LMFDB - Embedded newform 309.2.k.a.80.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,2,Mod(80,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([17, 25]))

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

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

chi := DirichletCharacter("309.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	309.k (of order $34$, degree $16$, 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:	$2.46737742246$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{34})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{34}]$

Embedding invariants

Embedding label			80.19
Character	$\chi$	$=$	309.80
Dual form			309.2.k.a.197.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.339807 - 0.169204i) q^{2} +(0.161612 - 1.72449i) q^{3} +(-1.11843 + 1.48104i) q^{4} +(1.86326 + 1.69858i) q^{5} +(-0.236874 - 0.613340i) q^{6} +(1.76047 - 0.329088i) q^{7} +(-0.268956 + 1.43879i) q^{8} +(-2.94776 - 0.557399i) q^{9} +O(q^{10})$	\(q+(0.339807 - 0.169204i) q^{2} +(0.161612 - 1.72449i) q^{3} +(-1.11843 + 1.48104i) q^{4} +(1.86326 + 1.69858i) q^{5} +(-0.236874 - 0.613340i) q^{6} +(1.76047 - 0.329088i) q^{7} +(-0.268956 + 1.43879i) q^{8} +(-2.94776 - 0.557399i) q^{9} +(0.920554 + 0.261920i) q^{10} +(1.47203 + 2.95623i) q^{11} +(2.37330 + 2.16808i) q^{12} +(5.74661 - 1.07423i) q^{13} +(0.542536 - 0.409704i) q^{14} +(3.23032 - 2.93866i) q^{15} +(-0.863728 - 3.03569i) q^{16} +(-2.31139 + 0.214181i) q^{17} +(-1.09598 + 0.309364i) q^{18} +(0.466922 - 0.289106i) q^{19} +(-4.59959 + 0.859813i) q^{20} +(-0.282998 - 3.08910i) q^{21} +(1.00041 + 0.755473i) q^{22} +(-1.65750 - 0.825338i) q^{23} +(2.43772 + 0.696340i) q^{24} +(0.125200 + 1.35112i) q^{25} +(1.77097 - 1.33738i) q^{26} +(-1.43763 + 4.99332i) q^{27} +(-1.48157 + 2.97539i) q^{28} +(6.25004 - 6.85596i) q^{29} +(0.600453 - 1.54516i) q^{30} +(-5.69587 + 1.62062i) q^{31} +(-2.77934 - 3.04879i) q^{32} +(5.33589 - 2.06074i) q^{33} +(-0.749184 + 0.463875i) q^{34} +(3.83918 + 2.37712i) q^{35} +(4.12240 - 3.74235i) q^{36} +(1.27659 + 3.29526i) q^{37} +(0.109745 - 0.177245i) q^{38} +(-0.923776 - 10.0836i) q^{39} +(-2.94504 + 2.22399i) q^{40} +(3.74280 + 4.10565i) q^{41} +(-0.618852 - 1.00181i) q^{42} +(0.764844 - 1.97429i) q^{43} +(-6.02465 - 1.12620i) q^{44} +(-4.54565 - 6.04560i) q^{45} -0.702881 q^{46} -11.7834 q^{47} +(-5.37462 + 0.998889i) q^{48} +(-3.53636 + 1.36999i) q^{49} +(0.271158 + 0.437935i) q^{50} +(-0.00419369 + 4.02059i) q^{51} +(-4.83621 + 9.71241i) q^{52} +(-5.53888 + 3.42953i) q^{53} +(0.356373 + 1.94002i) q^{54} +(-2.27863 + 8.00856i) q^{55} +2.62145i q^{56} +(-0.423101 - 0.851928i) q^{57} +(0.963751 - 3.38723i) q^{58} +(2.32349 - 12.4296i) q^{59} +(0.739392 + 8.07093i) q^{60} +(-0.176496 - 1.90469i) q^{61} +(-1.66128 + 1.51446i) q^{62} +(-5.37287 - 0.0112084i) q^{63} +(4.42578 + 1.71456i) q^{64} +(12.5321 + 7.75953i) q^{65} +(1.46449 - 1.60311i) q^{66} +(-2.15489 + 11.5276i) q^{67} +(2.26791 - 3.66280i) q^{68} +(-1.69116 + 2.72497i) q^{69} +(1.70680 + 0.158158i) q^{70} +(-4.33671 + 3.95343i) q^{71} +(1.59480 - 4.09130i) q^{72} +(-0.738037 - 0.809588i) q^{73} +(0.991366 + 0.903749i) q^{74} +(2.35023 + 0.00245142i) q^{75} +(-0.0940421 + 1.01488i) q^{76} +(3.56431 + 4.71991i) q^{77} +(-2.02009 - 3.27017i) q^{78} +(-8.24146 - 7.51308i) q^{79} +(3.54702 - 7.12338i) q^{80} +(8.37861 + 3.28616i) q^{81} +(1.96652 + 0.761833i) q^{82} +(-2.33241 - 12.4773i) q^{83} +(4.89160 + 3.03581i) q^{84} +(-4.67051 - 3.52700i) q^{85} +(-0.0741579 - 0.800291i) q^{86} +(-10.8130 - 11.8862i) q^{87} +(-4.64930 + 1.32284i) q^{88} +(-2.21739 - 2.93629i) q^{89} +(-2.56758 - 1.28519i) q^{90} +(9.76319 - 3.78228i) q^{91} +(3.07616 - 1.53175i) q^{92} +(1.87422 + 10.0844i) q^{93} +(-4.00409 + 1.99380i) q^{94} +(1.36107 + 0.254427i) q^{95} +(-5.70681 + 4.30024i) q^{96} +(-1.17316 + 12.6604i) q^{97} +(-0.969872 + 1.06390i) q^{98} +(-2.69138 - 9.53476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q - 17 q^{3} - 2 q^{4} - 17 q^{6} - 18 q^{7} - 13 q^{9}+O(q^{10}) $ 512 * q - 17 * q^3 - 2 * q^4 - 17 * q^6 - 18 * q^7 - 13 * q^9	$ 512 q - 17 q^{3} - 2 q^{4} - 17 q^{6} - 18 q^{7} - 13 q^{9} + 34 q^{10} - 17 q^{12} - 38 q^{13} - 23 q^{15} - 50 q^{16} + 5 q^{18} - 22 q^{19} - 51 q^{21} - 34 q^{22} - 17 q^{24} + 6 q^{25} - 17 q^{27} - 152 q^{28} - 21 q^{30} - 34 q^{31} - 11 q^{33} - 128 q^{34} + 149 q^{36} + 68 q^{37} + 119 q^{39} - 34 q^{40} - 17 q^{42} - 34 q^{43} - 17 q^{45} - 96 q^{46} - 187 q^{48} - 34 q^{49} - 17 q^{51} + 2 q^{52} - 17 q^{54} - 80 q^{55} - 14 q^{58} - 172 q^{60} - 38 q^{61} - 61 q^{63} + 56 q^{64} + 101 q^{66} - 136 q^{67} + 119 q^{69} - 34 q^{70} - 101 q^{72} - 136 q^{73} - 255 q^{75} - 114 q^{76} - 17 q^{78} - 54 q^{79} - 5 q^{81} - 66 q^{82} - 17 q^{84} - 17 q^{87} - 17 q^{90} + 244 q^{91} + 35 q^{93} - 34 q^{94} - 17 q^{96} + 236 q^{97} - 17 q^{99}+O(q^{100}) $ 512 * q - 17 * q^3 - 2 * q^4 - 17 * q^6 - 18 * q^7 - 13 * q^9 + 34 * q^10 - 17 * q^12 - 38 * q^13 - 23 * q^15 - 50 * q^16 + 5 * q^18 - 22 * q^19 - 51 * q^21 - 34 * q^22 - 17 * q^24 + 6 * q^25 - 17 * q^27 - 152 * q^28 - 21 * q^30 - 34 * q^31 - 11 * q^33 - 128 * q^34 + 149 * q^36 + 68 * q^37 + 119 * q^39 - 34 * q^40 - 17 * q^42 - 34 * q^43 - 17 * q^45 - 96 * q^46 - 187 * q^48 - 34 * q^49 - 17 * q^51 + 2 * q^52 - 17 * q^54 - 80 * q^55 - 14 * q^58 - 172 * q^60 - 38 * q^61 - 61 * q^63 + 56 * q^64 + 101 * q^66 - 136 * q^67 + 119 * q^69 - 34 * q^70 - 101 * q^72 - 136 * q^73 - 255 * q^75 - 114 * q^76 - 17 * q^78 - 54 * q^79 - 5 * q^81 - 66 * q^82 - 17 * q^84 - 17 * q^87 - 17 * q^90 + 244 * q^91 + 35 * q^93 - 34 * q^94 - 17 * q^96 + 236 * q^97 - 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/309\mathbb{Z}\right)^\times$.

$n$	$104$	$211$
$\chi(n)$	$-1$	$e\left(\frac{25}{34}\right)$

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 $

$2$	0.339807	−	0.169204i	0.240280	−	0.119645i	−0.321566	−	0.946887i	$-0.604209\pi$
$2$	0.339807	−	0.169204i	0.240280	−	0.119645i	0.561846	+	0.827242i	$0.310092\pi$
$3$	0.161612	−	1.72449i	0.0933069	−	0.995637i
$3$	0.161612	−	1.72449i	0.0933069	−	0.995637i
$4$	−1.11843	+	1.48104i	−0.559215	+	0.740521i
$5$	1.86326	+	1.69858i	0.833274	+	0.759629i	0.973060	−	0.230552i	$-0.0740533\pi$
$5$	1.86326	+	1.69858i	0.833274	+	0.759629i	−0.139786	+	0.990182i	$0.544642\pi$
$6$	−0.236874	−	0.613340i	−0.0967034	−	0.250395i
$7$	1.76047	−	0.329088i	0.665394	−	0.124384i	0.159792	−	0.987151i	$-0.448918\pi$
$7$	1.76047	−	0.329088i	0.665394	−	0.124384i	0.505602	+	0.862767i	$0.331271\pi$
$8$	−0.268956	+	1.43879i	−0.0950905	+	0.508689i
$9$	−2.94776	−	0.557399i	−0.982588	−	0.185800i
$10$	0.920554	+	0.261920i	0.291105	+	0.0828264i
$11$	1.47203	+	2.95623i	0.443832	+	0.891335i	0.998252	+	0.0590983i	$0.0188226\pi$
$11$	1.47203	+	2.95623i	0.443832	+	0.891335i	−0.554420	+	0.832237i	$0.687060\pi$
$12$	2.37330	+	2.16808i	0.685111	+	0.625871i
$13$	5.74661	−	1.07423i	1.59382	−	0.297937i	0.689336	−	0.724441i	$-0.257902\pi$
$13$	5.74661	−	1.07423i	1.59382	−	0.297937i	0.904485	+	0.426504i	$0.140255\pi$
$14$	0.542536	−	0.409704i	0.144999	−	0.109498i
$15$	3.23032	−	2.93866i	0.834066	−	0.758760i
$16$	−0.863728	−	3.03569i	−0.215932	−	0.758922i
$17$	−2.31139	+	0.214181i	−0.560593	+	0.0519466i	−0.368834	−	0.929495i	$-0.620243\pi$
$17$	−2.31139	+	0.214181i	−0.560593	+	0.0519466i	−0.191759	+	0.981442i	$0.561419\pi$
$18$	−1.09598	+	0.309364i	−0.258326	+	0.0729179i
$19$	0.466922	−	0.289106i	0.107119	−	0.0663254i	−0.471827	−	0.881691i	$-0.656405\pi$
$19$	0.466922	−	0.289106i	0.107119	−	0.0663254i	0.578946	+	0.815366i	$0.303464\pi$
$20$	−4.59959	+	0.859813i	−1.02850	+	0.192260i
$21$	−0.282998	−	3.08910i	−0.0617552	−	0.674097i
$22$	1.00041	+	0.755473i	0.213288	+	0.161067i
$23$	−1.65750	−	0.825338i	−0.345613	−	0.172095i	0.264548	−	0.964373i	$-0.414777\pi$
$23$	−1.65750	−	0.825338i	−0.345613	−	0.172095i	−0.610161	+	0.792278i	$0.708895\pi$
$24$	2.43772	+	0.696340i	0.497597	+	0.142140i
$25$	0.125200	+	1.35112i	0.0250399	+	0.270224i
$26$	1.77097	−	1.33738i	0.347316	−	0.262281i
$27$	−1.43763	+	4.99332i	−0.276671	+	0.960965i
$28$	−1.48157	+	2.97539i	−0.279990	+	0.562295i
$29$	6.25004	−	6.85596i	1.16060	−	1.27312i	0.204901	−	0.978783i	$-0.434313\pi$
$29$	6.25004	−	6.85596i	1.16060	−	1.27312i	0.955701	−	0.294338i	$-0.0950991\pi$
$30$	0.600453	−	1.54516i	0.109627	−	0.282106i
$31$	−5.69587	+	1.62062i	−1.02301	+	0.291071i	−0.743260	−	0.669002i	$-0.766722\pi$
$31$	−5.69587	+	1.62062i	−1.02301	+	0.291071i	−0.279748	+	0.960073i	$0.590251\pi$
$32$	−2.77934	−	3.04879i	−0.491323	−	0.538956i
$33$	5.33589	−	2.06074i	0.928860	−	0.358728i
$34$	−0.749184	+	0.463875i	−0.128484	+	0.0795539i
$35$	3.83918	+	2.37712i	0.648941	+	0.401807i
$36$	4.12240	−	3.74235i	0.687067	−	0.623724i
$37$	1.27659	+	3.29526i	0.209870	+	0.541738i	0.997199	−	0.0747957i	$-0.0238305\pi$
$37$	1.27659	+	3.29526i	0.209870	+	0.541738i	−0.787328	+	0.616534i	$0.788536\pi$
$38$	0.109745	−	0.177245i	0.0178031	−	0.0287529i
$39$	−0.923776	−	10.0836i	−0.147923	−	1.61467i
$40$	−2.94504	+	2.22399i	−0.465651	+	0.351644i
$41$	3.74280	+	4.10565i	0.584526	+	0.641195i	0.958110	−	0.286402i	$-0.0924592\pi$
$41$	3.74280	+	4.10565i	0.584526	+	0.641195i	−0.373583	+	0.927597i	$0.621871\pi$
$42$	−0.618852	−	1.00181i	−0.0954909	−	0.154583i
$43$	0.764844	−	1.97429i	0.116638	−	0.301076i	−0.861922	−	0.507041i	$-0.830739\pi$
$43$	0.764844	−	1.97429i	0.116638	−	0.301076i	0.978559	+	0.205965i	$0.0660333\pi$
$44$	−6.02465	−	1.12620i	−0.908250	−	0.169781i
$45$	−4.54565	−	6.04560i	−0.677625	−	0.901224i
$46$	−0.702881			−0.103634
$47$	−11.7834			−1.71879			−0.859394	−	0.511313i	$-0.829159\pi$
$47$	−11.7834			−1.71879			−0.859394	+	0.511313i	$0.829159\pi$
$48$	−5.37462	+	0.998889i	−0.775759	+	0.144177i
$49$	−3.53636	+	1.36999i	−0.505195	+	0.195713i
$50$	0.271158	+	0.437935i	0.0383476	+	0.0619334i
$51$	−0.00419369	+	4.02059i	−0.000587235	+	0.562995i
$52$	−4.83621	+	9.71241i	−0.670661	+	1.34687i
$53$	−5.53888	+	3.42953i	−0.760824	+	0.471082i	−0.851210	−	0.524825i	$-0.824131\pi$
$53$	−5.53888	+	3.42953i	−0.760824	+	0.471082i	0.0903866	+	0.995907i	$0.471190\pi$
$54$	0.356373	+	1.94002i	0.0484962	+	0.264003i
$55$	−2.27863	+	8.00856i	−0.307251	+	1.07987i
$56$			2.62145i			0.350306i
$57$	−0.423101	−	0.851928i	−0.0560411	−	0.112841i
$58$	0.963751	−	3.38723i	0.126547	−	0.444765i
$59$	2.32349	−	12.4296i	0.302493	−	1.61820i	−0.406962	−	0.913445i	$-0.633412\pi$
$59$	2.32349	−	12.4296i	0.302493	−	1.61820i	0.709455	−	0.704750i	$-0.248941\pi$
$60$	0.739392	+	8.07093i	0.0954551	+	1.04195i
$61$	−0.176496	−	1.90469i	−0.0225979	−	0.243871i	−0.999539	−	0.0303614i	$-0.990334\pi$
$61$	−0.176496	−	1.90469i	−0.0225979	−	0.243871i	0.976941	−	0.213509i	$-0.0684893\pi$
$62$	−1.66128	+	1.51446i	−0.210983	+	0.192336i
$63$	−5.37287	−	0.0112084i	−0.676918	−	0.00141213i
$64$	4.42578	+	1.71456i	0.553223	+	0.214320i
$65$	12.5321	+	7.75953i	1.55441	+	0.962451i
$66$	1.46449	−	1.60311i	0.180266	−	0.197329i
$67$	−2.15489	+	11.5276i	−0.263261	+	1.40832i	0.554220	+	0.832370i	$0.313017\pi$
$67$	−2.15489	+	11.5276i	−0.263261	+	1.40832i	−0.817482	+	0.575954i	$0.804631\pi$
$68$	2.26791	−	3.66280i	0.275025	−	0.444180i
$69$	−1.69116	+	2.72497i	−0.203592	+	0.328048i
$70$	1.70680	+	0.158158i	0.204001	+	0.0189035i
$71$	−4.33671	+	3.95343i	−0.514673	+	0.469186i	−0.888868	−	0.458164i	$-0.848507\pi$
$71$	−4.33671	+	3.95343i	−0.514673	+	0.469186i	0.374195	+	0.927350i	$0.377919\pi$
$72$	1.59480	−	4.09130i	0.187949	−	0.482164i
$73$	−0.738037	−	0.809588i	−0.0863807	−	0.0947551i	0.694298	−	0.719687i	$-0.255715\pi$
$73$	−0.738037	−	0.809588i	−0.0863807	−	0.0947551i	−0.780679	+	0.624932i	$0.785127\pi$
$74$	0.991366	+	0.903749i	0.115244	+	0.105059i
$75$	2.35023	+	0.00245142i	0.271381	+	0.000283066i
$76$	−0.0940421	+	1.01488i	−0.0107874	+	0.116414i
$77$	3.56431	+	4.71991i	0.406191	+	0.537884i
$78$	−2.02009	−	3.27017i	−0.228730	−	0.370274i
$79$	−8.24146	−	7.51308i	−0.927237	−	0.845288i	0.0610127	−	0.998137i	$-0.480567\pi$
$79$	−8.24146	−	7.51308i	−0.927237	−	0.845288i	−0.988250	+	0.152849i	$0.951155\pi$
$80$	3.54702	−	7.12338i	0.396569	−	0.796418i
$81$	8.37861	+	3.28616i	0.930957	+	0.365129i
$82$	1.96652	+	0.761833i	0.217166	+	0.0841304i
$83$	−2.33241	−	12.4773i	−0.256015	−	1.36956i	−0.833211	−	0.552955i	$-0.813500\pi$
$83$	−2.33241	−	12.4773i	−0.256015	−	1.36956i	0.577196	−	0.816606i	$-0.304147\pi$
$84$	4.89160	+	3.03581i	0.533717	+	0.331234i
$85$	−4.67051	−	3.52700i	−0.506588	−	0.382557i
$86$	−0.0741579	−	0.800291i	−0.00799665	−	0.0862976i
$87$	−10.8130	−	11.8862i	−1.15927	−	1.27433i
$88$	−4.64930	+	1.32284i	−0.495617	+	0.141015i
$89$	−2.21739	−	2.93629i	−0.235042	−	0.311246i	0.665175	−	0.746688i	$-0.268357\pi$
$89$	−2.21739	−	2.93629i	−0.235042	−	0.311246i	−0.900217	+	0.435441i	$0.856592\pi$
$90$	−2.56758	−	1.28519i	−0.270647	−	0.135471i
$91$	9.76319	−	3.78228i	1.02346	−	0.396491i
$92$	3.07616	−	1.53175i	0.320712	−	0.159696i
$93$	1.87422	+	10.0844i	0.194347	+	1.04570i
$94$	−4.00409	+	1.99380i	−0.412990	+	0.205645i
$95$	1.36107	+	0.254427i	0.139642	+	0.0261037i
$96$	−5.70681	+	4.30024i	−0.582448	+	0.438891i
$97$	−1.17316	+	12.6604i	−0.119116	+	1.28547i	0.700954	+	0.713206i	$0.252758\pi$
$97$	−1.17316	+	12.6604i	−0.119116	+	1.28547i	−0.820071	+	0.572262i	$0.806066\pi$
$98$	−0.969872	+	1.06390i	−0.0979719	+	0.107470i
$99$	−2.69138	−	9.53476i	−0.270494	−	0.958279i
$100$	−2.14109	−	1.32571i	−0.214109	−	0.132571i
$101$	−5.91848	−	11.8859i	−0.588911	−	1.18269i	−0.966487	−	0.256714i	$-0.917360\pi$
$101$	−5.91848	−	11.8859i	−0.588911	−	1.18269i	0.377577	−	0.925978i	$-0.376757\pi$
$102$	0.678873	+	1.36693i	0.0672184	+	0.135346i
$103$	−8.78310	−	5.08499i	−0.865425	−	0.501039i
$103$	−8.78310	−	5.08499i	−0.865425	−	0.501039i
$104$			8.55708i			0.839091i
$105$	4.71979	−	6.23648i	0.460605	−	0.608618i
$106$	−1.30186	+	2.10258i	−0.126448	+	0.204220i
$107$	3.69987	+	2.79401i	0.357680	+	0.270107i	0.766146	−	0.642666i	$-0.222172\pi$
$107$	3.69987	+	2.79401i	0.357680	+	0.270107i	−0.408467	+	0.912773i	$0.633936\pi$
$108$	−5.78743	−	7.71386i	−0.556895	−	0.742267i
$109$	16.8404	+	1.56049i	1.61302	+	0.149468i	0.860623	−	0.509243i	$-0.170074\pi$
$109$	16.8404	+	1.56049i	1.61302	+	0.149468i	0.752396	+	0.658711i	$0.228898\pi$
$110$	0.580783	+	3.10692i	0.0553755	+	0.296233i
$111$	5.88898	−	1.66892i	0.558957	−	0.158407i
$112$	−2.51957	−	5.05998i	−0.238077	−	0.478124i
$113$	0.537604	−	1.88948i	0.0505735	−	0.177747i	−0.932424	−	0.361366i	$-0.882311\pi$
$113$	0.537604	−	1.88948i	0.0505735	−	0.177747i	0.982998	+	0.183618i	$0.0587811\pi$
$114$	−0.287922	−	0.217900i	−0.0269664	−	0.0204083i
$115$	−1.68645	−	4.35322i	−0.157262	−	0.405940i
$116$	3.16373	+	16.9245i	0.293745	+	1.57140i
$117$	−17.5384	−	0.0365871i	−1.62143	−	0.00338248i
$118$	−1.31359	−	4.61680i	−0.120926	−	0.425011i
$119$	−3.99863	+	1.13771i	−0.366554	+	0.104294i
$120$	3.35930	+	5.43813i	0.306661	+	0.496431i
$121$	0.0565714	−	0.0749126i	0.00514285	−	0.00681024i
$122$	−0.382255	−	0.617363i	−0.0346077	−	0.0558934i
$123$	7.68505	−	5.79091i	0.692938	−	0.522148i
$124$	3.97024	−	10.2484i	0.356538	−	0.920331i
$125$	5.53538	−	7.33002i	0.495099	−	0.655617i
$126$	−1.82763	+	0.905301i	−0.162819	+	0.0806506i
$127$	14.1131	−	15.4813i	1.25234	−	1.37375i	0.353515	−	0.935429i	$-0.384986\pi$
$127$	14.1131	−	15.4813i	1.25234	−	1.37375i	0.898820	−	0.438318i	$-0.144425\pi$
$128$	10.0099	−	0.927550i	0.884755	−	0.0819846i
$129$	−3.28104	−	1.63804i	−0.288880	−	0.144221i
$130$	5.57142	+	0.516268i	0.488646	+	0.0452797i
$131$	1.65870	+	0.825936i	0.144922	+	0.0721624i	0.516736	−	0.856145i	$-0.327147\pi$
$131$	1.65870	+	0.825936i	0.144922	+	0.0721624i	−0.371815	+	0.928307i	$0.621264\pi$
$132$	−2.91579	+	10.2075i	−0.253787	+	0.888446i
$133$	0.726859	−	0.662620i	0.0630267	−	0.0574564i
$134$	1.21827	+	4.28178i	0.105243	+	0.369890i
$135$	−11.1602	+	6.86191i	−0.960520	+	0.590579i
$136$	0.313500	−	3.38320i	0.0268824	−	0.290107i
$137$	−6.89901	−	11.1423i	−0.589422	−	0.951949i	−0.999209	−	0.0397680i	$-0.987338\pi$
$137$	−6.89901	−	11.1423i	−0.589422	−	0.951949i	0.409787	−	0.912181i	$-0.365603\pi$
$138$	−0.113594	+	1.21211i	−0.00966978	+	0.103182i
$139$	−1.83665	−	0.343329i	−0.155783	−	0.0291208i	0.105280	−	0.994443i	$-0.466426\pi$
$139$	−1.83665	−	0.343329i	−0.155783	−	0.0291208i	−0.261063	+	0.965322i	$0.584073\pi$
$140$	−7.81448	+	3.02734i	−0.660444	+	0.255857i
$141$	−1.90435	+	20.3204i	−0.160375	+	1.71129i
$142$	−0.804708	+	2.07719i	−0.0675296	+	0.174314i
$143$	11.6348	+	15.4070i	0.972951	+	1.28840i
$144$	0.853975	+	9.42993i	0.0711646	+	0.785828i
$145$	23.2908	−	2.15821i	1.93420	−	0.179230i
$146$	−0.387775	−	0.150225i	−0.0320925	−	0.0124327i
$147$	1.79103	+	6.31985i	0.147721	+	0.521252i
$148$	−6.30820	−	1.79484i	−0.518531	−	0.147535i
$149$			7.49281i			0.613835i	0.951736	+	0.306918i	$0.0992976\pi$
$149$			7.49281i			0.613835i	−0.951736	+	0.306918i	$0.900702\pi$
$150$	0.799040	−	0.396835i	0.0652413	−	0.0324014i
$151$	−2.90928	−	0.827762i	−0.236754	−	0.0673624i	0.153205	−	0.988194i	$-0.451040\pi$
$151$	−2.90928	−	0.827762i	−0.236754	−	0.0673624i	−0.389959	+	0.920832i	$0.627511\pi$
$152$	0.290381	+	0.749560i	0.0235530	+	0.0607973i
$153$	6.93280	+	0.657008i	0.560484	+	0.0531160i
$154$	2.00980	+	1.00076i	0.161955	+	0.0806438i
$155$	−13.3656	−	6.65529i	−1.07355	−	0.534566i
$156$	15.9674	+	9.90965i	1.27842	+	0.793407i
$157$	0.0374707	+	0.0967229i	0.00299048	+	0.00771933i	0.933959	−	0.357379i	$-0.116330\pi$
$157$	0.0374707	+	0.0967229i	0.00299048	+	0.00771933i	−0.930969	+	0.365098i	$0.881035\pi$
$158$	−4.07175	−	1.15851i	−0.323931	−	0.0921662i
$159$	5.01905	+	10.1060i	0.398037	+	0.801460i
$160$		−	10.4016i		−	0.822321i
$161$	−3.18958	−	0.907515i	−0.251375	−	0.0715222i
$162$	3.40314	−	0.301032i	0.267376	−	0.0236513i
$163$	2.06863	+	0.801392i	0.162028	+	0.0627698i	0.440890	−	0.897561i	$-0.354663\pi$
$163$	2.06863	+	0.801392i	0.162028	+	0.0627698i	−0.278862	+	0.960331i	$0.589957\pi$
$164$	−10.2667	+	0.951349i	−0.801694	+	0.0742879i
$165$	13.4425	+	5.22377i	1.04649	+	0.406670i
$166$	−2.90377	−	3.84522i	−0.225376	−	0.298447i
$167$	−2.00205	+	5.16788i	−0.154923	+	0.399902i	−0.988244	−	0.152888i	$-0.951143\pi$
$167$	−2.00205	+	5.16788i	−0.154923	+	0.399902i	0.833321	+	0.552790i	$0.186437\pi$
$168$	4.52068	+	0.423659i	0.348778	+	0.0326860i
$169$	19.7474	−	7.65018i	1.51903	−	0.588475i
$170$	−2.18385	−	0.408233i	−0.167494	−	0.0313100i
$171$	−1.53752	+	0.591954i	−0.117577	+	0.0452678i
$172$	2.06858	+	3.34087i	0.157728	+	0.254739i
$173$	−1.46341	+	15.7927i	−0.111261	+	1.20070i	0.738767	+	0.673961i	$0.235408\pi$
$173$	−1.46341	+	15.7927i	−0.111261	+	1.20070i	−0.850028	+	0.526738i	$0.823415\pi$
$174$	−5.68551	−	2.20940i	−0.431017	−	0.167494i
$175$	0.665047	+	2.33740i	0.0502729	+	0.176691i
$176$	7.70275	−	7.02198i	0.580617	−	0.529302i
$177$	−21.0593	−	6.01563i	−1.58291	−	0.452162i
$178$	−1.25031	−	0.622583i	−0.0937150	−	0.0466645i
$179$	−0.622490	−	0.0576822i	−0.0465271	−	0.00431137i	0.0689796	−	0.997618i	$-0.478026\pi$
$179$	−0.622490	−	0.0576822i	−0.0465271	−	0.00431137i	−0.115507	+	0.993307i	$0.536849\pi$
$180$	14.0378	+	0.0292844i	1.04631	+	0.00218273i
$181$	5.80550	−	0.537959i	0.431520	−	0.0399862i	0.125684	−	0.992070i	$-0.459888\pi$
$181$	5.80550	−	0.537959i	0.431520	−	0.0399862i	0.305836	+	0.952084i	$0.401064\pi$
$182$	2.67762	−	2.93721i	0.198479	−	0.217721i
$183$	−3.31315	−	0.00345580i	−0.244915	−	0.000255460i
$184$	1.63328	−	2.16282i	0.120407	−	0.159445i
$185$	−3.21866	+	8.30832i	−0.236641	+	0.610840i
$186$	2.34319	+	3.10963i	0.171811	+	0.228009i
$187$	−4.03559	−	6.51769i	−0.295111	−	0.476621i
$188$	13.1789	−	17.4517i	0.961173	−	1.27280i
$189$	−0.887651	+	9.26368i	−0.0645671	+	0.673833i
$190$	0.505549	−	0.143841i	0.0366764	−	0.0104353i
$191$	1.27928	+	4.49620i	0.0925654	+	0.325334i	0.994253	−	0.107054i	$-0.0341418\pi$
$191$	1.27928	+	4.49620i	0.0925654	+	0.325334i	−0.901688	+	0.432388i	$0.857671\pi$
$192$	3.67200	−	7.35514i	0.265004	−	0.530812i
$193$	−0.627226	−	3.35536i	−0.0451487	−	0.241524i	0.952952	−	0.303120i	$-0.0980282\pi$
$193$	−0.627226	−	3.35536i	−0.0451487	−	0.241524i	−0.998101	+	0.0615955i	$0.980381\pi$
$194$	1.74354	+	4.50059i	0.125179	+	0.323124i
$195$	15.4066	−	20.3574i	1.10329	−	1.45783i
$196$	1.92616	−	6.76974i	0.137583	−	0.483553i
$197$	−8.70751	−	17.4870i	−0.620385	−	1.24590i	−0.953038	−	0.302851i	$-0.902062\pi$
$197$	−8.70751	−	17.4870i	−0.620385	−	1.24590i	0.332653	−	0.943049i	$-0.392056\pi$
$198$	−2.52787	−	2.78458i	−0.179648	−	0.197892i
$199$	2.65624	+	14.2097i	0.188296	+	1.00730i	0.938290	+	0.345850i	$0.112410\pi$
$199$	2.65624	+	14.2097i	0.188296	+	1.00730i	−0.749994	+	0.661445i	$0.769943\pi$
$200$	−1.97765	−	0.183256i	−0.139841	−	0.0129582i
$201$	19.5311	+	5.57910i	1.37762	+	0.393519i
$202$	−4.02228	−	3.03748i	−0.283007	−	0.213717i
$203$	8.74676	−	14.1265i	0.613902	−	0.991486i
$204$	−5.94996	−	4.50296i	−0.416581	−	0.315270i
$205$			14.0073i			0.978314i
$206$	−3.84496	−	0.241780i	−0.267891	−	0.0168456i
$207$	4.42588	+	3.35679i	0.307620	+	0.233313i
$208$	−8.22452	−	16.5171i	−0.570268	−	1.14525i
$209$	1.54198	+	0.954756i	0.106661	+	0.0660418i
$210$	0.548583	−	2.91780i	0.0378558	−	0.201348i
$211$	−15.0339	+	16.4914i	−1.03498	+	1.13532i	−0.0443092	+	0.999018i	$0.514109\pi$
$211$	−15.0339	+	16.4914i	−1.03498	+	1.13532i	−0.990668	+	0.136298i	$0.956480\pi$
$212$	1.11558	−	12.0390i	0.0766182	−	0.826842i
$213$	6.11681	+	8.11756i	0.419117	+	0.556206i
$214$	1.73000	+	0.323392i	0.118260	+	0.0221067i
$215$	4.77859	−	2.37946i	0.325897	−	0.162278i
$216$	−6.79768	−	3.41143i	−0.462523	−	0.232118i
$217$	−9.49407	+	4.72748i	−0.644499	+	0.320922i
$218$	5.98653	−	2.31919i	0.405459	−	0.157076i
$219$	−1.51541	+	1.14190i	−0.102402	+	0.0771626i
$220$	−9.31252	−	12.3318i	−0.627850	−	0.831408i
$221$	−13.0525	+	3.71377i	−0.878009	+	0.249815i
$222$	1.71873	−	1.56355i	0.115353	−	0.104938i
$223$	−0.969050	−	10.4577i	−0.0648924	−	0.700300i	−0.964584	−	0.263775i	$-0.915032\pi$
$223$	−0.969050	−	10.4577i	−0.0648924	−	0.700300i	0.899692	−	0.436526i	$-0.143791\pi$
$224$	−5.89626	−	4.45265i	−0.393961	−	0.297505i
$225$	0.384054	−	4.05257i	0.0256036	−	0.270171i
$226$	−0.137026	−	0.733023i	−0.00911482	−	0.0487600i
$227$	11.2351	+	4.35251i	0.745702	+	0.288886i	0.703958	−	0.710242i	$-0.251414\pi$
$227$	11.2351	+	4.35251i	0.745702	+	0.288886i	0.0417442	+	0.999128i	$0.486709\pi$
$228$	1.73495	+	0.326191i	0.114900	+	0.0216026i
$229$	−5.50662	+	11.0588i	−0.363888	+	0.730785i	−0.999138	−	0.0415219i	$-0.986779\pi$
$229$	−5.50662	+	11.0588i	−0.363888	+	0.730785i	0.635250	+	0.772307i	$0.280897\pi$
$230$	−1.30965	−	1.19390i	−0.0863555	−	0.0787235i
$231$	8.71549	−	5.38384i	0.573437	−	0.354231i
$232$	8.18330	+	10.8364i	0.537260	+	0.711447i
$233$	−2.01991	+	21.7983i	−0.132329	+	1.42805i	0.627847	+	0.778337i	$0.283937\pi$
$233$	−2.01991	+	21.7983i	−0.132329	+	1.42805i	−0.760175	+	0.649718i	$0.774887\pi$
$234$	−5.96586	+	2.95513i	−0.390000	+	0.193183i
$235$	−21.9555	−	20.0151i	−1.43222	−	1.30564i
$236$	15.8101	+	17.3428i	1.02915	+	1.12892i
$237$	−14.2882	+	12.9981i	−0.928118	+	0.844320i
$238$	−1.16626	+	1.06318i	−0.0755973	+	0.0689160i
$239$	16.5849	+	1.53681i	1.07279	+	0.0994083i	0.614129	−	0.789205i	$-0.289507\pi$
$239$	16.5849	+	1.53681i	1.07279	+	0.0994083i	0.458657	+	0.888614i	$0.348331\pi$
$240$	−11.7110	−	7.26804i	−0.755941	−	0.469150i
$241$	3.54012	−	5.71749i	0.228039	−	0.368296i	−0.716016	−	0.698084i	$-0.754036\pi$
$241$	3.54012	−	5.71749i	0.228039	−	0.368296i	0.944055	+	0.329788i	$0.106977\pi$
$242$	0.00654785	−	0.0350279i	0.000420912	−	0.00225168i
$243$	7.02105	−	13.9178i	0.450401	−	0.892826i
$244$	3.01832	+	1.86887i	0.193228	+	0.119642i
$245$	−8.91620	−	3.45415i	−0.569635	−	0.220678i
$246$	1.63159	−	3.26813i	0.104026	−	0.208368i
$247$	2.37265	−	2.16296i	0.150968	−	0.137626i
$248$	−0.799783	−	8.63104i	−0.0507863	−	0.548071i
$249$	−21.8940	+	2.00574i	−1.38747	+	0.127109i
$250$	0.640692	−	3.42740i	0.0405209	−	0.216768i
$251$	−1.20407	+	4.23188i	−0.0760004	+	0.267114i	−0.990508	−	0.137455i	$-0.956108\pi$
$251$	−1.20407	+	4.23188i	−0.0760004	+	0.267114i	0.914508	+	0.404569i	$0.132578\pi$
$252$	6.02578	−	7.94491i	0.379589	−	0.500482i
$253$		−	6.11487i		−	0.384438i
$254$	2.17623	−	7.64865i	0.136549	−	0.479919i
$255$	−6.83711	+	7.48426i	−0.428156	+	0.468682i
$256$	−4.82628	+	2.98830i	−0.301642	+	0.186769i
$257$	−12.8410	+	25.7881i	−0.800997	+	1.60862i	−0.00755707	+	0.999971i	$0.502406\pi$
$257$	−12.8410	+	25.7881i	−0.800997	+	1.60862i	−0.793440	+	0.608648i	$0.791712\pi$
$258$	−1.39208	−	0.00145202i	−0.0866673	−	9.03988e-5i
$259$	3.33183	+	5.38109i	0.207030	+	0.334365i
$260$	−25.5084	+	9.88202i	−1.58197	+	0.612857i
$261$	−22.2451	+	16.7260i	−1.37694	+	1.03531i
$262$	0.703390			0.0434556
$263$	−0.418935			−0.0258327			−0.0129163	−	0.999917i	$-0.504112\pi$
$263$	−0.418935			−0.0258327			−0.0129163	+	0.999917i	$0.504112\pi$
$264$	1.52985	+	8.23148i	0.0941555	+	0.506612i
$265$	−16.1457	−	3.01815i	−0.991822	−	0.185404i
$266$	0.134874	−	0.348150i	0.00826966	−	0.0213464i
$267$	−5.42198	+	3.34933i	−0.331820	+	0.204976i
$268$	−14.6628	−	16.0843i	−0.895674	−	0.982507i
$269$	13.8359	−	10.4484i	0.843588	−	0.637048i	−0.0897828	−	0.995961i	$-0.528617\pi$
$269$	13.8359	−	10.4484i	0.843588	−	0.637048i	0.933371	+	0.358913i	$0.116853\pi$
$270$	−2.63126	+	4.22007i	−0.160134	+	0.256826i
$271$	−1.65234	+	2.66863i	−0.100373	+	0.162107i	−0.896531	−	0.442981i	$-0.853921\pi$
$271$	−1.65234	+	2.66863i	−0.100373	+	0.162107i	0.796158	+	0.605088i	$0.206862\pi$
$272$	2.64660	+	6.83165i	0.160473	+	0.414230i
$273$	−4.94467	−	17.4478i	−0.299265	−	1.05599i
$274$	−4.22964	−	2.61889i	−0.255522	−	0.158213i
$275$	−3.80992	+	2.35900i	−0.229747	+	0.142253i
$276$	−2.14434	−	5.55237i	−0.129074	−	0.334213i
$277$	21.0294	+	23.0682i	1.26354	+	1.38603i	0.888404	+	0.459063i	$0.151815\pi$
$277$	21.0294	+	23.0682i	1.26354	+	1.38603i	0.375133	+	0.926971i	$0.377597\pi$
$278$	−0.682198	+	0.194102i	−0.0409155	+	0.0116415i
$279$	17.6934	−	1.60232i	1.05928	−	0.0959281i
$280$	−4.45275	+	4.88444i	−0.266103	+	0.291901i
$281$	10.6690	−	21.4263i	0.636462	−	1.27819i	−0.308568	−	0.951202i	$-0.599850\pi$
$281$	10.6690	−	21.4263i	0.636462	−	1.27819i	0.945030	−	0.326985i	$-0.106033\pi$
$282$	2.79118	+	7.22725i	0.166213	+	0.430376i
$283$	−19.7236	+	14.8946i	−1.17244	+	0.885389i	−0.995111	−	0.0987615i	$-0.968512\pi$
$283$	−19.7236	+	14.8946i	−1.17244	+	0.885389i	−0.177334	+	0.984151i	$0.556747\pi$
$284$	−1.00489	−	10.8445i	−0.0596293	−	0.643502i
$285$	0.658723	−	2.30603i	0.0390194	−	0.136598i
$286$	6.56050	+	3.26674i	0.387931	+	0.193167i
$287$	7.94019	+	5.99615i	0.468694	+	0.353942i
$288$	6.49345	+	10.5363i	0.382630	+	0.620859i
$289$	−11.4139	+	2.13363i	−0.671407	+	0.125508i
$290$	7.54921	−	4.67427i	0.443305	−	0.274483i
$291$	21.6432	+	4.06918i	1.26875	+	0.238540i
$292$	2.02448	−	0.187595i	0.118474	−	0.0109782i
$293$	−4.84446	−	17.0265i	−0.283016	−	0.994700i	−0.964765	−	0.263113i	$-0.915251\pi$
$293$	−4.84446	−	17.0265i	−0.283016	−	0.994700i	0.681749	−	0.731587i	$-0.261220\pi$
$294$	1.67794	+	1.84448i	0.0978597	+	0.107572i
$295$	25.4420	−	19.2129i	1.48129	−	1.11862i
$296$	−5.08454	+	0.950465i	−0.295533	+	0.0552447i
$297$	−16.8776	+	3.10034i	−0.979338	+	0.179900i
$298$	1.26781	+	2.54611i	0.0734423	+	0.147492i
$299$	−10.4116	−	2.96236i	−0.602119	−	0.171318i
$300$	−2.63220	+	3.47805i	−0.151970	+	0.200805i
$301$	0.696766	−	3.72737i	0.0401610	−	0.214842i
$302$	−1.12865	+	0.210982i	−0.0649468	+	0.0121407i
$303$	−21.4537	+	8.28547i	−1.23248	+	0.475988i
$304$	−1.28093	−	1.16772i	−0.0734663	−	0.0669734i
$305$	2.90642	−	3.84872i	0.166421	−	0.220377i
$306$	2.46698	−	0.949799i	0.141028	−	0.0542964i
$307$	4.08166	−	2.03243i	0.232953	−	0.115997i	−0.325473	−	0.945551i	$-0.605523\pi$
$307$	4.08166	−	2.03243i	0.232953	−	0.115997i	0.558425	+	0.829555i	$0.311406\pi$
$308$	−10.9768			−0.625462
$309$	−10.1885	+	14.3246i	−0.579603	+	0.814899i
$310$	−5.66783			−0.321911
$311$	3.77697	−	1.88071i	0.214172	−	0.106645i	−0.335451	−	0.942058i	$-0.608889\pi$
$311$	3.77697	−	1.88071i	0.214172	−	0.106645i	0.549624	+	0.835412i	$0.314771\pi$
$312$	14.7566	+	1.38293i	0.835430	+	0.0782930i
$313$	7.42933	−	9.83802i	0.419931	−	0.556078i	−0.538049	−	0.842913i	$-0.680839\pi$
$313$	7.42933	−	9.83802i	0.419931	−	0.556078i	0.957980	+	0.286835i	$0.0926033\pi$
$314$	0.0290987	+	0.0265269i	0.00164213	+	0.00149700i
$315$	−9.99200	−	9.14715i	−0.562985	−	0.515384i
$316$	20.3447	−	3.80308i	1.14448	−	0.213940i
$317$	−4.86714	+	26.0369i	−0.273366	+	1.46238i	0.520279	+	0.853996i	$0.325828\pi$
$317$	−4.86714	+	26.0369i	−0.273366	+	1.46238i	−0.793645	+	0.608381i	$0.791819\pi$
$318$	3.41548	+	2.58485i	0.191531	+	0.144951i
$319$	29.4680	+	8.38436i	1.64989	+	0.469434i
$320$	5.33405	+	10.7122i	0.298182	+	0.598831i
$321$	5.41620	−	5.92885i	0.302303	−	0.330916i
$322$	−1.23740	+	0.231310i	−0.0689575	+	0.0128904i
$323$	−1.01732	+	0.768241i	−0.0566049	+	0.0427461i
$324$	−14.2378	+	8.73373i	−0.790991	+	0.485207i
$325$	2.17088	+	7.62986i	0.120419	+	0.423229i
$326$	0.838533	−	0.0777015i	0.0464420	−	0.00430349i
$327$	5.41268	−	28.7890i	0.299322	−	1.59204i
$328$	−6.91382	+	4.28085i	−0.381752	+	0.236371i
$329$	−20.7443	+	3.87779i	−1.14367	+	0.213789i
$330$	5.45172	−	0.499442i	0.300108	−	0.0274934i
$331$	−9.93949	−	7.50595i	−0.546324	−	0.412565i	0.293068	−	0.956092i	$-0.405324\pi$
$331$	−9.93949	−	7.50595i	−0.546324	−	0.412565i	−0.839392	+	0.543527i	$0.817089\pi$
$332$	21.0880	+	10.5006i	1.15736	+	0.576294i
$333$	−1.92631	−	10.4252i	−0.105561	−	0.571299i
$334$	0.194115	+	2.09483i	0.0106215	+	0.114624i
$335$	−23.5957	+	17.8187i	−1.28917	+	0.973539i
$336$	−9.13311	+	3.52723i	−0.498252	+	0.192426i
$337$	−5.69341	+	11.4339i	−0.310140	+	0.622844i	−0.994316	−	0.106473i	$-0.966044\pi$
$337$	−5.69341	+	11.4339i	−0.310140	+	0.622844i	0.684176	+	0.729317i	$0.260162\pi$
$338$	5.41586	−	5.94091i	0.294584	−	0.323143i
$339$	−3.17152	−	1.23246i	−0.172253	−	0.0669380i
$340$	10.4473	−	2.97251i	0.566583	−	0.161207i
$341$	−13.1754	−	14.4527i	−0.713486	−	0.782657i
$342$	−0.422300	+	0.461304i	−0.0228354	+	0.0249445i
$343$	−16.4337	+	10.1753i	−0.887338	+	0.549417i
$344$	2.63488	+	1.63145i	0.142063	+	0.0879618i
$345$	−7.77965	+	2.20473i	−0.418843	+	0.118699i
$346$	2.17491	+	5.61409i	0.116924	+	0.301815i
$347$	5.82528	−	9.40815i	0.312717	−	0.505056i	−0.655490	−	0.755204i	$-0.727538\pi$
$347$	5.82528	−	9.40815i	0.312717	−	0.505056i	0.968208	+	0.250148i	$0.0804792\pi$
$348$	29.6975	−	2.72064i	1.59195	−	0.145841i
$349$	7.35152	−	5.55161i	0.393518	−	0.297171i	−0.387271	−	0.921966i	$-0.626582\pi$
$349$	7.35152	−	5.55161i	0.393518	−	0.297171i	0.780789	+	0.624795i	$0.214817\pi$
$350$	0.621484	+	0.681736i	0.0332197	+	0.0364403i
$351$	−2.89752	+	30.2390i	−0.154658	+	1.61404i
$352$	4.92166	−	12.7043i	0.262325	−	0.677140i
$353$	−0.0694071	−	0.0129744i	−0.00369417	−	0.000690560i	0.181902	−	0.983317i	$-0.441775\pi$
$353$	−0.0694071	−	0.0129744i	−0.00369417	−	0.000690560i	−0.185596	+	0.982626i	$0.559422\pi$
$354$	−8.17395	+	1.51915i	−0.434440	+	0.0807421i
$355$	−14.7956			−0.785271
$356$	6.82876			0.361924
$357$	1.31574	+	7.07949i	0.0696366	+	0.374686i
$358$	−0.221286	+	0.0857267i	−0.0116953	+	0.00453080i
$359$	−13.5916	−	21.9511i	−0.717335	−	1.15854i	−0.981016	−	0.193926i	$-0.937878\pi$
$359$	−13.5916	−	21.9511i	−0.717335	−	1.15854i	0.263681	−	0.964610i	$-0.415063\pi$
$360$	9.92093	−	4.91423i	0.522879	−	0.259003i
$361$	−8.33459	+	16.7381i	−0.438663	+	0.880954i
$362$	1.88172	−	1.16511i	0.0989012	−	0.0612371i
$363$	−0.120044	−	0.109664i	−0.00630066	−	0.00575586i
$364$	−5.31774	+	18.6899i	−0.278725	+	0.979617i
$365$		−	2.76209i		−	0.144574i
$366$	−1.12642	+	0.559423i	−0.0588787	+	0.0292415i
$367$	−3.98506	+	14.0060i	−0.208018	+	0.731109i	0.785642	+	0.618682i	$0.212333\pi$
$367$	−3.98506	+	14.0060i	−0.208018	+	0.731109i	−0.993660	+	0.112427i	$0.964138\pi$
$368$	−1.07384	+	5.74453i	−0.0559777	+	0.299454i
$369$	−8.74439	−	14.1887i	−0.455215	−	0.738635i
$370$	0.312076	+	3.36783i	0.0162240	+	0.175085i
$371$	−8.62240	+	7.86035i	−0.447652	+	0.408089i
$372$	−17.0316	−	8.50292i	−0.883048	−	0.440856i
$373$	−11.4880	−	4.45048i	−0.594827	−	0.230437i	0.0449609	−	0.998989i	$-0.485684\pi$
$373$	−11.4880	−	4.45048i	−0.594827	−	0.230437i	−0.639788	+	0.768552i	$0.720978\pi$
$374$	−2.47414	−	1.53192i	−0.127935	−	0.0792138i
$375$	−11.7460	−	10.7303i	−0.606561	−	0.554113i
$376$	3.16923	−	16.9539i	0.163440	−	0.874329i
$377$	28.5516	−	46.1125i	1.47048	−	2.37491i
$378$	1.26582	+	3.29805i	0.0651067	+	0.169634i
$379$	−13.3227	−	1.23453i	−0.684343	−	0.0634137i	−0.255522	−	0.966803i	$-0.582247\pi$
$379$	−13.3227	−	1.23453i	−0.684343	−	0.0634137i	−0.428821	+	0.903389i	$0.641071\pi$
$380$	−1.89907	+	1.73124i	−0.0974205	+	0.0888105i
$381$	−24.4166	−	26.8399i	−1.25090	−	1.37505i
$382$	1.19548	+	1.31138i	0.0611662	+	0.0670961i
$383$	14.8940	+	13.5777i	0.761048	+	0.693787i	0.958045	−	0.286617i	$-0.0925308\pi$
$383$	14.8940	+	13.5777i	0.761048	+	0.693787i	−0.196997	+	0.980404i	$0.563119\pi$
$384$	0.0181615	−	17.4118i	0.000926802	−	0.888545i
$385$	−1.37593	+	14.8487i	−0.0701240	+	0.756759i
$386$	−0.780875	−	1.03405i	−0.0397455	−	0.0526315i
$387$	−3.35505	+	5.39341i	−0.170547	+	0.274163i
$388$	−17.4385	−	15.8973i	−0.885304	−	0.807061i
$389$	−10.3559	+	20.7975i	−0.525067	+	1.05448i	0.460887	+	0.887459i	$0.347531\pi$
$389$	−10.3559	+	20.7975i	−0.525067	+	1.05448i	−0.985954	+	0.167017i	$0.946586\pi$
$390$	1.79071	−	9.52445i	0.0906762	−	0.482289i
$391$	4.00790	+	1.55267i	0.202688	+	0.0785218i
$392$	−1.02001	−	5.45655i	−0.0515181	−	0.275597i
$393$	1.69239	−	2.72694i	0.0853697	−	0.137556i
$394$	−5.91774	−	4.46887i	−0.298132	−	0.225139i
$395$	−2.59436	−	27.9976i	−0.130536	−	1.40871i
$396$	17.1315	+	6.67791i	0.860890	+	0.335578i
$397$	22.8434	−	6.49950i	1.14648	−	0.326200i	0.353488	−	0.935439i	$-0.384995\pi$
$397$	22.8434	−	6.49950i	1.14648	−	0.326200i	0.792987	+	0.609239i	$0.208525\pi$
$398$	3.30694	+	4.37909i	0.165762	+	0.219504i
$399$	−1.02521	−	1.36055i	−0.0513249	−	0.0681128i
$400$	3.99344	−	1.54707i	0.199672	−	0.0773533i
$401$	14.7810	−	7.36005i	0.738126	−	0.367543i	−0.0370288	−	0.999314i	$-0.511789\pi$
$401$	14.7810	−	7.36005i	0.738126	−	0.367543i	0.775155	+	0.631771i	$0.217672\pi$
$402$	7.58080	−	1.40892i	0.378096	−	0.0702703i
$403$	−30.9910	+	15.4317i	−1.54377	+	0.768708i
$404$	24.2229	+	4.52805i	1.20514	+	0.225279i
$405$	10.0297	+	20.3547i	0.498379	+	1.01143i
$406$	0.581953	−	6.28027i	0.0288818	−	0.311684i
$407$	−7.86237	+	8.62461i	−0.389723	+	0.427506i
$408$	−5.78365	−	1.08740i	−0.286333	−	0.0538341i
$409$	0.0416757	+	0.0258045i	0.00206073	+	0.00127595i	0.527462	−	0.849579i	$-0.323144\pi$
$409$	0.0416757	+	0.0258045i	0.00206073	+	0.00127595i	−0.525401	+	0.850854i	$0.676085\pi$
$410$	2.37009	+	4.75979i	0.117050	+	0.235069i
$411$	−20.3298	+	10.0966i	−1.00279	+	0.498027i
$412$	17.3544	−	7.32093i	0.854988	−	0.360677i
$413$		−	22.6465i		−	1.11436i
$414$	2.07193	+	0.391785i	0.101830	+	0.0192552i
$415$	16.8478	−	27.2102i	0.827027	−	1.33570i
$416$	−19.2469	−	14.5346i	−0.943656	−	0.712616i
$417$	−0.888894	+	3.11181i	−0.0435294	+	0.152386i
$418$	0.685524	+	0.0635232i	0.0335301	+	0.00310702i
$419$	4.29276	+	22.9642i	0.209715	+	1.12188i	0.912065	+	0.410045i	$0.134487\pi$
$419$	4.29276	+	22.9642i	0.209715	+	1.12188i	−0.702350	+	0.711832i	$0.747866\pi$
$420$	3.95772	+	13.9653i	0.193117	+	0.681436i
$421$	16.0888	+	32.3107i	0.784122	+	1.57473i	0.817941	+	0.575301i	$0.195115\pi$
$421$	16.0888	+	32.3107i	0.784122	+	1.57473i	−0.0338194	+	0.999428i	$0.510767\pi$
$422$	−2.31822	+	8.14769i	−0.112849	+	0.396623i
$423$	34.7347	+	6.56807i	1.68886	+	0.319350i
$424$	−3.44465	−	8.89168i	−0.167287	−	0.431818i
$425$	−0.578769	−	3.09614i	−0.0280744	−	0.150185i
$426$	3.45205	+	1.72341i	0.167253	+	0.0834997i
$427$	−0.937525	−	3.29506i	−0.0453700	−	0.159459i
$428$	−8.27609	+	2.35475i	−0.400040	+	0.113821i
$429$	28.4496	−	17.5742i	1.37356	−	0.848491i
$430$	1.22119	−	1.61711i	0.0588908	−	0.0779840i
$431$	6.29691	+	10.1699i	0.303311	+	0.489865i	0.965828	−	0.259182i	$-0.0834530\pi$
$431$	6.29691	+	10.1699i	0.303311	+	0.489865i	−0.662517	+	0.749047i	$0.730512\pi$
$432$	16.3999	+	0.0513181i	0.789039	+	0.00246904i
$433$	10.4427	−	26.9558i	0.501845	−	1.29541i	−0.419884	−	0.907578i	$-0.637929\pi$
$433$	10.4427	−	26.9558i	0.501845	−	1.29541i	0.921729	−	0.387834i	$-0.126777\pi$
$434$	−2.42624	+	3.21286i	−0.116463	+	0.154222i
$435$	0.0422581	−	40.5137i	0.00202612	−	1.94248i
$436$	−21.1460	+	23.1960i	−1.01271	+	1.11089i
$437$	−1.01253	+	0.0938251i	−0.0484361	+	0.00448826i
$438$	−0.321731	+	0.644438i	−0.0153729	+	0.0307925i
$439$	28.2901	+	2.62147i	1.35021	+	0.125116i	0.742930	−	0.669369i	$-0.233435\pi$
$439$	28.2901	+	2.62147i	1.35021	+	0.125116i	0.607284	+	0.794485i	$0.292259\pi$
$440$	−10.9098	−	5.43243i	−0.520104	−	0.258981i
$441$	11.1880	−	2.06725i	0.532762	−	0.0984406i
$442$	−3.80696	+	3.47050i	−0.181079	+	0.165075i
$443$	−4.07617	−	14.3262i	−0.193665	−	0.680660i	−0.996434	−	0.0843712i	$-0.973112\pi$
$443$	−4.07617	−	14.3262i	−0.193665	−	0.680660i	0.802770	−	0.596289i	$-0.203359\pi$
$444$	−4.11467	+	10.5884i	−0.195274	+	0.502503i
$445$	0.855979	−	9.23748i	0.0405773	−	0.437899i
$446$	−2.09877	−	3.38964i	−0.0993798	−	0.160504i
$447$	12.9213	+	1.21093i	0.611157	+	0.0572751i
$448$	8.35568	+	1.56195i	0.394769	+	0.0737951i
$449$	11.5066	−	4.45769i	0.543031	−	0.210371i	−0.0740731	−	0.997253i	$-0.523600\pi$
$449$	11.5066	−	4.45769i	0.543031	−	0.210371i	0.617104	+	0.786881i	$0.288306\pi$
$450$	−0.555205	−	1.44207i	−0.0261726	−	0.0679800i
$451$	−6.62774	+	17.1082i	−0.312088	+	0.805592i
$452$	2.19713	+	2.90947i	0.103344	+	0.136850i
$453$	−1.89765	+	4.88327i	−0.0891593	+	0.229436i
$454$	4.55424	−	0.422012i	0.213741	−	0.0198060i
$455$	24.6158	+	9.53623i	1.15401	+	0.447065i
$456$	1.33954	−	0.379622i	0.0627297	−	0.0177774i
$457$	37.5425	+	10.6818i	1.75616	+	0.499672i	0.989767	−	0.142696i	$-0.0455771\pi$
$457$	37.5425	+	10.6818i	1.75616	+	0.499672i	0.766397	+	0.642368i	$0.222048\pi$
$458$			4.68959i			0.219130i
$459$	2.25343	−	11.8494i	0.105181	−	0.553082i
$460$	8.33347	+	2.37108i	0.388550	+	0.110552i
$461$	9.19465	+	23.7341i	0.428237	+	1.10541i	0.965133	+	0.261760i	$0.0843028\pi$
$461$	9.19465	+	23.7341i	0.428237	+	1.10541i	−0.536896	+	0.843649i	$0.680403\pi$
$462$	2.05062	−	3.30416i	0.0954034	−	0.153723i
$463$	−19.8190	−	9.86871i	−0.921069	−	0.458638i	−0.0783101	−	0.996929i	$-0.524952\pi$
$463$	−19.8190	−	9.86871i	−0.921069	−	0.458638i	−0.842759	+	0.538291i	$0.819070\pi$
$464$	−26.2109	−	13.0515i	−1.21681	−	0.605900i
$465$	−13.6371	+	21.9734i	−0.632403	+	1.01899i
$466$	3.00198	+	7.74899i	0.139064	+	0.358965i
$467$	37.0429	+	10.5396i	1.71414	+	0.487715i	0.981267	−	0.192651i	$-0.0617084\pi$
$467$	37.0429	+	10.5396i	1.71414	+	0.487715i	0.732873	+	0.680366i	$0.238179\pi$
$468$	19.6697	−	25.9342i	0.909231	−	1.19881i
$469$			21.0032i			0.969836i
$470$	−10.8473	−	3.08632i	−0.500347	−	0.142361i
$471$	0.172854	−	0.0489863i	0.00796469	−	0.00225717i
$472$	17.2587	+	6.68604i	0.794394	+	0.307750i
$473$	6.96231	−	0.645153i	0.320128	−	0.0296642i
$474$	−2.65589	+	6.83447i	−0.121989	+	0.313918i
$475$	0.449075	+	0.594672i	0.0206050	+	0.0272854i
$476$	2.78720	−	7.19459i	0.127751	−	0.329763i
$477$	18.2389	−	7.02207i	0.835103	−	0.321519i
$478$	5.89569	−	2.28400i	0.269662	−	0.104468i
$479$	23.0041	+	4.30021i	1.05108	+	0.196482i	0.680824	−	0.732447i	$-0.261622\pi$
$479$	23.0041	+	4.30021i	1.05108	+	0.196482i	0.370259	+	0.928928i	$0.379269\pi$
$480$	−17.9376	−	1.68103i	−0.818734	−	0.0767282i
$481$	10.8759	+	17.5652i	0.495900	+	0.800906i
$482$	0.235537	−	2.54184i	0.0107284	−	0.115778i
$483$	−2.08048	+	5.35376i	−0.0946652	+	0.243604i
$484$	0.0476775	+	0.167569i	0.00216716	+	0.00761678i
$485$	−23.6906	+	21.5969i	−1.07574	+	0.980663i
$486$	0.0308609	−	5.91735i	0.00139988	−	0.268416i
$487$	−22.0210	−	10.9651i	−0.997865	−	0.496878i	−0.128850	−	0.991664i	$-0.541129\pi$
$487$	−22.0210	−	10.9651i	−0.997865	−	0.496878i	−0.869015	+	0.494786i	$0.835246\pi$
$488$	2.78792	+	0.258339i	0.126203	+	0.0116944i
$489$	1.71631	−	3.43783i	0.0776143	−	0.155464i
$490$	−3.61424	+	0.334909i	−0.163275	+	0.0151296i
$491$	−6.23199	+	6.83617i	−0.281246	+	0.308512i	−0.863353	−	0.504600i	$-0.831640\pi$
$491$	−6.23199	+	6.83617i	−0.281246	+	0.308512i	0.582108	+	0.813112i	$0.302228\pi$
$492$	−0.0186275	+	17.8586i	−0.000839794	+	0.805128i
$493$	−12.9778	+	17.1854i	−0.584492	+	0.773992i
$494$	0.440263	−	1.13645i	0.0198084	−	0.0511313i
$495$	11.1808	−	22.3372i	0.502541	−	1.00398i
$496$	9.83937	+	15.8911i	0.441801	+	0.713532i
$497$	−6.33361	+	8.38705i	−0.284101	+	0.376211i
$498$	−7.10034	+	4.38610i	−0.318174	+	0.196546i
$499$	24.3263	−	6.92142i	1.08899	−	0.309845i	0.318907	−	0.947786i	$-0.396684\pi$
$499$	24.3263	−	6.92142i	1.08899	−	0.309845i	0.770085	+	0.637941i	$0.220214\pi$
$500$	4.66513	+	16.3962i	0.208631	+	0.733262i
$501$	8.58842	+	4.28771i	0.383702	+	0.191561i
$502$	0.306897	+	1.64175i	0.0136975	+	0.0732751i
$503$	−11.7370	−	30.2968i	−0.523329	−	1.35087i	−0.904544	−	0.426381i	$-0.859788\pi$
$503$	−11.7370	−	30.2968i	−0.523329	−	1.35087i	0.381215	−	0.924486i	$-0.375506\pi$
$504$	1.46119	−	7.72742i	0.0650868	−	0.344207i
$505$	9.16155	−	32.1995i	0.407684	−	1.43286i
$506$	−1.03466	−	2.07787i	−0.0459962	−	0.0923727i
$507$	−10.0013	−	35.2906i	−0.444172	−	1.56731i
$508$	7.14397	+	38.2169i	0.316963	+	1.69560i
$509$	−37.6979	−	3.49322i	−1.67093	−	0.154834i	−0.785265	−	0.619160i	$-0.787473\pi$
$509$	−37.6979	−	3.49322i	−1.67093	−	0.154834i	−0.885665	+	0.464325i	$0.846297\pi$
$510$	−1.05693	+	3.70007i	−0.0468018	+	0.163842i
$511$	−1.56572	−	1.18237i	−0.0692632	−	0.0523051i
$512$	−11.7185	+	18.9261i	−0.517891	+	0.836423i
$513$	0.772338	+	2.74712i	0.0340996	+	0.121288i
$514$			10.9357i			0.482354i
$515$	−7.72790	−	24.3935i	−0.340532	−	1.07490i
$516$	6.09562	−	3.02733i	0.268345	−	0.133271i
$517$	−17.3455	−	34.8345i	−0.762854	−	1.53202i
$518$	2.04268	+	1.26477i	0.0897502	+	0.0555709i
$519$	26.9980	+	5.07594i	1.18508	+	0.222809i
$520$	−14.5349	+	15.9440i	−0.637398	+	0.699192i
$521$	−2.17199	+	23.4395i	−0.0951565	+	1.02690i	0.805566	+	0.592507i	$0.201862\pi$
$521$	−2.17199	+	23.4395i	−0.0951565	+	1.02690i	−0.900722	+	0.434396i	$0.856962\pi$
$522$	−4.72895	+	9.44756i	−0.206980	+	0.413509i
$523$	6.52506	+	1.21975i	0.285321	+	0.0533358i	0.324465	−	0.945898i	$-0.394816\pi$
$523$	6.52506	+	1.21975i	0.285321	+	0.0533358i	−0.0391435	+	0.999234i	$0.512463\pi$
$524$	−3.07839	+	1.53286i	−0.134480	+	0.0669631i
$525$	4.13831	−	0.769118i	0.180611	−	0.0335671i
$526$	−0.142357	+	0.0708854i	−0.00620706	+	0.00309075i
$527$	12.8182	−	4.96582i	0.558372	−	0.216314i
$528$	−10.8645	−	14.4182i	−0.472817	−	0.627471i
$529$	−11.7945	−	15.6184i	−0.512803	−	0.679061i
$530$	−5.99710	+	1.70632i	−0.260497	+	0.0741179i
$531$	−13.7774	+	35.3444i	−0.597886	+	1.53382i
$532$	0.168426	+	1.81760i	0.00730218	+	0.0788031i
$533$	25.9188	+	19.5729i	1.12267	+	0.847799i
$534$	−1.27571	+	2.05554i	−0.0552052	+	0.0889521i
$535$	2.14794	+	11.4905i	0.0928637	+	0.496777i
$536$	−16.0063	−	6.20086i	−0.691366	−	0.267836i
$537$	−0.200075	+	1.06416i	−0.00863385	+	0.0459218i
$538$	2.93362	−	5.89151i	0.126477	−	0.254001i
$539$	−9.25563	−	8.43762i	−0.398668	−	0.363434i
$540$	2.31918	−	24.2033i	0.0998015	−	1.04155i
$541$	21.2979	+	28.2029i	0.915667	+	1.21254i	0.976745	+	0.214406i	$0.0687814\pi$
$541$	21.2979	+	28.2029i	0.915667	+	1.21254i	−0.0610781	+	0.998133i	$0.519454\pi$
$542$	−0.109936	+	1.18640i	−0.00472216	+	0.0509602i
$543$	0.0105333	−	10.0985i	0.000452027	−	0.433368i
$544$	7.07713	+	6.45165i	0.303429	+	0.276612i
$545$	28.7274	+	31.5124i	1.23055	+	1.34984i
$546$	−4.63247	−	5.09224i	−0.198251	−	0.217928i
$547$	−23.5936	+	21.5084i	−1.00879	+	0.919635i	−0.996771	−	0.0802929i	$-0.974414\pi$
$547$	−23.5936	+	21.5084i	−1.00879	+	0.919635i	−0.0120201	+	0.999928i	$0.503826\pi$
$548$	24.2182	+	2.24415i	1.03455	+	0.0958654i
$549$	−0.541406	+	5.71295i	−0.0231066	+	0.243823i
$550$	−0.895484	+	1.44626i	−0.0381836	+	0.0616686i
$551$	0.936180	−	5.00812i	0.0398826	−	0.213353i
$552$	−3.46581	−	3.16613i	−0.147515	−	0.134759i
$553$	−16.9813	−	10.5144i	−0.722118	−	0.447116i
$554$	11.0492	+	4.28047i	0.469434	+	0.181860i
$555$	13.8075	+	6.89329i	0.586095	+	0.292604i
$556$	2.56265	−	2.33616i	0.108681	−	0.0990754i
$557$	2.93994	+	31.7270i	0.124569	+	1.34432i	0.796920	+	0.604085i	$0.206461\pi$
$557$	2.93994	+	31.7270i	0.124569	+	1.34432i	−0.672351	+	0.740233i	$0.734715\pi$
$558$	5.74122	−	3.53827i	0.243045	−	0.149787i
$559$	2.27442	−	12.1671i	0.0961978	−	0.514613i
$560$	3.90019	−	13.7078i	0.164813	−	0.579258i
$561$	−11.8919	+	5.90601i	−0.502078	+	0.249352i
$562$		−	9.08605i		−	0.383272i
$563$	0.463120	−	1.62770i	0.0195182	−	0.0685992i	−0.951455	−	0.307789i	$-0.900411\pi$
$563$	0.463120	−	1.62770i	0.0195182	−	0.0685992i	0.970973	+	0.239189i	$0.0768817\pi$
$564$	−27.9655	−	25.5474i	−1.17756	−	1.07574i
$565$	4.21113	−	2.60742i	0.177164	−	0.109695i
$566$	−4.18199	+	8.39857i	−0.175782	+	0.353018i
$567$	15.8317	+	3.02787i	0.664869	+	0.127159i
$568$	−4.52178	−	7.30292i	−0.189729	−	0.306424i
$569$	42.1131	−	16.3147i	1.76547	−	0.683949i	0.766337	−	0.642439i	$-0.222077\pi$
$569$	42.1131	−	16.3147i	1.76547	−	0.683949i	0.999138	−	0.0415096i	$-0.0132167\pi$
$570$	−0.166350	−	0.895064i	−0.00696765	−	0.0374901i
$571$	−30.9467			−1.29508			−0.647539	−	0.762032i	$-0.724202\pi$
$571$	−30.9467			−1.29508			−0.647539	+	0.762032i	$0.724202\pi$
$572$	−35.8311			−1.49817
$573$	7.96042	−	1.47947i	0.332551	−	0.0618057i
$574$	3.71270	+	0.694024i	0.154965	+	0.0289680i
$575$	0.907612	−	2.34282i	0.0378500	−	0.0977022i
$576$	−12.0905	−	7.52103i	−0.503769	−	0.313376i
$577$	−6.10802	−	6.70018i	−0.254280	−	0.278932i	0.598589	−	0.801056i	$-0.295728\pi$
$577$	−6.10802	−	6.70018i	−0.254280	−	0.278932i	−0.852870	+	0.522124i	$0.825140\pi$
$578$	−3.51751	+	2.65630i	−0.146309	+	0.110487i
$579$	−5.88767	+	0.539380i	−0.244683	+	0.0224159i
$580$	−22.8528	+	36.9085i	−0.948910	+	1.53254i
$581$	−8.21226	−	21.1983i	−0.340702	−	0.879453i
$582$	8.04302	−	2.27937i	0.333394	−	0.0944830i
$583$	−18.2918	−	11.3258i	−0.757570	−	0.469068i
$584$	1.36333	−	0.844136i	0.0564149	−	0.0349306i
$585$	−32.6164	−	29.8586i	−1.34852	−	1.23450i
$586$	−4.52713	−	4.96603i	−0.187014	−	0.205145i
$587$	21.3058	−	6.06203i	0.879385	−	0.250207i	0.196298	−	0.980544i	$-0.437108\pi$
$587$	21.3058	−	6.06203i	0.879385	−	0.250207i	0.683086	+	0.730338i	$0.260637\pi$
$588$	−11.3631	−	4.41572i	−0.468606	−	0.182101i
$589$	−2.19100	+	2.40341i	−0.0902785	+	0.0990308i
$590$	5.39446	−	10.8335i	0.222086	−	0.446010i
$591$	−31.5636	+	12.1899i	−1.29835	+	0.501427i
$592$	8.90077	−	6.72155i	0.365819	−	0.276254i
$593$	0.486170	+	5.24661i	0.0199646	+	0.215452i	0.999872	+	0.0159993i	$0.00509296\pi$
$593$	0.486170	+	5.24661i	0.0199646	+	0.215452i	−0.979907	+	0.199453i	$0.936084\pi$
$594$	−5.21053	+	3.90927i	−0.213791	+	0.160399i
$595$	−9.38297	−	4.67216i	−0.384664	−	0.191540i
$596$	−11.0972	−	8.38019i	−0.454558	−	0.343266i
$597$	24.9337	−	2.28422i	1.02047	−	0.0934871i
$598$	−4.03918	+	0.755053i	−0.165174	+	0.0308764i
$599$	−18.5087	+	11.4601i	−0.756243	+	0.468246i	−0.849627	−	0.527384i	$-0.823173\pi$
$599$	−18.5087	+	11.4601i	−0.756243	+	0.468246i	0.0933836	+	0.995630i	$0.470232\pi$
$600$	−0.635637	+	3.38083i	−0.0259498	+	0.138022i
$601$	−0.263470	+	0.0244141i	−0.0107472	+	0.000995871i	−0.0976406	−	0.995222i	$-0.531130\pi$
$601$	−0.263470	+	0.0244141i	−0.0107472	+	0.000995871i	0.0868934	+	0.996218i	$0.472306\pi$
$602$	−0.393919	−	1.38448i	−0.0160549	−	0.0564273i
$603$	12.7776	−	32.7796i	0.520344	−	1.33489i
$604$	4.47978	−	3.38297i	0.182280	−	0.137651i
$605$	0.232652	−	0.0434903i	0.00945866	−	0.00176813i
$606$	−5.88817	+	6.44550i	−0.239191	+	0.261831i
$607$	−14.7492	−	29.6203i	−0.598650	−	1.20225i	−0.962624	−	0.270842i	$-0.912698\pi$
$607$	−14.7492	−	29.6203i	−0.598650	−	1.20225i	0.363974	−	0.931409i	$-0.381420\pi$
$608$	−2.17916	−	0.620025i	−0.0883766	−	0.0251453i
$609$	−22.9475	−	17.3668i	−0.929880	−	0.703737i
$610$	0.336403	−	1.79960i	0.0136206	−	0.0728636i
$611$	−67.7147	+	12.6581i	−2.73944	+	0.512091i
$612$	−8.72691	+	9.53295i	−0.352764	+	0.385346i
$613$	13.1458	+	11.9840i	0.530953	+	0.484027i	0.894201	−	0.447665i	$-0.147744\pi$
$613$	13.1458	+	11.9840i	0.530953	+	0.484027i	−0.363249	+	0.931692i	$0.618333\pi$
$614$	1.04308	−	1.38126i	0.0420954	−	0.0557433i
$615$	24.1556	+	2.26376i	0.974046	+	0.0912835i
$616$	−7.74960	+	3.85884i	−0.312240	+	0.155477i
$617$	6.07866			0.244718			0.122359	−	0.992486i	$-0.460954\pi$
$617$	6.07866			0.244718			0.122359	+	0.992486i	$0.460954\pi$
$618$	−1.03834	+	6.59153i	−0.0417682	+	0.265150i
$619$	−32.4800			−1.30548			−0.652740	−	0.757582i	$-0.726381\pi$
$619$	−32.4800			−1.30548			−0.652740	+	0.757582i	$0.726381\pi$
$620$	24.8053	−	12.3516i	0.996204	−	0.496051i
$621$	6.50404	−	7.08991i	0.260998	−	0.284508i
$622$	0.965218	−	1.27815i	0.0387017	−	0.0512493i
$623$	−4.86993	−	4.43953i	−0.195110	−	0.177866i
$624$	−29.8128	+	11.5138i	−1.19347	+	0.460920i
$625$	29.4335	−	5.50207i	1.17734	−	0.220083i
$626$	0.859907	−	4.60010i	0.0343688	−	0.183857i
$627$	1.89567	−	2.50484i	0.0757059	−	0.100034i
$628$	−0.185159	−	0.0526823i	−0.00738865	−	0.00210225i
$629$	−3.65648	−	7.34320i	−0.145793	−	0.292793i
$630$	−4.94308	−	1.41758i	−0.196937	−	0.0564778i
$631$	10.2897	−	1.92348i	0.409628	−	0.0765727i	0.0250973	−	0.999685i	$-0.492010\pi$
$631$	10.2897	−	1.92348i	0.409628	−	0.0765727i	0.384530	+	0.923112i	$0.374363\pi$
$632$	13.0263	−	9.83704i	0.518160	−	0.391296i
$633$	26.0097	+	28.5911i	1.03379	+	1.13639i
$634$	2.75165	+	9.67105i	0.109282	+	0.384087i
$635$	52.5927	−	4.87343i	2.08708	−	0.193396i
$636$	−20.5809	−	3.86946i	−0.816086	−	0.153434i
$637$	−18.8504	+	11.6717i	−0.746880	+	0.462449i
$638$	11.4321	−	2.13703i	0.452601	−	0.0846057i
$639$	14.9872	−	9.23651i	0.592886	−	0.365391i
$640$	20.2265	+	15.2743i	0.799521	+	0.603770i
$641$	−21.3579	−	10.6350i	−0.843588	−	0.420057i	−0.0286393	−	0.999590i	$-0.509117\pi$
$641$	−21.3579	−	10.6350i	−0.843588	−	0.420057i	−0.814949	+	0.579533i	$0.803235\pi$
$642$	0.837277	−	2.93111i	0.0330447	−	0.115682i
$643$	−1.42509	−	15.3791i	−0.0561999	−	0.606494i	−0.976534	−	0.215362i	$-0.930907\pi$
$643$	−1.42509	−	15.3791i	−0.0561999	−	0.606494i	0.920334	−	0.391132i	$-0.127917\pi$
$644$	4.91140	−	3.70891i	0.193536	−	0.146152i
$645$	−3.33108	−	8.62521i	−0.131161	−	0.339617i
$646$	−0.215702	+	0.433187i	−0.00848666	+	0.0170435i
$647$	11.2541	−	12.3452i	0.442446	−	0.485340i	−0.476807	−	0.879008i	$-0.658206\pi$
$647$	11.2541	−	12.3452i	0.442446	−	0.485340i	0.919253	+	0.393668i	$0.128794\pi$
$648$	−6.98158	+	11.1712i	−0.274262	+	0.438847i
$649$	40.1649	−	11.4279i	1.57661	−	0.448585i
$650$	2.02868	+	2.22536i	0.0795714	+	0.0872857i
$651$	6.61816	+	17.1365i	0.259386	+	0.671632i
$652$	−3.50051	+	2.16743i	−0.137091	+	0.0848829i
$653$	−20.3082	−	12.5743i	−0.794723	−	0.492072i	0.0680386	−	0.997683i	$-0.478326\pi$
$653$	−20.3082	−	12.5743i	−0.794723	−	0.492072i	−0.862762	+	0.505611i	$0.831267\pi$
$654$	−3.03194	−	10.6985i	−0.118558	−	0.418346i
$655$	1.68767	+	4.35638i	0.0659427	+	0.170218i
$656$	9.23072	−	14.9081i	0.360399	−	0.582064i
$657$	1.72429	+	2.79786i	0.0672711	+	0.109155i
$658$	−6.39293	+	4.82771i	−0.249222	+	0.188204i
$659$	8.69946	+	9.54285i	0.338883	+	0.371737i	0.884695	−	0.466171i	$-0.154367\pi$
$659$	8.69946	+	9.54285i	0.338883	+	0.371737i	−0.545812	+	0.837908i	$0.683779\pi$
$660$	−22.7711	+	14.0664i	−0.886363	+	0.547535i
$661$	10.7771	−	27.8188i	0.419179	−	1.08203i	−0.549890	−	0.835237i	$-0.685330\pi$
$661$	10.7771	−	27.8188i	0.419179	−	1.08203i	0.969069	−	0.246789i	$-0.0793756\pi$
$662$	−4.64754	−	0.868776i	−0.180632	−	0.0337659i
$663$	4.29492	+	23.1092i	0.166801	+	0.897488i
$664$	18.5795			0.721025
$665$	2.47984			0.0961640
$666$	−2.41856	−	3.21662i	−0.0937174	−	0.124642i
$667$	−16.0179	+	6.20538i	−0.620217	+	0.240273i
$668$	−5.41469	−	8.74502i	−0.209501	−	0.338355i
$669$	−18.1909	−	0.0189741i	−0.703300	−	0.000733581i
$670$	−5.00301	+	10.0474i	−0.193283	+	0.388165i
$671$	5.37089	−	3.32551i	0.207341	−	0.128380i
$672$	−8.63148	+	9.44847i	−0.332967	+	0.364483i
$673$	−3.44885	+	12.1214i	−0.132943	+	0.467247i	−0.999493	−	0.0318439i	$-0.989862\pi$
$673$	−3.44885	+	12.1214i	−0.132943	+	0.467247i	0.866550	+	0.499091i	$0.166333\pi$
$674$			4.84866i			0.186764i
$675$	−6.92656	−	1.31724i	−0.266603	−	0.0507007i
$676$	−10.7558	+	37.8029i	−0.413686	+	1.45396i
$677$	0.419244	−	2.24276i	0.0161129	−	0.0861962i	−0.973971	−	0.226671i	$-0.927216\pi$
$677$	0.419244	−	2.24276i	0.0161129	−	0.0861962i	0.990084	+	0.140475i	$0.0448629\pi$
$678$	−1.28624	+	0.117835i	−0.0493977	+	0.00452541i
$679$	2.10108	+	22.6743i	0.0806321	+	0.870159i
$680$	6.33078	−	5.77127i	0.242774	−	0.221318i
$681$	9.32162	−	18.6715i	0.357205	−	0.715494i
$682$	−6.92253	−	2.68180i	−0.265077	−	0.102692i
$683$	−42.9410	−	26.5879i	−1.64309	−	1.01736i	−0.957105	−	0.289743i	$-0.906430\pi$
$683$	−42.9410	−	26.5879i	−1.64309	−	1.01736i	−0.685985	−	0.727615i	$-0.740629\pi$
$684$	0.842905	−	2.93919i	0.0322293	−	0.112383i
$685$	6.07146	−	32.4795i	0.231979	−	1.24098i
$686$	−3.86259	+	6.23830i	−0.147474	+	0.238179i
$687$	18.1809	+	11.2834i	0.693643	+	0.430487i
$688$	−6.65394	−	0.616579i	−0.253679	−	0.0235068i
$689$	−28.1457	+	25.6582i	−1.07226	+	0.977498i
$690$	−2.27053	+	2.06553i	−0.0864376	+	0.0786334i
$691$	−20.4519	−	22.4347i	−0.778027	−	0.853455i	0.214342	−	0.976759i	$-0.431239\pi$
$691$	−20.4519	−	22.4347i	−0.778027	−	0.853455i	−0.992369	+	0.123304i	$0.960651\pi$
$692$	−21.7530	−	19.8304i	−0.826923	−	0.753840i
$693$	−7.87587	−	15.8999i	−0.299179	−	0.603988i
$694$	0.387576	−	4.18261i	0.0147122	−	0.158770i
$695$	−2.83898	−	3.75941i	−0.107688	−	0.142603i
$696$	20.0099	−	12.3608i	0.758474	−	0.468533i
$697$	−9.53040	−	8.68810i	−0.360989	−	0.329085i
$698$	1.55874	−	3.13038i	0.0589993	−	0.118487i
$699$	37.2646	+	7.00620i	1.40948	+	0.264999i
$700$	−4.20559	−	1.62926i	−0.158957	−	0.0615801i
$701$	1.85987	+	9.94944i	0.0702464	+	0.375785i	0.999972	+	0.00753109i	$0.00239724\pi$
$701$	1.85987	+	9.94944i	0.0702464	+	0.375785i	−0.929725	+	0.368254i	$0.879956\pi$
$702$	4.13195	+	10.7657i	0.155950	+	0.406324i
$703$	1.54875	+	1.16956i	0.0584122	+	0.0441108i
$704$	1.44625	+	15.6075i	0.0545074	+	0.588229i
$705$	−38.0642	+	34.6275i	−1.43358	+	1.30415i
$706$	−0.0257803	+	0.00733514i	−0.000970256	+	0.000276062i
$707$	−14.3308	−	18.9770i	−0.538965	−	0.713705i
$708$	32.4627	−	24.4616i	1.22002	−	0.919322i
$709$	19.1610	−	7.42301i	0.719607	−	0.278777i	0.0265372	−	0.999648i	$-0.491552\pi$
$709$	19.1610	−	7.42301i	0.719607	−	0.278777i	0.693070	+	0.720871i	$0.256258\pi$
$710$	−5.02766	+	2.50348i	−0.188685	+	0.0939538i
$711$	20.1061	+	26.7406i	0.754037	+	1.00285i
$712$	4.82109	−	2.40062i	0.180678	−	0.0899669i
$713$	10.7785	+	2.01485i	0.403657	+	0.0754566i
$714$	1.64497	+	2.18303i	0.0615616	+	0.0816978i
$715$	−4.49139	+	48.4698i	−0.167968	+	1.81267i
$716$	0.781641	−	0.857419i	0.0292113	−	0.0320433i
$717$	5.33055	−	28.3521i	0.199073	−	1.05883i
$718$	−8.33271	−	5.15940i	−0.310974	−	0.192547i
$719$	19.3885	+	38.9373i	0.723068	+	1.45212i	0.885134	+	0.465336i	$0.154067\pi$
$719$	19.3885	+	38.9373i	0.723068	+	1.45212i	−0.162066	+	0.986780i	$0.551816\pi$
$720$	−14.4263	+	19.0209i	−0.537638	+	0.708868i
$721$	−17.1358	−	6.06153i	−0.638169	−	0.225743i
$722$			7.09797i			0.264159i
$723$	−9.28766	−	7.02894i	−0.345412	−	0.261409i
$724$	−5.69631	+	9.19986i	−0.211702	+	0.341910i
$725$	10.0457	+	7.58618i	0.373089	+	0.281744i
$726$	−0.0593472	−	0.0169527i	−0.00220258	−	0.000629173i
$727$	−4.28618	−	0.397173i	−0.158966	−	0.0147303i	0.0124911	−	0.999922i	$-0.496024\pi$
$727$	−4.28618	−	0.397173i	−0.158966	−	0.0147303i	−0.171457	+	0.985192i	$0.554847\pi$
$728$	2.81603	+	15.0645i	0.104369	+	0.558326i
$729$	−22.8665	−	14.3571i	−0.846906	−	0.531743i
$730$	−0.467355	−	0.938576i	−0.0172976	−	0.0347383i
$731$	−1.34499	+	4.72716i	−0.0497463	+	0.174840i
$732$	3.71065	−	4.90305i	0.137149	−	0.181222i
$733$	0.734658	+	1.89637i	0.0271352	+	0.0700440i	0.945382	−	0.325965i	$-0.105689\pi$
$733$	0.734658	+	1.89637i	0.0271352	+	0.0700440i	−0.918247	+	0.396009i	$0.870395\pi$
$734$	1.01572	+	5.43363i	0.0374910	+	0.200559i
$735$	−7.39764	+	14.8177i	−0.272866	+	0.546559i
$736$	2.09048	+	7.34728i	0.0770562	+	0.270824i
$737$	−37.2503	+	10.5986i	−1.37213	+	0.390406i
$738$	−5.37219	−	3.34184i	−0.197753	−	0.123015i
$739$	2.36626	−	3.13344i	0.0870443	−	0.115265i	−0.752411	−	0.658694i	$-0.771109\pi$
$739$	2.36626	−	3.13344i	0.0870443	−	0.115265i	0.839456	+	0.543428i	$0.182874\pi$
$740$	−8.70512	−	14.0592i	−0.320006	−	0.516828i
$741$	−3.34656	−	4.44119i	−0.122939	−	0.163151i
$742$	−1.59995	+	4.12994i	−0.0587359	+	0.151615i
$743$	−19.5180	+	25.8460i	−0.716046	+	0.948198i	−0.999943	−	0.0106570i	$-0.996608\pi$
$743$	−19.5180	+	25.8460i	−0.716046	+	0.948198i	0.283898	+	0.958855i	$0.408372\pi$
$744$	−15.0134	−	0.0156598i	−0.550419	−	0.000574118i
$745$	−12.7272	+	13.9610i	−0.466287	+	0.511493i
$746$	−4.65674	+	0.431511i	−0.170495	+	0.0157987i
$747$	−0.0794396	+	38.0802i	−0.00290654	+	1.39328i
$748$	14.1665	+	1.31272i	0.517978	+	0.0479978i
$749$	7.43297	+	3.70118i	0.271595	+	0.135238i
$750$	−5.80699	−	1.65878i	−0.212041	−	0.0605700i
$751$	13.7256	−	12.5125i	0.500853	−	0.456587i	−0.383409	−	0.923578i	$-0.625250\pi$
$751$	13.7256	−	12.5125i	0.500853	−	0.456587i	0.884262	+	0.466991i	$0.154662\pi$
$752$	10.1777	+	35.7708i	0.371141	+	1.30443i
$753$	7.10326	+	2.76034i	0.258857	+	0.100592i
$754$	1.89964	−	20.5004i	0.0691808	−	0.746580i
$755$	−4.01472	−	6.48399i	−0.146111	−	0.235977i
$756$	−12.7271	−	11.6754i	−0.462881	−	0.424631i
$757$	−15.6330	−	2.92232i	−0.568191	−	0.106213i	−0.108188	−	0.994130i	$-0.534505\pi$
$757$	−15.6330	−	2.92232i	−0.568191	−	0.106213i	−0.460004	+	0.887917i	$0.652152\pi$
$758$	−4.73605	+	1.83475i	−0.172021	+	0.0666413i
$759$	−10.5451	−	0.988238i	−0.382761	−	0.0358708i
$760$	−0.732135	+	1.88986i	−0.0265573	+	0.0685523i
$761$	−25.1138	−	33.2561i	−0.910375	−	1.20553i	−0.978165	−	0.207831i	$-0.933359\pi$
$761$	−25.1138	−	33.2561i	−0.910375	−	1.20553i	0.0677900	−	0.997700i	$-0.478405\pi$
$762$	−12.8384	−	4.98901i	−0.465084	−	0.180733i
$763$	30.1605	−	2.79478i	1.09188	−	0.101178i
$764$	−8.08985	−	3.13402i	−0.292680	−	0.113385i
$765$	11.8016	+	13.0001i	0.426688	+	0.470020i
$766$	7.35847	+	2.09367i	0.265873	+	0.0756472i
$767$		−	73.9239i		−	2.66924i
$768$	4.37333	+	8.80583i	0.157809	+	0.317753i
$769$	4.03494	+	1.14804i	0.145504	+	0.0413993i	0.345631	−	0.938371i	$-0.387665\pi$
$769$	4.03494	+	1.14804i	0.145504	+	0.0413993i	−0.200127	+	0.979770i	$0.564136\pi$
$770$	2.04490	+	5.27849i	0.0736931	+	0.190224i
$771$	42.3962	+	26.3119i	1.52686	+	0.947598i
$772$	5.67094	+	2.82379i	0.204102	+	0.101630i
$773$	2.70059	+	1.34474i	0.0971336	+	0.0483668i	0.493649	−	0.869661i	$-0.335663\pi$
$773$	2.70059	+	1.34474i	0.0971336	+	0.0483668i	−0.396515	+	0.918028i	$0.629781\pi$
$774$	−0.227482	+	2.40040i	−0.00817666	+	0.0862808i
$775$	−2.90277	−	7.49290i	−0.104270	−	0.269153i
$776$	−17.9001	−	5.09302i	−0.642577	−	0.182829i
$777$	9.81813	−	4.87607i	0.352223	−	0.174928i
$778$			8.81940i			0.316191i
$779$	2.93456	+	0.834955i	0.105142	+	0.0299154i
$780$	12.9190	+	45.5862i	0.462575	+	1.63225i
$781$	−18.0710	−	7.00074i	−0.646631	−	0.250506i
$782$	1.62463	−	0.150544i	0.0580966	−	0.00538344i
$783$	25.2488	+	41.0647i	0.902318	+	1.46753i
$784$	7.21333	+	9.55199i	0.257619	+	0.341143i
$785$	−0.0944744	+	0.243867i	−0.00337194	+	0.00870397i
$786$	0.113676	−	1.21299i	0.00405471	−	0.0432660i
$787$	19.8563	−	7.69237i	0.707800	−	0.274203i	0.0196865	−	0.999806i	$-0.493733\pi$
$787$	19.8563	−	7.69237i	0.707800	−	0.274203i	0.688114	+	0.725603i	$0.258439\pi$
$788$	35.6378	+	6.66186i	1.26954	+	0.237319i
$789$	−0.0677051	+	0.722452i	−0.00241037	+	0.0257200i
$790$	−5.61888	−	9.07480i	−0.199911	−	0.322867i
$791$	0.324627	−	3.50329i	0.0115424	−	0.124563i
$792$	14.4424	−	1.30790i	0.513188	−	0.0464743i
$793$	−3.06032	−	10.7559i	−0.108675	−	0.381953i
$794$	6.66259	−	6.07375i	0.236447	−	0.215549i
$795$	−7.81413	+	27.3554i	−0.277139	+	0.970196i
$796$	−24.0159	−	11.9585i	−0.851221	−	0.423858i
$797$	−20.9824	−	1.94431i	−0.743236	−	0.0688710i	−0.286017	−	0.958225i	$-0.592331\pi$
$797$	−20.9824	−	1.94431i	−0.743236	−	0.0688710i	−0.457220	+	0.889354i	$0.651155\pi$
$798$	−0.578585	−	0.288855i	−0.0204817	−	0.0102253i
$799$	27.2360	−	2.52379i	0.963541	−	0.0892853i
$800$	3.77131	−	4.13693i	0.133336	−	0.146263i
$801$	4.89964	+	9.89146i	0.173120	+	0.349498i
$802$	3.77733	−	5.00199i	0.133382	−	0.176626i
$803$	1.30692	−	3.37354i	0.0461201	−	0.119050i
$804$	−30.1070	+	22.6865i	−1.06179	+	0.800091i
$805$	−4.40153	−	7.10871i	−0.155133	−	0.250549i
$806$	−7.91986	+	10.4876i	−0.278965	+	0.369410i
$807$	−15.7821	−	25.5485i	−0.555556	−	0.899349i
$808$	18.6931	−	5.31866i	0.657622	−	0.187110i
$809$	9.09581	+	31.9685i	0.319792	+	1.12395i	0.940467	+	0.339884i	$0.110388\pi$
$809$	9.09581	+	31.9685i	0.319792	+	1.12395i	−0.620676	+	0.784067i	$0.713142\pi$
$810$	6.85225	+	5.21961i	0.240764	+	0.183399i
$811$	−6.82390	−	36.5046i	−0.239619	−	1.28185i	−0.865095	−	0.501607i	$-0.832742\pi$
$811$	−6.82390	−	36.5046i	−0.239619	−	1.28185i	0.625476	−	0.780243i	$-0.284905\pi$
$812$	11.1393	+	28.7538i	0.390913	+	1.00906i
$813$	4.33499	+	3.28074i	0.152035	+	0.115061i
$814$	−1.21237	+	4.26104i	−0.0424936	+	0.149349i
$815$	2.49316	+	5.00694i	0.0873315	+	0.175385i
$816$	12.2089	−	3.45996i	0.427396	−	0.121123i
$817$	−0.213656	−	1.14296i	−0.00747489	−	0.0399871i
$818$	0.0185279	+	0.00171686i	0.000647813	+	6.00287e-5i
$819$	−30.8878	+	5.70727i	−1.07931	+	0.199428i
$820$	−20.7454	−	15.6662i	−0.724462	−	0.547088i
$821$	21.5722	−	34.8403i	0.752874	−	1.21593i	−0.217907	−	0.975969i	$-0.569923\pi$
$821$	21.5722	−	34.8403i	0.752874	−	1.21593i	0.970782	−	0.239964i	$-0.0771357\pi$
$822$	−5.19982	+	6.87076i	−0.181364	+	0.239645i
$823$			4.39932i			0.153351i	0.997056	+	0.0766754i	$0.0244305\pi$
$823$			4.39932i			0.153351i	−0.997056	+	0.0766754i	$0.975569\pi$
$824$	9.67850	−	11.2694i	0.337167	−	0.392588i
$825$	3.45235	+	6.95143i	0.120196	+	0.242018i
$826$	−3.83187	−	7.69544i	−0.133328	−	0.267759i
$827$	13.9572	+	8.64194i	0.485340	+	0.300510i	0.747204	−	0.664595i	$-0.231396\pi$
$827$	13.9572	+	8.64194i	0.485340	+	0.300510i	−0.261864	+	0.965105i	$0.584337\pi$
$828$	−9.92158	+	2.80057i	−0.344799	+	0.0973267i
$829$	13.1570	−	14.4325i	0.456960	−	0.501262i	−0.466731	−	0.884399i	$-0.654568\pi$
$829$	13.1570	−	14.4325i	0.456960	−	0.501262i	0.923691	+	0.383138i	$0.125157\pi$
$830$	1.12094	−	12.0969i	0.0389086	−	0.419890i
$831$	43.1796	−	32.5371i	1.49788	−	1.12870i
$832$	27.2750	+	5.09859i	0.945592	+	0.176762i
$833$	7.88047	−	3.92401i	0.273042	−	0.135959i
$834$	0.224477	+	1.20782i	0.00777299	+	0.0418233i
$835$	−12.5084	+	6.22844i	−0.432871	+	0.215544i
$836$	−3.13863	+	1.21591i	−0.108552	+	0.0420532i
$837$	0.0962883	−	30.7711i	0.00332821	−	1.06361i
$838$	5.34434	+	7.07705i	0.184617	+	0.244473i
$839$	−19.6591	+	5.59350i	−0.678708	+	0.193109i	−0.595418	−	0.803416i	$-0.703013\pi$
$839$	−19.6591	+	5.59350i	−0.678708	+	0.193109i	−0.0832901	+	0.996525i	$0.526543\pi$
$840$	7.70356	+	8.46813i	0.265798	+	0.292178i
$841$	−5.26550	−	56.8238i	−0.181569	−	1.95944i
$842$	10.9342	+	8.25712i	0.376817	+	0.284559i
$843$	−35.2253	−	21.8615i	−1.21322	−	0.752949i
$844$	−7.61008	−	40.7103i	−0.261950	−	1.40131i
$845$	49.7889	+	19.2883i	1.71279	+	0.663538i
$846$	12.9144	−	3.64537i	0.444008	−	0.125330i
$847$	0.0749392	−	0.150498i	0.00257494	−	0.00517118i
$848$	15.1951	+	13.8521i	0.521801	+	0.475684i
$849$	22.4980	+	36.4203i	0.772129	+	1.24994i
$850$	−0.720549	−	0.954160i	−0.0247146	−	0.0327274i
$851$	0.603752	−	6.51553i	0.0206964	−	0.223349i
$852$	−18.8637	−	0.0196759i	−0.646259	−	0.000674084i
$853$	−34.9067	−	31.8217i	−1.19518	−	1.08955i	−0.993930	−	0.110014i	$-0.964910\pi$
$853$	−34.9067	−	31.8217i	−1.19518	−	1.08955i	−0.201253	−	0.979539i	$-0.564501\pi$
$854$	−0.876114	−	0.961051i	−0.0299800	−	0.0328865i
$855$	−3.87028	−	1.50865i	−0.132361	−	0.0515947i
$856$	−5.01510	+	4.57186i	−0.171412	+	0.156263i
$857$	−18.2757	−	1.69350i	−0.624287	−	0.0578487i	−0.224526	−	0.974468i	$-0.572083\pi$
$857$	−18.2757	−	1.69350i	−0.624287	−	0.0578487i	−0.399761	+	0.916619i	$0.630907\pi$
$858$	6.69374	−	10.7856i	0.228520	−	0.368215i
$859$	8.12424	−	13.1211i	0.277195	−	0.447686i	−0.681624	−	0.731703i	$-0.738726\pi$
$859$	8.12424	−	13.1211i	0.277195	−	0.447686i	0.958819	+	0.284017i	$0.0916671\pi$
$860$	−1.82045	+	9.73855i	−0.0620769	+	0.332082i
$861$	11.6236	−	12.7238i	0.396130	−	0.433625i
$862$	3.86051	+	2.39033i	0.131489	+	0.0814148i
$863$	1.05767	+	0.409744i	0.0360035	+	0.0139478i	0.379176	−	0.925325i	$-0.376207\pi$
$863$	1.05767	+	0.409744i	0.0360035	+	0.0139478i	−0.343173	+	0.939272i	$0.611502\pi$
$864$	19.2193	−	9.49512i	0.653853	−	0.323031i
$865$	−29.5520	+	26.9402i	−1.00480	+	0.915993i
$866$	−1.01251	−	10.9267i	−0.0344064	−	0.371304i
$867$	1.83480	+	20.0281i	0.0623132	+	0.680188i
$868$	3.61685	−	19.3485i	0.122764	−	0.656730i
$869$	10.0787	−	35.4231i	0.341898	−	1.20165i
$870$	−6.84071	−	13.7740i	−0.231922	−	0.466982i
$871$			68.5596i			2.32305i
$872$	−6.77456	+	23.8101i	−0.229416	+	0.806312i
$873$	10.5151	−	36.6659i	0.355882	−	1.24095i
$874$	−0.328190	+	0.203207i	−0.0111012	+	0.00687358i
$875$	7.33262	−	14.7259i	0.247888	−	0.497826i
$876$	0.00367314	−	3.52152i	0.000124104	−	0.118981i
$877$	−10.8619	−	17.5426i	−0.366781	−	0.592371i	0.613568	−	0.789642i	$-0.289734\pi$
$877$	−10.8619	−	17.5426i	−0.366781	−	0.592371i	−0.980349	+	0.197270i	$0.936792\pi$
$878$	10.0567	−	3.89600i	0.339399	−	0.131484i
$879$	−30.1451	+	5.60255i	−1.01677	+	0.188969i
$880$	26.2796			0.885886
$881$	12.0496			0.405962			0.202981	−	0.979183i	$-0.434937\pi$
$881$	12.0496			0.405962			0.202981	+	0.979183i	$0.434937\pi$
$882$	3.45197	−	2.59552i	0.116234	−	0.0873956i
$883$	48.5071	+	9.06755i	1.63239	+	0.305147i	0.918594	−	0.395203i	$-0.129326\pi$
$883$	48.5071	+	9.06755i	1.63239	+	0.305147i	0.713800	+	0.700350i	$0.246973\pi$
$884$	9.09812	−	23.4849i	0.306003	−	0.789884i
$885$	−29.0208	−	46.9796i	−0.975522	−	1.57920i
$886$	−3.80916	−	4.17845i	−0.127971	−	0.140378i
$887$	20.8462	−	15.7424i	0.699948	−	0.528576i	−0.191616	−	0.981470i	$-0.561373\pi$
$887$	20.8462	−	15.7424i	0.699948	−	0.528576i	0.891565	+	0.452893i	$0.149608\pi$
$888$	0.817348	+	8.92187i	0.0274284	+	0.299398i
$889$	19.7509	−	31.8988i	0.662424	−	1.06985i
$890$	−1.27215	−	3.28379i	−0.0426425	−	0.110073i
$891$	2.61890	+	29.6064i	0.0877364	+	0.991851i
$892$	16.5721	+	10.2610i	0.554876	+	0.343565i
$893$	−5.50194	+	3.40666i	−0.184115	+	0.113999i
$894$	4.59564	−	1.77485i	0.153701	−	0.0593599i
$895$	−1.06188	−	1.16483i	−0.0354947	−	0.0389359i
$896$	17.3168	−	4.92705i	0.578513	−	0.164601i
$897$	−6.79122	+	17.4760i	−0.226752	+	0.583507i
$898$	3.15577	−	3.46172i	0.105309	−	0.115519i
$899$	−24.4885	+	49.1796i	−0.816738	+	1.64023i
$900$	5.57248	+	5.10131i	0.185749	+	0.170044i
$901$	12.0679	−	9.11329i	0.402042	−	0.303608i
$902$	0.642614	+	6.93491i	0.0213967	+	0.230907i
$903$	−6.31523	−	1.80396i	−0.210158	−	0.0600320i
$904$	2.57398	+	1.28169i	0.0856091	+	0.0426283i
$905$	11.7309	+	8.85877i	0.389949	+	0.294475i
$906$	0.181433	+	1.98046i	0.00602771	+	0.0657963i
$907$	−17.7468	+	3.31746i	−0.589274	+	0.110154i	−0.469938	−	0.882699i	$-0.655724\pi$
$907$	−17.7468	+	3.31746i	−0.589274	+	0.110154i	−0.119336	+	0.992854i	$0.538077\pi$
$908$	−19.0120	+	11.7717i	−0.630934	+	0.390658i
$909$	10.8211	+	38.3358i	0.358912	+	1.27152i
$910$	9.97820	−	0.924616i	0.330774	−	0.0306507i
$911$	13.8132	+	48.5484i	0.457653	+	1.60848i	0.756373	+	0.654141i	$0.226970\pi$
$911$	13.8132	+	48.5484i	0.457653	+	1.60848i	−0.298720	+	0.954341i	$0.596560\pi$
$912$	−2.22074	+	2.02024i	−0.0735361	+	0.0668967i
$913$	33.4523	−	25.2620i	1.10711	−	0.836051i
$914$	14.5646	−	2.72259i	0.481754	−	0.0900554i
$915$	−6.16738	−	5.63410i	−0.203887	−	0.186258i
$916$	−10.2197	−	20.5240i	−0.337670	−	0.678132i
$917$	3.19190	+	0.908173i	0.105406	+	0.0299905i
$918$	−1.23923	−	4.40779i	−0.0409007	−	0.145479i
$919$	−6.94076	+	37.1298i	−0.228955	+	1.22480i	0.654420	+	0.756131i	$0.272913\pi$
$919$	−6.94076	+	37.1298i	−0.228955	+	1.22480i	−0.883375	+	0.468667i	$0.844734\pi$
$920$	6.71695	−	1.25562i	0.221451	−	0.0413964i
$921$	−2.84526	−	7.36727i	−0.0937545	−	0.242760i
$922$	7.14031	+	6.50925i	0.235153	+	0.214371i
$923$	−20.6745	+	27.3774i	−0.680509	+	0.901140i
$924$	−1.77399	+	18.9295i	−0.0583599	+	0.622733i
$925$	−4.29247	+	2.13740i	−0.141135	+	0.0702771i
$926$	−8.40447			−0.276188
$927$	23.0561	+	19.8850i	0.757263	+	0.653110i
$928$	−38.2734			−1.25639
$929$	18.2213	−	9.07313i	0.597822	−	0.297680i	−0.121243	−	0.992623i	$-0.538688\pi$
$929$	18.2213	−	9.07313i	0.597822	−	0.297680i	0.719065	+	0.694943i	$0.244570\pi$
$930$	−0.915991	+	9.77414i	−0.0300365	+	0.320507i
$931$	−1.25513	+	1.66206i	−0.0411353	+	0.0544719i
$932$	−30.0251	−	27.3715i	−0.983504	−	0.896582i
$933$	−2.63287	−	6.81731i	−0.0861962	−	0.223189i
$934$	14.3708	−	2.68636i	0.470226	−	0.0879004i
$935$	3.55151	−	18.9989i	0.116147	−	0.621331i
$936$	4.76971	−	25.2242i	0.155903	−	0.824480i
$937$	−11.6294	−	3.30884i	−0.379915	−	0.108095i	0.0783155	−	0.996929i	$-0.475046\pi$
$937$	−11.6294	−	3.30884i	−0.379915	−	0.108095i	−0.458230	+	0.888834i	$0.651516\pi$
$938$	3.55381	+	7.13702i	0.116036	+	0.233032i
$939$	−15.7649	−	14.4018i	−0.514470	−	0.469984i
$940$	54.1990	−	10.1315i	1.76778	−	0.330454i
$941$	34.0537	−	25.7161i	1.11012	−	0.838322i	0.122078	−	0.992521i	$-0.461044\pi$
$941$	34.0537	−	25.7161i	1.11012	−	0.838322i	0.988040	+	0.154199i	$0.0492796\pi$
$942$	0.0504483	−	0.0458934i	0.00164369	−	0.00149529i
$943$	−2.81514	−	9.89419i	−0.0916736	−	0.322199i
$944$	−39.7392	+	3.68238i	−1.29340	+	0.119851i
$945$	−17.3890	+	15.7529i	−0.565666	+	0.512440i
$946$	2.25668	−	1.39728i	0.0733710	−	0.0454294i
$947$	−28.0972	+	5.25227i	−0.913035	+	0.170676i	−0.619248	−	0.785195i	$-0.712563\pi$
$947$	−28.0972	+	5.25227i	−0.913035	+	0.170676i	−0.293787	+	0.955871i	$0.594916\pi$
$948$	−3.27044	−	35.6989i	−0.106219	−	1.15945i
$949$	−5.11089	−	3.85957i	−0.165907	−	0.125287i
$950$	0.253219	+	0.126088i	0.00821552	+	0.00409084i
$951$	44.1139	+	12.6012i	1.43049	+	0.408623i
$952$	−0.561466	−	6.05918i	−0.0181972	−	0.196379i
$953$	−12.7350	+	9.61702i	−0.412527	+	0.311526i	−0.788420	−	0.615137i	$-0.789101\pi$
$953$	−12.7350	+	9.61702i	−0.412527	+	0.311526i	0.375893	+	0.926663i	$0.377336\pi$
$954$	5.00955	−	5.47224i	0.162190	−	0.177170i
$955$	−5.25354	+	10.5505i	−0.170001	+	0.341407i
$956$	−20.8251	+	22.8441i	−0.673532	+	0.738830i
$957$	19.2212	−	49.4624i	0.621333	−	1.59889i
$958$	8.54456	−	2.43114i	0.276062	−	0.0785465i
$959$	−15.8123	−	17.3452i	−0.510605	−	0.560107i
$960$	19.3352	−	7.46731i	0.624041	−	0.241006i
$961$	3.45983	−	2.14224i	0.111607	−	0.0691044i
$962$	6.66782	+	4.12854i	0.214979	+	0.133109i
$963$	−9.34895	−	10.2984i	−0.301266	−	0.331861i
$964$	4.50846	+	11.6377i	0.145208	+	0.374825i
$965$	4.53068	−	7.31729i	0.145848	−	0.235552i
$966$	0.198914	+	2.17127i	0.00639994	+	0.0698594i
$967$	−42.4459	+	32.0536i	−1.36497	+	1.03078i	−0.370163	+	0.928967i	$0.620698\pi$
$967$	−42.4459	+	32.0536i	−1.36497	+	1.03078i	−0.994804	+	0.101808i	$0.967537\pi$
$968$	0.0925683	+	0.101543i	0.00297526	+	0.00326370i
$969$	1.16042	+	1.87851i	0.0372780	+	0.0603465i
$970$	−4.39597	+	11.3473i	−0.141146	+	0.364340i
$971$	43.3771	+	8.10858i	1.39204	+	0.260217i	0.825771	−	0.564006i	$-0.190740\pi$
$971$	43.3771	+	8.10858i	1.39204	+	0.260217i	0.566266	+	0.824222i	$0.308387\pi$
$972$	12.7603	+	25.9645i	0.409285	+	0.832813i
$973$	−3.34634			−0.107279
$974$	−9.33821			−0.299216
$975$	13.5085	−	2.51060i	0.432618	−	0.0804034i
$976$	−5.62960	+	2.18092i	−0.180199	+	0.0698095i
$977$	−6.41360	−	10.3583i	−0.205189	−	0.331392i	0.731320	−	0.682034i	$-0.238904\pi$
$977$	−6.41360	−	10.3583i	−0.205189	−	0.331392i	−0.936509	+	0.350642i	$0.885963\pi$
$978$	0.00152140	−	1.45860i	4.86491e−5	−	0.0466410i
$979$	5.41630	−	10.8774i	0.173106	−	0.347643i
$980$	15.0879	−	9.34203i	0.481965	−	0.298420i
$981$	−48.7717	−	13.9868i	−1.55716	−	0.446564i
$982$	−0.960968	+	3.37745i	−0.0306657	+	0.107779i
$983$			47.5048i			1.51517i	0.652737	+	0.757585i	$0.273621\pi$
$983$			47.5048i			1.51517i	−0.652737	+	0.757585i	$0.726379\pi$
$984$	6.26495	+	12.6147i	0.199719	+	0.402141i
$985$	13.4789	−	47.3733i	0.429472	−	1.50944i
$986$	−1.50212	+	8.03562i	−0.0478371	+	0.255906i
$987$	3.33468	+	36.4002i	0.106144	+	1.15863i
$988$	0.549784	+	5.93311i	0.0174910	+	0.188757i
$989$	−2.89719	+	2.64113i	−0.0921251	+	0.0839832i
$990$	0.0197809	−	9.48218i	0.000628679	−	0.301364i
$991$	41.9872	+	16.2659i	1.33377	+	0.516704i	0.919371	−	0.393392i	$-0.128698\pi$
$991$	41.9872	+	16.2659i	1.33377	+	0.516704i	0.414397	+	0.910096i	$0.363993\pi$
$992$	20.7717	+	12.8613i	0.659502	+	0.408347i
$993$	−14.5503	+	15.9275i	−0.461740	+	0.505445i
$994$	−0.733083	+	3.92165i	−0.0232520	+	0.124387i
$995$	−19.1870	+	30.9881i	−0.608269	+	0.982388i
$996$	21.5163	−	34.6691i	0.681770	−	1.09853i
$997$	−5.99322	−	0.555353i	−0.189807	−	0.0175882i	−0.00305525	−	0.999995i	$-0.500973\pi$
$997$	−5.99322	−	0.555353i	−0.189807	−	0.0175882i	−0.186752	+	0.982407i	$0.559796\pi$
$998$	7.09510	−	6.46804i	0.224591	−	0.204742i
$999$	−18.2896	+	1.63707i	−0.578656	+	0.0517947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.2.k.a.80.19	yes	512
3.2	odd	2	inner	309.2.k.a.80.14	✓	512
103.94	odd	34	inner	309.2.k.a.197.14	yes	512
309.197	even	34	inner	309.2.k.a.197.19	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.k.a.80.14	✓	512	3.2	odd	2	inner
309.2.k.a.80.19	yes	512	1.1	even	1	trivial
309.2.k.a.197.14	yes	512	103.94	odd	34	inner
309.2.k.a.197.19	yes	512	309.197	even	34	inner

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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	309.k (of order \(34\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.339807 - 0.169204i) q^{2} +(0.161612 - 1.72449i) q^{3} +(-1.11843 + 1.48104i) q^{4} +(1.86326 + 1.69858i) q^{5} +(-0.236874 - 0.613340i) q^{6} +(1.76047 - 0.329088i) q^{7} +(-0.268956 + 1.43879i) q^{8} +(-2.94776 - 0.557399i) q^{9} +O(q^{10})\)	\(q+(0.339807 - 0.169204i) q^{2} +(0.161612 - 1.72449i) q^{3} +(-1.11843 + 1.48104i) q^{4} +(1.86326 + 1.69858i) q^{5} +(-0.236874 - 0.613340i) q^{6} +(1.76047 - 0.329088i) q^{7} +(-0.268956 + 1.43879i) q^{8} +(-2.94776 - 0.557399i) q^{9} +(0.920554 + 0.261920i) q^{10} +(1.47203 + 2.95623i) q^{11} +(2.37330 + 2.16808i) q^{12} +(5.74661 - 1.07423i) q^{13} +(0.542536 - 0.409704i) q^{14} +(3.23032 - 2.93866i) q^{15} +(-0.863728 - 3.03569i) q^{16} +(-2.31139 + 0.214181i) q^{17} +(-1.09598 + 0.309364i) q^{18} +(0.466922 - 0.289106i) q^{19} +(-4.59959 + 0.859813i) q^{20} +(-0.282998 - 3.08910i) q^{21} +(1.00041 + 0.755473i) q^{22} +(-1.65750 - 0.825338i) q^{23} +(2.43772 + 0.696340i) q^{24} +(0.125200 + 1.35112i) q^{25} +(1.77097 - 1.33738i) q^{26} +(-1.43763 + 4.99332i) q^{27} +(-1.48157 + 2.97539i) q^{28} +(6.25004 - 6.85596i) q^{29} +(0.600453 - 1.54516i) q^{30} +(-5.69587 + 1.62062i) q^{31} +(-2.77934 - 3.04879i) q^{32} +(5.33589 - 2.06074i) q^{33} +(-0.749184 + 0.463875i) q^{34} +(3.83918 + 2.37712i) q^{35} +(4.12240 - 3.74235i) q^{36} +(1.27659 + 3.29526i) q^{37} +(0.109745 - 0.177245i) q^{38} +(-0.923776 - 10.0836i) q^{39} +(-2.94504 + 2.22399i) q^{40} +(3.74280 + 4.10565i) q^{41} +(-0.618852 - 1.00181i) q^{42} +(0.764844 - 1.97429i) q^{43} +(-6.02465 - 1.12620i) q^{44} +(-4.54565 - 6.04560i) q^{45} -0.702881 q^{46} -11.7834 q^{47} +(-5.37462 + 0.998889i) q^{48} +(-3.53636 + 1.36999i) q^{49} +(0.271158 + 0.437935i) q^{50} +(-0.00419369 + 4.02059i) q^{51} +(-4.83621 + 9.71241i) q^{52} +(-5.53888 + 3.42953i) q^{53} +(0.356373 + 1.94002i) q^{54} +(-2.27863 + 8.00856i) q^{55} +2.62145i q^{56} +(-0.423101 - 0.851928i) q^{57} +(0.963751 - 3.38723i) q^{58} +(2.32349 - 12.4296i) q^{59} +(0.739392 + 8.07093i) q^{60} +(-0.176496 - 1.90469i) q^{61} +(-1.66128 + 1.51446i) q^{62} +(-5.37287 - 0.0112084i) q^{63} +(4.42578 + 1.71456i) q^{64} +(12.5321 + 7.75953i) q^{65} +(1.46449 - 1.60311i) q^{66} +(-2.15489 + 11.5276i) q^{67} +(2.26791 - 3.66280i) q^{68} +(-1.69116 + 2.72497i) q^{69} +(1.70680 + 0.158158i) q^{70} +(-4.33671 + 3.95343i) q^{71} +(1.59480 - 4.09130i) q^{72} +(-0.738037 - 0.809588i) q^{73} +(0.991366 + 0.903749i) q^{74} +(2.35023 + 0.00245142i) q^{75} +(-0.0940421 + 1.01488i) q^{76} +(3.56431 + 4.71991i) q^{77} +(-2.02009 - 3.27017i) q^{78} +(-8.24146 - 7.51308i) q^{79} +(3.54702 - 7.12338i) q^{80} +(8.37861 + 3.28616i) q^{81} +(1.96652 + 0.761833i) q^{82} +(-2.33241 - 12.4773i) q^{83} +(4.89160 + 3.03581i) q^{84} +(-4.67051 - 3.52700i) q^{85} +(-0.0741579 - 0.800291i) q^{86} +(-10.8130 - 11.8862i) q^{87} +(-4.64930 + 1.32284i) q^{88} +(-2.21739 - 2.93629i) q^{89} +(-2.56758 - 1.28519i) q^{90} +(9.76319 - 3.78228i) q^{91} +(3.07616 - 1.53175i) q^{92} +(1.87422 + 10.0844i) q^{93} +(-4.00409 + 1.99380i) q^{94} +(1.36107 + 0.254427i) q^{95} +(-5.70681 + 4.30024i) q^{96} +(-1.17316 + 12.6604i) q^{97} +(-0.969872 + 1.06390i) q^{98} +(-2.69138 - 9.53476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 17 q^{3} - 2 q^{4} - 17 q^{6} - 18 q^{7} - 13 q^{9}+O(q^{10}) \) 512 * q - 17 * q^3 - 2 * q^4 - 17 * q^6 - 18 * q^7 - 13 * q^9	\( 512 q - 17 q^{3} - 2 q^{4} - 17 q^{6} - 18 q^{7} - 13 q^{9} + 34 q^{10} - 17 q^{12} - 38 q^{13} - 23 q^{15} - 50 q^{16} + 5 q^{18} - 22 q^{19} - 51 q^{21} - 34 q^{22} - 17 q^{24} + 6 q^{25} - 17 q^{27} - 152 q^{28} - 21 q^{30} - 34 q^{31} - 11 q^{33} - 128 q^{34} + 149 q^{36} + 68 q^{37} + 119 q^{39} - 34 q^{40} - 17 q^{42} - 34 q^{43} - 17 q^{45} - 96 q^{46} - 187 q^{48} - 34 q^{49} - 17 q^{51} + 2 q^{52} - 17 q^{54} - 80 q^{55} - 14 q^{58} - 172 q^{60} - 38 q^{61} - 61 q^{63} + 56 q^{64} + 101 q^{66} - 136 q^{67} + 119 q^{69} - 34 q^{70} - 101 q^{72} - 136 q^{73} - 255 q^{75} - 114 q^{76} - 17 q^{78} - 54 q^{79} - 5 q^{81} - 66 q^{82} - 17 q^{84} - 17 q^{87} - 17 q^{90} + 244 q^{91} + 35 q^{93} - 34 q^{94} - 17 q^{96} + 236 q^{97} - 17 q^{99}+O(q^{100}) \) 512 * q - 17 * q^3 - 2 * q^4 - 17 * q^6 - 18 * q^7 - 13 * q^9 + 34 * q^10 - 17 * q^12 - 38 * q^13 - 23 * q^15 - 50 * q^16 + 5 * q^18 - 22 * q^19 - 51 * q^21 - 34 * q^22 - 17 * q^24 + 6 * q^25 - 17 * q^27 - 152 * q^28 - 21 * q^30 - 34 * q^31 - 11 * q^33 - 128 * q^34 + 149 * q^36 + 68 * q^37 + 119 * q^39 - 34 * q^40 - 17 * q^42 - 34 * q^43 - 17 * q^45 - 96 * q^46 - 187 * q^48 - 34 * q^49 - 17 * q^51 + 2 * q^52 - 17 * q^54 - 80 * q^55 - 14 * q^58 - 172 * q^60 - 38 * q^61 - 61 * q^63 + 56 * q^64 + 101 * q^66 - 136 * q^67 + 119 * q^69 - 34 * q^70 - 101 * q^72 - 136 * q^73 - 255 * q^75 - 114 * q^76 - 17 * q^78 - 54 * q^79 - 5 * q^81 - 66 * q^82 - 17 * q^84 - 17 * q^87 - 17 * q^90 + 244 * q^91 + 35 * q^93 - 34 * q^94 - 17 * q^96 + 236 * q^97 - 17 * q^99

Introduction

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