LMFDB - Embedded newform 93.2.m.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	93.49
Dual form			93.2.m.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.731871 + 0.531736i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.365141 + 1.12379i) q^{4} +(0.192370 + 0.333194i) q^{5} +(-0.452321 + 0.783444i) q^{6} +(2.25360 + 2.50288i) q^{7} +(-0.889422 - 2.73736i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.731871 + 0.531736i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.365141 + 1.12379i) q^{4} +(0.192370 + 0.333194i) q^{5} +(-0.452321 + 0.783444i) q^{6} +(2.25360 + 2.50288i) q^{7} +(-0.889422 - 2.73736i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.317961 - 0.141565i) q^{10} +(0.374247 - 0.0795487i) q^{11} +(0.123513 + 1.17515i) q^{12} +(-0.0199864 + 0.190158i) q^{13} +(-2.98022 - 0.633465i) q^{14} +(0.311261 + 0.226144i) q^{15} +(0.194591 + 0.141379i) q^{16} +(-3.62477 - 0.770470i) q^{17} +(-0.0945609 + 0.899687i) q^{18} +(-0.469692 - 4.46882i) q^{19} +(-0.444682 + 0.0945201i) q^{20} +(3.07678 + 1.36987i) q^{21} +(-0.231602 + 0.257220i) q^{22} +(-1.34979 - 4.15422i) q^{23} +(-1.92591 - 2.13894i) q^{24} +(2.42599 - 4.20193i) q^{25} +(-0.0864864 - 0.149799i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-3.63559 + 1.61867i) q^{28} +(-2.26475 + 1.64544i) q^{29} -0.348052 q^{30} +(-5.05659 - 2.33043i) q^{31} +5.53887 q^{32} +(0.309536 - 0.224891i) q^{33} +(3.06255 - 1.36354i) q^{34} +(-0.400420 + 1.23237i) q^{35} +(0.590811 + 1.02331i) q^{36} +(-2.60863 + 4.51829i) q^{37} +(2.71999 + 3.02085i) q^{38} +(0.0590858 + 0.181847i) q^{39} +(0.740975 - 0.822936i) q^{40} +(11.6300 + 5.17799i) q^{41} +(-2.98022 + 0.633465i) q^{42} +(0.0695595 + 0.661814i) q^{43} +(-0.0472571 + 0.449621i) q^{44} +(0.376332 + 0.0799918i) q^{45} +(3.19682 + 2.32262i) q^{46} +(2.71166 + 1.97013i) q^{47} +(0.235271 + 0.0500085i) q^{48} +(-0.453982 + 4.31935i) q^{49} +(0.458807 + 4.36526i) q^{50} +(-3.62477 + 0.770470i) q^{51} +(-0.206400 - 0.0918952i) q^{52} +(-8.39237 + 9.32067i) q^{53} +(0.279550 + 0.860366i) q^{54} +(0.0984990 + 0.109394i) q^{55} +(4.84688 - 8.39504i) q^{56} +(-2.24672 - 3.89143i) q^{57} +(0.782570 - 2.40850i) q^{58} +(-4.84432 + 2.15683i) q^{59} +(-0.367792 + 0.267217i) q^{60} +11.6660 q^{61} +(4.93995 - 0.983193i) q^{62} +3.36796 q^{63} +(-4.44292 + 3.22797i) q^{64} +(-0.0672044 + 0.0299213i) q^{65} +(-0.106958 + 0.329183i) q^{66} +(-5.15789 - 8.93373i) q^{67} +(2.18940 - 3.79215i) q^{68} +(-2.92276 - 3.24606i) q^{69} +(-0.362237 - 1.11485i) q^{70} +(9.09104 - 10.0966i) q^{71} +(-2.62939 - 1.17068i) q^{72} +(-14.2866 + 3.03670i) q^{73} +(-0.493350 - 4.69391i) q^{74} +(0.507170 - 4.82540i) q^{75} +(5.19352 + 1.10392i) q^{76} +(1.04251 + 0.757425i) q^{77} +(-0.139938 - 0.101671i) q^{78} +(4.92560 + 1.04697i) q^{79} +(-0.00967311 + 0.0920335i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-11.2650 + 2.39444i) q^{82} +(-9.09203 - 4.04803i) q^{83} +(-2.66291 + 2.95746i) q^{84} +(-0.440581 - 1.35597i) q^{85} +(-0.402819 - 0.447375i) q^{86} +(-1.39970 + 2.42434i) q^{87} +(-0.550617 - 0.953697i) q^{88} +(-3.06122 + 9.42147i) q^{89} +(-0.317961 + 0.141565i) q^{90} +(-0.520985 + 0.378518i) q^{91} +5.16133 q^{92} +(-5.56730 - 0.0722548i) q^{93} -3.03217 q^{94} +(1.39863 - 1.01617i) q^{95} +(5.06001 - 2.25286i) q^{96} +(1.44230 - 4.43894i) q^{97} +(-1.96449 - 3.40260i) q^{98} +(0.191304 - 0.331348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{13}{15}\right)$

Coefficient data

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

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

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

$2$	−0.731871	+	0.531736i	−0.517511	+	0.375994i	−0.815666	−	0.578524i	$-0.803629\pi$
$2$	−0.731871	+	0.531736i	−0.517511	+	0.375994i	0.298154	+	0.954518i	$0.403629\pi$
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$4$	−0.365141	+	1.12379i	−0.182571	+	0.561894i
$5$	0.192370	+	0.333194i	0.0860304	+	0.149009i	0.905830	−	0.423642i	$-0.139248\pi$
$5$	0.192370	+	0.333194i	0.0860304	+	0.149009i	−0.819799	+	0.572651i	$0.805915\pi$
$6$	−0.452321	+	0.783444i	−0.184659	+	0.319840i
$7$	2.25360	+	2.50288i	0.851782	+	0.946000i	0.999071	−	0.0430937i	$-0.0137214\pi$
$7$	2.25360	+	2.50288i	0.851782	+	0.946000i	−0.147289	+	0.989093i	$0.547055\pi$
$8$	−0.889422	−	2.73736i	−0.314458	−	0.967803i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	−0.317961	−	0.141565i	−0.100548	−	0.0447669i
$11$	0.374247	−	0.0795487i	0.112840	−	0.0239848i	−0.151146	−	0.988512i	$-0.548296\pi$
$11$	0.374247	−	0.0795487i	0.112840	−	0.0239848i	0.263985	+	0.964527i	$0.414963\pi$
$12$	0.123513	+	1.17515i	0.0356552	+	0.339236i
$13$	−0.0199864	+	0.190158i	−0.00554324	+	0.0527404i	−0.996944	−	0.0781215i	$-0.975108\pi$
$13$	−0.0199864	+	0.190158i	−0.00554324	+	0.0527404i	0.991401	+	0.130862i	$0.0417745\pi$
$14$	−2.98022	−	0.633465i	−0.796497	−	0.169301i
$15$	0.311261	+	0.226144i	0.0803672	+	0.0583902i
$16$	0.194591	+	0.141379i	0.0486477	+	0.0353446i
$17$	−3.62477	−	0.770470i	−0.879137	−	0.186866i	−0.253833	−	0.967248i	$-0.581692\pi$
$17$	−3.62477	−	0.770470i	−0.879137	−	0.186866i	−0.625304	+	0.780382i	$0.715025\pi$
$18$	−0.0945609	+	0.899687i	−0.0222882	+	0.212058i
$19$	−0.469692	−	4.46882i	−0.107755	−	1.02522i	−0.906113	−	0.423036i	$-0.860965\pi$
$19$	−0.469692	−	4.46882i	−0.107755	−	1.02522i	0.798358	−	0.602183i	$-0.205702\pi$
$20$	−0.444682	+	0.0945201i	−0.0994339	+	0.0211353i
$21$	3.07678	+	1.36987i	0.671409	+	0.298931i
$22$	−0.231602	+	0.257220i	−0.0493777	+	0.0548395i
$23$	−1.34979	−	4.15422i	−0.281450	−	0.866214i	−0.987440	−	0.157993i	$-0.949498\pi$
$23$	−1.34979	−	4.15422i	−0.281450	−	0.866214i	0.705990	−	0.708222i	$-0.250502\pi$
$24$	−1.92591	−	2.13894i	−0.393125	−	0.436610i
$25$	2.42599	−	4.20193i	0.485198	−	0.840387i
$26$	−0.0864864	−	0.149799i	−0.0169614	−	0.0293780i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−3.63559	+	1.61867i	−0.687062	+	0.305900i
$29$	−2.26475	+	1.64544i	−0.420554	+	0.305551i	−0.777861	−	0.628437i	$-0.783695\pi$
$29$	−2.26475	+	1.64544i	−0.420554	+	0.305551i	0.357306	+	0.933987i	$0.383695\pi$
$30$	−0.348052			−0.0635453
$31$	−5.05659	−	2.33043i	−0.908190	−	0.418558i
$31$	−5.05659	−	2.33043i	−0.908190	−	0.418558i
$32$	5.53887			0.979143
$33$	0.309536	−	0.224891i	0.0538834	−	0.0391486i
$34$	3.06255	−	1.36354i	0.525224	−	0.233845i
$35$	−0.400420	+	1.23237i	−0.0676833	+	0.208308i
$36$	0.590811	+	1.02331i	0.0984685	+	0.170552i
$37$	−2.60863	+	4.51829i	−0.428857	+	0.742802i	−0.996772	−	0.0802854i	$-0.974417\pi$
$37$	−2.60863	+	4.51829i	−0.428857	+	0.742802i	0.567915	+	0.823087i	$0.307750\pi$
$38$	2.71999	+	3.02085i	0.441240	+	0.490047i
$39$	0.0590858	+	0.181847i	0.00946130	+	0.0291189i
$40$	0.740975	−	0.822936i	0.117158	−	0.130118i
$41$	11.6300	+	5.17799i	1.81630	+	0.808667i	0.952297	+	0.305172i	$0.0987139\pi$
$41$	11.6300	+	5.17799i	1.81630	+	0.808667i	0.863998	+	0.503495i	$0.167953\pi$
$42$	−2.98022	+	0.633465i	−0.459858	+	0.0977458i
$43$	0.0695595	+	0.661814i	0.0106077	+	0.100926i	0.998545	−	0.0539310i	$-0.0171751\pi$
$43$	0.0695595	+	0.661814i	0.0106077	+	0.100926i	−0.987937	+	0.154857i	$0.950508\pi$
$44$	−0.0472571	+	0.449621i	−0.00712428	+	0.0677830i
$45$	0.376332	+	0.0799918i	0.0561003	+	0.0119245i
$46$	3.19682	+	2.32262i	0.471345	+	0.342452i
$47$	2.71166	+	1.97013i	0.395536	+	0.287374i	0.767720	−	0.640785i	$-0.221391\pi$
$47$	2.71166	+	1.97013i	0.395536	+	0.287374i	−0.372184	+	0.928159i	$0.621391\pi$
$48$	0.235271	+	0.0500085i	0.0339585	+	0.00721810i
$49$	−0.453982	+	4.31935i	−0.0648545	+	0.617049i
$50$	0.458807	+	4.36526i	0.0648851	+	0.617341i
$51$	−3.62477	+	0.770470i	−0.507570	+	0.107887i
$52$	−0.206400	−	0.0918952i	−0.0286225	−	0.0127436i
$53$	−8.39237	+	9.32067i	−1.15278	+	1.28029i	−0.198929	+	0.980014i	$0.563746\pi$
$53$	−8.39237	+	9.32067i	−1.15278	+	1.28029i	−0.953852	+	0.300279i	$0.902920\pi$
$54$	0.279550	+	0.860366i	0.0380419	+	0.117081i
$55$	0.0984990	+	0.109394i	0.0132816	+	0.0147507i
$56$	4.84688	−	8.39504i	0.647692	−	1.12183i
$57$	−2.24672	−	3.89143i	−0.297585	−	0.515433i
$58$	0.782570	−	2.40850i	0.102756	−	0.316252i
$59$	−4.84432	+	2.15683i	−0.630677	+	0.280795i	−0.697075	−	0.716998i	$-0.745516\pi$
$59$	−4.84432	+	2.15683i	−0.630677	+	0.280795i	0.0663987	+	0.997793i	$0.478849\pi$
$60$	−0.367792	+	0.267217i	−0.0474818	+	0.0344975i
$61$	11.6660			1.49367			0.746837	−	0.665007i	$-0.231571\pi$
$61$	11.6660			1.49367			0.746837	+	0.665007i	$0.231571\pi$
$62$	4.93995	−	0.983193i	0.627374	−	0.124866i
$63$	3.36796			0.424323
$64$	−4.44292	+	3.22797i	−0.555365	+	0.403496i
$65$	−0.0672044	+	0.0299213i	−0.00833568	+	0.00371129i
$66$	−0.106958	+	0.329183i	−0.0131656	+	0.0405196i
$67$	−5.15789	−	8.93373i	−0.630137	−	1.09143i	−0.987523	−	0.157472i	$-0.949665\pi$
$67$	−5.15789	−	8.93373i	−0.630137	−	1.09143i	0.357387	−	0.933957i	$-0.383668\pi$
$68$	2.18940	−	3.79215i	0.265504	−	0.459866i
$69$	−2.92276	−	3.24606i	−0.351859	−	0.390780i
$70$	−0.362237	−	1.11485i	−0.0432956	−	0.133250i
$71$	9.09104	−	10.0966i	1.07891	−	1.19825i	0.0997790	−	0.995010i	$-0.468186\pi$
$71$	9.09104	−	10.0966i	1.07891	−	1.19825i	0.979129	−	0.203239i	$-0.0651469\pi$
$72$	−2.62939	−	1.17068i	−0.309877	−	0.137966i
$73$	−14.2866	+	3.03670i	−1.67211	+	0.355419i	−0.943977	−	0.330012i	$-0.892947\pi$
$73$	−14.2866	+	3.03670i	−1.67211	+	0.355419i	−0.728138	+	0.685431i	$0.759614\pi$
$74$	−0.493350	−	4.69391i	−0.0573507	−	0.545656i
$75$	0.507170	−	4.82540i	0.0585629	−	0.557189i
$76$	5.19352	+	1.10392i	0.595737	+	0.126628i
$77$	1.04251	+	0.757425i	0.118805	+	0.0863165i
$78$	−0.139938	−	0.101671i	−0.0158449	−	0.0115120i
$79$	4.92560	+	1.04697i	0.554173	+	0.117793i	0.476482	−	0.879184i	$-0.341912\pi$
$79$	4.92560	+	1.04697i	0.554173	+	0.117793i	0.0776915	+	0.996977i	$0.475245\pi$
$80$	−0.00967311	+	0.0920335i	−0.00108149	+	0.0102897i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−11.2650	+	2.39444i	−1.24401	+	0.264422i
$83$	−9.09203	−	4.04803i	−0.997980	−	0.444329i	−0.158288	−	0.987393i	$-0.550598\pi$
$83$	−9.09203	−	4.04803i	−0.997980	−	0.444329i	−0.839692	+	0.543064i	$0.817264\pi$
$84$	−2.66291	+	2.95746i	−0.290547	+	0.322685i
$85$	−0.440581	−	1.35597i	−0.0477877	−	0.147075i
$86$	−0.402819	−	0.447375i	−0.0434371	−	0.0482417i
$87$	−1.39970	+	2.42434i	−0.150063	+	0.259917i
$88$	−0.550617	−	0.953697i	−0.0586960	−	0.101664i
$89$	−3.06122	+	9.42147i	−0.324489	+	0.998674i	0.647182	+	0.762336i	$0.275947\pi$
$89$	−3.06122	+	9.42147i	−0.324489	+	0.998674i	−0.971671	+	0.236339i	$0.924053\pi$
$90$	−0.317961	+	0.141565i	−0.0335160	+	0.0149223i
$91$	−0.520985	+	0.378518i	−0.0546141	+	0.0396794i
$92$	5.16133			0.538105
$93$	−5.56730	−	0.0722548i	−0.577302	−	0.00749248i
$94$	−3.03217			−0.312745
$95$	1.39863	−	1.01617i	0.143497	−	0.104256i
$96$	5.06001	−	2.25286i	0.516435	−	0.229932i
$97$	1.44230	−	4.43894i	0.146443	−	0.450706i	−0.850751	−	0.525570i	$-0.823852\pi$
$97$	1.44230	−	4.43894i	0.146443	−	0.450706i	0.997194	+	0.0748638i	$0.0238522\pi$
$98$	−1.96449	−	3.40260i	−0.198444	−	0.343715i
$99$	0.191304	−	0.331348i	0.0192268	−	0.0333018i
$100$	3.83626	+	4.26060i	0.383626	+	0.426060i
$101$	4.64077	+	14.2828i	0.461773	+	1.42119i	0.862996	+	0.505212i	$0.168586\pi$
$101$	4.64077	+	14.2828i	0.461773	+	1.42119i	−0.401222	+	0.915981i	$0.631414\pi$
$102$	2.24318	−	2.49131i	0.222108	−	0.246676i
$103$	10.3706	+	4.61727i	1.02184	+	0.454953i	0.848099	−	0.529838i	$-0.177747\pi$
$103$	10.3706	+	4.61727i	1.02184	+	0.454953i	0.173743	+	0.984791i	$0.444414\pi$
$104$	0.538308	−	0.114421i	0.0527855	−	0.0112199i
$105$	0.135447	+	1.28869i	0.0132182	+	0.125763i
$106$	1.18600	−	11.2841i	0.115195	−	1.09600i
$107$	−14.0962	−	2.99623i	−1.36273	−	0.289656i	−0.532192	−	0.846624i	$-0.678632\pi$
$107$	−14.0962	−	2.99623i	−1.36273	−	0.289656i	−0.830534	+	0.556967i	$0.811965\pi$
$108$	0.955952	+	0.694540i	0.0919865	+	0.0668321i
$109$	−0.481021	−	0.349482i	−0.0460735	−	0.0334743i	0.564510	−	0.825426i	$-0.309065\pi$
$109$	−0.481021	−	0.349482i	−0.0460735	−	0.0334743i	−0.610584	+	0.791952i	$0.709065\pi$
$110$	−0.130257	−	0.0276871i	−0.0124196	−	0.00263986i
$111$	−0.545353	+	5.18869i	−0.0517626	+	0.492488i
$112$	0.0846771	+	0.805649i	0.00800123	+	0.0761267i
$113$	−2.63545	+	0.560182i	−0.247922	+	0.0526975i	−0.330197	−	0.943912i	$-0.607115\pi$
$113$	−2.63545	+	0.560182i	−0.247922	+	0.0526975i	0.0822742	+	0.996610i	$0.473782\pi$
$114$	3.71352	+	1.65337i	0.347803	+	0.154852i
$115$	1.12450	−	1.24889i	0.104860	−	0.116459i
$116$	−1.02217	−	3.14592i	−0.0949064	−	0.292092i
$117$	0.127942	+	0.142094i	0.0118282	+	0.0131366i
$118$	2.39856	−	4.15442i	0.220805	−	0.382445i
$119$	−6.24041	−	10.8087i	−0.572058	−	0.990833i
$120$	0.342196	−	1.05317i	0.0312381	−	0.0961409i
$121$	−9.91527	+	4.41456i	−0.901388	+	0.401324i
$122$	−8.53799	+	6.20321i	−0.772993	+	0.561612i
$123$	12.7306			1.14788
$124$	4.46528	−	4.83160i	0.400994	−	0.433891i
$125$	3.79044			0.339028
$126$	−2.46491	+	1.79086i	−0.219592	+	0.159543i
$127$	−2.10789	+	0.938493i	−0.187045	+	0.0832778i	−0.498122	−	0.867107i	$-0.665977\pi$
$127$	−2.10789	+	0.938493i	−0.187045	+	0.0832778i	0.311077	+	0.950385i	$0.399310\pi$
$128$	−1.88799	+	5.81064i	−0.166876	+	0.513593i
$129$	0.332730	+	0.576305i	0.0292952	+	0.0507408i
$130$	0.0332748	−	0.0576336i	0.00291839	−	0.00505480i
$131$	0.609290	+	0.676685i	0.0532339	+	0.0591222i	0.769174	−	0.639040i	$-0.220668\pi$
$131$	0.609290	+	0.676685i	0.0532339	+	0.0591222i	−0.715940	+	0.698162i	$0.754001\pi$
$132$	0.139706	+	0.429971i	0.0121598	+	0.0374241i
$133$	10.1264	−	11.2465i	0.878073	−	0.975199i
$134$	8.52530	+	3.79571i	0.736473	+	0.327899i
$135$	0.376332	−	0.0799918i	0.0323895	−	0.00688460i
$136$	1.11490	+	10.6076i	0.0956021	+	0.909593i
$137$	−0.0427543	+	0.406780i	−0.00365275	+	0.0347536i	−0.996196	−	0.0871357i	$-0.972229\pi$
$137$	−0.0427543	+	0.406780i	−0.00365275	+	0.0347536i	0.992544	+	0.121889i	$0.0388953\pi$
$138$	3.86513	+	0.821559i	0.329022	+	0.0699358i
$139$	12.5136	+	9.09165i	1.06139	+	0.771143i	0.974345	−	0.225061i	$-0.0722582\pi$
$139$	12.5136	+	9.09165i	1.06139	+	0.771143i	0.0870431	+	0.996205i	$0.472258\pi$
$140$	−1.23871	−	0.899975i	−0.104690	−	0.0760618i
$141$	3.27855	+	0.696877i	0.276103	+	0.0586876i
$142$	−1.28474	+	12.2235i	−0.107813	+	1.02577i
$143$	0.00764697	+	0.0727561i	0.000639472	+	0.00608417i
$144$	0.235271	−	0.0500085i	0.0196060	−	0.00416737i
$145$	−0.983922	−	0.438070i	−0.0817102	−	0.0363797i
$146$	8.84120	−	9.81914i	0.731703	−	0.812638i
$147$	1.34210	+	4.13057i	0.110695	+	0.340684i
$148$	−4.12508	−	4.58137i	−0.339080	−	0.376586i
$149$	5.59998	−	9.69945i	0.458768	−	0.794610i	−0.540128	−	0.841583i	$-0.681624\pi$
$149$	5.59998	−	9.69945i	0.458768	−	0.794610i	0.998896	+	0.0469728i	$0.0149574\pi$
$150$	2.19465	+	3.80125i	0.179193	+	0.310371i
$151$	−1.61705	+	4.97676i	−0.131593	+	0.405003i	−0.995045	−	0.0994295i	$-0.968298\pi$
$151$	−1.61705	+	4.97676i	−0.131593	+	0.405003i	0.863451	+	0.504432i	$0.168298\pi$
$152$	−11.8150	+	5.26039i	−0.958325	+	0.426674i
$153$	−2.99802	+	2.17819i	−0.242375	+	0.176096i
$154$	−1.16573			−0.0939372
$155$	−0.196249	−	2.13313i	−0.0157631	−	0.171337i
$156$	−0.225933			−0.0180891
$157$	−12.5240	+	9.09919i	−0.999521	+	0.726195i	−0.961985	−	0.273101i	$-0.911951\pi$
$157$	−12.5240	+	9.09919i	−0.999521	+	0.726195i	−0.0375356	+	0.999295i	$0.511951\pi$
$158$	−4.16162	+	1.85287i	−0.331080	+	0.147407i
$159$	−3.87575	+	11.9283i	−0.307367	+	0.945979i
$160$	1.06551	+	1.84552i	0.0842360	+	0.145901i
$161$	7.35562	−	12.7403i	0.579704	−	1.00408i
$162$	0.605324	+	0.672281i	0.0475588	+	0.0528193i
$163$	−2.65489	−	8.17091i	−0.207947	−	0.639995i	−0.999579	−	0.0289975i	$-0.990769\pi$
$163$	−2.65489	−	8.17091i	−0.207947	−	0.639995i	0.791632	−	0.610998i	$-0.209231\pi$
$164$	−10.0656	+	11.1789i	−0.785987	+	0.872928i
$165$	0.134478	+	0.0598734i	0.0104691	+	0.00466114i
$166$	8.80668	−	1.87192i	0.683531	−	0.145289i
$167$	−0.322086	−	3.06444i	−0.0249237	−	0.237134i	−0.999891	−	0.0147838i	$-0.995294\pi$
$167$	−0.322086	−	3.06444i	−0.0249237	−	0.237134i	0.974967	−	0.222350i	$-0.0713727\pi$
$168$	1.01327	−	9.64066i	0.0781758	−	0.743793i
$169$	12.6802	+	2.69525i	0.975397	+	0.207327i
$170$	1.04347	+	0.758122i	0.0800302	+	0.0581453i
$171$	−3.63527	−	2.64118i	−0.277996	−	0.201976i
$172$	−0.769138	−	0.163485i	−0.0586462	−	0.0124656i
$173$	−1.24623	+	11.8571i	−0.0947491	+	0.901477i	0.839140	+	0.543915i	$0.183059\pi$
$173$	−1.24623	+	11.8571i	−0.0947491	+	0.901477i	−0.933889	+	0.357562i	$0.883608\pi$
$174$	−0.264713	−	2.51858i	−0.0200678	−	0.190933i
$175$	15.9842	−	3.39754i	1.20829	−	0.256830i
$176$	0.0840715	+	0.0374311i	0.00633713	+	0.00282147i
$177$	−3.54824	+	3.94073i	−0.266702	+	0.296203i
$178$	−2.76931	−	8.52307i	−0.207569	−	0.638831i
$179$	−12.4318	−	13.8069i	−0.929199	−	1.03198i	−0.999407	−	0.0344473i	$-0.989033\pi$
$179$	−12.4318	−	13.8069i	−0.929199	−	1.03198i	0.0702078	−	0.997532i	$-0.477634\pi$
$180$	−0.227308	+	0.393709i	−0.0169426	+	0.0293454i
$181$	−3.38279	−	5.85916i	−0.251441	−	0.435508i	0.712482	−	0.701690i	$-0.247571\pi$
$181$	−3.38279	−	5.85916i	−0.251441	−	0.435508i	−0.963923	+	0.266182i	$0.914238\pi$
$182$	0.180023	−	0.554053i	0.0133442	−	0.0410691i
$183$	10.6574	−	4.74498i	0.787817	−	0.350759i
$184$	−10.1711	+	7.38971i	−0.749820	+	0.544776i
$185$	−2.00729			−0.147579
$186$	4.11296	−	2.90745i	0.301577	−	0.213184i
$187$	−1.41785			−0.103684
$188$	−3.20415	+	2.32795i	−0.233687	+	0.169783i
$189$	3.07678	−	1.36987i	0.223803	−	0.0996435i
$190$	−0.483287	+	1.48740i	−0.0350613	+	0.107908i
$191$	0.212212	+	0.367562i	0.0153551	+	0.0265958i	0.873601	−	0.486643i	$-0.161779\pi$
$191$	0.212212	+	0.367562i	0.0153551	+	0.0265958i	−0.858246	+	0.513239i	$0.828445\pi$
$192$	−2.74588	+	4.75600i	−0.198167	+	0.343235i
$193$	5.38523	+	5.98090i	0.387637	+	0.430515i	0.905105	−	0.425188i	$-0.139792\pi$
$193$	5.38523	+	5.98090i	0.387637	+	0.430515i	−0.517468	+	0.855703i	$0.673125\pi$
$194$	1.30477	+	4.01565i	0.0936767	+	0.288307i
$195$	−0.0492242	+	0.0546690i	−0.00352502	+	0.00391493i
$196$	−4.68827	−	2.08735i	−0.334876	−	0.149096i
$197$	18.4978	−	3.93183i	1.31791	−	0.280131i	0.505305	−	0.862941i	$-0.331380\pi$
$197$	18.4978	−	3.93183i	1.31791	−	0.280131i	0.812609	+	0.582809i	$0.198047\pi$
$198$	0.0361798	+	0.344227i	0.00257118	+	0.0244632i
$199$	0.757698	−	7.20902i	0.0537118	−	0.511034i	−0.934281	−	0.356536i	$-0.883958\pi$
$199$	0.757698	−	7.20902i	0.0537118	−	0.511034i	0.987993	−	0.154497i	$-0.0493758\pi$
$200$	−13.6599	−	2.90351i	−0.965903	−	0.205309i
$201$	−8.34564	−	6.06347i	−0.588656	−	0.427684i
$202$	−10.9911	−	7.98552i	−0.773333	−	0.561859i
$203$	−9.22220	−	1.96024i	−0.647272	−	0.137582i
$204$	0.457709	−	4.35481i	0.0320461	−	0.304898i
$205$	0.511976	+	4.87113i	0.0357580	+	0.340214i
$206$	−10.0451	+	2.13515i	−0.699874	+	0.148763i
$207$	−3.99037	−	1.77663i	−0.277350	−	0.123484i
$208$	−0.0307735	+	0.0341774i	−0.00213376	+	0.00236978i
$209$	−0.531270	−	1.63508i	−0.0367487	−	0.113101i
$210$	−0.784371	−	0.871132i	−0.0541267	−	0.0601138i
$211$	−12.2668	+	21.2468i	−0.844483	+	1.46269i	0.0415869	+	0.999135i	$0.486759\pi$
$211$	−12.2668	+	21.2468i	−0.844483	+	1.46269i	−0.886070	+	0.463552i	$0.846575\pi$
$212$	−7.41007	−	12.8346i	−0.508925	−	0.881485i
$213$	4.19841	−	12.9214i	0.287670	−	0.885359i
$214$	11.9098	−	5.30257i	0.814135	−	0.362476i
$215$	−0.207131	+	0.150490i	−0.0141262	+	0.0102633i
$216$	−2.87823			−0.195839
$217$	−5.56276	−	17.9079i	−0.377624	−	1.21567i
$218$	0.537878			0.0364297
$219$	−11.8163	+	8.58503i	−0.798470	+	0.580122i
$220$	−0.158902	+	0.0707477i	−0.0107132	+	0.00476981i
$221$	0.218958	−	0.673882i	0.0147287	−	0.0453302i
$222$	−2.35988	−	4.08743i	−0.158385	−	0.274331i
$223$	−3.73850	+	6.47528i	−0.250349	+	0.433617i	−0.963622	−	0.267270i	$-0.913879\pi$
$223$	−3.73850	+	6.47528i	−0.250349	+	0.433617i	0.713273	+	0.700886i	$0.247212\pi$
$224$	12.4824	+	13.8631i	0.834017	+	0.926269i
$225$	−1.49934	−	4.61450i	−0.0999562	−	0.307634i
$226$	1.63094	−	1.81134i	0.108489	−	0.120489i
$227$	4.40212	+	1.95995i	0.292179	+	0.130086i	0.547592	−	0.836746i	$-0.315545\pi$
$227$	4.40212	+	1.95995i	0.292179	+	0.130086i	−0.255413	+	0.966832i	$0.582211\pi$
$228$	5.19352	−	1.10392i	0.343949	−	0.0731086i
$229$	−1.49970	−	14.2687i	−0.0991028	−	0.942900i	−0.925228	−	0.379413i	$-0.876126\pi$
$229$	−1.49970	−	14.2687i	−0.0991028	−	0.942900i	0.826125	−	0.563487i	$-0.190541\pi$
$230$	−0.158914	+	1.51196i	−0.0104785	+	0.0996959i
$231$	1.26045	+	0.267917i	0.0829314	+	0.0176276i
$232$	6.51849	+	4.73596i	0.427960	+	0.310931i
$233$	23.2382	+	16.8835i	1.52238	+	1.10608i	0.960291	+	0.279000i	$0.0900029\pi$
$233$	23.2382	+	16.8835i	1.52238	+	1.10608i	0.562091	+	0.827075i	$0.309997\pi$
$234$	−0.169193	−	0.0359631i	−0.0110605	−	0.00235098i
$235$	−0.134796	+	1.28250i	−0.00879315	+	0.0836612i
$236$	−0.654961	−	6.23154i	−0.0426343	−	0.405639i
$237$	4.92560	−	1.04697i	0.319952	−	0.0680079i
$238$	10.3146	+	4.59234i	0.668593	+	0.297677i
$239$	15.4074	−	17.1116i	0.996620	−	1.10686i	0.00234658	−	0.999997i	$-0.499253\pi$
$239$	15.4074	−	17.1116i	0.996620	−	1.10686i	0.994274	−	0.106862i	$-0.0340803\pi$
$240$	0.0285966	+	0.0880112i	0.00184590	+	0.00568110i
$241$	−5.62504	−	6.24724i	−0.362341	−	0.402420i	0.534217	−	0.845348i	$-0.320607\pi$
$241$	−5.62504	−	6.24724i	−0.362341	−	0.402420i	−0.896558	+	0.442927i	$0.853940\pi$
$242$	4.90932	−	8.50319i	0.315583	−	0.546606i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.25973	+	13.1101i	−0.272701	+	0.839287i
$245$	−1.52651	+	0.679647i	−0.0975253	+	0.0434211i
$246$	−9.31715	+	6.76930i	−0.594040	+	0.431595i
$247$	0.859171			0.0546678
$248$	−1.88179	+	15.9144i	−0.119494	+	1.01057i
$249$	−9.95247			−0.630712
$250$	−2.77412	+	2.01551i	−0.175451	+	0.127472i
$251$	13.8867	−	6.18277i	0.876523	−	0.390253i	0.0813857	−	0.996683i	$-0.474065\pi$
$251$	13.8867	−	6.18277i	0.876523	−	0.390253i	0.795137	+	0.606429i	$0.207399\pi$
$252$	−1.22978	+	3.78487i	−0.0774688	+	0.238425i
$253$	−0.835616	−	1.44733i	−0.0525348	−	0.0909929i
$254$	1.04367	−	1.80770i	0.0654859	−	0.113425i
$255$	−0.954013	−	1.05954i	−0.0597426	−	0.0663509i
$256$	−5.10205	−	15.7025i	−0.318878	−	0.981405i
$257$	−0.643011	+	0.714136i	−0.0401099	+	0.0445466i	−0.762866	−	0.646557i	$-0.776208\pi$
$257$	−0.643011	+	0.714136i	−0.0401099	+	0.0445466i	0.722756	+	0.691103i	$0.242875\pi$
$258$	−0.549957	−	0.244857i	−0.0342388	−	0.0152441i
$259$	−17.1876	+	3.65333i	−1.06798	+	0.227007i
$260$	−0.00908617	−	0.0864491i	−0.000563500	−	0.00536135i
$261$	−0.292616	+	2.78406i	−0.0181125	+	0.172329i
$262$	−0.805739	−	0.171265i	−0.0497787	−	0.0105808i
$263$	22.5837	+	16.4080i	1.39257	+	1.01176i	0.995578	+	0.0939379i	$0.0299455\pi$
$263$	22.5837	+	16.4080i	1.39257	+	1.01176i	0.396991	+	0.917823i	$0.370054\pi$
$264$	−0.890917	−	0.647289i	−0.0548322	−	0.0398379i
$265$	−4.72003	−	1.00327i	−0.289949	−	0.0616306i
$266$	−1.43106	+	13.6156i	−0.0877438	+	0.834826i
$267$	1.03549	+	9.85206i	0.0633711	+	0.602936i
$268$	11.9230	−	2.53431i	0.728312	−	0.154808i
$269$	−13.5132	−	6.01647i	−0.823915	−	0.366830i	−0.0489236	−	0.998803i	$-0.515579\pi$
$269$	−13.5132	−	6.01647i	−0.823915	−	0.366830i	−0.774991	+	0.631972i	$0.782246\pi$
$270$	−0.232892	+	0.258653i	−0.0141734	+	0.0157411i
$271$	6.59940	+	20.3109i	0.400885	+	1.23380i	0.924283	+	0.381708i	$0.124664\pi$
$271$	6.59940	+	20.3109i	0.400885	+	1.23380i	−0.523398	+	0.852088i	$0.675336\pi$
$272$	−0.596420	−	0.662392i	−0.0361633	−	0.0401634i
$273$	−0.321986	+	0.557697i	−0.0194875	+	0.0337533i
$274$	−0.185009	−	0.320445i	−0.0111768	−	0.0193588i
$275$	0.573661	−	1.76555i	0.0345930	−	0.106466i
$276$	4.71511	−	2.09930i	0.283816	−	0.126363i
$277$	10.3733	−	7.53666i	0.623272	−	0.452834i	−0.230791	−	0.973003i	$-0.574131\pi$
$277$	10.3733	−	7.53666i	0.623272	−	0.452834i	0.854063	+	0.520169i	$0.174131\pi$
$278$	−13.9927			−0.839225
$279$	−5.11537	+	2.19842i	−0.306249	+	0.131616i
$280$	3.72957			0.222885
$281$	15.3468	−	11.1501i	0.915512	−	0.665158i	−0.0268912	−	0.999638i	$-0.508561\pi$
$281$	15.3468	−	11.1501i	0.915512	−	0.665158i	0.942403	+	0.334480i	$0.108561\pi$
$282$	−2.77003	+	1.23330i	−0.164953	+	0.0734417i
$283$	−4.39371	+	13.5224i	−0.261179	+	0.803825i	0.731370	+	0.681980i	$0.238881\pi$
$283$	−4.39371	+	13.5224i	−0.261179	+	0.803825i	−0.992549	+	0.121845i	$0.961119\pi$
$284$	8.02696	+	13.9031i	0.476312	+	0.824997i
$285$	0.864402	−	1.49719i	0.0512027	−	0.0886857i
$286$	−0.0442836	−	0.0491819i	−0.00261854	−	0.00290819i
$287$	13.2494	+	40.7776i	0.782089	+	2.40702i
$288$	3.70623	−	4.11618i	0.218392	−	0.242548i
$289$	−2.98490	−	1.32896i	−0.175583	−	0.0781744i
$290$	0.953042	−	0.202575i	0.0559645	−	0.0118956i
$291$	−0.487874	−	4.64181i	−0.0285997	−	0.272108i
$292$	1.80400	−	17.1639i	0.105571	−	1.00444i
$293$	−11.3884	−	2.42069i	−0.665320	−	0.141418i	−0.137141	−	0.990551i	$-0.543791\pi$
$293$	−11.3884	−	2.42069i	−0.665320	−	0.141418i	−0.528178	+	0.849133i	$0.677125\pi$
$294$	−3.17862	−	2.30940i	−0.185381	−	0.134687i
$295$	−1.65054	−	1.19919i	−0.0960984	−	0.0698196i
$296$	14.6884	+	3.12211i	0.853743	+	0.181469i
$297$	0.0399934	−	0.380512i	0.00232065	−	0.0220795i
$298$	1.05908	+	10.0765i	0.0613508	+	0.583714i
$299$	0.816936	−	0.173645i	0.0472447	−	0.0100422i
$300$	5.23754	+	2.33190i	0.302389	+	0.134632i
$301$	−1.49968	+	1.66557i	−0.0864402	+	0.0960016i
$302$	−1.46285	−	4.50219i	−0.0841775	−	0.259072i
$303$	10.0489	+	11.1604i	0.577294	+	0.641150i
$304$	0.540398	−	0.935997i	0.0309939	−	0.0536831i
$305$	2.24418	+	3.88703i	0.128501	+	0.222571i
$306$	1.03594	−	3.18831i	0.0592210	−	0.182263i
$307$	5.22091	−	2.32450i	0.297973	−	0.132666i	−0.252305	−	0.967648i	$-0.581188\pi$
$307$	5.22091	−	2.32450i	0.297973	−	0.132666i	0.550278	+	0.834982i	$0.314522\pi$
$308$	−1.23185	+	0.894989i	−0.0701910	+	0.0509967i
$309$	11.3520			0.645792
$310$	1.27789	+	1.45682i	0.0725793	+	0.0827421i
$311$	−4.36507			−0.247520			−0.123760	−	0.992312i	$-0.539495\pi$
$311$	−4.36507			−0.247520			−0.123760	+	0.992312i	$0.539495\pi$
$312$	0.445230	−	0.323478i	0.0252062	−	0.0183134i
$313$	−18.4341	+	8.20738i	−1.04196	+	0.463908i	−0.855091	−	0.518477i	$-0.826499\pi$
$313$	−18.4341	+	8.20738i	−1.04196	+	0.463908i	−0.186864	+	0.982386i	$0.559832\pi$
$314$	4.32756	−	13.3189i	0.244219	−	0.751628i
$315$	0.647893	+	1.12218i	0.0365046	+	0.0632279i
$316$	−2.97511	+	5.15304i	−0.167363	+	0.289881i
$317$	−16.6491	−	18.4907i	−0.935107	−	1.03854i	−0.999176	−	0.0405958i	$-0.987074\pi$
$317$	−16.6491	−	18.4907i	−0.935107	−	1.03854i	0.0640689	−	0.997945i	$-0.479592\pi$
$318$	−3.50617	−	10.7909i	−0.196616	−	0.605123i
$319$	−0.716685	+	0.795960i	−0.0401267	+	0.0445652i
$320$	−1.93023	−	0.859392i	−0.107903	−	0.0480415i
$321$	−14.0962	+	2.99623i	−0.786770	+	0.167233i
$322$	1.39111	+	13.2355i	0.0775235	+	0.737587i
$323$	−1.74056	+	16.5604i	−0.0968476	+	0.921443i
$324$	1.15580	+	0.245673i	0.0642111	+	0.0136485i
$325$	0.750546	+	0.545303i	0.0416328	+	0.0302480i
$326$	6.28780	+	4.56836i	0.348249	+	0.253018i
$327$	−0.581582	−	0.123619i	−0.0321616	−	0.00683615i
$328$	3.83009	−	36.4408i	0.211481	−	2.01211i
$329$	1.17999	+	11.2269i	0.0650549	+	0.618956i
$330$	−0.130257	+	0.0276871i	−0.00717043	+	0.00152412i
$331$	−30.1018	−	13.4022i	−1.65454	−	0.736651i	−0.654729	−	0.755863i	$-0.727217\pi$
$331$	−30.1018	−	13.4022i	−1.65454	−	0.736651i	−0.999815	+	0.0192125i	$0.993884\pi$
$332$	7.86901	−	8.73942i	0.431868	−	0.479638i
$333$	1.61222	+	4.96192i	0.0883494	+	0.271911i
$334$	1.86520	+	2.07151i	0.102059	+	0.113348i
$335$	1.98444	−	3.43716i	0.108422	−	0.187792i
$336$	0.405043	+	0.701555i	0.0220969	+	0.0382730i
$337$	4.57959	−	14.0945i	0.249466	−	0.767778i	−0.745404	−	0.666613i	$-0.767743\pi$
$337$	4.57959	−	14.0945i	0.249466	−	0.767778i	0.994870	−	0.101164i	$-0.0322568\pi$
$338$	−10.7134	+	4.76992i	−0.582732	+	0.259449i
$339$	−2.17976	+	1.58369i	−0.118388	+	0.0860140i
$340$	1.68470			0.0913655
$341$	−2.07780	−	0.469912i	−0.112519	−	0.0254472i
$342$	4.06496			0.219808
$343$	7.23925	−	5.25962i	0.390883	−	0.283993i
$344$	1.74976	−	0.779041i	0.0943405	−	0.0420031i
$345$	0.519316	−	1.59829i	0.0279591	−	0.0860491i
$346$	−5.39275	−	9.34052i	−0.289916	−	0.502150i
$347$	9.18921	−	15.9162i	0.493303	−	0.854425i	−0.506668	−	0.862141i	$-0.669123\pi$
$347$	9.18921	−	15.9162i	0.493303	−	0.854425i	0.999970	+	0.00771632i	$0.00245621\pi$
$348$	−2.21336	−	2.45819i	−0.118649	−	0.131773i
$349$	−2.32552	−	7.15723i	−0.124482	−	0.383118i	0.869324	−	0.494243i	$-0.164555\pi$
$349$	−2.32552	−	7.15723i	−0.124482	−	0.383118i	−0.993806	+	0.111125i	$0.964555\pi$
$350$	−9.89175	+	10.9859i	−0.528736	+	0.587221i
$351$	0.174675	+	0.0777704i	0.00932347	+	0.00415108i
$352$	2.07291	−	0.440610i	0.110486	−	0.0234846i
$353$	−1.89704	−	18.0491i	−0.100969	−	0.960656i	−0.921323	−	0.388799i	$-0.872890\pi$
$353$	−1.89704	−	18.0491i	−0.100969	−	0.960656i	0.820354	−	0.571857i	$-0.193777\pi$
$354$	0.501435	−	4.77083i	0.0266510	−	0.253567i
$355$	5.11298	+	1.08680i	0.271369	+	0.0576812i
$356$	−9.46997	−	6.88034i	−0.501907	−	0.364657i
$357$	−10.0972	−	7.33604i	−0.534400	−	0.388265i
$358$	16.4401	+	3.49446i	0.868889	+	0.184688i
$359$	2.54116	−	24.1775i	0.134117	−	1.27604i	−0.695833	−	0.718204i	$-0.744964\pi$
$359$	2.54116	−	24.1775i	0.134117	−	1.27604i	0.829950	−	0.557838i	$-0.188369\pi$
$360$	−0.115752	−	1.10130i	−0.00610064	−	0.0580438i
$361$	−1.16497	+	0.247622i	−0.0613141	+	0.0130327i
$362$	5.59129	+	2.48940i	0.293872	+	0.130840i
$363$	−7.26248	+	8.06580i	−0.381182	+	0.423345i
$364$	−0.235141	−	0.723689i	−0.0123247	−	0.0379316i
$365$	−3.76011	−	4.17603i	−0.196813	−	0.218583i
$366$	−5.27677	+	9.13963i	−0.275821	+	0.477736i
$367$	12.4734	+	21.6046i	0.651107	+	1.12775i	0.982855	+	0.184383i	$0.0590286\pi$
$367$	12.4734	+	21.6046i	0.651107	+	1.12775i	−0.331747	+	0.943368i	$0.607638\pi$
$368$	0.324661	−	0.999204i	0.0169241	−	0.0520871i
$369$	11.6300	−	5.17799i	0.605432	−	0.269556i
$370$	1.46908	−	1.06735i	0.0763737	−	0.0554887i
$371$	−42.2416			−2.19307
$372$	2.11405	−	6.23008i	0.109608	−	0.323015i
$373$	−4.77307			−0.247140			−0.123570	−	0.992336i	$-0.539434\pi$
$373$	−4.77307			−0.247140			−0.123570	+	0.992336i	$0.539434\pi$
$374$	1.03768	−	0.753922i	0.0536574	−	0.0389844i
$375$	3.46274	−	1.54171i	0.178815	−	0.0796137i
$376$	2.98116	−	9.17506i	0.153741	−	0.473168i
$377$	−0.267630	−	0.463548i	−0.0137836	−	0.0238740i
$378$	−1.52340	+	2.63860i	−0.0783552	+	0.135715i
$379$	−13.7606	−	15.2827i	−0.706836	−	0.785021i	0.277613	−	0.960693i	$-0.410457\pi$
$379$	−13.7606	−	15.2827i	−0.706836	−	0.785021i	−0.984449	+	0.175672i	$0.943790\pi$
$380$	0.631257	+	1.94281i	0.0323828	+	0.0996640i
$381$	−1.54393	+	1.71471i	−0.0790981	+	0.0878473i
$382$	−0.350758	−	0.156167i	−0.0179463	−	0.00799022i
$383$	−32.7847	+	6.96861i	−1.67522	+	0.356080i	−0.944985	−	0.327114i	$-0.893924\pi$
$383$	−32.7847	+	6.96861i	−1.67522	+	0.356080i	−0.730237	+	0.683193i	$0.760591\pi$
$384$	0.638634	+	6.07620i	0.0325902	+	0.310075i
$385$	−0.0518229	+	0.493062i	−0.00264114	+	0.0251288i
$386$	−7.12155	−	1.51373i	−0.362477	−	0.0770469i
$387$	0.538368	+	0.391147i	0.0273668	+	0.0198831i
$388$	4.46179	+	3.24168i	0.226513	+	0.164571i
$389$	−5.48073	−	1.16497i	−0.277884	−	0.0590661i	0.0668614	−	0.997762i	$-0.478701\pi$
$389$	−5.48073	−	1.16497i	−0.277884	−	0.0590661i	−0.344746	+	0.938696i	$0.612035\pi$
$390$	0.00695632	−	0.0661849i	0.000352247	−	0.00335140i
$391$	1.69198	+	16.0981i	0.0855669	+	0.814115i
$392$	12.2274	−	2.59901i	0.617576	−	0.131270i
$393$	0.831846	+	0.370362i	0.0419611	+	0.0186823i
$394$	−11.4473	+	12.7135i	−0.576708	+	0.640499i
$395$	0.598693	+	1.84259i	0.0301235	+	0.0927106i
$396$	0.302513	+	0.335974i	0.0152018	+	0.0168833i
$397$	−1.67053	+	2.89345i	−0.0838416	+	0.145218i	−0.904897	−	0.425631i	$-0.860052\pi$
$397$	−1.67053	+	2.89345i	−0.0838416	+	0.145218i	0.821055	+	0.570849i	$0.193386\pi$
$398$	3.27875	+	5.67897i	0.164349	+	0.284661i
$399$	4.67657	−	14.3930i	0.234122	−	0.720552i
$400$	1.06614	−	0.474675i	0.0533069	−	0.0237338i
$401$	25.2130	−	18.3183i	1.25907	−	0.914771i	0.260363	−	0.965511i	$-0.416158\pi$
$401$	25.2130	−	18.3183i	1.25907	−	0.914771i	0.998712	+	0.0507393i	$0.0161578\pi$
$402$	9.33210			0.465443
$403$	0.544214	−	0.914975i	0.0271092	−	0.0455782i
$404$	−17.7454			−0.882866
$405$	0.311261	−	0.226144i	0.0154667	−	0.0112372i
$406$	7.79179	−	3.46913i	0.386700	−	0.172170i
$407$	−0.616850	+	1.89847i	−0.0305761	+	0.0941036i
$408$	5.33301	+	9.23704i	0.264023	+	0.457302i
$409$	−1.85729	+	3.21692i	−0.0918372	+	0.159067i	−0.908284	−	0.418354i	$-0.862607\pi$
$409$	−1.85729	+	3.21692i	−0.0918372	+	0.159067i	0.816447	+	0.577420i	$0.195941\pi$
$410$	−2.96485	−	3.29280i	−0.146424	−	0.162620i
$411$	0.126394	+	0.389002i	0.00623457	+	0.0191880i
$412$	−8.97555	+	9.96836i	−0.442194	+	0.491106i
$413$	−16.3155	−	7.26411i	−0.802832	−	0.357444i
$414$	3.86513	−	0.821559i	0.189961	−	0.0403774i
$415$	−0.400251	−	3.80813i	−0.0196475	−	0.186934i
$416$	−0.110702	+	1.05326i	−0.00542763	+	0.0516404i
$417$	15.1296	+	3.21590i	0.740901	+	0.157483i
$418$	1.25825	+	0.914174i	0.0615431	+	0.0447137i
$419$	6.96322	+	5.05907i	0.340175	+	0.247152i	0.744736	−	0.667359i	$-0.232575\pi$
$419$	6.96322	+	5.05907i	0.340175	+	0.247152i	−0.404560	+	0.914511i	$0.632575\pi$
$420$	−1.49767	−	0.318340i	−0.0730788	−	0.0155334i
$421$	−1.42599	+	13.5674i	−0.0694985	+	0.661234i	0.903209	+	0.429200i	$0.141205\pi$
$421$	−1.42599	+	13.5674i	−0.0694985	+	0.661234i	−0.972708	+	0.232034i	$0.925462\pi$
$422$	−2.31992	−	22.0726i	−0.112932	−	1.07448i
$423$	3.27855	−	0.696877i	0.159408	−	0.0338833i
$424$	32.9784	+	14.6829i	1.60157	+	0.713066i
$425$	−12.0311	+	13.3619i	−0.583595	+	0.648148i
$426$	3.79806	+	11.6892i	0.184017	+	0.566345i
$427$	26.2905	+	29.1985i	1.27228	+	1.41302i
$428$	8.51421	−	14.7471i	0.411550	−	0.712826i
$429$	0.0365784	+	0.0633557i	0.00176602	+	0.00305884i
$430$	0.0715728	−	0.220278i	0.00345155	−	0.0106228i
$431$	1.66200	−	0.739970i	0.0800557	−	0.0356431i	−0.366318	−	0.930490i	$-0.619382\pi$
$431$	1.66200	−	0.739970i	0.0800557	−	0.0356431i	0.446374	+	0.894847i	$0.352715\pi$
$432$	0.194591	−	0.141379i	0.00936226	−	0.00680208i
$433$	19.0176			0.913926			0.456963	−	0.889486i	$-0.348937\pi$
$433$	19.0176			0.913926			0.456963	+	0.889486i	$0.348937\pi$
$434$	13.5935	+	10.1484i	0.652509	+	0.487137i
$435$	−1.07704			−0.0516399
$436$	0.568385	−	0.412956i	0.0272207	−	0.0197770i
$437$	−17.9305	+	7.98316i	−0.857731	+	0.381887i
$438$	4.08303	−	12.5663i	0.195095	−	0.600440i
$439$	11.0874	+	19.2039i	0.529171	+	0.916552i	0.999421	+	0.0340184i	$0.0108305\pi$
$439$	11.0874	+	19.2039i	0.529171	+	0.916552i	−0.470250	+	0.882533i	$0.655836\pi$
$440$	0.211844	−	0.366925i	0.0100993	−	0.0174925i
$441$	2.90613	+	3.22758i	0.138387	+	0.153694i
$442$	0.198078	+	0.609623i	0.00942163	+	0.0289968i
$443$	−4.16283	+	4.62329i	−0.197782	+	0.219659i	−0.833875	−	0.551953i	$-0.813883\pi$
$443$	−4.16283	+	4.62329i	−0.197782	+	0.219659i	0.636093	+	0.771612i	$0.280549\pi$
$444$	−5.63186	−	2.50746i	−0.267276	−	0.118999i
$445$	−3.72807	+	0.792425i	−0.176727	+	0.0375646i
$446$	−0.707033	−	6.72697i	−0.0334790	−	0.318531i
$447$	1.17072	−	11.1386i	0.0553729	−	0.526838i
$448$	−18.0918	−	3.84553i	−0.854758	−	0.181684i
$449$	−4.39877	−	3.19589i	−0.207591	−	0.150823i	0.479132	−	0.877743i	$-0.340951\pi$
$449$	−4.39877	−	3.19589i	−0.207591	−	0.150823i	−0.686723	+	0.726919i	$0.740951\pi$
$450$	3.55102	+	2.57997i	0.167397	+	0.121621i
$451$	4.76438	+	1.01270i	0.224346	+	0.0476862i
$452$	0.332785	−	3.16624i	0.0156529	−	0.148927i
$453$	0.546984	+	5.20421i	0.0256996	+	0.244515i
$454$	−4.26396	+	0.906332i	−0.200117	+	0.0425363i
$455$	−0.226342	−	0.100774i	−0.0106111	−	0.00472435i
$456$	−8.65397	+	9.61121i	−0.405259	+	0.450086i
$457$	4.94030	+	15.2047i	0.231098	+	0.711246i	0.997615	+	0.0690221i	$0.0219879\pi$
$457$	4.94030	+	15.2047i	0.231098	+	0.711246i	−0.766517	+	0.642224i	$0.778012\pi$
$458$	8.68474	+	9.64539i	0.405811	+	0.450699i
$459$	−1.85288	+	3.20928i	−0.0864849	+	0.149796i
$460$	0.992883	+	1.71972i	0.0462934	+	0.0801825i
$461$	−10.9710	+	33.7653i	−0.510970	+	1.57260i	0.279526	+	0.960138i	$0.409823\pi$
$461$	−10.9710	+	33.7653i	−0.510970	+	1.57260i	−0.790497	+	0.612466i	$0.790177\pi$
$462$	−1.06495	+	0.474145i	−0.0495458	+	0.0220592i
$463$	8.77928	−	6.37852i	0.408008	−	0.296435i	−0.364787	−	0.931091i	$-0.618858\pi$
$463$	8.77928	−	6.37852i	0.408008	−	0.296435i	0.772795	+	0.634656i	$0.218858\pi$
$464$	−0.673331			−0.0312586
$465$	−1.04690	−	1.86889i	−0.0485490	−	0.0866677i
$466$	−25.9849			−1.20373
$467$	6.81122	−	4.94864i	0.315186	−	0.228996i	−0.418933	−	0.908017i	$-0.637596\pi$
$467$	6.81122	−	4.94864i	0.315186	−	0.228996i	0.734118	+	0.679021i	$0.237596\pi$
$468$	−0.206400	+	0.0918952i	−0.00954084	+	0.00424786i
$469$	10.7362	−	33.0427i	0.495752	−	1.52577i
$470$	−0.583299	−	1.01030i	−0.0269056	−	0.0466018i
$471$	−7.74023	+	13.4065i	−0.356651	+	0.617738i
$472$	10.2127	+	11.3423i	0.470076	+	0.522072i
$473$	0.0786789	+	0.242149i	0.00361766	+	0.0111340i
$474$	−3.04820	+	3.38536i	−0.140008	+	0.155495i
$475$	−19.9172	−	8.86770i	−0.913862	−	0.406878i
$476$	14.4253	−	3.06620i	0.661184	−	0.140539i
$477$	1.31102	+	12.4735i	0.0600273	+	0.571122i
$478$	−2.17736	+	20.7162i	−0.0995900	+	0.947535i
$479$	−2.49035	−	0.529339i	−0.113787	−	0.0241861i	0.150666	−	0.988585i	$-0.451858\pi$
$479$	−2.49035	−	0.529339i	−0.113787	−	0.0241861i	−0.264453	+	0.964399i	$0.585191\pi$
$480$	1.72403	+	1.25258i	0.0786910	+	0.0571723i
$481$	−0.807052	−	0.586358i	−0.0367984	−	0.0267356i
$482$	7.43869	+	1.58114i	0.338823	+	0.0720191i
$483$	1.53774	−	14.6307i	0.0699698	−	0.665718i
$484$	−1.34056	−	12.7546i	−0.0609347	−	0.579755i
$485$	1.75648	−	0.373352i	0.0797578	−	0.0169530i
$486$	0.826432	+	0.367951i	0.0374877	+	0.0166906i
$487$	17.3032	−	19.2171i	0.784083	−	0.870812i	−0.210193	−	0.977660i	$-0.567409\pi$
$487$	17.3032	−	19.2171i	0.784083	−	0.870812i	0.994275	+	0.106848i	$0.0340758\pi$
$488$	−10.3760	−	31.9340i	−0.469698	−	1.44558i
$489$	−5.74877	−	6.38466i	−0.259968	−	0.288724i
$490$	0.755818	−	1.30912i	0.0341444	−	0.0591398i
$491$	−5.18805	−	8.98597i	−0.234133	−	0.405531i	0.724887	−	0.688868i	$-0.241892\pi$
$491$	−5.18805	−	8.98597i	−0.234133	−	0.405531i	−0.959020	+	0.283337i	$0.908559\pi$
$492$	−4.64846	+	14.3065i	−0.209569	+	0.644986i
$493$	9.47699	−	4.21943i	0.426822	−	0.190033i
$494$	−0.628803	+	0.456852i	−0.0282912	+	0.0205547i
$495$	0.147204			0.00661635
$496$	−0.654493	−	1.16837i	−0.0293876	−	0.0524615i
$497$	45.7582			2.05254
$498$	7.28393	−	5.29208i	0.326400	−	0.237144i
$499$	13.8094	−	6.14835i	0.618195	−	0.275238i	−0.0736501	−	0.997284i	$-0.523465\pi$
$499$	13.8094	−	6.14835i	0.618195	−	0.275238i	0.691845	+	0.722046i	$0.256798\pi$
$500$	−1.38405	+	4.25966i	−0.0618965	+	0.190498i
$501$	−1.54066	−	2.66850i	−0.0688316	−	0.119220i
$502$	−6.87570	+	11.9091i	−0.306878	+	0.531528i
$503$	−11.3234	−	12.5759i	−0.504884	−	0.560731i	0.435787	−	0.900050i	$-0.356470\pi$
$503$	−11.3234	−	12.5759i	−0.504884	−	0.560731i	−0.940671	+	0.339319i	$0.889803\pi$
$504$	−2.99554	−	9.21931i	−0.133432	−	0.410661i
$505$	−3.86621	+	4.29386i	−0.172044	+	0.191074i
$506$	1.38116	+	0.614932i	0.0614001	+	0.0273371i
$507$	12.6802	−	2.69525i	0.563146	−	0.119700i
$508$	−0.284991	−	2.71151i	−0.0126444	−	0.120304i
$509$	−4.02979	+	38.3409i	−0.178617	+	1.69943i	0.427469	+	0.904030i	$0.359405\pi$
$509$	−4.02979	+	38.3409i	−0.178617	+	1.69943i	−0.606086	+	0.795399i	$0.707261\pi$
$510$	1.26161	+	0.268163i	0.0558650	+	0.0118745i
$511$	−39.7967	−	28.9140i	−1.76050	−	1.27908i
$512$	2.19797	+	1.59692i	0.0971374	+	0.0705744i
$513$	−4.39525	−	0.934238i	−0.194055	−	0.0412476i
$514$	0.0908697	−	0.864567i	0.00400809	−	0.0381344i
$515$	0.456534	+	4.34363i	0.0201173	+	0.191403i
$516$	−0.769138	+	0.163485i	−0.0338594	+	0.00719704i
$517$	1.17155	+	0.521608i	0.0515248	+	0.0229403i
$518$	10.6365	−	11.8130i	0.467340	−	0.519034i
$519$	3.68422	+	11.3389i	0.161719	+	0.497721i
$520$	0.141679	+	0.157350i	0.00621302	+	0.00690025i
$521$	−3.22645	+	5.58837i	−0.141353	+	0.244831i	−0.928006	−	0.372564i	$-0.878479\pi$
$521$	−3.22645	+	5.58837i	−0.141353	+	0.244831i	0.786653	+	0.617395i	$0.211812\pi$
$522$	−1.26622	−	2.19316i	−0.0554211	−	0.0959922i
$523$	11.6674	−	35.9085i	0.510179	−	1.57017i	−0.281707	−	0.959500i	$-0.590901\pi$
$523$	11.6674	−	35.9085i	0.510179	−	1.57017i	0.791886	−	0.610669i	$-0.209099\pi$
$524$	−0.982927	+	0.437627i	−0.0429394	+	0.0191178i
$525$	13.2203	−	9.60514i	0.576983	−	0.419203i
$526$	−25.2531			−1.10109
$527$	16.5335	+	12.3432i	0.720209	+	0.537680i
$528$	0.0920278			0.00400499
$529$	3.17179	−	2.30444i	0.137904	−	0.100193i
$530$	3.98793	−	1.77554i	0.173225	−	0.0771246i
$531$	−1.63865	+	5.04323i	−0.0711112	+	0.218858i
$532$	8.94116	+	15.4865i	0.387648	+	0.671427i
$533$	−1.21708	+	2.10804i	−0.0527176	+	0.0913096i
$534$	−5.99654	−	6.65983i	−0.259496	−	0.288199i
$535$	−1.71335	−	5.27314i	−0.0740744	−	0.227978i
$536$	−19.8673	+	22.0649i	−0.858136	+	0.953057i
$537$	−16.9728	−	7.55679i	−0.732432	−	0.326100i
$538$	13.0891	−	2.78217i	0.564311	−	0.119948i
$539$	0.173697	+	1.65262i	0.00748166	+	0.0711832i
$540$	−0.0475204	+	0.452126i	−0.00204495	+	0.0194564i
$541$	25.6826	+	5.45900i	1.10418	+	0.234701i	0.723718	−	0.690096i	$-0.242432\pi$
$541$	25.6826	+	5.45900i	1.10418	+	0.234701i	0.380462	+	0.924797i	$0.375765\pi$
$542$	−15.6299	−	11.3558i	−0.671362	−	0.487773i
$543$	−5.47346	−	3.97670i	−0.234889	−	0.170657i
$544$	−20.0772	−	4.26753i	−0.860801	−	0.182969i
$545$	0.0239116	−	0.227503i	0.00102426	−	0.00974517i
$546$	−0.0608947	−	0.579374i	−0.00260605	−	0.0247949i
$547$	−12.6086	+	2.68005i	−0.539106	+	0.114590i	−0.469414	−	0.882978i	$-0.655535\pi$
$547$	−12.6086	+	2.68005i	−0.539106	+	0.114590i	−0.0696916	+	0.997569i	$0.522202\pi$
$548$	−0.441524	−	0.196579i	−0.0188610	−	0.00839744i
$549$	7.80606	−	8.66950i	0.333154	−	0.370005i
$550$	0.518958	+	1.59719i	0.0221284	+	0.0681043i
$551$	8.41692	+	9.34794i	0.358573	+	0.398236i
$552$	−6.28606	+	10.8878i	−0.267552	+	0.463415i
$553$	8.47991	+	14.6876i	0.360603	+	0.624582i
$554$	−3.58443	+	11.0317i	−0.152288	+	0.468693i
$555$	−1.83375	+	0.816438i	−0.0778383	+	0.0346559i
$556$	−14.7863	+	10.7429i	−0.627079	+	0.455600i
$557$	−33.5051			−1.41966			−0.709829	−	0.704375i	$-0.751228\pi$
$557$	−33.5051			−1.41966			−0.709829	+	0.704375i	$0.751228\pi$
$558$	2.57481	−	4.32898i	0.109001	−	0.183260i
$559$	−0.127240			−0.00538166
$560$	−0.252148	+	0.183196i	−0.0106552	+	0.00774146i
$561$	−1.29527	+	0.576692i	−0.0546864	+	0.0243480i
$562$	−5.30297	+	16.3208i	−0.223692	+	0.688453i
$563$	10.3818	+	17.9817i	0.437539	+	0.757839i	0.997499	−	0.0706802i	$-0.0225170\pi$
$563$	10.3818	+	17.9817i	0.437539	+	0.757839i	−0.559960	+	0.828519i	$0.689184\pi$
$564$	−1.98027	+	3.42994i	−0.0833846	+	0.144426i
$565$	−0.693631	−	0.770355i	−0.0291813	−	0.0324091i
$566$	−3.97473	−	12.2330i	−0.167071	−	0.514190i
$567$	2.25360	−	2.50288i	0.0946424	−	0.105111i
$568$	−35.7239	−	15.9053i	−1.49894	−	0.667371i
$569$	27.1606	−	5.77316i	1.13863	−	0.242024i	0.400249	−	0.916406i	$-0.368924\pi$
$569$	27.1606	−	5.77316i	1.13863	−	0.242024i	0.738382	+	0.674383i	$0.235590\pi$
$570$	0.163477	+	1.55538i	0.00684731	+	0.0651478i
$571$	−0.768705	+	7.31374i	−0.0321693	+	0.306071i	0.966592	+	0.256319i	$0.0825097\pi$
$571$	−0.768705	+	7.31374i	−0.0321693	+	0.306071i	−0.998762	+	0.0497518i	$0.984157\pi$
$572$	−0.0845547	−	0.0179727i	−0.00353541	−	0.000751475i
$573$	0.343366	+	0.249470i	0.0143443	+	0.0104218i
$574$	−31.3798	−	22.7987i	−1.30977	−	0.951601i
$575$	−20.7303	−	4.40636i	−0.864514	−	0.183758i
$576$	−0.574045	+	5.46167i	−0.0239185	+	0.227570i
$577$	−4.46905	−	42.5201i	−0.186049	−	1.77014i	−0.546597	−	0.837396i	$-0.684077\pi$
$577$	−4.46905	−	42.5201i	−0.186049	−	1.77014i	0.360549	−	0.932740i	$-0.382589\pi$
$578$	2.89122	−	0.614549i	0.120259	−	0.0255619i
$579$	7.35230	+	3.27345i	0.305551	+	0.136040i
$580$	0.851569	−	0.945763i	0.0353595	−	0.0392707i
$581$	−10.3581	−	31.8789i	−0.429726	−	1.32256i
$582$	2.82528	+	3.13779i	0.117111	+	0.130065i
$583$	−2.39937	+	4.15584i	−0.0993719	+	0.172117i
$584$	21.0193	+	36.4065i	0.869786	+	1.50651i
$585$	−0.0227327	+	0.0699639i	−0.000939879	+	0.00289265i
$586$	9.62204	−	4.28401i	0.397483	−	0.176971i
$587$	33.8974	−	24.6279i	1.39910	−	1.01650i	0.404299	−	0.914627i	$-0.367515\pi$
$587$	33.8974	−	24.6279i	1.39910	−	1.01650i	0.994797	−	0.101876i	$-0.0324846\pi$
$588$	−5.13195			−0.211638
$589$	−8.03924	+	23.6916i	−0.331251	+	0.976195i
$590$	1.84564			0.0759837
$591$	15.2994	−	11.1156i	0.629332	−	0.457236i
$592$	−1.14640	+	0.510412i	−0.0471170	+	0.0209778i
$593$	−2.00666	+	6.17587i	−0.0824037	+	0.253613i	−0.983767	−	0.179452i	$-0.942568\pi$
$593$	−2.00666	+	6.17587i	−0.0824037	+	0.253613i	0.901363	+	0.433064i	$0.142568\pi$
$594$	0.173062	+	0.299752i	0.00710081	+	0.0122990i
$595$	2.40093	−	4.15854i	0.0984286	−	0.170483i
$596$	8.85535	+	9.83487i	0.362729	+	0.402852i
$597$	−2.23998	−	6.89395i	−0.0916763	−	0.282151i
$598$	−0.505559	+	0.561480i	−0.0206738	+	0.0229606i
$599$	37.4107	+	16.6563i	1.52856	+	0.680559i	0.987091	−	0.160161i	$-0.0512015\pi$
$599$	37.4107	+	16.6563i	1.52856	+	0.680559i	0.541470	+	0.840720i	$0.317868\pi$
$600$	−13.6599	+	2.90351i	−0.557664	+	0.118535i
$601$	3.20431	+	30.4870i	0.130707	+	1.24359i	0.841527	+	0.540216i	$0.181657\pi$
$601$	3.20431	+	30.4870i	0.130707	+	1.24359i	−0.710820	+	0.703374i	$0.751676\pi$
$602$	0.211934	−	2.01641i	0.00863777	−	0.0821829i
$603$	−10.0904	−	2.14477i	−0.410911	−	0.0873419i
$604$	−5.00238	−	3.63444i	−0.203544	−	0.147883i
$605$	−3.37830	−	2.45448i	−0.137348	−	0.0997888i
$606$	−13.2889	−	2.82464i	−0.539824	−	0.114743i
$607$	3.12170	−	29.7010i	0.126706	−	1.20553i	−0.727691	−	0.685906i	$-0.759406\pi$
$607$	3.12170	−	29.7010i	0.126706	−	1.20553i	0.854397	−	0.519621i	$-0.173927\pi$
$608$	−2.60156	−	24.7522i	−0.105507	−	1.00384i
$609$	−9.22220	+	1.96024i	−0.373702	+	0.0794329i
$610$	−3.70932	−	1.65150i	−0.150186	−	0.0668672i
$611$	−0.428834	+	0.476268i	−0.0173488	+	0.0192677i
$612$	−1.35312	−	4.16449i	−0.0546968	−	0.168339i
$613$	−5.73519	−	6.36958i	−0.231642	−	0.257265i	0.616106	−	0.787663i	$-0.288709\pi$
$613$	−5.73519	−	6.36958i	−0.231642	−	0.257265i	−0.847749	+	0.530398i	$0.822042\pi$
$614$	−2.58502	+	4.47738i	−0.104323	+	0.180692i
$615$	2.44898	+	4.24176i	0.0987524	+	0.171044i
$616$	1.14612	−	3.52738i	0.0461783	−	0.142122i
$617$	12.3208	−	5.48559i	0.496018	−	0.220841i	−0.143452	−	0.989657i	$-0.545820\pi$
$617$	12.3208	−	5.48559i	0.496018	−	0.220841i	0.639470	+	0.768816i	$0.279154\pi$
$618$	−8.30820	+	6.03626i	−0.334205	+	0.242814i
$619$	−0.715069			−0.0287410			−0.0143705	−	0.999897i	$-0.504574\pi$
$619$	−0.715069			−0.0287410			−0.0143705	+	0.999897i	$0.504574\pi$
$620$	2.46885	+	0.558352i	0.0991513	+	0.0224239i
$621$	−4.36800			−0.175282
$622$	3.19467	−	2.32106i	0.128094	−	0.0930661i
$623$	−30.4796	+	13.5704i	−1.22114	+	0.543686i
$624$	−0.0142118	+	0.0437393i	−0.000568926	+	0.00175097i
$625$	−11.4008	−	19.7467i	−0.456031	−	0.789869i
$626$	9.12721	−	15.8088i	0.364797	−	0.631847i
$627$	−1.15039	−	1.27763i	−0.0459420	−	0.0510238i
$628$	−5.65256	−	17.3968i	−0.225562	−	0.694207i
$629$	12.9369	−	14.3679i	0.515828	−	0.572886i
$630$	−1.07088	−	0.476786i	−0.0426649	−	0.0189956i
$631$	14.5542	−	3.09358i	0.579392	−	0.123153i	0.0911119	−	0.995841i	$-0.470958\pi$
$631$	14.5542	−	3.09358i	0.579392	−	0.123153i	0.488280	+	0.872687i	$0.337625\pi$
$632$	−1.51501	−	14.4143i	−0.0602638	−	0.573372i
$633$	−2.56446	+	24.3992i	−0.101928	+	0.969783i
$634$	22.0172	+	4.67989i	0.874413	+	0.185862i
$635$	−0.718195	−	0.521799i	−0.0285007	−	0.0207070i
$636$	−11.9897	−	8.71106i	−0.475424	−	0.345416i
$637$	−0.812286	−	0.172657i	−0.0321839	−	0.00684091i
$638$	0.101281	−	0.963627i	0.00400977	−	0.0381504i
$639$	−1.42016	−	13.5119i	−0.0561807	−	0.534523i
$640$	−2.29926	+	0.488723i	−0.0908863	+	0.0193185i
$641$	−5.01391	−	2.23234i	−0.198038	−	0.0881721i	0.305322	−	0.952249i	$-0.401236\pi$
$641$	−5.01391	−	2.23234i	−0.198038	−	0.0881721i	−0.503359	+	0.864077i	$0.667903\pi$
$642$	8.72337	−	9.68828i	0.344284	−	0.382366i
$643$	11.5179	+	35.4486i	0.454224	+	1.39796i	0.872044	+	0.489427i	$0.162794\pi$
$643$	11.5179	+	35.4486i	0.454224	+	1.39796i	−0.417821	+	0.908529i	$0.637206\pi$
$644$	11.6316	+	12.9182i	0.458349	+	0.509048i
$645$	−0.128014	+	0.221727i	−0.00504056	+	0.00873050i
$646$	−7.53187	−	13.0456i	−0.296337	−	0.513271i
$647$	−4.52856	+	13.9375i	−0.178036	+	0.547939i	−0.999759	−	0.0219481i	$-0.993013\pi$
$647$	−4.52856	+	13.9375i	−0.178036	+	0.547939i	0.821723	+	0.569887i	$0.193013\pi$
$648$	−2.62939	+	1.17068i	−0.103292	+	0.0459887i
$649$	−1.64140	+	1.19255i	−0.0644306	+	0.0468116i
$650$	−0.839260			−0.0329185
$651$	−12.3656	−	14.0971i	−0.484647	−	0.552509i
$652$	10.1518			0.397575
$653$	12.2873	−	8.92726i	0.480840	−	0.349351i	−0.320811	−	0.947143i	$-0.603955\pi$
$653$	12.2873	−	8.92726i	0.480840	−	0.349351i	0.801651	+	0.597793i	$0.203955\pi$
$654$	0.491376	−	0.218775i	0.0192143	−	0.00855477i
$655$	−0.108258	+	0.333185i	−0.00423001	+	0.0130186i
$656$	1.53103	+	2.65182i	0.0597766	+	0.103536i
$657$	−7.30286	+	12.6489i	−0.284912	+	0.493482i
$658$	−6.83332	−	7.58917i	−0.266390	−	0.295857i
$659$	−6.04866	−	18.6159i	−0.235622	−	0.725171i	−0.997038	−	0.0769075i	$-0.975495\pi$
$659$	−6.04866	−	18.6159i	−0.235622	−	0.725171i	0.761416	−	0.648264i	$-0.224505\pi$
$660$	−0.116389	+	0.129263i	−0.00453042	+	0.00503154i
$661$	26.2069	+	11.6681i	1.01933	+	0.453835i	0.847219	−	0.531243i	$-0.178275\pi$
$661$	26.2069	+	11.6681i	1.01933	+	0.453835i	0.172110	+	0.985078i	$0.444942\pi$
$662$	29.1571	−	6.19753i	1.13322	−	0.240874i
$663$	−0.0740648	−	0.704680i	−0.00287644	−	0.0273675i
$664$	−2.99427	+	28.4886i	−0.116200	+	1.10557i
$665$	5.69530	+	1.21057i	0.220854	+	0.0469440i
$666$	−3.81837	−	2.77421i	−0.147959	−	0.107498i
$667$	9.89246	+	7.18729i	0.383037	+	0.278293i
$668$	3.56139	+	0.756997i	0.137794	+	0.0292891i
$669$	−0.781560	+	7.43605i	−0.0302169	+	0.287494i
$670$	0.375302	+	3.57076i	0.0144992	+	0.137950i
$671$	4.36596	−	0.928012i	0.168546	−	0.0358255i
$672$	17.0419	+	7.58754i	0.657405	+	0.292696i
$673$	−17.7315	+	19.6929i	−0.683501	+	0.759105i	−0.980659	−	0.195724i	$-0.937294\pi$
$673$	−17.7315	+	19.6929i	−0.683501	+	0.759105i	0.297158	+	0.954828i	$0.403961\pi$
$674$	4.14289	+	12.7505i	0.159578	+	0.491131i
$675$	−3.24661	−	3.60572i	−0.124962	−	0.138784i
$676$	−7.65894	+	13.2657i	−0.294575	+	0.510218i
$677$	14.7737	+	25.5888i	0.567800	+	0.983459i	0.996783	+	0.0801464i	$0.0255388\pi$
$677$	14.7737	+	25.5888i	0.567800	+	0.983459i	−0.428983	+	0.903313i	$0.641128\pi$
$678$	0.753199	−	2.31811i	0.0289265	−	0.0890265i
$679$	14.3605	−	6.39371i	0.551105	−	0.245368i
$680$	−3.31991	+	2.41206i	−0.127313	+	0.0924982i
$681$	4.81872			0.184654
$682$	1.77055	−	0.760923i	0.0677978	−	0.0291373i
$683$	−12.7938			−0.489541			−0.244771	−	0.969581i	$-0.578713\pi$
$683$	−12.7938			−0.489541			−0.244771	+	0.969581i	$0.578713\pi$
$684$	4.29551	−	3.12087i	0.164243	−	0.119330i
$685$	−0.143761	+	0.0640067i	−0.00549284	+	0.00244557i
$686$	−2.50147	+	7.69873i	−0.0955065	+	0.293939i
$687$	−7.17363	−	12.4251i	−0.273691	−	0.474047i
$688$	−0.0800307	+	0.138617i	−0.00305114	+	0.00528473i
$689$	−1.60467	−	1.78217i	−0.0611330	−	0.0678951i
$690$	0.469796	+	1.44588i	0.0178848	+	0.0550438i
$691$	−7.03790	+	7.81638i	−0.267734	+	0.297349i	−0.861988	−	0.506929i	$-0.830781\pi$
$691$	−7.03790	+	7.81638i	−0.267734	+	0.297349i	0.594254	+	0.804278i	$0.297447\pi$
$692$	−12.8698	−	5.73001i	−0.489237	−	0.217822i
$693$	1.26045	−	0.267917i	0.0478805	−	0.0101773i
$694$	1.73788	+	16.5348i	0.0659690	+	0.627653i
$695$	−0.622050	+	5.91841i	−0.0235957	+	0.224498i
$696$	7.88122	+	1.67521i	0.298737	+	0.0634985i
$697$	−38.1665	−	27.7296i	−1.44566	−	1.05033i
$698$	5.50774	+	4.00161i	0.208471	+	0.151463i
$699$	28.0963	+	5.97204i	1.06270	+	0.225883i
$700$	−2.01836	+	19.2034i	−0.0762868	+	0.725820i
$701$	1.04962	+	9.98651i	0.0396438	+	0.377185i	0.996299	+	0.0859608i	$0.0273960\pi$
$701$	1.04962	+	9.98651i	0.0396438	+	0.377185i	−0.956655	+	0.291224i	$0.905937\pi$
$702$	−0.169193	+	0.0359631i	−0.00638578	+	0.00135734i
$703$	21.4167	+	9.53532i	0.807745	+	0.359631i
$704$	−1.40597	+	1.56149i	−0.0529895	+	0.0588508i
$705$	0.398498	+	1.22645i	0.0150083	+	0.0461908i
$706$	10.9857	+	12.2009i	0.413453	+	0.459186i
$707$	−25.2897	+	43.8031i	−0.951117	+	1.64738i
$708$	−3.13293	−	5.42640i	−0.117743	−	0.203937i
$709$	4.07493	−	12.5413i	0.153037	−	0.471000i	−0.844920	−	0.534893i	$-0.820352\pi$
$709$	4.07493	−	12.5413i	0.153037	−	0.471000i	0.997957	+	0.0638935i	$0.0203518\pi$
$710$	−4.31993	+	1.92336i	−0.162124	+	0.0721823i
$711$	4.07392	−	2.95988i	0.152784	−	0.111004i
$712$	28.5127			1.06856
$713$	−2.85580	+	24.1518i	−0.106951	+	0.904490i
$714$	11.2907			0.422543
$715$	−0.0227709	+	0.0165440i	−0.000851582	+	0.000618710i
$716$	20.0555	−	8.92927i	0.749508	−	0.333702i
$717$	7.11541	−	21.8990i	0.265730	−	0.817833i
$718$	10.9963	+	19.0461i	0.410377	+	0.710793i
$719$	0.00762333	−	0.0132040i	0.000284302	−	0.000492426i	−0.865883	−	0.500246i	$-0.833243\pi$
$719$	0.00762333	−	0.0132040i	0.000284302	−	0.000492426i	0.866168	+	0.499754i	$0.166576\pi$
$720$	0.0619216	+	0.0687709i	0.00230768	+	0.00256294i
$721$	11.8147	+	36.3618i	0.440001	+	1.35418i
$722$	0.720937	−	0.800682i	0.0268305	−	0.0297983i
$723$	−7.67971	−	3.41923i	−0.285612	−	0.127163i
$724$	7.81965	−	1.66212i	0.290615	−	0.0617721i
$725$	1.41977	+	13.5082i	0.0527288	+	0.501681i
$726$	1.02633	−	9.76485i	0.0380906	−	0.362408i
$727$	−2.58698	−	0.549880i	−0.0959459	−	0.0203939i	0.159689	−	0.987167i	$-0.448951\pi$
$727$	−2.58698	−	0.549880i	−0.0959459	−	0.0203939i	−0.255634	+	0.966774i	$0.582284\pi$
$728$	1.49951	+	1.08946i	0.0555757	+	0.0403781i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	4.97246	+	1.05693i	0.184039	+	0.0391187i
$731$	0.257770	−	2.45252i	0.00953398	−	0.0907097i
$732$	1.44090	+	13.7092i	0.0532572	+	0.506708i
$733$	−8.69308	+	1.84777i	−0.321086	+	0.0682490i	−0.365635	−	0.930758i	$-0.619148\pi$
$733$	−8.69308	+	1.84777i	−0.321086	+	0.0682490i	0.0445491	+	0.999007i	$0.485815\pi$
$734$	−20.6169	−	9.17922i	−0.760983	−	0.338811i
$735$	−1.11810	+	1.24178i	−0.0412418	+	0.0458037i
$736$	−7.47630	−	23.0097i	−0.275580	−	0.848148i
$737$	−2.64099	−	2.93312i	−0.0972822	−	0.108043i
$738$	−5.75831	+	9.97369i	−0.211966	+	0.367137i
$739$	−5.02245	−	8.69914i	−0.184754	−	0.320003i	0.758740	−	0.651394i	$-0.225815\pi$
$739$	−5.02245	−	8.69914i	−0.184754	−	0.320003i	−0.943494	+	0.331391i	$0.892482\pi$
$740$	0.732944	−	2.25577i	0.0269435	−	0.0829237i
$741$	0.784892	−	0.349456i	0.0288337	−	0.0128376i
$742$	30.9154	−	22.4614i	1.13494	−	0.824583i
$743$	−37.1172			−1.36170			−0.680849	−	0.732424i	$-0.738389\pi$
$743$	−37.1172			−1.36170			−0.680849	+	0.732424i	$0.738389\pi$
$744$	4.75389	+	15.3040i	0.174286	+	0.561070i
$745$	4.30907			0.157872
$746$	3.49327	−	2.53801i	0.127898	−	0.0929232i
$747$	−9.09203	+	4.04803i	−0.332660	+	0.148110i
$748$	0.517716	−	1.59337i	0.0189296	−	0.0582592i
$749$	−24.2679	−	42.0333i	−0.886731	−	1.53586i
$750$	−1.71450	+	2.96960i	−0.0626046	+	0.108434i
$751$	−10.2017	−	11.3302i	−0.372267	−	0.413444i	0.527680	−	0.849443i	$-0.323062\pi$
$751$	−10.2017	−	11.3302i	−0.372267	−	0.413444i	−0.899947	+	0.435999i	$0.856395\pi$
$752$	0.249129	+	0.766740i	0.00908480	+	0.0279601i
$753$	10.1714	−	11.2965i	0.370667	−	0.411667i
$754$	0.442356	+	0.196950i	0.0161096	+	0.00717248i
$755$	−1.96930	+	0.418587i	−0.0716701	+	0.0152339i
$756$	0.415987	+	3.95785i	0.0151293	+	0.143946i
$757$	−3.34410	+	31.8170i	−0.121544	+	1.15641i	0.748396	+	0.663252i	$0.230824\pi$
$757$	−3.34410	+	31.8170i	−0.121544	+	1.15641i	−0.869940	+	0.493158i	$0.835843\pi$
$758$	18.1974	+	3.86797i	0.660958	+	0.140491i
$759$	−1.35206	−	0.982326i	−0.0490765	−	0.0356562i
$760$	−4.02558	−	2.92476i	−0.146023	−	0.106092i
$761$	2.76427	+	0.587563i	0.100205	+	0.0212991i	0.257741	−	0.966214i	$-0.417022\pi$
$761$	2.76427	+	0.587563i	0.100205	+	0.0212991i	−0.157536	+	0.987513i	$0.550355\pi$
$762$	0.218187	−	2.07591i	0.00790409	−	0.0752024i
$763$	−0.209319	−	1.99153i	−0.00757784	−	0.0720983i
$764$	−0.490549	+	0.104269i	−0.0177475	+	0.00377234i
$765$	−1.30249	−	0.579905i	−0.0470915	−	0.0209665i
$766$	20.2888	−	22.5329i	0.733063	−	0.814148i
$767$	−0.313318	−	0.964295i	−0.0113133	−	0.0348187i
$768$	−11.0477	−	12.2697i	−0.398651	−	0.442746i
$769$	−10.5973	+	18.3550i	−0.382148	+	0.661899i	−0.991369	−	0.131101i	$-0.958149\pi$
$769$	−10.5973	+	18.3550i	−0.382148	+	0.661899i	0.609221	+	0.793000i	$0.291482\pi$
$770$	−0.224251	−	0.388414i	−0.00808145	−	0.0139975i
$771$	−0.296954	+	0.913932i	−0.0106946	+	0.0329144i
$772$	−8.68764	+	3.86798i	−0.312675	+	0.139212i
$773$	10.1303	−	7.36010i	0.364362	−	0.264724i	−0.390507	−	0.920600i	$-0.627700\pi$
$773$	10.1303	−	7.36010i	0.364362	−	0.264724i	0.754869	+	0.655875i	$0.227700\pi$
$774$	−0.602003			−0.0216386
$775$	−22.0595	+	15.5939i	−0.792402	+	0.560148i
$776$	−13.4338			−0.482245
$777$	−14.2157	+	10.3283i	−0.509984	+	0.370525i
$778$	4.63064	−	2.06170i	0.166017	−	0.0739154i
$779$	17.6770	−	54.4043i	0.633346	−	1.94924i
$780$	−0.0434626	−	0.0752795i	−0.00155621	−	0.00269544i
$781$	2.59912	−	4.50181i	0.0930039	−	0.161088i
$782$	−9.79823	−	10.8820i	−0.350384	−	0.389141i
$783$	0.865059	+	2.66238i	0.0309147	+	0.0951457i
$784$	−0.699003	+	0.776322i	−0.0249644	+	0.0277258i
$785$	−5.44103	−	2.42250i	−0.194199	−	0.0864628i
$786$	−0.805739	+	0.171265i	−0.0287398	+	0.00610882i
$787$	−5.55143	−	52.8183i	−0.197887	−	1.88277i	−0.419673	−	0.907675i	$-0.637855\pi$
$787$	−5.55143	−	52.8183i	−0.197887	−	1.88277i	0.221786	−	0.975095i	$-0.428811\pi$
$788$	−2.33576	+	22.2233i	−0.0832081	+	0.791672i
$789$	27.3049	+	5.80385i	0.972082	+	0.206622i
$790$	−1.41794	−	1.03019i	−0.0504479	−	0.0366525i
$791$	−7.34133	−	5.33379i	−0.261028	−	0.189648i
$792$	−1.07717	−	0.228959i	−0.0382756	−	0.00813572i
$793$	−0.233161	+	2.21838i	−0.00827980	+	0.0787770i
$794$	−0.315934	−	3.00591i	−0.0112121	−	0.106676i
$795$	−4.72003	+	1.00327i	−0.167402	+	0.0355824i
$796$	7.82475	+	3.48380i	0.277341	+	0.123480i
$797$	−16.1361	+	17.9210i	−0.571570	+	0.634793i	−0.957740	−	0.287635i	$-0.907131\pi$
$797$	−16.1361	+	17.9210i	−0.571570	+	0.634793i	0.386170	+	0.922428i	$0.373798\pi$
$798$	4.23063	+	13.0205i	0.149763	+	0.460922i
$799$	−8.31122	−	9.23054i	−0.294030	−	0.326553i
$800$	13.4372	−	23.2740i	0.475078	−	0.822859i
$801$	4.95316	+	8.57913i	0.175011	+	0.303129i
$802$	−8.71215	+	26.8133i	−0.307637	+	0.946809i
$803$	−5.10514	+	2.27295i	−0.180156	+	0.0802108i
$804$	9.86139	−	7.16472i	0.347785	−	0.252680i
$805$	5.66000			0.199489
$806$	0.0882303	+	0.959022i	0.00310778	+	0.0337801i
$807$	−14.7920			−0.520705
$808$	34.9696	−	25.4069i	1.23023	−	0.893811i
$809$	−38.3065	+	17.0552i	−1.34678	+	0.599627i	−0.948250	−	0.317526i	$-0.897148\pi$
$809$	−38.3065	+	17.0552i	−1.34678	+	0.599627i	−0.398535	+	0.917153i	$0.630481\pi$
$810$	−0.107554	+	0.331017i	−0.00377906	+	0.0116307i
$811$	−19.5238	−	33.8162i	−0.685573	−	1.18745i	−0.973256	−	0.229722i	$-0.926218\pi$
$811$	−19.5238	−	33.8162i	−0.685573	−	1.18745i	0.287683	−	0.957726i	$-0.407115\pi$
$812$	5.57030	−	9.64804i	0.195479	−	0.338580i
$813$	14.2900	+	15.8707i	0.501173	+	0.556609i
$814$	−0.558029	−	1.71744i	−0.0195589	−	0.0601961i
$815$	2.21178	−	2.45643i	0.0774752	−	0.0860450i
$816$	−0.814276	−	0.362539i	−0.0285054	−	0.0126914i
$817$	2.92486	−	0.621698i	0.102328	−	0.0217505i
$818$	−0.351254	−	3.34196i	−0.0122813	−	0.116849i
$819$	−0.0673135	+	0.640445i	−0.00235212	+	0.0223790i
$820$	−5.66106	−	1.20330i	−0.197693	−	0.0420209i
$821$	−29.3643	−	21.3344i	−1.02482	−	0.744577i	−0.0575565	−	0.998342i	$-0.518331\pi$
$821$	−29.3643	−	21.3344i	−1.02482	−	0.744577i	−0.967266	+	0.253765i	$0.918331\pi$
$822$	−0.299351	−	0.217491i	−0.0104410	−	0.00758587i
$823$	−22.4445	−	4.77072i	−0.782365	−	0.166297i	−0.200621	−	0.979669i	$-0.564296\pi$
$823$	−22.4445	−	4.77072i	−0.782365	−	0.166297i	−0.581744	+	0.813372i	$0.697629\pi$
$824$	3.41533	−	32.4947i	0.118979	−	1.13200i
$825$	−0.194047	−	1.84624i	−0.00675585	−	0.0642777i
$826$	15.8034	−	3.35912i	0.549871	−	0.116879i
$827$	2.21642	+	0.986814i	0.0770725	+	0.0343149i	0.444911	−	0.895575i	$-0.353235\pi$
$827$	2.21642	+	0.986814i	0.0770725	+	0.0343149i	−0.367838	+	0.929890i	$0.619902\pi$
$828$	3.45360	−	3.83561i	0.120021	−	0.133297i
$829$	−0.0754426	−	0.232188i	−0.00262023	−	0.00806424i	0.949738	−	0.313046i	$-0.101350\pi$
$829$	−0.0754426	−	0.232188i	−0.00262023	−	0.00806424i	−0.952358	+	0.304982i	$0.901350\pi$
$830$	2.31785	+	2.57423i	0.0804538	+	0.0893530i
$831$	6.41107	−	11.1043i	0.222397	−	0.385204i
$832$	−0.525027	−	0.909374i	−0.0182021	−	0.0315269i
$833$	4.97351	−	15.3069i	0.172322	−	0.530352i
$834$	−12.7829	+	5.69134i	−0.442637	+	0.197075i
$835$	0.959094	−	0.696823i	0.0331908	−	0.0241145i
$836$	2.03147			0.0702600
$837$	−3.77894	+	4.08896i	−0.130619	+	0.141335i
$838$	−7.78627			−0.268972
$839$	4.83191	−	3.51059i	0.166816	−	0.121199i	−0.501245	−	0.865305i	$-0.667124\pi$
$839$	4.83191	−	3.51059i	0.166816	−	0.121199i	0.668061	+	0.744106i	$0.267124\pi$
$840$	3.40713	−	1.51695i	0.117557	−	0.0523399i
$841$	−6.53985	+	20.1276i	−0.225512	+	0.694055i
$842$	−6.17062	−	10.6878i	−0.212654	−	0.368327i
$843$	9.48483	−	16.4282i	0.326675	−	0.565817i
$844$	−19.3977	−	21.5434i	−0.667698	−	0.741554i
$845$	1.54124	+	4.74344i	0.0530202	+	0.163179i
$846$	−2.02892	+	2.25334i	−0.0697557	+	0.0774716i
$847$	−33.3942	−	14.8681i	−1.14744	−	0.510872i
$848$	−2.95082	+	0.627216i	−0.101332	+	0.0215387i
$849$	1.48622	+	14.1404i	0.0510070	+	0.485299i
$850$	1.70023	−	16.1766i	0.0583173	−	0.554852i
$851$	22.2910	+	4.73811i	0.764127	+	0.162420i
$852$	12.9879	+	9.43626i	0.444958	+	0.323281i
$853$	17.4768	+	12.6976i	0.598394	+	0.434759i	0.845308	−	0.534279i	$-0.179417\pi$
$853$	17.4768	+	12.6976i	0.598394	+	0.434759i	−0.246915	+	0.969037i	$0.579417\pi$
$854$	−34.7671	−	7.38998i	−1.18971	−	0.252880i
$855$	0.180709	−	1.71933i	0.00618012	−	0.0587999i
$856$	4.33567	+	41.2512i	0.148190	+	1.40994i
$857$	−24.4262	+	5.19195i	−0.834383	+	0.177354i	−0.605244	−	0.796040i	$-0.706924\pi$
$857$	−24.4262	+	5.19195i	−0.834383	+	0.177354i	−0.229139	+	0.973394i	$0.573591\pi$
$858$	−0.0604592	−	0.0269182i	−0.00206404	−	0.000918971i
$859$	−23.5080	+	26.1083i	−0.802082	+	0.890803i	−0.995921	−	0.0902307i	$-0.971240\pi$
$859$	−23.5080	+	26.1083i	−0.802082	+	0.890803i	0.193838	+	0.981033i	$0.437906\pi$
$860$	−0.0934865	−	0.287722i	−0.00318786	−	0.00981124i
$861$	28.6897	+	31.8631i	0.977742	+	1.08589i
$862$	−0.822902	+	1.42531i	−0.0280281	+	0.0485462i
$863$	−9.92611	−	17.1925i	−0.337889	−	0.585240i	0.646147	−	0.763213i	$-0.276379\pi$
$863$	−9.92611	−	17.1925i	−0.337889	−	0.585240i	−0.984035	+	0.177973i	$0.943046\pi$
$864$	1.71160	−	5.26778i	0.0582300	−	0.179213i
$865$	−4.19045	+	1.86571i	−0.142479	+	0.0634360i
$866$	−13.9184	+	10.1123i	−0.472967	+	0.343631i
$867$	−3.26738			−0.110966
$868$	22.1559	+	0.287549i	0.752020	+	0.00976005i
$869$	1.92668			0.0653580
$870$	0.788252	−	0.572699i	0.0267242	−	0.0194163i
$871$	1.80191	−	0.802262i	0.0610554	−	0.0271836i
$872$	−0.528828	+	1.62757i	−0.0179084	+	0.0551163i
$873$	−2.33369	−	4.04207i	−0.0789834	−	0.136803i
$874$	8.87787	−	15.3769i	0.300298	−	0.520132i
$875$	8.54216	+	9.48703i	0.288778	+	0.320720i
$876$	−5.33315	−	16.4137i	−0.180190	−	0.554569i
$877$	6.33998	−	7.04126i	0.214086	−	0.237766i	−0.626531	−	0.779396i	$-0.715526\pi$
$877$	6.33998	−	7.04126i	0.214086	−	0.237766i	0.840617	+	0.541630i	$0.182193\pi$
$878$	−18.3259	−	8.15923i	−0.618470	−	0.275361i
$879$	−11.3884	+	2.42069i	−0.384123	+	0.0816478i
$880$	0.00370101	+	0.0352128i	0.000124761	+	0.00118702i
$881$	1.30134	−	12.3814i	0.0438433	−	0.417141i	−0.950484	−	0.310775i	$-0.899412\pi$
$881$	1.30134	−	12.3814i	0.0438433	−	0.417141i	0.994327	−	0.106367i	$-0.0339218\pi$
$882$	−3.84313	−	0.816883i	−0.129405	−	0.0275059i
$883$	15.2049	+	11.0470i	0.511686	+	0.371761i	0.813463	−	0.581617i	$-0.197580\pi$
$883$	15.2049	+	11.0470i	0.511686	+	0.371761i	−0.301777	+	0.953379i	$0.597580\pi$
$884$	0.677351	+	0.492124i	0.0227818	+	0.0165519i
$885$	−1.99560	−	0.424178i	−0.0670814	−	0.0142586i
$886$	0.588287	−	5.59718i	0.0197639	−	0.188041i
$887$	3.11200	+	29.6087i	0.104491	+	0.994164i	0.913630	+	0.406547i	$0.133267\pi$
$887$	3.11200	+	29.6087i	0.104491	+	0.994164i	−0.809139	+	0.587617i	$0.800066\pi$
$888$	14.6884	−	3.12211i	0.492909	−	0.104771i
$889$	−7.09928	−	3.16080i	−0.238102	−	0.106010i
$890$	2.30710	−	2.56230i	0.0773343	−	0.0858885i
$891$	−0.118232	−	0.363882i	−0.00396093	−	0.0121905i
$892$	−5.91176	−	6.56568i	−0.197940	−	0.219835i
$893$	7.53054	−	13.0433i	0.252000	−	0.436476i
$894$	5.06598	+	8.77454i	0.169432	+	0.293465i
$895$	2.20889	−	6.79825i	0.0738349	−	0.227241i
$896$	−18.7981	+	8.36946i	−0.628001	+	0.279604i
$897$	0.675681	−	0.490911i	0.0225603	−	0.0163910i
$898$	4.91870			0.164139
$899$	15.2865	−	3.04246i	0.509834	−	0.101472i
$900$	5.73320			0.191107
$901$	37.6017	−	27.3193i	1.25270	−	0.910137i
$902$	−4.02541	+	1.79223i	−0.134031	+	0.0596746i
$903$	−0.692581	+	2.13154i	−0.0230477	+	0.0709334i
$904$	3.87745	+	6.71594i	0.128962	+	0.223369i
$905$	1.30149	−	2.25425i	0.0432630	−	0.0749338i
$906$	−3.16759	−	3.51796i	−0.105236	−	0.116876i
$907$	11.9652	+	36.8252i	0.397299	+	1.22276i	0.927157	+	0.374674i	$0.122245\pi$
$907$	11.9652	+	36.8252i	0.397299	+	1.22276i	−0.529858	+	0.848087i	$0.677755\pi$
$908$	−3.80996	+	4.23139i	−0.126438	+	0.140424i
$909$	13.7195	+	6.10830i	0.455046	+	0.202600i
$910$	0.219238	−	0.0466005i	0.00726767	−	0.00154479i
$911$	1.37696	+	13.1009i	0.0456206	+	0.434051i	0.993364	+	0.115016i	$0.0366920\pi$
$911$	1.37696	+	13.1009i	0.0456206	+	0.434051i	−0.947743	+	0.319035i	$0.896641\pi$
$912$	0.112974	−	1.07488i	0.00374094	−	0.0355927i
$913$	−3.72468	−	0.791706i	−0.123269	−	0.0262016i
$914$	−11.7005	−	8.50094i	−0.387020	−	0.281186i
$915$	3.63116	+	2.63819i	0.120042	+	0.0872159i
$916$	16.5826	+	3.52473i	0.547903	+	0.116460i
$917$	−0.320563	+	3.04996i	−0.0105859	+	0.100718i
$918$	−0.350420	−	3.33402i	−0.0115656	−	0.110039i
$919$	−4.84552	+	1.02995i	−0.159839	+	0.0339748i	−0.287136	−	0.957890i	$-0.592703\pi$
$919$	−4.84552	+	1.02995i	−0.159839	+	0.0339748i	0.127297	+	0.991865i	$0.459370\pi$
$920$	−4.41881	−	1.96738i	−0.145684	−	0.0648626i
$921$	3.82408	−	4.24707i	0.126008	−	0.139946i
$922$	−9.92483	−	30.5455i	−0.326857	−	1.00596i
$923$	1.73826	+	1.93053i	0.0572155	+	0.0635443i
$924$	−0.761323	+	1.31865i	−0.0250457	+	0.0433804i
$925$	12.6570	+	21.9226i	0.416160	+	0.720811i
$926$	−3.03362	+	9.33651i	−0.0996908	+	0.306817i
$927$	10.3706	−	4.61727i	0.340614	−	0.151651i
$928$	−12.5442	+	9.11388i	−0.411783	+	0.299178i
$929$	54.0755			1.77416			0.887080	−	0.461616i	$-0.152730\pi$
$929$	54.0755			1.77416			0.887080	+	0.461616i	$0.152730\pi$
$930$	1.75995	+	0.811111i	0.0577112	+	0.0265974i
$931$	19.5156			0.639599
$932$	−27.4587	+	19.9499i	−0.899440	+	0.653481i
$933$	−3.98769	+	1.77543i	−0.130551	+	0.0581251i
$934$	−2.35357	+	7.24354i	−0.0770111	+	0.237016i
$935$	−0.272752	−	0.472420i	−0.00891993	−	0.0154498i
$936$	0.275167	−	0.476603i	0.00899412	−	0.0155783i
$937$	−11.9375	−	13.2579i	−0.389981	−	0.433118i	0.515901	−	0.856648i	$-0.327457\pi$
$937$	−11.9375	−	13.2579i	−0.389981	−	0.433118i	−0.905882	+	0.423531i	$0.860791\pi$
$938$	9.71244	+	29.8918i	0.317122	+	0.976002i
$939$	−13.5021	+	14.9956i	−0.440625	+	0.489364i
$940$	−1.39204	−	0.619777i	−0.0454034	−	0.0202149i
$941$	−39.6604	+	8.43009i	−1.29289	+	0.274813i	−0.802481	−	0.596678i	$-0.796487\pi$
$941$	−39.6604	+	8.43009i	−1.29289	+	0.274813i	−0.490412	+	0.871491i	$0.663154\pi$
$942$	−1.46385	−	13.9276i	−0.0476947	−	0.453785i
$943$	5.81254	−	55.3026i	0.189282	−	1.80090i
$944$	−1.24759	−	0.265183i	−0.0406056	−	0.00863099i
$945$	1.04831	+	0.761644i	0.0341016	+	0.0247763i
$946$	−0.186342	−	0.135385i	−0.00605850	−	0.00440176i
$947$	49.2338	+	10.4650i	1.59988	+	0.340066i	0.919592	−	0.392875i	$-0.128520\pi$
$947$	49.2338	+	10.4650i	1.59988	+	0.340066i	0.680292	+	0.732941i	$0.261853\pi$
$948$	−0.621968	+	5.91763i	−0.0202006	+	0.192196i
$949$	−0.291916	−	2.77740i	−0.00947601	−	0.0901582i
$950$	19.2921	−	4.10066i	0.625918	−	0.133043i
$951$	−22.7306	−	10.1203i	−0.737089	−	0.328173i
$952$	−24.0370	+	26.6958i	−0.779043	+	0.865215i
$953$	−4.38858	−	13.5067i	−0.142160	−	0.437524i	0.854475	−	0.519493i	$-0.173879\pi$
$953$	−4.38858	−	13.5067i	−0.142160	−	0.437524i	−0.996635	+	0.0819689i	$0.973879\pi$
$954$	−7.59210	−	8.43188i	−0.245803	−	0.272992i
$955$	−0.0816463	+	0.141416i	−0.00264201	+	0.00457610i
$956$	13.6040	+	23.5628i	0.439984	+	0.762075i
$957$	−0.330979	+	1.01865i	−0.0106990	+	0.0329282i
$958$	2.10408	−	0.936797i	0.0679798	−	0.0302665i
$959$	−1.11447	+	0.809712i	−0.0359882	+	0.0261470i
$960$	−2.11289			−0.0681934
$961$	20.1382	+	23.5681i	0.649619	+	0.760260i
$962$	0.902446			0.0290960
$963$	−11.6588	+	8.47061i	−0.375700	+	0.272962i
$964$	9.07452	−	4.04023i	0.292270	−	0.130127i
$965$	−0.956846	+	2.94487i	−0.0308020	+	0.0947987i
$966$	6.65421	+	11.5254i	0.214096	+	0.370825i
$967$	−8.30158	+	14.3788i	−0.266961	+	0.462390i	−0.968075	−	0.250659i	$-0.919353\pi$
$967$	−8.30158	+	14.3788i	−0.266961	+	0.462390i	0.701115	+	0.713049i	$0.252686\pi$
$968$	20.9031	+	23.2152i	0.671851	+	0.746166i
$969$	5.14562	+	15.8366i	0.165301	+	0.508745i
$970$	−1.08700	+	1.20723i	−0.0349013	+	0.0387618i
$971$	16.0501	+	7.14596i	0.515072	+	0.229325i	0.647776	−	0.761831i	$-0.275699\pi$
$971$	16.0501	+	7.14596i	0.515072	+	0.229325i	−0.132704	+	0.991156i	$0.542366\pi$
$972$	1.15580	−	0.245673i	0.0370723	−	0.00787996i
$973$	5.44534	+	51.8089i	0.174570	+	1.66092i
$974$	−2.44527	+	23.2652i	−0.0783516	+	0.745465i
$975$	0.907453	+	0.192885i	0.0290617	+	0.00617726i
$976$	2.27009	+	1.64932i	0.0726638	+	0.0527934i
$977$	−27.2126	−	19.7711i	−0.870610	−	0.632535i	0.0601408	−	0.998190i	$-0.480845\pi$
$977$	−27.2126	−	19.7711i	−0.870610	−	0.632535i	−0.930750	+	0.365655i	$0.880845\pi$
$978$	7.60231	+	1.61592i	0.243095	+	0.0516715i
$979$	−0.396188	+	3.76948i	−0.0126622	+	0.120473i
$980$	−0.206387	−	1.96365i	−0.00659281	−	0.0627264i
$981$	−0.581582	+	0.123619i	−0.0185685	+	0.00394685i
$982$	8.57514	+	3.81790i	0.273644	+	0.121834i
$983$	23.3853	−	25.9720i	0.745874	−	0.828377i	−0.244082	−	0.969755i	$-0.578487\pi$
$983$	23.3853	−	25.9720i	0.745874	−	0.828377i	0.989956	+	0.141378i	$0.0451533\pi$
$984$	−11.3229	−	34.8482i	−0.360960	−	1.11092i
$985$	4.86848	+	5.40700i	0.155123	+	0.172281i
$986$	−4.69232	+	8.12733i	−0.149434	+	0.258827i
$987$	5.64435	+	9.77629i	0.179662	+	0.311183i
$988$	−0.313719	+	0.965527i	−0.00998072	+	0.0307175i
$989$	2.65543	−	1.18227i	0.0844377	−	0.0375941i
$990$	−0.107735	+	0.0782738i	−0.00342403	+	0.00248771i
$991$	−22.5471			−0.716231			−0.358115	−	0.933677i	$-0.616581\pi$
$991$	−22.5471			−0.716231			−0.358115	+	0.933677i	$0.616581\pi$
$992$	−28.0078	−	12.9080i	−0.889248	−	0.409828i
$993$	−32.9505			−1.04565
$994$	−33.4891	+	24.3313i	−1.06221	+	0.771742i
$995$	2.54776	−	1.13434i	0.0807695	−	0.0359609i
$996$	3.63405	−	11.1845i	0.115149	−	0.354394i
$997$	3.29515	+	5.70736i	0.104358	+	0.180754i	0.913476	−	0.406893i	$-0.133388\pi$
$997$	3.29515	+	5.70736i	0.104358	+	0.180754i	−0.809117	+	0.587647i	$0.800054\pi$
$998$	−6.83743	+	11.8428i	−0.216435	+	0.374876i
$999$	3.49103	+	3.87719i	0.110451	+	0.122669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.49.2	yes	24
3.2	odd	2		279.2.y.d.235.2		24
31.9	even	15		2883.2.a.t.1.7		12
31.19	even	15	inner	93.2.m.b.19.2	✓	24
31.22	odd	30		2883.2.a.s.1.7		12
93.50	odd	30		279.2.y.d.19.2		24
93.53	even	30		8649.2.a.bl.1.6		12
93.71	odd	30		8649.2.a.bk.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.19.2	✓	24	31.19	even	15	inner
93.2.m.b.49.2	yes	24	1.1	even	1	trivial
279.2.y.d.19.2		24	93.50	odd	30
279.2.y.d.235.2		24	3.2	odd	2
2883.2.a.s.1.7		12	31.22	odd	30
2883.2.a.t.1.7		12	31.9	even	15
8649.2.a.bk.1.6		12	93.71	odd	30
8649.2.a.bl.1.6		12	93.53	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.731871 + 0.531736i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.365141 + 1.12379i) q^{4} +(0.192370 + 0.333194i) q^{5} +(-0.452321 + 0.783444i) q^{6} +(2.25360 + 2.50288i) q^{7} +(-0.889422 - 2.73736i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.731871 + 0.531736i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.365141 + 1.12379i) q^{4} +(0.192370 + 0.333194i) q^{5} +(-0.452321 + 0.783444i) q^{6} +(2.25360 + 2.50288i) q^{7} +(-0.889422 - 2.73736i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.317961 - 0.141565i) q^{10} +(0.374247 - 0.0795487i) q^{11} +(0.123513 + 1.17515i) q^{12} +(-0.0199864 + 0.190158i) q^{13} +(-2.98022 - 0.633465i) q^{14} +(0.311261 + 0.226144i) q^{15} +(0.194591 + 0.141379i) q^{16} +(-3.62477 - 0.770470i) q^{17} +(-0.0945609 + 0.899687i) q^{18} +(-0.469692 - 4.46882i) q^{19} +(-0.444682 + 0.0945201i) q^{20} +(3.07678 + 1.36987i) q^{21} +(-0.231602 + 0.257220i) q^{22} +(-1.34979 - 4.15422i) q^{23} +(-1.92591 - 2.13894i) q^{24} +(2.42599 - 4.20193i) q^{25} +(-0.0864864 - 0.149799i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-3.63559 + 1.61867i) q^{28} +(-2.26475 + 1.64544i) q^{29} -0.348052 q^{30} +(-5.05659 - 2.33043i) q^{31} +5.53887 q^{32} +(0.309536 - 0.224891i) q^{33} +(3.06255 - 1.36354i) q^{34} +(-0.400420 + 1.23237i) q^{35} +(0.590811 + 1.02331i) q^{36} +(-2.60863 + 4.51829i) q^{37} +(2.71999 + 3.02085i) q^{38} +(0.0590858 + 0.181847i) q^{39} +(0.740975 - 0.822936i) q^{40} +(11.6300 + 5.17799i) q^{41} +(-2.98022 + 0.633465i) q^{42} +(0.0695595 + 0.661814i) q^{43} +(-0.0472571 + 0.449621i) q^{44} +(0.376332 + 0.0799918i) q^{45} +(3.19682 + 2.32262i) q^{46} +(2.71166 + 1.97013i) q^{47} +(0.235271 + 0.0500085i) q^{48} +(-0.453982 + 4.31935i) q^{49} +(0.458807 + 4.36526i) q^{50} +(-3.62477 + 0.770470i) q^{51} +(-0.206400 - 0.0918952i) q^{52} +(-8.39237 + 9.32067i) q^{53} +(0.279550 + 0.860366i) q^{54} +(0.0984990 + 0.109394i) q^{55} +(4.84688 - 8.39504i) q^{56} +(-2.24672 - 3.89143i) q^{57} +(0.782570 - 2.40850i) q^{58} +(-4.84432 + 2.15683i) q^{59} +(-0.367792 + 0.267217i) q^{60} +11.6660 q^{61} +(4.93995 - 0.983193i) q^{62} +3.36796 q^{63} +(-4.44292 + 3.22797i) q^{64} +(-0.0672044 + 0.0299213i) q^{65} +(-0.106958 + 0.329183i) q^{66} +(-5.15789 - 8.93373i) q^{67} +(2.18940 - 3.79215i) q^{68} +(-2.92276 - 3.24606i) q^{69} +(-0.362237 - 1.11485i) q^{70} +(9.09104 - 10.0966i) q^{71} +(-2.62939 - 1.17068i) q^{72} +(-14.2866 + 3.03670i) q^{73} +(-0.493350 - 4.69391i) q^{74} +(0.507170 - 4.82540i) q^{75} +(5.19352 + 1.10392i) q^{76} +(1.04251 + 0.757425i) q^{77} +(-0.139938 - 0.101671i) q^{78} +(4.92560 + 1.04697i) q^{79} +(-0.00967311 + 0.0920335i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-11.2650 + 2.39444i) q^{82} +(-9.09203 - 4.04803i) q^{83} +(-2.66291 + 2.95746i) q^{84} +(-0.440581 - 1.35597i) q^{85} +(-0.402819 - 0.447375i) q^{86} +(-1.39970 + 2.42434i) q^{87} +(-0.550617 - 0.953697i) q^{88} +(-3.06122 + 9.42147i) q^{89} +(-0.317961 + 0.141565i) q^{90} +(-0.520985 + 0.378518i) q^{91} +5.16133 q^{92} +(-5.56730 - 0.0722548i) q^{93} -3.03217 q^{94} +(1.39863 - 1.01617i) q^{95} +(5.06001 - 2.25286i) q^{96} +(1.44230 - 4.43894i) q^{97} +(-1.96449 - 3.40260i) q^{98} +(0.191304 - 0.331348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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