LMFDB - Embedded newform 507.2.q.b.490.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			490.11
Character	$\chi$	$=$	507.490
Dual form			507.2.q.b.328.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222298 + 1.08889i) q^{2} +(0.987050 + 0.160411i) q^{3} +(0.703694 - 0.299816i) q^{4} +(2.41330 - 0.594826i) q^{5} +(0.0447495 + 1.11045i) q^{6} +(-0.108935 + 0.229576i) q^{7} +(1.74553 + 2.52884i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(0.222298 + 1.08889i) q^{2} +(0.987050 + 0.160411i) q^{3} +(0.703694 - 0.299816i) q^{4} +(2.41330 - 0.594826i) q^{5} +(0.0447495 + 1.11045i) q^{6} +(-0.108935 + 0.229576i) q^{7} +(1.74553 + 2.52884i) q^{8} +(0.948536 + 0.316668i) q^{9} +(1.18417 + 2.49559i) q^{10} +(-3.57428 + 1.19327i) q^{11} +(0.742675 - 0.183053i) q^{12} +(-3.29356 + 1.46714i) q^{13} +(-0.274199 - 0.0675841i) q^{14} +(2.47747 - 0.200002i) q^{15} +(-1.30587 + 1.35955i) q^{16} +(2.03797 - 4.29493i) q^{17} +(-0.133958 + 1.10325i) q^{18} +(0.777804 + 1.34720i) q^{19} +(1.51989 - 1.14212i) q^{20} +(-0.144351 + 0.209129i) q^{21} +(-2.09390 - 3.62674i) q^{22} +(3.76314 - 6.51795i) q^{23} +(1.31727 + 2.77610i) q^{24} +(1.04294 - 0.547375i) q^{25} +(-2.32970 - 3.26018i) q^{26} +(0.885456 + 0.464723i) q^{27} +(-0.00782648 + 0.194212i) q^{28} +(0.585042 + 2.86573i) q^{29} +(0.768518 + 2.65323i) q^{30} +(-1.53321 - 0.804689i) q^{31} +(3.42346 + 2.16486i) q^{32} +(-3.71941 + 0.604463i) q^{33} +(5.12975 + 1.26437i) q^{34} +(-0.126336 + 0.618835i) q^{35} +(0.762422 - 0.0615490i) q^{36} +(-1.60533 + 1.01515i) q^{37} +(-1.29404 + 1.14642i) q^{38} +(-3.48625 + 0.919814i) q^{39} +(5.71672 + 5.06458i) q^{40} +(-4.45573 - 0.724127i) q^{41} +(-0.259807 - 0.110694i) q^{42} +(-8.44382 - 5.33955i) q^{43} +(-2.15744 + 1.91133i) q^{44} +(2.47747 + 0.200002i) q^{45} +(7.93387 + 2.64872i) q^{46} +(0.00188909 + 0.0155581i) q^{47} +(-1.50705 + 1.13247i) q^{48} +(4.38628 + 5.37222i) q^{49} +(0.827874 + 1.01396i) q^{50} +(2.70053 - 3.91240i) q^{51} +(-1.87778 + 2.01988i) q^{52} +(-1.15396 - 1.67180i) q^{53} +(-0.309197 + 1.06747i) q^{54} +(-7.91605 + 5.00580i) q^{55} +(-0.770712 + 0.125253i) q^{56} +(0.551626 + 1.45452i) q^{57} +(-2.99041 + 1.27409i) q^{58} +(-10.3240 - 10.7484i) q^{59} +(1.68342 - 0.883525i) q^{60} +(-1.60597 - 0.129647i) q^{61} +(0.535388 - 1.84837i) q^{62} +(-0.176029 + 0.183265i) q^{63} +(-2.93321 + 7.73425i) q^{64} +(-7.07566 + 5.49974i) q^{65} +(-1.48501 - 3.91566i) q^{66} +(-5.95660 - 2.53787i) q^{67} +(0.146418 - 3.63333i) q^{68} +(4.75996 - 5.82990i) q^{69} -0.701927 q^{70} +(4.41073 - 5.40216i) q^{71} +(0.854899 + 2.95145i) q^{72} +(11.1313 + 9.86148i) q^{73} +(-1.46224 - 1.52236i) q^{74} +(1.11724 - 0.372988i) q^{75} +(0.951247 + 0.714816i) q^{76} +(0.115419 - 0.950560i) q^{77} +(-1.77656 - 3.59167i) q^{78} +(1.15375 + 9.50195i) q^{79} +(-2.34276 + 4.05778i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.202008 - 5.01278i) q^{82} +(-4.29266 + 11.3188i) q^{83} +(-0.0388789 + 0.190442i) q^{84} +(2.36350 - 11.5772i) q^{85} +(3.93713 - 10.3814i) q^{86} +(0.117771 + 2.92246i) q^{87} +(-9.25663 - 6.95591i) q^{88} +(8.37814 - 14.5114i) q^{89} +(0.332957 + 2.74215i) q^{90} +(0.0219647 - 0.915945i) q^{91} +(0.693914 - 5.71490i) q^{92} +(-1.38427 - 1.04021i) q^{93} +(-0.0165211 + 0.00551556i) q^{94} +(2.67842 + 2.78854i) q^{95} +(3.03186 + 2.68599i) q^{96} +(3.84463 + 13.2732i) q^{97} +(-4.87469 + 5.97041i) q^{98} -3.76821 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{17}{39}\right)$

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 $

$2$	0.222298	+	1.08889i	0.157189	+	0.769961i	0.979582	+	0.201043i	$0.0644330\pi$
$2$	0.222298	+	1.08889i	0.157189	+	0.769961i	−0.822394	+	0.568919i	$0.807362\pi$
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$3$	0.987050	+	0.160411i	0.569874	+	0.0926135i
$4$	0.703694	−	0.299816i	0.351847	−	0.149908i
$5$	2.41330	−	0.594826i	1.07926	−	0.266014i	0.340681	−	0.940179i	$-0.389342\pi$
$5$	2.41330	−	0.594826i	1.07926	−	0.266014i	0.738581	+	0.674165i	$0.235496\pi$
$6$	0.0447495	+	1.11045i	0.0182689	+	0.453339i
$7$	−0.108935	+	0.229576i	−0.0411737	+	0.0867717i	−0.922995	−	0.384812i	$-0.874266\pi$
$7$	−0.108935	+	0.229576i	−0.0411737	+	0.0867717i	0.881821	+	0.471584i	$0.156318\pi$
$8$	1.74553	+	2.52884i	0.617139	+	0.894081i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	1.18417	+	2.49559i	0.374469	+	0.789176i
$11$	−3.57428	+	1.19327i	−1.07769	+	0.359785i	−0.799453	−	0.600728i	$-0.794877\pi$
$11$	−3.57428	+	1.19327i	−1.07769	+	0.359785i	−0.278234	+	0.960513i	$0.589749\pi$
$12$	0.742675	−	0.183053i	0.214392	−	0.0528429i
$13$	−3.29356	+	1.46714i	−0.913468	+	0.406911i
$13$	−3.29356	+	1.46714i	−0.913468	+	0.406911i
$14$	−0.274199	−	0.0675841i	−0.0732829	−	0.0180626i
$15$	2.47747	−	0.200002i	0.639680	−	0.0516403i
$16$	−1.30587	+	1.35955i	−0.326467	+	0.339888i
$17$	2.03797	−	4.29493i	0.494280	−	1.04167i	−0.491068	−	0.871121i	$-0.663393\pi$
$17$	2.03797	−	4.29493i	0.494280	−	1.04167i	0.985349	−	0.170553i	$-0.0545553\pi$
$18$	−0.133958	+	1.10325i	−0.0315743	+	0.260038i
$19$	0.777804	+	1.34720i	0.178440	+	0.309068i	0.941347	−	0.337441i	$-0.109561\pi$
$19$	0.777804	+	1.34720i	0.178440	+	0.309068i	−0.762906	+	0.646509i	$0.776228\pi$
$20$	1.51989	−	1.14212i	0.339858	−	0.255386i
$21$	−0.144351	+	0.209129i	−0.0315000	+	0.0456357i
$22$	−2.09390	−	3.62674i	−0.446421	−	0.773224i
$23$	3.76314	−	6.51795i	0.784669	−	1.35909i	−0.144527	−	0.989501i	$-0.546166\pi$
$23$	3.76314	−	6.51795i	0.784669	−	1.35909i	0.929196	−	0.369586i	$-0.120501\pi$
$24$	1.31727	+	2.77610i	0.268888	+	0.566669i
$25$	1.04294	−	0.547375i	0.208587	−	0.109475i
$26$	−2.32970	−	3.26018i	−0.456892	−	0.639373i
$27$	0.885456	+	0.464723i	0.170406	+	0.0894360i
$28$	−0.00782648	+	0.194212i	−0.00147907	+	0.0367026i
$29$	0.585042	+	2.86573i	0.108640	+	0.532152i	0.997290	+	0.0735673i	$0.0234384\pi$
$29$	0.585042	+	2.86573i	0.108640	+	0.532152i	−0.888651	+	0.458585i	$0.848356\pi$
$30$	0.768518	+	2.65323i	0.140311	+	0.484411i
$31$	−1.53321	−	0.804689i	−0.275372	−	0.144526i	0.321384	−	0.946949i	$-0.395852\pi$
$31$	−1.53321	−	0.804689i	−0.275372	−	0.144526i	−0.596756	+	0.802422i	$0.703544\pi$
$32$	3.42346	+	2.16486i	0.605187	+	0.382697i
$33$	−3.71941	+	0.604463i	−0.647467	+	0.105224i
$34$	5.12975	+	1.26437i	0.879744	+	0.216837i
$35$	−0.126336	+	0.618835i	−0.0213547	+	0.104602i
$36$	0.762422	−	0.0615490i	0.127070	−	0.0102582i
$37$	−1.60533	+	1.01515i	−0.263914	+	0.166889i	−0.659869	−	0.751381i	$-0.729388\pi$
$37$	−1.60533	+	1.01515i	−0.263914	+	0.166889i	0.395955	+	0.918270i	$0.370414\pi$
$38$	−1.29404	+	1.14642i	−0.209922	+	0.185974i
$39$	−3.48625	+	0.919814i	−0.558247	+	0.147288i
$40$	5.71672	+	5.06458i	0.903893	+	0.800780i
$41$	−4.45573	−	0.724127i	−0.695869	−	0.113090i	−0.197819	−	0.980238i	$-0.563386\pi$
$41$	−4.45573	−	0.724127i	−0.695869	−	0.113090i	−0.498049	+	0.867149i	$0.665950\pi$
$42$	−0.259807	−	0.110694i	−0.0400891	−	0.0170804i
$43$	−8.44382	−	5.33955i	−1.28767	−	0.814274i	−0.297579	−	0.954697i	$-0.596179\pi$
$43$	−8.44382	−	5.33955i	−1.28767	−	0.814274i	−0.990092	+	0.140423i	$0.955154\pi$
$44$	−2.15744	+	1.91133i	−0.325247	+	0.288143i
$45$	2.47747	+	0.200002i	0.369319	+	0.0298145i
$46$	7.93387	+	2.64872i	1.16979	+	0.390532i
$47$	0.00188909	+	0.0155581i	0.000275553	+	0.00226938i	0.992846	−	0.119402i	$-0.0380977\pi$
$47$	0.00188909	+	0.0155581i	0.000275553	+	0.00226938i	−0.992570	+	0.121671i	$0.961175\pi$
$48$	−1.50705	+	1.13247i	−0.217523	+	0.163458i
$49$	4.38628	+	5.37222i	0.626611	+	0.767460i
$50$	0.827874	+	1.01396i	0.117079	+	0.143396i
$51$	2.70053	−	3.91240i	0.378150	−	0.547846i
$52$	−1.87778	+	2.01988i	−0.260402	+	0.280106i
$53$	−1.15396	−	1.67180i	−0.158508	−	0.229639i	0.735681	−	0.677328i	$-0.236862\pi$
$53$	−1.15396	−	1.67180i	−0.158508	−	0.229639i	−0.894189	+	0.447689i	$0.852247\pi$
$54$	−0.309197	+	1.06747i	−0.0420764	+	0.145264i
$55$	−7.91605	+	5.00580i	−1.06740	+	0.674982i
$56$	−0.770712	+	0.125253i	−0.102991	+	0.0167376i
$57$	0.551626	+	1.45452i	0.0730647	+	0.192656i
$58$	−2.99041	+	1.27409i	−0.392660	+	0.167297i
$59$	−10.3240	−	10.7484i	−1.34407	−	1.39932i	−0.846983	−	0.531619i	$-0.821584\pi$
$59$	−10.3240	−	10.7484i	−1.34407	−	1.39932i	−0.497084	−	0.867703i	$-0.665596\pi$
$60$	1.68342	−	0.883525i	0.217328	−	0.114063i
$61$	−1.60597	−	0.129647i	−0.205623	−	0.0165996i	−0.0227742	−	0.999741i	$-0.507250\pi$
$61$	−1.60597	−	0.129647i	−0.205623	−	0.0165996i	−0.182849	+	0.983141i	$0.558532\pi$
$62$	0.535388	−	1.84837i	0.0679944	−	0.234744i
$63$	−0.176029	+	0.183265i	−0.0221775	+	0.0230892i
$64$	−2.93321	+	7.73425i	−0.366652	+	0.966781i
$65$	−7.07566	+	5.49974i	−0.877627	+	0.682159i
$66$	−1.48501	−	3.91566i	−0.182793	−	0.481984i
$67$	−5.95660	−	2.53787i	−0.727714	−	0.310050i	−0.00385008	−	0.999993i	$-0.501226\pi$
$67$	−5.95660	−	2.53787i	−0.727714	−	0.310050i	−0.723864	+	0.689943i	$0.757636\pi$
$68$	0.146418	−	3.63333i	0.0177558	−	0.440607i
$69$	4.75996	−	5.82990i	0.573032	−	0.701837i
$70$	−0.701927			−0.0838964
$71$	4.41073	−	5.40216i	0.523457	−	0.641118i	−0.443434	−	0.896307i	$-0.646240\pi$
$71$	4.41073	−	5.40216i	0.523457	−	0.641118i	0.966891	+	0.255188i	$0.0821375\pi$
$72$	0.854899	+	2.95145i	0.100751	+	0.347832i
$73$	11.1313	+	9.86148i	1.30282	+	1.15420i	0.978042	+	0.208410i	$0.0668288\pi$
$73$	11.1313	+	9.86148i	1.30282	+	1.15420i	0.324780	+	0.945790i	$0.394710\pi$
$74$	−1.46224	−	1.52236i	−0.169982	−	0.176970i
$75$	1.11724	−	0.372988i	0.129007	−	0.0430689i
$76$	0.951247	+	0.714816i	0.109116	+	0.0819950i
$77$	0.115419	−	0.950560i	0.0131532	−	0.108326i
$78$	−1.77656	−	3.59167i	−0.201156	−	0.406677i
$79$	1.15375	+	9.50195i	0.129807	+	1.06905i	0.901415	+	0.432956i	$0.142529\pi$
$79$	1.15375	+	9.50195i	0.129807	+	1.06905i	−0.771609	+	0.636097i	$0.780548\pi$
$80$	−2.34276	+	4.05778i	−0.261929	+	0.453674i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	−0.202008	−	5.01278i	−0.0223080	−	0.553568i
$83$	−4.29266	+	11.3188i	−0.471180	+	1.24240i	0.463241	+	0.886232i	$0.346686\pi$
$83$	−4.29266	+	11.3188i	−0.471180	+	1.24240i	−0.934422	+	0.356169i	$0.884083\pi$
$84$	−0.0388789	+	0.190442i	−0.00424204	+	0.0207789i
$85$	2.36350	−	11.5772i	0.256358	−	1.25572i
$86$	3.93713	−	10.3814i	0.424552	−	1.11945i
$87$	0.117771	+	2.92246i	0.0126264	+	0.313321i
$88$	−9.25663	−	6.95591i	−0.986760	−	0.741502i
$89$	8.37814	−	14.5114i	0.888081	−	1.53820i	0.0459401	−	0.998944i	$-0.485372\pi$
$89$	8.37814	−	14.5114i	0.888081	−	1.53820i	0.842141	−	0.539257i	$-0.181295\pi$
$90$	0.332957	+	2.74215i	0.0350968	+	0.289048i
$91$	0.0219647	−	0.915945i	0.00230252	−	0.0960172i
$92$	0.693914	−	5.71490i	0.0723455	−	0.595819i
$93$	−1.38427	−	1.04021i	−0.143542	−	0.107865i
$94$	−0.0165211	+	0.00551556i	−0.00170402	+	0.000568886i
$95$	2.67842	+	2.78854i	0.274801	+	0.286098i
$96$	3.03186	+	2.68599i	0.309438	+	0.274138i
$97$	3.84463	+	13.2732i	0.390363	+	1.34769i	0.879672	+	0.475580i	$0.157762\pi$
$97$	3.84463	+	13.2732i	0.390363	+	1.34769i	−0.489309	+	0.872110i	$0.662751\pi$
$98$	−4.87469	+	5.97041i	−0.492418	+	0.603103i
$99$	−3.76821			−0.378719
$100$	0.569796	−	0.697874i	0.0569796	−	0.0697874i
$101$	0.467423	−	11.5990i	0.0465103	−	1.15414i	−0.792446	−	0.609943i	$-0.791193\pi$
$101$	0.467423	−	11.5990i	0.0465103	−	1.15414i	0.838956	−	0.544199i	$-0.183166\pi$
$102$	4.86050	+	2.07086i	0.481261	+	0.205046i
$103$	−1.58443	−	4.17780i	−0.156119	−	0.411651i	0.834021	−	0.551732i	$-0.186033\pi$
$103$	−1.58443	−	4.17780i	−0.156119	−	0.411651i	−0.990140	+	0.140081i	$0.955264\pi$
$104$	−9.45917	−	5.76795i	−0.927548	−	0.565594i
$105$	−0.223968	+	0.590555i	−0.0218570	+	0.0576323i
$106$	1.56388	−	1.62817i	0.151897	−	0.158142i
$107$	−1.33761	+	4.61797i	−0.129312	+	0.446436i	−0.998877	−	0.0473823i	$-0.984912\pi$
$107$	−1.33761	+	4.61797i	−0.129312	+	0.446436i	0.869565	+	0.493818i	$0.164399\pi$
$108$	0.762422	+	0.0615490i	0.0733641	+	0.00592256i
$109$	−2.21110	+	1.16047i	−0.211785	+	0.111153i	−0.567280	−	0.823525i	$-0.692004\pi$
$109$	−2.21110	+	1.16047i	−0.211785	+	0.111153i	0.355496	+	0.934678i	$0.384312\pi$
$110$	−7.21049	−	7.50692i	−0.687494	−	0.715757i
$111$	−1.74738	+	0.744488i	−0.165854	+	0.0706637i
$112$	−0.169866	−	0.447900i	−0.0160508	−	0.0423226i
$113$	5.31627	−	0.863977i	0.500112	−	0.0812761i	0.0948777	−	0.995489i	$-0.469754\pi$
$113$	5.31627	−	0.863977i	0.500112	−	0.0812761i	0.405234	+	0.914213i	$0.367190\pi$
$114$	−1.46119	+	0.923998i	−0.136853	+	0.0865403i
$115$	5.20456	−	17.9682i	0.485327	−	1.67554i
$116$	1.27088	+	1.84119i	0.117998	+	0.170950i
$117$	−3.58865	+	0.348669i	−0.331771	+	0.0322345i
$118$	9.40882	−	13.6310i	0.866152	−	1.25484i
$119$	0.764007	+	0.935739i	0.0700364	+	0.0857791i
$120$	4.83028	+	5.91602i	0.440942	+	0.540056i
$121$	2.55774	−	1.92202i	0.232522	−	0.174729i
$122$	−0.215833	−	1.77754i	−0.0195406	−	0.160931i
$123$	−4.28187	−	1.42950i	−0.386084	−	0.128894i
$124$	−1.32017	−	0.106575i	−0.118555	−	0.00957071i
$125$	−7.11090	+	6.29970i	−0.636018	+	0.563463i
$126$	−0.238686	−	0.150936i	−0.0212639	−	0.0134465i
$127$	−17.5524	−	7.47838i	−1.55752	−	0.663599i	−0.570084	−	0.821587i	$-0.693089\pi$
$127$	−17.5524	−	7.47838i	−1.55752	−	0.663599i	−0.987441	+	0.157987i	$0.949499\pi$
$128$	−1.07767	−	0.175138i	−0.0952533	−	0.0154802i
$129$	−7.47795	−	6.62489i	−0.658397	−	0.583289i
$130$	−7.56152	−	6.48203i	−0.663189	−	0.568512i
$131$	9.11452	−	8.07476i	0.796340	−	0.705495i	−0.163347	−	0.986569i	$-0.552229\pi$
$131$	9.11452	−	8.07476i	0.796340	−	0.705495i	0.959686	+	0.281073i	$0.0906905\pi$
$132$	−2.43610	+	1.54050i	−0.212035	+	0.134083i
$133$	−0.394015	+	0.0318081i	−0.0341654	+	0.00275812i
$134$	1.43932	−	7.05024i	0.124338	−	0.609048i
$135$	2.41330	+	0.594826i	0.207704	+	0.0511945i
$136$	14.4186	−	2.34324i	1.23638	−	0.200931i
$137$	0.698917	+	0.441968i	0.0597125	+	0.0377599i	0.563989	−	0.825783i	$-0.309266\pi$
$137$	0.698917	+	0.441968i	0.0597125	+	0.0377599i	−0.504276	+	0.863543i	$0.668241\pi$
$138$	7.40625	+	3.88710i	0.630462	+	0.330892i
$139$	−4.20927	−	14.5321i	−0.357025	−	1.23259i	−0.915244	−	0.402900i	$-0.868002\pi$
$139$	−4.20927	−	14.5321i	−0.357025	−	1.23259i	0.558219	−	0.829694i	$-0.311485\pi$
$140$	0.0966347	+	0.473348i	0.00816712	+	0.0400052i
$141$	−0.000631063		0.0156597i	−5.31451e−5		0.00131878i
$142$	6.86285	+	3.60190i	0.575918	+	0.302265i
$143$	10.0214	−	9.17407i	0.838033	−	0.767174i
$144$	−1.66919	+	0.876059i	−0.139099	+	0.0730049i
$145$	3.11649	+	6.56787i	0.258811	+	0.545432i
$146$	−8.26360	+	14.3130i	−0.683900	+	1.18455i
$147$	3.46771	+	6.00626i	0.286012	+	0.495388i
$148$	−0.825301	+	1.19566i	−0.0678393	+	0.0982823i
$149$	−4.91974	+	3.69695i	−0.403041	+	0.302866i	−0.782863	−	0.622194i	$-0.786242\pi$
$149$	−4.91974	+	3.69695i	−0.403041	+	0.302866i	0.379822	+	0.925060i	$0.375985\pi$
$150$	0.654503	+	1.13363i	0.0534399	+	0.0925606i
$151$	−0.283665	+	2.33619i	−0.0230843	+	0.190117i	−0.999689	−	0.0249245i	$-0.992065\pi$
$151$	−0.283665	+	2.33619i	−0.0230843	+	0.190117i	0.976605	+	0.215041i	$0.0689885\pi$
$152$	−2.04916	+	4.31852i	−0.166209	+	0.350278i
$153$	3.29316	−	3.42854i	0.266236	−	0.277181i
$154$	1.06071	−	0.0856296i	0.0854747	−	0.00690023i
$155$	−4.17874	−	1.02997i	−0.335645	−	0.0827290i
$156$	−2.17748	+	1.69250i	−0.174338	+	0.135509i
$157$	2.96446	−	0.730673i	0.236590	−	0.0583141i	−0.119238	−	0.992866i	$-0.538045\pi$
$157$	2.96446	−	0.730673i	0.236590	−	0.0583141i	0.355828	+	0.934552i	$0.384199\pi$
$158$	−10.0901	+	3.36857i	−0.802725	+	0.267989i
$159$	−0.870840	−	1.83526i	−0.0690621	−	0.145545i
$160$	9.54956	+	3.18811i	0.754959	+	0.252042i
$161$	1.08643	+	1.57396i	0.0856225	+	0.124046i
$162$	−0.476427	+	1.00405i	−0.0374317	+	0.0788856i
$163$	0.244402	+	6.06477i	0.0191430	+	0.475030i	0.980121	+	0.198403i	$0.0635755\pi$
$163$	0.244402	+	6.06477i	0.0191430	+	0.475030i	−0.960977	+	0.276627i	$0.910783\pi$
$164$	−3.35258	+	0.826336i	−0.261792	+	0.0645260i
$165$	−8.61652	+	3.67116i	−0.670795	+	0.285799i
$166$	−13.2792	−	2.15808i	−1.03066	−	0.167499i
$167$	4.80992	+	23.5605i	0.372203	+	1.82317i	0.545272	+	0.838259i	$0.316426\pi$
$167$	4.80992	+	23.5605i	0.372203	+	1.82317i	−0.173070	+	0.984910i	$0.555369\pi$
$168$	−0.780824			−0.0602419
$169$	8.69502	−	9.66419i	0.668848	−	0.743400i
$170$	13.1317			1.00716
$171$	0.311162	+	1.52417i	0.0237951	+	0.116556i
$172$	−7.54275	−	1.22582i	−0.575129	−	0.0934676i
$173$	9.70669	−	4.13563i	0.737986	−	0.314426i	0.00993608	−	0.999951i	$-0.496837\pi$
$173$	9.70669	−	4.13563i	0.737986	−	0.314426i	0.728050	+	0.685524i	$0.240427\pi$
$174$	−3.15606	+	0.777899i	−0.239260	+	0.0589724i
$175$	0.0120518	+	0.299062i	0.000911029	+	0.0226069i
$176$	3.04523	−	6.41769i	0.229543	−	0.483751i
$177$	−8.46612	−	12.2653i	−0.636352	−	0.921916i
$178$	17.6637	+	5.89702i	1.32395	+	0.442000i
$179$	−6.69070	−	14.1003i	−0.500086	−	1.05391i	−0.983897	−	0.178736i	$-0.942799\pi$
$179$	−6.69070	−	14.1003i	−0.500086	−	1.05391i	0.483811	−	0.875173i	$-0.339252\pi$
$180$	1.80334	−	0.602045i	0.134413	−	0.0448738i
$181$	−8.07116	+	1.98936i	−0.599924	+	0.147868i	−0.527571	−	0.849511i	$-0.676897\pi$
$181$	−8.07116	+	1.98936i	−0.599924	+	0.147868i	−0.0723535	+	0.997379i	$0.523051\pi$
$182$	1.00225	−	0.179696i	0.0742914	−	0.0133200i
$183$	−1.56437	−	0.385584i	−0.115642	−	0.0285032i
$184$	23.0516	−	1.86091i	1.69938	−	0.137188i
$185$	−3.27030	+	3.40475i	−0.240437	+	0.250322i
$186$	0.824955	−	1.73856i	0.0604887	−	0.127477i
$187$	−2.15927	+	17.7832i	−0.157901	+	1.30043i
$188$	0.00599391	+	0.0103818i	0.000437151	+	0.000757168i
$189$	−0.203147	+	0.152655i	−0.0147768	+	0.0111040i
$190$	−2.44100	+	3.53640i	−0.177089	+	0.256557i
$191$	7.43817	+	12.8833i	0.538207	+	0.932201i	0.999001	+	0.0446943i	$0.0142314\pi$
$191$	7.43817	+	12.8833i	0.538207	+	0.932201i	−0.460794	+	0.887507i	$0.652435\pi$
$192$	−4.13589	+	7.16357i	−0.298482	+	0.516986i
$193$	0.604565	+	1.27409i	0.0435176	+	0.0917113i	0.924045	−	0.382284i	$-0.124863\pi$
$193$	0.604565	+	1.27409i	0.0435176	+	0.0917113i	−0.880527	+	0.473996i	$0.842811\pi$
$194$	−13.5984	+	7.13700i	−0.976309	+	0.512406i
$195$	−7.86625	+	4.29350i	−0.563314	+	0.307464i
$196$	4.69728	+	2.46532i	0.335520	+	0.176094i
$197$	0.121067	−	3.00424i	0.00862565	−	0.214043i	−0.989128	−	0.147056i	$-0.953020\pi$
$197$	0.121067	−	3.00424i	0.00862565	−	0.214043i	0.997754	−	0.0669874i	$-0.0213387\pi$
$198$	−0.837667	−	4.10317i	−0.0595304	−	0.291599i
$199$	−3.96064	−	13.6737i	−0.280762	−	0.969303i	−0.969663	−	0.244447i	$-0.921393\pi$
$199$	−3.96064	−	13.6737i	−0.280762	−	0.969303i	0.688900	−	0.724856i	$-0.258094\pi$
$200$	3.20471	+	1.68196i	0.226607	+	0.118932i
$201$	−5.47236	−	3.46051i	−0.385990	−	0.244086i
$202$	12.7339	−	2.06946i	0.895956	−	0.145607i
$203$	−0.721635	−	0.177867i	−0.0506488	−	0.0124838i
$204$	0.727350	−	3.56280i	0.0509247	−	0.249446i
$205$	−11.1838	+	0.902847i	−0.781108	+	0.0630576i
$206$	4.19695	−	2.65399i	0.292415	−	0.184912i
$207$	5.63350	−	4.99085i	0.391556	−	0.346888i
$208$	2.30630	−	6.39365i	0.159913	−	0.443320i
$209$	−4.38766	−	3.88713i	−0.303501	−	0.268878i
$210$	−0.692837	−	0.112597i	−0.0478103	−	0.00776993i
$211$	0.541748	+	0.230817i	0.0372955	+	0.0158901i	0.410534	−	0.911845i	$-0.365342\pi$
$211$	0.541748	+	0.230817i	0.0372955	+	0.0158901i	−0.373238	+	0.927735i	$0.621753\pi$
$212$	−1.31327	−	0.830459i	−0.0901955	−	0.0570362i
$213$	5.22018	−	4.62467i	0.357681	−	0.316877i
$214$	−5.32581	−	0.429944i	−0.364065	−	0.0293904i
$215$	−23.5536	−	7.86335i	−1.60634	−	0.536276i
$216$	0.370382	+	3.05037i	0.0252013	+	0.207551i
$217$	0.351758	−	0.264329i	0.0238789	−	0.0179438i
$218$	−1.75515	−	2.14967i	−0.118874	−	0.145594i
$219$	9.40527	+	11.5194i	0.635549	+	0.778407i
$220$	−4.06965	+	5.89591i	−0.274376	+	0.397502i
$221$	−0.410917	+	17.1356i	−0.0276413	+	1.15266i
$222$	−1.19911	−	1.73720i	−0.0804787	−	0.116593i
$223$	−3.59872	+	12.4242i	−0.240988	+	0.831988i	0.745268	+	0.666765i	$0.232322\pi$
$223$	−3.59872	+	12.4242i	−0.240988	+	0.831988i	−0.986256	+	0.165223i	$0.947166\pi$
$224$	−0.869937	+	0.550115i	−0.0581251	+	0.0367561i
$225$	1.16260	−	0.188941i	0.0775066	−	0.0125960i
$226$	2.12257	+	5.59677i	0.141192	+	0.372291i
$227$	−14.0339	+	5.97928i	−0.931462	+	0.396859i	−0.803760	−	0.594954i	$-0.797170\pi$
$227$	−14.0339	+	5.97928i	−0.931462	+	0.396859i	−0.127702	+	0.991813i	$0.540760\pi$
$228$	0.824264	+	0.858150i	0.0545882	+	0.0568324i
$229$	7.33934	−	3.85198i	0.484997	−	0.254546i	−0.204457	−	0.978876i	$-0.565543\pi$
$229$	7.33934	−	3.85198i	0.484997	−	0.254546i	0.689454	+	0.724329i	$0.257850\pi$
$230$	20.7224	+	1.67288i	1.36639	+	0.110307i
$231$	0.266405	−	0.919736i	0.0175282	−	0.0605142i
$232$	−6.22576	+	6.48170i	−0.408741	+	0.425545i
$233$	0.308112	−	0.812423i	0.0201851	−	0.0532236i	−0.924545	−	0.381073i	$-0.875555\pi$
$233$	0.308112	−	0.812423i	0.0201851	−	0.0532236i	0.944730	+	0.327849i	$0.106324\pi$
$234$	−1.17741	−	3.83014i	−0.0769700	−	0.250384i
$235$	0.0138133	+	0.0364227i	0.000901082	+	0.00237596i
$236$	−10.4875	−	4.46829i	−0.682676	−	0.290861i
$237$	−0.385415	+	9.56398i	−0.0250354	+	0.621247i
$238$	−0.849079	+	1.03993i	−0.0550376	+	0.0674089i
$239$	20.2989			1.31302			0.656512	−	0.754315i	$-0.272031\pi$
$239$	20.2989			1.31302			0.656512	+	0.754315i	$0.272031\pi$
$240$	−2.96334	+	3.62943i	−0.191283	+	0.234279i
$241$	−5.81899	−	20.0895i	−0.374834	−	1.29408i	−0.897301	−	0.441418i	$-0.854476\pi$
$241$	−5.81899	−	20.0895i	−0.374834	−	1.29408i	0.522467	−	0.852659i	$-0.325012\pi$
$242$	2.66145	+	2.35784i	0.171085	+	0.151568i
$243$	0.692724	+	0.721202i	0.0444383	+	0.0462652i
$244$	−1.16898	+	0.390263i	−0.0748363	+	0.0249840i
$245$	13.7810	+	10.3557i	0.880433	+	0.661603i
$246$	0.604714	−	4.98027i	0.0385551	−	0.317530i
$247$	−4.53826	−	3.29592i	−0.288763	−	0.209714i
$248$	−0.641333	−	5.28185i	−0.0407247	−	0.335398i
$249$	−6.05273	+	10.4836i	−0.383576	+	0.664374i
$250$	−8.44043	−	6.34257i	−0.533819	−	0.401139i
$251$	0.155820	+	3.86663i	0.00983527	+	0.244060i	0.996627	+	0.0820653i	$0.0261516\pi$
$251$	0.155820	+	3.86663i	0.00983527	+	0.244060i	−0.986792	+	0.161994i	$0.948207\pi$
$252$	−0.0689244	+	0.181739i	−0.00434183	+	0.0114485i
$253$	−5.67285	+	27.7875i	−0.356649	+	1.74698i
$254$	4.24126	−	20.7751i	0.266120	−	1.30354i
$255$	4.19001	−	11.0482i	0.262389	−	0.691862i
$256$	0.617284	+	15.3178i	0.0385803	+	0.957360i
$257$	18.2952	+	13.7479i	1.14122	+	0.857573i	0.991365	−	0.131135i	$-0.0418621\pi$
$257$	18.2952	+	13.7479i	1.14122	+	0.857573i	0.149858	+	0.988708i	$0.452118\pi$
$258$	5.55144	−	9.61537i	0.345617	−	0.598627i
$259$	−0.0581769	−	0.479130i	−0.00361494	−	0.0297717i
$260$	−3.33019	+	5.99153i	−0.206530	+	0.371579i
$261$	−0.352550	+	2.90351i	−0.0218223	+	0.179723i
$262$	10.8187	+	8.12970i	0.668380	+	0.502255i
$263$	−18.7146	+	6.24785i	−1.15399	+	0.385259i	−0.828337	−	0.560230i	$-0.810713\pi$
$263$	−18.7146	+	6.24785i	−1.15399	+	0.385259i	−0.325654	+	0.945489i	$0.605584\pi$
$264$	−8.02095	−	8.35070i	−0.493656	−	0.513950i
$265$	−3.77928	−	3.34815i	−0.232159	−	0.205675i
$266$	−0.122224	−	0.421968i	−0.00749406	−	0.0258725i
$267$	10.5974	−	12.9795i	0.648552	−	0.794332i
$268$	−4.95252			−0.302523
$269$	−9.14621	+	11.2021i	−0.557654	+	0.683002i	−0.974089	−	0.226163i	$-0.927382\pi$
$269$	−9.14621	+	11.2021i	−0.557654	+	0.683002i	0.416435	+	0.909165i	$0.363279\pi$
$270$	−0.111226	+	2.76005i	−0.00676901	+	0.167971i
$271$	25.8982	+	11.0342i	1.57321	+	0.670280i	0.989873	−	0.141953i	$-0.0453383\pi$
$271$	25.8982	+	11.0342i	1.57321	+	0.670280i	0.583332	+	0.812234i	$0.301749\pi$
$272$	3.17787	+	8.37935i	0.192687	+	0.508073i
$273$	0.168608	−	0.900561i	0.0102046	−	0.0545044i
$274$	−0.325887	+	0.859292i	−0.0196875	+	0.0519117i
$275$	−3.07458	+	3.20098i	−0.185404	+	0.193026i
$276$	1.60166	−	5.52958i	0.0964087	−	0.332841i
$277$	4.02351	+	0.324811i	0.241749	+	0.0195160i	0.200747	−	0.979643i	$-0.435663\pi$
$277$	4.02351	+	0.324811i	0.241749	+	0.0195160i	0.0410018	+	0.999159i	$0.486945\pi$
$278$	14.8881	−	7.81388i	0.892930	−	0.468646i
$279$	−1.19948	−	1.24879i	−0.0718112	−	0.0747634i
$280$	−1.78546	+	0.760713i	−0.106702	+	0.0454613i
$281$	9.61802	+	25.3606i	0.573763	+	1.51289i	0.836470	+	0.548013i	$0.184616\pi$
$281$	9.61802	+	25.3606i	0.573763	+	1.51289i	−0.262707	+	0.964876i	$0.584615\pi$
$282$	−0.0171919	+	0.00279396i	−0.00102376	+	0.000166378i
$283$	1.85404	−	1.17243i	0.110211	−	0.0696935i	−0.478223	−	0.878238i	$-0.658719\pi$
$283$	1.85404	−	1.17243i	0.110211	−	0.0696935i	0.588434	+	0.808545i	$0.299745\pi$
$284$	1.48415	−	5.12387i	0.0880680	−	0.304046i
$285$	2.19643	+	3.18207i	0.130105	+	0.188490i
$286$	12.2173	+	8.87283i	0.722424	+	0.524662i
$287$	0.651629	−	0.944048i	0.0384644	−	0.0557254i
$288$	2.56173	+	3.13755i	0.150951	+	0.184882i
$289$	−3.54154	−	4.33760i	−0.208326	−	0.255153i
$290$	−6.45890	+	4.85355i	−0.379280	+	0.285010i
$291$	1.66567	+	13.7180i	0.0976435	+	0.804166i
$292$	10.7897	+	3.60212i	0.631418	+	0.210798i
$293$	26.2020	+	2.11525i	1.53074	+	0.123574i	0.816918	−	0.576754i	$-0.195681\pi$
$293$	26.2020	+	2.11525i	1.53074	+	0.123574i	0.713821	+	0.700328i	$0.246963\pi$
$294$	−5.76928	+	5.11114i	−0.336472	+	0.298088i
$295$	−31.3083	−	19.7982i	−1.82284	−	1.15269i
$296$	−5.36930	−	2.28764i	−0.312084	−	0.132967i
$297$	−3.71941	−	0.604463i	−0.215822	−	0.0350745i
$298$	−5.11922	−	4.53523i	−0.296548	−	0.262719i
$299$	−2.83139	+	26.9883i	−0.163743	+	1.56077i
$300$	0.674364	−	0.597435i	0.0389344	−	0.0344929i
$301$	2.14566	−	1.35684i	0.123674	−	0.0782067i
$302$	−2.60691	+	0.210452i	−0.150011	+	0.0121101i
$303$	2.32198	−	11.3738i	0.133394	−	0.653408i
$304$	−2.84730	−	0.701795i	−0.163304	−	0.0402507i
$305$	−3.95281	+	0.642394i	−0.226337	+	0.0367834i
$306$	4.46537	+	2.82373i	0.255268	+	0.161422i
$307$	14.1745	+	7.43934i	0.808980	+	0.424586i	0.817890	−	0.575375i	$-0.195144\pi$
$307$	14.1745	+	7.43934i	0.808980	+	0.424586i	−0.00890974	+	0.999960i	$0.502836\pi$
$308$	−0.203774	−	0.703508i	−0.0116111	−	0.0400861i
$309$	−0.893747	−	4.37786i	−0.0508435	−	0.249048i
$310$	0.192593	−	4.77915i	0.0109386	−	0.271438i
$311$	26.0768	+	13.6862i	1.47868	+	0.776072i	0.995067	−	0.0992080i	$-0.0316309\pi$
$311$	26.0768	+	13.6862i	1.47868	+	0.776072i	0.483616	+	0.875280i	$0.339323\pi$
$312$	−8.41143	−	7.21061i	−0.476204	−	0.408220i
$313$	−7.02810	+	3.68863i	−0.397252	+	0.208494i	−0.651506	−	0.758644i	$-0.725862\pi$
$313$	−7.02810	+	3.68863i	−0.397252	+	0.208494i	0.254254	+	0.967137i	$0.418170\pi$
$314$	1.45462	+	3.06554i	0.0820888	+	0.172999i
$315$	−0.315799	+	0.546981i	−0.0177933	+	0.0308189i
$316$	3.66072	+	6.34056i	0.205932	+	0.356684i
$317$	6.73676	−	9.75988i	0.378374	−	0.548169i	−0.586816	−	0.809721i	$-0.699619\pi$
$317$	6.73676	−	9.75988i	0.378374	−	0.548169i	0.965190	+	0.261551i	$0.0842340\pi$
$318$	1.80481	−	1.35622i	0.101208	−	0.0760532i
$319$	−5.51070	−	9.54481i	−0.308540	−	0.534407i
$320$	−2.47820	+	20.4098i	−0.138536	+	1.14095i
$321$	−2.06106	+	4.34360i	−0.115037	+	0.242436i
$322$	−1.47236	+	1.53289i	−0.0820515	+	0.0854246i
$323$	7.37126	−	0.595069i	0.410148	−	0.0331105i
$324$	0.742675	+	0.183053i	0.0412597	+	0.0101696i
$325$	−2.63189	+	3.33294i	−0.145991	+	0.184878i
$326$	−6.54954	+	1.61432i	−0.362746	+	0.0894087i
$327$	−2.36862	+	0.790761i	−0.130985	+	0.0437292i
$328$	−5.94643	−	12.5318i	−0.328337	−	0.691955i
$329$	−0.00377756	−	0.00126113i	−0.000208264	−	6.95286e-5i
$330$	−5.91293	−	8.56635i	−0.325496	−	0.471562i
$331$	−3.69182	+	7.78034i	−0.202921	+	0.427646i	−0.979243	−	0.202690i	$-0.935032\pi$
$331$	−3.69182	+	7.78034i	−0.202921	+	0.427646i	0.776322	+	0.630336i	$0.217083\pi$
$332$	0.372842	+	9.25199i	0.0204624	+	0.507769i
$333$	−1.84417	+	0.454548i	−0.101060	+	0.0249091i
$334$	−24.5856	+	10.4749i	−1.34526	+	0.573163i
$335$	−15.8847	−	2.58151i	−0.867872	−	0.141043i
$336$	−0.0958181	−	0.469348i	−0.00522731	−	0.0256050i
$337$	−11.8406			−0.644997			−0.322498	−	0.946570i	$-0.604523\pi$
$337$	−11.8406			−0.644997			−0.322498	+	0.946570i	$0.604523\pi$
$338$	12.4561	+	7.31958i	0.677524	+	0.398133i
$339$	5.38601			0.292528
$340$	−1.80785	−	8.85543i	−0.0980444	−	0.480253i
$341$	6.44033	+	1.04666i	0.348763	+	0.0566796i
$342$	−1.59048	+	0.677641i	−0.0860035	+	0.0366427i
$343$	−3.43824	+	0.847450i	−0.185648	+	0.0457580i
$344$	−1.23610	−	30.6735i	−0.0666459	−	1.65380i
$345$	8.01946	−	16.9007i	0.431753	−	0.909901i
$346$	6.66103	+	9.65017i	0.358099	+	0.518796i
$347$	17.1758	+	5.73413i	0.922046	+	0.307824i	0.737772	−	0.675050i	$-0.235878\pi$
$347$	17.1758	+	5.73413i	0.922046	+	0.307824i	0.184275	+	0.982875i	$0.441006\pi$
$348$	0.959077	+	2.02121i	0.0514119	+	0.108348i
$349$	2.22305	−	0.742164i	0.118997	−	0.0397271i	−0.256546	−	0.966532i	$-0.582584\pi$
$349$	2.22305	−	0.742164i	0.118997	−	0.0397271i	0.375543	+	0.926805i	$0.377456\pi$
$350$	−0.322966	+	0.0796040i	−0.0172633	+	0.00425502i
$351$	−3.59811	−	0.231507i	−0.192053	−	0.0123569i
$352$	−14.8197	−	3.65272i	−0.789892	−	0.194691i
$353$	14.9426	−	1.20629i	0.795315	−	0.0642045i	0.323872	−	0.946101i	$-0.395015\pi$
$353$	14.9426	−	1.20629i	0.795315	−	0.0642045i	0.471443	+	0.881896i	$0.343733\pi$
$354$	11.4735	−	11.9452i	0.609812	−	0.634882i
$355$	7.43108	−	15.6607i	0.394401	−	0.831182i
$356$	1.54491	−	12.7235i	0.0818800	−	0.674342i
$357$	0.604011	+	1.04618i	0.0319676	+	0.0553696i
$358$	13.8664	−	10.4199i	0.732861	−	0.550710i
$359$	1.87849	−	2.72147i	0.0991430	−	0.143633i	−0.770273	−	0.637714i	$-0.779880\pi$
$359$	1.87849	−	2.72147i	0.0991430	−	0.143633i	0.869416	+	0.494081i	$0.164495\pi$
$360$	3.81873	+	6.61424i	0.201265	+	0.348601i
$361$	8.29004	−	14.3588i	0.436318	−	0.755725i
$362$	−3.96040	−	8.34637i	−0.208154	−	0.438675i
$363$	2.83294	−	1.48684i	0.148691	−	0.0780388i
$364$	−0.259159	−	0.651131i	−0.0135836	−	0.0341285i
$365$	32.7291	+	17.1776i	1.71312	+	0.899115i
$366$	0.0721001	−	1.78915i	0.00376874	−	0.0935202i
$367$	−1.65594	−	8.11134i	−0.0864395	−	0.423409i	−0.999865	−	0.0164037i	$-0.994778\pi$
$367$	−1.65594	−	8.11134i	−0.0864395	−	0.423409i	0.913426	−	0.407005i	$-0.133427\pi$
$368$	3.94734	+	13.6278i	0.205769	+	0.710397i
$369$	−3.99712	−	2.09785i	−0.208082	−	0.109210i
$370$	−4.43438	−	2.80413i	−0.230532	−	0.145780i
$371$	0.509512	−	0.0828037i	0.0264525	−	0.00429896i
$372$	−1.28598	−	0.316965i	−0.0666747	−	0.0164338i
$373$	0.313776	−	1.53698i	0.0162467	−	0.0795816i	−0.970859	−	0.239651i	$-0.922967\pi$
$373$	0.313776	−	1.53698i	0.0162467	−	0.0795816i	0.987106	+	0.160070i	$0.0511719\pi$
$374$	−19.8439	+	1.60197i	−1.02610	+	0.0828357i
$375$	−8.02935	+	5.07746i	−0.414634	+	0.262199i
$376$	−0.0360465	+	0.0319344i	−0.00185896	+	0.00164689i
$377$	−6.13128	−	8.58010i	−0.315777	−	0.441897i
$378$	−0.211384	−	0.187270i	−0.0108724	−	0.00963211i
$379$	7.81507	+	1.27007i	0.401433	+	0.0652392i	0.357776	−	0.933807i	$-0.383535\pi$
$379$	7.81507	+	1.27007i	0.401433	+	0.0652392i	0.0436569	+	0.999047i	$0.486099\pi$
$380$	2.72084	+	1.15924i	0.139576	+	0.0594678i
$381$	−16.1255	−	10.1971i	−0.826134	−	0.522416i
$382$	−12.3750	+	10.9633i	−0.633159	+	0.560930i
$383$	−19.6459	−	1.58598i	−1.00386	−	0.0810399i	−0.432410	−	0.901677i	$-0.642337\pi$
$383$	−19.6459	−	1.58598i	−1.00386	−	0.0810399i	−0.571450	+	0.820637i	$0.693619\pi$
$384$	−1.03562	−	0.345740i	−0.0528487	−	0.0176435i
$385$	−0.286877	−	2.36264i	−0.0146206	−	0.120412i
$386$	−1.25295	+	0.941534i	−0.0637737	+	0.0479228i
$387$	−6.31841	−	7.73865i	−0.321183	−	0.393377i
$388$	6.68497	+	8.18760i	0.339378	+	0.415662i
$389$	6.67399	−	9.66894i	0.338385	−	0.490235i	−0.616441	−	0.787401i	$-0.711426\pi$
$389$	6.67399	−	9.66894i	0.338385	−	0.490235i	0.954826	+	0.297166i	$0.0960416\pi$
$390$	−6.42381	−	7.61104i	−0.325282	−	0.385400i
$391$	−20.3250	−	29.4458i	−1.02788	−	1.48914i
$392$	−5.92909	+	20.4696i	−0.299464	+	1.03387i
$393$	10.2918	−	6.50812i	0.519151	−	0.328291i
$394$	3.29820	−	0.536010i	0.166161	−	0.0270038i
$395$	8.43634	+	22.2448i	0.424479	+	1.11926i
$396$	−2.65167	+	1.12977i	−0.133251	+	0.0567731i
$397$	−18.1806	−	18.9281i	−0.912460	−	0.949972i	0.0864683	−	0.996255i	$-0.472442\pi$
$397$	−18.1806	−	18.9281i	−0.912460	−	0.949972i	−0.998928	+	0.0462830i	$0.985262\pi$
$398$	14.0087	−	7.35234i	0.702194	−	0.368540i
$399$	−0.394015	−	0.0318081i	−0.0197254	−	0.00159240i
$400$	−0.617752	+	2.13273i	−0.0308876	+	0.106636i
$401$	3.84944	−	4.00769i	0.192232	−	0.200134i	−0.618111	−	0.786091i	$-0.712102\pi$
$401$	3.84944	−	4.00769i	0.192232	−	0.200134i	0.810342	+	0.585957i	$0.199281\pi$
$402$	2.55162	−	6.72806i	0.127263	−	0.335565i
$403$	6.23029	+	0.400864i	0.310353	+	0.0199685i
$404$	−3.14864	−	8.30228i	−0.156651	−	0.413054i
$405$	2.28664	+	0.974244i	0.113624	+	0.0484106i
$406$	0.0332593	−	0.825320i	0.00165063	−	0.0409600i
$407$	4.52655	−	5.54401i	0.224373	−	0.274806i
$408$	14.6077			0.723190
$409$	−5.71378	+	6.99810i	−0.282528	+	0.346034i	−0.896299	−	0.443450i	$-0.853754\pi$
$409$	−5.71378	+	6.99810i	−0.282528	+	0.346034i	0.613771	+	0.789484i	$0.289652\pi$
$410$	−3.46924	−	11.9772i	−0.171333	−	0.591511i
$411$	0.618969	+	0.548359i	0.0305315	+	0.0270486i
$412$	−2.36753	−	2.46486i	−0.116640	−	0.121435i
$413$	3.59222	−	1.19926i	0.176762	−	0.0590117i
$414$	6.68680	+	5.02481i	0.328638	+	0.246956i
$415$	−3.62677	+	29.8691i	−0.178031	+	1.46622i
$416$	−14.4515	−	2.10742i	−0.708543	−	0.103325i
$417$	−1.82365	−	15.0191i	−0.0893045	−	0.735488i
$418$	3.25729	−	5.64179i	0.159319	−	0.275949i
$419$	−22.4200	−	16.8475i	−1.09529	−	0.823057i	−0.109997	−	0.993932i	$-0.535084\pi$
$419$	−22.4200	−	16.8475i	−1.09529	−	0.823057i	−0.985293	+	0.170875i	$0.945340\pi$
$420$	0.0194529	+	0.482720i	0.000949206	+	0.0235543i
$421$	−0.999180	+	2.63462i	−0.0486971	+	0.128404i	−0.957158	−	0.289566i	$-0.906489\pi$
$421$	−0.999180	+	2.63462i	−0.0486971	+	0.128404i	0.908461	+	0.417970i	$0.137258\pi$
$422$	−0.130905	+	0.641214i	−0.00637235	+	0.0312138i
$423$	−0.00313488	+	0.0153556i	−0.000152423	+	0.000746617i
$424$	2.21344	−	5.83636i	0.107494	−	0.283439i
$425$	−0.225466	−	5.59487i	−0.0109367	−	0.271391i
$426$	6.19620	+	4.65614i	0.300207	+	0.225591i
$427$	0.204711	−	0.354569i	0.00990664	−	0.0171588i
$428$	0.443272	+	3.65068i	0.0214264	+	0.176462i
$429$	11.3633	−	7.44772i	0.548624	−	0.359579i
$430$	3.32639	−	27.3953i	0.160413	−	1.32112i
$431$	−16.1522	−	12.1376i	−0.778026	−	0.584649i	0.135808	−	0.990735i	$-0.456637\pi$
$431$	−16.1522	−	12.1376i	−0.778026	−	0.584649i	−0.913835	+	0.406086i	$0.866893\pi$
$432$	−1.78811	+	0.596957i	−0.0860303	+	0.0287211i
$433$	23.4954	+	24.4613i	1.12912	+	1.17554i	0.982485	+	0.186344i	$0.0596639\pi$
$433$	23.4954	+	24.4613i	1.12912	+	1.17554i	0.146632	+	0.989191i	$0.453157\pi$
$434$	0.366020	+	0.324266i	0.0175695	+	0.0155653i
$435$	2.02258	+	6.98274i	0.0969751	+	0.334797i
$436$	−1.20801	+	1.47954i	−0.0578531	+	0.0708572i
$437$	11.7079			0.560067
$438$	−10.4525	+	12.8020i	−0.499442	+	0.611705i
$439$	−1.03671	+	25.7257i	−0.0494796	+	1.22782i	0.763608	+	0.645681i	$0.223426\pi$
$439$	−1.03671	+	25.7257i	−0.0494796	+	1.22782i	−0.813087	+	0.582142i	$0.802215\pi$
$440$	−26.4766	−	11.2806i	−1.26222	−	0.537783i
$441$	2.45934	+	6.48474i	0.117111	+	0.308797i
$442$	−18.7501	+	3.36177i	−0.891852	+	0.159903i
$443$	2.88054	−	7.59535i	0.136858	−	0.360866i	−0.849013	−	0.528373i	$-0.822802\pi$
$443$	2.88054	−	7.59535i	0.136858	−	0.360866i	0.985871	+	0.167507i	$0.0535716\pi$
$444$	−1.00641	+	1.04778i	−0.0477621	+	0.0497256i
$445$	11.5873	−	40.0039i	0.549289	−	1.89637i
$446$	−14.3286	−	1.15672i	−0.678479	−	0.0547725i
$447$	−5.44907	+	2.85989i	−0.257732	+	0.135268i
$448$	−1.45607	−	1.51593i	−0.0687928	−	0.0716209i
$449$	−36.2509	+	15.4451i	−1.71079	+	0.728898i	−0.711121	+	0.703069i	$0.751812\pi$
$449$	−36.2509	+	15.4451i	−1.71079	+	0.728898i	−0.999666	+	0.0258291i	$0.991777\pi$
$450$	0.464180	+	1.22394i	0.0218816	+	0.0576971i
$451$	16.7901	−	2.72866i	0.790617	−	0.128488i
$452$	3.48199	−	2.20188i	0.163779	−	0.103568i
$453$	−0.654743	+	2.26044i	−0.0307625	+	0.106205i
$454$	−9.63049	−	13.9522i	−0.451981	−	0.654808i
$455$	−0.491821	−	2.22352i	−0.0230569	−	0.104240i
$456$	−2.71537	+	3.93389i	−0.127159	+	0.184221i
$457$	6.45116	+	7.90123i	0.301772	+	0.369604i	0.903124	−	0.429381i	$-0.141268\pi$
$457$	6.45116	+	7.90123i	0.301772	+	0.369604i	−0.601351	+	0.798985i	$0.705371\pi$
$458$	5.82591	+	7.13545i	0.272227	+	0.333418i
$459$	3.80049	−	2.85588i	0.177392	−	0.133301i
$460$	−1.72474	−	14.2045i	−0.0804166	−	0.662290i
$461$	5.74468	+	1.91785i	0.267556	+	0.0893234i	0.447281	−	0.894394i	$-0.352392\pi$
$461$	5.74468	+	1.91785i	0.267556	+	0.0893234i	−0.179725	+	0.983717i	$0.557521\pi$
$462$	1.06071	+	0.0856296i	0.0493488	+	0.00398385i
$463$	16.5610	−	14.6718i	0.769656	−	0.681856i	−0.183943	−	0.982937i	$-0.558886\pi$
$463$	16.5610	−	14.6718i	0.769656	−	0.681856i	0.953598	+	0.301081i	$0.0973476\pi$
$464$	−4.66010	−	2.94687i	−0.216340	−	0.136805i
$465$	−3.95941	−	1.68695i	−0.183613	−	0.0782303i
$466$	0.953132	+	0.154899i	0.0441530	+	0.00717556i
$467$	6.00840	+	5.32298i	0.278035	+	0.246318i	0.790603	−	0.612329i	$-0.209767\pi$
$467$	6.00840	+	5.32298i	0.278035	+	0.246318i	−0.512568	+	0.858647i	$0.671306\pi$
$468$	−2.42078	+	1.32129i	−0.111900	+	0.0610768i
$469$	1.23152	−	1.09103i	0.0568662	−	0.0503791i
$470$	−0.0365897	+	0.0231379i	−0.00168776	+	0.00106727i
$471$	3.04328	−	0.245679i	0.140227	−	0.0113203i
$472$	9.16015	−	44.8694i	0.421630	−	2.06528i
$473$	36.5522	+	9.00930i	1.68067	+	0.414248i
$474$	−10.4998	+	1.70638i	−0.482272	+	0.0783768i
$475$	1.54862	+	0.979289i	0.0710556	+	0.0449329i
$476$	0.818177	+	0.429413i	0.0375011	+	0.0196821i
$477$	−0.565167	−	1.95118i	−0.0258772	−	0.0893385i
$478$	4.51241	+	22.1032i	0.206393	+	1.01098i
$479$	0.0388695	−	0.964536i	0.00177599	−	0.0440708i	−0.998058	−	0.0622915i	$-0.980159\pi$
$479$	0.0388695	−	0.964536i	0.00177599	−	0.0440708i	0.999834	+	0.0182208i	$0.00580017\pi$
$480$	8.91449	+	4.67868i	0.406889	+	0.213552i
$481$	3.79787	−	5.69867i	0.173168	−	0.259837i
$482$	20.5817	−	10.8021i	0.937470	−	0.492022i
$483$	0.819878	+	1.72786i	0.0373057	+	0.0786202i
$484$	1.22362	−	2.11937i	0.0556190	−	0.0963349i
$485$	17.1735	+	29.7454i	0.779809	+	1.35067i
$486$	−0.631319	+	0.914623i	−0.0286372	+	0.0414881i
$487$	−34.7723	+	26.1297i	−1.57568	+	1.18405i	−0.685874	+	0.727720i	$0.740580\pi$
$487$	−34.7723	+	26.1297i	−1.57568	+	1.18405i	−0.889810	+	0.456330i	$0.849164\pi$
$488$	−2.47542	−	4.28755i	−0.112057	−	0.194088i
$489$	−0.731621	+	6.02544i	−0.0330850	+	0.272480i
$490$	−8.21275	+	17.3080i	−0.371014	+	0.781896i
$491$	24.3703	−	25.3722i	1.09982	−	1.14503i	0.111323	−	0.993784i	$-0.464491\pi$
$491$	24.3703	−	25.3722i	1.09982	−	1.14503i	0.988496	−	0.151248i	$-0.0483292\pi$
$492$	−3.44172	+	0.277844i	−0.155165	+	0.0125262i
$493$	13.5004	+	3.32755i	0.608028	+	0.149865i
$494$	2.58005	−	5.67435i	0.116082	−	0.255301i
$495$	−9.09383	+	2.24143i	−0.408737	+	0.100745i
$496$	3.09618	−	1.03366i	0.139023	−	0.0464126i
$497$	0.759724	+	1.60108i	0.0340783	+	0.0718184i
$498$	−12.7610	−	4.26026i	−0.571836	−	0.190907i
$499$	−13.0507	−	18.9072i	−0.584229	−	0.846402i	0.413720	−	0.910404i	$-0.364229\pi$
$499$	−13.0507	−	18.9072i	−0.584229	−	0.846402i	−0.997950	+	0.0640016i	$0.979614\pi$
$500$	−3.11514	+	6.56503i	−0.139313	+	0.293597i
$501$	0.968255	+	24.0270i	0.0432584	+	1.07345i
$502$	−4.17570	+	1.02922i	−0.186370	+	0.0459362i
$503$	−24.7000	+	10.5237i	−1.10132	+	0.469227i	−0.864656	−	0.502365i	$-0.832463\pi$
$503$	−24.7000	+	10.5237i	−1.10132	+	0.469227i	−0.236661	+	0.971592i	$0.576053\pi$
$504$	−0.770712	−	0.125253i	−0.0343303	−	0.00557921i
$505$	−5.77134	−	28.2699i	−0.256821	−	1.25799i
$506$	−31.5186			−1.40117
$507$	10.1327	−	8.14427i	0.450008	−	0.361700i
$508$	−14.5937			−0.647489
$509$	4.16082	+	20.3810i	0.184425	+	0.903373i	0.961677	+	0.274184i	$0.0884077\pi$
$509$	4.16082	+	20.3810i	0.184425	+	0.903373i	−0.777252	+	0.629189i	$0.783387\pi$
$510$	12.9617	+	2.10647i	0.573952	+	0.0932763i
$511$	−3.47656	+	1.48122i	−0.153794	+	0.0655254i
$512$	−18.6623	+	4.59984i	−0.824764	+	0.203286i
$513$	0.0626380	+	1.55435i	0.00276554	+	0.0686261i
$514$	−10.9030	+	22.9776i	−0.480911	+	1.01350i
$515$	−6.30878	−	9.13984i	−0.277998	−	0.402750i
$516$	−7.24844	−	2.41988i	−0.319095	−	0.106529i
$517$	−0.0253172	−	0.0533549i	−0.00111345	−	0.00234654i
$518$	0.508787	−	0.169858i	0.0223548	−	0.00746314i
$519$	10.2444	−	2.52502i	0.449679	−	0.110836i
$520$	−26.2588	−	8.29325i	−1.15152	−	0.363683i
$521$	35.7798	+	8.81894i	1.56754	+	0.386365i	0.925025	−	0.379906i	$-0.124044\pi$
$521$	35.7798	+	8.81894i	1.56754	+	0.386365i	0.642518	+	0.766271i	$0.277890\pi$
$522$	−3.23998	+	0.261558i	−0.141810	+	0.0114481i
$523$	−24.7991	+	25.8186i	−1.08439	+	1.12897i	−0.0933184	+	0.995636i	$0.529747\pi$
$523$	−24.7991	+	25.8186i	−1.08439	+	1.12897i	−0.991071	+	0.133333i	$0.957432\pi$
$524$	3.99289	−	8.41484i	0.174430	−	0.367604i
$525$	−0.0360772	+	0.297122i	−0.00157454	+	0.0129675i
$526$	−10.9634	−	18.9892i	−0.478029	−	0.827970i
$527$	−6.58071	+	4.94509i	−0.286660	+	0.215411i
$528$	4.03527	−	5.84609i	0.175612	−	0.254418i
$529$	−16.8225	−	29.1374i	−0.731412	−	1.26684i
$530$	2.80564	−	4.85951i	0.121869	−	0.211084i
$531$	−6.38899	−	13.4645i	−0.277259	−	0.584310i
$532$	−0.267729	+	0.140515i	−0.0116075	+	0.00609210i
$533$	15.7376	−	4.15222i	0.681671	−	0.179852i
$534$	16.4890	+	8.65411i	0.713550	+	0.374500i
$535$	−0.481174	+	11.9402i	−0.0208030	+	0.516220i
$536$	−3.97957	−	19.4932i	−0.171891	−	0.841979i
$537$	−4.34220	−	14.9910i	−0.187380	−	0.646910i
$538$	−14.2310	−	7.46901i	−0.613543	−	0.322012i
$539$	−22.0883	−	13.9678i	−0.951411	−	0.601636i
$540$	1.87657	−	0.304972i	0.0807545	−	0.0131239i
$541$	−17.6550	−	4.35157i	−0.759048	−	0.187089i	−0.159248	−	0.987239i	$-0.550907\pi$
$541$	−17.6550	−	4.35157i	−0.759048	−	0.187089i	−0.599800	+	0.800150i	$0.704753\pi$
$542$	−6.25790	+	30.6532i	−0.268800	+	1.31667i
$543$	−8.28575	+	0.668895i	−0.355576	+	0.0287050i
$544$	16.2748	−	10.2916i	0.697778	−	0.441248i
$545$	−4.64577	+	4.11579i	−0.199003	+	0.176301i
$546$	1.01809	−	0.0165975i	0.0435703	−	0.000710307i
$547$	28.5256	+	25.2715i	1.21967	+	1.08053i	0.994340	+	0.106247i	$0.0338834\pi$
$547$	28.5256	+	25.2715i	1.21967	+	1.08053i	0.225327	+	0.974283i	$0.427655\pi$
$548$	0.624333	+	0.101464i	0.0266702	+	0.00433433i
$549$	−1.48226	−	0.631534i	−0.0632615	−	0.0269532i
$550$	−4.16899	−	2.63631i	−0.177766	−	0.112413i
$551$	−3.40565	+	3.01714i	−0.145086	+	0.128535i
$552$	23.0516	+	1.86091i	0.981140	+	0.0792058i
$553$	−2.30711	−	0.770225i	−0.0981081	−	0.0327533i
$554$	0.540736	+	4.45336i	0.0229737	+	0.189205i
$555$	−3.77411	+	2.83606i	−0.160202	+	0.120384i
$556$	−7.31899	−	8.96413i	−0.310394	−	0.380164i
$557$	−6.75586	−	8.27443i	−0.286255	−	0.350599i	0.611381	−	0.791337i	$-0.290614\pi$
$557$	−6.75586	−	8.27443i	−0.286255	−	0.350599i	−0.897636	+	0.440738i	$0.854717\pi$
$558$	1.09316	−	1.58371i	0.0462770	−	0.0670438i
$559$	35.6440	+	5.19786i	1.50758	+	0.219846i
$560$	−0.676361	−	0.979878i	−0.0285815	−	0.0414074i
$561$	−4.98392	+	17.2065i	−0.210421	+	0.726459i
$562$	−25.4769	+	16.1106i	−1.07468	+	0.679585i
$563$	−36.9922	+	6.01182i	−1.55904	+	0.253368i	−0.877920	−	0.478808i	$-0.841069\pi$
$563$	−36.9922	+	6.01182i	−1.55904	+	0.253368i	−0.681116	+	0.732176i	$0.738505\pi$
$564$	0.00425094	+	0.0112088i	0.000178997	+	0.000471976i
$565$	12.3158	−	5.24729i	0.518132	−	0.220755i
$566$	1.68879	+	1.75822i	0.0709853	+	0.0739035i
$567$	−0.225004	+	0.118091i	−0.00944927	+	0.00495936i
$568$	21.3603	+	1.72438i	0.896258	+	0.0723534i
$569$	6.97988	−	24.0974i	0.292612	−	1.01021i	−0.670678	−	0.741749i	$-0.733997\pi$
$569$	6.97988	−	24.0974i	0.292612	−	1.01021i	0.963290	−	0.268465i	$-0.0865163\pi$
$570$	−2.97667	+	3.09904i	−0.124679	+	0.129804i
$571$	−6.46131	+	17.0371i	−0.270397	+	0.712979i	0.729192	+	0.684309i	$0.239896\pi$
$571$	−6.46131	+	17.0371i	−0.270397	+	0.712979i	−0.999589	+	0.0286694i	$0.990873\pi$
$572$	4.30148	−	9.46032i	0.179854	−	0.395556i
$573$	5.27522	+	13.9096i	0.220375	+	0.581082i
$574$	1.17282	+	0.499692i	0.0489526	+	0.0208567i
$575$	0.356951	−	8.85766i	0.0148859	−	0.369390i
$576$	−5.23145	+	6.40736i	−0.217977	+	0.266973i
$577$	−10.2767			−0.427823			−0.213911	−	0.976853i	$-0.568620\pi$
$577$	−10.2767			−0.427823			−0.213911	+	0.976853i	$0.568620\pi$
$578$	3.93589	−	4.82059i	0.163712	−	0.200510i
$579$	0.392357	+	1.35457i	0.0163058	+	0.0562942i
$580$	4.16221	+	3.68740i	0.172826	+	0.153111i
$581$	−2.13091	−	2.21851i	−0.0884050	−	0.0920393i
$582$	−14.5672	+	4.86324i	−0.603829	+	0.201588i
$583$	6.11949	+	4.59849i	0.253443	+	0.190450i
$584$	−5.50805	+	45.3629i	−0.227925	+	1.87713i
$585$	−8.45311	+	2.97607i	−0.349493	+	0.123045i
$586$	3.52140	+	29.0013i	0.145468	+	1.19803i
$587$	14.7915	−	25.6197i	0.610511	−	1.05744i	−0.380643	−	0.924722i	$-0.624297\pi$
$587$	14.7915	−	25.6197i	0.610511	−	1.05744i	0.991154	−	0.132714i	$-0.0423693\pi$
$588$	4.24098	+	3.18689i	0.174895	+	0.131425i
$589$	−0.108461	−	2.69142i	−0.00446904	−	0.110898i
$590$	14.5982	−	38.4924i	0.601000	−	1.58471i
$591$	0.601413	−	2.94592i	0.0247388	−	0.121179i
$592$	0.716199	−	3.50817i	0.0294356	−	0.144185i
$593$	4.04374	−	10.6625i	0.166056	−	0.437855i	−0.825997	−	0.563675i	$-0.809387\pi$
$593$	4.04374	−	10.6625i	0.166056	−	0.437855i	0.992053	+	0.125820i	$0.0401562\pi$
$594$	−0.168626	−	4.18440i	−0.00691879	−	0.171688i
$595$	2.40038	+	1.80377i	0.0984061	+	0.0739474i
$596$	−2.35359	+	4.07654i	−0.0964068	+	0.166982i
$597$	−1.71593	−	14.1320i	−0.0702284	−	0.578383i
$598$	−30.0167	+	2.91638i	−1.22747	+	0.119260i
$599$	0.682942	−	5.62453i	0.0279042	−	0.229812i	−0.972084	−	0.234633i	$-0.924611\pi$
$599$	0.682942	−	5.62453i	0.0279042	−	0.229812i	0.999988	+	0.00482040i	$0.00153439\pi$
$600$	2.89340	+	2.17425i	0.118123	+	0.0887633i
$601$	37.8075	−	12.6220i	1.54220	−	0.514862i	0.586688	−	0.809813i	$-0.300432\pi$
$601$	37.8075	−	12.6220i	1.54220	−	0.514862i	0.955512	+	0.294951i	$0.0953033\pi$
$602$	1.95442	+	2.03477i	0.0796563	+	0.0829310i
$603$	−4.84639	−	4.29353i	−0.197360	−	0.174846i
$604$	0.500814	+	1.72901i	0.0203778	+	0.0703525i
$605$	5.02934	−	6.15983i	0.204472	−	0.250433i
$606$	12.9010			0.524067
$607$	−17.8892	+	21.9103i	−0.726099	+	0.889310i	−0.997317	−	0.0732078i	$-0.976676\pi$
$607$	−17.8892	+	21.9103i	−0.726099	+	0.889310i	0.271217	+	0.962518i	$0.412574\pi$
$608$	−0.253716	+	6.29591i	−0.0102896	+	0.255333i
$609$	−0.683758	−	0.291322i	−0.0277073	−	0.0118050i
$610$	−1.57820	−	4.16137i	−0.0638994	−	0.168489i
$611$	−0.0290477	−	0.0484699i	−0.00117514	−	0.00196088i
$612$	1.28944	−	3.39998i	0.0521227	−	0.137436i
$613$	0.612819	−	0.638012i	0.0247515	−	0.0257691i	−0.708712	−	0.705498i	$-0.750723\pi$
$613$	0.612819	−	0.638012i	0.0247515	−	0.0257691i	0.733463	+	0.679729i	$0.237903\pi$
$614$	−4.94966	+	17.0882i	−0.199752	+	0.689624i
$615$	−11.1838	−	0.902847i	−0.450973	−	0.0364063i
$616$	2.60528	−	1.36736i	0.104970	−	0.0550925i
$617$	−10.4723	−	10.9028i	−0.421599	−	0.438931i	0.476200	−	0.879337i	$-0.342014\pi$
$617$	−10.4723	−	10.9028i	−0.421599	−	0.438931i	−0.897799	+	0.440406i	$0.854834\pi$
$618$	4.56833	−	1.94638i	0.183765	−	0.0782950i
$619$	−15.1514	−	39.9509i	−0.608986	−	1.60576i	−0.783697	−	0.621144i	$-0.786668\pi$
$619$	−15.1514	−	39.9509i	−0.608986	−	1.60576i	0.174711	−	0.984620i	$-0.444101\pi$
$620$	−3.24936	+	0.528072i	−0.130497	+	0.0212079i
$621$	6.36114	−	4.02254i	0.255264	−	0.161419i
$622$	−9.10591	+	31.4372i	−0.365114	+	1.26052i
$623$	2.41879	+	3.50422i	0.0969068	+	0.140394i
$624$	3.30205	−	5.94090i	0.132188	−	0.237826i
$625$	−16.7590	+	24.2796i	−0.670360	+	0.971184i
$626$	−5.57885	−	6.83285i	−0.222976	−	0.273096i
$627$	−3.70731	−	4.54062i	−0.148056	−	0.181335i
$628$	1.86700	−	1.40296i	0.0745016	−	0.0559843i
$629$	1.08838	+	8.96360i	0.0433965	+	0.357402i
$630$	−0.665804	−	0.222278i	−0.0265262	−	0.00885576i
$631$	−14.4194	−	1.16405i	−0.574025	−	0.0463401i	−0.209954	−	0.977711i	$-0.567331\pi$
$631$	−14.4194	−	1.16405i	−0.574025	−	0.0463401i	−0.364071	+	0.931371i	$0.618614\pi$
$632$	−22.0150	+	19.5036i	−0.875711	+	0.775812i
$633$	0.497707	+	0.314731i	0.0197821	+	0.0125094i
$634$	12.1250	+	5.16598i	0.481546	+	0.205167i
$635$	−46.8076	−	7.60698i	−1.85750	−	0.301874i
$636$	−1.16304	−	1.03037i	−0.0461177	−	0.0408567i
$637$	−22.3282	−	11.2584i	−0.884677	−	0.446075i
$638$	9.16823	−	8.12234i	0.362974	−	0.321567i
$639$	5.89443	−	3.72741i	0.233180	−	0.147454i
$640$	−2.70492	+	0.218363i	−0.106921	+	0.00863157i
$641$	1.59768	−	7.82595i	0.0631045	−	0.309106i	−0.935972	−	0.352075i	$-0.885476\pi$
$641$	1.59768	−	7.82595i	0.0631045	−	0.309106i	0.999076	+	0.0429682i	$0.0136814\pi$
$642$	−5.18788	−	1.27870i	−0.204749	−	0.0504661i
$643$	38.3299	−	6.22922i	1.51158	−	0.245656i	0.652617	−	0.757688i	$-0.273671\pi$
$643$	38.3299	−	6.22922i	1.51158	−	0.245656i	0.858967	+	0.512031i	$0.171107\pi$
$644$	1.23641	+	0.781860i	0.0487215	+	0.0308096i
$645$	−21.9872	−	11.5398i	−0.865746	−	0.454379i
$646$	2.28658	+	7.89420i	0.0899645	+	0.310593i
$647$	−3.06682	−	15.0223i	−0.120569	−	0.590586i	−0.994518	−	0.104568i	$-0.966654\pi$
$647$	−3.06682	−	15.0223i	−0.120569	−	0.590586i	0.873949	−	0.486018i	$-0.161551\pi$
$648$	−0.123728	+	3.07028i	−0.00486050	+	0.120612i
$649$	49.7266	+	26.0985i	1.95194	+	1.02446i
$650$	−4.21427	−	2.12494i	−0.165297	−	0.0833468i
$651$	0.389604	−	0.204480i	0.0152698	−	0.00801420i
$652$	1.99030	+	4.19447i	0.0779462	+	0.164268i
$653$	4.07172	−	7.05242i	0.159339	−	0.275983i	−0.775292	−	0.631603i	$-0.782397\pi$
$653$	4.07172	−	7.05242i	0.159339	−	0.275983i	0.934630	+	0.355621i	$0.115731\pi$
$654$	−1.38759	−	2.40338i	−0.0542591	−	0.0939796i
$655$	17.1930	−	24.9084i	0.671787	−	0.973252i
$656$	6.80309	−	5.11219i	0.265616	−	0.199598i
$657$	7.43564	+	12.8789i	0.290092	+	0.502454i
$658$	0.000533491	−	0.00439369i	2.07976e−5	−	0.000171284i
$659$	19.7682	−	41.6606i	0.770060	−	1.62287i	−0.0122072	−	0.999925i	$-0.503886\pi$
$659$	19.7682	−	41.6606i	0.770060	−	1.62287i	0.782268	−	0.622943i	$-0.214063\pi$
$660$	−4.96272	+	5.16674i	−0.193174	+	0.201115i
$661$	39.0224	−	3.15022i	1.51780	−	0.122529i	0.706730	−	0.707483i	$-0.250169\pi$
$661$	39.0224	−	3.15022i	1.51780	−	0.122529i	0.811067	+	0.584954i	$0.198887\pi$
$662$	−9.29262	−	2.29042i	−0.361168	−	0.0890199i
$663$	−3.15434	+	16.8478i	−0.122504	+	0.654313i
$664$	−36.1165	+	8.90191i	−1.40159	+	0.345461i
$665$	−0.931957	+	0.311133i	−0.0361397	+	0.0120652i
$666$	−0.904910	−	1.90706i	−0.0350646	−	0.0738970i
$667$	20.8803	+	6.97086i	0.808487	+	0.269913i
$668$	10.4485	+	15.1373i	0.404266	+	0.585680i
$669$	−5.54511	+	11.6861i	−0.214386	+	0.451809i
$670$	−0.720157	−	17.8705i	−0.0278221	−	0.690398i
$671$	5.89489	−	1.45296i	0.227570	−	0.0560909i
$672$	−0.946916	+	0.403443i	−0.0365281	+	0.0155632i
$673$	45.8319	+	7.44840i	1.76669	+	0.287115i	0.954920	−	0.296864i	$-0.0959409\pi$
$673$	45.8319	+	7.44840i	1.76669	+	0.287115i	0.811769	+	0.583979i	$0.198505\pi$
$674$	−2.63214	−	12.8931i	−0.101386	−	0.496623i
$675$	1.17785			0.0453355
$676$	3.22115	−	9.40754i	0.123891	−	0.361829i
$677$	−19.2878			−0.741291			−0.370646	−	0.928774i	$-0.620864\pi$
$677$	−19.2878			−0.741291			−0.370646	+	0.928774i	$0.620864\pi$
$678$	1.19730	+	5.86478i	0.0459821	+	0.225235i
$679$	−3.46603	−	0.563285i	−0.133014	−	0.0216169i
$680$	33.4025	−	14.2315i	1.28093	−	0.545752i
$681$	−14.8113	+	3.65066i	−0.567570	+	0.139893i
$682$	0.291983	+	7.24548i	0.0111806	+	0.277444i
$683$	−16.2431	+	34.2317i	−0.621527	+	1.30984i	0.311573	+	0.950222i	$0.399144\pi$
$683$	−16.2431	+	34.2317i	−0.621527	+	1.30984i	−0.933100	+	0.359618i	$0.882907\pi$
$684$	0.675933	+	0.979259i	0.0258450	+	0.0374429i
$685$	1.94959	+	0.650870i	0.0744901	+	0.0248685i
$686$	−1.68710	−	3.55548i	−0.0644136	−	0.135749i
$687$	7.86220	−	2.62479i	0.299962	−	0.100142i
$688$	18.2859	−	4.50708i	0.697144	−	0.171831i
$689$	6.25338	+	3.81314i	0.238235	+	0.145269i
$690$	20.1857	+	4.97532i	0.768455	+	0.189407i
$691$	40.9270	−	3.30397i	1.55694	−	0.125689i	0.728214	−	0.685349i	$-0.240350\pi$
$691$	40.9270	−	3.30397i	1.55694	−	0.125689i	0.828722	+	0.559660i	$0.189068\pi$
$692$	5.59061	−	5.82044i	0.212523	−	0.221260i
$693$	0.410491	−	0.865092i	0.0155933	−	0.0328621i
$694$	−2.42568	+	19.9773i	−0.0920775	+	0.758327i
$695$	−18.8023	−	32.5665i	−0.713212	−	1.23532i
$696$	−7.18488	+	5.39909i	−0.272342	+	0.204652i
$697$	−12.1907	+	17.6613i	−0.461757	+	0.668970i
$698$	1.30232	+	2.25568i	0.0492934	+	0.0853786i
$699$	0.434443	−	0.752478i	0.0164322	−	0.0284613i
$700$	0.0981443	+	0.206835i	0.00370951	+	0.00781762i
$701$	−18.6597	+	9.79339i	−0.704769	+	0.369891i	−0.778721	−	0.627371i	$-0.784131\pi$
$701$	−18.6597	+	9.79339i	−0.704769	+	0.369891i	0.0739521	+	0.997262i	$0.476439\pi$
$702$	−0.547769	−	3.96941i	−0.0206742	−	0.149816i
$703$	−2.61623	−	1.37310i	−0.0986730	−	0.0517876i
$704$	1.25508	−	31.1445i	0.0473027	−	1.17380i
$705$	0.00779182	+	0.0381669i	0.000293457	+	0.00143745i
$706$	4.63524	+	16.0027i	0.174450	+	0.602270i
$707$	2.61193	+	1.37085i	0.0982318	+	0.0515560i
$708$	−9.63489	−	6.09273i	−0.362101	−	0.228979i
$709$	−31.0608	+	5.04787i	−1.16651	+	0.189577i	−0.712666	−	0.701503i	$-0.752513\pi$
$709$	−31.0608	+	5.04787i	−1.16651	+	0.189577i	−0.453846	+	0.891080i	$0.649948\pi$
$710$	18.7047	+	4.61028i	0.701973	+	0.173021i
$711$	−1.91459	+	9.37830i	−0.0718029	+	0.351714i
$712$	51.3213	−	4.14308i	1.92335	−	0.155269i
$713$	−11.0146	+	6.96521i	−0.412500	+	0.260849i
$714$	−1.00490	+	0.890265i	−0.0376075	+	0.0333173i
$715$	18.7277	−	28.1008i	0.700378	−	1.05091i
$716$	−8.93571	−	7.91635i	−0.333943	−	0.295848i
$717$	20.0360	+	3.25617i	0.748258	+	0.121604i
$718$	3.38096	+	1.44049i	0.126176	+	0.0537587i
$719$	0.668635	+	0.422819i	0.0249359	+	0.0157685i	0.546876	−	0.837214i	$-0.315817\pi$
$719$	0.668635	+	0.422819i	0.0249359	+	0.0157685i	−0.521940	+	0.852982i	$0.674791\pi$
$720$	−3.50716	+	3.10707i	−0.130704	+	0.115794i
$721$	1.13172	+	0.0913623i	0.0421476	+	0.00340251i
$722$	17.4780	+	5.83501i	0.650463	+	0.217157i
$723$	−2.52106	−	20.7628i	−0.0937591	−	0.772176i
$724$	−5.08318	+	3.81977i	−0.188915	+	0.141960i
$725$	2.17879	+	2.66853i	0.0809182	+	0.0991068i
$726$	2.24876	+	2.75423i	0.0834594	+	0.102219i
$727$	−18.2826	+	26.4869i	−0.678064	+	0.982345i	0.321310	+	0.946974i	$0.395877\pi$
$727$	−18.2826	+	26.4869i	−0.678064	+	0.982345i	−0.999374	+	0.0353714i	$0.988739\pi$
$728$	2.35462	−	1.54327i	0.0872681	−	0.0571973i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	−11.4288	+	39.4569i	−0.423000	+	1.46037i
$731$	−40.1413	+	25.3838i	−1.48468	+	0.938854i
$732$	−1.21645	+	0.197692i	−0.0449611	+	0.00730689i
$733$	18.5537	+	48.9220i	0.685296	+	1.80698i	0.583407	+	0.812180i	$0.301719\pi$
$733$	18.5537	+	48.9220i	0.685296	+	1.80698i	0.101889	+	0.994796i	$0.467511\pi$
$734$	8.46425	−	3.60628i	0.312421	−	0.133110i
$735$	11.9413	+	12.4322i	0.440462	+	0.458570i
$736$	26.9934	−	14.1672i	0.994991	−	0.522212i
$737$	24.3189	+	1.96323i	0.895800	+	0.0723164i
$738$	1.39577	−	4.81877i	0.0513791	−	0.177381i
$739$	5.84368	−	6.08392i	0.214963	−	0.223800i	−0.604987	−	0.796235i	$-0.706822\pi$
$739$	5.84368	−	6.08392i	0.214963	−	0.223800i	0.819950	+	0.572435i	$0.194001\pi$
$740$	−1.28050	+	3.37639i	−0.0470720	+	0.124119i
$741$	−3.95079	−	3.98123i	−0.145136	−	0.146254i
$742$	0.203428	+	0.536395i	0.00746807	+	0.0196917i
$743$	−25.8161	−	10.9992i	−0.947099	−	0.403521i	−0.137498	−	0.990502i	$-0.543906\pi$
$743$	−25.8161	−	10.9992i	−0.947099	−	0.403521i	−0.809601	+	0.586981i	$0.800316\pi$
$744$	0.214241	−	5.31633i	0.00785445	−	0.194906i
$745$	−9.67379	+	11.8482i	−0.354420	+	0.434086i
$746$	1.74335			0.0638286
$747$	−7.65605	+	9.37696i	−0.280120	+	0.343085i
$748$	3.81221	+	13.1613i	0.139388	+	0.481224i
$749$	−0.914463	−	0.810144i	−0.0334138	−	0.0296020i
$750$	−7.31370	−	7.61437i	−0.267059	−	0.278038i
$751$	2.15215	−	0.718492i	0.0785329	−	0.0262181i	−0.277130	−	0.960832i	$-0.589383\pi$
$751$	2.15215	−	0.718492i	0.0785329	−	0.0262181i	0.355663	+	0.934614i	$0.384255\pi$
$752$	−0.0236190	−	0.0177485i	−0.000861295	−	0.000647222i
$753$	−0.466449	+	3.84155i	−0.0169984	+	0.139994i
$754$	7.97980	−	8.58364i	0.290607	−	0.312598i
$755$	0.705057	+	5.80667i	0.0256597	+	0.211326i
$756$	−0.0971848	+	0.168329i	−0.00353458	+	0.00612207i
$757$	36.8745	+	27.7094i	1.34023	+	1.00711i	0.997712	+	0.0676012i	$0.0215345\pi$
$757$	36.8745	+	27.7094i	1.34023	+	1.00711i	0.342513	+	0.939513i	$0.388722\pi$
$758$	0.354309	+	8.79209i	0.0128691	+	0.319343i
$759$	−10.0568	+	26.5176i	−0.365039	+	0.962529i
$760$	−2.37649	+	11.6408i	−0.0862042	+	0.422256i
$761$	−6.46757	+	31.6803i	−0.234449	+	1.14841i	0.676676	+	0.736281i	$0.263420\pi$
$761$	−6.46757	+	31.6803i	−0.234449	+	1.14841i	−0.911126	+	0.412128i	$0.864786\pi$
$762$	7.51890	−	19.8257i	0.272381	−	0.718209i
$763$	−0.0255506	−	0.634032i	−0.000924995	−	0.0229535i
$764$	9.09681	+	6.83581i	0.329111	+	0.247311i
$765$	5.90800	−	10.2330i	0.213604	−	0.369973i
$766$	−2.64030	−	21.7448i	−0.0953978	−	0.785672i
$767$	49.7720	+	20.2538i	1.79716	+	0.731321i
$768$	−1.84785	+	15.2184i	−0.0666785	+	0.549147i
$769$	−13.4493	−	10.1065i	−0.484992	−	0.364448i	0.329942	−	0.944001i	$-0.392971\pi$
$769$	−13.4493	−	10.1065i	−0.484992	−	0.364448i	−0.814935	+	0.579553i	$0.803227\pi$
$770$	2.50889	−	0.837590i	0.0904140	−	0.0301846i
$771$	15.8529	+	16.5047i	0.570930	+	0.594401i
$772$	0.807423	+	0.715314i	0.0290598	+	0.0257447i
$773$	−6.27409	−	21.6607i	−0.225663	−	0.779080i	−0.990814	−	0.135229i	$-0.956823\pi$
$773$	−6.27409	−	21.6607i	−0.225663	−	0.779080i	0.765151	−	0.643851i	$-0.222664\pi$
$774$	7.02196	−	8.60034i	0.252399	−	0.309133i
$775$	−2.03950			−0.0732611
$776$	−26.8549	+	32.8913i	−0.964036	+	1.18073i
$777$	0.0194343	−	0.482258i	0.000697202	−	0.0173009i
$778$	12.0120	+	5.11785i	0.430652	+	0.183484i
$779$	−2.49015	−	6.56598i	−0.0892187	−	0.235250i
$780$	−4.24817	+	5.37974i	−0.152109	+	0.192626i
$781$	−9.31895	+	24.5720i	−0.333458	+	0.879257i
$782$	27.5451	−	28.6774i	0.985009	−	1.02550i
$783$	−0.813741	+	2.80936i	−0.0290807	+	0.100398i
$784$	−13.0317	−	1.05203i	−0.465419	−	0.0375725i
$785$	6.71951	−	3.52667i	0.239830	−	0.125872i
$786$	9.37448	+	9.75986i	0.334377	+	0.348123i
$787$	29.8157	−	12.7033i	1.06281	−	0.452823i	0.211445	−	0.977390i	$-0.432183\pi$
$787$	29.8157	−	12.7033i	1.06281	−	0.452823i	0.851369	+	0.524567i	$0.175773\pi$
$788$	−0.815526	−	2.15037i	−0.0290519	−	0.0766036i
$789$	−19.4745	+	3.16491i	−0.693309	+	0.112674i
$790$	−22.3468	+	14.1312i	−0.795062	+	0.502767i
$791$	−0.380780	+	1.31461i	−0.0135390	+	0.0467420i
$792$	−6.57754	−	9.52921i	−0.233723	−	0.338606i
$793$	5.47956	−	1.92918i	0.194585	−	0.0685070i
$794$	16.5690	−	24.0044i	0.588013	−	0.851884i
$795$	−3.19326	−	3.91103i	−0.113253	−	0.138710i
$796$	−6.88668	−	8.43465i	−0.244092	−	0.298958i
$797$	−12.1022	+	9.09418i	−0.428680	+	0.322132i	−0.793088	−	0.609107i	$-0.791528\pi$
$797$	−12.1022	+	9.09418i	−0.428680	+	0.322132i	0.364408	+	0.931240i	$0.381272\pi$
$798$	−0.0529533	−	0.436109i	−0.00187453	−	0.0154381i
$799$	0.0706709	+	0.0235934i	0.00250016	+	0.000834675i
$800$	4.75544	+	0.383899i	0.168130	+	0.0135729i
$801$	12.5423	−	11.1115i	0.443159	−	0.392604i
$802$	5.21966	+	3.30071i	0.184312	+	0.116552i
$803$	−51.5539	−	21.9651i	−1.81930	−	0.775130i
$804$	−4.88838	−	0.794440i	−0.172400	−	0.0280177i
$805$	3.55811	+	3.15221i	0.125407	+	0.111101i
$806$	0.948487	+	6.87321i	0.0334090	+	0.242099i
$807$	−10.8247	+	9.58985i	−0.381048	+	0.337579i
$808$	30.1479	−	19.0644i	1.06060	−	0.670682i
$809$	−32.9081	+	2.65662i	−1.15699	+	0.0934017i	−0.644022	−	0.765007i	$-0.722735\pi$
$809$	−32.9081	+	2.65662i	−1.15699	+	0.0934017i	−0.512966	+	0.858409i	$0.671453\pi$
$810$	−0.552529	+	2.70647i	−0.0194139	+	0.0950956i
$811$	25.4843	+	6.28131i	0.894873	+	0.220566i	0.659827	−	0.751418i	$-0.270630\pi$
$811$	25.4843	+	6.28131i	0.894873	+	0.220566i	0.235046	+	0.971984i	$0.424476\pi$
$812$	−0.561138	+	0.0911937i	−0.0196921	+	0.00320027i
$813$	23.7928	+	15.0457i	0.834452	+	0.527675i
$814$	7.04306	+	3.69648i	0.246859	+	0.129562i
$815$	4.19730	+	14.4908i	0.147025	+	0.507589i
$816$	1.79257	+	8.78060i	0.0627526	+	0.307383i
$817$	0.625782	−	15.5286i	0.0218933	−	0.543277i
$818$	−8.89033	−	4.66600i	−0.310843	−	0.163143i
$819$	0.310885	−	0.861852i	0.0108632	−	0.0301155i
$820$	−7.59926	+	3.98840i	−0.265378	+	0.139281i
$821$	2.73141	+	5.75632i	0.0953268	+	0.200897i	0.945512	−	0.325586i	$-0.105562\pi$
$821$	2.73141	+	5.75632i	0.0953268	+	0.200897i	−0.850186	+	0.526483i	$0.823510\pi$
$822$	−0.459507	+	0.795889i	−0.0160271	+	0.0277598i
$823$	−13.6428	−	23.6301i	−0.475560	−	0.823693i	0.524048	−	0.851688i	$-0.324421\pi$
$823$	−13.6428	−	23.6301i	−0.475560	−	0.823693i	−0.999608	+	0.0279951i	$0.991088\pi$
$824$	7.79932	−	11.2993i	0.271702	−	0.393629i
$825$	−3.54824	+	2.66633i	−0.123534	+	0.0928297i
$826$	2.10441	+	3.64494i	0.0732217	+	0.126824i
$827$	0.345894	−	2.84869i	0.0120279	−	0.0990587i	−0.985459	−	0.169916i	$-0.945650\pi$
$827$	0.345894	−	2.84869i	0.0120279	−	0.0990587i	0.997486	+	0.0708572i	$0.0225735\pi$
$828$	2.46793	−	5.20105i	0.0857664	−	0.180749i
$829$	−39.5450	+	41.1707i	−1.37346	+	1.42992i	−0.592039	+	0.805910i	$0.701677\pi$
$829$	−39.5450	+	41.1707i	−1.37346	+	1.42992i	−0.781417	+	0.624009i	$0.785503\pi$
$830$	−33.3304	+	2.69071i	−1.15691	+	0.0933958i
$831$	3.91930	+	0.966021i	0.135959	+	0.0335109i
$832$	−1.68650	−	29.7766i	−0.0584688	−	1.03232i
$833$	32.0124	−	7.89035i	1.10916	−	0.273384i
$834$	15.9488	−	5.32448i	0.552260	−	0.184372i
$835$	25.6222	+	53.9977i	0.886693	+	1.86867i
$836$	−4.25300	−	1.41986i	−0.147093	−	0.0491069i
$837$	−0.983630	−	1.42503i	−0.0339992	−	0.0492564i
$838$	13.3612	−	28.1581i	0.461555	−	0.972706i
$839$	1.04745	+	25.9921i	0.0361619	+	0.897348i	0.910869	+	0.412696i	$0.135413\pi$
$839$	1.04745	+	25.9921i	0.0361619	+	0.897348i	−0.874707	+	0.484652i	$0.838946\pi$
$840$	−1.88437	+	0.464454i	−0.0650168	+	0.0160252i
$841$	18.8093	−	8.01389i	0.648596	−	0.276341i
$842$	−3.09093	−	0.502325i	−0.106520	−	0.0173113i
$843$	5.42534	+	26.5751i	0.186859	+	0.915294i
$844$	0.450428			0.0155044
$845$	15.2352	−	28.4947i	0.524107	−	0.980246i
$846$	−0.0174175			−0.000598825
$847$	0.162622	+	0.796573i	0.00558774	+	0.0273706i
$848$	3.77982	+	0.614280i	0.129799	+	0.0210945i
$849$	2.01810	−	0.859834i	0.0692611	−	0.0295094i
$850$	6.04208	−	1.48924i	0.207242	−	0.0510805i
$851$	0.575608	+	14.2836i	0.0197316	+	0.489635i
$852$	2.28686	−	4.81945i	0.0783464	−	0.165112i
$853$	0.0699237	+	0.101302i	0.00239414	+	0.00346851i	0.824179	−	0.566329i	$-0.191637\pi$
$853$	0.0699237	+	0.101302i	0.00239414	+	0.00346851i	−0.821785	+	0.569798i	$0.807022\pi$
$854$	0.431594	+	0.144087i	0.0147688	+	0.00493056i
$855$	1.65754	+	3.49320i	0.0566868	+	0.119465i
$856$	−14.0130	+	4.67822i	−0.478953	+	0.159898i
$857$	52.8028	−	13.0147i	1.80371	−	0.444574i	0.813196	−	0.581990i	$-0.197726\pi$
$857$	52.8028	−	13.0147i	1.80371	−	0.444574i	0.990513	+	0.137416i	$0.0438797\pi$
$858$	10.6358	+	10.7177i	0.363100	+	0.365897i
$859$	−26.9721	−	6.64802i	−0.920276	−	0.226828i	−0.249403	−	0.968400i	$-0.580234\pi$
$859$	−26.9721	−	6.64802i	−0.920276	−	0.226828i	−0.670873	+	0.741572i	$0.734080\pi$
$860$	−18.9321	+	1.52836i	−0.645579	+	0.0521165i
$861$	0.794626	−	0.827294i	0.0270808	−	0.0281941i
$862$	9.62592	−	20.2862i	0.327860	−	0.690951i
$863$	0.508349	−	4.18663i	0.0173044	−	0.142515i	−0.981496	−	0.191483i	$-0.938670\pi$
$863$	0.508349	−	4.18663i	0.0173044	−	0.142515i	0.998800	+	0.0489685i	$0.0155934\pi$
$864$	2.02526	+	3.50785i	0.0689007	+	0.119340i
$865$	20.9652	−	15.7543i	0.712838	−	0.535663i
$866$	−21.4127	+	31.0216i	−0.727632	+	1.05416i
$867$	−2.79988	−	4.84953i	−0.0950889	−	0.164699i
$868$	0.168280	−	0.291469i	0.00571179	−	0.00989311i
$869$	−15.4622	−	32.5859i	−0.524520	−	1.10540i
$870$	−7.15382	+	3.75461i	−0.242537	+	0.127293i
$871$	23.3418	−	0.380530i	0.790906	−	0.0128938i
$872$	−6.79420	−	3.56587i	−0.230081	−	0.120756i
$873$	−0.556427	+	13.8076i	−0.0188322	+	0.467316i
$874$	2.60266	+	12.7487i	0.0880362	+	0.431230i
$875$	−0.671635	−	2.31875i	−0.0227054	−	0.0783882i
$876$	10.0721	+	5.28626i	0.340306	+	0.178606i
$877$	−46.3581	−	29.3151i	−1.56540	−	0.989900i	−0.984389	−	0.176006i	$-0.943682\pi$
$877$	−46.3581	−	29.3151i	−1.56540	−	0.989900i	−0.581013	−	0.813894i	$-0.697344\pi$
$878$	−28.2430	+	4.58993i	−0.953154	+	0.154903i
$879$	25.5234	+	6.29095i	0.860883	+	0.212189i
$880$	3.53166	−	17.2992i	0.119052	−	0.583156i
$881$	37.0492	−	2.99092i	1.24822	−	0.100767i	0.561369	−	0.827566i	$-0.310275\pi$
$881$	37.0492	−	2.99092i	1.24822	−	0.100767i	0.686850	+	0.726799i	$0.258993\pi$
$882$	−6.51446	+	4.11949i	−0.219353	+	0.138711i
$883$	19.5660	−	17.3340i	0.658449	−	0.583335i	−0.266310	−	0.963887i	$-0.585805\pi$
$883$	19.5660	−	17.3340i	0.658449	−	0.583335i	0.924759	+	0.380552i	$0.124266\pi$
$884$	4.84836	+	12.1814i	0.163068	+	0.409705i
$885$	−27.7270	−	24.5640i	−0.932034	−	0.825710i
$886$	8.91084	+	1.44815i	0.299365	+	0.0486516i
$887$	−11.9391	−	5.08677i	−0.400875	−	0.170797i	0.182113	−	0.983278i	$-0.441706\pi$
$887$	−11.9391	−	5.08677i	−0.400875	−	0.170797i	−0.582988	+	0.812481i	$0.698117\pi$
$888$	−4.93280	−	3.11931i	−0.165534	−	0.104677i
$889$	3.62894	−	3.21496i	0.121711	−	0.107826i
$890$	46.1356	+	3.72445i	1.54647	+	0.124844i
$891$	−3.57428	−	1.19327i	−0.119743	−	0.0399761i
$892$	1.19258	+	9.82181i	0.0399307	+	0.328859i
$893$	−0.0194905	+	0.0146461i	−0.000652223	+	0.000490114i
$894$	−4.32542	−	5.29768i	−0.144664	−	0.177181i
$895$	−24.5339	−	30.0486i	−0.820079	−	1.00441i
$896$	0.157604	−	0.228328i	0.00526517	−	0.00762791i
$897$	−7.12395	+	26.1846i	−0.237862	+	0.874278i
$898$	−24.8765	−	36.0399i	−0.830140	−	1.20267i
$899$	1.40903	−	4.86453i	0.0469937	−	0.162241i
$900$	0.761467	−	0.481522i	0.0253822	−	0.0160507i
$901$	−9.53199	+	1.54910i	−0.317557	+	0.0516080i
$902$	6.70364	+	17.6760i	0.223207	+	0.588548i
$903$	2.33553	−	0.995076i	0.0777216	−	0.0331141i
$904$	11.4646	+	11.9359i	0.381306	+	0.396982i
$905$	−18.2948	+	9.60187i	−0.608141	+	0.319177i
$906$	−2.60691	−	0.210452i	−0.0866089	−	0.00699179i
$907$	6.81338	−	23.5225i	0.226234	−	0.781052i	−0.764427	−	0.644710i	$-0.776978\pi$
$907$	6.81338	−	23.5225i	0.226234	−	0.781052i	0.990662	−	0.136342i	$-0.0435346\pi$
$908$	−8.08288	+	8.41517i	−0.268240	+	0.279267i
$909$	4.11639	−	10.8540i	0.136532	−	0.360006i
$910$	2.31184	−	1.02982i	0.0766366	−	0.0341383i
$911$	−9.81833	−	25.8888i	−0.325296	−	0.857734i	−0.993508	−	0.113763i	$-0.963709\pi$
$911$	−9.81833	−	25.8888i	−0.325296	−	0.857734i	0.668212	−	0.743971i	$-0.267060\pi$
$912$	−2.69785	−	1.14945i	−0.0893347	−	0.0380619i
$913$	1.83677	−	45.5790i	0.0607882	−	1.50844i
$914$	−7.16949	+	8.78103i	−0.237146	+	0.290451i
$915$	−4.00467			−0.132390
$916$	4.00977	−	4.91107i	0.132486	−	0.162266i
$917$	0.860881	+	2.97210i	0.0284288	+	0.0981475i
$918$	3.95458	+	3.50345i	0.130521	+	0.115631i
$919$	−30.2309	−	31.4737i	−0.997227	−	1.03822i	−0.999269	−	0.0382252i	$-0.987830\pi$
$919$	−30.2309	−	31.4737i	−0.997227	−	1.03822i	0.00204234	−	0.999998i	$-0.499350\pi$
$920$	54.5235	−	18.2026i	1.79759	−	0.600123i
$921$	12.7976	+	9.61675i	0.421694	+	0.316883i
$922$	−0.811300	+	6.68166i	−0.0267187	+	0.220049i
$923$	−6.60127	+	24.2635i	−0.217283	+	0.798641i
$924$	−0.0882842	−	0.727086i	−0.00290434	−	0.0239194i
$925$	−1.11859	+	1.93745i	−0.0367789	+	0.0637029i
$926$	19.6574	+	14.7716i	0.645984	+	0.485425i
$927$	−0.179915	−	4.46454i	−0.00590917	−	0.146635i
$928$	−4.20104	+	11.0772i	−0.137906	+	0.363628i
$929$	0.596962	−	2.92412i	0.0195857	−	0.0959371i	−0.968823	−	0.247754i	$-0.920307\pi$
$929$	0.596962	−	2.92412i	0.0195857	−	0.0959371i	0.988409	+	0.151817i	$0.0485125\pi$
$930$	0.956729	−	4.68637i	0.0313724	−	0.153672i
$931$	−3.82576	+	10.0877i	−0.125384	+	0.330611i
$932$	−0.0267613	−	0.664074i	−0.000876595	−	0.0217525i
$933$	23.5437	+	17.6920i	0.770788	+	0.579209i
$934$	−4.46048	+	7.72577i	−0.145951	+	0.252795i
$935$	5.36692	+	44.2006i	0.175517	+	1.44551i
$936$	−7.14584	−	8.46652i	−0.233569	−	0.276737i
$937$	−4.45359	+	36.6786i	−0.145493	+	1.19824i	0.718788	+	0.695229i	$0.244697\pi$
$937$	−4.45359	+	36.6786i	−0.145493	+	1.19824i	−0.864281	+	0.503010i	$0.832226\pi$
$938$	1.46178	+	1.09845i	0.0477287	+	0.0358658i
$939$	−7.52879	+	2.51348i	−0.245693	+	0.0820243i
$940$	0.0206405	+	0.0214890i	0.000673218	+	0.000700894i
$941$	−16.6035	−	14.7094i	−0.541258	−	0.479513i	0.347634	−	0.937630i	$-0.386985\pi$
$941$	−16.6035	−	14.7094i	−0.541258	−	0.479513i	−0.888892	+	0.458118i	$0.848524\pi$
$942$	0.944033	+	3.25918i	0.0307583	+	0.106190i
$943$	−21.4874	+	26.3173i	−0.699725	+	0.857008i
$944$	28.0948			0.914407
$945$	−0.399452	+	0.489240i	−0.0129942	+	0.0159150i
$946$	−1.68464	+	41.8040i	−0.0547725	+	1.35917i
$947$	3.46030	+	1.47430i	0.112445	+	0.0479082i	0.447456	−	0.894306i	$-0.352330\pi$
$947$	3.46030	+	1.47430i	0.112445	+	0.0479082i	−0.335012	+	0.942214i	$0.608740\pi$
$948$	2.59622	+	6.84567i	0.0843213	+	0.222337i
$949$	−51.1297	−	16.1482i	−1.65974	−	0.524192i
$950$	−0.722082	+	1.90397i	−0.0234274	+	0.0617730i
$951$	8.21511	−	8.55284i	0.266393	−	0.277345i
$952$	−1.03274	+	3.56542i	−0.0334712	+	0.115556i
$953$	10.1716	+	0.821140i	0.329492	+	0.0265993i	0.244106	−	0.969749i	$-0.421506\pi$
$953$	10.1716	+	0.821140i	0.329492	+	0.0265993i	0.0853860	+	0.996348i	$0.472788\pi$
$954$	1.99899	−	1.04915i	0.0647196	−	0.0339675i
$955$	25.6139	+	26.6669i	0.828845	+	0.862919i
$956$	14.2842	−	6.08593i	0.461984	−	0.196833i
$957$	−3.90824	−	10.3052i	−0.126336	−	0.333119i
$958$	1.05891	−	0.172090i	0.0342120	−	0.00555999i
$959$	−0.177602	+	0.112309i	−0.00573507	+	0.00362664i
$960$	−5.72008	+	19.7480i	−0.184615	+	0.637364i
$961$	−15.9068	−	23.0450i	−0.513123	−	0.743387i
$962$	7.04949	+	2.86866i	0.227285	+	0.0924892i
$963$	−2.73114	+	3.95673i	−0.0880097	+	0.127504i
$964$	−10.1179	−	12.3922i	−0.325877	−	0.399127i
$965$	2.21686	+	2.71516i	0.0713634	+	0.0874042i
$966$	−1.69919	+	1.27686i	−0.0546705	+	0.0410822i
$967$	−5.86396	−	48.2941i	−0.188572	−	1.55303i	−0.712747	−	0.701421i	$-0.752549\pi$
$967$	−5.86396	−	48.2941i	−0.188572	−	1.55303i	0.524175	−	0.851611i	$-0.324374\pi$
$968$	9.32511	+	3.11318i	0.299720	+	0.100061i
$969$	7.37126	+	0.595069i	0.236799	+	0.0191164i
$970$	−28.5718	+	25.3124i	−0.917386	+	0.812733i
$971$	−5.28009	−	3.33893i	−0.169446	−	0.107151i	0.447051	−	0.894509i	$-0.352474\pi$
$971$	−5.28009	−	3.33893i	−0.169446	−	0.107151i	−0.616497	+	0.787357i	$0.711449\pi$
$972$	0.703694	+	0.299816i	0.0225710	+	0.00961661i
$973$	3.79476	+	0.616708i	0.121654	+	0.0197708i
$974$	−36.1822	−	32.0546i	−1.15935	−	1.02710i
$975$	−3.13245	+	2.86759i	−0.100319	+	0.0918365i
$976$	2.27345	−	2.01410i	0.0727713	−	0.0644697i
$977$	−7.68659	+	4.86070i	−0.245916	+	0.155508i	−0.651738	−	0.758445i	$-0.725960\pi$
$977$	−7.68659	+	4.86070i	−0.245916	+	0.155508i	0.405822	+	0.913952i	$0.366985\pi$
$978$	−6.72368	+	0.542792i	−0.215000	+	0.0173566i
$979$	−12.6299	+	61.8651i	−0.403652	+	1.97722i
$980$	12.8024	+	3.15551i	0.408957	+	0.100799i
$981$	−2.46479	+	0.400568i	−0.0786947	+	0.0127891i
$982$	33.0450	+	20.8964i	1.05451	+	0.666832i
$983$	−22.1721	−	11.6368i	−0.707180	−	0.371157i	0.0724712	−	0.997371i	$-0.476911\pi$
$983$	−22.1721	−	11.6368i	−0.707180	−	0.371157i	−0.779652	+	0.626214i	$0.784604\pi$
$984$	−3.85918	−	13.3234i	−0.123026	−	0.424735i
$985$	−1.49483	−	7.32216i	−0.0476292	−	0.233303i
$986$	−0.622217	+	15.4402i	−0.0198154	+	0.491715i
$987$	−0.00352634	−	0.00185077i	−0.000112245	−	5.89105e-5i
$988$	−4.18172	−	0.958676i	−0.133038	−	0.0304996i
$989$	−66.5782	+	34.9429i	−2.11706	+	1.11112i
$990$	−4.46222	−	9.40392i	−0.141819	−	0.298876i
$991$	20.9263	−	36.2454i	0.664746	−	1.15137i	−0.314608	−	0.949222i	$-0.601873\pi$
$991$	20.9263	−	36.2454i	0.664746	−	1.15137i	0.979354	−	0.202152i	$-0.0647936\pi$
$992$	−3.50683	−	6.07400i	−0.111342	−	0.192850i
$993$	−4.89206	+	7.08738i	−0.155245	+	0.224911i
$994$	−1.57452	+	1.18317i	−0.0499407	+	0.0375280i
$995$	−17.6917	−	30.6429i	−0.560865	−	0.971446i
$996$	−1.11611	+	9.19199i	−0.0353653	+	0.291259i
$997$	−5.38950	+	11.3581i	−0.170687	+	0.359716i	−0.970710	−	0.240254i	$-0.922769\pi$
$997$	−5.38950	+	11.3581i	−0.170687	+	0.359716i	0.800023	+	0.599969i	$0.204821\pi$
$998$	17.6867	−	18.4138i	0.559863	−	0.582879i
$999$	−1.89321	+	0.152836i	−0.0598984	+	0.00483550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.490.11	yes	384
169.159	even	39	inner	507.2.q.b.328.11	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.328.11	✓	384	169.159	even	39	inner
507.2.q.b.490.11	yes	384	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222298 + 1.08889i) q^{2} +(0.987050 + 0.160411i) q^{3} +(0.703694 - 0.299816i) q^{4} +(2.41330 - 0.594826i) q^{5} +(0.0447495 + 1.11045i) q^{6} +(-0.108935 + 0.229576i) q^{7} +(1.74553 + 2.52884i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(0.222298 + 1.08889i) q^{2} +(0.987050 + 0.160411i) q^{3} +(0.703694 - 0.299816i) q^{4} +(2.41330 - 0.594826i) q^{5} +(0.0447495 + 1.11045i) q^{6} +(-0.108935 + 0.229576i) q^{7} +(1.74553 + 2.52884i) q^{8} +(0.948536 + 0.316668i) q^{9} +(1.18417 + 2.49559i) q^{10} +(-3.57428 + 1.19327i) q^{11} +(0.742675 - 0.183053i) q^{12} +(-3.29356 + 1.46714i) q^{13} +(-0.274199 - 0.0675841i) q^{14} +(2.47747 - 0.200002i) q^{15} +(-1.30587 + 1.35955i) q^{16} +(2.03797 - 4.29493i) q^{17} +(-0.133958 + 1.10325i) q^{18} +(0.777804 + 1.34720i) q^{19} +(1.51989 - 1.14212i) q^{20} +(-0.144351 + 0.209129i) q^{21} +(-2.09390 - 3.62674i) q^{22} +(3.76314 - 6.51795i) q^{23} +(1.31727 + 2.77610i) q^{24} +(1.04294 - 0.547375i) q^{25} +(-2.32970 - 3.26018i) q^{26} +(0.885456 + 0.464723i) q^{27} +(-0.00782648 + 0.194212i) q^{28} +(0.585042 + 2.86573i) q^{29} +(0.768518 + 2.65323i) q^{30} +(-1.53321 - 0.804689i) q^{31} +(3.42346 + 2.16486i) q^{32} +(-3.71941 + 0.604463i) q^{33} +(5.12975 + 1.26437i) q^{34} +(-0.126336 + 0.618835i) q^{35} +(0.762422 - 0.0615490i) q^{36} +(-1.60533 + 1.01515i) q^{37} +(-1.29404 + 1.14642i) q^{38} +(-3.48625 + 0.919814i) q^{39} +(5.71672 + 5.06458i) q^{40} +(-4.45573 - 0.724127i) q^{41} +(-0.259807 - 0.110694i) q^{42} +(-8.44382 - 5.33955i) q^{43} +(-2.15744 + 1.91133i) q^{44} +(2.47747 + 0.200002i) q^{45} +(7.93387 + 2.64872i) q^{46} +(0.00188909 + 0.0155581i) q^{47} +(-1.50705 + 1.13247i) q^{48} +(4.38628 + 5.37222i) q^{49} +(0.827874 + 1.01396i) q^{50} +(2.70053 - 3.91240i) q^{51} +(-1.87778 + 2.01988i) q^{52} +(-1.15396 - 1.67180i) q^{53} +(-0.309197 + 1.06747i) q^{54} +(-7.91605 + 5.00580i) q^{55} +(-0.770712 + 0.125253i) q^{56} +(0.551626 + 1.45452i) q^{57} +(-2.99041 + 1.27409i) q^{58} +(-10.3240 - 10.7484i) q^{59} +(1.68342 - 0.883525i) q^{60} +(-1.60597 - 0.129647i) q^{61} +(0.535388 - 1.84837i) q^{62} +(-0.176029 + 0.183265i) q^{63} +(-2.93321 + 7.73425i) q^{64} +(-7.07566 + 5.49974i) q^{65} +(-1.48501 - 3.91566i) q^{66} +(-5.95660 - 2.53787i) q^{67} +(0.146418 - 3.63333i) q^{68} +(4.75996 - 5.82990i) q^{69} -0.701927 q^{70} +(4.41073 - 5.40216i) q^{71} +(0.854899 + 2.95145i) q^{72} +(11.1313 + 9.86148i) q^{73} +(-1.46224 - 1.52236i) q^{74} +(1.11724 - 0.372988i) q^{75} +(0.951247 + 0.714816i) q^{76} +(0.115419 - 0.950560i) q^{77} +(-1.77656 - 3.59167i) q^{78} +(1.15375 + 9.50195i) q^{79} +(-2.34276 + 4.05778i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.202008 - 5.01278i) q^{82} +(-4.29266 + 11.3188i) q^{83} +(-0.0388789 + 0.190442i) q^{84} +(2.36350 - 11.5772i) q^{85} +(3.93713 - 10.3814i) q^{86} +(0.117771 + 2.92246i) q^{87} +(-9.25663 - 6.95591i) q^{88} +(8.37814 - 14.5114i) q^{89} +(0.332957 + 2.74215i) q^{90} +(0.0219647 - 0.915945i) q^{91} +(0.693914 - 5.71490i) q^{92} +(-1.38427 - 1.04021i) q^{93} +(-0.0165211 + 0.00551556i) q^{94} +(2.67842 + 2.78854i) q^{95} +(3.03186 + 2.68599i) q^{96} +(3.84463 + 13.2732i) q^{97} +(-4.87469 + 5.97041i) q^{98} -3.76821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

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