LMFDB - Embedded newform 76.2.k.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	76.3
Dual form			76.2.k.a.51.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33647 - 0.462424i) q^{2} +(-0.855656 + 0.311433i) q^{3} +(1.57233 - 1.23604i) q^{4} +(-0.00805719 + 0.0456946i) q^{5} +(-0.999548 + 0.811899i) q^{6} +(-1.20959 + 0.698356i) q^{7} +(1.52980 - 2.37901i) q^{8} +(-1.66298 + 1.39540i) q^{9} +O(q^{10})$	\(q+(1.33647 - 0.462424i) q^{2} +(-0.855656 + 0.311433i) q^{3} +(1.57233 - 1.23604i) q^{4} +(-0.00805719 + 0.0456946i) q^{5} +(-0.999548 + 0.811899i) q^{6} +(-1.20959 + 0.698356i) q^{7} +(1.52980 - 2.37901i) q^{8} +(-1.66298 + 1.39540i) q^{9} +(0.0103621 + 0.0647955i) q^{10} +(-1.13484 - 0.655201i) q^{11} +(-0.960429 + 1.54730i) q^{12} +(-0.681875 + 1.87343i) q^{13} +(-1.29365 + 1.49268i) q^{14} +(-0.00733663 - 0.0416081i) q^{15} +(0.944429 - 3.88691i) 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} +(-1.81967 - 0.350881i) q^{22} +(8.42847 - 1.48617i) q^{23} +(-0.568081 + 2.51205i) q^{24} +(4.69644 + 1.70936i) q^{25} +(-0.0449862 + 2.81911i) q^{26} +(2.35422 - 4.07762i) q^{27} +(-1.03868 + 2.59314i) q^{28} +(-3.45448 - 4.11689i) q^{29} +(-0.0290458 - 0.0522155i) q^{30} +(3.06782 + 5.31361i) q^{31} +(-0.535196 - 5.63148i) q^{32} +(1.17509 + 0.207199i) q^{33} +(-1.56980 - 0.599894i) q^{34} +(-0.0221652 - 0.0608984i) q^{35} +(-0.889975 + 4.24953i) q^{36} -4.41365i q^{37} +(-5.73226 + 2.26743i) q^{38} -1.81537i q^{39} +(0.0963821 + 0.0890718i) q^{40} +(-2.39968 - 6.59307i) q^{41} +(0.642047 - 1.68010i) q^{42} +(-0.406170 - 0.0716188i) q^{43} +(-2.59419 + 0.372514i) q^{44} +(-0.0503634 - 0.0872320i) q^{45} +(10.5772 - 5.88375i) q^{46} +(5.36271 + 6.39102i) q^{47} +(0.402407 + 3.61998i) q^{48} +(-2.52460 + 4.37273i) q^{49} +(7.06712 + 0.112774i) q^{50} +(1.01678 + 0.370078i) q^{51} +(1.24350 + 3.78848i) q^{52} +(5.17907 - 0.913210i) q^{53} +(1.26076 - 6.53828i) 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} +(-0.0629647 - 0.0563533i) q^{60} +(2.12915 + 12.0750i) q^{61} +(6.55720 + 5.68288i) q^{62} +(1.03703 - 2.84921i) q^{63} +(-3.31941 - 7.27884i) q^{64} +(-0.0801118 - 0.0462526i) q^{65} +(1.66629 - 0.266471i) q^{66} +(-8.40871 + 7.05575i) q^{67} +(-2.37540 - 0.0758305i) q^{68} +(-6.74903 + 3.89655i) q^{69} +(-0.0577841 - 0.0711394i) q^{70} +(1.06152 - 6.02019i) q^{71} +(0.775657 + 6.09094i) q^{72} +(-6.09478 + 2.21832i) q^{73} +(-2.04098 - 5.89873i) q^{74} -4.55089 q^{75} +(-6.61250 + 5.68109i) q^{76} +1.83025 q^{77} +(-0.839473 - 2.42620i) q^{78} +(-10.3375 + 3.76254i) q^{79} +(0.170001 + 0.0744728i) q^{80} +(0.386407 - 2.19142i) q^{81} +(-6.25591 - 7.70180i) q^{82} +(-0.635962 + 0.367173i) q^{83} +(0.0811589 - 2.54231i) q^{84} +(0.0422372 - 0.0354412i) q^{85} +(-0.575954 + 0.0921063i) q^{86} +(4.23798 + 2.44680i) q^{87} +(-3.29481 + 1.69747i) q^{88} +(-4.73119 + 12.9988i) q^{89} +(-0.107648 - 0.0932941i) q^{90} +(-0.483537 - 2.74227i) q^{91} +(11.4154 - 12.7546i) 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} +(-1.35200 + 7.01148i) 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.33647	−	0.462424i	0.945030	−	0.326983i
$2$	1.33647	−	0.462424i	0.945030	−	0.326983i
$3$	−0.855656	+	0.311433i	−0.494013	+	0.179806i	−0.576999	−	0.816745i	$-0.695777\pi$
$3$	−0.855656	+	0.311433i	−0.494013	+	0.179806i	0.0829861	+	0.996551i	$0.473554\pi$
$4$	1.57233	−	1.23604i	0.786164	−	0.618018i
$5$	−0.00805719	+	0.0456946i	−0.00360328	+	0.0204352i	−0.986556	−	0.163421i	$-0.947747\pi$
$5$	−0.00805719	+	0.0456946i	−0.00360328	+	0.0204352i	0.982953	+	0.183856i	$0.0588582\pi$
$6$	−0.999548	+	0.811899i	−0.408064	+	0.331456i
$7$	−1.20959	+	0.698356i	−0.457181	+	0.263954i	−0.710858	−	0.703335i	$-0.751693\pi$
$7$	−1.20959	+	0.698356i	−0.457181	+	0.263954i	0.253677	+	0.967289i	$0.418360\pi$
$8$	1.52980	−	2.37901i	0.540867	−	0.841108i
$9$	−1.66298	+	1.39540i	−0.554326	+	0.465134i
$10$	0.0103621	+	0.0647955i	0.00327677	+	0.0204901i
$11$	−1.13484	−	0.655201i	−0.342167	−	0.197550i	0.319063	−	0.947734i	$-0.396632\pi$
$11$	−1.13484	−	0.655201i	−0.342167	−	0.197550i	−0.661230	+	0.750183i	$0.729965\pi$
$12$	−0.960429	+	1.54730i	−0.277252	+	0.446666i
$13$	−0.681875	+	1.87343i	−0.189118	+	0.519597i	−0.997624	−	0.0688902i	$-0.978054\pi$
$13$	−0.681875	+	1.87343i	−0.189118	+	0.519597i	0.808506	+	0.588488i	$0.200276\pi$
$14$	−1.29365	+	1.49268i	−0.345742	+	0.398935i
$15$	−0.00733663	−	0.0416081i	−0.00189431	−	0.0107432i
$16$	0.944429	−	3.88691i	0.236107	−	0.971727i
$17$	−0.910294	−	0.763828i	−0.220779	−	0.185255i	0.525689	−	0.850677i	$-0.323807\pi$
$17$	−0.910294	−	0.763828i	−0.220779	−	0.185255i	−0.746468	+	0.665421i	$0.768252\pi$
$18$	−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
$22$	−1.81967	−	0.350881i	−0.387954	−	0.0748081i
$23$	8.42847	−	1.48617i	1.75746	−	0.309887i	0.800331	−	0.599559i	$-0.204657\pi$
$23$	8.42847	−	1.48617i	1.75746	−	0.309887i	0.957126	+	0.289672i	$0.0935461\pi$
$24$	−0.568081	+	2.51205i	−0.115959	+	0.512770i
$25$	4.69644	+	1.70936i	0.939288	+	0.341873i
$26$	−0.0449862	+	2.81911i	−0.00882252	+	0.552874i
$27$	2.35422	−	4.07762i	0.453069	−	0.784739i
$28$	−1.03868	+	2.59314i	−0.196291	+	0.490057i
$29$	−3.45448	−	4.11689i	−0.641480	−	0.764487i	0.343123	−	0.939291i	$-0.388515\pi$
$29$	−3.45448	−	4.11689i	−0.641480	−	0.764487i	−0.984603	+	0.174804i	$0.944071\pi$
$30$	−0.0290458	−	0.0522155i	−0.00530302	−	0.00953321i
$31$	3.06782	+	5.31361i	0.550996	+	0.954353i	0.998203	+	0.0599227i	$0.0190854\pi$
$31$	3.06782	+	5.31361i	0.550996	+	0.954353i	−0.447207	+	0.894431i	$0.647581\pi$
$32$	−0.535196	−	5.63148i	−0.0946101	−	0.995514i
$33$	1.17509	+	0.207199i	0.204556	+	0.0360688i
$34$	−1.56980	−	0.599894i	−0.269218	−	0.102881i
$35$	−0.0221652	−	0.0608984i	−0.00374660	−	0.0102937i
$36$	−0.889975	+	4.24953i	−0.148329	+	0.708255i
$37$		−	4.41365i		−	0.725599i	−0.931867	−	0.362800i	$-0.881821\pi$
$37$		−	4.41365i		−	0.725599i	0.931867	−	0.362800i	$-0.118179\pi$
$38$	−5.73226	+	2.26743i	−0.929895	+	0.367825i
$39$		−	1.81537i		−	0.290693i
$40$	0.0963821	+	0.0890718i	0.0152393	+	0.0140835i
$41$	−2.39968	−	6.59307i	−0.374767	−	1.02966i	−0.973494	−	0.228712i	$-0.926549\pi$
$41$	−2.39968	−	6.59307i	−0.374767	−	1.02966i	0.598727	−	0.800953i	$-0.295673\pi$
$42$	0.642047	−	1.68010i	0.0990700	−	0.259246i
$43$	−0.406170	−	0.0716188i	−0.0619404	−	0.0109218i	0.142592	−	0.989782i	$-0.454456\pi$
$43$	−0.406170	−	0.0716188i	−0.0619404	−	0.0109218i	−0.204532	+	0.978860i	$0.565567\pi$
$44$	−2.59419	+	0.372514i	−0.391089	+	0.0561587i
$45$	−0.0503634	−	0.0872320i	−0.00750774	−	0.0130038i
$46$	10.5772	−	5.88375i	1.55952	−	0.867512i
$47$	5.36271	+	6.39102i	0.782231	+	0.932227i	0.999032	−	0.0439892i	$-0.0140067\pi$
$47$	5.36271	+	6.39102i	0.782231	+	0.932227i	−0.216801	+	0.976216i	$0.569562\pi$
$48$	0.402407	+	3.61998i	0.0580824	+	0.522500i
$49$	−2.52460	+	4.37273i	−0.360657	+	0.624676i
$50$	7.06712	+	0.112774i	0.999442	+	0.0159487i
$51$	1.01678	+	0.370078i	0.142378	+	0.0518213i
$52$	1.24350	+	3.78848i	0.172443	+	0.525367i
$53$	5.17907	−	0.913210i	0.711400	−	0.125439i	0.193774	−	0.981046i	$-0.437927\pi$
$53$	5.17907	−	0.913210i	0.711400	−	0.125439i	0.517626	+	0.855607i	$0.326816\pi$
$54$	1.26076	−	6.53828i	0.171568	−	0.889748i
$55$	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	$-0.554111\pi$
$59$	−8.98054	−	7.53557i	−1.16917	−	0.981048i	−0.999990	+	0.00453778i	$0.998556\pi$
$60$	−0.0629647	−	0.0563533i	−0.00812871	−	0.00727517i
$61$	2.12915	+	12.0750i	0.272610	+	1.54605i	0.746452	+	0.665440i	$0.231756\pi$
$61$	2.12915	+	12.0750i	0.272610	+	1.54605i	−0.473841	+	0.880610i	$0.657133\pi$
$62$	6.55720	+	5.68288i	0.832765	+	0.721726i
$63$	1.03703	−	2.84921i	0.130653	−	0.358967i
$64$	−3.31941	−	7.27884i	−0.414926	−	0.909855i
$65$	−0.0801118	−	0.0462526i	−0.00993665	−	0.00573693i
$66$	1.66629	−	0.266471i	0.205106	−	0.0328004i
$67$	−8.40871	+	7.05575i	−1.02729	+	0.861997i	−0.990526	−	0.137327i	$-0.956149\pi$
$67$	−8.40871	+	7.05575i	−1.02729	+	0.861997i	−0.0367622	+	0.999324i	$0.511704\pi$
$68$	−2.37540	−	0.0758305i	−0.288060	−	0.00919580i
$69$	−6.74903	+	3.89655i	−0.812487	+	0.469090i
$70$	−0.0577841	−	0.0711394i	−0.00690652	−	0.00850279i
$71$	1.06152	−	6.02019i	0.125979	−	0.714465i	−0.854742	−	0.519053i	$-0.826285\pi$
$71$	1.06152	−	6.02019i	0.125979	−	0.714465i	0.980721	−	0.195412i	$-0.0626043\pi$
$72$	0.775657	+	6.09094i	0.0914120	+	0.717824i
$73$	−6.09478	+	2.21832i	−0.713341	+	0.259635i	−0.673096	−	0.739555i	$-0.735036\pi$
$73$	−6.09478	+	2.21832i	−0.713341	+	0.259635i	−0.0402446	+	0.999190i	$0.512814\pi$
$74$	−2.04098	−	5.89873i	−0.237259	−	0.685713i
$75$	−4.55089			−0.525492
$76$	−6.61250	+	5.68109i	−0.758506	+	0.651666i
$77$	1.83025			0.208577
$78$	−0.839473	−	2.42620i	−0.0950516	−	0.274713i
$79$	−10.3375	+	3.76254i	−1.16306	+	0.423319i	−0.850189	−	0.526477i	$-0.823512\pi$
$79$	−10.3375	+	3.76254i	−1.16306	+	0.423319i	−0.312870	+	0.949796i	$0.601290\pi$
$80$	0.170001	+	0.0744728i	0.0190067	+	0.00832631i
$81$	0.386407	−	2.19142i	0.0429341	−	0.243491i
$82$	−6.25591	−	7.70180i	−0.690850	−	0.850522i
$83$	−0.635962	+	0.367173i	−0.0698060	+	0.0403025i	−0.534497	−	0.845171i	$-0.679499\pi$
$83$	−0.635962	+	0.367173i	−0.0698060	+	0.0403025i	0.464691	+	0.885473i	$0.346165\pi$
$84$	0.0811589	−	2.54231i	0.00885516	−	0.277389i
$85$	0.0422372	−	0.0354412i	0.00458127	−	0.00384414i
$86$	−0.575954	+	0.0921063i	−0.0621067	+	0.00993208i
$87$	4.23798	+	2.44680i	0.454359	+	0.262324i
$88$	−3.29481	+	1.69747i	−0.351228	+	0.180951i
$89$	−4.73119	+	12.9988i	−0.501506	+	1.37788i	0.388299	+	0.921533i	$0.373063\pi$
$89$	−4.73119	+	12.9988i	−0.501506	+	1.37788i	−0.889805	+	0.456342i	$0.849159\pi$
$90$	−0.107648	−	0.0932941i	−0.0113471	−	0.00983406i
$91$	−0.483537	−	2.74227i	−0.0506885	−	0.287469i
$92$	11.4154	−	12.7546i	1.19013	−	1.32976i
$93$	−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	−0.414000	−	0.910277i	$-0.635869\pi$
$97$	5.45960	−	6.50649i	0.554338	−	0.660634i	0.968338	+	0.249642i	$0.0803131\pi$
$98$	−1.35200	+	7.01148i	−0.136573	+	0.708266i
$99$	2.80148	−	0.493977i	0.281560	−	0.0496466i
$100$	9.49718	−	3.11729i	0.949718	−	0.311729i
$101$	9.90522	+	3.60521i	0.985606	+	0.358731i	0.784017	−	0.620739i	$-0.213167\pi$
$101$	9.90522	+	3.60521i	0.985606	+	0.358731i	0.201589	+	0.979470i	$0.435389\pi$
$102$	1.53003	+	0.0244156i	0.151496	+	0.00241751i
$103$	0.289877	−	0.502082i	0.0285624	−	0.0494716i	−0.851391	−	0.524532i	$-0.824240\pi$
$103$	0.289877	−	0.502082i	0.0285624	−	0.0494716i	0.879953	+	0.475060i	$0.157574\pi$
$104$	3.41379	+	4.48817i	0.334750	+	0.440102i
$105$	0.0379316	+	0.0452051i	0.00370174	+	0.00441157i
$106$	6.49940	−	3.61541i	0.631278	−	0.351160i
$107$	0.422452	+	0.731708i	0.0408400	+	0.0707369i	0.885723	−	0.464214i	$-0.153663\pi$
$107$	0.422452	+	0.731708i	0.0408400	+	0.0707369i	−0.844883	+	0.534951i	$0.820330\pi$
$108$	−1.33849	−	9.32126i	−0.128796	−	0.896938i
$109$	7.99713	+	1.41011i	0.765986	+	0.135064i	0.542971	−	0.839751i	$-0.317299\pi$
$109$	7.99713	+	1.41011i	0.765986	+	0.135064i	0.223014	+	0.974815i	$0.428410\pi$
$110$	0.0306948	−	0.0803218i	0.00292663	−	0.00765838i
$111$	1.37456	+	3.77656i	0.130467	+	0.358456i
$112$	1.57208	+	5.36110i	0.148547	+	0.506577i
$113$		−	14.2204i		−	1.33774i	−0.743378	−	0.668872i	$-0.766777\pi$
$113$		−	14.2204i		−	1.33774i	0.743378	−	0.668872i	$-0.233223\pi$
$114$	4.19869	−	3.72535i	0.393243	−	0.348911i
$115$			0.397110i			0.0370307i
$116$	−10.5202	−	2.20323i	−0.976775	−	0.204565i
$117$	−1.48026	−	4.06697i	−0.136850	−	0.375991i
$118$	−15.4869	−	5.91828i	−1.42568	−	0.544822i
$119$	1.63450	+	0.288207i	0.149835	+	0.0264199i
$120$	−0.110210	−	0.0461983i	−0.0100607	−	0.00421730i
$121$	−4.64142	−	8.03918i	−0.421948	−	0.730835i
$122$	8.42935	+	15.1534i	0.763157	+	1.37192i
$123$	4.10660	+	4.89406i	0.370280	+	0.441283i
$124$	11.3914	+	4.56281i	1.02298	+	0.409752i
$125$	−0.231948	+	0.401745i	−0.0207460	+	0.0359332i
$126$	0.0684172	−	4.28745i	0.00609509	−	0.381956i
$127$	12.3119	+	4.48118i	1.09251	+	0.397641i	0.824550	−	0.565790i	$-0.191429\pi$
$127$	12.3119	+	4.48118i	1.09251	+	0.397641i	0.267959	+	0.963430i	$0.413651\pi$
$128$	−7.80222	−	8.19301i	−0.689625	−	0.724167i
$129$	0.369846	−	0.0652139i	0.0325632	−	0.00574176i
$130$	−0.128456	−	0.0247697i	−0.0112663	−	0.00217245i
$131$	−0.872574	+	1.03989i	−0.0762372	+	0.0908559i	−0.802815	−	0.596228i	$-0.796665\pi$
$131$	−0.872574	+	1.03989i	−0.0762372	+	0.0908559i	0.726578	+	0.687084i	$0.241110\pi$
$132$	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
$136$	−3.20973	+	0.997097i	−0.275232	+	0.0855004i
$137$	1.33938	+	7.59599i	0.114431	+	0.648969i	0.987030	+	0.160533i	$0.0513213\pi$
$137$	1.33938	+	7.59599i	0.114431	+	0.648969i	−0.872600	+	0.488436i	$0.837568\pi$
$138$	−7.21804	+	8.32856i	−0.614440	+	0.708974i
$139$	5.84051	−	16.0467i	0.495386	−	1.36106i	−0.400304	−	0.916382i	$-0.631096\pi$
$139$	5.84051	−	16.0467i	0.495386	−	1.36106i	0.895690	−	0.444679i	$-0.146682\pi$
$140$	−0.110124	−	0.0683552i	−0.00930714	−	0.00577707i
$141$	−6.57901	−	3.79839i	−0.554053	−	0.319882i
$142$	−1.36518	−	8.53670i	−0.114564	−	0.716384i
$143$	2.00130	−	1.67929i	0.167357	−	0.140429i
$144$	3.85324	+	7.78170i	0.321103	+	0.648475i
$145$	0.215953	−	0.124680i	0.0179339	−	0.0103541i
$146$	−7.11972	+	5.78310i	−0.589232	+	0.478613i
$147$	0.798373	−	4.52780i	0.0658487	−	0.373447i
$148$	−5.45543	−	6.93970i	−0.448433	−	0.570440i
$149$	−12.5718	+	4.57575i	−1.02992	+	0.374860i	−0.801051	−	0.598597i	$-0.795725\pi$
$149$	−12.5718	+	4.57575i	−1.02992	+	0.374860i	−0.228870	+	0.973457i	$0.573503\pi$
$150$	−6.08215	+	2.10444i	−0.496605	+	0.171827i
$151$	0.552457			0.0449583			0.0224792	−	0.999747i	$-0.492844\pi$
$151$	0.552457			0.0449583			0.0224792	+	0.999747i	$0.492844\pi$
$152$	−6.21037	+	10.6504i	−0.503727	+	0.863863i
$153$	2.57965			0.208552
$154$	2.44609	−	0.846353i	0.197111	−	0.0682011i
$155$	−0.267521	+	0.0973698i	−0.0214878	+	0.00782093i
$156$	−2.24387	−	2.85436i	−0.179653	−	0.228532i
$157$	1.20691	−	6.84471i	0.0963216	−	0.546267i	−0.898013	−	0.439970i	$-0.854989\pi$
$157$	1.20691	−	6.84471i	0.0963216	−	0.546267i	0.994334	−	0.106298i	$-0.0338996\pi$
$158$	−12.0759	+	9.80884i	−0.960707	+	0.780350i
$159$	−4.14710	+	2.39433i	−0.328886	+	0.189883i
$160$	0.261640	+	0.0209183i	0.0206845	+	0.00165374i
$161$	−9.15710	+	7.68372i	−0.721680	+	0.605562i
$162$	−0.496944	−	3.10746i	−0.0390436	−	0.244145i
$163$	14.1181	+	8.15109i	1.10582	+	0.638443i	0.937742	−	0.347332i	$-0.112912\pi$
$163$	14.1181	+	8.15109i	1.10582	+	0.638443i	0.168073	+	0.985775i	$0.446245\pi$
$164$	−11.9224	−	7.40038i	−0.930980	−	0.577872i
$165$	−0.0189358	+	0.0520256i	−0.00147415	+	0.00405019i
$166$	−0.680158	+	0.784802i	−0.0527905	+	0.0609124i
$167$	−2.56785	−	14.5630i	−0.198706	−	1.12692i	−0.907041	−	0.421042i	$-0.861664\pi$
$167$	−2.56785	−	14.5630i	−0.198706	−	1.12692i	0.708335	−	0.705876i	$-0.249447\pi$
$168$	−1.06716	−	3.43527i	−0.0823332	−	0.265037i
$169$	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	−0.811932	−	0.583752i	$-0.801584\pi$
$173$	−1.26345	+	1.50572i	−0.0960586	+	0.114478i	0.715874	+	0.698230i	$0.246029\pi$
$174$	6.79541	+	1.31034i	0.515159	+	0.0993366i
$175$	−6.87450	+	1.21216i	−0.519663	+	0.0916307i
$176$	−3.61848	+	3.79223i	−0.272753	+	0.285850i
$177$	10.0311	+	3.65102i	0.753983	+	0.274427i
$178$	−0.312137	+	19.5604i	−0.0233957	+	1.46612i
$179$	−11.4727	+	19.8714i	−0.857512	+	1.48526i	0.0167821	+	0.999859i	$0.494658\pi$
$179$	−11.4727	+	19.8714i	−0.857512	+	1.48526i	−0.874294	+	0.485396i	$0.838675\pi$
$180$	−0.187010	−	0.0749063i	−0.0139389	−	0.00558319i
$181$	−13.8104	−	16.4586i	−1.02652	−	1.22336i	−0.974425	−	0.224715i	$-0.927855\pi$
$181$	−13.8104	−	16.4586i	−1.02652	−	1.22336i	−0.0520937	−	0.998642i	$-0.516589\pi$
$182$	−1.91433	−	3.44138i	−0.141900	−	0.255092i
$183$	−5.58239	−	9.66899i	−0.412662	−	0.714752i
$184$	9.35828	−	22.3250i	0.689902	−	1.64582i
$185$	0.201680	+	0.0355616i	0.0148278	+	0.00261454i
$186$	−7.38055	−	2.82046i	−0.541168	−	0.206806i
$187$	0.532579	+	1.46325i	0.0389460	+	0.107003i
$188$	16.3315	+	3.42028i	1.19109	+	0.249450i
$189$			6.57632i			0.478357i
$190$	−0.0574232	−	0.280202i	−0.00416592	−	0.0203280i
$191$			7.68079i			0.555762i	0.960615	+	0.277881i	$0.0896321\pi$
$191$			7.68079i			0.555762i	−0.960615	+	0.277881i	$0.910368\pi$
$192$	5.10715	+	5.19441i	0.368576	+	0.374874i
$193$	1.33031	+	3.65500i	0.0957578	+	0.263093i	0.978318	−	0.207106i	$-0.0664045\pi$
$193$	1.33031	+	3.65500i	0.0957578	+	0.263093i	−0.882561	+	0.470199i	$0.844182\pi$
$194$	4.28785	−	11.2204i	0.307850	−	0.805579i
$195$	0.0829528	+	0.0146268i	0.00594037	+	0.00104745i
$196$	1.43536	+	9.99586i	0.102526	+	0.713990i
$197$	5.83464	+	10.1059i	0.415701	+	0.720015i	0.995502	−	0.0947432i	$-0.0302030\pi$
$197$	5.83464	+	10.1059i	0.415701	+	0.720015i	−0.579801	+	0.814758i	$0.696870\pi$
$198$	3.51568	−	1.95566i	0.249849	−	0.138983i
$199$	−13.9328	−	16.6044i	−0.987668	−	1.17706i	−0.984200	−	0.177063i	$-0.943340\pi$
$199$	−13.9328	−	16.6044i	−0.987668	−	1.17706i	−0.00346853	−	0.999994i	$-0.501104\pi$
$200$	11.2512	−	8.55790i	0.795582	−	0.605135i
$201$	4.99757	−	8.65605i	0.352502	−	0.610551i
$202$	14.9052	+	0.237851i	1.04873	+	0.0167351i
$203$	7.05354	+	2.56728i	0.495062	+	0.180188i
$204$	2.05614	−	0.674894i	0.143959	−	0.0472520i
$205$	0.320602	−	0.0565308i	0.0223918	−	0.00394828i
$206$	0.155238	−	0.805066i	0.0108160	−	0.0560916i
$207$	−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	$-0.147990\pi$
$211$	8.82488	+	7.40495i	0.607530	+	0.509778i	−0.286326	+	0.958132i	$0.592434\pi$
$212$	7.01443	−	7.83738i	0.481753	−	0.538274i
$213$	0.966590	+	5.48181i	0.0662297	+	0.375607i
$214$	0.902956	+	0.782557i	0.0617248	+	0.0534945i
$215$	0.00654518	−	0.0179827i	0.000446377	−	0.00122641i
$216$	−6.09923	−	11.8387i	−0.415000	−	0.805519i
$217$	−7.42159	−	4.28485i	−0.503810	−	0.290875i
$218$	11.3400	−	1.81349i	0.768043	−	0.122825i
$219$	4.52418	−	3.79624i	0.305716	−	0.256526i
$220$	0.00388002	−	0.121542i	0.000261591	−	0.00819436i
$221$	2.05169	−	1.18454i	0.138011	−	0.0796810i
$222$	3.58343	+	4.41165i	0.240504	+	0.296091i
$223$	−0.353870	+	2.00689i	−0.0236969	+	0.134392i	−0.994361	−	0.106048i	$-0.966180\pi$
$223$	−0.353870	+	2.00689i	−0.0236969	+	0.134392i	0.970664	+	0.240439i	$0.0772915\pi$
$224$	4.58014	+	6.43801i	0.306024	+	0.430158i
$225$	−10.1953	+	3.71079i	−0.679688	+	0.247386i
$226$	−6.57586	−	19.0052i	−0.437420	−	1.26421i
$227$	−12.3915			−0.822456			−0.411228	−	0.911533i	$-0.634900\pi$
$227$	−12.3915			−0.822456			−0.411228	+	0.911533i	$0.634900\pi$
$228$	3.88875	−	6.92041i	0.257539	−	0.458316i
$229$	9.29197			0.614031			0.307015	−	0.951705i	$-0.400670\pi$
$229$	9.29197			0.614031			0.307015	+	0.951705i	$0.400670\pi$
$230$	0.183633	+	0.530727i	0.0121084	+	0.0349951i
$231$	−1.56607	+	0.570002i	−0.103040	+	0.0375034i
$232$	−15.0788	+	1.92023i	−0.989971	+	0.126069i
$233$	1.38093	−	7.83166i	0.0904679	−	0.513069i	−0.905574	−	0.424188i	$-0.860560\pi$
$233$	1.38093	−	7.83166i	0.0904679	−	0.513069i	0.996042	−	0.0888814i	$-0.0283292\pi$
$234$	−3.85899	−	4.75089i	−0.252270	−	0.310576i
$235$	−0.335243	+	0.193553i	−0.0218689	+	0.0126260i
$236$	−23.4346	−	0.748109i	−1.52546	−	0.0486977i
$237$	7.67356	−	6.43888i	0.498451	−	0.418250i
$238$	2.31775	−	0.370653i	0.150237	−	0.0240259i
$239$	−18.1412	−	10.4738i	−1.17346	−	0.677496i	−0.218966	−	0.975732i	$-0.570268\pi$
$239$	−18.1412	−	10.4738i	−1.17346	−	0.677496i	−0.954492	+	0.298236i	$0.903602\pi$
$240$	−0.168656	−	0.0107791i	−0.0108867	−	0.000695786i
$241$	−3.23683	+	8.89311i	−0.208502	+	0.572856i	−0.999227	−	0.0393166i	$-0.987482\pi$
$241$	−3.23683	+	8.89311i	−0.208502	+	0.572856i	0.790724	+	0.612172i	$0.209704\pi$
$242$	−9.92066	−	8.59785i	−0.637724	−	0.552691i
$243$	2.80468	+	15.9061i	0.179920	+	1.02038i
$244$	18.2729	+	16.3542i	1.16980	+	1.04697i
$245$	−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
$250$	−0.124215	+	0.644180i	−0.00785607	+	0.0407415i
$251$	5.25705	−	0.926959i	0.331822	−	0.0585091i	−0.00525525	−	0.999986i	$-0.501673\pi$
$251$	5.25705	−	0.926959i	0.331822	−	0.0585091i	0.337077	+	0.941477i	$0.390562\pi$
$252$	−1.89118	−	5.76170i	−0.119133	−	0.362953i
$253$	−10.5387	−	3.83578i	−0.662563	−	0.241153i
$254$	18.5268	+	0.295643i	1.16248	+	0.0185503i
$255$	−0.0251029	+	0.0434796i	−0.00157201	+	0.00272280i
$256$	−14.2161	−	7.34181i	−0.888507	−	0.458863i
$257$	8.86041	+	10.5594i	0.552697	+	0.658679i	0.967984	−	0.251011i	$-0.0807632\pi$
$257$	8.86041	+	10.5594i	0.552697	+	0.658679i	−0.415287	+	0.909691i	$0.636319\pi$
$258$	0.464134	−	0.258183i	0.0288957	−	0.0160738i
$259$	3.08230	+	5.33869i	0.191525	+	0.331730i
$260$	−0.183132	+	0.0262969i	−0.0113574	+	0.00163086i
$261$	11.4894	+	2.02590i	0.711178	+	0.125400i
$262$	−0.685301	+	1.79329i	−0.0423380	+	0.110790i
$263$	4.72312	+	12.9767i	0.291240	+	0.800175i	0.995886	+	0.0906161i	$0.0288836\pi$
$263$	4.72312	+	12.9767i	0.291240	+	0.800175i	−0.704646	+	0.709559i	$0.748894\pi$
$264$	2.29058	−	2.47857i	0.140975	−	0.152545i
$265$			0.244013i			0.0149896i
$266$	5.35020	−	6.74581i	0.328042	−	0.413612i
$267$		−	12.5960i		−	0.770862i
$268$	−4.50009	+	21.4874i	−0.274887	+	1.31255i
$269$	0.0765103	+	0.210210i	0.00466491	+	0.0128167i	0.942003	−	0.335604i	$-0.108940\pi$
$269$	0.0765103	+	0.210210i	0.00466491	+	0.0128167i	−0.937338	+	0.348421i	$0.886718\pi$
$270$	0.288606	+	0.110290i	0.0175640	+	0.00671204i
$271$	−14.0034	−	2.46917i	−0.850644	−	0.149992i	−0.268704	−	0.963223i	$-0.586595\pi$
$271$	−14.0034	−	2.46917i	−0.850644	−	0.149992i	−0.581941	+	0.813231i	$0.697706\pi$
$272$	−3.82864	+	2.81685i	−0.232145	+	0.170797i
$273$	1.26778	+	2.19585i	0.0767294	+	0.132899i
$274$	5.30261	+	9.53248i	0.320343	+	0.575878i
$275$	−4.20974	−	5.01697i	−0.253857	−	0.302535i
$276$	−5.79540	+	14.4687i	−0.348842	+	0.870913i
$277$	−10.5953	+	18.3516i	−0.636609	+	1.10264i	0.349563	+	0.936913i	$0.386330\pi$
$277$	−10.5953	+	18.3516i	−0.636609	+	1.10264i	−0.986172	+	0.165726i	$0.947003\pi$
$278$	0.385324	−	24.1468i	0.0231102	−	1.44823i
$279$	−12.5163	−	4.55558i	−0.749334	−	0.272735i
$280$	−0.178786	−	0.0404312i	−0.0106845	−	0.00241623i
$281$	7.25757	−	1.27971i	0.432950	−	0.0763408i	0.0470741	−	0.998891i	$-0.485010\pi$
$281$	7.25757	−	1.27971i	0.432950	−	0.0763408i	0.385876	+	0.922551i	$0.373899\pi$
$282$	−10.5491	−	2.03416i	−0.628193	−	0.121133i
$283$	15.7071	−	18.7190i	0.933691	−	1.11273i	−0.0597309	−	0.998215i	$-0.519024\pi$
$283$	15.7071	−	18.7190i	0.933691	−	1.11273i	0.993422	−	0.114515i	$-0.0365313\pi$
$284$	−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
$288$	8.74820	+	8.61821i	0.515493	+	0.507833i
$289$	−2.70682	−	15.3511i	−0.159224	−	0.903007i
$290$	0.230960	−	0.266494i	0.0135624	−	0.0156491i
$291$	−2.64520	+	7.26762i	−0.155064	+	0.426036i
$292$	−6.84107	+	11.0213i	−0.400344	+	0.644973i
$293$	−11.5307	−	6.65724i	−0.673630	−	0.388920i	0.123821	−	0.992305i	$-0.460485\pi$
$293$	−11.5307	−	6.65724i	−0.673630	−	0.388920i	−0.797451	+	0.603384i	$0.793819\pi$
$294$	−1.02676	−	6.42047i	−0.0598818	−	0.374450i
$295$	0.416693	−	0.349647i	0.0242608	−	0.0203572i
$296$	−10.5001	−	6.75201i	−0.610307	−	0.392453i
$297$	−5.34332	+	3.08497i	−0.310051	+	0.179008i
$298$	−14.6859	+	11.9289i	−0.850733	+	0.691021i
$299$	−2.96292	+	16.8036i	−0.171350	+	0.971775i
$300$	−7.15549	+	5.62507i	−0.413122	+	0.324763i
$301$	0.541314	−	0.197022i	0.0312008	−	0.0113562i
$302$	0.738345	−	0.255470i	0.0424870	−	0.0147006i
$303$	−9.59824			−0.551405
$304$	−3.37499	+	17.1058i	−0.193569	+	0.981087i
$305$	−0.568919			−0.0325762
$306$	3.44763	−	1.19289i	0.197088	−	0.0681930i
$307$	26.7916	−	9.75134i	1.52908	−	0.556538i	0.565681	−	0.824624i	$-0.308613\pi$
$307$	26.7916	−	9.75134i	1.52908	−	0.556538i	0.963395	+	0.268086i	$0.0863910\pi$
$308$	2.87776	−	2.26226i	0.163975	−	0.128904i
$309$	−0.0916701	+	0.519887i	−0.00521493	+	0.0295753i
$310$	−0.312509	+	0.253841i	−0.0177493	+	0.0144172i
$311$	22.6396	−	13.0710i	1.28377	−	0.741188i	0.306239	−	0.951955i	$-0.400929\pi$
$311$	22.6396	−	13.0710i	1.28377	−	0.741188i	0.977536	+	0.210767i	$0.0675961\pi$
$312$	−4.31880	−	2.77716i	−0.244504	−	0.157226i
$313$	−2.72269	+	2.28461i	−0.153895	+	0.129134i	−0.716484	−	0.697603i	$-0.754250\pi$
$313$	−2.72269	+	2.28461i	−0.153895	+	0.129134i	0.562589	+	0.826737i	$0.309805\pi$
$314$	−1.55216	−	9.70588i	−0.0875934	−	0.547735i
$315$	0.121838	+	0.0703432i	0.00686479	+	0.00396339i
$316$	−11.6033	+	18.6935i	−0.652736	+	1.05159i
$317$	4.75523	−	13.0649i	0.267080	−	0.733798i	−0.731565	−	0.681771i	$-0.761210\pi$
$317$	4.75523	−	13.0649i	0.267080	−	0.733798i	0.998646	−	0.0520261i	$-0.0165679\pi$
$318$	−4.43530	+	5.11768i	−0.248719	+	0.286985i
$319$	1.22290	+	6.93539i	0.0684690	+	0.388307i
$320$	0.359349	−	0.0930320i	0.0200882	−	0.00520065i
$321$	−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
$326$	22.6378	+	4.36517i	1.25379	+	0.241765i
$327$	−7.28194	+	1.28400i	−0.402692	+	0.0710055i
$328$	−19.3560	−	4.37722i	−1.06876	−	0.241692i
$329$	−10.9499	−	3.98543i	−0.603686	−	0.219724i
$330$	−0.00124927	+	0.0782872i	−6.87702e−5	+	0.00430957i
$331$	3.55440	−	6.15641i	0.195368	−	0.338387i	−0.751653	−	0.659558i	$-0.770743\pi$
$331$	3.55440	−	6.15641i	0.195368	−	0.338387i	0.947021	+	0.321172i	$0.104077\pi$
$332$	−0.546102	+	1.36339i	−0.0299712	+	0.0748257i
$333$	6.15882	+	7.33979i	0.337501	+	0.402218i
$334$	−10.1661	−	18.2756i	−0.556267	−	0.999998i
$335$	−0.254659	−	0.441082i	−0.0139135	−	0.0240989i
$336$	−3.01478	−	4.09766i	−0.164470	−	0.223546i
$337$	−29.9028	−	5.27267i	−1.62891	−	0.287220i	−0.716833	−	0.697245i	$-0.754409\pi$
$337$	−29.9028	−	5.27267i	−1.62891	−	0.287220i	−0.912075	+	0.410024i	$0.865520\pi$
$338$	11.9228	+	4.55625i	0.648513	+	0.247827i
$339$	4.42871	+	12.1678i	0.240535	+	0.660863i
$340$	0.0226041	−	0.107932i	0.00122588	−	0.00585343i
$341$		−	8.04014i		−	0.435398i
$342$	6.36864	−	11.7695i	0.344376	−	0.636421i
$343$		−	16.8293i		−	0.908694i
$344$	−0.791742	+	0.856722i	−0.0426879	+	0.0461913i
$345$	−0.123673	−	0.339789i	−0.00665834	−	0.0182936i
$346$	−0.992289	+	2.59661i	−0.0533458	+	0.139595i
$347$	−0.491581	−	0.0866790i	−0.0263895	−	0.00465317i	0.160438	−	0.987046i	$-0.448709\pi$
$347$	−0.491581	−	0.0866790i	−0.0263895	−	0.00465317i	−0.186827	+	0.982393i	$0.559820\pi$
$348$	9.68783	−	1.39113i	0.519322	−	0.0745723i
$349$	−1.36569	−	2.36545i	−0.0731040	−	0.126620i	0.827156	−	0.561972i	$-0.189957\pi$
$349$	−1.36569	−	2.36545i	−0.0731040	−	0.126620i	−0.900260	+	0.435352i	$0.856624\pi$
$350$	−8.62706	+	4.79896i	−0.461136	+	0.256515i
$351$	6.03388	+	7.19090i	0.322065	+	0.383822i
$352$	−3.08239	+	6.74150i	−0.164292	+	0.359323i
$353$	12.5409	−	21.7215i	0.667484	−	1.15612i	−0.311121	−	0.950370i	$-0.600704\pi$
$353$	12.5409	−	21.7215i	0.667484	−	1.15612i	0.978605	−	0.205747i	$-0.0659623\pi$
$354$	15.0946	+	0.240873i	0.802269	+	0.0128023i
$355$	0.266537	+	0.0970116i	0.0141463	+	0.00514884i
$356$	8.62806	+	26.2864i	0.457286	+	1.39318i
$357$	−1.48833	+	0.262433i	−0.0787708	+	0.0138894i
$358$	−6.14402	+	31.8628i	−0.324721	+	1.68400i
$359$	5.00752	−	5.96773i	0.264287	−	0.314965i	−0.617539	−	0.786540i	$-0.711870\pi$
$359$	5.00752	−	5.96773i	0.264287	−	0.314965i	0.881826	+	0.471576i	$0.156315\pi$
$360$	−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
$364$	−4.14983	−	3.71409i	−0.217510	−	0.194671i
$365$	−0.0522584	−	0.296372i	−0.00273533	−	0.0155128i
$366$	−11.9319	−	10.3409i	−0.623690	−	0.540529i
$367$	−2.87685	+	7.90408i	−0.150170	+	0.412590i	−0.991854	−	0.127382i	$-0.959343\pi$
$367$	−2.87685	+	7.90408i	−0.150170	+	0.412590i	0.841683	+	0.539971i	$0.181565\pi$
$368$	2.18349	−	34.1643i	0.113823	−	1.78093i
$369$	13.1906	+	7.61560i	0.686676	+	0.396452i
$370$	0.285984	−	0.0457345i	0.0148676	−	0.00237762i
$371$	−5.62679	+	4.72144i	−0.292129	+	0.245125i
$372$	−11.1682	−	0.356524i	−0.579042	−	0.0184849i
$373$	17.6598	−	10.1959i	0.914391	−	0.527924i	0.0325499	−	0.999470i	$-0.489637\pi$
$373$	17.6598	−	10.1959i	0.914391	−	0.527924i	0.881841	+	0.471546i	$0.156304\pi$
$374$	1.38842	+	1.70932i	0.0717935	+	0.0883867i
$375$	0.0733505	−	0.415992i	0.00378781	−	0.0214817i
$376$	23.4082	−	2.98094i	1.20719	−	0.153730i
$377$	10.0682	−	3.66454i	0.518541	−	0.188733i
$378$	3.04105	+	8.78909i	0.156415	+	0.452062i
$379$	17.8645			0.917638			0.458819	−	0.888530i	$-0.348273\pi$
$379$	17.8645			0.917638			0.458819	+	0.888530i	$0.348273\pi$
$380$	−0.206317	−	0.347929i	−0.0105838	−	0.0178484i
$381$	−11.9304			−0.611212
$382$	3.55178	+	10.2652i	0.181725	+	0.525212i
$383$	11.4496	−	4.16732i	0.585047	−	0.212940i	−0.0325023	−	0.999472i	$-0.510348\pi$
$383$	11.4496	−	4.16732i	0.585047	−	0.212940i	0.617550	+	0.786532i	$0.288125\pi$
$384$	9.22759	+	4.58053i	0.470894	+	0.233749i
$385$	−0.0147467	+	0.0836327i	−0.000751561	+	0.00426231i
$386$	3.46809	+	4.26964i	0.176521	+	0.217319i
$387$	0.775389	−	0.447671i	0.0394152	−	0.0227564i
$388$	0.542012	−	16.9786i	0.0275165	−	0.861958i
$389$	15.3327	−	12.8656i	0.777398	−	0.652314i	−0.165194	−	0.986261i	$-0.552825\pi$
$389$	15.3327	−	12.8656i	0.777398	−	0.652314i	0.942592	+	0.333947i	$0.108381\pi$
$390$	0.117628	−	0.0188110i	0.00595633	−	0.000952533i
$391$	−8.80756	−	5.08505i	−0.445418	−	0.257162i
$392$	6.54065	+	12.6955i	0.330353	+	0.641218i
$393$	0.422766	−	1.16154i	0.0213257	−	0.0585919i
$394$	12.4711	+	10.8082i	0.628283	+	0.544509i
$395$	−0.0886365	−	0.502683i	−0.00445979	−	0.0252927i
$396$	3.79428	−	4.23943i	0.190670	−	0.213039i
$397$	3.50279	+	2.93919i	0.175800	+	0.147514i	0.726442	−	0.687228i	$-0.241173\pi$
$397$	3.50279	+	2.93919i	0.175800	+	0.147514i	−0.550642	+	0.834742i	$0.685617\pi$
$398$	−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	−0.879536	−	0.475833i	$-0.842147\pi$
$401$	−5.17049	+	6.16195i	−0.258202	+	0.307713i	0.621334	+	0.783546i	$0.286591\pi$
$402$	2.67636	−	13.8796i	0.133485	−	0.692251i
$403$	−12.0466	+	2.12414i	−0.600083	+	0.105811i
$404$	20.0304	−	6.57465i	0.996551	−	0.327101i
$405$	0.0970227	+	0.0353134i	0.00482110	+	0.00175474i
$406$	10.6141	+	0.169375i	0.526767	+	0.00840592i
$407$	−2.89183	+	5.00879i	−0.143342	+	0.248276i
$408$	2.43589	−	1.85279i	0.120595	−	0.0917267i
$409$	8.35432	+	9.95629i	0.413094	+	0.492307i	0.931966	−	0.362545i	$-0.118092\pi$
$409$	8.35432	+	9.95629i	0.413094	+	0.492307i	−0.518872	+	0.854852i	$0.673648\pi$
$410$	0.402336	−	0.223806i	0.0198699	−	0.0110530i
$411$	−3.51169	−	6.08243i	−0.173219	−	0.300024i
$412$	−0.164810	−	1.14774i	−0.00811959	−	0.0565449i
$413$	16.1253	+	2.84332i	0.793472	+	0.139911i
$414$	−9.37942	+	24.5440i	−0.460973	+	1.20627i
$415$	−0.0116538	−	0.0320184i	−0.000572060	−	0.00157172i
$416$	10.9151	+	2.83731i	0.535159	+	0.139110i
$417$			15.5494i			0.761456i
$418$	7.99082	+	1.18261i	0.390844	+	0.0578434i
$419$			1.47508i			0.0720624i	0.999351	+	0.0360312i	$0.0114716\pi$
$419$			1.47508i			0.0720624i	−0.999351	+	0.0360312i	$0.988528\pi$
$420$	0.115516	+	0.0241924i	0.00563660	+	0.00118047i
$421$	7.00572	+	19.2481i	0.341438	+	0.938093i	0.984978	+	0.172680i	$0.0552428\pi$
$421$	7.00572	+	19.2481i	0.341438	+	0.938093i	−0.643540	+	0.765412i	$0.722535\pi$
$422$	15.2185	+	5.81569i	0.740823	+	0.283103i
$423$	−17.8361	−	3.14499i	−0.867221	−	0.152915i
$424$	5.75042	−	13.7181i	0.279265	−	0.666210i
$425$	−2.96948	−	5.14330i	−0.144041	−	0.249487i
$426$	3.82674	+	6.87932i	0.185406	+	0.333304i
$427$	−11.0081	−	13.1189i	−0.532718	−	0.634868i
$428$	1.56865	+	0.628319i	0.0758236	+	0.0303710i
$429$	−1.18943	+	2.06016i	−0.0574265	+	0.0994655i
$430$	0.000431814	−	0.0270601i	2.08239e−5	−	0.00130495i
$431$	−15.5185	−	5.64828i	−0.747501	−	0.272068i	−0.0599469	−	0.998202i	$-0.519093\pi$
$431$	−15.5185	−	5.64828i	−0.747501	−	0.272068i	−0.687554	+	0.726134i	$0.741315\pi$
$432$	−13.6260	−	13.0016i	−0.655579	−	0.625542i
$433$	−29.9167	+	5.27512i	−1.43770	+	0.253506i	−0.837542	−	0.546373i	$-0.816008\pi$
$433$	−29.9167	+	5.27512i	−1.43770	+	0.253506i	−0.600161	+	0.799879i	$0.704897\pi$
$434$	−11.9002	−	2.29468i	−0.571227	−	0.110148i
$435$	−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	$-0.220785\pi$
$439$	5.71692	+	4.79706i	0.272854	+	0.228951i	−0.496085	+	0.868274i	$0.665230\pi$
$440$	−0.0510184	−	0.164232i	−0.00243221	−	0.00782945i
$441$	−1.90338	−	10.7946i	−0.0906370	−	0.514028i
$442$	2.19427	−	2.53186i	0.104371	−	0.120428i
$443$	−11.1704	+	30.6904i	−0.530721	+	1.45814i	0.327494	+	0.944853i	$0.393796\pi$
$443$	−11.1704	+	30.6904i	−0.530721	+	1.45814i	−0.858215	+	0.513290i	$0.828426\pi$
$444$	6.82922	+	4.23899i	0.324101	+	0.201174i
$445$	−0.555857	−	0.320924i	−0.0263501	−	0.0152133i
$446$	0.455099	+	2.84580i	0.0215496	+	0.134753i
$447$	9.33208	−	7.83054i	0.441392	−	0.370372i
$448$	9.09834	+	6.48627i	0.429856	+	0.306447i
$449$	−4.49778	+	2.59680i	−0.212264	+	0.122550i	−0.602363	−	0.798222i	$-0.705774\pi$
$449$	−4.49778	+	2.59680i	−0.212264	+	0.122550i	0.390099	+	0.920773i	$0.372441\pi$
$450$	−11.9098	+	9.67395i	−0.561435	+	0.456034i
$451$	−1.59653	+	9.05436i	−0.0751776	+	0.426353i
$452$	−17.5769	−	22.3591i	−0.826750	−	1.05169i
$453$	−0.472714	+	0.172054i	−0.0222100	+	0.00808379i
$454$	−16.5610	+	5.73015i	−0.777246	+	0.268929i
$455$	0.129203			0.00605713
$456$	1.99704	−	11.0472i	0.0935201	−	0.517333i
$457$	−13.2130			−0.618078			−0.309039	−	0.951049i	$-0.600007\pi$
$457$	−13.2130			−0.618078			−0.309039	+	0.951049i	$0.600007\pi$
$458$	12.4185	−	4.29683i	0.580278	−	0.200778i
$459$	−5.25763	+	1.91362i	−0.245405	+	0.0893202i
$460$	0.490842	+	0.624386i	0.0228856	+	0.0291122i
$461$	−4.56893	+	25.9117i	−0.212796	+	1.20683i	0.671894	+	0.740648i	$0.265481\pi$
$461$	−4.56893	+	25.9117i	−0.212796	+	1.20683i	−0.884690	+	0.466180i	$0.845630\pi$
$462$	−1.82943	+	1.48598i	−0.0851126	+	0.0691341i
$463$	−18.3103	+	10.5715i	−0.850954	+	0.491298i	−0.860972	−	0.508652i	$-0.830144\pi$
$463$	−18.3103	+	10.5715i	−0.850954	+	0.491298i	0.0100189	+	0.999950i	$0.496811\pi$
$464$	−19.2645	+	9.53913i	−0.894330	+	0.442843i
$465$	0.198582	−	0.166630i	0.00920902	−	0.00772729i
$466$	−1.77597	−	11.1054i	−0.0822701	−	0.514447i
$467$	−27.4162	−	15.8287i	−1.26867	−	0.732467i	−0.293934	−	0.955826i	$-0.594964\pi$
$467$	−27.4162	−	15.8287i	−1.26867	−	0.732467i	−0.974736	+	0.223359i	$0.928298\pi$
$468$	−7.35437	−	4.56496i	−0.339956	−	0.211015i
$469$	5.24365	−	14.4068i	0.242129	−	0.665245i
$470$	−0.358541	+	0.413703i	−0.0165383	+	0.0190827i
$471$	1.09897	+	6.23259i	0.0506380	+	0.287182i
$472$	−31.6657	+	9.83690i	−1.45753	+	0.452780i
$473$	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
$478$	−29.0886	−	5.60908i	−1.33048	−	0.256553i
$479$	13.3251	−	2.34958i	0.608840	−	0.107355i	0.139276	−	0.990254i	$-0.455522\pi$
$479$	13.3251	−	2.34958i	0.608840	−	0.107355i	0.469563	+	0.882899i	$0.344411\pi$
$480$	−0.230389	+	0.0635846i	−0.0105158	+	0.00290223i
$481$	8.26868	+	3.00955i	0.377019	+	0.137224i
$482$	−0.213547	+	13.3822i	−0.00972682	+	0.609543i
$483$	5.44236	−	9.42644i	0.247636	−	0.428918i
$484$	−17.2346	−	6.90326i	−0.783389	−	0.313785i
$485$	0.253323	+	0.301898i	0.0115028	+	0.0137085i
$486$	11.1038	+	19.9612i	0.503677	+	0.905459i
$487$	6.49642	+	11.2521i	0.294381	+	0.509883i	0.974841	−	0.222903i	$-0.0715532\pi$
$487$	6.49642	+	11.2521i	0.294381	+	0.509883i	−0.680460	+	0.732786i	$0.738220\pi$
$488$	31.9839	+	13.4071i	1.44784	+	0.606912i
$489$	−14.6188	−	2.57768i	−0.661084	−	0.116567i
$490$	−0.309493	−	0.118272i	−0.0139815	−	0.00534299i
$491$	−11.1325	−	30.5862i	−0.502401	−	1.38033i	−0.888924	−	0.458055i	$-0.848546\pi$
$491$	−11.1325	−	30.5862i	−0.502401	−	1.38033i	0.386523	−	0.922280i	$-0.373676\pi$
$492$	12.5062	+	2.61915i	0.563821	+	0.118081i
$493$			6.38620i			0.287620i
$494$	−0.339194	−	12.2851i	−0.0152611	−	0.552733i
$495$			0.131993i			0.00593263i
$496$	23.5509	−	6.90599i	1.05746	−	0.310088i
$497$	2.92023	+	8.02327i	0.130990	+	0.359893i
$498$	0.337568	−	0.883344i	0.0151268	−	0.0395836i
$499$	4.07989	+	0.719394i	0.182641	+	0.0322045i	0.264220	−	0.964462i	$-0.414885\pi$
$499$	4.07989	+	0.719394i	0.182641	+	0.0322045i	−0.0815796	+	0.996667i	$0.525996\pi$
$500$	0.131874	+	0.918370i	0.00589757	+	0.0410708i
$501$	6.73260	+	11.6612i	0.300790	+	0.520984i
$502$	6.59726	−	3.66984i	0.294450	−	0.163793i
$503$	14.9435	+	17.8090i	0.666298	+	0.794063i	0.988275	−	0.152685i	$-0.0487919\pi$
$503$	14.9435	+	17.8090i	0.666298	+	0.794063i	−0.321977	+	0.946747i	$0.604347\pi$
$504$	−5.19186	−	6.82584i	−0.231264	−	0.304047i
$505$	−0.244547	+	0.423567i	−0.0108822	+	0.0188485i
$506$	−15.8585	−	0.253063i	−0.704995	−	0.0112500i
$507$	−7.72254	−	2.81078i	−0.342970	−	0.124831i
$508$	24.8973	−	8.17213i	1.10464	−	0.362579i
$509$	13.7146	−	2.41826i	0.607891	−	0.107188i	0.138775	−	0.990324i	$-0.455684\pi$
$509$	13.7146	−	2.41826i	0.607891	−	0.107188i	0.469116	+	0.883136i	$0.344573\pi$
$510$	−0.0134434	+	0.0697175i	−0.000595285	+	0.00308714i
$511$	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
$516$	0.500913	−	0.559681i	0.0220515	−	0.0246386i
$517$	−1.89841	−	10.7664i	−0.0834922	−	0.473508i
$518$	6.58815	+	5.70970i	0.289467	+	0.250870i
$519$	0.612148	−	1.68186i	0.0268703	−	0.0738256i
$520$	−0.232591	+	0.119830i	−0.0101998	+	0.00525488i
$521$	14.7143	+	8.49530i	0.644645	+	0.372186i	0.786402	−	0.617716i	$-0.211942\pi$
$521$	14.7143	+	8.49530i	0.644645	+	0.372186i	−0.141757	+	0.989902i	$0.545275\pi$
$522$	16.2922	−	2.60543i	0.713088	−	0.114037i
$523$	−2.73927	+	2.29852i	−0.119780	+	0.100507i	−0.700710	−	0.713446i	$-0.747133\pi$
$523$	−2.73927	+	2.29852i	−0.119780	+	0.100507i	0.580930	+	0.813953i	$0.302689\pi$
$524$	−0.0866265	+	2.71359i	−0.00378430	+	0.118544i
$525$	5.50470	−	3.17814i	0.240245	−	0.138705i
$526$	12.3131	+	15.1589i	0.536875	+	0.660959i
$527$	1.26607	−	7.18024i	0.0551508	−	0.312776i
$528$	1.91515	−	4.37176i	0.0833461	−	0.190257i
$529$	47.2174	−	17.1857i	2.05293	−	0.747206i
$530$	0.112838	+	0.326118i	0.00490135	+	0.0141656i
$531$	25.4496			1.10442
$532$	4.03098	−	11.4897i	0.174765	−	0.498140i
$533$	13.9880			0.605886
$534$	−5.82469	−	16.8342i	−0.252059	−	0.728488i
$535$	−0.0368389	+	0.0134083i	−0.00159268	+	0.000579689i
$536$	3.92205	+	30.7983i	0.169407	+	1.33029i
$537$	3.62811	−	20.5760i	0.156565	−	0.887922i
$538$	0.199460	+	0.245560i	0.00859934	+	0.0105869i
$539$	5.73004	−	3.30824i	0.246810	−	0.142496i
$540$	0.436715	+	0.0139414i	0.0187932	+	0.000599941i
$541$	15.2062	−	12.7595i	0.653766	−	0.548575i	−0.254445	−	0.967087i	$-0.581893\pi$
$541$	15.2062	−	12.7595i	0.653766	−	0.548575i	0.908211	+	0.418513i	$0.137448\pi$
$542$	−19.8570	+	3.17551i	−0.852929	+	0.136400i
$543$	16.9427	+	9.78187i	0.727081	+	0.419780i
$544$	−3.81429	+	5.53510i	−0.163537	+	0.237316i
$545$	−0.128869	+	0.354064i	−0.00552013	+	0.0151664i
$546$	2.70977	+	2.34845i	0.115967	+	0.100504i
$547$	−0.130482	−	0.740000i	−0.00557901	−	0.0316401i	0.981891	−	0.189446i	$-0.0606691\pi$
$547$	−0.130482	−	0.740000i	−0.00557901	−	0.0316401i	−0.987470	+	0.157806i	$0.949558\pi$
$548$	11.4949	+	10.2879i	0.491036	+	0.439476i
$549$	−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
$554$	−5.67411	+	29.4259i	−0.241070	+	1.25019i
$555$	−0.183644	+	0.0323813i	−0.00779524	+	0.00137451i
$556$	−10.6511	−	32.4497i	−0.451706	−	1.37617i
$557$	−31.8977	−	11.6098i	−1.35155	−	0.491923i	−0.438117	−	0.898918i	$-0.644354\pi$
$557$	−31.8977	−	11.6098i	−1.35155	−	0.491923i	−0.913430	+	0.406995i	$0.866577\pi$
$558$	−18.8344	−	0.300551i	−0.797323	−	0.0127233i
$559$	0.411130	−	0.712098i	0.0173890	−	0.0301186i
$560$	−0.257640	+	0.0286399i	−0.0108873	+	0.00121026i
$561$	−0.911409	−	1.08617i	−0.0384797	−	0.0458583i
$562$	9.10779	−	5.06637i	0.384189	−	0.213712i
$563$	−16.1201	−	27.9209i	−0.679383	−	1.17673i	−0.975167	−	0.221471i	$-0.928914\pi$
$563$	−16.1201	−	27.9209i	−0.679383	−	1.17673i	0.295784	−	0.955255i	$-0.404419\pi$
$564$	−15.0393	+	2.15958i	−0.633269	+	0.0909346i
$565$	0.649796	+	0.114577i	0.0273371	+	0.00482027i
$566$	12.3360	−	32.2808i	0.518522	−	1.35686i
$567$	1.06300	+	2.92057i	0.0446418	+	0.122652i
$568$	−12.6982	−	11.7351i	−0.532804	−	0.492393i
$569$			17.8706i			0.749175i	0.927192	+	0.374587i	$0.122216\pi$
$569$			17.8706i			0.749175i	−0.927192	+	0.374587i	$0.877784\pi$
$570$	0.136399	+	0.221873i	0.00571312	+	0.00929325i
$571$			35.9863i			1.50598i	0.658032	+	0.752990i	$0.271389\pi$
$571$			35.9863i			1.50598i	−0.658032	+	0.752990i	$0.728611\pi$
$572$	1.07103	−	5.11406i	0.0447822	−	0.213830i
$573$	−2.39205	−	6.57211i	−0.0999295	−	0.274554i
$574$	12.9457	+	4.94715i	0.540342	+	0.206490i
$575$	42.1242	+	7.42763i	1.75670	+	0.309754i
$576$	15.6770	+	7.47263i	0.653209	+	0.311360i
$577$	−7.40172	−	12.8202i	−0.308138	−	0.533710i	0.669817	−	0.742526i	$-0.266372\pi$
$577$	−7.40172	−	12.8202i	−0.308138	−	0.533710i	−0.977955	+	0.208816i	$0.933039\pi$
$578$	−10.7163	−	19.2647i	−0.445740	−	0.801305i
$579$	−2.27658	−	2.71312i	−0.0946113	−	0.112753i
$580$	0.185439	−	0.462964i	0.00769994	−	0.0192235i
$581$	0.512835	−	0.888256i	0.0212760	−	0.0368511i
$582$	−0.174515	+	10.9362i	−0.00723388	+	0.453320i
$583$	−6.47576	−	2.35698i	−0.268198	−	0.0976162i
$584$	−4.04640	+	17.8932i	−0.167441	+	0.740424i
$585$	0.197765	−	0.0348713i	0.00817658	−	0.00144175i
$586$	−18.4889	−	3.56517i	−0.763771	−	0.147276i
$587$	−12.8463	+	15.3096i	−0.530222	+	0.631894i	−0.962966	−	0.269623i	$-0.913101\pi$
$587$	−12.8463	+	15.3096i	−0.530222	+	0.631894i	0.432744	+	0.901517i	$0.357545\pi$
$588$	−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
$592$	−17.1554	−	4.16838i	−0.705084	−	0.171319i
$593$	−5.76362	−	32.6871i	−0.236683	−	1.34230i	−0.839039	−	0.544071i	$-0.816882\pi$
$593$	−5.76362	−	32.6871i	−0.236683	−	1.34230i	0.602356	−	0.798228i	$-0.294229\pi$
$594$	−5.71465	+	6.59386i	−0.234475	+	0.270550i
$595$	−0.0263390	+	0.0723659i	−0.00107979	+	0.00296671i
$596$	−14.1112	+	22.7338i	−0.578016	+	0.931211i
$597$	17.0928	+	9.86855i	0.699563	+	0.403893i
$598$	3.81051	+	23.8277i	0.155823	+	0.974385i
$599$	24.4486	−	20.5148i	0.998941	−	0.838211i	0.0121038	−	0.999927i	$-0.496147\pi$
$599$	24.4486	−	20.5148i	0.998941	−	0.838211i	0.986837	+	0.161716i	$0.0517027\pi$
$600$	−6.96196	+	10.8266i	−0.284221	+	0.441995i
$601$	−0.700958	+	0.404698i	−0.0285927	+	0.0165080i	−0.514228	−	0.857653i	$-0.671922\pi$
$601$	−0.700958	+	0.404698i	−0.0285927	+	0.0165080i	0.485636	+	0.874161i	$0.338588\pi$
$602$	0.632344	−	0.513632i	0.0257724	−	0.0209341i
$603$	4.13788	−	23.4671i	0.168508	−	0.955654i
$604$	0.868644	−	0.682857i	0.0353446	−	0.0277851i
$605$	0.404744	−	0.147315i	0.0164552	−	0.00598919i
$606$	−12.8278	+	4.43846i	−0.521094	+	0.180300i
$607$	37.1238			1.50681			0.753404	−	0.657558i	$-0.228410\pi$
$607$	37.1238			1.50681			0.753404	+	0.657558i	$0.228410\pi$
$608$	3.39957	+	24.4222i	0.137871	+	0.990450i
$609$	−6.83495			−0.276966
$610$	−0.760345	+	0.263082i	−0.0307855	+	0.0106519i
$611$	−15.6299	+	5.68880i	−0.632316	+	0.230144i
$612$	4.05605	−	3.18854i	0.163956	−	0.128889i
$613$	−6.54618	+	37.1252i	−0.264398	+	1.49947i	0.506347	+	0.862330i	$0.330996\pi$
$613$	−6.54618	+	37.1252i	−0.264398	+	1.49947i	−0.770745	+	0.637144i	$0.780116\pi$
$614$	31.2970	−	25.4215i	1.26304	−	1.02593i
$615$	−0.256720	+	0.148217i	−0.0103519	+	0.00597669i
$616$	2.79993	−	4.35420i	0.112812	−	0.175436i
$617$	−24.7371	+	20.7569i	−0.995877	+	0.835640i	−0.986408	−	0.164315i	$-0.947459\pi$
$617$	−24.7371	+	20.7569i	−0.995877	+	0.835640i	−0.00946884	+	0.999955i	$0.503014\pi$
$618$	0.117894	+	0.737206i	0.00474237	+	0.0296548i
$619$	36.7309	+	21.2066i	1.47634	+	0.852365i	0.999643	−	0.0267023i	$-0.00850062\pi$
$619$	36.7309	+	21.2066i	1.47634	+	0.852365i	0.476697	+	0.879068i	$0.341834\pi$
$620$	−0.300279	+	0.483763i	−0.0120595	+	0.0194284i
$621$	13.7824	−	37.8669i	0.553069	−	1.51954i
$622$	24.2129	−	27.9382i	0.970850	−	1.12022i
$623$	−3.35503	−	19.0273i	−0.134416	−	0.762313i
$624$	−7.05619	−	1.71449i	−0.282474	−	0.0686346i
$625$	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
$630$	0.195362	+	0.0376711i	0.00778340	+	0.00150085i
$631$	−20.4902	+	3.61298i	−0.815704	+	0.143831i	−0.565908	−	0.824468i	$-0.691474\pi$
$631$	−20.4902	+	3.61298i	−0.815704	+	0.143831i	−0.249795	+	0.968299i	$0.580363\pi$
$632$	−6.86319	+	30.3490i	−0.273003	+	1.20722i
$633$	−9.85721	−	3.58773i	−0.391789	−	0.142599i
$634$	0.313723	−	19.6598i	0.0124595	−	0.780792i
$635$	−0.303965	+	0.526483i	−0.0120625	+	0.0208929i
$636$	−3.56112	+	8.89063i	−0.141208	+	0.352536i
$637$	−6.47057	−	7.71133i	−0.256373	−	0.305534i
$638$	4.84146	+	8.70347i	0.191675	+	0.344574i
$639$	6.63531	+	11.4927i	0.262489	+	0.454644i
$640$	0.437240	−	0.290506i	0.0172834	−	0.0114833i
$641$	−25.6534	−	4.52338i	−1.01325	−	0.178663i	−0.357715	−	0.933831i	$-0.616444\pi$
$641$	−25.6534	−	4.52338i	−1.01325	−	0.178663i	−0.655531	+	0.755168i	$0.727555\pi$
$642$	−1.01633	−	0.388389i	−0.0401115	−	0.0153285i
$643$	−9.65370	−	26.5233i	−0.380705	−	1.04598i	−0.971060	−	0.238835i	$-0.923235\pi$
$643$	−9.65370	−	26.5233i	−0.380705	−	1.04598i	0.590355	−	0.807144i	$-0.298988\pi$
$644$	−4.90060	+	23.3998i	−0.193111	+	0.922082i
$645$			0.0174254i			0.000686125i
$646$	6.94997	+	2.31443i	0.273443	+	0.0910601i
$647$			31.9737i			1.25702i	0.777803	+	0.628508i	$0.216334\pi$
$647$			31.9737i			1.25702i	−0.777803	+	0.628508i	$0.783666\pi$
$648$	−4.62229	−	4.27171i	−0.181581	−	0.167809i
$649$	5.25418	+	14.4357i	0.206245	+	0.566652i
$650$	−5.03017	+	13.1629i	−0.197299	+	0.516291i
$651$	7.68477	+	1.35503i	0.301190	+	0.0531079i
$652$	32.2733	−	4.63430i	1.26392	−	0.181493i
$653$	8.32093	+	14.4123i	0.325623	+	0.563996i	0.981638	−	0.190752i	$-0.0610926\pi$
$653$	8.32093	+	14.4123i	0.325623	+	0.563996i	−0.656015	+	0.754748i	$0.727759\pi$
$654$	−9.13838	+	5.08338i	−0.357339	+	0.198776i
$655$	−0.0404870	−	0.0482505i	−0.00158196	−	0.00188530i
$656$	−27.8930	+	3.10066i	−1.08904	+	0.121060i
$657$	7.04003	−	12.1937i	0.274658	−	0.475721i
$658$	−16.4772	−	0.262936i	−0.642347	−	0.0102503i
$659$	4.28405	+	1.55927i	0.166883	+	0.0607404i	0.424111	−	0.905610i	$-0.360587\pi$
$659$	4.28405	+	1.55927i	0.166883	+	0.0607404i	−0.257228	+	0.966351i	$0.582809\pi$
$660$	0.0345323	+	0.105207i	0.00134417	+	0.00409516i
$661$	−22.6492	+	3.99366i	−0.880951	+	0.155335i	−0.595786	−	0.803143i	$-0.703159\pi$
$661$	−22.6492	+	3.99366i	−0.880951	+	0.155335i	−0.285165	+	0.958479i	$0.592048\pi$
$662$	1.90350	−	9.87153i	0.0739816	−	0.383668i
$663$	−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
$668$	−22.0379	−	19.7238i	−0.852672	−	0.763139i
$669$	−0.322223	−	1.82742i	−0.0124579	−	0.0706521i
$670$	−0.544312	−	0.471735i	−0.0210286	−	0.0182247i
$671$	5.49532	−	15.0983i	0.212145	−	0.582862i
$672$	−5.92404	−	4.08231i	−0.228525	−	0.157479i
$673$	23.9900	+	13.8506i	0.924745	+	0.533902i	0.885146	−	0.465314i	$-0.154058\pi$
$673$	23.9900	+	13.8506i	0.924745	+	0.533902i	0.0395995	+	0.999216i	$0.487392\pi$
$674$	−42.4025	+	6.78098i	−1.63328	+	0.261194i
$675$	18.0266	−	15.1261i	0.693843	−	0.582204i
$676$	18.0414	+	0.575940i	0.693900	+	0.0221515i
$677$	3.28430	−	1.89619i	0.126226	−	0.0728765i	−0.435558	−	0.900161i	$-0.643449\pi$
$677$	3.28430	−	1.89619i	0.126226	−	0.0728765i	0.561783	+	0.827284i	$0.310115\pi$
$678$	11.5455	+	14.2140i	0.443404	+	0.545885i
$679$	−2.06001	+	11.6829i	−0.0790561	+	0.448349i
$680$	−0.0197006	−	0.154701i	−0.000755482	−	0.00593251i
$681$	10.6029	−	3.85914i	0.406304	−	0.147883i
$682$	−3.71796	−	10.7454i	−0.142368	−	0.411464i
$683$	−34.1213			−1.30561			−0.652807	−	0.757524i	$-0.726409\pi$
$683$	−34.1213			−1.30561			−0.652807	+	0.757524i	$0.726409\pi$
$684$	3.06903	−	18.6746i	0.117347	−	0.714042i
$685$	−0.357887			−0.0136742
$686$	−7.78225	−	22.4919i	−0.297128	−	0.858743i
$687$	−7.95073	+	2.89383i	−0.303339	+	0.110406i
$688$	−0.661974	+	1.51111i	−0.0252375	+	0.0576104i
$689$	−1.82064	+	10.3253i	−0.0693607	+	0.393364i
$690$	−0.322413	−	0.396930i	−0.0122740	−	0.0151109i
$691$	−28.6806	+	16.5587i	−1.09106	+	0.629924i	−0.933859	−	0.357642i	$-0.883581\pi$
$691$	−28.6806	+	16.5587i	−1.09106	+	0.629924i	−0.157202	+	0.987566i	$0.550247\pi$
$692$	−0.125432	+	3.92917i	−0.00476820	+	0.149365i
$693$	−3.04367	+	2.55394i	−0.115619	+	0.0970162i
$694$	−0.697068	+	0.111475i	−0.0264603	+	0.00423152i
$695$	0.686188	+	0.396171i	0.0260286	+	0.0150276i
$696$	12.3042	−	6.33909i	0.466391	−	0.240283i
$697$	−2.85155	+	7.83458i	−0.108010	+	0.296756i
$698$	−2.91906	−	2.52984i	−0.110488	−	0.0957557i
$699$	1.25744	+	7.13128i	0.0475606	+	0.269730i
$700$	−9.31069	+	10.4030i	−0.351911	+	0.393198i
$701$	5.75372	+	4.82795i	0.217315	+	0.182349i	0.744946	−	0.667125i	$-0.232475\pi$
$701$	5.75372	+	4.82795i	0.217315	+	0.182349i	−0.527631	+	0.849474i	$0.676920\pi$
$702$	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
$706$	6.71605	−	34.8294i	0.252762	−	1.31082i
$707$	−14.4990	+	2.55656i	−0.545289	+	0.0961492i
$708$	20.2849	−	6.65819i	0.762355	−	0.250230i
$709$	−19.0347	−	6.92805i	−0.714862	−	0.260188i	−0.0411190	−	0.999154i	$-0.513092\pi$
$709$	−19.0347	−	6.92805i	−0.714862	−	0.260188i	−0.673743	+	0.738966i	$0.735314\pi$
$710$	0.401081	+	0.00640027i	0.0150523	+	0.000240198i
$711$	11.9407	−	20.6820i	0.447813	−	0.775635i
$712$	23.6866	+	31.1412i	0.887694	+	1.16707i
$713$	33.7539	+	40.2263i	1.26409	+	1.50649i
$714$	−1.86776	+	1.03898i	−0.0698992	+	0.0388827i
$715$	0.0606095	+	0.104979i	0.00226667	+	0.00392598i
$716$	6.52282	+	45.4250i	0.243769	+	1.69761i
$717$	18.7846	+	3.31222i	0.701522	+	0.123697i
$718$	3.93280	−	10.2913i	0.146771	−	0.384069i
$719$	−9.88743	−	27.1655i	−0.368739	−	1.01310i	−0.975842	−	0.218479i	$-0.929891\pi$
$719$	−9.88743	−	27.1655i	−0.368739	−	1.01310i	0.607103	−	0.794623i	$-0.292332\pi$
$720$	−0.386628	+	0.113374i	−0.0144088	+	0.00422519i
$721$			0.809749i			0.0301566i
$722$	24.5322	−	10.9622i	0.912996	−	0.407969i
$723$		−	8.61750i		−	0.320488i
$724$	−42.0579	−	8.80814i	−1.56307	−	0.327352i
$725$	−9.18649	−	25.2397i	−0.341178	−	0.937378i
$726$	11.1663	+	4.26718i	0.414421	+	0.158370i
$727$	12.6244	+	2.22602i	0.468212	+	0.0825584i	0.402776	−	0.915298i	$-0.368045\pi$
$727$	12.6244	+	2.22602i	0.468212	+	0.0825584i	0.0654356	+	0.997857i	$0.479156\pi$
$728$	−7.26362	−	3.04480i	−0.269208	−	0.112848i
$729$	−4.01571	−	6.95541i	−0.148730	−	0.257608i
$730$	−0.206892	−	0.371928i	−0.00765740	−	0.0137657i
$731$	0.315030	+	0.375438i	0.0116518	+	0.0138861i
$732$	−20.7286	−	8.30278i	−0.766150	−	0.306879i
$733$	−25.7324	+	44.5699i	−0.950450	+	1.64623i	−0.205996	+	0.978553i	$0.566044\pi$
$733$	−25.7324	+	44.5699i	−0.950450	+	1.64623i	−0.744453	+	0.667674i	$0.767290\pi$
$734$	−0.189798	+	11.8939i	−0.00700558	+	0.439013i
$735$	0.200463	+	0.0729627i	0.00739420	+	0.00269127i
$736$	−12.8802	−	46.6693i	−0.474770	−	1.72026i
$737$	14.1655	−	2.49776i	0.521792	−	0.0920061i
$738$	21.1505	+	4.07840i	0.778562	+	0.150128i
$739$	−3.33185	+	3.97074i	−0.122564	+	0.146066i	−0.823837	−	0.566827i	$-0.808171\pi$
$739$	−3.33185	+	3.97074i	−0.122564	+	0.146066i	0.701273	+	0.712893i	$0.252615\pi$
$740$	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	$-0.370989\pi$
$743$	−12.0551	−	10.1154i	−0.442259	−	0.371099i	−0.836554	+	0.547885i	$0.815433\pi$
$744$	−15.0908	+	4.68794i	−0.553256	+	0.171868i
$745$	−0.107794	−	0.611330i	−0.00394927	−	0.0223974i
$746$	18.8871	−	21.7929i	0.691505	−	0.797895i
$747$	0.545236	−	1.49802i	0.0199492	−	0.0548098i
$748$	2.64602	+	1.64242i	0.0967480	+	0.0600528i
$749$	−1.02199	−	0.590044i	−0.0373425	−	0.0215597i
$750$	−0.0943335	−	0.589881i	−0.00344457	−	0.0215394i
$751$	−37.8228	+	31.7371i	−1.38017	+	1.15810i	−0.411026	+	0.911624i	$0.634829\pi$
$751$	−37.8228	+	31.7371i	−1.38017	+	1.15810i	−0.969148	+	0.246479i	$0.920726\pi$
$752$	29.9060	−	14.8085i	1.09056	−	0.540010i
$753$	−4.20954	+	2.43038i	−0.153404	+	0.0885679i
$754$	11.7614	−	9.55336i	0.428324	−	0.347913i
$755$	−0.00445125	+	0.0252443i	−0.000161998	+	0.000918734i
$756$	8.12857	+	10.3401i	0.295633	+	0.376067i
$757$	45.1863	−	16.4465i	1.64232	−	0.597757i	0.654881	−	0.755732i	$-0.272719\pi$
$757$	45.1863	−	16.4465i	1.64232	−	0.597757i	0.987443	+	0.157975i	$0.0504965\pi$
$758$	23.8755	−	8.26098i	0.867196	−	0.300052i
$759$	10.2121			0.370676
$760$	−0.436628	−	0.369592i	−0.0158382	−	0.0134065i
$761$	−48.4854			−1.75759			−0.878797	−	0.477196i	$-0.841653\pi$
$761$	−48.4854			−1.75759			−0.878797	+	0.477196i	$0.841653\pi$
$762$	−15.9446	+	5.51690i	−0.577614	+	0.199856i
$763$	−10.6580	+	3.87919i	−0.385845	+	0.140436i
$764$	9.49373	+	12.0767i	0.343471	+	0.436920i
$765$	−0.0207847	+	0.117876i	−0.000751472	+	0.00426181i
$766$	13.3750	−	10.8641i	0.483260	−	0.392535i
$767$	20.2410	−	11.6862i	0.730860	−	0.421962i
$768$	14.4506	+	1.85470i	0.521441	+	0.0669256i
$769$	3.06662	−	2.57320i	0.110585	−	0.0927919i	−0.585818	−	0.810442i	$-0.699227\pi$
$769$	3.06662	−	2.57320i	0.110585	−	0.0927919i	0.696404	+	0.717650i	$0.254782\pi$
$770$	0.0189652	+	0.118592i	0.000683458	+	0.00427376i
$771$	−10.8700	−	6.27581i	−0.391474	−	0.226018i
$772$	6.60939	+	4.10254i	0.237877	+	0.147654i
$773$	8.87283	−	24.3779i	0.319133	−	0.876812i	−0.671591	−	0.740922i	$-0.734389\pi$
$773$	8.87283	−	24.3779i	0.319133	−	0.876812i	0.990724	−	0.135889i	$-0.0433892\pi$
$774$	0.829273	−	0.956859i	0.0298076	−	0.0343936i
$775$	5.32491	+	30.1991i	0.191277	+	1.08478i
$776$	−7.12693	−	22.9421i	−0.255842	−	0.823574i
$777$	−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
$782$	−14.1225	−	2.72321i	−0.505021	−	0.0973817i
$783$	−24.9197	+	4.39401i	−0.890557	+	0.157029i
$784$	14.6121	+	13.9426i	0.521861	+	0.497951i
$785$	0.303042	+	0.110298i	0.0108160	+	0.00393671i
$786$	0.0278917	−	1.74787i	0.000994863	−	0.0623443i
$787$	7.04209	−	12.1973i	0.251023	−	0.434785i	−0.712785	−	0.701383i	$-0.752566\pi$
$787$	7.04209	−	12.1973i	0.251023	−	0.434785i	0.963808	+	0.266598i	$0.0858996\pi$
$788$	21.6652	+	8.67795i	0.771791	+	0.309139i
$789$	−8.08273	−	9.63262i	−0.287753	−	0.342930i
$790$	−0.350913	−	0.630835i	−0.0124849	−	0.0224441i
$791$	9.93091	+	17.2008i	0.353102	+	0.611591i
$792$	3.11054	−	7.42045i	0.110528	−	0.263674i
$793$	−24.0736	−	4.24483i	−0.854879	−	0.150738i
$794$	6.04055	+	2.30838i	0.214371	+	0.0819213i
$795$	−0.0759939	−	0.208791i	−0.00269522	−	0.00740507i
$796$	−42.4306	−	8.88620i	−1.50391	−	0.314963i
$797$			42.2792i			1.49761i	0.662792	+	0.748804i	$0.269371\pi$
$797$			42.2792i			1.49761i	−0.662792	+	0.748804i	$0.730629\pi$
$798$	−2.47706	+	7.43832i	−0.0876870	+	0.263314i
$799$		−	9.91390i		−	0.350728i
$800$	7.11274	−	27.3628i	0.251473	−	0.967419i
$801$	−10.2708	−	28.2187i	−0.362900	−	0.997059i
$802$	−4.06079	+	10.6262i	−0.143392	+	0.375226i
$803$	8.37006	+	1.47587i	0.295373	+	0.0520822i
$804$	−2.84137	−	19.7873i	−0.100207	−	0.697845i
$805$	−0.277324	−	0.480339i	−0.00977438	−	0.0169297i
$806$	−15.1177	+	8.40948i	−0.532498	+	0.296211i
$807$	−0.130933	−	0.156040i	−0.00460906	−	0.00549286i
$808$	23.7299	−	18.0494i	0.834814	−	0.634976i
$809$	21.3717	−	37.0168i	0.751388	−	1.30144i	−0.195762	−	0.980651i	$-0.562718\pi$
$809$	21.3717	−	37.0168i	0.751388	−	1.30144i	0.947150	−	0.320791i	$-0.103949\pi$
$810$	0.145998	+	0.00232978i	0.00512985	+	8.18600e-5i
$811$	−19.8838	−	7.23710i	−0.698213	−	0.254129i	−0.0315655	−	0.999502i	$-0.510049\pi$
$811$	−19.8838	−	7.23710i	−0.698213	−	0.254129i	−0.666648	+	0.745373i	$0.732272\pi$
$812$	14.2637	−	4.68183i	0.500559	−	0.164300i
$813$	12.7511	−	2.24836i	0.447199	−	0.0788533i
$814$	−1.54867	+	8.03137i	−0.0542807	+	0.281499i
$815$	−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
$820$	0.434218	−	0.485161i	0.0151635	−	0.0169426i
$821$	3.63805	+	20.6324i	0.126969	+	0.720076i	0.980119	+	0.198411i	$0.0635780\pi$
$821$	3.63805	+	20.6324i	0.126969	+	0.720076i	−0.853150	+	0.521666i	$0.825311\pi$
$822$	−7.50595	−	6.50512i	−0.261800	−	0.226892i
$823$	−6.64061	+	18.2449i	−0.231477	+	0.635978i	−0.999993	−	0.00385332i	$-0.998773\pi$
$823$	−6.64061	+	18.2449i	−0.231477	+	0.635978i	0.768516	+	0.639831i	$0.220996\pi$
$824$	−0.751005	−	1.45771i	−0.0261625	−	0.0507816i
$825$	5.16454	+	2.98175i	0.179806	+	0.103811i
$826$	22.8658	−	3.65669i	0.795604	−	0.127233i
$827$	−11.1754	+	9.37729i	−0.388608	+	0.326080i	−0.816070	−	0.577952i	$-0.803852\pi$
$827$	−11.1754	+	9.37729i	−0.388608	+	0.326080i	0.427463	+	0.904033i	$0.359407\pi$
$828$	−1.18562	+	37.1397i	−0.0412031	+	1.29069i
$829$	8.11069	−	4.68271i	0.281696	−	0.162637i	−0.352495	−	0.935814i	$-0.614667\pi$
$829$	8.11069	−	4.68271i	0.281696	−	0.162637i	0.634191	+	0.773177i	$0.281333\pi$
$830$	−0.0303810	−	0.0374028i	−0.00105454	−	0.00129827i
$831$	3.35063	−	19.0023i	0.116232	−	0.659184i
$832$	15.8999	−	1.25544i	0.551228	−	0.0435245i
$833$	5.63814	−	2.05212i	0.195350	−	0.0711016i
$834$	7.19040	+	20.7813i	0.248983	+	0.719599i
$835$	0.686140			0.0237448
$836$	11.2264	−	2.11462i	0.388273	−	0.0731356i
$837$	28.8892			0.998557
$838$	0.682113	+	1.97141i	0.0235632	+	0.0681012i
$839$	−10.1232	+	3.68454i	−0.349492	+	0.127205i	−0.510800	−	0.859699i	$-0.670651\pi$
$839$	−10.1232	+	3.68454i	−0.349492	+	0.127205i	0.161309	+	0.986904i	$0.448429\pi$
$840$	0.165571	−	0.0210849i	0.00571275	−	0.000727497i
$841$	0.0204617	−	0.116044i	0.000705577	−	0.00400153i
$842$	18.2637	+	22.4849i	0.629410	+	0.774882i
$843$	−5.81144	+	3.35524i	−0.200157	+	0.115560i
$844$	23.0284	+	0.735141i	0.792670	+	0.0253046i
$845$	−0.320796	+	0.269179i	−0.0110357	+	0.00926005i
$846$	−25.2918	+	4.04465i	−0.869551	+	0.139058i
$847$	11.2284	+	6.48273i	0.385813	+	0.222749i
$848$	1.34170	−	20.9930i	0.0460741	−	0.720904i
$849$	−7.61016	+	20.9087i	−0.261180	+	0.717586i
$850$	−6.34702	−	5.50072i	−0.217701	−	0.188673i
$851$	−6.55941	−	37.2003i	−0.224854	−	1.27521i
$852$	8.29551	+	7.42445i	0.284199	+	0.254358i
$853$	−7.36168	−	6.17719i	−0.252059	−	0.211503i	0.507999	−	0.861358i	$-0.330385\pi$
$853$	−7.36168	−	6.17719i	−0.252059	−	0.211503i	−0.760058	+	0.649855i	$0.774830\pi$
$854$	−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	−0.189520	−	0.981877i	$-0.560693\pi$
$857$	23.7226	−	28.2715i	0.810349	−	0.965737i	0.999870	+	0.0161401i	$0.00513779\pi$
$858$	−0.636981	+	3.30338i	−0.0217462	+	0.112775i
$859$	23.0371	−	4.06206i	0.786015	−	0.138596i	0.233786	−	0.972288i	$-0.424889\pi$
$859$	23.0371	−	4.06206i	0.786015	−	0.138596i	0.552229	+	0.833693i	$0.313777\pi$
$860$	−0.0119361	−	0.0363648i	−0.000407019	−	0.00124003i
$861$	−8.38509	−	3.05192i	−0.285763	−	0.104009i
$862$	−23.3520	−	0.372641i	−0.795372	−	0.0126922i
$863$	16.2551	−	28.1546i	0.553329	−	0.958394i	−0.444703	−	0.895678i	$-0.646691\pi$
$863$	16.2551	−	28.1546i	0.553329	−	0.958394i	0.998031	−	0.0627154i	$-0.0199760\pi$
$864$	−24.2230	−	11.0754i	−0.824084	−	0.376793i
$865$	−0.0586236	−	0.0698649i	−0.00199326	−	0.00237548i
$866$	−37.5435	+	20.8842i	−1.27578	+	0.709676i
$867$	7.09695	+	12.2923i	0.241025	+	0.417468i
$868$	−16.9654	+	2.43615i	−0.575843	+	0.0826885i
$869$	14.1966	+	2.50325i	0.481588	+	0.0849169i
$870$	−0.114627	+	0.299956i	−0.00388623	+	0.0101695i
$871$	−7.48480	−	20.5643i	−0.253613	−	0.696795i
$872$	15.5887	−	16.8681i	0.527900	−	0.571225i
$873$			18.4385i			0.624048i
$874$	−44.9444	+	27.6300i	−1.52027	+	0.934599i
$875$		−	0.647928i		−	0.0219039i
$876$	2.42121	−	11.5610i	0.0818050	−	0.390609i
$877$	13.6046	+	37.3782i	0.459393	+	1.26217i	0.925938	+	0.377675i	$0.123276\pi$
$877$	13.6046	+	37.3782i	0.459393	+	1.26217i	−0.466545	+	0.884497i	$0.654501\pi$
$878$	9.85879	+	3.76751i	0.332718	+	0.127147i
$879$	11.9396	+	2.10527i	0.402712	+	0.0710090i
$880$	−0.144130	−	0.195900i	−0.00485861	−	0.00660378i
$881$	−0.220653	−	0.382182i	−0.00743398	−	0.0128760i	0.862284	−	0.506424i	$-0.169033\pi$
$881$	−0.220653	−	0.382182i	−0.00743398	−	0.0128760i	−0.869718	+	0.493548i	$0.835700\pi$
$882$	−7.53549	−	13.5465i	−0.253733	−	0.456135i
$883$	22.6148	+	26.9512i	0.761048	+	0.906981i	0.997914	−	0.0645611i	$-0.0205647\pi$
$883$	22.6148	+	26.9512i	0.761048	+	0.906981i	−0.236866	+	0.971542i	$0.576120\pi$
$884$	1.76179	−	4.39845i	0.0592554	−	0.147936i
$885$	−0.247654	+	0.428949i	−0.00832480	+	0.0144190i
$886$	−0.736958	+	46.1823i	−0.0247586	+	1.55153i
$887$	30.0097	+	10.9226i	1.00763	+	0.366746i	0.792521	−	0.609845i	$-0.208768\pi$
$887$	30.0097	+	10.9226i	1.00763	+	0.366746i	0.215105	+	0.976591i	$0.430991\pi$
$888$	11.0873	+	2.50731i	0.372065	+	0.0841398i
$889$	−18.0218	+	3.17774i	−0.604433	+	0.106578i
$890$	−0.891291	−	0.171865i	−0.0298762	−	0.00576093i
$891$	−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
$896$	15.1591	+	4.46144i	0.506430	+	0.149046i
$897$	−2.69795	−	15.3008i	−0.0900819	−	0.510880i
$898$	−4.81035	+	5.55044i	−0.160524	+	0.185220i
$899$	11.2778	−	30.9856i	0.376137	−	1.03343i
$900$	−11.4437	+	18.4364i	−0.381457	+	0.614546i
$901$	−5.41201	−	3.12463i	−0.180300	−	0.104096i
$902$	2.05324	+	12.8392i	0.0683653	+	0.427499i
$903$	−0.401819	+	0.337166i	−0.0133717	+	0.0112202i
$904$	−33.8305	−	21.7544i	−1.12519	−	0.723541i
$905$	0.863341	−	0.498450i	0.0286984	−	0.0165690i
$906$	−0.552208	+	0.448539i	−0.0183459	+	0.0149017i
$907$	−2.47076	+	14.0124i	−0.0820404	+	0.465274i	0.915916	+	0.401371i	$0.131466\pi$
$907$	−2.47076	+	14.0124i	−0.0820404	+	0.465274i	−0.997956	+	0.0639034i	$0.979645\pi$
$908$	−19.4836	+	15.3164i	−0.646585	+	0.508293i
$909$	−21.5029	+	7.82640i	−0.713205	+	0.259585i
$910$	0.172677	−	0.0597466i	0.00572417	−	0.00198058i
$911$	−6.23491			−0.206572			−0.103286	−	0.994652i	$-0.532936\pi$
$911$	−6.23491			−0.206572			−0.103286	+	0.994652i	$0.532936\pi$
$912$	−2.43950	−	15.6878i	−0.0807799	−	0.519475i
$913$	0.962289			0.0318471
$914$	−17.6588	+	6.11002i	−0.584103	+	0.202101i
$915$	0.486799	−	0.177180i	0.0160931	−	0.00585740i
$916$	14.6100	−	11.4852i	0.482729	−	0.379482i
$917$	0.329239	−	1.86721i	0.0108724	−	0.0616607i
$918$	−6.14178	+	4.98876i	−0.202709	+	0.164654i
$919$	1.40693	−	0.812293i	0.0464104	−	0.0267951i	−0.476615	−	0.879112i	$-0.658137\pi$
$919$	1.40693	−	0.812293i	0.0464104	−	0.0267951i	0.523026	+	0.852317i	$0.324803\pi$
$920$	0.944729	+	0.607499i	0.0311468	+	0.0200287i
$921$	−19.8875	+	16.6876i	−0.655315	+	0.549875i
$922$	5.87594	+	36.7431i	0.193514	+	1.21007i
$923$	10.5546	+	6.09371i	0.347409	+	0.200577i
$924$	−1.75783	+	2.83195i	−0.0578283	+	0.0931642i
$925$	7.54453	−	20.7284i	0.248063	−	0.681547i
$926$	−19.5828	+	22.5957i	−0.643530	+	0.742539i
$927$	0.218548	+	1.23945i	0.00717805	+	0.0407087i
$928$	−21.3353	+	21.6572i	−0.700367	+	0.710931i
$929$	−14.7421	−	12.3701i	−0.483672	−	0.405849i	0.368080	−	0.929794i	$-0.380015\pi$
$929$	−14.7421	−	12.3701i	−0.483672	−	0.405849i	−0.851752	+	0.523945i	$0.824460\pi$
$930$	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
$934$	−43.9606	−	8.47680i	−1.43844	−	0.277369i
$935$	−0.0711536	+	0.0125463i	−0.00232697	+	0.000410308i
$936$	−11.9399	−	2.70011i	−0.390267	−	0.0882559i
$937$	7.32200	+	2.66499i	0.239199	+	0.0870615i	0.458838	−	0.888520i	$-0.348266\pi$
$937$	7.32200	+	2.66499i	0.239199	+	0.0870615i	−0.219639	+	0.975581i	$0.570488\pi$
$938$	0.345946	−	21.6791i	0.0112956	−	0.707849i
$939$	1.61818	−	2.80277i	0.0528074	−	0.0914650i
$940$	−0.287874	+	0.718702i	−0.00938942	+	0.0234415i
$941$	−15.8110	−	18.8429i	−0.515425	−	0.614260i	0.444068	−	0.895993i	$-0.353535\pi$
$941$	−15.8110	−	18.8429i	−0.515425	−	0.614260i	−0.959493	+	0.281734i	$0.909091\pi$
$942$	4.35085	+	7.82150i	0.141758	+	0.254838i
$943$	−30.0240	−	52.0032i	−0.977717	−	1.69346i
$944$	−37.7716	+	27.7897i	−1.22936	+	0.904479i
$945$	−0.300502	−	0.0529867i	−0.00977534	−	0.00172366i
$946$	0.713965	+	0.272840i	0.0232130	+	0.00887079i
$947$	−1.99484	−	5.48078i	−0.0648236	−	0.178101i	0.903052	−	0.429532i	$-0.141321\pi$
$947$	−1.99484	−	5.48078i	−0.0648236	−	0.178101i	−0.967875	+	0.251430i	$0.919099\pi$
$948$	4.10666	−	19.6088i	0.133378	−	0.636865i
$949$		−	12.9308i		−	0.419751i
$950$	−30.7971	+	0.850313i	−0.999189	+	0.0275878i
$951$			12.6600i			0.410528i
$952$	3.18612	−	3.44761i	0.103263	−	0.111738i
$953$	0.622993	+	1.71166i	0.0201807	+	0.0554461i	0.949374	−	0.314148i	$-0.101719\pi$
$953$	0.622993	+	1.71166i	0.0201807	+	0.0554461i	−0.929193	+	0.369594i	$0.879497\pi$
$954$	−5.76340	+	15.0816i	−0.186597	+	0.488286i
$955$	−0.350970	−	0.0618855i	−0.0113571	−	0.00200257i
$956$	−41.4700	+	5.95490i	−1.34124	+	0.192595i
$957$	−3.20629	−	5.55346i	−0.103645	−	0.179518i
$958$	16.7222	−	9.30200i	0.540269	−	0.300534i
$959$	−6.92480	−	8.25265i	−0.223613	−	0.266492i
$960$	−0.278506	+	0.191517i	−0.00898873	+	0.00618117i
$961$	−3.32299	+	5.75559i	−0.107193	+	0.185664i
$962$	12.4426	+	0.198553i	0.401165	+	0.00640161i
$963$	−1.72356	−	0.627323i	−0.0555408	−	0.0202152i
$964$	5.90285	+	17.9837i	0.190118	+	0.579217i
$965$	−0.177732	+	0.0313390i	−0.00572140	+	0.00100884i
$966$	2.91456	−	15.1149i	0.0937744	−	0.486313i
$967$	−12.3518	+	14.7203i	−0.397208	+	0.473375i	−0.927167	−	0.374649i	$-0.877763\pi$
$967$	−12.3518	+	14.7203i	−0.397208	+	0.473375i	0.529958	+	0.848024i	$0.322208\pi$
$968$	−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	0.970963	+	0.239230i	$0.0768948\pi$
$971$	42.8513	+	35.9565i	1.37516	+	1.15390i	0.404201	+	0.914670i	$0.367550\pi$
$972$	24.0705	+	21.5430i	0.772060	+	0.690992i
$973$	4.14168	+	23.4886i	0.132776	+	0.753011i
$974$	13.8856	+	12.0341i	0.444922	+	0.385597i
$975$	3.10314	−	8.52580i	0.0993799	−	0.273044i
$976$	48.9454	+	3.12818i	1.56670	+	0.100131i
$977$	−10.5268	−	6.07767i	−0.336783	−	0.194442i	0.322065	−	0.946717i	$-0.395623\pi$
$977$	−10.5268	−	6.07767i	−0.336783	−	0.194442i	−0.658849	+	0.752275i	$0.728956\pi$
$978$	−20.7296	+	3.31506i	−0.662859	+	0.106004i
$979$	13.8860	−	11.6517i	0.443799	−	0.372391i
$980$	−0.468322	−	0.0149504i	−0.0149600	−	0.000477572i
$981$	−15.2667	+	8.81424i	−0.487428	+	0.281417i
$982$	−29.0220	−	35.7297i	−0.926130	−	1.14018i
$983$	−4.91750	+	27.8885i	−0.156844	+	0.889506i	0.800237	+	0.599684i	$0.204707\pi$
$983$	−4.91750	+	27.8885i	−0.156844	+	0.889506i	−0.957081	+	0.289822i	$0.906404\pi$
$984$	17.9253	−	2.28272i	0.571439	−	0.0727705i
$985$	−0.508795	+	0.185186i	−0.0162116	+	0.00590053i
$986$	2.95314	+	8.53500i	0.0940470	+	0.271810i
$987$	10.6105			0.337737
$988$	−6.13426	−	16.2619i	−0.195157	−	0.517360i
$989$	−3.52983			−0.112242
$990$	0.0610366	+	0.176405i	0.00193987	+	0.00560651i
$991$	28.8710	−	10.5082i	0.917116	−	0.333803i	0.160026	−	0.987113i	$-0.448842\pi$
$991$	28.8710	−	10.5082i	0.917116	−	0.333803i	0.757091	+	0.653310i	$0.226620\pi$
$992$	28.2816	−	20.1202i	0.897943	−	0.638816i
$993$	−1.12404	+	6.37473i	−0.0356702	+	0.202296i
$994$	7.61297	+	9.37251i	0.241469	+	0.297278i
$995$	0.870991	−	0.502867i	0.0276123	−	0.0159420i
$996$	0.0426708	−	1.33667i	0.00135207	−	0.0423539i
$997$	42.8223	−	35.9321i	1.35619	−	1.13798i	0.379057	−	0.925373i	$-0.376248\pi$
$997$	42.8223	−	35.9321i	1.35619	−	1.13798i	0.977137	−	0.212609i	$-0.0681961\pi$
$998$	5.78533	−	0.925187i	0.183131	−	0.0292863i
$999$	−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.3.8	yes	48
3.2	odd	2		684.2.cf.a.307.1		48
4.3	odd	2	inner	76.2.k.a.3.5	✓	48
12.11	even	2		684.2.cf.a.307.4		48
19.13	odd	18	inner	76.2.k.a.51.5	yes	48
57.32	even	18		684.2.cf.a.127.4		48
76.51	even	18	inner	76.2.k.a.51.8	yes	48
228.203	odd	18		684.2.cf.a.127.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.5	✓	48	4.3	odd	2	inner
76.2.k.a.3.8	yes	48	1.1	even	1	trivial
76.2.k.a.51.5	yes	48	19.13	odd	18	inner
76.2.k.a.51.8	yes	48	76.51	even	18	inner
684.2.cf.a.127.1		48	228.203	odd	18
684.2.cf.a.127.4		48	57.32	even	18
684.2.cf.a.307.1		48	3.2	odd	2
684.2.cf.a.307.4		48	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.33647 - 0.462424i) q^{2} +(-0.855656 + 0.311433i) q^{3} +(1.57233 - 1.23604i) q^{4} +(-0.00805719 + 0.0456946i) q^{5} +(-0.999548 + 0.811899i) q^{6} +(-1.20959 + 0.698356i) q^{7} +(1.52980 - 2.37901i) q^{8} +(-1.66298 + 1.39540i) q^{9} +O(q^{10})\)	\(q+(1.33647 - 0.462424i) q^{2} +(-0.855656 + 0.311433i) q^{3} +(1.57233 - 1.23604i) q^{4} +(-0.00805719 + 0.0456946i) q^{5} +(-0.999548 + 0.811899i) q^{6} +(-1.20959 + 0.698356i) q^{7} +(1.52980 - 2.37901i) q^{8} +(-1.66298 + 1.39540i) q^{9} +(0.0103621 + 0.0647955i) q^{10} +(-1.13484 - 0.655201i) q^{11} +(-0.960429 + 1.54730i) q^{12} +(-0.681875 + 1.87343i) q^{13} +(-1.29365 + 1.49268i) q^{14} +(-0.00733663 - 0.0416081i) q^{15} +(0.944429 - 3.88691i) 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} +(-1.81967 - 0.350881i) q^{22} +(8.42847 - 1.48617i) q^{23} +(-0.568081 + 2.51205i) q^{24} +(4.69644 + 1.70936i) q^{25} +(-0.0449862 + 2.81911i) q^{26} +(2.35422 - 4.07762i) q^{27} +(-1.03868 + 2.59314i) q^{28} +(-3.45448 - 4.11689i) q^{29} +(-0.0290458 - 0.0522155i) q^{30} +(3.06782 + 5.31361i) q^{31} +(-0.535196 - 5.63148i) q^{32} +(1.17509 + 0.207199i) q^{33} +(-1.56980 - 0.599894i) q^{34} +(-0.0221652 - 0.0608984i) q^{35} +(-0.889975 + 4.24953i) q^{36} -4.41365i q^{37} +(-5.73226 + 2.26743i) q^{38} -1.81537i q^{39} +(0.0963821 + 0.0890718i) q^{40} +(-2.39968 - 6.59307i) q^{41} +(0.642047 - 1.68010i) q^{42} +(-0.406170 - 0.0716188i) q^{43} +(-2.59419 + 0.372514i) q^{44} +(-0.0503634 - 0.0872320i) q^{45} +(10.5772 - 5.88375i) q^{46} +(5.36271 + 6.39102i) q^{47} +(0.402407 + 3.61998i) q^{48} +(-2.52460 + 4.37273i) q^{49} +(7.06712 + 0.112774i) q^{50} +(1.01678 + 0.370078i) q^{51} +(1.24350 + 3.78848i) q^{52} +(5.17907 - 0.913210i) q^{53} +(1.26076 - 6.53828i) 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} +(-0.0629647 - 0.0563533i) q^{60} +(2.12915 + 12.0750i) q^{61} +(6.55720 + 5.68288i) q^{62} +(1.03703 - 2.84921i) q^{63} +(-3.31941 - 7.27884i) q^{64} +(-0.0801118 - 0.0462526i) q^{65} +(1.66629 - 0.266471i) q^{66} +(-8.40871 + 7.05575i) q^{67} +(-2.37540 - 0.0758305i) q^{68} +(-6.74903 + 3.89655i) q^{69} +(-0.0577841 - 0.0711394i) q^{70} +(1.06152 - 6.02019i) q^{71} +(0.775657 + 6.09094i) q^{72} +(-6.09478 + 2.21832i) q^{73} +(-2.04098 - 5.89873i) q^{74} -4.55089 q^{75} +(-6.61250 + 5.68109i) q^{76} +1.83025 q^{77} +(-0.839473 - 2.42620i) q^{78} +(-10.3375 + 3.76254i) q^{79} +(0.170001 + 0.0744728i) q^{80} +(0.386407 - 2.19142i) q^{81} +(-6.25591 - 7.70180i) q^{82} +(-0.635962 + 0.367173i) q^{83} +(0.0811589 - 2.54231i) q^{84} +(0.0422372 - 0.0354412i) q^{85} +(-0.575954 + 0.0921063i) q^{86} +(4.23798 + 2.44680i) q^{87} +(-3.29481 + 1.69747i) q^{88} +(-4.73119 + 12.9988i) q^{89} +(-0.107648 - 0.0932941i) q^{90} +(-0.483537 - 2.74227i) q^{91} +(11.4154 - 12.7546i) 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} +(-1.35200 + 7.01148i) 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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