LMFDB - Embedded newform 294.2.m.b.205.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			205.1
Character	$\chi$	$=$	294.205
Dual form			294.2.m.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(-1.49873 - 3.81871i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-0.683647 + 2.55590i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})$	\(q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(-1.49873 - 3.81871i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-0.683647 + 2.55590i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +(-1.49873 + 3.81871i) q^{10} +(-4.24363 + 1.30899i) q^{11} +(0.0747301 - 0.997204i) q^{12} +(0.268726 - 1.17736i) q^{13} +(2.23960 - 1.40861i) q^{14} +(0.912843 + 3.99943i) q^{15} +(-0.988831 + 0.149042i) q^{16} +(2.98698 + 2.03649i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.10108 + 3.63917i) q^{19} +(3.69603 - 1.77991i) q^{20} +(1.05695 - 2.42546i) q^{21} +(4.00114 + 1.92685i) q^{22} +(-6.13408 + 4.18215i) q^{23} +(-0.733052 + 0.680173i) q^{24} +(-8.67106 + 8.04556i) q^{25} +(-0.997801 + 0.680290i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-2.59984 - 0.490733i) q^{28} +(-0.564030 + 0.271623i) q^{29} +(2.05114 - 3.55268i) q^{30} +(-3.64081 - 6.30607i) q^{31} +(0.826239 + 0.563320i) q^{32} +(4.39133 - 0.661887i) q^{33} +(-0.804447 - 3.52451i) q^{34} +(10.7848 - 1.21996i) q^{35} +(-0.222521 + 0.974928i) q^{36} +(0.162291 - 2.16562i) q^{37} +(4.01547 - 1.23861i) q^{38} +(-0.441202 + 1.12416i) q^{39} +(-3.92003 - 1.20917i) q^{40} +(-3.15756 + 3.95945i) q^{41} +(-2.42453 + 1.05908i) q^{42} +(1.92190 + 2.40998i) q^{43} +(-1.62245 - 4.13395i) q^{44} +(-0.306564 - 4.09081i) q^{45} +(7.34119 + 1.10651i) q^{46} +(-0.154351 - 0.143217i) q^{47} +1.00000 q^{48} +(-6.06525 - 3.49467i) q^{49} +11.8287 q^{50} +(-2.65009 - 2.45893i) q^{51} +(1.19415 + 0.179990i) q^{52} +(-0.299625 - 3.99822i) q^{53} +(0.365341 + 0.930874i) q^{54} +(11.3587 + 14.2434i) q^{55} +(1.57204 + 2.12807i) q^{56} +(2.62000 - 3.28538i) q^{57} +(0.598214 + 0.184524i) q^{58} +(5.59962 - 14.2676i) q^{59} +(-3.92003 + 1.20917i) q^{60} +(0.253707 - 3.38549i) q^{61} +(-1.62031 + 7.09906i) q^{62} +(-1.40664 + 2.24084i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-4.89876 + 0.738369i) q^{65} +(-3.66927 - 2.50167i) q^{66} +(-0.294061 - 0.509329i) q^{67} +(-1.80757 + 3.13081i) q^{68} +(6.68889 - 3.22120i) q^{69} +(-8.73563 - 6.44125i) q^{70} +(-12.1420 - 5.84729i) q^{71} +(0.826239 - 0.563320i) q^{72} +(5.40695 - 5.01692i) q^{73} +(-1.59196 + 1.47713i) q^{74} +(9.77334 - 6.66335i) q^{75} +(-3.78601 - 1.82325i) q^{76} +(-0.444495 - 11.7412i) q^{77} +(1.08805 - 0.523977i) q^{78} +(1.23248 - 2.13472i) q^{79} +(2.05114 + 3.55268i) q^{80} +(0.826239 + 0.563320i) q^{81} +(5.00777 - 0.754799i) q^{82} +(1.48571 + 6.50930i) q^{83} +(2.49766 + 0.872738i) q^{84} +(3.30007 - 14.4585i) q^{85} +(0.230354 - 3.07387i) q^{86} +(0.598214 - 0.184524i) q^{87} +(-1.62245 + 4.13395i) q^{88} +(-11.9694 - 3.69208i) q^{89} +(-2.55773 + 3.20729i) q^{90} +(2.82551 + 1.49174i) q^{91} +(-4.62885 - 5.80440i) q^{92} +(2.66028 + 6.77827i) q^{93} +(0.0157351 + 0.209971i) q^{94} +(17.0459 + 2.56925i) q^{95} +(-0.733052 - 0.680173i) q^{96} -9.91836 q^{97} +(2.06917 + 6.68719i) q^{98} -4.44093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−0.733052	−	0.680173i	−0.518346	−	0.480955i
$2$	−0.733052	−	0.680173i	−0.518346	−	0.480955i
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$4$	0.0747301	+	0.997204i	0.0373650	+	0.498602i
$5$	−1.49873	−	3.81871i	−0.670253	−	1.70778i	−0.705802	−	0.708409i	$-0.749413\pi$
$5$	−1.49873	−	3.81871i	−0.670253	−	1.70778i	0.0355490	−	0.999368i	$-0.488682\pi$
$6$	0.623490	+	0.781831i	0.254539	+	0.319181i
$7$	−0.683647	+	2.55590i	−0.258394	+	0.966040i
$7$	−0.683647	+	2.55590i	−0.258394	+	0.966040i
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	0.955573	+	0.294755i	0.318524	+	0.0982517i
$10$	−1.49873	+	3.81871i	−0.473941	+	1.20758i
$11$	−4.24363	+	1.30899i	−1.27950	+	0.394675i	−0.858701	−	0.512477i	$-0.828728\pi$
$11$	−4.24363	+	1.30899i	−1.27950	+	0.394675i	−0.420803	+	0.907152i	$0.638252\pi$
$12$	0.0747301	−	0.997204i	0.0215727	−	0.287868i
$13$	0.268726	−	1.17736i	0.0745311	−	0.326542i	−0.923894	−	0.382649i	$-0.875012\pi$
$13$	0.268726	−	1.17736i	0.0745311	−	0.326542i	0.998425	+	0.0561072i	$0.0178689\pi$
$14$	2.23960	−	1.40861i	0.598559	−	0.376467i
$15$	0.912843	+	3.99943i	0.235695	+	1.03265i
$16$	−0.988831	+	0.149042i	−0.247208	+	0.0372606i
$17$	2.98698	+	2.03649i	0.724448	+	0.493921i	0.868525	−	0.495646i	$-0.165069\pi$
$17$	2.98698	+	2.03649i	0.724448	+	0.493921i	−0.144076	+	0.989567i	$0.546021\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−2.10108	+	3.63917i	−0.482020	+	0.834884i	−0.999787	−	0.0206381i	$-0.993430\pi$
$19$	−2.10108	+	3.63917i	−0.482020	+	0.834884i	0.517767	+	0.855522i	$0.326764\pi$
$20$	3.69603	−	1.77991i	0.826457	−	0.398001i
$21$	1.05695	−	2.42546i	0.230645	−	0.529279i
$22$	4.00114	+	1.92685i	0.853046	+	0.410805i
$23$	−6.13408	+	4.18215i	−1.27905	+	0.872038i	−0.996197	−	0.0871267i	$-0.972232\pi$
$23$	−6.13408	+	4.18215i	−1.27905	+	0.872038i	−0.282848	+	0.959165i	$0.591279\pi$
$24$	−0.733052	+	0.680173i	−0.149634	+	0.138840i
$25$	−8.67106	+	8.04556i	−1.73421	+	1.60911i
$26$	−0.997801	+	0.680290i	−0.195685	+	0.133416i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	−2.59984	−	0.490733i	−0.491324	−	0.0927398i
$29$	−0.564030	+	0.271623i	−0.104738	+	0.0504390i	−0.485519	−	0.874226i	$-0.661369\pi$
$29$	−0.564030	+	0.271623i	−0.104738	+	0.0504390i	0.380781	+	0.924665i	$0.375655\pi$
$30$	2.05114	−	3.55268i	0.374485	−	0.648628i
$31$	−3.64081	−	6.30607i	−0.653909	−	1.13260i	−0.982166	−	0.188015i	$-0.939794\pi$
$31$	−3.64081	−	6.30607i	−0.653909	−	1.13260i	0.328257	−	0.944588i	$-0.393539\pi$
$32$	0.826239	+	0.563320i	0.146060	+	0.0995819i
$33$	4.39133	−	0.661887i	0.764433	−	0.115220i
$34$	−0.804447	−	3.52451i	−0.137961	−	0.604449i
$35$	10.7848	−	1.21996i	1.82297	−	0.206211i
$36$	−0.222521	+	0.974928i	−0.0370868	+	0.162488i
$37$	0.162291	−	2.16562i	0.0266805	−	0.356026i	−0.967846	−	0.251543i	$-0.919062\pi$
$37$	0.162291	−	2.16562i	0.0266805	−	0.356026i	0.994527	−	0.104483i	$-0.0333189\pi$
$38$	4.01547	−	1.23861i	0.651395	−	0.200929i
$39$	−0.441202	+	1.12416i	−0.0706488	+	0.180010i
$40$	−3.92003	−	1.20917i	−0.619811	−	0.191186i
$41$	−3.15756	+	3.95945i	−0.493128	+	0.618363i	−0.964664	−	0.263484i	$-0.915128\pi$
$41$	−3.15756	+	3.95945i	−0.493128	+	0.618363i	0.471536	+	0.881847i	$0.343700\pi$
$42$	−2.42453	+	1.05908i	−0.374113	+	0.163420i
$43$	1.92190	+	2.40998i	0.293087	+	0.367519i	0.906473	−	0.422264i	$-0.138764\pi$
$43$	1.92190	+	2.40998i	0.293087	+	0.367519i	−0.613386	+	0.789783i	$0.710193\pi$
$44$	−1.62245	−	4.13395i	−0.244594	−	0.623216i
$45$	−0.306564	−	4.09081i	−0.0456998	−	0.609822i
$46$	7.34119	+	1.10651i	1.08240	+	0.163145i
$47$	−0.154351	−	0.143217i	−0.0225144	−	0.0208903i	0.668835	−	0.743411i	$-0.266793\pi$
$47$	−0.154351	−	0.143217i	−0.0225144	−	0.0208903i	−0.691350	+	0.722520i	$0.742984\pi$
$48$	1.00000			0.144338
$49$	−6.06525	−	3.49467i	−0.866465	−	0.499238i
$50$	11.8287			1.67283
$51$	−2.65009	−	2.45893i	−0.371087	−	0.344319i
$52$	1.19415	+	0.179990i	0.165599	+	0.0249601i
$53$	−0.299625	−	3.99822i	−0.0411567	−	0.549198i	−0.979229	−	0.202758i	$-0.935009\pi$
$53$	−0.299625	−	3.99822i	−0.0411567	−	0.549198i	0.938072	−	0.346440i	$-0.112610\pi$
$54$	0.365341	+	0.930874i	0.0497166	+	0.126676i
$55$	11.3587	+	14.2434i	1.53161	+	1.92058i
$56$	1.57204	+	2.12807i	0.210072	+	0.284376i
$57$	2.62000	−	3.28538i	0.347028	−	0.435159i
$58$	0.598214	+	0.184524i	0.0785493	+	0.0242292i
$59$	5.59962	−	14.2676i	0.729009	−	1.85748i	0.301542	−	0.953453i	$-0.402499\pi$
$59$	5.59962	−	14.2676i	0.729009	−	1.85748i	0.427467	−	0.904031i	$-0.359406\pi$
$60$	−3.92003	+	1.20917i	−0.506073	+	0.156103i
$61$	0.253707	−	3.38549i	0.0324839	−	0.433467i	−0.957124	−	0.289677i	$-0.906452\pi$
$61$	0.253707	−	3.38549i	0.0324839	−	0.433467i	0.989608	−	0.143790i	$-0.0459289\pi$
$62$	−1.62031	+	7.09906i	−0.205780	+	0.901581i
$63$	−1.40664	+	2.24084i	−0.177220	+	0.282319i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−4.89876	+	0.738369i	−0.607616	+	0.0915834i
$66$	−3.66927	−	2.50167i	−0.451656	−	0.307934i
$67$	−0.294061	−	0.509329i	−0.0359253	−	0.0622244i	0.847504	−	0.530789i	$-0.178104\pi$
$67$	−0.294061	−	0.509329i	−0.0359253	−	0.0622244i	−0.883429	+	0.468565i	$0.844771\pi$
$68$	−1.80757	+	3.13081i	−0.219201	+	0.379667i
$69$	6.68889	−	3.22120i	0.805248	−	0.387787i
$70$	−8.73563	−	6.44125i	−1.04411	−	0.769877i
$71$	−12.1420	−	5.84729i	−1.44099	−	0.693946i	−0.459988	−	0.887925i	$-0.652146\pi$
$71$	−12.1420	−	5.84729i	−1.44099	−	0.693946i	−0.981006	+	0.193979i	$0.937861\pi$
$72$	0.826239	−	0.563320i	0.0973732	−	0.0663879i
$73$	5.40695	−	5.01692i	0.632836	−	0.587186i	−0.297128	−	0.954838i	$-0.596029\pi$
$73$	5.40695	−	5.01692i	0.632836	−	0.587186i	0.929963	+	0.367652i	$0.119838\pi$
$74$	−1.59196	+	1.47713i	−0.185062	+	0.171713i
$75$	9.77334	−	6.66335i	1.12853	−	0.769417i
$76$	−3.78601	−	1.82325i	−0.434285	−	0.209141i
$77$	−0.444495	−	11.7412i	−0.0506549	−	1.33803i
$78$	1.08805	−	0.523977i	0.123197	−	0.0593287i
$79$	1.23248	−	2.13472i	0.138665	−	0.240174i	−0.788327	−	0.615257i	$-0.789052\pi$
$79$	1.23248	−	2.13472i	0.138665	−	0.240174i	0.926991	+	0.375083i	$0.122386\pi$
$80$	2.05114	+	3.55268i	0.229324	+	0.397202i
$81$	0.826239	+	0.563320i	0.0918043	+	0.0625911i
$82$	5.00777	−	0.754799i	0.553015	−	0.0833536i
$83$	1.48571	+	6.50930i	0.163077	+	0.714489i	0.988656	+	0.150201i	$0.0479920\pi$
$83$	1.48571	+	6.50930i	0.163077	+	0.714489i	−0.825578	+	0.564288i	$0.809151\pi$
$84$	2.49766	+	0.872738i	0.272518	+	0.0952235i
$85$	3.30007	−	14.4585i	0.357942	−	1.56825i
$86$	0.230354	−	3.07387i	0.0248398	−	0.331463i
$87$	0.598214	−	0.184524i	0.0641352	−	0.0197831i
$88$	−1.62245	+	4.13395i	−0.172954	+	0.440680i
$89$	−11.9694	−	3.69208i	−1.26876	−	0.391359i	−0.413946	−	0.910301i	$-0.635850\pi$
$89$	−11.9694	−	3.69208i	−1.26876	−	0.391359i	−0.854809	+	0.518942i	$0.826326\pi$
$90$	−2.55773	+	3.20729i	−0.269608	+	0.338078i
$91$	2.82551	+	1.49174i	0.296194	+	0.156377i
$92$	−4.62885	−	5.80440i	−0.482591	−	0.605151i
$93$	2.66028	+	6.77827i	0.275858	+	0.702874i
$94$	0.0157351	+	0.209971i	0.00162295	+	0.0216568i
$95$	17.0459	+	2.56925i	1.74887	+	0.263600i
$96$	−0.733052	−	0.680173i	−0.0748168	−	0.0694198i
$97$	−9.91836			−1.00706			−0.503528	−	0.863979i	$-0.667965\pi$
$97$	−9.91836			−1.00706			−0.503528	+	0.863979i	$0.667965\pi$
$98$	2.06917	+	6.68719i	0.209018	+	0.675508i
$99$	−4.44093			−0.446331
$100$	−8.67106	−	8.04556i	−0.867106	−	0.804556i
$101$	−0.136972	−	0.0206452i	−0.0136292	−	0.00205428i	0.142224	−	0.989834i	$-0.454575\pi$
$101$	−0.136972	−	0.0206452i	−0.0136292	−	0.00205428i	−0.155853	+	0.987780i	$0.549813\pi$
$102$	0.270160	+	3.60504i	0.0267499	+	0.356952i
$103$	5.98828	+	15.2579i	0.590043	+	1.50341i	0.844084	+	0.536212i	$0.180145\pi$
$103$	5.98828	+	15.2579i	0.590043	+	1.50341i	−0.254040	+	0.967194i	$0.581760\pi$
$104$	−0.752953	−	0.944173i	−0.0738331	−	0.0925838i
$105$	−10.8462	−	0.401060i	−1.05848	−	0.0391395i
$106$	−2.49984	+	3.13470i	−0.242806	+	0.304469i
$107$	−13.7102	−	4.22904i	−1.32542	−	0.408837i	−0.450355	−	0.892850i	$-0.648703\pi$
$107$	−13.7102	−	4.22904i	−1.32542	−	0.408837i	−0.875061	+	0.484013i	$0.839179\pi$
$108$	0.365341	−	0.930874i	0.0351550	−	0.0895734i
$109$	−16.7175	+	5.15668i	−1.60125	+	0.493920i	−0.961533	−	0.274690i	$-0.911425\pi$
$109$	−16.7175	+	5.15668i	−1.60125	+	0.493920i	−0.639717	+	0.768610i	$0.720949\pi$
$110$	1.36143	−	18.1670i	0.129807	−	1.73216i
$111$	−0.483247	+	2.11725i	−0.0458678	+	0.200960i
$112$	0.295074	−	2.62925i	0.0278819	−	0.248440i
$113$	4.24590	+	18.6025i	0.399421	+	1.74998i	0.629688	+	0.776848i	$0.283183\pi$
$113$	4.24590	+	18.6025i	0.399421	+	1.74998i	−0.230267	+	0.973127i	$0.573960\pi$
$114$	−4.15522	+	0.626299i	−0.389172	+	0.0586583i
$115$	25.1637	+	17.1563i	2.34653	+	1.59984i
$116$	−0.313013	−	0.542155i	−0.0290625	−	0.0503378i
$117$	0.603822	−	1.04585i	0.0558233	−	0.0966888i
$118$	−13.8092	+	6.65018i	−1.27124	+	0.612199i
$119$	−7.24709	+	6.24218i	−0.664340	+	0.572220i
$120$	3.69603	+	1.77991i	0.337400	+	0.162483i
$121$	7.20636	−	4.91321i	0.655124	−	0.446656i
$122$	−2.48870	+	2.30917i	−0.225316	+	0.209063i
$123$	3.71242	−	3.44462i	0.334737	−	0.310591i
$124$	6.01636	−	4.10189i	0.540285	−	0.368360i
$125$	25.2391	+	12.1545i	2.25745	+	1.08713i
$126$	2.55530	−	0.685895i	0.227644	−	0.0611043i
$127$	15.1002	−	7.27188i	1.33993	−	0.645275i	0.379860	−	0.925044i	$-0.375972\pi$
$127$	15.1002	−	7.27188i	1.33993	−	0.645275i	0.960067	+	0.279769i	$0.0902580\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.54124	−	2.66951i	−0.135699	−	0.235037i
$130$	4.09326	+	2.79074i	0.359003	+	0.244764i
$131$	6.51336	−	0.981731i	0.569075	−	0.0857742i	0.141799	−	0.989895i	$-0.454711\pi$
$131$	6.51336	−	0.981731i	0.569075	−	0.0857742i	0.427276	+	0.904121i	$0.359473\pi$
$132$	0.988201	+	4.32959i	0.0860118	+	0.376842i
$133$	−7.86497	−	7.85806i	−0.681979	−	0.681380i
$134$	−0.130869	+	0.573377i	−0.0113054	+	0.0495322i
$135$	−0.306564	+	4.09081i	−0.0263848	+	0.352081i
$136$	3.45454	−	1.06558i	0.296224	−	0.0913731i
$137$	−3.60382	+	9.18239i	−0.307895	+	0.784504i	0.690247	+	0.723574i	$0.257502\pi$
$137$	−3.60382	+	9.18239i	−0.307895	+	0.784504i	−0.998142	+	0.0609302i	$0.980593\pi$
$138$	−7.09427	−	2.18829i	−0.603905	−	0.186280i
$139$	−5.72958	+	7.18467i	−0.485977	+	0.609396i	−0.963002	−	0.269494i	$-0.913144\pi$
$139$	−5.72958	+	7.18467i	−0.485977	+	0.609396i	0.477025	+	0.878890i	$0.341715\pi$
$140$	2.02250	+	10.6635i	0.170933	+	0.901231i
$141$	0.131282	+	0.164622i	0.0110559	+	0.0138637i
$142$	4.92357	+	12.5450i	0.413177	+	1.05276i
$143$	0.400782	+	5.34807i	0.0335151	+	0.447228i
$144$	−0.988831	−	0.149042i	−0.0824026	−	0.0124202i
$145$	1.88258	+	1.74678i	0.156339	+	0.145062i
$146$	−7.37595			−0.610438
$147$	5.47666	+	4.35961i	0.451707	+	0.359575i
$148$	2.17169			0.178512
$149$	4.31662	+	4.00523i	0.353631	+	0.328122i	0.836906	−	0.547347i	$-0.184362\pi$
$149$	4.31662	+	4.00523i	0.353631	+	0.328122i	−0.483275	+	0.875469i	$0.660553\pi$
$150$	−11.6966	−	1.76298i	−0.955023	−	0.143947i
$151$	−1.27349	−	16.9935i	−0.103635	−	1.38291i	−0.770359	−	0.637610i	$-0.779923\pi$
$151$	−1.27349	−	16.9935i	−0.103635	−	1.38291i	0.666724	−	0.745304i	$-0.267696\pi$
$152$	1.53522	+	3.91168i	0.124523	+	0.317279i
$153$	2.25401	+	2.82644i	0.182226	+	0.228504i
$154$	−7.66020	+	8.90924i	−0.617277	+	0.717927i
$155$	−18.6244	+	23.3543i	−1.49595	+	1.87586i
$156$	−1.15399	−	0.355959i	−0.0923932	−	0.0284995i
$157$	4.62850	−	11.7932i	0.369395	−	0.941202i	−0.618459	−	0.785817i	$-0.712243\pi$
$157$	4.62850	−	11.7932i	0.369395	−	0.941202i	0.987854	−	0.155385i	$-0.0496619\pi$
$158$	−2.35545	+	0.726559i	−0.187389	+	0.0578019i
$159$	−0.299625	+	3.99822i	−0.0237618	+	0.317080i
$160$	0.912843	−	3.99943i	0.0721666	−	0.316183i
$161$	−6.49561	−	18.5372i	−0.511925	−	1.46094i
$162$	−0.222521	−	0.974928i	−0.0174829	−	0.0765976i
$163$	−4.41432	+	0.665351i	−0.345756	+	0.0521143i	−0.319625	−	0.947544i	$-0.603557\pi$
$163$	−4.41432	+	0.665351i	−0.345756	+	0.0521143i	−0.0261312	+	0.999659i	$0.508319\pi$
$164$	−4.18435	−	2.85284i	−0.326743	−	0.222769i
$165$	−9.10898	−	15.7772i	−0.709133	−	1.22825i
$166$	3.33835	−	5.78219i	0.259106	−	0.448785i
$167$	5.01922	−	2.41713i	0.388399	−	0.187043i	−0.229486	−	0.973312i	$-0.573704\pi$
$167$	5.01922	−	2.41713i	0.388399	−	0.187043i	0.617884	+	0.786269i	$0.287990\pi$
$168$	−1.23731	−	2.33861i	−0.0954602	−	0.180427i
$169$	10.3986	+	5.00771i	0.799894	+	0.385209i
$170$	−12.2534	+	8.35424i	−0.939794	+	0.640741i
$171$	−3.08040	+	2.85819i	−0.235564	+	0.218571i
$172$	−2.25962	+	2.09662i	−0.172295	+	0.159866i
$173$	−12.9065	+	8.79949i	−0.981262	+	0.669013i	−0.943880	−	0.330288i	$-0.892854\pi$
$173$	−12.9065	+	8.79949i	−0.981262	+	0.669013i	−0.0373816	+	0.999301i	$0.511902\pi$
$174$	−0.564030	−	0.271623i	−0.0427590	−	0.0205917i
$175$	−14.6357	−	27.6627i	−1.10636	−	2.09110i
$176$	4.00114	−	1.92685i	0.301597	−	0.145242i
$177$	−7.66356	+	13.2737i	−0.576028	+	0.997710i
$178$	6.26295	+	10.8478i	0.469428	+	0.813073i
$179$	−6.94682	−	4.73626i	−0.519230	−	0.354005i	0.275174	−	0.961394i	$-0.411264\pi$
$179$	−6.94682	−	4.73626i	−0.519230	−	0.354005i	−0.794404	+	0.607389i	$0.792217\pi$
$180$	4.05646	−	0.611413i	0.302351	−	0.0455721i
$181$	−3.13024	−	13.7145i	−0.232669	−	1.01939i	−0.947416	−	0.320005i	$-0.896315\pi$
$181$	−3.13024	−	13.7145i	−0.232669	−	1.01939i	0.714747	−	0.699383i	$-0.246542\pi$
$182$	−1.05661	−	3.01536i	−0.0783210	−	0.223513i
$183$	−0.755454	+	3.30986i	−0.0558448	+	0.244672i
$184$	−0.554804	+	7.40335i	−0.0409007	+	0.545782i
$185$	−8.51310	+	2.62594i	−0.625896	+	0.193063i
$186$	2.66028	−	6.77827i	0.195061	−	0.497007i
$187$	−15.3414	−	4.73219i	−1.12187	−	0.346052i
$188$	0.131282	−	0.164622i	0.00957470	−	0.0120063i
$189$	1.72491	−	2.00616i	0.125469	−	0.145927i
$190$	−10.7480	−	13.4775i	−0.779741	−	0.977764i
$191$	1.85292	+	4.72115i	0.134072	+	0.341611i	0.982105	−	0.188333i	$-0.0603084\pi$
$191$	1.85292	+	4.72115i	0.134072	+	0.341611i	−0.848033	+	0.529943i	$0.822213\pi$
$192$	0.0747301	+	0.997204i	0.00539318	+	0.0719670i
$193$	10.1349	+	1.52758i	0.729523	+	0.109958i	0.503293	−	0.864116i	$-0.332122\pi$
$193$	10.1349	+	1.52758i	0.729523	+	0.109958i	0.226230	+	0.974074i	$0.427360\pi$
$194$	7.27067	+	6.74620i	0.522004	+	0.484349i
$195$	4.95409			0.354770
$196$	3.03164	−	6.30945i	0.216546	−	0.450675i
$197$	11.2228			0.799588			0.399794	−	0.916605i	$-0.369082\pi$
$197$	11.2228			0.799588			0.399794	+	0.916605i	$0.369082\pi$
$198$	3.25543	+	3.02060i	0.231354	+	0.214665i
$199$	−7.40715	−	1.11645i	−0.525079	−	0.0791430i	−0.118847	−	0.992913i	$-0.537920\pi$
$199$	−7.40715	−	1.11645i	−0.525079	−	0.0791430i	−0.406233	+	0.913770i	$0.633158\pi$
$200$	0.883960	+	11.7956i	0.0625054	+	0.834077i
$201$	0.214865	+	0.547467i	0.0151554	+	0.0386154i
$202$	0.0863653	+	0.108299i	0.00607664	+	0.00761987i
$203$	−0.308643	−	1.62730i	−0.0216625	−	0.114214i
$204$	2.25401	−	2.82644i	0.157812	−	0.197890i
$205$	19.8523	+	6.12363i	1.38655	+	0.427693i
$206$	5.98828	−	15.2579i	0.417223	−	1.06307i
$207$	−7.09427	+	2.18829i	−0.493086	+	0.152097i
$208$	−0.0902473	+	1.20427i	−0.00625752	+	0.0835008i
$209$	4.15257	−	18.1936i	0.287239	−	1.25848i
$210$	7.67804	+	7.67129i	0.529835	+	0.529369i
$211$	2.12041	+	9.29012i	0.145975	+	0.639558i	0.993979	+	0.109569i	$0.0349470\pi$
$211$	2.12041	+	9.29012i	0.145975	+	0.639558i	−0.848004	+	0.529989i	$0.822196\pi$
$212$	3.96465	−	0.597575i	0.272293	−	0.0410416i
$213$	11.1349	+	7.59166i	0.762952	+	0.520172i
$214$	7.17382	+	12.4254i	0.490392	+	0.849384i
$215$	6.32261	−	10.9511i	0.431198	−	0.746857i
$216$	−0.900969	+	0.433884i	−0.0613032	+	0.0295220i
$217$	18.6067	−	4.99443i	1.26311	−	0.339044i
$218$	15.7623	+	7.59070i	1.06755	+	0.514107i
$219$	−6.09429	+	4.15502i	−0.411814	+	0.280770i
$220$	−13.3547	+	12.3914i	−0.900374	+	0.835425i
$221$	3.20037	−	2.96951i	0.215280	−	0.199751i
$222$	1.79434	−	1.22336i	0.120428	−	0.0821065i
$223$	4.36861	+	2.10381i	0.292544	+	0.140882i	0.574399	−	0.818575i	$-0.305236\pi$
$223$	4.36861	+	2.10381i	0.292544	+	0.140882i	−0.281856	+	0.959457i	$0.590950\pi$
$224$	−2.00465	+	1.72667i	−0.133941	+	0.115368i
$225$	−10.6573	+	5.13228i	−0.710486	+	0.342152i
$226$	9.54045	−	16.5245i	0.634621	−	1.09920i
$227$	−7.97854	−	13.8192i	−0.529554	−	0.917215i	−0.999406	−	0.0344693i	$-0.989026\pi$
$227$	−7.97854	−	13.8192i	−0.529554	−	0.917215i	0.469852	−	0.882745i	$-0.344307\pi$
$228$	3.47198	+	2.36716i	0.229938	+	0.156769i
$229$	−12.6731	+	1.91016i	−0.837461	+	0.126227i	−0.553750	−	0.832683i	$-0.686804\pi$
$229$	−12.6731	+	1.91016i	−0.837461	+	0.126227i	−0.283711	+	0.958910i	$0.591566\pi$
$230$	−6.77705	−	29.6922i	−0.446865	−	1.95784i
$231$	−1.31040	+	11.6763i	−0.0862183	+	0.768244i
$232$	−0.139304	+	0.610330i	−0.00914575	+	0.0400702i
$233$	−2.07614	+	27.7042i	−0.136012	+	1.81496i	0.345390	+	0.938459i	$0.387747\pi$
$233$	−2.07614	+	27.7042i	−0.136012	+	1.81496i	−0.481402	+	0.876500i	$0.659872\pi$
$234$	−1.15399	+	0.355959i	−0.0754387	+	0.0232698i
$235$	−0.315572	+	0.804065i	−0.0205857	+	0.0524514i
$236$	14.6462	+	4.51775i	0.953384	+	0.294080i
$237$	−1.53688	+	1.92718i	−0.0998308	+	0.125184i
$238$	9.55826	+	0.353436i	0.619570	+	0.0229098i
$239$	10.2126	+	12.8062i	0.660596	+	0.828362i	0.993408	−	0.114632i	$-0.0365688\pi$
$239$	10.2126	+	12.8062i	0.660596	+	0.828362i	−0.332812	+	0.942993i	$0.607997\pi$
$240$	−1.49873	−	3.81871i	−0.0967427	−	0.246496i
$241$	1.10719	+	14.7745i	0.0713207	+	0.951708i	0.912004	+	0.410181i	$0.134535\pi$
$241$	1.10719	+	14.7745i	0.0713207	+	0.951708i	−0.840683	+	0.541527i	$0.817846\pi$
$242$	−8.62447	−	1.29993i	−0.554402	−	0.0835626i
$243$	−0.733052	−	0.680173i	−0.0470253	−	0.0436331i
$244$	3.39498			0.217341
$245$	−4.25492	+	28.3990i	−0.271837	+	1.81434i
$246$	−5.06433			−0.322890
$247$	3.72002	+	3.45168i	0.236699	+	0.219625i
$248$	−7.20029	−	1.08527i	−0.457219	−	0.0689147i
$249$	−0.498950	−	6.65803i	−0.0316197	−	0.421935i
$250$	−10.2344	−	26.0768i	−0.647280	−	1.64924i
$251$	−18.8535	−	23.6415i	−1.19002	−	1.49224i	−0.828605	−	0.559834i	$-0.810865\pi$
$251$	−18.8535	−	23.6415i	−1.19002	−	1.49224i	−0.361416	−	0.932405i	$-0.617707\pi$
$252$	−2.33969	−	1.23525i	−0.147387	−	0.0778133i
$253$	20.5564	−	25.7770i	1.29237	−	1.62058i
$254$	−16.0154	−	4.94009i	−1.00489	−	0.309969i
$255$	−5.41814	+	13.8052i	−0.339297	+	0.864515i
$256$	0.955573	−	0.294755i	0.0597233	−	0.0184222i
$257$	2.33762	−	31.1933i	0.145817	−	1.94579i	−0.145940	−	0.989293i	$-0.546621\pi$
$257$	2.33762	−	31.1933i	0.145817	−	1.94579i	0.291756	−	0.956493i	$-0.405760\pi$
$258$	−0.685917	+	3.00520i	−0.0427034	+	0.187096i
$259$	5.42416	+	1.89532i	0.337041	+	0.117769i
$260$	−1.10239	−	4.82988i	−0.0683673	−	0.299537i
$261$	−0.619034	+	0.0933044i	−0.0383172	+	0.00577539i
$262$	−5.44238	−	3.71055i	−0.336231	−	0.229239i
$263$	−7.09250	−	12.2846i	−0.437342	−	0.757499i	0.560141	−	0.828397i	$-0.310747\pi$
$263$	−7.09250	−	12.2846i	−0.437342	−	0.757499i	−0.997484	+	0.0708979i	$0.977414\pi$
$264$	2.22047	−	3.84596i	0.136660	−	0.236703i
$265$	−14.8190	+	7.13644i	−0.910322	+	0.438388i
$266$	0.420595	+	11.1099i	0.0257884	+	0.681192i
$267$	11.2854	+	5.43479i	0.690658	+	0.332604i
$268$	0.485929	−	0.331301i	0.0296829	−	0.0202374i
$269$	1.62758	−	1.51017i	0.0992353	−	0.0920769i	−0.628995	−	0.777409i	$-0.716534\pi$
$269$	1.62758	−	1.51017i	0.0992353	−	0.0920769i	0.728230	+	0.685332i	$0.240343\pi$
$270$	3.00718	−	2.79026i	0.183011	−	0.169810i
$271$	−10.1386	+	6.91240i	−0.615878	+	0.419898i	−0.830673	−	0.556761i	$-0.812044\pi$
$271$	−10.1386	+	6.91240i	−0.615878	+	0.419898i	0.214795	+	0.976659i	$0.431092\pi$
$272$	−3.25714	−	1.56855i	−0.197493	−	0.0951076i
$273$	−2.57162	−	1.89620i	−0.155642	−	0.114763i
$274$	8.88740	−	4.27994i	0.536907	−	0.258561i
$275$	26.2652	−	45.4927i	1.58385	−	2.74332i
$276$	3.71205	+	6.42946i	0.223439	+	0.387008i
$277$	19.9618	+	13.6098i	1.19939	+	0.817731i	0.987198	−	0.159497i	$-0.0509873\pi$
$277$	19.9618	+	13.6098i	1.19939	+	0.817731i	0.212192	+	0.977228i	$0.431940\pi$
$278$	9.08690	−	1.36963i	0.544996	−	0.0821449i
$279$	−1.62031	−	7.09906i	−0.0970057	−	0.425010i
$280$	5.77043	−	9.19256i	0.344849	−	0.549360i
$281$	0.603904	−	2.64587i	0.0360259	−	0.157840i	−0.953715	−	0.300710i	$-0.902776\pi$
$281$	0.603904	−	2.64587i	0.0360259	−	0.157840i	0.989741	+	0.142871i	$0.0456334\pi$
$282$	0.0157351	−	0.209971i	0.000937013	−	0.0125036i
$283$	11.7347	−	3.61968i	0.697556	−	0.215167i	0.0743577	−	0.997232i	$-0.476309\pi$
$283$	11.7347	−	3.61968i	0.697556	−	0.215167i	0.623198	+	0.782064i	$0.285833\pi$
$284$	4.92357	−	12.5450i	0.292160	−	0.744411i
$285$	−16.4726	−	5.08111i	−0.975751	−	0.300979i
$286$	3.34381	−	4.19301i	0.197724	−	0.247938i
$287$	−7.96131	−	10.7773i	−0.469941	−	0.636162i
$288$	0.623490	+	0.781831i	0.0367395	+	0.0460699i
$289$	−1.43604	−	3.65898i	−0.0844731	−	0.215234i
$290$	−0.191917	−	2.56095i	−0.0112698	−	0.150384i
$291$	9.80758	+	1.47825i	0.574930	+	0.0866568i
$292$	5.40695	+	5.01692i	0.316418	+	0.293593i
$293$	13.1697			0.769382			0.384691	−	0.923045i	$-0.374308\pi$
$293$	13.1697			0.769382			0.384691	+	0.923045i	$0.374308\pi$
$294$	−1.04938	−	6.92090i	−0.0612013	−	0.403635i
$295$	−62.8761			−3.66079
$296$	−1.59196	−	1.47713i	−0.0925311	−	0.0858563i
$297$	4.39133	+	0.661887i	0.254811	+	0.0384066i
$298$	−0.440052	−	5.87209i	−0.0254915	−	0.340161i
$299$	3.27553	+	8.34591i	0.189429	+	0.482656i
$300$	7.37508	+	9.24806i	0.425800	+	0.533937i
$301$	−7.47358	+	3.26460i	−0.430770	+	0.188168i
$302$	−10.6250	+	13.3233i	−0.611400	+	0.766672i
$303$	0.132365	+	0.0408292i	0.00760418	+	0.00234558i
$304$	1.53522	−	3.91168i	0.0880509	−	0.224350i
$305$	−13.3084	+	4.10510i	−0.762038	+	0.235058i
$306$	0.270160	−	3.60504i	0.0154440	−	0.206086i
$307$	3.58092	−	15.6890i	0.204374	−	0.895419i	−0.763862	−	0.645380i	$-0.776699\pi$
$307$	3.58092	−	15.6890i	0.204374	−	0.895419i	0.968236	−	0.250040i	$-0.0804437\pi$
$308$	11.6751	−	1.32067i	0.665253	−	0.0752523i
$309$	−3.64733	−	15.9800i	−0.207489	−	0.909070i
$310$	29.5376	−	4.45208i	1.67762	−	0.252861i
$311$	1.52635	+	1.04065i	0.0865514	+	0.0590097i	0.605823	−	0.795600i	$-0.292844\pi$
$311$	1.52635	+	1.04065i	0.0865514	+	0.0590097i	−0.519271	+	0.854610i	$0.673797\pi$
$312$	0.603822	+	1.04585i	0.0341847	+	0.0592096i
$313$	3.12318	−	5.40950i	0.176532	−	0.305763i	−0.764158	−	0.645029i	$-0.776845\pi$
$313$	3.12318	−	5.40950i	0.176532	−	0.305763i	0.940691	+	0.339266i	$0.110179\pi$
$314$	−11.4144	+	5.49687i	−0.644150	+	0.310206i
$315$	10.6653	+	2.01312i	0.600921	+	0.113427i
$316$	2.22085	+	1.06951i	0.124933	+	0.0601644i
$317$	3.64362	−	2.48418i	0.204646	−	0.139525i	−0.456660	−	0.889641i	$-0.650955\pi$
$317$	3.64362	−	2.48418i	0.204646	−	0.139525i	0.661307	+	0.750116i	$0.270002\pi$
$318$	2.93912	−	2.72711i	0.164818	−	0.152929i
$319$	2.03799	−	1.89098i	0.114105	−	0.105874i
$320$	−3.38946	+	2.31090i	−0.189477	+	0.129183i
$321$	12.9268	+	6.22520i	0.721502	+	0.347457i
$322$	−7.84690	+	18.0069i	−0.437290	+	1.00348i
$323$	−13.6870	+	6.59131i	−0.761565	+	0.366750i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	7.14243	+	12.3710i	0.396191	+	0.686222i
$326$	3.68848	+	2.51476i	0.204286	+	0.139280i
$327$	17.2994	−	2.60746i	0.956658	−	0.144193i
$328$	1.12692	+	4.93736i	0.0622237	+	0.272620i
$329$	0.471569	−	0.296596i	0.0259985	−	0.0163519i
$330$	−4.05388	+	17.7612i	−0.223159	+	0.977721i
$331$	−1.61494	+	21.5498i	−0.0887650	+	1.18449i	0.757904	+	0.652366i	$0.226224\pi$
$331$	−1.61494	+	21.5498i	−0.0887650	+	1.18449i	−0.846669	+	0.532120i	$0.821395\pi$
$332$	−6.38007	+	1.96799i	−0.350152	+	0.108008i
$333$	0.793409	−	2.02157i	0.0434786	−	0.110782i
$334$	−5.32341	−	1.64205i	−0.291284	−	0.0898492i
$335$	−1.50426	+	1.88628i	−0.0821864	+	0.103058i
$336$	−0.683647	+	2.55590i	−0.0372960	+	0.139436i
$337$	−16.4479	−	20.6250i	−0.895972	−	1.12351i	−0.991760	−	0.128111i	$-0.959108\pi$
$337$	−16.4479	−	20.6250i	−0.895972	−	1.12351i	0.0957879	−	0.995402i	$-0.469463\pi$
$338$	−4.21662	−	10.7438i	−0.229354	−	0.584384i
$339$	−1.42592	−	19.0275i	−0.0774452	−	1.03343i
$340$	14.6647	+	2.21035i	0.795306	+	0.119873i
$341$	23.7048	+	21.9949i	1.28369	+	1.19109i
$342$	4.20216			0.227227
$343$	13.0785	−	13.1131i	0.706173	−	0.708039i
$344$	3.08248			0.166196
$345$	−22.3257	−	20.7152i	−1.20197	−	1.11527i
$346$	15.4463	+	2.32815i	0.830398	+	0.125162i
$347$	1.83023	+	24.4227i	0.0982517	+	1.31108i	0.800580	+	0.599225i	$0.204525\pi$
$347$	1.83023	+	24.4227i	0.0982517	+	1.31108i	−0.702329	+	0.711853i	$0.747856\pi$
$348$	0.228713	+	0.582751i	0.0122603	+	0.0312387i
$349$	−2.80183	−	3.51339i	−0.149979	−	0.188067i	0.701167	−	0.712997i	$-0.252663\pi$
$349$	−2.80183	−	3.51339i	−0.149979	−	0.188067i	−0.851145	+	0.524930i	$0.824091\pi$
$350$	−8.08666	+	30.2330i	−0.432250	+	1.61602i
$351$	−0.752953	+	0.944173i	−0.0401897	+	0.0503962i
$352$	−4.24363	−	1.30899i	−0.226186	−	0.0697693i
$353$	−4.77274	+	12.1607i	−0.254027	+	0.647251i	−0.999821	−	0.0189259i	$-0.993975\pi$
$353$	−4.77274	+	12.1607i	−0.254027	+	0.647251i	0.745793	+	0.666177i	$0.232071\pi$
$354$	14.6462	−	4.51775i	0.778435	−	0.240115i
$355$	−4.13145	+	55.1303i	−0.219275	+	2.92602i
$356$	2.78728	−	12.2119i	0.147725	−	0.647227i
$357$	8.09650	−	5.09233i	0.428512	−	0.269515i
$358$	1.87090	+	8.19697i	0.0988804	+	0.433223i
$359$	23.0918	−	3.48053i	1.21874	−	0.183695i	0.491992	−	0.870600i	$-0.336269\pi$
$359$	23.0918	−	3.48053i	1.21874	−	0.183695i	0.726748	+	0.686905i	$0.241031\pi$
$360$	−3.38946	−	2.31090i	−0.178640	−	0.121795i
$361$	0.670941	+	1.16210i	0.0353127	+	0.0611634i
$362$	−7.03358	+	12.1825i	−0.369677	+	0.640299i
$363$	−7.85815	+	3.78428i	−0.412446	+	0.198623i
$364$	−1.27642	+	2.92909i	−0.0669024	+	0.153526i
$365$	−27.2617	−	13.1285i	−1.42694	−	0.687179i
$366$	2.80506	−	1.91246i	0.146623	−	0.0999659i
$367$	5.58297	−	5.18024i	0.291429	−	0.270406i	−0.520885	−	0.853627i	$-0.674398\pi$
$367$	5.58297	−	5.18024i	0.291429	−	0.270406i	0.812314	+	0.583220i	$0.198208\pi$
$368$	5.44226	−	5.04967i	0.283697	−	0.263232i
$369$	−4.18435	+	2.85284i	−0.217828	+	0.148513i
$370$	8.02664	+	3.86543i	0.417285	+	0.200954i
$371$	10.4239	+	1.96756i	0.541182	+	0.102151i
$372$	−6.56052	+	3.15938i	−0.340147	+	0.163806i
$373$	−7.91530	+	13.7097i	−0.409839	+	0.709861i	−0.994871	−	0.101148i	$-0.967748\pi$
$373$	−7.91530	+	13.7097i	−0.409839	+	0.709861i	0.585033	+	0.811010i	$0.301082\pi$
$374$	8.02732	+	13.9037i	0.415083	+	0.718944i
$375$	−23.1457	−	15.7804i	−1.19524	−	0.814898i
$376$	−0.208208	+	0.0313823i	−0.0107375	+	0.00161842i
$377$	0.168229	+	0.737061i	0.00866426	+	0.0379606i
$378$	−2.62898	+	0.297386i	−0.135220	+	0.0152959i
$379$	2.70510	−	11.8518i	0.138952	−	0.608788i	−0.856714	−	0.515791i	$-0.827498\pi$
$379$	2.70510	−	11.8518i	0.138952	−	0.608788i	0.995666	−	0.0929971i	$-0.0296447\pi$
$380$	−1.28823	+	17.1902i	−0.0660848	+	0.881840i
$381$	−16.0154	+	4.94009i	−0.820492	+	0.253088i
$382$	1.85292	−	4.72115i	0.0948034	−	0.241555i
$383$	30.9913	+	9.55956i	1.58358	+	0.488471i	0.956806	−	0.290727i	$-0.0938972\pi$
$383$	30.9913	+	9.55956i	1.58358	+	0.488471i	0.626778	+	0.779198i	$0.284373\pi$
$384$	0.623490	−	0.781831i	0.0318173	−	0.0398977i
$385$	−44.1700	+	19.2943i	−2.25111	+	0.983328i
$386$	−6.39035	−	8.01325i	−0.325260	−	0.407864i
$387$	1.12616	+	2.86940i	0.0572458	+	0.145860i
$388$	−0.741200	−	9.89062i	−0.0376287	−	0.502120i
$389$	27.1336	+	4.08973i	1.37573	+	0.207357i	0.794935	−	0.606695i	$-0.207505\pi$
$389$	27.1336	+	4.08973i	1.37573	+	0.207357i	0.580792	+	0.814052i	$0.302743\pi$
$390$	−3.63161	−	3.36964i	−0.183893	−	0.170628i
$391$	−26.8393			−1.35732
$392$	−6.51386	+	2.56312i	−0.329000	+	0.129457i
$393$	−6.58693			−0.332267
$394$	−8.22686	−	7.63341i	−0.414463	−	0.384566i
$395$	−9.99901	−	1.50711i	−0.503105	−	0.0758308i
$396$	−0.331871	−	4.42852i	−0.0166772	−	0.222541i
$397$	0.772298	+	1.96778i	0.0387605	+	0.0987602i	0.948943	−	0.315447i	$-0.102154\pi$
$397$	0.772298	+	1.96778i	0.0387605	+	0.0987602i	−0.910183	+	0.414207i	$0.864059\pi$
$398$	4.67045	+	5.85656i	0.234109	+	0.293563i
$399$	6.60594	+	8.94250i	0.330711	+	0.447685i
$400$	7.37508	−	9.24806i	0.368754	−	0.462403i
$401$	7.88833	+	2.43323i	0.393925	+	0.121510i	0.485388	−	0.874299i	$-0.338678\pi$
$401$	7.88833	+	2.43323i	0.393925	+	0.121510i	−0.0914636	+	0.995808i	$0.529155\pi$
$402$	0.214865	−	0.547467i	0.0107165	−	0.0273052i
$403$	−8.40293	+	2.59196i	−0.418580	+	0.129115i
$404$	0.0103515	−	0.138132i	0.000515009	−	0.00687232i
$405$	0.912843	−	3.99943i	0.0453596	−	0.198733i
$406$	−0.880593	+	1.40282i	−0.0437031	+	0.0696210i
$407$	2.14607	+	9.40255i	0.106377	+	0.466067i
$408$	−3.57477	+	0.538810i	−0.176978	+	0.0266751i
$409$	−7.94682	−	5.41805i	−0.392945	−	0.267905i	0.350690	−	0.936492i	$-0.385947\pi$
$409$	−7.94682	−	5.41805i	−0.392945	−	0.267905i	−0.743634	+	0.668587i	$0.766900\pi$
$410$	−10.3877	−	17.9919i	−0.513010	−	0.888559i
$411$	4.93213	−	8.54270i	0.243284	−	0.421381i
$412$	−14.7677	+	7.11176i	−0.727554	+	0.350371i
$413$	32.6384	+	24.0661i	1.60603	+	1.18421i
$414$	6.68889	+	3.22120i	0.328741	+	0.158313i
$415$	22.6304	−	15.4292i	1.11088	−	0.757388i
$416$	0.885265	−	0.821406i	0.0434037	−	0.0402727i
$417$	6.73641	−	6.25047i	0.329883	−	0.306087i
$418$	−15.4188	+	10.5124i	−0.754161	+	0.514178i
$419$	15.1113	+	7.27722i	0.738236	+	0.355516i	0.764917	−	0.644128i	$-0.222780\pi$
$419$	15.1113	+	7.27722i	0.738236	+	0.355516i	−0.0266816	+	0.999644i	$0.508494\pi$
$420$	−0.410599	−	10.8458i	−0.0200352	−	0.529223i
$421$	0.316957	−	0.152638i	0.0154475	−	0.00743914i	−0.426144	−	0.904655i	$-0.640128\pi$
$421$	0.316957	−	0.152638i	0.0154475	−	0.00743914i	0.441592	+	0.897216i	$0.354414\pi$
$422$	4.76451	−	8.25238i	0.231933	−	0.401720i
$423$	−0.105280	−	0.182350i	−0.00511888	−	0.00886615i
$424$	−3.31275	−	2.25859i	−0.160881	−	0.109687i
$425$	−42.2849	+	6.37343i	−2.05112	+	0.309157i
$426$	−2.99883	−	13.1387i	−0.145294	−	0.636574i
$427$	8.47952	+	2.96293i	0.410353	+	0.143386i
$428$	3.19265	−	13.9879i	0.154323	−	0.676131i
$429$	0.400782	−	5.34807i	0.0193499	−	0.258207i
$430$	−12.0834	+	3.72724i	−0.582715	+	0.179744i
$431$	3.55743	−	9.06419i	0.171355	−	0.436606i	−0.819236	−	0.573456i	$-0.805602\pi$
$431$	3.55743	−	9.06419i	0.171355	−	0.436606i	0.990592	+	0.136849i	$0.0436976\pi$
$432$	0.955573	+	0.294755i	0.0459750	+	0.0141814i
$433$	−16.3142	+	20.4574i	−0.784011	+	0.983119i	0.215966	+	0.976401i	$0.430710\pi$
$433$	−16.3142	+	20.4574i	−0.784011	+	0.983119i	−0.999977	+	0.00671801i	$0.997862\pi$
$434$	−17.0368	−	8.99461i	−0.817791	−	0.431755i
$435$	−1.60121	−	2.00785i	−0.0767720	−	0.0962690i
$436$	−6.39156	−	16.2854i	−0.306100	−	0.779931i
$437$	−2.33137	−	31.1100i	−0.111525	−	1.48819i
$438$	7.29356	+	1.09933i	0.348500	+	0.0525279i
$439$	−0.264568	−	0.245484i	−0.0126272	−	0.0117163i	0.673834	−	0.738883i	$-0.264646\pi$
$439$	−0.264568	−	0.245484i	−0.0126272	−	0.0117163i	−0.686461	+	0.727167i	$0.740837\pi$
$440$	18.2180			0.868507
$441$	−4.76572	−	5.12717i	−0.226939	−	0.244151i
$442$	−4.36581			−0.207660
$443$	−13.8306	−	12.8329i	−0.657112	−	0.609711i	0.279472	−	0.960154i	$-0.409840\pi$
$443$	−13.8306	−	12.8329i	−0.657112	−	0.609711i	−0.936584	+	0.350443i	$0.886031\pi$
$444$	−2.14744	−	0.323674i	−0.101913	−	0.0153609i
$445$	3.83999	+	51.2411i	0.182033	+	2.42906i
$446$	−1.77146	−	4.51361i	−0.0838811	−	0.213726i
$447$	−3.67145	−	4.60386i	−0.173654	−	0.217755i
$448$	2.64394	+	0.0977652i	0.124915	+	0.00461897i
$449$	−12.0428	+	15.1011i	−0.568333	+	0.712667i	−0.980074	−	0.198634i	$-0.936350\pi$
$449$	−12.0428	+	15.1011i	−0.568333	+	0.712667i	0.411741	+	0.911301i	$0.364921\pi$
$450$	11.3032	+	3.48657i	0.532838	+	0.164359i
$451$	8.21665	−	20.9357i	0.386907	−	0.985823i
$452$	−18.2332	+	5.62419i	−0.857617	+	0.264540i
$453$	−1.27349	+	16.9935i	−0.0598338	+	0.798426i
$454$	−3.55078	+	15.5570i	−0.166647	+	0.730126i
$455$	1.46182	−	13.0255i	0.0685313	−	0.610646i
$456$	−0.935068	−	4.09680i	−0.0437886	−	0.191850i
$457$	1.07217	−	0.161604i	0.0501540	−	0.00755950i	−0.123917	−	0.992293i	$-0.539546\pi$
$457$	1.07217	−	0.161604i	0.0501540	−	0.00755950i	0.174071	+	0.984733i	$0.444308\pi$
$458$	10.5893	+	7.21964i	0.494804	+	0.337352i
$459$	−1.80757	−	3.13081i	−0.0843704	−	0.146134i
$460$	−15.2279	+	26.3755i	−0.710004	+	1.22976i
$461$	−18.8621	+	9.08350i	−0.878495	+	0.423061i	−0.818075	−	0.575112i	$-0.804958\pi$
$461$	−18.8621	+	9.08350i	−0.878495	+	0.423061i	−0.0604205	+	0.998173i	$0.519244\pi$
$462$	8.90250	−	7.66803i	0.414182	−	0.356749i
$463$	−15.2811	−	7.35901i	−0.710175	−	0.342002i	0.0436779	−	0.999046i	$-0.486092\pi$
$463$	−15.2811	−	7.35901i	−0.710175	−	0.342002i	−0.753853	+	0.657044i	$0.771807\pi$
$464$	0.517247	−	0.352653i	0.0240126	−	0.0163715i
$465$	21.8972	−	20.3176i	1.01546	−	0.942207i
$466$	20.3655	−	18.8964i	0.943415	−	0.875361i
$467$	−19.9816	+	13.6233i	−0.924640	+	0.630409i	−0.929199	−	0.369580i	$-0.879501\pi$
$467$	−19.9816	+	13.6233i	−0.924640	+	0.630409i	0.00455836	+	0.999990i	$0.498549\pi$
$468$	1.08805	+	0.523977i	0.0502951	+	0.0242208i
$469$	1.50283	−	0.403390i	0.0693941	−	0.0186268i
$470$	0.778234	−	0.374778i	0.0358972	−	0.0172872i
$471$	−6.33449	+	10.9717i	−0.291878	+	0.505548i
$472$	−7.66356	−	13.2737i	−0.352744	−	0.610970i
$473$	−11.3105	−	7.71135i	−0.520056	−	0.354568i
$474$	2.43743	−	0.367383i	0.111955	−	0.0168745i
$475$	−11.0606	−	48.4598i	−0.507497	−	2.22349i
$476$	−6.76630	−	6.76035i	−0.310133	−	0.309860i
$477$	0.892183	−	3.90891i	0.0408502	−	0.178977i
$478$	1.22406	−	16.3339i	0.0559870	−	0.747095i
$479$	−29.8376	+	9.20368i	−1.36331	+	0.420527i	−0.888224	−	0.459410i	$-0.848061\pi$
$479$	−29.8376	+	9.20368i	−1.36331	+	0.420527i	−0.475090	+	0.879937i	$0.657585\pi$
$480$	−1.49873	+	3.81871i	−0.0684074	+	0.174299i
$481$	−2.50612	−	0.773034i	−0.114269	−	0.0352473i
$482$	9.23757	−	11.5835i	0.420760	−	0.527616i
$483$	3.66023	+	19.2983i	0.166546	+	0.878103i
$484$	5.43801	+	6.81904i	0.247182	+	0.309957i
$485$	14.8650	+	37.8753i	0.674983	+	1.71983i
$486$	0.0747301	+	0.997204i	0.00338983	+	0.0452341i
$487$	−15.2961	−	2.30551i	−0.693131	−	0.104473i	−0.206977	−	0.978346i	$-0.566362\pi$
$487$	−15.2961	−	2.30551i	−0.693131	−	0.104473i	−0.486154	+	0.873873i	$0.661601\pi$
$488$	−2.48870	−	2.30917i	−0.112658	−	0.104531i
$489$	4.46418			0.201877
$490$	22.4353	−	17.9238i	1.01352	−	0.809717i
$491$	5.70609			0.257512			0.128756	−	0.991676i	$-0.458902\pi$
$491$	5.70609			0.257512			0.128756	+	0.991676i	$0.458902\pi$
$492$	3.71242	+	3.44462i	0.167369	+	0.155295i
$493$	−2.23790	−	0.337309i	−0.100790	−	0.0151916i
$494$	−0.379233	−	5.06051i	−0.0170625	−	0.227683i
$495$	6.65577	+	16.9586i	0.299154	+	0.762233i
$496$	4.54002	+	5.69300i	0.203853	+	0.255623i
$497$	23.2460	−	27.0363i	1.04272	−	1.21275i
$498$	−4.16285	+	5.22005i	−0.186542	+	0.233916i
$499$	14.8782	+	4.58933i	0.666042	+	0.205447i	0.609297	−	0.792942i	$-0.291452\pi$
$499$	14.8782	+	4.58933i	0.666042	+	0.205447i	0.0567446	+	0.998389i	$0.481928\pi$
$500$	−10.2344	+	26.0768i	−0.457696	+	1.16619i
$501$	−5.32341	+	1.64205i	−0.237832	+	0.0733616i
$502$	−2.25974	+	30.1541i	−0.100857	+	1.34584i
$503$	−0.206761	+	0.905879i	−0.00921901	+	0.0403911i	−0.979328	−	0.202278i	$-0.935166\pi$
$503$	−0.206761	+	0.905879i	−0.00921901	+	0.0403911i	0.970109	+	0.242669i	$0.0780228\pi$
$504$	0.874934	+	2.49690i	0.0389727	+	0.111221i
$505$	0.126446	+	0.553997i	0.00562679	+	0.0246526i
$506$	−32.6017	+	4.91392i	−1.44932	+	0.218450i
$507$	−9.53612	−	6.50161i	−0.423514	−	0.288747i
$508$	8.37998	+	14.5146i	0.371802	+	0.643979i
$509$	3.06730	−	5.31272i	0.135956	−	0.235482i	−0.790006	−	0.613099i	$-0.789923\pi$
$509$	3.06730	−	5.31272i	0.135956	−	0.235482i	0.925962	+	0.377616i	$0.123256\pi$
$510$	13.3617	−	6.43465i	0.591666	−	0.284931i
$511$	9.12630	+	17.2494i	0.403724	+	0.763070i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	3.47198	−	2.36716i	0.153292	−	0.104513i
$514$	−22.9304	+	21.2763i	−1.01142	+	0.938459i
$515$	49.2906	−	45.7350i	2.17200	−	2.01532i
$516$	2.54687	−	1.73643i	0.112120	−	0.0764419i
$517$	0.842478	+	0.405716i	0.0370522	+	0.0178434i
$518$	−2.68705	−	5.07874i	−0.118062	−	0.223147i
$519$	14.0738	−	6.77760i	0.617772	−	0.297503i
$520$	−2.47705	+	4.29037i	−0.108626	+	0.188145i
$521$	6.61161	+	11.4516i	0.289660	+	0.501706i	0.973729	−	0.227712i	$-0.0731245\pi$
$521$	6.61161	+	11.4516i	0.289660	+	0.501706i	−0.684069	+	0.729418i	$0.739791\pi$
$522$	0.517247	+	0.352653i	0.0226393	+	0.0154352i
$523$	−30.5794	+	4.60911i	−1.33715	+	0.201542i	−0.778385	−	0.627787i	$-0.783961\pi$
$523$	−30.5794	+	4.60911i	−1.33715	+	0.201542i	−0.558760	+	0.829329i	$0.688723\pi$
$524$	1.46573	+	6.42178i	0.0640307	+	0.280537i
$525$	10.3493	+	29.5351i	0.451682	+	1.28902i
$526$	−3.15646	+	13.8294i	−0.137628	+	0.602989i
$527$	1.96721	−	26.2506i	0.0856929	−	1.14349i
$528$	−4.24363	+	1.30899i	−0.184680	+	0.0569664i
$529$	11.7338	−	29.8972i	0.510165	−	1.29988i
$530$	15.7171	+	4.84808i	0.682707	+	0.210587i
$531$	9.55630	−	11.9832i	0.414708	−	0.520027i
$532$	7.24833	−	8.43021i	0.314255	−	0.365496i
$533$	3.81320	+	4.78161i	0.165168	+	0.207114i
$534$	−4.57623	−	11.6600i	−0.198033	−	0.504579i
$535$	4.39847	+	58.6934i	0.190162	+	2.53754i
$536$	−0.581553	−	0.0876551i	−0.0251193	−	0.00378612i
$537$	6.16333	+	5.71873i	0.265967	+	0.246782i
$538$	−2.22028			−0.0957230
$539$	30.3132	+	6.89075i	1.30568	+	0.296805i
$540$	−4.10228			−0.176534
$541$	−3.59933	−	3.33969i	−0.154747	−	0.143585i	0.599000	−	0.800749i	$-0.295565\pi$
$541$	−3.59933	−	3.33969i	−0.154747	−	0.143585i	−0.753747	+	0.657165i	$0.771756\pi$
$542$	12.1338	+	1.82887i	0.521190	+	0.0785567i
$543$	1.05124	+	14.0278i	0.0451130	+	0.601992i
$544$	1.32076	+	3.36525i	0.0566272	+	0.144284i
$545$	44.7469	+	56.1109i	1.91675	+	2.40353i
$546$	0.595391	+	3.13916i	0.0254804	+	0.134344i
$547$	−15.9372	+	19.9846i	−0.681424	+	0.854479i	−0.995485	−	0.0949240i	$-0.969739\pi$
$547$	−15.9372	+	19.9846i	−0.681424	+	0.854479i	0.314060	+	0.949403i	$0.398311\pi$
$548$	−9.42602	−	2.90754i	−0.402660	−	0.124204i
$549$	1.24033	−	3.16030i	0.0529358	−	0.134878i
$550$	−50.1967	+	15.4836i	−2.14040	+	0.660224i
$551$	0.196589	−	2.62330i	0.00837499	−	0.111757i
$552$	1.65202	−	7.23797i	0.0703146	−	0.308068i
$553$	4.61354	+	4.60949i	0.196188	+	0.196015i
$554$	−5.37608	−	23.5542i	−0.228408	−	1.00072i
$555$	8.80940	−	1.32780i	0.373938	−	0.0563621i
$556$	−7.59275	−	5.17665i	−0.322004	−	0.219539i
$557$	−13.2139	−	22.8871i	−0.559889	−	0.969756i	−0.997505	−	0.0705940i	$-0.977511\pi$
$557$	−13.2139	−	22.8871i	−0.559889	−	0.969756i	0.437616	−	0.899162i	$-0.355823\pi$
$558$	−3.64081	+	6.30607i	−0.154128	+	0.266957i
$559$	3.35389	−	1.61515i	0.141855	−	0.0683136i
$560$	−10.4826	+	2.81373i	−0.442969	+	0.118902i
$561$	14.4647	+	6.96585i	0.610701	+	0.294098i
$562$	−2.24234	+	1.52880i	−0.0945876	+	0.0644887i
$563$	−20.5870	+	19.1020i	−0.867639	+	0.805051i	−0.982097	−	0.188377i	$-0.939677\pi$
$563$	−20.5870	+	19.1020i	−0.867639	+	0.805051i	0.114458	+	0.993428i	$0.463487\pi$
$564$	−0.154351	+	0.143217i	−0.00649935	+	0.00603052i
$565$	64.6740	−	44.0940i	2.72086	−	1.85505i
$566$	−11.0641	−	5.32821i	−0.465061	−	0.223962i
$567$	−2.00465	+	1.72667i	−0.0841872	+	0.0725134i
$568$	−12.1420	+	5.84729i	−0.509468	+	0.245347i
$569$	−1.63327	+	2.82890i	−0.0684701	+	0.118594i	−0.898228	−	0.439530i	$-0.855145\pi$
$569$	−1.63327	+	2.82890i	−0.0684701	+	0.118594i	0.829758	+	0.558123i	$0.188478\pi$
$570$	8.61921	+	14.9289i	0.361019	+	0.625303i
$571$	−12.1395	−	8.27660i	−0.508024	−	0.346365i	0.282027	−	0.959407i	$-0.408993\pi$
$571$	−12.1395	−	8.27660i	−0.508024	−	0.346365i	−0.790050	+	0.613042i	$0.789946\pi$
$572$	−5.30316	+	0.799323i	−0.221736	+	0.0334214i
$573$	−1.12857	−	4.94458i	−0.0471466	−	0.206563i
$574$	−1.49435	+	13.3154i	−0.0623731	+	0.555773i
$575$	19.5413	−	85.6158i	0.814926	−	3.57043i
$576$	0.0747301	−	0.997204i	0.00311375	−	0.0415502i
$577$	−37.9376	+	11.7022i	−1.57936	+	0.487169i	−0.955655	−	0.294487i	$-0.904851\pi$
$577$	−37.9376	+	11.7022i	−1.57936	+	0.487169i	−0.623709	+	0.781657i	$0.714375\pi$
$578$	−1.43604	+	3.65898i	−0.0597315	+	0.152193i
$579$	−9.79398	−	3.02104i	−0.407024	−	0.125550i
$580$	−1.60121	+	2.00785i	−0.0664865	+	0.0833714i
$581$	−17.6528	−	0.652749i	−0.732362	−	0.0270806i
$582$	−6.18400	−	7.75449i	−0.256335	−	0.321434i
$583$	6.50512	+	16.5748i	0.269415	+	0.686458i
$584$	−0.551205	−	7.35532i	−0.0228090	−	0.304365i
$585$	−4.89876	−	0.738369i	−0.202539	−	0.0305278i
$586$	−9.65407	−	8.95767i	−0.398806	−	0.370038i
$587$	−30.0536			−1.24045			−0.620223	−	0.784425i	$-0.712958\pi$
$587$	−30.0536			−1.24045			−0.620223	+	0.784425i	$0.712958\pi$
$588$	−3.93815	+	5.78714i	−0.162407	+	0.238658i
$589$	30.5985			1.26079
$590$	46.0915	+	42.7666i	1.89755	+	1.76067i
$591$	−11.0974	−	1.67266i	−0.456486	−	0.0688042i
$592$	0.162291	+	2.16562i	0.00667012	+	0.0890065i
$593$	−2.29441	−	5.84606i	−0.0942200	−	0.240069i	0.875992	−	0.482325i	$-0.160208\pi$
$593$	−2.29441	−	5.84606i	−0.0942200	−	0.240069i	−0.970212	+	0.242257i	$0.922112\pi$
$594$	−2.76888	−	3.47206i	−0.113608	−	0.142460i
$595$	34.6985	+	18.3192i	1.42250	+	0.751013i
$596$	−3.67145	+	4.60386i	−0.150389	+	0.188581i
$597$	7.15802	+	2.20796i	0.292958	+	0.0903657i
$598$	3.27553	−	8.34591i	0.133946	−	0.341290i
$599$	17.6643	−	5.44872i	0.721745	−	0.222629i	0.0879443	−	0.996125i	$-0.471970\pi$
$599$	17.6643	−	5.44872i	0.721745	−	0.222629i	0.633800	+	0.773497i	$0.281494\pi$
$600$	0.883960	−	11.7956i	0.0360875	−	0.481555i
$601$	7.77251	−	34.0536i	0.317047	−	1.38907i	−0.525656	−	0.850697i	$-0.676180\pi$
$601$	7.77251	−	34.0536i	0.317047	−	1.38907i	0.842704	−	0.538378i	$-0.180963\pi$
$602$	7.69901	+	2.69020i	0.313788	+	0.109644i
$603$	−0.130869	−	0.573377i	−0.00532942	−	0.0233497i
$604$	16.8509	−	2.53986i	0.685651	−	0.103345i
$605$	−29.5625	−	20.1554i	−1.20189	−	0.819433i
$606$	−0.0692596	−	0.119961i	−0.00281348	−	0.00487309i
$607$	18.0549	−	31.2720i	0.732826	−	1.26929i	−0.222844	−	0.974854i	$-0.571534\pi$
$607$	18.0549	−	31.2720i	0.732826	−	1.26929i	0.955670	−	0.294438i	$-0.0951325\pi$
$608$	−3.78601	+	1.82325i	−0.153543	+	0.0739424i
$609$	0.0626592	+	1.65512i	0.00253908	+	0.0670690i
$610$	12.5479	+	6.04277i	0.508051	+	0.244665i
$611$	−0.210097	+	0.143241i	−0.00849960	+	0.00579493i
$612$	−2.65009	+	2.45893i	−0.107124	+	0.0993962i
$613$	−1.48352	+	1.37650i	−0.0599187	+	0.0555964i	−0.709564	−	0.704641i	$-0.751108\pi$
$613$	−1.48352	+	1.37650i	−0.0599187	+	0.0555964i	0.649645	+	0.760238i	$0.274917\pi$
$614$	−13.2962	+	9.06522i	−0.536592	+	0.365843i
$615$	−18.7179	−	9.01407i	−0.754779	−	0.363482i
$616$	−9.45677	−	6.97299i	−0.381024	−	0.280950i
$617$	39.8231	−	19.1778i	1.60322	−	0.772068i	0.603536	−	0.797336i	$-0.293758\pi$
$617$	39.8231	−	19.1778i	1.60322	−	0.772068i	0.999681	+	0.0252676i	$0.00804379\pi$
$618$	−8.19547	+	14.1950i	−0.329670	+	0.571005i
$619$	15.0312	+	26.0348i	0.604156	+	1.04643i	0.992184	+	0.124781i	$0.0398228\pi$
$619$	15.0312	+	26.0348i	0.604156	+	1.04643i	−0.388029	+	0.921647i	$0.626844\pi$
$620$	−24.6808	−	16.8271i	−0.991205	−	0.675792i
$621$	7.34119	−	1.10651i	0.294592	−	0.0444025i
$622$	−0.411074	−	1.80103i	−0.0164825	−	0.0722148i
$623$	17.6194	−	28.0686i	0.705908	−	1.12454i
$624$	0.268726	−	1.17736i	0.0107576	−	0.0471323i
$625$	4.16806	−	55.6188i	0.166722	−	2.22475i
$626$	−5.96885	+	1.84115i	−0.238563	+	0.0735870i
$627$	−6.81781	+	17.3715i	−0.272277	+	0.693751i
$628$	12.1061	+	3.73425i	0.483088	+	0.149013i
$629$	4.89502	−	6.13816i	0.195177	−	0.244744i
$630$	−6.44893	−	8.72996i	−0.256932	−	0.347810i
$631$	8.13794	+	10.2047i	0.323966	+	0.406241i	0.916968	−	0.398960i	$-0.130629\pi$
$631$	8.13794	+	10.2047i	0.323966	+	0.406241i	−0.593002	+	0.805201i	$0.702057\pi$
$632$	−0.900550	−	2.29456i	−0.0358220	−	0.0912729i
$633$	−0.712105	−	9.50238i	−0.0283036	−	0.377686i
$634$	−4.36063	−	0.657260i	−0.173183	−	0.0261031i
$635$	−50.4003	−	46.7647i	−2.00008	−	1.85580i
$636$	−4.00943			−0.158984
$637$	−5.74439	+	6.20191i	−0.227601	+	0.245729i
$638$	−2.78014			−0.110067
$639$	−9.87907	−	9.16644i	−0.390810	−	0.362619i
$640$	4.05646	+	0.611413i	0.160346	+	0.0241682i
$641$	0.857254	+	11.4393i	0.0338595	+	0.451824i	0.988207	+	0.153125i	$0.0489336\pi$
$641$	0.857254	+	11.4393i	0.0338595	+	0.451824i	−0.954347	+	0.298699i	$0.903447\pi$
$642$	−5.24178	−	13.3558i	−0.206877	−	0.527113i
$643$	−7.73247	−	9.69621i	−0.304939	−	0.382381i	0.605625	−	0.795750i	$-0.292923\pi$
$643$	−7.73247	−	9.69621i	−0.304939	−	0.382381i	−0.910564	+	0.413369i	$0.864352\pi$
$644$	18.0000	−	7.86273i	0.709298	−	0.309835i
$645$	−7.88416	+	9.88643i	−0.310439	+	0.389278i
$646$	14.5165	+	4.47775i	0.571145	+	0.176175i
$647$	−9.75698	+	24.8604i	−0.383586	+	0.977362i	0.600493	+	0.799630i	$0.294971\pi$
$647$	−9.75698	+	24.8604i	−0.383586	+	0.977362i	−0.984079	+	0.177732i	$0.943124\pi$
$648$	0.955573	−	0.294755i	0.0375384	−	0.0115791i
$649$	−5.08663	+	67.8763i	−0.199668	+	2.66438i
$650$	3.17868	−	13.9267i	0.124678	−	0.546250i
$651$	−19.1433	+	2.16545i	−0.750284	+	0.0848709i
$652$	−0.993373	−	4.35225i	−0.0389035	−	0.170447i
$653$	−20.6899	+	3.11850i	−0.809659	+	0.122036i	−0.540809	−	0.841146i	$-0.681882\pi$
$653$	−20.6899	+	3.11850i	−0.809659	+	0.122036i	−0.268850	+	0.963182i	$0.586644\pi$
$654$	−14.4549	−	9.85516i	−0.565230	−	0.385367i
$655$	−13.5107	−	23.4012i	−0.527907	−	0.914362i
$656$	2.53217	−	4.38584i	0.0988645	−	0.171238i
$657$	6.64550	−	3.20030i	0.259266	−	0.124856i
$658$	−0.547421	−	0.103328i	−0.0213407	−	0.00402816i
$659$	0.295827	+	0.142463i	0.0115238	+	0.00554956i	0.439637	−	0.898176i	$-0.355107\pi$
$659$	0.295827	+	0.142463i	0.0115238	+	0.00554956i	−0.428113	+	0.903725i	$0.640821\pi$
$660$	15.0524	−	10.2625i	0.585913	−	0.399469i
$661$	16.5900	−	15.3933i	0.645276	−	0.598729i	−0.288112	−	0.957597i	$-0.593028\pi$
$661$	16.5900	−	15.3933i	0.645276	−	0.598729i	0.933388	+	0.358868i	$0.116837\pi$
$662$	15.8414	−	14.6987i	0.615695	−	0.571282i
$663$	−3.60720	+	2.45935i	−0.140092	+	0.0955132i
$664$	6.01550	+	2.89691i	0.233447	+	0.112422i
$665$	−18.2201	+	41.8111i	−0.706546	+	1.62137i
$666$	−1.95663	+	0.942263i	−0.0758178	+	0.0365119i
$667$	2.32384	−	4.02501i	0.0899795	−	0.155849i
$668$	2.78545	+	4.82455i	0.107772	+	0.186667i
$669$	−4.00626	−	2.73142i	−0.154891	−	0.105603i
$670$	2.38569	−	0.359586i	0.0921674	−	0.0138920i
$671$	3.35492	+	14.6989i	0.129515	+	0.567444i
$672$	2.23960	−	1.40861i	0.0863945	−	0.0543383i
$673$	−1.76717	+	7.74249i	−0.0681195	+	0.298451i	−0.997500	−	0.0706733i	$-0.977485\pi$
$673$	−1.76717	+	7.74249i	−0.0681195	+	0.298451i	0.929380	+	0.369124i	$0.120342\pi$
$674$	−1.97140	+	26.3066i	−0.0759356	+	1.01329i
$675$	11.3032	−	3.48657i	0.435060	−	0.134198i
$676$	−4.21662	+	10.7438i	−0.162178	+	0.413222i
$677$	19.0770	+	5.88447i	0.733188	+	0.226159i	0.638796	−	0.769377i	$-0.279433\pi$
$677$	19.0770	+	5.88447i	0.733188	+	0.226159i	0.0943925	+	0.995535i	$0.469909\pi$
$678$	−11.8967	+	14.9180i	−0.456892	+	0.572924i
$679$	6.78066	−	25.3503i	0.260218	−	0.972857i
$680$	−9.24658	−	11.5948i	−0.354590	−	0.444642i
$681$	5.82977	+	14.8540i	0.223397	+	0.569207i
$682$	−2.41656	−	32.2468i	−0.0925350	−	1.23479i
$683$	−15.1877	−	2.28917i	−0.581140	−	0.0875928i	−0.148108	−	0.988971i	$-0.547318\pi$
$683$	−15.1877	−	2.28917i	−0.581140	−	0.0875928i	−0.433032	+	0.901378i	$0.642556\pi$
$684$	−3.08040	−	2.85819i	−0.117782	−	0.109286i
$685$	40.4660			1.54613
$686$	−18.5064	+	0.716908i	−0.706577	+	0.0273717i
$687$	12.8162			0.488970
$688$	−2.25962	−	2.09662i	−0.0861473	−	0.0799330i
$689$	−4.78788	−	0.721657i	−0.182404	−	0.0274930i
$690$	2.27596	+	30.3706i	0.0866444	+	1.15619i
$691$	−9.34213	−	23.8034i	−0.355391	−	0.905523i	−0.991043	−	0.133546i	$-0.957364\pi$
$691$	−9.34213	−	23.8034i	−0.355391	−	0.905523i	0.635651	−	0.771976i	$-0.280732\pi$
$692$	−9.73939	−	12.2128i	−0.370236	−	0.464261i
$693$	3.03603	−	11.3506i	0.115329	−	0.431173i
$694$	15.2700	−	19.1480i	0.579641	−	0.726847i
$695$	36.0232	+	11.1117i	1.36644	+	0.421491i
$696$	0.228713	−	0.582751i	0.00866935	−	0.0220891i
$697$	−17.4949	+	5.39647i	−0.662668	+	0.204406i
$698$	−0.335822	+	4.48123i	−0.0127110	+	0.169617i
$699$	6.18204	−	27.0853i	0.233826	−	1.02446i
$700$	26.4916	−	16.6620i	1.00129	−	0.629766i
$701$	8.46073	+	37.0689i	0.319557	+	1.40007i	0.838331	+	0.545161i	$0.183531\pi$
$701$	8.46073	+	37.0689i	0.319557	+	1.40007i	−0.518774	+	0.854911i	$0.673611\pi$
$702$	1.19415	−	0.179990i	0.0450705	−	0.00679328i
$703$	7.54009	+	5.14075i	0.284380	+	0.193887i
$704$	2.22047	+	3.84596i	0.0836870	+	0.144950i
$705$	0.431887	−	0.748050i	0.0162658	−	0.0281732i
$706$	11.7701	−	5.66817i	0.442973	−	0.213324i
$707$	0.146408	−	0.335973i	0.00550622	−	0.0126356i
$708$	−13.8092	−	6.65018i	−0.518983	−	0.249929i
$709$	−35.4271	+	24.1538i	−1.33049	+	0.907115i	−0.999335	−	0.0364603i	$-0.988392\pi$
$709$	−35.4271	+	24.1538i	−1.33049	+	0.907115i	−0.331158	+	0.943575i	$0.607439\pi$
$710$	40.5267	−	37.6033i	1.52094	−	1.41123i
$711$	1.80694	−	1.67660i	0.0677656	−	0.0628773i
$712$	−10.3494	+	7.05609i	−0.387860	+	0.264438i
$713$	48.7060	+	23.4556i	1.82405	+	0.878418i
$714$	−9.39882	−	1.77407i	−0.351742	−	0.0663930i
$715$	19.8220	−	9.54578i	0.741302	−	0.356992i
$716$	4.20388	−	7.28134i	0.157107	−	0.272116i
$717$	−8.18985	−	14.1852i	−0.305855	−	0.529757i
$718$	−19.2949	−	13.1550i	−0.720078	−	0.490941i
$719$	16.4270	−	2.47597i	0.612623	−	0.0923380i	0.164600	−	0.986360i	$-0.447367\pi$
$719$	16.4270	−	2.47597i	0.612623	−	0.0923380i	0.448022	+	0.894022i	$0.352129\pi$
$720$	0.912843	+	3.99943i	0.0340197	+	0.149050i
$721$	−43.0915	+	4.87444i	−1.60481	+	0.181534i
$722$	0.298597	−	1.30824i	0.0111126	−	0.0486876i
$723$	1.10719	−	14.7745i	0.0411770	−	0.549469i
$724$	13.4422	−	4.14637i	0.499575	−	0.154099i
$725$	2.70538	−	6.89319i	0.100475	−	0.256007i
$726$	8.33440	+	2.57082i	0.309318	+	0.0954121i
$727$	4.16612	−	5.22415i	0.154513	−	0.193753i	−0.698550	−	0.715561i	$-0.746171\pi$
$727$	4.16612	−	5.22415i	0.154513	−	0.193753i	0.853063	+	0.521808i	$0.174742\pi$
$728$	2.92797	−	1.27899i	0.108518	−	0.0474026i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	11.0546	+	28.1666i	0.409148	+	1.04249i
$731$	0.832766	+	11.1125i	0.0308009	+	0.411010i
$732$	−3.35706	−	0.505996i	−0.124081	−	0.0187021i
$733$	−23.3484	−	21.6642i	−0.862393	−	0.800184i	0.118859	−	0.992911i	$-0.462076\pi$
$733$	−23.3484	−	21.6642i	−0.862393	−	0.800184i	−0.981252	+	0.192727i	$0.938267\pi$
$734$	−7.61607			−0.281114
$735$	8.44004	−	27.4476i	0.311316	−	1.01242i
$736$	−7.42411			−0.273656
$737$	1.91459	+	1.77648i	0.0705249	+	0.0654376i
$738$	5.00777	+	0.754799i	0.184338	+	0.0277845i
$739$	1.72262	+	22.9867i	0.0633675	+	0.845581i	0.934825	+	0.355109i	$0.115556\pi$
$739$	1.72262	+	22.9867i	0.0633675	+	0.845581i	−0.871457	+	0.490472i	$0.836825\pi$
$740$	−3.25479	−	8.29306i	−0.119648	−	0.304859i
$741$	−3.16403	−	3.96756i	−0.116233	−	0.145752i
$742$	−6.30298	−	8.53237i	−0.231389	−	0.313233i
$743$	−15.4177	+	19.3332i	−0.565620	+	0.709265i	−0.979586	−	0.201028i	$-0.935572\pi$
$743$	−15.4177	+	19.3332i	−0.565620	+	0.709265i	0.413966	+	0.910292i	$0.364143\pi$
$744$	6.95812	+	2.14630i	0.255097	+	0.0786870i
$745$	8.82536	−	22.4867i	0.323336	−	0.823847i
$746$	15.1273	−	4.66615i	0.553849	−	0.170840i
$747$	−0.498950	+	6.65803i	−0.0182556	+	0.243605i
$748$	3.57249	−	15.6521i	0.130623	−	0.572298i
$749$	20.1819	−	32.1508i	0.737432	−	1.17476i
$750$	6.23354	+	27.3109i	0.227617	+	0.997254i
$751$	−35.6836	+	5.37843i	−1.30211	+	0.196262i	−0.763234	−	0.646122i	$-0.776390\pi$
$751$	−35.6836	+	5.37843i	−1.30211	+	0.196262i	−0.538878	+	0.842384i	$0.681152\pi$
$752$	0.173972	+	0.118612i	0.00634412	+	0.00432535i
$753$	15.1193	+	26.1874i	0.550978	+	0.954323i
$754$	0.378008	−	0.654729i	0.0137662	−	0.0238438i
$755$	−62.9847	+	30.3318i	−2.29225	+	1.10389i
$756$	2.12946	+	1.57016i	0.0774476	+	0.0571063i
$757$	21.7800	+	10.4887i	0.791609	+	0.381219i	0.785578	−	0.618763i	$-0.212366\pi$
$757$	21.7800	+	10.4887i	0.791609	+	0.381219i	0.00603138	+	0.999982i	$0.498080\pi$
$758$	−10.0443	+	6.84807i	−0.364825	+	0.248733i
$759$	−24.1687	+	22.4253i	−0.877268	+	0.813986i
$760$	12.6367	−	11.7251i	0.458380	−	0.425314i
$761$	23.3924	−	15.9486i	0.847972	−	0.578138i	−0.0595103	−	0.998228i	$-0.518954\pi$
$761$	23.3924	−	15.9486i	0.847972	−	0.578138i	0.907482	+	0.420090i	$0.138002\pi$
$762$	15.1002	+	7.27188i	0.547023	+	0.263432i
$763$	−1.75106	−	46.2537i	−0.0633926	−	1.67450i
$764$	−4.56948	+	2.20055i	−0.165318	+	0.0796130i
$765$	7.41518	−	12.8435i	0.268096	−	0.464357i
$766$	−16.2161	−	28.0871i	−0.585912	−	1.01483i
$767$	−15.2934	−	10.4269i	−0.552213	−	0.376493i
$768$	−0.988831	+	0.149042i	−0.0356814	+	0.00537810i
$769$	−4.74774	−	20.8012i	−0.171208	−	0.750111i	−0.985503	−	0.169659i	$-0.945733\pi$
$769$	−4.74774	−	20.8012i	−0.171208	−	0.750111i	0.814295	−	0.580451i	$-0.197124\pi$
$770$	45.5023	+	15.8995i	1.63979	+	0.572978i
$771$	−6.96063	+	30.4965i	−0.250681	+	1.09831i
$772$	−0.765933	+	10.2207i	−0.0275665	+	0.367850i
$773$	6.98794	−	2.15549i	0.251339	−	0.0775277i	−0.166526	−	0.986037i	$-0.553255\pi$
$773$	6.98794	−	2.15549i	0.251339	−	0.0775277i	0.417864	+	0.908509i	$0.362779\pi$
$774$	1.12616	−	2.86940i	0.0404789	−	0.103139i
$775$	82.3056	+	25.3879i	2.95650	+	0.911961i
$776$	−6.18400	+	7.75449i	−0.221993	+	0.278370i
$777$	−5.08110	−	2.68258i	−0.182283	−	0.0962371i
$778$	−17.1086	−	21.4535i	−0.613373	−	0.769145i
$779$	−7.77486	−	19.8100i	−0.278563	−	0.709768i
$780$	0.370220	+	4.94024i	0.0132560	+	0.176889i
$781$	59.1804	+	8.92000i	2.11764	+	0.319183i
$782$	19.6746	+	18.2553i	0.703561	+	0.652809i
$783$	0.626026			0.0223723
$784$	6.51836	+	2.55166i	0.232799	+	0.0911306i
$785$	−51.9717			−1.85495
$786$	4.82856	+	4.48025i	0.172229	+	0.159805i
$787$	−20.0441	−	3.02116i	−0.714494	−	0.107693i	−0.218272	−	0.975888i	$-0.570042\pi$
$787$	−20.0441	−	3.02116i	−0.714494	−	0.107693i	−0.496222	+	0.868195i	$0.665280\pi$
$788$	0.838677	+	11.1914i	0.0298766	+	0.398676i
$789$	5.18236	+	13.2044i	0.184497	+	0.470091i
$790$	6.30470	+	7.90584i	0.224311	+	0.281277i
$791$	−50.4488	−	1.86545i	−1.79375	−	0.0663277i
$792$	−2.76888	+	3.47206i	−0.0983877	+	0.123374i
$793$	−3.91778	−	1.20847i	−0.139124	−	0.0429142i
$794$	0.772298	−	1.96778i	0.0274078	−	0.0698340i
$795$	15.7171	−	4.84808i	0.557428	−	0.171944i
$796$	0.559790	−	7.46987i	0.0198412	−	0.264763i
$797$	−4.51894	+	19.7988i	−0.160069	+	0.701309i	0.829650	+	0.558284i	$0.188540\pi$
$797$	−4.51894	+	19.7988i	−0.160069	+	0.701309i	−0.989719	+	0.143025i	$0.954317\pi$
$798$	1.23995	−	11.0485i	0.0438937	−	0.391113i
$799$	−0.169384	−	0.742119i	−0.00599237	−	0.0262543i
$800$	−11.6966	+	1.76298i	−0.413537	+	0.0623307i
$801$	−10.3494	−	7.05609i	−0.365678	−	0.249315i
$802$	−4.12754	−	7.14911i	−0.145749	−	0.252444i
$803$	−16.3780	+	28.3676i	−0.577969	+	1.00107i
$804$	−0.529880	+	0.255177i	−0.0186874	+	0.00899939i
$805$	−61.0530	+	52.5871i	−2.15184	+	1.85345i
$806$	7.92276	+	3.81540i	0.279067	+	0.134392i
$807$	−1.83448	+	1.25073i	−0.0645768	+	0.0440277i
$808$	−0.101542	+	0.0942170i	−0.00357223	+	0.00331454i
$809$	−11.8563	+	11.0010i	−0.416845	+	0.386776i	−0.860524	−	0.509410i	$-0.829864\pi$
$809$	−11.8563	+	11.0010i	−0.416845	+	0.386776i	0.443679	+	0.896186i	$0.353673\pi$
$810$	−3.38946	+	2.31090i	−0.119094	+	0.0811966i
$811$	−13.1089	−	6.31293i	−0.460317	−	0.221677i	0.189329	−	0.981914i	$-0.439369\pi$
$811$	−13.1089	−	6.31293i	−0.460317	−	0.221677i	−0.649646	+	0.760237i	$0.725083\pi$
$812$	1.59968	−	0.429388i	0.0561379	−	0.0150686i
$813$	11.0556	−	5.32411i	0.387738	−	0.186725i
$814$	4.82217	−	8.35225i	0.169017	−	0.292746i
$815$	9.15665	+	15.8598i	0.320744	+	0.555544i
$816$	2.98698	+	2.03649i	0.104565	+	0.0712913i
$817$	−12.8084	+	1.93056i	−0.448109	+	0.0675416i
$818$	2.14022	+	9.37692i	0.0748311	+	0.327856i
$819$	2.26029	+	2.25830i	0.0789808	+	0.0789114i
$820$	−4.62294	+	20.2544i	−0.161440	+	0.707315i
$821$	3.05140	−	40.7180i	0.106494	−	1.42107i	−0.646435	−	0.762969i	$-0.723741\pi$
$821$	3.05140	−	40.7180i	0.106494	−	1.42107i	0.752930	−	0.658101i	$-0.228640\pi$
$822$	−9.42602	+	2.90754i	−0.328770	+	0.101412i
$823$	11.5891	−	29.5286i	0.403972	−	1.02930i	−0.573681	−	0.819079i	$-0.694485\pi$
$823$	11.5891	−	29.5286i	0.403972	−	1.02930i	0.977653	−	0.210225i	$-0.0674197\pi$
$824$	15.6627	+	4.83131i	0.545637	+	0.168307i
$825$	−32.7522	+	41.0700i	−1.14029	+	1.42987i
$826$	−7.55656	−	39.8414i	−0.262926	−	1.38626i
$827$	−17.1915	−	21.5575i	−0.597809	−	0.749628i	0.387226	−	0.921985i	$-0.373433\pi$
$827$	−17.1915	−	21.5575i	−0.597809	−	0.749628i	−0.985035	+	0.172357i	$0.944862\pi$
$828$	−2.71233	−	6.91091i	−0.0942600	−	0.240171i
$829$	−1.67500	−	22.3513i	−0.0581752	−	0.776294i	−0.947650	−	0.319310i	$-0.896549\pi$
$829$	−1.67500	−	22.3513i	−0.0581752	−	0.776294i	0.889475	−	0.456984i	$-0.151070\pi$
$830$	−27.0838	−	4.08222i	−0.940092	−	0.141696i
$831$	−17.7105	−	16.4329i	−0.614369	−	0.570051i
$832$	−1.20764			−0.0418675
$833$	−10.9999	−	22.7903i	−0.381125	−	0.789637i
$834$	−9.18954			−0.318208
$835$	−16.7528	−	15.5443i	−0.579753	−	0.537932i
$836$	18.4531	+	2.78135i	0.638212	+	0.0961950i
$837$	0.544156	+	7.26126i	0.0188088	+	0.250986i
$838$	−6.12761	−	15.6129i	−0.211675	−	0.539338i
$839$	−22.2781	−	27.9359i	−0.769127	−	0.964455i	0.230836	−	0.972993i	$-0.425854\pi$
$839$	−22.2781	−	27.9359i	−0.769127	−	0.964455i	−0.999964	+	0.00853769i	$0.997282\pi$
$840$	−7.07606	+	8.22985i	−0.244147	+	0.283957i
$841$	−17.8369	+	22.3667i	−0.615064	+	0.771266i
$842$	−0.336166	−	0.103694i	−0.0115851	−	0.00357352i
$843$	−0.991506	+	2.52632i	−0.0341493	+	0.0870109i
$844$	−9.10568	+	2.80873i	−0.313430	+	0.0966805i
$845$	3.53824	−	47.2145i	0.121719	−	1.62423i
$846$	−0.0468539	+	0.205280i	−0.00161087	+	0.00705768i
$847$	7.63108	+	21.7776i	0.262207	+	0.748289i
$848$	0.892183	+	3.90891i	0.0306377	+	0.134232i
$849$	−12.1431	+	1.83028i	−0.416751	+	0.0628151i
$850$	35.3321	+	24.0890i	1.21188	+	0.826246i
$851$	8.06145	+	13.9628i	0.276343	+	0.478640i
$852$	−6.73832	+	11.6711i	−0.230851	+	0.399846i
$853$	−15.9066	+	7.66021i	−0.544631	+	0.262281i	−0.685906	−	0.727690i	$-0.740594\pi$
$853$	−15.9066	+	7.66021i	−0.544631	+	0.262281i	0.141275	+	0.989970i	$0.454880\pi$
$854$	−4.20063	−	7.93952i	−0.143742	−	0.271685i
$855$	15.5313	+	7.47947i	0.531159	+	0.255793i
$856$	−11.8546	+	8.08231i	−0.405181	+	0.276248i
$857$	−19.6538	+	18.2360i	−0.671360	+	0.622931i	−0.940349	−	0.340212i	$-0.889501\pi$
$857$	−19.6538	+	18.2360i	−0.671360	+	0.622931i	0.268989	+	0.963143i	$0.413311\pi$
$858$	−3.93140	+	3.64781i	−0.134216	+	0.124534i
$859$	−16.9759	+	11.5740i	−0.579211	+	0.394900i	−0.817188	−	0.576371i	$-0.804468\pi$
$859$	−16.9759	+	11.5740i	−0.579211	+	0.394900i	0.237977	+	0.971271i	$0.423516\pi$
$860$	11.3929	+	5.48655i	0.388496	+	0.187090i
$861$	6.26612	+	11.8435i	0.213549	+	0.403624i
$862$	−8.77299	+	4.22485i	−0.298809	+	0.143899i
$863$	−5.06145	+	8.76669i	−0.172294	+	0.298422i	−0.939221	−	0.343312i	$-0.888451\pi$
$863$	−5.06145	+	8.76669i	−0.172294	+	0.298422i	0.766928	+	0.641734i	$0.221785\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	52.9460	+	36.0980i	1.80022	+	1.22737i
$866$	25.8737	−	3.89984i	0.879225	−	0.132522i
$867$	0.874661	+	3.83214i	0.0297050	+	0.130146i
$868$	6.37094	+	18.1815i	0.216244	+	0.617119i
$869$	−2.43587	+	10.6723i	−0.0826313	+	0.362032i
$870$	−0.191917	+	2.56095i	−0.00650659	+	0.0868245i
$871$	−0.678688	+	0.209347i	−0.0229965	+	0.00709347i
$872$	−6.39156	+	16.2854i	−0.216446	+	0.551494i
$873$	−9.47771	−	2.92349i	−0.320772	−	0.0989451i
$874$	−19.4512	+	24.3910i	−0.657946	+	0.825038i
$875$	−48.3203	+	56.1992i	−1.63353	+	1.89988i
$876$	−4.59883	−	5.76675i	−0.155380	−	0.194840i
$877$	−19.1895	−	48.8939i	−0.647982	−	1.65103i	−0.754165	−	0.656685i	$-0.771958\pi$
$877$	−19.1895	−	48.8939i	−0.647982	−	1.65103i	0.106183	−	0.994347i	$-0.466137\pi$
$878$	0.0269711	+	0.359904i	0.000910230	+	0.0121462i
$879$	−13.0226	−	1.96284i	−0.439242	−	0.0662050i
$880$	−13.3547	−	12.3914i	−0.450187	−	0.417713i
$881$	−4.83214			−0.162799			−0.0813994	−	0.996682i	$-0.525939\pi$
$881$	−4.83214			−0.162799			−0.0813994	+	0.996682i	$0.525939\pi$
$882$	0.00615617	+	7.00000i	0.000207289	+	0.235702i
$883$	32.0773			1.07949			0.539744	−	0.841829i	$-0.318521\pi$
$883$	32.0773			1.07949			0.539744	+	0.841829i	$0.318521\pi$
$884$	3.20037	+	2.96951i	0.107640	+	0.0998753i
$885$	62.1738	+	9.37120i	2.08995	+	0.315009i
$886$	1.40994	+	18.8144i	0.0473680	+	0.632082i
$887$	11.4661	+	29.2151i	0.384994	+	0.980948i	0.983674	+	0.179960i	$0.0575968\pi$
$887$	11.4661	+	29.2151i	0.384994	+	0.980948i	−0.598680	+	0.800988i	$0.704308\pi$
$888$	1.35403	+	1.69790i	0.0454383	+	0.0569778i
$889$	8.26298	+	43.5660i	0.277132	+	1.46116i
$890$	32.0379	−	40.1742i	1.07391	−	1.34664i
$891$	−4.24363	−	1.30899i	−0.142167	−	0.0438527i
$892$	−1.77146	+	4.51361i	−0.0593129	+	0.151127i
$893$	0.845494	−	0.260800i	0.0282934	−	0.00872736i
$894$	−0.440052	+	5.87209i	−0.0147175	+	0.196392i
$895$	−7.67497	+	33.6263i	−0.256546	+	1.12400i
$896$	−1.87165	−	1.87001i	−0.0625275	−	0.0624725i
$897$	−1.99505	−	8.74088i	−0.0666128	−	0.291850i
$898$	19.0994	−	2.87877i	0.637354	−	0.0960656i
$899$	3.76640	+	2.56789i	0.125616	+	0.0856438i
$900$	−5.91435	−	10.2440i	−0.197145	−	0.341465i
$901$	7.24735	−	12.5528i	0.241444	−	0.418194i
$902$	−20.2631	+	9.75820i	−0.674688	+	0.324912i
$903$	7.87667	−	2.11426i	0.262119	−	0.0703581i
$904$	17.1913	+	8.27889i	0.571774	+	0.275352i
$905$	−47.6801	+	32.5078i	−1.58494	+	1.08059i
$906$	12.4921	−	11.5910i	0.415021	−	0.385084i
$907$	5.44564	−	5.05282i	0.180819	−	0.167776i	−0.584570	−	0.811343i	$-0.698737\pi$
$907$	5.44564	−	5.05282i	0.180819	−	0.167776i	0.765390	+	0.643567i	$0.222546\pi$
$908$	13.1844	−	8.98894i	0.437538	−	0.298308i
$909$	−0.124801	−	0.0601012i	−0.00413940	−	0.00199343i
$910$	−9.93120	+	8.55409i	−0.329216	+	0.283565i
$911$	12.5454	−	6.04153i	0.415646	−	0.200165i	−0.214360	−	0.976755i	$-0.568767\pi$
$911$	12.5454	−	6.04153i	0.415646	−	0.200165i	0.630006	+	0.776590i	$0.283052\pi$
$912$	−2.10108	+	3.63917i	−0.0695736	+	0.120505i
$913$	−14.8254	−	25.6783i	−0.490649	−	0.849828i
$914$	−0.895874	−	0.610797i	−0.0296329	−	0.0202034i
$915$	13.7716	−	2.07574i	0.455275	−	0.0686217i
$916$	−2.85188	−	12.4949i	−0.0942288	−	0.412843i
$917$	−1.94363	+	17.3187i	−0.0641844	+	0.571912i
$918$	−0.804447	+	3.52451i	−0.0265507	+	0.116326i
$919$	−1.29262	+	17.2488i	−0.0426395	+	0.568984i	0.934442	+	0.356117i	$0.115899\pi$
$919$	−1.29262	+	17.2488i	−0.0426395	+	0.568984i	−0.977081	+	0.212868i	$0.931720\pi$
$920$	29.1027	−	8.97700i	0.959488	−	0.295963i
$921$	−5.87925	+	14.9801i	−0.193728	+	0.493610i
$922$	20.0052	+	6.17080i	0.658838	+	0.203224i
$923$	−10.1473	+	12.7243i	−0.334002	+	0.418825i
$924$	−11.7416	−	0.434169i	−0.386270	−	0.0142831i
$925$	16.0164	+	20.0840i	0.526617	+	0.660356i
$926$	6.19647	+	15.7883i	0.203629	+	0.518837i
$927$	1.22490	+	16.3451i	0.0402309	+	0.536844i
$928$	−0.619034	−	0.0933044i	−0.0203208	−	0.00306287i
$929$	−4.13607	−	3.83771i	−0.135700	−	0.125911i	0.609403	−	0.792861i	$-0.291409\pi$
$929$	−4.13607	−	3.83771i	−0.135700	−	0.125911i	−0.745103	+	0.666949i	$0.767600\pi$
$930$	−29.8713			−0.979517
$931$	25.4613	−	14.7299i	0.834460	−	0.482754i
$932$	−27.7818			−0.910024
$933$	−1.35420	−	1.25652i	−0.0443346	−	0.0411365i
$934$	23.9138	+	3.60442i	0.782482	+	0.117940i
$935$	4.92177	+	65.6765i	0.160959	+	2.14785i
$936$	−0.441202	−	1.12416i	−0.0144211	−	0.0367444i
$937$	29.3136	+	36.7581i	0.957633	+	1.20083i	0.979576	+	0.201075i	$0.0644434\pi$
$937$	29.3136	+	36.7581i	0.957633	+	1.20083i	−0.0219429	+	0.999759i	$0.506985\pi$
$938$	−1.37603	−	0.726477i	−0.0449288	−	0.0237203i
$939$	−3.89454	+	4.88360i	−0.127093	+	0.159370i
$940$	−0.825399	−	0.254602i	−0.0269215	−	0.00830420i
$941$	−8.46154	+	21.5596i	−0.275838	+	0.702824i	0.724076	+	0.689720i	$0.242266\pi$
$941$	−8.46154	+	21.5596i	−0.275838	+	0.702824i	−0.999914	+	0.0131040i	$0.995829\pi$
$942$	12.1061	−	3.73425i	0.394439	−	0.121668i
$943$	2.80971	−	37.4930i	0.0914968	−	1.22094i
$944$	−3.41060	+	14.9428i	−0.111006	+	0.486348i
$945$	−10.2461	−	3.58022i	−0.333306	−	0.116464i
$946$	3.04611	+	13.3459i	0.0990377	+	0.433912i
$947$	3.74061	−	0.563807i	0.121554	−	0.0183213i	−0.0879837	−	0.996122i	$-0.528042\pi$
$947$	3.74061	−	0.563807i	0.121554	−	0.0183213i	0.209537	+	0.977801i	$0.432804\pi$
$948$	−2.03664	−	1.38856i	−0.0661471	−	0.0450983i
$949$	−4.45376	−	7.71413i	−0.144575	−	0.250411i
$950$	−24.8530	+	43.0467i	−0.806339	+	1.39662i
$951$	−3.97317	+	1.91338i	−0.128839	+	0.0620456i
$952$	0.361842	+	9.55794i	0.0117274	+	0.309775i
$953$	15.9366	+	7.67467i	0.516237	+	0.248607i	0.673815	−	0.738900i	$-0.264654\pi$
$953$	15.9366	+	7.67467i	0.516237	+	0.248607i	−0.157578	+	0.987507i	$0.550369\pi$
$954$	−3.31275	+	2.25859i	−0.107254	+	0.0731247i
$955$	15.2517	−	14.1515i	0.493532	−	0.457931i
$956$	−12.0072	+	11.1410i	−0.388339	+	0.360326i
$957$	−2.29706	+	1.56611i	−0.0742534	+	0.0506251i
$958$	28.1326	+	13.5479i	0.908923	+	0.437714i
$959$	−21.0055	−	15.4885i	−0.678304	−	0.500150i
$960$	3.69603	−	1.77991i	0.119289	−	0.0574464i
$961$	−11.0110	+	19.0717i	−0.355194	+	0.615215i
$962$	1.31132	+	2.27127i	0.0422785	+	0.0732285i
$963$	−11.8546	−	8.08231i	−0.382008	−	0.260449i
$964$	−14.6504	+	2.20820i	−0.471859	+	0.0711213i
$965$	−9.35603	−	40.9915i	−0.301181	−	1.31956i
$966$	10.4430	−	16.6362i	0.335999	−	0.535262i
$967$	5.35572	−	23.4649i	0.172228	−	0.754581i	−0.812850	−	0.582473i	$-0.802085\pi$
$967$	5.35572	−	23.4649i	0.172228	−	0.754581i	0.985078	−	0.172108i	$-0.0550578\pi$
$968$	0.651787	−	8.69750i	0.0209492	−	0.279548i
$969$	14.5165	−	4.47775i	0.466338	−	0.143846i
$970$	14.8650	−	37.8753i	0.477285	−	1.21610i
$971$	−4.63642	−	1.43015i	−0.148790	−	0.0458955i	0.219466	−	0.975620i	$-0.429569\pi$
$971$	−4.63642	−	1.43015i	−0.148790	−	0.0458955i	−0.368255	+	0.929725i	$0.620045\pi$
$972$	0.623490	−	0.781831i	0.0199984	−	0.0250773i
$973$	−14.4463	−	19.5560i	−0.463127	−	0.626937i
$974$	9.64466	+	12.0940i	0.309035	+	0.387517i
$975$	−5.21884	−	13.2974i	−0.167137	−	0.425858i
$976$	0.253707	+	3.38549i	0.00812097	+	0.108367i
$977$	27.4297	+	4.13436i	0.877554	+	0.132270i	0.572342	−	0.820015i	$-0.306035\pi$
$977$	27.4297	+	4.13436i	0.877554	+	0.132270i	0.305211	+	0.952285i	$0.401273\pi$
$978$	−3.27247	−	3.03641i	−0.104642	−	0.0970937i
$979$	55.6267			1.77784
$980$	−28.6375	−	2.12076i	−0.914793	−	0.0677453i
$981$	−17.4948			−0.558566
$982$	−4.18286	−	3.88113i	−0.133481	−	0.123852i
$983$	39.6548	+	5.97700i	1.26479	+	0.190637i	0.746973	−	0.664854i	$-0.231506\pi$
$983$	39.6548	+	5.97700i	1.26479	+	0.190637i	0.517818	+	0.855491i	$0.326744\pi$
$984$	−0.378458	−	5.05017i	−0.0120648	−	0.160994i
$985$	−16.8199	−	42.8564i	−0.535926	−	1.36552i
$986$	1.41107	+	1.76942i	0.0449376	+	0.0563499i
$987$	−0.510508	+	0.223000i	−0.0162496	+	0.00709815i
$988$	−3.16403	+	3.96756i	−0.100661	+	0.126225i
$989$	−21.8680	−	6.74538i	−0.695362	−	0.214491i
$990$	6.65577	−	16.9586i	0.211534	−	0.538980i
$991$	−17.0155	+	5.24859i	−0.540516	+	0.166727i	−0.552979	−	0.833195i	$-0.686509\pi$
$991$	−17.0155	+	5.24859i	−0.540516	+	0.166727i	0.0124631	+	0.999922i	$0.496033\pi$
$992$	0.544156	−	7.26126i	0.0172770	−	0.230545i
$993$	4.80874	−	21.0685i	0.152601	−	0.668587i
$994$	−35.4299	+	4.00777i	−1.12377	+	0.127119i
$995$	6.83795	+	29.9590i	0.216777	+	0.949764i
$996$	6.60213	−	0.995110i	0.209196	−	0.0315313i
$997$	−11.1067	−	7.57242i	−0.351753	−	0.239821i	0.374533	−	0.927213i	$-0.377803\pi$
$997$	−11.1067	−	7.57242i	−0.351753	−	0.239821i	−0.726286	+	0.687392i	$0.758755\pi$
$998$	−7.78499	−	13.4840i	−0.246429	−	0.426828i
$999$	−1.08585	+	1.88074i	−0.0343547	+	0.0595041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.205.1	yes	24
3.2	odd	2		882.2.z.a.793.2		24
49.11	even	21	inner	294.2.m.b.109.1	✓	24
147.11	odd	42		882.2.z.a.109.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.109.1	✓	24	49.11	even	21	inner
294.2.m.b.205.1	yes	24	1.1	even	1	trivial
882.2.z.a.109.2		24	147.11	odd	42
882.2.z.a.793.2		24	3.2	odd	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(-1.49873 - 3.81871i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-0.683647 + 2.55590i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})\)	\(q+(-0.733052 - 0.680173i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(-1.49873 - 3.81871i) q^{5} +(0.623490 + 0.781831i) q^{6} +(-0.683647 + 2.55590i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.955573 + 0.294755i) q^{9} +(-1.49873 + 3.81871i) q^{10} +(-4.24363 + 1.30899i) q^{11} +(0.0747301 - 0.997204i) q^{12} +(0.268726 - 1.17736i) q^{13} +(2.23960 - 1.40861i) q^{14} +(0.912843 + 3.99943i) q^{15} +(-0.988831 + 0.149042i) q^{16} +(2.98698 + 2.03649i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.10108 + 3.63917i) q^{19} +(3.69603 - 1.77991i) q^{20} +(1.05695 - 2.42546i) q^{21} +(4.00114 + 1.92685i) q^{22} +(-6.13408 + 4.18215i) q^{23} +(-0.733052 + 0.680173i) q^{24} +(-8.67106 + 8.04556i) q^{25} +(-0.997801 + 0.680290i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-2.59984 - 0.490733i) q^{28} +(-0.564030 + 0.271623i) q^{29} +(2.05114 - 3.55268i) q^{30} +(-3.64081 - 6.30607i) q^{31} +(0.826239 + 0.563320i) q^{32} +(4.39133 - 0.661887i) q^{33} +(-0.804447 - 3.52451i) q^{34} +(10.7848 - 1.21996i) q^{35} +(-0.222521 + 0.974928i) q^{36} +(0.162291 - 2.16562i) q^{37} +(4.01547 - 1.23861i) q^{38} +(-0.441202 + 1.12416i) q^{39} +(-3.92003 - 1.20917i) q^{40} +(-3.15756 + 3.95945i) q^{41} +(-2.42453 + 1.05908i) q^{42} +(1.92190 + 2.40998i) q^{43} +(-1.62245 - 4.13395i) q^{44} +(-0.306564 - 4.09081i) q^{45} +(7.34119 + 1.10651i) q^{46} +(-0.154351 - 0.143217i) q^{47} +1.00000 q^{48} +(-6.06525 - 3.49467i) q^{49} +11.8287 q^{50} +(-2.65009 - 2.45893i) q^{51} +(1.19415 + 0.179990i) q^{52} +(-0.299625 - 3.99822i) q^{53} +(0.365341 + 0.930874i) q^{54} +(11.3587 + 14.2434i) q^{55} +(1.57204 + 2.12807i) q^{56} +(2.62000 - 3.28538i) q^{57} +(0.598214 + 0.184524i) q^{58} +(5.59962 - 14.2676i) q^{59} +(-3.92003 + 1.20917i) q^{60} +(0.253707 - 3.38549i) q^{61} +(-1.62031 + 7.09906i) q^{62} +(-1.40664 + 2.24084i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-4.89876 + 0.738369i) q^{65} +(-3.66927 - 2.50167i) q^{66} +(-0.294061 - 0.509329i) q^{67} +(-1.80757 + 3.13081i) q^{68} +(6.68889 - 3.22120i) q^{69} +(-8.73563 - 6.44125i) q^{70} +(-12.1420 - 5.84729i) q^{71} +(0.826239 - 0.563320i) q^{72} +(5.40695 - 5.01692i) q^{73} +(-1.59196 + 1.47713i) q^{74} +(9.77334 - 6.66335i) q^{75} +(-3.78601 - 1.82325i) q^{76} +(-0.444495 - 11.7412i) q^{77} +(1.08805 - 0.523977i) q^{78} +(1.23248 - 2.13472i) q^{79} +(2.05114 + 3.55268i) q^{80} +(0.826239 + 0.563320i) q^{81} +(5.00777 - 0.754799i) q^{82} +(1.48571 + 6.50930i) q^{83} +(2.49766 + 0.872738i) q^{84} +(3.30007 - 14.4585i) q^{85} +(0.230354 - 3.07387i) q^{86} +(0.598214 - 0.184524i) q^{87} +(-1.62245 + 4.13395i) q^{88} +(-11.9694 - 3.69208i) q^{89} +(-2.55773 + 3.20729i) q^{90} +(2.82551 + 1.49174i) q^{91} +(-4.62885 - 5.80440i) q^{92} +(2.66028 + 6.77827i) q^{93} +(0.0157351 + 0.209971i) q^{94} +(17.0459 + 2.56925i) q^{95} +(-0.733052 - 0.680173i) q^{96} -9.91836 q^{97} +(2.06917 + 6.68719i) q^{98} -4.44093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more