LMFDB - Embedded newform 61.4.b.a.60.7

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			60.7
Root			$-1.28937i$ of defining polynomial
Character	$\chi$	$=$	61.60
Dual form			61.4.b.a.60.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28937i q^{2} +5.54789 q^{3} +6.33752 q^{4} +0.0273216 q^{5} -7.15328i q^{6} +21.0031i q^{7} -18.4864i q^{8} +3.77903 q^{9} +O(q^{10})$	\(q-1.28937i q^{2} +5.54789 q^{3} +6.33752 q^{4} +0.0273216 q^{5} -7.15328i q^{6} +21.0031i q^{7} -18.4864i q^{8} +3.77903 q^{9} -0.0352277i q^{10} -20.2234i q^{11} +35.1599 q^{12} -9.47849 q^{13} +27.0808 q^{14} +0.151577 q^{15} +26.8644 q^{16} -90.4116i q^{17} -4.87257i q^{18} -54.9725 q^{19} +0.173152 q^{20} +116.523i q^{21} -26.0755 q^{22} +142.946i q^{23} -102.560i q^{24} -124.999 q^{25} +12.2213i q^{26} -128.827 q^{27} +133.108i q^{28} +115.845i q^{29} -0.195439i q^{30} +104.790i q^{31} -182.529i q^{32} -112.197i q^{33} -116.574 q^{34} +0.573840i q^{35} +23.9497 q^{36} -73.2424i q^{37} +70.8799i q^{38} -52.5856 q^{39} -0.505078i q^{40} +206.026 q^{41} +150.241 q^{42} -17.9583i q^{43} -128.166i q^{44} +0.103249 q^{45} +184.311 q^{46} +36.1835 q^{47} +149.041 q^{48} -98.1310 q^{49} +161.170i q^{50} -501.593i q^{51} -60.0702 q^{52} -361.507i q^{53} +166.106i q^{54} -0.552537i q^{55} +388.272 q^{56} -304.981 q^{57} +149.367 q^{58} +78.4496i q^{59} +0.960625 q^{60} +(429.877 + 205.394i) q^{61} +135.114 q^{62} +79.3714i q^{63} -20.4325 q^{64} -0.258968 q^{65} -144.664 q^{66} +1035.85i q^{67} -572.986i q^{68} +793.050i q^{69} +0.739892 q^{70} -837.087i q^{71} -69.8606i q^{72} -13.7542 q^{73} -94.4366 q^{74} -693.482 q^{75} -348.390 q^{76} +424.755 q^{77} +67.8023i q^{78} -1103.67i q^{79} +0.733980 q^{80} -816.753 q^{81} -265.644i q^{82} +503.365 q^{83} +738.467i q^{84} -2.47019i q^{85} -23.1550 q^{86} +642.696i q^{87} -373.858 q^{88} +308.852i q^{89} -0.133127i q^{90} -199.078i q^{91} +905.926i q^{92} +581.365i q^{93} -46.6539i q^{94} -1.50194 q^{95} -1012.65i q^{96} -1434.67 q^{97} +126.527i q^{98} -76.4249i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.28937i		−	0.455861i	−0.973677	−	0.227931i	$-0.926804\pi$
$2$		−	1.28937i		−	0.455861i	0.973677	−	0.227931i	$-0.0731959\pi$
$3$	5.54789			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$3$	5.54789			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$4$	6.33752			0.792190
$5$	0.0273216			0.00244372			0.00122186	−	0.999999i	$-0.499611\pi$
$5$	0.0273216			0.00244372			0.00122186	+	0.999999i	$0.499611\pi$
$6$		−	7.15328i		−	0.486719i
$7$			21.0031i			1.13406i	0.823697	+	0.567031i	$0.191908\pi$
$7$			21.0031i			1.13406i	−0.823697	+	0.567031i	$0.808092\pi$
$8$		−	18.4864i		−	0.816990i
$9$	3.77903			0.139964
$10$		−	0.0352277i		−	0.00111400i
$11$		−	20.2234i		−	0.554327i	−0.960823	−	0.277163i	$-0.910606\pi$
$11$		−	20.2234i		−	0.554327i	0.960823	−	0.277163i	$-0.0893943\pi$
$12$	35.1599			0.845815
$13$	−9.47849			−0.202220			−0.101110	−	0.994875i	$-0.532239\pi$
$13$	−9.47849			−0.202220			−0.101110	+	0.994875i	$0.532239\pi$
$14$	27.0808			0.516975
$15$	0.151577			0.00260914
$16$	26.8644			0.419756
$17$		−	90.4116i		−	1.28988i	−0.764231	−	0.644942i	$-0.776881\pi$
$17$		−	90.4116i		−	1.28988i	0.764231	−	0.644942i	$-0.223119\pi$
$18$		−	4.87257i		−	0.0638042i
$19$	−54.9725			−0.663766			−0.331883	−	0.943320i	$-0.607684\pi$
$19$	−54.9725			−0.663766			−0.331883	+	0.943320i	$0.607684\pi$
$20$	0.173152			0.00193589
$21$			116.523i			1.21083i
$22$	−26.0755			−0.252696
$23$			142.946i			1.29593i	0.761671	+	0.647964i	$0.224379\pi$
$23$			142.946i			1.29593i	−0.761671	+	0.647964i	$0.775621\pi$
$24$		−	102.560i		−	0.872293i
$25$	−124.999			−0.999994
$26$			12.2213i			0.0921843i
$27$	−128.827			−0.918253
$28$			133.108i			0.898393i
$29$			115.845i			0.741790i	0.928675	+	0.370895i	$0.120949\pi$
$29$			115.845i			0.741790i	−0.928675	+	0.370895i	$0.879051\pi$
$30$		−	0.195439i		−	0.00118941i
$31$			104.790i			0.607126i	0.952811	+	0.303563i	$0.0981763\pi$
$31$			104.790i			0.607126i	−0.952811	+	0.303563i	$0.901824\pi$
$32$		−	182.529i		−	1.00834i
$33$		−	112.197i		−	0.591849i
$34$	−116.574			−0.588008
$35$			0.573840i			0.00277133i
$36$	23.9497			0.110878
$37$		−	73.2424i		−	0.325432i	−0.986673	−	0.162716i	$-0.947975\pi$
$37$		−	73.2424i		−	0.325432i	0.986673	−	0.162716i	$-0.0520254\pi$
$38$			70.8799i			0.302585i
$39$	−52.5856			−0.215909
$40$		−	0.505078i		−	0.00199650i
$41$	206.026			0.784778			0.392389	−	0.919799i	$-0.371649\pi$
$41$	206.026			0.784778			0.392389	+	0.919799i	$0.371649\pi$
$42$	150.241			0.551969
$43$		−	17.9583i		−	0.0636889i	−0.999493	−	0.0318444i	$-0.989862\pi$
$43$		−	17.9583i		−	0.0636889i	0.999493	−	0.0318444i	$-0.0101381\pi$
$44$		−	128.166i		−	0.439132i
$45$	0.103249			0.000342033
$46$	184.311			0.590764
$47$	36.1835			0.112296			0.0561479	−	0.998422i	$-0.482118\pi$
$47$	36.1835			0.112296			0.0561479	+	0.998422i	$0.482118\pi$
$48$	149.041			0.448170
$49$	−98.1310			−0.286096
$50$			161.170i			0.455859i
$51$		−	501.593i		−	1.37720i
$52$	−60.0702			−0.160197
$53$		−	361.507i		−	0.936920i	−0.883485	−	0.468460i	$-0.844809\pi$
$53$		−	361.507i		−	0.936920i	0.883485	−	0.468460i	$-0.155191\pi$
$54$			166.106i			0.418596i
$55$		−	0.552537i		−	0.00135462i
$56$	388.272			0.926517
$57$	−304.981			−0.708697
$58$	149.367			0.338153
$59$			78.4496i			0.173106i	0.996247	+	0.0865531i	$0.0275852\pi$
$59$			78.4496i			0.173106i	−0.996247	+	0.0865531i	$0.972415\pi$
$60$	0.960625			0.00206694
$61$	429.877	+	205.394i	0.902297	+	0.431114i
$61$	429.877	+	205.394i	0.902297	+	0.431114i
$62$	135.114			0.276765
$63$			79.3714i			0.158728i
$64$	−20.4325			−0.0399073
$65$	−0.258968			−0.000494170
$66$	−144.664			−0.269801
$67$			1035.85i			1.88880i	0.328796	+	0.944401i	$0.393357\pi$
$67$			1035.85i			1.88880i	−0.328796	+	0.944401i	$0.606643\pi$
$68$		−	572.986i		−	1.02183i
$69$			793.050i			1.38365i
$70$	0.739892			0.00126334
$71$		−	837.087i		−	1.39921i	−0.714529	−	0.699605i	$-0.753359\pi$
$71$		−	837.087i		−	1.39921i	0.714529	−	0.699605i	$-0.246641\pi$
$72$		−	69.8606i		−	0.114349i
$73$	−13.7542			−0.0220522			−0.0110261	−	0.999939i	$-0.503510\pi$
$73$	−13.7542			−0.0220522			−0.0110261	+	0.999939i	$0.503510\pi$
$74$	−94.4366			−0.148352
$75$	−693.482			−1.06768
$76$	−348.390			−0.525829
$77$	424.755			0.628641
$78$			67.8023i			0.0984243i
$79$		−	1103.67i		−	1.57181i	−0.618348	−	0.785904i	$-0.712198\pi$
$79$		−	1103.67i		−	1.57181i	0.618348	−	0.785904i	$-0.287802\pi$
$80$	0.733980			0.00102577
$81$	−816.753			−1.12037
$82$		−	265.644i		−	0.357750i
$83$	503.365			0.665681			0.332840	−	0.942983i	$-0.391993\pi$
$83$	503.365			0.665681			0.332840	+	0.942983i	$0.391993\pi$
$84$			738.467i			0.959206i
$85$		−	2.47019i		−	0.00315212i
$86$	−23.1550			−0.0290333
$87$			642.696i			0.792003i
$88$	−373.858			−0.452879
$89$			308.852i			0.367845i	0.982941	+	0.183923i	$0.0588796\pi$
$89$			308.852i			0.367845i	−0.982941	+	0.183923i	$0.941120\pi$
$90$		−	0.133127i		−	0.000155920i
$91$		−	199.078i		−	0.229330i
$92$			905.926i			1.02662i
$93$			581.365i			0.648223i
$94$		−	46.6539i		−	0.0511913i
$95$	−1.50194			−0.00162206
$96$		−	1012.65i		−	1.07660i
$97$	−1434.67			−1.50174			−0.750872	−	0.660448i	$-0.770366\pi$
$97$	−1434.67			−1.50174			−0.750872	+	0.660448i	$0.770366\pi$
$98$			126.527i			0.130420i
$99$		−	76.4249i		−	0.0775858i
$100$	−792.186			−0.792186
$101$		−	880.180i		−	0.867141i	−0.901120	−	0.433570i	$-0.857254\pi$
$101$		−	880.180i		−	0.867141i	0.901120	−	0.433570i	$-0.142746\pi$
$102$	−646.739			−0.627811
$103$	965.766			0.923881			0.461941	−	0.886911i	$-0.347153\pi$
$103$	965.766			0.923881			0.461941	+	0.886911i	$0.347153\pi$
$104$			175.223i			0.165212i
$105$			3.18360i			0.00295893i
$106$	−466.116			−0.427106
$107$	1549.30			1.39978			0.699888	−	0.714252i	$-0.253233\pi$
$107$	1549.30			1.39978			0.699888	+	0.714252i	$0.253233\pi$
$108$	−816.446			−0.727431
$109$	−209.911			−0.184457			−0.0922284	−	0.995738i	$-0.529399\pi$
$109$	−209.911			−0.184457			−0.0922284	+	0.995738i	$0.529399\pi$
$110$	−0.712425			−0.000617519
$111$		−	406.341i		−	0.347461i
$112$			564.236i			0.476030i
$113$	319.389			0.265890			0.132945	−	0.991123i	$-0.457557\pi$
$113$	319.389			0.265890			0.132945	+	0.991123i	$0.457557\pi$
$114$			393.234i			0.323068i
$115$			3.90553i			0.00316689i
$116$			734.172i			0.587639i
$117$	−35.8195			−0.0283035
$118$	101.151			0.0789124
$119$	1898.93			1.46281
$120$		−	2.80212i		−	0.00213164i
$121$	922.013			0.692722
$122$	264.828	−	554.271i	0.196528	−	0.411322i
$123$	1143.01			0.837900
$124$			664.112i			0.480960i
$125$	−6.83039			−0.00488743
$126$	102.339			0.0723579
$127$	1384.98			0.967694			0.483847	−	0.875153i	$-0.339239\pi$
$127$	1384.98			0.967694			0.483847	+	0.875153i	$0.339239\pi$
$128$		−	1433.89i		−	0.990149i
$129$		−	99.6308i		−	0.0680000i
$130$			0.333906i			0.000225273i
$131$	1948.32			1.29943			0.649715	−	0.760178i	$-0.274888\pi$
$131$	1948.32			1.29943			0.649715	+	0.760178i	$0.274888\pi$
$132$		−	711.053i		−	0.468858i
$133$		−	1154.59i		−	0.752752i
$134$	1335.60			0.861032
$135$	−3.51977			−0.00224395
$136$	−1671.38			−1.05382
$137$	−2540.31			−1.58419			−0.792094	−	0.610400i	$-0.791009\pi$
$137$	−2540.31			−1.58419			−0.792094	+	0.610400i	$0.791009\pi$
$138$	1022.53			0.630753
$139$		−	1902.41i		−	1.16086i	−0.814309	−	0.580432i	$-0.802884\pi$
$139$		−	1902.41i		−	1.16086i	0.814309	−	0.580432i	$-0.197116\pi$
$140$			3.63672i			0.00219542i
$141$	200.742			0.119897
$142$	−1079.32			−0.637846
$143$			191.688i			0.112096i
$144$	101.521			0.0587508
$145$			3.16508i			0.00181273i
$146$			17.7343i			0.0100527i
$147$	−544.419			−0.305462
$148$		−	464.176i		−	0.257804i
$149$	−562.734			−0.309402			−0.154701	−	0.987961i	$-0.549441\pi$
$149$	−562.734			−0.309402			−0.154701	+	0.987961i	$0.549441\pi$
$150$			894.155i			0.486716i
$151$			2134.37i			1.15028i	0.818054	+	0.575142i	$0.195053\pi$
$151$			2134.37i			1.15028i	−0.818054	+	0.575142i	$0.804947\pi$
$152$			1016.24i			0.542291i
$153$		−	341.668i		−	0.180537i
$154$		−	547.666i		−	0.286573i
$155$			2.86305i			0.00148365i
$156$	−333.262			−0.171041
$157$			3205.05i			1.62924i	0.579993	+	0.814621i	$0.303055\pi$
$157$			3205.05i			1.62924i	−0.579993	+	0.814621i	$0.696945\pi$
$158$	−1423.04			−0.716527
$159$		−	2005.60i		−	1.00034i
$160$		−	4.98700i		−	0.00246411i
$161$	−3002.32			−1.46966
$162$			1053.10i			0.510735i
$163$	735.113			0.353242			0.176621	−	0.984279i	$-0.443483\pi$
$163$	735.113			0.353242			0.176621	+	0.984279i	$0.443483\pi$
$164$	1305.70			0.621694
$165$		−	3.06541i		−	0.00144632i
$166$		−	649.024i		−	0.303458i
$167$	−2693.71			−1.24818			−0.624088	−	0.781354i	$-0.714530\pi$
$167$	−2693.71			−1.24818			−0.624088	+	0.781354i	$0.714530\pi$
$168$	2154.09			0.989234
$169$	−2107.16			−0.959107
$170$	−3.18499			−0.00143693
$171$	−207.743			−0.0929035
$172$		−	113.811i		−	0.0504537i
$173$			1131.93i			0.497452i	0.968574	+	0.248726i	$0.0800119\pi$
$173$			1131.93i			0.497452i	−0.968574	+	0.248726i	$0.919988\pi$
$174$	828.673			0.361043
$175$		−	2625.37i		−	1.13405i
$176$		−	543.290i		−	0.232682i
$177$			435.229i			0.184824i
$178$	398.224			0.167686
$179$	−1496.49			−0.624875			−0.312437	−	0.949938i	$-0.601145\pi$
$179$	−1496.49			−0.624875			−0.312437	+	0.949938i	$0.601145\pi$
$180$	0.654345			0.000270956
$181$			802.000i			0.329349i	0.986348	+	0.164675i	$0.0526574\pi$
$181$			802.000i			0.329349i	−0.986348	+	0.164675i	$0.947343\pi$
$182$	−256.685			−0.104543
$183$	2384.91	+	1139.50i	0.963375	+	0.460297i
$184$	2642.56			1.05876
$185$		−	2.00110i		−	0.000795266i
$186$	749.595			0.295500
$187$	−1828.43			−0.715017
$188$	229.314			0.0889596
$189$		−	2705.77i		−	1.04136i
$190$			1.93656i			0.000739435i
$191$		−	822.017i		−	0.311409i	−0.987804	−	0.155704i	$-0.950235\pi$
$191$		−	822.017i		−	0.311409i	0.987804	−	0.155704i	$-0.0497647\pi$
$192$	−113.357			−0.0426086
$193$			4604.54i			1.71732i	0.512550	+	0.858658i	$0.328701\pi$
$193$			4604.54i			1.71732i	−0.512550	+	0.858658i	$0.671299\pi$
$194$			1849.83i			0.684587i
$195$	−1.43672			−0.000527621
$196$	−621.907			−0.226643
$197$	−4375.63			−1.58249			−0.791246	−	0.611499i	$-0.790567\pi$
$197$	−4375.63			−1.58249			−0.791246	+	0.611499i	$0.790567\pi$
$198$	−98.5400			−0.0353684
$199$	3729.76			1.32862			0.664310	−	0.747457i	$-0.268725\pi$
$199$	3729.76			1.32862			0.664310	+	0.747457i	$0.268725\pi$
$200$			2310.78i			0.816985i
$201$			5746.80i			2.01666i
$202$	−1134.88			−0.395296
$203$	−2433.11			−0.841236
$204$		−	3178.86i		−	1.09100i
$205$	5.62898			0.00191778
$206$		−	1245.23i		−	0.421162i
$207$			540.198i			0.181383i
$208$	−254.634			−0.0848831
$209$			1111.73i			0.367943i
$210$	4.10484			0.00134886
$211$		−	5318.56i		−	1.73528i	−0.497191	−	0.867641i	$-0.665635\pi$
$211$		−	5318.56i		−	1.73528i	0.497191	−	0.867641i	$-0.334365\pi$
$212$		−	2291.06i		−	0.742219i
$213$		−	4644.06i		−	1.49392i
$214$		−	1997.62i		−	0.638104i
$215$		−	0.490652i		−	0.000155638i
$216$			2381.55i			0.750203i
$217$	−2200.92			−0.688519
$218$			270.652i			0.0840867i
$219$	−76.3068			−0.0235449
$220$		−	3.50172i		−	0.00107312i
$221$			856.966i			0.260840i
$222$	−523.924			−0.158394
$223$		−	285.512i		−	0.0857368i	−0.999081	−	0.0428684i	$-0.986350\pi$
$223$		−	285.512i		−	0.0857368i	0.999081	−	0.0428684i	$-0.0136496\pi$
$224$	3833.68			1.14352
$225$	−472.376			−0.139963
$226$		−	411.811i		−	0.121209i
$227$			4939.30i			1.44420i	0.691789	+	0.722099i	$0.256823\pi$
$227$			4939.30i			1.44420i	−0.691789	+	0.722099i	$0.743177\pi$
$228$	−1932.83			−0.561423
$229$	4652.26			1.34249			0.671245	−	0.741236i	$-0.265760\pi$
$229$	4652.26			1.34249			0.671245	+	0.741236i	$0.265760\pi$
$230$	5.03567			0.00144366
$231$	2356.49			0.671194
$232$	2141.56			0.606035
$233$		−	2096.09i		−	0.589353i	−0.955597	−	0.294676i	$-0.904788\pi$
$233$		−	2096.09i		−	0.589353i	0.955597	−	0.294676i	$-0.0952119\pi$
$234$			46.1846i			0.0129025i
$235$	0.988592			0.000274420
$236$			497.176i			0.137133i
$237$		−	6123.05i		−	1.67821i
$238$		−	2448.42i		−	0.666838i
$239$	3391.83			0.917989			0.458994	−	0.888439i	$-0.348210\pi$
$239$	3391.83			0.917989			0.458994	+	0.888439i	$0.348210\pi$
$240$	4.07204			0.00109520
$241$	5359.57			1.43253			0.716266	−	0.697827i	$-0.245850\pi$
$241$	5359.57			1.43253			0.716266	+	0.697827i	$0.245850\pi$
$242$		−	1188.82i		−	0.315785i
$243$	−1052.91			−0.277961
$244$	2724.36	+	1301.69i	0.714791	+	0.341525i
$245$	−2.68110			−0.000699139
$246$		−	1473.76i		−	0.381966i
$247$	521.057			0.134227
$248$	1937.19			0.496016
$249$	2792.61			0.710741
$250$			8.80690i			0.00222799i
$251$			2755.66i			0.692970i	0.938055	+	0.346485i	$0.112625\pi$
$251$			2755.66i			0.692970i	−0.938055	+	0.346485i	$0.887375\pi$
$252$			503.018i			0.125743i
$253$	2890.86			0.718368
$254$		−	1785.75i		−	0.441134i
$255$		−	13.7044i		−	0.00336549i
$256$	−2012.27			−0.491278
$257$	−6484.37			−1.57387			−0.786934	−	0.617037i	$-0.788333\pi$
$257$	−6484.37			−1.57387			−0.786934	+	0.617037i	$0.788333\pi$
$258$	−128.461			−0.0309986
$259$	1538.32			0.369060
$260$	−1.64122			−0.000391477
$261$			437.783i			0.103824i
$262$		−	2512.10i		−	0.592360i
$263$	−5014.28			−1.17564			−0.587820	−	0.808991i	$-0.700014\pi$
$263$	−5014.28			−1.17564			−0.587820	+	0.808991i	$0.700014\pi$
$264$	−2074.12			−0.483535
$265$		−	9.87696i		−	0.00228957i
$266$	−1488.70			−0.343151
$267$			1713.47i			0.392745i
$268$			6564.75i			1.49629i
$269$	817.491			0.185291			0.0926456	−	0.995699i	$-0.470468\pi$
$269$	817.491			0.185291			0.0926456	+	0.995699i	$0.470468\pi$
$270$			4.53829i			0.00102293i
$271$	−3039.35			−0.681282			−0.340641	−	0.940193i	$-0.610644\pi$
$271$	−3039.35			−0.681282			−0.340641	+	0.940193i	$0.610644\pi$
$272$		−	2428.85i		−	0.541437i
$273$		−	1104.46i		−	0.244854i
$274$			3275.40i			0.722170i
$275$			2527.91i			0.554323i
$276$			5025.97i			1.09612i
$277$			2178.23i			0.472480i	0.971695	+	0.236240i	$0.0759151\pi$
$277$			2178.23i			0.472480i	−0.971695	+	0.236240i	$0.924085\pi$
$278$	−2452.91			−0.529193
$279$			396.006i			0.0849758i
$280$	10.6082			0.00226415
$281$		−	266.215i		−	0.0565163i	−0.999601	−	0.0282581i	$-0.991004\pi$
$281$		−	266.215i		−	0.0565163i	0.999601	−	0.0282581i	$-0.00899604\pi$
$282$		−	258.830i		−	0.0546565i
$283$	−1589.82			−0.333939			−0.166970	−	0.985962i	$-0.553398\pi$
$283$	−1589.82			−0.333939			−0.166970	+	0.985962i	$0.553398\pi$
$284$		−	5305.06i		−	1.10844i
$285$	−8.33259			−0.00173186
$286$	247.156			0.0511002
$287$			4327.19i			0.889987i
$288$		−	689.783i		−	0.141132i
$289$	−3261.26			−0.663801
$290$	4.08096			0.000826353
$291$	−7959.41			−1.60340
$292$	−87.1676			−0.0174695
$293$	860.807			0.171634			0.0858172	−	0.996311i	$-0.472650\pi$
$293$	860.807			0.171634			0.0858172	+	0.996311i	$0.472650\pi$
$294$			701.958i			0.139248i
$295$			2.14337i			0.000423024i
$296$	−1353.99			−0.265875
$297$			2605.33i			0.509012i
$298$			725.572i			0.141045i
$299$		−	1354.92i		−	0.262063i
$300$	−4394.96			−0.845810
$301$	377.181			0.0722271
$302$	2752.00			0.524370
$303$		−	4883.14i		−	0.925838i
$304$	−1476.80			−0.278620
$305$	11.7450	+	5.61169i	0.00220496	+	0.00105352i
$306$	−440.537			−0.0823000
$307$			4782.80i			0.889149i	0.895742	+	0.444574i	$0.146645\pi$
$307$			4782.80i			0.889149i	−0.895742	+	0.444574i	$0.853355\pi$
$308$	2691.89			0.498003
$309$	5357.96			0.986420
$310$	3.69153			0.000676338
$311$		−	7476.79i		−	1.36325i	−0.731703	−	0.681623i	$-0.761274\pi$
$311$		−	7476.79i		−	1.36325i	0.731703	−	0.681623i	$-0.238726\pi$
$312$			972.117i			0.176395i
$313$		−	792.792i		−	0.143167i	−0.997435	−	0.0715835i	$-0.977195\pi$
$313$		−	792.792i		−	0.143167i	0.997435	−	0.0715835i	$-0.0228052\pi$
$314$	4132.50			0.742709
$315$			2.16856i			0.000387887i
$316$		−	6994.55i		−	1.24517i
$317$	−8892.74			−1.57560			−0.787802	−	0.615929i	$-0.788781\pi$
$317$	−8892.74			−1.57560			−0.787802	+	0.615929i	$0.788781\pi$
$318$	−2585.96			−0.456017
$319$	2342.79			0.411194
$320$	−0.558250			−9.75223e−5
$321$	8595.32			1.49453
$322$			3871.10i			0.669963i
$323$			4970.15i			0.856182i
$324$	−5176.19			−0.887550
$325$	1184.80			0.202219
$326$		−	947.833i		−	0.161029i
$327$	−1164.56			−0.196943
$328$		−	3808.68i		−	0.641156i
$329$			759.966i			0.127350i
$330$	−3.95245			−0.000659319
$331$		−	1012.48i		−	0.168130i	−0.996460	−	0.0840648i	$-0.973210\pi$
$331$		−	1012.48i		−	0.168130i	0.996460	−	0.0840648i	$-0.0267903\pi$
$332$	3190.09			0.527346
$333$		−	276.785i		−	0.0455488i
$334$			3473.19i			0.568996i
$335$			28.3012i			0.00461571i
$336$			3130.32i			0.508252i
$337$		−	10448.2i		−	1.68888i	−0.535653	−	0.844438i	$-0.679935\pi$
$337$		−	10448.2i		−	1.68888i	0.535653	−	0.844438i	$-0.320065\pi$
$338$			2716.91i			0.437220i
$339$	1771.93			0.283889
$340$		−	15.6549i		−	0.00249708i
$341$	2119.22			0.336546
$342$			267.857i			0.0423511i
$343$			5143.01i			0.809611i
$344$	−331.985			−0.0520332
$345$			21.6674i			0.00338126i
$346$	1459.48			0.226769
$347$	−11795.4			−1.82481			−0.912405	−	0.409288i	$-0.865777\pi$
$347$	−11795.4			−1.82481			−0.912405	+	0.409288i	$0.865777\pi$
$348$			4073.10i			0.627417i
$349$		−	9196.05i		−	1.41047i	−0.708975	−	0.705234i	$-0.750842\pi$
$349$		−	9196.05i		−	1.41047i	0.708975	−	0.705234i	$-0.249158\pi$
$350$	−3385.08			−0.516972
$351$	1221.09			0.185689
$352$	−3691.37			−0.558950
$353$	5621.48			0.847596			0.423798	−	0.905757i	$-0.360697\pi$
$353$	5621.48			0.847596			0.423798	+	0.905757i	$0.360697\pi$
$354$	561.172			0.0842541
$355$		−	22.8706i		−	0.00341928i
$356$			1957.36i			0.291404i
$357$	10535.0			1.56183
$358$			1929.52i			0.284856i
$359$			4719.83i			0.693880i	0.937887	+	0.346940i	$0.112779\pi$
$359$			4719.83i			0.693880i	−0.937887	+	0.346940i	$0.887221\pi$
$360$		−	1.90871i		−	0.000279438i
$361$	−3837.02			−0.559414
$362$	1034.08			0.150138
$363$	5115.22			0.739613
$364$		−	1261.66i		−	0.181673i
$365$	−0.375788			−5.38894e−5
$366$	1469.24	−	3075.03i	0.209831	−	0.439165i
$367$	5424.34			0.771522			0.385761	−	0.922599i	$-0.373939\pi$
$367$	5424.34			0.771522			0.385761	+	0.922599i	$0.373939\pi$
$368$			3840.17i			0.543974i
$369$	778.579			0.109841
$370$	−2.58016			−0.000362531
$371$	7592.77			1.06253
$372$			3684.41i			0.513516i
$373$		−	8920.24i		−	1.23826i	−0.785287	−	0.619132i	$-0.787485\pi$
$373$		−	8920.24i		−	1.23826i	0.785287	−	0.619132i	$-0.212515\pi$
$374$			2357.53i			0.325949i
$375$	−37.8942			−0.00521827
$376$		−	668.901i		−	0.0917445i
$377$		−	1098.04i		−	0.150005i
$378$	−3488.75			−0.474713
$379$	−8212.42			−1.11304			−0.556522	−	0.830833i	$-0.687864\pi$
$379$	−8212.42			−1.11304			−0.556522	+	0.830833i	$0.687864\pi$
$380$	−9.51858			−0.00128498
$381$	7683.71			1.03320
$382$	−1059.88			−0.141959
$383$		−	12050.4i		−	1.60770i	−0.594832	−	0.803850i	$-0.702781\pi$
$383$		−	12050.4i		−	1.60770i	0.594832	−	0.803850i	$-0.297219\pi$
$384$		−	7955.05i		−	1.05717i
$385$	11.6050			0.00153622
$386$	5936.95			0.782857
$387$		−	67.8651i		−	0.00891416i
$388$	−9092.28			−1.18967
$389$			13751.0i			1.79230i	0.443749	+	0.896151i	$0.353648\pi$
$389$			13751.0i			1.79230i	−0.443749	+	0.896151i	$0.646352\pi$
$390$			1.85247i			0.000240522i
$391$	12924.0			1.67160
$392$			1814.09i			0.233738i
$393$	10809.0			1.38739
$394$			5641.81i			0.721396i
$395$		−	30.1542i		−	0.00384106i
$396$		−	484.345i		−	0.0614627i
$397$			6812.28i			0.861205i	0.902542	+	0.430603i	$0.141699\pi$
$397$			6812.28i			0.861205i	−0.902542	+	0.430603i	$0.858301\pi$
$398$		−	4809.04i		−	0.605667i
$399$		−	6405.56i		−	0.803707i
$400$	−3358.03			−0.419754
$401$			3395.48i			0.422849i	0.977394	+	0.211424i	$0.0678102\pi$
$401$			3395.48i			0.422849i	−0.977394	+	0.211424i	$0.932190\pi$
$402$	7409.75			0.919316
$403$		−	993.255i		−	0.122773i
$404$		−	5578.16i		−	0.686941i
$405$	−22.3150			−0.00273788
$406$			3137.18i			0.383487i
$407$	−1481.21			−0.180396
$408$	−9272.64			−1.12516
$409$		−	10132.8i		−	1.22502i	−0.790462	−	0.612511i	$-0.790160\pi$
$409$		−	10132.8i		−	1.22502i	0.790462	−	0.612511i	$-0.209840\pi$
$410$		−	7.25784i		−	0.000874241i
$411$	−14093.4			−1.69142
$412$	6120.57			0.731890
$413$	−1647.69			−0.196313
$414$	696.516			0.0826857
$415$	13.7528			0.00162674
$416$			1730.10i			0.203907i
$417$		−	10554.3i		−	1.23944i
$418$	1433.44			0.167731
$419$		−	11785.8i		−	1.37416i	−0.726581	−	0.687081i	$-0.758892\pi$
$419$		−	11785.8i		−	1.37416i	0.726581	−	0.687081i	$-0.241108\pi$
$420$			20.1761i			0.00234403i
$421$			7125.71i			0.824907i	0.910979	+	0.412453i	$0.135328\pi$
$421$			7125.71i			0.824907i	−0.910979	+	0.412453i	$0.864672\pi$
$422$	−6857.59			−0.791048
$423$	136.738			0.0157174
$424$	−6682.95			−0.765455
$425$			11301.4i			1.28988i
$426$	−5987.92			−0.681023
$427$	−4313.91	+	9028.76i	−0.488910	+	1.02326i
$428$	9818.70			1.10889
$429$			1063.46i			0.119684i
$430$	−0.632632			−7.09493e−5
$431$	6691.93			0.747886			0.373943	−	0.927452i	$-0.378006\pi$
$431$	6691.93			0.747886			0.373943	+	0.927452i	$0.378006\pi$
$432$	−3460.87			−0.385442
$433$			12760.4i			1.41622i	0.706100	+	0.708112i	$0.250453\pi$
$433$			12760.4i			1.41622i	−0.706100	+	0.708112i	$0.749547\pi$
$434$			2837.81i			0.313869i
$435$			17.5595i			0.00193543i
$436$	−1330.31			−0.146125
$437$		−	7858.12i		−	0.860194i
$438$			98.3877i			0.0107332i
$439$	−17068.3			−1.85563			−0.927817	−	0.373035i	$-0.878317\pi$
$439$	−17068.3			−1.85563			−0.927817	+	0.373035i	$0.878317\pi$
$440$	−10.2144			−0.00110671
$441$	−370.840			−0.0400432
$442$	1104.95			0.118907
$443$	−4403.80			−0.472305			−0.236152	−	0.971716i	$-0.575886\pi$
$443$	−4403.80			−0.472305			−0.236152	+	0.971716i	$0.575886\pi$
$444$		−	2575.19i		−	0.275255i
$445$			8.43834i			0.000898912i
$446$	−368.131			−0.0390841
$447$	−3121.98			−0.330346
$448$		−	429.147i		−	0.0452573i
$449$	−12133.3			−1.27530			−0.637648	−	0.770328i	$-0.720092\pi$
$449$	−12133.3			−1.27530			−0.637648	+	0.770328i	$0.720092\pi$
$450$			609.068i			0.0638038i
$451$		−	4166.56i		−	0.435023i
$452$	2024.14			0.210636
$453$			11841.3i			1.22815i
$454$	6368.59			0.658354
$455$		−	5.43914i		−	0.000560419i
$456$			5638.00i			0.578999i
$457$		−	12347.7i		−	1.26389i	−0.775012	−	0.631947i	$-0.782256\pi$
$457$		−	12347.7i		−	1.26389i	0.775012	−	0.631947i	$-0.217744\pi$
$458$		−	5998.49i		−	0.611989i
$459$			11647.5i			1.18444i
$460$			24.7514i			0.00250878i
$461$	−2715.96			−0.274392			−0.137196	−	0.990544i	$-0.543809\pi$
$461$	−2715.96			−0.274392			−0.137196	+	0.990544i	$0.543809\pi$
$462$		−	3038.39i		−	0.305971i
$463$	7874.95			0.790453			0.395227	−	0.918584i	$-0.370666\pi$
$463$	7874.95			0.790453			0.395227	+	0.918584i	$0.370666\pi$
$464$			3112.11i			0.311371i
$465$			15.8839i			0.00158408i
$466$	−2702.63			−0.268663
$467$			3260.37i			0.323066i	0.986867	+	0.161533i	$0.0516438\pi$
$467$			3260.37i			0.323066i	−0.986867	+	0.161533i	$0.948356\pi$
$468$	−227.007			−0.0224218
$469$	−21756.2			−2.14202
$470$		−	1.27466i		−	0.000125097i
$471$			17781.3i			1.73953i
$472$	1450.25			0.141426
$473$	−363.179			−0.0353044
$474$	−7894.88			−0.765029
$475$	6871.52			0.663762
$476$	12034.5			1.15882
$477$		−	1366.14i		−	0.131135i
$478$		−	4373.33i		−	0.418476i
$479$	12654.2			1.20707			0.603533	−	0.797338i	$-0.293759\pi$
$479$	12654.2			1.20707			0.603533	+	0.797338i	$0.293759\pi$
$480$		−	27.6673i		−	0.00263090i
$481$			694.228i			0.0658089i
$482$		−	6910.47i		−	0.653036i
$483$	−16656.5			−1.56915
$484$	5843.28			0.548768
$485$	−39.1977			−0.00366984
$486$			1357.60i			0.126712i
$487$	−9883.43			−0.919633			−0.459816	−	0.888014i	$-0.652085\pi$
$487$	−9883.43			−0.919633			−0.459816	+	0.888014i	$0.652085\pi$
$488$	3796.98	−	7946.87i	0.352216	−	0.737168i
$489$	4078.32			0.377154
$490$			3.45693i			0.000318711i
$491$	−11726.1			−1.07779			−0.538893	−	0.842374i	$-0.681157\pi$
$491$	−11726.1			−1.07779			−0.538893	+	0.842374i	$0.681157\pi$
$492$	7243.85			0.663777
$493$	10473.8			0.956824
$494$		−	671.835i		−	0.0611888i
$495$		−	2.08805i		−	0.000189598i
$496$			2815.13i			0.254845i
$497$	17581.4			1.58679
$498$		−	3600.71i		−	0.323999i
$499$			12325.8i			1.10577i	0.833257	+	0.552885i	$0.186473\pi$
$499$			12325.8i			1.10577i	−0.833257	+	0.552885i	$0.813527\pi$
$500$	−43.2878			−0.00387178
$501$	−14944.4			−1.33267
$502$	3553.06			0.315898
$503$	19023.3			1.68629			0.843146	−	0.537684i	$-0.180701\pi$
$503$	19023.3			1.68629			0.843146	+	0.537684i	$0.180701\pi$
$504$	1467.29			0.129679
$505$		−	24.0480i		−	0.00211905i
$506$		−	3727.39i		−	0.327476i
$507$	−11690.3			−1.02403
$508$	8777.35			0.766598
$509$			623.453i			0.0542909i	0.999631	+	0.0271455i	$0.00864173\pi$
$509$			623.453i			0.0542909i	−0.999631	+	0.0271455i	$0.991358\pi$
$510$	−17.6700			−0.00153420
$511$		−	288.881i		−	0.0250085i
$512$		−	8876.54i		−	0.766194i
$513$	7081.96			0.609505
$514$			8360.76i			0.717465i
$515$	26.3863			0.00225771
$516$		−	631.413i		−	0.0538690i
$517$		−	731.754i		−	0.0622485i
$518$		−	1983.46i		−	0.168240i
$519$			6279.83i			0.531125i
$520$			4.78738i			0.000403732i
$521$		−	18923.8i		−	1.59130i	−0.605755	−	0.795651i	$-0.707129\pi$
$521$		−	18923.8i		−	1.59130i	0.605755	−	0.795651i	$-0.292871\pi$
$522$	564.464			0.0473293
$523$		−	4269.87i		−	0.356995i	−0.983940	−	0.178497i	$-0.942876\pi$
$523$		−	4269.87i		−	0.356995i	0.983940	−	0.178497i	$-0.0571236\pi$
$524$	12347.5			1.02940
$525$		−	14565.3i		−	1.21082i
$526$			6465.26i			0.535929i
$527$	9474.27			0.783122
$528$		−	3014.11i		−	0.248433i
$529$	−8266.64			−0.679431
$530$	−12.7351			−0.00104373
$531$			296.463i			0.0242287i
$532$		−	7317.27i		−	0.596323i
$533$	−1952.82			−0.158698
$534$	2209.30			0.179037
$535$	42.3293			0.00342067
$536$	19149.2			1.54313
$537$	−8302.33			−0.667173
$538$		−	1054.05i		−	0.0844670i
$539$			1984.54i			0.158591i
$540$	−22.3066			−0.00177764
$541$			2117.72i			0.168296i	0.996453	+	0.0841478i	$0.0268168\pi$
$541$			2117.72i			0.168296i	−0.996453	+	0.0841478i	$0.973183\pi$
$542$			3918.85i			0.310570i
$543$			4449.40i			0.351643i
$544$	−16502.8			−1.30064
$545$	−5.73510			−0.000450761
$546$	−1424.06			−0.111619
$547$		−	10070.9i		−	0.787207i	−0.919280	−	0.393604i	$-0.871228\pi$
$547$		−	10070.9i		−	0.787207i	0.919280	−	0.393604i	$-0.128772\pi$
$548$	−16099.3			−1.25498
$549$	1624.52	+	776.189i	0.126289	+	0.0603405i
$550$	3259.42			0.252694
$551$		−	6368.30i		−	0.492375i
$552$	14660.6			1.13043
$553$	23180.6			1.78253
$554$	2808.54			0.215385
$555$		−	11.1019i		−	0.000849098i
$556$		−	12056.5i		−	0.919625i
$557$			18330.0i			1.39438i	0.716887	+	0.697189i	$0.245566\pi$
$557$			18330.0i			1.39438i	−0.716887	+	0.697189i	$0.754434\pi$
$558$	510.598			0.0387372
$559$			170.218i			0.0128792i
$560$			15.4159i			0.00116328i
$561$	−10143.9			−0.763417
$562$	−343.250			−0.0257636
$563$	7775.75			0.582076			0.291038	−	0.956711i	$-0.405999\pi$
$563$	7775.75			0.582076			0.291038	+	0.956711i	$0.405999\pi$
$564$	1272.21			0.0949814
$565$	8.72623			0.000649762
$566$			2049.86i			0.152230i
$567$		−	17154.4i		−	1.27057i
$568$	−15474.7			−1.14314
$569$	−1396.12			−0.102862			−0.0514309	−	0.998677i	$-0.516378\pi$
$569$	−1396.12			−0.102862			−0.0514309	+	0.998677i	$0.516378\pi$
$570$			10.7438i			0.000789488i
$571$	−12089.3			−0.886028			−0.443014	−	0.896515i	$-0.646091\pi$
$571$	−12089.3			−0.886028			−0.443014	+	0.896515i	$0.646091\pi$
$572$			1214.82i			0.0888013i
$573$		−	4560.46i		−	0.332488i
$574$	5579.36			0.405710
$575$		−	17868.2i		−	1.29592i
$576$	−77.2151			−0.00558558
$577$			16713.0i			1.20584i	0.797800	+	0.602922i	$0.205997\pi$
$577$			16713.0i			1.20584i	−0.797800	+	0.602922i	$0.794003\pi$
$578$			4204.97i			0.302601i
$579$			25545.4i			1.83356i
$580$			20.0588i			0.00143603i
$581$			10572.2i			0.754923i
$582$			10262.6i			0.730927i
$583$	−7310.90			−0.519360
$584$			254.266i			0.0180164i
$585$	−0.978648			−6.91660e−5
$586$		−	1109.90i		−	0.0782415i
$587$		−	9057.09i		−	0.636842i	−0.947949	−	0.318421i	$-0.896847\pi$
$587$		−	9057.09i		−	0.636842i	0.947949	−	0.318421i	$-0.103153\pi$
$588$	−3450.27			−0.241984
$589$		−	5760.59i		−	0.402990i
$590$	2.76360			0.000192840
$591$	−24275.5			−1.68961
$592$		−	1967.61i		−	0.136602i
$593$		−	12882.8i		−	0.892132i	−0.895000	−	0.446066i	$-0.852825\pi$
$593$		−	12882.8i		−	0.892132i	0.895000	−	0.446066i	$-0.147175\pi$
$594$	3359.23			0.232039
$595$	51.8818			0.00357470
$596$	−3566.34			−0.245106
$597$	20692.3			1.41856
$598$	−1746.99			−0.119464
$599$		−	402.919i		−	0.0274838i	−0.999906	−	0.0137419i	$-0.995626\pi$
$599$		−	402.919i		−	0.0274838i	0.999906	−	0.0137419i	$-0.00437433\pi$
$600$			12820.0i			0.872288i
$601$	19727.1			1.33891			0.669454	−	0.742853i	$-0.266528\pi$
$601$	19727.1			1.33891			0.669454	+	0.742853i	$0.266528\pi$
$602$		−	486.326i		−	0.0329256i
$603$			3914.52i			0.264364i
$604$			13526.6i			0.911244i
$605$	25.1909			0.00169282
$606$	−6296.18			−0.422054
$607$	24709.2			1.65225			0.826126	−	0.563485i	$-0.190540\pi$
$607$	24709.2			1.65225			0.826126	+	0.563485i	$0.190540\pi$
$608$			10034.1i			0.669303i
$609$	−13498.6			−0.898180
$610$	7.23555	−	15.1436i	0.000480260	−	0.00100516i
$611$	−342.965			−0.0227085
$612$		−	2165.33i		−	0.143020i
$613$	−24131.2			−1.58997			−0.794984	−	0.606631i	$-0.792521\pi$
$613$	−24131.2			−1.58997			−0.794984	+	0.606631i	$0.792521\pi$
$614$	6166.80			0.405328
$615$	31.2289			0.00204760
$616$		−	7852.18i		−	0.513593i
$617$			18525.3i			1.20875i	0.796700	+	0.604375i	$0.206577\pi$
$617$			18525.3i			1.20875i	−0.796700	+	0.604375i	$0.793423\pi$
$618$		−	6908.40i		−	0.449671i
$619$	7162.17			0.465060			0.232530	−	0.972589i	$-0.425300\pi$
$619$	7162.17			0.465060			0.232530	+	0.972589i	$0.425300\pi$
$620$			18.1446i			0.00117533i
$621$		−	18415.4i		−	1.18999i
$622$	−9640.35			−0.621451
$623$	−6486.85			−0.417159
$624$	−1412.68			−0.0906290
$625$	15624.7			0.999982
$626$	−1022.20			−0.0652643
$627$			6167.77i			0.392850i
$628$			20312.1i			1.29067i
$629$	−6621.97			−0.419770
$630$	2.79607			0.000176823
$631$		−	3358.78i		−	0.211903i	−0.994371	−	0.105952i	$-0.966211\pi$
$631$		−	3358.78i		−	0.211903i	0.994371	−	0.105952i	$-0.0337888\pi$
$632$	−20402.9			−1.28415
$633$		−	29506.7i		−	1.85275i
$634$			11466.0i			0.718257i
$635$	37.8399			0.00236478
$636$		−	12710.5i		−	0.792461i
$637$	930.134			0.0578544
$638$		−	3020.72i		−	0.187447i
$639$		−	3163.38i		−	0.195839i
$640$		−	39.1762i		−	0.00241965i
$641$		−	18734.3i		−	1.15438i	−0.816609	−	0.577191i	$-0.804149\pi$
$641$		−	18734.3i		−	1.15438i	0.816609	−	0.577191i	$-0.195851\pi$
$642$		−	11082.5i		−	0.681298i
$643$			22240.1i			1.36402i	0.731343	+	0.682010i	$0.238894\pi$
$643$			22240.1i			1.36402i	−0.731343	+	0.682010i	$0.761106\pi$
$644$	−19027.3			−1.16425
$645$		−	2.72208i		−	0.000166173i
$646$	6408.37			0.390300
$647$			17078.9i			1.03778i	0.854842	+	0.518888i	$0.173654\pi$
$647$			17078.9i			1.03778i	−0.854842	+	0.518888i	$0.826346\pi$
$648$			15098.8i			0.915335i
$649$	1586.52			0.0959574
$650$		−	1527.65i		−	0.0921837i
$651$	−12210.5			−0.735125
$652$	4658.80			0.279835
$653$			20503.3i			1.22872i	0.789024	+	0.614362i	$0.210587\pi$
$653$			20503.3i			1.22872i	−0.789024	+	0.614362i	$0.789413\pi$
$654$			1501.55i			0.0897786i
$655$	53.2312			0.00317545
$656$	5534.77			0.329415
$657$	−51.9776			−0.00308651
$658$	979.877			0.0580541
$659$	−11822.8			−0.698865			−0.349433	−	0.936962i	$-0.613626\pi$
$659$	−11822.8			−0.698865			−0.349433	+	0.936962i	$0.613626\pi$
$660$		−	19.4271i		−	0.00114576i
$661$			19978.5i			1.17561i	0.809004	+	0.587803i	$0.200007\pi$
$661$			19978.5i			1.17561i	−0.809004	+	0.587803i	$0.799993\pi$
$662$	−1305.46			−0.0766438
$663$			4754.35i			0.278497i
$664$		−	9305.40i		−	0.543855i
$665$		−	31.5454i		−	0.00183952i
$666$	−356.879			−0.0207639
$667$	−16559.6			−0.961307
$668$	−17071.5			−0.988794
$669$		−	1583.99i		−	0.0915404i
$670$	36.4908			0.00210412
$671$	4153.76	−	8693.59i	0.238978	−	0.500167i
$672$	21268.8			1.22093
$673$		−	8899.33i		−	0.509724i	−0.966977	−	0.254862i	$-0.917970\pi$
$673$		−	8899.33i		−	0.509724i	0.966977	−	0.254862i	$-0.0820300\pi$
$674$	−13471.6			−0.769893
$675$	16103.3			0.918247
$676$	−13354.2			−0.759795
$677$		−	2030.96i		−	0.115297i	−0.998337	−	0.0576484i	$-0.981640\pi$
$677$		−	2030.96i		−	0.115297i	0.998337	−	0.0576484i	$-0.0183602\pi$
$678$		−	2284.68i		−	0.129414i
$679$		−	30132.6i		−	1.70307i
$680$	−45.6649			−0.00257525
$681$			27402.7i			1.54196i
$682$		−	2732.46i		−	0.153418i
$683$	−24480.5			−1.37148			−0.685739	−	0.727847i	$-0.740521\pi$
$683$	−24480.5			−1.37148			−0.685739	+	0.727847i	$0.740521\pi$
$684$	−1316.58			−0.0735972
$685$	−69.4055			−0.00387131
$686$	6631.25			0.369070
$687$	25810.2			1.43336
$688$		−	482.440i		−	0.0267338i
$689$			3426.54i			0.189464i
$690$	27.9373			0.00154139
$691$	−11839.1			−0.651782			−0.325891	−	0.945407i	$-0.605664\pi$
$691$	−11839.1			−0.651782			−0.325891	+	0.945407i	$0.605664\pi$
$692$			7173.65i			0.394077i
$693$	1605.16			0.0879871
$694$			15208.6i			0.831860i
$695$		−	51.9769i		−	0.00283683i
$696$	11881.1			0.647059
$697$		−	18627.2i		−	1.01227i
$698$	−11857.1			−0.642977
$699$		−	11628.9i		−	0.629247i
$700$		−	16638.4i		−	0.898388i
$701$			3663.28i			0.197375i	0.995118	+	0.0986877i	$0.0314645\pi$
$701$			3663.28i			0.197375i	−0.995118	+	0.0986877i	$0.968536\pi$
$702$		−	1574.44i		−	0.0846485i
$703$			4026.32i			0.216011i
$704$			413.216i			0.0221217i
$705$	5.48459			0.000292995
$706$		−	7248.17i		−	0.386386i
$707$	18486.5			0.983391
$708$			2758.28i			0.146416i
$709$		−	26815.0i		−	1.42039i	−0.704004	−	0.710196i	$-0.748606\pi$
$709$		−	26815.0i		−	1.42039i	0.704004	−	0.710196i	$-0.251394\pi$
$710$	−29.4887			−0.00155872
$711$		−	4170.81i		−	0.219997i
$712$	5709.55			0.300526
$713$	−14979.4			−0.786792
$714$		−	13583.5i		−	0.711977i
$715$			5.23722i			0.000273931i
$716$	−9484.01			−0.495020
$717$	18817.5			0.980129
$718$	6085.61			0.316313
$719$	19113.0			0.991370			0.495685	−	0.868502i	$-0.334917\pi$
$719$	19113.0			0.991370			0.495685	+	0.868502i	$0.334917\pi$
$720$	2.77373			0.000143571
$721$			20284.1i			1.04774i
$722$			4947.34i			0.255015i
$723$	29734.3			1.52950
$724$			5082.70i			0.260907i
$725$		−	14480.6i		−	0.741786i
$726$		−	6595.42i		−	0.337161i
$727$	1391.10			0.0709673			0.0354836	−	0.999370i	$-0.488703\pi$
$727$	1391.10			0.0709673			0.0354836	+	0.999370i	$0.488703\pi$
$728$	−3680.23			−0.187360
$729$	16210.9			0.823598
$730$			0.484529i			2.45661e-5i
$731$	−1623.64			−0.0821513
$732$	15114.4	+	7221.61i	0.763176	+	0.364643i
$733$	18278.9			0.921072			0.460536	−	0.887641i	$-0.347657\pi$
$733$	18278.9			0.921072			0.460536	+	0.887641i	$0.347657\pi$
$734$		−	6993.99i		−	0.351707i
$735$	−14.8744			−0.000746465
$736$	26091.9			1.30674
$737$	20948.5			1.04701
$738$		−	1003.88i		−	0.0500721i
$739$		−	11021.9i		−	0.548643i	−0.961638	−	0.274321i	$-0.911547\pi$
$739$		−	11021.9i		−	0.548643i	0.961638	−	0.274321i	$-0.0884532\pi$
$740$		−	12.6820i		−	0.000630002i
$741$	2890.76			0.143313
$742$		−	9789.89i		−	0.484364i
$743$			16138.0i			0.796832i	0.917205	+	0.398416i	$0.130440\pi$
$743$			16138.0i			0.796832i	−0.917205	+	0.398416i	$0.869560\pi$
$744$	10747.3			0.529592
$745$	−15.3748			−0.000756093
$746$	−11501.5			−0.564477
$747$	1902.23			0.0931714
$748$	−11587.7			−0.566430
$749$			32540.0i			1.58743i
$750$			48.8597i			0.00237881i
$751$	15561.9			0.756141			0.378071	−	0.925777i	$-0.376588\pi$
$751$	15561.9			0.756141			0.378071	+	0.925777i	$0.376588\pi$
$752$	972.047			0.0471368
$753$			15288.1i			0.739878i
$754$	−1415.78			−0.0683814
$755$			58.3146i			0.00281097i
$756$		−	17147.9i		−	0.824952i
$757$	−611.565			−0.0293629			−0.0146814	−	0.999892i	$-0.504673\pi$
$757$	−611.565			−0.0293629			−0.0146814	+	0.999892i	$0.504673\pi$
$758$			10588.8i			0.507393i
$759$	16038.2			0.766995
$760$			27.7654i			0.00132521i
$761$		−	12887.2i		−	0.613880i	−0.951729	−	0.306940i	$-0.900695\pi$
$761$		−	12887.2i		−	0.613880i	0.951729	−	0.306940i	$-0.0993050\pi$
$762$		−	9907.15i		−	0.470995i
$763$		−	4408.78i		−	0.209185i
$764$		−	5209.55i		−	0.246695i
$765$		−	9.33494i		−	0.000441183i
$766$	−15537.5			−0.732888
$767$		−	743.584i		−	0.0350056i
$768$	−11163.9			−0.524533
$769$			7784.51i			0.365041i	0.983202	+	0.182520i	$0.0584256\pi$
$769$			7784.51i			0.365041i	−0.983202	+	0.182520i	$0.941574\pi$
$770$		−	14.9632i		−	0.000700305i
$771$	−35974.6			−1.68040
$772$			29181.4i			1.36044i
$773$	−11166.4			−0.519569			−0.259784	−	0.965667i	$-0.583651\pi$
$773$	−11166.4			−0.519569			−0.259784	+	0.965667i	$0.583651\pi$
$774$	−87.5033			−0.00406362
$775$		−	13098.7i		−	0.607122i
$776$			26521.9i			1.22691i
$777$	8534.42			0.394042
$778$	17730.2			0.817041
$779$	−11325.8			−0.520909
$780$	−9.10528			−0.000417976
$781$	−16928.8			−0.775620
$782$		−	16663.8i		−	0.762017i
$783$		−	14924.0i		−	0.681151i
$784$	−2636.23			−0.120091
$785$			87.5673i			0.00398142i
$786$		−	13936.9i		−	0.632457i
$787$		−	28063.2i		−	1.27109i	−0.772065	−	0.635543i	$-0.780776\pi$
$787$		−	28063.2i		−	1.27109i	0.772065	−	0.635543i	$-0.219224\pi$
$788$	−27730.7			−1.25363
$789$	−27818.6			−1.25522
$790$	−38.8799			−0.00175099
$791$			6708.16i			0.301536i
$792$	−1412.82			−0.0633868
$793$	−4074.59	−	1946.82i	−0.182463	−	0.0871799i
$794$	8783.55			0.392590
$795$		−	54.7962i		−	0.00244456i
$796$	23637.4			1.05252
$797$	−8072.26			−0.358763			−0.179381	−	0.983780i	$-0.557410\pi$
$797$	−8072.26			−0.358763			−0.179381	+	0.983780i	$0.557410\pi$
$798$	−8259.14			−0.366379
$799$		−	3271.40i		−	0.144849i
$800$			22816.0i			1.00833i
$801$			1167.16i			0.0514851i
$802$	4378.04			0.192760
$803$			278.157i			0.0122241i
$804$			36420.5i			1.59758i
$805$	−82.0283			−0.00359145
$806$	−1280.67			−0.0559675
$807$	4535.35			0.197834
$808$	−16271.3			−0.708446
$809$	3223.09			0.140072			0.0700358	−	0.997544i	$-0.477689\pi$
$809$	3223.09			0.140072			0.0700358	+	0.997544i	$0.477689\pi$
$810$			28.7723i			0.00124810i
$811$			32774.2i			1.41906i	0.704675	+	0.709530i	$0.251093\pi$
$811$			32774.2i			1.41906i	−0.704675	+	0.709530i	$0.748907\pi$
$812$	−15419.9			−0.666419
$813$	−16862.0			−0.727399
$814$			1909.83i			0.0822354i
$815$	20.0845			0.000863226
$816$		−	13475.0i		−	0.578087i
$817$			987.216i			0.0422745i
$818$	−13064.9			−0.558440
$819$		−	752.321i		−	0.0320980i
$820$	35.6738			0.00151925
$821$		−	23369.4i		−	0.993421i	−0.867916	−	0.496711i	$-0.834541\pi$
$821$		−	23369.4i		−	0.993421i	0.867916	−	0.496711i	$-0.165459\pi$
$822$			18171.6i			0.771054i
$823$			820.030i			0.0347320i	0.999849	+	0.0173660i	$0.00552805\pi$
$823$			820.030i			0.0347320i	−0.999849	+	0.0173660i	$0.994472\pi$
$824$		−	17853.5i		−	0.754802i
$825$			14024.6i			0.591846i
$826$			2124.48i			0.0894916i
$827$	19332.1			0.812870			0.406435	−	0.913680i	$-0.366772\pi$
$827$	19332.1			0.812870			0.406435	+	0.913680i	$0.366772\pi$
$828$			3423.52i			0.143690i
$829$	−23504.6			−0.984740			−0.492370	−	0.870386i	$-0.663869\pi$
$829$	−23504.6			−0.984740			−0.492370	+	0.870386i	$0.663869\pi$
$830$		−	17.7324i		−	0.000741567i
$831$			12084.5i			0.504462i
$832$	193.670			0.00807005
$833$			8872.18i			0.369031i
$834$	−13608.4			−0.565014
$835$	−73.5966			−0.00305020
$836$			7045.63i			0.291481i
$837$		−	13499.9i		−	0.557495i
$838$	−15196.3			−0.626427
$839$	25601.4			1.05347			0.526734	−	0.850030i	$-0.323416\pi$
$839$	25601.4			1.05347			0.526734	+	0.850030i	$0.323416\pi$
$840$	58.8532			0.00241741
$841$	10968.9			0.449747
$842$	9187.67			0.376043
$843$		−	1476.93i		−	0.0603419i
$844$		−	33706.5i		−	1.37467i
$845$	−57.5710			−0.00234379
$846$		−	176.306i		−	0.00716494i
$847$			19365.1i			0.785590i
$848$		−	9711.66i		−	0.393278i
$849$	−8820.12			−0.356544
$850$	14571.7			0.588005
$851$	10469.7			0.421737
$852$		−	29431.9i		−	1.18347i
$853$	8567.55			0.343901			0.171950	−	0.985106i	$-0.444993\pi$
$853$	8567.55			0.343901			0.171950	+	0.985106i	$0.444993\pi$
$854$	11641.4	+	5562.22i	0.466465	+	0.222875i
$855$	−5.67588			−0.000227030
$856$		−	28640.9i		−	1.14360i
$857$	−34438.0			−1.37267			−0.686336	−	0.727285i	$-0.740782\pi$
$857$	−34438.0			−1.37267			−0.686336	+	0.727285i	$0.740782\pi$
$858$	1371.19			0.0545592
$859$	19586.5			0.777976			0.388988	−	0.921243i	$-0.372825\pi$
$859$	19586.5			0.777976			0.388988	+	0.921243i	$0.372825\pi$
$860$		−	3.10952i		−	0.000123295i
$861$			24006.8i			0.950231i
$862$		−	8628.37i		−	0.340932i
$863$	22934.6			0.904637			0.452318	−	0.891856i	$-0.350597\pi$
$863$	22934.6			0.904637			0.452318	+	0.891856i	$0.350597\pi$
$864$			23514.7i			0.925912i
$865$			30.9263i			0.00121564i
$866$	16452.9			0.645602
$867$	−18093.1			−0.708735
$868$	−13948.4			−0.545438
$869$	−22320.0			−0.871295
$870$	22.6407			0.000882290
$871$		−	9818.34i		−	0.381954i
$872$			3880.49i			0.150699i
$873$	−5421.68			−0.210190
$874$	−10132.0			−0.392129
$875$		−	143.460i		−	0.00554265i
$876$	−483.596			−0.0186520
$877$		−	39338.8i		−	1.51468i	−0.653019	−	0.757341i	$-0.726498\pi$
$877$		−	39338.8i		−	1.51468i	0.653019	−	0.757341i	$-0.273502\pi$
$878$			22007.3i			0.845912i
$879$	4775.66			0.183253
$880$		−	14.8436i		−	0.000568610i
$881$	−38415.6			−1.46907			−0.734536	−	0.678569i	$-0.762600\pi$
$881$	−38415.6			−1.46907			−0.734536	+	0.678569i	$0.762600\pi$
$882$			478.150i			0.0182541i
$883$		−	21523.2i		−	0.820288i	−0.912021	−	0.410144i	$-0.865479\pi$
$883$		−	21523.2i		−	0.820288i	0.912021	−	0.410144i	$-0.134521\pi$
$884$			5431.04i			0.206635i
$885$			11.8912i			0.000451658i
$886$			5678.13i			0.215305i
$887$		−	29417.8i		−	1.11359i	−0.830650	−	0.556794i	$-0.812031\pi$
$887$		−	29417.8i		−	1.11359i	0.830650	−	0.556794i	$-0.187969\pi$
$888$	−7511.77			−0.283872
$889$			29088.9i			1.09742i
$890$	10.8801			0.000409779
$891$			16517.5i			0.621053i
$892$		−	1809.44i		−	0.0679199i
$893$	−1989.10			−0.0745381
$894$			4025.39i			0.150592i
$895$	−40.8864			−0.00152702
$896$	30116.1			1.12289
$897$		−	7516.91i		−	0.279802i
$898$			15644.4i			0.581358i
$899$	−12139.5			−0.450360
$900$	−2993.69			−0.110878
$901$	−32684.4			−1.20852
$902$	−5372.23			−0.198310
$903$	2092.56			0.0771163
$904$		−	5904.35i		−	0.217230i
$905$			21.9120i			0.000804838i
$906$	15267.8			0.559865
$907$			47921.7i			1.75437i	0.480151	+	0.877186i	$0.340582\pi$
$907$			47921.7i			1.75437i	−0.480151	+	0.877186i	$0.659418\pi$
$908$			31303.0i			1.14408i
$909$		−	3326.23i		−	0.121369i
$910$	−7.01306			−0.000255473
$911$	35938.1			1.30701			0.653504	−	0.756923i	$-0.273298\pi$
$911$	35938.1			1.30701			0.653504	+	0.756923i	$0.273298\pi$
$912$	−8193.14			−0.297480
$913$		−	10179.8i		−	0.369005i
$914$	−15920.7			−0.576160
$915$	65.1597	+	31.1330i	0.00235422	+	0.00112484i
$916$	29483.8			1.06351
$917$			40920.7i			1.47363i
$918$	15017.9			0.539940
$919$	−1425.67			−0.0511737			−0.0255868	−	0.999673i	$-0.508145\pi$
$919$	−1425.67			−0.0511737			−0.0255868	+	0.999673i	$0.508145\pi$
$920$	72.1991			0.00258732
$921$			26534.4i			0.949336i
$922$			3501.87i			0.125085i
$923$			7934.33i			0.282949i
$924$	14934.3			0.531713
$925$			9155.25i			0.325430i
$926$		−	10153.7i		−	0.360337i
$927$	3649.66			0.129310
$928$	21145.1			0.747977
$929$	−41722.5			−1.47349			−0.736744	−	0.676172i	$-0.763638\pi$
$929$	−41722.5			−1.47349			−0.736744	+	0.676172i	$0.763638\pi$
$930$	20.4802			0.000722119
$931$	5394.51			0.189901
$932$		−	13284.0i		−	0.466880i
$933$		−	41480.4i		−	1.45553i
$934$	4203.82			0.147273
$935$	−49.9558			−0.00174730
$936$			662.173i			0.0231237i
$937$	−5311.67			−0.185192			−0.0925958	−	0.995704i	$-0.529516\pi$
$937$	−5311.67			−0.185192			−0.0925958	+	0.995704i	$0.529516\pi$
$938$			28051.8i			0.976463i
$939$		−	4398.32i		−	0.152858i
$940$	6.26522			0.000217393
$941$		−	2163.11i		−	0.0749365i	−0.999298	−	0.0374682i	$-0.988071\pi$
$941$		−	2163.11i		−	0.0749365i	0.999298	−	0.0374682i	$-0.0119293\pi$
$942$	22926.6			0.792983
$943$			29450.7i			1.01702i
$944$			2107.50i			0.0726624i
$945$		−	73.9262i		−	0.00254478i
$946$			468.273i			0.0160939i
$947$		−	54309.9i		−	1.86360i	−0.362967	−	0.931802i	$-0.618236\pi$
$947$		−	54309.9i		−	1.86360i	0.362967	−	0.931802i	$-0.381764\pi$
$948$		−	38805.0i		−	1.32946i
$949$	130.369			0.00445939
$950$		−	8859.94i		−	0.302584i
$951$	−49335.9			−1.68226
$952$		−	35104.3i		−	1.19510i
$953$		−	14375.9i		−	0.488646i	−0.969694	−	0.244323i	$-0.921434\pi$
$953$		−	14375.9i		−	0.488646i	0.969694	−	0.244323i	$-0.0785658\pi$
$954$	−1761.47			−0.0597794
$955$		−	22.4589i		−	0.000760996i
$956$	21495.8			0.727222
$957$	12997.5			0.439028
$958$		−	16315.9i		−	0.550255i
$959$		−	53354.5i		−	1.79657i
$960$	−3.09711			−0.000104124
$961$	18810.0			0.631398
$962$	895.117			0.0299997
$963$	5854.84			0.195918
$964$	33966.4			1.13484
$965$			125.804i			0.00419664i
$966$			21476.4i			0.715313i
$967$	−5438.16			−0.180847			−0.0904237	−	0.995903i	$-0.528822\pi$
$967$	−5438.16			−0.180847			−0.0904237	+	0.995903i	$0.528822\pi$
$968$		−	17044.7i		−	0.565947i
$969$			27573.8i			0.914138i
$970$			50.5403i			0.00167294i
$971$	48709.4			1.60985			0.804923	−	0.593380i	$-0.202207\pi$
$971$	48709.4			1.60985			0.804923	+	0.593380i	$0.202207\pi$
$972$	−6672.87			−0.220198
$973$	39956.5			1.31649
$974$			12743.4i			0.419225i
$975$	6573.16			0.215907
$976$	11548.4	+	5517.78i	0.378745	+	0.180963i
$977$	−6837.14			−0.223889			−0.111944	−	0.993714i	$-0.535708\pi$
$977$	−6837.14			−0.223889			−0.111944	+	0.993714i	$0.535708\pi$
$978$		−	5258.47i		−	0.171930i
$979$	6246.04			0.203906
$980$	−16.9915			−0.000553852
$981$	−793.258			−0.0258173
$982$			15119.3i			0.491321i
$983$		−	49814.3i		−	1.61631i	−0.588972	−	0.808154i	$-0.700467\pi$
$983$		−	49814.3i		−	1.61631i	0.588972	−	0.808154i	$-0.299533\pi$
$984$		−	21130.1i		−	0.684556i
$985$	−119.549			−0.00386717
$986$		−	13504.5i		−	0.436179i
$987$			4216.20i			0.135971i
$988$	3302.21			0.106333
$989$	2567.08			0.0825363
$990$	−2.69228			−8.64305e−5
$991$	−20028.9			−0.642016			−0.321008	−	0.947077i	$-0.604022\pi$
$991$	−20028.9			−0.642016			−0.321008	+	0.947077i	$0.604022\pi$
$992$	19127.3			0.612190
$993$		−	5617.12i		−	0.179510i
$994$		−	22669.0i		−	0.723357i
$995$	101.903			0.00324678
$996$	17698.2			0.563043
$997$			16547.5i			0.525640i	0.964845	+	0.262820i	$0.0846526\pi$
$997$			16547.5i			0.525640i	−0.964845	+	0.262820i	$0.915347\pi$
$998$	15892.5			0.504078
$999$			9435.63i			0.298829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.4.b.a.60.7	✓	14
3.2	odd	2		549.4.c.c.487.8		14
4.3	odd	2		976.4.h.a.609.3		14
61.60	even	2	inner	61.4.b.a.60.8	yes	14
183.182	odd	2		549.4.c.c.487.7		14
244.243	odd	2		976.4.h.a.609.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.4.b.a.60.7	✓	14	1.1	even	1	trivial
61.4.b.a.60.8	yes	14	61.60	even	2	inner
549.4.c.c.487.7		14	183.182	odd	2
549.4.c.c.487.8		14	3.2	odd	2
976.4.h.a.609.3		14	4.3	odd	2
976.4.h.a.609.4		14	244.243	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)

\(f(q)\)	\(=\)	\(q-1.28937i q^{2} +5.54789 q^{3} +6.33752 q^{4} +0.0273216 q^{5} -7.15328i q^{6} +21.0031i q^{7} -18.4864i q^{8} +3.77903 q^{9} +O(q^{10})\)	\(q-1.28937i q^{2} +5.54789 q^{3} +6.33752 q^{4} +0.0273216 q^{5} -7.15328i q^{6} +21.0031i q^{7} -18.4864i q^{8} +3.77903 q^{9} -0.0352277i q^{10} -20.2234i q^{11} +35.1599 q^{12} -9.47849 q^{13} +27.0808 q^{14} +0.151577 q^{15} +26.8644 q^{16} -90.4116i q^{17} -4.87257i q^{18} -54.9725 q^{19} +0.173152 q^{20} +116.523i q^{21} -26.0755 q^{22} +142.946i q^{23} -102.560i q^{24} -124.999 q^{25} +12.2213i q^{26} -128.827 q^{27} +133.108i q^{28} +115.845i q^{29} -0.195439i q^{30} +104.790i q^{31} -182.529i q^{32} -112.197i q^{33} -116.574 q^{34} +0.573840i q^{35} +23.9497 q^{36} -73.2424i q^{37} +70.8799i q^{38} -52.5856 q^{39} -0.505078i q^{40} +206.026 q^{41} +150.241 q^{42} -17.9583i q^{43} -128.166i q^{44} +0.103249 q^{45} +184.311 q^{46} +36.1835 q^{47} +149.041 q^{48} -98.1310 q^{49} +161.170i q^{50} -501.593i q^{51} -60.0702 q^{52} -361.507i q^{53} +166.106i q^{54} -0.552537i q^{55} +388.272 q^{56} -304.981 q^{57} +149.367 q^{58} +78.4496i q^{59} +0.960625 q^{60} +(429.877 + 205.394i) q^{61} +135.114 q^{62} +79.3714i q^{63} -20.4325 q^{64} -0.258968 q^{65} -144.664 q^{66} +1035.85i q^{67} -572.986i q^{68} +793.050i q^{69} +0.739892 q^{70} -837.087i q^{71} -69.8606i q^{72} -13.7542 q^{73} -94.4366 q^{74} -693.482 q^{75} -348.390 q^{76} +424.755 q^{77} +67.8023i q^{78} -1103.67i q^{79} +0.733980 q^{80} -816.753 q^{81} -265.644i q^{82} +503.365 q^{83} +738.467i q^{84} -2.47019i q^{85} -23.1550 q^{86} +642.696i q^{87} -373.858 q^{88} +308.852i q^{89} -0.133127i q^{90} -199.078i q^{91} +905.926i q^{92} +581.365i q^{93} -46.6539i q^{94} -1.50194 q^{95} -1012.65i q^{96} -1434.67 q^{97} +126.527i q^{98} -76.4249i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9}+O(q^{10}) \) 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