LMFDB - Embedded newform 76.2.k.a.67.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.8
Character	$\chi$	$=$	76.67
Dual form			76.2.k.a.59.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33760 + 0.459147i) q^{2} +(0.220673 - 0.185167i) q^{3} +(1.57837 + 1.22831i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(0.380192 - 0.146358i) q^{6} +(-3.55057 - 2.04992i) q^{7} +(1.54725 + 2.36770i) q^{8} +(-0.506535 + 2.87270i) q^{9} +O(q^{10})$	\(q+(1.33760 + 0.459147i) q^{2} +(0.220673 - 0.185167i) q^{3} +(1.57837 + 1.22831i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(0.380192 - 0.146358i) q^{6} +(-3.55057 - 2.04992i) q^{7} +(1.54725 + 2.36770i) q^{8} +(-0.506535 + 2.87270i) q^{9} +(-2.50567 - 2.02510i) q^{10} +(3.61965 - 2.08981i) q^{11} +(0.575746 - 0.0212054i) q^{12} +(-0.374492 + 0.446302i) q^{13} +(-3.80804 - 4.37222i) q^{14} +(-0.616669 + 0.224449i) q^{15} +(0.982490 + 3.87746i) q^{16} +(-0.573106 - 3.25025i) q^{17} +(-1.99653 + 3.60996i) q^{18} +(-0.458280 + 4.33474i) q^{19} +(-2.42178 - 3.85925i) q^{20} +(-1.16309 + 0.205085i) q^{21} +(5.80119 - 1.13338i) q^{22} +(-0.862701 - 2.37025i) q^{23} +(0.779857 + 0.235988i) q^{24} +(0.145317 + 0.121936i) q^{25} +(-0.705840 + 0.425028i) q^{26} +(0.852252 + 1.47614i) q^{27} +(-3.08616 - 7.59675i) q^{28} +(8.34798 + 1.47197i) q^{29} +(-0.927914 + 0.0170823i) q^{30} +(-0.386863 + 0.670066i) q^{31} +(-0.466142 + 5.63762i) q^{32} +(0.411797 - 1.13140i) q^{33} +(0.725752 - 4.61068i) q^{34} +(6.00353 + 7.15472i) q^{35} +(-4.32808 + 3.91200i) q^{36} +1.23521i q^{37} +(-2.60328 + 5.58775i) q^{38} +0.167830i q^{39} +(-1.46741 - 6.27410i) q^{40} +(-4.51238 - 5.37764i) q^{41} +(-1.64992 - 0.259709i) q^{42} +(-1.55737 + 4.27884i) q^{43} +(8.28008 + 1.14758i) q^{44} +(3.32261 - 5.75494i) q^{45} +(-0.0656581 - 3.56656i) q^{46} +(4.84679 + 0.854620i) q^{47} +(0.934786 + 0.673727i) q^{48} +(4.90438 + 8.49464i) q^{49} +(0.138391 + 0.229824i) q^{50} +(-0.728306 - 0.611122i) q^{51} +(-1.13928 + 0.244435i) q^{52} +(-0.232598 - 0.639058i) q^{53} +(0.462209 + 2.36581i) q^{54} +(-9.37689 + 1.65340i) q^{55} +(-0.640033 - 11.5784i) q^{56} +(0.701520 + 1.04142i) q^{57} +(10.4904 + 5.80187i) q^{58} +(-0.368113 - 2.08767i) q^{59} +(-1.24902 - 0.403200i) q^{60} +(-2.91217 + 1.05994i) q^{61} +(-0.825128 + 0.718656i) q^{62} +(7.68731 - 9.16138i) q^{63} +(-3.21201 + 7.32687i) q^{64} +(1.14941 - 0.663614i) q^{65} +(1.07030 - 1.32429i) q^{66} +(2.44691 - 13.8771i) q^{67} +(3.08775 - 5.83404i) q^{68} +(-0.629267 - 0.363307i) q^{69} +(4.74527 + 12.3267i) q^{70} +(-12.4034 - 4.51448i) q^{71} +(-7.58543 + 3.24548i) q^{72} +(-8.59023 + 7.20806i) q^{73} +(-0.567143 + 1.65222i) q^{74} +0.0546461 q^{75} +(-6.04776 + 6.27890i) q^{76} -17.1358 q^{77} +(-0.0770587 + 0.224490i) q^{78} +(-7.91111 + 6.63821i) q^{79} +(0.917914 - 9.06601i) q^{80} +(-7.76190 - 2.82510i) q^{81} +(-3.56664 - 9.26500i) q^{82} +(1.29416 + 0.747183i) q^{83} +(-2.08770 - 1.10494i) q^{84} +(-1.30559 + 7.40436i) q^{85} +(-4.04776 + 5.00833i) q^{86} +(2.11474 - 1.22094i) q^{87} +(10.5486 + 5.33679i) q^{88} +(9.52313 - 11.3492i) q^{89} +(7.08670 - 6.17226i) q^{90} +(2.24455 - 0.816948i) q^{91} +(1.54975 - 4.80080i) q^{92} +(0.0387037 + 0.219500i) q^{93} +(6.09069 + 3.36853i) q^{94} +(4.35847 - 8.92233i) q^{95} +(0.941034 + 1.33038i) q^{96} +(10.1050 - 1.78178i) q^{97} +(2.65983 + 13.6143i) q^{98} +(4.16991 + 11.4567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	1.33760	+	0.459147i	0.945829	+	0.324666i
$2$	1.33760	+	0.459147i	0.945829	+	0.324666i
$3$	0.220673	−	0.185167i	0.127406	−	0.106906i	−0.576858	−	0.816844i	$-0.695722\pi$
$3$	0.220673	−	0.185167i	0.127406	−	0.106906i	0.704264	+	0.709938i	$0.251277\pi$
$4$	1.57837	+	1.22831i	0.789184	+	0.614157i
$5$	−2.14071	−	0.779153i	−0.957352	−	0.348448i	−0.184357	−	0.982859i	$-0.559020\pi$
$5$	−2.14071	−	0.779153i	−0.957352	−	0.348448i	−0.772995	+	0.634412i	$0.781242\pi$
$6$	0.380192	−	0.146358i	0.155213	−	0.0597505i
$7$	−3.55057	−	2.04992i	−1.34199	−	0.774799i	−0.354891	−	0.934908i	$-0.615482\pi$
$7$	−3.55057	−	2.04992i	−1.34199	−	0.774799i	−0.987099	+	0.160109i	$0.948815\pi$
$8$	1.54725	+	2.36770i	0.547037	+	0.837108i
$9$	−0.506535	+	2.87270i	−0.168845	+	0.957567i
$10$	−2.50567	−	2.02510i	−0.792362	−	0.640392i
$11$	3.61965	−	2.08981i	1.09137	−	0.630101i	0.157426	−	0.987531i	$-0.449680\pi$
$11$	3.61965	−	2.08981i	1.09137	−	0.630101i	0.933940	+	0.357430i	$0.116347\pi$
$12$	0.575746	−	0.0212054i	0.166204	−	0.00612147i
$13$	−0.374492	+	0.446302i	−0.103865	+	0.123782i	−0.815473	−	0.578795i	$-0.803523\pi$
$13$	−0.374492	+	0.446302i	−0.103865	+	0.123782i	0.711608	+	0.702577i	$0.247967\pi$
$14$	−3.80804	−	4.37222i	−1.01774	−	1.16853i
$15$	−0.616669	+	0.224449i	−0.159223	+	0.0579525i
$16$	0.982490	+	3.87746i	0.245623	+	0.969366i
$17$	−0.573106	−	3.25025i	−0.138999	−	0.788301i	−0.971991	−	0.235017i	$-0.924486\pi$
$17$	−0.573106	−	3.25025i	−0.138999	−	0.788301i	0.832993	−	0.553284i	$-0.186626\pi$
$18$	−1.99653	+	3.60996i	−0.470588	+	0.850876i
$19$	−0.458280	+	4.33474i	−0.105137	+	0.994458i
$19$	−0.458280	+	4.33474i	−0.105137	+	0.994458i
$20$	−2.42178	−	3.85925i	−0.541526	−	0.862954i
$21$	−1.16309	+	0.205085i	−0.253808	+	0.0447532i
$22$	5.80119	−	1.13338i	1.23682	−	0.241638i
$23$	−0.862701	−	2.37025i	−0.179886	−	0.494232i	0.816675	−	0.577098i	$-0.195815\pi$
$23$	−0.862701	−	2.37025i	−0.179886	−	0.494232i	−0.996561	+	0.0828661i	$0.973593\pi$
$24$	0.779857	+	0.235988i	0.159188	+	0.0481708i
$25$	0.145317	+	0.121936i	0.0290635	+	0.0243872i
$26$	−0.705840	+	0.425028i	−0.138427	+	0.0833549i
$27$	0.852252	+	1.47614i	0.164016	+	0.284084i
$28$	−3.08616	−	7.59675i	−0.583230	−	1.43565i
$29$	8.34798	+	1.47197i	1.55018	+	0.273339i	0.882213	−	0.470850i	$-0.156053\pi$
$29$	8.34798	+	1.47197i	1.55018	+	0.273339i	0.667969	+	0.744189i	$0.267164\pi$
$30$	−0.927914	+	0.0170823i	−0.169413	+	0.00311878i
$31$	−0.386863	+	0.670066i	−0.0694826	+	0.120347i	−0.898674	−	0.438618i	$-0.855468\pi$
$31$	−0.386863	+	0.670066i	−0.0694826	+	0.120347i	0.829191	+	0.558965i	$0.188801\pi$
$32$	−0.466142	+	5.63762i	−0.0824031	+	0.996599i
$33$	0.411797	−	1.13140i	0.0716847	−	0.196952i
$34$	0.725752	−	4.61068i	0.124465	−	0.790725i
$35$	6.00353	+	7.15472i	1.01478	+	1.20937i
$36$	−4.32808	+	3.91200i	−0.721346	+	0.651999i
$37$			1.23521i			0.203067i	0.994832	+	0.101534i	$0.0323749\pi$
$37$			1.23521i			0.203067i	−0.994832	+	0.101534i	$0.967625\pi$
$38$	−2.60328	+	5.58775i	−0.422308	+	0.906452i
$39$			0.167830i			0.0268743i
$40$	−1.46741	−	6.27410i	−0.232019	−	0.992022i
$41$	−4.51238	−	5.37764i	−0.704715	−	0.839847i	0.288336	−	0.957529i	$-0.406898\pi$
$41$	−4.51238	−	5.37764i	−0.704715	−	0.839847i	−0.993051	+	0.117683i	$0.962453\pi$
$42$	−1.64992	−	0.259709i	−0.254589	−	0.0400739i
$43$	−1.55737	+	4.27884i	−0.237497	+	0.652517i	0.762488	+	0.647002i	$0.223978\pi$
$43$	−1.55737	+	4.27884i	−0.237497	+	0.652517i	−0.999985	+	0.00551486i	$0.998245\pi$
$44$	8.28008	+	1.14758i	1.24827	+	0.173005i
$45$	3.32261	−	5.75494i	0.495306	−	0.857895i
$46$	−0.0656581	−	3.56656i	−0.00968075	−	0.525861i
$47$	4.84679	+	0.854620i	0.706977	+	0.124659i	0.515565	−	0.856851i	$-0.327582\pi$
$47$	4.84679	+	0.854620i	0.706977	+	0.124659i	0.191412	+	0.981510i	$0.438693\pi$
$48$	0.934786	+	0.673727i	0.134925	+	0.0972441i
$49$	4.90438	+	8.49464i	0.700626	+	1.21352i
$50$	0.138391	+	0.229824i	0.0195714	+	0.0325020i
$51$	−0.728306	−	0.611122i	−0.101983	−	0.0855742i
$52$	−1.13928	+	0.244435i	−0.157990	+	0.0338971i
$53$	−0.232598	−	0.639058i	−0.0319498	−	0.0877814i	0.922692	−	0.385538i	$-0.125984\pi$
$53$	−0.232598	−	0.639058i	−0.0319498	−	0.0877814i	−0.954642	+	0.297756i	$0.903762\pi$
$54$	0.462209	+	2.36581i	0.0628986	+	0.321945i
$55$	−9.37689	+	1.65340i	−1.26438	+	0.222944i
$56$	−0.640033	−	11.5784i	−0.0855280	−	1.54724i
$57$	0.701520	+	1.04142i	0.0929185	+	0.137939i
$58$	10.4904	+	5.80187i	1.37746	+	0.761823i
$59$	−0.368113	−	2.08767i	−0.0479243	−	0.271792i	0.951424	−	0.307883i	$-0.0996205\pi$
$59$	−0.368113	−	2.08767i	−0.0479243	−	0.271792i	−0.999349	+	0.0360909i	$0.988509\pi$
$60$	−1.24902	−	0.403200i	−0.161248	−	0.0520529i
$61$	−2.91217	+	1.05994i	−0.372866	+	0.135712i	−0.521654	−	0.853157i	$-0.674685\pi$
$61$	−2.91217	+	1.05994i	−0.372866	+	0.135712i	0.148789	+	0.988869i	$0.452463\pi$
$62$	−0.825128	+	0.718656i	−0.104791	+	0.0912693i
$63$	7.68731	−	9.16138i	0.968510	−	1.15423i
$64$	−3.21201	+	7.32687i	−0.401501	+	0.915859i
$65$	1.14941	−	0.663614i	0.142567	−	0.0823112i
$66$	1.07030	−	1.32429i	0.131745	−	0.163009i
$67$	2.44691	−	13.8771i	0.298938	−	1.69536i	−0.351813	−	0.936070i	$-0.614435\pi$
$67$	2.44691	−	13.8771i	0.298938	−	1.69536i	0.650751	−	0.759291i	$-0.274454\pi$
$68$	3.08775	−	5.83404i	0.374445	−	0.707481i
$69$	−0.629267	−	0.363307i	−0.0757548	−	0.0437370i
$70$	4.74527	+	12.3267i	0.567168	+	1.47332i
$71$	−12.4034	−	4.51448i	−1.47202	−	0.535771i	−0.523370	−	0.852105i	$-0.675326\pi$
$71$	−12.4034	−	4.51448i	−1.47202	−	0.535771i	−0.948648	+	0.316335i	$0.897548\pi$
$72$	−7.58543	+	3.24548i	−0.893952	+	0.382483i
$73$	−8.59023	+	7.20806i	−1.00541	+	0.843639i	−0.987725	−	0.156205i	$-0.950074\pi$
$73$	−8.59023	+	7.20806i	−1.00541	+	0.843639i	−0.0176852	+	0.999844i	$0.505630\pi$
$74$	−0.567143	+	1.65222i	−0.0659290	+	0.192067i
$75$	0.0546461			0.00630999
$76$	−6.04776	+	6.27890i	−0.693725	+	0.720240i
$77$	−17.1358			−1.95280
$78$	−0.0770587	+	0.224490i	−0.00872518	+	0.0254185i
$79$	−7.91111	+	6.63821i	−0.890069	+	0.746857i	−0.968224	−	0.250085i	$-0.919542\pi$
$79$	−7.91111	+	6.63821i	−0.890069	+	0.746857i	0.0781550	+	0.996941i	$0.475097\pi$
$80$	0.917914	−	9.06601i	0.102626	−	1.01361i
$81$	−7.76190	−	2.82510i	−0.862433	−	0.313900i
$82$	−3.56664	−	9.26500i	−0.393870	−	1.02315i
$83$	1.29416	+	0.747183i	0.142052	+	0.0820140i	0.569342	−	0.822101i	$-0.307198\pi$
$83$	1.29416	+	0.747183i	0.142052	+	0.0820140i	−0.427289	+	0.904115i	$0.640531\pi$
$84$	−2.08770	−	1.10494i	−0.227787	−	0.120559i
$85$	−1.30559	+	7.40436i	−0.141611	+	0.803115i
$86$	−4.04776	+	5.00833i	−0.436482	+	0.540062i
$87$	2.11474	−	1.22094i	0.226723	−	0.130899i
$88$	10.5486	+	5.33679i	1.12448	+	0.568904i
$89$	9.52313	−	11.3492i	1.00945	−	1.20302i	0.0303703	−	0.999539i	$-0.490331\pi$
$89$	9.52313	−	11.3492i	1.00945	−	1.20302i	0.979080	−	0.203477i	$-0.0652242\pi$
$90$	7.08670	−	6.17226i	0.747004	−	0.650613i
$91$	2.24455	−	0.816948i	0.235292	−	0.0856394i
$92$	1.54975	−	4.80080i	0.161573	−	0.500518i
$93$	0.0387037	+	0.219500i	0.00401339	+	0.0227610i
$94$	6.09069	+	3.36853i	0.628206	+	0.347438i
$95$	4.35847	−	8.92233i	0.447169	−	0.915412i
$96$	0.941034	+	1.33038i	0.0960438	+	0.135782i
$97$	10.1050	−	1.78178i	1.02601	−	0.180913i	0.364776	−	0.931095i	$-0.381146\pi$
$97$	10.1050	−	1.78178i	1.02601	−	0.180913i	0.661230	+	0.750183i	$0.270035\pi$
$98$	2.65983	+	13.6143i	0.268684	+	1.37525i
$99$	4.16991	+	11.4567i	0.419092	+	1.15145i
$100$	0.0795889	+	0.370955i	0.00795889	+	0.0370955i
$101$	6.70325	+	5.62470i	0.666999	+	0.559678i	0.912175	−	0.409800i	$-0.134402\pi$
$101$	6.70325	+	5.62470i	0.666999	+	0.559678i	−0.245177	+	0.969478i	$0.578846\pi$
$102$	−0.693591	−	1.15184i	−0.0686757	−	0.114049i
$103$	−4.40079	−	7.62240i	−0.433623	−	0.751057i	0.563559	−	0.826076i	$-0.309432\pi$
$103$	−4.40079	−	7.62240i	−0.433623	−	0.751057i	−0.997182	+	0.0750187i	$0.976098\pi$
$104$	−1.63614	−	0.196142i	−0.160437	−	0.0192333i
$105$	2.64963	+	0.467202i	0.258578	+	0.0455942i
$106$	−0.0177025	−	0.961604i	−0.00171942	−	0.0933992i
$107$	−0.252753	+	0.437781i	−0.0244346	+	0.0423219i	−0.877984	−	0.478690i	$-0.841112\pi$
$107$	−0.252753	+	0.437781i	−0.0244346	+	0.0423219i	0.853550	+	0.521012i	$0.174445\pi$
$108$	−0.468001	+	3.37673i	−0.0450334	+	0.324926i
$109$	2.13914	−	5.87723i	0.204892	−	0.562937i	−0.794102	−	0.607785i	$-0.792058\pi$
$109$	2.13914	−	5.87723i	0.204892	−	0.562937i	0.998994	+	0.0448483i	$0.0142805\pi$
$110$	−13.3017	−	2.09378i	−1.26827	−	0.199634i
$111$	0.228720	+	0.272577i	0.0217091	+	0.0258719i
$112$	4.46010	−	15.7812i	0.421440	−	1.49119i
$113$			7.26696i			0.683618i	0.939769	+	0.341809i	$0.111040\pi$
$113$			7.26696i			0.683618i	−0.939769	+	0.341809i	$0.888960\pi$
$114$	0.460191	+	1.71511i	0.0431008	+	0.160634i
$115$			5.74619i			0.535835i
$116$	11.3681	+	12.5773i	1.05551	+	1.16777i
$117$	−1.09240	−	1.30187i	−0.100992	−	0.120358i
$118$	0.466160	−	2.96150i	0.0429135	−	0.272628i
$119$	−4.62790	+	12.7151i	−0.424239	+	1.16559i
$120$	−1.48557	−	1.11281i	−0.135614	−	0.101585i
$121$	3.23459	−	5.60247i	0.294054	−	0.509316i
$122$	−4.38201	+	0.0806698i	−0.396728	+	0.00730350i
$123$	−1.99152	−	0.351159i	−0.179569	−	0.0316629i
$124$	−1.43366	+	0.582421i	−0.128747	+	0.0523030i
$125$	5.47915	+	9.49017i	0.490070	+	0.848827i
$126$	14.4890	−	8.72469i	1.29078	−	0.777257i
$127$	6.88695	+	5.77884i	0.611118	+	0.512789i	0.894998	−	0.446071i	$-0.147177\pi$
$127$	6.88695	+	5.77884i	0.611118	+	0.512789i	−0.283879	+	0.958860i	$0.591622\pi$
$128$	−7.66051	+	8.32566i	−0.677099	+	0.735892i
$129$	0.448629	+	1.23260i	0.0394996	+	0.108524i
$130$	1.84216	−	0.359903i	0.161568	−	0.0315656i
$131$	13.5834	−	2.39512i	1.18679	−	0.209262i	0.454807	−	0.890590i	$-0.349708\pi$
$131$	13.5834	−	2.39512i	1.18679	−	0.209262i	0.731979	+	0.681328i	$0.238597\pi$
$132$	2.03969	−	1.27995i	0.177532	−	0.111406i
$133$	10.5130	−	14.4514i	0.911597	−	1.25309i
$134$	9.64465	−	17.4386i	0.833171	−	1.50647i
$135$	−0.674279	−	3.82402i	−0.0580327	−	0.329120i
$136$	6.80887	−	6.38590i	0.583856	−	0.547587i
$137$	−7.03294	+	2.55978i	−0.600865	+	0.218697i	−0.624501	−	0.781024i	$-0.714698\pi$
$137$	−7.03294	+	2.55978i	−0.600865	+	0.218697i	0.0236365	+	0.999721i	$0.492476\pi$
$138$	−0.674898	−	0.774887i	−0.0574511	−	0.0659628i
$139$	−12.3852	+	14.7601i	−1.05050	+	1.25194i	−0.0836787	+	0.996493i	$0.526667\pi$
$139$	−12.3852	+	14.7601i	−1.05050	+	1.25194i	−0.966823	+	0.255447i	$0.917777\pi$
$140$	0.687527	+	18.6670i	0.0581066	+	1.57765i
$141$	1.22780	−	0.708872i	0.103400	−	0.0596978i
$142$	−14.5181	−	11.7336i	−1.21833	−	0.984662i
$143$	−0.422845	+	2.39807i	−0.0353601	+	0.200537i
$144$	−11.6365	+	0.858332i	−0.969704	+	0.0715277i
$145$	−16.7237	−	9.65542i	−1.38883	−	0.801839i
$146$	−14.7999	+	5.69735i	−1.22485	+	0.471516i
$147$	2.65519	+	0.966410i	0.218996	+	0.0797081i
$148$	−1.51722	+	1.94961i	−0.124715	+	0.160257i
$149$	1.56368	−	1.31208i	0.128101	−	0.107490i	−0.576486	−	0.817107i	$-0.695576\pi$
$149$	1.56368	−	1.31208i	0.128101	−	0.107490i	0.704588	+	0.709617i	$0.251132\pi$
$150$	0.0730948	+	0.0250906i	0.00596817	+	0.00204864i
$151$	9.61868			0.782757			0.391378	−	0.920230i	$-0.371998\pi$
$151$	9.61868			0.782757			0.391378	+	0.920230i	$0.371998\pi$
$152$	−10.9724	+	5.62188i	−0.889983	+	0.455994i
$153$	9.62728			0.778320
$154$	−22.9209	−	7.86785i	−1.84702	−	0.634009i
$155$	1.35024	−	1.13299i	0.108454	−	0.0910038i
$156$	−0.206148	+	0.264898i	−0.0165051	+	0.0212088i
$157$	−7.10221	−	2.58499i	−0.566818	−	0.206305i	0.0426851	−	0.999089i	$-0.486409\pi$
$157$	−7.10221	−	2.58499i	−0.566818	−	0.206305i	−0.609503	+	0.792784i	$0.708631\pi$
$158$	−13.6298	+	5.24693i	−1.08433	+	0.417423i
$159$	−0.169660	−	0.0979535i	−0.0134549	−	0.00776822i
$160$	5.39044	−	11.7053i	0.426152	−	0.925383i
$161$	−1.79575	+	10.1842i	−0.141525	+	0.802629i
$162$	−9.08520	−	7.34271i	−0.713801	−	0.576898i
$163$	14.3484	−	8.28406i	1.12385	−	0.648858i	0.181472	−	0.983396i	$-0.441914\pi$
$163$	14.3484	−	8.28406i	1.12385	−	0.648858i	0.942382	+	0.334538i	$0.108580\pi$
$164$	−0.516760	−	14.0305i	−0.0403522	−	1.09560i
$165$	−1.76307	+	2.10115i	−0.137255	+	0.163574i
$166$	1.38801	+	1.59364i	0.107730	+	0.123691i
$167$	−7.24993	+	2.63876i	−0.561016	+	0.204193i	−0.606934	−	0.794752i	$-0.707601\pi$
$167$	−7.24993	+	2.63876i	−0.561016	+	0.204193i	0.0459180	+	0.998945i	$0.485379\pi$
$168$	−2.28518	−	2.43654i	−0.176306	−	0.187983i
$169$	2.19849	+	12.4682i	0.169114	+	0.959094i
$170$	−5.14605	+	9.30464i	−0.394684	+	0.713633i
$171$	−12.2203	−	3.51220i	−0.934508	−	0.268585i
$172$	−7.71387	+	4.84065i	−0.588177	+	0.369096i
$173$	−9.18629	+	1.61979i	−0.698421	+	0.123150i	−0.511575	−	0.859239i	$-0.670938\pi$
$173$	−9.18629	+	1.61979i	−0.698421	+	0.123150i	−0.186846	+	0.982389i	$0.559827\pi$
$174$	3.38927	−	0.662164i	0.256940	−	0.0501985i
$175$	−0.266001	−	0.730832i	−0.0201078	−	0.0552457i
$176$	11.6594	+	11.9818i	0.878862	+	0.903166i
$177$	−0.467801	−	0.392531i	−0.0351620	−	0.0295045i
$178$	17.9491	−	10.8083i	1.34535	−	0.810113i
$179$	0.791374	+	1.37070i	0.0591501	+	0.102451i	0.894084	−	0.447899i	$-0.147828\pi$
$179$	0.791374	+	1.37070i	0.0591501	+	0.102451i	−0.834934	+	0.550350i	$0.814494\pi$
$180$	12.3132	−	5.00220i	0.917770	−	0.372842i
$181$	13.1059	+	2.31093i	0.974156	+	0.171770i	0.638000	−	0.770036i	$-0.279762\pi$
$181$	13.1059	+	2.31093i	0.974156	+	0.171770i	0.336156	+	0.941806i	$0.390873\pi$
$182$	3.37741	−	0.0621759i	0.250350	−	0.00460878i
$183$	−0.446372	+	0.773139i	−0.0329968	+	0.0571521i
$184$	4.27723	−	5.71000i	0.315321	−	0.420947i
$185$	0.962417	−	2.64422i	0.0707583	−	0.194407i
$186$	−0.0490124	+	0.311374i	−0.00359376	+	0.0228311i
$187$	−8.86683	−	10.5671i	−0.648407	−	0.772742i
$188$	6.60028	+	7.30228i	0.481375	+	0.532574i
$189$		−	6.98821i		−	0.508318i
$190$	9.92657	−	9.93337i	0.720149	−	0.720642i
$191$			12.6803i			0.917517i	0.888561	+	0.458759i	$0.151706\pi$
$191$			12.6803i			0.917517i	−0.888561	+	0.458759i	$0.848294\pi$
$192$	0.647888	+	2.21160i	0.0467573	+	0.159608i
$193$	−14.1194	−	16.8269i	−1.01634	−	1.21123i	−0.977272	−	0.211989i	$-0.932006\pi$
$193$	−14.1194	−	16.8269i	−1.01634	−	1.21123i	−0.0390670	−	0.999237i	$-0.512439\pi$
$194$	14.3346	+	2.25636i	1.02916	+	0.161997i
$195$	0.130765	−	0.359275i	0.00936430	−	0.0257282i
$196$	−2.69316	+	19.4318i	−0.192369	+	1.38798i
$197$	2.27195	−	3.93514i	0.161870	−	0.280367i	−0.773669	−	0.633590i	$-0.781581\pi$
$197$	2.27195	−	3.93514i	0.161870	−	0.280367i	0.935539	+	0.353223i	$0.114914\pi$
$198$	0.317362	+	17.2392i	0.0225539	+	1.22514i
$199$	11.9982	+	2.11561i	0.850530	+	0.149971i	0.581888	−	0.813269i	$-0.302314\pi$
$199$	11.9982	+	2.11561i	0.850530	+	0.149971i	0.268642	+	0.963240i	$0.413425\pi$
$200$	−0.0638644	+	0.532734i	−0.00451590	+	0.0376700i
$201$	−2.02962	−	3.51540i	−0.143158	−	0.247957i
$202$	6.38373	+	10.6014i	0.449158	+	0.745912i
$203$	−26.6227	−	22.3391i	−1.86855	−	1.56790i
$204$	−0.398886	−	1.85916i	−0.0279276	−	0.130167i
$205$	5.46966	+	15.0278i	0.382018	+	1.04959i
$206$	−2.38672	−	12.2164i	−0.166290	−	0.851154i
$207$	7.24601	−	1.27767i	0.503633	−	0.0888040i
$208$	−2.09845	−	1.01359i	−0.145502	−	0.0702798i
$209$	7.39996	+	16.6480i	0.511866	+	1.15156i
$210$	3.32965	+	1.84150i	0.229767	+	0.127076i
$211$	−0.635579	−	3.60455i	−0.0437551	−	0.248147i	0.955083	−	0.296338i	$-0.0957656\pi$
$211$	−0.635579	−	3.60455i	−0.0437551	−	0.248147i	−0.998838	+	0.0481908i	$0.984654\pi$
$212$	0.417839	−	1.29437i	0.0286973	−	0.0888979i
$213$	−3.57304	+	1.30048i	−0.244821	+	0.0891074i
$214$	−0.539089	+	0.469527i	−0.0368514	+	0.0320962i
$215$	6.66775	−	7.94631i	0.454736	−	0.541934i
$216$	−2.17642	+	4.30185i	−0.148086	+	0.292704i
$217$	2.74717	−	1.58608i	0.186490	−	0.107670i
$218$	5.55983	−	6.87923i	0.376559	−	0.465920i
$219$	−0.560940	+	3.18125i	−0.0379048	+	0.214969i
$220$	−16.8311	−	8.90809i	−1.13475	−	0.600583i
$221$	1.66521	+	0.961412i	0.112014	+	0.0646716i
$222$	0.180783	+	0.469616i	0.0121334	+	0.0315186i
$223$	26.3079	+	9.57530i	1.76171	+	0.641210i	0.999978	−	0.00668309i	$-0.00212731\pi$
$223$	26.3079	+	9.57530i	1.76171	+	0.641210i	0.761732	+	0.647893i	$0.224350\pi$
$224$	13.2118	−	19.0612i	0.882748	−	1.27358i
$225$	−0.423893	+	0.355689i	−0.0282596	+	0.0237126i
$226$	−3.33660	+	9.72032i	−0.221948	+	0.646586i
$227$	−6.26652			−0.415924			−0.207962	−	0.978137i	$-0.566683\pi$
$227$	−6.26652			−0.415924			−0.207962	+	0.978137i	$0.566683\pi$
$228$	−0.171933	+	2.50543i	−0.0113865	+	0.165926i
$229$	−12.6430			−0.835472			−0.417736	−	0.908569i	$-0.637176\pi$
$229$	−12.6430			−0.835472			−0.417736	+	0.908569i	$0.637176\pi$
$230$	−2.63834	+	7.68612i	−0.173967	+	0.506808i
$231$	−3.78141	+	3.17298i	−0.248798	+	0.208767i
$232$	9.43126	+	22.0430i	0.619192	+	1.44720i
$233$	6.32647	+	2.30265i	0.414461	+	0.150851i	0.540830	−	0.841132i	$-0.318110\pi$
$233$	6.32647	+	2.30265i	0.414461	+	0.150851i	−0.126369	+	0.991983i	$0.540332\pi$
$234$	−0.863447	−	2.24296i	−0.0564453	−	0.146627i
$235$	−9.70967	−	5.60588i	−0.633389	−	0.365687i
$236$	1.98330	−	3.74728i	0.129102	−	0.243927i
$237$	−0.516593	+	2.92975i	−0.0335563	+	0.190307i
$238$	−12.0284	+	14.8828i	−0.779685	+	0.964711i
$239$	−8.72510	+	5.03744i	−0.564380	+	0.325845i	−0.754901	−	0.655838i	$-0.772315\pi$
$239$	−8.72510	+	5.03744i	−0.564380	+	0.325845i	0.190522	+	0.981683i	$0.438982\pi$
$240$	−1.47616	−	2.17059i	−0.0952860	−	0.140111i
$241$	5.43427	−	6.47631i	0.350052	−	0.417176i	−0.562073	−	0.827088i	$-0.689996\pi$
$241$	5.43427	−	6.47631i	0.350052	−	0.417176i	0.912125	+	0.409912i	$0.134440\pi$
$242$	6.89896	−	6.00874i	0.443482	−	0.386256i
$243$	−7.04109	+	2.56275i	−0.451686	+	0.164400i
$244$	−5.89843	−	1.90408i	−0.377608	−	0.121896i
$245$	−3.88021	−	22.0058i	−0.247898	−	1.40590i
$246$	−2.50263	−	1.38411i	−0.159562	−	0.0882478i
$247$	−1.76298	−	1.82786i	−0.112176	−	0.116304i
$248$	−2.18509	+	0.120787i	−0.138753	+	0.00767000i
$249$	0.423939	−	0.0747520i	0.0268661	−	0.00473721i
$250$	2.97155	+	15.2098i	0.187937	+	0.961954i
$251$	−2.91664	−	8.01342i	−0.184097	−	0.505802i	0.812973	−	0.582302i	$-0.197848\pi$
$251$	−2.91664	−	8.01342i	−0.184097	−	0.505802i	−0.997070	+	0.0764996i	$0.975626\pi$
$252$	23.3864	−	5.01760i	1.47321	−	0.316079i
$253$	−8.07605	−	6.77661i	−0.507737	−	0.426042i
$254$	6.55868	+	10.8919i	0.411528	+	0.683420i
$255$	1.08293	+	1.87569i	0.0678158	+	0.117460i
$256$	−14.0694	+	7.61914i	−0.879339	+	0.476196i
$257$	−2.70278	−	0.476573i	−0.168595	−	0.0297278i	0.0887134	−	0.996057i	$-0.471724\pi$
$257$	−2.70278	−	0.476573i	−0.168595	−	0.0297278i	−0.257308	+	0.966329i	$0.582836\pi$
$258$	0.0341441	+	1.85472i	0.00212572	+	0.115470i
$259$	2.53208	−	4.38570i	0.157336	−	0.272514i
$260$	2.62932	+	0.364413i	0.163064	+	0.0225999i
$261$	−8.45709	+	23.2357i	−0.523481	+	1.43825i
$262$	19.2689	+	3.03305i	1.19044	+	0.187383i
$263$	−1.42151	−	1.69409i	−0.0876540	−	0.104462i	0.720435	−	0.693523i	$-0.243942\pi$
$263$	−1.42151	−	1.69409i	−0.0876540	−	0.104462i	−0.808089	+	0.589061i	$0.799498\pi$
$264$	3.31598	−	0.775556i	0.204084	−	0.0477322i
$265$			1.54926i			0.0951706i
$266$	20.6976	−	14.5032i	1.26905	−	0.889247i
$267$		−	4.26784i		−	0.261187i
$268$	20.9076	−	18.8976i	1.27714	−	1.15436i
$269$	9.64383	+	11.4931i	0.587995	+	0.700745i	0.975219	−	0.221241i	$-0.0710106\pi$
$269$	9.64383	+	11.4931i	0.587995	+	0.700745i	−0.387225	+	0.921985i	$0.626566\pi$
$270$	0.853872	−	5.42462i	0.0519650	−	0.330132i
$271$	8.76172	−	24.0726i	0.532237	−	1.46231i	−0.324166	−	0.946000i	$-0.605084\pi$
$271$	8.76172	−	24.0726i	0.532237	−	1.46231i	0.856403	−	0.516308i	$-0.172694\pi$
$272$	12.0396	−	5.41553i	0.730010	−	0.328365i
$273$	0.344039	−	0.595893i	0.0208222	−	0.0360651i
$274$	−10.5826	+	0.194819i	−0.639319	+	0.0117694i
$275$	0.780821	+	0.137680i	0.0470853	+	0.00830240i
$276$	−0.546959	−	1.34637i	−0.0329231	−	0.0810419i
$277$	−4.24573	−	7.35381i	−0.255101	−	0.441848i	0.709822	−	0.704381i	$-0.248775\pi$
$277$	−4.24573	−	7.35381i	−0.255101	−	0.441848i	−0.964923	+	0.262533i	$0.915442\pi$
$278$	−23.3436	+	14.0566i	−1.40006	+	0.843058i
$279$	−1.72894	−	1.45075i	−0.103509	−	0.0868542i
$280$	−7.65126	+	25.2847i	−0.457250	+	1.51105i
$281$	−0.393696	−	1.08167i	−0.0234859	−	0.0645270i	0.927396	−	0.374082i	$-0.122042\pi$
$281$	−0.393696	−	1.08167i	−0.0234859	−	0.0645270i	−0.950882	+	0.309555i	$0.899820\pi$
$282$	1.96779	−	0.384448i	0.117180	−	0.0228936i
$283$	−9.24245	+	1.62969i	−0.549407	+	0.0968752i	−0.441459	−	0.897281i	$-0.645539\pi$
$283$	−9.24245	+	1.62969i	−0.549407	+	0.0968752i	−0.107948	+	0.994157i	$0.534428\pi$
$284$	−14.0320	−	22.3608i	−0.832646	−	1.32687i
$285$	−0.690322	−	2.77596i	−0.0408911	−	0.164434i
$286$	−1.66667	+	3.01352i	−0.0985521	+	0.178193i
$287$	4.99777	+	28.3437i	0.295009	+	1.67308i
$288$	−15.9591	−	4.19474i	−0.940397	−	0.247177i
$289$	5.73912	−	2.08887i	0.337595	−	0.122875i
$290$	−17.9364	−	20.5938i	−1.05326	−	1.20931i
$291$	1.89997	−	2.26430i	0.111378	−	0.132736i
$292$	−22.4123	+	0.825470i	−1.31158	+	0.0483070i
$293$	−15.9687	+	9.21954i	−0.932902	+	0.538611i	−0.887728	−	0.460368i	$-0.847717\pi$
$293$	−15.9687	+	9.21954i	−0.932902	+	0.538611i	−0.0451738	+	0.998979i	$0.514384\pi$
$294$	3.10787	+	2.51180i	0.181254	+	0.146491i
$295$	−0.838596	+	4.75591i	−0.0488249	+	0.276900i
$296$	−2.92460	+	1.91118i	−0.169989	+	0.111085i
$297$	6.16971	+	3.56209i	0.358003	+	0.206693i
$298$	2.69402	−	1.03709i	0.156060	−	0.0600768i
$299$	1.38092	+	0.502615i	0.0798608	+	0.0290669i
$300$	0.0862516	+	0.0671225i	0.00497974	+	0.00387532i
$301$	14.3009	−	11.9999i	0.824288	−	0.691660i
$302$	12.8660	+	4.41639i	0.740354	+	0.254135i
$303$	2.52073			0.144812
$304$	−17.2580	+	2.48188i	−0.989817	+	0.142345i
$305$	7.05996			0.404252
$306$	12.8775	+	4.42034i	0.736157	+	0.252694i
$307$	−4.28349	+	3.59427i	−0.244471	+	0.205136i	−0.756787	−	0.653661i	$-0.773232\pi$
$307$	−4.28349	+	3.59427i	−0.244471	+	0.205136i	0.512316	+	0.858797i	$0.328788\pi$
$308$	−27.0466	−	21.0481i	−1.54112	−	1.19933i
$309$	−2.38255	−	0.867177i	−0.135539	−	0.0493320i
$310$	2.32630	−	0.895529i	0.132125	−	0.0508626i
$311$	10.3643	+	5.98382i	0.587704	+	0.339311i	0.764189	−	0.644992i	$-0.223139\pi$
$311$	10.3643	+	5.98382i	0.587704	+	0.339311i	−0.176485	+	0.984303i	$0.556473\pi$
$312$	−0.397372	+	0.259676i	−0.0224967	+	0.0147013i
$313$	−2.75949	+	15.6499i	−0.155976	+	0.884582i	0.801913	+	0.597441i	$0.203816\pi$
$313$	−2.75949	+	15.6499i	−0.155976	+	0.884582i	−0.957888	+	0.287141i	$0.907295\pi$
$314$	−8.31305	−	6.71865i	−0.469133	−	0.379156i
$315$	−23.5944	+	13.6222i	−1.32939	+	0.767525i
$316$	−20.6404	+	0.760211i	−1.16112	+	0.0427652i
$317$	10.8229	−	12.8982i	0.607875	−	0.724437i	−0.371060	−	0.928609i	$-0.621006\pi$
$317$	10.8229	−	12.8982i	0.607875	−	0.724437i	0.978935	+	0.204172i	$0.0654500\pi$
$318$	−0.181963	−	0.208922i	−0.0102040	−	0.0117158i
$319$	33.2929	−	12.1176i	1.86405	−	0.678458i
$320$	12.5847	−	13.1820i	0.703507	−	0.736897i
$321$	0.0252867	+	0.143408i	0.00141137	+	0.00800425i
$322$	−7.07806	+	12.7979i	−0.394445	+	0.713202i
$323$	14.3516	−	0.994743i	0.798546	−	0.0553490i
$324$	−8.78102	−	13.9931i	−0.487834	−	0.777394i
$325$	−0.108840	+	0.0191915i	−0.00603738	+	0.00106455i
$326$	22.9961	−	4.49276i	1.27364	−	0.248831i
$327$	−0.616218	−	1.69304i	−0.0340769	−	0.0936255i
$328$	5.75085	−	19.0045i	0.317538	−	1.04935i
$329$	−15.4570	−	12.9699i	−0.852171	−	0.715056i
$330$	−3.32303	+	2.00099i	−0.182927	+	0.110151i
$331$	7.28237	+	12.6134i	0.400275	+	0.693297i	0.993759	−	0.111549i	$-0.0355811\pi$
$331$	7.28237	+	12.6134i	0.400275	+	0.693297i	−0.593484	+	0.804846i	$0.702248\pi$
$332$	1.12488	+	2.76896i	0.0617360	+	0.151967i
$333$	−3.54839	−	0.625676i	−0.194450	−	0.0342868i
$334$	−10.9091	+	0.200829i	−0.596920	+	0.0109889i
$335$	−16.0505	+	27.8003i	−0.876934	+	1.51889i
$336$	−1.93794	−	4.30836i	−0.105723	−	0.235040i
$337$	0.136737	−	0.375681i	0.00744853	−	0.0204647i	−0.935913	−	0.352232i	$-0.885423\pi$
$337$	0.136737	−	0.375681i	0.00744853	−	0.0204647i	0.943361	+	0.331768i	$0.107645\pi$
$338$	−2.78405	+	17.6870i	−0.151432	+	0.962045i
$339$	1.34560	+	1.60362i	0.0730829	+	0.0870968i
$340$	−11.1556	+	10.0831i	−0.604996	+	0.546834i
$341$			3.23387i			0.175124i
$342$	−14.7333	−	10.3088i	−0.796684	−	0.557438i
$343$		−	11.5155i		−	0.621779i
$344$	−12.5407	+	2.93307i	−0.676147	+	0.158140i
$345$	1.06400	+	1.26803i	0.0572840	+	0.0682684i
$346$	−13.0313	−	2.05122i	−0.700569	−	0.110274i
$347$	6.38859	−	17.5525i	0.342958	−	0.942268i	−0.641574	−	0.767061i	$-0.721718\pi$
$347$	6.38859	−	17.5525i	0.342958	−	0.942268i	0.984532	−	0.175207i	$-0.0560595\pi$
$348$	4.83753	+	0.670461i	0.259319	+	0.0359405i
$349$	−3.47936	+	6.02643i	−0.186246	+	0.322587i	−0.943996	−	0.329958i	$-0.892965\pi$
$349$	−3.47936	+	6.02643i	−0.186246	+	0.322587i	0.757750	+	0.652545i	$0.226299\pi$
$350$	−0.0202447	−	1.09970i	−0.00108212	−	0.0587813i
$351$	−0.977967	−	0.172442i	−0.0522000	−	0.00920427i
$352$	10.0943	+	21.3804i	0.538026	+	1.13958i
$353$	−2.82935	−	4.90058i	−0.150591	−	0.260831i	0.780854	−	0.624714i	$-0.214784\pi$
$353$	−2.82935	−	4.90058i	−0.150591	−	0.260831i	−0.931445	+	0.363882i	$0.881451\pi$
$354$	−0.445502	−	0.739841i	−0.0236782	−	0.0393221i
$355$	23.0346	+	19.3284i	1.22255	+	1.02584i
$356$	28.9714	−	6.21586i	1.53548	−	0.329440i
$357$	1.33315	+	3.66281i	0.0705579	+	0.193856i
$358$	0.429192	+	2.19681i	0.0226835	+	0.116105i
$359$	−22.1724	+	3.90959i	−1.17022	+	0.206340i	−0.724784	−	0.688976i	$-0.758061\pi$
$359$	−22.1724	+	3.90959i	−1.17022	+	0.206340i	−0.445431	+	0.895316i	$0.646949\pi$
$360$	18.7669	−	1.03740i	0.989102	−	0.0546756i
$361$	−18.5800	−	3.97305i	−0.977893	−	0.209108i
$362$	16.4695	+	9.10865i	0.865617	+	0.478740i
$363$	−0.323605	−	1.83525i	−0.0169848	−	0.0963258i
$364$	4.54619	+	1.46756i	0.238285	+	0.0769211i
$365$	24.0053	−	8.73722i	1.25650	−	0.457327i
$366$	−0.952053	+	0.829203i	−0.0497646	+	0.0433431i
$367$	−19.3515	+	23.0622i	−1.01014	+	1.20384i	−0.0312345	+	0.999512i	$0.509944\pi$
$367$	−19.3515	+	23.0622i	−1.01014	+	1.20384i	−0.978903	+	0.204323i	$0.934501\pi$
$368$	8.34297	−	5.67384i	0.434907	−	0.295769i
$369$	17.7340	−	10.2387i	0.923197	−	0.533008i
$370$	2.50142	−	3.09503i	0.130042	−	0.160903i
$371$	−0.484164	+	2.74583i	−0.0251366	+	0.142557i
$372$	−0.208526	+	0.393991i	−0.0108115	+	0.0204275i
$373$	15.0172	+	8.67020i	0.777562	+	0.448926i	0.835566	−	0.549391i	$-0.185140\pi$
$373$	15.0172	+	8.67020i	0.777562	+	0.448926i	−0.0580034	+	0.998316i	$0.518473\pi$
$374$	−7.00847	−	18.2057i	−0.362399	−	0.941397i
$375$	2.96636	+	1.07967i	0.153182	+	0.0557538i
$376$	5.47573	+	12.7981i	0.282389	+	0.660009i
$377$	−3.78320	+	3.17448i	−0.194844	+	0.163494i
$378$	3.20862	−	9.34746i	0.165033	−	0.480781i
$379$	−13.0139			−0.668480			−0.334240	−	0.942488i	$-0.608480\pi$
$379$	−13.0139			−0.668480			−0.334240	+	0.942488i	$0.608480\pi$
$380$	17.8387	−	8.72916i	0.915106	−	0.447796i
$381$	2.58981			0.132680
$382$	−5.82214	+	16.9613i	−0.297887	+	0.867814i
$383$	21.9719	−	18.4366i	1.12271	−	0.942068i	0.123975	−	0.992285i	$-0.460436\pi$
$383$	21.9719	−	18.4366i	1.12271	−	0.942068i	0.998738	+	0.0502175i	$0.0159915\pi$
$384$	−0.148832	+	3.25572i	−0.00759504	+	0.166143i
$385$	36.6827	+	13.3514i	1.86952	+	0.680450i
$386$	−11.1602	−	28.9906i	−0.568039	−	1.47558i
$387$	−11.5030	−	6.64124i	−0.584729	−	0.337593i
$388$	18.1380	+	9.59979i	0.920816	+	0.487355i
$389$	5.59981	−	31.7581i	0.283921	−	1.61020i	−0.425191	−	0.905104i	$-0.639793\pi$
$389$	5.59981	−	31.7581i	0.283921	−	1.61020i	0.709113	−	0.705095i	$-0.249096\pi$
$390$	0.339872	−	0.420527i	0.0172101	−	0.0212942i
$391$	−7.20948	+	4.16240i	−0.364599	+	0.210501i
$392$	−12.5244	+	24.7555i	−0.632579	+	1.25034i
$393$	2.55399	−	3.04373i	0.128832	−	0.153536i
$394$	4.84578	−	4.22049i	0.244127	−	0.212625i
$395$	22.1075	−	8.04648i	1.11235	−	0.404862i
$396$	−7.49081	+	23.2049i	−0.376428	+	1.16609i
$397$	2.86736	+	16.2616i	0.143909	+	0.816146i	0.968237	+	0.250034i	$0.0804419\pi$
$397$	2.86736	+	16.2616i	0.143909	+	0.816146i	−0.824328	+	0.566112i	$0.808447\pi$
$398$	15.0775	+	8.33878i	0.755765	+	0.417985i
$399$	−0.355967	−	5.13570i	−0.0178206	−	0.257106i
$400$	−0.330028	+	0.683264i	−0.0165014	+	0.0341632i
$401$	−22.0221	+	3.88308i	−1.09973	+	0.193912i	−0.693925	−	0.720048i	$-0.744120\pi$
$401$	−22.0221	+	3.88308i	−1.09973	+	0.193912i	−0.405805	+	0.913960i	$0.633009\pi$
$402$	−1.10074	−	5.63410i	−0.0548998	−	0.281003i
$403$	−0.154175	−	0.423591i	−0.00767999	−	0.0211006i
$404$	3.67131	+	17.1115i	0.182654	+	0.851331i
$405$	14.4147	+	12.0954i	0.716274	+	0.601026i
$406$	−25.3537	−	42.1046i	−1.25828	−	2.08962i
$407$	2.58135	+	4.47103i	0.127953	+	0.221621i
$408$	0.320078	−	2.66997i	0.0158462	−	0.132183i
$409$	−21.3931	−	3.77218i	−1.05782	−	0.186522i	−0.382431	−	0.923984i	$-0.624913\pi$
$409$	−21.3931	−	3.77218i	−1.05782	−	0.186522i	−0.675389	+	0.737462i	$0.736024\pi$
$410$	0.416283	+	22.6126i	0.0205587	+	1.11676i
$411$	−1.07799	+	1.86714i	−0.0531736	+	0.0920993i
$412$	2.41662	−	17.4365i	0.119059	−	0.859035i
$413$	−2.97256	+	8.16705i	−0.146270	+	0.401874i
$414$	10.2789	+	1.61797i	0.505182	+	0.0795190i
$415$	−2.18824	−	2.60785i	−0.107417	−	0.128014i
$416$	−2.34151	−	2.31928i	−0.114802	−	0.113712i
$417$			5.55050i			0.271809i
$418$	2.25434	+	25.6661i	0.110264	+	1.25537i
$419$		−	13.1962i		−	0.644678i	−0.946624	−	0.322339i	$-0.895531\pi$
$419$		−	13.1962i		−	0.644678i	0.946624	−	0.322339i	$-0.104469\pi$
$420$	3.60823	+	3.99200i	0.176063	+	0.194790i
$421$	−4.59262	−	5.47327i	−0.223830	−	0.266751i	0.642429	−	0.766345i	$-0.277927\pi$
$421$	−4.59262	−	5.47327i	−0.223830	−	0.266751i	−0.866259	+	0.499595i	$0.833482\pi$
$422$	0.804865	−	5.11328i	0.0391802	−	0.248911i
$423$	−4.91013	+	13.4905i	−0.238739	+	0.655930i
$424$	1.15321	−	1.53951i	0.0560048	−	0.0747651i
$425$	0.313039	−	0.542200i	0.0151846	−	0.0263005i
$426$	−5.37642	+	0.0989763i	−0.260488	+	0.00479542i
$427$	12.5127	+	2.20633i	0.605532	+	0.106772i
$428$	−0.936670	+	0.380520i	−0.0452756	+	0.0183931i
$429$	0.350733	+	0.607487i	0.0169335	+	0.0293297i
$430$	12.5673	−	7.56754i	0.606050	−	0.364939i
$431$	−10.9959	−	9.22664i	−0.529653	−	0.444432i	0.338329	−	0.941028i	$-0.390138\pi$
$431$	−10.9959	−	9.22664i	−0.529653	−	0.444432i	−0.867982	+	0.496596i	$0.834583\pi$
$432$	−4.88636	+	4.75487i	−0.235095	+	0.228769i
$433$	−9.93835	−	27.3054i	−0.477607	−	1.31221i	−0.911519	−	0.411258i	$-0.865089\pi$
$433$	−9.93835	−	27.3054i	−0.477607	−	1.31221i	0.433912	−	0.900955i	$-0.357133\pi$
$434$	4.40287	−	0.860190i	0.211344	−	0.0412904i
$435$	−5.47833	+	0.965977i	−0.262666	+	0.0463151i
$436$	10.5954	−	6.64890i	0.507429	−	0.318425i
$437$	10.6698	−	2.65335i	0.510405	−	0.126927i
$438$	−2.21098	+	3.99769i	−0.105644	+	0.191017i
$439$	−4.75454	−	26.9643i	−0.226922	−	1.28694i	−0.858977	−	0.512014i	$-0.828900\pi$
$439$	−4.75454	−	26.9643i	−0.226922	−	1.28694i	0.632055	−	0.774923i	$-0.282212\pi$
$440$	−18.4232	−	19.6434i	−0.878291	−	0.936464i
$441$	−26.8868	+	9.78599i	−1.28032	+	0.466000i
$442$	1.78597	+	2.05057i	0.0849498	+	0.0975355i
$443$	9.24631	−	11.0193i	0.439305	−	0.523544i	−0.500278	−	0.865865i	$-0.666769\pi$
$443$	9.24631	−	11.0193i	0.439305	−	0.523544i	0.939583	+	0.342321i	$0.111213\pi$
$444$	0.0261931	+	0.711167i	0.00124307	+	0.0337505i
$445$	−29.2290	+	16.8754i	−1.38559	+	0.799969i
$446$	30.7931	+	24.8872i	1.45810	+	1.17844i
$447$	0.102108	−	0.579082i	0.00482953	−	0.0273896i
$448$	26.4240	−	19.4302i	1.24842	−	0.917991i
$449$	−19.6084	−	11.3209i	−0.925380	−	0.534268i	−0.0400325	−	0.999198i	$-0.512746\pi$
$449$	−19.6084	−	11.3209i	−0.925380	−	0.534268i	−0.885347	+	0.464930i	$0.846079\pi$
$450$	−0.730315	+	0.281141i	−0.0344274	+	0.0132531i
$451$	−27.5715	−	10.0352i	−1.29829	−	0.472539i
$452$	−8.92611	+	11.4699i	−0.419849	+	0.539501i
$453$	2.12258	−	1.78106i	0.0997276	−	0.0836814i
$454$	−8.38213	−	2.87726i	−0.393393	−	0.135036i
$455$	−5.44144			−0.255099
$456$	−1.38034	+	3.27233i	−0.0646403	+	0.153241i
$457$	20.3699			0.952862			0.476431	−	0.879212i	$-0.341930\pi$
$457$	20.3699			0.952862			0.476431	+	0.879212i	$0.341930\pi$
$458$	−16.9113	−	5.80499i	−0.790213	−	0.271249i
$459$	4.30940	−	3.61602i	0.201146	−	0.168781i
$460$	−7.05812	+	9.06960i	−0.329087	+	0.422872i
$461$	−17.2074	−	6.26298i	−0.801429	−	0.291696i	−0.0913504	−	0.995819i	$-0.529118\pi$
$461$	−17.2074	−	6.26298i	−0.801429	−	0.291696i	−0.710078	+	0.704123i	$0.751341\pi$
$462$	−6.51489	+	2.50796i	−0.303100	+	0.116681i
$463$	−8.71218	−	5.02998i	−0.404890	−	0.233763i	0.283702	−	0.958912i	$-0.408437\pi$
$463$	−8.71218	−	5.02998i	−0.404890	−	0.233763i	−0.688592	+	0.725149i	$0.741771\pi$
$464$	2.49429	+	33.8152i	0.115794	+	1.56983i
$465$	0.0881705	−	0.500040i	0.00408881	−	0.0231888i
$466$	7.40506	+	5.98481i	0.343033	+	0.277241i
$467$	4.54318	−	2.62300i	0.210233	−	0.121378i	−0.391187	−	0.920311i	$-0.627935\pi$
$467$	4.54318	−	2.62300i	0.210233	−	0.121378i	0.601420	+	0.798933i	$0.294602\pi$
$468$	−0.125102	−	3.39664i	−0.00578285	−	0.157010i
$469$	−37.1350	+	44.2558i	−1.71474	+	2.04354i
$470$	−10.4138	−	11.9566i	−0.480351	−	0.551517i
$471$	−2.04592	+	0.744654i	−0.0942711	+	0.0343119i
$472$	4.37342	−	4.10175i	0.201303	−	0.188798i
$473$	3.30481	+	18.7425i	0.151955	+	0.861782i
$474$	−2.03618	+	3.68165i	−0.0935249	+	0.169104i
$475$	−0.595156	+	0.574033i	−0.0273076	+	0.0263384i
$476$	−22.9226	+	14.3845i	−1.05066	+	0.659314i
$477$	1.95364	−	0.344480i	0.0894511	−	0.0157726i
$478$	−13.9836	+	2.73199i	−0.639597	+	0.124958i
$479$	1.67304	+	4.59663i	0.0764430	+	0.210025i	0.972028	−	0.234865i	$-0.0754648\pi$
$479$	1.67304	+	4.59663i	0.0764430	+	0.210025i	−0.895585	+	0.444890i	$0.853243\pi$
$480$	−0.977903	−	3.58117i	−0.0446350	−	0.163457i
$481$	−0.551276	−	0.462575i	−0.0251360	−	0.0210916i
$482$	10.2425	−	6.16761i	0.466532	−	0.280927i
$483$	1.48950	+	2.57990i	0.0677748	+	0.117389i
$484$	11.9870	−	4.86967i	0.544862	−	0.221349i
$485$	−23.0201	−	4.05906i	−1.04529	−	0.184312i
$486$	−10.5949	+	0.195044i	−0.480593	+	0.00884739i
$487$	9.66172	−	16.7346i	0.437814	−	0.758317i	−0.559706	−	0.828691i	$-0.689086\pi$
$487$	9.66172	−	16.7346i	0.437814	−	0.758317i	0.997521	+	0.0703744i	$0.0224194\pi$
$488$	−7.01550	−	5.25515i	−0.317577	−	0.237890i
$489$	1.63238	−	4.48492i	0.0738186	−	0.202815i
$490$	4.91370	−	31.2166i	0.221978	−	1.41022i
$491$	−14.7254	−	17.5490i	−0.664547	−	0.791977i	0.323483	−	0.946234i	$-0.395146\pi$
$491$	−14.7254	−	17.5490i	−0.664547	−	0.791977i	−0.988031	+	0.154257i	$0.950702\pi$
$492$	−2.71202	−	3.00047i	−0.122267	−	0.135272i
$493$		−	27.9766i		−	1.26000i
$494$	−1.51891	−	3.25441i	−0.0683392	−	0.146423i
$495$		−	27.7745i		−	1.24837i
$496$	−2.97824	−	0.841712i	−0.133727	−	0.0377940i
$497$	34.7850	+	41.4551i	1.56032	+	1.85952i
$498$	0.601385	+	0.0946620i	0.0269487	+	0.00424191i
$499$	0.869506	−	2.38895i	0.0389245	−	0.106944i	−0.918708	−	0.394938i	$-0.870766\pi$
$499$	0.869506	−	2.38895i	0.0389245	−	0.106944i	0.957632	+	0.287994i	$0.0929883\pi$
$500$	−3.00879	+	21.7091i	−0.134557	+	0.970860i
$501$	−1.11125	+	1.92475i	−0.0496472	+	0.0859914i
$502$	−0.221979	−	12.0579i	−0.00990740	−	0.538172i
$503$	−39.8057	−	7.01881i	−1.77485	−	0.312953i	−0.812132	−	0.583473i	$-0.801693\pi$
$503$	−39.8057	−	7.01881i	−1.77485	−	0.312953i	−0.962714	+	0.270520i	$0.912804\pi$
$504$	33.5856	+	4.02626i	1.49602	+	0.179344i
$505$	−9.96719	−	17.2637i	−0.443534	−	0.768224i
$506$	−7.69109	−	12.7725i	−0.341911	−	0.567807i
$507$	2.79385	+	2.34432i	0.124079	+	0.104115i
$508$	3.77192	+	17.5805i	0.167352	+	0.780008i
$509$	2.34020	+	6.42964i	0.103728	+	0.284989i	0.980690	−	0.195570i	$-0.0626558\pi$
$509$	2.34020	+	6.42964i	0.103728	+	0.284989i	−0.876962	+	0.480559i	$0.840434\pi$
$510$	0.587315	+	3.00616i	0.0260067	+	0.133115i
$511$	45.2762	−	7.98342i	2.00290	−	0.353166i
$512$	−22.3176	+	3.73145i	−0.986309	+	0.164909i
$513$	−6.78927	+	3.01781i	−0.299754	+	0.133239i
$514$	−3.39643	−	1.87844i	−0.149810	−	0.0828545i
$515$	3.48179	+	19.7462i	0.153426	+	0.870121i
$516$	−0.805916	+	2.49655i	−0.0354785	+	0.109905i
$517$	19.3297	−	7.03543i	0.850118	−	0.309418i
$518$	5.40061	−	4.70373i	0.237289	−	0.206670i
$519$	−1.72724	+	2.05844i	−0.0758173	+	0.0903555i
$520$	3.34967	+	1.69469i	0.146893	+	0.0743169i
$521$	32.2497	−	18.6194i	1.41288	−	0.815729i	0.417225	−	0.908803i	$-0.363003\pi$
$521$	32.2497	−	18.6194i	1.41288	−	0.815729i	0.995659	+	0.0930744i	$0.0296694\pi$
$522$	−21.9808	+	27.1971i	−0.962074	+	1.19038i
$523$	−7.68298	+	43.5724i	−0.335953	+	1.90529i	0.0816571	+	0.996660i	$0.473979\pi$
$523$	−7.68298	+	43.5724i	−0.335953	+	1.90529i	−0.417611	+	0.908626i	$0.637132\pi$
$524$	24.3815	+	12.9043i	1.06511	+	0.563726i
$525$	−0.194025	−	0.112020i	−0.00846794	−	0.00488897i
$526$	−1.12358	−	2.91870i	−0.0489904	−	0.127261i
$527$	2.39959	+	0.873380i	0.104528	+	0.0380450i
$528$	4.79156	+	0.485135i	0.208526	+	0.0211128i
$529$	12.7452	−	10.6945i	0.554138	−	0.464977i
$530$	−0.711340	+	2.07230i	−0.0308987	+	0.0900151i
$531$	6.18373			0.268351
$532$	34.3443	−	9.89627i	1.48901	−	0.429058i
$533$	4.08990			0.177153
$534$	1.95956	−	5.70867i	0.0847986	−	0.247038i
$535$	0.882168	−	0.740227i	0.0381395	−	0.0320028i
$536$	36.6429	−	15.6779i	1.58273	−	0.677182i
$537$	0.428443	+	0.155940i	0.0184887	+	0.00672933i
$538$	7.62261	+	19.8011i	0.328634	+	0.853686i
$539$	35.5043	+	20.4984i	1.52928	+	0.882930i
$540$	3.63284	−	6.86394i	0.156333	−	0.295377i
$541$	6.37799	−	36.1714i	0.274211	−	1.55513i	−0.467245	−	0.884128i	$-0.654753\pi$
$541$	6.37799	−	36.1714i	0.274211	−	1.55513i	0.741456	−	0.671001i	$-0.234135\pi$
$542$	22.7726	−	28.1767i	0.978167	−	1.21029i
$543$	3.32003	−	1.91682i	0.142476	−	0.0822587i
$544$	18.5908	−	1.71587i	0.797074	−	0.0735675i
$545$	−9.15853	+	10.9147i	−0.392308	+	0.467535i
$546$	0.733791	−	0.639105i	0.0314033	−	0.0273512i
$547$	−30.6008	+	11.1378i	−1.30840	+	0.476217i	−0.899722	−	0.436464i	$-0.856231\pi$
$547$	−30.6008	+	11.1378i	−1.30840	+	0.476217i	−0.408673	+	0.912681i	$0.634008\pi$
$548$	−14.2448	−	4.59838i	−0.608507	−	0.196433i
$549$	−1.56979	−	8.90270i	−0.0669969	−	0.379958i
$550$	0.981214	+	0.542673i	0.0418391	+	0.0231396i
$551$	−10.2063	+	35.5118i	−0.434805	+	1.51285i
$552$	−0.113433	−	2.05204i	−0.00482802	−	0.0873408i
$553$	41.6968	−	7.35227i	1.77313	−	0.312650i
$554$	−2.30262	−	11.7859i	−0.0978288	−	0.500735i
$555$	−0.277242	−	0.761715i	−0.0117683	−	0.0323330i
$556$	−37.6786	+	8.08399i	−1.59793	+	0.342838i
$557$	9.87223	+	8.28378i	0.418300	+	0.350995i	0.827516	−	0.561442i	$-0.189753\pi$
$557$	9.87223	+	8.28378i	0.418300	+	0.350995i	−0.409216	+	0.912438i	$0.634198\pi$
$558$	−1.64653	−	2.73437i	−0.0697030	−	0.115755i
$559$	−1.32643	−	2.29745i	−0.0561021	−	0.0971717i
$560$	−21.8438	+	30.3079i	−0.923068	+	1.28074i
$561$	−3.91334	−	0.690028i	−0.165221	−	0.0291330i
$562$	−0.0299632	−	1.62761i	−0.00126392	−	0.0686566i
$563$	2.06206	−	3.57160i	0.0869055	−	0.150525i	−0.819296	−	0.573371i	$-0.805635\pi$
$563$	2.06206	−	3.57160i	0.0869055	−	0.150525i	0.906202	+	0.422846i	$0.138969\pi$
$564$	2.80864	+	0.389266i	0.118265	+	0.0163911i
$565$	5.66208	−	15.5564i	0.238205	−	0.654464i
$566$	−13.1110	−	2.06376i	−0.551097	−	0.0867463i
$567$	21.7679	+	25.9420i	0.914168	+	1.08946i
$568$	−8.50234	−	36.3527i	−0.356750	−	1.52533i
$569$			2.71200i			0.113693i	0.998383	+	0.0568466i	$0.0181046\pi$
$569$			2.71200i			0.113693i	−0.998383	+	0.0568466i	$0.981895\pi$
$570$	0.351197	−	4.03010i	0.0147100	−	0.168802i
$571$			27.8695i			1.16630i	0.812363	+	0.583152i	$0.198181\pi$
$571$			27.8695i			1.16630i	−0.812363	+	0.583152i	$0.801819\pi$
$572$	−3.61299	+	3.26565i	−0.151067	+	0.136544i
$573$	2.34798	+	2.79821i	0.0980881	+	0.116897i
$574$	−6.32892	+	40.2074i	−0.264164	+	1.67823i
$575$	0.163653	−	0.449633i	0.00682480	−	0.0187510i
$576$	−19.4209	−	12.9385i	−0.809204	−	0.539102i
$577$	−20.7062	+	35.8643i	−0.862012	+	1.49305i	0.00797112	+	0.999968i	$0.497463\pi$
$577$	−20.7062	+	35.8643i	−0.862012	+	1.49305i	−0.869983	+	0.493081i	$0.835871\pi$
$578$	8.63577	−	0.158979i	0.359201	−	0.00661265i
$579$	−6.23156	−	1.09879i	−0.258975	−	0.0456642i
$580$	−14.5362	−	35.7817i	−0.603584	−	1.48576i
$581$	−3.06334	−	5.30586i	−0.127089	−	0.220124i
$582$	3.58106	−	2.15637i	0.148440	−	0.0893843i
$583$	−2.17743	−	1.82708i	−0.0901801	−	0.0756701i
$584$	−30.3578	−	9.18639i	−1.25621	−	0.380135i
$585$	1.32415	+	3.63807i	0.0547468	+	0.150415i
$586$	−25.5929	+	5.00010i	−1.05723	+	0.206552i
$587$	14.7610	−	2.60276i	0.609252	−	0.107428i	0.139494	−	0.990223i	$-0.455452\pi$
$587$	14.7610	−	2.60276i	0.609252	−	0.107428i	0.469758	+	0.882795i	$0.344341\pi$
$588$	3.00381	+	4.78676i	0.123875	+	0.197402i
$589$	−2.72727	−	1.98403i	−0.112375	−	0.0817504i
$590$	−3.30537	+	5.97649i	−0.136080	+	0.246048i
$591$	−0.227298	−	1.28907i	−0.00934977	−	0.0530252i
$592$	−4.78948	+	1.21358i	−0.196846	+	0.0498779i
$593$	−7.47341	+	2.72010i	−0.306896	+	0.111701i	−0.490877	−	0.871229i	$-0.663324\pi$
$593$	−7.47341	+	2.72010i	−0.306896	+	0.111701i	0.183981	+	0.982930i	$0.441101\pi$
$594$	6.61711	+	7.59747i	0.271503	+	0.311728i
$595$	19.8140	−	23.6134i	0.812293	−	0.968053i
$596$	4.07971	−	0.150260i	0.167111	−	0.00615490i
$597$	3.03942	−	1.75481i	0.124395	−	0.0718195i
$598$	1.61635	+	1.30635i	0.0660976	+	0.0534204i
$599$	4.61115	−	26.1511i	0.188407	−	1.06851i	−0.733093	−	0.680128i	$-0.761924\pi$
$599$	4.61115	−	26.1511i	0.188407	−	1.06851i	0.921500	−	0.388379i	$-0.126965\pi$
$600$	0.0845514	+	0.129386i	0.00345180	+	0.00528214i
$601$	22.0067	+	12.7056i	0.897673	+	0.518272i	0.876444	−	0.481503i	$-0.159909\pi$
$601$	22.0067	+	12.7056i	0.897673	+	0.518272i	0.0212282	+	0.999775i	$0.493242\pi$
$602$	24.6386	−	9.48485i	1.00419	−	0.386573i
$603$	38.6254	+	14.0585i	1.57295	+	0.572506i
$604$	15.1818	+	11.8148i	0.617739	+	0.480735i
$605$	−11.2895	+	9.47300i	−0.458983	+	0.385132i
$606$	3.37174	+	1.15739i	0.136968	+	0.0470157i
$607$	−13.6931			−0.555787			−0.277894	−	0.960612i	$-0.589636\pi$
$607$	−13.6931			−0.555787			−0.277894	+	0.960612i	$0.589636\pi$
$608$	−24.2240	−	4.60421i	−0.982412	−	0.186726i
$609$	−10.0114			−0.405681
$610$	9.44344	+	3.24156i	0.382354	+	0.131247i
$611$	−2.19650	+	1.84308i	−0.0888609	+	0.0745631i
$612$	15.1954	+	11.8253i	0.614237	+	0.478010i
$613$	18.5018	+	6.73412i	0.747282	+	0.271988i	0.687462	−	0.726221i	$-0.258725\pi$
$613$	18.5018	+	6.73412i	0.747282	+	0.271988i	0.0598205	+	0.998209i	$0.480947\pi$
$614$	−7.37991	+	2.84096i	−0.297829	+	0.114652i
$615$	3.98965	+	2.30343i	0.160878	+	0.0928831i
$616$	−26.5134	−	40.5724i	−1.06826	−	1.63471i
$617$	0.953161	−	5.40564i	0.0383728	−	0.217623i	−0.959592	−	0.281396i	$-0.909202\pi$
$617$	0.953161	−	5.40564i	0.0383728	−	0.217623i	0.997964	+	0.0637735i	$0.0203135\pi$
$618$	−2.78875	−	2.25388i	−0.112180	−	0.0906644i
$619$	−12.3997	+	7.15899i	−0.498388	+	0.287744i	−0.728047	−	0.685527i	$-0.759572\pi$
$619$	−12.3997	+	7.15899i	−0.498388	+	0.287744i	0.229660	+	0.973271i	$0.426239\pi$
$620$	3.52284	−	0.129750i	0.141481	−	0.00521090i
$621$	2.76359	−	3.29352i	0.110899	−	0.132165i
$622$	11.1158	+	12.7627i	0.445705	+	0.511738i
$623$	−57.0776	+	20.7746i	−2.28677	+	0.832315i
$624$	−0.650755	+	0.164892i	−0.0260511	+	0.00660094i
$625$	−4.49966	−	25.5188i	−0.179986	−	1.02075i
$626$	−10.8767	+	19.6663i	−0.434720	+	0.786023i
$627$	4.71562	+	2.30353i	0.188324	+	0.0919943i
$628$	−8.03472	−	12.8038i	−0.320620	−	0.510928i
$629$	4.01473	−	0.707906i	0.160078	−	0.0282261i
$630$	−37.8145	+	7.38784i	−1.50657	+	0.294339i
$631$	−0.896513	−	2.46315i	−0.0356896	−	0.0980565i	0.920568	−	0.390583i	$-0.127726\pi$
$631$	−0.896513	−	2.46315i	−0.0356896	−	0.0980565i	−0.956258	+	0.292526i	$0.905504\pi$
$632$	−27.9578	−	8.46013i	−1.11210	−	0.336526i
$633$	−0.807698	−	0.677739i	−0.0321031	−	0.0269377i
$634$	20.3990	−	12.2834i	0.810146	−	0.487837i
$635$	−10.2403	−	17.7368i	−0.406375	−	0.703863i
$636$	−0.147469	−	0.363003i	−0.00584752	−	0.0143940i
$637$	−5.62782	−	0.992337i	−0.222982	−	0.0393178i
$638$	50.0966	−	0.922244i	1.98334	−	0.0365120i
$639$	19.2515	−	33.3446i	0.761579	−	1.31909i
$640$	22.8858	−	11.8541i	0.904643	−	0.468574i
$641$	12.1986	−	33.5152i	0.481814	−	1.32377i	−0.426123	−	0.904665i	$-0.640121\pi$
$641$	12.1986	−	33.5152i	0.481814	−	1.32377i	0.907937	−	0.419107i	$-0.137657\pi$
$642$	−0.0320218	+	0.203433i	−0.00126380	+	0.00802887i
$643$	15.4800	+	18.4484i	0.610472	+	0.727532i	0.979401	−	0.201925i	$-0.0647198\pi$
$643$	15.4800	+	18.4484i	0.610472	+	0.727532i	−0.368929	+	0.929458i	$0.620275\pi$
$644$	−15.3438	+	13.8687i	−0.604630	+	0.546504i
$645$		−	2.98818i		−	0.117660i
$646$	19.6535	+	5.25893i	0.773257	+	0.206910i
$647$			28.8314i			1.13348i	0.823897	+	0.566740i	$0.191796\pi$
$647$			28.8314i			1.13348i	−0.823897	+	0.566740i	$0.808204\pi$
$648$	−5.32064	−	22.7490i	−0.209014	−	0.893665i
$649$	−5.69528	−	6.78737i	−0.223559	−	0.266428i
$650$	−0.154397	−	0.0243031i	−0.00605595	−	0.000953247i
$651$	0.312537	−	0.858689i	0.0122493	−	0.0336547i
$652$	32.8225	+	4.54906i	1.28543	+	0.178155i
$653$	−21.8194	+	37.7923i	−0.853859	+	1.47893i	0.0238403	+	0.999716i	$0.492411\pi$
$653$	−21.8194	+	37.7923i	−0.853859	+	1.47893i	−0.877699	+	0.479212i	$0.840923\pi$
$654$	−0.0468988	−	2.54756i	−0.00183389	−	0.0996173i
$655$	−30.9442	−	5.45629i	−1.20909	−	0.213195i
$656$	16.4182	−	22.7801i	0.641024	−	0.889412i
$657$	−16.3553	−	28.3283i	−0.638083	−	1.10519i
$658$	−14.7202	−	24.4457i	−0.573853	−	0.952991i
$659$	30.8465	+	25.8833i	1.20161	+	1.00827i	0.999583	+	0.0288882i	$0.00919669\pi$
$659$	30.8465	+	25.8833i	1.20161	+	1.00827i	0.202025	+	0.979380i	$0.435248\pi$
$660$	−5.36365	+	1.15078i	−0.208780	+	0.0447940i
$661$	5.51264	+	15.1459i	0.214417	+	0.589106i	0.999543	−	0.0302304i	$-0.00962411\pi$
$661$	5.51264	+	15.1459i	0.214417	+	0.589106i	−0.785126	+	0.619336i	$0.787402\pi$
$662$	3.94951	+	20.2155i	0.153502	+	0.785696i
$663$	0.545489	−	0.0961845i	0.0211851	−	0.00373550i
$664$	0.233288	+	4.22026i	0.00905331	+	0.163778i
$665$	−33.7652	+	22.7449i	−1.30936	+	0.882008i
$666$	−4.45906	−	2.46614i	−0.172785	−	0.0955609i
$667$	−3.71286	−	21.0567i	−0.143763	−	0.815319i
$668$	−14.6843	−	4.74026i	−0.568152	−	0.183406i
$669$	7.57848	−	2.75834i	0.293001	−	0.106644i
$670$	−34.2337	+	29.8163i	−1.32256	+	1.15190i
$671$	−8.32598	+	9.92251i	−0.321421	+	0.383054i
$672$	−0.614022	−	6.65267i	−0.0236864	−	0.256632i
$673$	−20.0030	+	11.5487i	−0.771058	+	0.445171i	−0.833252	−	0.552894i	$-0.813524\pi$
$673$	−20.0030	+	11.5487i	−0.771058	+	0.445171i	0.0621939	+	0.998064i	$0.480190\pi$
$674$	0.355392	−	0.439730i	0.0136892	−	0.0169378i
$675$	−0.0561477	+	0.318430i	−0.00216113	+	0.0122564i
$676$	−11.8449	+	22.3799i	−0.455572	+	0.860765i
$677$	25.2730	+	14.5914i	0.971321	+	0.560792i	0.899639	−	0.436635i	$-0.143830\pi$
$677$	25.2730	+	14.5914i	0.971321	+	0.560792i	0.0716821	+	0.997428i	$0.477163\pi$
$678$	1.06358	+	2.76284i	0.0408465	+	0.106106i
$679$	−39.5310	−	14.3881i	−1.51706	−	0.552165i
$680$	−19.5514	+	8.36518i	−0.749761	+	0.320790i
$681$	−1.38285	+	1.16035i	−0.0529910	+	0.0444648i
$682$	−1.48482	+	4.32564i	−0.0568568	+	0.165637i
$683$	32.3508			1.23787			0.618934	−	0.785443i	$-0.287565\pi$
$683$	32.3508			1.23787			0.618934	+	0.785443i	$0.287565\pi$
$684$	−14.9740	−	20.5539i	−0.572546	−	0.785897i
$685$	17.0499			0.651444
$686$	5.28731	−	15.4032i	0.201871	−	0.588097i
$687$	−2.78996	+	2.34106i	−0.106444	+	0.0893170i
$688$	−18.1212	−	1.83473i	−0.690862	−	0.0699483i
$689$	0.372319	+	0.135513i	0.0141842	+	0.00516263i
$690$	0.841002	+	2.18465i	0.0320164	+	0.0831683i
$691$	13.6086	+	7.85694i	0.517696	+	0.298892i	0.735992	−	0.676991i	$-0.236716\pi$
$691$	13.6086	+	7.85694i	0.517696	+	0.298892i	−0.218295	+	0.975883i	$0.570050\pi$
$692$	−16.4890	−	8.72703i	−0.626816	−	0.331752i
$693$	8.67987	−	49.2260i	0.329721	−	1.86994i
$694$	16.6046	−	20.5450i	0.630302	−	0.779878i
$695$	38.0136	−	21.9471i	1.44194	−	0.832502i
$696$	6.16286	+	3.11795i	0.233603	+	0.118186i
$697$	−14.8926	+	17.7483i	−0.564097	+	0.672265i
$698$	−7.42102	+	6.46344i	−0.280890	+	0.244645i
$699$	1.82246	−	0.663319i	0.0689316	−	0.0250890i
$700$	0.477843	−	1.48025i	0.0180608	−	0.0559483i
$701$	3.32956	+	18.8829i	0.125756	+	0.713196i	0.980856	+	0.194734i	$0.0623842\pi$
$701$	3.32956	+	18.8829i	0.125756	+	0.713196i	−0.855100	+	0.518462i	$0.826505\pi$
$702$	−1.22896	−	0.679690i	−0.0463840	−	0.0256532i
$703$	−5.35431	−	0.566072i	−0.201942	−	0.0213498i
$704$	3.68539	+	33.2332i	0.138898	+	1.25252i
$705$	−3.18068	+	0.560840i	−0.119791	+	0.0211225i
$706$	−1.53446	−	7.85412i	−0.0577503	−	0.295594i
$707$	−12.2702	−	33.7121i	−0.461468	−	1.26787i
$708$	−0.256210	−	1.19416i	−0.00962895	−	0.0448795i
$709$	−13.0269	−	10.9309i	−0.489235	−	0.410517i	0.364517	−	0.931197i	$-0.381234\pi$
$709$	−13.0269	−	10.9309i	−0.489235	−	0.410517i	−0.853752	+	0.520680i	$0.825679\pi$
$710$	21.9367	+	36.4300i	0.823268	+	1.36719i
$711$	−15.0623	−	26.0887i	−0.564881	−	0.978403i
$712$	41.6063	+	4.98778i	1.55926	+	0.186925i
$713$	1.92197	+	0.338895i	0.0719784	+	0.0126917i
$714$	0.101463	+	5.51150i	0.00379716	+	0.206263i
$715$	2.77365	−	4.80411i	0.103729	−	0.179663i
$716$	−0.434570	+	3.13552i	−0.0162407	+	0.117180i
$717$	−0.992628	+	2.72722i	−0.0370704	+	0.101850i
$718$	−31.4530	−	4.95091i	−1.17381	−	0.184766i
$719$	−25.6259	−	30.5397i	−0.955684	−	1.13894i	−0.990217	−	0.139536i	$-0.955439\pi$
$719$	−25.6259	−	30.5397i	−0.955684	−	1.13894i	0.0345328	−	0.999404i	$-0.489006\pi$
$720$	25.5790	+	7.22914i	0.953273	+	0.269414i
$721$			36.0852i			1.34388i
$722$	−23.0284	−	13.8453i	−0.857029	−	0.515269i
$723$		−	2.43539i		−	0.0905733i
$724$	17.8474	+	19.7457i	0.663294	+	0.733843i
$725$	1.03362	+	1.23182i	0.0383877	+	0.0457487i
$726$	0.409796	−	2.60342i	0.0152090	−	0.0966221i
$727$	−2.73410	+	7.51188i	−0.101402	+	0.278600i	−0.980011	−	0.198941i	$-0.936250\pi$
$727$	−2.73410	+	7.51188i	−0.101402	+	0.278600i	0.878609	+	0.477541i	$0.158472\pi$
$728$	5.40717	+	4.05038i	0.200403	+	0.150117i
$729$	11.3108	−	19.5909i	0.418919	−	0.725589i
$730$	36.1213	−	0.664969i	1.33691	−	0.0246116i
$731$	14.7998	+	2.60961i	0.547392	+	0.0965199i
$732$	−1.65420	+	0.672013i	−0.0611408	+	0.0248383i
$733$	14.5869	+	25.2652i	0.538779	+	0.933193i	0.998970	+	0.0453728i	$0.0144476\pi$
$733$	14.5869	+	25.2652i	0.538779	+	0.933193i	−0.460191	+	0.887820i	$0.652219\pi$
$734$	−36.4735	+	21.9629i	−1.34626	+	0.810665i
$735$	−4.93100	−	4.13760i	−0.181883	−	0.152618i
$736$	13.7647	−	3.75870i	0.507374	−	0.138548i
$737$	−20.1436	−	55.3440i	−0.741998	−	2.03862i
$738$	28.4222	−	5.55286i	1.04624	−	0.204404i
$739$	−18.2045	+	3.20994i	−0.669663	+	0.118080i	−0.498135	−	0.867100i	$-0.665981\pi$
$739$	−18.2045	+	3.20994i	−0.669663	+	0.118080i	−0.171528	+	0.985179i	$0.554870\pi$
$740$	4.76698	−	2.99140i	0.175238	−	0.109966i
$741$	−0.727500	−	0.0769132i	−0.0267254	−	0.00282548i
$742$	−1.90836	+	3.45053i	−0.0700581	+	0.126673i
$743$	−1.20332	−	6.82439i	−0.0441457	−	0.250363i	0.954746	−	0.297421i	$-0.0961264\pi$
$743$	−1.20332	−	6.82439i	−0.0441457	−	0.250363i	−0.998892	+	0.0470583i	$0.985015\pi$
$744$	−0.459825	+	0.431260i	−0.0168580	+	0.0158108i
$745$	−4.36969	+	1.59044i	−0.160093	+	0.0582690i
$746$	16.1062	+	18.4924i	0.589690	+	0.677055i
$747$	−2.80197	+	3.33926i	−0.102519	+	0.122177i
$748$	−1.01543	−	27.5700i	−0.0371280	−	1.00806i
$749$	1.79484	−	1.03625i	0.0655819	−	0.0378637i
$750$	3.47209	+	2.80617i	0.126783	+	0.102467i
$751$	−1.76031	+	9.98320i	−0.0642345	+	0.364292i	0.935699	+	0.352798i	$0.114770\pi$
$751$	−1.76031	+	9.98320i	−0.0642345	+	0.364292i	−0.999934	+	0.0114939i	$0.996341\pi$
$752$	1.44817	+	19.6329i	0.0528093	+	0.715938i
$753$	−2.12744	−	1.22828i	−0.0775283	−	0.0447610i
$754$	−6.51797	+	2.50915i	−0.237370	+	0.0913779i
$755$	−20.5908	−	7.49442i	−0.749374	−	0.272750i
$756$	8.58372	−	11.0300i	0.312187	−	0.401156i
$757$	−15.0952	+	12.6664i	−0.548646	+	0.460368i	−0.874482	−	0.485058i	$-0.838799\pi$
$757$	−15.0952	+	12.6664i	−0.548646	+	0.460368i	0.325836	+	0.945426i	$0.394354\pi$
$758$	−17.4075	−	5.97530i	−0.632267	−	0.217033i
$759$	−3.03697			−0.110235
$760$	27.8691	−	3.48557i	1.01092	−	0.126435i
$761$	19.6304			0.711603			0.355801	−	0.934562i	$-0.384208\pi$
$761$	19.6304			0.711603			0.355801	+	0.934562i	$0.384208\pi$
$762$	3.46414	+	1.18911i	0.125493	+	0.0430767i
$763$	−19.6430	+	16.4825i	−0.711126	+	0.596706i
$764$	−15.5754	+	20.0142i	−0.563500	+	0.724090i
$765$	−20.6092	−	7.50113i	−0.745126	−	0.271204i
$766$	37.8549	−	14.5726i	1.36775	−	0.526528i
$767$	1.06959	+	0.617527i	0.0386206	+	0.0222976i
$768$	−1.69393	+	4.28653i	−0.0611245	+	0.154677i
$769$	−6.67065	+	37.8311i	−0.240550	+	1.36423i	0.590055	+	0.807363i	$0.299106\pi$
$769$	−6.67065	+	37.8311i	−0.240550	+	1.36423i	−0.830605	+	0.556863i	$0.812005\pi$
$770$	42.9366	+	34.7016i	1.54733	+	1.25056i
$771$	−0.684677	+	0.395298i	−0.0246580	+	0.0142363i
$772$	−1.61697	−	43.9021i	−0.0581958	−	1.58007i
$773$	−10.1209	+	12.0616i	−0.364024	+	0.433827i	−0.916704	−	0.399567i	$-0.869161\pi$
$773$	−10.1209	+	12.0616i	−0.364024	+	0.433827i	0.552680	+	0.833393i	$0.313605\pi$
$774$	−12.3371	−	14.1649i	−0.443448	−	0.509147i
$775$	−0.137923	+	0.0501998i	−0.00495434	+	0.00180323i
$776$	19.8537	+	21.1687i	0.712707	+	0.759912i
$777$	−0.253323	−	1.43666i	−0.00908790	−	0.0515400i
$778$	22.0720	−	39.9086i	0.791318	−	1.43079i
$779$	25.3786	−	17.0955i	0.909283	−	0.612511i
$780$	0.647698	−	0.406447i	0.0231913	−	0.0145531i
$781$	−54.3306	+	9.57994i	−1.94410	+	0.342797i
$782$	−11.5546	+	2.25743i	−0.413191	+	0.0807254i
$783$	4.94174	+	13.5773i	0.176603	+	0.485214i
$784$	−28.1191	+	27.3625i	−1.00425	+	0.977231i
$785$	13.1896	+	11.0674i	0.470758	+	0.395013i
$786$	4.81375	−	2.89864i	0.171701	−	0.103391i
$787$	−11.5582	−	20.0194i	−0.412005	−	0.713614i	0.583104	−	0.812398i	$-0.301838\pi$
$787$	−11.5582	−	20.0194i	−0.412005	−	0.713614i	−0.995109	+	0.0987836i	$0.968505\pi$
$788$	8.41956	−	3.42042i	0.299934	−	0.121848i
$789$	−0.627377	−	0.110624i	−0.0223352	−	0.00393830i
$790$	33.2656	−	0.612398i	1.18354	−	0.0217881i
$791$	14.8967	−	25.8019i	0.529667	−	0.917409i
$792$	−20.6742	+	27.5996i	−0.734626	+	0.980709i
$793$	0.617530	−	1.69665i	0.0219291	−	0.0602498i
$794$	−3.63108	+	23.0681i	−0.128862	+	0.818657i
$795$	0.286872	+	0.341881i	0.0101743	+	0.0121253i
$796$	16.3389	+	18.0768i	0.579118	+	0.640714i
$797$		−	54.7609i		−	1.93973i	−0.243642	−	0.969865i	$-0.578342\pi$
$797$		−	54.7609i		−	1.93973i	0.243642	−	0.969865i	$-0.421658\pi$
$798$	1.88190	−	7.03297i	0.0666184	−	0.248964i
$799$		−	16.2430i		−	0.574638i
$800$	−0.755166	+	0.762404i	−0.0266991	+	0.0269551i
$801$	27.7791	+	33.1059i	0.981528	+	1.16974i
$802$	−31.2397	−	4.91734i	−1.10311	−	0.173637i
$803$	−16.0302	+	44.0426i	−0.565693	+	1.55423i
$804$	1.11453	−	8.04159i	0.0393065	−	0.283605i
$805$	11.7792	−	20.4023i	0.415164	−	0.719085i
$806$	−0.0117339	−	0.637386i	−0.000413308	−	0.0224510i
$807$	4.25627	+	0.750495i	0.149828	+	0.0264187i
$808$	−2.94596	+	24.5741i	−0.103639	+	0.864515i
$809$	−4.43960	−	7.68961i	−0.156088	−	0.270352i	0.777367	−	0.629048i	$-0.216555\pi$
$809$	−4.43960	−	7.68961i	−0.156088	−	0.270352i	−0.933455	+	0.358695i	$0.883222\pi$
$810$	13.7276	+	22.7974i	0.482340	+	0.801017i
$811$	37.3268	+	31.3209i	1.31072	+	1.09982i	0.988185	+	0.153268i	$0.0489796\pi$
$811$	37.3268	+	31.3209i	1.31072	+	1.09982i	0.322536	+	0.946557i	$0.395465\pi$
$812$	−14.5810	−	67.9603i	−0.511692	−	2.38494i
$813$	−2.52397	−	6.93456i	−0.0885196	−	0.243206i
$814$	1.39996	+	7.16568i	0.0490687	+	0.251157i
$815$	−37.1703	+	6.55412i	−1.30202	+	0.229581i
$816$	1.65405	−	3.42440i	0.0579032	−	0.119878i
$817$	−17.8340	−	8.71171i	−0.623931	−	0.304784i
$818$	−26.8835	−	14.8683i	−0.939960	−	0.519857i
$819$	1.20991	+	6.86172i	0.0422775	+	0.239768i
$820$	−9.82569	+	30.4378i	−0.343128	+	1.06294i
$821$	13.9797	−	5.08819i	0.487894	−	0.177579i	−0.0863471	−	0.996265i	$-0.527519\pi$
$821$	13.9797	−	5.08819i	0.487894	−	0.177579i	0.574241	+	0.818686i	$0.305297\pi$
$822$	−2.29922	+	2.00254i	−0.0801946	+	0.0698465i
$823$	1.64912	−	1.96535i	0.0574848	−	0.0685077i	−0.736536	−	0.676399i	$-0.763540\pi$
$823$	1.64912	−	1.96535i	0.0574848	−	0.0685077i	0.794021	+	0.607891i	$0.207984\pi$
$824$	11.2384	−	22.2135i	0.391508	−	0.773845i
$825$	0.197800	−	0.114200i	0.00688651	−	0.00397593i
$826$	−7.72599	+	9.55943i	−0.268821	+	0.332615i
$827$	0.878109	−	4.98000i	0.0305348	−	0.173172i	−0.965727	−	0.259562i	$-0.916422\pi$
$827$	0.878109	−	4.98000i	0.0305348	−	0.173172i	0.996261	+	0.0863899i	$0.0275331\pi$
$828$	13.0062	+	6.88375i	0.451998	+	0.239227i
$829$	43.3520	+	25.0293i	1.50568	+	0.869303i	0.999978	+	0.00659184i	$0.00209826\pi$
$829$	43.3520	+	25.0293i	1.50568	+	0.869303i	0.505698	+	0.862711i	$0.331235\pi$
$830$	−1.72962	−	4.49299i	−0.0600359	−	0.155954i
$831$	−2.29860	−	0.836621i	−0.0797375	−	0.0290221i
$832$	−2.06712	−	4.17738i	−0.0716646	−	0.144824i
$833$	24.7989	−	20.8088i	0.859232	−	0.720982i
$834$	−2.54850	+	7.42437i	−0.0882472	+	0.257085i
$835$	17.5760			0.608241
$836$	−8.76908	+	35.3661i	−0.303285	+	1.22316i
$837$	−1.31882			−0.0455850
$838$	6.05901	−	17.6513i	0.209305	−	0.609755i
$839$	33.0449	−	27.7279i	1.14084	−	0.957275i	0.141370	−	0.989957i	$-0.454849\pi$
$839$	33.0449	−	27.7279i	1.14084	−	0.957275i	0.999466	+	0.0326821i	$0.0104049\pi$
$840$	2.99346	+	6.99642i	0.103284	+	0.241399i
$841$	40.2710	+	14.6575i	1.38866	+	0.505430i
$842$	−3.63007	−	9.42975i	−0.125100	−	0.324971i
$843$	−0.287167	−	0.165796i	−0.00989056	−	0.00571032i
$844$	3.42434	−	6.47000i	0.117871	−	0.222706i
$845$	5.00835	−	28.4038i	0.172292	−	0.977119i
$846$	−12.7619	+	15.7904i	−0.438764	+	0.542887i
$847$	−22.9693	+	13.2613i	−0.789234	+	0.455665i
$848$	2.24940	−	1.52976i	0.0772447	−	0.0525321i
$849$	−1.73779	+	2.07102i	−0.0596410	+	0.0710773i
$850$	0.667672	−	0.581517i	0.0229009	−	0.0199459i
$851$	2.92776	−	1.06562i	0.100362	−	0.0365288i
$852$	−7.23697	−	2.33618i	−0.247934	−	0.0800361i
$853$	−0.190369	−	1.07963i	−0.00651809	−	0.0369659i	0.981375	−	0.192101i	$-0.0615300\pi$
$853$	−0.190369	−	1.07963i	−0.00651809	−	0.0369659i	−0.987893	+	0.155135i	$0.950419\pi$
$854$	15.7240	+	8.69636i	0.538064	+	0.297583i
$855$	23.4235	+	17.0400i	0.801066	+	0.582757i
$856$	−1.42761	+	0.0789152i	−0.0487946	+	0.00269727i
$857$	17.0456	−	3.00560i	0.582267	−	0.102669i	0.125246	−	0.992126i	$-0.460028\pi$
$857$	17.0456	−	3.00560i	0.582267	−	0.102669i	0.457020	+	0.889456i	$0.348917\pi$
$858$	0.190216	+	0.973615i	0.00649385	+	0.0332387i
$859$	2.68429	+	7.37504i	0.0915869	+	0.251633i	0.977025	−	0.213124i	$-0.0683639\pi$
$859$	2.68429	+	7.37504i	0.0915869	+	0.251633i	−0.885438	+	0.464757i	$0.846142\pi$
$860$	20.2847	−	4.35212i	0.691703	−	0.148406i
$861$	6.35119	+	5.32928i	0.216448	+	0.181621i
$862$	−10.4717	−	17.3903i	−0.356669	−	0.592317i
$863$	14.7692	+	25.5810i	0.502750	+	0.870789i	0.999995	+	0.00317851i	$0.00101175\pi$
$863$	14.7692	+	25.5810i	0.502750	+	0.870789i	−0.497245	+	0.867610i	$0.665655\pi$
$864$	−8.71920	+	4.11658i	−0.296633	+	0.140049i
$865$	20.9272	+	3.69003i	0.711547	+	0.125465i
$866$	−0.756383	−	41.0870i	−0.0257030	−	1.39619i
$867$	0.879681	−	1.52365i	0.0298755	−	0.0517459i
$868$	6.28424	+	0.870970i	0.213301	+	0.0295626i
$869$	−14.7629	+	40.5607i	−0.500796	+	1.37593i
$870$	−7.77136	−	1.22326i	−0.263474	−	0.0414725i
$871$	5.27704	+	6.28893i	0.178806	+	0.213092i
$872$	17.2253	−	4.02874i	0.583323	−	0.136430i
$873$			29.9311i			1.01302i
$874$	15.4902	+	1.34987i	0.523965	+	0.0456602i
$875$		−	44.9274i		−	1.51882i
$876$	−4.79294	+	4.33217i	−0.161938	+	0.146370i
$877$	−18.0457	−	21.5060i	−0.609359	−	0.726206i	0.369843	−	0.929094i	$-0.379412\pi$
$877$	−18.0457	−	21.5060i	−0.609359	−	0.726206i	−0.979202	+	0.202888i	$0.934967\pi$
$878$	6.02091	−	38.2506i	0.203196	−	1.29090i
$879$	−1.81671	+	4.99138i	−0.0612762	+	0.168355i
$880$	−15.6237	−	34.7341i	−0.526675	−	1.17089i
$881$	−0.307651	+	0.532868i	−0.0103650	+	0.0179528i	−0.871161	−	0.490997i	$-0.836633\pi$
$881$	−0.307651	+	0.532868i	−0.0103650	+	0.0179528i	0.860796	+	0.508950i	$0.169966\pi$
$882$	−40.4571	+	0.744788i	−1.36226	+	0.0250783i
$883$	−20.1205	−	3.54779i	−0.677110	−	0.119393i	−0.175491	−	0.984481i	$-0.556151\pi$
$883$	−20.1205	−	3.54779i	−0.677110	−	0.119393i	−0.501620	+	0.865088i	$0.667262\pi$
$884$	1.44741	+	3.56287i	0.0486815	+	0.119832i
$885$	0.695581	+	1.20478i	0.0233817	+	0.0404983i
$886$	17.4274	−	10.4941i	0.585484	−	0.352555i
$887$	21.2538	+	17.8341i	0.713634	+	0.598810i	0.925616	−	0.378463i	$-0.123547\pi$
$887$	21.2538	+	17.8341i	0.713634	+	0.598810i	−0.211982	+	0.977274i	$0.567992\pi$
$888$	−0.291494	+	0.963286i	−0.00978190	+	0.0323257i
$889$	−12.6064	−	34.6359i	−0.422807	−	1.16165i
$890$	−46.8451	+	9.15215i	−1.57025	+	0.306781i
$891$	−33.9993	+	5.99499i	−1.13902	+	0.200840i
$892$	29.7621	+	47.4277i	0.996509	+	1.58800i
$893$	−5.92574	+	20.6179i	−0.198297	+	0.689952i
$894$	0.402464	−	0.727700i	0.0134604	−	0.0243379i
$895$	−0.626113	−	3.55087i	−0.0209287	−	0.118692i
$896$	44.2662	−	13.8574i	1.47883	−	0.462944i
$897$	0.397800	−	0.144787i	0.0132821	−	0.00483431i
$898$	−21.0304	−	24.1461i	−0.701792	−	0.805766i
$899$	−4.21584	+	5.02425i	−0.140606	+	0.167568i
$900$	−1.10596	+	0.0407337i	−0.0368652	+	0.00135779i
$901$	−1.94379	+	1.12225i	−0.0647571	+	0.0373876i
$902$	−32.2721	−	26.0825i	−1.07454	−	0.868451i
$903$	0.933843	−	5.29609i	0.0310764	−	0.176243i
$904$	−17.2060	+	11.2438i	−0.572263	+	0.373965i
$905$	−26.2554	−	15.1585i	−0.872758	−	0.503887i
$906$	3.65694	−	1.40777i	0.121494	−	0.0467701i
$907$	−28.1356	−	10.2405i	−0.934228	−	0.340031i	−0.170344	−	0.985385i	$-0.554488\pi$
$907$	−28.1356	−	10.2405i	−0.934228	−	0.340031i	−0.763884	+	0.645354i	$0.776710\pi$
$908$	−9.89088	−	7.69726i	−0.328240	−	0.255442i
$909$	−19.5535	+	16.4073i	−0.648549	+	0.544197i
$910$	−7.27849	−	2.49842i	−0.241280	−	0.0828218i
$911$	−30.9988			−1.02704			−0.513518	−	0.858079i	$-0.671658\pi$
$911$	−30.9988			−1.02704			−0.513518	+	0.858079i	$0.671658\pi$
$912$	−3.34883	+	3.74330i	−0.110891	+	0.123953i
$913$	6.24587			0.206708
$914$	27.2468	+	9.35276i	0.901244	+	0.309362i
$915$	1.55794	−	1.30727i	0.0515040	−	0.0432170i
$916$	−19.9553	−	15.5295i	−0.659341	−	0.513111i
$917$	−53.1386	−	19.3409i	−1.75479	−	0.638692i
$918$	7.42456	−	2.85815i	0.245047	−	0.0943330i
$919$	19.5649	+	11.2958i	0.645385	+	0.372613i	0.786686	−	0.617353i	$-0.211795\pi$
$919$	19.5649	+	11.2958i	0.645385	+	0.372613i	−0.141301	+	0.989967i	$0.545128\pi$
$920$	−13.6052	+	8.89081i	−0.448552	+	0.293121i
$921$	−0.279711	+	1.58632i	−0.00921678	+	0.0522709i
$922$	−20.1411	−	16.2781i	−0.663311	−	0.536091i
$923$	6.65981	−	3.84504i	0.219210	−	0.126561i
$924$	−9.86586	+	0.363371i	−0.324563	+	0.0119540i
$925$	−0.150616	+	0.179497i	−0.00495223	+	0.00590184i
$926$	−9.34395	−	10.7283i	−0.307061	−	0.352554i
$927$	24.1260	−	8.78115i	0.792402	−	0.288411i
$928$	−12.1898	+	46.3766i	−0.400149	+	1.52239i
$929$	−2.89978	−	16.4455i	−0.0951388	−	0.539559i	−0.994705	−	0.102774i	$-0.967228\pi$
$929$	−2.89978	−	16.4455i	−0.0951388	−	0.539559i	0.899566	−	0.436785i	$-0.143883\pi$
$930$	0.347529	−	0.628372i	0.0113959	−	0.0206051i
$931$	−39.0696	+	17.3663i	−1.28046	+	0.569158i
$932$	7.15712	+	11.4053i	0.234439	+	0.373594i
$933$	3.39512	−	0.598652i	0.111151	−	0.0195990i
$934$	7.28131	−	1.42255i	0.238252	−	0.0465474i
$935$	10.7479	+	29.5296i	0.351494	+	0.965722i
$936$	1.39222	−	4.60080i	0.0455061	−	0.150382i
$937$	−39.7274	−	33.3352i	−1.29784	−	1.08901i	−0.990515	−	0.137408i	$-0.956123\pi$
$937$	−39.7274	−	33.3352i	−1.29784	−	1.08901i	−0.307322	−	0.951606i	$-0.599433\pi$
$938$	−69.9919	+	42.1463i	−2.28532	+	1.37613i
$939$	2.28889	+	3.96447i	0.0746950	+	0.129376i
$940$	−8.43965	−	20.7747i	−0.275271	−	0.677595i
$941$	−25.8232	−	4.55332i	−0.841811	−	0.148434i	−0.263917	−	0.964545i	$-0.585014\pi$
$941$	−25.8232	−	4.55332i	−0.841811	−	0.148434i	−0.577895	+	0.816111i	$0.696126\pi$
$942$	−3.07854	+	0.0566738i	−0.100304	+	0.00184653i
$943$	−8.85353	+	15.3348i	−0.288311	+	0.499369i
$944$	7.73321	−	3.47847i	0.251695	−	0.113214i
$945$	−5.44489	+	14.9597i	−0.177122	+	0.486639i
$946$	−4.18505	+	26.5875i	−0.136068	+	0.864433i
$947$	9.64551	+	11.4951i	0.313437	+	0.373540i	0.899646	−	0.436620i	$-0.143825\pi$
$947$	9.64551	+	11.4951i	0.313437	+	0.373540i	−0.586209	+	0.810160i	$0.699380\pi$
$948$	−4.41402	+	3.98968i	−0.143361	+	0.129579i
$949$		−	6.53319i		−	0.212076i
$950$	−1.05965	+	0.494564i	−0.0343795	+	0.0160458i
$951$		−	4.85034i		−	0.157283i
$952$	−37.2660	+	8.71595i	−1.20780	+	0.282485i
$953$	−5.08743	−	6.06296i	−0.164798	−	0.196399i	0.677325	−	0.735684i	$-0.263139\pi$
$953$	−5.08743	−	6.06296i	−0.164798	−	0.196399i	−0.842123	+	0.539285i	$0.818695\pi$
$954$	2.77137	+	0.436232i	0.0897263	+	0.0141235i
$955$	9.87993	−	27.1449i	0.319707	−	0.878388i
$956$	−19.9590	−	2.76623i	−0.645519	−	0.0894662i
$957$	5.10307	−	8.83878i	0.164959	−	0.285717i
$958$	0.127331	+	6.91664i	0.00411387	+	0.223466i
$959$	30.2183	+	5.32831i	0.975801	+	0.172060i
$960$	0.336237	−	5.23919i	0.0108520	−	0.169094i
$961$	15.2007	+	26.3283i	0.490344	+	0.849301i
$962$	−0.524999	−	0.871859i	−0.0169266	−	0.0281099i
$963$	−1.12959	−	0.947835i	−0.0364004	−	0.0305436i
$964$	16.5322	−	3.54701i	0.532467	−	0.114242i
$965$	17.1148	+	47.0226i	0.550946	+	1.51371i
$966$	0.807815	+	4.13478i	0.0259910	+	0.133034i
$967$	39.9648	−	7.04688i	1.28518	−	0.226612i	0.511003	−	0.859579i	$-0.329274\pi$
$967$	39.9648	−	7.04688i	1.28518	−	0.226612i	0.774179	+	0.632967i	$0.218163\pi$
$968$	18.2697	−	1.00991i	0.587211	−	0.0324598i
$969$	2.98282	−	2.87695i	0.0958221	−	0.0924211i
$970$	−28.9280	−	15.9990i	−0.928823	−	0.513698i
$971$	7.47160	+	42.3736i	0.239775	+	1.35983i	0.832320	+	0.554295i	$0.187012\pi$
$971$	7.47160	+	42.3736i	0.239775	+	1.35983i	−0.592545	+	0.805537i	$0.701877\pi$
$972$	−14.2613	−	4.60371i	−0.457431	−	0.147664i
$973$	74.2319	−	27.0182i	2.37976	−	0.866164i
$974$	20.6072	−	17.9481i	0.660297	−	0.575094i
$975$	−0.0204645	+	0.0243886i	−0.000655389	+	0.000781062i
$976$	−6.97108	−	10.2505i	−0.223139	−	0.328109i
$977$	28.8945	−	16.6822i	0.924415	−	0.533712i	0.0393744	−	0.999225i	$-0.487463\pi$
$977$	28.8945	−	16.6822i	0.924415	−	0.533712i	0.885041	+	0.465513i	$0.154130\pi$
$978$	4.24271	−	5.24954i	0.135667	−	0.167862i
$979$	10.7527	−	60.9818i	0.343659	−	1.94899i
$980$	20.9056	−	39.4993i	0.667805	−	1.26176i
$981$	15.8000	+	9.12212i	0.504455	+	0.291247i
$982$	−11.6391	−	30.2348i	−0.371420	−	0.964830i
$983$	27.6780	+	10.0740i	0.882790	+	0.321309i	0.743335	−	0.668919i	$-0.233243\pi$
$983$	27.6780	+	10.0740i	0.882790	+	0.321309i	0.139455	+	0.990228i	$0.455465\pi$
$984$	−2.24995	−	5.25865i	−0.0717258	−	0.167640i
$985$	−7.92965	+	6.65377i	−0.252660	+	0.212007i
$986$	12.8454	−	37.4216i	0.409080	−	1.19175i
$987$	−5.81254			−0.185015
$988$	−0.537452	−	5.05052i	−0.0170986	−	0.160679i
$989$	11.4855			0.365217
$990$	12.7526	−	37.1513i	0.405304	−	1.18074i
$991$	−14.8234	+	12.4383i	−0.470882	+	0.395117i	−0.847116	−	0.531408i	$-0.821663\pi$
$991$	−14.8234	+	12.4383i	−0.470882	+	0.395117i	0.376234	+	0.926525i	$0.377219\pi$
$992$	−3.59724	−	2.49333i	−0.114212	−	0.0791633i
$993$	3.94261	+	1.43499i	0.125115	+	0.0455381i
$994$	27.4945	+	71.4220i	0.872073	+	2.26537i
$995$	−24.0362	−	13.8773i	−0.761999	−	0.439941i
$996$	0.760951	+	0.402745i	0.0241117	+	0.0127614i
$997$	−8.02691	+	45.5229i	−0.254215	+	1.44172i	0.543865	+	0.839173i	$0.316960\pi$
$997$	−8.02691	+	45.5229i	−0.254215	+	1.44172i	−0.798080	+	0.602551i	$0.794151\pi$
$998$	2.25993	−	2.79624i	0.0715370	−	0.0885133i
$999$	−1.82335	+	1.05271i	−0.0576881	+	0.0333063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.67.8	yes	48
3.2	odd	2		684.2.cf.a.523.1		48
4.3	odd	2	inner	76.2.k.a.67.7	yes	48
12.11	even	2		684.2.cf.a.523.2		48
19.2	odd	18	inner	76.2.k.a.59.7	✓	48
57.2	even	18		684.2.cf.a.667.2		48
76.59	even	18	inner	76.2.k.a.59.8	yes	48
228.59	odd	18		684.2.cf.a.667.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.59.7	✓	48	19.2	odd	18	inner
76.2.k.a.59.8	yes	48	76.59	even	18	inner
76.2.k.a.67.7	yes	48	4.3	odd	2	inner
76.2.k.a.67.8	yes	48	1.1	even	1	trivial
684.2.cf.a.523.1		48	3.2	odd	2
684.2.cf.a.523.2		48	12.11	even	2
684.2.cf.a.667.1		48	228.59	odd	18
684.2.cf.a.667.2		48	57.2	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33760 + 0.459147i) q^{2} +(0.220673 - 0.185167i) q^{3} +(1.57837 + 1.22831i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(0.380192 - 0.146358i) q^{6} +(-3.55057 - 2.04992i) q^{7} +(1.54725 + 2.36770i) q^{8} +(-0.506535 + 2.87270i) q^{9} +O(q^{10})\)	\(q+(1.33760 + 0.459147i) q^{2} +(0.220673 - 0.185167i) q^{3} +(1.57837 + 1.22831i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(0.380192 - 0.146358i) q^{6} +(-3.55057 - 2.04992i) q^{7} +(1.54725 + 2.36770i) q^{8} +(-0.506535 + 2.87270i) q^{9} +(-2.50567 - 2.02510i) q^{10} +(3.61965 - 2.08981i) q^{11} +(0.575746 - 0.0212054i) q^{12} +(-0.374492 + 0.446302i) q^{13} +(-3.80804 - 4.37222i) q^{14} +(-0.616669 + 0.224449i) q^{15} +(0.982490 + 3.87746i) q^{16} +(-0.573106 - 3.25025i) q^{17} +(-1.99653 + 3.60996i) q^{18} +(-0.458280 + 4.33474i) q^{19} +(-2.42178 - 3.85925i) q^{20} +(-1.16309 + 0.205085i) q^{21} +(5.80119 - 1.13338i) q^{22} +(-0.862701 - 2.37025i) q^{23} +(0.779857 + 0.235988i) q^{24} +(0.145317 + 0.121936i) q^{25} +(-0.705840 + 0.425028i) q^{26} +(0.852252 + 1.47614i) q^{27} +(-3.08616 - 7.59675i) q^{28} +(8.34798 + 1.47197i) q^{29} +(-0.927914 + 0.0170823i) q^{30} +(-0.386863 + 0.670066i) q^{31} +(-0.466142 + 5.63762i) q^{32} +(0.411797 - 1.13140i) q^{33} +(0.725752 - 4.61068i) q^{34} +(6.00353 + 7.15472i) q^{35} +(-4.32808 + 3.91200i) q^{36} +1.23521i q^{37} +(-2.60328 + 5.58775i) q^{38} +0.167830i q^{39} +(-1.46741 - 6.27410i) q^{40} +(-4.51238 - 5.37764i) q^{41} +(-1.64992 - 0.259709i) q^{42} +(-1.55737 + 4.27884i) q^{43} +(8.28008 + 1.14758i) q^{44} +(3.32261 - 5.75494i) q^{45} +(-0.0656581 - 3.56656i) q^{46} +(4.84679 + 0.854620i) q^{47} +(0.934786 + 0.673727i) q^{48} +(4.90438 + 8.49464i) q^{49} +(0.138391 + 0.229824i) q^{50} +(-0.728306 - 0.611122i) q^{51} +(-1.13928 + 0.244435i) q^{52} +(-0.232598 - 0.639058i) q^{53} +(0.462209 + 2.36581i) q^{54} +(-9.37689 + 1.65340i) q^{55} +(-0.640033 - 11.5784i) q^{56} +(0.701520 + 1.04142i) q^{57} +(10.4904 + 5.80187i) q^{58} +(-0.368113 - 2.08767i) q^{59} +(-1.24902 - 0.403200i) q^{60} +(-2.91217 + 1.05994i) q^{61} +(-0.825128 + 0.718656i) q^{62} +(7.68731 - 9.16138i) q^{63} +(-3.21201 + 7.32687i) q^{64} +(1.14941 - 0.663614i) q^{65} +(1.07030 - 1.32429i) q^{66} +(2.44691 - 13.8771i) q^{67} +(3.08775 - 5.83404i) q^{68} +(-0.629267 - 0.363307i) q^{69} +(4.74527 + 12.3267i) q^{70} +(-12.4034 - 4.51448i) q^{71} +(-7.58543 + 3.24548i) q^{72} +(-8.59023 + 7.20806i) q^{73} +(-0.567143 + 1.65222i) q^{74} +0.0546461 q^{75} +(-6.04776 + 6.27890i) q^{76} -17.1358 q^{77} +(-0.0770587 + 0.224490i) q^{78} +(-7.91111 + 6.63821i) q^{79} +(0.917914 - 9.06601i) q^{80} +(-7.76190 - 2.82510i) q^{81} +(-3.56664 - 9.26500i) q^{82} +(1.29416 + 0.747183i) q^{83} +(-2.08770 - 1.10494i) q^{84} +(-1.30559 + 7.40436i) q^{85} +(-4.04776 + 5.00833i) q^{86} +(2.11474 - 1.22094i) q^{87} +(10.5486 + 5.33679i) q^{88} +(9.52313 - 11.3492i) q^{89} +(7.08670 - 6.17226i) q^{90} +(2.24455 - 0.816948i) q^{91} +(1.54975 - 4.80080i) q^{92} +(0.0387037 + 0.219500i) q^{93} +(6.09069 + 3.36853i) q^{94} +(4.35847 - 8.92233i) q^{95} +(0.941034 + 1.33038i) q^{96} +(10.1050 - 1.78178i) q^{97} +(2.65983 + 13.6143i) q^{98} +(4.16991 + 11.4567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

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