LMFDB - Embedded newform 61.4.b.a.60.10

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			60.10
Root			$1.94645i$ of defining polynomial
Character	$\chi$	$=$	61.60
Dual form			61.4.b.a.60.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.94645i q^{2} -2.22484 q^{3} +4.21134 q^{4} -18.8131 q^{5} -4.33054i q^{6} +26.8280i q^{7} +23.7687i q^{8} -22.0501 q^{9} +O(q^{10})$	\(q+1.94645i q^{2} -2.22484 q^{3} +4.21134 q^{4} -18.8131 q^{5} -4.33054i q^{6} +26.8280i q^{7} +23.7687i q^{8} -22.0501 q^{9} -36.6188i q^{10} -41.1668i q^{11} -9.36956 q^{12} -17.5813 q^{13} -52.2192 q^{14} +41.8562 q^{15} -12.5739 q^{16} +117.663i q^{17} -42.9193i q^{18} +82.6063 q^{19} -79.2284 q^{20} -59.6880i q^{21} +80.1292 q^{22} -42.5687i q^{23} -52.8817i q^{24} +228.933 q^{25} -34.2211i q^{26} +109.129 q^{27} +112.982i q^{28} -0.654118i q^{29} +81.4710i q^{30} +92.9433i q^{31} +165.675i q^{32} +91.5898i q^{33} -229.024 q^{34} -504.717i q^{35} -92.8603 q^{36} +24.8498i q^{37} +160.789i q^{38} +39.1156 q^{39} -447.164i q^{40} +31.2050 q^{41} +116.180 q^{42} +271.529i q^{43} -173.368i q^{44} +414.831 q^{45} +82.8578 q^{46} -415.060 q^{47} +27.9750 q^{48} -376.739 q^{49} +445.607i q^{50} -261.781i q^{51} -74.0408 q^{52} -684.790i q^{53} +212.413i q^{54} +774.476i q^{55} -637.667 q^{56} -183.786 q^{57} +1.27321 q^{58} +579.185i q^{59} +176.271 q^{60} +(-459.978 - 124.103i) q^{61} -180.909 q^{62} -591.559i q^{63} -423.070 q^{64} +330.759 q^{65} -178.275 q^{66} +363.230i q^{67} +495.517i q^{68} +94.7086i q^{69} +982.406 q^{70} -243.725i q^{71} -524.103i q^{72} +1085.75 q^{73} -48.3689 q^{74} -509.340 q^{75} +347.883 q^{76} +1104.42 q^{77} +76.1365i q^{78} +248.994i q^{79} +236.555 q^{80} +352.558 q^{81} +60.7389i q^{82} -946.175 q^{83} -251.366i q^{84} -2213.60i q^{85} -528.518 q^{86} +1.45531i q^{87} +978.484 q^{88} +1316.75i q^{89} +807.446i q^{90} -471.670i q^{91} -179.271i q^{92} -206.784i q^{93} -807.893i q^{94} -1554.08 q^{95} -368.602i q^{96} -499.038 q^{97} -733.304i q^{98} +907.732i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.94645i			0.688174i	0.938938	+	0.344087i	$0.111811\pi$
$2$			1.94645i			0.688174i	−0.938938	+	0.344087i	$0.888189\pi$
$3$	−2.22484			−0.428171			−0.214086	−	0.976815i	$-0.568677\pi$
$3$	−2.22484			−0.428171			−0.214086	+	0.976815i	$0.568677\pi$
$4$	4.21134			0.526417
$5$	−18.8131			−1.68270			−0.841348	−	0.540494i	$-0.818237\pi$
$5$	−18.8131			−1.68270			−0.841348	+	0.540494i	$0.818237\pi$
$6$		−	4.33054i		−	0.294656i
$7$			26.8280i			1.44857i	0.689499	+	0.724287i	$0.257831\pi$
$7$			26.8280i			1.44857i	−0.689499	+	0.724287i	$0.742169\pi$
$8$			23.7687i			1.05044i
$9$	−22.0501			−0.816669
$10$		−	36.6188i		−	1.15799i
$11$		−	41.1668i		−	1.12839i	−0.825642	−	0.564194i	$-0.809187\pi$
$11$		−	41.1668i		−	1.12839i	0.825642	−	0.564194i	$-0.190813\pi$
$12$	−9.36956			−0.225397
$13$	−17.5813			−0.375090			−0.187545	−	0.982256i	$-0.560053\pi$
$13$	−17.5813			−0.375090			−0.187545	+	0.982256i	$0.560053\pi$
$14$	−52.2192			−0.996870
$15$	41.8562			0.720482
$16$	−12.5739			−0.196468
$17$			117.663i			1.67867i	0.543615	+	0.839335i	$0.317055\pi$
$17$			117.663i			1.67867i	−0.543615	+	0.839335i	$0.682945\pi$
$18$		−	42.9193i		−	0.562010i
$19$	82.6063			0.997431			0.498715	−	0.866766i	$-0.333805\pi$
$19$	82.6063			0.997431			0.498715	+	0.866766i	$0.333805\pi$
$20$	−79.2284			−0.885800
$21$		−	59.6880i		−	0.620238i
$22$	80.1292			0.776527
$23$		−	42.5687i		−	0.385921i	−0.981207	−	0.192961i	$-0.938191\pi$
$23$		−	42.5687i		−	0.385921i	0.981207	−	0.192961i	$-0.0618089\pi$
$24$		−	52.8817i		−	0.449768i
$25$	228.933			1.83147
$26$		−	34.2211i		−	0.258127i
$27$	109.129			0.777846
$28$			112.982i			0.762554i
$29$		−	0.654118i		−	0.00418850i	−0.999998	−	0.00209425i	$-0.999333\pi$
$29$		−	0.654118i		−	0.00418850i	0.999998	−	0.00209425i	$-0.000666621\pi$
$30$			81.4710i			0.495817i
$31$			92.9433i			0.538487i	0.963072	+	0.269244i	$0.0867737\pi$
$31$			92.9433i			0.538487i	−0.963072	+	0.269244i	$0.913226\pi$
$32$			165.675i			0.915236i
$33$			91.5898i			0.483143i
$34$	−229.024			−1.15522
$35$		−	504.717i		−	2.43751i
$36$	−92.8603			−0.429909
$37$			24.8498i			0.110413i	0.998475	+	0.0552065i	$0.0175817\pi$
$37$			24.8498i			0.110413i	−0.998475	+	0.0552065i	$0.982418\pi$
$38$			160.789i			0.686405i
$39$	39.1156			0.160603
$40$		−	447.164i		−	1.76757i
$41$	31.2050			0.118863			0.0594317	−	0.998232i	$-0.481071\pi$
$41$	31.2050			0.118863			0.0594317	+	0.998232i	$0.481071\pi$
$42$	116.180			0.426831
$43$			271.529i			0.962973i	0.876454	+	0.481486i	$0.159903\pi$
$43$			271.529i			0.962973i	−0.876454	+	0.481486i	$0.840097\pi$
$44$		−	173.368i		−	0.594003i
$45$	414.831			1.37421
$46$	82.8578			0.265581
$47$	−415.060			−1.28814			−0.644071	−	0.764965i	$-0.722756\pi$
$47$	−415.060			−1.28814			−0.644071	+	0.764965i	$0.722756\pi$
$48$	27.9750			0.0841218
$49$	−376.739			−1.09837
$50$			445.607i			1.26037i
$51$		−	261.781i		−	0.718758i
$52$	−74.0408			−0.197454
$53$		−	684.790i		−	1.77478i	−0.461023	−	0.887388i	$-0.652517\pi$
$53$		−	684.790i		−	1.77478i	0.461023	−	0.887388i	$-0.347483\pi$
$54$			212.413i			0.535293i
$55$			774.476i			1.89873i
$56$	−637.667			−1.52164
$57$	−183.786			−0.427071
$58$	1.27321			0.00288242
$59$			579.185i			1.27802i	0.769197	+	0.639012i	$0.220657\pi$
$59$			579.185i			1.27802i	−0.769197	+	0.639012i	$0.779343\pi$
$60$	176.271			0.379274
$61$	−459.978	−	124.103i	−0.965477	−	0.260488i
$61$	−459.978	−	124.103i	−0.965477	−	0.260488i
$62$	−180.909			−0.370573
$63$		−	591.559i		−	1.18301i
$64$	−423.070			−0.826309
$65$	330.759			0.631163
$66$	−178.275			−0.332486
$67$			363.230i			0.662323i	0.943574	+	0.331162i	$0.107441\pi$
$67$			363.230i			0.662323i	−0.943574	+	0.331162i	$0.892559\pi$
$68$			495.517i			0.883681i
$69$			94.7086i			0.165240i
$70$	982.406			1.67743
$71$		−	243.725i		−	0.407391i	−0.979034	−	0.203696i	$-0.934705\pi$
$71$		−	243.725i		−	0.407391i	0.979034	−	0.203696i	$-0.0652953\pi$
$72$		−	524.103i		−	0.857862i
$73$	1085.75			1.74079			0.870393	−	0.492358i	$-0.163865\pi$
$73$	1085.75			1.74079			0.870393	+	0.492358i	$0.163865\pi$
$74$	−48.3689			−0.0759833
$75$	−509.340			−0.784181
$76$	347.883			0.525065
$77$	1104.42			1.63455
$78$			76.1365i			0.110523i
$79$			248.994i			0.354608i	0.984156	+	0.177304i	$0.0567376\pi$
$79$			248.994i			0.354608i	−0.984156	+	0.177304i	$0.943262\pi$
$80$	236.555			0.330595
$81$	352.558			0.483618
$82$			60.7389i			0.0817986i
$83$	−946.175			−1.25128			−0.625640	−	0.780112i	$-0.715162\pi$
$83$	−946.175			−1.25128			−0.625640	+	0.780112i	$0.715162\pi$
$84$		−	251.366i		−	0.326504i
$85$		−	2213.60i		−	2.82469i
$86$	−528.518			−0.662692
$87$			1.45531i			0.00179340i
$88$	978.484			1.18530
$89$			1316.75i			1.56827i	0.620593	+	0.784133i	$0.286892\pi$
$89$			1316.75i			1.56827i	−0.620593	+	0.784133i	$0.713108\pi$
$90$			807.446i			0.945692i
$91$		−	471.670i		−	0.543346i
$92$		−	179.271i		−	0.203155i
$93$		−	206.784i		−	0.230565i
$94$		−	807.893i		−	0.886466i
$95$	−1554.08			−1.67837
$96$		−	368.602i		−	0.391878i
$97$	−499.038			−0.522368			−0.261184	−	0.965289i	$-0.584113\pi$
$97$	−499.038			−0.522368			−0.261184	+	0.965289i	$0.584113\pi$
$98$		−	733.304i		−	0.755866i
$99$			907.732i			0.921520i
$100$	964.115			0.964115
$101$			887.994i			0.874839i	0.899258	+	0.437419i	$0.144107\pi$
$101$			887.994i			0.874839i	−0.899258	+	0.437419i	$0.855893\pi$
$102$	509.543			0.494630
$103$	−807.562			−0.772538			−0.386269	−	0.922386i	$-0.626236\pi$
$103$	−807.562			−0.772538			−0.386269	+	0.922386i	$0.626236\pi$
$104$		−	417.885i		−	0.394010i
$105$			1122.92i			1.04367i
$106$	1332.91			1.22135
$107$	1998.76			1.80586			0.902932	−	0.429783i	$-0.141410\pi$
$107$	1998.76			1.80586			0.902932	+	0.429783i	$0.141410\pi$
$108$	459.578			0.409471
$109$	986.675			0.867031			0.433515	−	0.901146i	$-0.357273\pi$
$109$	986.675			0.867031			0.433515	+	0.901146i	$0.357273\pi$
$110$	−1507.48			−1.30666
$111$		−	55.2869i		−	0.0472757i
$112$		−	337.333i		−	0.284598i
$113$	−255.206			−0.212458			−0.106229	−	0.994342i	$-0.533878\pi$
$113$	−255.206			−0.212458			−0.106229	+	0.994342i	$0.533878\pi$
$114$		−	357.730i		−	0.293899i
$115$			800.849i			0.649388i
$116$		−	2.75471i		−	0.00220490i
$117$	387.669			0.306325
$118$	−1127.35			−0.879503
$119$	−3156.65			−2.43168
$120$			994.870i			0.756823i
$121$	−363.709			−0.273260
$122$	241.560	−	895.323i	0.179261	−	0.664416i
$123$	−69.4262			−0.0508939
$124$			391.416i			0.283469i
$125$	−1955.31			−1.39910
$126$	1151.44			0.814113
$127$	−268.179			−0.187378			−0.0936890	−	0.995602i	$-0.529866\pi$
$127$	−268.179			−0.187378			−0.0936890	+	0.995602i	$0.529866\pi$
$128$			501.919i			0.346592i
$129$		−	604.110i		−	0.412317i
$130$			643.805i			0.434350i
$131$	1275.71			0.850831			0.425416	−	0.904998i	$-0.360128\pi$
$131$	1275.71			0.850831			0.425416	+	0.904998i	$0.360128\pi$
$132$			385.715i			0.254335i
$133$			2216.16i			1.44485i
$134$	−707.009			−0.455793
$135$	−2053.05			−1.30888
$136$	−2796.69			−1.76334
$137$	1541.73			0.961452			0.480726	−	0.876871i	$-0.340373\pi$
$137$	1541.73			0.961452			0.480726	+	0.876871i	$0.340373\pi$
$138$	−184.345			−0.113714
$139$		−	2373.22i		−	1.44816i	−0.689718	−	0.724078i	$-0.742266\pi$
$139$		−	2373.22i		−	1.44816i	0.689718	−	0.724078i	$-0.257734\pi$
$140$		−	2125.54i		−	1.28315i
$141$	923.443			0.551546
$142$	474.397			0.280356
$143$			723.767i			0.423248i
$144$	277.256			0.160449
$145$			12.3060i			0.00704798i
$146$			2113.36i			1.19796i
$147$	838.186			0.470289
$148$			104.651i			0.0581233i
$149$	294.809			0.162092			0.0810460	−	0.996710i	$-0.474174\pi$
$149$	294.809			0.162092			0.0810460	+	0.996710i	$0.474174\pi$
$150$		−	991.405i		−	0.539652i
$151$		−	2279.83i		−	1.22867i	−0.789044	−	0.614336i	$-0.789424\pi$
$151$		−	2279.83i		−	1.22867i	0.789044	−	0.614336i	$-0.210576\pi$
$152$			1963.45i			1.04774i
$153$		−	2594.47i		−	1.37092i
$154$			2149.70i			1.12486i
$155$		−	1748.55i		−	0.906110i
$156$	164.729			0.0845441
$157$			446.224i			0.226831i	0.993548	+	0.113416i	$0.0361792\pi$
$157$			446.224i			0.226831i	−0.993548	+	0.113416i	$0.963821\pi$
$158$	−484.654			−0.244032
$159$			1523.55i			0.759908i
$160$		−	3116.87i		−	1.54006i
$161$	1142.03			0.559035
$162$			686.236i			0.332813i
$163$	−430.041			−0.206647			−0.103323	−	0.994648i	$-0.532948\pi$
$163$	−430.041			−0.206647			−0.103323	+	0.994648i	$0.532948\pi$
$164$	131.415			0.0625717
$165$		−	1723.09i		−	0.812983i
$166$		−	1841.68i		−	0.861097i
$167$	645.363			0.299040			0.149520	−	0.988759i	$-0.452227\pi$
$167$	645.363			0.299040			0.149520	+	0.988759i	$0.452227\pi$
$168$	1418.71			0.651522
$169$	−1887.90			−0.859307
$170$	4308.66			1.94388
$171$	−1821.47			−0.814571
$172$			1143.50i			0.506925i
$173$			2863.11i			1.25826i	0.777302	+	0.629128i	$0.216588\pi$
$173$			2863.11i			1.25826i	−0.777302	+	0.629128i	$0.783412\pi$
$174$	−2.83268			−0.00123417
$175$			6141.81i			2.65301i
$176$			517.629i			0.221692i
$177$		−	1288.60i		−	0.547213i
$178$	−2562.99			−1.07924
$179$	1556.78			0.650052			0.325026	−	0.945705i	$-0.394627\pi$
$179$	1556.78			0.650052			0.325026	+	0.945705i	$0.394627\pi$
$180$	1746.99			0.723406
$181$		−	3077.06i		−	1.26363i	−0.775121	−	0.631813i	$-0.782311\pi$
$181$		−	3077.06i		−	1.26363i	0.775121	−	0.631813i	$-0.217689\pi$
$182$	918.082			0.373916
$183$	1023.38	+	276.110i	0.413389	+	0.111533i
$184$	1011.80			0.405387
$185$		−	467.502i		−	0.185792i
$186$	402.495			0.158669
$187$	4843.80			1.89419
$188$	−1747.96			−0.678101
$189$			2927.70i			1.12677i
$190$		−	3024.94i		−	1.15501i
$191$		−	2216.08i		−	0.839530i	−0.907633	−	0.419765i	$-0.862112\pi$
$191$		−	2216.08i		−	0.839530i	0.907633	−	0.419765i	$-0.137888\pi$
$192$	941.265			0.353802
$193$			203.421i			0.0758680i	0.999280	+	0.0379340i	$0.0120777\pi$
$193$			203.421i			0.0758680i	−0.999280	+	0.0379340i	$0.987922\pi$
$194$		−	971.353i		−	0.359480i
$195$	−735.887			−0.270246
$196$	−1586.58			−0.578199
$197$	4568.01			1.65207			0.826033	−	0.563622i	$-0.190592\pi$
$197$	4568.01			1.65207			0.826033	+	0.563622i	$0.190592\pi$
$198$	−1766.85			−0.634166
$199$	−537.898			−0.191611			−0.0958055	−	0.995400i	$-0.530543\pi$
$199$	−537.898			−0.191611			−0.0958055	+	0.995400i	$0.530543\pi$
$200$			5441.45i			1.92384i
$201$		−	808.131i		−	0.283588i
$202$	−1728.43			−0.602041
$203$	17.5486			0.00606736
$204$		−	1102.45i		−	0.378367i
$205$	−587.063			−0.200011
$206$		−	1571.88i		−	0.531640i
$207$			938.643i			0.315170i
$208$	221.066			0.0736931
$209$		−	3400.64i		−	1.12549i
$210$	−2185.70			−0.718227
$211$			429.877i			0.140256i	0.997538	+	0.0701279i	$0.0223407\pi$
$211$			429.877i			0.140256i	−0.997538	+	0.0701279i	$0.977659\pi$
$212$		−	2883.88i		−	0.934273i
$213$			542.249i			0.174433i
$214$			3890.48i			1.24275i
$215$		−	5108.31i		−	1.62039i
$216$			2593.85i			0.817080i
$217$	−2493.48			−0.780039
$218$			1920.51i			0.596668i
$219$	−2415.62			−0.745354
$220$			3261.58i			0.999526i
$221$		−	2068.66i		−	0.629653i
$222$	107.613			0.0325339
$223$			4472.77i			1.34313i	0.740944	+	0.671566i	$0.234378\pi$
$223$			4472.77i			1.34313i	−0.740944	+	0.671566i	$0.765622\pi$
$224$	−4444.73			−1.32579
$225$	−5047.99			−1.49570
$226$		−	496.746i		−	0.146208i
$227$		−	198.031i		−	0.0579020i	−0.999581	−	0.0289510i	$-0.990783\pi$
$227$		−	198.031i		−	0.0579020i	0.999581	−	0.0289510i	$-0.00921668\pi$
$228$	−773.985			−0.224818
$229$	436.886			0.126071			0.0630355	−	0.998011i	$-0.479922\pi$
$229$	436.886			0.126071			0.0630355	+	0.998011i	$0.479922\pi$
$230$	−1558.81			−0.446891
$231$	−2457.17			−0.699869
$232$	15.5476			0.00439977
$233$		−	3700.94i		−	1.04059i	−0.853988	−	0.520293i	$-0.825823\pi$
$233$		−	3700.94i		−	1.04059i	0.853988	−	0.520293i	$-0.174177\pi$
$234$			754.578i			0.210805i
$235$	7808.57			2.16755
$236$			2439.14i			0.672774i
$237$		−	553.973i		−	0.151833i
$238$		−	6144.26i		−	1.67342i
$239$	−1793.35			−0.485364			−0.242682	−	0.970106i	$-0.578027\pi$
$239$	−1793.35			−0.485364			−0.242682	+	0.970106i	$0.578027\pi$
$240$	−526.297			−0.141551
$241$	4766.00			1.27388			0.636940	−	0.770913i	$-0.280200\pi$
$241$	4766.00			1.27388			0.636940	+	0.770913i	$0.280200\pi$
$242$		−	707.942i		−	0.188050i
$243$	−3730.86			−0.984917
$244$	−1937.12	−	522.640i	−0.508244	−	0.137125i
$245$	7087.64			1.84822
$246$		−	135.134i		−	0.0350238i
$247$	−1452.33			−0.374127
$248$	−2209.15			−0.565649
$249$	2105.09			0.535762
$250$		−	3805.90i		−	0.962826i
$251$			5991.18i			1.50661i	0.657670	+	0.753306i	$0.271542\pi$
$251$			5991.18i			1.50661i	−0.657670	+	0.753306i	$0.728458\pi$
$252$		−	2491.25i		−	0.622755i
$253$	−1752.42			−0.435469
$254$		−	521.996i		−	0.128949i
$255$			4924.91i			1.20945i
$256$	−4361.52			−1.06482
$257$	4718.54			1.14527			0.572635	−	0.819810i	$-0.305921\pi$
$257$	4718.54			1.14527			0.572635	+	0.819810i	$0.305921\pi$
$258$	1175.87			0.283746
$259$	−666.670			−0.159941
$260$	1392.94			0.332255
$261$			14.4233i			0.00342062i
$262$			2483.10i			0.585520i
$263$	−3932.95			−0.922115			−0.461058	−	0.887370i	$-0.652530\pi$
$263$	−3932.95			−0.922115			−0.461058	+	0.887370i	$0.652530\pi$
$264$	−2176.97			−0.507513
$265$			12883.0i			2.98641i
$266$	−4313.64			−0.994309
$267$		−	2929.57i		−	0.671486i
$268$			1529.69i			0.348658i
$269$	1631.56			0.369806			0.184903	−	0.982757i	$-0.440803\pi$
$269$	1631.56			0.369806			0.184903	+	0.982757i	$0.440803\pi$
$270$		−	3996.16i		−	0.900735i
$271$	2958.73			0.663210			0.331605	−	0.943418i	$-0.392410\pi$
$271$	2958.73			0.663210			0.331605	+	0.943418i	$0.392410\pi$
$272$		−	1479.48i		−	0.329804i
$273$			1049.39i			0.232645i
$274$			3000.90i			0.661646i
$275$		−	9424.46i		−	2.06660i
$276$			398.850i			0.0869853i
$277$			1774.62i			0.384932i	0.981304	+	0.192466i	$0.0616486\pi$
$277$			1774.62i			0.384932i	−0.981304	+	0.192466i	$0.938351\pi$
$278$	4619.35			0.996583
$279$		−	2049.41i		−	0.439766i
$280$	11996.5			2.56046
$281$			6500.11i			1.37994i	0.723837	+	0.689971i	$0.242377\pi$
$281$			6500.11i			1.37994i	−0.723837	+	0.689971i	$0.757623\pi$
$282$			1797.43i			0.379559i
$283$	−7697.10			−1.61677			−0.808383	−	0.588657i	$-0.799657\pi$
$283$	−7697.10			−1.61677			−0.808383	+	0.588657i	$0.799657\pi$
$284$		−	1026.41i		−	0.214458i
$285$	3457.59			0.718631
$286$	−1408.77			−0.291268
$287$			837.166i			0.172182i
$288$		−	3653.16i		−	0.747445i
$289$	−8931.50			−1.81793
$290$	−23.9530			−0.00485023
$291$	1110.28			0.223663
$292$	4572.46			0.916379
$293$	7962.81			1.58769			0.793844	−	0.608122i	$-0.208077\pi$
$293$	7962.81			1.58769			0.793844	+	0.608122i	$0.208077\pi$
$294$			1631.49i			0.323640i
$295$		−	10896.3i		−	2.15053i
$296$	−590.649			−0.115982
$297$		−	4492.48i		−	0.877712i
$298$			573.831i			0.111547i
$299$			748.413i			0.144755i
$300$	−2145.00			−0.412806
$301$	−7284.58			−1.39494
$302$	4437.56			0.845540
$303$		−	1975.65i		−	0.374581i
$304$	−1038.69			−0.195963
$305$	8653.61	+	2334.76i	1.62460	+	0.438322i
$306$	5050.00			0.943430
$307$		−	9376.22i		−	1.74309i	−0.490314	−	0.871546i	$-0.663118\pi$
$307$		−	9376.22i		−	1.74309i	0.490314	−	0.871546i	$-0.336882\pi$
$308$	4651.10			0.860457
$309$	1796.70			0.330779
$310$	3403.47			0.623561
$311$			4947.74i			0.902125i	0.892492	+	0.451062i	$0.148955\pi$
$311$			4947.74i			0.902125i	−0.892492	+	0.451062i	$0.851045\pi$
$312$			929.729i			0.168704i
$313$		−	8919.58i		−	1.61075i	−0.592766	−	0.805374i	$-0.701964\pi$
$313$		−	8919.58i		−	1.61075i	0.592766	−	0.805374i	$-0.298036\pi$
$314$	−868.552			−0.156099
$315$			11129.1i			1.99064i
$316$			1048.60i			0.186672i
$317$	−7545.20			−1.33685			−0.668423	−	0.743781i	$-0.733031\pi$
$317$	−7545.20			−1.33685			−0.668423	+	0.743781i	$0.733031\pi$
$318$	−2965.51			−0.522949
$319$	−26.9280			−0.00472626
$320$	7959.27			1.39043
$321$	−4446.93			−0.773219
$322$			2222.90i			0.384713i
$323$			9719.68i			1.67436i
$324$	1484.74			0.254585
$325$	−4024.94			−0.686965
$326$		−	837.053i		−	0.142209i
$327$	−2195.20			−0.371238
$328$			741.703i			0.124859i
$329$		−	11135.2i		−	1.86597i
$330$	3353.90			0.559474
$331$			5472.94i			0.908822i	0.890792	+	0.454411i	$0.150150\pi$
$331$			5472.94i			0.908822i	−0.890792	+	0.454411i	$0.849850\pi$
$332$	−3984.66			−0.658695
$333$		−	547.940i		−	0.0901710i
$334$			1256.17i			0.205791i
$335$		−	6833.50i		−	1.11449i
$336$			750.513i			0.121857i
$337$			2446.86i			0.395516i	0.980251	+	0.197758i	$0.0633660\pi$
$337$			2446.86i			0.395516i	−0.980251	+	0.197758i	$0.936634\pi$
$338$		−	3674.70i		−	0.591352i
$339$	567.794			0.0909686
$340$		−	9322.22i		−	1.48697i
$341$	3826.18			0.607623
$342$		−	3545.41i		−	0.560566i
$343$		−	905.160i		−	0.142490i
$344$	−6453.91			−1.01154
$345$		−	1781.76i		−	0.278049i
$346$	−5572.90			−0.865898
$347$	−6094.66			−0.942878			−0.471439	−	0.881899i	$-0.656265\pi$
$347$	−6094.66			−0.942878			−0.471439	+	0.881899i	$0.656265\pi$
$348$			6.12880i			0.000944075i
$349$			4728.06i			0.725179i	0.931949	+	0.362589i	$0.118107\pi$
$349$			4728.06i			0.725179i	−0.931949	+	0.362589i	$0.881893\pi$
$350$	−11954.7			−1.82573
$351$	−1918.62			−0.291762
$352$	6820.33			1.03274
$353$	2013.89			0.303650			0.151825	−	0.988407i	$-0.451485\pi$
$353$	2013.89			0.303650			0.151825	+	0.988407i	$0.451485\pi$
$354$	2508.18			0.376578
$355$			4585.22i			0.685516i
$356$			5545.30i			0.825562i
$357$	7023.05			1.04117
$358$			3030.19i			0.447348i
$359$			4997.77i			0.734741i	0.930075	+	0.367371i	$0.119742\pi$
$359$			4997.77i			0.734741i	−0.930075	+	0.367371i	$0.880258\pi$
$360$			9860.00i			1.44352i
$361$	−35.2013			−0.00513213
$362$	5989.35			0.869594
$363$	809.196			0.117002
$364$		−	1986.36i		−	0.286027i
$365$	−20426.3			−2.92921
$366$	−537.433	+	1991.95i	−0.0767543	+	0.284484i
$367$	−4786.61			−0.680815			−0.340407	−	0.940278i	$-0.610565\pi$
$367$	−4786.61			−0.680815			−0.340407	+	0.940278i	$0.610565\pi$
$368$			535.256i			0.0758210i
$369$	−688.072			−0.0970721
$370$	909.969			0.127857
$371$	18371.5			2.57089
$372$		−	870.838i		−	0.121373i
$373$			9895.37i			1.37363i	0.726834	+	0.686813i	$0.240991\pi$
$373$			9895.37i			1.37363i	−0.726834	+	0.686813i	$0.759009\pi$
$374$			9428.21i			1.30353i
$375$	4350.25			0.599056
$376$		−	9865.45i		−	1.35312i
$377$			11.5002i			0.00157107i
$378$	−5698.62			−0.775411
$379$	−852.186			−0.115498			−0.0577491	−	0.998331i	$-0.518392\pi$
$379$	−852.186			−0.115498			−0.0577491	+	0.998331i	$0.518392\pi$
$380$	−6544.76			−0.883524
$381$	596.656			0.0802299
$382$	4313.49			0.577742
$383$			5068.86i			0.676258i	0.941100	+	0.338129i	$0.109794\pi$
$383$			5068.86i			0.676258i	−0.941100	+	0.338129i	$0.890206\pi$
$384$		−	1116.69i		−	0.148401i
$385$	−20777.6			−2.75046
$386$	−395.948			−0.0522104
$387$		−	5987.24i		−	0.786430i
$388$	−2101.62			−0.274983
$389$		−	10409.2i		−	1.35672i	−0.734727	−	0.678362i	$-0.762690\pi$
$389$		−	10409.2i		−	1.35672i	0.734727	−	0.678362i	$-0.237310\pi$
$390$		−	1432.37i		−	0.185976i
$391$	5008.74			0.647834
$392$		−	8954.62i		−	1.15377i
$393$	−2838.24			−0.364301
$394$			8891.39i			1.13691i
$395$		−	4684.36i		−	0.596697i
$396$			3822.77i			0.485104i
$397$			1450.16i			0.183328i	0.995790	+	0.0916641i	$0.0292186\pi$
$397$			1450.16i			0.183328i	−0.995790	+	0.0916641i	$0.970781\pi$
$398$		−	1046.99i		−	0.131862i
$399$		−	4930.60i		−	0.618644i
$400$	−2878.59			−0.359824
$401$			1767.66i			0.220132i	0.993924	+	0.110066i	$0.0351061\pi$
$401$			1767.66i			0.220132i	−0.993924	+	0.110066i	$0.964894\pi$
$402$	1572.98			0.195158
$403$		−	1634.06i		−	0.201981i
$404$			3739.64i			0.460530i
$405$	−6632.71			−0.813783
$406$			34.1575i			0.00417539i
$407$	1022.99			0.124589
$408$	6222.20			0.755012
$409$		−	6878.13i		−	0.831545i	−0.909469	−	0.415772i	$-0.863511\pi$
$409$		−	6878.13i		−	0.831545i	0.909469	−	0.415772i	$-0.136489\pi$
$410$		−	1142.69i		−	0.137642i
$411$	−3430.11			−0.411666
$412$	−3400.92			−0.406677
$413$	−15538.3			−1.85131
$414$	−1827.02			−0.216892
$415$	17800.5			2.10552
$416$		−	2912.79i		−	0.343296i
$417$			5280.04i			0.620059i
$418$	6619.17			0.774532
$419$		−	7900.37i		−	0.921142i	−0.887623	−	0.460571i	$-0.847645\pi$
$419$		−	7900.37i		−	0.921142i	0.887623	−	0.460571i	$-0.152355\pi$
$420$			4728.98i			0.549406i
$421$		−	1873.85i		−	0.216926i	−0.994100	−	0.108463i	$-0.965407\pi$
$421$		−	1873.85i		−	0.216926i	0.994100	−	0.108463i	$-0.0345929\pi$
$422$	−836.734			−0.0965203
$423$	9152.10			1.05199
$424$	16276.6			1.86430
$425$			26936.9i			3.07443i
$426$	−1055.46			−0.120040
$427$	3329.43	−	12340.3i	0.377336	−	1.39856i
$428$	8417.46			0.950638
$429$		−	1610.27i		−	0.181222i
$430$	9943.06			1.11511
$431$	11511.8			1.28655			0.643277	−	0.765633i	$-0.277574\pi$
$431$	11511.8			1.28655			0.643277	+	0.765633i	$0.277574\pi$
$432$	−1372.18			−0.152821
$433$			4780.81i			0.530603i	0.964165	+	0.265302i	$0.0854716\pi$
$433$			4780.81i			0.530603i	−0.964165	+	0.265302i	$0.914528\pi$
$434$		−	4853.43i		−	0.536802i
$435$		−	27.3789i		−	0.00301774i
$436$	4155.22			0.456420
$437$		−	3516.44i		−	0.384929i
$438$		−	4701.88i		−	0.512933i
$439$	−6382.06			−0.693848			−0.346924	−	0.937893i	$-0.612774\pi$
$439$	−6382.06			−0.693848			−0.346924	+	0.937893i	$0.612774\pi$
$440$	−18408.3			−1.99451
$441$	8307.13			0.897002
$442$	4026.54			0.433310
$443$	7566.64			0.811516			0.405758	−	0.913980i	$-0.367008\pi$
$443$	7566.64			0.811516			0.405758	+	0.913980i	$0.367008\pi$
$444$		−	232.832i		−	0.0248867i
$445$		−	24772.2i		−	2.63891i
$446$	−8706.01			−0.924309
$447$	−655.904			−0.0694032
$448$		−	11350.1i		−	1.19697i
$449$	−8356.23			−0.878296			−0.439148	−	0.898415i	$-0.644720\pi$
$449$	−8356.23			−0.878296			−0.439148	+	0.898415i	$0.644720\pi$
$450$		−	9825.66i		−	1.02930i
$451$		−	1284.61i		−	0.134124i
$452$	−1074.76			−0.111842
$453$			5072.25i			0.526082i
$454$	385.456			0.0398466
$455$			8873.59i			0.914286i
$456$		−	4368.36i		−	0.448612i
$457$			7740.53i			0.792312i	0.918183	+	0.396156i	$0.129656\pi$
$457$			7740.53i			0.792312i	−0.918183	+	0.396156i	$0.870344\pi$
$458$			850.376i			0.0867587i
$459$			12840.4i			1.30575i
$460$			3372.65i			0.341849i
$461$	−3489.11			−0.352503			−0.176252	−	0.984345i	$-0.556397\pi$
$461$	−3489.11			−0.352503			−0.176252	+	0.984345i	$0.556397\pi$
$462$		−	4782.75i		−	0.481631i
$463$	−107.298			−0.0107701			−0.00538507	−	0.999986i	$-0.501714\pi$
$463$	−107.298			−0.0107701			−0.00538507	+	0.999986i	$0.501714\pi$
$464$			8.22483i			0.000822905i
$465$			3890.25i			0.387970i
$466$	7203.69			0.716104
$467$			2579.97i			0.255646i	0.991797	+	0.127823i	$0.0407989\pi$
$467$			2579.97i			0.255646i	−0.991797	+	0.127823i	$0.959201\pi$
$468$	1632.60			0.161255
$469$	−9744.73			−0.959424
$470$			15199.0i			1.49165i
$471$		−	992.778i		−	0.0971227i
$472$	−13766.5			−1.34249
$473$	11178.0			1.08661
$474$	1078.28			0.104487
$475$	18911.3			1.82676
$476$	−13293.7			−1.28008
$477$			15099.7i			1.44941i
$478$		−	3490.66i		−	0.334014i
$479$	3675.44			0.350595			0.175298	−	0.984515i	$-0.443911\pi$
$479$	3675.44			0.350595			0.175298	+	0.984515i	$0.443911\pi$
$480$			6934.55i			0.659411i
$481$		−	436.892i		−	0.0414149i
$482$			9276.78i			0.876651i
$483$	−2540.84			−0.239363
$484$	−1531.70			−0.143849
$485$	9388.46			0.878986
$486$		−	7261.93i		−	0.677794i
$487$	11758.6			1.09411			0.547055	−	0.837097i	$-0.315749\pi$
$487$	11758.6			1.09411			0.547055	+	0.837097i	$0.315749\pi$
$488$	2949.77	−	10933.1i	0.273627	−	1.01418i
$489$	956.773			0.0884801
$490$			13795.7i			1.27189i
$491$	−8460.89			−0.777667			−0.388834	−	0.921308i	$-0.627122\pi$
$491$	−8460.89			−0.777667			−0.388834	+	0.921308i	$0.627122\pi$
$492$	−292.377			−0.0267914
$493$	76.9652			0.00703111
$494$		−	2826.88i		−	0.257464i
$495$		−	17077.3i		−	1.55064i
$496$		−	1168.66i		−	0.105795i
$497$	6538.63			0.590136
$498$			4097.45i			0.368697i
$499$		−	5536.55i		−	0.496693i	−0.968671	−	0.248347i	$-0.920113\pi$
$499$		−	5536.55i		−	0.496693i	0.968671	−	0.248347i	$-0.0798872\pi$
$500$	−8234.45			−0.736512
$501$	−1435.83			−0.128040
$502$	−11661.5			−1.03681
$503$	−8397.57			−0.744392			−0.372196	−	0.928154i	$-0.621395\pi$
$503$	−8397.57			−0.744392			−0.372196	+	0.928154i	$0.621395\pi$
$504$	14060.6			1.24268
$505$		−	16705.9i		−	1.47209i
$506$		−	3410.99i		−	0.299678i
$507$	4200.28			0.367931
$508$	−1129.39			−0.0986391
$509$		−	4192.59i		−	0.365094i	−0.983197	−	0.182547i	$-0.941566\pi$
$509$		−	4192.59i		−	0.365094i	0.983197	−	0.182547i	$-0.0584342\pi$
$510$	−9586.09			−0.832312
$511$			29128.4i			2.52166i
$512$		−	4474.12i		−	0.386192i
$513$	9014.72			0.775847
$514$			9184.40i			0.788145i
$515$	15192.8			1.29995
$516$		−	2544.11i		−	0.217051i
$517$			17086.7i			1.45353i
$518$		−	1297.64i		−	0.110067i
$519$		−	6369.97i		−	0.538749i
$520$			7861.72i			0.662999i
$521$		−	14382.1i		−	1.20939i	−0.796459	−	0.604693i	$-0.793296\pi$
$521$		−	14382.1i		−	1.20939i	0.796459	−	0.604693i	$-0.206704\pi$
$522$	−28.0743			−0.00235398
$523$		−	9531.84i		−	0.796938i	−0.917182	−	0.398469i	$-0.869542\pi$
$523$		−	9531.84i		−	0.796938i	0.917182	−	0.398469i	$-0.130458\pi$
$524$	5372.43			0.447892
$525$		−	13664.6i		−	1.13594i
$526$		−	7655.29i		−	0.634575i
$527$	−10936.0			−0.903943
$528$		−	1151.64i		−	0.0949221i
$529$	10354.9			0.851065
$530$	−25076.2			−2.05517
$531$		−	12771.1i		−	1.04372i
$532$			9332.99i			0.760595i
$533$	−548.624			−0.0445845
$534$	5702.26			0.462099
$535$	−37602.9			−3.03872
$536$	−8633.53			−0.695731
$537$	−3463.59			−0.278333
$538$			3175.75i			0.254491i
$539$			15509.2i			1.23938i
$540$	−8646.09			−0.689016
$541$			7881.62i			0.626354i	0.949695	+	0.313177i	$0.101393\pi$
$541$			7881.62i			0.626354i	−0.949695	+	0.313177i	$0.898607\pi$
$542$			5759.01i			0.456404i
$543$			6845.98i			0.541048i
$544$	−19493.8			−1.53638
$545$	−18562.4			−1.45895
$546$	−2042.59			−0.160100
$547$		−	12526.1i		−	0.979119i	−0.871970	−	0.489559i	$-0.837158\pi$
$547$		−	12526.1i		−	0.979119i	0.871970	−	0.489559i	$-0.162842\pi$
$548$	6492.75			0.506125
$549$	10142.5	+	2736.48i	0.788476	+	0.212732i
$550$	18344.2			1.42218
$551$		−	54.0342i		−	0.00417774i
$552$	−2251.10			−0.173575
$553$	−6680.01			−0.513676
$554$	−3454.20			−0.264900
$555$			1040.12i			0.0795506i
$556$		−	9994.42i		−	0.762334i
$557$			17536.9i			1.33404i	0.745038	+	0.667022i	$0.232431\pi$
$557$			17536.9i			1.33404i	−0.745038	+	0.667022i	$0.767569\pi$
$558$	3989.06			0.302635
$559$		−	4773.84i		−	0.361202i
$560$			6346.28i			0.478892i
$561$	−10776.7			−0.811038
$562$	−12652.1			−0.949640
$563$	−4691.83			−0.351220			−0.175610	−	0.984460i	$-0.556190\pi$
$563$	−4691.83			−0.351220			−0.175610	+	0.984460i	$0.556190\pi$
$564$	3888.93			0.290343
$565$	4801.23			0.357503
$566$		−	14982.0i		−	1.11262i
$567$			9458.41i			0.700557i
$568$	5793.03			0.427940
$569$	4629.65			0.341098			0.170549	−	0.985349i	$-0.445446\pi$
$569$	4629.65			0.341098			0.170549	+	0.985349i	$0.445446\pi$
$570$			6730.01i			0.494543i
$571$	10644.3			0.780125			0.390063	−	0.920788i	$-0.372453\pi$
$571$	10644.3			0.780125			0.390063	+	0.920788i	$0.372453\pi$
$572$			3048.03i			0.222805i
$573$			4930.44i			0.359463i
$574$	−1629.50			−0.118491
$575$		−	9745.38i		−	0.706801i
$576$	9328.73			0.674821
$577$		−	9343.78i		−	0.674153i	−0.941477	−	0.337077i	$-0.890562\pi$
$577$		−	9343.78i		−	0.674153i	0.941477	−	0.337077i	$-0.109438\pi$
$578$		−	17384.7i		−	1.25105i
$579$		−	452.579i		−	0.0324845i
$580$			51.8247i			0.00371018i
$581$		−	25383.9i		−	1.81257i
$582$			2161.11i			0.153919i
$583$	−28190.7			−2.00264
$584$			25806.9i			1.82859i
$585$	−7293.26			−0.515451
$586$			15499.2i			1.09260i
$587$		−	709.791i		−	0.0499084i	−0.999689	−	0.0249542i	$-0.992056\pi$
$587$		−	709.791i		−	0.0499084i	0.999689	−	0.0249542i	$-0.00794399\pi$
$588$	3529.88			0.247568
$589$			7677.70i			0.537104i
$590$	21209.0			1.47994
$591$	−10163.1			−0.707367
$592$		−	312.460i		−	0.0216926i
$593$			1216.65i			0.0842529i	0.999112	+	0.0421264i	$0.0134132\pi$
$593$			1216.65i			0.0842529i	−0.999112	+	0.0421264i	$0.986587\pi$
$594$	8744.39			0.604018
$595$	59386.4			4.09177
$596$	1241.54			0.0853281
$597$	1196.74			0.0820423
$598$	−1456.75			−0.0996167
$599$		−	14979.7i		−	1.02179i	−0.859643	−	0.510895i	$-0.829314\pi$
$599$		−	14979.7i		−	1.02179i	0.859643	−	0.510895i	$-0.170686\pi$
$600$		−	12106.4i		−	0.823735i
$601$	23145.0			1.57089			0.785444	−	0.618933i	$-0.212435\pi$
$601$	23145.0			1.57089			0.785444	+	0.618933i	$0.212435\pi$
$602$		−	14179.1i		−	0.959959i
$603$		−	8009.26i		−	0.540899i
$604$		−	9601.11i		−	0.646794i
$605$	6842.50			0.459814
$606$	3845.50			0.257777
$607$	−12482.5			−0.834676			−0.417338	−	0.908751i	$-0.637037\pi$
$607$	−12482.5			−0.834676			−0.417338	+	0.908751i	$0.637037\pi$
$608$			13685.8i			0.912884i
$609$	−39.0430			−0.00259787
$610$	−4544.50	+	16843.8i	−0.301642	+	1.11801i
$611$	7297.29			0.483170
$612$		−	10926.2i		−	0.721675i
$613$	11371.7			0.749264			0.374632	−	0.927174i	$-0.377769\pi$
$613$	11371.7			0.749264			0.374632	+	0.927174i	$0.377769\pi$
$614$	18250.3			1.19955
$615$	1306.12			0.0856389
$616$			26250.7i			1.71700i
$617$			21202.5i			1.38344i	0.722168	+	0.691718i	$0.243146\pi$
$617$			21202.5i			1.38344i	−0.722168	+	0.691718i	$0.756854\pi$
$618$			3497.18i			0.227633i
$619$	8767.48			0.569297			0.284648	−	0.958632i	$-0.408123\pi$
$619$	8767.48			0.569297			0.284648	+	0.958632i	$0.408123\pi$
$620$		−	7363.75i		−	0.476992i
$621$		−	4645.47i		−	0.300187i
$622$	−9630.53			−0.620818
$623$	−35325.8			−2.27175
$624$	−491.837			−0.0315533
$625$	8168.74			0.522800
$626$	17361.5			1.10847
$627$			7565.89i			0.481902i
$628$			1879.20i			0.119408i
$629$	−2923.89			−0.185347
$630$	−21662.1			−1.36991
$631$			16112.9i			1.01655i	0.861194	+	0.508276i	$0.169717\pi$
$631$			16112.9i			1.01655i	−0.861194	+	0.508276i	$0.830283\pi$
$632$	−5918.28			−0.372494
$633$		−	956.409i		−	0.0600535i
$634$		−	14686.3i		−	0.919983i
$635$	5045.28			0.315300
$636$			6416.19i			0.400029i
$637$	6623.57			0.411986
$638$		−	52.4139i		−	0.00325249i
$639$			5374.15i			0.332704i
$640$		−	9442.66i		−	0.583209i
$641$			18734.3i			1.15438i	0.816609	+	0.577191i	$0.195851\pi$
$641$			18734.3i			1.15438i	−0.816609	+	0.577191i	$0.804149\pi$
$642$		−	8655.72i		−	0.532109i
$643$		−	6.59556i		−	0.000404516i	−1.00000		0.000202258i	$-0.999936\pi$
$643$		−	6.59556i		−	0.000404516i	1.00000		0.000202258i	$-6.43807e-5\pi$
$644$	4809.48			0.294286
$645$			11365.2i			0.693804i
$646$	−18918.8			−1.15225
$647$		−	17963.6i		−	1.09153i	−0.837938	−	0.545766i	$-0.816239\pi$
$647$		−	17963.6i		−	1.09153i	0.837938	−	0.545766i	$-0.183761\pi$
$648$			8379.86i			0.508012i
$649$	23843.2			1.44211
$650$		−	7834.34i		−	0.472751i
$651$	5547.60			0.333990
$652$	−1811.05			−0.108782
$653$		−	5993.95i		−	0.359206i	−0.983739	−	0.179603i	$-0.942519\pi$
$653$		−	5993.95i		−	0.359206i	0.983739	−	0.179603i	$-0.0574813\pi$
$654$		−	4272.84i		−	0.255476i
$655$	−24000.0			−1.43169
$656$	−392.369			−0.0233528
$657$	−23940.9			−1.42165
$658$	21674.1			1.28411
$659$	−14506.7			−0.857512			−0.428756	−	0.903420i	$-0.641048\pi$
$659$	−14506.7			−0.857512			−0.428756	+	0.903420i	$0.641048\pi$
$660$		−	7256.51i		−	0.427968i
$661$		−	18092.3i		−	1.06462i	−0.846551	−	0.532308i	$-0.821325\pi$
$661$		−	18092.3i		−	1.06462i	0.846551	−	0.532308i	$-0.178675\pi$
$662$	−10652.8			−0.625427
$663$			4602.45i			0.269599i
$664$		−	22489.4i		−	1.31439i
$665$		−	41692.8i		−	2.43125i
$666$	1066.54			0.0620533
$667$	−27.8449			−0.00161643
$668$	2717.84			0.157420
$669$		−	9951.20i		−	0.575091i
$670$	13301.0			0.766962
$671$	−5108.93	+	18935.8i	−0.293931	+	1.08943i
$672$	9888.83			0.567664
$673$			19903.7i			1.14002i	0.821639	+	0.570008i	$0.193060\pi$
$673$			19903.7i			1.14002i	−0.821639	+	0.570008i	$0.806940\pi$
$674$	−4762.68			−0.272183
$675$	24983.2			1.42460
$676$	−7950.58			−0.452354
$677$		−	27101.0i		−	1.53852i	−0.638936	−	0.769260i	$-0.720625\pi$
$677$		−	27101.0i		−	1.53852i	0.638936	−	0.769260i	$-0.279375\pi$
$678$			1105.18i			0.0626022i
$679$		−	13388.2i		−	0.756688i
$680$	52614.5			2.96717
$681$			440.587i			0.0247920i
$682$			7447.47i			0.418150i
$683$	24959.7			1.39832			0.699162	−	0.714963i	$-0.253557\pi$
$683$	24959.7			1.39832			0.699162	+	0.714963i	$0.253557\pi$
$684$	−7670.85			−0.428804
$685$	−29004.7			−1.61783
$686$	1761.85			0.0980578
$687$	−972.003			−0.0539799
$688$		−	3414.19i		−	0.189193i
$689$			12039.5i			0.665702i
$690$	3468.11			0.191346
$691$	20934.6			1.15252			0.576258	−	0.817268i	$-0.304512\pi$
$691$	20934.6			1.15252			0.576258	+	0.817268i	$0.304512\pi$
$692$			12057.5i			0.662367i
$693$	−24352.6			−1.33489
$694$		−	11862.9i		−	0.648863i
$695$			44647.6i			2.43681i
$696$	−34.5909			−0.00188386
$697$			3671.66i			0.199532i
$698$	−9202.93			−0.499049
$699$			8234.01i			0.445549i
$700$			25865.2i			1.39659i
$701$		−	15683.5i		−	0.845018i	−0.906359	−	0.422509i	$-0.861150\pi$
$701$		−	15683.5i		−	0.845018i	0.906359	−	0.422509i	$-0.138850\pi$
$702$		−	3734.50i		−	0.200783i
$703$			2052.75i			0.110129i
$704$			17416.5i			0.932397i
$705$	−17372.8			−0.928084
$706$			3919.93i			0.208964i
$707$	−23823.1			−1.26727
$708$		−	5426.71i		−	0.288062i
$709$			13891.4i			0.735828i	0.929860	+	0.367914i	$0.119928\pi$
$709$			13891.4i			0.735828i	−0.929860	+	0.367914i	$0.880072\pi$
$710$	−8924.89			−0.471754
$711$		−	5490.34i		−	0.289598i
$712$	−31297.6			−1.64737
$713$	3956.47			0.207814
$714$			13670.0i			0.716508i
$715$		−	13616.3i		−	0.712197i
$716$	6556.13			0.342199
$717$	3989.91			0.207819
$718$	−9727.90			−0.505629
$719$	26701.0			1.38495			0.692475	−	0.721442i	$-0.256520\pi$
$719$	26701.0			1.38495			0.692475	+	0.721442i	$0.256520\pi$
$720$	−5216.05			−0.269987
$721$		−	21665.2i		−	1.11908i
$722$		−	68.5175i		−	0.00353180i
$723$	−10603.6			−0.545439
$724$		−	12958.6i		−	0.665195i
$725$		−	149.749i		−	0.00767110i
$726$			1575.06i			0.0805178i
$727$	−36523.4			−1.86324			−0.931620	−	0.363433i	$-0.881605\pi$
$727$	−36523.4			−1.86324			−0.931620	+	0.363433i	$0.881605\pi$
$728$	11211.0			0.570752
$729$	−1218.48			−0.0619053
$730$		−	39758.8i		−	2.01581i
$731$	−31948.9			−1.61651
$732$	4309.79	+	1162.79i	0.217615	+	0.0587131i
$733$	−19349.7			−0.975031			−0.487515	−	0.873114i	$-0.662097\pi$
$733$	−19349.7			−0.975031			−0.487515	+	0.873114i	$0.662097\pi$
$734$		−	9316.89i		−	0.468519i
$735$	−15768.9			−0.791353
$736$	7052.58			0.353209
$737$	14953.1			0.747358
$738$		−	1339.30i		−	0.0668025i
$739$		−	27872.9i		−	1.38744i	−0.720243	−	0.693722i	$-0.755970\pi$
$739$		−	27872.9i		−	1.38744i	0.720243	−	0.693722i	$-0.244030\pi$
$740$		−	1968.81i		−	0.0978039i
$741$	3231.20			0.160190
$742$			35759.2i			1.76922i
$743$			8058.01i			0.397873i	0.980012	+	0.198937i	$0.0637488\pi$
$743$			8058.01i			0.397873i	−0.980012	+	0.198937i	$0.936251\pi$
$744$	4915.00			0.242194
$745$	−5546.28			−0.272752
$746$	−19260.8			−0.945293
$747$	20863.2			1.02188
$748$	20398.9			0.997135
$749$			53622.7i			2.61593i
$750$			8467.53i			0.412254i
$751$	−34051.8			−1.65455			−0.827276	−	0.561796i	$-0.810111\pi$
$751$	−34051.8			−1.65455			−0.827276	+	0.561796i	$0.810111\pi$
$752$	5218.94			0.253078
$753$		−	13329.4i		−	0.645088i
$754$	−22.3846			−0.00108117
$755$			42890.6i			2.06748i
$756$			12329.5i			0.593149i
$757$	−1411.58			−0.0677737			−0.0338868	−	0.999426i	$-0.510789\pi$
$757$	−1411.58			−0.0677737			−0.0338868	+	0.999426i	$0.510789\pi$
$758$		−	1658.74i		−	0.0794828i
$759$	3898.86			0.186455
$760$		−	36938.6i		−	1.76303i
$761$		−	9031.77i		−	0.430225i	−0.976589	−	0.215113i	$-0.930988\pi$
$761$		−	9031.77i		−	0.430225i	0.976589	−	0.215113i	$-0.0690118\pi$
$762$			1161.36i			0.0552121i
$763$			26470.5i			1.25596i
$764$		−	9332.68i		−	0.441943i
$765$			48810.1i			2.30684i
$766$	−9866.28			−0.465383
$767$		−	10182.8i		−	0.479375i
$768$	9703.70			0.455927
$769$			21170.1i			0.992737i	0.868112	+	0.496368i	$0.165333\pi$
$769$			21170.1i			0.992737i	−0.868112	+	0.496368i	$0.834667\pi$
$770$		−	40442.6i		−	1.89279i
$771$	−10498.0			−0.490372
$772$			856.672i			0.0399382i
$773$	28917.1			1.34550			0.672752	−	0.739868i	$-0.265112\pi$
$773$	28917.1			1.34550			0.672752	+	0.739868i	$0.265112\pi$
$774$	11653.9			0.541200
$775$			21277.8i			0.986221i
$776$		−	11861.5i		−	0.548716i
$777$	1483.24			0.0684823
$778$	20260.9			0.933662
$779$	2577.73			0.118558
$780$	−3099.07			−0.142262
$781$	−10033.4			−0.459696
$782$			9749.26i			0.445822i
$783$		−	71.3830i		−	0.00325801i
$784$	4737.10			0.215793
$785$		−	8394.86i		−	0.381688i
$786$		−	5524.50i		−	0.250703i
$787$			30019.7i			1.35970i	0.733349	+	0.679852i	$0.237956\pi$
$787$			30019.7i			1.35970i	−0.733349	+	0.679852i	$0.762044\pi$
$788$	19237.4			0.869676
$789$	8750.20			0.394823
$790$	9117.86			0.410631
$791$		−	6846.67i		−	0.307762i
$792$	−21575.6			−0.968002
$793$	8087.00	+	2181.89i	0.362141	+	0.0977065i
$794$	−2822.66			−0.126162
$795$		−	28662.7i		−	1.27869i
$796$	−2265.27			−0.100867
$797$	4393.97			0.195285			0.0976426	−	0.995222i	$-0.468870\pi$
$797$	4393.97			0.195285			0.0976426	+	0.995222i	$0.468870\pi$
$798$	9597.17			0.425734
$799$		−	48837.1i		−	2.16237i
$800$			37928.6i			1.67622i
$801$		−	29034.5i		−	1.28075i
$802$	−3440.66			−0.151489
$803$		−	44696.9i		−	1.96428i
$804$		−	3403.31i		−	0.149285i
$805$	−21485.2			−0.940686
$806$	3180.62			0.138998
$807$	−3629.96			−0.158340
$808$	−21106.5			−0.918965
$809$	17776.3			0.772535			0.386267	−	0.922387i	$-0.373764\pi$
$809$	17776.3			0.772535			0.386267	+	0.922387i	$0.373764\pi$
$810$		−	12910.2i		−	0.560024i
$811$			1827.67i			0.0791348i	0.999217	+	0.0395674i	$0.0125980\pi$
$811$			1827.67i			0.0791348i	−0.999217	+	0.0395674i	$0.987402\pi$
$812$	73.9033			0.00319396
$813$	−6582.71			−0.283968
$814$			1991.19i			0.0857387i
$815$	8090.41			0.347723
$816$			3291.62i			0.141213i
$817$			22430.0i			0.960498i
$818$	13387.9			0.572247
$819$			10400.4i			0.443734i
$820$	−2472.32			−0.105289
$821$		−	27664.2i		−	1.17599i	−0.808866	−	0.587994i	$-0.799918\pi$
$821$		−	27664.2i		−	1.17599i	0.808866	−	0.587994i	$-0.200082\pi$
$822$		−	6676.53i		−	0.283298i
$823$			34905.7i			1.47842i	0.673476	+	0.739209i	$0.264800\pi$
$823$			34905.7i			1.47842i	−0.673476	+	0.739209i	$0.735200\pi$
$824$		−	19194.7i		−	0.811505i
$825$			20967.9i			0.884860i
$826$		−	30244.6i		−	1.27402i
$827$	−4865.75			−0.204593			−0.102297	−	0.994754i	$-0.532619\pi$
$827$	−4865.75			−0.204593			−0.102297	+	0.994754i	$0.532619\pi$
$828$			3952.94i			0.165911i
$829$	7536.40			0.315742			0.157871	−	0.987460i	$-0.449537\pi$
$829$	7536.40			0.315742			0.157871	+	0.987460i	$0.449537\pi$
$830$			34647.7i			1.44896i
$831$		−	3948.24i		−	0.164817i
$832$	7438.12			0.309940
$833$		−	44328.2i		−	1.84379i
$834$	−10277.3			−0.426708
$835$	−12141.3			−0.503193
$836$		−	14321.2i		−	0.592477i
$837$			10142.8i			0.418860i
$838$	15377.7			0.633905
$839$	−6573.44			−0.270489			−0.135245	−	0.990812i	$-0.543182\pi$
$839$	−6573.44			−0.270489			−0.135245	+	0.990812i	$0.543182\pi$
$840$	−26690.3			−1.09631
$841$	24388.6			0.999982
$842$	3647.36			0.149283
$843$		−	14461.7i		−	0.590852i
$844$			1810.36i			0.0738330i
$845$	35517.2			1.44595
$846$			17814.1i			0.723950i
$847$		−	9757.58i		−	0.395838i
$848$			8610.50i			0.348686i
$849$	17124.8			0.692253
$850$	−52431.3			−2.11574
$851$	1057.82			0.0426107
$852$			2283.59i			0.0918247i
$853$	17013.9			0.682936			0.341468	−	0.939893i	$-0.389076\pi$
$853$	17013.9			0.682936			0.341468	+	0.939893i	$0.389076\pi$
$854$	24019.7	+	6480.57i	0.962455	+	0.259673i
$855$	34267.6			1.37068
$856$			47508.0i			1.89695i
$857$	−23708.9			−0.945019			−0.472509	−	0.881326i	$-0.656652\pi$
$857$	−23708.9			−0.945019			−0.472509	+	0.881326i	$0.656652\pi$
$858$	3134.30			0.124712
$859$	25978.5			1.03187			0.515934	−	0.856628i	$-0.327445\pi$
$859$	25978.5			1.03187			0.515934	+	0.856628i	$0.327445\pi$
$860$		−	21512.8i		−	0.853001i
$861$		−	1862.56i		−	0.0737235i
$862$			22407.2i			0.885373i
$863$	11228.2			0.442889			0.221444	−	0.975173i	$-0.428923\pi$
$863$	11228.2			0.442889			0.221444	+	0.975173i	$0.428923\pi$
$864$			18079.9i			0.711912i
$865$		−	53864.0i		−	2.11726i
$866$	−9305.61			−0.365147
$867$	19871.2			0.778386
$868$	−10500.9			−0.410626
$869$	10250.3			0.400136
$870$	53.2916			0.00207673
$871$		−	6386.06i		−	0.248431i
$872$			23452.0i			0.910764i
$873$	11003.8			0.426602
$874$	6844.57			0.264898
$875$		−	52456.9i		−	2.02670i
$876$	−10173.0			−0.392367
$877$		−	47930.5i		−	1.84550i	−0.385405	−	0.922748i	$-0.625938\pi$
$877$		−	47930.5i		−	1.84550i	0.385405	−	0.922748i	$-0.374062\pi$
$878$		−	12422.4i		−	0.477488i
$879$	−17716.0			−0.679802
$880$		−	9738.21i		−	0.373040i
$881$	26236.9			1.00334			0.501670	−	0.865059i	$-0.332719\pi$
$881$	26236.9			1.00334			0.501670	+	0.865059i	$0.332719\pi$
$882$			16169.4i			0.617293i
$883$			14795.1i			0.563868i	0.959434	+	0.281934i	$0.0909760\pi$
$883$			14795.1i			0.563868i	−0.959434	+	0.281934i	$0.909024\pi$
$884$		−	8711.84i		−	0.331460i
$885$			24242.5i			0.920793i
$886$			14728.1i			0.558464i
$887$			34712.4i			1.31401i	0.753886	+	0.657005i	$0.228177\pi$
$887$			34712.4i			1.31401i	−0.753886	+	0.657005i	$0.771823\pi$
$888$	1314.10			0.0496603
$889$		−	7194.69i		−	0.271431i
$890$	48217.9			1.81603
$891$		−	14513.7i		−	0.545709i
$892$			18836.3i			0.707048i
$893$	−34286.6			−1.28483
$894$		−	1276.68i		−	0.0477614i
$895$	−29287.9			−1.09384
$896$	−13465.5			−0.502064
$897$		−	1665.10i		−	0.0619800i
$898$		−	16265.0i		−	0.604420i
$899$	60.7958			0.00225546
$900$	−21258.8			−0.787363
$901$	80574.2			2.97926
$902$	2500.43			0.0923006
$903$	16207.0			0.597272
$904$		−	6065.94i		−	0.223175i
$905$			57889.2i			2.12630i
$906$	−9872.88			−0.362036
$907$		−	15528.2i		−	0.568473i	−0.958754	−	0.284236i	$-0.908260\pi$
$907$		−	15528.2i		−	0.568473i	0.958754	−	0.284236i	$-0.0917401\pi$
$908$		−	833.974i		−	0.0304806i
$909$		−	19580.3i		−	0.714454i
$910$	−17272.0			−0.629187
$911$	9430.12			0.342957			0.171478	−	0.985188i	$-0.445146\pi$
$911$	9430.12			0.342957			0.171478	+	0.985188i	$0.445146\pi$
$912$	2310.91			0.0839057
$913$			38951.0i			1.41193i
$914$	−15066.5			−0.545248
$915$	−19252.9	−	5194.48i	−0.695609	−	0.187677i
$916$	1839.87			0.0663659
$917$			34224.6i			1.23249i
$918$	−24993.1			−0.898580
$919$	−27656.1			−0.992701			−0.496350	−	0.868122i	$-0.665327\pi$
$919$	−27656.1			−0.992701			−0.496350	+	0.868122i	$0.665327\pi$
$920$	−19035.2			−0.682143
$921$			20860.6i			0.746342i
$922$		−	6791.37i		−	0.242583i
$923$			4284.99i			0.152809i
$924$	−10348.0			−0.368423
$925$			5688.94i			0.202218i
$926$		−	208.851i		−	0.00741172i
$927$	17806.8			0.630908
$928$	108.371			0.00383347
$929$	13166.4			0.464988			0.232494	−	0.972598i	$-0.425311\pi$
$929$	13166.4			0.464988			0.232494	+	0.972598i	$0.425311\pi$
$930$	−7572.18			−0.266991
$931$	−31121.0			−1.09554
$932$		−	15585.9i		−	0.547782i
$933$		−	11007.9i		−	0.386264i
$934$	−5021.77			−0.175929
$935$	−91127.0			−3.18735
$936$			9214.40i			0.321776i
$937$	−24625.6			−0.858572			−0.429286	−	0.903169i	$-0.641235\pi$
$937$	−24625.6			−0.858572			−0.429286	+	0.903169i	$0.641235\pi$
$938$		−	18967.6i		−	0.660250i
$939$			19844.7i			0.689676i
$940$	32884.5			1.14104
$941$			23504.0i			0.814249i	0.913373	+	0.407124i	$0.133468\pi$
$941$			23504.0i			0.814249i	−0.913373	+	0.407124i	$0.866532\pi$
$942$	1932.39			0.0668373
$943$		−	1328.36i		−	0.0458719i
$944$		−	7282.63i		−	0.251090i
$945$		−	55079.2i		−	1.89601i
$946$			21757.4i			0.747774i
$947$		−	8249.55i		−	0.283078i	−0.989933	−	0.141539i	$-0.954795\pi$
$947$		−	8249.55i		−	0.283078i	0.989933	−	0.141539i	$-0.0452050\pi$
$948$		−	2332.97i		−	0.0799275i
$949$	−19088.9			−0.652952
$950$			36809.9i			1.25713i
$951$	16786.9			0.572399
$952$		−	75029.6i		−	2.55433i
$953$			12996.1i			0.441748i	0.975302	+	0.220874i	$0.0708909\pi$
$953$			12996.1i			0.441748i	−0.975302	+	0.220874i	$0.929109\pi$
$954$	−29390.7			−0.997443
$955$			41691.4i			1.41267i
$956$	−7552.39			−0.255504
$957$	59.9105			0.00202365
$958$			7154.05i			0.241270i
$959$			41361.5i			1.39273i
$960$	−17708.1			−0.595341
$961$	21152.5			0.710031
$962$	850.388			0.0285006
$963$	−44072.8			−1.47479
$964$	20071.3			0.670593
$965$		−	3826.97i		−	0.127663i
$966$		−	4945.61i		−	0.164723i
$967$	32460.4			1.07948			0.539739	−	0.841833i	$-0.318523\pi$
$967$	32460.4			1.07948			0.539739	+	0.841833i	$0.318523\pi$
$968$		−	8644.91i		−	0.287043i
$969$		−	21624.7i		−	0.716911i
$970$			18274.2i			0.604895i
$971$	−45897.1			−1.51690			−0.758450	−	0.651732i	$-0.774043\pi$
$971$	−45897.1			−1.51690			−0.758450	+	0.651732i	$0.774043\pi$
$972$	−15711.9			−0.518477
$973$	63668.6			2.09776
$974$			22887.4i			0.752937i
$975$	8954.86			0.294139
$976$	5783.73	+	1560.46i	0.189685	+	0.0511774i
$977$	19432.9			0.636348			0.318174	−	0.948032i	$-0.396930\pi$
$977$	19432.9			0.636348			0.318174	+	0.948032i	$0.396930\pi$
$978$			1862.31i			0.0608897i
$979$	54206.6			1.76961
$980$	29848.5			0.972932
$981$	−21756.3			−0.708078
$982$		−	16468.7i		−	0.535170i
$983$		−	28759.1i		−	0.933135i	−0.884486	−	0.466568i	$-0.845490\pi$
$983$		−	28759.1i		−	0.933135i	0.884486	−	0.466568i	$-0.154510\pi$
$984$		−	1650.17i		−	0.0534610i
$985$	−85938.4			−2.77992
$986$			149.809i			0.00483863i
$987$			24774.1i			0.798955i
$988$	−6116.23			−0.196947
$989$	11558.6			0.371631
$990$	33240.0			1.06711
$991$	27622.8			0.885436			0.442718	−	0.896661i	$-0.354014\pi$
$991$	27622.8			0.885436			0.442718	+	0.896661i	$0.354014\pi$
$992$	−15398.4			−0.492843
$993$		−	12176.4i		−	0.389131i
$994$			12727.1i			0.406116i
$995$	10119.5			0.322423
$996$	8865.24			0.282034
$997$		−	48369.4i		−	1.53648i	−0.640160	−	0.768242i	$-0.721132\pi$
$997$		−	48369.4i		−	1.53648i	0.640160	−	0.768242i	$-0.278868\pi$
$998$	10776.6			0.341811
$999$			2711.83i			0.0858843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.4.b.a.60.10	yes	14
3.2	odd	2		549.4.c.c.487.5		14
4.3	odd	2		976.4.h.a.609.7		14
61.60	even	2	inner	61.4.b.a.60.5	✓	14
183.182	odd	2		549.4.c.c.487.10		14
244.243	odd	2		976.4.h.a.609.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.4.b.a.60.5	✓	14	61.60	even	2	inner
61.4.b.a.60.10	yes	14	1.1	even	1	trivial
549.4.c.c.487.5		14	3.2	odd	2
549.4.c.c.487.10		14	183.182	odd	2
976.4.h.a.609.7		14	4.3	odd	2
976.4.h.a.609.8		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)

\(f(q)\)	\(=\)	\(q+1.94645i q^{2} -2.22484 q^{3} +4.21134 q^{4} -18.8131 q^{5} -4.33054i q^{6} +26.8280i q^{7} +23.7687i q^{8} -22.0501 q^{9} +O(q^{10})\)	\(q+1.94645i q^{2} -2.22484 q^{3} +4.21134 q^{4} -18.8131 q^{5} -4.33054i q^{6} +26.8280i q^{7} +23.7687i q^{8} -22.0501 q^{9} -36.6188i q^{10} -41.1668i q^{11} -9.36956 q^{12} -17.5813 q^{13} -52.2192 q^{14} +41.8562 q^{15} -12.5739 q^{16} +117.663i q^{17} -42.9193i q^{18} +82.6063 q^{19} -79.2284 q^{20} -59.6880i q^{21} +80.1292 q^{22} -42.5687i q^{23} -52.8817i q^{24} +228.933 q^{25} -34.2211i q^{26} +109.129 q^{27} +112.982i q^{28} -0.654118i q^{29} +81.4710i q^{30} +92.9433i q^{31} +165.675i q^{32} +91.5898i q^{33} -229.024 q^{34} -504.717i q^{35} -92.8603 q^{36} +24.8498i q^{37} +160.789i q^{38} +39.1156 q^{39} -447.164i q^{40} +31.2050 q^{41} +116.180 q^{42} +271.529i q^{43} -173.368i q^{44} +414.831 q^{45} +82.8578 q^{46} -415.060 q^{47} +27.9750 q^{48} -376.739 q^{49} +445.607i q^{50} -261.781i q^{51} -74.0408 q^{52} -684.790i q^{53} +212.413i q^{54} +774.476i q^{55} -637.667 q^{56} -183.786 q^{57} +1.27321 q^{58} +579.185i q^{59} +176.271 q^{60} +(-459.978 - 124.103i) q^{61} -180.909 q^{62} -591.559i q^{63} -423.070 q^{64} +330.759 q^{65} -178.275 q^{66} +363.230i q^{67} +495.517i q^{68} +94.7086i q^{69} +982.406 q^{70} -243.725i q^{71} -524.103i q^{72} +1085.75 q^{73} -48.3689 q^{74} -509.340 q^{75} +347.883 q^{76} +1104.42 q^{77} +76.1365i q^{78} +248.994i q^{79} +236.555 q^{80} +352.558 q^{81} +60.7389i q^{82} -946.175 q^{83} -251.366i q^{84} -2213.60i q^{85} -528.518 q^{86} +1.45531i q^{87} +978.484 q^{88} +1316.75i q^{89} +807.446i q^{90} -471.670i q^{91} -179.271i q^{92} -206.784i q^{93} -807.893i q^{94} -1554.08 q^{95} -368.602i q^{96} -499.038 q^{97} -733.304i q^{98} +907.732i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9}+O(q^{10}) \) 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

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