LMFDB - Embedded newform 76.2.k.a.67.7

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			67.7
Character	$\chi$	$=$	76.67
Dual form			76.2.k.a.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09990 - 0.888945i) q^{2} +(-0.220673 + 0.185167i) q^{3} +(0.419555 - 1.95550i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(-0.0781151 + 0.399831i) q^{6} +(3.55057 + 2.04992i) q^{7} +(-1.27686 - 2.52381i) q^{8} +(-0.506535 + 2.87270i) q^{9} +O(q^{10})$	\(q+(1.09990 - 0.888945i) q^{2} +(-0.220673 + 0.185167i) q^{3} +(0.419555 - 1.95550i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(-0.0781151 + 0.399831i) q^{6} +(3.55057 + 2.04992i) q^{7} +(-1.27686 - 2.52381i) q^{8} +(-0.506535 + 2.87270i) q^{9} +(-3.04718 + 1.04598i) q^{10} +(-3.61965 + 2.08981i) q^{11} +(0.269509 + 0.509213i) q^{12} +(-0.374492 + 0.446302i) q^{13} +(5.72754 - 0.901553i) q^{14} +(0.616669 - 0.224449i) q^{15} +(-3.64795 - 1.64088i) 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} +(-2.12353 + 5.51625i) q^{22} +(0.862701 + 2.37025i) q^{23} +(0.749095 + 0.320505i) q^{24} +(0.145317 + 0.121936i) q^{25} +(-0.0151654 + 0.823789i) q^{26} +(-0.852252 - 1.47614i) q^{27} +(5.49829 - 6.08308i) q^{28} +(8.34798 + 1.47197i) q^{29} +(0.478751 - 0.795056i) q^{30} +(0.386863 - 0.670066i) q^{31} +(-5.47102 + 1.43802i) q^{32} +(0.411797 - 1.13140i) q^{33} +(-3.51965 - 3.06548i) q^{34} +(-6.00353 - 7.15472i) q^{35} +(5.40504 + 2.19578i) q^{36} +1.23521i q^{37} +(-3.34928 - 5.17516i) q^{38} -0.167830i q^{39} +(0.766949 + 6.39761i) q^{40} +(-4.51238 - 5.37764i) q^{41} +(-1.09698 + 1.25950i) q^{42} +(1.55737 - 4.27884i) q^{43} +(2.56797 + 7.95501i) q^{44} +(3.32261 - 5.75494i) q^{45} +(3.05591 + 1.84014i) q^{46} +(-4.84679 - 0.854620i) q^{47} +(1.10884 - 0.313381i) q^{48} +(4.90438 + 8.49464i) q^{49} +(0.268229 + 0.00493791i) q^{50} +(0.728306 + 0.611122i) q^{51} +(0.715623 + 0.919566i) q^{52} +(-0.232598 - 0.639058i) q^{53} +(-2.24960 - 0.866004i) 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} +(-0.180183 - 1.30006i) q^{60} +(-2.91217 + 1.05994i) q^{61} +(-0.170142 - 1.08090i) q^{62} +(-7.68731 + 9.16138i) q^{63} +(-4.73925 + 6.44512i) q^{64} +(1.14941 - 0.663614i) q^{65} +(-0.552820 - 1.61049i) q^{66} +(-2.44691 + 13.8771i) q^{67} +(-6.59630 - 0.242949i) q^{68} +(-0.629267 - 0.363307i) q^{69} +(-12.9634 - 2.53267i) q^{70} +(12.4034 + 4.51448i) q^{71} +(7.89693 - 2.38964i) q^{72} +(-8.59023 + 7.20806i) q^{73} +(1.09803 + 1.35860i) q^{74} -0.0546461 q^{75} +(-8.28430 - 2.71483i) q^{76} -17.1358 q^{77} +(-0.149192 - 0.184596i) q^{78} +(7.91111 - 6.63821i) q^{79} +(6.53068 + 6.35495i) q^{80} +(-7.76190 - 2.82510i) q^{81} +(-9.74358 - 1.90361i) q^{82} +(-1.29416 - 0.747183i) q^{83} +(-0.0869389 + 2.36047i) q^{84} +(-1.30559 + 7.40436i) q^{85} +(-2.09070 - 6.09071i) q^{86} +(-2.11474 + 1.22094i) q^{87} +(9.89607 + 6.46693i) q^{88} +(9.52313 - 11.3492i) q^{89} +(-1.46128 - 9.28347i) q^{90} +(-2.24455 + 0.816948i) q^{91} +(4.99697 - 0.692559i) 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} +(12.9456 + 4.98352i) 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 $

$2$	1.09990	−	0.888945i	0.777746	−	0.628579i
$2$	1.09990	−	0.888945i	0.777746	−	0.628579i
$3$	−0.220673	+	0.185167i	−0.127406	+	0.106906i	−0.704264	−	0.709938i	$-0.748723\pi$
$3$	−0.220673	+	0.185167i	−0.127406	+	0.106906i	0.576858	+	0.816844i	$0.304278\pi$
$4$	0.419555	−	1.95550i	0.209778	−	0.977749i
$5$	−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	$0.781242\pi$
$6$	−0.0781151	+	0.399831i	−0.0318904	+	0.163230i
$7$	3.55057	+	2.04992i	1.34199	+	0.774799i	0.987099	−	0.160109i	$-0.0511845\pi$
$7$	3.55057	+	2.04992i	1.34199	+	0.774799i	0.354891	+	0.934908i	$0.384518\pi$
$8$	−1.27686	−	2.52381i	−0.451439	−	0.892302i
$9$	−0.506535	+	2.87270i	−0.168845	+	0.957567i
$10$	−3.04718	+	1.04598i	−0.963604	+	0.330768i
$11$	−3.61965	+	2.08981i	−1.09137	+	0.630101i	−0.933940	−	0.357430i	$-0.883653\pi$
$11$	−3.61965	+	2.08981i	−1.09137	+	0.630101i	−0.157426	+	0.987531i	$0.550320\pi$
$12$	0.269509	+	0.509213i	0.0778004	+	0.146997i
$13$	−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	$0.247967\pi$
$14$	5.72754	−	0.901553i	1.53075	−	0.240950i
$15$	0.616669	−	0.224449i	0.159223	−	0.0579525i
$16$	−3.64795	−	1.64088i	−0.911987	−	0.410220i
$17$	−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
$22$	−2.12353	+	5.51625i	−0.452738	+	1.17607i
$23$	0.862701	+	2.37025i	0.179886	+	0.494232i	0.996561	−	0.0828661i	$-0.0264074\pi$
$23$	0.862701	+	2.37025i	0.179886	+	0.494232i	−0.816675	+	0.577098i	$0.804185\pi$
$24$	0.749095	+	0.320505i	0.152908	+	0.0654228i
$25$	0.145317	+	0.121936i	0.0290635	+	0.0243872i
$26$	−0.0151654	+	0.823789i	−0.00297418	+	0.161558i
$27$	−0.852252	−	1.47614i	−0.164016	−	0.284084i
$28$	5.49829	−	6.08308i	1.03908	−	1.14959i
$29$	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	$0.267164\pi$
$30$	0.478751	−	0.795056i	0.0874075	−	0.145157i
$31$	0.386863	−	0.670066i	0.0694826	−	0.120347i	−0.829191	−	0.558965i	$-0.811199\pi$
$31$	0.386863	−	0.670066i	0.0694826	−	0.120347i	0.898674	+	0.438618i	$0.144532\pi$
$32$	−5.47102	+	1.43802i	−0.967149	+	0.254209i
$33$	0.411797	−	1.13140i	0.0716847	−	0.196952i
$34$	−3.51965	−	3.06548i	−0.603615	−	0.525726i
$35$	−6.00353	−	7.15472i	−1.01478	−	1.20937i
$36$	5.40504	+	2.19578i	0.900840	+	0.365964i
$37$			1.23521i			0.203067i	0.994832	+	0.101534i	$0.0323749\pi$
$37$			1.23521i			0.203067i	−0.994832	+	0.101534i	$0.967625\pi$
$38$	−3.34928	−	5.17516i	−0.543325	−	0.839522i
$39$		−	0.167830i		−	0.0268743i
$40$	0.766949	+	6.39761i	0.121265	+	1.01155i
$41$	−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	$0.962453\pi$
$42$	−1.09698	+	1.25950i	−0.169267	+	0.194345i
$43$	1.55737	−	4.27884i	0.237497	−	0.652517i	−0.762488	−	0.647002i	$-0.776022\pi$
$43$	1.55737	−	4.27884i	0.237497	−	0.652517i	0.999985	−	0.00551486i	$-0.00175544\pi$
$44$	2.56797	+	7.95501i	0.387136	+	1.19926i
$45$	3.32261	−	5.75494i	0.495306	−	0.857895i
$46$	3.05591	+	1.84014i	0.450569	+	0.271314i
$47$	−4.84679	−	0.854620i	−0.706977	−	0.124659i	−0.191412	−	0.981510i	$-0.561307\pi$
$47$	−4.84679	−	0.854620i	−0.706977	−	0.124659i	−0.515565	+	0.856851i	$0.672418\pi$
$48$	1.10884	−	0.313381i	0.160047	−	0.0452326i
$49$	4.90438	+	8.49464i	0.700626	+	1.21352i
$50$	0.268229	+	0.00493791i	0.0379333	+	0.000698326i
$51$	0.728306	+	0.611122i	0.101983	+	0.0855742i
$52$	0.715623	+	0.919566i	0.0992390	+	0.127521i
$53$	−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	$0.903762\pi$
$54$	−2.24960	−	0.866004i	−0.306132	−	0.117848i
$55$	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	$-0.0114906\pi$
$59$	0.368113	+	2.08767i	0.0479243	+	0.271792i	−0.951424	+	0.307883i	$0.900379\pi$
$60$	−0.180183	−	1.30006i	−0.0232616	−	0.167838i
$61$	−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	$0.452463\pi$
$62$	−0.170142	−	1.08090i	−0.0216080	−	0.137275i
$63$	−7.68731	+	9.16138i	−0.968510	+	1.15423i
$64$	−4.73925	+	6.44512i	−0.592406	+	0.805639i
$65$	1.14941	−	0.663614i	0.142567	−	0.0823112i
$66$	−0.552820	−	1.61049i	−0.0680474	−	0.198238i
$67$	−2.44691	+	13.8771i	−0.298938	+	1.69536i	0.351813	+	0.936070i	$0.385565\pi$
$67$	−2.44691	+	13.8771i	−0.298938	+	1.69536i	−0.650751	+	0.759291i	$0.725546\pi$
$68$	−6.59630	−	0.242949i	−0.799919	−	0.0294619i
$69$	−0.629267	−	0.363307i	−0.0757548	−	0.0437370i
$70$	−12.9634	−	2.53267i	−1.54943	−	0.302712i
$71$	12.4034	+	4.51448i	1.47202	+	0.535771i	0.948648	−	0.316335i	$-0.102452\pi$
$71$	12.4034	+	4.51448i	1.47202	+	0.535771i	0.523370	+	0.852105i	$0.324674\pi$
$72$	7.89693	−	2.38964i	0.930662	−	0.281622i
$73$	−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	$0.505630\pi$
$74$	1.09803	+	1.35860i	0.127644	+	0.157935i
$75$	−0.0546461			−0.00630999
$76$	−8.28430	−	2.71483i	−0.950275	−	0.311412i
$77$	−17.1358			−1.95280
$78$	−0.149192	−	0.184596i	−0.0168926	−	0.0209014i
$79$	7.91111	−	6.63821i	0.890069	−	0.746857i	−0.0781550	−	0.996941i	$-0.524903\pi$
$79$	7.91111	−	6.63821i	0.890069	−	0.746857i	0.968224	+	0.250085i	$0.0804585\pi$
$80$	6.53068	+	6.35495i	0.730153	+	0.710505i
$81$	−7.76190	−	2.82510i	−0.862433	−	0.313900i
$82$	−9.74358	−	1.90361i	−1.07600	−	0.210218i
$83$	−1.29416	−	0.747183i	−0.142052	−	0.0820140i	0.427289	−	0.904115i	$-0.359469\pi$
$83$	−1.29416	−	0.747183i	−0.142052	−	0.0820140i	−0.569342	+	0.822101i	$0.692802\pi$
$84$	−0.0869389	+	2.36047i	−0.00948581	+	0.257549i
$85$	−1.30559	+	7.40436i	−0.141611	+	0.803115i
$86$	−2.09070	−	6.09071i	−0.225446	−	0.656778i
$87$	−2.11474	+	1.22094i	−0.226723	+	0.130899i
$88$	9.89607	+	6.46693i	1.05493	+	0.689377i
$89$	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	$-0.0652242\pi$
$90$	−1.46128	−	9.28347i	−0.154032	−	0.978564i
$91$	−2.24455	+	0.816948i	−0.235292	+	0.0856394i
$92$	4.99697	−	0.692559i	0.520971	−	0.0722043i
$93$	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	$0.270035\pi$
$98$	12.9456	+	4.98352i	1.30770	+	0.503412i
$99$	−4.16991	−	11.4567i	−0.419092	−	1.15145i
$100$	0.299414	−	0.233009i	0.0299414	−	0.0233009i
$101$	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	$0.578846\pi$
$102$	1.34432	+	0.0247480i	0.133107	+	0.00245041i
$103$	4.40079	+	7.62240i	0.433623	+	0.751057i	0.997182	−	0.0750187i	$-0.0239016\pi$
$103$	4.40079	+	7.62240i	0.433623	+	0.751057i	−0.563559	+	0.826076i	$0.690568\pi$
$104$	1.60456	+	0.375281i	0.157340	+	0.0367993i
$105$	2.64963	+	0.467202i	0.258578	+	0.0455942i
$106$	−0.823922	−	0.496133i	−0.0800264	−	0.0481887i
$107$	0.252753	−	0.437781i	0.0244346	−	0.0423219i	−0.853550	−	0.521012i	$-0.825555\pi$
$107$	0.252753	−	0.437781i	0.0244346	−	0.0423219i	0.877984	+	0.478690i	$0.158888\pi$
$108$	−3.24416	+	1.04725i	−0.312170	+	0.100772i
$109$	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	$0.0142805\pi$
$110$	8.84385	−	10.1541i	0.843228	−	0.968156i
$111$	−0.228720	−	0.272577i	−0.0217091	−	0.0258719i
$112$	−9.58863	−	13.3041i	−0.906040	−	1.25712i
$113$			7.26696i			0.683618i	0.939769	+	0.341809i	$0.111040\pi$
$113$			7.26696i			0.683618i	−0.939769	+	0.341809i	$0.888960\pi$
$114$	1.69736	+	0.521843i	0.158973	+	0.0488751i
$115$		−	5.74619i		−	0.535835i
$116$	6.38088	−	15.7069i	0.592450	−	1.45835i
$117$	−1.09240	−	1.30187i	−0.100992	−	0.120358i
$118$	2.26071	+	1.96900i	0.208116	+	0.181261i
$119$	4.62790	−	12.7151i	0.424239	−	1.16559i
$120$	−1.35387	−	1.26977i	−0.123591	−	0.115913i
$121$	3.23459	−	5.60247i	0.294054	−	0.509316i
$122$	−2.26086	+	3.75459i	−0.204689	+	0.339925i
$123$	1.99152	+	0.351159i	0.179569	+	0.0316629i
$124$	−1.14800	−	1.03764i	−0.103094	−	0.0931827i
$125$	5.47915	+	9.49017i	0.490070	+	0.848827i
$126$	−0.311305	+	16.9102i	−0.0277333	+	1.50648i
$127$	−6.88695	−	5.77884i	−0.611118	−	0.512789i	0.283879	−	0.958860i	$-0.408378\pi$
$127$	−6.88695	−	5.77884i	−0.611118	−	0.512789i	−0.894998	+	0.446071i	$0.852823\pi$
$128$	0.516655	+	11.3019i	0.0456663	+	0.998957i
$129$	0.448629	+	1.23260i	0.0394996	+	0.108524i
$130$	0.674323	−	1.75167i	0.0591420	−	0.153632i
$131$	−13.5834	+	2.39512i	−1.18679	+	0.209262i	−0.731979	−	0.681328i	$-0.761403\pi$
$131$	−13.5834	+	2.39512i	−1.18679	+	0.209262i	−0.454807	+	0.890590i	$0.650292\pi$
$132$	−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
$136$	−7.47123	+	5.59653i	−0.640653	+	0.479898i
$137$	−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	$0.492476\pi$
$138$	−1.01509	+	0.159782i	−0.0864102	+	0.0136015i
$139$	12.3852	−	14.7601i	1.05050	−	1.25194i	0.0836787	−	0.996493i	$-0.473333\pi$
$139$	12.3852	−	14.7601i	1.05050	−	1.25194i	0.966823	−	0.255447i	$-0.0822225\pi$
$140$	−16.5099	+	8.73809i	−1.39534	+	0.738503i
$141$	1.22780	−	0.708872i	0.103400	−	0.0596978i
$142$	17.6557	−	6.06050i	1.48163	−	0.508586i
$143$	0.422845	−	2.39807i	0.0353601	−	0.200537i
$144$	6.56156	−	9.64830i	0.546797	−	0.804025i
$145$	−16.7237	−	9.65542i	−1.38883	−	0.801839i
$146$	−3.04082	+	15.5644i	−0.251660	+	1.28812i
$147$	−2.65519	−	0.966410i	−0.218996	−	0.0797081i
$148$	2.41545	+	0.518238i	0.198549	+	0.0425989i
$149$	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	$0.251132\pi$
$150$	−0.0601052	+	0.0485773i	−0.00490757	+	0.00396632i
$151$	−9.61868			−0.782757			−0.391378	−	0.920230i	$-0.628002\pi$
$151$	−9.61868			−0.782757			−0.391378	+	0.920230i	$0.628002\pi$
$152$	−11.5252	+	4.37825i	−0.934820	+	0.355123i
$153$	9.62728			0.778320
$154$	−18.8476	+	15.2328i	−1.51879	+	1.22749i
$155$	−1.35024	+	1.13299i	−0.108454	+	0.0910038i
$156$	−0.328192	−	0.0704140i	−0.0262764	−	0.00563763i
$157$	−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	$0.708631\pi$
$158$	2.80042	−	14.3339i	0.222789	−	1.14034i
$159$	0.169660	+	0.0979535i	0.0134549	+	0.00776822i
$160$	12.8323	+	1.18438i	1.01448	+	0.0936336i
$161$	−1.79575	+	10.1842i	−0.141525	+	0.802629i
$162$	−11.0487	+	3.79257i	−0.868064	+	0.297973i
$163$	−14.3484	+	8.28406i	−1.12385	+	0.648858i	−0.942382	−	0.334538i	$-0.891420\pi$
$163$	−14.3484	+	8.28406i	−1.12385	+	0.648858i	−0.181472	+	0.983396i	$0.558086\pi$
$164$	−12.4092	+	6.56773i	−0.968993	+	0.512853i
$165$	−1.76307	+	2.10115i	−0.137255	+	0.163574i
$166$	−2.08765	+	0.328610i	−0.162033	+	0.0255051i
$167$	7.24993	−	2.63876i	0.561016	−	0.204193i	−0.0459180	−	0.998945i	$-0.514621\pi$
$167$	7.24993	−	2.63876i	0.561016	−	0.204193i	0.606934	+	0.794752i	$0.292399\pi$
$168$	2.00270	+	2.67356i	0.154512	+	0.206270i
$169$	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	$0.559827\pi$
$174$	−1.24064	+	3.22280i	−0.0940530	+	0.244320i
$175$	0.266001	+	0.730832i	0.0201078	+	0.0552457i
$176$	16.6334	−	1.68410i	1.25379	−	0.126944i
$177$	−0.467801	−	0.392531i	−0.0351620	−	0.0295045i
$178$	0.385649	−	20.9485i	0.0289056	−	1.57016i
$179$	−0.791374	−	1.37070i	−0.0591501	−	0.102451i	0.834934	−	0.550350i	$-0.185506\pi$
$179$	−0.791374	−	1.37070i	−0.0591501	−	0.102451i	−0.894084	+	0.447899i	$0.852172\pi$
$180$	−9.85975	−	8.91188i	−0.734902	−	0.664252i
$181$	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	$0.390873\pi$
$182$	−1.74255	+	2.89384i	−0.129167	+	0.214505i
$183$	0.446372	−	0.773139i	0.0329968	−	0.0571521i
$184$	4.88052	−	5.20378i	0.359797	−	0.383628i
$185$	0.962417	−	2.64422i	0.0707583	−	0.194407i
$186$	0.237693	+	0.207022i	0.0174285	+	0.0151796i
$187$	8.86683	+	10.5671i	0.648407	+	0.772742i
$188$	−3.70470	+	9.11933i	−0.270193	+	0.665095i
$189$		−	6.98821i		−	0.508318i
$190$	3.13758	+	13.6881i	0.227624	+	0.993039i
$191$		−	12.6803i		−	0.917517i	−0.888561	−	0.458759i	$-0.848294\pi$
$191$		−	12.6803i		−	0.917517i	0.888561	−	0.458759i	$-0.151706\pi$
$192$	−0.147596	−	2.29981i	−0.0106518	−	0.165975i
$193$	−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	$-0.512439\pi$
$194$	9.53056	−	10.9426i	0.684254	−	0.785630i
$195$	−0.130765	+	0.359275i	−0.00936430	+	0.0257282i
$196$	18.6689	−	6.02654i	1.33349	−	0.430467i
$197$	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	$0.114914\pi$
$198$	−14.7709	−	8.89443i	−1.04972	−	0.632100i
$199$	−11.9982	−	2.11561i	−0.850530	−	0.149971i	−0.268642	−	0.963240i	$-0.586575\pi$
$199$	−11.9982	−	2.11561i	−0.850530	−	0.149971i	−0.581888	+	0.813269i	$0.697686\pi$
$200$	0.122193	−	0.522449i	0.00864033	−	0.0369427i
$201$	−2.02962	−	3.51540i	−0.143158	−	0.247957i
$202$	12.3729	+	0.227778i	0.870557	+	0.0160264i
$203$	26.6227	+	22.3391i	1.86855	+	1.56790i
$204$	1.50061	−	1.16780i	0.105064	−	0.0817626i
$205$	5.46966	+	15.0278i	0.382018	+	1.04959i
$206$	11.6163	+	4.47180i	0.809347	+	0.311565i
$207$	−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	$-0.0153456\pi$
$211$	0.635579	+	3.60455i	0.0437551	+	0.248147i	−0.955083	+	0.296338i	$0.904234\pi$
$212$	−1.34727	+	0.186725i	−0.0925305	+	0.0128243i
$213$	−3.57304	+	1.30048i	−0.244821	+	0.0891074i
$214$	−0.111160	−	0.706198i	−0.00759877	−	0.0482747i
$215$	−6.66775	+	7.94631i	−0.454736	+	0.541934i
$216$	−2.63730	+	4.03576i	−0.179446	+	0.274598i
$217$	2.74717	−	1.58608i	0.186490	−	0.107670i
$218$	−2.87170	−	8.36594i	−0.194496	−	0.566613i
$219$	0.560940	−	3.18125i	0.0379048	−	0.214969i
$220$	0.700903	−	19.0302i	0.0472549	−	1.28301i
$221$	1.66521	+	0.961412i	0.112014	+	0.0646716i
$222$	−0.493874	−	0.0964885i	−0.0331467	−	0.00647588i
$223$	−26.3079	−	9.57530i	−1.76171	−	0.641210i	−0.761732	−	0.647893i	$-0.775650\pi$
$223$	−26.3079	−	9.57530i	−1.76171	−	0.641210i	−0.999978	+	0.00668309i	$0.997873\pi$
$224$	−22.3731	−	6.10938i	−1.49487	−	0.408200i
$225$	−0.423893	+	0.355689i	−0.0282596	+	0.0237126i
$226$	6.45993	+	7.99292i	0.429708	+	0.531681i
$227$	6.26652			0.415924			0.207962	−	0.978137i	$-0.433317\pi$
$227$	6.26652			0.415924			0.207962	+	0.978137i	$0.433317\pi$
$228$	2.33082	−	0.934888i	0.154362	−	0.0619144i
$229$	−12.6430			−0.835472			−0.417736	−	0.908569i	$-0.637176\pi$
$229$	−12.6430			−0.835472			−0.417736	+	0.908569i	$0.637176\pi$
$230$	−5.10804	−	6.32022i	−0.336814	−	0.416743i
$231$	3.78141	−	3.17298i	0.248798	−	0.208767i
$232$	−6.94423	−	22.9482i	−0.455911	−	1.50663i
$233$	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	$0.540332\pi$
$234$	−2.35882	−	0.460843i	−0.154201	−	0.0301263i
$235$	9.70967	+	5.60588i	0.633389	+	0.365687i
$236$	4.23689	+	0.156049i	0.275798	+	0.0101580i
$237$	−0.516593	+	2.92975i	−0.0335563	+	0.190307i
$238$	−6.21276	−	18.0992i	−0.402713	−	1.17320i
$239$	8.72510	−	5.03744i	0.564380	−	0.325845i	−0.190522	−	0.981683i	$-0.561018\pi$
$239$	8.72510	−	5.03744i	0.564380	−	0.325845i	0.754901	+	0.655838i	$0.227685\pi$
$240$	−2.61787	−	0.193100i	−0.168983	−	0.0124646i
$241$	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	$0.134440\pi$
$242$	−1.42257	−	9.03752i	−0.0914460	−	0.580954i
$243$	7.04109	−	2.56275i	0.451686	−	0.164400i
$244$	0.850902	+	6.13946i	0.0544735	+	0.393038i
$245$	−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
$250$	14.4627	+	5.56756i	0.914705	+	0.352124i
$251$	2.91664	+	8.01342i	0.184097	+	0.505802i	0.997070	−	0.0764996i	$-0.0243744\pi$
$251$	2.91664	+	8.01342i	0.184097	+	0.505802i	−0.812973	+	0.582302i	$0.802152\pi$
$252$	14.6898	+	18.8762i	0.925371	+	1.18909i
$253$	−8.07605	−	6.77661i	−0.507737	−	0.426042i
$254$	−12.7120	−	0.234020i	−0.797623	−	0.0146837i
$255$	−1.08293	−	1.87569i	−0.0678158	−	0.117460i
$256$	10.6150	+	11.9717i	0.663440	+	0.748230i
$257$	−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	$0.582836\pi$
$258$	1.58916	+	0.956927i	0.0989367	+	0.0595757i
$259$	−2.53208	+	4.38570i	−0.157336	+	0.272514i
$260$	−0.815454	−	2.52610i	−0.0505723	−	0.156662i
$261$	−8.45709	+	23.2357i	−0.523481	+	1.43825i
$262$	−12.8112	+	14.7093i	−0.791480	+	0.908741i
$263$	1.42151	+	1.69409i	0.0876540	+	0.104462i	0.808089	−	0.589061i	$-0.200502\pi$
$263$	1.42151	+	1.69409i	0.0876540	+	0.104462i	−0.720435	+	0.693523i	$0.756058\pi$
$264$	−3.38126	+	0.405347i	−0.208102	+	0.0249474i
$265$			1.54926i			0.0951706i
$266$	−1.28318	−	25.2406i	−0.0786769	−	1.54760i
$267$			4.26784i			0.261187i
$268$	26.1101	+	10.6072i	1.59493	+	0.647935i
$269$	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	$0.626566\pi$
$270$	4.14098	+	3.60664i	0.252012	+	0.219493i
$271$	−8.76172	+	24.0726i	−0.532237	+	1.46231i	0.324166	+	0.946000i	$0.394916\pi$
$271$	−8.76172	+	24.0726i	−0.532237	+	1.46231i	−0.856403	+	0.516308i	$0.827306\pi$
$272$	−3.24260	+	12.7971i	−0.196611	+	0.775940i
$273$	0.344039	−	0.595893i	0.0208222	−	0.0360651i
$274$	−5.46002	+	9.06740i	−0.329852	+	0.547782i
$275$	−0.780821	−	0.137680i	−0.0470853	−	0.00830240i
$276$	−0.974459	+	1.07810i	−0.0586555	+	0.0648941i
$277$	−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	$0.915442\pi$
$278$	0.501552	−	27.2445i	0.0300811	−	1.63401i
$279$	1.72894	+	1.45075i	0.103509	+	0.0868542i
$280$	−10.3915	+	24.2874i	−0.621011	+	1.45145i
$281$	−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	$0.899820\pi$
$282$	0.720311	−	1.87114i	0.0428939	−	0.111425i
$283$	9.24245	−	1.62969i	0.549407	−	0.0968752i	0.107948	−	0.994157i	$-0.465572\pi$
$283$	9.24245	−	1.62969i	0.549407	−	0.0968752i	0.441459	+	0.897281i	$0.354461\pi$
$284$	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
$288$	−1.35975	−	16.4450i	−0.0801238	−	0.969032i
$289$	5.73912	−	2.08887i	0.337595	−	0.122875i
$290$	−26.9775	+	4.24644i	−1.58417	+	0.249359i
$291$	−1.89997	+	2.26430i	−0.111378	+	0.132736i
$292$	10.4913	+	19.8223i	0.613955	+	1.16002i
$293$	−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	$0.514384\pi$
$294$	−3.77952	+	1.29736i	−0.220426	+	0.0756637i
$295$	0.838596	−	4.75591i	0.0488249	−	0.276900i
$296$	3.11743	−	1.57719i	0.181197	−	0.0916723i
$297$	6.16971	+	3.56209i	0.358003	+	0.206693i
$298$	0.553520	−	2.83318i	0.0320645	−	0.164122i
$299$	−1.38092	−	0.502615i	−0.0798608	−	0.0290669i
$300$	−0.0229270	+	0.106860i	−0.00132369	+	0.00616958i
$301$	14.3009	−	11.9999i	0.824288	−	0.691660i
$302$	−10.5796	+	8.55047i	−0.608786	+	0.492024i
$303$	−2.52073			−0.144812
$304$	−8.78456	+	15.0609i	−0.503829	+	0.863803i
$305$	7.05996			0.404252
$306$	10.5890	−	8.55812i	0.605335	−	0.489235i
$307$	4.28349	−	3.59427i	0.244471	−	0.205136i	−0.512316	−	0.858797i	$-0.671212\pi$
$307$	4.28349	−	3.59427i	0.244471	−	0.205136i	0.756787	+	0.653661i	$0.226768\pi$
$308$	−7.18941	+	33.5090i	−0.409655	+	1.90935i
$309$	−2.38255	−	0.867177i	−0.135539	−	0.0493320i
$310$	−0.477967	+	2.44646i	−0.0271467	+	0.138950i
$311$	−10.3643	−	5.98382i	−0.587704	−	0.339311i	0.176485	−	0.984303i	$-0.443527\pi$
$311$	−10.3643	−	5.98382i	−0.587704	−	0.339311i	−0.764189	+	0.644992i	$0.776861\pi$
$312$	−0.423572	+	0.214296i	−0.0239800	+	0.0121321i
$313$	−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	$0.907295\pi$
$314$	−10.1096	+	3.47024i	−0.570519	+	0.195837i
$315$	23.5944	−	13.6222i	1.32939	−	0.767525i
$316$	−9.66186	−	18.2552i	−0.543522	−	1.02694i
$317$	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	$0.0654500\pi$
$318$	0.273685	−	0.0430798i	0.0153475	−	0.00241579i
$319$	−33.2929	+	12.1176i	−1.86405	+	0.678458i
$320$	15.1671	−	10.1045i	0.847865	−	0.564858i
$321$	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
$326$	−8.41773	+	21.8666i	−0.466215	+	1.21108i
$327$	0.616218	+	1.69304i	0.0340769	+	0.0936255i
$328$	−7.81047	+	18.2549i	−0.431261	+	1.00796i
$329$	−15.4570	−	12.9699i	−0.852171	−	0.715056i
$330$	−0.0713974	+	3.87832i	−0.00393029	+	0.213495i
$331$	−7.28237	−	12.6134i	−0.400275	−	0.693297i	0.593484	−	0.804846i	$-0.297752\pi$
$331$	−7.28237	−	12.6134i	−0.400275	−	0.693297i	−0.993759	+	0.111549i	$0.964419\pi$
$332$	−2.00409	+	2.21724i	−0.109989	+	0.121687i
$333$	−3.54839	−	0.625676i	−0.194450	−	0.0342868i
$334$	5.62848	−	9.34715i	0.307977	−	0.511453i
$335$	16.0505	−	27.8003i	0.876934	−	1.51889i
$336$	4.57942	+	1.16036i	0.249828	+	0.0633027i
$337$	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	$0.107645\pi$
$338$	13.5017	+	11.7595i	0.734394	+	0.639630i
$339$	−1.34560	−	1.60362i	−0.0730829	−	0.0870968i
$340$	13.9314	+	5.65961i	0.755539	+	0.306935i
$341$			3.23387i			0.175124i
$342$	16.5632	−	7.00009i	0.895636	−	0.378521i
$343$			11.5155i			0.621779i
$344$	−12.7875	+	1.53298i	−0.689458	+	0.0826526i
$345$	1.06400	+	1.26803i	0.0572840	+	0.0682684i
$346$	−8.66409	+	9.94771i	−0.465784	+	0.534792i
$347$	−6.38859	+	17.5525i	−0.342958	+	0.942268i	0.641574	+	0.767061i	$0.278282\pi$
$347$	−6.38859	+	17.5525i	−0.342958	+	0.942268i	−0.984532	+	0.175207i	$0.943941\pi$
$348$	1.50030	+	4.64762i	0.0804248	+	0.249138i
$349$	−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	$0.226299\pi$
$350$	0.942243	+	0.567381i	0.0503650	+	0.0303278i
$351$	0.977967	+	0.172442i	0.0522000	+	0.00920427i
$352$	16.7980	−	16.6385i	0.895337	−	0.886836i
$353$	−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	$0.881451\pi$
$354$	−0.863472	−	0.0158959i	−0.0458930	−	0.000844860i
$355$	−23.0346	−	19.3284i	−1.22255	−	1.02584i
$356$	−18.1979	−	23.3841i	−0.964488	−	1.23935i
$357$	1.33315	+	3.66281i	0.0705579	+	0.193856i
$358$	−2.08891	−	0.804144i	−0.110402	−	0.0425003i
$359$	22.1724	−	3.90959i	1.17022	−	0.206340i	0.445431	−	0.895316i	$-0.353051\pi$
$359$	22.1724	−	3.90959i	1.17022	−	0.206340i	0.724784	+	0.688976i	$0.241939\pi$
$360$	−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
$364$	0.655829	+	4.73196i	0.0343748	+	0.248022i
$365$	24.0053	−	8.73722i	1.25650	−	0.457327i
$366$	−0.196314	−	1.24717i	−0.0102615	−	0.0651908i
$367$	19.3515	−	23.0622i	1.01014	−	1.20384i	0.0312345	−	0.999512i	$-0.490056\pi$
$367$	19.3515	−	23.0622i	1.01014	−	1.20384i	0.978903	−	0.204323i	$-0.0654994\pi$
$368$	0.742207	−	10.0621i	0.0386902	−	0.524525i
$369$	17.7340	−	10.2387i	0.923197	−	0.533008i
$370$	−1.29200	−	3.76391i	−0.0671680	−	0.195676i
$371$	0.484164	−	2.74583i	0.0251366	−	0.142557i
$372$	0.445469	+	0.0164071i	0.0230965	+	0.000850671i
$373$	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	$0.518473\pi$
$374$	19.1462	+	3.74060i	0.990025	+	0.193422i
$375$	−2.96636	−	1.07967i	−0.153182	−	0.0557538i
$376$	4.03178	+	13.3236i	0.207923	+	0.687113i
$377$	−3.78320	+	3.17448i	−0.194844	+	0.163494i
$378$	−6.21213	−	7.68633i	−0.319518	−	0.395342i
$379$	13.0139			0.668480			0.334240	−	0.942488i	$-0.391520\pi$
$379$	13.0139			0.668480			0.334240	+	0.942488i	$0.391520\pi$
$380$	15.6190	+	12.2664i	0.801237	+	0.629252i
$381$	2.58981			0.132680
$382$	−11.2721	−	13.9471i	−0.576732	−	0.713595i
$383$	−21.9719	+	18.4366i	−1.12271	+	0.942068i	−0.998738	−	0.0502175i	$-0.984009\pi$
$383$	−21.9719	+	18.4366i	−1.12271	+	0.942068i	−0.123975	+	0.992285i	$0.539564\pi$
$384$	−2.20675	−	2.39836i	−0.112613	−	0.122391i
$385$	36.6827	+	13.3514i	1.86952	+	0.680450i
$386$	−30.4881	−	5.95648i	−1.55180	−	0.303177i
$387$	11.5030	+	6.64124i	0.584729	+	0.337593i
$388$	0.755327	−	20.5078i	0.0383459	−	1.04113i
$389$	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	$-0.249096\pi$
$390$	0.175547	+	0.511409i	0.00888916	+	0.0258962i
$391$	7.20948	−	4.16240i	0.364599	−	0.210501i
$392$	15.1767	−	23.2242i	0.766537	−	1.17300i
$393$	2.55399	−	3.04373i	0.128832	−	0.153536i
$394$	−0.999201	−	6.34789i	−0.0503390	−	0.319802i
$395$	−22.1075	+	8.04648i	−1.11235	+	0.404862i
$396$	−24.1531	+	3.34752i	−1.21374	+	0.168219i
$397$	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	$0.633009\pi$
$402$	−5.35736	−	2.06237i	−0.267201	−	0.102861i
$403$	0.154175	+	0.423591i	0.00767999	+	0.0211006i
$404$	13.8115	−	10.7483i	0.687146	−	0.534749i
$405$	14.4147	+	12.0954i	0.716274	+	0.601026i
$406$	49.1405	+	0.904644i	2.43880	+	0.0448967i
$407$	−2.58135	−	4.47103i	−0.127953	−	0.221621i
$408$	0.612410	−	2.61843i	0.0303188	−	0.129631i
$409$	−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	$0.736024\pi$
$410$	19.3749	+	11.6668i	0.956860	+	0.576183i
$411$	1.07799	−	1.86714i	0.0531736	−	0.0920993i
$412$	16.7520	−	5.40773i	0.825310	−	0.266420i
$413$	−2.97256	+	8.16705i	−0.146270	+	0.401874i
$414$	−6.83410	+	7.84661i	−0.335878	+	0.385640i
$415$	2.18824	+	2.60785i	0.107417	+	0.128014i
$416$	1.40706	−	2.98025i	0.0689868	−	0.146119i
$417$			5.55050i			0.271809i
$418$	22.9383	+	11.7329i	1.12195	+	0.573877i
$419$			13.1962i			0.644678i	0.946624	+	0.322339i	$0.104469\pi$
$419$			13.1962i			0.644678i	−0.946624	+	0.322339i	$0.895531\pi$
$420$	2.02528	−	4.98534i	0.0988235	−	0.243260i
$421$	−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	$0.833482\pi$
$422$	3.90332	+	3.39965i	0.190011	+	0.165492i
$423$	4.91013	−	13.4905i	0.238739	−	0.655930i
$424$	−1.31587	+	1.40302i	−0.0639041	+	0.0681368i
$425$	0.313039	−	0.542200i	0.0151846	−	0.0263005i
$426$	−2.77393	+	4.60663i	−0.134397	+	0.223192i
$427$	−12.5127	−	2.20633i	−0.605532	−	0.106772i
$428$	−0.750036	−	0.677931i	−0.0362544	−	0.0327691i
$429$	0.350733	+	0.607487i	0.0169335	+	0.0293297i
$430$	−0.270017	+	14.6674i	−0.0130214	+	0.707325i
$431$	10.9959	+	9.22664i	0.529653	+	0.444432i	0.867982	−	0.496596i	$-0.165417\pi$
$431$	10.9959	+	9.22664i	0.529653	+	0.444432i	−0.338329	+	0.941028i	$0.609862\pi$
$432$	0.686798	+	6.78334i	0.0330436	+	0.326364i
$433$	−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	$-0.357133\pi$
$434$	1.61167	−	4.18661i	0.0773627	−	0.200964i
$435$	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	$0.171100\pi$
$439$	4.75454	+	26.9643i	0.226922	+	1.28694i	−0.632055	+	0.774923i	$0.717788\pi$
$440$	−16.1459	−	21.5543i	−0.769723	−	1.02756i
$441$	−26.8868	+	9.78599i	−1.28032	+	0.466000i
$442$	2.68621	−	0.422827i	0.127770	−	0.0201118i
$443$	−9.24631	+	11.0193i	−0.439305	+	0.523544i	−0.939583	−	0.342321i	$-0.888787\pi$
$443$	−9.24631	+	11.0193i	−0.439305	+	0.523544i	0.500278	+	0.865865i	$0.333231\pi$
$444$	−0.628985	+	0.332899i	−0.0298503	+	0.0157987i
$445$	−29.2290	+	16.8754i	−1.38559	+	0.799969i
$446$	−37.4480	+	12.8544i	−1.77321	+	0.608675i
$447$	−0.102108	+	0.579082i	−0.00482953	+	0.0273896i
$448$	−30.0391	+	13.1688i	−1.41921	+	0.622165i
$449$	−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	$0.846079\pi$
$450$	−0.150052	+	0.768039i	−0.00707353	+	0.0362057i
$451$	27.5715	+	10.0352i	1.29829	+	0.472539i
$452$	14.2105	+	3.04889i	0.668407	+	0.143408i
$453$	2.12258	−	1.78106i	0.0997276	−	0.0836814i
$454$	6.89254	−	5.57059i	0.323483	−	0.261441i
$455$	5.44144			0.255099
$456$	1.73260	−	3.10025i	0.0811365	−	0.145183i
$457$	20.3699			0.952862			0.476431	−	0.879212i	$-0.341930\pi$
$457$	20.3699			0.952862			0.476431	+	0.879212i	$0.341930\pi$
$458$	−13.9060	+	11.2389i	−0.649785	+	0.525160i
$459$	−4.30940	+	3.61602i	−0.201146	+	0.168781i
$460$	−11.2367	−	2.41084i	−0.523912	−	0.112406i
$461$	−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	$0.751341\pi$
$462$	1.33856	−	6.85142i	0.0622757	−	0.318757i
$463$	8.71218	+	5.02998i	0.404890	+	0.233763i	0.688592	−	0.725149i	$-0.258229\pi$
$463$	8.71218	+	5.02998i	0.404890	+	0.233763i	−0.283702	+	0.958912i	$0.591563\pi$
$464$	−28.0377	−	19.0677i	−1.30162	−	0.885196i
$465$	0.0881705	−	0.500040i	0.00408881	−	0.0231888i
$466$	9.00540	−	3.09120i	0.417167	−	0.143197i
$467$	−4.54318	+	2.62300i	−0.210233	+	0.121378i	−0.601420	−	0.798933i	$-0.705398\pi$
$467$	−4.54318	+	2.62300i	−0.210233	+	0.121378i	0.391187	+	0.920311i	$0.372065\pi$
$468$	−3.00413	+	1.58998i	−0.138866	+	0.0734967i
$469$	−37.1350	+	44.2558i	−1.71474	+	2.04354i
$470$	15.6630	−	2.46546i	0.722479	−	0.113723i
$471$	2.04592	−	0.744654i	0.0942711	−	0.0343119i
$472$	4.79887	−	3.59472i	0.220886	−	0.165460i
$473$	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
$478$	5.11872	−	13.2968i	0.234125	−	0.608181i
$479$	−1.67304	−	4.59663i	−0.0764430	−	0.210025i	0.895585	−	0.444890i	$-0.146757\pi$
$479$	−1.67304	−	4.59663i	−0.0764430	−	0.210025i	−0.972028	+	0.234865i	$0.924535\pi$
$480$	−3.05105	+	2.11475i	−0.139261	+	0.0965247i
$481$	−0.551276	−	0.462575i	−0.0251360	−	0.0210916i
$482$	0.220066	−	11.9541i	0.0100237	−	0.544492i
$483$	−1.48950	−	2.57990i	−0.0677748	−	0.117389i
$484$	−9.59854	−	8.67578i	−0.436297	−	0.394354i
$485$	−23.0201	−	4.05906i	−1.04529	−	0.184312i
$486$	5.46634	−	9.07790i	0.247958	−	0.411782i
$487$	−9.66172	+	16.7346i	−0.437814	+	0.758317i	−0.997521	−	0.0703744i	$-0.977581\pi$
$487$	−9.66172	+	16.7346i	−0.437814	+	0.758317i	0.559706	+	0.828691i	$0.310914\pi$
$488$	6.39354	+	5.99638i	0.289422	+	0.271443i
$489$	1.63238	−	4.48492i	0.0738186	−	0.202815i
$490$	−23.8298	−	20.7548i	−1.07652	−	0.937608i
$491$	14.7254	+	17.5490i	0.664547	+	0.791977i	0.988031	−	0.154257i	$-0.0492984\pi$
$491$	14.7254	+	17.5490i	0.664547	+	0.791977i	−0.323483	+	0.946234i	$0.604854\pi$
$492$	1.52224	−	3.74708i	0.0686280	−	0.168932i
$493$		−	27.9766i		−	1.26000i
$494$	3.56396	+	0.443264i	0.160350	+	0.0199434i
$495$			27.7745i			1.24837i
$496$	−2.51075	+	1.80957i	−0.112736	+	0.0812521i
$497$	34.7850	+	41.4551i	1.56032	+	1.85952i
$498$	0.399840	−	0.459078i	0.0179173	−	0.0205718i
$499$	−0.869506	+	2.38895i	−0.0389245	+	0.106944i	−0.957632	−	0.287994i	$-0.907012\pi$
$499$	−0.869506	+	2.38895i	−0.0389245	+	0.106944i	0.918708	+	0.394938i	$0.129234\pi$
$500$	20.8568	−	6.73282i	0.932745	−	0.301101i
$501$	−1.11125	+	1.92475i	−0.0496472	+	0.0859914i
$502$	10.3315	+	6.22121i	0.461117	+	0.277666i
$503$	39.8057	+	7.01881i	1.77485	+	0.312953i	0.962714	−	0.270520i	$-0.0871955\pi$
$503$	39.8057	+	7.01881i	1.77485	+	0.312953i	0.812132	+	0.583473i	$0.198307\pi$
$504$	32.9372	+	7.70351i	1.46714	+	0.343142i
$505$	−9.96719	−	17.2637i	−0.443534	−	0.768224i
$506$	−14.9069	−	0.274425i	−0.662691	−	0.0121997i
$507$	−2.79385	−	2.34432i	−0.124079	−	0.104115i
$508$	−14.1900	+	11.0429i	−0.629578	+	0.489949i
$509$	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	$0.840434\pi$
$510$	−2.85850	−	1.10041i	−0.126577	−	0.0487268i
$511$	−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
$516$	2.59857	−	0.360151i	0.114396	−	0.0158547i
$517$	19.3297	−	7.03543i	0.850118	−	0.309418i
$518$	1.11361	+	7.07471i	0.0489291	+	0.310845i
$519$	1.72724	−	2.05844i	0.0758173	−	0.0903555i
$520$	−3.14248	−	2.05356i	−0.137807	−	0.0900546i
$521$	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	$0.0296694\pi$
$522$	11.3533	+	33.0748i	0.496919	+	1.44764i
$523$	7.68298	−	43.5724i	0.335953	−	1.90529i	−0.0816571	−	0.996660i	$-0.526021\pi$
$523$	7.68298	−	43.5724i	0.335953	−	1.90529i	0.417611	−	0.908626i	$-0.362868\pi$
$524$	−1.01533	+	27.5672i	−0.0443549	+	1.20428i
$525$	−0.194025	−	0.112020i	−0.00846794	−	0.00488897i
$526$	3.06947	+	0.599683i	0.133835	+	0.0261474i
$527$	−2.39959	−	0.873380i	−0.104528	−	0.0380450i
$528$	−3.35871	+	3.45159i	−0.146169	+	0.150211i
$529$	12.7452	−	10.6945i	0.554138	−	0.464977i
$530$	1.37721	+	1.70403i	0.0598222	+	0.0740185i
$531$	−6.18373			−0.268351
$532$	−23.8488	−	26.6214i	−1.03398	−	1.15418i
$533$	4.08990			0.177153
$534$	3.79387	+	4.69419i	0.164177	+	0.203137i
$535$	−0.882168	+	0.740227i	−0.0381395	+	0.0320028i
$536$	38.1476	−	11.5436i	1.64773	−	0.498609i
$537$	0.428443	+	0.155940i	0.0184887	+	0.00672933i
$538$	20.8239	+	4.06838i	0.897784	+	0.175400i
$539$	−35.5043	−	20.4984i	−1.52928	−	0.882930i
$540$	7.76077	+	0.285838i	0.333970	+	0.0123005i
$541$	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	$-0.234135\pi$
$542$	11.7622	+	34.2662i	0.505231	+	1.47186i
$543$	−3.32003	+	1.91682i	−0.142476	+	0.0822587i
$544$	7.80940	+	16.9580i	0.334825	+	0.727070i
$545$	−9.15853	+	10.9147i	−0.392308	+	0.467535i
$546$	−0.151308	−	0.961254i	−0.00647538	−	0.0411379i
$547$	30.6008	−	11.1378i	1.30840	−	0.476217i	0.408673	−	0.912681i	$-0.365992\pi$
$547$	30.6008	−	11.1378i	1.30840	−	0.476217i	0.899722	+	0.436464i	$0.143769\pi$
$548$	2.05494	+	14.8269i	0.0877828	+	0.633373i
$549$	−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
$554$	−11.2070	−	4.31424i	−0.476140	−	0.183294i
$555$	0.277242	+	0.761715i	0.0117683	+	0.0323330i
$556$	−23.6672	−	30.4120i	−1.00371	−	1.28976i
$557$	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	$0.634198\pi$
$558$	3.19130	+	0.0587496i	0.135098	+	0.00248707i
$559$	1.32643	+	2.29745i	0.0561021	+	0.0971717i
$560$	10.1605	+	35.9511i	0.429360	+	1.51921i
$561$	−3.91334	−	0.690028i	−0.165221	−	0.0291330i
$562$	−1.39457	−	0.839754i	−0.0588264	−	0.0354229i
$563$	−2.06206	+	3.57160i	−0.0869055	+	0.150525i	−0.906202	−	0.422846i	$-0.861031\pi$
$563$	−2.06206	+	3.57160i	−0.0869055	+	0.150525i	0.819296	+	0.573371i	$0.194365\pi$
$564$	−0.871068	−	2.69838i	−0.0366786	−	0.113622i
$565$	5.66208	−	15.5564i	0.238205	−	0.654464i
$566$	8.71705	−	10.0085i	0.366405	−	0.420690i
$567$	−21.7679	−	25.9420i	−0.914168	−	1.08946i
$568$	−4.44377	−	37.0683i	−0.186456	−	1.55535i
$569$			2.71200i			0.113693i	0.998383	+	0.0568466i	$0.0181046\pi$
$569$			2.71200i			0.113693i	−0.998383	+	0.0568466i	$0.981895\pi$
$570$	−3.22696	−	2.43962i	−0.135162	−	0.102184i
$571$		−	27.8695i		−	1.16630i	−0.812363	−	0.583152i	$-0.801819\pi$
$571$		−	27.8695i		−	1.16630i	0.812363	−	0.583152i	$-0.198181\pi$
$572$	−4.51202	−	1.83300i	−0.188657	−	0.0766414i
$573$	2.34798	+	2.79821i	0.0980881	+	0.116897i
$574$	−30.6931	−	26.7325i	−1.28110	−	1.11579i
$575$	−0.163653	+	0.449633i	−0.00682480	+	0.0187510i
$576$	−16.1143	−	16.8791i	−0.671429	−	0.703297i
$577$	−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	$0.835871\pi$
$578$	4.45556	−	7.39931i	0.185327	−	0.307771i
$579$	6.23156	+	1.09879i	0.258975	+	0.0456642i
$580$	−25.8977	+	28.6521i	−1.07534	+	1.18972i
$581$	−3.06334	−	5.30586i	−0.127089	−	0.220124i
$582$	−0.0769412	+	4.17947i	−0.00318932	+	0.173245i
$583$	2.17743	+	1.82708i	0.0901801	+	0.0756701i
$584$	29.1603	+	12.4764i	1.20666	+	0.516278i
$585$	1.32415	+	3.63807i	0.0547468	+	0.150415i
$586$	−9.36831	+	24.3359i	−0.387001	+	1.00531i
$587$	−14.7610	+	2.60276i	−0.609252	+	0.107428i	−0.469758	−	0.882795i	$-0.655659\pi$
$587$	−14.7610	+	2.60276i	−0.609252	+	0.107428i	−0.139494	+	0.990223i	$0.544548\pi$
$588$	−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
$592$	2.02683	−	4.50598i	0.0833021	−	0.185194i
$593$	−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	$0.441101\pi$
$594$	9.95256	−	1.56660i	0.408358	−	0.0642783i
$595$	−19.8140	+	23.6134i	−0.812293	+	0.968053i
$596$	−1.90972	−	3.60826i	−0.0782253	−	0.147800i
$597$	3.03942	−	1.75481i	0.124395	−	0.0718195i
$598$	−1.96567	+	0.674738i	−0.0803823	+	0.0275921i
$599$	−4.61115	+	26.1511i	−0.188407	+	1.06851i	0.733093	+	0.680128i	$0.238076\pi$
$599$	−4.61115	+	26.1511i	−0.188407	+	1.06851i	−0.921500	+	0.388379i	$0.873035\pi$
$600$	0.0697755	+	0.137916i	0.00284857	+	0.00563041i
$601$	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	$0.493242\pi$
$602$	5.06230	−	25.9113i	0.206324	−	1.05607i
$603$	−38.6254	−	14.0585i	−1.57295	−	0.572506i
$604$	−4.03556	+	18.8093i	−0.164205	+	0.765340i
$605$	−11.2895	+	9.47300i	−0.458983	+	0.385132i
$606$	−2.77255	+	2.24079i	−0.112627	+	0.0910260i
$607$	13.6931			0.555787			0.277894	−	0.960612i	$-0.410364\pi$
$607$	13.6931			0.555787			0.277894	+	0.960612i	$0.410364\pi$
$608$	3.72619	+	24.3745i	0.151117	+	0.988516i
$609$	−10.0114			−0.405681
$610$	7.76525	−	6.27592i	0.314406	−	0.254104i
$611$	2.19650	−	1.84308i	0.0888609	−	0.0745631i
$612$	4.03918	−	18.8261i	0.163274	−	0.761001i
$613$	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	$0.480947\pi$
$614$	1.51629	−	7.76112i	0.0611926	−	0.313213i
$615$	−3.98965	−	2.30343i	−0.160878	−	0.0928831i
$616$	21.8800	+	43.2475i	0.881571	+	1.74249i
$617$	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	$0.0203135\pi$
$618$	−3.39144	+	1.16415i	−0.136424	+	0.0468289i
$619$	12.3997	−	7.15899i	0.498388	−	0.287744i	−0.229660	−	0.973271i	$-0.573761\pi$
$619$	12.3997	−	7.15899i	0.498388	−	0.287744i	0.728047	+	0.685527i	$0.240428\pi$
$620$	1.64905	+	3.11575i	0.0662276	+	0.125131i
$621$	2.76359	−	3.29352i	0.110899	−	0.132165i
$622$	−16.7189	+	2.63167i	−0.670369	+	0.105521i
$623$	57.0776	−	20.7746i	2.28677	−	0.832315i
$624$	−0.275389	+	0.612236i	−0.0110244	+	0.0245090i
$625$	−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
$630$	13.8420	−	35.9572i	0.551480	−	1.43257i
$631$	0.896513	+	2.46315i	0.0356896	+	0.0980565i	0.956258	−	0.292526i	$-0.0944958\pi$
$631$	0.896513	+	2.46315i	0.0356896	+	0.0980565i	−0.920568	+	0.390583i	$0.872274\pi$
$632$	−26.8550	−	11.4901i	−1.06823	−	0.457050i
$633$	−0.807698	−	0.677739i	−0.0321031	−	0.0269377i
$634$	0.438284	−	23.8077i	0.0174065	−	0.945526i
$635$	10.2403	+	17.7368i	0.406375	+	0.703863i
$636$	0.262730	−	0.290674i	0.0104179	−	0.0115260i
$637$	−5.62782	−	0.992337i	−0.222982	−	0.0393178i
$638$	−25.8470	+	42.9238i	−1.02329	+	1.69937i
$639$	−19.2515	+	33.3446i	−0.761579	+	1.31909i
$640$	7.69991	−	24.5966i	0.304366	−	0.972266i
$641$	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	$-0.137657\pi$
$642$	0.155295	+	0.135256i	0.00612899	+	0.00533812i
$643$	−15.4800	−	18.4484i	−0.610472	−	0.727532i	0.368929	−	0.929458i	$-0.379725\pi$
$643$	−15.4800	−	18.4484i	−0.610472	−	0.727532i	−0.979401	+	0.201925i	$0.935280\pi$
$644$	19.1618	+	7.78444i	0.755081	+	0.306750i
$645$		−	2.98818i		−	0.117660i
$646$	−14.9011	+	13.8519i	−0.586274	+	0.544996i
$647$		−	28.8314i		−	1.13348i	−0.823897	−	0.566740i	$-0.808204\pi$
$647$		−	28.8314i		−	1.13348i	0.823897	−	0.566740i	$-0.191796\pi$
$648$	2.78085	+	23.1968i	0.109242	+	0.911257i
$649$	−5.69528	−	6.78737i	−0.223559	−	0.266428i
$650$	−0.102653	+	0.117862i	−0.00402639	+	0.00462292i
$651$	−0.312537	+	0.858689i	−0.0122493	+	0.0336547i
$652$	10.1795	+	31.5339i	0.398661	+	1.23496i
$653$	−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	$0.840923\pi$
$654$	2.18280	+	1.31439i	0.0853542	+	0.0513969i
$655$	30.9442	+	5.45629i	1.20909	+	0.213195i
$656$	7.63686	+	27.0216i	0.298169	+	1.05502i
$657$	−16.3553	−	28.3283i	−0.638083	−	1.10519i
$658$	−28.5307	−	0.525231i	−1.11224	−	0.0204756i
$659$	−30.8465	−	25.8833i	−1.20161	−	1.00827i	−0.999583	−	0.0288882i	$-0.990803\pi$
$659$	−30.8465	−	25.8833i	−1.20161	−	1.00827i	−0.202025	−	0.979380i	$-0.564752\pi$
$660$	3.36908	+	4.32923i	0.131141	+	0.168515i
$661$	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	$0.787402\pi$
$662$	−19.2225	−	7.39988i	−0.747105	−	0.287605i
$663$	−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
$668$	−2.11834	−	15.2843i	−0.0819611	−	0.591368i
$669$	7.57848	−	2.75834i	0.293001	−	0.106644i
$670$	−7.05900	−	44.8456i	−0.272713	−	1.73254i
$671$	8.32598	−	9.92251i	0.321421	−	0.383054i
$672$	6.06840	−	2.79458i	0.234093	−	0.107803i
$673$	−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	$0.480190\pi$
$674$	−0.183563	−	0.534763i	−0.00707059	−	0.0205983i
$675$	0.0561477	−	0.318430i	0.00216113	−	0.0122564i
$676$	25.3040	+	0.931975i	0.973230	+	0.0358452i
$677$	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	$0.477163\pi$
$678$	−2.90556	−	0.567660i	−0.111587	−	0.0218008i
$679$	39.5310	+	14.3881i	1.51706	+	0.552165i
$680$	20.3543	−	6.15928i	0.780550	−	0.236198i
$681$	−1.38285	+	1.16035i	−0.0529910	+	0.0444648i
$682$	2.87473	+	3.55693i	0.110079	+	0.136202i
$683$	−32.3508			−1.23787			−0.618934	−	0.785443i	$-0.712435\pi$
$683$	−32.3508			−1.23787			−0.618934	+	0.785443i	$0.712435\pi$
$684$	11.9952	−	22.4232i	0.458647	−	0.857371i
$685$	17.0499			0.651444
$686$	10.2367	+	12.6659i	0.390837	+	0.483586i
$687$	2.78996	−	2.34106i	0.106444	−	0.0893170i
$688$	−12.7023	+	13.0535i	−0.484269	+	0.497661i
$689$	0.372319	+	0.135513i	0.0141842	+	0.00516263i
$690$	2.29750	+	0.448864i	0.0874644	+	0.0170880i
$691$	−13.6086	−	7.85694i	−0.517696	−	0.298892i	0.218295	−	0.975883i	$-0.429950\pi$
$691$	−13.6086	−	7.85694i	−0.517696	−	0.298892i	−0.735992	+	0.676991i	$0.763284\pi$
$692$	−0.686657	+	18.6434i	−0.0261028	+	0.708715i
$693$	8.67987	−	49.2260i	0.329721	−	1.86994i
$694$	8.57640	+	24.9851i	0.325556	+	0.948421i
$695$	−38.0136	+	21.9471i	−1.44194	+	0.832502i
$696$	5.78166	+	3.77822i	0.219153	+	0.143213i
$697$	−14.8926	+	17.7483i	−0.564097	+	0.672265i
$698$	1.53022	+	9.72142i	0.0579196	+	0.367961i
$699$	−1.82246	+	0.663319i	−0.0689316	+	0.0250890i
$700$	1.54074	−	0.213540i	0.0582346	−	0.00807107i
$701$	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
$706$	−7.46834	−	2.87500i	−0.281075	−	0.108202i
$707$	12.2702	+	33.7121i	0.461468	+	1.26787i
$708$	−0.963862	+	0.750095i	−0.0362242	+	0.0281903i
$709$	−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	$0.825679\pi$
$710$	−42.5176	−	0.782721i	−1.59566	−	0.0293750i
$711$	15.0623	+	26.0887i	0.564881	+	0.978403i
$712$	−40.8030	−	9.54320i	−1.52916	−	0.357647i
$713$	1.92197	+	0.338895i	0.0719784	+	0.0126917i
$714$	4.72236	+	2.84362i	0.176730	+	0.106420i
$715$	−2.77365	+	4.80411i	−0.103729	+	0.179663i
$716$	−3.01243	+	0.972446i	−0.112580	+	0.0363420i
$717$	−0.992628	+	2.72722i	−0.0370704	+	0.101850i
$718$	20.9120	−	24.0102i	0.780429	−	0.896053i
$719$	25.6259	+	30.5397i	0.955684	+	1.13894i	0.990217	+	0.139536i	$0.0445612\pi$
$719$	25.6259	+	30.5397i	0.955684	+	1.13894i	−0.0345328	+	0.999404i	$0.510994\pi$
$720$	−21.5639	+	15.5417i	−0.803638	+	0.579205i
$721$			36.0852i			1.34388i
$722$	−23.9679	+	12.1466i	−0.891993	+	0.452050i
$723$			2.43539i			0.0905733i
$724$	10.0177	−	24.6591i	0.372304	−	0.916447i
$725$	1.03362	+	1.23182i	0.0383877	+	0.0457487i
$726$	1.98737	+	1.73093i	0.0737582	+	0.0642407i
$727$	2.73410	−	7.51188i	0.101402	−	0.278600i	−0.878609	−	0.477541i	$-0.841528\pi$
$727$	2.73410	−	7.51188i	0.101402	−	0.278600i	0.980011	+	0.198941i	$0.0637503\pi$
$728$	4.92780	+	4.62168i	0.182636	+	0.171291i
$729$	11.3108	−	19.5909i	0.418919	−	0.725589i
$730$	18.6365	−	30.9495i	0.689768	−	1.14549i
$731$	−14.7998	−	2.60961i	−0.547392	−	0.0965199i
$732$	−1.32459	−	1.19725i	−0.0489584	−	0.0442518i
$733$	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	$0.652219\pi$
$734$	0.783656	−	42.5684i	0.0289253	−	1.57123i
$735$	4.93100	+	4.13760i	0.181883	+	0.152618i
$736$	−8.12833	−	11.7271i	−0.299614	−	0.432267i
$737$	−20.1436	−	55.3440i	−0.741998	−	2.03862i
$738$	10.4040	−	27.0262i	0.382975	−	0.994847i
$739$	18.2045	−	3.20994i	0.669663	−	0.118080i	0.171528	−	0.985179i	$-0.445130\pi$
$739$	18.2045	−	3.20994i	0.669663	−	0.118080i	0.498135	+	0.867100i	$0.334019\pi$
$740$	−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	$-0.0149847\pi$
$743$	1.20332	+	6.82439i	0.0441457	+	0.250363i	−0.954746	+	0.297421i	$0.903874\pi$
$744$	0.504556	−	0.377951i	0.0184979	−	0.0138564i
$745$	−4.36969	+	1.59044i	−0.160093	+	0.0582690i
$746$	24.2248	−	3.81314i	0.886931	−	0.139609i
$747$	2.80197	−	3.33926i	0.102519	−	0.122177i
$748$	24.3840	−	12.9056i	0.891569	−	0.471876i
$749$	1.79484	−	1.03625i	0.0655819	−	0.0378637i
$750$	−4.22247	+	1.44941i	−0.154183	+	0.0529249i
$751$	1.76031	−	9.98320i	0.0642345	−	0.364292i	−0.935699	−	0.352798i	$-0.885230\pi$
$751$	1.76031	−	9.98320i	0.0642345	−	0.364292i	0.999934	−	0.0114939i	$-0.00365869\pi$
$752$	16.2785	+	11.0706i	0.593616	+	0.403703i
$753$	−2.12744	−	1.22828i	−0.0775283	−	0.0447610i
$754$	−1.33920	+	6.85466i	−0.0487707	+	0.249632i
$755$	20.5908	+	7.49442i	0.749374	+	0.272750i
$756$	−13.6654	−	2.93194i	−0.497007	−	0.106634i
$757$	−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	$0.394354\pi$
$758$	14.3140	−	11.5686i	0.519907	−	0.420192i
$759$	3.03697			0.110235
$760$	28.0834	−	0.392627i	1.01869	−	0.0142421i
$761$	19.6304			0.711603			0.355801	−	0.934562i	$-0.384208\pi$
$761$	19.6304			0.711603			0.355801	+	0.934562i	$0.384208\pi$
$762$	2.84853	−	2.30220i	0.103191	−	0.0833999i
$763$	19.6430	−	16.4825i	0.711126	−	0.596706i
$764$	−24.7964	−	5.32010i	−0.897102	−	0.192475i
$765$	−20.6092	−	7.50113i	−0.745126	−	0.271204i
$766$	−7.77775	+	39.8103i	−0.281021	+	1.43840i
$767$	−1.06959	−	0.617527i	−0.0386206	−	0.0222976i
$768$	−4.55921	−	0.676275i	−0.164516	−	0.0244030i
$769$	−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	$0.812005\pi$
$770$	52.2159	−	17.9237i	1.88173	−	0.645924i
$771$	0.684677	−	0.395298i	0.0246580	−	0.0142363i
$772$	−38.8288	+	20.5507i	−1.39748	+	0.739637i
$773$	−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	$0.313605\pi$
$774$	18.5558	−	2.92081i	0.666975	−	0.104986i
$775$	0.137923	−	0.0501998i	0.00495434	−	0.00180323i
$776$	−17.3996	−	23.2280i	−0.624607	−	0.833837i
$777$	−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
$782$	4.22956	−	10.9870i	0.151249	−	0.392896i
$783$	−4.94174	−	13.5773i	−0.176603	−	0.485214i
$784$	−3.95226	−	39.0355i	−0.141152	−	1.39412i
$785$	13.1896	+	11.0674i	0.470758	+	0.395013i
$786$	0.103426	−	5.61815i	0.00368910	−	0.200393i
$787$	11.5582	+	20.0194i	0.412005	+	0.713614i	0.995109	−	0.0987836i	$-0.0314952\pi$
$787$	11.5582	+	20.0194i	0.412005	+	0.713614i	−0.583104	+	0.812398i	$0.698162\pi$
$788$	−6.74194	−	6.09381i	−0.240172	−	0.217083i
$789$	−0.627377	−	0.110624i	−0.0223352	−	0.00393830i
$790$	−17.1632	+	28.5027i	−0.610638	+	1.01408i
$791$	−14.8967	+	25.8019i	−0.529667	+	0.917409i
$792$	−23.5902	+	25.1527i	−0.838243	+	0.893764i
$793$	0.617530	−	1.69665i	0.0219291	−	0.0602498i
$794$	17.6095	+	15.3372i	0.624937	+	0.544297i
$795$	−0.286872	−	0.341881i	−0.0101743	−	0.0121253i
$796$	−9.17097	+	22.5748i	−0.325056	+	0.800144i
$797$		−	54.7609i		−	1.93973i	−0.243642	−	0.969865i	$-0.578342\pi$
$797$		−	54.7609i		−	1.93973i	0.243642	−	0.969865i	$-0.421658\pi$
$798$	4.95688	+	5.33231i	0.175472	+	0.188762i
$799$			16.2430i			0.574638i
$800$	−0.970381	−	0.458144i	−0.0343082	−	0.0161978i
$801$	27.7791	+	33.1059i	0.981528	+	1.16974i
$802$	−20.7702	+	23.8474i	−0.733421	+	0.842081i
$803$	16.0302	−	44.0426i	0.565693	−	1.55423i
$804$	−7.72589	+	2.49401i	−0.272471	+	0.0879568i
$805$	11.7792	−	20.4023i	0.415164	−	0.719085i
$806$	0.546126	+	0.328855i	0.0192365	+	0.0115834i
$807$	−4.25627	−	0.750495i	−0.149828	−	0.0264187i
$808$	5.63655	−	24.0997i	0.198293	−	0.847825i
$809$	−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	$0.883222\pi$
$810$	26.6069	+	0.489815i	0.934872	+	0.0172104i
$811$	−37.3268	−	31.3209i	−1.31072	−	1.09982i	−0.988185	−	0.153268i	$-0.951020\pi$
$811$	−37.3268	−	31.3209i	−1.31072	−	1.09982i	−0.322536	−	0.946557i	$-0.604535\pi$
$812$	54.8537	−	42.6882i	1.92499	−	1.49806i
$813$	−2.52397	−	6.93456i	−0.0885196	−	0.243206i
$814$	−6.81372	−	2.62300i	−0.238821	−	0.0919361i
$815$	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
$820$	31.6816	−	4.39094i	1.10637	−	0.153338i
$821$	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	$0.305297\pi$
$822$	−0.474100	−	3.01194i	−0.0165361	−	0.105054i
$823$	−1.64912	+	1.96535i	−0.0574848	+	0.0685077i	−0.794021	−	0.607891i	$-0.792016\pi$
$823$	−1.64912	+	1.96535i	−0.0574848	+	0.0685077i	0.736536	+	0.676399i	$0.236460\pi$
$824$	13.6183	−	20.8395i	0.474416	−	0.725979i
$825$	0.197800	−	0.114200i	0.00688651	−	0.00397593i
$826$	3.99054	+	11.6254i	0.138848	+	0.404498i
$827$	−0.878109	+	4.98000i	−0.0305348	+	0.173172i	−0.996261	−	0.0863899i	$-0.972467\pi$
$827$	−0.878109	+	4.98000i	−0.0305348	+	0.173172i	0.965727	+	0.259562i	$0.0835780\pi$
$828$	−0.541625	+	14.7056i	−0.0188228	+	0.511055i
$829$	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	$0.331235\pi$
$830$	4.72508	+	0.923141i	0.164010	+	0.0320427i
$831$	2.29860	+	0.836621i	0.0797375	+	0.0290221i
$832$	−1.10166	−	4.52878i	−0.0381931	−	0.157007i
$833$	24.7989	−	20.8088i	0.859232	−	0.720982i
$834$	4.93409	+	6.10499i	0.170853	+	0.211398i
$835$	−17.5760			−0.608241
$836$	35.6598	−	7.48586i	1.23332	−	0.258904i
$837$	−1.31882			−0.0455850
$838$	11.7307	+	14.5145i	0.405231	+	0.501396i
$839$	−33.0449	+	27.7279i	−1.14084	+	0.957275i	−0.999466	−	0.0326821i	$-0.989595\pi$
$839$	−33.0449	+	27.7279i	−1.14084	+	0.957275i	−0.141370	+	0.989957i	$0.545151\pi$
$840$	−2.20409	−	7.28373i	−0.0760482	−	0.251312i
$841$	40.2710	+	14.6575i	1.38866	+	0.505430i
$842$	−9.91685	−	1.93746i	−0.341757	−	0.0667693i
$843$	0.287167	+	0.165796i	0.00989056	+	0.00571032i
$844$	7.31535	+	0.269433i	0.251805	+	0.00927426i
$845$	5.00835	−	28.4038i	0.172292	−	0.977119i
$846$	−6.59164	−	19.2030i	−0.226625	−	0.660213i
$847$	22.9693	−	13.2613i	0.789234	−	0.455665i
$848$	−0.200111	+	2.71292i	−0.00687184	+	0.0931619i
$849$	−1.73779	+	2.07102i	−0.0596410	+	0.0710773i
$850$	−0.137674	−	0.874639i	−0.00472218	−	0.0299999i
$851$	−2.92776	+	1.06562i	−0.100362	+	0.0365288i
$852$	1.04400	+	7.53269i	0.0357668	+	0.258066i
$853$	−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	$0.348917\pi$
$858$	0.925793	+	0.356392i	0.0316060	+	0.0121670i
$859$	−2.68429	−	7.37504i	−0.0915869	−	0.251633i	0.885438	−	0.464757i	$-0.153858\pi$
$859$	−2.68429	−	7.37504i	−0.0915869	−	0.251633i	−0.977025	+	0.213124i	$0.931636\pi$
$860$	12.7415	+	16.3727i	0.434482	+	0.558304i
$861$	6.35119	+	5.32928i	0.216448	+	0.181621i
$862$	20.2963	+	0.373642i	0.691296	+	0.0127263i
$863$	−14.7692	−	25.5810i	−0.502750	−	0.870789i	−0.999995	−	0.00317851i	$-0.998988\pi$
$863$	−14.7692	−	25.5810i	−0.502750	−	0.870789i	0.497245	−	0.867610i	$-0.334345\pi$
$864$	6.78542	+	6.85046i	0.230845	+	0.233057i
$865$	20.9272	+	3.69003i	0.711547	+	0.125465i
$866$	−35.2042	−	21.1985i	−1.19629	−	0.720355i
$867$	−0.879681	+	1.52365i	−0.0298755	+	0.0517459i
$868$	−1.94899	−	6.03753i	−0.0661529	−	0.204927i
$869$	−14.7629	+	40.5607i	−0.500796	+	1.37593i
$870$	5.16691	−	5.93241i	0.175175	−	0.201127i
$871$	−5.27704	−	6.28893i	−0.178806	−	0.213092i
$872$	−17.5644	+	2.10563i	−0.594806	+	0.0713057i
$873$			29.9311i			1.01302i
$874$	9.37701	−	12.4033i	0.317182	−	0.419547i
$875$			44.9274i			1.51882i
$876$	−5.98558	−	2.43163i	−0.202234	−	0.0821570i
$877$	−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	$0.934967\pi$
$878$	29.1993	+	25.4315i	0.985429	+	0.858272i
$879$	1.81671	−	4.99138i	0.0612762	−	0.168355i
$880$	−36.9194	−	9.35482i	−1.24455	−	0.315351i
$881$	−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	$0.169966\pi$
$882$	−20.8735	+	34.6645i	−0.702849	+	1.16721i
$883$	20.1205	+	3.54779i	0.677110	+	0.119393i	0.501620	−	0.865088i	$-0.332738\pi$
$883$	20.1205	+	3.54779i	0.677110	+	0.119393i	0.175491	+	0.984481i	$0.443849\pi$
$884$	2.57869	−	2.85296i	0.0867307	−	0.0959554i
$885$	0.695581	+	1.20478i	0.0233817	+	0.0404983i
$886$	−0.374438	+	20.3396i	−0.0125795	+	0.683322i
$887$	−21.2538	−	17.8341i	−0.713634	−	0.598810i	0.211982	−	0.977274i	$-0.432008\pi$
$887$	−21.2538	−	17.8341i	−0.713634	−	0.598810i	−0.925616	+	0.378463i	$0.876453\pi$
$888$	−0.395891	+	0.925288i	−0.0132852	+	0.0310506i
$889$	−12.6064	−	34.6359i	−0.422807	−	1.16165i
$890$	−17.1477	+	44.5442i	−0.574791	+	1.49312i
$891$	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
$896$	−21.3336	+	41.1874i	−0.712707	+	1.37597i
$897$	0.397800	−	0.144787i	0.0132821	−	0.00483431i
$898$	−31.6310	+	4.97893i	−1.05554	+	0.166149i
$899$	4.21584	−	5.02425i	0.140606	−	0.167568i
$900$	0.517702	+	0.978154i	0.0172567	+	0.0326051i
$901$	−1.94379	+	1.12225i	−0.0647571	+	0.0373876i
$902$	39.2466	−	13.4718i	1.30677	−	0.448562i
$903$	−0.933843	+	5.29609i	−0.0310764	+	0.176243i
$904$	18.3404	−	9.27890i	0.609994	−	0.308612i
$905$	−26.2554	−	15.1585i	−0.872758	−	0.503887i
$906$	0.751364	−	3.84584i	0.0249624	−	0.127770i
$907$	28.1356	+	10.2405i	0.934228	+	0.340031i	0.763884	−	0.645354i	$-0.223290\pi$
$907$	28.1356	+	10.2405i	0.934228	+	0.340031i	0.170344	+	0.985385i	$0.445512\pi$
$908$	2.62915	−	12.2542i	0.0872515	−	0.406669i
$909$	−19.5535	+	16.4073i	−0.648549	+	0.544197i
$910$	5.98503	−	4.83714i	0.198402	−	0.160350i
$911$	30.9988			1.02704			0.513518	−	0.858079i	$-0.328342\pi$
$911$	30.9988			1.02704			0.513518	+	0.858079i	$0.328342\pi$
$912$	−0.850264	−	4.95015i	−0.0281551	−	0.163916i
$913$	6.24587			0.206708
$914$	22.4048	−	18.1077i	0.741085	−	0.598949i
$915$	−1.55794	+	1.30727i	−0.0515040	+	0.0432170i
$916$	−5.30443	+	24.7233i	−0.175263	+	0.816882i
$917$	−53.1386	−	19.3409i	−1.75479	−	0.638692i
$918$	−1.52547	+	7.80807i	−0.0503479	+	0.257705i
$919$	−19.5649	−	11.2958i	−0.645385	−	0.372613i	0.141301	−	0.989967i	$-0.454872\pi$
$919$	−19.5649	−	11.2958i	−0.645385	−	0.372613i	−0.786686	+	0.617353i	$0.788205\pi$
$920$	−14.5023	+	7.33708i	−0.478126	+	0.241896i
$921$	−0.279711	+	1.58632i	−0.00921678	+	0.0522709i
$922$	−24.4939	+	8.40778i	−0.806662	+	0.276896i
$923$	−6.65981	+	3.84504i	−0.219210	+	0.126561i
$924$	−4.61824	−	8.72577i	−0.151929	−	0.287057i
$925$	−0.150616	+	0.179497i	−0.00495223	+	0.00590184i
$926$	14.0539	−	2.21218i	0.461840	−	0.0726967i
$927$	−24.1260	+	8.78115i	−0.792402	+	0.288411i
$928$	−47.7887	+	3.95138i	−1.56874	+	0.129710i
$929$	−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
$934$	−2.66533	+	6.92367i	−0.0872122	+	0.226549i
$935$	−10.7479	−	29.5296i	−0.351494	−	0.965722i
$936$	−1.89083	+	4.41932i	−0.0618038	+	0.144450i
$937$	−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	$-0.599433\pi$
$938$	−1.50382	+	81.6879i	−0.0491014	+	2.66720i
$939$	−2.28889	−	3.96447i	−0.0746950	−	0.129376i
$940$	15.0360	−	16.6353i	0.490421	−	0.542582i
$941$	−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	$0.696126\pi$
$942$	1.58835	−	2.63775i	0.0517512	−	0.0859427i
$943$	8.85353	−	15.3348i	0.288311	−	0.499369i
$944$	2.08276	−	8.21976i	0.0677881	−	0.267530i
$945$	−5.44489	+	14.9597i	−0.177122	+	0.486639i
$946$	20.2960	+	17.6771i	0.659881	+	0.574732i
$947$	−9.64551	−	11.4951i	−0.313437	−	0.373540i	0.586209	−	0.810160i	$-0.300620\pi$
$947$	−9.64551	−	11.4951i	−0.313437	−	0.373540i	−0.899646	+	0.436620i	$0.856175\pi$
$948$	5.51237	+	2.23939i	0.179034	+	0.0727319i
$949$		−	6.53319i		−	0.212076i
$950$	0.144328	−	1.16044i	0.00468263	−	0.0376496i
$951$			4.85034i			0.157283i
$952$	−37.9996	+	4.55542i	−1.23157	+	0.147642i
$953$	−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	$0.818695\pi$
$954$	1.84259	−	2.11557i	0.0596559	−	0.0684942i
$955$	−9.87993	+	27.1449i	−0.319707	+	0.878388i
$956$	−6.19004	−	19.1754i	−0.200200	−	0.620177i
$957$	5.10307	−	8.83878i	0.164959	−	0.285717i
$958$	−5.92632	−	3.56859i	−0.191471	−	0.115296i
$959$	−30.2183	−	5.32831i	−0.975801	−	0.172060i
$960$	−1.47595	+	5.03822i	−0.0476360	+	0.162608i
$961$	15.2007	+	26.3283i	0.490344	+	0.849301i
$962$	−1.01755	−	0.0187324i	−0.0328072	−	0.000603958i
$963$	1.12959	+	0.947835i	0.0364004	+	0.0305436i
$964$	−10.3844	−	13.3439i	−0.334460	−	0.429777i
$965$	17.1148	+	47.0226i	0.550946	+	1.51371i
$966$	−3.93169	−	1.51354i	−0.126500	−	0.0486973i
$967$	−39.9648	+	7.04688i	−1.28518	+	0.226612i	−0.774179	−	0.632967i	$-0.781837\pi$
$967$	−39.9648	+	7.04688i	−1.28518	+	0.226612i	−0.511003	+	0.859579i	$0.670726\pi$
$968$	−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	$-0.812988\pi$
$971$	−7.47160	−	42.3736i	−0.239775	−	1.35983i	0.592545	−	0.805537i	$-0.298123\pi$
$972$	−2.05732	−	14.8440i	−0.0659886	−	0.476123i
$973$	74.2319	−	27.0182i	2.37976	−	0.866164i
$974$	4.24921	+	26.9951i	0.136153	+	0.864978i
$975$	0.0204645	−	0.0243886i	0.000655389	−	0.000781062i
$976$	12.3627	+	0.911902i	0.395720	+	0.0291893i
$977$	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	$0.154130\pi$
$978$	−2.19139	−	6.38405i	−0.0700731	−	0.204139i
$979$	−10.7527	+	60.9818i	−0.343659	+	1.94899i
$980$	−44.6602	−	1.64489i	−1.42662	−	0.0525440i
$981$	15.8000	+	9.12212i	0.504455	+	0.291247i
$982$	31.7966	+	6.21211i	1.01467	+	0.198236i
$983$	−27.6780	−	10.0740i	−0.882790	−	0.321309i	−0.139455	−	0.990228i	$-0.544535\pi$
$983$	−27.6780	−	10.0740i	−0.882790	−	0.321309i	−0.743335	+	0.668919i	$0.766757\pi$
$984$	−1.65664	−	5.47460i	−0.0528117	−	0.174524i
$985$	−7.92965	+	6.65377i	−0.252660	+	0.212007i
$986$	−24.8697	−	30.7714i	−0.792011	−	0.979962i
$987$	5.81254			0.185015
$988$	4.31404	−	2.68062i	0.137248	−	0.0852819i
$989$	11.4855			0.365217
$990$	24.6900	+	30.5491i	0.784699	+	0.970915i
$991$	14.8234	−	12.4383i	0.470882	−	0.395117i	−0.376234	−	0.926525i	$-0.622781\pi$
$991$	14.8234	−	12.4383i	0.470882	−	0.395117i	0.847116	+	0.531408i	$0.178337\pi$
$992$	−1.15296	+	4.22226i	−0.0366067	+	0.134057i
$993$	3.94261	+	1.43499i	0.125115	+	0.0455381i
$994$	75.1113	+	14.6745i	2.38239	+	0.465448i
$995$	24.0362	+	13.8773i	0.761999	+	0.439941i
$996$	0.0316886	−	0.860375i	0.00100409	−	0.0272620i
$997$	−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	$0.794151\pi$
$998$	1.16727	+	3.40055i	0.0369494	+	0.107642i
$999$	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.67.7	yes	48
3.2	odd	2		684.2.cf.a.523.2		48
4.3	odd	2	inner	76.2.k.a.67.8	yes	48
12.11	even	2		684.2.cf.a.523.1		48
19.2	odd	18	inner	76.2.k.a.59.8	yes	48
57.2	even	18		684.2.cf.a.667.1		48
76.59	even	18	inner	76.2.k.a.59.7	✓	48
228.59	odd	18		684.2.cf.a.667.2		48

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

\(f(q)\)	\(=\)	\(q+(1.09990 - 0.888945i) q^{2} +(-0.220673 + 0.185167i) q^{3} +(0.419555 - 1.95550i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(-0.0781151 + 0.399831i) q^{6} +(3.55057 + 2.04992i) q^{7} +(-1.27686 - 2.52381i) q^{8} +(-0.506535 + 2.87270i) q^{9} +O(q^{10})\)	\(q+(1.09990 - 0.888945i) q^{2} +(-0.220673 + 0.185167i) q^{3} +(0.419555 - 1.95550i) q^{4} +(-2.14071 - 0.779153i) q^{5} +(-0.0781151 + 0.399831i) q^{6} +(3.55057 + 2.04992i) q^{7} +(-1.27686 - 2.52381i) q^{8} +(-0.506535 + 2.87270i) q^{9} +(-3.04718 + 1.04598i) q^{10} +(-3.61965 + 2.08981i) q^{11} +(0.269509 + 0.509213i) q^{12} +(-0.374492 + 0.446302i) q^{13} +(5.72754 - 0.901553i) q^{14} +(0.616669 - 0.224449i) q^{15} +(-3.64795 - 1.64088i) 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} +(-2.12353 + 5.51625i) q^{22} +(0.862701 + 2.37025i) q^{23} +(0.749095 + 0.320505i) q^{24} +(0.145317 + 0.121936i) q^{25} +(-0.0151654 + 0.823789i) q^{26} +(-0.852252 - 1.47614i) q^{27} +(5.49829 - 6.08308i) q^{28} +(8.34798 + 1.47197i) q^{29} +(0.478751 - 0.795056i) q^{30} +(0.386863 - 0.670066i) q^{31} +(-5.47102 + 1.43802i) q^{32} +(0.411797 - 1.13140i) q^{33} +(-3.51965 - 3.06548i) q^{34} +(-6.00353 - 7.15472i) q^{35} +(5.40504 + 2.19578i) q^{36} +1.23521i q^{37} +(-3.34928 - 5.17516i) q^{38} -0.167830i q^{39} +(0.766949 + 6.39761i) q^{40} +(-4.51238 - 5.37764i) q^{41} +(-1.09698 + 1.25950i) q^{42} +(1.55737 - 4.27884i) q^{43} +(2.56797 + 7.95501i) q^{44} +(3.32261 - 5.75494i) q^{45} +(3.05591 + 1.84014i) q^{46} +(-4.84679 - 0.854620i) q^{47} +(1.10884 - 0.313381i) q^{48} +(4.90438 + 8.49464i) q^{49} +(0.268229 + 0.00493791i) q^{50} +(0.728306 + 0.611122i) q^{51} +(0.715623 + 0.919566i) q^{52} +(-0.232598 - 0.639058i) q^{53} +(-2.24960 - 0.866004i) 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} +(-0.180183 - 1.30006i) q^{60} +(-2.91217 + 1.05994i) q^{61} +(-0.170142 - 1.08090i) q^{62} +(-7.68731 + 9.16138i) q^{63} +(-4.73925 + 6.44512i) q^{64} +(1.14941 - 0.663614i) q^{65} +(-0.552820 - 1.61049i) q^{66} +(-2.44691 + 13.8771i) q^{67} +(-6.59630 - 0.242949i) q^{68} +(-0.629267 - 0.363307i) q^{69} +(-12.9634 - 2.53267i) q^{70} +(12.4034 + 4.51448i) q^{71} +(7.89693 - 2.38964i) q^{72} +(-8.59023 + 7.20806i) q^{73} +(1.09803 + 1.35860i) q^{74} -0.0546461 q^{75} +(-8.28430 - 2.71483i) q^{76} -17.1358 q^{77} +(-0.149192 - 0.184596i) q^{78} +(7.91111 - 6.63821i) q^{79} +(6.53068 + 6.35495i) q^{80} +(-7.76190 - 2.82510i) q^{81} +(-9.74358 - 1.90361i) q^{82} +(-1.29416 - 0.747183i) q^{83} +(-0.0869389 + 2.36047i) q^{84} +(-1.30559 + 7.40436i) q^{85} +(-2.09070 - 6.09071i) q^{86} +(-2.11474 + 1.22094i) q^{87} +(9.89607 + 6.46693i) q^{88} +(9.52313 - 11.3492i) q^{89} +(-1.46128 - 9.28347i) q^{90} +(-2.24455 + 0.816948i) q^{91} +(4.99697 - 0.692559i) 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} +(12.9456 + 4.98352i) 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

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