16616
$928$	33685.7			1.19158
$929$	9380.60			0.331289			0.165645	−	0.986186i	$-0.447030\pi$
$929$	9380.60			0.331289			0.165645	+	0.986186i	$0.447030\pi$
$930$	−44814.9			−1.58015
$931$	19762.8			0.695702
$932$		−	49298.3i		−	1.73264i
$933$			51680.3i			1.81344i
$934$	−44014.2			−1.54196
$935$	2117.06			0.0740483
$936$			21624.6i			0.755151i
$937$	42912.5			1.49615			0.748074	−	0.663616i	$-0.230979\pi$
$937$	42912.5			1.49615			0.748074	+	0.663616i	$0.230979\pi$
$938$		−	6735.80i		−	0.234469i
$939$		−	46674.9i		−	1.62213i
$940$	−57400.6			−1.99170
$941$			5369.56i			0.186018i	0.995665	+	0.0930088i	$0.0296485\pi$
$941$			5369.56i			0.186018i	−0.995665	+	0.0930088i	$0.970352\pi$
$942$	−56438.8			−1.95210
$943$		−	53942.3i		−	1.86278i
$944$		−	5485.69i		−	0.189136i
$945$			35545.6i			1.22360i
$946$		−	1014.60i		−	0.0348704i
$947$		−	30465.1i		−	1.04539i	−0.852521	−	0.522694i	$-0.824927\pi$
$947$		−	30465.1i		−	1.04539i	0.852521	−	0.522694i	$-0.175073\pi$
$948$		−	19434.0i		−	0.665810i
$949$	−12471.8			−0.426611
$950$			4158.69i			0.142027i
$951$	21852.5			0.745128
$952$			17930.0i			0.610414i
$953$			6640.52i			0.225716i	0.993611	+	0.112858i	$0.0360005\pi$
$953$			6640.52i			0.225716i	−0.993611	+	0.112858i	$0.963999\pi$
$954$	−69842.4			−2.37026
$955$			36837.9i			1.24821i
$956$	32775.3			1.10882
$957$	1910.98			0.0645488
$958$			3584.99i			0.120904i
$959$		−	26160.6i		−	0.880885i
$960$	−77227.0			−2.59634
$961$	18813.7			0.631523
$962$	−57677.2			−1.93304
$963$	−23863.7			−0.798542
$964$	4349.19			0.145309
$965$			35807.7i			1.19450i
$966$		−	76415.5i		−	2.54516i
$967$	−46373.1			−1.54215			−0.771075	−	0.636745i	$-0.780281\pi$
$967$	−46373.1			−1.54215			−0.771075	+	0.636745i	$0.780281\pi$
$968$			15685.6i			0.520820i
$969$			114430.i			3.79363i
$970$			7890.77i			0.261193i
$971$	6989.82			0.231013			0.115507	−	0.993307i	$-0.463151\pi$
$971$	6989.82			0.231013			0.115507	+	0.993307i	$0.463151\pi$
$972$	−23398.4			−0.772125
$973$	19029.8			0.626997
$974$		−	9542.36i		−	0.313919i
$975$	−2957.40			−0.0971412
$976$	8319.68	−	14305.9i	0.272855	−	0.469181i
$977$	40881.8			1.33871			0.669357	−	0.742941i	$-0.266570\pi$
$977$	40881.8			1.33871			0.669357	+	0.742941i	$0.266570\pi$
$978$		−	89408.0i		−	2.92326i
$979$	−558.252			−0.0182245
$980$	24031.6			0.783329
$981$	3705.50			0.120599
$982$			45511.7i			1.47896i
$983$			3702.10i			0.120121i	0.998195	+	0.0600604i	$0.0191293\pi$
$983$			3702.10i			0.120121i	−0.998195	+	0.0600604i	$0.980871\pi$
$984$		−	35507.9i		−	1.15036i
$985$	45806.6			1.48175
$986$		−	78158.7i		−	2.52442i
$987$			53302.1i			1.71897i
$988$	−31992.2			−1.03017
$989$	25760.1			0.828235
$990$	−4054.25			−0.130154
$991$	30501.3			0.977705			0.488853	−	0.872366i	$-0.337416\pi$
$991$	30501.3			0.977705			0.488853	+	0.872366i	$0.337416\pi$
$992$	−25644.4			−0.820776
$993$		−	10712.5i		−	0.342349i
$994$			32761.0i			1.04539i
$995$	−18605.7			−0.592803
$996$	−84835.6			−2.69892
$997$			5181.00i			0.164578i	0.996609	+	0.0822888i	$0.0262230\pi$
$997$			5181.00i			0.164578i	−0.996609	+	0.0822888i	$0.973777\pi$
$998$	−32155.7			−1.01991
$999$		−	121089.i		−	3.83493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.4.b.a.60.2	✓	14
3.2	odd	2		549.4.c.c.487.13		14
4.3	odd	2		976.4.h.a.609.2		14
61.60	even	2	inner	61.4.b.a.60.13	yes	14
183.182	odd	2		549.4.c.c.487.2		14
244.243	odd	2		976.4.h.a.609.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.4.b.a.60.2	✓	14	1.1	even	1	trivial
61.4.b.a.60.13	yes	14	61.60	even	2	inner
549.4.c.c.487.2		14	183.182	odd	2
549.4.c.c.487.13		14	3.2	odd	2
976.4.h.a.609.1		14	244.243	odd	2
976.4.h.a.609.2		14	4.3	odd	2

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	61.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.32757i q^{2} +9.22345 q^{3} -10.7278 q^{4} -10.7161 q^{5} -39.9151i q^{6} -11.5740i q^{7} +11.8049i q^{8} +58.0721 q^{9} +O(q^{10})\)	\(q-4.32757i q^{2} +9.22345 q^{3} -10.7278 q^{4} -10.7161 q^{5} -39.9151i q^{6} -11.5740i q^{7} +11.8049i q^{8} +58.0721 q^{9} +46.3747i q^{10} +1.50544i q^{11} -98.9477 q^{12} +31.5441 q^{13} -50.0874 q^{14} -98.8396 q^{15} -34.7362 q^{16} +131.230i q^{17} -251.311i q^{18} +94.5397 q^{19} +114.961 q^{20} -106.752i q^{21} +6.51487 q^{22} +165.409i q^{23} +108.882i q^{24} -10.1648 q^{25} -136.509i q^{26} +286.592 q^{27} +124.164i q^{28} -137.626i q^{29} +427.735i q^{30} +104.773i q^{31} +244.762i q^{32} +13.8853i q^{33} +567.906 q^{34} +124.029i q^{35} -622.988 q^{36} -422.515i q^{37} -409.127i q^{38} +290.945 q^{39} -126.503i q^{40} -326.114 q^{41} -461.978 q^{42} -155.736i q^{43} -16.1501i q^{44} -622.307 q^{45} +715.820 q^{46} -499.306 q^{47} -320.388 q^{48} +209.042 q^{49} +43.9888i q^{50} +1210.39i q^{51} -338.400 q^{52} -277.912i q^{53} -1240.24i q^{54} -16.1324i q^{55} +136.630 q^{56} +871.982 q^{57} -595.586 q^{58} +157.924i q^{59} +1060.34 q^{60} +(-239.510 + 411.844i) q^{61} +453.410 q^{62} -672.127i q^{63} +781.336 q^{64} -338.030 q^{65} +60.0896 q^{66} +134.481i q^{67} -1407.81i q^{68} +1525.64i q^{69} +536.742 q^{70} -654.077i q^{71} +685.535i q^{72} -395.378 q^{73} -1828.46 q^{74} -93.7545 q^{75} -1014.21 q^{76} +17.4239 q^{77} -1259.09i q^{78} +196.407i q^{79} +372.237 q^{80} +1075.42 q^{81} +1411.28i q^{82} +857.379 q^{83} +1145.22i q^{84} -1406.28i q^{85} -673.957 q^{86} -1269.39i q^{87} -17.7715 q^{88} +370.824i q^{89} +2693.08i q^{90} -365.092i q^{91} -1774.48i q^{92} +966.365i q^{93} +2160.78i q^{94} -1013.10 q^{95} +2257.55i q^{96} +170.152 q^{97} -904.643i q^{98} +87.4237i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9}+O(q^{10}) \) 14 * q - 2 * q^3 - 38 * q^4 - 14 * q^5 + 116 * q^9	\( 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9} - 150 q^{12} - 86 q^{13} - 8 q^{14} - 28 q^{15} - 158 q^{16} + 166 q^{19} + 54 q^{20} + 242 q^{22} + 204 q^{25} + 88 q^{27} + 824 q^{34} - 572 q^{36} + 1160 q^{39} - 64 q^{41} - 1936 q^{42} - 1310 q^{45} + 488 q^{46} - 1308 q^{47} + 230 q^{48} + 254 q^{49} - 50 q^{52} - 172 q^{56} + 1736 q^{57} - 470 q^{58} + 772 q^{60} - 630 q^{61} + 1546 q^{62} + 1098 q^{64} - 390 q^{65} - 292 q^{66} + 1390 q^{70} - 3032 q^{73} - 3806 q^{74} + 1978 q^{75} + 162 q^{76} - 82 q^{77} - 1682 q^{80} + 4238 q^{81} - 1822 q^{83} - 104 q^{86} + 3274 q^{88} - 1648 q^{95} + 3890 q^{97}+O(q^{100}) \) 14 * q - 2 * q^3 - 38 * q^4 - 14 * q^5 + 116 * q^9 - 150 * q^12 - 86 * q^13 - 8 * q^14 - 28 * q^15 - 158 * q^16 + 166 * q^19 + 54 * q^20 + 242 * q^22 + 204 * q^25 + 88 * q^27 + 824 * q^34 - 572 * q^36 + 1160 * q^39 - 64 * q^41 - 1936 * q^42 - 1310 * q^45 + 488 * q^46 - 1308 * q^47 + 230 * q^48 + 254 * q^49 - 50 * q^52 - 172 * q^56 + 1736 * q^57 - 470 * q^58 + 772 * q^60 - 630 * q^61 + 1546 * q^62 + 1098 * q^64 - 390 * q^65 - 292 * q^66 + 1390 * q^70 - 3032 * q^73 - 3806 * q^74 + 1978 * q^75 + 162 * q^76 - 82 * q^77 - 1682 * q^80 + 4238 * q^81 - 1822 * q^83 - 104 * q^86 + 3274 * q^88 - 1648 * q^95 + 3890 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more