LMFDB - Embedded newform 76.2.k.a.51.5

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			51.5
Character	$\chi$	$=$	76.51
Dual form			76.2.k.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.223323 + 1.39647i) q^{2} +(0.855656 + 0.311433i) q^{3} +(-1.90025 + 0.623726i) q^{4} +(-0.00805719 - 0.0456946i) q^{5} +(-0.243820 + 1.26445i) q^{6} +(1.20959 + 0.698356i) q^{7} +(-1.29538 - 2.51435i) q^{8} +(-1.66298 - 1.39540i) q^{9} +O(q^{10})$	\(q+(0.223323 + 1.39647i) q^{2} +(0.855656 + 0.311433i) q^{3} +(-1.90025 + 0.623726i) q^{4} +(-0.00805719 - 0.0456946i) q^{5} +(-0.243820 + 1.26445i) q^{6} +(1.20959 + 0.698356i) q^{7} +(-1.29538 - 2.51435i) q^{8} +(-1.66298 - 1.39540i) q^{9} +(0.0620117 - 0.0214562i) q^{10} +(1.13484 - 0.655201i) q^{11} +(-1.82021 - 0.0581071i) q^{12} +(-0.681875 - 1.87343i) q^{13} +(-0.705104 + 1.84511i) q^{14} +(0.00733663 - 0.0416081i) q^{15} +(3.22193 - 2.37048i) q^{16} +(-0.910294 + 0.763828i) q^{17} +(1.57726 - 2.63392i) q^{18} +(4.35476 + 0.189811i) q^{19} +(0.0438116 + 0.0818058i) q^{20} +(0.817500 + 0.974258i) q^{21} +(1.16840 + 1.43845i) q^{22} +(-8.42847 - 1.48617i) q^{23} +(-0.325350 - 2.55485i) q^{24} +(4.69644 - 1.70936i) q^{25} +(2.46392 - 1.37060i) q^{26} +(-2.35422 - 4.07762i) q^{27} +(-2.73411 - 0.572602i) q^{28} +(-3.45448 + 4.11689i) q^{29} +(0.0597429 + 0.000953352i) q^{30} +(-3.06782 + 5.31361i) q^{31} +(4.02983 + 3.96995i) q^{32} +(1.17509 - 0.207199i) q^{33} +(-1.26995 - 1.10062i) q^{34} +(0.0221652 - 0.0608984i) q^{35} +(4.03043 + 1.61438i) q^{36} +4.41365i q^{37} +(0.707452 + 6.12368i) q^{38} -1.81537i q^{39} +(-0.104455 + 0.0794507i) q^{40} +(-2.39968 + 6.59307i) q^{41} +(-1.17796 + 1.35919i) q^{42} +(0.406170 - 0.0716188i) q^{43} +(-1.74782 + 1.95288i) q^{44} +(-0.0503634 + 0.0872320i) q^{45} +(0.193118 - 12.1020i) q^{46} +(-5.36271 + 6.39102i) q^{47} +(3.49511 - 1.02490i) q^{48} +(-2.52460 - 4.37273i) q^{49} +(3.43590 + 6.17670i) q^{50} +(-1.01678 + 0.370078i) q^{51} +(2.46425 + 3.13470i) q^{52} +(5.17907 + 0.913210i) q^{53} +(5.16853 - 4.19822i) q^{54} +(-0.0390828 - 0.0465770i) q^{55} +(0.189033 - 3.94597i) q^{56} +(3.66707 + 1.51863i) q^{57} +(-6.52057 - 3.90468i) q^{58} +(8.98054 - 7.53557i) q^{59} +(0.0120106 + 0.0836420i) q^{60} +(2.12915 - 12.0750i) q^{61} +(-8.10541 - 3.09746i) q^{62} +(-1.03703 - 2.84921i) q^{63} +(-4.64396 + 6.51411i) q^{64} +(-0.0801118 + 0.0462526i) q^{65} +(0.551770 + 1.59470i) q^{66} +(8.40871 + 7.05575i) q^{67} +(1.25337 - 2.01924i) q^{68} +(-6.74903 - 3.89655i) q^{69} +(0.0899927 + 0.0173530i) q^{70} +(-1.06152 - 6.02019i) q^{71} +(-1.35434 + 5.98890i) q^{72} +(-6.09478 - 2.21832i) q^{73} +(-6.16352 + 0.985667i) q^{74} +4.55089 q^{75} +(-8.39355 + 2.35549i) q^{76} +1.83025 q^{77} +(2.53511 - 0.405414i) q^{78} +(10.3375 + 3.76254i) q^{79} +(-0.134278 - 0.128125i) q^{80} +(0.386407 + 2.19142i) q^{81} +(-9.74293 - 1.87870i) q^{82} +(0.635962 + 0.367173i) q^{83} +(-2.16113 - 1.34144i) q^{84} +(0.0422372 + 0.0354412i) q^{85} +(0.190720 + 0.551210i) q^{86} +(-4.23798 + 2.44680i) q^{87} +(-3.11746 - 2.00466i) q^{88} +(-4.73119 - 12.9988i) q^{89} +(-0.133064 - 0.0508501i) q^{90} +(0.483537 - 2.74227i) q^{91} +(16.9432 - 2.43296i) q^{92} +(-4.27983 + 3.59121i) q^{93} +(-10.1225 - 6.06159i) q^{94} +(-0.0264138 - 0.200518i) q^{95} +(2.21177 + 4.65193i) q^{96} +(5.45960 + 6.50649i) q^{97} +(5.54259 - 4.50205i) q^{98} +(-2.80148 - 0.493977i) 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	0.223323	+	1.39647i	0.157913	+	0.987453i
$2$	0.223323	+	1.39647i	0.157913	+	0.987453i
$3$	0.855656	+	0.311433i	0.494013	+	0.179806i	0.576999	−	0.816745i	$-0.304223\pi$
$3$	0.855656	+	0.311433i	0.494013	+	0.179806i	−0.0829861	+	0.996551i	$0.526446\pi$
$4$	−1.90025	+	0.623726i	−0.950127	+	0.311863i
$5$	−0.00805719	−	0.0456946i	−0.00360328	−	0.0204352i	0.982953	−	0.183856i	$-0.0588582\pi$
$5$	−0.00805719	−	0.0456946i	−0.00360328	−	0.0204352i	−0.986556	+	0.163421i	$0.947747\pi$
$6$	−0.243820	+	1.26445i	−0.0995390	+	0.516209i
$7$	1.20959	+	0.698356i	0.457181	+	0.263954i	0.710858	−	0.703335i	$-0.248307\pi$
$7$	1.20959	+	0.698356i	0.457181	+	0.263954i	−0.253677	+	0.967289i	$0.581640\pi$
$8$	−1.29538	−	2.51435i	−0.457988	−	0.888959i
$9$	−1.66298	−	1.39540i	−0.554326	−	0.465134i
$10$	0.0620117	−	0.0214562i	0.0196098	−	0.00678506i
$11$	1.13484	−	0.655201i	0.342167	−	0.197550i	−0.319063	−	0.947734i	$-0.603368\pi$
$11$	1.13484	−	0.655201i	0.342167	−	0.197550i	0.661230	+	0.750183i	$0.270035\pi$
$12$	−1.82021	−	0.0581071i	−0.525450	−	0.0167741i
$13$	−0.681875	−	1.87343i	−0.189118	−	0.519597i	0.808506	−	0.588488i	$-0.200276\pi$
$13$	−0.681875	−	1.87343i	−0.189118	−	0.519597i	−0.997624	+	0.0688902i	$0.978054\pi$
$14$	−0.705104	+	1.84511i	−0.188447	+	0.493127i
$15$	0.00733663	−	0.0416081i	0.00189431	−	0.0107432i
$16$	3.22193	−	2.37048i	0.805483	−	0.592619i
$17$	−0.910294	+	0.763828i	−0.220779	+	0.185255i	−0.746468	−	0.665421i	$-0.768252\pi$
$17$	−0.910294	+	0.763828i	−0.220779	+	0.185255i	0.525689	+	0.850677i	$0.323807\pi$
$18$	1.57726	−	2.63392i	0.371763	−	0.620821i
$19$	4.35476	+	0.189811i	0.999051	+	0.0435456i
$19$	4.35476	+	0.189811i	0.999051	+	0.0435456i
$20$	0.0438116	+	0.0818058i	0.00979658	+	0.0182923i
$21$	0.817500	+	0.974258i	0.178393	+	0.212601i
$22$	1.16840	+	1.43845i	0.249105	+	0.306679i
$23$	−8.42847	−	1.48617i	−1.75746	−	0.309887i	−0.800331	−	0.599559i	$-0.795343\pi$
$23$	−8.42847	−	1.48617i	−1.75746	−	0.309887i	−0.957126	+	0.289672i	$0.906454\pi$
$24$	−0.325350	−	2.55485i	−0.0664118	−	0.521506i
$25$	4.69644	−	1.70936i	0.939288	−	0.341873i
$26$	2.46392	−	1.37060i	0.483214	−	0.268796i
$27$	−2.35422	−	4.07762i	−0.453069	−	0.784739i
$28$	−2.73411	−	0.572602i	−0.516698	−	0.108212i
$29$	−3.45448	+	4.11689i	−0.641480	+	0.764487i	−0.984603	−	0.174804i	$-0.944071\pi$
$29$	−3.45448	+	4.11689i	−0.641480	+	0.764487i	0.343123	+	0.939291i	$0.388515\pi$
$30$	0.0597429		0.000953352i	0.0109075		0.000174057i
$31$	−3.06782	+	5.31361i	−0.550996	+	0.954353i	0.447207	+	0.894431i	$0.352419\pi$
$31$	−3.06782	+	5.31361i	−0.550996	+	0.954353i	−0.998203	+	0.0599227i	$0.980915\pi$
$32$	4.02983	+	3.96995i	0.712380	+	0.701794i
$33$	1.17509	−	0.207199i	0.204556	−	0.0360688i
$34$	−1.26995	−	1.10062i	−0.217795	−	0.188754i
$35$	0.0221652	−	0.0608984i	0.00374660	−	0.0102937i
$36$	4.03043	+	1.61438i	0.671738	+	0.269063i
$37$			4.41365i			0.725599i	0.931867	+	0.362800i	$0.118179\pi$
$37$			4.41365i			0.725599i	−0.931867	+	0.362800i	$0.881821\pi$
$38$	0.707452	+	6.12368i	0.114764	+	0.993393i
$39$		−	1.81537i		−	0.290693i
$40$	−0.104455	+	0.0794507i	−0.0165158	+	0.0125623i
$41$	−2.39968	+	6.59307i	−0.374767	+	1.02966i	0.598727	+	0.800953i	$0.295673\pi$
$41$	−2.39968	+	6.59307i	−0.374767	+	1.02966i	−0.973494	+	0.228712i	$0.926549\pi$
$42$	−1.17796	+	1.35919i	−0.181763	+	0.209727i
$43$	0.406170	−	0.0716188i	0.0619404	−	0.0109218i	−0.142592	−	0.989782i	$-0.545544\pi$
$43$	0.406170	−	0.0716188i	0.0619404	−	0.0109218i	0.204532	+	0.978860i	$0.434433\pi$
$44$	−1.74782	+	1.95288i	−0.263494	+	0.294408i
$45$	−0.0503634	+	0.0872320i	−0.00750774	+	0.0130038i
$46$	0.193118	−	12.1020i	0.0284737	−	1.78434i
$47$	−5.36271	+	6.39102i	−0.782231	+	0.932227i	−0.999032	−	0.0439892i	$-0.985993\pi$
$47$	−5.36271	+	6.39102i	−0.782231	+	0.932227i	0.216801	+	0.976216i	$0.430438\pi$
$48$	3.49511	−	1.02490i	0.504476	−	0.147931i
$49$	−2.52460	−	4.37273i	−0.360657	−	0.624676i
$50$	3.43590	+	6.17670i	0.485909	+	0.873517i
$51$	−1.01678	+	0.370078i	−0.142378	+	0.0518213i
$52$	2.46425	+	3.13470i	0.341729	+	0.434705i
$53$	5.17907	+	0.913210i	0.711400	+	0.125439i	0.517626	−	0.855607i	$-0.326816\pi$
$53$	5.17907	+	0.913210i	0.711400	+	0.125439i	0.193774	+	0.981046i	$0.437927\pi$
$54$	5.16853	−	4.19822i	0.703347	−	0.571305i
$55$	−0.0390828	−	0.0465770i	−0.00526992	−	0.00628044i
$56$	0.189033	−	3.94597i	0.0252606	−	0.527303i
$57$	3.66707	+	1.51863i	0.485715	+	0.201148i
$58$	−6.52057	−	3.90468i	−0.856193	−	0.512709i
$59$	8.98054	−	7.53557i	1.16917	−	0.981048i	0.169178	−	0.985586i	$-0.445889\pi$
$59$	8.98054	−	7.53557i	1.16917	−	0.981048i	0.999990	+	0.00453778i	$0.00144442\pi$
$60$	0.0120106	+	0.0836420i	0.00155056	+	0.0107981i
$61$	2.12915	−	12.0750i	0.272610	−	1.54605i	−0.473841	−	0.880610i	$-0.657133\pi$
$61$	2.12915	−	12.0750i	0.272610	−	1.54605i	0.746452	−	0.665440i	$-0.231756\pi$
$62$	−8.10541	−	3.09746i	−1.02939	−	0.393378i
$63$	−1.03703	−	2.84921i	−0.130653	−	0.358967i
$64$	−4.64396	+	6.51411i	−0.580495	+	0.814264i
$65$	−0.0801118	+	0.0462526i	−0.00993665	+	0.00573693i
$66$	0.551770	+	1.59470i	0.0679182	+	0.196294i
$67$	8.40871	+	7.05575i	1.02729	+	0.861997i	0.990526	−	0.137327i	$-0.0438511\pi$
$67$	8.40871	+	7.05575i	1.02729	+	0.861997i	0.0367622	+	0.999324i	$0.488296\pi$
$68$	1.25337	−	2.01924i	0.151994	−	0.244869i
$69$	−6.74903	−	3.89655i	−0.812487	−	0.469090i
$70$	0.0899927	+	0.0173530i	0.0107562	+	0.00207408i
$71$	−1.06152	−	6.02019i	−0.125979	−	0.714465i	−0.980721	−	0.195412i	$-0.937396\pi$
$71$	−1.06152	−	6.02019i	−0.125979	−	0.714465i	0.854742	−	0.519053i	$-0.173715\pi$
$72$	−1.35434	+	5.98890i	−0.159611	+	0.705798i
$73$	−6.09478	−	2.21832i	−0.713341	−	0.259635i	−0.0402446	−	0.999190i	$-0.512814\pi$
$73$	−6.09478	−	2.21832i	−0.713341	−	0.259635i	−0.673096	+	0.739555i	$0.735036\pi$
$74$	−6.16352	+	0.985667i	−0.716495	+	0.114581i
$75$	4.55089			0.525492
$76$	−8.39355	+	2.35549i	−0.962806	+	0.270194i
$77$	1.83025			0.208577
$78$	2.53511	−	0.405414i	0.287045	−	0.0459041i
$79$	10.3375	+	3.76254i	1.16306	+	0.423319i	0.850189	−	0.526477i	$-0.176488\pi$
$79$	10.3375	+	3.76254i	1.16306	+	0.423319i	0.312870	+	0.949796i	$0.398710\pi$
$80$	−0.134278	−	0.128125i	−0.0150127	−	0.0143249i
$81$	0.386407	+	2.19142i	0.0429341	+	0.243491i
$82$	−9.74293	−	1.87870i	−1.07593	−	0.207468i
$83$	0.635962	+	0.367173i	0.0698060	+	0.0403025i	0.534497	−	0.845171i	$-0.320501\pi$
$83$	0.635962	+	0.367173i	0.0698060	+	0.0403025i	−0.464691	+	0.885473i	$0.653835\pi$
$84$	−2.16113	−	1.34144i	−0.235798	−	0.146363i
$85$	0.0422372	+	0.0354412i	0.00458127	+	0.00384414i
$86$	0.190720	+	0.551210i	0.0205659	+	0.0594385i
$87$	−4.23798	+	2.44680i	−0.454359	+	0.262324i
$88$	−3.11746	−	2.00466i	−0.332323	−	0.213697i
$89$	−4.73119	−	12.9988i	−0.501506	−	1.37788i	−0.889805	−	0.456342i	$-0.849159\pi$
$89$	−4.73119	−	12.9988i	−0.501506	−	1.37788i	0.388299	−	0.921533i	$-0.373063\pi$
$90$	−0.133064	−	0.0508501i	−0.0140262	−	0.00536007i
$91$	0.483537	−	2.74227i	0.0506885	−	0.287469i
$92$	16.9432	−	2.43296i	1.76645	−	0.253654i
$93$	−4.27983	+	3.59121i	−0.443798	+	0.372391i
$94$	−10.1225	−	6.06159i	−1.04405	−	0.625206i
$95$	−0.0264138	−	0.200518i	−0.00271000	−	0.0205728i
$96$	2.21177	+	4.65193i	0.225738	+	0.474786i
$97$	5.45960	+	6.50649i	0.554338	+	0.660634i	0.968338	−	0.249642i	$-0.0803131\pi$
$97$	5.45960	+	6.50649i	0.554338	+	0.660634i	−0.414000	+	0.910277i	$0.635869\pi$
$98$	5.54259	−	4.50205i	0.559886	−	0.454776i
$99$	−2.80148	−	0.493977i	−0.281560	−	0.0496466i
$100$	−7.85825	+	6.17752i	−0.785825	+	0.617752i
$101$	9.90522	−	3.60521i	0.985606	−	0.358731i	0.201589	−	0.979470i	$-0.435389\pi$
$101$	9.90522	−	3.60521i	0.985606	−	0.358731i	0.784017	+	0.620739i	$0.213167\pi$
$102$	−0.743872	−	1.33726i	−0.0736543	−	0.132408i
$103$	−0.289877	−	0.502082i	−0.0285624	−	0.0494716i	0.851391	−	0.524532i	$-0.175760\pi$
$103$	−0.289877	−	0.502082i	−0.0285624	−	0.0494716i	−0.879953	+	0.475060i	$0.842426\pi$
$104$	−3.82719	+	4.14129i	−0.375287	+	0.406087i
$105$	0.0379316	−	0.0452051i	0.00370174	−	0.00441157i
$106$	−0.118666	+	7.43635i	−0.0115259	+	0.722282i
$107$	−0.422452	+	0.731708i	−0.0408400	+	0.0707369i	−0.885723	−	0.464214i	$-0.846337\pi$
$107$	−0.422452	+	0.731708i	−0.0408400	+	0.0707369i	0.844883	+	0.534951i	$0.179670\pi$
$108$	7.01693	+	6.28013i	0.675204	+	0.604306i
$109$	7.99713	−	1.41011i	0.765986	−	0.135064i	0.223014	−	0.974815i	$-0.428410\pi$
$109$	7.99713	−	1.41011i	0.765986	−	0.135064i	0.542971	+	0.839751i	$0.317299\pi$
$110$	0.0563153	−	0.0649796i	0.00536945	−	0.00619556i
$111$	−1.37456	+	3.77656i	−0.130467	+	0.358456i
$112$	5.55264	−	0.617246i	0.524676	−	0.0583243i
$113$			14.2204i			1.33774i	0.743378	+	0.668872i	$0.233223\pi$
$113$			14.2204i			1.33774i	−0.743378	+	0.668872i	$0.766777\pi$
$114$	−1.30178	+	5.46009i	−0.121923	+	0.511384i
$115$			0.397110i			0.0370307i
$116$	3.99657	−	9.97778i	0.371073	−	0.926413i
$117$	−1.48026	+	4.06697i	−0.136850	+	0.375991i
$118$	12.5288	+	10.8582i	1.15337	+	0.999578i
$119$	−1.63450	+	0.288207i	−0.149835	+	0.0264199i
$120$	−0.114121	+	0.0354516i	−0.0104178	+	0.00323628i
$121$	−4.64142	+	8.03918i	−0.421948	+	0.730835i
$122$	17.3379	+	0.276671i	1.56970	+	0.0250486i
$123$	−4.10660	+	4.89406i	−0.370280	+	0.441283i
$124$	2.51539	−	12.0107i	0.225889	−	1.07859i
$125$	−0.231948	−	0.401745i	−0.0207460	−	0.0359332i
$126$	3.74725	−	2.08447i	0.333831	−	0.185700i
$127$	−12.3119	+	4.48118i	−1.09251	+	0.397641i	−0.824550	−	0.565790i	$-0.808571\pi$
$127$	−12.3119	+	4.48118i	−1.09251	+	0.397641i	−0.267959	+	0.963430i	$0.586349\pi$
$128$	−10.1339	−	5.03040i	−0.895715	−	0.444628i
$129$	0.369846	+	0.0652139i	0.0325632	+	0.00574176i
$130$	−0.0824811	−	0.101544i	−0.00723407	−	0.00890604i
$131$	0.872574	+	1.03989i	0.0762372	+	0.0908559i	0.802815	−	0.596228i	$-0.203335\pi$
$131$	0.872574	+	1.03989i	0.0762372	+	0.0908559i	−0.726578	+	0.687084i	$0.758890\pi$
$132$	−2.10372	+	1.12666i	−0.183106	+	0.0980634i
$133$	5.13491	+	3.27077i	0.445253	+	0.283612i
$134$	−7.97528	+	13.3182i	−0.688959	+	1.15052i
$135$	−0.167357	+	0.140429i	−0.0144038	+	0.0120862i
$136$	3.09972	+	1.29935i	0.265798	+	0.111419i
$137$	1.33938	−	7.59599i	0.114431	−	0.648969i	−0.872600	−	0.488436i	$-0.837568\pi$
$137$	1.33938	−	7.59599i	0.114431	−	0.648969i	0.987030	−	0.160533i	$-0.0513213\pi$
$138$	3.93421	−	10.2950i	0.334902	−	0.876368i
$139$	−5.84051	−	16.0467i	−0.495386	−	1.36106i	−0.895690	−	0.444679i	$-0.853318\pi$
$139$	−5.84051	−	16.0467i	−0.495386	−	1.36106i	0.400304	−	0.916382i	$-0.368904\pi$
$140$	−0.00413558	+	0.129547i	−0.000349520	+	0.0109488i
$141$	−6.57901	+	3.79839i	−0.554053	+	0.319882i
$142$	8.16995	−	2.82683i	0.685607	−	0.237222i
$143$	−2.00130	−	1.67929i	−0.167357	−	0.140429i
$144$	−8.66577	−	0.553844i	−0.722147	−	0.0461536i
$145$	0.215953	+	0.124680i	0.0179339	+	0.0103541i
$146$	1.73671	−	9.00658i	0.143731	−	0.745390i
$147$	−0.798373	−	4.52780i	−0.0658487	−	0.373447i
$148$	−2.75291	−	8.38705i	−0.226288	−	0.689411i
$149$	−12.5718	−	4.57575i	−1.02992	−	0.374860i	−0.228870	−	0.973457i	$-0.573503\pi$
$149$	−12.5718	−	4.57575i	−1.02992	−	0.374860i	−0.801051	+	0.598597i	$0.795725\pi$
$150$	1.01632	+	6.35518i	0.0829819	+	0.518898i
$151$	−0.552457			−0.0449583			−0.0224792	−	0.999747i	$-0.507156\pi$
$151$	−0.552457			−0.0449583			−0.0224792	+	0.999747i	$0.507156\pi$
$152$	−5.16384	−	11.1953i	−0.418843	−	0.908059i
$153$	2.57965			0.208552
$154$	0.408737	+	2.55589i	0.0329370	+	0.205960i
$155$	0.267521	+	0.0973698i	0.0214878	+	0.00782093i
$156$	1.13230	+	3.44967i	0.0906563	+	0.276195i
$157$	1.20691	+	6.84471i	0.0963216	+	0.546267i	0.994334	+	0.106298i	$0.0338996\pi$
$157$	1.20691	+	6.84471i	0.0963216	+	0.546267i	−0.898013	+	0.439970i	$0.854989\pi$
$158$	−2.94568	+	15.2763i	−0.234345	+	1.21531i
$159$	4.14710	+	2.39433i	0.328886	+	0.189883i
$160$	0.148936	−	0.216128i	0.0117744	−	0.0170864i
$161$	−9.15710	−	7.68372i	−0.721680	−	0.605562i
$162$	−2.97396	+	1.02900i	−0.233656	+	0.0808458i
$163$	−14.1181	+	8.15109i	−1.10582	+	0.638443i	−0.937742	−	0.347332i	$-0.887088\pi$
$163$	−14.1181	+	8.15109i	−1.10582	+	0.638443i	−0.168073	+	0.985775i	$0.553755\pi$
$164$	0.447732	−	14.0253i	0.0349620	−	1.09519i
$165$	−0.0189358	−	0.0520256i	−0.00147415	−	0.00405019i
$166$	−0.370721	+	0.970100i	−0.0287735	+	0.0752944i
$167$	2.56785	−	14.5630i	0.198706	−	1.12692i	−0.708335	−	0.705876i	$-0.750553\pi$
$167$	2.56785	−	14.5630i	0.198706	−	1.12692i	0.907041	−	0.421042i	$-0.138336\pi$
$168$	1.39065	−	3.31752i	0.107291	−	0.255953i
$169$	6.91377	−	5.80134i	0.531829	−	0.446257i
$170$	−0.0400601	+	0.0668978i	−0.00307247	+	0.00513083i
$171$	−6.97701	−	6.39230i	−0.533545	−	0.488832i
$172$	−0.727156	+	0.389433i	−0.0554451	+	0.0296940i
$173$	−1.26345	−	1.50572i	−0.0960586	−	0.114478i	0.715874	−	0.698230i	$-0.246029\pi$
$173$	−1.26345	−	1.50572i	−0.0960586	−	0.114478i	−0.811932	+	0.583752i	$0.801584\pi$
$174$	−4.36332	−	5.37178i	−0.330782	−	0.407234i
$175$	6.87450	+	1.21216i	0.519663	+	0.0916307i
$176$	2.10324	−	4.80113i	0.158538	−	0.361899i
$177$	10.0311	−	3.65102i	0.753983	−	0.274427i
$178$	17.0959	−	9.50990i	1.28139	−	0.712797i
$179$	11.4727	+	19.8714i	0.857512	+	1.48526i	0.874294	+	0.485396i	$0.161325\pi$
$179$	11.4727	+	19.8714i	0.857512	+	1.48526i	−0.0167821	+	0.999859i	$0.505342\pi$
$180$	0.0412944	−	0.197176i	0.00307790	−	0.0146966i
$181$	−13.8104	+	16.4586i	−1.02652	+	1.22336i	−0.0520937	+	0.998642i	$0.516589\pi$
$181$	−13.8104	+	16.4586i	−1.02652	+	1.22336i	−0.974425	+	0.224715i	$0.927855\pi$
$182$	3.93749	+	0.0628327i	0.291866	+	0.00465747i
$183$	5.58239	−	9.66899i	0.412662	−	0.714752i
$184$	7.18136	+	23.1173i	0.529417	+	1.70423i
$185$	0.201680	−	0.0355616i	0.0148278	−	0.00261454i
$186$	−5.97079	−	5.17466i	−0.437800	−	0.379424i
$187$	−0.532579	+	1.46325i	−0.0389460	+	0.107003i
$188$	6.20425	−	15.4894i	0.452492	−	1.12968i
$189$		−	6.57632i		−	0.478357i
$190$	0.274119	−	0.0816664i	0.0198867	−	0.00592470i
$191$			7.68079i			0.555762i	0.960615	+	0.277881i	$0.0896321\pi$
$191$			7.68079i			0.555762i	−0.960615	+	0.277881i	$0.910368\pi$
$192$	−6.00234	+	4.12756i	−0.433182	+	0.297881i
$193$	1.33031	−	3.65500i	0.0957578	−	0.263093i	−0.882561	−	0.470199i	$-0.844182\pi$
$193$	1.33031	−	3.65500i	0.0957578	−	0.263093i	0.978318	+	0.207106i	$0.0664045\pi$
$194$	−7.86687	+	9.07721i	−0.564808	+	0.651706i
$195$	−0.0829528	+	0.0146268i	−0.00594037	+	0.00104745i
$196$	7.52477	+	6.73464i	0.537483	+	0.481046i
$197$	5.83464	−	10.1059i	0.415701	−	0.720015i	−0.579801	−	0.814758i	$-0.696870\pi$
$197$	5.83464	−	10.1059i	0.415701	−	0.720015i	0.995502	+	0.0947432i	$0.0302030\pi$
$198$	0.0641894	−	4.02250i	0.00456174	−	0.285867i
$199$	13.9328	−	16.6044i	0.987668	−	1.17706i	0.00346853	−	0.999994i	$-0.498896\pi$
$199$	13.9328	−	16.6044i	0.987668	−	1.17706i	0.984200	−	0.177063i	$-0.0566596\pi$
$200$	−10.3816	−	9.59423i	−0.734093	−	0.678415i
$201$	4.99757	+	8.65605i	0.352502	+	0.610551i
$202$	7.24662	+	13.0272i	0.509870	+	0.916592i
$203$	−7.05354	+	2.56728i	−0.495062	+	0.180188i
$204$	1.70131	−	1.33743i	0.119116	−	0.0936392i
$205$	0.320602	+	0.0565308i	0.0223918	+	0.00394828i
$206$	0.636406	−	0.516931i	0.0443405	−	0.0360163i
$207$	11.9425	+	14.2326i	0.830064	+	0.989232i
$208$	−6.63789	−	4.41971i	−0.460255	−	0.306452i
$209$	5.06633	−	2.63784i	0.350445	−	0.182463i
$210$	0.0715985	+	0.0428750i	0.00494077	+	0.00295865i
$211$	−8.82488	+	7.40495i	−0.607530	+	0.509778i	−0.893856	−	0.448354i	$-0.852010\pi$
$211$	−8.82488	+	7.40495i	−0.607530	+	0.509778i	0.286326	+	0.958132i	$0.407566\pi$
$212$	−10.4111	+	1.49499i	−0.715040	+	0.102676i
$213$	0.966590	−	5.48181i	0.0662297	−	0.375607i
$214$	−1.11615	−	0.426534i	−0.0762985	−	0.0291573i
$215$	−0.00654518	−	0.0179827i	−0.000446377	−	0.00122641i
$216$	−7.20297	+	11.2014i	−0.490100	+	0.762160i
$217$	−7.42159	+	4.28485i	−0.503810	+	0.290875i
$218$	3.75511	+	10.8528i	0.254328	+	0.735047i
$219$	−4.52418	−	3.79624i	−0.305716	−	0.256526i
$220$	0.103318	+	0.0641312i	0.00696573	+	0.00432373i
$221$	2.05169	+	1.18454i	0.138011	+	0.0796810i
$222$	−5.58083	−	1.07613i	−0.374561	−	0.0722254i
$223$	0.353870	+	2.00689i	0.0236969	+	0.134392i	0.994361	−	0.106048i	$-0.0338196\pi$
$223$	0.353870	+	2.00689i	0.0236969	+	0.134392i	−0.970664	+	0.240439i	$0.922709\pi$
$224$	2.10200	+	7.61625i	0.140446	+	0.508882i
$225$	−10.1953	−	3.71079i	−0.679688	−	0.247386i
$226$	−19.8584	+	3.17574i	−1.32096	+	0.211247i
$227$	12.3915			0.822456			0.411228	−	0.911533i	$-0.365100\pi$
$227$	12.3915			0.822456			0.411228	+	0.911533i	$0.365100\pi$
$228$	−7.91557	−	0.598539i	−0.524221	−	0.0396392i
$229$	9.29197			0.614031			0.307015	−	0.951705i	$-0.400670\pi$
$229$	9.29197			0.614031			0.307015	+	0.951705i	$0.400670\pi$
$230$	−0.554551	+	0.0886835i	−0.0365660	+	0.00584762i
$231$	1.56607	+	0.570002i	0.103040	+	0.0375034i
$232$	14.8262	+	3.35283i	0.973387	+	0.220124i
$233$	1.38093	+	7.83166i	0.0904679	+	0.513069i	0.996042	+	0.0888814i	$0.0283292\pi$
$233$	1.38093	+	7.83166i	0.0904679	+	0.513069i	−0.905574	+	0.424188i	$0.860560\pi$
$234$	−6.00997	−	1.15889i	−0.392884	−	0.0757587i
$235$	0.335243	+	0.193553i	0.0218689	+	0.0126260i
$236$	−12.3652	+	19.9209i	−0.804905	+	1.29674i
$237$	7.67356	+	6.43888i	0.498451	+	0.418250i
$238$	−0.767494	−	2.21817i	−0.0497493	−	0.143783i
$239$	18.1412	−	10.4738i	1.17346	−	0.677496i	0.218966	−	0.975732i	$-0.429732\pi$
$239$	18.1412	−	10.4738i	1.17346	−	0.677496i	0.954492	+	0.298236i	$0.0963983\pi$
$240$	−0.0749930	−	0.151450i	−0.00484078	−	0.00977604i
$241$	−3.23683	−	8.89311i	−0.208502	−	0.572856i	0.790724	−	0.612172i	$-0.209704\pi$
$241$	−3.23683	−	8.89311i	−0.208502	−	0.572856i	−0.999227	+	0.0393166i	$0.987482\pi$
$242$	−12.2630	−	4.68628i	−0.788296	−	0.301245i
$243$	−2.80468	+	15.9061i	−0.179920	+	1.02038i
$244$	3.48558	+	24.2736i	0.223142	+	1.55396i
$245$	−0.179469	+	0.150592i	−0.0114659	+	0.00962099i
$246$	−7.75150	−	4.64179i	−0.494218	−	0.295950i
$247$	−2.61380	−	8.28779i	−0.166312	−	0.527340i
$248$	17.3343	+	0.830404i	1.10073	+	0.0527307i
$249$	0.429815	+	0.512234i	0.0272384	+	0.0324615i
$250$	0.509225	−	0.413626i	0.0322062	−	0.0261600i
$251$	−5.25705	−	0.926959i	−0.331822	−	0.0585091i	0.00525525	−	0.999986i	$-0.498327\pi$
$251$	−5.25705	−	0.926959i	−0.331822	−	0.0585091i	−0.337077	+	0.941477i	$0.609438\pi$
$252$	3.74775	+	4.76740i	0.236086	+	0.300318i
$253$	−10.5387	+	3.83578i	−0.662563	+	0.241153i
$254$	−9.00737	−	16.1925i	−0.565173	−	1.01601i
$255$	0.0251029	+	0.0434796i	0.00157201	+	0.00272280i
$256$	4.76167	−	15.2750i	0.297605	−	0.954689i
$257$	8.86041	−	10.5594i	0.552697	−	0.658679i	−0.415287	−	0.909691i	$-0.636319\pi$
$257$	8.86041	−	10.5594i	0.552697	−	0.658679i	0.967984	+	0.251011i	$0.0807632\pi$
$258$	−0.00847416	+	0.531043i	−0.000527578	+	0.0330613i
$259$	−3.08230	+	5.33869i	−0.191525	+	0.331730i
$260$	0.123384	−	0.137860i	0.00765194	−	0.00854968i
$261$	11.4894	−	2.02590i	0.711178	−	0.125400i
$262$	−1.25731	+	1.45075i	−0.0776771	+	0.0896279i
$263$	−4.72312	+	12.9767i	−0.291240	+	0.800175i	0.704646	+	0.709559i	$0.251106\pi$
$263$	−4.72312	+	12.9767i	−0.291240	+	0.800175i	−0.995886	+	0.0906161i	$0.971116\pi$
$264$	−2.04316	−	2.68618i	−0.125748	−	0.165323i
$265$		−	0.244013i		−	0.0149896i
$266$	−3.42079	+	7.90119i	−0.209742	+	0.484453i
$267$		−	12.5960i		−	0.770862i
$268$	−20.3796	−	8.16298i	−1.24488	−	0.498633i
$269$	0.0765103	−	0.210210i	0.00466491	−	0.0128167i	−0.937338	−	0.348421i	$-0.886718\pi$
$269$	0.0765103	−	0.210210i	0.00466491	−	0.0128167i	0.942003	+	0.335604i	$0.108940\pi$
$270$	−0.233480	−	0.202348i	−0.0142091	−	0.0123145i
$271$	14.0034	−	2.46917i	0.850644	−	0.149992i	0.268704	−	0.963223i	$-0.413405\pi$
$271$	14.0034	−	2.46917i	0.850644	−	0.149992i	0.581941	+	0.813231i	$0.302294\pi$
$272$	−1.12227	+	4.61883i	−0.0680476	+	0.280058i
$273$	1.26778	−	2.19585i	0.0767294	−	0.132899i
$274$	10.9067	+	0.174044i	0.658897	+	0.0105144i
$275$	4.20974	−	5.01697i	0.253857	−	0.302535i
$276$	15.2552	+	3.19489i	0.918258	+	0.192310i
$277$	−10.5953	−	18.3516i	−0.636609	−	1.10264i	−0.986172	−	0.165726i	$-0.947003\pi$
$277$	−10.5953	−	18.3516i	−0.636609	−	1.10264i	0.349563	−	0.936913i	$-0.386330\pi$
$278$	21.1044	−	11.7397i	1.26576	−	0.704099i
$279$	12.5163	−	4.55558i	0.749334	−	0.272735i
$280$	−0.181833	+	0.0231557i	−0.0108666	+	0.00138382i
$281$	7.25757	+	1.27971i	0.432950	+	0.0763408i	0.385876	−	0.922551i	$-0.373899\pi$
$281$	7.25757	+	1.27971i	0.432950	+	0.0763408i	0.0470741	+	0.998891i	$0.485010\pi$
$282$	−6.77358	−	8.33912i	−0.403361	−	0.496587i
$283$	−15.7071	−	18.7190i	−0.933691	−	1.11273i	−0.993422	−	0.114515i	$-0.963469\pi$
$283$	−15.7071	−	18.7190i	−0.933691	−	1.11273i	0.0597309	−	0.998215i	$-0.480976\pi$
$284$	5.77211	+	10.7778i	0.342512	+	0.639544i
$285$	0.0398470	−	0.179801i	0.00236033	−	0.0106505i
$286$	1.89814	−	3.16977i	0.112239	−	0.187432i
$287$	−7.50694	+	6.29907i	−0.443120	+	0.371822i
$288$	−1.16184	−	12.2252i	−0.0684619	−	0.720375i
$289$	−2.70682	+	15.3511i	−0.159224	+	0.903007i
$290$	−0.125885	+	0.329415i	−0.00739223	+	0.0193439i
$291$	2.64520	+	7.26762i	0.155064	+	0.426036i
$292$	12.9653	+	0.413894i	0.758735	+	0.0242213i
$293$	−11.5307	+	6.65724i	−0.673630	+	0.388920i	−0.797451	−	0.603384i	$-0.793819\pi$
$293$	−11.5307	+	6.65724i	−0.673630	+	0.388920i	0.123821	+	0.992305i	$0.460485\pi$
$294$	6.14464	−	2.12606i	0.358363	−	0.123995i
$295$	−0.416693	−	0.349647i	−0.0242608	−	0.0203572i
$296$	11.0975	−	5.71737i	0.645028	−	0.332315i
$297$	−5.34332	−	3.08497i	−0.310051	−	0.179008i
$298$	3.58234	−	18.5780i	0.207519	−	1.07619i
$299$	2.96292	+	16.8036i	0.171350	+	0.971775i
$300$	−8.64785	+	2.83851i	−0.499284	+	0.163881i
$301$	0.541314	+	0.197022i	0.0312008	+	0.0113562i
$302$	−0.123376	−	0.771490i	−0.00709950	−	0.0443943i
$303$	9.59824			0.551405
$304$	14.4807	−	9.71131i	0.830525	−	0.556982i
$305$	−0.568919			−0.0325762
$306$	0.576093	+	3.60240i	0.0329331	+	0.205935i
$307$	−26.7916	−	9.75134i	−1.52908	−	0.556538i	−0.565681	−	0.824624i	$-0.691387\pi$
$307$	−26.7916	−	9.75134i	−1.52908	−	0.556538i	−0.963395	+	0.268086i	$0.913609\pi$
$308$	−3.47795	+	1.14158i	−0.198174	+	0.0650474i
$309$	−0.0916701	−	0.519887i	−0.00521493	−	0.0295753i
$310$	−0.0762304	+	0.395330i	−0.00432959	+	0.0224532i
$311$	−22.6396	−	13.0710i	−1.28377	−	0.741188i	−0.306239	−	0.951955i	$-0.599071\pi$
$311$	−22.6396	−	13.0710i	−1.28377	−	0.741188i	−0.977536	+	0.210767i	$0.932404\pi$
$312$	−4.56449	+	2.35161i	−0.258414	+	0.133134i
$313$	−2.72269	−	2.28461i	−0.153895	−	0.129134i	0.562589	−	0.826737i	$-0.309805\pi$
$313$	−2.72269	−	2.28461i	−0.153895	−	0.129134i	−0.716484	+	0.697603i	$0.754250\pi$
$314$	−9.28890	+	3.21399i	−0.524203	+	0.181376i
$315$	−0.121838	+	0.0703432i	−0.00686479	+	0.00396339i
$316$	−21.9907	−	0.702014i	−1.23707	−	0.0394913i
$317$	4.75523	+	13.0649i	0.267080	+	0.733798i	0.998646	+	0.0520261i	$0.0165679\pi$
$317$	4.75523	+	13.0649i	0.267080	+	0.733798i	−0.731565	+	0.681771i	$0.761210\pi$
$318$	−2.41747	+	6.32600i	−0.135565	+	0.354745i
$319$	−1.22290	+	6.93539i	−0.0684690	+	0.388307i
$320$	0.335077	+	0.159718i	0.0187314	+	0.00892852i
$321$	−0.589352	+	0.494525i	−0.0328944	+	0.0276017i
$322$	8.68509	−	14.5036i	0.484001	−	0.808251i
$323$	−4.10910	+	3.15351i	−0.228636	+	0.175466i
$324$	−2.10112	−	3.92325i	−0.116729	−	0.217958i
$325$	−6.40477	−	7.63290i	−0.355272	−	0.423397i
$326$	−14.5356	−	17.8952i	−0.805055	−	0.991123i
$327$	7.28194	+	1.28400i	0.402692	+	0.0710055i
$328$	19.6858	−	2.50691i	1.08697	−	0.138421i
$329$	−10.9499	+	3.98543i	−0.603686	+	0.219724i
$330$	0.0684233	−	0.0380617i	0.00376658	−	0.00209523i
$331$	−3.55440	−	6.15641i	−0.195368	−	0.338387i	0.751653	−	0.659558i	$-0.229257\pi$
$331$	−3.55440	−	6.15641i	−0.195368	−	0.338387i	−0.947021	+	0.321172i	$0.895923\pi$
$332$	−1.43751	−	0.301056i	−0.0788934	−	0.0165226i
$333$	6.15882	−	7.33979i	0.337501	−	0.402218i
$334$	20.9102	+	0.333677i	1.14416	+	0.0182580i
$335$	0.254659	−	0.441082i	0.0139135	−	0.0240989i
$336$	4.94338	+	1.20113i	0.269684	+	0.0655269i
$337$	−29.9028	+	5.27267i	−1.62891	+	0.287220i	−0.912075	−	0.410024i	$-0.865520\pi$
$337$	−29.9028	+	5.27267i	−1.62891	+	0.287220i	−0.716833	+	0.697245i	$0.754409\pi$
$338$	9.64540	+	8.35930i	0.524641	+	0.454686i
$339$	−4.42871	+	12.1678i	−0.240535	+	0.660863i
$340$	−0.102367	−	0.0410029i	−0.00555163	−	0.00222369i
$341$			8.04014i			0.435398i
$342$	7.36853	−	11.1707i	0.398445	−	0.604044i
$343$		−	16.8293i		−	0.908694i
$344$	−0.706222	−	0.928482i	−0.0380769	−	0.0500604i
$345$	−0.123673	+	0.339789i	−0.00665834	+	0.0182936i
$346$	1.82054	−	2.10064i	0.0978729	−	0.112931i
$347$	0.491581	−	0.0866790i	0.0263895	−	0.00465317i	−0.160438	−	0.987046i	$-0.551291\pi$
$347$	0.491581	−	0.0866790i	0.0263895	−	0.00465317i	0.186827	+	0.982393i	$0.440180\pi$
$348$	6.52711	−	7.29288i	0.349890	−	0.390939i
$349$	−1.36569	+	2.36545i	−0.0731040	+	0.126620i	−0.900260	−	0.435352i	$-0.856624\pi$
$349$	−1.36569	+	2.36545i	−0.0731040	+	0.126620i	0.827156	+	0.561972i	$0.189957\pi$
$350$	−0.157513	+	9.87073i	−0.00841942	+	0.527613i
$351$	−6.03388	+	7.19090i	−0.322065	+	0.383822i
$352$	7.17433	+	1.86491i	0.382393	+	0.0994001i
$353$	12.5409	+	21.7215i	0.667484	+	1.15612i	0.978605	+	0.205747i	$0.0659623\pi$
$353$	12.5409	+	21.7215i	0.667484	+	1.15612i	−0.311121	+	0.950370i	$0.600704\pi$
$354$	7.33870	+	13.1927i	0.390048	+	0.701187i
$355$	−0.266537	+	0.0970116i	−0.0141463	+	0.00514884i
$356$	17.0982	+	21.7501i	0.906202	+	1.15276i
$357$	−1.48833	−	0.262433i	−0.0787708	−	0.0138894i
$358$	−25.1876	+	20.4590i	−1.33121	+	1.08129i
$359$	−5.00752	−	5.96773i	−0.264287	−	0.314965i	0.617539	−	0.786540i	$-0.288130\pi$
$359$	−5.00752	−	5.96773i	−0.264287	−	0.314965i	−0.881826	+	0.471576i	$0.843685\pi$
$360$	0.284572	+	0.0136325i	0.0149983	+	0.000718496i
$361$	18.9279	+	1.65316i	0.996208	+	0.0870087i
$362$	−26.0681	−	15.6102i	−1.37011	−	0.820455i
$363$	−6.47513	+	5.43328i	−0.339856	+	0.285173i
$364$	0.791586	+	5.51261i	0.0414904	+	0.288939i
$365$	−0.0522584	+	0.296372i	−0.00273533	+	0.0155128i
$366$	14.7491	+	5.63634i	0.770949	+	0.294616i
$367$	2.87685	+	7.90408i	0.150170	+	0.412590i	0.991854	−	0.127382i	$-0.0406573\pi$
$367$	2.87685	+	7.90408i	0.150170	+	0.412590i	−0.841683	+	0.539971i	$0.818435\pi$
$368$	−30.6789	+	15.1912i	−1.59925	+	0.791894i
$369$	13.1906	−	7.61560i	0.686676	−	0.396452i
$370$	0.0947003	+	0.273698i	0.00492324	+	0.0142289i
$371$	5.62679	+	4.72144i	0.292129	+	0.245125i
$372$	5.89284	−	9.49365i	0.305529	−	0.492223i
$373$	17.6598	+	10.1959i	0.914391	+	0.527924i	0.881841	−	0.471546i	$-0.156304\pi$
$373$	17.6598	+	10.1959i	0.914391	+	0.527924i	0.0325499	+	0.999470i	$0.489637\pi$
$374$	−2.16232	−	0.416954i	−0.111811	−	0.0215602i
$375$	−0.0733505	−	0.415992i	−0.00378781	−	0.0214817i
$376$	23.0161	+	5.20491i	1.18696	+	0.268423i
$377$	10.0682	+	3.66454i	0.518541	+	0.188733i
$378$	9.18363	−	1.46864i	0.472355	−	0.0755388i
$379$	−17.8645			−0.917638			−0.458819	−	0.888530i	$-0.651727\pi$
$379$	−17.8645			−0.917638			−0.458819	+	0.888530i	$0.651727\pi$
$380$	0.175262	+	0.364561i	0.00899073	+	0.0187016i
$381$	−11.9304			−0.611212
$382$	−10.7260	+	1.71529i	−0.548789	+	0.0877620i
$383$	−11.4496	−	4.16732i	−0.585047	−	0.212940i	0.0325023	−	0.999472i	$-0.489652\pi$
$383$	−11.4496	−	4.16732i	−0.585047	−	0.212940i	−0.617550	+	0.786532i	$0.711875\pi$
$384$	−7.10447	−	7.46031i	−0.362548	−	0.380707i
$385$	−0.0147467	−	0.0836327i	−0.000751561	−	0.00426231i
$386$	5.40118	+	1.04149i	0.274913	+	0.0530107i
$387$	−0.775389	−	0.447671i	−0.0394152	−	0.0227564i
$388$	−14.4329	−	8.95870i	−0.732719	−	0.454809i
$389$	15.3327	+	12.8656i	0.777398	+	0.652314i	0.942592	−	0.333947i	$-0.108381\pi$
$389$	15.3327	+	12.8656i	0.777398	+	0.652314i	−0.165194	+	0.986261i	$0.552825\pi$
$390$	−0.0389511	−	0.112575i	−0.00197237	−	0.00570043i
$391$	8.80756	−	5.08505i	0.445418	−	0.257162i
$392$	−7.72427	+	12.0121i	−0.390135	+	0.606703i
$393$	0.422766	+	1.16154i	0.0213257	+	0.0585919i
$394$	15.4156	+	5.89102i	0.776626	+	0.296785i
$395$	0.0886365	−	0.502683i	0.00445979	−	0.0252927i
$396$	5.63164	−	0.808677i	0.283000	−	0.0406376i
$397$	3.50279	−	2.93919i	0.175800	−	0.147514i	−0.550642	−	0.834742i	$-0.685617\pi$
$397$	3.50279	−	2.93919i	0.175800	−	0.147514i	0.726442	+	0.687228i	$0.241173\pi$
$398$	26.2991	+	15.7485i	1.31825	+	0.789403i
$399$	3.37509	+	4.39784i	0.168966	+	0.220167i
$400$	11.0796	−	16.6403i	0.553980	−	0.832013i
$401$	−5.17049	−	6.16195i	−0.258202	−	0.307713i	0.621334	−	0.783546i	$-0.286591\pi$
$401$	−5.17049	−	6.16195i	−0.258202	−	0.307713i	−0.879536	+	0.475833i	$0.842147\pi$
$402$	−10.9718	+	8.91205i	−0.547225	+	0.444493i
$403$	12.0466	+	2.12414i	0.600083	+	0.105811i
$404$	−16.5738	+	13.0290i	−0.824576	+	0.648215i
$405$	0.0970227	−	0.0353134i	0.00482110	−	0.00175474i
$406$	−5.16034	−	9.27673i	−0.256104	−	0.460396i
$407$	2.89183	+	5.00879i	0.143342	+	0.248276i
$408$	2.24763	+	2.07715i	0.111274	+	0.102834i
$409$	8.35432	−	9.95629i	0.413094	−	0.492307i	−0.518872	−	0.854852i	$-0.673648\pi$
$409$	8.35432	−	9.95629i	0.413094	−	0.492307i	0.931966	+	0.362545i	$0.118092\pi$
$410$	−0.00734584	+	0.460336i	−0.000362785	+	0.0227344i
$411$	3.51169	−	6.08243i	0.173219	−	0.300024i
$412$	0.864002	+	0.773279i	0.0425663	+	0.0380967i
$413$	16.1253	−	2.84332i	0.793472	−	0.139911i
$414$	−17.2083	+	19.8559i	−0.845742	+	0.975862i
$415$	0.0116538	−	0.0320184i	0.000572060	−	0.00157172i
$416$	4.68960	−	10.2566i	0.229926	−	0.502873i
$417$		−	15.5494i		−	0.761456i
$418$	4.81509	+	6.48589i	0.235514	+	0.317235i
$419$			1.47508i			0.0720624i	0.999351	+	0.0360312i	$0.0114716\pi$
$419$			1.47508i			0.0720624i	−0.999351	+	0.0360312i	$0.988528\pi$
$420$	−0.0438840	+	0.109560i	−0.00214132	+	0.00534598i
$421$	7.00572	−	19.2481i	0.341438	−	0.938093i	−0.643540	−	0.765412i	$-0.722535\pi$
$421$	7.00572	−	19.2481i	0.341438	−	0.938093i	0.984978	−	0.172680i	$-0.0552428\pi$
$422$	−12.3116	−	10.6700i	−0.599319	−	0.519406i
$423$	17.8361	−	3.14499i	0.867221	−	0.152915i
$424$	−4.41275	−	14.2050i	−0.214302	−	0.689855i
$425$	−2.96948	+	5.14330i	−0.144041	+	0.249487i
$426$	7.87104	+	0.125603i	0.381353	+	0.00608547i
$427$	11.0081	−	13.1189i	0.532718	−	0.634868i
$428$	0.346380	−	1.65393i	0.0167429	−	0.0799455i
$429$	−1.18943	−	2.06016i	−0.0574265	−	0.0994655i
$430$	0.0236506	−	0.0131561i	0.00114054	−	0.000634443i
$431$	15.5185	−	5.64828i	0.747501	−	0.272068i	0.0599469	−	0.998202i	$-0.480907\pi$
$431$	15.5185	−	5.64828i	0.747501	−	0.272068i	0.687554	+	0.726134i	$0.258685\pi$
$432$	−17.2510	−	7.55720i	−0.829991	−	0.363596i
$433$	−29.9167	−	5.27512i	−1.43770	−	0.253506i	−0.600161	−	0.799879i	$-0.704897\pi$
$433$	−29.9167	−	5.27512i	−1.43770	−	0.253506i	−0.837542	+	0.546373i	$0.816008\pi$
$434$	−7.64108	−	9.40711i	−0.366783	−	0.451556i
$435$	0.145952	+	0.173938i	0.00699785	+	0.00833971i
$436$	−14.3170	+	7.66758i	−0.685662	+	0.367211i
$437$	−36.4219	−	8.07172i	−1.74230	−	0.386123i
$438$	4.29098	−	7.16567i	0.205031	−	0.342389i
$439$	−5.71692	+	4.79706i	−0.272854	+	0.228951i	−0.768939	−	0.639323i	$-0.779215\pi$
$439$	−5.71692	+	4.79706i	−0.272854	+	0.228951i	0.496085	+	0.868274i	$0.334770\pi$
$440$	−0.0664839	+	0.158603i	−0.00316950	+	0.00756110i
$441$	−1.90338	+	10.7946i	−0.0906370	+	0.514028i
$442$	−1.19599	+	3.12965i	−0.0568874	+	0.148863i
$443$	11.1704	+	30.6904i	0.530721	+	1.45814i	0.858215	+	0.513290i	$0.171574\pi$
$443$	11.1704	+	30.6904i	0.530721	+	1.45814i	−0.327494	+	0.944853i	$0.606204\pi$
$444$	0.256464	−	8.03378i	0.0121713	−	0.381266i
$445$	−0.555857	+	0.320924i	−0.0263501	+	0.0152133i
$446$	−2.72354	+	0.942353i	−0.128963	+	0.0446217i
$447$	−9.33208	−	7.83054i	−0.441392	−	0.370372i
$448$	−10.1664	+	4.63626i	−0.480319	+	0.219043i
$449$	−4.49778	−	2.59680i	−0.212264	−	0.122550i	0.390099	−	0.920773i	$-0.372441\pi$
$449$	−4.49778	−	2.59680i	−0.212264	−	0.122550i	−0.602363	+	0.798222i	$0.705774\pi$
$450$	2.90516	−	15.0662i	0.136951	−	0.710226i
$451$	1.59653	+	9.05436i	0.0751776	+	0.426353i
$452$	−8.86965	−	27.0224i	−0.417193	−	1.27103i
$453$	−0.472714	−	0.172054i	−0.0222100	−	0.00808379i
$454$	2.76731	+	17.3044i	0.129876	+	0.812137i
$455$	−0.129203			−0.00605713
$456$	−0.931884	−	11.1875i	−0.0436394	−	0.523904i
$457$	−13.2130			−0.618078			−0.309039	−	0.951049i	$-0.600007\pi$
$457$	−13.2130			−0.618078			−0.309039	+	0.951049i	$0.600007\pi$
$458$	2.07511	+	12.9760i	0.0969634	+	0.606327i
$459$	5.25763	+	1.91362i	0.245405	+	0.0893202i
$460$	−0.247688	−	0.754609i	−0.0115485	−	0.0351838i
$461$	−4.56893	−	25.9117i	−0.212796	−	1.20683i	−0.884690	−	0.466180i	$-0.845630\pi$
$461$	−4.56893	−	25.9117i	−0.212796	−	1.20683i	0.671894	−	0.740648i	$-0.265481\pi$
$462$	−0.446252	+	2.31426i	−0.0207615	+	0.107669i
$463$	18.3103	+	10.5715i	0.850954	+	0.491298i	0.860972	−	0.508652i	$-0.169856\pi$
$463$	18.3103	+	10.5715i	0.850954	+	0.491298i	−0.0100189	+	0.999950i	$0.503189\pi$
$464$	−1.37110	+	21.4531i	−0.0636518	+	0.995934i
$465$	0.198582	+	0.166630i	0.00920902	+	0.00772729i
$466$	−10.6283	+	3.67742i	−0.492346	+	0.170353i
$467$	27.4162	−	15.8287i	1.26867	−	0.732467i	0.293934	−	0.955826i	$-0.405036\pi$
$467$	27.4162	−	15.8287i	1.26867	−	0.732467i	0.974736	+	0.223359i	$0.0717022\pi$
$468$	0.276186	−	8.65155i	0.0127667	−	0.399918i
$469$	5.24365	+	14.4068i	0.242129	+	0.665245i
$470$	−0.195423	+	0.511382i	−0.00901420	+	0.0235883i
$471$	−1.09897	+	6.23259i	−0.0506380	+	0.287182i
$472$	−30.5804	−	12.8188i	−1.40757	−	0.590033i
$473$	0.414014	−	0.347399i	0.0190364	−	0.0159734i
$474$	−7.27802	+	12.1538i	−0.334290	+	0.558244i
$475$	20.7763	−	6.55244i	0.953284	−	0.300647i
$476$	2.92621	−	1.56715i	0.134123	−	0.0718302i
$477$	−7.33838	−	8.74554i	−0.336001	−	0.400431i
$478$	18.6777	+	22.9946i	0.854300	+	1.05175i
$479$	−13.3251	−	2.34958i	−0.608840	−	0.107355i	−0.139276	−	0.990254i	$-0.544478\pi$
$479$	−13.3251	−	2.34958i	−0.608840	−	0.107355i	−0.469563	+	0.882899i	$0.655589\pi$
$480$	0.194747	−	0.138548i	0.00888896	−	0.00632380i
$481$	8.26868	−	3.00955i	0.377019	−	0.137224i
$482$	11.6961	−	6.50616i	0.532743	−	0.296348i
$483$	−5.44236	−	9.42644i	−0.247636	−	0.428918i
$484$	3.80563	−	18.1715i	0.172983	−	0.825976i
$485$	0.253323	−	0.301898i	0.0115028	−	0.0137085i
$486$	−22.8388	−	0.364452i	−1.03599	−	0.0165319i
$487$	−6.49642	+	11.2521i	−0.294381	+	0.509883i	−0.974841	−	0.222903i	$-0.928447\pi$
$487$	−6.49642	+	11.2521i	−0.294381	+	0.509883i	0.680460	+	0.732786i	$0.261780\pi$
$488$	−33.1190	+	10.2884i	−1.49923	+	0.465732i
$489$	−14.6188	+	2.57768i	−0.661084	+	0.116567i
$490$	−0.250377	−	0.216992i	−0.0113109	−	0.00980271i
$491$	11.1325	−	30.5862i	0.502401	−	1.38033i	−0.386523	−	0.922280i	$-0.626324\pi$
$491$	11.1325	−	30.5862i	0.502401	−	1.38033i	0.888924	−	0.458055i	$-0.151454\pi$
$492$	4.75104	−	11.8614i	0.214193	−	0.534751i
$493$		−	6.38620i		−	0.287620i
$494$	10.9899	−	5.50095i	0.494460	−	0.247499i
$495$			0.131993i			0.00593263i
$496$	2.71151	+	24.3923i	0.121750	+	1.09525i
$497$	2.92023	−	8.02327i	0.130990	−	0.359893i
$498$	−0.619331	+	0.714617i	−0.0277529	+	0.0320228i
$499$	−4.07989	+	0.719394i	−0.182641	+	0.0322045i	−0.264220	−	0.964462i	$-0.585115\pi$
$499$	−4.07989	+	0.719394i	−0.182641	+	0.0322045i	0.0815796	+	0.996667i	$0.474004\pi$
$500$	0.691338	+	0.618746i	0.0309176	+	0.0276711i
$501$	6.73260	−	11.6612i	0.300790	−	0.520984i
$502$	0.120453	−	7.54832i	0.00537607	−	0.336898i
$503$	−14.9435	+	17.8090i	−0.666298	+	0.794063i	−0.988275	−	0.152685i	$-0.951208\pi$
$503$	−14.9435	+	17.8090i	−0.666298	+	0.794063i	0.321977	+	0.946747i	$0.395653\pi$
$504$	−5.82058	+	6.29828i	−0.259269	+	0.280548i
$505$	−0.244547	−	0.423567i	−0.0108822	−	0.0188485i
$506$	−7.71008	−	13.8604i	−0.342755	−	0.616169i
$507$	7.72254	−	2.81078i	0.342970	−	0.124831i
$508$	20.6008	−	16.1947i	0.914012	−	0.718522i
$509$	13.7146	+	2.41826i	0.607891	+	0.107188i	0.469116	−	0.883136i	$-0.344573\pi$
$509$	13.7146	+	2.41826i	0.607891	+	0.107188i	0.138775	+	0.990324i	$0.455684\pi$
$510$	−0.0551118	+	0.0447655i	−0.00244039	+	0.00198225i
$511$	−5.82300	−	6.93958i	−0.257594	−	0.306989i
$512$	22.3945	+	3.23827i	0.989706	+	0.143113i
$513$	−9.47808	−	18.2039i	−0.418467	−	0.803724i
$514$	16.7247	+	10.0151i	0.737693	+	0.441749i
$515$	−0.0206068	+	0.0172912i	−0.000908045	+	0.000761940i
$516$	−0.743478	+	0.106760i	−0.0327298	+	0.00469985i
$517$	−1.89841	+	10.7664i	−0.0834922	+	0.473508i
$518$	−8.14367	−	3.11208i	−0.357812	−	0.136737i
$519$	−0.612148	−	1.68186i	−0.0268703	−	0.0738256i
$520$	0.220071	+	0.141515i	0.00965075	+	0.00620583i
$521$	14.7143	−	8.49530i	0.644645	−	0.372186i	−0.141757	−	0.989902i	$-0.545275\pi$
$521$	14.7143	−	8.49530i	0.644645	−	0.372186i	0.786402	+	0.617716i	$0.211942\pi$
$522$	5.39495	+	15.5922i	0.236131	+	0.682453i
$523$	2.73927	+	2.29852i	0.119780	+	0.100507i	0.700710	−	0.713446i	$-0.252867\pi$
$523$	2.73927	+	2.29852i	0.119780	+	0.100507i	−0.580930	+	0.813953i	$0.697311\pi$
$524$	−2.30672	−	1.43181i	−0.100770	−	0.0625491i
$525$	5.50470	+	3.17814i	0.240245	+	0.138705i
$526$	−19.1763	−	3.69771i	−0.836126	−	0.161228i
$527$	−1.26607	−	7.18024i	−0.0551508	−	0.312776i
$528$	3.29488	−	3.45309i	0.143391	−	0.150277i
$529$	47.2174	+	17.1857i	2.05293	+	0.747206i
$530$	0.340757	−	0.0544937i	0.0148015	−	0.00236705i
$531$	−25.4496			−1.10442
$532$	−11.7977	−	3.01251i	−0.511495	−	0.130609i
$533$	13.9880			0.605886
$534$	17.5899	−	2.81297i	0.761190	−	0.121729i
$535$	0.0368389	+	0.0134083i	0.00159268	+	0.000579689i
$536$	6.84814	−	30.2824i	0.295794	−	1.30800i
$537$	3.62811	+	20.5760i	0.156565	+	0.887922i
$538$	0.310639	+	0.0598996i	0.0133926	+	0.00258245i
$539$	−5.73004	−	3.30824i	−0.246810	−	0.142496i
$540$	0.230431	−	0.371236i	0.00991618	−	0.0159754i
$541$	15.2062	+	12.7595i	0.653766	+	0.548575i	0.908211	−	0.418513i	$-0.137448\pi$
$541$	15.2062	+	12.7595i	0.653766	+	0.548575i	−0.254445	+	0.967087i	$0.581893\pi$
$542$	6.57539	+	19.0039i	0.282437	+	0.816286i
$543$	−16.9427	+	9.78187i	−0.727081	+	0.419780i
$544$	−6.70069	−	0.535725i	−0.287290	−	0.0229690i
$545$	−0.128869	−	0.354064i	−0.00552013	−	0.0151664i
$546$	3.34957	+	1.28003i	0.143348	+	0.0547802i
$547$	0.130482	−	0.740000i	0.00557901	−	0.0316401i	−0.981891	−	0.189446i	$-0.939331\pi$
$547$	0.130482	−	0.740000i	0.00557901	−	0.0316401i	0.987470	+	0.157806i	$0.0504420\pi$
$548$	2.19266	+	15.2697i	0.0936658	+	0.652290i
$549$	−20.3903	+	17.1095i	−0.870236	+	0.730215i
$550$	7.94617	+	4.75837i	0.338826	+	0.202897i
$551$	−15.8249	+	17.2724i	−0.674162	+	0.735828i
$552$	−1.05473	+	22.0170i	−0.0448922	+	0.937105i
$553$	9.87651	+	11.7704i	0.419992	+	0.500527i
$554$	23.2612	−	18.8943i	0.988275	−	0.802742i
$555$	0.183644	+	0.0323813i	0.00779524	+	0.00137451i
$556$	21.1072	+	26.8499i	0.895144	+	1.13869i
$557$	−31.8977	+	11.6098i	−1.35155	+	0.491923i	−0.913430	−	0.406995i	$-0.866577\pi$
$557$	−31.8977	+	11.6098i	−1.35155	+	0.491923i	−0.438117	+	0.898918i	$0.644354\pi$
$558$	9.15690	+	16.4613i	0.387643	+	0.696863i
$559$	−0.411130	−	0.712098i	−0.0173890	−	0.0301186i
$560$	−0.0729435	−	0.248752i	−0.00308243	−	0.0105117i
$561$	−0.911409	+	1.08617i	−0.0384797	+	0.0458583i
$562$	−0.166290	+	10.4208i	−0.00701452	+	0.439573i
$563$	16.1201	−	27.9209i	0.679383	−	1.17673i	−0.295784	−	0.955255i	$-0.595581\pi$
$563$	16.1201	−	27.9209i	0.679383	−	1.17673i	0.975167	−	0.221471i	$-0.0710859\pi$
$564$	10.1326	−	11.3214i	0.426661	−	0.476718i
$565$	0.649796	−	0.114577i	0.0273371	−	0.00482027i
$566$	22.6328	−	26.1149i	0.951326	−	1.09769i
$567$	−1.06300	+	2.92057i	−0.0446418	+	0.122652i
$568$	−13.7618	+	10.4675i	−0.577433	+	0.439207i
$569$		−	17.8706i		−	0.749175i	−0.927192	−	0.374587i	$-0.877784\pi$
$569$		−	17.8706i		−	0.749175i	0.927192	−	0.374587i	$-0.122216\pi$
$570$	0.259985	+	0.0154915i	0.0108896	+	0.000648867i
$571$			35.9863i			1.50598i	0.658032	+	0.752990i	$0.271389\pi$
$571$			35.9863i			1.50598i	−0.658032	+	0.752990i	$0.728611\pi$
$572$	4.85038	+	1.94281i	0.202805	+	0.0812330i
$573$	−2.39205	+	6.57211i	−0.0999295	+	0.274554i
$574$	−10.4729	−	9.07648i	−0.437131	−	0.378845i
$575$	−42.1242	+	7.42763i	−1.75670	+	0.309754i
$576$	16.8126	−	4.35262i	0.700525	−	0.181359i
$577$	−7.40172	+	12.8202i	−0.308138	+	0.533710i	−0.977955	−	0.208816i	$-0.933039\pi$
$577$	−7.40172	+	12.8202i	−0.308138	+	0.533710i	0.669817	+	0.742526i	$0.266372\pi$
$578$	−22.0419	−	0.351734i	−0.916820	−	0.0146302i
$579$	2.27658	−	2.71312i	0.0946113	−	0.112753i
$580$	−0.488132	−	0.102229i	−0.0202686	−	0.00424483i
$581$	0.512835	+	0.888256i	0.0212760	+	0.0368511i
$582$	−9.55828	+	5.31696i	−0.396203	+	0.220395i
$583$	6.47576	−	2.35698i	0.268198	−	0.0976162i
$584$	2.31745	+	18.1980i	0.0958966	+	0.753040i
$585$	0.197765	+	0.0348713i	0.00817658	+	0.00144175i
$586$	−11.8717	−	14.6155i	−0.490415	−	0.603762i
$587$	12.8463	+	15.3096i	0.530222	+	0.631894i	0.962966	−	0.269623i	$-0.0868991\pi$
$587$	12.8463	+	15.3096i	0.530222	+	0.631894i	−0.432744	+	0.901517i	$0.642455\pi$
$588$	4.34122	+	8.10600i	0.179029	+	0.334286i
$589$	−14.3682	+	22.5572i	−0.592031	+	0.929454i
$590$	0.395214	−	0.659983i	0.0162707	−	0.0271711i
$591$	8.13976	−	6.83007i	0.334825	−	0.280951i
$592$	10.4625	+	14.2205i	0.430004	+	0.584458i
$593$	−5.76362	+	32.6871i	−0.236683	+	1.34230i	0.602356	+	0.798228i	$0.294229\pi$
$593$	−5.76362	+	32.6871i	−0.236683	+	1.34230i	−0.839039	+	0.544071i	$0.816882\pi$
$594$	3.11478	−	8.15073i	0.127801	−	0.334429i
$595$	0.0263390	+	0.0723659i	0.00107979	+	0.00296671i
$596$	26.7436	+	0.853743i	1.09546	+	0.0349707i
$597$	17.0928	−	9.86855i	0.699563	−	0.403893i
$598$	−22.8040	+	7.89024i	−0.932524	+	0.322656i
$599$	−24.4486	−	20.5148i	−0.998941	−	0.838211i	−0.0121038	−	0.999927i	$-0.503853\pi$
$599$	−24.4486	−	20.5148i	−0.998941	−	0.838211i	−0.986837	+	0.161716i	$0.948297\pi$
$600$	−5.89515	−	11.4426i	−0.240669	−	0.467140i
$601$	−0.700958	−	0.404698i	−0.0285927	−	0.0165080i	0.485636	−	0.874161i	$-0.338588\pi$
$601$	−0.700958	−	0.404698i	−0.0285927	−	0.0165080i	−0.514228	+	0.857653i	$0.671922\pi$
$602$	−0.154248	+	0.799928i	−0.00628667	+	0.0326026i
$603$	−4.13788	−	23.4671i	−0.168508	−	0.955654i
$604$	1.04981	−	0.344582i	0.0427161	−	0.0140209i
$605$	0.404744	+	0.147315i	0.0164552	+	0.00598919i
$606$	2.14350	+	13.4037i	0.0870739	+	0.544486i
$607$	−37.1238			−1.50681			−0.753404	−	0.657558i	$-0.771590\pi$
$607$	−37.1238			−1.50681			−0.753404	+	0.657558i	$0.771590\pi$
$608$	16.7954	+	18.0531i	0.681144	+	0.732149i
$609$	−6.83495			−0.276966
$610$	−0.127052	−	0.794477i	−0.00514420	−	0.0321675i
$611$	15.6299	+	5.68880i	0.632316	+	0.230144i
$612$	−4.90198	+	1.60899i	−0.198151	+	0.0650397i
$613$	−6.54618	−	37.1252i	−0.264398	−	1.49947i	−0.770745	−	0.637144i	$-0.780116\pi$
$613$	−6.54618	−	37.1252i	−0.264398	−	1.49947i	0.506347	−	0.862330i	$-0.330996\pi$
$614$	7.63428	−	39.5913i	0.308094	−	1.59778i
$615$	0.256720	+	0.148217i	0.0103519	+	0.00597669i
$616$	−2.37088	−	4.60191i	−0.0955256	−	0.185416i
$617$	−24.7371	−	20.7569i	−0.995877	−	0.835640i	−0.00946884	−	0.999955i	$-0.503014\pi$
$617$	−24.7371	−	20.7569i	−0.995877	−	0.835640i	−0.986408	+	0.164315i	$0.947459\pi$
$618$	0.705534	−	0.244117i	0.0283807	−	0.00981982i
$619$	−36.7309	+	21.2066i	−1.47634	+	0.852365i	−0.999643	−	0.0267023i	$-0.991499\pi$
$619$	−36.7309	+	21.2066i	−1.47634	+	0.852365i	−0.476697	+	0.879068i	$0.658166\pi$
$620$	−0.569091	−	0.0181672i	−0.0228552	−	0.000729613i
$621$	13.7824	+	37.8669i	0.553069	+	1.51954i
$622$	13.1973	−	34.5346i	0.529163	−	1.38471i
$623$	3.35503	−	19.0273i	0.134416	−	0.762313i
$624$	−4.30330	−	5.84901i	−0.172270	−	0.234148i
$625$	19.1264	−	16.0489i	0.765055	−	0.641957i
$626$	2.58234	−	4.31235i	0.103211	−	0.172356i
$627$	5.15655	−	0.679260i	0.205933	−	0.0271270i
$628$	−6.56265	−	12.2539i	−0.261878	−	0.488984i
$629$	−3.37127	−	4.01772i	−0.134421	−	0.160197i
$630$	−0.125441	−	0.154434i	−0.00499770	−	0.00615279i
$631$	20.4902	+	3.61298i	0.815704	+	0.143831i	0.565908	−	0.824468i	$-0.308526\pi$
$631$	20.4902	+	3.61298i	0.815704	+	0.143831i	0.249795	+	0.968299i	$0.419637\pi$
$632$	−3.93067	−	30.8661i	−0.156354	−	1.22779i
$633$	−9.85721	+	3.58773i	−0.391789	+	0.142599i
$634$	−17.1828	+	9.55822i	−0.682415	+	0.379606i
$635$	0.303965	+	0.526483i	0.0120625	+	0.0208929i
$636$	−9.37395	−	1.96318i	−0.371701	−	0.0778450i
$637$	−6.47057	+	7.71133i	−0.256373	+	0.305534i
$638$	−9.95816	−	0.158908i	−0.394247	−	0.00629123i
$639$	−6.63531	+	11.4927i	−0.262489	+	0.454644i
$640$	−0.148211	+	0.503593i	−0.00585857	+	0.0199063i
$641$	−25.6534	+	4.52338i	−1.01325	+	0.178663i	−0.655531	−	0.755168i	$-0.727555\pi$
$641$	−25.6534	+	4.52338i	−1.01325	+	0.178663i	−0.357715	+	0.933831i	$0.616444\pi$
$642$	−0.822205	−	0.712573i	−0.0324498	−	0.0281230i
$643$	9.65370	−	26.5233i	0.380705	−	1.04598i	−0.590355	−	0.807144i	$-0.701012\pi$
$643$	9.65370	−	26.5233i	0.380705	−	1.04598i	0.971060	−	0.238835i	$-0.0767654\pi$
$644$	22.1933	+	8.88949i	0.874540	+	0.350295i
$645$		−	0.0174254i		−	0.000686125i
$646$	−5.32143	−	5.03398i	−0.209369	−	0.198059i
$647$			31.9737i			1.25702i	0.777803	+	0.628508i	$0.216334\pi$
$647$			31.9737i			1.25702i	−0.777803	+	0.628508i	$0.783666\pi$
$648$	5.00947	−	3.81030i	0.196790	−	0.149683i
$649$	5.25418	−	14.4357i	0.206245	−	0.566652i
$650$	9.22879	−	10.6487i	0.361983	−	0.417675i
$651$	−7.68477	+	1.35503i	−0.301190	+	0.0531079i
$652$	21.7439	−	24.2950i	0.851558	−	0.951465i
$653$	8.32093	−	14.4123i	0.325623	−	0.563996i	−0.656015	−	0.754748i	$-0.727759\pi$
$653$	8.32093	−	14.4123i	0.325623	−	0.563996i	0.981638	+	0.190752i	$0.0610926\pi$
$654$	−0.166848	+	10.4558i	−0.00652429	+	0.408853i
$655$	0.0404870	−	0.0482505i	0.00158196	−	0.00188530i
$656$	7.89712	+	26.9308i	0.308331	+	1.05147i
$657$	7.04003	+	12.1937i	0.274658	+	0.475721i
$658$	−8.01088	−	14.4011i	−0.312297	−	0.561414i
$659$	−4.28405	+	1.55927i	−0.166883	+	0.0607404i	−0.424111	−	0.905610i	$-0.639413\pi$
$659$	−4.28405	+	1.55927i	−0.166883	+	0.0607404i	0.257228	+	0.966351i	$0.417191\pi$
$660$	0.0684325	+	0.0870511i	0.00266373	+	0.00338846i
$661$	−22.6492	−	3.99366i	−0.880951	−	0.155335i	−0.285165	−	0.958479i	$-0.592048\pi$
$661$	−22.6492	−	3.99366i	−0.880951	−	0.155335i	−0.595786	+	0.803143i	$0.703159\pi$
$662$	7.80346	−	6.33848i	0.303290	−	0.246352i
$663$	1.38663	+	1.65253i	0.0538524	+	0.0641788i
$664$	0.0993873	−	2.07467i	0.00385698	−	0.0805126i
$665$	0.108083	−	0.260991i	0.00419129	−	0.0101208i
$666$	11.6252	+	6.96146i	0.450467	+	0.269751i
$667$	35.2343	−	29.5651i	1.36428	−	1.14477i
$668$	4.20376	+	29.2750i	0.162648	+	1.13268i
$669$	−0.322223	+	1.82742i	−0.0124579	+	0.0706521i
$670$	0.672829	+	0.257120i	0.0259936	+	0.00993340i
$671$	−5.49532	−	15.0983i	−0.212145	−	0.582862i
$672$	−0.573369	+	7.17153i	−0.0221182	+	0.276648i
$673$	23.9900	−	13.8506i	0.924745	−	0.533902i	0.0395995	−	0.999216i	$-0.487392\pi$
$673$	23.9900	−	13.8506i	0.924745	−	0.533902i	0.885146	+	0.465314i	$0.154058\pi$
$674$	−14.0411	−	40.5808i	−0.540842	−	1.56311i
$675$	−18.0266	−	15.1261i	−0.693843	−	0.582204i
$676$	−9.51947	+	15.3363i	−0.366134	+	0.589859i
$677$	3.28430	+	1.89619i	0.126226	+	0.0728765i	0.561783	−	0.827284i	$-0.310115\pi$
$677$	3.28430	+	1.89619i	0.126226	+	0.0728765i	−0.435558	+	0.900161i	$0.643449\pi$
$678$	−17.9810	−	3.46722i	−0.690555	−	0.133158i
$679$	2.06001	+	11.6829i	0.0790561	+	0.448349i
$680$	0.0343984	−	0.152109i	0.00131912	−	0.00583313i
$681$	10.6029	+	3.85914i	0.406304	+	0.147883i
$682$	−11.2278	+	1.79555i	−0.429935	+	0.0687550i
$683$	34.1213			1.30561			0.652807	−	0.757524i	$-0.273591\pi$
$683$	34.1213			1.30561			0.652807	+	0.757524i	$0.273591\pi$
$684$	17.2451	+	7.79526i	0.659384	+	0.298059i
$685$	−0.357887			−0.0136742
$686$	23.5015	−	3.75835i	0.897293	−	0.143495i
$687$	7.95073	+	2.89383i	0.303339	+	0.110406i
$688$	1.13888	−	1.19357i	0.0434195	−	0.0455043i
$689$	−1.82064	−	10.3253i	−0.0693607	−	0.393364i
$690$	−0.502124	−	0.0968232i	−0.0191155	−	0.00368600i
$691$	28.6806	+	16.5587i	1.09106	+	0.629924i	0.933859	−	0.357642i	$-0.116419\pi$
$691$	28.6806	+	16.5587i	1.09106	+	0.629924i	0.157202	+	0.987566i	$0.449753\pi$
$692$	3.34004	+	2.07321i	0.126969	+	0.0788116i
$693$	−3.04367	−	2.55394i	−0.115619	−	0.0970162i
$694$	0.230826	+	0.667121i	0.00876203	+	0.0253236i
$695$	−0.686188	+	0.396171i	−0.0260286	+	0.0150276i
$696$	11.6419	+	7.48624i	0.441286	+	0.283765i
$697$	−2.85155	−	7.83458i	−0.108010	−	0.296756i
$698$	−3.60827	−	1.37889i	−0.136575	−	0.0521918i
$699$	−1.25744	+	7.13128i	−0.0475606	+	0.269730i
$700$	−13.8194	+	1.98440i	−0.522322	+	0.0750031i
$701$	5.75372	−	4.82795i	0.217315	−	0.182349i	−0.527631	−	0.849474i	$-0.676920\pi$
$701$	5.75372	−	4.82795i	0.217315	−	0.182349i	0.744946	+	0.667125i	$0.232475\pi$
$702$	−11.3894	−	6.82024i	−0.429864	−	0.257413i
$703$	−0.837759	+	19.2204i	−0.0315967	+	0.724911i
$704$	−1.00210	+	10.4352i	−0.0377681	+	0.393292i
$705$	0.226574	+	0.270021i	0.00853328	+	0.0101696i
$706$	−27.5327	+	22.3639i	−1.03621	+	0.841675i
$707$	14.4990	+	2.55656i	0.545289	+	0.0961492i
$708$	−16.7844	+	13.1945i	−0.630795	+	0.495880i
$709$	−19.0347	+	6.92805i	−0.714862	+	0.260188i	−0.673743	−	0.738966i	$-0.735314\pi$
$709$	−19.0347	+	6.92805i	−0.714862	+	0.260188i	−0.0411190	+	0.999154i	$0.513092\pi$
$710$	−0.194998	−	0.350546i	−0.00731813	−	0.0131558i
$711$	−11.9407	−	20.6820i	−0.447813	−	0.775635i
$712$	−26.5550	+	28.7344i	−0.995191	+	1.07687i
$713$	33.7539	−	40.2263i	1.26409	−	1.50649i
$714$	0.0341016	−	2.13702i	0.00127622	−	0.0799758i
$715$	−0.0606095	+	0.104979i	−0.00226667	+	0.00392598i
$716$	−34.1954	−	30.6048i	−1.27794	−	1.14375i
$717$	18.7846	−	3.31222i	0.701522	−	0.123697i
$718$	7.21546	−	8.32558i	0.269279	−	0.310708i
$719$	9.88743	−	27.1655i	0.368739	−	1.01310i	−0.607103	−	0.794623i	$-0.707668\pi$
$719$	9.88743	−	27.1655i	0.368739	−	1.01310i	0.975842	−	0.218479i	$-0.0701094\pi$
$720$	0.0445141	+	0.400441i	0.00165894	+	0.0149236i
$721$		−	0.809749i		−	0.0301566i
$722$	1.91844	+	26.8015i	0.0713971	+	0.997448i
$723$		−	8.61750i		−	0.320488i
$724$	15.9776	−	39.8894i	0.593803	−	1.48248i
$725$	−9.18649	+	25.2397i	−0.341178	+	0.937378i
$726$	−9.03345	−	7.82895i	−0.335263	−	0.290560i
$727$	−12.6244	+	2.22602i	−0.468212	+	0.0825584i	−0.402776	−	0.915298i	$-0.631955\pi$
$727$	−12.6244	+	2.22602i	−0.468212	+	0.0825584i	−0.0654356	+	0.997857i	$0.520844\pi$
$728$	−7.52142	+	2.33652i	−0.278762	+	0.0865971i
$729$	−4.01571	+	6.95541i	−0.148730	+	0.257608i
$730$	−0.425545	−	0.00679066i	−0.0157501	−	0.000251334i
$731$	−0.315030	+	0.375438i	−0.0116518	+	0.0138861i
$732$	−4.57716	+	21.8554i	−0.169177	+	0.807799i
$733$	−25.7324	−	44.5699i	−0.950450	−	1.64623i	−0.744453	−	0.667674i	$-0.767290\pi$
$733$	−25.7324	−	44.5699i	−0.950450	−	1.64623i	−0.205996	−	0.978553i	$-0.566044\pi$
$734$	−10.3953	+	5.78260i	−0.383699	+	0.213440i
$735$	−0.200463	+	0.0729627i	−0.00739420	+	0.00269127i
$736$	−28.0653	−	39.4496i	−1.03450	−	1.45413i
$737$	14.1655	+	2.49776i	0.521792	+	0.0920061i
$738$	13.5807	+	16.7195i	0.499913	+	0.615455i
$739$	3.33185	+	3.97074i	0.122564	+	0.146066i	0.823837	−	0.566827i	$-0.191829\pi$
$739$	3.33185	+	3.97074i	0.122564	+	0.146066i	−0.701273	+	0.712893i	$0.747385\pi$
$740$	−0.361062	+	0.193369i	−0.0132729	+	0.00710839i
$741$	0.344578	−	7.90553i	0.0126584	−	0.290417i
$742$	−5.33676	+	8.91205i	−0.195919	+	0.327172i
$743$	12.0551	−	10.1154i	0.442259	−	0.371099i	−0.394295	−	0.918984i	$-0.629011\pi$
$743$	12.0551	−	10.1154i	0.442259	−	0.371099i	0.836554	+	0.547885i	$0.184567\pi$
$744$	14.5736	+	6.10902i	0.534294	+	0.223968i
$745$	−0.107794	+	0.611330i	−0.00394927	+	0.0223974i
$746$	−10.2944	+	26.9384i	−0.376906	+	0.986285i
$747$	−0.545236	−	1.49802i	−0.0199492	−	0.0548098i
$748$	0.0993684	−	3.11273i	0.00363327	−	0.113813i
$749$	−1.02199	+	0.590044i	−0.0373425	+	0.0215597i
$750$	0.564539	−	0.195332i	0.0206140	−	0.00713252i
$751$	37.8228	+	31.7371i	1.38017	+	1.15810i	0.969148	+	0.246479i	$0.0792737\pi$
$751$	37.8228	+	31.7371i	1.38017	+	1.15810i	0.411026	+	0.911624i	$0.365171\pi$
$752$	−2.12849	+	33.3036i	−0.0776180	+	1.21446i
$753$	−4.20954	−	2.43038i	−0.153404	−	0.0885679i
$754$	−2.86895	+	14.8784i	−0.104481	+	0.541838i
$755$	0.00445125	+	0.0252443i	0.000161998	+	0.000918734i
$756$	4.10183	+	12.4967i	0.149182	+	0.454500i
$757$	45.1863	+	16.4465i	1.64232	+	0.597757i	0.987443	−	0.157975i	$-0.0504965\pi$
$757$	45.1863	+	16.4465i	1.64232	+	0.597757i	0.654881	+	0.755732i	$0.272719\pi$
$758$	−3.98955	−	24.9472i	−0.144907	−	0.906124i
$759$	−10.2121			−0.370676
$760$	−0.469958	+	0.326162i	−0.0170472	+	0.0118311i
$761$	−48.4854			−1.75759			−0.878797	−	0.477196i	$-0.841653\pi$
$761$	−48.4854			−1.75759			−0.878797	+	0.477196i	$0.841653\pi$
$762$	−2.66432	−	16.6604i	−0.0965183	−	0.603543i
$763$	10.6580	+	3.87919i	0.385845	+	0.140436i
$764$	−4.79071	−	14.5954i	−0.173322	−	0.528045i
$765$	−0.0207847	−	0.117876i	−0.000751472	−	0.00426181i
$766$	3.26257	−	16.9197i	0.117882	−	0.611333i
$767$	−20.2410	−	11.6862i	−0.730860	−	0.421962i
$768$	8.83151	−	11.5872i	0.318680	−	0.418118i
$769$	3.06662	+	2.57320i	0.110585	+	0.0927919i	0.696404	−	0.717650i	$-0.254782\pi$
$769$	3.06662	+	2.57320i	0.110585	+	0.0927919i	−0.585818	+	0.810442i	$0.699227\pi$
$770$	0.113497	−	0.0392704i	0.00409015	−	0.00141521i
$771$	10.8700	−	6.27581i	0.391474	−	0.226018i
$772$	−0.248209	+	7.77517i	−0.00893324	+	0.279835i
$773$	8.87283	+	24.3779i	0.319133	+	0.876812i	0.990724	+	0.135889i	$0.0433892\pi$
$773$	8.87283	+	24.3779i	0.319133	+	0.876812i	−0.671591	+	0.740922i	$0.734389\pi$
$774$	0.451997	−	1.18278i	0.0162467	−	0.0425142i
$775$	−5.32491	+	30.1991i	−0.191277	+	1.08478i
$776$	9.28736	−	22.1558i	0.333397	−	0.795346i
$777$	−4.30003	+	3.60816i	−0.154263	+	0.129442i
$778$	−14.5423	+	24.2848i	−0.521368	+	0.870653i
$779$	−11.7015	+	28.2558i	−0.419249	+	1.01237i
$780$	0.148508	−	0.0795345i	0.00531745	−	0.00284779i
$781$	−5.14909	−	6.13645i	−0.184249	−	0.219579i
$782$	9.06804	+	11.1639i	0.324273	+	0.399220i
$783$	24.9197	+	4.39401i	0.890557	+	0.157029i
$784$	−18.4995	−	8.10414i	−0.660698	−	0.289434i
$785$	0.303042	−	0.110298i	0.0108160	−	0.00393671i
$786$	−1.52764	+	0.849778i	−0.0544892	+	0.0303106i
$787$	−7.04209	−	12.1973i	−0.251023	−	0.434785i	0.712785	−	0.701383i	$-0.247434\pi$
$787$	−7.04209	−	12.1973i	−0.251023	−	0.434785i	−0.963808	+	0.266598i	$0.914100\pi$
$788$	−4.78399	+	22.8430i	−0.170422	+	0.813748i
$789$	−8.08273	+	9.63262i	−0.287753	+	0.342930i
$790$	0.721776	+	0.0115178i	0.0256796	+	0.000409784i
$791$	−9.93091	+	17.2008i	−0.353102	+	0.611591i
$792$	2.38697	+	7.68381i	0.0848171	+	0.273032i
$793$	−24.0736	+	4.24483i	−0.854879	+	0.150738i
$794$	4.88675	+	4.23516i	0.173424	+	0.150300i
$795$	0.0759939	−	0.208791i	0.00269522	−	0.00740507i
$796$	−16.1192	+	40.2429i	−0.571329	+	1.42637i
$797$		−	42.2792i		−	1.49761i	−0.662792	−	0.748804i	$-0.730629\pi$
$797$		−	42.2792i		−	1.49761i	0.662792	−	0.748804i	$-0.269371\pi$
$798$	−5.38771	+	5.69535i	−0.190723	+	0.201613i
$799$		−	9.91390i		−	0.350728i
$800$	25.7119	+	11.7562i	0.909054	+	0.415643i
$801$	−10.2708	+	28.2187i	−0.362900	+	0.997059i
$802$	7.45029	−	8.59653i	0.263079	−	0.303554i
$803$	−8.37006	+	1.47587i	−0.295373	+	0.0520822i
$804$	−14.8957	−	13.3316i	−0.525330	−	0.470168i
$805$	−0.277324	+	0.480339i	−0.00977438	+	0.0169297i
$806$	−0.276019	+	17.2970i	−0.00972235	+	0.609262i
$807$	0.130933	−	0.156040i	0.00460906	−	0.00549286i
$808$	−21.8958	−	20.2351i	−0.770293	−	0.711869i
$809$	21.3717	+	37.0168i	0.751388	+	1.30144i	0.947150	+	0.320791i	$0.103949\pi$
$809$	21.3717	+	37.0168i	0.751388	+	1.30144i	−0.195762	+	0.980651i	$0.562718\pi$
$810$	0.0709814	+	0.127603i	0.00249403	+	0.00448351i
$811$	19.8838	−	7.23710i	0.698213	−	0.254129i	0.0315655	−	0.999502i	$-0.489951\pi$
$811$	19.8838	−	7.23710i	0.698213	−	0.254129i	0.666648	+	0.745373i	$0.267728\pi$
$812$	11.8022	−	9.27797i	0.414178	−	0.325593i
$813$	12.7511	+	2.24836i	0.447199	+	0.0788533i
$814$	−6.34881	+	5.15692i	−0.222526	+	0.180750i
$815$	0.486213	+	0.579446i	0.0170313	+	0.0202971i
$816$	−2.39873	+	3.60262i	−0.0839725	+	0.126117i
$817$	1.78237	−	0.234787i	0.0623572	−	0.00821417i
$818$	15.7694	+	9.44308i	0.551363	+	0.330170i
$819$	−4.63069	+	3.88561i	−0.161809	+	0.135774i
$820$	−0.644486	+	0.0925452i	−0.0225064	+	0.00323182i
$821$	3.63805	−	20.6324i	0.126969	−	0.720076i	−0.853150	−	0.521666i	$-0.825311\pi$
$821$	3.63805	−	20.6324i	0.126969	−	0.720076i	0.980119	−	0.198411i	$-0.0635780\pi$
$822$	9.27816	+	3.54563i	0.323613	+	0.123668i
$823$	6.64061	+	18.2449i	0.231477	+	0.635978i	0.999993	−	0.00385332i	$-0.00122655\pi$
$823$	6.64061	+	18.2449i	0.231477	+	0.635978i	−0.768516	+	0.639831i	$0.779004\pi$
$824$	−0.886909	+	1.37924i	−0.0308970	+	0.0480482i
$825$	5.16454	−	2.98175i	0.179806	−	0.103811i
$826$	7.57175	+	21.8835i	0.263455	+	0.761423i
$827$	11.1754	+	9.37729i	0.388608	+	0.326080i	0.816070	−	0.577952i	$-0.196148\pi$
$827$	11.1754	+	9.37729i	0.388608	+	0.326080i	−0.427463	+	0.904033i	$0.640593\pi$
$828$	−31.5711	−	19.5966i	−1.09717	−	0.681029i
$829$	8.11069	+	4.68271i	0.281696	+	0.162637i	0.634191	−	0.773177i	$-0.281333\pi$
$829$	8.11069	+	4.68271i	0.281696	+	0.162637i	−0.352495	+	0.935814i	$0.614667\pi$
$830$	0.0473153	+	0.00912367i	0.00164234	+	0.000316687i
$831$	−3.35063	−	19.0023i	−0.116232	−	0.659184i
$832$	15.3704	+	4.25834i	0.532871	+	0.147632i
$833$	5.63814	+	2.05212i	0.195350	+	0.0711016i
$834$	21.7142	−	3.47253i	0.751902	−	0.120244i
$835$	−0.686140			−0.0237448
$836$	−7.98202	+	8.17257i	−0.276064	+	0.282654i
$837$	28.8892			0.998557
$838$	−2.05991	+	0.329419i	−0.0711583	+	0.0113796i
$839$	10.1232	+	3.68454i	0.349492	+	0.127205i	0.510800	−	0.859699i	$-0.329349\pi$
$839$	10.1232	+	3.68454i	0.349492	+	0.127205i	−0.161309	+	0.986904i	$0.551571\pi$
$840$	−0.162798	−	0.0368154i	−0.00561705	−	0.00127025i
$841$	0.0204617	+	0.116044i	0.000705577	+	0.00400153i
$842$	28.4439	+	5.48475i	0.980240	+	0.189017i
$843$	5.81144	+	3.35524i	0.200157	+	0.115560i
$844$	12.1508	−	19.5756i	0.418249	−	0.673820i
$845$	−0.320796	−	0.269179i	−0.0110357	−	0.00926005i
$846$	8.37509	+	24.2052i	0.287941	+	0.832193i
$847$	−11.2284	+	6.48273i	−0.385813	+	0.222749i
$848$	18.8513	−	9.33457i	0.647358	−	0.320550i
$849$	−7.61016	−	20.9087i	−0.261180	−	0.717586i
$850$	−7.84561	−	2.99818i	−0.269102	−	0.102837i
$851$	6.55941	−	37.2003i	0.224854	−	1.27521i
$852$	1.58238	+	11.0197i	0.0542115	+	0.377529i
$853$	−7.36168	+	6.17719i	−0.252059	+	0.211503i	−0.760058	−	0.649855i	$-0.774830\pi$
$853$	−7.36168	+	6.17719i	−0.252059	+	0.211503i	0.507999	+	0.861358i	$0.330385\pi$
$854$	20.7785	+	12.4427i	0.711026	+	0.425780i
$855$	−0.235879	+	0.370315i	−0.00806688	+	0.0126645i
$856$	2.38701	+	0.114350i	0.0815864	+	0.00390842i
$857$	23.7226	+	28.2715i	0.810349	+	0.965737i	0.999870	−	0.0161401i	$-0.00513779\pi$
$857$	23.7226	+	28.2715i	0.810349	+	0.965737i	−0.189520	+	0.981877i	$0.560693\pi$
$858$	2.61133	−	2.12109i	0.0891492	−	0.0724128i
$859$	−23.0371	−	4.06206i	−0.786015	−	0.138596i	−0.233786	−	0.972288i	$-0.575111\pi$
$859$	−23.0371	−	4.06206i	−0.786015	−	0.138596i	−0.552229	+	0.833693i	$0.686223\pi$
$860$	0.0236538	+	0.0300894i	0.000806588	+	0.00102604i
$861$	−8.38509	+	3.05192i	−0.285763	+	0.104009i
$862$	11.3533	+	20.4097i	0.386694	+	0.695159i
$863$	−16.2551	−	28.1546i	−0.553329	−	0.958394i	−0.998031	−	0.0627154i	$-0.980024\pi$
$863$	−16.2551	−	28.1546i	−0.553329	−	0.958394i	0.444703	−	0.895678i	$-0.353309\pi$
$864$	6.70085	−	25.7782i	0.227968	−	0.876993i
$865$	−0.0586236	+	0.0698649i	−0.00199326	+	0.00237548i
$866$	0.685470	−	42.9558i	0.0232932	−	1.45970i
$867$	−7.09695	+	12.2923i	−0.241025	+	0.417468i
$868$	11.4303	−	12.7714i	0.387970	−	0.433488i
$869$	14.1966	−	2.50325i	0.481588	−	0.0849169i
$870$	−0.210305	+	0.242661i	−0.00713002	+	0.00822699i
$871$	7.48480	−	20.5643i	0.253613	−	0.696795i
$872$	−13.9049	−	18.2810i	−0.470878	−	0.619072i
$873$		−	18.4385i		−	0.624048i
$874$	3.13808	−	52.6647i	0.106147	−	1.78141i
$875$		−	0.647928i		−	0.0219039i
$876$	10.9649	+	4.39197i	0.370470	+	0.148391i
$877$	13.6046	−	37.3782i	0.459393	−	1.26217i	−0.466545	−	0.884497i	$-0.654501\pi$
$877$	13.6046	−	37.3782i	0.459393	−	1.26217i	0.925938	−	0.377675i	$-0.123276\pi$
$878$	−7.97567	−	6.91221i	−0.269166	−	0.233276i
$879$	−11.9396	+	2.10527i	−0.402712	+	0.0710090i
$880$	−0.236332	−	0.0574231i	−0.00796674	−	0.00193573i
$881$	−0.220653	+	0.382182i	−0.00743398	+	0.0128760i	−0.869718	−	0.493548i	$-0.835700\pi$
$881$	−0.220653	+	0.382182i	−0.00743398	+	0.0128760i	0.862284	+	0.506424i	$0.169033\pi$
$882$	−15.4994	−	0.247332i	−0.521891	−	0.00832811i
$883$	−22.6148	+	26.9512i	−0.761048	+	0.906981i	−0.997914	−	0.0645611i	$-0.979435\pi$
$883$	−22.6148	+	26.9512i	−0.761048	+	0.906981i	0.236866	+	0.971542i	$0.423880\pi$
$884$	−4.63756	−	0.971240i	−0.155978	−	0.0326663i
$885$	−0.247654	−	0.428949i	−0.00832480	−	0.0144190i
$886$	−40.3636	+	22.4529i	−1.35604	+	0.754322i
$887$	−30.0097	+	10.9226i	−1.00763	+	0.366746i	−0.792521	−	0.609845i	$-0.791232\pi$
$887$	−30.0097	+	10.9226i	−1.00763	+	0.366746i	−0.215105	+	0.976591i	$0.569009\pi$
$888$	11.2762	−	1.43598i	0.378405	−	0.0481883i
$889$	−18.0218	−	3.17774i	−0.604433	−	0.106578i
$890$	−0.572296	−	0.704567i	−0.0191834	−	0.0236172i
$891$	1.87433	+	2.23374i	0.0627925	+	0.0748331i
$892$	−1.92420	−	3.59289i	−0.0644268	−	0.120299i
$893$	−24.5664	+	26.8135i	−0.822083	+	0.897280i
$894$	8.85105	−	14.7807i	0.296023	−	0.494341i
$895$	0.815575	−	0.684349i	0.0272617	−	0.0228753i
$896$	−8.74479	−	13.1617i	−0.292143	−	0.439703i
$897$	−2.69795	+	15.3008i	−0.0900819	+	0.510880i
$898$	2.62189	−	6.86094i	0.0874936	−	0.228953i
$899$	−11.2778	−	30.9856i	−0.376137	−	1.03343i
$900$	21.6882	+	0.692359i	0.722941	+	0.0230786i
$901$	−5.41201	+	3.12463i	−0.180300	+	0.104096i
$902$	−12.2876	+	4.25155i	−0.409132	+	0.141561i
$903$	0.401819	+	0.337166i	0.0133717	+	0.0112202i
$904$	35.7552	−	18.4209i	1.18920	−	0.612670i
$905$	0.863341	+	0.498450i	0.0286984	+	0.0165690i
$906$	0.134700	−	0.698553i	0.00447511	−	0.0232079i
$907$	2.47076	+	14.0124i	0.0820404	+	0.465274i	0.997956	+	0.0639034i	$0.0203549\pi$
$907$	2.47076	+	14.0124i	0.0820404	+	0.465274i	−0.915916	+	0.401371i	$0.868534\pi$
$908$	−23.5471	+	7.72894i	−0.781438	+	0.256494i
$909$	−21.5029	−	7.82640i	−0.713205	−	0.259585i
$910$	−0.0288540	−	0.180428i	−0.000956500	−	0.00598113i
$911$	6.23491			0.206572			0.103286	−	0.994652i	$-0.467064\pi$
$911$	6.23491			0.206572			0.103286	+	0.994652i	$0.467064\pi$
$912$	15.4149	−	3.79977i	0.510439	−	0.125823i
$913$	0.962289			0.0318471
$914$	−2.95076	−	18.4516i	−0.0976026	−	0.610323i
$915$	−0.486799	−	0.177180i	−0.0160931	−	0.00585740i
$916$	−17.6571	+	5.79565i	−0.583407	+	0.191494i
$917$	0.329239	+	1.86721i	0.0108724	+	0.0616607i
$918$	−1.49817	+	7.76948i	−0.0494468	+	0.256431i
$919$	−1.40693	−	0.812293i	−0.0464104	−	0.0267951i	0.476615	−	0.879112i	$-0.341863\pi$
$919$	−1.40693	−	0.812293i	−0.0464104	−	0.0267951i	−0.523026	+	0.852317i	$0.675197\pi$
$920$	0.998474	−	0.514410i	0.0329187	−	0.0169596i
$921$	−19.8875	−	16.6876i	−0.655315	−	0.549875i
$922$	35.1645	−	12.1670i	1.15808	−	0.400700i
$923$	−10.5546	+	6.09371i	−0.347409	+	0.200577i
$924$	−3.33145	−	0.106351i	−0.109597	−	0.00349868i
$925$	7.54453	+	20.7284i	0.248063	+	0.681547i
$926$	−10.6736	+	27.9307i	−0.350757	+	0.917859i
$927$	−0.218548	+	1.23945i	−0.00717805	+	0.0407087i
$928$	−30.2648	+	2.87626i	−0.993490	+	0.0944177i
$929$	−14.7421	+	12.3701i	−0.483672	+	0.405849i	−0.851752	−	0.523945i	$-0.824460\pi$
$929$	−14.7421	+	12.3701i	−0.483672	+	0.405849i	0.368080	+	0.929794i	$0.380015\pi$
$930$	−0.188346	+	0.314526i	−0.00617611	+	0.0103137i
$931$	−10.1640	−	19.5214i	−0.333113	−	0.639789i
$932$	−7.50894	−	14.0208i	−0.245963	−	0.459267i
$933$	−15.3010	−	18.2350i	−0.500932	−	0.596987i
$934$	28.2270	+	34.7510i	0.923616	+	1.13709i
$935$	0.0711536	+	0.0125463i	0.00232697	+	0.000410308i
$936$	12.1433	−	1.54640i	0.396916	−	0.0505457i
$937$	7.32200	−	2.66499i	0.239199	−	0.0870615i	−0.219639	−	0.975581i	$-0.570488\pi$
$937$	7.32200	−	2.66499i	0.239199	−	0.0870615i	0.458838	+	0.888520i	$0.348266\pi$
$938$	−18.9477	+	10.5400i	−0.618663	+	0.344142i
$939$	−1.61818	−	2.80277i	−0.0528074	−	0.0914650i
$940$	−0.757772	−	0.158699i	−0.0247158	−	0.00517621i
$941$	−15.8110	+	18.8429i	−0.515425	+	0.614260i	−0.959493	−	0.281734i	$-0.909091\pi$
$941$	−15.8110	+	18.8429i	−0.515425	+	0.614260i	0.444068	+	0.895993i	$0.353535\pi$
$942$	−8.94904	−	0.142805i	−0.291576	−	0.00465284i
$943$	30.0240	−	52.0032i	0.977717	−	1.69346i
$944$	11.0718	−	45.5673i	0.360356	−	1.48309i
$945$	−0.300502	+	0.0529867i	−0.00977534	+	0.00172366i
$946$	0.577591	+	0.500576i	0.0187791	+	0.0162751i
$947$	1.99484	−	5.48078i	0.0648236	−	0.178101i	−0.903052	−	0.429532i	$-0.858679\pi$
$947$	1.99484	−	5.48078i	0.0648236	−	0.178101i	0.967875	+	0.251430i	$0.0809009\pi$
$948$	−18.5978	−	7.44931i	−0.604029	−	0.241942i
$949$			12.9308i			0.419751i
$950$	13.7901	+	27.5502i	0.447410	+	0.893847i
$951$			12.6600i			0.410528i
$952$	2.84197	+	3.73638i	0.0921087	+	0.121097i
$953$	0.622993	−	1.71166i	0.0201807	−	0.0554461i	−0.929193	−	0.369594i	$-0.879497\pi$
$953$	0.622993	−	1.71166i	0.0201807	−	0.0554461i	0.949374	+	0.314148i	$0.101719\pi$
$954$	10.5740	−	12.2009i	0.342347	−	0.395019i
$955$	0.350970	−	0.0618855i	0.0113571	−	0.00200257i
$956$	−27.9401	+	31.2181i	−0.903648	+	1.00967i
$957$	−3.20629	+	5.55346i	−0.103645	+	0.179518i
$958$	0.305313	−	19.1328i	0.00986422	−	0.618153i
$959$	6.92480	−	8.25265i	0.223613	−	0.266492i
$960$	0.236969	+	0.241018i	0.00764814	+	0.00777882i
$961$	−3.32299	−	5.75559i	−0.107193	−	0.185664i
$962$	6.04933	+	10.8749i	0.195038	+	0.350620i
$963$	1.72356	−	0.627323i	0.0555408	−	0.0202152i
$964$	11.6977	+	14.8803i	0.376756	+	0.479261i
$965$	−0.177732	−	0.0313390i	−0.00572140	−	0.00100884i
$966$	11.9483	−	9.70523i	0.384432	−	0.312261i
$967$	12.3518	+	14.7203i	0.397208	+	0.473375i	0.927167	−	0.374649i	$-0.122237\pi$
$967$	12.3518	+	14.7203i	0.397208	+	0.473375i	−0.529958	+	0.848024i	$0.677792\pi$
$968$	26.2258	+	1.25635i	0.842929	+	0.0403807i
$969$	−4.49808	+	1.41861i	−0.144499	+	0.0455722i
$970$	0.478164	+	0.286337i	0.0153529	+	0.00919371i
$971$	−42.8513	+	35.9565i	−1.37516	+	1.15390i	−0.404201	+	0.914670i	$0.632450\pi$
$971$	−42.8513	+	35.9565i	−1.37516	+	1.15390i	−0.970963	+	0.239230i	$0.923105\pi$
$972$	−4.59147	−	31.9751i	−0.147272	−	1.02560i
$973$	4.14168	−	23.4886i	0.132776	−	0.753011i
$974$	−17.1641	−	6.55920i	−0.549972	−	0.210170i
$975$	−3.10314	−	8.52580i	−0.0993799	−	0.273044i
$976$	−21.7636	−	43.9520i	−0.696636	−	1.40687i
$977$	−10.5268	+	6.07767i	−0.336783	+	0.194442i	−0.658849	−	0.752275i	$-0.728956\pi$
$977$	−10.5268	+	6.07767i	−0.336783	+	0.194442i	0.322065	+	0.946717i	$0.395623\pi$
$978$	−6.86436	−	19.8390i	−0.219498	−	0.634382i
$979$	−13.8860	−	11.6517i	−0.443799	−	0.372391i
$980$	0.247108	−	0.398103i	0.00789358	−	0.0127169i
$981$	−15.2667	−	8.81424i	−0.487428	−	0.281417i
$982$	45.1988	+	8.71555i	1.44235	+	0.278124i
$983$	4.91750	+	27.8885i	0.156844	+	0.889506i	0.957081	+	0.289822i	$0.0935960\pi$
$983$	4.91750	+	27.8885i	0.156844	+	0.889506i	−0.800237	+	0.599684i	$0.795293\pi$
$984$	17.6250	+	3.98577i	0.561866	+	0.127062i
$985$	−0.508795	−	0.185186i	−0.0162116	−	0.00590053i
$986$	8.91814	−	1.42618i	0.284011	−	0.0454189i
$987$	−10.6105			−0.337737
$988$	10.1362	+	14.1186i	0.322476	+	0.449173i
$989$	−3.52983			−0.112242
$990$	−0.184324	+	0.0294770i	−0.00585819	+	0.000936839i
$991$	−28.8710	−	10.5082i	−0.917116	−	0.333803i	−0.160026	−	0.987113i	$-0.551158\pi$
$991$	−28.8710	−	10.5082i	−0.917116	−	0.333803i	−0.757091	+	0.653310i	$0.773380\pi$
$992$	−33.4575	+	9.23389i	−1.06228	+	0.293176i
$993$	−1.12404	−	6.37473i	−0.0356702	−	0.202296i
$994$	11.8564	+	2.28624i	0.376062	+	0.0725150i
$995$	−0.870991	−	0.502867i	−0.0276123	−	0.0159420i
$996$	−1.13625	−	0.705287i	−0.0360035	−	0.0223479i
$997$	42.8223	+	35.9321i	1.35619	+	1.13798i	0.977137	+	0.212609i	$0.0681961\pi$
$997$	42.8223	+	35.9321i	1.35619	+	1.13798i	0.379057	+	0.925373i	$0.376248\pi$
$998$	−1.91574	−	5.53678i	−0.0606418	−	0.175264i
$999$	17.9972	−	10.3907i	0.569406	−	0.328747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.51.5	yes	48
3.2	odd	2		684.2.cf.a.127.4		48
4.3	odd	2	inner	76.2.k.a.51.8	yes	48
12.11	even	2		684.2.cf.a.127.1		48
19.3	odd	18	inner	76.2.k.a.3.8	yes	48
57.41	even	18		684.2.cf.a.307.1		48
76.3	even	18	inner	76.2.k.a.3.5	✓	48
228.155	odd	18		684.2.cf.a.307.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.5	✓	48	76.3	even	18	inner
76.2.k.a.3.8	yes	48	19.3	odd	18	inner
76.2.k.a.51.5	yes	48	1.1	even	1	trivial
76.2.k.a.51.8	yes	48	4.3	odd	2	inner
684.2.cf.a.127.1		48	12.11	even	2
684.2.cf.a.127.4		48	3.2	odd	2
684.2.cf.a.307.1		48	57.41	even	18
684.2.cf.a.307.4		48	228.155	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)

\(f(q)\)	\(=\)	\(q+(0.223323 + 1.39647i) q^{2} +(0.855656 + 0.311433i) q^{3} +(-1.90025 + 0.623726i) q^{4} +(-0.00805719 - 0.0456946i) q^{5} +(-0.243820 + 1.26445i) q^{6} +(1.20959 + 0.698356i) q^{7} +(-1.29538 - 2.51435i) q^{8} +(-1.66298 - 1.39540i) q^{9} +O(q^{10})\)	\(q+(0.223323 + 1.39647i) q^{2} +(0.855656 + 0.311433i) q^{3} +(-1.90025 + 0.623726i) q^{4} +(-0.00805719 - 0.0456946i) q^{5} +(-0.243820 + 1.26445i) q^{6} +(1.20959 + 0.698356i) q^{7} +(-1.29538 - 2.51435i) q^{8} +(-1.66298 - 1.39540i) q^{9} +(0.0620117 - 0.0214562i) q^{10} +(1.13484 - 0.655201i) q^{11} +(-1.82021 - 0.0581071i) q^{12} +(-0.681875 - 1.87343i) q^{13} +(-0.705104 + 1.84511i) q^{14} +(0.00733663 - 0.0416081i) q^{15} +(3.22193 - 2.37048i) q^{16} +(-0.910294 + 0.763828i) q^{17} +(1.57726 - 2.63392i) q^{18} +(4.35476 + 0.189811i) q^{19} +(0.0438116 + 0.0818058i) q^{20} +(0.817500 + 0.974258i) q^{21} +(1.16840 + 1.43845i) q^{22} +(-8.42847 - 1.48617i) q^{23} +(-0.325350 - 2.55485i) q^{24} +(4.69644 - 1.70936i) q^{25} +(2.46392 - 1.37060i) q^{26} +(-2.35422 - 4.07762i) q^{27} +(-2.73411 - 0.572602i) q^{28} +(-3.45448 + 4.11689i) q^{29} +(0.0597429 + 0.000953352i) q^{30} +(-3.06782 + 5.31361i) q^{31} +(4.02983 + 3.96995i) q^{32} +(1.17509 - 0.207199i) q^{33} +(-1.26995 - 1.10062i) q^{34} +(0.0221652 - 0.0608984i) q^{35} +(4.03043 + 1.61438i) q^{36} +4.41365i q^{37} +(0.707452 + 6.12368i) q^{38} -1.81537i q^{39} +(-0.104455 + 0.0794507i) q^{40} +(-2.39968 + 6.59307i) q^{41} +(-1.17796 + 1.35919i) q^{42} +(0.406170 - 0.0716188i) q^{43} +(-1.74782 + 1.95288i) q^{44} +(-0.0503634 + 0.0872320i) q^{45} +(0.193118 - 12.1020i) q^{46} +(-5.36271 + 6.39102i) q^{47} +(3.49511 - 1.02490i) q^{48} +(-2.52460 - 4.37273i) q^{49} +(3.43590 + 6.17670i) q^{50} +(-1.01678 + 0.370078i) q^{51} +(2.46425 + 3.13470i) q^{52} +(5.17907 + 0.913210i) q^{53} +(5.16853 - 4.19822i) q^{54} +(-0.0390828 - 0.0465770i) q^{55} +(0.189033 - 3.94597i) q^{56} +(3.66707 + 1.51863i) q^{57} +(-6.52057 - 3.90468i) q^{58} +(8.98054 - 7.53557i) q^{59} +(0.0120106 + 0.0836420i) q^{60} +(2.12915 - 12.0750i) q^{61} +(-8.10541 - 3.09746i) q^{62} +(-1.03703 - 2.84921i) q^{63} +(-4.64396 + 6.51411i) q^{64} +(-0.0801118 + 0.0462526i) q^{65} +(0.551770 + 1.59470i) q^{66} +(8.40871 + 7.05575i) q^{67} +(1.25337 - 2.01924i) q^{68} +(-6.74903 - 3.89655i) q^{69} +(0.0899927 + 0.0173530i) q^{70} +(-1.06152 - 6.02019i) q^{71} +(-1.35434 + 5.98890i) q^{72} +(-6.09478 - 2.21832i) q^{73} +(-6.16352 + 0.985667i) q^{74} +4.55089 q^{75} +(-8.39355 + 2.35549i) q^{76} +1.83025 q^{77} +(2.53511 - 0.405414i) q^{78} +(10.3375 + 3.76254i) q^{79} +(-0.134278 - 0.128125i) q^{80} +(0.386407 + 2.19142i) q^{81} +(-9.74293 - 1.87870i) q^{82} +(0.635962 + 0.367173i) q^{83} +(-2.16113 - 1.34144i) q^{84} +(0.0422372 + 0.0354412i) q^{85} +(0.190720 + 0.551210i) q^{86} +(-4.23798 + 2.44680i) q^{87} +(-3.11746 - 2.00466i) q^{88} +(-4.73119 - 12.9988i) q^{89} +(-0.133064 - 0.0508501i) q^{90} +(0.483537 - 2.74227i) q^{91} +(16.9432 - 2.43296i) q^{92} +(-4.27983 + 3.59121i) q^{93} +(-10.1225 - 6.06159i) q^{94} +(-0.0264138 - 0.200518i) q^{95} +(2.21177 + 4.65193i) q^{96} +(5.45960 + 6.50649i) q^{97} +(5.54259 - 4.50205i) q^{98} +(-2.80148 - 0.493977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

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