LMFDB - Embedded newform 76.2.k.a.59.8

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			59.8
Character	$\chi$	$=$	76.59
Dual form			76.2.k.a.67.8

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

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

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	0.704264	−	0.709938i	$-0.251277\pi$
$3$	0.220673	+	0.185167i	0.127406	+	0.106906i	−0.576858	+	0.816844i	$0.695722\pi$
$4$	1.57837	−	1.22831i	0.789184	−	0.614157i
$5$	−2.14071	+	0.779153i	−0.957352	+	0.348448i	−0.772995	−	0.634412i	$-0.781242\pi$
$5$	−2.14071	+	0.779153i	−0.957352	+	0.348448i	−0.184357	+	0.982859i	$0.559020\pi$
$6$	0.380192	+	0.146358i	0.155213	+	0.0597505i
$7$	−3.55057	+	2.04992i	−1.34199	+	0.774799i	−0.987099	−	0.160109i	$-0.948815\pi$
$7$	−3.55057	+	2.04992i	−1.34199	+	0.774799i	−0.354891	+	0.934908i	$0.615482\pi$
$8$	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	0.933940	−	0.357430i	$-0.116347\pi$
$11$	3.61965	+	2.08981i	1.09137	+	0.630101i	0.157426	+	0.987531i	$0.449680\pi$
$12$	0.575746	+	0.0212054i	0.166204	+	0.00612147i
$13$	−0.374492	−	0.446302i	−0.103865	−	0.123782i	0.711608	−	0.702577i	$-0.247967\pi$
$13$	−0.374492	−	0.446302i	−0.103865	−	0.123782i	−0.815473	+	0.578795i	$0.803523\pi$
$14$	−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	0.832993	+	0.553284i	$0.186626\pi$
$17$	−0.573106	+	3.25025i	−0.138999	+	0.788301i	−0.971991	+	0.235017i	$0.924486\pi$
$18$	−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	−0.996561	−	0.0828661i	$-0.973593\pi$
$23$	−0.862701	+	2.37025i	−0.179886	+	0.494232i	0.816675	+	0.577098i	$0.195815\pi$
$24$	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	0.667969	−	0.744189i	$-0.267164\pi$
$29$	8.34798	−	1.47197i	1.55018	−	0.273339i	0.882213	+	0.470850i	$0.156053\pi$
$30$	−0.927914	−	0.0170823i	−0.169413	−	0.00311878i
$31$	−0.386863	−	0.670066i	−0.0694826	−	0.120347i	0.829191	−	0.558965i	$-0.188801\pi$
$31$	−0.386863	−	0.670066i	−0.0694826	−	0.120347i	−0.898674	+	0.438618i	$0.855468\pi$
$32$	−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	$-0.967625\pi$
$37$		−	1.23521i		−	0.203067i	0.994832	−	0.101534i	$-0.0323749\pi$
$38$	−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	−0.993051	−	0.117683i	$-0.962453\pi$
$41$	−4.51238	+	5.37764i	−0.704715	+	0.839847i	0.288336	+	0.957529i	$0.406898\pi$
$42$	−1.64992	+	0.259709i	−0.254589	+	0.0400739i
$43$	−1.55737	−	4.27884i	−0.237497	−	0.652517i	−0.999985	−	0.00551486i	$-0.998245\pi$
$43$	−1.55737	−	4.27884i	−0.237497	−	0.652517i	0.762488	−	0.647002i	$-0.223978\pi$
$44$	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	0.191412	−	0.981510i	$-0.438693\pi$
$47$	4.84679	−	0.854620i	0.706977	−	0.124659i	0.515565	+	0.856851i	$0.327582\pi$
$48$	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	−0.954642	−	0.297756i	$-0.903762\pi$
$53$	−0.232598	+	0.639058i	−0.0319498	+	0.0877814i	0.922692	+	0.385538i	$0.125984\pi$
$54$	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	−0.999349	−	0.0360909i	$-0.988509\pi$
$59$	−0.368113	+	2.08767i	−0.0479243	+	0.271792i	0.951424	+	0.307883i	$0.0996205\pi$
$60$	−1.24902	+	0.403200i	−0.161248	+	0.0520529i
$61$	−2.91217	−	1.05994i	−0.372866	−	0.135712i	0.148789	−	0.988869i	$-0.452463\pi$
$61$	−2.91217	−	1.05994i	−0.372866	−	0.135712i	−0.521654	+	0.853157i	$0.674685\pi$
$62$	−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	0.650751	+	0.759291i	$0.274454\pi$
$67$	2.44691	+	13.8771i	0.298938	+	1.69536i	−0.351813	+	0.936070i	$0.614435\pi$
$68$	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	−0.948648	−	0.316335i	$-0.897548\pi$
$71$	−12.4034	+	4.51448i	−1.47202	+	0.535771i	−0.523370	+	0.852105i	$0.675326\pi$
$72$	−7.58543	−	3.24548i	−0.893952	−	0.382483i
$73$	−8.59023	−	7.20806i	−1.00541	−	0.843639i	−0.0176852	−	0.999844i	$-0.505630\pi$
$73$	−8.59023	−	7.20806i	−1.00541	−	0.843639i	−0.987725	+	0.156205i	$0.950074\pi$
$74$	−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	0.0781550	−	0.996941i	$-0.475097\pi$
$79$	−7.91111	−	6.63821i	−0.890069	−	0.746857i	−0.968224	+	0.250085i	$0.919542\pi$
$80$	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	−0.427289	−	0.904115i	$-0.640531\pi$
$83$	1.29416	−	0.747183i	0.142052	−	0.0820140i	0.569342	+	0.822101i	$0.307198\pi$
$84$	−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	0.979080	+	0.203477i	$0.0652242\pi$
$89$	9.52313	+	11.3492i	1.00945	+	1.20302i	0.0303703	+	0.999539i	$0.490331\pi$
$90$	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	0.661230	−	0.750183i	$-0.270035\pi$
$97$	10.1050	+	1.78178i	1.02601	+	0.180913i	0.364776	+	0.931095i	$0.381146\pi$
$98$	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	−0.245177	−	0.969478i	$-0.578846\pi$
$101$	6.70325	−	5.62470i	0.666999	−	0.559678i	0.912175	+	0.409800i	$0.134402\pi$
$102$	−0.693591	+	1.15184i	−0.0686757	+	0.114049i
$103$	−4.40079	+	7.62240i	−0.433623	+	0.751057i	−0.997182	−	0.0750187i	$-0.976098\pi$
$103$	−4.40079	+	7.62240i	−0.433623	+	0.751057i	0.563559	+	0.826076i	$0.309432\pi$
$104$	−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	0.853550	−	0.521012i	$-0.174445\pi$
$107$	−0.252753	−	0.437781i	−0.0244346	−	0.0423219i	−0.877984	+	0.478690i	$0.841112\pi$
$108$	−0.468001	−	3.37673i	−0.0450334	−	0.324926i
$109$	2.13914	+	5.87723i	0.204892	+	0.562937i	0.998994	−	0.0448483i	$-0.0142805\pi$
$109$	2.13914	+	5.87723i	0.204892	+	0.562937i	−0.794102	+	0.607785i	$0.792058\pi$
$110$	−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	$-0.888960\pi$
$113$		−	7.26696i		−	0.683618i	0.939769	−	0.341809i	$-0.111040\pi$
$114$	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	−0.283879	−	0.958860i	$-0.591622\pi$
$127$	6.88695	−	5.77884i	0.611118	−	0.512789i	0.894998	+	0.446071i	$0.147177\pi$
$128$	−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	0.731979	−	0.681328i	$-0.238597\pi$
$131$	13.5834	+	2.39512i	1.18679	+	0.209262i	0.454807	+	0.890590i	$0.349708\pi$
$132$	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	0.0236365	−	0.999721i	$-0.492476\pi$
$137$	−7.03294	−	2.55978i	−0.600865	−	0.218697i	−0.624501	+	0.781024i	$0.714698\pi$
$138$	−0.674898	+	0.774887i	−0.0574511	+	0.0659628i
$139$	−12.3852	−	14.7601i	−1.05050	−	1.25194i	−0.966823	−	0.255447i	$-0.917777\pi$
$139$	−12.3852	−	14.7601i	−1.05050	−	1.25194i	−0.0836787	−	0.996493i	$-0.526667\pi$
$140$	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	0.704588	−	0.709617i	$-0.251132\pi$
$149$	1.56368	+	1.31208i	0.128101	+	0.107490i	−0.576486	+	0.817107i	$0.695576\pi$
$150$	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	−0.609503	−	0.792784i	$-0.708631\pi$
$157$	−7.10221	+	2.58499i	−0.566818	+	0.206305i	0.0426851	+	0.999089i	$0.486409\pi$
$158$	−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	0.942382	−	0.334538i	$-0.108580\pi$
$163$	14.3484	+	8.28406i	1.12385	+	0.648858i	0.181472	+	0.983396i	$0.441914\pi$
$164$	−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	0.0459180	−	0.998945i	$-0.485379\pi$
$167$	−7.24993	−	2.63876i	−0.561016	−	0.204193i	−0.606934	+	0.794752i	$0.707601\pi$
$168$	−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	−0.186846	−	0.982389i	$-0.559827\pi$
$173$	−9.18629	−	1.61979i	−0.698421	−	0.123150i	−0.511575	+	0.859239i	$0.670938\pi$
$174$	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	−0.834934	−	0.550350i	$-0.814494\pi$
$179$	0.791374	−	1.37070i	0.0591501	−	0.102451i	0.894084	+	0.447899i	$0.147828\pi$
$180$	12.3132	+	5.00220i	0.917770	+	0.372842i
$181$	13.1059	−	2.31093i	0.974156	−	0.171770i	0.336156	−	0.941806i	$-0.390873\pi$
$181$	13.1059	−	2.31093i	0.974156	−	0.171770i	0.638000	+	0.770036i	$0.279762\pi$
$182$	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	$-0.848294\pi$
$191$		−	12.6803i		−	0.917517i	0.888561	−	0.458759i	$-0.151706\pi$
$192$	0.647888	−	2.21160i	0.0467573	−	0.159608i
$193$	−14.1194	+	16.8269i	−1.01634	+	1.21123i	−0.0390670	+	0.999237i	$0.512439\pi$
$193$	−14.1194	+	16.8269i	−1.01634	+	1.21123i	−0.977272	+	0.211989i	$0.932006\pi$
$194$	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	0.935539	−	0.353223i	$-0.114914\pi$
$197$	2.27195	+	3.93514i	0.161870	+	0.280367i	−0.773669	+	0.633590i	$0.781581\pi$
$198$	0.317362	−	17.2392i	0.0225539	−	1.22514i
$199$	11.9982	−	2.11561i	0.850530	−	0.149971i	0.268642	−	0.963240i	$-0.413425\pi$
$199$	11.9982	−	2.11561i	0.850530	−	0.149971i	0.581888	+	0.813269i	$0.302314\pi$
$200$	−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	−0.998838	−	0.0481908i	$-0.984654\pi$
$211$	−0.635579	+	3.60455i	−0.0437551	+	0.248147i	0.955083	+	0.296338i	$0.0957656\pi$
$212$	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	0.761732	−	0.647893i	$-0.224350\pi$
$223$	26.3079	−	9.57530i	1.76171	−	0.641210i	0.999978	+	0.00668309i	$0.00212731\pi$
$224$	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	−0.126369	−	0.991983i	$-0.540332\pi$
$233$	6.32647	−	2.30265i	0.414461	−	0.150851i	0.540830	+	0.841132i	$0.318110\pi$
$234$	−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	0.190522	−	0.981683i	$-0.438982\pi$
$239$	−8.72510	−	5.03744i	−0.564380	−	0.325845i	−0.754901	+	0.655838i	$0.772315\pi$
$240$	−1.47616	+	2.17059i	−0.0952860	+	0.140111i
$241$	5.43427	+	6.47631i	0.350052	+	0.417176i	0.912125	−	0.409912i	$-0.134440\pi$
$241$	5.43427	+	6.47631i	0.350052	+	0.417176i	−0.562073	+	0.827088i	$0.689996\pi$
$242$	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	−0.997070	−	0.0764996i	$-0.975626\pi$
$251$	−2.91664	+	8.01342i	−0.184097	+	0.505802i	0.812973	+	0.582302i	$0.197848\pi$
$252$	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	−0.257308	−	0.966329i	$-0.582836\pi$
$257$	−2.70278	+	0.476573i	−0.168595	+	0.0297278i	0.0887134	+	0.996057i	$0.471724\pi$
$258$	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	−0.808089	−	0.589061i	$-0.799498\pi$
$263$	−1.42151	+	1.69409i	−0.0876540	+	0.104462i	0.720435	+	0.693523i	$0.243942\pi$
$264$	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	−0.387225	−	0.921985i	$-0.626566\pi$
$269$	9.64383	−	11.4931i	0.587995	−	0.700745i	0.975219	+	0.221241i	$0.0710106\pi$
$270$	0.853872	+	5.42462i	0.0519650	+	0.330132i
$271$	8.76172	+	24.0726i	0.532237	+	1.46231i	0.856403	+	0.516308i	$0.172694\pi$
$271$	8.76172	+	24.0726i	0.532237	+	1.46231i	−0.324166	+	0.946000i	$0.605084\pi$
$272$	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	−0.964923	−	0.262533i	$-0.915442\pi$
$277$	−4.24573	+	7.35381i	−0.255101	+	0.441848i	0.709822	+	0.704381i	$0.248775\pi$
$278$	−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	−0.950882	−	0.309555i	$-0.899820\pi$
$281$	−0.393696	+	1.08167i	−0.0234859	+	0.0645270i	0.927396	+	0.374082i	$0.122042\pi$
$282$	1.96779	+	0.384448i	0.117180	+	0.0228936i
$283$	−9.24245	−	1.62969i	−0.549407	−	0.0968752i	−0.107948	−	0.994157i	$-0.534428\pi$
$283$	−9.24245	−	1.62969i	−0.549407	−	0.0968752i	−0.441459	+	0.897281i	$0.645539\pi$
$284$	−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	−0.0451738	−	0.998979i	$-0.514384\pi$
$293$	−15.9687	−	9.21954i	−0.932902	−	0.538611i	−0.887728	+	0.460368i	$0.847717\pi$
$294$	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	0.512316	−	0.858797i	$-0.328788\pi$
$307$	−4.28349	−	3.59427i	−0.244471	−	0.205136i	−0.756787	+	0.653661i	$0.773232\pi$
$308$	−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	−0.176485	−	0.984303i	$-0.556473\pi$
$311$	10.3643	−	5.98382i	0.587704	−	0.339311i	0.764189	+	0.644992i	$0.223139\pi$
$312$	−0.397372	−	0.259676i	−0.0224967	−	0.0147013i
$313$	−2.75949	−	15.6499i	−0.155976	−	0.884582i	−0.957888	−	0.287141i	$-0.907295\pi$
$313$	−2.75949	−	15.6499i	−0.155976	−	0.884582i	0.801913	−	0.597441i	$-0.203816\pi$
$314$	−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	0.978935	−	0.204172i	$-0.0654500\pi$
$317$	10.8229	+	12.8982i	0.607875	+	0.724437i	−0.371060	+	0.928609i	$0.621006\pi$
$318$	−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	−0.593484	−	0.804846i	$-0.702248\pi$
$331$	7.28237	−	12.6134i	0.400275	−	0.693297i	0.993759	+	0.111549i	$0.0355811\pi$
$332$	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	0.943361	−	0.331768i	$-0.107645\pi$
$337$	0.136737	+	0.375681i	0.00744853	+	0.0204647i	−0.935913	+	0.352232i	$0.885423\pi$
$338$	−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	0.984532	+	0.175207i	$0.0560595\pi$
$347$	6.38859	+	17.5525i	0.342958	+	0.942268i	−0.641574	+	0.767061i	$0.721718\pi$
$348$	4.83753	−	0.670461i	0.259319	−	0.0359405i
$349$	−3.47936	−	6.02643i	−0.186246	−	0.322587i	0.757750	−	0.652545i	$-0.226299\pi$
$349$	−3.47936	−	6.02643i	−0.186246	−	0.322587i	−0.943996	+	0.329958i	$0.892965\pi$
$350$	−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	−0.931445	−	0.363882i	$-0.881451\pi$
$353$	−2.82935	+	4.90058i	−0.150591	+	0.260831i	0.780854	+	0.624714i	$0.214784\pi$
$354$	−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	−0.445431	−	0.895316i	$-0.646949\pi$
$359$	−22.1724	−	3.90959i	−1.17022	−	0.206340i	−0.724784	+	0.688976i	$0.758061\pi$
$360$	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	−0.978903	−	0.204323i	$-0.934501\pi$
$367$	−19.3515	−	23.0622i	−1.01014	−	1.20384i	−0.0312345	−	0.999512i	$-0.509944\pi$
$368$	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	−0.0580034	−	0.998316i	$-0.518473\pi$
$373$	15.0172	−	8.67020i	0.777562	−	0.448926i	0.835566	+	0.549391i	$0.185140\pi$
$374$	−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	0.998738	−	0.0502175i	$-0.0159915\pi$
$383$	21.9719	+	18.4366i	1.12271	+	0.942068i	0.123975	+	0.992285i	$0.460436\pi$
$384$	−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	0.709113	+	0.705095i	$0.249096\pi$
$389$	5.59981	+	31.7581i	0.283921	+	1.61020i	−0.425191	+	0.905104i	$0.639793\pi$
$390$	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	−0.824328	−	0.566112i	$-0.808447\pi$
$397$	2.86736	−	16.2616i	0.143909	−	0.816146i	0.968237	−	0.250034i	$-0.0804419\pi$
$398$	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	−0.405805	−	0.913960i	$-0.633009\pi$
$401$	−22.0221	−	3.88308i	−1.09973	−	0.193912i	−0.693925	+	0.720048i	$0.744120\pi$
$402$	−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	−0.675389	−	0.737462i	$-0.736024\pi$
$409$	−21.3931	+	3.77218i	−1.05782	+	0.186522i	−0.382431	+	0.923984i	$0.624913\pi$
$410$	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	$0.104469\pi$
$419$			13.1962i			0.644678i	−0.946624	+	0.322339i	$0.895531\pi$
$420$	3.60823	−	3.99200i	0.176063	−	0.194790i
$421$	−4.59262	+	5.47327i	−0.223830	+	0.266751i	−0.866259	−	0.499595i	$-0.833482\pi$
$421$	−4.59262	+	5.47327i	−0.223830	+	0.266751i	0.642429	+	0.766345i	$0.277927\pi$
$422$	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	−0.867982	−	0.496596i	$-0.834583\pi$
$431$	−10.9959	+	9.22664i	−0.529653	+	0.444432i	0.338329	+	0.941028i	$0.390138\pi$
$432$	−4.88636	−	4.75487i	−0.235095	−	0.228769i
$433$	−9.93835	+	27.3054i	−0.477607	+	1.31221i	0.433912	+	0.900955i	$0.357133\pi$
$433$	−9.93835	+	27.3054i	−0.477607	+	1.31221i	−0.911519	+	0.411258i	$0.865089\pi$
$434$	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	0.632055	+	0.774923i	$0.282212\pi$
$439$	−4.75454	+	26.9643i	−0.226922	+	1.28694i	−0.858977	+	0.512014i	$0.828900\pi$
$440$	−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	0.939583	−	0.342321i	$-0.111213\pi$
$443$	9.24631	+	11.0193i	0.439305	+	0.523544i	−0.500278	+	0.865865i	$0.666769\pi$
$444$	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	−0.885347	−	0.464930i	$-0.846079\pi$
$449$	−19.6084	+	11.3209i	−0.925380	+	0.534268i	−0.0400325	+	0.999198i	$0.512746\pi$
$450$	−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	−0.710078	−	0.704123i	$-0.751341\pi$
$461$	−17.2074	+	6.26298i	−0.801429	+	0.291696i	−0.0913504	+	0.995819i	$0.529118\pi$
$462$	−6.51489	−	2.50796i	−0.303100	−	0.116681i
$463$	−8.71218	+	5.02998i	−0.404890	+	0.233763i	−0.688592	−	0.725149i	$-0.741771\pi$
$463$	−8.71218	+	5.02998i	−0.404890	+	0.233763i	0.283702	+	0.958912i	$0.408437\pi$
$464$	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	0.601420	−	0.798933i	$-0.294602\pi$
$467$	4.54318	+	2.62300i	0.210233	+	0.121378i	−0.391187	+	0.920311i	$0.627935\pi$
$468$	−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	−0.895585	−	0.444890i	$-0.853243\pi$
$479$	1.67304	−	4.59663i	0.0764430	−	0.210025i	0.972028	+	0.234865i	$0.0754648\pi$
$480$	−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	0.997521	−	0.0703744i	$-0.0224194\pi$
$487$	9.66172	+	16.7346i	0.437814	+	0.758317i	−0.559706	+	0.828691i	$0.689086\pi$
$488$	−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	−0.988031	−	0.154257i	$-0.950702\pi$
$491$	−14.7254	+	17.5490i	−0.664547	+	0.791977i	0.323483	+	0.946234i	$0.395146\pi$
$492$	−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	0.957632	−	0.287994i	$-0.0929883\pi$
$499$	0.869506	+	2.38895i	0.0389245	+	0.106944i	−0.918708	+	0.394938i	$0.870766\pi$
$500$	−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	−0.962714	−	0.270520i	$-0.912804\pi$
$503$	−39.8057	+	7.01881i	−1.77485	+	0.312953i	−0.812132	+	0.583473i	$0.801693\pi$
$504$	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	−0.876962	−	0.480559i	$-0.840434\pi$
$509$	2.34020	−	6.42964i	0.103728	−	0.284989i	0.980690	+	0.195570i	$0.0626558\pi$
$510$	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	0.995659	−	0.0930744i	$-0.0296694\pi$
$521$	32.2497	+	18.6194i	1.41288	+	0.815729i	0.417225	+	0.908803i	$0.363003\pi$
$522$	−21.9808	−	27.1971i	−0.962074	−	1.19038i
$523$	−7.68298	−	43.5724i	−0.335953	−	1.90529i	−0.417611	−	0.908626i	$-0.637132\pi$
$523$	−7.68298	−	43.5724i	−0.335953	−	1.90529i	0.0816571	−	0.996660i	$-0.473979\pi$
$524$	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	0.741456	+	0.671001i	$0.234135\pi$
$541$	6.37799	+	36.1714i	0.274211	+	1.55513i	−0.467245	+	0.884128i	$0.654753\pi$
$542$	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	−0.408673	−	0.912681i	$-0.634008\pi$
$547$	−30.6008	−	11.1378i	−1.30840	−	0.476217i	−0.899722	+	0.436464i	$0.856231\pi$
$548$	−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	−0.409216	−	0.912438i	$-0.634198\pi$
$557$	9.87223	−	8.28378i	0.418300	−	0.350995i	0.827516	+	0.561442i	$0.189753\pi$
$558$	−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	0.906202	−	0.422846i	$-0.138969\pi$
$563$	2.06206	+	3.57160i	0.0869055	+	0.150525i	−0.819296	+	0.573371i	$0.805635\pi$
$564$	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	$-0.981895\pi$
$569$		−	2.71200i		−	0.113693i	0.998383	−	0.0568466i	$-0.0181046\pi$
$570$	0.351197	+	4.03010i	0.0147100	+	0.168802i
$571$		−	27.8695i		−	1.16630i	−0.812363	−	0.583152i	$-0.801819\pi$
$571$		−	27.8695i		−	1.16630i	0.812363	−	0.583152i	$-0.198181\pi$
$572$	−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	−0.869983	−	0.493081i	$-0.835871\pi$
$577$	−20.7062	−	35.8643i	−0.862012	−	1.49305i	0.00797112	−	0.999968i	$-0.497463\pi$
$578$	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	0.469758	−	0.882795i	$-0.344341\pi$
$587$	14.7610	+	2.60276i	0.609252	+	0.107428i	0.139494	+	0.990223i	$0.455452\pi$
$588$	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	0.183981	−	0.982930i	$-0.441101\pi$
$593$	−7.47341	−	2.72010i	−0.306896	−	0.111701i	−0.490877	+	0.871229i	$0.663324\pi$
$594$	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	0.921500	+	0.388379i	$0.126965\pi$
$599$	4.61115	+	26.1511i	0.188407	+	1.06851i	−0.733093	+	0.680128i	$0.761924\pi$
$600$	0.0845514	−	0.129386i	0.00345180	−	0.00528214i
$601$	22.0067	−	12.7056i	0.897673	−	0.518272i	0.0212282	−	0.999775i	$-0.493242\pi$
$601$	22.0067	−	12.7056i	0.897673	−	0.518272i	0.876444	+	0.481503i	$0.159909\pi$
$602$	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	0.0598205	−	0.998209i	$-0.480947\pi$
$613$	18.5018	−	6.73412i	0.747282	−	0.271988i	0.687462	+	0.726221i	$0.258725\pi$
$614$	−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	0.997964	−	0.0637735i	$-0.0203135\pi$
$617$	0.953161	+	5.40564i	0.0383728	+	0.217623i	−0.959592	+	0.281396i	$0.909202\pi$
$618$	−2.78875	+	2.25388i	−0.112180	+	0.0906644i
$619$	−12.3997	−	7.15899i	−0.498388	−	0.287744i	0.229660	−	0.973271i	$-0.426239\pi$
$619$	−12.3997	−	7.15899i	−0.498388	−	0.287744i	−0.728047	+	0.685527i	$0.759572\pi$
$620$	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	−0.956258	−	0.292526i	$-0.905504\pi$
$631$	−0.896513	+	2.46315i	−0.0356896	+	0.0980565i	0.920568	+	0.390583i	$0.127726\pi$
$632$	−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	0.907937	+	0.419107i	$0.137657\pi$
$641$	12.1986	+	33.5152i	0.481814	+	1.32377i	−0.426123	+	0.904665i	$0.640121\pi$
$642$	−0.0320218	−	0.203433i	−0.00126380	−	0.00802887i
$643$	15.4800	−	18.4484i	0.610472	−	0.727532i	−0.368929	−	0.929458i	$-0.620275\pi$
$643$	15.4800	−	18.4484i	0.610472	−	0.727532i	0.979401	+	0.201925i	$0.0647198\pi$
$644$	−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	$-0.808204\pi$
$647$		−	28.8314i		−	1.13348i	0.823897	−	0.566740i	$-0.191796\pi$
$648$	−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	−0.877699	−	0.479212i	$-0.840923\pi$
$653$	−21.8194	−	37.7923i	−0.853859	−	1.47893i	0.0238403	−	0.999716i	$-0.492411\pi$
$654$	−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	0.202025	−	0.979380i	$-0.435248\pi$
$659$	30.8465	−	25.8833i	1.20161	−	1.00827i	0.999583	−	0.0288882i	$-0.00919669\pi$
$660$	−5.36365	−	1.15078i	−0.208780	−	0.0447940i
$661$	5.51264	−	15.1459i	0.214417	−	0.589106i	−0.785126	−	0.619336i	$-0.787402\pi$
$661$	5.51264	−	15.1459i	0.214417	−	0.589106i	0.999543	+	0.0302304i	$0.00962411\pi$
$662$	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	0.0621939	−	0.998064i	$-0.480190\pi$
$673$	−20.0030	−	11.5487i	−0.771058	−	0.445171i	−0.833252	+	0.552894i	$0.813524\pi$
$674$	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	0.0716821	−	0.997428i	$-0.477163\pi$
$677$	25.2730	−	14.5914i	0.971321	−	0.560792i	0.899639	+	0.436635i	$0.143830\pi$
$678$	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	−0.218295	−	0.975883i	$-0.570050\pi$
$691$	13.6086	−	7.85694i	0.517696	−	0.298892i	0.735992	+	0.676991i	$0.236716\pi$
$692$	−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	−0.855100	−	0.518462i	$-0.826505\pi$
$701$	3.32956	−	18.8829i	0.125756	−	0.713196i	0.980856	−	0.194734i	$-0.0623842\pi$
$702$	−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	−0.853752	−	0.520680i	$-0.825679\pi$
$709$	−13.0269	+	10.9309i	−0.489235	+	0.410517i	0.364517	+	0.931197i	$0.381234\pi$
$710$	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	0.0345328	+	0.999404i	$0.489006\pi$
$719$	−25.6259	+	30.5397i	−0.955684	+	1.13894i	−0.990217	+	0.139536i	$0.955439\pi$
$720$	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	0.878609	−	0.477541i	$-0.158472\pi$
$727$	−2.73410	−	7.51188i	−0.101402	−	0.278600i	−0.980011	+	0.198941i	$0.936250\pi$
$728$	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	−0.460191	−	0.887820i	$-0.652219\pi$
$733$	14.5869	−	25.2652i	0.538779	−	0.933193i	0.998970	−	0.0453728i	$-0.0144476\pi$
$734$	−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	−0.171528	−	0.985179i	$-0.554870\pi$
$739$	−18.2045	−	3.20994i	−0.669663	−	0.118080i	−0.498135	+	0.867100i	$0.665981\pi$
$740$	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	−0.998892	−	0.0470583i	$-0.985015\pi$
$743$	−1.20332	+	6.82439i	−0.0441457	+	0.250363i	0.954746	+	0.297421i	$0.0961264\pi$
$744$	−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	−0.999934	−	0.0114939i	$-0.996341\pi$
$751$	−1.76031	−	9.98320i	−0.0642345	−	0.364292i	0.935699	−	0.352798i	$-0.114770\pi$
$752$	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	0.325836	−	0.945426i	$-0.394354\pi$
$757$	−15.0952	−	12.6664i	−0.548646	−	0.460368i	−0.874482	+	0.485058i	$0.838799\pi$
$758$	−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	−0.830605	−	0.556863i	$-0.812005\pi$
$769$	−6.67065	−	37.8311i	−0.240550	−	1.36423i	0.590055	−	0.807363i	$-0.299106\pi$
$770$	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	0.552680	−	0.833393i	$-0.313605\pi$
$773$	−10.1209	−	12.0616i	−0.364024	−	0.433827i	−0.916704	+	0.399567i	$0.869161\pi$
$774$	−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	−0.995109	−	0.0987836i	$-0.968505\pi$
$787$	−11.5582	+	20.0194i	−0.412005	+	0.713614i	0.583104	+	0.812398i	$0.301838\pi$
$788$	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	$0.421658\pi$
$797$			54.7609i			1.93973i	−0.243642	+	0.969865i	$0.578342\pi$
$798$	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	−0.933455	−	0.358695i	$-0.883222\pi$
$809$	−4.43960	+	7.68961i	−0.156088	+	0.270352i	0.777367	+	0.629048i	$0.216555\pi$
$810$	13.7276	−	22.7974i	0.482340	−	0.801017i
$811$	37.3268	−	31.3209i	1.31072	−	1.09982i	0.322536	−	0.946557i	$-0.395465\pi$
$811$	37.3268	−	31.3209i	1.31072	−	1.09982i	0.988185	−	0.153268i	$-0.0489796\pi$
$812$	−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	0.574241	−	0.818686i	$-0.305297\pi$
$821$	13.9797	+	5.08819i	0.487894	+	0.177579i	−0.0863471	+	0.996265i	$0.527519\pi$
$822$	−2.29922	−	2.00254i	−0.0801946	−	0.0698465i
$823$	1.64912	+	1.96535i	0.0574848	+	0.0685077i	0.794021	−	0.607891i	$-0.207984\pi$
$823$	1.64912	+	1.96535i	0.0574848	+	0.0685077i	−0.736536	+	0.676399i	$0.763540\pi$
$824$	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	0.996261	−	0.0863899i	$-0.0275331\pi$
$827$	0.878109	+	4.98000i	0.0305348	+	0.173172i	−0.965727	+	0.259562i	$0.916422\pi$
$828$	13.0062	−	6.88375i	0.451998	−	0.239227i
$829$	43.3520	−	25.0293i	1.50568	−	0.869303i	0.505698	−	0.862711i	$-0.331235\pi$
$829$	43.3520	−	25.0293i	1.50568	−	0.869303i	0.999978	−	0.00659184i	$-0.00209826\pi$
$830$	−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	0.999466	−	0.0326821i	$-0.0104049\pi$
$839$	33.0449	+	27.7279i	1.14084	+	0.957275i	0.141370	+	0.989957i	$0.454849\pi$
$840$	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	−0.987893	−	0.155135i	$-0.950419\pi$
$853$	−0.190369	+	1.07963i	−0.00651809	+	0.0369659i	0.981375	+	0.192101i	$0.0615300\pi$
$854$	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	0.457020	−	0.889456i	$-0.348917\pi$
$857$	17.0456	+	3.00560i	0.582267	+	0.102669i	0.125246	+	0.992126i	$0.460028\pi$
$858$	0.190216	−	0.973615i	0.00649385	−	0.0332387i
$859$	2.68429	−	7.37504i	0.0915869	−	0.251633i	−0.885438	−	0.464757i	$-0.846142\pi$
$859$	2.68429	−	7.37504i	0.0915869	−	0.251633i	0.977025	+	0.213124i	$0.0683639\pi$
$860$	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	−0.497245	−	0.867610i	$-0.665655\pi$
$863$	14.7692	−	25.5810i	0.502750	−	0.870789i	0.999995	−	0.00317851i	$-0.00101175\pi$
$864$	−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	−0.979202	−	0.202888i	$-0.934967\pi$
$877$	−18.0457	+	21.5060i	−0.609359	+	0.726206i	0.369843	+	0.929094i	$0.379412\pi$
$878$	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	0.860796	−	0.508950i	$-0.169966\pi$
$881$	−0.307651	−	0.532868i	−0.0103650	−	0.0179528i	−0.871161	+	0.490997i	$0.836633\pi$
$882$	−40.4571	−	0.744788i	−1.36226	−	0.0250783i
$883$	−20.1205	+	3.54779i	−0.677110	+	0.119393i	−0.501620	−	0.865088i	$-0.667262\pi$
$883$	−20.1205	+	3.54779i	−0.677110	+	0.119393i	−0.175491	+	0.984481i	$0.556151\pi$
$884$	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	−0.211982	−	0.977274i	$-0.567992\pi$
$887$	21.2538	−	17.8341i	0.713634	−	0.598810i	0.925616	+	0.378463i	$0.123547\pi$
$888$	−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	−0.763884	−	0.645354i	$-0.776710\pi$
$907$	−28.1356	+	10.2405i	−0.934228	+	0.340031i	−0.170344	+	0.985385i	$0.554488\pi$
$908$	−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	−0.141301	−	0.989967i	$-0.545128\pi$
$919$	19.5649	−	11.2958i	0.645385	−	0.372613i	0.786686	+	0.617353i	$0.211795\pi$
$920$	−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	0.899566	+	0.436785i	$0.143883\pi$
$929$	−2.89978	+	16.4455i	−0.0951388	+	0.539559i	−0.994705	+	0.102774i	$0.967228\pi$
$930$	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	−0.307322	+	0.951606i	$0.599433\pi$
$937$	−39.7274	+	33.3352i	−1.29784	+	1.08901i	−0.990515	+	0.137408i	$0.956123\pi$
$938$	−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	−0.577895	−	0.816111i	$-0.696126\pi$
$941$	−25.8232	+	4.55332i	−0.841811	+	0.148434i	−0.263917	+	0.964545i	$0.585014\pi$
$942$	−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	−0.586209	−	0.810160i	$-0.699380\pi$
$947$	9.64551	−	11.4951i	0.313437	−	0.373540i	0.899646	+	0.436620i	$0.143825\pi$
$948$	−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	−0.842123	−	0.539285i	$-0.818695\pi$
$953$	−5.08743	+	6.06296i	−0.164798	+	0.196399i	0.677325	+	0.735684i	$0.263139\pi$
$954$	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	0.774179	−	0.632967i	$-0.218163\pi$
$967$	39.9648	+	7.04688i	1.28518	+	0.226612i	0.511003	+	0.859579i	$0.329274\pi$
$968$	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	−0.592545	−	0.805537i	$-0.701877\pi$
$971$	7.47160	−	42.3736i	0.239775	−	1.35983i	0.832320	−	0.554295i	$-0.187012\pi$
$972$	−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	0.885041	−	0.465513i	$-0.154130\pi$
$977$	28.8945	+	16.6822i	0.924415	+	0.533712i	0.0393744	+	0.999225i	$0.487463\pi$
$978$	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	0.139455	−	0.990228i	$-0.455465\pi$
$983$	27.6780	−	10.0740i	0.882790	−	0.321309i	0.743335	+	0.668919i	$0.233243\pi$
$984$	−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	0.376234	−	0.926525i	$-0.377219\pi$
$991$	−14.8234	−	12.4383i	−0.470882	−	0.395117i	−0.847116	+	0.531408i	$0.821663\pi$
$992$	−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	−0.798080	−	0.602551i	$-0.794151\pi$
$997$	−8.02691	−	45.5229i	−0.254215	−	1.44172i	0.543865	−	0.839173i	$-0.316960\pi$
$998$	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.59.8	yes	48
3.2	odd	2		684.2.cf.a.667.1		48
4.3	odd	2	inner	76.2.k.a.59.7	✓	48
12.11	even	2		684.2.cf.a.667.2		48
19.10	odd	18	inner	76.2.k.a.67.7	yes	48
57.29	even	18		684.2.cf.a.523.2		48
76.67	even	18	inner	76.2.k.a.67.8	yes	48
228.143	odd	18		684.2.cf.a.523.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.59.7	✓	48	4.3	odd	2	inner
76.2.k.a.59.8	yes	48	1.1	even	1	trivial
76.2.k.a.67.7	yes	48	19.10	odd	18	inner
76.2.k.a.67.8	yes	48	76.67	even	18	inner
684.2.cf.a.523.1		48	228.143	odd	18
684.2.cf.a.523.2		48	57.29	even	18
684.2.cf.a.667.1		48	3.2	odd	2
684.2.cf.a.667.2		48	12.11	even	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
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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