LMFDB - Embedded newform 61.4.b.a.60.9

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			60.9
Root			$1.56667i$ of defining polynomial
Character	$\chi$	$=$	61.60
Dual form			61.4.b.a.60.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56667i q^{2} -4.69850 q^{3} +5.54555 q^{4} +9.67822 q^{5} -7.36099i q^{6} +14.1375i q^{7} +21.2214i q^{8} -4.92407 q^{9} +O(q^{10})$	\(q+1.56667i q^{2} -4.69850 q^{3} +5.54555 q^{4} +9.67822 q^{5} -7.36099i q^{6} +14.1375i q^{7} +21.2214i q^{8} -4.92407 q^{9} +15.1625i q^{10} +58.4904i q^{11} -26.0558 q^{12} +55.0957 q^{13} -22.1487 q^{14} -45.4731 q^{15} +11.1176 q^{16} -94.2261i q^{17} -7.71437i q^{18} +0.352876 q^{19} +53.6711 q^{20} -66.4250i q^{21} -91.6350 q^{22} -46.1716i q^{23} -99.7087i q^{24} -31.3321 q^{25} +86.3166i q^{26} +149.995 q^{27} +78.4001i q^{28} +66.1215i q^{29} -71.2412i q^{30} -150.522i q^{31} +187.189i q^{32} -274.818i q^{33} +147.621 q^{34} +136.826i q^{35} -27.3067 q^{36} -279.299i q^{37} +0.552840i q^{38} -258.867 q^{39} +205.385i q^{40} -459.595 q^{41} +104.066 q^{42} -287.772i q^{43} +324.362i q^{44} -47.6562 q^{45} +72.3355 q^{46} +337.708 q^{47} -52.2362 q^{48} +143.132 q^{49} -49.0870i q^{50} +442.722i q^{51} +305.536 q^{52} -162.313i q^{53} +234.993i q^{54} +566.083i q^{55} -300.017 q^{56} -1.65799 q^{57} -103.590 q^{58} +795.023i q^{59} -252.174 q^{60} +(80.6463 - 469.550i) q^{61} +235.818 q^{62} -69.6139i q^{63} -204.321 q^{64} +533.228 q^{65} +430.548 q^{66} -19.9848i q^{67} -522.536i q^{68} +216.937i q^{69} -214.360 q^{70} +53.4847i q^{71} -104.495i q^{72} -123.920 q^{73} +437.568 q^{74} +147.214 q^{75} +1.95690 q^{76} -826.907 q^{77} -405.559i q^{78} -754.594i q^{79} +107.599 q^{80} -571.804 q^{81} -720.032i q^{82} -42.8735 q^{83} -368.363i q^{84} -911.941i q^{85} +450.842 q^{86} -310.672i q^{87} -1241.25 q^{88} +786.766i q^{89} -74.6614i q^{90} +778.914i q^{91} -256.047i q^{92} +707.229i q^{93} +529.077i q^{94} +3.41521 q^{95} -879.506i q^{96} +991.717 q^{97} +224.240i q^{98} -288.011i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.56667i			0.553900i	0.960884	+	0.276950i	$0.0893237\pi$
$2$			1.56667i			0.553900i	−0.960884	+	0.276950i	$0.910676\pi$
$3$	−4.69850			−0.904227			−0.452114	−	0.891960i	$-0.649330\pi$
$3$	−4.69850			−0.904227			−0.452114	+	0.891960i	$0.649330\pi$
$4$	5.54555			0.693194
$5$	9.67822			0.865646			0.432823	−	0.901479i	$-0.357518\pi$
$5$	9.67822			0.865646			0.432823	+	0.901479i	$0.357518\pi$
$6$		−	7.36099i		−	0.500852i
$7$			14.1375i			0.763352i	0.924296	+	0.381676i	$0.124653\pi$
$7$			14.1375i			0.763352i	−0.924296	+	0.381676i	$0.875347\pi$
$8$			21.2214i			0.937861i
$9$	−4.92407			−0.182373
$10$			15.1625i			0.479482i
$11$			58.4904i			1.60323i	0.597840	+	0.801615i	$0.296026\pi$
$11$			58.4904i			1.60323i	−0.597840	+	0.801615i	$0.703974\pi$
$12$	−26.0558			−0.626805
$13$	55.0957			1.17545			0.587723	−	0.809062i	$-0.300024\pi$
$13$	55.0957			1.17545			0.587723	+	0.809062i	$0.300024\pi$
$14$	−22.1487			−0.422821
$15$	−45.4731			−0.782741
$16$	11.1176			0.173713
$17$		−	94.2261i		−	1.34431i	−0.740412	−	0.672153i	$-0.765370\pi$
$17$		−	94.2261i		−	1.34431i	0.740412	−	0.672153i	$-0.234630\pi$
$18$		−	7.71437i		−	0.101016i
$19$	0.352876			0.00426081			0.00213040	−	0.999998i	$-0.499322\pi$
$19$	0.352876			0.00426081			0.00213040	+	0.999998i	$0.499322\pi$
$20$	53.6711			0.600061
$21$		−	66.4250i		−	0.690244i
$22$	−91.6350			−0.888030
$23$		−	46.1716i		−	0.418584i	−0.977853	−	0.209292i	$-0.932884\pi$
$23$		−	46.1716i		−	0.418584i	0.977853	−	0.209292i	$-0.0671160\pi$
$24$		−	99.7087i		−	0.848040i
$25$	−31.3321			−0.250657
$26$			86.3166i			0.651080i
$27$	149.995			1.06913
$28$			78.4001i			0.529151i
$29$			66.1215i			0.423395i	0.977335	+	0.211697i	$0.0678991\pi$
$29$			66.1215i			0.423395i	−0.977335	+	0.211697i	$0.932101\pi$
$30$		−	71.2412i		−	0.433560i
$31$		−	150.522i		−	0.872083i	−0.899927	−	0.436041i	$-0.856380\pi$
$31$		−	150.522i		−	0.872083i	0.899927	−	0.436041i	$-0.143620\pi$
$32$			187.189i			1.03408i
$33$		−	274.818i		−	1.44968i
$34$	147.621			0.744611
$35$			136.826i			0.660792i
$36$	−27.3067			−0.126420
$37$		−	279.299i		−	1.24098i	−0.784213	−	0.620492i	$-0.786933\pi$
$37$		−	279.299i		−	1.24098i	0.784213	−	0.620492i	$-0.213067\pi$
$38$			0.552840i			0.00236006i
$39$	−258.867			−1.06287
$40$			205.385i			0.811856i
$41$	−459.595			−1.75065			−0.875325	−	0.483534i	$-0.839353\pi$
$41$	−459.595			−1.75065			−0.875325	+	0.483534i	$0.839353\pi$
$42$	104.066			0.382326
$43$		−	287.772i		−	1.02058i	−0.860004	−	0.510288i	$-0.829539\pi$
$43$		−	287.772i		−	1.02058i	0.860004	−	0.510288i	$-0.170461\pi$
$44$			324.362i			1.11135i
$45$	−47.6562			−0.157870
$46$	72.3355			0.231854
$47$	337.708			1.04808			0.524041	−	0.851693i	$-0.324424\pi$
$47$	337.708			1.04808			0.524041	+	0.851693i	$0.324424\pi$
$48$	−52.2362			−0.157076
$49$	143.132			0.417294
$50$		−	49.0870i		−	0.138839i
$51$			442.722i			1.21556i
$52$	305.536			0.814813
$53$		−	162.313i		−	0.420668i	−0.977630	−	0.210334i	$-0.932545\pi$
$53$		−	162.313i		−	0.420668i	0.977630	−	0.210334i	$-0.0674552\pi$
$54$			234.993i			0.592194i
$55$			566.083i			1.38783i
$56$	−300.017			−0.715918
$57$	−1.65799			−0.00385274
$58$	−103.590			−0.234519
$59$			795.023i			1.75429i	0.480225	+	0.877145i	$0.340555\pi$
$59$			795.023i			1.75429i	−0.480225	+	0.877145i	$0.659445\pi$
$60$	−252.174			−0.542591
$61$	80.6463	−	469.550i	0.169274	−	0.985569i
$61$	80.6463	−	469.550i	0.169274	−	0.985569i
$62$	235.818			0.483047
$63$		−	69.6139i		−	0.139215i
$64$	−204.321			−0.399065
$65$	533.228			1.01752
$66$	430.548			0.802981
$67$		−	19.9848i		−	0.0364407i	−0.999834	−	0.0182204i	$-0.994200\pi$
$67$		−	19.9848i		−	0.0364407i	0.999834	−	0.0182204i	$-0.00580004\pi$
$68$		−	522.536i		−	0.931865i
$69$			216.937i			0.378495i
$70$	−214.360			−0.366013
$71$			53.4847i			0.0894010i	0.999000	+	0.0447005i	$0.0142333\pi$
$71$			53.4847i			0.0894010i	−0.999000	+	0.0447005i	$0.985767\pi$
$72$		−	104.495i		−	0.171040i
$73$	−123.920			−0.198682			−0.0993409	−	0.995053i	$-0.531673\pi$
$73$	−123.920			−0.198682			−0.0993409	+	0.995053i	$0.531673\pi$
$74$	437.568			0.687381
$75$	147.214			0.226651
$76$	1.95690			0.00295357
$77$	−826.907			−1.22383
$78$		−	405.559i		−	0.588724i
$79$		−	754.594i		−	1.07466i	−0.843371	−	0.537332i	$-0.819432\pi$
$79$		−	754.594i		−	1.07466i	0.843371	−	0.537332i	$-0.180568\pi$
$80$	107.599			0.150374
$81$	−571.804			−0.784367
$82$		−	720.032i		−	0.969686i
$83$	−42.8735			−0.0566985			−0.0283492	−	0.999598i	$-0.509025\pi$
$83$	−42.8735			−0.0566985			−0.0283492	+	0.999598i	$0.509025\pi$
$84$		−	368.363i		−	0.478473i
$85$		−	911.941i		−	1.16369i
$86$	450.842			0.565297
$87$		−	310.672i		−	0.382845i
$88$	−1241.25			−1.50361
$89$			786.766i			0.937046i	0.883451	+	0.468523i	$0.155214\pi$
$89$			786.766i			0.937046i	−0.883451	+	0.468523i	$0.844786\pi$
$90$		−	74.6614i		−	0.0874445i
$91$			778.914i			0.897279i
$92$		−	256.047i		−	0.290160i
$93$			707.229i			0.788561i
$94$			529.077i			0.580533i
$95$	3.41521			0.00368835
$96$		−	879.506i		−	0.935044i
$97$	991.717			1.03808			0.519039	−	0.854750i	$-0.326290\pi$
$97$	991.717			1.03808			0.519039	+	0.854750i	$0.326290\pi$
$98$			224.240i			0.231139i
$99$		−	288.011i		−	0.292386i
$100$	−173.754			−0.173754
$101$		−	473.958i		−	0.466937i	−0.972364	−	0.233468i	$-0.924992\pi$
$101$		−	473.958i		−	0.466937i	0.972364	−	0.233468i	$-0.0750075\pi$
$102$	−693.598			−0.673298
$103$	−212.036			−0.202840			−0.101420	−	0.994844i	$-0.532339\pi$
$103$	−212.036			−0.202840			−0.101420	+	0.994844i	$0.532339\pi$
$104$			1169.21i			1.10240i
$105$		−	642.875i		−	0.597507i
$106$	254.290			0.233008
$107$	−1075.93			−0.972098			−0.486049	−	0.873932i	$-0.661562\pi$
$107$	−1075.93			−0.972098			−0.486049	+	0.873932i	$0.661562\pi$
$108$	831.807			0.741118
$109$	2010.85			1.76701			0.883506	−	0.468420i	$-0.155177\pi$
$109$	2010.85			1.76701			0.883506	+	0.468420i	$0.155177\pi$
$110$	−886.864			−0.768719
$111$			1312.29i			1.12213i
$112$			157.175i			0.132604i
$113$	1680.93			1.39937			0.699684	−	0.714452i	$-0.253324\pi$
$113$	1680.93			1.39937			0.699684	+	0.714452i	$0.253324\pi$
$114$		−	2.59752i		−	0.00213403i
$115$		−	446.858i		−	0.362346i
$116$			366.680i			0.293495i
$117$	−271.295			−0.214369
$118$	−1245.54			−0.971702
$119$	1332.12			1.02618
$120$		−	965.002i		−	0.734102i
$121$	−2090.13			−1.57035
$122$	735.628	+	126.346i	0.545907	+	0.0937608i
$123$	2159.41			1.58299
$124$		−	834.729i		−	0.604523i
$125$	−1513.02			−1.08263
$126$	109.062			0.0771111
$127$	−1715.24			−1.19845			−0.599224	−	0.800581i	$-0.704524\pi$
$127$	−1715.24			−1.19845			−0.599224	+	0.800581i	$0.704524\pi$
$128$			1177.41i			0.813038i
$129$			1352.10i			0.922833i
$130$			835.391i			0.563605i
$131$	−251.750			−0.167904			−0.0839522	−	0.996470i	$-0.526754\pi$
$131$	−251.750			−0.167904			−0.0839522	+	0.996470i	$0.526754\pi$
$132$		−	1524.02i		−	1.00491i
$133$			4.98878i			0.00325250i
$134$	31.3095			0.0201845
$135$	1451.69			0.925491
$136$	1999.61			1.26077
$137$	1198.09			0.747149			0.373574	−	0.927600i	$-0.378132\pi$
$137$	1198.09			0.747149			0.373574	+	0.927600i	$0.378132\pi$
$138$	−339.868			−0.209649
$139$			2442.26i			1.49029i	0.666905	+	0.745143i	$0.267619\pi$
$139$			2442.26i			1.49029i	−0.666905	+	0.745143i	$0.732381\pi$
$140$			758.773i			0.458058i
$141$	−1586.72			−0.947704
$142$	−83.7927			−0.0495192
$143$			3222.57i			1.88451i
$144$	−54.7439			−0.0316805
$145$			639.938i			0.366510i
$146$		−	194.142i		−	0.110050i
$147$	−672.505			−0.377329
$148$		−	1548.87i		−	0.860243i
$149$	−1019.11			−0.560326			−0.280163	−	0.959952i	$-0.590389\pi$
$149$	−1019.11			−0.560326			−0.280163	+	0.959952i	$0.590389\pi$
$150$			230.635i			0.125542i
$151$		−	247.144i		−	0.133194i	−0.997780	−	0.0665970i	$-0.978786\pi$
$151$		−	247.144i		−	0.133194i	0.997780	−	0.0665970i	$-0.0212142\pi$
$152$			7.48852i			0.00399605i
$153$			463.976i			0.245165i
$154$		−	1295.49i		−	0.677879i
$155$		−	1456.79i		−	0.754915i
$156$	−1435.56			−0.736776
$157$		−	1855.02i		−	0.942975i	−0.881873	−	0.471488i	$-0.843717\pi$
$157$		−	1855.02i		−	0.942975i	0.881873	−	0.471488i	$-0.156283\pi$
$158$	1182.20			0.595257
$159$			762.628i			0.380380i
$160$			1811.65i			0.895148i
$161$	652.749			0.319527
$162$		−	895.826i		−	0.434461i
$163$	−2289.01			−1.09993			−0.549965	−	0.835187i	$-0.685359\pi$
$163$	−2289.01			−1.09993			−0.549965	+	0.835187i	$0.685359\pi$
$164$	−2548.71			−1.21354
$165$		−	2659.74i		−	1.25491i
$166$		−	67.1684i		−	0.0314053i
$167$	1043.12			0.483346			0.241673	−	0.970358i	$-0.422304\pi$
$167$	1043.12			0.483346			0.241673	+	0.970358i	$0.422304\pi$
$168$	1409.63			0.647353
$169$	838.536			0.381673
$170$	1428.71			0.644570
$171$	−1.73759			−0.000777056
$172$		−	1595.85i		−	0.707458i
$173$		−	3268.03i		−	1.43621i	−0.695937	−	0.718103i	$-0.745011\pi$
$173$		−	3268.03i		−	1.43621i	0.695937	−	0.718103i	$-0.254989\pi$
$174$	486.720			0.212058
$175$		−	442.957i		−	0.191340i
$176$			650.274i			0.278502i
$177$		−	3735.42i		−	1.58628i
$178$	−1232.60			−0.519030
$179$	−1022.07			−0.426779			−0.213389	−	0.976967i	$-0.568450\pi$
$179$	−1022.07			−0.426779			−0.213389	+	0.976967i	$0.568450\pi$
$180$	−264.280			−0.109435
$181$			238.671i			0.0980127i	0.998798	+	0.0490064i	$0.0156055\pi$
$181$			238.671i			0.0980127i	−0.998798	+	0.0490064i	$0.984395\pi$
$182$	−1220.30			−0.497003
$183$	−378.917	+	2206.18i	−0.153062	+	0.891179i
$184$	979.824			0.392574
$185$		−	2703.11i		−	1.07425i
$186$	−1107.99			−0.436784
$187$	5511.33			2.15523
$188$	1872.78			0.726524
$189$			2120.56i			0.816125i
$190$			5.35050i			0.00204298i
$191$		−	4008.15i		−	1.51843i	−0.650841	−	0.759214i	$-0.725584\pi$
$191$		−	4008.15i		−	1.51843i	0.650841	−	0.759214i	$-0.274416\pi$
$192$	960.004			0.360845
$193$			4266.26i			1.59115i	0.605854	+	0.795576i	$0.292832\pi$
$193$			4266.26i			1.59115i	−0.605854	+	0.795576i	$0.707168\pi$
$194$			1553.69i			0.574992i
$195$	−2505.37			−0.920069
$196$	793.746			0.289266
$197$	−82.4733			−0.0298273			−0.0149136	−	0.999889i	$-0.504747\pi$
$197$	−82.4733			−0.0298273			−0.0149136	+	0.999889i	$0.504747\pi$
$198$	451.217			0.161953
$199$	−2081.81			−0.741585			−0.370793	−	0.928716i	$-0.620914\pi$
$199$	−2081.81			−0.741585			−0.370793	+	0.928716i	$0.620914\pi$
$200$		−	664.911i		−	0.235081i
$201$			93.8985i			0.0329507i
$202$	742.535			0.258636
$203$	−934.791			−0.323199
$204$			2455.14i			0.842618i
$205$	−4448.06			−1.51544
$206$		−	332.190i		−	0.112353i
$207$			227.352i			0.0763384i
$208$	612.533			0.204190
$209$			20.6399i			0.00683106i
$210$	1007.17			0.330959
$211$		−	380.461i		−	0.124133i	−0.998072	−	0.0620664i	$-0.980231\pi$
$211$		−	380.461i		−	0.124133i	0.998072	−	0.0620664i	$-0.0197691\pi$
$212$		−	900.116i		−	0.291605i
$213$		−	251.298i		−	0.0808388i
$214$		−	1685.63i		−	0.538445i
$215$		−	2785.12i		−	0.883458i
$216$			3183.11i			1.00270i
$217$	2128.00			0.665706
$218$			3150.33i			0.978749i
$219$	582.240			0.179654
$220$			3139.25i			0.962036i
$221$		−	5191.45i		−	1.58016i
$222$	−2055.91			−0.621549
$223$			6172.97i			1.85369i	0.375447	+	0.926844i	$0.377489\pi$
$223$			6172.97i			1.85369i	−0.375447	+	0.926844i	$0.622511\pi$
$224$	−2646.37			−0.789367
$225$	154.282			0.0457131
$226$			2633.46i			0.775111i
$227$		−	1900.76i		−	0.555762i	−0.960615	−	0.277881i	$-0.910368\pi$
$227$		−	1900.76i		−	0.555762i	0.960615	−	0.277881i	$-0.0896322\pi$
$228$	−9.19448			−0.00267070
$229$	3683.18			1.06284			0.531422	−	0.847107i	$-0.321658\pi$
$229$	3683.18			1.06284			0.531422	+	0.847107i	$0.321658\pi$
$230$	700.078			0.200703
$231$	3885.23			1.10662
$232$	−1403.19			−0.397086
$233$			508.911i			0.143090i	0.997437	+	0.0715448i	$0.0227929\pi$
$233$			508.911i			0.143090i	−0.997437	+	0.0715448i	$0.977207\pi$
$234$		−	425.029i		−	0.118739i
$235$	3268.42			0.907268
$236$			4408.84i			1.21606i
$237$			3545.46i			0.971741i
$238$			2086.99i			0.568400i
$239$	−6755.09			−1.82824			−0.914122	−	0.405440i	$-0.867118\pi$
$239$	−6755.09			−1.82824			−0.914122	+	0.405440i	$0.867118\pi$
$240$	−505.553			−0.135972
$241$	−4164.76			−1.11318			−0.556588	−	0.830788i	$-0.687890\pi$
$241$	−4164.76			−1.11318			−0.556588	+	0.830788i	$0.687890\pi$
$242$		−	3274.54i		−	0.869816i
$243$	−1363.25			−0.359888
$244$	447.229	−	2603.92i	0.117340	−	0.683191i
$245$	1385.26			0.361229
$246$			3383.07i			0.876817i
$247$	19.4420			0.00500835
$248$	3194.29			0.817893
$249$	201.441			0.0512683
$250$		−	2370.39i		−	0.599667i
$251$			1207.85i			0.303740i	0.988400	+	0.151870i	$0.0485295\pi$
$251$			1207.85i			0.303740i	−0.988400	+	0.151870i	$0.951471\pi$
$252$		−	386.048i		−	0.0965028i
$253$	2700.60			0.671087
$254$		−	2687.21i		−	0.663821i
$255$			4284.76i			1.05224i
$256$	−3479.17			−0.849407
$257$	−7509.98			−1.82280			−0.911400	−	0.411523i	$-0.864997\pi$
$257$	−7509.98			−1.82280			−0.911400	+	0.411523i	$0.864997\pi$
$258$	−2118.28			−0.511157
$259$	3948.58			0.947307
$260$	2957.05			0.705339
$261$		−	325.587i		−	0.0772157i
$262$		−	394.408i		−	0.0930023i
$263$	61.3343			0.0143804			0.00719018	−	0.999974i	$-0.497711\pi$
$263$	61.3343			0.0143804			0.00719018	+	0.999974i	$0.497711\pi$
$264$	5832.01			1.35960
$265$		−	1570.90i		−	0.364150i
$266$	−7.81576			−0.00180156
$267$		−	3696.62i		−	0.847302i
$268$		−	110.827i		−	0.0252605i
$269$	4922.78			1.11579			0.557894	−	0.829912i	$-0.311610\pi$
$269$	4922.78			1.11579			0.557894	+	0.829912i	$0.311610\pi$
$270$			2274.31i			0.512630i
$271$	7876.50			1.76555			0.882774	−	0.469798i	$-0.155673\pi$
$271$	7876.50			1.76555			0.882774	+	0.469798i	$0.155673\pi$
$272$		−	1047.57i		−	0.233523i
$273$		−	3659.73i		−	0.811344i
$274$			1877.00i			0.413846i
$275$		−	1832.63i		−	0.401861i
$276$			1203.04i			0.262371i
$277$		−	7239.41i		−	1.57030i	−0.619304	−	0.785152i	$-0.712585\pi$
$277$		−	7239.41i		−	1.57030i	0.619304	−	0.785152i	$-0.287415\pi$
$278$	−3826.21			−0.825470
$279$			741.181i			0.159044i
$280$	−2903.63			−0.619731
$281$			3660.84i			0.777179i	0.921411	+	0.388589i	$0.127038\pi$
$281$			3660.84i			0.777179i	−0.921411	+	0.388589i	$0.872962\pi$
$282$		−	2485.87i		−	0.524934i
$283$	810.466			0.170237			0.0851187	−	0.996371i	$-0.472873\pi$
$283$	810.466			0.170237			0.0851187	+	0.996371i	$0.472873\pi$
$284$			296.602i			0.0619723i
$285$	−16.0464			−0.00333511
$286$	−5048.70			−1.04383
$287$		−	6497.51i		−	1.33636i
$288$		−	921.729i		−	0.188588i
$289$	−3965.56			−0.807158
$290$	−1002.57			−0.203010
$291$	−4659.58			−0.938659
$292$	−687.207			−0.137725
$293$	−3244.89			−0.646991			−0.323496	−	0.946230i	$-0.604858\pi$
$293$	−3244.89			−0.646991			−0.323496	+	0.946230i	$0.604858\pi$
$294$		−	1053.59i		−	0.209002i
$295$			7694.40i			1.51859i
$296$	5927.10			1.16387
$297$			8773.29i			1.71407i
$298$		−	1596.60i		−	0.310365i
$299$		−	2543.85i		−	0.492023i
$300$	816.384			0.157113
$301$	4068.36			0.779059
$302$	387.192			0.0737762
$303$			2226.89i			0.422217i
$304$	3.92314			0.000740157
$305$	780.513	−	4544.41i	0.146531	−	0.853154i
$306$	−726.896			−0.135797
$307$			1068.34i			0.198610i	0.995057	+	0.0993052i	$0.0316620\pi$
$307$			1068.34i			0.198610i	−0.995057	+	0.0993052i	$0.968338\pi$
$308$	−4585.66			−0.848351
$309$	996.251			0.183413
$310$	2282.30			0.418148
$311$			192.990i			0.0351879i	0.999845	+	0.0175940i	$0.00560062\pi$
$311$			192.990i			0.0351879i	−0.999845	+	0.0175940i	$0.994399\pi$
$312$		−	5493.52i		−	0.996825i
$313$		−	5330.80i		−	0.962667i	−0.876538	−	0.481334i	$-0.840153\pi$
$313$		−	5330.80i		−	0.962667i	0.876538	−	0.481334i	$-0.159847\pi$
$314$	2906.21			0.522314
$315$		−	673.738i		−	0.120511i
$316$		−	4184.64i		−	0.744951i
$317$	−228.598			−0.0405027			−0.0202513	−	0.999795i	$-0.506447\pi$
$317$	−228.598			−0.0405027			−0.0202513	+	0.999795i	$0.506447\pi$
$318$	−1194.78			−0.210692
$319$	−3867.47			−0.678799
$320$	−1977.46			−0.345449
$321$	5055.28			0.878998
$322$			1022.64i			0.176986i
$323$		−	33.2502i		−	0.00572783i
$324$	−3170.97			−0.543719
$325$	−1726.27			−0.294634
$326$		−	3586.11i		−	0.609252i
$327$	−9447.98			−1.59778
$328$		−	9753.24i		−	1.64187i
$329$			4774.34i			0.800055i
$330$	4166.93			0.695097
$331$		−	7304.43i		−	1.21295i	−0.795101	−	0.606477i	$-0.792582\pi$
$331$		−	7304.43i		−	1.21295i	0.795101	−	0.606477i	$-0.207418\pi$
$332$	−237.757			−0.0393031
$333$			1375.29i			0.226322i
$334$			1634.22i			0.267726i
$335$		−	193.417i		−	0.0315448i
$336$		−	738.487i		−	0.119904i
$337$			9729.85i			1.57276i	0.617745	+	0.786378i	$0.288046\pi$
$337$			9729.85i			1.57276i	−0.617745	+	0.786378i	$0.711954\pi$
$338$			1313.71i			0.211409i
$339$	−7897.86			−1.26535
$340$		−	5057.22i		−	0.806665i
$341$	8804.11			1.39815
$342$		−	2.72222i		−	0.000430412i
$343$			6872.68i			1.08189i
$344$	6106.91			0.957159
$345$			2099.57i			0.327643i
$346$	5119.91			0.795515
$347$	−9876.71			−1.52798			−0.763991	−	0.645227i	$-0.776763\pi$
$347$	−9876.71			−1.52798			−0.763991	+	0.645227i	$0.776763\pi$
$348$		−	1722.85i		−	0.265386i
$349$			7854.49i			1.20470i	0.798231	+	0.602351i	$0.205769\pi$
$349$			7854.49i			1.20470i	−0.798231	+	0.602351i	$0.794231\pi$
$350$	693.966			0.105983
$351$	8264.10			1.25671
$352$	−10948.7			−1.65787
$353$	8849.16			1.33426			0.667129	−	0.744942i	$-0.267523\pi$
$353$	8849.16			1.33426			0.667129	+	0.744942i	$0.267523\pi$
$354$	5852.15			0.878640
$355$			517.637i			0.0773896i
$356$			4363.06i			0.649555i
$357$	−6258.97			−0.927898
$358$		−	1601.25i		−	0.236393i
$359$			8890.91i			1.30709i	0.756889	+	0.653544i	$0.226719\pi$
$359$			8890.91i			1.30709i	−0.756889	+	0.653544i	$0.773281\pi$
$360$		−	1011.33i		−	0.148060i
$361$	−6858.88			−0.999982
$362$	−373.919			−0.0542893
$363$	9820.49			1.41995
$364$			4319.51i			0.621989i
$365$	−1199.33			−0.171988
$366$	−3456.35	−	593.637i	−0.493624	−	0.0847811i
$367$	9039.36			1.28570			0.642849	−	0.765993i	$-0.277752\pi$
$367$	9039.36			1.28570			0.642849	+	0.765993i	$0.277752\pi$
$368$		−	513.318i		−	0.0727134i
$369$	2263.08			0.319271
$370$	4234.88			0.595029
$371$	2294.70			0.321118
$372$			3921.98i			0.546626i
$373$			7819.85i			1.08551i	0.839890	+	0.542757i	$0.182619\pi$
$373$			7819.85i			1.08551i	−0.839890	+	0.542757i	$0.817381\pi$
$374$			8634.42i			1.19378i
$375$	7108.91			0.978940
$376$			7166.64i			0.982955i
$377$			3643.01i			0.497678i
$378$	−3322.20			−0.452052
$379$	−12011.0			−1.62787			−0.813934	−	0.580958i	$-0.802678\pi$
$379$	−12011.0			−1.62787			−0.813934	+	0.580958i	$0.802678\pi$
$380$	18.9393			0.00255675
$381$	8059.06			1.08367
$382$	6279.44			0.841058
$383$		−	1404.06i		−	0.187321i	−0.995604	−	0.0936607i	$-0.970143\pi$
$383$		−	1404.06i		−	0.187321i	0.995604	−	0.0936607i	$-0.0298569\pi$
$384$		−	5532.04i		−	0.735172i
$385$	−8002.99			−1.05940
$386$	−6683.81			−0.881339
$387$			1417.01i			0.186125i
$388$	5499.62			0.719590
$389$			7428.10i			0.968173i	0.875020	+	0.484087i	$0.160848\pi$
$389$			7428.10i			0.968173i	−0.875020	+	0.484087i	$0.839152\pi$
$390$		−	3925.09i		−	0.509627i
$391$	−4350.57			−0.562705
$392$			3037.45i			0.391364i
$393$	1182.85			0.151824
$394$		−	129.208i		−	0.0165213i
$395$		−	7303.13i		−	0.930279i
$396$		−	1597.18i		−	0.202680i
$397$		−	11673.7i		−	1.47579i	−0.674916	−	0.737895i	$-0.735820\pi$
$397$		−	11673.7i		−	1.47579i	0.674916	−	0.737895i	$-0.264180\pi$
$398$		−	3261.50i		−	0.410764i
$399$		−	23.4398i		−	0.00294100i
$400$	−348.339			−0.0435423
$401$		−	4734.95i		−	0.589657i	−0.955550	−	0.294828i	$-0.904738\pi$
$401$		−	4734.95i		−	0.589657i	0.955550	−	0.294828i	$-0.0952625\pi$
$402$	−147.108			−0.0182514
$403$		−	8293.12i		−	1.02509i
$404$		−	2628.36i		−	0.323678i
$405$	−5534.04			−0.678984
$406$		−	1464.51i		−	0.179020i
$407$	16336.3			1.98958
$408$	−9395.16			−1.14002
$409$			7958.35i			0.962139i	0.876682	+	0.481070i	$0.159752\pi$
$409$			7958.35i			0.962139i	−0.876682	+	0.481070i	$0.840248\pi$
$410$		−	6968.63i		−	0.839405i
$411$	−5629.21			−0.675593
$412$	−1175.86			−0.140608
$413$	−11239.6			−1.33914
$414$	−356.185			−0.0422839
$415$	−414.939			−0.0490808
$416$			10313.3i			1.21551i
$417$		−	11475.0i		−	1.34756i
$418$	−32.3358			−0.00378373
$419$		−	8329.87i		−	0.971220i	−0.874176	−	0.485610i	$-0.838598\pi$
$419$		−	8329.87i		−	0.971220i	0.874176	−	0.485610i	$-0.161402\pi$
$420$		−	3565.10i		−	0.414188i
$421$			13528.4i			1.56612i	0.621947	+	0.783060i	$0.286342\pi$
$421$			13528.4i			1.56612i	−0.621947	+	0.783060i	$0.713658\pi$
$422$	596.056			0.0687572
$423$	−1662.90			−0.191142
$424$	3444.51			0.394528
$425$			2952.31i			0.336960i
$426$	393.700			0.0447766
$427$	6638.25	+	1140.14i	0.752336	+	0.129215i
$428$	−5966.65			−0.673853
$429$		−	15141.3i		−	1.70403i
$430$	4363.35			0.489347
$431$	−9659.41			−1.07953			−0.539765	−	0.841816i	$-0.681487\pi$
$431$	−9659.41			−1.07953			−0.539765	+	0.841816i	$0.681487\pi$
$432$	1667.59			0.185722
$433$			1203.26i			0.133545i	0.997768	+	0.0667724i	$0.0212701\pi$
$433$			1203.26i			0.133545i	−0.997768	+	0.0667724i	$0.978730\pi$
$434$			3333.87i			0.368735i
$435$		−	3006.75i		−	0.331408i
$436$	11151.3			1.22488
$437$		−	16.2929i		−	0.00178351i
$438$			912.176i			0.0995102i
$439$	−8723.97			−0.948456			−0.474228	−	0.880402i	$-0.657273\pi$
$439$	−8723.97			−0.948456			−0.474228	+	0.880402i	$0.657273\pi$
$440$	−12013.1			−1.30159
$441$	−704.791			−0.0761031
$442$	8133.28			0.875250
$443$	9714.97			1.04192			0.520962	−	0.853580i	$-0.325573\pi$
$443$	9714.97			1.04192			0.520962	+	0.853580i	$0.325573\pi$
$444$			7277.35i			0.777855i
$445$			7614.49i			0.811150i
$446$	−9670.98			−1.02676
$447$	4788.28			0.506662
$448$		−	2888.59i		−	0.304627i
$449$	−3132.22			−0.329217			−0.164608	−	0.986359i	$-0.552636\pi$
$449$	−3132.22			−0.329217			−0.164608	+	0.986359i	$0.552636\pi$
$450$			241.708i			0.0253205i
$451$		−	26881.9i		−	2.80670i
$452$	9321.69			0.970034
$453$			1161.21i			0.120438i
$454$	2977.86			0.307837
$455$			7538.50i			0.776726i
$456$		−	35.1848i		−	0.00361334i
$457$			6940.95i			0.710468i	0.934777	+	0.355234i	$0.115599\pi$
$457$			6940.95i			0.710468i	−0.934777	+	0.355234i	$0.884401\pi$
$458$			5770.31i			0.588709i
$459$		−	14133.5i		−	1.43724i
$460$		−	2478.08i		−	0.251176i
$461$	−8267.80			−0.835293			−0.417646	−	0.908610i	$-0.637145\pi$
$461$	−8267.80			−0.835293			−0.417646	+	0.908610i	$0.637145\pi$
$462$			6086.85i			0.612957i
$463$	−1691.87			−0.169823			−0.0849115	−	0.996388i	$-0.527061\pi$
$463$	−1691.87			−0.169823			−0.0849115	+	0.996388i	$0.527061\pi$
$464$			735.113i			0.0735491i
$465$			6844.71i			0.682615i
$466$	−797.295			−0.0792574
$467$		−	6274.27i		−	0.621711i	−0.950457	−	0.310855i	$-0.899385\pi$
$467$		−	6274.27i		−	0.621711i	0.950457	−	0.310855i	$-0.100615\pi$
$468$	−1504.48			−0.148600
$469$	282.534			0.0278171
$470$			5120.52i			0.502536i
$471$			8715.84i			0.852664i
$472$	−16871.5			−1.64528
$473$	16831.9			1.63622
$474$	−5554.56			−0.538248
$475$	−11.0564			−0.00106800
$476$	7387.34			0.711341
$477$			799.240i			0.0767185i
$478$		−	10583.0i		−	1.01266i
$479$	7046.62			0.672167			0.336084	−	0.941832i	$-0.390897\pi$
$479$	7046.62			0.672167			0.336084	+	0.941832i	$0.390897\pi$
$480$		−	8512.05i		−	0.809417i
$481$		−	15388.2i		−	1.45871i
$482$		−	6524.79i		−	0.616589i
$483$	−3066.94			−0.288925
$484$	−11590.9			−1.08856
$485$	9598.05			0.898608
$486$		−	2135.76i		−	0.199342i
$487$	−14741.0			−1.37162			−0.685808	−	0.727783i	$-0.740551\pi$
$487$	−14741.0			−1.37162			−0.685808	+	0.727783i	$0.740551\pi$
$488$	9964.49	+	1711.43i	0.924327	+	0.158755i
$489$	10754.9			0.994588
$490$			2170.24i			0.200085i
$491$	17417.5			1.60090			0.800450	−	0.599400i	$-0.204594\pi$
$491$	17417.5			1.60090			0.800450	+	0.599400i	$0.204594\pi$
$492$	11975.1			1.09732
$493$	6230.37			0.569172
$494$			30.4591i			0.00277413i
$495$		−	2787.43i		−	0.253103i
$496$		−	1673.45i		−	0.151492i
$497$	−756.139			−0.0682444
$498$			315.591i			0.0283975i
$499$		−	8231.42i		−	0.738455i	−0.929339	−	0.369227i	$-0.879622\pi$
$499$		−	8231.42i		−	0.738455i	0.929339	−	0.369227i	$-0.120378\pi$
$500$	−8390.51			−0.750470
$501$	−4901.09			−0.437055
$502$	−1892.30			−0.168242
$503$	−2731.69			−0.242147			−0.121074	−	0.992644i	$-0.538634\pi$
$503$	−2731.69			−0.242147			−0.121074	+	0.992644i	$0.538634\pi$
$504$	1477.30			0.130564
$505$		−	4587.07i		−	0.404202i
$506$			4230.93i			0.371715i
$507$	−3939.86			−0.345119
$508$	−9511.96			−0.830758
$509$			19612.4i			1.70787i	0.520380	+	0.853935i	$0.325790\pi$
$509$			19612.4i			1.70787i	−0.520380	+	0.853935i	$0.674210\pi$
$510$	−6712.79			−0.582838
$511$		−	1751.92i		−	0.151664i
$512$			3968.54i			0.342551i
$513$	52.9298			0.00455538
$514$		−	11765.6i		−	1.00965i
$515$	−2052.13			−0.175588
$516$			7498.12i			0.639702i
$517$			19752.7i			1.68032i
$518$			6186.10i			0.524714i
$519$			15354.8i			1.29866i
$520$			11315.8i			0.954292i
$521$			6045.40i			0.508357i	0.967157	+	0.254178i	$0.0818050\pi$
$521$			6045.40i			0.508357i	−0.967157	+	0.254178i	$0.918195\pi$
$522$	510.086			0.0427698
$523$		−	14849.0i		−	1.24149i	−0.784011	−	0.620747i	$-0.786829\pi$
$523$		−	14849.0i		−	1.24149i	0.784011	−	0.620747i	$-0.213171\pi$
$524$	−1396.09			−0.116390
$525$			2081.24i			0.173014i
$526$			96.0904i			0.00796529i
$527$	−14183.1			−1.17235
$528$		−	3055.32i		−	0.251829i
$529$	10035.2			0.824787
$530$	2461.08			0.201703
$531$		−	3914.75i		−	0.319935i
$532$			27.6656i			0.00225461i
$533$	−25321.7			−2.05780
$534$	5791.38			0.469321
$535$	−10413.1			−0.841493
$536$	424.104			0.0341763
$537$	4802.22			0.385905
$538$			7712.35i			0.618035i
$539$			8371.85i			0.669018i
$540$	8050.41			0.641545
$541$		−	9539.82i		−	0.758131i	−0.925370	−	0.379065i	$-0.876246\pi$
$541$		−	9539.82i		−	0.758131i	0.925370	−	0.379065i	$-0.123754\pi$
$542$			12339.9i			0.977938i
$543$		−	1121.40i		−	0.0886258i
$544$	17638.1			1.39012
$545$	19461.4			1.52961
$546$	5733.58			0.449404
$547$			4963.94i			0.388012i	0.981000	+	0.194006i	$0.0621482\pi$
$547$			4963.94i			0.388012i	−0.981000	+	0.194006i	$0.937852\pi$
$548$	6644.05			0.517919
$549$	−397.108	+	2312.10i	−0.0308710	+	0.179741i
$550$	2871.12			0.222591
$551$			23.3327i			0.00180400i
$552$	−4603.71			−0.354976
$553$	10668.1			0.820347
$554$	11341.7			0.869792
$555$			12700.6i			0.971369i
$556$			13543.7i			1.03306i
$557$			6474.12i			0.492491i	0.969208	+	0.246245i	$0.0791969\pi$
$557$			6474.12i			0.492491i	−0.969208	+	0.246245i	$0.920803\pi$
$558$	−1161.18			−0.0880947
$559$		−	15855.0i		−	1.19963i
$560$			1521.17i			0.114788i
$561$	−25895.0			−1.94882
$562$	−5735.31			−0.430480
$563$	−21156.7			−1.58374			−0.791872	−	0.610687i	$-0.790894\pi$
$563$	−21156.7			−1.58374			−0.791872	+	0.610687i	$0.790894\pi$
$564$	−8799.27			−0.656943
$565$	16268.4			1.21136
$566$			1269.73i			0.0942946i
$567$		−	8083.86i		−	0.598748i
$568$	−1135.02			−0.0838457
$569$	−490.448			−0.0361347			−0.0180674	−	0.999837i	$-0.505751\pi$
$569$	−490.448			−0.0361347			−0.0180674	+	0.999837i	$0.505751\pi$
$570$		−	25.1393i		−	0.00184732i
$571$	−22037.4			−1.61513			−0.807564	−	0.589780i	$-0.799215\pi$
$571$	−22037.4			−1.61513			−0.807564	+	0.589780i	$0.799215\pi$
$572$			17870.9i			1.30633i
$573$			18832.3i			1.37300i
$574$	10179.4			0.740212
$575$			1446.65i			0.104921i
$576$	1006.09			0.0727786
$577$		−	6019.28i		−	0.434291i	−0.976139	−	0.217145i	$-0.930325\pi$
$577$		−	6019.28i		−	0.434291i	0.976139	−	0.217145i	$-0.0696746\pi$
$578$		−	6212.72i		−	0.447085i
$579$		−	20045.0i		−	1.43876i
$580$			3548.81i			0.254063i
$581$		−	606.122i		−	0.0432809i
$582$		−	7300.02i		−	0.519923i
$583$	9493.76			0.674428
$584$		−	2629.76i		−	0.186336i
$585$	−2625.65			−0.185568
$586$		−	5083.66i		−	0.358369i
$587$			2855.51i			0.200783i	0.994948	+	0.100392i	$0.0320096\pi$
$587$			2855.51i			0.200783i	−0.994948	+	0.100392i	$0.967990\pi$
$588$	−3729.42			−0.261562
$589$		−	53.1157i		−	0.00371578i
$590$	−12054.6			−0.841150
$591$	387.501			0.0269707
$592$		−	3105.14i		−	0.215575i
$593$		−	20097.2i		−	1.39172i	−0.718176	−	0.695862i	$-0.755023\pi$
$593$		−	20097.2i		−	1.39172i	0.718176	−	0.695862i	$-0.244977\pi$
$594$	−13744.8			−0.949423
$595$	12892.5			0.888307
$596$	−5651.52			−0.388415
$597$	9781.38			0.670561
$598$	3985.37			0.272532
$599$		−	19521.5i		−	1.33160i	−0.746131	−	0.665799i	$-0.768091\pi$
$599$		−	19521.5i		−	1.33160i	0.746131	−	0.665799i	$-0.231909\pi$
$600$			3124.09i			0.212567i
$601$	6522.77			0.442711			0.221355	−	0.975193i	$-0.428952\pi$
$601$	6522.77			0.442711			0.221355	+	0.975193i	$0.428952\pi$
$602$			6373.77i			0.431521i
$603$			98.4064i			0.00664580i
$604$		−	1370.55i		−	0.0923293i
$605$	−20228.7			−1.35936
$606$	−3488.80			−0.233866
$607$	21651.9			1.44781			0.723906	−	0.689899i	$-0.242345\pi$
$607$	21651.9			1.44781			0.723906	+	0.689899i	$0.242345\pi$
$608$			66.0544i			0.00440602i
$609$	4392.12			0.292246
$610$	7119.57	+	1222.80i	0.472562	+	0.0811637i
$611$	18606.3			1.23196
$612$			2573.00i			0.169947i
$613$	11545.5			0.760716			0.380358	−	0.924839i	$-0.375801\pi$
$613$	11545.5			0.760716			0.380358	+	0.924839i	$0.375801\pi$
$614$	−1673.73			−0.110010
$615$	20899.2			1.37031
$616$		−	17548.1i		−	1.14778i
$617$		−	29455.5i		−	1.92193i	−0.276664	−	0.960967i	$-0.589229\pi$
$617$		−	29455.5i		−	1.92193i	0.276664	−	0.960967i	$-0.410771\pi$
$618$			1560.79i			0.101593i
$619$	1007.08			0.0653924			0.0326962	−	0.999465i	$-0.489591\pi$
$619$	1007.08			0.0653924			0.0326962	+	0.999465i	$0.489591\pi$
$620$		−	8078.68i		−	0.523303i
$621$		−	6925.52i		−	0.447523i
$622$	−302.351			−0.0194906
$623$	−11122.9			−0.715295
$624$	−2877.99			−0.184634
$625$	−10726.8			−0.686514
$626$	8351.59			0.533222
$627$		−	96.9766i		−	0.00617683i
$628$		−	10287.1i		−	0.653665i
$629$	−26317.2			−1.66826
$630$	1055.52			0.0667509
$631$		−	12441.1i		−	0.784901i	−0.919773	−	0.392451i	$-0.871627\pi$
$631$		−	12441.1i		−	0.784901i	0.919773	−	0.392451i	$-0.128373\pi$
$632$	16013.5			1.00789
$633$			1787.60i			0.112244i
$634$		−	358.137i		−	0.0224344i
$635$	−16600.5			−1.03743
$636$			4229.20i			0.263677i
$637$	7885.95			0.490507
$638$		−	6059.04i		−	0.375987i
$639$		−	263.362i		−	0.0163043i
$640$			11395.2i			0.703803i
$641$		−	21238.7i		−	1.30870i	−0.756192	−	0.654350i	$-0.772942\pi$
$641$		−	21238.7i		−	1.30870i	0.756192	−	0.654350i	$-0.227058\pi$
$642$			7919.94i			0.486877i
$643$			21339.9i			1.30881i	0.756146	+	0.654403i	$0.227080\pi$
$643$			21339.9i			1.30881i	−0.756146	+	0.654403i	$0.772920\pi$
$644$	3619.86			0.221494
$645$			13085.9i			0.798846i
$646$	52.0919			0.00317265
$647$			23482.7i			1.42689i	0.700709	+	0.713447i	$0.252867\pi$
$647$			23482.7i			1.42689i	−0.700709	+	0.713447i	$0.747133\pi$
$648$		−	12134.5i		−	0.735627i
$649$	−46501.2			−2.81253
$650$		−	2704.48i		−	0.163198i
$651$	−9998.43			−0.601950
$652$	−12693.8			−0.762466
$653$		−	1237.57i		−	0.0741650i	−0.999312	−	0.0370825i	$-0.988194\pi$
$653$		−	1237.57i		−	0.0741650i	0.999312	−	0.0370825i	$-0.0118064\pi$
$654$		−	14801.8i		−	0.885011i
$655$	−2436.49			−0.145346
$656$	−5109.60			−0.304110
$657$	610.192			0.0362342
$658$	−7479.81			−0.443151
$659$	16891.0			0.998452			0.499226	−	0.866472i	$-0.333618\pi$
$659$	16891.0			0.998452			0.499226	+	0.866472i	$0.333618\pi$
$660$		−	14749.8i		−	0.869899i
$661$			13016.7i			0.765948i	0.923759	+	0.382974i	$0.125100\pi$
$661$			13016.7i			0.765948i	−0.923759	+	0.382974i	$0.874900\pi$
$662$	11443.6			0.671855
$663$			24392.1i			1.42882i
$664$		−	909.834i		−	0.0531753i
$665$			48.2825i			0.00281551i
$666$	−2154.61			−0.125360
$667$	3052.93			0.177226
$668$	5784.67			0.335053
$669$		−	29003.7i		−	1.67616i
$670$	303.020			0.0174727
$671$	27464.2	+	4717.04i	1.58009	+	0.271385i
$672$	12434.0			0.713767
$673$			20202.9i			1.15715i	0.815629	+	0.578576i	$0.196391\pi$
$673$			20202.9i			1.15715i	−0.815629	+	0.578576i	$0.803609\pi$
$674$	−15243.4			−0.871150
$675$	−4699.67			−0.267986
$676$	4650.15			0.264574
$677$			1087.89i			0.0617594i	0.999523	+	0.0308797i	$0.00983088\pi$
$677$			1087.89i			0.0617594i	−0.999523	+	0.0308797i	$0.990169\pi$
$678$		−	12373.3i		−	0.700876i
$679$			14020.4i			0.792419i
$680$	19352.6			1.09138
$681$			8930.74i			0.502536i
$682$			13793.1i			0.774436i
$683$	12001.0			0.672333			0.336167	−	0.941803i	$-0.390869\pi$
$683$	12001.0			0.672333			0.336167	+	0.941803i	$0.390869\pi$
$684$	−9.63588			−0.000538651
$685$	11595.3			0.646766
$686$	−10767.2			−0.599261
$687$	−17305.4			−0.961052
$688$		−	3199.34i		−	0.177287i
$689$		−	8942.75i		−	0.494473i
$690$	−3289.32			−0.181482
$691$	−25827.7			−1.42190			−0.710949	−	0.703244i	$-0.751734\pi$
$691$	−25827.7			−1.42190			−0.710949	+	0.703244i	$0.751734\pi$
$692$		−	18123.0i		−	0.995570i
$693$	4071.75			0.223193
$694$		−	15473.5i		−	0.846350i
$695$			23636.7i			1.29006i
$696$	6592.89			0.359056
$697$			43305.9i			2.35341i
$698$	−12305.4			−0.667285
$699$		−	2391.12i		−	0.129386i
$700$		−	2456.44i		−	0.132635i
$701$		−	9300.39i		−	0.501100i	−0.968104	−	0.250550i	$-0.919389\pi$
$701$		−	9300.39i		−	0.501100i	0.968104	−	0.250550i	$-0.0806114\pi$
$702$			12947.1i			0.696092i
$703$		−	98.5579i		−	0.00528760i
$704$		−	11950.8i		−	0.639793i
$705$	−15356.7			−0.820376
$706$			13863.7i			0.739046i
$707$	6700.57			0.356437
$708$		−	20715.0i		−	1.09960i
$709$		−	22043.8i		−	1.16766i	−0.811876	−	0.583830i	$-0.801553\pi$
$709$		−	22043.8i		−	1.16766i	0.811876	−	0.583830i	$-0.198447\pi$
$710$	−810.964			−0.0428661
$711$			3715.67i			0.195990i
$712$	−16696.3			−0.878818
$713$	−6949.84			−0.365040
$714$		−	9805.72i		−	0.513963i
$715$			31188.7i			1.63132i
$716$	−5667.97			−0.295841
$717$	31738.8			1.65315
$718$	−13929.1			−0.723996
$719$	34095.1			1.76847			0.884236	−	0.467040i	$-0.154680\pi$
$719$	34095.1			1.76847			0.884236	+	0.467040i	$0.154680\pi$
$720$	−529.823			−0.0274241
$721$		−	2997.65i		−	0.154838i
$722$		−	10745.6i		−	0.553890i
$723$	19568.1			1.00657
$724$			1323.57i			0.0679419i
$725$		−	2071.73i		−	0.106127i
$726$			15385.4i			0.786511i
$727$	−3443.25			−0.175658			−0.0878289	−	0.996136i	$-0.527993\pi$
$727$	−3443.25			−0.175658			−0.0878289	+	0.996136i	$0.527993\pi$
$728$	−16529.6			−0.841523
$729$	21843.9			1.10979
$730$		−	1878.95i		−	0.0952643i
$731$	−27115.6			−1.37197
$732$	−2101.30	+	12234.5i	−0.106102	+	0.617760i
$733$	15742.8			0.793281			0.396641	−	0.917974i	$-0.370176\pi$
$733$	15742.8			0.793281			0.396641	+	0.917974i	$0.370176\pi$
$734$			14161.7i			0.712148i
$735$	−6508.65			−0.326633
$736$	8642.79			0.432850
$737$	1168.92			0.0584229
$738$			3545.49i			0.176844i
$739$			4056.35i			0.201915i	0.994891	+	0.100958i	$0.0321906\pi$
$739$			4056.35i			0.201915i	−0.994891	+	0.100958i	$0.967809\pi$
$740$		−	14990.3i		−	0.744666i
$741$	−91.3482			−0.00452869
$742$			3595.02i			0.177867i
$743$			8589.84i			0.424133i	0.977255	+	0.212066i	$0.0680193\pi$
$743$			8589.84i			0.424133i	−0.977255	+	0.212066i	$0.931981\pi$
$744$	−15008.4			−0.739561
$745$	−9863.15			−0.485044
$746$	−12251.1			−0.601266
$747$	211.112			0.0103403
$748$	30563.4			1.49399
$749$		−	15211.0i		−	0.742053i
$750$			11137.3i			0.542235i
$751$	4805.51			0.233496			0.116748	−	0.993162i	$-0.462753\pi$
$751$	4805.51			0.233496			0.116748	+	0.993162i	$0.462753\pi$
$752$	3754.51			0.182065
$753$		−	5675.08i		−	0.274650i
$754$	−5707.38			−0.275664
$755$		−	2391.91i		−	0.115299i
$756$			11759.7i			0.565733i
$757$	16085.8			0.772325			0.386162	−	0.922431i	$-0.373800\pi$
$757$	16085.8			0.772325			0.386162	+	0.922431i	$0.373800\pi$
$758$		−	18817.2i		−	0.901677i
$759$	−12688.8			−0.606815
$760$			72.4755i			0.00345916i
$761$			11922.7i			0.567934i	0.958834	+	0.283967i	$0.0916506\pi$
$761$			11922.7i			0.567934i	−0.958834	+	0.283967i	$0.908349\pi$
$762$			12625.9i			0.600245i
$763$			28428.3i			1.34885i
$764$		−	22227.4i		−	1.05257i
$765$			4490.46i			0.212226i
$766$	2199.69			0.103757
$767$			43802.3i			2.06207i
$768$	16346.9			0.768057
$769$		−	6194.49i		−	0.290480i	−0.989396	−	0.145240i	$-0.953605\pi$
$769$		−	6194.49i		−	0.290480i	0.989396	−	0.145240i	$-0.0463954\pi$
$770$		−	12538.0i		−	0.586803i
$771$	35285.6			1.64822
$772$			23658.8i			1.10298i
$773$	20699.6			0.963149			0.481575	−	0.876405i	$-0.340065\pi$
$773$	20699.6			0.963149			0.481575	+	0.876405i	$0.340065\pi$
$774$	−2219.98			−0.103095
$775$			4716.18i			0.218594i
$776$			21045.6i			0.973573i
$777$	−18552.4			−0.856581
$778$	−11637.4			−0.536272
$779$	−162.180			−0.00745919
$780$	−13893.7			−0.637787
$781$	−3128.35			−0.143330
$782$		−	6815.89i		−	0.311683i
$783$			9917.91i			0.452666i
$784$	1591.29			0.0724893
$785$		−	17953.3i		−	0.816283i
$786$			1853.13i			0.0840952i
$787$		−	35322.4i		−	1.59988i	−0.600078	−	0.799942i	$-0.704864\pi$
$787$		−	35322.4i		−	1.59988i	0.600078	−	0.799942i	$-0.295136\pi$
$788$	−457.360			−0.0206761
$789$	−288.179			−0.0130031
$790$	11441.6			0.515282
$791$			23764.1i			1.06821i
$792$	6111.99			0.274217
$793$	4443.27	−	25870.2i	0.198972	−	1.15848i
$794$	18288.9			0.817440
$795$			7380.88i			0.329274i
$796$	−11544.8			−0.514063
$797$	845.158			0.0375622			0.0187811	−	0.999824i	$-0.494021\pi$
$797$	845.158			0.0375622			0.0187811	+	0.999824i	$0.494021\pi$
$798$	36.7224			0.00162902
$799$		−	31821.0i		−	1.40894i
$800$		−	5865.02i		−	0.259200i
$801$		−	3874.09i		−	0.170892i
$802$	7418.10			0.326611
$803$		−	7248.15i		−	0.318533i
$804$			520.720i			0.0228412i
$805$	6317.45			0.276597
$806$	12992.6			0.567796
$807$	−23129.7			−1.00893
$808$	10058.0			0.437922
$809$	−25432.2			−1.10525			−0.552626	−	0.833429i	$-0.686374\pi$
$809$	−25432.2			−1.10525			−0.552626	+	0.833429i	$0.686374\pi$
$810$		−	8670.00i		−	0.376090i
$811$			6769.80i			0.293120i	0.989202	+	0.146560i	$0.0468201\pi$
$811$			6769.80i			0.293120i	−0.989202	+	0.146560i	$0.953180\pi$
$812$	−5183.93			−0.224040
$813$	−37007.8			−1.59646
$814$			25593.5i			1.10203i
$815$	−22153.5			−0.952151
$816$			4922.01i			0.211158i
$817$		−	101.548i		−	0.00434848i
$818$	−12468.1			−0.532929
$819$		−	3835.43i		−	0.163639i
$820$	−24667.0			−1.05050
$821$		−	44294.8i		−	1.88295i	−0.337089	−	0.941473i	$-0.609442\pi$
$821$		−	44294.8i		−	1.88295i	0.337089	−	0.941473i	$-0.390558\pi$
$822$		−	8819.10i		−	0.374211i
$823$		−	22262.8i		−	0.942933i	−0.881884	−	0.471466i	$-0.843725\pi$
$823$		−	22262.8i		−	0.942933i	0.881884	−	0.471466i	$-0.156275\pi$
$824$		−	4499.69i		−	0.190236i
$825$			8610.62i			0.363374i
$826$		−	17608.7i		−	0.741751i
$827$	−8728.30			−0.367005			−0.183502	−	0.983019i	$-0.558743\pi$
$827$	−8728.30			−0.367005			−0.183502	+	0.983019i	$0.558743\pi$
$828$			1260.79i			0.0529174i
$829$	−13930.0			−0.583605			−0.291803	−	0.956479i	$-0.594255\pi$
$829$	−13930.0			−0.583605			−0.291803	+	0.956479i	$0.594255\pi$
$830$		−	650.071i		−	0.0271859i
$831$			34014.4i			1.41991i
$832$	−11257.2			−0.469079
$833$		−	13486.8i		−	0.560971i
$834$	17977.4			0.746412
$835$	10095.5			0.418407
$836$			114.460i			0.00473525i
$837$		−	22577.6i		−	0.932373i
$838$	13050.1			0.537959
$839$	13633.1			0.560984			0.280492	−	0.959856i	$-0.409502\pi$
$839$	13633.1			0.560984			0.280492	+	0.959856i	$0.409502\pi$
$840$	13642.7			0.560378
$841$	20016.9			0.820737
$842$	−21194.6			−0.867474
$843$		−	17200.5i		−	0.702746i
$844$		−	2109.87i		−	0.0860482i
$845$	8115.53			0.330394
$846$		−	2605.21i		−	0.105873i
$847$		−	29549.2i		−	1.19873i
$848$		−	1804.53i		−	0.0730754i
$849$	−3807.98			−0.153933
$850$	−4625.28			−0.186642
$851$	−12895.7			−0.519456
$852$		−	1393.59i		−	0.0560370i
$853$	−33981.7			−1.36402			−0.682012	−	0.731341i	$-0.738895\pi$
$853$	−33981.7			−1.36402			−0.682012	+	0.731341i	$0.738895\pi$
$854$	−1786.21	+	10399.9i	−0.0715725	+	0.416719i
$855$	−16.8167			−0.000672656
$856$		−	22832.8i		−	0.911693i
$857$	2774.49			0.110589			0.0552945	−	0.998470i	$-0.482390\pi$
$857$	2774.49			0.110589			0.0552945	+	0.998470i	$0.482390\pi$
$858$	23721.3			0.943861
$859$	−25631.2			−1.01807			−0.509037	−	0.860744i	$-0.669999\pi$
$859$	−25631.2			−1.01807			−0.509037	+	0.860744i	$0.669999\pi$
$860$		−	15445.0i		−	0.612408i
$861$			30528.6i			1.20838i
$862$		−	15133.1i		−	0.597952i
$863$	−1333.79			−0.0526102			−0.0263051	−	0.999654i	$-0.508374\pi$
$863$	−1333.79			−0.0526102			−0.0263051	+	0.999654i	$0.508374\pi$
$864$			28077.4i			1.10557i
$865$		−	31628.7i		−	1.24325i
$866$	−1885.11			−0.0739705
$867$	18632.2			0.729854
$868$	11801.0			0.461464
$869$	44136.6			1.72293
$870$	4710.58			0.183567
$871$		−	1101.08i		−	0.0428341i
$872$			42673.0i			1.65721i
$873$	−4883.28			−0.189317
$874$	25.5255			0.000987886
$875$		−	21390.2i		−	0.826425i
$876$	3228.84			0.124535
$877$			47321.3i			1.82204i	0.412366	+	0.911018i	$0.364703\pi$
$877$			47321.3i			1.82204i	−0.412366	+	0.911018i	$0.635297\pi$
$878$		−	13667.6i		−	0.525350i
$879$	15246.1			0.585027
$880$			6293.50i			0.241084i
$881$	10405.9			0.397937			0.198968	−	0.980006i	$-0.436241\pi$
$881$	10405.9			0.397937			0.198968	+	0.980006i	$0.436241\pi$
$882$		−	1104.17i		−	0.0421535i
$883$			7822.47i			0.298128i	0.988828	+	0.149064i	$0.0476260\pi$
$883$			7822.47i			0.298128i	−0.988828	+	0.149064i	$0.952374\pi$
$884$		−	28789.5i		−	1.09536i
$885$		−	36152.2i		−	1.37315i
$886$			15220.1i			0.577122i
$887$			10387.6i			0.393216i	0.980482	+	0.196608i	$0.0629926\pi$
$887$			10387.6i			0.393216i	−0.980482	+	0.196608i	$0.937007\pi$
$888$	−27848.5			−1.05240
$889$		−	24249.2i		−	0.914838i
$890$	−11929.4			−0.449296
$891$		−	33445.1i		−	1.25752i
$892$			34232.5i			1.28497i
$893$	119.169			0.00446568
$894$			7501.64i			0.280640i
$895$	−9891.85			−0.369439
$896$	−16645.5			−0.620634
$897$			11952.3i			0.444901i
$898$		−	4907.14i		−	0.182353i
$899$	9952.75			0.369235
$900$	855.577			0.0316880
$901$	−15294.1			−0.565507
$902$	42115.0			1.55463
$903$	−19115.2			−0.704446
$904$			35671.7i			1.31241i
$905$			2309.91i			0.0848443i
$906$	−1819.22			−0.0667105
$907$			12753.4i			0.466891i	0.972370	+	0.233446i	$0.0750001\pi$
$907$			12753.4i			0.466891i	−0.972370	+	0.233446i	$0.925000\pi$
$908$		−	10540.8i		−	0.385251i
$909$			2333.80i			0.0851566i
$910$	−11810.3			−0.430229
$911$	−46480.0			−1.69040			−0.845198	−	0.534453i	$-0.820518\pi$
$911$	−46480.0			−1.69040			−0.845198	+	0.534453i	$0.820518\pi$
$912$	−18.4329			−0.000669270
$913$		−	2507.69i		−	0.0909007i
$914$	−10874.1			−0.393528
$915$	−3667.24	+	21351.9i	−0.132498	+	0.771445i
$916$	20425.3			0.736757
$917$		−	3559.10i		−	0.128170i
$918$	22142.5			0.796089
$919$	18650.1			0.669434			0.334717	−	0.942319i	$-0.391359\pi$
$919$	18650.1			0.669434			0.334717	+	0.942319i	$0.391359\pi$
$920$	9482.95			0.339830
$921$		−	5019.60i		−	0.179589i
$922$		−	12952.9i		−	0.462669i
$923$			2946.78i			0.105086i
$924$	21545.7			0.767102
$925$			8751.02i			0.311061i
$926$		−	2650.60i		−	0.0940650i
$927$	1044.08			0.0369925
$928$	−12377.2			−0.437824
$929$	19959.5			0.704899			0.352450	−	0.935831i	$-0.385349\pi$
$929$	19959.5			0.704899			0.352450	+	0.935831i	$0.385349\pi$
$930$	−10723.4			−0.378101
$931$	50.5078			0.00177801
$932$			2822.20i			0.0991889i
$933$		−	906.763i		−	0.0318179i
$934$	9829.70			0.344366
$935$	53339.8			1.86567
$936$		−	5757.25i		−	0.201049i
$937$	1782.45			0.0621454			0.0310727	−	0.999517i	$-0.490108\pi$
$937$	1782.45			0.0621454			0.0310727	+	0.999517i	$0.490108\pi$
$938$			442.637i			0.0154079i
$939$			25046.8i			0.870470i
$940$	18125.2			0.628913
$941$		−	8281.53i		−	0.286897i	−0.989658	−	0.143448i	$-0.954181\pi$
$941$		−	8281.53i		−	0.286897i	0.989658	−	0.143448i	$-0.0458191\pi$
$942$	−13654.8			−0.472291
$943$			21220.2i			0.732795i
$944$			8838.76i			0.304743i
$945$			20523.2i			0.706476i
$946$			26370.0i			0.906302i
$947$		−	35475.1i		−	1.21730i	−0.793438	−	0.608651i	$-0.791711\pi$
$947$		−	35475.1i		−	1.21730i	0.793438	−	0.608651i	$-0.208289\pi$
$948$			19661.6i			0.673605i
$949$	−6827.48			−0.233540
$950$		−	17.3216i		−	0.000591567i
$951$	1074.07			0.0366236
$952$			28269.4i			0.962412i
$953$			13456.6i			0.457399i	0.973497	+	0.228699i	$0.0734473\pi$
$953$			13456.6i			0.457399i	−0.973497	+	0.228699i	$0.926553\pi$
$954$	−1252.14			−0.0424944
$955$		−	38791.8i		−	1.31442i
$956$	−37460.7			−1.26733
$957$	18171.3			0.613789
$958$			11039.7i			0.372314i
$959$			16937.9i			0.570338i
$960$	9291.12			0.312364
$961$	7134.09			0.239471
$962$	24108.1			0.807980
$963$	5297.97			0.177284
$964$	−23095.9			−0.771648
$965$			41289.8i			1.37737i
$966$		−	4804.88i		−	0.160036i
$967$	10345.1			0.344029			0.172015	−	0.985094i	$-0.444972\pi$
$967$	10345.1			0.344029			0.172015	+	0.985094i	$0.444972\pi$
$968$		−	44355.5i		−	1.47277i
$969$			156.226i			0.00517926i
$970$			15036.9i			0.497739i
$971$	4263.77			0.140917			0.0704587	−	0.997515i	$-0.477554\pi$
$971$	4263.77			0.140917			0.0704587	+	0.997515i	$0.477554\pi$
$972$	−7559.99			−0.249472
$973$	−34527.4			−1.13761
$974$		−	23094.2i		−	0.759738i
$975$	8110.87			0.266416
$976$	896.595	−	5220.28i	0.0294050	−	0.171206i
$977$	−40607.0			−1.32972			−0.664859	−	0.746969i	$-0.731508\pi$
$977$	−40607.0			−1.32972			−0.664859	+	0.746969i	$0.731508\pi$
$978$			16849.3i			0.550902i
$979$	−46018.3			−1.50230
$980$	7682.04			0.250402
$981$	−9901.55			−0.322255
$982$			27287.5i			0.886739i
$983$			49479.8i			1.60545i	0.596348	+	0.802726i	$0.296618\pi$
$983$			49479.8i			1.60545i	−0.596348	+	0.802726i	$0.703382\pi$
$984$			45825.6i			1.48462i
$985$	−798.194			−0.0258199
$986$			9760.92i			0.315265i
$987$		−	22432.3i		−	0.723432i
$988$	107.817			0.00347176
$989$	−13286.9			−0.427197
$990$	4366.98			0.140194
$991$	20249.3			0.649083			0.324542	−	0.945871i	$-0.394790\pi$
$991$	20249.3			0.649083			0.324542	+	0.945871i	$0.394790\pi$
$992$	28176.0			0.901804
$993$			34319.9i			1.09679i
$994$		−	1184.62i		−	0.0378006i
$995$	−20148.2			−0.641950
$996$	1117.10			0.0355389
$997$		−	32871.7i		−	1.04419i	−0.852888	−	0.522094i	$-0.825151\pi$
$997$		−	32871.7i		−	1.04419i	0.852888	−	0.522094i	$-0.174849\pi$
$998$	12895.9			0.409030
$999$		−	41893.5i		−	1.32678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.4.b.a.60.9	yes	14
3.2	odd	2		549.4.c.c.487.6		14
4.3	odd	2		976.4.h.a.609.11		14
61.60	even	2	inner	61.4.b.a.60.6	✓	14
183.182	odd	2		549.4.c.c.487.9		14
244.243	odd	2		976.4.h.a.609.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.4.b.a.60.6	✓	14	61.60	even	2	inner
61.4.b.a.60.9	yes	14	1.1	even	1	trivial
549.4.c.c.487.6		14	3.2	odd	2
549.4.c.c.487.9		14	183.182	odd	2
976.4.h.a.609.11		14	4.3	odd	2
976.4.h.a.609.12		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)

\(f(q)\)	\(=\)	\(q+1.56667i q^{2} -4.69850 q^{3} +5.54555 q^{4} +9.67822 q^{5} -7.36099i q^{6} +14.1375i q^{7} +21.2214i q^{8} -4.92407 q^{9} +O(q^{10})\)	\(q+1.56667i q^{2} -4.69850 q^{3} +5.54555 q^{4} +9.67822 q^{5} -7.36099i q^{6} +14.1375i q^{7} +21.2214i q^{8} -4.92407 q^{9} +15.1625i q^{10} +58.4904i q^{11} -26.0558 q^{12} +55.0957 q^{13} -22.1487 q^{14} -45.4731 q^{15} +11.1176 q^{16} -94.2261i q^{17} -7.71437i q^{18} +0.352876 q^{19} +53.6711 q^{20} -66.4250i q^{21} -91.6350 q^{22} -46.1716i q^{23} -99.7087i q^{24} -31.3321 q^{25} +86.3166i q^{26} +149.995 q^{27} +78.4001i q^{28} +66.1215i q^{29} -71.2412i q^{30} -150.522i q^{31} +187.189i q^{32} -274.818i q^{33} +147.621 q^{34} +136.826i q^{35} -27.3067 q^{36} -279.299i q^{37} +0.552840i q^{38} -258.867 q^{39} +205.385i q^{40} -459.595 q^{41} +104.066 q^{42} -287.772i q^{43} +324.362i q^{44} -47.6562 q^{45} +72.3355 q^{46} +337.708 q^{47} -52.2362 q^{48} +143.132 q^{49} -49.0870i q^{50} +442.722i q^{51} +305.536 q^{52} -162.313i q^{53} +234.993i q^{54} +566.083i q^{55} -300.017 q^{56} -1.65799 q^{57} -103.590 q^{58} +795.023i q^{59} -252.174 q^{60} +(80.6463 - 469.550i) q^{61} +235.818 q^{62} -69.6139i q^{63} -204.321 q^{64} +533.228 q^{65} +430.548 q^{66} -19.9848i q^{67} -522.536i q^{68} +216.937i q^{69} -214.360 q^{70} +53.4847i q^{71} -104.495i q^{72} -123.920 q^{73} +437.568 q^{74} +147.214 q^{75} +1.95690 q^{76} -826.907 q^{77} -405.559i q^{78} -754.594i q^{79} +107.599 q^{80} -571.804 q^{81} -720.032i q^{82} -42.8735 q^{83} -368.363i q^{84} -911.941i q^{85} +450.842 q^{86} -310.672i q^{87} -1241.25 q^{88} +786.766i q^{89} -74.6614i q^{90} +778.914i q^{91} -256.047i q^{92} +707.229i q^{93} +529.077i q^{94} +3.41521 q^{95} -879.506i q^{96} +991.717 q^{97} +224.240i q^{98} -288.011i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9}+O(q^{10}) \) 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

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